LMFDB - Embedded newform 41.2.g.a.20.3

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			20.3
Character	$\chi$	$=$	41.20
Dual form			41.2.g.a.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14785 + 0.372958i) q^{2} +(-1.55151 + 1.55151i) q^{3} +(-0.439578 - 0.319372i) q^{4} +(1.49595 - 2.05900i) q^{5} +(-2.35955 + 1.20225i) q^{6} +(-1.01547 - 0.517405i) q^{7} +(-1.80427 - 2.48337i) q^{8} -1.81438i q^{9} +O(q^{10})$	\(q+(1.14785 + 0.372958i) q^{2} +(-1.55151 + 1.55151i) q^{3} +(-0.439578 - 0.319372i) q^{4} +(1.49595 - 2.05900i) q^{5} +(-2.35955 + 1.20225i) q^{6} +(-1.01547 - 0.517405i) q^{7} +(-1.80427 - 2.48337i) q^{8} -1.81438i q^{9} +(2.48504 - 1.80549i) q^{10} +(-0.807883 + 5.10077i) q^{11} +(1.17752 - 0.186501i) q^{12} +(1.17315 + 2.30243i) q^{13} +(-0.972629 - 0.972629i) q^{14} +(0.873576 + 5.51554i) q^{15} +(-0.809030 - 2.48994i) q^{16} +(-3.05576 - 0.483986i) q^{17} +(0.676690 - 2.08264i) q^{18} +(3.74044 - 7.34102i) q^{19} +(-1.31517 + 0.427326i) q^{20} +(2.37827 - 0.772746i) q^{21} +(-2.82970 + 5.55360i) q^{22} +(-1.17869 + 3.62763i) q^{23} +(6.65233 + 1.05363i) q^{24} +(-0.456519 - 1.40502i) q^{25} +(0.487884 + 3.08038i) q^{26} +(-1.83950 - 1.83950i) q^{27} +(0.281132 + 0.551752i) q^{28} +(5.72573 - 0.906866i) q^{29} +(-1.05433 + 6.65681i) q^{30} +(3.65641 - 2.65654i) q^{31} +2.97943i q^{32} +(-6.66047 - 9.16735i) q^{33} +(-3.32705 - 1.69521i) q^{34} +(-2.58442 + 1.31683i) q^{35} +(-0.579464 + 0.797564i) q^{36} +(0.584132 + 0.424397i) q^{37} +(7.03134 - 7.03134i) q^{38} +(-5.39241 - 1.75210i) q^{39} -7.81235 q^{40} +(-5.78336 + 2.74822i) q^{41} +3.01809 q^{42} +(1.75698 + 0.570876i) q^{43} +(1.98417 - 1.98417i) q^{44} +(-3.73581 - 2.71423i) q^{45} +(-2.70591 + 3.72436i) q^{46} +(-3.15704 + 1.60859i) q^{47} +(5.11839 + 2.60795i) q^{48} +(-3.35104 - 4.61230i) q^{49} -1.78301i q^{50} +(5.49197 - 3.99015i) q^{51} +(0.219643 - 1.38677i) q^{52} +(-5.52741 + 0.875456i) q^{53} +(-1.42541 - 2.79752i) q^{54} +(9.29392 + 9.29392i) q^{55} +(0.547268 + 3.45532i) q^{56} +(5.58635 + 17.1930i) q^{57} +(6.91048 + 1.09451i) q^{58} +(0.242763 - 0.747149i) q^{59} +(1.37751 - 2.70351i) q^{60} +(6.70623 - 2.17898i) q^{61} +(5.18778 - 1.68561i) q^{62} +(-0.938773 + 1.84244i) q^{63} +(-2.72926 + 8.39980i) q^{64} +(6.49567 + 1.02881i) q^{65} +(-4.22616 - 13.0068i) q^{66} +(-0.835907 - 5.27771i) q^{67} +(1.18868 + 1.18868i) q^{68} +(-3.79956 - 7.45706i) q^{69} +(-3.45764 + 0.547637i) q^{70} +(0.708805 - 4.47522i) q^{71} +(-4.50579 + 3.27365i) q^{72} -0.149836i q^{73} +(0.512213 + 0.705000i) q^{74} +(2.88820 + 1.47161i) q^{75} +(-3.98873 + 2.03236i) q^{76} +(3.45954 - 4.76165i) q^{77} +(-5.53620 - 4.02229i) q^{78} +(-11.4389 + 11.4389i) q^{79} +(-6.33704 - 2.05903i) q^{80} +11.1512 q^{81} +(-7.66339 + 0.997584i) q^{82} +4.27258 q^{83} +(-1.29223 - 0.419871i) q^{84} +(-5.56779 + 5.56779i) q^{85} +(1.80383 + 1.31056i) q^{86} +(-7.47653 + 10.2906i) q^{87} +(14.1247 - 7.19691i) q^{88} +(-1.51781 - 0.773362i) q^{89} +(-3.27585 - 4.50882i) q^{90} -2.94503i q^{91} +(1.67669 - 1.21819i) q^{92} +(-1.55132 + 9.79463i) q^{93} +(-4.22374 + 0.668975i) q^{94} +(-9.51963 - 18.6833i) q^{95} +(-4.62262 - 4.62262i) q^{96} +(0.687542 + 4.34097i) q^{97} +(-2.12628 - 6.54402i) q^{98} +(9.25476 + 1.46581i) 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 $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	1.14785	+	0.372958i	0.811651	+	0.263721i	0.685297	−	0.728264i	$-0.259673\pi$
$2$	1.14785	+	0.372958i	0.811651	+	0.263721i	0.126354	+	0.991985i	$0.459673\pi$
$3$	−1.55151	+	1.55151i	−0.895766	+	0.895766i	−0.995058	−	0.0992919i	$-0.968342\pi$
$3$	−1.55151	+	1.55151i	−0.895766	+	0.895766i	0.0992919	+	0.995058i	$0.468342\pi$
$4$	−0.439578	−	0.319372i	−0.219789	−	0.159686i
$5$	1.49595	−	2.05900i	0.669008	−	0.920811i	−0.330729	−	0.943726i	$-0.607295\pi$
$5$	1.49595	−	2.05900i	0.669008	−	0.920811i	0.999737	+	0.0229146i	$0.00729460\pi$
$6$	−2.35955	+	1.20225i	−0.963282	+	0.490817i
$7$	−1.01547	−	0.517405i	−0.383810	−	0.195561i	0.251431	−	0.967875i	$-0.419099\pi$
$7$	−1.01547	−	0.517405i	−0.383810	−	0.195561i	−0.635240	+	0.772314i	$0.719099\pi$
$8$	−1.80427	−	2.48337i	−0.637907	−	0.878004i
$9$		−	1.81438i		−	0.604795i
$10$	2.48504	−	1.80549i	0.785839	−	0.570945i
$11$	−0.807883	+	5.10077i	−0.243586	+	1.53794i	0.498057	+	0.867144i	$0.334047\pi$
$11$	−0.807883	+	5.10077i	−0.243586	+	1.53794i	−0.741642	+	0.670795i	$0.765953\pi$
$12$	1.17752	−	0.186501i	0.339921	−	0.0538382i
$13$	1.17315	+	2.30243i	0.325373	+	0.638580i	0.994520	−	0.104550i	$-0.0333403\pi$
$13$	1.17315	+	2.30243i	0.325373	+	0.638580i	−0.669147	+	0.743130i	$0.733340\pi$
$14$	−0.972629	−	0.972629i	−0.259946	−	0.259946i
$15$	0.873576	+	5.51554i	0.225556	+	1.42411i
$16$	−0.809030	−	2.48994i	−0.202257	−	0.622484i
$17$	−3.05576	−	0.483986i	−0.741132	−	0.117384i	−0.225559	−	0.974230i	$-0.572421\pi$
$17$	−3.05576	−	0.483986i	−0.741132	−	0.117384i	−0.515573	+	0.856846i	$0.672421\pi$
$18$	0.676690	−	2.08264i	0.159497	−	0.490882i
$19$	3.74044	−	7.34102i	0.858115	−	1.68415i	0.137842	−	0.990454i	$-0.455983\pi$
$19$	3.74044	−	7.34102i	0.858115	−	1.68415i	0.720273	−	0.693691i	$-0.244017\pi$
$20$	−1.31517	+	0.427326i	−0.294082	+	0.0955529i
$21$	2.37827	−	0.772746i	0.518981	−	0.168627i
$22$	−2.82970	+	5.55360i	−0.603294	+	1.18403i
$23$	−1.17869	+	3.62763i	−0.245773	+	0.756413i	0.749735	+	0.661738i	$0.230181\pi$
$23$	−1.17869	+	3.62763i	−0.245773	+	0.756413i	−0.995508	+	0.0946746i	$0.969819\pi$
$24$	6.65233	+	1.05363i	1.35790	+	0.215071i
$25$	−0.456519	−	1.40502i	−0.0913038	−	0.281004i
$26$	0.487884	+	3.08038i	0.0956819	+	0.604112i
$27$	−1.83950	−	1.83950i	−0.354011	−	0.354011i
$28$	0.281132	+	0.551752i	0.0531289	+	0.104271i
$29$	5.72573	−	0.906866i	1.06324	−	0.168401i	0.399780	−	0.916611i	$-0.369087\pi$
$29$	5.72573	−	0.906866i	1.06324	−	0.168401i	0.663461	+	0.748211i	$0.269087\pi$
$30$	−1.05433	+	6.65681i	−0.192494	+	1.21536i
$31$	3.65641	−	2.65654i	0.656711	−	0.477129i	−0.208840	−	0.977950i	$-0.566969\pi$
$31$	3.65641	−	2.65654i	0.656711	−	0.477129i	0.865551	+	0.500821i	$0.166969\pi$
$32$			2.97943i			0.526693i
$33$	−6.66047	−	9.16735i	−1.15944	−	1.59583i
$34$	−3.32705	−	1.69521i	−0.570584	−	0.290727i
$35$	−2.58442	+	1.31683i	−0.436847	+	0.222584i
$36$	−0.579464	+	0.797564i	−0.0965774	+	0.132927i
$37$	0.584132	+	0.424397i	0.0960308	+	0.0697704i	0.634765	−	0.772706i	$-0.281097\pi$
$37$	0.584132	+	0.424397i	0.0960308	+	0.0697704i	−0.538734	+	0.842476i	$0.681097\pi$
$38$	7.03134	−	7.03134i	1.14063	−	1.14063i
$39$	−5.39241	−	1.75210i	−0.863476	−	0.280561i
$40$	−7.81235			−1.23524
$41$	−5.78336	+	2.74822i	−0.903210	+	0.429200i
$41$	−5.78336	+	2.74822i	−0.903210	+	0.429200i
$42$	3.01809			0.465702
$43$	1.75698	+	0.570876i	0.267936	+	0.0870578i	0.439904	−	0.898045i	$-0.355012\pi$
$43$	1.75698	+	0.570876i	0.267936	+	0.0870578i	−0.171968	+	0.985103i	$0.555012\pi$
$44$	1.98417	−	1.98417i	0.299125	−	0.299125i
$45$	−3.73581	−	2.71423i	−0.556902	−	0.404613i
$46$	−2.70591	+	3.72436i	−0.398964	+	0.549127i
$47$	−3.15704	+	1.60859i	−0.460502	+	0.234638i	−0.668821	−	0.743423i	$-0.733201\pi$
$47$	−3.15704	+	1.60859i	−0.460502	+	0.234638i	0.208319	+	0.978061i	$0.433201\pi$
$48$	5.11839	+	2.60795i	0.738776	+	0.376425i
$49$	−3.35104	−	4.61230i	−0.478719	−	0.658901i
$50$		−	1.78301i		−	0.252156i
$51$	5.49197	−	3.99015i	0.769029	−	0.558733i
$52$	0.219643	−	1.38677i	0.0304590	−	0.192310i
$53$	−5.52741	+	0.875456i	−0.759249	+	0.120253i	−0.524042	−	0.851692i	$-0.675577\pi$
$53$	−5.52741	+	0.875456i	−0.759249	+	0.120253i	−0.235206	+	0.971945i	$0.575577\pi$
$54$	−1.42541	−	2.79752i	−0.193973	−	0.380694i
$55$	9.29392	+	9.29392i	1.25319	+	1.25319i
$56$	0.547268	+	3.45532i	0.0731318	+	0.461736i
$57$	5.58635	+	17.1930i	0.739930	+	2.27727i
$58$	6.91048	+	1.09451i	0.907391	+	0.143717i
$59$	0.242763	−	0.747149i	0.0316051	−	0.0972705i	−0.934010	−	0.357248i	$-0.883715\pi$
$59$	0.242763	−	0.747149i	0.0316051	−	0.0972705i	0.965615	+	0.259977i	$0.0837151\pi$
$60$	1.37751	−	2.70351i	0.177835	−	0.349022i
$61$	6.70623	−	2.17898i	0.858644	−	0.278990i	0.153582	−	0.988136i	$-0.450919\pi$
$61$	6.70623	−	2.17898i	0.858644	−	0.278990i	0.705062	+	0.709145i	$0.250919\pi$
$62$	5.18778	−	1.68561i	0.658849	−	0.214073i
$63$	−0.938773	+	1.84244i	−0.118274	+	0.232126i
$64$	−2.72926	+	8.39980i	−0.341158	+	1.04997i
$65$	6.49567	+	1.02881i	0.805689	+	0.127609i
$66$	−4.22616	−	13.0068i	−0.520205	−	1.60103i
$67$	−0.835907	−	5.27771i	−0.102122	−	0.644774i	−0.984654	−	0.174521i	$-0.944162\pi$
$67$	−0.835907	−	5.27771i	−0.102122	−	0.644774i	0.882531	−	0.470254i	$-0.155838\pi$
$68$	1.18868	+	1.18868i	0.144148	+	0.144148i
$69$	−3.79956	−	7.45706i	−0.457414	−	0.897725i
$70$	−3.45764	+	0.547637i	−0.413267	+	0.0654551i
$71$	0.708805	−	4.47522i	0.0841197	−	0.531111i	−0.909260	−	0.416230i	$-0.863351\pi$
$71$	0.708805	−	4.47522i	0.0841197	−	0.531111i	0.993379	−	0.114881i	$-0.0366487\pi$
$72$	−4.50579	+	3.27365i	−0.531012	+	0.385803i
$73$		−	0.149836i		−	0.0175369i	−0.999962	−	0.00876846i	$-0.997209\pi$
$73$		−	0.149836i		−	0.0175369i	0.999962	−	0.00876846i	$-0.00279112\pi$
$74$	0.512213	+	0.705000i	0.0595435	+	0.0819546i
$75$	2.88820	+	1.47161i	0.333501	+	0.169927i
$76$	−3.98873	+	2.03236i	−0.457539	+	0.233128i
$77$	3.45954	−	4.76165i	0.394251	−	0.542641i
$78$	−5.53620	−	4.02229i	−0.626851	−	0.455434i
$79$	−11.4389	+	11.4389i	−1.28698	+	1.28698i	−0.350367	+	0.936613i	$0.613943\pi$
$79$	−11.4389	+	11.4389i	−1.28698	+	1.28698i	−0.936613	+	0.350367i	$0.886057\pi$
$80$	−6.33704	−	2.05903i	−0.708502	−	0.230206i
$81$	11.1512			1.23902
$82$	−7.66339	+	0.997584i	−0.846280	+	0.110165i
$83$	4.27258			0.468977			0.234488	−	0.972119i	$-0.424659\pi$
$83$	4.27258			0.468977			0.234488	+	0.972119i	$0.424659\pi$
$84$	−1.29223	−	0.419871i	−0.140994	−	0.0458117i
$85$	−5.56779	+	5.56779i	−0.603912	+	0.603912i
$86$	1.80383	+	1.31056i	0.194512	+	0.141321i
$87$	−7.47653	+	10.2906i	−0.801568	+	1.10326i
$88$	14.1247	−	7.19691i	1.50570	−	0.767193i
$89$	−1.51781	−	0.773362i	−0.160887	−	0.0819762i	0.371693	−	0.928356i	$-0.378777\pi$
$89$	−1.51781	−	0.773362i	−0.160887	−	0.0819762i	−0.532580	+	0.846380i	$0.678777\pi$
$90$	−3.27585	−	4.50882i	−0.345305	−	0.475271i
$91$		−	2.94503i		−	0.308723i
$92$	1.67669	−	1.21819i	0.174807	−	0.127005i
$93$	−1.55132	+	9.79463i	−0.160864	+	1.01566i
$94$	−4.22374	+	0.668975i	−0.435646	+	0.0689995i
$95$	−9.51963	−	18.6833i	−0.976694	−	1.91687i
$96$	−4.62262	−	4.62262i	−0.471794	−	0.471794i
$97$	0.687542	+	4.34097i	0.0698093	+	0.440758i	0.997693	+	0.0678885i	$0.0216262\pi$
$97$	0.687542	+	4.34097i	0.0698093	+	0.440758i	−0.927884	+	0.372870i	$0.878374\pi$
$98$	−2.12628	−	6.54402i	−0.214787	−	0.661046i
$99$	9.25476	+	1.46581i	0.930138	+	0.147319i
$100$	−0.248049	+	0.763417i	−0.0248049	+	0.0763417i
$101$	1.40554	−	2.75854i	0.139857	−	0.274485i	−0.810445	−	0.585815i	$-0.800775\pi$
$101$	1.40554	−	2.75854i	0.139857	−	0.274485i	0.950302	+	0.311330i	$0.100775\pi$
$102$	7.79210	−	2.53181i	0.771533	−	0.250686i
$103$	2.80356	−	0.910931i	0.276243	−	0.0897567i	−0.167619	−	0.985852i	$-0.553608\pi$
$103$	2.80356	−	0.910931i	0.276243	−	0.0897567i	0.443862	+	0.896095i	$0.353608\pi$
$104$	3.60111	−	7.06758i	0.353118	−	0.693033i
$105$	1.96669	−	6.05284i	0.191929	−	0.590696i
$106$	−6.67114	−	1.05660i	−0.647958	−	0.102626i
$107$	−1.04654	−	3.22093i	−0.101173	−	0.311379i	0.887640	−	0.460538i	$-0.152344\pi$
$107$	−1.04654	−	3.22093i	−0.101173	−	0.311379i	−0.988813	+	0.149159i	$0.952344\pi$
$108$	0.221119	+	1.39609i	0.0212771	+	0.134339i
$109$	9.65686	+	9.65686i	0.924960	+	0.924960i	0.997375	−	0.0724148i	$-0.0230705\pi$
$109$	9.65686	+	9.65686i	0.924960	+	0.924960i	−0.0724148	+	0.997375i	$0.523071\pi$
$110$	7.20175	+	14.1342i	0.686660	+	1.34765i
$111$	−1.56475	+	0.247832i	−0.148519	+	0.0235231i
$112$	−0.466765	+	2.94704i	−0.0441052	+	0.278469i
$113$	−10.7162	+	7.78581i	−1.00810	+	0.732427i	−0.963810	−	0.266592i	$-0.914102\pi$
$113$	−10.7162	+	7.78581i	−1.00810	+	0.732427i	−0.0442897	+	0.999019i	$0.514102\pi$
$114$			21.8184i			2.04348i
$115$	5.70602	+	7.85366i	0.532089	+	0.732358i
$116$	−2.80653	−	1.43000i	−0.260580	−	0.132772i
$117$	4.17750	−	2.12854i	0.386210	−	0.196784i
$118$	0.557310	−	0.767072i	0.0513046	−	0.0706147i
$119$	2.85261	+	2.07254i	0.261498	+	0.189989i
$120$	12.1210	−	12.1210i	1.10649	−	1.10649i
$121$	−14.9036	−	4.84246i	−1.35487	−	0.440223i
$122$	8.51039			0.770495
$123$	4.70906	−	13.2369i	0.424602	−	1.19353i
$124$	−2.45570			−0.220529
$125$	8.52661	+	2.77046i	0.762643	+	0.247798i
$126$	−1.76472	+	1.76472i	−0.157214	+	0.157214i
$127$	−10.9310	−	7.94181i	−0.969966	−	0.704721i	−0.0145221	−	0.999895i	$-0.504623\pi$
$127$	−10.9310	−	7.94181i	−0.969966	−	0.704721i	−0.955444	+	0.295173i	$0.904623\pi$
$128$	−2.76302	+	3.80298i	−0.244219	+	0.336139i
$129$	−3.61169	+	1.84025i	−0.317992	+	0.162025i
$130$	7.07233	+	3.60353i	0.620285	+	0.316051i
$131$	6.01522	+	8.27923i	0.525552	+	0.723360i	0.986444	−	0.164096i	$-0.0524707\pi$
$131$	6.01522	+	8.27923i	0.525552	+	0.723360i	−0.460893	+	0.887456i	$0.652471\pi$
$132$			6.15694i			0.535893i
$133$	−7.59657	+	5.51923i	−0.658706	+	0.478578i
$134$	1.00887	−	6.36976i	0.0871532	−	0.550263i
$135$	−6.53931	+	1.03573i	−0.562814	+	0.0891410i
$136$	4.31152	+	8.46184i	0.369710	+	0.725596i
$137$	4.05839	+	4.05839i	0.346731	+	0.346731i	0.858891	−	0.512159i	$-0.171154\pi$
$137$	4.05839	+	4.05839i	0.346731	+	0.346731i	−0.512159	+	0.858891i	$0.671154\pi$
$138$	−1.58015	−	9.97665i	−0.134511	−	0.849269i
$139$	−4.98324	−	15.3368i	−0.422673	−	1.30085i	−0.905205	−	0.424975i	$-0.860283\pi$
$139$	−4.98324	−	15.3368i	−0.422673	−	1.30085i	0.482532	−	0.875878i	$-0.339717\pi$
$140$	1.55661	+	0.246543i	0.131558	+	0.0208367i
$141$	2.40244	−	7.39395i	0.202322	−	0.622683i
$142$	2.48267	−	4.87251i	0.208341	−	0.408892i
$143$	−12.6919	+	4.12386i	−1.06135	+	0.344855i
$144$	−4.51770	+	1.46789i	−0.376475	+	0.122324i
$145$	6.69816	−	13.1459i	0.556252	−	1.09171i
$146$	0.0558824	−	0.171988i	0.00462486	−	0.0142339i
$147$	12.3552	+	1.95688i	1.01904	+	0.161400i
$148$	−0.121231	−	0.373111i	−0.00996515	−	0.0306696i
$149$	0.849406	+	5.36294i	0.0695860	+	0.439349i	0.997742	+	0.0671583i	$0.0213932\pi$
$149$	0.849406	+	5.36294i	0.0695860	+	0.439349i	−0.928156	+	0.372191i	$0.878607\pi$
$150$	2.76637	+	2.76637i	0.225873	+	0.225873i
$151$	1.53796	+	3.01842i	0.125158	+	0.245636i	0.945080	−	0.326839i	$-0.105983\pi$
$151$	1.53796	+	3.01842i	0.125158	+	0.245636i	−0.819922	+	0.572475i	$0.805983\pi$
$152$	−24.9792	+	3.95632i	−2.02608	+	0.320900i
$153$	−0.878136	+	5.54433i	−0.0709931	+	0.448233i
$154$	5.74692	−	4.17538i	0.463100	−	0.336462i
$155$		−	11.5026i		−	0.923910i
$156$	1.81081	+	2.49237i	0.144981	+	0.199549i
$157$	−9.01316	−	4.59244i	−0.719329	−	0.366516i	0.0556954	−	0.998448i	$-0.482262\pi$
$157$	−9.01316	−	4.59244i	−0.719329	−	0.366516i	−0.775024	+	0.631931i	$0.782262\pi$
$158$	−17.3964	+	8.86390i	−1.38398	+	0.705174i
$159$	7.21757	−	9.93413i	0.572391	−	0.787828i
$160$	6.13463	+	4.45707i	0.484985	+	0.352362i
$161$	3.07387	−	3.07387i	0.242255	−	0.242255i
$162$	12.7998	+	4.15892i	1.00565	+	0.326755i
$163$	18.7430			1.46807			0.734033	−	0.679113i	$-0.237635\pi$
$163$	18.7430			1.46807			0.734033	+	0.679113i	$0.237635\pi$
$164$	3.41995	+	0.638988i	0.267053	+	0.0498966i
$165$	−28.8393			−2.24513
$166$	4.90427	+	1.59349i	0.380645	+	0.123679i
$167$	2.16228	−	2.16228i	0.167322	−	0.167322i	−0.618479	−	0.785801i	$-0.712251\pi$
$167$	2.16228	−	2.16228i	0.167322	−	0.167322i	0.785801	+	0.618479i	$0.212251\pi$
$168$	−6.21006	−	4.51187i	−0.479117	−	0.348099i
$169$	3.71629	−	5.11503i	0.285868	−	0.393464i
$170$	−8.46753	+	4.31442i	−0.649430	+	0.330901i
$171$	−13.3194	−	6.78659i	−1.01856	−	0.518983i
$172$	−0.590006	−	0.812074i	−0.0449876	−	0.0619201i
$173$			10.5897i			0.805117i	0.915394	+	0.402558i	$0.131879\pi$
$173$			10.5897i			0.805117i	−0.915394	+	0.402558i	$0.868121\pi$
$174$	−12.4199	+	9.02355i	−0.941547	+	0.684074i
$175$	−0.263386	+	1.66296i	−0.0199101	+	0.125708i
$176$	13.3542	−	2.11510i	1.00661	−	0.159431i
$177$	0.782560	+	1.53586i	0.0588208	+	0.115442i
$178$	−1.45378	−	1.45378i	−0.108965	−	0.108965i
$179$	−0.298749	−	1.88623i	−0.0223295	−	0.140983i	0.974005	−	0.226527i	$-0.0727372\pi$
$179$	−0.298749	−	1.88623i	−0.0223295	−	0.140983i	−0.996334	+	0.0855440i	$0.972737\pi$
$180$	0.775333	+	2.38623i	0.0577899	+	0.177859i
$181$	−5.82173	−	0.922071i	−0.432726	−	0.0685370i	−0.0637279	−	0.997967i	$-0.520299\pi$
$181$	−5.82173	−	0.922071i	−0.432726	−	0.0685370i	−0.368998	+	0.929430i	$0.620299\pi$
$182$	1.09837	−	3.38045i	0.0814169	−	0.250576i
$183$	−7.02407	+	13.7855i	−0.519234	+	1.01905i
$184$	11.1354	−	3.61812i	0.820914	−	0.266731i
$185$	1.74766	−	0.567850i	0.128491	−	0.0417492i
$186$	−5.43366	+	10.6642i	−0.398415	+	0.781934i
$187$	4.93740	−	15.1957i	0.361058	−	1.11122i
$188$	1.90151	+	0.301169i	0.138682	+	0.0219650i
$189$	0.916180	+	2.81971i	0.0666423	+	0.205104i
$190$	−3.95898	−	24.9960i	−0.287215	−	1.81340i
$191$	−2.23597	−	2.23597i	−0.161789	−	0.161789i	0.621570	−	0.783359i	$-0.286495\pi$
$191$	−2.23597	−	2.23597i	−0.161789	−	0.161789i	−0.783359	+	0.621570i	$0.786495\pi$
$192$	−8.79791	−	17.2669i	−0.634935	−	1.24613i
$193$	15.5972	−	2.47036i	1.12271	−	0.177820i	0.432645	−	0.901565i	$-0.357580\pi$
$193$	15.5972	−	2.47036i	1.12271	−	0.177820i	0.690068	+	0.723744i	$0.257580\pi$
$194$	−0.829806	+	5.23919i	−0.0595766	+	0.376152i
$195$	−11.6743	+	8.48190i	−0.836016	+	0.607401i
$196$			3.09770i			0.221264i
$197$	2.67161	+	3.67715i	0.190344	+	0.261986i	0.893514	−	0.449036i	$-0.148233\pi$
$197$	2.67161	+	3.67715i	0.190344	+	0.261986i	−0.703170	+	0.711022i	$0.748233\pi$
$198$	10.0764	+	5.13416i	0.716096	+	0.364869i
$199$	8.00456	−	4.07852i	0.567428	−	0.289119i	−0.146646	−	0.989189i	$-0.546848\pi$
$199$	8.00456	−	4.07852i	0.567428	−	0.289119i	0.714074	+	0.700070i	$0.246848\pi$
$200$	−2.66550	+	3.66875i	−0.188479	+	0.259420i
$201$	9.48535	+	6.89151i	0.669045	+	0.486090i
$202$	2.64217	−	2.64217i	0.185902	−	0.185902i
$203$	−6.28350	−	2.04163i	−0.441015	−	0.143294i
$204$	−3.68849			−0.258246
$205$	−2.99304	+	16.0191i	−0.209043	+	1.11882i
$206$	3.55779			0.247883
$207$	6.58192	+	2.13859i	0.457475	+	0.148643i
$208$	4.78380	−	4.78380i	0.331697	−	0.331697i
$209$	34.4230	+	25.0098i	2.38109	+	1.72996i
$210$	4.51491	−	6.21424i	0.311558	−	0.428823i
$211$	5.75578	−	2.93272i	0.396245	−	0.201897i	−0.244503	−	0.969649i	$-0.578625\pi$
$211$	5.75578	−	2.93272i	0.396245	−	0.201897i	0.640747	+	0.767752i	$0.278625\pi$
$212$	2.70933	+	1.38047i	0.186077	+	0.0948112i
$213$	5.84364	+	8.04308i	0.400399	+	0.551103i
$214$		−	4.08746i		−	0.279413i
$215$	3.80378	−	2.76361i	0.259415	−	0.188476i
$216$	−1.24920	+	7.88711i	−0.0849970	+	0.536650i
$217$	−5.08747	+	0.805776i	−0.345360	+	0.0546996i
$218$	7.48300	+	14.6862i	0.506813	+	0.994676i
$219$	0.232472	+	0.232472i	0.0157090	+	0.0157090i
$220$	−1.11718	−	7.05362i	−0.0753205	−	0.475555i
$221$	−2.47052	−	7.60348i	−0.166185	−	0.511465i
$222$	−1.88852	−	0.299112i	−0.126749	−	0.0200751i
$223$	−1.26478	+	3.89258i	−0.0846956	+	0.260666i	−0.984432	−	0.175768i	$-0.943759\pi$
$223$	−1.26478	+	3.89258i	−0.0846956	+	0.260666i	0.899736	+	0.436435i	$0.143759\pi$
$224$	1.54157	−	3.02550i	0.103001	−	0.202150i
$225$	−2.54925	+	0.828302i	−0.169950	+	0.0552201i
$226$	−15.2044	+	4.94021i	−1.01138	+	0.328618i
$227$	−0.260675	+	0.511604i	−0.0173016	+	0.0339564i	−0.899496	−	0.436930i	$-0.856066\pi$
$227$	−0.260675	+	0.511604i	−0.0173016	+	0.0339564i	0.882194	+	0.470886i	$0.156066\pi$
$228$	3.03534	−	9.34180i	0.201020	−	0.618676i
$229$	−23.7418	−	3.76033i	−1.56890	−	0.248490i	−0.689399	−	0.724382i	$-0.742125\pi$
$229$	−23.7418	−	3.76033i	−1.56890	−	0.248490i	−0.879504	+	0.475892i	$0.842125\pi$
$230$	3.62055	+	11.1429i	0.238732	+	0.734742i
$231$	2.02024	+	12.7553i	0.132922	+	0.839236i
$232$	−12.5829	−	12.5829i	−0.826105	−	0.826105i
$233$	−5.63580	−	11.0609i	−0.369213	−	0.724622i	0.629410	−	0.777073i	$-0.283297\pi$
$233$	−5.63580	−	11.0609i	−0.369213	−	0.724622i	−0.998623	+	0.0524514i	$0.983297\pi$
$234$	5.58899	−	0.885209i	0.365364	−	0.0578679i
$235$	−1.41069	+	8.90672i	−0.0920230	+	0.581010i
$236$	−0.345332	+	0.250898i	−0.0224792	+	0.0163321i
$237$		−	35.4953i		−	2.30567i
$238$	2.50139	+	3.44286i	0.162141	+	0.223168i
$239$	−6.04489	−	3.08002i	−0.391011	−	0.199230i	0.247421	−	0.968908i	$-0.420417\pi$
$239$	−6.04489	−	3.08002i	−0.391011	−	0.199230i	−0.638433	+	0.769678i	$0.720417\pi$
$240$	13.0266	−	6.63739i	0.840864	−	0.428441i
$241$	−11.2730	+	15.5159i	−0.726155	+	0.999467i	0.273142	+	0.961974i	$0.411937\pi$
$241$	−11.2730	+	15.5159i	−0.726155	+	0.999467i	−0.999297	+	0.0374932i	$0.988063\pi$
$242$	−15.3010	−	11.1168i	−0.983584	−	0.714615i
$243$	−11.7827	+	11.7827i	−0.755859	+	0.755859i
$244$	−3.64382	−	1.18395i	−0.233272	−	0.0757945i
$245$	−14.5097			−0.926990
$246$	10.3421	−	13.4376i	0.659387	−	0.856751i
$247$	21.2903			1.35467
$248$	−13.1943	−	4.28710i	−0.837841	−	0.272231i
$249$	−6.62896	+	6.62896i	−0.420093	+	0.420093i
$250$	8.75398	+	6.36014i	0.553650	+	0.402251i
$251$	1.10805	−	1.52510i	0.0699397	−	0.0962637i	−0.772614	−	0.634876i	$-0.781051\pi$
$251$	1.10805	−	1.52510i	0.0699397	−	0.0962637i	0.842554	+	0.538612i	$0.181051\pi$
$252$	1.00109	−	0.510081i	0.0630627	−	0.0321321i
$253$	−17.5515	−	8.94292i	−1.10345	−	0.562236i
$254$	−9.58511	−	13.1928i	−0.601423	−	0.827788i
$255$		−	17.2770i		−	1.08193i
$256$	9.70071	−	7.04798i	0.606294	−	0.440499i
$257$	4.37877	−	27.6464i	0.273140	−	1.72454i	−0.345116	−	0.938560i	$-0.612160\pi$
$257$	4.37877	−	27.6464i	0.273140	−	1.72454i	0.618256	−	0.785977i	$-0.287840\pi$
$258$	−4.83201	+	0.765315i	−0.300828	+	0.0476464i
$259$	−0.373581	−	0.733194i	−0.0232132	−	0.0455584i
$260$	−2.52678	−	2.52678i	−0.156704	−	0.156704i
$261$	−1.64540	−	10.3887i	−0.101848	−	0.643043i
$262$	3.81674	+	11.7467i	0.235799	+	0.725715i
$263$	4.08854	+	0.647561i	0.252110	+	0.0399303i	0.281210	−	0.959646i	$-0.409264\pi$
$263$	4.08854	+	0.647561i	0.252110	+	0.0399303i	−0.0291002	+	0.999576i	$0.509264\pi$
$264$	−10.7486	+	33.0808i	−0.661531	+	2.03598i
$265$	−6.46616	+	12.6906i	−0.397213	+	0.779575i
$266$	−10.7781	+	3.50203i	−0.660850	+	0.214723i
$267$	3.55478	−	1.15502i	0.217549	−	0.0706860i
$268$	−1.31811	+	2.58693i	−0.0805162	+	0.158022i
$269$	−9.19596	+	28.3022i	−0.560687	+	1.72562i	0.119742	+	0.992805i	$0.461793\pi$
$269$	−9.19596	+	28.3022i	−0.560687	+	1.72562i	−0.680430	+	0.732813i	$0.738207\pi$
$270$	−7.89241	−	1.25004i	−0.480317	−	0.0760747i
$271$	7.16633	+	22.0557i	0.435324	+	1.33979i	0.892754	+	0.450544i	$0.148770\pi$
$271$	7.16633	+	22.0557i	0.435324	+	1.33979i	−0.457431	+	0.889245i	$0.651230\pi$
$272$	1.26711	+	8.00022i	0.0768299	+	0.485085i
$273$	4.56926	+	4.56926i	0.276544	+	0.276544i
$274$	3.14480	+	6.17202i	0.189984	+	0.372865i
$275$	7.53551	−	1.19351i	0.454408	−	0.0719712i
$276$	−0.711374	+	4.49144i	−0.0428197	+	0.270353i
$277$	20.0368	−	14.5576i	1.20389	−	0.874680i	0.209231	−	0.977866i	$-0.432904\pi$
$277$	20.0368	−	14.5576i	1.20389	−	0.874680i	0.994662	+	0.103187i	$0.0329039\pi$
$278$		−	19.4629i		−	1.16731i
$279$	−4.81998	−	6.63414i	−0.288565	−	0.397176i
$280$	7.93317	+	4.04215i	0.474098	+	0.241565i
$281$	−0.189482	+	0.0965459i	−0.0113035	+	0.00575945i	−0.459633	−	0.888109i	$-0.652019\pi$
$281$	−0.189482	+	0.0965459i	−0.0113035	+	0.00575945i	0.448330	+	0.893868i	$0.352019\pi$
$282$	5.51527	−	7.59112i	0.328429	−	0.452044i
$283$	8.92649	+	6.48547i	0.530625	+	0.385521i	0.820591	−	0.571515i	$-0.193644\pi$
$283$	8.92649	+	6.48547i	0.530625	+	0.385521i	−0.289967	+	0.957037i	$0.593644\pi$
$284$	−1.74084	+	1.74084i	−0.103300	+	0.103300i
$285$	43.7573	+	14.2176i	2.59196	+	0.842178i
$286$	−16.1064			−0.952394
$287$	7.29475	+	0.201622i	0.430595	+	0.0119014i
$288$	5.40582			0.318541
$289$	−7.06450	−	2.29540i	−0.415559	−	0.135023i
$290$	12.5913	−	12.5913i	0.739388	−	0.739388i
$291$	−7.80180	−	5.66834i	−0.457349	−	0.332284i
$292$	−0.0478533	+	0.0658645i	−0.00280040	+	0.00385443i
$293$	6.77986	−	3.45451i	0.396083	−	0.201815i	−0.244593	−	0.969626i	$-0.578654\pi$
$293$	6.77986	−	3.45451i	0.396083	−	0.201815i	0.640676	+	0.767811i	$0.278654\pi$
$294$	13.4521	+	6.85418i	0.784541	+	0.399744i
$295$	−1.17521	−	1.61754i	−0.0684237	−	0.0941771i
$296$		−	2.21635i		−	0.128822i
$297$	10.8689	−	7.89675i	0.630680	−	0.458216i
$298$	−1.02516	+	6.47263i	−0.0593861	+	0.374949i
$299$	−9.73515	+	1.54190i	−0.562998	+	0.0891702i
$300$	−0.799599	−	1.56930i	−0.0461649	−	0.0906037i
$301$	−1.48877	−	1.48877i	−0.0858115	−	0.0858115i
$302$	0.639602	+	4.03829i	0.0368049	+	0.232377i
$303$	2.09919	+	6.46063i	0.120595	+	0.371153i
$304$	−21.3048	−	3.37435i	−1.22191	−	0.193532i
$305$	5.54565	−	17.0677i	0.317543	−	0.977296i
$306$	−3.07577	+	6.03654i	−0.175830	+	0.345086i
$307$	−29.8761	+	9.70732i	−1.70512	+	0.554026i	−0.989508	−	0.144476i	$-0.953850\pi$
$307$	−29.8761	+	9.70732i	−1.70512	+	0.554026i	−0.715608	+	0.698502i	$0.753850\pi$
$308$	−3.04148	+	0.988237i	−0.173304	+	0.0563100i
$309$	−2.93643	+	5.76308i	−0.167048	+	0.327850i
$310$	4.28998	−	13.2032i	0.243655	−	0.749892i
$311$	14.5714	+	2.30789i	0.826270	+	0.130868i	0.555227	−	0.831699i	$-0.312631\pi$
$311$	14.5714	+	2.30789i	0.826270	+	0.130868i	0.271043	+	0.962567i	$0.412631\pi$
$312$	5.37827	+	16.5526i	0.304485	+	0.937107i
$313$	−2.59799	−	16.4031i	−0.146847	−	0.927155i	−0.945561	−	0.325445i	$-0.894486\pi$
$313$	−2.59799	−	16.4031i	−0.146847	−	0.927155i	0.798714	−	0.601711i	$-0.205514\pi$
$314$	−8.63295	−	8.63295i	−0.487186	−	0.487186i
$315$	2.38923	+	4.68913i	0.134618	+	0.264203i
$316$	8.68158	−	1.37503i	0.488377	−	0.0773513i
$317$	5.09527	−	32.1703i	0.286179	−	1.80686i	−0.256085	−	0.966654i	$-0.582433\pi$
$317$	5.09527	−	32.1703i	0.286179	−	1.80686i	0.542264	−	0.840208i	$-0.317567\pi$
$318$	11.9897	−	8.71102i	0.672348	−	0.488490i
$319$			29.9383i			1.67622i
$320$	13.2123	+	18.1852i	0.738591	+	1.01658i
$321$	6.62105	+	3.37359i	0.369551	+	0.188296i
$322$	4.67476	−	2.38191i	0.260514	−	0.132739i
$323$	−14.9828	+	20.6221i	−0.833667	+	1.14744i
$324$	−4.90181	−	3.56137i	−0.272323	−	0.197854i
$325$	2.69940	−	2.69940i	0.149736	−	0.149736i
$326$	21.5141	+	6.99036i	1.19156	+	0.387160i
$327$	−29.9655			−1.65710
$328$	17.2596	+	9.40369i	0.953003	+	0.519232i
$329$	4.03816			0.222631
$330$	−33.1031	−	10.7558i	−1.82226	−	0.592089i
$331$	−1.33145	+	1.33145i	−0.0731829	+	0.0731829i	−0.742751	−	0.669568i	$-0.766479\pi$
$331$	−1.33145	+	1.33145i	−0.0731829	+	0.0731829i	0.669568	+	0.742751i	$0.266479\pi$
$332$	−1.87813	−	1.36454i	−0.103076	−	0.0748891i
$333$	0.770020	−	1.05984i	0.0421968	−	0.0580789i
$334$	3.28840	−	1.67553i	0.179934	−	0.0916807i
$335$	−12.1173	−	6.17405i	−0.662036	−	0.337324i
$336$	−3.84818	−	5.29657i	−0.209935	−	0.288951i
$337$			29.3757i			1.60020i	0.599870	+	0.800098i	$0.295219\pi$
$337$			29.3757i			1.60020i	−0.599870	+	0.800098i	$0.704781\pi$
$338$	6.17342	−	4.48526i	0.335790	−	0.243966i
$339$	4.54661	−	28.7062i	0.246938	−	1.55910i
$340$	4.22568	−	0.669282i	0.229170	−	0.0362969i
$341$	10.5964	+	20.7967i	0.573830	+	1.12620i
$342$	−12.7576	−	12.7576i	−0.689850	−	0.689850i
$343$	2.26443	+	14.2970i	0.122268	+	0.771968i
$344$	−1.75237	−	5.39324i	−0.0944814	−	0.290784i
$345$	−21.0380	−	3.33209i	−1.13265	−	0.179394i
$346$	−3.94950	+	12.1553i	−0.212326	+	0.653473i
$347$	−12.7217	+	24.9677i	−0.682936	+	1.34034i	0.245700	+	0.969346i	$0.420982\pi$
$347$	−12.7217	+	24.9677i	−0.682936	+	1.34034i	−0.928636	+	0.370992i	$0.879018\pi$
$348$	6.57304	−	2.13571i	0.352352	−	0.114486i
$349$	19.4391	−	6.31615i	1.04055	−	0.338096i	0.261598	−	0.965177i	$-0.415751\pi$
$349$	19.4391	−	6.31615i	1.04055	−	0.338096i	0.778954	+	0.627081i	$0.215751\pi$
$350$	−0.922541	+	1.81059i	−0.0493119	+	0.0967800i
$351$	2.07732	−	6.39332i	0.110879	−	0.341250i
$352$	−15.1974	−	2.40703i	−0.810022	−	0.128295i
$353$	−8.94631	−	27.5339i	−0.476164	−	1.46548i	−0.844381	−	0.535743i	$-0.820032\pi$
$353$	−8.94631	−	27.5339i	−0.476164	−	1.46548i	0.368217	−	0.929740i	$-0.379968\pi$
$354$	0.325448	+	2.05480i	0.0172974	+	0.109211i
$355$	−8.15412	−	8.15412i	−0.432776	−	0.432776i
$356$	0.420205	+	0.824699i	0.0222708	+	0.0437090i
$357$	−7.64143	+	1.21028i	−0.404427	+	0.0640550i
$358$	0.360565	−	2.27652i	0.0190565	−	0.120318i
$359$	17.5745	−	12.7687i	0.927549	−	0.673904i	−0.0178425	−	0.999841i	$-0.505680\pi$
$359$	17.5745	−	12.7687i	0.927549	−	0.673904i	0.945391	+	0.325937i	$0.105680\pi$
$360$			14.1746i			0.747067i
$361$	−28.7318	−	39.5459i	−1.51220	−	2.08136i
$362$	−6.33856	−	3.22966i	−0.333147	−	0.169747i
$363$	30.6362	−	15.6099i	1.60798	−	0.819308i
$364$	−0.940562	+	1.29457i	−0.0492989	+	0.0678541i
$365$	−0.308511	−	0.224146i	−0.0161482	−	0.0117324i
$366$	−13.2040	+	13.2040i	−0.690183	+	0.690183i
$367$	16.4047	+	5.33020i	0.856316	+	0.278234i	0.704089	−	0.710112i	$-0.251355\pi$
$367$	16.4047	+	5.33020i	0.856316	+	0.278234i	0.152227	+	0.988346i	$0.451355\pi$
$368$	9.98616			0.520565
$369$	4.98633	+	10.4932i	0.259578	+	0.546257i
$370$	2.21784			0.115300
$371$	6.06586	+	1.97092i	0.314924	+	0.102325i
$372$	3.81006	−	3.81006i	0.197542	−	0.197542i
$373$	−13.7898	−	10.0189i	−0.714007	−	0.518756i	0.170457	−	0.985365i	$-0.445476\pi$
$373$	−13.7898	−	10.0189i	−0.714007	−	0.518756i	−0.884464	+	0.466609i	$0.845476\pi$
$374$	11.3348	−	15.6010i	0.586106	−	0.806706i
$375$	−17.5276	+	8.93074i	−0.905119	+	0.461181i
$376$	9.69091	+	4.93776i	0.499770	+	0.254646i
$377$	8.80513	+	12.1192i	0.453487	+	0.624171i
$378$			3.57830i			0.184048i
$379$	−29.9726	+	21.7764i	−1.53959	+	1.11858i	−0.588995	+	0.808137i	$0.700476\pi$
$379$	−29.9726	+	21.7764i	−1.53959	+	1.11858i	−0.950593	+	0.310439i	$0.899524\pi$
$380$	−1.78231	+	11.2531i	−0.0914308	+	0.577271i
$381$	29.2813	−	4.63771i	1.50013	−	0.237597i
$382$	−1.73263	−	3.40048i	−0.0886491	−	0.173984i
$383$	−23.8870	−	23.8870i	−1.22057	−	1.22057i	−0.967430	−	0.253137i	$-0.918538\pi$
$383$	−23.8870	−	23.8870i	−1.22057	−	1.22057i	−0.253137	−	0.967430i	$-0.581462\pi$
$384$	−1.61350	−	10.1872i	−0.0823385	−	0.519865i
$385$	−4.62893	−	14.2464i	−0.235912	−	0.726062i
$386$	18.8246	+	2.98152i	0.958146	+	0.151755i
$387$	1.03579	−	3.18783i	0.0526521	−	0.162046i
$388$	1.08416	−	2.12778i	0.0550397	−	0.108021i
$389$	−8.46056	+	2.74900i	−0.428967	+	0.139380i	−0.515540	−	0.856866i	$-0.672409\pi$
$389$	−8.46056	+	2.74900i	−0.428967	+	0.139380i	0.0865726	+	0.996246i	$0.472409\pi$
$390$	−16.5637	+	5.38189i	−0.838738	+	0.272522i
$391$	5.35751	−	10.5147i	0.270941	−	0.531752i
$392$	−5.40787	+	16.6437i	−0.273139	+	0.840635i
$393$	−22.1780	−	3.51265i	−1.11873	−	0.177190i
$394$	1.69517	+	5.21721i	0.0854016	+	0.262839i
$395$	6.44066	+	40.6647i	0.324065	+	2.04606i
$396$	−3.60005	−	3.60005i	−0.180909	−	0.180909i
$397$	3.80671	+	7.47109i	0.191053	+	0.374963i	0.966585	−	0.256345i	$-0.0825183\pi$
$397$	3.80671	+	7.47109i	0.191053	+	0.374963i	−0.775532	+	0.631308i	$0.782518\pi$
$398$	10.7091	−	1.69616i	0.536800	−	0.0850208i
$399$	3.22302	−	20.3493i	0.161353	−	1.01874i
$400$	−3.12908	+	2.27341i	−0.156454	+	0.113670i
$401$		−	24.8940i		−	1.24315i	−0.783356	−	0.621573i	$-0.786494\pi$
$401$		−	24.8940i		−	1.24315i	0.783356	−	0.621573i	$-0.213506\pi$
$402$	8.31749	+	11.4480i	0.414839	+	0.570976i
$403$	10.4060	+	5.30213i	0.518361	+	0.264118i
$404$	−1.49885	+	0.763701i	−0.0745705	+	0.0379955i
$405$	16.6816	−	22.9602i	0.828914	−	1.14090i
$406$	−6.45105	−	4.68696i	−0.320160	−	0.232610i
$407$	−2.63666	+	2.63666i	−0.130694	+	0.130694i
$408$	−19.8180	−	6.43927i	−0.981139	−	0.318791i
$409$	−8.75194			−0.432756			−0.216378	−	0.976310i	$-0.569424\pi$
$409$	−8.75194			−0.432756			−0.216378	+	0.976310i	$0.569424\pi$
$410$	−9.41001	+	17.2712i	−0.464727	+	0.852965i
$411$	−12.5933			−0.621181
$412$	−1.52331	−	0.494953i	−0.0750480	−	0.0243846i
$413$	−0.633096	+	0.633096i	−0.0311526	+	0.0311526i
$414$	6.75743	+	4.90956i	0.332109	+	0.241292i
$415$	6.39156	−	8.79722i	0.313749	−	0.431839i
$416$	−6.85993	+	3.49531i	−0.336336	+	0.171372i
$417$	31.5269	+	16.0637i	1.54388	+	0.786645i
$418$	30.1848	+	41.5458i	1.47638	+	2.03207i
$419$		−	24.9286i		−	1.21784i	−0.793232	−	0.608920i	$-0.791603\pi$
$419$		−	24.9286i		−	1.21784i	0.793232	−	0.608920i	$-0.208397\pi$
$420$	−2.79762	+	2.03259i	−0.136510	+	0.0991803i
$421$	−1.70359	+	10.7560i	−0.0830279	+	0.524217i	0.910761	+	0.412934i	$0.135496\pi$
$421$	−1.70359	+	10.7560i	−0.0830279	+	0.524217i	−0.993789	+	0.111283i	$0.964504\pi$
$422$	7.70054	−	1.21965i	0.374857	−	0.0593714i
$423$	2.91861	+	5.72809i	0.141908	+	0.278509i
$424$	12.1470	+	12.1470i	0.589913	+	0.589913i
$425$	0.715005	+	4.51436i	0.0346828	+	0.218979i
$426$	3.70787	+	11.4117i	0.179647	+	0.552897i
$427$	−7.93736	−	1.25715i	−0.384116	−	0.0608380i
$428$	−0.568639	+	1.75009i	−0.0274862	+	0.0845938i
$429$	13.2935	−	26.0899i	0.641816	−	1.25963i
$430$	5.39686	−	1.75355i	0.260260	−	0.0845636i
$431$	−18.5078	+	6.01355i	−0.891490	+	0.289663i	−0.718720	−	0.695300i	$-0.755272\pi$
$431$	−18.5078	+	6.01355i	−0.891490	+	0.289663i	−0.172770	+	0.984962i	$0.555272\pi$
$432$	−3.09202	+	6.06844i	−0.148765	+	0.291968i
$433$	−1.43880	+	4.42816i	−0.0691441	+	0.212804i	−0.979658	−	0.200675i	$-0.935686\pi$
$433$	−1.43880	+	4.42816i	−0.0691441	+	0.212804i	0.910514	+	0.413479i	$0.135686\pi$
$434$	−6.14016	−	0.972505i	−0.294737	−	0.0466818i
$435$	10.0037	+	30.7883i	0.479642	+	1.47618i
$436$	−1.16081	−	7.32908i	−0.0555928	−	0.350999i
$437$	22.2217	+	22.2217i	1.06301	+	1.06301i
$438$	0.180140	+	0.353544i	0.00860742	+	0.0168930i
$439$	12.3177	−	1.95093i	0.587891	−	0.0931127i	0.144599	−	0.989490i	$-0.453811\pi$
$439$	12.3177	−	1.95093i	0.587891	−	0.0931127i	0.443291	+	0.896378i	$0.353811\pi$
$440$	6.31146	−	39.8490i	0.300887	−	1.89973i
$441$	−8.36849	+	6.08007i	−0.398500	+	0.289527i
$442$		−	9.64904i		−	0.458958i
$443$	8.10317	+	11.1531i	0.384993	+	0.529897i	0.956899	−	0.290422i	$-0.0937957\pi$
$443$	8.10317	+	11.1531i	0.384993	+	0.529897i	−0.571906	+	0.820319i	$0.693796\pi$
$444$	0.766979	+	0.390795i	0.0363992	+	0.0185463i
$445$	−3.86291	+	1.96825i	−0.183120	+	0.0933041i
$446$	−2.90354	+	3.99638i	−0.137487	+	0.189234i
$447$	−9.63853	−	7.00280i	−0.455887	−	0.331221i
$448$	7.11757	−	7.11757i	0.336274	−	0.336274i
$449$	−5.07254	−	1.64817i	−0.239388	−	0.0777819i	0.186866	−	0.982385i	$-0.440167\pi$
$449$	−5.07254	−	1.64817i	−0.239388	−	0.0777819i	−0.426254	+	0.904604i	$0.640167\pi$
$450$	−3.23507			−0.152503
$451$	−9.34576	−	31.7198i	−0.440075	−	1.49363i
$452$	7.19720			0.338528
$453$	−7.06929	−	2.29695i	−0.332144	−	0.107920i
$454$	−0.490022	+	0.490022i	−0.0229979	+	0.0229979i
$455$	−6.06381	−	4.40562i	−0.284276	−	0.206539i
$456$	32.6173	−	44.8939i	1.52745	−	2.10235i
$457$	−9.05273	+	4.61259i	−0.423469	+	0.215768i	−0.652720	−	0.757599i	$-0.726372\pi$
$457$	−9.05273	+	4.61259i	−0.423469	+	0.215768i	0.229251	+	0.973367i	$0.426372\pi$
$458$	−25.8495	−	13.1710i	−1.20787	−	0.615440i
$459$	4.73078	+	6.51136i	0.220814	+	0.303924i
$460$		−	5.27464i		−	0.245932i
$461$	−24.0238	+	17.4543i	−1.11890	+	0.812927i	−0.984042	−	0.177938i	$-0.943057\pi$
$461$	−24.0238	+	17.4543i	−1.11890	+	0.812927i	−0.134856	+	0.990865i	$0.543057\pi$
$462$	−2.43826	+	15.3946i	−0.113438	+	0.716221i
$463$	37.9429	−	6.00956i	1.76336	−	0.279288i	0.811171	−	0.584809i	$-0.198831\pi$
$463$	37.9429	−	6.00956i	1.76336	−	0.279288i	0.952185	+	0.305521i	$0.0988307\pi$
$464$	−6.89032	−	13.5230i	−0.319875	−	0.627790i
$465$	17.8464	+	17.8464i	0.827607	+	0.827607i
$466$	−2.34379	−	14.7981i	−0.108574	−	0.685509i
$467$	0.851187	+	2.61968i	0.0393882	+	0.121224i	0.968817	−	0.247777i	$-0.0796999\pi$
$467$	0.851187	+	2.61968i	0.0393882	+	0.121224i	−0.929429	+	0.369001i	$0.879700\pi$
$468$	−2.51614	−	0.398517i	−0.116308	−	0.0184214i
$469$	−1.88188	+	5.79183i	−0.0868971	+	0.267442i
$470$	−4.94108	+	9.69742i	−0.227915	+	0.447309i
$471$	21.1093	−	6.85882i	0.972664	−	0.316038i
$472$	−2.29346	+	0.745190i	−0.105565	+	0.0343001i
$473$	−4.33134	+	8.50073i	−0.199155	+	0.390864i
$474$	13.2383	−	40.7432i	0.608053	−	1.87139i
$475$	−12.0219	−	1.90408i	−0.551601	−	0.0873651i
$476$	−0.592032	−	1.82209i	−0.0271357	−	0.0835152i
$477$	1.58841	+	10.0289i	0.0727285	+	0.459190i
$478$	−5.78989	−	5.78989i	−0.264823	−	0.264823i
$479$	16.3580	+	32.1043i	0.747415	+	1.46688i	0.879628	+	0.475663i	$0.157792\pi$
$479$	16.3580	+	32.1043i	0.747415	+	1.46688i	−0.132213	+	0.991221i	$0.542208\pi$
$480$	−16.4331	+	2.60275i	−0.750067	+	0.118799i
$481$	−0.291872	+	1.84281i	−0.0133082	+	0.0840247i
$482$	−18.7264	+	13.6055i	−0.852965	+	0.619715i
$483$			9.53831i			0.434008i
$484$	5.00473	+	6.88842i	0.227488	+	0.313110i
$485$	9.96656	+	5.07822i	0.452558	+	0.230590i
$486$	−17.9192	+	9.13027i	−0.812830	+	0.414157i
$487$	−8.99982	+	12.3872i	−0.407821	+	0.561317i	−0.962685	−	0.270624i	$-0.912770\pi$
$487$	−8.99982	+	12.3872i	−0.407821	+	0.561317i	0.554865	+	0.831941i	$0.312770\pi$
$488$	−17.5111	−	12.7226i	−0.792690	−	0.575923i
$489$	−29.0800	+	29.0800i	−1.31505	+	1.31505i
$490$	−16.6549	−	5.41151i	−0.752392	−	0.244467i
$491$	8.39830			0.379010			0.189505	−	0.981880i	$-0.439312\pi$
$491$	8.39830			0.379010			0.189505	+	0.981880i	$0.439312\pi$
$492$	−6.29749	+	4.31469i	−0.283913	+	0.194521i
$493$	−17.9354			−0.807769
$494$	24.4380	+	7.94039i	1.09952	+	0.357255i
$495$	16.8627	−	16.8627i	0.757924	−	0.757924i
$496$	−9.57276	−	6.95502i	−0.429830	−	0.312290i
$497$	−3.03527	+	4.17769i	−0.136150	+	0.187395i
$498$	−10.0814	+	5.13671i	−0.451757	+	0.230182i
$499$	6.86475	+	3.49776i	0.307308	+	0.156581i	0.600843	−	0.799367i	$-0.294832\pi$
$499$	6.86475	+	3.49776i	0.307308	+	0.156581i	−0.293535	+	0.955948i	$0.594832\pi$
$500$	−2.86330	−	3.94100i	−0.128051	−	0.176247i
$501$			6.70961i			0.299763i
$502$	1.84068	−	1.33733i	0.0821534	−	0.0596879i
$503$	2.90709	−	18.3546i	0.129621	−	0.818392i	−0.834126	−	0.551574i	$-0.814028\pi$
$503$	2.90709	−	18.3546i	0.129621	−	0.818392i	0.963747	−	0.266818i	$-0.0859724\pi$
$504$	6.26927	−	0.992955i	0.279256	−	0.0442298i
$505$	−3.57720	−	7.02064i	−0.159183	−	0.312414i
$506$	−16.8111	−	16.8111i	−0.747343	−	0.747343i
$507$	2.17017	+	13.7019i	0.0963806	+	0.608523i
$508$	2.26862	+	6.98209i	0.100654	+	0.309780i
$509$	−17.4808	−	2.76869i	−0.774823	−	0.122720i	−0.243513	−	0.969898i	$-0.578300\pi$
$509$	−17.4808	−	2.76869i	−0.774823	−	0.122720i	−0.531310	+	0.847178i	$0.678300\pi$
$510$	6.44360	−	19.8314i	0.285327	−	0.878147i
$511$	−0.0775257	+	0.152153i	−0.00342954	+	0.00673085i
$512$	22.7049	−	7.37726i	1.00342	−	0.326032i
$513$	−20.3843	+	6.62326i	−0.899989	+	0.292424i
$514$	15.3371	−	30.1008i	0.676491	−	1.32769i
$515$	2.31837	−	7.13522i	0.102160	−	0.314415i
$516$	2.17535	+	0.344541i	0.0957643	+	0.0151676i
$517$	−5.65455	−	17.4029i	−0.248687	−	0.765379i
$518$	−0.155363	−	0.980925i	−0.00682627	−	0.0430994i
$519$	−16.4300	−	16.4300i	−0.721196	−	0.721196i
$520$	−9.16504	−	17.9874i	−0.401914	−	0.788800i
$521$	−25.2617	+	4.00106i	−1.10673	+	0.175289i	−0.682944	−	0.730471i	$-0.739301\pi$
$521$	−25.2617	+	4.00106i	−1.10673	+	0.175289i	−0.423790	+	0.905760i	$0.639301\pi$
$522$	1.98587	−	12.5383i	0.0869191	−	0.548786i
$523$	21.3827	−	15.5354i	0.934998	−	0.679316i	−0.0122132	−	0.999925i	$-0.503888\pi$
$523$	21.3827	−	15.5354i	0.934998	−	0.679316i	0.947211	+	0.320609i	$0.103888\pi$
$524$		−	5.56046i		−	0.242910i
$525$	−2.17145	−	2.98875i	−0.0947699	−	0.130440i
$526$	4.45150	+	2.26815i	0.194095	+	0.0988962i
$527$	−12.4589	+	6.34811i	−0.542717	+	0.276528i
$528$	−17.4376	+	24.0008i	−0.758875	+	1.04450i
$529$	6.83700	+	4.96737i	0.297261	+	0.215973i
$530$	−12.1552	+	12.1552i	−0.527989	+	0.527989i
$531$	−1.35562	−	0.440466i	−0.0588287	−	0.0191146i
$532$	5.10197			0.221199
$533$	−13.1123	−	10.0917i	−0.567958	−	0.437122i
$534$	4.51112			0.195215
$535$	−8.19747	−	2.66352i	−0.354407	−	0.115154i
$536$	−11.5983	+	11.5983i	−0.500970	+	0.500970i
$537$	3.39001	+	2.46299i	0.146290	+	0.106286i
$538$	−21.1111	+	29.0569i	−0.910165	+	1.25273i
$539$	26.2335	−	13.3667i	1.12996	−	0.575743i
$540$	3.20532	+	1.63319i	0.137935	+	0.0702814i
$541$	11.1474	+	15.3431i	0.479266	+	0.659653i	0.978364	−	0.206893i	$-0.0663351\pi$
$541$	11.1474	+	15.3431i	0.479266	+	0.659653i	−0.499098	+	0.866546i	$0.666335\pi$
$542$			27.9893i			1.20224i
$543$	10.4631	−	7.60188i	0.449014	−	0.326228i
$544$	1.44200	−	9.10442i	0.0618252	−	0.390349i
$545$	34.3296	−	5.43728i	1.47052	−	0.232907i
$546$	3.54067	+	6.94895i	0.151527	+	0.297388i
$547$	11.0744	+	11.0744i	0.473506	+	0.473506i	0.903047	−	0.429541i	$-0.141325\pi$
$547$	11.0744	+	11.0744i	0.473506	+	0.473506i	−0.429541	+	0.903047i	$0.641325\pi$
$548$	−0.487842	−	3.08011i	−0.0208396	−	0.131576i
$549$	−3.95352	−	12.1677i	−0.168732	−	0.519304i
$550$	9.09474	+	1.44047i	0.387801	+	0.0614216i
$551$	14.7594	−	45.4247i	0.628771	−	1.93516i
$552$	−11.6632	+	22.8903i	−0.496418	+	0.974276i
$553$	17.5344	−	5.69727i	0.745638	−	0.242273i
$554$	28.4285	−	9.23699i	1.20781	−	0.392442i
$555$	−1.83050	+	3.59255i	−0.0777002	+	0.152495i
$556$	−2.70764	+	8.33325i	−0.114829	+	0.353408i
$557$	30.3636	+	4.80913i	1.28655	+	0.203769i	0.761981	−	0.647600i	$-0.224227\pi$
$557$	30.3636	+	4.80913i	1.28655	+	0.203769i	0.524567	+	0.851369i	$0.324227\pi$
$558$	−3.05835	−	9.41263i	−0.129470	−	0.398468i
$559$	0.746789	+	4.71504i	0.0315858	+	0.199425i
$560$	5.36969	+	5.36969i	0.226911	+	0.226911i
$561$	15.9160	+	31.2368i	0.671973	+	1.31882i
$562$	−0.253504	+	0.0401511i	−0.0106934	+	0.00169367i
$563$	−3.47564	+	21.9443i	−0.146481	+	0.924844i	0.799510	+	0.600652i	$0.205092\pi$
$563$	−3.47564	+	21.9443i	−0.146481	+	0.924844i	−0.945991	+	0.324192i	$0.894908\pi$
$564$	−3.41748	+	2.48295i	−0.143902	+	0.104551i
$565$			33.7119i			1.41827i
$566$	7.82744	+	10.7735i	0.329012	+	0.452846i
$567$	−11.3236	−	5.76967i	−0.475547	−	0.242303i
$568$	−12.3925	+	6.31429i	−0.519978	+	0.264942i
$569$	2.76582	−	3.80682i	0.115949	−	0.159590i	−0.747098	−	0.664714i	$-0.768553\pi$
$569$	2.76582	−	3.80682i	0.115949	−	0.159590i	0.863047	+	0.505124i	$0.168553\pi$
$570$	44.9241	+	32.6393i	1.88166	+	1.36711i
$571$	9.49358	−	9.49358i	0.397294	−	0.397294i	−0.479983	−	0.877278i	$-0.659357\pi$
$571$	9.49358	−	9.49358i	0.397294	−	0.397294i	0.877278	+	0.479983i	$0.159357\pi$
$572$	6.89615	+	2.24070i	0.288343	+	0.0936882i
$573$	6.93828			0.289851
$574$	8.29806	+	2.95207i	0.346354	+	0.123217i
$575$	5.63499			0.234995
$576$	15.2405	+	4.95193i	0.635020	+	0.206330i
$577$	−11.7501	+	11.7501i	−0.489162	+	0.489162i	−0.908042	−	0.418880i	$-0.862423\pi$
$577$	−11.7501	+	11.7501i	−0.489162	+	0.489162i	0.418880	+	0.908042i	$0.362423\pi$
$578$	−7.25289	−	5.26953i	−0.301680	−	0.219184i
$579$	−20.3665	+	28.0321i	−0.846403	+	1.16497i
$580$	−7.14279	+	3.63944i	−0.296588	+	0.151119i
$581$	−4.33866	−	2.21066i	−0.179998	−	0.0917135i
$582$	−6.84122	−	9.41613i	−0.283578	−	0.390311i
$583$		−	28.9013i		−	1.19697i
$584$	−0.372097	+	0.270344i	−0.0153975	+	0.0111869i
$585$	1.86666	−	11.7856i	0.0771770	−	0.487276i
$586$	9.07063	−	1.43665i	0.374704	−	0.0593473i
$587$	−11.9109	−	23.3764i	−0.491615	−	0.964849i	−0.994913	−	0.100736i	$-0.967880\pi$
$587$	−11.9109	−	23.3764i	−0.491615	−	0.964849i	0.503298	−	0.864113i	$-0.332120\pi$
$588$	−4.80612	−	4.80612i	−0.198201	−	0.198201i
$589$	−5.82513	−	36.7784i	−0.240020	−	1.51543i
$590$	−0.745691	−	2.29500i	−0.0306996	−	0.0944837i
$591$	−9.85018	−	1.56012i	−0.405182	−	0.0641746i
$592$	0.584142	−	1.79780i	0.0240081	−	0.0738892i
$593$	1.10491	−	2.16850i	0.0453730	−	0.0890496i	−0.867207	−	0.497948i	$-0.834087\pi$
$593$	1.10491	−	2.16850i	0.0453730	−	0.0890496i	0.912580	+	0.408898i	$0.134087\pi$
$594$	15.4211	−	5.01060i	0.632734	−	0.205588i
$595$	8.53470	−	2.77309i	0.349889	−	0.113686i
$596$	1.33939	−	2.62871i	0.0548637	−	0.107676i
$597$	−6.09129	+	18.7471i	−0.249300	+	0.767266i
$598$	−11.7495	−	1.86094i	−0.480474	−	0.0760996i
$599$	5.18017	+	15.9429i	0.211656	+	0.651410i	0.999374	+	0.0353745i	$0.0112624\pi$
$599$	5.18017	+	15.9429i	0.211656	+	0.651410i	−0.787718	+	0.616036i	$0.788738\pi$
$600$	−1.55655	−	9.82767i	−0.0635459	−	0.401213i
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	0.509256	−	0.860615i	$-0.329921\pi$
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	−0.860615	+	0.509256i	$0.829921\pi$
$602$	−1.15363	−	2.26413i	−0.0470186	−	0.0922793i
$603$	−9.57579	+	1.51666i	−0.389956	+	0.0617630i
$604$	0.287946	−	1.81802i	0.0117163	−	0.0739740i
$605$	−32.2656	+	23.4423i	−1.31178	+	0.953065i
$606$			8.19872i			0.333050i
$607$	2.60922	+	3.59129i	0.105905	+	0.145766i	0.858680	−	0.512512i	$-0.171285\pi$
$607$	2.60922	+	3.59129i	0.105905	+	0.145766i	−0.752775	+	0.658278i	$0.771285\pi$
$608$	21.8720	+	11.1443i	0.887027	+	0.451963i
$609$	12.9165	−	6.58131i	0.523405	−	0.266688i
$610$	12.7311	−	17.5229i	0.515468	−	0.709480i
$611$	−7.40736	−	5.38176i	−0.299670	−	0.217723i
$612$	2.15672	−	2.15672i	0.0871801	−	0.0871801i
$613$	45.1753	+	14.6783i	1.82461	+	0.592852i	0.999616	+	0.0277136i	$0.00882263\pi$
$613$	45.1753	+	14.6783i	1.82461	+	0.592852i	0.824996	+	0.565139i	$0.191177\pi$
$614$	−37.9136			−1.53007
$615$	−20.2101	−	29.4976i	−0.814951	−	1.18946i
$616$	−18.0669			−0.727936
$617$	−35.6237	−	11.5748i	−1.43416	−	0.465985i	−0.514086	−	0.857739i	$-0.671869\pi$
$617$	−35.6237	−	11.5748i	−1.43416	−	0.465985i	−0.920070	+	0.391753i	$0.871869\pi$
$618$	−5.51996	+	5.51996i	−0.222046	+	0.222046i
$619$	−12.2778	−	8.92032i	−0.493485	−	0.358538i	0.313038	−	0.949741i	$-0.398653\pi$
$619$	−12.2778	−	8.92032i	−0.493485	−	0.358538i	−0.806523	+	0.591203i	$0.798653\pi$
$620$	−3.67361	+	5.05629i	−0.147536	+	0.203065i
$621$	8.84121	−	4.50482i	0.354785	−	0.180772i
$622$	15.8650	+	8.08364i	0.636130	+	0.324125i
$623$	1.14114	+	1.57064i	0.0457188	+	0.0629265i
$624$			14.8443i			0.594246i
$625$	24.4357	−	17.7535i	0.977427	−	0.710142i
$626$	3.13556	−	19.7971i	0.125322	−	0.791253i
$627$	−92.2107	+	14.6047i	−3.68254	+	0.583257i
$628$	2.49529	+	4.89729i	0.0995731	+	0.195423i
$629$	−1.57957	−	1.57957i	−0.0629816	−	0.0629816i
$630$	0.993623	+	6.27349i	0.0395869	+	0.249942i
$631$	−1.82817	−	5.62652i	−0.0727782	−	0.223988i	0.908050	−	0.418861i	$-0.137571\pi$
$631$	−1.82817	−	5.62652i	−0.0727782	−	0.223988i	−0.980829	+	0.194873i	$0.937571\pi$
$632$	49.0460	+	7.76813i	1.95095	+	0.308999i
$633$	−4.38002	+	13.4803i	−0.174090	+	0.535795i
$634$	17.8468	−	35.0262i	0.708785	−	1.39107i
$635$	−32.7043	+	10.6263i	−1.29783	+	0.421691i
$636$	−6.34538	+	2.06174i	−0.251611	+	0.0817532i
$637$	6.68826	−	13.1264i	0.264999	−	0.520089i
$638$	−11.1657	+	34.3646i	−0.442055	+	1.36051i
$639$	−8.11977	−	1.28604i	−0.321213	−	0.0508751i
$640$	3.69697	+	11.3781i	0.146136	+	0.449759i
$641$	−5.46005	−	34.4734i	−0.215659	−	1.36162i	−0.823391	−	0.567475i	$-0.807920\pi$
$641$	−5.46005	−	34.4734i	−0.215659	−	1.36162i	0.607732	−	0.794143i	$-0.292080\pi$
$642$	6.34174	+	6.34174i	0.250289	+	0.250289i
$643$	−14.6680	−	28.7876i	−0.578451	−	1.13527i	−0.976016	−	0.217700i	$-0.930145\pi$
$643$	−14.6680	−	28.7876i	−0.578451	−	1.13527i	0.397565	−	0.917574i	$-0.369855\pi$
$644$	−2.33292	+	0.369498i	−0.0919298	+	0.0145603i
$645$	−1.61384	+	10.1894i	−0.0635448	+	0.401206i
$646$	−24.8892	+	18.0831i	−0.979252	+	0.711468i
$647$		−	0.686839i		−	0.0270024i	−0.999909	−	0.0135012i	$-0.995702\pi$
$647$		−	0.686839i		−	0.0270024i	0.999909	−	0.0135012i	$-0.00429770\pi$
$648$	−20.1197	−	27.6925i	−0.790378	−	1.08786i
$649$	3.61491	+	1.84189i	0.141898	+	0.0723004i
$650$	4.10527	−	2.09174i	0.161022	−	0.0820447i
$651$	6.64310	−	9.14344i	0.260364	−	0.358360i
$652$	−8.23903	−	5.98600i	−0.322665	−	0.234430i
$653$	33.7065	−	33.7065i	1.31904	−	1.31904i	0.404500	−	0.914538i	$-0.367446\pi$
$653$	33.7065	−	33.7065i	1.31904	−	1.31904i	0.914538	−	0.404500i	$-0.132554\pi$
$654$	−34.3958	−	11.1759i	−1.34498	−	0.437011i
$655$	26.0454			1.01768
$656$	11.5218	+	12.1768i	0.449851	+	0.475425i
$657$	−0.271859			−0.0106062
$658$	4.63520	+	1.50607i	0.180699	+	0.0587126i
$659$	31.4326	−	31.4326i	1.22444	−	1.22444i	0.258404	−	0.966037i	$-0.416803\pi$
$659$	31.4326	−	31.4326i	1.22444	−	1.22444i	0.966037	−	0.258404i	$-0.0831967\pi$
$660$	12.6771	+	9.21046i	0.493456	+	0.358517i
$661$	−14.1153	+	19.4280i	−0.549020	+	0.755662i	−0.989879	−	0.141915i	$-0.954674\pi$
$661$	−14.1153	+	19.4280i	−0.549020	+	0.755662i	0.440859	+	0.897577i	$0.354674\pi$
$662$	−2.02487	+	1.03172i	−0.0786989	+	0.0400991i
$663$	15.6299	+	7.96385i	0.607017	+	0.309290i
$664$	−7.70890	−	10.6104i	−0.299163	−	0.411763i
$665$			23.8978i			0.926716i
$666$	1.27914	−	0.929351i	0.0495657	−	0.0360116i
$667$	−3.45907	+	21.8397i	−0.133936	+	0.845638i
$668$	−1.64106	+	0.259919i	−0.0634946	+	0.0100566i
$669$	−4.07707	−	8.00170i	−0.157629	−	0.309364i
$670$	−11.6061	−	11.6061i	−0.448382	−	0.448382i
$671$	5.69666	+	35.9673i	0.219917	+	1.38850i
$672$	2.30234	+	7.08587i	0.0888147	+	0.273344i
$673$	15.1756	+	2.40357i	0.584975	+	0.0926510i	0.441906	−	0.897062i	$-0.354303\pi$
$673$	15.1756	+	2.40357i	0.584975	+	0.0926510i	0.143070	+	0.989713i	$0.454303\pi$
$674$	−10.9559	+	33.7188i	−0.422006	+	1.29880i
$675$	−1.74477	+	3.42430i	−0.0671561	+	0.131801i
$676$	−3.26720	+	1.06158i	−0.125662	+	0.0408299i
$677$	−30.7055	+	9.97682i	−1.18011	+	0.383440i	−0.832407	−	0.554165i	$-0.813038\pi$
$677$	−30.7055	+	9.97682i	−1.18011	+	0.383440i	−0.347701	+	0.937605i	$0.613038\pi$
$678$	15.9250	−	31.2546i	0.611596	−	1.20033i
$679$	1.54787	−	4.76384i	0.0594016	−	0.182819i
$680$	23.8727	+	3.78106i	0.915476	+	0.144997i
$681$	−0.389319	−	1.19820i	−0.0149187	−	0.0459152i
$682$	4.40680	+	27.8235i	0.168745	+	1.06542i
$683$	11.8785	+	11.8785i	0.454518	+	0.454518i	0.896851	−	0.442333i	$-0.145849\pi$
$683$	11.8785	+	11.8785i	0.454518	+	0.454518i	−0.442333	+	0.896851i	$0.645849\pi$
$684$	3.68748	+	7.23710i	0.140994	+	0.276717i
$685$	14.4273	−	2.28507i	0.551240	−	0.0873079i
$686$	−2.73298	+	17.2554i	−0.104346	+	0.658813i
$687$	42.6699	−	31.0015i	1.62796	−	1.18278i
$688$		−	4.83661i		−	0.184394i
$689$	−8.50015	−	11.6995i	−0.323830	−	0.445714i
$690$	−22.9057	−	11.6710i	−0.872005	−	0.444309i
$691$	−23.1214	+	11.7810i	−0.879581	+	0.448169i	−0.834624	−	0.550820i	$-0.814315\pi$
$691$	−23.1214	+	11.7810i	−0.879581	+	0.448169i	−0.0449572	+	0.998989i	$0.514315\pi$
$692$	3.38204	−	4.65498i	0.128566	−	0.176956i
$693$	−8.63947	−	6.27694i	−0.328186	−	0.238441i
$694$	−23.9145	+	23.9145i	−0.907781	+	0.907781i
$695$	−39.0332	−	12.6826i	−1.48061	−	0.481080i
$696$	39.0450			1.48000
$697$	19.0027	−	5.59885i	0.719778	−	0.212072i
$698$	24.6688			0.933727
$699$	25.9051	+	8.41708i	0.979821	+	0.318363i
$700$	0.646881	−	0.646881i	0.0244498	−	0.0244498i
$701$	22.0790	+	16.0413i	0.833911	+	0.605872i	0.920663	−	0.390358i	$-0.127649\pi$
$701$	22.0790	+	16.0413i	0.833911	+	0.605872i	−0.0867523	+	0.996230i	$0.527649\pi$
$702$	4.76888	−	6.56381i	0.179990	−	0.247735i
$703$	5.30042	−	2.70070i	0.199909	−	0.101859i
$704$	−40.6405	−	20.7074i	−1.53170	−	0.780439i
$705$	−11.6302	−	16.0076i	−0.438018	−	0.602880i
$706$		−	34.9413i		−	1.31503i
$707$	−2.85456	+	2.07396i	−0.107357	+	0.0779994i
$708$	0.146515	−	0.925059i	0.00550637	−	0.0347659i
$709$	−44.8571	+	7.10466i	−1.68464	+	0.266821i	−0.924012	−	0.382364i	$-0.875110\pi$
$709$	−44.8571	+	7.10466i	−1.68464	+	0.266821i	−0.760631	+	0.649185i	$0.775110\pi$
$710$	−6.31854	−	12.4008i	−0.237131	−	0.465395i
$711$	20.7546	+	20.7546i	0.778359	+	0.778359i
$712$	0.817998	+	5.16463i	0.0306558	+	0.193553i
$713$	5.32717	+	16.3953i	0.199504	+	0.614010i
$714$	−9.22258	−	1.46071i	−0.345146	−	0.0546658i
$715$	−10.4955	+	32.3018i	−0.392509	+	1.20802i
$716$	−0.471085	+	0.924556i	−0.0176053	+	0.0345523i
$717$	14.1574	−	4.60002i	0.528719	−	0.171791i
$718$	24.9351	−	8.10189i	0.930569	−	0.302360i
$719$	−12.6131	+	24.7546i	−0.470390	+	0.923192i	0.526922	+	0.849914i	$0.323346\pi$
$719$	−12.6131	+	24.7546i	−0.470390	+	0.923192i	−0.997312	+	0.0732784i	$0.976654\pi$
$720$	−3.73587	+	11.4978i	−0.139228	+	0.428499i
$721$	−3.31824	−	0.525557i	−0.123578	−	0.0195728i
$722$	−18.2307	−	56.1084i	−0.678477	−	2.08814i
$723$	−6.58297	−	41.5633i	−0.244823	−	1.54575i
$724$	2.26462	+	2.26462i	0.0841640	+	0.0841640i
$725$	−3.88807	−	7.63077i	−0.144399	−	0.283400i
$726$	40.9875	−	6.49179i	1.52119	−	0.240933i
$727$	−2.75993	+	17.4255i	−0.102360	+	0.646276i	0.882153	+	0.470963i	$0.156094\pi$
$727$	−2.75993	+	17.4255i	−0.102360	+	0.646276i	−0.984513	+	0.175313i	$0.943906\pi$
$728$	−7.31361	+	5.31365i	−0.271060	+	0.196937i
$729$		−	3.10848i		−	0.115129i
$730$	−0.270526	−	0.372347i	−0.0100126	−	0.0137812i
$731$	−5.09261	−	2.59481i	−0.188357	−	0.0959726i
$732$	7.49034	−	3.81652i	0.276851	−	0.141063i
$733$	−5.53747	+	7.62168i	−0.204531	+	0.281513i	−0.898944	−	0.438064i	$-0.855664\pi$
$733$	−5.53747	+	7.62168i	−0.204531	+	0.281513i	0.694413	+	0.719577i	$0.255664\pi$
$734$	16.8421	+	12.2365i	0.621653	+	0.451658i
$735$	22.5120	−	22.5120i	0.830367	−	0.830367i
$736$	−10.8083	−	3.51181i	−0.398397	−	0.129447i
$737$	27.5957			1.01650
$738$	1.81000	+	13.9043i	0.0666271	+	0.511826i
$739$	0.347492			0.0127827			0.00639135	−	0.999980i	$-0.497966\pi$
$739$	0.347492			0.0127827			0.00639135	+	0.999980i	$0.497966\pi$
$740$	−0.949591	−	0.308541i	−0.0349077	−	0.0113422i
$741$	−33.0322	+	33.0322i	−1.21347	+	1.21347i
$742$	6.22761	+	4.52463i	0.228623	+	0.166104i
$743$	4.23794	−	5.83302i	0.155475	−	0.213993i	−0.724173	−	0.689618i	$-0.757778\pi$
$743$	4.23794	−	5.83302i	0.155475	−	0.213993i	0.879648	+	0.475626i	$0.157778\pi$
$744$	27.1227	−	13.8197i	0.994366	−	0.506655i
$745$	12.3129	+	6.27375i	0.451111	+	0.229853i
$746$	−12.0919	−	16.6431i	−0.442717	−	0.609348i
$747$		−	7.75210i		−	0.283635i
$748$	−7.02347	+	5.10285i	−0.256804	+	0.186579i
$749$	−0.603799	+	3.81223i	−0.0220623	+	0.139296i
$750$	−23.4498	+	3.71408i	−0.856264	+	0.135619i
$751$	8.85526	+	17.3794i	0.323133	+	0.634184i	0.994240	−	0.107176i	$-0.0341809\pi$
$751$	8.85526	+	17.3794i	0.323133	+	0.634184i	−0.671107	+	0.741361i	$0.734181\pi$
$752$	6.55944	+	6.55944i	0.239198	+	0.239198i
$753$	0.647060	+	4.08538i	0.0235802	+	0.148879i
$754$	5.58698	+	17.1950i	0.203466	+	0.626203i
$755$	8.51564	+	1.34874i	0.309916	+	0.0490858i
$756$	0.497805	−	1.53209i	0.0181050	−	0.0557215i
$757$	−7.98828	+	15.6779i	−0.290339	+	0.569823i	−0.989396	−	0.145244i	$-0.953603\pi$
$757$	−7.98828	+	15.6779i	−0.290339	+	0.569823i	0.699057	+	0.715066i	$0.253603\pi$
$758$	−42.5256	+	13.8174i	−1.54460	+	0.501871i
$759$	41.1064	−	13.3563i	1.49207	−	0.484802i
$760$	−29.2216	+	57.3506i	−1.05998	+	2.08032i
$761$	7.86010	−	24.1909i	0.284928	−	0.876919i	−0.701492	−	0.712678i	$-0.747482\pi$
$761$	7.86010	−	24.1909i	0.284928	−	0.876919i	0.986420	−	0.164242i	$-0.0525177\pi$
$762$	35.3402	+	5.59734i	1.28024	+	0.202770i
$763$	−4.80970	−	14.8027i	−0.174123	−	0.535895i
$764$	0.268777	+	1.69699i	0.00972402	+	0.0613950i
$765$	10.1021	+	10.1021i	0.365243	+	0.365243i
$766$	−18.5098	−	36.3274i	−0.668785	−	1.31256i
$767$	2.00506	−	0.317570i	0.0723984	−	0.0114668i
$768$	−4.11575	+	25.9858i	−0.148514	+	0.937682i
$769$	−10.8491	+	7.88236i	−0.391230	+	0.284245i	−0.765959	−	0.642889i	$-0.777736\pi$
$769$	−10.8491	+	7.88236i	−0.391230	+	0.284245i	0.374729	+	0.927134i	$0.377736\pi$
$770$		−	18.0791i		−	0.651524i
$771$	36.1001	+	49.6875i	1.30011	+	1.78945i
$772$	−7.64517	−	3.89541i	−0.275156	−	0.140199i
$773$	33.8688	−	17.2570i	1.21817	−	0.620691i	0.277737	−	0.960657i	$-0.410416\pi$
$773$	33.8688	−	17.2570i	1.21817	−	0.620691i	0.940438	+	0.339966i	$0.110416\pi$
$774$	2.37785	−	3.27284i	0.0854702	−	0.117640i
$775$	−5.40172	−	3.92458i	−0.194035	−	0.140975i
$776$	9.53971	−	9.53971i	0.342456	−	0.342456i
$777$	1.71718	+	0.557944i	0.0616033	+	0.0200161i
$778$	−10.7367			−0.384929
$779$	−1.45757	+	52.7353i	−0.0522228	+	1.88944i
$780$	7.84067			0.280741
$781$	22.2544	+	7.23090i	0.796326	+	0.258742i
$782$	10.0712	−	10.0712i	0.360144	−	0.360144i
$783$	−12.2006	−	8.86428i	−0.436015	−	0.316784i
$784$	−8.77326	+	12.0754i	−0.313331	+	0.431263i
$785$	−22.9390	+	11.6880i	−0.818729	+	0.417163i
$786$	−24.1469	−	12.3035i	−0.861292	−	0.438850i
$787$	−28.9010	−	39.7788i	−1.03021	−	1.41796i	−0.904791	−	0.425856i	$-0.859973\pi$
$787$	−28.9010	−	39.7788i	−1.03021	−	1.41796i	−0.125417	−	0.992104i	$-0.540027\pi$
$788$		−	2.46963i		−	0.0879771i
$789$	−7.34812	+	5.33872i	−0.261600	+	0.190063i
$790$	−7.77335	+	49.0790i	−0.276563	+	1.74615i
$791$	14.9104	−	2.36157i	0.530152	−	0.0839679i
$792$	−13.0580	−	25.6277i	−0.463995	−	0.910641i
$793$	12.8844	+	12.8844i	0.457537	+	0.457537i
$794$	1.58312	+	9.99541i	0.0561827	+	0.354724i
$795$	−9.65723	−	29.7219i	−0.342507	−	1.05413i
$796$	−4.82120	−	0.763603i	−0.170883	−	0.0270652i
$797$	1.66232	−	5.11611i	0.0588825	−	0.181222i	−0.917289	−	0.398222i	$-0.869627\pi$
$797$	1.66232	−	5.11611i	0.0588825	−	0.181222i	0.976172	+	0.217000i	$0.0696273\pi$
$798$	11.2890	−	22.1559i	0.399625	−	0.784309i
$799$	10.4257	−	3.38752i	0.368836	−	0.119842i
$800$	4.18616	−	1.36016i	0.148003	−	0.0480891i
$801$	−1.40318	+	2.75389i	−0.0495788	+	0.0973038i
$802$	9.28442	−	28.5745i	0.327844	−	1.00900i
$803$	0.764277	+	0.121050i	0.0269707	+	0.00427175i
$804$	−1.96860	−	6.05872i	−0.0694270	−	0.213674i
$805$	−1.73074	−	10.9274i	−0.0610005	−	0.385142i
$806$	9.96704	+	9.96704i	0.351074	+	0.351074i
$807$	−29.6437	−	58.1789i	−1.04351	−	2.04800i
$808$	−9.38645	+	1.48667i	−0.330214	+	0.0523008i
$809$	−4.90251	+	30.9532i	−0.172363	+	1.08826i	0.738107	+	0.674683i	$0.235720\pi$
$809$	−4.90251	+	30.9532i	−0.172363	+	1.08826i	−0.910470	+	0.413574i	$0.864280\pi$
$810$	27.7111	−	20.1333i	0.973668	−	0.707411i
$811$		−	18.8699i		−	0.662610i	−0.943524	−	0.331305i	$-0.892511\pi$
$811$		−	18.8699i		−	0.662610i	0.943524	−	0.331305i	$-0.107489\pi$
$812$	2.11005	+	2.90423i	0.0740482	+	0.101919i
$813$	−45.3384	−	23.1011i	−1.59009	−	0.810189i
$814$	−4.00985	+	2.04312i	−0.140545	+	0.0716113i
$815$	28.0386	−	38.5918i	0.982149	−	1.35181i
$816$	−14.3784	−	10.4465i	−0.503344	−	0.365701i
$817$	10.7627	−	10.7627i	0.376538	−	0.376538i
$818$	−10.0459	−	3.26411i	−0.351246	−	0.114127i
$819$	−5.34342			−0.186714
$820$	6.43174	−	6.08576i	0.224606	−	0.212524i
$821$	1.59911			0.0558094			0.0279047	−	0.999611i	$-0.491117\pi$
$821$	1.59911			0.0558094			0.0279047	+	0.999611i	$0.491117\pi$
$822$	−14.4552	−	4.69677i	−0.504182	−	0.163819i
$823$	−18.3789	+	18.3789i	−0.640647	+	0.640647i	−0.950715	−	0.310068i	$-0.899648\pi$
$823$	−18.3789	+	18.3789i	−0.640647	+	0.640647i	0.310068	+	0.950715i	$0.399648\pi$
$824$	−7.32056	−	5.31870i	−0.255024	−	0.185286i
$825$	−9.83969	+	13.5432i	−0.342574	+	0.471513i
$826$	−0.962817	+	0.490580i	−0.0335007	+	0.0170694i
$827$	7.57401	+	3.85915i	0.263374	+	0.134196i	0.580692	−	0.814124i	$-0.302782\pi$
$827$	7.57401	+	3.85915i	0.263374	+	0.134196i	−0.317318	+	0.948319i	$0.602782\pi$
$828$	−2.21026	−	3.04216i	−0.0768118	−	0.105722i
$829$		−	0.285264i		−	0.00990764i	−0.999988	−	0.00495382i	$-0.998423\pi$
$829$		−	0.285264i		−	0.00990764i	0.999988	−	0.00495382i	$-0.00157686\pi$
$830$	10.6175	−	7.71409i	0.368540	−	0.267760i
$831$	−8.50106	+	53.6736i	−0.294898	+	1.86192i
$832$	−22.5418	+	3.57027i	−0.781496	+	0.123777i
$833$	8.00769	+	15.7160i	0.277450	+	0.544526i
$834$	30.1969	+	30.1969i	1.04563	+	1.04563i
$835$	−1.21747	−	7.68678i	−0.0421322	−	0.266012i
$836$	−7.14418	−	21.9875i	−0.247087	−	0.760454i
$837$	−11.6127	−	1.83926i	−0.401392	−	0.0635743i
$838$	9.29731	−	28.6142i	0.321170	−	0.988460i
$839$	−5.30778	+	10.4171i	−0.183245	+	0.359638i	−0.964295	−	0.264830i	$-0.914684\pi$
$839$	−5.30778	+	10.4171i	−0.183245	+	0.359638i	0.781050	+	0.624468i	$0.214684\pi$
$840$	−18.5799	+	6.03696i	−0.641066	+	0.208295i
$841$	4.38091	−	1.42344i	0.151066	−	0.0490843i
$842$	−5.96702	+	11.7109i	−0.205637	+	0.403585i
$843$	0.144192	−	0.443776i	0.00496622	−	0.0152845i
$844$	−3.46675	−	0.549079i	−0.119330	−	0.0189001i
$845$	−4.97246	−	15.3036i	−0.171058	−	0.526461i
$846$	1.21378	+	7.66350i	0.0417306	+	0.263476i
$847$	12.6285	+	12.6285i	0.433921	+	0.433921i
$848$	6.65167	+	13.0546i	0.228419	+	0.448298i
$849$	−23.9119	+	3.78727i	−0.820653	+	0.129979i
$850$	−0.862953	+	5.44847i	−0.0295990	+	0.186881i
$851$	−2.22807	+	1.61878i	−0.0763771	+	0.0554912i
$852$		−	5.40186i		−	0.185065i
$853$	−14.3175	−	19.7064i	−0.490223	−	0.674734i	0.490206	−	0.871607i	$-0.336921\pi$
$853$	−14.3175	−	19.7064i	−0.490223	−	0.674734i	−0.980429	+	0.196873i	$0.936921\pi$
$854$	−8.64201	−	4.40332i	−0.295723	−	0.150679i
$855$	−33.8987	+	17.2723i	−1.15931	+	0.590699i
$856$	−6.11052	+	8.41040i	−0.208853	+	0.287462i
$857$	−4.13061	−	3.00106i	−0.141099	−	0.102514i	0.514997	−	0.857192i	$-0.327793\pi$
$857$	−4.13061	−	3.00106i	−0.141099	−	0.102514i	−0.656096	+	0.754678i	$0.727793\pi$
$858$	24.9894	−	24.9894i	0.853123	−	0.853123i
$859$	0.384709	+	0.125000i	0.0131261	+	0.00426493i	0.315573	−	0.948901i	$-0.397803\pi$
$859$	0.384709	+	0.125000i	0.0131261	+	0.00426493i	−0.302447	+	0.953166i	$0.597803\pi$
$860$	−2.55468			−0.0871137
$861$	−11.6307	+	11.0051i	−0.396374	+	0.375052i
$862$	−23.4869			−0.799969
$863$	36.1033	+	11.7307i	1.22897	+	0.399316i	0.850341	−	0.526232i	$-0.176396\pi$
$863$	36.1033	+	11.7307i	1.22897	+	0.399316i	0.378629	+	0.925549i	$0.376396\pi$
$864$	5.48064	−	5.48064i	0.186455	−	0.186455i
$865$	21.8041	+	15.8416i	0.741360	+	0.538630i
$866$	−3.30304	+	4.54624i	−0.112242	+	0.154488i
$867$	14.5220	−	7.39933i	0.493193	−	0.251294i
$868$	2.49368	+	1.27060i	0.0846411	+	0.0431268i
$869$	−49.1060	−	67.5886i	−1.66581	−	2.29279i
$870$			39.0712i			1.32464i
$871$	11.1709	−	8.11615i	0.378512	−	0.275005i
$872$	6.55794	−	41.4052i	0.222080	−	1.40216i
$873$	7.87618	−	1.24747i	0.266568	−	0.0422203i
$874$	17.2193	+	33.7949i	0.582453	+	1.14313i
$875$	−7.22503	−	7.22503i	−0.244250	−	0.244250i
$876$	−0.0279445	−	0.176435i	−0.000944157	−	0.00596117i
$877$	11.4052	+	35.1015i	0.385125	+	1.18529i	0.936389	+	0.350963i	$0.114146\pi$
$877$	11.4052	+	35.1015i	0.385125	+	1.18529i	−0.551264	+	0.834331i	$0.685854\pi$
$878$	14.8664	+	2.35461i	0.501718	+	0.0794643i
$879$	−5.15932	+	15.8788i	−0.174020	+	0.535577i
$880$	15.6222	−	30.6603i	0.526625	−	1.03356i
$881$	−10.6200	+	3.45065i	−0.357798	+	0.116255i	−0.482399	−	0.875951i	$-0.660235\pi$
$881$	−10.6200	+	3.45065i	−0.357798	+	0.116255i	0.124602	+	0.992207i	$0.460235\pi$
$882$	−11.8734	+	3.85789i	−0.399797	+	0.129902i
$883$	−10.6504	+	20.9026i	−0.358415	+	0.703429i	−0.997859	−	0.0654092i	$-0.979165\pi$
$883$	−10.6504	+	20.9026i	−0.358415	+	0.703429i	0.639444	+	0.768838i	$0.279165\pi$
$884$	−1.34235	+	4.13134i	−0.0451483	+	0.138952i
$885$	4.33300	+	0.686280i	0.145652	+	0.0230691i
$886$	5.14158	+	15.8241i	0.172735	+	0.531622i
$887$	4.35893	+	27.5212i	0.146358	+	0.924071i	0.946135	+	0.323773i	$0.104951\pi$
$887$	4.35893	+	27.5212i	0.146358	+	0.924071i	−0.799776	+	0.600298i	$0.795049\pi$
$888$	3.43869	+	3.43869i	0.115395	+	0.115395i
$889$	6.99088	+	13.7204i	0.234467	+	0.460166i
$890$	−5.16811	+	0.818548i	−0.173235	+	0.0274378i
$891$	−9.00883	+	56.8795i	−0.301807	+	1.90554i
$892$	1.79915	−	1.30716i	0.0602400	−	0.0437669i
$893$			29.1928i			0.976899i
$894$	−8.45181	−	11.6329i	−0.282671	−	0.389063i
$895$	−4.33064	−	2.20657i	−0.144757	−	0.0737576i
$896$	4.77344	−	2.43219i	0.159469	−	0.0812537i
$897$	12.7119	−	17.4965i	0.424439	−	0.584190i
$898$	−5.20780	−	3.78369i	−0.173787	−	0.126263i
$899$	18.5265	−	18.5265i	0.617893	−	0.617893i
$900$	1.38513	+	0.450057i	0.0461711	+	0.0150019i
$901$	17.3142			0.576819
$902$	1.10267	−	39.8951i	0.0367150	−	1.32836i
$903$	4.61970			0.153734
$904$	38.6701	+	12.5647i	1.28615	+	0.417895i
$905$	−10.6075	+	10.6075i	−0.352607	+	0.352607i
$906$	−7.25780	−	5.27310i	−0.241124	−	0.175187i
$907$	22.2821	−	30.6687i	0.739865	−	1.01834i	−0.258761	−	0.965941i	$-0.583314\pi$
$907$	22.2821	−	30.6687i	0.739865	−	1.01834i	0.998626	−	0.0523958i	$-0.0166857\pi$
$908$	0.277979	−	0.141638i	0.00922507	−	0.00470041i
$909$	−5.00505	−	2.55020i	−0.166007	−	0.0845848i
$910$	−5.31722	−	7.31853i	−0.176264	−	0.242607i
$911$		−	23.3777i		−	0.774537i	−0.921967	−	0.387269i	$-0.873419\pi$
$911$		−	23.3777i		−	0.774537i	0.921967	−	0.387269i	$-0.126581\pi$
$912$	38.2900	−	27.8193i	1.26791	−	0.921190i
$913$	−3.45174	+	21.7934i	−0.114236	+	0.721258i
$914$	−12.1115	+	1.91827i	−0.400611	+	0.0634506i
$915$	17.8767	+	35.0850i	0.590985	+	1.15987i
$916$	9.23544	+	9.23544i	0.305147	+	0.305147i
$917$	−1.82452	−	11.5196i	−0.0602510	−	0.380410i
$918$	3.00175	+	9.23843i	0.0990725	+	0.304914i
$919$	19.4344	+	3.07810i	0.641080	+	0.101537i	0.468507	−	0.883460i	$-0.344792\pi$
$919$	19.4344	+	3.07810i	0.641080	+	0.101537i	0.172573	+	0.984997i	$0.444792\pi$
$920$	9.20832	−	28.3403i	0.303589	−	0.934352i
$921$	31.2921	−	61.4141i	1.03111	−	2.02366i
$922$	−34.0853	+	11.0750i	−1.12254	+	0.364735i
$923$	11.1354	−	3.61812i	0.366527	−	0.119092i
$924$	3.18563	−	6.25216i	0.104800	−	0.205681i
$925$	0.329619	−	1.01446i	0.0108378	−	0.0333554i
$926$	45.7940	+	7.25305i	1.50488	+	0.238350i
$927$	−1.65278	−	5.08673i	−0.0542844	−	0.167070i
$928$	2.70194	+	17.0594i	0.0886955	+	0.560001i
$929$	5.06327	+	5.06327i	0.166120	+	0.166120i	0.785272	−	0.619151i	$-0.212523\pi$
$929$	5.06327	+	5.06327i	0.166120	+	0.166120i	−0.619151	+	0.785272i	$0.712523\pi$
$930$	13.8290	+	27.1409i	0.453470	+	0.889986i
$931$	−46.3933	+	7.34798i	−1.52048	+	0.240820i
$932$	−1.05516	+	6.66204i	−0.0345630	+	0.218222i
$933$	−26.1885	+	19.0271i	−0.857373	+	0.622918i
$934$			3.32445i			0.108779i
$935$	−23.9019	−	32.8981i	−0.781676	−	1.07588i
$936$	−12.8233	−	6.53380i	−0.419143	−	0.213564i
$937$	38.9861	−	19.8644i	1.27362	−	0.648942i	0.319280	−	0.947660i	$-0.396559\pi$
$937$	38.9861	−	19.8644i	1.27362	−	0.648942i	0.954341	+	0.298718i	$0.0965590\pi$
$938$	−4.32022	+	5.94627i	−0.141060	+	0.194153i
$939$	29.4804	+	21.4187i	0.962055	+	0.698974i
$940$	3.46467	−	3.46467i	0.113005	−	0.113005i
$941$	−24.9275	−	8.09943i	−0.812613	−	0.264034i	−0.126909	−	0.991914i	$-0.540506\pi$
$941$	−24.9275	−	8.09943i	−0.812613	−	0.264034i	−0.685704	+	0.727881i	$0.740506\pi$
$942$	26.7883			0.872809
$943$	−3.15274	−	24.2192i	−0.102667	−	0.788685i
$944$	−2.05676			−0.0669417
$945$	7.17633	+	2.33173i	0.233446	+	0.0758513i
$946$	−8.14213	+	8.14213i	−0.264723	+	0.264723i
$947$	26.7046	+	19.4020i	0.867781	+	0.630480i	0.929991	−	0.367583i	$-0.119815\pi$
$947$	26.7046	+	19.4020i	0.867781	+	0.630480i	−0.0622093	+	0.998063i	$0.519815\pi$
$948$	−11.3362	+	15.6030i	−0.368183	+	0.506760i
$949$	0.344986	−	0.175779i	0.0111987	−	0.00570604i
$950$	−13.0891	−	6.66925i	−0.424667	−	0.216379i
$951$	42.0072	+	57.8180i	1.36218	+	1.87488i
$952$		−	10.8235i		−	0.350792i
$953$	−2.15205	+	1.56356i	−0.0697119	+	0.0506486i	−0.622095	−	0.782941i	$-0.713718\pi$
$953$	−2.15205	+	1.56356i	−0.0697119	+	0.0506486i	0.552384	+	0.833590i	$0.313718\pi$
$954$	−1.91709	+	12.1040i	−0.0620680	+	0.391882i
$955$	−7.94876	+	1.25896i	−0.257216	+	0.0407390i
$956$	1.67353	+	3.28448i	0.0541257	+	0.106228i
$957$	−46.4496	−	46.4496i	−1.50150	−	1.50150i
$958$	6.80288	+	42.9517i	0.219791	+	1.38771i
$959$	−2.02132	−	6.22098i	−0.0652718	−	0.200886i
$960$	−48.7137	−	7.71549i	−1.57223	−	0.249016i
$961$	−3.26738	+	10.0559i	−0.105399	+	0.324385i
$962$	−1.02231	+	2.00640i	−0.0329607	+	0.0646891i
$963$	−5.84401	+	1.89884i	−0.188321	+	0.0611891i
$964$	9.91070	−	3.22018i	0.319202	−	0.103715i
$965$	18.2462	−	35.8102i	0.587366	−	1.15277i
$966$	−3.55739	+	10.9485i	−0.114457	+	0.352263i
$967$	12.8463	+	2.03466i	0.413110	+	0.0654303i	0.359531	−	0.933133i	$-0.382937\pi$
$967$	12.8463	+	2.03466i	0.413110	+	0.0654303i	0.0535799	+	0.998564i	$0.482937\pi$
$968$	14.8645	+	45.7482i	0.477762	+	1.47040i
$969$	−8.74940	−	55.2415i	−0.281071	−	1.77461i
$970$	9.54613	+	9.54613i	0.306508	+	0.306508i
$971$	−3.29747	−	6.47166i	−0.105821	−	0.207685i	0.832024	−	0.554739i	$-0.187182\pi$
$971$	−3.29747	−	6.47166i	−0.105821	−	0.207685i	−0.937845	+	0.347054i	$0.887182\pi$
$972$	8.94247	−	1.41635i	0.286830	−	0.0454294i
$973$	−2.87505	+	18.1524i	−0.0921700	+	0.581939i
$974$	−14.9503	+	10.8620i	−0.479039	+	0.348042i
$975$			8.37632i			0.268257i
$976$	−10.8511	−	14.9352i	−0.347334	−	0.478065i
$977$	26.7289	+	13.6190i	0.855132	+	0.435711i	0.825870	−	0.563860i	$-0.190684\pi$
$977$	26.7289	+	13.6190i	0.855132	+	0.435711i	0.0292617	+	0.999572i	$0.490684\pi$
$978$	−44.2251	+	22.5338i	−1.41416	+	0.720552i
$979$	5.17095	−	7.11720i	0.165264	−	0.227467i
$980$	6.37815	+	4.63399i	0.203742	+	0.148028i
$981$	17.5213	−	17.5213i	0.559411	−	0.559411i
$982$	9.63997	+	3.13222i	0.307624	+	0.0999530i
$983$	−47.8093			−1.52488			−0.762439	−	0.647060i	$-0.775998\pi$
$983$	−47.8093			−1.52488			−0.762439	+	0.647060i	$0.775998\pi$
$984$	−41.3685	+	12.1886i	−1.31878	+	0.388557i
$985$	11.5678			0.368582
$986$	−20.5871	−	6.68915i	−0.655626	−	0.213026i
$987$	−6.26526	+	6.26526i	−0.199426	+	0.199426i
$988$	−9.35875	−	6.79953i	−0.297741	−	0.216322i
$989$	−4.14185	+	5.70077i	−0.131703	+	0.181274i
$990$	25.6449	−	13.0668i	0.815050	−	0.415289i
$991$	−37.8416	−	19.2812i	−1.20208	−	0.612489i	−0.265894	−	0.964002i	$-0.585667\pi$
$991$	−37.8416	−	19.2812i	−1.20208	−	0.612489i	−0.936183	+	0.351513i	$0.885667\pi$
$992$	7.91496	+	10.8940i	0.251300	+	0.345885i
$993$		−	4.13151i		−	0.131110i
$994$	−5.04213	+	3.66332i	−0.159927	+	0.116193i
$995$	3.57673	−	22.5826i	0.113390	−	0.715917i
$996$	5.03106	−	0.796841i	0.159415	−	0.0252489i
$997$	−19.2309	−	37.7427i	−0.609048	−	1.19532i	−0.965351	−	0.260954i	$-0.915963\pi$
$997$	−19.2309	−	37.7427i	−0.609048	−	1.19532i	0.356303	−	0.934370i	$-0.384037\pi$
$998$	6.57516	+	6.57516i	0.208133	+	0.208133i
$999$	−0.293833	−	1.85519i	−0.00929646	−	0.0586955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.20.3	✓	24
3.2	odd	2		369.2.u.a.307.1		24
4.3	odd	2		656.2.bs.d.225.2		24
41.11	odd	40		1681.2.a.m.1.15		24
41.30	odd	40		1681.2.a.m.1.16		24
41.39	even	20	inner	41.2.g.a.39.3	yes	24
123.80	odd	20		369.2.u.a.244.1		24
164.39	odd	20		656.2.bs.d.449.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.3	✓	24	1.1	even	1	trivial
41.2.g.a.39.3	yes	24	41.39	even	20	inner
369.2.u.a.244.1		24	123.80	odd	20
369.2.u.a.307.1		24	3.2	odd	2
656.2.bs.d.225.2		24	4.3	odd	2
656.2.bs.d.449.2		24	164.39	odd	20
1681.2.a.m.1.15		24	41.11	odd	40
1681.2.a.m.1.16		24	41.30	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)

\(f(q)\)	\(=\)	\(q+(1.14785 + 0.372958i) q^{2} +(-1.55151 + 1.55151i) q^{3} +(-0.439578 - 0.319372i) q^{4} +(1.49595 - 2.05900i) q^{5} +(-2.35955 + 1.20225i) q^{6} +(-1.01547 - 0.517405i) q^{7} +(-1.80427 - 2.48337i) q^{8} -1.81438i q^{9} +O(q^{10})\)	\(q+(1.14785 + 0.372958i) q^{2} +(-1.55151 + 1.55151i) q^{3} +(-0.439578 - 0.319372i) q^{4} +(1.49595 - 2.05900i) q^{5} +(-2.35955 + 1.20225i) q^{6} +(-1.01547 - 0.517405i) q^{7} +(-1.80427 - 2.48337i) q^{8} -1.81438i q^{9} +(2.48504 - 1.80549i) q^{10} +(-0.807883 + 5.10077i) q^{11} +(1.17752 - 0.186501i) q^{12} +(1.17315 + 2.30243i) q^{13} +(-0.972629 - 0.972629i) q^{14} +(0.873576 + 5.51554i) q^{15} +(-0.809030 - 2.48994i) q^{16} +(-3.05576 - 0.483986i) q^{17} +(0.676690 - 2.08264i) q^{18} +(3.74044 - 7.34102i) q^{19} +(-1.31517 + 0.427326i) q^{20} +(2.37827 - 0.772746i) q^{21} +(-2.82970 + 5.55360i) q^{22} +(-1.17869 + 3.62763i) q^{23} +(6.65233 + 1.05363i) q^{24} +(-0.456519 - 1.40502i) q^{25} +(0.487884 + 3.08038i) q^{26} +(-1.83950 - 1.83950i) q^{27} +(0.281132 + 0.551752i) q^{28} +(5.72573 - 0.906866i) q^{29} +(-1.05433 + 6.65681i) q^{30} +(3.65641 - 2.65654i) q^{31} +2.97943i q^{32} +(-6.66047 - 9.16735i) q^{33} +(-3.32705 - 1.69521i) q^{34} +(-2.58442 + 1.31683i) q^{35} +(-0.579464 + 0.797564i) q^{36} +(0.584132 + 0.424397i) q^{37} +(7.03134 - 7.03134i) q^{38} +(-5.39241 - 1.75210i) q^{39} -7.81235 q^{40} +(-5.78336 + 2.74822i) q^{41} +3.01809 q^{42} +(1.75698 + 0.570876i) q^{43} +(1.98417 - 1.98417i) q^{44} +(-3.73581 - 2.71423i) q^{45} +(-2.70591 + 3.72436i) q^{46} +(-3.15704 + 1.60859i) q^{47} +(5.11839 + 2.60795i) q^{48} +(-3.35104 - 4.61230i) q^{49} -1.78301i q^{50} +(5.49197 - 3.99015i) q^{51} +(0.219643 - 1.38677i) q^{52} +(-5.52741 + 0.875456i) q^{53} +(-1.42541 - 2.79752i) q^{54} +(9.29392 + 9.29392i) q^{55} +(0.547268 + 3.45532i) q^{56} +(5.58635 + 17.1930i) q^{57} +(6.91048 + 1.09451i) q^{58} +(0.242763 - 0.747149i) q^{59} +(1.37751 - 2.70351i) q^{60} +(6.70623 - 2.17898i) q^{61} +(5.18778 - 1.68561i) q^{62} +(-0.938773 + 1.84244i) q^{63} +(-2.72926 + 8.39980i) q^{64} +(6.49567 + 1.02881i) q^{65} +(-4.22616 - 13.0068i) q^{66} +(-0.835907 - 5.27771i) q^{67} +(1.18868 + 1.18868i) q^{68} +(-3.79956 - 7.45706i) q^{69} +(-3.45764 + 0.547637i) q^{70} +(0.708805 - 4.47522i) q^{71} +(-4.50579 + 3.27365i) q^{72} -0.149836i q^{73} +(0.512213 + 0.705000i) q^{74} +(2.88820 + 1.47161i) q^{75} +(-3.98873 + 2.03236i) q^{76} +(3.45954 - 4.76165i) q^{77} +(-5.53620 - 4.02229i) q^{78} +(-11.4389 + 11.4389i) q^{79} +(-6.33704 - 2.05903i) q^{80} +11.1512 q^{81} +(-7.66339 + 0.997584i) q^{82} +4.27258 q^{83} +(-1.29223 - 0.419871i) q^{84} +(-5.56779 + 5.56779i) q^{85} +(1.80383 + 1.31056i) q^{86} +(-7.47653 + 10.2906i) q^{87} +(14.1247 - 7.19691i) q^{88} +(-1.51781 - 0.773362i) q^{89} +(-3.27585 - 4.50882i) q^{90} -2.94503i q^{91} +(1.67669 - 1.21819i) q^{92} +(-1.55132 + 9.79463i) q^{93} +(-4.22374 + 0.668975i) q^{94} +(-9.51963 - 18.6833i) q^{95} +(-4.62262 - 4.62262i) q^{96} +(0.687542 + 4.34097i) q^{97} +(-2.12628 - 6.54402i) q^{98} +(9.25476 + 1.46581i) 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