LMFDB - Embedded newform 41.2.g.a.21.2

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			21.2
Character	$\chi$	$=$	41.21
Dual form			41.2.g.a.2.2

$q$-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 $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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	−0.234151	−	0.972200i	$-0.575231\pi$
$2$	−1.40718	−	0.457221i	−0.995028	−	0.323304i	−0.760877	+	0.648896i	$0.775231\pi$
$3$	−1.90046	−	1.90046i	−1.09723	−	1.09723i	−0.994733	−	0.102497i	$-0.967317\pi$
$3$	−1.90046	−	1.90046i	−1.09723	−	1.09723i	−0.102497	−	0.994733i	$-0.532683\pi$
$4$	0.153075	+	0.111216i	0.0765376	+	0.0556078i
$5$	−0.455161	+	0.626475i	−0.203554	+	0.280168i	−0.898574	−	0.438823i	$-0.855396\pi$
$5$	−0.455161	+	0.626475i	−0.203554	+	0.280168i	0.695020	+	0.718991i	$0.255396\pi$
$6$	1.80536	+	3.54322i	0.737036	+	1.44651i
$7$	2.12336	−	4.16732i	0.802553	−	1.57510i	−0.0154469	−	0.999881i	$-0.504917\pi$
$7$	2.12336	−	4.16732i	0.802553	−	1.57510i	0.818000	−	0.575218i	$-0.195083\pi$
$8$	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	0.0747477	−	0.997202i	$-0.476185\pi$
$11$	−0.538340	−	0.0852647i	−0.162316	−	0.0257083i	−0.237063	+	0.971494i	$0.576185\pi$
$12$	−0.0795524	−	0.502274i	−0.0229648	−	0.144994i
$13$	−0.808560	+	0.411982i	−0.224254	+	0.114263i	−0.562508	−	0.826792i	$-0.690164\pi$
$13$	−0.808560	+	0.411982i	−0.224254	+	0.114263i	0.338254	+	0.941055i	$0.390164\pi$
$14$	−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	−0.564897	−	0.825161i	$-0.691084\pi$
$17$	0.937351	−	5.91820i	0.227341	−	1.43537i	0.792238	−	0.610212i	$-0.208916\pi$
$18$	1.93107	−	5.94322i	0.455157	−	1.40083i
$19$	3.90401	+	1.98919i	0.895641	+	0.456352i	0.840304	−	0.542116i	$-0.182377\pi$
$19$	3.90401	+	1.98919i	0.895641	+	0.456352i	0.0553374	+	0.998468i	$0.482377\pi$
$20$	−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	−0.979102	−	0.203370i	$-0.934811\pi$
$23$	−0.323498	+	0.995624i	−0.0674539	+	0.207602i	0.911648	+	0.410972i	$0.134811\pi$
$24$	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	0.999107	−	0.0422549i	$-0.0134542\pi$
$29$	0.193017	+	1.21866i	0.0358423	+	0.226299i	−0.963265	+	0.268554i	$0.913454\pi$
$30$	−3.04147	−	0.481721i	−0.555294	−	0.0879499i
$31$	1.22986	−	0.893547i	0.220890	−	0.160486i	−0.471837	−	0.881686i	$-0.656409\pi$
$31$	1.22986	−	0.893547i	0.220890	−	0.160486i	0.692727	+	0.721200i	$0.256409\pi$
$32$			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	0.954357	−	0.298668i	$-0.0965423\pi$
$37$	5.87120	+	4.26568i	0.965220	+	0.701273i	0.0108626	+	0.999941i	$0.496542\pi$
$38$	−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	−0.179092	−	0.983832i	$-0.557316\pi$
$43$	−5.91654	−	1.92240i	−0.902263	−	0.293163i	−0.723171	+	0.690669i	$0.757316\pi$
$44$	−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	0.721369	−	0.692551i	$-0.243513\pi$
$47$	−1.80254	−	3.53768i	−0.262927	−	0.516023i	−0.984296	+	0.176528i	$0.943513\pi$
$48$	−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	0.976024	+	0.217663i	$0.0698434\pi$
$53$	0.837443	+	5.28741i	0.115032	+	0.726281i	−0.860992	+	0.508618i	$0.830157\pi$
$54$	−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	−0.597769	−	0.801668i	$-0.703946\pi$
$59$	2.74251	−	8.44059i	0.357045	−	1.09887i	0.954814	−	0.297203i	$-0.0960538\pi$
$60$	0.350871	+	0.178778i	0.0452972	+	0.0230801i
$61$	1.31994	−	0.428873i	0.169001	−	0.0549116i	−0.223295	−	0.974751i	$-0.571681\pi$
$61$	1.31994	−	0.428873i	0.169001	−	0.0549116i	0.392295	+	0.919839i	$0.371681\pi$
$62$	−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	−0.486881	−	0.873468i	$-0.661866\pi$
$67$	−5.56618	+	0.881596i	−0.680017	+	0.107704i	−0.193135	+	0.981172i	$0.561866\pi$
$68$	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	0.0922409	−	0.995737i	$-0.470597\pi$
$71$	−1.07629	−	0.170468i	−0.127732	−	0.0202308i	−0.219973	+	0.975506i	$0.570597\pi$
$72$	−9.15463	+	6.65123i	−1.07888	+	0.783855i
$73$			5.61291i			0.656941i	0.944514	+	0.328471i	$0.106533\pi$
$73$			5.61291i			0.656941i	−0.944514	+	0.328471i	$0.893467\pi$
$74$	−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	0.999570	−	0.0293183i	$-0.00933364\pi$
$79$	8.62379	+	8.62379i	0.970252	+	0.970252i	−0.0293183	+	0.999570i	$0.509334\pi$
$80$	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	−0.933170	−	0.359436i	$-0.882969\pi$
$89$	−0.885629	+	1.73814i	−0.0938764	+	0.184243i	0.839293	+	0.543679i	$0.182969\pi$
$90$	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	−0.253084	−	0.967444i	$-0.581445\pi$
$97$	−1.91879	+	0.303907i	−0.194824	+	0.0308571i	0.0582598	+	0.998301i	$0.481445\pi$
$98$	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	0.785248	−	0.619181i	$-0.212535\pi$
$101$	7.49597	+	3.81939i	0.745877	+	0.380043i	−0.0393710	+	0.999225i	$0.512535\pi$
$102$	22.6617	−	7.36325i	2.24385	−	0.729070i
$103$	4.08634	−	1.32773i	0.402639	−	0.130825i	−0.100695	−	0.994917i	$-0.532107\pi$
$103$	4.08634	−	1.32773i	0.402639	−	0.130825i	0.503334	+	0.864092i	$0.332107\pi$
$104$	−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	0.946813	+	0.321785i	$0.104283\pi$
$107$	3.82695	+	11.7782i	0.369966	+	1.13864i	−0.576847	+	0.816852i	$0.695717\pi$
$108$	0.614527	−	0.0973316i	0.0591329	−	0.00936574i
$109$	1.22345	−	1.22345i	0.117185	−	0.117185i	−0.646082	−	0.763268i	$-0.723594\pi$
$109$	1.22345	−	1.22345i	0.117185	−	0.117185i	0.763268	+	0.646082i	$0.223594\pi$
$110$	−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	−0.542458	−	0.840083i	$-0.682506\pi$
$113$	0.944802	−	0.686439i	0.0888795	−	0.0645747i	0.631338	+	0.775508i	$0.282506\pi$
$114$			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	0.885571	−	0.464504i	$-0.153767\pi$
$127$	8.08534	+	5.87434i	0.717458	+	0.521264i	−0.168113	+	0.985768i	$0.553767\pi$
$128$	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	0.787579	−	0.616213i	$-0.211334\pi$
$131$	−0.478992	−	0.659276i	−0.0418497	−	0.0576012i	−0.829429	+	0.558612i	$0.811334\pi$
$132$			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	−0.825058	−	0.565048i	$-0.808858\pi$
$137$	−3.04334	+	3.04334i	−0.260010	+	0.260010i	0.565048	+	0.825058i	$0.308858\pi$
$138$	−4.11175	+	0.651237i	−0.350015	+	0.0554369i
$139$	1.55254	+	4.77824i	0.131685	+	0.405285i	0.995060	−	0.0992785i	$-0.0316535\pi$
$139$	1.55254	+	4.77824i	0.131685	+	0.405285i	−0.863375	+	0.504563i	$0.831653\pi$
$140$	−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	0.172685	−	0.984977i	$-0.444756\pi$
$149$	7.82798	−	1.23983i	0.641293	−	0.101571i	0.468608	+	0.883406i	$0.344756\pi$
$150$	−12.3734	+	12.3734i	−1.01029	+	1.01029i
$151$	−18.4200	+	9.38545i	−1.49900	+	0.763777i	−0.994995	−	0.0999253i	$-0.968140\pi$
$151$	−18.4200	+	9.38545i	−1.49900	+	0.763777i	−0.504002	+	0.863702i	$0.668140\pi$
$152$	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	−0.562177	−	0.827017i	$-0.690036\pi$
$157$	5.47977	−	10.7546i	0.437333	−	0.858314i	0.999510	−	0.0312976i	$-0.00996395\pi$
$158$	−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	0.998871	+	0.0475043i	$0.0151268\pi$
$167$	13.5221	+	13.5221i	1.04638	+	1.04638i	0.0475043	+	0.998871i	$0.484873\pi$
$168$	−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	$-0.926705\pi$
$173$		−	6.00388i		−	0.456467i	0.973606	−	0.228233i	$-0.0732949\pi$
$174$	−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	−0.484894	−	0.874573i	$-0.661142\pi$
$179$	−9.04156	+	1.43204i	−0.675798	+	0.107036i	−0.190904	+	0.981609i	$0.561142\pi$
$180$	−0.191226	−	0.588533i	−0.0142531	−	0.0438667i
$181$	2.98065	−	18.8191i	0.221550	−	1.39881i	−0.586619	−	0.809863i	$-0.699541\pi$
$181$	2.98065	−	18.8191i	0.221550	−	1.39881i	0.808169	−	0.588950i	$-0.200459\pi$
$182$	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	−0.357503	−	0.933912i	$-0.616372\pi$
$191$	7.96614	−	7.96614i	0.576410	−	0.576410i	0.933912	+	0.357503i	$0.116372\pi$
$192$	17.0186	−	8.67141i	1.22821	−	0.625805i
$193$	−1.82911	−	11.5486i	−0.131663	−	0.831285i	−0.961805	−	0.273734i	$-0.911741\pi$
$193$	−1.82911	−	11.5486i	−0.131663	−	0.831285i	0.830143	−	0.557551i	$-0.188259\pi$
$194$	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	0.543168	−	0.839624i	$-0.317225\pi$
$197$	−5.94003	−	8.17575i	−0.423210	−	0.582498i	−0.966378	+	0.257126i	$0.917225\pi$
$198$	−1.54632	+	3.03482i	−0.109892	+	0.215675i
$199$	3.82058	+	7.49832i	0.270834	+	0.531542i	0.985863	−	0.167553i	$-0.0535866\pi$
$199$	3.82058	+	7.49832i	0.270834	+	0.531542i	−0.715029	+	0.699095i	$0.753587\pi$
$200$	−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	0.594169	−	0.804340i	$-0.297481\pi$
$211$	−5.89458	−	11.5688i	−0.405800	−	0.796427i	−0.999969	+	0.00791335i	$0.997481\pi$
$212$	−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	0.589686	+	0.807632i	$0.299251\pi$
$223$	−5.40722	+	16.6417i	−0.362094	+	1.11441i	−0.951781	+	0.306779i	$0.900749\pi$
$224$	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	−0.999565	−	0.0294771i	$-0.990616\pi$
$227$	−24.2713	−	12.3668i	−1.61094	−	0.820816i	−0.611377	−	0.791339i	$-0.709384\pi$
$228$	0.688546	−	2.11913i	0.0456001	−	0.140343i
$229$	3.54084	−	22.3560i	0.233985	−	1.47733i	−0.538679	−	0.842511i	$-0.681077\pi$
$229$	3.54084	−	22.3560i	0.233985	−	1.47733i	0.772665	−	0.634815i	$-0.218923\pi$
$230$	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	0.430041	−	0.902809i	$-0.358499\pi$
$233$	21.5716	−	10.9913i	1.41320	−	0.720062i	0.983160	+	0.182747i	$0.0584990\pi$
$234$	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	0.290603	+	0.956844i	$0.406144\pi$
$239$	−10.1154	+	19.8526i	−0.654312	+	1.28416i	−0.944915	+	0.327316i	$0.893856\pi$
$240$	−4.10316	−	8.05290i	−0.264858	−	0.519813i
$241$	−7.10275	+	9.77610i	−0.457528	+	0.629734i	−0.973994	−	0.226574i	$-0.927247\pi$
$241$	−7.10275	+	9.77610i	−0.457528	+	0.629734i	0.516466	+	0.856308i	$0.327247\pi$
$242$	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	−0.635767	−	0.771881i	$-0.719316\pi$
$251$	4.67048	−	6.42836i	0.294798	−	0.405755i	0.930565	+	0.366126i	$0.119316\pi$
$252$	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	−0.617709	−	0.786407i	$-0.711939\pi$
$257$	−23.2164	−	3.67711i	−1.44820	−	0.229372i	−0.830489	+	0.557035i	$0.811939\pi$
$258$	−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	0.639656	+	0.768661i	$0.279077\pi$
$263$	−3.34437	+	21.1155i	−0.206222	+	1.30204i	−0.845878	+	0.533376i	$0.820923\pi$
$264$	−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	0.283943	+	0.958841i	$0.408357\pi$
$269$	−8.35420	+	25.7116i	−0.509364	+	1.56766i	−0.793308	+	0.608821i	$0.791643\pi$
$270$	0.589381	−	3.72121i	0.0358686	−	0.226466i
$271$	−3.68892	−	11.3533i	−0.224086	−	0.689666i	−0.998383	−	0.0568438i	$-0.981896\pi$
$271$	−3.68892	−	11.3533i	−0.224086	−	0.689666i	0.774297	−	0.632822i	$-0.218104\pi$
$272$	−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	−0.884121	−	0.467259i	$-0.845242\pi$
$277$	−11.8657	+	8.62092i	−0.712940	+	0.517981i	0.171181	+	0.985240i	$0.445242\pi$
$278$		−	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	0.989286	−	0.145989i	$-0.0466365\pi$
$281$	4.85610	+	9.53063i	0.289691	+	0.568550i	−0.699596	+	0.714539i	$0.746636\pi$
$282$	9.28054	−	12.7736i	0.552648	−	0.760655i
$283$	15.4306	+	11.2110i	0.917254	+	0.666424i	0.942839	−	0.333249i	$-0.108145\pi$
$283$	15.4306	+	11.2110i	0.917254	+	0.666424i	−0.0255849	+	0.999673i	$0.508145\pi$
$284$	−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	0.925475	+	0.378808i	$0.123666\pi$
$293$	11.7759	+	23.1115i	0.687957	+	1.35019i	−0.237519	+	0.971383i	$0.576334\pi$
$294$	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	−0.534390	−	0.845238i	$-0.679459\pi$
$307$	−8.23334	+	2.67517i	−0.469901	+	0.152680i	0.0644882	+	0.997918i	$0.479459\pi$
$308$	−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	−0.925595	−	0.378515i	$-0.876435\pi$
$311$	1.26384	−	7.97957i	0.0716658	−	0.452480i	0.997261	−	0.0739647i	$-0.0235652\pi$
$312$	2.01929	+	6.21473i	0.114320	+	0.351840i
$313$	−3.40878	+	0.539898i	−0.192676	+	0.0305168i	−0.252026	−	0.967720i	$-0.581097\pi$
$313$	−3.40878	+	0.539898i	−0.192676	+	0.0305168i	0.0593507	+	0.998237i	$0.481097\pi$
$314$	−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	0.871431	−	0.490519i	$-0.163193\pi$
$317$	27.5726	+	4.36707i	1.54863	+	0.245279i	0.677201	+	0.735798i	$0.263193\pi$
$318$	−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	0.115756	−	0.993278i	$-0.463071\pi$
$331$	−15.9651	−	15.9651i	−0.877522	−	0.877522i	−0.993278	+	0.115756i	$0.963071\pi$
$332$	−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	$0.235952\pi$
$337$			24.7909i			1.35045i	−0.737614	+	0.675223i	$0.764048\pi$
$338$	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	0.365895	−	0.930656i	$-0.380763\pi$
$347$	−3.20315	−	1.63209i	−0.171954	−	0.0876149i	−0.537849	+	0.843041i	$0.680763\pi$
$348$	0.596746	−	0.193894i	0.0319889	−	0.0103938i
$349$	−0.272833	+	0.0886489i	−0.0146044	+	0.00474526i	−0.316310	−	0.948656i	$-0.602444\pi$
$349$	−0.272833	+	0.0886489i	−0.0146044	+	0.00474526i	0.301706	+	0.953401i	$0.402444\pi$
$350$	−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	−0.935233	−	0.354033i	$-0.884810\pi$
$353$	−7.26560	−	22.3612i	−0.386709	−	1.19017i	0.548524	−	0.836135i	$-0.315190\pi$
$354$	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	0.485363	−	0.874313i	$-0.338687\pi$
$359$	27.7932	−	20.1929i	1.46687	−	1.06574i	0.981506	−	0.191430i	$-0.0613125\pi$
$360$		−	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	0.873804	−	0.486278i	$-0.161646\pi$
$367$	24.8067	+	8.06019i	1.29490	+	0.420738i	0.421096	+	0.907016i	$0.361646\pi$
$368$	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	0.778856	−	0.627203i	$-0.215800\pi$
$373$	8.17007	+	5.93590i	0.423030	+	0.307349i	−0.355826	+	0.934552i	$0.615800\pi$
$374$	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	−0.277816	−	0.960634i	$-0.589611\pi$
$379$	10.7064	−	7.77867i	0.549952	−	0.399563i	0.827768	+	0.561071i	$0.189611\pi$
$380$	−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	−0.571833	−	0.820370i	$-0.693767\pi$
$383$	4.86397	−	4.86397i	0.248537	−	0.248537i	0.820370	+	0.571833i	$0.193767\pi$
$384$	−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	0.539965	−	0.841687i	$-0.318437\pi$
$389$	29.0233	−	9.43023i	1.47154	−	0.478132i	0.931572	+	0.363556i	$0.118437\pi$
$390$	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	−0.899512	−	0.436896i	$-0.856078\pi$
$397$	−21.4147	+	10.9114i	−1.07477	+	0.547625i	−0.175263	+	0.984522i	$0.556078\pi$
$398$	−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	$0.0379717\pi$
$401$			4.76630i			0.238018i	−0.992893	+	0.119009i	$0.962028\pi$
$402$	−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	$0.0884281\pi$
$419$			11.2273i			0.548491i	−0.961660	+	0.274246i	$0.911572\pi$
$420$	1.49005	−	1.08258i	0.0727069	−	0.0528246i
$421$	−16.7385	−	2.65113i	−0.815787	−	0.129208i	−0.265422	−	0.964132i	$-0.585511\pi$
$421$	−16.7385	−	2.65113i	−0.815787	−	0.129208i	−0.550365	+	0.834924i	$0.685511\pi$
$422$	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	−0.735491	−	0.677534i	$-0.763048\pi$
$431$	−19.3545	+	6.28864i	−0.932271	+	0.302913i	−0.196780	+	0.980448i	$0.563048\pi$
$432$	−12.7235	−	6.48296i	−0.612160	−	0.311911i
$433$	6.55082	−	20.1613i	0.314812	−	0.968893i	−0.661019	−	0.750369i	$-0.729876\pi$
$433$	6.55082	−	20.1613i	0.314812	−	0.968893i	0.975832	−	0.218524i	$-0.0701241\pi$
$434$	−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	0.936360	+	0.351041i	$0.114172\pi$
$439$	3.23308	+	20.4129i	0.154306	+	0.974252i	−0.782054	+	0.623211i	$0.785828\pi$
$440$	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	0.996248	−	0.0865400i	$-0.0275810\pi$
$443$	12.7566	+	17.5580i	0.606086	+	0.834206i	−0.390162	+	0.920746i	$0.627581\pi$
$444$	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	0.181736	−	0.983347i	$-0.441829\pi$
$449$	−5.28118	−	1.71596i	−0.249234	−	0.0809812i	−0.430970	+	0.902366i	$0.641829\pi$
$450$	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	−0.789101	−	0.614264i	$-0.789453\pi$
$457$	−17.5772	−	34.4973i	−0.822229	−	1.61371i	−0.0331277	−	0.999451i	$-0.510547\pi$
$458$	−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	−0.679543	−	0.733636i	$-0.737822\pi$
$461$	−4.11822	+	2.99206i	−0.191805	+	0.139354i	0.487738	+	0.872990i	$0.337822\pi$
$462$	−10.0127	−	1.58585i	−0.465832	−	0.0737805i
$463$	−0.451109	−	2.84819i	−0.0209648	−	0.132367i	0.974986	−	0.222266i	$-0.0713454\pi$
$463$	−0.451109	−	2.84819i	−0.0209648	−	0.132367i	−0.995951	+	0.0898996i	$0.971345\pi$
$464$	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	0.760266	+	0.649612i	$0.225069\pi$
$467$	11.3892	+	35.0524i	0.527030	+	1.62203i	−0.233235	+	0.972420i	$0.574931\pi$
$468$	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	−0.960232	−	0.279203i	$-0.909930\pi$
$479$	−28.4248	+	14.4832i	−1.29876	+	0.661752i	−0.338530	+	0.940956i	$0.609930\pi$
$480$	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	−0.500424	−	0.865780i	$-0.666823\pi$
$487$	10.5402	−	14.5073i	0.477621	−	0.657389i	0.978046	+	0.208391i	$0.0668227\pi$
$488$	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	−0.464720	−	0.885458i	$-0.653845\pi$
$499$	11.7228	−	23.0074i	0.524786	−	1.02995i	0.989506	−	0.144493i	$-0.0461551\pi$
$500$	−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	−0.262792	−	0.964853i	$-0.584643\pi$
$503$	−18.1861	−	2.88039i	−0.810878	−	0.128430i	−0.548086	+	0.836422i	$0.684643\pi$
$504$	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	0.836015	+	0.548706i	$0.184879\pi$
$509$	−2.90230	+	18.3244i	−0.128642	+	0.812214i	−0.964657	+	0.263508i	$0.915121\pi$
$510$	−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	−0.999706	−	0.0242662i	$-0.992275\pi$
$521$	−1.28799	−	8.13203i	−0.0564277	−	0.356271i	0.943278	−	0.332005i	$-0.107725\pi$
$522$	7.61549	+	1.20617i	0.333321	+	0.0527928i
$523$	−27.7382	+	20.1530i	−1.21291	+	0.881229i	−0.995492	−	0.0948499i	$-0.969763\pi$
$523$	−27.7382	+	20.1530i	−1.21291	+	0.881229i	−0.217416	+	0.976079i	$0.569763\pi$
$524$		−	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	0.819435	−	0.573172i	$-0.194287\pi$
$541$	0.490706	+	0.675399i	0.0210971	+	0.0290377i	−0.798338	+	0.602209i	$0.794287\pi$
$542$			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	−0.0338377	−	0.999427i	$-0.510773\pi$
$547$	22.5832	−	22.5832i	0.965590	−	0.965590i	0.999427	+	0.0338377i	$0.0107729\pi$
$548$	−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	−0.705465	−	0.708744i	$-0.749262\pi$
$557$	4.35403	−	27.4903i	0.184486	−	1.16480i	0.889951	−	0.456055i	$-0.150738\pi$
$558$	−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	−0.492073	−	0.870554i	$-0.663761\pi$
$563$	−29.1631	−	4.61898i	−1.22908	−	0.194667i	−0.737005	+	0.675887i	$0.763761\pi$
$564$	−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	0.290535	+	0.956864i	$0.406167\pi$
$569$	−16.9189	+	23.2869i	−0.709278	+	0.976237i	−0.999812	+	0.0193726i	$0.993833\pi$
$570$	−10.9157	−	7.93071i	−0.457208	−	0.332181i
$571$	−19.3493	−	19.3493i	−0.809742	−	0.809742i	0.174853	−	0.984595i	$-0.444055\pi$
$571$	−19.3493	−	19.3493i	−0.809742	−	0.809742i	−0.984595	+	0.174853i	$0.944055\pi$
$572$	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	0.827700	−	0.561171i	$-0.189649\pi$
$577$	6.40224	+	6.40224i	0.266529	+	0.266529i	−0.561171	+	0.827700i	$0.689649\pi$
$578$	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	−0.546760	−	0.837289i	$-0.684139\pi$
$587$	−4.62167	+	2.35486i	−0.190757	+	0.0971955i	0.356003	+	0.934485i	$0.384139\pi$
$588$	−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	−0.0308006	−	0.999526i	$-0.509806\pi$
$593$	−20.8824	−	10.6401i	−0.857538	−	0.436937i	−0.826737	+	0.562588i	$0.809806\pi$
$594$	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	−0.934586	−	0.355739i	$-0.884229\pi$
$599$	−9.48601	−	29.1949i	−0.387588	−	1.19287i	0.546998	−	0.837134i	$-0.315771\pi$
$600$	31.2963	−	4.95685i	1.27767	−	0.202363i
$601$	5.21941	−	5.21941i	0.212904	−	0.212904i	−0.592596	−	0.805500i	$-0.701897\pi$
$601$	5.21941	−	5.21941i	0.212904	−	0.212904i	0.805500	+	0.592596i	$0.201897\pi$
$602$	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	0.998088	+	0.0618155i	$0.0196890\pi$
$607$	18.4399	+	25.3803i	0.748452	+	1.03016i	−0.249636	+	0.968340i	$0.580311\pi$
$608$	−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	0.627373	−	0.778719i	$-0.284130\pi$
$613$	16.7669	+	5.44789i	0.677208	+	0.220038i	0.0498354	+	0.998757i	$0.484130\pi$
$614$	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	0.150905	−	0.988548i	$-0.451781\pi$
$617$	−7.65218	−	2.48634i	−0.308065	−	0.100096i	−0.458970	+	0.888452i	$0.651781\pi$
$618$	12.0818	+	12.0818i	0.486000	+	0.486000i
$619$	−5.14200	−	3.73588i	−0.206675	−	0.150158i	0.479633	−	0.877469i	$-0.340770\pi$
$619$	−5.14200	−	3.73588i	−0.206675	−	0.150158i	−0.686308	+	0.727311i	$0.740770\pi$
$620$	−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	0.973485	−	0.228753i	$-0.0734647\pi$
$631$	1.29270	+	3.97853i	0.0514616	+	0.158383i	−0.922023	+	0.387135i	$0.873465\pi$
$632$	−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	0.238377	−	0.971173i	$-0.423385\pi$
$641$	19.3732	−	3.06842i	0.765196	−	0.121195i	0.526819	+	0.849978i	$0.323385\pi$
$642$	−34.8236	+	34.8236i	−1.37438	+	1.37438i
$643$	−9.90543	+	5.04707i	−0.390632	+	0.199037i	−0.638265	−	0.769817i	$-0.720347\pi$
$643$	−9.90543	+	5.04707i	−0.390632	+	0.199037i	0.247633	+	0.968854i	$0.420347\pi$
$644$	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	$-0.934230\pi$
$647$		−	10.4368i		−	0.410313i	0.978729	−	0.205157i	$-0.0657704\pi$
$648$	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	0.973877	−	0.227075i	$-0.0729163\pi$
$653$	19.0837	+	19.0837i	0.746802	+	0.746802i	−0.227075	+	0.973877i	$0.572916\pi$
$654$	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	0.463246	−	0.886230i	$-0.346685\pi$
$659$	−10.8584	−	10.8584i	−0.422984	−	0.422984i	−0.886230	+	0.463246i	$0.846685\pi$
$660$	−0.173644	−	0.126160i	−0.00675910	−	0.00491077i
$661$	0.199484	−	0.274566i	0.00775902	−	0.0106794i	−0.805120	−	0.593112i	$-0.797899\pi$
$661$	0.199484	−	0.274566i	0.00775902	−	0.0106794i	0.812879	+	0.582433i	$0.197899\pi$
$662$	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	−0.920705	−	0.390258i	$-0.872386\pi$
$673$	1.95952	−	12.3719i	0.0755340	−	0.476903i	0.996239	−	0.0866442i	$-0.0276143\pi$
$674$	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	−0.790140	−	0.612926i	$-0.789992\pi$
$677$	−27.8174	+	9.03841i	−1.06911	+	0.347374i	−0.278968	+	0.960300i	$0.589992\pi$
$678$	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	−0.310545	−	0.950559i	$-0.600512\pi$
$683$	16.7263	−	16.7263i	0.640013	−	0.640013i	0.950559	+	0.310545i	$0.100512\pi$
$684$	−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	0.700484	−	0.713668i	$-0.252967\pi$
$691$	−7.58691	−	14.8902i	−0.288620	−	0.566448i	−0.989104	+	0.147220i	$0.952967\pi$
$692$	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	−0.115656	−	0.993289i	$-0.536897\pi$
$701$	−29.0200	−	21.0843i	−1.09607	−	0.796342i	−0.980414	+	0.196948i	$0.936897\pi$
$702$	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	0.980396	+	0.197037i	$0.0631319\pi$
$709$	2.89893	+	18.3031i	0.108872	+	0.687389i	−0.871524	+	0.490352i	$0.836868\pi$
$710$	−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	−0.119104	−	0.992882i	$-0.538002\pi$
$719$	−26.6096	−	13.5583i	−0.992371	−	0.505638i	−0.873266	+	0.487244i	$0.838002\pi$
$720$	−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	0.249237	−	0.968443i	$-0.419820\pi$
$727$	5.04235	+	0.798630i	0.187010	+	0.0296195i	−0.0622267	+	0.998062i	$0.519820\pi$
$728$	−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	−0.967127	−	0.254293i	$-0.918157\pi$
$733$	−11.5449	+	15.8902i	−0.426421	+	0.586918i	0.540706	+	0.841212i	$0.318157\pi$
$734$	−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	−0.417492	−	0.908681i	$-0.637091\pi$
$743$	15.6932	−	21.5998i	0.575727	−	0.792420i	0.993219	+	0.116261i	$0.0370908\pi$
$744$	−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	−0.725470	−	0.688254i	$-0.758378\pi$
$751$	−16.3078	+	8.30926i	−0.595082	+	0.303209i	0.130388	+	0.991463i	$0.458378\pi$
$752$	−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	0.718765	−	0.695254i	$-0.244708\pi$
$757$	15.9241	+	8.11374i	0.578772	+	0.294899i	−0.139993	+	0.990153i	$0.544708\pi$
$758$	−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	−0.908096	−	0.418762i	$-0.862464\pi$
$761$	2.00583	−	6.17330i	0.0727111	−	0.223782i	0.980807	+	0.194980i	$0.0624642\pi$
$762$	−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	−0.349026	−	0.937113i	$-0.613487\pi$
$769$	12.0454	−	8.75147i	0.434367	−	0.315586i	0.783393	+	0.621527i	$0.213487\pi$
$770$			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	−0.985723	−	0.168375i	$-0.946148\pi$
$773$	−15.0844	−	29.6048i	−0.542548	−	1.06481i	0.443175	−	0.896435i	$-0.353852\pi$
$774$	−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	0.856626	+	0.515937i	$0.172556\pi$
$787$	30.3707	+	41.8017i	1.08260	+	1.49007i	0.225974	+	0.974133i	$0.427444\pi$
$788$		−	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	−0.841255	−	0.540639i	$-0.818183\pi$
$797$	4.43551	−	13.6511i	0.157114	−	0.483547i	0.998369	+	0.0570915i	$0.0181827\pi$
$798$	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	0.865513	−	0.500887i	$-0.166993\pi$
$809$	43.6281	+	6.91001i	1.53388	+	0.242943i	0.668369	+	0.743830i	$0.266993\pi$
$810$	3.55255	−	2.58108i	0.124824	−	0.0906899i
$811$		−	27.7113i		−	0.973074i	−0.873660	−	0.486537i	$-0.838260\pi$
$811$		−	27.7113i		−	0.973074i	0.873660	−	0.486537i	$-0.161740\pi$
$812$	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	0.00438414	−	0.999990i	$-0.498604\pi$
$823$	−28.5619	−	28.5619i	−0.995606	−	0.995606i	−0.999990	+	0.00438414i	$0.998604\pi$
$824$	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	−0.907110	−	0.420894i	$-0.861716\pi$
$827$	−0.960885	+	1.88584i	−0.0334133	+	0.0655772i	0.873696	+	0.486472i	$0.161716\pi$
$828$	−0.491729	−	0.676807i	−0.0170888	−	0.0235207i
$829$		−	22.5376i		−	0.782765i	−0.920228	−	0.391382i	$-0.871997\pi$
$829$		−	22.5376i		−	0.782765i	0.920228	−	0.391382i	$-0.128003\pi$
$830$	−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	0.853506	−	0.521083i	$-0.174472\pi$
$839$	27.0427	+	13.7790i	0.933619	+	0.475703i	0.0801132	+	0.996786i	$0.474472\pi$
$840$	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	0.578942	−	0.815369i	$-0.303466\pi$
$853$	−10.9647	−	15.0916i	−0.375423	−	0.516726i	−0.954365	+	0.298643i	$0.903466\pi$
$854$	−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	−0.999751	−	0.0223039i	$-0.992900\pi$
$857$	−38.9323	−	28.2860i	−1.32990	−	0.966232i	−0.330152	−	0.943928i	$-0.607100\pi$
$858$	1.39082	+	1.39082i	0.0474817	+	0.0474817i
$859$	−17.0896	−	5.55276i	−0.583091	−	0.189458i	0.00259400	−	0.999997i	$-0.499174\pi$
$859$	−17.0896	−	5.55276i	−0.583091	−	0.189458i	−0.585685	+	0.810539i	$0.699174\pi$
$860$	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	−0.294459	−	0.955664i	$-0.595139\pi$
$863$	−32.1502	−	10.4462i	−1.09441	−	0.355594i	−0.799947	+	0.600070i	$0.795139\pi$
$864$	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	−0.987198	−	0.159499i	$-0.949012\pi$
$877$	−8.35976	−	25.7287i	−0.282289	−	0.868796i	0.704909	−	0.709298i	$-0.250988\pi$
$878$	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	−0.564462	−	0.825459i	$-0.690916\pi$
$881$	−15.9073	+	5.16859i	−0.535930	+	0.174134i	0.0285328	+	0.999593i	$0.490916\pi$
$882$	−88.4065	+	28.7250i	−2.97680	+	0.967222i
$883$	22.7575	+	11.5955i	0.765852	+	0.390221i	0.792852	−	0.609414i	$-0.208595\pi$
$883$	22.7575	+	11.5955i	0.765852	+	0.390221i	−0.0269999	+	0.999635i	$0.508595\pi$
$884$	−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	0.547594	−	0.836744i	$-0.315544\pi$
$887$	39.5201	−	6.25936i	1.32695	−	0.210169i	0.779361	+	0.626576i	$0.215544\pi$
$888$	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	−0.977570	−	0.210610i	$-0.932455\pi$
$907$	−14.3108	+	19.6971i	−0.475182	+	0.654032i	0.502388	+	0.864642i	$0.332455\pi$
$908$	−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	$0.130663\pi$
$911$			24.0894i			0.798118i	−0.916925	+	0.399059i	$0.869337\pi$
$912$	−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	−0.962127	−	0.272603i	$-0.912115\pi$
$919$	1.12618	−	7.11039i	0.0371491	−	0.234550i	0.999276	+	0.0380527i	$0.0121155\pi$
$920$	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	−0.622594	−	0.782545i	$-0.713921\pi$
$929$	4.87523	−	4.87523i	0.159951	−	0.159951i	0.782545	+	0.622594i	$0.213921\pi$
$930$	−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	0.715803	+	0.698303i	$0.246061\pi$
$937$	26.3251	+	51.6659i	0.860003	+	1.68785i	0.144200	+	0.989549i	$0.453939\pi$
$938$	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	0.862663	−	0.505779i	$-0.168795\pi$
$941$	38.7521	+	12.5913i	1.26328	+	0.410466i	0.400620	+	0.916244i	$0.368795\pi$
$942$	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	0.154791	−	0.987947i	$-0.450530\pi$
$947$	−22.6790	−	16.4773i	−0.736970	−	0.535440i	−0.891761	+	0.452507i	$0.850530\pi$
$948$	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	−0.964184	−	0.265235i	$-0.914551\pi$
$953$	−31.1757	+	22.6505i	−1.00988	+	0.733721i	−0.0456960	+	0.998955i	$0.514551\pi$
$954$	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	0.618891	+	0.785477i	$0.287582\pi$
$967$	−6.60601	+	41.7087i	−0.212435	+	1.34126i	−0.831326	+	0.555785i	$0.812418\pi$
$968$	−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	−0.483554	−	0.875314i	$-0.660654\pi$
$971$	−1.85832	+	0.946862i	−0.0596364	+	0.0303863i	0.423918	+	0.905701i	$0.360654\pi$
$972$	−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	−0.566600	−	0.823993i	$-0.691742\pi$
$977$	13.5363	−	26.5664i	0.433063	−	0.849935i	0.999663	−	0.0259417i	$-0.00825842\pi$
$978$	−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	−0.772746	−	0.634716i	$-0.781117\pi$
$991$	6.13732	−	12.0452i	0.194959	−	0.382628i	0.967704	+	0.252088i	$0.0811172\pi$
$992$	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	−0.0143801	−	0.999897i	$-0.504577\pi$
$997$	24.8214	−	12.6471i	0.786101	−	0.400538i	0.800481	+	0.599358i	$0.204577\pi$
$998$	−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.21.2	yes	24
3.2	odd	2		369.2.u.a.226.2		24
4.3	odd	2		656.2.bs.d.513.3		24
41.2	even	20	inner	41.2.g.a.2.2	✓	24
41.17	odd	40		1681.2.a.m.1.18		24
41.24	odd	40		1681.2.a.m.1.17		24
123.2	odd	20		369.2.u.a.289.2		24
164.43	odd	20		656.2.bs.d.289.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.2	✓	24	41.2	even	20	inner
41.2.g.a.21.2	yes	24	1.1	even	1	trivial
369.2.u.a.226.2		24	3.2	odd	2
369.2.u.a.289.2		24	123.2	odd	20
656.2.bs.d.289.3		24	164.43	odd	20
656.2.bs.d.513.3		24	4.3	odd	2
1681.2.a.m.1.17		24	41.24	odd	40
1681.2.a.m.1.18		24	41.17	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

Related objects

Downloads

Learn more