LMFDB - Embedded newform 966.2.q.i.211.2

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:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.2
Character	$\chi$	$=$	966.211
Dual form			966.2.q.i.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.627520 - 0.403283i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.627520 - 0.403283i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.106158 - 0.738342i) q^{10} +(-0.872936 + 1.91146i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.471059 + 3.27629i) q^{13} +(0.841254 - 0.540641i) q^{14} +(0.715719 + 0.210154i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.19435 - 1.37835i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-2.06359 + 2.38151i) q^{19} +(0.715719 - 0.210154i) q^{20} +(0.415415 + 0.909632i) q^{21} -2.10136 q^{22} +(0.133298 - 4.79398i) q^{23} +1.00000 q^{24} +(-1.84593 - 4.04202i) q^{25} +(-3.17590 + 0.932529i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(-5.49797 - 6.34500i) q^{29} +(0.106158 + 0.738342i) q^{30} +(-6.69345 - 1.96538i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.299055 - 2.07997i) q^{33} +(0.757643 - 1.65901i) q^{34} +(-0.309873 + 0.678526i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-0.528750 + 0.339807i) q^{37} +(-3.02354 - 0.887791i) q^{38} +(-0.471059 - 3.27629i) q^{39} +(0.488484 + 0.563740i) q^{40} +(-4.26037 - 2.73797i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(-4.63005 + 1.35951i) q^{43} +(-0.872936 - 1.91146i) q^{44} -0.745935 q^{45} +(4.41613 - 1.87024i) q^{46} +8.15577 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(2.90993 - 3.35823i) q^{50} +(1.53430 + 0.986032i) q^{51} +(-2.16758 - 2.50152i) q^{52} +(-1.14047 - 7.93216i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(1.31865 - 0.847442i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(1.30905 - 2.86642i) q^{57} +(3.48767 - 7.63694i) q^{58} +(-0.895939 + 6.23139i) q^{59} +(-0.627520 + 0.403283i) q^{60} +(4.25042 + 1.24804i) q^{61} +(-0.992793 - 6.90503i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(1.61687 - 1.86597i) q^{65} +(2.01624 - 0.592021i) q^{66} +(1.31227 + 2.87347i) q^{67} +1.82382 q^{68} +(1.22272 + 4.63734i) q^{69} -0.745935 q^{70} +(-2.20851 - 4.83595i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-2.28777 + 2.64023i) q^{73} +(-0.528750 - 0.339807i) q^{74} +(2.90993 + 3.35823i) q^{75} +(-0.448460 - 3.11911i) q^{76} +(2.01624 + 0.592021i) q^{77} +(2.78453 - 1.78951i) q^{78} +(1.05600 - 7.34467i) q^{79} +(-0.309873 + 0.678526i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.720727 - 5.01277i) q^{82} +(-6.36396 + 4.08987i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(0.193613 + 1.34660i) q^{85} +(-3.16004 - 3.64688i) q^{86} +(7.06286 + 4.53902i) q^{87} +(1.37610 - 1.58810i) q^{88} +(9.52166 - 2.79581i) q^{89} +(-0.309873 - 0.678526i) q^{90} +3.30998 q^{91} +(3.53576 + 3.24013i) q^{92} +6.97603 q^{93} +(3.38803 + 7.41875i) q^{94} +(2.25536 - 0.662234i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-10.4570 - 6.72029i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.299055 + 2.07997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.627520	−	0.403283i	−0.280636	−	0.180354i	0.392749	−	0.919646i	$-0.371524\pi$
$5$	−0.627520	−	0.403283i	−0.280636	−	0.180354i	−0.673385	+	0.739292i	$0.735160\pi$
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.106158	−	0.738342i	0.0335700	−	0.233484i
$11$	−0.872936	+	1.91146i	−0.263200	+	0.576328i	−0.994382	−	0.105855i	$-0.966242\pi$
$11$	−0.872936	+	1.91146i	−0.263200	+	0.576328i	0.731181	+	0.682183i	$0.238969\pi$
$12$	0.415415	−	0.909632i	0.119920	−	0.262588i
$13$	−0.471059	+	3.27629i	−0.130648	+	0.908679i	0.814063	+	0.580776i	$0.197251\pi$
$13$	−0.471059	+	3.27629i	−0.130648	+	0.908679i	−0.944711	+	0.327903i	$0.893658\pi$
$14$	0.841254	−	0.540641i	0.224834	−	0.144492i
$15$	0.715719	+	0.210154i	0.184798	+	0.0542616i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−1.19435	−	1.37835i	−0.289672	−	0.334300i	0.592197	−	0.805793i	$-0.298261\pi$
$17$	−1.19435	−	1.37835i	−0.289672	−	0.334300i	−0.881870	+	0.471493i	$0.843715\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	−2.06359	+	2.38151i	−0.473419	+	0.546355i	−0.941359	−	0.337405i	$-0.890451\pi$
$19$	−2.06359	+	2.38151i	−0.473419	+	0.546355i	0.467940	+	0.883760i	$0.344996\pi$
$20$	0.715719	−	0.210154i	0.160040	−	0.0469919i
$21$	0.415415	+	0.909632i	0.0906510	+	0.198498i
$22$	−2.10136			−0.448011
$23$	0.133298	−	4.79398i	0.0277945	−	0.999614i
$23$	0.133298	−	4.79398i	0.0277945	−	0.999614i
$24$	1.00000			0.204124
$25$	−1.84593	−	4.04202i	−0.369186	−	0.808405i
$26$	−3.17590	+	0.932529i	−0.622846	+	0.182884i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	0.841254	+	0.540641i	0.158982	+	0.102172i
$29$	−5.49797	−	6.34500i	−1.02095	−	1.17824i	−0.983863	−	0.178925i	$-0.942738\pi$
$29$	−5.49797	−	6.34500i	−1.02095	−	1.17824i	−0.0370851	−	0.999312i	$-0.511807\pi$
$30$	0.106158	+	0.738342i	0.0193816	+	0.134802i
$31$	−6.69345	−	1.96538i	−1.20218	−	0.352992i	−0.381494	−	0.924371i	$-0.624590\pi$
$31$	−6.69345	−	1.96538i	−1.20218	−	0.352992i	−0.820686	+	0.571379i	$0.806408\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	0.299055	−	2.07997i	0.0520587	−	0.362076i
$34$	0.757643	−	1.65901i	0.129935	−	0.284517i
$35$	−0.309873	+	0.678526i	−0.0523780	+	0.114692i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−0.528750	+	0.339807i	−0.0869260	+	0.0558640i	−0.583382	−	0.812198i	$-0.698271\pi$
$37$	−0.528750	+	0.339807i	−0.0869260	+	0.0558640i	0.496456	+	0.868062i	$0.334634\pi$
$38$	−3.02354	−	0.887791i	−0.490483	−	0.144019i
$39$	−0.471059	−	3.27629i	−0.0754298	−	0.524626i
$40$	0.488484	+	0.563740i	0.0772360	+	0.0891351i
$41$	−4.26037	−	2.73797i	−0.665358	−	0.427600i	0.163891	−	0.986478i	$-0.447595\pi$
$41$	−4.26037	−	2.73797i	−0.665358	−	0.427600i	−0.829249	+	0.558879i	$0.811232\pi$
$42$	−0.654861	+	0.755750i	−0.101047	+	0.116615i
$43$	−4.63005	+	1.35951i	−0.706076	+	0.207323i	−0.615007	−	0.788522i	$-0.710847\pi$
$43$	−4.63005	+	1.35951i	−0.706076	+	0.207323i	−0.0910694	+	0.995845i	$0.529029\pi$
$44$	−0.872936	−	1.91146i	−0.131600	−	0.288164i
$45$	−0.745935			−0.111197
$46$	4.41613	−	1.87024i	0.651123	−	0.275752i
$47$	8.15577			1.18964			0.594820	−	0.803859i	$-0.297223\pi$
$47$	8.15577			1.18964			0.594820	+	0.803859i	$0.297223\pi$
$48$	0.415415	+	0.909632i	0.0599600	+	0.131294i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	2.90993	−	3.35823i	0.411526	−	0.474926i
$51$	1.53430	+	0.986032i	0.214844	+	0.138072i
$52$	−2.16758	−	2.50152i	−0.300589	−	0.346898i
$53$	−1.14047	−	7.93216i	−0.156656	−	1.08957i	−0.904741	−	0.425963i	$-0.859935\pi$
$53$	−1.14047	−	7.93216i	−0.156656	−	1.08957i	0.748085	−	0.663603i	$-0.230974\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	1.31865	−	0.847442i	0.177806	−	0.114269i
$56$	−0.142315	+	0.989821i	−0.0190176	+	0.132270i
$57$	1.30905	−	2.86642i	0.173388	−	0.379666i
$58$	3.48767	−	7.63694i	0.457954	−	1.00278i
$59$	−0.895939	+	6.23139i	−0.116641	+	0.811258i	0.844570	+	0.535445i	$0.179856\pi$
$59$	−0.895939	+	6.23139i	−0.116641	+	0.811258i	−0.961211	+	0.275813i	$0.911053\pi$
$60$	−0.627520	+	0.403283i	−0.0810125	+	0.0520636i
$61$	4.25042	+	1.24804i	0.544211	+	0.159795i	0.542271	−	0.840203i	$-0.317564\pi$
$61$	4.25042	+	1.24804i	0.544211	+	0.159795i	0.00193960	+	0.999998i	$0.499383\pi$
$62$	−0.992793	−	6.90503i	−0.126085	−	0.876939i
$63$	−0.654861	−	0.755750i	−0.0825047	−	0.0952155i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	1.61687	−	1.86597i	0.200548	−	0.231445i
$66$	2.01624	−	0.592021i	0.248182	−	0.0728728i
$67$	1.31227	+	2.87347i	0.160319	+	0.351050i	0.972696	−	0.232083i	$-0.0745541\pi$
$67$	1.31227	+	2.87347i	0.160319	+	0.351050i	−0.812377	+	0.583133i	$0.801827\pi$
$68$	1.82382			0.221171
$69$	1.22272	+	4.63734i	0.147198	+	0.558271i
$70$	−0.745935			−0.0891563
$71$	−2.20851	−	4.83595i	−0.262102	−	0.573922i	0.732132	−	0.681163i	$-0.238526\pi$
$71$	−2.20851	−	4.83595i	−0.262102	−	0.573922i	−0.994233	+	0.107241i	$0.965798\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	−2.28777	+	2.64023i	−0.267764	+	0.309016i	−0.873669	−	0.486521i	$-0.838266\pi$
$73$	−2.28777	+	2.64023i	−0.267764	+	0.309016i	0.605905	+	0.795537i	$0.292811\pi$
$74$	−0.528750	−	0.339807i	−0.0614660	−	0.0395018i
$75$	2.90993	+	3.35823i	0.336009	+	0.387776i
$76$	−0.448460	−	3.11911i	−0.0514419	−	0.357786i
$77$	2.01624	+	0.592021i	0.229772	+	0.0674671i
$78$	2.78453	−	1.78951i	0.315286	−	0.202622i
$79$	1.05600	−	7.34467i	0.118810	−	0.826340i	−0.840060	−	0.542494i	$-0.817480\pi$
$79$	1.05600	−	7.34467i	0.118810	−	0.826340i	0.958870	−	0.283847i	$-0.0916106\pi$
$80$	−0.309873	+	0.678526i	−0.0346448	+	0.0758616i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.720727	−	5.01277i	0.0795910	−	0.553567i
$83$	−6.36396	+	4.08987i	−0.698535	+	0.448921i	−0.841111	−	0.540863i	$-0.818098\pi$
$83$	−6.36396	+	4.08987i	−0.698535	+	0.448921i	0.142576	+	0.989784i	$0.454462\pi$
$84$	−0.959493	−	0.281733i	−0.104689	−	0.0307395i
$85$	0.193613	+	1.34660i	0.0210002	+	0.146060i
$86$	−3.16004	−	3.64688i	−0.340756	−	0.393254i
$87$	7.06286	+	4.53902i	0.757218	+	0.486634i
$88$	1.37610	−	1.58810i	0.146692	−	0.169292i
$89$	9.52166	−	2.79581i	1.00929	−	0.296355i	0.265029	−	0.964240i	$-0.414618\pi$
$89$	9.52166	−	2.79581i	1.00929	−	0.296355i	0.744264	+	0.667885i	$0.232800\pi$
$90$	−0.309873	−	0.678526i	−0.0326634	−	0.0715230i
$91$	3.30998			0.346980
$92$	3.53576	+	3.24013i	0.368628	+	0.337807i
$93$	6.97603			0.723381
$94$	3.38803	+	7.41875i	0.349448	+	0.765185i
$95$	2.25536	−	0.662234i	0.231395	−	0.0679438i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	−10.4570	−	6.72029i	−1.06175	−	0.682342i	−0.111475	−	0.993767i	$-0.535557\pi$
$97$	−10.4570	−	6.72029i	−1.06175	−	0.682342i	−0.950271	+	0.311425i	$0.899194\pi$
$98$	−0.654861	−	0.755750i	−0.0661509	−	0.0763422i
$99$	0.299055	+	2.07997i	0.0300561	+	0.209045i
$100$	4.26358	+	1.25190i	0.426358	+	0.125190i
$101$	−7.28119	+	4.67934i	−0.724506	+	0.465611i	−0.850202	−	0.526457i	$-0.823520\pi$
$101$	−7.28119	+	4.67934i	−0.724506	+	0.465611i	0.125696	+	0.992069i	$0.459884\pi$
$102$	−0.259557	+	1.80526i	−0.0257000	+	0.178747i
$103$	−7.37020	+	16.1385i	−0.726207	+	1.59017i	0.0787879	+	0.996891i	$0.474895\pi$
$103$	−7.37020	+	16.1385i	−0.726207	+	1.59017i	−0.804995	+	0.593281i	$0.797832\pi$
$104$	1.37502	−	3.01086i	0.134831	−	0.295239i
$105$	0.106158	−	0.738342i	0.0103599	−	0.0720548i
$106$	6.74158	−	4.33255i	0.654800	−	0.420814i
$107$	−7.72244	−	2.26751i	−0.746556	−	0.219209i	−0.113740	−	0.993511i	$-0.536283\pi$
$107$	−7.72244	−	2.26751i	−0.746556	−	0.219209i	−0.632816	+	0.774302i	$0.718101\pi$
$108$	−0.142315	−	0.989821i	−0.0136943	−	0.0952456i
$109$	1.01077	+	1.16650i	0.0968146	+	0.111730i	0.802089	−	0.597204i	$-0.203722\pi$
$109$	1.01077	+	1.16650i	0.0968146	+	0.111730i	−0.705275	+	0.708934i	$0.749176\pi$
$110$	1.31865	+	0.847442i	0.125728	+	0.0808004i
$111$	0.411598	−	0.475009i	0.0390671	−	0.0450858i
$112$	−0.959493	+	0.281733i	−0.0906636	+	0.0266212i
$113$	−4.16167	−	9.11279i	−0.391497	−	0.857259i	−0.998062	−	0.0622251i	$-0.980180\pi$
$113$	−4.16167	−	9.11279i	−0.391497	−	0.857259i	0.606565	−	0.795034i	$-0.292547\pi$
$114$	3.15118			0.295135
$115$	−2.01698	+	2.95456i	−0.188084	+	0.275514i
$116$	8.39564			0.779515
$117$	1.37502	+	3.01086i	0.127120	+	0.278354i
$118$	−6.04046	+	1.77364i	−0.556070	+	0.163277i
$119$	−1.19435	+	1.37835i	−0.109486	+	0.126353i
$120$	−0.627520	−	0.403283i	−0.0572845	−	0.0368145i
$121$	4.31179	+	4.97607i	0.391981	+	0.452370i
$122$	0.630436	+	4.38478i	0.0570770	+	0.396979i
$123$	4.85917	+	1.42678i	0.438137	+	0.128649i
$124$	5.86861	−	3.77153i	0.527017	−	0.338693i
$125$	−1.00251	+	6.97260i	−0.0896670	+	0.623648i
$126$	0.415415	−	0.909632i	0.0370081	−	0.0810365i
$127$	−8.48534	+	18.5803i	−0.752952	+	1.64874i	0.00803403	+	0.999968i	$0.497443\pi$
$127$	−8.48534	+	18.5803i	−0.752952	+	1.64874i	−0.760986	+	0.648768i	$0.775285\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	4.05948	−	2.60887i	0.357418	−	0.229698i
$130$	2.36902	+	0.695606i	0.207777	+	0.0610087i
$131$	−1.31482	−	9.14478i	−0.114876	−	0.798983i	−0.963061	−	0.269283i	$-0.913213\pi$
$131$	−1.31482	−	9.14478i	−0.114876	−	0.798983i	0.848185	−	0.529701i	$-0.177696\pi$
$132$	1.37610	+	1.58810i	0.119774	+	0.138226i
$133$	2.65094	+	1.70366i	0.229866	+	0.147726i
$134$	−2.06866	+	2.38736i	−0.178705	+	0.206237i
$135$	0.715719	−	0.210154i	0.0615993	−	0.0180872i
$136$	0.757643	+	1.65901i	0.0649673	+	0.142259i
$137$	−7.33861			−0.626980			−0.313490	−	0.949592i	$-0.601498\pi$
$137$	−7.33861			−0.626980			−0.313490	+	0.949592i	$0.601498\pi$
$138$	−3.71034	+	3.03865i	−0.315845	+	0.258667i
$139$	−3.40540			−0.288843			−0.144421	−	0.989516i	$-0.546132\pi$
$139$	−3.40540			−0.288843			−0.144421	+	0.989516i	$0.546132\pi$
$140$	−0.309873	−	0.678526i	−0.0261890	−	0.0573459i
$141$	−7.82540	+	2.29774i	−0.659018	+	0.193505i
$142$	3.48149	−	4.01786i	0.292160	−	0.337171i
$143$	−5.85130	−	3.76040i	−0.489310	−	0.314461i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	0.891261	+	6.19885i	0.0740152	+	0.514787i
$146$	−3.35201	−	0.984240i	−0.277415	−	0.0814563i
$147$	0.841254	−	0.540641i	0.0693854	−	0.0445913i
$148$	0.0894487	−	0.622129i	0.00735264	−	0.0511387i
$149$	5.00380	−	10.9568i	0.409927	−	0.897616i	−0.586239	−	0.810138i	$-0.699392\pi$
$149$	5.00380	−	10.9568i	0.409927	−	0.897616i	0.996166	−	0.0874776i	$-0.0278806\pi$
$150$	−1.84593	+	4.04202i	−0.150720	+	0.330030i
$151$	−1.12131	+	7.79885i	−0.0912506	+	0.634662i	0.891950	+	0.452134i	$0.149337\pi$
$151$	−1.12131	+	7.79885i	−0.0912506	+	0.634662i	−0.983201	+	0.182528i	$0.941572\pi$
$152$	2.65094	−	1.70366i	0.215020	−	0.138185i
$153$	−1.74994	−	0.513830i	−0.141475	−	0.0415407i
$154$	0.299055	+	2.07997i	0.0240985	+	0.167609i
$155$	3.40768	+	3.93267i	0.273711	+	0.315880i
$156$	2.78453	+	1.78951i	0.222941	+	0.143275i
$157$	−2.59298	+	2.99246i	−0.206942	+	0.238824i	−0.849727	−	0.527222i	$-0.823233\pi$
$157$	−2.59298	+	2.99246i	−0.206942	+	0.238824i	0.642785	+	0.766047i	$0.277779\pi$
$158$	7.11963	−	2.09051i	0.566407	−	0.166312i
$159$	3.32902	+	7.28954i	0.264009	+	0.578098i
$160$	−0.745935			−0.0589713
$161$	−4.76415	+	0.550314i	−0.375468	+	0.0433708i
$162$	1.00000			0.0785674
$163$	8.73678	+	19.1309i	0.684317	+	1.49845i	0.858003	+	0.513644i	$0.171705\pi$
$163$	8.73678	+	19.1309i	0.684317	+	1.49845i	−0.173686	+	0.984801i	$0.555568\pi$
$164$	4.85917	−	1.42678i	0.379438	−	0.111413i
$165$	−1.02648	+	1.18462i	−0.0799113	+	0.0922226i
$166$	−6.36396	−	4.08987i	−0.493939	−	0.317435i
$167$	−0.315083	−	0.363625i	−0.0243818	−	0.0281381i	0.743428	−	0.668816i	$-0.233199\pi$
$167$	−0.315083	−	0.363625i	−0.0243818	−	0.0281381i	−0.767810	+	0.640678i	$0.778653\pi$
$168$	−0.142315	−	0.989821i	−0.0109798	−	0.0763664i
$169$	1.96124	+	0.575871i	0.150864	+	0.0442978i
$170$	−1.14449	+	0.735516i	−0.0877780	+	0.0564115i
$171$	−0.448460	+	3.11911i	−0.0342946	+	0.238524i
$172$	2.00459	−	4.38945i	0.152849	−	0.334692i
$173$	−0.181092	+	0.396536i	−0.0137682	+	0.0301481i	−0.916391	−	0.400284i	$-0.868912\pi$
$173$	−0.181092	+	0.396536i	−0.0137682	+	0.0301481i	0.902623	+	0.430432i	$0.141639\pi$
$174$	−1.19482	+	8.31018i	−0.0905793	+	0.629993i
$175$	−3.73818	+	2.40238i	−0.282580	+	0.181603i
$176$	2.01624	+	0.592021i	0.151980	+	0.0446253i
$177$	−0.895939	−	6.23139i	−0.0673429	−	0.468380i
$178$	6.49860	+	7.49978i	0.487091	+	0.562132i
$179$	15.5926	+	10.0208i	1.16545	+	0.748989i	0.972656	−	0.232251i	$-0.0746090\pi$
$179$	15.5926	+	10.0208i	1.16545	+	0.748989i	0.192793	+	0.981239i	$0.438245\pi$
$180$	0.488484	−	0.563740i	0.0364094	−	0.0420187i
$181$	−4.76574	+	1.39935i	−0.354235	+	0.104013i	−0.454008	−	0.890997i	$-0.650006\pi$
$181$	−4.76574	+	1.39935i	−0.354235	+	0.104013i	0.0997736	+	0.995010i	$0.468188\pi$
$182$	1.37502	+	3.01086i	0.101923	+	0.223180i
$183$	−4.42987			−0.327465
$184$	−1.47852	+	4.56223i	−0.108998	+	0.336332i
$185$	0.468840			0.0344698
$186$	2.89795	+	6.34562i	0.212488	+	0.465284i
$187$	3.67726	−	1.07974i	0.268908	−	0.0789585i
$188$	−5.34089	+	6.16372i	−0.389524	+	0.449535i
$189$	0.841254	+	0.540641i	0.0611922	+	0.0393258i
$190$	1.53930	+	1.77645i	0.111673	+	0.128877i
$191$	−2.03574	−	14.1589i	−0.147301	−	1.02450i	−0.920614	−	0.390474i	$-0.872311\pi$
$191$	−2.03574	−	14.1589i	−0.147301	−	1.02450i	0.773313	−	0.634024i	$-0.218598\pi$
$192$	−0.959493	−	0.281733i	−0.0692454	−	0.0203323i
$193$	22.1887	−	14.2598i	1.59718	−	1.02644i	0.628600	−	0.777729i	$-0.283628\pi$
$193$	22.1887	−	14.2598i	1.59718	−	1.02644i	0.968577	−	0.248714i	$-0.0800080\pi$
$194$	1.76901	−	12.3037i	0.127007	−	0.883355i
$195$	−1.02567	+	2.24591i	−0.0734499	+	0.160833i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−0.181673	+	1.26356i	−0.0129436	+	0.0900250i	−0.995269	−	0.0971551i	$-0.969026\pi$
$197$	−0.181673	+	1.26356i	−0.0129436	+	0.0900250i	0.982326	+	0.187180i	$0.0599348\pi$
$198$	−1.76778	+	1.13608i	−0.125630	+	0.0807377i
$199$	2.43188	+	0.714063i	0.172391	+	0.0506186i	0.366789	−	0.930304i	$-0.380457\pi$
$199$	2.43188	+	0.714063i	0.172391	+	0.0506186i	−0.194398	+	0.980923i	$0.562275\pi$
$200$	0.632388	+	4.39835i	0.0447165	+	0.311010i
$201$	−2.06866	−	2.38736i	−0.145912	−	0.168392i
$202$	−7.28119	−	4.67934i	−0.512303	−	0.329237i
$203$	−5.49797	+	6.34500i	−0.385882	+	0.445332i
$204$	−1.74994	+	0.513830i	−0.122521	+	0.0359753i
$205$	1.56929	+	3.43627i	0.109604	+	0.240000i
$206$	−17.7418			−1.23613
$207$	−2.47968	−	4.10502i	−0.172350	−	0.285318i
$208$	3.30998			0.229506
$209$	−2.75078	−	6.02337i	−0.190276	−	0.416645i
$210$	0.715719	−	0.210154i	0.0493893	−	0.0145020i
$211$	−7.54406	+	8.70631i	−0.519355	+	0.599367i	−0.953469	−	0.301491i	$-0.902516\pi$
$211$	−7.54406	+	8.70631i	−0.519355	+	0.599367i	0.434115	+	0.900858i	$0.357061\pi$
$212$	6.74158	+	4.33255i	0.463013	+	0.297561i
$213$	3.48149	+	4.01786i	0.238548	+	0.275299i
$214$	−1.14541	−	7.96653i	−0.0782989	−	0.544581i
$215$	3.45372	+	1.01410i	0.235542	+	0.0691612i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.992793	+	6.90503i	−0.0673952	+	0.468744i
$218$	−0.641191	+	1.40401i	−0.0434269	+	0.0950917i
$219$	1.45126	−	3.17782i	0.0980673	−	0.214737i
$220$	−0.223075	+	1.55152i	−0.0150397	+	0.104604i
$221$	5.07849	−	3.26375i	0.341616	−	0.219543i
$222$	0.603067	+	0.177076i	0.0404752	+	0.0118846i
$223$	0.719551	+	5.00458i	0.0481847	+	0.335132i	0.999627	+	0.0273051i	$0.00869257\pi$
$223$	0.719551	+	5.00458i	0.0481847	+	0.335132i	−0.951442	+	0.307827i	$0.900398\pi$
$224$	−0.654861	−	0.755750i	−0.0437547	−	0.0504956i
$225$	−3.73818	−	2.40238i	−0.249212	−	0.160159i
$226$	6.56046	−	7.57118i	0.436395	−	0.503627i
$227$	−14.5614	+	4.27561i	−0.966474	+	0.283782i	−0.726630	−	0.687029i	$-0.758914\pi$
$227$	−14.5614	+	4.27561i	−0.966474	+	0.283782i	−0.239844	+	0.970811i	$0.577096\pi$
$228$	1.30905	+	2.86642i	0.0866939	+	0.189833i
$229$	16.3950			1.08341			0.541707	−	0.840567i	$-0.317778\pi$
$229$	16.3950			1.08341			0.541707	+	0.840567i	$0.317778\pi$
$230$	−3.52545	−	0.607337i	−0.232461	−	0.0400466i
$231$	−2.10136			−0.138259
$232$	3.48767	+	7.63694i	0.228977	+	0.501390i
$233$	−11.6021	+	3.40670i	−0.760081	+	0.223180i	−0.638731	−	0.769430i	$-0.720541\pi$
$233$	−11.6021	+	3.40670i	−0.760081	+	0.223180i	−0.121350	+	0.992610i	$0.538722\pi$
$234$	−2.16758	+	2.50152i	−0.141699	+	0.163529i
$235$	−5.11791	−	3.28908i	−0.333856	−	0.214556i
$236$	−4.12266	−	4.75780i	−0.268362	−	0.309706i
$237$	1.05600	+	7.34467i	0.0685949	+	0.477088i
$238$	−1.74994	−	0.513830i	−0.113432	−	0.0333066i
$239$	14.6990	−	9.44649i	0.950801	−	0.611043i	0.0293633	−	0.999569i	$-0.490652\pi$
$239$	14.6990	−	9.44649i	0.950801	−	0.611043i	0.921438	+	0.388526i	$0.127016\pi$
$240$	0.106158	−	0.738342i	0.00685244	−	0.0476598i
$241$	−8.64424	+	18.9282i	−0.556825	+	1.21928i	0.396697	+	0.917950i	$0.370156\pi$
$241$	−8.64424	+	18.9282i	−0.556825	+	1.21928i	−0.953521	+	0.301326i	$0.902571\pi$
$242$	−2.73521	+	5.98928i	−0.175826	+	0.385006i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	−3.72664	+	2.39497i	−0.238574	+	0.153322i
$245$	0.715719	+	0.210154i	0.0457256	+	0.0134263i
$246$	0.720727	+	5.01277i	0.0459519	+	0.319602i
$247$	−6.83043	−	7.88273i	−0.434610	−	0.501566i
$248$	5.86861	+	3.77153i	0.372657	+	0.239492i
$249$	4.95392	−	5.71713i	0.313942	−	0.362309i
$250$	−6.75895	+	1.98461i	−0.427474	+	0.125518i
$251$	12.6100	+	27.6120i	0.795935	+	1.74286i	0.658821	+	0.752300i	$0.271056\pi$
$251$	12.6100	+	27.6120i	0.795935	+	1.74286i	0.137114	+	0.990555i	$0.456217\pi$
$252$	1.00000			0.0629941
$253$	9.04715	+	4.43963i	0.568790	+	0.279117i
$254$	−20.4262			−1.28165
$255$	−0.565152	−	1.23751i	−0.0353912	−	0.0774959i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	3.14323	−	3.62748i	0.196069	−	0.226276i	−0.649198	−	0.760619i	$-0.724895\pi$
$257$	3.14323	−	3.62748i	0.196069	−	0.226276i	0.845268	+	0.534343i	$0.179441\pi$
$258$	4.05948	+	2.60887i	0.252732	+	0.162421i
$259$	0.411598	+	0.475009i	0.0255754	+	0.0295156i
$260$	0.351380	+	2.44390i	0.0217916	+	0.151564i
$261$	−8.05555	−	2.36532i	−0.498626	−	0.146410i
$262$	7.77219	−	4.99488i	0.480167	−	0.308585i
$263$	0.249359	−	1.73433i	0.0153761	−	0.106943i	−0.980688	−	0.195579i	$-0.937342\pi$
$263$	0.249359	−	1.73433i	0.0153761	−	0.106943i	0.996064	+	0.0886354i	$0.0282506\pi$
$264$	−0.872936	+	1.91146i	−0.0537255	+	0.117642i
$265$	−2.48323	+	5.43753i	−0.152544	+	0.334025i
$266$	−0.448460	+	3.11911i	−0.0274969	+	0.191245i
$267$	−8.34829	+	5.36512i	−0.510907	+	0.328340i
$268$	−3.03097	−	0.889974i	−0.185146	−	0.0543638i
$269$	−2.64779	−	18.4158i	−0.161439	−	1.12283i	−0.895924	−	0.444207i	$-0.853485\pi$
$269$	−2.64779	−	18.4158i	−0.161439	−	1.12283i	0.734485	−	0.678625i	$-0.237424\pi$
$270$	0.488484	+	0.563740i	0.0297282	+	0.0343081i
$271$	20.9577	+	13.4687i	1.27309	+	0.818166i	0.990019	−	0.140932i	$-0.0450100\pi$
$271$	20.9577	+	13.4687i	1.27309	+	0.818166i	0.283072	+	0.959099i	$0.408646\pi$
$272$	−1.19435	+	1.37835i	−0.0724180	+	0.0835749i
$273$	−3.17590	+	0.932529i	−0.192214	+	0.0564392i
$274$	−3.04857	−	6.67543i	−0.184171	−	0.403278i
$275$	9.33756			0.563076
$276$	−4.30538	−	2.11274i	−0.259154	−	0.127172i
$277$	0.768221			0.0461579			0.0230790	−	0.999734i	$-0.492653\pi$
$277$	0.768221			0.0461579			0.0230790	+	0.999734i	$0.492653\pi$
$278$	−1.41466	−	3.09766i	−0.0848454	−	0.185786i
$279$	−6.69345	+	1.96538i	−0.400727	+	0.117664i
$280$	0.488484	−	0.563740i	0.0291925	−	0.0336899i
$281$	−9.37932	−	6.02772i	−0.559523	−	0.359584i	0.230108	−	0.973165i	$-0.426092\pi$
$281$	−9.37932	−	6.02772i	−0.559523	−	0.359584i	−0.789632	+	0.613581i	$0.789728\pi$
$282$	−5.34089	−	6.16372i	−0.318045	−	0.367044i
$283$	−3.43443	−	23.8870i	−0.204155	−	1.41993i	−0.791784	−	0.610802i	$-0.790847\pi$
$283$	−3.43443	−	23.8870i	−0.204155	−	1.41993i	0.587628	−	0.809131i	$-0.300062\pi$
$284$	5.10103	+	1.49780i	0.302691	+	0.0888780i
$285$	−1.97743	+	1.27082i	−0.117133	+	0.0752768i
$286$	0.989865	−	6.88466i	0.0585319	−	0.407098i
$287$	−2.10379	+	4.60666i	−0.124183	+	0.271923i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	1.94597	−	13.5345i	0.114469	−	0.796147i
$290$	−5.26843	+	3.38582i	−0.309373	+	0.198822i
$291$	11.9267	+	3.50200i	0.699157	+	0.205291i
$292$	−0.497181	−	3.45797i	−0.0290953	−	0.202362i
$293$	−10.6344	−	12.2727i	−0.621267	−	0.716981i	0.354680	−	0.934988i	$-0.384590\pi$
$293$	−10.6344	−	12.2727i	−0.621267	−	0.716981i	−0.975947	+	0.218007i	$0.930044\pi$
$294$	0.841254	+	0.540641i	0.0490629	+	0.0315308i
$295$	3.07523	−	3.54901i	0.179047	−	0.206631i
$296$	0.603067	−	0.177076i	0.0350526	−	0.0102924i
$297$	−0.872936	−	1.91146i	−0.0506529	−	0.110914i
$298$	12.0453			0.697766
$299$	15.6437	+	2.69497i	0.904697	+	0.155854i
$300$	−4.44358			−0.256550
$301$	2.00459	+	4.38945i	0.115543	+	0.253003i
$302$	−7.55989	+	2.21978i	−0.435023	+	0.127734i
$303$	5.66793	−	6.54114i	0.325614	−	0.375779i
$304$	2.65094	+	1.70366i	0.152042	+	0.0977115i
$305$	−2.16392	−	2.49729i	−0.123905	−	0.142995i
$306$	−0.259557	−	1.80526i	−0.0148379	−	0.103200i
$307$	−12.8470	−	3.77223i	−0.733219	−	0.215292i	−0.106253	−	0.994339i	$-0.533885\pi$
$307$	−12.8470	−	3.77223i	−0.733219	−	0.215292i	−0.626966	+	0.779047i	$0.715704\pi$
$308$	−1.76778	+	1.13608i	−0.100728	+	0.0647342i
$309$	2.52492	−	17.5612i	0.143638	−	0.999021i
$310$	−2.16168	+	4.73342i	−0.122775	+	0.268840i
$311$	−13.3150	+	29.1557i	−0.755023	+	1.65327i	0.00210041	+	0.999998i	$0.499331\pi$
$311$	−13.3150	+	29.1557i	−0.755023	+	1.65327i	−0.757123	+	0.653272i	$0.773396\pi$
$312$	−0.471059	+	3.27629i	−0.0266685	+	0.185483i
$313$	−3.88900	+	2.49931i	−0.219819	+	0.141269i	−0.645916	−	0.763408i	$-0.723525\pi$
$313$	−3.88900	+	2.49931i	−0.219819	+	0.141269i	0.426097	+	0.904677i	$0.359888\pi$
$314$	−3.79920	−	1.11555i	−0.214401	−	0.0629539i
$315$	0.106158	+	0.738342i	0.00598130	+	0.0416009i
$316$	4.85920	+	5.60781i	0.273351	+	0.315464i
$317$	16.7015	+	10.7334i	0.938050	+	0.602848i	0.917841	−	0.396947i	$-0.129930\pi$
$317$	16.7015	+	10.7334i	0.938050	+	0.602848i	0.0202091	+	0.999796i	$0.493567\pi$
$318$	−5.24788	+	6.05637i	−0.294286	+	0.339624i
$319$	16.9276	−	4.97040i	0.947764	−	0.278289i
$320$	−0.309873	−	0.678526i	−0.0173224	−	0.0379308i
$321$	8.04845			0.449221
$322$	−2.47968	−	4.10502i	−0.138187	−	0.228764i
$323$	5.74719			0.319782
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	14.1124	−	4.14377i	0.782814	−	0.229855i
$326$	−13.7727	+	15.8945i	−0.762797	+	0.880315i
$327$	−1.29847	−	0.834477i	−0.0718056	−	0.0461467i
$328$	3.31642	+	3.82735i	0.183119	+	0.211330i
$329$	−1.16069	−	8.07275i	−0.0639907	−	0.445065i
$330$	−1.50398	−	0.441609i	−0.0827916	−	0.0243098i
$331$	21.4279	−	13.7709i	1.17779	−	0.756917i	0.202809	−	0.979218i	$-0.434993\pi$
$331$	21.4279	−	13.7709i	1.17779	−	0.756917i	0.974978	+	0.222301i	$0.0713567\pi$
$332$	1.07659	−	7.48785i	0.0590856	−	0.410949i
$333$	−0.261099	+	0.571728i	−0.0143082	+	0.0313305i
$334$	0.199875	−	0.437665i	0.0109367	−	0.0239479i
$335$	0.335345	−	2.33237i	0.0183218	−	0.127431i
$336$	0.841254	−	0.540641i	0.0458941	−	0.0294944i
$337$	−29.1946	−	8.57230i	−1.59033	−	0.466963i	−0.637496	−	0.770454i	$-0.720030\pi$
$337$	−29.1946	−	8.57230i	−1.59033	−	0.466963i	−0.952834	+	0.303491i	$0.901848\pi$
$338$	0.290896	+	2.02323i	0.0158227	+	0.110049i
$339$	6.56046	+	7.57118i	0.356315	+	0.411210i
$340$	−1.14449	−	0.735516i	−0.0620684	−	0.0398890i
$341$	9.59970	−	11.0786i	0.519853	−	0.599942i
$342$	−3.02354	+	0.887791i	−0.163494	+	0.0480062i
$343$	0.415415	+	0.909632i	0.0224303	+	0.0491155i
$344$	4.82552			0.260174
$345$	1.10288	−	3.40313i	0.0593770	−	0.183218i
$346$	−0.435930			−0.0234358
$347$	−5.24246	−	11.4794i	−0.281430	−	0.616246i	0.715142	−	0.698979i	$-0.246362\pi$
$347$	−5.24246	−	11.4794i	−0.281430	−	0.616246i	−0.996572	+	0.0827339i	$0.973635\pi$
$348$	−8.05555	+	2.36532i	−0.431823	+	0.126795i
$349$	7.64007	−	8.81711i	0.408963	−	0.471969i	−0.513480	−	0.858102i	$-0.671644\pi$
$349$	7.64007	−	8.81711i	0.408963	−	0.471969i	0.922443	+	0.386133i	$0.126189\pi$
$350$	−3.73818	−	2.40238i	−0.199814	−	0.128413i
$351$	−2.16758	−	2.50152i	−0.115697	−	0.133521i
$352$	0.299055	+	2.07997i	0.0159397	+	0.110863i
$353$	−23.6582	−	6.94669i	−1.25920	−	0.369735i	−0.417004	−	0.908905i	$-0.636920\pi$
$353$	−23.6582	−	6.94669i	−1.25920	−	0.369735i	−0.842197	+	0.539170i	$0.818738\pi$
$354$	5.29609	−	3.40359i	0.281484	−	0.180899i
$355$	−0.564375	+	3.92531i	−0.0299539	+	0.208334i
$356$	−4.12243	+	9.02686i	−0.218488	+	0.478422i
$357$	0.757643	−	1.65901i	0.0400987	−	0.0878039i
$358$	−2.63781	+	18.3464i	−0.139412	+	0.969635i
$359$	−17.8777	+	11.4893i	−0.943547	+	0.606381i	−0.919398	−	0.393328i	$-0.871324\pi$
$359$	−17.8777	+	11.4893i	−0.943547	+	0.606381i	−0.0241483	+	0.999708i	$0.507687\pi$
$360$	0.715719	+	0.210154i	0.0377217	+	0.0110761i
$361$	1.29080	+	8.97773i	0.0679370	+	0.472512i
$362$	−3.25265	−	3.75376i	−0.170956	−	0.197293i
$363$	−5.53906	−	3.55974i	−0.290725	−	0.186838i
$364$	−2.16758	+	2.50152i	−0.113612	+	0.131115i
$365$	2.50038	−	0.734179i	0.130876	−	0.0384287i
$366$	−1.84023	−	4.02955i	−0.0961905	−	0.210628i
$367$	−20.1656			−1.05264			−0.526318	−	0.850288i	$-0.676428\pi$
$367$	−20.1656			−1.05264			−0.526318	+	0.850288i	$0.676428\pi$
$368$	−4.76415	+	0.550314i	−0.248349	+	0.0286871i
$369$	−5.06431			−0.263638
$370$	0.194763	+	0.426472i	0.0101253	+	0.0221712i
$371$	−7.68912	+	2.25773i	−0.399199	+	0.117215i
$372$	−4.56833	+	5.27213i	−0.236857	+	0.273347i
$373$	−12.1675	−	7.81957i	−0.630009	−	0.404882i	0.186304	−	0.982492i	$-0.440349\pi$
$373$	−12.1675	−	7.81957i	−0.630009	−	0.404882i	−0.816313	+	0.577610i	$0.803985\pi$
$374$	2.50976	+	2.89641i	0.129776	+	0.149770i
$375$	−1.00251	−	6.97260i	−0.0517693	−	0.360063i
$376$	−7.82540	−	2.29774i	−0.403564	−	0.118497i
$377$	23.3779	−	15.0241i	1.20402	−	0.773779i
$378$	−0.142315	+	0.989821i	−0.00731989	+	0.0509109i
$379$	−7.43933	+	16.2899i	−0.382133	+	0.836754i	0.616641	+	0.787245i	$0.288493\pi$
$379$	−7.43933	+	16.2899i	−0.382133	+	0.836754i	−0.998774	+	0.0495096i	$0.984234\pi$
$380$	−0.976465	+	2.13816i	−0.0500916	+	0.109685i
$381$	2.90695	−	20.2183i	0.148927	−	1.03581i
$382$	12.0337	−	7.73357i	0.615696	−	0.395684i
$383$	−8.68317	−	2.54961i	−0.443689	−	0.130279i	0.0522541	−	0.998634i	$-0.483359\pi$
$383$	−8.68317	−	2.54961i	−0.443689	−	0.130279i	−0.495943	+	0.868355i	$0.665178\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−1.02648	−	1.18462i	−0.0523142	−	0.0603738i
$386$	22.1887	+	14.2598i	1.12937	+	0.725805i
$387$	−3.16004	+	3.64688i	−0.160634	+	0.185381i
$388$	11.9267	−	3.50200i	0.605488	−	0.177787i
$389$	−0.0534956	−	0.117139i	−0.00271233	−	0.00593918i	0.908271	−	0.418382i	$-0.137403\pi$
$389$	−0.0534956	−	0.117139i	−0.00271233	−	0.00593918i	−0.910983	+	0.412443i	$0.864676\pi$
$390$	−2.46903			−0.125024
$391$	−6.76700	+	5.54195i	−0.342222	+	0.280269i
$392$	1.00000			0.0505076
$393$	3.83794	+	8.40393i	0.193599	+	0.423922i
$394$	−1.22485	+	0.359647i	−0.0617068	+	0.0181188i
$395$	−3.62464	+	4.18306i	−0.182376	+	0.210473i
$396$	−1.76778	−	1.13608i	−0.0888341	−	0.0570902i
$397$	12.0439	+	13.8994i	0.604465	+	0.697590i	0.972680	−	0.232151i	$-0.0745763\pi$
$397$	12.0439	+	13.8994i	0.604465	+	0.697590i	−0.368215	+	0.929741i	$0.620031\pi$
$398$	0.360703	+	2.50875i	0.0180804	+	0.125752i
$399$	−3.02354	−	0.887791i	−0.151366	−	0.0444451i
$400$	−3.73818	+	2.40238i	−0.186909	+	0.120119i
$401$	−1.14784	+	7.98337i	−0.0573202	+	0.398671i	0.940882	+	0.338734i	$0.109999\pi$
$401$	−1.14784	+	7.98337i	−0.0573202	+	0.398671i	−0.998202	+	0.0599362i	$0.980910\pi$
$402$	1.31227	−	2.87347i	0.0654500	−	0.143315i
$403$	9.59215	−	21.0039i	0.477819	−	1.04628i
$404$	1.23176	−	8.56707i	0.0612823	−	0.426228i
$405$	−0.627520	+	0.403283i	−0.0311817	+	0.0200393i
$406$	−8.05555	−	2.36532i	−0.399790	−	0.117389i
$407$	−0.187964	−	1.30732i	−0.00931702	−	0.0648013i
$408$	−1.19435	−	1.37835i	−0.0591291	−	0.0682386i
$409$	−4.80295	−	3.08667i	−0.237491	−	0.152626i	0.416483	−	0.909144i	$-0.363263\pi$
$409$	−4.80295	−	3.08667i	−0.237491	−	0.152626i	−0.653973	+	0.756518i	$0.726899\pi$
$410$	−2.47383	+	2.85496i	−0.122174	+	0.140996i
$411$	7.04134	−	2.06752i	0.347324	−	0.101983i
$412$	−7.37020	−	16.1385i	−0.363104	−	0.795086i
$413$	6.29547			0.309780
$414$	2.70396	−	3.96089i	0.132892	−	0.194667i
$415$	5.64289			0.276998
$416$	1.37502	+	3.01086i	0.0674157	+	0.147620i
$417$	3.26746	−	0.959413i	0.160008	−	0.0469827i
$418$	4.33633	−	5.00440i	0.212097	−	0.244773i
$419$	19.5272	+	12.5494i	0.953966	+	0.613076i	0.922322	−	0.386423i	$-0.126289\pi$
$419$	19.5272	+	12.5494i	0.953966	+	0.613076i	0.0316438	+	0.999499i	$0.489926\pi$
$420$	0.488484	+	0.563740i	0.0238356	+	0.0275077i
$421$	−1.15435	−	8.02866i	−0.0562594	−	0.391293i	−0.998423	−	0.0561393i	$-0.982121\pi$
$421$	−1.15435	−	8.02866i	−0.0562594	−	0.391293i	0.942164	−	0.335154i	$-0.108788\pi$
$422$	−11.0535	−	3.24559i	−0.538074	−	0.157993i
$423$	6.86107	−	4.40934i	0.333596	−	0.214389i
$424$	−1.14047	+	7.93216i	−0.0553862	+	0.385220i
$425$	−3.36665	+	7.37193i	−0.163306	+	0.357591i
$426$	−2.20851	+	4.83595i	−0.107002	+	0.234303i
$427$	0.630436	−	4.38478i	0.0305089	−	0.212194i
$428$	6.77079	−	4.35132i	0.327279	−	0.210329i
$429$	6.67371	+	1.95958i	0.322210	+	0.0946093i
$430$	0.512265	+	3.56288i	0.0247036	+	0.171818i
$431$	21.6663	+	25.0042i	1.04363	+	1.20441i	0.978438	+	0.206539i	$0.0662199\pi$
$431$	21.6663	+	25.0042i	1.04363	+	1.20441i	0.0651900	+	0.997873i	$0.479235\pi$
$432$	0.841254	+	0.540641i	0.0404748	+	0.0260116i
$433$	20.4065	−	23.5503i	0.980673	−	1.13176i	−0.0106014	−	0.999944i	$-0.503375\pi$
$433$	20.4065	−	23.5503i	0.980673	−	1.13176i	0.991275	−	0.131813i	$-0.0420800\pi$
$434$	−6.69345	+	1.96538i	−0.321296	+	0.0943410i
$435$	−2.60158	−	5.69666i	−0.124736	−	0.273134i
$436$	−1.54350			−0.0739200
$437$	11.1418	+	10.2102i	0.532985	+	0.488422i
$438$	3.49353			0.166927
$439$	−8.90219	−	19.4931i	−0.424878	−	0.930353i	−0.994130	−	0.108190i	$-0.965494\pi$
$439$	−8.90219	−	19.4931i	−0.424878	−	0.930353i	0.569252	−	0.822163i	$-0.307233\pi$
$440$	−1.50398	+	0.441609i	−0.0716996	+	0.0210529i
$441$	−0.654861	+	0.755750i	−0.0311838	+	0.0359881i
$442$	5.07849	+	3.26375i	0.241559	+	0.155241i
$443$	9.19107	+	10.6071i	0.436681	+	0.503956i	0.930846	−	0.365412i	$-0.119072\pi$
$443$	9.19107	+	10.6071i	0.436681	+	0.503956i	−0.494165	+	0.869368i	$0.664526\pi$
$444$	0.0894487	+	0.622129i	0.00424505	+	0.0295249i
$445$	−7.10254	−	2.08549i	−0.336693	−	0.0988619i
$446$	−4.25342	+	2.73351i	−0.201405	+	0.129435i
$447$	−1.71423	+	11.9227i	−0.0810801	+	0.563924i
$448$	0.415415	−	0.909632i	0.0196265	−	0.0429761i
$449$	6.98750	−	15.3005i	0.329760	−	0.722074i	−0.670034	−	0.742330i	$-0.733721\pi$
$449$	6.98750	−	15.3005i	0.329760	−	0.722074i	0.999795	+	0.0202555i	$0.00644797\pi$
$450$	0.632388	−	4.39835i	0.0298110	−	0.207340i
$451$	8.95257	−	5.75347i	0.421560	−	0.270920i
$452$	9.61230	+	2.82243i	0.452125	+	0.132756i
$453$	−1.12131	−	7.79885i	−0.0526835	−	0.366422i
$454$	−9.93826	−	11.4694i	−0.466425	−	0.538284i
$455$	−2.07708	−	1.33486i	−0.0973750	−	0.0625791i
$456$	−2.06359	+	2.38151i	−0.0966363	+	0.111524i
$457$	−2.80432	+	0.823423i	−0.131181	+	0.0385181i	−0.346664	−	0.937989i	$-0.612686\pi$
$457$	−2.80432	+	0.823423i	−0.131181	+	0.0385181i	0.215483	+	0.976508i	$0.430867\pi$
$458$	6.81075	+	14.9135i	0.318245	+	0.696860i
$459$	1.82382			0.0851287
$460$	−0.912071	−	3.45916i	−0.0425255	−	0.161284i
$461$	14.6061			0.680275			0.340137	−	0.940376i	$-0.389526\pi$
$461$	14.6061			0.680275			0.340137	+	0.940376i	$0.389526\pi$
$462$	−0.872936	−	1.91146i	−0.0406127	−	0.0889293i
$463$	−13.1988	+	3.87550i	−0.613398	+	0.180110i	−0.573651	−	0.819100i	$-0.694473\pi$
$463$	−13.1988	+	3.87550i	−0.613398	+	0.180110i	−0.0397470	+	0.999210i	$0.512655\pi$
$464$	−5.49797	+	6.34500i	−0.255237	+	0.294559i
$465$	−4.37760	−	2.81331i	−0.203006	−	0.130464i
$466$	−7.91854	−	9.13848i	−0.366819	−	0.423332i
$467$	−4.90251	−	34.0977i	−0.226861	−	1.57785i	−0.711211	−	0.702979i	$-0.751853\pi$
$467$	−4.90251	−	34.0977i	−0.226861	−	1.57785i	0.484349	−	0.874875i	$-0.339056\pi$
$468$	−3.17590	−	0.932529i	−0.146806	−	0.0431062i
$469$	2.65746	−	1.70785i	0.122710	−	0.0788611i
$470$	0.865797	−	6.02175i	0.0399362	−	0.277763i
$471$	1.64487	−	3.60177i	0.0757918	−	0.165961i
$472$	2.61523	−	5.72656i	0.120376	−	0.263586i
$473$	1.44309	−	10.0369i	0.0663535	−	0.461499i
$474$	−6.24227	+	4.01166i	−0.286717	+	0.184262i
$475$	13.4353	+	3.94497i	0.616455	+	0.181008i
$476$	−0.259557	−	1.80526i	−0.0118968	−	0.0827438i
$477$	−5.24788	−	6.05637i	−0.240284	−	0.277302i
$478$	14.6990	+	9.44649i	0.672318	+	0.432072i
$479$	9.01364	−	10.4023i	0.411844	−	0.475293i	−0.511491	−	0.859289i	$-0.670907\pi$
$479$	9.01364	−	10.4023i	0.411844	−	0.475293i	0.923335	+	0.383995i	$0.125452\pi$
$480$	0.715719	−	0.210154i	0.0326680	−	0.00959218i
$481$	−0.864234	−	1.89241i	−0.0394057	−	0.0862864i
$482$	−20.8087			−0.947810
$483$	4.41613	−	1.87024i	0.200941	−	0.0850988i
$484$	−6.58429			−0.299286
$485$	3.85179	+	8.43424i	0.174901	+	0.382979i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	23.4007	−	27.0059i	1.06039	−	1.22375i	0.0866114	−	0.996242i	$-0.472396\pi$
$487$	23.4007	−	27.0059i	1.06039	−	1.22375i	0.973776	−	0.227510i	$-0.0730584\pi$
$488$	−3.72664	−	2.39497i	−0.168697	−	0.108415i
$489$	−13.7727	−	15.8945i	−0.622821	−	0.718774i
$490$	0.106158	+	0.738342i	0.00479571	+	0.0333549i
$491$	−23.5426	−	6.91274i	−1.06246	−	0.311967i	−0.296621	−	0.954995i	$-0.595860\pi$
$491$	−23.5426	−	6.91274i	−1.06246	−	0.311967i	−0.765843	+	0.643028i	$0.777678\pi$
$492$	−4.26037	+	2.73797i	−0.192072	+	0.123437i
$493$	−2.17915	+	15.1563i	−0.0981438	+	0.682605i
$494$	4.33292	−	9.48778i	0.194947	−	0.426875i
$495$	0.651154	−	1.42583i	0.0292672	−	0.0640862i
$496$	−0.992793	+	6.90503i	−0.0445777	+	0.310045i
$497$	−4.47243	+	2.87426i	−0.200616	+	0.128928i
$498$	7.25842	+	2.13126i	0.325258	+	0.0955042i
$499$	2.72309	+	18.9395i	0.121902	+	0.847850i	0.955397	+	0.295323i	$0.0954273\pi$
$499$	2.72309	+	18.9395i	0.121902	+	0.847850i	−0.833495	+	0.552527i	$0.813664\pi$
$500$	−4.61303	−	5.32372i	−0.206301	−	0.238084i
$501$	0.404765	+	0.260126i	0.0180836	+	0.0116216i
$502$	−19.8784	+	22.9409i	−0.887216	+	1.02390i
$503$	0.156088	−	0.0458316i	0.00695963	−	0.00204353i	−0.278251	−	0.960508i	$-0.589755\pi$
$503$	0.156088	−	0.0458316i	0.00695963	−	0.00204353i	0.285211	+	0.958465i	$0.407936\pi$
$504$	0.415415	+	0.909632i	0.0185041	+	0.0405182i
$505$	6.45619			0.287297
$506$	−0.280106	+	10.0739i	−0.0124522	+	0.447838i
$507$	−2.04403			−0.0907787
$508$	−8.48534	−	18.5803i	−0.376476	−	0.824368i
$509$	26.3802	−	7.74593i	1.16928	−	0.343332i	0.361250	−	0.932469i	$-0.382350\pi$
$509$	26.3802	−	7.74593i	1.16928	−	0.343332i	0.808033	+	0.589137i	$0.200532\pi$
$510$	0.890907	−	1.02816i	0.0394500	−	0.0455277i
$511$	2.93894	+	1.88874i	0.130011	+	0.0835531i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.448460	−	3.11911i	−0.0198000	−	0.137712i
$514$	4.60542	+	1.35227i	0.203136	+	0.0596462i
$515$	11.1333	−	7.15496i	0.490593	−	0.315285i
$516$	−0.686743	+	4.77640i	−0.0302322	+	0.210269i
$517$	−7.11946	+	15.5894i	−0.313114	+	0.685623i
$518$	−0.261099	+	0.571728i	−0.0114721	+	0.0251203i
$519$	0.0620393	−	0.431493i	0.00272322	−	0.0189404i
$520$	−2.07708	+	1.33486i	−0.0910860	+	0.0585374i
$521$	6.23803	+	1.83165i	0.273293	+	0.0802461i	0.415507	−	0.909590i	$-0.363604\pi$
$521$	6.23803	+	1.83165i	0.273293	+	0.0802461i	−0.142214	+	0.989836i	$0.545422\pi$
$522$	−1.19482	−	8.31018i	−0.0522960	−	0.363727i
$523$	−15.4094	−	17.7834i	−0.673807	−	0.777615i	0.311160	−	0.950358i	$-0.399283\pi$
$523$	−15.4094	−	17.7834i	−0.673807	−	0.777615i	−0.984967	+	0.172743i	$0.944737\pi$
$524$	7.77219	+	4.99488i	0.339530	+	0.218202i
$525$	2.90993	−	3.35823i	0.127000	−	0.146565i
$526$	1.68119	−	0.493641i	0.0733033	−	0.0215238i
$527$	5.28534	+	11.5733i	0.230233	+	0.504140i
$528$	−2.10136			−0.0914499
$529$	−22.9645	−	1.27805i	−0.998455	−	0.0555675i
$530$	−5.97772			−0.259656
$531$	2.61523	+	5.72656i	0.113491	+	0.248512i
$532$	−3.02354	+	0.887791i	−0.131087	+	0.0384906i
$533$	10.9773	−	12.6685i	0.475479	−	0.548732i
$534$	−8.34829	−	5.36512i	−0.361266	−	0.232172i
$535$	3.93154	+	4.53724i	0.169975	+	0.196162i
$536$	−0.449563	−	3.12678i	−0.0194182	−	0.135056i
$537$	−17.7842	−	5.22192i	−0.767446	−	0.225342i
$538$	15.6517	−	10.0587i	0.674792	−	0.433662i
$539$	0.299055	−	2.07997i	0.0128812	−	0.0895907i
$540$	−0.309873	+	0.678526i	−0.0133348	+	0.0291991i
$541$	0.699685	−	1.53210i	0.0300818	−	0.0658700i	−0.893995	−	0.448078i	$-0.852109\pi$
$541$	0.699685	−	1.53210i	0.0300818	−	0.0658700i	0.924076	+	0.382208i	$0.124836\pi$
$542$	−3.54542	+	24.6589i	−0.152289	+	1.05919i
$543$	4.17845	−	2.68533i	0.179315	−	0.115238i
$544$	−1.74994	−	0.513830i	−0.0750282	−	0.0220303i
$545$	−0.163854	−	1.13963i	−0.00701873	−	0.0488163i
$546$	−2.16758	−	2.50152i	−0.0927637	−	0.107055i
$547$	−8.18141	−	5.25787i	−0.349812	−	0.224810i	0.353921	−	0.935275i	$-0.384848\pi$
$547$	−8.18141	−	5.25787i	−0.349812	−	0.224810i	−0.703732	+	0.710465i	$0.748485\pi$
$548$	4.80577	−	5.54615i	0.205292	−	0.236920i
$549$	4.25042	−	1.24804i	0.181404	−	0.0532649i
$550$	3.87896	+	8.49374i	0.165400	+	0.362174i
$551$	26.4562			1.12707
$552$	0.133298	−	4.79398i	0.00567352	−	0.204045i
$553$	−7.42020			−0.315539
$554$	0.319131	+	0.698799i	0.0135586	+	0.0296891i
$555$	−0.449849	+	0.132088i	−0.0190950	+	0.00560680i
$556$	2.23007	−	2.57363i	0.0945758	−	0.109146i
$557$	−32.4883	−	20.8790i	−1.37657	−	0.884671i	−0.377430	−	0.926038i	$-0.623192\pi$
$557$	−32.4883	−	20.8790i	−1.37657	−	0.884671i	−0.999144	+	0.0413672i	$0.986829\pi$
$558$	−4.56833	−	5.27213i	−0.193393	−	0.223187i
$559$	−2.27310	−	15.8098i	−0.0961421	−	0.668683i
$560$	0.715719	+	0.210154i	0.0302447	+	0.00888063i
$561$	−3.22411	+	2.07201i	−0.136122	+	0.0874802i
$562$	1.58670	−	11.0357i	0.0669308	−	0.465514i
$563$	0.776173	−	1.69958i	0.0327118	−	0.0716288i	−0.892571	−	0.450907i	$-0.851100\pi$
$563$	0.776173	−	1.69958i	0.0327118	−	0.0716288i	0.925283	+	0.379278i	$0.123828\pi$
$564$	3.38803	−	7.41875i	0.142662	−	0.312386i
$565$	−1.06350	+	7.39679i	−0.0447417	+	0.311185i
$566$	20.3016	−	13.0471i	0.853341	−	0.548409i
$567$	−0.959493	−	0.281733i	−0.0402949	−	0.0118317i
$568$	0.756601	+	5.26227i	0.0317463	+	0.220800i
$569$	−23.3209	−	26.9138i	−0.977664	−	1.12828i	−0.991725	−	0.128383i	$-0.959021\pi$
$569$	−23.3209	−	26.9138i	−0.977664	−	1.12828i	0.0140604	−	0.999901i	$-0.495524\pi$
$570$	−1.97743	−	1.27082i	−0.0828255	−	0.0532287i
$571$	12.7812	−	14.7502i	0.534875	−	0.617278i	−0.422417	−	0.906401i	$-0.638818\pi$
$571$	12.7812	−	14.7502i	0.534875	−	0.617278i	0.957292	+	0.289123i	$0.0933638\pi$
$572$	6.67371	−	1.95958i	0.279042	−	0.0819341i
$573$	5.94228	+	13.0118i	0.248242	+	0.543575i
$574$	−5.06431			−0.211380
$575$	−19.6234	+	8.31056i	−0.818354	+	0.346574i
$576$	1.00000			0.0416667
$577$	−0.946559	−	2.07267i	−0.0394057	−	0.0862866i	0.888905	−	0.458091i	$-0.151467\pi$
$577$	−0.946559	−	2.07267i	−0.0394057	−	0.0862866i	−0.928311	+	0.371804i	$0.878739\pi$
$578$	13.1198	−	3.85232i	0.545712	−	0.160235i
$579$	−17.2724	+	19.9335i	−0.717818	+	0.828406i
$580$	−5.26843	−	3.38582i	−0.218760	−	0.140588i
$581$	4.95392	+	5.71713i	0.205523	+	0.237187i
$582$	1.76901	+	12.3037i	0.0733277	+	0.510005i
$583$	16.1576	+	4.74430i	0.669179	+	0.196489i
$584$	2.93894	−	1.88874i	0.121614	−	0.0781567i
$585$	0.351380	−	2.44390i	0.0145278	−	0.101043i
$586$	6.74599	−	14.7717i	0.278674	−	0.610211i
$587$	−10.0053	+	21.9085i	−0.412962	+	0.904260i	0.582828	+	0.812595i	$0.301946\pi$
$587$	−10.0053	+	21.9085i	−0.412962	+	0.904260i	−0.995790	+	0.0916647i	$0.970781\pi$
$588$	−0.142315	+	0.989821i	−0.00586897	+	0.0408195i
$589$	18.4931	−	11.8848i	0.761994	−	0.489704i
$590$	4.50579	+	1.32302i	0.185500	+	0.0544679i
$591$	−0.181673	−	1.26356i	−0.00747301	−	0.0519760i
$592$	0.411598	+	0.475009i	0.0169166	+	0.0195227i
$593$	25.3356	+	16.2822i	1.04041	+	0.668630i	0.945088	−	0.326816i	$-0.105976\pi$
$593$	25.3356	+	16.2822i	1.04041	+	0.668630i	0.0953214	+	0.995447i	$0.469612\pi$
$594$	1.37610	−	1.58810i	0.0564620	−	0.0651606i
$595$	1.30534	−	0.383284i	0.0535139	−	0.0157131i
$596$	5.00380	+	10.9568i	0.204964	+	0.448808i
$597$	−2.53454			−0.103732
$598$	4.04718	+	15.3495i	0.165502	+	0.627688i
$599$	24.3413			0.994559			0.497280	−	0.867590i	$-0.334332\pi$
$599$	24.3413			0.994559			0.497280	+	0.867590i	$0.334332\pi$
$600$	−1.84593	−	4.04202i	−0.0753598	−	0.165015i
$601$	−37.8614	+	11.1171i	−1.54440	+	0.453477i	−0.939421	−	0.342765i	$-0.888636\pi$
$601$	−37.8614	+	11.1171i	−1.54440	+	0.453477i	−0.604978	+	0.796242i	$0.706818\pi$
$602$	−3.16004	+	3.64688i	−0.128794	+	0.148636i
$603$	2.65746	+	1.70785i	0.108220	+	0.0695489i
$604$	−5.15968	−	5.95459i	−0.209944	−	0.242289i
$605$	−0.698973	−	4.86146i	−0.0284173	−	0.197646i
$606$	8.30457	+	2.43844i	0.337350	+	0.0990550i
$607$	−5.82495	+	3.74347i	−0.236428	+	0.151943i	−0.653490	−	0.756935i	$-0.726696\pi$
$607$	−5.82495	+	3.74347i	−0.236428	+	0.151943i	0.417063	+	0.908878i	$0.363060\pi$
$608$	−0.448460	+	3.11911i	−0.0181875	+	0.126497i
$609$	3.48767	−	7.63694i	0.141328	−	0.309464i
$610$	1.37269	−	3.00578i	0.0555787	−	0.121700i
$611$	−3.84185	+	26.7206i	−0.155425	+	1.08100i
$612$	1.53430	−	0.986032i	0.0620202	−	0.0398580i
$613$	1.42522	+	0.418483i	0.0575642	+	0.0169024i	0.310388	−	0.950610i	$-0.399541\pi$
$613$	1.42522	+	0.418483i	0.0575642	+	0.0169024i	−0.252824	+	0.967512i	$0.581359\pi$
$614$	−1.90551	−	13.2531i	−0.0769001	−	0.534852i
$615$	−2.47383	−	2.85496i	−0.0997546	−	0.115123i
$616$	−1.76778	−	1.13608i	−0.0712257	−	0.0457740i
$617$	−6.75914	+	7.80046i	−0.272113	+	0.314035i	−0.875315	−	0.483554i	$-0.839346\pi$
$617$	−6.75914	+	7.80046i	−0.272113	+	0.314035i	0.603202	+	0.797588i	$0.293891\pi$
$618$	17.0231	−	4.99844i	0.684770	−	0.201067i
$619$	−12.3775	−	27.1028i	−0.497492	−	1.08936i	−0.977276	−	0.211969i	$-0.932012\pi$
$619$	−12.3775	−	27.1028i	−0.497492	−	1.08936i	0.479785	−	0.877386i	$-0.340715\pi$
$620$	−5.20367			−0.208984
$621$	3.53576	+	3.24013i	0.141885	+	0.130022i
$622$	−32.0522			−1.28518
$623$	−4.12243	−	9.02686i	−0.165162	−	0.361653i
$624$	−3.17590	+	0.932529i	−0.127138	+	0.0373310i
$625$	−11.1086	+	12.8200i	−0.444344	+	0.512801i
$626$	−3.88900	−	2.49931i	−0.155436	−	0.0998925i
$627$	4.33633	+	5.00440i	0.173177	+	0.199856i
$628$	−0.563509	−	3.91929i	−0.0224864	−	0.156397i
$629$	1.09989	+	0.322956i	0.0438554	+	0.0128771i
$630$	−0.627520	+	0.403283i	−0.0250010	+	0.0160672i
$631$	6.11743	−	42.5477i	0.243531	−	1.69380i	−0.390592	−	0.920564i	$-0.627730\pi$
$631$	6.11743	−	42.5477i	0.243531	−	1.69380i	0.634123	−	0.773232i	$-0.281361\pi$
$632$	−3.08246	+	6.74965i	−0.122614	+	0.268487i
$633$	4.78562	−	10.4791i	0.190211	−	0.416505i
$634$	−2.82539	+	19.6511i	−0.112211	+	0.780443i
$635$	12.8178	−	8.23753i	0.508661	−	0.326896i
$636$	−7.68912	−	2.25773i	−0.304893	−	0.0895248i
$637$	−0.471059	−	3.27629i	−0.0186640	−	0.129811i
$638$	11.5532	+	13.3331i	0.457396	+	0.527863i
$639$	−4.47243	−	2.87426i	−0.176927	−	0.113704i
$640$	0.488484	−	0.563740i	0.0193090	−	0.0222838i
$641$	−10.7054	+	3.14338i	−0.422836	+	0.124156i	−0.486226	−	0.873833i	$-0.661627\pi$
$641$	−10.7054	+	3.14338i	−0.422836	+	0.124156i	0.0633900	+	0.997989i	$0.479809\pi$
$642$	3.34345	+	7.32113i	0.131955	+	0.288942i
$643$	−11.8341			−0.466690			−0.233345	−	0.972394i	$-0.574967\pi$
$643$	−11.8341			−0.466690			−0.233345	+	0.972394i	$0.574967\pi$
$644$	2.70396	−	3.96089i	0.106551	−	0.156081i
$645$	−3.59952			−0.141731
$646$	2.38747	+	5.22783i	0.0939338	+	0.205686i
$647$	−24.3354	+	7.14552i	−0.956723	+	0.280919i	−0.722583	−	0.691284i	$-0.757045\pi$
$647$	−24.3354	+	7.14552i	−0.956723	+	0.280919i	−0.234140	+	0.972203i	$0.575227\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	−11.1290	−	7.15216i	−0.436851	−	0.280747i
$650$	9.63180	+	11.1157i	0.377790	+	0.435993i
$651$	−0.992793	−	6.90503i	−0.0389106	−	0.270629i
$652$	−20.1795	−	5.92524i	−0.790291	−	0.232050i
$653$	21.6151	−	13.8912i	0.845863	−	0.543603i	−0.0444191	−	0.999013i	$-0.514144\pi$
$653$	21.6151	−	13.8912i	0.845863	−	0.543603i	0.890282	+	0.455410i	$0.150507\pi$
$654$	0.219662	−	1.52778i	0.00858948	−	0.0597411i
$655$	−2.86286	+	6.26878i	−0.111861	+	0.244942i
$656$	−2.10379	+	4.60666i	−0.0821393	+	0.179860i
$657$	−0.497181	+	3.45797i	−0.0193969	+	0.134908i
$658$	6.86107	−	4.40934i	0.267472	−	0.171894i
$659$	−14.8001	−	4.34570i	−0.576530	−	0.169284i	−0.0195476	−	0.999809i	$-0.506223\pi$
$659$	−14.8001	−	4.34570i	−0.576530	−	0.169284i	−0.556982	+	0.830525i	$0.688041\pi$
$660$	−0.223075	−	1.55152i	−0.00868319	−	0.0603929i
$661$	−29.4799	−	34.0216i	−1.14664	−	1.32329i	−0.938537	−	0.345180i	$-0.887818\pi$
$661$	−29.4799	−	34.0216i	−1.14664	−	1.32329i	−0.208099	−	0.978108i	$-0.566728\pi$
$662$	21.4279	+	13.7709i	0.832821	+	0.535221i
$663$	−3.95327	+	4.56232i	−0.153532	+	0.177186i
$664$	7.25842	−	2.13126i	0.281681	−	0.0827091i
$665$	−0.976465	−	2.13816i	−0.0378657	−	0.0829143i
$666$	−0.628527			−0.0243549
$667$	−31.1507	+	25.5114i	−1.20616	+	0.987805i
$668$	0.481145			0.0186160
$669$	−2.10036	−	4.59914i	−0.0812045	−	0.177813i
$670$	2.26091	−	0.663863i	0.0873465	−	0.0256473i
$671$	−6.09593	+	7.03507i	−0.235331	+	0.271586i
$672$	0.841254	+	0.540641i	0.0324521	+	0.0208557i
$673$	−0.146832	−	0.169453i	−0.00565996	−	0.00653194i	0.752913	−	0.658121i	$-0.228648\pi$
$673$	−0.146832	−	0.169453i	−0.00565996	−	0.00653194i	−0.758572	+	0.651589i	$0.774103\pi$
$674$	−4.33023	−	30.1174i	−0.166794	−	1.16008i
$675$	4.26358	+	1.25190i	0.164105	+	0.0481857i
$676$	−1.71955	+	1.10509i	−0.0661366	+	0.0425034i
$677$	3.20125	−	22.2652i	0.123034	−	0.855721i	−0.831053	−	0.556193i	$-0.812262\pi$
$677$	3.20125	−	22.2652i	0.123034	−	0.855721i	0.954087	−	0.299528i	$-0.0968293\pi$
$678$	−4.16167	+	9.11279i	−0.159828	+	0.349974i
$679$	−5.16371	+	11.3069i	−0.198165	+	0.433921i
$680$	0.193613	−	1.34660i	0.00742470	−	0.0516399i
$681$	12.7670	−	8.20484i	0.489232	−	0.314410i
$682$	14.0654	+	4.12996i	0.538590	+	0.158144i
$683$	1.33714	+	9.30001i	0.0511642	+	0.355855i	0.999280	+	0.0379309i	$0.0120767\pi$
$683$	1.33714	+	9.30001i	0.0511642	+	0.355855i	−0.948116	+	0.317924i	$0.897014\pi$
$684$	−2.06359	−	2.38151i	−0.0789032	−	0.0910591i
$685$	4.60513	+	2.95953i	0.175953	+	0.113078i
$686$	−0.654861	+	0.755750i	−0.0250027	+	0.0288547i
$687$	−15.7309	+	4.61902i	−0.600172	+	0.176226i
$688$	2.00459	+	4.38945i	0.0764244	+	0.167346i
$689$	26.5253			1.01053
$690$	3.55375	−	0.410498i	0.135289	−	0.0156274i
$691$	−27.7989			−1.05752			−0.528760	−	0.848771i	$-0.677343\pi$
$691$	−27.7989			−1.05752			−0.528760	+	0.848771i	$0.677343\pi$
$692$	−0.181092	−	0.396536i	−0.00688408	−	0.0150740i
$693$	2.01624	−	0.592021i	0.0765906	−	0.0224890i
$694$	8.26422	−	9.53742i	0.313705	−	0.362035i
$695$	2.13696	+	1.37334i	0.0810595	+	0.0520938i
$696$	−5.49797	−	6.34500i	−0.208400	−	0.240507i
$697$	1.31448	+	9.14239i	0.0497894	+	0.346293i
$698$	11.1941	+	3.28689i	0.423704	+	0.124411i
$699$	10.1724	−	6.53740i	0.384755	−	0.247267i
$700$	0.632388	−	4.39835i	0.0239020	−	0.166242i
$701$	−8.36099	+	18.3080i	−0.315790	+	0.691484i	−0.999259	−	0.0384960i	$-0.987743\pi$
$701$	−8.36099	+	18.3080i	−0.315790	+	0.691484i	0.683469	+	0.729980i	$0.260471\pi$
$702$	1.37502	−	3.01086i	0.0518966	−	0.113638i
$703$	0.281869	−	1.96044i	0.0106309	−	0.0739395i
$704$	−1.76778	+	1.13608i	−0.0666256	+	0.0428176i
$705$	5.83724	+	1.71397i	0.219843	+	0.0645518i
$706$	−3.50906	−	24.4060i	−0.132065	−	0.918534i
$707$	5.66793	+	6.54114i	0.213164	+	0.246005i
$708$	5.29609	+	3.40359i	0.199039	+	0.127915i
$709$	−8.27356	+	9.54819i	−0.310720	+	0.358590i	−0.889533	−	0.456870i	$-0.848970\pi$
$709$	−8.27356	+	9.54819i	−0.310720	+	0.358590i	0.578814	+	0.815460i	$0.303516\pi$
$710$	−3.80504	+	1.11726i	−0.142801	+	0.0419300i
$711$	−3.08246	−	6.74965i	−0.115601	−	0.253132i
$712$	−9.92363			−0.371904
$713$	−10.3142	+	31.8263i	−0.386269	+	1.19190i
$714$	1.82382			0.0682548
$715$	2.15531	+	4.71946i	0.0806038	+	0.176498i
$716$	−17.7842	+	5.22192i	−0.664627	+	0.195152i
$717$	−11.4422	+	13.2050i	−0.427318	+	0.493151i
$718$	−17.8777	−	11.4893i	−0.667188	−	0.428776i
$719$	24.1076	+	27.8217i	0.899063	+	1.03757i	0.999093	+	0.0425900i	$0.0135609\pi$
$719$	24.1076	+	27.8217i	0.899063	+	1.03757i	−0.100029	+	0.994985i	$0.531894\pi$
$720$	0.106158	+	0.738342i	0.00395626	+	0.0275164i
$721$	17.0231	+	4.99844i	0.633974	+	0.186152i
$722$	−7.63021	+	4.90364i	−0.283967	+	0.182494i
$723$	2.96138	−	20.5969i	0.110135	−	0.766006i
$724$	2.06334	−	4.51808i	0.0766834	−	0.167913i
$725$	−15.4978	+	33.9354i	−0.575572	+	1.26033i
$726$	0.937042	−	6.51727i	0.0347769	−	0.241879i
$727$	9.56229	−	6.14531i	0.354646	−	0.227917i	−0.351171	−	0.936311i	$-0.614216\pi$
$727$	9.56229	−	6.14531i	0.354646	−	0.227917i	0.705817	+	0.708394i	$0.250580\pi$
$728$	−3.17590	−	0.932529i	−0.117707	−	0.0345618i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	1.70653	+	1.96944i	0.0631615	+	0.0728923i
$731$	7.40377	+	4.75812i	0.273838	+	0.175985i
$732$	2.90094	−	3.34787i	0.107222	−	0.123741i
$733$	−12.1573	+	3.56971i	−0.449040	+	0.131850i	−0.498431	−	0.866929i	$-0.666090\pi$
$733$	−12.1573	+	3.56971i	−0.449040	+	0.131850i	0.0493907	+	0.998780i	$0.484272\pi$
$734$	−8.37709	−	18.3433i	−0.309204	−	0.677062i
$735$	−0.745935			−0.0275142
$736$	−2.47968	−	4.10502i	−0.0914023	−	0.151313i
$737$	−6.63805			−0.244516
$738$	−2.10379	−	4.60666i	−0.0774417	−	0.169574i
$739$	32.2558	−	9.47115i	1.18655	−	0.348402i	0.371853	−	0.928292i	$-0.378723\pi$
$739$	32.2558	−	9.47115i	1.18655	−	0.348402i	0.814695	+	0.579890i	$0.196904\pi$
$740$	−0.307025	+	0.354326i	−0.0112865	+	0.0130253i
$741$	8.77457	+	5.63907i	0.322342	+	0.207157i
$742$	−5.24788	−	6.05637i	−0.192656	−	0.222336i
$743$	−2.46682	−	17.1571i	−0.0904990	−	0.629434i	−0.983705	−	0.179788i	$-0.942459\pi$
$743$	−2.46682	−	17.1571i	−0.0904990	−	0.629434i	0.893206	−	0.449647i	$-0.148450\pi$
$744$	−6.69345	−	1.96538i	−0.245394	−	0.0720542i
$745$	−7.55868	+	4.85767i	−0.276928	+	0.177971i
$746$	2.05837	−	14.3163i	0.0753624	−	0.524157i
$747$	−3.14255	+	6.88123i	−0.114980	+	0.251771i
$748$	−1.59208	+	3.48617i	−0.0582122	+	0.127467i
$749$	−1.14541	+	7.96653i	−0.0418525	+	0.291091i
$750$	5.92604	−	3.80843i	0.216388	−	0.139064i
$751$	−17.7197	−	5.20296i	−0.646599	−	0.189859i	−0.0580419	−	0.998314i	$-0.518486\pi$
$751$	−17.7197	−	5.20296i	−0.646599	−	0.189859i	−0.588557	+	0.808455i	$0.700304\pi$
$752$	−1.16069	−	8.07275i	−0.0423259	−	0.294383i
$753$	−19.8784	−	22.9409i	−0.724409	−	0.836013i
$754$	23.3779	+	15.0241i	0.851374	+	0.547145i
$755$	3.84879	−	4.44174i	0.140072	−	0.161651i
$756$	−0.959493	+	0.281733i	−0.0348964	+	0.0102465i
$757$	21.5973	+	47.2915i	0.784967	+	1.71884i	0.690526	+	0.723308i	$0.257379\pi$
$757$	21.5973	+	47.2915i	0.784967	+	1.71884i	0.0944417	+	0.995530i	$0.469893\pi$
$758$	−17.9082			−0.650455
$759$	−9.93147	−	1.71092i	−0.360490	−	0.0621023i
$760$	−2.35058			−0.0852644
$761$	−12.5782	−	27.5424i	−0.455959	−	0.998410i	−0.988390	−	0.151937i	$-0.951449\pi$
$761$	−12.5782	−	27.5424i	−0.455959	−	0.998410i	0.532432	−	0.846473i	$-0.321278\pi$
$762$	19.5988	−	5.75472i	0.709989	−	0.208472i
$763$	1.01077	−	1.16650i	0.0365925	−	0.0422300i
$764$	12.0337	+	7.73357i	0.435363	+	0.279791i
$765$	0.890907	+	1.02816i	0.0322108	+	0.0371732i
$766$	−1.28791	−	8.95763i	−0.0465342	−	0.323652i
$767$	−19.9938	−	5.87071i	−0.721934	−	0.211979i
$768$	0.841254	−	0.540641i	0.0303561	−	0.0195087i
$769$	0.598723	−	4.16421i	0.0215905	−	0.150165i	−0.976174	−	0.216987i	$-0.930377\pi$
$769$	0.598723	−	4.16421i	0.0215905	−	0.150165i	0.997765	+	0.0668222i	$0.0212860\pi$
$770$	0.651154	−	1.42583i	0.0234659	−	0.0513833i
$771$	−1.99393	+	4.36610i	−0.0718096	+	0.157241i
$772$	−3.75366	+	26.1073i	−0.135097	+	0.939621i
$773$	3.41555	−	2.19504i	0.122849	−	0.0789501i	−0.477773	−	0.878483i	$-0.658556\pi$
$773$	3.41555	−	2.19504i	0.122849	−	0.0789501i	0.600622	+	0.799533i	$0.294920\pi$
$774$	−4.63005	−	1.35951i	−0.166424	−	0.0488664i
$775$	4.41156	+	30.6830i	0.158468	+	1.10217i
$776$	8.14007	+	9.39415i	0.292212	+	0.337230i
$777$	−0.528750	−	0.339807i	−0.0189688	−	0.0121905i
$778$	0.0843305	−	0.0973226i	0.00302339	−	0.00348918i
$779$	15.3121	−	4.49605i	0.548614	−	0.161088i
$780$	−1.02567	−	2.24591i	−0.0367249	−	0.0804164i
$781$	11.1716			0.399753
$782$	−7.85225	−	3.85326i	−0.280796	−	0.137792i
$783$	8.39564			0.300036
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	2.83396	−	0.832125i	0.101148	−	0.0296998i
$786$	−6.05014	+	6.98223i	−0.215801	+	0.249048i
$787$	−44.0677	−	28.3206i	−1.57084	−	1.00952i	−0.979097	−	0.203395i	$-0.934803\pi$
$787$	−44.0677	−	28.3206i	−1.57084	−	1.00952i	−0.591746	−	0.806125i	$-0.701561\pi$
$788$	−0.835965	−	0.964756i	−0.0297800	−	0.0343680i
$789$	0.249359	+	1.73433i	0.00887741	+	0.0617437i
$790$	−5.31078	−	1.55939i	−0.188949	−	0.0554805i
$791$	−8.42776	+	5.41620i	−0.299657	+	0.192578i
$792$	0.299055	−	2.07997i	0.0106264	−	0.0739085i
$793$	−6.09113	+	13.3377i	−0.216302	+	0.473636i
$794$	−7.64011	+	16.7295i	−0.271137	+	0.593708i
$795$	0.850718	−	5.91688i	0.0301719	−	0.209850i
$796$	−2.13219	+	1.37028i	−0.0755736	+	0.0485682i
$797$	29.8857	+	8.77525i	1.05861	+	0.310835i	0.764290	−	0.644873i	$-0.223090\pi$
$797$	29.8857	+	8.77525i	1.05861	+	0.310835i	0.294317	+	0.955708i	$0.404908\pi$
$798$	−0.448460	−	3.11911i	−0.0158753	−	0.110415i
$799$	−9.74083	−	11.2415i	−0.344606	−	0.397696i
$800$	−3.73818	−	2.40238i	−0.132165	−	0.0849370i
$801$	6.49860	−	7.49978i	0.229617	−	0.264992i
$802$	−7.73876	+	2.27230i	−0.273265	+	0.0802379i
$803$	−3.04962	−	6.67775i	−0.107619	−	0.235653i
$804$	3.15893			0.111407
$805$	3.21154	+	1.57597i	0.113192	+	0.0555456i
$806$	23.0905			0.813329
$807$	7.72888	+	16.9239i	0.272069	+	0.595749i
$808$	8.30457	−	2.43844i	0.292154	−	0.0857841i
$809$	−8.63346	+	9.96355i	−0.303536	+	0.350300i	−0.886942	−	0.461882i	$-0.847174\pi$
$809$	−8.63346	+	9.96355i	−0.303536	+	0.350300i	0.583405	+	0.812181i	$0.301720\pi$
$810$	−0.627520	−	0.403283i	−0.0220488	−	0.0141699i
$811$	18.5193	+	21.3725i	0.650302	+	0.750488i	0.981161	−	0.193192i	$-0.0618840\pi$
$811$	18.5193	+	21.3725i	0.650302	+	0.750488i	−0.330859	+	0.943680i	$0.607338\pi$
$812$	−1.19482	−	8.31018i	−0.0419301	−	0.291630i
$813$	−23.9034	−	7.01866i	−0.838328	−	0.246155i
$814$	1.11109	−	0.714057i	0.0389438	−	0.0250277i
$815$	2.23265	−	15.5284i	0.0782062	−	0.543936i
$816$	0.757643	−	1.65901i	0.0265228	−	0.0580768i
$817$	6.31684	−	13.8319i	0.220998	−	0.483919i
$818$	0.812515	−	5.65116i	0.0284089	−	0.197588i
$819$	2.78453	−	1.78951i	0.0972994	−	0.0625305i
$820$	−3.62463	−	1.06429i	−0.126577	−	0.0371665i
$821$	7.39954	+	51.4649i	0.258246	+	1.79614i	0.545319	+	0.838229i	$0.316409\pi$
$821$	7.39954	+	51.4649i	0.258246	+	1.79614i	−0.287073	+	0.957909i	$0.592682\pi$
$822$	4.80577	+	5.54615i	0.167620	+	0.193444i
$823$	−11.7487	−	7.55045i	−0.409535	−	0.263192i	0.319613	−	0.947548i	$-0.396447\pi$
$823$	−11.7487	−	7.55045i	−0.409535	−	0.263192i	−0.729148	+	0.684356i	$0.760083\pi$
$824$	11.6184	−	13.4083i	0.404746	−	0.467102i
$825$	−8.95932	+	2.63069i	−0.311924	+	0.0915890i
$826$	2.61523	+	5.72656i	0.0909956	+	0.199253i
$827$	8.38136			0.291449			0.145724	−	0.989325i	$-0.453449\pi$
$827$	8.38136			0.291449			0.145724	+	0.989325i	$0.453449\pi$
$828$	4.72621	+	0.814195i	0.164247	+	0.0282952i
$829$	−6.49607			−0.225618			−0.112809	−	0.993617i	$-0.535985\pi$
$829$	−6.49607			−0.225618			−0.112809	+	0.993617i	$0.535985\pi$
$830$	2.34414	+	5.13295i	0.0813663	+	0.178167i
$831$	−0.737103	+	0.216433i	−0.0255698	+	0.00750797i
$832$	−2.16758	+	2.50152i	−0.0751472	+	0.0867245i
$833$	1.53430	+	0.986032i	0.0531602	+	0.0341640i
$834$	2.23007	+	2.57363i	0.0772209	+	0.0891176i
$835$	0.0510772	+	0.355250i	0.00176760	+	0.0122939i
$836$	6.35354	+	1.86557i	0.219742	+	0.0645220i
$837$	5.86861	−	3.77153i	0.202849	−	0.130363i
$838$	−3.30341	+	22.9757i	−0.114115	+	0.793684i
$839$	11.7326	−	25.6907i	0.405053	−	0.886942i	−0.591680	−	0.806173i	$-0.701535\pi$
$839$	11.7326	−	25.6907i	0.405053	−	0.886942i	0.996733	−	0.0807691i	$-0.0257376\pi$
$840$	−0.309873	+	0.678526i	−0.0106916	+	0.0234114i
$841$	−5.90418	+	41.0644i	−0.203592	+	1.41602i
$842$	6.82359	−	4.38526i	0.235156	−	0.151126i
$843$	10.6976	+	3.14110i	0.368445	+	0.108185i
$844$	−1.63948	−	11.4028i	−0.0564333	−	0.392502i
$845$	−0.998477	−	1.15230i	−0.0343487	−	0.0396405i
$846$	6.86107	+	4.40934i	0.235888	+	0.151596i
$847$	4.31179	−	4.97607i	0.148155	−	0.170980i
$848$	−7.68912	+	2.25773i	−0.264045	+	0.0775307i
$849$	10.0250	+	21.9518i	0.344059	+	0.753383i
$850$	−8.10430			−0.277975
$851$	1.55855	+	2.58011i	0.0534263	+	0.0884452i
$852$	−5.31639			−0.182136
$853$	6.64735	+	14.5557i	0.227601	+	0.498377i	0.988635	−	0.150335i	$-0.0480353\pi$
$853$	6.64735	+	14.5557i	0.227601	+	0.498377i	−0.761034	+	0.648712i	$0.775308\pi$
$854$	4.25042	−	1.24804i	0.145447	−	0.0427070i
$855$	1.53930	−	1.77645i	0.0526430	−	0.0607532i
$856$	6.77079	+	4.35132i	0.231421	+	0.148725i
$857$	−9.94065	−	11.4721i	−0.339566	−	0.391880i	0.560124	−	0.828409i	$-0.310753\pi$
$857$	−9.94065	−	11.4721i	−0.339566	−	0.391880i	−0.899691	+	0.436528i	$0.856208\pi$
$858$	0.989865	+	6.88466i	0.0337934	+	0.235038i
$859$	−8.53448	−	2.50595i	−0.291193	−	0.0855018i	0.132874	−	0.991133i	$-0.457579\pi$
$859$	−8.53448	−	2.50595i	−0.291193	−	0.0855018i	−0.424066	+	0.905631i	$0.639398\pi$
$860$	−3.02811	+	1.94605i	−0.103258	+	0.0663597i
$861$	0.720727	−	5.01277i	0.0245623	−	0.170835i
$862$	−13.7441	+	30.0955i	−0.468128	+	1.02506i
$863$	−9.70971	+	21.2613i	−0.330522	+	0.723743i	−0.999815	−	0.0192561i	$-0.993870\pi$
$863$	−9.70971	+	21.2613i	−0.330522	+	0.723743i	0.669292	+	0.742999i	$0.266597\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	0.273555	−	0.175803i	0.00930115	−	0.00597749i
$866$	29.8993	+	8.77923i	1.01602	+	0.298330i
$867$	1.94597	+	13.5345i	0.0660885	+	0.459656i
$868$	−4.56833	−	5.27213i	−0.155059	−	0.178948i
$869$	13.1172	+	8.42994i	0.444972	+	0.285966i
$870$	4.10113	−	4.73296i	0.139041	−	0.160462i
$871$	−10.0325	+	2.94580i	−0.339937	+	0.0998145i
$872$	−0.641191	−	1.40401i	−0.0217135	−	0.0475459i
$873$	−12.4302			−0.420700
$874$	−4.65908	+	14.3764i	−0.157596	+	0.486290i
$875$	7.04430			0.238141
$876$	1.45126	+	3.17782i	0.0490336	+	0.107369i
$877$	5.77547	−	1.69583i	0.195024	−	0.0572641i	−0.182762	−	0.983157i	$-0.558504\pi$
$877$	5.77547	−	1.69583i	0.195024	−	0.0572641i	0.377786	+	0.925893i	$0.376686\pi$
$878$	14.0334	−	16.1954i	0.473605	−	0.546569i
$879$	13.6612	+	8.77955i	0.460782	+	0.296127i
$880$	−1.02648	−	1.18462i	−0.0346026	−	0.0399335i
$881$	0.629574	+	4.37879i	0.0212109	+	0.147525i	0.997675	−	0.0681566i	$-0.0217117\pi$
$881$	0.629574	+	4.37879i	0.0212109	+	0.147525i	−0.976464	+	0.215682i	$0.930803\pi$
$882$	−0.959493	−	0.281733i	−0.0323078	−	0.00948643i
$883$	−26.4243	+	16.9818i	−0.889247	+	0.571484i	−0.903583	−	0.428413i	$-0.859073\pi$
$883$	−26.4243	+	16.9818i	−0.889247	+	0.571484i	0.0143362	+	0.999897i	$0.495437\pi$
$884$	−0.859128	+	5.97537i	−0.0288956	+	0.200973i
$885$	−1.95079	+	4.27164i	−0.0655752	+	0.143590i
$886$	−5.83041	+	12.7668i	−0.195876	+	0.428910i
$887$	2.84606	−	19.7948i	0.0955613	−	0.664644i	−0.884587	−	0.466376i	$-0.845559\pi$
$887$	2.84606	−	19.7948i	0.0955613	−	0.664644i	0.980148	−	0.198268i	$-0.0635315\pi$
$888$	−0.528750	+	0.339807i	−0.0177437	+	0.0114032i
$889$	19.5988	+	5.75472i	0.657322	+	0.193007i
$890$	−1.05347	−	7.32704i	−0.0353124	−	0.245603i
$891$	1.37610	+	1.58810i	0.0461010	+	0.0532034i
$892$	−4.25342	−	2.73351i	−0.142415	−	0.0915245i
$893$	−16.8301	+	19.4230i	−0.563199	+	0.649966i
$894$	−11.5574	+	3.39355i	−0.386537	+	0.113497i
$895$	−5.74349	−	12.5765i	−0.191984	−	0.420386i
$896$	1.00000			0.0334077
$897$	−15.7693	+	1.82153i	−0.526520	+	0.0608190i
$898$	16.8205			0.561308
$899$	24.3301	+	53.2755i	0.811455	+	1.77684i
$900$	4.26358	−	1.25190i	0.142119	−	0.0417300i
$901$	−9.57119	+	11.0457i	−0.318863	+	0.367987i
$902$	8.95257	+	5.75347i	0.298088	+	0.191570i
$903$	−3.16004	−	3.64688i	−0.105160	−	0.121361i
$904$	1.42572	+	9.91613i	0.0474189	+	0.329806i
$905$	3.55493	+	1.04382i	0.118170	+	0.0346978i
$906$	6.62828	−	4.25974i	0.220210	−	0.141520i
$907$	5.74150	−	39.9330i	0.190643	−	1.32595i	−0.639667	−	0.768652i	$-0.720928\pi$
$907$	5.74150	−	39.9330i	0.190643	−	1.32595i	0.830311	−	0.557301i	$-0.188163\pi$
$908$	6.30440	−	13.8047i	0.209219	−	0.458125i
$909$	−3.59549	+	7.87302i	−0.119255	+	0.261132i
$910$	0.351380	−	2.44390i	0.0116481	−	0.0810144i
$911$	−21.5189	+	13.8293i	−0.712951	+	0.458186i	−0.846179	−	0.532900i	$-0.821102\pi$
$911$	−21.5189	+	13.8293i	−0.712951	+	0.458186i	0.133227	+	0.991086i	$0.457466\pi$
$912$	−3.02354	−	0.887791i	−0.100119	−	0.0293977i
$913$	−2.26230	−	15.7347i	−0.0748713	−	0.520741i
$914$	−1.91397	−	2.20884i	−0.0633085	−	0.0730619i
$915$	2.77983	+	1.78649i	0.0918984	+	0.0590595i
$916$	−10.7365	+	12.3905i	−0.354743	+	0.409395i
$917$	−8.86458	+	2.60288i	−0.292734	+	0.0859545i
$918$	0.757643	+	1.65901i	0.0250059	+	0.0547554i
$919$	56.6771			1.86961			0.934803	−	0.355168i	$-0.115576\pi$
$919$	56.6771			1.86961			0.934803	+	0.355168i	$0.115576\pi$
$920$	2.76767	−	2.26663i	0.0912474	−	0.0747287i
$921$	13.3894			0.441196
$922$	6.06760	+	13.2862i	0.199826	+	0.437558i
$923$	16.8843	−	4.95768i	0.555754	−	0.163184i
$924$	1.37610	−	1.58810i	0.0452703	−	0.0522447i
$925$	2.34955	+	1.50996i	0.0772526	+	0.0496472i
$926$	−9.00824	−	10.3961i	−0.296029	−	0.341636i
$927$	2.52492	+	17.5612i	0.0829292	+	0.576785i
$928$	−8.05555	−	2.36532i	−0.264437	−	0.0776456i
$929$	18.7810	−	12.0698i	0.616185	−	0.395998i	−0.194987	−	0.980806i	$-0.562466\pi$
$929$	18.7810	−	12.0698i	0.616185	−	0.395998i	0.811172	+	0.584808i	$0.198830\pi$
$930$	0.740559	−	5.15070i	0.0242839	−	0.168898i
$931$	1.30905	−	2.86642i	0.0429023	−	0.0939430i
$932$	5.02318	−	10.9992i	0.164540	−	0.360292i
$933$	4.56151	−	31.7260i	0.149337	−	1.03866i
$934$	28.9798	−	18.6242i	0.948248	−	0.609402i
$935$	−2.74300	−	0.805417i	−0.0897056	−	0.0263399i
$936$	−0.471059	−	3.27629i	−0.0153971	−	0.107089i
$937$	21.4966	+	24.8084i	0.702263	+	0.810455i	0.989056	−	0.147537i	$-0.0471347\pi$
$937$	21.4966	+	24.8084i	0.702263	+	0.810455i	−0.286793	+	0.957993i	$0.592589\pi$
$938$	2.65746	+	1.70785i	0.0867692	+	0.0557632i
$939$	3.02733	−	3.49373i	0.0987932	−	0.114013i
$940$	5.83724	−	1.71397i	0.190390	−	0.0559035i
$941$	6.79957	+	14.8890i	0.221660	+	0.485367i	0.987491	−	0.157674i	$-0.0503996\pi$
$941$	6.79957	+	14.8890i	0.221660	+	0.485367i	−0.765831	+	0.643041i	$0.777672\pi$
$942$	3.95959			0.129010
$943$	−13.6937	+	20.0592i	−0.445928	+	0.653216i
$944$	6.29547			0.204900
$945$	−0.309873	−	0.678526i	−0.0100802	−	0.0220725i
$946$	9.72940	−	2.85681i	0.316330	−	0.0928829i
$947$	−9.51456	+	10.9804i	−0.309182	+	0.356815i	−0.888981	−	0.457945i	$-0.848586\pi$
$947$	−9.51456	+	10.9804i	−0.309182	+	0.356815i	0.579799	+	0.814760i	$0.303131\pi$
$948$	−6.24227	−	4.01166i	−0.202739	−	0.130293i
$949$	−7.57248	−	8.73911i	−0.245813	−	0.283684i
$950$	1.99277	+	13.8600i	0.0646540	+	0.449678i
$951$	−19.0489	−	5.59327i	−0.617704	−	0.181374i
$952$	1.53430	−	0.986032i	0.0497268	−	0.0319575i
$953$	4.99130	−	34.7153i	0.161684	−	1.12454i	−0.733775	−	0.679393i	$-0.762243\pi$
$953$	4.99130	−	34.7153i	0.161684	−	1.12454i	0.895459	−	0.445144i	$-0.146848\pi$
$954$	3.32902	−	7.28954i	0.107781	−	0.236008i
$955$	−4.43256	+	9.70595i	−0.143434	+	0.314077i
$956$	−2.48663	+	17.2949i	−0.0804235	+	0.559358i
$957$	−14.8416	+	9.53812i	−0.479761	+	0.308324i
$958$	13.2067	+	3.87783i	0.426688	+	0.125287i
$959$	1.04439	+	7.26391i	0.0337252	+	0.234564i
$960$	0.488484	+	0.563740i	0.0157657	+	0.0181946i
$961$	14.8608	+	9.55044i	0.479380	+	0.308079i
$962$	1.36238	−	1.57227i	0.0439249	−	0.0506920i
$963$	−7.72244	+	2.26751i	−0.248852	+	0.0730695i
$964$	−8.64424	−	18.9282i	−0.278412	−	0.609638i
$965$	−19.6746			−0.633347
$966$	3.53576	+	3.24013i	0.113761	+	0.104249i
$967$	−20.9689			−0.674314			−0.337157	−	0.941448i	$-0.609465\pi$
$967$	−20.9689			−0.674314			−0.337157	+	0.941448i	$0.609465\pi$
$968$	−2.73521	−	5.98928i	−0.0879131	−	0.192503i
$969$	−5.51439	+	1.61917i	−0.177148	+	0.0520153i
$970$	−6.07197	+	7.00742i	−0.194959	+	0.224995i
$971$	51.2095	+	32.9104i	1.64339	+	1.05614i	0.937595	+	0.347730i	$0.113047\pi$
$971$	51.2095	+	32.9104i	1.64339	+	1.05614i	0.705797	+	0.708414i	$0.250589\pi$
$972$	−0.654861	−	0.755750i	−0.0210047	−	0.0242407i
$973$	0.484640	+	3.37074i	0.0155368	+	0.108061i
$974$	34.2864	+	10.0674i	1.09861	+	0.322580i
$975$	−12.3733	+	7.95183i	−0.396263	+	0.254662i
$976$	0.630436	−	4.38478i	0.0201798	−	0.140353i
$977$	−23.9257	+	52.3900i	−0.765452	+	1.67611i	−0.0290347	+	0.999578i	$0.509243\pi$
$977$	−23.9257	+	52.3900i	−0.765452	+	1.67611i	−0.736417	+	0.676528i	$0.763484\pi$
$978$	8.73678	−	19.1309i	0.279371	−	0.611738i
$979$	−2.96771	+	20.6409i	−0.0948484	+	0.659685i
$980$	−0.627520	+	0.403283i	−0.0200454	+	0.0128824i
$981$	1.48097	+	0.434853i	0.0472838	+	0.0138838i
$982$	−3.49191	−	24.2868i	−0.111431	−	0.775022i
$983$	−14.4244	−	16.6467i	−0.460067	−	0.530946i	0.477555	−	0.878602i	$-0.341523\pi$
$983$	−14.4244	−	16.6467i	−0.460067	−	0.530946i	−0.937622	+	0.347656i	$0.886978\pi$
$984$	−4.26037	−	2.73797i	−0.135816	−	0.0872834i
$985$	0.623576	−	0.719645i	0.0198688	−	0.0229298i
$986$	−14.6919	+	4.31393i	−0.467885	+	0.137383i
$987$	3.38803	+	7.41875i	0.107842	+	0.236141i
$988$	10.4304			0.331834
$989$	5.90027	+	22.3776i	0.187618	+	0.711566i
$990$	1.56748			0.0498177
$991$	−7.31638	−	16.0206i	−0.232413	−	0.508912i	0.757111	−	0.653287i	$-0.226610\pi$
$991$	−7.31638	−	16.0206i	−0.232413	−	0.508912i	−0.989523	+	0.144374i	$0.953883\pi$
$992$	−6.69345	+	1.96538i	−0.212517	+	0.0624007i
$993$	−16.6803	+	19.2500i	−0.529332	+	0.610882i
$994$	−4.47243	−	2.87426i	−0.141857	−	0.0911658i
$995$	−1.23808	−	1.42882i	−0.0392499	−	0.0452967i
$996$	1.07659	+	7.48785i	0.0341131	+	0.237262i
$997$	14.5824	+	4.28177i	0.461828	+	0.135605i	0.504366	−	0.863490i	$-0.331726\pi$
$997$	14.5824	+	4.28177i	0.461828	+	0.135605i	−0.0425382	+	0.999095i	$0.513544\pi$
$998$	−16.0968	+	10.3448i	−0.509535	+	0.327458i
$999$	0.0894487	−	0.622129i	0.00283003	−	0.0196833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.211.2	✓	40
23.6	even	11	inner	966.2.q.i.673.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.211.2	✓	40	1.1	even	1	trivial
966.2.q.i.673.2	yes	40	23.6	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)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.627520 - 0.403283i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.627520 - 0.403283i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.106158 - 0.738342i) q^{10} +(-0.872936 + 1.91146i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.471059 + 3.27629i) q^{13} +(0.841254 - 0.540641i) q^{14} +(0.715719 + 0.210154i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.19435 - 1.37835i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-2.06359 + 2.38151i) q^{19} +(0.715719 - 0.210154i) q^{20} +(0.415415 + 0.909632i) q^{21} -2.10136 q^{22} +(0.133298 - 4.79398i) q^{23} +1.00000 q^{24} +(-1.84593 - 4.04202i) q^{25} +(-3.17590 + 0.932529i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(-5.49797 - 6.34500i) q^{29} +(0.106158 + 0.738342i) q^{30} +(-6.69345 - 1.96538i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.299055 - 2.07997i) q^{33} +(0.757643 - 1.65901i) q^{34} +(-0.309873 + 0.678526i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-0.528750 + 0.339807i) q^{37} +(-3.02354 - 0.887791i) q^{38} +(-0.471059 - 3.27629i) q^{39} +(0.488484 + 0.563740i) q^{40} +(-4.26037 - 2.73797i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(-4.63005 + 1.35951i) q^{43} +(-0.872936 - 1.91146i) q^{44} -0.745935 q^{45} +(4.41613 - 1.87024i) q^{46} +8.15577 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(2.90993 - 3.35823i) q^{50} +(1.53430 + 0.986032i) q^{51} +(-2.16758 - 2.50152i) q^{52} +(-1.14047 - 7.93216i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(1.31865 - 0.847442i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(1.30905 - 2.86642i) q^{57} +(3.48767 - 7.63694i) q^{58} +(-0.895939 + 6.23139i) q^{59} +(-0.627520 + 0.403283i) q^{60} +(4.25042 + 1.24804i) q^{61} +(-0.992793 - 6.90503i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(1.61687 - 1.86597i) q^{65} +(2.01624 - 0.592021i) q^{66} +(1.31227 + 2.87347i) q^{67} +1.82382 q^{68} +(1.22272 + 4.63734i) q^{69} -0.745935 q^{70} +(-2.20851 - 4.83595i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(-2.28777 + 2.64023i) q^{73} +(-0.528750 - 0.339807i) q^{74} +(2.90993 + 3.35823i) q^{75} +(-0.448460 - 3.11911i) q^{76} +(2.01624 + 0.592021i) q^{77} +(2.78453 - 1.78951i) q^{78} +(1.05600 - 7.34467i) q^{79} +(-0.309873 + 0.678526i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.720727 - 5.01277i) q^{82} +(-6.36396 + 4.08987i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(0.193613 + 1.34660i) q^{85} +(-3.16004 - 3.64688i) q^{86} +(7.06286 + 4.53902i) q^{87} +(1.37610 - 1.58810i) q^{88} +(9.52166 - 2.79581i) q^{89} +(-0.309873 - 0.678526i) q^{90} +3.30998 q^{91} +(3.53576 + 3.24013i) q^{92} +6.97603 q^{93} +(3.38803 + 7.41875i) q^{94} +(2.25536 - 0.662234i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-10.4570 - 6.72029i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.299055 + 2.07997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more