LMFDB - Embedded newform 976.2.bw.c.321.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [976,2,Mod(225,976)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("976.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(976, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			321.4
Character	$\chi$	$=$	976.321
Dual form			976.2.bw.c.225.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.880961 + 2.71132i) q^{3} +(0.308047 + 2.93087i) q^{5} +(-2.02506 - 2.24905i) q^{7} +(-4.14811 + 3.01378i) q^{9} -0.399822 q^{11} +(0.149926 - 0.259680i) q^{13} +(-7.67516 + 3.41720i) q^{15} +(-7.00397 - 3.11837i) q^{17} +(-2.34027 + 2.59913i) q^{19} +(4.31391 - 7.47190i) q^{21} +(-1.24700 + 0.906001i) q^{23} +(-3.60439 + 0.766136i) q^{25} +(-4.90648 - 3.56477i) q^{27} +(3.91291 + 6.77736i) q^{29} +(3.05474 - 0.649305i) q^{31} +(-0.352228 - 1.08404i) q^{33} +(5.96788 - 6.62800i) q^{35} +(0.796081 - 2.45008i) q^{37} +(0.836154 + 0.177730i) q^{39} +(-2.21673 + 6.82240i) q^{41} +(-9.63795 + 4.29109i) q^{43} +(-10.1108 - 11.2292i) q^{45} +(2.86033 + 4.95423i) q^{47} +(-0.225687 + 2.14727i) q^{49} +(2.28467 - 21.7372i) q^{51} +(4.87318 + 3.54057i) q^{53} +(-0.123164 - 1.17183i) q^{55} +(-9.10877 - 4.05548i) q^{57} +(4.62950 + 0.984030i) q^{59} +(4.65863 - 6.26875i) q^{61} +(15.1783 + 3.22625i) q^{63} +(0.807272 + 0.359421i) q^{65} +(0.169933 + 1.61680i) q^{67} +(-3.55502 - 2.58287i) q^{69} +(0.194910 - 1.85445i) q^{71} +(0.0973672 - 0.926387i) q^{73} +(-5.25256 - 9.09771i) q^{75} +(0.809662 + 0.899221i) q^{77} +(2.35371 - 1.04794i) q^{79} +(0.589492 - 1.81427i) q^{81} +(7.51408 + 1.59717i) q^{83} +(6.98199 - 21.4884i) q^{85} +(-14.9285 + 16.5797i) q^{87} +(0.364222 + 1.12096i) q^{89} +(-0.887642 + 0.188674i) q^{91} +(4.45158 + 7.71036i) q^{93} +(-8.33864 - 6.05838i) q^{95} +(2.04807 - 0.435330i) q^{97} +(1.65851 - 1.20497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{15}\right)$

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			0
$2$		0			0
$3$	0.880961	+	2.71132i	0.508623	+	1.56538i	0.794593	+	0.607142i	$0.207684\pi$
$3$	0.880961	+	2.71132i	0.508623	+	1.56538i	−0.285970	+	0.958239i	$0.592316\pi$
$4$		0			0
$5$	0.308047	+	2.93087i	0.137763	+	1.31073i	0.816928	+	0.576740i	$0.195676\pi$
$5$	0.308047	+	2.93087i	0.137763	+	1.31073i	−0.679165	+	0.733986i	$0.737658\pi$
$6$		0			0
$7$	−2.02506	−	2.24905i	−0.765399	−	0.850062i	0.226901	−	0.973918i	$-0.427141\pi$
$7$	−2.02506	−	2.24905i	−0.765399	−	0.850062i	−0.992300	+	0.123856i	$0.960474\pi$
$8$		0			0
$9$	−4.14811	+	3.01378i	−1.38270	+	1.00459i
$10$		0			0
$11$	−0.399822			−0.120551			−0.0602754	−	0.998182i	$-0.519198\pi$
$11$	−0.399822			−0.120551			−0.0602754	+	0.998182i	$0.519198\pi$
$12$		0			0
$13$	0.149926	−	0.259680i	0.0415820	−	0.0720222i	−0.844485	−	0.535579i	$-0.820094\pi$
$13$	0.149926	−	0.259680i	0.0415820	−	0.0720222i	0.886067	+	0.463556i	$0.153427\pi$
$14$		0			0
$15$	−7.67516	+	3.41720i	−1.98172	+	0.882317i
$16$		0			0
$17$	−7.00397	−	3.11837i	−1.69871	−	0.756316i	−0.999127	−	0.0417664i	$-0.986701\pi$
$17$	−7.00397	−	3.11837i	−1.69871	−	0.756316i	−0.699585	−	0.714549i	$-0.746632\pi$
$18$		0			0
$19$	−2.34027	+	2.59913i	−0.536895	+	0.596282i	−0.949165	−	0.314780i	$-0.898069\pi$
$19$	−2.34027	+	2.59913i	−0.536895	+	0.596282i	0.412270	+	0.911062i	$0.364736\pi$
$20$		0			0
$21$	4.31391	−	7.47190i	0.941371	−	1.63050i
$22$		0			0
$23$	−1.24700	+	0.906001i	−0.260018	+	0.188914i	−0.710155	−	0.704045i	$-0.751375\pi$
$23$	−1.24700	+	0.906001i	−0.260018	+	0.188914i	0.450137	+	0.892960i	$0.351375\pi$
$24$		0			0
$25$	−3.60439	+	0.766136i	−0.720877	+	0.153227i
$26$		0			0
$27$	−4.90648	−	3.56477i	−0.944253	−	0.686040i
$28$		0			0
$29$	3.91291	+	6.77736i	0.726609	+	1.25852i	0.958308	+	0.285736i	$0.0922381\pi$
$29$	3.91291	+	6.77736i	0.726609	+	1.25852i	−0.231699	+	0.972787i	$0.574429\pi$
$30$		0			0
$31$	3.05474	−	0.649305i	0.548647	−	0.116619i	0.0747558	−	0.997202i	$-0.476182\pi$
$31$	3.05474	−	0.649305i	0.548647	−	0.116619i	0.473891	+	0.880583i	$0.342849\pi$
$32$		0			0
$33$	−0.352228	−	1.08404i	−0.0613149	−	0.188708i
$34$		0			0
$35$	5.96788	−	6.62800i	1.00876	−	1.12034i
$36$		0			0
$37$	0.796081	−	2.45008i	0.130875	−	0.402791i	−0.864051	−	0.503405i	$-0.832080\pi$
$37$	0.796081	−	2.45008i	0.130875	−	0.402791i	0.994926	+	0.100613i	$0.0320805\pi$
$38$		0			0
$39$	0.836154	+	0.177730i	0.133892	+	0.0284596i
$40$		0			0
$41$	−2.21673	+	6.82240i	−0.346195	+	1.06548i	0.614745	+	0.788726i	$0.289259\pi$
$41$	−2.21673	+	6.82240i	−0.346195	+	1.06548i	−0.960941	+	0.276754i	$0.910741\pi$
$42$		0			0
$43$	−9.63795	+	4.29109i	−1.46977	+	0.654385i	−0.976506	−	0.215492i	$-0.930864\pi$
$43$	−9.63795	+	4.29109i	−1.46977	+	0.654385i	−0.493268	+	0.869878i	$0.664198\pi$
$44$		0			0
$45$	−10.1108	−	11.2292i	−1.50723	−	1.67395i
$46$		0			0
$47$	2.86033	+	4.95423i	0.417221	+	0.722649i	0.995659	−	0.0930781i	$-0.0296706\pi$
$47$	2.86033	+	4.95423i	0.417221	+	0.722649i	−0.578437	+	0.815727i	$0.696337\pi$
$48$		0			0
$49$	−0.225687	+	2.14727i	−0.0322410	+	0.306752i
$50$		0			0
$51$	2.28467	−	21.7372i	0.319918	−	3.04381i
$52$		0			0
$53$	4.87318	+	3.54057i	0.669382	+	0.486335i	0.869818	−	0.493372i	$-0.164236\pi$
$53$	4.87318	+	3.54057i	0.669382	+	0.486335i	−0.200436	+	0.979707i	$0.564236\pi$
$54$		0			0
$55$	−0.123164	−	1.17183i	−0.0166074	−	0.158009i
$56$		0			0
$57$	−9.10877	−	4.05548i	−1.20649	−	0.537162i
$58$		0			0
$59$	4.62950	+	0.984030i	0.602709	+	0.128110i	0.499153	−	0.866514i	$-0.333645\pi$
$59$	4.62950	+	0.984030i	0.602709	+	0.128110i	0.103556	+	0.994624i	$0.466978\pi$
$60$		0			0
$61$	4.65863	−	6.26875i	0.596476	−	0.802631i
$61$	4.65863	−	6.26875i	0.596476	−	0.802631i
$62$		0			0
$63$	15.1783	+	3.22625i	1.91229	+	0.406469i
$64$		0			0
$65$	0.807272	+	0.359421i	0.100130	+	0.0445807i
$66$		0			0
$67$	0.169933	+	1.61680i	0.0207606	+	0.197524i	0.999986	−	0.00524993i	$-0.00167111\pi$
$67$	0.169933	+	1.61680i	0.0207606	+	0.197524i	−0.979226	+	0.202774i	$0.935004\pi$
$68$		0			0
$69$	−3.55502	−	2.58287i	−0.427974	−	0.310941i
$70$		0			0
$71$	0.194910	−	1.85445i	0.0231316	−	0.220082i	−0.976849	−	0.213928i	$-0.931374\pi$
$71$	0.194910	−	1.85445i	0.0231316	−	0.220082i	0.999981	−	0.00615449i	$-0.00195905\pi$
$72$		0			0
$73$	0.0973672	−	0.926387i	0.0113960	−	0.108425i	−0.987345	−	0.158586i	$-0.949307\pi$
$73$	0.0973672	−	0.926387i	0.0113960	−	0.108425i	0.998741	+	0.0501604i	$0.0159732\pi$
$74$		0			0
$75$	−5.25256	−	9.09771i	−0.606514	−	1.05051i
$76$		0			0
$77$	0.809662	+	0.899221i	0.0922695	+	0.102476i
$78$		0			0
$79$	2.35371	−	1.04794i	0.264813	−	0.117902i	−0.270035	−	0.962850i	$-0.587035\pi$
$79$	2.35371	−	1.04794i	0.264813	−	0.117902i	0.534848	+	0.844948i	$0.320369\pi$
$80$		0			0
$81$	0.589492	−	1.81427i	0.0654991	−	0.201586i
$82$		0			0
$83$	7.51408	+	1.59717i	0.824777	+	0.175312i	0.600919	−	0.799310i	$-0.294801\pi$
$83$	7.51408	+	1.59717i	0.824777	+	0.175312i	0.223858	+	0.974622i	$0.428135\pi$
$84$		0			0
$85$	6.98199	−	21.4884i	0.757303	−	2.33074i
$86$		0			0
$87$	−14.9285	+	16.5797i	−1.60050	+	1.77753i
$88$		0			0
$89$	0.364222	+	1.12096i	0.0386074	+	0.118821i	0.968503	−	0.249003i	$-0.0801028\pi$
$89$	0.364222	+	1.12096i	0.0386074	+	0.118821i	−0.929895	+	0.367824i	$0.880103\pi$
$90$		0			0
$91$	−0.887642	+	0.188674i	−0.0930502	+	0.0197784i
$92$		0			0
$93$	4.45158	+	7.71036i	0.461607	+	0.799527i
$94$		0			0
$95$	−8.33864	−	6.05838i	−0.855527	−	0.621577i
$96$		0			0
$97$	2.04807	−	0.435330i	0.207950	−	0.0442010i	−0.102759	−	0.994706i	$-0.532767\pi$
$97$	2.04807	−	0.435330i	0.207950	−	0.0442010i	0.310708	+	0.950505i	$0.399434\pi$
$98$		0			0
$99$	1.65851	−	1.20497i	0.166686	−	0.121105i
$100$		0			0
$101$	−0.535247	+	0.927075i	−0.0532591	+	0.0922474i	−0.891426	−	0.453167i	$-0.850294\pi$
$101$	−0.535247	+	0.927075i	−0.0532591	+	0.0922474i	0.838167	+	0.545414i	$0.183628\pi$
$102$		0			0
$103$	5.65477	−	6.28026i	0.557181	−	0.618812i	−0.397081	−	0.917784i	$-0.629977\pi$
$103$	5.65477	−	6.28026i	0.557181	−	0.618812i	0.954262	+	0.298971i	$0.0966435\pi$
$104$		0			0
$105$	23.2281	+	10.3418i	2.26683	+	1.00926i
$106$		0			0
$107$	−14.1419	+	6.29638i	−1.36715	+	0.608694i	−0.953403	−	0.301699i	$-0.902446\pi$
$107$	−14.1419	+	6.29638i	−1.36715	+	0.608694i	−0.413746	+	0.910393i	$0.635780\pi$
$108$		0			0
$109$	−9.89437	+	17.1376i	−0.947709	+	1.64148i	−0.197474	+	0.980308i	$0.563274\pi$
$109$	−9.89437	+	17.1376i	−0.947709	+	1.64148i	−0.750235	+	0.661172i	$0.770060\pi$
$110$		0			0
$111$	7.34428			0.697088
$112$		0			0
$113$	−6.19931	+	4.50406i	−0.583182	+	0.423706i	−0.839870	−	0.542788i	$-0.817369\pi$
$113$	−6.19931	+	4.50406i	−0.583182	+	0.423706i	0.256688	+	0.966494i	$0.417369\pi$
$114$		0			0
$115$	−3.03951	−	3.37572i	−0.283436	−	0.314787i
$116$		0			0
$117$	0.160707	+	1.52902i	0.0148574	+	0.141358i
$118$		0			0
$119$	7.17006	+	22.0672i	0.657278	+	2.02289i
$120$		0			0
$121$	−10.8401			−0.985467
$122$		0			0
$123$	−20.4506			−1.84397
$124$		0			0
$125$	1.19762	+	3.68591i	0.107119	+	0.329678i
$126$		0			0
$127$	−0.736109	−	7.00361i	−0.0653191	−	0.621470i	−0.977391	−	0.211439i	$-0.932185\pi$
$127$	−0.736109	−	7.00361i	−0.0653191	−	0.621470i	0.912072	−	0.410030i	$-0.134482\pi$
$128$		0			0
$129$	−20.1252	−	22.3513i	−1.77192	−	1.96792i
$130$		0			0
$131$	1.10032	−	0.799426i	0.0961350	−	0.0698461i	−0.538679	−	0.842511i	$-0.681077\pi$
$131$	1.10032	−	0.799426i	0.0961350	−	0.0698461i	0.634814	+	0.772665i	$0.281077\pi$
$132$		0			0
$133$	10.5848			0.917816
$134$		0			0
$135$	8.93645	−	15.4784i	0.769127	−	1.33217i
$136$		0			0
$137$	6.99524	−	3.11448i	0.597644	−	0.266088i	−0.0855400	−	0.996335i	$-0.527262\pi$
$137$	6.99524	−	3.11448i	0.597644	−	0.266088i	0.683184	+	0.730247i	$0.260595\pi$
$138$		0			0
$139$	−7.12471	−	3.17212i	−0.604310	−	0.269056i	0.0816900	−	0.996658i	$-0.473968\pi$
$139$	−7.12471	−	3.17212i	−0.604310	−	0.269056i	−0.686000	+	0.727602i	$0.740635\pi$
$140$		0			0
$141$	−10.9127	+	12.1197i	−0.919012	+	1.02067i
$142$		0			0
$143$	−0.0599437	+	0.103826i	−0.00501275	+	0.00868233i
$144$		0			0
$145$	−18.6582	+	13.5560i	−1.54948	+	1.12576i
$146$		0			0
$147$	−6.02075	+	1.27975i	−0.496583	+	0.105552i
$148$		0			0
$149$	−4.37795	−	3.18077i	−0.358655	−	0.260578i	0.393836	−	0.919181i	$-0.371148\pi$
$149$	−4.37795	−	3.18077i	−0.358655	−	0.260578i	−0.752491	+	0.658602i	$0.771148\pi$
$150$		0			0
$151$	2.89174	+	5.00863i	0.235326	+	0.407597i	0.959367	−	0.282160i	$-0.0910508\pi$
$151$	2.89174	+	5.00863i	0.235326	+	0.407597i	−0.724041	+	0.689757i	$0.757718\pi$
$152$		0			0
$153$	38.4513	−	8.17308i	3.10860	−	0.660754i
$154$		0			0
$155$	2.84403	+	8.75303i	0.228438	+	0.703061i
$156$		0			0
$157$	−2.17155	+	2.41175i	−0.173309	+	0.192479i	−0.823541	−	0.567256i	$-0.808005\pi$
$157$	−2.17155	+	2.41175i	−0.173309	+	0.192479i	0.650232	+	0.759735i	$0.274671\pi$
$158$		0			0
$159$	−5.30654	+	16.3318i	−0.420836	+	1.29520i
$160$		0			0
$161$	4.56290	+	0.969873i	0.359607	+	0.0764367i
$162$		0			0
$163$	−5.72526	+	17.6205i	−0.448437	+	1.38015i	0.430233	+	0.902718i	$0.358431\pi$
$163$	−5.72526	+	17.6205i	−0.448437	+	1.38015i	−0.878670	+	0.477429i	$0.841569\pi$
$164$		0			0
$165$	3.06870	−	1.36627i	0.238898	−	0.106364i
$166$		0			0
$167$	6.26513	+	6.95813i	0.484810	+	0.538436i	0.935071	−	0.354461i	$-0.115336\pi$
$167$	6.26513	+	6.95813i	0.484810	+	0.538436i	−0.450261	+	0.892897i	$0.648669\pi$
$168$		0			0
$169$	6.45504	+	11.1805i	0.496542	+	0.860036i
$170$		0			0
$171$	1.87449	−	17.8345i	0.143346	−	1.36384i
$172$		0			0
$173$	−0.130968	+	1.24607i	−0.00995729	+	0.0947373i	−0.998372	−	0.0570412i	$-0.981833\pi$
$173$	−0.130968	+	1.24607i	−0.00995729	+	0.0947373i	0.988415	+	0.151778i	$0.0485000\pi$
$174$		0			0
$175$	9.02217	+	6.55499i	0.682012	+	0.495510i
$176$		0			0
$177$	1.41039	+	13.4189i	0.106011	+	1.00863i
$178$		0			0
$179$	10.9570	+	4.87837i	0.818964	+	0.364626i	0.773071	−	0.634320i	$-0.218720\pi$
$179$	10.9570	+	4.87837i	0.818964	+	0.364626i	0.0458935	+	0.998946i	$0.485387\pi$
$180$		0			0
$181$	22.7000	+	4.82503i	1.68728	+	0.358642i	0.948858	−	0.315702i	$-0.102240\pi$
$181$	22.7000	+	4.82503i	1.68728	+	0.358642i	0.738418	+	0.674343i	$0.235573\pi$
$182$		0			0
$183$	21.1006	+	7.10850i	1.55980	+	0.525475i
$184$		0			0
$185$	7.42612	+	1.57847i	0.545979	+	0.116051i
$186$		0			0
$187$	2.80034	+	1.24679i	0.204781	+	0.0911745i
$188$		0			0
$189$	1.91855	+	18.2538i	0.139554	+	1.32777i
$190$		0			0
$191$	13.9507	+	10.1358i	1.00944	+	0.733399i	0.964091	−	0.265572i	$-0.0855609\pi$
$191$	13.9507	+	10.1358i	1.00944	+	0.733399i	0.0453462	+	0.998971i	$0.485561\pi$
$192$		0			0
$193$	2.29904	−	21.8739i	0.165489	−	1.57452i	−0.524952	−	0.851132i	$-0.675917\pi$
$193$	2.29904	−	21.8739i	0.165489	−	1.57452i	0.690441	−	0.723389i	$-0.257417\pi$
$194$		0			0
$195$	−0.263329	+	2.50541i	−0.0188574	+	0.179416i
$196$		0			0
$197$	−9.10581	−	15.7717i	−0.648762	−	1.12369i	−0.983419	−	0.181349i	$-0.941954\pi$
$197$	−9.10581	−	15.7717i	−0.648762	−	1.12369i	0.334656	−	0.942340i	$-0.391380\pi$
$198$		0			0
$199$	−2.55974	−	2.84288i	−0.181455	−	0.201526i	0.645554	−	0.763714i	$-0.276626\pi$
$199$	−2.55974	−	2.84288i	−0.181455	−	0.201526i	−0.827009	+	0.562188i	$0.809960\pi$
$200$		0			0
$201$	−4.23396	+	1.88508i	−0.298641	+	0.132963i
$202$		0			0
$203$	7.31877	−	22.5249i	0.513677	−	1.58094i
$204$		0			0
$205$	−20.6784	−	4.39534i	−1.44425	−	0.306984i
$206$		0			0
$207$	2.44222	−	7.51638i	0.169746	−	0.522425i
$208$		0			0
$209$	0.935691	−	1.03919i	0.0647231	−	0.0718823i
$210$		0			0
$211$	3.10456	+	9.55485i	0.213727	+	0.657783i	0.999242	+	0.0389404i	$0.0123982\pi$
$211$	3.10456	+	9.55485i	0.213727	+	0.657783i	−0.785515	+	0.618843i	$0.787602\pi$
$212$		0			0
$213$	5.19970	−	1.10523i	0.356278	−	0.0757292i
$214$		0			0
$215$	−15.5456	−	26.9257i	−1.06020	−	1.83632i
$216$		0			0
$217$	−7.64634	−	5.55539i	−0.519067	−	0.377124i
$218$		0			0
$219$	2.59751	−	0.552117i	0.175523	−	0.0373086i
$220$		0			0
$221$	−1.85986	+	1.35126i	−0.125107	+	0.0908958i
$222$		0			0
$223$	2.35430	−	4.07776i	0.157655	−	0.273067i	−0.776367	−	0.630281i	$-0.782940\pi$
$223$	2.35430	−	4.07776i	0.157655	−	0.273067i	0.934023	+	0.357214i	$0.116273\pi$
$224$		0			0
$225$	12.6424	−	14.0408i	0.842828	−	0.936056i
$226$		0			0
$227$	16.3441	+	7.27686i	1.08480	+	0.482982i	0.869685	−	0.493607i	$-0.164322\pi$
$227$	16.3441	+	7.27686i	1.08480	+	0.482982i	0.215111	+	0.976590i	$0.430989\pi$
$228$		0			0
$229$	−20.4903	+	9.12285i	−1.35403	+	0.602855i	−0.950103	−	0.311935i	$-0.899023\pi$
$229$	−20.4903	+	9.12285i	−1.35403	+	0.602855i	−0.403931	+	0.914790i	$0.632356\pi$
$230$		0			0
$231$	−1.72479	+	2.98743i	−0.113483	+	0.196559i
$232$		0			0
$233$	17.8701			1.17071			0.585356	−	0.810777i	$-0.300955\pi$
$233$	17.8701			1.17071			0.585356	+	0.810777i	$0.300955\pi$
$234$		0			0
$235$	−13.6391	+	9.90939i	−0.889717	+	0.646417i
$236$		0			0
$237$	4.91483	+	5.45847i	0.319252	+	0.354566i
$238$		0			0
$239$	−1.66876	−	15.8772i	−0.107943	−	1.02701i	−0.905668	−	0.423988i	$-0.860630\pi$
$239$	−1.66876	−	15.8772i	−0.107943	−	1.02701i	0.797724	−	0.603022i	$-0.206037\pi$
$240$		0			0
$241$	−1.04724	−	3.22309i	−0.0674589	−	0.207617i	0.911645	−	0.410979i	$-0.134813\pi$
$241$	−1.04724	−	3.22309i	−0.0674589	−	0.207617i	−0.979104	+	0.203362i	$0.934813\pi$
$242$		0			0
$243$	−12.7558			−0.818288
$244$		0			0
$245$	−6.36289			−0.406510
$246$		0			0
$247$	0.324074	+	0.997398i	0.0206204	+	0.0634629i
$248$		0			0
$249$	2.28918	+	21.7801i	0.145071	+	1.38026i
$250$		0			0
$251$	−14.2803	−	15.8599i	−0.901367	−	1.00107i	−0.999982	−	0.00594408i	$-0.998108\pi$
$251$	−14.2803	−	15.8599i	−0.901367	−	1.00107i	0.0986151	−	0.995126i	$-0.468559\pi$
$252$		0			0
$253$	0.498579	−	0.362239i	0.0313454	−	0.0227738i
$254$		0			0
$255$	64.4127			4.03368
$256$		0			0
$257$	1.47438	−	2.55371i	0.0919696	−	0.159296i	−0.816370	−	0.577529i	$-0.804017\pi$
$257$	1.47438	−	2.55371i	0.0919696	−	0.159296i	0.908340	+	0.418233i	$0.137350\pi$
$258$		0			0
$259$	−7.12248	+	3.17113i	−0.442569	+	0.197045i
$260$		0			0
$261$	−36.6566	−	16.3206i	−2.26899	−	1.01022i
$262$		0			0
$263$	0.194518	−	0.216034i	0.0119945	−	0.0133212i	−0.737118	−	0.675764i	$-0.763814\pi$
$263$	0.194518	−	0.216034i	0.0119945	−	0.0133212i	0.749112	+	0.662443i	$0.230480\pi$
$264$		0			0
$265$	−8.87579	+	15.3733i	−0.545236	+	0.944376i
$266$		0			0
$267$	−2.71841	+	1.97504i	−0.166364	+	0.120871i
$268$		0			0
$269$	21.9176	−	4.65874i	1.33634	−	0.284048i	0.516328	−	0.856391i	$-0.327299\pi$
$269$	21.9176	−	4.65874i	1.33634	−	0.284048i	0.820014	+	0.572343i	$0.193965\pi$
$270$		0			0
$271$	−6.74554	−	4.90092i	−0.409762	−	0.297710i	0.363743	−	0.931499i	$-0.381499\pi$
$271$	−6.74554	−	4.90092i	−0.409762	−	0.297710i	−0.773506	+	0.633790i	$0.781499\pi$
$272$		0			0
$273$	−1.29353	−	2.24047i	−0.0782882	−	0.135599i
$274$		0			0
$275$	1.44111	−	0.306318i	0.0869023	−	0.0184717i
$276$		0			0
$277$	3.62381	+	11.1529i	0.217734	+	0.670115i	0.998948	+	0.0458524i	$0.0146004\pi$
$277$	3.62381	+	11.1529i	0.217734	+	0.670115i	−0.781215	+	0.624262i	$0.785400\pi$
$278$		0			0
$279$	−10.7145	+	11.8997i	−0.641462	+	0.712416i
$280$		0			0
$281$	3.54416	−	10.9078i	0.211427	−	0.650706i	−0.787961	−	0.615725i	$-0.788863\pi$
$281$	3.54416	−	10.9078i	0.211427	−	0.650706i	0.999388	−	0.0349804i	$-0.0111369\pi$
$282$		0			0
$283$	−16.8149	−	3.57412i	−0.999542	−	0.212459i	−0.321046	−	0.947064i	$-0.604034\pi$
$283$	−16.8149	−	3.57412i	−0.999542	−	0.212459i	−0.678496	+	0.734604i	$0.737368\pi$
$284$		0			0
$285$	9.08018	−	27.9459i	0.537863	−	1.65537i
$286$		0			0
$287$	19.8329	−	8.83020i	1.17070	−	0.521230i
$288$		0			0
$289$	27.9562	+	31.0485i	1.64448	+	1.82638i
$290$		0			0
$291$	2.98458	+	5.16945i	0.174959	+	0.303039i
$292$		0			0
$293$	1.65109	−	15.7091i	0.0964578	−	0.917735i	−0.834106	−	0.551605i	$-0.814016\pi$
$293$	1.65109	−	15.7091i	0.0964578	−	0.917735i	0.930564	−	0.366130i	$-0.119318\pi$
$294$		0			0
$295$	−1.45796	+	13.8716i	−0.0848859	+	0.807635i
$296$		0			0
$297$	1.96172	+	1.42527i	0.113830	+	0.0827027i
$298$		0			0
$299$	0.0483116	+	0.459654i	0.00279393	+	0.0265825i
$300$		0			0
$301$	29.1683	+	12.9866i	1.68123	+	0.748533i
$302$		0			0
$303$	−2.98513	−	0.634509i	−0.171491	−	0.0364516i
$304$		0			0
$305$	19.8080	+	11.7228i	1.13420	+	0.671244i
$306$		0			0
$307$	32.4427	+	6.89591i	1.85160	+	0.393570i	0.992905	−	0.118912i	$-0.0379405\pi$
$307$	32.4427	+	6.89591i	1.85160	+	0.393570i	0.858698	+	0.512482i	$0.171274\pi$
$308$		0			0
$309$	22.0094	+	9.79923i	1.25207	+	0.557459i
$310$		0			0
$311$	2.27916	+	21.6847i	0.129239	+	1.22963i	0.846334	+	0.532653i	$0.178805\pi$
$311$	2.27916	+	21.6847i	0.129239	+	1.22963i	−0.717094	+	0.696976i	$0.754528\pi$
$312$		0			0
$313$	−21.2184	−	15.4161i	−1.19933	−	0.871367i	−0.205115	−	0.978738i	$-0.565757\pi$
$313$	−21.2184	−	15.4161i	−1.19933	−	0.871367i	−0.994219	+	0.107370i	$0.965757\pi$
$314$		0			0
$315$	−4.78009	+	45.4795i	−0.269328	+	2.56248i
$316$		0			0
$317$	−1.54496	+	14.6993i	−0.0867734	+	0.825594i	0.861419	+	0.507896i	$0.169576\pi$
$317$	−1.54496	+	14.6993i	−0.0867734	+	0.825594i	−0.948192	+	0.317698i	$0.897090\pi$
$318$		0			0
$319$	−1.56447	−	2.70974i	−0.0875933	−	0.151716i
$320$		0			0
$321$	−29.5300	−	32.7963i	−1.64820	−	1.83051i
$322$		0			0
$323$	24.4962	−	10.9064i	1.36301	−	0.606850i
$324$		0			0
$325$	−0.341442	+	1.05085i	−0.0189398	+	0.0582906i
$326$		0			0
$327$	−55.1819	−	11.7293i	−3.05157	−	0.648631i
$328$		0			0
$329$	5.35000	−	16.4656i	0.294955	−	0.907779i
$330$		0			0
$331$	−1.54116	+	1.71163i	−0.0847099	+	0.0940799i	−0.784009	−	0.620749i	$-0.786829\pi$
$331$	−1.54116	+	1.71163i	−0.0847099	+	0.0940799i	0.699300	+	0.714829i	$0.253495\pi$
$332$		0			0
$333$	4.08178	+	12.5624i	0.223680	+	0.688417i
$334$		0			0
$335$	−4.68629	+	0.996102i	−0.256039	+	0.0544229i
$336$		0			0
$337$	5.01937	+	8.69381i	0.273423	+	0.473582i	0.969736	−	0.244156i	$-0.0785109\pi$
$337$	5.01937	+	8.69381i	0.273423	+	0.473582i	−0.696313	+	0.717738i	$0.745178\pi$
$338$		0			0
$339$	−17.6733	−	12.8404i	−0.959882	−	0.697395i
$340$		0			0
$341$	−1.22135	+	0.259606i	−0.0661399	+	0.0140585i
$342$		0			0
$343$	−11.8525	+	8.61136i	−0.639976	+	0.464970i
$344$		0			0
$345$	6.47496	−	11.2150i	0.348600	−	0.603793i
$346$		0			0
$347$	16.6956	−	18.5424i	0.896267	−	0.995406i	−0.103732	−	0.994605i	$-0.533079\pi$
$347$	16.6956	−	18.5424i	0.896267	−	0.995406i	1.00000		0.000800339i	$-0.000254756\pi$
$348$		0			0
$349$	−3.21237	−	1.43024i	−0.171954	−	0.0765590i	0.318954	−	0.947770i	$-0.396668\pi$
$349$	−3.21237	−	1.43024i	−0.171954	−	0.0765590i	−0.490908	+	0.871211i	$0.663335\pi$
$350$		0			0
$351$	−1.66131	+	0.739661i	−0.0886740	+	0.0394802i
$352$		0			0
$353$	3.49617	−	6.05554i	0.186082	−	0.322304i	−0.757858	−	0.652419i	$-0.773754\pi$
$353$	3.49617	−	6.05554i	0.186082	−	0.322304i	0.943941	+	0.330115i	$0.107088\pi$
$354$		0			0
$355$	5.49519			0.291654
$356$		0			0
$357$	−53.5146	+	38.8807i	−2.83229	+	2.05778i
$358$		0			0
$359$	13.6064	+	15.1115i	0.718120	+	0.797554i	0.986150	−	0.165857i	$-0.0530391\pi$
$359$	13.6064	+	15.1115i	0.718120	+	0.797554i	−0.268029	+	0.963411i	$0.586372\pi$
$360$		0			0
$361$	0.707411	+	6.73057i	0.0372322	+	0.354240i
$362$		0			0
$363$	−9.54974	−	29.3911i	−0.501232	−	1.54263i
$364$		0			0
$365$	2.74512			0.143686
$366$		0			0
$367$	−3.22811			−0.168506			−0.0842531	−	0.996444i	$-0.526850\pi$
$367$	−3.22811			−0.168506			−0.0842531	+	0.996444i	$0.526850\pi$
$368$		0			0
$369$	−11.3660	−	34.9808i	−0.591688	−	1.82103i
$370$		0			0
$371$	−1.90553	−	18.1299i	−0.0989301	−	0.941257i
$372$		0			0
$373$	−1.51640	−	1.68413i	−0.0785161	−	0.0872009i	0.702607	−	0.711578i	$-0.252019\pi$
$373$	−1.51640	−	1.68413i	−0.0785161	−	0.0872009i	−0.781123	+	0.624378i	$0.785353\pi$
$374$		0			0
$375$	−8.93861	+	6.49428i	−0.461588	+	0.335363i
$376$		0			0
$377$	2.34659			0.120855
$378$		0			0
$379$	16.4822	−	28.5481i	0.846636	−	1.46642i	−0.0375567	−	0.999294i	$-0.511957\pi$
$379$	16.4822	−	28.5481i	0.846636	−	1.46642i	0.884193	−	0.467122i	$-0.154709\pi$
$380$		0			0
$381$	18.3405	−	8.16573i	0.939614	−	0.418343i
$382$		0			0
$383$	−13.3743	−	5.95464i	−0.683396	−	0.304268i	0.0355152	−	0.999369i	$-0.488693\pi$
$383$	−13.3743	−	5.95464i	−0.683396	−	0.304268i	−0.718912	+	0.695101i	$0.755359\pi$
$384$		0			0
$385$	−2.38609	+	2.65002i	−0.121606	+	0.135057i
$386$		0			0
$387$	27.0469	−	46.8466i	1.37487	−	2.38134i
$388$		0			0
$389$	11.9862	−	8.70851i	0.607726	−	0.441539i	−0.240887	−	0.970553i	$-0.577438\pi$
$389$	11.9862	−	8.70851i	0.607726	−	0.441539i	0.848613	+	0.529014i	$0.177438\pi$
$390$		0			0
$391$	11.5592	−	2.45699i	0.584575	−	0.124255i
$392$		0			0
$393$	3.13683	+	2.27904i	0.158232	+	0.114962i
$394$		0			0
$395$	3.79643	+	6.57561i	0.191019	+	0.330855i
$396$		0			0
$397$	−26.2969	+	5.58957i	−1.31980	+	0.280533i	−0.813370	−	0.581747i	$-0.802369\pi$
$397$	−26.2969	+	5.58957i	−1.31980	+	0.280533i	−0.506432	+	0.862280i	$0.669036\pi$
$398$		0			0
$399$	9.32477	+	28.6987i	0.466822	+	1.43673i
$400$		0			0
$401$	3.64626	−	4.04958i	0.182085	−	0.202226i	−0.645191	−	0.764021i	$-0.723222\pi$
$401$	3.64626	−	4.04958i	0.182085	−	0.202226i	0.827277	+	0.561795i	$0.189889\pi$
$402$		0			0
$403$	0.289374	−	0.890601i	0.0144147	−	0.0443640i
$404$		0			0
$405$	5.49899	+	1.16885i	0.273247	+	0.0580804i
$406$		0			0
$407$	−0.318291	+	0.979598i	−0.0157771	+	0.0485569i
$408$		0			0
$409$	−9.03661	+	4.02336i	−0.446832	+	0.198942i	−0.617802	−	0.786334i	$-0.711977\pi$
$409$	−9.03661	+	4.02336i	−0.446832	+	0.198942i	0.170970	+	0.985276i	$0.445310\pi$
$410$		0			0
$411$	14.6069	+	16.2226i	0.720505	+	0.800201i
$412$		0			0
$413$	−7.16185	−	12.4047i	−0.352412	−	0.610395i
$414$		0			0
$415$	−2.36640	+	22.5148i	−0.116162	+	1.10521i
$416$		0			0
$417$	2.32405	−	22.1119i	0.113809	−	1.08282i
$418$		0			0
$419$	−4.56538	−	3.31694i	−0.223034	−	0.162043i	0.470658	−	0.882316i	$-0.344017\pi$
$419$	−4.56538	−	3.31694i	−0.223034	−	0.162043i	−0.693691	+	0.720273i	$0.744017\pi$
$420$		0			0
$421$	−1.50531	−	14.3220i	−0.0733641	−	0.698013i	−0.967954	−	0.251126i	$-0.919199\pi$
$421$	−1.50531	−	14.3220i	−0.0733641	−	0.698013i	0.894590	−	0.446887i	$-0.147467\pi$
$422$		0			0
$423$	−26.7959	−	11.9303i	−1.30286	−	0.580071i
$424$		0			0
$425$	27.6341	+	5.87381i	1.34045	+	0.284922i
$426$		0			0
$427$	−23.5327	+	2.21707i	−1.13883	+	0.107292i
$428$		0			0
$429$	−0.334313	−	0.0710603i	−0.0161408	−	0.00343082i
$430$		0			0
$431$	−14.8855	−	6.62747i	−0.717012	−	0.319234i	0.0156027	−	0.999878i	$-0.495033\pi$
$431$	−14.8855	−	6.62747i	−0.717012	−	0.319234i	−0.732614	+	0.680644i	$0.761700\pi$
$432$		0			0
$433$	2.11501	+	20.1229i	0.101641	+	0.967047i	0.919888	+	0.392181i	$0.128279\pi$
$433$	2.11501	+	20.1229i	0.101641	+	0.967047i	−0.818247	+	0.574866i	$0.805054\pi$
$434$		0			0
$435$	−53.1918	−	38.6461i	−2.55035	−	1.85294i
$436$		0			0
$437$	0.563507	−	5.36141i	0.0269562	−	0.256471i
$438$		0			0
$439$	−0.819063	+	7.79286i	−0.0390917	+	0.371933i	0.957434	+	0.288651i	$0.0932068\pi$
$439$	−0.819063	+	7.79286i	−0.0390917	+	0.371933i	−0.996526	+	0.0832817i	$0.973460\pi$
$440$		0			0
$441$	−5.53521	−	9.58727i	−0.263581	−	0.456536i
$442$		0			0
$443$	−17.7434	−	19.7060i	−0.843014	−	0.936262i	0.155656	−	0.987811i	$-0.450251\pi$
$443$	−17.7434	−	19.7060i	−0.843014	−	0.936262i	−0.998670	+	0.0515493i	$0.983584\pi$
$444$		0			0
$445$	−3.17319	+	1.41280i	−0.150424	+	0.0669730i
$446$		0			0
$447$	4.76727	−	14.6721i	0.225484	−	0.693969i
$448$		0			0
$449$	3.69456	+	0.785304i	0.174357	+	0.0370608i	0.294263	−	0.955725i	$-0.404926\pi$
$449$	3.69456	+	0.785304i	0.174357	+	0.0370608i	−0.119906	+	0.992785i	$0.538259\pi$
$450$		0			0
$451$	0.886298	−	2.72775i	0.0417341	−	0.128445i
$452$		0			0
$453$	−11.0325	+	12.2528i	−0.518352	+	0.575688i
$454$		0			0
$455$	−0.826416	−	2.54345i	−0.0387430	−	0.119239i
$456$		0			0
$457$	10.0115	−	2.12802i	0.468319	−	0.0995444i	0.0322934	−	0.999478i	$-0.489719\pi$
$457$	10.0115	−	2.12802i	0.468319	−	0.0995444i	0.436026	+	0.899934i	$0.356386\pi$
$458$		0			0
$459$	23.2486	+	40.2677i	1.08515	+	1.87954i
$460$		0			0
$461$	10.5472	+	7.66299i	0.491232	+	0.356901i	0.805658	−	0.592381i	$-0.201812\pi$
$461$	10.5472	+	7.66299i	0.491232	+	0.356901i	−0.314426	+	0.949282i	$0.601812\pi$
$462$		0			0
$463$	15.9214	−	3.38421i	0.739932	−	0.157277i	0.177500	−	0.984121i	$-0.443199\pi$
$463$	15.9214	−	3.38421i	0.739932	−	0.157277i	0.562432	+	0.826843i	$0.309866\pi$
$464$		0			0
$465$	−21.2268	+	15.4222i	−0.984369	+	0.715186i
$466$		0			0
$467$	−6.74234	+	11.6781i	−0.311998	+	0.540397i	−0.978795	−	0.204843i	$-0.934332\pi$
$467$	−6.74234	+	11.6781i	−0.311998	+	0.540397i	0.666796	+	0.745240i	$0.267665\pi$
$468$		0			0
$469$	3.29215	−	3.65630i	0.152017	−	0.168832i
$470$		0			0
$471$	−8.45209	−	3.76311i	−0.389452	−	0.173395i
$472$		0			0
$473$	3.85346	−	1.71567i	0.177182	−	0.0788867i
$474$		0			0
$475$	6.44395	−	11.1612i	0.295669	−	0.512113i
$476$		0			0
$477$	−30.8850			−1.41413
$478$		0			0
$479$	−31.0521	+	22.5607i	−1.41881	+	1.03082i	−0.426841	+	0.904327i	$0.640374\pi$
$479$	−31.0521	+	22.5607i	−1.41881	+	1.03082i	−0.991967	+	0.126498i	$0.959626\pi$
$480$		0			0
$481$	−0.516884	−	0.574058i	−0.0235679	−	0.0261748i
$482$		0			0
$483$	1.39010	+	13.2259i	0.0632516	+	0.601799i
$484$		0			0
$485$	1.90680	+	5.86852i	0.0865832	+	0.266476i
$486$		0			0
$487$	11.6942			0.529913			0.264957	−	0.964260i	$-0.414642\pi$
$487$	11.6942			0.529913			0.264957	+	0.964260i	$0.414642\pi$
$488$		0			0
$489$	−52.8186			−2.38854
$490$		0			0
$491$	12.1170	+	37.2924i	0.546834	+	1.68298i	0.716590	+	0.697495i	$0.245702\pi$
$491$	12.1170	+	37.2924i	0.546834	+	1.68298i	−0.169756	+	0.985486i	$0.554298\pi$
$492$		0			0
$493$	−6.27160	−	59.6703i	−0.282459	−	2.68742i
$494$		0			0
$495$	4.04253	+	4.48968i	0.181698	+	0.201796i
$496$		0			0
$497$	−4.56545	+	3.31699i	−0.204788	+	0.148788i
$498$		0			0
$499$	−38.5025			−1.72361			−0.861804	−	0.507242i	$-0.830665\pi$
$499$	−38.5025			−1.72361			−0.861804	+	0.507242i	$0.830665\pi$
$500$		0			0
$501$	−13.3464	+	23.1166i	−0.596272	+	1.03277i
$502$		0			0
$503$	31.7869	−	14.1525i	1.41731	−	0.631027i	0.451972	−	0.892032i	$-0.350721\pi$
$503$	31.7869	−	14.1525i	1.41731	−	0.631027i	0.965337	+	0.261005i	$0.0840539\pi$
$504$		0			0
$505$	−2.88202	−	1.28316i	−0.128248	−	0.0570998i
$506$		0			0
$507$	−24.6272	+	27.3512i	−1.09373	+	1.21471i
$508$		0			0
$509$	12.2764	−	21.2634i	0.544143	−	0.942484i	−0.454517	−	0.890738i	$-0.650188\pi$
$509$	12.2764	−	21.2634i	0.544143	−	0.942484i	0.998660	−	0.0517456i	$-0.0164785\pi$
$510$		0			0
$511$	−2.28067	+	1.65700i	−0.100891	+	0.0733014i
$512$		0			0
$513$	20.7478	−	4.41008i	0.916037	−	0.194710i
$514$		0			0
$515$	20.1486	+	14.6388i	0.887852	+	0.645063i
$516$		0			0
$517$	−1.14362	−	1.98081i	−0.0502964	−	0.0871159i
$518$		0			0
$519$	−3.49388	+	0.742648i	−0.153364	+	0.0325986i
$520$		0			0
$521$	5.97906	+	18.4017i	0.261947	+	0.806191i	0.992381	+	0.123207i	$0.0393180\pi$
$521$	5.97906	+	18.4017i	0.261947	+	0.806191i	−0.730434	+	0.682984i	$0.760682\pi$
$522$		0			0
$523$	13.9413	−	15.4834i	0.609611	−	0.677041i	−0.356759	−	0.934196i	$-0.616118\pi$
$523$	13.9413	−	15.4834i	0.609611	−	0.677041i	0.966370	+	0.257155i	$0.0827851\pi$
$524$		0			0
$525$	−9.82449	+	30.2367i	−0.428776	+	1.31964i
$526$		0			0
$527$	−23.4201	−	4.97809i	−1.02019	−	0.216849i
$528$		0			0
$529$	−6.37321	+	19.6147i	−0.277096	+	0.852814i
$530$		0			0
$531$	−22.1693	+	9.87041i	−0.962066	+	0.428339i
$532$		0			0
$533$	1.43929	+	1.59850i	0.0623427	+	0.0692386i
$534$		0			0
$535$	−22.8103	−	39.5085i	−0.986173	−	1.70810i
$536$		0			0
$537$	−3.57413	+	34.0056i	−0.154235	+	1.46745i
$538$		0			0
$539$	0.0902345	−	0.858524i	0.00388668	−	0.0369793i
$540$		0			0
$541$	9.81786	+	7.13309i	0.422103	+	0.306676i	0.778483	−	0.627665i	$-0.215989\pi$
$541$	9.81786	+	7.13309i	0.422103	+	0.306676i	−0.356381	+	0.934341i	$0.615989\pi$
$542$		0			0
$543$	6.91560	+	65.7976i	0.296777	+	2.82364i
$544$		0			0
$545$	−53.2759	−	23.7200i	−2.28209	−	1.01605i
$546$		0			0
$547$	8.53976	+	1.81518i	0.365134	+	0.0776116i	0.386825	−	0.922153i	$-0.373572\pi$
$547$	8.53976	+	1.81518i	0.365134	+	0.0776116i	−0.0216912	+	0.999765i	$0.506905\pi$
$548$		0			0
$549$	−0.431875	+	40.0435i	−0.0184320	+	1.70902i
$550$		0			0
$551$	−26.7725	−	5.69067i	−1.14055	−	0.242431i
$552$		0			0
$553$	−7.12327	−	3.17148i	−0.302912	−	0.134865i
$554$		0			0
$555$	2.26238	+	21.5251i	0.0960329	+	0.913692i
$556$		0			0
$557$	−11.1633	−	8.11060i	−0.473004	−	0.343657i	0.325607	−	0.945505i	$-0.394431\pi$
$557$	−11.1633	−	8.11060i	−0.473004	−	0.343657i	−0.798611	+	0.601848i	$0.794431\pi$
$558$		0			0
$559$	−0.330671	+	3.14613i	−0.0139859	+	0.133067i
$560$		0			0
$561$	−0.913460	+	8.69100i	−0.0385663	+	0.366934i
$562$		0			0
$563$	−7.98048	−	13.8226i	−0.336337	−	0.582553i	0.647404	−	0.762147i	$-0.275855\pi$
$563$	−7.98048	−	13.8226i	−0.336337	−	0.582553i	−0.983741	+	0.179594i	$0.942521\pi$
$564$		0			0
$565$	−15.1105	−	16.7819i	−0.635704	−	0.706021i
$566$		0			0
$567$	−5.27415	+	2.34820i	−0.221493	+	0.0986152i
$568$		0			0
$569$	−12.0403	+	37.0562i	−0.504756	+	1.55348i	0.296426	+	0.955056i	$0.404205\pi$
$569$	−12.0403	+	37.0562i	−0.504756	+	1.55348i	−0.801181	+	0.598422i	$0.795795\pi$
$570$		0			0
$571$	37.6530	+	8.00340i	1.57573	+	0.334932i	0.911082	−	0.412225i	$-0.135248\pi$
$571$	37.6530	+	8.00340i	1.57573	+	0.334932i	0.664648	+	0.747157i	$0.268582\pi$
$572$		0			0
$573$	−15.1913	+	46.7540i	−0.634626	+	1.95318i
$574$		0			0
$575$	3.80056	−	4.22095i	0.158494	−	0.176026i
$576$		0			0
$577$	−2.62766	−	8.08712i	−0.109391	−	0.336671i	0.881345	−	0.472474i	$-0.156639\pi$
$577$	−2.62766	−	8.08712i	−0.109391	−	0.336671i	−0.990736	+	0.135802i	$0.956639\pi$
$578$		0			0
$579$	61.3326	−	13.0367i	2.54890	−	0.541785i
$580$		0			0
$581$	−11.6243	−	20.1339i	−0.482258	−	0.835296i
$582$		0			0
$583$	−1.94840	−	1.41560i	−0.0806946	−	0.0586281i
$584$		0			0
$585$	−4.43187	+	0.942023i	−0.183235	+	0.0389479i
$586$		0			0
$587$	−26.4320	+	19.2039i	−1.09096	+	0.792631i	−0.979562	−	0.201144i	$-0.935534\pi$
$587$	−26.4320	+	19.2039i	−1.09096	+	0.792631i	−0.111402	+	0.993775i	$0.535534\pi$
$588$		0			0
$589$	−5.46128	+	9.45922i	−0.225028	+	0.389760i
$590$		0			0
$591$	34.7403	−	38.5831i	1.42903	−	1.58709i
$592$		0			0
$593$	−5.00295	−	2.22746i	−0.205447	−	0.0914707i	0.301434	−	0.953487i	$-0.402535\pi$
$593$	−5.00295	−	2.22746i	−0.205447	−	0.0914707i	−0.506880	+	0.862016i	$0.669201\pi$
$594$		0			0
$595$	−62.4674	+	27.8123i	−2.56091	+	1.14019i
$596$		0			0
$597$	5.45292	−	9.44474i	0.223173	−	0.386547i
$598$		0			0
$599$	1.13106			0.0462139			0.0231070	−	0.999733i	$-0.492644\pi$
$599$	1.13106			0.0462139			0.0231070	+	0.999733i	$0.492644\pi$
$600$		0			0
$601$	3.46384	−	2.51662i	0.141293	−	0.102655i	−0.514894	−	0.857254i	$-0.672169\pi$
$601$	3.46384	−	2.51662i	0.141293	−	0.102655i	0.656186	+	0.754599i	$0.272169\pi$
$602$		0			0
$603$	−5.57758	−	6.19453i	−0.227137	−	0.252261i
$604$		0			0
$605$	−3.33928	−	31.7711i	−0.135761	−	1.29168i
$606$		0			0
$607$	−11.7554	−	36.1794i	−0.477137	−	1.46848i	−0.843053	−	0.537830i	$-0.819244\pi$
$607$	−11.7554	−	36.1794i	−0.477137	−	1.46848i	0.365916	−	0.930648i	$-0.380756\pi$
$608$		0			0
$609$	67.5197			2.73604
$610$		0			0
$611$	1.71535			0.0693956
$612$		0			0
$613$	−9.36834	−	28.8328i	−0.378384	−	1.16455i	−0.941167	−	0.337941i	$-0.890270\pi$
$613$	−9.36834	−	28.8328i	−0.378384	−	1.16455i	0.562784	−	0.826604i	$-0.309730\pi$
$614$		0			0
$615$	−6.29974	−	59.9380i	−0.254030	−	2.41693i
$616$		0			0
$617$	−21.7879	−	24.1979i	−0.877147	−	0.974170i	0.122686	−	0.992445i	$-0.460849\pi$
$617$	−21.7879	−	24.1979i	−0.877147	−	0.974170i	−0.999833	+	0.0182754i	$0.994182\pi$
$618$		0			0
$619$	−8.29811	+	6.02893i	−0.333529	+	0.242323i	−0.741927	−	0.670481i	$-0.766088\pi$
$619$	−8.29811	+	6.02893i	−0.333529	+	0.242323i	0.408397	+	0.912804i	$0.366088\pi$
$620$		0			0
$621$	9.34808			0.375125
$622$		0			0
$623$	1.78353	−	3.08916i	0.0714555	−	0.123765i
$624$		0			0
$625$	−27.2657	+	12.1395i	−1.09063	+	0.485578i
$626$		0			0
$627$	3.64188	+	1.62147i	0.145443	+	0.0647553i
$628$		0			0
$629$	−13.2160	+	14.6779i	−0.526956	+	0.585244i
$630$		0			0
$631$	1.78884	−	3.09836i	0.0712125	−	0.123344i	−0.828220	−	0.560402i	$-0.810646\pi$
$631$	1.78884	−	3.09836i	0.0712125	−	0.123344i	0.899433	+	0.437059i	$0.143980\pi$
$632$		0			0
$633$	−23.1713	+	16.8349i	−0.920975	+	0.669128i
$634$		0			0
$635$	20.2999	−	4.31488i	0.805578	−	0.171231i
$636$		0			0
$637$	0.523765	+	0.380538i	0.0207523	+	0.0150774i
$638$		0			0
$639$	4.78038	+	8.27986i	0.189109	+	0.327546i
$640$		0			0
$641$	11.0052	−	2.33923i	0.434679	−	0.0923940i	0.0146254	−	0.999893i	$-0.495344\pi$
$641$	11.0052	−	2.33923i	0.434679	−	0.0923940i	0.420054	+	0.907499i	$0.362011\pi$
$642$		0			0
$643$	7.97652	+	24.5492i	0.314563	+	0.968126i	0.975934	+	0.218067i	$0.0699750\pi$
$643$	7.97652	+	24.5492i	0.314563	+	0.968126i	−0.661371	+	0.750059i	$0.730025\pi$
$644$		0			0
$645$	59.3092	−	65.8696i	2.33530	−	2.59361i
$646$		0			0
$647$	1.52794	−	4.70250i	0.0600694	−	0.184875i	−0.916519	−	0.399991i	$-0.869013\pi$
$647$	1.52794	−	4.70250i	0.0600694	−	0.184875i	0.976588	+	0.215117i	$0.0690132\pi$
$648$		0			0
$649$	−1.85097	−	0.393437i	−0.0726571	−	0.0154437i
$650$		0			0
$651$	8.32631	−	25.6257i	0.326334	−	1.00435i
$652$		0			0
$653$	34.9778	−	15.5731i	1.36879	−	0.609423i	0.414977	−	0.909832i	$-0.363790\pi$
$653$	34.9778	−	15.5731i	1.36879	−	0.609423i	0.953811	+	0.300409i	$0.0971231\pi$
$654$		0			0
$655$	2.68196	+	2.97862i	0.104793	+	0.116384i
$656$		0			0
$657$	2.38803	+	4.13620i	0.0931661	+	0.161368i
$658$		0			0
$659$	1.99488	−	18.9801i	0.0777096	−	0.739358i	−0.884406	−	0.466718i	$-0.845436\pi$
$659$	1.99488	−	18.9801i	0.0777096	−	0.739358i	0.962116	−	0.272640i	$-0.0878969\pi$
$660$		0			0
$661$	1.69390	−	16.1164i	0.0658850	−	0.626854i	−0.910899	−	0.412629i	$-0.864611\pi$
$661$	1.69390	−	16.1164i	0.0658850	−	0.626854i	0.976784	−	0.214225i	$-0.0687227\pi$
$662$		0			0
$663$	−5.30217	−	3.85225i	−0.205919	−	0.149609i
$664$		0			0
$665$	3.26061	+	31.0226i	0.126441	+	1.20301i
$666$		0			0
$667$	−11.0197	−	4.90629i	−0.426684	−	0.189972i
$668$		0			0
$669$	13.1302	+	2.79090i	0.507641	+	0.107902i
$670$		0			0
$671$	−1.86262	+	2.50638i	−0.0719057	+	0.0967578i
$672$		0			0
$673$	28.0725	+	5.96699i	1.08211	+	0.230010i	0.714265	−	0.699875i	$-0.246761\pi$
$673$	28.0725	+	5.96699i	1.08211	+	0.230010i	0.367849	+	0.929886i	$0.380094\pi$
$674$		0			0
$675$	20.4159	+	9.08976i	0.785810	+	0.349865i
$676$		0			0
$677$	−4.11774	−	39.1777i	−0.158258	−	1.50572i	−0.728956	−	0.684561i	$-0.759994\pi$
$677$	−4.11774	−	39.1777i	−0.158258	−	1.50572i	0.570698	−	0.821160i	$-0.306673\pi$
$678$		0			0
$679$	−5.12653	−	3.72464i	−0.196738	−	0.142939i
$680$		0			0
$681$	−5.33138	+	50.7247i	−0.204299	+	1.94377i
$682$		0			0
$683$	0.0207977	−	0.197877i	0.000795801	−	0.00757154i	−0.994117	−	0.108313i	$-0.965455\pi$
$683$	0.0207977	−	0.197877i	0.000795801	−	0.00757154i	0.994913	+	0.100742i	$0.0321216\pi$
$684$		0			0
$685$	11.2830	+	19.5428i	0.431102	+	0.746690i
$686$		0			0
$687$	−42.7861	−	47.5187i	−1.63239	−	1.81295i
$688$		0			0
$689$	1.65003	−	0.734641i	0.0628611	−	0.0279876i
$690$		0			0
$691$	−5.16059	+	15.8827i	−0.196318	+	0.604205i	0.803641	+	0.595115i	$0.202893\pi$
$691$	−5.16059	+	15.8827i	−0.196318	+	0.604205i	−0.999959	+	0.00908993i	$0.997107\pi$
$692$		0			0
$693$	−6.06862	−	1.28992i	−0.230528	−	0.0490002i
$694$		0			0
$695$	7.10235	−	21.8588i	0.269407	−	0.829151i
$696$		0			0
$697$	36.8007	−	40.8713i	1.39393	−	1.54811i
$698$		0			0
$699$	15.7429	+	48.4516i	0.595451	+	1.83261i
$700$		0			0
$701$	37.4901	−	7.96877i	1.41598	−	0.300976i	0.564531	−	0.825412i	$-0.309057\pi$
$701$	37.4901	−	7.96877i	1.41598	−	0.300976i	0.851450	+	0.524436i	$0.175724\pi$
$702$		0			0
$703$	4.50505	+	7.80298i	0.169911	+	0.294295i
$704$		0			0
$705$	−38.8830	−	28.2502i	−1.46442	−	1.06396i
$706$		0			0
$707$	3.16895	−	0.673581i	0.119181	−	0.0253326i
$708$		0			0
$709$	24.1861	−	17.5722i	0.908328	−	0.659939i	−0.0322633	−	0.999479i	$-0.510272\pi$
$709$	24.1861	−	17.5722i	0.908328	−	0.659939i	0.940591	+	0.339540i	$0.110272\pi$
$710$		0			0
$711$	−6.60519	+	11.4405i	−0.247714	+	0.429053i
$712$		0			0
$713$	−3.22100	+	3.57728i	−0.120627	+	0.133970i
$714$		0			0
$715$	−0.322765	−	0.143704i	−0.0120707	−	0.00537424i
$716$		0			0
$717$	41.5780	−	18.5117i	1.55276	−	0.691333i
$718$		0			0
$719$	−23.9267	+	41.4423i	−0.892315	+	1.54554i	−0.0552231	+	0.998474i	$0.517587\pi$
$719$	−23.9267	+	41.4423i	−0.892315	+	1.54554i	−0.837092	+	0.547062i	$0.815746\pi$
$720$		0			0
$721$	−25.5759			−0.952495
$722$		0			0
$723$	7.81624	−	5.67883i	0.290689	−	0.211198i
$724$		0			0
$725$	−19.2960	−	21.4304i	−0.716636	−	0.795905i
$726$		0			0
$727$	−3.99403	−	38.0007i	−0.148130	−	1.40937i	−0.775845	−	0.630923i	$-0.782676\pi$
$727$	−3.99403	−	38.0007i	−0.148130	−	1.40937i	0.627715	−	0.778443i	$-0.283990\pi$
$728$		0			0
$729$	−13.0059	−	40.0280i	−0.481699	−	1.48252i
$730$		0			0
$731$	80.8851			2.99164
$732$		0			0
$733$	−41.8494			−1.54574			−0.772871	−	0.634563i	$-0.781180\pi$
$733$	−41.8494			−1.54574			−0.772871	+	0.634563i	$0.781180\pi$
$734$		0			0
$735$	−5.60546	−	17.2518i	−0.206760	−	0.636343i
$736$		0			0
$737$	−0.0679428	−	0.646433i	−0.00250271	−	0.0238116i
$738$		0			0
$739$	22.8634	+	25.3924i	0.841045	+	0.934075i	0.998571	−	0.0534399i	$-0.0170186\pi$
$739$	22.8634	+	25.3924i	0.841045	+	0.934075i	−0.157526	+	0.987515i	$0.550352\pi$
$740$		0			0
$741$	−2.41877	+	1.75734i	−0.0888557	+	0.0645574i
$742$		0			0
$743$	17.0680			0.626165			0.313082	−	0.949726i	$-0.398638\pi$
$743$	17.0680			0.626165			0.313082	+	0.949726i	$0.398638\pi$
$744$		0			0
$745$	7.97380	−	13.8110i	0.292138	−	0.505997i
$746$		0			0
$747$	−35.9827	+	16.0205i	−1.31654	+	0.586161i
$748$		0			0
$749$	42.7990	+	19.0554i	1.56384	+	0.696268i
$750$		0			0
$751$	9.39979	−	10.4395i	0.343003	−	0.380943i	−0.546819	−	0.837251i	$-0.684162\pi$
$751$	9.39979	−	10.4395i	0.343003	−	0.380943i	0.889822	+	0.456307i	$0.150828\pi$
$752$		0			0
$753$	30.4209	−	52.6905i	1.10860	−	1.92015i
$754$		0			0
$755$	−13.7889	+	10.0182i	−0.501829	+	0.364600i
$756$		0			0
$757$	14.1935	−	3.01692i	0.515872	−	0.109652i	0.0573833	−	0.998352i	$-0.481724\pi$
$757$	14.1935	−	3.01692i	0.515872	−	0.109652i	0.458489	+	0.888700i	$0.348391\pi$
$758$		0			0
$759$	1.42137	+	1.03269i	0.0515926	+	0.0374842i
$760$		0			0
$761$	2.12245	+	3.67619i	0.0769387	+	0.133262i	0.901928	−	0.431887i	$-0.142152\pi$
$761$	2.12245	+	3.67619i	0.0769387	+	0.133262i	−0.824989	+	0.565149i	$0.808819\pi$
$762$		0			0
$763$	58.5799	−	12.4515i	2.12074	−	0.450776i
$764$		0			0
$765$	35.7991	+	110.178i	1.29432	+	3.98350i
$766$		0			0
$767$	0.949615	−	1.05465i	0.0342886	−	0.0380813i
$768$		0			0
$769$	−10.5372	+	32.4303i	−0.379982	+	1.16947i	0.560073	+	0.828443i	$0.310773\pi$
$769$	−10.5372	+	32.4303i	−0.379982	+	1.16947i	−0.940055	+	0.341022i	$0.889227\pi$
$770$		0			0
$771$	8.22279	+	1.74781i	0.296137	+	0.0629458i
$772$		0			0
$773$	−6.50037	+	20.0061i	−0.233802	+	0.719568i	0.763476	+	0.645836i	$0.223491\pi$
$773$	−6.50037	+	20.0061i	−0.233802	+	0.719568i	−0.997278	+	0.0737323i	$0.976509\pi$
$774$		0			0
$775$	−10.5130	+	4.68069i	−0.377638	+	0.168135i
$776$		0			0
$777$	−14.8726	−	16.5177i	−0.533551	−	0.592568i
$778$		0			0
$779$	−12.5446	−	21.7278i	−0.449456	−	0.778481i
$780$		0			0
$781$	−0.0779293	+	0.741448i	−0.00278853	+	0.0265311i
$782$		0			0
$783$	4.96109	−	47.2016i	0.177295	−	1.68685i
$784$		0			0
$785$	−7.73748	−	5.62161i	−0.276163	−	0.200644i
$786$		0			0
$787$	−4.39936	−	41.8571i	−0.156820	−	1.49205i	−0.736075	−	0.676900i	$-0.763323\pi$
$787$	−4.39936	−	41.8571i	−0.156820	−	1.49205i	0.579255	−	0.815147i	$-0.303344\pi$
$788$		0			0
$789$	0.757101	+	0.337083i	0.0269535	+	0.0120005i
$790$		0			0
$791$	22.6838	+	4.82159i	0.806544	+	0.171436i
$792$		0			0
$793$	−0.929417	−	2.14960i	−0.0330046	−	0.0763345i
$794$		0			0
$795$	−49.5012	−	10.5218i	−1.75563	−	0.373170i
$796$		0			0
$797$	48.2610	+	21.4872i	1.70949	+	0.761114i	0.998311	+	0.0581046i	$0.0185057\pi$
$797$	48.2610	+	21.4872i	1.70949	+	0.761114i	0.711180	+	0.703010i	$0.248161\pi$
$798$		0			0
$799$	−4.58452	−	43.6188i	−0.162189	−	1.54312i
$800$		0			0
$801$	−4.88916	−	3.55218i	−0.172750	−	0.125510i
$802$		0			0
$803$	−0.0389295	+	0.370390i	−0.00137379	+	0.0130708i
$804$		0			0
$805$	−1.43699	+	13.6720i	−0.0506472	+	0.481876i
$806$		0			0
$807$	31.9399	+	55.3216i	1.12434	+	1.94741i
$808$		0			0
$809$	1.43828	+	1.59737i	0.0505671	+	0.0561604i	0.767898	−	0.640573i	$-0.221303\pi$
$809$	1.43828	+	1.59737i	0.0505671	+	0.0561604i	−0.717331	+	0.696733i	$0.754636\pi$
$810$		0			0
$811$	−34.2125	+	15.2324i	−1.20136	+	0.534882i	−0.907130	−	0.420851i	$-0.861731\pi$
$811$	−34.2125	+	15.2324i	−1.20136	+	0.534882i	−0.294235	+	0.955733i	$0.595065\pi$
$812$		0			0
$813$	7.34540	−	22.6068i	0.257615	−	0.792856i
$814$		0			0
$815$	−53.4072	−	11.3521i	−1.87077	−	0.397645i
$816$		0			0
$817$	11.4023	−	35.0926i	0.398915	−	1.22774i
$818$		0			0
$819$	3.11342	−	3.45780i	0.108792	−	0.120825i
$820$		0			0
$821$	−6.94124	−	21.3629i	−0.242251	−	0.745571i	−0.996076	−	0.0884968i	$-0.971794\pi$
$821$	−6.94124	−	21.3629i	−0.242251	−	0.745571i	0.753826	−	0.657074i	$-0.228206\pi$
$822$		0			0
$823$	6.04547	−	1.28500i	0.210732	−	0.0447924i	−0.101336	−	0.994852i	$-0.532312\pi$
$823$	6.04547	−	1.28500i	0.210732	−	0.0447924i	0.312068	+	0.950060i	$0.398978\pi$
$824$		0			0
$825$	2.10009	+	3.63746i	0.0731157	+	0.126640i
$826$		0			0
$827$	28.4531	+	20.6724i	0.989412	+	0.718850i	0.959792	−	0.280712i	$-0.0905704\pi$
$827$	28.4531	+	20.6724i	0.989412	+	0.718850i	0.0296195	+	0.999561i	$0.490570\pi$
$828$		0			0
$829$	43.1132	−	9.16400i	1.49738	−	0.318279i	0.614894	−	0.788610i	$-0.289199\pi$
$829$	43.1132	−	9.16400i	1.49738	−	0.318279i	0.882490	+	0.470331i	$0.155865\pi$
$830$		0			0
$831$	−27.0467	+	19.6506i	−0.938241	+	0.681672i
$832$		0			0
$833$	8.27667	−	14.3356i	0.286770	−	0.496700i
$834$		0			0
$835$	−18.4634	+	20.5057i	−0.638954	+	0.709630i
$836$		0			0
$837$	−17.3026	−	7.70363i	−0.598067	−	0.266276i
$838$		0			0
$839$	38.2712	−	17.0394i	1.32127	−	0.588267i	0.379707	−	0.925107i	$-0.376025\pi$
$839$	38.2712	−	17.0394i	1.32127	−	0.588267i	0.941562	+	0.336840i	$0.109358\pi$
$840$		0			0
$841$	−16.1217	+	27.9236i	−0.555921	+	0.962884i
$842$		0			0
$843$	32.6968			1.12614
$844$		0			0
$845$	−30.7801	+	22.3630i	−1.05887	+	0.769311i
$846$		0			0
$847$	21.9519	+	24.3801i	0.754276	+	0.837709i
$848$		0			0
$849$	−5.12270	−	48.7392i	−0.175811	−	1.67273i
$850$		0			0
$851$	1.22706	+	3.77651i	0.0420632	+	0.129457i
$852$		0			0
$853$	45.4221			1.55522			0.777612	−	0.628745i	$-0.216431\pi$
$853$	45.4221			1.55522			0.777612	+	0.628745i	$0.216431\pi$
$854$		0			0
$855$	52.8482			1.80737
$856$		0			0
$857$	10.0708	+	30.9949i	0.344014	+	1.05876i	0.962110	+	0.272662i	$0.0879042\pi$
$857$	10.0708	+	30.9949i	0.344014	+	1.05876i	−0.618096	+	0.786102i	$0.712096\pi$
$858$		0			0
$859$	−4.50812	−	42.8919i	−0.153815	−	1.46345i	−0.750444	−	0.660934i	$-0.770160\pi$
$859$	−4.50812	−	42.8919i	−0.153815	−	1.46345i	0.596629	−	0.802517i	$-0.296506\pi$
$860$		0			0
$861$	41.4135	+	45.9944i	1.41137	+	1.56748i
$862$		0			0
$863$	15.0924	−	10.9653i	0.513752	−	0.373263i	−0.300493	−	0.953784i	$-0.597151\pi$
$863$	15.0924	−	10.9653i	0.513752	−	0.373263i	0.814245	+	0.580521i	$0.197151\pi$
$864$		0			0
$865$	−3.69243			−0.125546
$866$		0			0
$867$	−59.5540	+	103.151i	−2.02256	+	3.50318i
$868$		0			0
$869$	−0.941065	+	0.418989i	−0.0319234	+	0.0142132i
$870$		0			0
$871$	0.445328	+	0.198273i	0.0150894	+	0.00671821i
$872$		0			0
$873$	−7.18361	+	7.97821i	−0.243128	+	0.270021i
$874$		0			0
$875$	5.86455	−	10.1577i	0.198258	−	0.343393i
$876$		0			0
$877$	−23.6587	+	17.1891i	−0.798899	+	0.580434i	−0.910591	−	0.413309i	$-0.864373\pi$
$877$	−23.6587	+	17.1891i	−0.798899	+	0.580434i	0.111692	+	0.993743i	$0.464373\pi$
$878$		0			0
$879$	44.0469	−	9.36246i	1.48567	−	0.315788i
$880$		0			0
$881$	−12.1004	−	8.79144i	−0.407672	−	0.296191i	0.364987	−	0.931013i	$-0.381074\pi$
$881$	−12.1004	−	8.79144i	−0.407672	−	0.296191i	−0.772659	+	0.634822i	$0.781074\pi$
$882$		0			0
$883$	−21.7091	−	37.6013i	−0.730570	−	1.26539i	−0.956640	−	0.291274i	$-0.905921\pi$
$883$	−21.7091	−	37.6013i	−0.730570	−	1.26539i	0.226069	−	0.974111i	$-0.427412\pi$
$884$		0			0
$885$	−38.8947	+	8.26733i	−1.30743	+	0.277903i
$886$		0			0
$887$	−18.1772	−	55.9436i	−0.610330	−	1.87840i	−0.454867	−	0.890559i	$-0.650313\pi$
$887$	−18.1772	−	55.9436i	−0.610330	−	1.87840i	−0.155463	−	0.987842i	$-0.549687\pi$
$888$		0			0
$889$	−14.2608	+	15.8382i	−0.478293	+	0.531198i
$890$		0			0
$891$	−0.235692	+	0.725385i	−0.00789598	+	0.0243013i
$892$		0			0
$893$	−19.5706	−	4.15987i	−0.654906	−	0.139205i
$894$		0			0
$895$	−10.9226	+	33.6163i	−0.365102	+	1.12367i
$896$		0			0
$897$	−1.20371	+	0.535926i	−0.0401907	+	0.0178940i
$898$		0			0
$899$	16.3535	+	18.1624i	0.545419	+	0.605749i
$900$		0			0
$901$	−23.0908	−	39.9944i	−0.769266	−	1.33241i
$902$		0			0
$903$	−9.51458	+	90.5252i	−0.316625	+	3.01249i
$904$		0			0
$905$	−7.14889	+	68.0171i	−0.237637	+	2.26096i
$906$		0			0
$907$	32.6510	+	23.7223i	1.08416	+	0.787688i	0.978403	−	0.206705i	$-0.0662739\pi$
$907$	32.6510	+	23.7223i	1.08416	+	0.787688i	0.105756	+	0.994392i	$0.466274\pi$
$908$		0			0
$909$	−0.573735	−	5.45873i	−0.0190296	−	0.181055i
$910$		0			0
$911$	−8.47793	−	3.77462i	−0.280886	−	0.125059i	0.261458	−	0.965215i	$-0.415797\pi$
$911$	−8.47793	−	3.77462i	−0.280886	−	0.125059i	−0.542345	+	0.840156i	$0.682463\pi$
$912$		0			0
$913$	−3.00429	−	0.638582i	−0.0994276	−	0.0211340i
$914$		0			0
$915$	−14.3341	+	64.0331i	−0.473871	+	2.11687i
$916$		0			0
$917$	−4.02615	−	0.855785i	−0.132955	−	0.0282605i
$918$		0			0
$919$	27.1997	+	12.1101i	0.897236	+	0.399475i	0.802934	−	0.596068i	$-0.203271\pi$
$919$	27.1997	+	12.1101i	0.897236	+	0.399475i	0.0943024	+	0.995544i	$0.469938\pi$
$920$		0			0
$921$	9.88375	+	94.0376i	0.325680	+	3.09864i
$922$		0			0
$923$	−0.452340	−	0.328644i	−0.0148889	−	0.0108175i
$924$		0			0
$925$	−0.992285	+	9.44096i	−0.0326261	+	0.310417i
$926$		0			0
$927$	−4.52930	+	43.0934i	−0.148762	+	1.41537i
$928$		0			0
$929$	5.86998	+	10.1671i	0.192588	+	0.333572i	0.946107	−	0.323854i	$-0.104979\pi$
$929$	5.86998	+	10.1671i	0.192588	+	0.333572i	−0.753519	+	0.657426i	$0.771645\pi$
$930$		0			0
$931$	−5.05286	−	5.61177i	−0.165601	−	0.183918i
$932$		0			0
$933$	−56.7864	+	25.2829i	−1.85910	+	0.827727i
$934$		0			0
$935$	−2.79155	+	8.59152i	−0.0912935	+	0.280973i
$936$		0			0
$937$	−39.0015	−	8.29004i	−1.27413	−	0.270824i	−0.479294	−	0.877654i	$-0.659107\pi$
$937$	−39.0015	−	8.29004i	−1.27413	−	0.270824i	−0.794831	+	0.606831i	$0.792441\pi$
$938$		0			0
$939$	23.1053	−	71.1108i	0.754013	−	2.32061i
$940$		0			0
$941$	−8.85595	+	9.83552i	−0.288696	+	0.320629i	−0.869995	−	0.493061i	$-0.835878\pi$
$941$	−8.85595	+	9.83552i	−0.288696	+	0.320629i	0.581299	+	0.813690i	$0.302545\pi$
$942$		0			0
$943$	−3.41683	−	10.5159i	−0.111267	−	0.342445i
$944$		0			0
$945$	−52.9085	+	11.2461i	−1.72111	+	0.365834i
$946$		0			0
$947$	23.2179	+	40.2146i	0.754480	+	1.30680i	0.945632	+	0.325237i	$0.105444\pi$
$947$	23.2179	+	40.2146i	0.754480	+	1.30680i	−0.191152	+	0.981560i	$0.561222\pi$
$948$		0			0
$949$	−0.225966	−	0.164174i	−0.00733516	−	0.00532931i
$950$		0			0
$951$	−41.2155	+	8.76062i	−1.33650	+	0.284083i
$952$		0			0
$953$	−5.72862	+	4.16208i	−0.185568	+	0.134823i	−0.676691	−	0.736267i	$-0.736587\pi$
$953$	−5.72862	+	4.16208i	−0.185568	+	0.134823i	0.491123	+	0.871090i	$0.336587\pi$
$954$		0			0
$955$	−25.4092	+	44.0100i	−0.822222	+	1.42413i
$956$		0			0
$957$	5.96873	−	6.62894i	0.192941	−	0.214283i
$958$		0			0
$959$	−21.1704	−	9.42566i	−0.683627	−	0.304371i
$960$		0			0
$961$	−19.4101	+	8.64192i	−0.626132	+	0.278772i
$962$		0			0
$963$	39.6863	−	68.7386i	1.27887	−	2.21507i
$964$		0			0
$965$	64.8180			2.08656
$966$		0			0
$967$	2.46303	−	1.78950i	0.0792057	−	0.0575463i	−0.547478	−	0.836820i	$-0.684412\pi$
$967$	2.46303	−	1.78950i	0.0792057	−	0.0575463i	0.626683	+	0.779274i	$0.284412\pi$
$968$		0			0
$969$	51.1510	+	56.8090i	1.64321	+	1.82497i
$970$		0			0
$971$	−0.484622	−	4.61087i	−0.0155523	−	0.147970i	0.983990	−	0.178224i	$-0.0570351\pi$
$971$	−0.484622	−	4.61087i	−0.0155523	−	0.147970i	−0.999542	+	0.0302539i	$0.990368\pi$
$972$		0			0
$973$	7.29366	+	22.4476i	0.233824	+	0.719636i
$974$		0			0
$975$	−3.14999			−0.100880
$976$		0			0
$977$	9.58007			0.306494			0.153247	−	0.988188i	$-0.451027\pi$
$977$	9.58007			0.306494			0.153247	+	0.988188i	$0.451027\pi$
$978$		0			0
$979$	−0.145624	−	0.448184i	−0.00465416	−	0.0143240i
$980$		0			0
$981$	−10.6058	−	100.908i	−0.338619	−	3.22174i
$982$		0			0
$983$	−23.1081	−	25.6642i	−0.737035	−	0.818560i	0.251768	−	0.967788i	$-0.418988\pi$
$983$	−23.1081	−	25.6642i	−0.737035	−	0.818560i	−0.988803	+	0.149227i	$0.952321\pi$
$984$		0			0
$985$	43.4199	−	31.5464i	1.38347	−	1.00515i
$986$		0			0
$987$	49.3567			1.57104
$988$		0			0
$989$	8.13082	−	14.0830i	0.258545	−	0.447813i
$990$		0			0
$991$	29.9992	−	13.3565i	0.952958	−	0.424284i	0.129448	−	0.991586i	$-0.458680\pi$
$991$	29.9992	−	13.3565i	0.952958	−	0.424284i	0.823510	+	0.567302i	$0.192013\pi$
$992$		0			0
$993$	−5.99849	−	2.67070i	−0.190356	−	0.0847521i
$994$		0			0
$995$	7.54359	−	8.37801i	0.239148	−	0.265601i
$996$		0			0
$997$	14.3243	−	24.8104i	0.453655	−	0.785753i	−0.544955	−	0.838465i	$-0.683453\pi$
$997$	14.3243	−	24.8104i	0.453655	−	0.785753i	0.998610	+	0.0527125i	$0.0167867\pi$
$998$		0			0
$999$	−12.6399	+	9.18345i	−0.399910	+	0.290552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.321.4		32
4.3	odd	2		61.2.i.a.16.4	✓	32
12.11	even	2		549.2.bl.b.199.1		32
61.42	even	15	inner	976.2.bw.c.225.4		32
244.15	odd	30		3721.2.a.j.1.6		16
244.103	odd	30		61.2.i.a.42.4	yes	32
244.107	odd	30		3721.2.a.l.1.11		16
732.347	even	30		549.2.bl.b.469.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.4	✓	32	4.3	odd	2
61.2.i.a.42.4	yes	32	244.103	odd	30
549.2.bl.b.199.1		32	12.11	even	2
549.2.bl.b.469.1		32	732.347	even	30
976.2.bw.c.225.4		32	61.42	even	15	inner
976.2.bw.c.321.4		32	1.1	even	1	trivial
3721.2.a.j.1.6		16	244.15	odd	30
3721.2.a.l.1.11		16	244.107	odd	30

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:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.880961 + 2.71132i) q^{3} +(0.308047 + 2.93087i) q^{5} +(-2.02506 - 2.24905i) q^{7} +(-4.14811 + 3.01378i) q^{9} -0.399822 q^{11} +(0.149926 - 0.259680i) q^{13} +(-7.67516 + 3.41720i) q^{15} +(-7.00397 - 3.11837i) q^{17} +(-2.34027 + 2.59913i) q^{19} +(4.31391 - 7.47190i) q^{21} +(-1.24700 + 0.906001i) q^{23} +(-3.60439 + 0.766136i) q^{25} +(-4.90648 - 3.56477i) q^{27} +(3.91291 + 6.77736i) q^{29} +(3.05474 - 0.649305i) q^{31} +(-0.352228 - 1.08404i) q^{33} +(5.96788 - 6.62800i) q^{35} +(0.796081 - 2.45008i) q^{37} +(0.836154 + 0.177730i) q^{39} +(-2.21673 + 6.82240i) q^{41} +(-9.63795 + 4.29109i) q^{43} +(-10.1108 - 11.2292i) q^{45} +(2.86033 + 4.95423i) q^{47} +(-0.225687 + 2.14727i) q^{49} +(2.28467 - 21.7372i) q^{51} +(4.87318 + 3.54057i) q^{53} +(-0.123164 - 1.17183i) q^{55} +(-9.10877 - 4.05548i) q^{57} +(4.62950 + 0.984030i) q^{59} +(4.65863 - 6.26875i) q^{61} +(15.1783 + 3.22625i) q^{63} +(0.807272 + 0.359421i) q^{65} +(0.169933 + 1.61680i) q^{67} +(-3.55502 - 2.58287i) q^{69} +(0.194910 - 1.85445i) q^{71} +(0.0973672 - 0.926387i) q^{73} +(-5.25256 - 9.09771i) q^{75} +(0.809662 + 0.899221i) q^{77} +(2.35371 - 1.04794i) q^{79} +(0.589492 - 1.81427i) q^{81} +(7.51408 + 1.59717i) q^{83} +(6.98199 - 21.4884i) q^{85} +(-14.9285 + 16.5797i) q^{87} +(0.364222 + 1.12096i) q^{89} +(-0.887642 + 0.188674i) q^{91} +(4.45158 + 7.71036i) q^{93} +(-8.33864 - 6.05838i) q^{95} +(2.04807 - 0.435330i) q^{97} +(1.65851 - 1.20497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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