LMFDB - Embedded newform 41.2.g.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, 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:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	41.2
Dual form			41.2.g.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40718 + 0.457221i) q^{2} +(-1.90046 + 1.90046i) q^{3} +(0.153075 - 0.111216i) q^{4} +(-0.455161 - 0.626475i) q^{5} +(1.80536 - 3.54322i) q^{6} +(2.12336 + 4.16732i) q^{7} +(1.57482 - 2.16755i) q^{8} -4.22349i q^{9} +O(q^{10})$	\(q+(-1.40718 + 0.457221i) q^{2} +(-1.90046 + 1.90046i) q^{3} +(0.153075 - 0.111216i) q^{4} +(-0.455161 - 0.626475i) q^{5} +(1.80536 - 3.54322i) q^{6} +(2.12336 + 4.16732i) q^{7} +(1.57482 - 2.16755i) q^{8} -4.22349i q^{9} +(0.926931 + 0.673455i) q^{10} +(-0.538340 + 0.0852647i) q^{11} +(-0.0795524 + 0.502274i) q^{12} +(-0.808560 - 0.411982i) q^{13} +(-4.89333 - 4.89333i) q^{14} +(2.05560 + 0.325576i) q^{15} +(-1.34194 + 4.13008i) q^{16} +(0.937351 + 5.91820i) q^{17} +(1.93107 + 5.94322i) q^{18} +(3.90401 - 1.98919i) q^{19} +(-0.139348 - 0.0452768i) q^{20} +(-11.9552 - 3.88447i) q^{21} +(0.718557 - 0.366123i) q^{22} +(-0.323498 - 0.995624i) q^{23} +(1.12646 + 7.11222i) q^{24} +(1.35979 - 4.18499i) q^{25} +(1.32616 + 0.210043i) q^{26} +(2.32519 + 2.32519i) q^{27} +(0.788504 + 0.401763i) q^{28} +(0.193017 - 1.21866i) q^{29} +(-3.04147 + 0.481721i) q^{30} +(1.22986 + 0.893547i) q^{31} -1.06686i q^{32} +(0.861051 - 1.18514i) q^{33} +(-4.02495 - 7.89940i) q^{34} +(1.64425 - 3.22703i) q^{35} +(-0.469718 - 0.646511i) q^{36} +(5.87120 - 4.26568i) q^{37} +(-4.58415 + 4.58415i) q^{38} +(2.31959 - 0.753680i) q^{39} -2.07471 q^{40} +(6.21116 - 1.55612i) q^{41} +18.5992 q^{42} +(-5.91654 + 1.92240i) q^{43} +(-0.0729237 + 0.0729237i) q^{44} +(-2.64591 + 1.92237i) q^{45} +(0.910440 + 1.25311i) q^{46} +(-1.80254 + 3.53768i) q^{47} +(-5.29874 - 10.3994i) q^{48} +(-8.74342 + 12.0343i) q^{49} +6.51076i q^{50} +(-13.0287 - 9.46590i) q^{51} +(-0.169589 + 0.0268603i) q^{52} +(0.837443 - 5.28741i) q^{53} +(-4.33510 - 2.20884i) q^{54} +(0.298447 + 0.298447i) q^{55} +(12.3768 + 1.96029i) q^{56} +(-3.63903 + 11.1998i) q^{57} +(0.285587 + 1.80313i) q^{58} +(2.74251 + 8.44059i) q^{59} +(0.350871 - 0.178778i) q^{60} +(1.31994 + 0.428873i) q^{61} +(-2.13919 - 0.695064i) q^{62} +(17.6006 - 8.96797i) q^{63} +(-2.19610 - 6.75890i) q^{64} +(0.109928 + 0.694060i) q^{65} +(-0.669787 + 2.06139i) q^{66} +(-5.56618 - 0.881596i) q^{67} +(0.801681 + 0.801681i) q^{68} +(2.50694 + 1.27735i) q^{69} +(-0.838297 + 5.29280i) q^{70} +(-1.07629 + 0.170468i) q^{71} +(-9.15463 - 6.65123i) q^{72} -5.61291i q^{73} +(-6.31149 + 8.68702i) q^{74} +(5.36919 + 10.5376i) q^{75} +(0.376378 - 0.738683i) q^{76} +(-1.49841 - 2.06239i) q^{77} +(-2.91948 + 2.12113i) q^{78} +(8.62379 - 8.62379i) q^{79} +(3.19819 - 1.03915i) q^{80} +3.83260 q^{81} +(-8.02874 + 5.02962i) q^{82} -13.1576 q^{83} +(-2.26205 + 0.734986i) q^{84} +(3.28096 - 3.28096i) q^{85} +(7.44668 - 5.41033i) q^{86} +(1.94919 + 2.68283i) q^{87} +(-0.662972 + 1.30116i) q^{88} +(-0.885629 - 1.73814i) q^{89} +(2.84433 - 3.91488i) q^{90} -4.24431i q^{91} +(-0.160248 - 0.116427i) q^{92} +(-4.03545 + 0.639153i) q^{93} +(0.918996 - 5.80231i) q^{94} +(-3.02313 - 1.54036i) q^{95} +(2.02752 + 2.02752i) q^{96} +(-1.91879 - 0.303907i) q^{97} +(6.80125 - 20.9321i) q^{98} +(0.360115 + 2.27367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.40718	+	0.457221i	−0.995028	+	0.323304i	−0.760877	−	0.648896i	$-0.775231\pi$
$2$	−1.40718	+	0.457221i	−0.995028	+	0.323304i	−0.234151	+	0.972200i	$0.575231\pi$
$3$	−1.90046	+	1.90046i	−1.09723	+	1.09723i	−0.102497	+	0.994733i	$0.532683\pi$
$3$	−1.90046	+	1.90046i	−1.09723	+	1.09723i	−0.994733	+	0.102497i	$0.967317\pi$
$4$	0.153075	−	0.111216i	0.0765376	−	0.0556078i
$5$	−0.455161	−	0.626475i	−0.203554	−	0.280168i	0.695020	−	0.718991i	$-0.255396\pi$
$5$	−0.455161	−	0.626475i	−0.203554	−	0.280168i	−0.898574	+	0.438823i	$0.855396\pi$
$6$	1.80536	−	3.54322i	0.737036	−	1.44651i
$7$	2.12336	+	4.16732i	0.802553	+	1.57510i	0.818000	+	0.575218i	$0.195083\pi$
$7$	2.12336	+	4.16732i	0.802553	+	1.57510i	−0.0154469	+	0.999881i	$0.504917\pi$
$8$	1.57482	−	2.16755i	0.556782	−	0.766345i
$9$		−	4.22349i		−	1.40783i
$10$	0.926931	+	0.673455i	0.293121	+	0.212965i
$11$	−0.538340	+	0.0852647i	−0.162316	+	0.0257083i	−0.237063	−	0.971494i	$-0.576185\pi$
$11$	−0.538340	+	0.0852647i	−0.162316	+	0.0257083i	0.0747477	+	0.997202i	$0.476185\pi$
$12$	−0.0795524	+	0.502274i	−0.0229648	+	0.144994i
$13$	−0.808560	−	0.411982i	−0.224254	−	0.114263i	0.338254	−	0.941055i	$-0.390164\pi$
$13$	−0.808560	−	0.411982i	−0.224254	−	0.114263i	−0.562508	+	0.826792i	$0.690164\pi$
$14$	−4.89333	−	4.89333i	−1.30780	−	1.30780i
$15$	2.05560	+	0.325576i	0.530755	+	0.0840633i
$16$	−1.34194	+	4.13008i	−0.335486	+	1.03252i
$17$	0.937351	+	5.91820i	0.227341	+	1.43537i	0.792238	+	0.610212i	$0.208916\pi$
$17$	0.937351	+	5.91820i	0.227341	+	1.43537i	−0.564897	+	0.825161i	$0.691084\pi$
$18$	1.93107	+	5.94322i	0.455157	+	1.40083i
$19$	3.90401	−	1.98919i	0.895641	−	0.456352i	0.0553374	−	0.998468i	$-0.482377\pi$
$19$	3.90401	−	1.98919i	0.895641	−	0.456352i	0.840304	+	0.542116i	$0.182377\pi$
$20$	−0.139348	−	0.0452768i	−0.0311591	−	0.0101242i
$21$	−11.9552	−	3.88447i	−2.60883	−	0.847661i
$22$	0.718557	−	0.366123i	0.153197	−	0.0780577i
$23$	−0.323498	−	0.995624i	−0.0674539	−	0.207602i	0.911648	−	0.410972i	$-0.134811\pi$
$23$	−0.323498	−	0.995624i	−0.0674539	−	0.207602i	−0.979102	+	0.203370i	$0.934811\pi$
$24$	1.12646	+	7.11222i	0.229939	+	1.45178i
$25$	1.35979	−	4.18499i	0.271957	−	0.836998i
$26$	1.32616	+	0.210043i	0.260081	+	0.0411927i
$27$	2.32519	+	2.32519i	0.447484	+	0.447484i
$28$	0.788504	+	0.401763i	0.149013	+	0.0759260i
$29$	0.193017	−	1.21866i	0.0358423	−	0.226299i	−0.963265	−	0.268554i	$-0.913454\pi$
$29$	0.193017	−	1.21866i	0.0358423	−	0.226299i	0.999107	+	0.0422549i	$0.0134542\pi$
$30$	−3.04147	+	0.481721i	−0.555294	+	0.0879499i
$31$	1.22986	+	0.893547i	0.220890	+	0.160486i	0.692727	−	0.721200i	$-0.256409\pi$
$31$	1.22986	+	0.893547i	0.220890	+	0.160486i	−0.471837	+	0.881686i	$0.656409\pi$
$32$		−	1.06686i		−	0.188595i
$33$	0.861051	−	1.18514i	0.149890	−	0.206306i
$34$	−4.02495	−	7.89940i	−0.690273	−	1.35474i
$35$	1.64425	−	3.22703i	0.277929	−	0.545467i
$36$	−0.469718	−	0.646511i	−0.0782863	−	0.107752i
$37$	5.87120	−	4.26568i	0.965220	−	0.701273i	0.0108626	−	0.999941i	$-0.496542\pi$
$37$	5.87120	−	4.26568i	0.965220	−	0.701273i	0.954357	+	0.298668i	$0.0965423\pi$
$38$	−4.58415	+	4.58415i	−0.743647	+	0.743647i
$39$	2.31959	−	0.753680i	0.371431	−	0.120685i
$40$	−2.07471			−0.328041
$41$	6.21116	−	1.55612i	0.970020	−	0.243025i
$41$	6.21116	−	1.55612i	0.970020	−	0.243025i
$42$	18.5992			2.86991
$43$	−5.91654	+	1.92240i	−0.902263	+	0.293163i	−0.723171	−	0.690669i	$-0.757316\pi$
$43$	−5.91654	+	1.92240i	−0.902263	+	0.293163i	−0.179092	+	0.983832i	$0.557316\pi$
$44$	−0.0729237	+	0.0729237i	−0.0109937	+	0.0109937i
$45$	−2.64591	+	1.92237i	−0.394429	+	0.286569i
$46$	0.910440	+	1.25311i	0.134237	+	0.184761i
$47$	−1.80254	+	3.53768i	−0.262927	+	0.516023i	−0.984296	−	0.176528i	$-0.943513\pi$
$47$	−1.80254	+	3.53768i	−0.262927	+	0.516023i	0.721369	+	0.692551i	$0.243513\pi$
$48$	−5.29874	−	10.3994i	−0.764807	−	1.50102i
$49$	−8.74342	+	12.0343i	−1.24906	+	1.71918i
$50$			6.51076i			0.920761i
$51$	−13.0287	−	9.46590i	−1.82438	−	1.32549i
$52$	−0.169589	+	0.0268603i	−0.0235178	+	0.00372485i
$53$	0.837443	−	5.28741i	0.115032	−	0.726281i	−0.860992	−	0.508618i	$-0.830157\pi$
$53$	0.837443	−	5.28741i	0.115032	−	0.726281i	0.976024	−	0.217663i	$-0.0698434\pi$
$54$	−4.33510	−	2.20884i	−0.589932	−	0.300585i
$55$	0.298447	+	0.298447i	0.0402426	+	0.0402426i
$56$	12.3768	+	1.96029i	1.65392	+	0.261955i
$57$	−3.63903	+	11.1998i	−0.482002	+	1.48345i
$58$	0.285587	+	1.80313i	0.0374994	+	0.236762i
$59$	2.74251	+	8.44059i	0.357045	+	1.09887i	0.954814	+	0.297203i	$0.0960538\pi$
$59$	2.74251	+	8.44059i	0.357045	+	1.09887i	−0.597769	+	0.801668i	$0.703946\pi$
$60$	0.350871	−	0.178778i	0.0452972	−	0.0230801i
$61$	1.31994	+	0.428873i	0.169001	+	0.0549116i	0.392295	−	0.919839i	$-0.371681\pi$
$61$	1.31994	+	0.428873i	0.169001	+	0.0549116i	−0.223295	+	0.974751i	$0.571681\pi$
$62$	−2.13919	−	0.695064i	−0.271677	−	0.0882732i
$63$	17.6006	−	8.96797i	2.21747	−	1.12986i
$64$	−2.19610	−	6.75890i	−0.274512	−	0.844862i
$65$	0.109928	+	0.694060i	0.0136349	+	0.0860875i
$66$	−0.669787	+	2.06139i	−0.0824450	+	0.253740i
$67$	−5.56618	−	0.881596i	−0.680017	−	0.107704i	−0.193135	−	0.981172i	$-0.561866\pi$
$67$	−5.56618	−	0.881596i	−0.680017	−	0.107704i	−0.486881	+	0.873468i	$0.661866\pi$
$68$	0.801681	+	0.801681i	0.0972181	+	0.0972181i
$69$	2.50694	+	1.27735i	0.301800	+	0.153775i
$70$	−0.838297	+	5.29280i	−0.100196	+	0.632611i
$71$	−1.07629	+	0.170468i	−0.127732	+	0.0202308i	−0.219973	−	0.975506i	$-0.570597\pi$
$71$	−1.07629	+	0.170468i	−0.127732	+	0.0202308i	0.0922409	+	0.995737i	$0.470597\pi$
$72$	−9.15463	−	6.65123i	−1.07888	−	0.783855i
$73$		−	5.61291i		−	0.656941i	−0.944514	−	0.328471i	$-0.893467\pi$
$73$		−	5.61291i		−	0.656941i	0.944514	−	0.328471i	$-0.106533\pi$
$74$	−6.31149	+	8.68702i	−0.733696	+	1.00985i
$75$	5.36919	+	10.5376i	0.619980	+	1.21678i
$76$	0.376378	−	0.738683i	0.0431735	−	0.0847327i
$77$	−1.49841	−	2.06239i	−0.170760	−	0.235031i
$78$	−2.91948	+	2.12113i	−0.330567	+	0.240171i
$79$	8.62379	−	8.62379i	0.970252	−	0.970252i	−0.0293183	−	0.999570i	$-0.509334\pi$
$79$	8.62379	−	8.62379i	0.970252	−	0.970252i	0.999570	+	0.0293183i	$0.00933364\pi$
$80$	3.19819	−	1.03915i	0.357568	−	0.116181i
$81$	3.83260			0.425844
$82$	−8.02874	+	5.02962i	−0.886626	+	0.555428i
$83$	−13.1576			−1.44423			−0.722116	−	0.691772i	$-0.756830\pi$
$83$	−13.1576			−1.44423			−0.722116	+	0.691772i	$0.756830\pi$
$84$	−2.26205	+	0.734986i	−0.246810	+	0.0801935i
$85$	3.28096	−	3.28096i	0.355870	−	0.355870i
$86$	7.44668	−	5.41033i	0.802996	−	0.583411i
$87$	1.94919	+	2.68283i	0.208975	+	0.287630i
$88$	−0.662972	+	1.30116i	−0.0706730	+	0.138704i
$89$	−0.885629	−	1.73814i	−0.0938764	−	0.184243i	0.839293	−	0.543679i	$-0.182969\pi$
$89$	−0.885629	−	1.73814i	−0.0938764	−	0.184243i	−0.933170	+	0.359436i	$0.882969\pi$
$90$	2.84433	−	3.91488i	0.299819	−	0.412665i
$91$		−	4.24431i		−	0.444925i
$92$	−0.160248	−	0.116427i	−0.0167070	−	0.0121384i
$93$	−4.03545	+	0.639153i	−0.418457	+	0.0662770i
$94$	0.918996	−	5.80231i	0.0947872	−	0.598463i
$95$	−3.02313	−	1.54036i	−0.310167	−	0.158038i
$96$	2.02752	+	2.02752i	0.206932	+	0.206932i
$97$	−1.91879	−	0.303907i	−0.194824	−	0.0308571i	0.0582598	−	0.998301i	$-0.481445\pi$
$97$	−1.91879	−	0.303907i	−0.194824	−	0.0308571i	−0.253084	+	0.967444i	$0.581445\pi$
$98$	6.80125	−	20.9321i	0.687030	−	2.11446i
$99$	0.360115	+	2.27367i	0.0361929	+	0.228513i
$100$	−0.257287	−	0.791847i	−0.0257287	−	0.0791847i
$101$	7.49597	−	3.81939i	0.745877	−	0.380043i	−0.0393710	−	0.999225i	$-0.512535\pi$
$101$	7.49597	−	3.81939i	0.745877	−	0.380043i	0.785248	+	0.619181i	$0.212535\pi$
$102$	22.6617	+	7.36325i	2.24385	+	0.729070i
$103$	4.08634	+	1.32773i	0.402639	+	0.130825i	0.503334	−	0.864092i	$-0.332107\pi$
$103$	4.08634	+	1.32773i	0.402639	+	0.130825i	−0.100695	+	0.994917i	$0.532107\pi$
$104$	−2.16632	+	1.10380i	−0.212426	+	0.108236i
$105$	3.00800	+	9.25767i	0.293551	+	0.903456i
$106$	1.23908	+	7.82324i	0.120350	+	0.759860i
$107$	3.82695	−	11.7782i	0.369966	−	1.13864i	−0.576847	−	0.816852i	$-0.695717\pi$
$107$	3.82695	−	11.7782i	0.369966	−	1.13864i	0.946813	−	0.321785i	$-0.104283\pi$
$108$	0.614527	+	0.0973316i	0.0591329	+	0.00936574i
$109$	1.22345	+	1.22345i	0.117185	+	0.117185i	0.763268	−	0.646082i	$-0.223594\pi$
$109$	1.22345	+	1.22345i	0.117185	+	0.117185i	−0.646082	+	0.763268i	$0.723594\pi$
$110$	−0.556426	−	0.283513i	−0.0530531	−	0.0270319i
$111$	−3.05123	+	19.2647i	−0.289610	+	1.82853i
$112$	−20.0608	+	3.17732i	−1.89557	+	0.300228i
$113$	0.944802	+	0.686439i	0.0888795	+	0.0645747i	0.631338	−	0.775508i	$-0.282506\pi$
$113$	0.944802	+	0.686439i	0.0888795	+	0.0645747i	−0.542458	+	0.840083i	$0.682506\pi$
$114$		−	17.4240i		−	1.63191i
$115$	−0.476490	+	0.655832i	−0.0444329	+	0.0611566i
$116$	−0.105988	−	0.208013i	−0.00984073	−	0.0193135i
$117$	−1.74000	+	3.41494i	−0.160863	+	0.315712i
$118$	−7.71843	−	10.6235i	−0.710539	−	0.977973i
$119$	−22.6727	+	16.4727i	−2.07840	+	1.51005i
$120$	3.94290	−	3.94290i	0.359936	−	0.359936i
$121$	−10.1791	+	3.30738i	−0.925371	+	0.300671i
$122$	−2.05348			−0.185913
$123$	−8.84671	+	14.7614i	−0.797681	+	1.33099i
$124$	0.287638			0.0258306
$125$	−6.92304	+	2.24943i	−0.619215	+	0.201195i
$126$	−20.6669	+	20.6669i	−1.84116	+	1.84116i
$127$	8.08534	−	5.87434i	0.717458	−	0.521264i	−0.168113	−	0.985768i	$-0.553767\pi$
$127$	8.08534	−	5.87434i	0.717458	−	0.521264i	0.885571	+	0.464504i	$0.153767\pi$
$128$	7.43478	+	10.2331i	0.657148	+	0.904487i
$129$	7.59069	−	14.8976i	0.668323	−	1.31166i
$130$	−0.472028	−	0.926407i	−0.0413996	−	0.0812513i
$131$	−0.478992	+	0.659276i	−0.0418497	+	0.0576012i	−0.829429	−	0.558612i	$-0.811334\pi$
$131$	−0.478992	+	0.659276i	−0.0418497	+	0.0576012i	0.787579	+	0.616213i	$0.211334\pi$
$132$		−	0.277177i		−	0.0241252i
$133$	16.5792	+	12.0455i	1.43760	+	1.04448i
$134$	8.23570	−	1.30441i	0.711456	−	0.112684i
$135$	0.398339	−	2.51501i	0.0342835	−	0.216458i
$136$	14.3042	+	7.28833i	1.22657	+	0.624969i
$137$	−3.04334	−	3.04334i	−0.260010	−	0.260010i	0.565048	−	0.825058i	$-0.308858\pi$
$137$	−3.04334	−	3.04334i	−0.260010	−	0.260010i	−0.825058	+	0.565048i	$0.808858\pi$
$138$	−4.11175	−	0.651237i	−0.350015	−	0.0554369i
$139$	1.55254	−	4.77824i	0.131685	−	0.405285i	−0.863375	−	0.504563i	$-0.831653\pi$
$139$	1.55254	−	4.77824i	0.131685	−	0.405285i	0.995060	+	0.0992785i	$0.0316535\pi$
$140$	−0.107202	−	0.676844i	−0.00906019	−	0.0572038i
$141$	−3.29756	−	10.1489i	−0.277705	−	0.854688i
$142$	1.43660	−	0.731983i	0.120557	−	0.0614266i
$143$	0.470407	+	0.152845i	0.0393374	+	0.0127815i
$144$	17.4433	+	5.66769i	1.45361	+	0.472307i
$145$	−0.851313	+	0.433765i	−0.0706977	+	0.0360223i
$146$	2.56634	+	7.89838i	0.212392	+	0.653675i
$147$	−6.25416	−	39.4872i	−0.515834	−	3.25685i
$148$	0.424325	−	1.30594i	0.0348793	−	0.107347i
$149$	7.82798	+	1.23983i	0.641293	+	0.101571i	0.468608	−	0.883406i	$-0.344756\pi$
$149$	7.82798	+	1.23983i	0.641293	+	0.101571i	0.172685	+	0.984977i	$0.444756\pi$
$150$	−12.3734	−	12.3734i	−1.01029	−	1.01029i
$151$	−18.4200	−	9.38545i	−1.49900	−	0.763777i	−0.504002	−	0.863702i	$-0.668140\pi$
$151$	−18.4200	−	9.38545i	−1.49900	−	0.763777i	−0.994995	+	0.0999253i	$0.968140\pi$
$152$	1.83643	−	11.5948i	0.148954	−	0.940459i
$153$	24.9955	−	3.95889i	2.02076	−	0.320057i
$154$	3.05151	+	2.21705i	0.245897	+	0.178655i
$155$		−	1.17718i		−	0.0945537i
$156$	0.271250	−	0.373344i	0.0217174	−	0.0298915i
$157$	5.47977	+	10.7546i	0.437333	+	0.858314i	0.999510	+	0.0312976i	$0.00996395\pi$
$157$	5.47977	+	10.7546i	0.437333	+	0.858314i	−0.562177	+	0.827017i	$0.690036\pi$
$158$	−8.19226	+	16.0782i	−0.651741	+	1.27911i
$159$	8.45697	+	11.6400i	0.670682	+	0.923114i
$160$	−0.668358	+	0.485591i	−0.0528384	+	0.0383893i
$161$	3.46218	−	3.46218i	0.272858	−	0.272858i
$162$	−5.39316	+	1.75234i	−0.423727	+	0.137677i
$163$	−2.00089			−0.156722			−0.0783609	−	0.996925i	$-0.524969\pi$
$163$	−2.00089			−0.156722			−0.0783609	+	0.996925i	$0.524969\pi$
$164$	0.777709	−	0.928981i	0.0607289	−	0.0725413i
$165$	−1.13437			−0.0883109
$166$	18.5151	−	6.01592i	1.43705	−	0.466926i
$167$	13.5221	−	13.5221i	1.04638	−	1.04638i	0.0475043	−	0.998871i	$-0.484873\pi$
$167$	13.5221	−	13.5221i	1.04638	−	1.04638i	0.998871	−	0.0475043i	$-0.0151268\pi$
$168$	−27.2470	+	19.7961i	−2.10215	+	1.52730i
$169$	−7.15717	−	9.85100i	−0.550551	−	0.757769i
$170$	−3.11678	+	6.11702i	−0.239046	+	0.469154i
$171$	−8.40134	−	16.4885i	−0.642466	−	1.26091i
$172$	−0.691874	+	0.952283i	−0.0527549	+	0.0726109i
$173$			6.00388i			0.456467i	0.973606	+	0.228233i	$0.0732949\pi$
$173$			6.00388i			0.456467i	−0.973606	+	0.228233i	$0.926705\pi$
$174$	−3.96951	−	2.88402i	−0.300928	−	0.218637i
$175$	20.3275	−	3.21956i	1.53661	−	0.243376i
$176$	0.370272	−	2.33781i	0.0279103	−	0.176219i
$177$	−21.2530	−	10.8290i	−1.59748	−	0.813954i
$178$	2.04096	+	2.04096i	0.152976	+	0.152976i
$179$	−9.04156	−	1.43204i	−0.675798	−	0.107036i	−0.190904	−	0.981609i	$-0.561142\pi$
$179$	−9.04156	−	1.43204i	−0.675798	−	0.107036i	−0.484894	+	0.874573i	$0.661142\pi$
$180$	−0.191226	+	0.588533i	−0.0142531	+	0.0438667i
$181$	2.98065	+	18.8191i	0.221550	+	1.39881i	0.808169	+	0.588950i	$0.200459\pi$
$181$	2.98065	+	18.8191i	0.221550	+	1.39881i	−0.586619	+	0.809863i	$0.699541\pi$
$182$	1.94059	+	5.97252i	0.143846	+	0.442712i
$183$	−3.32354	+	1.69343i	−0.245683	+	0.125182i
$184$	−2.66751	−	0.866728i	−0.196652	−	0.0638960i
$185$	−5.34468	−	1.73659i	−0.392949	−	0.127677i
$186$	5.38638	−	2.74450i	0.394948	−	0.201236i
$187$	−1.00923	−	3.10608i	−0.0738019	−	0.227139i
$188$	0.117521	+	0.742000i	0.00857112	+	0.0541159i
$189$	−4.75262	+	14.6270i	−0.345702	+	1.06396i
$190$	4.95838	+	0.785330i	0.359719	+	0.0569738i
$191$	7.96614	+	7.96614i	0.576410	+	0.576410i	0.933912	−	0.357503i	$-0.116372\pi$
$191$	7.96614	+	7.96614i	0.576410	+	0.576410i	−0.357503	+	0.933912i	$0.616372\pi$
$192$	17.0186	+	8.67141i	1.22821	+	0.625805i
$193$	−1.82911	+	11.5486i	−0.131663	+	0.831285i	0.830143	+	0.557551i	$0.188259\pi$
$193$	−1.82911	+	11.5486i	−0.131663	+	0.831285i	−0.961805	+	0.273734i	$0.911741\pi$
$194$	2.83904	−	0.449660i	0.203831	−	0.0322837i
$195$	−1.52795	−	1.11012i	−0.109419	−	0.0794972i
$196$			2.81456i			0.201040i
$197$	−5.94003	+	8.17575i	−0.423210	+	0.582498i	−0.966378	−	0.257126i	$-0.917225\pi$
$197$	−5.94003	+	8.17575i	−0.423210	+	0.582498i	0.543168	+	0.839624i	$0.317225\pi$
$198$	−1.54632	−	3.03482i	−0.109892	−	0.215675i
$199$	3.82058	−	7.49832i	0.270834	−	0.531542i	−0.715029	−	0.699095i	$-0.753587\pi$
$199$	3.82058	−	7.49832i	0.270834	−	0.531542i	0.985863	+	0.167553i	$0.0535866\pi$
$200$	−6.92976	−	9.53800i	−0.490008	−	0.674438i
$201$	12.2537	−	8.90285i	0.864311	−	0.627959i
$202$	−8.80189	+	8.80189i	−0.619299	+	0.619299i
$203$	5.48839	−	1.78328i	0.385209	−	0.125162i
$204$	−3.04712			−0.213341
$205$	−3.80195	−	3.18285i	−0.265539	−	0.222300i
$206$	−6.35728			−0.442933
$207$	−4.20501	+	1.36629i	−0.292268	+	0.0949637i
$208$	2.78656	−	2.78656i	0.193213	−	0.193213i
$209$	−1.93208	+	1.40374i	−0.133645	+	0.0970984i
$210$	−8.46560	−	11.6519i	−0.584182	−	0.804058i
$211$	−5.89458	+	11.5688i	−0.405800	+	0.796427i	−0.999969	−	0.00791335i	$-0.997481\pi$
$211$	−5.89458	+	11.5688i	−0.405800	+	0.796427i	0.594169	+	0.804340i	$0.297481\pi$
$212$	−0.459850	−	0.902507i	−0.0315827	−	0.0619845i
$213$	1.72148	−	2.36942i	0.117954	−	0.162350i
$214$			18.3238i			1.25259i
$215$	3.89731	+	2.83156i	0.265794	+	0.193111i
$216$	8.70173	−	1.37822i	0.592078	−	0.0937760i
$217$	−1.11226	+	7.02254i	−0.0755052	+	0.476721i
$218$	−2.28100	−	1.16223i	−0.154489	−	0.0787160i
$219$	10.6671	+	10.6671i	0.720816	+	0.720816i
$220$	0.0788768	+	0.0124929i	0.00531788	+	0.000842269i
$221$	1.68029	−	5.17139i	0.113028	−	0.347865i
$222$	−4.51460	−	28.5041i	−0.303000	−	1.91307i
$223$	−5.40722	−	16.6417i	−0.362094	−	1.11441i	−0.951781	−	0.306779i	$-0.900749\pi$
$223$	−5.40722	−	16.6417i	−0.362094	−	1.11441i	0.589686	−	0.807632i	$-0.299251\pi$
$224$	4.44593	−	2.26531i	0.297056	−	0.151358i
$225$	−17.6753	−	5.74304i	−1.17835	−	0.382869i
$226$	−1.64336	−	0.533961i	−0.109315	−	0.0355185i
$227$	−24.2713	+	12.3668i	−1.61094	+	0.820816i	−0.611377	+	0.791339i	$0.709384\pi$
$227$	−24.2713	+	12.3668i	−1.61094	+	0.820816i	−0.999565	+	0.0294771i	$0.990616\pi$
$228$	0.688546	+	2.11913i	0.0456001	+	0.140343i
$229$	3.54084	+	22.3560i	0.233985	+	1.47733i	0.772665	+	0.634815i	$0.218923\pi$
$229$	3.54084	+	22.3560i	0.233985	+	1.47733i	−0.538679	+	0.842511i	$0.681077\pi$
$230$	0.370647	−	1.14074i	0.0244398	−	0.0752179i
$231$	6.76715	+	1.07181i	0.445246	+	0.0705201i
$232$	−2.33754	−	2.33754i	−0.153467	−	0.153467i
$233$	21.5716	+	10.9913i	1.41320	+	0.720062i	0.983160	−	0.182747i	$-0.0584990\pi$
$233$	21.5716	+	10.9913i	1.41320	+	0.720062i	0.430041	+	0.902809i	$0.358499\pi$
$234$	0.887113	−	5.60101i	0.0579924	−	0.366150i
$235$	3.03671	−	0.480967i	0.198093	−	0.0313748i
$236$	1.35854	+	0.987034i	0.0884332	+	0.0642504i
$237$			32.7783i			2.12918i
$238$	24.3729	−	33.5465i	1.57986	−	2.17450i
$239$	−10.1154	−	19.8526i	−0.654312	−	1.28416i	−0.944915	−	0.327316i	$-0.893856\pi$
$239$	−10.1154	−	19.8526i	−0.654312	−	1.28416i	0.290603	−	0.956844i	$-0.406144\pi$
$240$	−4.10316	+	8.05290i	−0.264858	+	0.519813i
$241$	−7.10275	−	9.77610i	−0.457528	−	0.629734i	0.516466	−	0.856308i	$-0.327247\pi$
$241$	−7.10275	−	9.77610i	−0.457528	−	0.629734i	−0.973994	+	0.226574i	$0.927247\pi$
$242$	12.8116	−	9.30818i	0.823562	−	0.598353i
$243$	−14.2593	+	14.2593i	−0.914733	+	0.914733i
$244$	0.249747	−	0.0811477i	0.0159884	−	0.00519495i
$245$	11.5188			0.735911
$246$	5.69970	−	24.8169i	0.363400	−	1.58227i
$247$	−3.97613			−0.252995
$248$	3.87361	−	1.25861i	0.245975	−	0.0799221i
$249$	25.0054	−	25.0054i	1.58466	−	1.58466i
$250$	8.71348	−	6.33072i	0.551089	−	0.400390i
$251$	4.67048	+	6.42836i	0.294798	+	0.405755i	0.930565	−	0.366126i	$-0.119316\pi$
$251$	4.67048	+	6.42836i	0.294798	+	0.405755i	−0.635767	+	0.771881i	$0.719316\pi$
$252$	1.69684	−	3.33024i	0.106891	−	0.209785i
$253$	0.259043	+	0.508401i	0.0162859	+	0.0319629i
$254$	−8.69167	+	11.9631i	−0.545364	+	0.750629i
$255$			12.4706i			0.780942i
$256$	−3.64196	−	2.64604i	−0.227622	−	0.165377i
$257$	−23.2164	+	3.67711i	−1.44820	+	0.229372i	−0.830489	−	0.557035i	$-0.811939\pi$
$257$	−23.2164	+	3.67711i	−1.44820	+	0.229372i	−0.617709	+	0.786407i	$0.711939\pi$
$258$	−3.87000	+	24.4342i	−0.240936	+	1.52121i
$259$	30.2431	+	15.4096i	1.87921	+	0.957508i
$260$	0.0940176	+	0.0940176i	0.00583072	+	0.00583072i
$261$	−5.14700	−	0.815204i	−0.318591	−	0.0504599i
$262$	0.372594	−	1.14673i	0.0230189	−	0.0708450i
$263$	−3.34437	−	21.1155i	−0.206222	−	1.30204i	−0.845878	−	0.533376i	$-0.820923\pi$
$263$	−3.34437	−	21.1155i	−0.206222	−	1.30204i	0.639656	−	0.768661i	$-0.279077\pi$
$264$	−1.21284	−	3.73274i	−0.0746453	−	0.229734i
$265$	−3.69360	+	1.88198i	−0.226896	+	0.115609i
$266$	−28.8374	−	9.36984i	−1.76813	−	0.574502i
$267$	4.98637	+	1.62017i	0.305161	+	0.0991528i
$268$	−0.950090	+	0.484095i	−0.0580360	+	0.0295708i
$269$	−8.35420	−	25.7116i	−0.509364	−	1.56766i	−0.793308	−	0.608821i	$-0.791643\pi$
$269$	−8.35420	−	25.7116i	−0.509364	−	1.56766i	0.283943	−	0.958841i	$-0.408357\pi$
$270$	0.589381	+	3.72121i	0.0358686	+	0.226466i
$271$	−3.68892	+	11.3533i	−0.224086	+	0.689666i	0.774297	+	0.632822i	$0.218104\pi$
$271$	−3.68892	+	11.3533i	−0.224086	+	0.689666i	−0.998383	+	0.0568438i	$0.981896\pi$
$272$	−25.7005	−	4.07056i	−1.55832	−	0.246814i
$273$	8.06614	+	8.06614i	0.488185	+	0.488185i
$274$	5.67401	+	2.89105i	0.342780	+	0.174655i
$275$	−0.375195	+	2.36889i	−0.0226251	+	0.142849i
$276$	0.525811	−	0.0832802i	0.0316501	−	0.00501288i
$277$	−11.8657	−	8.62092i	−0.712940	−	0.517981i	0.171181	−	0.985240i	$-0.445242\pi$
$277$	−11.8657	−	8.62092i	−0.712940	−	0.517981i	−0.884121	+	0.467259i	$0.845242\pi$
$278$			7.43371i			0.445844i
$279$	3.77389	−	5.19431i	0.225937	−	0.310975i
$280$	−4.40535	−	8.64598i	−0.263270	−	0.516696i
$281$	4.85610	−	9.53063i	0.289691	−	0.568550i	−0.699596	−	0.714539i	$-0.746636\pi$
$281$	4.85610	−	9.53063i	0.289691	−	0.568550i	0.989286	+	0.145989i	$0.0466365\pi$
$282$	9.28054	+	12.7736i	0.552648	+	0.760655i
$283$	15.4306	−	11.2110i	0.917254	−	0.666424i	−0.0255849	−	0.999673i	$-0.508145\pi$
$283$	15.4306	−	11.2110i	0.917254	−	0.666424i	0.942839	+	0.333249i	$0.108145\pi$
$284$	−0.145795	+	0.145795i	−0.00865133	+	0.00865133i
$285$	8.67273	−	2.81794i	0.513728	−	0.166920i
$286$	−0.731832			−0.0432742
$287$	19.6734	+	22.5797i	1.16128	+	1.33284i
$288$	−4.50586			−0.265510
$289$	−17.9785	+	5.84156i	−1.05756	+	0.343621i
$290$	0.999625	−	0.999625i	0.0587000	−	0.0587000i
$291$	4.22415	−	3.06903i	0.247624	−	0.179909i
$292$	−0.624243	−	0.859197i	−0.0365311	−	0.0502807i
$293$	11.7759	−	23.1115i	0.687957	−	1.35019i	−0.237519	−	0.971383i	$-0.576334\pi$
$293$	11.7759	−	23.1115i	0.687957	−	1.35019i	0.925475	−	0.378808i	$-0.123666\pi$
$294$	26.8551	+	52.7061i	1.56622	+	3.07388i
$295$	4.03953	−	5.55994i	0.235191	−	0.323712i
$296$		−	19.4438i		−	1.13015i
$297$	−1.45000	−	1.05349i	−0.0841376	−	0.0611296i
$298$	−11.5823	+	1.83445i	−0.670943	+	0.106267i
$299$	−0.148612	+	0.938296i	−0.00859443	+	0.0542631i
$300$	1.99384	+	1.01591i	0.115114	+	0.0586536i
$301$	−20.5742	−	20.5742i	−1.18587	−	1.18587i
$302$	30.2115	+	4.78503i	1.73848	+	0.275348i
$303$	−6.98720	+	21.5044i	−0.401404	+	1.23539i
$304$	2.97656	+	18.7933i	0.170717	+	1.07787i
$305$	−0.332105	−	1.02211i	−0.0190163	−	0.0585260i
$306$	−33.3631	+	16.9993i	−1.90724	+	0.971787i
$307$	−8.23334	−	2.67517i	−0.469901	−	0.152680i	0.0644882	−	0.997918i	$-0.479459\pi$
$307$	−8.23334	−	2.67517i	−0.469901	−	0.152680i	−0.534390	+	0.845238i	$0.679459\pi$
$308$	−0.458739	−	0.149053i	−0.0261391	−	0.00849311i
$309$	−10.2892	+	5.24262i	−0.585333	+	0.298242i
$310$	0.538233	+	1.65651i	0.0305696	+	0.0940836i
$311$	1.26384	+	7.97957i	0.0716658	+	0.452480i	0.997261	+	0.0739647i	$0.0235652\pi$
$311$	1.26384	+	7.97957i	0.0716658	+	0.452480i	−0.925595	+	0.378515i	$0.876435\pi$
$312$	2.01929	−	6.21473i	0.114320	−	0.351840i
$313$	−3.40878	−	0.539898i	−0.192676	−	0.0305168i	0.0593507	−	0.998237i	$-0.481097\pi$
$313$	−3.40878	−	0.539898i	−0.192676	−	0.0305168i	−0.252026	+	0.967720i	$0.581097\pi$
$314$	−12.6283	−	12.6283i	−0.712655	−	0.712655i
$315$	−13.6293	−	6.94449i	−0.767925	−	0.391278i
$316$	0.360988	−	2.27919i	0.0203071	−	0.128214i
$317$	27.5726	−	4.36707i	1.54863	−	0.245279i	0.677201	−	0.735798i	$-0.263193\pi$
$317$	27.5726	−	4.36707i	1.54863	−	0.245279i	0.871431	+	0.490519i	$0.163193\pi$
$318$	−17.2226	−	12.5129i	−0.965794	−	0.701690i
$319$			0.672510i			0.0376534i
$320$	−3.23470	+	4.45218i	−0.180825	+	0.248885i
$321$	15.1109	+	29.6569i	0.843410	+	1.65529i
$322$	−3.28894	+	6.45490i	−0.183285	+	0.359718i
$323$	15.4319	+	21.2401i	0.858652	+	1.18183i
$324$	0.586675	−	0.426245i	0.0325931	−	0.0236803i
$325$	−2.82361	+	2.82361i	−0.156625	+	0.156625i
$326$	2.81562	−	0.914849i	0.155943	−	0.0506688i
$327$	−4.65023			−0.257158
$328$	6.40847	−	15.9136i	0.353848	−	0.878682i
$329$	−18.5701			−1.02380
$330$	1.59627	−	0.518659i	0.0878718	−	0.0285513i
$331$	−15.9651	+	15.9651i	−0.877522	+	0.877522i	−0.993278	−	0.115756i	$-0.963071\pi$
$331$	−15.9651	+	15.9651i	−0.877522	+	0.877522i	0.115756	+	0.993278i	$0.463071\pi$
$332$	−2.01410	+	1.46333i	−0.110538	+	0.0803106i
$333$	−18.0161	−	24.7970i	−0.987274	−	1.35887i
$334$	−12.8455	+	25.2107i	−0.702875	+	1.37947i
$335$	1.98121	+	3.88834i	0.108245	+	0.212442i
$336$	32.0863	−	44.1631i	1.75045	−	2.40929i
$337$		−	24.7909i		−	1.35045i	−0.737614	−	0.675223i	$-0.764048\pi$
$337$		−	24.7909i		−	1.35045i	0.737614	−	0.675223i	$-0.235952\pi$
$338$	14.5755	+	10.5897i	0.792804	+	0.576006i
$339$	−3.10011	+	0.491008i	−0.168375	+	0.0266679i
$340$	0.137339	−	0.867127i	0.00744827	−	0.0470265i
$341$	−0.738271	−	0.376168i	−0.0399796	−	0.0203706i
$342$	19.3611	+	19.3611i	1.04693	+	1.04693i
$343$	−36.3795	−	5.76195i	−1.96431	−	0.311116i
$344$	−5.15057	+	15.8518i	−0.277700	+	0.854673i
$345$	−0.340832	−	2.15193i	−0.0183498	−	0.115856i
$346$	−2.74510	−	8.44855i	−0.147578	−	0.454197i
$347$	−3.20315	+	1.63209i	−0.171954	+	0.0876149i	−0.537849	−	0.843041i	$-0.680763\pi$
$347$	−3.20315	+	1.63209i	−0.171954	+	0.0876149i	0.365895	+	0.930656i	$0.380763\pi$
$348$	0.596746	+	0.193894i	0.0319889	+	0.0103938i
$349$	−0.272833	−	0.0886489i	−0.0146044	−	0.00474526i	0.301706	−	0.953401i	$-0.402444\pi$
$349$	−0.272833	−	0.0886489i	−0.0146044	−	0.00474526i	−0.316310	+	0.948656i	$0.602444\pi$
$350$	−27.1324	+	13.8247i	−1.45029	+	0.738959i
$351$	−0.922121	−	2.83800i	−0.0492192	−	0.151481i
$352$	0.0909651	+	0.574331i	0.00484846	+	0.0306119i
$353$	−7.26560	+	22.3612i	−0.386709	+	1.19017i	0.548524	+	0.836135i	$0.315190\pi$
$353$	−7.26560	+	22.3612i	−0.386709	+	1.19017i	−0.935233	+	0.354033i	$0.884810\pi$
$354$	34.8581	+	5.52098i	1.85269	+	0.293437i
$355$	0.596679	+	0.596679i	0.0316685	+	0.0316685i
$356$	−0.328876	−	0.167571i	−0.0174304	−	0.00888124i
$357$	11.7829	−	74.3942i	0.623616	−	3.93736i
$358$	13.3779	−	2.11885i	0.707043	−	0.111985i
$359$	27.7932	+	20.1929i	1.46687	+	1.06574i	0.981506	+	0.191430i	$0.0613125\pi$
$359$	27.7932	+	20.1929i	1.46687	+	1.06574i	0.485363	+	0.874313i	$0.338687\pi$
$360$			8.76252i			0.461825i
$361$	0.116485	−	0.160328i	0.00613080	−	0.00843832i
$362$	−12.7988	−	25.1191i	−0.672691	−	1.32023i
$363$	13.0594	−	25.6305i	0.685440	−	1.34525i
$364$	−0.472033	−	0.649698i	−0.0247413	−	0.0340534i
$365$	−3.51635	+	2.55477i	−0.184054	+	0.133723i
$366$	3.90256	−	3.90256i	0.203990	−	0.203990i
$367$	24.8067	−	8.06019i	1.29490	−	0.420738i	0.421096	−	0.907016i	$-0.361646\pi$
$367$	24.8067	−	8.06019i	1.29490	−	0.420738i	0.873804	+	0.486278i	$0.161646\pi$
$368$	4.54612			0.236983
$369$	−6.57227	−	26.2328i	−0.342139	−	1.36562i
$370$	8.31494			0.432273
$371$	23.8125	−	7.73715i	1.23628	−	0.401693i
$372$	−0.546643	+	0.546643i	−0.0283421	+	0.0283421i
$373$	8.17007	−	5.93590i	0.423030	−	0.307349i	−0.355826	−	0.934552i	$-0.615800\pi$
$373$	8.17007	−	5.93590i	0.423030	−	0.307349i	0.778856	+	0.627203i	$0.215800\pi$
$374$	2.84033	+	3.90938i	0.146870	+	0.202149i
$375$	8.88200	−	17.4319i	0.458664	−	0.900180i
$376$	4.82943	+	9.47828i	0.249059	+	0.488805i
$377$	−0.658131	+	0.905839i	−0.0338955	+	0.0466531i
$378$		−	22.7559i		−	1.17044i
$379$	10.7064	+	7.77867i	0.549952	+	0.399563i	0.827768	−	0.561071i	$-0.189611\pi$
$379$	10.7064	+	7.77867i	0.549952	+	0.399563i	−0.277816	+	0.960634i	$0.589611\pi$
$380$	−0.634078	+	0.100428i	−0.0325275	+	0.00515185i
$381$	−4.20191	+	26.5298i	−0.215270	+	1.35916i
$382$	−14.8521	−	7.56752i	−0.759899	−	0.387188i
$383$	4.86397	+	4.86397i	0.248537	+	0.248537i	0.820370	−	0.571833i	$-0.193767\pi$
$383$	4.86397	+	4.86397i	0.248537	+	0.248537i	−0.571833	+	0.820370i	$0.693767\pi$
$384$	−33.5771	−	5.31809i	−1.71347	−	0.271388i
$385$	−0.610016	+	1.87743i	−0.0310893	+	0.0956829i
$386$	−2.70636	−	17.0873i	−0.137750	−	0.869718i
$387$	8.11923	+	24.9884i	0.412724	+	1.27023i
$388$	−0.327519	+	0.166879i	−0.0166272	+	0.00847201i
$389$	29.0233	+	9.43023i	1.47154	+	0.478132i	0.931572	−	0.363556i	$-0.118437\pi$
$389$	29.0233	+	9.43023i	1.47154	+	0.478132i	0.539965	+	0.841687i	$0.318437\pi$
$390$	2.65767	+	0.863529i	0.134576	+	0.0437265i
$391$	5.58907	−	2.84777i	0.282651	−	0.144018i
$392$	12.3156	+	37.9036i	0.622033	+	1.91442i
$393$	−0.342622	−	2.16323i	−0.0172830	−	0.109121i
$394$	4.62058	−	14.2207i	0.232781	−	0.716427i
$395$	−9.32779	−	1.47738i	−0.469332	−	0.0743349i
$396$	0.307993	+	0.307993i	0.0154772	+	0.0154772i
$397$	−21.4147	−	10.9114i	−1.07477	−	0.547625i	−0.175263	−	0.984522i	$-0.556078\pi$
$397$	−21.4147	−	10.9114i	−1.07477	−	0.547625i	−0.899512	+	0.436896i	$0.856078\pi$
$398$	−1.94787	+	12.2983i	−0.0976377	+	0.616460i
$399$	−54.4001	+	8.61612i	−2.72341	+	0.431346i
$400$	15.4596	+	11.2320i	0.772979	+	0.561602i
$401$		−	4.76630i		−	0.238018i	−0.992893	−	0.119009i	$-0.962028\pi$
$401$		−	4.76630i		−	0.238018i	0.992893	−	0.119009i	$-0.0379717\pi$
$402$	−13.1726	+	18.1306i	−0.656992	+	0.904272i
$403$	−0.626291	−	1.22917i	−0.0311978	−	0.0612291i
$404$	0.722671	−	1.41832i	0.0359542	−	0.0705642i
$405$	−1.74445	−	2.40103i	−0.0866823	−	0.119308i
$406$	−6.90780	+	5.01881i	−0.342828	+	0.249079i
$407$	−2.79699	+	2.79699i	−0.138642	+	0.138642i
$408$	−41.0356	+	13.3333i	−2.03157	+	0.660096i
$409$	−37.1120			−1.83507			−0.917534	−	0.397657i	$-0.869824\pi$
$409$	−37.1120			−1.83507			−0.917534	+	0.397657i	$0.869824\pi$
$410$	6.80529	+	2.74052i	0.336089	+	0.135344i
$411$	11.5675			0.570582
$412$	0.773181	−	0.251222i	0.0380919	−	0.0123768i
$413$	−29.3513	+	29.3513i	−1.44428	+	1.44428i
$414$	5.29251	−	3.84524i	0.260113	−	0.188983i
$415$	5.98881	+	8.24289i	0.293979	+	0.404628i
$416$	−0.439525	+	0.862616i	−0.0215495	+	0.0422933i
$417$	6.13030	+	12.0314i	0.300202	+	0.589180i
$418$	2.07696	−	2.85870i	0.101588	−	0.139823i
$419$		−	11.2273i		−	0.548491i	−0.961660	−	0.274246i	$-0.911572\pi$
$419$		−	11.2273i		−	0.548491i	0.961660	−	0.274246i	$-0.0884281\pi$
$420$	1.49005	+	1.08258i	0.0727069	+	0.0528246i
$421$	−16.7385	+	2.65113i	−0.815787	+	0.129208i	−0.550365	−	0.834924i	$-0.685511\pi$
$421$	−16.7385	+	2.65113i	−0.815787	+	0.129208i	−0.265422	+	0.964132i	$0.585511\pi$
$422$	3.00526	−	18.9745i	0.146294	−	0.923664i
$423$	14.9413	+	7.61299i	0.726473	+	0.370156i
$424$	−10.1419	−	10.1419i	−0.492534	−	0.492534i
$425$	26.0422	+	4.12468i	1.26323	+	0.200076i
$426$	−1.33909	+	4.12130i	−0.0648792	+	0.199677i
$427$	1.01544	+	6.41125i	0.0491407	+	0.310262i
$428$	−0.724103	−	2.22856i	−0.0350008	−	0.107722i
$429$	−1.18446	+	0.603515i	−0.0571865	+	0.0291380i
$430$	−6.77887	−	2.20259i	−0.326906	−	0.106218i
$431$	−19.3545	−	6.28864i	−0.932271	−	0.302913i	−0.196780	−	0.980448i	$-0.563048\pi$
$431$	−19.3545	−	6.28864i	−0.932271	−	0.302913i	−0.735491	+	0.677534i	$0.763048\pi$
$432$	−12.7235	+	6.48296i	−0.612160	+	0.311911i
$433$	6.55082	+	20.1613i	0.314812	+	0.968893i	0.975832	+	0.218524i	$0.0701241\pi$
$433$	6.55082	+	20.1613i	0.314812	+	0.968893i	−0.661019	+	0.750369i	$0.729876\pi$
$434$	−1.64570	−	10.3905i	−0.0789961	−	0.498762i
$435$	0.793531	−	2.44224i	0.0380469	−	0.117096i
$436$	0.323346	+	0.0512130i	0.0154855	+	0.00245266i
$437$	−3.24343	−	3.24343i	−0.155154	−	0.155154i
$438$	−19.8878	−	10.1333i	−0.950275	−	0.484189i
$439$	3.23308	−	20.4129i	0.154306	−	0.974252i	−0.782054	−	0.623211i	$-0.785828\pi$
$439$	3.23308	−	20.4129i	0.154306	−	0.974252i	0.936360	−	0.351041i	$-0.114172\pi$
$440$	1.11690	−	0.176900i	0.0532461	−	0.00843335i
$441$	50.8267	+	36.9278i	2.42032	+	1.75846i
$442$			8.04534i			0.382678i
$443$	12.7566	−	17.5580i	0.606086	−	0.834206i	−0.390162	−	0.920746i	$-0.627581\pi$
$443$	12.7566	−	17.5580i	0.606086	−	0.834206i	0.996248	+	0.0865400i	$0.0275810\pi$
$444$	1.67547	+	3.28830i	0.0795143	+	0.156056i
$445$	−0.685800	+	1.34596i	−0.0325100	+	0.0638045i
$446$	15.2179	+	20.9456i	0.720588	+	0.991804i
$447$	−17.2330	+	12.5205i	−0.815093	+	0.592200i
$448$	23.5034	−	23.5034i	1.11043	−	1.11043i
$449$	−5.28118	+	1.71596i	−0.249234	+	0.0809812i	−0.430970	−	0.902366i	$-0.641829\pi$
$449$	−5.28118	+	1.71596i	−0.249234	+	0.0809812i	0.181736	+	0.983347i	$0.441829\pi$
$450$	27.4981			1.29628
$451$	−3.21103	+	1.36731i	−0.151202	+	0.0643843i
$452$	0.220968			0.0103935
$453$	52.8431	−	17.1698i	2.48279	−	0.806706i
$454$	28.4997	−	28.4997i	1.33756	−	1.33756i
$455$	−2.65895	+	1.93184i	−0.124654	+	0.0905662i
$456$	18.5453	+	25.5254i	0.868463	+	1.19534i
$457$	−17.5772	+	34.4973i	−0.822229	+	1.61371i	−0.0331277	+	0.999451i	$0.510547\pi$
$457$	−17.5772	+	34.4973i	−0.822229	+	1.61371i	−0.789101	+	0.614264i	$0.789453\pi$
$458$	−15.2042	−	29.8400i	−0.710447	−	1.39433i
$459$	−11.5814	+	15.9405i	−0.540575	+	0.744038i
$460$			0.153385i			0.00715160i
$461$	−4.11822	−	2.99206i	−0.191805	−	0.139354i	0.487738	−	0.872990i	$-0.337822\pi$
$461$	−4.11822	−	2.99206i	−0.191805	−	0.139354i	−0.679543	+	0.733636i	$0.737822\pi$
$462$	−10.0127	+	1.58585i	−0.465832	+	0.0737805i
$463$	−0.451109	+	2.84819i	−0.0209648	+	0.132367i	−0.995951	−	0.0898996i	$-0.971345\pi$
$463$	−0.451109	+	2.84819i	−0.0209648	+	0.132367i	0.974986	+	0.222266i	$0.0713454\pi$
$464$	4.77414	+	2.43255i	0.221634	+	0.112928i
$465$	2.23719	+	2.23719i	0.103747	+	0.103747i
$466$	−35.3806	−	5.60373i	−1.63897	−	0.259588i
$467$	11.3892	−	35.0524i	0.527030	−	1.62203i	−0.233235	−	0.972420i	$-0.574931\pi$
$467$	11.3892	−	35.0524i	0.527030	−	1.62203i	0.760266	−	0.649612i	$-0.225069\pi$
$468$	0.113444	+	0.716258i	0.00524396	+	0.0331090i
$469$	−8.14508	−	25.0680i	−0.376105	−	1.15753i
$470$	−4.05329	+	2.06525i	−0.186964	+	0.0952631i
$471$	−30.8528	−	10.0247i	−1.42162	−	0.461914i
$472$	22.6144	+	7.34785i	1.04091	+	0.338212i
$473$	3.02119	−	1.53938i	0.138915	−	0.0707806i
$474$	−14.9869	−	46.1250i	−0.688373	−	2.11859i
$475$	−3.01613	−	19.0431i	−0.138390	−	0.873758i
$476$	−1.63861	+	5.04312i	−0.0751055	+	0.231151i
$477$	−22.3313	−	3.53693i	−1.02248	−	0.161945i
$478$	23.3113	+	23.3113i	1.06623	+	1.06623i
$479$	−28.4248	−	14.4832i	−1.29876	−	0.661752i	−0.338530	−	0.940956i	$-0.609930\pi$
$479$	−28.4248	−	14.4832i	−1.29876	−	0.661752i	−0.960232	+	0.279203i	$0.909930\pi$
$480$	0.347342	−	2.19303i	0.0158539	−	0.100098i
$481$	−6.50460	+	1.03023i	−0.296584	+	0.0469743i
$482$	14.4647	+	10.5092i	0.658849	+	0.478682i
$483$			13.1595i			0.598777i
$484$	−1.19033	+	1.63835i	−0.0541060	+	0.0744705i
$485$	0.682969	+	1.34040i	0.0310120	+	0.0608645i
$486$	13.5458	−	26.5850i	0.614448	−	1.20592i
$487$	10.5402	+	14.5073i	0.477621	+	0.657389i	0.978046	−	0.208391i	$-0.0668227\pi$
$487$	10.5402	+	14.5073i	0.477621	+	0.657389i	−0.500424	+	0.865780i	$0.666823\pi$
$488$	3.00826	−	2.18563i	0.136178	−	0.0989389i
$489$	3.80261	−	3.80261i	0.171960	−	0.171960i
$490$	−16.2091	+	5.26665i	−0.732252	+	0.237923i
$491$	25.0172			1.12901			0.564505	−	0.825430i	$-0.309067\pi$
$491$	25.0172			1.12901			0.564505	+	0.825430i	$0.309067\pi$
$492$	0.287487	+	3.24350i	0.0129609	+	0.146228i
$493$	7.39319			0.332973
$494$	5.59514	−	1.81797i	0.251737	−	0.0817944i
$495$	1.26049	−	1.26049i	0.0566548	−	0.0566548i
$496$	−5.34082	+	3.88033i	−0.239810	+	0.174232i
$497$	−2.99575	−	4.12329i	−0.134378	−	0.184955i
$498$	−23.7542	+	46.6202i	−1.06445	+	2.08910i
$499$	11.7228	+	23.0074i	0.524786	+	1.02995i	0.989506	+	0.144493i	$0.0461551\pi$
$499$	11.7228	+	23.0074i	0.524786	+	1.02995i	−0.464720	+	0.885458i	$0.653845\pi$
$500$	−0.809573	+	1.11428i	−0.0362052	+	0.0498322i
$501$			51.3966i			2.29623i
$502$	−9.51139	−	6.91043i	−0.424514	−	0.308428i
$503$	−18.1861	+	2.88039i	−0.810878	+	0.128430i	−0.548086	−	0.836422i	$-0.684643\pi$
$503$	−18.1861	+	2.88039i	−0.810878	+	0.128430i	−0.262792	+	0.964853i	$0.584643\pi$
$504$	8.27926	−	52.2732i	0.368788	−	2.32843i
$505$	−5.80462	−	2.95760i	−0.258302	−	0.131612i
$506$	−0.596973	−	0.596973i	−0.0265387	−	0.0265387i
$507$	32.3233	+	5.11951i	1.43553	+	0.227366i
$508$	0.584346	−	1.79843i	0.0259262	−	0.0797925i
$509$	−2.90230	−	18.3244i	−0.128642	−	0.812214i	−0.964657	−	0.263508i	$-0.915121\pi$
$509$	−2.90230	−	18.3244i	−0.128642	−	0.812214i	0.836015	−	0.548706i	$-0.184879\pi$
$510$	−5.70184	−	17.5485i	−0.252482	−	0.777059i
$511$	23.3908	−	11.9182i	1.03475	−	0.527230i
$512$	−17.7247	−	5.75912i	−0.783330	−	0.254519i
$513$	13.7028	+	4.45232i	0.604995	+	0.196575i
$514$	30.9884	−	15.7894i	1.36684	−	0.696440i
$515$	−1.02815	−	3.16432i	−0.0453057	−	0.139436i
$516$	−0.494896	−	3.12465i	−0.0217866	−	0.137555i
$517$	0.668738	−	2.05816i	0.0294111	−	0.0905180i
$518$	−49.6031	−	7.85636i	−2.17944	−	0.345189i
$519$	−11.4101	−	11.4101i	−0.500849	−	0.500849i
$520$	1.67753	+	0.854743i	0.0735644	+	0.0374829i
$521$	−1.28799	+	8.13203i	−0.0564277	+	0.356271i	0.943278	+	0.332005i	$0.107725\pi$
$521$	−1.28799	+	8.13203i	−0.0564277	+	0.356271i	−0.999706	+	0.0242662i	$0.992275\pi$
$522$	7.61549	−	1.20617i	0.333321	−	0.0527928i
$523$	−27.7382	−	20.1530i	−1.21291	−	0.881229i	−0.217416	−	0.976079i	$-0.569763\pi$
$523$	−27.7382	−	20.1530i	−1.21291	−	0.881229i	−0.995492	+	0.0948499i	$0.969763\pi$
$524$			0.154190i			0.00673583i
$525$	−32.5129	+	44.7502i	−1.41898	+	1.95306i
$526$	14.3606	+	28.1842i	0.626151	+	1.22889i
$527$	−4.13537	+	8.11613i	−0.180140	+	0.353544i
$528$	3.73922	+	5.14659i	0.162729	+	0.223977i
$529$	17.7208	−	12.8749i	0.770468	−	0.559778i
$530$	4.33708	−	4.33708i	0.188391	−	0.188391i
$531$	35.6487	−	11.5830i	1.54702	−	0.502659i
$532$	3.87751			0.168111
$533$	−5.66318	−	1.30067i	−0.245300	−	0.0563381i
$534$	−7.75751			−0.335700
$535$	−9.12060	+	2.96346i	−0.394318	+	0.128122i
$536$	−10.6766	+	10.6766i	−0.461160	+	0.461160i
$537$	19.9047	−	14.4616i	0.858950	−	0.624063i
$538$	23.5117	+	32.3611i	1.01366	+	1.39519i
$539$	3.68083	−	7.22404i	0.158545	−	0.311162i
$540$	−0.218733	−	0.429287i	−0.00941276	−	0.0184736i
$541$	0.490706	−	0.675399i	0.0210971	−	0.0290377i	−0.798338	−	0.602209i	$-0.794287\pi$
$541$	0.490706	−	0.675399i	0.0210971	−	0.0290377i	0.819435	+	0.573172i	$0.194287\pi$
$542$		−	17.6629i		−	0.758685i
$543$	−41.4296	−	30.1003i	−1.77791	−	1.29173i
$544$	6.31386	−	1.00002i	0.270705	−	0.0428754i
$545$	0.209594	−	1.32332i	0.00897802	−	0.0566850i
$546$	−15.0385	−	7.66251i	−0.643590	−	0.327925i
$547$	22.5832	+	22.5832i	0.965590	+	0.965590i	0.999427	−	0.0338377i	$-0.0107729\pi$
$547$	22.5832	+	22.5832i	0.965590	+	0.965590i	−0.0338377	+	0.999427i	$0.510773\pi$
$548$	−0.804327	−	0.127393i	−0.0343591	−	0.00544195i
$549$	1.81134	−	5.57474i	0.0773062	−	0.237924i
$550$	−0.555138	−	3.50500i	−0.0236712	−	0.149454i
$551$	−1.67061	−	5.14160i	−0.0711703	−	0.219040i
$552$	6.71668	−	3.42232i	0.285881	−	0.145664i
$553$	54.2494	+	17.6267i	2.30692	+	0.749564i
$554$	20.6388	+	6.70597i	0.876860	+	0.284909i
$555$	13.4577	−	6.85702i	0.571246	−	0.291064i
$556$	−0.293759	−	0.904097i	−0.0124581	−	0.0383422i
$557$	4.35403	+	27.4903i	0.184486	+	1.16480i	0.889951	+	0.456055i	$0.150738\pi$
$557$	4.35403	+	27.4903i	0.184486	+	1.16480i	−0.705465	+	0.708744i	$0.749262\pi$
$558$	−2.93560	+	9.03483i	−0.124274	+	0.382475i
$559$	5.57586	+	0.883130i	0.235834	+	0.0373524i
$560$	11.1214	+	11.1214i	0.469964	+	0.469964i
$561$	7.82097	+	3.98498i	0.330202	+	0.168246i
$562$	−2.47581	+	15.6316i	−0.104436	+	0.659381i
$563$	−29.1631	+	4.61898i	−1.22908	+	0.194667i	−0.737005	−	0.675887i	$-0.763761\pi$
$563$	−29.1631	+	4.61898i	−1.22908	+	0.194667i	−0.492073	+	0.870554i	$0.663761\pi$
$564$	−1.63349	−	1.18680i	−0.0687822	−	0.0499732i
$565$		−	0.904334i		−	0.0380456i
$566$	−16.5878	+	22.8311i	−0.697236	+	0.959662i
$567$	8.13797	+	15.9717i	0.341763	+	0.670747i
$568$	−1.32547	+	2.60137i	−0.0556153	+	0.109151i
$569$	−16.9189	−	23.2869i	−0.709278	−	0.976237i	−0.999812	−	0.0193726i	$-0.993833\pi$
$569$	−16.9189	−	23.2869i	−0.709278	−	0.976237i	0.290535	−	0.956864i	$-0.406167\pi$
$570$	−10.9157	+	7.93071i	−0.457208	+	0.332181i
$571$	−19.3493	+	19.3493i	−0.809742	+	0.809742i	−0.984595	−	0.174853i	$-0.944055\pi$
$571$	−19.3493	+	19.3493i	−0.809742	+	0.809742i	0.174853	+	0.984595i	$0.444055\pi$
$572$	0.0890064	−	0.0289199i	0.00372154	−	0.00120920i
$573$	−30.2786			−1.26491
$574$	−38.0079	−	22.7786i	−1.58642	−	0.950762i
$575$	−4.60656			−0.192107
$576$	−28.5461	+	9.27520i	−1.18942	+	0.386467i
$577$	6.40224	−	6.40224i	0.266529	−	0.266529i	−0.561171	−	0.827700i	$-0.689649\pi$
$577$	6.40224	−	6.40224i	0.266529	−	0.266529i	0.827700	+	0.561171i	$0.189649\pi$
$578$	22.6281	−	16.4403i	0.941205	−	0.683826i
$579$	−18.4714	−	25.4238i	−0.767647	−	1.05658i
$580$	−0.0820733	+	0.161078i	−0.00340791	+	0.00668840i
$581$	−27.9382	−	54.8318i	−1.15907	−	2.27481i
$582$	−4.54093	+	6.25005i	−0.188227	+	0.259073i
$583$			2.91783i			0.120844i
$584$	−12.1663	−	8.83931i	−0.503444	−	0.365773i
$585$	2.93136	−	0.464281i	0.121197	−	0.0191957i
$586$	−6.00377	+	37.9063i	−0.248014	+	1.56590i
$587$	−4.62167	−	2.35486i	−0.190757	−	0.0971955i	0.356003	−	0.934485i	$-0.384139\pi$
$587$	−4.62167	−	2.35486i	−0.190757	−	0.0971955i	−0.546760	+	0.837289i	$0.684139\pi$
$588$	−5.34895	−	5.34895i	−0.220587	−	0.220587i
$589$	6.57883	+	1.04198i	0.271076	+	0.0429342i
$590$	−3.14223	+	9.67080i	−0.129364	+	0.398141i
$591$	−4.24890	−	26.8265i	−0.174776	−	1.10349i
$592$	9.73876	+	29.9728i	0.400261	+	1.23188i
$593$	−20.8824	+	10.6401i	−0.857538	+	0.436937i	−0.826737	−	0.562588i	$-0.809806\pi$
$593$	−20.8824	+	10.6401i	−0.857538	+	0.436937i	−0.0308006	+	0.999526i	$0.509806\pi$
$594$	2.52209	+	0.819478i	0.103483	+	0.0336236i
$595$	20.6394	+	6.70616i	0.846134	+	0.274926i
$596$	1.33616	−	0.680807i	0.0547312	−	0.0278869i
$597$	6.98938	+	21.5111i	0.286056	+	0.880391i
$598$	−0.219885	−	1.38830i	−0.00899178	−	0.0567719i
$599$	−9.48601	+	29.1949i	−0.387588	+	1.19287i	0.546998	+	0.837134i	$0.315771\pi$
$599$	−9.48601	+	29.1949i	−0.387588	+	1.19287i	−0.934586	+	0.355739i	$0.884229\pi$
$600$	31.2963	+	4.95685i	1.27767	+	0.202363i
$601$	5.21941	+	5.21941i	0.212904	+	0.212904i	0.805500	−	0.592596i	$-0.201897\pi$
$601$	5.21941	+	5.21941i	0.212904	+	0.212904i	−0.592596	+	0.805500i	$0.701897\pi$
$602$	38.3585	+	19.5446i	1.56338	+	0.796580i
$603$	−3.72341	+	23.5087i	−0.151629	+	0.957348i
$604$	−3.86345	+	0.611910i	−0.157202	+	0.0248983i
$605$	6.70511	+	4.87155i	0.272601	+	0.198057i
$606$		−	33.4553i		−	1.35903i
$607$	18.4399	−	25.3803i	0.748452	−	1.03016i	−0.249636	−	0.968340i	$-0.580311\pi$
$607$	18.4399	−	25.3803i	0.748452	−	1.03016i	0.998088	−	0.0618155i	$-0.0196890\pi$
$608$	−2.12218	−	4.16502i	−0.0860658	−	0.168914i
$609$	−7.04139	+	13.8195i	−0.285332	+	0.559995i
$610$	0.934663	+	1.28645i	0.0378434	+	0.0520870i
$611$	2.91492	−	2.11781i	0.117925	−	0.0856774i
$612$	3.38589	−	3.38589i	0.136867	−	0.136867i
$613$	16.7669	−	5.44789i	0.677208	−	0.220038i	0.0498354	−	0.998757i	$-0.484130\pi$
$613$	16.7669	−	5.44789i	0.677208	−	0.220038i	0.627373	+	0.778719i	$0.284130\pi$
$614$	12.8089			0.516927
$615$	13.2743	−	1.17657i	0.535272	−	0.0474438i
$616$	−6.83006			−0.275191
$617$	−7.65218	+	2.48634i	−0.308065	+	0.100096i	−0.458970	−	0.888452i	$-0.651781\pi$
$617$	−7.65218	+	2.48634i	−0.308065	+	0.100096i	0.150905	+	0.988548i	$0.451781\pi$
$618$	12.0818	−	12.0818i	0.486000	−	0.486000i
$619$	−5.14200	+	3.73588i	−0.206675	+	0.150158i	−0.686308	−	0.727311i	$-0.740770\pi$
$619$	−5.14200	+	3.73588i	−0.206675	+	0.150158i	0.479633	+	0.877469i	$0.340770\pi$
$620$	−0.130921	−	0.180198i	−0.00525792	−	0.00723691i
$621$	1.56282	−	3.06721i	0.0627140	−	0.123083i
$622$	−5.42688	−	10.6509i	−0.217598	−	0.427060i
$623$	5.36290	−	7.38140i	0.214860	−	0.295729i
$624$			10.5915i			0.423999i
$625$	−13.2395	−	9.61907i	−0.529581	−	0.384763i
$626$	5.04362	−	0.798832i	0.201584	−	0.0319277i
$627$	1.00409	−	6.33957i	0.0400995	−	0.253178i
$628$	2.03490	+	1.03683i	0.0812014	+	0.0413742i
$629$	30.7485	+	30.7485i	1.22602	+	1.22602i
$630$	22.3541	+	3.54054i	0.890609	+	0.141059i
$631$	1.29270	−	3.97853i	0.0514616	−	0.158383i	−0.922023	−	0.387135i	$-0.873465\pi$
$631$	1.29270	−	3.97853i	0.0514616	−	0.158383i	0.973485	+	0.228753i	$0.0734647\pi$
$632$	−5.11160	−	32.2734i	−0.203329	−	1.28377i
$633$	−10.7836	−	33.1884i	−0.428608	−	1.31912i
$634$	−36.8030	+	18.7520i	−1.46163	+	0.744739i
$635$	−7.36026	−	2.39149i	−0.292083	−	0.0949035i
$636$	2.58911	+	0.841251i	0.102665	+	0.0333578i
$637$	12.0275	−	6.12831i	0.476546	−	0.242812i
$638$	−0.307486	−	0.946344i	−0.0121735	−	0.0374661i
$639$	0.719970	+	4.54571i	0.0284816	+	0.179825i
$640$	3.02676	−	9.31541i	0.119643	−	0.368224i
$641$	19.3732	+	3.06842i	0.765196	+	0.121195i	0.526819	−	0.849978i	$-0.323385\pi$
$641$	19.3732	+	3.06842i	0.765196	+	0.121195i	0.238377	+	0.971173i	$0.423385\pi$
$642$	−34.8236	−	34.8236i	−1.37438	−	1.37438i
$643$	−9.90543	−	5.04707i	−0.390632	−	0.199037i	0.247633	−	0.968854i	$-0.420347\pi$
$643$	−9.90543	−	5.04707i	−0.390632	−	0.199037i	−0.638265	+	0.769817i	$0.720347\pi$
$644$	0.144925	−	0.915023i	0.00571086	−	0.0360569i
$645$	−12.7879	+	2.02541i	−0.503525	+	0.0797505i
$646$	−31.4269	−	22.8330i	−1.23647	−	0.898351i
$647$			10.4368i			0.410313i	0.978729	+	0.205157i	$0.0657704\pi$
$647$			10.4368i			0.410313i	−0.978729	+	0.205157i	$0.934230\pi$
$648$	6.03564	−	8.30735i	0.237102	−	0.326344i
$649$	−2.19609	−	4.31007i	−0.0862040	−	0.169185i
$650$	2.68231	−	5.26434i	0.105209	−	0.206484i
$651$	−11.2322	−	15.4599i	−0.440227	−	0.605920i
$652$	−0.306287	+	0.222530i	−0.0119951	+	0.00871496i
$653$	19.0837	−	19.0837i	0.746802	−	0.746802i	−0.227075	−	0.973877i	$-0.572916\pi$
$653$	19.0837	−	19.0837i	0.746802	−	0.746802i	0.973877	+	0.227075i	$0.0729163\pi$
$654$	6.54371	−	2.12618i	0.255879	−	0.0831403i
$655$	0.631038			0.0246567
$656$	−1.90812	+	27.7408i	−0.0744995	+	1.08310i
$657$	−23.7061			−0.924862
$658$	26.1314	−	8.49062i	1.01871	−	0.330999i
$659$	−10.8584	+	10.8584i	−0.422984	+	0.422984i	−0.886230	−	0.463246i	$-0.846685\pi$
$659$	−10.8584	+	10.8584i	−0.422984	+	0.422984i	0.463246	+	0.886230i	$0.346685\pi$
$660$	−0.173644	+	0.126160i	−0.00675910	+	0.00491077i
$661$	0.199484	+	0.274566i	0.00775902	+	0.0106794i	0.812879	−	0.582433i	$-0.197899\pi$
$661$	0.199484	+	0.274566i	0.00775902	+	0.0106794i	−0.805120	+	0.593112i	$0.797899\pi$
$662$	15.1662	−	29.7654i	0.589452	−	1.15686i
$663$	6.63470	+	13.0213i	0.257670	+	0.505706i
$664$	−20.7208	+	28.5197i	−0.804123	+	1.10678i
$665$		−	15.8691i		−	0.615377i
$666$	36.6896	+	26.6565i	1.42169	+	1.03292i
$667$	−1.27577	+	0.202062i	−0.0493979	+	0.00782385i
$668$	0.566031	−	3.57378i	0.0219004	−	0.138274i
$669$	41.9031	+	21.3507i	1.62007	+	0.825466i
$670$	−4.56575	−	4.56575i	−0.176390	−	0.176390i
$671$	−0.747142	−	0.118336i	−0.0288431	−	0.00456830i
$672$	−4.14417	+	12.7544i	−0.159865	+	0.492013i
$673$	1.95952	+	12.3719i	0.0755340	+	0.476903i	0.996239	+	0.0866442i	$0.0276143\pi$
$673$	1.95952	+	12.3719i	0.0755340	+	0.476903i	−0.920705	+	0.390258i	$0.872386\pi$
$674$	11.3349	+	34.8853i	0.436604	+	1.34373i
$675$	12.8927	−	6.56915i	0.496240	−	0.252847i
$676$	−2.19117	−	0.711954i	−0.0842757	−	0.0273828i
$677$	−27.8174	−	9.03841i	−1.06911	−	0.347374i	−0.278968	−	0.960300i	$-0.589992\pi$
$677$	−27.8174	−	9.03841i	−1.06911	−	0.347374i	−0.790140	+	0.612926i	$0.789992\pi$
$678$	4.13791	−	2.10837i	0.158916	−	0.0809715i
$679$	−2.80780	−	8.64153i	−0.107754	−	0.331631i
$680$	−1.94473	−	12.2785i	−0.0745770	−	0.470861i
$681$	22.6239	−	69.6293i	0.866951	−	2.66820i
$682$	1.21087	+	0.191784i	0.0463668	+	0.00734377i
$683$	16.7263	+	16.7263i	0.640013	+	0.640013i	0.950559	−	0.310545i	$-0.100512\pi$
$683$	16.7263	+	16.7263i	0.640013	+	0.640013i	−0.310545	+	0.950559i	$0.600512\pi$
$684$	−3.11982	−	1.58963i	−0.119289	−	0.0607809i
$685$	−0.521367	+	3.29178i	−0.0199204	+	0.125773i
$686$	53.8271	−	8.52538i	2.05513	−	0.325500i
$687$	−49.2159	−	35.7574i	−1.87770	−	1.36423i
$688$		−	27.0155i		−	1.02996i
$689$	−2.85544	+	3.93017i	−0.108783	+	0.149728i
$690$	1.46352	+	2.87232i	0.0557153	+	0.109347i
$691$	−7.58691	+	14.8902i	−0.288620	+	0.566448i	−0.989104	−	0.147220i	$-0.952967\pi$
$691$	−7.58691	+	14.8902i	−0.288620	+	0.566448i	0.700484	+	0.713668i	$0.252967\pi$
$692$	0.667725	+	0.919045i	0.0253831	+	0.0349369i
$693$	−8.71047	+	6.32853i	−0.330884	+	0.240401i
$694$	3.76119	−	3.76119i	0.142773	−	0.142773i
$695$	−3.70010	+	1.20224i	−0.140353	+	0.0456034i
$696$	8.88480			0.336777
$697$	15.0315	+	35.3002i	0.569358	+	1.33709i
$698$	0.424458			0.0160660
$699$	−61.8844	+	20.1075i	−2.34068	+	0.760534i
$700$	2.75357	−	2.75357i	0.104075	−	0.104075i
$701$	−29.0200	+	21.0843i	−1.09607	+	0.796342i	−0.980414	−	0.196948i	$-0.936897\pi$
$701$	−29.0200	+	21.0843i	−1.09607	+	0.796342i	−0.115656	+	0.993289i	$0.536897\pi$
$702$	2.59518	+	3.57196i	0.0979489	+	0.134815i
$703$	14.4360	−	28.3322i	0.544463	−	1.06857i
$704$	1.75854	+	3.45133i	0.0662776	+	0.130077i
$705$	−4.85708	+	6.68520i	−0.182928	+	0.251779i
$706$		−	34.7883i		−	1.30927i
$707$	31.8332	+	23.1282i	1.19721	+	0.869825i
$708$	−4.45766	+	0.706024i	−0.167529	+	0.0265340i
$709$	2.89893	−	18.3031i	0.108872	−	0.687389i	−0.871524	−	0.490352i	$-0.836868\pi$
$709$	2.89893	−	18.3031i	0.108872	−	0.687389i	0.980396	−	0.197037i	$-0.0631319\pi$
$710$	−1.11245	−	0.566822i	−0.0417495	−	0.0212725i
$711$	−36.4225	−	36.4225i	−1.36595	−	1.36595i
$712$	−5.16222	−	0.817615i	−0.193462	−	0.0306414i
$713$	0.491779	−	1.51354i	0.0184173	−	0.0566825i
$714$	17.4339	+	110.074i	0.652449	+	4.11940i
$715$	−0.118358	−	0.364267i	−0.00442632	−	0.0136228i
$716$	−1.54330	+	0.786353i	−0.0576760	+	0.0293874i
$717$	56.9530	+	18.5052i	2.12695	+	0.691088i
$718$	−48.3427	−	15.7075i	−1.80413	−	0.586199i
$719$	−26.6096	+	13.5583i	−0.992371	+	0.505638i	−0.873266	−	0.487244i	$-0.838002\pi$
$719$	−26.6096	+	13.5583i	−0.992371	+	0.505638i	−0.119104	+	0.992882i	$0.538002\pi$
$720$	−4.38886	−	13.5075i	−0.163563	−	0.503396i
$721$	3.14366	+	19.8483i	0.117076	+	0.739190i
$722$	−0.0906104	+	0.278870i	−0.00337217	+	0.0103785i
$723$	32.0776	+	5.08059i	1.19298	+	0.188949i
$724$	2.54924	+	2.54924i	0.0947418	+	0.0947418i
$725$	−4.83761	−	2.46489i	−0.179664	−	0.0915436i
$726$	−6.65813	+	42.0378i	−0.247106	+	1.56017i
$727$	5.04235	−	0.798630i	0.187010	−	0.0296195i	−0.0622267	−	0.998062i	$-0.519820\pi$
$727$	5.04235	−	0.798630i	0.187010	−	0.0296195i	0.249237	+	0.968443i	$0.419820\pi$
$728$	−9.19976	−	6.68401i	−0.340966	−	0.247726i
$729$		−	42.7006i		−	1.58150i
$730$	3.78004	−	5.20278i	0.139906	−	0.192564i
$731$	−16.9230	−	33.2133i	−0.625920	−	1.22844i
$732$	−0.320416	+	0.628852i	−0.0118429	+	0.0232430i
$733$	−11.5449	−	15.8902i	−0.426421	−	0.586918i	0.540706	−	0.841212i	$-0.318157\pi$
$733$	−11.5449	−	15.8902i	−0.426421	−	0.586918i	−0.967127	+	0.254293i	$0.918157\pi$
$734$	−31.2223	+	22.6843i	−1.15243	+	0.837293i
$735$	−21.8911	+	21.8911i	−0.807465	+	0.807465i
$736$	−1.06219	+	0.345125i	−0.0391527	+	0.0127215i
$737$	3.07166			0.113146
$738$	21.2425	+	33.9093i	0.781949	+	1.24822i
$739$	21.4364			0.788552			0.394276	−	0.918992i	$-0.370995\pi$
$739$	21.4364			0.788552			0.394276	+	0.918992i	$0.370995\pi$
$740$	−1.01127	+	0.328583i	−0.0371752	+	0.0120789i
$741$	7.55648	−	7.55648i	0.277594	−	0.277594i
$742$	−29.9709	+	21.7752i	−1.10027	+	0.799391i
$743$	15.6932	+	21.5998i	0.575727	+	0.792420i	0.993219	−	0.116261i	$-0.0370908\pi$
$743$	15.6932	+	21.5998i	0.575727	+	0.792420i	−0.417492	+	0.908681i	$0.637091\pi$
$744$	−4.96970	+	9.75359i	−0.182198	+	0.357584i
$745$	−2.78627	−	5.46835i	−0.102081	−	0.200345i
$746$	−8.78275	+	12.0884i	−0.321559	+	0.442588i
$747$			55.5709i			2.03323i
$748$	−0.499932	−	0.363222i	−0.0182793	−	0.0132807i
$749$	57.2093	−	9.06107i	2.09038	−	0.331084i
$750$	−4.52835	+	28.5909i	−0.165352	+	1.04399i
$751$	−16.3078	−	8.30926i	−0.595082	−	0.303209i	0.130388	−	0.991463i	$-0.458378\pi$
$751$	−16.3078	−	8.30926i	−0.595082	−	0.303209i	−0.725470	+	0.688254i	$0.758378\pi$
$752$	−12.1920	−	12.1920i	−0.444596	−	0.444596i
$753$	−21.0929	−	3.34079i	−0.768668	−	0.121745i
$754$	0.511941	−	1.57559i	0.0186438	−	0.0573797i
$755$	2.50430	+	15.8115i	0.0911409	+	0.575441i
$756$	0.899248	+	2.76760i	0.0327053	+	0.100657i
$757$	15.9241	−	8.11374i	0.578772	−	0.294899i	−0.139993	−	0.990153i	$-0.544708\pi$
$757$	15.9241	−	8.11374i	0.578772	−	0.294899i	0.718765	+	0.695254i	$0.244708\pi$
$758$	−18.6224	−	6.05080i	−0.676398	−	0.219775i
$759$	−1.45850	−	0.473894i	−0.0529401	−	0.0172013i
$760$	−8.09969	+	4.12700i	−0.293807	+	0.149702i
$761$	2.00583	+	6.17330i	0.0727111	+	0.223782i	0.980807	−	0.194980i	$-0.0624642\pi$
$761$	2.00583	+	6.17330i	0.0727111	+	0.223782i	−0.908096	+	0.418762i	$0.862464\pi$
$762$	−6.21714	−	39.2535i	−0.225223	−	1.42200i
$763$	−2.50068	+	7.69632i	−0.0905309	+	0.278625i
$764$	2.10538	+	0.333459i	0.0761699	+	0.0120641i
$765$	−13.8571	−	13.8571i	−0.501004	−	0.501004i
$766$	−9.06839	−	4.62058i	−0.327654	−	0.166948i
$767$	1.25988	−	7.95458i	0.0454917	−	0.287223i
$768$	11.9501	−	1.89271i	0.431211	−	0.0682972i
$769$	12.0454	+	8.75147i	0.434367	+	0.315586i	0.783393	−	0.621527i	$-0.213487\pi$
$769$	12.0454	+	8.75147i	0.434367	+	0.315586i	−0.349026	+	0.937113i	$0.613487\pi$
$770$		−	2.92080i		−	0.105258i
$771$	37.1336	−	51.1100i	1.33733	−	1.84068i
$772$	1.00439	+	1.97123i	0.0361488	+	0.0709460i
$773$	−15.0844	+	29.6048i	−0.542548	+	1.06481i	0.443175	+	0.896435i	$0.353852\pi$
$773$	−15.0844	+	29.6048i	−0.542548	+	1.06481i	−0.985723	+	0.168375i	$0.946148\pi$
$774$	−22.8505	−	31.4510i	−0.821343	−	1.13048i
$775$	5.41183	−	3.93192i	0.194399	−	0.141239i
$776$	−3.68048	+	3.68048i	−0.132122	+	0.132122i
$777$	−86.7611	+	28.1904i	−3.11254	+	1.01133i
$778$	−45.1527			−1.61880
$779$	21.1530	−	18.4303i	0.757885	−	0.660334i
$780$	−0.357353			−0.0127953
$781$	0.564876	−	0.183539i	0.0202129	−	0.00656755i
$782$	−6.56277	+	6.56277i	−0.234684	+	0.234684i
$783$	3.28242	−	2.38482i	0.117304	−	0.0852265i
$784$	−37.9694	−	52.2604i	−1.35605	−	1.86644i
$785$	4.24334	−	8.32803i	0.151451	−	0.297240i
$786$	1.47121	+	2.88741i	0.0524762	+	0.102990i
$787$	30.3707	−	41.8017i	1.08260	−	1.49007i	0.225974	−	0.974133i	$-0.427444\pi$
$787$	30.3707	−	41.8017i	1.08260	−	1.49007i	0.856626	−	0.515937i	$-0.172556\pi$
$788$			1.91213i			0.0681168i
$789$	46.4850	+	33.7733i	1.65491	+	1.20236i
$790$	13.8014	−	2.18592i	0.491031	−	0.0777717i
$791$	−0.854459	+	5.39484i	−0.0303811	+	0.191819i
$792$	5.49542	+	2.80006i	0.195271	+	0.0994956i
$793$	−0.890559	−	0.890559i	−0.0316247	−	0.0316247i
$794$	35.1233	+	5.56299i	1.24648	+	0.197423i
$795$	3.44290	−	10.5962i	0.122107	−	0.375807i
$796$	−0.249093	−	1.57271i	−0.00882888	−	0.0557434i
$797$	4.43551	+	13.6511i	0.157114	+	0.483547i	0.998369	−	0.0570915i	$-0.0181827\pi$
$797$	4.43551	+	13.6511i	0.157114	+	0.483547i	−0.841255	+	0.540639i	$0.818183\pi$
$798$	72.6113	−	36.9973i	2.57041	−	1.30969i
$799$	−22.6263	−	7.35172i	−0.800460	−	0.260085i
$800$	−4.46478	−	1.45070i	−0.157854	−	0.0512898i
$801$	−7.34104	+	3.74044i	−0.259383	+	0.132162i
$802$	2.17925	+	6.70706i	0.0769521	+	0.236834i
$803$	0.478583	+	3.02165i	0.0168888	+	0.106632i
$804$	0.885605	−	2.72561i	0.0312329	−	0.0961249i
$805$	−3.74482	−	0.593121i	−0.131987	−	0.0209048i
$806$	1.44331	+	1.44331i	0.0508383	+	0.0508383i
$807$	64.7406	+	32.9870i	2.27898	+	1.16120i
$808$	3.52607	−	22.2627i	0.124047	−	0.783200i
$809$	43.6281	−	6.91001i	1.53388	−	0.242943i	0.668369	−	0.743830i	$-0.266993\pi$
$809$	43.6281	−	6.91001i	1.53388	−	0.242943i	0.865513	+	0.500887i	$0.166993\pi$
$810$	3.55255	+	2.58108i	0.124824	+	0.0906899i
$811$			27.7113i			0.973074i	0.873660	+	0.486537i	$0.161740\pi$
$811$			27.7113i			0.973074i	−0.873660	+	0.486537i	$0.838260\pi$
$812$	0.641806	−	0.883371i	0.0225230	−	0.0310002i
$813$	−14.5659	−	28.5872i	−0.510849	−	1.00260i
$814$	2.65703	−	5.21472i	0.0931289	−	0.182776i
$815$	0.910726	+	1.25351i	0.0319014	+	0.0439084i
$816$	56.5787	−	41.1068i	1.98065	−	1.43903i
$817$	−19.2742	+	19.2742i	−0.674319	+	0.674319i
$818$	52.2233	−	16.9684i	1.82594	−	0.593285i
$819$	−17.9258			−0.626378
$820$	−0.935966	−	0.0643793i	−0.0326853	−	0.00224822i
$821$	11.1582			0.389424			0.194712	−	0.980860i	$-0.437623\pi$
$821$	11.1582			0.389424			0.194712	+	0.980860i	$0.437623\pi$
$822$	−16.2776	+	5.28890i	−0.567745	+	0.184472i
$823$	−28.5619	+	28.5619i	−0.995606	+	0.995606i	−0.999990	−	0.00438414i	$-0.998604\pi$
$823$	−28.5619	+	28.5619i	−0.995606	+	0.995606i	0.00438414	+	0.999990i	$0.498604\pi$
$824$	9.31316	−	6.76641i	0.324439	−	0.235719i
$825$	−3.78893	−	5.21502i	−0.131914	−	0.181564i
$826$	27.8826	−	54.7226i	0.970159	−	1.90404i
$827$	−0.960885	−	1.88584i	−0.0334133	−	0.0655772i	0.873696	−	0.486472i	$-0.161716\pi$
$827$	−0.960885	−	1.88584i	−0.0334133	−	0.0655772i	−0.907110	+	0.420894i	$0.861716\pi$
$828$	−0.491729	+	0.676807i	−0.0170888	+	0.0235207i
$829$			22.5376i			0.782765i	0.920228	+	0.391382i	$0.128003\pi$
$829$			22.5376i			0.782765i	−0.920228	+	0.391382i	$0.871997\pi$
$830$	−12.1962	−	8.86103i	−0.423335	−	0.307571i
$831$	38.9340	−	6.16653i	1.35060	−	0.213915i
$832$	−1.00887	+	6.36972i	−0.0349761	+	0.220830i
$833$	−79.4169	−	40.4650i	−2.75163	−	1.40203i
$834$	−14.1275	−	14.1275i	−0.489194	−	0.489194i
$835$	−14.6260	−	2.31654i	−0.506155	−	0.0801670i
$836$	−0.139636	+	0.429754i	−0.00482940	+	0.0148634i
$837$	0.781997	+	4.93734i	0.0270298	+	0.170659i
$838$	5.13337	+	15.7989i	0.177329	+	0.545764i
$839$	27.0427	−	13.7790i	0.933619	−	0.475703i	0.0801132	−	0.996786i	$-0.474472\pi$
$839$	27.0427	−	13.7790i	0.933619	−	0.475703i	0.853506	+	0.521083i	$0.174472\pi$
$840$	24.8035	+	8.05915i	0.855803	+	0.278067i
$841$	26.1328	+	8.49105i	0.901130	+	0.292795i
$842$	22.3420	−	11.3838i	0.769957	−	0.392313i
$843$	8.88376	+	27.3414i	0.305973	+	0.941688i
$844$	0.384314	+	2.42646i	0.0132286	+	0.0835222i
$845$	−2.91374	+	8.96757i	−0.100236	+	0.308494i
$846$	−24.5060	−	3.88137i	−0.842534	−	0.133444i
$847$	−35.3967	−	35.3967i	−1.21625	−	1.21625i
$848$	20.7136	+	10.5541i	0.711308	+	0.362430i
$849$	−8.01920	+	50.6313i	−0.275218	+	1.73766i
$850$	−38.5320	+	6.10287i	−1.32164	+	0.209327i
$851$	−6.14633	−	4.46557i	−0.210694	−	0.153078i
$852$		−	0.554154i		−	0.0189850i
$853$	−10.9647	+	15.0916i	−0.375423	+	0.516726i	−0.954365	−	0.298643i	$-0.903466\pi$
$853$	−10.9647	+	15.0916i	−0.375423	+	0.516726i	0.578942	+	0.815369i	$0.303466\pi$
$854$	−4.36027	−	8.55751i	−0.149205	−	0.292832i
$855$	−6.50570	+	12.7682i	−0.222490	+	0.436662i
$856$	−19.5030	−	26.8436i	−0.666599	−	0.917494i
$857$	−38.9323	+	28.2860i	−1.32990	+	0.966232i	−0.330152	+	0.943928i	$0.607100\pi$
$857$	−38.9323	+	28.2860i	−1.32990	+	0.966232i	−0.999751	+	0.0223039i	$0.992900\pi$
$858$	1.39082	−	1.39082i	0.0474817	−	0.0474817i
$859$	−17.0896	+	5.55276i	−0.583091	+	0.189458i	−0.585685	−	0.810539i	$-0.699174\pi$
$859$	−17.0896	+	5.55276i	−0.583091	+	0.189458i	0.00259400	+	0.999997i	$0.499174\pi$
$860$	0.911495			0.0310817
$861$	−80.3002	−	5.52336i	−2.73662	−	0.188235i
$862$	30.1105			1.02557
$863$	−32.1502	+	10.4462i	−1.09441	+	0.355594i	−0.799947	−	0.600070i	$-0.795139\pi$
$863$	−32.1502	+	10.4462i	−1.09441	+	0.355594i	−0.294459	+	0.955664i	$0.595139\pi$
$864$	2.48065	−	2.48065i	0.0843933	−	0.0843933i
$865$	3.76128	−	2.73273i	0.127887	−	0.0929156i
$866$	−18.4364	−	25.3755i	−0.626494	−	0.862295i
$867$	23.0657	−	45.2690i	0.783353	−	1.53742i
$868$	0.610757	+	1.19868i	0.0207304	+	0.0406858i
$869$	−3.90722	+	5.37783i	−0.132544	+	0.182430i
$870$			3.79949i			0.128815i
$871$	4.13738	+	3.00598i	0.140190	+	0.101854i
$872$	4.57859	−	0.725178i	0.155051	−	0.0245576i
$873$	−1.28355	+	8.10401i	−0.0434415	+	0.274279i
$874$	6.04705	+	3.08113i	0.204545	+	0.104221i
$875$	−24.0742	−	24.0742i	−0.813855	−	0.813855i
$876$	2.81922	+	0.446520i	0.0952525	+	0.0150865i
$877$	−8.35976	+	25.7287i	−0.282289	+	0.868796i	0.704909	+	0.709298i	$0.250988\pi$
$877$	−8.35976	+	25.7287i	−0.282289	+	0.868796i	−0.987198	+	0.159499i	$0.949012\pi$
$878$	4.78366	+	30.2028i	0.161441	+	1.01930i
$879$	21.5429	+	66.3022i	0.726624	+	2.23632i
$880$	−1.63311	+	0.832111i	−0.0550521	+	0.0280505i
$881$	−15.9073	−	5.16859i	−0.535930	−	0.174134i	0.0285328	−	0.999593i	$-0.490916\pi$
$881$	−15.9073	−	5.16859i	−0.535930	−	0.174134i	−0.564462	+	0.825459i	$0.690916\pi$
$882$	−88.4065	−	28.7250i	−2.97680	−	0.967222i
$883$	22.7575	−	11.5955i	0.765852	−	0.390221i	−0.0269999	−	0.999635i	$-0.508595\pi$
$883$	22.7575	−	11.5955i	0.765852	−	0.390221i	0.792852	+	0.609414i	$0.208595\pi$
$884$	−0.317929	−	0.978485i	−0.0106931	−	0.0329100i
$885$	2.88947	+	18.2434i	0.0971285	+	0.613245i
$886$	−9.92302	+	30.5399i	−0.333370	+	1.02601i
$887$	39.5201	+	6.25936i	1.32695	+	0.210169i	0.779361	−	0.626576i	$-0.215544\pi$
$887$	39.5201	+	6.25936i	1.32695	+	0.210169i	0.547594	+	0.836744i	$0.315544\pi$
$888$	36.9521	+	36.9521i	1.24003	+	1.24003i
$889$	41.6483	+	21.2209i	1.39684	+	0.711726i
$890$	0.349645	−	2.20757i	0.0117201	−	0.0739979i
$891$	−2.06324	+	0.326785i	−0.0691211	+	0.0109477i
$892$	−2.67853	−	1.94607i	−0.0896838	−	0.0651591i
$893$			17.3967i			0.582159i
$894$	18.5253	−	25.4979i	0.619580	−	0.852778i
$895$	3.21822	+	6.31612i	0.107573	+	0.211125i
$896$	−26.8579	+	52.7116i	−0.897260	+	1.76097i
$897$	−1.50076	−	2.06562i	−0.0501090	−	0.0689692i
$898$	6.64701	−	4.82933i	0.221814	−	0.161157i
$899$	1.32631	−	1.32631i	0.0442350	−	0.0442350i
$900$	−3.34436	+	1.08665i	−0.111479	+	0.0362216i
$901$	32.0769			1.06864
$902$	3.89334	−	3.39221i	0.129634	−	0.112948i
$903$	78.2007			2.60236
$904$	2.97578	−	0.966890i	0.0989730	−	0.0321583i
$905$	10.4330	−	10.4330i	0.346805	−	0.346805i
$906$	−66.5095	+	48.3220i	−2.20963	+	1.60539i
$907$	−14.3108	−	19.6971i	−0.475182	−	0.654032i	0.502388	−	0.864642i	$-0.332455\pi$
$907$	−14.3108	−	19.6971i	−0.475182	−	0.654032i	−0.977570	+	0.210610i	$0.932455\pi$
$908$	−2.33995	+	4.59240i	−0.0776539	+	0.152404i
$909$	−16.1312	−	31.6592i	−0.535037	−	1.05007i
$910$	2.85835	−	3.93418i	0.0947534	−	0.130417i
$911$		−	24.0894i		−	0.798118i	−0.916925	−	0.399059i	$-0.869337\pi$
$911$		−	24.0894i		−	0.798118i	0.916925	−	0.399059i	$-0.130663\pi$
$912$	−41.3726	−	30.0590i	−1.36998	−	0.995352i
$913$	7.08325	−	1.12188i	0.234421	−	0.0371287i
$914$	8.96149	−	56.5806i	0.296420	−	1.87152i
$915$	2.57364	+	1.31133i	0.0850818	+	0.0433513i
$916$	3.02835	+	3.02835i	0.100059	+	0.100059i
$917$	−3.76449	−	0.596236i	−0.124314	−	0.0196894i
$918$	9.00887	−	27.7264i	0.297337	−	0.915109i
$919$	1.12618	+	7.11039i	0.0371491	+	0.234550i	0.999276	−	0.0380527i	$-0.0121155\pi$
$919$	1.12618	+	7.11039i	0.0371491	+	0.234550i	−0.962127	+	0.272603i	$0.912115\pi$
$920$	0.671164	+	2.06563i	0.0221276	+	0.0681018i
$921$	20.7312	−	10.5631i	0.683116	−	0.348065i
$922$	7.16312	+	2.32744i	0.235905	+	0.0766501i
$923$	0.940476	+	0.305579i	0.0309561	+	0.0100583i
$924$	1.15509	−	0.588545i	0.0379995	−	0.0193617i
$925$	−9.86824	−	30.3713i	−0.324466	−	0.998603i
$926$	−0.667460	−	4.21418i	−0.0219341	−	0.138486i
$927$	5.60766	−	17.2586i	0.184180	−	0.566847i
$928$	−1.30013	−	0.205921i	−0.0426790	−	0.00675969i
$929$	4.87523	+	4.87523i	0.159951	+	0.159951i	0.782545	−	0.622594i	$-0.213921\pi$
$929$	4.87523	+	4.87523i	0.159951	+	0.159951i	−0.622594	+	0.782545i	$0.713921\pi$
$930$	−4.17102	−	2.12524i	−0.136773	−	0.0696895i
$931$	−10.1959	+	64.3743i	−0.334157	+	2.10978i
$932$	4.52447	−	0.716606i	0.148204	−	0.0234732i
$933$	−17.5667	−	12.7630i	−0.575109	−	0.417841i
$934$			54.5325i			1.78436i
$935$	−1.48652	+	2.04602i	−0.0486144	+	0.0669120i
$936$	4.66188	+	9.14945i	0.152378	+	0.299059i
$937$	26.3251	−	51.6659i	0.860003	−	1.68785i	0.144200	−	0.989549i	$-0.453939\pi$
$937$	26.3251	−	51.6659i	0.860003	−	1.68785i	0.715803	−	0.698303i	$-0.246061\pi$
$938$	22.9232	+	31.5511i	0.748469	+	1.03018i
$939$	7.50430	−	5.45219i	0.244894	−	0.177926i
$940$	0.411353	−	0.411353i	0.0134169	−	0.0134169i
$941$	38.7521	−	12.5913i	1.26328	−	0.410466i	0.400620	−	0.916244i	$-0.368795\pi$
$941$	38.7521	−	12.5913i	1.26328	−	0.410466i	0.862663	+	0.505779i	$0.168795\pi$
$942$	47.9991			1.56389
$943$	−3.55861	−	5.68057i	−0.115884	−	0.184985i
$944$	−38.5406			−1.25439
$945$	11.3267	−	3.68026i	0.368457	−	0.119719i
$946$	−3.54753	+	3.54753i	−0.115340	+	0.115340i
$947$	−22.6790	+	16.4773i	−0.736970	+	0.535440i	−0.891761	−	0.452507i	$-0.850530\pi$
$947$	−22.6790	+	16.4773i	−0.736970	+	0.535440i	0.154791	+	0.987947i	$0.450530\pi$
$948$	3.64546	+	5.01754i	0.118399	+	0.162962i
$949$	−2.31242	+	4.53837i	−0.0750642	+	0.147322i
$950$	12.9512	+	25.4181i	0.420191	+	0.824671i
$951$	−44.1012	+	60.7001i	−1.43008	+	1.96833i
$952$			75.0857i			2.43354i
$953$	−31.1757	−	22.6505i	−1.00988	−	0.733721i	−0.0456960	−	0.998955i	$-0.514551\pi$
$953$	−31.1757	−	22.6505i	−1.00988	−	0.733721i	−0.964184	+	0.265235i	$0.914551\pi$
$954$	33.0414	−	5.23324i	1.06975	−	0.169432i
$955$	1.36471	−	8.61646i	0.0441611	−	0.278822i
$956$	−3.75634	−	1.91395i	−0.121489	−	0.0619016i
$957$	−1.27808	−	1.27808i	−0.0413144	−	0.0413144i
$958$	46.6208	+	7.38402i	1.50625	+	0.238567i
$959$	6.22048	−	19.1447i	0.200870	−	0.618213i
$960$	−2.31378	−	14.6086i	−0.0746768	−	0.471491i
$961$	−8.86539	−	27.2849i	−0.285980	−	0.880157i
$962$	8.68211	−	4.42376i	0.279922	−	0.142628i
$963$	−49.7449	−	16.1631i	−1.60301	−	0.520849i
$964$	−2.17451	−	0.706541i	−0.0700362	−	0.0227561i
$965$	8.06743	−	4.11056i	0.259700	−	0.132324i
$966$	−6.01679	−	18.5178i	−0.193587	−	0.595799i
$967$	−6.60601	−	41.7087i	−0.212435	−	1.34126i	−0.831326	−	0.555785i	$-0.812418\pi$
$967$	−6.60601	−	41.7087i	−0.212435	−	1.34126i	0.618891	−	0.785477i	$-0.287582\pi$
$968$	−8.86128	+	27.2722i	−0.284812	+	0.876562i
$969$	−69.6936	−	11.0384i	−2.23888	−	0.354604i
$970$	−1.57392	−	1.57392i	−0.0505356	−	0.0505356i
$971$	−1.85832	−	0.946862i	−0.0596364	−	0.0303863i	0.423918	−	0.905701i	$-0.360654\pi$
$971$	−1.85832	−	0.946862i	−0.0596364	−	0.0303863i	−0.483554	+	0.875314i	$0.660654\pi$
$972$	−0.596887	+	3.76860i	−0.0191452	+	0.120878i
$973$	23.2091	−	3.67595i	0.744048	−	0.117846i
$974$	−21.4650	−	15.5952i	−0.687783	−	0.499703i
$975$		−	10.7323i		−	0.343709i
$976$	−3.54256	+	4.87592i	−0.113395	+	0.156074i
$977$	13.5363	+	26.5664i	0.433063	+	0.849935i	0.999663	+	0.0259417i	$0.00825842\pi$
$977$	13.5363	+	26.5664i	0.433063	+	0.849935i	−0.566600	+	0.823993i	$0.691742\pi$
$978$	−3.61233	+	7.08960i	−0.115510	+	0.226700i
$979$	0.624971	+	0.860199i	0.0199742	+	0.0274921i
$980$	1.76325	−	1.28107i	0.0563249	−	0.0409224i
$981$	5.16722	−	5.16722i	0.164977	−	0.164977i
$982$	−35.2037	+	11.4384i	−1.12340	+	0.365013i
$983$	−36.2484			−1.15615			−0.578073	−	0.815985i	$-0.696195\pi$
$983$	−36.2484			−1.15615			−0.578073	+	0.815985i	$0.696195\pi$
$984$	18.0641	+	42.4222i	0.575863	+	1.35237i
$985$	7.82557			0.249343
$986$	−10.4036	+	3.38032i	−0.331317	+	0.107651i
$987$	35.2916	−	35.2916i	1.12334	−	1.12334i
$988$	−0.608647	+	0.442208i	−0.0193637	+	0.0140685i
$989$	3.82797	+	5.26875i	0.121722	+	0.167537i
$990$	−1.19742	+	2.35006i	−0.0380563	+	0.0746898i
$991$	6.13732	+	12.0452i	0.194959	+	0.382628i	0.967704	−	0.252088i	$-0.0811172\pi$
$991$	6.13732	+	12.0452i	0.194959	+	0.382628i	−0.772746	+	0.634716i	$0.781117\pi$
$992$	0.953285	−	1.31208i	0.0302668	−	0.0416587i
$993$		−	60.6821i		−	1.92569i
$994$	6.10081	+	4.43250i	0.193506	+	0.140590i
$995$	−6.43648	+	1.01944i	−0.204050	+	0.0323184i
$996$	1.04672	−	6.60871i	0.0331665	−	0.209405i
$997$	24.8214	+	12.6471i	0.786101	+	0.400538i	0.800481	−	0.599358i	$-0.204577\pi$
$997$	24.8214	+	12.6471i	0.786101	+	0.400538i	−0.0143801	+	0.999897i	$0.504577\pi$
$998$	−27.0156	−	27.0156i	−0.855164	−	0.855164i
$999$	23.5702	+	3.73316i	0.745729	+	0.118112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.2.2	✓	24
3.2	odd	2		369.2.u.a.289.2		24
4.3	odd	2		656.2.bs.d.289.3		24
41.12	odd	40		1681.2.a.m.1.17		24
41.21	even	20	inner	41.2.g.a.21.2	yes	24
41.29	odd	40		1681.2.a.m.1.18		24
123.62	odd	20		369.2.u.a.226.2		24
164.103	odd	20		656.2.bs.d.513.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.2	✓	24	1.1	even	1	trivial
41.2.g.a.21.2	yes	24	41.21	even	20	inner
369.2.u.a.226.2		24	123.62	odd	20
369.2.u.a.289.2		24	3.2	odd	2
656.2.bs.d.289.3		24	4.3	odd	2
656.2.bs.d.513.3		24	164.103	odd	20
1681.2.a.m.1.17		24	41.12	odd	40
1681.2.a.m.1.18		24	41.29	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40718 + 0.457221i) q^{2} +(-1.90046 + 1.90046i) q^{3} +(0.153075 - 0.111216i) q^{4} +(-0.455161 - 0.626475i) q^{5} +(1.80536 - 3.54322i) q^{6} +(2.12336 + 4.16732i) q^{7} +(1.57482 - 2.16755i) q^{8} -4.22349i q^{9} +O(q^{10})\)	\(q+(-1.40718 + 0.457221i) q^{2} +(-1.90046 + 1.90046i) q^{3} +(0.153075 - 0.111216i) q^{4} +(-0.455161 - 0.626475i) q^{5} +(1.80536 - 3.54322i) q^{6} +(2.12336 + 4.16732i) q^{7} +(1.57482 - 2.16755i) q^{8} -4.22349i q^{9} +(0.926931 + 0.673455i) q^{10} +(-0.538340 + 0.0852647i) q^{11} +(-0.0795524 + 0.502274i) q^{12} +(-0.808560 - 0.411982i) q^{13} +(-4.89333 - 4.89333i) q^{14} +(2.05560 + 0.325576i) q^{15} +(-1.34194 + 4.13008i) q^{16} +(0.937351 + 5.91820i) q^{17} +(1.93107 + 5.94322i) q^{18} +(3.90401 - 1.98919i) q^{19} +(-0.139348 - 0.0452768i) q^{20} +(-11.9552 - 3.88447i) q^{21} +(0.718557 - 0.366123i) q^{22} +(-0.323498 - 0.995624i) q^{23} +(1.12646 + 7.11222i) q^{24} +(1.35979 - 4.18499i) q^{25} +(1.32616 + 0.210043i) q^{26} +(2.32519 + 2.32519i) q^{27} +(0.788504 + 0.401763i) q^{28} +(0.193017 - 1.21866i) q^{29} +(-3.04147 + 0.481721i) q^{30} +(1.22986 + 0.893547i) q^{31} -1.06686i q^{32} +(0.861051 - 1.18514i) q^{33} +(-4.02495 - 7.89940i) q^{34} +(1.64425 - 3.22703i) q^{35} +(-0.469718 - 0.646511i) q^{36} +(5.87120 - 4.26568i) q^{37} +(-4.58415 + 4.58415i) q^{38} +(2.31959 - 0.753680i) q^{39} -2.07471 q^{40} +(6.21116 - 1.55612i) q^{41} +18.5992 q^{42} +(-5.91654 + 1.92240i) q^{43} +(-0.0729237 + 0.0729237i) q^{44} +(-2.64591 + 1.92237i) q^{45} +(0.910440 + 1.25311i) q^{46} +(-1.80254 + 3.53768i) q^{47} +(-5.29874 - 10.3994i) q^{48} +(-8.74342 + 12.0343i) q^{49} +6.51076i q^{50} +(-13.0287 - 9.46590i) q^{51} +(-0.169589 + 0.0268603i) q^{52} +(0.837443 - 5.28741i) q^{53} +(-4.33510 - 2.20884i) q^{54} +(0.298447 + 0.298447i) q^{55} +(12.3768 + 1.96029i) q^{56} +(-3.63903 + 11.1998i) q^{57} +(0.285587 + 1.80313i) q^{58} +(2.74251 + 8.44059i) q^{59} +(0.350871 - 0.178778i) q^{60} +(1.31994 + 0.428873i) q^{61} +(-2.13919 - 0.695064i) q^{62} +(17.6006 - 8.96797i) q^{63} +(-2.19610 - 6.75890i) q^{64} +(0.109928 + 0.694060i) q^{65} +(-0.669787 + 2.06139i) q^{66} +(-5.56618 - 0.881596i) q^{67} +(0.801681 + 0.801681i) q^{68} +(2.50694 + 1.27735i) q^{69} +(-0.838297 + 5.29280i) q^{70} +(-1.07629 + 0.170468i) q^{71} +(-9.15463 - 6.65123i) q^{72} -5.61291i q^{73} +(-6.31149 + 8.68702i) q^{74} +(5.36919 + 10.5376i) q^{75} +(0.376378 - 0.738683i) q^{76} +(-1.49841 - 2.06239i) q^{77} +(-2.91948 + 2.12113i) q^{78} +(8.62379 - 8.62379i) q^{79} +(3.19819 - 1.03915i) q^{80} +3.83260 q^{81} +(-8.02874 + 5.02962i) q^{82} -13.1576 q^{83} +(-2.26205 + 0.734986i) q^{84} +(3.28096 - 3.28096i) q^{85} +(7.44668 - 5.41033i) q^{86} +(1.94919 + 2.68283i) q^{87} +(-0.662972 + 1.30116i) q^{88} +(-0.885629 - 1.73814i) q^{89} +(2.84433 - 3.91488i) q^{90} -4.24431i q^{91} +(-0.160248 - 0.116427i) q^{92} +(-4.03545 + 0.639153i) q^{93} +(0.918996 - 5.80231i) q^{94} +(-3.02313 - 1.54036i) q^{95} +(2.02752 + 2.02752i) q^{96} +(-1.91879 - 0.303907i) q^{97} +(6.80125 - 20.9321i) q^{98} +(0.360115 + 2.27367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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