LMFDB - Embedded newform 966.2.q.j.85.2

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			85.2
Character	$\chi$	$=$	966.85
Dual form			966.2.q.j.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.568699 - 1.24528i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.568699 - 1.24528i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.31354 + 0.385689i) q^{10} +(-2.37303 - 2.73862i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-5.15124 - 1.51254i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(1.15167 + 0.740131i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.946027 + 6.57976i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.212597 + 1.47864i) q^{19} +(-1.15167 + 0.740131i) q^{20} +(-0.654861 + 0.755750i) q^{21} +3.62371 q^{22} +(3.63723 + 3.12579i) q^{23} -1.00000 q^{24} +(2.04701 - 2.36237i) q^{25} +(4.51644 - 2.90254i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.636609 + 4.42771i) q^{29} +(-1.31354 + 0.385689i) q^{30} +(7.53236 + 4.84076i) q^{31} +(0.415415 - 0.909632i) q^{32} +(3.47693 + 1.02092i) q^{33} +(-4.35313 - 5.02379i) q^{34} +(-0.896497 - 1.03461i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.717923 - 1.57203i) q^{37} +(-1.25670 - 0.807635i) q^{38} +(5.15124 - 1.51254i) q^{39} +(0.194827 - 1.35505i) q^{40} +(5.15905 + 11.2967i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-2.04459 + 1.31398i) q^{43} +(-2.37303 + 2.73862i) q^{44} -1.36899 q^{45} +(-4.74419 + 0.701884i) q^{46} -13.0590 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.444858 + 3.09405i) q^{50} +(-2.76144 - 6.04671i) q^{51} +(-0.764047 + 5.31406i) q^{52} +(-3.94865 + 1.15943i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-2.06080 + 4.51252i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-0.978262 - 1.12897i) q^{57} +(-2.92935 - 3.38065i) q^{58} +(-2.73431 - 0.802865i) q^{59} +(0.568699 - 1.24528i) q^{60} +(7.12582 + 4.57949i) q^{61} +(-8.59105 + 2.52256i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.04597 + 7.27489i) q^{65} +(-3.04846 + 1.95913i) q^{66} +(-2.17226 + 2.50692i) q^{67} +6.64742 q^{68} +(-4.74976 - 0.663141i) q^{69} +1.36899 q^{70} +(-10.3604 + 11.9565i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-0.561205 - 3.90327i) q^{73} +(0.717923 + 1.57203i) q^{74} +(-0.444858 + 3.09405i) q^{75} +(1.43334 - 0.420865i) q^{76} +(-3.04846 - 1.95913i) q^{77} +(-2.23024 + 4.88355i) q^{78} +(1.23033 + 0.361258i) q^{79} +(0.896497 + 1.03461i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-11.9160 - 3.49884i) q^{82} +(-3.91195 + 8.56597i) q^{83} +(0.841254 + 0.540641i) q^{84} +(8.73162 - 2.56384i) q^{85} +(0.345883 - 2.40567i) q^{86} +(-1.85825 - 4.06901i) q^{87} +(-0.515708 - 3.58683i) q^{88} +(6.12242 - 3.93464i) q^{89} +(0.896497 - 1.03461i) q^{90} -5.36871 q^{91} +(2.57634 - 4.04506i) q^{92} -8.95374 q^{93} +(8.55186 - 9.86937i) q^{94} +(1.72041 - 1.10564i) q^{95} +(0.142315 + 0.989821i) q^{96} +(6.30470 + 13.8054i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-3.47693 + 1.02092i) 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	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 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 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.568699	−	1.24528i	−0.254330	−	0.556904i	0.738800	−	0.673925i	$-0.235393\pi$
$5$	−0.568699	−	1.24528i	−0.254330	−	0.556904i	−0.993129	+	0.117021i	$0.962666\pi$
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	1.31354	+	0.385689i	0.415376	+	0.121965i
$11$	−2.37303	−	2.73862i	−0.715494	−	0.825725i	0.275263	−	0.961369i	$-0.411235\pi$
$11$	−2.37303	−	2.73862i	−0.715494	−	0.825725i	−0.990758	+	0.135644i	$0.956690\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	−5.15124	−	1.51254i	−1.42870	−	0.419503i	−0.526259	−	0.850324i	$-0.676406\pi$
$13$	−5.15124	−	1.51254i	−1.42870	−	0.419503i	−0.902437	+	0.430821i	$0.858224\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	1.15167	+	0.740131i	0.297359	+	0.191101i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.946027	+	6.57976i	−0.229445	+	1.59583i	0.471009	+	0.882128i	$0.343890\pi$
$17$	−0.946027	+	6.57976i	−0.229445	+	1.59583i	−0.700454	+	0.713698i	$0.747019\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	0.212597	+	1.47864i	0.0487730	+	0.339224i	0.999568	+	0.0294019i	$0.00936028\pi$
$19$	0.212597	+	1.47864i	0.0487730	+	0.339224i	−0.950795	+	0.309822i	$0.899731\pi$
$20$	−1.15167	+	0.740131i	−0.257521	+	0.165498i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	3.62371			0.772578
$23$	3.63723	+	3.12579i	0.758416	+	0.651771i
$23$	3.63723	+	3.12579i	0.758416	+	0.651771i
$24$	−1.00000			−0.204124
$25$	2.04701	−	2.36237i	0.409402	−	0.472475i
$26$	4.51644	−	2.90254i	0.885748	−	0.569235i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−0.415415	−	0.909632i	−0.0785061	−	0.171904i
$29$	−0.636609	+	4.42771i	−0.118215	+	0.822206i	0.841304	+	0.540563i	$0.181789\pi$
$29$	−0.636609	+	4.42771i	−0.118215	+	0.822206i	−0.959519	+	0.281643i	$0.909120\pi$
$30$	−1.31354	+	0.385689i	−0.239818	+	0.0704168i
$31$	7.53236	+	4.84076i	1.35285	+	0.869425i	0.997856	−	0.0654426i	$-0.0208459\pi$
$31$	7.53236	+	4.84076i	1.35285	+	0.869425i	0.354996	+	0.934868i	$0.384482\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	3.47693	+	1.02092i	0.605255	+	0.177719i
$34$	−4.35313	−	5.02379i	−0.746556	−	0.861572i
$35$	−0.896497	−	1.03461i	−0.151536	−	0.174881i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.717923	−	1.57203i	0.118026	−	0.258441i	−0.841394	−	0.540422i	$-0.818264\pi$
$37$	0.717923	−	1.57203i	0.118026	−	0.258441i	0.959420	+	0.281982i	$0.0909918\pi$
$38$	−1.25670	−	0.807635i	−0.203864	−	0.131016i
$39$	5.15124	−	1.51254i	0.824858	−	0.242200i
$40$	0.194827	−	1.35505i	0.0308049	−	0.214253i
$41$	5.15905	+	11.2967i	0.805708	+	1.76425i	0.624849	+	0.780746i	$0.285161\pi$
$41$	5.15905	+	11.2967i	0.805708	+	1.76425i	0.180859	+	0.983509i	$0.442112\pi$
$42$	−0.142315	−	0.989821i	−0.0219597	−	0.152733i
$43$	−2.04459	+	1.31398i	−0.311797	+	0.200380i	−0.687175	−	0.726492i	$-0.741149\pi$
$43$	−2.04459	+	1.31398i	−0.311797	+	0.200380i	0.375378	+	0.926872i	$0.377513\pi$
$44$	−2.37303	+	2.73862i	−0.357747	+	0.412862i
$45$	−1.36899			−0.204077
$46$	−4.74419	+	0.701884i	−0.699493	+	0.103487i
$47$	−13.0590			−1.90486			−0.952429	−	0.304761i	$-0.901423\pi$
$47$	−13.0590			−1.90486			−0.952429	+	0.304761i	$0.901423\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.444858	+	3.09405i	0.0629124	+	0.437565i
$51$	−2.76144	−	6.04671i	−0.386679	−	0.846708i
$52$	−0.764047	+	5.31406i	−0.105954	+	0.736928i
$53$	−3.94865	+	1.15943i	−0.542389	+	0.159260i	−0.541439	−	0.840740i	$-0.682120\pi$
$53$	−3.94865	+	1.15943i	−0.542389	+	0.159260i	−0.000949555		1.00000i	$0.500302\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	−2.06080	+	4.51252i	−0.277878	+	0.608468i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−0.978262	−	1.12897i	−0.129574	−	0.149536i
$58$	−2.92935	−	3.38065i	−0.384643	−	0.443902i
$59$	−2.73431	−	0.802865i	−0.355976	−	0.104524i	0.0988545	−	0.995102i	$-0.468482\pi$
$59$	−2.73431	−	0.802865i	−0.355976	−	0.104524i	−0.454831	+	0.890578i	$0.650300\pi$
$60$	0.568699	−	1.24528i	0.0734187	−	0.160764i
$61$	7.12582	+	4.57949i	0.912368	+	0.586343i	0.910434	−	0.413655i	$-0.135748\pi$
$61$	7.12582	+	4.57949i	0.912368	+	0.586343i	0.00193425	+	0.999998i	$0.499384\pi$
$62$	−8.59105	+	2.52256i	−1.09106	+	0.320365i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	1.04597	+	7.27489i	0.129737	+	0.902339i
$66$	−3.04846	+	1.95913i	−0.375240	+	0.241152i
$67$	−2.17226	+	2.50692i	−0.265384	+	0.306270i	−0.872764	−	0.488142i	$-0.837675\pi$
$67$	−2.17226	+	2.50692i	−0.265384	+	0.306270i	0.607380	+	0.794411i	$0.292220\pi$
$68$	6.64742			0.806118
$69$	−4.74976	−	0.663141i	−0.571804	−	0.0798328i
$70$	1.36899			0.163625
$71$	−10.3604	+	11.9565i	−1.22955	+	1.41898i	−0.354427	+	0.935084i	$0.615324\pi$
$71$	−10.3604	+	11.9565i	−1.22955	+	1.41898i	−0.875126	+	0.483896i	$0.839221\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	−0.561205	−	3.90327i	−0.0656841	−	0.456843i	−0.995946	−	0.0899479i	$-0.971330\pi$
$73$	−0.561205	−	3.90327i	−0.0656841	−	0.456843i	0.930262	−	0.366895i	$-0.119579\pi$
$74$	0.717923	+	1.57203i	0.0834569	+	0.182745i
$75$	−0.444858	+	3.09405i	−0.0513677	+	0.357270i
$76$	1.43334	−	0.420865i	0.164415	−	0.0482766i
$77$	−3.04846	−	1.95913i	−0.347404	−	0.223263i
$78$	−2.23024	+	4.88355i	−0.252525	+	0.552953i
$79$	1.23033	+	0.361258i	0.138423	+	0.0406447i	0.350210	−	0.936671i	$-0.386110\pi$
$79$	1.23033	+	0.361258i	0.138423	+	0.0406447i	−0.211787	+	0.977316i	$0.567928\pi$
$80$	0.896497	+	1.03461i	0.100231	+	0.115673i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−11.9160	−	3.49884i	−1.31590	−	0.386383i
$83$	−3.91195	+	8.56597i	−0.429392	+	0.940238i	0.564033	+	0.825752i	$0.309249\pi$
$83$	−3.91195	+	8.56597i	−0.429392	+	0.940238i	−0.993425	+	0.114485i	$0.963478\pi$
$84$	0.841254	+	0.540641i	0.0917883	+	0.0589887i
$85$	8.73162	−	2.56384i	0.947077	−	0.278087i
$86$	0.345883	−	2.40567i	0.0372975	−	0.259410i
$87$	−1.85825	−	4.06901i	−0.199226	−	0.436243i
$88$	−0.515708	−	3.58683i	−0.0549747	−	0.382357i
$89$	6.12242	−	3.93464i	0.648975	−	0.417071i	−0.174317	−	0.984690i	$-0.555772\pi$
$89$	6.12242	−	3.93464i	0.648975	−	0.417071i	0.823292	+	0.567619i	$0.192135\pi$
$90$	0.896497	−	1.03461i	0.0944991	−	0.109058i
$91$	−5.36871			−0.562794
$92$	2.57634	−	4.04506i	0.268602	−	0.421726i
$93$	−8.95374			−0.928459
$94$	8.55186	−	9.86937i	0.882057	−	1.01795i
$95$	1.72041	−	1.10564i	0.176511	−	0.113437i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	6.30470	+	13.8054i	0.640145	+	1.40172i	0.899921	+	0.436054i	$0.143624\pi$
$97$	6.30470	+	13.8054i	0.640145	+	1.40172i	−0.259776	+	0.965669i	$0.583649\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	−3.47693	+	1.02092i	−0.349444	+	0.102606i
$100$	−2.62965	−	1.68997i	−0.262965	−	0.168997i
$101$	3.14191	−	6.87983i	0.312632	−	0.684568i	−0.686460	−	0.727167i	$-0.740837\pi$
$101$	3.14191	−	6.87983i	0.312632	−	0.684568i	0.999092	+	0.0425990i	$0.0135638\pi$
$102$	6.37815	+	1.87279i	0.631531	+	0.185434i
$103$	2.25754	+	2.60534i	0.222442	+	0.256712i	0.855991	−	0.516991i	$-0.172948\pi$
$103$	2.25754	+	2.60534i	0.222442	+	0.256712i	−0.633549	+	0.773703i	$0.718402\pi$
$104$	−3.51576	−	4.05740i	−0.344748	−	0.397861i
$105$	1.31354	+	0.385689i	0.128188	+	0.0376394i
$106$	1.70958	−	3.74346i	0.166049	−	0.363597i
$107$	−16.5553	−	10.6395i	−1.60046	−	1.02855i	−0.966998	−	0.254782i	$-0.917996\pi$
$107$	−16.5553	−	10.6395i	−1.60046	−	1.02855i	−0.633464	−	0.773772i	$-0.718367\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	1.37185	−	9.54141i	0.131399	−	0.913901i	−0.812334	−	0.583193i	$-0.801803\pi$
$109$	1.37185	−	9.54141i	0.131399	−	0.913901i	0.943733	−	0.330708i	$-0.107288\pi$
$110$	−2.06080	−	4.51252i	−0.196490	−	0.430252i
$111$	0.245950	+	1.71062i	0.0233445	+	0.162365i
$112$	−0.841254	+	0.540641i	−0.0794910	+	0.0510858i
$113$	−3.68011	+	4.24708i	−0.346196	+	0.399532i	−0.901968	−	0.431803i	$-0.857877\pi$
$113$	−3.68011	+	4.24708i	−0.346196	+	0.399532i	0.555772	+	0.831335i	$0.312423\pi$
$114$	1.49385			0.139912
$115$	1.82398	−	6.30699i	0.170087	−	0.588130i
$116$	4.47325			0.415330
$117$	−3.51576	+	4.05740i	−0.325032	+	0.375107i
$118$	2.39736	−	1.54069i	0.220694	−	0.141832i
$119$	0.946027	+	6.57976i	0.0867221	+	0.603166i
$120$	0.568699	+	1.24528i	0.0519148	+	0.113678i
$121$	−0.303314	+	2.10959i	−0.0275740	+	0.191781i
$122$	−8.12737	+	2.38641i	−0.735817	+	0.216055i
$123$	−10.4475	−	6.71423i	−0.942024	−	0.605402i
$124$	3.71952	−	8.14460i	0.334022	−	0.731407i
$125$	−10.6736	−	3.13406i	−0.954677	−	0.280319i
$126$	0.654861	+	0.755750i	0.0583396	+	0.0673275i
$127$	−7.47308	−	8.62439i	−0.663128	−	0.765291i	0.320156	−	0.947365i	$-0.396265\pi$
$127$	−7.47308	−	8.62439i	−0.663128	−	0.765291i	−0.983285	+	0.182074i	$0.941719\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	1.00963	−	2.21078i	0.0888927	−	0.194648i
$130$	−6.18296	−	3.97355i	−0.542282	−	0.348503i
$131$	17.3321	−	5.08916i	1.51431	−	0.444642i	0.584104	−	0.811679i	$-0.301446\pi$
$131$	17.3321	−	5.08916i	1.51431	−	0.444642i	0.930206	+	0.367037i	$0.119628\pi$
$132$	0.515708	−	3.58683i	0.0448866	−	0.312193i
$133$	0.620566	+	1.35885i	0.0538099	+	0.117827i
$134$	−0.472078	−	3.28337i	−0.0407813	−	0.283640i
$135$	1.15167	−	0.740131i	0.0991197	−	0.0637004i
$136$	−4.35313	+	5.02379i	−0.373278	+	0.430786i
$137$	6.35674			0.543093			0.271546	−	0.962425i	$-0.412465\pi$
$137$	6.35674			0.543093			0.271546	+	0.962425i	$0.412465\pi$
$138$	3.61160	−	3.15537i	0.307440	−	0.268603i
$139$	−16.2351			−1.37705			−0.688523	−	0.725214i	$-0.741741\pi$
$139$	−16.2351			−1.37705			−0.688523	+	0.725214i	$0.741741\pi$
$140$	−0.896497	+	1.03461i	−0.0757678	+	0.0874407i
$141$	10.9860	−	7.06025i	0.925185	−	0.594581i
$142$	−2.25153	−	15.6597i	−0.188944	−	1.31414i
$143$	8.08175	+	17.6966i	0.675830	+	1.47986i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	5.87577	−	1.72528i	0.487956	−	0.143277i
$146$	3.31740	+	2.13197i	0.274550	+	0.176443i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	−1.65820	−	0.486892i	−0.136303	−	0.0400223i
$149$	10.3616	+	11.9579i	0.848851	+	0.979627i	0.999960	−	0.00889035i	$-0.00282992\pi$
$149$	10.3616	+	11.9579i	0.848851	+	0.979627i	−0.151109	+	0.988517i	$0.548284\pi$
$150$	−2.04701	−	2.36237i	−0.167138	−	0.192887i
$151$	7.40982	+	2.17572i	0.603002	+	0.177057i	0.568963	−	0.822363i	$-0.307345\pi$
$151$	7.40982	+	2.17572i	0.603002	+	0.177057i	0.0340393	+	0.999420i	$0.489163\pi$
$152$	−0.620566	+	1.35885i	−0.0503346	+	0.110217i
$153$	5.59217	+	3.59387i	0.452100	+	0.290547i
$154$	3.47693	−	1.02092i	0.280179	−	0.0822679i
$155$	1.74443	−	12.1328i	0.140116	−	0.974530i
$156$	−2.23024	−	4.88355i	−0.178562	−	0.390997i
$157$	2.34306	+	16.2963i	0.186996	+	1.30059i	0.839731	+	0.543002i	$0.182712\pi$
$157$	2.34306	+	16.2963i	0.186996	+	1.30059i	−0.652735	+	0.757586i	$0.726378\pi$
$158$	−1.07872	+	0.693248i	−0.0858180	+	0.0551519i
$159$	2.69498	−	3.11018i	0.213726	−	0.246653i
$160$	−1.36899			−0.108228
$161$	4.37054	+	1.97444i	0.344446	+	0.155608i
$162$	1.00000			0.0785674
$163$	1.20299	−	1.38833i	0.0942257	−	0.108742i	−0.706678	−	0.707535i	$-0.749807\pi$
$163$	1.20299	−	1.38833i	0.0942257	−	0.108742i	0.800904	+	0.598793i	$0.204353\pi$
$164$	10.4475	−	6.71423i	0.815817	−	0.524293i
$165$	−0.705999	−	4.91033i	−0.0549619	−	0.382268i
$166$	−3.91195	−	8.56597i	−0.303626	−	0.664848i
$167$	−0.690987	+	4.80592i	−0.0534701	+	0.371893i	0.945464	+	0.325728i	$0.105609\pi$
$167$	−0.690987	+	4.80592i	−0.0534701	+	0.371893i	−0.998934	+	0.0461654i	$0.985300\pi$
$168$	−0.959493	+	0.281733i	−0.0740265	+	0.0217361i
$169$	13.3112	+	8.55458i	1.02394	+	0.658044i
$170$	−3.78038	+	8.27787i	−0.289942	+	0.634884i
$171$	1.43334	+	0.420865i	0.109610	+	0.0321844i
$172$	1.59158	+	1.83678i	0.121357	+	0.140053i
$173$	8.78418	+	10.1375i	0.667849	+	0.770739i	0.984038	−	0.177957i	$-0.0569489\pi$
$173$	8.78418	+	10.1375i	0.667849	+	0.770739i	−0.316189	+	0.948696i	$0.602403\pi$
$174$	4.29205	+	1.26026i	0.325379	+	0.0955400i
$175$	1.29853	−	2.84339i	0.0981599	−	0.214940i
$176$	3.04846	+	1.95913i	0.229786	+	0.147675i
$177$	2.73431	−	0.802865i	0.205523	−	0.0603470i
$178$	−1.03573	+	7.20365i	−0.0776312	+	0.539937i
$179$	5.30896	+	11.6250i	0.396810	+	0.868893i	0.997584	+	0.0694739i	$0.0221320\pi$
$179$	5.30896	+	11.6250i	0.396810	+	0.868893i	−0.600774	+	0.799419i	$0.705141\pi$
$180$	0.194827	+	1.35505i	0.0145216	+	0.101000i
$181$	−17.9934	+	11.5636i	−1.33744	+	0.859518i	−0.996742	−	0.0806555i	$-0.974299\pi$
$181$	−17.9934	+	11.5636i	−1.33744	+	0.859518i	−0.340695	+	0.940174i	$0.610662\pi$
$182$	3.51576	−	4.05740i	0.260605	−	0.300754i
$183$	−8.47048			−0.626156
$184$	1.36991	+	4.59601i	0.100991	+	0.338823i
$185$	−2.36590			−0.173944
$186$	5.86345	−	6.76678i	0.429929	−	0.496165i
$187$	20.2644	−	13.0231i	1.48188	−	0.952346i
$188$	1.85850	+	12.9261i	0.135545	+	0.942734i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	−0.291042	+	2.02424i	−0.0211144	+	0.146854i
$191$	2.94061	−	0.863440i	0.212775	−	0.0624763i	−0.173608	−	0.984815i	$-0.555543\pi$
$191$	2.94061	−	0.863440i	0.212775	−	0.0624763i	0.386383	+	0.922339i	$0.373724\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	9.33313	−	20.4367i	0.671813	−	1.47107i	−0.199277	−	0.979943i	$-0.563859\pi$
$193$	9.33313	−	20.4367i	0.671813	−	1.47107i	0.871090	−	0.491123i	$-0.163413\pi$
$194$	−14.5621	−	4.27582i	−1.04550	−	0.306986i
$195$	−4.81303	−	5.55453i	−0.344668	−	0.397768i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−9.13722	−	2.68293i	−0.651000	−	0.191151i	−0.0604743	−	0.998170i	$-0.519261\pi$
$197$	−9.13722	−	2.68293i	−0.651000	−	0.191151i	−0.590526	+	0.807019i	$0.701080\pi$
$198$	1.50534	−	3.29624i	0.106980	−	0.234254i
$199$	−17.9123	−	11.5115i	−1.26977	−	0.816031i	−0.280179	−	0.959948i	$-0.590394\pi$
$199$	−17.9123	−	11.5115i	−1.26977	−	0.816031i	−0.989590	+	0.143917i	$0.954030\pi$
$200$	2.99925	−	0.880659i	0.212079	−	0.0622720i
$201$	0.472078	−	3.28337i	0.0332978	−	0.231591i
$202$	3.14191	+	6.87983i	0.221064	+	0.484063i
$203$	0.636609	+	4.42771i	0.0446812	+	0.310765i
$204$	−5.59217	+	3.59387i	−0.391530	+	0.251621i
$205$	11.1336	−	12.8489i	0.777606	−	0.897405i
$206$	−3.44736			−0.240189
$207$	4.35428	−	2.01005i	0.302643	−	0.139708i
$208$	5.36871			0.372253
$209$	3.54494	−	4.09108i	0.245209	−	0.282986i
$210$	−1.15167	+	0.740131i	−0.0794726	+	0.0510739i
$211$	1.85867	+	12.9273i	0.127956	+	0.889954i	0.948140	+	0.317854i	$0.102962\pi$
$211$	1.85867	+	12.9273i	0.127956	+	0.889954i	−0.820184	+	0.572100i	$0.806129\pi$
$212$	1.70958	+	3.74346i	0.117414	+	0.257102i
$213$	2.25153	−	15.6597i	0.154272	−	1.07299i
$214$	18.8822	−	5.54431i	1.29076	−	0.379001i
$215$	2.79902	+	1.79882i	0.190891	+	0.122678i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	8.59105	+	2.52256i	0.583198	+	0.171242i
$218$	6.31255	+	7.28507i	0.427540	+	0.493407i
$219$	2.58238	+	2.98023i	0.174501	+	0.201385i
$220$	4.75987	+	1.39762i	0.320911	+	0.0942279i
$221$	14.8254	−	32.4630i	0.997261	−	2.18370i
$222$	−1.45386	−	0.934340i	−0.0975767	−	0.0627088i
$223$	−12.8346	+	3.76858i	−0.859469	+	0.252363i	−0.681630	−	0.731697i	$-0.738729\pi$
$223$	−12.8346	+	3.76858i	−0.859469	+	0.252363i	−0.177839	+	0.984060i	$0.556911\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−1.29853	−	2.84339i	−0.0865689	−	0.189559i
$226$	−0.799765	−	5.56249i	−0.0531996	−	0.370011i
$227$	3.54545	−	2.27852i	0.235320	−	0.151231i	−0.417667	−	0.908600i	$-0.637152\pi$
$227$	3.54545	−	2.27852i	0.235320	−	0.151231i	0.652987	+	0.757369i	$0.273516\pi$
$228$	−0.978262	+	1.12897i	−0.0647870	+	0.0747681i
$229$	−6.08721			−0.402254			−0.201127	−	0.979565i	$-0.564460\pi$
$229$	−6.08721			−0.402254			−0.201127	+	0.979565i	$0.564460\pi$
$230$	3.57205	+	5.50867i	0.235534	+	0.363231i
$231$	3.62371			0.238423
$232$	−2.92935	+	3.38065i	−0.192321	+	0.221951i
$233$	0.764826	−	0.491524i	0.0501054	−	0.0322008i	−0.515348	−	0.856981i	$-0.672337\pi$
$233$	0.764826	−	0.491524i	0.0501054	−	0.0322008i	0.565454	+	0.824780i	$0.308701\pi$
$234$	−0.764047	−	5.31406i	−0.0499473	−	0.347391i
$235$	7.42666	+	16.2621i	0.484462	+	1.06082i
$236$	−0.405561	+	2.82074i	−0.0263997	+	0.183614i
$237$	−1.23033	+	0.361258i	−0.0799186	+	0.0234662i
$238$	−5.59217	−	3.59387i	−0.362486	−	0.232956i
$239$	−0.302623	+	0.662652i	−0.0195751	+	0.0428634i	−0.919167	−	0.393868i	$-0.871137\pi$
$239$	−0.302623	+	0.662652i	−0.0195751	+	0.0428634i	0.899592	+	0.436731i	$0.143864\pi$
$240$	−1.31354	−	0.385689i	−0.0847883	−	0.0248961i
$241$	3.15557	+	3.64173i	0.203268	+	0.234584i	0.848226	−	0.529634i	$-0.177671\pi$
$241$	3.15557	+	3.64173i	0.203268	+	0.234584i	−0.644958	+	0.764218i	$0.723125\pi$
$242$	−1.39570	−	1.61072i	−0.0897188	−	0.103541i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	3.51877	−	7.70502i	0.225266	−	0.493263i
$245$	−1.15167	−	0.740131i	−0.0735773	−	0.0472853i
$246$	11.9160	−	3.49884i	0.759734	−	0.223078i
$247$	1.14137	−	7.93840i	0.0726236	−	0.505108i
$248$	3.71952	+	8.14460i	0.236190	+	0.517183i
$249$	−1.34017	−	9.32111i	−0.0849301	−	0.590702i
$250$	9.35829	−	6.01421i	0.591870	−	0.380372i
$251$	3.94233	−	4.54969i	0.248838	−	0.287174i	−0.617565	−	0.786520i	$-0.711881\pi$
$251$	3.94233	−	4.54969i	0.248838	−	0.287174i	0.866403	+	0.499346i	$0.166426\pi$
$252$	−1.00000			−0.0629941
$253$	−0.0709177	−	17.3786i	−0.00445856	−	1.09258i
$254$	11.4117			0.716034
$255$	−5.95939	+	6.87751i	−0.373192	+	0.430686i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	1.51555	+	10.5408i	0.0945371	+	0.657520i	0.980898	+	0.194524i	$0.0623164\pi$
$257$	1.51555	+	10.5408i	0.0945371	+	0.657520i	−0.886361	+	0.462996i	$0.846775\pi$
$258$	1.00963	+	2.21078i	0.0628566	+	0.137637i
$259$	0.245950	−	1.71062i	0.0152826	−	0.106293i
$260$	7.05199	−	2.07065i	0.437346	−	0.128416i
$261$	3.76313	+	2.41842i	0.232932	+	0.149696i
$262$	−7.50397	+	16.4314i	−0.463597	+	1.01513i
$263$	−26.8750	−	7.89120i	−1.65718	−	0.486592i	−0.686533	−	0.727099i	$-0.740868\pi$
$263$	−26.8750	−	7.89120i	−1.65718	−	0.486592i	−0.970648	+	0.240506i	$0.922687\pi$
$264$	2.37303	+	2.73862i	0.146050	+	0.168550i
$265$	3.68940	+	4.25780i	0.226638	+	0.261554i
$266$	−1.43334	−	0.420865i	−0.0878834	−	0.0258049i
$267$	−3.02328	+	6.62006i	−0.185022	+	0.405141i
$268$	2.79055	+	1.79338i	0.170460	+	0.109548i
$269$	4.59754	−	1.34996i	0.280317	−	0.0823085i	−0.138552	−	0.990355i	$-0.544245\pi$
$269$	4.59754	−	1.34996i	0.280317	−	0.0823085i	0.418869	+	0.908047i	$0.362427\pi$
$270$	−0.194827	+	1.35505i	−0.0118568	+	0.0824660i
$271$	−11.3556	−	24.8654i	−0.689807	−	1.51047i	−0.851908	−	0.523691i	$-0.824554\pi$
$271$	−11.3556	−	24.8654i	−0.689807	−	1.51047i	0.162102	−	0.986774i	$-0.448173\pi$
$272$	−0.946027	−	6.57976i	−0.0573613	−	0.398956i
$273$	4.51644	−	2.90254i	0.273348	−	0.175670i
$274$	−4.16278	+	4.80410i	−0.251483	+	0.290227i
$275$	−11.3272			−0.683059
$276$	0.0195705	+	4.79579i	0.00117800	+	0.288673i
$277$	22.3145			1.34075			0.670375	−	0.742023i	$-0.266133\pi$
$277$	22.3145			1.34075			0.670375	+	0.742023i	$0.266133\pi$
$278$	10.6318	−	12.2697i	0.637650	−	0.735887i
$279$	7.53236	−	4.84076i	0.450951	−	0.289808i
$280$	−0.194827	−	1.35505i	−0.0116432	−	0.0809800i
$281$	−8.41649	−	18.4295i	−0.502086	−	1.09941i	−0.975786	−	0.218728i	$-0.929809\pi$
$281$	−8.41649	−	18.4295i	−0.502086	−	1.09941i	0.473700	−	0.880686i	$-0.342918\pi$
$282$	−1.85850	+	12.9261i	−0.110672	+	0.769739i
$283$	7.79854	−	2.28986i	0.463575	−	0.136118i	−0.0416007	−	0.999134i	$-0.513246\pi$
$283$	7.79854	−	2.28986i	0.463575	−	0.136118i	0.505176	+	0.863016i	$0.331428\pi$
$284$	13.3093	+	8.55335i	0.789760	+	0.507548i
$285$	−0.849549	+	1.86025i	−0.0503229	+	0.110192i
$286$	−18.6666	−	5.48101i	−1.10378	−	0.324099i
$287$	8.13273	+	9.38567i	0.480060	+	0.554019i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−26.0869	−	7.65980i	−1.53452	−	0.450576i
$290$	−2.54393	+	5.57043i	−0.149385	+	0.327107i
$291$	−12.7676	−	8.20524i	−0.748450	−	0.480999i
$292$	−3.78367	+	1.11099i	−0.221422	+	0.0650155i
$293$	3.60500	−	25.0733i	0.210606	−	1.46480i	−0.560533	−	0.828132i	$-0.689404\pi$
$293$	3.60500	−	25.0733i	0.210606	−	1.46480i	0.771139	−	0.636666i	$-0.219687\pi$
$294$	−0.415415	−	0.909632i	−0.0242275	−	0.0530508i
$295$	0.555208	+	3.86156i	0.0323255	+	0.224828i
$296$	1.45386	−	0.934340i	0.0845039	−	0.0543074i
$297$	2.37303	−	2.73862i	0.137697	−	0.158911i
$298$	−15.8225			−0.916574
$299$	−14.0084	−	21.6031i	−0.810125	−	1.24934i
$300$	3.12587			0.180472
$301$	−1.59158	+	1.83678i	−0.0917370	+	0.105870i
$302$	−6.49670	+	4.17517i	−0.373843	+	0.240254i
$303$	1.07637	+	7.48632i	0.0618359	+	0.430078i
$304$	−0.620566	−	1.35885i	−0.0355919	−	0.0779354i
$305$	1.65028	−	11.4780i	0.0944949	−	0.657226i
$306$	−6.37815	+	1.87279i	−0.364615	+	0.107061i
$307$	16.7472	+	10.7628i	0.955814	+	0.614264i	0.922836	−	0.385192i	$-0.125865\pi$
$307$	16.7472	+	10.7628i	0.955814	+	0.614264i	0.0329772	+	0.999456i	$0.489501\pi$
$308$	−1.50534	+	3.29624i	−0.0857750	+	0.187821i
$309$	−3.30772	−	0.971234i	−0.188170	−	0.0552516i
$310$	8.02700	+	9.26365i	0.455903	+	0.526140i
$311$	21.8098	+	25.1698i	1.23672	+	1.42725i	0.867152	+	0.498044i	$0.165948\pi$
$311$	21.8098	+	25.1698i	1.23672	+	1.42725i	0.369566	+	0.929204i	$0.379506\pi$
$312$	5.15124	+	1.51254i	0.291631	+	0.0856307i
$313$	−7.41033	+	16.2263i	−0.418856	+	0.917167i	0.576149	+	0.817345i	$0.304555\pi$
$313$	−7.41033	+	16.2263i	−0.418856	+	0.917167i	−0.995005	+	0.0998227i	$0.968172\pi$
$314$	−13.8503	−	8.90106i	−0.781619	−	0.502316i
$315$	−1.31354	+	0.385689i	−0.0740093	+	0.0217311i
$316$	0.182486	−	1.26922i	0.0102657	−	0.0713992i
$317$	12.5019	+	27.3754i	0.702177	+	1.53755i	0.837311	+	0.546727i	$0.184126\pi$
$317$	12.5019	+	27.3754i	0.702177	+	1.53755i	−0.135134	+	0.990827i	$0.543146\pi$
$318$	0.585676	+	4.07346i	0.0328431	+	0.228428i
$319$	13.6365	−	8.76365i	0.763498	−	0.490670i
$320$	0.896497	−	1.03461i	0.0501157	−	0.0578366i
$321$	19.6793			1.09839
$322$	−4.35428	+	2.01005i	−0.242654	+	0.112015i
$323$	−9.93023			−0.552533
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−14.1178	+	9.07297i	−0.783116	+	0.503278i
$326$	0.261435	+	1.81832i	0.0144796	+	0.100708i
$327$	4.00440	+	8.76842i	0.221444	+	0.484895i
$328$	−1.76741	+	12.2926i	−0.0975890	+	0.678746i
$329$	−12.5301	+	3.67916i	−0.690805	+	0.202839i
$330$	4.17331	+	2.68202i	0.229733	+	0.147640i
$331$	−10.6514	+	23.3233i	−0.585453	+	1.28196i	0.352698	+	0.935737i	$0.385264\pi$
$331$	−10.6514	+	23.3233i	−0.585453	+	1.28196i	−0.938151	+	0.346226i	$0.887463\pi$
$332$	9.03551	+	2.65307i	0.495888	+	0.145606i
$333$	−1.13174	−	1.30609i	−0.0620187	−	0.0715734i
$334$	−3.17957	−	3.66942i	−0.173978	−	0.200782i
$335$	4.35717	+	1.27938i	0.238058	+	0.0699001i
$336$	0.415415	−	0.909632i	0.0226627	−	0.0496245i
$337$	10.0610	+	6.46580i	0.548056	+	0.352214i	0.785183	−	0.619264i	$-0.212569\pi$
$337$	10.0610	+	6.46580i	0.548056	+	0.352214i	−0.237126	+	0.971479i	$0.576205\pi$
$338$	−15.1821	+	4.45786i	−0.825797	+	0.242476i
$339$	0.799765	−	5.56249i	0.0434373	−	0.302113i
$340$	−3.78038	−	8.27787i	−0.205020	−	0.448931i
$341$	−4.61751	−	32.1155i	−0.250052	−	1.73915i
$342$	−1.25670	+	0.807635i	−0.0679548	+	0.0436719i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−2.43041			−0.131039
$345$	1.87539	+	6.29189i	0.100968	+	0.338744i
$346$	−13.4138			−0.721131
$347$	−4.39003	+	5.06637i	−0.235669	+	0.271977i	−0.861249	−	0.508184i	$-0.830317\pi$
$347$	−4.39003	+	5.06637i	−0.235669	+	0.271977i	0.625580	+	0.780160i	$0.284863\pi$
$348$	−3.76313	+	2.41842i	−0.201725	+	0.129641i
$349$	−0.179695	−	1.24981i	−0.00961887	−	0.0669007i	0.984447	−	0.175684i	$-0.0562137\pi$
$349$	−0.179695	−	1.24981i	−0.00961887	−	0.0669007i	−0.994065	+	0.108783i	$0.965305\pi$
$350$	1.29853	+	2.84339i	0.0694095	+	0.151986i
$351$	0.764047	−	5.31406i	0.0407818	−	0.283644i
$352$	−3.47693	+	1.02092i	−0.185321	+	0.0544151i
$353$	−7.86421	−	5.05402i	−0.418570	−	0.268998i	0.314359	−	0.949304i	$-0.398211\pi$
$353$	−7.86421	−	5.05402i	−0.418570	−	0.268998i	−0.732928	+	0.680306i	$0.761847\pi$
$354$	−1.18383	+	2.59222i	−0.0629196	+	0.137775i
$355$	20.7811	+	6.10189i	1.10295	+	0.323855i
$356$	−4.76590	−	5.50014i	−0.252592	−	0.291507i
$357$	−4.35313	−	5.02379i	−0.230392	−	0.265887i
$358$	−12.2622	−	3.60051i	−0.648078	−	0.190293i
$359$	11.8316	−	25.9076i	0.624449	−	1.36735i	−0.287790	−	0.957693i	$-0.592921\pi$
$359$	11.8316	−	25.9076i	0.624449	−	1.36735i	0.912239	−	0.409659i	$-0.134352\pi$
$360$	−1.15167	−	0.740131i	−0.0606982	−	0.0390083i
$361$	16.0892	−	4.72421i	0.846799	−	0.248643i
$362$	3.04394	−	21.1711i	0.159986	−	1.11273i
$363$	−0.885369	−	1.93869i	−0.0464698	−	0.101755i
$364$	0.764047	+	5.31406i	0.0400469	+	0.278533i
$365$	−4.54149	+	2.91864i	−0.237712	+	0.152768i
$366$	5.54699	−	6.40156i	0.289946	−	0.334615i
$367$	−35.0166			−1.82785			−0.913927	−	0.405878i	$-0.866966\pi$
$367$	−35.0166			−1.82785			−0.913927	+	0.405878i	$0.866966\pi$
$368$	−4.37054	−	1.97444i	−0.227830	−	0.102925i
$369$	12.4190			0.646509
$370$	1.54933	−	1.78803i	0.0805460	−	0.0929550i
$371$	−3.46205	+	2.22493i	−0.179741	+	0.115512i
$372$	1.27425	+	8.86260i	0.0660668	+	0.459504i
$373$	−5.57366	−	12.2046i	−0.288593	−	0.631931i	0.708696	−	0.705514i	$-0.249284\pi$
$373$	−5.57366	−	12.2046i	−0.288593	−	0.631931i	−0.997289	+	0.0735831i	$0.976557\pi$
$374$	−3.42813	+	23.8432i	−0.177264	+	1.23290i
$375$	10.6736	−	3.13406i	0.551183	−	0.161842i
$376$	−10.9860	−	7.06025i	−0.566558	−	0.364105i
$377$	9.97642	−	21.8453i	0.513812	−	1.12509i
$378$	−0.959493	−	0.281733i	−0.0493510	−	0.0144908i
$379$	−1.59490	−	1.84062i	−0.0819247	−	0.0945461i	0.713307	−	0.700851i	$-0.247196\pi$
$379$	−1.59490	−	1.84062i	−0.0819247	−	0.0945461i	−0.795232	+	0.606305i	$0.792651\pi$
$380$	−1.33923	−	1.54555i	−0.0687010	−	0.0792852i
$381$	10.9495	+	3.21505i	0.560957	+	0.164712i
$382$	−1.27314	+	2.78779i	−0.0651397	+	0.142636i
$383$	−15.8506	−	10.1866i	−0.809930	−	0.520510i	0.0689123	−	0.997623i	$-0.478047\pi$
$383$	−15.8506	−	10.1866i	−0.809930	−	0.520510i	−0.878842	+	0.477112i	$0.841683\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	−0.705999	+	4.91033i	−0.0359810	+	0.250253i
$386$	9.33313	+	20.4367i	0.475044	+	1.04020i
$387$	0.345883	+	2.40567i	0.0175822	+	0.122287i
$388$	12.7676	−	8.20524i	0.648176	−	0.416558i
$389$	13.7238	−	15.8381i	0.695822	−	0.803021i	−0.292360	−	0.956308i	$-0.594440\pi$
$389$	13.7238	−	15.8381i	0.695822	−	0.803021i	0.988182	+	0.153287i	$0.0489859\pi$
$390$	7.34970			0.372167
$391$	−24.0078	+	20.9750i	−1.21413	+	1.06075i
$392$	1.00000			0.0505076
$393$	−11.8293	+	13.6517i	−0.596707	+	0.688637i
$394$	8.01123	−	5.14850i	0.403600	−	0.259378i
$395$	−0.249822	−	1.73755i	−0.0125699	−	0.0874255i
$396$	1.50534	+	3.29624i	0.0756464	+	0.165643i
$397$	−4.28414	+	29.7969i	−0.215015	+	1.49546i	0.541064	+	0.840981i	$0.318022\pi$
$397$	−4.28414	+	29.7969i	−0.215015	+	1.49546i	−0.756079	+	0.654480i	$0.772887\pi$
$398$	20.4299	−	5.99876i	1.02406	−	0.300691i
$399$	−1.25670	−	0.807635i	−0.0629139	−	0.0404323i
$400$	−1.29853	+	2.84339i	−0.0649267	+	0.142170i
$401$	−7.46907	−	2.19312i	−0.372987	−	0.109519i	0.0898659	−	0.995954i	$-0.471356\pi$
$401$	−7.46907	−	2.19312i	−0.372987	−	0.109519i	−0.462853	+	0.886435i	$0.653174\pi$
$402$	2.17226	+	2.50692i	0.108343	+	0.125034i
$403$	−31.4792	−	36.3289i	−1.56809	−	1.80967i
$404$	−7.25694	−	2.13083i	−0.361046	−	0.106013i
$405$	−0.568699	+	1.24528i	−0.0282589	+	0.0618783i
$406$	−3.76313	−	2.41842i	−0.186761	−	0.120024i
$407$	−6.00885	+	1.76436i	−0.297848	+	0.0874560i
$408$	0.946027	−	6.57976i	0.0468353	−	0.325747i
$409$	−3.45455	−	7.56440i	−0.170816	−	0.374036i	0.804791	−	0.593558i	$-0.202277\pi$
$409$	−3.45455	−	7.56440i	−0.170816	−	0.374036i	−0.975607	+	0.219523i	$0.929550\pi$
$410$	2.41957	+	16.8285i	0.119494	+	0.831098i
$411$	−5.34763	+	3.43671i	−0.263779	+	0.169521i
$412$	2.25754	−	2.60534i	0.111221	−	0.128356i
$413$	−2.84974			−0.140227
$414$	−1.33235	+	4.60704i	−0.0654816	+	0.226424i
$415$	12.8917			0.632830
$416$	−3.51576	+	4.05740i	−0.172374	+	0.198930i
$417$	13.6579	−	8.77738i	0.668829	−	0.429830i
$418$	0.770389	+	5.35817i	0.0376809	+	0.262077i
$419$	13.5260	+	29.6177i	0.660786	+	1.44692i	0.881788	+	0.471647i	$0.156340\pi$
$419$	13.5260	+	29.6177i	0.660786	+	1.44692i	−0.221001	+	0.975274i	$0.570932\pi$
$420$	0.194827	−	1.35505i	0.00950661	−	0.0661199i
$421$	−22.9538	+	6.73985i	−1.11870	+	0.328480i	−0.788258	−	0.615345i	$-0.789017\pi$
$421$	−22.9538	+	6.73985i	−1.11870	+	0.328480i	−0.330444	+	0.943826i	$0.607198\pi$
$422$	−10.9870	−	7.06091i	−0.534839	−	0.343720i
$423$	−5.42492	+	11.8789i	−0.263769	+	0.577573i
$424$	−3.94865	−	1.15943i	−0.191763	−	0.0563068i
$425$	13.6073	+	15.7037i	0.660052	+	0.761741i
$426$	10.3604	+	11.9565i	0.501963	+	0.579296i
$427$	8.12737	+	2.38641i	0.393311	+	0.115486i
$428$	−8.17509	+	17.9010i	−0.395158	+	0.865275i
$429$	−16.3663	−	10.5180i	−0.790172	−	0.507813i
$430$	−3.19242	+	0.937380i	−0.153952	+	0.0452045i
$431$	−4.40359	+	30.6277i	−0.212114	+	1.47528i	0.553967	+	0.832538i	$0.313113\pi$
$431$	−4.40359	+	30.6277i	−0.212114	+	1.47528i	−0.766081	+	0.642744i	$0.777796\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	5.00793	+	34.8309i	0.240666	+	1.67387i	0.648810	+	0.760950i	$0.275267\pi$
$433$	5.00793	+	34.8309i	0.240666	+	1.67387i	−0.408145	+	0.912917i	$0.633824\pi$
$434$	−7.53236	+	4.84076i	−0.361565	+	0.232364i
$435$	−4.01025	+	4.62808i	−0.192277	+	0.221899i
$436$	−9.63952			−0.461649
$437$	−3.84865	+	6.04270i	−0.184106	+	0.289061i
$438$	−3.94340			−0.188423
$439$	−21.0907	+	24.3399i	−1.00660	+	1.16168i	−0.0197919	+	0.999804i	$0.506300\pi$
$439$	−21.0907	+	24.3399i	−1.00660	+	1.16168i	−0.986811	+	0.161877i	$0.948245\pi$
$440$	−4.17331	+	2.68202i	−0.198955	+	0.127860i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	14.8254	+	32.4630i	0.705170	+	1.54411i
$443$	1.72324	−	11.9854i	0.0818738	−	0.569445i	−0.907050	−	0.421022i	$-0.861671\pi$
$443$	1.72324	−	11.9854i	0.0818738	−	0.569445i	0.988924	−	0.148422i	$-0.0474195\pi$
$444$	1.65820	−	0.486892i	0.0786948	−	0.0231069i
$445$	−8.38152	−	5.38648i	−0.397322	−	0.255343i
$446$	5.55678	−	12.1676i	0.263121	−	0.576155i
$447$	−15.1816	−	4.45772i	−0.718065	−	0.210843i
$448$	0.654861	+	0.755750i	0.0309393	+	0.0357058i
$449$	−12.2732	−	14.1641i	−0.579210	−	0.668444i	0.388225	−	0.921565i	$-0.373088\pi$
$449$	−12.2732	−	14.1641i	−0.579210	−	0.668444i	−0.967435	+	0.253121i	$0.918543\pi$
$450$	2.99925	+	0.880659i	0.141386	+	0.0415147i
$451$	18.6949	−	40.9361i	0.880309	−	1.92761i
$452$	4.72758	+	3.03823i	0.222367	+	0.142907i
$453$	−7.40982	+	2.17572i	−0.348144	+	0.102224i
$454$	−0.599784	+	4.17159i	−0.0281493	+	0.195782i
$455$	3.05318	+	6.68552i	0.143135	+	0.313422i
$456$	−0.212597	−	1.47864i	−0.00995575	−	0.0692437i
$457$	22.0515	−	14.1716i	1.03152	−	0.662921i	0.0886482	−	0.996063i	$-0.471745\pi$
$457$	22.0515	−	14.1716i	1.03152	−	0.662921i	0.942877	+	0.333142i	$0.108109\pi$
$458$	3.98628	−	4.60041i	0.186266	−	0.214963i
$459$	−6.64742			−0.310275
$460$	−6.50237	−	0.907833i	−0.303175	−	0.0423279i
$461$	1.10466			0.0514493			0.0257246	−	0.999669i	$-0.491811\pi$
$461$	1.10466			0.0514493			0.0257246	+	0.999669i	$0.491811\pi$
$462$	−2.37303	+	2.73862i	−0.110403	+	0.127412i
$463$	25.0441	−	16.0948i	1.16390	−	0.747991i	0.191538	−	0.981485i	$-0.438652\pi$
$463$	25.0441	−	16.0948i	1.16390	−	0.747991i	0.972358	+	0.233494i	$0.0750160\pi$
$464$	−0.636609	−	4.42771i	−0.0295538	−	0.205551i
$465$	5.09198	+	11.1499i	0.236135	+	0.517063i
$466$	−0.129386	+	0.899896i	−0.00599367	+	0.0416869i
$467$	−17.9870	+	5.28147i	−0.832341	+	0.244397i	−0.670022	−	0.742341i	$-0.733715\pi$
$467$	−17.9870	+	5.28147i	−0.832341	+	0.244397i	−0.162319	+	0.986738i	$0.551897\pi$
$468$	4.51644	+	2.90254i	0.208773	+	0.134170i
$469$	−1.37799	+	3.01737i	−0.0636296	+	0.139329i
$470$	−17.1535	−	5.03673i	−0.791233	−	0.232327i
$471$	−10.7816	−	12.4426i	−0.496788	−	0.573324i
$472$	−1.86618	−	2.15369i	−0.0858981	−	0.0991317i
$473$	8.45034	+	2.48124i	0.388547	+	0.114088i
$474$	0.532675	−	1.16640i	0.0244666	−	0.0535743i
$475$	3.92829	+	2.52456i	0.180242	+	0.115835i
$476$	6.37815	−	1.87279i	0.292342	−	0.0858394i
$477$	−0.585676	+	4.07346i	−0.0268162	+	0.186511i
$478$	−0.302623	−	0.662652i	−0.0138417	−	0.0303090i
$479$	−1.41166	−	9.81832i	−0.0645005	−	0.448611i	−0.996322	−	0.0856927i	$-0.972690\pi$
$479$	−1.41166	−	9.81832i	−0.0645005	−	0.448611i	0.931821	−	0.362918i	$-0.118219\pi$
$480$	1.15167	−	0.740131i	0.0525662	−	0.0337822i
$481$	−6.07596	+	7.01203i	−0.277040	+	0.319721i
$482$	−4.81870			−0.219486
$483$	−4.74419	+	0.701884i	−0.215868	+	0.0319368i
$484$	2.13129			0.0968767
$485$	13.6060	−	15.7022i	0.617818	−	0.712999i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−0.00631039	−	0.0438898i	−0.000285951	−	0.00198883i	0.989678	−	0.143309i	$-0.0457743\pi$
$487$	−0.00631039	−	0.0438898i	−0.000285951	−	0.00198883i	−0.989964	+	0.141320i	$0.954865\pi$
$488$	3.51877	+	7.70502i	0.159287	+	0.348790i
$489$	−0.261435	+	1.81832i	−0.0118225	+	0.0822274i
$490$	1.31354	−	0.385689i	0.0593395	−	0.0174236i
$491$	−24.7978	−	15.9366i	−1.11911	−	0.719207i	−0.155849	−	0.987781i	$-0.549811\pi$
$491$	−24.7978	−	15.9366i	−1.11911	−	0.719207i	−0.963259	+	0.268573i	$0.913448\pi$
$492$	−5.15905	+	11.2967i	−0.232588	+	0.509296i
$493$	−28.5310	−	8.37747i	−1.28497	−	0.377302i
$494$	5.25200	+	6.06113i	0.236299	+	0.272703i
$495$	3.24865	+	3.74914i	0.146016	+	0.168511i
$496$	−8.59105	−	2.52256i	−0.385749	−	0.113266i
$497$	−6.57218	+	14.3911i	−0.294803	+	0.645528i
$498$	7.92205	+	5.09120i	0.354996	+	0.228142i
$499$	4.45269	−	1.30743i	0.199330	−	0.0585284i	−0.180544	−	0.983567i	$-0.557786\pi$
$499$	4.45269	−	1.30743i	0.199330	−	0.0585284i	0.379873	+	0.925039i	$0.375968\pi$
$500$	−1.58314	+	11.0110i	−0.0708003	+	0.492427i
$501$	−2.01698	−	4.41657i	−0.0901120	−	0.197318i
$502$	0.856750	+	5.95883i	0.0382386	+	0.265955i
$503$	−10.1135	+	6.49958i	−0.450941	+	0.289802i	−0.746331	−	0.665574i	$-0.768187\pi$
$503$	−10.1135	+	6.49958i	−0.450941	+	0.289802i	0.295391	+	0.955377i	$0.404550\pi$
$504$	0.654861	−	0.755750i	0.0291698	−	0.0336638i
$505$	−10.3541			−0.460751
$506$	13.1803	+	11.3269i	0.585935	+	0.503544i
$507$	−15.8230			−0.702725
$508$	−7.47308	+	8.62439i	−0.331564	+	0.382645i
$509$	35.9595	−	23.1098i	1.59388	−	1.02432i	0.623783	−	0.781598i	$-0.285595\pi$
$509$	35.9595	−	23.1098i	1.59388	−	1.02432i	0.970095	−	0.242725i	$-0.0780413\pi$
$510$	−1.29510	−	9.00762i	−0.0573480	−	0.398864i
$511$	−1.63815	−	3.58705i	−0.0724675	−	0.158682i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	−1.43334	+	0.420865i	−0.0632833	+	0.0185817i
$514$	−8.95871	−	5.75742i	−0.395152	−	0.253949i
$515$	1.96051	−	4.29292i	0.0863903	−	0.189168i
$516$	−2.33196	−	0.684725i	−0.102659	−	0.0301433i
$517$	30.9895	+	35.7637i	1.36292	+	1.57289i
$518$	1.13174	+	1.30609i	0.0497256	+	0.0573864i
$519$	−12.8705	−	3.77911i	−0.564951	−	0.165884i
$520$	−3.05318	+	6.68552i	−0.133891	+	0.293180i
$521$	−14.6424	−	9.41007i	−0.641493	−	0.412263i	0.179056	−	0.983839i	$-0.442696\pi$
$521$	−14.6424	−	9.41007i	−0.641493	−	0.412263i	−0.820549	+	0.571576i	$0.806332\pi$
$522$	−4.29205	+	1.26026i	−0.187858	+	0.0551600i
$523$	2.08816	−	14.5235i	0.0913089	−	0.635067i	−0.891852	−	0.452327i	$-0.850594\pi$
$523$	2.08816	−	14.5235i	0.0913089	−	0.635067i	0.983161	−	0.182740i	$-0.0584968\pi$
$524$	−7.50397	−	16.4314i	−0.327812	−	0.717809i
$525$	0.444858	+	3.09405i	0.0194152	+	0.135036i
$526$	23.5631	−	15.1431i	1.02740	−	0.660270i
$527$	−38.9768	+	44.9816i	−1.69786	+	1.95943i
$528$	−3.62371			−0.157702
$529$	3.45893	+	22.7384i	0.150388	+	0.988627i
$530$	−5.63387			−0.244720
$531$	−1.86618	+	2.15369i	−0.0809855	+	0.0934622i
$532$	1.25670	−	0.807635i	0.0544850	−	0.0350154i
$533$	−9.48872	−	65.9955i	−0.411002	−	2.85858i
$534$	−3.02328	−	6.62006i	−0.130830	−	0.286478i
$535$	−3.83407	+	26.6666i	−0.165762	+	1.15290i
$536$	−3.18277	+	0.934545i	−0.137475	+	0.0403662i
$537$	−10.7511	−	6.90933i	−0.463945	−	0.298160i
$538$	−1.99052	+	4.35863i	−0.0858173	+	0.187914i
$539$	−3.47693	−	1.02092i	−0.149762	−	0.0439740i
$540$	−0.896497	−	1.03461i	−0.0385791	−	0.0445226i
$541$	4.98310	+	5.75080i	0.214240	+	0.247246i	0.852690	−	0.522417i	$-0.174970\pi$
$541$	4.98310	+	5.75080i	0.214240	+	0.247246i	−0.638450	+	0.769663i	$0.720424\pi$
$542$	26.2284	+	7.70135i	1.12661	+	0.330801i
$543$	8.88521	−	19.4559i	0.381301	−	0.834933i
$544$	5.59217	+	3.59387i	0.239762	+	0.154086i
$545$	−12.6619	+	3.71786i	−0.542374	+	0.159255i
$546$	−0.764047	+	5.31406i	−0.0326982	+	0.227421i
$547$	13.8679	+	30.3665i	0.592949	+	1.29838i	0.933643	+	0.358204i	$0.116611\pi$
$547$	13.8679	+	30.3665i	0.592949	+	1.29838i	−0.340694	+	0.940174i	$0.610662\pi$
$548$	−0.904658	−	6.29204i	−0.0386451	−	0.268783i
$549$	7.12582	−	4.57949i	0.304123	−	0.195448i
$550$	7.41777	−	8.56056i	0.316295	−	0.365024i
$551$	−6.68234			−0.284677
$552$	−3.63723	−	3.12579i	−0.154811	−	0.133042i
$553$	1.28227			0.0545277
$554$	−14.6129	+	16.8642i	−0.620843	+	0.716491i
$555$	1.99032	−	1.27910i	0.0844843	−	0.0542948i
$556$	2.31050	+	16.0699i	0.0979871	+	0.681515i
$557$	3.15145	+	6.90072i	0.133531	+	0.292393i	0.964572	−	0.263818i	$-0.0849819\pi$
$557$	3.15145	+	6.90072i	0.133531	+	0.292393i	−0.831041	+	0.556211i	$0.812255\pi$
$558$	−1.27425	+	8.86260i	−0.0539433	+	0.375184i
$559$	12.5196	−	3.67609i	0.529523	−	0.155482i
$560$	1.15167	+	0.740131i	0.0486668	+	0.0312763i
$561$	−10.0067	+	21.9115i	−0.422481	+	0.925105i
$562$	19.4398	+	5.70803i	0.820016	+	0.240779i
$563$	−16.9331	−	19.5419i	−0.713646	−	0.823592i	0.276881	−	0.960904i	$-0.410699\pi$
$563$	−16.9331	−	19.5419i	−0.713646	−	0.823592i	−0.990528	+	0.137312i	$0.956154\pi$
$564$	−8.55186	−	9.86937i	−0.360098	−	0.415575i
$565$	7.38166	+	2.16745i	0.310549	+	0.0911854i
$566$	−3.37640	+	7.39329i	−0.141921	+	0.310763i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−15.1799	+	4.45722i	−0.636935	+	0.187021i
$569$	3.14601	−	21.8810i	0.131887	−	0.917297i	−0.811204	−	0.584763i	$-0.801187\pi$
$569$	3.14601	−	21.8810i	0.131887	−	0.917297i	0.943091	−	0.332534i	$-0.107904\pi$
$570$	−0.849549	−	1.86025i	−0.0355837	−	0.0779174i
$571$	−0.312758	−	2.17528i	−0.0130885	−	0.0910326i	0.982230	−	0.187681i	$-0.0600970\pi$
$571$	−0.312758	−	2.17528i	−0.0130885	−	0.0910326i	−0.995319	+	0.0966480i	$0.969188\pi$
$572$	16.3663	−	10.5180i	0.684309	−	0.439779i
$573$	−2.00698	+	2.31618i	−0.0838430	+	0.0967599i
$574$	−12.4190			−0.518360
$575$	14.8297	−	2.19400i	0.618442	−	0.0914960i
$576$	1.00000			0.0416667
$577$	−22.8136	+	26.3283i	−0.949744	+	1.09606i	0.0455311	+	0.998963i	$0.485502\pi$
$577$	−22.8136	+	26.3283i	−0.949744	+	1.09606i	−0.995275	+	0.0970996i	$0.969043\pi$
$578$	22.8722	−	14.6990i	0.951357	−	0.611400i
$579$	3.19739	+	22.2383i	0.132879	+	0.924193i
$580$	−2.54393	−	5.57043i	−0.105631	−	0.231299i
$581$	−1.34017	+	9.32111i	−0.0555998	+	0.386705i
$582$	14.5621	−	4.27582i	0.603618	−	0.177238i
$583$	12.5455	+	8.06249i	0.519581	+	0.333914i
$584$	1.63815	−	3.58705i	0.0677871	−	0.148433i
$585$	7.05199	+	2.07065i	0.291564	+	0.0856109i
$586$	16.5884	+	19.1440i	0.685259	+	0.790831i
$587$	−16.4294	−	18.9606i	−0.678116	−	0.782587i	0.307508	−	0.951546i	$-0.400505\pi$
$587$	−16.4294	−	18.9606i	−0.678116	−	0.782587i	−0.985623	+	0.168959i	$0.945960\pi$
$588$	0.959493	+	0.281733i	0.0395688	+	0.0116185i
$589$	−5.55639	+	12.1668i	−0.228947	+	0.501324i
$590$	−3.28195	−	2.10918i	−0.135116	−	0.0868337i
$591$	9.13722	−	2.68293i	0.375855	−	0.110361i
$592$	−0.245950	+	1.71062i	−0.0101085	+	0.0703059i
$593$	−5.77698	−	12.6498i	−0.237232	−	0.519465i	0.753146	−	0.657853i	$-0.228535\pi$
$593$	−5.77698	−	12.6498i	−0.237232	−	0.519465i	−0.990378	+	0.138388i	$0.955808\pi$
$594$	0.515708	+	3.58683i	0.0211598	+	0.147169i
$595$	7.65561	−	4.91996i	0.313850	−	0.201699i
$596$	10.3616	−	11.9579i	0.424426	−	0.489813i
$597$	21.2924			0.871439
$598$	25.5001	+	3.56021i	1.04278	+	0.145588i
$599$	−18.5403			−0.757537			−0.378768	−	0.925492i	$-0.623652\pi$
$599$	−18.5403			−0.757537			−0.378768	+	0.925492i	$0.623652\pi$
$600$	−2.04701	+	2.36237i	−0.0835688	+	0.0964435i
$601$	12.1589	−	7.81404i	0.495971	−	0.318741i	−0.268632	−	0.963243i	$-0.586571\pi$
$601$	12.1589	−	7.81404i	0.495971	−	0.318741i	0.764603	+	0.644502i	$0.222935\pi$
$602$	−0.345883	−	2.40567i	−0.0140971	−	0.0980477i
$603$	1.37799	+	3.01737i	0.0561160	+	0.122877i
$604$	1.09905	−	7.64403i	0.0447196	−	0.311031i
$605$	2.79952	−	0.822014i	0.113817	−	0.0334196i
$606$	−6.36266	−	4.08903i	−0.258465	−	0.166106i
$607$	0.932587	−	2.04208i	0.0378525	−	0.0828855i	−0.889761	−	0.456426i	$-0.849129\pi$
$607$	0.932587	−	2.04208i	0.0378525	−	0.0828855i	0.927614	+	0.373541i	$0.121856\pi$
$608$	1.43334	+	0.420865i	0.0581294	+	0.0170683i
$609$	−2.92935	−	3.38065i	−0.118703	−	0.136991i
$610$	7.59376	+	8.76367i	0.307462	+	0.354831i
$611$	67.2703	+	19.7523i	2.72146	+	0.799094i
$612$	2.76144	−	6.04671i	0.111625	−	0.244424i
$613$	−18.8839	−	12.1360i	−0.762715	−	0.490167i	0.100541	−	0.994933i	$-0.467943\pi$
$613$	−18.8839	−	12.1360i	−0.762715	−	0.490167i	−0.863256	+	0.504766i	$0.831579\pi$
$614$	−19.1011	+	5.60858i	−0.770856	+	0.226344i
$615$	−2.41957	+	16.8285i	−0.0975664	+	0.678589i
$616$	−1.50534	−	3.29624i	−0.0606521	−	0.132809i
$617$	−1.94975	−	13.5608i	−0.0784939	−	0.545937i	−0.990685	−	0.136172i	$-0.956520\pi$
$617$	−1.94975	−	13.5608i	−0.0784939	−	0.545937i	0.912191	−	0.409765i	$-0.134389\pi$
$618$	2.90010	−	1.86378i	0.116659	−	0.0749724i
$619$	−1.44082	+	1.66279i	−0.0579113	+	0.0668332i	−0.783966	−	0.620804i	$-0.786806\pi$
$619$	−1.44082	+	1.66279i	−0.0579113	+	0.0668332i	0.726055	+	0.687637i	$0.241352\pi$
$620$	−12.2576			−0.492276
$621$	−2.57634	+	4.04506i	−0.103385	+	0.162323i
$622$	−33.3044			−1.33539
$623$	4.76590	−	5.50014i	0.190942	−	0.220359i
$624$	−4.51644	+	2.90254i	−0.180802	+	0.116195i
$625$	−0.0569836	−	0.396330i	−0.00227935	−	0.0158532i
$626$	−7.41033	−	16.2263i	−0.296176	−	0.648535i
$627$	−0.770389	+	5.35817i	−0.0307664	+	0.213985i
$628$	15.7970	−	4.63842i	0.630369	−	0.185093i
$629$	9.66442	+	6.21095i	0.385346	+	0.247647i
$630$	0.568699	−	1.24528i	0.0226575	−	0.0496130i
$631$	−5.45232	−	1.60095i	−0.217054	−	0.0637327i	0.171398	−	0.985202i	$-0.445172\pi$
$631$	−5.45232	−	1.60095i	−0.217054	−	0.0637327i	−0.388451	+	0.921469i	$0.626990\pi$
$632$	0.839709	+	0.969076i	0.0334018	+	0.0385478i
$633$	−8.55266	−	9.87029i	−0.339938	−	0.392309i
$634$	−28.8759	−	8.47874i	−1.14681	−	0.336734i
$635$	−6.48982	+	14.2107i	−0.257541	+	0.563935i
$636$	−3.46205	−	2.22493i	−0.137279	−	0.0882241i
$637$	−5.15124	+	1.51254i	−0.204099	+	0.0599290i
$638$	−2.30689	+	16.0448i	−0.0913306	+	0.635218i
$639$	6.57218	+	14.3911i	0.259991	+	0.569302i
$640$	0.194827	+	1.35505i	0.00770123	+	0.0535632i
$641$	7.95006	−	5.10919i	0.314008	−	0.201801i	−0.374138	−	0.927373i	$-0.622061\pi$
$641$	7.95006	−	5.10919i	0.314008	−	0.201801i	0.688146	+	0.725572i	$0.258425\pi$
$642$	−12.8872	+	14.8726i	−0.508618	+	0.586977i
$643$	22.9642			0.905621			0.452811	−	0.891607i	$-0.350421\pi$
$643$	22.9642			0.905621			0.452811	+	0.891607i	$0.350421\pi$
$644$	1.33235	−	4.60704i	0.0525021	−	0.181543i
$645$	−3.32720			−0.131008
$646$	6.50292	−	7.50477i	0.255854	−	0.295271i
$647$	−20.6509	+	13.2715i	−0.811870	+	0.521757i	−0.879469	−	0.475955i	$-0.842102\pi$
$647$	−20.6509	+	13.2715i	−0.811870	+	0.521757i	0.0675994	+	0.997713i	$0.478466\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	4.28984	+	9.39345i	0.168391	+	0.368725i
$650$	2.38831	−	16.6111i	0.0936772	−	0.651540i
$651$	−8.59105	+	2.52256i	−0.336710	+	0.0988669i
$652$	−1.54540	−	0.993168i	−0.0605225	−	0.0388955i
$653$	−16.7815	+	36.7464i	−0.656711	+	1.43800i	0.228844	+	0.973463i	$0.426505\pi$
$653$	−16.7815	+	36.7464i	−0.656711	+	1.43800i	−0.885555	+	0.464534i	$0.846222\pi$
$654$	−9.24906	−	2.71577i	−0.361667	−	0.106195i
$655$	−16.1941	−	18.6890i	−0.632757	−	0.730240i
$656$	−8.13273	−	9.38567i	−0.317530	−	0.366449i
$657$	−3.78367	−	1.11099i	−0.147615	−	0.0433437i
$658$	5.42492	−	11.8789i	0.211486	−	0.463089i
$659$	−7.76628	−	4.99108i	−0.302531	−	0.194425i	0.380563	−	0.924755i	$-0.375730\pi$
$659$	−7.76628	−	4.99108i	−0.302531	−	0.194425i	−0.683095	+	0.730330i	$0.739366\pi$
$660$	−4.75987	+	1.39762i	−0.185278	+	0.0544025i
$661$	3.13499	−	21.8043i	0.121937	−	0.848091i	−0.833421	−	0.552639i	$-0.813621\pi$
$661$	3.13499	−	21.8043i	0.121937	−	0.848091i	0.955358	−	0.295452i	$-0.0954701\pi$
$662$	−10.6514	−	23.3233i	−0.413978	−	0.906485i
$663$	5.07894	+	35.3248i	0.197250	+	1.37190i
$664$	−7.92205	+	5.09120i	−0.307435	+	0.197577i
$665$	1.33923	−	1.54555i	0.0519331	−	0.0599340i
$666$	1.72821			0.0669667
$667$	−16.1556	+	14.1147i	−0.625547	+	0.546524i
$668$	4.85534			0.187859
$669$	8.75971	−	10.1092i	0.338670	−	0.390846i
$670$	−3.82024	+	2.45512i	−0.147589	+	0.0948494i
$671$	−4.36829	−	30.3822i	−0.168636	−	1.17289i
$672$	0.415415	+	0.909632i	0.0160250	+	0.0350898i
$673$	−1.78813	+	12.4367i	−0.0689274	+	0.479401i	0.925896	+	0.377779i	$0.123312\pi$
$673$	−1.78813	+	12.4367i	−0.0689274	+	0.479401i	−0.994823	+	0.101621i	$0.967597\pi$
$674$	−11.4751	+	3.36938i	−0.442003	+	0.129784i
$675$	2.62965	+	1.68997i	0.101215	+	0.0650471i
$676$	6.57312	−	14.3931i	0.252812	−	0.553582i
$677$	−12.2927	−	3.60946i	−0.472447	−	0.138723i	0.0368373	−	0.999321i	$-0.488272\pi$
$677$	−12.2927	−	3.60946i	−0.472447	−	0.138723i	−0.509284	+	0.860598i	$0.670090\pi$
$678$	3.68011	+	4.24708i	0.141334	+	0.163108i
$679$	9.93874	+	11.4699i	0.381414	+	0.440175i
$680$	8.73162	+	2.56384i	0.334842	+	0.0983186i
$681$	−1.75076	+	3.83363i	−0.0670893	+	0.146905i
$682$	27.2951	+	17.5415i	1.04518	+	0.671699i
$683$	12.0524	−	3.53890i	0.461172	−	0.135412i	−0.0428898	−	0.999080i	$-0.513656\pi$
$683$	12.0524	−	3.53890i	0.461172	−	0.135412i	0.504062	+	0.863667i	$0.331838\pi$
$684$	0.212597	−	1.47864i	0.00812883	−	0.0565373i
$685$	−3.61507	−	7.91590i	−0.138125	−	0.302451i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	5.12089	−	3.29099i	0.195374	−	0.125559i
$688$	1.59158	−	1.83678i	0.0606783	−	0.0700265i
$689$	22.0941			0.841719
$690$	−5.98321	−	2.70299i	−0.227777	−	0.102901i
$691$	7.16023			0.272388			0.136194	−	0.990682i	$-0.456513\pi$
$691$	7.16023			0.272388			0.136194	+	0.990682i	$0.456513\pi$
$692$	8.78418	−	10.1375i	0.333925	−	0.385369i
$693$	−3.04846	+	1.95913i	−0.115801	+	0.0744211i
$694$	−0.954045	−	6.63553i	−0.0362150	−	0.251881i
$695$	9.23290	+	20.2172i	0.350224	+	0.766883i
$696$	0.636609	−	4.42771i	0.0241306	−	0.167832i
$697$	−79.2104	+	23.2583i	−3.00031	+	0.880970i
$698$	1.06222	+	0.682646i	0.0402055	+	0.0258385i
$699$	−0.377675	+	0.826992i	−0.0142850	+	0.0312797i
$700$	−2.99925	−	0.880659i	−0.113361	−	0.0332858i
$701$	3.69774	+	4.26742i	0.139662	+	0.161178i	0.821271	−	0.570538i	$-0.193265\pi$
$701$	3.69774	+	4.26742i	0.139662	+	0.161178i	−0.681610	+	0.731716i	$0.738720\pi$
$702$	3.51576	+	4.05740i	0.132694	+	0.153137i
$703$	2.47710	+	0.727343i	0.0934256	+	0.0274322i
$704$	1.50534	−	3.29624i	0.0567348	−	0.124232i
$705$	−15.0397	−	9.66541i	−0.566427	−	0.364020i
$706$	8.96953	−	2.63369i	0.337573	−	0.0991203i
$707$	1.07637	−	7.48632i	0.0404811	−	0.281552i
$708$	−1.18383	−	2.59222i	−0.0444909	−	0.0974215i
$709$	−6.41360	−	44.6076i	−0.240868	−	1.67527i	−0.647797	−	0.761813i	$-0.724310\pi$
$709$	−6.41360	−	44.6076i	−0.240868	−	1.67527i	0.406930	−	0.913459i	$-0.366599\pi$
$710$	−18.2202	+	11.7094i	−0.683794	+	0.439447i
$711$	0.839709	−	0.969076i	0.0314916	−	0.0363432i
$712$	7.27773			0.272745
$713$	12.2658	+	41.1515i	0.459358	+	1.54114i
$714$	6.64742			0.248773
$715$	17.4410	−	20.1280i	0.652258	−	0.752746i
$716$	10.7511	−	6.90933i	0.401789	−	0.258214i
$717$	−0.103674	−	0.721069i	−0.00387178	−	0.0269288i
$718$	11.8316	+	25.9076i	0.441552	+	0.966864i
$719$	5.49944	−	38.2495i	0.205095	−	1.42646i	−0.583781	−	0.811911i	$-0.698427\pi$
$719$	5.49944	−	38.2495i	0.205095	−	1.42646i	0.788876	−	0.614553i	$-0.210664\pi$
$720$	1.31354	−	0.385689i	0.0489526	−	0.0143738i
$721$	2.90010	+	1.86378i	0.108006	+	0.0694109i
$722$	−6.96585	+	15.2531i	−0.259242	+	0.567661i
$723$	−4.62350	−	1.35758i	−0.171950	−	0.0504891i
$724$	14.0067	+	16.1645i	0.520553	+	0.600751i
$725$	9.15677	+	10.5675i	0.340074	+	0.392466i
$726$	2.04496	+	0.600453i	0.0758954	+	0.0222849i
$727$	10.5931	−	23.1956i	0.392876	−	0.860279i	−0.605067	−	0.796174i	$-0.706854\pi$
$727$	10.5931	−	23.1956i	0.392876	−	0.860279i	0.997943	−	0.0641042i	$-0.0204190\pi$
$728$	−4.51644	−	2.90254i	−0.167391	−	0.107575i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.768283	−	5.34353i	0.0284354	−	0.197773i
$731$	−6.71142	−	14.6960i	−0.248231	−	0.543549i
$732$	1.20548	+	8.38426i	0.0445556	+	0.309891i
$733$	2.45170	−	1.57561i	0.0905555	−	0.0581965i	−0.494579	−	0.869132i	$-0.664678\pi$
$733$	2.45170	−	1.57561i	0.0905555	−	0.0581965i	0.585135	+	0.810936i	$0.301042\pi$
$734$	22.9310	−	26.4638i	0.846400	−	0.976797i
$735$	1.36899			0.0504959
$736$	4.35428	−	2.01005i	0.160501	−	0.0740913i
$737$	12.0203			0.442775
$738$	−8.13273	+	9.38567i	−0.299370	+	0.345491i
$739$	−12.9227	+	8.30493i	−0.475370	+	0.305502i	−0.756298	−	0.654227i	$-0.772994\pi$
$739$	−12.9227	+	8.30493i	−0.475370	+	0.305502i	0.280928	+	0.959729i	$0.409358\pi$
$740$	0.336702	+	2.34182i	0.0123774	+	0.0860869i
$741$	3.33164	+	7.29527i	0.122391	+	0.267999i
$742$	0.585676	−	4.07346i	0.0215008	−	0.149542i
$743$	34.8718	−	10.2393i	1.27932	−	0.375643i	0.429670	−	0.902986i	$-0.358630\pi$
$743$	34.8718	−	10.2393i	1.27932	−	0.375643i	0.849652	+	0.527343i	$0.176812\pi$
$744$	−7.53236	−	4.84076i	−0.276150	−	0.177471i
$745$	8.99825	−	19.7034i	0.329670	−	0.721877i
$746$	12.8736	+	3.78003i	0.471336	+	0.138397i
$747$	6.16680	+	7.11687i	0.225631	+	0.260393i
$748$	−15.7745	−	18.2047i	−0.576773	−	0.665632i
$749$	−18.8822	−	5.54431i	−0.689940	−	0.202585i
$750$	−4.62117	+	10.1190i	−0.168741	+	0.369492i
$751$	−19.4804	−	12.5193i	−0.710850	−	0.456836i	0.134593	−	0.990901i	$-0.457027\pi$
$751$	−19.4804	−	12.5193i	−0.710850	−	0.456836i	−0.845443	+	0.534065i	$0.820664\pi$
$752$	12.5301	−	3.67916i	0.456924	−	0.134165i
$753$	−0.856750	+	5.95883i	−0.0312217	+	0.217152i
$754$	9.97642	+	21.8453i	0.363320	+	0.795559i
$755$	−1.50458	−	10.4646i	−0.0547573	−	0.380846i
$756$	0.841254	−	0.540641i	0.0305961	−	0.0196629i
$757$	−29.9544	+	34.5692i	−1.08871	+	1.25644i	−0.124241	+	0.992252i	$0.539650\pi$
$757$	−29.9544	+	34.5692i	−1.08871	+	1.25644i	−0.964471	+	0.264189i	$0.914896\pi$
$758$	2.43548			0.0884608
$759$	9.45522	+	14.5814i	0.343203	+	0.529273i
$760$	2.04506			0.0741821
$761$	−7.20705	+	8.31738i	−0.261255	+	0.301505i	−0.871189	−	0.490948i	$-0.836651\pi$
$761$	−7.20705	+	8.31738i	−0.261255	+	0.301505i	0.609934	+	0.792453i	$0.291196\pi$
$762$	−9.60014	+	6.16963i	−0.347776	+	0.223502i
$763$	−1.37185	−	9.54141i	−0.0496642	−	0.345422i
$764$	−1.27314	−	2.78779i	−0.0460607	−	0.100859i
$765$	1.29510	−	9.00762i	0.0468244	−	0.325671i
$766$	18.0785	−	5.30832i	0.653202	−	0.191797i
$767$	12.8707	+	8.27150i	0.464734	+	0.298666i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	45.0444	+	13.2262i	1.62434	+	0.476950i	0.962181	−	0.272412i	$-0.0878212\pi$
$769$	45.0444	+	13.2262i	1.62434	+	0.476950i	0.662161	+	0.749361i	$0.269639\pi$
$770$	−3.24865	−	3.74914i	−0.117073	−	0.135110i
$771$	−6.97377	−	8.04816i	−0.251154	−	0.289847i
$772$	−21.5569	−	6.32968i	−0.775851	−	0.227810i
$773$	−10.2949	+	22.5427i	−0.370282	+	0.810805i	0.629156	+	0.777279i	$0.283401\pi$
$773$	−10.2949	+	22.5427i	−0.370282	+	0.810805i	−0.999438	+	0.0335257i	$0.989326\pi$
$774$	−2.04459	−	1.31398i	−0.0734912	−	0.0472299i
$775$	26.8545	−	7.88519i	0.964642	−	0.283244i
$776$	−2.15989	+	15.0224i	−0.0775357	+	0.539272i
$777$	0.717923	+	1.57203i	0.0257554	+	0.0563964i
$778$	2.98246	+	20.7434i	0.106926	+	0.743688i
$779$	−15.6070	+	10.0300i	−0.559180	+	0.359363i
$780$	−4.81303	+	5.55453i	−0.172334	+	0.198884i
$781$	57.3299			2.05142
$782$	−0.130093	−	31.8796i	−0.00465212	−	1.14001i
$783$	−4.47325			−0.159861
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	18.9609	−	12.1855i	0.676745	−	0.434917i
$786$	−2.57074	−	17.8799i	−0.0916954	−	0.637756i
$787$	7.09538	+	15.5367i	0.252923	+	0.553824i	0.992920	−	0.118786i	$-0.0379003\pi$
$787$	7.09538	+	15.5367i	0.252923	+	0.553824i	−0.739997	+	0.672610i	$0.765173\pi$
$788$	−1.35526	+	9.42604i	−0.0482791	+	0.335789i
$789$	26.8750	−	7.89120i	0.956774	−	0.280934i
$790$	1.47675	+	0.949049i	0.0525404	+	0.0337657i
$791$	−2.33450	+	5.11185i	−0.0830054	+	0.181756i
$792$	−3.47693	−	1.02092i	−0.123547	−	0.0362767i
$793$	−29.7801	−	34.3681i	−1.05752	−	1.22045i
$794$	−19.7135	−	22.7505i	−0.699604	−	0.807386i
$795$	−5.40566	−	1.58724i	−0.191719	−	0.0562938i
$796$	−8.84518	+	19.3682i	−0.313509	+	0.686489i
$797$	−0.464768	−	0.298688i	−0.0164629	−	0.0105801i	0.532383	−	0.846503i	$-0.321296\pi$
$797$	−0.464768	−	0.298688i	−0.0164629	−	0.0105801i	−0.548846	+	0.835923i	$0.684933\pi$
$798$	1.43334	−	0.420865i	0.0507395	−	0.0148985i
$799$	12.3542	−	85.9254i	0.437060	−	3.03982i
$800$	−1.29853	−	2.84339i	−0.0459101	−	0.100529i
$801$	−1.03573	−	7.20365i	−0.0365957	−	0.254529i
$802$	6.54864	−	4.20856i	0.231241	−	0.148609i
$803$	−9.35780	+	10.7995i	−0.330230	+	0.381105i
$804$	−3.31714			−0.116986
$805$	−0.0267917	−	6.56539i	−0.000944285	−	0.231399i
$806$	48.0700			1.69319
$807$	−3.13785	+	3.62128i	−0.110458	+	0.127475i
$808$	6.36266	−	4.08903i	0.223838	−	0.143852i
$809$	0.948284	+	6.59546i	0.0333399	+	0.231884i	0.999678	−	0.0253932i	$-0.00808377\pi$
$809$	0.948284	+	6.59546i	0.0333399	+	0.231884i	−0.966338	+	0.257277i	$0.917175\pi$
$810$	−0.568699	−	1.24528i	−0.0199820	−	0.0437545i
$811$	−1.30029	+	9.04369i	−0.0456592	+	0.317567i	0.954173	+	0.299255i	$0.0967382\pi$
$811$	−1.30029	+	9.04369i	−0.0456592	+	0.317567i	−0.999832	+	0.0183116i	$0.994171\pi$
$812$	4.29205	−	1.26026i	0.150621	−	0.0442264i
$813$	22.9962	+	14.7788i	0.806513	+	0.518314i
$814$	2.60155	−	5.69659i	0.0911842	−	0.199666i
$815$	−2.41299	−	0.708518i	−0.0845234	−	0.0248183i
$816$	4.35313	+	5.02379i	0.152390	+	0.175868i
$817$	−2.37757	−	2.74387i	−0.0831808	−	0.0959957i
$818$	7.97904	+	2.34286i	0.278981	+	0.0819161i
$819$	−2.23024	+	4.88355i	−0.0779310	+	0.170645i
$820$	−14.3026	−	9.19171i	−0.499468	−	0.320988i
$821$	12.6390	−	3.71113i	0.441103	−	0.129519i	−0.0536372	−	0.998560i	$-0.517081\pi$
$821$	12.6390	−	3.71113i	0.441103	−	0.129519i	0.494740	+	0.869041i	$0.335263\pi$
$822$	0.904658	−	6.29204i	0.0315536	−	0.219460i
$823$	4.92846	+	10.7918i	0.171795	+	0.376179i	0.975871	−	0.218347i	$-0.0700666\pi$
$823$	4.92846	+	10.7918i	0.171795	+	0.376179i	−0.804076	+	0.594527i	$0.797339\pi$
$824$	0.490611	+	3.41227i	0.0170912	+	0.118872i
$825$	9.52909	−	6.12397i	0.331760	−	0.213209i
$826$	1.86618	−	2.15369i	0.0649328	−	0.0749365i
$827$	48.1027			1.67269			0.836347	−	0.548201i	$-0.184687\pi$
$827$	48.1027			1.67269			0.836347	+	0.548201i	$0.184687\pi$
$828$	−2.60926	−	4.02390i	−0.0906782	−	0.139840i
$829$	−42.8371			−1.48779			−0.743897	−	0.668294i	$-0.767025\pi$
$829$	−42.8371			−1.48779			−0.743897	+	0.668294i	$0.767025\pi$
$830$	−8.44228	+	9.74291i	−0.293036	+	0.338181i
$831$	−18.7722	+	12.0641i	−0.651199	+	0.418500i
$832$	−0.764047	−	5.31406i	−0.0264886	−	0.184232i
$833$	2.76144	+	6.04671i	0.0956782	+	0.209506i
$834$	−2.31050	+	16.0699i	−0.0800061	+	0.556455i
$835$	6.37766	−	1.87265i	0.220708	−	0.0648057i
$836$	−4.55393	−	2.92663i	−0.157501	−	0.101220i
$837$	−3.71952	+	8.14460i	−0.128565	+	0.281519i
$838$	−31.2412	−	9.17324i	−1.07921	−	0.316884i
$839$	−19.2069	−	22.1659i	−0.663094	−	0.765252i	0.320185	−	0.947355i	$-0.396255\pi$
$839$	−19.2069	−	22.1659i	−0.663094	−	0.765252i	−0.983279	+	0.182103i	$0.941709\pi$
$840$	0.896497	+	1.03461i	0.0309321	+	0.0356975i
$841$	8.62591	+	2.53280i	0.297445	+	0.0873378i
$842$	9.93792	−	21.7610i	0.342483	−	0.749934i
$843$	17.0442	+	10.9536i	0.587032	+	0.377263i
$844$	12.5312	−	3.67950i	0.431343	−	0.126654i
$845$	3.08276	−	21.4411i	0.106050	−	0.737595i
$846$	−5.42492	−	11.8789i	−0.186513	−	0.408406i
$847$	0.303314	+	2.10959i	0.0104220	+	0.0724865i
$848$	3.46205	−	2.22493i	0.118887	−	0.0764043i
$849$	−5.32256	+	6.14256i	−0.182670	+	0.210812i
$850$	−20.7790			−0.712713
$851$	7.52509	−	3.47378i	0.257957	−	0.119080i
$852$	−15.8208			−0.542010
$853$	−22.0726	+	25.4731i	−0.755751	+	0.872184i	−0.995113	−	0.0987470i	$-0.968517\pi$
$853$	−22.0726	+	25.4731i	−0.755751	+	0.872184i	0.239361	+	0.970931i	$0.423062\pi$
$854$	−7.12582	+	4.57949i	−0.243841	+	0.156707i
$855$	−0.291042	−	2.02424i	−0.00995344	−	0.0692277i
$856$	−8.17509	−	17.9010i	−0.279419	−	0.611842i
$857$	−7.80945	+	54.3159i	−0.266766	+	1.85540i	0.211760	+	0.977322i	$0.432081\pi$
$857$	−7.80945	+	54.3159i	−0.266766	+	1.85540i	−0.478525	+	0.878074i	$0.658829\pi$
$858$	18.6666	−	5.48101i	0.637267	−	0.187119i
$859$	28.4265	+	18.2686i	0.969900	+	0.623317i	0.926721	−	0.375750i	$-0.122615\pi$
$859$	28.4265	+	18.2686i	0.969900	+	0.623317i	0.0431794	+	0.999067i	$0.486251\pi$
$860$	1.38217	−	3.02653i	0.0471316	−	0.103204i
$861$	−11.9160	−	3.49884i	−0.406095	−	0.119240i
$862$	−20.2631	−	23.3849i	−0.690164	−	0.796492i
$863$	18.2725	+	21.0876i	0.622005	+	0.717831i	0.976086	−	0.217383i	$-0.0697520\pi$
$863$	18.2725	+	21.0876i	0.622005	+	0.717831i	−0.354082	+	0.935214i	$0.615207\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	7.62842	−	16.7039i	0.259374	−	0.567950i
$866$	−29.6030	−	19.0247i	−1.00595	−	0.646484i
$867$	26.0869	−	7.65980i	0.885957	−	0.260140i
$868$	1.27425	−	8.86260i	0.0432508	−	0.300816i
$869$	−1.93026	−	4.22668i	−0.0654796	−	0.143380i
$870$	−0.871511	−	6.06149i	−0.0295470	−	0.205504i
$871$	14.9817	−	9.62813i	0.507634	−	0.326237i
$872$	6.31255	−	7.28507i	0.213770	−	0.246703i
$873$	15.1769			0.513659
$874$	−2.04643	−	6.86574i	−0.0692216	−	0.232237i
$875$	−11.1242			−0.376067
$876$	2.58238	−	2.98023i	0.0872506	−	0.100693i
$877$	27.5258	−	17.6898i	0.929482	−	0.597342i	0.0140878	−	0.999901i	$-0.495516\pi$
$877$	27.5258	−	17.6898i	0.929482	−	0.597342i	0.915394	+	0.402559i	$0.131879\pi$
$878$	−4.58344	−	31.8785i	−0.154684	−	1.07585i
$879$	10.5229	+	23.0420i	0.354930	+	0.777188i
$880$	0.705999	−	4.91033i	0.0237992	−	0.165527i
$881$	−6.21705	+	1.82549i	−0.209458	+	0.0615023i	−0.384778	−	0.923009i	$-0.625722\pi$
$881$	−6.21705	+	1.82549i	−0.209458	+	0.0615023i	0.175320	+	0.984511i	$0.443904\pi$
$882$	0.841254	+	0.540641i	0.0283265	+	0.0182043i
$883$	−1.54309	+	3.37890i	−0.0519292	+	0.113709i	−0.933818	−	0.357748i	$-0.883545\pi$
$883$	−1.54309	+	3.37890i	−0.0519292	+	0.113709i	0.881889	+	0.471457i	$0.156272\pi$
$884$	−34.2424	−	10.0545i	−1.15170	−	0.338169i
$885$	−2.55479	−	2.94838i	−0.0858782	−	0.0991087i
$886$	7.92950	+	9.15113i	0.266397	+	0.307438i
$887$	−25.5489	−	7.50182i	−0.857847	−	0.251887i	−0.176909	−	0.984227i	$-0.556610\pi$
$887$	−25.5489	−	7.50182i	−0.857847	−	0.251887i	−0.680938	+	0.732341i	$0.738428\pi$
$888$	−0.717923	+	1.57203i	−0.0240919	+	0.0527540i
$889$	−9.60014	−	6.16963i	−0.321978	−	0.206923i
$890$	9.55956	−	2.80694i	0.320437	−	0.0940888i
$891$	−0.515708	+	3.58683i	−0.0172769	+	0.120163i
$892$	5.55678	+	12.1676i	0.186055	+	0.407403i
$893$	−2.77631	−	19.3096i	−0.0929056	−	0.646173i
$894$	13.3108	−	8.55430i	0.445178	−	0.286099i
$895$	11.4571	−	13.2222i	0.382970	−	0.441971i
$896$	−1.00000			−0.0334077
$897$	23.4641	+	10.6002i	0.783444	+	0.353930i
$898$	18.7418			0.625420
$899$	−26.2287	+	30.2695i	−0.874775	+	1.00954i
$900$	−2.62965	+	1.68997i	−0.0876550	+	0.0563324i
$901$	−3.89323	−	27.0780i	−0.129702	−	0.902100i
$902$	18.6949	+	40.9361i	0.622472	+	1.36302i
$903$	0.345883	−	2.40567i	0.0115103	−	0.0800556i
$904$	−5.39205	+	1.58325i	−0.179337	+	0.0526581i
$905$	24.6327	+	15.8305i	0.818820	+	0.526223i
$906$	3.20810	−	7.02476i	0.106582	−	0.233382i
$907$	2.71122	+	0.796085i	0.0900245	+	0.0264336i	0.326435	−	0.945220i	$-0.394153\pi$
$907$	2.71122	+	0.796085i	0.0900245	+	0.0264336i	−0.236410	+	0.971653i	$0.575971\pi$
$908$	−2.75990	−	3.18510i	−0.0915906	−	0.105701i
$909$	−4.95291	−	5.71597i	−0.164278	−	0.189587i
$910$	−7.05199	−	2.07065i	−0.233771	−	0.0686414i
$911$	2.21194	−	4.84348i	0.0732849	−	0.160472i	−0.869444	−	0.494032i	$-0.835523\pi$
$911$	2.21194	−	4.84348i	0.0732849	−	0.160472i	0.942729	+	0.333560i	$0.108250\pi$
$912$	1.25670	+	0.807635i	0.0416136	+	0.0267435i
$913$	32.7421	−	9.61394i	1.08361	−	0.318175i
$914$	−3.73045	+	25.9458i	−0.123392	+	0.858212i
$915$	4.81715	+	10.5481i	0.159250	+	0.348709i
$916$	0.866300	+	6.02525i	0.0286234	+	0.199080i
$917$	15.1962	−	9.76602i	0.501823	−	0.322502i
$918$	4.35313	−	5.02379i	0.143675	−	0.165810i
$919$	31.4940			1.03889			0.519445	−	0.854504i	$-0.326139\pi$
$919$	31.4940			1.03889			0.519445	+	0.854504i	$0.326139\pi$
$920$	4.94424	−	4.31966i	0.163007	−	0.142415i
$921$	−19.9074			−0.655973
$922$	−0.723400	+	0.834849i	−0.0238239	+	0.0274943i
$923$	71.4536	−	45.9204i	2.35192	−	1.51149i
$924$	−0.515708	−	3.58683i	−0.0169655	−	0.117998i
$925$	−2.24413	−	4.91397i	−0.0737867	−	0.161570i
$926$	−4.23670	+	29.4669i	−0.139227	+	0.968343i
$927$	3.30772	−	0.971234i	0.108640	−	0.0318995i
$928$	3.76313	+	2.41842i	0.123531	+	0.0793885i
$929$	11.0073	−	24.1027i	0.361139	−	0.790785i	−0.638634	−	0.769510i	$-0.720500\pi$
$929$	11.0073	−	24.1027i	0.361139	−	0.790785i	0.999774	−	0.0212746i	$-0.00677243\pi$
$930$	−11.7610	−	3.45336i	−0.385660	−	0.113240i
$931$	0.978262	+	1.12897i	0.0320612	+	0.0370006i
$932$	−0.595367	−	0.687090i	−0.0195019	−	0.0225064i
$933$	−31.9554	−	9.38294i	−1.04617	−	0.307184i
$934$	7.78754	−	17.0523i	0.254816	−	0.557969i
$935$	−27.7417	−	17.8285i	−0.907252	−	0.583055i
$936$	−5.15124	+	1.51254i	−0.168373	+	0.0494389i
$937$	2.57812	−	17.9312i	0.0842236	−	0.585788i	−0.903383	−	0.428835i	$-0.858924\pi$
$937$	2.57812	−	17.9312i	0.0842236	−	0.585788i	0.987606	−	0.156952i	$-0.0501669\pi$
$938$	−1.37799	−	3.01737i	−0.0449929	−	0.0985207i
$939$	−2.53866	−	17.6568i	−0.0828462	−	0.576208i
$940$	15.0397	−	9.66541i	0.490540	−	0.315251i
$941$	5.09416	−	5.87897i	0.166065	−	0.191649i	−0.666618	−	0.745400i	$-0.732259\pi$
$941$	5.09416	−	5.87897i	0.166065	−	0.191649i	0.832682	+	0.553751i	$0.186804\pi$
$942$	16.4639			0.536423
$943$	−16.5465	+	57.2150i	−0.538829	+	1.86318i
$944$	2.84974			0.0927512
$945$	0.896497	−	1.03461i	0.0291631	−	0.0336560i
$946$	−7.40900	+	4.76147i	−0.240887	+	0.154809i
$947$	−3.97971	−	27.6795i	−0.129323	−	0.899463i	−0.946415	−	0.322954i	$-0.895324\pi$
$947$	−3.97971	−	27.6795i	−0.129323	−	0.899463i	0.817091	−	0.576508i	$-0.195585\pi$
$948$	0.532675	+	1.16640i	0.0173005	+	0.0378828i
$949$	−3.01295	+	20.9555i	−0.0978044	+	0.680244i
$950$	−4.48042	+	1.31557i	−0.145364	+	0.0426827i
$951$	−25.3175	−	16.2706i	−0.820977	−	0.527610i
$952$	−2.76144	+	6.04671i	−0.0894987	+	0.195975i
$953$	9.07023	+	2.66326i	0.293814	+	0.0862715i	0.425318	−	0.905044i	$-0.360162\pi$
$953$	9.07023	+	2.66326i	0.293814	+	0.0862715i	−0.131504	+	0.991316i	$0.541981\pi$
$954$	−2.69498	−	3.11018i	−0.0872533	−	0.100696i
$955$	−2.74754	−	3.17083i	−0.0889083	−	0.102606i
$956$	0.698975	+	0.205238i	0.0226065	+	0.00663786i
$957$	−6.73378	+	14.7449i	−0.217672	+	0.476635i
$958$	8.34463	+	5.36277i	0.269603	+	0.173263i
$959$	6.09925	−	1.79090i	0.196955	−	0.0578312i
$960$	−0.194827	+	1.35505i	−0.00628803	+	0.0437342i
$961$	20.4257	+	44.7260i	0.658894	+	1.44278i
$962$	−1.32043	−	9.18380i	−0.0425724	−	0.296098i
$963$	−16.5553	+	10.6395i	−0.533487	+	0.342852i
$964$	3.15557	−	3.64173i	0.101634	−	0.117292i
$965$	−30.7571			−0.990105
$966$	2.57634	−	4.04506i	0.0828923	−	0.130148i
$967$	6.33679			0.203777			0.101889	−	0.994796i	$-0.467511\pi$
$967$	6.33679			0.203777			0.101889	+	0.994796i	$0.467511\pi$
$968$	−1.39570	+	1.61072i	−0.0448594	+	0.0517705i
$969$	8.35384	−	5.36869i	0.268364	−	0.172467i
$970$	2.95687	+	20.5655i	0.0949394	+	0.660318i
$971$	−7.71464	−	16.8927i	−0.247575	−	0.542113i	0.744521	−	0.667599i	$-0.232678\pi$
$971$	−7.71464	−	16.8927i	−0.247575	−	0.542113i	−0.992095	+	0.125487i	$0.959951\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−15.5775	+	4.57397i	−0.499392	+	0.146635i
$974$	0.0373021	+	0.0239726i	0.00119524	+	0.000768132i
$975$	6.97145	−	15.2653i	0.223265	−	0.488882i
$976$	−8.12737	−	2.38641i	−0.260151	−	0.0763871i
$977$	33.2374	+	38.3580i	1.06336	+	1.22718i	0.972887	+	0.231282i	$0.0742919\pi$
$977$	33.2374	+	38.3580i	1.06336	+	1.22718i	0.0904712	+	0.995899i	$0.471163\pi$
$978$	−1.20299	−	1.38833i	−0.0384675	−	0.0443938i
$979$	−25.3041	−	7.42996i	−0.808724	−	0.237463i
$980$	−0.568699	+	1.24528i	−0.0181664	+	0.0397789i
$981$	−8.10928	−	5.21152i	−0.258909	−	0.166391i
$982$	28.2832	−	8.30468i	0.902552	−	0.265013i
$983$	2.60295	−	18.1039i	0.0830214	−	0.577426i	−0.905269	−	0.424839i	$-0.860331\pi$
$983$	2.60295	−	18.1039i	0.0830214	−	0.577426i	0.988290	−	0.152587i	$-0.0487604\pi$
$984$	−5.15905	−	11.2967i	−0.164464	−	0.360127i
$985$	1.85534	+	12.9041i	0.0591159	+	0.411160i
$986$	25.0151	−	16.0762i	0.796644	−	0.511972i
$987$	8.55186	−	9.86937i	0.272209	−	0.314145i
$988$	−8.02003			−0.255151
$989$	−11.5439	−	1.61170i	−0.367073	−	0.0512491i
$990$	−4.96082			−0.157665
$991$	−14.1399	+	16.3183i	−0.449169	+	0.518369i	−0.934501	−	0.355961i	$-0.884154\pi$
$991$	−14.1399	+	16.3183i	−0.449169	+	0.518369i	0.485331	+	0.874330i	$0.338699\pi$
$992$	7.53236	−	4.84076i	0.239153	−	0.153694i
$993$	−3.64900	−	25.3794i	−0.115798	−	0.805390i
$994$	−6.57218	−	14.3911i	−0.208457	−	0.456457i
$995$	−4.14834	+	28.8523i	−0.131511	+	0.914681i
$996$	−9.03551	+	2.65307i	−0.286301	+	0.0840656i
$997$	18.2269	+	11.7137i	0.577252	+	0.370977i	0.796451	−	0.604703i	$-0.206708\pi$
$997$	18.2269	+	11.7137i	0.577252	+	0.370977i	−0.219199	+	0.975680i	$0.570344\pi$
$998$	−1.92780	+	4.22130i	−0.0610235	+	0.133623i
$999$	1.65820	+	0.486892i	0.0524632	+	0.0154046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.j.85.2	✓	40
23.13	even	11	inner	966.2.q.j.841.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.j.85.2	✓	40	1.1	even	1	trivial
966.2.q.j.841.2	yes	40	23.13	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.568699 - 1.24528i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.568699 - 1.24528i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.31354 + 0.385689i) q^{10} +(-2.37303 - 2.73862i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-5.15124 - 1.51254i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(1.15167 + 0.740131i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.946027 + 6.57976i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.212597 + 1.47864i) q^{19} +(-1.15167 + 0.740131i) q^{20} +(-0.654861 + 0.755750i) q^{21} +3.62371 q^{22} +(3.63723 + 3.12579i) q^{23} -1.00000 q^{24} +(2.04701 - 2.36237i) q^{25} +(4.51644 - 2.90254i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.636609 + 4.42771i) q^{29} +(-1.31354 + 0.385689i) q^{30} +(7.53236 + 4.84076i) q^{31} +(0.415415 - 0.909632i) q^{32} +(3.47693 + 1.02092i) q^{33} +(-4.35313 - 5.02379i) q^{34} +(-0.896497 - 1.03461i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.717923 - 1.57203i) q^{37} +(-1.25670 - 0.807635i) q^{38} +(5.15124 - 1.51254i) q^{39} +(0.194827 - 1.35505i) q^{40} +(5.15905 + 11.2967i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-2.04459 + 1.31398i) q^{43} +(-2.37303 + 2.73862i) q^{44} -1.36899 q^{45} +(-4.74419 + 0.701884i) q^{46} -13.0590 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.444858 + 3.09405i) q^{50} +(-2.76144 - 6.04671i) q^{51} +(-0.764047 + 5.31406i) q^{52} +(-3.94865 + 1.15943i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-2.06080 + 4.51252i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-0.978262 - 1.12897i) q^{57} +(-2.92935 - 3.38065i) q^{58} +(-2.73431 - 0.802865i) q^{59} +(0.568699 - 1.24528i) q^{60} +(7.12582 + 4.57949i) q^{61} +(-8.59105 + 2.52256i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.04597 + 7.27489i) q^{65} +(-3.04846 + 1.95913i) q^{66} +(-2.17226 + 2.50692i) q^{67} +6.64742 q^{68} +(-4.74976 - 0.663141i) q^{69} +1.36899 q^{70} +(-10.3604 + 11.9565i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-0.561205 - 3.90327i) q^{73} +(0.717923 + 1.57203i) q^{74} +(-0.444858 + 3.09405i) q^{75} +(1.43334 - 0.420865i) q^{76} +(-3.04846 - 1.95913i) q^{77} +(-2.23024 + 4.88355i) q^{78} +(1.23033 + 0.361258i) q^{79} +(0.896497 + 1.03461i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-11.9160 - 3.49884i) q^{82} +(-3.91195 + 8.56597i) q^{83} +(0.841254 + 0.540641i) q^{84} +(8.73162 - 2.56384i) q^{85} +(0.345883 - 2.40567i) q^{86} +(-1.85825 - 4.06901i) q^{87} +(-0.515708 - 3.58683i) q^{88} +(6.12242 - 3.93464i) q^{89} +(0.896497 - 1.03461i) q^{90} -5.36871 q^{91} +(2.57634 - 4.04506i) q^{92} -8.95374 q^{93} +(8.55186 - 9.86937i) q^{94} +(1.72041 - 1.10564i) q^{95} +(0.142315 + 0.989821i) q^{96} +(6.30470 + 13.8054i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-3.47693 + 1.02092i) 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	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 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 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more