LMFDB - Embedded newform 804.2.o.d.365.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.3
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53706 + 0.798403i) q^{3} -3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 - 2.45439i) q^{9} +O(q^{10})$	\(q+(-1.53706 + 0.798403i) q^{3} -3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 - 2.45439i) q^{9} +(-0.987044 + 1.70961i) q^{11} +(-4.07559 + 2.35304i) q^{13} +(4.92452 - 2.55797i) q^{15} +(-2.01339 + 1.16243i) q^{17} +(-3.36730 - 5.83233i) q^{19} +(-5.05028 - 0.225008i) q^{21} +(4.96371 - 2.86580i) q^{23} +5.26471 q^{25} +(-0.692002 + 5.14987i) q^{27} +(7.75975 + 4.48009i) q^{29} +(-0.441467 - 0.254881i) q^{31} +(0.152188 - 3.41583i) q^{33} +(-8.09821 - 4.67550i) q^{35} +(-5.77782 - 10.0075i) q^{37} +(4.38575 - 6.87073i) q^{39} +(4.44499 - 7.69895i) q^{41} -11.8911i q^{43} +(-5.52699 + 7.86350i) q^{45} +(-10.8496 - 6.26403i) q^{47} +(0.759320 + 1.31518i) q^{49} +(2.16661 - 3.39423i) q^{51} +3.44912 q^{53} +(3.16235 - 5.47735i) q^{55} +(9.83229 + 6.27618i) q^{57} -3.19468i q^{59} +(4.86430 - 2.80840i) q^{61} +(7.94222 - 3.68630i) q^{63} +(13.0576 - 7.53882i) q^{65} +(-2.26878 + 7.86464i) q^{67} +(-5.34146 + 8.36795i) q^{69} +(-7.69380 - 4.44202i) q^{71} +(0.977450 + 1.69299i) q^{73} +(-8.09217 + 4.20336i) q^{75} +(-4.98979 + 2.88086i) q^{77} +(8.79520 + 5.07791i) q^{79} +(-3.04802 - 8.46815i) q^{81} +(-11.1516 + 6.43837i) q^{83} +(6.45062 - 3.72427i) q^{85} +(-15.5041 - 0.690765i) q^{87} +1.87132i q^{89} -13.7355 q^{91} +(0.882060 + 0.0392990i) q^{93} +(10.7884 + 18.6860i) q^{95} +(-5.04464 + 2.91252i) q^{97} +(2.49329 + 5.37185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.53706	+	0.798403i	−0.887422	+	0.460958i
$3$	−1.53706	+	0.798403i	−0.887422	+	0.460958i
$4$		0			0
$5$	−3.20386			−1.43281			−0.716404	−	0.697685i	$-0.754213\pi$
$5$	−3.20386			−1.43281			−0.716404	+	0.697685i	$0.754213\pi$
$6$		0			0
$7$	2.52764	+	1.45934i	0.955359	+	0.551577i	0.894742	−	0.446584i	$-0.147360\pi$
$7$	2.52764	+	1.45934i	0.955359	+	0.551577i	0.0606176	+	0.998161i	$0.480693\pi$
$8$		0			0
$9$	1.72511	−	2.45439i	0.575035	−	0.818129i
$10$		0			0
$11$	−0.987044	+	1.70961i	−0.297605	+	0.515467i	−0.975588	−	0.219611i	$-0.929521\pi$
$11$	−0.987044	+	1.70961i	−0.297605	+	0.515467i	0.677982	+	0.735078i	$0.262855\pi$
$12$		0			0
$13$	−4.07559	+	2.35304i	−1.13037	+	0.652617i	−0.944027	−	0.329869i	$-0.892995\pi$
$13$	−4.07559	+	2.35304i	−1.13037	+	0.652617i	−0.186339	+	0.982486i	$0.559662\pi$
$14$		0			0
$15$	4.92452	−	2.55797i	1.27151	−	0.660465i
$16$		0			0
$17$	−2.01339	+	1.16243i	−0.488319	+	0.281931i	−0.723877	−	0.689929i	$-0.757642\pi$
$17$	−2.01339	+	1.16243i	−0.488319	+	0.281931i	0.235558	+	0.971860i	$0.424308\pi$
$18$		0			0
$19$	−3.36730	−	5.83233i	−0.772512	−	1.33803i	−0.936183	−	0.351514i	$-0.885667\pi$
$19$	−3.36730	−	5.83233i	−0.772512	−	1.33803i	0.163671	−	0.986515i	$-0.447666\pi$
$20$		0			0
$21$	−5.05028	−	0.225008i	−1.10206	−	0.0491009i
$22$		0			0
$23$	4.96371	−	2.86580i	1.03501	−	0.597561i	0.116591	−	0.993180i	$-0.462803\pi$
$23$	4.96371	−	2.86580i	1.03501	−	0.597561i	0.918415	+	0.395619i	$0.129470\pi$
$24$		0			0
$25$	5.26471			1.05294
$26$		0			0
$27$	−0.692002	+	5.14987i	−0.133176	+	0.991092i
$28$		0			0
$29$	7.75975	+	4.48009i	1.44095	+	0.831932i	0.997913	−	0.0645717i	$-0.0205681\pi$
$29$	7.75975	+	4.48009i	1.44095	+	0.831932i	0.443036	+	0.896504i	$0.353901\pi$
$30$		0			0
$31$	−0.441467	−	0.254881i	−0.0792899	−	0.0457780i	0.459831	−	0.888007i	$-0.347910\pi$
$31$	−0.441467	−	0.254881i	−0.0792899	−	0.0457780i	−0.539121	+	0.842228i	$0.681243\pi$
$32$		0			0
$33$	0.152188	−	3.41583i	0.0264925	−	0.594620i
$34$		0			0
$35$	−8.09821	−	4.67550i	−1.36885	−	0.790304i
$36$		0			0
$37$	−5.77782	−	10.0075i	−0.949867	−	1.64522i	−0.745699	−	0.666282i	$-0.767885\pi$
$37$	−5.77782	−	10.0075i	−0.949867	−	1.64522i	−0.204168	−	0.978936i	$-0.565449\pi$
$38$		0			0
$39$	4.38575	−	6.87073i	0.702282	−	1.10020i
$40$		0			0
$41$	4.44499	−	7.69895i	0.694191	−	1.20237i	−0.276262	−	0.961083i	$-0.589096\pi$
$41$	4.44499	−	7.69895i	0.694191	−	1.20237i	0.970453	−	0.241292i	$-0.0775711\pi$
$42$		0			0
$43$		−	11.8911i		−	1.81338i	−0.421797	−	0.906690i	$-0.638600\pi$
$43$		−	11.8911i		−	1.81338i	0.421797	−	0.906690i	$-0.361400\pi$
$44$		0			0
$45$	−5.52699	+	7.86350i	−0.823916	+	1.17222i
$46$		0			0
$47$	−10.8496	−	6.26403i	−1.58258	−	0.913702i	−0.994481	−	0.104912i	$-0.966544\pi$
$47$	−10.8496	−	6.26403i	−1.58258	−	0.913702i	−0.588097	−	0.808790i	$-0.700123\pi$
$48$		0			0
$49$	0.759320	+	1.31518i	0.108474	+	0.187883i
$50$		0			0
$51$	2.16661	−	3.39423i	0.303387	−	0.475287i
$52$		0			0
$53$	3.44912			0.473774			0.236887	−	0.971537i	$-0.423873\pi$
$53$	3.44912			0.473774			0.236887	+	0.971537i	$0.423873\pi$
$54$		0			0
$55$	3.16235	−	5.47735i	0.426411	−	0.738566i
$56$		0			0
$57$	9.83229	+	6.27618i	1.30232	+	0.831301i
$58$		0			0
$59$		−	3.19468i		−	0.415911i	−0.978138	−	0.207956i	$-0.933319\pi$
$59$		−	3.19468i		−	0.415911i	0.978138	−	0.207956i	$-0.0666810\pi$
$60$		0			0
$61$	4.86430	−	2.80840i	0.622810	−	0.359579i	−0.155152	−	0.987891i	$-0.549587\pi$
$61$	4.86430	−	2.80840i	0.622810	−	0.359579i	0.777962	+	0.628311i	$0.216254\pi$
$62$		0			0
$63$	7.94222	−	3.68630i	1.00063	−	0.464431i
$64$		0			0
$65$	13.0576	−	7.53882i	1.61960	−	0.935075i
$66$		0			0
$67$	−2.26878	+	7.86464i	−0.277176	+	0.960819i
$67$	−2.26878	+	7.86464i	−0.277176	+	0.960819i
$68$		0			0
$69$	−5.34146	+	8.36795i	−0.643036	+	1.00738i
$70$		0			0
$71$	−7.69380	−	4.44202i	−0.913086	−	0.527171i	−0.0316634	−	0.999499i	$-0.510080\pi$
$71$	−7.69380	−	4.44202i	−0.913086	−	0.527171i	−0.881423	+	0.472328i	$0.843414\pi$
$72$		0			0
$73$	0.977450	+	1.69299i	0.114402	+	0.198150i	0.917540	−	0.397642i	$-0.130172\pi$
$73$	0.977450	+	1.69299i	0.114402	+	0.198150i	−0.803139	+	0.595792i	$0.796838\pi$
$74$		0			0
$75$	−8.09217	+	4.20336i	−0.934403	+	0.485362i
$76$		0			0
$77$	−4.98979	+	2.88086i	−0.568639	+	0.328304i
$78$		0			0
$79$	8.79520	+	5.07791i	0.989538	+	0.571310i	0.905136	−	0.425122i	$-0.139769\pi$
$79$	8.79520	+	5.07791i	0.989538	+	0.571310i	0.0844016	+	0.996432i	$0.473102\pi$
$80$		0			0
$81$	−3.04802	−	8.46815i	−0.338669	−	0.940906i
$82$		0			0
$83$	−11.1516	+	6.43837i	−1.22404	+	0.706702i	−0.965778	−	0.259371i	$-0.916485\pi$
$83$	−11.1516	+	6.43837i	−1.22404	+	0.706702i	−0.258267	+	0.966074i	$0.583151\pi$
$84$		0			0
$85$	6.45062	−	3.72427i	0.699668	−	0.403954i
$86$		0			0
$87$	−15.5041	−	0.690765i	−1.66222	−	0.0740578i
$88$		0			0
$89$			1.87132i			0.198360i	0.995070	+	0.0991798i	$0.0316219\pi$
$89$			1.87132i			0.198360i	−0.995070	+	0.0991798i	$0.968378\pi$
$90$		0			0
$91$	−13.7355			−1.43987
$92$		0			0
$93$	0.882060	+	0.0392990i	0.0914654	+	0.00407512i
$94$		0			0
$95$	10.7884	+	18.6860i	1.10686	+	1.91714i
$96$		0			0
$97$	−5.04464	+	2.91252i	−0.512205	+	0.295722i	−0.733740	−	0.679431i	$-0.762227\pi$
$97$	−5.04464	+	2.91252i	−0.512205	+	0.295722i	0.221534	+	0.975153i	$0.428894\pi$
$98$		0			0
$99$	2.49329	+	5.37185i	0.250585	+	0.539891i
$100$		0			0
$101$	6.46599	−	11.1994i	0.643390	−	1.11438i	−0.341281	−	0.939961i	$-0.610861\pi$
$101$	6.46599	−	11.1994i	0.643390	−	1.11438i	0.984671	−	0.174423i	$-0.0558061\pi$
$102$		0			0
$103$	2.00365	−	3.47042i	0.197425	−	0.341951i	−0.750268	−	0.661134i	$-0.770075\pi$
$103$	2.00365	−	3.47042i	0.197425	−	0.341951i	0.947693	+	0.319184i	$0.103409\pi$
$104$		0			0
$105$	16.1804	+	0.720895i	1.57904	+	0.0703522i
$106$		0			0
$107$		−	2.64243i		−	0.255453i	−0.991809	−	0.127726i	$-0.959232\pi$
$107$		−	2.64243i		−	0.255453i	0.991809	−	0.127726i	$-0.0407680\pi$
$108$		0			0
$109$			9.40209i			0.900557i	0.892888	+	0.450279i	$0.148675\pi$
$109$			9.40209i			0.900557i	−0.892888	+	0.450279i	$0.851325\pi$
$110$		0			0
$111$	16.8708	+	10.7691i	1.60131	+	1.02215i
$112$		0			0
$113$	−6.41107	+	11.1043i	−0.603103	+	1.04461i	0.389245	+	0.921134i	$0.372736\pi$
$113$	−6.41107	+	11.1043i	−0.603103	+	1.04461i	−0.992348	+	0.123471i	$0.960597\pi$
$114$		0			0
$115$	−15.9030	+	9.18162i	−1.48297	+	0.856190i
$116$		0			0
$117$	−1.25555	+	14.0623i	−0.116076	+	1.30006i
$118$		0			0
$119$	−6.78551			−0.622027
$120$		0			0
$121$	3.55149	+	6.15136i	0.322862	+	0.559214i
$122$		0			0
$123$	−0.685354	+	15.3826i	−0.0617962	+	1.38701i
$124$		0			0
$125$	−0.848087			−0.0758552
$126$		0			0
$127$	−1.32461	+	2.29429i	−0.117540	+	0.203586i	−0.918792	−	0.394741i	$-0.870834\pi$
$127$	−1.32461	+	2.29429i	−0.117540	+	0.203586i	0.801252	+	0.598327i	$0.204168\pi$
$128$		0			0
$129$	9.49392	+	18.2774i	0.835893	+	1.60923i
$130$		0			0
$131$		−	4.66707i		−	0.407764i	−0.978995	−	0.203882i	$-0.934644\pi$
$131$		−	4.66707i		−	0.407764i	0.978995	−	0.203882i	$-0.0653559\pi$
$132$		0			0
$133$		−	19.6561i		−	1.70440i
$134$		0			0
$135$	2.21708	−	16.4994i	0.190816	−	1.42005i
$136$		0			0
$137$	−5.38077			−0.459710			−0.229855	−	0.973225i	$-0.573825\pi$
$137$	−5.38077			−0.459710			−0.229855	+	0.973225i	$0.573825\pi$
$138$		0			0
$139$		−	7.85597i		−	0.666335i	−0.942868	−	0.333167i	$-0.891883\pi$
$139$		−	7.85597i		−	0.666335i	0.942868	−	0.333167i	$-0.108117\pi$
$140$		0			0
$141$	21.6777	+	0.965823i	1.82559	+	0.0813369i
$142$		0			0
$143$		−	9.29023i		−	0.776888i
$144$		0			0
$145$	−24.8611	−	14.3536i	−2.06460	−	1.19200i
$146$		0			0
$147$	−2.21716	−	1.41527i	−0.182869	−	0.116729i
$148$		0			0
$149$			10.2426i			0.839104i	0.907731	+	0.419552i	$0.137813\pi$
$149$			10.2426i			0.839104i	−0.907731	+	0.419552i	$0.862187\pi$
$150$		0			0
$151$	−11.2120	−	19.4198i	−0.912420	−	1.58036i	−0.810636	−	0.585551i	$-0.800878\pi$
$151$	−11.2120	−	19.4198i	−0.912420	−	1.58036i	−0.101784	−	0.994807i	$-0.532455\pi$
$152$		0			0
$153$	−0.620256	+	6.94696i	−0.0501448	+	0.561628i
$154$		0			0
$155$	1.41440	+	0.816604i	0.113607	+	0.0655912i
$156$		0			0
$157$	5.15104	+	8.92186i	0.411098	+	0.712042i	0.995010	−	0.0997745i	$-0.0318121\pi$
$157$	5.15104	+	8.92186i	0.411098	+	0.712042i	−0.583912	+	0.811817i	$0.698479\pi$
$158$		0			0
$159$	−5.30151	+	2.75379i	−0.420437	+	0.218390i
$160$		0			0
$161$	16.7287			1.31840
$162$		0			0
$163$	7.12151	−	12.3348i	0.557800	−	0.966138i	−0.439880	−	0.898057i	$-0.644979\pi$
$163$	7.12151	−	12.3348i	0.557800	−	0.966138i	0.997680	−	0.0680812i	$-0.0216877\pi$
$164$		0			0
$165$	−0.487589	+	10.9438i	−0.0379587	+	0.851977i
$166$		0			0
$167$	−4.17054	−	2.40786i	−0.322726	−	0.186326i	0.329881	−	0.944023i	$-0.392991\pi$
$167$	−4.17054	−	2.40786i	−0.322726	−	0.186326i	−0.652607	+	0.757697i	$0.726325\pi$
$168$		0			0
$169$	4.57362	−	7.92175i	0.351817	−	0.609365i
$170$		0			0
$171$	−20.1237	−	1.79674i	−1.53890	−	0.137400i
$172$		0			0
$173$	−7.52908	+	4.34692i	−0.572425	+	0.330490i	−0.758117	−	0.652118i	$-0.773881\pi$
$173$	−7.52908	+	4.34692i	−0.572425	+	0.330490i	0.185692	+	0.982608i	$0.440547\pi$
$174$		0			0
$175$	13.3073	+	7.68297i	1.00594	+	0.580778i
$176$		0			0
$177$	2.55064	+	4.91041i	0.191718	+	0.369089i
$178$		0			0
$179$	−5.10471			−0.381544			−0.190772	−	0.981634i	$-0.561099\pi$
$179$	−5.10471			−0.381544			−0.190772	+	0.981634i	$0.561099\pi$
$180$		0			0
$181$	0.232900	−	0.403395i	0.0173113	−	0.0299841i	−0.857240	−	0.514917i	$-0.827823\pi$
$181$	0.232900	−	0.403395i	0.0173113	−	0.0299841i	0.874551	+	0.484933i	$0.161156\pi$
$182$		0			0
$183$	−5.23448	+	8.20036i	−0.386944	+	0.606188i
$184$		0			0
$185$	18.5113	+	32.0625i	1.36098	+	2.35728i
$186$		0			0
$187$		−	4.58949i		−	0.335617i
$188$		0			0
$189$	−9.26452	+	12.0072i	−0.673895	+	0.873393i
$190$		0			0
$191$	−7.02138	−	12.1614i	−0.508050	−	0.879968i	−0.999957	−	0.00931986i	$-0.997033\pi$
$191$	−7.02138	−	12.1614i	−0.508050	−	0.879968i	0.491907	−	0.870648i	$-0.336300\pi$
$192$		0			0
$193$	−22.8992			−1.64832			−0.824161	−	0.566356i	$-0.808353\pi$
$193$	−22.8992			−1.64832			−0.824161	+	0.566356i	$0.808353\pi$
$194$		0			0
$195$	−14.0513	+	22.0128i	−1.00624	+	1.57637i
$196$		0			0
$197$	7.48173	−	12.9587i	0.533051	−	0.923272i	−0.466204	−	0.884677i	$-0.654379\pi$
$197$	7.48173	−	12.9587i	0.533051	−	0.923272i	0.999255	−	0.0385943i	$-0.0122880\pi$
$198$		0			0
$199$	1.02061	+	1.76776i	0.0723494	+	0.125313i	0.899931	−	0.436033i	$-0.143617\pi$
$199$	1.02061	+	1.76776i	0.0723494	+	0.125313i	−0.827581	+	0.561346i	$0.810284\pi$
$200$		0			0
$201$	−2.79191	−	13.8998i	−0.196926	−	0.980418i
$202$		0			0
$203$	13.0759	+	22.6481i	0.917749	+	1.58959i
$204$		0			0
$205$	−14.2411	+	24.6664i	−0.994643	+	1.72277i
$206$		0			0
$207$	1.52915	−	17.1267i	0.106283	−	1.19039i
$208$		0			0
$209$	13.2947			0.919613
$210$		0			0
$211$	−5.61946	−	9.73320i	−0.386860	−	0.670061i	0.605165	−	0.796100i	$-0.293107\pi$
$211$	−5.61946	−	9.73320i	−0.386860	−	0.670061i	−0.992025	+	0.126039i	$0.959774\pi$
$212$		0			0
$213$	15.3724	+	0.684895i	1.05330	+	0.0469282i
$214$		0			0
$215$			38.0975i			2.59823i
$216$		0			0
$217$	−0.743915	−	1.28850i	−0.0505002	−	0.0874690i
$218$		0			0
$219$	−2.85409	−	1.82183i	−0.192861	−	0.123108i
$220$		0			0
$221$	5.47051	−	9.47519i	0.367986	−	0.637371i
$222$		0			0
$223$	−2.71436			−0.181767			−0.0908836	−	0.995862i	$-0.528969\pi$
$223$	−2.71436			−0.181767			−0.0908836	+	0.995862i	$0.528969\pi$
$224$		0			0
$225$	9.08218	−	12.9216i	0.605479	−	0.861442i
$226$		0			0
$227$	−1.37699	−	0.795008i	−0.0913943	−	0.0527665i	0.453606	−	0.891202i	$-0.350137\pi$
$227$	−1.37699	−	0.795008i	−0.0913943	−	0.0527665i	−0.545001	+	0.838436i	$0.683471\pi$
$228$		0			0
$229$	−16.9492	+	9.78563i	−1.12003	+	0.646652i	−0.941410	−	0.337265i	$-0.890498\pi$
$229$	−16.9492	+	9.78563i	−1.12003	+	0.646652i	−0.178625	+	0.983917i	$0.557165\pi$
$230$		0			0
$231$	5.36952	−	8.41191i	0.353289	−	0.553463i
$232$		0			0
$233$	−7.15629	+	12.3951i	−0.468824	+	0.812027i	−0.999365	−	0.0356320i	$-0.988656\pi$
$233$	−7.15629	+	12.3951i	−0.468824	+	0.812027i	0.530541	+	0.847659i	$0.321989\pi$
$234$		0			0
$235$	34.7606	+	20.0691i	2.26753	+	1.30916i
$236$		0			0
$237$	−17.5730	−	0.782941i	−1.14149	−	0.0508575i
$238$		0			0
$239$	0.671399	−	1.16290i	0.0434292	−	0.0752216i	−0.843494	−	0.537139i	$-0.819505\pi$
$239$	0.671399	−	1.16290i	0.0434292	−	0.0752216i	0.886923	+	0.461917i	$0.152838\pi$
$240$		0			0
$241$	−16.4061			−1.05681			−0.528406	−	0.848992i	$-0.677210\pi$
$241$	−16.4061			−1.05681			−0.528406	+	0.848992i	$0.677210\pi$
$242$		0			0
$243$	11.4460	+	10.5825i	0.734260	+	0.678868i
$244$		0			0
$245$	−2.43275	−	4.21365i	−0.155423	−	0.269200i
$246$		0			0
$247$	27.4475	+	15.8468i	1.74644	+	1.00831i
$248$		0			0
$249$	12.0002	−	18.7996i	0.760484	−	1.19138i
$250$		0			0
$251$	−4.36026	−	7.55219i	−0.275217	−	0.476690i	0.694973	−	0.719036i	$-0.255416\pi$
$251$	−4.36026	−	7.55219i	−0.275217	−	0.476690i	−0.970190	+	0.242346i	$0.922083\pi$
$252$		0			0
$253$			11.3147i			0.711348i
$254$		0			0
$255$	−6.94152	+	10.8746i	−0.434695	+	0.680995i
$256$		0			0
$257$	12.8887	+	7.44127i	0.803973	+	0.464174i	0.844858	−	0.534990i	$-0.179685\pi$
$257$	12.8887	+	7.44127i	0.803973	+	0.464174i	−0.0408856	+	0.999164i	$0.513018\pi$
$258$		0			0
$259$		−	33.7271i		−	2.09570i
$260$		0			0
$261$	24.3823	−	11.3168i	1.50922	−	0.700491i
$262$		0			0
$263$		−	11.5112i		−	0.709810i	−0.934902	−	0.354905i	$-0.884513\pi$
$263$		−	11.5112i		−	0.709810i	0.934902	−	0.354905i	$-0.115487\pi$
$264$		0			0
$265$	−11.0505			−0.678827
$266$		0			0
$267$	−1.49407	−	2.87633i	−0.0914355	−	0.176029i
$268$		0			0
$269$		−	28.4279i		−	1.73328i	−0.498933	−	0.866641i	$-0.666275\pi$
$269$		−	28.4279i		−	1.73328i	0.498933	−	0.866641i	$-0.333725\pi$
$270$		0			0
$271$		−	17.3458i		−	1.05368i	−0.849963	−	0.526842i	$-0.823376\pi$
$271$		−	17.3458i		−	1.05368i	0.849963	−	0.526842i	$-0.176624\pi$
$272$		0			0
$273$	21.1123	−	10.9665i	1.27778	−	0.663721i
$274$		0			0
$275$	−5.19650	+	9.00060i	−0.313361	+	0.542757i
$276$		0			0
$277$	−5.75928			−0.346042			−0.173021	−	0.984918i	$-0.555353\pi$
$277$	−5.75928			−0.346042			−0.173021	+	0.984918i	$0.555353\pi$
$278$		0			0
$279$	−1.38716	+	0.643834i	−0.0830468	+	0.0385453i
$280$		0			0
$281$	9.90115	+	17.1493i	0.590653	+	1.02304i	0.994145	+	0.108058i	$0.0344631\pi$
$281$	9.90115	+	17.1493i	0.590653	+	1.02304i	−0.403492	+	0.914983i	$0.632204\pi$
$282$		0			0
$283$	12.5205			0.744265			0.372133	−	0.928180i	$-0.378627\pi$
$283$	12.5205			0.744265			0.372133	+	0.928180i	$0.378627\pi$
$284$		0			0
$285$	−31.5013	−	20.1080i	−1.86597	−	1.19110i
$286$		0			0
$287$	22.4707	−	12.9735i	1.32640	−	0.765800i
$288$		0			0
$289$	−5.79750	+	10.0416i	−0.341030	+	0.590681i
$290$		0			0
$291$	5.42854	−	8.50438i	0.318227	−	0.498535i
$292$		0			0
$293$		−	6.13214i		−	0.358243i	−0.983827	−	0.179122i	$-0.942674\pi$
$293$		−	6.13214i		−	0.358243i	0.983827	−	0.179122i	$-0.0573256\pi$
$294$		0			0
$295$			10.2353i			0.595921i
$296$		0			0
$297$	−8.12123	−	6.26620i	−0.471242	−	0.363602i
$298$		0			0
$299$	−13.4867	+	23.3597i	−0.779956	+	1.35092i
$300$		0			0
$301$	17.3532	−	30.0565i	1.00022	−	1.73243i
$302$		0			0
$303$	−0.996963	+	22.3767i	−0.0572740	+	1.28551i
$304$		0			0
$305$	−15.5845	+	8.99773i	−0.892367	+	0.515209i
$306$		0			0
$307$	14.1653	+	24.5350i	0.808455	+	1.40029i	0.913934	+	0.405864i	$0.133029\pi$
$307$	14.1653	+	24.5350i	0.808455	+	1.40029i	−0.105479	+	0.994422i	$0.533637\pi$
$308$		0			0
$309$	−0.308934	+	6.93397i	−0.0175746	+	0.394460i
$310$		0			0
$311$	4.02974			0.228506			0.114253	−	0.993452i	$-0.463553\pi$
$311$	4.02974			0.228506			0.114253	+	0.993452i	$0.463553\pi$
$312$		0			0
$313$			4.30403i			0.243278i	0.992574	+	0.121639i	$0.0388150\pi$
$313$			4.30403i			0.243278i	−0.992574	+	0.121639i	$0.961185\pi$
$314$		0			0
$315$	−25.4458	+	11.8104i	−1.43371	+	0.665440i
$316$		0			0
$317$	4.44287	−	2.56509i	0.249536	−	0.144070i	−0.370016	−	0.929026i	$-0.620648\pi$
$317$	4.44287	−	2.56509i	0.249536	−	0.144070i	0.619552	+	0.784956i	$0.287314\pi$
$318$		0			0
$319$	−15.3184	+	8.84410i	−0.857667	+	0.495174i
$320$		0			0
$321$	2.10972	+	4.06157i	0.117753	+	0.226695i
$322$		0			0
$323$	13.5594	+	7.82851i	0.754464	+	0.435590i
$324$		0			0
$325$	−21.4568	+	12.3881i	−1.19021	+	0.687167i
$326$		0			0
$327$	−7.50666	−	14.4516i	−0.415119	−	0.799174i
$328$		0			0
$329$	−18.2826	−	31.6665i	−1.00795	−	1.74583i
$330$		0			0
$331$	−6.85838	−	3.95969i	−0.376971	−	0.217644i	0.299529	−	0.954087i	$-0.403171\pi$
$331$	−6.85838	−	3.95969i	−0.376971	−	0.217644i	−0.676499	+	0.736443i	$0.736504\pi$
$332$		0			0
$333$	−34.5295	−	3.08296i	−1.89221	−	0.168945i
$334$		0			0
$335$	7.26885	−	25.1972i	0.397140	−	1.37667i
$336$		0			0
$337$	29.7888	−	17.1986i	1.62270	−	0.936867i	0.636508	−	0.771270i	$-0.280378\pi$
$337$	29.7888	−	17.1986i	1.62270	−	0.936867i	0.986193	−	0.165597i	$-0.0529552\pi$
$338$		0			0
$339$	0.988495	−	22.1866i	0.0536877	−	1.20501i
$340$		0			0
$341$	0.871496	−	0.503158i	0.0471941	−	0.0272476i
$342$		0			0
$343$		−	15.9983i		−	0.863826i
$344$		0			0
$345$	17.1133	−	26.8097i	0.921348	−	1.44339i
$346$		0			0
$347$	−13.4672	+	23.3259i	−0.722957	+	1.25220i	0.236852	+	0.971546i	$0.423884\pi$
$347$	−13.4672	+	23.3259i	−0.722957	+	1.25220i	−0.959809	+	0.280653i	$0.909449\pi$
$348$		0			0
$349$	13.6050			0.728261			0.364130	−	0.931348i	$-0.381366\pi$
$349$	13.6050			0.728261			0.364130	+	0.931348i	$0.381366\pi$
$350$		0			0
$351$	−9.29754	−	22.6171i	−0.496266	−	1.20721i
$352$		0			0
$353$	−7.19818	−	12.4676i	−0.383120	−	0.663584i	0.608386	−	0.793641i	$-0.291817\pi$
$353$	−7.19818	−	12.4676i	−0.383120	−	0.663584i	−0.991507	+	0.130057i	$0.958484\pi$
$354$		0			0
$355$	24.6499	+	14.2316i	1.30828	+	0.755335i
$356$		0			0
$357$	10.4297	−	5.41757i	0.552000	−	0.286728i
$358$		0			0
$359$		−	20.5974i		−	1.08709i	−0.839381	−	0.543544i	$-0.817082\pi$
$359$		−	20.5974i		−	1.08709i	0.839381	−	0.543544i	$-0.182918\pi$
$360$		0			0
$361$	−13.1774	+	22.8240i	−0.693548	+	1.20126i
$362$		0			0
$363$	−10.3701	−	6.61949i	−0.544290	−	0.347433i
$364$		0			0
$365$	−3.13161	−	5.42411i	−0.163916	−	0.283911i
$366$		0			0
$367$	10.8988	+	6.29240i	0.568911	+	0.328461i	0.756714	−	0.653746i	$-0.226803\pi$
$367$	10.8988	+	6.29240i	0.568911	+	0.328461i	−0.187803	+	0.982207i	$0.560137\pi$
$368$		0			0
$369$	−11.2281	−	24.1912i	−0.584512	−	1.25935i
$370$		0			0
$371$	8.71815	+	5.03343i	0.452624	+	0.261323i
$372$		0			0
$373$	−18.5514	−	10.7107i	−0.960556	−	0.554578i	−0.0642122	−	0.997936i	$-0.520453\pi$
$373$	−18.5514	−	10.7107i	−0.960556	−	0.554578i	−0.896344	+	0.443359i	$0.853787\pi$
$374$		0			0
$375$	1.30356	−	0.677115i	0.0673156	−	0.0349661i
$376$		0			0
$377$	−42.1674			−2.17173
$378$		0			0
$379$	−0.845081	+	0.487908i	−0.0434089	+	0.0250621i	−0.521547	−	0.853222i	$-0.674645\pi$
$379$	−0.845081	+	0.487908i	−0.0434089	+	0.0250621i	0.478139	+	0.878284i	$0.341312\pi$
$380$		0			0
$381$	0.204236	−	4.58404i	0.0104633	−	0.234848i
$382$		0			0
$383$	0.216664	+	0.375273i	0.0110710	+	0.0191755i	0.871508	−	0.490382i	$-0.163143\pi$
$383$	0.216664	+	0.375273i	0.0110710	+	0.0191755i	−0.860437	+	0.509557i	$0.829809\pi$
$384$		0			0
$385$	15.9866	−	9.22986i	0.814752	−	0.470397i
$386$		0			0
$387$	−29.1854	−	20.5135i	−1.48358	−	1.04276i
$388$		0			0
$389$	7.74886	−	4.47381i	0.392883	−	0.226831i	−0.290526	−	0.956867i	$-0.593830\pi$
$389$	7.74886	−	4.47381i	0.392883	−	0.226831i	0.683409	+	0.730036i	$0.260497\pi$
$390$		0			0
$391$	−6.66260	+	11.5400i	−0.336942	+	0.583601i
$392$		0			0
$393$	3.72621	+	7.17357i	0.187962	+	0.361859i
$394$		0			0
$395$	−28.1786	−	16.2689i	−1.41782	−	0.818578i
$396$		0			0
$397$	24.1534			1.21223			0.606113	−	0.795378i	$-0.292728\pi$
$397$	24.1534			1.21223			0.606113	+	0.795378i	$0.292728\pi$
$398$		0			0
$399$	15.6935	+	30.2126i	0.785656	+	1.51252i
$400$		0			0
$401$	−27.2167			−1.35914			−0.679569	−	0.733611i	$-0.737833\pi$
$401$	−27.2167			−1.35914			−0.679569	+	0.733611i	$0.737833\pi$
$402$		0			0
$403$	2.39899			0.119502
$404$		0			0
$405$	9.76542	+	27.1308i	0.485248	+	1.34814i
$406$		0			0
$407$	22.8118			1.13074
$408$		0			0
$409$	3.81181	+	2.20075i	0.188482	+	0.108820i	0.591272	−	0.806472i	$-0.298626\pi$
$409$	3.81181	+	2.20075i	0.188482	+	0.108820i	−0.402790	+	0.915293i	$0.631959\pi$
$410$		0			0
$411$	8.27056	−	4.29602i	0.407957	−	0.211907i
$412$		0			0
$413$	4.66210	−	8.07500i	0.229407	−	0.397345i
$414$		0			0
$415$	35.7281	−	20.6276i	1.75382	−	1.01257i
$416$		0			0
$417$	6.27223	+	12.0751i	0.307152	+	0.591320i
$418$		0			0
$419$	14.1367	−	8.16182i	0.690622	−	0.398731i	−0.113223	−	0.993570i	$-0.536117\pi$
$419$	14.1367	−	8.16182i	0.690622	−	0.398731i	0.803845	+	0.594839i	$0.202784\pi$
$420$		0			0
$421$	3.71634	+	6.43689i	0.181123	+	0.313715i	0.942263	−	0.334873i	$-0.108693\pi$
$421$	3.71634	+	6.43689i	0.181123	+	0.313715i	−0.761140	+	0.648588i	$0.775360\pi$
$422$		0			0
$423$	−34.0911	+	15.8230i	−1.65756	+	0.769342i
$424$		0			0
$425$	−10.5999	+	6.11987i	−0.514172	+	0.296857i
$426$		0			0
$427$	16.3936			0.793343
$428$		0			0
$429$	7.41735	+	14.2796i	0.358113	+	0.689427i
$430$		0			0
$431$	−26.6502	−	15.3865i	−1.28370	−	0.741142i	−0.306174	−	0.951976i	$-0.599049\pi$
$431$	−26.6502	−	15.3865i	−1.28370	−	0.741142i	−0.977522	+	0.210834i	$0.932382\pi$
$432$		0			0
$433$	−3.19421	−	1.84418i	−0.153504	−	0.0886255i	0.421281	−	0.906930i	$-0.361581\pi$
$433$	−3.19421	−	1.84418i	−0.153504	−	0.0886255i	−0.574784	+	0.818305i	$0.694914\pi$
$434$		0			0
$435$	49.6730	+	2.21311i	2.38164	+	0.106111i
$436$		0			0
$437$	−33.4286	−	19.3000i	−1.59911	−	0.923245i
$438$		0			0
$439$	9.88666	+	17.1242i	0.471865	+	0.817294i	0.999482	−	0.0321887i	$-0.0102477\pi$
$439$	9.88666	+	17.1242i	0.471865	+	0.817294i	−0.527617	+	0.849482i	$0.676914\pi$
$440$		0			0
$441$	4.53787	+	0.405162i	0.216089	+	0.0192934i
$442$		0			0
$443$	−6.50699	+	11.2704i	−0.309157	+	0.535475i	−0.978178	−	0.207768i	$-0.933380\pi$
$443$	−6.50699	+	11.2704i	−0.309157	+	0.535475i	0.669022	+	0.743243i	$0.266713\pi$
$444$		0			0
$445$		−	5.99545i		−	0.284211i
$446$		0			0
$447$	−8.17769	−	15.7434i	−0.386792	−	0.744639i
$448$		0			0
$449$	−6.01808	−	3.47454i	−0.284011	−	0.163974i	0.351227	−	0.936290i	$-0.385765\pi$
$449$	−6.01808	−	3.47454i	−0.284011	−	0.163974i	−0.635238	+	0.772317i	$0.719098\pi$
$450$		0			0
$451$	8.77481	+	15.1984i	0.413190	+	0.715665i
$452$		0			0
$453$	32.7383	+	20.8976i	1.53818	+	0.981856i
$454$		0			0
$455$	44.0066			2.06306
$456$		0			0
$457$	1.09725	−	1.90048i	0.0513270	−	0.0889009i	−0.839220	−	0.543791i	$-0.816988\pi$
$457$	1.09725	−	1.90048i	0.0513270	−	0.0889009i	0.890547	+	0.454890i	$0.150322\pi$
$458$		0			0
$459$	−4.59310	−	11.1731i	−0.214388	−	0.521516i
$460$		0			0
$461$			3.44843i			0.160609i	0.996770	+	0.0803047i	$0.0255893\pi$
$461$			3.44843i			0.160609i	−0.996770	+	0.0803047i	$0.974411\pi$
$462$		0			0
$463$	−35.5673	+	20.5348i	−1.65295	+	0.954331i	−0.677100	+	0.735891i	$0.736764\pi$
$463$	−35.5673	+	20.5348i	−1.65295	+	0.954331i	−0.975850	+	0.218441i	$0.929903\pi$
$464$		0			0
$465$	−2.82599	−	0.125909i	−0.131052	−	0.00583887i
$466$		0			0
$467$	0.832464	−	0.480623i	0.0385218	−	0.0222406i	−0.480615	−	0.876931i	$-0.659587\pi$
$467$	0.832464	−	0.480623i	0.0385218	−	0.0222406i	0.519137	+	0.854691i	$0.326253\pi$
$468$		0			0
$469$	−17.2118	+	16.5681i	−0.794768	+	0.765044i
$470$		0			0
$471$	−15.0407	−	9.60083i	−0.693039	−	0.442383i
$472$		0			0
$473$	20.3292	+	11.7371i	0.934738	+	0.539671i
$474$		0			0
$475$	−17.7278	−	30.7055i	−0.813410	−	1.40887i
$476$		0			0
$477$	5.95010	−	8.46548i	0.272437	−	0.387608i
$478$		0			0
$479$	−21.0787	+	12.1698i	−0.963111	+	0.556052i	−0.897129	−	0.441768i	$-0.854351\pi$
$479$	−21.0787	+	12.1698i	−0.963111	+	0.556052i	−0.0659819	+	0.997821i	$0.521018\pi$
$480$		0			0
$481$	47.0960	+	27.1909i	2.14739	+	1.23980i
$482$		0			0
$483$	−25.7129	+	13.3562i	−1.16998	+	0.607728i
$484$		0			0
$485$	16.1623	−	9.33131i	0.733892	−	0.423713i
$486$		0			0
$487$	7.77489	−	4.48884i	0.352314	−	0.203409i	−0.313390	−	0.949625i	$-0.601465\pi$
$487$	7.77489	−	4.48884i	0.352314	−	0.203409i	0.665704	+	0.746216i	$0.268131\pi$
$488$		0			0
$489$	−1.09803	+	24.6452i	−0.0496548	+	1.11449i
$490$		0			0
$491$		−	13.0618i		−	0.589470i	−0.955579	−	0.294735i	$-0.904769\pi$
$491$		−	13.0618i		−	0.589470i	0.955579	−	0.294735i	$-0.0952314\pi$
$492$		0			0
$493$	−20.8312			−0.938191
$494$		0			0
$495$	−7.98814	−	17.2106i	−0.359040	−	0.773561i
$496$		0			0
$497$	−12.9648	−	22.4557i	−0.581550	−	1.00727i
$498$		0			0
$499$	−21.0939	+	12.1786i	−0.944293	+	0.545188i	−0.891304	−	0.453407i	$-0.850208\pi$
$499$	−21.0939	+	12.1786i	−0.944293	+	0.545188i	−0.0529899	+	0.998595i	$0.516875\pi$
$500$		0			0
$501$	8.33281	+	0.371258i	0.372283	+	0.0165866i
$502$		0			0
$503$	10.8279	−	18.7544i	0.482791	−	0.836219i	−0.517013	−	0.855977i	$-0.672956\pi$
$503$	10.8279	−	18.7544i	0.482791	−	0.836219i	0.999805	+	0.0197581i	$0.00628961\pi$
$504$		0			0
$505$	−20.7161	+	35.8814i	−0.921855	+	1.59670i
$506$		0			0
$507$	−0.705187	+	15.8278i	−0.0313184	+	0.702937i
$508$		0			0
$509$		−	3.86563i		−	0.171341i	−0.996324	−	0.0856705i	$-0.972697\pi$
$509$		−	3.86563i		−	0.171341i	0.996324	−	0.0856705i	$-0.0273032\pi$
$510$		0			0
$511$			5.70571i			0.252406i
$512$		0			0
$513$	32.3659	−	13.3052i	1.42899	−	0.587437i
$514$		0			0
$515$	−6.41941	+	11.1187i	−0.282873	+	0.489950i
$516$		0			0
$517$	21.4181	−	12.3657i	0.941967	−	0.543845i
$518$		0			0
$519$	8.10206	−	12.6927i	0.355641	−	0.557148i
$520$		0			0
$521$	−11.9852			−0.525081			−0.262541	−	0.964921i	$-0.584560\pi$
$521$	−11.9852			−0.525081			−0.262541	+	0.964921i	$0.584560\pi$
$522$		0			0
$523$	−8.87338	−	15.3691i	−0.388006	−	0.672046i	0.604175	−	0.796851i	$-0.293503\pi$
$523$	−8.87338	−	15.3691i	−0.388006	−	0.672046i	−0.992181	+	0.124806i	$0.960169\pi$
$524$		0			0
$525$	−26.5882	−	1.18460i	−1.16041	−	0.0517003i
$526$		0			0
$527$	1.18513			0.0516250
$528$		0			0
$529$	4.92563	−	8.53144i	0.214158	−	0.370932i
$530$		0			0
$531$	−7.84097	−	5.51115i	−0.340269	−	0.239164i
$532$		0			0
$533$			41.8370i			1.81216i
$534$		0			0
$535$			8.46596i			0.366015i
$536$		0			0
$537$	7.84625	−	4.07562i	0.338591	−	0.175876i
$538$		0			0
$539$	−2.99793			−0.129130
$540$		0			0
$541$		−	0.595897i		−	0.0256196i	−0.999918	−	0.0128098i	$-0.995922\pi$
$541$		−	0.595897i		−	0.0256196i	0.999918	−	0.0128098i	$-0.00407760\pi$
$542$		0			0
$543$	−0.0359099	+	0.805991i	−0.00154104	+	0.0345884i
$544$		0			0
$545$		−	30.1230i		−	1.29033i
$546$		0			0
$547$	−31.7116	−	18.3087i	−1.35589	−	0.782824i	−0.366824	−	0.930290i	$-0.619555\pi$
$547$	−31.7116	−	18.3087i	−1.35589	−	0.782824i	−0.989067	+	0.147466i	$0.952888\pi$
$548$		0			0
$549$	1.49852	−	16.7837i	0.0639554	−	0.716309i
$550$		0			0
$551$		−	60.3433i		−	2.57071i
$552$		0			0
$553$	14.8208	+	25.6703i	0.630243	+	1.09161i
$554$		0			0
$555$	−54.0518	−	34.5025i	−2.29437	−	1.46455i
$556$		0			0
$557$	−7.01612	−	4.05076i	−0.297283	−	0.171636i	0.343939	−	0.938992i	$-0.388239\pi$
$557$	−7.01612	−	4.05076i	−0.297283	−	0.171636i	−0.641221	+	0.767356i	$0.721572\pi$
$558$		0			0
$559$	27.9804	+	48.4634i	1.18344	+	2.04978i
$560$		0			0
$561$	3.66426	+	7.05432i	0.154705	+	0.297834i
$562$		0			0
$563$	−4.35191			−0.183411			−0.0917055	−	0.995786i	$-0.529232\pi$
$563$	−4.35191			−0.183411			−0.0917055	+	0.995786i	$0.529232\pi$
$564$		0			0
$565$	20.5402	−	35.5766i	0.864132	−	1.49672i
$566$		0			0
$567$	4.65357	−	25.8525i	0.195431	−	1.08570i
$568$		0			0
$569$	37.1223	+	21.4326i	1.55625	+	0.898500i	0.997611	+	0.0690877i	$0.0220088\pi$
$569$	37.1223	+	21.4326i	1.55625	+	0.898500i	0.558637	+	0.829412i	$0.311325\pi$
$570$		0			0
$571$	1.40481	−	2.43321i	0.0587897	−	0.101827i	−0.835133	−	0.550049i	$-0.814609\pi$
$571$	1.40481	−	2.43321i	0.0587897	−	0.101827i	0.893922	+	0.448222i	$0.147943\pi$
$572$		0			0
$573$	20.5020	+	13.0869i	0.856482	+	0.546713i
$574$		0			0
$575$	26.1325	−	15.0876i	1.08980	−	0.629197i
$576$		0			0
$577$	−25.6115	−	14.7868i	−1.06622	−	0.615582i	−0.139073	−	0.990282i	$-0.544412\pi$
$577$	−25.6115	−	14.7868i	−1.06622	−	0.615582i	−0.927146	+	0.374700i	$0.877746\pi$
$578$		0			0
$579$	35.1975	−	18.2828i	1.46276	−	0.759807i
$580$		0			0
$581$	−37.5829			−1.55920
$582$		0			0
$583$	−3.40444	+	5.89666i	−0.140997	+	0.244215i
$584$		0			0
$585$	4.02260	−	45.0537i	0.166314	−	1.86274i
$586$		0			0
$587$	−6.48911	−	11.2395i	−0.267834	−	0.463903i	0.700468	−	0.713684i	$-0.252975\pi$
$587$	−6.48911	−	11.2395i	−0.267834	−	0.463903i	−0.968302	+	0.249781i	$0.919641\pi$
$588$		0			0
$589$			3.43305i			0.141456i
$590$		0			0
$591$	−1.15357	+	25.8918i	−0.0474517	+	1.06505i
$592$		0			0
$593$	10.8855	+	18.8542i	0.447013	+	0.774250i	0.998190	−	0.0601388i	$-0.0191543\pi$
$593$	10.8855	+	18.8542i	0.447013	+	0.774250i	−0.551177	+	0.834389i	$0.685821\pi$
$594$		0			0
$595$	21.7398			0.891246
$596$		0			0
$597$	−2.98013	−	1.90228i	−0.121968	−	0.0778553i
$598$		0			0
$599$	0.356374	−	0.617258i	0.0145610	−	0.0252205i	−0.858653	−	0.512557i	$-0.828698\pi$
$599$	0.356374	−	0.617258i	0.0145610	−	0.0252205i	0.873214	+	0.487337i	$0.162032\pi$
$600$		0			0
$601$	−12.3893	−	21.4589i	−0.505369	−	0.875326i	−0.999981	−	0.00621128i	$-0.998023\pi$
$601$	−12.3893	−	21.4589i	−0.505369	−	0.875326i	0.494611	−	0.869114i	$-0.335310\pi$
$602$		0			0
$603$	15.3890	+	19.1358i	0.626688	+	0.779270i
$604$		0			0
$605$	−11.3785	−	19.7081i	−0.462600	−	0.801247i
$606$		0			0
$607$	−10.6326	+	18.4162i	−0.431565	+	0.747492i	−0.997008	−	0.0772949i	$-0.975372\pi$
$607$	−10.6326	+	18.4162i	−0.431565	+	0.747492i	0.565443	+	0.824787i	$0.308705\pi$
$608$		0			0
$609$	−38.1808	−	24.3717i	−1.54716	−	0.987592i
$610$		0			0
$611$	58.9581			2.38519
$612$		0			0
$613$	5.60084	+	9.70094i	0.226216	+	0.391817i	0.956683	−	0.291130i	$-0.0940312\pi$
$613$	5.60084	+	9.70094i	0.226216	+	0.391817i	−0.730468	+	0.682947i	$0.760698\pi$
$614$		0			0
$615$	2.19578	−	49.2838i	0.0885422	−	1.98732i
$616$		0			0
$617$			22.9497i			0.923921i	0.886901	+	0.461960i	$0.152854\pi$
$617$			22.9497i			0.923921i	−0.886901	+	0.461960i	$0.847146\pi$
$618$		0			0
$619$	−12.6873	−	21.9750i	−0.509944	−	0.883249i	−0.999934	−	0.0115210i	$-0.996333\pi$
$619$	−12.6873	−	21.9750i	−0.509944	−	0.883249i	0.489989	−	0.871728i	$-0.337001\pi$
$620$		0			0
$621$	11.3236	+	27.5456i	0.454400	+	1.10537i
$622$		0			0
$623$	−2.73088	+	4.73003i	−0.109411	+	0.189505i
$624$		0			0
$625$	−23.6064			−0.944256
$626$		0			0
$627$	−20.4347	+	10.6145i	−0.816085	+	0.423903i
$628$		0			0
$629$	23.2660	+	13.4326i	0.927677	+	0.535594i
$630$		0			0
$631$	28.3908	−	16.3914i	1.13022	−	0.652533i	0.186230	−	0.982506i	$-0.440373\pi$
$631$	28.3908	−	16.3914i	1.13022	−	0.652533i	0.943990	+	0.329973i	$0.107040\pi$
$632$		0			0
$633$	16.4085	+	10.4739i	0.652178	+	0.416301i
$634$		0			0
$635$	4.24387	−	7.35059i	0.168413	−	0.291699i
$636$		0			0
$637$	−6.18935	−	3.57342i	−0.245231	−	0.141584i
$638$		0			0
$639$	−24.1751	+	11.2206i	−0.956350	+	0.443880i
$640$		0			0
$641$	−9.92337	+	17.1878i	−0.391950	+	0.678877i	−0.992707	−	0.120555i	$-0.961533\pi$
$641$	−9.92337	+	17.1878i	−0.391950	+	0.678877i	0.600757	+	0.799432i	$0.294866\pi$
$642$		0			0
$643$	−20.7556			−0.818521			−0.409260	−	0.912418i	$-0.634213\pi$
$643$	−20.7556			−0.818521			−0.409260	+	0.912418i	$0.634213\pi$
$644$		0			0
$645$	−30.4172	−	58.5582i	−1.19767	−	2.30572i
$646$		0			0
$647$	15.6324	+	27.0761i	0.614572	+	1.06447i	0.990459	+	0.137805i	$0.0440046\pi$
$647$	15.6324	+	27.0761i	0.614572	+	1.06447i	−0.375887	+	0.926665i	$0.622662\pi$
$648$		0			0
$649$	5.46165	+	3.15329i	0.214389	+	0.123777i
$650$		0			0
$651$	2.17218	+	1.38656i	0.0851345	+	0.0543434i
$652$		0			0
$653$	−4.12647	−	7.14725i	−0.161481	−	0.279693i	0.773919	−	0.633285i	$-0.218294\pi$
$653$	−4.12647	−	7.14725i	−0.161481	−	0.279693i	−0.935400	+	0.353591i	$0.884960\pi$
$654$		0			0
$655$			14.9526i			0.584248i
$656$		0			0
$657$	5.84146	+	0.521553i	0.227897	+	0.0203477i
$658$		0			0
$659$	−18.5290	−	10.6977i	−0.721789	−	0.416725i	0.0936220	−	0.995608i	$-0.470155\pi$
$659$	−18.5290	−	10.6977i	−0.721789	−	0.416725i	−0.815411	+	0.578883i	$0.803489\pi$
$660$		0			0
$661$		−	32.6187i		−	1.26872i	−0.773038	−	0.634359i	$-0.781264\pi$
$661$		−	32.6187i		−	1.26872i	0.773038	−	0.634359i	$-0.218736\pi$
$662$		0			0
$663$	−0.843473	+	18.9316i	−0.0327578	+	0.735243i
$664$		0			0
$665$			62.9753i			2.44208i
$666$		0			0
$667$	51.3562			1.98852
$668$		0			0
$669$	4.17214	−	2.16716i	0.161304	−	0.0837871i
$670$		0			0
$671$			11.0881i			0.428051i
$672$		0			0
$673$		−	1.33460i		−	0.0514450i	−0.999669	−	0.0257225i	$-0.991811\pi$
$673$		−	1.33460i		−	0.0514450i	0.999669	−	0.0257225i	$-0.00818863\pi$
$674$		0			0
$675$	−3.64319	+	27.1125i	−0.140226	+	1.04356i
$676$		0			0
$677$	−17.8648	+	30.9427i	−0.686599	+	1.18923i	0.286332	+	0.958131i	$0.407564\pi$
$677$	−17.8648	+	30.9427i	−0.686599	+	1.18923i	−0.972931	+	0.231095i	$0.925769\pi$
$678$		0			0
$679$	−17.0014			−0.652454
$680$		0			0
$681$	2.75126	+	0.122579i	0.105428	+	0.00469723i
$682$		0			0
$683$	23.4072	+	40.5424i	0.895651	+	1.55131i	0.832997	+	0.553277i	$0.186623\pi$
$683$	23.4072	+	40.5424i	0.895651	+	1.55131i	0.0626538	+	0.998035i	$0.480044\pi$
$684$		0			0
$685$	17.2392			0.658677
$686$		0			0
$687$	18.2391	−	28.5734i	0.695864	−	1.09014i
$688$		0			0
$689$	−14.0572	+	8.11594i	−0.535537	+	0.309193i
$690$		0			0
$691$	0.509742	−	0.882900i	0.0193915	−	0.0335871i	−0.856167	−	0.516700i	$-0.827160\pi$
$691$	0.509742	−	0.882900i	0.0193915	−	0.0335871i	0.875558	+	0.483112i	$0.160494\pi$
$692$		0			0
$693$	−1.53718	+	17.2167i	−0.0583927	+	0.654007i
$694$		0			0
$695$			25.1694i			0.954730i
$696$		0			0
$697$			20.6680i			0.782857i
$698$		0			0
$699$	1.10340	−	24.7656i	0.0417343	−	0.936719i
$700$		0			0
$701$	−0.684260	+	1.18517i	−0.0258442	+	0.0447634i	−0.878658	−	0.477451i	$-0.841561\pi$
$701$	−0.684260	+	1.18517i	−0.0258442	+	0.0447634i	0.852814	+	0.522215i	$0.174894\pi$
$702$		0			0
$703$	−38.9113	+	67.3963i	−1.46757	+	2.54190i
$704$		0			0
$705$	−69.4524	−	3.09436i	−2.61573	−	0.116540i
$706$		0			0
$707$	32.6874	−	18.8721i	1.22934	−	0.709758i
$708$		0			0
$709$	−9.74597	−	16.8805i	−0.366018	−	0.633961i	0.622921	−	0.782285i	$-0.285946\pi$
$709$	−9.74597	−	16.8805i	−0.366018	−	0.633961i	−0.988939	+	0.148323i	$0.952612\pi$
$710$		0			0
$711$	27.6358	−	12.8269i	1.03642	−	0.481046i
$712$		0			0
$713$	−2.92176			−0.109421
$714$		0			0
$715$			29.7646i			1.11313i
$716$		0			0
$717$	−0.103520	+	2.32349i	−0.00386603	+	0.0867723i
$718$		0			0
$719$	−7.42309	+	4.28572i	−0.276835	+	0.159831i	−0.631990	−	0.774977i	$-0.717761\pi$
$719$	−7.42309	+	4.28572i	−0.276835	+	0.159831i	0.355155	+	0.934807i	$0.384428\pi$
$720$		0			0
$721$	10.1290	−	5.84799i	0.377224	−	0.217791i
$722$		0			0
$723$	25.2172	−	13.0987i	0.937839	−	0.487146i
$724$		0			0
$725$	40.8528	+	23.5864i	1.51724	+	0.875976i
$726$		0			0
$727$	−3.91641	+	2.26114i	−0.145252	+	0.0838610i	−0.570864	−	0.821044i	$-0.693392\pi$
$727$	−3.91641	+	2.26114i	−0.145252	+	0.0838610i	0.425613	+	0.904905i	$0.360059\pi$
$728$		0			0
$729$	−26.0423	−	7.12744i	−0.964528	−	0.263979i
$730$		0			0
$731$	13.8226	+	23.9415i	0.511249	+	0.885509i
$732$		0			0
$733$	19.3552	+	11.1747i	0.714902	+	0.412749i	0.812873	−	0.582440i	$-0.197902\pi$
$733$	19.3552	+	11.1747i	0.714902	+	0.412749i	−0.0979715	+	0.995189i	$0.531235\pi$
$734$		0			0
$735$	7.10348	+	4.53432i	0.262016	+	0.167251i
$736$		0			0
$737$	−11.2061	−	11.6415i	−0.412782	−	0.428819i
$738$		0			0
$739$	7.14264	−	4.12381i	0.262746	−	0.151697i	−0.362840	−	0.931851i	$-0.618193\pi$
$739$	7.14264	−	4.12381i	0.262746	−	0.151697i	0.625587	+	0.780155i	$0.284860\pi$
$740$		0			0
$741$	−54.8405	−	2.44335i	−2.01462	−	0.0897586i
$742$		0			0
$743$	36.6126	−	21.1383i	1.34319	−	0.775489i	0.355912	−	0.934519i	$-0.384170\pi$
$743$	36.6126	−	21.1383i	1.34319	−	0.775489i	0.987274	+	0.159030i	$0.0508368\pi$
$744$		0			0
$745$		−	32.8157i		−	1.20228i
$746$		0			0
$747$	−3.43542	+	38.4771i	−0.125695	+	1.40780i
$748$		0			0
$749$	3.85619	−	6.67911i	0.140902	−	0.244049i
$750$		0			0
$751$	42.6819			1.55749			0.778743	−	0.627343i	$-0.215858\pi$
$751$	42.6819			1.55749			0.778743	+	0.627343i	$0.215858\pi$
$752$		0			0
$753$	12.7317	+	8.12692i	0.463968	+	0.296161i
$754$		0			0
$755$	35.9217	+	62.2181i	1.30732	+	2.26435i
$756$		0			0
$757$	−15.6349	−	9.02681i	−0.568260	−	0.328085i	0.188194	−	0.982132i	$-0.439737\pi$
$757$	−15.6349	−	9.02681i	−0.568260	−	0.328085i	−0.756454	+	0.654047i	$0.773070\pi$
$758$		0			0
$759$	−9.03368	−	17.3914i	−0.327902	−	0.631266i
$760$		0			0
$761$		−	41.7005i		−	1.51164i	−0.654779	−	0.755821i	$-0.727238\pi$
$761$		−	41.7005i		−	1.51164i	0.654779	−	0.755821i	$-0.272762\pi$
$762$		0			0
$763$	−13.7208	+	23.7651i	−0.496727	+	0.860356i
$764$		0			0
$765$	1.98721	−	22.2571i	0.0718479	−	0.804706i
$766$		0			0
$767$	7.51721	+	13.0202i	0.271431	+	0.470132i
$768$		0			0
$769$	13.4222	+	7.74931i	0.484017	+	0.279447i	0.722089	−	0.691800i	$-0.243182\pi$
$769$	13.4222	+	7.74931i	0.484017	+	0.279447i	−0.238072	+	0.971247i	$0.576515\pi$
$770$		0			0
$771$	−25.7518	−	1.14734i	−0.927428	−	0.0413203i
$772$		0			0
$773$	44.5890	+	25.7434i	1.60375	+	0.925927i	0.990727	+	0.135865i	$0.0433812\pi$
$773$	44.5890	+	25.7434i	1.60375	+	0.925927i	0.613026	+	0.790063i	$0.289952\pi$
$774$		0			0
$775$	−2.32420	−	1.34188i	−0.0834876	−	0.0482016i
$776$		0			0
$777$	26.9278	+	51.8406i	0.966030	+	1.85977i
$778$		0			0
$779$	−59.8705			−2.14508
$780$		0			0
$781$	15.1882	−	8.76894i	0.543478	−	0.313777i
$782$		0			0
$783$	−28.4416	+	36.8614i	−1.01642	+	1.31732i
$784$		0			0
$785$	−16.5032	−	28.5844i	−0.589025	−	1.02022i
$786$		0			0
$787$	−34.1786	+	19.7330i	−1.21834	+	0.703407i	−0.964562	−	0.263857i	$-0.915005\pi$
$787$	−34.1786	+	19.7330i	−1.21834	+	0.703407i	−0.253774	+	0.967264i	$0.581672\pi$
$788$		0			0
$789$	9.19056	+	17.6934i	0.327193	+	0.629901i
$790$		0			0
$791$	−32.4098	+	18.7118i	−1.15236	+	0.665316i
$792$		0			0
$793$	−13.2166	+	22.8918i	−0.469335	+	0.812912i
$794$		0			0
$795$	16.9853	−	8.82275i	0.602406	−	0.312911i
$796$		0			0
$797$	−35.3173	−	20.3905i	−1.25100	−	0.722268i	−0.279696	−	0.960089i	$-0.590234\pi$
$797$	−35.3173	−	20.3905i	−1.25100	−	0.722268i	−0.971309	+	0.237821i	$0.923567\pi$
$798$		0			0
$799$	29.1260			1.03040
$800$		0			0
$801$	4.59294	+	3.22823i	0.162284	+	0.114064i
$802$		0			0
$803$	−3.85914			−0.136186
$804$		0			0
$805$	−53.5962			−1.88902
$806$		0			0
$807$	22.6969	+	43.6954i	0.798970	+	1.53815i
$808$		0			0
$809$	−40.2433			−1.41488			−0.707440	−	0.706773i	$-0.750150\pi$
$809$	−40.2433			−1.41488			−0.707440	+	0.706773i	$0.750150\pi$
$810$		0			0
$811$	−11.4449	−	6.60772i	−0.401885	−	0.232029i	0.285412	−	0.958405i	$-0.407870\pi$
$811$	−11.4449	−	6.60772i	−0.401885	−	0.232029i	−0.687297	+	0.726376i	$0.741203\pi$
$812$		0			0
$813$	13.8489	+	26.6616i	0.485704	+	0.935062i
$814$		0			0
$815$	−22.8163	+	39.5190i	−0.799221	+	1.38429i
$816$		0			0
$817$	−69.3531	+	40.0410i	−2.42636	+	1.40086i
$818$		0			0
$819$	−23.6952	+	33.7123i	−0.827978	+	1.17800i
$820$		0			0
$821$	38.8196	−	22.4125i	1.35481	−	0.782202i	0.365894	−	0.930657i	$-0.380763\pi$
$821$	38.8196	−	22.4125i	1.35481	−	0.782202i	0.988919	+	0.148455i	$0.0474300\pi$
$822$		0			0
$823$	−1.92591	−	3.33578i	−0.0671331	−	0.116278i	0.830505	−	0.557011i	$-0.188052\pi$
$823$	−1.92591	−	3.33578i	−0.0671331	−	0.116278i	−0.897638	+	0.440733i	$0.854719\pi$
$824$		0			0
$825$	0.801225	−	17.9834i	0.0278951	−	0.626100i
$826$		0			0
$827$	−14.5840	+	8.42009i	−0.507136	+	0.292795i	−0.731656	−	0.681674i	$-0.761252\pi$
$827$	−14.5840	+	8.42009i	−0.507136	+	0.292795i	0.224519	+	0.974470i	$0.427919\pi$
$828$		0			0
$829$	53.3153			1.85172			0.925859	−	0.377870i	$-0.123343\pi$
$829$	53.3153			1.85172			0.925859	+	0.377870i	$0.123343\pi$
$830$		0			0
$831$	8.85236	−	4.59823i	0.307085	−	0.159511i
$832$		0			0
$833$	−3.05762	−	1.76532i	−0.105940	−	0.0611645i
$834$		0			0
$835$	13.3618	+	7.71445i	0.462405	+	0.266969i
$836$		0			0
$837$	1.61810	−	2.09712i	0.0559298	−	0.0724871i
$838$		0			0
$839$	38.7325	+	22.3622i	1.33720	+	0.772031i	0.986391	−	0.164418i	$-0.0525746\pi$
$839$	38.7325	+	22.3622i	1.33720	+	0.772031i	0.350805	+	0.936448i	$0.385908\pi$
$840$		0			0
$841$	25.6424	+	44.4140i	0.884222	+	1.53152i
$842$		0			0
$843$	−28.9107	−	18.4544i	−0.995737	−	0.635603i
$844$		0			0
$845$	−14.6532	+	25.3802i	−0.504087	+	0.873104i
$846$		0			0
$847$			20.7312i			0.712334i
$848$		0			0
$849$	−19.2447	+	9.99639i	−0.660477	+	0.343075i
$850$		0			0
$851$	−57.3588	−	33.1161i	−1.96624	−	1.13521i
$852$		0			0
$853$	−5.06303	−	8.76942i	−0.173355	−	0.300259i	0.766236	−	0.642559i	$-0.222127\pi$
$853$	−5.06303	−	8.76942i	−0.173355	−	0.300259i	−0.939591	+	0.342300i	$0.888794\pi$
$854$		0			0
$855$	64.4736	+	5.75650i	2.20495	+	0.196868i
$856$		0			0
$857$	−20.3805			−0.696184			−0.348092	−	0.937460i	$-0.613170\pi$
$857$	−20.3805			−0.696184			−0.348092	+	0.937460i	$0.613170\pi$
$858$		0			0
$859$	−15.1111	+	26.1733i	−0.515586	+	0.893021i	0.484251	+	0.874929i	$0.339092\pi$
$859$	−15.1111	+	26.1733i	−0.515586	+	0.893021i	−0.999836	+	0.0180914i	$0.994241\pi$
$860$		0			0
$861$	−24.1808	+	37.8817i	−0.824078	+	1.29100i
$862$		0			0
$863$		−	50.1250i		−	1.70628i	−0.521686	−	0.853138i	$-0.674697\pi$
$863$		−	50.1250i		−	1.70628i	0.521686	−	0.853138i	$-0.325303\pi$
$864$		0			0
$865$	24.1221	−	13.9269i	0.820176	−	0.473529i
$866$		0			0
$867$	0.893891	−	20.0632i	0.0303581	−	0.681383i
$868$		0			0
$869$	−17.3625	+	10.0242i	−0.588983	+	0.340049i
$870$		0			0
$871$	−9.25923	−	37.3916i	−0.313737	−	1.26697i
$872$		0			0
$873$	−1.55408	+	17.4059i	−0.0525976	+	0.589100i
$874$		0			0
$875$	−2.14366	−	1.23764i	−0.0724690	−	0.0418400i
$876$		0			0
$877$	16.7943	+	29.0886i	0.567103	+	0.982251i	0.996851	+	0.0793017i	$0.0252691\pi$
$877$	16.7943	+	29.0886i	0.567103	+	0.982251i	−0.429748	+	0.902949i	$0.641398\pi$
$878$		0			0
$879$	4.89592	+	9.42546i	0.165135	+	0.317913i
$880$		0			0
$881$	4.93257	−	2.84782i	0.166183	−	0.0959456i	−0.414602	−	0.910003i	$-0.636079\pi$
$881$	4.93257	−	2.84782i	0.166183	−	0.0959456i	0.580785	+	0.814057i	$0.302746\pi$
$882$		0			0
$883$	−7.53399	−	4.34975i	−0.253539	−	0.146381i	0.367845	−	0.929887i	$-0.380096\pi$
$883$	−7.53399	−	4.34975i	−0.253539	−	0.146381i	−0.621384	+	0.783506i	$0.713429\pi$
$884$		0			0
$885$	−8.17188	−	15.7322i	−0.274695	−	0.528834i
$886$		0			0
$887$	17.9553	−	10.3665i	0.602879	−	0.348072i	−0.167295	−	0.985907i	$-0.553503\pi$
$887$	17.9553	−	10.3665i	0.602879	−	0.348072i	0.770173	+	0.637835i	$0.220170\pi$
$888$		0			0
$889$	−6.69629	+	3.86611i	−0.224586	+	0.129665i
$890$		0			0
$891$	17.4858	+	3.14751i	0.585795	+	0.105446i
$892$		0			0
$893$			84.3714i			2.82338i
$894$		0			0
$895$	16.3548			0.546680
$896$		0			0
$897$	2.07946	−	46.6730i	0.0694310	−	1.55837i
$898$		0			0
$899$	−2.28378	−	3.95563i	−0.0761685	−	0.131928i
$900$		0			0
$901$	−6.94444	+	4.00937i	−0.231353	+	0.133572i
$902$		0			0
$903$	−2.67561	+	60.0535i	−0.0890386	+	1.99846i
$904$		0			0
$905$	−0.746179	+	1.29242i	−0.0248038	+	0.0429615i
$906$		0			0
$907$	15.0799	−	26.1192i	0.500721	−	0.867273i	−0.499279	−	0.866441i	$-0.666402\pi$
$907$	15.0799	−	26.1192i	0.500721	−	0.867273i	1.00000		0.000832243i	$-0.000264911\pi$
$908$		0			0
$909$	−16.3332	−	35.1902i	−0.541738	−	1.16719i
$910$		0			0
$911$		−	36.0923i		−	1.19579i	−0.801574	−	0.597895i	$-0.796004\pi$
$911$		−	36.0923i		−	1.19579i	0.801574	−	0.597895i	$-0.203996\pi$
$912$		0			0
$913$		−	25.4198i		−	0.841273i
$914$		0			0
$915$	16.7705	−	26.2728i	0.554417	−	0.868551i
$916$		0			0
$917$	6.81083	−	11.7967i	0.224913	−	0.389561i
$918$		0			0
$919$	16.2239	−	9.36686i	0.535176	−	0.308984i	−0.207945	−	0.978140i	$-0.566678\pi$
$919$	16.2239	−	9.36686i	0.535176	−	0.308984i	0.743122	+	0.669156i	$0.233344\pi$
$920$		0			0
$921$	−41.3617	−	26.4021i	−1.36291	−	0.869980i
$922$		0			0
$923$	41.8090			1.37616
$924$		0			0
$925$	−30.4185	−	52.6864i	−1.00015	−	1.73232i
$926$		0			0
$927$	−5.06125	−	10.9046i	−0.166233	−	0.358153i
$928$		0			0
$929$	26.1800			0.858937			0.429468	−	0.903082i	$-0.358701\pi$
$929$	26.1800			0.858937			0.429468	+	0.903082i	$0.358701\pi$
$930$		0			0
$931$	5.11371	−	8.85721i	0.167595	−	0.290283i
$932$		0			0
$933$	−6.19395	+	3.21736i	−0.202781	+	0.105332i
$934$		0			0
$935$			14.7041i			0.480874i
$936$		0			0
$937$		−	14.4685i		−	0.472667i	−0.971672	−	0.236333i	$-0.924054\pi$
$937$		−	14.4685i		−	0.472667i	0.971672	−	0.236333i	$-0.0759458\pi$
$938$		0			0
$939$	−3.43635	−	6.61555i	−0.112141	−	0.215890i
$940$		0			0
$941$	52.1415			1.69976			0.849881	−	0.526974i	$-0.176673\pi$
$941$	52.1415			1.69976			0.849881	+	0.526974i	$0.176673\pi$
$942$		0			0
$943$		−	50.9538i		−	1.65929i
$944$		0			0
$945$	29.6822	−	38.4692i	0.965562	−	1.25140i
$946$		0			0
$947$		−	1.99689i		−	0.0648903i	−0.999474	−	0.0324451i	$-0.989671\pi$
$947$		−	1.99689i		−	0.0648903i	0.999474	−	0.0324451i	$-0.0103294\pi$
$948$		0			0
$949$	−7.96737	−	4.59996i	−0.258632	−	0.149321i
$950$		0			0
$951$	−4.78098	+	7.48989i	−0.155034	+	0.242876i
$952$		0			0
$953$		−	9.50442i		−	0.307878i	−0.988080	−	0.153939i	$-0.950804\pi$
$953$		−	9.50442i		−	0.307878i	0.988080	−	0.153939i	$-0.0491960\pi$
$954$		0			0
$955$	22.4955	+	38.9634i	0.727938	+	1.26083i
$956$		0			0
$957$	16.4842	−	25.8242i	0.532858	−	0.834777i
$958$		0			0
$959$	−13.6007	−	7.85235i	−0.439188	−	0.253565i
$960$		0			0
$961$	−15.3701	−	26.6217i	−0.495809	−	0.858766i
$962$		0			0
$963$	−6.48553	−	4.55846i	−0.208993	−	0.146894i
$964$		0			0
$965$	73.3659			2.36173
$966$		0			0
$967$	9.05985	−	15.6921i	0.291345	−	0.504624i	−0.682783	−	0.730621i	$-0.739231\pi$
$967$	9.05985	−	15.6921i	0.291345	−	0.504624i	0.974128	+	0.225997i	$0.0725639\pi$
$968$		0			0
$969$	−27.0919	−	1.20704i	−0.870317	−	0.0387758i
$970$		0			0
$971$	−15.9602	−	9.21463i	−0.512187	−	0.295711i	0.221545	−	0.975150i	$-0.428890\pi$
$971$	−15.9602	−	9.21463i	−0.512187	−	0.295711i	−0.733732	+	0.679439i	$0.762223\pi$
$972$		0			0
$973$	11.4645	−	19.8571i	0.367535	−	0.636589i
$974$		0			0
$975$	23.0897	−	36.1724i	0.739462	−	1.15844i
$976$		0			0
$977$	30.8018	−	17.7834i	0.985437	−	0.568942i	0.0815295	−	0.996671i	$-0.474020\pi$
$977$	30.8018	−	17.7834i	0.985437	−	0.568942i	0.903907	+	0.427729i	$0.140686\pi$
$978$		0			0
$979$	−3.19923	−	1.84708i	−0.102248	−	0.0590328i
$980$		0			0
$981$	23.0764	+	16.2196i	0.736772	+	0.517852i
$982$		0			0
$983$	−23.8068			−0.759320			−0.379660	−	0.925126i	$-0.623959\pi$
$983$	−23.8068			−0.759320			−0.379660	+	0.925126i	$0.623959\pi$
$984$		0			0
$985$	−23.9704	+	41.5180i	−0.763760	+	1.32287i
$986$		0			0
$987$	53.3841	+	34.0763i	1.69923	+	1.08466i
$988$		0			0
$989$	−34.0776	−	59.0242i	−1.08361	−	1.87686i
$990$		0			0
$991$		−	7.49694i		−	0.238148i	−0.992885	−	0.119074i	$-0.962007\pi$
$991$		−	7.49694i		−	0.238148i	0.992885	−	0.119074i	$-0.0379926\pi$
$992$		0			0
$993$	13.7032	+	0.610526i	0.434857	+	0.0193745i
$994$		0			0
$995$	−3.26990	−	5.66364i	−0.103663	−	0.179549i
$996$		0			0
$997$	−26.8584			−0.850616			−0.425308	−	0.905049i	$-0.639834\pi$
$997$	−26.8584			−0.850616			−0.425308	+	0.905049i	$0.639834\pi$
$998$		0			0
$999$	55.5354	−	22.8298i	1.75706	−	0.722303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.3	✓	36
3.2	odd	2	inner	804.2.o.d.365.16	yes	36
67.38	odd	6	inner	804.2.o.d.641.16	yes	36
201.38	even	6	inner	804.2.o.d.641.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.3	✓	36	1.1	even	1	trivial
804.2.o.d.365.16	yes	36	3.2	odd	2	inner
804.2.o.d.641.3	yes	36	201.38	even	6	inner
804.2.o.d.641.16	yes	36	67.38	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53706 + 0.798403i) q^{3} -3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 - 2.45439i) q^{9} +O(q^{10})\)	\(q+(-1.53706 + 0.798403i) q^{3} -3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 - 2.45439i) q^{9} +(-0.987044 + 1.70961i) q^{11} +(-4.07559 + 2.35304i) q^{13} +(4.92452 - 2.55797i) q^{15} +(-2.01339 + 1.16243i) q^{17} +(-3.36730 - 5.83233i) q^{19} +(-5.05028 - 0.225008i) q^{21} +(4.96371 - 2.86580i) q^{23} +5.26471 q^{25} +(-0.692002 + 5.14987i) q^{27} +(7.75975 + 4.48009i) q^{29} +(-0.441467 - 0.254881i) q^{31} +(0.152188 - 3.41583i) q^{33} +(-8.09821 - 4.67550i) q^{35} +(-5.77782 - 10.0075i) q^{37} +(4.38575 - 6.87073i) q^{39} +(4.44499 - 7.69895i) q^{41} -11.8911i q^{43} +(-5.52699 + 7.86350i) q^{45} +(-10.8496 - 6.26403i) q^{47} +(0.759320 + 1.31518i) q^{49} +(2.16661 - 3.39423i) q^{51} +3.44912 q^{53} +(3.16235 - 5.47735i) q^{55} +(9.83229 + 6.27618i) q^{57} -3.19468i q^{59} +(4.86430 - 2.80840i) q^{61} +(7.94222 - 3.68630i) q^{63} +(13.0576 - 7.53882i) q^{65} +(-2.26878 + 7.86464i) q^{67} +(-5.34146 + 8.36795i) q^{69} +(-7.69380 - 4.44202i) q^{71} +(0.977450 + 1.69299i) q^{73} +(-8.09217 + 4.20336i) q^{75} +(-4.98979 + 2.88086i) q^{77} +(8.79520 + 5.07791i) q^{79} +(-3.04802 - 8.46815i) q^{81} +(-11.1516 + 6.43837i) q^{83} +(6.45062 - 3.72427i) q^{85} +(-15.5041 - 0.690765i) q^{87} +1.87132i q^{89} -13.7355 q^{91} +(0.882060 + 0.0392990i) q^{93} +(10.7884 + 18.6860i) q^{95} +(-5.04464 + 2.91252i) q^{97} +(2.49329 + 5.37185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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