LMFDB - Embedded newform 31.2.g.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(7,31)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("31.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			10.2
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	31.10
Dual form			31.2.g.a.28.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.284315 - 0.206567i) q^{2} +(0.302431 + 2.87744i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(1.05848 + 0.224987i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(-5.25377 + 1.11672i) q^{9} +O(q^{10})$	\(q+(-0.284315 - 0.206567i) q^{2} +(0.302431 + 2.87744i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(1.05848 + 0.224987i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(-5.25377 + 1.11672i) q^{9} +(-0.109221 + 1.03917i) q^{10} +(-1.62690 + 1.80686i) q^{11} +(4.95987 - 2.20827i) q^{12} +(2.62521 + 1.16882i) q^{13} +(-0.254466 - 0.282614i) q^{14} +(6.95951 - 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(-1.22101 - 1.35606i) q^{17} +(1.72440 + 0.767753i) q^{18} +(1.93514 - 0.861580i) q^{19} +(-3.73325 + 4.14619i) q^{20} +(-0.327269 + 3.11375i) q^{21} +(0.835790 - 0.177653i) q^{22} +(-0.136652 + 0.420572i) q^{23} +(-3.85547 - 0.819506i) q^{24} +(-1.92005 + 3.32562i) q^{25} +(-0.504947 - 0.874594i) q^{26} +(-2.11998 - 6.52462i) q^{27} +(-0.212256 - 2.01948i) q^{28} +(2.55579 + 1.85689i) q^{29} -3.02317 q^{30} +(1.15354 - 5.44696i) q^{31} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(0.0670322 + 0.637769i) q^{34} +(-0.994234 - 3.05994i) q^{35} +(5.03946 + 8.72860i) q^{36} +(-1.57338 + 2.72517i) q^{37} +(-0.728163 - 0.154776i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(3.96200 - 0.842148i) q^{40} +(0.726079 - 6.90818i) q^{41} +(0.736246 - 0.817684i) q^{42} +(-7.68509 + 3.42162i) q^{43} +(4.16801 + 1.85572i) q^{44} +(10.6858 + 11.8677i) q^{45} +(0.125728 - 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(-6.33887 - 7.04003i) q^{48} +(-5.32506 - 2.37087i) q^{49} +(1.23286 - 0.548905i) q^{50} +(3.53273 - 3.92349i) q^{51} +(0.563659 - 5.36285i) q^{52} +(4.86824 - 1.03478i) q^{53} +(-0.745029 + 2.29296i) q^{54} +(7.07105 + 1.50300i) q^{55} +(-0.737104 + 1.27670i) q^{56} +(3.06439 + 5.30768i) q^{57} +(-0.343078 - 1.05588i) q^{58} +(1.25580 + 11.9481i) q^{59} +(-13.0595 - 9.48827i) q^{60} -14.4351 q^{61} +(-1.45313 + 1.31037i) q^{62} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(-0.893094 - 8.49722i) q^{65} +(0.763955 + 2.35121i) q^{66} +(3.21879 + 5.57511i) q^{67} +(-1.71208 + 2.96541i) q^{68} +(-1.25150 - 0.266015i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(-1.64121 + 0.348850i) q^{71} +(0.764860 - 7.27716i) q^{72} +(9.60883 - 10.6717i) q^{73} +(1.01026 - 0.449798i) q^{74} +(-10.1500 - 4.51905i) q^{75} +(-2.65975 - 2.95395i) q^{76} +(-2.12856 + 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(-2.30692 - 2.56210i) q^{79} +(8.89339 + 3.95959i) q^{80} +(3.41274 - 1.51945i) q^{81} +(-1.63344 + 1.81412i) q^{82} +(-1.34357 + 12.7832i) q^{83} +(5.74674 - 1.22151i) q^{84} +(-1.67655 + 5.15991i) q^{85} +(2.89178 + 0.614667i) q^{86} +(-4.57015 + 7.91573i) q^{87} +(-1.65616 - 2.86855i) q^{88} +(0.698188 + 2.14880i) q^{89} +(-0.586639 - 5.58150i) q^{90} +(2.51576 + 1.82781i) q^{91} +0.829816 q^{92} +(16.0222 + 1.67190i) q^{93} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(1.17202 + 11.1510i) q^{96} +(1.05463 + 3.24582i) q^{97} +(1.02425 + 1.77405i) q^{98} +(6.52961 - 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	0.482710	−	0.875780i	$-0.339653\pi$
$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	−0.683751	+	0.729715i	$0.739653\pi$
$3$	0.302431	+	2.87744i	0.174609	+	1.66129i	0.634206	+	0.773164i	$0.281327\pi$
$3$	0.302431	+	2.87744i	0.174609	+	1.66129i	−0.459597	+	0.888128i	$0.652006\pi$
$4$	−0.579869	−	1.78465i	−0.289934	−	0.892327i
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	−0.979330	−	0.202268i	$-0.935169\pi$
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	0.314496	−	0.949259i	$-0.398165\pi$
$6$	0.508398	−	0.880572i	0.207553	−	0.359492i
$7$	1.05848	+	0.224987i	0.400067	+	0.0850369i	0.403551	−	0.914957i	$-0.367776\pi$
$7$	1.05848	+	0.224987i	0.400067	+	0.0850369i	−0.00348400	+	0.999994i	$0.501109\pi$
$8$	−0.420982	+	1.29565i	−0.148840	+	0.458081i
$9$	−5.25377	+	1.11672i	−1.75126	+	0.372241i
$10$	−0.109221	+	1.03917i	−0.0345386	+	0.328613i
$11$	−1.62690	+	1.80686i	−0.490530	+	0.544789i	−0.936688	−	0.350165i	$-0.886125\pi$
$11$	−1.62690	+	1.80686i	−0.490530	+	0.544789i	0.446158	+	0.894954i	$0.352792\pi$
$12$	4.95987	−	2.20827i	1.43179	−	0.637474i
$13$	2.62521	+	1.16882i	0.728103	+	0.324172i	0.737097	−	0.675787i	$-0.236196\pi$
$13$	2.62521	+	1.16882i	0.728103	+	0.324172i	−0.00899389	+	0.999960i	$0.502863\pi$
$14$	−0.254466	−	0.282614i	−0.0680090	−	0.0755317i
$15$	6.95951	−	5.05638i	1.79694	−	1.30555i
$16$	−2.64890	+	1.92454i	−0.662226	+	0.481135i
$17$	−1.22101	−	1.35606i	−0.296137	−	0.328894i	0.576653	−	0.816989i	$-0.304359\pi$
$17$	−1.22101	−	1.35606i	−0.296137	−	0.328894i	−0.872790	+	0.488095i	$0.837692\pi$
$18$	1.72440	+	0.767753i	0.406445	+	0.180961i
$19$	1.93514	−	0.861580i	0.443951	−	0.197660i	−0.172571	−	0.984997i	$-0.555208\pi$
$19$	1.93514	−	0.861580i	0.443951	−	0.197660i	0.616523	+	0.787337i	$0.288541\pi$
$20$	−3.73325	+	4.14619i	−0.834780	+	0.927117i
$21$	−0.327269	+	3.11375i	−0.0714159	+	0.679477i
$22$	0.835790	−	0.177653i	0.178191	−	0.0378757i
$23$	−0.136652	+	0.420572i	−0.0284939	+	0.0876953i	−0.964292	−	0.264841i	$-0.914681\pi$
$23$	−0.136652	+	0.420572i	−0.0284939	+	0.0876953i	0.935798	+	0.352536i	$0.114681\pi$
$24$	−3.85547	−	0.819506i	−0.786995	−	0.167281i
$25$	−1.92005	+	3.32562i	−0.384010	+	0.665124i
$26$	−0.504947	−	0.874594i	−0.0990283	−	0.171522i
$27$	−2.11998	−	6.52462i	−0.407990	−	1.25566i
$28$	−0.212256	−	2.01948i	−0.0401126	−	0.381646i
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	0.799231	−	0.601024i	$-0.205240\pi$
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	−0.324632	+	0.945840i	$0.605240\pi$
$30$	−3.02317			−0.551953
$31$	1.15354	−	5.44696i	0.207181	−	0.978303i
$31$	1.15354	−	5.44696i	0.207181	−	0.978303i
$32$	3.87532			0.685067
$33$	−5.69116	−	4.13487i	−0.990704	−	0.719789i
$34$	0.0670322	+	0.637769i	0.0114959	+	0.109376i
$35$	−0.994234	−	3.05994i	−0.168056	−	0.517224i
$36$	5.03946	+	8.72860i	0.839910	+	1.45477i
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	−0.965884	−	0.258977i	$-0.916615\pi$
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	0.707222	+	0.706991i	$0.249948\pi$
$38$	−0.728163	−	0.154776i	−0.118124	−	0.0251079i
$39$	−2.56926	+	7.90738i	−0.411412	+	1.26619i
$40$	3.96200	−	0.842148i	0.626447	−	0.133155i
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	−0.778814	−	0.627254i	$-0.784179\pi$
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	0.892209	−	0.451623i	$-0.149155\pi$
$42$	0.736246	−	0.817684i	0.113605	−	0.126171i
$43$	−7.68509	+	3.42162i	−1.17197	+	0.521793i	−0.898021	−	0.439953i	$-0.854995\pi$
$43$	−7.68509	+	3.42162i	−1.17197	+	0.521793i	−0.273944	+	0.961746i	$0.588328\pi$
$44$	4.16801	+	1.85572i	0.628351	+	0.279760i
$45$	10.6858	+	11.8677i	1.59294	+	1.76914i
$46$	0.125728	−	0.0913471i	0.0185377	−	0.0134684i
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	−0.00873953	−	0.999962i	$-0.502782\pi$
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	0.948320	+	0.317317i	$0.102782\pi$
$48$	−6.33887	−	7.04003i	−0.914937	−	1.01614i
$49$	−5.32506	−	2.37087i	−0.760723	−	0.338696i
$50$	1.23286	−	0.548905i	0.174353	−	0.0776269i
$51$	3.53273	−	3.92349i	0.494681	−	0.549399i
$52$	0.563659	−	5.36285i	0.0781654	−	0.743694i
$53$	4.86824	−	1.03478i	0.668704	−	0.142137i	0.138964	−	0.990297i	$-0.455623\pi$
$53$	4.86824	−	1.03478i	0.668704	−	0.142137i	0.529740	+	0.848160i	$0.322289\pi$
$54$	−0.745029	+	2.29296i	−0.101386	+	0.312033i
$55$	7.07105	+	1.50300i	0.953460	+	0.202664i
$56$	−0.737104	+	1.27670i	−0.0984997	+	0.170606i
$57$	3.06439	+	5.30768i	0.405889	+	0.703020i
$58$	−0.343078	−	1.05588i	−0.0450483	−	0.138644i
$59$	1.25580	+	11.9481i	0.163491	+	1.55551i	0.701559	+	0.712612i	$0.252488\pi$
$59$	1.25580	+	11.9481i	0.163491	+	1.55551i	−0.538068	+	0.842902i	$0.680846\pi$
$60$	−13.0595	−	9.48827i	−1.68597	−	1.22493i
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$	−1.45313	+	1.31037i	−0.184548	+	0.166417i
$63$	−5.81225			−0.732274
$64$	4.19600	+	3.04857i	0.524499	+	0.381071i
$65$	−0.893094	−	8.49722i	−0.110775	−	1.05395i
$66$	0.763955	+	2.35121i	0.0940363	+	0.289414i
$67$	3.21879	+	5.57511i	0.393238	+	0.681108i	0.992875	−	0.119164i	$-0.0380215\pi$
$67$	3.21879	+	5.57511i	0.393238	+	0.681108i	−0.599636	+	0.800273i	$0.704688\pi$
$68$	−1.71208	+	2.96541i	−0.207620	+	0.359609i
$69$	−1.25150	−	0.266015i	−0.150663	−	0.0320244i
$70$	−0.349406	+	1.07536i	−0.0417620	+	0.128530i
$71$	−1.64121	+	0.348850i	−0.194776	+	0.0414009i	−0.304266	−	0.952587i	$-0.598411\pi$
$71$	−1.64121	+	0.348850i	−0.194776	+	0.0414009i	0.109491	+	0.993988i	$0.465078\pi$
$72$	0.764860	−	7.27716i	0.0901396	−	0.857621i
$73$	9.60883	−	10.6717i	1.12463	−	1.24903i	0.159514	−	0.987196i	$-0.449007\pi$
$73$	9.60883	−	10.6717i	1.12463	−	1.24903i	0.965114	−	0.261830i	$-0.0843261\pi$
$74$	1.01026	−	0.449798i	0.117441	−	0.0522880i
$75$	−10.1500	−	4.51905i	−1.17202	−	0.521815i
$76$	−2.65975	−	2.95395i	−0.305094	−	0.338841i
$77$	−2.12856	+	1.54649i	−0.242572	+	0.176239i
$78$	2.36388	−	1.71746i	0.267657	−	0.194464i
$79$	−2.30692	−	2.56210i	−0.259549	−	0.288259i	0.599260	−	0.800555i	$-0.295462\pi$
$79$	−2.30692	−	2.56210i	−0.259549	−	0.288259i	−0.858809	+	0.512296i	$0.828795\pi$
$80$	8.89339	+	3.95959i	0.994311	+	0.442696i
$81$	3.41274	−	1.51945i	0.379194	−	0.168828i
$82$	−1.63344	+	1.81412i	−0.180383	+	0.200336i
$83$	−1.34357	+	12.7832i	−0.147476	+	1.40314i	0.631155	+	0.775657i	$0.282581\pi$
$83$	−1.34357	+	12.7832i	−0.147476	+	1.40314i	−0.778631	+	0.627482i	$0.784086\pi$
$84$	5.74674	−	1.22151i	0.627021	−	0.133277i
$85$	−1.67655	+	5.15991i	−0.181848	+	0.559670i
$86$	2.89178	+	0.614667i	0.311829	+	0.0662812i
$87$	−4.57015	+	7.91573i	−0.489972	+	0.848656i
$88$	−1.65616	−	2.86855i	−0.176547	−	0.305789i
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	0.981217	−	0.192907i	$-0.0617916\pi$
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	−0.907209	+	0.420680i	$0.861792\pi$
$90$	−0.586639	−	5.58150i	−0.0618372	−	0.588342i
$91$	2.51576	+	1.82781i	0.263724	+	0.191606i
$92$	0.829816			0.0865143
$93$	16.0222	+	1.67190i	1.66142	+	0.173368i
$94$	−2.79812			−0.288604
$95$	−5.09528	−	3.70194i	−0.522765	−	0.379811i
$96$	1.17202	+	11.1510i	0.119619	+	1.13810i
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	0.990213	−	0.139562i	$-0.0445693\pi$
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	−0.883132	+	0.469125i	$0.844569\pi$
$98$	1.02425	+	1.77405i	0.103465	+	0.179207i
$99$	6.52961	−	11.3096i	0.656251	−	1.13666i
$100$	7.04845	+	1.49820i	0.704845	+	0.149820i
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	−0.176741	−	0.984257i	$-0.556555\pi$
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	0.721518	−	0.692395i	$-0.243445\pi$
$102$	−1.81487	+	0.385763i	−0.179699	+	0.0381962i
$103$	−0.843947	+	8.02962i	−0.0831566	+	0.791182i	0.870881	+	0.491494i	$0.163549\pi$
$103$	−0.843947	+	8.02962i	−0.0831566	+	0.791182i	−0.954037	+	0.299688i	$0.903118\pi$
$104$	−2.61955	+	2.90930i	−0.256868	+	0.285281i
$105$	8.50411	−	3.78627i	0.829916	−	0.369502i
$106$	−1.59786	−	0.711414i	−0.155198	−	0.0690987i
$107$	−8.13074	−	9.03010i	−0.786028	−	0.872972i	0.208438	−	0.978036i	$-0.433162\pi$
$107$	−8.13074	−	9.03010i	−0.786028	−	0.872972i	−0.994466	+	0.105063i	$0.966495\pi$
$108$	−10.4149	+	7.56685i	−1.00217	+	0.728121i
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	−0.563025	−	0.826440i	$-0.690363\pi$
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	0.612007	+	0.790853i	$0.290363\pi$
$110$	−1.69994	−	1.88797i	−0.162082	−	0.180011i
$111$	−8.31735	−	3.70312i	−0.789448	−	0.351485i
$112$	−3.23680	+	1.44112i	−0.305849	+	0.136173i
$113$	−7.56140	+	8.39779i	−0.711317	+	0.789998i	−0.985135	−	0.171784i	$-0.945047\pi$
$113$	−7.56140	+	8.39779i	−0.711317	+	0.789998i	0.273818	+	0.961782i	$0.411714\pi$
$114$	0.225139	−	2.14205i	0.0210862	−	0.200622i
$115$	1.28608	−	0.273364i	0.119927	−	0.0254913i
$116$	1.83188	−	5.63796i	0.170086	−	0.523472i
$117$	−15.0975	−	3.20907i	−1.39576	−	0.296679i
$118$	2.11104	−	3.65643i	0.194337	−	0.336602i
$119$	−0.987313	−	1.71008i	−0.0905068	−	0.156762i
$120$	3.62146	+	11.1457i	0.330593	+	1.01746i
$121$	0.531887	+	5.06056i	0.0483533	+	0.460051i
$122$	4.10412	+	2.98182i	0.371570	+	0.269961i
$123$	20.0975			1.81213
$124$	−10.3898	+	1.09986i	−0.933034	+	0.0987702i
$125$	−3.44866			−0.308458
$126$	1.65251	+	1.20062i	0.147217	+	0.106960i
$127$	−0.0123141	−	0.117161i	−0.00109270	−	0.0103963i	0.993962	−	0.109725i	$-0.0349971\pi$
$127$	−0.0123141	−	0.117161i	−0.00109270	−	0.0103963i	−0.995055	+	0.0993289i	$0.968330\pi$
$128$	−2.95833	−	9.10481i	−0.261482	−	0.804759i
$129$	−12.1697	−	21.0786i	−1.07149	−	1.85587i
$130$	−1.50132	+	2.60037i	−0.131675	+	0.228068i
$131$	−5.65756	−	1.20255i	−0.494303	−	0.105067i	−0.0459863	−	0.998942i	$-0.514643\pi$
$131$	−5.65756	−	1.20255i	−0.494303	−	0.105067i	−0.448317	+	0.893875i	$0.647976\pi$
$132$	−4.07918	+	12.5544i	−0.355047	+	1.09272i
$133$	2.24215	−	0.476583i	0.194419	−	0.0413250i
$134$	0.236483	−	2.24998i	0.0204290	−	0.194369i
$135$	−13.6486	+	15.1583i	−1.17469	+	1.30462i
$136$	2.27101	−	1.01112i	0.194737	−	0.0867026i
$137$	10.7848	+	4.80170i	0.921407	+	0.410237i	0.811931	−	0.583753i	$-0.198416\pi$
$137$	10.7848	+	4.80170i	0.921407	+	0.410237i	0.109475	+	0.993990i	$0.465083\pi$
$138$	0.300870	+	0.334150i	0.0256118	+	0.0284448i
$139$	12.4767	−	9.06482i	1.05826	−	0.768868i	0.0844915	−	0.996424i	$-0.473073\pi$
$139$	12.4767	−	9.06482i	1.05826	−	0.768868i	0.973765	+	0.227556i	$0.0730734\pi$
$140$	−4.88440	+	3.54873i	−0.412807	+	0.299922i
$141$	15.4145	+	17.1195i	1.29813	+	1.44172i
$142$	0.538681	+	0.239836i	0.0452051	+	0.0201266i
$143$	−6.38286	+	2.84183i	−0.533762	+	0.237646i
$144$	11.7675	−	13.0692i	0.980628	−	1.08910i
$145$	0.981819	−	9.34138i	0.0815356	−	0.775759i
$146$	−4.93635	+	1.04925i	−0.408535	+	0.0868368i
$147$	5.21157	−	16.0396i	0.429843	−	1.32292i
$148$	5.77583	+	1.22769i	0.474770	+	0.100916i
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	−0.510427	−	0.859921i	$-0.670512\pi$
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	0.999927	+	0.0120817i	$0.00384583\pi$
$150$	1.95230	+	3.38148i	0.159404	+	0.276097i
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	0.881888	−	0.471458i	$-0.156272\pi$
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	−0.990579	+	0.136943i	$0.956272\pi$
$152$	0.301646	+	2.86997i	0.0244667	+	0.232785i
$153$	7.92923	+	5.76092i	0.641040	+	0.465743i
$154$	0.924636			0.0745093
$155$	−15.7402	+	5.12730i	−1.26428	+	0.411834i
$156$	15.6018			1.24914
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	0.832196	−	0.554481i	$-0.187083\pi$
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	−0.270180	+	0.962810i	$0.587083\pi$
$158$	0.126648	+	1.20498i	0.0100756	+	0.0958628i
$159$	4.44982	+	13.6951i	0.352893	+	1.08609i
$160$	−5.76111	−	9.97854i	−0.455456	−	0.788873i
$161$	−0.239267	+	0.414422i	−0.0188568	+	0.0326610i
$162$	−1.28416	−	0.272957i	−0.100893	−	0.0214455i
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	−0.906040	−	0.423192i	$-0.860909\pi$
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	0.981748	+	0.190187i	$0.0609095\pi$
$164$	−12.7497	+	2.71004i	−0.995588	+	0.211619i
$165$	−2.18628	+	20.8011i	−0.170202	+	1.61936i
$166$	3.02258	−	3.35692i	0.234598	−	0.260547i
$167$	−12.2003	+	5.43194i	−0.944090	+	0.420336i	−0.820275	−	0.571969i	$-0.806180\pi$
$167$	−12.2003	+	5.43194i	−0.944090	+	0.420336i	−0.123815	+	0.992305i	$0.539513\pi$
$168$	−3.89656	−	1.73486i	−0.300626	−	0.133847i
$169$	−3.17310	−	3.52408i	−0.244085	−	0.271083i
$170$	1.54253	−	1.12072i	0.118307	−	0.0859551i
$171$	−9.20462	+	6.68755i	−0.703895	+	0.511410i
$172$	10.5628	+	11.7311i	0.805402	+	0.894490i
$173$	17.3982	+	7.74619i	1.32276	+	0.588932i	0.941960	−	0.335724i	$-0.108981\pi$
$173$	17.3982	+	7.74619i	1.32276	+	0.588932i	0.380803	+	0.924656i	$0.375648\pi$
$174$	2.93449	−	1.30652i	0.222463	−	0.0990469i
$175$	−2.78055	+	3.08811i	−0.210190	+	0.233439i
$176$	0.832136	−	7.91724i	0.0627246	−	0.596785i
$177$	−34.0002	+	7.22697i	−2.55561	+	0.543213i
$178$	0.245366	−	0.755159i	0.0183910	−	0.0566016i
$179$	0.0775964	+	0.0164936i	0.00579983	+	0.00123279i	0.210811	−	0.977527i	$-0.432390\pi$
$179$	0.0775964	+	0.0164936i	0.00579983	+	0.00123279i	−0.205011	+	0.978760i	$0.565723\pi$
$180$	14.9835	−	25.9521i	1.11680	−	1.93436i
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	0.823032	−	0.567995i	$-0.192281\pi$
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	−0.903414	+	0.428769i	$0.858947\pi$
$182$	−0.337704	−	1.03935i	−0.0250323	−	0.0770415i
$183$	−4.36564	−	41.5363i	−0.322717	−	3.07045i
$184$	−0.487386	−	0.354107i	−0.0359306	−	0.0261051i
$185$	9.35601			0.687868
$186$	−4.20998	−	3.78500i	−0.308691	−	0.277529i
$187$	4.43668			0.324442
$188$	−12.0873	−	8.78195i	−0.881559	−	0.640490i
$189$	−0.776000	−	7.38314i	−0.0564457	−	0.537045i
$190$	0.683966	+	2.10503i	0.0496201	+	0.152715i
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	0.946327	−	0.323210i	$-0.104762\pi$
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	−0.753072	+	0.657939i	$0.771429\pi$
$192$	−7.50308	+	12.9957i	−0.541488	+	0.937885i
$193$	2.08705	+	0.443616i	0.150229	+	0.0319322i	0.282412	−	0.959293i	$-0.408865\pi$
$193$	2.08705	+	0.443616i	0.150229	+	0.0319322i	−0.132183	+	0.991225i	$0.542199\pi$
$194$	0.370632	−	1.14069i	0.0266098	−	0.0818966i
$195$	24.1802	−	5.13965i	1.73158	−	0.368058i
$196$	−1.14334	+	10.8782i	−0.0816673	+	0.777013i
$197$	−3.93163	+	4.36652i	−0.280117	+	0.311102i	−0.866742	−	0.498758i	$-0.833790\pi$
$197$	−3.93163	+	4.36652i	−0.280117	+	0.311102i	0.586624	+	0.809859i	$0.300456\pi$
$198$	−4.19266	+	1.86669i	−0.297959	+	0.132660i
$199$	6.32901	+	2.81786i	0.448652	+	0.199753i	0.618609	−	0.785699i	$-0.287696\pi$
$199$	6.32901	+	2.81786i	0.448652	+	0.199753i	−0.169958	+	0.985451i	$0.554363\pi$
$200$	−3.50053	−	3.88773i	−0.247525	−	0.274904i
$201$	−15.0686	+	10.9480i	−1.06286	+	0.772211i
$202$	−5.03729	+	3.65981i	−0.354423	+	0.257503i
$203$	2.28748	+	2.54050i	0.160549	+	0.178308i
$204$	−9.05059	−	4.02958i	−0.633668	−	0.282127i
$205$	−18.8672	+	8.40023i	−1.31774	+	0.586698i
$206$	1.89860	−	2.10861i	0.132282	−	0.146914i
$207$	0.248276	−	2.36219i	0.0172564	−	0.164184i
$208$	−9.20337	+	1.95624i	−0.638139	+	0.135641i
$209$	−1.59153	+	4.89823i	−0.110089	+	0.338818i
$210$	−3.19996	−	0.680173i	−0.220818	−	0.0469364i
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	0.420888	+	0.907113i	$0.361719\pi$
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	−0.996027	+	0.0890568i	$0.971615\pi$
$212$	−4.66966	−	8.08808i	−0.320713	−	0.555492i
$213$	−1.50015	−	4.61698i	−0.102788	−	0.316350i
$214$	0.446370	+	4.24693i	0.0305133	+	0.290314i
$215$	20.2351	+	14.7016i	1.38002	+	1.00264i
$216$	9.34610			0.635921
$217$	2.44649	−	5.50596i	0.166078	−	0.373769i
$218$	−0.222141			−0.0150453
$219$	33.6132	+	24.4214i	2.27137	+	1.65024i
$220$	−1.41795	−	13.4909i	−0.0955983	−	0.909557i
$221$	−1.62040	−	4.98709i	−0.109000	−	0.335468i
$222$	1.59980	+	2.77094i	0.107372	+	0.185973i
$223$	3.13078	−	5.42267i	0.209653	−	0.363129i	−0.741952	−	0.670453i	$-0.766100\pi$
$223$	3.13078	−	5.42267i	0.209653	−	0.363129i	0.951605	+	0.307323i	$0.0994333\pi$
$224$	4.10195	+	0.871895i	0.274073	+	0.0582560i
$225$	6.37369	−	19.6162i	0.424912	−	1.30775i
$226$	3.88452	−	0.825681i	0.258395	−	0.0549235i
$227$	0.820289	−	7.80452i	0.0544445	−	0.518004i	−0.932982	−	0.359924i	$-0.882803\pi$
$227$	0.820289	−	7.80452i	0.0544445	−	0.518004i	0.987426	−	0.158081i	$-0.0505306\pi$
$228$	7.69543	−	8.54664i	0.509642	−	0.566015i
$229$	11.6687	−	5.19524i	0.771089	−	0.343311i	0.0168049	−	0.999859i	$-0.494651\pi$
$229$	11.6687	−	5.19524i	0.771089	−	0.343311i	0.754285	+	0.656548i	$0.227984\pi$
$230$	−0.422119	−	0.187939i	−0.0278337	−	0.0123924i
$231$	−5.09368	−	5.65711i	−0.335140	−	0.372210i
$232$	−3.48183	+	2.52969i	−0.228593	+	0.166083i
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	−0.871373	−	0.490622i	$-0.836770\pi$
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	0.197340	+	0.980335i	$0.436770\pi$
$234$	3.62955	+	4.03103i	0.237271	+	0.263517i
$235$	−21.6264	−	9.62868i	−1.41075	−	0.628106i
$236$	20.5951	−	9.16951i	1.34062	−	0.596884i
$237$	6.67460	−	7.41290i	0.433562	−	0.481520i
$238$	−0.0725373	+	0.690146i	−0.00470189	+	0.0447355i
$239$	24.8690	−	5.28607i	1.60864	−	0.341928i	0.686006	−	0.727596i	$-0.259362\pi$
$239$	24.8690	−	5.28607i	1.60864	−	0.341928i	0.922638	+	0.385668i	$0.126029\pi$
$240$	−8.70385	+	26.7877i	−0.561831	+	1.72914i
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	0.132929	−	0.991126i	$-0.457562\pi$
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	−0.281690	+	0.959505i	$0.590895\pi$
$242$	0.894121	−	1.54866i	0.0574763	−	0.0995519i
$243$	−4.88634	−	8.46339i	−0.313459	−	0.542927i
$244$	8.37048	+	25.7617i	0.535865	+	1.64922i
$245$	1.81158	+	17.2360i	0.115738	+	1.10117i
$246$	−5.71401	−	4.15147i	−0.364312	−	0.264688i
$247$	6.08718			0.387318
$248$	6.57173	+	3.78765i	0.417305	+	0.240516i
$249$	−37.1893			−2.35677
$250$	0.980506	+	0.712379i	0.0620126	+	0.0450548i
$251$	−0.246336	−	2.34373i	−0.0155486	−	0.147935i	0.983993	−	0.178206i	$-0.0570294\pi$
$251$	−0.246336	−	2.34373i	−0.0155486	−	0.147935i	−0.999542	+	0.0302716i	$0.990363\pi$
$252$	3.37034	+	10.3728i	0.212312	+	0.653428i
$253$	−0.537595	−	0.931142i	−0.0337983	−	0.0585404i
$254$	−0.0207005	+	0.0358542i	−0.00129886	+	0.00224970i
$255$	−15.3544	−	3.26367i	−0.961528	−	0.204379i
$256$	2.16580	−	6.66565i	0.135363	−	0.416603i
$257$	25.4455	−	5.40862i	1.58725	−	0.337380i	0.672089	−	0.740470i	$-0.265397\pi$
$257$	25.4455	−	5.40862i	1.58725	−	0.337380i	0.915160	+	0.403090i	$0.132064\pi$
$258$	−0.894103	+	8.50682i	−0.0556644	+	0.529612i
$259$	−2.27851	+	2.53054i	−0.141580	+	0.157240i
$260$	−14.6467	+	6.52114i	−0.908351	+	0.404424i
$261$	−15.5012	−	6.90157i	−0.959499	−	0.427196i
$262$	1.36012	+	1.51057i	0.0840285	+	0.0933232i
$263$	−18.5552	+	13.4812i	−1.14417	+	0.831285i	−0.987694	−	0.156398i	$-0.950012\pi$
$263$	−18.5552	+	13.4812i	−1.14417	+	0.831285i	−0.156471	+	0.987683i	$0.550012\pi$
$264$	7.75322	−	5.63304i	0.477178	−	0.346690i
$265$	−9.90163	−	10.9969i	−0.608253	−	0.675533i
$266$	−0.735922	−	0.327654i	−0.0451223	−	0.0200897i
$267$	−5.97190	+	2.65886i	−0.365474	+	0.162720i
$268$	8.08316	−	8.97726i	0.493758	−	0.548374i
$269$	1.78193	−	16.9539i	0.108646	−	1.03370i	−0.795347	−	0.606154i	$-0.792712\pi$
$269$	1.78193	−	16.9539i	0.108646	−	1.03370i	0.903994	−	0.427546i	$-0.140622\pi$
$270$	7.01171	−	1.49038i	0.426719	−	0.0907019i
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	−0.859721	−	0.510764i	$-0.829363\pi$
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	0.995748	+	0.0921146i	$0.0293626\pi$
$272$	5.84413	+	1.24221i	0.354352	+	0.0753199i
$273$	−4.49857	+	7.79175i	−0.272266	+	0.471578i
$274$	−2.07440	−	3.59297i	−0.125319	−	0.217059i
$275$	−2.88520	−	8.87972i	−0.173984	−	0.535467i
$276$	0.250962	+	2.38775i	0.0151062	+	0.143725i
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	0.156719	−	0.987643i	$-0.449908\pi$
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	−0.890876	+	0.454247i	$0.849908\pi$
$278$	−5.41979			−0.325058
$279$	0.0223278	+	29.9052i	0.00133673	+	1.79038i
$280$	4.38316			0.261944
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	0.646181	−	0.763184i	$-0.276365\pi$
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	−0.526150	+	0.850392i	$0.676365\pi$
$282$	−0.846240	−	8.05144i	−0.0503929	−	0.479456i
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	0.898216	−	0.439554i	$-0.144863\pi$
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	−0.985035	+	0.172352i	$0.944863\pi$
$284$	1.57426	+	2.72670i	0.0934153	+	0.161800i
$285$	9.11114	−	15.7810i	0.539697	−	0.934783i
$286$	2.40177	+	0.510512i	0.142020	+	0.0301872i
$287$	2.32279	−	7.14881i	0.137110	−	0.421981i
$288$	−20.3600	+	4.32766i	−1.19973	+	0.255010i
$289$	1.42893	−	13.5953i	0.0840546	−	0.799726i
$290$	−2.20877	+	2.45308i	−0.129703	+	0.144050i
$291$	−9.02071	+	4.01628i	−0.528804	+	0.235439i
$292$	−24.6171	−	10.9602i	−1.44061	−	0.641400i
$293$	−7.05858	−	7.83935i	−0.412367	−	0.457980i	0.500802	−	0.865562i	$-0.333039\pi$
$293$	−7.05858	−	7.83935i	−0.412367	−	0.457980i	−0.913169	+	0.407582i	$0.866372\pi$
$294$	−4.79497	+	3.48375i	−0.279648	+	0.203177i
$295$	28.8982	−	20.9958i	1.68252	−	1.22242i
$296$	−2.86850	−	3.18579i	−0.166728	−	0.185170i
$297$	15.2381	+	6.78443i	0.884203	+	0.393673i
$298$	−3.83662	+	1.70817i	−0.222249	+	0.0989517i
$299$	−0.850314	+	0.944369i	−0.0491749	+	0.0546143i
$300$	−2.17930	+	20.7346i	−0.125822	+	1.19711i
$301$	−8.90432	+	1.89267i	−0.513237	+	0.109092i
$302$	−0.469377	+	1.44459i	−0.0270096	+	0.0831271i
$303$	50.1411	+	10.6578i	2.88053	+	0.612276i
$304$	−3.46785	+	6.00650i	−0.198895	+	0.344496i
$305$	21.4595	+	37.1689i	1.22877	+	2.12829i
$306$	−1.06438	−	3.27583i	−0.0608467	−	0.187267i
$307$	−0.276844	−	2.63399i	−0.0158003	−	0.150330i	0.983777	−	0.179394i	$-0.0574138\pi$
$307$	−0.276844	−	2.63399i	−0.0158003	−	0.150330i	−0.999578	+	0.0290645i	$0.990747\pi$
$308$	3.99424	+	2.90198i	0.227593	+	0.165356i
$309$	−23.3600			−1.32890
$310$	5.53430	+	1.79364i	0.314327	+	0.101872i
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	−9.16358	−	6.65773i	−0.518786	−	0.376920i
$313$	2.78834	+	26.5293i	0.157607	+	1.49953i	0.732201	+	0.681088i	$0.238493\pi$
$313$	2.78834	+	26.5293i	0.157607	+	1.49953i	−0.574595	+	0.818438i	$0.694840\pi$
$314$	−0.945290	−	2.90930i	−0.0533458	−	0.164181i
$315$	8.64057	+	14.9659i	0.486841	+	0.843234i
$316$	−3.23474	+	5.60274i	−0.181969	+	0.315179i
$317$	−10.5055	−	2.23302i	−0.590050	−	0.125419i	−0.0967957	−	0.995304i	$-0.530859\pi$
$317$	−10.5055	−	2.23302i	−0.590050	−	0.125419i	−0.493254	+	0.869885i	$0.664193\pi$
$318$	1.56381	−	4.81291i	0.0876941	−	0.269895i
$319$	−7.51318	+	1.59698i	−0.420657	+	0.0894135i
$320$	1.61191	−	15.3363i	0.0901084	−	0.857324i
$321$	23.5246	−	26.1267i	1.31301	−	1.45825i
$322$	0.153633	−	0.0684017i	0.00856162	−	0.00381188i
$323$	−3.53117	−	1.57218i	−0.196480	−	0.0874784i
$324$	−4.69064	−	5.20948i	−0.260591	−	0.289416i
$325$	−8.92758	+	6.48627i	−0.495213	+	0.359793i
$326$	−0.889309	+	0.646121i	−0.0492543	+	0.0357853i
$327$	1.22374	+	1.35911i	0.0676732	+	0.0751587i
$328$	8.64492	+	3.84897i	0.477336	+	0.212524i
$329$	7.87106	−	3.50442i	0.433945	−	0.193205i
$330$	4.91841	−	5.46245i	0.270750	−	0.300698i
$331$	−2.05373	+	19.5400i	−0.112883	+	1.07401i	0.780635	+	0.624987i	$0.214896\pi$
$331$	−2.05373	+	19.5400i	−0.112883	+	1.07401i	−0.893518	+	0.449027i	$0.851771\pi$
$332$	23.5927	−	5.01478i	1.29482	−	0.275222i
$333$	5.22289	−	16.0744i	0.286213	−	0.880872i
$334$	4.59080	+	0.975804i	0.251197	+	0.0533936i
$335$	9.57021	−	16.5761i	0.522876	−	0.905649i
$336$	−5.12565	−	8.87788i	−0.279627	−	0.484328i
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	0.972406	+	0.233294i	$0.0749505\pi$
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	−0.649566	+	0.760305i	$0.725050\pi$
$338$	0.174200	+	1.65741i	0.00947525	+	0.0901510i
$339$	−26.4510	−	19.2178i	−1.43662	−	1.04376i
$340$	10.1808			0.552133
$341$	7.96520	+	10.9460i	0.431340	+	0.592757i
$342$	3.99844			0.216211
$343$	−11.2313	−	8.15999i	−0.606431	−	0.440598i
$344$	−1.19794	−	11.3976i	−0.0645885	−	0.614519i
$345$	1.17554	+	3.61794i	0.0632889	+	0.194783i
$346$	−3.34647	−	5.79626i	−0.179907	−	0.311609i
$347$	−5.32998	+	9.23180i	−0.286128	+	0.495589i	−0.972882	−	0.231301i	$-0.925702\pi$
$347$	−5.32998	+	9.23180i	−0.286128	+	0.495589i	0.686754	+	0.726890i	$0.259035\pi$
$348$	16.7769	+	3.56605i	0.899338	+	0.191160i
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	0.668671	+	0.743559i	$0.266864\pi$
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	−0.978019	+	0.208517i	$0.933136\pi$
$350$	1.42845	−	0.303627i	0.0763540	−	0.0162296i
$351$	2.06072	−	19.6064i	0.109993	−	1.04651i
$352$	−6.30478	+	7.00216i	−0.336046	+	0.373217i
$353$	−11.5675	+	5.15020i	−0.615678	+	0.274117i	−0.690787	−	0.723058i	$-0.742736\pi$
$353$	−11.5675	+	5.15020i	−0.615678	+	0.274117i	0.0751097	+	0.997175i	$0.476069\pi$
$354$	11.1596	+	4.96859i	0.593127	+	0.264077i
$355$	3.33810	+	3.70733i	0.177168	+	0.196765i
$356$	3.43001	−	2.49205i	0.181790	−	0.132078i
$357$	4.62205	−	3.35812i	0.244625	−	0.177730i
$358$	−0.0186548	−	0.0207182i	−0.000985936	−	0.00109499i
$359$	−20.7175	−	9.22402i	−1.09343	−	0.486825i	−0.220853	−	0.975307i	$-0.570884\pi$
$359$	−20.7175	−	9.22402i	−1.09343	−	0.486825i	−0.872574	+	0.488482i	$0.837551\pi$
$360$	−19.8750	+	8.84890i	−1.04750	+	0.466378i
$361$	−9.71104	+	10.7852i	−0.511107	+	0.567642i
$362$	−0.0794517	+	0.755932i	−0.00417589	+	0.0397309i
$363$	−14.4006	+	3.06095i	−0.755837	+	0.160658i
$364$	1.80319	−	5.54965i	0.0945129	−	0.290881i
$365$	−41.7631	−	8.87701i	−2.18598	−	0.464644i
$366$	−7.33880	+	12.7112i	−0.383605	+	0.664424i
$367$	−4.35984	−	7.55147i	−0.227582	−	0.394183i	0.729509	−	0.683971i	$-0.239749\pi$
$367$	−4.35984	−	7.55147i	−0.227582	−	0.394183i	−0.957091	+	0.289788i	$0.906415\pi$
$368$	−0.447430	−	1.37705i	−0.0233239	−	0.0717836i
$369$	3.89987	+	37.1048i	0.203019	+	1.93160i
$370$	−2.66005	−	1.93264i	−0.138290	−	0.100473i
$371$	5.38574			0.279614
$372$	−6.30699	−	29.5635i	−0.327002	−	1.53280i
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	−1.26141	−	0.916471i	−0.0652262	−	0.0473896i
$375$	−1.04298	−	9.92333i	−0.0538594	−	0.512438i
$376$	3.35188	+	10.3160i	0.172860	+	0.532009i
$377$	4.53913	+	7.86200i	0.233777	+	0.404914i
$378$	−1.30448	+	2.25943i	−0.0670954	+	0.116213i
$379$	−21.6150	−	4.59441i	−1.11029	−	0.235999i	−0.383961	−	0.923349i	$-0.625440\pi$
$379$	−21.6150	−	4.59441i	−1.11029	−	0.235999i	−0.726326	+	0.687350i	$0.758774\pi$
$380$	−3.65208	+	11.2399i	−0.187348	+	0.576597i
$381$	0.333399	−	0.0708662i	0.0170806	−	0.00363059i
$382$	0.196226	−	1.86696i	0.0100398	−	0.0955220i
$383$	−17.8274	+	19.7993i	−0.910938	+	1.01170i	0.0889398	+	0.996037i	$0.471652\pi$
$383$	−17.8274	+	19.7993i	−0.910938	+	1.01170i	−0.999877	+	0.0156617i	$0.995015\pi$
$384$	25.3039	−	11.2660i	1.29128	−	0.574916i
$385$	7.14640	+	3.18178i	0.364214	+	0.162159i
$386$	−0.501743	−	0.557242i	−0.0255380	−	0.0283629i
$387$	36.5547	−	26.5585i	1.85818	−	1.35005i
$388$	5.18112	−	3.76430i	0.263032	−	0.191104i
$389$	−8.66862	−	9.62748i	−0.439517	−	0.488133i	0.482165	−	0.876081i	$-0.339851\pi$
$389$	−8.66862	−	9.62748i	−0.439517	−	0.488133i	−0.921681	+	0.387948i	$0.873184\pi$
$390$	−7.93646	−	3.53354i	−0.401878	−	0.178928i
$391$	0.737176	−	0.328212i	0.0372806	−	0.0165984i
$392$	5.31357	−	5.90132i	0.268376	−	0.298062i
$393$	1.74925	−	16.6430i	0.0882379	−	0.839528i
$394$	2.01980	−	0.429321i	0.101756	−	0.0216289i
$395$	−3.16762	+	9.74894i	−0.159380	+	0.490522i
$396$	−23.9701	−	5.09500i	−1.20454	−	0.256033i
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	−0.826957	−	0.562265i	$-0.809930\pi$
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	0.900414	+	0.435033i	$0.143263\pi$
$398$	−1.21736	−	2.10852i	−0.0610205	−	0.105691i
$399$	2.04944	+	6.30752i	0.102600	+	0.315771i
$400$	−1.31427	−	12.5045i	−0.0657136	−	0.625223i
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	0.807446	−	0.589942i	$-0.200849\pi$
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	−0.311553	+	0.950229i	$0.600849\pi$
$402$	6.54572			0.326471
$403$	9.39479	−	12.9511i	0.467988	−	0.645142i
$404$	−33.2464			−1.65407
$405$	−8.98586	−	6.52861i	−0.446511	−	0.324409i
$406$	−0.125581	−	1.19482i	−0.00623246	−	0.0592979i
$407$	−2.36426	−	7.27645i	−0.117192	−	0.360680i
$408$	3.59625	+	6.22889i	0.178041	+	0.308376i
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	−0.571263	−	0.820767i	$-0.693546\pi$
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	0.996437	+	0.0843442i	$0.0268795\pi$
$410$	7.09944	+	1.50903i	0.350617	+	0.0745258i
$411$	−10.5549	+	32.4848i	−0.520637	+	1.60236i
$412$	14.8195	−	3.14997i	0.730102	−	0.155188i
$413$	−1.35893	+	12.9294i	−0.0668687	+	0.636213i
$414$	−0.558539	+	0.620320i	−0.0274507	+	0.0304871i
$415$	34.9127	−	15.5442i	1.71380	−	0.763032i
$416$	10.1735	+	4.52955i	0.498799	+	0.222080i
$417$	29.8568	+	33.1594i	1.46210	+	1.62382i
$418$	1.46431	−	1.06388i	0.0716217	−	0.0520362i
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	−0.942220	−	0.334996i	$-0.891265\pi$
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	0.0274378	+	0.999624i	$0.491265\pi$
$420$	−11.6884	−	12.9813i	−0.570338	−	0.633424i
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.935609	−	0.353038i	$-0.114851\pi$
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.363686	+	0.931522i	$0.381518\pi$
$422$	5.36434	−	2.38836i	0.261132	−	0.116263i
$423$	−28.6156	+	31.7808i	−1.39134	+	1.54524i
$424$	−0.708734	+	6.74315i	−0.0344192	+	0.327476i
$425$	6.85415	−	1.45689i	0.332475	−	0.0706697i
$426$	−0.527201	+	1.62256i	−0.0255430	+	0.0786132i
$427$	−15.2793	−	3.24771i	−0.739416	−	0.157168i
$428$	−11.4008	+	19.7468i	−0.551080	+	0.954498i
$429$	−10.1076	−	17.5069i	−0.487999	−	0.845239i
$430$	−2.71626	−	8.35979i	−0.130990	−	0.403145i
$431$	−3.17267	−	30.1859i	−0.152822	−	1.45401i	−0.755042	−	0.655676i	$-0.772384\pi$
$431$	−3.17267	−	30.1859i	−0.152822	−	1.45401i	0.602220	−	0.798330i	$-0.294283\pi$
$432$	18.1725	+	13.2031i	0.874326	+	0.635235i
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$	−1.83292	+	1.06006i	−0.0879830	+	0.0508846i
$435$	27.1762			1.30300
$436$	−0.959605	−	0.697194i	−0.0459567	−	0.0333895i
$437$	0.0979154	+	0.931602i	0.00468393	+	0.0445646i
$438$	−4.51207	−	13.8867i	−0.215595	−	0.663534i
$439$	−6.46006	−	11.1892i	−0.308322	−	0.534029i	0.669674	−	0.742656i	$-0.266434\pi$
$439$	−6.46006	−	11.1892i	−0.308322	−	0.534029i	−0.977995	+	0.208626i	$0.933101\pi$
$440$	−4.92414	+	8.52887i	−0.234749	+	0.406598i
$441$	30.6242	+	6.50938i	1.45830	+	0.309970i
$442$	−0.569463	+	1.75263i	−0.0270866	+	0.0833639i
$443$	−23.2391	+	4.93962i	−1.10412	+	0.234688i	−0.723693	−	0.690122i	$-0.757557\pi$
$443$	−23.2391	+	4.93962i	−1.10412	+	0.234688i	−0.380429	+	0.924810i	$0.624224\pi$
$444$	−1.78582	+	16.9909i	−0.0847511	+	0.806353i
$445$	4.49500	−	4.99220i	0.213083	−	0.236653i
$446$	−2.01027	+	0.895031i	−0.0951892	+	0.0423809i
$447$	31.5863	+	14.0631i	1.49398	+	0.665163i
$448$	3.75549	+	4.17089i	0.177430	+	0.197056i
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	−0.151900	−	0.988396i	$-0.548539\pi$
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	0.893081	+	0.449896i	$0.148539\pi$
$450$	−5.86419	+	4.26058i	−0.276440	+	0.200846i
$451$	11.3009	+	12.5509i	0.532137	+	0.590998i
$452$	19.3718	+	8.62487i	0.911171	+	0.405680i
$453$	11.4241	−	5.08632i	0.536749	−	0.238976i
$454$	−1.84538	+	2.04950i	−0.0866078	+	0.0961877i
$455$	0.966440	−	9.19507i	0.0453074	−	0.431071i
$456$	−8.16695	+	1.73594i	−0.382452	+	0.0812928i
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	−0.605935	−	0.795514i	$-0.707201\pi$
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	0.957803	−	0.287424i	$-0.0927990\pi$
$458$	−4.39075	−	0.933283i	−0.205166	−	0.0436094i
$459$	−6.25931	+	10.8414i	−0.292159	+	0.506035i
$460$	−1.23362	−	2.13669i	−0.0575177	−	0.0996235i
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	−0.704126	−	0.710075i	$-0.748661\pi$
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	0.152279	−	0.988338i	$-0.451339\pi$
$462$	0.279639	+	2.66059i	0.0130100	+	0.123782i
$463$	5.33489	+	3.87603i	0.247934	+	0.180134i	0.704810	−	0.709396i	$-0.251032\pi$
$463$	5.33489	+	3.87603i	0.247934	+	0.180134i	−0.456877	+	0.889530i	$0.651032\pi$
$464$	−10.3437			−0.480195
$465$	−19.5138	−	43.7409i	−0.904932	−	2.02843i
$466$	4.46933			0.207038
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.988532	−	0.151014i	$-0.951746\pi$
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.449096	−	0.893484i	$-0.648254\pi$
$468$	3.02749	+	28.8046i	0.139946	+	1.33149i
$469$	2.15270	+	6.62532i	0.0994024	+	0.305929i
$470$	4.15973	+	7.20487i	0.191874	+	0.332336i
$471$	−12.5922	+	21.8104i	−0.580220	+	1.00497i
$472$	−16.0092	−	3.40287i	−0.736885	−	0.156630i
$473$	6.32051	−	19.4525i	0.290617	−	0.894429i
$474$	−3.42895	+	0.728845i	−0.157497	+	0.0334770i
$475$	−0.850274	+	8.08981i	−0.0390132	+	0.371186i
$476$	−2.47938	+	2.75363i	−0.113642	+	0.126212i
$477$	−24.4210	+	10.8729i	−1.11816	+	0.497838i
$478$	−8.16256	−	3.63421i	−0.373347	−	0.166225i
$479$	5.03531	+	5.59228i	0.230069	+	0.255518i	0.847115	−	0.531409i	$-0.178337\pi$
$479$	5.03531	+	5.59228i	0.230069	+	0.255518i	−0.617046	+	0.786927i	$0.711671\pi$
$480$	26.9703	−	19.5951i	1.23102	−	0.894389i
$481$	−7.31567	+	5.31515i	−0.333566	+	0.242350i
$482$	0.555195	+	0.616606i	0.0252884	+	0.0280856i
$483$	−1.26484	−	0.563141i	−0.0575520	−	0.0256238i
$484$	8.72293	−	3.88370i	0.396497	−	0.176532i
$485$	6.78981	−	7.54085i	0.308310	−	0.342412i
$486$	−0.358996	+	3.41562i	−0.0162844	+	0.154936i
$487$	−24.4852	+	5.20450i	−1.10953	+	0.235838i	−0.726004	−	0.687691i	$-0.758625\pi$
$487$	−24.4852	+	5.20450i	−1.10953	+	0.235838i	−0.383528	+	0.923529i	$0.625291\pi$
$488$	6.07693	−	18.7029i	0.275090	−	0.846639i
$489$	8.85217	+	1.88159i	0.400309	+	0.0850883i
$490$	3.04533	−	5.27467i	0.137574	−	0.238285i
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.832507	+	0.554015i	$0.186905\pi$
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.0635377	+	0.997979i	$0.479762\pi$
$492$	−11.6539	−	35.8670i	−0.525399	−	1.61701i
$493$	−0.602573	−	5.73310i	−0.0271385	−	0.258206i
$494$	−1.73068	−	1.25741i	−0.0778668	−	0.0565735i
$495$	−38.8281			−1.74519
$496$	7.42729	+	16.6485i	0.333495	+	0.747539i
$497$	−1.81567			−0.0814440
$498$	10.5735	+	7.68207i	0.473808	+	0.344242i
$499$	2.47252	+	23.5245i	0.110685	+	1.05310i	0.899036	+	0.437875i	$0.144269\pi$
$499$	2.47252	+	23.5245i	0.110685	+	1.05310i	−0.788351	+	0.615226i	$0.789065\pi$
$500$	1.99977	+	6.15467i	0.0894325	+	0.275245i
$501$	−19.3199	−	33.4630i	−0.863148	−	1.49502i
$502$	−0.414099	+	0.717241i	−0.0184822	+	0.0320120i
$503$	19.7453	+	4.19699i	0.880400	+	0.187135i	0.625867	−	0.779930i	$-0.284745\pi$
$503$	19.7453	+	4.19699i	0.880400	+	0.187135i	0.254532	+	0.967064i	$0.418078\pi$
$504$	2.44685	−	7.53063i	0.108991	−	0.335441i
$505$	−51.5265	+	10.9523i	−2.29290	+	0.487370i
$506$	−0.0394968	+	0.375787i	−0.00175585	+	0.0167058i
$507$	9.18070	−	10.1962i	0.407729	−	0.452829i
$508$	−0.201951	+	0.0899143i	−0.00896012	+	0.00398930i
$509$	10.8155	+	4.81536i	0.479387	+	0.213437i	0.632180	−	0.774821i	$-0.282160\pi$
$509$	10.8155	+	4.81536i	0.479387	+	0.213437i	−0.152793	+	0.988258i	$0.548827\pi$
$510$	3.69131	+	4.09961i	0.163454	+	0.181534i
$511$	12.5717	−	9.13389i	0.556140	−	0.404060i
$512$	−17.4827	+	12.7019i	−0.772633	+	0.561351i
$513$	−9.72394	−	10.7995i	−0.429322	−	0.476811i
$514$	−8.35179	−	3.71845i	−0.368381	−	0.164014i
$515$	21.9300	−	9.76388i	0.966352	−	0.430248i
$516$	−30.5611	+	33.9416i	−1.34538	+	1.49419i
$517$	−2.02354	+	19.2526i	−0.0889950	+	0.846731i
$518$	1.17054	−	0.248806i	0.0514306	−	0.0109319i
$519$	−17.0275	+	52.4051i	−0.747422	+	2.30033i
$520$	11.3854	+	2.42004i	0.499283	+	0.106126i
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	0.962039	−	0.272911i	$-0.0879865\pi$
$522$	2.98158	+	5.16425i	0.130500	+	0.226033i
$523$	−9.11682	−	28.0587i	−0.398651	−	1.22692i	−0.926082	−	0.377323i	$-0.876845\pi$
$523$	−9.11682	−	28.0587i	−0.398651	−	1.22692i	0.527431	−	0.849598i	$-0.323155\pi$
$524$	1.13451	+	10.7941i	0.0495611	+	0.471543i
$525$	−9.72679	−	7.06693i	−0.424512	−	0.308426i
$526$	8.06030			0.351446
$527$	−8.79490	+	5.08650i	−0.383112	+	0.221571i
$528$	23.0331			1.00239
$529$	18.4492	+	13.4041i	0.802138	+	0.582788i
$530$	0.543591	+	5.17193i	0.0236121	+	0.224654i
$531$	−19.9404	−	61.3703i	−0.865340	−	2.66324i
$532$	−2.15069	−	3.72510i	−0.0932441	−	0.161504i
$533$	9.98053	−	17.2868i	0.432305	−	0.748774i
$534$	2.24713	+	0.477643i	0.0972430	+	0.0206696i
$535$	−11.1643	+	34.3600i	−0.482673	+	1.48551i
$536$	−8.57845	+	1.82340i	−0.370532	+	0.0787591i
$537$	−0.0239919	+	0.228267i	−0.00103533	+	0.00985047i
$538$	−4.00875	+	4.45217i	−0.172830	+	0.191947i
$539$	12.9472	−	5.76446i	0.557675	−	0.248293i
$540$	34.9668	+	15.5682i	1.50473	+	0.669949i
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	0.903104	−	0.429423i	$-0.141283\pi$
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	−0.521470	+	0.853270i	$0.674616\pi$
$542$	−2.06029	+	1.49689i	−0.0884970	+	0.0642968i
$543$	5.06264	−	3.67822i	0.217258	−	0.157848i
$544$	−4.73179	−	5.25519i	−0.202874	−	0.225314i
$545$	−1.71690	−	0.764415i	−0.0735441	−	0.0327439i
$546$	2.88853	−	1.28605i	0.123618	−	0.0550381i
$547$	25.2689	−	28.0640i	1.08042	−	1.19993i	0.101684	−	0.994817i	$-0.467577\pi$
$547$	25.2689	−	28.0640i	1.08042	−	1.19993i	0.978738	−	0.205114i	$-0.0657564\pi$
$548$	2.31560	−	22.0315i	0.0989175	−	0.941137i
$549$	75.8388	−	16.1200i	3.23672	−	0.687986i
$550$	−1.01395	+	3.12062i	−0.0432351	+	0.133064i
$551$	6.54568	+	1.39133i	0.278855	+	0.0592725i
$552$	0.871520	−	1.50952i	0.0370944	−	0.0642493i
$553$	−1.86539	−	3.23095i	−0.0793245	−	0.137394i
$554$	1.64019	+	5.04800i	0.0696852	+	0.214469i
$555$	2.82955	+	26.9214i	0.120108	+	1.14275i
$556$	−23.4124	−	17.0101i	−0.992907	−	0.721389i
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$	6.17108	−	8.50711i	0.261243	−	0.360135i
$559$	−24.1743			−1.02246
$560$	8.52261	+	6.19204i	0.360146	+	0.261661i
$561$	1.34179	+	12.7663i	0.0566505	+	0.538993i
$562$	−0.270094	−	0.831262i	−0.0113932	−	0.0350647i
$563$	10.0933	+	17.4821i	0.425381	+	0.736781i	0.996456	−	0.0841167i	$-0.0268068\pi$
$563$	10.0933	+	17.4821i	0.425381	+	0.736781i	−0.571075	+	0.820898i	$0.693474\pi$
$564$	21.6140	−	37.4365i	0.910113	−	1.57636i
$565$	32.8643	+	6.98552i	1.38261	+	0.293883i
$566$	−0.513276	+	1.57970i	−0.0215746	+	0.0663998i
$567$	3.95417	−	0.840485i	0.166060	−	0.0352971i
$568$	0.238933	−	2.27329i	0.0100254	−	0.0953852i
$569$	−20.7361	+	23.0298i	−0.869304	+	0.965460i	−0.999662	−	0.0260074i	$-0.991721\pi$
$569$	−20.7361	+	23.0298i	−0.869304	+	0.965460i	0.130358	+	0.991467i	$0.458387\pi$
$570$	−5.85026	+	2.60470i	−0.245040	+	0.109099i
$571$	−9.50060	−	4.22994i	−0.397588	−	0.177017i	0.198196	−	0.980162i	$-0.436492\pi$
$571$	−9.50060	−	4.22994i	−0.397588	−	0.177017i	−0.595784	+	0.803145i	$0.703158\pi$
$572$	8.77291	+	9.74330i	0.366814	+	0.407388i
$573$	−12.5034	+	9.08427i	−0.522338	+	0.379501i
$574$	−2.13711	+	1.55270i	−0.0892012	+	0.0648085i
$575$	−1.13628	−	1.26197i	−0.0473863	−	0.0526279i
$576$	−25.4492	−	11.3307i	−1.06038	−	0.472113i
$577$	4.94581	−	2.20201i	0.205897	−	0.0916711i	−0.301197	−	0.953562i	$-0.597386\pi$
$577$	4.94581	−	2.20201i	0.205897	−	0.0916711i	0.507094	+	0.861891i	$0.330720\pi$
$578$	−3.21461	+	3.57019i	−0.133710	+	0.148500i
$579$	−0.645291	+	6.13953i	−0.0268174	+	0.255150i
$580$	−17.2404	+	3.66457i	−0.715871	+	0.152163i
$581$	−4.29819	+	13.2285i	−0.178319	+	0.548809i
$582$	3.39435	+	0.721492i	0.140700	+	0.0299068i
$583$	−6.05046	+	10.4797i	−0.250585	+	0.434025i
$584$	9.78162	+	16.9423i	0.404766	+	0.701076i
$585$	14.1811	+	43.6451i	0.586318	+	1.80450i
$586$	0.387510	+	3.68691i	0.0160079	+	0.152305i
$587$	10.1635	+	7.38424i	0.419494	+	0.304780i	0.777434	−	0.628964i	$-0.216521\pi$
$587$	10.1635	+	7.38424i	0.419494	+	0.304780i	−0.357940	+	0.933744i	$0.616521\pi$
$588$	−31.6471			−1.30510
$589$	−2.46073	−	11.5345i	−0.101393	−	0.475270i
$590$	−12.5532			−0.516809
$591$	−13.7535	−	9.99247i	−0.565741	−	0.411035i
$592$	−1.07697	−	10.2467i	−0.0442634	−	0.421138i
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	0.962375	+	0.271726i	$0.0875943\pi$
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	−0.618861	+	0.785500i	$0.712406\pi$
$594$	−2.93098	−	5.07660i	−0.120259	−	0.208295i
$595$	−2.93551	+	5.08445i	−0.120344	+	0.208442i
$596$	−21.9345	−	4.66233i	−0.898473	−	0.190976i
$597$	−6.19413	+	19.0636i	−0.253509	+	0.780220i
$598$	0.436832	−	0.0928516i	0.0178634	−	0.00379698i
$599$	1.50051	−	14.2764i	0.0613094	−	0.583320i	−0.920139	−	0.391592i	$-0.871924\pi$
$599$	1.50051	−	14.2764i	0.0613094	−	0.583320i	0.981448	−	0.191727i	$-0.0614089\pi$
$600$	10.1281	−	11.2484i	0.413476	−	0.459212i
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	−0.394777	−	0.918777i	$-0.629178\pi$
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	0.418627	+	0.908158i	$0.362512\pi$
$602$	2.92260	+	1.30122i	0.119116	+	0.0530339i
$603$	−23.1366	−	25.6958i	−0.942197	−	1.04642i
$604$	−6.56150	+	4.76721i	−0.266984	+	0.193975i
$605$	12.2397	−	8.89266i	0.497614	−	0.361538i
$606$	−12.0543	−	13.3877i	−0.489673	−	0.543837i
$607$	−5.95432	−	2.65104i	−0.241679	−	0.107602i	0.282323	−	0.959319i	$-0.408895\pi$
$607$	−5.95432	−	2.65104i	−0.241679	−	0.107602i	−0.524002	+	0.851717i	$0.675562\pi$
$608$	7.49929	−	3.33890i	0.304136	−	0.135410i
$609$	−6.61834	+	7.35041i	−0.268189	+	0.297854i
$610$	1.57662	−	15.0005i	0.0638353	−	0.607352i
$611$	22.3802	−	4.75706i	0.905405	−	0.192450i
$612$	5.68333	−	17.4915i	0.229735	−	0.707052i
$613$	−10.2171	−	2.17170i	−0.412663	−	0.0877143i	−0.00309833	−	0.999995i	$-0.500986\pi$
$613$	−10.2171	−	2.17170i	−0.412663	−	0.0877143i	−0.409565	+	0.912281i	$0.634320\pi$
$614$	−0.465385	+	0.806070i	−0.0187814	+	0.0325303i
$615$	−29.8772	−	51.7489i	−1.20477	−	2.08672i
$616$	−1.10762	−	3.40892i	−0.0446274	−	0.137349i
$617$	−2.26862	−	21.5845i	−0.0913311	−	0.868958i	−0.940262	−	0.340453i	$-0.889420\pi$
$617$	−2.26862	−	21.5845i	−0.0913311	−	0.868958i	0.848930	−	0.528505i	$-0.177247\pi$
$618$	6.64159	+	4.82540i	0.267164	+	0.194106i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$	18.2777	+	25.1176i	0.734050	+	1.00875i
$621$	3.03377			0.121741
$622$	−1.56738	−	1.13877i	−0.0628462	−	0.0456604i
$623$	0.255566	+	2.43155i	0.0102390	+	0.0974178i
$624$	−8.41235	−	25.8906i	−0.336764	−	1.03645i
$625$	14.7271	+	25.5080i	0.589083	+	1.02032i
$626$	4.68731	−	8.11866i	0.187343	−	0.324487i
$627$	−14.5757	−	3.09816i	−0.582098	−	0.123729i
$628$	5.04743	−	15.5344i	0.201414	−	0.619890i
$629$	5.61660	−	1.19385i	0.223949	−	0.0476018i
$630$	0.634818	−	6.03989i	0.0252917	−	0.240635i
$631$	18.2275	−	20.2436i	0.725624	−	0.805887i	−0.261609	−	0.965174i	$-0.584253\pi$
$631$	18.2275	−	20.2436i	0.725624	−	0.805887i	0.987232	+	0.159287i	$0.0509196\pi$
$632$	4.29075	−	1.91037i	0.170677	−	0.0759903i
$633$	−44.1638	−	19.6630i	−1.75535	−	0.781533i
$634$	2.52561	+	2.80498i	0.100305	+	0.111400i
$635$	−0.283370	+	0.205880i	−0.0112452	+	0.00817012i
$636$	21.8607	−	15.8828i	0.866835	−	0.629792i
$637$	−11.2083	−	12.4481i	−0.444089	−	0.493210i
$638$	2.46599	+	1.09793i	0.0976295	+	0.0434675i
$639$	8.23296	−	3.66555i	0.325691	−	0.145007i
$640$	−19.0460	+	21.1527i	−0.752859	+	0.836135i
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	0.492880	+	0.870097i	$0.335944\pi$
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	−0.663013	+	0.748608i	$0.730722\pi$
$642$	−12.0853	+	2.56881i	−0.476969	+	0.101383i
$643$	−9.52156	+	29.3044i	−0.375494	+	1.15565i	0.567651	+	0.823269i	$0.307852\pi$
$643$	−9.52156	+	29.3044i	−0.375494	+	1.15565i	−0.943145	+	0.332382i	$0.892148\pi$
$644$	0.878342	+	0.186697i	0.0346115	+	0.00735691i
$645$	−36.1834	+	62.6715i	−1.42472	+	2.46769i
$646$	0.679205	+	1.17642i	0.0267230	+	0.0462855i
$647$	2.75525	+	8.47978i	0.108320	+	0.333375i	0.990495	−	0.137547i	$-0.0439217\pi$
$647$	2.75525	+	8.47978i	0.108320	+	0.333375i	−0.882175	+	0.470921i	$0.843922\pi$
$648$	0.531973	+	5.06138i	0.0208979	+	0.198830i
$649$	−23.6317	−	17.1694i	−0.927623	−	0.673958i
$650$	3.87809			0.152111
$651$	16.5830	+	5.37445i	0.649938	+	0.210641i
$652$	−5.86949			−0.229867
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.244601	−	0.969624i	$-0.578657\pi$
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.997753	+	0.0670010i	$0.978657\pi$
$654$	−0.0671825	−	0.639199i	−0.00262704	−	0.0249946i
$655$	5.31417	+	16.3553i	0.207642	+	0.639056i
$656$	11.3718	+	19.6965i	0.443993	+	0.769018i
$657$	−38.5652	+	66.7969i	−1.50457	+	2.60600i
$658$	−2.96175	−	0.629540i	−0.115461	−	0.0245420i
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	−0.530963	−	0.847395i	$-0.678170\pi$
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	0.927644	−	0.373465i	$-0.121830\pi$
$660$	38.3905	−	8.16015i	1.49435	−	0.317633i
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	−0.994172	−	0.107810i	$-0.965616\pi$
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	0.994861	+	0.101246i	$0.0322830\pi$
$662$	4.62022	−	5.13127i	0.179570	−	0.199433i
$663$	13.8600	−	6.17087i	0.538278	−	0.239657i
$664$	−15.9969	−	7.12229i	−0.620801	−	0.276398i
$665$	−4.56036	−	5.06479i	−0.176843	−	0.196404i
$666$	−4.80539	+	3.49132i	−0.186205	+	0.135286i
$667$	−1.13021	+	0.821147i	−0.0437620	+	0.0317950i
$668$	16.7687	+	18.6236i	0.648801	+	0.720567i
$669$	16.5503	+	7.36866i	0.639871	+	0.284889i
$670$	−6.14502	+	2.73594i	−0.237403	+	0.105699i
$671$	23.4846	−	26.0823i	0.906612	−	1.00689i
$672$	−1.26827	+	12.0668i	−0.0489246	+	0.465487i
$673$	14.2676	−	3.03267i	0.549976	−	0.116901i	0.0754613	−	0.997149i	$-0.475957\pi$
$673$	14.2676	−	3.03267i	0.549976	−	0.116901i	0.474514	+	0.880248i	$0.342624\pi$
$674$	2.08278	−	6.41015i	0.0802258	−	0.246910i
$675$	25.7689	+	5.47735i	0.991845	+	0.210823i
$676$	−4.44929	+	7.70639i	−0.171126	+	0.296400i
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	0.673826	−	0.738890i	$-0.264650\pi$
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	−0.976810	+	0.214106i	$0.931316\pi$
$678$	3.55065	+	10.9278i	0.136362	+	0.419679i
$679$	0.386039	+	3.67291i	0.0148148	+	0.140953i
$680$	−5.97963	−	4.34445i	−0.229308	−	0.166602i
$681$	22.7051			0.870063
$682$	−0.00355200	−	4.75744i	−0.000136013	−	0.182172i
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	17.2724	+	12.5492i	0.660428	+	0.479829i
$685$	−3.66897	−	34.9079i	−0.140184	−	1.33376i
$686$	1.50763	+	4.64001i	0.0575616	+	0.177156i
$687$	18.4780	+	32.0048i	0.704979	+	1.22106i
$688$	13.7720	−	23.8538i	0.525053	−	0.909418i
$689$	13.9896	+	2.97359i	0.532962	+	0.113285i
$690$	0.413123	−	1.27146i	0.0157273	−	0.0484037i
$691$	5.82165	−	1.23743i	0.221466	−	0.0470741i	−0.0958421	−	0.995397i	$-0.530554\pi$
$691$	5.82165	−	1.23743i	0.221466	−	0.0470741i	0.317308	+	0.948322i	$0.397221\pi$
$692$	3.73557	−	35.5416i	0.142005	−	1.35109i
$693$	9.45597	−	10.5019i	0.359203	−	0.398935i
$694$	3.42238	−	1.52374i	0.129912	−	0.0578404i
$695$	−41.8889	−	18.6502i	−1.58894	−	0.707441i
$696$	−8.33206	−	9.25369i	−0.315826	−	0.350760i
$697$	−10.2545	+	7.45032i	−0.388417	+	0.282201i
$698$	5.31713	−	3.86312i	0.201256	−	0.146221i
$699$	−24.6209	−	27.3443i	−0.931248	−	1.03426i
$700$	7.12357	+	3.17162i	0.269245	+	0.119876i
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.810988	−	0.585062i	$-0.801070\pi$
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.107871	+	0.994165i	$0.534403\pi$
$702$	−4.63592	+	5.14871i	−0.174972	+	0.194326i
$703$	−0.696753	+	6.62916i	−0.0262785	+	0.250024i
$704$	−12.3348	+	2.62185i	−0.464886	+	0.0988146i
$705$	21.1655	−	65.1407i	0.797138	−	2.45334i
$706$	4.35268	+	0.925191i	0.163815	+	0.0348200i
$707$	9.58617	−	16.6037i	0.360525	−	0.624448i
$708$	32.6133	+	56.4879i	1.22568	+	2.12295i
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	0.934550	−	0.355833i	$-0.115803\pi$
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	−0.965220	+	0.261439i	$0.915803\pi$
$710$	−0.183259	−	1.74359i	−0.00687757	−	0.0654357i
$711$	14.9812	+	10.8845i	0.561839	+	0.408200i
$712$	−3.07802			−0.115354
$713$	2.13321	+	1.22948i	0.0798892	+	0.0460445i
$714$	−2.00779			−0.0751398
$715$	16.8063	+	12.2105i	0.628519	+	0.456646i
$716$	−0.0155603	−	0.148047i	−0.000581518	−	0.00553277i
$717$	22.7315	+	69.9605i	0.848925	+	2.61272i
$718$	3.98491	+	6.90207i	0.148716	+	0.257583i
$719$	−2.59912	+	4.50181i	−0.0969308	+	0.167889i	−0.910413	−	0.413701i	$-0.864236\pi$
$719$	−2.59912	+	4.50181i	−0.0969308	+	0.167889i	0.813482	+	0.581590i	$0.197569\pi$
$720$	−51.1455	−	10.8713i	−1.90608	−	0.405150i
$721$	−2.69986	+	8.30930i	−0.100548	+	0.309455i
$722$	4.98886	−	1.06041i	0.185666	−	0.0394645i
$723$	0.714035	−	6.79359i	0.0265552	−	0.252656i
$724$	−2.71572	+	3.01611i	−0.100929	+	0.112093i
$725$	−11.0826	+	4.93428i	−0.411596	+	0.183254i
$726$	4.72660	+	2.10442i	0.175421	+	0.0781023i
$727$	16.1973	+	17.9889i	0.600723	+	0.667171i	0.964429	−	0.264343i	$-0.0851551\pi$
$727$	16.1973	+	17.9889i	0.600723	+	0.667171i	−0.363705	+	0.931514i	$0.618488\pi$
$728$	−3.42729	+	2.49007i	−0.127024	+	0.0922882i
$729$	31.9419	−	23.2071i	1.18303	−	0.859524i
$730$	10.0402	+	11.1507i	0.371603	+	0.412707i
$731$	14.0235	+	6.24366i	0.518677	+	0.230930i
$732$	−71.5963	+	31.8767i	−2.64628	+	1.17820i
$733$	27.0080	−	29.9954i	0.997562	−	1.10790i	0.00340093	−	0.999994i	$-0.498917\pi$
$733$	27.0080	−	29.9954i	0.997562	−	1.10790i	0.994161	−	0.107910i	$-0.0344159\pi$
$734$	−0.320315	+	3.04759i	−0.0118230	+	0.112489i
$735$	−49.0478	+	10.4254i	−1.80916	+	0.384548i
$736$	−0.529571	+	1.62985i	−0.0195202	+	0.0600771i
$737$	−15.3101	−	3.25427i	−0.563955	−	0.119872i
$738$	6.55583	−	11.3550i	0.241324	−	0.417985i
$739$	−3.04893	−	5.28089i	−0.112157	−	0.194261i	0.804483	−	0.593976i	$-0.202442\pi$
$739$	−3.04893	−	5.28089i	−0.112157	−	0.194261i	−0.916640	+	0.399715i	$0.869109\pi$
$740$	−5.42526	−	16.6972i	−0.199437	−	0.613803i
$741$	1.84095	+	17.5155i	0.0676292	+	0.643449i
$742$	−1.53125	−	1.11251i	−0.0562138	−	0.0408417i
$743$	16.2263			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$744$	−8.91125	+	20.0553i	−0.326702	+	0.735262i
$745$	−35.5308			−1.30175
$746$	−7.22540	−	5.24956i	−0.264541	−	0.192200i
$747$	−7.21649	−	68.6603i	−0.264038	−	2.51215i
$748$	−2.57269	−	7.91793i	−0.0940670	−	0.289508i
$749$	−6.57456	−	11.3875i	−0.240229	−	0.416089i
$750$	−1.75329	+	3.03680i	−0.0640213	+	0.110888i
$751$	−35.6481	−	7.57723i	−1.30082	−	0.276497i	−0.495119	−	0.868825i	$-0.664876\pi$
$751$	−35.6481	−	7.57723i	−1.30082	−	0.276497i	−0.805697	+	0.592328i	$0.798209\pi$
$752$	−8.05593	+	24.7936i	−0.293770	+	0.904130i
$753$	6.66944	−	1.41763i	0.243048	−	0.0516614i
$754$	0.333487	−	3.17292i	0.0121449	−	0.115551i
$755$	−8.59879	+	9.54992i	−0.312942	+	0.347557i
$756$	−12.7264	+	5.66615i	−0.462854	+	0.206076i
$757$	39.7960	+	17.7183i	1.44641	+	0.643984i	0.971713	−	0.236164i	$-0.0758904\pi$
$757$	39.7960	+	17.7183i	1.44641	+	0.643984i	0.474699	+	0.880148i	$0.342557\pi$
$758$	5.19641	+	5.77120i	0.188742	+	0.209619i
$759$	2.51672	−	1.82851i	0.0913512	−	0.0663705i
$760$	6.94144	−	5.04325i	0.251792	−	0.182938i
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	0.781828	−	0.623494i	$-0.214287\pi$
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	−0.701801	+	0.712373i	$0.747621\pi$
$762$	−0.109429	−	0.0487209i	−0.00396419	−	0.00176497i
$763$	0.624878	−	0.278214i	0.0226221	−	0.0100720i
$764$	6.70714	−	7.44903i	0.242656	−	0.269497i
$765$	3.04605	−	28.9812i	0.110130	−	1.04782i
$766$	9.15848	−	1.94669i	0.330909	−	0.0703369i
$767$	−10.6685	+	32.8342i	−0.385216	+	1.18557i
$768$	19.8350	+	4.21607i	0.715735	+	0.152134i
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	−0.0782634	−	0.996933i	$-0.524938\pi$
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	0.902501	−	0.430688i	$-0.141729\pi$
$770$	−1.37458	−	2.38084i	−0.0495363	−	0.0857995i
$771$	23.2585	+	71.5823i	0.837635	+	2.57798i
$772$	−0.418515	−	3.98190i	−0.0150627	−	0.143312i
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	0.0584131	−	0.998292i	$-0.481396\pi$
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	−0.931382	+	0.364044i	$0.881396\pi$
$774$	−15.8791			−0.570764
$775$	15.8997	+	14.2946i	0.571133	+	0.513479i
$776$	−4.64943			−0.166905
$777$	−7.97058	−	5.79097i	−0.285943	−	0.207750i
$778$	0.475900	+	4.52789i	0.0170618	+	0.162333i
$779$	−4.54689	−	13.9939i	−0.162909	−	0.501383i
$780$	−23.1938	−	40.1729i	−0.830472	−	1.43842i
$781$	2.03977	−	3.53298i	0.0729886	−	0.126420i
$782$	−0.277388	−	0.0589606i	−0.00991937	−	0.00210843i
$783$	6.69730	−	20.6122i	0.239342	−	0.736619i
$784$	18.6684	−	3.96809i	0.666729	−	0.141718i
$785$	2.70523	−	25.7385i	0.0965537	−	0.918647i
$786$	−3.93523	+	4.37051i	−0.140365	+	0.155891i
$787$	−39.4944	+	17.5840i	−1.40782	+	0.626803i	−0.963168	−	0.268899i	$-0.913340\pi$
$787$	−39.4944	+	17.5840i	−1.40782	+	0.626803i	−0.444654	+	0.895702i	$0.646673\pi$
$788$	10.0725	+	4.48459i	0.358820	+	0.159757i
$789$	−44.4030	−	49.3145i	−1.58079	−	1.75564i
$790$	2.91441	−	2.11744i	0.103690	−	0.0753352i
$791$	−9.89298	+	7.18767i	−0.351754	+	0.255564i
$792$	11.9045	+	13.2212i	0.423006	+	0.469796i
$793$	−37.8953	−	16.8721i	−1.34570	−	0.599145i
$794$	−0.939794	+	0.418423i	−0.0333520	+	0.0148493i
$795$	28.6483	−	31.8172i	1.01605	−	1.12844i
$796$	1.35890	−	12.9291i	0.0481649	−	0.458259i
$797$	−22.3250	+	4.74532i	−0.790792	+	0.168088i	−0.585564	−	0.810626i	$-0.699127\pi$
$797$	−22.3250	+	4.74532i	−0.790792	+	0.168088i	−0.205228	+	0.978714i	$0.565794\pi$
$798$	0.720239	−	2.21667i	0.0254962	−	0.0784691i
$799$	−14.2114	−	3.02072i	−0.502763	−	0.106865i
$800$	−7.44080	+	12.8878i	−0.263072	+	0.455654i
$801$	−6.06773	−	10.5096i	−0.214393	−	0.371339i
$802$	−1.33299	−	4.10252i	−0.0470695	−	0.144865i
$803$	3.64960	+	34.7236i	0.128792	+	1.22537i
$804$	28.2762	+	20.5438i	0.997223	+	0.724525i
$805$	1.42279			0.0501467
$806$	−5.34635	+	1.74155i	−0.188317	+	0.0613435i
$807$	49.3229			1.73625
$808$	19.5270	+	14.1872i	0.686959	+	0.499105i
$809$	2.22002	+	21.1221i	0.0780517	+	0.742613i	0.961634	+	0.274336i	$0.0884581\pi$
$809$	2.22002	+	21.1221i	0.0780517	+	0.742613i	−0.883582	+	0.468276i	$0.844875\pi$
$810$	1.20622	+	3.71236i	0.0423822	+	0.130439i
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	0.846785	−	0.531935i	$-0.178535\pi$
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	−0.884062	+	0.467370i	$0.845202\pi$
$812$	3.20748	−	5.55551i	0.112560	−	0.194960i
$813$	20.5081	+	4.35913i	0.719250	+	0.152881i
$814$	−0.830879	+	2.55718i	−0.0291223	+	0.0896292i
$815$	−9.09675	+	1.93357i	−0.318645	+	0.0677301i
$816$	−1.80693	+	17.1918i	−0.0632553	+	0.601834i
$817$	−11.9237	+	13.2426i	−0.417158	+	0.463301i
$818$	−5.52116	+	2.45818i	−0.193043	+	0.0859482i
$819$	−15.2584	−	6.79347i	−0.533171	−	0.237383i
$820$	25.9320	+	28.8004i	0.905586	+	1.00575i
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.992171	−	0.124891i	$-0.960142\pi$
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.187819	+	0.982204i	$0.560142\pi$
$822$	9.71121	−	7.05561i	0.338717	−	0.246093i
$823$	10.9058	+	12.1121i	0.380153	+	0.422203i	0.902608	−	0.430464i	$-0.141650\pi$
$823$	10.9058	+	12.1121i	0.380153	+	0.422203i	−0.522454	+	0.852667i	$0.674984\pi$
$824$	−10.0483	−	4.47378i	−0.350049	−	0.155852i
$825$	24.6783	−	10.9875i	0.859189	−	0.382535i
$826$	3.05714	−	3.39530i	0.106372	−	0.118138i
$827$	3.24974	−	30.9192i	0.113005	−	1.07517i	−0.780205	−	0.625524i	$-0.784885\pi$
$827$	3.24974	−	30.9192i	0.113005	−	1.07517i	0.893209	−	0.449642i	$-0.148448\pi$
$828$	−4.35966	+	0.926674i	−0.151509	+	0.0322041i
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	0.680090	+	0.733129i	$0.261941\pi$
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	−0.981126	+	0.193367i	$0.938059\pi$
$830$	−13.1371	−	2.79238i	−0.455996	−	0.0969249i
$831$	21.8491	−	37.8437i	0.757936	−	1.31278i
$832$	7.45215	+	12.9075i	0.258357	+	0.447487i
$833$	3.28688	+	10.1160i	0.113884	+	0.350498i
$834$	−1.63912	−	15.5951i	−0.0567579	−	0.540015i
$835$	32.1239	+	23.3394i	1.11169	+	0.807692i
$836$	9.66453			0.334255
$837$	−37.9848	+	4.02104i	−1.31295	+	0.138988i
$838$	8.13409			0.280987
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	0.861320	−	0.508062i	$-0.169638\pi$
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	−0.217034	+	0.976164i	$0.569638\pi$
$840$	1.32561	+	12.6123i	0.0457377	+	0.435165i
$841$	−5.87746	−	18.0890i	−0.202671	−	0.623757i
$842$	−5.12779	−	8.88160i	−0.176715	−	0.306080i
$843$	−3.59793	+	6.23179i	−0.123919	+	0.214634i
$844$	30.6687	+	6.51884i	1.05566	+	0.224388i
$845$	−4.35696	+	13.4093i	−0.149884	+	0.461296i
$846$	14.7007	−	3.12473i	0.505420	−	0.107430i
$847$	−0.575568	+	5.47617i	−0.0197768	+	0.188163i
$848$	−10.9040	+	12.1101i	−0.374446	+	0.415864i
$849$	12.4925	−	5.56202i	0.428741	−	0.190888i
$850$	−2.24968	−	1.00162i	−0.0771634	−	0.0343554i
$851$	−0.931124	−	1.03412i	−0.0319185	−	0.0354491i
$852$	−7.36982	+	5.35449i	−0.252486	+	0.183442i
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	−0.920007	−	0.391901i	$-0.871818\pi$
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	0.0884221	+	0.996083i	$0.471818\pi$
$854$	3.67326	+	4.07957i	0.125696	+	0.139600i
$855$	30.9035	+	13.7591i	1.05688	+	0.470551i
$856$	15.1227	−	6.73307i	0.516884	−	0.230132i
$857$	−36.5261	+	40.5663i	−1.24771	+	1.38572i	−0.355135	+	0.934815i	$0.615565\pi$
$857$	−36.5261	+	40.5663i	−1.24771	+	1.38572i	−0.892572	+	0.450904i	$0.851102\pi$
$858$	−0.742598	+	7.06535i	−0.0253519	+	0.241207i
$859$	−9.13238	+	1.94115i	−0.311593	+	0.0662311i	−0.361054	−	0.932545i	$-0.617583\pi$
$859$	−9.13238	+	1.94115i	−0.311593	+	0.0662311i	0.0494610	+	0.998776i	$0.484250\pi$
$860$	14.5036	−	44.6376i	0.494570	−	1.52213i
$861$	21.2728	+	4.52167i	0.724974	+	0.154098i
$862$	−5.33338	+	9.23768i	−0.181656	+	0.314637i
$863$	−6.65836	−	11.5326i	−0.226653	−	0.392575i	0.730161	−	0.683275i	$-0.239445\pi$
$863$	−6.65836	−	11.5326i	−0.226653	−	0.392575i	−0.956814	+	0.290700i	$0.906112\pi$
$864$	−8.21560	−	25.2850i	−0.279500	−	0.860214i
$865$	−5.91886	−	56.3142i	−0.201247	−	1.91474i
$866$	3.93491	+	2.85888i	0.133714	+	0.0971487i
$867$	39.5520			1.34326
$868$	−11.2449	−	1.17340i	−0.381676	−	0.0398276i
$869$	8.38250			0.284357
$870$	−7.72660	−	5.61370i	−0.261956	−	0.190322i
$871$	1.93371	+	18.3980i	0.0655213	+	0.623394i
$872$	0.266104	+	0.818983i	0.00901141	+	0.0277343i
$873$	−9.16547	−	15.8751i	−0.310204	−	0.537290i
$874$	0.164599	−	0.285094i	0.00556766	−	0.00964346i
$875$	−3.65034	−	0.775903i	−0.123404	−	0.0262303i
$876$	24.0925	−	74.1490i	0.814010	−	2.50526i
$877$	41.6359	−	8.84998i	1.40594	−	0.298843i	0.558402	−	0.829571i	$-0.311415\pi$
$877$	41.6359	−	8.84998i	1.40594	−	0.298843i	0.847542	+	0.530728i	$0.178081\pi$
$878$	−0.474617	+	4.51568i	−0.0160175	+	0.152397i
$879$	20.4225	−	22.6815i	0.688835	−	0.765029i
$880$	−21.6231	+	9.62723i	−0.728915	+	0.324534i
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	0.315966	−	0.948771i	$-0.397672\pi$
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	−0.493652	+	0.869660i	$0.664338\pi$
$882$	−7.36230	−	8.17666i	−0.247902	−	0.275323i
$883$	−22.0029	+	15.9860i	−0.740457	+	0.537973i	−0.892854	−	0.450346i	$-0.851301\pi$
$883$	−22.0029	+	15.9860i	−0.740457	+	0.537973i	0.152397	+	0.988319i	$0.451301\pi$
$884$	−7.96061	+	5.78372i	−0.267744	+	0.194528i
$885$	69.1539	+	76.8032i	2.32458	+	2.58171i
$886$	7.62758	+	3.39602i	0.256254	+	0.114091i
$887$	−6.73437	+	2.99834i	−0.226118	+	0.100674i	−0.516669	−	0.856185i	$-0.672828\pi$
$887$	−6.73437	+	2.99834i	−0.226118	+	0.100674i	0.290551	+	0.956860i	$0.406161\pi$
$888$	8.29940	−	9.21742i	0.278510	−	0.309316i
$889$	0.0133254	−	0.126783i	0.000446920	−	0.00425216i
$890$	−2.30922	+	0.490840i	−0.0774052	+	0.0164530i
$891$	−2.80677	+	8.63835i	−0.0940304	+	0.289396i
$892$	−11.4930	−	2.44292i	−0.384815	−	0.0817950i
$893$	8.43290	−	14.6062i	0.282196	−	0.488778i
$894$	−6.07548	−	10.5230i	−0.203194	−	0.351943i
$895$	−0.0728867	−	0.224322i	−0.00243633	−	0.00749826i
$896$	−1.08287	−	10.3028i	−0.0361762	−	0.344193i
$897$	−2.97453	−	2.16112i	−0.0993166	−	0.0721578i
$898$	−6.82232			−0.227664
$899$	13.0626	−	11.7793i	0.435663	−	0.392862i
$900$	−38.7040			−1.29013
$901$	−7.34737	−	5.33818i	−0.244776	−	0.177841i
$902$	−0.620408	−	5.90278i	−0.0206573	−	0.196541i
$903$	−8.13900	−	25.0493i	−0.270849	−	0.833588i
$904$	−7.69738	−	13.3322i	−0.256011	−	0.443424i
$905$	−3.21533	+	5.56911i	−0.106881	+	0.185123i
$906$	−4.29869	−	0.913715i	−0.142814	−	0.0303562i
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	−0.830189	−	0.557482i	$-0.811767\pi$
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	0.999317	+	0.0369599i	$0.0117674\pi$
$908$	−14.4040	+	3.06167i	−0.478014	+	0.101605i
$909$	−9.94714	+	94.6408i	−0.329926	+	3.13904i
$910$	−2.17417	+	2.41466i	−0.0720730	+	0.0800452i
$911$	40.9333	−	18.2247i	1.35618	−	0.603810i	0.405531	−	0.914081i	$-0.367087\pi$
$911$	40.9333	−	18.2247i	1.35618	−	0.603810i	0.950648	+	0.310271i	$0.100420\pi$
$912$	−18.3321	−	8.16199i	−0.607038	−	0.270271i
$913$	−20.9116	−	23.2247i	−0.692073	−	0.768625i
$914$	−6.92078	+	5.02824i	−0.228919	+	0.166319i
$915$	−100.461	+	72.9895i	−3.32115	+	2.41296i
$916$	−16.0380	−	17.8120i	−0.529911	−	0.588526i
$917$	−5.71785	−	2.54575i	−0.188820	−	0.0840681i
$918$	4.01909	−	1.78942i	0.132650	−	0.0590595i
$919$	−6.93006	+	7.69662i	−0.228602	+	0.253888i	−0.846523	−	0.532352i	$-0.821308\pi$
$919$	−6.93006	+	7.69662i	−0.228602	+	0.253888i	0.617921	+	0.786240i	$0.287975\pi$
$920$	−0.187231	+	1.78139i	−0.00617283	+	0.0587306i
$921$	7.49544	−	1.59320i	0.246983	−	0.0524979i
$922$	−4.16401	+	12.8155i	−0.137134	+	0.422056i
$923$	−4.71626	−	1.00247i	−0.155238	−	0.0329968i
$924$	−7.14231	+	12.3708i	−0.234965	+	0.406971i
$925$	−6.04191	−	10.4649i	−0.198657	−	0.344084i
$926$	−0.716131	−	2.20402i	−0.0235335	−	0.0724287i
$927$	−4.53296	−	43.1282i	−0.148882	−	1.41652i
$928$	9.90452	+	7.19606i	0.325132	+	0.236222i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$	−3.48734	+	16.4671i	−0.114354	+	0.539977i
$931$	−12.3474			−0.404671
$932$	19.3066	+	14.0271i	0.632409	+	0.459472i
$933$	1.66725	+	15.8629i	0.0545834	+	0.519327i
$934$	4.17034	+	12.8350i	0.136458	+	0.419974i
$935$	−6.59563	−	11.4240i	−0.215700	−	0.373604i
$936$	10.5136	−	18.2101i	0.343648	−	0.595216i
$937$	33.8116	+	7.18687i	1.10458	+	0.234785i	0.723887	−	0.689918i	$-0.242354\pi$
$937$	33.8116	+	7.18687i	1.10458	+	0.234785i	0.380689	+	0.924703i	$0.375687\pi$
$938$	0.756528	−	2.32835i	0.0247015	−	0.0760235i
$939$	−75.4933	+	16.0466i	−2.46363	+	0.523661i
$940$	−4.64339	+	44.1789i	−0.151451	+	1.44096i
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	−0.934595	−	0.355713i	$-0.884238\pi$
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	0.451457	+	0.892293i	$0.350905\pi$
$942$	8.08546	−	3.59988i	0.263439	−	0.117290i
$943$	2.80617	+	1.24939i	0.0913814	+	0.0406856i
$944$	−26.3211	−	29.2326i	−0.856680	−	0.951440i
$945$	−17.8572	+	12.9740i	−0.580894	+	0.422044i
$946$	−5.81526	+	4.22504i	−0.189071	+	0.137368i
$947$	−18.7909	−	20.8694i	−0.610622	−	0.678165i	0.355966	−	0.934499i	$-0.384152\pi$
$947$	−18.7909	−	20.8694i	−0.610622	−	0.678165i	−0.966588	+	0.256334i	$0.917485\pi$
$948$	−17.0998	−	7.61334i	−0.555377	−	0.247270i
$949$	37.6985	−	16.7844i	1.22374	−	0.544846i
$950$	1.91283	−	2.12442i	0.0620605	−	0.0689251i
$951$	3.24818	−	30.9044i	0.105330	−	1.00214i
$952$	2.63130	−	0.559300i	0.0852809	−	0.0181270i
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	−0.905323	−	0.424723i	$-0.860371\pi$
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	0.982068	+	0.188527i	$0.0603715\pi$
$954$	9.18925	+	1.95324i	0.297513	+	0.0632383i
$955$	7.94104	−	13.7543i	0.256966	−	0.445078i
$956$	−23.8546	−	41.3173i	−0.771512	−	1.33630i
$957$	−6.86743	−	21.1358i	−0.221992	−	0.683222i
$958$	−0.276434	−	2.63009i	−0.00893118	−	0.0849745i
$959$	10.3352	+	7.50893i	0.333740	+	0.242476i
$960$	44.6168			1.44000
$961$	−28.3387	−	12.5665i	−0.914152	−	0.405372i
$962$	3.17789			0.102459
$963$	52.8011	+	38.3622i	1.70149	+	1.23621i
$964$	0.463100	+	4.40610i	0.0149154	+	0.141911i
$965$	−1.96038	−	6.03342i	−0.0631067	−	0.194223i
$966$	0.243285	+	0.421383i	0.00782758	+	0.0135578i
$967$	0.925182	−	1.60246i	0.0297518	−	0.0515317i	−0.850766	−	0.525545i	$-0.823862\pi$
$967$	0.925182	−	1.60246i	0.0297518	−	0.0515317i	0.880518	+	0.474013i	$0.157195\pi$
$968$	−6.78063	−	1.44127i	−0.217938	−	0.0463241i
$969$	3.45592	−	10.6362i	0.111020	−	0.341685i
$970$	−3.48813	+	0.741426i	−0.111997	+	0.0238058i
$971$	−5.16072	+	49.1010i	−0.165615	+	1.57573i	0.524107	+	0.851652i	$0.324399\pi$
$971$	−5.16072	+	49.1010i	−0.165615	+	1.57573i	−0.689723	+	0.724074i	$0.742268\pi$
$972$	−12.2708	+	13.6281i	−0.393585	+	0.437121i
$973$	15.2457	−	6.78784i	0.488756	−	0.217608i
$974$	8.03659	+	3.57812i	0.257509	+	0.114650i
$975$	−21.3638	−	23.7270i	−0.684191	−	0.759871i
$976$	38.2373	−	27.7810i	1.22395	−	0.889248i
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	−0.0220160	−	0.999758i	$-0.507008\pi$
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	0.944023	+	0.329881i	$0.107008\pi$
$978$	−2.12813	−	2.36353i	−0.0680501	−	0.0755773i
$979$	−5.01847	−	2.23437i	−0.160391	−	0.0714107i
$980$	29.7098	−	13.2277i	0.949046	−	0.422543i
$981$	−2.27177	+	2.52306i	−0.0725321	+	0.0805550i
$982$	1.45874	−	13.8789i	0.0465501	−	0.442895i
$983$	6.24409	−	1.32722i	0.199156	−	0.0423318i	−0.107254	−	0.994232i	$-0.534206\pi$
$983$	6.24409	−	1.32722i	0.199156	−	0.0423318i	0.306409	+	0.951900i	$0.400872\pi$
$984$	−8.46068	+	26.0393i	−0.269717	+	0.830103i
$985$	17.0881	+	3.63220i	0.544473	+	0.115731i
$986$	−1.01295	+	1.75448i	−0.0322588	+	0.0558739i
$987$	12.4642	+	21.5887i	0.396740	+	0.687175i
$988$	−3.52977	−	10.8635i	−0.112297	−	0.345614i
$989$	−0.388855	−	3.69971i	−0.0123649	−	0.117644i
$990$	11.0394	+	8.02059i	0.350855	+	0.254911i
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$	4.47033	−	21.1087i	0.141933	−	0.670202i
$993$	−56.8463			−1.80396
$994$	0.516222	+	0.375058i	0.0163736	+	0.0118961i
$995$	−2.15312	−	20.4856i	−0.0682586	−	0.649437i
$996$	21.5649	+	66.3699i	0.683310	+	2.10301i
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	0.820797	−	0.571220i	$-0.193530\pi$
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	−0.905090	+	0.425221i	$0.860197\pi$
$998$	4.15641	−	7.19911i	0.131569	−	0.227884i
$999$	21.1162	+	4.48839i	0.668087	+	0.142006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.g.a.10.2	✓	16
3.2	odd	2		279.2.y.c.10.1		16
4.3	odd	2		496.2.bg.c.289.1		16
5.2	odd	4		775.2.ck.a.599.3		32
5.3	odd	4		775.2.ck.a.599.2		32
5.4	even	2		775.2.bl.a.351.1		16
31.2	even	5		961.2.g.t.846.1		16
31.3	odd	30		961.2.g.l.338.2		16
31.4	even	5		961.2.c.j.439.4		16
31.5	even	3		961.2.d.o.374.3		16
31.6	odd	6		961.2.g.j.732.2		16
31.7	even	15		961.2.c.j.521.4		16
31.8	even	5		961.2.g.s.547.1		16
31.9	even	15		961.2.d.p.531.2		16
31.10	even	15		961.2.d.p.628.2		16
31.11	odd	30		961.2.a.j.1.4		8
31.12	odd	30		961.2.g.m.448.1		16
31.13	odd	30		961.2.d.n.388.3		16
31.14	even	15		961.2.g.t.844.1		16
31.15	odd	10		961.2.g.j.235.2		16
31.16	even	5		961.2.g.k.235.2		16
31.17	odd	30		961.2.g.n.844.1		16
31.18	even	15		961.2.d.o.388.3		16
31.19	even	15		961.2.g.s.448.1		16
31.20	even	15		961.2.a.i.1.4		8
31.21	odd	30		961.2.d.q.628.2		16
31.22	odd	30		961.2.d.q.531.2		16
31.23	odd	10		961.2.g.m.547.1		16
31.24	odd	30		961.2.c.i.521.4		16
31.25	even	3		961.2.g.k.732.2		16
31.26	odd	6		961.2.d.n.374.3		16
31.27	odd	10		961.2.c.i.439.4		16
31.28	even	15	inner	31.2.g.a.28.2	yes	16
31.29	odd	10		961.2.g.n.846.1		16
31.30	odd	2		961.2.g.l.816.2		16
93.11	even	30		8649.2.a.be.1.5		8
93.20	odd	30		8649.2.a.bf.1.5		8
93.59	odd	30		279.2.y.c.28.1		16
124.59	odd	30		496.2.bg.c.369.1		16
155.28	odd	60		775.2.ck.a.524.3		32
155.59	even	30		775.2.bl.a.276.1		16
155.152	odd	60		775.2.ck.a.524.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	1.1	even	1	trivial
31.2.g.a.28.2	yes	16	31.28	even	15	inner
279.2.y.c.10.1		16	3.2	odd	2
279.2.y.c.28.1		16	93.59	odd	30
496.2.bg.c.289.1		16	4.3	odd	2
496.2.bg.c.369.1		16	124.59	odd	30
775.2.bl.a.276.1		16	155.59	even	30
775.2.bl.a.351.1		16	5.4	even	2
775.2.ck.a.524.2		32	155.152	odd	60
775.2.ck.a.524.3		32	155.28	odd	60
775.2.ck.a.599.2		32	5.3	odd	4
775.2.ck.a.599.3		32	5.2	odd	4
961.2.a.i.1.4		8	31.20	even	15
961.2.a.j.1.4		8	31.11	odd	30
961.2.c.i.439.4		16	31.27	odd	10
961.2.c.i.521.4		16	31.24	odd	30
961.2.c.j.439.4		16	31.4	even	5
961.2.c.j.521.4		16	31.7	even	15
961.2.d.n.374.3		16	31.26	odd	6
961.2.d.n.388.3		16	31.13	odd	30
961.2.d.o.374.3		16	31.5	even	3
961.2.d.o.388.3		16	31.18	even	15
961.2.d.p.531.2		16	31.9	even	15
961.2.d.p.628.2		16	31.10	even	15
961.2.d.q.531.2		16	31.22	odd	30
961.2.d.q.628.2		16	31.21	odd	30
961.2.g.j.235.2		16	31.15	odd	10
961.2.g.j.732.2		16	31.6	odd	6
961.2.g.k.235.2		16	31.16	even	5
961.2.g.k.732.2		16	31.25	even	3
961.2.g.l.338.2		16	31.3	odd	30
961.2.g.l.816.2		16	31.30	odd	2
961.2.g.m.448.1		16	31.12	odd	30
961.2.g.m.547.1		16	31.23	odd	10
961.2.g.n.844.1		16	31.17	odd	30
961.2.g.n.846.1		16	31.29	odd	10
961.2.g.s.448.1		16	31.19	even	15
961.2.g.s.547.1		16	31.8	even	5
961.2.g.t.844.1		16	31.14	even	15
961.2.g.t.846.1		16	31.2	even	5
8649.2.a.be.1.5		8	93.11	even	30
8649.2.a.bf.1.5		8	93.20	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.284315 - 0.206567i) q^{2} +(0.302431 + 2.87744i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(1.05848 + 0.224987i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(-5.25377 + 1.11672i) q^{9} +O(q^{10})\)	\(q+(-0.284315 - 0.206567i) q^{2} +(0.302431 + 2.87744i) q^{3} +(-0.579869 - 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(1.05848 + 0.224987i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(-5.25377 + 1.11672i) q^{9} +(-0.109221 + 1.03917i) q^{10} +(-1.62690 + 1.80686i) q^{11} +(4.95987 - 2.20827i) q^{12} +(2.62521 + 1.16882i) q^{13} +(-0.254466 - 0.282614i) q^{14} +(6.95951 - 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(-1.22101 - 1.35606i) q^{17} +(1.72440 + 0.767753i) q^{18} +(1.93514 - 0.861580i) q^{19} +(-3.73325 + 4.14619i) q^{20} +(-0.327269 + 3.11375i) q^{21} +(0.835790 - 0.177653i) q^{22} +(-0.136652 + 0.420572i) q^{23} +(-3.85547 - 0.819506i) q^{24} +(-1.92005 + 3.32562i) q^{25} +(-0.504947 - 0.874594i) q^{26} +(-2.11998 - 6.52462i) q^{27} +(-0.212256 - 2.01948i) q^{28} +(2.55579 + 1.85689i) q^{29} -3.02317 q^{30} +(1.15354 - 5.44696i) q^{31} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(0.0670322 + 0.637769i) q^{34} +(-0.994234 - 3.05994i) q^{35} +(5.03946 + 8.72860i) q^{36} +(-1.57338 + 2.72517i) q^{37} +(-0.728163 - 0.154776i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(3.96200 - 0.842148i) q^{40} +(0.726079 - 6.90818i) q^{41} +(0.736246 - 0.817684i) q^{42} +(-7.68509 + 3.42162i) q^{43} +(4.16801 + 1.85572i) q^{44} +(10.6858 + 11.8677i) q^{45} +(0.125728 - 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(-6.33887 - 7.04003i) q^{48} +(-5.32506 - 2.37087i) q^{49} +(1.23286 - 0.548905i) q^{50} +(3.53273 - 3.92349i) q^{51} +(0.563659 - 5.36285i) q^{52} +(4.86824 - 1.03478i) q^{53} +(-0.745029 + 2.29296i) q^{54} +(7.07105 + 1.50300i) q^{55} +(-0.737104 + 1.27670i) q^{56} +(3.06439 + 5.30768i) q^{57} +(-0.343078 - 1.05588i) q^{58} +(1.25580 + 11.9481i) q^{59} +(-13.0595 - 9.48827i) q^{60} -14.4351 q^{61} +(-1.45313 + 1.31037i) q^{62} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(-0.893094 - 8.49722i) q^{65} +(0.763955 + 2.35121i) q^{66} +(3.21879 + 5.57511i) q^{67} +(-1.71208 + 2.96541i) q^{68} +(-1.25150 - 0.266015i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(-1.64121 + 0.348850i) q^{71} +(0.764860 - 7.27716i) q^{72} +(9.60883 - 10.6717i) q^{73} +(1.01026 - 0.449798i) q^{74} +(-10.1500 - 4.51905i) q^{75} +(-2.65975 - 2.95395i) q^{76} +(-2.12856 + 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(-2.30692 - 2.56210i) q^{79} +(8.89339 + 3.95959i) q^{80} +(3.41274 - 1.51945i) q^{81} +(-1.63344 + 1.81412i) q^{82} +(-1.34357 + 12.7832i) q^{83} +(5.74674 - 1.22151i) q^{84} +(-1.67655 + 5.15991i) q^{85} +(2.89178 + 0.614667i) q^{86} +(-4.57015 + 7.91573i) q^{87} +(-1.65616 - 2.86855i) q^{88} +(0.698188 + 2.14880i) q^{89} +(-0.586639 - 5.58150i) q^{90} +(2.51576 + 1.82781i) q^{91} +0.829816 q^{92} +(16.0222 + 1.67190i) q^{93} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(1.17202 + 11.1510i) q^{96} +(1.05463 + 3.24582i) q^{97} +(1.02425 + 1.77405i) q^{98} +(6.52961 - 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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