LMFDB - Embedded newform 966.2.q.h.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	966.127
Dual form			966.2.q.h.715.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-3.32453 + 0.976169i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-3.32453 + 0.976169i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(2.26901 - 2.61858i) q^{10} +(2.54487 + 1.63549i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-1.59644 + 1.84240i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.493104 + 3.42961i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.30076 + 5.03796i) q^{17} +(0.959493 - 0.281733i) q^{18} +(1.44193 - 3.15739i) q^{19} +(-0.493104 + 3.42961i) q^{20} +(-0.841254 + 0.540641i) q^{21} -3.02510 q^{22} +(-1.26039 - 4.62725i) q^{23} +1.00000 q^{24} +(5.89331 - 3.78740i) q^{25} +(0.346941 - 2.41302i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-0.427245 - 0.935536i) q^{29} +(-2.26901 - 2.61858i) q^{30} +(-1.08734 - 7.56259i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.98102 - 2.28622i) q^{33} +(-4.65925 - 2.99432i) q^{34} +(2.91484 + 1.87326i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.29441 + 0.380074i) q^{37} +(0.493984 + 3.43573i) q^{38} +(1.59644 + 1.84240i) q^{39} +(-1.43936 - 3.15177i) q^{40} +(10.4718 - 3.07479i) q^{41} +(0.415415 - 0.909632i) q^{42} +(1.83622 - 12.7712i) q^{43} +(2.54487 - 1.63549i) q^{44} +3.46488 q^{45} +(3.56199 + 3.21127i) q^{46} -6.57110 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-2.91015 + 6.37233i) q^{50} +(5.31411 - 1.56036i) q^{51} +(1.01271 + 2.21754i) q^{52} +(4.54133 + 5.24097i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-10.0570 - 2.95301i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-2.92004 - 1.87660i) q^{57} +(0.865210 + 0.556037i) q^{58} +(1.52911 - 1.76469i) q^{59} +(3.32453 + 0.976169i) q^{60} +(-0.547998 - 3.81141i) q^{61} +(5.00337 + 5.77420i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(3.50893 - 7.68349i) q^{65} +(-0.430516 + 2.99431i) q^{66} +(9.99784 - 6.42522i) q^{67} +5.53846 q^{68} +(-4.75952 + 0.589038i) q^{69} -3.46488 q^{70} +(4.76164 - 3.06012i) q^{71} +(0.142315 - 0.989821i) q^{72} +(-3.46027 + 7.57694i) q^{73} +(-1.29441 + 0.380074i) q^{74} +(-2.91015 - 6.37233i) q^{75} +(-2.27306 - 2.62325i) q^{76} +(-0.430516 - 2.99431i) q^{77} +(-2.33909 - 0.686818i) q^{78} +(4.08418 - 4.71339i) q^{79} +(2.91484 + 1.87326i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-7.14705 + 8.24814i) q^{82} +(-14.2252 - 4.17690i) q^{83} +(0.142315 + 0.989821i) q^{84} +(-12.5668 - 14.5029i) q^{85} +(5.35991 + 11.7366i) q^{86} +(-0.986817 + 0.289756i) q^{87} +(-1.25667 + 2.75172i) q^{88} +(0.207928 - 1.44617i) q^{89} +(-2.91484 + 1.87326i) q^{90} +2.43784 q^{91} +(-4.73268 - 0.775734i) q^{92} -7.64036 q^{93} +(5.52796 - 3.55261i) q^{94} +(-1.71159 + 11.9044i) q^{95} +(0.415415 - 0.909632i) q^{96} +(6.69423 - 1.96560i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(-1.98102 - 2.28622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−3.32453	+	0.976169i	−1.48677	+	0.436556i	−0.921510	−	0.388354i	$-0.873044\pi$
$5$	−3.32453	+	0.976169i	−1.48677	+	0.436556i	−0.565264	+	0.824910i	$0.691226\pi$
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	2.26901	−	2.61858i	0.717525	−	0.828068i
$11$	2.54487	+	1.63549i	0.767308	+	0.493119i	0.864799	−	0.502117i	$-0.167445\pi$
$11$	2.54487	+	1.63549i	0.767308	+	0.493119i	−0.0974913	+	0.995236i	$0.531082\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	−1.59644	+	1.84240i	−0.442774	+	0.510988i	−0.932640	−	0.360810i	$-0.882500\pi$
$13$	−1.59644	+	1.84240i	−0.442774	+	0.510988i	0.489865	+	0.871798i	$0.337046\pi$
$14$	0.959493	+	0.281733i	0.256435	+	0.0752962i
$15$	0.493104	+	3.42961i	0.127319	+	0.885522i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	2.30076	+	5.03796i	0.558016	+	1.22188i	0.952937	+	0.303170i	$0.0980448\pi$
$17$	2.30076	+	5.03796i	0.558016	+	1.22188i	−0.394921	+	0.918715i	$0.629228\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	1.44193	−	3.15739i	0.330802	−	0.724355i	−0.669020	−	0.743245i	$-0.733286\pi$
$19$	1.44193	−	3.15739i	0.330802	−	0.724355i	0.999822	+	0.0188898i	$0.00601317\pi$
$20$	−0.493104	+	3.42961i	−0.110261	+	0.766885i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	−3.02510			−0.644953
$23$	−1.26039	−	4.62725i	−0.262810	−	0.964848i
$23$	−1.26039	−	4.62725i	−0.262810	−	0.964848i
$24$	1.00000			0.204124
$25$	5.89331	−	3.78740i	1.17866	−	0.757480i
$26$	0.346941	−	2.41302i	0.0680406	−	0.473233i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	−0.427245	−	0.935536i	−0.0793374	−	0.173725i	0.865806	−	0.500379i	$-0.166806\pi$
$29$	−0.427245	−	0.935536i	−0.0793374	−	0.173725i	−0.945144	+	0.326654i	$0.894079\pi$
$30$	−2.26901	−	2.61858i	−0.414263	−	0.478085i
$31$	−1.08734	−	7.56259i	−0.195291	−	1.35828i	−0.817725	−	0.575609i	$-0.804765\pi$
$31$	−1.08734	−	7.56259i	−0.195291	−	1.35828i	0.622434	−	0.782672i	$-0.286144\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	1.98102	−	2.28622i	0.344851	−	0.397979i
$34$	−4.65925	−	2.99432i	−0.799055	−	0.513521i
$35$	2.91484	+	1.87326i	0.492698	+	0.316638i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	1.29441	+	0.380074i	0.212800	+	0.0624838i	0.386395	−	0.922333i	$-0.373720\pi$
$37$	1.29441	+	0.380074i	0.212800	+	0.0624838i	−0.173595	+	0.984817i	$0.555538\pi$
$38$	0.493984	+	3.43573i	0.0801347	+	0.557349i
$39$	1.59644	+	1.84240i	0.255636	+	0.295019i
$40$	−1.43936	−	3.15177i	−0.227583	−	0.498338i
$41$	10.4718	−	3.07479i	1.63542	−	0.480201i	0.670314	−	0.742078i	$-0.266160\pi$
$41$	10.4718	−	3.07479i	1.63542	−	0.480201i	0.965101	+	0.261877i	$0.0843414\pi$
$42$	0.415415	−	0.909632i	0.0640999	−	0.140359i
$43$	1.83622	−	12.7712i	0.280022	−	1.94759i	−0.0373798	−	0.999301i	$-0.511901\pi$
$43$	1.83622	−	12.7712i	0.280022	−	1.94759i	0.317401	−	0.948291i	$-0.397190\pi$
$44$	2.54487	−	1.63549i	0.383654	−	0.246559i
$45$	3.46488			0.516514
$46$	3.56199	+	3.21127i	0.525186	+	0.473476i
$47$	−6.57110			−0.958493			−0.479247	−	0.877680i	$-0.659090\pi$
$47$	−6.57110			−0.958493			−0.479247	+	0.877680i	$0.659090\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−2.91015	+	6.37233i	−0.411557	+	0.901183i
$51$	5.31411	−	1.56036i	0.744125	−	0.218495i
$52$	1.01271	+	2.21754i	0.140438	+	0.307517i
$53$	4.54133	+	5.24097i	0.623799	+	0.719903i	0.976424	−	0.215862i	$-0.0692562\pi$
$53$	4.54133	+	5.24097i	0.623799	+	0.719903i	−0.352625	+	0.935765i	$0.614711\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	−10.0570	−	2.95301i	−1.35609	−	0.398183i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	−2.92004	−	1.87660i	−0.386769	−	0.248561i
$58$	0.865210	+	0.556037i	0.113608	+	0.0730112i
$59$	1.52911	−	1.76469i	0.199074	−	0.229743i	−0.647432	−	0.762124i	$-0.724157\pi$
$59$	1.52911	−	1.76469i	0.199074	−	0.229743i	0.846505	+	0.532380i	$0.178702\pi$
$60$	3.32453	+	0.976169i	0.429195	+	0.126023i
$61$	−0.547998	−	3.81141i	−0.0701640	−	0.488001i	−0.994358	−	0.106077i	$-0.966171\pi$
$61$	−0.547998	−	3.81141i	−0.0701640	−	0.488001i	0.924194	−	0.381924i	$-0.124738\pi$
$62$	5.00337	+	5.77420i	0.635429	+	0.733324i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	3.50893	−	7.68349i	0.435230	−	0.953020i
$66$	−0.430516	+	2.99431i	−0.0529929	+	0.368574i
$67$	9.99784	−	6.42522i	1.22143	−	0.784966i	0.238896	−	0.971045i	$-0.423215\pi$
$67$	9.99784	−	6.42522i	1.22143	−	0.784966i	0.982535	+	0.186080i	$0.0595782\pi$
$68$	5.53846			0.671637
$69$	−4.75952	+	0.589038i	−0.572979	+	0.0709118i
$70$	−3.46488			−0.414132
$71$	4.76164	−	3.06012i	0.565103	−	0.363169i	−0.226683	−	0.973969i	$-0.572788\pi$
$71$	4.76164	−	3.06012i	0.565103	−	0.363169i	0.791786	+	0.610799i	$0.209152\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	−3.46027	+	7.57694i	−0.404994	+	0.886814i	0.591745	+	0.806125i	$0.298439\pi$
$73$	−3.46027	+	7.57694i	−0.404994	+	0.886814i	−0.996739	+	0.0806885i	$0.974288\pi$
$74$	−1.29441	+	0.380074i	−0.150473	+	0.0441827i
$75$	−2.91015	−	6.37233i	−0.336035	−	0.735813i
$76$	−2.27306	−	2.62325i	−0.260738	−	0.300908i
$77$	−0.430516	−	2.99431i	−0.0490619	−	0.341233i
$78$	−2.33909	−	0.686818i	−0.264850	−	0.0777669i
$79$	4.08418	−	4.71339i	0.459506	−	0.530298i	−0.477957	−	0.878383i	$-0.658623\pi$
$79$	4.08418	−	4.71339i	0.459506	−	0.530298i	0.937463	+	0.348085i	$0.113168\pi$
$80$	2.91484	+	1.87326i	0.325889	+	0.209436i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−7.14705	+	8.24814i	−0.789260	+	0.910855i
$83$	−14.2252	−	4.17690i	−1.56142	−	0.458474i	−0.616930	−	0.787018i	$-0.711624\pi$
$83$	−14.2252	−	4.17690i	−1.56142	−	0.458474i	−0.944489	+	0.328544i	$0.893442\pi$
$84$	0.142315	+	0.989821i	0.0155278	+	0.107998i
$85$	−12.5668	−	14.5029i	−1.36307	−	1.57306i
$86$	5.35991	+	11.7366i	0.577974	+	1.26559i
$87$	−0.986817	+	0.289756i	−0.105798	+	0.0310651i
$88$	−1.25667	+	2.75172i	−0.133962	+	0.293335i
$89$	0.207928	−	1.44617i	0.0220404	−	0.153294i	−0.975829	−	0.218535i	$-0.929872\pi$
$89$	0.207928	−	1.44617i	0.0220404	−	0.153294i	0.997870	+	0.0652405i	$0.0207815\pi$
$90$	−2.91484	+	1.87326i	−0.307251	+	0.197458i
$91$	2.43784			0.255555
$92$	−4.73268	−	0.775734i	−0.493416	−	0.0808759i
$93$	−7.64036			−0.792268
$94$	5.52796	−	3.55261i	0.570166	−	0.366423i
$95$	−1.71159	+	11.9044i	−0.175606	+	1.22137i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	6.69423	−	1.96560i	0.679696	−	0.199577i	0.0763797	−	0.997079i	$-0.475664\pi$
$97$	6.69423	−	1.96560i	0.679696	−	0.199577i	0.603316	+	0.797502i	$0.293846\pi$
$98$	−0.415415	−	0.909632i	−0.0419633	−	0.0918867i
$99$	−1.98102	−	2.28622i	−0.199100	−	0.229773i
$100$	−0.996971	−	6.93409i	−0.0996971	−	0.693409i
$101$	−6.36937	−	1.87022i	−0.633776	−	0.186093i	−0.0509639	−	0.998700i	$-0.516229\pi$
$101$	−6.36937	−	1.87022i	−0.633776	−	0.186093i	−0.582812	+	0.812607i	$0.698048\pi$
$102$	−3.62692	+	4.18569i	−0.359119	+	0.414445i
$103$	10.1165	+	6.50149i	0.996810	+	0.640611i	0.933947	−	0.357411i	$-0.116341\pi$
$103$	10.1165	+	6.50149i	0.996810	+	0.640611i	0.0628628	+	0.998022i	$0.479977\pi$
$104$	−2.05084	−	1.31799i	−0.201101	−	0.129240i
$105$	2.26901	−	2.61858i	0.221433	−	0.255547i
$106$	−6.65389	−	1.95376i	−0.646283	−	0.189766i
$107$	−0.300833	−	2.09234i	−0.0290826	−	0.202274i	0.970100	−	0.242707i	$-0.0780354\pi$
$107$	−0.300833	−	2.09234i	−0.0290826	−	0.202274i	−0.999182	+	0.0404330i	$0.987126\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	5.46583	+	11.9685i	0.523531	+	1.14637i	0.968085	+	0.250622i	$0.0806350\pi$
$109$	5.46583	+	11.9685i	0.523531	+	1.14637i	−0.444554	+	0.895752i	$0.646638\pi$
$110$	10.0570	−	2.95301i	0.958899	−	0.281558i
$111$	0.560420	−	1.22715i	0.0531927	−	0.116476i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	7.47179	−	4.80183i	0.702887	−	0.451718i	−0.139760	−	0.990185i	$-0.544633\pi$
$113$	7.47179	−	4.80183i	0.702887	−	0.451718i	0.842646	+	0.538468i	$0.180997\pi$
$114$	3.47106			0.325095
$115$	8.70719	+	14.1531i	0.811949	+	1.31978i
$116$	−1.02848			−0.0954917
$117$	2.05084	−	1.31799i	0.189600	−	0.121849i
$118$	−0.332308	+	2.31125i	−0.0305915	+	0.212768i
$119$	2.30076	−	5.03796i	0.210910	−	0.461829i
$120$	−3.32453	+	0.976169i	−0.303486	+	0.0891117i
$121$	−0.768015	−	1.68172i	−0.0698196	−	0.152884i
$122$	2.52161	+	2.91009i	0.228296	+	0.263467i
$123$	−1.55320	−	10.8028i	−0.140048	−	0.974053i
$124$	−7.33087	−	2.15254i	−0.658331	−	0.193304i
$125$	−4.55026	+	5.25128i	−0.406988	+	0.469689i
$126$	−0.841254	−	0.540641i	−0.0749448	−	0.0481641i
$127$	16.2608	+	10.4502i	1.44291	+	0.927302i	0.999520	+	0.0309730i	$0.00986058\pi$
$127$	16.2608	+	10.4502i	1.44291	+	0.927302i	0.443390	+	0.896329i	$0.353776\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	−12.3799	−	3.63507i	−1.08999	−	0.320050i
$130$	1.20211	+	8.36084i	0.105432	+	0.733294i
$131$	3.82972	+	4.41974i	0.334604	+	0.386154i	0.897972	−	0.440052i	$-0.145040\pi$
$131$	3.82972	+	4.41974i	0.334604	+	0.386154i	−0.563368	+	0.826206i	$0.690495\pi$
$132$	−1.25667	−	2.75172i	−0.109379	−	0.239507i
$133$	−3.33046	+	0.977911i	−0.288787	+	0.0847957i
$134$	−4.93698	+	10.8105i	−0.426490	+	0.933883i
$135$	0.493104	−	3.42961i	0.0424396	−	0.295174i
$136$	−4.65925	+	2.99432i	−0.399527	+	0.256761i
$137$	15.6052			1.33324			0.666620	−	0.745398i	$-0.267740\pi$
$137$	15.6052			1.33324			0.666620	+	0.745398i	$0.267740\pi$
$138$	3.68551	−	3.06872i	0.313731	−	0.261227i
$139$	−5.74154			−0.486991			−0.243496	−	0.969902i	$-0.578294\pi$
$139$	−5.74154			−0.486991			−0.243496	+	0.969902i	$0.578294\pi$
$140$	2.91484	−	1.87326i	0.246349	−	0.158319i
$141$	−0.935165	+	6.50422i	−0.0787551	+	0.547754i
$142$	−2.35132	+	5.14867i	−0.197318	+	0.432067i
$143$	−7.07597	+	2.07769i	−0.591722	+	0.173745i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	2.33363	+	2.69315i	0.193797	+	0.223654i
$146$	−1.18544	−	8.24489i	−0.0981074	−	0.682352i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	0.883447	−	1.01955i	0.0726189	−	0.0838067i
$149$	−7.31786	−	4.70291i	−0.599503	−	0.385277i	0.205405	−	0.978677i	$-0.434149\pi$
$149$	−7.31786	−	4.70291i	−0.599503	−	0.385277i	−0.804908	+	0.593400i	$0.797785\pi$
$150$	5.89331	+	3.78740i	0.481187	+	0.309240i
$151$	12.3292	−	14.2286i	1.00333	−	1.15791i	0.0158984	−	0.999874i	$-0.494939\pi$
$151$	12.3292	−	14.2286i	1.00333	−	1.15791i	0.987434	−	0.158033i	$-0.0505154\pi$
$152$	3.33046	+	0.977911i	0.270136	+	0.0793191i
$153$	−0.788205	−	5.48209i	−0.0637226	−	0.443200i
$154$	1.98102	+	2.28622i	0.159635	+	0.184228i
$155$	10.9972	+	24.0806i	0.883320	+	1.93420i
$156$	2.33909	−	0.686818i	0.187277	−	0.0549895i
$157$	2.66767	−	5.84139i	0.212904	−	0.466194i	−0.772807	−	0.634641i	$-0.781148\pi$
$157$	2.66767	−	5.84139i	0.212904	−	0.466194i	0.985711	+	0.168447i	$0.0538753\pi$
$158$	−0.887577	+	6.17323i	−0.0706118	+	0.491116i
$159$	5.83392	−	3.74923i	0.462660	−	0.297334i
$160$	−3.46488			−0.273923
$161$	−2.67166	+	3.98274i	−0.210556	+	0.313884i
$162$	−1.00000			−0.0785674
$163$	−12.8831	+	8.27948i	−1.00908	+	0.648499i	−0.937156	−	0.348911i	$-0.886552\pi$
$163$	−12.8831	+	8.27948i	−1.00908	+	0.648499i	−0.0719284	+	0.997410i	$0.522915\pi$
$164$	1.55320	−	10.8028i	0.121285	−	0.843554i
$165$	−4.35421	+	9.53440i	−0.338975	+	0.742252i
$166$	14.2252	−	4.17690i	1.10409	−	0.324190i
$167$	1.70612	+	3.73589i	0.132024	+	0.289092i	0.964086	−	0.265591i	$-0.0855670\pi$
$167$	1.70612	+	3.73589i	0.132024	+	0.289092i	−0.832062	+	0.554683i	$0.812840\pi$
$168$	−0.654861	−	0.755750i	−0.0505236	−	0.0583073i
$169$	1.00431	+	6.98512i	0.0772545	+	0.537317i
$170$	18.4128	+	5.40648i	1.41219	+	0.414658i
$171$	−2.27306	+	2.62325i	−0.173825	+	0.200605i
$172$	−10.8543	−	6.97564i	−0.827634	−	0.531888i
$173$	1.74344	+	1.12044i	0.132551	+	0.0851855i	0.605236	−	0.796046i	$-0.293079\pi$
$173$	1.74344	+	1.12044i	0.132551	+	0.0851855i	−0.472685	+	0.881232i	$0.656715\pi$
$174$	0.673509	−	0.777271i	0.0510586	−	0.0589248i
$175$	−6.72162	−	1.97365i	−0.508107	−	0.149194i
$176$	−0.430516	−	2.99431i	−0.0324514	−	0.225704i
$177$	−1.52911	−	1.76469i	−0.114935	−	0.132642i
$178$	0.606940	+	1.32901i	0.0454921	+	0.0996137i
$179$	19.7854	−	5.80951i	1.47883	−	0.434223i	0.559871	−	0.828580i	$-0.310851\pi$
$179$	19.7854	−	5.80951i	1.47883	−	0.434223i	0.918958	+	0.394356i	$0.129032\pi$
$180$	1.43936	−	3.15177i	0.107284	−	0.234919i
$181$	−0.924782	+	6.43200i	−0.0687385	+	0.478087i	0.926154	+	0.377146i	$0.123094\pi$
$181$	−0.924782	+	6.43200i	−0.0687385	+	0.478087i	−0.994892	+	0.100941i	$0.967815\pi$
$182$	−2.05084	+	1.31799i	−0.152018	+	0.0976963i
$183$	−3.85060			−0.284645
$184$	4.40078	−	1.90609i	0.324429	−	0.140519i
$185$	−4.67433			−0.343664
$186$	6.42748	−	4.13069i	0.471285	−	0.302877i
$187$	−2.38440	+	16.5838i	−0.174364	+	1.21273i
$188$	−2.72973	+	5.97728i	−0.199086	+	0.435938i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	−4.99612	−	10.9400i	−0.362457	−	0.793669i
$191$	−14.2443	−	16.4387i	−1.03068	−	1.18947i	−0.981654	−	0.190668i	$-0.938934\pi$
$191$	−14.2443	−	16.4387i	−1.03068	−	1.18947i	−0.0490238	−	0.998798i	$-0.515611\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	−18.5607	−	5.44992i	−1.33603	−	0.392294i	−0.465778	−	0.884902i	$-0.654225\pi$
$193$	−18.5607	−	5.44992i	−1.33603	−	0.392294i	−0.870251	+	0.492608i	$0.836044\pi$
$194$	−4.56886	+	5.27274i	−0.328025	+	0.378561i
$195$	−7.10591	−	4.56669i	−0.508865	−	0.327028i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−10.6143	+	12.2496i	−0.756238	+	0.872745i	−0.995157	−	0.0982941i	$-0.968661\pi$
$197$	−10.6143	+	12.2496i	−0.756238	+	0.872745i	0.238919	+	0.971039i	$0.423207\pi$
$198$	2.90256	+	0.852268i	0.206276	+	0.0605681i
$199$	−2.55161	−	17.7469i	−0.180879	−	1.25804i	−0.854690	−	0.519138i	$-0.826253\pi$
$199$	−2.55161	−	17.7469i	−0.180879	−	1.25804i	0.673811	−	0.738904i	$-0.264656\pi$
$200$	4.58756	+	5.29432i	0.324389	+	0.374365i
$201$	−4.93698	−	10.8105i	−0.348228	−	0.762512i
$202$	6.36937	−	1.87022i	0.448147	−	0.131588i
$203$	−0.427245	+	0.935536i	−0.0299867	+	0.0656617i
$204$	0.788205	−	5.48209i	0.0551854	−	0.383823i
$205$	−31.8122	+	20.4444i	−2.22186	+	1.42790i
$206$	−12.0255			−0.837858
$207$	−0.0943081	+	4.79490i	−0.00655487	+	0.333269i
$208$	2.43784			0.169034
$209$	8.83341	−	5.67689i	0.611020	−	0.392679i
$210$	−0.493104	+	3.42961i	−0.0340274	+	0.236666i
$211$	3.72431	−	8.15510i	0.256392	−	0.561420i	−0.737039	−	0.675850i	$-0.763777\pi$
$211$	3.72431	−	8.15510i	0.256392	−	0.561420i	0.993431	+	0.114430i	$0.0365040\pi$
$212$	6.65389	−	1.95376i	0.456991	−	0.134185i
$213$	−2.35132	−	5.14867i	−0.161110	−	0.352781i
$214$	1.38428	+	1.59754i	0.0946275	+	0.109206i
$215$	6.36230	+	44.2507i	0.433905	+	3.01788i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−5.00337	+	5.77420i	−0.339651	+	0.391978i
$218$	−11.0688	−	7.11349i	−0.749674	−	0.481786i
$219$	7.00737	+	4.50336i	0.473514	+	0.304309i
$220$	−6.86399	+	7.92146i	−0.462770	+	0.534065i
$221$	−12.9549	−	3.80392i	−0.871444	−	0.255879i
$222$	0.191991	+	1.33533i	0.0128856	+	0.0896214i
$223$	3.95353	+	4.56262i	0.264748	+	0.305535i	0.872522	−	0.488574i	$-0.162483\pi$
$223$	3.95353	+	4.56262i	0.264748	+	0.305535i	−0.607774	+	0.794110i	$0.707937\pi$
$224$	−0.415415	−	0.909632i	−0.0277561	−	0.0607773i
$225$	−6.72162	+	1.97365i	−0.448108	+	0.131576i
$226$	−3.68960	+	8.07911i	−0.245429	+	0.537414i
$227$	−3.58785	+	24.9541i	−0.238134	+	1.65626i	0.423102	+	0.906082i	$0.360941\pi$
$227$	−3.58785	+	24.9541i	−0.238134	+	1.65626i	−0.661236	+	0.750178i	$0.729968\pi$
$228$	−2.92004	+	1.87660i	−0.193385	+	0.124281i
$229$	−0.264513			−0.0174795			−0.00873976	−	0.999962i	$-0.502782\pi$
$229$	−0.264513			−0.0174795			−0.00873976	+	0.999962i	$0.502782\pi$
$230$	−14.9767	−	7.19885i	−0.987532	−	0.474678i
$231$	−3.02510			−0.199037
$232$	0.865210	−	0.556037i	0.0568038	−	0.0365056i
$233$	1.68829	−	11.7423i	0.110603	−	0.769263i	−0.856732	−	0.515762i	$-0.827509\pi$
$233$	1.68829	−	11.7423i	0.110603	−	0.769263i	0.967335	−	0.253501i	$-0.0815820\pi$
$234$	−1.01271	+	2.21754i	−0.0662032	+	0.144965i
$235$	21.8458	−	6.41451i	1.42506	−	0.418436i
$236$	−0.970003	−	2.12401i	−0.0631418	−	0.138261i
$237$	−4.08418	−	4.71339i	−0.265296	−	0.306168i
$238$	0.788205	+	5.48209i	0.0510917	+	0.355351i
$239$	−17.7007	−	5.19738i	−1.14496	−	0.336191i	−0.346389	−	0.938091i	$-0.612592\pi$
$239$	−17.7007	−	5.19738i	−1.14496	−	0.336191i	−0.798571	+	0.601900i	$0.794411\pi$
$240$	2.26901	−	2.61858i	0.146464	−	0.169029i
$241$	2.83424	+	1.82146i	0.182570	+	0.117330i	0.628733	−	0.777621i	$-0.283574\pi$
$241$	2.83424	+	1.82146i	0.182570	+	0.117330i	−0.446164	+	0.894951i	$0.647210\pi$
$242$	1.55530	+	0.999532i	0.0999786	+	0.0642523i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−3.69463	−	1.08484i	−0.236524	−	0.0694498i
$245$	−0.493104	−	3.42961i	−0.0315032	−	0.219110i
$246$	7.14705	+	8.24814i	0.455680	+	0.525882i
$247$	3.51519	+	7.69720i	0.223666	+	0.489761i
$248$	7.33087	−	2.15254i	0.465511	−	0.136686i
$249$	−6.15884	+	13.4860i	−0.390300	+	0.854639i
$250$	0.988867	−	6.87772i	0.0625414	−	0.434985i
$251$	−17.9332	+	11.5249i	−1.13193	+	0.727448i	−0.965962	−	0.258683i	$-0.916712\pi$
$251$	−17.9332	+	11.5249i	−1.13193	+	0.727448i	−0.165969	+	0.986131i	$0.553075\pi$
$252$	1.00000			0.0629941
$253$	4.36028	−	13.8371i	0.274128	−	0.869932i
$254$	−19.3292			−1.21282
$255$	−16.1437	+	10.3749i	−1.01096	+	0.649705i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−6.07211	+	13.2961i	−0.378768	+	0.829386i	0.620221	+	0.784427i	$0.287043\pi$
$257$	−6.07211	+	13.2961i	−0.378768	+	0.829386i	−0.998989	+	0.0449586i	$0.985684\pi$
$258$	12.3799	−	3.63507i	0.770739	−	0.226309i
$259$	−0.560420	−	1.22715i	−0.0348228	−	0.0762513i
$260$	−5.53149	−	6.38368i	−0.343048	−	0.395899i
$261$	0.146368	+	1.01801i	0.00905993	+	0.0630132i
$262$	−5.61126	−	1.64761i	−0.346665	−	0.101790i
$263$	12.2176	−	14.0999i	0.753370	−	0.869436i	−0.241520	−	0.970396i	$-0.577646\pi$
$263$	12.2176	−	14.0999i	0.753370	−	0.869436i	0.994890	+	0.100960i	$0.0321915\pi$
$264$	2.54487	+	1.63549i	0.156626	+	0.100657i
$265$	−20.2138	−	12.9906i	−1.24173	−	0.798009i
$266$	2.27306	−	2.62325i	0.139370	−	0.160842i
$267$	−1.40186	−	0.411624i	−0.0857926	−	0.0251910i
$268$	−1.69133	−	11.7635i	−0.103315	−	0.718569i
$269$	−18.0100	−	20.7847i	−1.09809	−	1.26726i	−0.960953	−	0.276713i	$-0.910755\pi$
$269$	−18.0100	−	20.7847i	−1.09809	−	1.26726i	−0.137139	−	0.990552i	$-0.543791\pi$
$270$	1.43936	+	3.15177i	0.0875968	+	0.191810i
$271$	0.605973	−	0.177930i	0.0368103	−	0.0108085i	−0.263276	−	0.964721i	$-0.584803\pi$
$271$	0.605973	−	0.177930i	0.0368103	−	0.0108085i	0.300086	+	0.953912i	$0.402985\pi$
$272$	2.30076	−	5.03796i	0.139504	−	0.305471i
$273$	0.346941	−	2.41302i	0.0209978	−	0.146043i
$274$	−13.1279	+	8.43680i	−0.793086	+	0.509685i
$275$	21.1920			1.27792
$276$	−1.44137	+	4.57411i	−0.0867602	+	0.275329i
$277$	2.72716			0.163859			0.0819294	−	0.996638i	$-0.473892\pi$
$277$	2.72716			0.163859			0.0819294	+	0.996638i	$0.473892\pi$
$278$	4.83009	−	3.10411i	0.289690	−	0.186172i
$279$	−1.08734	+	7.56259i	−0.0650971	+	0.452760i
$280$	−1.43936	+	3.15177i	−0.0860184	+	0.188354i
$281$	7.37495	−	2.16548i	0.439953	−	0.129182i	−0.0542520	−	0.998527i	$-0.517277\pi$
$281$	7.37495	−	2.16548i	0.439953	−	0.129182i	0.494205	+	0.869345i	$0.335459\pi$
$282$	−2.72973	−	5.97728i	−0.162553	−	0.355942i
$283$	−15.2099	−	17.5531i	−0.904134	−	1.04343i	−0.998851	−	0.0479220i	$-0.984740\pi$
$283$	−15.2099	−	17.5531i	−0.904134	−	1.04343i	0.0947171	−	0.995504i	$-0.469805\pi$
$284$	−0.805526	−	5.60256i	−0.0477992	−	0.332451i
$285$	11.5396	+	3.38834i	0.683549	+	0.200708i
$286$	4.82940	−	5.57342i	0.285568	−	0.329563i
$287$	−9.18132	−	5.90047i	−0.541956	−	0.348294i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	−8.95492	+	10.3345i	−0.526760	+	0.607913i
$290$	−3.41920	−	1.00397i	−0.200782	−	0.0589550i
$291$	−0.992908	−	6.90583i	−0.0582053	−	0.404827i
$292$	5.45478	+	6.29515i	0.319217	+	0.368396i
$293$	0.139653	+	0.305797i	0.00815861	+	0.0178649i	0.913667	−	0.406463i	$-0.133238\pi$
$293$	0.139653	+	0.305797i	0.00815861	+	0.0178649i	−0.905509	+	0.424327i	$0.860511\pi$
$294$	−0.959493	+	0.281733i	−0.0559588	+	0.0164310i
$295$	−3.36094	+	7.35944i	−0.195682	+	0.428483i
$296$	−0.191991	+	1.33533i	−0.0111593	+	0.0776144i
$297$	−2.54487	+	1.63549i	−0.147669	+	0.0949008i
$298$	8.69876			0.503906
$299$	10.5374	+	5.06500i	0.609391	+	0.292917i
$300$	−7.00539			−0.404457
$301$	−10.8543	+	6.97564i	−0.625632	+	0.402069i
$302$	−2.67938	+	18.6355i	−0.154181	+	1.07235i
$303$	−2.75763	+	6.03838i	−0.158422	+	0.346896i
$304$	−3.33046	+	0.977911i	−0.191015	+	0.0560871i
$305$	5.54242	+	12.1362i	0.317358	+	0.694917i
$306$	3.62692	+	4.18569i	0.207337	+	0.239280i
$307$	2.98584	+	20.7670i	0.170411	+	1.18523i	0.878018	+	0.478628i	$0.158866\pi$
$307$	2.98584	+	20.7670i	0.170411	+	1.18523i	−0.707607	+	0.706607i	$0.750225\pi$
$308$	−2.90256	−	0.852268i	−0.165389	−	0.0485625i
$309$	7.87504	−	9.08829i	0.447996	−	0.517015i
$310$	−22.2704	−	14.3123i	−1.26488	−	0.812886i
$311$	14.2545	+	9.16079i	0.808297	+	0.519461i	0.878314	−	0.478085i	$-0.158669\pi$
$311$	14.2545	+	9.16079i	0.808297	+	0.519461i	−0.0700169	+	0.997546i	$0.522305\pi$
$312$	−1.59644	+	1.84240i	−0.0903809	+	0.104305i
$313$	21.2144	+	6.22910i	1.19911	+	0.352090i	0.819512	−	0.573063i	$-0.194245\pi$
$313$	21.2144	+	6.22910i	1.19911	+	0.352090i	0.379596	+	0.925152i	$0.376063\pi$
$314$	0.913904	+	6.35634i	0.0515746	+	0.358709i
$315$	−2.26901	−	2.61858i	−0.127844	−	0.147540i
$316$	−2.59082	−	5.67311i	−0.145745	−	0.319138i
$317$	−11.8789	+	3.48795i	−0.667183	+	0.195903i	−0.597748	−	0.801684i	$-0.703938\pi$
$317$	−11.8789	+	3.48795i	−0.667183	+	0.195903i	−0.0694348	+	0.997586i	$0.522120\pi$
$318$	−2.88082	+	6.30811i	−0.161548	+	0.353741i
$319$	0.442776	−	3.07958i	0.0247907	−	0.172423i
$320$	2.91484	−	1.87326i	0.162945	−	0.104718i
$321$	−2.11385			−0.117984
$322$	0.0943081	−	4.79490i	0.00525558	−	0.267210i
$323$	19.2243			1.06967
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−2.43045	+	16.9042i	−0.134817	+	0.937675i
$326$	6.36175	−	13.9303i	0.352345	−	0.771527i
$327$	12.6245	−	3.70690i	0.698139	−	0.204992i
$328$	4.53378	+	9.92759i	0.250336	+	0.548159i
$329$	4.30316	+	4.96611i	0.237241	+	0.273790i
$330$	−1.49169	−	10.3749i	−0.0821146	−	0.571120i
$331$	−3.78772	−	1.11217i	−0.208192	−	0.0611306i	0.175974	−	0.984395i	$-0.443693\pi$
$331$	−3.78772	−	1.11217i	−0.208192	−	0.0611306i	−0.384165	+	0.923264i	$0.625511\pi$
$332$	−9.70880	+	11.2046i	−0.532840	+	0.614930i
$333$	−1.13490	−	0.729357i	−0.0621923	−	0.0399685i
$334$	−3.45506	−	2.22043i	−0.189052	−	0.121497i
$335$	−26.9660	+	31.1204i	−1.47331	+	1.70029i
$336$	0.959493	+	0.281733i	0.0523446	+	0.0153698i
$337$	−5.22302	−	36.3269i	−0.284516	−	1.97885i	−0.170211	−	0.985408i	$-0.554445\pi$
$337$	−5.22302	−	36.3269i	−0.284516	−	1.97885i	−0.114305	−	0.993446i	$-0.536464\pi$
$338$	−4.62132	−	5.33328i	−0.251366	−	0.290092i
$339$	−3.68960	−	8.07911i	−0.200392	−	0.438797i
$340$	−18.4128	+	5.40648i	−0.998572	+	0.293207i
$341$	9.60141	−	21.0242i	0.519946	−	1.13852i
$342$	0.493984	−	3.43573i	0.0267116	−	0.185783i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	12.9025			0.695659
$345$	15.2482	−	6.60437i	0.820933	−	0.355567i
$346$	−2.07243			−0.111415
$347$	−2.91119	+	1.87091i	−0.156281	+	0.100436i	−0.616444	−	0.787399i	$-0.711427\pi$
$347$	−2.91119	+	1.87091i	−0.156281	+	0.100436i	0.460163	+	0.887834i	$0.347791\pi$
$348$	−0.146368	+	1.01801i	−0.00784613	+	0.0545710i
$349$	−9.46718	+	20.7302i	−0.506766	+	1.10966i	0.467444	+	0.884023i	$0.345175\pi$
$349$	−9.46718	+	20.7302i	−0.506766	+	1.10966i	−0.974211	+	0.225641i	$0.927552\pi$
$350$	6.72162	−	1.97365i	0.359286	−	0.105496i
$351$	−1.01271	−	2.21754i	−0.0540547	−	0.118363i
$352$	1.98102	+	2.28622i	0.105589	+	0.121856i
$353$	−0.721386	−	5.01735i	−0.0383955	−	0.267046i	0.961576	−	0.274537i	$-0.0885247\pi$
$353$	−0.721386	−	5.01735i	−0.0383955	−	0.267046i	−0.999972	+	0.00749081i	$0.997616\pi$
$354$	2.24044	+	0.657852i	0.119078	+	0.0349644i
$355$	−12.8430	+	14.8216i	−0.681636	+	0.786650i
$356$	−1.22911	−	0.789900i	−0.0651426	−	0.0418646i
$357$	−4.65925	−	2.99432i	−0.246594	−	0.158476i
$358$	−13.5037	+	15.5841i	−0.713691	+	0.823643i
$359$	−32.0771	−	9.41869i	−1.69296	−	0.497099i	−0.713831	−	0.700318i	$-0.753042\pi$
$359$	−32.0771	−	9.41869i	−1.69296	−	0.497099i	−0.979133	+	0.203218i	$0.934860\pi$
$360$	0.493104	+	3.42961i	0.0259889	+	0.180756i
$361$	4.55241	+	5.25377i	0.239601	+	0.276514i
$362$	−2.69943	−	5.91092i	−0.141879	−	0.310671i
$363$	−1.77390	+	0.520865i	−0.0931057	+	0.0273383i
$364$	1.01271	−	2.21754i	0.0530807	−	0.116230i
$365$	4.10739	−	28.5676i	0.214991	−	1.49529i
$366$	3.23933	−	2.08179i	0.169323	−	0.108817i
$367$	−3.72519			−0.194454			−0.0972268	−	0.995262i	$-0.530997\pi$
$367$	−3.72519			−0.194454			−0.0972268	+	0.995262i	$0.530997\pi$
$368$	−2.67166	+	3.98274i	−0.139270	+	0.207615i
$369$	−10.9139			−0.568153
$370$	3.93230	−	2.52714i	0.204431	−	0.131380i
$371$	0.986925	−	6.86421i	0.0512386	−	0.356372i
$372$	−3.17392	+	6.94991i	−0.164560	+	0.360336i
$373$	−0.681523	+	0.200113i	−0.0352879	+	0.0103615i	−0.299329	−	0.954150i	$-0.596763\pi$
$373$	−0.681523	+	0.200113i	−0.0352879	+	0.0103615i	0.264041	+	0.964511i	$0.414945\pi$
$374$	−6.96002	−	15.2403i	−0.359894	−	0.788058i
$375$	4.55026	+	5.25128i	0.234975	+	0.271175i
$376$	−0.935165	−	6.50422i	−0.0482275	−	0.335429i
$377$	2.40570	+	0.706377i	0.123900	+	0.0363803i
$378$	−0.654861	+	0.755750i	−0.0336824	+	0.0388716i
$379$	26.9084	+	17.2930i	1.38219	+	0.888281i	0.999368	−	0.0355401i	$-0.0113151\pi$
$379$	26.9084	+	17.2930i	1.38219	+	0.888281i	0.382824	+	0.923821i	$0.374951\pi$
$380$	10.1176	+	6.50219i	0.519022	+	0.333555i
$381$	12.6579	−	14.6080i	0.648486	−	0.748393i
$382$	20.8705	+	6.12813i	1.06783	+	0.313542i
$383$	−0.264890	−	1.84235i	−0.0135353	−	0.0941398i	0.981934	−	0.189224i	$-0.0605971\pi$
$383$	−0.264890	−	1.84235i	−0.0135353	−	0.0941398i	−0.995469	+	0.0950839i	$0.969688\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	4.35421	+	9.53440i	0.221911	+	0.485918i
$386$	18.5607	−	5.44992i	0.944715	−	0.277393i
$387$	−5.35991	+	11.7366i	−0.272460	+	0.596603i
$388$	0.992908	−	6.90583i	0.0504073	−	0.350590i
$389$	21.8002	−	14.0101i	1.10531	−	0.710341i	0.145046	−	0.989425i	$-0.453667\pi$
$389$	21.8002	−	14.0101i	1.10531	−	0.710341i	0.960267	+	0.279084i	$0.0900307\pi$
$390$	8.44682			0.427721
$391$	20.4120	−	16.9960i	1.03228	−	0.859524i
$392$	−1.00000			−0.0505076
$393$	4.91978	−	3.16175i	0.248170	−	0.159489i
$394$	2.30671	−	16.0435i	0.116210	−	0.808261i
$395$	−8.97689	+	19.6567i	−0.451677	+	0.989034i
$396$	−2.90256	+	0.852268i	−0.145859	+	0.0428281i
$397$	−6.69638	−	14.6630i	−0.336082	−	0.735916i	0.663847	−	0.747868i	$-0.268923\pi$
$397$	−6.69638	−	14.6630i	−0.336082	−	0.735916i	−0.999929	+	0.0119524i	$0.996195\pi$
$398$	11.7412	+	13.5501i	0.588535	+	0.679205i
$399$	0.493984	+	3.43573i	0.0247301	+	0.172002i
$400$	−6.72162	−	1.97365i	−0.336081	−	0.0986824i
$401$	11.6366	−	13.4293i	0.581102	−	0.670628i	−0.386739	−	0.922189i	$-0.626399\pi$
$401$	11.6366	−	13.4293i	0.581102	−	0.670628i	0.967841	+	0.251561i	$0.0809440\pi$
$402$	9.99784	+	6.42522i	0.498647	+	0.320461i
$403$	15.6691	+	10.0699i	0.780536	+	0.501620i
$404$	−4.34714	+	5.01687i	−0.216278	+	0.249598i
$405$	−3.32453	−	0.976169i	−0.165197	−	0.0485063i
$406$	−0.146368	−	1.01801i	−0.00726410	−	0.0505229i
$407$	2.67251	+	3.08424i	0.132472	+	0.152880i
$408$	2.30076	+	5.03796i	0.113905	+	0.249416i
$409$	35.9924	−	10.5683i	1.77971	−	0.522569i	0.784480	−	0.620154i	$-0.212930\pi$
$409$	35.9924	−	10.5683i	1.77971	−	0.522569i	0.995227	+	0.0975849i	$0.0311117\pi$
$410$	15.7090	−	34.3979i	0.775812	−	1.69879i
$411$	2.22085	−	15.4463i	0.109546	−	0.761912i
$412$	10.1165	−	6.50149i	0.498405	−	0.320305i
$413$	−2.33502			−0.114899
$414$	−2.51298	−	4.08472i	−0.123506	−	0.200753i
$415$	51.3694			2.52163
$416$	−2.05084	+	1.31799i	−0.100551	+	0.0646200i
$417$	−0.817107	+	5.68310i	−0.0400139	+	0.278303i
$418$	−4.36198	+	9.55141i	−0.213351	+	0.467175i
$419$	16.7753	−	4.92567i	0.819526	−	0.240635i	0.155014	−	0.987912i	$-0.450458\pi$
$419$	16.7753	−	4.92567i	0.819526	−	0.240635i	0.664512	+	0.747278i	$0.268639\pi$
$420$	−1.43936	−	3.15177i	−0.0702337	−	0.153790i
$421$	−1.49797	−	1.72875i	−0.0730066	−	0.0842541i	0.718071	−	0.695970i	$-0.245025\pi$
$421$	−1.49797	−	1.72875i	−0.0730066	−	0.0842541i	−0.791078	+	0.611716i	$0.790480\pi$
$422$	1.27589	+	8.87402i	0.0621094	+	0.431981i
$423$	6.30492	+	1.85129i	0.306556	+	0.0900129i
$424$	−4.54133	+	5.24097i	−0.220546	+	0.254524i
$425$	32.6399	+	20.9764i	1.58327	+	1.01750i
$426$	4.76164	+	3.06012i	0.230702	+	0.148263i
$427$	−2.52161	+	2.91009i	−0.122029	+	0.140829i
$428$	−2.02823	−	0.595542i	−0.0980381	−	0.0287866i
$429$	1.04953	+	7.29963i	0.0506717	+	0.352430i
$430$	−29.2761	−	33.7864i	−1.41182	−	1.62932i
$431$	6.56562	+	14.3767i	0.316255	+	0.692502i	0.999282	−	0.0378915i	$-0.0120641\pi$
$431$	6.56562	+	14.3767i	0.316255	+	0.692502i	−0.683027	+	0.730393i	$0.739337\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	11.1489	−	24.4126i	0.535781	−	1.17320i	−0.427331	−	0.904095i	$-0.640546\pi$
$433$	11.1489	−	24.4126i	0.535781	−	1.17320i	0.963112	−	0.269101i	$-0.0867266\pi$
$434$	1.08734	−	7.56259i	0.0521938	−	0.363016i
$435$	2.99785	−	1.92660i	0.143736	−	0.0923734i
$436$	13.1575			0.630131
$437$	−16.4274	−	2.69262i	−0.785830	−	0.128806i
$438$	−8.32968			−0.398007
$439$	8.08611	−	5.19663i	0.385929	−	0.248022i	−0.333262	−	0.942834i	$-0.608149\pi$
$439$	8.08611	−	5.19663i	0.385929	−	0.248022i	0.719191	+	0.694813i	$0.244513\pi$
$440$	1.49169	−	10.3749i	0.0711134	−	0.494604i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	12.9549	−	3.80392i	0.616204	−	0.180934i
$443$	−0.156998	−	0.343778i	−0.00745921	−	0.0163334i	0.905866	−	0.423565i	$-0.139221\pi$
$443$	−0.156998	−	0.343778i	−0.00745921	−	0.0163334i	−0.913325	+	0.407232i	$0.866494\pi$
$444$	−0.883447	−	1.01955i	−0.0419265	−	0.0483858i
$445$	0.720447	+	5.01082i	0.0341524	+	0.237535i
$446$	−5.79266	−	1.70088i	−0.274290	−	0.0805389i
$447$	−5.69648	+	6.57409i	−0.269434	+	0.310944i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−24.4170	−	15.6919i	−1.15231	−	0.740544i	−0.182212	−	0.983259i	$-0.558326\pi$
$449$	−24.4170	−	15.6919i	−1.15231	−	0.740544i	−0.970098	+	0.242715i	$0.921962\pi$
$450$	4.58756	−	5.29432i	0.216259	−	0.249577i
$451$	31.6781	+	9.30153i	1.49166	+	0.437992i
$452$	−1.26400	−	8.79133i	−0.0594537	−	0.413509i
$453$	−12.3292	−	14.2286i	−0.579274	−	0.668518i
$454$	−10.4729	−	22.9324i	−0.491517	−	1.07627i
$455$	−8.10466	+	2.37974i	−0.379952	+	0.111564i
$456$	1.44193	−	3.15739i	0.0675246	−	0.147858i
$457$	−4.16580	+	28.9738i	−0.194868	+	1.35534i	0.624031	+	0.781399i	$0.285494\pi$
$457$	−4.16580	+	28.9738i	−0.194868	+	1.35534i	−0.818899	+	0.573937i	$0.805415\pi$
$458$	0.222523	−	0.143007i	0.0103978	−	0.00668226i
$459$	−5.53846			−0.258513
$460$	16.4912	−	2.04095i	0.768905	−	0.0951596i
$461$	−18.4974			−0.861510			−0.430755	−	0.902469i	$-0.641753\pi$
$461$	−18.4974			−0.861510			−0.430755	+	0.902469i	$0.641753\pi$
$462$	2.54487	−	1.63549i	0.118398	−	0.0760899i
$463$	−5.05534	+	35.1606i	−0.234941	+	1.63405i	0.441290	+	0.897364i	$0.354521\pi$
$463$	−5.05534	+	35.1606i	−0.234941	+	1.63405i	−0.676232	+	0.736689i	$0.736388\pi$
$464$	−0.427245	+	0.935536i	−0.0198343	+	0.0434312i
$465$	25.4006	−	7.45828i	1.17792	−	0.345870i
$466$	4.92808	+	10.7910i	0.228289	+	0.499883i
$467$	12.8552	+	14.8357i	0.594869	+	0.686515i	0.970734	−	0.240159i	$-0.0771997\pi$
$467$	12.8552	+	14.8357i	0.594869	+	0.686515i	−0.375865	+	0.926675i	$0.622654\pi$
$468$	−0.346941	−	2.41302i	−0.0160373	−	0.111542i
$469$	−11.4031	−	3.34824i	−0.526544	−	0.154607i
$470$	−14.9099	+	17.2070i	−0.687743	+	0.793698i
$471$	−5.40228	−	3.47184i	−0.248924	−	0.159974i
$472$	1.96435	+	1.26241i	0.0904163	+	0.0581070i
$473$	25.5602	−	29.4980i	1.17526	−	1.35632i
$474$	5.98408	+	1.75708i	0.274858	+	0.0807056i
$475$	−3.46055	−	24.0686i	−0.158781	−	1.10435i
$476$	−3.62692	−	4.18569i	−0.166240	−	0.191851i
$477$	−2.88082	−	6.30811i	−0.131904	−	0.288829i
$478$	17.7007	−	5.19738i	0.809610	−	0.237723i
$479$	15.3349	−	33.5788i	0.700670	−	1.53425i	−0.138487	−	0.990364i	$-0.544224\pi$
$479$	15.3349	−	33.5788i	0.700670	−	1.53425i	0.839157	−	0.543889i	$-0.183049\pi$
$480$	−0.493104	+	3.42961i	−0.0225070	+	0.156540i
$481$	−2.76671	+	1.77806i	−0.126151	+	0.0810723i
$482$	−3.36907			−0.153457
$483$	3.56199	+	3.21127i	0.162076	+	0.146118i
$484$	−1.84879			−0.0840359
$485$	−20.3364	+	13.0694i	−0.923428	+	0.593451i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	4.63988	−	10.1599i	0.210253	−	0.460390i	−0.774896	−	0.632088i	$-0.782198\pi$
$487$	4.63988	−	10.1599i	0.210253	−	0.460390i	0.985150	+	0.171698i	$0.0549253\pi$
$488$	3.69463	−	1.08484i	0.167248	−	0.0491084i
$489$	6.36175	+	13.9303i	0.287688	+	0.629949i
$490$	2.26901	+	2.61858i	0.102504	+	0.118295i
$491$	0.542332	+	3.77200i	0.0244751	+	0.170228i	0.998393	−	0.0566737i	$-0.0180495\pi$
$491$	0.542332	+	3.77200i	0.0244751	+	0.170228i	−0.973918	+	0.226902i	$0.927140\pi$
$492$	−10.4718	−	3.07479i	−0.472104	−	0.138622i
$493$	3.73020	−	4.30489i	0.168000	−	0.193882i
$494$	−7.11859	−	4.57484i	−0.320281	−	0.205832i
$495$	8.81768	+	5.66678i	0.396325	+	0.254703i
$496$	−5.00337	+	5.77420i	−0.224658	+	0.259269i
$497$	−5.43090	−	1.59465i	−0.243609	−	0.0715300i
$498$	−2.10992	−	14.6748i	−0.0945479	−	0.657595i
$499$	19.8117	+	22.8639i	0.886893	+	1.02353i	0.999553	+	0.0298951i	$0.00951732\pi$
$499$	19.8117	+	22.8639i	0.886893	+	1.02353i	−0.112660	+	0.993634i	$0.535937\pi$
$500$	2.88649	+	6.32053i	0.129088	+	0.282663i
$501$	3.94067	−	1.15709i	0.176056	−	0.0516948i
$502$	8.85548	−	19.3908i	0.395240	−	0.865454i
$503$	0.271679	−	1.88957i	0.0121135	−	0.0842516i	−0.982868	−	0.184312i	$-0.940994\pi$
$503$	0.271679	−	1.88957i	0.0121135	−	0.0842516i	0.994981	+	0.100060i	$0.0319035\pi$
$504$	−0.841254	+	0.540641i	−0.0374724	+	0.0240821i
$505$	23.0008			1.02352
$506$	3.81281	+	13.9979i	0.169500	+	0.622281i
$507$	7.05695			0.313410
$508$	16.2608	−	10.4502i	0.721455	−	0.463651i
$509$	−1.42322	+	9.89870i	−0.0630831	+	0.438752i	0.933663	+	0.358152i	$0.116593\pi$
$509$	−1.42322	+	9.89870i	−0.0630831	+	0.438752i	−0.996746	+	0.0806006i	$0.974316\pi$
$510$	7.97185	−	17.4559i	0.353000	−	0.772961i
$511$	7.99226	−	2.34674i	0.353557	−	0.103814i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	2.27306	+	2.62325i	0.100358	+	0.115819i
$514$	−2.08021	−	14.4682i	−0.0917542	−	0.638164i
$515$	−39.9792	−	11.7390i	−1.76169	−	0.517280i
$516$	−8.44937	+	9.75109i	−0.371963	+	0.429268i
$517$	−16.7226	−	10.7470i	−0.735460	−	0.472651i
$518$	1.13490	+	0.729357i	0.0498647	+	0.0320461i
$519$	1.35715	−	1.56624i	0.0595724	−	0.0687503i
$520$	8.10466	+	2.37974i	0.355413	+	0.104359i
$521$	−1.81584	−	12.6295i	−0.0795535	−	0.553306i	−0.990150	−	0.140010i	$-0.955286\pi$
$521$	−1.81584	−	12.6295i	−0.0795535	−	0.553306i	0.910597	−	0.413296i	$-0.135623\pi$
$522$	−0.673509	−	0.777271i	−0.0294787	−	0.0340202i
$523$	−4.41096	−	9.65866i	−0.192878	−	0.422344i	0.788342	−	0.615238i	$-0.210940\pi$
$523$	−4.41096	−	9.65866i	−0.192878	−	0.422344i	−0.981220	+	0.192894i	$0.938213\pi$
$524$	5.61126	−	1.64761i	0.245129	−	0.0719763i
$525$	−2.91015	+	6.37233i	−0.127009	+	0.278111i
$526$	−2.65514	+	18.4669i	−0.115770	+	0.805196i
$527$	35.5983	−	22.8777i	1.55069	−	0.996566i
$528$	−3.02510			−0.131650
$529$	−19.8228	+	11.6643i	−0.861862	+	0.507143i
$530$	24.0282			1.04372
$531$	−1.96435	+	1.26241i	−0.0852453	+	0.0547839i
$532$	−0.493984	+	3.43573i	−0.0214169	+	0.148958i
$533$	−11.0526	+	24.2019i	−0.478742	+	1.04830i
$534$	1.40186	−	0.411624i	0.0606645	−	0.0178127i
$535$	3.04260	+	6.66237i	0.131543	+	0.288040i
$536$	7.78266	+	8.98167i	0.336160	+	0.387949i
$537$	−2.93463	−	20.4108i	−0.126638	−	0.880790i
$538$	26.3881	+	7.74823i	1.13767	+	0.334050i
$539$	−1.98102	+	2.28622i	−0.0853284	+	0.0984743i
$540$	−2.91484	−	1.87326i	−0.125435	−	0.0806121i
$541$	18.0464	+	11.5977i	0.775876	+	0.498625i	0.867662	−	0.497154i	$-0.165621\pi$
$541$	18.0464	+	11.5977i	0.775876	+	0.498625i	−0.0917869	+	0.995779i	$0.529258\pi$
$542$	−0.413581	+	0.477298i	−0.0177648	+	0.0205017i
$543$	6.23492	+	1.83074i	0.267566	+	0.0785645i
$544$	0.788205	+	5.48209i	0.0337940	+	0.235043i
$545$	−29.8546	−	34.4540i	−1.27883	−	1.47585i
$546$	1.01271	+	2.21754i	0.0433402	+	0.0949018i
$547$	−23.5549	+	6.91636i	−1.00714	+	0.295722i	−0.743382	−	0.668868i	$-0.766779\pi$
$547$	−23.5549	+	6.91636i	−1.00714	+	0.295722i	−0.263755	+	0.964590i	$0.584961\pi$
$548$	6.48262	−	14.1950i	0.276924	−	0.606379i
$549$	−0.547998	+	3.81141i	−0.0233880	+	0.162667i
$550$	−17.8278	+	11.4573i	−0.760181	+	0.488539i
$551$	−3.56991			−0.152083
$552$	−1.26039	−	4.62725i	−0.0536459	−	0.196949i
$553$	−6.23671			−0.265212
$554$	−2.29423	+	1.47441i	−0.0974725	+	0.0626417i
$555$	−0.665227	+	4.62676i	−0.0282373	+	0.196395i
$556$	−2.38512	+	5.22269i	−0.101152	+	0.221491i
$557$	6.61433	−	1.94214i	0.280258	−	0.0822912i	−0.138583	−	0.990351i	$-0.544255\pi$
$557$	6.61433	−	1.94214i	0.280258	−	0.0822912i	0.418841	+	0.908060i	$0.362436\pi$
$558$	−3.17392	−	6.94991i	−0.134363	−	0.294213i
$559$	20.5982	+	23.7716i	0.871211	+	1.00543i
$560$	−0.493104	−	3.42961i	−0.0208374	−	0.144928i
$561$	16.0757	+	4.72025i	0.678717	+	0.199289i
$562$	−5.03346	+	5.80892i	−0.212324	+	0.245035i
$563$	−25.3227	−	16.2739i	−1.06722	−	0.685862i	−0.115651	−	0.993290i	$-0.536895\pi$
$563$	−25.3227	−	16.2739i	−1.06722	−	0.685862i	−0.951572	+	0.307427i	$0.900532\pi$
$564$	5.52796	+	3.55261i	0.232769	+	0.149592i
$565$	−20.1528	+	23.2575i	−0.847833	+	0.978452i
$566$	22.2853	+	6.54356i	0.936722	+	0.275046i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	3.70662	+	4.27767i	0.155527	+	0.179487i
$569$	−6.29034	−	13.7739i	−0.263705	−	0.577433i	0.730744	−	0.682651i	$-0.239173\pi$
$569$	−6.29034	−	13.7739i	−0.263705	−	0.577433i	−0.994449	+	0.105218i	$0.966446\pi$
$570$	−11.5396	+	3.38834i	−0.483342	+	0.141922i
$571$	10.4323	−	22.8436i	0.436579	−	0.955975i	−0.555634	−	0.831427i	$-0.687524\pi$
$571$	10.4323	−	22.8436i	0.436579	−	0.955975i	0.992214	−	0.124549i	$-0.0397482\pi$
$572$	−1.04953	+	7.29963i	−0.0438830	+	0.305213i
$573$	−18.2986	+	11.7598i	−0.764435	+	0.491272i
$574$	10.9139			0.455535
$575$	−24.9531	−	22.4962i	−1.04062	−	0.938156i
$576$	1.00000			0.0416667
$577$	−24.7886	+	15.9306i	−1.03196	+	0.663201i	−0.942986	−	0.332833i	$-0.891996\pi$
$577$	−24.7886	+	15.9306i	−1.03196	+	0.663201i	−0.0889751	+	0.996034i	$0.528359\pi$
$578$	1.94609	−	13.5353i	0.0809466	−	0.562996i
$579$	−8.03591	+	17.5962i	−0.333961	+	0.731273i
$580$	3.41920	−	1.00397i	0.141975	−	0.0416875i
$581$	6.15884	+	13.4860i	0.255512	+	0.559492i
$582$	4.56886	+	5.27274i	0.189385	+	0.218562i
$583$	2.98554	+	20.7649i	0.123649	+	0.859994i
$584$	−7.99226	−	2.34674i	−0.330722	−	0.0971088i
$585$	−5.53149	+	6.38368i	−0.228699	+	0.263933i
$586$	−0.282810	−	0.181751i	−0.0116828	−	0.00750806i
$587$	−22.1066	−	14.2070i	−0.912435	−	0.586387i	−0.00198191	−	0.999998i	$-0.500631\pi$
$587$	−22.1066	−	14.2070i	−0.912435	−	0.586387i	−0.910454	+	0.413611i	$0.864267\pi$
$588$	0.654861	−	0.755750i	0.0270060	−	0.0311666i
$589$	−25.4459	−	7.47159i	−1.04848	−	0.307861i
$590$	−1.15141	−	8.00822i	−0.0474027	−	0.329693i
$591$	10.6143	+	12.2496i	0.436614	+	0.503880i
$592$	−0.560420	−	1.22715i	−0.0230331	−	0.0504355i
$593$	3.80979	−	1.11866i	0.156449	−	0.0459377i	−0.202570	−	0.979268i	$-0.564929\pi$
$593$	3.80979	−	1.11866i	0.156449	−	0.0459377i	0.359019	+	0.933330i	$0.383111\pi$
$594$	1.25667	−	2.75172i	0.0515618	−	0.112905i
$595$	−2.73104	+	18.9948i	−0.111962	+	0.778710i
$596$	−7.31786	+	4.70291i	−0.299751	+	0.192639i
$597$	−17.9294			−0.733800
$598$	−11.6029	+	1.43598i	−0.474480	+	0.0587215i
$599$	−0.492388			−0.0201184			−0.0100592	−	0.999949i	$-0.503202\pi$
$599$	−0.492388			−0.0201184			−0.0100592	+	0.999949i	$0.503202\pi$
$600$	5.89331	−	3.78740i	0.240593	−	0.154620i
$601$	5.30193	−	36.8758i	0.216270	−	1.50419i	−0.535368	−	0.844619i	$-0.679827\pi$
$601$	5.30193	−	36.8758i	0.216270	−	1.50419i	0.751639	−	0.659575i	$-0.229264\pi$
$602$	5.35991	−	11.7366i	0.218454	−	0.478347i
$603$	−11.4031	+	3.34824i	−0.464368	+	0.136351i
$604$	−7.82108	−	17.1258i	−0.318235	−	0.696838i
$605$	4.19493	+	4.84121i	0.170548	+	0.196823i
$606$	−0.944724	−	6.57070i	−0.0383768	−	0.266916i
$607$	−14.7172	−	4.32136i	−0.597353	−	0.175399i	−0.0309414	−	0.999521i	$-0.509851\pi$
$607$	−14.7172	−	4.32136i	−0.597353	−	0.175399i	−0.566412	+	0.824123i	$0.691669\pi$
$608$	2.27306	−	2.62325i	0.0921848	−	0.106387i
$609$	0.865210	+	0.556037i	0.0350601	+	0.0225318i
$610$	−11.2239	−	7.21316i	−0.454443	−	0.292052i
$611$	10.4904	−	12.1066i	0.424396	−	0.489779i
$612$	−5.31411	−	1.56036i	−0.214810	−	0.0630740i
$613$	2.12255	+	14.7626i	0.0857288	+	0.596257i	0.986721	+	0.162422i	$0.0519307\pi$
$613$	2.12255	+	14.7626i	0.0857288	+	0.596257i	−0.900993	+	0.433835i	$0.857160\pi$
$614$	−13.7393	−	15.8560i	−0.554474	−	0.639898i
$615$	15.7090	+	34.3979i	0.633448	+	1.38706i
$616$	2.90256	−	0.852268i	0.116947	−	0.0343389i
$617$	0.0203896	−	0.0446471i	0.000820856	−	0.00179742i	−0.909221	−	0.416314i	$-0.863322\pi$
$617$	0.0203896	−	0.0446471i	0.000820856	−	0.00179742i	0.910042	+	0.414516i	$0.136049\pi$
$618$	−1.71141	+	11.9031i	−0.0688430	+	0.478814i
$619$	−18.3878	+	11.8171i	−0.739070	+	0.474971i	−0.855223	−	0.518260i	$-0.826580\pi$
$619$	−18.3878	+	11.8171i	−0.739070	+	0.474971i	0.116153	+	0.993231i	$0.462944\pi$
$620$	26.4729			1.06318
$621$	4.73268	+	0.775734i	0.189916	+	0.0311291i
$622$	−16.9443			−0.679405
$623$	−1.22911	+	0.789900i	−0.0492432	+	0.0316467i
$624$	0.346941	−	2.41302i	0.0138887	−	0.0965983i
$625$	−4.54939	+	9.96178i	−0.181976	+	0.398471i
$626$	−21.2144	+	6.22910i	−0.847897	+	0.248965i
$627$	−4.36198	−	9.55141i	−0.174201	−	0.381446i
$628$	−4.20532	−	4.85320i	−0.167811	−	0.193664i
$629$	1.06334	+	7.39567i	0.0423980	+	0.294885i
$630$	3.32453	+	0.976169i	0.132452	+	0.0388915i
$631$	−0.520147	+	0.600282i	−0.0207067	+	0.0238968i	−0.766008	−	0.642830i	$-0.777760\pi$
$631$	−0.520147	+	0.600282i	−0.0207067	+	0.0238968i	0.745302	+	0.666727i	$0.232305\pi$
$632$	5.24666	+	3.37182i	0.208701	+	0.134124i
$633$	−7.54207	−	4.84699i	−0.299770	−	0.192651i
$634$	8.10740	−	9.35644i	0.321986	−	0.371592i
$635$	−64.2605	−	18.8686i	−2.55010	−	0.748777i
$636$	−0.986925	−	6.86421i	−0.0391341	−	0.272184i
$637$	−1.59644	−	1.84240i	−0.0632534	−	0.0729984i
$638$	1.29246	+	2.83009i	0.0511689	+	0.112044i
$639$	−5.43090	+	1.59465i	−0.214843	+	0.0630836i
$640$	−1.43936	+	3.15177i	−0.0568958	+	0.124584i
$641$	3.59387	−	24.9959i	0.141949	−	0.987278i	−0.786969	−	0.616993i	$-0.788351\pi$
$641$	3.59387	−	24.9959i	0.141949	−	0.987278i	0.928918	−	0.370286i	$-0.120740\pi$
$642$	1.77829	−	1.14284i	0.0701834	−	0.0451041i
$643$	32.6586			1.28793			0.643965	−	0.765055i	$-0.277288\pi$
$643$	32.6586			1.28793			0.643965	+	0.765055i	$0.277288\pi$
$644$	2.51298	+	4.08472i	0.0990254	+	0.160960i
$645$	44.7058			1.76029
$646$	−16.1725	+	10.3935i	−0.636300	+	0.408925i
$647$	4.45535	−	30.9876i	0.175158	−	1.21825i	−0.692622	−	0.721300i	$-0.743545\pi$
$647$	4.45535	−	30.9876i	0.175158	−	1.21825i	0.867780	−	0.496948i	$-0.165546\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	6.77754	−	1.99007i	0.266042	−	0.0781169i
$650$	−7.09446	−	15.5347i	−0.278268	−	0.609321i
$651$	5.00337	+	5.77420i	0.196097	+	0.226309i
$652$	2.17944	+	15.1583i	0.0853534	+	0.593646i
$653$	35.9049	+	10.5426i	1.40507	+	0.412564i	0.894420	−	0.447227i	$-0.147588\pi$
$653$	35.9049	+	10.5426i	1.40507	+	0.412564i	0.510645	+	0.859792i	$0.329407\pi$
$654$	−8.61634	+	9.94378i	−0.336926	+	0.388833i
$655$	−17.0464	−	10.9551i	−0.666059	−	0.428050i
$656$	−9.18132	−	5.90047i	−0.358470	−	0.230375i
$657$	5.45478	−	6.29515i	0.212811	−	0.245597i
$658$	−6.30492	−	1.85129i	−0.245792	−	0.0721709i
$659$	4.75167	+	33.0486i	0.185099	+	1.28739i	0.844482	+	0.535583i	$0.179908\pi$
$659$	4.75167	+	33.0486i	0.185099	+	1.28739i	−0.659384	+	0.751807i	$0.729183\pi$
$660$	6.86399	+	7.92146i	0.267180	+	0.308342i
$661$	−7.26479	−	15.9077i	−0.282568	−	0.618737i	0.714123	−	0.700020i	$-0.246826\pi$
$661$	−7.26479	−	15.9077i	−0.282568	−	0.618737i	−0.996691	+	0.0812829i	$0.974098\pi$
$662$	3.78772	−	1.11217i	0.147214	−	0.0432259i
$663$	−5.60888	+	12.2817i	−0.217831	+	0.476983i
$664$	2.10992	−	14.6748i	0.0818809	−	0.569494i
$665$	10.1176	−	6.50219i	0.392344	−	0.252144i
$666$	1.34906			0.0522750
$667$	−3.79046	+	3.15611i	−0.146767	+	0.122205i
$668$	4.10703			0.158906
$669$	5.07882	−	3.26396i	0.196359	−	0.126192i
$670$	5.86027	−	40.7591i	0.226402	−	1.57466i
$671$	4.83894	−	10.5958i	0.186805	−	0.409046i
$672$	−0.959493	+	0.281733i	−0.0370132	+	0.0108681i
$673$	4.05539	+	8.88007i	0.156324	+	0.342302i	0.971548	−	0.236845i	$-0.0761133\pi$
$673$	4.05539	+	8.88007i	0.156324	+	0.342302i	−0.815224	+	0.579146i	$0.803386\pi$
$674$	24.0337	+	27.7364i	0.925744	+	1.06837i
$675$	0.996971	+	6.93409i	0.0383734	+	0.266893i
$676$	6.77109	+	1.98817i	0.260427	+	0.0764681i
$677$	−20.0152	+	23.0987i	−0.769245	+	0.887756i	−0.996284	−	0.0861295i	$-0.972550\pi$
$677$	−20.0152	+	23.0987i	−0.769245	+	0.887756i	0.227039	+	0.973886i	$0.427096\pi$
$678$	7.47179	+	4.80183i	0.286952	+	0.184413i
$679$	−5.86929	−	3.77196i	−0.225243	−	0.144755i
$680$	12.5668	−	14.5029i	0.481916	−	0.556161i
$681$	24.1895	+	7.10267i	0.926942	+	0.272175i
$682$	3.28930	+	22.8776i	0.125954	+	0.876027i
$683$	−23.6785	−	27.3264i	−0.906032	−	1.04562i	−0.998753	−	0.0499244i	$-0.984102\pi$
$683$	−23.6785	−	27.3264i	−0.906032	−	1.04562i	0.0927211	−	0.995692i	$-0.470443\pi$
$684$	1.44193	+	3.15739i	0.0551336	+	0.120726i
$685$	−51.8798	+	15.2333i	−1.98223	+	0.582034i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	−0.0376442	+	0.261821i	−0.00143621	+	0.00998909i
$688$	−10.8543	+	6.97564i	−0.413817	+	0.265944i
$689$	−16.9059			−0.644064
$690$	−9.25697	+	13.7997i	−0.352407	+	0.525347i
$691$	41.2387			1.56879			0.784397	−	0.620259i	$-0.212972\pi$
$691$	41.2387			1.56879			0.784397	+	0.620259i	$0.212972\pi$
$692$	1.74344	−	1.12044i	0.0662757	−	0.0425928i
$693$	−0.430516	+	2.99431i	−0.0163540	+	0.113744i
$694$	1.43756	−	3.14781i	0.0545690	−	0.119489i
$695$	19.0879	−	5.60472i	0.724046	−	0.212599i
$696$	−0.427245	−	0.935536i	−0.0161947	−	0.0354614i
$697$	39.5837	+	45.6820i	1.49934	+	1.73033i
$698$	−3.24331	−	22.5577i	−0.122761	−	0.853822i
$699$	−11.3825	−	3.34220i	−0.430526	−	0.126414i
$700$	−4.58756	+	5.29432i	−0.173393	+	0.200107i
$701$	−29.1378	−	18.7257i	−1.10052	−	0.707260i	−0.141312	−	0.989965i	$-0.545132\pi$
$701$	−29.1378	−	18.7257i	−1.10052	−	0.707260i	−0.959207	+	0.282705i	$0.908768\pi$
$702$	2.05084	+	1.31799i	0.0774040	+	0.0497445i
$703$	3.06650	−	3.53893i	0.115655	−	0.133473i
$704$	−2.90256	−	0.852268i	−0.109394	−	0.0321211i
$705$	−3.24023	−	22.5363i	−0.122034	−	0.848767i
$706$	3.31945	+	3.83085i	0.124929	+	0.144176i
$707$	2.75763	+	6.03838i	0.103712	+	0.227097i
$708$	−2.24044	+	0.657852i	−0.0842008	+	0.0247236i
$709$	8.50852	−	18.6311i	0.319544	−	0.699704i	−0.679891	−	0.733313i	$-0.737973\pi$
$709$	8.50852	−	18.6311i	0.319544	−	0.699704i	0.999435	+	0.0336091i	$0.0107001\pi$
$710$	2.79105	−	19.4122i	0.104746	−	0.728527i
$711$	−5.24666	+	3.37182i	−0.196765	+	0.126453i
$712$	1.46104			0.0547550
$713$	−33.6235	+	14.5632i	−1.25921	+	0.545396i
$714$	5.53846			0.207272
$715$	21.4961	−	13.8147i	0.803908	−	0.516640i
$716$	2.93463	−	20.4108i	0.109672	−	0.762787i
$717$	−7.66355	+	16.7808i	−0.286201	+	0.626692i
$718$	32.0771	−	9.41869i	1.19711	−	0.351502i
$719$	−0.405404	−	0.887710i	−0.0151190	−	0.0331060i	0.901922	−	0.431899i	$-0.142156\pi$
$719$	−0.405404	−	0.887710i	−0.0151190	−	0.0331060i	−0.917041	+	0.398793i	$0.869429\pi$
$720$	−2.26901	−	2.61858i	−0.0845612	−	0.0975888i
$721$	−1.71141	−	11.9031i	−0.0637363	−	0.443295i
$722$	−6.67014	−	1.95853i	−0.248237	−	0.0728889i
$723$	2.20627	−	2.54617i	0.0820522	−	0.0946932i
$724$	5.46659	+	3.51316i	0.203164	+	0.130566i
$725$	−6.06114	−	3.89526i	−0.225105	−	0.144666i
$726$	1.21070	−	1.39722i	0.0449333	−	0.0518558i
$727$	−1.53871	−	0.451805i	−0.0570674	−	0.0167565i	0.253074	−	0.967447i	$-0.418558\pi$
$727$	−1.53871	−	0.451805i	−0.0570674	−	0.0167565i	−0.310142	+	0.950690i	$0.600376\pi$
$728$	0.346941	+	2.41302i	0.0128585	+	0.0894326i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	11.9894	+	26.2532i	0.443749	+	0.971674i
$731$	68.5656	−	20.1327i	2.53599	−	0.744634i
$732$	−1.59960	+	3.50263i	−0.0591229	+	0.129461i
$733$	2.41353	−	16.7865i	0.0891457	−	0.620022i	−0.895448	−	0.445166i	$-0.853145\pi$
$733$	2.41353	−	16.7865i	0.0891457	−	0.620022i	0.984594	−	0.174856i	$-0.0559461\pi$
$734$	3.13383	−	2.01399i	0.115672	−	0.0743378i
$735$	−3.46488			−0.127804
$736$	0.0943081	−	4.79490i	0.00347624	−	0.176743i
$737$	35.9516			1.32429
$738$	9.18132	−	5.90047i	0.337969	−	0.217199i
$739$	−1.40560	+	9.77615i	−0.0517057	+	0.359621i	0.947499	+	0.319758i	$0.103601\pi$
$739$	−1.40560	+	9.77615i	−0.0517057	+	0.359621i	−0.999205	+	0.0398637i	$0.987308\pi$
$740$	−1.94179	+	4.25192i	−0.0713816	+	0.156304i
$741$	8.11912	−	2.38399i	0.298263	−	0.0875780i
$742$	2.88082	+	6.30811i	0.105758	+	0.231578i
$743$	13.8315	+	15.9624i	0.507428	+	0.585603i	0.950438	−	0.310913i	$-0.100635\pi$
$743$	13.8315	+	15.9624i	0.507428	+	0.585603i	−0.443010	+	0.896517i	$0.646089\pi$
$744$	−1.08734	−	7.56259i	−0.0398637	−	0.277258i
$745$	28.9193	+	8.49147i	1.05952	+	0.311103i
$746$	0.465144	−	0.536805i	0.0170301	−	0.0196538i
$747$	12.4722	+	8.01540i	0.456334	+	0.293268i
$748$	14.0947	+	9.05810i	0.515352	+	0.331197i
$749$	−1.38428	+	1.59754i	−0.0505805	+	0.0583730i
$750$	−6.66698	−	1.95760i	−0.243444	−	0.0714815i
$751$	−1.71969	−	11.9607i	−0.0627522	−	0.436451i	−0.996842	−	0.0794126i	$-0.974696\pi$
$751$	−1.71969	−	11.9607i	−0.0627522	−	0.436451i	0.934090	−	0.357039i	$-0.116214\pi$
$752$	4.30316	+	4.96611i	0.156920	+	0.181095i
$753$	8.85548	+	19.3908i	0.322712	+	0.706640i
$754$	−2.40570	+	0.706377i	−0.0876104	+	0.0257247i
$755$	−27.0991	+	59.3387i	−0.986237	+	2.15956i
$756$	0.142315	−	0.989821i	0.00517594	−	0.0359995i
$757$	−35.3099	+	22.6923i	−1.28336	+	0.824766i	−0.991299	−	0.131633i	$-0.957978\pi$
$757$	−35.3099	+	22.6923i	−1.28336	+	0.824766i	−0.292063	+	0.956399i	$0.594342\pi$
$758$	−31.9861			−1.16179
$759$	−13.0757	−	6.28512i	−0.474619	−	0.228136i
$760$	−12.0268			−0.436258
$761$	−42.3675	+	27.2280i	−1.53582	+	0.987013i	−0.547131	+	0.837047i	$0.684280\pi$
$761$	−42.3675	+	27.2280i	−1.53582	+	0.987013i	−0.988691	+	0.149966i	$0.952084\pi$
$762$	−2.75083	+	19.1325i	−0.0996522	+	0.693096i
$763$	5.46583	−	11.9685i	0.197876	−	0.433289i
$764$	−20.8705	+	6.12813i	−0.755068	+	0.221708i
$765$	7.97185	+	17.4559i	0.288223	+	0.631120i
$766$	1.21889	+	1.40668i	0.0440403	+	0.0508252i
$767$	0.810114	+	5.63447i	0.0292515	+	0.203449i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	25.5239	−	29.4562i	0.920416	−	1.06222i	−0.0774549	−	0.996996i	$-0.524679\pi$
$769$	25.5239	−	29.4562i	0.920416	−	1.06222i	0.997871	−	0.0652207i	$-0.0207752\pi$
$770$	−8.81768	−	5.66678i	−0.317767	−	0.204217i
$771$	12.2966	+	7.90253i	0.442850	+	0.284603i
$772$	−12.6678	+	14.6194i	−0.455925	+	0.526165i
$773$	−15.0480	−	4.41848i	−0.541238	−	0.158922i	−0.000324106	−	1.00000i	$-0.500103\pi$
$773$	−15.0480	−	4.41848i	−0.541238	−	0.158922i	−0.540913	+	0.841078i	$0.681921\pi$
$774$	−1.83622	−	12.7712i	−0.0660017	−	0.459052i
$775$	−35.0506	−	40.4505i	−1.25905	−	1.45303i
$776$	2.89828	+	6.34636i	0.104042	+	0.227821i
$777$	−1.29441	+	0.380074i	−0.0464369	+	0.0136351i
$778$	−10.7650	+	23.5721i	−0.385945	+	0.845102i
$779$	5.39126	−	37.4971i	0.193162	−	1.34347i
$780$	−7.10591	+	4.56669i	−0.254433	+	0.163514i
$781$	17.1226			0.612694
$782$	−7.98296	+	25.3335i	−0.285470	+	0.905924i
$783$	1.02848			0.0367548
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−3.16657	+	22.0240i	−0.113020	+	0.786069i
$786$	−2.42941	+	5.31966i	−0.0866541	+	0.189746i
$787$	−28.2031	+	8.28118i	−1.00533	+	0.295192i	−0.742642	−	0.669688i	$-0.766428\pi$
$787$	−28.2031	+	8.28118i	−1.00533	+	0.295192i	−0.262690	+	0.964880i	$0.584610\pi$
$788$	6.73325	+	14.7438i	0.239862	+	0.525225i
$789$	−12.2176	−	14.0999i	−0.434958	−	0.501969i
$790$	−3.07535	−	21.3895i	−0.109416	−	0.761004i
$791$	−8.52196	−	2.50227i	−0.303006	−	0.0889706i
$792$	1.98102	−	2.28622i	0.0703924	−	0.0812371i
$793$	7.89697	+	5.07508i	0.280430	+	0.180221i
$794$	13.5608	+	8.71498i	0.481254	+	0.309283i
$795$	−15.7351	+	18.1593i	−0.558068	+	0.644045i
$796$	−17.2031	−	5.05128i	−0.609748	−	0.179038i
$797$	−4.60176	−	32.0059i	−0.163003	−	1.13371i	−0.892934	−	0.450187i	$-0.851357\pi$
$797$	−4.60176	−	32.0059i	−0.163003	−	1.13371i	0.729932	−	0.683520i	$-0.239552\pi$
$798$	−2.27306	−	2.62325i	−0.0804655	−	0.0928622i
$799$	−15.1185	−	33.1049i	−0.534855	−	1.17117i
$800$	6.72162	−	1.97365i	0.237645	−	0.0697790i
$801$	−0.606940	+	1.32901i	−0.0214452	+	0.0469584i
$802$	−2.52887	+	17.5887i	−0.0892974	+	0.621077i
$803$	−21.1980	+	13.6231i	−0.748060	+	0.480749i
$804$	−11.8845			−0.419132
$805$	4.99417	−	15.8487i	0.176021	−	0.558594i
$806$	−18.6260			−0.656071
$807$	−23.1362	+	14.8687i	−0.814434	+	0.523405i
$808$	0.944724	−	6.57070i	0.0332353	−	0.231156i
$809$	−12.2228	+	26.7642i	−0.429731	+	0.940980i	0.563639	+	0.826021i	$0.309401\pi$
$809$	−12.2228	+	26.7642i	−0.429731	+	0.940980i	−0.993370	+	0.114959i	$0.963326\pi$
$810$	3.32453	−	0.976169i	0.116812	−	0.0342991i
$811$	−18.4874	−	40.4818i	−0.649181	−	1.42151i	−0.892270	−	0.451503i	$-0.850888\pi$
$811$	−18.4874	−	40.4818i	−0.649181	−	1.42151i	0.243089	−	0.970004i	$-0.421839\pi$
$812$	0.673509	+	0.777271i	0.0236355	+	0.0272769i
$813$	−0.0898797	−	0.625127i	−0.00315222	−	0.0219242i
$814$	−3.91573	−	1.14976i	−0.137246	−	0.0402991i
$815$	34.7481	−	40.1015i	1.21717	−	1.40469i
$816$	−4.65925	−	2.99432i	−0.163106	−	0.104822i
$817$	−37.6760	−	24.2129i	−1.31812	−	0.847102i
$818$	−24.5650	+	28.3496i	−0.858896	+	0.991219i
$819$	−2.33909	−	0.686818i	−0.0817344	−	0.0239994i
$820$	5.38166	+	37.4303i	0.187936	+	1.30712i
$821$	25.0429	+	28.9010i	0.874003	+	1.00865i	0.999862	+	0.0166054i	$0.00528591\pi$
$821$	25.0429	+	28.9010i	0.874003	+	1.00865i	−0.125859	+	0.992048i	$0.540169\pi$
$822$	6.48262	+	14.1950i	0.226107	+	0.495106i
$823$	−11.0343	+	3.23997i	−0.384633	+	0.112938i	−0.468332	−	0.883553i	$-0.655145\pi$
$823$	−11.0343	+	3.23997i	−0.384633	+	0.112938i	0.0836990	+	0.996491i	$0.473327\pi$
$824$	−4.99558	+	10.9388i	−0.174029	+	0.381071i
$825$	3.01593	−	20.9763i	0.105001	−	0.730300i
$826$	1.96435	−	1.26241i	0.0683483	−	0.0439248i
$827$	56.4987			1.96465			0.982327	−	0.187175i	$-0.0599331\pi$
$827$	56.4987			1.96465			0.982327	+	0.187175i	$0.0599331\pi$
$828$	4.32242	+	2.07766i	0.150215	+	0.0722037i
$829$	33.0692			1.14854			0.574270	−	0.818666i	$-0.305286\pi$
$829$	33.0692			1.14854			0.574270	+	0.818666i	$0.305286\pi$
$830$	−43.2147	+	27.7724i	−1.50000	+	0.963994i
$831$	0.388115	−	2.69940i	0.0134635	−	0.0936410i
$832$	1.01271	−	2.21754i	0.0351096	−	0.0768792i
$833$	−5.31411	+	1.56036i	−0.184123	+	0.0540634i
$834$	−2.38512	−	5.22269i	−0.0825901	−	0.180847i
$835$	−9.31892	−	10.7546i	−0.322494	−	0.372178i
$836$	−1.49435	−	10.3934i	−0.0516831	−	0.359464i
$837$	7.33087	+	2.15254i	0.253392	+	0.0744026i
$838$	−11.4492	+	13.2131i	−0.395508	+	0.456440i
$839$	−0.332657	−	0.213786i	−0.0114846	−	0.00738071i	0.534886	−	0.844924i	$-0.320355\pi$
$839$	−0.332657	−	0.213786i	−0.0114846	−	0.00738071i	−0.546371	+	0.837544i	$0.683991\pi$
$840$	2.91484	+	1.87326i	0.100572	+	0.0646335i
$841$	18.2983	−	21.1173i	0.630975	−	0.728184i
$842$	2.19480	+	0.644453i	0.0756380	+	0.0222093i
$843$	−1.09388	−	7.60807i	−0.0376751	−	0.262036i
$844$	−5.87101	−	6.77550i	−0.202088	−	0.233222i
$845$	−10.1575	−	22.2418i	−0.349429	−	0.765142i
$846$	−6.30492	+	1.85129i	−0.216768	+	0.0636488i
$847$	−0.768015	+	1.68172i	−0.0263893	+	0.0577846i
$848$	0.986925	−	6.86421i	0.0338911	−	0.235718i
$849$	−19.5391	+	12.5570i	−0.670579	+	0.430955i
$850$	−38.7991			−1.33080
$851$	0.127227	−	6.46862i	0.00436130	−	0.221741i
$852$	−5.66017			−0.193914
$853$	43.9055	−	28.2163i	1.50330	−	0.966109i	0.508850	−	0.860855i	$-0.330071\pi$
$853$	43.9055	−	28.2163i	1.50330	−	0.966109i	0.994445	−	0.105254i	$-0.0335655\pi$
$854$	0.547998	−	3.81141i	0.0187521	−	0.130424i
$855$	4.99612	−	10.9400i	0.170864	−	0.374139i
$856$	2.02823	−	0.595542i	0.0693234	−	0.0203552i
$857$	6.51133	+	14.2578i	0.222423	+	0.487038i	0.987641	−	0.156733i	$-0.0500962\pi$
$857$	6.51133	+	14.2578i	0.222423	+	0.487038i	−0.765218	+	0.643771i	$0.777369\pi$
$858$	−4.82940	−	5.57342i	−0.164873	−	0.190274i
$859$	−6.78650	−	47.2012i	−0.231552	−	1.61048i	−0.691392	−	0.722480i	$-0.743002\pi$
$859$	−6.78650	−	47.2012i	−0.231552	−	1.61048i	0.459839	−	0.888002i	$-0.347907\pi$
$860$	42.8949	+	12.5951i	1.46270	+	0.429488i
$861$	−7.14705	+	8.24814i	−0.243571	+	0.281096i
$862$	−13.2960	−	8.54481i	−0.452863	−	0.291038i
$863$	−8.90314	−	5.72170i	−0.303066	−	0.194769i	0.380264	−	0.924878i	$-0.375833\pi$
$863$	−8.90314	−	5.72170i	−0.303066	−	0.194769i	−0.683331	+	0.730109i	$0.739469\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−6.88986	−	2.02304i	−0.234262	−	0.0687856i
$866$	3.81943	+	26.5648i	0.129790	+	0.902707i
$867$	8.95492	+	10.3345i	0.304125	+	0.350979i
$868$	3.17392	+	6.94991i	0.107730	+	0.235895i
$869$	18.1024	−	5.31535i	0.614083	−	0.180311i
$870$	−1.48035	+	3.24152i	−0.0501886	+	0.109898i
$871$	−4.12320	+	28.6775i	−0.139709	+	0.971699i
$872$	−11.0688	+	7.11349i	−0.374837	+	0.240893i
$873$	−6.97684			−0.236130
$874$	15.2754	−	6.61615i	0.516697	−	0.223795i
$875$	6.94844			0.234900
$876$	7.00737	−	4.50336i	0.236757	−	0.152155i
$877$	−0.506739	+	3.52445i	−0.0171114	+	0.119012i	−0.996587	−	0.0825513i	$-0.973693\pi$
$877$	−0.506739	+	3.52445i	−0.0171114	+	0.119012i	0.979475	+	0.201564i	$0.0646023\pi$
$878$	−3.99296	+	8.74336i	−0.134756	+	0.295074i
$879$	0.322559	−	0.0947120i	0.0108797	−	0.00319456i
$880$	4.35421	+	9.53440i	0.146780	+	0.321404i
$881$	17.9185	+	20.6791i	0.603690	+	0.696695i	0.972525	−	0.232800i	$-0.0747887\pi$
$881$	17.9185	+	20.6791i	0.603690	+	0.696695i	−0.368835	+	0.929495i	$0.620243\pi$
$882$	0.142315	+	0.989821i	0.00479199	+	0.0333290i
$883$	−11.0760	−	3.25220i	−0.372737	−	0.109445i	0.0899986	−	0.995942i	$-0.471314\pi$
$883$	−11.0760	−	3.25220i	−0.372737	−	0.109445i	−0.462735	+	0.886497i	$0.653132\pi$
$884$	−8.84184	+	10.2040i	−0.297383	+	0.343199i
$885$	6.80622	+	4.37409i	0.228789	+	0.147034i
$886$	0.317936	+	0.204325i	0.0106813	+	0.00686443i
$887$	−34.7544	+	40.1087i	−1.16694	+	1.34672i	−0.240328	+	0.970692i	$0.577255\pi$
$887$	−34.7544	+	40.1087i	−1.16694	+	1.34672i	−0.926609	+	0.376025i	$0.877291\pi$
$888$	1.29441	+	0.380074i	0.0434377	+	0.0127545i
$889$	−2.75083	−	19.1325i	−0.0922600	−	0.641682i
$890$	−3.31513	−	3.82586i	−0.111123	−	0.128243i
$891$	1.25667	+	2.75172i	0.0421000	+	0.0921862i
$892$	5.79266	−	1.70088i	0.193953	−	0.0569496i
$893$	−9.47507	+	20.7475i	−0.317071	+	0.694289i
$894$	1.23796	−	8.61022i	0.0414037	−	0.287969i
$895$	−60.1060	+	38.6278i	−2.00912	+	1.29118i
$896$	−1.00000			−0.0334077
$897$	6.51307	−	9.70928i	0.217465	−	0.324184i
$898$	29.0245			0.968562
$899$	−6.61051	+	4.24832i	−0.220473	+	0.141689i
$900$	−0.996971	+	6.93409i	−0.0332324	+	0.231136i
$901$	−15.9553	+	34.9372i	−0.531548	+	1.16393i
$902$	−31.6781	+	9.30153i	−1.05477	+	0.309707i
$903$	5.35991	+	11.7366i	0.178367	+	0.390569i
$904$	5.81630	+	6.71236i	0.193447	+	0.223250i
$905$	−3.20426	−	22.2861i	−0.106513	−	0.740815i
$906$	18.0645	+	5.30422i	0.600153	+	0.176221i
$907$	−18.9380	+	21.8556i	−0.628826	+	0.725704i	−0.977358	−	0.211593i	$-0.932135\pi$
$907$	−18.9380	+	21.8556i	−0.628826	+	0.725704i	0.348532	+	0.937297i	$0.386680\pi$
$908$	21.2086	+	13.6299i	0.703831	+	0.452325i
$909$	5.58446	+	3.58892i	0.185225	+	0.119037i
$910$	5.53149	−	6.38368i	0.183367	−	0.211617i
$911$	15.0000	+	4.40441i	0.496973	+	0.145924i	0.520607	−	0.853796i	$-0.325706\pi$
$911$	15.0000	+	4.40441i	0.496973	+	0.145924i	−0.0236343	+	0.999721i	$0.507524\pi$
$912$	0.493984	+	3.43573i	0.0163574	+	0.113768i
$913$	−29.3701	−	33.8949i	−0.972007	−	1.12176i
$914$	−12.1599	−	26.6265i	−0.402214	−	0.880726i
$915$	12.8014	−	3.75884i	0.423202	−	0.124263i
$916$	−0.109883	+	0.240610i	−0.00363063	+	0.00794997i
$917$	0.832278	−	5.78862i	0.0274842	−	0.191157i
$918$	4.65925	−	2.99432i	0.153778	−	0.0988272i
$919$	−17.1523			−0.565803			−0.282901	−	0.959149i	$-0.591297\pi$
$919$	−17.1523			−0.565803			−0.282901	+	0.959149i	$0.591297\pi$
$920$	−12.7698	+	10.6328i	−0.421009	+	0.350551i
$921$	20.9805			0.691332
$922$	15.5610	−	10.0004i	0.512474	−	0.329347i
$923$	−1.96374	+	13.6581i	−0.0646374	+	0.449563i
$924$	−1.25667	+	2.75172i	−0.0413414	+	0.0905251i
$925$	9.06788	−	2.66257i	0.298150	−	0.0875448i
$926$	−14.7565	−	32.3121i	−0.484927	−	1.06184i
$927$	−7.87504	−	9.08829i	−0.258650	−	0.298498i
$928$	−0.146368	−	1.01801i	−0.00480475	−	0.0334178i
$929$	10.6235	+	3.11933i	0.348545	+	0.102342i	0.451319	−	0.892363i	$-0.350954\pi$
$929$	10.6235	+	3.11933i	0.348545	+	0.102342i	−0.102774	+	0.994705i	$0.532772\pi$
$930$	−17.3361	+	20.0069i	−0.568472	+	0.656052i
$931$	2.92004	+	1.87660i	0.0957005	+	0.0615030i
$932$	−9.97982	−	6.41364i	−0.326900	−	0.210086i
$933$	11.0962	−	12.8057i	0.363272	−	0.419238i
$934$	−18.8353	−	5.53054i	−0.616310	−	0.180965i
$935$	−8.26165	−	57.4610i	−0.270185	−	1.87918i
$936$	1.59644	+	1.84240i	0.0521814	+	0.0602206i
$937$	19.8468	+	43.4583i	0.648365	+	1.41972i	0.892978	+	0.450101i	$0.148612\pi$
$937$	19.8468	+	43.4583i	0.648365	+	1.41972i	−0.244613	+	0.969621i	$0.578661\pi$
$938$	11.4031	−	3.34824i	0.372323	−	0.109324i
$939$	9.18482	−	20.1120i	0.299735	−	0.656329i
$940$	3.24023	−	22.5363i	0.105685	−	0.735054i
$941$	−47.4455	+	30.4914i	−1.54668	+	0.993990i	−0.560528	+	0.828135i	$0.689402\pi$
$941$	−47.4455	+	30.4914i	−1.54668	+	0.993990i	−0.986150	+	0.165855i	$0.946962\pi$
$942$	6.42171			0.209231
$943$	−27.4263	−	44.5800i	−0.893124	−	1.45172i
$944$	−2.33502			−0.0759985
$945$	−2.91484	+	1.87326i	−0.0948198	+	0.0609370i
$946$	−5.55475	+	38.6342i	−0.180601	+	1.25611i
$947$	−20.8212	+	45.5921i	−0.676598	+	1.48154i	0.189610	+	0.981860i	$0.439278\pi$
$947$	−20.8212	+	45.5921i	−0.676598	+	1.48154i	−0.866208	+	0.499684i	$0.833450\pi$
$948$	−5.98408	+	1.75708i	−0.194354	+	0.0570675i
$949$	−8.43558	−	18.4714i	−0.273831	−	0.599605i
$950$	15.9237	+	18.3769i	0.516633	+	0.596226i
$951$	1.76191	+	12.2543i	0.0571338	+	0.397374i
$952$	5.31411	+	1.56036i	0.172231	+	0.0505717i
$953$	25.9863	−	29.9898i	0.841778	−	0.971464i	−0.158094	−	0.987424i	$-0.550535\pi$
$953$	25.9863	−	29.9898i	0.841778	−	0.971464i	0.999873	+	0.0159600i	$0.00508044\pi$
$954$	5.83392	+	3.74923i	0.188880	+	0.121386i
$955$	63.4024	+	40.7463i	2.05165	+	1.31852i
$956$	−12.0808	+	13.9420i	−0.390722	+	0.450917i
$957$	−2.98522	−	0.876539i	−0.0964983	−	0.0283345i
$958$	5.25351	+	36.5389i	0.169733	+	1.18052i
$959$	−10.2192	−	11.7936i	−0.329996	−	0.380835i
$960$	−1.43936	−	3.15177i	−0.0464552	−	0.101723i
$961$	−26.2662	+	7.71244i	−0.847295	+	0.248788i
$962$	1.36621	−	2.99159i	0.0440485	−	0.0964527i
$963$	−0.300833	+	2.09234i	−0.00969420	+	0.0674247i
$964$	2.83424	−	1.82146i	0.0912848	−	0.0586652i
$965$	67.0256			2.15763
$966$	−4.73268	−	0.775734i	−0.152271	−	0.0249588i
$967$	−32.7114			−1.05193			−0.525964	−	0.850507i	$-0.676295\pi$
$967$	−32.7114			−1.05193			−0.525964	+	0.850507i	$0.676295\pi$
$968$	1.55530	−	0.999532i	0.0499893	−	0.0321262i
$969$	2.73591	−	19.0287i	0.0878900	−	0.611289i
$970$	10.0422	−	21.9894i	0.322436	−	0.706036i
$971$	−34.1346	+	10.0228i	−1.09543	+	0.321648i	−0.779036	−	0.626979i	$-0.784291\pi$
$971$	−34.1346	+	10.0228i	−1.09543	+	0.321648i	−0.316396	+	0.948627i	$0.602473\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	3.75991	+	4.33917i	0.120537	+	0.139107i
$974$	1.58955	+	11.0556i	0.0509326	+	0.354244i
$975$	16.3862	+	4.81143i	0.524779	+	0.154089i
$976$	−2.52161	+	2.91009i	−0.0807147	+	0.0931498i
$977$	−10.0928	−	6.48622i	−0.322896	−	0.207513i	0.369143	−	0.929372i	$-0.379651\pi$
$977$	−10.0928	−	6.48622i	−0.322896	−	0.207513i	−0.692039	+	0.721860i	$0.743288\pi$
$978$	−12.8831	−	8.27948i	−0.411957	−	0.264749i
$979$	2.89435	−	3.34026i	0.0925039	−	0.106755i
$980$	−3.32453	−	0.976169i	−0.106198	−	0.0311826i
$981$	−1.87251	−	13.0236i	−0.0597846	−	0.415811i
$982$	−2.49554	−	2.88000i	−0.0796357	−	0.0919045i
$983$	−3.60647	−	7.89706i	−0.115028	−	0.251877i	0.843358	−	0.537353i	$-0.180576\pi$
$983$	−3.60647	−	7.89706i	−0.115028	−	0.251877i	−0.958386	+	0.285476i	$0.907848\pi$
$984$	10.4718	−	3.07479i	0.333828	−	0.0980207i
$985$	23.3299	−	51.0854i	0.743353	−	1.62772i
$986$	−0.810651	+	5.63820i	−0.0258164	+	0.179557i
$987$	5.52796	−	3.55261i	0.175957	−	0.113081i
$988$	8.46189			0.269208
$989$	−61.4099	+	7.60009i	−1.95272	+	0.241669i
$990$	−10.4816			−0.333127
$991$	6.38411	−	4.10282i	0.202798	−	0.130330i	−0.435300	−	0.900285i	$-0.643358\pi$
$991$	6.38411	−	4.10282i	0.202798	−	0.130330i	0.638098	+	0.769955i	$0.279721\pi$
$992$	1.08734	−	7.56259i	0.0345230	−	0.240112i
$993$	−1.63990	+	3.59088i	−0.0520407	+	0.113953i
$994$	5.43090	−	1.59465i	0.172258	−	0.0505794i
$995$	25.8069	+	56.5091i	0.818132	+	1.79146i
$996$	9.70880	+	11.2046i	0.307635	+	0.355030i
$997$	6.29500	+	43.7827i	0.199365	+	1.38661i	0.806133	+	0.591734i	$0.201556\pi$
$997$	6.29500	+	43.7827i	0.199365	+	1.38661i	−0.606769	+	0.794878i	$0.707535\pi$
$998$	−29.0278	−	8.52333i	−0.918859	−	0.269801i
$999$	−0.883447	+	1.01955i	−0.0279510	+	0.0322572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.127.1	✓	30
23.2	even	11	inner	966.2.q.h.715.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.127.1	✓	30	1.1	even	1	trivial
966.2.q.h.715.1	yes	30	23.2	even	11	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-3.32453 + 0.976169i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-3.32453 + 0.976169i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(2.26901 - 2.61858i) q^{10} +(2.54487 + 1.63549i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-1.59644 + 1.84240i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.493104 + 3.42961i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.30076 + 5.03796i) q^{17} +(0.959493 - 0.281733i) q^{18} +(1.44193 - 3.15739i) q^{19} +(-0.493104 + 3.42961i) q^{20} +(-0.841254 + 0.540641i) q^{21} -3.02510 q^{22} +(-1.26039 - 4.62725i) q^{23} +1.00000 q^{24} +(5.89331 - 3.78740i) q^{25} +(0.346941 - 2.41302i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-0.427245 - 0.935536i) q^{29} +(-2.26901 - 2.61858i) q^{30} +(-1.08734 - 7.56259i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.98102 - 2.28622i) q^{33} +(-4.65925 - 2.99432i) q^{34} +(2.91484 + 1.87326i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.29441 + 0.380074i) q^{37} +(0.493984 + 3.43573i) q^{38} +(1.59644 + 1.84240i) q^{39} +(-1.43936 - 3.15177i) q^{40} +(10.4718 - 3.07479i) q^{41} +(0.415415 - 0.909632i) q^{42} +(1.83622 - 12.7712i) q^{43} +(2.54487 - 1.63549i) q^{44} +3.46488 q^{45} +(3.56199 + 3.21127i) q^{46} -6.57110 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-2.91015 + 6.37233i) q^{50} +(5.31411 - 1.56036i) q^{51} +(1.01271 + 2.21754i) q^{52} +(4.54133 + 5.24097i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-10.0570 - 2.95301i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-2.92004 - 1.87660i) q^{57} +(0.865210 + 0.556037i) q^{58} +(1.52911 - 1.76469i) q^{59} +(3.32453 + 0.976169i) q^{60} +(-0.547998 - 3.81141i) q^{61} +(5.00337 + 5.77420i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(3.50893 - 7.68349i) q^{65} +(-0.430516 + 2.99431i) q^{66} +(9.99784 - 6.42522i) q^{67} +5.53846 q^{68} +(-4.75952 + 0.589038i) q^{69} -3.46488 q^{70} +(4.76164 - 3.06012i) q^{71} +(0.142315 - 0.989821i) q^{72} +(-3.46027 + 7.57694i) q^{73} +(-1.29441 + 0.380074i) q^{74} +(-2.91015 - 6.37233i) q^{75} +(-2.27306 - 2.62325i) q^{76} +(-0.430516 - 2.99431i) q^{77} +(-2.33909 - 0.686818i) q^{78} +(4.08418 - 4.71339i) q^{79} +(2.91484 + 1.87326i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-7.14705 + 8.24814i) q^{82} +(-14.2252 - 4.17690i) q^{83} +(0.142315 + 0.989821i) q^{84} +(-12.5668 - 14.5029i) q^{85} +(5.35991 + 11.7366i) q^{86} +(-0.986817 + 0.289756i) q^{87} +(-1.25667 + 2.75172i) q^{88} +(0.207928 - 1.44617i) q^{89} +(-2.91484 + 1.87326i) q^{90} +2.43784 q^{91} +(-4.73268 - 0.775734i) q^{92} -7.64036 q^{93} +(5.52796 - 3.55261i) q^{94} +(-1.71159 + 11.9044i) q^{95} +(0.415415 - 0.909632i) q^{96} +(6.69423 - 1.96560i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(-1.98102 - 2.28622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more