LMFDB - Embedded newform 804.2.o.d.365.16

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			365.16
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53706 + 0.798403i) q^{3} +3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 + 2.45439i) q^{9} +O(q^{10})$	\(q+(1.53706 + 0.798403i) q^{3} +3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 + 2.45439i) q^{9} +(0.987044 - 1.70961i) q^{11} +(-4.07559 + 2.35304i) q^{13} +(4.92452 + 2.55797i) q^{15} +(2.01339 - 1.16243i) q^{17} +(-3.36730 - 5.83233i) q^{19} +(2.72000 + 4.26116i) q^{21} +(-4.96371 + 2.86580i) q^{23} +5.26471 q^{25} +(0.692002 + 5.14987i) q^{27} +(-7.75975 - 4.48009i) q^{29} +(-0.441467 - 0.254881i) q^{31} +(2.88210 - 1.83972i) q^{33} +(8.09821 + 4.67550i) q^{35} +(-5.77782 - 10.0075i) q^{37} +(-8.14310 + 0.362805i) q^{39} +(-4.44499 + 7.69895i) q^{41} -11.8911i q^{43} +(5.52699 + 7.86350i) q^{45} +(10.8496 + 6.26403i) q^{47} +(0.759320 + 1.31518i) q^{49} +(4.02279 - 0.179230i) q^{51} -3.44912 q^{53} +(3.16235 - 5.47735i) q^{55} +(-0.519189 - 11.6531i) q^{57} +3.19468i q^{59} +(4.86430 - 2.80840i) q^{61} +(0.778680 + 8.72132i) q^{63} +(-13.0576 + 7.53882i) q^{65} +(-2.26878 + 7.86464i) q^{67} +(-9.91759 + 0.441865i) q^{69} +(7.69380 + 4.44202i) q^{71} +(0.977450 + 1.69299i) q^{73} +(8.09217 + 4.20336i) q^{75} +(4.98979 - 2.88086i) q^{77} +(8.79520 + 5.07791i) q^{79} +(-3.04802 + 8.46815i) q^{81} +(11.1516 - 6.43837i) q^{83} +(6.45062 - 3.72427i) q^{85} +(-8.35028 - 13.0816i) q^{87} -1.87132i q^{89} -13.7355 q^{91} +(-0.475064 - 0.744237i) q^{93} +(-10.7884 - 18.6860i) q^{95} +(-5.04464 + 2.91252i) q^{97} +(5.89880 - 0.526672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.245787\pi$
$5$	3.20386			1.43281			0.716404	+	0.697685i	$0.245787\pi$
$6$		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	−0.677982	−	0.735078i	$-0.737145\pi$
$11$	0.987044	−	1.70961i	0.297605	−	0.515467i	0.975588	+	0.219611i	$0.0704788\pi$
$12$		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	−0.235558	−	0.971860i	$-0.575692\pi$
$17$	2.01339	−	1.16243i	0.488319	−	0.281931i	0.723877	+	0.689929i	$0.242358\pi$
$18$		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
$21$	2.72000	+	4.26116i	0.593553	+	0.929862i
$22$		0			0
$23$	−4.96371	+	2.86580i	−1.03501	+	0.597561i	−0.918415	−	0.395619i	$-0.870530\pi$
$23$	−4.96371	+	2.86580i	−1.03501	+	0.597561i	−0.116591	+	0.993180i	$0.537197\pi$
$24$		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	−0.443036	−	0.896504i	$-0.646099\pi$
$29$	−7.75975	−	4.48009i	−1.44095	−	0.831932i	−0.997913	+	0.0645717i	$0.979432\pi$
$30$		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
$33$	2.88210	−	1.83972i	0.501710	−	0.320253i
$34$		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
$39$	−8.14310	+	0.362805i	−1.30394	+	0.0580953i
$40$		0			0
$41$	−4.44499	+	7.69895i	−0.694191	+	1.20237i	0.276262	+	0.961083i	$0.410904\pi$
$41$	−4.44499	+	7.69895i	−0.694191	+	1.20237i	−0.970453	+	0.241292i	$0.922429\pi$
$42$		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	$0.0334561\pi$
$47$	10.8496	+	6.26403i	1.58258	+	0.913702i	0.588097	+	0.808790i	$0.299877\pi$
$48$		0			0
$49$	0.759320	+	1.31518i	0.108474	+	0.187883i
$50$		0			0
$51$	4.02279	−	0.179230i	0.563304	−	0.0250973i
$52$		0			0
$53$	−3.44912			−0.473774			−0.236887	−	0.971537i	$-0.576127\pi$
$53$	−3.44912			−0.473774			−0.236887	+	0.971537i	$0.576127\pi$
$54$		0			0
$55$	3.16235	−	5.47735i	0.426411	−	0.738566i
$56$		0			0
$57$	−0.519189	−	11.6531i	−0.0687683	−	1.54349i
$58$		0			0
$59$			3.19468i			0.415911i	0.978138	+	0.207956i	$0.0666810\pi$
$59$			3.19468i			0.415911i	−0.978138	+	0.207956i	$0.933319\pi$
$60$		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
$63$	0.778680	+	8.72132i	0.0981044	+	1.09878i
$64$		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
$69$	−9.91759	+	0.441865i	−1.19394	+	0.0531943i
$70$		0			0
$71$	7.69380	+	4.44202i	0.913086	+	0.527171i	0.881423	−	0.472328i	$-0.156586\pi$
$71$	7.69380	+	4.44202i	0.913086	+	0.527171i	0.0316634	+	0.999499i	$0.489920\pi$
$72$		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	0.258267	−	0.966074i	$-0.416849\pi$
$83$	11.1516	−	6.43837i	1.22404	−	0.706702i	0.965778	+	0.259371i	$0.0835153\pi$
$84$		0			0
$85$	6.45062	−	3.72427i	0.699668	−	0.403954i
$86$		0			0
$87$	−8.35028	−	13.0816i	−0.895244	−	1.40249i
$88$		0			0
$89$		−	1.87132i		−	0.198360i	−0.995070	−	0.0991798i	$-0.968378\pi$
$89$		−	1.87132i		−	0.198360i	0.995070	−	0.0991798i	$-0.0316219\pi$
$90$		0			0
$91$	−13.7355			−1.43987
$92$		0			0
$93$	−0.475064	−	0.744237i	−0.0492618	−	0.0771738i
$94$		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
$99$	5.89880	−	0.526672i	0.592852	−	0.0529325i
$100$		0			0
$101$	−6.46599	+	11.1994i	−0.643390	+	1.11438i	0.341281	+	0.939961i	$0.389139\pi$
$101$	−6.46599	+	11.1994i	−0.643390	+	1.11438i	−0.984671	+	0.174423i	$0.944194\pi$
$102$		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
$105$	8.71450	+	13.6522i	0.850448	+	1.33231i
$106$		0			0
$107$			2.64243i			0.255453i	0.991809	+	0.127726i	$0.0407680\pi$
$107$			2.64243i			0.255453i	−0.991809	+	0.127726i	$0.959232\pi$
$108$		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
$111$	−0.890856	−	19.9951i	−0.0845563	−	1.89785i
$112$		0			0
$113$	6.41107	−	11.1043i	0.603103	−	1.04461i	−0.389245	−	0.921134i	$-0.627264\pi$
$113$	6.41107	−	11.1043i	0.603103	−	1.04461i	0.992348	−	0.123471i	$-0.0394026\pi$
$114$		0			0
$115$	−15.9030	+	9.18162i	−1.48297	+	0.856190i
$116$		0			0
$117$	−12.8061	−	5.94382i	−1.18392	−	0.549507i
$118$		0			0
$119$	6.78551			0.622027
$120$		0			0
$121$	3.55149	+	6.15136i	0.322862	+	0.559214i
$122$		0			0
$123$	−12.9791	+	8.28486i	−1.17028	+	0.747020i
$124$		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	$0.0653559\pi$
$131$			4.66707i			0.407764i	−0.978995	+	0.203882i	$0.934644\pi$
$132$		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	$-0.426175\pi$
$137$	5.38077			0.459710			0.229855	+	0.973225i	$0.426175\pi$
$138$		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
$141$	11.6753	+	18.2905i	0.983237	+	1.54034i
$142$		0			0
$143$			9.29023i			0.776888i
$144$		0			0
$145$	−24.8611	−	14.3536i	−2.06460	−	1.19200i
$146$		0			0
$147$	0.117076	+	2.62775i	0.00965628	+	0.216733i
$148$		0			0
$149$		−	10.2426i		−	0.839104i	−0.907731	−	0.419552i	$-0.862187\pi$
$149$		−	10.2426i		−	0.839104i	0.907731	−	0.419552i	$-0.137813\pi$
$150$		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
$153$	6.32637	+	2.93632i	0.511457	+	0.237387i
$154$		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
$165$	9.23385	−	5.89419i	0.718854	−	0.458862i
$166$		0			0
$167$	4.17054	+	2.40786i	0.322726	+	0.186326i	0.652607	−	0.757697i	$-0.273675\pi$
$167$	4.17054	+	2.40786i	0.322726	+	0.186326i	−0.329881	+	0.944023i	$0.607009\pi$
$168$		0			0
$169$	4.57362	−	7.92175i	0.351817	−	0.609365i
$170$		0			0
$171$	8.50585	−	18.3260i	0.650459	−	1.40143i
$172$		0			0
$173$	7.52908	−	4.34692i	0.572425	−	0.330490i	−0.185692	−	0.982608i	$-0.559453\pi$
$173$	7.52908	−	4.34692i	0.572425	−	0.330490i	0.758117	+	0.652118i	$0.226119\pi$
$174$		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	$-0.438901\pi$
$179$	5.10471			0.381544			0.190772	+	0.981634i	$0.438901\pi$
$180$		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
$183$	9.71896	−	0.433015i	0.718446	−	0.0320094i
$184$		0			0
$185$	−18.5113	−	32.0625i	−1.36098	−	2.35728i
$186$		0			0
$187$		−	4.58949i		−	0.335617i
$188$		0			0
$189$	−5.76625	+	14.0269i	−0.419433	+	1.02031i
$190$		0			0
$191$	7.02138	+	12.1614i	0.508050	+	0.879968i	0.999957	+	0.00931986i	$0.00296665\pi$
$191$	7.02138	+	12.1614i	0.508050	+	0.879968i	−0.491907	+	0.870648i	$0.663700\pi$
$192$		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
$195$	−26.0893	+	1.16238i	−1.86830	+	0.0832395i
$196$		0			0
$197$	−7.48173	+	12.9587i	−0.533051	+	0.923272i	0.466204	+	0.884677i	$0.345621\pi$
$197$	−7.48173	+	12.9587i	−0.533051	+	0.923272i	−0.999255	+	0.0385943i	$0.987712\pi$
$198$		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
$201$	−9.76640	+	10.2770i	−0.688869	+	0.724886i
$202$		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
$207$	−15.5967	−	7.23906i	−1.08405	−	0.503149i
$208$		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
$213$	8.27931	+	12.9704i	0.567289	+	0.888717i
$214$		0			0
$215$		−	38.0975i		−	2.59823i
$216$		0			0
$217$	−0.743915	−	1.28850i	−0.0505002	−	0.0874690i
$218$		0			0
$219$	0.150709	+	3.38263i	0.0101839	+	0.228577i
$220$		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	0.545001	−	0.838436i	$-0.316529\pi$
$227$	1.37699	+	0.795008i	0.0913943	+	0.0527665i	−0.453606	+	0.891202i	$0.649863\pi$
$228$		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
$231$	9.96969	−	0.444187i	0.655958	−	0.0292253i
$232$		0			0
$233$	7.15629	−	12.3951i	0.468824	−	0.812027i	−0.530541	−	0.847659i	$-0.678011\pi$
$233$	7.15629	−	12.3951i	0.468824	−	0.812027i	0.999365	+	0.0356320i	$0.0113444\pi$
$234$		0			0
$235$	34.7606	+	20.0691i	2.26753	+	1.30916i
$236$		0			0
$237$	9.46453	+	14.8272i	0.614788	+	0.963128i
$238$		0			0
$239$	−0.671399	+	1.16290i	−0.0434292	+	0.0752216i	−0.886923	−	0.461917i	$-0.847162\pi$
$239$	−0.671399	+	1.16290i	−0.0434292	+	0.0752216i	0.843494	+	0.537139i	$0.180495\pi$
$240$		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
$249$	22.2810	−	0.992703i	1.41200	−	0.0629100i
$250$		0			0
$251$	4.36026	+	7.55219i	0.275217	+	0.476690i	0.970190	−	0.242346i	$-0.0779170\pi$
$251$	4.36026	+	7.55219i	0.275217	+	0.476690i	−0.694973	+	0.719036i	$0.744584\pi$
$252$		0			0
$253$			11.3147i			0.711348i
$254$		0			0
$255$	12.8885	−	0.574228i	0.807106	−	0.0359596i
$256$		0			0
$257$	−12.8887	−	7.44127i	−0.803973	−	0.464174i	0.0408856	−	0.999164i	$-0.486982\pi$
$257$	−12.8887	−	7.44127i	−0.803973	−	0.464174i	−0.844858	+	0.534990i	$0.820315\pi$
$258$		0			0
$259$		−	33.7271i		−	2.09570i
$260$		0			0
$261$	−2.39051	−	26.7740i	−0.147969	−	1.65727i
$262$		0			0
$263$			11.5112i			0.709810i	0.934902	+	0.354905i	$0.115487\pi$
$263$			11.5112i			0.709810i	−0.934902	+	0.354905i	$0.884513\pi$
$264$		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	$0.333725\pi$
$269$			28.4279i			1.73328i	−0.498933	+	0.866641i	$0.666275\pi$
$270$		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
$279$	−0.136001	−	1.52323i	−0.00814216	−	0.0911933i
$280$		0			0
$281$	−9.90115	−	17.1493i	−0.590653	−	1.02304i	−0.994145	−	0.108058i	$-0.965537\pi$
$281$	−9.90115	−	17.1493i	−0.590653	−	1.02304i	0.403492	−	0.914983i	$-0.367796\pi$
$282$		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
$285$	−1.66341	−	37.3349i	−0.0985318	−	2.21153i
$286$		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
$291$	−10.0793	+	0.449069i	−0.590858	+	0.0263249i
$292$		0			0
$293$			6.13214i			0.358243i	0.983827	+	0.179122i	$0.0573256\pi$
$293$			6.13214i			0.358243i	−0.983827	+	0.179122i	$0.942674\pi$
$294$		0			0
$295$			10.2353i			0.595921i
$296$		0			0
$297$	9.48731	+	3.90009i	0.550509	+	0.226306i
$298$		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
$303$	−18.8803	+	12.0517i	−1.08464	+	0.692353i
$304$		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
$309$	5.85052	−	3.73453i	0.332825	−	0.212450i
$310$		0			0
$311$	−4.02974			−0.228506			−0.114253	−	0.993452i	$-0.536447\pi$
$311$	−4.02974			−0.228506			−0.114253	+	0.993452i	$0.536447\pi$
$312$		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
$315$	2.49478	+	27.9419i	0.140565	+	1.57435i
$316$		0			0
$317$	−4.44287	+	2.56509i	−0.249536	+	0.144070i	−0.619552	−	0.784956i	$-0.712686\pi$
$317$	−4.44287	+	2.56509i	−0.249536	+	0.144070i	0.370016	+	0.929026i	$0.379352\pi$
$318$		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
$333$	14.5949	−	31.4449i	0.799793	−	1.72317i
$334$		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
$339$	18.7199	−	11.9494i	1.01673	−	0.649000i
$340$		0			0
$341$	−0.871496	+	0.503158i	−0.0471941	+	0.0272476i
$342$		0			0
$343$		−	15.9983i		−	0.863826i
$344$		0			0
$345$	−31.7745	+	1.41567i	−1.71068	+	0.0762173i
$346$		0			0
$347$	13.4672	−	23.3259i	0.722957	−	1.25220i	−0.236852	−	0.971546i	$-0.576116\pi$
$347$	13.4672	−	23.3259i	0.722957	−	1.25220i	0.959809	−	0.280653i	$-0.0905509\pi$
$348$		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
$351$	−14.9382	−	19.3604i	−0.797341	−	1.03338i
$352$		0			0
$353$	7.19818	+	12.4676i	0.383120	+	0.663584i	0.991507	−	0.130057i	$-0.0415161\pi$
$353$	7.19818	+	12.4676i	0.383120	+	0.663584i	−0.608386	+	0.793641i	$0.708183\pi$
$354$		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	$0.182918\pi$
$359$			20.5974i			1.08709i	−0.839381	+	0.543544i	$0.817082\pi$
$360$		0			0
$361$	−13.1774	+	22.8240i	−0.693548	+	1.20126i
$362$		0			0
$363$	0.547588	+	12.2905i	0.0287409	+	0.645085i
$364$		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
$369$	−26.5643	+	2.37178i	−1.38288	+	0.123470i
$370$		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
$381$	−3.86778	+	2.46889i	−0.198152	+	0.126485i
$382$		0			0
$383$	−0.216664	−	0.375273i	−0.0110710	−	0.0191755i	0.860437	−	0.509557i	$-0.170191\pi$
$383$	−0.216664	−	0.375273i	−0.0110710	−	0.0191755i	−0.871508	+	0.490382i	$0.836857\pi$
$384$		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	−0.683409	−	0.730036i	$-0.739503\pi$
$389$	−7.74886	+	4.47381i	−0.392883	+	0.226831i	0.290526	+	0.956867i	$0.406170\pi$
$390$		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	$-0.262167\pi$
$401$	27.2167			1.35914			0.679569	+	0.733611i	$0.262167\pi$
$402$		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	−0.803845	−	0.594839i	$-0.797216\pi$
$419$	−14.1367	+	8.16182i	−0.690622	+	0.398731i	0.113223	+	0.993570i	$0.463883\pi$
$420$		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
$423$	3.34239	+	37.4352i	0.162513	+	1.82016i
$424$		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	0.977522	−	0.210834i	$-0.0676179\pi$
$431$	26.6502	+	15.3865i	1.28370	+	0.741142i	0.306174	+	0.951976i	$0.400951\pi$
$432$		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
$435$	−26.7531	−	41.9115i	−1.28271	−	2.00950i
$436$		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
$441$	−1.91805	+	4.13249i	−0.0913358	+	0.196785i
$442$		0			0
$443$	6.50699	−	11.2704i	0.309157	−	0.535475i	−0.669022	−	0.743243i	$-0.733287\pi$
$443$	6.50699	−	11.2704i	0.309157	−	0.535475i	0.978178	+	0.207768i	$0.0666199\pi$
$444$		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	0.635238	−	0.772317i	$-0.280902\pi$
$449$	6.01808	+	3.47454i	0.284011	+	0.163974i	−0.351227	+	0.936290i	$0.614235\pi$
$450$		0			0
$451$	8.77481	+	15.1984i	0.413190	+	0.715665i
$452$		0			0
$453$	−1.72873	−	38.8010i	−0.0812227	−	1.82303i
$454$		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
$459$	7.37964	+	9.56429i	0.344452	+	0.446423i
$460$		0			0
$461$		−	3.44843i		−	0.160609i	−0.996770	−	0.0803047i	$-0.974411\pi$
$461$		−	3.44843i		−	0.160609i	0.996770	−	0.0803047i	$-0.0255893\pi$
$462$		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
$465$	−1.52204	−	2.38443i	−0.0705828	−	0.110575i
$466$		0			0
$467$	−0.832464	+	0.480623i	−0.0385218	+	0.0222406i	−0.519137	−	0.854691i	$-0.673747\pi$
$467$	−0.832464	+	0.480623i	−0.0385218	+	0.0222406i	0.480615	+	0.876931i	$0.340413\pi$
$468$		0			0
$469$	−17.2118	+	16.5681i	−0.794768	+	0.765044i
$470$		0			0
$471$	0.794216	+	17.8260i	0.0365955	+	0.821381i
$472$		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	0.0659819	−	0.997821i	$-0.478982\pi$
$479$	21.0787	−	12.1698i	0.963111	−	0.556052i	0.897129	+	0.441768i	$0.145649\pi$
$480$		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
$489$	20.7943	−	13.2735i	0.940353	−	0.600249i
$490$		0			0
$491$			13.0618i			0.589470i	0.955579	+	0.294735i	$0.0952314\pi$
$491$			13.0618i			0.589470i	−0.955579	+	0.294735i	$0.904769\pi$
$492$		0			0
$493$	−20.8312			−0.938191
$494$		0			0
$495$	18.8989	−	1.68738i	0.849443	−	0.0758422i
$496$		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
$501$	4.48792	+	7.03080i	0.200506	+	0.314113i
$502$		0			0
$503$	−10.8279	+	18.7544i	−0.482791	+	0.836219i	−0.999805	−	0.0197581i	$-0.993710\pi$
$503$	−10.8279	+	18.7544i	−0.482791	+	0.836219i	0.517013	+	0.855977i	$0.327044\pi$
$504$		0			0
$505$	−20.7161	+	35.8814i	−0.921855	+	1.59670i
$506$		0			0
$507$	13.3547	−	8.52461i	0.593102	−	0.378591i
$508$		0			0
$509$			3.86563i			0.171341i	0.996324	+	0.0856705i	$0.0273032\pi$
$509$			3.86563i			0.171341i	−0.996324	+	0.0856705i	$0.972697\pi$
$510$		0			0
$511$			5.70571i			0.252406i
$512$		0			0
$513$	27.7056	−	21.3771i	1.22323	−	0.943824i
$514$		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
$519$	15.0432	−	0.670232i	0.660325	−	0.0294199i
$520$		0			0
$521$	11.9852			0.525081			0.262541	−	0.964921i	$-0.415440\pi$
$521$	11.9852			0.525081			0.262541	+	0.964921i	$0.415440\pi$
$522$		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
$525$	14.3200	+	22.4338i	0.624977	+	0.979090i
$526$		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
$543$	0.680053	−	0.434094i	0.0291839	−	0.0186288i
$544$		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
$549$	15.2843	+	7.09407i	0.652320	+	0.302768i
$550$		0			0
$551$			60.3433i			2.57071i
$552$		0			0
$553$	14.8208	+	25.6703i	0.630243	+	1.09161i
$554$		0			0
$555$	−2.85418	−	64.0615i	−0.121153	−	2.71926i
$556$		0			0
$557$	7.01612	+	4.05076i	0.297283	+	0.171636i	0.641221	−	0.767356i	$-0.278428\pi$
$557$	7.01612	+	4.05076i	0.297283	+	0.171636i	−0.343939	+	0.938992i	$0.611761\pi$
$558$		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	$-0.470768\pi$
$563$	4.35191			0.183411			0.0917055	+	0.995786i	$0.470768\pi$
$564$		0			0
$565$	20.5402	−	35.5766i	0.864132	−	1.49672i
$566$		0			0
$567$	−20.0622	+	16.9564i	−0.842532	+	0.712101i
$568$		0			0
$569$	−37.1223	−	21.4326i	−1.55625	−	0.898500i	−0.997611	−	0.0690877i	$-0.977991\pi$
$569$	−37.1223	−	21.4326i	−1.55625	−	0.898500i	−0.558637	−	0.829412i	$-0.688675\pi$
$570$		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
$573$	1.08260	+	24.2987i	0.0452261	+	1.01509i
$574$		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
$585$	−41.0289	−	19.0432i	−1.69634	−	0.787338i
$586$		0			0
$587$	6.48911	+	11.2395i	0.267834	+	0.463903i	0.968302	−	0.249781i	$-0.0803587\pi$
$587$	6.48911	+	11.2395i	0.267834	+	0.463903i	−0.700468	+	0.713684i	$0.747025\pi$
$588$		0			0
$589$			3.43305i			0.141456i
$590$		0			0
$591$	−21.8462	+	13.9449i	−0.898631	+	0.573617i
$592$		0			0
$593$	−10.8855	−	18.8542i	−0.447013	−	0.774250i	0.551177	−	0.834389i	$-0.314179\pi$
$593$	−10.8855	−	18.8542i	−0.447013	−	0.774250i	−0.998190	+	0.0601388i	$0.980846\pi$
$594$		0			0
$595$	21.7398			0.891246
$596$		0			0
$597$	0.157364	+	3.53201i	0.00644048	+	0.144555i
$598$		0			0
$599$	−0.356374	+	0.617258i	−0.0145610	+	0.0252205i	−0.873214	−	0.487337i	$-0.837968\pi$
$599$	−0.356374	+	0.617258i	−0.0145610	+	0.0252205i	0.858653	+	0.512557i	$0.171302\pi$
$600$		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
$603$	−23.2168	+	7.99888i	−0.945459	+	0.325740i
$604$		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
$609$	−2.01612	−	45.2514i	−0.0816972	−	1.83368i
$610$		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
$615$	−41.5831	+	26.5435i	−1.67679	+	1.07034i
$616$		0			0
$617$		−	22.9497i		−	0.923921i	−0.886901	−	0.461960i	$-0.847146\pi$
$617$		−	22.9497i		−	0.923921i	0.886901	−	0.461960i	$-0.152854\pi$
$618$		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
$621$	−18.1934	−	23.5793i	−0.730076	−	0.946205i
$622$		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
$633$	−0.866440	−	19.4471i	−0.0344379	−	0.772953i
$634$		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
$639$	2.37020	+	26.5465i	0.0937635	+	1.05016i
$640$		0			0
$641$	9.92337	−	17.1878i	0.391950	−	0.678877i	−0.600757	−	0.799432i	$-0.705134\pi$
$641$	9.92337	−	17.1878i	0.391950	−	0.678877i	0.992707	+	0.120555i	$0.0384674\pi$
$642$		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	$-0.955995\pi$
$647$	−15.6324	−	27.0761i	−0.614572	−	1.06447i	0.375887	−	0.926665i	$-0.377338\pi$
$648$		0			0
$649$	5.46165	+	3.15329i	0.214389	+	0.123777i
$650$		0			0
$651$	−0.114701	−	2.57444i	−0.00449548	−	0.100900i
$652$		0			0
$653$	4.12647	+	7.14725i	0.161481	+	0.279693i	0.935400	−	0.353591i	$-0.115040\pi$
$653$	4.12647	+	7.14725i	0.161481	+	0.279693i	−0.773919	+	0.633285i	$0.781706\pi$
$654$		0			0
$655$			14.9526i			0.584248i
$656$		0			0
$657$	−2.46905	+	5.31963i	−0.0963269	+	0.207539i
$658$		0			0
$659$	18.5290	+	10.6977i	0.721789	+	0.416725i	0.815411	−	0.578883i	$-0.196511\pi$
$659$	18.5290	+	10.6977i	0.721789	+	0.416725i	−0.0936220	+	0.995608i	$0.529845\pi$
$660$		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
$663$	−15.9735	+	10.1963i	−0.620360	+	0.395990i
$664$		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	$-0.592436\pi$
$677$	17.8648	−	30.9427i	0.686599	−	1.18923i	0.972931	−	0.231095i	$-0.0742307\pi$
$678$		0			0
$679$	−17.0014			−0.652454
$680$		0			0
$681$	1.48179	+	2.32137i	0.0567821	+	0.0889551i
$682$		0			0
$683$	−23.4072	−	40.5424i	−0.895651	−	1.55131i	−0.832997	−	0.553277i	$-0.813377\pi$
$683$	−23.4072	−	40.5424i	−0.895651	−	1.55131i	−0.0626538	−	0.998035i	$-0.519956\pi$
$684$		0			0
$685$	17.2392			0.658677
$686$		0			0
$687$	−33.8648	+	1.50880i	−1.29202	+	0.0575644i
$688$		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
$693$	15.6787	+	7.27709i	0.595583	+	0.276434i
$694$		0			0
$695$		−	25.1694i		−	0.954730i
$696$		0			0
$697$			20.6680i			0.782857i
$698$		0			0
$699$	20.8959	−	13.3383i	0.790355	−	0.504503i
$700$		0			0
$701$	0.684260	−	1.18517i	0.0258442	−	0.0447634i	−0.852814	−	0.522215i	$-0.825106\pi$
$701$	0.684260	−	1.18517i	0.0258442	−	0.0447634i	0.878658	+	0.477451i	$0.158439\pi$
$702$		0			0
$703$	−38.9113	+	67.3963i	−1.46757	+	2.54190i
$704$		0			0
$705$	37.4060	+	58.6003i	1.40879	+	2.20702i
$706$		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
$711$	2.70950	+	30.3468i	0.101614	+	1.13809i
$712$		0			0
$713$	2.92176			0.109421
$714$		0			0
$715$			29.7646i			1.11313i
$716$		0			0
$717$	−1.96044	+	1.25140i	−0.0732140	+	0.0467342i
$718$		0			0
$719$	7.42309	−	4.28572i	0.276835	−	0.159831i	−0.355155	−	0.934807i	$-0.615572\pi$
$719$	7.42309	−	4.28572i	0.276835	−	0.159831i	0.631990	+	0.774977i	$0.282239\pi$
$720$		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
$735$	0.375095	+	8.41895i	0.0138356	+	0.310538i
$736$		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
$741$	29.5363	+	46.2716i	1.08504	+	1.69983i
$742$		0			0
$743$	−36.6126	+	21.1383i	−1.34319	+	0.775489i	−0.987274	−	0.159030i	$-0.949163\pi$
$743$	−36.6126	+	21.1383i	−1.34319	+	0.775489i	−0.355912	+	0.934519i	$0.615830\pi$
$744$		0			0
$745$		−	32.8157i		−	1.20228i
$746$		0			0
$747$	35.0399	+	16.2634i	1.28204	+	0.595047i
$748$		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
$753$	0.672289	+	15.0894i	0.0244996	+	0.549888i
$754$		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	$0.272762\pi$
$761$			41.7005i			1.51164i	−0.654779	+	0.755821i	$0.727238\pi$
$762$		0			0
$763$	−13.7208	+	23.7651i	−0.496727	+	0.860356i
$764$		0			0
$765$	20.2688	+	9.40756i	0.732820	+	0.340131i
$766$		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
$771$	−13.8695	−	21.7280i	−0.499498	−	0.782516i
$772$		0			0
$773$	−44.5890	−	25.7434i	−1.60375	−	0.925927i	−0.990727	−	0.135865i	$-0.956619\pi$
$773$	−44.5890	−	25.7434i	−1.60375	−	0.925927i	−0.613026	−	0.790063i	$-0.710048\pi$
$774$		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
$783$	17.7021	−	43.0619i	0.632622	−	1.53891i
$784$		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	0.971309	−	0.237821i	$-0.0764331\pi$
$797$	35.3173	+	20.3905i	1.25100	+	0.722268i	0.279696	+	0.960089i	$0.409766\pi$
$798$		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	$-0.249850\pi$
$809$	40.2433			1.41488			0.707440	+	0.706773i	$0.249850\pi$
$810$		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	−0.988919	−	0.148455i	$-0.952570\pi$
$821$	−38.8196	+	22.4125i	−1.35481	+	0.782202i	−0.365894	+	0.930657i	$0.619237\pi$
$822$		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
$825$	15.1734	−	9.68556i	0.528271	−	0.337208i
$826$		0			0
$827$	14.5840	−	8.42009i	0.507136	−	0.292795i	−0.224519	−	0.974470i	$-0.572081\pi$
$827$	14.5840	−	8.42009i	0.507136	−	0.292795i	0.731656	+	0.681674i	$0.238748\pi$
$828$		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
$837$	1.00711	−	2.44988i	0.0348108	−	0.0846801i
$838$		0			0
$839$	−38.7325	−	22.3622i	−1.33720	−	0.772031i	−0.350805	−	0.936448i	$-0.614092\pi$
$839$	−38.7325	−	22.3622i	−1.33720	−	0.772031i	−0.986391	+	0.164418i	$0.947425\pi$
$840$		0			0
$841$	25.6424	+	44.4140i	0.884222	+	1.53152i
$842$		0			0
$843$	−1.52661	−	34.2646i	−0.0525794	−	1.18014i
$844$		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
$855$	27.2515	−	58.7141i	0.931983	−	2.00798i
$856$		0			0
$857$	20.3805			0.696184			0.348092	−	0.937460i	$-0.386830\pi$
$857$	20.3805			0.696184			0.348092	+	0.937460i	$0.386830\pi$
$858$		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
$861$	−44.8969	+	2.00032i	−1.53008	+	0.0681708i
$862$		0			0
$863$			50.1250i			1.70628i	0.521686	+	0.853138i	$0.325303\pi$
$863$			50.1250i			1.70628i	−0.521686	+	0.853138i	$0.674697\pi$
$864$		0			0
$865$	24.1221	−	13.9269i	0.820176	−	0.473529i
$866$		0			0
$867$	−16.9283	+	10.8058i	−0.574916	+	0.366983i
$868$		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
$873$	−15.8510	−	7.35708i	−0.536475	−	0.248999i
$874$		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	−0.580785	−	0.814057i	$-0.697254\pi$
$881$	−4.93257	+	2.84782i	−0.166183	+	0.0959456i	0.414602	+	0.910003i	$0.363921\pi$
$882$		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	−0.770173	−	0.637835i	$-0.779830\pi$
$887$	−17.9553	+	10.3665i	−0.602879	+	0.348072i	0.167295	+	0.985907i	$0.446497\pi$
$888$		0			0
$889$	−6.69629	+	3.86611i	−0.224586	+	0.129665i
$890$		0			0
$891$	11.4687	+	13.5694i	0.384216	+	0.454591i
$892$		0			0
$893$		−	84.3714i		−	2.82338i
$894$		0			0
$895$	16.3548			0.546680
$896$		0			0
$897$	39.3803	−	25.1374i	1.31487	−	0.839312i
$898$		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
$903$	50.6701	−	32.3439i	1.68619	−	1.07634i
$904$		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
$909$	−38.6422	+	3.45016i	−1.28168	+	0.114434i
$910$		0			0
$911$			36.0923i			1.19579i	0.801574	+	0.597895i	$0.203996\pi$
$911$			36.0923i			1.19579i	−0.801574	+	0.597895i	$0.796004\pi$
$912$		0			0
$913$		−	25.4198i		−	0.841273i
$914$		0			0
$915$	31.1382	−	1.38732i	1.02940	−	0.0458634i
$916$		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
$921$	2.18408	+	49.0213i	0.0719679	+	1.61531i
$922$		0			0
$923$	−41.8090			−1.37616
$924$		0			0
$925$	−30.4185	−	52.6864i	−1.00015	−	1.73232i
$926$		0			0
$927$	11.9743	−	1.06912i	0.393286	−	0.0351144i
$928$		0			0
$929$	−26.1800			−0.858937			−0.429468	−	0.903082i	$-0.641299\pi$
$929$	−26.1800			−0.858937			−0.429468	+	0.903082i	$0.641299\pi$
$930$		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	$-0.823327\pi$
$941$	−52.1415			−1.69976			−0.849881	+	0.526974i	$0.823327\pi$
$942$		0			0
$943$		−	50.9538i		−	1.65929i
$944$		0			0
$945$	−18.4742	+	44.9402i	−0.600967	+	1.46190i
$946$		0			0
$947$			1.99689i			0.0648903i	0.999474	+	0.0324451i	$0.0103294\pi$
$947$			1.99689i			0.0648903i	−0.999474	+	0.0324451i	$0.989671\pi$
$948$		0			0
$949$	−7.96737	−	4.59996i	−0.258632	−	0.149321i
$950$		0			0
$951$	−8.87692	+	0.395500i	−0.287854	+	0.0128250i
$952$		0			0
$953$			9.50442i			0.307878i	0.988080	+	0.153939i	$0.0491960\pi$
$953$			9.50442i			0.307878i	−0.988080	+	0.153939i	$0.950804\pi$
$954$		0			0
$955$	22.4955	+	38.9634i	0.727938	+	1.26083i
$956$		0			0
$957$	−30.6065	+	1.36363i	−0.989367	+	0.0440800i
$958$		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
$969$	−14.5913	−	22.8587i	−0.468739	−	0.734329i
$970$		0			0
$971$	15.9602	+	9.21463i	0.512187	+	0.295711i	0.733732	−	0.679439i	$-0.237777\pi$
$971$	15.9602	+	9.21463i	0.512187	+	0.295711i	−0.221545	+	0.975150i	$0.571110\pi$
$972$		0			0
$973$	11.4645	−	19.8571i	0.367535	−	0.636589i
$974$		0			0
$975$	−42.8711	+	1.91006i	−1.37297	+	0.0611710i
$976$		0			0
$977$	−30.8018	+	17.7834i	−0.985437	+	0.568942i	−0.903907	−	0.427729i	$-0.859314\pi$
$977$	−30.8018	+	17.7834i	−0.985437	+	0.568942i	−0.0815295	+	0.996671i	$0.525980\pi$
$978$		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	$-0.376041\pi$
$983$	23.8068			0.759320			0.379660	+	0.925126i	$0.376041\pi$
$984$		0			0
$985$	−23.9704	+	41.5180i	−0.763760	+	1.32287i
$986$		0			0
$987$	2.81892	+	63.2701i	0.0897272	+	2.01391i
$988$		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
$993$	−7.38031	−	11.5620i	−0.234207	−	0.366910i
$994$		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
$999$	47.5389	−	36.6802i	1.50406	−	1.16051i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.53706 + 0.798403i) q^{3} +3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 + 2.45439i) q^{9} +O(q^{10})\)	\(q+(1.53706 + 0.798403i) q^{3} +3.20386 q^{5} +(2.52764 + 1.45934i) q^{7} +(1.72511 + 2.45439i) q^{9} +(0.987044 - 1.70961i) q^{11} +(-4.07559 + 2.35304i) q^{13} +(4.92452 + 2.55797i) q^{15} +(2.01339 - 1.16243i) q^{17} +(-3.36730 - 5.83233i) q^{19} +(2.72000 + 4.26116i) q^{21} +(-4.96371 + 2.86580i) q^{23} +5.26471 q^{25} +(0.692002 + 5.14987i) q^{27} +(-7.75975 - 4.48009i) q^{29} +(-0.441467 - 0.254881i) q^{31} +(2.88210 - 1.83972i) q^{33} +(8.09821 + 4.67550i) q^{35} +(-5.77782 - 10.0075i) q^{37} +(-8.14310 + 0.362805i) q^{39} +(-4.44499 + 7.69895i) q^{41} -11.8911i q^{43} +(5.52699 + 7.86350i) q^{45} +(10.8496 + 6.26403i) q^{47} +(0.759320 + 1.31518i) q^{49} +(4.02279 - 0.179230i) q^{51} -3.44912 q^{53} +(3.16235 - 5.47735i) q^{55} +(-0.519189 - 11.6531i) q^{57} +3.19468i q^{59} +(4.86430 - 2.80840i) q^{61} +(0.778680 + 8.72132i) q^{63} +(-13.0576 + 7.53882i) q^{65} +(-2.26878 + 7.86464i) q^{67} +(-9.91759 + 0.441865i) q^{69} +(7.69380 + 4.44202i) q^{71} +(0.977450 + 1.69299i) q^{73} +(8.09217 + 4.20336i) q^{75} +(4.98979 - 2.88086i) q^{77} +(8.79520 + 5.07791i) q^{79} +(-3.04802 + 8.46815i) q^{81} +(11.1516 - 6.43837i) q^{83} +(6.45062 - 3.72427i) q^{85} +(-8.35028 - 13.0816i) q^{87} -1.87132i q^{89} -13.7355 q^{91} +(-0.475064 - 0.744237i) q^{93} +(-10.7884 - 18.6860i) q^{95} +(-5.04464 + 2.91252i) q^{97} +(5.89880 - 0.526672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 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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