LMFDB - Embedded newform 966.2.y.b.121.6

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			121.6
Character	$\chi$	$=$	966.121
Dual form			966.2.y.b.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0618096 + 1.29754i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.05626 - 2.42576i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0618096 + 1.29754i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.05626 - 2.42576i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(1.02109 - 0.802998i) q^{10} +(-0.839986 + 1.17960i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.0709830 - 0.493698i) q^{13} +(-1.36328 + 2.26748i) q^{14} +(-1.24640 + 0.365975i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.82416 - 1.12251i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.66793 + 0.899670i) q^{19} +(-1.24640 - 0.365975i) q^{20} +(2.10836 - 1.59838i) q^{21} +1.44811 q^{22} +(0.610413 + 4.75683i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.29756 - 0.314879i) q^{25} +(-0.360980 + 0.344194i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.63781 - 0.204776i) q^{28} +(3.79071 - 4.37471i) q^{29} +(1.02109 + 0.802998i) q^{30} +(-4.72819 - 4.50832i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.34438 - 0.538208i) q^{33} +(2.46397 + 5.39534i) q^{34} +(3.08224 - 1.52048i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.77356 + 3.49201i) q^{37} +(3.44052 + 3.28052i) q^{38} +(0.463046 - 0.185376i) q^{39} +(0.424866 + 1.22757i) q^{40} +(1.87372 - 1.20417i) q^{41} +(-2.52497 - 0.790269i) q^{42} +(-10.0338 - 2.94619i) q^{43} +(-0.839986 - 1.17960i) q^{44} +(-0.649507 - 1.12498i) q^{45} +(3.52072 - 3.25646i) q^{46} +(2.70142 - 4.67899i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-4.76864 + 5.12446i) q^{49} +(-2.16927 - 2.50347i) q^{50} +(-0.282225 - 5.92463i) q^{51} +(0.489761 + 0.0943937i) q^{52} +(-9.62864 + 3.85473i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-1.58250 - 1.01701i) q^{55} +(-1.69689 - 2.02992i) q^{56} +(-1.97482 - 4.32424i) q^{57} +(-5.76236 - 0.550239i) q^{58} +(-2.07163 + 1.62915i) q^{59} +(0.0618096 - 1.29754i) q^{60} +(3.19386 - 13.1653i) q^{61} +(-0.929749 + 6.46655i) q^{62} +(2.05039 + 1.67210i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.636207 - 0.122619i) q^{65} +(0.341405 + 1.40729i) q^{66} +(-6.23227 + 0.595110i) q^{67} +(2.96567 - 5.13669i) q^{68} +(-4.47883 + 1.71467i) q^{69} +(-3.02642 - 1.62876i) q^{70} +(-3.70704 + 8.11729i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(3.09709 - 8.94847i) q^{73} +(6.77356 + 3.49201i) q^{74} +(1.08343 + 3.13037i) q^{75} +(0.676542 - 4.70545i) q^{76} +(3.74866 + 0.791648i) q^{77} +(-0.419596 - 0.269658i) q^{78} +(-8.64564 - 3.46119i) q^{79} +(0.753502 - 1.05815i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-2.06775 - 0.827803i) q^{82} +(11.0748 + 7.11732i) q^{83} +(0.820892 + 2.51518i) q^{84} +(1.09652 - 7.62648i) q^{85} +(3.42028 + 9.88224i) q^{86} +(5.14509 + 2.65248i) q^{87} +(-0.473630 + 1.36847i) q^{88} +(-1.23096 + 1.17372i) q^{89} +(-0.539630 + 1.18163i) q^{90} +(-1.12262 + 0.693660i) q^{91} +(-4.69485 - 0.978964i) q^{92} +(3.26652 - 5.65778i) q^{93} +(-5.37837 + 0.513572i) q^{94} +(-1.45588 - 6.00124i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-4.31185 + 2.77106i) q^{97} +(6.94034 + 0.911938i) q^{98} +(0.206088 - 1.43337i) 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
$5$	0.0618096	+	1.29754i	0.0276421	+	0.580279i	0.969622	+	0.244609i	$0.0786596\pi$
$5$	0.0618096	+	1.29754i	0.0276421	+	0.580279i	−0.941980	+	0.335670i	$0.891037\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−1.05626	−	2.42576i	−0.399228	−	0.916852i
$7$	−1.05626	−	2.42576i	−0.399228	−	0.916852i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	1.02109	−	0.802998i	0.322898	−	0.253930i
$11$	−0.839986	+	1.17960i	−0.253265	+	0.355661i	−0.921560	−	0.388235i	$-0.873085\pi$
$11$	−0.839986	+	1.17960i	−0.253265	+	0.355661i	0.668295	+	0.743896i	$0.267024\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	−0.0709830	−	0.493698i	−0.0196871	−	0.136927i	0.977607	−	0.210438i	$-0.0674889\pi$
$13$	−0.0709830	−	0.493698i	−0.0196871	−	0.136927i	−0.997294	+	0.0735105i	$0.976580\pi$
$14$	−1.36328	+	2.26748i	−0.364351	+	0.606010i
$15$	−1.24640	+	0.365975i	−0.321818	+	0.0944943i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−5.82416	−	1.12251i	−1.41257	−	0.272250i	−0.574806	−	0.818290i	$-0.694923\pi$
$17$	−5.82416	−	1.12251i	−1.41257	−	0.272250i	−0.837759	+	0.546040i	$0.816135\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	−4.66793	+	0.899670i	−1.07090	+	0.206398i	−0.694086	−	0.719892i	$-0.744191\pi$
$19$	−4.66793	+	0.899670i	−1.07090	+	0.206398i	−0.376811	+	0.926290i	$0.622979\pi$
$20$	−1.24640	−	0.365975i	−0.278702	−	0.0818344i
$21$	2.10836	−	1.59838i	0.460082	−	0.348795i
$22$	1.44811			0.308738
$23$	0.610413	+	4.75683i	0.127280	+	0.991867i
$23$	0.610413	+	4.75683i	0.127280	+	0.991867i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	3.29756	−	0.314879i	0.659512	−	0.0629758i
$26$	−0.360980	+	0.344194i	−0.0707940	+	0.0675020i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	2.63781	−	0.204776i	0.498500	−	0.0386991i
$29$	3.79071	−	4.37471i	0.703917	−	0.812364i	−0.285359	−	0.958421i	$-0.592113\pi$
$29$	3.79071	−	4.37471i	0.703917	−	0.812364i	0.989276	+	0.146057i	$0.0466583\pi$
$30$	1.02109	+	0.802998i	0.186426	+	0.146607i
$31$	−4.72819	−	4.50832i	−0.849207	−	0.809718i	0.134233	−	0.990950i	$-0.457143\pi$
$31$	−4.72819	−	4.50832i	−0.849207	−	0.809718i	−0.983440	+	0.181232i	$0.941991\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	−1.34438	−	0.538208i	−0.234026	−	0.0936900i
$34$	2.46397	+	5.39534i	0.422567	+	0.925293i
$35$	3.08224	−	1.52048i	0.520994	−	0.257007i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−6.77356	+	3.49201i	−1.11357	+	0.574084i	−0.913965	−	0.405793i	$-0.866995\pi$
$37$	−6.77356	+	3.49201i	−1.11357	+	0.574084i	−0.199602	+	0.979877i	$0.563965\pi$
$38$	3.44052	+	3.28052i	0.558125	+	0.532171i
$39$	0.463046	−	0.185376i	0.0741467	−	0.0296839i
$40$	0.424866	+	1.22757i	0.0671772	+	0.194096i
$41$	1.87372	−	1.20417i	0.292626	−	0.188059i	−0.386088	−	0.922462i	$-0.626174\pi$
$41$	1.87372	−	1.20417i	0.292626	−	0.188059i	0.678714	+	0.734403i	$0.262538\pi$
$42$	−2.52497	−	0.790269i	−0.389611	−	0.121941i
$43$	−10.0338	−	2.94619i	−1.53014	−	0.449289i	−0.595045	−	0.803692i	$-0.702866\pi$
$43$	−10.0338	−	2.94619i	−1.53014	−	0.449289i	−0.935093	+	0.354403i	$0.884684\pi$
$44$	−0.839986	−	1.17960i	−0.126633	−	0.177831i
$45$	−0.649507	−	1.12498i	−0.0968228	−	0.167702i
$46$	3.52072	−	3.25646i	0.519102	−	0.480139i
$47$	2.70142	−	4.67899i	0.394042	−	0.682501i	−0.598936	−	0.800797i	$-0.704410\pi$
$47$	2.70142	−	4.67899i	0.394042	−	0.682501i	0.992978	+	0.118296i	$0.0377430\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−4.76864	+	5.12446i	−0.681234	+	0.732066i
$50$	−2.16927	−	2.50347i	−0.306781	−	0.354044i
$51$	−0.282225	−	5.92463i	−0.0395194	−	0.829613i
$52$	0.489761	+	0.0943937i	0.0679176	+	0.0130900i
$53$	−9.62864	+	3.85473i	−1.32260	+	0.529487i	−0.922150	−	0.386833i	$-0.873569\pi$
$53$	−9.62864	+	3.85473i	−1.32260	+	0.529487i	−0.400446	+	0.916320i	$0.631145\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	−1.58250	−	1.01701i	−0.213384	−	0.137133i
$56$	−1.69689	−	2.02992i	−0.226756	−	0.271259i
$57$	−1.97482	−	4.32424i	−0.261571	−	0.572760i
$58$	−5.76236	−	0.550239i	−0.756635	−	0.0722499i
$59$	−2.07163	+	1.62915i	−0.269703	+	0.212097i	−0.743846	−	0.668351i	$-0.767000\pi$
$59$	−2.07163	+	1.62915i	−0.269703	+	0.212097i	0.474143	+	0.880448i	$0.342758\pi$
$60$	0.0618096	−	1.29754i	0.00797959	−	0.167512i
$61$	3.19386	−	13.1653i	0.408932	−	1.68564i	−0.279342	−	0.960192i	$-0.590116\pi$
$61$	3.19386	−	13.1653i	0.408932	−	1.68564i	0.688275	−	0.725450i	$-0.258368\pi$
$62$	−0.929749	+	6.46655i	−0.118078	+	0.821252i
$63$	2.05039	+	1.67210i	0.258325	+	0.210664i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	0.636207	−	0.122619i	0.0789117	−	0.0152090i
$66$	0.341405	+	1.40729i	0.0420240	+	0.173225i
$67$	−6.23227	+	0.595110i	−0.761393	+	0.0727042i	−0.468527	−	0.883449i	$-0.655215\pi$
$67$	−6.23227	+	0.595110i	−0.761393	+	0.0727042i	−0.292866	+	0.956153i	$0.594609\pi$
$68$	2.96567	−	5.13669i	0.359641	−	0.622916i
$69$	−4.47883	+	1.71467i	−0.539188	+	0.206422i
$70$	−3.02642	−	1.62876i	−0.361726	−	0.194674i
$71$	−3.70704	+	8.11729i	−0.439945	+	0.963346i	0.551663	+	0.834067i	$0.313993\pi$
$71$	−3.70704	+	8.11729i	−0.439945	+	0.963346i	−0.991608	+	0.129279i	$0.958734\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	3.09709	−	8.94847i	0.362488	−	1.04734i	−0.605393	−	0.795927i	$-0.706984\pi$
$73$	3.09709	−	8.94847i	0.362488	−	1.04734i	0.967880	−	0.251412i	$-0.0808949\pi$
$74$	6.77356	+	3.49201i	0.787411	+	0.405938i
$75$	1.08343	+	3.13037i	0.125104	+	0.361464i
$76$	0.676542	−	4.70545i	0.0776047	−	0.539752i
$77$	3.74866	+	0.791648i	0.427199	+	0.0902167i
$78$	−0.419596	−	0.269658i	−0.0475099	−	0.0305327i
$79$	−8.64564	−	3.46119i	−0.972711	−	0.389415i	−0.169777	−	0.985483i	$-0.554305\pi$
$79$	−8.64564	−	3.46119i	−0.972711	−	0.389415i	−0.802934	+	0.596068i	$0.796729\pi$
$80$	0.753502	−	1.05815i	0.0842441	−	0.118304i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−2.06775	−	0.827803i	−0.228345	−	0.0914155i
$83$	11.0748	+	7.11732i	1.21561	+	0.781228i	0.981589	−	0.191003i	$-0.0611740\pi$
$83$	11.0748	+	7.11732i	1.21561	+	0.781228i	0.234025	+	0.972231i	$0.424810\pi$
$84$	0.820892	+	2.51518i	0.0895667	+	0.274429i
$85$	1.09652	−	7.62648i	0.118935	−	0.827208i
$86$	3.42028	+	9.88224i	0.368818	+	1.06563i
$87$	5.14509	+	2.65248i	0.551611	+	0.284375i
$88$	−0.473630	+	1.36847i	−0.0504892	+	0.145879i
$89$	−1.23096	+	1.17372i	−0.130482	+	0.124414i	−0.752510	−	0.658580i	$-0.771157\pi$
$89$	−1.23096	+	1.17372i	−0.130482	+	0.124414i	0.622029	+	0.782994i	$0.286309\pi$
$90$	−0.539630	+	1.18163i	−0.0568820	+	0.124554i
$91$	−1.12262	+	0.693660i	−0.117682	+	0.0727153i
$92$	−4.69485	−	0.978964i	−0.489472	−	0.102064i
$93$	3.26652	−	5.65778i	0.338723	−	0.586685i
$94$	−5.37837	+	0.513572i	−0.554737	+	0.0529709i
$95$	−1.45588	−	6.00124i	−0.149371	−	0.615714i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	−4.31185	+	2.77106i	−0.437802	+	0.281358i	−0.740918	−	0.671595i	$-0.765609\pi$
$97$	−4.31185	+	2.77106i	−0.437802	+	0.281358i	0.303116	+	0.952954i	$0.401973\pi$
$98$	6.94034	+	0.911938i	0.701081	+	0.0921196i
$99$	0.206088	−	1.43337i	0.0207126	−	0.144059i
$100$	−0.780966	+	3.21918i	−0.0780966	+	0.321918i
$101$	0.561400	−	11.7852i	0.0558614	−	1.17267i	−0.780738	−	0.624859i	$-0.785156\pi$
$101$	0.561400	−	11.7852i	0.0558614	−	1.17267i	0.836599	−	0.547816i	$-0.184541\pi$
$102$	−4.66235	+	3.66651i	−0.461642	+	0.363039i
$103$	10.5504	+	1.00744i	1.03956	+	0.0992658i	0.600849	−	0.799363i	$-0.294829\pi$
$103$	10.5504	+	1.00744i	1.03956	+	0.0992658i	0.438710	+	0.898629i	$0.355436\pi$
$104$	−0.207198	−	0.453701i	−0.0203175	−	0.0444891i
$105$	2.20428	+	2.63689i	0.215116	+	0.257335i
$106$	8.72513	+	5.60730i	0.847459	+	0.544629i
$107$	−2.28521	+	9.41975i	−0.220919	+	0.910642i	0.748086	+	0.663602i	$0.230973\pi$
$107$	−2.28521	+	9.41975i	−0.220919	+	0.910642i	−0.969005	+	0.247040i	$0.920542\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	−18.5907	−	3.58306i	−1.78066	−	0.343195i	−0.810517	−	0.585715i	$-0.800814\pi$
$109$	−18.5907	−	3.58306i	−1.78066	−	0.343195i	−0.970146	+	0.242520i	$0.922026\pi$
$110$	0.0895071	+	1.87899i	0.00853417	+	0.179154i
$111$	−4.99051	−	5.75935i	−0.473678	−	0.546654i
$112$	−0.669231	+	2.55971i	−0.0632364	+	0.241870i
$113$	−1.86380	+	4.08115i	−0.175331	+	0.383922i	−0.976812	−	0.214098i	$-0.931319\pi$
$113$	−1.86380	+	4.08115i	−0.175331	+	0.383922i	0.801481	+	0.598021i	$0.204046\pi$
$114$	−2.37692	+	4.11695i	−0.222619	+	0.385587i
$115$	−6.13446	+	1.08606i	−0.572041	+	0.101275i
$116$	2.89429	+	5.01305i	0.268728	+	0.465450i
$117$	0.289318	+	0.406290i	0.0267474	+	0.0375615i
$118$	2.52873	+	0.742502i	0.232788	+	0.0683528i
$119$	3.42886	+	15.3137i	0.314323	+	1.40380i
$120$	−1.09280	+	0.702300i	−0.0997586	+	0.0641110i
$121$	2.91188	+	8.41332i	0.264716	+	0.764847i
$122$	−12.5767	+	5.03497i	−1.13864	+	0.455845i
$123$	1.61197	+	1.53701i	0.145347	+	0.138588i
$124$	5.80680	−	2.99361i	0.521466	−	0.268835i
$125$	1.53674	+	10.6882i	0.137450	+	0.955984i
$126$	0.172708	−	2.64011i	0.0153861	−	0.235200i
$127$	2.96428	+	6.49087i	0.263038	+	0.575972i	0.994360	−	0.106060i	$-0.0338237\pi$
$127$	2.96428	+	6.49087i	0.263038	+	0.575972i	−0.731322	+	0.682032i	$0.761096\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	0.497582	−	10.4455i	0.0438097	−	0.919678i
$130$	−0.468918	−	0.447113i	−0.0411269	−	0.0392144i
$131$	−10.3564	−	8.14436i	−0.904843	−	0.711576i	0.0530836	−	0.998590i	$-0.483095\pi$
$131$	−10.3564	−	8.14436i	−0.904843	−	0.711576i	−0.957926	+	0.287014i	$0.907337\pi$
$132$	0.948310	−	1.09441i	0.0825398	−	0.0952560i
$133$	7.11293	+	10.3730i	0.616769	+	0.899454i
$134$	4.09983	+	4.73146i	0.354172	+	0.408736i
$135$	0.940141	−	0.896423i	0.0809145	−	0.0771518i
$136$	−5.90449	+	0.563810i	−0.506305	+	0.0483463i
$137$	7.75553	+	13.4330i	0.662599	+	1.14766i	0.979930	+	0.199341i	$0.0638801\pi$
$137$	7.75553	+	13.4330i	0.662599	+	1.14766i	−0.317331	+	0.948315i	$0.602787\pi$
$138$	3.99471	+	2.65374i	0.340052	+	0.225901i
$139$	−16.1168			−1.36701			−0.683503	−	0.729948i	$-0.739544\pi$
$139$	−16.1168			−1.36701			−0.683503	+	0.729948i	$0.739544\pi$
$140$	0.428748	+	3.41002i	0.0362358	+	0.288199i
$141$	5.18398	+	1.52215i	0.436570	+	0.128189i
$142$	8.76245	−	1.68882i	0.735328	−	0.141723i
$143$	0.641988	+	0.330968i	0.0536858	+	0.0276769i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	5.91068	+	4.64821i	0.490855	+	0.386013i
$146$	−9.08570	+	2.66780i	−0.751938	+	0.220789i
$147$	−6.10426	−	3.42608i	−0.503471	−	0.282578i
$148$	−1.08454	−	7.54315i	−0.0891487	−	0.620043i
$149$	21.1784	+	2.02229i	1.73500	+	0.165673i	0.914125	−	0.405432i	$-0.132879\pi$
$149$	21.1784	+	2.02229i	1.73500	+	0.165673i	0.820877	+	0.571105i	$0.193485\pi$
$150$	1.92147	−	2.69833i	0.156888	−	0.220318i
$151$	5.53022	−	4.34901i	0.450043	−	0.353918i	−0.367267	−	0.930115i	$-0.619707\pi$
$151$	5.53022	−	4.34901i	0.450043	−	0.353918i	0.817310	+	0.576198i	$0.195464\pi$
$152$	−4.22538	+	2.17834i	−0.342724	+	0.176686i
$153$	5.69108	−	1.67105i	0.460097	−	0.135097i
$154$	−1.52958	−	3.51277i	−0.123257	−	0.283067i
$155$	5.55749	−	6.41368i	0.446388	−	0.515160i
$156$	0.0237326	+	0.498210i	0.00190013	+	0.0398887i
$157$	−0.587925	+	1.69870i	−0.0469216	+	0.135571i	−0.966027	−	0.258440i	$-0.916792\pi$
$157$	−0.587925	+	1.69870i	−0.0469216	+	0.135571i	0.919106	+	0.394011i	$0.128913\pi$
$158$	2.19556	+	9.05022i	0.174669	+	0.719997i
$159$	−6.01611	−	8.44844i	−0.477108	−	0.670005i
$160$	−1.29901			−0.102696
$161$	10.8942	−	6.50515i	0.858581	−	0.512678i
$162$	−1.00000			−0.0785674
$163$	0.264573	+	0.371540i	0.0207229	+	0.0291013i	0.824807	−	0.565414i	$-0.191283\pi$
$163$	0.264573	+	0.371540i	0.0207229	+	0.0291013i	−0.804085	+	0.594515i	$0.797344\pi$
$164$	0.525105	+	2.16451i	0.0410038	+	0.169020i
$165$	0.615253	−	1.77766i	0.0478974	−	0.138390i
$166$	−0.626397	−	13.1497i	−0.0486178	−	1.02061i
$167$	−6.38534	+	7.36908i	−0.494113	+	0.570236i	−0.946960	−	0.321352i	$-0.895863\pi$
$167$	−6.38534	+	7.36908i	−0.494113	+	0.570236i	0.452847	+	0.891588i	$0.350408\pi$
$168$	1.57264	−	2.12763i	0.121332	−	0.164150i
$169$	12.2347	−	3.59243i	0.941132	−	0.276341i
$170$	−6.84839	+	3.53059i	−0.525248	+	0.270784i
$171$	3.73677	−	2.93863i	0.285758	−	0.224723i
$172$	6.06588	−	8.51833i	0.462519	−	0.649517i
$173$	−0.000180050	0	1.71926e-5i	−1.36889e−5	0	1.30713e-6i	0.0950492	−	0.995473i	$-0.469699\pi$
$173$	−0.000180050	0	1.71926e-5i	−1.36889e−5	0	1.30713e-6i	−0.0950629	+	0.995471i	$0.530305\pi$
$174$	−0.823800	−	5.72965i	−0.0624521	−	0.434364i
$175$	−4.24690	−	7.66650i	−0.321035	−	0.579533i
$176$	1.38945	−	0.407980i	0.104734	−	0.0307526i
$177$	−2.07163	−	1.62915i	−0.155713	−	0.122454i
$178$	1.67011	+	0.321888i	0.125180	+	0.0241265i
$179$	−6.64414	−	3.42529i	−0.496606	−	0.256018i	0.191680	−	0.981457i	$-0.438606\pi$
$179$	−6.64414	−	3.42529i	−0.496606	−	0.256018i	−0.688286	+	0.725439i	$0.741637\pi$
$180$	1.27554	−	0.245840i	0.0950731	−	0.0183238i
$181$	25.2156	+	7.40396i	1.87426	+	0.550332i	0.997602	+	0.0692135i	$0.0220490\pi$
$181$	25.2156	+	7.40396i	1.87426	+	0.550332i	0.876656	+	0.481118i	$0.159769\pi$
$182$	1.21622	+	0.512094i	0.0901522	+	0.0379589i
$183$	13.5472			1.00143
$184$	1.92584	+	4.39217i	0.141975	+	0.323795i
$185$	−4.94971	−	8.57315i	−0.363910	−	0.630311i
$186$	−6.50346	+	0.621005i	−0.476857	+	0.0455343i
$187$	6.21632	−	5.92725i	0.454583	−	0.433444i
$188$	3.53810	+	4.08319i	0.258043	+	0.297797i
$189$	−1.14157	+	2.38680i	−0.0830367	+	0.173614i
$190$	−4.04397	+	4.66699i	−0.293380	+	0.338579i
$191$	5.11345	+	4.02126i	0.369996	+	0.290968i	0.785793	−	0.618489i	$-0.212255\pi$
$191$	5.11345	+	4.02126i	0.369996	+	0.290968i	−0.415797	+	0.909457i	$0.636497\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	−0.732377	+	15.3745i	−0.0527176	+	1.10668i	0.805237	+	0.592953i	$0.202038\pi$
$193$	−0.732377	+	15.3745i	−0.0527176	+	1.10668i	−0.857954	+	0.513726i	$0.828265\pi$
$194$	4.75836	+	1.90496i	0.341630	+	0.136768i
$195$	0.269154	+	0.589365i	0.0192745	+	0.0422053i
$196$	−3.28295	−	6.18241i	−0.234497	−	0.441601i
$197$	0.678120	+	4.71643i	0.0483141	+	0.336032i	0.999614	+	0.0277662i	$0.00883940\pi$
$197$	0.678120	+	4.71643i	0.0483141	+	0.336032i	−0.951300	+	0.308265i	$0.900252\pi$
$198$	−1.28713	+	0.663562i	−0.0914724	+	0.0471573i
$199$	16.4108	+	15.6476i	1.16333	+	1.10923i	0.992286	+	0.123967i	$0.0395617\pi$
$199$	16.4108	+	15.6476i	1.16333	+	1.10923i	0.171042	+	0.985264i	$0.445287\pi$
$200$	3.07528	−	1.23115i	0.217455	−	0.0870558i
$201$	−2.04765	−	5.91629i	−0.144430	−	0.417303i
$202$	−9.92561	+	6.37881i	−0.698364	+	0.448811i
$203$	−14.6160	−	4.57453i	−1.02584	−	0.321069i
$204$	5.69108	+	1.67105i	0.398455	+	0.116997i
$205$	1.67827	+	2.35681i	0.117216	+	0.164607i
$206$	−5.29918	−	9.17845i	−0.369211	−	0.639493i
$207$	−2.72226	−	3.94833i	−0.189210	−	0.274428i
$208$	−0.249387	+	0.431951i	−0.0172919	+	0.0299504i
$209$	2.85975	−	6.26198i	0.197813	−	0.433150i
$210$	0.869341	−	3.32510i	0.0599902	−	0.229454i
$211$	−17.9387	−	20.7024i	−1.23495	−	1.42521i	−0.869171	−	0.494511i	$-0.835347\pi$
$211$	−17.9387	−	20.7024i	−1.23495	−	1.42521i	−0.365782	−	0.930701i	$-0.619198\pi$
$212$	−0.493500	−	10.3598i	−0.0338937	−	0.711516i
$213$	−8.76245	−	1.68882i	−0.600393	−	0.115716i
$214$	8.99866	−	3.60252i	0.615135	−	0.246263i
$215$	3.20262	−	13.2014i	0.218417	−	0.900326i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−5.94191	+	16.2314i	−0.403363	+	1.10186i
$218$	7.86497	+	17.2219i	0.532683	+	1.16641i
$219$	9.42639	+	0.900111i	0.636977	+	0.0608239i
$220$	1.47866	−	1.16283i	0.0996910	−	0.0783979i
$221$	−0.140766	+	2.95505i	−0.00946898	+	0.198778i
$222$	−1.79665	+	7.40590i	−0.120583	+	0.497052i
$223$	3.08686	−	21.4696i	0.206711	−	1.43771i	−0.577082	−	0.816686i	$-0.695809\pi$
$223$	3.08686	−	21.4696i	0.206711	−	1.43771i	0.783793	−	0.621022i	$-0.213282\pi$
$224$	2.47327	−	0.939640i	0.165252	−	0.0627823i
$225$	−2.78670	+	1.79091i	−0.185780	+	0.119394i
$226$	4.40551	−	0.849093i	0.293050	−	0.0564808i
$227$	−3.42083	−	14.1009i	−0.227049	−	0.935907i	−0.965250	−	0.261327i	$-0.915840\pi$
$227$	−3.42083	−	14.1009i	−0.227049	−	0.935907i	0.738202	−	0.674580i	$-0.235675\pi$
$228$	4.73231	−	0.451881i	0.313405	−	0.0299266i
$229$	4.03838	−	6.99468i	0.266864	−	0.462221i	−0.701187	−	0.712978i	$-0.747346\pi$
$229$	4.03838	−	6.99468i	0.266864	−	0.462221i	0.968050	+	0.250757i	$0.0806794\pi$
$230$	4.44301	+	4.36701i	0.292963	+	0.287952i
$231$	0.114447	+	3.82963i	0.00753005	+	0.251971i
$232$	2.40466	−	5.26547i	0.157874	−	0.345695i
$233$	10.4622	−	9.97569i	0.685401	−	0.653529i	−0.265110	−	0.964218i	$-0.585408\pi$
$233$	10.4622	−	9.97569i	0.685401	−	0.653529i	0.950512	+	0.310689i	$0.100560\pi$
$234$	0.163133	−	0.471342i	0.0106643	−	0.0308126i
$235$	6.23817	+	3.21600i	0.406933	+	0.209789i
$236$	−0.861983	−	2.49054i	−0.0561103	−	0.162120i
$237$	1.32534	−	9.21794i	0.0860901	−	0.598770i
$238$	10.4852	−	11.6759i	0.679656	−	0.756834i
$239$	1.22597	+	0.787884i	0.0793015	+	0.0509640i	0.579691	−	0.814837i	$-0.303173\pi$
$239$	1.22597	+	0.787884i	0.0793015	+	0.0509640i	−0.500389	+	0.865801i	$0.666810\pi$
$240$	1.20596	+	0.482795i	0.0778446	+	0.0311643i
$241$	4.00729	−	5.62746i	0.258132	−	0.362496i	−0.665089	−	0.746764i	$-0.731607\pi$
$241$	4.00729	−	5.62746i	0.258132	−	0.362496i	0.923222	+	0.384267i	$0.125546\pi$
$242$	5.16423	−	7.25215i	0.331970	−	0.466186i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	11.3966	+	7.32415i	0.729592	+	0.468880i
$245$	−6.94396	−	5.87077i	−0.443633	−	0.375070i
$246$	0.316978	−	2.20463i	0.0202097	−	0.140562i
$247$	0.775509	+	2.24069i	0.0493444	+	0.142571i
$248$	−5.80680	−	2.99361i	−0.368732	−	0.190095i
$249$	−4.30572	+	12.4406i	−0.272864	+	0.788389i
$250$	7.81498	−	7.45157i	0.494263	−	0.471279i
$251$	0.527118	−	1.15423i	0.0332714	−	0.0728542i	−0.892267	−	0.451509i	$-0.850886\pi$
$251$	0.527118	−	1.15423i	0.0332714	−	0.0728542i	0.925538	+	0.378655i	$0.123613\pi$
$252$	−2.25075	+	1.39073i	−0.141784	+	0.0876077i
$253$	−6.12387	−	3.27563i	−0.385004	−	0.205937i
$254$	3.56786	−	6.17971i	0.223867	−	0.387749i
$255$	7.67001	−	0.732398i	0.480315	−	0.0458645i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	11.4235	−	2.20171i	0.712581	−	0.137339i	0.179937	−	0.983678i	$-0.442411\pi$
$257$	11.4235	−	2.20171i	0.712581	−	0.137339i	0.532644	+	0.846340i	$0.321199\pi$
$258$	−8.79731	+	5.65369i	−0.547697	+	0.351983i
$259$	15.6254	+	12.7426i	0.970917	+	0.791785i
$260$	−0.0922080	+	0.641320i	−0.00571850	+	0.0397730i
$261$	−1.36471	+	5.62540i	−0.0844733	+	0.348204i
$262$	−0.626901	+	13.1603i	−0.0387301	+	0.813044i
$263$	−18.9586	+	14.9092i	−1.16904	+	0.919340i	−0.997827	−	0.0658952i	$-0.979010\pi$
$263$	−18.9586	+	14.9092i	−1.16904	+	0.919340i	−0.171209	+	0.985235i	$0.554767\pi$
$264$	−1.44155	−	0.137652i	−0.0887214	−	0.00847187i
$265$	−5.59682	−	12.2553i	−0.343810	−	0.752838i
$266$	4.32370	−	11.8110i	0.265103	−	0.724176i
$267$	−1.43084	−	0.919548i	−0.0875663	−	0.0562754i
$268$	1.47600	−	6.08414i	0.0901609	−	0.371648i
$269$	−1.87466	+	0.750499i	−0.114300	+	0.0457587i	−0.428107	−	0.903728i	$-0.640820\pi$
$269$	−1.87466	+	0.750499i	−0.114300	+	0.0457587i	0.313808	+	0.949487i	$0.398395\pi$
$270$	−1.27554	−	0.245840i	−0.0776269	−	0.0149614i
$271$	0.892487	+	18.7356i	0.0542148	+	1.13811i	0.848030	+	0.529948i	$0.177789\pi$
$271$	0.892487	+	18.7356i	0.0542148	+	1.13811i	−0.793815	+	0.608159i	$0.791908\pi$
$272$	3.88420	+	4.48261i	0.235514	+	0.271798i
$273$	−0.938774	−	0.927435i	−0.0568172	−	0.0561309i
$274$	6.44352	−	14.1093i	0.389267	−	0.852377i
$275$	−2.39848	+	4.15428i	−0.144634	+	0.250513i
$276$	−0.155484	−	4.79331i	−0.00935904	−	0.288523i
$277$	−6.53582	−	11.3204i	−0.392699	−	0.680175i	0.600105	−	0.799921i	$-0.295125\pi$
$277$	−6.53582	−	11.3204i	−0.392699	−	0.680175i	−0.992805	+	0.119746i	$0.961792\pi$
$278$	9.34864	+	13.1283i	0.560694	+	0.787384i
$279$	6.26841	+	1.84057i	0.375280	+	0.110192i
$280$	2.52902	−	2.32725i	0.151138	−	0.139080i
$281$	22.6528	−	14.5581i	1.35135	−	0.868462i	0.353597	−	0.935398i	$-0.384959\pi$
$281$	22.6528	−	14.5581i	1.35135	−	0.868462i	0.997757	+	0.0669357i	$0.0213222\pi$
$282$	−1.76709	−	5.10568i	−0.105229	−	0.304039i
$283$	−16.3714	+	6.55412i	−0.973179	+	0.389602i	−0.803111	−	0.595830i	$-0.796823\pi$
$283$	−16.3714	+	6.55412i	−0.973179	+	0.389602i	−0.170069	+	0.985432i	$0.554399\pi$
$284$	−6.45839	−	6.15807i	−0.383235	−	0.365414i
$285$	5.48883	−	2.82969i	0.325130	−	0.167616i
$286$	−0.102791	−	0.714928i	−0.00607817	−	0.0422746i
$287$	−4.90016	−	3.27329i	−0.289247	−	0.193216i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	16.8785	+	6.75713i	0.992853	+	0.397478i
$290$	0.357789	−	7.51092i	0.0210101	−	0.441057i
$291$	−3.70950	−	3.53701i	−0.217455	−	0.207343i
$292$	7.44335	+	5.85351i	0.435589	+	0.342551i
$293$	−18.0393	+	20.8184i	−1.05387	+	1.21623i	−0.0782057	+	0.996937i	$0.524919\pi$
$293$	−18.0393	+	20.8184i	−1.05387	+	1.21623i	−0.975660	+	0.219289i	$0.929626\pi$
$294$	0.750017	+	6.95970i	0.0437419	+	0.405898i
$295$	−2.24194	−	2.58733i	−0.130531	−	0.150640i
$296$	−5.51537	+	5.25890i	−0.320574	+	0.305667i
$297$	1.44155	−	0.137652i	0.0836474	−	0.00798736i
$298$	−10.6374	−	18.4245i	−0.616206	−	1.06730i
$299$	2.30510	−	0.639013i	0.133308	−	0.0369551i
$300$	−3.31256			−0.191251
$301$	3.45153	+	27.4515i	0.198943	+	1.58228i
$302$	−6.75044	−	1.98211i	−0.388444	−	0.114058i
$303$	11.5854	−	2.23290i	0.665563	−	0.128277i
$304$	4.22538	+	2.17834i	0.242342	+	0.124936i
$305$	17.2799	+	3.33043i	0.989446	+	0.190700i
$306$	−4.66235	−	3.66651i	−0.266529	−	0.209601i
$307$	−10.4548	+	3.06980i	−0.596686	+	0.175203i	−0.566110	−	0.824330i	$-0.691552\pi$
$307$	−10.4548	+	3.06980i	−0.596686	+	0.175203i	−0.0305760	+	0.999532i	$0.509734\pi$
$308$	−1.97417	+	3.28356i	−0.112489	+	0.187098i
$309$	1.50830	+	10.4905i	0.0858044	+	0.596783i
$310$	−8.44809	−	0.806695i	−0.479819	−	0.0458172i
$311$	8.39044	−	11.7827i	0.475778	−	0.668137i	−0.505033	−	0.863100i	$-0.668520\pi$
$311$	8.39044	−	11.7827i	0.475778	−	0.668137i	0.980810	+	0.194964i	$0.0624589\pi$
$312$	0.392063	−	0.308322i	0.0221962	−	0.0174553i
$313$	7.32081	−	3.77414i	0.413797	−	0.213327i	−0.238741	−	0.971083i	$-0.576735\pi$
$313$	7.32081	−	3.77414i	0.413797	−	0.213327i	0.652538	+	0.757756i	$0.273704\pi$
$314$	1.72475	−	0.506432i	0.0973332	−	0.0285796i
$315$	−2.04288	+	2.76382i	−0.115104	+	0.155724i
$316$	6.09854	−	7.03810i	0.343070	−	0.395924i
$317$	1.42197	+	29.8509i	0.0798660	+	1.67659i	0.583067	+	0.812424i	$0.301852\pi$
$317$	1.42197	+	29.8509i	0.0798660	+	1.67659i	−0.503202	+	0.864169i	$0.667845\pi$
$318$	−3.39221	+	9.80115i	−0.190226	+	0.549621i
$319$	1.97625	+	8.14620i	0.110649	+	0.456100i
$320$	0.753502	+	1.05815i	0.0421221	+	0.0591522i
$321$	−9.69298			−0.541010
$322$	−11.6182	−	5.10077i	−0.647456	−	0.284255i
$323$	28.1967			1.56890
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−0.389526	−	1.60565i	−0.0216070	−	0.0890653i
$326$	0.149181	−	0.431029i	0.00826235	−	0.0238725i
$327$	−0.900859	−	18.9114i	−0.0498176	−	1.04580i
$328$	1.45857	−	1.68328i	0.0805360	−	0.0929436i
$329$	−14.2035	−	1.61077i	−0.783065	−	0.0888046i
$330$	−1.80492	+	0.529972i	−0.0993574	+	0.0291740i
$331$	−14.6012	+	7.52744i	−0.802554	+	0.413745i	−0.810148	−	0.586226i	$-0.800613\pi$
$331$	−14.6012	+	7.52744i	−0.802554	+	0.413745i	0.00759374	+	0.999971i	$0.497583\pi$
$332$	−10.3481	+	8.13782i	−0.567925	+	0.446621i
$333$	4.42045	−	6.20765i	0.242239	−	0.340177i
$334$	9.70653	+	0.926862i	0.531118	+	0.0507156i
$335$	−1.15739	−	8.04986i	−0.0632352	−	0.439811i
$336$	−2.64534	−	0.0468913i	−0.144315	−	0.00255813i
$337$	27.3370	−	8.02686i	1.48914	−	0.437251i	0.566874	−	0.823805i	$-0.308153\pi$
$337$	27.3370	−	8.02686i	1.48914	−	0.437251i	0.922267	+	0.386554i	$0.126335\pi$
$338$	−10.0231	−	7.88228i	−0.545187	−	0.428740i
$339$	−4.40551	−	0.849093i	−0.239275	−	0.0461164i
$340$	6.84839	+	3.53059i	0.371406	+	0.191473i
$341$	9.28960	−	1.79042i	0.503060	−	0.0969569i
$342$	−4.56128	−	1.33931i	−0.246646	−	0.0724217i
$343$	17.4676	+	6.15482i	0.943164	+	0.332329i
$344$	−10.4574			−0.563824
$345$	−2.50169	−	5.70549i	−0.134687	−	0.307173i
$346$	9.04343e−5	0	0.000156637i	4.86178e−6	0	8.42084e-6i
$347$	−11.4684	+	1.09510i	−0.615657	+	0.0587881i	−0.398226	−	0.917287i	$-0.630374\pi$
$347$	−11.4684	+	1.09510i	−0.615657	+	0.0587881i	−0.217431	+	0.976076i	$0.569768\pi$
$348$	−4.18939	+	3.99457i	−0.224575	+	0.214132i
$349$	4.79828	+	5.53751i	0.256846	+	0.296416i	0.869498	−	0.493937i	$-0.164443\pi$
$349$	4.79828	+	5.53751i	0.256846	+	0.296416i	−0.612652	+	0.790353i	$0.709897\pi$
$350$	−3.78151	+	7.90643i	−0.202130	+	0.422616i
$351$	−0.326628	+	0.376949i	−0.0174341	+	0.0201200i
$352$	−1.13829	−	0.895162i	−0.0606711	−	0.0477123i
$353$	−14.6037	−	13.9246i	−0.777277	−	0.741132i	0.193504	−	0.981099i	$-0.438015\pi$
$353$	−14.6037	−	13.9246i	−0.777277	−	0.741132i	−0.970781	+	0.239967i	$0.922863\pi$
$354$	−0.125401	+	2.63250i	−0.00666501	+	0.139916i
$355$	−10.7617	−	4.30832i	−0.571170	−	0.228662i
$356$	−0.706558	−	1.54715i	−0.0374475	−	0.0819986i
$357$	−14.0736	+	6.94254i	−0.744855	+	0.367438i
$358$	1.06382	+	7.39902i	0.0562245	+	0.391050i
$359$	−31.4511	+	16.2142i	−1.65992	+	0.855750i	−0.665967	+	0.745981i	$0.731981\pi$
$359$	−31.4511	+	16.2142i	−1.65992	+	0.855750i	−0.993957	+	0.109769i	$0.964989\pi$
$360$	−0.940141	−	0.896423i	−0.0495498	−	0.0472456i
$361$	3.34119	−	1.33761i	0.175852	−	0.0704005i
$362$	−8.59537	−	24.8347i	−0.451763	−	1.30528i
$363$	−7.48966	+	4.81331i	−0.393105	+	0.252633i
$364$	−0.288338	−	1.28775i	−0.0151130	−	0.0674963i
$365$	11.8025	+	3.46551i	0.617769	+	0.181393i
$366$	−7.85812	−	11.0352i	−0.410751	−	0.576818i
$367$	7.99089	+	13.8406i	0.417121	+	0.722475i	0.995649	−	0.0931878i	$-0.0297057\pi$
$367$	7.99089	+	13.8406i	0.417121	+	0.722475i	−0.578527	+	0.815663i	$0.696372\pi$
$368$	2.46066	−	4.11645i	0.128271	−	0.214585i
$369$	−1.11365	+	1.92890i	−0.0579742	+	0.100414i
$370$	−4.11237	+	9.00483i	−0.213792	+	0.468139i
$371$	19.5210	+	19.2852i	1.01348	+	1.00124i
$372$	4.27823	+	4.93735i	0.221816	+	0.255989i
$373$	0.0814307	+	1.70944i	0.00421632	+	0.0885115i	0.999995	−	0.00327944i	$-0.00104388\pi$
$373$	0.0814307	+	1.70944i	0.00421632	+	0.0885115i	−0.995778	+	0.0917909i	$0.970741\pi$
$374$	−8.43402	−	1.62552i	−0.436113	−	0.0840538i
$375$	−10.0246	+	4.01326i	−0.517670	+	0.207244i
$376$	1.27377	−	5.25054i	0.0656895	−	0.270776i
$377$	−2.42886	−	1.56093i	−0.125093	−	0.0803922i
$378$	2.60641	−	0.454589i	0.134059	−	0.0233815i
$379$	−4.25040	−	9.30708i	−0.218329	−	0.478073i	0.768499	−	0.639852i	$-0.221004\pi$
$379$	−4.25040	−	9.30708i	−0.218329	−	0.478073i	−0.986827	+	0.161779i	$0.948277\pi$
$380$	6.14735	+	0.587000i	0.315352	+	0.0301125i
$381$	−5.60905	+	4.41101i	−0.287360	+	0.225983i
$382$	0.309531	−	6.49785i	0.0158370	−	0.332459i
$383$	−1.08945	+	4.49079i	−0.0556685	+	0.229469i	−0.992849	−	0.119376i	$-0.961911\pi$
$383$	−1.08945	+	4.49079i	−0.0556685	+	0.229469i	0.937181	+	0.348844i	$0.113426\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−0.795495	+	4.91298i	−0.0405422	+	0.250389i
$386$	12.9485	−	8.32150i	0.659061	−	0.423553i
$387$	10.2684	−	1.97907i	0.521972	−	0.100602i
$388$	−1.20838	−	4.98103i	−0.0613464	−	0.252873i
$389$	7.30542	−	0.697583i	0.370400	−	0.0353689i	0.0918033	−	0.995777i	$-0.470737\pi$
$389$	7.30542	−	0.697583i	0.370400	−	0.0353689i	0.278596	+	0.960408i	$0.410131\pi$
$390$	0.323958	−	0.561111i	0.0164042	−	0.0284130i
$391$	1.78446	−	28.3897i	0.0902442	−	1.43573i
$392$	−3.13175	+	6.26036i	−0.158177	+	0.316196i
$393$	5.47317	−	11.9846i	0.276085	−	0.604542i
$394$	3.44854	−	3.28818i	0.173735	−	0.165656i
$395$	3.95667	−	11.4320i	0.199081	−	0.575208i
$396$	1.28713	+	0.663562i	0.0646808	+	0.0333453i
$397$	6.13985	+	17.7399i	0.308150	+	0.890341i	0.987651	+	0.156667i	$0.0500750\pi$
$397$	6.13985	+	17.7399i	0.308150	+	0.890341i	−0.679501	+	0.733674i	$0.737804\pi$
$398$	3.22701	−	22.4443i	0.161755	−	1.12503i
$399$	−8.40367	+	9.35795i	−0.420710	+	0.468484i
$400$	−2.78670	−	1.79091i	−0.139335	−	0.0895453i
$401$	13.1902	+	5.28055i	0.658686	+	0.263698i	0.676832	−	0.736137i	$-0.263352\pi$
$401$	13.1902	+	5.28055i	0.658686	+	0.263698i	−0.0181464	+	0.999835i	$0.505776\pi$
$402$	−3.63152	+	5.09975i	−0.181124	+	0.254352i
$403$	−1.89012	+	2.65431i	−0.0941538	+	0.132221i
$404$	10.9534	+	4.38510i	0.544954	+	0.218167i
$405$	1.09280	+	0.702300i	0.0543017	+	0.0348976i
$406$	4.75179	+	14.5593i	0.235828	+	0.722566i
$407$	1.57053	−	10.9233i	0.0778485	−	0.541448i
$408$	−1.93995	−	5.60512i	−0.0960420	−	0.277495i
$409$	7.15642	+	3.68939i	0.353862	+	0.182429i	0.625987	−	0.779833i	$-0.284696\pi$
$409$	7.15642	+	3.68939i	0.353862	+	0.182429i	−0.272125	+	0.962262i	$0.587726\pi$
$410$	0.946303	−	2.73416i	0.0467346	−	0.135031i
$411$	−11.2259	+	10.7039i	−0.553732	+	0.527982i
$412$	−4.40272	+	9.64060i	−0.216906	+	0.474959i
$413$	6.14010	+	3.30448i	0.302135	+	0.162603i
$414$	−1.63715	+	4.50774i	−0.0804614	+	0.221543i
$415$	−8.55051	+	14.8099i	−0.419728	+	0.726990i
$416$	0.496516	−	0.0474115i	0.0243437	−	0.00232454i
$417$	−3.79967	−	15.6625i	−0.186071	−	0.766994i
$418$	−6.75968	+	1.30282i	−0.330627	+	0.0637231i
$419$	8.13677	−	5.22918i	0.397507	−	0.255462i	−0.326582	−	0.945169i	$-0.605897\pi$
$419$	8.13677	−	5.22918i	0.397507	−	0.255462i	0.724089	+	0.689707i	$0.242261\pi$
$420$	−3.21282	+	1.22061i	−0.156769	+	0.0595595i
$421$	0.263342	−	1.83158i	0.0128345	−	0.0892660i	−0.982397	−	0.186803i	$-0.940187\pi$
$421$	0.263342	−	1.83158i	0.0128345	−	0.0892660i	0.995232	+	0.0975371i	$0.0310965\pi$
$422$	−6.45819	+	26.6210i	−0.314380	+	1.29589i
$423$	−0.257077	+	5.39672i	−0.0124995	+	0.262397i
$424$	−8.15261	+	6.41128i	−0.395926	+	0.311360i
$425$	−19.5590	−	1.86766i	−0.948749	−	0.0905946i
$426$	3.70704	+	8.11729i	0.179607	+	0.393284i
$427$	−35.3094	+	6.15839i	−1.70874	+	0.298025i
$428$	−8.15426	−	5.24042i	−0.394151	−	0.253305i
$429$	−0.170284	+	0.701920i	−0.00822139	+	0.0338890i
$430$	−12.6112	+	5.04877i	−0.608167	+	0.243473i
$431$	8.87435	+	1.71039i	0.427463	+	0.0823867i	0.398445	−	0.917192i	$-0.369550\pi$
$431$	8.87435	+	1.71039i	0.427463	+	0.0823867i	0.0290176	+	0.999579i	$0.490762\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	−16.6217	−	19.1824i	−0.798786	−	0.921848i	0.199528	−	0.979892i	$-0.436059\pi$
$433$	−16.6217	−	19.1824i	−0.798786	−	0.921848i	−0.998314	+	0.0580438i	$0.981514\pi$
$434$	16.6684	−	4.57500i	0.800107	−	0.219607i
$435$	−3.12369	+	6.83992i	−0.149769	+	0.327949i
$436$	9.46641	−	16.3963i	0.453359	−	0.785240i
$437$	−7.12894	−	21.6554i	−0.341023	−	1.03592i
$438$	−4.73463	−	8.20063i	−0.226230	−	0.391841i
$439$	−5.03924	−	7.07662i	−0.240510	−	0.337749i	0.676624	−	0.736329i	$-0.263442\pi$
$439$	−5.03924	−	7.07662i	−0.240510	−	0.337749i	−0.917133	+	0.398580i	$0.869503\pi$
$440$	−1.80492	−	0.529972i	−0.0860461	−	0.0252654i
$441$	1.89037	−	6.73992i	0.0900176	−	0.320949i
$442$	2.48877	−	1.59943i	0.118379	−	0.0760773i
$443$	0.718944	+	2.07725i	0.0341581	+	0.0986933i	0.960791	−	0.277275i	$-0.0894313\pi$
$443$	0.718944	+	2.07725i	0.0341581	+	0.0986933i	−0.926632	+	0.375968i	$0.877310\pi$
$444$	7.07483	−	2.83233i	0.335757	−	0.134417i
$445$	−1.59904	−	1.52468i	−0.0758016	−	0.0722767i
$446$	−19.2791	+	9.93909i	−0.912894	+	0.470630i
$447$	3.02771	+	21.0582i	0.143206	+	0.996018i
$448$	−2.20005	−	1.46962i	−0.103942	−	0.0694332i
$449$	−10.9332	−	23.9404i	−0.515970	−	1.12982i	−0.970943	−	0.239312i	$-0.923078\pi$
$449$	−10.9332	−	23.9404i	−0.515970	−	1.12982i	0.454973	−	0.890505i	$-0.349649\pi$
$450$	3.07528	+	1.23115i	0.144970	+	0.0580372i
$451$	−0.153469	+	3.22172i	−0.00722659	+	0.151705i
$452$	−3.24710	−	3.09610i	−0.152731	−	0.145628i
$453$	5.53022	+	4.34901i	0.259832	+	0.204334i
$454$	−9.50195	+	10.9658i	−0.445949	+	0.514652i
$455$	−0.969443	−	1.41377i	−0.0454482	−	0.0662785i
$456$	−3.11310	−	3.59271i	−0.145784	−	0.168244i
$457$	−14.5809	+	13.9028i	−0.682064	+	0.650347i	−0.949696	−	0.313175i	$-0.898608\pi$
$457$	−14.5809	+	13.9028i	−0.682064	+	0.650347i	0.267632	+	0.963521i	$0.413759\pi$
$458$	−8.04018	+	0.767744i	−0.375693	+	0.0358743i
$459$	2.96567	+	5.13669i	0.138426	+	0.239760i
$460$	0.980062	−	6.15228i	0.0456956	−	0.286852i
$461$	11.3825			0.530137			0.265068	−	0.964230i	$-0.414605\pi$
$461$	11.3825			0.530137			0.265068	+	0.964230i	$0.414605\pi$
$462$	3.05314	−	2.31463i	0.142045	−	0.107686i
$463$	12.9485	+	3.80202i	0.601767	+	0.176695i	0.568405	−	0.822749i	$-0.307561\pi$
$463$	12.9485	+	3.80202i	0.601767	+	0.176695i	0.0333614	+	0.999443i	$0.489379\pi$
$464$	−5.68397	+	1.09549i	−0.263872	+	0.0508571i
$465$	7.54312	+	3.88875i	0.349804	+	0.180336i
$466$	−14.1946	−	2.73579i	−0.657553	−	0.126733i
$467$	−19.1420	−	15.0535i	−0.885788	−	0.696591i	0.0678024	−	0.997699i	$-0.478401\pi$
$467$	−19.1420	−	15.0535i	−0.885788	−	0.696591i	−0.953590	+	0.301108i	$0.902644\pi$
$468$	−0.478571	+	0.140521i	−0.0221219	+	0.00649559i
$469$	8.02648	+	14.4894i	0.370628	+	0.669059i
$470$	−0.998817	−	6.94693i	−0.0460720	−	0.320438i
$471$	−1.78942	−	0.170869i	−0.0824523	−	0.00787324i
$472$	−1.52873	+	2.14680i	−0.0703656	+	0.0988146i
$473$	11.9035	−	9.36105i	0.547326	−	0.430422i
$474$	−8.27749	+	4.26734i	−0.380198	+	0.196006i
$475$	−15.1095	+	4.43655i	−0.693272	+	0.203563i
$476$	−15.5929	−	1.76834i	−0.714700	−	0.0810515i
$477$	6.79194	−	7.83832i	0.310982	−	0.358892i
$478$	−0.0693418	−	1.45566i	−0.00317162	−	0.0665805i
$479$	−3.23864	+	9.35745i	−0.147977	+	0.427553i	−0.994492	−	0.104813i	$-0.966576\pi$
$479$	−3.23864	+	9.35745i	−0.147977	+	0.427553i	0.846515	+	0.532366i	$0.178697\pi$
$480$	−0.306254	−	1.26240i	−0.0139785	−	0.0576203i
$481$	2.20481	+	3.09622i	0.100531	+	0.141175i
$482$	−6.90845			−0.314671
$483$	8.89018	+	9.05343i	0.404517	+	0.411945i
$484$	−8.90298			−0.404681
$485$	−3.86208	−	5.42354i	−0.175368	−	0.246270i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	−2.19647	+	6.34628i	−0.0995315	+	0.287577i	−0.983763	−	0.179471i	$-0.942561\pi$
$487$	−2.19647	+	6.34628i	−0.0995315	+	0.287577i	0.884232	+	0.467048i	$0.154683\pi$
$488$	−0.644600	−	13.5318i	−0.0291797	−	0.612556i
$489$	−0.298692	+	0.344709i	−0.0135073	+	0.0155883i
$490$	−0.754299	+	9.06176i	−0.0340757	+	0.409369i
$491$	−32.7419	+	9.61388i	−1.47762	+	0.433869i	−0.918568	−	0.395264i	$-0.870653\pi$
$491$	−32.7419	+	9.61388i	−1.47762	+	0.433869i	−0.559053	+	0.829132i	$0.688835\pi$
$492$	−1.97970	+	1.02061i	−0.0892518	+	0.0460125i
$493$	−26.9884	+	21.2239i	−1.21549	+	0.955876i
$494$	1.37537	−	1.93144i	0.0618808	−	0.0868994i
$495$	1.87260	+	0.178811i	0.0841670	+	0.00803698i
$496$	0.929749	+	6.46655i	0.0417470	+	0.290357i
$497$	23.6062	+	0.418445i	1.05888	+	0.0187698i
$498$	12.6313	−	3.70890i	0.566024	−	0.166200i
$499$	−15.0016	−	11.7974i	−0.671566	−	0.528125i	0.223137	−	0.974787i	$-0.428370\pi$
$499$	−15.0016	−	11.7974i	−0.671566	−	0.528125i	−0.894703	+	0.446662i	$0.852613\pi$
$500$	−10.6030	−	2.04356i	−0.474181	−	0.0913908i
$501$	−8.66675	−	4.46802i	−0.387202	−	0.199617i
$502$	−1.24596	+	0.240140i	−0.0556101	+	0.0107180i
$503$	−17.0437	−	5.00447i	−0.759940	−	0.223138i	−0.121270	−	0.992620i	$-0.538697\pi$
$503$	−17.0437	−	5.00447i	−0.759940	−	0.223138i	−0.638670	+	0.769481i	$0.720515\pi$
$504$	2.43842	+	1.02670i	0.108616	+	0.0457330i
$505$	15.3266			0.682023
$506$	0.883945	+	6.88841i	0.0392962	+	0.306227i
$507$	6.37561	+	11.0429i	0.283151	+	0.490432i
$508$	−7.10340	+	0.678293i	−0.315162	+	0.0300944i
$509$	−20.9004	+	19.9285i	−0.926394	+	0.883315i	−0.993431	−	0.114435i	$-0.963494\pi$
$509$	−20.9004	+	19.9285i	−0.926394	+	0.883315i	0.0670363	+	0.997751i	$0.478646\pi$
$510$	−5.04564	−	5.82298i	−0.223425	−	0.257846i
$511$	−24.9782	+	1.93908i	−1.10497	+	0.0857799i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	3.73677	+	2.93863i	0.164982	+	0.129744i
$514$	−8.41976	−	8.02822i	−0.371380	−	0.354110i
$515$	−0.655080	+	13.7518i	−0.0288663	+	0.605978i
$516$	9.70830	+	3.88662i	0.427384	+	0.171099i
$517$	3.25017	+	7.11687i	0.142942	+	0.313000i
$518$	1.31616	−	20.1195i	0.0578288	−	0.884001i
$519$	−2.57403e−5	0	0.000179028i	−1.12987e−6	0	7.85844e-6i
$520$	0.575890	−	0.296892i	0.0252545	−	0.0130196i
$521$	−6.65957	−	6.34988i	−0.291761	−	0.278193i	0.530035	−	0.847976i	$-0.322179\pi$
$521$	−6.65957	−	6.34988i	−0.291761	−	0.278193i	−0.821795	+	0.569783i	$0.807027\pi$
$522$	5.37393	−	2.15140i	0.235210	−	0.0941640i
$523$	2.33213	+	6.73823i	0.101977	+	0.294642i	0.984435	−	0.175748i	$-0.0562343\pi$
$523$	2.33213	+	6.73823i	0.101977	+	0.294642i	−0.882458	+	0.470390i	$0.844113\pi$
$524$	11.0837	−	7.12305i	0.484193	−	0.311172i
$525$	6.44915	−	5.93463i	0.281464	−	0.259009i
$526$	23.1417	+	6.79502i	1.00903	+	0.296277i
$527$	22.4771	+	31.5646i	0.979116	+	1.37498i
$528$	0.724055	+	1.25410i	0.0315104	+	0.0545777i
$529$	−22.2548	+	5.80726i	−0.967600	+	0.252490i
$530$	−6.73642	+	11.6678i	−0.292611	+	0.506818i
$531$	1.09482	−	2.39732i	0.0475111	−	0.104035i
$532$	−12.1289	+	3.32904i	−0.525855	+	0.144332i
$533$	−0.727497	−	0.839577i	−0.0315114	−	0.0363661i
$534$	0.0809296	+	1.69892i	0.00350217	+	0.0735195i
$535$	−12.3638	−	2.38292i	−0.534533	−	0.103023i
$536$	−5.81216	+	2.32684i	−0.251047	+	0.100504i
$537$	1.76232	−	7.26439i	0.0760498	−	0.313482i
$538$	1.69875	+	1.09172i	0.0732381	+	0.0470673i
$539$	−2.03920	−	9.92954i	−0.0878347	−	0.427696i
$540$	0.539630	+	1.18163i	0.0232220	+	0.0508491i
$541$	19.8113	+	1.89175i	0.851753	+	0.0813325i	0.511794	−	0.859108i	$-0.328981\pi$
$541$	19.8113	+	1.89175i	0.851753	+	0.0813325i	0.339958	+	0.940440i	$0.389587\pi$
$542$	14.7439	−	11.5947i	0.633304	−	0.498036i
$543$	−1.25046	+	26.2503i	−0.0536622	+	1.12651i
$544$	1.39837	−	5.76415i	0.0599545	−	0.247136i
$545$	3.50009	−	24.3437i	0.149927	−	1.04277i
$546$	−0.210924	+	1.30267i	−0.00902671	+	0.0557490i
$547$	5.99137	−	3.85042i	0.256173	−	0.164632i	−0.406251	−	0.913761i	$-0.633164\pi$
$547$	5.99137	−	3.85042i	0.256173	−	0.164632i	0.662424	+	0.749129i	$0.269528\pi$
$548$	−15.2307	+	2.93549i	−0.650625	+	0.125398i
$549$	3.19386	+	13.1653i	0.136311	+	0.561881i
$550$	4.77523	−	0.455979i	0.203617	−	0.0194430i
$551$	−13.7590	+	23.8312i	−0.586152	+	1.01525i
$552$	−3.81433	+	2.90705i	−0.162348	+	0.123732i
$553$	0.736003	+	24.6282i	0.0312980	+	1.04730i
$554$	−5.43015	+	11.8904i	−0.230705	+	0.505174i
$555$	7.16455	−	6.83138i	0.304118	−	0.289976i
$556$	5.27127	−	15.2303i	0.223552	−	0.645911i
$557$	−21.0761	−	10.8655i	−0.893024	−	0.460386i	−0.0503013	−	0.998734i	$-0.516018\pi$
$557$	−21.0761	−	10.8655i	−0.893024	−	0.460386i	−0.842722	+	0.538348i	$0.819048\pi$
$558$	−2.13675	−	6.17373i	−0.0904558	−	0.261355i
$559$	−0.742296	+	5.16279i	−0.0313958	+	0.218363i
$560$	−3.36270	−	0.710141i	−0.142100	−	0.0300090i
$561$	7.22573	+	4.64369i	0.305070	+	0.196057i
$562$	−24.9986	−	10.0079i	−1.05450	−	0.422159i
$563$	−1.84612	+	2.59251i	−0.0778045	+	0.109261i	−0.851644	−	0.524120i	$-0.824394\pi$
$563$	−1.84612	+	2.59251i	−0.0778045	+	0.109261i	0.773840	+	0.633381i	$0.218334\pi$
$564$	−3.13395	+	4.40102i	−0.131963	+	0.185316i
$565$	−5.41067	−	2.16610i	−0.227628	−	0.0911287i
$566$	14.8352	+	9.53399i	0.623569	+	0.400744i
$567$	−2.58866	−	0.546677i	−0.108713	−	0.0229583i
$568$	−1.26998	+	8.83288i	−0.0532870	+	0.370619i
$569$	1.71894	+	4.96654i	0.0720615	+	0.208208i	0.975280	−	0.220973i	$-0.0709233\pi$
$569$	1.71894	+	4.96654i	0.0720615	+	0.208208i	−0.903218	+	0.429181i	$0.858802\pi$
$570$	−5.48883	−	2.82969i	−0.229902	−	0.118523i
$571$	5.47706	−	15.8249i	0.229208	−	0.662253i	−0.770485	−	0.637458i	$-0.779986\pi$
$571$	5.47706	−	15.8249i	0.229208	−	0.662253i	0.999693	−	0.0247941i	$-0.00789303\pi$
$572$	−0.522739	+	0.498430i	−0.0218568	+	0.0208404i
$573$	−2.70237	+	5.91736i	−0.112893	+	0.247201i
$574$	0.176028	+	5.89025i	0.00734725	+	0.245854i
$575$	3.51070	+	15.4937i	0.146406	+	0.646133i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.52441	+	0.813983i	−0.354876	+	0.0338865i	−0.270972	−	0.962587i	$-0.587345\pi$
$577$	−8.52441	+	0.813983i	−0.354876	+	0.0338865i	−0.0839042	+	0.996474i	$0.526739\pi$
$578$	−4.28629	−	17.6683i	−0.178286	−	0.734906i
$579$	−15.1138	+	2.91294i	−0.628106	+	0.121058i
$580$	−6.32576	+	4.06532i	−0.262663	+	0.168803i
$581$	5.56711	−	34.3825i	0.230963	−	1.42643i
$582$	−0.729436	+	5.07334i	−0.0302361	+	0.210297i
$583$	3.54091	−	14.5958i	0.146649	−	0.604497i
$584$	0.450566	−	9.45854i	0.0186446	−	0.391397i
$585$	−0.509296	+	0.400515i	−0.0210568	+	0.0165592i
$586$	27.4220	+	2.61848i	1.13279	+	0.108169i
$587$	−15.3245	−	33.5560i	−0.632510	−	1.38500i	−0.906061	−	0.423147i	$-0.860925\pi$
$587$	−15.3245	−	33.5560i	−0.632510	−	1.38500i	0.273551	−	0.961858i	$-0.411802\pi$
$588$	5.23415	−	4.64797i	0.215853	−	0.191679i
$589$	26.1269	+	16.7907i	1.07654	+	0.691849i
$590$	−0.807129	+	3.32703i	−0.0332290	+	0.136972i
$591$	−4.42361	+	1.77095i	−0.181963	+	0.0728470i
$592$	7.48300	+	1.44223i	0.307549	+	0.0592753i
$593$	0.244964	+	5.14243i	0.0100595	+	0.211174i	0.998301	+	0.0582719i	$0.0185590\pi$
$593$	0.244964	+	5.14243i	0.0100595	+	0.211174i	−0.988241	+	0.152903i	$0.951138\pi$
$594$	−0.948310	−	1.09441i	−0.0389096	−	0.0449041i
$595$	−19.6582	+	5.39563i	−0.805909	+	0.221199i
$596$	−8.83784	+	19.3522i	−0.362012	+	0.792696i
$597$	−11.3376	+	19.6372i	−0.464016	+	0.803698i
$598$	−1.85762	−	1.50702i	−0.0759636	−	0.0616266i
$599$	17.8913	+	30.9886i	0.731018	+	1.26616i	0.956448	+	0.291901i	$0.0942879\pi$
$599$	17.8913	+	30.9886i	0.731018	+	1.26616i	−0.225430	+	0.974259i	$0.572379\pi$
$600$	1.92147	+	2.69833i	0.0784438	+	0.110159i
$601$	−4.27193	−	1.25435i	−0.174255	−	0.0511660i	0.193441	−	0.981112i	$-0.438035\pi$
$601$	−4.27193	−	1.25435i	−0.174255	−	0.0511660i	−0.367696	+	0.929946i	$0.619853\pi$
$602$	20.3593	−	18.7350i	0.829781	−	0.763580i
$603$	5.26677	−	3.38475i	0.214479	−	0.137838i
$604$	2.30106	+	6.64849i	0.0936289	+	0.270523i
$605$	−10.7367	+	4.29831i	−0.436508	+	0.174751i
$606$	−8.53905	−	8.14197i	−0.346875	−	0.330745i
$607$	−38.2394	+	19.7138i	−1.55209	+	0.800157i	−0.999447	−	0.0332611i	$-0.989411\pi$
$607$	−38.2394	+	19.7138i	−1.55209	+	0.800157i	−0.552642	+	0.833419i	$0.686380\pi$
$608$	−0.676542	−	4.70545i	−0.0274374	−	0.190831i
$609$	0.999735	−	15.2825i	0.0405113	−	0.619277i
$610$	−7.31045	−	16.0077i	−0.295992	−	0.648131i
$611$	−2.50176	−	1.00155i	−0.101210	−	0.0405186i
$612$	−0.282225	+	5.92463i	−0.0114083	+	0.239489i
$613$	−6.05396	−	5.77244i	−0.244517	−	0.233146i	0.557903	−	0.829906i	$-0.311606\pi$
$613$	−6.05396	−	5.77244i	−0.244517	−	0.233146i	−0.802420	+	0.596760i	$0.796455\pi$
$614$	8.56496	+	6.73556i	0.345654	+	0.271825i
$615$	−1.89470	+	2.18660i	−0.0764018	+	0.0881724i
$616$	3.81985	−	0.296538i	0.153906	−	0.0119479i
$617$	−23.2636	−	26.8477i	−0.936559	−	1.08085i	−0.996579	−	0.0826495i	$-0.973662\pi$
$617$	−23.2636	−	26.8477i	−0.936559	−	1.08085i	0.0600197	−	0.998197i	$-0.480884\pi$
$618$	7.67039	−	7.31370i	0.308548	−	0.294200i
$619$	25.9328	−	2.47628i	1.04233	−	0.0995302i	0.440176	−	0.897912i	$-0.354916\pi$
$619$	25.9328	−	2.47628i	1.04233	−	0.0995302i	0.602152	+	0.798381i	$0.294310\pi$
$620$	4.24326	+	7.34954i	0.170413	+	0.295165i
$621$	3.19523	−	3.57638i	0.128220	−	0.143515i
$622$	−14.4648			−0.579988
$623$	4.14738	+	1.74627i	0.166161	+	0.0699628i
$624$	−0.478571	−	0.140521i	−0.0191582	−	0.00562534i
$625$	2.49004	−	0.479915i	0.0996015	−	0.0191966i
$626$	−7.32081	−	3.77414i	−0.292598	−	0.150845i
$627$	6.75968	+	1.30282i	0.269956	+	0.0520297i
$628$	−1.41298	−	1.11118i	−0.0563841	−	0.0443409i
$629$	43.3701	−	12.7346i	1.72928	−	0.507762i
$630$	3.43633	+	0.0609125i	0.136907	+	0.00242681i
$631$	1.01948	+	7.09062i	0.0405848	+	0.282273i	1.00000		0.000275895i	$8.78202e-5\pi$
$631$	1.01948	+	7.09062i	0.0405848	+	0.282273i	−0.959415	+	0.281997i	$0.909003\pi$
$632$	−9.27057	−	0.885232i	−0.368763	−	0.0352126i
$633$	15.8896	−	22.3138i	0.631555	−	0.886896i
$634$	23.4910	−	18.4735i	0.932946	−	0.733677i
$635$	−8.23897	+	4.24748i	−0.326953	+	0.168556i
$636$	9.95146	−	2.92201i	0.394601	−	0.115865i
$637$	2.86843	+	1.99052i	0.113651	+	0.0788671i
$638$	5.48936	−	6.33506i	0.217326	−	0.250808i
$639$	−0.424607	−	8.91360i	−0.0167972	−	0.352617i
$640$	0.424866	−	1.22757i	0.0167943	−	0.0485240i
$641$	−0.882321	−	3.63698i	−0.0348496	−	0.143652i	0.951729	−	0.306940i	$-0.0993051\pi$
$641$	−0.882321	−	3.63698i	−0.0348496	−	0.143652i	−0.986578	+	0.163288i	$0.947790\pi$
$642$	5.62248	+	7.89567i	0.221902	+	0.311617i
$643$	33.7737			1.33190			0.665952	−	0.745995i	$-0.268026\pi$
$643$	33.7737			1.33190			0.665952	+	0.745995i	$0.268026\pi$
$644$	2.58424	+	12.4226i	0.101833	+	0.489520i
$645$	13.5843			0.534881
$646$	−16.3557	−	22.9683i	−0.643505	−	0.903676i
$647$	−11.4046	−	47.0106i	−0.448363	−	1.84818i	−0.524979	−	0.851115i	$-0.675927\pi$
$647$	−11.4046	−	47.0106i	−0.448363	−	1.84818i	0.0766165	−	0.997061i	$-0.475588\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	−0.181595	−	3.81215i	−0.00712823	−	0.149640i
$650$	−1.08197	+	1.24867i	−0.0424385	+	0.0489767i
$651$	−17.1747	−	1.94772i	−0.673130	−	0.0763373i
$652$	−0.437639	+	0.128502i	−0.0171393	+	0.00503255i
$653$	−39.1440	+	20.1801i	−1.53182	+	0.789710i	−0.998422	−	0.0561520i	$-0.982117\pi$
$653$	−39.1440	+	20.1801i	−1.53182	+	0.789710i	−0.533402	+	0.845862i	$0.679087\pi$
$654$	−14.8822	+	11.7035i	−0.581940	+	0.457643i
$655$	9.92754	−	13.9413i	0.387901	−	0.544731i
$656$	−2.21721	−	0.211718i	−0.0865676	−	0.00826620i
$657$	1.34762	+	9.37289i	0.0525756	+	0.365671i
$658$	6.92675	+	12.5042i	0.270033	+	0.487464i
$659$	20.8655	−	6.12667i	0.812805	−	0.238661i	0.151190	−	0.988505i	$-0.451689\pi$
$659$	20.8655	−	6.12667i	0.812805	−	0.238661i	0.661615	+	0.749844i	$0.269871\pi$
$660$	1.47866	+	1.16283i	0.0575566	+	0.0452630i
$661$	−35.6724	−	6.87530i	−1.38750	−	0.267418i	−0.559816	−	0.828617i	$-0.689128\pi$
$661$	−35.6724	−	6.87530i	−1.38750	−	0.267418i	−0.827681	+	0.561199i	$0.810340\pi$
$662$	14.6012	+	7.52744i	0.567491	+	0.292562i
$663$	−2.90494	+	0.559881i	−0.112819	+	0.0217440i
$664$	12.6313	+	3.70890i	0.490191	+	0.143933i
$665$	−13.0198	+	9.87048i	−0.504885	+	0.382761i
$666$	−7.62072			−0.295297
$667$	23.1236	+	15.3614i	0.895351	+	0.594794i
$668$	−4.87534	−	8.44434i	−0.188633	−	0.326721i
$669$	21.5921	−	2.06180i	0.834800	−	0.0797137i
$670$	−5.88587	+	5.61216i	−0.227391	+	0.216817i
$671$	12.8469	+	14.8261i	0.495949	+	0.572356i
$672$	1.49625	+	2.18203i	0.0577190	+	0.0841735i
$673$	12.6112	−	14.5540i	0.486124	−	0.561017i	−0.458702	−	0.888590i	$-0.651685\pi$
$673$	12.6112	−	14.5540i	0.486124	−	0.561017i	0.944826	+	0.327573i	$0.106231\pi$
$674$	−22.3955	−	17.6120i	−0.862642	−	0.678389i
$675$	−2.39741	−	2.28593i	−0.0922765	−	0.0879854i
$676$	−0.606728	+	12.7368i	−0.0233357	+	0.489876i
$677$	−31.6236	−	12.6602i	−1.21539	−	0.486570i	−0.326724	−	0.945120i	$-0.605945\pi$
$677$	−31.6236	−	12.6602i	−1.21539	−	0.486570i	−0.888669	+	0.458550i	$0.848369\pi$
$678$	1.86380	+	4.08115i	0.0715787	+	0.156736i
$679$	11.2764	+	7.53257i	0.432747	+	0.289073i
$680$	−1.09652	−	7.62648i	−0.0420497	−	0.292462i
$681$	12.8969	−	6.64881i	0.494210	−	0.254783i
$682$	−6.84693	−	6.52854i	−0.262183	−	0.249991i
$683$	21.7060	−	8.68979i	0.830559	−	0.332506i	0.0828746	−	0.996560i	$-0.473590\pi$
$683$	21.7060	−	8.68979i	0.830559	−	0.332506i	0.747684	+	0.664054i	$0.231166\pi$
$684$	1.55483	+	4.49238i	0.0594504	+	0.171771i
$685$	−16.9505	+	10.8934i	−0.647645	+	0.416216i
$686$	−5.11865	−	17.7989i	−0.195431	−	0.679564i
$687$	7.74959	+	2.27549i	0.295665	+	0.0868152i
$688$	6.06588	+	8.51833i	0.231259	+	0.324758i
$689$	2.58654	+	4.48002i	0.0985393	+	0.170675i
$690$	−3.19643	+	5.34733i	−0.121686	+	0.203569i
$691$	1.07231	−	1.85729i	0.0407925	−	0.0706546i	−0.844908	−	0.534911i	$-0.820345\pi$
$691$	1.07231	−	1.85729i	0.0407925	−	0.0706546i	0.885701	+	0.464257i	$0.153678\pi$
$692$	7.51355e−5	0	0.000164524i	2.85622e−6	0	6.25426e-6i
$693$	−3.69470	+	1.01409i	−0.140350	+	0.0385221i
$694$	7.54438	+	8.70668i	0.286381	+	0.330501i
$695$	−0.996170	−	20.9122i	−0.0377869	−	0.793245i
$696$	5.68397	+	1.09549i	0.215450	+	0.0415246i
$697$	−12.2645	+	4.90998i	−0.464553	+	0.185979i
$698$	1.72745	−	7.12064i	0.0653849	−	0.269520i
$699$	12.1610	+	7.81543i	0.459973	+	0.295607i
$700$	8.63388	−	1.50585i	0.326330	−	0.0569159i
$701$	−17.5501	−	38.4294i	−0.662859	−	1.45146i	−0.879834	−	0.475281i	$-0.842346\pi$
$701$	−17.5501	−	38.4294i	−0.662859	−	1.45146i	0.216975	−	0.976177i	$-0.430381\pi$
$702$	0.496516	+	0.0474115i	0.0187398	+	0.00178943i
$703$	28.4769	−	22.3945i	1.07403	−	0.844623i
$704$	−0.0689038	+	1.44647i	−0.00259691	+	0.0545159i
$705$	−1.65464	+	6.82053i	−0.0623174	+	0.256876i
$706$	−2.87167	+	19.9729i	−0.108077	+	0.751690i
$707$	−29.1812	+	11.0864i	−1.09747	+	0.416948i
$708$	2.21711	−	1.42485i	0.0833241	−	0.0535492i
$709$	32.9804	−	6.35645i	1.23861	−	0.238722i	0.472439	−	0.881364i	$-0.343374\pi$
$709$	32.9804	−	6.35645i	1.23861	−	0.238722i	0.766167	+	0.642642i	$0.222162\pi$
$710$	2.73293	+	11.2653i	0.102565	+	0.422778i
$711$	9.27057	−	0.885232i	0.347673	−	0.0331988i
$712$	−0.850424	+	1.47298i	−0.0318710	+	0.0552022i
$713$	18.5591	−	25.2431i	0.695045	−	0.945362i
$714$	13.8187	+	7.43697i	0.517153	+	0.278321i
$715$	−0.389764	+	0.853465i	−0.0145764	+	0.0319178i
$716$	5.40999	−	5.15841i	0.202181	−	0.192779i
$717$	−0.476641	+	1.37716i	−0.0178005	+	0.0514311i
$718$	31.4511	+	16.2142i	1.17374	+	0.605107i
$719$	0.301779	+	0.871932i	0.0112544	+	0.0325176i	0.950488	−	0.310761i	$-0.100584\pi$
$719$	0.301779	+	0.871932i	0.0112544	+	0.0325176i	−0.939234	+	0.343278i	$0.888463\pi$
$720$	−0.184869	+	1.28579i	−0.00688966	+	0.0479187i
$721$	−8.70011	−	26.6568i	−0.324009	−	0.992751i
$722$	−3.02766	−	1.94576i	−0.112678	−	0.0724137i
$723$	6.41358	+	2.56761i	0.238524	+	0.0954905i
$724$	−15.2439	+	21.4071i	−0.566537	+	0.795590i
$725$	11.1226	−	15.6195i	0.413083	−	0.580093i
$726$	8.26524	+	3.30890i	0.306752	+	0.122805i
$727$	−40.8073	−	26.2253i	−1.51346	−	0.972642i	−0.992918	−	0.118806i	$-0.962093\pi$
$727$	−40.8073	−	26.2253i	−1.51346	−	0.972642i	−0.520542	−	0.853836i	$-0.674270\pi$
$728$	−0.881716	+	0.981840i	−0.0326786	+	0.0363894i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−4.02317	−	11.6242i	−0.148904	−	0.430231i
$731$	55.1312	+	28.4221i	2.03910	+	1.05123i
$732$	−4.43084	+	12.8021i	−0.163769	+	0.473178i
$733$	26.7918	−	25.5459i	0.989577	−	0.943559i	−0.00883159	−	0.999961i	$-0.502811\pi$
$733$	26.7918	−	25.5459i	0.989577	−	0.943559i	0.998408	+	0.0564017i	$0.0179627\pi$
$734$	6.63907	−	14.5375i	0.245053	−	0.536591i
$735$	4.06818	−	8.13231i	0.150057	−	0.299965i
$736$	−4.78048	+	0.383383i	−0.176211	+	0.0141317i
$737$	4.53303	−	7.85144i	0.166976	−	0.289212i
$738$	2.21721	−	0.211718i	0.0816167	−	0.00779345i
$739$	−2.95557	−	12.1830i	−0.108722	−	0.448159i	0.891264	−	0.453486i	$-0.149820\pi$
$739$	−2.95557	−	12.1830i	−0.108722	−	0.448159i	−0.999986	+	0.00532641i	$0.998305\pi$
$740$	9.72053	−	1.87348i	0.357334	−	0.0688704i
$741$	−1.99469	+	1.28191i	−0.0732768	+	0.0470921i
$742$	4.38598	−	27.0878i	0.161014	−	0.994426i
$743$	−3.08607	+	21.4641i	−0.113217	+	0.787441i	0.851538	+	0.524292i	$0.175670\pi$
$743$	−3.08607	+	21.4641i	−0.113217	+	0.787441i	−0.964755	+	0.263149i	$0.915239\pi$
$744$	1.54022	−	6.34889i	0.0564673	−	0.232762i
$745$	−1.31498	+	27.6049i	−0.0481772	+	1.01136i
$746$	1.34524	−	1.05790i	0.0492526	−	0.0387326i
$747$	−13.1050	−	1.25138i	−0.479487	−	0.0457854i
$748$	3.56810	+	7.81304i	0.130463	+	0.285673i
$749$	25.2638	−	4.40633i	0.923121	−	0.161004i
$750$	9.08397	+	5.83791i	0.331700	+	0.213170i
$751$	11.3642	−	46.8440i	0.414687	−	1.70936i	−0.255190	−	0.966891i	$-0.582138\pi$
$751$	11.3642	−	46.8440i	0.414687	−	1.70936i	0.669877	−	0.742472i	$-0.266347\pi$
$752$	−5.01582	+	2.00803i	−0.182908	+	0.0732254i
$753$	1.24596	+	0.240140i	0.0454055	+	0.00875119i
$754$	0.137378	+	2.88392i	0.00500302	+	0.105026i
$755$	5.98485	+	6.90689i	0.217811	+	0.251367i
$756$	−1.88216	−	1.85943i	−0.0684535	−	0.0676267i
$757$	−11.9883	+	26.2506i	−0.435721	+	0.954095i	0.556643	+	0.830752i	$0.312089\pi$
$757$	−11.9883	+	26.2506i	−0.435721	+	0.954095i	−0.992364	+	0.123344i	$0.960638\pi$
$758$	−5.11585	+	8.86092i	−0.185816	+	0.321843i
$759$	1.73954	−	6.72351i	0.0631411	−	0.244048i
$760$	−3.08765	−	5.34797i	−0.112001	−	0.193991i
$761$	−5.79319	−	8.13539i	−0.210003	−	0.294908i	0.696117	−	0.717928i	$-0.254909\pi$
$761$	−5.79319	−	8.13539i	−0.210003	−	0.294908i	−0.906120	+	0.423020i	$0.860970\pi$
$762$	6.84667	+	2.01036i	0.248029	+	0.0728278i
$763$	10.9449	+	48.8812i	0.396232	+	1.76962i
$764$	−5.47254	+	3.51699i	−0.197990	+	0.127240i
$765$	2.52003	+	7.28114i	0.0911118	+	0.263250i
$766$	4.29004	−	1.71747i	0.155005	−	0.0620548i
$767$	0.951358	+	0.907118i	0.0343515	+	0.0327541i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	−5.76384	−	40.0884i	−0.207850	−	1.44563i	−0.780156	−	0.625585i	$-0.784860\pi$
$769$	−5.76384	−	40.0884i	−0.207850	−	1.44563i	0.572306	−	0.820040i	$-0.306049\pi$
$770$	4.46343	−	2.20182i	0.160851	−	0.0793480i
$771$	4.83284	+	10.5825i	0.174051	+	0.381118i
$772$	−14.2894	−	5.72060i	−0.514285	−	0.205889i
$773$	1.52488	−	32.0112i	0.0548462	−	1.15136i	−0.788865	−	0.614566i	$-0.789331\pi$
$773$	1.52488	−	32.0112i	0.0548462	−	1.15136i	0.843712	−	0.536797i	$-0.180366\pi$
$774$	−7.56836	−	7.21642i	−0.272039	−	0.259389i
$775$	−17.0111	−	13.3776i	−0.611055	−	0.480539i
$776$	−3.35649	+	3.87360i	−0.120491	+	0.139054i
$777$	−8.69955	+	18.1891i	−0.312095	+	0.652532i
$778$	−4.80580	−	5.54619i	−0.172296	−	0.198840i
$779$	−7.66305	+	7.30671i	−0.274557	+	0.261790i
$780$	−0.644982	+	0.0615883i	−0.0230940	+	0.00220521i
$781$	−6.46126	−	11.1912i	−0.231202	−	0.400454i
$782$	−24.1607	+	15.0141i	−0.863983	+	0.536902i
$783$	−5.78857			−0.206867
$784$	6.91613	−	1.08032i	0.247005	−	0.0385830i
$785$	−2.24048	−	0.657863i	−0.0799660	−	0.0234801i
$786$	−12.9371	+	2.49342i	−0.461451	+	0.0889374i
$787$	32.1541	+	16.5766i	1.14617	+	0.590891i	0.923346	−	0.383968i	$-0.125443\pi$
$787$	32.1541	+	16.5766i	1.14617	+	0.590891i	0.222822	+	0.974859i	$0.428473\pi$
$788$	−4.67882	−	0.901769i	−0.166676	−	0.0321242i
$789$	−18.9586	−	14.9092i	−0.674943	−	0.530781i
$790$	−11.6073	+	3.40823i	−0.412971	+	0.121259i
$791$	11.8685	+	0.210382i	0.421997	+	0.00748033i
$792$	−0.206088	−	1.43337i	−0.00732300	−	0.0509326i
$793$	−6.72638	−	0.642291i	−0.238861	−	0.0228084i
$794$	10.8891	−	15.2915i	0.386438	−	0.542676i
$795$	10.5904	−	8.32835i	0.375601	−	0.295376i
$796$	−20.1545	+	10.3903i	−0.714356	+	0.368276i
$797$	−2.77929	+	0.816073i	−0.0984475	+	0.0289068i	−0.330585	−	0.943776i	$-0.607246\pi$
$797$	−2.77929	+	0.816073i	−0.0984475	+	0.0289068i	0.232138	+	0.972683i	$0.425428\pi$
$798$	12.4974	+	1.41728i	0.442402	+	0.0501712i
$799$	−20.9857	+	24.2188i	−0.742421	+	0.856800i
$800$	0.157618	+	3.30881i	0.00557264	+	0.116984i
$801$	0.556293	−	1.60730i	0.0196556	−	0.0567913i
$802$	−3.34964	−	13.8074i	−0.118280	−	0.487557i
$803$	7.95406	+	11.1699i	0.280693	+	0.394177i
$804$	6.26062			0.220795
$805$	9.11408	+	13.7336i	0.321229	+	0.484045i
$806$	3.25852			0.114776
$807$	−1.17131	−	1.64488i	−0.0412321	−	0.0579024i
$808$	−2.78163	−	11.4660i	−0.0978572	−	0.403373i
$809$	16.0426	−	46.3519i	0.564026	−	1.62965i	−0.196620	−	0.980480i	$-0.562996\pi$
$809$	16.0426	−	46.3519i	0.564026	−	1.62965i	0.760646	−	0.649167i	$-0.224882\pi$
$810$	−0.0618096	−	1.29754i	−0.00217177	−	0.0455910i
$811$	2.16580	−	2.49946i	0.0760514	−	0.0877680i	−0.716449	−	0.697640i	$-0.754234\pi$
$811$	2.16580	−	2.49946i	0.0760514	−	0.0877680i	0.792500	+	0.609872i	$0.208779\pi$
$812$	9.10335	−	12.3159i	0.319465	−	0.432204i
$813$	−17.9971	+	5.28442i	−0.631185	+	0.185333i
$814$	−9.80886	+	5.05682i	−0.343801	+	0.177241i
$815$	−0.465737	+	0.366259i	−0.0163140	+	0.0128295i
$816$	−3.44052	+	4.83153i	−0.120442	+	0.169137i
$817$	49.4876	+	4.72549i	1.73135	+	0.165324i
$818$	−1.14584	−	7.96950i	−0.0400634	−	0.278647i
$819$	0.679968	−	1.13096i	0.0237600	−	0.0395190i
$820$	−2.77609	+	0.815135i	−0.0969454	+	0.0284657i
$821$	39.2837	+	30.8931i	1.37101	+	1.07818i	0.988004	+	0.154431i	$0.0493543\pi$
$821$	39.2837	+	30.8931i	1.37101	+	1.07818i	0.383008	+	0.923745i	$0.374888\pi$
$822$	15.2307	+	2.93549i	0.531233	+	0.102387i
$823$	−29.8626	−	15.3952i	−1.04094	−	0.536644i	−0.149023	−	0.988834i	$-0.547613\pi$
$823$	−29.8626	−	15.3952i	−1.04094	−	0.536644i	−0.891922	+	0.452189i	$0.850643\pi$
$824$	10.4068	−	2.00575i	0.362539	−	0.0698737i
$825$	−4.60264	−	1.35146i	−0.160243	−	0.0470517i
$826$	−0.869859	−	6.91837i	−0.0302663	−	0.240721i
$827$	−10.3793			−0.360925			−0.180462	−	0.983582i	$-0.557759\pi$
$827$	−10.3793			−0.360925			−0.180462	+	0.983582i	$0.557759\pi$
$828$	4.62154	−	1.28117i	0.160610	−	0.0445236i
$829$	11.0790	+	19.1894i	0.384791	+	0.666477i	0.991740	−	0.128263i	$-0.0409403\pi$
$829$	11.0790	+	19.1894i	0.384791	+	0.666477i	−0.606950	+	0.794740i	$0.707607\pi$
$830$	17.0236	−	1.62555i	0.590897	−	0.0564238i
$831$	9.46039	−	9.02046i	0.328177	−	0.312916i
$832$	−0.326628	−	0.376949i	−0.0113238	−	0.0130683i
$833$	33.5256	−	24.4928i	1.16159	−	0.848625i
$834$	−10.5542	+	12.1802i	−0.365463	+	0.421767i
$835$	−9.95637	−	7.82978i	−0.344554	−	0.270961i
$836$	4.98224	+	4.75056i	0.172315	+	0.164302i
$837$	−0.310855	+	6.52565i	−0.0107447	+	0.225559i
$838$	−8.97935	−	3.59479i	−0.310187	−	0.124180i
$839$	8.58402	+	18.7964i	0.296353	+	0.648923i	0.997974	−	0.0636278i	$-0.0202671\pi$
$839$	8.58402	+	18.7964i	0.296353	+	0.648923i	−0.701620	+	0.712551i	$0.747540\pi$
$840$	2.85789	+	1.90906i	0.0986067	+	0.0658689i
$841$	−0.641496	−	4.46170i	−0.0221205	−	0.153852i
$842$	−1.64472	+	0.847911i	−0.0566807	+	0.0292210i
$843$	19.4883	+	18.5821i	0.671213	+	0.640001i
$844$	25.4310	−	10.1810i	0.875370	−	0.350445i
$845$	5.41756	+	15.6530i	0.186370	+	0.538480i
$846$	4.54515	−	2.92099i	0.156266	−	0.100426i
$847$	17.3330	−	15.9502i	0.595569	−	0.548054i
$848$	9.95146	+	2.92201i	0.341734	+	0.100342i
$849$	−10.2291	−	14.3647i	−0.351061	−	0.492996i
$850$	9.82397	+	17.0156i	0.336959	+	0.583631i
$851$	−20.7456	−	30.0891i	−0.711149	−	1.03144i
$852$	4.46186	−	7.72816i	0.152861	−	0.264762i
$853$	−0.577541	+	1.26464i	−0.0197746	+	0.0433004i	−0.919262	−	0.393647i	$-0.871213\pi$
$853$	−0.577541	+	1.26464i	−0.0197746	+	0.0433004i	0.899487	+	0.436948i	$0.143940\pi$
$854$	25.4979	+	25.1900i	0.872521	+	0.861982i
$855$	4.04397	+	4.66699i	0.138301	+	0.159608i
$856$	0.461211	+	9.68201i	0.0157639	+	0.330924i
$857$	−23.0812	−	4.44853i	−0.788438	−	0.151959i	−0.220889	−	0.975299i	$-0.570896\pi$
$857$	−23.0812	−	4.44853i	−0.788438	−	0.151959i	−0.567548	+	0.823340i	$0.692108\pi$
$858$	0.670542	−	0.268444i	0.0228919	−	0.00916454i
$859$	7.08166	−	29.1910i	0.241623	−	0.995984i	−0.713707	−	0.700444i	$-0.752985\pi$
$859$	7.08166	−	29.1910i	0.241623	−	0.995984i	0.955330	−	0.295540i	$-0.0954996\pi$
$860$	11.4278	+	7.34422i	0.389686	+	0.250436i
$861$	2.02577	−	5.53374i	0.0690379	−	0.188589i
$862$	−3.75439	−	8.22096i	−0.127875	−	0.280007i
$863$	−8.46722	−	0.808522i	−0.288228	−	0.0275224i	−0.0500591	−	0.998746i	$-0.515941\pi$
$863$	−8.46722	−	0.808522i	−0.288228	−	0.0275224i	−0.238168	+	0.971224i	$0.576547\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	1.11794e−5	0	0.000234685i	3.80111e−7	0	7.97952e-6i
$866$	−5.98403	+	24.6665i	−0.203346	+	0.838202i
$867$	−2.58740	+	17.9958i	−0.0878728	+	0.611169i
$868$	−13.3953	−	10.9239i	−0.454665	−	0.370781i
$869$	11.3450	−	7.29101i	0.384854	−	0.247331i
$870$	7.38356	−	1.42306i	0.250326	−	0.0482464i
$871$	0.736190	+	3.03461i	0.0249448	+	0.102824i
$872$	−18.8471	+	1.79968i	−0.638243	+	0.0609448i
$873$	2.56275	−	4.43882i	0.0867361	−	0.150231i
$874$	−13.5048	+	18.3684i	−0.456805	+	0.621321i
$875$	24.3039	−	15.0173i	0.821622	−	0.507677i
$876$	−3.93368	+	8.61355i	−0.132907	+	0.291025i
$877$	15.0605	−	14.3602i	0.508558	−	0.484909i	−0.391805	−	0.920048i	$-0.628149\pi$
$877$	15.0605	−	14.3602i	0.508558	−	0.484909i	0.900363	+	0.435139i	$0.143301\pi$
$878$	−2.84140	+	8.20969i	−0.0958926	+	0.277063i
$879$	−24.4845	−	12.6226i	−0.825842	−	0.425751i
$880$	0.615253	+	1.77766i	0.0207402	+	0.0599248i
$881$	−6.21204	+	43.2057i	−0.209289	+	1.45564i	0.566195	+	0.824271i	$0.308415\pi$
$881$	−6.21204	+	43.2057i	−0.209289	+	1.45564i	−0.775485	+	0.631367i	$0.782494\pi$
$882$	−6.58670	+	2.36969i	−0.221786	+	0.0797915i
$883$	−10.3175	−	6.63064i	−0.347211	−	0.223139i	0.355398	−	0.934715i	$-0.384345\pi$
$883$	−10.3175	−	6.63064i	−0.347211	−	0.223139i	−0.702609	+	0.711576i	$0.747982\pi$
$884$	−2.74649	−	1.09953i	−0.0923743	−	0.0369811i
$885$	1.98584	−	2.78873i	0.0667534	−	0.0937421i
$886$	1.27505	−	1.79056i	0.0428362	−	0.0601550i
$887$	24.4310	+	9.78068i	0.820311	+	0.328403i	0.743579	−	0.668649i	$-0.233127\pi$
$887$	24.4310	+	9.78068i	0.820311	+	0.328403i	0.0767328	+	0.997052i	$0.475551\pi$
$888$	−6.41096	−	4.12007i	−0.215138	−	0.138261i
$889$	12.6143	−	14.0467i	0.423069	−	0.471111i
$890$	−0.314434	+	2.18694i	−0.0105399	+	0.0733063i
$891$	0.473630	+	1.36847i	0.0158672	+	0.0458453i
$892$	19.2791	+	9.93909i	0.645513	+	0.332785i
$893$	−8.40048	+	24.2716i	−0.281111	+	0.812218i
$894$	15.3972	−	14.6812i	0.514961	−	0.491014i
$895$	4.03379	−	8.83277i	0.134835	−	0.295247i
$896$	0.0790319	+	2.64457i	0.00264027	+	0.0883489i
$897$	1.16445	+	2.08947i	0.0388798	+	0.0697655i
$898$	−13.1594	+	22.7927i	−0.439134	+	0.760603i
$899$	−37.6458	+	3.59474i	−1.25556	+	0.119891i
$900$	−0.780966	−	3.21918i	−0.0260322	−	0.107306i
$901$	60.4057	−	11.6422i	2.01241	−	0.387859i
$902$	2.71336	−	1.74377i	0.0903449	−	0.0580611i
$903$	−25.8640	+	9.82617i	−0.860699	+	0.326994i
$904$	−0.638509	+	4.44093i	−0.0212365	+	0.147703i
$905$	−8.04839	+	33.1759i	−0.267538	+	1.10280i
$906$	0.334759	−	7.02746i	0.0111216	−	0.233472i
$907$	−15.2525	+	11.9947i	−0.506451	+	0.398277i	−0.838430	−	0.545009i	$-0.816526\pi$
$907$	−15.2525	+	11.9947i	−0.506451	+	0.398277i	0.331979	+	0.943287i	$0.392284\pi$
$908$	14.4442	+	1.37925i	0.479347	+	0.0457721i
$909$	4.90132	+	10.7324i	0.162566	+	0.355971i
$910$	−0.589290	+	1.60975i	−0.0195348	+	0.0533627i
$911$	−6.26243	−	4.02462i	−0.207483	−	0.133341i	0.432773	−	0.901503i	$-0.357535\pi$
$911$	−6.26243	−	4.02462i	−0.207483	−	0.133341i	−0.640256	+	0.768162i	$0.721172\pi$
$912$	−1.12076	+	4.61984i	−0.0371121	+	0.152978i
$913$	−17.6982	+	7.08530i	−0.585725	+	0.234489i
$914$	19.7826	+	3.81279i	0.654352	+	0.126116i
$915$	0.837344	+	17.5780i	0.0276818	+	0.581111i
$916$	5.28915	+	6.10400i	0.174758	+	0.201682i
$917$	−8.81725	+	33.7247i	−0.291171	+	1.11369i
$918$	2.46397	−	5.39534i	0.0813231	−	0.178073i
$919$	16.5730	−	28.7053i	0.546693	−	0.946900i	−0.451805	−	0.892116i	$-0.649220\pi$
$919$	16.5730	−	28.7053i	0.546693	−	0.946900i	0.998498	−	0.0547833i	$-0.0174468\pi$
$920$	−5.57999	+	2.77034i	−0.183967	+	0.0913354i
$921$	−5.44808	−	9.43635i	−0.179520	−	0.310938i
$922$	−6.60251	−	9.27193i	−0.217442	−	0.305355i
$923$	4.27063	+	1.25397i	0.140569	+	0.0412749i
$924$	−3.65643	−	1.14440i	−0.120288	−	0.0376479i
$925$	−21.2367	+	13.6480i	−0.698258	+	0.448743i
$926$	−4.41382	−	12.7529i	−0.145047	−	0.419086i
$927$	−9.83917	+	3.93901i	−0.323161	+	0.129374i
$928$	4.18939	+	3.99457i	0.137523	+	0.131128i
$929$	−31.2560	+	16.1136i	−1.02548	+	0.528670i	−0.887036	−	0.461701i	$-0.847239\pi$
$929$	−31.2560	+	16.1136i	−1.02548	+	0.528670i	−0.138441	+	0.990371i	$0.544209\pi$
$930$	−1.20776	−	8.40014i	−0.0396039	−	0.275451i
$931$	17.6493	−	28.2108i	0.578434	−	0.924573i
$932$	6.00518	+	13.1495i	0.196706	+	0.430727i
$933$	13.4287	+	5.37604i	0.439636	+	0.176004i
$934$	−1.15872	+	24.3245i	−0.0379144	+	0.795922i
$935$	8.07510	+	7.69959i	0.264084	+	0.251803i
$936$	0.392063	+	0.308322i	0.0128150	+	0.0100778i
$937$	−26.6593	+	30.7665i	−0.870921	+	1.00510i	0.128988	+	0.991646i	$0.458827\pi$
$937$	−26.6593	+	30.7665i	−0.870921	+	1.00510i	−0.999910	+	0.0134505i	$0.995718\pi$
$938$	7.14691	−	14.9429i	0.233355	−	0.487902i
$939$	5.39370	+	6.22466i	0.176017	+	0.203134i
$940$	−5.07943	+	4.84322i	−0.165673	+	0.157969i
$941$	−6.55530	+	0.625955i	−0.213697	+	0.0204055i	−0.201355	−	0.979518i	$-0.564535\pi$
$941$	−6.55530	+	0.625955i	−0.213697	+	0.0204055i	−0.0123414	+	0.999924i	$0.503928\pi$
$942$	0.898782	+	1.55674i	0.0292839	+	0.0507212i
$943$	6.87176	+	8.17793i	0.223775	+	0.266310i
$944$	2.63549			0.0857777
$945$	−3.16754	−	1.33370i	−0.103040	−	0.0433854i
$946$	−14.5300	−	4.26640i	−0.472412	−	0.138713i
$947$	−20.1910	+	3.89149i	−0.656119	+	0.126457i	−0.506436	−	0.862278i	$-0.669037\pi$
$947$	−20.1910	+	3.89149i	−0.656119	+	0.126457i	−0.149683	+	0.988734i	$0.547825\pi$
$948$	8.27749	+	4.26734i	0.268840	+	0.138597i
$949$	−4.63768	−	0.893839i	−0.150545	−	0.0290153i
$950$	12.3783	+	9.73439i	0.401604	+	0.315825i
$951$	−28.6742	+	8.41950i	−0.929824	+	0.273021i
$952$	7.60433	+	13.7273i	0.246458	+	0.444906i
$953$	0.638131	+	4.43830i	0.0206711	+	0.143771i	0.997543	−	0.0700537i	$-0.0223171\pi$
$953$	0.638131	+	4.43830i	0.0206711	+	0.143771i	−0.976872	+	0.213824i	$0.931408\pi$
$954$	−10.3246	−	0.985881i	−0.334272	−	0.0319191i
$955$	−4.90170	+	6.88348i	−0.158615	+	0.222744i
$956$	−1.14553	+	0.900852i	−0.0370490	+	0.0291356i
$957$	−7.45065	+	3.84108i	−0.240845	+	0.124164i
$958$	9.50095	−	2.78973i	0.306962	−	0.0901321i
$959$	24.3933	−	33.0017i	0.787702	−	1.06568i
$960$	−0.850674	+	0.981730i	−0.0274554	+	0.0316852i
$961$	0.555789	+	11.6674i	0.0179287	+	0.376369i
$962$	1.24319	−	3.59197i	0.0400821	−	0.115810i
$963$	−2.28521	−	9.41975i	−0.0736398	−	0.303547i
$964$	4.00729	+	5.62746i	0.129066	+	0.181248i
$965$	−19.9943			−0.643640
$966$	2.21790	−	12.4932i	0.0713597	−	0.401963i
$967$	−19.6421			−0.631648			−0.315824	−	0.948818i	$-0.602281\pi$
$967$	−19.6421			−0.631648			−0.315824	+	0.948818i	$0.602281\pi$
$968$	5.16423	+	7.25215i	0.165985	+	0.233093i
$969$	6.64761	+	27.4018i	0.213552	+	0.880274i
$970$	−2.17765	+	6.29192i	−0.0699203	+	0.202021i
$971$	0.430421	+	9.03565i	0.0138129	+	0.289968i	0.995196	+	0.0979059i	$0.0312144\pi$
$971$	0.430421	+	9.03565i	0.0138129	+	0.289968i	−0.981383	+	0.192062i	$0.938483\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	17.0235	+	39.0954i	0.545747	+	1.25334i
$974$	6.44360	−	1.89201i	0.206466	−	0.0606240i
$975$	1.46855	−	0.757091i	0.0470313	−	0.0242463i
$976$	−10.6488	+	8.37430i	−0.340859	+	0.268055i
$977$	15.6717	−	22.0078i	0.501382	−	0.704093i	−0.483882	−	0.875133i	$-0.660774\pi$
$977$	15.6717	−	22.0078i	0.501382	−	0.704093i	0.985264	+	0.171041i	$0.0547130\pi$
$978$	0.454050	+	0.0433565i	0.0145189	+	0.00138639i
$979$	−0.350524	−	2.43794i	−0.0112028	−	0.0779171i
$980$	7.81903	−	4.64190i	0.249770	−	0.148280i
$981$	18.1659	−	5.33399i	0.579993	−	0.170301i
$982$	26.8234	+	21.0942i	0.855969	+	0.673141i
$983$	−36.6311	−	7.06007i	−1.16835	−	0.225181i	−0.432060	−	0.901845i	$-0.642213\pi$
$983$	−36.6311	−	7.06007i	−1.16835	−	0.225181i	−0.736292	+	0.676664i	$0.763425\pi$
$984$	1.97970	+	1.02061i	0.0631106	+	0.0325358i
$985$	−6.07786	+	1.17141i	−0.193657	+	0.0373243i
$986$	32.9432	+	9.67301i	1.04913	+	0.308051i
$987$	−1.78324	−	14.1829i	−0.0567612	−	0.451446i
$988$	−2.37109			−0.0754345
$989$	7.88974	−	49.5274i	0.250879	−	1.57488i
$990$	−0.940558	−	1.62909i	−0.0298929	−	0.0517760i
$991$	20.1868	−	1.92760i	0.641254	−	0.0612323i	0.230636	−	0.973040i	$-0.425919\pi$
$991$	20.1868	−	1.92760i	0.641254	−	0.0612323i	0.410618	+	0.911808i	$0.365313\pi$
$992$	4.72819	−	4.50832i	0.150120	−	0.143139i
$993$	−10.7576	−	12.4149i	−0.341382	−	0.393976i
$994$	−13.3521	−	19.4718i	−0.423503	−	0.617607i
$995$	−19.2891	+	22.2608i	−0.611507	+	0.705716i
$996$	−10.3481	−	8.13782i	−0.327891	−	0.257857i
$997$	−28.3153	−	26.9986i	−0.896755	−	0.855054i	0.0933142	−	0.995637i	$-0.470254\pi$
$997$	−28.3153	−	26.9986i	−0.896755	−	0.855054i	−0.990069	+	0.140583i	$0.955102\pi$
$998$	−0.908090	+	19.0632i	−0.0287451	+	0.603433i
$999$	7.07483	+	2.83233i	0.223838	+	0.0896111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.121.6	✓	160
7.4	even	3	inner	966.2.y.b.949.3	yes	160
23.4	even	11	inner	966.2.y.b.625.3	yes	160
161.4	even	33	inner	966.2.y.b.487.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.121.6	✓	160	1.1	even	1	trivial
966.2.y.b.487.6	yes	160	161.4	even	33	inner
966.2.y.b.625.3	yes	160	23.4	even	11	inner
966.2.y.b.949.3	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0618096 + 1.29754i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.05626 - 2.42576i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0618096 + 1.29754i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.05626 - 2.42576i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(1.02109 - 0.802998i) q^{10} +(-0.839986 + 1.17960i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.0709830 - 0.493698i) q^{13} +(-1.36328 + 2.26748i) q^{14} +(-1.24640 + 0.365975i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.82416 - 1.12251i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.66793 + 0.899670i) q^{19} +(-1.24640 - 0.365975i) q^{20} +(2.10836 - 1.59838i) q^{21} +1.44811 q^{22} +(0.610413 + 4.75683i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.29756 - 0.314879i) q^{25} +(-0.360980 + 0.344194i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.63781 - 0.204776i) q^{28} +(3.79071 - 4.37471i) q^{29} +(1.02109 + 0.802998i) q^{30} +(-4.72819 - 4.50832i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.34438 - 0.538208i) q^{33} +(2.46397 + 5.39534i) q^{34} +(3.08224 - 1.52048i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.77356 + 3.49201i) q^{37} +(3.44052 + 3.28052i) q^{38} +(0.463046 - 0.185376i) q^{39} +(0.424866 + 1.22757i) q^{40} +(1.87372 - 1.20417i) q^{41} +(-2.52497 - 0.790269i) q^{42} +(-10.0338 - 2.94619i) q^{43} +(-0.839986 - 1.17960i) q^{44} +(-0.649507 - 1.12498i) q^{45} +(3.52072 - 3.25646i) q^{46} +(2.70142 - 4.67899i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-4.76864 + 5.12446i) q^{49} +(-2.16927 - 2.50347i) q^{50} +(-0.282225 - 5.92463i) q^{51} +(0.489761 + 0.0943937i) q^{52} +(-9.62864 + 3.85473i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-1.58250 - 1.01701i) q^{55} +(-1.69689 - 2.02992i) q^{56} +(-1.97482 - 4.32424i) q^{57} +(-5.76236 - 0.550239i) q^{58} +(-2.07163 + 1.62915i) q^{59} +(0.0618096 - 1.29754i) q^{60} +(3.19386 - 13.1653i) q^{61} +(-0.929749 + 6.46655i) q^{62} +(2.05039 + 1.67210i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.636207 - 0.122619i) q^{65} +(0.341405 + 1.40729i) q^{66} +(-6.23227 + 0.595110i) q^{67} +(2.96567 - 5.13669i) q^{68} +(-4.47883 + 1.71467i) q^{69} +(-3.02642 - 1.62876i) q^{70} +(-3.70704 + 8.11729i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(3.09709 - 8.94847i) q^{73} +(6.77356 + 3.49201i) q^{74} +(1.08343 + 3.13037i) q^{75} +(0.676542 - 4.70545i) q^{76} +(3.74866 + 0.791648i) q^{77} +(-0.419596 - 0.269658i) q^{78} +(-8.64564 - 3.46119i) q^{79} +(0.753502 - 1.05815i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-2.06775 - 0.827803i) q^{82} +(11.0748 + 7.11732i) q^{83} +(0.820892 + 2.51518i) q^{84} +(1.09652 - 7.62648i) q^{85} +(3.42028 + 9.88224i) q^{86} +(5.14509 + 2.65248i) q^{87} +(-0.473630 + 1.36847i) q^{88} +(-1.23096 + 1.17372i) q^{89} +(-0.539630 + 1.18163i) q^{90} +(-1.12262 + 0.693660i) q^{91} +(-4.69485 - 0.978964i) q^{92} +(3.26652 - 5.65778i) q^{93} +(-5.37837 + 0.513572i) q^{94} +(-1.45588 - 6.00124i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-4.31185 + 2.77106i) q^{97} +(6.94034 + 0.911938i) q^{98} +(0.206088 - 1.43337i) 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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