LMFDB - Embedded newform 966.2.y.b.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.4
Character	$\chi$	$=$	966.121
Dual form			966.2.y.b.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0296258 - 0.621921i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.62091 - 0.361724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0296258 - 0.621921i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.62091 - 0.361724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-0.489417 + 0.384882i) q^{10} +(-1.00708 + 1.41425i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.302322 - 2.10270i) q^{13} +(1.22562 + 2.34475i) q^{14} +(0.597406 - 0.175414i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(1.25114 + 0.241137i) q^{17} +(0.888835 + 0.458227i) q^{18} +(6.10592 - 1.17682i) q^{19} +(0.597406 + 0.175414i) q^{20} +(-0.266375 - 2.63231i) q^{21} +1.73618 q^{22} +(4.49666 - 1.66735i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.59145 - 0.438430i) q^{25} +(-1.53744 + 1.46595i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.19904 - 2.35845i) q^{28} +(0.137091 - 0.158211i) q^{29} +(-0.489417 - 0.384882i) q^{30} +(4.81762 + 4.59359i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.61181 - 0.645271i) q^{33} +(-0.529306 - 1.15902i) q^{34} +(-0.147318 + 1.64071i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.230590 + 0.118877i) q^{37} +(-4.50039 - 4.29111i) q^{38} +(1.97215 - 0.789530i) q^{39} +(-0.203641 - 0.588383i) q^{40} +(-4.08481 + 2.62515i) q^{41} +(-1.98970 + 1.74387i) q^{42} +(7.04930 + 2.06986i) q^{43} +(-1.00708 - 1.41425i) q^{44} +(0.311313 + 0.539210i) q^{45} +(-3.96650 - 2.69571i) q^{46} +(1.30838 - 2.26618i) q^{47} +(0.415415 - 0.909632i) q^{48} +(6.73831 + 1.89609i) q^{49} +(-3.02044 - 3.48577i) q^{50} +(0.0606271 + 1.27272i) q^{51} +(2.08593 + 0.402030i) q^{52} +(-3.51484 + 1.40713i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(0.909386 + 0.584427i) q^{55} +(-2.61665 + 0.391323i) q^{56} +(2.58317 + 5.65636i) q^{57} +(-0.208395 - 0.0198993i) q^{58} +(5.11332 - 4.02116i) q^{59} +(-0.0296258 + 0.621921i) q^{60} +(-1.87449 + 7.72677i) q^{61} +(0.947336 - 6.58886i) q^{62} +(2.49531 - 0.879456i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.29876 + 0.250315i) q^{65} +(0.409319 + 1.68724i) q^{66} +(12.8572 - 1.22772i) q^{67} +(-0.637081 + 1.10346i) q^{68} +(2.68048 + 3.97681i) q^{69} +(1.42194 - 0.831706i) q^{70} +(-0.611246 + 1.33844i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(1.13928 - 3.29173i) q^{73} +(0.230590 + 0.118877i) q^{74} +(1.50855 + 4.35866i) q^{75} +(-0.884955 + 6.15500i) q^{76} +(3.15103 - 3.34233i) q^{77} +(-1.78709 - 1.14849i) q^{78} +(-1.55887 - 0.624076i) q^{79} +(-0.361159 + 0.507177i) q^{80} +(0.580057 - 0.814576i) q^{81} +(4.50780 + 1.80465i) q^{82} +(-5.95775 - 3.82881i) q^{83} +(2.57466 + 0.609219i) q^{84} +(0.112902 - 0.785252i) q^{85} +(-2.40294 - 6.94283i) q^{86} +(0.186072 + 0.0959266i) q^{87} +(-0.567847 + 1.64069i) q^{88} +(4.97317 - 4.74191i) q^{89} +(0.258648 - 0.566361i) q^{90} +(0.0317620 + 5.62033i) q^{91} +(0.104935 + 4.79468i) q^{92} +(-3.32831 + 5.76480i) q^{93} +(-2.60491 + 0.248739i) q^{94} +(-0.912782 - 3.76254i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(5.01365 - 3.22208i) q^{97} +(-2.36409 - 6.58871i) q^{98} +(0.247084 - 1.71850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	−0.0296258	−	0.621921i	−0.0132490	−	0.278132i	−0.995764	−	0.0919473i	$-0.970691\pi$
$5$	−0.0296258	−	0.621921i	−0.0132490	−	0.278132i	0.982515	−	0.186184i	$-0.0596122\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−2.62091	−	0.361724i	−0.990610	−	0.136719i
$7$	−2.62091	−	0.361724i	−0.990610	−	0.136719i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−0.489417	+	0.384882i	−0.154767	+	0.121710i
$11$	−1.00708	+	1.41425i	−0.303646	+	0.426412i	−0.938002	−	0.346630i	$-0.887326\pi$
$11$	−1.00708	+	1.41425i	−0.303646	+	0.426412i	0.634356	+	0.773041i	$0.281265\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	−0.302322	−	2.10270i	−0.0838491	−	0.583183i	−0.987821	−	0.155592i	$-0.950271\pi$
$13$	−0.302322	−	2.10270i	−0.0838491	−	0.583183i	0.903972	−	0.427591i	$-0.140638\pi$
$14$	1.22562	+	2.34475i	0.327562	+	0.626660i
$15$	0.597406	−	0.175414i	0.154249	−	0.0452917i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	1.25114	+	0.241137i	0.303445	+	0.0584843i	0.338701	−	0.940894i	$-0.390012\pi$
$17$	1.25114	+	0.241137i	0.303445	+	0.0584843i	−0.0352559	+	0.999378i	$0.511225\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	6.10592	−	1.17682i	1.40079	−	0.269981i	0.567756	−	0.823197i	$-0.307812\pi$
$19$	6.10592	−	1.17682i	1.40079	−	0.269981i	0.833038	+	0.553216i	$0.186600\pi$
$20$	0.597406	+	0.175414i	0.133584	+	0.0392238i
$21$	−0.266375	−	2.63231i	−0.0581277	−	0.574417i
$22$	1.73618			0.370154
$23$	4.49666	−	1.66735i	0.937618	−	0.347667i
$23$	4.49666	−	1.66735i	0.937618	−	0.347667i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.59145	−	0.438430i	0.918290	−	0.0876861i
$26$	−1.53744	+	1.46595i	−0.301517	+	0.287496i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	1.19904	−	2.35845i	0.226598	−	0.445705i
$29$	0.137091	−	0.158211i	0.0254571	−	0.0293790i	−0.742878	−	0.669427i	$-0.766540\pi$
$29$	0.137091	−	0.158211i	0.0254571	−	0.0293790i	0.768335	+	0.640048i	$0.221085\pi$
$30$	−0.489417	−	0.384882i	−0.0893550	−	0.0702695i
$31$	4.81762	+	4.59359i	0.865270	+	0.825034i	0.985843	−	0.167671i	$-0.0536246\pi$
$31$	4.81762	+	4.59359i	0.865270	+	0.825034i	−0.120573	+	0.992705i	$0.538473\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	−1.61181	−	0.645271i	−0.280580	−	0.112327i
$34$	−0.529306	−	1.15902i	−0.0907752	−	0.198770i
$35$	−0.147318	+	1.64071i	−0.0249012	+	0.277331i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.230590	+	0.118877i	−0.0379087	+	0.0195433i	−0.477077	−	0.878862i	$-0.658304\pi$
$37$	−0.230590	+	0.118877i	−0.0379087	+	0.0195433i	0.439168	+	0.898405i	$0.355273\pi$
$38$	−4.50039	−	4.29111i	−0.730060	−	0.696110i
$39$	1.97215	−	0.789530i	0.315797	−	0.126426i
$40$	−0.203641	−	0.588383i	−0.0321985	−	0.0930314i
$41$	−4.08481	+	2.62515i	−0.637940	+	0.409979i	−0.819242	−	0.573449i	$-0.805605\pi$
$41$	−4.08481	+	2.62515i	−0.637940	+	0.409979i	0.181302	+	0.983427i	$0.441969\pi$
$42$	−1.98970	+	1.74387i	−0.307018	+	0.269085i
$43$	7.04930	+	2.06986i	1.07501	+	0.315651i	0.770880	−	0.636980i	$-0.219817\pi$
$43$	7.04930	+	2.06986i	1.07501	+	0.315651i	0.304128	+	0.952631i	$0.401635\pi$
$44$	−1.00708	−	1.41425i	−0.151823	−	0.213206i
$45$	0.311313	+	0.539210i	0.0464078	+	0.0803807i
$46$	−3.96650	−	2.69571i	−0.584829	−	0.397461i
$47$	1.30838	−	2.26618i	0.190847	−	0.330556i	−0.754684	−	0.656088i	$-0.772210\pi$
$47$	1.30838	−	2.26618i	0.190847	−	0.330556i	0.945531	+	0.325532i	$0.105543\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	6.73831	+	1.89609i	0.962616	+	0.270870i
$50$	−3.02044	−	3.48577i	−0.427154	−	0.492962i
$51$	0.0606271	+	1.27272i	0.00848949	+	0.178216i
$52$	2.08593	+	0.402030i	0.289267	+	0.0557515i
$53$	−3.51484	+	1.40713i	−0.482801	+	0.193284i	−0.600278	−	0.799791i	$-0.704943\pi$
$53$	−3.51484	+	1.40713i	−0.482801	+	0.193284i	0.117477	+	0.993076i	$0.462519\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	0.909386	+	0.584427i	0.122622	+	0.0788041i
$56$	−2.61665	+	0.391323i	−0.349665	+	0.0522927i
$57$	2.58317	+	5.65636i	0.342149	+	0.749203i
$58$	−0.208395	−	0.0198993i	−0.0273636	−	0.00261291i
$59$	5.11332	−	4.02116i	0.665697	−	0.523510i	−0.227156	−	0.973858i	$-0.572943\pi$
$59$	5.11332	−	4.02116i	0.665697	−	0.523510i	0.892853	+	0.450348i	$0.148700\pi$
$60$	−0.0296258	+	0.621921i	−0.00382467	+	0.0802897i
$61$	−1.87449	+	7.72677i	−0.240004	+	0.989311i	0.716499	+	0.697589i	$0.245744\pi$
$61$	−1.87449	+	7.72677i	−0.240004	+	0.989311i	−0.956503	+	0.291723i	$0.905771\pi$
$62$	0.947336	−	6.58886i	0.120312	−	0.836787i
$63$	2.49531	−	0.879456i	0.314379	−	0.110801i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−1.29876	+	0.250315i	−0.161091	+	0.0310477i
$66$	0.409319	+	1.68724i	0.0503837	+	0.207684i
$67$	12.8572	−	1.22772i	1.57076	−	0.149989i	0.726972	−	0.686667i	$-0.240927\pi$
$67$	12.8572	−	1.22772i	1.57076	−	0.149989i	0.843788	+	0.536677i	$0.180321\pi$
$68$	−0.637081	+	1.10346i	−0.0772574	+	0.133814i
$69$	2.68048	+	3.97681i	0.322692	+	0.478752i
$70$	1.42194	−	0.831706i	0.169954	−	0.0994079i
$71$	−0.611246	+	1.33844i	−0.0725415	+	0.158844i	−0.942429	−	0.334407i	$-0.891464\pi$
$71$	−0.611246	+	1.33844i	−0.0725415	+	0.158844i	0.869887	+	0.493250i	$0.164191\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	1.13928	−	3.29173i	0.133342	−	0.385268i	−0.858488	−	0.512834i	$-0.828596\pi$
$73$	1.13928	−	3.29173i	0.133342	−	0.385268i	0.991830	+	0.127567i	$0.0407167\pi$
$74$	0.230590	+	0.118877i	0.0268055	+	0.0138192i
$75$	1.50855	+	4.35866i	0.174192	+	0.503295i
$76$	−0.884955	+	6.15500i	−0.101511	+	0.706027i
$77$	3.15103	−	3.34233i	0.359094	−	0.380893i
$78$	−1.78709	−	1.14849i	−0.202348	−	0.130041i
$79$	−1.55887	−	0.624076i	−0.175386	−	0.0702141i	0.282308	−	0.959324i	$-0.408900\pi$
$79$	−1.55887	−	0.624076i	−0.175386	−	0.0702141i	−0.457694	+	0.889110i	$0.651324\pi$
$80$	−0.361159	+	0.507177i	−0.0403788	+	0.0567041i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	4.50780	+	1.80465i	0.497803	+	0.199290i
$83$	−5.95775	−	3.82881i	−0.653947	−	0.420267i	0.171159	−	0.985243i	$-0.445249\pi$
$83$	−5.95775	−	3.82881i	−0.653947	−	0.420267i	−0.825107	+	0.564977i	$0.808885\pi$
$84$	2.57466	+	0.609219i	0.280918	+	0.0664713i
$85$	0.112902	−	0.785252i	0.0122460	−	0.0851725i
$86$	−2.40294	−	6.94283i	−0.259115	−	0.748665i
$87$	0.186072	+	0.0959266i	0.0199490	+	0.0102844i
$88$	−0.567847	+	1.64069i	−0.0605327	+	0.174898i
$89$	4.97317	−	4.74191i	0.527155	−	0.502641i	−0.379110	−	0.925352i	$-0.623770\pi$
$89$	4.97317	−	4.74191i	0.527155	−	0.502641i	0.906265	+	0.422711i	$0.138921\pi$
$90$	0.258648	−	0.566361i	0.0272639	−	0.0596997i
$91$	0.0317620	+	5.62033i	0.00332957	+	0.589171i
$92$	0.104935	+	4.79468i	0.0109402	+	0.499880i
$93$	−3.32831	+	5.76480i	−0.345130	+	0.597782i
$94$	−2.60491	+	0.248739i	−0.268676	+	0.0256555i
$95$	−0.912782	−	3.76254i	−0.0936494	−	0.386028i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	5.01365	−	3.22208i	0.509059	−	0.327152i	−0.260772	−	0.965401i	$-0.583977\pi$
$97$	5.01365	−	3.22208i	0.509059	−	0.327152i	0.769831	+	0.638248i	$0.220341\pi$
$98$	−2.36409	−	6.58871i	−0.238810	−	0.665560i
$99$	0.247084	−	1.71850i	0.0248328	−	0.172716i
$100$	−1.08740	+	4.48232i	−0.108740	+	0.448232i
$101$	0.310288	−	6.51374i	0.0308748	−	0.648141i	−0.929398	−	0.369079i	$-0.879673\pi$
$101$	0.310288	−	6.51374i	0.0308748	−	0.648141i	0.960273	−	0.279063i	$-0.0900237\pi$
$102$	1.00156	−	0.787635i	0.0991691	−	0.0779875i
$103$	9.42884	+	0.900345i	0.929051	+	0.0887136i	0.548598	−	0.836087i	$-0.315162\pi$
$103$	9.42884	+	0.900345i	0.929051	+	0.0887136i	0.380453	+	0.924800i	$0.375768\pi$
$104$	−0.882474	−	1.93235i	−0.0865337	−	0.189482i
$105$	−1.62920	+	0.243648i	−0.158993	+	0.0237776i
$106$	3.18502	+	2.04689i	0.309357	+	0.198812i
$107$	0.773093	−	3.18673i	0.0747377	−	0.308073i	−0.922157	−	0.386815i	$-0.873575\pi$
$107$	0.773093	−	3.18673i	0.0747377	−	0.308073i	0.996895	+	0.0787420i	$0.0250903\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	−13.7471	−	2.64953i	−1.31673	−	0.253779i	−0.517954	−	0.855409i	$-0.673306\pi$
$109$	−13.7471	−	2.64953i	−1.31673	−	0.253779i	−0.798775	+	0.601630i	$0.794518\pi$
$110$	−0.0514355	−	1.07976i	−0.00490419	−	0.102952i
$111$	−0.169890	−	0.196063i	−0.0161252	−	0.0186095i
$112$	1.83657	+	1.90447i	0.173539	+	0.179956i
$113$	−2.32043	+	5.08102i	−0.218287	+	0.477983i	−0.986819	−	0.161829i	$-0.948261\pi$
$113$	−2.32043	+	5.08102i	−0.218287	+	0.477983i	0.768531	+	0.639812i	$0.220988\pi$
$114$	3.10915	−	5.38520i	0.291198	−	0.504370i
$115$	−1.17018	−	2.74717i	−0.109120	−	0.256175i
$116$	0.104672	+	0.181296i	0.00971851	+	0.0168330i
$117$	1.23223	+	1.73042i	0.113919	+	0.159977i
$118$	−6.24155	−	1.83269i	−0.574582	−	0.168712i
$119$	−3.19189	−	1.08456i	−0.292600	−	0.0994218i
$120$	0.523787	−	0.336617i	0.0478150	−	0.0307288i
$121$	2.61186	+	7.54649i	0.237442	+	0.686044i
$122$	7.38135	−	2.95505i	0.668276	−	0.267538i
$123$	−3.51418	−	3.35076i	−0.316863	−	0.302128i
$124$	−5.91664	+	3.05024i	−0.531330	+	0.273920i
$125$	−0.851739	−	5.92398i	−0.0761819	−	0.529857i
$126$	−2.16380	−	1.52248i	−0.192767	−	0.135634i
$127$	−2.37361	−	5.19749i	−0.210624	−	0.461203i	0.774605	−	0.632446i	$-0.217949\pi$
$127$	−2.37361	−	5.19749i	−0.210624	−	0.461203i	−0.985229	+	0.171243i	$0.945222\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	−0.349580	+	7.33858i	−0.0307788	+	0.646126i
$130$	0.957252	+	0.912738i	0.0839566	+	0.0800524i
$131$	10.6510	+	8.37604i	0.930582	+	0.731818i	0.963519	−	0.267640i	$-0.0862437\pi$
$131$	10.6510	+	8.37604i	0.930582	+	0.731818i	−0.0329371	+	0.999457i	$0.510486\pi$
$132$	1.13695	−	1.31211i	0.0989591	−	0.114205i
$133$	−16.4287	+	0.875676i	−1.42455	+	0.0759307i
$134$	−8.45799	−	9.76104i	−0.730659	−	0.843226i
$135$	−0.450616	+	0.429661i	−0.0387828	+	0.0369794i
$136$	1.26839	−	0.121117i	0.108764	−	0.0103857i
$137$	−9.31904	−	16.1411i	−0.796180	−	1.37902i	−0.922087	−	0.386982i	$-0.873518\pi$
$137$	−9.31904	−	16.1411i	−0.796180	−	1.37902i	0.125908	−	0.992042i	$-0.459816\pi$
$138$	1.68459	−	4.49023i	0.143401	−	0.382234i
$139$	10.7949			0.915615			0.457808	−	0.889051i	$-0.348635\pi$
$139$	10.7949			0.915615			0.457808	+	0.889051i	$0.348635\pi$
$140$	−1.50229	−	0.675840i	−0.126967	−	0.0571189i
$141$	2.51076	+	0.737227i	0.211444	+	0.0620857i
$142$	1.44482	−	0.278466i	0.121247	−	0.0233684i
$143$	3.27820	+	1.69003i	0.274137	+	0.141327i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−0.102456	−	0.0805724i	−0.00850852	−	0.00669118i
$146$	−3.34221	+	0.981361i	−0.276603	+	0.0812180i
$147$	−0.254026	+	6.99539i	−0.0209517	+	0.576970i
$148$	−0.0369206	−	0.256788i	−0.00303485	−	0.0211079i
$149$	−9.34771	−	0.892598i	−0.765794	−	0.0731245i	−0.295154	−	0.955450i	$-0.595371\pi$
$149$	−9.34771	−	0.892598i	−0.765794	−	0.0731245i	−0.470640	+	0.882325i	$0.655977\pi$
$150$	2.67542	−	3.75710i	0.218447	−	0.306766i
$151$	0.496749	−	0.390648i	0.0404249	−	0.0317905i	−0.597742	−	0.801688i	$-0.703935\pi$
$151$	0.496749	−	0.390648i	0.0404249	−	0.0317905i	0.638167	+	0.769898i	$0.279693\pi$
$152$	5.52704	−	2.84939i	0.448302	−	0.231116i
$153$	−1.22255	+	0.358973i	−0.0988373	+	0.0290212i
$154$	−4.55036	−	0.628017i	−0.366678	−	0.0506070i
$155$	2.71413	−	3.13227i	0.218004	−	0.251590i
$156$	0.101079	+	2.12191i	0.00809281	+	0.169889i
$157$	4.22830	−	12.2169i	0.337455	−	0.975011i	−0.640819	−	0.767692i	$-0.721405\pi$
$157$	4.22830	−	12.2169i	0.337455	−	0.975011i	0.978273	−	0.207319i	$-0.0664738\pi$
$158$	0.395874	+	1.63182i	0.0314941	+	0.129820i
$159$	−2.19612	−	3.08402i	−0.174164	−	0.244579i
$160$	0.622626			0.0492229
$161$	−12.3884	+	2.74342i	−0.976346	+	0.216212i
$162$	−1.00000			−0.0785674
$163$	−2.72076	−	3.82077i	−0.213106	−	0.299266i	0.694162	−	0.719819i	$-0.255775\pi$
$163$	−2.72076	−	3.82077i	−0.213106	−	0.299266i	−0.907268	+	0.420553i	$0.861836\pi$
$164$	−1.14476	−	4.71875i	−0.0893904	−	0.368472i
$165$	−0.353557	+	1.02154i	−0.0275244	+	0.0795264i
$166$	0.336974	+	7.07396i	0.0261543	+	0.549046i
$167$	−7.08925	+	8.18143i	−0.548582	+	0.633098i	−0.960552	−	0.278100i	$-0.910295\pi$
$167$	−7.08925	+	8.18143i	−0.548582	+	0.633098i	0.411970	+	0.911198i	$0.364841\pi$
$168$	−0.997191	−	2.45063i	−0.0769350	−	0.189071i
$169$	8.14347	−	2.39114i	0.626421	−	0.183934i
$170$	−0.705137	+	0.363523i	−0.0540816	+	0.0278810i
$171$	−4.88791	+	3.84389i	−0.373788	+	0.293950i
$172$	−4.26162	+	5.98461i	−0.324946	+	0.456322i
$173$	13.5323	+	1.29218i	1.02884	+	0.0982426i	0.595802	−	0.803132i	$-0.296834\pi$
$173$	13.5323	+	1.29218i	1.02884	+	0.0982426i	0.433041	+	0.901374i	$0.357441\pi$
$174$	−0.0297926	−	0.207212i	−0.00225857	−	0.0157087i
$175$	−12.1924	−	0.511754i	−0.921656	−	0.0386849i
$176$	1.66585	−	0.489137i	0.125568	−	0.0368701i
$177$	5.11332	+	4.02116i	0.384341	+	0.302249i
$178$	−6.74736	−	1.30045i	−0.505736	−	0.0974727i
$179$	−13.9332	−	7.18306i	−1.04142	−	0.536887i	−0.149346	−	0.988785i	$-0.547717\pi$
$179$	−13.9332	−	7.18306i	−1.04142	−	0.536887i	−0.892070	+	0.451898i	$0.850747\pi$
$180$	−0.611375	+	0.117833i	−0.0455692	+	0.00878274i
$181$	−15.9072	−	4.67076i	−1.18237	−	0.347175i	−0.369283	−	0.929317i	$-0.620397\pi$
$181$	−15.9072	−	4.67076i	−1.18237	−	0.347175i	−0.813087	+	0.582142i	$0.802215\pi$
$182$	4.55976	−	3.28598i	0.337992	−	0.243573i
$183$	−7.95089			−0.587747
$184$	3.84477	−	2.86667i	0.283440	−	0.211333i
$185$	0.0807637	+	0.139887i	0.00593786	+	0.0102847i
$186$	6.62648	−	0.632752i	0.485877	−	0.0463956i
$187$	−1.60102	+	1.52657i	−0.117078	+	0.111634i
$188$	1.71361	+	1.97762i	0.124978	+	0.144232i
$189$	1.44296	+	2.21763i	0.104960	+	0.161309i
$190$	−2.53541	+	2.92602i	−0.183938	+	0.212275i
$191$	−15.6275	−	12.2896i	−1.13077	−	0.889244i	−0.135927	−	0.990719i	$-0.543401\pi$
$191$	−15.6275	−	12.2896i	−1.13077	−	0.889244i	−0.994838	+	0.101475i	$0.967644\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	−0.0675815	+	1.41871i	−0.00486462	+	0.102121i	0.995129	+	0.0985802i	$0.0314301\pi$
$193$	−0.0675815	+	1.41871i	−0.00486462	+	0.102121i	−0.999994	+	0.00354078i	$0.998873\pi$
$194$	−5.53283	−	2.21501i	−0.397234	−	0.159029i
$195$	−0.549452	−	1.20313i	−0.0393471	−	0.0861581i
$196$	−3.99569	+	5.74756i	−0.285407	+	0.410540i
$197$	3.24557	+	22.5734i	0.231237	+	1.60829i	0.692764	+	0.721164i	$0.256393\pi$
$197$	3.24557	+	22.5734i	0.231237	+	1.60829i	−0.461527	+	0.887126i	$0.652698\pi$
$198$	−1.54317	+	0.795562i	−0.109669	+	0.0565381i
$199$	11.4324	+	10.9008i	0.810424	+	0.772738i	0.976988	−	0.213293i	$-0.0684189\pi$
$199$	11.4324	+	10.9008i	0.810424	+	0.772738i	−0.166564	+	0.986031i	$0.553267\pi$
$200$	4.28195	−	1.71423i	0.302779	−	0.121215i
$201$	4.22431	+	12.2054i	0.297960	+	0.860899i
$202$	−5.48592	+	3.52559i	−0.385988	+	0.248059i
$203$	−0.416530	+	0.365067i	−0.0292347	+	0.0256227i
$204$	−1.22255	−	0.358973i	−0.0855956	−	0.0251331i
$205$	1.75365	+	2.46266i	0.122480	+	0.171999i
$206$	−4.73586	−	8.20275i	−0.329963	−	0.571513i
$207$	−3.23277	+	3.54249i	−0.224693	+	0.246220i
$208$	−1.06216	+	1.83971i	−0.0736475	+	0.127561i
$209$	−4.48484	+	9.82043i	−0.310223	+	0.679293i
$210$	1.14350	+	1.18577i	0.0789088	+	0.0818262i
$211$	12.4779	+	14.4003i	0.859016	+	0.991357i	0.999999	+	0.00134513i	$0.000428167\pi$
$211$	12.4779	+	14.4003i	0.859016	+	0.991357i	−0.140983	+	0.990012i	$0.545026\pi$
$212$	−0.180147	−	3.78176i	−0.0123726	−	0.259732i
$213$	−1.44482	−	0.278466i	−0.0989974	−	0.0190802i
$214$	−3.04427	+	1.21874i	−0.208102	+	0.0833116i
$215$	1.07845	−	4.44543i	0.0735497	−	0.303176i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−10.9649	−	13.7820i	−0.744348	−	0.935585i
$218$	5.81583	+	12.7349i	0.393898	+	0.862516i
$219$	3.46753	+	0.331109i	0.234314	+	0.0223743i
$220$	−0.849715	+	0.668223i	−0.0572878	+	0.0450516i
$221$	0.128791	−	2.70366i	0.00866344	−	0.181868i
$222$	−0.0611627	+	0.252116i	−0.00410497	+	0.0169209i
$223$	2.12026	−	14.7467i	0.141983	−	0.987513i	−0.786884	−	0.617100i	$-0.788307\pi$
$223$	2.12026	−	14.7467i	0.141983	−	0.987513i	0.928867	−	0.370413i	$-0.120784\pi$
$224$	0.486022	−	2.60073i	0.0324737	−	0.173768i
$225$	−3.88014	+	2.49362i	−0.258676	+	0.166241i
$226$	5.48486	−	1.05712i	0.364847	−	0.0703186i
$227$	3.07257	+	12.6653i	0.203934	+	0.840626i	0.978183	+	0.207745i	$0.0666125\pi$
$227$	3.07257	+	12.6653i	0.203934	+	0.840626i	−0.774249	+	0.632881i	$0.781872\pi$
$228$	−6.19014	+	0.591086i	−0.409952	+	0.0391456i
$229$	−6.66503	+	11.5442i	−0.440438	+	0.762860i	−0.997722	−	0.0674616i	$-0.978510\pi$
$229$	−6.66503	+	11.5442i	−0.440438	+	0.762860i	0.557284	+	0.830322i	$0.311843\pi$
$230$	−1.55901	+	2.54671i	−0.102798	+	0.167925i
$231$	3.99099	+	2.27423i	0.262588	+	0.149633i
$232$	0.0869643	−	0.190425i	0.00570948	−	0.0125020i
$233$	−17.0250	+	16.2333i	−1.11534	+	1.06348i	−0.117827	+	0.993034i	$0.537593\pi$
$233$	−17.0250	+	16.2333i	−1.11534	+	1.06348i	−0.997516	+	0.0704433i	$0.977559\pi$
$234$	0.694797	−	2.00748i	0.0454203	−	0.131233i
$235$	−1.44815	−	0.746572i	−0.0944667	−	0.0487010i
$236$	2.12759	+	6.14728i	0.138495	+	0.400154i
$237$	0.238968	−	1.66206i	0.0155226	−	0.107962i
$238$	0.968017	+	3.22914i	0.0627472	+	0.209314i
$239$	−7.75540	−	4.98409i	−0.501655	−	0.322394i	0.265223	−	0.964187i	$-0.414554\pi$
$239$	−7.75540	−	4.98409i	−0.501655	−	0.322394i	−0.766878	+	0.641793i	$0.778191\pi$
$240$	−0.578026	−	0.231407i	−0.0373114	−	0.0149373i
$241$	−4.47755	+	6.28784i	−0.288424	+	0.405035i	−0.933212	−	0.359327i	$-0.883006\pi$
$241$	−4.47755	+	6.28784i	−0.288424	+	0.405035i	0.644788	+	0.764362i	$0.276946\pi$
$242$	4.63216	−	6.50495i	0.297766	−	0.418154i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	−6.68872	−	4.29858i	−0.428201	−	0.275188i
$245$	0.979592	−	4.24687i	0.0625838	−	0.271323i
$246$	−0.691027	+	4.80620i	−0.0440583	+	0.306432i
$247$	−4.32045	−	12.4831i	−0.274904	−	0.794282i
$248$	5.91664	+	3.05024i	0.375707	+	0.193690i
$249$	2.31629	−	6.69248i	0.146789	−	0.424119i
$250$	−4.33147	+	4.13005i	−0.273946	+	0.261207i
$251$	−7.08983	+	15.5246i	−0.447506	+	0.979901i	0.542653	+	0.839957i	$0.317420\pi$
$251$	−7.08983	+	15.5246i	−0.447506	+	0.979901i	−0.990159	+	0.139945i	$0.955308\pi$
$252$	0.0149516	+	2.64571i	0.000941864	+	0.166664i
$253$	−2.17045	+	8.03854i	−0.136455	+	0.505379i
$254$	−2.85692	+	4.94833i	−0.179259	+	0.310486i
$255$	0.789735	−	0.0754105i	0.0494551	−	0.00472239i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	15.3508	−	2.95862i	0.957554	−	0.184553i	0.313547	−	0.949573i	$-0.398483\pi$
$257$	15.3508	−	2.95862i	0.957554	−	0.184553i	0.644007	+	0.765019i	$0.277271\pi$
$258$	6.18061	−	3.97204i	0.384788	−	0.247288i
$259$	0.647355	−	0.228156i	0.0402247	−	0.0141769i
$260$	0.188234	−	1.30919i	0.0116738	−	0.0811928i
$261$	−0.0493545	+	0.203442i	−0.00305497	+	0.0125927i
$262$	0.644734	−	13.5346i	0.0398318	−	0.836172i
$263$	−18.2176	+	14.3265i	−1.12335	+	0.883411i	−0.994129	−	0.108205i	$-0.965490\pi$
$263$	−18.2176	+	14.3265i	−1.12335	+	0.883411i	−0.129219	+	0.991616i	$0.541247\pi$
$264$	−1.72831	−	0.165034i	−0.106370	−	0.0101571i
$265$	0.979255	+	2.14427i	0.0601551	+	0.131721i
$266$	10.2429	+	12.8745i	0.628033	+	0.789387i
$267$	5.78071	+	3.71504i	0.353774	+	0.227357i
$268$	−3.04499	+	12.5516i	−0.186003	+	0.766713i
$269$	11.6020	−	4.64473i	0.707385	−	0.283194i	0.0100601	−	0.999949i	$-0.496798\pi$
$269$	11.6020	−	4.64473i	0.707385	−	0.283194i	0.697325	+	0.716755i	$0.254373\pi$
$270$	0.611375	+	0.117833i	0.0372071	+	0.00717108i
$271$	1.26310	+	26.5157i	0.0767278	+	1.61072i	0.629240	+	0.777211i	$0.283366\pi$
$271$	1.26310	+	26.5157i	0.0767278	+	1.61072i	−0.552512	+	0.833505i	$0.686331\pi$
$272$	−0.834399	−	0.962947i	−0.0505928	−	0.0583873i
$273$	−5.45442	+	1.35591i	−0.330116	+	0.0820634i
$274$	−7.74254	+	16.9538i	−0.467744	+	1.02422i
$275$	−4.00391	+	6.93498i	−0.241445	+	0.418195i
$276$	−4.63479	+	1.23237i	−0.278982	+	0.0741797i
$277$	−7.88213	−	13.6522i	−0.473591	−	0.820284i	0.525952	−	0.850514i	$-0.323709\pi$
$277$	−7.88213	−	13.6522i	−0.473591	−	0.820284i	−0.999543	+	0.0302303i	$0.990376\pi$
$278$	−6.26168	−	8.79330i	−0.375551	−	0.527387i
$279$	−6.38698	−	1.87539i	−0.382378	−	0.112276i
$280$	0.320892	+	1.61576i	0.0191770	+	0.0965600i
$281$	−2.22886	+	1.43240i	−0.132963	+	0.0854498i	−0.605431	−	0.795898i	$-0.706999\pi$
$281$	−2.22886	+	1.43240i	−0.132963	+	0.0854498i	0.472469	+	0.881347i	$0.343363\pi$
$282$	−0.855858	−	2.47284i	−0.0509656	−	0.147256i
$283$	10.4236	−	4.17300i	0.619621	−	0.248059i	−0.0405457	−	0.999178i	$-0.512910\pi$
$283$	10.4236	−	4.17300i	0.619621	−	0.248059i	0.660167	+	0.751119i	$0.270485\pi$
$284$	−1.06491	−	1.01539i	−0.0631908	−	0.0602523i
$285$	3.44128	−	1.77410i	0.203844	−	0.105089i
$286$	−0.524885	−	3.65065i	−0.0310371	−	0.215868i
$287$	11.6555	−	5.40269i	0.688001	−	0.318911i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−14.2751	−	5.71487i	−0.839709	−	0.336169i
$290$	−0.00620195	+	0.130195i	−0.000364191	+	0.00764531i
$291$	4.31327	+	4.11269i	0.252848	+	0.241090i
$292$	2.73806	+	2.15324i	0.160233	+	0.126009i
$293$	−2.54343	+	2.93527i	−0.148589	+	0.171480i	−0.825165	−	0.564892i	$-0.808918\pi$
$293$	−2.54343	+	2.93527i	−0.148589	+	0.171480i	0.676576	+	0.736373i	$0.263463\pi$
$294$	5.84563	−	3.85080i	0.340924	−	0.224583i
$295$	−2.65233	−	3.06095i	−0.154425	−	0.178215i
$296$	−0.187758	+	0.179026i	−0.0109132	+	0.0104057i
$297$	1.72831	−	0.165034i	0.100287	−	0.00957624i
$298$	4.69512	+	8.13218i	0.271981	+	0.471084i
$299$	−4.86537	−	8.95103i	−0.281372	−	0.517652i
$300$	−4.61234			−0.266293
$301$	−17.7268	−	7.97482i	−1.02176	−	0.459661i
$302$	−0.606355	−	0.178042i	−0.0348918	−	0.0102452i
$303$	6.40328	−	1.23413i	0.367859	−	0.0708990i
$304$	−5.52704	−	2.84939i	−0.316997	−	0.163424i
$305$	4.86098	+	0.936876i	0.278339	+	0.0536454i
$306$	1.00156	+	0.787635i	0.0572553	+	0.0450261i
$307$	26.5530	−	7.79666i	1.51546	−	0.444979i	0.584895	−	0.811109i	$-0.301136\pi$
$307$	26.5530	−	7.79666i	1.51546	−	0.444979i	0.930564	+	0.366130i	$0.119317\pi$
$308$	2.12790	+	4.07090i	0.121248	+	0.231961i
$309$	1.34797	+	9.37532i	0.0766832	+	0.533343i
$310$	−4.12582	−	0.393968i	−0.234331	−	0.0223759i
$311$	18.5507	−	26.0508i	1.05191	−	1.47721i	0.182447	−	0.983216i	$-0.441598\pi$
$311$	18.5507	−	26.0508i	1.05191	−	1.47721i	0.869467	−	0.493991i	$-0.164462\pi$
$312$	1.66983	−	1.31317i	0.0945354	−	0.0743435i
$313$	−11.9967	+	6.18472i	−0.678093	+	0.349581i	−0.762626	−	0.646840i	$-0.776090\pi$
$313$	−11.9967	+	6.18472i	−0.678093	+	0.349581i	0.0845334	+	0.996421i	$0.473060\pi$
$314$	−12.4042	+	3.64220i	−0.700010	+	0.205541i
$315$	−0.620878	−	1.52583i	−0.0349825	−	0.0859708i
$316$	1.09961	−	1.26902i	0.0618578	−	0.0713877i
$317$	0.282813	+	5.93697i	0.0158844	+	0.333454i	0.992797	+	0.119812i	$0.0382293\pi$
$317$	0.282813	+	5.93697i	0.0158844	+	0.333454i	−0.976912	+	0.213641i	$0.931468\pi$
$318$	−1.23829	+	3.57782i	−0.0694401	+	0.200634i
$319$	0.0856881	+	0.353211i	0.00479761	+	0.0197760i
$320$	−0.361159	−	0.507177i	−0.0201894	−	0.0283520i
$321$	3.27917			0.183025
$322$	9.42073	+	8.49999i	0.524997	+	0.473686i
$323$	7.92311			0.440854
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.30998	−	9.52188i	−0.128135	−	0.528179i
$326$	−1.53411	+	4.43253i	−0.0849667	+	0.245495i
$327$	−0.666149	−	13.9842i	−0.0368381	−	0.773328i
$328$	−3.17975	+	3.66963i	−0.175573	+	0.202622i
$329$	−4.24888	+	5.46618i	−0.234248	+	0.301360i
$330$	1.03720	−	0.304550i	0.0570961	−	0.0167649i
$331$	−18.6799	+	9.63016i	−1.02674	+	0.529322i	−0.887437	−	0.460928i	$-0.847517\pi$
$331$	−18.6799	+	9.63016i	−1.02674	+	0.529322i	−0.139303	+	0.990250i	$0.544486\pi$
$332$	5.56682	−	4.37779i	0.305519	−	0.240263i
$333$	0.150484	−	0.211325i	0.00824645	−	0.0115805i
$334$	10.7766	+	1.02904i	0.589667	+	0.0563064i
$335$	−1.14445	−	7.95981i	−0.0625279	−	0.434891i
$336$	−1.41780	+	2.23380i	−0.0773473	+	0.121864i
$337$	14.1491	−	4.15454i	0.770749	−	0.226312i	0.127365	−	0.991856i	$-0.459348\pi$
$337$	14.1491	−	4.15454i	0.770749	−	0.226312i	0.643384	+	0.765543i	$0.277530\pi$
$338$	−6.67144	−	5.24648i	−0.362879	−	0.285371i
$339$	−5.48486	−	1.05712i	−0.297897	−	0.0574149i
$340$	0.705137	+	0.363523i	0.0382414	+	0.0197148i
$341$	−11.3482	+	2.18719i	−0.614540	+	0.118443i
$342$	5.96641	+	1.75190i	0.322626	+	0.0947317i
$343$	−16.9746	−	7.40689i	−0.916544	−	0.399934i
$344$	7.34690			0.396118
$345$	2.39385	−	1.78486i	0.128881	−	0.0960938i
$346$	−6.79693	−	11.7726i	−0.365405	−	0.632901i
$347$	13.4511	−	1.28442i	0.722091	−	0.0689513i	0.272462	−	0.962167i	$-0.412162\pi$
$347$	13.4511	−	1.28442i	0.722091	−	0.0689513i	0.449629	+	0.893215i	$0.351556\pi$
$348$	−0.151509	+	0.144463i	−0.00812172	+	0.00774405i
$349$	3.17540	+	3.66461i	0.169975	+	0.196162i	0.834346	−	0.551241i	$-0.185846\pi$
$349$	3.17540	+	3.66461i	0.169975	+	0.196162i	−0.664370	+	0.747404i	$0.731300\pi$
$350$	6.65540	+	10.2284i	0.355746	+	0.546734i
$351$	−1.39113	+	1.60545i	−0.0742532	+	0.0856928i
$352$	−1.36473	−	1.07323i	−0.0727402	−	0.0572035i
$353$	2.50393	+	2.38750i	0.133271	+	0.127074i	0.753783	−	0.657123i	$-0.228227\pi$
$353$	2.50393	+	2.38750i	0.133271	+	0.127074i	−0.620512	+	0.784197i	$0.713075\pi$
$354$	0.309523	−	6.49769i	0.0164510	−	0.345348i
$355$	0.850514	+	0.340494i	0.0451406	+	0.0180716i
$356$	2.85454	+	6.25057i	0.151290	+	0.331280i
$357$	0.301475	−	3.35761i	0.0159558	−	0.177703i
$358$	2.23090	+	15.5162i	0.117907	+	0.820058i
$359$	−11.5457	+	5.95221i	−0.609358	+	0.314146i	−0.735143	−	0.677912i	$-0.762885\pi$
$359$	−11.5457	+	5.95221i	−0.609358	+	0.314146i	0.125786	+	0.992057i	$0.459855\pi$
$360$	0.450616	+	0.429661i	0.0237495	+	0.0226451i
$361$	18.2584	−	7.30955i	0.960966	−	0.384713i
$362$	5.42237	+	15.6669i	0.284993	+	0.823434i
$363$	−6.71799	+	4.31739i	−0.352603	+	0.226604i
$364$	−5.32161	−	1.80822i	−0.278928	−	0.0947762i
$365$	−2.08095	−	0.611021i	−0.108922	−	0.0319823i
$366$	4.61197	+	6.47661i	0.241072	+	0.338538i
$367$	9.26085	+	16.0403i	0.483413	+	0.837295i	0.999819	−	0.0190487i	$-0.00606377\pi$
$367$	9.26085	+	16.0403i	0.483413	+	0.837295i	−0.516406	+	0.856344i	$0.672730\pi$
$368$	−4.56530	−	1.46902i	−0.237983	−	0.0765782i
$369$	2.42781	−	4.20509i	0.126387	−	0.218908i
$370$	0.0671009	−	0.146930i	0.00348841	−	0.00763855i
$371$	9.72107	−	2.41656i	0.504693	−	0.125461i
$372$	−4.35916	−	5.03074i	−0.226012	−	0.260832i
$373$	−0.543220	−	11.4036i	−0.0281269	−	0.590456i	−0.968305	−	0.249772i	$-0.919644\pi$
$373$	−0.543220	−	11.4036i	−0.0281269	−	0.590456i	0.940178	−	0.340684i	$-0.110659\pi$
$374$	2.17219	+	0.418656i	0.112321	+	0.0216482i
$375$	5.55618	−	2.22436i	0.286920	−	0.114865i
$376$	0.616925	−	2.54300i	0.0318155	−	0.131145i
$377$	−0.374115	−	0.240429i	−0.0192679	−	0.0123827i
$378$	0.969430	−	2.46175i	0.0498621	−	0.126619i
$379$	−8.24281	−	18.0492i	−0.423405	−	0.927127i	−0.994351	−	0.106139i	$-0.966151\pi$
$379$	−8.24281	−	18.0492i	−0.423405	−	0.927127i	0.570947	−	0.820987i	$-0.306576\pi$
$380$	3.85414	+	0.368026i	0.197713	+	0.0188793i
$381$	4.49138	−	3.53206i	0.230100	−	0.180953i
$382$	−0.945974	+	19.8584i	−0.0484002	+	1.01605i
$383$	1.62016	−	6.67838i	0.0827861	−	0.341249i	−0.915323	−	0.402721i	$-0.868064\pi$
$383$	1.62016	−	6.67838i	0.0827861	−	0.341249i	0.998109	+	0.0614722i	$0.0195795\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−2.17201	−	1.86068i	−0.110696	−	0.0948288i
$386$	1.19485	−	0.767882i	0.0608162	−	0.0390842i
$387$	−7.21413	+	1.39041i	−0.366715	+	0.0706785i
$388$	1.40506	+	5.79174i	0.0713312	+	0.294031i
$389$	−9.80945	+	0.936689i	−0.497359	+	0.0474920i	−0.340722	−	0.940164i	$-0.610671\pi$
$389$	−9.80945	+	0.936689i	−0.497359	+	0.0474920i	−0.156637	+	0.987656i	$0.550065\pi$
$390$	−0.661329	+	1.14546i	−0.0334877	+	0.0580024i
$391$	6.02799	−	1.00177i	0.304849	−	0.0506618i
$392$	6.99955	−	0.0791153i	0.353531	−	0.00399593i
$393$	−5.62886	+	12.3255i	−0.283939	+	0.621739i
$394$	16.5052	−	15.7376i	0.831518	−	0.792851i
$395$	−0.341944	+	0.987981i	−0.0172051	+	0.0497107i
$396$	1.54317	+	0.795562i	0.0775474	+	0.0399785i
$397$	−5.96457	−	17.2335i	−0.299353	−	0.864924i	−0.989917	−	0.141652i	$-0.954759\pi$
$397$	−5.96457	−	17.2335i	−0.299353	−	0.864924i	0.690564	−	0.723272i	$-0.257363\pi$
$398$	2.24807	−	15.6357i	0.112686	−	0.783746i
$399$	−4.72421	−	15.7592i	−0.236506	−	0.788946i
$400$	−3.88014	−	2.49362i	−0.194007	−	0.124681i
$401$	−29.2562	−	11.7124i	−1.46099	−	0.584890i	−0.501127	−	0.865374i	$-0.667081\pi$
$401$	−29.2562	−	11.7124i	−1.46099	−	0.584890i	−0.959859	+	0.280483i	$0.909505\pi$
$402$	7.49185	−	10.5208i	0.373659	−	0.524731i
$403$	8.20246	−	11.5187i	0.408594	−	0.573790i
$404$	6.05400	+	2.42366i	0.301198	+	0.120581i
$405$	−0.523787	−	0.336617i	−0.0260272	−	0.0167266i
$406$	0.538986	+	0.127536i	0.0267494	+	0.00632950i
$407$	0.0641006	−	0.445830i	0.00317735	−	0.0220990i
$408$	0.416738	+	1.20408i	0.0206316	+	0.0596110i
$409$	−12.6395	−	6.51614i	−0.624985	−	0.322202i	0.116480	−	0.993193i	$-0.462839\pi$
$409$	−12.6395	−	6.51614i	−0.624985	−	0.322202i	−0.741466	+	0.670991i	$0.765869\pi$
$410$	0.988804	−	2.85696i	0.0488336	−	0.141095i
$411$	13.4890	−	12.8618i	0.665364	−	0.634424i
$412$	−3.93470	+	8.61578i	−0.193849	+	0.424469i
$413$	−14.8561	+	8.68947i	−0.731020	+	0.427581i
$414$	4.76081	+	0.578488i	0.233981	+	0.0284311i
$415$	−2.20472	+	3.81868i	−0.108225	+	0.187452i
$416$	2.11470	−	0.201929i	0.103682	−	0.00990040i
$417$	2.54500	+	10.4907i	0.124629	+	0.513729i
$418$	10.6010	−	2.04317i	0.518509	−	0.0999345i
$419$	26.0015	−	16.7101i	1.27026	−	0.816344i	0.280602	−	0.959824i	$-0.409466\pi$
$419$	26.0015	−	16.7101i	1.27026	−	0.816344i	0.989653	+	0.143480i	$0.0458294\pi$
$420$	0.302610	−	1.61928i	0.0147659	−	0.0790129i
$421$	−1.97572	+	13.7414i	−0.0962905	+	0.669715i	0.883314	+	0.468781i	$0.155307\pi$
$421$	−1.97572	+	13.7414i	−0.0962905	+	0.669715i	−0.979605	+	0.200934i	$0.935602\pi$
$422$	4.49223	−	18.5172i	0.218678	−	0.901404i
$423$	−0.124510	+	2.61380i	−0.00605391	+	0.127087i
$424$	−2.97603	+	2.34038i	−0.144529	+	0.113659i
$425$	5.85025	+	0.558631i	0.283779	+	0.0270976i
$426$	0.611246	+	1.33844i	0.0296150	+	0.0648477i
$427$	7.70784	−	19.5731i	0.373008	−	0.947209i
$428$	2.75861	+	1.77285i	0.133343	+	0.0856940i
$429$	−0.869524	+	3.58423i	−0.0419810	+	0.173048i
$430$	−4.24670	+	1.70012i	−0.204794	+	0.0819873i
$431$	−11.3751	−	2.19237i	−0.547919	−	0.105603i	−0.0922232	−	0.995738i	$-0.529397\pi$
$431$	−11.3751	−	2.19237i	−0.547919	−	0.105603i	−0.455696	+	0.890136i	$0.650609\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	−0.575076	−	0.663673i	−0.0276364	−	0.0318941i	0.741763	−	0.670662i	$-0.233990\pi$
$433$	−0.575076	−	0.663673i	−0.0276364	−	0.0318941i	−0.769399	+	0.638768i	$0.779444\pi$
$434$	−4.86623	+	16.9261i	−0.233587	+	0.812480i
$435$	0.0541463	−	0.118564i	0.00259611	−	0.00568470i
$436$	7.00003	−	12.1244i	0.335240	−	0.580653i
$437$	25.4941	−	15.4725i	1.21955	−	0.740148i
$438$	−1.74165	−	3.01663i	−0.0832194	−	0.144140i
$439$	−4.15411	−	5.83363i	−0.198265	−	0.278424i	0.703460	−	0.710735i	$-0.251638\pi$
$439$	−4.15411	−	5.83363i	−0.198265	−	0.278424i	−0.901724	+	0.432311i	$0.857698\pi$
$440$	1.03720	+	0.304550i	0.0494466	+	0.0145188i
$441$	−6.85809	+	1.40236i	−0.326576	+	0.0667790i
$442$	−2.27704	+	1.46337i	−0.108308	+	0.0696053i
$443$	−3.98830	−	11.5234i	−0.189490	−	0.547495i	0.809738	−	0.586792i	$-0.199609\pi$
$443$	−3.98830	−	11.5234i	−0.189490	−	0.547495i	−0.999228	+	0.0392968i	$0.987488\pi$
$444$	0.240845	−	0.0964200i	0.0114300	−	0.00457589i
$445$	−3.09643	−	2.95244i	−0.146785	−	0.139959i
$446$	−13.2422	+	6.82682i	−0.627036	+	0.323259i
$447$	−1.33637	−	9.29465i	−0.0632081	−	0.439622i
$448$	−2.40041	+	1.11267i	−0.113409	+	0.0525686i
$449$	12.6278	+	27.6511i	0.595945	+	1.30494i	0.931783	+	0.363017i	$0.118253\pi$
$449$	12.6278	+	27.6511i	0.595945	+	1.30494i	−0.335838	+	0.941920i	$0.609019\pi$
$450$	4.28195	+	1.71423i	0.201853	+	0.0808097i
$451$	0.401126	−	8.42066i	0.0188883	−	0.396513i
$452$	−4.04264	−	3.85465i	−0.190150	−	0.181307i
$453$	0.496749	+	0.390648i	0.0233393	+	0.0183542i
$454$	8.53459	−	9.84944i	0.400548	−	0.462257i
$455$	3.49446	−	0.186260i	0.163823	−	0.00873201i
$456$	4.07212	+	4.69947i	0.190694	+	0.220073i
$457$	−11.8621	+	11.3105i	−0.554887	+	0.529083i	−0.914803	−	0.403901i	$-0.867654\pi$
$457$	−11.8621	+	11.3105i	−0.554887	+	0.529083i	0.359916	+	0.932985i	$0.382805\pi$
$458$	13.2697	−	1.26710i	0.620052	−	0.0592078i
$459$	−0.637081	−	1.10346i	−0.0297364	−	0.0515049i
$460$	2.97881	−	0.207307i	0.138888	−	0.00966575i
$461$	0.805774			0.0375286			0.0187643	−	0.999824i	$-0.494027\pi$
$461$	0.805774			0.0375286			0.0187643	+	0.999824i	$0.494027\pi$
$462$	−0.462473	−	4.57015i	−0.0215162	−	0.212623i
$463$	29.6810	+	8.71512i	1.37939	+	0.405026i	0.885557	−	0.464530i	$-0.153777\pi$
$463$	29.6810	+	8.71512i	1.37939	+	0.405026i	0.493835	+	0.869556i	$0.335595\pi$
$464$	−0.205560	+	0.0396184i	−0.00954288	+	0.00183924i
$465$	3.68386	+	1.89916i	0.170835	+	0.0880714i
$466$	23.0987	+	4.45191i	1.07003	+	0.206231i
$467$	−25.1537	−	19.7811i	−1.16397	−	0.915360i	−0.166476	−	0.986046i	$-0.553239\pi$
$467$	−25.1537	−	19.7811i	−1.16397	−	0.915360i	−0.997499	+	0.0706860i	$0.977481\pi$
$468$	−2.03827	+	0.598490i	−0.0942191	+	0.0276652i
$469$	−34.1417	−	1.43304i	−1.57652	−	0.0661716i
$470$	0.231868	+	1.61268i	0.0106953	+	0.0743874i
$471$	12.8693	+	1.22887i	0.592988	+	0.0566235i
$472$	3.77330	−	5.29886i	0.173680	−	0.243900i
$473$	−10.0265	+	7.88494i	−0.461020	+	0.362550i
$474$	−1.49249	+	0.769430i	−0.0685522	+	0.0353411i
$475$	27.5191	−	8.08033i	1.26266	−	0.370751i
$476$	2.06888	−	2.66161i	0.0948268	−	0.121995i
$477$	2.47933	−	2.86130i	0.113521	−	0.131010i
$478$	0.438651	+	9.20842i	0.0200634	+	0.421183i
$479$	−2.45578	+	7.09550i	−0.112207	+	0.324202i	−0.987098	−	0.160119i	$-0.948812\pi$
$479$	−2.45578	+	7.09550i	−0.112207	+	0.324202i	0.874890	+	0.484321i	$0.160933\pi$
$480$	0.146790	+	0.605076i	0.00670000	+	0.0276178i
$481$	0.319675	+	0.448921i	0.0145759	+	0.0204690i
$482$	7.71915			0.351598
$483$	−5.58678	−	11.3925i	−0.254207	−	0.518374i
$484$	−7.98569			−0.362986
$485$	−2.15241	−	3.02264i	−0.0977360	−	0.137251i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	11.3672	−	32.8435i	0.515099	−	1.48828i	−0.324929	−	0.945738i	$-0.605340\pi$
$487$	11.3672	−	32.8435i	0.515099	−	1.48828i	0.840028	−	0.542543i	$-0.182538\pi$
$488$	0.378319	+	7.94189i	0.0171257	+	0.359512i
$489$	3.07163	−	3.54484i	0.138904	−	0.160303i
$490$	−4.02762	+	1.66548i	−0.181949	+	0.0752385i
$491$	9.97725	−	2.92959i	0.450267	−	0.132210i	−0.0487339	−	0.998812i	$-0.515519\pi$
$491$	9.97725	−	2.92959i	0.450267	−	0.132210i	0.499001	+	0.866601i	$0.333700\pi$
$492$	4.31585	−	2.22497i	0.194573	−	0.100310i
$493$	0.209669	−	0.164886i	0.00944304	−	0.00742609i
$494$	−7.66234	+	10.7603i	−0.344745	+	0.484127i
$495$	−1.07609	−	0.102755i	−0.0483668	−	0.00461847i
$496$	−0.947336	−	6.58886i	−0.0425366	−	0.295849i
$497$	2.08617	−	3.28683i	0.0935773	−	0.147434i
$498$	−6.79512	+	1.99523i	−0.304496	+	0.0894082i
$499$	0.286133	+	0.225017i	0.0128091	+	0.0100732i	0.624543	−	0.780990i	$-0.285285\pi$
$499$	0.286133	+	0.225017i	0.0128091	+	0.0100732i	−0.611734	+	0.791064i	$0.709528\pi$
$500$	5.87674	+	1.13265i	0.262816	+	0.0506536i
$501$	−9.62216	−	4.96057i	−0.429886	−	0.221622i
$502$	16.7584	−	3.22992i	0.747966	−	0.144159i
$503$	23.6552	+	6.94581i	1.05474	+	0.309698i	0.762729	−	0.646718i	$-0.223859\pi$
$503$	23.6552	+	6.94581i	1.05474	+	0.309698i	0.292006	+	0.956416i	$0.405677\pi$
$504$	2.14646	−	1.54684i	0.0956108	−	0.0689018i
$505$	−4.06023			−0.180678
$506$	7.80699	−	2.89481i	0.347063	−	0.128690i
$507$	4.24363	+	7.35019i	0.188466	+	0.326433i
$508$	5.68797	−	0.543135i	0.252363	−	0.0240977i
$509$	16.4748	−	15.7087i	0.730233	−	0.696276i	−0.230709	−	0.973023i	$-0.574105\pi$
$509$	16.4748	−	15.7087i	0.730233	−	0.696276i	0.960943	+	0.276746i	$0.0892562\pi$
$510$	−0.519519	−	0.599557i	−0.0230047	−	0.0265488i
$511$	−4.17664	+	8.21521i	−0.184764	+	0.363419i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−4.88791	−	3.84389i	−0.215806	−	0.169712i
$514$	−11.3143	−	10.7882i	−0.499054	−	0.475847i
$515$	0.280607	−	5.89067i	0.0123650	−	0.259574i
$516$	−6.82063	−	2.73057i	−0.300261	−	0.120207i
$517$	1.88730	+	4.13260i	0.0830031	+	0.181752i
$518$	−0.561353	−	0.394976i	−0.0246644	−	0.0173542i
$519$	1.93461	+	13.4555i	0.0849199	+	0.590631i
$520$	−1.17563	+	0.606077i	−0.0515546	+	0.0265782i
$521$	30.8566	+	29.4217i	1.35185	+	1.28899i	0.922577	+	0.385812i	$0.126079\pi$
$521$	30.8566	+	29.4217i	1.35185	+	1.28899i	0.429273	+	0.903175i	$0.358770\pi$
$522$	0.194347	−	0.0778050i	0.00850636	−	0.00340543i
$523$	−9.52286	−	27.5145i	−0.416406	−	1.20312i	−0.937003	−	0.349322i	$-0.886412\pi$
$523$	−9.52286	−	27.5145i	−0.416406	−	1.20312i	0.520597	−	0.853802i	$-0.325709\pi$
$524$	−11.3990	+	7.32567i	−0.497966	+	0.320023i
$525$	−2.37713	−	11.9693i	−0.103746	−	0.522384i
$526$	22.2373	+	6.52946i	0.969592	+	0.284698i
$527$	4.91982	+	6.90892i	0.214311	+	0.300957i
$528$	0.868088	+	1.50357i	0.0377787	+	0.0654346i
$529$	17.4399	−	14.9950i	0.758256	−	0.651957i
$530$	1.17865	−	2.04147i	0.0511971	−	0.0886760i
$531$	−2.70230	+	5.91721i	−0.117270	+	0.256785i
$532$	4.54580	−	15.8116i	0.197085	−	0.685519i
$533$	6.75482	+	7.79547i	0.292584	+	0.337659i
$534$	−0.326961	−	6.86376i	−0.0141490	−	0.297024i
$535$	−2.00480	−	0.386394i	−0.0866751	−	0.0167053i
$536$	11.9905	−	4.80028i	0.517912	−	0.207341i
$537$	3.69571	−	15.2339i	0.159482	−	0.657392i
$538$	−10.5133	−	6.75648i	−0.453260	−	0.291293i
$539$	−9.46757	+	7.62012i	−0.407797	+	0.328222i
$540$	−0.258648	−	0.566361i	−0.0111305	−	0.0243723i
$541$	22.0629	+	2.10675i	0.948557	+	0.0905763i	0.557853	−	0.829940i	$-0.311625\pi$
$541$	22.0629	+	2.10675i	0.948557	+	0.0905763i	0.390705	+	0.920516i	$0.372231\pi$
$542$	20.8664	−	16.4095i	0.896289	−	0.704849i
$543$	0.788847	−	16.5599i	0.0338527	−	0.710655i
$544$	−0.300395	+	1.23825i	−0.0128793	+	0.0530893i
$545$	−1.24053	+	8.62808i	−0.0531385	+	0.369586i
$546$	4.26836	+	3.65653i	0.182669	+	0.156485i
$547$	−6.13661	+	3.94376i	−0.262382	+	0.168623i	−0.665217	−	0.746650i	$-0.731661\pi$
$547$	−6.13661	+	3.94376i	−0.262382	+	0.168623i	0.402835	+	0.915273i	$0.368025\pi$
$548$	18.3013	−	3.52728i	0.781792	−	0.150678i
$549$	−1.87449	−	7.72677i	−0.0800015	−	0.329770i
$550$	7.97157	−	0.761192i	0.339909	−	0.0324573i
$551$	0.650878	−	1.12735i	0.0277284	−	0.0480269i
$552$	3.69230	+	3.06055i	0.157155	+	0.130265i
$553$	3.85990	+	2.19953i	0.164140	+	0.0935333i
$554$	−6.54871	+	14.3397i	−0.278228	+	0.609234i
$555$	−0.116903	+	0.111467i	−0.00496225	+	0.00473149i
$556$	−3.53068	+	10.2012i	−0.149734	+	0.432629i
$557$	29.3271	+	15.1192i	1.24263	+	0.640619i	0.948993	−	0.315299i	$-0.102105\pi$
$557$	29.3271	+	15.1192i	1.24263	+	0.640619i	0.293635	+	0.955918i	$0.405135\pi$
$558$	2.17717	+	6.29051i	0.0921668	+	0.266299i
$559$	2.22113	−	15.4483i	0.0939439	−	0.653394i
$560$	1.13002	−	1.19862i	0.0477521	−	0.0506511i
$561$	−1.86100	−	1.19599i	−0.0785713	−	0.0504947i
$562$	2.45966	+	0.984700i	0.103755	+	0.0415371i
$563$	16.2966	−	22.8853i	0.686818	−	0.964501i	−0.313073	−	0.949729i	$-0.601358\pi$
$563$	16.2966	−	22.8853i	0.686818	−	0.964501i	0.999891	−	0.0147722i	$-0.00470231\pi$
$564$	−1.51787	+	2.13155i	−0.0639139	+	0.0897544i
$565$	3.22874	+	1.29259i	0.135834	+	0.0543798i
$566$	−9.44553	−	6.07028i	−0.397025	−	0.255153i
$567$	−1.81493	+	1.92511i	−0.0762198	+	0.0808469i
$568$	−0.209404	+	1.45643i	−0.00878638	+	0.0611106i
$569$	−4.82236	−	13.9333i	−0.202164	−	0.584114i	0.797656	−	0.603113i	$-0.206073\pi$
$569$	−4.82236	−	13.9333i	−0.202164	−	0.584114i	−0.999820	+	0.0189990i	$0.993952\pi$
$570$	−3.44128	−	1.77410i	−0.144139	−	0.0743090i
$571$	−9.62958	+	27.8228i	−0.402985	+	1.16435i	0.542886	+	0.839807i	$0.317332\pi$
$571$	−9.62958	+	27.8228i	−0.402985	+	1.16435i	−0.945871	+	0.324543i	$0.894790\pi$
$572$	−2.66927	+	2.54514i	−0.111608	+	0.106418i
$573$	8.25885	−	18.0844i	0.345018	−	0.755485i
$574$	−11.1617	−	6.36041i	−0.465882	−	0.265478i
$575$	19.9152	−	9.62703i	0.830520	−	0.401475i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−14.2914	+	1.36466i	−0.594957	+	0.0568115i	−0.388191	−	0.921579i	$-0.626900\pi$
$577$	−14.2914	+	1.36466i	−0.594957	+	0.0568115i	−0.206766	+	0.978390i	$0.566294\pi$
$578$	3.62515	+	14.9431i	0.150786	+	0.621550i
$579$	−1.39465	+	0.268797i	−0.0579597	+	0.0111708i
$580$	0.109651	−	0.0704685i	0.00455302	−	0.00292605i
$581$	14.2297	+	12.1900i	0.590348	+	0.505727i
$582$	0.848159	−	5.89908i	0.0351573	−	0.244525i
$583$	1.54970	−	6.38795i	0.0641820	−	0.264562i
$584$	0.165742	−	3.47936i	0.00685847	−	0.143977i
$585$	1.03968	−	0.817613i	0.0429854	−	0.0338041i
$586$	3.86634	+	0.369190i	0.159717	+	0.0152511i
$587$	5.19081	+	11.3663i	0.214248	+	0.469137i	0.985991	−	0.166797i	$-0.0533424\pi$
$587$	5.19081	+	11.3663i	0.214248	+	0.469137i	−0.771744	+	0.635934i	$0.780615\pi$
$588$	−6.52756	−	2.52802i	−0.269192	−	0.104254i
$589$	34.8218	+	22.3786i	1.43481	+	0.922096i
$590$	−0.954875	+	3.93605i	−0.0393116	+	0.162045i
$591$	−21.1720	+	8.47597i	−0.870898	+	0.348655i
$592$	0.254741	+	0.0490972i	0.0104698	+	0.00201788i
$593$	1.53895	+	32.3066i	0.0631973	+	1.32667i	0.778405	+	0.627762i	$0.216029\pi$
$593$	1.53895	+	32.3066i	0.0631973	+	1.32667i	−0.715208	+	0.698912i	$0.753668\pi$
$594$	−1.13695	−	1.31211i	−0.0466498	−	0.0538367i
$595$	−0.579951	+	2.01723i	−0.0237757	+	0.0826985i
$596$	3.90084	−	8.54166i	0.159785	−	0.349880i
$597$	−7.89823	+	13.6801i	−0.323253	+	0.559891i
$598$	−4.46910	+	9.15533i	−0.182755	+	0.374389i
$599$	15.6871	+	27.1709i	0.640958	+	1.11017i	0.985219	+	0.171298i	$0.0547959\pi$
$599$	15.6871	+	27.1709i	0.640958	+	1.11017i	−0.344262	+	0.938874i	$0.611871\pi$
$600$	2.67542	+	3.75710i	0.109223	+	0.153383i
$601$	−3.70581	−	1.08812i	−0.151163	−	0.0443855i	0.205275	−	0.978704i	$-0.434191\pi$
$601$	−3.70581	−	1.08812i	−0.151163	−	0.0443855i	−0.356439	+	0.934319i	$0.616009\pi$
$602$	3.78648	+	19.0657i	0.154326	+	0.777060i
$603$	−10.8654	+	6.98276i	−0.442473	+	0.284360i
$604$	0.206692	+	0.597197i	0.00841017	+	0.0242996i
$605$	4.61594	−	1.84794i	0.187665	−	0.0751296i
$606$	−4.71956	−	4.50009i	−0.191719	−	0.182804i
$607$	−17.2600	+	8.89817i	−0.700563	+	0.361166i	−0.771425	−	0.636321i	$-0.780456\pi$
$607$	−17.2600	+	8.89817i	−0.700563	+	0.361166i	0.0708613	+	0.997486i	$0.477425\pi$
$608$	0.884955	+	6.15500i	0.0358897	+	0.249618i
$609$	−0.452977	−	0.318721i	−0.0183556	−	0.0129152i
$610$	−2.05649	−	4.50308i	−0.0832647	−	0.182324i
$611$	−5.16064	−	2.06601i	−0.208777	−	0.0835818i
$612$	0.0606271	−	1.27272i	0.00245070	−	0.0514466i
$613$	−20.9104	−	19.9380i	−0.844563	−	0.805289i	0.138153	−	0.990411i	$-0.455884\pi$
$613$	−20.9104	−	19.9380i	−0.844563	−	0.805289i	−0.982716	+	0.185122i	$0.940732\pi$
$614$	−21.7532	−	17.1069i	−0.877888	−	0.690379i
$615$	−1.97980	+	2.28481i	−0.0798332	+	0.0921324i
$616$	2.08175	−	4.09469i	0.0838762	−	0.164980i
$617$	−7.72845	−	8.91911i	−0.311136	−	0.359070i	0.578547	−	0.815649i	$-0.303620\pi$
$617$	−7.72845	−	8.91911i	−0.311136	−	0.359070i	−0.889683	+	0.456579i	$0.849074\pi$
$618$	6.85501	−	6.53624i	0.275749	−	0.262926i
$619$	−23.4676	+	2.24088i	−0.943242	+	0.0900687i	−0.555332	−	0.831629i	$-0.687409\pi$
$619$	−23.4676	+	2.24088i	−0.943242	+	0.0900687i	−0.387910	+	0.921697i	$0.626803\pi$
$620$	2.07229	+	3.58932i	0.0832253	+	0.144150i
$621$	−4.20478	−	2.30647i	−0.168732	−	0.0925553i
$622$	−31.9808			−1.28231
$623$	−14.7495	+	10.6292i	−0.590925	+	0.425849i
$624$	−2.03827	−	0.598490i	−0.0815961	−	0.0239588i
$625$	18.9859	−	3.65923i	0.759437	−	0.146369i
$626$	11.9967	+	6.18472i	0.479484	+	0.247191i
$627$	−10.6010	−	2.04317i	−0.423361	−	0.0815962i
$628$	10.1620	+	7.99148i	0.405508	+	0.318895i
$629$	−0.317165	+	0.0931280i	−0.0126462	+	0.00371325i
$630$	−0.882760	+	1.39082i	−0.0351700	+	0.0554116i
$631$	−5.06911	−	35.2565i	−0.201798	−	1.40354i	−0.798944	−	0.601405i	$-0.794608\pi$
$631$	−5.06911	−	35.2565i	−0.201798	−	1.40354i	0.597146	−	0.802133i	$-0.296301\pi$
$632$	−1.67154	−	0.159613i	−0.0664905	−	0.00634907i
$633$	−11.0526	+	15.5212i	−0.439301	+	0.616912i
$634$	4.67207	−	3.67415i	0.185552	−	0.145919i
$635$	−3.16211	+	1.63018i	−0.125484	+	0.0646917i
$636$	3.63268	−	1.06665i	0.144045	−	0.0422955i
$637$	1.94976	−	14.7419i	0.0772525	−	0.584094i
$638$	0.238013	−	0.274682i	0.00942304	−	0.0108748i
$639$	−0.0700125	−	1.46974i	−0.00276965	−	0.0581422i
$640$	−0.203641	+	0.588383i	−0.00804962	+	0.0232579i
$641$	7.86660	+	32.4266i	0.310712	+	1.28077i	0.886330	+	0.463054i	$0.153246\pi$
$641$	7.86660	+	32.4266i	0.310712	+	1.28077i	−0.575618	+	0.817719i	$0.695238\pi$
$642$	−1.90210	−	2.67113i	−0.0750701	−	0.105421i
$643$	36.1867			1.42706			0.713532	−	0.700623i	$-0.247094\pi$
$643$	36.1867			1.42706			0.713532	+	0.700623i	$0.247094\pi$
$644$	1.45933	−	12.6044i	0.0575056	−	0.496682i
$645$	4.57438			0.180116
$646$	−4.59586	−	6.45398i	−0.180822	−	0.253928i
$647$	6.13804	+	25.3014i	0.241311	+	0.994699i	0.955558	+	0.294804i	$0.0952545\pi$
$647$	6.13804	+	25.3014i	0.241311	+	0.994699i	−0.714246	+	0.699894i	$0.753230\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	0.537386	+	11.2811i	0.0210943	+	0.442823i
$650$	−6.41638	+	7.40489i	−0.251671	+	0.290444i
$651$	10.8085	−	13.9051i	0.423617	−	0.544983i
$652$	4.50050	−	1.32147i	0.176253	−	0.0517526i
$653$	−30.7495	+	15.8525i	−1.20332	+	0.620355i	−0.938946	−	0.344065i	$-0.888196\pi$
$653$	−30.7495	+	15.8525i	−1.20332	+	0.620355i	−0.264375	+	0.964420i	$0.585166\pi$
$654$	−11.0048	+	8.65426i	−0.430321	+	0.338408i
$655$	4.89369	−	6.87223i	0.191212	−	0.268520i
$656$	4.83363	+	0.461556i	0.188722	+	0.0180207i
$657$	0.495726	+	3.44785i	0.0193401	+	0.134513i
$658$	6.91721	+	0.290338i	0.269661	+	0.0113186i
$659$	−10.3052	+	3.02588i	−0.401434	+	0.117872i	−0.476216	−	0.879328i	$-0.657992\pi$
$659$	−10.3052	+	3.02588i	−0.401434	+	0.117872i	0.0747821	+	0.997200i	$0.476174\pi$
$660$	−0.849715	−	0.668223i	−0.0330751	−	0.0260105i
$661$	−40.7299	−	7.85005i	−1.58421	−	0.305332i	−0.680261	−	0.732970i	$-0.738134\pi$
$661$	−40.7299	−	7.85005i	−1.58421	−	0.305332i	−0.903950	+	0.427638i	$0.859346\pi$
$662$	18.6799	+	9.63016i	0.726015	+	0.374287i
$663$	2.65781	−	0.512252i	0.103221	−	0.0198942i
$664$	−6.79512	−	1.99523i	−0.263702	−	0.0774298i
$665$	1.03132	+	10.1914i	0.0399927	+	0.395207i
$666$	−0.259429			−0.0100527
$667$	0.352656	−	0.939999i	0.0136549	−	0.0363969i
$668$	−5.41279	−	9.37523i	−0.209427	−	0.362738i
$669$	14.8309	−	1.41618i	0.573396	−	0.0547526i
$670$	−5.82002	+	5.54938i	−0.224847	+	0.214391i
$671$	−9.03979	−	10.4325i	−0.348977	−	0.402741i
$672$	2.64200	−	0.140823i	0.101917	−	0.00543235i
$673$	−16.8666	+	19.4651i	−0.650161	+	0.750325i	−0.981137	−	0.193314i	$-0.938077\pi$
$673$	−16.8666	+	19.4651i	−0.650161	+	0.750325i	0.330976	+	0.943639i	$0.392622\pi$
$674$	−11.5915	−	9.11563i	−0.446486	−	0.351121i
$675$	−3.33810	−	3.18288i	−0.128484	−	0.122509i
$676$	−0.403840	+	8.47765i	−0.0155323	+	0.326064i
$677$	−20.8875	−	8.36208i	−0.802770	−	0.321381i	−0.0662559	−	0.997803i	$-0.521105\pi$
$677$	−20.8875	−	8.36208i	−0.802770	−	0.321381i	−0.736514	+	0.676422i	$0.763530\pi$
$678$	2.32043	+	5.08102i	0.0891154	+	0.195136i
$679$	−14.3058	+	6.63121i	−0.549007	+	0.254482i
$680$	−0.112902	−	0.785252i	−0.00432960	−	0.0301130i
$681$	−11.5839	+	5.97192i	−0.443896	+	0.228844i
$682$	8.36424	+	7.97528i	0.320283	+	0.305389i
$683$	25.0708	−	10.0368i	0.959307	−	0.384048i	0.161440	−	0.986883i	$-0.448386\pi$
$683$	25.0708	−	10.0368i	0.959307	−	0.384048i	0.797867	+	0.602834i	$0.205962\pi$
$684$	−2.03380	−	5.87629i	−0.0777644	−	0.224686i
$685$	−9.76238	+	6.27390i	−0.373002	+	0.239714i
$686$	3.81278	+	18.1235i	0.145572	+	0.691960i
$687$	−12.7901	−	3.75551i	−0.487973	−	0.143282i
$688$	−4.26162	−	5.98461i	−0.162473	−	0.228161i
$689$	4.02139	+	6.96524i	0.153203	+	0.265355i
$690$	−2.84248	−	0.914653i	−0.108211	−	0.0348203i
$691$	−6.02635	+	10.4379i	−0.229253	+	0.397078i	−0.957587	−	0.288144i	$-0.906962\pi$
$691$	−6.02635	+	10.4379i	−0.229253	+	0.397078i	0.728334	+	0.685222i	$0.240295\pi$
$692$	−5.64710	+	12.3654i	−0.214670	+	0.470063i
$693$	−1.26921	+	4.41466i	−0.0482132	+	0.167699i
$694$	−8.84864	−	10.2119i	−0.335890	−	0.387637i
$695$	−0.319808	−	6.71361i	−0.0121310	−	0.254662i
$696$	0.205560	+	0.0396184i	0.00779173	+	0.00150173i
$697$	−5.74367	+	2.29942i	−0.217557	+	0.0870967i
$698$	1.14319	−	4.71229i	0.0432703	−	0.178363i
$699$	−19.7895	−	12.7179i	−0.748507	−	0.481036i
$700$	4.47134	−	11.3544i	0.169001	−	0.429156i
$701$	−3.00869	−	6.58810i	−0.113636	−	0.248829i	0.844265	−	0.535926i	$-0.180037\pi$
$701$	−3.00869	−	6.58810i	−0.113636	−	0.248829i	−0.957902	+	0.287096i	$0.907310\pi$
$702$	2.11470	+	0.201929i	0.0798142	+	0.00762133i
$703$	−1.26806	+	0.997217i	−0.0478260	+	0.0376108i
$704$	−0.0826106	+	1.73421i	−0.00311350	+	0.0653605i
$705$	0.384114	−	1.58334i	0.0144666	−	0.0596320i
$706$	0.492373	−	3.42453i	0.0185307	−	0.128884i
$707$	−3.16941	+	16.9597i	−0.119198	+	0.637834i
$708$	−5.47240	+	3.51690i	−0.205665	+	0.132173i
$709$	34.1898	−	6.58954i	1.28402	−	0.247475i	0.498817	−	0.866708i	$-0.333768\pi$
$709$	34.1898	−	6.58954i	1.28402	−	0.247475i	0.785208	+	0.619232i	$0.212556\pi$
$710$	−0.215988	−	0.890314i	−0.00810588	−	0.0334129i
$711$	1.67154	−	0.159613i	0.0626878	−	0.00598596i
$712$	3.43577	−	5.95093i	0.128761	−	0.223021i
$713$	29.3223	+	12.6232i	1.09813	+	0.472741i
$714$	−2.90990	+	1.70203i	−0.108900	+	0.0636969i
$715$	0.953945	−	2.08885i	0.0356755	−	0.0781185i
$716$	11.3451	−	10.8175i	0.423986	−	0.404270i
$717$	3.01519	−	8.71183i	0.112604	−	0.325349i
$718$	11.5457	+	5.95221i	0.430881	+	0.222135i
$719$	−6.70572	−	19.3749i	−0.250081	−	0.722562i	−0.998255	−	0.0590586i	$-0.981190\pi$
$719$	−6.70572	−	19.3749i	−0.250081	−	0.722562i	0.748173	−	0.663503i	$-0.230931\pi$
$720$	0.0886090	−	0.616289i	0.00330226	−	0.0229677i
$721$	−24.3864	−	5.77036i	−0.908198	−	0.214899i
$722$	−16.5451	−	10.6329i	−0.615744	−	0.395714i
$723$	−7.16621	−	2.86892i	−0.266514	−	0.106696i
$724$	9.61660	−	13.5046i	0.357398	−	0.501895i
$725$	0.560080	−	0.786523i	0.0208009	−	0.0292107i
$726$	7.41366	+	2.96798i	0.275147	+	0.110152i
$727$	15.1687	+	9.74834i	0.562577	+	0.361546i	0.790811	−	0.612060i	$-0.209659\pi$
$727$	15.1687	+	9.74834i	0.562577	+	0.361546i	−0.228235	+	0.973606i	$0.573295\pi$
$728$	1.61391	+	5.38372i	0.0598153	+	0.199534i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	0.709345	+	2.04952i	0.0262540	+	0.0758560i
$731$	8.32052	+	4.28952i	0.307745	+	0.158654i
$732$	2.60048	−	7.51360i	0.0961166	−	0.277711i
$733$	−6.53598	+	6.23205i	−0.241412	+	0.230186i	−0.801120	−	0.598504i	$-0.795762\pi$
$733$	−6.53598	+	6.23205i	−0.241412	+	0.230186i	0.559708	+	0.828690i	$0.310913\pi$
$734$	7.69419	−	16.8479i	0.283998	−	0.621869i
$735$	4.35811	−	0.0492593i	0.160751	−	0.00181696i
$736$	1.45150	+	4.57090i	0.0535031	+	0.168486i
$737$	−11.2120	+	19.4197i	−0.412998	+	0.715334i
$738$	−4.83363	+	0.461556i	−0.177928	+	0.0169901i
$739$	4.85140	+	19.9977i	0.178461	+	0.735628i	0.988748	+	0.149594i	$0.0477965\pi$
$739$	4.85140	+	19.9977i	0.178461	+	0.735628i	−0.810286	+	0.586034i	$0.800688\pi$
$740$	−0.158608	+	0.0305692i	−0.00583056	+	0.00112375i
$741$	11.1127	−	7.14167i	0.408234	−	0.262356i
$742$	−7.60724	−	6.51681i	−0.279271	−	0.239240i
$743$	2.57440	−	17.9053i	0.0944455	−	0.656883i	−0.886519	−	0.462693i	$-0.846883\pi$
$743$	2.57440	−	17.9053i	0.0944455	−	0.656883i	0.980964	−	0.194190i	$-0.0622077\pi$
$744$	−1.56936	+	6.46898i	−0.0575354	+	0.237164i
$745$	−0.278193	+	5.83998i	−0.0101922	+	0.213960i
$746$	−8.97400	+	7.05723i	−0.328561	+	0.258384i
$747$	7.04992	+	0.673185i	0.257943	+	0.0246306i
$748$	−0.918968	−	2.01226i	−0.0336008	−	0.0735755i
$749$	−3.17892	+	8.07249i	−0.116155	+	0.294962i
$750$	−5.03481	−	3.23568i	−0.183845	−	0.118150i
$751$	−11.1401	+	45.9199i	−0.406506	+	1.67564i	0.289163	+	0.957280i	$0.406623\pi$
$751$	−11.1401	+	45.9199i	−0.406506	+	1.67564i	−0.695669	+	0.718362i	$0.744892\pi$
$752$	−2.42932	+	0.972552i	−0.0885881	+	0.0354653i
$753$	−16.7584	−	3.22992i	−0.610711	−	0.117705i
$754$	0.0211602	+	0.444208i	0.000770610	+	0.0161771i
$755$	−0.257669	−	0.297366i	−0.00937753	−	0.0108222i
$756$	−2.56761	+	0.638280i	−0.0933829	+	0.0232140i
$757$	−15.6947	+	34.3665i	−0.570432	+	1.24907i	0.376135	+	0.926565i	$0.377253\pi$
$757$	−15.6947	+	34.3665i	−0.570432	+	1.24907i	−0.946567	+	0.322507i	$0.895474\pi$
$758$	−9.92117	+	17.1840i	−0.360353	+	0.624150i
$759$	−8.32365	−	0.214113i	−0.302129	−	0.00777181i
$760$	−1.93584	−	3.35297i	−0.0702202	−	0.121625i
$761$	−15.2804	−	21.4583i	−0.553914	−	0.777863i	0.438771	−	0.898599i	$-0.355414\pi$
$761$	−15.2804	−	21.4583i	−0.553914	−	0.777863i	−0.992685	+	0.120736i	$0.961475\pi$
$762$	−5.48239	−	1.60977i	−0.198606	−	0.0583160i
$763$	35.0713	+	11.9168i	1.26967	+	0.431417i
$764$	16.7249	−	10.7485i	0.605087	−	0.388866i
$765$	0.259472	+	0.749695i	0.00938122	+	0.0271053i
$766$	−6.37983	+	2.55410i	−0.230513	+	0.0922833i
$767$	−10.0011	−	9.53607i	−0.361120	−	0.344328i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	−1.07130	−	7.45106i	−0.0386321	−	0.268692i	0.961346	−	0.275344i	$-0.0887917\pi$
$769$	−1.07130	−	7.45106i	−0.0386321	−	0.268692i	−0.999978	+	0.00665188i	$0.997883\pi$
$770$	−0.255769	+	2.84857i	−0.00921728	+	0.102655i
$771$	6.49429	+	14.2205i	0.233886	+	0.512139i
$772$	−1.31858	−	0.527879i	−0.0474567	−	0.0189988i
$773$	2.32489	−	48.8055i	0.0836206	−	1.75541i	−0.435020	−	0.900421i	$-0.643259\pi$
$773$	2.32489	−	48.8055i	0.0836206	−	1.75541i	0.518641	−	0.854992i	$-0.326438\pi$
$774$	5.31720	+	5.06994i	0.191123	+	0.182235i
$775$	24.1338	+	18.9791i	0.866913	+	0.681748i
$776$	3.90280	−	4.50407i	0.140102	−	0.161687i
$777$	0.374345	+	0.575317i	0.0134295	+	0.0206394i
$778$	6.45304	+	7.44721i	0.231353	+	0.266995i
$779$	−21.8522	+	20.8360i	−0.782936	+	0.746528i
$780$	1.31667	−	0.125727i	0.0471443	−	0.00450173i
$781$	−1.27731	−	2.21237i	−0.0457059	−	0.0791649i
$782$	−4.31260	−	4.32917i	−0.154218	−	0.154811i
$783$	−0.209343			−0.00748131
$784$	−4.12458	−	5.65578i	−0.147307	−	0.201992i
$785$	−7.72319	−	2.26773i	−0.275652	−	0.0809389i
$786$	13.3051	−	2.56435i	0.474577	−	0.0914673i
$787$	−3.66166	−	1.88772i	−0.130524	−	0.0672898i	0.391728	−	0.920081i	$-0.371878\pi$
$787$	−3.66166	−	1.88772i	−0.130524	−	0.0672898i	−0.522252	+	0.852791i	$0.674908\pi$
$788$	−22.3934	−	4.31598i	−0.797733	−	0.153750i
$789$	−18.2176	−	14.3265i	−0.648565	−	0.510037i
$790$	1.00313	−	0.294546i	0.0356899	−	0.0104795i
$791$	7.91955	−	12.4775i	0.281587	−	0.443650i
$792$	−0.247084	−	1.71850i	−0.00877973	−	0.0610644i
$793$	16.8138	+	1.60552i	0.597074	+	0.0570137i
$794$	−10.5782	+	14.8550i	−0.375406	+	0.527184i
$795$	−1.85296	+	1.45718i	−0.0657176	+	0.0516809i
$796$	−14.0405	+	7.23836i	−0.497651	+	0.256557i
$797$	−20.6832	+	6.07314i	−0.732637	+	0.215122i	−0.626710	−	0.779252i	$-0.715599\pi$
$797$	−20.6832	+	6.07314i	−0.732637	+	0.215122i	−0.105927	+	0.994374i	$0.533781\pi$
$798$	−10.0967	+	12.9895i	−0.357421	+	0.459822i
$799$	2.18342	−	2.51980i	0.0772439	−	0.0891442i
$800$	0.219464	+	4.60711i	0.00775922	+	0.162886i
$801$	−2.24746	+	6.49361i	−0.0794101	+	0.229441i
$802$	7.42961	+	30.6253i	0.262349	+	1.08142i
$803$	3.50797	+	4.92626i	0.123794	+	0.173844i
$804$	−12.9157			−0.455502
$805$	2.07321	+	7.62336i	0.0730710	+	0.268688i
$806$	−14.1408			−0.498088
$807$	7.24907	+	10.1799i	0.255179	+	0.358349i
$808$	−1.53741	−	6.33730i	−0.0540860	−	0.222946i
$809$	−18.0323	+	52.1008i	−0.633980	+	1.83177i	−0.0842126	+	0.996448i	$0.526837\pi$
$809$	−18.0323	+	52.1008i	−0.633980	+	1.83177i	−0.549768	+	0.835318i	$0.685284\pi$
$810$	0.0296258	+	0.621921i	0.00104094	+	0.0218521i
$811$	−27.8670	+	32.1603i	−0.978544	+	1.12930i	0.0130509	+	0.999915i	$0.495846\pi$
$811$	−27.8670	+	32.1603i	−0.978544	+	1.12930i	−0.991594	+	0.129385i	$0.958700\pi$
$812$	−0.208755	−	0.513023i	−0.00732587	−	0.0180036i
$813$	−25.4705	+	7.47881i	−0.893290	+	0.262293i
$814$	−0.400344	+	0.206392i	−0.0140321	+	0.00723403i
$815$	−2.29561	+	1.80529i	−0.0804118	+	0.0632366i
$816$	0.739086	−	1.03790i	0.0258732	−	0.0363338i
$817$	45.4783	+	4.34265i	1.59109	+	0.151930i
$818$	2.02377	+	14.0756i	0.0707593	+	0.492142i
$819$	−2.60362	−	4.98100i	−0.0909777	−	0.174050i
$820$	−2.90078	+	0.851744i	−0.101299	+	0.0297442i
$821$	−22.4206	−	17.6318i	−0.782486	−	0.615354i	0.144906	−	0.989445i	$-0.453712\pi$
$821$	−22.4206	−	17.6318i	−0.782486	−	0.615354i	−0.927392	+	0.374092i	$0.877954\pi$
$822$	−18.3013	−	3.52728i	−0.638330	−	0.123028i
$823$	10.5913	+	5.46018i	0.369188	+	0.190330i	0.632830	−	0.774291i	$-0.281893\pi$
$823$	10.5913	+	5.46018i	0.369188	+	0.190330i	−0.263641	+	0.964621i	$0.584924\pi$
$824$	9.30056	−	1.79254i	0.324000	−	0.0624459i
$825$	−7.68345	−	2.25607i	−0.267504	−	0.0785461i
$826$	15.6956	+	7.06102i	0.546120	+	0.245684i
$827$	−18.0099			−0.626265			−0.313133	−	0.949709i	$-0.601378\pi$
$827$	−18.0099			−0.626265			−0.313133	+	0.949709i	$0.601378\pi$
$828$	−2.29032	−	4.21360i	−0.0795941	−	0.146433i
$829$	−21.8960	−	37.9250i	−0.760480	−	1.31719i	−0.942603	−	0.333915i	$-0.891630\pi$
$829$	−21.8960	−	37.9250i	−0.760480	−	1.31719i	0.182123	−	0.983276i	$-0.441703\pi$
$830$	4.38947	−	0.419143i	0.152361	−	0.0145487i
$831$	11.4091	−	10.8786i	0.395778	−	0.377374i
$832$	−1.39113	−	1.60545i	−0.0482289	−	0.0556591i
$833$	7.97333	+	3.99712i	0.276259	+	0.138492i
$834$	7.06919	−	8.15827i	0.244786	−	0.282498i
$835$	5.29823	+	4.16657i	0.183353	+	0.144190i
$836$	−7.81347	−	7.45013i	−0.270234	−	0.257668i
$837$	0.316735	−	6.64908i	0.0109480	−	0.229826i
$838$	−28.6940	−	11.4874i	−0.991218	−	0.396824i
$839$	15.4733	+	33.8818i	0.534197	+	1.16973i	0.963779	+	0.266701i	$0.0859335\pi$
$839$	15.4733	+	33.8818i	0.534197	+	1.16973i	−0.429582	+	0.903028i	$0.641339\pi$
$840$	−1.49456	+	0.692776i	−0.0515672	+	0.0239031i
$841$	4.12089	+	28.6614i	0.142100	+	0.988326i
$842$	12.3394	−	6.36143i	0.425245	−	0.219229i
$843$	−1.91750	−	1.82833i	−0.0660421	−	0.0629710i
$844$	−17.6894	+	7.08178i	−0.608895	+	0.243765i
$845$	−1.72836	−	4.99376i	−0.0594573	−	0.171791i
$846$	2.20136	−	1.41473i	0.0756843	−	0.0486393i
$847$	−4.11571	−	20.7234i	−0.141417	−	0.712065i
$848$	3.63268	+	1.06665i	0.124747	+	0.0366290i
$849$	6.51284	+	9.14600i	0.223520	+	0.313890i
$850$	−2.93843	−	5.08951i	−0.100787	−	0.174569i
$851$	−0.838673	+	0.919024i	−0.0287493	+	0.0315037i
$852$	0.735705	−	1.27428i	0.0252048	−	0.0436561i
$853$	8.65350	−	18.9485i	0.296290	−	0.648785i	−0.701678	−	0.712494i	$-0.747566\pi$
$853$	8.65350	−	18.9485i	0.296290	−	0.648785i	0.997969	+	0.0637089i	$0.0202929\pi$
$854$	−20.4148	+	5.07489i	−0.698579	+	0.173659i
$855$	2.53541	+	2.92602i	0.0867091	+	0.100068i
$856$	−0.156029	−	3.27545i	−0.00533296	−	0.111953i
$857$	39.2809	+	7.57076i	1.34181	+	0.258612i	0.809092	−	0.587682i	$-0.199959\pi$
$857$	39.2809	+	7.57076i	1.34181	+	0.258612i	0.532716	+	0.846294i	$0.321171\pi$
$858$	3.42400	−	1.37076i	0.116893	−	0.0467971i
$859$	10.0987	−	41.6274i	0.344563	−	1.42031i	−0.491118	−	0.871093i	$-0.663412\pi$
$859$	10.0987	−	41.6274i	0.344563	−	1.42031i	0.835681	−	0.549215i	$-0.185073\pi$
$860$	3.84821	+	2.47309i	0.131223	+	0.0843318i
$861$	7.99828	+	10.0532i	0.272581	+	0.342612i
$862$	4.81235	+	10.5376i	0.163909	+	0.358911i
$863$	14.7782	+	1.41115i	0.503055	+	0.0480359i	0.343499	−	0.939153i	$-0.388388\pi$
$863$	14.7782	+	1.41115i	0.503055	+	0.0480359i	0.159556	+	0.987189i	$0.448994\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	0.402729	−	8.45431i	0.0136932	−	0.287455i
$866$	−0.207035	+	0.853411i	−0.00703534	+	0.0290001i
$867$	2.18831	−	15.2200i	0.0743188	−	0.516898i
$868$	16.6103	−	5.85420i	0.563791	−	0.198705i
$869$	2.45250	−	1.57613i	0.0831955	−	0.0534665i
$870$	−0.127987	+	0.0246675i	−0.00433917	+	0.000836306i
$871$	−6.46854	−	26.6637i	−0.219178	−	0.903464i
$872$	−13.9367	+	1.33079i	−0.471955	+	0.0450662i
$873$	−2.97987	+	5.16129i	−0.100853	+	0.174683i
$874$	−27.3915	−	11.7919i	−0.926532	−	0.398868i
$875$	0.0894839	+	15.8343i	0.00302511	+	0.535297i
$876$	−1.44702	+	3.16853i	−0.0488902	+	0.107055i
$877$	21.7397	−	20.7288i	0.734098	−	0.699961i	−0.227697	−	0.973732i	$-0.573119\pi$
$877$	21.7397	−	20.7288i	0.734098	−	0.699961i	0.961795	+	0.273771i	$0.0882710\pi$
$878$	−2.34231	+	6.76767i	−0.0790493	+	0.228398i
$879$	−3.45217	−	1.77972i	−0.116439	−	0.0600283i
$880$	−0.353557	−	1.02154i	−0.0119184	−	0.0344360i
$881$	0.274318	−	1.90792i	0.00924199	−	0.0642795i	−0.984679	−	0.174380i	$-0.944208\pi$
$881$	0.274318	−	1.90792i	0.00924199	−	0.0642795i	0.993921	+	0.110100i	$0.0351171\pi$
$882$	5.12041	+	4.77299i	0.172413	+	0.160715i
$883$	−41.1037	−	26.4157i	−1.38325	−	0.888960i	−0.383842	−	0.923399i	$-0.625399\pi$
$883$	−41.1037	−	26.4157i	−1.38325	−	0.888960i	−0.999407	+	0.0344383i	$0.989036\pi$
$884$	2.51284	+	1.00599i	0.0845159	+	0.0338351i
$885$	2.34936	−	3.29921i	0.0789728	−	0.110902i
$886$	−7.07328	+	9.93303i	−0.237631	+	0.333707i
$887$	32.9627	+	13.1963i	1.10678	+	0.443088i	0.851805	−	0.523859i	$-0.175508\pi$
$887$	32.9627	+	13.1963i	1.10678	+	0.443088i	0.254976	+	0.966947i	$0.417932\pi$
$888$	−0.218245	−	0.140258i	−0.00732384	−	0.00470675i
$889$	4.34097	+	14.4807i	0.145591	+	0.485668i
$890$	−0.608880	+	4.23486i	−0.0204097	+	0.141953i
$891$	0.567847	+	1.64069i	0.0190236	+	0.0549651i
$892$	13.2422	+	6.82682i	0.443381	+	0.228579i
$893$	5.32198	−	15.3768i	0.178093	−	0.514567i
$894$	−6.79603	+	6.48000i	−0.227293	+	0.216724i
$895$	−4.05452	+	8.87815i	−0.135528	+	0.296764i
$896$	2.29873	+	1.30991i	0.0767951	+	0.0437609i
$897$	7.55166	−	6.83851i	0.252143	−	0.228331i
$898$	15.1991	−	26.3256i	0.507199	−	0.878495i
$899$	1.38721	−	0.132462i	0.0462660	−	0.00441786i
$900$	−1.08740	−	4.48232i	−0.0362466	−	0.149411i
$901$	−4.73686	+	0.912955i	−0.157808	+	0.0304149i
$902$	−7.09194	+	4.55772i	−0.236136	+	0.151755i
$903$	3.57076	−	19.1073i	0.118827	−	0.635851i
$904$	−0.794943	+	5.52895i	−0.0264394	+	0.183890i
$905$	−2.43359	+	10.0314i	−0.0808951	+	0.333454i
$906$	0.0300696	−	0.631238i	0.000998994	−	0.0209715i
$907$	12.7059	−	9.99207i	0.421894	−	0.331781i	−0.384537	−	0.923110i	$-0.625639\pi$
$907$	12.7059	−	9.99207i	0.421894	−	0.331781i	0.806431	+	0.591329i	$0.201396\pi$
$908$	−12.9737	−	1.23884i	−0.430546	−	0.0411122i
$909$	2.70897	+	5.93182i	0.0898510	+	0.196746i
$910$	−2.17871	−	2.73846i	−0.0722235	−	0.0907792i
$911$	−39.4637	−	25.3618i	−1.30749	−	0.840272i	−0.313483	−	0.949594i	$-0.601496\pi$
$911$	−39.4637	−	25.3618i	−1.30749	−	0.840272i	−0.994006	+	0.109322i	$0.965132\pi$
$912$	1.46602	−	6.04301i	0.0485447	−	0.200104i
$913$	11.4148	−	4.56980i	0.377775	−	0.151238i
$914$	16.0940	+	3.10186i	0.532341	+	0.102600i
$915$	0.235551	+	4.94483i	0.00778708	+	0.163471i
$916$	−8.72933	−	10.0742i	−0.288425	−	0.332860i
$917$	−24.8855	−	25.8055i	−0.821790	−	0.852174i
$918$	−0.529306	+	1.15902i	−0.0174697	+	0.0382533i
$919$	−4.62457	+	8.00999i	−0.152551	+	0.264225i	−0.932164	−	0.362035i	$-0.882082\pi$
$919$	−4.62457	+	8.00999i	−0.152551	+	0.264225i	0.779614	+	0.626260i	$0.215415\pi$
$920$	−1.89674	−	2.30621i	−0.0625338	−	0.0760336i
$921$	13.8370	+	23.9664i	0.455944	+	0.789719i
$922$	−0.467395	−	0.656364i	−0.0153928	−	0.0216162i
$923$	2.99913	+	0.880624i	0.0987176	+	0.0289861i
$924$	−3.45447	+	3.02767i	−0.113644	+	0.0996029i
$925$	−1.00662	+	0.646916i	−0.0330975	+	0.0212705i
$926$	−10.1175	−	29.2327i	−0.332483	−	0.960645i
$927$	−8.79325	+	3.52028i	−0.288808	+	0.115621i
$928$	0.151509	+	0.144463i	0.00497352	+	0.00474224i
$929$	−26.3191	+	13.5684i	−0.863501	+	0.445166i	−0.832286	−	0.554347i	$-0.812968\pi$
$929$	−26.3191	+	13.5684i	−0.863501	+	0.445166i	−0.0312153	+	0.999513i	$0.509938\pi$
$930$	−0.589836	−	4.10240i	−0.0193415	−	0.134523i
$931$	43.3749	+	3.64761i	1.42156	+	0.119545i
$932$	−9.77214	−	21.3980i	−0.320097	−	0.700915i
$933$	29.6900	+	11.8861i	0.972006	+	0.389133i
$934$	−1.52262	+	31.9638i	−0.0498217	+	1.04589i
$935$	0.996839	+	0.950484i	0.0326001	+	0.0310841i
$936$	1.66983	+	1.31317i	0.0545800	+	0.0429222i
$937$	9.96038	−	11.4949i	0.325392	−	0.375522i	−0.569358	−	0.822089i	$-0.692808\pi$
$937$	9.96038	−	11.4949i	0.325392	−	0.375522i	0.894750	+	0.446568i	$0.147354\pi$
$938$	18.6368	+	28.6422i	0.608513	+	0.935202i
$939$	−8.83871	−	10.2004i	−0.288440	−	0.332878i
$940$	1.17915	−	1.12432i	0.0384598	−	0.0366713i
$941$	−13.8658	+	1.32403i	−0.452013	+	0.0431620i	−0.318580	−	0.947896i	$-0.603206\pi$
$941$	−13.8658	+	1.32403i	−0.452013	+	0.0431620i	−0.133433	+	0.991058i	$0.542600\pi$
$942$	−6.46394	−	11.1959i	−0.210607	−	0.364781i
$943$	−13.9909	+	18.6152i	−0.455608	+	0.606194i
$944$	−6.50505			−0.211721
$945$	1.33644	−	0.963104i	0.0434745	−	0.0313298i
$946$	12.2388	+	3.59364i	0.397919	+	0.116839i
$947$	−0.528669	+	0.101893i	−0.0171794	+	0.00331106i	−0.197834	−	0.980236i	$-0.563391\pi$
$947$	−0.528669	+	0.101893i	−0.0171794	+	0.00331106i	0.180654	+	0.983547i	$0.442178\pi$
$948$	1.49249	+	0.769430i	0.0484737	+	0.0249899i
$949$	−7.26593	−	1.40039i	−0.235862	−	0.0454587i
$950$	−22.5447	−	17.7293i	−0.731446	−	0.575215i
$951$	−5.70294	+	1.67454i	−0.184931	+	0.0543005i
$952$	−3.36815	−	0.141372i	−0.109162	−	0.00458190i
$953$	−3.53796	−	24.6070i	−0.114606	−	0.797100i	−0.963341	−	0.268281i	$-0.913544\pi$
$953$	−3.53796	−	24.6070i	−0.114606	−	0.797100i	0.848735	−	0.528818i	$-0.177365\pi$
$954$	−3.76890	−	0.359887i	−0.122023	−	0.0116518i
$955$	−7.18018	+	10.0832i	−0.232345	+	0.326283i
$956$	7.24652	−	5.69872i	0.234369	−	0.184310i
$957$	−0.323053	+	0.166545i	−0.0104428	+	0.00538365i
$958$	7.20431	−	2.11538i	0.232761	−	0.0683447i
$959$	18.5857	+	45.6751i	0.600165	+	1.47493i
$960$	0.407734	−	0.470550i	0.0131595	−	0.0151869i
$961$	0.633343	+	13.2955i	0.0204304	+	0.428887i
$962$	0.180250	−	0.520799i	0.00581151	−	0.0167912i
$963$	0.773093	+	3.18673i	0.0249126	+	0.102691i
$964$	−4.47755	−	6.28784i	−0.144212	−	0.202518i
$965$	0.884328			0.0284675
$966$	−6.03937	+	11.1591i	−0.194314	+	0.359039i
$967$	−34.1012			−1.09662			−0.548311	−	0.836275i	$-0.684729\pi$
$967$	−34.1012			−1.09662			−0.548311	+	0.836275i	$0.684729\pi$
$968$	4.63216	+	6.50495i	0.148883	+	0.209077i
$969$	1.86794	+	7.69977i	0.0600070	+	0.247352i
$970$	−1.21365	+	3.50661i	−0.0389679	+	0.112590i
$971$	−0.184826	−	3.87998i	−0.00593136	−	0.124515i	−0.999891	−	0.0147679i	$-0.995299\pi$
$971$	−0.184826	−	3.87998i	−0.00593136	−	0.124515i	0.993960	−	0.109747i	$-0.0350040\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−28.2926	−	3.90479i	−0.907018	−	0.125182i
$974$	−33.3472	+	9.79162i	−1.06851	+	0.313744i
$975$	8.70888	−	4.48974i	0.278907	−	0.143787i
$976$	6.24982	−	4.91492i	0.200052	−	0.157323i
$977$	28.6639	−	40.2527i	0.917038	−	1.28780i	−0.0404070	−	0.999183i	$-0.512865\pi$
$977$	28.6639	−	40.2527i	0.917038	−	1.28780i	0.957445	−	0.288616i	$-0.0931951\pi$
$978$	−4.66926	−	0.445861i	−0.149307	−	0.0142570i
$979$	1.69785	+	11.8088i	0.0542634	+	0.377410i
$980$	3.69290	+	2.31473i	0.117966	+	0.0739414i
$981$	13.4329	−	3.94427i	0.428881	−	0.125931i
$982$	−8.17374	−	6.42790i	−0.260835	−	0.205123i
$983$	−41.1756	−	7.93595i	−1.31330	−	0.253118i	−0.515941	−	0.856624i	$-0.672558\pi$
$983$	−41.1756	−	7.93595i	−1.31330	−	0.253118i	−0.797358	+	0.603506i	$0.793770\pi$
$984$	−4.31585	−	2.22497i	−0.137584	−	0.0709296i
$985$	13.9427	−	2.68724i	0.444253	−	0.0856227i
$986$	−0.255932	−	0.0751485i	−0.00815055	−	0.00239322i
$987$	−6.31380	−	2.84041i	−0.200971	−	0.0904111i
$988$	13.2096			0.420255
$989$	35.1495	−	2.44619i	1.11769	−	0.0777845i
$990$	0.540495	+	0.936164i	0.0171780	+	0.0297532i
$991$	21.3513	−	2.03880i	0.678247	−	0.0647648i	0.249753	−	0.968309i	$-0.419650\pi$
$991$	21.3513	−	2.03880i	0.678247	−	0.0647648i	0.428494	+	0.903545i	$0.359044\pi$
$992$	−4.81762	+	4.59359i	−0.152960	+	0.145847i
$993$	−13.7627	−	15.8830i	−0.436745	−	0.504030i
$994$	−3.88747	+	0.207208i	−0.123303	+	0.00657223i
$995$	6.44075	−	7.43302i	0.204185	−	0.235643i
$996$	5.56682	+	4.37779i	0.176391	+	0.138716i
$997$	−20.7882	−	19.8215i	−0.658370	−	0.627754i	0.285380	−	0.958414i	$-0.407880\pi$
$997$	−20.7882	−	19.8215i	−0.658370	−	0.627754i	−0.943750	+	0.330660i	$0.892729\pi$
$998$	0.0173204	−	0.363600i	0.000548268	−	0.0115096i
$999$	0.240845	+	0.0964200i	0.00762001	+	0.00305059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.121.4	✓	160
7.4	even	3	inner	966.2.y.b.949.5	yes	160
23.4	even	11	inner	966.2.y.b.625.5	yes	160
161.4	even	33	inner	966.2.y.b.487.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.121.4	✓	160	1.1	even	1	trivial
966.2.y.b.487.4	yes	160	161.4	even	33	inner
966.2.y.b.625.5	yes	160	23.4	even	11	inner
966.2.y.b.949.5	yes	160	7.4	even	3	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0296258 - 0.621921i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.62091 - 0.361724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0296258 - 0.621921i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-2.62091 - 0.361724i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-0.489417 + 0.384882i) q^{10} +(-1.00708 + 1.41425i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.302322 - 2.10270i) q^{13} +(1.22562 + 2.34475i) q^{14} +(0.597406 - 0.175414i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(1.25114 + 0.241137i) q^{17} +(0.888835 + 0.458227i) q^{18} +(6.10592 - 1.17682i) q^{19} +(0.597406 + 0.175414i) q^{20} +(-0.266375 - 2.63231i) q^{21} +1.73618 q^{22} +(4.49666 - 1.66735i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.59145 - 0.438430i) q^{25} +(-1.53744 + 1.46595i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.19904 - 2.35845i) q^{28} +(0.137091 - 0.158211i) q^{29} +(-0.489417 - 0.384882i) q^{30} +(4.81762 + 4.59359i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.61181 - 0.645271i) q^{33} +(-0.529306 - 1.15902i) q^{34} +(-0.147318 + 1.64071i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.230590 + 0.118877i) q^{37} +(-4.50039 - 4.29111i) q^{38} +(1.97215 - 0.789530i) q^{39} +(-0.203641 - 0.588383i) q^{40} +(-4.08481 + 2.62515i) q^{41} +(-1.98970 + 1.74387i) q^{42} +(7.04930 + 2.06986i) q^{43} +(-1.00708 - 1.41425i) q^{44} +(0.311313 + 0.539210i) q^{45} +(-3.96650 - 2.69571i) q^{46} +(1.30838 - 2.26618i) q^{47} +(0.415415 - 0.909632i) q^{48} +(6.73831 + 1.89609i) q^{49} +(-3.02044 - 3.48577i) q^{50} +(0.0606271 + 1.27272i) q^{51} +(2.08593 + 0.402030i) q^{52} +(-3.51484 + 1.40713i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(0.909386 + 0.584427i) q^{55} +(-2.61665 + 0.391323i) q^{56} +(2.58317 + 5.65636i) q^{57} +(-0.208395 - 0.0198993i) q^{58} +(5.11332 - 4.02116i) q^{59} +(-0.0296258 + 0.621921i) q^{60} +(-1.87449 + 7.72677i) q^{61} +(0.947336 - 6.58886i) q^{62} +(2.49531 - 0.879456i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.29876 + 0.250315i) q^{65} +(0.409319 + 1.68724i) q^{66} +(12.8572 - 1.22772i) q^{67} +(-0.637081 + 1.10346i) q^{68} +(2.68048 + 3.97681i) q^{69} +(1.42194 - 0.831706i) q^{70} +(-0.611246 + 1.33844i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(1.13928 - 3.29173i) q^{73} +(0.230590 + 0.118877i) q^{74} +(1.50855 + 4.35866i) q^{75} +(-0.884955 + 6.15500i) q^{76} +(3.15103 - 3.34233i) q^{77} +(-1.78709 - 1.14849i) q^{78} +(-1.55887 - 0.624076i) q^{79} +(-0.361159 + 0.507177i) q^{80} +(0.580057 - 0.814576i) q^{81} +(4.50780 + 1.80465i) q^{82} +(-5.95775 - 3.82881i) q^{83} +(2.57466 + 0.609219i) q^{84} +(0.112902 - 0.785252i) q^{85} +(-2.40294 - 6.94283i) q^{86} +(0.186072 + 0.0959266i) q^{87} +(-0.567847 + 1.64069i) q^{88} +(4.97317 - 4.74191i) q^{89} +(0.258648 - 0.566361i) q^{90} +(0.0317620 + 5.62033i) q^{91} +(0.104935 + 4.79468i) q^{92} +(-3.32831 + 5.76480i) q^{93} +(-2.60491 + 0.248739i) q^{94} +(-0.912782 - 3.76254i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(5.01365 - 3.22208i) q^{97} +(-2.36409 - 6.58871i) q^{98} +(0.247084 - 1.71850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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