LMFDB - Embedded newform 756.2.bp.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72645 + 0.139144i) q^{3} +(-0.604458 + 0.220005i) q^{5} +(-2.43449 - 1.03598i) q^{7} +(2.96128 - 0.480450i) q^{9} +O(q^{10})$	\(q+(-1.72645 + 0.139144i) q^{3} +(-0.604458 + 0.220005i) q^{5} +(-2.43449 - 1.03598i) q^{7} +(2.96128 - 0.480450i) q^{9} +(3.29749 + 1.20019i) q^{11} +(3.30070 - 1.20136i) q^{13} +(1.01296 - 0.463934i) q^{15} +(-3.32777 - 5.76387i) q^{17} +(-3.85167 + 6.67129i) q^{19} +(4.34718 + 1.44983i) q^{21} +(-0.950630 + 5.39129i) q^{23} +(-3.51325 + 2.94797i) q^{25} +(-5.04565 + 1.24152i) q^{27} +(-4.55828 - 1.65908i) q^{29} +(-2.08254 + 0.757984i) q^{31} +(-5.85995 - 1.61324i) q^{33} +(1.69947 + 0.0906102i) q^{35} -0.0346577 q^{37} +(-5.53135 + 2.53336i) q^{39} +(-10.3758 + 3.77650i) q^{41} +(1.18835 + 6.73949i) q^{43} +(-1.68427 + 0.941907i) q^{45} +(1.51245 + 0.550488i) q^{47} +(4.85347 + 5.04419i) q^{49} +(6.54725 + 9.48802i) q^{51} +(-0.109688 + 0.189985i) q^{53} -2.25724 q^{55} +(5.72146 - 12.0536i) q^{57} +(-8.00526 - 6.71721i) q^{59} +(5.71836 + 2.08131i) q^{61} +(-7.70694 - 1.89819i) q^{63} +(-1.73083 + 1.45234i) q^{65} +(1.88174 - 10.6719i) q^{67} +(0.891053 - 9.44008i) q^{69} +(-6.84419 + 11.8545i) q^{71} +3.55317 q^{73} +(5.65528 - 5.57838i) q^{75} +(-6.78432 - 6.33798i) q^{77} +(2.62111 + 14.8650i) q^{79} +(8.53834 - 2.84549i) q^{81} +(-11.6151 - 4.22756i) q^{83} +(3.27958 + 2.75189i) q^{85} +(8.10051 + 2.23007i) q^{87} +(2.25492 - 3.90564i) q^{89} +(-9.28011 - 0.494786i) q^{91} +(3.48995 - 1.59840i) q^{93} +(0.860458 - 4.87990i) q^{95} +(2.53604 + 14.3826i) q^{97} +(10.3414 + 1.96981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.72645	+	0.139144i	−0.996768	+	0.0803347i
$3$	−1.72645	+	0.139144i	−0.996768	+	0.0803347i
$4$		0			0
$5$	−0.604458	+	0.220005i	−0.270322	+	0.0983891i	−0.473625	−	0.880727i	$-0.657055\pi$
$5$	−0.604458	+	0.220005i	−0.270322	+	0.0983891i	0.203303	+	0.979116i	$0.434832\pi$
$6$		0			0
$7$	−2.43449	−	1.03598i	−0.920150	−	0.391565i
$7$	−2.43449	−	1.03598i	−0.920150	−	0.391565i
$8$		0			0
$9$	2.96128	−	0.480450i	0.987093	−	0.160150i
$10$		0			0
$11$	3.29749	+	1.20019i	0.994229	+	0.361870i	0.787356	−	0.616498i	$-0.211449\pi$
$11$	3.29749	+	1.20019i	0.994229	+	0.361870i	0.206873	+	0.978368i	$0.433671\pi$
$12$		0			0
$13$	3.30070	−	1.20136i	0.915450	−	0.333197i	0.159023	−	0.987275i	$-0.449166\pi$
$13$	3.30070	−	1.20136i	0.915450	−	0.333197i	0.756427	+	0.654078i	$0.226943\pi$
$14$		0			0
$15$	1.01296	−	0.463934i	0.261544	−	0.119787i
$16$		0			0
$17$	−3.32777	−	5.76387i	−0.807104	−	1.39794i	−0.914862	−	0.403768i	$-0.867700\pi$
$17$	−3.32777	−	5.76387i	−0.807104	−	1.39794i	0.107758	−	0.994177i	$-0.465633\pi$
$18$		0			0
$19$	−3.85167	+	6.67129i	−0.883634	+	1.53050i	−0.0363620	+	0.999339i	$0.511577\pi$
$19$	−3.85167	+	6.67129i	−0.883634	+	1.53050i	−0.847272	+	0.531160i	$0.821756\pi$
$20$		0			0
$21$	4.34718	+	1.44983i	0.948633	+	0.316380i
$22$		0			0
$23$	−0.950630	+	5.39129i	−0.198220	+	1.12416i	0.709538	+	0.704667i	$0.248904\pi$
$23$	−0.950630	+	5.39129i	−0.198220	+	1.12416i	−0.907758	+	0.419494i	$0.862207\pi$
$24$		0			0
$25$	−3.51325	+	2.94797i	−0.702651	+	0.589594i
$26$		0			0
$27$	−5.04565	+	1.24152i	−0.971037	+	0.238930i
$28$		0			0
$29$	−4.55828	−	1.65908i	−0.846452	−	0.308083i	−0.117859	−	0.993030i	$-0.537603\pi$
$29$	−4.55828	−	1.65908i	−0.846452	−	0.308083i	−0.728593	+	0.684947i	$0.759825\pi$
$30$		0			0
$31$	−2.08254	+	0.757984i	−0.374036	+	0.136138i	−0.522196	−	0.852825i	$-0.674887\pi$
$31$	−2.08254	+	0.757984i	−0.374036	+	0.136138i	0.148160	+	0.988963i	$0.452665\pi$
$32$		0			0
$33$	−5.85995	−	1.61324i	−1.02009	−	0.280829i
$34$		0			0
$35$	1.69947	+	0.0906102i	0.287263	+	0.0153159i
$36$		0			0
$37$	−0.0346577			−0.00569769			−0.00284885	−	0.999996i	$-0.500907\pi$
$37$	−0.0346577			−0.00569769			−0.00284885	+	0.999996i	$0.500907\pi$
$38$		0			0
$39$	−5.53135	+	2.53336i	−0.885724	+	0.405662i
$40$		0			0
$41$	−10.3758	+	3.77650i	−1.62044	+	0.589790i	−0.983465	−	0.181098i	$-0.942035\pi$
$41$	−10.3758	+	3.77650i	−1.62044	+	0.589790i	−0.636970	+	0.770888i	$0.719813\pi$
$42$		0			0
$43$	1.18835	+	6.73949i	0.181222	+	1.02776i	0.930714	+	0.365748i	$0.119187\pi$
$43$	1.18835	+	6.73949i	0.181222	+	1.02776i	−0.749492	+	0.662014i	$0.769702\pi$
$44$		0			0
$45$	−1.68427	+	0.941907i	−0.251076	+	0.140411i
$46$		0			0
$47$	1.51245	+	0.550488i	0.220614	+	0.0802969i	0.449962	−	0.893047i	$-0.351437\pi$
$47$	1.51245	+	0.550488i	0.220614	+	0.0802969i	−0.229349	+	0.973344i	$0.573660\pi$
$48$		0			0
$49$	4.85347	+	5.04419i	0.693353	+	0.720598i
$50$		0			0
$51$	6.54725	+	9.48802i	0.916799	+	1.32859i
$52$		0			0
$53$	−0.109688	+	0.189985i	−0.0150668	+	0.0260964i	−0.873460	−	0.486895i	$-0.838129\pi$
$53$	−0.109688	+	0.189985i	−0.0150668	+	0.0260964i	0.858394	+	0.512991i	$0.171463\pi$
$54$		0			0
$55$	−2.25724			−0.304366
$56$		0			0
$57$	5.72146	−	12.0536i	0.757826	−	1.59654i
$58$		0			0
$59$	−8.00526	−	6.71721i	−1.04220	−	0.874507i	−0.0499448	−	0.998752i	$-0.515905\pi$
$59$	−8.00526	−	6.71721i	−1.04220	−	0.874507i	−0.992252	+	0.124245i	$0.960349\pi$
$60$		0			0
$61$	5.71836	+	2.08131i	0.732161	+	0.266485i	0.681079	−	0.732210i	$-0.261511\pi$
$61$	5.71836	+	2.08131i	0.732161	+	0.266485i	0.0510814	+	0.998694i	$0.483733\pi$
$62$		0			0
$63$	−7.70694	−	1.89819i	−0.970983	−	0.239149i
$64$		0			0
$65$	−1.73083	+	1.45234i	−0.214683	+	0.180141i
$66$		0			0
$67$	1.88174	−	10.6719i	0.229892	−	1.30378i	−0.623218	−	0.782048i	$-0.714175\pi$
$67$	1.88174	−	10.6719i	0.229892	−	1.30378i	0.853110	−	0.521732i	$-0.174714\pi$
$68$		0			0
$69$	0.891053	−	9.44008i	0.107270	−	1.13645i
$70$		0			0
$71$	−6.84419	+	11.8545i	−0.812256	+	1.40687i	0.0990264	+	0.995085i	$0.468427\pi$
$71$	−6.84419	+	11.8545i	−0.812256	+	1.40687i	−0.911282	+	0.411783i	$0.864906\pi$
$72$		0			0
$73$	3.55317			0.415867			0.207934	−	0.978143i	$-0.433326\pi$
$73$	3.55317			0.415867			0.207934	+	0.978143i	$0.433326\pi$
$74$		0			0
$75$	5.65528	−	5.57838i	0.653015	−	0.644136i
$76$		0			0
$77$	−6.78432	−	6.33798i	−0.773145	−	0.722280i
$78$		0			0
$79$	2.62111	+	14.8650i	0.294898	+	1.67245i	0.667618	+	0.744504i	$0.267314\pi$
$79$	2.62111	+	14.8650i	0.294898	+	1.67245i	−0.372720	+	0.927944i	$0.621575\pi$
$80$		0			0
$81$	8.53834	−	2.84549i	0.948704	−	0.316166i
$82$		0			0
$83$	−11.6151	−	4.22756i	−1.27493	−	0.464035i	−0.386175	−	0.922426i	$-0.626204\pi$
$83$	−11.6151	−	4.22756i	−1.27493	−	0.464035i	−0.888751	+	0.458391i	$0.848426\pi$
$84$		0			0
$85$	3.27958	+	2.75189i	0.355720	+	0.298485i
$86$		0			0
$87$	8.10051	+	2.23007i	0.868466	+	0.239088i
$88$		0			0
$89$	2.25492	−	3.90564i	0.239021	−	0.413997i	−0.721413	−	0.692506i	$-0.756507\pi$
$89$	2.25492	−	3.90564i	0.239021	−	0.413997i	0.960434	+	0.278509i	$0.0898401\pi$
$90$		0			0
$91$	−9.28011	−	0.494786i	−0.972820	−	0.0518676i
$92$		0			0
$93$	3.48995	−	1.59840i	0.361891	−	0.165746i
$94$		0			0
$95$	0.860458	−	4.87990i	0.0882811	−	0.500667i
$96$		0			0
$97$	2.53604	+	14.3826i	0.257495	+	1.46033i	0.789585	+	0.613641i	$0.210296\pi$
$97$	2.53604	+	14.3826i	0.257495	+	1.46033i	−0.532090	+	0.846688i	$0.678593\pi$
$98$		0			0
$99$	10.3414	+	1.96981i	1.03935	+	0.197973i
$100$		0			0
$101$	2.26854	+	12.8656i	0.225729	+	1.28017i	0.861287	+	0.508118i	$0.169659\pi$
$101$	2.26854	+	12.8656i	0.225729	+	1.28017i	−0.635559	+	0.772052i	$0.719230\pi$
$102$		0			0
$103$	−7.54733	+	2.74700i	−0.743661	+	0.270670i	−0.685936	−	0.727662i	$-0.740607\pi$
$103$	−7.54733	+	2.74700i	−0.743661	+	0.270670i	−0.0577250	+	0.998333i	$0.518385\pi$
$104$		0			0
$105$	−2.94666	+	0.0800362i	−0.287565	+	0.00781073i
$106$		0			0
$107$	−1.89331	−	3.27931i	−0.183033	−	0.317023i	0.759879	−	0.650065i	$-0.225258\pi$
$107$	−1.89331	−	3.27931i	−0.183033	−	0.317023i	−0.942912	+	0.333042i	$0.891925\pi$
$108$		0			0
$109$	−5.73912	+	9.94045i	−0.549708	+	0.952122i	0.448586	+	0.893740i	$0.351928\pi$
$109$	−5.73912	+	9.94045i	−0.549708	+	0.952122i	−0.998294	+	0.0583829i	$0.981406\pi$
$110$		0			0
$111$	0.0598349	−	0.00482240i	0.00567928	−	0.000457722i
$112$		0			0
$113$	1.57495	−	8.93197i	0.148159	−	0.840249i	−0.816618	−	0.577179i	$-0.804154\pi$
$113$	1.57495	−	8.93197i	0.148159	−	0.840249i	0.964777	−	0.263071i	$-0.0847352\pi$
$114$		0			0
$115$	−0.611493	−	3.46795i	−0.0570221	−	0.323388i
$116$		0			0
$117$	9.19711	−	5.14338i	0.850273	−	0.475505i
$118$		0			0
$119$	2.13014	+	17.4796i	0.195270	+	1.60235i
$120$		0			0
$121$	1.00647	+	0.844530i	0.0914974	+	0.0767754i
$122$		0			0
$123$	17.3879	−	7.96368i	1.56782	−	0.718061i
$124$		0			0
$125$	3.08318	−	5.34022i	0.275768	−	0.477643i
$126$		0			0
$127$	−8.02947	−	13.9074i	−0.712500	−	1.23409i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$	−8.02947	−	13.9074i	−0.712500	−	1.23409i	0.251416	−	0.967879i	$-0.419104\pi$
$128$		0			0
$129$	−2.98939	−	11.4701i	−0.263201	−	1.00988i
$130$		0			0
$131$	3.47167	−	19.6888i	0.303321	−	1.72022i	−0.327983	−	0.944684i	$-0.606369\pi$
$131$	3.47167	−	19.6888i	0.303321	−	1.72022i	0.631304	−	0.775535i	$-0.282520\pi$
$132$		0			0
$133$	16.2882	−	12.2509i	1.41237	−	1.06229i
$134$		0			0
$135$	2.77675	−	1.86051i	0.238984	−	0.160128i
$136$		0			0
$137$	3.27993	−	2.75219i	0.280223	−	0.235135i	−0.491833	−	0.870690i	$-0.663673\pi$
$137$	3.27993	−	2.75219i	0.280223	−	0.235135i	0.772056	+	0.635554i	$0.219228\pi$
$138$		0			0
$139$	4.15561	+	3.48697i	0.352474	+	0.295761i	0.801783	−	0.597616i	$-0.203885\pi$
$139$	4.15561	+	3.48697i	0.352474	+	0.295761i	−0.449308	+	0.893377i	$0.648330\pi$
$140$		0			0
$141$	−2.68777	−	0.739943i	−0.226351	−	0.0623144i
$142$		0			0
$143$	12.3259			1.03074
$144$		0			0
$145$	3.12030			0.259127
$146$		0			0
$147$	−9.08116	−	8.03322i	−0.749001	−	0.662569i
$148$		0			0
$149$	5.10221	+	4.28126i	0.417990	+	0.350735i	0.827398	−	0.561616i	$-0.189820\pi$
$149$	5.10221	+	4.28126i	0.417990	+	0.350735i	−0.409408	+	0.912351i	$0.634265\pi$
$150$		0			0
$151$	13.8838	+	5.05328i	1.12985	+	0.411230i	0.838236	−	0.545307i	$-0.183587\pi$
$151$	13.8838	+	5.05328i	1.12985	+	0.411230i	0.291610	+	0.956537i	$0.405809\pi$
$152$		0			0
$153$	−12.6237	−	15.4696i	−1.02057	−	1.25064i
$154$		0			0
$155$	1.09205	−	0.916340i	0.0877157	−	0.0736022i
$156$		0			0
$157$	−13.2972	−	11.1576i	−1.06123	−	0.890476i	−0.0669990	−	0.997753i	$-0.521342\pi$
$157$	−13.2972	−	11.1576i	−1.06123	−	0.890476i	−0.994229	+	0.107277i	$0.965787\pi$
$158$		0			0
$159$	0.162936	−	0.343262i	0.0129216	−	0.0272225i
$160$		0			0
$161$	7.89959	−	12.1402i	0.622575	−	0.956781i
$162$		0			0
$163$	7.05815	+	12.2251i	0.552837	+	0.957542i	0.998068	+	0.0621265i	$0.0197882\pi$
$163$	7.05815	+	12.2251i	0.552837	+	0.957542i	−0.445231	+	0.895416i	$0.646878\pi$
$164$		0			0
$165$	3.89702	−	0.314081i	0.303382	−	0.0244511i
$166$		0			0
$167$	−2.33330	+	13.2328i	−0.180556	+	1.02398i	0.750977	+	0.660328i	$0.229583\pi$
$167$	−2.33330	+	13.2328i	−0.180556	+	1.02398i	−0.931533	+	0.363656i	$0.881528\pi$
$168$		0			0
$169$	−0.507199	+	0.425590i	−0.0390153	+	0.0327377i
$170$		0			0
$171$	−8.20064	+	21.6061i	−0.627119	+	1.65226i
$172$		0			0
$173$	1.82568	−	1.53192i	0.138804	−	0.116470i	−0.570742	−	0.821129i	$-0.693345\pi$
$173$	1.82568	−	1.53192i	0.138804	−	0.116470i	0.709546	+	0.704659i	$0.248900\pi$
$174$		0			0
$175$	11.6070	−	3.53712i	0.877409	−	0.267381i
$176$		0			0
$177$	14.7554	+	10.4831i	1.10908	+	0.787956i
$178$		0			0
$179$	−5.44831	−	9.43676i	−0.407226	−	0.705336i	0.587352	−	0.809332i	$-0.300171\pi$
$179$	−5.44831	−	9.43676i	−0.407226	−	0.705336i	−0.994578	+	0.103995i	$0.966837\pi$
$180$		0			0
$181$	−4.37784	−	7.58264i	−0.325402	−	0.563613i	0.656192	−	0.754594i	$-0.272166\pi$
$181$	−4.37784	−	7.58264i	−0.325402	−	0.563613i	−0.981594	+	0.190981i	$0.938833\pi$
$182$		0			0
$183$	−10.1621	−	2.79761i	−0.751202	−	0.206805i
$184$		0			0
$185$	0.0209491	−	0.00762487i	0.00154021	−	0.000560591i
$186$		0			0
$187$	−4.05556	−	23.0002i	−0.296572	−	1.68194i
$188$		0			0
$189$	13.5698	+	2.20476i	0.987057	+	0.160373i
$190$		0			0
$191$	−2.36119	−	13.3910i	−0.170850	−	0.968937i	−0.942826	−	0.333286i	$-0.891843\pi$
$191$	−2.36119	−	13.3910i	−0.170850	−	0.968937i	0.771976	−	0.635652i	$-0.219268\pi$
$192$		0			0
$193$	14.2146	−	5.17369i	1.02319	−	0.372410i	0.224705	−	0.974427i	$-0.427858\pi$
$193$	14.2146	−	5.17369i	1.02319	−	0.372410i	0.798484	+	0.602017i	$0.205636\pi$
$194$		0			0
$195$	2.78612	−	2.74823i	0.199518	−	0.196805i
$196$		0			0
$197$	−0.378230	−	0.655113i	−0.0269478	−	0.0466749i	0.852237	−	0.523156i	$-0.175245\pi$
$197$	−0.378230	−	0.655113i	−0.0269478	−	0.0466749i	−0.879185	+	0.476481i	$0.841912\pi$
$198$		0			0
$199$	9.62859	+	16.6772i	0.682552	+	1.18222i	0.974199	+	0.225689i	$0.0724634\pi$
$199$	9.62859	+	16.6772i	0.682552	+	1.18222i	−0.291647	+	0.956526i	$0.594203\pi$
$200$		0			0
$201$	−1.76381	+	18.6864i	−0.124410	+	1.31803i
$202$		0			0
$203$	9.37831	+	8.76132i	0.658228	+	0.614924i
$204$		0			0
$205$	5.44092	−	4.56547i	0.380010	−	0.318866i
$206$		0			0
$207$	−0.224833	+	16.4218i	−0.0156270	+	1.14140i
$208$		0			0
$209$	−20.7076	+	17.3758i	−1.43238	+	1.20191i
$210$		0			0
$211$	2.46519	−	13.9808i	0.169711	−	0.962478i	−0.774362	−	0.632742i	$-0.781929\pi$
$211$	2.46519	−	13.9808i	0.169711	−	0.962478i	0.944073	−	0.329736i	$-0.106960\pi$
$212$		0			0
$213$	10.1667	−	21.4185i	0.696610	−	1.46757i
$214$		0			0
$215$	−2.20103	−	3.81229i	−0.150109	−	0.259996i
$216$		0			0
$217$	5.85519	+	0.312180i	0.397476	+	0.0211922i
$218$		0			0
$219$	−6.13438	+	0.494402i	−0.414523	+	0.0334086i
$220$		0			0
$221$	−17.9085	−	15.0270i	−1.20465	−	1.01082i
$222$		0			0
$223$	−11.2980	+	9.48011i	−0.756567	+	0.634835i	−0.937231	−	0.348710i	$-0.886620\pi$
$223$	−11.2980	+	9.48011i	−0.756567	+	0.634835i	0.180664	+	0.983545i	$0.442175\pi$
$224$		0			0
$225$	−8.98737	+	10.4177i	−0.599158	+	0.694514i
$226$		0			0
$227$	4.36866	+	1.59006i	0.289958	+	0.105536i	0.482904	−	0.875673i	$-0.339582\pi$
$227$	4.36866	+	1.59006i	0.289958	+	0.105536i	−0.192946	+	0.981209i	$0.561804\pi$
$228$		0			0
$229$	−3.98379	−	3.34279i	−0.263256	−	0.220898i	0.501599	−	0.865100i	$-0.332745\pi$
$229$	−3.98379	−	3.34279i	−0.263256	−	0.220898i	−0.764855	+	0.644202i	$0.777190\pi$
$230$		0			0
$231$	12.5947	+	9.99823i	0.828670	+	0.657836i
$232$		0			0
$233$	4.44351			0.291104			0.145552	−	0.989351i	$-0.453504\pi$
$233$	4.44351			0.291104			0.145552	+	0.989351i	$0.453504\pi$
$234$		0			0
$235$	−1.03532			−0.0675371
$236$		0			0
$237$	−6.59360	−	25.2991i	−0.428300	−	1.64335i
$238$		0			0
$239$	−10.6008	−	8.89510i	−0.685706	−	0.575376i	0.231961	−	0.972725i	$-0.425486\pi$
$239$	−10.6008	−	8.89510i	−0.685706	−	0.575376i	−0.917668	+	0.397349i	$0.869930\pi$
$240$		0			0
$241$	−9.13000	+	7.66098i	−0.588115	+	0.493487i	−0.887601	−	0.460614i	$-0.847629\pi$
$241$	−9.13000	+	7.66098i	−0.588115	+	0.493487i	0.299486	+	0.954101i	$0.403185\pi$
$242$		0			0
$243$	−14.3451	+	6.10066i	−0.920239	+	0.391358i
$244$		0			0
$245$	−4.04347	−	1.98121i	−0.258328	−	0.126575i
$246$		0			0
$247$	−4.69862	+	26.6472i	−0.298966	+	1.69552i
$248$		0			0
$249$	20.6412	+	5.68251i	1.30808	+	0.360114i
$250$		0			0
$251$	2.12742	+	3.68480i	0.134282	+	0.232583i	0.925323	−	0.379180i	$-0.123794\pi$
$251$	2.12742	+	3.68480i	0.134282	+	0.232583i	−0.791041	+	0.611763i	$0.790461\pi$
$252$		0			0
$253$	−9.60524	+	16.6368i	−0.603876	+	1.04594i
$254$		0			0
$255$	−6.04495	−	4.29468i	−0.378549	−	0.268943i
$256$		0			0
$257$	12.9993	+	10.9077i	0.810873	+	0.680403i	0.950816	−	0.309756i	$-0.100248\pi$
$257$	12.9993	+	10.9077i	0.810873	+	0.680403i	−0.139943	+	0.990160i	$0.544692\pi$
$258$		0			0
$259$	0.0843738	+	0.0359049i	0.00524274	+	0.00223102i
$260$		0			0
$261$	−14.2955	−	2.72297i	−0.884866	−	0.168548i
$262$		0			0
$263$	−2.12014	−	12.0239i	−0.130733	−	0.741426i	−0.977736	−	0.209838i	$-0.932706\pi$
$263$	−2.12014	−	12.0239i	−0.130733	−	0.741426i	0.847003	−	0.531588i	$-0.178405\pi$
$264$		0			0
$265$	0.0245041	−	0.138970i	0.00150528	−	0.00853684i
$266$		0			0
$267$	−3.34957	+	7.05666i	−0.204990	+	0.431860i
$268$		0			0
$269$	−1.67259	+	2.89702i	−0.101980	+	0.176634i	−0.912500	−	0.409076i	$-0.865851\pi$
$269$	−1.67259	+	2.89702i	−0.101980	+	0.176634i	0.810520	+	0.585710i	$0.199184\pi$
$270$		0			0
$271$	−9.41919	−	16.3145i	−0.572175	−	0.991036i	−0.996342	−	0.0854522i	$-0.972767\pi$
$271$	−9.41919	−	16.3145i	−0.572175	−	0.991036i	0.424167	−	0.905584i	$-0.360567\pi$
$272$		0			0
$273$	16.0905	−	0.437046i	0.973843	−	0.0264512i
$274$		0			0
$275$	−15.1230	+	5.50433i	−0.911952	+	0.331924i
$276$		0			0
$277$	4.21488	+	23.9038i	0.253248	+	1.43624i	0.800531	+	0.599291i	$0.204551\pi$
$277$	4.21488	+	23.9038i	0.253248	+	1.43624i	−0.547283	+	0.836947i	$0.684338\pi$
$278$		0			0
$279$	−5.80282	+	3.24516i	−0.347406	+	0.194283i
$280$		0			0
$281$	0.196436	+	1.11404i	0.0117184	+	0.0664583i	0.990106	−	0.140320i	$-0.0448132\pi$
$281$	0.196436	+	1.11404i	0.0117184	+	0.0664583i	−0.978388	+	0.206778i	$0.933702\pi$
$282$		0			0
$283$	−0.100536	+	0.570166i	−0.00597623	+	0.0338929i	−0.987650	−	0.156676i	$-0.949922\pi$
$283$	−0.100536	+	0.570166i	−0.00597623	+	0.0338929i	0.981674	+	0.190569i	$0.0610333\pi$
$284$		0			0
$285$	−0.806533	+	8.54464i	−0.0477749	+	0.506141i
$286$		0			0
$287$	29.1723	+	1.55537i	1.72199	+	0.0918107i
$288$		0			0
$289$	−13.6482	+	23.6393i	−0.802833	+	1.39055i
$290$		0			0
$291$	−6.37959	−	24.4780i	−0.373978	−	1.43492i
$292$		0			0
$293$	−19.8331	−	16.6419i	−1.15866	−	0.972231i	−0.158774	−	0.987315i	$-0.550754\pi$
$293$	−19.8331	−	16.6419i	−1.15866	−	0.972231i	−0.999886	+	0.0150836i	$0.995199\pi$
$294$		0			0
$295$	6.31666	+	2.29908i	0.367770	+	0.133857i
$296$		0			0
$297$	−18.1280	−	1.96184i	−1.05189	−	0.113838i
$298$		0			0
$299$	3.33912	+	18.9371i	0.193106	+	1.09516i
$300$		0			0
$301$	4.08897	−	17.6383i	0.235684	−	1.01666i
$302$		0			0
$303$	−5.70670	−	21.8961i	−0.327841	−	1.25790i
$304$		0			0
$305$	−3.91441			−0.224138
$306$		0			0
$307$	10.8315	−	18.7608i	0.618189	−	1.07073i	−0.371627	−	0.928382i	$-0.621200\pi$
$307$	10.8315	−	18.7608i	0.618189	−	1.07073i	0.989816	−	0.142352i	$-0.0454666\pi$
$308$		0			0
$309$	12.6479	−	5.79274i	0.719513	−	0.329537i
$310$		0			0
$311$	−2.69978	+	15.3112i	−0.153091	+	0.868220i	0.807420	+	0.589977i	$0.200863\pi$
$311$	−2.69978	+	15.3112i	−0.153091	+	0.868220i	−0.960511	+	0.278243i	$0.910248\pi$
$312$		0			0
$313$	0.272167	−	0.228375i	0.0153838	−	0.0129085i	−0.635063	−	0.772460i	$-0.719026\pi$
$313$	0.272167	−	0.228375i	0.0153838	−	0.0129085i	0.650447	+	0.759552i	$0.274582\pi$
$314$		0			0
$315$	5.07613	−	0.548188i	0.286008	−	0.0308869i
$316$		0			0
$317$	12.5862	+	4.58100i	0.706911	+	0.257294i	0.670359	−	0.742037i	$-0.266140\pi$
$317$	12.5862	+	4.58100i	0.706911	+	0.257294i	0.0365520	+	0.999332i	$0.488363\pi$
$318$		0			0
$319$	−13.0397	−	10.9416i	−0.730081	−	0.612611i
$320$		0			0
$321$	3.72501	+	5.39813i	0.207910	+	0.301294i
$322$		0			0
$323$	51.2700			2.85274
$324$		0			0
$325$	−8.05464	+	13.9511i	−0.446791	+	0.773865i
$326$		0			0
$327$	8.52517	−	17.9603i	0.471443	−	0.993206i
$328$		0			0
$329$	−3.11175	−	2.90703i	−0.171556	−	0.160270i
$330$		0			0
$331$	−8.57117	−	3.11965i	−0.471114	−	0.171472i	0.0955427	−	0.995425i	$-0.469541\pi$
$331$	−8.57117	−	3.11965i	−0.471114	−	0.171472i	−0.566657	+	0.823954i	$0.691764\pi$
$332$		0			0
$333$	−0.102631	+	0.0166513i	−0.00562415	+	0.000912486i
$334$		0			0
$335$	1.21043	+	6.86471i	0.0661331	+	0.375059i
$336$		0			0
$337$	−15.7322	+	5.72604i	−0.856986	+	0.311917i	−0.732885	−	0.680352i	$-0.761827\pi$
$337$	−15.7322	+	5.72604i	−0.856986	+	0.311917i	−0.124101	+	0.992270i	$0.539605\pi$
$338$		0			0
$339$	−1.47624	+	15.6398i	−0.0801786	+	0.849436i
$340$		0			0
$341$	−7.77688			−0.421142
$342$		0			0
$343$	−6.59002	−	17.3081i	−0.355828	−	0.934552i
$344$		0			0
$345$	1.53826	+	5.90217i	0.0828170	+	0.317762i
$346$		0			0
$347$	17.5808	−	6.39888i	0.943785	−	0.343510i	0.176126	−	0.984368i	$-0.443644\pi$
$347$	17.5808	−	6.39888i	0.943785	−	0.343510i	0.767659	+	0.640858i	$0.221421\pi$
$348$		0			0
$349$	21.0027	+	7.64437i	1.12425	+	0.409194i	0.836202	−	0.548422i	$-0.184771\pi$
$349$	21.0027	+	7.64437i	1.12425	+	0.409194i	0.288049	+	0.957616i	$0.406993\pi$
$350$		0			0
$351$	−15.1627	+	10.1595i	−0.809325	+	0.542275i
$352$		0			0
$353$	−16.2524	+	13.6374i	−0.865030	+	0.725846i	−0.963046	−	0.269339i	$-0.913195\pi$
$353$	−16.2524	+	13.6374i	−0.865030	+	0.725846i	0.0980158	+	0.995185i	$0.468750\pi$
$354$		0			0
$355$	1.52898	−	8.67129i	0.0811500	−	0.460224i
$356$		0			0
$357$	−6.10977	−	29.8813i	−0.323363	−	1.58149i
$358$		0			0
$359$	−12.3632	+	21.4137i	−0.652505	+	1.13017i	0.330008	+	0.943978i	$0.392948\pi$
$359$	−12.3632	+	21.4137i	−0.652505	+	1.13017i	−0.982513	+	0.186194i	$0.940385\pi$
$360$		0			0
$361$	−20.1707	−	34.9367i	−1.06162	−	1.83877i
$362$		0			0
$363$	−1.85514	−	1.31800i	−0.0973694	−	0.0691769i
$364$		0			0
$365$	−2.14774	+	0.781715i	−0.112418	+	0.0409168i
$366$		0			0
$367$	6.64324	+	2.41794i	0.346774	+	0.126216i	0.509535	−	0.860450i	$-0.329818\pi$
$367$	6.64324	+	2.41794i	0.346774	+	0.126216i	−0.162760	+	0.986666i	$0.552040\pi$
$368$		0			0
$369$	−28.9113	+	16.1683i	−1.50506	+	0.841690i
$370$		0			0
$371$	0.463855	−	0.348881i	0.0240821	−	0.0181130i
$372$		0			0
$373$	19.5537	−	7.11696i	1.01245	−	0.368502i	0.218078	−	0.975931i	$-0.430021\pi$
$373$	19.5537	−	7.11696i	1.01245	−	0.368502i	0.794374	+	0.607429i	$0.207799\pi$
$374$		0			0
$375$	−4.57990	+	9.64864i	−0.236505	+	0.498253i
$376$		0			0
$377$	−17.0387			−0.877537
$378$		0			0
$379$	−18.4427			−0.947340			−0.473670	−	0.880702i	$-0.657071\pi$
$379$	−18.4427			−0.947340			−0.473670	+	0.880702i	$0.657071\pi$
$380$		0			0
$381$	15.7976	+	22.8933i	0.809337	+	1.17286i
$382$		0			0
$383$	−15.4119	+	5.60946i	−0.787510	+	0.286630i	−0.704300	−	0.709902i	$-0.748739\pi$
$383$	−15.4119	+	5.60946i	−0.787510	+	0.286630i	−0.0832093	+	0.996532i	$0.526517\pi$
$384$		0			0
$385$	5.49522	+	2.33846i	0.280062	+	0.119179i
$386$		0			0
$387$	6.75703	+	19.3865i	0.343479	+	0.985474i
$388$		0			0
$389$	4.20058	+	1.52889i	0.212978	+	0.0775176i	0.446306	−	0.894881i	$-0.352739\pi$
$389$	4.20058	+	1.52889i	0.212978	+	0.0775176i	−0.233328	+	0.972398i	$0.574962\pi$
$390$		0			0
$391$	34.2382	−	12.4617i	1.73150	−	0.630214i
$392$		0			0
$393$	−3.25410	+	34.4749i	−0.164147	+	1.73903i
$394$		0			0
$395$	−4.85473	−	8.40864i	−0.244268	−	0.423085i
$396$		0			0
$397$	15.1255	−	26.1981i	0.759126	−	1.31485i	−0.184170	−	0.982894i	$-0.558960\pi$
$397$	15.1255	−	26.1981i	0.759126	−	1.31485i	0.943297	−	0.331951i	$-0.107707\pi$
$398$		0			0
$399$	−26.4162	+	23.4170i	−1.32246	+	1.17232i
$400$		0			0
$401$	−1.36169	+	7.72255i	−0.0679998	+	0.385646i	0.931746	+	0.363110i	$0.118285\pi$
$401$	−1.36169	+	7.72255i	−0.0679998	+	0.385646i	−0.999746	+	0.0225358i	$0.992826\pi$
$402$		0			0
$403$	−5.96325	+	5.00376i	−0.297051	+	0.249255i
$404$		0			0
$405$	−4.53504	+	3.59846i	−0.225348	+	0.178809i
$406$		0			0
$407$	−0.114283	−	0.0415957i	−0.00566481	−	0.00206182i
$408$		0			0
$409$	9.02518	−	3.28490i	0.446266	−	0.162428i	−0.109105	−	0.994030i	$-0.534798\pi$
$409$	9.02518	−	3.28490i	0.446266	−	0.162428i	0.555371	+	0.831603i	$0.312576\pi$
$410$		0			0
$411$	−5.27970	+	5.20791i	−0.260428	+	0.256887i
$412$		0			0
$413$	12.5298	+	24.6463i	0.616551	+	1.21277i
$414$		0			0
$415$	7.95094			0.390296
$416$		0			0
$417$	−7.65965	−	5.44186i	−0.375095	−	0.266489i
$418$		0			0
$419$	18.2101	−	6.62792i	0.889620	−	0.323795i	0.143534	−	0.989645i	$-0.454153\pi$
$419$	18.2101	−	6.62792i	0.889620	−	0.323795i	0.746085	+	0.665850i	$0.231931\pi$
$420$		0			0
$421$	2.48404	+	14.0877i	0.121065	+	0.686592i	0.983568	+	0.180540i	$0.0577845\pi$
$421$	2.48404	+	14.0877i	0.121065	+	0.686592i	−0.862503	+	0.506052i	$0.831104\pi$
$422$		0			0
$423$	4.74327	+	0.903489i	0.230626	+	0.0439291i
$424$		0			0
$425$	28.6831	+	10.4398i	1.39133	+	0.506404i
$426$		0			0
$427$	−11.7651	−	10.9911i	−0.569352	−	0.531895i
$428$		0			0
$429$	−21.2800	+	1.71507i	−1.02741	+	0.0828043i
$430$		0			0
$431$	18.5086	−	32.0579i	0.891529	−	1.54417i	0.0534863	−	0.998569i	$-0.482967\pi$
$431$	18.5086	−	32.0579i	0.891529	−	1.54417i	0.838043	−	0.545605i	$-0.183700\pi$
$432$		0			0
$433$	−8.01327			−0.385093			−0.192546	−	0.981288i	$-0.561675\pi$
$433$	−8.01327			−0.385093			−0.192546	+	0.981288i	$0.561675\pi$
$434$		0			0
$435$	−5.38705	+	0.434170i	−0.258289	+	0.0208169i
$436$		0			0
$437$	−32.3053	−	27.1074i	−1.54537	−	1.29672i
$438$		0			0
$439$	−11.9641	−	4.35457i	−0.571015	−	0.207832i	0.0403440	−	0.999186i	$-0.487155\pi$
$439$	−11.9641	−	4.35457i	−0.571015	−	0.207832i	−0.611359	+	0.791353i	$0.709377\pi$
$440$		0			0
$441$	16.7960	+	12.6054i	0.799808	+	0.600256i
$442$		0			0
$443$	−20.4003	+	17.1179i	−0.969248	+	0.813296i	−0.982433	−	0.186617i	$-0.940248\pi$
$443$	−20.4003	+	17.1179i	−0.969248	+	0.813296i	0.0131847	+	0.999913i	$0.495803\pi$
$444$		0			0
$445$	−0.503747	+	2.85689i	−0.0238799	+	0.135430i
$446$		0			0
$447$	−9.40444	−	6.68146i	−0.444815	−	0.316022i
$448$		0			0
$449$	6.81423	−	11.8026i	0.321584	−	0.556999i	−0.659231	−	0.751940i	$-0.729118\pi$
$449$	6.81423	−	11.8026i	0.321584	−	0.556999i	0.980815	+	0.194941i	$0.0624516\pi$
$450$		0			0
$451$	−38.7467			−1.82451
$452$		0			0
$453$	−24.6728	−	6.79241i	−1.15923	−	0.319135i
$454$		0			0
$455$	5.71829	−	1.74259i	0.268078	−	0.0816940i
$456$		0			0
$457$	−1.85769	−	10.5355i	−0.0868990	−	0.492828i	−0.996931	−	0.0782898i	$-0.975054\pi$
$457$	−1.85769	−	10.5355i	−0.0868990	−	0.492828i	0.910032	−	0.414539i	$-0.136057\pi$
$458$		0			0
$459$	23.9468	+	24.9510i	1.11774	+	1.16461i
$460$		0			0
$461$	31.7576	+	11.5588i	1.47910	+	0.538347i	0.950554	−	0.310559i	$-0.100516\pi$
$461$	31.7576	+	11.5588i	1.47910	+	0.538347i	0.528543	+	0.848906i	$0.322738\pi$
$462$		0			0
$463$	−19.4003	−	16.2788i	−0.901610	−	0.756541i	0.0688943	−	0.997624i	$-0.478053\pi$
$463$	−19.4003	−	16.2788i	−0.901610	−	0.756541i	−0.970504	+	0.241083i	$0.922497\pi$
$464$		0			0
$465$	−1.75787	+	1.73397i	−0.0815194	+	0.0804109i
$466$		0			0
$467$	4.87995	−	8.45233i	0.225817	−	0.391127i	−0.730747	−	0.682648i	$-0.760828\pi$
$467$	4.87995	−	8.45233i	0.225817	−	0.391127i	0.956564	+	0.291521i	$0.0941614\pi$
$468$		0			0
$469$	−15.6370	+	24.0312i	−0.722050	+	1.10966i
$470$		0			0
$471$	24.5094	+	17.4129i	1.12933	+	0.802345i
$472$		0			0
$473$	−4.17006	+	23.6496i	−0.191740	+	1.08741i
$474$		0			0
$475$	−6.13486	−	34.7925i	−0.281487	−	1.59639i
$476$		0			0
$477$	−0.233538	+	0.615297i	−0.0106930	+	0.0281725i
$478$		0			0
$479$	1.94737	+	11.0441i	0.0889777	+	0.504617i	0.996427	+	0.0844563i	$0.0269153\pi$
$479$	1.94737	+	11.0441i	0.0889777	+	0.504617i	−0.907450	+	0.420161i	$0.861974\pi$
$480$		0			0
$481$	−0.114395	+	0.0416363i	−0.00521596	+	0.00189845i
$482$		0			0
$483$	−11.9490	+	22.0586i	−0.543700	+	1.00370i
$484$		0			0
$485$	−4.69716	−	8.13572i	−0.213287	−	0.369424i
$486$		0			0
$487$	−14.8740	+	25.7625i	−0.674005	+	1.16741i	0.302754	+	0.953069i	$0.402094\pi$
$487$	−14.8740	+	25.7625i	−0.674005	+	1.16741i	−0.976759	+	0.214342i	$0.931239\pi$
$488$		0			0
$489$	−13.8866	−	20.1239i	−0.627974	−	0.910035i
$490$		0			0
$491$	6.17255	−	35.0063i	0.278563	−	1.57981i	−0.448847	−	0.893608i	$-0.648165\pi$
$491$	6.17255	−	35.0063i	0.278563	−	1.57981i	0.727411	−	0.686202i	$-0.240724\pi$
$492$		0			0
$493$	5.60621	+	31.7944i	0.252491	+	1.43195i
$494$		0			0
$495$	−6.68431	+	1.08449i	−0.300437	+	0.0487442i
$496$		0			0
$497$	28.9432	−	21.7691i	1.29828	−	0.976479i
$498$		0			0
$499$	−12.4294	−	10.4295i	−0.556417	−	0.466890i	0.320690	−	0.947184i	$-0.396085\pi$
$499$	−12.4294	−	10.4295i	−0.556417	−	0.466890i	−0.877107	+	0.480295i	$0.840530\pi$
$500$		0			0
$501$	2.18707	−	23.1704i	0.0977110	−	1.03518i
$502$		0			0
$503$	−10.2619	+	17.7741i	−0.457555	+	0.792508i	−0.998831	−	0.0483367i	$-0.984608\pi$
$503$	−10.2619	+	17.7741i	−0.457555	+	0.792508i	0.541276	+	0.840845i	$0.317941\pi$
$504$		0			0
$505$	−4.20172	−	7.27760i	−0.186974	−	0.323849i
$506$		0			0
$507$	0.816436	−	0.805335i	0.0362592	−	0.0357662i
$508$		0			0
$509$	−6.05085	+	34.3161i	−0.268199	+	1.52103i	0.491568	+	0.870839i	$0.336424\pi$
$509$	−6.05085	+	34.3161i	−0.268199	+	1.52103i	−0.759767	+	0.650195i	$0.774687\pi$
$510$		0			0
$511$	−8.65016	−	3.68103i	−0.382660	−	0.162839i
$512$		0			0
$513$	11.1517	−	38.4429i	0.492358	−	1.69730i
$514$		0			0
$515$	3.95769	−	3.32090i	0.174397	−	0.146336i
$516$		0			0
$517$	4.32660	+	3.63045i	0.190284	+	0.159667i
$518$		0			0
$519$	−2.93878	+	2.89883i	−0.128998	+	0.127244i
$520$		0			0
$521$	24.4632			1.07175			0.535876	−	0.844296i	$-0.319981\pi$
$521$	24.4632			1.07175			0.535876	+	0.844296i	$0.319981\pi$
$522$		0			0
$523$	33.1299			1.44867			0.724334	−	0.689449i	$-0.242147\pi$
$523$	33.1299			1.44867			0.724334	+	0.689449i	$0.242147\pi$
$524$		0			0
$525$	−19.5468	+	7.72172i	−0.853093	+	0.337004i
$526$		0			0
$527$	11.2992	+	9.48113i	0.492199	+	0.413004i
$528$		0			0
$529$	−6.54936	−	2.38377i	−0.284755	−	0.103642i
$530$		0			0
$531$	−26.9331	−	16.0454i	−1.16880	−	0.696311i
$532$		0			0
$533$	−29.7107	+	24.9302i	−1.28691	+	1.07985i
$534$		0			0
$535$	1.86589	+	1.56567i	0.0806695	+	0.0676897i
$536$		0			0
$537$	10.7193	+	15.5340i	0.462573	+	0.670342i
$538$		0			0
$539$	9.95029	+	22.4582i	0.428589	+	0.967343i
$540$		0			0
$541$	−2.41583	−	4.18433i	−0.103864	−	0.179899i	0.809409	−	0.587245i	$-0.199787\pi$
$541$	−2.41583	−	4.18433i	−0.103864	−	0.179899i	−0.913274	+	0.407346i	$0.866454\pi$
$542$		0			0
$543$	8.61321	+	12.4819i	0.369628	+	0.535650i
$544$		0			0
$545$	1.28211	−	7.27122i	0.0549197	−	0.311465i
$546$		0			0
$547$	14.2069	−	11.9210i	0.607443	−	0.509705i	−0.286385	−	0.958115i	$-0.592454\pi$
$547$	14.2069	−	11.9210i	0.607443	−	0.509705i	0.893828	+	0.448409i	$0.148009\pi$
$548$		0			0
$549$	17.9336	+	3.41596i	0.765388	+	0.145789i
$550$		0			0
$551$	28.6252	−	24.0194i	1.21947	−	1.02326i
$552$		0			0
$553$	9.01889	−	38.9042i	0.383522	−	1.65437i
$554$		0			0
$555$	−0.0351068	+	0.0160789i	−0.00149020	+	0.000682512i
$556$		0			0
$557$	−12.3461	−	21.3841i	−0.523121	−	0.906073i	−0.999638	−	0.0269072i	$-0.991434\pi$
$557$	−12.3461	−	21.3841i	−0.523121	−	0.906073i	0.476517	−	0.879165i	$-0.341899\pi$
$558$		0			0
$559$	12.0189	+	20.8174i	0.508347	+	0.880482i
$560$		0			0
$561$	10.2021	+	39.1445i	0.430732	+	1.65268i
$562$		0			0
$563$	22.1106	−	8.04758i	0.931849	−	0.339165i	0.168907	−	0.985632i	$-0.445976\pi$
$563$	22.1106	−	8.04758i	0.931849	−	0.339165i	0.762942	+	0.646467i	$0.223754\pi$
$564$		0			0
$565$	1.01309	+	5.74550i	0.0426209	+	0.241715i
$566$		0			0
$567$	−23.7344	−	1.91826i	−0.996750	−	0.0805595i
$568$		0			0
$569$	2.36321	+	13.4024i	0.0990711	+	0.561860i	0.993424	+	0.114497i	$0.0365256\pi$
$569$	2.36321	+	13.4024i	0.0990711	+	0.561860i	−0.894353	+	0.447363i	$0.852363\pi$
$570$		0			0
$571$	−32.4943	+	11.8270i	−1.35985	+	0.494943i	−0.916007	−	0.401163i	$-0.868606\pi$
$571$	−32.4943	+	11.8270i	−1.35985	+	0.494943i	−0.443839	+	0.896107i	$0.646384\pi$
$572$		0			0
$573$	5.93976	+	22.7903i	0.248137	+	0.952080i
$574$		0			0
$575$	−12.5536	−	21.7434i	−0.523519	−	0.906762i
$576$		0			0
$577$	−5.22053	−	9.04223i	−0.217334	−	0.376433i	0.736658	−	0.676265i	$-0.236403\pi$
$577$	−5.22053	−	9.04223i	−0.217334	−	0.376433i	−0.953992	+	0.299832i	$0.903069\pi$
$578$		0			0
$579$	−23.8209	+	10.9100i	−0.989964	+	0.453404i
$580$		0			0
$581$	23.8972	+	22.3250i	0.991423	+	0.926199i
$582$		0			0
$583$	−0.589711	+	0.494826i	−0.0244233	+	0.0204936i
$584$		0			0
$585$	−4.42770	+	5.13236i	−0.183063	+	0.212197i
$586$		0			0
$587$	−12.4120	+	10.4149i	−0.512298	+	0.429869i	−0.861937	−	0.507016i	$-0.830749\pi$
$587$	−12.4120	+	10.4149i	−0.512298	+	0.429869i	0.349639	+	0.936884i	$0.386304\pi$
$588$		0			0
$589$	2.96454	−	16.8128i	0.122152	−	0.692758i
$590$		0			0
$591$	0.744151	+	1.07839i	0.0306103	+	0.0443592i
$592$		0			0
$593$	−9.82904	−	17.0244i	−0.403630	−	0.699108i	0.590531	−	0.807015i	$-0.298918\pi$
$593$	−9.82904	−	17.0244i	−0.403630	−	0.699108i	−0.994161	+	0.107907i	$0.965585\pi$
$594$		0			0
$595$	−5.13318	−	10.0971i	−0.210440	−	0.413939i
$596$		0			0
$597$	−18.9438	−	27.4526i	−0.775319	−	1.12356i
$598$		0			0
$599$	10.9050	+	9.15037i	0.445566	+	0.373874i	0.837787	−	0.545997i	$-0.183849\pi$
$599$	10.9050	+	9.15037i	0.445566	+	0.373874i	−0.392221	+	0.919871i	$0.628293\pi$
$600$		0			0
$601$	−4.04380	+	3.39315i	−0.164950	+	0.138410i	−0.721526	−	0.692387i	$-0.756559\pi$
$601$	−4.04380	+	3.39315i	−0.164950	+	0.138410i	0.556576	+	0.830796i	$0.312115\pi$
$602$		0			0
$603$	0.445051	−	32.5065i	0.0181239	−	1.32377i
$604$		0			0
$605$	−0.794171	−	0.289054i	−0.0322876	−	0.0117517i
$606$		0			0
$607$	−2.43258	−	2.04117i	−0.0987352	−	0.0828487i	0.592084	−	0.805876i	$-0.298305\pi$
$607$	−2.43258	−	2.04117i	−0.0987352	−	0.0828487i	−0.690819	+	0.723028i	$0.742750\pi$
$608$		0			0
$609$	−17.4103	−	13.8211i	−0.705501	−	0.560058i
$610$		0			0
$611$	5.65349			0.228716
$612$		0			0
$613$	−12.0925			−0.488413			−0.244207	−	0.969723i	$-0.578527\pi$
$613$	−12.0925			−0.488413			−0.244207	+	0.969723i	$0.578527\pi$
$614$		0			0
$615$	−8.75823	+	8.63914i	−0.353166	+	0.348364i
$616$		0			0
$617$	−3.46111	−	2.90422i	−0.139339	−	0.116919i	0.570454	−	0.821329i	$-0.306767\pi$
$617$	−3.46111	−	2.90422i	−0.139339	−	0.116919i	−0.709793	+	0.704410i	$0.751212\pi$
$618$		0			0
$619$	33.1367	−	27.8050i	1.33188	−	1.11758i	0.348243	−	0.937404i	$-0.386778\pi$
$619$	33.1367	−	27.8050i	1.33188	−	1.11758i	0.983635	−	0.180174i	$-0.0576662\pi$
$620$		0			0
$621$	−1.89683	−	28.3828i	−0.0761172	−	1.13896i
$622$		0			0
$623$	−9.53576	+	7.17217i	−0.382042	+	0.287347i
$624$		0			0
$625$	3.29317	−	18.6765i	0.131727	−	0.747061i
$626$		0			0
$627$	33.3330	−	32.8797i	1.33119	−	1.31309i
$628$		0			0
$629$	0.115333	+	0.199763i	0.00459863	+	0.00796506i
$630$		0			0
$631$	0.853275	−	1.47792i	0.0339683	−	0.0588349i	−0.848541	−	0.529129i	$-0.822519\pi$
$631$	0.853275	−	1.47792i	0.0339683	−	0.0588349i	0.882510	+	0.470294i	$0.155852\pi$
$632$		0			0
$633$	−2.31070	+	24.4802i	−0.0918420	+	0.973001i
$634$		0			0
$635$	7.91318	+	6.63995i	0.314025	+	0.263498i
$636$		0			0
$637$	22.0797	+	10.8186i	0.874831	+	0.428649i
$638$		0			0
$639$	−14.5721	+	38.3927i	−0.576462	+	1.51879i
$640$		0			0
$641$	−5.08966	−	28.8649i	−0.201029	−	1.14009i	−0.903567	−	0.428448i	$-0.859061\pi$
$641$	−5.08966	−	28.8649i	−0.201029	−	1.14009i	0.702537	−	0.711647i	$-0.252050\pi$
$642$		0			0
$643$	−1.83540	+	10.4091i	−0.0723811	+	0.410494i	0.926992	+	0.375082i	$0.122385\pi$
$643$	−1.83540	+	10.4091i	−0.0723811	+	0.410494i	−0.999373	+	0.0354119i	$0.988726\pi$
$644$		0			0
$645$	4.33043	+	6.27549i	0.170511	+	0.247097i
$646$		0			0
$647$	−8.67133	+	15.0192i	−0.340905	+	0.590465i	−0.984601	−	0.174816i	$-0.944067\pi$
$647$	−8.67133	+	15.0192i	−0.340905	+	0.590465i	0.643696	+	0.765281i	$0.277400\pi$
$648$		0			0
$649$	−18.3353	−	31.7577i	−0.719724	−	1.24660i
$650$		0			0
$651$	−10.1522	+	0.275749i	−0.397894	+	0.0108075i
$652$		0			0
$653$	−39.4522	+	14.3594i	−1.54388	+	0.561928i	−0.966973	−	0.254880i	$-0.917964\pi$
$653$	−39.4522	+	14.3594i	−1.54388	+	0.561928i	−0.576911	+	0.816807i	$0.695742\pi$
$654$		0			0
$655$	2.23315	+	12.6648i	0.0872565	+	0.494856i
$656$		0			0
$657$	10.5219	−	1.70712i	0.410500	−	0.0666012i
$658$		0			0
$659$	2.92502	+	16.5886i	0.113943	+	0.646201i	0.987268	+	0.159064i	$0.0508476\pi$
$659$	2.92502	+	16.5886i	0.113943	+	0.646201i	−0.873326	+	0.487137i	$0.838041\pi$
$660$		0			0
$661$	−1.50486	+	8.53449i	−0.0585323	+	0.331953i	−0.999987	−	0.00518758i	$-0.998349\pi$
$661$	−1.50486	+	8.53449i	−0.0585323	+	0.331953i	0.941454	+	0.337141i	$0.109460\pi$
$662$		0			0
$663$	33.0090	+	23.4515i	1.28196	+	0.910782i
$664$		0			0
$665$	−7.15028	+	10.9886i	−0.277276	+	0.426121i
$666$		0			0
$667$	13.2778	−	22.9979i	0.514119	−	0.890481i
$668$		0			0
$669$	18.1863	−	17.9390i	0.703122	−	0.693562i
$670$		0			0
$671$	16.3582	+	13.7262i	0.631503	+	0.529894i
$672$		0			0
$673$	−18.7908	−	6.83929i	−0.724332	−	0.263635i	−0.0465685	−	0.998915i	$-0.514829\pi$
$673$	−18.7908	−	6.83929i	−0.724332	−	0.263635i	−0.677764	+	0.735280i	$0.737051\pi$
$674$		0			0
$675$	14.0667	−	19.2362i	0.541428	−	0.740402i
$676$		0			0
$677$	2.16397	+	12.2725i	0.0831682	+	0.471670i	0.997737	+	0.0672395i	$0.0214192\pi$
$677$	2.16397	+	12.2725i	0.0831682	+	0.471670i	−0.914569	+	0.404431i	$0.867470\pi$
$678$		0			0
$679$	8.72617	−	37.6415i	0.334880	−	1.44455i
$680$		0			0
$681$	−7.76353	−	2.13730i	−0.297499	−	0.0819014i
$682$		0			0
$683$	−9.80042			−0.375003			−0.187501	−	0.982264i	$-0.560039\pi$
$683$	−9.80042			−0.375003			−0.187501	+	0.982264i	$0.560039\pi$
$684$		0			0
$685$	−1.37709	+	2.38518i	−0.0526158	+	0.0911332i
$686$		0			0
$687$	7.34295	+	5.21686i	0.280151	+	0.199036i
$688$		0			0
$689$	−0.133807	+	0.758858i	−0.00509764	+	0.0289102i
$690$		0			0
$691$	−0.396250	+	0.332493i	−0.0150741	+	0.0126486i	−0.650294	−	0.759683i	$-0.725354\pi$
$691$	−0.396250	+	0.332493i	−0.0150741	+	0.0126486i	0.635219	+	0.772332i	$0.280910\pi$
$692$		0			0
$693$	−23.1353	−	15.5090i	−0.878839	−	0.589138i
$694$		0			0
$695$	−3.27904	−	1.19347i	−0.124381	−	0.0452710i
$696$		0			0
$697$	56.2958	+	47.2377i	2.13235	+	1.78926i
$698$		0			0
$699$	−7.67151	+	0.618287i	−0.290163	+	0.0233858i
$700$		0			0
$701$	38.7926			1.46518			0.732588	−	0.680673i	$-0.238312\pi$
$701$	38.7926			1.46518			0.732588	+	0.680673i	$0.238312\pi$
$702$		0			0
$703$	0.133490	−	0.231212i	0.00503467	−	0.00872031i
$704$		0			0
$705$	1.78744	−	0.144059i	0.0673188	−	0.00542557i
$706$		0			0
$707$	7.80577	−	33.6712i	0.293566	−	1.26634i
$708$		0			0
$709$	12.4456	+	4.52983i	0.467405	+	0.170121i	0.564976	−	0.825107i	$-0.308885\pi$
$709$	12.4456	+	4.52983i	0.467405	+	0.170121i	−0.0975716	+	0.995229i	$0.531108\pi$
$710$		0			0
$711$	14.9037	+	42.7602i	0.558934	+	1.60363i
$712$		0			0
$713$	−2.10678	−	11.9482i	−0.0788997	−	0.447462i
$714$		0			0
$715$	−7.45047	+	2.71175i	−0.278632	+	0.101414i
$716$		0			0
$717$	19.5394	+	13.8819i	0.729713	+	0.518430i
$718$		0			0
$719$	44.9946			1.67801			0.839007	−	0.544121i	$-0.183137\pi$
$719$	44.9946			1.67801			0.839007	+	0.544121i	$0.183137\pi$
$720$		0			0
$721$	21.2198	+	1.13137i	0.790265	+	0.0421344i
$722$		0			0
$723$	14.6965	−	14.4967i	0.546570	−	0.539138i
$724$		0			0
$725$	20.9053	−	7.60892i	0.776405	−	0.282588i
$726$		0			0
$727$	−1.51497	−	0.551405i	−0.0561872	−	0.0204505i	0.313774	−	0.949498i	$-0.398407\pi$
$727$	−1.51497	−	0.551405i	−0.0561872	−	0.0204505i	−0.369961	+	0.929047i	$0.620629\pi$
$728$		0			0
$729$	23.9173	−	12.5285i	0.885825	−	0.464020i
$730$		0			0
$731$	34.8910	−	29.2770i	1.29049	−	1.08285i
$732$		0			0
$733$	−5.73411	+	32.5197i	−0.211794	+	1.20114i	0.674590	+	0.738193i	$0.264321\pi$
$733$	−5.73411	+	32.5197i	−0.211794	+	1.20114i	−0.886384	+	0.462951i	$0.846791\pi$
$734$		0			0
$735$	7.25653	+	2.85785i	0.267661	+	0.105413i
$736$		0			0
$737$	19.0133	−	32.9320i	0.700364	−	1.21307i
$738$		0			0
$739$	0.109588	+	0.189812i	0.00403126	+	0.00698234i	0.868034	−	0.496505i	$-0.165383\pi$
$739$	0.109588	+	0.189812i	0.00403126	+	0.00698234i	−0.864003	+	0.503487i	$0.832050\pi$
$740$		0			0
$741$	4.40415	−	46.6589i	0.161791	−	1.71406i
$742$		0			0
$743$	13.1398	−	4.78250i	0.482053	−	0.175453i	−0.0895517	−	0.995982i	$-0.528543\pi$
$743$	13.1398	−	4.78250i	0.482053	−	0.175453i	0.571604	+	0.820529i	$0.306321\pi$
$744$		0			0
$745$	−4.02597	−	1.46533i	−0.147500	−	0.0536857i
$746$		0			0
$747$	−36.4267	−	6.93849i	−1.33278	−	0.253866i
$748$		0			0
$749$	1.21193	+	9.94488i	0.0442829	+	0.363378i
$750$		0			0
$751$	−2.14018	+	0.778962i	−0.0780963	+	0.0284247i	−0.380773	−	0.924669i	$-0.624342\pi$
$751$	−2.14018	+	0.778962i	−0.0780963	+	0.0284247i	0.302677	+	0.953093i	$0.402120\pi$
$752$		0			0
$753$	−4.18561	−	6.06562i	−0.152532	−	0.221043i
$754$		0			0
$755$	−9.50391			−0.345883
$756$		0			0
$757$	23.0895			0.839202			0.419601	−	0.907709i	$-0.362170\pi$
$757$	23.0895			0.839202			0.419601	+	0.907709i	$0.362170\pi$
$758$		0			0
$759$	14.2681	−	30.0591i	0.517899	−	1.09108i
$760$		0			0
$761$	−17.7685	+	6.46720i	−0.644107	+	0.234436i	−0.643360	−	0.765564i	$-0.722460\pi$
$761$	−17.7685	+	6.46720i	−0.644107	+	0.234436i	−0.000747278		1.00000i	$0.500238\pi$
$762$		0			0
$763$	24.2700	−	18.2543i	0.878632	−	0.660849i
$764$		0			0
$765$	11.0339	+	6.57345i	0.398931	+	0.237664i
$766$		0			0
$767$	−34.4928	−	12.5543i	−1.24546	−	0.453311i
$768$		0			0
$769$	16.9420	−	6.16640i	0.610945	−	0.222366i	−0.0179714	−	0.999839i	$-0.505721\pi$
$769$	16.9420	−	6.16640i	0.610945	−	0.222366i	0.628917	+	0.777473i	$0.283499\pi$
$770$		0			0
$771$	−23.9604	−	17.0228i	−0.862912	−	0.613063i
$772$		0			0
$773$	−20.8656	−	36.1403i	−0.750483	−	1.29987i	−0.947589	−	0.319492i	$-0.896488\pi$
$773$	−20.8656	−	36.1403i	−0.750483	−	1.29987i	0.197106	−	0.980382i	$-0.436846\pi$
$774$		0			0
$775$	5.08200	−	8.80227i	0.182551	−	0.316187i
$776$		0			0
$777$	−0.150663	−	0.0502480i	−0.00540502	−	0.00180264i
$778$		0			0
$779$	14.7702	−	83.7661i	0.529198	−	3.00123i
$780$		0			0
$781$	−36.7962	+	30.8757i	−1.31667	+	1.10482i
$782$		0			0
$783$	25.0593	+	2.71195i	0.895547	+	0.0969173i
$784$		0			0
$785$	10.4923	+	3.81889i	0.374486	+	0.136302i
$786$		0			0
$787$	20.4511	−	7.44360i	0.729004	−	0.265336i	0.0492606	−	0.998786i	$-0.484314\pi$
$787$	20.4511	−	7.44360i	0.729004	−	0.265336i	0.679743	+	0.733450i	$0.262091\pi$
$788$		0			0
$789$	5.33337	+	20.4637i	0.189873	+	0.728527i
$790$		0			0
$791$	−13.0876	+	20.1132i	−0.465341	+	0.715142i
$792$		0			0
$793$	21.3750			0.759048
$794$		0			0
$795$	−0.0229684	+	0.243334i	−0.000814606	+	0.00863017i
$796$		0			0
$797$	−44.7024	+	16.2704i	−1.58344	+	0.576326i	−0.975949	−	0.218000i	$-0.930047\pi$
$797$	−44.7024	+	16.2704i	−1.58344	+	0.576326i	−0.607493	+	0.794325i	$0.707825\pi$
$798$		0			0
$799$	−1.86016	−	10.5495i	−0.0658077	−	0.373214i
$800$		0			0
$801$	4.80098	−	12.6491i	0.169634	−	0.446932i
$802$		0			0
$803$	11.7165	+	4.26447i	0.413467	+	0.150490i
$804$		0			0
$805$	−2.10407	+	9.07619i	−0.0741587	+	0.319894i
$806$		0			0
$807$	2.48455	−	5.23429i	0.0874604	−	0.184256i
$808$		0			0
$809$	−18.8057	+	32.5724i	−0.661173	+	1.14518i	0.319135	+	0.947709i	$0.396608\pi$
$809$	−18.8057	+	32.5724i	−0.661173	+	1.14518i	−0.980308	+	0.197476i	$0.936726\pi$
$810$		0			0
$811$	34.0214			1.19465			0.597326	−	0.801998i	$-0.296230\pi$
$811$	34.0214			1.19465			0.597326	+	0.801998i	$0.296230\pi$
$812$		0			0
$813$	18.5318	+	26.8556i	0.649940	+	0.941867i
$814$		0			0
$815$	−6.95594	−	5.83672i	−0.243656	−	0.204451i
$816$		0			0
$817$	−49.5382	−	18.0304i	−1.73312	−	0.630805i
$818$		0			0
$819$	−27.7187	+	2.99343i	−0.968570	+	0.104599i
$820$		0			0
$821$	13.3396	−	11.1933i	0.465556	−	0.390648i	−0.379615	−	0.925145i	$-0.623943\pi$
$821$	13.3396	−	11.1933i	0.465556	−	0.390648i	0.845170	+	0.534497i	$0.179499\pi$
$822$		0			0
$823$	−1.50719	+	8.54768i	−0.0525372	+	0.297953i	−0.999743	−	0.0226731i	$-0.992782\pi$
$823$	−1.50719	+	8.54768i	−0.0525372	+	0.297953i	0.947206	+	0.320626i	$0.103893\pi$
$824$		0			0
$825$	25.3433	−	11.6072i	0.882340	−	0.404112i
$826$		0			0
$827$	−2.05196	+	3.55410i	−0.0713537	+	0.123588i	−0.899495	−	0.436931i	$-0.856065\pi$
$827$	−2.05196	+	3.55410i	−0.0713537	+	0.123588i	0.828141	+	0.560520i	$0.189399\pi$
$828$		0			0
$829$	−1.08877			−0.0378147			−0.0189073	−	0.999821i	$-0.506019\pi$
$829$	−1.08877			−0.0378147			−0.0189073	+	0.999821i	$0.506019\pi$
$830$		0			0
$831$	−10.6029	−	40.6823i	−0.367809	−	1.41125i
$832$		0			0
$833$	12.9228	−	44.7607i	0.447748	−	1.55087i
$834$		0			0
$835$	−1.50090	−	8.51200i	−0.0519406	−	0.294570i
$836$		0			0
$837$	9.56675	−	6.41004i	0.330675	−	0.221564i
$838$		0			0
$839$	11.8890	+	4.32723i	0.410453	+	0.149393i	0.538990	−	0.842312i	$-0.318806\pi$
$839$	11.8890	+	4.32723i	0.410453	+	0.149393i	−0.128537	+	0.991705i	$0.541028\pi$
$840$		0			0
$841$	−4.18988	−	3.51572i	−0.144478	−	0.121232i
$842$		0			0
$843$	−0.494150	−	1.89601i	−0.0170194	−	0.0653021i
$844$		0			0
$845$	0.212948	−	0.368838i	0.00732565	−	0.0126884i
$846$		0			0
$847$	−1.57532	−	3.09869i	−0.0541288	−	0.106472i
$848$		0			0
$849$	0.0942350	−	0.998354i	0.00323414	−	0.0342634i
$850$		0			0
$851$	0.0329467	−	0.186850i	0.00112940	−	0.00640513i
$852$		0			0
$853$	4.19359	+	23.7830i	0.143586	+	0.814314i	0.968492	+	0.249045i	$0.0801167\pi$
$853$	4.19359	+	23.7830i	0.143586	+	0.814314i	−0.824906	+	0.565269i	$0.808772\pi$
$854$		0			0
$855$	0.203507	−	14.8641i	0.00695979	−	0.508343i
$856$		0			0
$857$	−3.37374	−	19.1334i	−0.115245	−	0.653585i	−0.986629	−	0.162984i	$-0.947888\pi$
$857$	−3.37374	−	19.1334i	−0.115245	−	0.653585i	0.871384	−	0.490602i	$-0.163223\pi$
$858$		0			0
$859$	−12.6624	+	4.60873i	−0.432035	+	0.157248i	−0.548878	−	0.835903i	$-0.684945\pi$
$859$	−12.6624	+	4.60873i	−0.432035	+	0.157248i	0.116843	+	0.993150i	$0.462723\pi$
$860$		0			0
$861$	−50.5810	+	1.37386i	−1.72380	+	0.0468212i
$862$		0			0
$863$	1.79029	+	3.10087i	0.0609422	+	0.105555i	0.894887	−	0.446293i	$-0.147256\pi$
$863$	1.79029	+	3.10087i	0.0609422	+	0.105555i	−0.833945	+	0.551848i	$0.813923\pi$
$864$		0			0
$865$	−0.766514	+	1.32764i	−0.0260623	+	0.0451412i
$866$		0			0
$867$	20.2737	−	42.7112i	0.688529	−	1.45055i
$868$		0			0
$869$	−9.19776	+	52.1631i	−0.312012	+	1.76951i
$870$		0			0
$871$	−6.60969	−	37.4854i	−0.223961	−	1.27014i
$872$		0			0
$873$	14.4200	+	41.3724i	0.488044	+	1.40024i
$874$		0			0
$875$	−13.0383	+	9.80657i	−0.440776	+	0.331523i
$876$		0			0
$877$	21.1576	+	17.7533i	0.714442	+	0.599488i	0.925842	−	0.377912i	$-0.123358\pi$
$877$	21.1576	+	17.7533i	0.714442	+	0.599488i	−0.211400	+	0.977400i	$0.567802\pi$
$878$		0			0
$879$	36.5565	+	25.9718i	1.23302	+	0.876008i
$880$		0			0
$881$	−21.7266	+	37.6316i	−0.731989	+	1.26784i	0.224043	+	0.974579i	$0.428074\pi$
$881$	−21.7266	+	37.6316i	−0.731989	+	1.26784i	−0.956032	+	0.293263i	$0.905259\pi$
$882$		0			0
$883$	14.9311	+	25.8615i	0.502472	+	0.870308i	0.999996	+	0.00285721i	$0.000909481\pi$
$883$	14.9311	+	25.8615i	0.502472	+	0.870308i	−0.497524	+	0.867450i	$0.665757\pi$
$884$		0			0
$885$	−11.2253	−	3.09032i	−0.377335	−	0.103880i
$886$		0			0
$887$	6.60722	−	37.4714i	0.221849	−	1.25817i	−0.646770	−	0.762685i	$-0.723881\pi$
$887$	6.60722	−	37.4714i	0.221849	−	1.25817i	0.868619	−	0.495481i	$-0.165008\pi$
$888$		0			0
$889$	5.13975	+	42.1759i	0.172382	+	1.41453i
$890$		0			0
$891$	31.5702	+	0.864623i	1.05764	+	0.0289660i
$892$		0			0
$893$	−9.49793	+	7.96971i	−0.317836	+	0.266696i
$894$		0			0
$895$	5.36941	+	4.50547i	0.179480	+	0.150601i
$896$		0			0
$897$	−8.39981	−	32.2294i	−0.280461	−	1.07611i
$898$		0			0
$899$	10.7504			0.358546
$900$		0			0
$901$	1.46006			0.0486418
$902$		0			0
$903$	−4.60515	+	31.0207i	−0.153250	+	1.03230i
$904$		0			0
$905$	4.31444	+	3.62024i	0.143417	+	0.120341i
$906$		0			0
$907$	−8.57787	−	3.12209i	−0.284824	−	0.103667i	0.195658	−	0.980672i	$-0.437316\pi$
$907$	−8.57787	−	3.12209i	−0.284824	−	0.103667i	−0.480481	+	0.877005i	$0.659538\pi$
$908$		0			0
$909$	12.8990	+	37.0086i	0.427834	+	1.22750i
$910$		0			0
$911$	−0.0485039	+	0.0406996i	−0.00160700	+	0.00134844i	−0.643591	−	0.765370i	$-0.722556\pi$
$911$	−0.0485039	+	0.0406996i	−0.00160700	+	0.00134844i	0.641984	+	0.766718i	$0.278112\pi$
$912$		0			0
$913$	−33.2268	−	27.8806i	−1.09965	−	0.922714i
$914$		0			0
$915$	6.75804	−	0.544665i	0.223414	−	0.0180061i
$916$		0			0
$917$	−28.8490	+	44.3356i	−0.952679	+	1.46409i
$918$		0			0
$919$	6.65858	+	11.5330i	0.219646	+	0.380439i	0.954700	−	0.297570i	$-0.0961763\pi$
$919$	6.65858	+	11.5330i	0.219646	+	0.380439i	−0.735053	+	0.678009i	$0.762843\pi$
$920$		0			0
$921$	−16.0897	+	33.8967i	−0.530174	+	1.11694i
$922$		0			0
$923$	−8.34916	+	47.3504i	−0.274816	+	1.55856i
$924$		0			0
$925$	0.121761	−	0.102170i	0.00400349	−	0.00335933i
$926$		0			0
$927$	−21.0300	+	11.7608i	−0.690714	+	0.386274i
$928$		0			0
$929$	12.1069	−	10.1589i	0.397214	−	0.333302i	−0.422202	−	0.906502i	$-0.638743\pi$
$929$	12.1069	−	10.1589i	0.397214	−	0.333302i	0.819416	+	0.573200i	$0.194298\pi$
$930$		0			0
$931$	−52.3452	+	12.9504i	−1.71554	+	0.424431i
$932$		0			0
$933$	2.53058	−	26.8098i	0.0828476	−	0.877712i
$934$		0			0
$935$	7.51158	+	13.0104i	0.245655	+	0.425487i
$936$		0			0
$937$	8.36232	+	14.4840i	0.273185	+	0.473170i	0.969676	−	0.244396i	$-0.0785896\pi$
$937$	8.36232	+	14.4840i	0.273185	+	0.473170i	−0.696491	+	0.717566i	$0.745256\pi$
$938$		0			0
$939$	−0.438106	+	0.432149i	−0.0142970	+	0.0141026i
$940$		0			0
$941$	−18.9375	+	6.89269i	−0.617345	+	0.224695i	−0.631714	−	0.775202i	$-0.717648\pi$
$941$	−18.9375	+	6.89269i	−0.617345	+	0.224695i	0.0143690	+	0.999897i	$0.495426\pi$
$942$		0			0
$943$	−10.4966	−	59.5292i	−0.341817	−	1.93854i
$944$		0			0
$945$	−8.68742	+	1.65273i	−0.282602	+	0.0537634i
$946$		0			0
$947$	−1.86769	−	10.5922i	−0.0606916	−	0.344199i	−0.999999	−	0.00112364i	$-0.999642\pi$
$947$	−1.86769	−	10.5922i	−0.0606916	−	0.344199i	0.939308	−	0.343076i	$-0.111469\pi$
$948$		0			0
$949$	11.7280	−	4.26863i	0.380706	−	0.138566i
$950$		0			0
$951$	−22.3669	−	6.15759i	−0.725295	−	0.199673i
$952$		0			0
$953$	11.1902	+	19.3819i	0.362485	+	0.627842i	0.988369	−	0.152074i	$-0.0485951\pi$
$953$	11.1902	+	19.3819i	0.362485	+	0.627842i	−0.625884	+	0.779916i	$0.715262\pi$
$954$		0			0
$955$	4.37332	+	7.57481i	0.141517	+	0.245115i
$956$		0			0
$957$	24.0348	+	17.0757i	0.776936	+	0.551980i
$958$		0			0
$959$	−10.8362	+	3.30222i	−0.349919	+	0.106634i
$960$		0			0
$961$	−19.9849	+	16.7693i	−0.644675	+	0.540947i
$962$		0			0
$963$	−7.18216	−	8.80131i	−0.231442	−	0.283618i
$964$		0			0
$965$	−7.45389	+	6.25456i	−0.239949	+	0.201341i
$966$		0			0
$967$	1.22166	−	6.92838i	0.0392859	−	0.222802i	−0.958844	−	0.283934i	$-0.908360\pi$
$967$	1.22166	−	6.92838i	0.0392859	−	0.222802i	0.998130	+	0.0611328i	$0.0194713\pi$
$968$		0			0
$969$	−88.5152	+	7.13389i	−2.84352	+	0.229174i
$970$		0			0
$971$	7.74120	+	13.4081i	0.248427	+	0.430288i	0.963090	−	0.269181i	$-0.0867531\pi$
$971$	7.74120	+	13.4081i	0.248427	+	0.430288i	−0.714663	+	0.699469i	$0.753420\pi$
$972$		0			0
$973$	−6.50434	−	12.7941i	−0.208519	−	0.410161i
$974$		0			0
$975$	11.9648	−	25.2066i	0.383179	−	0.807257i
$976$		0			0
$977$	−3.07287	−	2.57845i	−0.0983099	−	0.0824918i	0.592308	−	0.805712i	$-0.298217\pi$
$977$	−3.07287	−	2.57845i	−0.0983099	−	0.0824918i	−0.690618	+	0.723220i	$0.742661\pi$
$978$		0			0
$979$	12.1231	−	10.1725i	0.387455	−	0.325113i
$980$		0			0
$981$	−12.2192	+	32.1938i	−0.390130	+	1.02787i
$982$		0			0
$983$	−27.0379	−	9.84100i	−0.862376	−	0.313879i	−0.127300	−	0.991864i	$-0.540631\pi$
$983$	−27.0379	−	9.84100i	−0.862376	−	0.313879i	−0.735076	+	0.677985i	$0.762853\pi$
$984$		0			0
$985$	0.372752	+	0.312776i	0.0118769	+	0.00996588i
$986$		0			0
$987$	5.77679	+	4.58588i	0.183877	+	0.145970i
$988$		0			0
$989$	−37.4642			−1.19129
$990$		0			0
$991$	−44.6552			−1.41852			−0.709260	−	0.704947i	$-0.750971\pi$
$991$	−44.6552			−1.41852			−0.709260	+	0.704947i	$0.750971\pi$
$992$		0			0
$993$	15.2318	+	4.19331i	0.483367	+	0.133071i
$994$		0			0
$995$	−9.48914	−	7.96234i	−0.300826	−	0.252423i
$996$		0			0
$997$	−6.37024	+	5.34526i	−0.201747	+	0.169286i	−0.738064	−	0.674731i	$-0.764260\pi$
$997$	−6.37024	+	5.34526i	−0.201747	+	0.169286i	0.536317	+	0.844017i	$0.319815\pi$
$998$		0			0
$999$	0.174871	−	0.0430282i	0.00553267	−	0.00136135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.1	✓	144
7.2	even	3		756.2.bq.a.625.16	yes	144
27.7	even	9		756.2.bq.a.277.16	yes	144
189.142	even	9	inner	756.2.bp.a.709.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.1	✓	144	1.1	even	1	trivial
756.2.bp.a.709.1	yes	144	189.142	even	9	inner
756.2.bq.a.277.16	yes	144	27.7	even	9
756.2.bq.a.625.16	yes	144	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72645 + 0.139144i) q^{3} +(-0.604458 + 0.220005i) q^{5} +(-2.43449 - 1.03598i) q^{7} +(2.96128 - 0.480450i) q^{9} +O(q^{10})\)	\(q+(-1.72645 + 0.139144i) q^{3} +(-0.604458 + 0.220005i) q^{5} +(-2.43449 - 1.03598i) q^{7} +(2.96128 - 0.480450i) q^{9} +(3.29749 + 1.20019i) q^{11} +(3.30070 - 1.20136i) q^{13} +(1.01296 - 0.463934i) q^{15} +(-3.32777 - 5.76387i) q^{17} +(-3.85167 + 6.67129i) q^{19} +(4.34718 + 1.44983i) q^{21} +(-0.950630 + 5.39129i) q^{23} +(-3.51325 + 2.94797i) q^{25} +(-5.04565 + 1.24152i) q^{27} +(-4.55828 - 1.65908i) q^{29} +(-2.08254 + 0.757984i) q^{31} +(-5.85995 - 1.61324i) q^{33} +(1.69947 + 0.0906102i) q^{35} -0.0346577 q^{37} +(-5.53135 + 2.53336i) q^{39} +(-10.3758 + 3.77650i) q^{41} +(1.18835 + 6.73949i) q^{43} +(-1.68427 + 0.941907i) q^{45} +(1.51245 + 0.550488i) q^{47} +(4.85347 + 5.04419i) q^{49} +(6.54725 + 9.48802i) q^{51} +(-0.109688 + 0.189985i) q^{53} -2.25724 q^{55} +(5.72146 - 12.0536i) q^{57} +(-8.00526 - 6.71721i) q^{59} +(5.71836 + 2.08131i) q^{61} +(-7.70694 - 1.89819i) q^{63} +(-1.73083 + 1.45234i) q^{65} +(1.88174 - 10.6719i) q^{67} +(0.891053 - 9.44008i) q^{69} +(-6.84419 + 11.8545i) q^{71} +3.55317 q^{73} +(5.65528 - 5.57838i) q^{75} +(-6.78432 - 6.33798i) q^{77} +(2.62111 + 14.8650i) q^{79} +(8.53834 - 2.84549i) q^{81} +(-11.6151 - 4.22756i) q^{83} +(3.27958 + 2.75189i) q^{85} +(8.10051 + 2.23007i) q^{87} +(2.25492 - 3.90564i) q^{89} +(-9.28011 - 0.494786i) q^{91} +(3.48995 - 1.59840i) q^{93} +(0.860458 - 4.87990i) q^{95} +(2.53604 + 14.3826i) q^{97} +(10.3414 + 1.96981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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