LMFDB - Embedded newform 680.2.h.c.509.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.32
Character	$\chi$	$=$	680.509
Dual form			680.2.h.c.509.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.483690 + 1.32893i) q^{2} +2.44428i q^{3} +(-1.53209 + 1.28558i) q^{4} +(-0.380200 + 2.20351i) q^{5} +(-3.24827 + 1.18227i) q^{6} +2.45108 q^{7} +(-2.44949 - 1.41421i) q^{8} -2.97453 q^{9} +(-3.11220 + 0.560555i) q^{10} -2.47628 q^{11} +(-3.14231 - 3.74486i) q^{12} -2.44949 q^{13} +(1.18556 + 3.25730i) q^{14} +(-5.38600 - 0.929318i) q^{15} +(0.694593 - 3.93923i) q^{16} +(4.12307 - 0.0180128i) q^{17} +(-1.43875 - 3.95293i) q^{18} +1.36808i q^{19} +(-2.25027 - 3.86475i) q^{20} +5.99113i q^{21} +(-1.19775 - 3.29080i) q^{22} +1.43193 q^{23} +(3.45674 - 5.98725i) q^{24} +(-4.71090 - 1.67555i) q^{25} +(-1.18479 - 3.25519i) q^{26} +0.0622655i q^{27} +(-3.75527 + 3.15104i) q^{28} +7.23197 q^{29} +(-1.37016 - 7.60710i) q^{30} +6.21204i q^{31} +(5.57091 - 0.982302i) q^{32} -6.05274i q^{33} +(2.01822 + 5.47054i) q^{34} +(-0.931901 + 5.40097i) q^{35} +(4.55724 - 3.82398i) q^{36} +2.43556i q^{37} +(-1.81808 + 0.661726i) q^{38} -5.98725i q^{39} +(4.04753 - 4.85979i) q^{40} -7.78600i q^{41} +(-7.96177 + 2.89785i) q^{42} +5.04731 q^{43} +(3.79389 - 3.18345i) q^{44} +(1.13092 - 6.55439i) q^{45} +(0.692608 + 1.90292i) q^{46} +0.293016i q^{47} +(9.62860 + 1.69778i) q^{48} -0.992220 q^{49} +(-0.0519291 - 7.07088i) q^{50} +(0.0440284 + 10.0779i) q^{51} +(3.75284 - 3.14900i) q^{52} -9.16076 q^{53} +(-0.0827463 + 0.0301172i) q^{54} +(0.941484 - 5.45651i) q^{55} +(-6.00389 - 3.46635i) q^{56} -3.34398 q^{57} +(3.49803 + 9.61075i) q^{58} -12.4453i q^{59} +(9.44654 - 5.50031i) q^{60} -5.56012 q^{61} +(-8.25535 + 3.00470i) q^{62} -7.29079 q^{63} +(4.00000 + 6.92820i) q^{64} +(0.931297 - 5.39747i) q^{65} +(8.04364 - 2.92765i) q^{66} +8.90074 q^{67} +(-6.29375 + 5.32811i) q^{68} +3.50003i q^{69} +(-7.62824 + 1.37396i) q^{70} +10.8712i q^{71} +(7.28607 + 4.20662i) q^{72} -4.79712 q^{73} +(-3.23668 + 1.17806i) q^{74} +(4.09552 - 11.5148i) q^{75} +(-1.75877 - 2.09602i) q^{76} -6.06956 q^{77} +(7.95661 - 2.89597i) q^{78} +8.84615i q^{79} +(8.41604 + 3.02824i) q^{80} -9.07577 q^{81} +(10.3470 - 3.76601i) q^{82} +13.7781 q^{83} +(-7.70205 - 9.17894i) q^{84} +(-1.52790 + 9.09206i) q^{85} +(2.44133 + 6.70750i) q^{86} +17.6770i q^{87} +(6.06563 + 3.50199i) q^{88} +13.8497 q^{89} +(9.25731 - 1.66739i) q^{90} -6.00389 q^{91} +(-2.19384 + 1.84085i) q^{92} -15.1840 q^{93} +(-0.389397 + 0.141729i) q^{94} +(-3.01458 - 0.520145i) q^{95} +(2.40103 + 13.6169i) q^{96} -3.27942 q^{97} +(-0.479926 - 1.31859i) q^{98} +7.36577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) $ 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.483690	+	1.32893i	0.342020	+	0.939693i
$2$	0.483690	+	1.32893i	0.342020	+	0.939693i
$3$			2.44428i			1.41121i	0.708606	+	0.705604i	$0.249324\pi$
$3$			2.44428i			1.41121i	−0.708606	+	0.705604i	$0.750676\pi$
$4$	−1.53209	+	1.28558i	−0.766044	+	0.642788i
$5$	−0.380200	+	2.20351i	−0.170031	+	0.985439i
$5$	−0.380200	+	2.20351i	−0.170031	+	0.985439i
$6$	−3.24827	+	1.18227i	−1.32610	+	0.482662i
$7$	2.45108			0.926420			0.463210	−	0.886249i	$-0.346698\pi$
$7$	2.45108			0.926420			0.463210	+	0.886249i	$0.346698\pi$
$8$	−2.44949	−	1.41421i	−0.866025	−	0.500000i
$9$	−2.97453			−0.991509
$10$	−3.11220	+	0.560555i	−0.984163	+	0.177263i
$11$	−2.47628			−0.746627			−0.373314	−	0.927705i	$-0.621778\pi$
$11$	−2.47628			−0.746627			−0.373314	+	0.927705i	$0.621778\pi$
$12$	−3.14231	−	3.74486i	−0.907107	−	1.08105i
$13$	−2.44949			−0.679366			−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949			−0.679366			−0.339683	+	0.940540i	$0.610320\pi$
$14$	1.18556	+	3.25730i	0.316854	+	0.870550i
$15$	−5.38600	−	0.929318i	−1.39066	−	0.239949i
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	4.12307	−	0.0180128i	0.999990	−	0.00436874i
$17$	4.12307	−	0.0180128i	0.999990	−	0.00436874i
$18$	−1.43875	−	3.95293i	−0.339116	−	0.931713i
$19$			1.36808i			0.313859i	0.987610	+	0.156930i	$0.0501596\pi$
$19$			1.36808i			0.313859i	−0.987610	+	0.156930i	$0.949840\pi$
$20$	−2.25027	−	3.86475i	−0.503177	−	0.864184i
$21$			5.99113i			1.30737i
$22$	−1.19775	−	3.29080i	−0.255362	−	0.701600i
$23$	1.43193			0.298577			0.149289	−	0.988794i	$-0.452302\pi$
$23$	1.43193			0.298577			0.149289	+	0.988794i	$0.452302\pi$
$24$	3.45674	−	5.98725i	0.705604	−	1.22214i
$25$	−4.71090	−	1.67555i	−0.942179	−	0.335110i
$26$	−1.18479	−	3.25519i	−0.232357	−	0.638395i
$27$			0.0622655i			0.0119830i
$28$	−3.75527	+	3.15104i	−0.709679	+	0.595491i
$29$	7.23197			1.34294			0.671472	−	0.741030i	$-0.265662\pi$
$29$	7.23197			1.34294			0.671472	+	0.741030i	$0.265662\pi$
$30$	−1.37016	−	7.60710i	−0.250155	−	1.38886i
$31$			6.21204i			1.11572i	0.829936	+	0.557858i	$0.188377\pi$
$31$			6.21204i			1.11572i	−0.829936	+	0.557858i	$0.811623\pi$
$32$	5.57091	−	0.982302i	0.984808	−	0.173648i
$33$		−	6.05274i		−	1.05365i
$34$	2.01822	+	5.47054i	0.346122	+	0.938189i
$35$	−0.931901	+	5.40097i	−0.157520	+	0.912930i
$36$	4.55724	−	3.82398i	0.759540	−	0.637330i
$37$			2.43556i			0.400404i	0.979755	+	0.200202i	$0.0641599\pi$
$37$			2.43556i			0.400404i	−0.979755	+	0.200202i	$0.935840\pi$
$38$	−1.81808	+	0.661726i	−0.294931	+	0.107346i
$39$		−	5.98725i		−	0.958727i
$40$	4.04753	−	4.85979i	0.639970	−	0.768400i
$41$		−	7.78600i		−	1.21597i	−0.793949	−	0.607985i	$-0.791978\pi$
$41$		−	7.78600i		−	1.21597i	0.793949	−	0.607985i	$-0.208022\pi$
$42$	−7.96177	+	2.89785i	−1.22853	+	0.447147i
$43$	5.04731			0.769708			0.384854	−	0.922978i	$-0.374252\pi$
$43$	5.04731			0.769708			0.384854	+	0.922978i	$0.374252\pi$
$44$	3.79389	−	3.18345i	0.571950	−	0.479923i
$45$	1.13092	−	6.55439i	0.168587	−	0.977071i
$46$	0.692608	+	1.90292i	0.102119	+	0.280571i
$47$			0.293016i			0.0427408i	0.999772	+	0.0213704i	$0.00680293\pi$
$47$			0.293016i			0.0427408i	−0.999772	+	0.0213704i	$0.993197\pi$
$48$	9.62860	+	1.69778i	1.38977	+	0.245054i
$49$	−0.992220			−0.141746
$50$	−0.0519291	−	7.07088i	−0.00734388	−	0.999973i
$51$	0.0440284	+	10.0779i	0.00616520	+	1.41119i
$52$	3.75284	−	3.14900i	0.520425	−	0.436688i
$53$	−9.16076			−1.25833			−0.629163	−	0.777273i	$-0.716602\pi$
$53$	−9.16076			−1.25833			−0.629163	+	0.777273i	$0.716602\pi$
$54$	−0.0827463	+	0.0301172i	−0.0112603	+	0.00409843i
$55$	0.941484	−	5.45651i	0.126950	−	0.735756i
$56$	−6.00389	−	3.46635i	−0.802303	−	0.463210i
$57$	−3.34398			−0.442921
$58$	3.49803	+	9.61075i	0.459314	+	1.26195i
$59$		−	12.4453i		−	1.62024i	−0.586265	−	0.810119i	$-0.699402\pi$
$59$		−	12.4453i		−	1.62024i	0.586265	−	0.810119i	$-0.300598\pi$
$60$	9.44654	−	5.50031i	1.21954	−	0.710087i
$61$	−5.56012			−0.711900			−0.355950	−	0.934505i	$-0.615843\pi$
$61$	−5.56012			−0.711900			−0.355950	+	0.934505i	$0.615843\pi$
$62$	−8.25535	+	3.00470i	−1.04843	+	0.381597i
$63$	−7.29079			−0.918554
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	0.931297	−	5.39747i	0.115513	−	0.669474i
$66$	8.04364	−	2.92765i	0.990104	−	0.360368i
$67$	8.90074			1.08740			0.543699	−	0.839280i	$-0.317023\pi$
$67$	8.90074			1.08740			0.543699	+	0.839280i	$0.317023\pi$
$68$	−6.29375	+	5.32811i	−0.763229	+	0.646128i
$69$			3.50003i			0.421355i
$70$	−7.62824	+	1.37396i	−0.911749	+	0.164220i
$71$			10.8712i			1.29017i	0.764109	+	0.645087i	$0.223179\pi$
$71$			10.8712i			1.29017i	−0.764109	+	0.645087i	$0.776821\pi$
$72$	7.28607	+	4.20662i	0.858672	+	0.495754i
$73$	−4.79712			−0.561461			−0.280730	−	0.959787i	$-0.590577\pi$
$73$	−4.79712			−0.561461			−0.280730	+	0.959787i	$0.590577\pi$
$74$	−3.23668	+	1.17806i	−0.376257	+	0.136946i
$75$	4.09552	−	11.5148i	0.472910	−	1.32961i
$76$	−1.75877	−	2.09602i	−0.201745	−	0.240430i
$77$	−6.06956			−0.691691
$78$	7.95661	−	2.89597i	0.900909	−	0.327904i
$79$			8.84615i			0.995270i	0.867387	+	0.497635i	$0.165798\pi$
$79$			8.84615i			0.995270i	−0.867387	+	0.497635i	$0.834202\pi$
$80$	8.41604	+	3.02824i	0.940942	+	0.338567i
$81$	−9.07577			−1.00842
$82$	10.3470	−	3.76601i	1.14264	−	0.415886i
$83$	13.7781			1.51234			0.756169	−	0.654377i	$-0.227069\pi$
$83$	13.7781			1.51234			0.756169	+	0.654377i	$0.227069\pi$
$84$	−7.70205	−	9.17894i	−0.840362	−	1.00150i
$85$	−1.52790	+	9.09206i	−0.165724	+	0.986172i
$86$	2.44133	+	6.70750i	0.263255	+	0.723289i
$87$			17.6770i			1.89517i
$88$	6.06563	+	3.50199i	0.646598	+	0.373314i
$89$	13.8497			1.46806			0.734032	−	0.679115i	$-0.237636\pi$
$89$	13.8497			1.46806			0.734032	+	0.679115i	$0.237636\pi$
$90$	9.25731	−	1.66739i	0.975807	−	0.175758i
$91$	−6.00389			−0.629379
$92$	−2.19384	+	1.84085i	−0.228723	+	0.191922i
$93$	−15.1840			−1.57451
$94$	−0.389397	+	0.141729i	−0.0401633	+	0.0146182i
$95$	−3.01458	−	0.520145i	−0.309289	−	0.0533657i
$96$	2.40103	+	13.6169i	0.245054	+	1.38977i
$97$	−3.27942			−0.332974			−0.166487	−	0.986044i	$-0.553242\pi$
$97$	−3.27942			−0.332974			−0.166487	+	0.986044i	$0.553242\pi$
$98$	−0.479926	−	1.31859i	−0.0484799	−	0.133197i
$99$	7.36577			0.740288
$100$	9.37156	−	3.48912i	0.937156	−	0.348912i
$101$			1.56858i			0.156080i	0.996950	+	0.0780398i	$0.0248661\pi$
$101$			1.56858i			0.156080i	−0.996950	+	0.0780398i	$0.975134\pi$
$102$	−13.3715	+	4.93311i	−1.32398	+	0.488450i
$103$			9.63770i			0.949631i	0.880085	+	0.474815i	$0.157485\pi$
$103$			9.63770i			0.949631i	−0.880085	+	0.474815i	$0.842515\pi$
$104$	6.00000	+	3.46410i	0.588348	+	0.339683i
$105$	−13.2015	−	2.27783i	−1.28833	−	0.222293i
$106$	−4.43096	−	12.1740i	−0.430373	−	1.18244i
$107$			7.16085i			0.692266i	0.938185	+	0.346133i	$0.112505\pi$
$107$			7.16085i			0.692266i	−0.938185	+	0.346133i	$0.887495\pi$
$108$	−0.0800470	−	0.0953963i	−0.00770253	−	0.00917951i
$109$	−15.7018			−1.50396			−0.751978	−	0.659188i	$-0.770900\pi$
$109$	−15.7018			−1.50396			−0.751978	+	0.659188i	$0.770900\pi$
$110$	7.70668	−	1.38809i	0.734803	−	0.132350i
$111$	−5.95321			−0.565054
$112$	1.70250	−	9.65536i	0.160871	−	0.912346i
$113$	6.91519			0.650526			0.325263	−	0.945624i	$-0.394547\pi$
$113$	6.91519			0.650526			0.325263	+	0.945624i	$0.394547\pi$
$114$	−1.61745	−	4.44390i	−0.151488	−	0.416209i
$115$	−0.544419	+	3.15526i	−0.0507673	+	0.294230i
$116$	−11.0800	+	9.29724i	−1.02875	+	0.863227i
$117$	7.28607			0.673598
$118$	16.5389	−	6.01965i	1.52253	−	0.554154i
$119$	10.1060	−	0.0441507i	0.926411	−	0.00404729i
$120$	11.8787	+	9.89331i	1.08437	+	0.903131i
$121$	−4.86802			−0.442548
$122$	−2.68937	−	7.38899i	−0.243484	−	0.668967i
$123$	19.0312			1.71599
$124$	−7.98605	−	9.51740i	−0.717169	−	0.854688i
$125$	5.48317	−	9.74345i	0.490430	−	0.871481i
$126$	−3.52648	−	9.68893i	−0.314164	−	0.863158i
$127$			1.30318i			0.115638i	0.998327	+	0.0578192i	$0.0184147\pi$
$127$			1.30318i			0.115638i	−0.998327	+	0.0578192i	$0.981585\pi$
$128$	−7.27231	+	8.66680i	−0.642788	+	0.766044i
$129$			12.3371i			1.08622i
$130$	7.62330	−	1.37307i	0.668607	−	0.120427i
$131$	−18.7031			−1.63410			−0.817051	−	0.576566i	$-0.804393\pi$
$131$	−18.7031			−1.63410			−0.817051	+	0.576566i	$0.804393\pi$
$132$	7.78125	+	9.27334i	0.677271	+	0.807140i
$133$			3.35327i			0.290765i
$134$	4.30520	+	11.8284i	0.371912	+	1.02182i
$135$	−0.137203	−	0.0236734i	−0.0118085	−	0.00203748i
$136$	−10.1249	−	5.78677i	−0.868202	−	0.496212i
$137$		−	10.0090i		−	0.855124i	−0.903986	−	0.427562i	$-0.859373\pi$
$137$		−	10.0090i		−	0.855124i	0.903986	−	0.427562i	$-0.140627\pi$
$138$	−4.65129	+	1.69293i	−0.395944	+	0.144112i
$139$	9.40241			0.797502			0.398751	−	0.917059i	$-0.369444\pi$
$139$	9.40241			0.797502			0.398751	+	0.917059i	$0.369444\pi$
$140$	−5.51560	−	9.47279i	−0.466153	−	0.800597i
$141$	−0.716216			−0.0603162
$142$	−14.4470	+	5.25829i	−1.21237	+	0.441266i
$143$	6.06563			0.507233
$144$	−2.06608	+	11.7173i	−0.172174	+	0.976445i
$145$	−2.74960	+	15.9357i	−0.228342	+	1.32339i
$146$	−2.32032	−	6.37502i	−0.192031	−	0.527601i
$147$		−	2.42527i		−	0.200033i
$148$	−3.13110	−	3.73150i	−0.257375	−	0.306727i
$149$		−	6.92001i		−	0.566910i	−0.958986	−	0.283455i	$-0.908519\pi$
$149$		−	6.92001i		−	0.566910i	0.958986	−	0.283455i	$-0.0914806\pi$
$150$	17.2832	−	0.126929i	1.41117	−	0.0103637i
$151$	−17.1983			−1.39957			−0.699787	−	0.714351i	$-0.746722\pi$
$151$	−17.1983			−1.39957			−0.699787	+	0.714351i	$0.746722\pi$
$152$	1.93476	−	3.35110i	0.156930	−	0.271810i
$153$	−12.2642	+	0.0535795i	−0.991499	+	0.00433165i
$154$	−2.93578	−	8.06600i	−0.236572	−	0.649977i
$155$	−13.6883	−	2.36182i	−1.09947	−	0.189706i
$156$	7.69706	+	9.17300i	0.616258	+	0.734428i
$157$	8.48882			0.677482			0.338741	−	0.940880i	$-0.389999\pi$
$157$	8.48882			0.677482			0.338741	+	0.940880i	$0.389999\pi$
$158$	−11.7559	+	4.27879i	−0.935248	+	0.340402i
$159$		−	22.3915i		−	1.77576i
$160$	0.0464471	+	12.6490i	0.00367196	+	0.999993i
$161$	3.50976			0.276608
$162$	−4.38986	−	12.0610i	−0.344900	−	0.947604i
$163$			9.90706i			0.775981i	0.921663	+	0.387991i	$0.126831\pi$
$163$			9.90706i			0.775981i	−0.921663	+	0.387991i	$0.873169\pi$
$164$	10.0095	+	11.9288i	0.781610	+	0.931486i
$165$	13.3373	+	2.30125i	1.03830	+	0.179152i
$166$	6.66430	+	18.3100i	0.517250	+	1.42113i
$167$	21.1938			1.64003			0.820013	−	0.572345i	$-0.193966\pi$
$167$	21.1938			1.64003			0.820013	+	0.572345i	$0.193966\pi$
$168$	8.47274	−	14.6752i	0.653686	−	1.13222i
$169$	−7.00000			−0.538462
$170$	−12.8217	+	2.36727i	−0.983380	+	0.181561i
$171$		−	4.06939i		−	0.311194i
$172$	−7.73293	+	6.48870i	−0.589630	+	0.494758i
$173$			0.675738i			0.0513754i	0.999670	+	0.0256877i	$0.00817755\pi$
$173$			0.675738i			0.0513754i	−0.999670	+	0.0256877i	$0.991822\pi$
$174$	−23.4914	+	8.55018i	−1.78088	+	0.648187i
$175$	−11.5468	−	4.10690i	−0.872854	−	0.310453i
$176$	−1.72001	+	9.75465i	−0.129650	+	0.735284i
$177$	30.4198			2.28649
$178$	6.69894	+	18.4052i	0.502107	+	1.37953i
$179$			3.55235i			0.265515i	0.991149	+	0.132757i	$0.0423831\pi$
$179$			3.55235i			0.265515i	−0.991149	+	0.132757i	$0.957617\pi$
$180$	6.69350	+	11.4958i	0.498904	+	0.856846i
$181$	7.46849			0.555128			0.277564	−	0.960707i	$-0.410473\pi$
$181$	7.46849			0.555128			0.277564	+	0.960707i	$0.410473\pi$
$182$	−2.90402	−	7.97872i	−0.215260	−	0.591422i
$183$		−	13.5905i		−	1.00464i
$184$	−3.50749	−	2.02505i	−0.258575	−	0.149289i
$185$	−5.36678	−	0.926002i	−0.394574	−	0.0680811i
$186$	−7.34434	−	20.1784i	−0.538513	−	1.47955i
$187$	−10.2099	+	0.0446047i	−0.746620	+	0.00326182i
$188$	−0.376695	−	0.448927i	−0.0274733	−	0.0327414i
$189$			0.152618i			0.0111013i
$190$	−0.766885	−	4.25774i	−0.0556357	−	0.308889i
$191$	12.0831			0.874305			0.437152	−	0.899388i	$-0.355987\pi$
$191$	12.0831			0.874305			0.437152	+	0.899388i	$0.355987\pi$
$192$	−16.9345	+	9.77714i	−1.22214	+	0.705604i
$193$	12.8832			0.927350			0.463675	−	0.886005i	$-0.346530\pi$
$193$	12.8832			0.927350			0.463675	+	0.886005i	$0.346530\pi$
$194$	−1.58622	−	4.35810i	−0.113884	−	0.312893i
$195$	13.1930	+	2.27636i	0.944767	+	0.163013i
$196$	1.52017	−	1.27557i	0.108584	−	0.0911124i
$197$			13.9686i			0.995224i	0.867400	+	0.497612i	$0.165790\pi$
$197$			13.9686i			0.995224i	−0.867400	+	0.497612i	$0.834210\pi$
$198$	3.56274	+	9.78856i	0.253193	+	0.695643i
$199$		−	21.4009i		−	1.51707i	−0.651634	−	0.758533i	$-0.725916\pi$
$199$		−	21.4009i		−	1.51707i	0.651634	−	0.758533i	$-0.274084\pi$
$200$	9.16970	+	10.7665i	0.648396	+	0.761303i
$201$			21.7559i			1.53455i
$202$	−2.08453	+	0.758706i	−0.146667	+	0.0533823i
$203$	17.7261			1.24413
$204$	−13.0234	−	15.3837i	−0.911821	−	1.07707i
$205$	17.1565	+	2.96024i	1.19826	+	0.206752i
$206$	−12.8078	+	4.66165i	−0.892361	+	0.324793i
$207$	−4.25930			−0.296042
$208$	−1.70140	+	9.64911i	−0.117971	+	0.669045i
$209$		−	3.38775i		−	0.234336i
$210$	−3.35836	−	18.6456i	−0.231749	−	1.28667i
$211$	16.3619			1.12640			0.563201	−	0.826320i	$-0.309570\pi$
$211$	16.3619			1.12640			0.563201	+	0.826320i	$0.309570\pi$
$212$	14.0351	−	11.7768i	0.963934	−	0.808837i
$213$	−26.5723			−1.82070
$214$	−9.51625	+	3.46363i	−0.650517	+	0.236769i
$215$	−1.91899	+	11.1218i	−0.130874	+	0.758500i
$216$	0.0880567	−	0.152519i	0.00599150	−	0.0103776i
$217$			15.2262i			1.03362i
$218$	−7.59478	−	20.8665i	−0.514383	−	1.41326i
$219$		−	11.7255i		−	0.792338i
$220$	5.57232	+	9.57021i	0.375685	+	0.645223i
$221$	−10.0994	+	0.0441221i	−0.679360	+	0.00296798i
$222$	−2.87951	−	7.91138i	−0.193260	−	0.530977i
$223$			26.3574i			1.76502i	0.470291	+	0.882512i	$0.344149\pi$
$223$			26.3574i			1.76502i	−0.470291	+	0.882512i	$0.655851\pi$
$224$	13.6547	−	2.40770i	0.912346	−	0.160871i
$225$	14.0127	+	4.98397i	0.934179	+	0.332264i
$226$	3.34480	+	9.18977i	0.222493	+	0.611295i
$227$		−	3.49638i		−	0.232063i	−0.993246	−	0.116031i	$-0.962983\pi$
$227$		−	3.49638i		−	0.232063i	0.993246	−	0.116031i	$-0.0370173\pi$
$228$	5.12327	−	4.29894i	0.339297	−	0.284704i
$229$		−	21.9131i		−	1.44806i	−0.689771	−	0.724028i	$-0.742289\pi$
$229$		−	21.9131i		−	1.44806i	0.689771	−	0.724028i	$-0.257711\pi$
$230$	−4.45644	+	0.802674i	−0.293849	+	0.0529267i
$231$		−	14.8357i		−	0.976120i
$232$	−17.7146	−	10.2276i	−1.16302	−	0.671472i
$233$	−1.45722			−0.0954658			−0.0477329	−	0.998860i	$-0.515200\pi$
$233$	−1.45722			−0.0954658			−0.0477329	+	0.998860i	$0.515200\pi$
$234$	3.52420	+	9.68265i	0.230384	+	0.632975i
$235$	−0.645664	−	0.111405i	−0.0421185	−	0.00726726i
$236$	15.9994	+	19.0673i	1.04147	+	1.24117i
$237$	−21.6225			−1.40453
$238$	4.94682	+	13.4087i	0.320655	+	0.869158i
$239$	14.0395			0.908143			0.454071	−	0.890965i	$-0.349971\pi$
$239$	14.0395			0.908143			0.454071	+	0.890965i	$0.349971\pi$
$240$	−7.40188	+	20.5712i	−0.477789	+	1.32787i
$241$			6.51814i			0.419870i	0.977715	+	0.209935i	$0.0673253\pi$
$241$			6.51814i			0.419870i	−0.977715	+	0.209935i	$0.932675\pi$
$242$	−2.35461	−	6.46924i	−0.151360	−	0.415859i
$243$		−	21.9970i		−	1.41111i
$244$	8.51859	−	7.14795i	0.545347	−	0.457601i
$245$	0.377243	−	2.18636i	0.0241011	−	0.139682i
$246$	9.20519	+	25.2911i	0.586902	+	1.61250i
$247$		−	3.35110i		−	0.213225i
$248$	8.78516	−	15.2163i	0.557858	−	0.966239i
$249$			33.6775i			2.13422i
$250$	15.6005	+	2.57392i	0.986661	+	0.162789i
$251$		−	26.4287i		−	1.66816i	−0.551640	−	0.834082i	$-0.685998\pi$
$251$		−	26.4287i		−	1.66816i	0.551640	−	0.834082i	$-0.314002\pi$
$252$	11.1701	−	9.37286i	0.703653	−	0.590435i
$253$	−3.54585			−0.222926
$254$	−1.73183	+	0.630334i	−0.108665	+	0.0395506i
$255$	−22.2236	−	3.73462i	−1.39169	−	0.233871i
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$		−	30.8915i		−	1.92696i	−0.267784	−	0.963479i	$-0.586291\pi$
$257$		−	30.8915i		−	1.92696i	0.267784	−	0.963479i	$-0.413709\pi$
$258$	−16.3950	+	5.96731i	−1.02071	+	0.371508i
$259$			5.96975i			0.370943i
$260$	5.51202	+	9.46666i	0.341841	+	0.587097i
$261$	−21.5117			−1.33154
$262$	−9.04652	−	24.8551i	−0.558896	−	1.53555i
$263$			14.3910i			0.887385i	0.896179	+	0.443692i	$0.146332\pi$
$263$			14.3910i			0.887385i	−0.896179	+	0.443692i	$0.853668\pi$
$264$	−8.55987	+	14.8261i	−0.526823	+	0.912485i
$265$	3.48292	−	20.1858i	0.213954	−	1.24000i
$266$	−4.45625	+	1.62194i	−0.273230	+	0.0994477i
$267$			33.8526i			2.07174i
$268$	−13.6367	+	11.4426i	−0.832996	+	0.698966i
$269$	12.3788			0.754750			0.377375	−	0.926061i	$-0.376827\pi$
$269$	12.3788			0.754750			0.377375	+	0.926061i	$0.376827\pi$
$270$	−0.0349033	−	0.193783i	−0.00212415	−	0.0117932i
$271$	25.9852			1.57849			0.789243	−	0.614081i	$-0.210473\pi$
$271$	25.9852			1.57849			0.789243	+	0.614081i	$0.210473\pi$
$272$	2.79290	−	16.2542i	0.169344	−	0.985557i
$273$		−	14.6752i		−	0.888184i
$274$	13.3012	−	4.84123i	0.803553	−	0.292470i
$275$	11.6655	+	4.14914i	0.703457	+	0.250202i
$276$	−4.49956	−	5.36236i	−0.270842	−	0.322776i
$277$		−	8.30576i		−	0.499045i	−0.968369	−	0.249522i	$-0.919726\pi$
$277$		−	8.30576i		−	0.499045i	0.968369	−	0.249522i	$-0.0802736\pi$
$278$	4.54785	+	12.4951i	0.272762	+	0.749406i
$279$		−	18.4779i		−	1.10624i
$280$	9.92080	−	11.9117i	0.592881	−	0.711861i
$281$	21.5720			1.28688			0.643439	−	0.765498i	$-0.277507\pi$
$281$	21.5720			1.28688			0.643439	+	0.765498i	$0.277507\pi$
$282$	−0.346426	−	0.951797i	−0.0206294	−	0.0566787i
$283$		−	13.2294i		−	0.786403i	−0.919452	−	0.393202i	$-0.871367\pi$
$283$		−	13.2294i		−	0.786403i	0.919452	−	0.393202i	$-0.128633\pi$
$284$	−13.9757	−	16.6556i	−0.829308	−	0.988331i
$285$	1.27138	−	7.36848i	0.0753102	−	0.436471i
$286$	2.93388	+	8.06077i	0.173484	+	0.476644i
$287$		−	19.0841i		−	1.12650i
$288$	−16.5708	+	2.92188i	−0.976445	+	0.172174i
$289$	16.9994	−	0.148536i	0.999962	−	0.00873740i
$290$	−22.5073	+	4.05392i	−1.32168	+	0.238054i
$291$		−	8.01582i		−	0.469896i
$292$	7.34962	−	6.16706i	0.430104	−	0.360900i
$293$	−19.3453			−1.13016			−0.565082	−	0.825035i	$-0.691155\pi$
$293$	−19.3453			−1.13016			−0.565082	+	0.825035i	$0.691155\pi$
$294$	3.22300	−	1.17308i	0.187969	−	0.0684152i
$295$	27.4233	+	4.73170i	1.59665	+	0.275490i
$296$	3.44441	−	5.96589i	0.200202	−	0.346760i
$297$		−	0.154187i		−	0.00894684i
$298$	9.19619	−	3.34714i	0.532721	−	0.193895i
$299$	−3.50749			−0.202843
$300$	8.52840	+	22.9067i	0.492387	+	1.32252i
$301$	12.3713			0.713073
$302$	−8.31862	−	22.8552i	−0.478683	−	1.31517i
$303$	−3.83406			−0.220261
$304$	5.38919	+	0.950259i	0.309091	+	0.0545011i
$305$	2.11396	−	12.2518i	0.121045	−	0.701534i
$306$	−6.00325	−	16.2723i	−0.343183	−	0.930223i
$307$	−5.10218			−0.291197			−0.145598	−	0.989344i	$-0.546511\pi$
$307$	−5.10218			−0.291197			−0.145598	+	0.989344i	$0.546511\pi$
$308$	9.29911	−	7.80288i	0.529866	−	0.444610i
$309$	−23.5573			−1.34013
$310$	−3.48220	−	19.3331i	−0.197775	−	1.09805i
$311$			4.35179i			0.246767i	0.992359	+	0.123384i	$0.0393745\pi$
$311$			4.35179i			0.246767i	−0.992359	+	0.123384i	$0.960625\pi$
$312$	−8.46725	+	14.6657i	−0.479364	+	0.830282i
$313$	−20.8861			−1.18055			−0.590275	−	0.807202i	$-0.700981\pi$
$313$	−20.8861			−1.18055			−0.590275	+	0.807202i	$0.700981\pi$
$314$	4.10595	+	11.2810i	0.231712	+	0.636625i
$315$	2.77196	−	16.0653i	0.156182	−	0.905178i
$316$	−11.3724	−	13.5531i	−0.639747	−	0.762421i
$317$			20.4837i			1.15048i	0.817985	+	0.575240i	$0.195091\pi$
$317$			20.4837i			1.15048i	−0.817985	+	0.575240i	$0.804909\pi$
$318$	29.7566	−	10.8305i	1.66867	−	0.607346i
$319$	−17.9084			−1.00268
$320$	−16.7872	+	6.17993i	−0.938430	+	0.345468i
$321$	−17.5032			−0.976931
$322$	1.69763	+	4.66421i	0.0946055	+	0.259926i
$323$	0.0246429	+	5.64069i	0.00137117	+	0.313856i
$324$	13.9049	−	11.6676i	0.772494	−	0.648199i
$325$	11.5393	+	4.10424i	0.640085	+	0.227662i
$326$	−13.1658	+	4.79194i	−0.729184	+	0.265401i
$327$		−	38.3796i		−	2.12240i
$328$	−11.0111	+	19.0717i	−0.607985	+	1.05306i
$329$			0.718206i			0.0395960i
$330$	3.39290	+	18.8373i	0.186773	+	1.03696i
$331$			6.60254i			0.362908i	0.983399	+	0.181454i	$0.0580804\pi$
$331$			6.60254i			0.362908i	−0.983399	+	0.181454i	$0.941920\pi$
$332$	−21.1092	+	17.7127i	−1.15852	+	0.972112i
$333$		−	7.24465i		−	0.397004i
$334$	10.2512	+	28.1650i	0.560922	+	1.54112i
$335$	−3.38407	+	19.6129i	−0.184891	+	1.07156i
$336$	23.6004	+	4.16140i	1.28751	+	0.227023i
$337$	26.9787			1.46962			0.734811	−	0.678272i	$-0.237271\pi$
$337$	26.9787			1.46962			0.734811	+	0.678272i	$0.237271\pi$
$338$	−3.38583	−	9.30248i	−0.184165	−	0.505988i
$339$			16.9027i			0.918028i
$340$	−9.34765	−	15.8941i	−0.506947	−	0.861977i
$341$		−	15.3828i		−	0.833024i
$342$	5.40792	−	1.96832i	0.292427	−	0.106435i
$343$	−19.5895			−1.05774
$344$	−12.3633	−	7.13797i	−0.666586	−	0.384854i
$345$	−7.71235	−	1.33071i	−0.415219	−	0.0716433i
$346$	−0.898006	+	0.326847i	−0.0482771	+	0.0175714i
$347$			8.20630i			0.440537i	0.975439	+	0.220269i	$0.0706934\pi$
$347$			8.20630i			0.440537i	−0.975439	+	0.220269i	$0.929307\pi$
$348$	−22.7251	−	27.0827i	−1.21819	−	1.45179i
$349$			25.1107i			1.34415i	0.740485	+	0.672073i	$0.234596\pi$
$349$			25.1107i			1.34415i	−0.740485	+	0.672073i	$0.765404\pi$
$350$	−0.127282	−	17.3313i	−0.00680352	−	0.926395i
$351$		−	0.152519i		−	0.00814085i
$352$	−13.7952	+	2.43246i	−0.735284	+	0.129650i
$353$			28.8119i			1.53350i	0.641944	+	0.766752i	$0.278128\pi$
$353$			28.8119i			1.53350i	−0.641944	+	0.766752i	$0.721872\pi$
$354$	14.7137	+	40.4257i	0.782027	+	2.14860i
$355$	−23.9548	−	4.13324i	−1.27139	−	0.219369i
$356$	−21.2189	+	17.8048i	−1.12460	+	0.943653i
$357$	0.107917	+	24.7018i	0.00571157	+	1.30736i
$358$	−4.72080	+	1.71823i	−0.249502	+	0.0908114i
$359$	−6.11200			−0.322579			−0.161290	−	0.986907i	$-0.551565\pi$
$359$	−6.11200			−0.322579			−0.161290	+	0.986907i	$0.551565\pi$
$360$	−12.0395	+	14.4556i	−0.634536	+	0.761875i
$361$	17.1284			0.901492
$362$	3.61243	+	9.92507i	0.189865	+	0.521650i
$363$		−	11.8988i		−	0.624527i
$364$	9.19849	−	7.71845i	0.482132	−	0.404557i
$365$	1.82387	−	10.5705i	0.0954657	−	0.553285i
$366$	18.0608	−	6.57359i	0.944052	−	0.343607i
$367$	20.2183			1.05539			0.527695	−	0.849434i	$-0.323057\pi$
$367$	20.2183			1.05539			0.527695	+	0.849434i	$0.323057\pi$
$368$	0.994605	−	5.64069i	0.0518474	−	0.294041i
$369$			23.1597i			1.20564i
$370$	−1.36527	−	7.57996i	−0.0709769	−	0.394063i
$371$	−22.4537			−1.16574
$372$	23.2632	−	19.5202i	1.20614	−	1.01207i
$373$	35.3438			1.83003			0.915016	−	0.403419i	$-0.132178\pi$
$373$	35.3438			1.83003			0.915016	+	0.403419i	$0.132178\pi$
$374$	−4.99769	−	13.5466i	−0.258424	−	0.700478i
$375$	23.8158	+	13.4024i	1.22984	+	0.692099i
$376$	0.414388	−	0.717741i	0.0213704	−	0.0370147i
$377$	−17.7146			−0.912350
$378$	−0.202817	+	0.0738195i	−0.0104318	+	0.00379687i
$379$	−17.6653			−0.907404			−0.453702	−	0.891153i	$-0.649897\pi$
$379$	−17.6653			−0.907404			−0.453702	+	0.891153i	$0.649897\pi$
$380$	5.28728	−	3.07856i	0.271232	−	0.157927i
$381$	−3.18534			−0.163190
$382$	5.84448	+	16.0576i	0.299030	+	0.821578i
$383$		−	28.5067i		−	1.45662i	−0.685246	−	0.728312i	$-0.740305\pi$
$383$		−	28.5067i		−	1.45662i	0.685246	−	0.728312i	$-0.259695\pi$
$384$	−21.1841	−	17.7756i	−1.08105	−	0.907107i
$385$	2.30765	−	13.3743i	0.117609	−	0.681619i
$386$	6.23145	+	17.1208i	0.317172	+	0.871424i
$387$	−15.0134			−0.763172
$388$	5.02436	−	4.21594i	0.255073	−	0.214032i
$389$		−	18.5485i		−	0.940445i	−0.882548	−	0.470223i	$-0.844174\pi$
$389$		−	18.5485i		−	0.940445i	0.882548	−	0.470223i	$-0.155826\pi$
$390$	3.35619	+	18.6335i	0.169947	+	0.943544i
$391$	5.90393	−	0.0257930i	0.298574	−	0.00130441i
$392$	2.43043	+	1.40321i	0.122755	+	0.0708729i
$393$		−	45.7158i		−	2.30606i
$394$	−18.5633	+	6.75648i	−0.935204	+	0.340387i
$395$	−19.4926	−	3.36331i	−0.980777	−	0.169227i
$396$	−11.2850	+	9.46925i	−0.567093	+	0.475848i
$397$		−	10.8537i		−	0.544732i	−0.962194	−	0.272366i	$-0.912194\pi$
$397$		−	10.8537i		−	0.544732i	0.962194	−	0.272366i	$-0.0878062\pi$
$398$	28.4402	−	10.3514i	1.42558	−	0.518867i
$399$	−8.19635			−0.410331
$400$	−9.87253	+	17.3935i	−0.493627	+	0.869674i
$401$		−	35.9604i		−	1.79578i	−0.440222	−	0.897889i	$-0.645100\pi$
$401$		−	35.9604i		−	1.79578i	0.440222	−	0.897889i	$-0.354900\pi$
$402$	−28.9120	+	10.5231i	−1.44200	+	0.524846i
$403$		−	15.2163i		−	0.757980i
$404$	−2.01653	−	2.40320i	−0.100326	−	0.119564i
$405$	3.45061	−	19.9985i	0.171462	−	0.993735i
$406$	8.57394	+	23.5567i	0.425517	+	1.16910i
$407$		−	6.03114i		−	0.298953i
$408$	14.1445	−	24.7481i	0.700258	−	1.22521i
$409$	−2.08221			−0.102959			−0.0514794	−	0.998674i	$-0.516394\pi$
$409$	−2.08221			−0.102959			−0.0514794	+	0.998674i	$0.516394\pi$
$410$	4.36449	+	24.2316i	0.215547	+	1.19671i
$411$	24.4648			1.20676
$412$	−12.3900	−	14.7658i	−0.610411	−	0.727459i
$413$		−	30.5044i		−	1.50102i
$414$	−2.06018	−	5.66030i	−0.101252	−	0.278188i
$415$	−5.23842	+	30.3600i	−0.257144	+	1.49032i
$416$	−13.6459	+	2.40614i	−0.669045	+	0.117971i
$417$			22.9822i			1.12544i
$418$	4.50208	−	1.63862i	0.220204	−	0.0801476i
$419$	39.7488			1.94186			0.970928	−	0.239373i	$-0.0769418\pi$
$419$	39.7488			1.94186			0.970928	+	0.239373i	$0.0769418\pi$
$420$	23.1542	−	13.4817i	1.12981	−	0.657839i
$421$		−	24.6387i		−	1.20082i	−0.799694	−	0.600408i	$-0.795005\pi$
$421$		−	24.6387i		−	1.20082i	0.799694	−	0.600408i	$-0.204995\pi$
$422$	7.91410	+	21.7438i	0.385252	+	1.05847i
$423$		−	0.871585i		−	0.0423779i
$424$	22.4392	+	12.9553i	1.08974	+	0.629163i
$425$	−19.4535	−	6.82355i	−0.943634	−	0.330991i
$426$	−12.8527	−	35.3126i	−0.622718	−	1.71090i
$427$	−13.6283			−0.659519
$428$	−9.20582	−	10.9711i	−0.444980	−	0.530306i
$429$			14.8261i			0.715812i
$430$	−15.7082	+	2.82930i	−0.757518	+	0.136441i
$431$			18.3142i			0.882162i	0.897467	+	0.441081i	$0.145405\pi$
$431$			18.3142i			0.882162i	−0.897467	+	0.441081i	$0.854595\pi$
$432$	0.245278	+	0.0432492i	0.0118010	+	0.00208083i
$433$		−	9.79590i		−	0.470761i	−0.971903	−	0.235381i	$-0.924366\pi$
$433$		−	9.79590i		−	0.470761i	0.971903	−	0.235381i	$-0.0756336\pi$
$434$	−20.2345	+	7.36475i	−0.971287	+	0.353520i
$435$	−38.9514	−	6.72080i	−1.86758	−	0.322238i
$436$	24.0565	−	20.1858i	1.15210	−	0.966724i
$437$			1.95899i			0.0937112i
$438$	15.5824	−	5.67152i	0.744554	−	0.270996i
$439$			12.7651i			0.609245i	0.952473	+	0.304622i	$0.0985302\pi$
$439$			12.7651i			0.609245i	−0.952473	+	0.304622i	$0.901470\pi$
$440$	−10.0228	+	12.0342i	−0.477819	+	0.573708i
$441$	2.95138			0.140542
$442$	−4.94361	−	13.4000i	−0.235144	−	0.637374i
$443$	−24.8545			−1.18087			−0.590437	−	0.807084i	$-0.701044\pi$
$443$	−24.8545			−1.18087			−0.590437	+	0.807084i	$0.701044\pi$
$444$	9.12085	−	7.65330i	0.432856	−	0.363210i
$445$	−5.26566	+	30.5179i	−0.249616	+	1.44669i
$446$	−35.0271	+	12.7488i	−1.65858	+	0.603673i
$447$	16.9145			0.800027
$448$	9.80431	+	16.9816i	0.463210	+	0.802303i
$449$		−	23.8359i		−	1.12489i	−0.826836	−	0.562443i	$-0.809862\pi$
$449$		−	23.8359i		−	1.12489i	0.826836	−	0.562443i	$-0.190138\pi$
$450$	0.154464	+	21.0325i	0.00728152	+	0.991482i
$451$			19.2803i			0.907876i
$452$	−10.5947	+	8.88999i	−0.498332	+	0.418150i
$453$		−	42.0374i		−	1.97509i
$454$	4.64643	−	1.69116i	0.218068	−	0.0793701i
$455$	2.28268	−	13.2296i	0.107014	−	0.620214i
$456$	8.19104	+	4.72910i	0.383581	+	0.221460i
$457$			31.5870i			1.47758i	0.673937	+	0.738789i	$0.264602\pi$
$457$			31.5870i			1.47758i	−0.673937	+	0.738789i	$0.735398\pi$
$458$	29.1208	−	10.5991i	1.36073	−	0.495264i
$459$	0.00112158	+	0.256725i	5.23506e−5	+	0.0119829i
$460$	−3.22223	−	5.53403i	−0.150237	−	0.258026i
$461$		−	25.4407i		−	1.18489i	−0.805610	−	0.592447i	$-0.798162\pi$
$461$		−	25.4407i		−	1.18489i	0.805610	−	0.592447i	$-0.201838\pi$
$462$	19.7156	−	7.17589i	0.917252	−	0.333853i
$463$		−	6.77616i		−	0.314915i	−0.987526	−	0.157457i	$-0.949670\pi$
$463$		−	6.77616i		−	0.314915i	0.987526	−	0.157457i	$-0.0503297\pi$
$464$	5.02327	−	28.4884i	0.233200	−	1.32254i
$465$	5.77297	−	33.4581i	0.267715	−	1.55158i
$466$	−0.704843	−	1.93654i	−0.0326512	−	0.0897085i
$467$	0.322265			0.0149126			0.00745632	−	0.999972i	$-0.497627\pi$
$467$	0.322265			0.0149126			0.00745632	+	0.999972i	$0.497627\pi$
$468$	−11.1629	+	9.36679i	−0.516006	+	0.432980i
$469$	21.8164			1.00739
$470$	−0.164252	−	0.911925i	−0.00757638	−	0.0420640i
$471$			20.7491i			0.956068i
$472$	−17.6003	+	30.4846i	−0.810119	+	1.40317i
$473$	−12.4986			−0.574685
$474$	−10.4586	−	28.7347i	−0.480379	−	1.31983i
$475$	2.29229	−	6.44488i	0.105177	−	0.295712i
$476$	−15.4265	+	13.0596i	−0.707071	+	0.598586i
$477$	27.2489			1.24764
$478$	6.79078	+	18.6575i	0.310603	+	0.853375i
$479$		−	2.74216i		−	0.125292i	−0.998036	−	0.0626462i	$-0.980046\pi$
$479$		−	2.74216i		−	0.125292i	0.998036	−	0.0626462i	$-0.0199540\pi$
$480$	−30.9178	+	0.113530i	−1.41120	+	0.00518190i
$481$		−	5.96589i		−	0.272021i
$482$	−8.66213	+	3.15276i	−0.394549	+	0.143604i
$483$			8.57885i			0.390351i
$484$	7.45824	−	6.25821i	0.339011	−	0.284464i
$485$	1.24684	−	7.22622i	0.0566159	−	0.328126i
$486$	29.2324	−	10.6397i	1.32601	−	0.482627i
$487$	12.7568			0.578064			0.289032	−	0.957319i	$-0.406667\pi$
$487$	12.7568			0.578064			0.289032	+	0.957319i	$0.406667\pi$
$488$	13.6195	+	7.86319i	0.616524	+	0.355950i
$489$	−24.2157			−1.09507
$490$	3.08799	−	0.556194i	0.139501	−	0.0251263i
$491$		−	20.5459i		−	0.927224i	−0.886038	−	0.463612i	$-0.846553\pi$
$491$		−	20.5459i		−	0.927224i	0.886038	−	0.463612i	$-0.153447\pi$
$492$	−29.1575	+	24.4660i	−1.31452	+	1.10301i
$493$	29.8179	−	0.130268i	1.34293	−	0.00586697i
$494$	4.45336	−	1.62089i	0.200366	−	0.0729274i
$495$	−2.80047	+	16.2305i	−0.125872	+	0.729508i
$496$	24.4707	+	4.31484i	1.09877	+	0.193742i
$497$			26.6462i			1.19524i
$498$	−44.7549	+	16.2894i	−2.00551	+	0.729947i
$499$	2.77678			0.124306			0.0621529	−	0.998067i	$-0.480203\pi$
$499$	2.77678			0.124306			0.0621529	+	0.998067i	$0.480203\pi$
$500$	4.12523	+	21.9769i	0.184486	+	0.982835i
$501$			51.8037i			2.31442i
$502$	35.1218	−	12.7833i	1.56756	−	0.570546i
$503$	−31.4367			−1.40169			−0.700846	−	0.713313i	$-0.747194\pi$
$503$	−31.4367			−1.40169			−0.700846	+	0.713313i	$0.747194\pi$
$504$	17.8587	+	10.3107i	0.795491	+	0.459277i
$505$	−3.45638	−	0.596375i	−0.153807	−	0.0265383i
$506$	−1.71509	−	4.71218i	−0.0762452	−	0.209482i
$507$		−	17.1100i		−	0.759881i
$508$	−1.67533	−	1.99658i	−0.0743309	−	0.0885841i
$509$			25.2633i			1.11978i	0.828568	+	0.559889i	$0.189156\pi$
$509$			25.2633i			1.11978i	−0.828568	+	0.559889i	$0.810844\pi$
$510$	−5.78627	−	31.3399i	−0.256220	−	1.38775i
$511$	−11.7581			−0.520149
$512$		−	22.6274i		−	1.00000i
$513$	−0.0851842			−0.00376098
$514$	41.0525	−	14.9419i	1.81075	−	0.659058i
$515$	−21.2367	−	3.66426i	−0.935803	−	0.161467i
$516$	−15.8602	−	18.9015i	−0.698207	−	0.832091i
$517$		−	0.725592i		−	0.0319115i
$518$	−7.93336	+	2.88751i	−0.348572	+	0.126870i
$519$	−1.65170			−0.0725014
$520$	−9.91438	+	11.9040i	−0.434774	+	0.522025i
$521$		−	6.70567i		−	0.293781i	−0.989153	−	0.146890i	$-0.953074\pi$
$521$		−	6.70567i		−	0.293781i	0.989153	−	0.146890i	$-0.0469264\pi$
$522$	−10.4050	−	28.5874i	−0.455414	−	1.25124i
$523$	−22.0466			−0.964029			−0.482015	−	0.876163i	$-0.660095\pi$
$523$	−22.0466			−0.964029			−0.482015	+	0.876163i	$0.660095\pi$
$524$	28.6549	−	24.0443i	1.25179	−	1.05038i
$525$	10.0384	−	28.2236i	0.438113	−	1.23178i
$526$	−19.1245	+	6.96076i	−0.833869	+	0.303503i
$527$	0.111896	+	25.6127i	0.00487428	+	1.11571i
$528$	−23.8431	−	4.20419i	−1.03764	−	0.182964i
$529$	−20.9496			−0.910852
$530$	28.5101	−	5.13511i	1.23840	−	0.223055i
$531$			37.0188i			1.60648i
$532$	−4.31088	−	5.13751i	−0.186900	−	0.222739i
$533$			19.0717i			0.826088i
$534$	−44.9875	+	16.3741i	−1.94680	+	0.708578i
$535$	−15.7790	−	2.72256i	−0.682186	−	0.117707i
$536$	−21.8023	−	12.5875i	−0.941715	−	0.543699i
$537$	−8.68294			−0.374697
$538$	5.98750	+	16.4505i	0.258140	+	0.709233i
$539$	2.45702			0.105831
$540$	0.240640	−	0.140114i	0.0103555	−	0.00602957i
$541$	33.6997			1.44886			0.724431	−	0.689348i	$-0.242103\pi$
$541$	33.6997			1.44886			0.724431	+	0.689348i	$0.242103\pi$
$542$	12.5688	+	34.5324i	0.539874	+	1.48329i
$543$			18.2551i			0.783402i
$544$	22.9516	−	4.15045i	0.984040	−	0.177949i
$545$	5.96982	−	34.5990i	0.255719	−	1.48206i
$546$	19.5023	−	7.09825i	0.834620	−	0.303777i
$547$			19.4137i			0.830070i	0.909805	+	0.415035i	$0.136231\pi$
$547$			19.4137i			0.830070i	−0.909805	+	0.415035i	$0.863769\pi$
$548$	12.8673	+	15.3346i	0.549663	+	0.655063i
$549$	16.5387			0.705855
$550$	0.128591	+	17.5095i	0.00548314	+	0.746607i
$551$			9.89392i			0.421495i
$552$	4.94980	−	8.57330i	0.210677	−	0.364904i
$553$			21.6826i			0.922038i
$554$	11.0377	−	4.01741i	0.468949	−	0.170683i
$555$	2.26341	−	13.1179i	0.0960765	−	0.556826i
$556$	−14.4053	+	12.0875i	−0.610922	+	0.512624i
$557$	−6.56797			−0.278294			−0.139147	−	0.990272i	$-0.544436\pi$
$557$	−6.56797			−0.278294			−0.139147	+	0.990272i	$0.544436\pi$
$558$	24.5557	−	8.93756i	1.03953	−	0.378357i
$559$	−12.3633			−0.522913
$560$	20.6284	+	7.42245i	0.871708	+	0.313656i
$561$	−0.109027	−	24.9558i	−0.00460311	−	1.05364i
$562$	10.4341	+	28.6676i	0.440138	+	1.20927i
$563$	5.91485			0.249281			0.124641	−	0.992202i	$-0.460222\pi$
$563$	5.91485			0.249281			0.124641	+	0.992202i	$0.460222\pi$
$564$	1.09731	−	0.920749i	0.0462049	−	0.0387705i
$565$	−2.62916	+	15.2377i	−0.110610	+	0.641054i
$566$	17.5808	−	6.39890i	0.738977	−	0.268966i
$567$	−22.2454			−0.934220
$568$	15.3742	−	26.6289i	0.645087	−	1.11732i
$569$	−25.7452			−1.07929			−0.539647	−	0.841892i	$-0.681442\pi$
$569$	−25.7452			−1.07929			−0.539647	+	0.841892i	$0.681442\pi$
$570$	10.4071	−	1.87448i	0.435906	−	0.0785135i
$571$	−5.12821			−0.214609			−0.107305	−	0.994226i	$-0.534222\pi$
$571$	−5.12821			−0.214609			−0.107305	+	0.994226i	$0.534222\pi$
$572$	−9.29308	+	7.79782i	−0.388563	+	0.326043i
$573$			29.5346i			1.23383i
$574$	25.3613	−	9.23078i	1.05856	−	0.385285i
$575$	−6.74565	−	2.39926i	−0.281313	−	0.100056i
$576$	−11.8981	−	20.6081i	−0.495754	−	0.858672i
$577$			15.5372i			0.646822i	0.946259	+	0.323411i	$0.104830\pi$
$577$			15.5372i			0.646822i	−0.946259	+	0.323411i	$0.895170\pi$
$578$	8.41980	+	22.5190i	0.350218	+	0.936668i
$579$			31.4901i			1.30868i
$580$	−16.2739	−	27.9497i	−0.675738	−	1.16055i
$581$	33.7711			1.40106
$582$	10.6524	−	3.87717i	0.441558	−	0.160714i
$583$	22.6846			0.939501
$584$	11.7505	+	6.78416i	0.486239	+	0.280730i
$585$	−2.77017	+	16.0549i	−0.114532	+	0.663789i
$586$	−9.35712	−	25.7085i	−0.386539	−	1.06201i
$587$	28.1980			1.16386			0.581929	−	0.813240i	$-0.302298\pi$
$587$	28.1980			1.16386			0.581929	+	0.813240i	$0.302298\pi$
$588$	3.11786	+	3.71573i	0.128579	+	0.153234i
$589$	−8.49858			−0.350178
$590$	6.97627	+	38.7322i	0.287209	+	1.59458i
$591$	−34.1433			−1.40447
$592$	9.59425	+	1.69172i	0.394321	+	0.0695295i
$593$			7.05467i			0.289701i	0.989454	+	0.144850i	$0.0462701\pi$
$593$			7.05467i			0.289701i	−0.989454	+	0.144850i	$0.953730\pi$
$594$	0.204903	−	0.0745786i	0.00840728	−	0.00306000i
$595$	−3.74500	+	22.2853i	−0.153530	+	0.913610i
$596$	8.89620	+	10.6021i	0.364402	+	0.434278i
$597$	52.3098			2.14090
$598$	−1.69654	−	4.66119i	−0.0693765	−	0.190610i
$599$	−4.07024			−0.166306			−0.0831528	−	0.996537i	$-0.526499\pi$
$599$	−4.07024			−0.166306			−0.0831528	+	0.996537i	$0.526499\pi$
$600$	−26.3163	+	22.4134i	−1.07436	+	0.915022i
$601$		−	44.7775i		−	1.82651i	−0.407388	−	0.913255i	$-0.633560\pi$
$601$		−	44.7775i		−	1.82651i	0.407388	−	0.913255i	$-0.366440\pi$
$602$	5.98389	+	16.4406i	0.243885	+	0.670069i
$603$	−26.4755			−1.07817
$604$	26.3493	−	22.1097i	1.07214	−	0.899629i
$605$	1.85082	−	10.7267i	0.0752467	−	0.436103i
$606$	−1.85449	−	5.09518i	−0.0753336	−	0.206977i
$607$	−29.5562			−1.19965			−0.599824	−	0.800132i	$-0.704763\pi$
$607$	−29.5562			−1.19965			−0.599824	+	0.800132i	$0.704763\pi$
$608$	1.34387	+	7.62146i	0.0545011	+	0.309091i
$609$			43.3277i			1.75573i
$610$	17.3042	−	3.11675i	0.700626	−	0.126194i
$611$		−	0.717741i		−	0.0290367i
$612$	18.7209	−	15.8486i	0.756748	−	0.640642i
$613$	5.16244			0.208509			0.104254	−	0.994551i	$-0.466754\pi$
$613$	5.16244			0.208509			0.104254	+	0.994551i	$0.466754\pi$
$614$	−2.46787	−	6.78042i	−0.0995952	−	0.273636i
$615$	−7.23567	+	41.9354i	−0.291770	+	1.69100i
$616$	14.8673	+	8.58366i	0.599022	+	0.345845i
$617$	27.0679			1.08971			0.544857	−	0.838529i	$-0.316584\pi$
$617$	27.0679			1.08971			0.544857	+	0.838529i	$0.316584\pi$
$618$	−11.3944	−	31.3059i	−0.458350	−	1.25931i
$619$	−9.40241			−0.377915			−0.188957	−	0.981985i	$-0.560511\pi$
$619$	−9.40241			−0.377915			−0.188957	+	0.981985i	$0.560511\pi$
$620$	24.0080	−	13.9788i	0.964184	−	0.561402i
$621$			0.0891596i			0.00357785i
$622$	−5.78320	+	2.10491i	−0.231885	+	0.0843993i
$623$	33.9466			1.36004
$624$	−23.5852	−	4.15870i	−0.944162	−	0.166481i
$625$	19.3851	+	15.7867i	0.775403	+	0.631467i
$626$	−10.1024	−	27.7560i	−0.403772	−	1.10935i
$627$	8.28064			0.330697
$628$	−13.0056	+	10.9130i	−0.518981	+	0.435477i
$629$	0.0438713	+	10.0420i	0.00174926	+	0.400400i
$630$	22.6904	−	4.08689i	0.904007	−	0.162826i
$631$	11.0504			0.439910			0.219955	−	0.975510i	$-0.429409\pi$
$631$	11.0504			0.439910			0.219955	+	0.975510i	$0.429409\pi$
$632$	12.5103	−	21.6686i	0.497635	−	0.861929i
$633$			39.9932i			1.58959i
$634$	−27.2213	+	9.90775i	−1.08110	+	0.393487i
$635$	−2.87156	−	0.495469i	−0.113955	−	0.0196621i
$636$	28.7859	+	34.3058i	1.14144	+	1.36031i
$637$	2.43043			0.0962973
$638$	−8.66211	−	23.7989i	−0.342936	−	0.942209i
$639$		−	32.3367i		−	1.27922i
$640$	−16.3324	−	19.3197i	−0.645596	−	0.763679i
$641$			18.8190i			0.743306i	0.928372	+	0.371653i	$0.121209\pi$
$641$			18.8190i			0.743306i	−0.928372	+	0.371653i	$0.878791\pi$
$642$	−8.46610	−	23.2604i	−0.334130	−	0.918015i
$643$			27.0209i			1.06560i	0.846241	+	0.532801i	$0.178861\pi$
$643$			27.0209i			1.06560i	−0.846241	+	0.532801i	$0.821139\pi$
$644$	−5.37727	+	4.51206i	−0.211894	+	0.177800i
$645$	−27.1848	−	4.69056i	−1.07040	−	0.184690i
$646$	−7.48414	+	2.76109i	−0.294459	+	0.108634i
$647$			24.0203i			0.944335i	0.881509	+	0.472168i	$0.156528\pi$
$647$			24.0203i			0.944335i	−0.881509	+	0.472168i	$0.843472\pi$
$648$	22.2310	+	12.8351i	0.873317	+	0.504210i
$649$			30.8180i			1.20971i
$650$	0.127200	+	17.3200i	0.00498918	+	0.679348i
$651$	−37.2172			−1.45866
$652$	−12.7363	−	15.1785i	−0.498791	−	0.594436i
$653$			0.294016i			0.0115057i	0.999983	+	0.00575286i	$0.00183120\pi$
$653$			0.294016i			0.0115057i	−0.999983	+	0.00575286i	$0.998169\pi$
$654$	51.0036	−	18.5638i	1.99440	−	0.725902i
$655$	7.11095	−	41.2125i	0.277848	−	1.61031i
$656$	−30.6709	−	5.40810i	−1.19750	−	0.211151i
$657$	14.2692			0.556693
$658$	−0.954443	+	0.347389i	−0.0372080	+	0.0135426i
$659$			7.63585i			0.297451i	0.988879	+	0.148725i	$0.0475170\pi$
$659$			7.63585i			0.297451i	−0.988879	+	0.148725i	$0.952483\pi$
$660$	−23.3923	+	13.6203i	−0.910544	+	0.530170i
$661$			21.3029i			0.828588i	0.910143	+	0.414294i	$0.135971\pi$
$661$			21.3029i			0.828588i	−0.910143	+	0.414294i	$0.864029\pi$
$662$	−8.77429	+	3.19358i	−0.341022	+	0.124122i
$663$	−0.107847	−	24.6858i	−0.00418843	−	0.958718i
$664$	−33.7492	−	19.4851i	−1.30972	−	0.756169i
$665$	−7.38896	−	1.27492i	−0.286532	−	0.0494391i
$666$	9.62760	−	3.50416i	0.373062	−	0.135783i
$667$	10.3556			0.400972
$668$	−32.4708	+	27.2462i	−1.25633	+	1.05419i
$669$	−64.4250			−2.49082
$670$	−27.7009	+	4.98936i	−1.07018	+	0.192756i
$671$	13.7684			0.531524
$672$	5.88510	+	33.3761i	0.227023	+	1.28751i
$673$	−10.3584			−0.399286			−0.199643	−	0.979869i	$-0.563978\pi$
$673$	−10.3584			−0.399286			−0.199643	+	0.979869i	$0.563978\pi$
$674$	13.0493	+	35.8526i	0.502640	+	1.38099i
$675$	0.104329	−	0.293326i	0.00401562	−	0.0112901i
$676$	10.7246	−	8.99903i	0.412485	−	0.346116i
$677$		−	25.4377i		−	0.977652i	−0.872381	−	0.488826i	$-0.837425\pi$
$677$		−	25.4377i		−	0.977652i	0.872381	−	0.488826i	$-0.162575\pi$
$678$	−22.4624	+	8.17565i	−0.862664	+	0.313984i
$679$	−8.03810			−0.308474
$680$	16.6007	−	20.1101i	0.636607	−	0.771188i
$681$	8.54614			0.327489
$682$	20.4426	−	7.44049i	0.782787	−	0.284911i
$683$			13.0714i			0.500165i	0.968225	+	0.250082i	$0.0804577\pi$
$683$			13.0714i			0.500165i	−0.968225	+	0.250082i	$0.919542\pi$
$684$	5.23151	+	6.23467i	0.200032	+	0.238389i
$685$	22.0548	+	3.80541i	0.842672	+	0.145397i
$686$	−9.47526	−	26.0331i	−0.361767	−	0.993947i
$687$	53.5618			2.04351
$688$	3.50582	−	19.8825i	0.133658	−	0.758014i
$689$	22.4392			0.854865
$690$	−1.96196	−	10.8928i	−0.0746907	−	0.414682i
$691$	−18.6715			−0.710297			−0.355148	−	0.934810i	$-0.615570\pi$
$691$	−18.6715			−0.710297			−0.355148	+	0.934810i	$0.615570\pi$
$692$	−0.868712	−	1.03529i	−0.0330235	−	0.0393559i
$693$	18.0541			0.685817
$694$	−10.9056	+	3.96930i	−0.413970	+	0.150673i
$695$	−3.57480	+	20.7183i	−0.135600	+	0.785889i
$696$	24.9990	−	43.2996i	0.947586	−	1.64127i
$697$	−0.140248	−	32.1022i	−0.00531225	−	1.21596i
$698$	−33.3703	+	12.1458i	−1.26308	+	0.459725i
$699$		−	3.56187i		−	0.134722i
$700$	22.9704	−	8.55210i	0.868200	−	0.323239i
$701$			4.47088i			0.168863i	0.996429	+	0.0844313i	$0.0269074\pi$
$701$			4.47088i			0.168863i	−0.996429	+	0.0844313i	$0.973093\pi$
$702$	0.202686	−	0.0737717i	0.00764989	−	0.00278433i
$703$	−3.33205			−0.125671
$704$	−9.90513	−	17.1562i	−0.373314	−	0.646598i
$705$	0.272305	−	1.57819i	0.0102556	−	0.0594379i
$706$	−38.2889	+	13.9360i	−1.44102	+	0.524489i
$707$			3.84471i			0.144595i
$708$	−46.6059	+	39.1070i	−1.75156	+	1.46973i
$709$	−29.3419			−1.10196			−0.550978	−	0.834520i	$-0.685745\pi$
$709$	−29.3419			−1.10196			−0.550978	+	0.834520i	$0.685745\pi$
$710$	−6.09391	−	33.8333i	−0.228700	−	1.26974i
$711$		−	26.3131i		−	0.986819i
$712$	−33.9246	−	19.5864i	−1.27138	−	0.734032i
$713$			8.89519i			0.333127i
$714$	−32.7747	+	12.0914i	−1.22656	+	0.452510i
$715$	−2.30616	+	13.3657i	−0.0862453	+	0.499847i
$716$	−4.56681	−	5.44251i	−0.170670	−	0.203396i
$717$			34.3166i			1.28158i
$718$	−2.95631	−	8.12240i	−0.110329	−	0.303125i
$719$		−	40.6462i		−	1.51585i	−0.652343	−	0.757924i	$-0.726214\pi$
$719$		−	40.6462i		−	1.51585i	0.652343	−	0.757924i	$-0.273786\pi$
$720$	−25.0337	−	9.00757i	−0.932952	−	0.335692i
$721$			23.6227i			0.879757i
$722$	8.28481	+	22.7623i	0.308329	+	0.847126i
$723$	−15.9322			−0.592525
$724$	−11.4424	+	9.60130i	−0.425253	+	0.356830i
$725$	−34.0691	−	12.1175i	−1.26529	−	0.450034i
$726$	15.8127	−	5.75534i	0.586863	−	0.213601i
$727$		−	12.6204i		−	0.468064i	−0.972229	−	0.234032i	$-0.924808\pi$
$727$		−	12.6204i		−	0.468064i	0.972229	−	0.234032i	$-0.0751921\pi$
$728$	14.7065	+	8.49078i	0.545058	+	0.314689i
$729$	26.5395			0.982946
$730$	14.9296	−	2.68905i	0.552569	−	0.0995263i
$731$	20.8104	−	0.0909161i	0.769700	−	0.00336265i
$732$	17.4716	+	20.8219i	0.645770	+	0.769598i
$733$	27.9511			1.03240			0.516198	−	0.856469i	$-0.327347\pi$
$733$	27.9511			1.03240			0.516198	+	0.856469i	$0.327347\pi$
$734$	9.77940	+	26.8687i	0.360964	+	0.991741i
$735$	5.34410	+	0.922088i	0.197120	+	0.0340117i
$736$	7.97714	−	1.40658i	0.294041	−	0.0518474i
$737$	−22.0408			−0.811882
$738$	−30.7775	+	11.2021i	−1.13293	+	0.412355i
$739$		−	6.33410i		−	0.233004i	−0.993190	−	0.116502i	$-0.962832\pi$
$739$		−	6.33410i		−	0.233004i	0.993190	−	0.116502i	$-0.0371681\pi$
$740$	9.41284	−	5.48069i	0.346023	−	0.201474i
$741$	8.19104			0.300905
$742$	−10.8606	−	29.8393i	−0.398706	−	1.09544i
$743$	26.0637			0.956185			0.478093	−	0.878309i	$-0.341328\pi$
$743$	26.0637			0.956185			0.478093	+	0.878309i	$0.341328\pi$
$744$	37.1931	+	21.4734i	1.36356	+	0.787254i
$745$	15.2483	+	2.63099i	0.558655	+	0.0963921i
$746$	17.0954	+	46.9693i	0.625908	+	1.71967i
$747$	−40.9832			−1.49950
$748$	15.5851	−	13.1939i	0.569848	−	0.482417i
$749$			17.5518i			0.641329i
$750$	−6.29140	+	38.1320i	−0.229730	+	1.39238i
$751$			1.56092i			0.0569587i	0.999594	+	0.0284794i	$0.00906649\pi$
$751$			1.56092i			0.0569587i	−0.999594	+	0.0284794i	$0.990934\pi$
$752$	1.15426	+	0.203527i	0.0420915	+	0.00742187i
$753$	64.5993			2.35413
$754$	−8.56839	−	23.5414i	−0.312042	−	0.857329i
$755$	6.53878	−	37.8965i	0.237971	−	1.37919i
$756$	−0.196201	−	0.233824i	−0.00713577	−	0.00850409i
$757$	26.8691			0.976574			0.488287	−	0.872683i	$-0.337622\pi$
$757$	26.8691			0.976574			0.488287	+	0.872683i	$0.337622\pi$
$758$	−8.54451	−	23.4758i	−0.310351	−	0.852681i
$759$		−	8.66707i		−	0.314595i
$760$	6.64858	+	5.53734i	0.241169	+	0.200861i
$761$	−14.3215			−0.519155			−0.259578	−	0.965722i	$-0.583583\pi$
$761$	−14.3215			−0.519155			−0.259578	+	0.965722i	$0.583583\pi$
$762$	−1.54071	−	4.23308i	−0.0558142	−	0.153348i
$763$	−38.4862			−1.39330
$764$	−18.5124	+	15.5338i	−0.669756	+	0.561992i
$765$	4.54478	−	27.0446i	0.164317	−	0.977798i
$766$	37.8833	−	13.7884i	1.36878	−	0.498195i
$767$			30.4846i			1.10074i
$768$	13.3759	−	36.7500i	0.482662	−	1.32610i
$769$	−44.1777			−1.59309			−0.796543	−	0.604581i	$-0.793340\pi$
$769$	−44.1777			−1.59309			−0.796543	+	0.604581i	$0.793340\pi$
$770$	18.8897	−	3.40233i	0.680737	−	0.122611i
$771$	75.5076			2.71934
$772$	−19.7382	+	16.5623i	−0.710392	+	0.596089i
$773$	42.6576			1.53429			0.767144	−	0.641475i	$-0.221677\pi$
$773$	42.6576			1.53429			0.767144	+	0.641475i	$0.221677\pi$
$774$	−7.26180	−	19.9516i	−0.261020	−	0.717147i
$775$	10.4086	−	29.2643i	0.373888	−	1.05120i
$776$	8.03289	+	4.63779i	0.288364	+	0.166487i
$777$	−14.5918			−0.523477
$778$	24.6496	−	8.97170i	0.883729	−	0.321651i
$779$	10.6519			0.381643
$780$	−23.1392	+	13.4730i	−0.828516	+	0.482409i
$781$		−	26.9202i		−	0.963279i
$782$	2.88994	+	7.83340i	0.103344	+	0.280122i
$783$			0.450302i			0.0160925i
$784$	−0.689189	+	3.90858i	−0.0246139	+	0.139592i
$785$	−3.22745	+	18.7052i	−0.115193	+	0.667617i
$786$	60.7529	−	22.1123i	2.16699	−	0.788718i
$787$		−	19.7394i		−	0.703632i	−0.936069	−	0.351816i	$-0.885564\pi$
$787$		−	19.7394i		−	0.703632i	0.936069	−	0.351816i	$-0.114436\pi$
$788$	−17.9577	−	21.4012i	−0.639718	−	0.762386i
$789$	−35.1756			−1.25228
$790$	−4.95876	−	27.5310i	−0.176425	−	0.979508i
$791$	16.9497			0.602661
$792$	−18.0424	−	10.4168i	−0.641108	−	0.370144i
$793$	13.6195			0.483641
$794$	14.4238	−	5.24983i	0.511881	−	0.186309i
$795$	49.3398	+	8.51326i	1.74990	+	0.301934i
$796$	27.5124	+	32.7880i	0.975152	+	1.16214i
$797$	−31.3920			−1.11196			−0.555981	−	0.831195i	$-0.687657\pi$
$797$	−31.3920			−1.11196			−0.555981	+	0.831195i	$0.687657\pi$
$798$	−3.96449	−	10.8923i	−0.140341	−	0.385585i
$799$	0.00527804	+	1.20813i	0.000186724	+	0.0427404i
$800$	−27.8899	−	4.70682i	−0.986056	−	0.166411i
$801$	−41.1962			−1.45560
$802$	47.7887	−	17.3937i	1.68748	−	0.614192i
$803$	11.8790			0.419202
$804$	−27.9689	−	33.3320i	−0.986387	−	1.17553i
$805$	−1.33441	+	7.73379i	−0.0470319	+	0.272580i
$806$	20.2214	−	7.35998i	0.712268	−	0.259244i
$807$			30.2573i			1.06511i
$808$	2.21831	−	3.84222i	0.0780398	−	0.135169i
$809$			48.9537i			1.72112i	0.509349	+	0.860560i	$0.329886\pi$
$809$			48.9537i			1.72112i	−0.509349	+	0.860560i	$0.670114\pi$
$810$	28.2456	−	5.08747i	0.992449	−	0.178756i
$811$	19.6878			0.691334			0.345667	−	0.938357i	$-0.387653\pi$
$811$	19.6878			0.691334			0.345667	+	0.938357i	$0.387653\pi$
$812$	−27.1580	+	22.7883i	−0.953059	+	0.799711i
$813$			63.5151i			2.22757i
$814$	8.01495	−	2.91720i	0.280924	−	0.102248i
$815$	−21.8303	−	3.76667i	−0.764682	−	0.131941i
$816$	39.7299	+	6.82663i	1.39083	+	0.238980i
$817$			6.90513i			0.241580i
$818$	−1.00715	−	2.76711i	−0.0352140	−	0.0967497i
$819$	17.8587			0.624034
$820$	−30.0909	+	17.5206i	−1.05082	+	0.611847i
$821$	15.0022			0.523580			0.261790	−	0.965125i	$-0.415687\pi$
$821$	15.0022			0.523580			0.261790	+	0.965125i	$0.415687\pi$
$822$	11.8333	+	32.5119i	0.412735	+	1.13398i
$823$	−36.7195			−1.27996			−0.639981	−	0.768390i	$-0.721058\pi$
$823$	−36.7195			−1.27996			−0.639981	+	0.768390i	$0.721058\pi$
$824$	13.6298	−	23.6074i	0.474815	−	0.822404i
$825$	−10.1417	+	28.5138i	−0.353087	+	0.992724i
$826$	40.5380	−	14.7546i	1.41050	−	0.513380i
$827$		−	24.7896i		−	0.862019i	−0.902347	−	0.431009i	$-0.858158\pi$
$827$		−	24.7896i		−	0.862019i	0.902347	−	0.431009i	$-0.141842\pi$
$828$	6.52563	−	5.47565i	0.226781	−	0.190292i
$829$			21.9879i			0.763672i	0.924230	+	0.381836i	$0.124708\pi$
$829$			21.9879i			0.763672i	−0.924230	+	0.381836i	$0.875292\pi$
$830$	−42.8800	+	7.72336i	−1.48839	+	0.268082i
$831$	20.3016			0.704256
$832$	−9.79796	−	16.9706i	−0.339683	−	0.588348i
$833$	−4.09099	+	0.0178726i	−0.141744	+	0.000619250i
$834$	−30.5416	+	11.1162i	−1.05757	+	0.384923i
$835$	−8.05789	+	46.7007i	−0.278855	+	1.61614i
$836$	4.35521	+	5.19034i	0.150628	+	0.179512i
$837$	−0.386796			−0.0133696
$838$	19.2261	+	52.8232i	0.664154	+	1.82475i
$839$		−	24.2884i		−	0.838528i	−0.907864	−	0.419264i	$-0.862288\pi$
$839$		−	24.2884i		−	0.838528i	0.907864	−	0.419264i	$-0.137712\pi$
$840$	29.1156	+	24.2493i	1.00458	+	0.836679i
$841$	23.3014			0.803497
$842$	32.7430	−	11.9175i	1.12840	−	0.410703i
$843$			52.7281i			1.81605i
$844$	−25.0679	+	21.0345i	−0.862874	+	0.724037i
$845$	2.66140	−	15.4246i	0.0915551	−	0.530621i
$846$	1.15827	−	0.421577i	0.0398222	−	0.0144941i
$847$	−11.9319			−0.409985
$848$	−6.36299	+	36.0863i	−0.218506	+	1.23921i
$849$	32.3363			1.10978
$850$	−0.341473	−	29.1528i	−0.0117124	−	0.999931i
$851$			3.48755i			0.119552i
$852$	40.7111	−	34.1607i	1.39474	−	1.17033i
$853$		−	12.7808i		−	0.437605i	−0.975769	−	0.218803i	$-0.929785\pi$
$853$		−	12.7808i		−	0.437605i	0.975769	−	0.218803i	$-0.0702151\pi$
$854$	−6.59186	−	18.1110i	−0.225569	−	0.619745i
$855$	8.96694	+	1.54718i	0.306663	+	0.0529126i
$856$	10.1270	−	17.5404i	0.346133	−	0.599520i
$857$	8.58247			0.293172			0.146586	−	0.989198i	$-0.453172\pi$
$857$	8.58247			0.293172			0.146586	+	0.989198i	$0.453172\pi$
$858$	−19.7028	+	7.17124i	−0.672643	+	0.244822i
$859$			9.06471i			0.309284i	0.987971	+	0.154642i	$0.0494224\pi$
$859$			9.06471i			0.309284i	−0.987971	+	0.154642i	$0.950578\pi$
$860$	−11.3578	−	19.5066i	−0.387299	−	0.665169i
$861$	46.6469			1.58972
$862$	−24.3382	+	8.85837i	−0.828961	+	0.301717i
$863$		−	55.9115i		−	1.90325i	−0.307264	−	0.951624i	$-0.599413\pi$
$863$		−	55.9115i		−	1.90325i	0.307264	−	0.951624i	$-0.400587\pi$
$864$	0.0611636	+	0.346876i	0.00208083	+	0.0118010i
$865$	−1.48899	−	0.256916i	−0.0506273	−	0.00873541i
$866$	13.0180	−	4.73818i	0.442371	−	0.161010i
$867$	0.363064	+	41.5512i	0.0123303	+	1.41115i
$868$	−19.5744	−	23.3279i	−0.664399	−	0.791800i
$869$		−	21.9056i		−	0.743096i
$870$	−9.90893	−	55.0143i	−0.335944	−	1.86516i
$871$	−21.8023			−0.738742
$872$	38.4613	+	22.2056i	1.30246	+	0.751978i
$873$	9.75471			0.330147
$874$	−2.60335	+	0.947543i	−0.0880597	+	0.0320511i
$875$	13.4397	−	23.8820i	0.454344	−	0.807357i
$876$	15.0741	+	17.9646i	0.509305	+	0.606966i
$877$		−	9.07425i		−	0.306416i	−0.988194	−	0.153208i	$-0.951040\pi$
$877$		−	9.07425i		−	0.306416i	0.988194	−	0.153208i	$-0.0489604\pi$
$878$	−16.9639	+	6.17434i	−0.572503	+	0.208374i
$879$		−	47.2854i		−	1.59490i
$880$	−20.8405	−	7.49877i	−0.702533	−	0.252784i
$881$		−	22.6662i		−	0.763642i	−0.924236	−	0.381821i	$-0.875297\pi$
$881$		−	22.6662i		−	0.763642i	0.924236	−	0.381821i	$-0.124703\pi$
$882$	1.42755	+	3.92217i	0.0480682	+	0.132066i
$883$	−46.7195			−1.57224			−0.786119	−	0.618075i	$-0.787913\pi$
$883$	−46.7195			−1.57224			−0.786119	+	0.618075i	$0.787913\pi$
$884$	15.4165	−	13.0511i	0.518512	−	0.438958i
$885$	−11.5656	+	67.0303i	−0.388774	+	2.25320i
$886$	−12.0219	−	33.0298i	−0.403882	−	1.10966i
$887$	−52.8203			−1.77353			−0.886765	−	0.462220i	$-0.847053\pi$
$887$	−52.8203			−1.77353			−0.886765	+	0.462220i	$0.847053\pi$
$888$	14.5823	+	8.41911i	0.489351	+	0.282527i
$889$			3.19419i			0.107130i
$890$	−43.1029	+	7.76351i	−1.44481	+	0.260234i
$891$	22.4742			0.752913
$892$	−33.8844	−	40.3819i	−1.13453	−	1.35209i
$893$	−0.400870			−0.0134146
$894$	8.18136	+	22.4781i	0.273626	+	0.751780i
$895$	−7.82762	−	1.35060i	−0.261649	−	0.0451457i
$896$	−17.8250	+	21.2430i	−0.595491	+	0.709679i
$897$		−	8.57330i		−	0.286254i
$898$	31.6762	−	11.5292i	1.05705	−	0.384734i
$899$			44.9253i			1.49834i
$900$	−27.8759	+	10.3785i	−0.929198	+	0.345949i
$901$	−37.7704	+	0.165011i	−1.25831	+	0.00549730i
$902$	−25.6222	+	9.32570i	−0.853124	+	0.310512i
$903$			30.2391i			1.00629i
$904$	−16.9387	−	9.77955i	−0.563372	−	0.325263i
$905$	−2.83952	+	16.4569i	−0.0943889	+	0.547045i
$906$	55.8646	−	20.3331i	1.85598	−	0.675521i
$907$		−	37.9689i		−	1.26074i	−0.776296	−	0.630369i	$-0.782904\pi$
$907$		−	37.9689i		−	1.26074i	0.776296	−	0.630369i	$-0.217096\pi$
$908$	4.49486	+	5.35676i	0.149167	+	0.177770i
$909$		−	4.66578i		−	0.154754i
$910$	18.6853	−	3.36551i	0.619411	−	0.111566i
$911$		−	0.938913i		−	0.0311076i	−0.999879	−	0.0155538i	$-0.995049\pi$
$911$		−	0.938913i		−	0.0311076i	0.999879	−	0.0155538i	$-0.00495113\pi$
$912$	−2.32270	+	13.1727i	−0.0769124	+	0.436192i
$913$	−34.1184			−1.12915
$914$	−41.9768	+	15.2783i	−1.38847	+	0.505361i
$915$	29.9468	+	5.16712i	0.990010	+	0.170820i
$916$	28.1709	+	33.5728i	0.930793	+	1.10928i
$917$	−45.8429			−1.51386
$918$	−0.340626	+	0.125666i	−0.0112423	+	0.00414758i
$919$	7.54759			0.248972			0.124486	−	0.992221i	$-0.460272\pi$
$919$	7.54759			0.248972			0.124486	+	0.992221i	$0.460272\pi$
$920$	5.79576	−	6.95885i	0.191081	−	0.229427i
$921$		−	12.4712i		−	0.410939i
$922$	33.8089	−	12.3054i	1.11344	−	0.405258i
$923$		−	26.6289i		−	0.876501i
$924$	19.0725	+	22.7297i	0.627438	+	0.747751i
$925$	4.08091	−	11.4737i	0.134179	−	0.377252i
$926$	9.00501	−	3.27756i	0.295923	−	0.107707i
$927$		−	28.6676i		−	0.941567i
$928$	40.2887	−	7.10398i	1.32254	−	0.233200i
$929$			44.5382i			1.46125i	0.682778	+	0.730625i	$0.260771\pi$
$929$			44.5382i			1.46125i	−0.682778	+	0.730625i	$0.739229\pi$
$930$	47.2556	−	8.51148i	1.54957	−	0.279102i
$931$		−	1.35744i		−	0.0444882i
$932$	2.23259	−	1.87337i	0.0731310	−	0.0613642i
$933$	−10.6370			−0.348240
$934$	0.155876	+	0.428266i	0.00510043	+	0.0140133i
$935$	3.78351	−	22.5145i	0.123734	−	0.736303i
$936$	−17.8472	−	10.3041i	−0.583353	−	0.336799i
$937$		−	58.9476i		−	1.92574i	−0.269974	−	0.962868i	$-0.587015\pi$
$937$		−	58.9476i		−	1.92574i	0.269974	−	0.962868i	$-0.412985\pi$
$938$	10.5524	+	28.9924i	0.344547	+	0.946635i
$939$		−	51.0515i		−	1.66600i
$940$	1.13243	−	0.659367i	0.0369359	−	0.0215062i
$941$	−51.6074			−1.68235			−0.841177	−	0.540760i	$-0.818137\pi$
$941$	−51.6074			−1.68235			−0.841177	+	0.540760i	$0.818137\pi$
$942$	−27.5740	+	10.0361i	−0.898410	+	0.326994i
$943$		−	11.1490i		−	0.363061i
$944$	−49.0249	−	8.64440i	−1.59562	−	0.281351i
$945$	−0.336294	−	0.0580253i	−0.0109396	−	0.00188756i
$946$	−6.04543	−	16.6097i	−0.196554	−	0.540027i
$947$		−	3.86021i		−	0.125440i	−0.998031	−	0.0627201i	$-0.980022\pi$
$947$		−	3.86021i		−	0.125440i	0.998031	−	0.0627201i	$-0.0199775\pi$
$948$	33.1276	−	27.7974i	1.07593	−	0.902816i
$949$	11.7505			0.381438
$950$	9.67353	−	0.0710431i	0.313851	−	0.00230494i
$951$	−50.0680			−1.62357
$952$	−24.8169	−	14.1838i	−0.804319	−	0.459701i
$953$		−	4.23440i		−	0.137166i	−0.997645	−	0.0685828i	$-0.978152\pi$
$953$		−	4.23440i		−	0.137166i	0.997645	−	0.0685828i	$-0.0218477\pi$
$954$	13.1800	+	36.2118i	0.426719	+	1.17240i
$955$	−4.59401	+	26.6253i	−0.148659	+	0.861574i
$956$	−21.5098	+	18.0489i	−0.695678	+	0.583743i
$957$		−	43.7732i		−	1.41499i
$958$	3.64412	−	1.32635i	0.117736	−	0.0428525i
$959$		−	24.5327i		−	0.792204i
$960$	−15.1055	−	41.0326i	−0.487528	−	1.32432i
$961$	−7.58950			−0.244823
$962$	7.92822	−	2.88564i	0.255616	−	0.0930367i
$963$		−	21.3001i		−	0.686388i
$964$	−8.37956	−	9.98637i	−0.269888	−	0.321639i
$965$	−4.89818	+	28.3882i	−0.157678	+	0.913847i
$966$	−11.4007	+	4.14950i	−0.366810	+	0.133508i
$967$		−	22.9341i		−	0.737511i	−0.929527	−	0.368755i	$-0.879784\pi$
$967$		−	22.9341i		−	0.737511i	0.929527	−	0.368755i	$-0.120216\pi$
$968$	11.9242	+	6.88442i	0.383257	+	0.221274i
$969$	−13.7874	+	0.0602343i	−0.442916	+	0.00193501i
$970$	10.2062	−	1.83829i	0.327701	−	0.0590241i
$971$		−	48.6846i		−	1.56236i	−0.624304	−	0.781182i	$-0.714617\pi$
$971$		−	48.6846i		−	1.56236i	0.624304	−	0.781182i	$-0.285383\pi$
$972$	28.2788	+	33.7013i	0.907042	+	1.08097i
$973$	23.0460			0.738822
$974$	6.17031	+	16.9528i	0.197710	+	0.543202i
$975$	−10.0319	+	28.2053i	−0.321279	+	0.903293i
$976$	−3.86202	+	21.9026i	−0.123620	+	0.701085i
$977$		−	18.2712i		−	0.584547i	−0.956335	−	0.292274i	$-0.905588\pi$
$977$		−	18.2712i		−	0.584547i	0.956335	−	0.292274i	$-0.0944118\pi$
$978$	−11.7129	−	32.1808i	−0.374536	−	1.02903i
$979$	−34.2957			−1.09610
$980$	2.23277	+	3.83468i	0.0713231	+	0.122494i
$981$	46.7053			1.49119
$982$	27.3040	−	9.93784i	0.871306	−	0.317129i
$983$	−40.5244			−1.29253			−0.646264	−	0.763114i	$-0.723670\pi$
$983$	−40.5244			−1.29253			−0.646264	+	0.763114i	$0.723670\pi$
$984$	−46.6167	−	26.9142i	−1.48609	−	0.857993i
$985$	−30.7800	−	5.31088i	−0.980732	−	0.169219i
$986$	14.5957	+	39.5628i	0.464822	+	1.25994i
$987$	−1.75550			−0.0558782
$988$	4.30809	+	5.13418i	0.137059	+	0.163340i
$989$	7.22737			0.229817
$990$	−22.9237	+	4.12892i	−0.728564	+	0.131226i
$991$		−	29.5223i		−	0.937807i	−0.883249	−	0.468903i	$-0.844649\pi$
$991$		−	29.5223i		−	0.937807i	0.883249	−	0.468903i	$-0.155351\pi$
$992$	6.10211	+	34.6068i	0.193742	+	1.09877i
$993$	−16.1385			−0.512139
$994$	−35.4108	+	12.8885i	−1.12316	+	0.408797i
$995$	47.1570	+	8.13662i	1.49498	+	0.257948i
$996$	−43.2949	−	51.5969i	−1.37185	−	1.63491i
$997$		−	36.1931i		−	1.14625i	−0.819469	−	0.573123i	$-0.805732\pi$
$997$		−	36.1931i		−	1.14625i	0.819469	−	0.573123i	$-0.194268\pi$
$998$	1.34310	+	3.69014i	0.0425151	+	0.116809i
$999$	−0.151652			−0.00479804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.c.509.32	yes	48
5.4	even	2	inner	680.2.h.c.509.17	✓	48
8.5	even	2	inner	680.2.h.c.509.21	yes	48
17.16	even	2	inner	680.2.h.c.509.29	yes	48
40.29	even	2	inner	680.2.h.c.509.28	yes	48
85.84	even	2	inner	680.2.h.c.509.20	yes	48
136.101	even	2	inner	680.2.h.c.509.24	yes	48
680.509	even	2	inner	680.2.h.c.509.25	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.c.509.17	✓	48	5.4	even	2	inner
680.2.h.c.509.20	yes	48	85.84	even	2	inner
680.2.h.c.509.21	yes	48	8.5	even	2	inner
680.2.h.c.509.24	yes	48	136.101	even	2	inner
680.2.h.c.509.25	yes	48	680.509	even	2	inner
680.2.h.c.509.28	yes	48	40.29	even	2	inner
680.2.h.c.509.29	yes	48	17.16	even	2	inner
680.2.h.c.509.32	yes	48	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483690 + 1.32893i) q^{2} +2.44428i q^{3} +(-1.53209 + 1.28558i) q^{4} +(-0.380200 + 2.20351i) q^{5} +(-3.24827 + 1.18227i) q^{6} +2.45108 q^{7} +(-2.44949 - 1.41421i) q^{8} -2.97453 q^{9} +(-3.11220 + 0.560555i) q^{10} -2.47628 q^{11} +(-3.14231 - 3.74486i) q^{12} -2.44949 q^{13} +(1.18556 + 3.25730i) q^{14} +(-5.38600 - 0.929318i) q^{15} +(0.694593 - 3.93923i) q^{16} +(4.12307 - 0.0180128i) q^{17} +(-1.43875 - 3.95293i) q^{18} +1.36808i q^{19} +(-2.25027 - 3.86475i) q^{20} +5.99113i q^{21} +(-1.19775 - 3.29080i) q^{22} +1.43193 q^{23} +(3.45674 - 5.98725i) q^{24} +(-4.71090 - 1.67555i) q^{25} +(-1.18479 - 3.25519i) q^{26} +0.0622655i q^{27} +(-3.75527 + 3.15104i) q^{28} +7.23197 q^{29} +(-1.37016 - 7.60710i) q^{30} +6.21204i q^{31} +(5.57091 - 0.982302i) q^{32} -6.05274i q^{33} +(2.01822 + 5.47054i) q^{34} +(-0.931901 + 5.40097i) q^{35} +(4.55724 - 3.82398i) q^{36} +2.43556i q^{37} +(-1.81808 + 0.661726i) q^{38} -5.98725i q^{39} +(4.04753 - 4.85979i) q^{40} -7.78600i q^{41} +(-7.96177 + 2.89785i) q^{42} +5.04731 q^{43} +(3.79389 - 3.18345i) q^{44} +(1.13092 - 6.55439i) q^{45} +(0.692608 + 1.90292i) q^{46} +0.293016i q^{47} +(9.62860 + 1.69778i) q^{48} -0.992220 q^{49} +(-0.0519291 - 7.07088i) q^{50} +(0.0440284 + 10.0779i) q^{51} +(3.75284 - 3.14900i) q^{52} -9.16076 q^{53} +(-0.0827463 + 0.0301172i) q^{54} +(0.941484 - 5.45651i) q^{55} +(-6.00389 - 3.46635i) q^{56} -3.34398 q^{57} +(3.49803 + 9.61075i) q^{58} -12.4453i q^{59} +(9.44654 - 5.50031i) q^{60} -5.56012 q^{61} +(-8.25535 + 3.00470i) q^{62} -7.29079 q^{63} +(4.00000 + 6.92820i) q^{64} +(0.931297 - 5.39747i) q^{65} +(8.04364 - 2.92765i) q^{66} +8.90074 q^{67} +(-6.29375 + 5.32811i) q^{68} +3.50003i q^{69} +(-7.62824 + 1.37396i) q^{70} +10.8712i q^{71} +(7.28607 + 4.20662i) q^{72} -4.79712 q^{73} +(-3.23668 + 1.17806i) q^{74} +(4.09552 - 11.5148i) q^{75} +(-1.75877 - 2.09602i) q^{76} -6.06956 q^{77} +(7.95661 - 2.89597i) q^{78} +8.84615i q^{79} +(8.41604 + 3.02824i) q^{80} -9.07577 q^{81} +(10.3470 - 3.76601i) q^{82} +13.7781 q^{83} +(-7.70205 - 9.17894i) q^{84} +(-1.52790 + 9.09206i) q^{85} +(2.44133 + 6.70750i) q^{86} +17.6770i q^{87} +(6.06563 + 3.50199i) q^{88} +13.8497 q^{89} +(9.25731 - 1.66739i) q^{90} -6.00389 q^{91} +(-2.19384 + 1.84085i) q^{92} -15.1840 q^{93} +(-0.389397 + 0.141729i) q^{94} +(-3.01458 - 0.520145i) q^{95} +(2.40103 + 13.6169i) q^{96} -3.27942 q^{97} +(-0.479926 - 1.31859i) q^{98} +7.36577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) \) 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more