LMFDB - Embedded newform 41.2.g.a.21.3

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			21.3
Character	$\chi$	$=$	41.21
Dual form			41.2.g.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.698642 + 0.227002i) q^{2} +(0.0432913 + 0.0432913i) q^{3} +(-1.18146 - 0.858384i) q^{4} +(-0.422124 + 0.581004i) q^{5} +(0.0204179 + 0.0400723i) q^{6} +(-1.42228 + 2.79137i) q^{7} +(-1.49413 - 2.05650i) q^{8} -2.99625i q^{9} +O(q^{10})$	\(q+(0.698642 + 0.227002i) q^{2} +(0.0432913 + 0.0432913i) q^{3} +(-1.18146 - 0.858384i) q^{4} +(-0.422124 + 0.581004i) q^{5} +(0.0204179 + 0.0400723i) q^{6} +(-1.42228 + 2.79137i) q^{7} +(-1.49413 - 2.05650i) q^{8} -2.99625i q^{9} +(-0.426803 + 0.310091i) q^{10} +(3.06970 + 0.486193i) q^{11} +(-0.0139866 - 0.0883076i) q^{12} +(-1.79162 + 0.912875i) q^{13} +(-1.62731 + 1.62731i) q^{14} +(-0.0434267 + 0.00687812i) q^{15} +(0.325524 + 1.00186i) q^{16} +(0.304435 - 1.92213i) q^{17} +(0.680157 - 2.09331i) q^{18} +(3.91204 + 1.99329i) q^{19} +(0.997449 - 0.324091i) q^{20} +(-0.182414 + 0.0592700i) q^{21} +(2.03426 + 1.03651i) q^{22} +(0.275748 - 0.848664i) q^{23} +(0.0243455 - 0.153711i) q^{24} +(1.38571 + 4.26477i) q^{25} +(-1.45892 + 0.231071i) q^{26} +(0.259585 - 0.259585i) q^{27} +(4.07644 - 2.07705i) q^{28} +(-1.43151 - 9.03822i) q^{29} +(-0.0319011 - 0.00505263i) q^{30} +(-5.64731 + 4.10301i) q^{31} +5.85778i q^{32} +(0.111844 + 0.153939i) q^{33} +(0.649020 - 1.27377i) q^{34} +(-1.02142 - 2.00465i) q^{35} +(-2.57193 + 3.53996i) q^{36} +(-3.49299 - 2.53781i) q^{37} +(2.28064 + 2.28064i) q^{38} +(-0.117081 - 0.0380419i) q^{39} +1.82554 q^{40} +(-2.53101 - 5.88167i) q^{41} -0.140897 q^{42} +(-10.3243 - 3.35457i) q^{43} +(-3.20940 - 3.20940i) q^{44} +(1.74083 + 1.26479i) q^{45} +(0.385298 - 0.530317i) q^{46} +(5.24325 + 10.2905i) q^{47} +(-0.0292795 + 0.0574642i) q^{48} +(-1.65440 - 2.27709i) q^{49} +3.29411i q^{50} +(0.0963909 - 0.0700321i) q^{51} +(2.90033 + 0.459367i) q^{52} +(0.465724 + 2.94046i) q^{53} +(0.240284 - 0.122431i) q^{54} +(-1.57828 + 1.57828i) q^{55} +(7.86552 - 1.24578i) q^{56} +(0.0830655 + 0.255649i) q^{57} +(1.05158 - 6.63944i) q^{58} +(1.37512 - 4.23218i) q^{59} +(0.0572112 + 0.0291505i) q^{60} +(11.3577 - 3.69033i) q^{61} +(-4.87684 + 1.58458i) q^{62} +(8.36366 + 4.26150i) q^{63} +(-0.678682 + 2.08877i) q^{64} +(0.225901 - 1.42628i) q^{65} +(0.0431939 + 0.132937i) q^{66} +(8.00079 - 1.26720i) q^{67} +(-2.00960 + 2.00960i) q^{68} +(0.0486772 - 0.0248023i) q^{69} +(-0.258547 - 1.63240i) q^{70} +(-0.988102 - 0.156500i) q^{71} +(-6.16179 + 4.47680i) q^{72} +6.49752i q^{73} +(-1.86426 - 2.56593i) q^{74} +(-0.124638 + 0.244616i) q^{75} +(-2.91093 - 5.71303i) q^{76} +(-5.72311 + 7.87719i) q^{77} +(-0.0731620 - 0.0531553i) q^{78} +(-4.43337 - 4.43337i) q^{79} +(-0.719497 - 0.233779i) q^{80} -8.96628 q^{81} +(-0.433113 - 4.68372i) q^{82} +7.83744 q^{83} +(0.266392 + 0.0865561i) q^{84} +(0.988256 + 0.988256i) q^{85} +(-6.45150 - 4.68729i) q^{86} +(0.329304 - 0.453248i) q^{87} +(-3.58669 - 7.03928i) q^{88} +(-6.40964 + 12.5796i) q^{89} +(0.929109 + 1.27881i) q^{90} -6.29943i q^{91} +(-1.05426 + 0.765968i) q^{92} +(-0.422104 - 0.0668547i) q^{93} +(1.32719 + 8.37958i) q^{94} +(-2.80948 + 1.43150i) q^{95} +(-0.253591 + 0.253591i) q^{96} +(6.34053 - 1.00424i) q^{97} +(-0.638929 - 1.96642i) q^{98} +(1.45676 - 9.19761i) 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 $

$2$	0.698642	+	0.227002i	0.494014	+	0.160515i	0.545420	−	0.838163i	$-0.316370\pi$
$2$	0.698642	+	0.227002i	0.494014	+	0.160515i	−0.0514057	+	0.998678i	$0.516370\pi$
$3$	0.0432913	+	0.0432913i	0.0249942	+	0.0249942i	0.719493	−	0.694499i	$-0.244374\pi$
$3$	0.0432913	+	0.0432913i	0.0249942	+	0.0249942i	−0.694499	+	0.719493i	$0.744374\pi$
$4$	−1.18146	−	0.858384i	−0.590732	−	0.429192i
$5$	−0.422124	+	0.581004i	−0.188780	+	0.259833i	−0.892907	−	0.450240i	$-0.851338\pi$
$5$	−0.422124	+	0.581004i	−0.188780	+	0.259833i	0.704128	+	0.710073i	$0.251338\pi$
$6$	0.0204179	+	0.0400723i	0.00833556	+	0.0163595i
$7$	−1.42228	+	2.79137i	−0.537570	+	1.05504i	0.449279	+	0.893392i	$0.351681\pi$
$7$	−1.42228	+	2.79137i	−0.537570	+	1.05504i	−0.986848	+	0.161648i	$0.948319\pi$
$8$	−1.49413	−	2.05650i	−0.528256	−	0.727082i
$9$		−	2.99625i		−	0.998751i
$10$	−0.426803	+	0.310091i	−0.134967	+	0.0980592i
$11$	3.06970	+	0.486193i	0.925551	+	0.146593i	0.600976	−	0.799267i	$-0.294779\pi$
$11$	3.06970	+	0.486193i	0.925551	+	0.146593i	0.324575	+	0.945860i	$0.394779\pi$
$12$	−0.0139866	−	0.0883076i	−0.00403757	−	0.0254922i
$13$	−1.79162	+	0.912875i	−0.496905	+	0.253186i	−0.684436	−	0.729073i	$-0.739952\pi$
$13$	−1.79162	+	0.912875i	−0.496905	+	0.253186i	0.187531	+	0.982259i	$0.439952\pi$
$14$	−1.62731	+	1.62731i	−0.434917	+	0.434917i
$15$	−0.0434267	+	0.00687812i	−0.0112127	+	0.00177592i
$16$	0.325524	+	1.00186i	0.0813810	+	0.250465i
$17$	0.304435	−	1.92213i	0.0738365	−	0.466185i	−0.922871	−	0.385108i	$-0.874164\pi$
$17$	0.304435	−	1.92213i	0.0738365	−	0.466185i	0.996708	−	0.0810768i	$-0.0258359\pi$
$18$	0.680157	−	2.09331i	0.160314	−	0.493397i
$19$	3.91204	+	1.99329i	0.897485	+	0.457291i	0.840952	−	0.541109i	$-0.181996\pi$
$19$	3.91204	+	1.99329i	0.897485	+	0.457291i	0.0565325	+	0.998401i	$0.481996\pi$
$20$	0.997449	−	0.324091i	0.223036	−	0.0724689i
$21$	−0.182414	+	0.0592700i	−0.0398061	+	0.0129338i
$22$	2.03426	+	1.03651i	0.433705	+	0.220984i
$23$	0.275748	−	0.848664i	0.0574973	−	0.176959i	−0.918183	−	0.396156i	$-0.870344\pi$
$23$	0.275748	−	0.848664i	0.0574973	−	0.176959i	0.975681	+	0.219198i	$0.0703439\pi$
$24$	0.0243455	−	0.153711i	0.00496950	−	0.0313762i
$25$	1.38571	+	4.26477i	0.277142	+	0.852954i
$26$	−1.45892	+	0.231071i	−0.286119	+	0.0453167i
$27$	0.259585	−	0.259585i	0.0499572	−	0.0499572i
$28$	4.07644	−	2.07705i	0.770374	−	0.392525i
$29$	−1.43151	−	9.03822i	−0.265825	−	1.67836i	−0.653786	−	0.756680i	$-0.726820\pi$
$29$	−1.43151	−	9.03822i	−0.265825	−	1.67836i	0.387961	−	0.921676i	$-0.373180\pi$
$30$	−0.0319011	−	0.00505263i	−0.00582431	−	0.000922480i
$31$	−5.64731	+	4.10301i	−1.01429	+	0.736922i	−0.965104	−	0.261868i	$-0.915662\pi$
$31$	−5.64731	+	4.10301i	−1.01429	+	0.736922i	−0.0491827	+	0.998790i	$0.515662\pi$
$32$			5.85778i			1.03552i
$33$	0.111844	+	0.153939i	0.0194695	+	0.0267974i
$34$	0.649020	−	1.27377i	0.111306	−	0.218450i
$35$	−1.02142	−	2.00465i	−0.172652	−	0.338848i
$36$	−2.57193	+	3.53996i	−0.428656	+	0.589994i
$37$	−3.49299	−	2.53781i	−0.574244	−	0.417213i	0.262400	−	0.964959i	$-0.415486\pi$
$37$	−3.49299	−	2.53781i	−0.574244	−	0.417213i	−0.836644	+	0.547746i	$0.815486\pi$
$38$	2.28064	+	2.28064i	0.369968	+	0.369968i
$39$	−0.117081	−	0.0380419i	−0.0187480	−	0.00609158i
$40$	1.82554			0.288644
$41$	−2.53101	−	5.88167i	−0.395277	−	0.918562i
$41$	−2.53101	−	5.88167i	−0.395277	−	0.918562i
$42$	−0.140897			−0.0217408
$43$	−10.3243	−	3.35457i	−1.57444	−	0.511568i	−0.613826	−	0.789441i	$-0.710370\pi$
$43$	−10.3243	−	3.35457i	−1.57444	−	0.511568i	−0.960618	+	0.277874i	$0.910370\pi$
$44$	−3.20940	−	3.20940i	−0.483836	−	0.483836i
$45$	1.74083	+	1.26479i	0.259508	+	0.188544i
$46$	0.385298	−	0.530317i	0.0568090	−	0.0781909i
$47$	5.24325	+	10.2905i	0.764807	+	1.50102i	0.862642	+	0.505815i	$0.168808\pi$
$47$	5.24325	+	10.2905i	0.764807	+	1.50102i	−0.0978352	+	0.995203i	$0.531192\pi$
$48$	−0.0292795	+	0.0574642i	−0.00422612	+	0.00829424i
$49$	−1.65440	−	2.27709i	−0.236343	−	0.325298i
$50$			3.29411i			0.465857i
$51$	0.0963909	−	0.0700321i	0.0134974	−	0.00980645i
$52$	2.90033	+	0.459367i	0.402203	+	0.0637027i
$53$	0.465724	+	2.94046i	0.0639721	+	0.403904i	0.998807	+	0.0488225i	$0.0155469\pi$
$53$	0.465724	+	2.94046i	0.0639721	+	0.403904i	−0.934835	+	0.355081i	$0.884453\pi$
$54$	0.240284	−	0.122431i	0.0326985	−	0.0166607i
$55$	−1.57828	+	1.57828i	−0.212815	+	0.212815i
$56$	7.86552	−	1.24578i	1.05107	−	0.166474i
$57$	0.0830655	+	0.255649i	0.0110023	+	0.0338616i
$58$	1.05158	−	6.63944i	0.138080	−	0.871801i
$59$	1.37512	−	4.23218i	0.179025	−	0.550982i	−0.820769	−	0.571260i	$-0.806455\pi$
$59$	1.37512	−	4.23218i	0.179025	−	0.550982i	0.999794	+	0.0202774i	$0.00645493\pi$
$60$	0.0572112	+	0.0291505i	0.00738593	+	0.00376332i
$61$	11.3577	−	3.69033i	1.45420	−	0.472499i	0.527908	−	0.849301i	$-0.322977\pi$
$61$	11.3577	−	3.69033i	1.45420	−	0.472499i	0.926294	+	0.376803i	$0.122977\pi$
$62$	−4.87684	+	1.58458i	−0.619359	+	0.201242i
$63$	8.36366	+	4.26150i	1.05372	+	0.536898i
$64$	−0.678682	+	2.08877i	−0.0848353	+	0.261096i
$65$	0.225901	−	1.42628i	0.0280196	−	0.176909i
$66$	0.0431939	+	0.132937i	0.00531680	+	0.0163634i
$67$	8.00079	−	1.26720i	0.977452	−	0.154813i	0.352785	−	0.935704i	$-0.385235\pi$
$67$	8.00079	−	1.26720i	0.977452	−	0.154813i	0.624667	+	0.780891i	$0.285235\pi$
$68$	−2.00960	+	2.00960i	−0.243700	+	0.243700i
$69$	0.0486772	−	0.0248023i	0.00586005	−	0.00298584i
$70$	−0.258547	−	1.63240i	−0.0309023	−	0.195109i
$71$	−0.988102	−	0.156500i	−0.117266	−	0.0185731i	0.0975255	−	0.995233i	$-0.468907\pi$
$71$	−0.988102	−	0.156500i	−0.117266	−	0.0185731i	−0.214792	+	0.976660i	$0.568907\pi$
$72$	−6.16179	+	4.47680i	−0.726174	+	0.527596i
$73$			6.49752i			0.760477i	0.924889	+	0.380238i	$0.124158\pi$
$73$			6.49752i			0.760477i	−0.924889	+	0.380238i	$0.875842\pi$
$74$	−1.86426	−	2.56593i	−0.216716	−	0.298284i
$75$	−0.124638	+	0.244616i	−0.0143920	+	0.0282459i
$76$	−2.91093	−	5.71303i	−0.333907	−	0.655330i
$77$	−5.72311	+	7.87719i	−0.652209	+	0.897689i
$78$	−0.0731620	−	0.0531553i	−0.00828397	−	0.00601866i
$79$	−4.43337	−	4.43337i	−0.498793	−	0.498793i	0.412269	−	0.911062i	$-0.364736\pi$
$79$	−4.43337	−	4.43337i	−0.498793	−	0.498793i	−0.911062	+	0.412269i	$0.864736\pi$
$80$	−0.719497	−	0.233779i	−0.0804422	−	0.0261372i
$81$	−8.96628			−0.996253
$82$	−0.433113	−	4.68372i	−0.0478294	−	0.517231i
$83$	7.83744			0.860271			0.430136	−	0.902764i	$-0.358466\pi$
$83$	7.83744			0.860271			0.430136	+	0.902764i	$0.358466\pi$
$84$	0.266392	+	0.0865561i	0.0290658	+	0.00944404i
$85$	0.988256	+	0.988256i	0.107191	+	0.107191i
$86$	−6.45150	−	4.68729i	−0.695683	−	0.505444i
$87$	0.329304	−	0.453248i	0.0353051	−	0.0485933i
$88$	−3.58669	−	7.03928i	−0.382343	−	0.750390i
$89$	−6.40964	+	12.5796i	−0.679420	+	1.33344i	0.251373	+	0.967890i	$0.419118\pi$
$89$	−6.40964	+	12.5796i	−0.679420	+	1.33344i	−0.930793	+	0.365547i	$0.880882\pi$
$90$	0.929109	+	1.27881i	0.0979367	+	0.134798i
$91$		−	6.29943i		−	0.660360i
$92$	−1.05426	+	0.765968i	−0.109915	+	0.0798577i
$93$	−0.422104	−	0.0668547i	−0.0437701	−	0.00693251i
$94$	1.32719	+	8.37958i	0.136890	+	0.864287i
$95$	−2.80948	+	1.43150i	−0.288246	+	0.146869i
$96$	−0.253591	+	0.253591i	−0.0258820	+	0.0258820i
$97$	6.34053	−	1.00424i	0.643783	−	0.101965i	0.173998	−	0.984746i	$-0.444331\pi$
$97$	6.34053	−	1.00424i	0.643783	−	0.101965i	0.469785	+	0.882781i	$0.344331\pi$
$98$	−0.638929	−	1.96642i	−0.0645415	−	0.198638i
$99$	1.45676	−	9.19761i	0.146410	−	0.924394i
$100$	2.02365	−	6.22814i	0.202365	−	0.622814i
$101$	10.7210	+	5.46262i	1.06678	+	0.543551i	0.897045	−	0.441938i	$-0.145709\pi$
$101$	10.7210	+	5.46262i	1.06678	+	0.543551i	0.169734	+	0.985490i	$0.445709\pi$
$102$	0.0832402	−	0.0270464i	0.00824200	−	0.00267799i
$103$	−14.6231	+	4.75134i	−1.44086	+	0.468163i	−0.922165	−	0.386797i	$-0.873581\pi$
$103$	−14.6231	+	4.75134i	−1.44086	+	0.468163i	−0.518694	+	0.854960i	$0.673581\pi$
$104$	4.55424	+	2.32050i	0.446580	+	0.227544i
$105$	0.0425654	−	0.131003i	0.00415396	−	0.0127846i
$106$	−0.342119	+	2.16005i	−0.0332295	+	0.209803i
$107$	−0.344730	−	1.06097i	−0.0333263	−	0.102568i	0.933010	−	0.359851i	$-0.117173\pi$
$107$	−0.344730	−	1.06097i	−0.0333263	−	0.102568i	−0.966336	+	0.257284i	$0.917173\pi$
$108$	−0.529515	+	0.0838669i	−0.0509526	+	0.00807009i
$109$	4.18654	−	4.18654i	0.400998	−	0.400998i	−0.477587	−	0.878585i	$-0.658488\pi$
$109$	4.18654	−	4.18654i	0.400998	−	0.400998i	0.878585	+	0.477587i	$0.158488\pi$
$110$	−1.46092	+	0.744378i	−0.139294	+	0.0709736i
$111$	−0.0413511	−	0.261081i	−0.00392488	−	0.0247807i
$112$	−3.25955	−	0.516262i	−0.307999	−	0.0487822i
$113$	12.4975	−	9.07995i	1.17566	−	0.854170i	0.183988	−	0.982928i	$-0.441099\pi$
$113$	12.4975	−	9.07995i	1.17566	−	0.854170i	0.991676	+	0.128759i	$0.0410992\pi$
$114$			0.197463i			0.0184941i
$115$	0.376677	+	0.518452i	0.0351254	+	0.0483459i
$116$	−6.06698	+	11.9071i	−0.563305	+	1.10555i
$117$	2.73520	+	5.36814i	0.252870	+	0.496285i
$118$	1.92143	−	2.64462i	0.176882	−	0.243457i
$119$	4.93239	+	3.58359i	0.452152	+	0.328507i
$120$	0.0790301	+	0.0790301i	0.00721443	+	0.00721443i
$121$	−1.27492	−	0.414247i	−0.115902	−	0.0376588i
$122$	8.77266			0.794240
$123$	0.145054	−	0.364195i	0.0130791	−	0.0328384i
$124$	10.1940			0.915452
$125$	−6.47785	−	2.10478i	−0.579396	−	0.188257i
$126$	4.87583	+	4.87583i	0.434373	+	0.434373i
$127$	3.50780	+	2.54857i	0.311267	+	0.226149i	0.732440	−	0.680832i	$-0.238381\pi$
$127$	3.50780	+	2.54857i	0.311267	+	0.226149i	−0.421173	+	0.906980i	$0.638381\pi$
$128$	5.93792	−	8.17285i	0.524843	−	0.722384i
$129$	−0.301729	−	0.592177i	−0.0265658	−	0.0521383i
$130$	0.481594	−	0.945182i	0.0422386	−	0.0828979i
$131$	−9.74217	−	13.4090i	−0.851178	−	1.17155i	−0.983602	−	0.180352i	$-0.942276\pi$
$131$	−9.74217	−	13.4090i	−0.851178	−	1.17155i	0.132424	−	0.991193i	$-0.457724\pi$
$132$		−	0.277878i		−	0.0241862i
$133$	−11.1280	+	8.08497i	−0.964921	+	0.701056i
$134$	5.87734	+	0.930880i	0.507725	+	0.0804157i
$135$	0.0412429	+	0.260398i	0.00354963	+	0.0224115i
$136$	−4.40772	+	2.24585i	−0.377959	+	0.192580i
$137$	−0.166857	+	0.166857i	−0.0142555	+	0.0142555i	−0.714199	−	0.699943i	$-0.753209\pi$
$137$	−0.166857	+	0.166857i	−0.0142555	+	0.0142555i	0.699943	+	0.714199i	$0.253209\pi$
$138$	0.0396381	−	0.00627806i	0.00337422	−	0.000534424i
$139$	−0.727856	−	2.24011i	−0.0617360	−	0.190004i	0.915432	−	0.402473i	$-0.131849\pi$
$139$	−0.727856	−	2.24011i	−0.0617360	−	0.190004i	−0.977168	+	0.212470i	$0.931849\pi$
$140$	−0.513989	+	3.24520i	−0.0434400	+	0.274269i
$141$	−0.218500	+	0.672474i	−0.0184010	+	0.0566325i
$142$	−0.654803	−	0.333639i	−0.0549499	−	0.0279984i
$143$	−5.94357	+	1.93118i	−0.497026	+	0.161494i
$144$	3.00182	−	0.975352i	0.250152	−	0.0812793i
$145$	5.85552	+	2.98354i	0.486275	+	0.247769i
$146$	−1.47495	+	4.53944i	−0.122068	+	0.375686i
$147$	0.0269569	−	0.170199i	0.00222337	−	0.0140378i
$148$	1.94843	+	5.99665i	0.160160	+	0.492922i
$149$	−8.28803	+	1.31270i	−0.678982	+	0.107540i	−0.486394	−	0.873739i	$-0.661688\pi$
$149$	−8.28803	+	1.31270i	−0.678982	+	0.107540i	−0.192588	+	0.981280i	$0.561688\pi$
$150$	−0.142606	+	0.142606i	−0.0116437	+	0.0116437i
$151$	3.22750	−	1.64449i	0.262650	−	0.133827i	−0.317707	−	0.948189i	$-0.602913\pi$
$151$	3.22750	−	1.64449i	0.262650	−	0.133827i	0.580357	+	0.814362i	$0.302913\pi$
$152$	−1.74593	−	11.0233i	−0.141613	−	0.894112i
$153$	−5.75919	−	0.912165i	−0.465603	−	0.0737442i
$154$	−5.78655	+	4.20417i	−0.466293	+	0.338782i
$155$		−	5.01309i		−	0.402661i
$156$	0.105672	+	0.145446i	0.00846056	+	0.0116450i
$157$	6.25608	−	12.2783i	0.499290	−	0.979911i	−0.494557	−	0.869145i	$-0.664670\pi$
$157$	6.25608	−	12.2783i	0.499290	−	0.979911i	0.993847	−	0.110766i	$-0.0353304\pi$
$158$	−2.09095	−	4.10373i	−0.166347	−	0.326475i
$159$	−0.107135	+	0.147458i	−0.00849633	+	0.0116942i
$160$	−3.40339	−	2.47271i	−0.269062	−	0.195485i
$161$	1.97675	+	1.97675i	0.155790	+	0.155790i
$162$	−6.26422	−	2.03537i	−0.492163	−	0.159914i
$163$	−0.923374			−0.0723243			−0.0361621	−	0.999346i	$-0.511513\pi$
$163$	−0.923374			−0.0723243			−0.0361621	+	0.999346i	$0.511513\pi$
$164$	−2.05844	+	9.12155i	−0.160737	+	0.712273i
$165$	−0.136651			−0.0106383
$166$	5.47557	+	1.77912i	0.424986	+	0.138086i
$167$	−12.0223	−	12.0223i	−0.930315	−	0.930315i	0.0674099	−	0.997725i	$-0.478526\pi$
$167$	−12.0223	−	12.0223i	−0.930315	−	0.930315i	−0.997725	+	0.0674099i	$0.978526\pi$
$168$	0.394440	+	0.286577i	0.0304317	+	0.0221099i
$169$	−5.26465	+	7.24617i	−0.404973	+	0.557398i
$170$	0.466100	+	0.914774i	0.0357483	+	0.0701599i
$171$	5.97239	−	11.7215i	0.456720	−	0.896363i
$172$	9.31829	+	12.8255i	0.710513	+	0.977938i
$173$			12.1428i			0.923198i	0.887089	+	0.461599i	$0.152724\pi$
$173$			12.1428i			0.923198i	−0.887089	+	0.461599i	$0.847276\pi$
$174$	0.332954	−	0.241905i	0.0252412	−	0.0183388i
$175$	−13.8754	−	2.19765i	−1.04888	−	0.166127i
$176$	0.512165	+	3.23368i	0.0386059	+	0.243748i
$177$	0.242747	−	0.123686i	0.0182460	−	0.00929679i
$178$	−7.33365	+	7.33365i	−0.549680	+	0.549680i
$179$	−2.11231	+	0.334557i	−0.157881	+	0.0250060i	−0.234875	−	0.972026i	$-0.575468\pi$
$179$	−2.11231	+	0.334557i	−0.157881	+	0.0250060i	0.0769933	+	0.997032i	$0.475468\pi$
$180$	−0.971058	−	2.98861i	−0.0723784	−	0.222758i
$181$	−0.878821	+	5.54866i	−0.0653222	+	0.412428i	0.933260	+	0.359201i	$0.116951\pi$
$181$	−0.878821	+	5.54866i	−0.0653222	+	0.412428i	−0.998582	+	0.0532273i	$0.983049\pi$
$182$	1.42999	−	4.40105i	0.105998	−	0.326227i
$183$	0.651448	+	0.331929i	0.0481564	+	0.0245369i
$184$	−2.15728	+	0.700942i	−0.159037	+	0.0516742i
$185$	2.94895	−	0.958172i	0.216811	−	0.0704462i
$186$	−0.279723	−	0.142526i	−0.0205103	−	0.0104505i
$187$	1.86905	−	5.75236i	0.136679	−	0.420654i
$188$	2.63845	−	16.6585i	0.192429	−	1.21495i
$189$	0.355398	+	1.09380i	0.0258514	+	0.0795624i
$190$	−2.28777	+	0.362347i	−0.165972	+	0.0262875i
$191$	9.27794	−	9.27794i	0.671328	−	0.671328i	−0.286694	−	0.958022i	$-0.592556\pi$
$191$	9.27794	−	9.27794i	0.671328	−	0.671328i	0.958022	+	0.286694i	$0.0925564\pi$
$192$	−0.119807	+	0.0610445i	−0.00864629	+	0.00440551i
$193$	2.59319	+	16.3728i	0.186662	+	1.17854i	0.885979	+	0.463726i	$0.153488\pi$
$193$	2.59319	+	16.3728i	0.186662	+	1.17854i	−0.699317	+	0.714812i	$0.746512\pi$
$194$	4.65772	+	0.737711i	0.334405	+	0.0529646i
$195$	0.0715252	−	0.0519661i	0.00512203	−	0.00372137i
$196$			4.11040i			0.293600i
$197$	−8.51171	−	11.7154i	−0.606434	−	0.834685i	0.389844	−	0.920881i	$-0.372529\pi$
$197$	−8.51171	−	11.7154i	−0.606434	−	0.834685i	−0.996278	+	0.0861961i	$0.972529\pi$
$198$	3.10563	−	6.09515i	0.220708	−	0.433163i
$199$	8.18953	+	16.0729i	0.580541	+	1.13938i	0.975361	+	0.220617i	$0.0708070\pi$
$199$	8.18953	+	16.0729i	0.580541	+	1.13938i	−0.394820	+	0.918759i	$0.629193\pi$
$200$	6.70006	−	9.22184i	0.473766	−	0.652083i
$201$	0.401223	+	0.291506i	0.0283001	+	0.0205612i
$202$	6.25011	+	6.25011i	0.439756	+	0.439756i
$203$	27.2651	+	8.85895i	1.91363	+	0.621777i
$204$	−0.173997			−0.0121822
$205$	4.48567	+	1.01227i	0.313293	+	0.0707000i
$206$	−11.2949			−0.786952
$207$	−2.54281	−	0.826209i	−0.176738	−	0.0574255i
$208$	−1.49779	−	1.49779i	−0.103853	−	0.103853i
$209$	11.0397	+	8.02081i	0.763632	+	0.554811i
$210$	0.0594759	−	0.0818616i	0.00410423	−	0.00564898i
$211$	6.12962	+	12.0301i	0.421980	+	0.828183i	0.999927	+	0.0121083i	$0.00385430\pi$
$211$	6.12962	+	12.0301i	0.421980	+	0.828183i	−0.577946	+	0.816075i	$0.696146\pi$
$212$	1.97381	−	3.87382i	0.135562	−	0.266055i
$213$	−0.0360011	−	0.0495513i	−0.00246676	−	0.00339520i
$214$		−	0.819492i		−	0.0560193i
$215$	6.30717	−	4.58242i	0.430145	−	0.312519i
$216$	−0.921692	−	0.145982i	−0.0627132	−	0.00993280i
$217$	−3.42100	−	21.5994i	−0.232233	−	1.46626i
$218$	3.87525	−	1.97454i	0.262465	−	0.133733i
$219$	−0.281286	+	0.281286i	−0.0190075	+	0.0190075i
$220$	3.21944	−	0.509910i	0.217055	−	0.0343781i
$221$	1.20923	+	3.72163i	0.0813418	+	0.250344i
$222$	0.0303764	−	0.191789i	0.00203873	−	0.0128720i
$223$	−2.34538	+	7.21835i	−0.157059	+	0.483377i	−0.998364	−	0.0571840i	$-0.981788\pi$
$223$	−2.34538	+	7.21835i	−0.157059	+	0.483377i	0.841305	+	0.540561i	$0.181788\pi$
$224$	−16.3512	−	8.33138i	−1.09251	−	0.556664i
$225$	12.7783	−	4.15193i	0.851888	−	0.276795i
$226$	10.7924	−	3.50667i	0.717902	−	0.233260i
$227$	−19.3474	−	9.85797i	−1.28413	−	0.654297i	−0.327293	−	0.944923i	$-0.606136\pi$
$227$	−19.3474	−	9.85797i	−1.28413	−	0.654297i	−0.956837	+	0.290626i	$0.906136\pi$
$228$	0.121306	−	0.373343i	0.00803371	−	0.0247252i
$229$	−0.463354	+	2.92550i	−0.0306193	+	0.193323i	−0.998257	−	0.0590222i	$-0.981202\pi$
$229$	−0.463354	+	2.92550i	−0.0306193	+	0.193323i	0.967637	+	0.252345i	$0.0812017\pi$
$230$	0.145473	+	0.447719i	0.00959219	+	0.0295217i
$231$	−0.588775	+	0.0932527i	−0.0387385	+	0.00613558i
$232$	−16.4482	+	16.4482i	−1.07988	+	1.07988i
$233$	−15.5044	+	7.89988i	−1.01573	+	0.517538i	−0.880886	−	0.473329i	$-0.843052\pi$
$233$	−15.5044	+	7.89988i	−1.01573	+	0.517538i	−0.134840	+	0.990867i	$0.543052\pi$
$234$	0.692347	+	4.37130i	0.0452601	+	0.285761i
$235$	−8.19210	−	1.29750i	−0.534394	−	0.0846397i
$236$	−5.25748	+	3.81978i	−0.342233	+	0.248647i
$237$		−	0.383853i		−	0.0249339i
$238$	2.63249	+	3.62331i	0.170639	+	0.234864i
$239$	−2.69685	+	5.29286i	−0.174444	+	0.342366i	−0.961630	−	0.274350i	$-0.911537\pi$
$239$	−2.69685	+	5.29286i	−0.174444	+	0.342366i	0.787186	+	0.616716i	$0.211537\pi$
$240$	−0.0210274	−	0.0412685i	−0.00135731	−	0.00266387i
$241$	5.16221	−	7.10518i	0.332527	−	0.457685i	−0.609713	−	0.792622i	$-0.708715\pi$
$241$	5.16221	−	7.10518i	0.332527	−	0.457685i	0.942240	+	0.334938i	$0.108715\pi$
$242$	−0.796678	−	0.578820i	−0.0512124	−	0.0372080i
$243$	−1.16692	−	1.16692i	−0.0748578	−	0.0748578i
$244$	−16.5864	−	5.38925i	−1.06184	−	0.345011i
$245$	2.02136			0.129140
$246$	0.184014	−	0.221514i	0.0117323	−	0.0141232i
$247$	−8.82851			−0.561745
$248$	16.8757	+	5.48324i	1.07161	+	0.348186i
$249$	0.339293	+	0.339293i	0.0215018	+	0.0215018i
$250$	−4.04790	−	2.94098i	−0.256012	−	0.186004i
$251$	−3.01355	+	4.14780i	−0.190214	+	0.261807i	−0.893463	−	0.449137i	$-0.851732\pi$
$251$	−3.01355	+	4.14780i	−0.190214	+	0.261807i	0.703250	+	0.710943i	$0.251732\pi$
$252$	−6.22336	−	12.2140i	−0.392035	−	0.769412i
$253$	1.25908	−	2.47108i	0.0791576	−	0.155355i
$254$	1.87216	+	2.57681i	0.117470	+	0.161684i
$255$			0.0855657i			0.00535833i
$256$	9.55736	−	6.94383i	0.597335	−	0.433989i
$257$	−1.08576	−	0.171967i	−0.0677277	−	0.0107270i	0.122479	−	0.992471i	$-0.460916\pi$
$257$	−1.08576	−	0.171967i	−0.0677277	−	0.0107270i	−0.190206	+	0.981744i	$0.560916\pi$
$258$	−0.0763750	−	0.482213i	−0.00475490	−	0.0300212i
$259$	12.0520	−	6.14078i	0.748872	−	0.381569i
$260$	−1.49119	+	1.49119i	−0.0924799	+	0.0924799i
$261$	−27.0808	+	4.28917i	−1.67626	+	0.265493i
$262$	−3.76242	−	11.5796i	−0.232443	−	0.715387i
$263$	−1.99659	+	12.6060i	−0.123115	+	0.777317i	0.846447	+	0.532472i	$0.178737\pi$
$263$	−1.99659	+	12.6060i	−0.123115	+	0.777317i	−0.969562	+	0.244845i	$0.921263\pi$
$264$	0.149467	−	0.460012i	0.00919905	−	0.0283118i
$265$	−1.90502	−	0.970654i	−0.117024	−	0.0596268i
$266$	−9.60980	+	3.12241i	−0.589215	+	0.191448i
$267$	−0.822069	+	0.267107i	−0.0503098	+	0.0163467i
$268$	−10.5404	−	5.37059i	−0.643856	−	0.328061i
$269$	0.170602	−	0.525059i	0.0104018	−	0.0320134i	−0.945721	−	0.324980i	$-0.894642\pi$
$269$	0.170602	−	0.525059i	0.0104018	−	0.0320134i	0.956123	+	0.292967i	$0.0946425\pi$
$270$	−0.0302969	+	0.191287i	−0.00184381	+	0.0116413i
$271$	−0.852971	−	2.62518i	−0.0518143	−	0.159468i	0.921801	−	0.387663i	$-0.126718\pi$
$271$	−0.852971	−	2.62518i	−0.0518143	−	0.159468i	−0.973615	+	0.228195i	$0.926718\pi$
$272$	2.02481	−	0.320698i	0.122772	−	0.0194452i
$273$	0.272711	−	0.272711i	0.0165052	−	0.0165052i
$274$	−0.154450	+	0.0786962i	−0.00933067	+	0.00475421i
$275$	2.18021	+	13.7653i	0.131472	+	0.830079i
$276$	−0.0788002	−	0.0124807i	−0.00474322	−	0.000751252i
$277$	17.2011	−	12.4974i	1.03352	−	0.750894i	0.0645072	−	0.997917i	$-0.479452\pi$
$277$	17.2011	−	12.4974i	1.03352	−	0.750894i	0.969010	+	0.247023i	$0.0794525\pi$
$278$		−	1.73026i		−	0.103774i
$279$	12.2936	+	16.9208i	0.736002	+	1.01302i
$280$	−2.59643	+	5.09578i	−0.155166	+	0.304531i
$281$	−0.813754	−	1.59708i	−0.0485445	−	0.0952739i	0.865460	−	0.500978i	$-0.167026\pi$
$281$	−0.813754	−	1.59708i	−0.0485445	−	0.0952739i	−0.914004	+	0.405704i	$0.867026\pi$
$282$	−0.305307	+	0.420219i	−0.0181807	+	0.0250236i
$283$	−3.00831	−	2.18566i	−0.178825	−	0.129924i	0.494772	−	0.869023i	$-0.335252\pi$
$283$	−3.00831	−	2.18566i	−0.178825	−	0.129924i	−0.673597	+	0.739099i	$0.735252\pi$
$284$	1.03307	+	1.03307i	0.0613014	+	0.0613014i
$285$	−0.183597	−	0.0596544i	−0.0108754	−	0.00353362i
$286$	−4.59081			−0.271460
$287$	20.0177	+	1.30037i	1.18161	+	0.0767585i
$288$	17.5514			1.03423
$289$	12.5661	+	4.08296i	0.739180	+	0.240174i
$290$	3.41364	+	3.41364i	0.200456	+	0.200456i
$291$	0.317965	+	0.231015i	0.0186394	+	0.0135423i
$292$	5.57736	−	7.67658i	0.326390	−	0.449238i
$293$	−6.31176	−	12.3875i	−0.368737	−	0.723687i	0.629856	−	0.776712i	$-0.283114\pi$
$293$	−6.31176	−	12.3875i	−0.368737	−	0.723687i	−0.998593	+	0.0530245i	$0.983114\pi$
$294$	0.0574688	−	0.112789i	0.00335165	−	0.00657798i
$295$	1.87844	+	2.58545i	0.109367	+	0.150531i
$296$			10.9751i			0.637917i
$297$	0.923059	−	0.670642i	0.0535613	−	0.0389146i
$298$	−6.08835	−	0.964300i	−0.352689	−	0.0558604i
$299$	0.280690	+	1.77220i	0.0162327	+	0.102489i
$300$	0.357230	−	0.182018i	0.0206247	−	0.0105088i
$301$	24.0479	−	24.0479i	1.38610	−	1.38610i
$302$	2.62817	−	0.416261i	0.151234	−	0.0239532i
$303$	0.227642	+	0.700610i	0.0130777	+	0.0402490i
$304$	−0.723529	+	4.56818i	−0.0414973	+	0.262003i
$305$	−2.65025	+	8.15664i	−0.151753	+	0.467048i
$306$	−3.81654	−	1.94463i	−0.218177	−	0.111167i
$307$	−20.7993	+	6.75809i	−1.18708	+	0.385705i	−0.834991	−	0.550263i	$-0.814527\pi$
$307$	−20.7993	+	6.75809i	−1.18708	+	0.385705i	−0.352086	+	0.935968i	$0.614527\pi$
$308$	13.5233	−	4.39399i	0.770562	−	0.250371i
$309$	−0.838745	−	0.427362i	−0.0477145	−	0.0243118i
$310$	1.13798	−	3.50235i	0.0646331	−	0.198920i
$311$	−2.49509	+	15.7534i	−0.141483	+	0.893291i	0.810188	+	0.586171i	$0.199365\pi$
$311$	−2.49509	+	15.7534i	−0.141483	+	0.893291i	−0.951671	+	0.307120i	$0.900635\pi$
$312$	0.0967015	+	0.297617i	0.00547464	+	0.0168492i
$313$	−0.811177	+	0.128478i	−0.0458504	+	0.00726199i	−0.179318	−	0.983791i	$-0.557389\pi$
$313$	−0.811177	+	0.128478i	−0.0458504	+	0.00726199i	0.133467	+	0.991053i	$0.457389\pi$
$314$	7.15796	−	7.15796i	0.403947	−	0.403947i
$315$	−6.00645	+	3.06044i	−0.338425	+	0.172436i
$316$	1.43233	+	9.04340i	0.0805751	+	0.508731i
$317$	27.9438	+	4.42587i	1.56948	+	0.248582i	0.879734	−	0.475467i	$-0.157721\pi$
$317$	27.9438	+	4.42587i	1.56948	+	0.248582i	0.689749	+	0.724048i	$0.257721\pi$
$318$	−0.108322	+	0.0787007i	−0.00607441	+	0.00441331i
$319$		−	28.4407i		−	1.59237i
$320$	−0.927096	−	1.27604i	−0.0518262	−	0.0713327i
$321$	0.0310069	−	0.0608545i	0.00173064	−	0.00339657i
$322$	0.932312	+	1.82977i	0.0519557	+	0.101969i
$323$	5.02232	−	6.91263i	0.279449	−	0.384629i
$324$	10.5933	+	7.69651i	0.588519	+	0.427584i
$325$	−6.37586	−	6.37586i	−0.353669	−	0.353669i
$326$	−0.645108	−	0.209608i	−0.0357292	−	0.0116091i
$327$	0.362481			0.0200453
$328$	−8.31398	+	13.9930i	−0.459063	+	0.772634i
$329$	−36.1819			−1.99477
$330$	−0.0954703	−	0.0310202i	−0.00525547	−	0.00170760i
$331$	21.7469	+	21.7469i	1.19532	+	1.19532i	0.975554	+	0.219762i	$0.0705281\pi$
$331$	21.7469	+	21.7469i	1.19532	+	1.19532i	0.219762	+	0.975554i	$0.429472\pi$
$332$	−9.25966	−	6.72753i	−0.508190	−	0.369221i
$333$	−7.60390	+	10.4659i	−0.416691	+	0.573526i
$334$	−5.67020	−	11.1284i	−0.310260	−	0.608919i
$335$	−2.64108	+	5.18341i	−0.144297	+	0.283200i
$336$	−0.118760	−	0.163460i	−0.00647891	−	0.00891746i
$337$		−	26.0552i		−	1.41932i	−0.704546	−	0.709658i	$-0.748849\pi$
$337$		−	26.0552i		−	1.41932i	0.704546	−	0.709658i	$-0.251151\pi$
$338$	−5.32301	+	3.86739i	−0.289533	+	0.210358i
$339$	0.934115	+	0.147949i	0.0507341	+	0.00803550i
$340$	−0.319286	−	2.01589i	−0.0173157	−	0.109327i
$341$	−19.3304	+	9.84934i	−1.04680	+	0.533372i
$342$	6.83336	−	6.83336i	0.369506	−	0.369506i
$343$	−12.9506	+	2.05118i	−0.699268	+	0.110753i
$344$	8.52723	+	26.2441i	0.459758	+	1.41499i
$345$	−0.00613760	+	0.0387513i	−0.000330437	+	0.00208630i
$346$	−2.75644	+	8.48345i	−0.148187	+	0.456073i
$347$	−5.78097	−	2.94555i	−0.310339	−	0.158126i	0.291884	−	0.956454i	$-0.405718\pi$
$347$	−5.78097	−	2.94555i	−0.310339	−	0.158126i	−0.602223	+	0.798328i	$0.705718\pi$
$348$	−0.778122	+	0.252827i	−0.0417117	+	0.0135530i
$349$	7.18918	−	2.33591i	0.384828	−	0.125038i	−0.110213	−	0.993908i	$-0.535153\pi$
$349$	7.18918	−	2.33591i	0.384828	−	0.125038i	0.495041	+	0.868870i	$0.335153\pi$
$350$	−9.19508	−	4.68513i	−0.491498	−	0.250431i
$351$	−0.228109	+	0.702047i	−0.0121756	+	0.0374725i
$352$	−2.84801	+	17.9817i	−0.151800	+	0.958425i
$353$	−11.4959	−	35.3808i	−0.611866	−	1.88313i	−0.439967	−	0.898014i	$-0.645010\pi$
$353$	−11.4959	−	35.3808i	−0.611866	−	1.88313i	−0.171899	−	0.985115i	$-0.554990\pi$
$354$	0.197670	−	0.0313079i	0.0105060	−	0.00166399i
$355$	0.508029	−	0.508029i	0.0269634	−	0.0269634i
$356$	18.3709	−	9.36044i	0.973655	−	0.496102i
$357$	0.0583912	+	0.368668i	0.00309039	+	0.0195120i
$358$	−1.55169	−	0.245764i	−0.0820095	−	0.0129890i
$359$	17.5992	−	12.7866i	0.928849	−	0.674848i	−0.0168617	−	0.999858i	$-0.505367\pi$
$359$	17.5992	−	12.7866i	0.928849	−	0.674848i	0.945711	+	0.325009i	$0.105367\pi$
$360$		−	5.46979i		−	0.288283i
$361$	0.162984	+	0.224329i	0.00857813	+	0.0118068i
$362$	−1.87354	+	3.67703i	−0.0984711	+	0.193260i
$363$	−0.0372597	−	0.0731262i	−0.00195563	−	0.00383813i
$364$	−5.40733	+	7.44255i	−0.283421	+	0.390096i
$365$	−3.77508	−	2.74276i	−0.197597	−	0.143563i
$366$	0.379780	+	0.379780i	0.0198514	+	0.0198514i
$367$	−16.6389	−	5.40631i	−0.868544	−	0.282207i	−0.159352	−	0.987222i	$-0.550940\pi$
$367$	−16.6389	−	5.40631i	−0.868544	−	0.282207i	−0.709193	+	0.705015i	$0.750940\pi$
$368$	0.940005			0.0490011
$369$	−17.6230	+	7.58353i	−0.917414	+	0.394783i
$370$	2.27777			0.118416
$371$	−8.87032	−	2.88214i	−0.460524	−	0.149633i
$372$	0.441313	+	0.441313i	0.0228810	+	0.0228810i
$373$	5.79680	+	4.21162i	0.300147	+	0.218070i	0.727657	−	0.685941i	$-0.240609\pi$
$373$	5.79680	+	4.21162i	0.300147	+	0.218070i	−0.427510	+	0.904011i	$0.640609\pi$
$374$	2.61160	−	3.59456i	0.135043	−	0.185870i
$375$	−0.189316	−	0.371553i	−0.00977622	−	0.0191869i
$376$	13.3282	−	26.1581i	0.687349	−	1.34900i
$377$	10.8155	+	14.8862i	0.557026	+	0.766681i
$378$			0.844852i			0.0434545i
$379$	6.38423	−	4.63842i	0.327936	−	0.238260i	−0.411618	−	0.911356i	$-0.635036\pi$
$379$	6.38423	−	4.63842i	0.327936	−	0.238260i	0.739554	+	0.673097i	$0.235036\pi$
$380$	4.54807	+	0.720344i	0.233311	+	0.0369529i
$381$	0.0415265	+	0.262188i	0.00212747	+	0.0134323i
$382$	8.58807	−	4.37584i	0.439404	−	0.223887i
$383$	−4.35320	+	4.35320i	−0.222438	+	0.222438i	−0.809524	−	0.587086i	$-0.800275\pi$
$383$	−4.35320	+	4.35320i	−0.222438	+	0.222438i	0.587086	+	0.809524i	$0.300275\pi$
$384$	0.610873	−	0.0967528i	0.0311735	−	0.00493740i
$385$	−2.16082	−	6.65031i	−0.110125	−	0.338931i
$386$	−1.90495	+	12.0274i	−0.0969592	+	0.612177i
$387$	−10.0511	+	30.9343i	−0.510929	+	1.57248i
$388$	−8.35313	−	4.25613i	−0.424066	−	0.216072i
$389$	−21.1299	+	6.86553i	−1.07133	+	0.348096i	−0.791005	−	0.611809i	$-0.790442\pi$
$389$	−21.1299	+	6.86553i	−1.07133	+	0.348096i	−0.280324	+	0.959905i	$0.590442\pi$
$390$	0.0617670	−	0.0200693i	0.00312769	−	0.00101625i
$391$	−1.54729	−	0.788386i	−0.0782501	−	0.0398704i
$392$	−2.21093	+	6.80454i	−0.111669	+	0.343681i
$393$	0.158740	−	1.00224i	0.00800735	−	0.0505564i
$394$	−3.28722	−	10.1170i	−0.165608	−	0.509688i
$395$	4.44724	−	0.704374i	0.223765	−	0.0354409i
$396$	−9.61618	+	9.61618i	−0.483231	+	0.483231i
$397$	5.81775	−	2.96429i	0.291984	−	0.148773i	−0.301863	−	0.953351i	$-0.597608\pi$
$397$	5.81775	−	2.96429i	0.291984	−	0.148773i	0.593847	+	0.804578i	$0.297608\pi$
$398$	2.07297	+	13.0882i	0.103909	+	0.656053i
$399$	−0.831755	−	0.131737i	−0.0416398	−	0.00659510i
$400$	−3.82162	+	2.77657i	−0.191081	+	0.138829i
$401$		−	21.3099i		−	1.06416i	−0.846693	−	0.532082i	$-0.821410\pi$
$401$		−	21.3099i		−	1.06416i	0.846693	−	0.532082i	$-0.178590\pi$
$402$	0.214139	+	0.294737i	0.0106803	+	0.0147001i
$403$	6.37228	−	12.5063i	0.317426	−	0.622984i
$404$	−7.97745	−	15.6566i	−0.396893	−	0.778946i
$405$	3.78488	−	5.20945i	0.188072	−	0.258859i
$406$	17.0375	+	12.3785i	0.845557	+	0.614333i
$407$	−9.48858	−	9.48858i	−0.470331	−	0.470331i
$408$	−0.288042	−	0.0935904i	−0.0142602	−	0.00463342i
$409$	3.89625			0.192657			0.0963287	−	0.995350i	$-0.469290\pi$
$409$	3.89625			0.192657			0.0963287	+	0.995350i	$0.469290\pi$
$410$	2.90409	+	1.72547i	0.143423	+	0.0852150i
$411$	−0.0144469			−0.000712613
$412$	21.3552	+	6.93871i	1.05209	+	0.341846i
$413$	9.85779	+	9.85779i	0.485070	+	0.485070i
$414$	−1.58896	−	1.15445i	−0.0780932	−	0.0567380i
$415$	−3.30838	+	4.55359i	−0.162402	+	0.223527i
$416$	−5.34742	−	10.4949i	−0.262179	−	0.514555i
$417$	0.0654675	−	0.128487i	0.00320596	−	0.00629204i
$418$	5.89205	+	8.10971i	0.288190	+	0.396659i
$419$			14.8236i			0.724179i	0.932143	+	0.362089i	$0.117937\pi$
$419$			14.8236i			0.724179i	−0.932143	+	0.362089i	$0.882063\pi$
$420$	−0.162740	+	0.118238i	−0.00794090	+	0.00576940i
$421$	−10.9908	−	1.74076i	−0.535657	−	0.0848397i	−0.117255	−	0.993102i	$-0.537410\pi$
$421$	−10.9908	−	1.74076i	−0.535657	−	0.0848397i	−0.418402	+	0.908262i	$0.637410\pi$
$422$	1.55156	+	9.79614i	0.0755286	+	0.476869i
$423$	30.8328	−	15.7101i	1.49914	−	0.763851i
$424$	5.35121	−	5.35121i	0.259878	−	0.259878i
$425$	8.61930	−	1.36516i	0.418098	−	0.0662202i
$426$	−0.0139036	−	0.0427909i	−0.000673633	−	0.00207323i
$427$	−5.85265	+	36.9522i	−0.283230	+	1.78824i
$428$	−0.503433	+	1.54941i	−0.0243343	+	0.0748934i
$429$	−0.340908	−	0.173701i	−0.0164592	−	0.00838638i
$430$	5.44667	−	1.76973i	0.262662	−	0.0853440i
$431$	25.1750	−	8.17986i	1.21264	−	0.394010i	0.368242	−	0.929730i	$-0.379960\pi$
$431$	25.1750	−	8.17986i	1.21264	−	0.394010i	0.844396	+	0.535720i	$0.179960\pi$
$432$	0.344570	+	0.175567i	0.0165781	+	0.00844697i
$433$	0.144494	−	0.444707i	0.00694395	−	0.0213713i	−0.947525	−	0.319683i	$-0.896424\pi$
$433$	0.144494	−	0.444707i	0.00694395	−	0.0213713i	0.954468	+	0.298312i	$0.0964235\pi$
$434$	2.51305	−	15.8668i	0.120630	−	0.761630i
$435$	0.124332	+	0.382654i	0.00596126	+	0.0183469i
$436$	−8.53990	+	1.35259i	−0.408987	+	0.0647772i
$437$	2.77037	−	2.77037i	0.132525	−	0.132525i
$438$	−0.260371	+	0.132665i	−0.0124410	+	0.00633900i
$439$	−3.05677	−	19.2997i	−0.145892	−	0.921123i	−0.946680	−	0.322176i	$-0.895586\pi$
$439$	−3.05677	−	19.2997i	−0.145892	−	0.921123i	0.800788	−	0.598947i	$-0.204414\pi$
$440$	5.60388	+	0.887568i	0.267155	+	0.0423131i
$441$	−6.82272	+	4.95700i	−0.324891	+	0.236047i
$442$			2.87459i			0.136730i
$443$	4.37823	+	6.02611i	0.208016	+	0.286309i	0.900259	−	0.435355i	$-0.143377\pi$
$443$	4.37823	+	6.02611i	0.208016	+	0.286309i	−0.692243	+	0.721665i	$0.743377\pi$
$444$	−0.175253	+	0.343953i	−0.00831712	+	0.0163233i
$445$	−4.60315	−	9.03419i	−0.218210	−	0.428262i
$446$	−3.27717	+	4.51063i	−0.155178	+	0.213585i
$447$	−0.415628	−	0.301971i	−0.0196585	−	0.0142828i
$448$	−4.86526	−	4.86526i	−0.229862	−	0.229862i
$449$	24.2920	+	7.89296i	1.14641	+	0.372492i	0.819790	−	0.572664i	$-0.194090\pi$
$449$	24.2920	+	7.89296i	1.14641	+	0.372492i	0.326621	+	0.945155i	$0.394090\pi$
$450$	9.86997			0.465275
$451$	−4.90981	−	19.2855i	−0.231194	−	0.908121i
$452$	−22.5594			−1.06110
$453$	0.210915	+	0.0685304i	0.00990964	+	0.00321984i
$454$	−11.2791	−	11.2791i	−0.529354	−	0.529354i
$455$	3.66000	+	2.65914i	0.171583	+	0.124663i
$456$	0.401632	−	0.552798i	0.0188081	−	0.0258872i
$457$	16.0293	+	31.4593i	0.749820	+	1.47161i	0.877391	+	0.479776i	$0.159282\pi$
$457$	16.0293	+	31.4593i	0.749820	+	1.47161i	−0.127571	+	0.991829i	$0.540718\pi$
$458$	−0.987815	+	1.93870i	−0.0461576	+	0.0905893i
$459$	−0.419930	−	0.577984i	−0.0196007	−	0.0269780i
$460$		−	0.935866i		−	0.0436350i
$461$	23.0488	−	16.7459i	1.07349	−	0.779936i	0.0969530	−	0.995289i	$-0.469090\pi$
$461$	23.0488	−	16.7459i	1.07349	−	0.779936i	0.976536	+	0.215353i	$0.0690903\pi$
$462$	−0.432511	−	0.0685030i	−0.0201222	−	0.00318705i
$463$	−2.00832	−	12.6801i	−0.0933348	−	0.589293i	−0.989383	−	0.145335i	$-0.953574\pi$
$463$	−2.00832	−	12.6801i	−0.0933348	−	0.589293i	0.896048	−	0.443958i	$-0.146426\pi$
$464$	8.58904	−	4.37633i	0.398736	−	0.203166i
$465$	0.217023	−	0.217023i	0.0100642	−	0.0100642i
$466$	−12.6253	+	1.99965i	−0.584856	+	0.0926321i
$467$	9.10432	+	28.0202i	0.421297	+	1.29662i	0.906495	+	0.422216i	$0.138748\pi$
$467$	9.10432	+	28.0202i	0.421297	+	1.29662i	−0.485198	+	0.874404i	$0.661252\pi$
$468$	1.37638	−	8.69011i	0.0636231	−	0.401701i
$469$	−7.84210	+	24.1355i	−0.362114	+	1.11447i
$470$	−5.42881	−	2.76612i	−0.250412	−	0.127591i
$471$	0.802375	−	0.260708i	0.0369715	−	0.0120128i
$472$	−10.7581	+	3.49551i	−0.495180	+	0.160894i
$473$	−30.0616	−	15.3172i	−1.38224	−	0.704284i
$474$	0.0871355	−	0.268176i	0.00400227	−	0.0123177i
$475$	−3.07996	+	19.4461i	−0.141318	+	0.892248i
$476$	−2.75134	−	8.46777i	−0.126108	−	0.388120i
$477$	8.81037	−	1.39543i	0.403399	−	0.0638922i
$478$	−3.08562	+	3.08562i	−0.141133	+	0.141133i
$479$	−23.8053	+	12.1294i	−1.08769	+	0.554207i	−0.903459	−	0.428675i	$-0.858980\pi$
$479$	−23.8053	+	12.1294i	−1.08769	+	0.554207i	−0.184234	+	0.982882i	$0.558980\pi$
$480$	−0.0402905	−	0.254384i	−0.00183900	−	0.0116110i
$481$	8.57480	+	1.35812i	0.390977	+	0.0619247i
$482$	5.21943	−	3.79214i	0.237739	−	0.172727i
$483$			0.171152i			0.00778768i
$484$	1.15069	+	1.58379i	0.0523041	+	0.0719904i
$485$	−2.09302	+	4.10779i	−0.0950393	+	0.186525i
$486$	−0.550364	−	1.08015i	−0.0249650	−	0.0489966i
$487$	6.82210	−	9.38981i	0.309139	−	0.425493i	−0.625974	−	0.779844i	$-0.715298\pi$
$487$	6.82210	−	9.38981i	0.309139	−	0.425493i	0.935112	+	0.354351i	$0.115298\pi$
$488$	−24.5591	−	17.8432i	−1.11174	−	0.807724i
$489$	−0.0399741	−	0.0399741i	−0.00180769	−	0.00180769i
$490$	1.41221	+	0.458853i	0.0637969	+	0.0207289i
$491$	−26.8852			−1.21331			−0.606656	−	0.794964i	$-0.707489\pi$
$491$	−26.8852			−1.21331			−0.606656	+	0.794964i	$0.707489\pi$
$492$	−0.483996	+	0.305771i	−0.0218202	+	0.0137852i
$493$	−17.8084			−0.802052
$494$	−6.16797	−	2.00409i	−0.277510	−	0.0901685i
$495$	4.72892	+	4.72892i	0.212549	+	0.212549i
$496$	−5.94898	−	4.32218i	−0.267117	−	0.194072i
$497$	1.84220	−	2.53557i	0.0826341	−	0.113736i
$498$	0.160024	+	0.314065i	0.00717084	+	0.0140736i
$499$	5.83710	−	11.4559i	0.261304	−	0.512839i	−0.722660	−	0.691204i	$-0.757081\pi$
$499$	5.83710	−	11.4559i	0.261304	−	0.512839i	0.983964	+	0.178365i	$0.0570808\pi$
$500$	5.84663	+	8.04720i	0.261469	+	0.359882i
$501$		−	1.04092i		−	0.0465050i
$502$	−3.04695	+	2.21374i	−0.135992	+	0.0988041i
$503$	11.9300	+	1.88953i	0.531934	+	0.0842501i	0.416623	−	0.909079i	$-0.363214\pi$
$503$	11.9300	+	1.88953i	0.531934	+	0.0842501i	0.115311	+	0.993329i	$0.463214\pi$
$504$	−3.73266	−	23.5671i	−0.166266	−	1.04976i
$505$	−7.69940	+	3.92304i	−0.342619	+	0.174573i
$506$	1.44059	−	1.44059i	0.0640419	−	0.0640419i
$507$	−0.541610	+	0.0857826i	−0.0240537	+	0.00380974i
$508$	−1.95669	−	6.02208i	−0.0868141	−	0.267186i
$509$	4.55017	−	28.7287i	0.201683	−	1.27338i	−0.654246	−	0.756282i	$-0.727014\pi$
$509$	4.55017	−	28.7287i	0.201683	−	1.27338i	0.855929	−	0.517094i	$-0.172986\pi$
$510$	−0.0194236	+	0.0597798i	−0.000860093	+	0.00264709i
$511$	−18.1370	−	9.24126i	−0.802333	−	0.408809i
$512$	−10.9621	+	3.56179i	−0.484460	+	0.157411i
$513$	1.53294	−	0.498082i	0.0676809	−	0.0219908i
$514$	−0.719519	−	0.366613i	−0.0317366	−	0.0161706i
$515$	3.41223	−	10.5017i	0.150361	−	0.462762i
$516$	−0.151833	+	0.958635i	−0.00668407	+	0.0422015i
$517$	11.0921	+	34.1379i	0.487829	+	1.50138i
$518$	9.81397	−	1.55438i	0.431201	−	0.0682956i
$519$	−0.525676	+	0.525676i	−0.0230746	+	0.0230746i
$520$	−3.27068	+	1.66649i	−0.143429	+	0.0730806i
$521$	3.39562	+	21.4391i	0.148765	+	0.939264i	0.943275	+	0.332013i	$0.107728\pi$
$521$	3.39562	+	21.4391i	0.148765	+	0.939264i	−0.794510	+	0.607251i	$0.792272\pi$
$522$	−19.8934	−	3.15081i	−0.870711	−	0.137907i
$523$	−12.7639	+	9.27355i	−0.558128	+	0.405504i	−0.830773	−	0.556611i	$-0.812102\pi$
$523$	−12.7639	+	9.27355i	−0.558128	+	0.405504i	0.272645	+	0.962115i	$0.412102\pi$
$524$			24.2047i			1.05739i
$525$	−0.505546	−	0.695824i	−0.0220638	−	0.0303683i
$526$	−4.25648	+	8.35382i	−0.185592	+	0.364244i
$527$	6.16728	+	12.1040i	0.268651	+	0.527257i
$528$	−0.117818	+	0.162163i	−0.00512737	+	0.00705722i
$529$	17.9632	+	13.0510i	0.781009	+	0.567436i
$530$	−1.11058	−	1.11058i	−0.0482406	−	0.0482406i
$531$	−12.6807	−	4.12020i	−0.550294	−	0.178801i
$532$	20.0874			0.870897
$533$	9.90382	+	8.22721i	0.428982	+	0.356360i
$534$	−0.634966			−0.0274777
$535$	0.761946	+	0.247571i	0.0329418	+	0.0107034i
$536$	−14.5602	−	14.5602i	−0.628907	−	0.628907i
$537$	−0.105928	−	0.0769612i	−0.00457113	−	0.00332112i
$538$	0.238379	−	0.328101i	0.0102773	−	0.0141454i
$539$	−3.97141	−	7.79434i	−0.171061	−	0.335726i
$540$	0.174794	−	0.343052i	0.00752193	−	0.0147626i
$541$	2.48515	+	3.42051i	0.106845	+	0.147059i	0.859091	−	0.511823i	$-0.171030\pi$
$541$	2.48515	+	3.42051i	0.106845	+	0.147059i	−0.752246	+	0.658882i	$0.771030\pi$
$542$		−	2.02768i		−	0.0870965i
$543$	−0.278254	+	0.202163i	−0.0119410	+	0.00867565i
$544$	11.2594	+	1.78332i	0.482743	+	0.0764590i
$545$	0.665157	+	4.19964i	0.0284922	+	0.179893i
$546$	0.252433	−	0.128621i	0.0108031	−	0.00550447i
$547$	−1.68661	+	1.68661i	−0.0721143	+	0.0721143i	−0.742244	−	0.670130i	$-0.766238\pi$
$547$	−1.68661	+	1.68661i	−0.0721143	+	0.0721143i	0.670130	+	0.742244i	$0.266238\pi$
$548$	0.340362	−	0.0539081i	0.0145396	−	0.00230284i
$549$	−11.0572	−	34.0305i	−0.471908	−	1.45238i
$550$	−1.60157	+	10.1119i	−0.0682913	+	0.431174i
$551$	12.4156	−	38.2113i	0.528923	−	1.62786i
$552$	−0.123736	−	0.0630467i	−0.00526656	−	0.00268344i
$553$	18.6807	−	6.06972i	0.794383	−	0.258111i
$554$	14.8544	−	4.82648i	0.631102	−	0.205057i
$555$	0.169144	+	0.0861834i	0.00717978	+	0.00365828i
$556$	−1.06294	+	3.27139i	−0.0450787	+	0.138738i
$557$	1.20951	−	7.63657i	0.0512487	−	0.323572i	−0.948723	−	0.316107i	$-0.897624\pi$
$557$	1.20951	−	7.63657i	0.0512487	−	0.323572i	0.999972	−	0.00746438i	$-0.00237601\pi$
$558$	4.74780	+	14.6122i	0.200991	+	0.618585i
$559$	21.5595	−	3.41470i	0.911871	−	0.144426i
$560$	1.67589	−	1.67589i	0.0708191	−	0.0708191i
$561$	0.329941	−	0.168113i	0.0139301	−	0.00709774i
$562$	−0.205981	−	1.30051i	−0.00868878	−	0.0548588i
$563$	29.4356	+	4.66214i	1.24056	+	0.196486i	0.742019	−	0.670379i	$-0.233869\pi$
$563$	29.4356	+	4.66214i	1.24056	+	0.196486i	0.498543	+	0.866865i	$0.333869\pi$
$564$	0.835391	−	0.606947i	0.0351763	−	0.0255571i
$565$			11.0940i			0.466726i
$566$	−1.60558	−	2.20989i	−0.0674875	−	0.0928885i
$567$	12.7525	−	25.0282i	0.535556	−	1.05109i
$568$	1.15451	+	2.26586i	0.0484423	+	0.0950734i
$569$	−5.19710	+	7.15320i	−0.217874	+	0.299878i	−0.903938	−	0.427663i	$-0.859337\pi$
$569$	−5.19710	+	7.15320i	−0.217874	+	0.299878i	0.686064	+	0.727541i	$0.259337\pi$
$570$	−0.114727	−	0.0833541i	−0.00480539	−	0.00349132i
$571$	15.7965	+	15.7965i	0.661063	+	0.661063i	0.955631	−	0.294567i	$-0.0951756\pi$
$571$	15.7965	+	15.7965i	0.661063	+	0.661063i	−0.294567	+	0.955631i	$0.595176\pi$
$572$	8.67981	+	2.82024i	0.362921	+	0.117920i
$573$	0.803308			0.0335587
$574$	13.6900	+	5.45256i	0.571411	+	0.227586i
$575$	4.00146			0.166872
$576$	6.25848	+	2.03350i	0.260770	+	0.0847293i
$577$	8.51989	+	8.51989i	0.354688	+	0.354688i	0.861850	−	0.507163i	$-0.169306\pi$
$577$	8.51989	+	8.51989i	0.354688	+	0.354688i	−0.507163	+	0.861850i	$0.669306\pi$
$578$	7.85233	+	5.70505i	0.326614	+	0.237299i
$579$	−0.596536	+	0.821061i	−0.0247912	+	0.0341221i
$580$	−4.35707	−	8.55122i	−0.180917	−	0.355070i
$581$	−11.1470	+	21.8772i	−0.462456	+	0.907621i
$582$	0.169702	+	0.233575i	0.00703439	+	0.00968201i
$583$			9.25279i			0.383211i
$584$	13.3621	−	9.70816i	0.552929	−	0.401726i
$585$	−4.27351	−	0.676857i	−0.176688	−	0.0279846i
$586$	−1.59766	−	10.0872i	−0.0659988	−	0.416700i
$587$	−22.9909	+	11.7145i	−0.948936	+	0.483507i	−0.858737	−	0.512417i	$-0.828750\pi$
$587$	−22.9909	+	11.7145i	−0.948936	+	0.483507i	−0.0901991	+	0.995924i	$0.528750\pi$
$588$	−0.177945	+	0.177945i	−0.00733831	+	0.00733831i
$589$	−30.2710	+	4.79445i	−1.24729	+	0.197552i
$590$	0.725454	+	2.23272i	0.0298664	+	0.0919195i
$591$	0.138690	−	0.875656i	0.00570495	−	0.0360197i
$592$	1.40547	−	4.32560i	0.0577646	−	0.177781i
$593$	18.5585	+	9.45605i	0.762108	+	0.388313i	0.791432	−	0.611257i	$-0.209336\pi$
$593$	18.5585	+	9.45605i	0.762108	+	0.388313i	−0.0293248	+	0.999570i	$0.509336\pi$
$594$	0.797125	−	0.259002i	0.0327064	−	0.0106270i
$595$	−4.16416	+	1.35302i	−0.170714	+	0.0554684i
$596$	10.9188	+	5.56341i	0.447252	+	0.227886i
$597$	−0.341280	+	1.05035i	−0.0139676	+	0.0429880i
$598$	−0.206193	+	1.30185i	−0.00843187	+	0.0532367i
$599$	−5.67622	−	17.4696i	−0.231924	−	0.713789i	−0.997515	−	0.0704605i	$-0.977553\pi$
$599$	−5.67622	−	17.4696i	−0.231924	−	0.713789i	0.765591	−	0.643328i	$-0.222447\pi$
$600$	0.689280	−	0.109171i	0.0281397	−	0.00445689i
$601$	−7.61945	+	7.61945i	−0.310804	+	0.310804i	−0.845221	−	0.534417i	$-0.820531\pi$
$601$	−7.61945	+	7.61945i	−0.310804	+	0.310804i	0.534417	+	0.845221i	$0.320531\pi$
$602$	22.2598	−	11.3419i	0.907241	−	0.462263i
$603$	−3.79685	−	23.9724i	−0.154620	−	0.976230i
$604$	−5.22478	−	0.827524i	−0.212593	−	0.0336715i
$605$	0.778854	−	0.565870i	0.0316649	−	0.0230059i
$606$			0.541151i			0.0219827i
$607$	−8.17357	−	11.2500i	−0.331755	−	0.456622i	0.610256	−	0.792205i	$-0.291067\pi$
$607$	−8.17357	−	11.2500i	−0.331755	−	0.456622i	−0.942011	+	0.335583i	$0.891067\pi$
$608$	−11.6762	+	22.9159i	−0.473534	+	0.929362i
$609$	0.796824	+	1.56385i	0.0322889	+	0.0633706i
$610$	−3.70315	+	5.09695i	−0.149936	+	0.206370i
$611$	−18.7878	−	13.6501i	−0.760073	−	0.552226i
$612$	6.02128	+	6.02128i	0.243396	+	0.243396i
$613$	−14.1988	−	4.61346i	−0.573482	−	0.186336i	0.00789628	−	0.999969i	$-0.497487\pi$
$613$	−14.1988	−	4.61346i	−0.573482	−	0.186336i	−0.581379	+	0.813633i	$0.697487\pi$
$614$	−16.0653			−0.648344
$615$	0.150368	+	0.238013i	0.00606343	+	0.00959761i
$616$	24.7505			0.997227
$617$	7.99439	+	2.59753i	0.321842	+	0.104573i	0.465482	−	0.885057i	$-0.345881\pi$
$617$	7.99439	+	2.59753i	0.321842	+	0.104573i	−0.143640	+	0.989630i	$0.545881\pi$
$618$	−0.488970	−	0.488970i	−0.0196693	−	0.0196693i
$619$	−22.0401	−	16.0131i	−0.885866	−	0.643619i	0.0489312	−	0.998802i	$-0.484418\pi$
$619$	−22.0401	−	16.0131i	−0.885866	−	0.643619i	−0.934797	+	0.355183i	$0.884418\pi$
$620$	−4.30315	+	5.92278i	−0.172819	+	0.237865i
$621$	−0.148721	−	0.291881i	−0.00596796	−	0.0117128i
$622$	−5.31922	+	10.4396i	−0.213281	+	0.418588i
$623$	−25.9981	−	35.7834i	−1.04159	−	1.43363i
$624$		−	0.129682i		−	0.00519145i
$625$	−14.1818	+	10.3037i	−0.567272	+	0.412148i
$626$	−0.595887	−	0.0943792i	−0.0238164	−	0.00377215i
$627$	0.130692	+	0.825154i	0.00521932	+	0.0329535i
$628$	−17.9308	+	9.13619i	−0.715516	+	0.364574i
$629$	−5.94138	+	5.94138i	−0.236898	+	0.236898i
$630$	−4.89108	+	0.774672i	−0.194865	+	0.0308637i
$631$	0.989181	+	3.04439i	0.0393787	+	0.121195i	0.968813	−	0.247792i	$-0.0797048\pi$
$631$	0.989181	+	3.04439i	0.0393787	+	0.121195i	−0.929435	+	0.368987i	$0.879705\pi$
$632$	−2.49317	+	15.7413i	−0.0991731	+	0.626154i
$633$	−0.255437	+	0.786156i	−0.0101527	+	0.0312469i
$634$	18.5181	+	9.43542i	0.735446	+	0.374728i
$635$	−2.96145	+	0.962235i	−0.117522	+	0.0381851i
$636$	0.253152	−	0.0822539i	0.0100381	−	0.00326158i
$637$	5.04275	+	2.56941i	0.199801	+	0.101804i
$638$	6.45610	−	19.8698i	0.255599	−	0.786654i
$639$	−0.468913	+	2.96060i	−0.0185499	+	0.117120i
$640$	2.24192	+	6.89991i	0.0886196	+	0.272743i
$641$	−42.6511	+	6.75528i	−1.68462	+	0.266817i	−0.924003	−	0.382385i	$-0.875103\pi$
$641$	−42.6511	+	6.75528i	−1.68462	+	0.266817i	−0.760615	+	0.649203i	$0.775103\pi$
$642$	0.0354769	−	0.0354769i	0.00140016	−	0.00140016i
$643$	−3.56855	+	1.81827i	−0.140730	+	0.0717054i	−0.522937	−	0.852371i	$-0.675164\pi$
$643$	−3.56855	+	1.81827i	−0.140730	+	0.0717054i	0.382208	+	0.924076i	$0.375164\pi$
$644$	−0.638648	−	4.03226i	−0.0251663	−	0.158893i
$645$	0.471424	+	0.0746663i	0.0185623	+	0.00293998i
$646$	5.07799	−	3.68937i	0.199791	−	0.145156i
$647$		−	16.9523i		−	0.666465i	−0.942845	−	0.333232i	$-0.891861\pi$
$647$		−	16.9523i		−	0.666465i	0.942845	−	0.333232i	$-0.108139\pi$
$648$	13.3968	+	18.4391i	0.526277	+	0.724358i
$649$	6.27886	−	12.3230i	0.246467	−	0.483718i
$650$	−3.00711	−	5.90178i	−0.117948	−	0.231487i
$651$	0.786964	−	1.08316i	0.0308436	−	0.0424525i
$652$	1.09093	+	0.792609i	0.0427242	+	0.0310410i
$653$	12.3449	+	12.3449i	0.483092	+	0.483092i	0.906118	−	0.423026i	$-0.139032\pi$
$653$	12.3449	+	12.3449i	0.483092	+	0.483092i	−0.423026	+	0.906118i	$0.639032\pi$
$654$	0.253245	+	0.0822842i	0.00990265	+	0.00321757i
$655$	11.9031			0.465091
$656$	5.06870	−	4.45034i	0.197900	−	0.173757i
$657$	19.4682			0.759527
$658$	−25.2782	−	8.21337i	−0.985445	−	0.320191i
$659$	−19.4232	−	19.4232i	−0.756620	−	0.756620i	0.219086	−	0.975706i	$-0.429692\pi$
$659$	−19.4232	−	19.4232i	−0.756620	−	0.756620i	−0.975706	+	0.219086i	$0.929692\pi$
$660$	0.161449	+	0.117299i	0.00628438	+	0.00456587i
$661$	−4.42412	+	6.08928i	−0.172078	+	0.236846i	−0.886342	−	0.463031i	$-0.846762\pi$
$661$	−4.42412	+	6.08928i	−0.172078	+	0.236846i	0.714264	+	0.699877i	$0.246762\pi$
$662$	10.2567	+	20.1299i	0.398637	+	0.782369i
$663$	−0.108765	+	0.213464i	−0.00422409	+	0.00829024i
$664$	−11.7102	−	16.1177i	−0.454443	−	0.625488i
$665$		−	9.87829i		−	0.383063i
$666$	−7.68818	+	5.58579i	−0.297911	+	0.216445i
$667$	−8.06515	−	1.27739i	−0.312284	−	0.0494609i
$668$	3.88417	+	24.5237i	0.150283	+	0.948851i
$669$	−0.414026	+	0.210957i	−0.0160072	+	0.00815607i
$670$	−3.02181	+	3.02181i	−0.116743	+	0.116743i
$671$	36.6589	−	5.80620i	1.41520	−	0.224146i
$672$	−0.347191	−	1.06854i	−0.0133932	−	0.0412199i
$673$	6.65260	−	42.0029i	0.256439	−	1.61909i	−0.437610	−	0.899165i	$-0.644175\pi$
$673$	6.65260	−	42.0029i	0.256439	−	1.61909i	0.694049	−	0.719927i	$-0.255825\pi$
$674$	5.91459	−	18.2032i	0.227822	−	0.701163i
$675$	1.46678	+	0.747363i	0.0564565	+	0.0287660i
$676$	12.4400	−	4.04200i	0.478461	−	0.155462i
$677$	−44.0320	+	14.3069i	−1.69229	+	0.549857i	−0.987231	−	0.159294i	$-0.949078\pi$
$677$	−44.0320	+	14.3069i	−1.69229	+	0.549857i	−0.705056	+	0.709152i	$0.749078\pi$
$678$	0.619027	+	0.315410i	0.0237736	+	0.0121132i
$679$	−6.21477	+	19.1271i	−0.238501	+	0.734030i
$680$	0.555760	−	3.50893i	0.0213124	−	0.134561i
$681$	−0.410808	−	1.26434i	−0.0157422	−	0.0484495i
$682$	−15.7409	+	2.49311i	−0.602749	+	0.0954661i
$683$	10.8884	−	10.8884i	0.416633	−	0.416633i	−0.467409	−	0.884041i	$-0.654812\pi$
$683$	10.8884	−	10.8884i	0.416633	−	0.416633i	0.884041	+	0.467409i	$0.154812\pi$
$684$	−17.1177	+	8.72189i	−0.654511	+	0.333490i
$685$	−0.0265102	−	0.167379i	−0.00101290	−	0.00639522i
$686$	−9.51347	−	1.50679i	−0.363226	−	0.0575293i
$687$	−0.146708	+	0.106590i	−0.00559726	+	0.00406665i
$688$		−	11.4355i		−	0.435975i
$689$	−3.51868	−	4.84304i	−0.134051	−	0.184505i
$690$	−0.0130846	+	0.0256800i	−0.000498123	+	0.000977622i
$691$	19.4697	+	38.2115i	0.740664	+	1.45363i	0.885724	+	0.464212i	$0.153662\pi$
$691$	19.4697	+	38.2115i	0.740664	+	1.45363i	−0.145060	+	0.989423i	$0.546338\pi$
$692$	10.4232	−	14.3462i	0.396229	−	0.545363i
$693$	23.6020	+	17.1479i	0.896567	+	0.651394i
$694$	−3.37018	−	3.37018i	−0.127930	−	0.127930i
$695$	1.60876	+	0.522718i	0.0610237	+	0.0198278i
$696$	−1.42413			−0.0539815
$697$	−12.0759	+	3.07433i	−0.457406	+	0.116449i
$698$	5.55292			0.210181
$699$	−1.01320	−	0.329209i	−0.0383228	−	0.0124518i
$700$	14.5069	+	14.5069i	0.548309	+	0.548309i
$701$	23.6599	+	17.1899i	0.893623	+	0.649255i	0.936820	−	0.349812i	$-0.113754\pi$
$701$	23.6599	+	17.1899i	0.893623	+	0.649255i	−0.0431974	+	0.999067i	$0.513754\pi$
$702$	−0.318733	+	0.438698i	−0.0120298	+	0.0165576i
$703$	−8.60616	−	16.8905i	−0.324587	−	0.637039i
$704$	−3.09890	+	6.08193i	−0.116794	+	0.229222i
$705$	−0.298476	−	0.410817i	−0.0112413	−	0.0154723i
$706$		−	27.3281i		−	1.02851i
$707$	−30.4964	+	22.1570i	−1.14694	+	0.833298i
$708$	−0.392966	−	0.0622398i	−0.0147686	−	0.00233911i
$709$	1.32698	+	8.37821i	0.0498357	+	0.314650i	0.999996	+	0.00288796i	$0.000919268\pi$
$709$	1.32698	+	8.37821i	0.0498357	+	0.314650i	−0.950160	+	0.311762i	$0.899081\pi$
$710$	0.470254	−	0.239606i	0.0176483	−	0.00899227i
$711$	−13.2835	+	13.2835i	−0.498170	+	0.498170i
$712$	35.4468	−	5.61423i	1.32843	−	0.210402i
$713$	1.92484	+	5.92406i	0.0720860	+	0.221858i
$714$	−0.0428939	+	0.270822i	−0.00160527	+	0.0101352i
$715$	1.38690	−	4.26844i	0.0518671	−	0.159631i
$716$	2.78279	+	1.41790i	0.103998	+	0.0529896i
$717$	−0.345884	+	0.112385i	−0.0129173	+	0.00419708i
$718$	15.1981	−	4.93816i	0.567188	−	0.184291i
$719$	34.3184	+	17.4861i	1.27986	+	0.652121i	0.955828	−	0.293926i	$-0.0949618\pi$
$719$	34.3184	+	17.4861i	1.27986	+	0.652121i	0.324031	+	0.946046i	$0.394962\pi$
$720$	−0.700460	+	2.15579i	−0.0261046	+	0.0803417i
$721$	7.53535	−	47.5763i	0.280631	−	1.77183i
$722$	0.0629445	+	0.193723i	0.00234255	+	0.00720964i
$723$	0.531071	−	0.0841134i	0.0197507	−	0.00312821i
$724$	5.80117	−	5.80117i	0.215599	−	0.215599i
$725$	36.5623	−	18.6294i	1.35789	−	0.691879i
$726$	−0.00943133	−	0.0595471i	−0.000350029	−	0.00221000i
$727$	−51.1019	−	8.09374i	−1.89526	−	0.300180i	−0.903533	−	0.428518i	$-0.859036\pi$
$727$	−51.1019	−	8.09374i	−1.89526	−	0.300180i	−0.991730	+	0.128338i	$0.959036\pi$
$728$	−12.9548	+	9.41220i	−0.480136	+	0.348839i
$729$			26.7978i			0.992511i
$730$	−2.01482	−	2.77316i	−0.0745718	−	0.102639i
$731$	−9.59102	+	18.8234i	−0.354737	+	0.696210i
$732$	−0.484739	−	0.951354i	−0.0179165	−	0.0351631i
$733$	0.369332	−	0.508342i	0.0136416	−	0.0187760i	−0.802142	−	0.597134i	$-0.796306\pi$
$733$	0.369332	−	0.508342i	0.0136416	−	0.0187760i	0.815783	+	0.578358i	$0.196306\pi$
$734$	−10.3974	−	7.55415i	−0.383775	−	0.278829i
$735$	0.0875072	+	0.0875072i	0.00322775	+	0.00322775i
$736$	4.97128	+	1.61527i	0.183244	+	0.0595396i
$737$	25.1762			0.927376
$738$	−14.0336	+	1.29772i	−0.516584	+	0.0477696i
$739$	40.6971			1.49707			0.748533	−	0.663097i	$-0.230758\pi$
$739$	40.6971			1.49707			0.748533	+	0.663097i	$0.230758\pi$
$740$	−4.30656	−	1.39929i	−0.158312	−	0.0514388i
$741$	−0.382198	−	0.382198i	−0.0140404	−	0.0140404i
$742$	−5.54292	−	4.02717i	−0.203487	−	0.147842i
$743$	9.43650	−	12.9882i	0.346192	−	0.476492i	−0.600045	−	0.799966i	$-0.704851\pi$
$743$	9.43650	−	12.9882i	0.346192	−	0.476492i	0.946237	+	0.323474i	$0.104851\pi$
$744$	0.493193	+	0.967945i	0.0180813	+	0.0354866i
$745$	2.73590	−	5.36950i	0.100236	−	0.196723i
$746$	3.09384	+	4.25830i	0.113273	+	0.155908i
$747$		−	23.4830i		−	0.859196i
$748$	−7.14595	+	5.19184i	−0.261282	+	0.189832i
$749$	3.45186	+	0.546721i	0.126128	+	0.0199768i
$750$	−0.0479204	−	0.302558i	−0.00174981	−	0.0110478i
$751$	26.2079	−	13.3536i	0.956339	−	0.487279i	0.0950935	−	0.995468i	$-0.469685\pi$
$751$	26.2079	−	13.3536i	0.956339	−	0.487279i	0.861245	+	0.508189i	$0.169685\pi$
$752$	−8.60280	+	8.60280i	−0.313712	+	0.313712i
$753$	−0.310024	+	0.0491030i	−0.0112979	+	0.00178941i
$754$	4.17694	+	12.8553i	0.152115	+	0.468162i
$755$	−0.406949	+	2.56937i	−0.0148104	+	0.0935090i
$756$	0.519012	−	1.59735i	0.0188763	−	0.0580952i
$757$	32.6350	+	16.6284i	1.18614	+	0.604369i	0.931880	−	0.362767i	$-0.118168\pi$
$757$	32.6350	+	16.6284i	1.18614	+	0.604369i	0.254260	+	0.967136i	$0.418168\pi$
$758$	5.51323	−	1.79136i	0.200249	−	0.0650650i
$759$	0.161483	−	0.0524691i	0.00586147	−	0.00190451i
$760$	7.14161	+	3.63883i	0.259053	+	0.131994i
$761$	−8.21482	+	25.2826i	−0.297787	+	0.916494i	0.684484	+	0.729028i	$0.260028\pi$
$761$	−8.21482	+	25.2826i	−0.297787	+	0.916494i	−0.982271	+	0.187466i	$0.939972\pi$
$762$	−0.0305052	+	0.192602i	−0.00110509	+	0.00697723i
$763$	5.73178	+	17.6406i	0.207504	+	0.638633i
$764$	−18.9256	+	2.99752i	−0.684703	+	0.108446i
$765$	2.96106	−	2.96106i	0.107057	−	0.107057i
$766$	−4.02951	+	2.05314i	−0.145592	+	0.0741830i
$767$	1.39976	+	8.83775i	0.0505425	+	0.319113i
$768$	0.714358	+	0.113143i	0.0257772	+	0.00408270i
$769$	−17.8728	+	12.9853i	−0.644509	+	0.468263i	−0.861396	−	0.507933i	$-0.830410\pi$
$769$	−17.8728	+	12.9853i	−0.644509	+	0.468263i	0.216887	+	0.976197i	$0.430410\pi$
$770$		−	5.13669i		−	0.185114i
$771$	−0.0395592	−	0.0544485i	−0.00142469	−	0.00196091i
$772$	10.9904	−	21.5698i	0.395552	−	0.776314i
$773$	−15.6700	−	30.7541i	−0.563610	−	1.10615i	−0.980377	−	0.197133i	$-0.936837\pi$
$773$	−15.6700	−	30.7541i	−0.563610	−	1.10615i	0.416767	−	0.909014i	$-0.363163\pi$
$774$	−14.0443	+	19.3303i	−0.504812	+	0.694814i
$775$	−25.3239	−	18.3989i	−0.909662	−	0.660908i
$776$	−11.5388	−	11.5388i	−0.414219	−	0.414219i
$777$	0.787587	+	0.255902i	0.0282545	+	0.00918045i
$778$	−16.3207			−0.585127
$779$	1.82244	−	28.0544i	0.0652957	−	1.00515i
$780$	−0.129111			−0.00462293
$781$	−2.95709	−	0.960817i	−0.105813	−	0.0343807i
$782$	−0.902039	−	0.902039i	−0.0322569	−	0.0322569i
$783$	−2.71779	−	1.97459i	−0.0971259	−	0.0705661i
$784$	1.74277	−	2.39872i	0.0622419	−	0.0856687i
$785$	4.49287	+	8.81776i	0.160358	+	0.314719i
$786$	0.338413	−	0.664174i	0.0120708	−	0.0236903i
$787$	4.79695	+	6.60244i	0.170993	+	0.235351i	0.885909	−	0.463858i	$-0.153535\pi$
$787$	4.79695	+	6.60244i	0.170993	+	0.235351i	−0.714917	+	0.699210i	$0.753535\pi$
$788$			21.1476i			0.753351i
$789$	−0.632163	+	0.459293i	−0.0225056	+	0.0163513i
$790$	3.26692	+	0.517430i	0.116232	+	0.0184093i
$791$	7.57067	+	47.7993i	0.269182	+	1.69955i
$792$	−21.0915	+	10.7466i	−0.749452	+	0.381865i
$793$	−16.9798	+	16.9798i	−0.602971	+	0.602971i
$794$	4.73742	−	0.750334i	0.168125	−	0.0266284i
$795$	−0.0404497	−	0.124491i	−0.00143460	−	0.00441526i
$796$	4.12105	−	26.0193i	0.146067	−	0.922229i
$797$	14.2797	−	43.9483i	0.505812	−	1.55673i	−0.293590	−	0.955931i	$-0.594850\pi$
$797$	14.2797	−	43.9483i	0.505812	−	1.55673i	0.799402	−	0.600797i	$-0.205150\pi$
$798$	−0.551194	−	0.280847i	−0.0195121	−	0.00994189i
$799$	21.3758	−	6.94543i	0.756223	−	0.245712i
$800$	−24.9821	+	8.11717i	−0.883250	+	0.286985i
$801$	37.6917	+	19.2049i	1.33177	+	0.678571i
$802$	4.83739	−	14.8880i	0.170814	−	0.525712i
$803$	−3.15905	+	19.9455i	−0.111480	+	0.703860i
$804$	−0.223807	−	0.688807i	−0.00789306	−	0.0242923i
$805$	−1.98293	+	0.314066i	−0.0698892	+	0.0110694i
$806$	7.29091	−	7.29091i	0.256811	−	0.256811i
$807$	0.0301160	−	0.0153449i	0.00106014	−	0.000540166i
$808$	−4.78473	−	30.2096i	−0.168326	−	1.06277i
$809$	0.358629	+	0.0568012i	0.0126087	+	0.00199703i	0.162736	−	0.986670i	$-0.447968\pi$
$809$	0.358629	+	0.0568012i	0.0126087	+	0.00199703i	−0.150127	+	0.988667i	$0.547968\pi$
$810$	3.82684	−	2.78036i	0.134461	−	0.0976918i
$811$			22.6805i			0.796419i	0.917295	+	0.398209i	$0.130368\pi$
$811$			22.6805i			0.796419i	−0.917295	+	0.398209i	$0.869632\pi$
$812$	−24.6083	−	33.8704i	−0.863582	−	1.18862i
$813$	0.0767210	−	0.150573i	0.00269072	−	0.00528084i
$814$	−4.47519	−	8.78305i	−0.156855	−	0.307846i
$815$	0.389779	−	0.536484i	0.0136534	−	0.0187922i
$816$	0.101540	+	0.0737730i	0.00355461	+	0.00258257i
$817$	−33.7026	−	33.7026i	−1.17910	−	1.17910i
$818$	2.72209	+	0.884459i	0.0951755	+	0.0309244i
$819$	−18.8747			−0.659535
$820$	−4.43074	−	5.04639i	−0.154728	−	0.176227i
$821$	−12.5246			−0.437111			−0.218556	−	0.975824i	$-0.570135\pi$
$821$	−12.5246			−0.437111			−0.218556	+	0.975824i	$0.570135\pi$
$822$	−0.0100932	−	0.00327948i	−0.000352041	−	0.000114385i
$823$	−21.7847	−	21.7847i	−0.759365	−	0.759365i	0.216842	−	0.976207i	$-0.430425\pi$
$823$	−21.7847	−	21.7847i	−0.759365	−	0.759365i	−0.976207	+	0.216842i	$0.930425\pi$
$824$	31.6200	+	22.9733i	1.10154	+	0.800312i
$825$	−0.501534	+	0.690302i	−0.0174612	+	0.0240332i
$826$	4.64932	+	9.12480i	0.161771	+	0.317493i
$827$	−5.75807	+	11.3008i	−0.200228	+	0.392969i	−0.969186	−	0.246330i	$-0.920775\pi$
$827$	−5.75807	+	11.3008i	−0.200228	+	0.392969i	0.768958	+	0.639299i	$0.220775\pi$
$828$	2.29503	+	3.15884i	0.0797579	+	0.109777i
$829$			47.8117i			1.66057i	0.557341	+	0.830284i	$0.311822\pi$
$829$			47.8117i			1.66057i	−0.557341	+	0.830284i	$0.688178\pi$
$830$	−3.34505	+	2.43032i	−0.116108	+	0.0843576i
$831$	1.28569	+	0.203633i	0.0446000	+	0.00706394i
$832$	−0.690846	−	4.36183i	−0.0239508	−	0.151219i
$833$	−4.88051	+	2.48675i	−0.169100	+	0.0861606i
$834$	0.0749052	−	0.0749052i	0.00259376	−	0.00259376i
$835$	12.0599	−	1.91011i	0.417351	−	0.0661020i
$836$	−6.15807	−	18.9526i	−0.212981	−	0.655489i
$837$	−0.400877	+	2.53104i	−0.0138563	+	0.0874856i
$838$	−3.36499	+	10.3564i	−0.116242	+	0.357755i
$839$	−5.31936	−	2.71035i	−0.183645	−	0.0935717i	0.359751	−	0.933048i	$-0.382862\pi$
$839$	−5.31936	−	2.71035i	−0.183645	−	0.0935717i	−0.543396	+	0.839477i	$0.682862\pi$
$840$	−0.333005	+	0.108200i	−0.0114898	+	0.00373325i
$841$	−52.0596	+	16.9152i	−1.79516	+	0.583282i
$842$	−7.28344	−	3.71110i	−0.251004	−	0.127893i
$843$	0.0339113	−	0.104368i	0.00116797	−	0.00359463i
$844$	3.08448	−	19.4746i	0.106172	−	0.670345i
$845$	−1.98772	−	6.11757i	−0.0683796	−	0.210451i
$846$	25.1073	−	3.97661i	0.863207	−	0.136719i
$847$	2.96961	−	2.96961i	0.102037	−	0.102037i
$848$	−2.79433	+	1.42378i	−0.0959577	+	0.0488929i
$849$	−0.0356133	−	0.224854i	−0.00122225	−	0.00771695i
$850$	6.33170	+	1.00284i	0.217176	+	0.0343972i
$851$	−3.11693	+	2.26458i	−0.106847	+	0.0776288i
$852$			0.0894458i			0.00306436i
$853$	−3.50643	−	4.82618i	−0.120058	−	0.165245i	0.744758	−	0.667335i	$-0.232565\pi$
$853$	−3.50643	−	4.82618i	−0.120058	−	0.165245i	−0.864816	+	0.502089i	$0.832565\pi$
$854$	−12.4771	+	24.4878i	−0.426959	+	0.837955i
$855$	4.28913	+	8.41790i	0.146685	+	0.287886i
$856$	−1.66681	+	2.29417i	−0.0569704	+	0.0784130i
$857$	6.99504	+	5.08219i	0.238946	+	0.173604i	0.700814	−	0.713344i	$-0.252820\pi$
$857$	6.99504	+	5.08219i	0.238946	+	0.173604i	−0.461868	+	0.886949i	$0.652820\pi$
$858$	−0.198742	−	0.198742i	−0.00678494	−	0.00678494i
$859$	34.4964	+	11.2086i	1.17700	+	0.382432i	0.831253	−	0.555895i	$-0.187624\pi$
$859$	34.4964	+	11.2086i	1.17700	+	0.382432i	0.345751	+	0.938326i	$0.387624\pi$
$860$	−11.3852			−0.388231
$861$	0.810298	+	0.922887i	0.0276149	+	0.0314519i
$862$	19.4452			0.662305
$863$	−32.6565	−	10.6107i	−1.11164	−	0.361193i	−0.305068	−	0.952331i	$-0.598679\pi$
$863$	−32.6565	−	10.6107i	−1.11164	−	0.361193i	−0.806571	+	0.591137i	$0.798679\pi$
$864$	1.52059	+	1.52059i	0.0517317	+	0.0517317i
$865$	−7.05500	−	5.12576i	−0.239877	−	0.174281i
$866$	0.201899	−	0.277891i	0.00686082	−	0.00944311i
$867$	0.367244	+	0.720757i	0.0124723	+	0.0244782i
$868$	−14.4987	+	28.4554i	−0.492119	+	0.965839i
$869$	−11.4537	−	15.7646i	−0.388539	−	0.534778i
$870$			0.295562i			0.0100205i
$871$	−13.1776	+	9.57406i	−0.446505	+	0.324405i
$872$	−14.8649	−	2.35436i	−0.503388	−	0.0797288i
$873$	−3.00896	−	18.9978i	−0.101838	−	0.642979i
$874$	2.56437	−	1.30661i	0.0867412	−	0.0441969i
$875$	15.0885	−	15.0885i	0.510085	−	0.510085i
$876$	0.573780	−	0.0908778i	0.0193862	−	0.00307048i
$877$	−13.8957	−	42.7666i	−0.469225	−	1.44413i	−0.853591	−	0.520944i	$-0.825580\pi$
$877$	−13.8957	−	42.7666i	−0.469225	−	1.44413i	0.384366	−	0.923181i	$-0.374420\pi$
$878$	2.24549	−	14.1775i	0.0757815	−	0.478466i
$879$	0.263028	−	0.809517i	0.00887171	−	0.0273043i
$880$	−2.09498	−	1.06745i	−0.0706218	−	0.0359836i
$881$	26.6642	−	8.66372i	0.898339	−	0.291888i	0.176788	−	0.984249i	$-0.443429\pi$
$881$	26.6642	−	8.66372i	0.898339	−	0.291888i	0.721551	+	0.692361i	$0.243429\pi$
$882$	−5.89189	+	1.91439i	−0.198390	+	0.0644609i
$883$	34.0612	+	17.3551i	1.14625	+	0.584044i	0.920733	−	0.390194i	$-0.127592\pi$
$883$	34.0612	+	17.3551i	1.14625	+	0.584044i	0.225519	+	0.974239i	$0.427592\pi$
$884$	1.76593	−	5.43496i	0.0593945	−	0.182798i
$885$	−0.0306074	+	0.193248i	−0.00102886	+	0.00649595i
$886$	1.69087	+	5.20396i	0.0568059	+	0.174830i
$887$	15.7052	−	2.48746i	0.527329	−	0.0835207i	0.112907	−	0.993606i	$-0.463984\pi$
$887$	15.7052	−	2.48746i	0.527329	−	0.0835207i	0.414422	+	0.910085i	$0.363984\pi$
$888$	−0.475128	+	0.475128i	−0.0159443	+	0.0159443i
$889$	−12.1031	+	6.16682i	−0.405923	+	0.206828i
$890$	−1.16517	−	7.35659i	−0.0390566	−	0.246593i
$891$	−27.5238	−	4.35935i	−0.922083	−	0.146044i
$892$	8.96710	−	6.51498i	0.300241	−	0.218138i
$893$			50.7080i			1.69688i
$894$	−0.221827	−	0.305318i	−0.00741900	−	0.0102114i
$895$	0.697278	−	1.36849i	0.0233074	−	0.0457434i
$896$	14.3681	+	28.1990i	0.480005	+	0.942062i
$897$	−0.0645696	+	0.0888724i	−0.00215592	+	0.00296736i
$898$	15.1797	+	11.0287i	0.506553	+	0.368032i
$899$	45.1681	+	45.1681i	1.50644	+	1.50644i
$900$	−18.6611	−	6.06335i	−0.622036	−	0.202112i
$901$	5.79374			0.193017
$902$	0.947666	−	14.5882i	0.0315538	−	0.485735i
$903$	2.08213			0.0692889
$904$	−37.3458	−	12.1344i	−1.24210	−	0.403584i
$905$	−2.85282	−	2.85282i	−0.0948310	−	0.0948310i
$906$	0.131797	+	0.0957564i	0.00437867	+	0.00318129i
$907$	25.3442	−	34.8834i	0.841542	−	1.15828i	−0.144122	−	0.989560i	$-0.546036\pi$
$907$	25.3442	−	34.8834i	0.841542	−	1.15828i	0.985664	−	0.168723i	$-0.0539643\pi$
$908$	14.3963	+	28.2543i	0.477757	+	0.937652i
$909$	16.3674	−	32.1228i	0.542872	−	1.06545i
$910$	1.95340	+	2.68862i	0.0647544	+	0.0891268i
$911$			26.3499i			0.873010i	0.899702	+	0.436505i	$0.143784\pi$
$911$			26.3499i			0.873010i	−0.899702	+	0.436505i	$0.856216\pi$
$912$	−0.229085	+	0.166440i	−0.00758576	+	0.00551138i
$913$	24.0586	+	3.81051i	0.796225	+	0.126110i
$914$	4.05741	+	25.6175i	0.134207	+	0.847352i
$915$	−0.467844	+	0.238379i	−0.0154665	+	0.00788055i
$916$	3.05864	−	3.05864i	0.101060	−	0.101060i
$917$	51.2854	−	8.12282i	1.69359	−	0.268239i
$918$	−0.162177	−	0.499129i	−0.00535263	−	0.0164737i
$919$	4.74106	−	29.9339i	0.156393	−	0.987427i	−0.777242	−	0.629202i	$-0.783382\pi$
$919$	4.74106	−	29.9339i	0.156393	−	0.987427i	0.933635	−	0.358226i	$-0.116618\pi$
$920$	0.503389	−	1.54927i	0.0165963	−	0.0510780i
$921$	−1.19299	−	0.607860i	−0.0393105	−	0.0200297i
$922$	19.9042	−	6.46727i	0.655510	−	0.212988i
$923$	1.91317	−	0.621625i	0.0629726	−	0.0204610i
$924$	0.775662	+	0.395220i	0.0255174	+	0.0130018i
$925$	5.98289	−	18.4135i	0.196716	−	0.605431i
$926$	1.47531	−	9.31472i	0.0484816	−	0.306101i
$927$	14.2362	+	43.8145i	0.467578	+	1.43906i
$928$	52.9439	−	8.38549i	1.73797	−	0.275267i
$929$	−14.3945	+	14.3945i	−0.472267	+	0.472267i	−0.902647	−	0.430381i	$-0.858379\pi$
$929$	−14.3945	+	14.3945i	−0.472267	+	0.472267i	0.430381	+	0.902647i	$0.358379\pi$
$930$	0.200886	−	0.102357i	0.00658732	−	0.00335641i
$931$	−1.93320	−	12.2058i	−0.0633581	−	0.400027i
$932$	25.0990	+	3.97529i	0.822145	+	0.130215i
$933$	−0.789998	+	0.573967i	−0.0258634	+	0.0187908i
$934$			21.6428i			0.708174i
$935$	2.55317	+	3.51414i	0.0834976	+	0.114925i
$936$	6.95281	−	13.6457i	0.227260	−	0.446022i
$937$	−16.9622	−	33.2901i	−0.554130	−	1.08754i	−0.982902	−	0.184129i	$-0.941054\pi$
$937$	−16.9622	−	33.2901i	−0.554130	−	1.08754i	0.428772	−	0.903413i	$-0.358946\pi$
$938$	−10.9576	+	15.0819i	−0.357779	+	0.492441i
$939$	−0.0406789	−	0.0295549i	−0.00132750	−	0.000964488i
$940$	8.56492	+	8.56492i	0.279357	+	0.279357i
$941$	−23.3267	−	7.57929i	−0.760427	−	0.247078i	−0.0969652	−	0.995288i	$-0.530914\pi$
$941$	−23.3267	−	7.57929i	−0.760427	−	0.247078i	−0.663462	+	0.748210i	$0.730914\pi$
$942$	0.619754			0.0201927
$943$	−5.68948	+	0.526117i	−0.185275	+	0.0171327i
$944$	4.68768			0.152571
$945$	−0.785525	−	0.255233i	−0.0255531	−	0.00830272i
$946$	−17.5253	−	17.5253i	−0.569796	−	0.569796i
$947$	−46.3059	−	33.6432i	−1.50474	−	1.09326i	−0.968446	−	0.249224i	$-0.919825\pi$
$947$	−46.3059	−	33.6432i	−1.50474	−	1.09326i	−0.536292	−	0.844032i	$-0.680175\pi$
$948$	−0.329493	+	0.453508i	−0.0107014	+	0.0147293i
$949$	−5.93142	−	11.6411i	−0.192542	−	0.377885i
$950$	−6.56610	+	12.8867i	−0.213032	+	0.418099i
$951$	1.01812	+	1.40133i	0.0330149	+	0.0454411i
$952$		−	15.4978i		−	0.502287i
$953$	20.8828	−	15.1723i	0.676461	−	0.491478i	−0.195721	−	0.980660i	$-0.562705\pi$
$953$	20.8828	−	15.1723i	0.676461	−	0.491478i	0.872182	+	0.489182i	$0.162705\pi$
$954$	6.47206	+	1.02507i	0.209541	+	0.0331880i
$955$	1.47408	+	9.30696i	0.0477000	+	0.301166i
$956$	7.72953	−	3.93839i	0.249991	−	0.127377i
$957$	1.23123	−	1.23123i	0.0398001	−	0.0398001i
$958$	−19.3848	+	3.07025i	−0.626294	+	0.0991953i
$959$	−0.228443	−	0.703076i	−0.00737682	−	0.0227035i
$960$	0.0151061	−	0.0953765i	0.000487549	−	0.00307826i
$961$	5.47787	−	16.8592i	0.176706	−	0.543844i
$962$	5.68242	+	2.89534i	0.183209	+	0.0933494i
$963$	−3.17893	+	1.03290i	−0.102440	+	0.0332846i
$964$	−12.1979	+	3.96335i	−0.392869	+	0.127651i
$965$	−10.6073	−	5.40469i	−0.341461	−	0.173983i
$966$	−0.0388519	+	0.119574i	−0.00125004	+	0.00384723i
$967$	−7.85597	+	49.6006i	−0.252631	+	1.59505i	0.456336	+	0.889807i	$0.349161\pi$
$967$	−7.85597	+	49.6006i	−0.252631	+	1.59505i	−0.708967	+	0.705241i	$0.750839\pi$
$968$	1.05300	+	3.24081i	0.0338448	+	0.104164i
$969$	0.516679	−	0.0818340i	0.0165981	−	0.00262889i
$970$	−2.39475	+	2.39475i	−0.0768908	+	0.0768908i
$971$	−21.9048	+	11.1611i	−0.702960	+	0.358176i	−0.768655	−	0.639664i	$-0.779074\pi$
$971$	−21.9048	+	11.1611i	−0.702960	+	0.358176i	0.0656949	+	0.997840i	$0.479074\pi$
$972$	0.377008	+	2.38033i	0.0120925	+	0.0763493i
$973$	7.28820	+	1.15434i	0.233649	+	0.0370064i
$974$	6.89771	−	5.01148i	0.221017	−	0.160578i
$975$		−	0.552038i		−	0.0176794i
$976$	7.39440	+	10.1775i	0.236689	+	0.325774i
$977$	−16.7259	+	32.8265i	−0.535110	+	1.05021i	0.452275	+	0.891878i	$0.350612\pi$
$977$	−16.7259	+	32.8265i	−0.535110	+	1.05021i	−0.987386	+	0.158334i	$0.949388\pi$
$978$	−0.0188533	−	0.0370018i	−0.000602863	−	0.00118319i
$979$	−25.7918	+	35.4994i	−0.824310	+	1.13457i
$980$	−2.38816	−	1.73510i	−0.0762870	−	0.0554258i
$981$	−12.5439	−	12.5439i	−0.400497	−	0.400497i
$982$	−18.7831	−	6.10301i	−0.599394	−	0.194755i
$983$	24.1327			0.769713			0.384857	−	0.922976i	$-0.374251\pi$
$983$	24.1327			0.769713			0.384857	+	0.922976i	$0.374251\pi$
$984$	−0.965698	+	0.245852i	−0.0307853	+	0.00783749i
$985$	10.3997			0.331361
$986$	−12.4417	−	4.04256i	−0.396225	−	0.128741i
$987$	−1.56636	−	1.56636i	−0.0498578	−	0.0498578i
$988$	10.4306	+	7.57825i	0.331841	+	0.241096i
$989$	−5.69381	+	7.83686i	−0.181053	+	0.249198i
$990$	2.23034	+	4.37729i	0.0708849	+	0.139120i
$991$	−3.15702	+	6.19601i	−0.100286	+	0.196823i	−0.935698	−	0.352802i	$-0.885229\pi$
$991$	−3.15702	+	6.19601i	−0.100286	+	0.196823i	0.835412	+	0.549624i	$0.185229\pi$
$992$	−24.0345	−	33.0807i	−0.763097	−	1.05031i
$993$			1.88290i			0.0597520i
$994$	1.86262	−	1.35327i	0.0590788	−	0.0429232i
$995$	−12.7954	−	2.02659i	−0.405642	−	0.0642473i
$996$	−0.109619	−	0.692106i	−0.00347341	−	0.0219302i
$997$	−29.1900	+	14.8731i	−0.924458	+	0.471035i	−0.850351	−	0.526216i	$-0.823610\pi$
$997$	−29.1900	+	14.8731i	−0.924458	+	0.471035i	−0.0741065	+	0.997250i	$0.523610\pi$
$998$	6.67857	−	6.67857i	0.211406	−	0.211406i
$999$	−1.56551	+	0.247952i	−0.0495304	+	0.00784485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.21.3	yes	24
3.2	odd	2		369.2.u.a.226.1		24
4.3	odd	2		656.2.bs.d.513.2		24
41.2	even	20	inner	41.2.g.a.2.3	✓	24
41.17	odd	40		1681.2.a.m.1.9		24
41.24	odd	40		1681.2.a.m.1.10		24
123.2	odd	20		369.2.u.a.289.1		24
164.43	odd	20		656.2.bs.d.289.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.3	✓	24	41.2	even	20	inner
41.2.g.a.21.3	yes	24	1.1	even	1	trivial
369.2.u.a.226.1		24	3.2	odd	2
369.2.u.a.289.1		24	123.2	odd	20
656.2.bs.d.289.2		24	164.43	odd	20
656.2.bs.d.513.2		24	4.3	odd	2
1681.2.a.m.1.9		24	41.17	odd	40
1681.2.a.m.1.10		24	41.24	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)

\(f(q)\)	\(=\)	\(q+(0.698642 + 0.227002i) q^{2} +(0.0432913 + 0.0432913i) q^{3} +(-1.18146 - 0.858384i) q^{4} +(-0.422124 + 0.581004i) q^{5} +(0.0204179 + 0.0400723i) q^{6} +(-1.42228 + 2.79137i) q^{7} +(-1.49413 - 2.05650i) q^{8} -2.99625i q^{9} +O(q^{10})\)	\(q+(0.698642 + 0.227002i) q^{2} +(0.0432913 + 0.0432913i) q^{3} +(-1.18146 - 0.858384i) q^{4} +(-0.422124 + 0.581004i) q^{5} +(0.0204179 + 0.0400723i) q^{6} +(-1.42228 + 2.79137i) q^{7} +(-1.49413 - 2.05650i) q^{8} -2.99625i q^{9} +(-0.426803 + 0.310091i) q^{10} +(3.06970 + 0.486193i) q^{11} +(-0.0139866 - 0.0883076i) q^{12} +(-1.79162 + 0.912875i) q^{13} +(-1.62731 + 1.62731i) q^{14} +(-0.0434267 + 0.00687812i) q^{15} +(0.325524 + 1.00186i) q^{16} +(0.304435 - 1.92213i) q^{17} +(0.680157 - 2.09331i) q^{18} +(3.91204 + 1.99329i) q^{19} +(0.997449 - 0.324091i) q^{20} +(-0.182414 + 0.0592700i) q^{21} +(2.03426 + 1.03651i) q^{22} +(0.275748 - 0.848664i) q^{23} +(0.0243455 - 0.153711i) q^{24} +(1.38571 + 4.26477i) q^{25} +(-1.45892 + 0.231071i) q^{26} +(0.259585 - 0.259585i) q^{27} +(4.07644 - 2.07705i) q^{28} +(-1.43151 - 9.03822i) q^{29} +(-0.0319011 - 0.00505263i) q^{30} +(-5.64731 + 4.10301i) q^{31} +5.85778i q^{32} +(0.111844 + 0.153939i) q^{33} +(0.649020 - 1.27377i) q^{34} +(-1.02142 - 2.00465i) q^{35} +(-2.57193 + 3.53996i) q^{36} +(-3.49299 - 2.53781i) q^{37} +(2.28064 + 2.28064i) q^{38} +(-0.117081 - 0.0380419i) q^{39} +1.82554 q^{40} +(-2.53101 - 5.88167i) q^{41} -0.140897 q^{42} +(-10.3243 - 3.35457i) q^{43} +(-3.20940 - 3.20940i) q^{44} +(1.74083 + 1.26479i) q^{45} +(0.385298 - 0.530317i) q^{46} +(5.24325 + 10.2905i) q^{47} +(-0.0292795 + 0.0574642i) q^{48} +(-1.65440 - 2.27709i) q^{49} +3.29411i q^{50} +(0.0963909 - 0.0700321i) q^{51} +(2.90033 + 0.459367i) q^{52} +(0.465724 + 2.94046i) q^{53} +(0.240284 - 0.122431i) q^{54} +(-1.57828 + 1.57828i) q^{55} +(7.86552 - 1.24578i) q^{56} +(0.0830655 + 0.255649i) q^{57} +(1.05158 - 6.63944i) q^{58} +(1.37512 - 4.23218i) q^{59} +(0.0572112 + 0.0291505i) q^{60} +(11.3577 - 3.69033i) q^{61} +(-4.87684 + 1.58458i) q^{62} +(8.36366 + 4.26150i) q^{63} +(-0.678682 + 2.08877i) q^{64} +(0.225901 - 1.42628i) q^{65} +(0.0431939 + 0.132937i) q^{66} +(8.00079 - 1.26720i) q^{67} +(-2.00960 + 2.00960i) q^{68} +(0.0486772 - 0.0248023i) q^{69} +(-0.258547 - 1.63240i) q^{70} +(-0.988102 - 0.156500i) q^{71} +(-6.16179 + 4.47680i) q^{72} +6.49752i q^{73} +(-1.86426 - 2.56593i) q^{74} +(-0.124638 + 0.244616i) q^{75} +(-2.91093 - 5.71303i) q^{76} +(-5.72311 + 7.87719i) q^{77} +(-0.0731620 - 0.0531553i) q^{78} +(-4.43337 - 4.43337i) q^{79} +(-0.719497 - 0.233779i) q^{80} -8.96628 q^{81} +(-0.433113 - 4.68372i) q^{82} +7.83744 q^{83} +(0.266392 + 0.0865561i) q^{84} +(0.988256 + 0.988256i) q^{85} +(-6.45150 - 4.68729i) q^{86} +(0.329304 - 0.453248i) q^{87} +(-3.58669 - 7.03928i) q^{88} +(-6.40964 + 12.5796i) q^{89} +(0.929109 + 1.27881i) q^{90} -6.29943i q^{91} +(-1.05426 + 0.765968i) q^{92} +(-0.422104 - 0.0668547i) q^{93} +(1.32719 + 8.37958i) q^{94} +(-2.80948 + 1.43150i) q^{95} +(-0.253591 + 0.253591i) q^{96} +(6.34053 - 1.00424i) q^{97} +(-0.638929 - 1.96642i) q^{98} +(1.45676 - 9.19761i) 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

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