LMFDB - Embedded newform 804.2.q.a.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, degree $10$, 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:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.2
Character	$\chi$	$=$	804.265
Dual form			804.2.q.a.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(-1.15584 - 2.53094i) q^{5} +(2.78570 + 0.817955i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.15584 - 2.53094i) q^{5} +(2.78570 + 0.817955i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(0.528186 + 1.15657i) q^{11} +(-2.90827 + 3.35633i) q^{13} +(2.66967 - 0.783886i) q^{15} +(2.15357 - 1.38402i) q^{17} +(6.68126 - 1.96180i) q^{19} +(-1.20608 + 2.64094i) q^{21} +(0.796817 - 5.54198i) q^{23} +(-1.79538 + 2.07198i) q^{25} +(0.415415 - 0.909632i) q^{27} +4.22718 q^{29} +(1.94303 + 2.24237i) q^{31} +(-1.21996 + 0.358213i) q^{33} +(-1.14963 - 7.99586i) q^{35} +8.27611 q^{37} +(-2.90827 - 3.35633i) q^{39} +(0.808447 - 0.519558i) q^{41} +(-1.37925 + 0.886389i) q^{43} +(0.395973 + 2.75406i) q^{45} +(0.821978 - 5.71698i) q^{47} +(1.20229 + 0.772666i) q^{49} +(1.06345 + 2.32862i) q^{51} +(5.37728 + 3.45577i) q^{53} +(2.31670 - 2.67361i) q^{55} +(0.990985 + 6.89245i) q^{57} +(3.80877 + 4.39555i) q^{59} +(-3.67372 + 8.04433i) q^{61} +(-2.44241 - 1.56964i) q^{63} +(11.8562 + 3.48128i) q^{65} +(6.62493 + 4.80732i) q^{67} +(5.37217 + 1.57741i) q^{69} +(-7.25738 - 4.66403i) q^{71} +(3.86842 - 8.47066i) q^{73} +(-1.79538 - 2.07198i) q^{75} +(0.525348 + 3.65388i) q^{77} +(-5.88412 + 6.79063i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.52238 + 12.0923i) q^{83} +(-5.99206 - 3.85086i) q^{85} +(-0.601590 + 4.18415i) q^{87} +(-1.46913 - 10.2181i) q^{89} +(-10.8469 + 6.97088i) q^{91} +(-2.49607 + 1.60413i) q^{93} +(-12.6877 - 14.6423i) q^{95} -2.24239 q^{97} +(-0.180948 - 1.25852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	$ 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$	$1$

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
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	−1.15584	−	2.53094i	−0.516908	−	1.13187i	−0.970597	−	0.240710i	$-0.922620\pi$
$5$	−1.15584	−	2.53094i	−0.516908	−	1.13187i	0.453689	−	0.891160i	$-0.350108\pi$
$6$		0			0
$7$	2.78570	+	0.817955i	1.05290	+	0.309158i	0.761986	−	0.647593i	$-0.224224\pi$
$7$	2.78570	+	0.817955i	1.05290	+	0.309158i	0.290909	+	0.956751i	$0.406042\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	0.528186	+	1.15657i	0.159254	+	0.348718i	0.972392	−	0.233353i	$-0.0749699\pi$
$11$	0.528186	+	1.15657i	0.159254	+	0.348718i	−0.813138	+	0.582071i	$0.802243\pi$
$12$		0			0
$13$	−2.90827	+	3.35633i	−0.806610	+	0.930877i	−0.998724	−	0.0504951i	$-0.983920\pi$
$13$	−2.90827	+	3.35633i	−0.806610	+	0.930877i	0.192114	+	0.981373i	$0.438466\pi$
$14$		0			0
$15$	2.66967	−	0.783886i	0.689306	−	0.202399i
$16$		0			0
$17$	2.15357	−	1.38402i	0.522319	−	0.335674i	−0.252770	−	0.967526i	$-0.581342\pi$
$17$	2.15357	−	1.38402i	0.522319	−	0.335674i	0.775089	+	0.631853i	$0.217705\pi$
$18$		0			0
$19$	6.68126	−	1.96180i	1.53279	−	0.450067i	0.596885	−	0.802327i	$-0.296405\pi$
$19$	6.68126	−	1.96180i	1.53279	−	0.450067i	0.935902	+	0.352260i	$0.114587\pi$
$20$		0			0
$21$	−1.20608	+	2.64094i	−0.263187	+	0.576300i
$22$		0			0
$23$	0.796817	−	5.54198i	0.166148	−	1.15558i	−0.720607	−	0.693343i	$-0.756137\pi$
$23$	0.796817	−	5.54198i	0.166148	−	1.15558i	0.886755	−	0.462240i	$-0.152954\pi$
$24$		0			0
$25$	−1.79538	+	2.07198i	−0.359076	+	0.414396i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	4.22718			0.784968			0.392484	−	0.919759i	$-0.371616\pi$
$29$	4.22718			0.784968			0.392484	+	0.919759i	$0.371616\pi$
$30$		0			0
$31$	1.94303	+	2.24237i	0.348978	+	0.402742i	0.902917	−	0.429815i	$-0.141421\pi$
$31$	1.94303	+	2.24237i	0.348978	+	0.402742i	−0.553939	+	0.832557i	$0.686876\pi$
$32$		0			0
$33$	−1.21996	+	0.358213i	−0.212368	+	0.0623569i
$34$		0			0
$35$	−1.14963	−	7.99586i	−0.194323	−	1.35155i
$36$		0			0
$37$	8.27611			1.36058			0.680292	−	0.732941i	$-0.261853\pi$
$37$	8.27611			1.36058			0.680292	+	0.732941i	$0.261853\pi$
$38$		0			0
$39$	−2.90827	−	3.35633i	−0.465696	−	0.537442i
$40$		0			0
$41$	0.808447	−	0.519558i	0.126258	−	0.0811413i	−0.475987	−	0.879452i	$-0.657909\pi$
$41$	0.808447	−	0.519558i	0.126258	−	0.0811413i	0.602246	+	0.798311i	$0.294273\pi$
$42$		0			0
$43$	−1.37925	+	0.886389i	−0.210333	+	0.135173i	−0.641566	−	0.767068i	$-0.721715\pi$
$43$	−1.37925	+	0.886389i	−0.210333	+	0.135173i	0.431233	+	0.902241i	$0.358079\pi$
$44$		0			0
$45$	0.395973	+	2.75406i	0.0590282	+	0.410550i
$46$		0			0
$47$	0.821978	−	5.71698i	0.119898	−	0.833907i	−0.837768	−	0.546026i	$-0.816140\pi$
$47$	0.821978	−	5.71698i	0.119898	−	0.833907i	0.957666	−	0.287881i	$-0.0929509\pi$
$48$		0			0
$49$	1.20229	+	0.772666i	0.171756	+	0.110381i
$50$		0			0
$51$	1.06345	+	2.32862i	0.148912	+	0.326072i
$52$		0			0
$53$	5.37728	+	3.45577i	0.738627	+	0.474686i	0.855071	−	0.518511i	$-0.173513\pi$
$53$	5.37728	+	3.45577i	0.738627	+	0.474686i	−0.116445	+	0.993197i	$0.537150\pi$
$54$		0			0
$55$	2.31670	−	2.67361i	0.312383	−	0.360510i
$56$		0			0
$57$	0.990985	+	6.89245i	0.131259	+	0.912927i
$58$		0			0
$59$	3.80877	+	4.39555i	0.495859	+	0.572252i	0.947422	−	0.319987i	$-0.103679\pi$
$59$	3.80877	+	4.39555i	0.495859	+	0.572252i	−0.451563	+	0.892239i	$0.649133\pi$
$60$		0			0
$61$	−3.67372	+	8.04433i	−0.470372	+	1.02997i	0.514627	+	0.857414i	$0.327930\pi$
$61$	−3.67372	+	8.04433i	−0.470372	+	1.02997i	−0.984999	+	0.172557i	$0.944797\pi$
$62$		0			0
$63$	−2.44241	−	1.56964i	−0.307715	−	0.197757i
$64$		0			0
$65$	11.8562	+	3.48128i	1.47058	+	0.431800i
$66$		0			0
$67$	6.62493	+	4.80732i	0.809364	+	0.587307i
$67$	6.62493	+	4.80732i	0.809364	+	0.587307i
$68$		0			0
$69$	5.37217	+	1.57741i	0.646734	+	0.189898i
$70$		0			0
$71$	−7.25738	−	4.66403i	−0.861292	−	0.553519i	0.0337854	−	0.999429i	$-0.489244\pi$
$71$	−7.25738	−	4.66403i	−0.861292	−	0.553519i	−0.895078	+	0.445910i	$0.852880\pi$
$72$		0			0
$73$	3.86842	−	8.47066i	0.452764	−	0.991416i	−0.536313	−	0.844019i	$-0.680183\pi$
$73$	3.86842	−	8.47066i	0.452764	−	0.991416i	0.989077	−	0.147396i	$-0.0470893\pi$
$74$		0			0
$75$	−1.79538	−	2.07198i	−0.207313	−	0.239251i
$76$		0			0
$77$	0.525348	+	3.65388i	0.0598690	+	0.416398i
$78$		0			0
$79$	−5.88412	+	6.79063i	−0.662015	+	0.764006i	−0.983105	−	0.183043i	$-0.941405\pi$
$79$	−5.88412	+	6.79063i	−0.662015	+	0.764006i	0.321090	+	0.947049i	$0.395951\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	5.52238	+	12.0923i	0.606160	+	1.32731i	0.925169	+	0.379554i	$0.123923\pi$
$83$	5.52238	+	12.0923i	0.606160	+	1.32731i	−0.319009	+	0.947752i	$0.603350\pi$
$84$		0			0
$85$	−5.99206	−	3.85086i	−0.649930	−	0.417685i
$86$		0			0
$87$	−0.601590	+	4.18415i	−0.0644973	+	0.448588i
$88$		0			0
$89$	−1.46913	−	10.2181i	−0.155728	−	1.08311i	−0.906395	−	0.422431i	$-0.861177\pi$
$89$	−1.46913	−	10.2181i	−0.155728	−	1.08311i	0.750667	−	0.660681i	$-0.229732\pi$
$90$		0			0
$91$	−10.8469	+	6.97088i	−1.13706	+	0.730746i
$92$		0			0
$93$	−2.49607	+	1.60413i	−0.258831	+	0.166340i
$94$		0			0
$95$	−12.6877	−	14.6423i	−1.30173	−	1.50227i
$96$		0			0
$97$	−2.24239			−0.227680			−0.113840	−	0.993499i	$-0.536315\pi$
$97$	−2.24239			−0.227680			−0.113840	+	0.993499i	$0.536315\pi$
$98$		0			0
$99$	−0.180948	−	1.25852i	−0.0181860	−	0.126486i
$100$		0			0
$101$	−6.15079	+	1.80603i	−0.612026	+	0.179707i	−0.573033	−	0.819532i	$-0.694233\pi$
$101$	−6.15079	+	1.80603i	−0.612026	+	0.179707i	−0.0389934	+	0.999239i	$0.512415\pi$
$102$		0			0
$103$	−9.55095	−	11.0224i	−0.941083	−	1.08607i	−0.996157	−	0.0875855i	$-0.972085\pi$
$103$	−9.55095	−	11.0224i	−0.941083	−	1.08607i	0.0550739	−	0.998482i	$-0.482461\pi$
$104$		0			0
$105$	8.07808			0.788340
$106$		0			0
$107$	0.196718	−	0.430752i	0.0190174	−	0.0416423i	−0.899885	−	0.436127i	$-0.856350\pi$
$107$	0.196718	−	0.430752i	0.0190174	−	0.0416423i	0.918902	+	0.394485i	$0.129077\pi$
$108$		0			0
$109$	−1.45675	+	1.68118i	−0.139531	+	0.161027i	−0.821214	−	0.570620i	$-0.806703\pi$
$109$	−1.45675	+	1.68118i	−0.139531	+	0.161027i	0.681683	+	0.731648i	$0.261248\pi$
$110$		0			0
$111$	−1.17781	+	8.19187i	−0.111793	+	0.777538i
$112$		0			0
$113$	−5.89439	+	12.9069i	−0.554498	+	1.21418i	0.400152	+	0.916449i	$0.368957\pi$
$113$	−5.89439	+	12.9069i	−0.554498	+	1.21418i	−0.954650	+	0.297732i	$0.903770\pi$
$114$		0			0
$115$	−14.9474	+	4.38896i	−1.39385	+	0.409272i
$116$		0			0
$117$	3.73605	−	2.40102i	0.345398	−	0.221974i
$118$		0			0
$119$	7.13128	−	2.09393i	0.653723	−	0.191950i
$120$		0			0
$121$	6.14480	−	7.09148i	0.558619	−	0.644680i
$122$		0			0
$123$	0.399215	+	0.874159i	0.0359960	+	0.0788203i
$124$		0			0
$125$	−6.02913	−	1.77031i	−0.539262	−	0.158342i
$126$		0			0
$127$	−7.98102	−	2.34344i	−0.708201	−	0.207947i	−0.0922555	−	0.995735i	$-0.529408\pi$
$127$	−7.98102	−	2.34344i	−0.708201	−	0.207947i	−0.615945	+	0.787789i	$0.711226\pi$
$128$		0			0
$129$	−0.681079	−	1.49136i	−0.0599657	−	0.131307i
$130$		0			0
$131$	2.91572	−	20.2793i	0.254748	−	1.77181i	−0.314122	−	0.949383i	$-0.601710\pi$
$131$	2.91572	−	20.2793i	0.254748	−	1.77181i	0.568870	−	0.822427i	$-0.307381\pi$
$132$		0			0
$133$	20.2166			1.75301
$134$		0			0
$135$	−2.78238			−0.239469
$136$		0			0
$137$	−0.805290	+	5.60092i	−0.0688006	+	0.478519i	0.926069	+	0.377354i	$0.123166\pi$
$137$	−0.805290	+	5.60092i	−0.0688006	+	0.478519i	−0.994870	+	0.101165i	$0.967743\pi$
$138$		0			0
$139$	−2.97675	−	6.51818i	−0.252485	−	0.552865i	0.740369	−	0.672200i	$-0.234651\pi$
$139$	−2.97675	−	6.51818i	−0.252485	−	0.552865i	−0.992854	+	0.119336i	$0.961923\pi$
$140$		0			0
$141$	5.54181	+	1.62722i	0.466705	+	0.137037i
$142$		0			0
$143$	−5.41792	−	1.59084i	−0.453069	−	0.133033i
$144$		0			0
$145$	−4.88595	−	10.6987i	−0.405756	−	0.888482i
$146$		0			0
$147$	−0.935905	+	1.08009i	−0.0771922	+	0.0890845i
$148$		0			0
$149$	6.23845	−	1.83177i	0.511074	−	0.150065i	−0.0160205	−	0.999872i	$-0.505100\pi$
$149$	6.23845	−	1.83177i	0.511074	−	0.150065i	0.527094	+	0.849807i	$0.323282\pi$
$150$		0			0
$151$	−20.1576	+	12.9545i	−1.64040	+	1.05422i	−0.700007	+	0.714136i	$0.746820\pi$
$151$	−20.1576	+	12.9545i	−1.64040	+	1.05422i	−0.940394	+	0.340086i	$0.889544\pi$
$152$		0			0
$153$	−2.45626	+	0.721224i	−0.198577	+	0.0583075i
$154$		0			0
$155$	3.42948	−	7.50951i	0.275462	−	0.603179i
$156$		0			0
$157$	−1.20524	+	8.38262i	−0.0961885	+	0.669006i	0.883493	+	0.468445i	$0.155185\pi$
$157$	−1.20524	+	8.38262i	−0.0961885	+	0.669006i	−0.979681	+	0.200561i	$0.935724\pi$
$158$		0			0
$159$	−4.18586	+	4.83074i	−0.331960	+	0.383103i
$160$		0			0
$161$	6.75278	−	14.7865i	0.532194	−	1.16534i
$162$		0			0
$163$	13.1748			1.03193			0.515966	−	0.856609i	$-0.327433\pi$
$163$	13.1748			1.03193			0.515966	+	0.856609i	$0.327433\pi$
$164$		0			0
$165$	2.31670	+	2.67361i	0.180355	+	0.208140i
$166$		0			0
$167$	−0.791735	+	0.232474i	−0.0612663	+	0.0179894i	−0.312222	−	0.950009i	$-0.601073\pi$
$167$	−0.791735	+	0.232474i	−0.0612663	+	0.0179894i	0.250956	+	0.967999i	$0.419255\pi$
$168$		0			0
$169$	−0.956780	−	6.65455i	−0.0735985	−	0.511888i
$170$		0			0
$171$	−6.96333			−0.532499
$172$		0			0
$173$	−7.41481	−	8.55715i	−0.563738	−	0.650588i	0.400290	−	0.916388i	$-0.368909\pi$
$173$	−7.41481	−	8.55715i	−0.563738	−	0.650588i	−0.964028	+	0.265800i	$0.914364\pi$
$174$		0			0
$175$	−6.69617	+	4.30337i	−0.506183	+	0.325304i
$176$		0			0
$177$	−4.89286	+	3.14445i	−0.367770	+	0.236351i
$178$		0			0
$179$	−1.68165	−	11.6962i	−0.125693	−	0.874211i	−0.950926	−	0.309419i	$-0.899865\pi$
$179$	−1.68165	−	11.6962i	−0.125693	−	0.874211i	0.825233	−	0.564792i	$-0.191044\pi$
$180$		0			0
$181$	−2.56828	+	17.8628i	−0.190899	+	1.32773i	0.638736	+	0.769426i	$0.279458\pi$
$181$	−2.56828	+	17.8628i	−0.190899	+	1.32773i	−0.829635	+	0.558306i	$0.811451\pi$
$182$		0			0
$183$	−7.43963	−	4.78116i	−0.549953	−	0.353433i
$184$		0			0
$185$	−9.56587	−	20.9463i	−0.703297	−	1.54000i
$186$		0			0
$187$	2.73820	+	1.75973i	0.200237	+	0.128684i
$188$		0			0
$189$	1.90126	−	2.19417i	0.138296	−	0.159602i
$190$		0			0
$191$	−2.12592	−	14.7861i	−0.153826	−	1.06989i	−0.909729	−	0.415203i	$-0.863711\pi$
$191$	−2.12592	−	14.7861i	−0.153826	−	1.06989i	0.755903	−	0.654684i	$-0.227198\pi$
$192$		0			0
$193$	4.36520	+	5.03771i	0.314214	+	0.362622i	0.890785	−	0.454425i	$-0.150155\pi$
$193$	4.36520	+	5.03771i	0.314214	+	0.362622i	−0.576571	+	0.817047i	$0.695610\pi$
$194$		0			0
$195$	−5.13316	+	11.2400i	−0.367593	+	0.804916i
$196$		0			0
$197$	−11.8450	−	7.61235i	−0.843925	−	0.542358i	0.0457497	−	0.998953i	$-0.485432\pi$
$197$	−11.8450	−	7.61235i	−0.843925	−	0.542358i	−0.889674	+	0.456595i	$0.849069\pi$
$198$		0			0
$199$	2.75884	+	0.810068i	0.195569	+	0.0574242i	0.378050	−	0.925785i	$-0.376595\pi$
$199$	2.75884	+	0.810068i	0.195569	+	0.0574242i	−0.182481	+	0.983209i	$0.558413\pi$
$200$		0			0
$201$	−5.70121	+	5.87334i	−0.402133	+	0.414274i
$202$		0			0
$203$	11.7756	+	3.45764i	0.826489	+	0.242679i
$204$		0			0
$205$	−2.24941	−	1.44561i	−0.157105	−	0.100965i
$206$		0			0
$207$	−2.32590	+	5.09300i	−0.161661	+	0.353988i
$208$		0			0
$209$	5.79789	+	6.69112i	0.401049	+	0.462835i
$210$		0			0
$211$	−1.57238	−	10.9362i	−0.108247	−	0.752877i	−0.969569	−	0.244817i	$-0.921272\pi$
$211$	−1.57238	−	10.9362i	−0.108247	−	0.752877i	0.861322	−	0.508060i	$-0.169637\pi$
$212$		0			0
$213$	5.64939	−	6.51975i	0.387090	−	0.446726i
$214$		0			0
$215$	3.83759	+	2.46627i	0.261721	+	0.168198i
$216$		0			0
$217$	3.57853	+	7.83589i	0.242926	+	0.531935i
$218$		0			0
$219$	7.83391	+	5.03455i	0.529366	+	0.340203i
$220$		0			0
$221$	−1.61797	+	11.2532i	−0.108836	+	0.756972i
$222$		0			0
$223$	1.16800	+	8.12362i	0.0782151	+	0.543998i	0.990823	+	0.135163i	$0.0431558\pi$
$223$	1.16800	+	8.12362i	0.0782151	+	0.543998i	−0.912608	+	0.408835i	$0.865935\pi$
$224$		0			0
$225$	2.30640	−	1.48223i	0.153760	−	0.0988154i
$226$		0			0
$227$	−16.8159	+	10.8069i	−1.11611	+	0.717279i	−0.962616	−	0.270871i	$-0.912688\pi$
$227$	−16.8159	+	10.8069i	−1.11611	+	0.717279i	−0.153492	+	0.988150i	$0.549052\pi$
$228$		0			0
$229$	2.67648	+	3.08882i	0.176866	+	0.204115i	0.837260	−	0.546805i	$-0.184156\pi$
$229$	2.67648	+	3.08882i	0.176866	+	0.204115i	−0.660394	+	0.750920i	$0.729611\pi$
$230$		0			0
$231$	−3.69145			−0.242880
$232$		0			0
$233$	1.64186	+	11.4194i	0.107562	+	0.748110i	0.970203	+	0.242294i	$0.0778997\pi$
$233$	1.64186	+	11.4194i	0.107562	+	0.748110i	−0.862641	+	0.505817i	$0.831191\pi$
$234$		0			0
$235$	−15.4194	+	4.52755i	−1.00585	+	0.295345i
$236$		0			0
$237$	−5.88412	−	6.79063i	−0.382214	−	0.441099i
$238$		0			0
$239$	−5.65320			−0.365675			−0.182838	−	0.983143i	$-0.558528\pi$
$239$	−5.65320			−0.365675			−0.182838	+	0.983143i	$0.558528\pi$
$240$		0			0
$241$	−5.08954	+	11.1445i	−0.327846	+	0.717883i	−0.999741	−	0.0227636i	$-0.992753\pi$
$241$	−5.08954	+	11.1445i	−0.327846	+	0.717883i	0.671895	+	0.740647i	$0.265481\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	0.565912	−	3.93601i	0.0361548	−	0.251462i
$246$		0			0
$247$	−12.8465	+	28.1299i	−0.817404	+	1.78986i
$248$		0			0
$249$	−12.7552	+	3.74526i	−0.808326	+	0.237346i
$250$		0			0
$251$	−22.4145	+	14.4049i	−1.41479	+	0.909231i	−1.00000		0.000684832i	$-0.999782\pi$
$251$	−22.4145	+	14.4049i	−1.41479	+	0.909231i	−0.414792	+	0.909916i	$0.636146\pi$
$252$		0			0
$253$	6.83053	−	2.00563i	0.429432	−	0.126093i
$254$		0			0
$255$	4.66442	−	5.38303i	0.292098	−	0.337098i
$256$		0			0
$257$	11.6798	+	25.5752i	0.728566	+	1.59534i	0.801496	+	0.598000i	$0.204038\pi$
$257$	11.6798	+	25.5752i	0.728566	+	1.59534i	−0.0729295	+	0.997337i	$0.523235\pi$
$258$		0			0
$259$	23.0547	+	6.76948i	1.43255	+	0.420635i
$260$		0			0
$261$	−4.05595	−	1.19093i	−0.251057	−	0.0737170i
$262$		0			0
$263$	−2.17551	−	4.76370i	−0.134148	−	0.293742i	0.830623	−	0.556835i	$-0.187985\pi$
$263$	−2.17551	−	4.76370i	−0.134148	−	0.293742i	−0.964770	+	0.263093i	$0.915257\pi$
$264$		0			0
$265$	2.53106	−	17.6039i	0.155482	−	1.08140i
$266$		0			0
$267$	10.3231			0.631765
$268$		0			0
$269$	−26.6782			−1.62660			−0.813299	−	0.581847i	$-0.802330\pi$
$269$	−26.6782			−1.62660			−0.813299	+	0.581847i	$0.802330\pi$
$270$		0			0
$271$	2.39688	−	16.6707i	0.145600	−	1.01267i	−0.777712	−	0.628621i	$-0.783620\pi$
$271$	2.39688	−	16.6707i	0.145600	−	1.01267i	0.923312	−	0.384050i	$-0.125471\pi$
$272$		0			0
$273$	−5.35625	−	11.7286i	−0.324175	−	0.709844i
$274$		0			0
$275$	−3.34467	−	0.982084i	−0.201691	−	0.0592219i
$276$		0			0
$277$	−2.10084	−	0.616861i	−0.126227	−	0.0370636i	0.218009	−	0.975947i	$-0.430044\pi$
$277$	−2.10084	−	0.616861i	−0.126227	−	0.0370636i	−0.344236	+	0.938883i	$0.611862\pi$
$278$		0			0
$279$	−1.23257	−	2.69896i	−0.0737922	−	0.161582i
$280$		0			0
$281$	−18.9404	+	21.8584i	−1.12989	+	1.30396i	−0.182746	+	0.983160i	$0.558498\pi$
$281$	−18.9404	+	21.8584i	−1.12989	+	1.30396i	−0.947146	+	0.320804i	$0.896047\pi$
$282$		0			0
$283$	21.1212	−	6.20175i	1.25553	−	0.368656i	0.414699	−	0.909959i	$-0.363887\pi$
$283$	21.1212	−	6.20175i	1.25553	−	0.368656i	0.840828	+	0.541303i	$0.182069\pi$
$284$		0			0
$285$	16.2989	−	10.4747i	0.965466	−	0.620467i
$286$		0			0
$287$	2.67707	−	0.786057i	0.158022	−	0.0463995i
$288$		0			0
$289$	−4.33968	+	9.50257i	−0.255275	+	0.558975i
$290$		0			0
$291$	0.319126	−	2.21957i	0.0187075	−	0.130113i
$292$		0			0
$293$	−11.9347	+	13.7734i	−0.697231	+	0.804648i	−0.988376	−	0.152031i	$-0.951419\pi$
$293$	−11.9347	+	13.7734i	−0.697231	+	0.804648i	0.291144	+	0.956679i	$0.405964\pi$
$294$		0			0
$295$	6.72254	−	14.7203i	0.391402	−	0.857050i
$296$		0			0
$297$	1.27147			0.0737779
$298$		0			0
$299$	16.2833	+	18.7920i	0.941690	+	1.08677i
$300$		0			0
$301$	−4.56720	+	1.34105i	−0.263249	+	0.0772968i
$302$		0			0
$303$	−0.912303	−	6.34521i	−0.0524104	−	0.364523i
$304$		0			0
$305$	24.6060			1.40893
$306$		0			0
$307$	−14.5202	−	16.7573i	−0.828714	−	0.956387i	0.170868	−	0.985294i	$-0.445343\pi$
$307$	−14.5202	−	16.7573i	−0.828714	−	0.956387i	−0.999582	+	0.0289069i	$0.990797\pi$
$308$		0			0
$309$	12.2694	−	7.88509i	0.697984	−	0.448567i
$310$		0			0
$311$	5.49310	−	3.53020i	0.311485	−	0.200179i	−0.375553	−	0.926801i	$-0.622547\pi$
$311$	5.49310	−	3.53020i	0.311485	−	0.200179i	0.687038	+	0.726622i	$0.258911\pi$
$312$		0			0
$313$	−1.86114	−	12.9445i	−0.105198	−	0.731666i	−0.972334	−	0.233595i	$-0.924951\pi$
$313$	−1.86114	−	12.9445i	−0.105198	−	0.731666i	0.867136	−	0.498071i	$-0.165958\pi$
$314$		0			0
$315$	−1.14963	+	7.99586i	−0.0647744	+	0.450516i
$316$		0			0
$317$	4.54055	+	2.91803i	0.255022	+	0.163893i	0.661906	−	0.749587i	$-0.269748\pi$
$317$	4.54055	+	2.91803i	0.255022	+	0.163893i	−0.406883	+	0.913480i	$0.633384\pi$
$318$		0			0
$319$	2.23274	+	4.88901i	0.125009	+	0.273732i
$320$		0			0
$321$	0.398371	+	0.256018i	0.0222349	+	0.0142895i
$322$		0			0
$323$	11.6734	−	13.4719i	0.649527	−	0.749595i
$324$		0			0
$325$	−1.73278	−	12.0518i	−0.0961174	−	0.668511i
$326$		0			0
$327$	−1.45675	−	1.68118i	−0.0805583	−	0.0929693i
$328$		0			0
$329$	6.96602	−	15.2534i	0.384049	−	0.840950i
$330$		0			0
$331$	28.4287	+	18.2700i	1.56258	+	1.00421i	0.981747	+	0.190193i	$0.0609113\pi$
$331$	28.4287	+	18.2700i	1.56258	+	1.00421i	0.580838	+	0.814019i	$0.302725\pi$
$332$		0			0
$333$	−7.94087	−	2.33165i	−0.435157	−	0.127774i
$334$		0			0
$335$	4.50966	−	22.3238i	0.246389	−	1.21968i
$336$		0			0
$337$	27.8538	+	8.17861i	1.51729	+	0.445517i	0.931133	−	0.364679i	$-0.118821\pi$
$337$	27.8538	+	8.17861i	1.51729	+	0.445517i	0.586159	+	0.810196i	$0.300639\pi$
$338$		0			0
$339$	−11.9367	−	7.67124i	−0.648312	−	0.416645i
$340$		0			0
$341$	−1.56717	+	3.43163i	−0.0848672	+	0.185833i
$342$		0			0
$343$	−10.5916	−	12.2234i	−0.571892	−	0.659999i
$344$		0			0
$345$	−2.21704	−	15.4199i	−0.119362	−	0.830179i
$346$		0			0
$347$	5.10601	−	5.89265i	0.274105	−	0.316334i	−0.601961	−	0.798526i	$-0.705614\pi$
$347$	5.10601	−	5.89265i	0.274105	−	0.316334i	0.876066	+	0.482192i	$0.160159\pi$
$348$		0			0
$349$	−0.401553	−	0.258063i	−0.0214947	−	0.0138138i	0.529849	−	0.848092i	$-0.322248\pi$
$349$	−0.401553	−	0.258063i	−0.0214947	−	0.0138138i	−0.551344	+	0.834278i	$0.685885\pi$
$350$		0			0
$351$	1.84488	+	4.03973i	0.0984725	+	0.215625i
$352$		0			0
$353$	22.3023	+	14.3328i	1.18703	+	0.762858i	0.976666	−	0.214765i	$-0.0688987\pi$
$353$	22.3023	+	14.3328i	1.18703	+	0.762858i	0.210364	+	0.977623i	$0.432535\pi$
$354$		0			0
$355$	−3.41601	+	23.7589i	−0.181303	+	1.26099i
$356$		0			0
$357$	1.05773	+	7.35669i	0.0559811	+	0.389357i
$358$		0			0
$359$	21.4493	−	13.7846i	1.13205	−	0.727524i	0.166063	−	0.986115i	$-0.446895\pi$
$359$	21.4493	−	13.7846i	1.13205	−	0.727524i	0.965987	+	0.258591i	$0.0832583\pi$
$360$		0			0
$361$	24.8068	−	15.9424i	1.30562	−	0.839072i
$362$		0			0
$363$	6.14480	+	7.09148i	0.322519	+	0.372206i
$364$		0			0
$365$	−25.9100			−1.35619
$366$		0			0
$367$	−3.93612	−	27.3763i	−0.205464	−	1.42903i	−0.787724	−	0.616029i	$-0.788741\pi$
$367$	−3.93612	−	27.3763i	−0.205464	−	1.42903i	0.582260	−	0.813003i	$-0.302169\pi$
$368$		0			0
$369$	−0.922076	+	0.270746i	−0.0480014	+	0.0140945i
$370$		0			0
$371$	12.1528	+	14.0251i	0.630943	+	0.728147i
$372$		0			0
$373$	1.95588			0.101272			0.0506358	−	0.998717i	$-0.483875\pi$
$373$	1.95588			0.101272			0.0506358	+	0.998717i	$0.483875\pi$
$374$		0			0
$375$	2.61033	−	5.71582i	0.134797	−	0.295164i
$376$		0			0
$377$	−12.2938	+	14.1878i	−0.633163	+	0.730709i
$378$		0			0
$379$	−0.0597674	+	0.415691i	−0.00307004	+	0.0213526i	−0.991299	−	0.131630i	$-0.957979\pi$
$379$	−0.0597674	+	0.415691i	−0.00307004	+	0.0213526i	0.988229	+	0.152983i	$0.0488879\pi$
$380$		0			0
$381$	3.45540	−	7.56628i	0.177026	−	0.387632i
$382$		0			0
$383$	31.1253	−	9.13922i	1.59043	−	0.466992i	0.637568	−	0.770394i	$-0.279941\pi$
$383$	31.1253	−	9.13922i	1.59043	−	0.466992i	0.952863	+	0.303402i	$0.0981225\pi$
$384$		0			0
$385$	8.64052	−	5.55292i	0.440361	−	0.283003i
$386$		0			0
$387$	1.57310	−	0.461905i	0.0799654	−	0.0234799i
$388$		0			0
$389$	6.97012	−	8.04395i	0.353399	−	0.407844i	−0.551018	−	0.834493i	$-0.685760\pi$
$389$	6.97012	−	8.04395i	0.353399	−	0.407844i	0.904417	+	0.426649i	$0.140306\pi$
$390$		0			0
$391$	−5.95420	−	13.0379i	−0.301117	−	0.659354i
$392$		0			0
$393$	19.6579	+	5.77209i	0.991611	+	0.291163i
$394$		0			0
$395$	23.9878	+	7.04345i	1.20696	+	0.354394i
$396$		0			0
$397$	−1.56828	−	3.43405i	−0.0787095	−	0.172350i	0.866186	−	0.499722i	$-0.166564\pi$
$397$	−1.56828	−	3.43405i	−0.0787095	−	0.172350i	−0.944896	+	0.327372i	$0.893837\pi$
$398$		0			0
$399$	−2.87713	+	20.0109i	−0.144037	+	1.00180i
$400$		0			0
$401$	13.2681			0.662577			0.331288	−	0.943530i	$-0.392517\pi$
$401$	13.2681			0.662577			0.331288	+	0.943530i	$0.392517\pi$
$402$		0			0
$403$	−13.1770			−0.656393
$404$		0			0
$405$	0.395973	−	2.75406i	0.0196761	−	0.136850i
$406$		0			0
$407$	4.37132	+	9.57186i	0.216678	+	0.474460i
$408$		0			0
$409$	−30.4832	−	8.95067i	−1.50730	−	0.442582i	−0.579282	−	0.815127i	$-0.696667\pi$
$409$	−30.4832	−	8.95067i	−1.50730	−	0.442582i	−0.928014	+	0.372545i	$0.878485\pi$
$410$		0			0
$411$	−5.42930	−	1.59419i	−0.267808	−	0.0786355i
$412$		0			0
$413$	7.01472	+	15.3601i	0.345172	+	0.755820i
$414$		0			0
$415$	24.2220	−	27.9536i	1.18901	−	1.37219i
$416$		0			0
$417$	6.87547	−	2.01882i	0.336693	−	0.0988620i
$418$		0			0
$419$	−29.1081	+	18.7067i	−1.42202	+	0.913880i	−0.422051	+	0.906572i	$0.638690\pi$
$419$	−29.1081	+	18.7067i	−1.42202	+	0.913880i	−0.999973	+	0.00730795i	$0.997674\pi$
$420$		0			0
$421$	11.1415	−	3.27143i	0.543002	−	0.159440i	0.00128246	−	0.999999i	$-0.499592\pi$
$421$	11.1415	−	3.27143i	0.543002	−	0.159440i	0.541719	+	0.840559i	$0.317774\pi$
$422$		0			0
$423$	−2.39934	+	5.25383i	−0.116660	+	0.255450i
$424$		0			0
$425$	−0.998828	+	6.94700i	−0.0484503	+	0.336979i
$426$		0			0
$427$	−16.8138	+	19.4041i	−0.813676	+	0.939032i
$428$		0			0
$429$	2.34570	−	5.13637i	0.113252	−	0.247986i
$430$		0			0
$431$	−15.5338			−0.748239			−0.374120	−	0.927380i	$-0.622055\pi$
$431$	−15.5338			−0.748239			−0.374120	+	0.927380i	$0.622055\pi$
$432$		0			0
$433$	−11.7447	−	13.5541i	−0.564414	−	0.651369i	0.399766	−	0.916617i	$-0.369091\pi$
$433$	−11.7447	−	13.5541i	−0.564414	−	0.651369i	−0.964180	+	0.265249i	$0.914546\pi$
$434$		0			0
$435$	11.2852	−	3.31363i	0.541083	−	0.158876i
$436$		0			0
$437$	−5.54849	−	38.5906i	−0.265420	−	1.84604i
$438$		0			0
$439$	−24.1317			−1.15174			−0.575872	−	0.817540i	$-0.695337\pi$
$439$	−24.1317			−1.15174			−0.575872	+	0.817540i	$0.695337\pi$
$440$		0			0
$441$	−0.935905	−	1.08009i	−0.0445669	−	0.0514330i
$442$		0			0
$443$	1.15123	−	0.739849i	0.0546965	−	0.0351513i	−0.513007	−	0.858385i	$-0.671468\pi$
$443$	1.15123	−	0.739849i	0.0546965	−	0.0351513i	0.567703	+	0.823233i	$0.307832\pi$
$444$		0			0
$445$	−24.1632	+	15.5287i	−1.14545	+	0.736133i
$446$		0			0
$447$	0.925305	+	6.43564i	0.0437654	+	0.304395i
$448$		0			0
$449$	−5.42757	+	37.7496i	−0.256143	+	1.78151i	0.303554	+	0.952814i	$0.401827\pi$
$449$	−5.42757	+	37.7496i	−0.256143	+	1.78151i	−0.559697	+	0.828698i	$0.689082\pi$
$450$		0			0
$451$	1.02791	+	0.660600i	0.0484025	+	0.0311064i
$452$		0			0
$453$	−9.95392	−	21.7960i	−0.467676	−	1.02407i
$454$		0			0
$455$	30.1802	+	19.3956i	1.41487	+	0.909280i
$456$		0			0
$457$	23.8036	−	27.4708i	1.11348	−	1.28503i	0.158832	−	0.987306i	$-0.449227\pi$
$457$	23.8036	−	27.4708i	1.11348	−	1.28503i	0.954652	−	0.297723i	$-0.0962273\pi$
$458$		0			0
$459$	−0.364320	−	2.53390i	−0.0170050	−	0.118272i
$460$		0			0
$461$	17.1110	+	19.7472i	0.796940	+	0.919718i	0.998209	−	0.0598180i	$-0.0190520\pi$
$461$	17.1110	+	19.7472i	0.796940	+	0.919718i	−0.201269	+	0.979536i	$0.564507\pi$
$462$		0			0
$463$	5.99769	−	13.1331i	0.278736	−	0.610348i	−0.717544	−	0.696513i	$-0.754734\pi$
$463$	5.99769	−	13.1331i	0.278736	−	0.610348i	0.996281	+	0.0861651i	$0.0274613\pi$
$464$		0			0
$465$	6.94501	+	4.46329i	0.322067	+	0.206980i
$466$		0			0
$467$	−26.3465	−	7.73604i	−1.21917	−	0.357981i	−0.392018	−	0.919957i	$-0.628223\pi$
$467$	−26.3465	−	7.73604i	−1.21917	−	0.357981i	−0.827153	+	0.561976i	$0.810041\pi$
$468$		0			0
$469$	14.5229	+	18.8106i	0.670605	+	0.868594i
$470$		0			0
$471$	−8.12577	−	2.38594i	−0.374416	−	0.109938i
$472$		0			0
$473$	−1.75367	−	1.12701i	−0.0806337	−	0.0518201i
$474$		0			0
$475$	−7.93060	+	17.3656i	−0.363881	+	0.796788i
$476$		0			0
$477$	−4.18586	−	4.83074i	−0.191657	−	0.221184i
$478$		0			0
$479$	−1.07752	−	7.49432i	−0.0492332	−	0.342424i	−0.999518	−	0.0310424i	$-0.990117\pi$
$479$	−1.07752	−	7.49432i	−0.0492332	−	0.342424i	0.950285	−	0.311382i	$-0.100792\pi$
$480$		0			0
$481$	−24.0692	+	27.7773i	−1.09746	+	1.26654i
$482$		0			0
$483$	13.6750	+	8.78839i	0.622234	+	0.399886i
$484$		0			0
$485$	2.59185	+	5.67536i	0.117690	+	0.257705i
$486$		0			0
$487$	10.1269	+	6.50819i	0.458896	+	0.294914i	0.749591	−	0.661901i	$-0.230250\pi$
$487$	10.1269	+	6.50819i	0.458896	+	0.294914i	−0.290695	+	0.956816i	$0.593887\pi$
$488$		0			0
$489$	−1.87497	+	13.0407i	−0.0847892	+	0.589722i
$490$		0			0
$491$	−0.0633668	−	0.440726i	−0.00285970	−	0.0198897i	0.988342	−	0.152252i	$-0.0486527\pi$
$491$	−0.0633668	−	0.440726i	−0.00285970	−	0.0198897i	−0.991201	+	0.132363i	$0.957744\pi$
$492$		0			0
$493$	9.10355	−	5.85050i	0.410003	−	0.263493i
$494$		0			0
$495$	−2.97610	+	1.91262i	−0.133766	+	0.0859660i
$496$		0			0
$497$	−16.4019	−	18.9288i	−0.735726	−	0.849073i
$498$		0			0
$499$	13.6974			0.613178			0.306589	−	0.951842i	$-0.400812\pi$
$499$	13.6974			0.613178			0.306589	+	0.951842i	$0.400812\pi$
$500$		0			0
$501$	−0.117432	−	0.816761i	−0.00524650	−	0.0364902i
$502$		0			0
$503$	11.0144	−	3.23412i	0.491108	−	0.144202i	−0.0267964	−	0.999641i	$-0.508531\pi$
$503$	11.0144	−	3.23412i	0.491108	−	0.144202i	0.517904	+	0.855439i	$0.326712\pi$
$504$		0			0
$505$	11.6803	+	13.4798i	0.519766	+	0.599842i
$506$		0			0
$507$	6.72298			0.298578
$508$		0			0
$509$	−16.9927	+	37.2089i	−0.753189	+	1.64925i	0.00736024	+	0.999973i	$0.497657\pi$
$509$	−16.9927	+	37.2089i	−0.753189	+	1.64925i	−0.760549	+	0.649280i	$0.775070\pi$
$510$		0			0
$511$	17.7049	−	20.4325i	0.783217	−	0.903881i
$512$		0			0
$513$	0.990985	−	6.89245i	0.0437530	−	0.304309i
$514$		0			0
$515$	−16.8576	+	36.9130i	−0.742835	+	1.62658i
$516$		0			0
$517$	7.04622	−	2.06896i	0.309892	−	0.0909926i
$518$		0			0
$519$	9.52529	−	6.12153i	0.418114	−	0.268705i
$520$		0			0
$521$	−27.5597	+	8.09225i	−1.20741	+	0.354528i	−0.822682	−	0.568502i	$-0.807523\pi$
$521$	−27.5597	+	8.09225i	−1.20741	+	0.354528i	−0.384729	+	0.923030i	$0.625705\pi$
$522$		0			0
$523$	15.1042	−	17.4312i	0.660462	−	0.762214i	−0.322390	−	0.946607i	$-0.604486\pi$
$523$	15.1042	−	17.4312i	0.660462	−	0.762214i	0.982853	+	0.184393i	$0.0590318\pi$
$524$		0			0
$525$	−3.30660	−	7.24045i	−0.144312	−	0.315999i
$526$		0			0
$527$	7.28794	+	2.13993i	0.317468	+	0.0932170i
$528$		0			0
$529$	−8.01031	−	2.35204i	−0.348274	−	0.102263i
$530$		0			0
$531$	−2.41612	−	5.29056i	−0.104850	−	0.229591i
$532$		0			0
$533$	−0.607381	+	4.22443i	−0.0263086	+	0.182980i
$534$		0			0
$535$	−1.31758			−0.0569640
$536$		0			0
$537$	11.8164			0.509916
$538$		0			0
$539$	−0.258605	+	1.79864i	−0.0111389	+	0.0774729i
$540$		0			0
$541$	−12.4681	−	27.3012i	−0.536044	−	1.17377i	−0.963000	−	0.269500i	$-0.913142\pi$
$541$	−12.4681	−	27.3012i	−0.536044	−	1.17377i	0.426957	−	0.904272i	$-0.359586\pi$
$542$		0			0
$543$	−17.3155	−	5.08429i	−0.743079	−	0.218188i
$544$		0			0
$545$	5.93872	+	1.74377i	0.254387	+	0.0746948i
$546$		0			0
$547$	5.02545	+	11.0042i	0.214873	+	0.470506i	0.986121	−	0.166029i	$-0.0530945\pi$
$547$	5.02545	+	11.0042i	0.214873	+	0.470506i	−0.771248	+	0.636535i	$0.780367\pi$
$548$		0			0
$549$	5.79126	−	6.68347i	0.247165	−	0.285244i
$550$		0			0
$551$	28.2429	−	8.29286i	1.20319	−	0.353288i
$552$		0			0
$553$	−21.9458	+	14.1037i	−0.933231	+	0.599751i
$554$		0			0
$555$	22.0945	−	6.48753i	0.937859	−	0.275380i
$556$		0			0
$557$	4.22712	−	9.25610i	0.179109	−	0.392194i	−0.798689	−	0.601744i	$-0.794473\pi$
$557$	4.22712	−	9.25610i	0.179109	−	0.392194i	0.977798	+	0.209550i	$0.0672000\pi$
$558$		0			0
$559$	1.03622	−	7.20707i	0.0438274	−	0.304827i
$560$		0			0
$561$	−2.13151	+	2.45989i	−0.0899923	+	0.103857i
$562$		0			0
$563$	7.34541	−	16.0842i	0.309572	−	0.677869i	−0.689343	−	0.724435i	$-0.742101\pi$
$563$	7.34541	−	16.0842i	0.309572	−	0.677869i	0.998915	+	0.0465664i	$0.0148279\pi$
$564$		0			0
$565$	39.4796			1.66092
$566$		0			0
$567$	1.90126	+	2.19417i	0.0798454	+	0.0921465i
$568$		0			0
$569$	−14.0657	+	4.13005i	−0.589663	+	0.173141i	−0.562934	−	0.826502i	$-0.690327\pi$
$569$	−14.0657	+	4.13005i	−0.589663	+	0.173141i	−0.0267295	+	0.999643i	$0.508509\pi$
$570$		0			0
$571$	5.25812	+	36.5710i	0.220045	+	1.53045i	0.737858	+	0.674956i	$0.235837\pi$
$571$	5.25812	+	36.5710i	0.220045	+	1.53045i	−0.517813	+	0.855494i	$0.673254\pi$
$572$		0			0
$573$	14.9382			0.624051
$574$		0			0
$575$	10.0523	+	11.6009i	0.419209	+	0.483793i
$576$		0			0
$577$	29.8028	−	19.1531i	1.24071	−	0.797354i	0.255183	−	0.966893i	$-0.417864\pi$
$577$	29.8028	−	19.1531i	1.24071	−	0.797354i	0.985523	+	0.169539i	$0.0542279\pi$
$578$		0			0
$579$	−5.60766	+	3.60383i	−0.233047	+	0.149770i
$580$		0			0
$581$	5.49271	+	38.2027i	0.227876	+	1.58491i
$582$		0			0
$583$	−1.15662	+	8.04447i	−0.0479023	+	0.333168i
$584$		0			0
$585$	−10.3951	−	6.68053i	−0.429785	−	0.276206i
$586$		0			0
$587$	−3.87466	−	8.48431i	−0.159924	−	0.350185i	0.812659	−	0.582739i	$-0.198019\pi$
$587$	−3.87466	−	8.48431i	−0.159924	−	0.350185i	−0.972583	+	0.232554i	$0.925292\pi$
$588$		0			0
$589$	17.3810	+	11.1701i	0.716170	+	0.460254i
$590$		0			0
$591$	9.22059	−	10.6411i	0.379285	−	0.437718i
$592$		0			0
$593$	−5.95952	−	41.4494i	−0.244728	−	1.70212i	−0.627777	−	0.778394i	$-0.716035\pi$
$593$	−5.95952	−	41.4494i	−0.244728	−	1.70212i	0.383048	−	0.923728i	$-0.374874\pi$
$594$		0			0
$595$	−13.5422	−	15.6286i	−0.555177	−	0.640709i
$596$		0			0
$597$	−1.19445	+	2.61547i	−0.0488854	+	0.107044i
$598$		0			0
$599$	−3.05114	−	1.96085i	−0.124666	−	0.0801182i	0.476821	−	0.879000i	$-0.341789\pi$
$599$	−3.05114	−	1.96085i	−0.124666	−	0.0801182i	−0.601488	+	0.798882i	$0.705425\pi$
$600$		0			0
$601$	−26.2979	−	7.72175i	−1.07271	−	0.314977i	−0.302753	−	0.953069i	$-0.597906\pi$
$601$	−26.2979	−	7.72175i	−1.07271	−	0.314977i	−0.769960	+	0.638092i	$0.779724\pi$
$602$		0			0
$603$	−5.00220	−	6.47905i	−0.203705	−	0.263847i
$604$		0			0
$605$	−25.0505	−	7.35550i	−1.01845	−	0.299044i
$606$		0			0
$607$	−0.757437	−	0.486775i	−0.0307434	−	0.0197576i	0.525179	−	0.850992i	$-0.323998\pi$
$607$	−0.757437	−	0.486775i	−0.0307434	−	0.0197576i	−0.555922	+	0.831234i	$0.687635\pi$
$608$		0			0
$609$	−5.09830	+	11.1637i	−0.206593	+	0.452377i
$610$		0			0
$611$	16.7975	+	19.3854i	0.679555	+	0.784248i
$612$		0			0
$613$	−4.79841	−	33.3737i	−0.193806	−	1.34795i	−0.821819	−	0.569748i	$-0.807041\pi$
$613$	−4.79841	−	33.3737i	−0.193806	−	1.34795i	0.628013	−	0.778202i	$-0.283868\pi$
$614$		0			0
$615$	1.75101	−	2.02078i	0.0706077	−	0.0814857i
$616$		0			0
$617$	33.7580	+	21.6950i	1.35905	+	0.873407i	0.998244	−	0.0592350i	$-0.0188661\pi$
$617$	33.7580	+	21.6950i	1.35905	+	0.873407i	0.360804	+	0.932642i	$0.382502\pi$
$618$		0			0
$619$	−9.86522	−	21.6018i	−0.396517	−	0.868251i	−0.997612	−	0.0690730i	$-0.977996\pi$
$619$	−9.86522	−	21.6018i	−0.396517	−	0.868251i	0.601095	−	0.799178i	$-0.294731\pi$
$620$		0			0
$621$	−4.71015	−	3.02703i	−0.189012	−	0.121471i
$622$		0			0
$623$	4.26534	−	29.6661i	0.170887	−	1.18855i
$624$		0			0
$625$	4.43903	+	30.8741i	0.177561	+	1.23497i
$626$		0			0
$627$	−7.44814	+	4.78663i	−0.297450	+	0.191160i
$628$		0			0
$629$	17.8232	−	11.4543i	0.710658	−	0.456712i
$630$		0			0
$631$	−8.68524	−	10.0233i	−0.345754	−	0.399021i	0.556063	−	0.831140i	$-0.312311\pi$
$631$	−8.68524	−	10.0233i	−0.345754	−	0.399021i	−0.901817	+	0.432119i	$0.857766\pi$
$632$		0			0
$633$	11.0486			0.439143
$634$		0			0
$635$	3.29369	+	22.9081i	0.130706	+	0.909081i
$636$		0			0
$637$	−6.08991	+	1.78816i	−0.241291	+	0.0708495i
$638$		0			0
$639$	5.64939	+	6.51975i	0.223487	+	0.257917i
$640$		0			0
$641$	−14.8740			−0.587486			−0.293743	−	0.955884i	$-0.594901\pi$
$641$	−14.8740			−0.587486			−0.293743	+	0.955884i	$0.594901\pi$
$642$		0			0
$643$	−9.68022	+	21.1967i	−0.381751	+	0.835917i	0.617049	+	0.786925i	$0.288328\pi$
$643$	−9.68022	+	21.1967i	−0.381751	+	0.835917i	−0.998799	+	0.0489922i	$0.984399\pi$
$644$		0			0
$645$	−2.98731	+	3.44754i	−0.117625	+	0.135747i
$646$		0			0
$647$	−5.12070	+	35.6152i	−0.201315	+	1.40018i	0.599072	+	0.800695i	$0.295536\pi$
$647$	−5.12070	+	35.6152i	−0.201315	+	1.40018i	−0.800387	+	0.599484i	$0.795373\pi$
$648$		0			0
$649$	−3.07201	+	6.72676i	−0.120587	+	0.264048i
$650$		0			0
$651$	−8.26541	+	2.42694i	−0.323947	+	0.0951194i
$652$		0			0
$653$	−12.2185	+	7.85234i	−0.478146	+	0.307286i	−0.757423	−	0.652925i	$-0.773542\pi$
$653$	−12.2185	+	7.85234i	−0.478146	+	0.307286i	0.279277	+	0.960211i	$0.409905\pi$
$654$		0			0
$655$	−54.6958	+	16.0601i	−2.13714	+	0.627521i
$656$		0			0
$657$	−6.09818	+	7.03768i	−0.237913	+	0.274566i
$658$		0			0
$659$	−0.751225	−	1.64495i	−0.0292636	−	0.0640783i	0.894436	−	0.447196i	$-0.147578\pi$
$659$	−0.751225	−	1.64495i	−0.0292636	−	0.0640783i	−0.923699	+	0.383118i	$0.874850\pi$
$660$		0			0
$661$	−47.4626	−	13.9363i	−1.84608	−	0.542058i	−0.999959	−	0.00906733i	$-0.997114\pi$
$661$	−47.4626	−	13.9363i	−1.84608	−	0.542058i	−0.846121	−	0.532991i	$-0.821068\pi$
$662$		0			0
$663$	−10.9084	−	3.20300i	−0.423647	−	0.124394i
$664$		0			0
$665$	−23.3672	−	51.1671i	−0.906142	−	1.98417i
$666$		0			0
$667$	3.36829	−	23.4270i	0.130421	−	0.907095i
$668$		0			0
$669$	−8.20716			−0.317307
$670$		0			0
$671$	−11.2442			−0.434078
$672$		0			0
$673$	2.62237	−	18.2390i	0.101085	−	0.703061i	−0.874754	−	0.484568i	$-0.838977\pi$
$673$	2.62237	−	18.2390i	0.101085	−	0.703061i	0.975839	−	0.218493i	$-0.0701140\pi$
$674$		0			0
$675$	1.13891	+	2.49387i	0.0438367	+	0.0959889i
$676$		0			0
$677$	−23.7850	−	6.98390i	−0.914131	−	0.268413i	−0.209352	−	0.977840i	$-0.567135\pi$
$677$	−23.7850	−	6.98390i	−0.914131	−	0.268413i	−0.704779	+	0.709427i	$0.748954\pi$
$678$		0			0
$679$	−6.24663	−	1.83418i	−0.239724	−	0.0703892i
$680$		0			0
$681$	−8.30375	−	18.1827i	−0.318200	−	0.696762i
$682$		0			0
$683$	−2.63165	+	3.03708i	−0.100697	+	0.116211i	−0.803861	−	0.594817i	$-0.797225\pi$
$683$	−2.63165	+	3.03708i	−0.100697	+	0.116211i	0.703164	+	0.711028i	$0.251770\pi$
$684$		0			0
$685$	15.1064	−	4.43563i	0.577185	−	0.169477i
$686$		0			0
$687$	−3.43828	+	2.20965i	−0.131179	+	0.0843033i
$688$		0			0
$689$	−27.2373	+	7.99759i	−1.03766	+	0.304684i
$690$		0			0
$691$	−1.57507	+	3.44892i	−0.0599184	+	0.131203i	−0.937223	−	0.348732i	$-0.886612\pi$
$691$	−1.57507	+	3.44892i	−0.0599184	+	0.131203i	0.877304	+	0.479935i	$0.159340\pi$
$692$		0			0
$693$	0.525348	−	3.65388i	0.0199563	−	0.138799i
$694$		0			0
$695$	−13.0565	+	15.0680i	−0.495260	+	0.571560i
$696$		0			0
$697$	1.02197	−	2.23781i	0.0387101	−	0.0847632i
$698$		0			0
$699$	−11.5368			−0.436363
$700$		0			0
$701$	−19.8768	−	22.9390i	−0.750736	−	0.866396i	0.243903	−	0.969800i	$-0.421572\pi$
$701$	−19.8768	−	22.9390i	−0.750736	−	0.866396i	−0.994639	+	0.103404i	$0.967027\pi$
$702$		0			0
$703$	55.2949	−	16.2360i	2.08549	−	0.612354i
$704$		0			0
$705$	−2.28705	−	15.9068i	−0.0861354	−	0.599085i
$706$		0			0
$707$	−18.6115			−0.699957
$708$		0			0
$709$	13.4453	+	15.5167i	0.504947	+	0.582740i	0.949798	−	0.312865i	$-0.101289\pi$
$709$	13.4453	+	15.5167i	0.504947	+	0.582740i	−0.444850	+	0.895605i	$0.646743\pi$
$710$		0			0
$711$	7.55891	−	4.85782i	0.283481	−	0.182182i
$712$		0			0
$713$	13.9754	−	8.98147i	0.523384	−	0.336359i
$714$		0			0
$715$	2.23592	+	15.5512i	0.0836188	+	0.581581i
$716$		0			0
$717$	0.804535	−	5.59566i	0.0300459	−	0.208974i
$718$		0			0
$719$	3.98959	+	2.56395i	0.148787	+	0.0956193i	0.612916	−	0.790148i	$-0.289996\pi$
$719$	3.98959	+	2.56395i	0.148787	+	0.0956193i	−0.464129	+	0.885767i	$0.653633\pi$
$720$		0			0
$721$	−17.5903	−	38.5173i	−0.655095	−	1.43446i
$722$		0			0
$723$	−10.3068	−	6.62377i	−0.383314	−	0.246341i
$724$		0			0
$725$	−7.58939	+	8.75862i	−0.281863	+	0.325287i
$726$		0			0
$727$	6.18304	+	43.0040i	0.229316	+	1.59493i	0.701000	+	0.713162i	$0.252737\pi$
$727$	6.18304	+	43.0040i	0.229316	+	1.59493i	−0.471683	+	0.881768i	$0.656353\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	−1.74354	+	3.81781i	−0.0644870	+	0.141207i
$732$		0			0
$733$	5.16763	+	3.32104i	0.190871	+	0.122665i	0.632586	−	0.774490i	$-0.281993\pi$
$733$	5.16763	+	3.32104i	0.190871	+	0.122665i	−0.441715	+	0.897155i	$0.645630\pi$
$734$		0			0
$735$	3.81541	+	1.12030i	0.140733	+	0.0413230i
$736$		0			0
$737$	−2.06078	+	10.2013i	−0.0759100	+	0.375771i
$738$		0			0
$739$	8.75852	+	2.57173i	0.322187	+	0.0946027i	0.438827	−	0.898572i	$-0.355394\pi$
$739$	8.75852	+	2.57173i	0.322187	+	0.0946027i	−0.116640	+	0.993174i	$0.537212\pi$
$740$		0			0
$741$	−26.0154	−	16.7191i	−0.955698	−	0.614190i
$742$		0			0
$743$	−9.74138	+	21.3306i	−0.357377	+	0.782546i	0.642491	+	0.766293i	$0.277901\pi$
$743$	−9.74138	+	21.3306i	−0.357377	+	0.782546i	−0.999868	+	0.0162526i	$0.994826\pi$
$744$		0			0
$745$	−11.8468	−	13.6719i	−0.434032	−	0.500899i
$746$		0			0
$747$	−1.89188	−	13.1583i	−0.0692204	−	0.481439i
$748$		0			0
$749$	0.900332	−	1.03904i	0.0328974	−	0.0379656i
$750$		0			0
$751$	30.0322	+	19.3005i	1.09589	+	0.704286i	0.958174	−	0.286186i	$-0.0923875\pi$
$751$	30.0322	+	19.3005i	1.09589	+	0.704286i	0.137716	+	0.990472i	$0.456024\pi$
$752$		0			0
$753$	−11.0684	−	24.2364i	−0.403355	−	0.883224i
$754$		0			0
$755$	56.0860	+	36.0443i	2.04118	+	1.31179i
$756$		0			0
$757$	−4.20324	+	29.2342i	−0.152769	+	1.06254i	0.758781	+	0.651346i	$0.225795\pi$
$757$	−4.20324	+	29.2342i	−0.152769	+	1.06254i	−0.911550	+	0.411189i	$0.865114\pi$
$758$		0			0
$759$	1.01312	+	7.04644i	0.0367741	+	0.255770i
$760$		0			0
$761$	−30.7789	+	19.7804i	−1.11574	+	0.717040i	−0.962536	−	0.271155i	$-0.912594\pi$
$761$	−30.7789	+	19.7804i	−1.11574	+	0.717040i	−0.153200	+	0.988195i	$0.548958\pi$
$762$		0			0
$763$	−5.43319	+	3.49170i	−0.196695	+	0.126408i
$764$		0			0
$765$	4.66442	+	5.38303i	0.168643	+	0.194624i
$766$		0			0
$767$	−25.8298			−0.932662
$768$		0			0
$769$	4.80637	+	33.4290i	0.173322	+	1.20548i	0.871804	+	0.489854i	$0.162950\pi$
$769$	4.80637	+	33.4290i	0.173322	+	1.20548i	−0.698482	+	0.715628i	$0.746141\pi$
$770$		0			0
$771$	−26.9771	+	7.92119i	−0.971556	+	0.285275i
$772$		0			0
$773$	22.8248	+	26.3413i	0.820952	+	0.947429i	0.999332	−	0.0365323i	$-0.0116312\pi$
$773$	22.8248	+	26.3413i	0.820952	+	0.947429i	−0.178380	+	0.983962i	$0.557086\pi$
$774$		0			0
$775$	−8.13462			−0.292204
$776$		0			0
$777$	−9.98161	+	21.8567i	−0.358088	+	0.784104i
$778$		0			0
$779$	4.38218	−	5.05731i	0.157008	−	0.181197i
$780$		0			0
$781$	1.56102	−	10.8571i	0.0558576	−	0.388498i
$782$		0			0
$783$	1.75603	−	3.84518i	0.0627555	−	0.137415i
$784$		0			0
$785$	22.6089	−	6.63859i	0.806948	−	0.236941i
$786$		0			0
$787$	−5.69410	+	3.65938i	−0.202973	+	0.130443i	−0.638179	−	0.769888i	$-0.720312\pi$
$787$	−5.69410	+	3.65938i	−0.202973	+	0.130443i	0.435206	+	0.900331i	$0.356676\pi$
$788$		0			0
$789$	5.02482	−	1.47542i	0.178888	−	0.0525263i
$790$		0			0
$791$	−26.9773	+	31.1334i	−0.959201	+	1.10698i
$792$		0			0
$793$	−16.3152	−	35.7253i	−0.579370	−	1.26864i
$794$		0			0
$795$	17.0645	+	5.01059i	0.605216	+	0.177707i
$796$		0			0
$797$	−0.0485585	−	0.0142581i	−0.00172003	−	0.000505047i	0.280872	−	0.959745i	$-0.409376\pi$
$797$	−0.0485585	−	0.0142581i	−0.00172003	−	0.000505047i	−0.282592	+	0.959240i	$0.591194\pi$
$798$		0			0
$799$	−6.14222	−	13.4496i	−0.217296	−	0.475812i
$800$		0			0
$801$	−1.46913	+	10.2181i	−0.0519093	+	0.361037i
$802$		0			0
$803$	11.8401			0.417829
$804$		0			0
$805$	−45.2290			−1.59411
$806$		0			0
$807$	3.79670	−	26.4066i	0.133650	−	0.929557i
$808$		0			0
$809$	−17.9174	−	39.2336i	−0.629942	−	1.37938i	−0.908063	−	0.418834i	$-0.862439\pi$
$809$	−17.9174	−	39.2336i	−0.629942	−	1.37938i	0.278121	−	0.960546i	$-0.410288\pi$
$810$		0			0
$811$	−7.90459	−	2.32100i	−0.277568	−	0.0815012i	0.139986	−	0.990153i	$-0.455294\pi$
$811$	−7.90459	−	2.32100i	−0.277568	−	0.0815012i	−0.417554	+	0.908652i	$0.637112\pi$
$812$		0			0
$813$	16.1599	+	4.74497i	0.566751	+	0.166413i
$814$		0			0
$815$	−15.2280	−	33.3447i	−0.533413	−	1.16801i
$816$		0			0
$817$	−7.47620	+	8.62800i	−0.261559	+	0.301855i
$818$		0			0
$819$	12.3714	−	3.63258i	0.432293	−	0.126933i
$820$		0			0
$821$	−42.7725	+	27.4882i	−1.49277	+	0.959345i	−0.496973	+	0.867766i	$0.665555\pi$
$821$	−42.7725	+	27.4882i	−1.49277	+	0.959345i	−0.995798	+	0.0915793i	$0.970808\pi$
$822$		0			0
$823$	35.0907	−	10.3035i	1.22318	−	0.359159i	0.394510	−	0.918892i	$-0.370914\pi$
$823$	35.0907	−	10.3035i	1.22318	−	0.359159i	0.828673	+	0.559733i	$0.189096\pi$
$824$		0			0
$825$	1.44808	−	3.17086i	0.0504158	−	0.110395i
$826$		0			0
$827$	−4.00382	+	27.8471i	−0.139226	+	0.968340i	0.793709	+	0.608297i	$0.208147\pi$
$827$	−4.00382	+	27.8471i	−0.139226	+	0.968340i	−0.932936	+	0.360043i	$0.882762\pi$
$828$		0			0
$829$	27.5239	−	31.7642i	0.955943	−	1.10322i	−0.0386383	−	0.999253i	$-0.512302\pi$
$829$	27.5239	−	31.7642i	0.955943	−	1.10322i	0.994581	−	0.103964i	$-0.0331525\pi$
$830$		0			0
$831$	0.909563	−	1.99166i	0.0315524	−	0.0690901i
$832$		0			0
$833$	3.65861			0.126763
$834$		0			0
$835$	1.50350	+	1.73513i	0.0520307	+	0.0600466i
$836$		0			0
$837$	2.84690	−	0.835925i	0.0984032	−	0.0288938i
$838$		0			0
$839$	−6.78224	−	47.1715i	−0.234149	−	1.62854i	−0.679845	−	0.733356i	$-0.737953\pi$
$839$	−6.78224	−	47.1715i	−0.234149	−	1.62854i	0.445696	−	0.895184i	$-0.352956\pi$
$840$		0			0
$841$	−11.1309			−0.383826
$842$		0			0
$843$	−18.9404	−	21.8584i	−0.652343	−	0.752844i
$844$		0			0
$845$	−15.7364	+	10.1132i	−0.541348	+	0.347903i
$846$		0			0
$847$	22.9181	−	14.7286i	0.787475	−	0.506079i
$848$		0			0
$849$	3.13276	+	21.7888i	0.107516	+	0.747791i
$850$		0			0
$851$	6.59454	−	45.8661i	0.226058	−	1.57227i
$852$		0			0
$853$	−26.6027	−	17.0965i	−0.910860	−	0.585374i	−0.000867553	−	1.00000i	$-0.500276\pi$
$853$	−26.6027	−	17.0965i	−0.910860	−	0.585374i	−0.909992	+	0.414626i	$0.863913\pi$
$854$		0			0
$855$	8.04850	+	17.6238i	0.275253	+	0.602720i
$856$		0			0
$857$	−10.8638	−	6.98173i	−0.371100	−	0.238491i	0.341776	−	0.939781i	$-0.388971\pi$
$857$	−10.8638	−	6.98173i	−0.371100	−	0.238491i	−0.712876	+	0.701290i	$0.752608\pi$
$858$		0			0
$859$	−1.92887	+	2.22603i	−0.0658120	+	0.0759511i	−0.787701	−	0.616058i	$-0.788729\pi$
$859$	−1.92887	+	2.22603i	−0.0658120	+	0.0759511i	0.721889	+	0.692009i	$0.243274\pi$
$860$		0			0
$861$	0.397070	+	2.76168i	0.0135321	+	0.0941180i
$862$		0			0
$863$	27.0579	+	31.2265i	0.921063	+	1.06296i	0.997825	+	0.0659140i	$0.0209963\pi$
$863$	27.0579	+	31.2265i	0.921063	+	1.06296i	−0.0767622	+	0.997049i	$0.524458\pi$
$864$		0			0
$865$	−13.0873	+	28.6571i	−0.444981	+	0.974372i
$866$		0			0
$867$	−8.78825	−	5.64786i	−0.298464	−	0.191811i
$868$		0			0
$869$	−10.9617	−	3.21865i	−0.371851	−	0.109185i
$870$		0			0
$871$	−35.4020	+	8.25443i	−1.19955	+	0.279691i
$872$		0			0
$873$	2.15156	+	0.631755i	0.0728193	+	0.0213817i
$874$		0			0
$875$	−15.3473	−	9.86312i	−0.518834	−	0.333434i
$876$		0			0
$877$	0.887434	−	1.94321i	0.0299665	−	0.0656175i	−0.894057	−	0.447953i	$-0.852153\pi$
$877$	0.887434	−	1.94321i	0.0299665	−	0.0656175i	0.924023	+	0.382336i	$0.124880\pi$
$878$		0			0
$879$	−11.9347	−	13.7734i	−0.402547	−	0.464564i
$880$		0			0
$881$	7.37402	+	51.2875i	0.248437	+	1.72792i	0.607252	+	0.794510i	$0.292272\pi$
$881$	7.37402	+	51.2875i	0.248437	+	1.72792i	−0.358815	+	0.933409i	$0.616819\pi$
$882$		0			0
$883$	8.15857	−	9.41550i	0.274558	−	0.316857i	−0.601678	−	0.798738i	$-0.705501\pi$
$883$	8.15857	−	9.41550i	0.274558	−	0.316857i	0.876236	+	0.481882i	$0.160047\pi$
$884$		0			0
$885$	13.6138	+	8.74904i	0.457622	+	0.294096i
$886$		0			0
$887$	−24.0529	−	52.6685i	−0.807617	−	1.76843i	−0.617328	−	0.786706i	$-0.711785\pi$
$887$	−24.0529	−	52.6685i	−0.807617	−	1.76843i	−0.190289	−	0.981728i	$-0.560942\pi$
$888$		0			0
$889$	−20.3159	−	13.0562i	−0.681373	−	0.437892i
$890$		0			0
$891$	−0.180948	+	1.25852i	−0.00606200	+	0.0421621i
$892$		0			0
$893$	−5.72370	−	39.8092i	−0.191536	−	1.33216i
$894$		0			0
$895$	−27.6585	+	17.7751i	−0.924522	+	0.594154i
$896$		0			0
$897$	−20.9181	+	13.4432i	−0.698434	+	0.448856i
$898$		0			0
$899$	8.21353	+	9.47892i	0.273937	+	0.316140i
$900$		0			0
$901$	16.3632			0.545138
$902$		0			0
$903$	−0.677420	−	4.71156i	−0.0225431	−	0.156791i
$904$		0			0
$905$	48.1782	−	14.1464i	1.60150	−	0.470242i
$906$		0			0
$907$	20.8682	+	24.0832i	0.692918	+	0.799670i	0.987778	−	0.155870i	$-0.0498182\pi$
$907$	20.8682	+	24.0832i	0.692918	+	0.799670i	−0.294859	+	0.955541i	$0.595273\pi$
$908$		0			0
$909$	6.41046			0.212621
$910$		0			0
$911$	−8.87772	+	19.4395i	−0.294132	+	0.644059i	−0.997788	−	0.0664820i	$-0.978822\pi$
$911$	−8.87772	+	19.4395i	−0.294132	+	0.644059i	0.703656	+	0.710541i	$0.251550\pi$
$912$		0			0
$913$	−11.0687	+	12.7740i	−0.366322	+	0.422758i
$914$		0			0
$915$	−3.50179	+	24.3555i	−0.115766	+	0.805168i
$916$		0			0
$917$	24.7099	−	54.1071i	0.815992	−	1.78677i
$918$		0			0
$919$	20.5629	−	6.03782i	0.678309	−	0.199169i	0.0756091	−	0.997138i	$-0.475910\pi$
$919$	20.5629	−	6.03782i	0.678309	−	0.199169i	0.602700	+	0.797968i	$0.294092\pi$
$920$		0			0
$921$	18.6531	−	11.9876i	0.614642	−	0.395006i
$922$		0			0
$923$	36.7605	−	10.7938i	1.20999	−	0.355284i
$924$		0			0
$925$	−14.8588	+	17.1479i	−0.488553	+	0.563820i
$926$		0			0
$927$	6.05870	+	13.2667i	0.198994	+	0.435736i
$928$		0			0
$929$	−2.10510	−	0.618112i	−0.0690660	−	0.0202796i	0.247017	−	0.969011i	$-0.420550\pi$
$929$	−2.10510	−	0.618112i	−0.0690660	−	0.0202796i	−0.316083	+	0.948732i	$0.602368\pi$
$930$		0			0
$931$	9.54864	+	2.80373i	0.312944	+	0.0918886i
$932$		0			0
$933$	2.71252	+	5.93959i	0.0888039	+	0.194453i
$934$		0			0
$935$	1.28885	−	8.96418i	0.0421500	−	0.293160i
$936$		0			0
$937$	35.0227			1.14414			0.572071	−	0.820204i	$-0.306140\pi$
$937$	35.0227			1.14414			0.572071	+	0.820204i	$0.306140\pi$
$938$		0			0
$939$	13.0776			0.426771
$940$		0			0
$941$	−5.26607	+	36.6263i	−0.171669	+	1.19398i	0.703689	+	0.710508i	$0.251535\pi$
$941$	−5.26607	+	36.6263i	−0.171669	+	1.19398i	−0.875358	+	0.483476i	$0.839374\pi$
$942$		0			0
$943$	−2.23519	−	4.89439i	−0.0727880	−	0.159383i
$944$		0			0
$945$	−7.75086	−	2.27586i	−0.252136	−	0.0740337i
$946$		0			0
$947$	−34.6452	−	10.1727i	−1.12582	−	0.330570i	−0.334755	−	0.942305i	$-0.608654\pi$
$947$	−34.6452	−	10.1727i	−1.12582	−	0.330570i	−0.791063	+	0.611735i	$0.790472\pi$
$948$		0			0
$949$	17.1799	+	37.6187i	0.557682	+	1.22115i
$950$		0			0
$951$	−3.53452	+	4.07905i	−0.114615	+	0.132272i
$952$		0			0
$953$	22.9214	−	6.73034i	0.742498	−	0.218017i	0.111460	−	0.993769i	$-0.464447\pi$
$953$	22.9214	−	6.73034i	0.742498	−	0.218017i	0.631038	+	0.775752i	$0.282629\pi$
$954$		0			0
$955$	−34.9656	+	22.4710i	−1.13146	+	0.727144i
$956$		0			0
$957$	−5.15700	+	1.51423i	−0.166702	+	0.0489482i
$958$		0			0
$959$	−6.82459	+	14.9438i	−0.220378	+	0.482560i
$960$		0			0
$961$	3.15888	−	21.9705i	0.101899	−	0.708725i
$962$		0			0
$963$	−0.310106	+	0.357881i	−0.00999303	+	0.0115326i
$964$		0			0
$965$	7.70466	−	16.8708i	0.248022	−	0.543092i
$966$		0			0
$967$	−23.0378			−0.740845			−0.370423	−	0.928863i	$-0.620787\pi$
$967$	−23.0378			−0.740845			−0.370423	+	0.928863i	$0.620787\pi$
$968$		0			0
$969$	11.6734	+	13.4719i	0.375005	+	0.432779i
$970$		0			0
$971$	36.0369	−	10.5814i	1.15648	−	0.339573i	0.353416	−	0.935466i	$-0.385020\pi$
$971$	36.0369	−	10.5814i	1.15648	−	0.339573i	0.803063	+	0.595894i	$0.203202\pi$
$972$		0			0
$973$	−2.96076	−	20.5925i	−0.0949175	−	0.660166i
$974$		0			0
$975$	12.1757			0.389934
$976$		0			0
$977$	7.27552	+	8.39640i	0.232765	+	0.268625i	0.860101	−	0.510124i	$-0.170400\pi$
$977$	7.27552	+	8.39640i	0.232765	+	0.268625i	−0.627336	+	0.778748i	$0.715855\pi$
$978$		0			0
$979$	11.0419	−	7.09618i	0.352900	−	0.226795i
$980$		0			0
$981$	1.87138	−	1.20266i	0.0597486	−	0.0383981i
$982$		0			0
$983$	−4.90727	−	34.1308i	−0.156518	−	1.08860i	−0.904989	−	0.425436i	$-0.860121\pi$
$983$	−4.90727	−	34.1308i	−0.156518	−	1.08860i	0.748471	−	0.663168i	$-0.230788\pi$
$984$		0			0
$985$	−5.57540	+	38.7778i	−0.177647	+	1.23556i
$986$		0			0
$987$	14.1068	+	9.06590i	0.449025	+	0.288571i
$988$		0			0
$989$	3.81334	+	8.35006i	0.121257	+	0.265516i
$990$		0			0
$991$	34.7024	+	22.3019i	1.10236	+	0.708443i	0.959615	−	0.281317i	$-0.0907712\pi$
$991$	34.7024	+	22.3019i	1.10236	+	0.708443i	0.142744	+	0.989760i	$0.454408\pi$
$992$		0			0
$993$	−22.1299	+	25.5393i	−0.702271	+	0.810464i
$994$		0			0
$995$	−1.13855	−	7.91876i	−0.0360943	−	0.251042i
$996$		0			0
$997$	−5.83307	−	6.73172i	−0.184735	−	0.213196i	0.655826	−	0.754912i	$-0.272320\pi$
$997$	−5.83307	−	6.73172i	−0.184735	−	0.213196i	−0.840562	+	0.541716i	$0.817775\pi$
$998$		0			0
$999$	3.43802	−	7.52821i	0.108774	−	0.238182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.a.265.2	✓	60
67.22	even	11	inner	804.2.q.a.625.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.a.265.2	✓	60	1.1	even	1	trivial
804.2.q.a.625.2	yes	60	67.22	even	11	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.15584 - 2.53094i) q^{5} +(2.78570 + 0.817955i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-1.15584 - 2.53094i) q^{5} +(2.78570 + 0.817955i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(0.528186 + 1.15657i) q^{11} +(-2.90827 + 3.35633i) q^{13} +(2.66967 - 0.783886i) q^{15} +(2.15357 - 1.38402i) q^{17} +(6.68126 - 1.96180i) q^{19} +(-1.20608 + 2.64094i) q^{21} +(0.796817 - 5.54198i) q^{23} +(-1.79538 + 2.07198i) q^{25} +(0.415415 - 0.909632i) q^{27} +4.22718 q^{29} +(1.94303 + 2.24237i) q^{31} +(-1.21996 + 0.358213i) q^{33} +(-1.14963 - 7.99586i) q^{35} +8.27611 q^{37} +(-2.90827 - 3.35633i) q^{39} +(0.808447 - 0.519558i) q^{41} +(-1.37925 + 0.886389i) q^{43} +(0.395973 + 2.75406i) q^{45} +(0.821978 - 5.71698i) q^{47} +(1.20229 + 0.772666i) q^{49} +(1.06345 + 2.32862i) q^{51} +(5.37728 + 3.45577i) q^{53} +(2.31670 - 2.67361i) q^{55} +(0.990985 + 6.89245i) q^{57} +(3.80877 + 4.39555i) q^{59} +(-3.67372 + 8.04433i) q^{61} +(-2.44241 - 1.56964i) q^{63} +(11.8562 + 3.48128i) q^{65} +(6.62493 + 4.80732i) q^{67} +(5.37217 + 1.57741i) q^{69} +(-7.25738 - 4.66403i) q^{71} +(3.86842 - 8.47066i) q^{73} +(-1.79538 - 2.07198i) q^{75} +(0.525348 + 3.65388i) q^{77} +(-5.88412 + 6.79063i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.52238 + 12.0923i) q^{83} +(-5.99206 - 3.85086i) q^{85} +(-0.601590 + 4.18415i) q^{87} +(-1.46913 - 10.2181i) q^{89} +(-10.8469 + 6.97088i) q^{91} +(-2.49607 + 1.60413i) q^{93} +(-12.6877 - 14.6423i) q^{95} -2.24239 q^{97} +(-0.180948 - 1.25852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9	\( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 2 * q^5 - 2 * q^7 - 6 * q^9 + 7 * q^11 - 2 * q^13 + 9 * q^15 - 19 * q^17 + 2 * q^19 - 2 * q^21 + 4 * q^23 + 16 * q^25 - 6 * q^27 + 16 * q^29 - 28 * q^31 - 4 * q^33 + 28 * q^35 + 2 * q^37 - 2 * q^39 + 32 * q^41 + 19 * q^43 - 2 * q^45 + 2 * q^47 - 70 * q^49 - 19 * q^51 + 31 * q^53 - 5 * q^55 + 13 * q^57 + 59 * q^59 + 32 * q^61 + 9 * q^63 + 28 * q^65 + 7 * q^67 + 4 * q^69 + 16 * q^71 + 19 * q^73 + 16 * q^75 - 46 * q^77 + 48 * q^79 - 6 * q^81 + 60 * q^83 - 66 * q^85 + 5 * q^87 - 22 * q^89 + 24 * q^91 + 5 * q^93 + 103 * q^95 - 46 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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