LMFDB - Embedded newform 804.2.q.b.241.4

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			241.4
Character	$\chi$	$=$	804.241
Dual form			804.2.q.b.397.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-4.86843 - 1.42950i) q^{11} +(-1.52774 - 0.981818i) q^{13} +(-1.09898 + 1.26829i) q^{15} +(-0.741435 - 5.15679i) q^{17} +(-5.41739 + 6.25200i) q^{19} +(2.54000 - 0.745811i) q^{21} +(-1.76573 + 3.86640i) q^{23} +(-1.83702 - 1.18058i) q^{25} +(0.959493 - 0.281733i) q^{27} -5.92850 q^{29} +(5.48491 - 3.52494i) q^{31} +(3.32273 - 3.83464i) q^{33} +(-1.84551 - 4.04109i) q^{35} +3.97126 q^{37} +(1.52774 - 0.981818i) q^{39} +(-0.509333 - 3.54249i) q^{41} +(0.150600 + 1.04744i) q^{43} +(-0.697146 - 1.52654i) q^{45} +(-2.23155 + 4.88641i) q^{47} +(-0.00111521 + 0.00775643i) q^{49} +(4.99879 + 1.46778i) q^{51} +(-0.275366 + 1.91521i) q^{53} +(-7.16333 - 4.60359i) q^{55} +(-3.43656 - 7.52501i) q^{57} +(-0.666382 + 0.428258i) q^{59} +(0.419761 - 0.123253i) q^{61} +(-0.376740 + 2.62029i) q^{63} +(-1.99578 - 2.30325i) q^{65} +(-1.49365 - 8.04792i) q^{67} +(-2.78350 - 3.21232i) q^{69} +(0.458922 - 3.19187i) q^{71} +(6.68618 - 1.96324i) q^{73} +(1.83702 - 1.18058i) q^{75} +(5.57983 + 12.2181i) q^{77} +(-9.05517 - 5.81941i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-16.4522 - 4.83081i) q^{83} +(1.24427 - 8.65408i) q^{85} +(2.46279 - 5.39276i) q^{87} +(4.61371 + 10.1026i) q^{89} +(0.684170 + 4.75851i) q^{91} +(0.927882 + 6.45356i) q^{93} +(-11.6791 + 7.50571i) q^{95} +11.4218 q^{97} +(2.10780 + 4.61543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$		0			0
$5$	1.61021	+	0.472801i	0.720109	+	0.211443i	0.621198	−	0.783653i	$-0.286646\pi$
$5$	1.61021	+	0.472801i	0.720109	+	0.211443i	0.0989104	+	0.995096i	$0.468464\pi$
$6$		0			0
$7$	−1.73357	−	2.00064i	−0.655227	−	0.756172i	0.326763	−	0.945106i	$-0.394042\pi$
$7$	−1.73357	−	2.00064i	−0.655227	−	0.756172i	−0.981990	+	0.188934i	$0.939497\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−4.86843	−	1.42950i	−1.46789	−	0.431010i	−0.552474	−	0.833530i	$-0.686316\pi$
$11$	−4.86843	−	1.42950i	−1.46789	−	0.431010i	−0.915411	+	0.402520i	$0.868134\pi$
$12$		0			0
$13$	−1.52774	−	0.981818i	−0.423718	−	0.272307i	0.311357	−	0.950293i	$-0.399217\pi$
$13$	−1.52774	−	0.981818i	−0.423718	−	0.272307i	−0.735075	+	0.677986i	$0.762853\pi$
$14$		0			0
$15$	−1.09898	+	1.26829i	−0.283756	+	0.327472i
$16$		0			0
$17$	−0.741435	−	5.15679i	−0.179824	−	1.25071i	−0.857167	−	0.515038i	$-0.827778\pi$
$17$	−0.741435	−	5.15679i	−0.179824	−	1.25071i	0.677343	−	0.735668i	$-0.263131\pi$
$18$		0			0
$19$	−5.41739	+	6.25200i	−1.24284	+	1.43431i	−0.382991	+	0.923752i	$0.625106\pi$
$19$	−5.41739	+	6.25200i	−1.24284	+	1.43431i	−0.859845	+	0.510556i	$0.829440\pi$
$20$		0			0
$21$	2.54000	−	0.745811i	0.554274	−	0.162749i
$22$		0			0
$23$	−1.76573	+	3.86640i	−0.368180	+	0.806201i	0.631349	+	0.775499i	$0.282502\pi$
$23$	−1.76573	+	3.86640i	−0.368180	+	0.806201i	−0.999529	+	0.0307021i	$0.990226\pi$
$24$		0			0
$25$	−1.83702	−	1.18058i	−0.367405	−	0.236117i
$26$		0			0
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$		0			0
$29$	−5.92850			−1.10090			−0.550448	−	0.834870i	$-0.685543\pi$
$29$	−5.92850			−1.10090			−0.550448	+	0.834870i	$0.685543\pi$
$30$		0			0
$31$	5.48491	−	3.52494i	0.985119	−	0.633098i	0.0542796	−	0.998526i	$-0.482714\pi$
$31$	5.48491	−	3.52494i	0.985119	−	0.633098i	0.930840	+	0.365428i	$0.119077\pi$
$32$		0			0
$33$	3.32273	−	3.83464i	0.578414	−	0.667525i
$34$		0			0
$35$	−1.84551	−	4.04109i	−0.311947	−	0.683070i
$36$		0			0
$37$	3.97126			0.652870			0.326435	−	0.945220i	$-0.394152\pi$
$37$	3.97126			0.652870			0.326435	+	0.945220i	$0.394152\pi$
$38$		0			0
$39$	1.52774	−	0.981818i	0.244634	−	0.157217i
$40$		0			0
$41$	−0.509333	−	3.54249i	−0.0795444	−	0.553243i	−0.990155	−	0.139977i	$-0.955297\pi$
$41$	−0.509333	−	3.54249i	−0.0795444	−	0.553243i	0.910610	−	0.413266i	$-0.135612\pi$
$42$		0			0
$43$	0.150600	+	1.04744i	0.0229662	+	0.159734i	0.998077	−	0.0619840i	$-0.0197428\pi$
$43$	0.150600	+	1.04744i	0.0229662	+	0.159734i	−0.975111	+	0.221718i	$0.928834\pi$
$44$		0			0
$45$	−0.697146	−	1.52654i	−0.103924	−	0.227563i
$46$		0			0
$47$	−2.23155	+	4.88641i	−0.325505	+	0.712756i	−0.999666	−	0.0258281i	$-0.991778\pi$
$47$	−2.23155	+	4.88641i	−0.325505	+	0.712756i	0.674162	+	0.738584i	$0.264505\pi$
$48$		0			0
$49$	−0.00111521	+	0.00775643i	−0.000159315	+	0.00110806i
$50$		0			0
$51$	4.99879	+	1.46778i	0.699970	+	0.205530i
$52$		0			0
$53$	−0.275366	+	1.91521i	−0.0378244	+	0.263074i	−0.999955	−	0.00951541i	$-0.996971\pi$
$53$	−0.275366	+	1.91521i	−0.0378244	+	0.263074i	0.962130	+	0.272590i	$0.0878802\pi$
$54$		0			0
$55$	−7.16333	−	4.60359i	−0.965903	−	0.620748i
$56$		0			0
$57$	−3.43656	−	7.52501i	−0.455183	−	0.996712i
$58$		0			0
$59$	−0.666382	+	0.428258i	−0.0867556	+	0.0557544i	−0.583299	−	0.812257i	$-0.698239\pi$
$59$	−0.666382	+	0.428258i	−0.0867556	+	0.0557544i	0.496544	+	0.868012i	$0.334602\pi$
$60$		0			0
$61$	0.419761	−	0.123253i	0.0537449	−	0.0157809i	−0.254750	−	0.967007i	$-0.581993\pi$
$61$	0.419761	−	0.123253i	0.0537449	−	0.0157809i	0.308494	+	0.951226i	$0.400175\pi$
$62$		0			0
$63$	−0.376740	+	2.62029i	−0.0474648	+	0.330125i
$64$		0			0
$65$	−1.99578	−	2.30325i	−0.247546	−	0.285683i
$66$		0			0
$67$	−1.49365	−	8.04792i	−0.182479	−	0.983210i
$67$	−1.49365	−	8.04792i	−0.182479	−	0.983210i
$68$		0			0
$69$	−2.78350	−	3.21232i	−0.335093	−	0.386718i
$70$		0			0
$71$	0.458922	−	3.19187i	0.0544640	−	0.378805i	−0.944299	−	0.329088i	$-0.893259\pi$
$71$	0.458922	−	3.19187i	0.0544640	−	0.378805i	0.998763	−	0.0497176i	$-0.0158321\pi$
$72$		0			0
$73$	6.68618	−	1.96324i	0.782558	−	0.229780i	0.134037	−	0.990976i	$-0.457206\pi$
$73$	6.68618	−	1.96324i	0.782558	−	0.229780i	0.648521	+	0.761196i	$0.275388\pi$
$74$		0			0
$75$	1.83702	−	1.18058i	0.212121	−	0.136322i
$76$		0			0
$77$	5.57983	+	12.2181i	0.635881	+	1.39238i
$78$		0			0
$79$	−9.05517	−	5.81941i	−1.01879	−	0.654734i	−0.0791338	−	0.996864i	$-0.525215\pi$
$79$	−9.05517	−	5.81941i	−1.01879	−	0.654734i	−0.939653	+	0.342130i	$0.888852\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	−16.4522	−	4.83081i	−1.80587	−	0.530250i	−0.807633	−	0.589686i	$-0.799252\pi$
$83$	−16.4522	−	4.83081i	−1.80587	−	0.530250i	−0.998232	+	0.0594357i	$0.981070\pi$
$84$		0			0
$85$	1.24427	−	8.65408i	0.134960	−	0.938667i
$86$		0			0
$87$	2.46279	−	5.39276i	0.264039	−	0.578164i
$88$		0			0
$89$	4.61371	+	10.1026i	0.489053	+	1.07088i	0.979874	+	0.199616i	$0.0639694\pi$
$89$	4.61371	+	10.1026i	0.489053	+	1.07088i	−0.490822	+	0.871260i	$0.663303\pi$
$90$		0			0
$91$	0.684170	+	4.75851i	0.0717205	+	0.498827i
$92$		0			0
$93$	0.927882	+	6.45356i	0.0962169	+	0.669203i
$94$		0			0
$95$	−11.6791	+	7.50571i	−1.19825	+	0.770069i
$96$		0			0
$97$	11.4218			1.15971			0.579853	−	0.814721i	$-0.303110\pi$
$97$	11.4218			1.15971			0.579853	+	0.814721i	$0.303110\pi$
$98$		0			0
$99$	2.10780	+	4.61543i	0.211842	+	0.463869i
$100$		0			0
$101$	−3.93723	+	4.54381i	−0.391769	+	0.452126i	−0.917032	−	0.398815i	$-0.869422\pi$
$101$	−3.93723	+	4.54381i	−0.391769	+	0.452126i	0.525262	+	0.850940i	$0.323967\pi$
$102$		0			0
$103$	14.1228	−	9.07620i	1.39157	−	0.894305i	0.391896	−	0.920009i	$-0.371819\pi$
$103$	14.1228	−	9.07620i	1.39157	−	0.894305i	0.999670	+	0.0257045i	$0.00818289\pi$
$104$		0			0
$105$	4.44256			0.433549
$106$		0			0
$107$	−10.2521	+	3.01029i	−0.991108	+	0.291016i	−0.736802	−	0.676108i	$-0.763665\pi$
$107$	−10.2521	+	3.01029i	−0.991108	+	0.291016i	−0.254306	+	0.967124i	$0.581847\pi$
$108$		0			0
$109$	−6.17414	−	3.96788i	−0.591375	−	0.380054i	0.210457	−	0.977603i	$-0.432505\pi$
$109$	−6.17414	−	3.96788i	−0.591375	−	0.380054i	−0.801832	+	0.597549i	$0.796141\pi$
$110$		0			0
$111$	−1.64972	+	3.61238i	−0.156584	+	0.342872i
$112$		0			0
$113$	4.11880	−	1.20939i	0.387464	−	0.113770i	−0.0821981	−	0.996616i	$-0.526194\pi$
$113$	4.11880	−	1.20939i	0.387464	−	0.113770i	0.469662	+	0.882846i	$0.344376\pi$
$114$		0			0
$115$	−4.67124	+	5.39089i	−0.435595	+	0.502703i
$116$		0			0
$117$	0.258447	+	1.79754i	0.0238935	+	0.166183i
$118$		0			0
$119$	−9.03158	+	10.4230i	−0.827924	+	0.955475i
$120$		0			0
$121$	12.4043	+	7.97177i	1.12766	+	0.724706i
$122$		0			0
$123$	3.43394	+	1.00830i	0.309628	+	0.0909150i
$124$		0			0
$125$	−7.89472	−	9.11100i	−0.706126	−	0.814912i
$126$		0			0
$127$	8.62104	+	9.94922i	0.764994	+	0.882850i	0.995931	−	0.0901186i	$-0.0287246\pi$
$127$	8.62104	+	9.94922i	0.764994	+	0.882850i	−0.230937	+	0.972969i	$0.574179\pi$
$128$		0			0
$129$	−1.01535	−	0.298134i	−0.0893965	−	0.0262492i
$130$		0			0
$131$	2.47822	−	5.42653i	0.216523	−	0.474119i	−0.769938	−	0.638119i	$-0.779713\pi$
$131$	2.47822	−	5.42653i	0.216523	−	0.474119i	0.986460	+	0.164001i	$0.0524399\pi$
$132$		0			0
$133$	21.8995			1.89892
$134$		0			0
$135$	1.67819			0.144436
$136$		0			0
$137$	−6.13483	+	13.4334i	−0.524134	+	1.14769i	0.443716	+	0.896167i	$0.353660\pi$
$137$	−6.13483	+	13.4334i	−0.524134	+	1.14769i	−0.967850	+	0.251526i	$0.919068\pi$
$138$		0			0
$139$	16.6169	+	4.87916i	1.40943	+	0.413845i	0.895910	−	0.444235i	$-0.146524\pi$
$139$	16.6169	+	4.87916i	1.40943	+	0.413845i	0.513516	+	0.858080i	$0.328343\pi$
$140$		0			0
$141$	−3.51781	−	4.05977i	−0.296253	−	0.341895i
$142$		0			0
$143$	6.03417	+	6.96381i	0.504603	+	0.582343i
$144$		0			0
$145$	−9.54615	−	2.80300i	−0.792764	−	0.232777i
$146$		0			0
$147$	−0.00659222	−	0.00423657i	−0.000543717	−	0.000349426i
$148$		0			0
$149$	7.35489	−	8.48800i	0.602536	−	0.695364i	−0.369757	−	0.929128i	$-0.620559\pi$
$149$	7.35489	−	8.48800i	0.602536	−	0.695364i	0.972293	+	0.233765i	$0.0751045\pi$
$150$		0			0
$151$	1.29080	+	8.97771i	0.105044	+	0.730595i	0.972470	+	0.233029i	$0.0748638\pi$
$151$	1.29080	+	8.97771i	0.105044	+	0.730595i	−0.867426	+	0.497566i	$0.834227\pi$
$152$		0			0
$153$	−3.41171	+	3.93732i	−0.275820	+	0.318313i
$154$		0			0
$155$	10.4985	−	3.08263i	0.843257	−	0.247603i
$156$		0			0
$157$	−6.63386	+	14.5261i	−0.529439	+	1.15931i	0.436301	+	0.899801i	$0.356288\pi$
$157$	−6.63386	+	14.5261i	−0.529439	+	1.15931i	−0.965740	+	0.259510i	$0.916439\pi$
$158$		0			0
$159$	−1.62775	−	1.04609i	−0.129089	−	0.0829602i
$160$		0			0
$161$	10.7963	−	3.17008i	0.850868	−	0.249837i
$162$		0			0
$163$	−1.49646			−0.117211			−0.0586057	−	0.998281i	$-0.518665\pi$
$163$	−1.49646			−0.117211			−0.0586057	+	0.998281i	$0.518665\pi$
$164$		0			0
$165$	7.16333	−	4.60359i	0.557665	−	0.358389i
$166$		0			0
$167$	7.41150	−	8.55333i	0.573519	−	0.661876i	−0.392679	−	0.919675i	$-0.628452\pi$
$167$	7.41150	−	8.55333i	0.573519	−	0.661876i	0.966199	+	0.257799i	$0.0829972\pi$
$168$		0			0
$169$	−4.03038	−	8.82529i	−0.310029	−	0.678869i
$170$		0			0
$171$	8.27259			0.632621
$172$		0			0
$173$	−16.9901	+	10.9188i	−1.29173	+	0.830144i	−0.992286	−	0.123970i	$-0.960437\pi$
$173$	−16.9901	+	10.9188i	−1.29173	+	0.830144i	−0.299444	+	0.954114i	$0.596801\pi$
$174$		0			0
$175$	0.822679	+	5.72186i	0.0621887	+	0.432532i
$176$		0			0
$177$	−0.112732	−	0.784067i	−0.00847345	−	0.0589341i
$178$		0			0
$179$	7.16229	+	15.6832i	0.535335	+	1.17222i	0.963301	+	0.268425i	$0.0865031\pi$
$179$	7.16229	+	15.6832i	0.535335	+	1.17222i	−0.427966	+	0.903795i	$0.640770\pi$
$180$		0			0
$181$	5.95049	−	13.0298i	0.442297	−	0.968495i	−0.548874	−	0.835905i	$-0.684943\pi$
$181$	5.95049	−	13.0298i	0.442297	−	0.968495i	0.991171	−	0.132590i	$-0.0423293\pi$
$182$		0			0
$183$	−0.0622602	+	0.433029i	−0.00460241	+	0.0320104i
$184$		0			0
$185$	6.39457	+	1.87761i	0.470138	+	0.138045i
$186$		0			0
$187$	−3.76201	+	26.1653i	−0.275105	+	1.91340i
$188$		0			0
$189$	−2.22699	−	1.43120i	−0.161990	−	0.104105i
$190$		0			0
$191$	−4.01728	−	8.79662i	−0.290680	−	0.636501i	0.706802	−	0.707411i	$-0.250137\pi$
$191$	−4.01728	−	8.79662i	−0.290680	−	0.636501i	−0.997483	+	0.0709098i	$0.977410\pi$
$192$		0			0
$193$	2.63028	−	1.69038i	0.189332	−	0.121676i	−0.442541	−	0.896748i	$-0.645923\pi$
$193$	2.63028	−	1.69038i	0.189332	−	0.121676i	0.631873	+	0.775072i	$0.282286\pi$
$194$		0			0
$195$	2.92419	−	0.858619i	0.209405	−	0.0614870i
$196$		0			0
$197$	−2.71248	+	18.8657i	−0.193256	+	1.34413i	0.630061	+	0.776546i	$0.283030\pi$
$197$	−2.71248	+	18.8657i	−0.193256	+	1.34413i	−0.823317	+	0.567582i	$0.807879\pi$
$198$		0			0
$199$	−14.2587	−	16.4554i	−1.01077	−	1.16650i	−0.985990	−	0.166802i	$-0.946656\pi$
$199$	−14.2587	−	16.4554i	−1.01077	−	1.16650i	−0.0247834	−	0.999693i	$-0.507890\pi$
$200$		0			0
$201$	7.94113	+	1.98455i	0.560124	+	0.139980i
$202$		0			0
$203$	10.2775	+	11.8608i	0.721336	+	0.832467i
$204$		0			0
$205$	0.854757	−	5.94497i	0.0596988	−	0.415215i
$206$		0			0
$207$	4.07834	−	1.19751i	0.283464	−	0.0832326i
$208$		0			0
$209$	35.3114	−	22.6933i	2.44254	−	1.56973i
$210$		0			0
$211$	4.55090	+	9.96509i	0.313297	+	0.686025i	0.999129	−	0.0417353i	$-0.0132886\pi$
$211$	4.55090	+	9.96509i	0.313297	+	0.686025i	−0.685832	+	0.727760i	$0.740561\pi$
$212$		0			0
$213$	2.71279	+	1.74340i	0.185877	+	0.119456i
$214$		0			0
$215$	−0.252735	+	1.75781i	−0.0172364	+	0.119882i
$216$		0			0
$217$	−16.5606	−	4.86264i	−1.12421	−	0.330097i
$218$		0			0
$219$	−0.991714	+	6.89752i	−0.0670138	+	0.466091i
$220$		0			0
$221$	−3.93031	+	8.60618i	−0.264381	+	0.578915i
$222$		0			0
$223$	7.95184	+	17.4121i	0.532495	+	1.16600i	0.964489	+	0.264124i	$0.0850828\pi$
$223$	7.95184	+	17.4121i	0.532495	+	1.16600i	−0.431994	+	0.901876i	$0.642190\pi$
$224$		0			0
$225$	0.310769	+	2.16145i	0.0207180	+	0.144097i
$226$		0			0
$227$	−2.92142	−	20.3189i	−0.193901	−	1.34861i	−0.821559	−	0.570123i	$-0.806895\pi$
$227$	−2.92142	−	20.3189i	−0.193901	−	1.34861i	0.627658	−	0.778489i	$-0.284014\pi$
$228$		0			0
$229$	−1.32079	+	0.848820i	−0.0872802	+	0.0560916i	−0.583553	−	0.812075i	$-0.698338\pi$
$229$	−1.32079	+	0.848820i	−0.0872802	+	0.0560916i	0.496273	+	0.868167i	$0.334702\pi$
$230$		0			0
$231$	−13.4319			−0.883757
$232$		0			0
$233$	2.19195	+	4.79970i	0.143599	+	0.314439i	0.967742	−	0.251944i	$-0.0810698\pi$
$233$	2.19195	+	4.79970i	0.143599	+	0.314439i	−0.824143	+	0.566382i	$0.808343\pi$
$234$		0			0
$235$	−5.90356	+	6.81307i	−0.385106	+	0.444436i
$236$		0			0
$237$	9.05517	−	5.81941i	0.588197	−	0.378011i
$238$		0			0
$239$	−19.0673			−1.23336			−0.616680	−	0.787214i	$-0.711523\pi$
$239$	−19.0673			−1.23336			−0.616680	+	0.787214i	$0.711523\pi$
$240$		0			0
$241$	−10.6389	+	3.12385i	−0.685309	+	0.201225i	−0.605809	−	0.795610i	$-0.707151\pi$
$241$	−10.6389	+	3.12385i	−0.685309	+	0.201225i	−0.0795001	+	0.996835i	$0.525332\pi$
$242$		0			0
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$		0			0
$245$	−0.00546297	+	0.0119622i	−0.000349016	+	0.000764239i
$246$		0			0
$247$	14.4147	−	4.23253i	0.917185	−	0.269310i
$248$		0			0
$249$	11.2288	−	12.9587i	0.711593	−	0.821222i
$250$		0			0
$251$	−3.15856	−	21.9683i	−0.199366	−	1.38662i	−0.806128	−	0.591741i	$-0.798441\pi$
$251$	−3.15856	−	21.9683i	−0.199366	−	1.38662i	0.606762	−	0.794884i	$-0.292468\pi$
$252$		0			0
$253$	14.1233	−	16.2992i	0.887926	−	1.02472i
$254$		0			0
$255$	7.35514	+	4.72686i	0.460597	+	0.296008i
$256$		0			0
$257$	−19.1886	−	5.63428i	−1.19695	−	0.351457i	−0.378265	−	0.925697i	$-0.623479\pi$
$257$	−19.1886	−	5.63428i	−1.19695	−	0.351457i	−0.818687	+	0.574240i	$0.805298\pi$
$258$		0			0
$259$	−6.88444	−	7.94507i	−0.427778	−	0.493683i
$260$		0			0
$261$	3.88234	+	4.48046i	0.240311	+	0.277334i
$262$		0			0
$263$	−13.8674	−	4.07184i	−0.855101	−	0.251080i	−0.175335	−	0.984509i	$-0.556101\pi$
$263$	−13.8674	−	4.07184i	−0.855101	−	0.251080i	−0.679767	+	0.733428i	$0.737919\pi$
$264$		0			0
$265$	−1.34891	+	2.95370i	−0.0828629	+	0.181445i
$266$		0			0
$267$	−11.1063			−0.679693
$268$		0			0
$269$	6.97062			0.425006			0.212503	−	0.977160i	$-0.431838\pi$
$269$	6.97062			0.425006			0.212503	+	0.977160i	$0.431838\pi$
$270$		0			0
$271$	0.0831706	−	0.182118i	0.00505226	−	0.0110629i	−0.907089	−	0.420939i	$-0.861701\pi$
$271$	0.0831706	−	0.182118i	0.00505226	−	0.0110629i	0.912141	+	0.409876i	$0.134428\pi$
$272$		0			0
$273$	−4.61271	−	1.35441i	−0.279174	−	0.0819728i
$274$		0			0
$275$	7.25578	+	8.37361i	0.437540	+	0.504948i
$276$		0			0
$277$	−10.2155	−	11.7893i	−0.613789	−	0.708350i	0.360726	−	0.932672i	$-0.382529\pi$
$277$	−10.2155	−	11.7893i	−0.613789	−	0.708350i	−0.974515	+	0.224322i	$0.927983\pi$
$278$		0			0
$279$	−6.25582	−	1.83688i	−0.374526	−	0.109971i
$280$		0			0
$281$	8.36473	+	5.37569i	0.498998	+	0.320687i	0.765815	−	0.643060i	$-0.222336\pi$
$281$	8.36473	+	5.37569i	0.498998	+	0.320687i	−0.266817	+	0.963747i	$0.585972\pi$
$282$		0			0
$283$	−16.5128	+	19.0567i	−0.981582	+	1.13281i	0.00955400	+	0.999954i	$0.496959\pi$
$283$	−16.5128	+	19.0567i	−0.981582	+	1.13281i	−0.991136	+	0.132852i	$0.957587\pi$
$284$		0			0
$285$	−1.97575	−	13.7417i	−0.117034	−	0.813986i
$286$		0			0
$287$	−6.20429	+	7.16013i	−0.366228	+	0.422649i
$288$		0			0
$289$	−9.73140	+	2.85740i	−0.572435	+	0.168082i
$290$		0			0
$291$	−4.74478	+	10.3896i	−0.278144	+	0.609050i
$292$		0			0
$293$	−17.8261	−	11.4561i	−1.04141	−	0.669274i	−0.0960754	−	0.995374i	$-0.530629\pi$
$293$	−17.8261	−	11.4561i	−1.04141	−	0.669274i	−0.945335	+	0.326100i	$0.894265\pi$
$294$		0			0
$295$	−1.27550	+	0.374520i	−0.0742624	+	0.0218054i
$296$		0			0
$297$	−5.07396			−0.294421
$298$		0			0
$299$	6.49367	−	4.17323i	0.375539	−	0.241344i
$300$		0			0
$301$	1.83449	−	2.11711i	0.105738	−	0.122028i
$302$		0			0
$303$	−2.49761	−	5.46900i	−0.143484	−	0.314186i
$304$		0			0
$305$	0.734178			0.0420389
$306$		0			0
$307$	7.21936	−	4.63960i	0.412030	−	0.264796i	−0.318163	−	0.948036i	$-0.603066\pi$
$307$	7.21936	−	4.63960i	0.412030	−	0.264796i	0.730194	+	0.683240i	$0.239430\pi$
$308$		0			0
$309$	2.38916	+	16.6170i	0.135915	+	0.945307i
$310$		0			0
$311$	−3.63552	−	25.2856i	−0.206151	−	1.43381i	−0.785565	−	0.618779i	$-0.787627\pi$
$311$	−3.63552	−	25.2856i	−0.206151	−	1.43381i	0.579414	−	0.815034i	$-0.303282\pi$
$312$		0			0
$313$	6.72899	+	14.7344i	0.380345	+	0.832839i	0.998891	+	0.0470902i	$0.0149948\pi$
$313$	6.72899	+	14.7344i	0.380345	+	0.832839i	−0.618546	+	0.785749i	$0.712278\pi$
$314$		0			0
$315$	−1.84551	+	4.04109i	−0.103982	+	0.227690i
$316$		0			0
$317$	−1.02496	+	7.12874i	−0.0575674	+	0.400390i	0.940581	+	0.339569i	$0.110281\pi$
$317$	−1.02496	+	7.12874i	−0.0575674	+	0.400390i	−0.998149	+	0.0608214i	$0.980628\pi$
$318$		0			0
$319$	28.8625	+	8.47479i	1.61599	+	0.474497i
$320$		0			0
$321$	1.52062	−	10.5762i	0.0848728	−	0.590303i
$322$		0			0
$323$	36.2569	+	23.3009i	2.01739	+	1.29650i
$324$		0			0
$325$	1.64737	+	3.60725i	0.0913799	+	0.200094i
$326$		0			0
$327$	6.17414	−	3.96788i	0.341431	−	0.219424i
$328$		0			0
$329$	13.6445	−	4.00639i	0.752246	−	0.220879i
$330$		0			0
$331$	4.99668	−	34.7527i	0.274642	−	1.91018i	−0.122585	−	0.992458i	$-0.539118\pi$
$331$	4.99668	−	34.7527i	0.274642	−	1.91018i	0.397227	−	0.917720i	$-0.369973\pi$
$332$		0			0
$333$	−2.60062	−	3.00128i	−0.142513	−	0.164469i
$334$		0			0
$335$	1.39997	−	13.6651i	0.0764883	−	0.746602i
$336$		0			0
$337$	1.36067	+	1.57030i	0.0741207	+	0.0855398i	0.791599	−	0.611041i	$-0.209249\pi$
$337$	1.36067	+	1.57030i	0.0741207	+	0.0855398i	−0.717478	+	0.696581i	$0.754704\pi$
$338$		0			0
$339$	−0.610912	+	4.24899i	−0.0331802	+	0.230773i
$340$		0			0
$341$	−31.7418	+	9.32023i	−1.71891	+	0.504719i
$342$		0			0
$343$	−15.5715	+	10.0072i	−0.840782	+	0.540338i
$344$		0			0
$345$	−2.96323	−	6.48856i	−0.159535	−	0.349333i
$346$		0			0
$347$	18.1731	+	11.6792i	0.975585	+	0.626971i	0.928269	−	0.371909i	$-0.121297\pi$
$347$	18.1731	+	11.6792i	0.975585	+	0.626971i	0.0473163	+	0.998880i	$0.484933\pi$
$348$		0			0
$349$	−1.61808	+	11.2540i	−0.0866140	+	0.602414i	0.899572	+	0.436773i	$0.143879\pi$
$349$	−1.61808	+	11.2540i	−0.0866140	+	0.602414i	−0.986186	+	0.165641i	$0.947031\pi$
$350$		0			0
$351$	−1.74246	−	0.511634i	−0.0930059	−	0.0273090i
$352$		0			0
$353$	−3.46565	+	24.1041i	−0.184458	+	1.28293i	0.661605	+	0.749852i	$0.269875\pi$
$353$	−3.46565	+	24.1041i	−0.184458	+	1.28293i	−0.846064	+	0.533082i	$0.821034\pi$
$354$		0			0
$355$	2.24808	−	4.92261i	0.119316	−	0.261265i
$356$		0			0
$357$	−5.72924	−	12.5453i	−0.303223	−	0.663967i
$358$		0			0
$359$	−3.01852	−	20.9942i	−0.159311	−	1.10803i	−0.899907	−	0.436082i	$-0.856366\pi$
$359$	−3.01852	−	20.9942i	−0.159311	−	1.10803i	0.740596	−	0.671951i	$-0.234543\pi$
$360$		0			0
$361$	−7.03543	−	48.9325i	−0.370286	−	2.57540i
$362$		0			0
$363$	−12.4043	+	7.97177i	−0.651058	+	0.418409i
$364$		0			0
$365$	11.6944			0.612113
$366$		0			0
$367$	−10.0305	−	21.9636i	−0.523586	−	1.14649i	−0.968064	−	0.250703i	$-0.919338\pi$
$367$	−10.0305	−	21.9636i	−0.523586	−	1.14649i	0.444478	−	0.895790i	$-0.353389\pi$
$368$		0			0
$369$	−2.34369	+	2.70476i	−0.122008	+	0.140804i
$370$		0			0
$371$	4.30902	−	2.76924i	0.223713	−	0.143772i
$372$		0			0
$373$	21.0568			1.09028			0.545140	−	0.838345i	$-0.316476\pi$
$373$	21.0568			1.09028			0.545140	+	0.838345i	$0.316476\pi$
$374$		0			0
$375$	11.5672	−	3.39645i	0.597330	−	0.175392i
$376$		0			0
$377$	9.05720	+	5.82071i	0.466469	+	0.299782i
$378$		0			0
$379$	−11.1517	+	24.4189i	−0.572826	+	1.25431i	0.372452	+	0.928051i	$0.378517\pi$
$379$	−11.1517	+	24.4189i	−0.572826	+	1.25431i	−0.945279	+	0.326264i	$0.894210\pi$
$380$		0			0
$381$	−12.6314	+	3.70892i	−0.647128	+	0.190014i
$382$		0			0
$383$	−0.620007	+	0.715526i	−0.0316809	+	0.0365617i	−0.771369	−	0.636388i	$-0.780428\pi$
$383$	−0.620007	+	0.715526i	−0.0316809	+	0.0365617i	0.739688	+	0.672950i	$0.234973\pi$
$384$		0			0
$385$	3.20797	+	22.3119i	0.163493	+	1.13712i
$386$		0			0
$387$	0.692983	−	0.799745i	0.0352263	−	0.0406533i
$388$		0			0
$389$	13.8761	+	8.91765i	0.703548	+	0.452143i	0.842879	−	0.538103i	$-0.180859\pi$
$389$	13.8761	+	8.91765i	0.703548	+	0.452143i	−0.139331	+	0.990246i	$0.544495\pi$
$390$		0			0
$391$	21.2474	+	6.23880i	1.07453	+	0.315510i
$392$		0			0
$393$	3.90666	+	4.50853i	0.197065	+	0.227425i
$394$		0			0
$395$	−11.8293	−	13.6518i	−0.595198	−	0.686895i
$396$		0			0
$397$	−20.8431	−	6.12008i	−1.04608	−	0.307158i	−0.286850	−	0.957976i	$-0.592608\pi$
$397$	−20.8431	−	6.12008i	−1.04608	−	0.307158i	−0.759234	+	0.650818i	$0.774426\pi$
$398$		0			0
$399$	−9.09736	+	19.9204i	−0.455438	+	0.997270i
$400$		0			0
$401$	−7.88131			−0.393574			−0.196787	−	0.980446i	$-0.563051\pi$
$401$	−7.88131			−0.393574			−0.196787	+	0.980446i	$0.563051\pi$
$402$		0			0
$403$	−11.8404			−0.589810
$404$		0			0
$405$	−0.697146	+	1.52654i	−0.0346414	+	0.0758542i
$406$		0			0
$407$	−19.3338	−	5.67691i	−0.958339	−	0.281394i
$408$		0			0
$409$	−25.0522	−	28.9118i	−1.23875	−	1.42960i	−0.864774	−	0.502160i	$-0.832539\pi$
$409$	−25.0522	−	28.9118i	−1.23875	−	1.42960i	−0.373979	−	0.927437i	$-0.622007\pi$
$410$		0			0
$411$	−9.67096	−	11.1609i	−0.477033	−	0.550526i
$412$		0			0
$413$	2.01201	+	0.590780i	0.0990046	+	0.0290704i
$414$		0			0
$415$	−24.2075	−	15.5572i	−1.18830	−	0.763675i
$416$		0			0
$417$	−11.3411	+	13.0884i	−0.555378	+	0.640941i
$418$		0			0
$419$	3.86162	+	26.8582i	0.188652	+	1.31211i	0.835501	+	0.549489i	$0.185177\pi$
$419$	3.86162	+	26.8582i	0.188652	+	1.31211i	−0.646849	+	0.762618i	$0.723913\pi$
$420$		0			0
$421$	15.0416	−	17.3590i	0.733084	−	0.846024i	−0.259731	−	0.965681i	$-0.583634\pi$
$421$	15.0416	−	17.3590i	0.733084	−	0.846024i	0.992815	+	0.119657i	$0.0381794\pi$
$422$		0			0
$423$	5.15425	−	1.51342i	0.250608	−	0.0735852i
$424$		0			0
$425$	−4.72599	+	10.3485i	−0.229244	+	0.501975i
$426$		0			0
$427$	−0.974269	−	0.626125i	−0.0471482	−	0.0303003i
$428$		0			0
$429$	−8.84119	+	2.59601i	−0.426857	+	0.125336i
$430$		0			0
$431$	−3.96385			−0.190932			−0.0954659	−	0.995433i	$-0.530434\pi$
$431$	−3.96385			−0.190932			−0.0954659	+	0.995433i	$0.530434\pi$
$432$		0			0
$433$	−13.0531	+	8.38873i	−0.627293	+	0.403137i	−0.815306	−	0.579030i	$-0.803432\pi$
$433$	−13.0531	+	8.38873i	−0.627293	+	0.403137i	0.188013	+	0.982166i	$0.439795\pi$
$434$		0			0
$435$	6.51531	−	7.51907i	0.312385	−	0.360512i
$436$		0			0
$437$	−14.6071	−	31.9852i	−0.698754	−	1.53006i
$438$		0			0
$439$	−36.9397			−1.76303			−0.881517	−	0.472153i	$-0.843477\pi$
$439$	−36.9397			−1.76303			−0.881517	+	0.472153i	$0.843477\pi$
$440$		0			0
$441$	0.00659222	−	0.00423657i	0.000313915	−	0.000201741i
$442$		0			0
$443$	1.29625	+	9.01564i	0.0615869	+	0.428346i	0.997166	+	0.0752296i	$0.0239690\pi$
$443$	1.29625	+	9.01564i	0.0615869	+	0.428346i	−0.935579	+	0.353116i	$0.885122\pi$
$444$		0			0
$445$	2.65253	+	18.4487i	0.125742	+	0.874554i
$446$		0			0
$447$	4.66562	+	10.2163i	0.220676	+	0.483214i
$448$		0			0
$449$	17.3679	−	38.0304i	0.819642	−	1.79477i	0.261046	−	0.965326i	$-0.415932\pi$
$449$	17.3679	−	38.0304i	0.819642	−	1.79477i	0.558596	−	0.829440i	$-0.311340\pi$
$450$		0			0
$451$	−2.58433	+	17.9744i	−0.121691	+	0.846382i
$452$		0			0
$453$	−8.70263	−	2.55532i	−0.408885	−	0.120059i
$454$		0			0
$455$	−1.14817	+	7.98569i	−0.0538270	+	0.374375i
$456$		0			0
$457$	−13.6356	−	8.76304i	−0.637845	−	0.409918i	0.181362	−	0.983416i	$-0.441949\pi$
$457$	−13.6356	−	8.76304i	−0.637845	−	0.409918i	−0.819207	+	0.573499i	$0.805586\pi$
$458$		0			0
$459$	−2.16424	−	4.73902i	−0.101018	−	0.221199i
$460$		0			0
$461$	13.6537	−	8.77472i	0.635918	−	0.408680i	−0.182579	−	0.983191i	$-0.558444\pi$
$461$	13.6537	−	8.77472i	0.635918	−	0.408680i	0.818496	+	0.574512i	$0.194808\pi$
$462$		0			0
$463$	−12.9356	+	3.79825i	−0.601170	+	0.176519i	−0.568136	−	0.822935i	$-0.692335\pi$
$463$	−12.9356	+	3.79825i	−0.601170	+	0.176519i	−0.0330342	+	0.999454i	$0.510517\pi$
$464$		0			0
$465$	−1.55716	+	10.8303i	−0.0722117	+	0.502244i
$466$		0			0
$467$	−15.3044	−	17.6622i	−0.708202	−	0.817309i	0.281634	−	0.959522i	$-0.409124\pi$
$467$	−15.3044	−	17.6622i	−0.708202	−	0.817309i	−0.989836	+	0.142213i	$0.954578\pi$
$468$		0			0
$469$	−13.5117	+	16.9399i	−0.623911	+	0.782211i
$470$		0			0
$471$	−10.4576	−	12.0687i	−0.481862	−	0.556098i
$472$		0			0
$473$	0.764136	−	5.31468i	0.0351350	−	0.244369i
$474$		0			0
$475$	17.3329	−	5.08940i	0.795288	−	0.233518i
$476$		0			0
$477$	1.62775	−	1.04609i	0.0745294	−	0.0478971i
$478$		0			0
$479$	−4.75082	−	10.4028i	−0.217070	−	0.475318i	0.769502	−	0.638645i	$-0.220505\pi$
$479$	−4.75082	−	10.4028i	−0.217070	−	0.475318i	−0.986572	+	0.163327i	$0.947777\pi$
$480$		0			0
$481$	−6.06704	−	3.89905i	−0.276633	−	0.177781i
$482$		0			0
$483$	−1.60134	+	11.1376i	−0.0728635	+	0.506777i
$484$		0			0
$485$	18.3915	+	5.40023i	0.835114	+	0.245212i
$486$		0			0
$487$	3.59573	−	25.0088i	0.162938	−	1.13326i	−0.730121	−	0.683318i	$-0.760536\pi$
$487$	3.59573	−	25.0088i	0.162938	−	1.13326i	0.893059	−	0.449940i	$-0.148555\pi$
$488$		0			0
$489$	0.621650	−	1.36122i	0.0281120	−	0.0615567i
$490$		0			0
$491$	−15.1560	−	33.1870i	−0.683980	−	1.49771i	−0.858370	−	0.513030i	$-0.828523\pi$
$491$	−15.1560	−	33.1870i	−0.683980	−	1.49771i	0.174391	−	0.984677i	$-0.444204\pi$
$492$		0			0
$493$	4.39560	+	30.5721i	0.197968	+	1.37690i
$494$		0			0
$495$	1.21182	+	8.42840i	0.0544673	+	0.378828i
$496$		0			0
$497$	−7.18137	+	4.61519i	−0.322129	+	0.207019i
$498$		0			0
$499$	−19.2669			−0.862505			−0.431252	−	0.902231i	$-0.641928\pi$
$499$	−19.2669			−0.862505			−0.431252	+	0.902231i	$0.641928\pi$
$500$		0			0
$501$	4.70153	+	10.2949i	0.210049	+	0.459943i
$502$		0			0
$503$	16.0562	−	18.5298i	0.715910	−	0.826204i	−0.274899	−	0.961473i	$-0.588644\pi$
$503$	16.0562	−	18.5298i	0.715910	−	0.826204i	0.990809	+	0.135269i	$0.0431898\pi$
$504$		0			0
$505$	−8.48809	+	5.45497i	−0.377715	+	0.242743i
$506$		0			0
$507$	9.70205			0.430883
$508$		0			0
$509$	2.78890	−	0.818895i	0.123616	−	0.0362969i	−0.219340	−	0.975649i	$-0.570390\pi$
$509$	2.78890	−	0.818895i	0.123616	−	0.0362969i	0.342955	+	0.939352i	$0.388572\pi$
$510$		0			0
$511$	−15.5187	−	9.97326i	−0.686507	−	0.441191i
$512$		0			0
$513$	−3.43656	+	7.52501i	−0.151728	+	0.332237i
$514$		0			0
$515$	27.0320	−	7.93732i	1.19117	−	0.349760i
$516$		0			0
$517$	17.8492	−	20.5991i	0.785008	−	0.905948i
$518$		0			0
$519$	−2.87421	−	19.9905i	−0.126164	−	0.877488i
$520$		0			0
$521$	4.68821	−	5.41048i	0.205394	−	0.237037i	−0.643702	−	0.765277i	$-0.722602\pi$
$521$	4.68821	−	5.41048i	0.205394	−	0.237037i	0.849096	+	0.528239i	$0.177148\pi$
$522$		0			0
$523$	31.9973	+	20.5634i	1.39914	+	0.899175i	0.999844	−	0.0176464i	$-0.00561730\pi$
$523$	31.9973	+	20.5634i	1.39914	+	0.899175i	0.399299	+	0.916821i	$0.369254\pi$
$524$		0			0
$525$	−5.54654	−	1.62861i	−0.242071	−	0.0710784i
$526$		0			0
$527$	−22.2441	−	25.6710i	−0.968967	−	1.11825i
$528$		0			0
$529$	3.23051	+	3.72821i	0.140457	+	0.162096i
$530$		0			0
$531$	0.760043	+	0.223169i	0.0329831	+	0.00968470i
$532$		0			0
$533$	−2.69995	+	5.91206i	−0.116948	+	0.256080i
$534$		0			0
$535$	−17.9313			−0.775239
$536$		0			0
$537$	−17.2413			−0.744017
$538$		0			0
$539$	0.0165171	−	0.0361674i	0.000711442	−	0.00155784i
$540$		0			0
$541$	0.843627	+	0.247711i	0.0362703	+	0.0106499i	0.299817	−	0.953997i	$-0.403074\pi$
$541$	0.843627	+	0.247711i	0.0362703	+	0.0106499i	−0.263547	+	0.964647i	$0.584892\pi$
$542$		0			0
$543$	9.38037	+	10.8255i	0.402550	+	0.464568i
$544$		0			0
$545$	−8.06566	−	9.30826i	−0.345495	−	0.398722i
$546$		0			0
$547$	33.2485	+	9.76265i	1.42160	+	0.417421i	0.900046	−	0.435794i	$-0.143533\pi$
$547$	33.2485	+	9.76265i	1.42160	+	0.417421i	0.521559	+	0.853215i	$0.325351\pi$
$548$		0			0
$549$	−0.368033	−	0.236521i	−0.0157073	−	0.0100945i
$550$		0			0
$551$	32.1170	−	37.0650i	1.36823	−	1.57902i
$552$		0			0
$553$	4.05520	+	28.2045i	0.172445	+	1.19938i
$554$		0			0
$555$	−4.36434	+	5.03671i	−0.185256	+	0.213797i
$556$		0			0
$557$	10.7331	−	3.15152i	0.454776	−	0.133534i	−0.0463187	−	0.998927i	$-0.514749\pi$
$557$	10.7331	−	3.15152i	0.454776	−	0.133534i	0.501095	+	0.865392i	$0.332931\pi$
$558$		0			0
$559$	0.798322	−	1.74808i	0.0337654	−	0.0739360i
$560$		0			0
$561$	−22.2380	−	14.2915i	−0.938891	−	0.603388i
$562$		0			0
$563$	1.22039	−	0.358338i	0.0514332	−	0.0151021i	−0.255915	−	0.966699i	$-0.582377\pi$
$563$	1.22039	−	0.358338i	0.0514332	−	0.0151021i	0.307348	+	0.951597i	$0.400558\pi$
$564$		0			0
$565$	7.20393			0.303072
$566$		0			0
$567$	2.22699	−	1.43120i	0.0935249	−	0.0601048i
$568$		0			0
$569$	−11.5191	+	13.2938i	−0.482907	+	0.557305i	−0.943957	−	0.330070i	$-0.892928\pi$
$569$	−11.5191	+	13.2938i	−0.482907	+	0.557305i	0.461049	+	0.887375i	$0.347473\pi$
$570$		0			0
$571$	−4.36488	−	9.55776i	−0.182665	−	0.399980i	0.796043	−	0.605241i	$-0.206923\pi$
$571$	−4.36488	−	9.55776i	−0.182665	−	0.399980i	−0.978707	+	0.205261i	$0.934196\pi$
$572$		0			0
$573$	9.67053			0.403992
$574$		0			0
$575$	7.80830	−	5.01809i	0.325629	−	0.209269i
$576$		0			0
$577$	1.26105	+	8.77078i	0.0524981	+	0.365132i	0.999088	+	0.0426931i	$0.0135938\pi$
$577$	1.26105	+	8.77078i	0.0524981	+	0.365132i	−0.946590	+	0.322439i	$0.895497\pi$
$578$		0			0
$579$	0.444965	+	3.09480i	0.0184921	+	0.128615i
$580$		0			0
$581$	18.8563	+	41.2896i	0.782292	+	1.71298i
$582$		0			0
$583$	4.07839	−	8.93043i	0.168910	−	0.369860i
$584$		0			0
$585$	−0.433724	+	3.01662i	−0.0179323	+	0.124722i
$586$		0			0
$587$	29.9078	+	8.78172i	1.23443	+	0.362460i	0.832919	−	0.553395i	$-0.186668\pi$
$587$	29.9078	+	8.78172i	1.23443	+	0.362460i	0.401508	+	0.915856i	$0.368486\pi$
$588$		0			0
$589$	−7.67599	+	53.3877i	−0.316284	+	2.19980i
$590$		0			0
$591$	−16.0341	−	10.3045i	−0.659553	−	0.423869i
$592$		0			0
$593$	6.36103	+	13.9287i	0.261216	+	0.571984i	0.994112	−	0.108357i	$-0.0345590\pi$
$593$	6.36103	+	13.9287i	0.261216	+	0.571984i	−0.732896	+	0.680341i	$0.761832\pi$
$594$		0			0
$595$	−19.4708	+	12.5131i	−0.798224	+	0.512987i
$596$		0			0
$597$	20.8917	−	6.13435i	0.855039	−	0.251062i
$598$		0			0
$599$	1.74042	−	12.1049i	0.0711115	−	0.494592i	−0.922876	−	0.385097i	$-0.874168\pi$
$599$	1.74042	−	12.1049i	0.0711115	−	0.494592i	0.993987	−	0.109494i	$-0.0349231\pi$
$600$		0			0
$601$	−10.0951	−	11.6504i	−0.411789	−	0.475230i	0.511529	−	0.859266i	$-0.329079\pi$
$601$	−10.0951	−	11.6504i	−0.411789	−	0.475230i	−0.923318	+	0.384036i	$0.874534\pi$
$602$		0			0
$603$	−5.10408	+	6.39909i	−0.207854	+	0.260591i
$604$		0			0
$605$	16.2045	+	18.7010i	0.658807	+	0.760304i
$606$		0			0
$607$	1.53254	−	10.6591i	0.0622039	−	0.432638i	−0.934793	−	0.355194i	$-0.884415\pi$
$607$	1.53254	−	10.6591i	0.0622039	−	0.432638i	0.996997	−	0.0774441i	$-0.0246759\pi$
$608$		0			0
$609$	−15.0584	+	4.42154i	−0.610197	+	0.179170i
$610$		0			0
$611$	8.20678	−	5.27418i	0.332011	−	0.213370i
$612$		0			0
$613$	−12.8600	−	28.1595i	−0.519411	−	1.13735i	−0.969662	−	0.244449i	$-0.921393\pi$
$613$	−12.8600	−	28.1595i	−0.519411	−	1.13735i	0.450252	−	0.892902i	$-0.351334\pi$
$614$		0			0
$615$	5.05265	+	3.24714i	0.203743	+	0.130937i
$616$		0			0
$617$	−1.94881	+	13.5543i	−0.0784562	+	0.545675i	0.912248	+	0.409639i	$0.134345\pi$
$617$	−1.94881	+	13.5543i	−0.0784562	+	0.545675i	−0.990704	+	0.136036i	$0.956564\pi$
$618$		0			0
$619$	26.2432	+	7.70571i	1.05480	+	0.309719i	0.762757	−	0.646685i	$-0.223845\pi$
$619$	26.2432	+	7.70571i	1.05480	+	0.309719i	0.292048	+	0.956404i	$0.405663\pi$
$620$		0			0
$621$	−0.604911	+	4.20725i	−0.0242743	+	0.168831i
$622$		0			0
$623$	12.2136	−	26.7440i	0.489326	−	1.07147i
$624$		0			0
$625$	−3.86884	−	8.47157i	−0.154753	−	0.338863i
$626$		0			0
$627$	5.97363	+	41.5475i	0.238564	+	1.65925i
$628$		0			0
$629$	−2.94443	−	20.4789i	−0.117402	−	0.816549i
$630$		0			0
$631$	16.9163	−	10.8714i	0.673426	−	0.432785i	−0.158733	−	0.987322i	$-0.550741\pi$
$631$	16.9163	−	10.8714i	0.673426	−	0.432785i	0.832159	+	0.554537i	$0.187104\pi$
$632$		0			0
$633$	−10.9551			−0.435425
$634$		0			0
$635$	9.17771	+	20.0964i	0.364206	+	0.797501i
$636$		0			0
$637$	0.00931915	−	0.0107549i	0.000369238	−	0.000426123i
$638$		0			0
$639$	−2.71279	+	1.74340i	−0.107316	+	0.0689679i
$640$		0			0
$641$	17.7914			0.702717			0.351358	−	0.936241i	$-0.385720\pi$
$641$	17.7914			0.702717			0.351358	+	0.936241i	$0.385720\pi$
$642$		0			0
$643$	44.5785	−	13.0894i	1.75800	−	0.516196i	0.766048	−	0.642784i	$-0.222221\pi$
$643$	44.5785	−	13.0894i	1.75800	−	0.516196i	0.991955	+	0.126587i	$0.0404024\pi$
$644$		0			0
$645$	−1.49397	−	0.960117i	−0.0588250	−	0.0378046i
$646$		0			0
$647$	−8.03423	+	17.5925i	−0.315858	+	0.691633i	−0.999262	−	0.0384076i	$-0.987771\pi$
$647$	−8.03423	+	17.5925i	−0.315858	+	0.691633i	0.683404	+	0.730040i	$0.260499\pi$
$648$		0			0
$649$	3.85643	−	1.13235i	0.151378	−	0.0444486i
$650$		0			0
$651$	11.3027	−	13.0441i	0.442989	−	0.511237i
$652$		0			0
$653$	0.492449	+	3.42506i	0.0192710	+	0.134033i	0.997186	−	0.0749718i	$-0.0238867\pi$
$653$	0.492449	+	3.42506i	0.0192710	+	0.134033i	−0.977915	+	0.209005i	$0.932978\pi$
$654$		0			0
$655$	6.55612	−	7.56617i	0.256169	−	0.295635i
$656$		0			0
$657$	−5.86224	−	3.76743i	−0.228708	−	0.146981i
$658$		0			0
$659$	5.53366	+	1.62483i	0.215561	+	0.0632943i	0.387730	−	0.921773i	$-0.373259\pi$
$659$	5.53366	+	1.62483i	0.215561	+	0.0632943i	−0.172169	+	0.985067i	$0.555078\pi$
$660$		0			0
$661$	−22.8765	−	26.4009i	−0.889793	−	1.02688i	−0.999458	−	0.0329074i	$-0.989523\pi$
$661$	−22.8765	−	26.4009i	−0.889793	−	1.02688i	0.109665	−	0.993969i	$-0.465022\pi$
$662$		0			0
$663$	−6.19575	−	7.15028i	−0.240623	−	0.277694i
$664$		0			0
$665$	35.2628	+	10.3541i	1.36743	+	0.401514i
$666$		0			0
$667$	10.4681	−	22.9220i	0.405327	−	0.887543i
$668$		0			0
$669$	−19.1419			−0.740069
$670$		0			0
$671$	−2.21976			−0.0856931
$672$		0			0
$673$	−5.22524	+	11.4417i	−0.201418	+	0.441044i	−0.983206	−	0.182501i	$-0.941581\pi$
$673$	−5.22524	+	11.4417i	−0.201418	+	0.441044i	0.781788	+	0.623545i	$0.214308\pi$
$674$		0			0
$675$	−2.09522	−	0.615213i	−0.0806451	−	0.0236795i
$676$		0			0
$677$	−5.33057	−	6.15181i	−0.204871	−	0.236433i	0.644011	−	0.765016i	$-0.277269\pi$
$677$	−5.33057	−	6.15181i	−0.204871	−	0.236433i	−0.848882	+	0.528583i	$0.822724\pi$
$678$		0			0
$679$	−19.8004	−	22.8509i	−0.759870	−	0.876937i
$680$		0			0
$681$	19.6963	+	5.78336i	0.754764	+	0.221619i
$682$		0			0
$683$	−29.3219	−	18.8441i	−1.12197	−	0.721048i	−0.158103	−	0.987423i	$-0.550538\pi$
$683$	−29.3219	−	18.8441i	−1.12197	−	0.721048i	−0.963870	+	0.266374i	$0.914174\pi$
$684$		0			0
$685$	−16.2297	+	18.7301i	−0.620105	+	0.715640i
$686$		0			0
$687$	−0.223438	−	1.55405i	−0.00852469	−	0.0592905i
$688$		0			0
$689$	2.30107	−	2.65558i	0.0876640	−	0.101170i
$690$		0			0
$691$	−5.91932	+	1.73807i	−0.225182	+	0.0661193i	−0.392377	−	0.919804i	$-0.628347\pi$
$691$	−5.91932	+	1.73807i	−0.225182	+	0.0661193i	0.167195	+	0.985924i	$0.446529\pi$
$692$		0			0
$693$	5.57983	−	12.2181i	0.211960	−	0.464128i
$694$		0			0
$695$	24.4499	+	15.7130i	0.927436	+	0.596027i
$696$		0			0
$697$	−17.8902	+	5.25305i	−0.677641	+	0.198973i
$698$		0			0
$699$	−5.27653			−0.199577
$700$		0			0
$701$	−34.0420	+	21.8775i	−1.28575	+	0.826300i	−0.991585	−	0.129455i	$-0.958677\pi$
$701$	−34.0420	+	21.8775i	−1.28575	+	0.826300i	−0.294163	+	0.955755i	$0.595041\pi$
$702$		0			0
$703$	−21.5139	+	24.8283i	−0.811410	+	0.936418i
$704$		0			0
$705$	−3.74496	−	8.20032i	−0.141043	−	0.308842i
$706$		0			0
$707$	15.9160			0.598583
$708$		0			0
$709$	37.5760	−	24.1486i	1.41120	−	0.906921i	0.411207	−	0.911542i	$-0.365107\pi$
$709$	37.5760	−	24.1486i	1.41120	−	0.906921i	0.999989	+	0.00462069i	$0.00147082\pi$
$710$		0			0
$711$	1.53186	+	10.6543i	0.0574494	+	0.399569i
$712$		0			0
$713$	3.94398	+	27.4310i	0.147703	+	1.02730i
$714$		0			0
$715$	6.42380	+	14.0662i	0.240237	+	0.526045i
$716$		0			0
$717$	7.92083	−	17.3442i	0.295809	−	0.647731i
$718$		0			0
$719$	2.73405	−	19.0158i	0.101963	−	0.709169i	−0.873149	−	0.487454i	$-0.837926\pi$
$719$	2.73405	−	19.0158i	0.101963	−	0.709169i	0.975112	−	0.221714i	$-0.0711653\pi$
$720$		0			0
$721$	−42.6412	−	12.5206i	−1.58804	−	0.466291i
$722$		0			0
$723$	1.57799	−	10.9751i	0.0586860	−	0.408170i
$724$		0			0
$725$	10.8908	+	6.99910i	0.404474	+	0.259940i
$726$		0			0
$727$	16.5275	+	36.1903i	0.612972	+	1.34222i	0.920522	+	0.390690i	$0.127764\pi$
$727$	16.5275	+	36.1903i	0.612972	+	1.34222i	−0.307550	+	0.951532i	$0.599509\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	5.28979	−	1.55322i	0.195650	−	0.0574480i
$732$		0			0
$733$	−0.552337	+	3.84159i	−0.0204010	+	0.141892i	−0.997476	−	0.0710026i	$-0.977380\pi$
$733$	−0.552337	+	3.84159i	−0.0204010	+	0.141892i	0.977075	+	0.212895i	$0.0682892\pi$
$734$		0			0
$735$	−0.00861183	−	0.00993858i	−0.000317652	−	0.000366590i
$736$		0			0
$737$	−4.23275	+	41.3159i	−0.155915	+	1.52189i
$738$		0			0
$739$	22.7304	+	26.2323i	0.836151	+	0.964970i	0.999768	−	0.0215544i	$-0.00686150\pi$
$739$	22.7304	+	26.2323i	0.836151	+	0.964970i	−0.163617	+	0.986524i	$0.552316\pi$
$740$		0			0
$741$	−2.13803	+	14.8703i	−0.0785425	+	0.546275i
$742$		0			0
$743$	−23.5115	+	6.90359i	−0.862552	+	0.253268i	−0.682945	−	0.730470i	$-0.739301\pi$
$743$	−23.5115	+	6.90359i	−0.862552	+	0.253268i	−0.179608	+	0.983738i	$0.557483\pi$
$744$		0			0
$745$	15.8561	−	10.1901i	0.580921	−	0.373336i
$746$		0			0
$747$	7.12303	+	15.5973i	0.260618	+	0.570674i
$748$		0			0
$749$	23.7952	+	15.2923i	0.869459	+	0.558767i
$750$		0			0
$751$	−3.68204	+	25.6091i	−0.134360	+	0.934491i	0.805419	+	0.592706i	$0.201940\pi$
$751$	−3.68204	+	25.6091i	−0.134360	+	0.934491i	−0.939778	+	0.341785i	$0.888969\pi$
$752$		0			0
$753$	21.2951	+	6.25282i	0.776038	+	0.227865i
$754$		0			0
$755$	−2.16621	+	15.0663i	−0.0788364	+	0.548319i
$756$		0			0
$757$	−2.17451	+	4.76152i	−0.0790341	+	0.173060i	−0.945024	−	0.327001i	$-0.893962\pi$
$757$	−2.17451	+	4.76152i	−0.0790341	+	0.173060i	0.865990	+	0.500061i	$0.166689\pi$
$758$		0			0
$759$	8.95923	+	19.6180i	0.325199	+	0.712087i
$760$		0			0
$761$	1.02457	+	7.12605i	0.0371407	+	0.258319i	0.999929	−	0.0119385i	$-0.00380023\pi$
$761$	1.02457	+	7.12605i	0.0371407	+	0.258319i	−0.962788	+	0.270258i	$0.912891\pi$
$762$		0			0
$763$	2.76498	+	19.2308i	0.100099	+	0.696203i
$764$		0			0
$765$	−7.35514	+	4.72686i	−0.265926	+	0.170900i
$766$		0			0
$767$	1.43853			0.0519423
$768$		0			0
$769$	14.6808	+	32.1465i	0.529404	+	1.15923i	0.965755	+	0.259456i	$0.0835433\pi$
$769$	14.6808	+	32.1465i	0.529404	+	1.15923i	−0.436351	+	0.899777i	$0.643729\pi$
$770$		0			0
$771$	13.0964	−	15.1140i	0.471654	−	0.544317i
$772$		0			0
$773$	−15.4667	+	9.93985i	−0.556299	+	0.357512i	−0.788384	−	0.615184i	$-0.789082\pi$
$773$	−15.4667	+	9.93985i	−0.556299	+	0.357512i	0.232085	+	0.972696i	$0.425445\pi$
$774$		0			0
$775$	−14.2374			−0.511423
$776$		0			0
$777$	10.0870	−	2.96181i	0.361869	−	0.106254i
$778$		0			0
$779$	24.9069	+	16.0067i	0.892382	+	0.573499i
$780$		0			0
$781$	−6.79700	+	14.8834i	−0.243216	+	0.532569i
$782$		0			0
$783$	−5.68836	+	1.67025i	−0.203285	+	0.0596899i
$784$		0			0
$785$	−17.5499	+	20.2536i	−0.626382	+	0.722883i
$786$		0			0
$787$	1.58388	+	11.0161i	0.0564591	+	0.392681i	0.998383	+	0.0568538i	$0.0181069\pi$
$787$	1.58388	+	11.0161i	0.0564591	+	0.392681i	−0.941923	+	0.335828i	$0.890984\pi$
$788$		0			0
$789$	9.46461	−	10.9227i	0.336949	−	0.388860i
$790$		0			0
$791$	−9.55977	−	6.14369i	−0.339906	−	0.218444i
$792$		0			0
$793$	−0.762297	−	0.223831i	−0.0270700	−	0.00794845i
$794$		0			0
$795$	−2.12642	−	2.45402i	−0.0754165	−	0.0870353i
$796$		0			0
$797$	−24.3198	−	28.0666i	−0.861452	−	0.994169i	−0.999993	−	0.00381229i	$-0.998787\pi$
$797$	−24.3198	−	28.0666i	−0.861452	−	0.994169i	0.138540	−	0.990357i	$-0.455759\pi$
$798$		0			0
$799$	26.8527	+	7.88467i	0.949981	+	0.278940i
$800$		0			0
$801$	4.61371	−	10.1026i	0.163018	−	0.356959i
$802$		0			0
$803$	−35.3576			−1.24774
$804$		0			0
$805$	18.8832			0.665544
$806$		0			0
$807$	−2.89570	+	6.34070i	−0.101934	+	0.223203i
$808$		0			0
$809$	30.1400	+	8.84991i	1.05967	+	0.311146i	0.764717	−	0.644366i	$-0.222879\pi$
$809$	30.1400	+	8.84991i	1.05967	+	0.311146i	0.294950	+	0.955513i	$0.404697\pi$
$810$		0			0
$811$	3.45640	+	3.98890i	0.121371	+	0.140069i	0.813183	−	0.582008i	$-0.197733\pi$
$811$	3.45640	+	3.98890i	0.121371	+	0.140069i	−0.691812	+	0.722077i	$0.743187\pi$
$812$		0			0
$813$	0.131110	+	0.151309i	0.00459824	+	0.00530665i
$814$		0			0
$815$	−2.40961	−	0.707526i	−0.0844050	−	0.0247836i
$816$		0			0
$817$	−7.36448	−	4.73286i	−0.257651	−	0.165582i
$818$		0			0
$819$	3.14820	−	3.63322i	0.110007	−	0.126955i
$820$		0			0
$821$	−3.40727	−	23.6980i	−0.118914	−	0.827068i	−0.958755	−	0.284234i	$-0.908261\pi$
$821$	−3.40727	−	23.6980i	−0.118914	−	0.827068i	0.839840	−	0.542833i	$-0.182648\pi$
$822$		0			0
$823$	2.17082	−	2.50526i	0.0756700	−	0.0873279i	−0.716652	−	0.697431i	$-0.754326\pi$
$823$	2.17082	−	2.50526i	0.0756700	−	0.0873279i	0.792322	+	0.610103i	$0.208872\pi$
$824$		0			0
$825$	−10.6311	+	3.12156i	−0.370126	+	0.108679i
$826$		0			0
$827$	20.2184	−	44.2720i	0.703061	−	1.53949i	−0.133158	−	0.991095i	$-0.542512\pi$
$827$	20.2184	−	44.2720i	0.703061	−	1.53949i	0.836219	−	0.548395i	$-0.184761\pi$
$828$		0			0
$829$	−37.0425	−	23.8057i	−1.28654	−	0.826807i	−0.294858	−	0.955541i	$-0.595272\pi$
$829$	−37.0425	−	23.8057i	−1.28654	−	0.826807i	−0.991679	+	0.128734i	$0.958909\pi$
$830$		0			0
$831$	14.9676	−	4.39488i	0.519220	−	0.152457i
$832$		0			0
$833$	0.0408252			0.00141451
$834$		0			0
$835$	15.9781	−	10.2685i	0.552945	−	0.355356i
$836$		0			0
$837$	4.26964	−	4.92743i	0.147580	−	0.170317i
$838$		0			0
$839$	−17.3986	−	38.0977i	−0.600667	−	1.31528i	−0.928777	−	0.370639i	$-0.879139\pi$
$839$	−17.3986	−	38.0977i	−0.600667	−	1.31528i	0.328110	−	0.944640i	$-0.393588\pi$
$840$		0			0
$841$	6.14714			0.211970
$842$		0			0
$843$	−8.36473	+	5.37569i	−0.288097	+	0.185149i
$844$		0			0
$845$	−2.31715	−	16.1162i	−0.0797125	−	0.554413i
$846$		0			0
$847$	−5.55505	−	38.6362i	−0.190874	−	1.32756i
$848$		0			0
$849$	−10.4750	−	22.9370i	−0.359500	−	0.787196i
$850$		0			0
$851$	−7.01216	+	15.3545i	−0.240374	+	0.526345i
$852$		0			0
$853$	−3.68721	+	25.6451i	−0.126248	+	0.878072i	0.824003	+	0.566586i	$0.191736\pi$
$853$	−3.68721	+	25.6451i	−0.126248	+	0.878072i	−0.950251	+	0.311487i	$0.899173\pi$
$854$		0			0
$855$	13.3206	+	3.91129i	0.455556	+	0.133763i
$856$		0			0
$857$	0.976749	−	6.79344i	0.0333651	−	0.232059i	−0.966315	−	0.257363i	$-0.917146\pi$
$857$	0.976749	−	6.79344i	0.0333651	−	0.232059i	0.999680	+	0.0253040i	$0.00805536\pi$
$858$		0			0
$859$	37.7938	+	24.2886i	1.28951	+	0.828717i	0.992029	−	0.126011i	$-0.0402174\pi$
$859$	37.7938	+	24.2886i	1.28951	+	0.828717i	0.297480	+	0.954728i	$0.403854\pi$
$860$		0			0
$861$	−3.93573	−	8.61805i	−0.134129	−	0.293702i
$862$		0			0
$863$	37.4206	−	24.0487i	1.27381	−	0.818629i	0.283700	−	0.958913i	$-0.408438\pi$
$863$	37.4206	−	24.0487i	1.27381	−	0.818629i	0.990111	+	0.140284i	$0.0448016\pi$
$864$		0			0
$865$	−32.5200	+	9.54874i	−1.10571	+	0.324667i
$866$		0			0
$867$	1.44339	−	10.0390i	0.0490201	−	0.340942i
$868$		0			0
$869$	35.7656	+	41.2757i	1.21327	+	1.40018i
$870$		0			0
$871$	−5.61968	+	13.7616i	−0.190416	+	0.466294i
$872$		0			0
$873$	−7.47967	−	8.63200i	−0.253149	−	0.292149i
$874$		0			0
$875$	−4.54182	+	31.5891i	−0.153542	+	1.06791i
$876$		0			0
$877$	26.8548	−	7.88529i	0.906824	−	0.266267i	0.205120	−	0.978737i	$-0.434241\pi$
$877$	26.8548	−	7.88529i	0.906824	−	0.266267i	0.701703	+	0.712469i	$0.252423\pi$
$878$		0			0
$879$	17.8261	−	11.4561i	0.601259	−	0.386406i
$880$		0			0
$881$	6.89586	+	15.0998i	0.232328	+	0.508726i	0.989508	−	0.144480i	$-0.0461508\pi$
$881$	6.89586	+	15.0998i	0.232328	+	0.508726i	−0.757180	+	0.653206i	$0.773424\pi$
$882$		0			0
$883$	−35.2941	−	22.6822i	−1.18774	−	0.763316i	−0.210949	−	0.977497i	$-0.567655\pi$
$883$	−35.2941	−	22.6822i	−1.18774	−	0.763316i	−0.976794	+	0.214181i	$0.931292\pi$
$884$		0			0
$885$	0.189186	−	1.31581i	0.00635940	−	0.0442306i
$886$		0			0
$887$	28.5572	+	8.38514i	0.958855	+	0.281545i	0.723469	−	0.690357i	$-0.242546\pi$
$887$	28.5572	+	8.38514i	0.958855	+	0.281545i	0.235386	+	0.971902i	$0.424365\pi$
$888$		0			0
$889$	4.95967	−	34.4953i	0.166342	−	1.15693i
$890$		0			0
$891$	2.10780	−	4.61543i	0.0706139	−	0.154623i
$892$		0			0
$893$	−18.4607	−	40.4232i	−0.617763	−	1.35271i
$894$		0			0
$895$	4.11776	+	28.6397i	0.137642	+	0.957319i
$896$		0			0
$897$	1.09853	+	7.64048i	0.0366790	+	0.255108i
$898$		0			0
$899$	−32.5173	+	20.8976i	−1.08451	+	0.696974i
$900$		0			0
$901$	10.0805			0.335830
$902$		0			0
$903$	1.16372	+	2.54819i	0.0387261	+	0.0847984i
$904$		0			0
$905$	15.7420	−	18.1673i	0.523283	−	0.603901i
$906$		0			0
$907$	2.96796	−	1.90739i	0.0985496	−	0.0633340i	−0.490438	−	0.871476i	$-0.663163\pi$
$907$	2.96796	−	1.90739i	0.0985496	−	0.0633340i	0.588987	+	0.808142i	$0.299527\pi$
$908$		0			0
$909$	6.01232			0.199416
$910$		0			0
$911$	−3.82526	+	1.12320i	−0.126736	+	0.0372132i	−0.344486	−	0.938792i	$-0.611947\pi$
$911$	−3.82526	+	1.12320i	−0.126736	+	0.0372132i	0.217749	+	0.976005i	$0.430128\pi$
$912$		0			0
$913$	73.1908	+	47.0368i	2.42226	+	1.55669i
$914$		0			0
$915$	−0.304989	+	0.667832i	−0.0100826	+	0.0220778i
$916$		0			0
$917$	−15.1527	+	4.44924i	−0.500387	+	0.146927i
$918$		0			0
$919$	−30.8200	+	35.5682i	−1.01666	+	1.17329i	−0.0318768	+	0.999492i	$0.510148\pi$
$919$	−30.8200	+	35.5682i	−1.01666	+	1.17329i	−0.984782	+	0.173795i	$0.944397\pi$
$920$		0			0
$921$	1.22130	+	8.49432i	0.0402432	+	0.279897i
$922$		0			0
$923$	−3.83495	+	4.42577i	−0.126229	+	0.145676i
$924$		0			0
$925$	−7.29530	−	4.68840i	−0.239868	−	0.154154i
$926$		0			0
$927$	−16.1078	−	4.72969i	−0.529051	−	0.155343i
$928$		0			0
$929$	−2.14014	−	2.46985i	−0.0702156	−	0.0810331i	0.719555	−	0.694436i	$-0.244346\pi$
$929$	−2.14014	−	2.46985i	−0.0702156	−	0.0810331i	−0.789771	+	0.613402i	$0.789800\pi$
$930$		0			0
$931$	−0.0424517	−	0.0489919i	−0.00139130	−	0.00160564i
$932$		0			0
$933$	24.5108	+	7.19702i	0.802448	+	0.235620i
$934$		0			0
$935$	−18.4286	+	40.3531i	−0.602681	+	1.31969i
$936$		0			0
$937$	−11.1153			−0.363120			−0.181560	−	0.983380i	$-0.558115\pi$
$937$	−11.1153			−0.363120			−0.181560	+	0.983380i	$0.558115\pi$
$938$		0			0
$939$	−16.1982			−0.528609
$940$		0			0
$941$	−21.4720	+	47.0172i	−0.699969	+	1.53272i	0.140041	+	0.990146i	$0.455277\pi$
$941$	−21.4720	+	47.0172i	−0.699969	+	1.53272i	−0.840009	+	0.542572i	$0.817451\pi$
$942$		0			0
$943$	14.5960	+	4.28578i	0.475312	+	0.139564i
$944$		0			0
$945$	−2.90926	−	3.35746i	−0.0946382	−	0.109218i
$946$		0			0
$947$	5.57693	+	6.43612i	0.181226	+	0.209146i	0.839093	−	0.543989i	$-0.183087\pi$
$947$	5.57693	+	6.43612i	0.181226	+	0.209146i	−0.657867	+	0.753134i	$0.728541\pi$
$948$		0			0
$949$	−12.1423	−	3.56529i	−0.394155	−	0.115734i
$950$		0			0
$951$	−6.05875	−	3.89372i	−0.196468	−	0.126263i
$952$		0			0
$953$	19.4253	−	22.4180i	0.629248	−	0.726191i	−0.348187	−	0.937425i	$-0.613203\pi$
$953$	19.4253	−	22.4180i	0.629248	−	0.726191i	0.977436	+	0.211234i	$0.0677481\pi$
$954$		0			0
$955$	−2.30963	−	16.0638i	−0.0747378	−	0.519813i
$956$		0			0
$957$	−19.6988	+	22.7337i	−0.636773	+	0.734875i
$958$		0			0
$959$	37.5106	−	11.0141i	1.21128	−	0.355664i
$960$		0			0
$961$	4.78119	−	10.4694i	0.154232	−	0.337721i
$962$		0			0
$963$	8.98872	+	5.77670i	0.289657	+	0.186152i
$964$		0			0
$965$	5.03453	−	1.47827i	0.162067	−	0.0475872i
$966$		0			0
$967$	−24.9715			−0.803031			−0.401515	−	0.915852i	$-0.631516\pi$
$967$	−24.9715			−0.803031			−0.401515	+	0.915852i	$0.631516\pi$
$968$		0			0
$969$	−36.2569	+	23.3009i	−1.16474	+	0.748533i
$970$		0			0
$971$	0.384304	−	0.443510i	0.0123329	−	0.0142329i	−0.749550	−	0.661948i	$-0.769730\pi$
$971$	0.384304	−	0.443510i	0.0123329	−	0.0142329i	0.761883	+	0.647715i	$0.224275\pi$
$972$		0			0
$973$	−19.0451	−	41.7028i	−0.610556	−	1.33693i
$974$		0			0
$975$	−3.96561			−0.127001
$976$		0			0
$977$	9.02416	−	5.79948i	0.288709	−	0.185542i	−0.388268	−	0.921547i	$-0.626926\pi$
$977$	9.02416	−	5.79948i	0.288709	−	0.185542i	0.676976	+	0.736005i	$0.263290\pi$
$978$		0			0
$979$	−8.01983	−	55.7792i	−0.256315	−	1.78271i
$980$		0			0
$981$	1.04448	+	7.26451i	0.0333476	+	0.231938i
$982$		0			0
$983$	16.9913	+	37.2057i	0.541937	+	1.18668i	0.960447	+	0.278464i	$0.0898253\pi$
$983$	16.9913	+	37.2057i	0.541937	+	1.18668i	−0.418510	+	0.908212i	$0.637447\pi$
$984$		0			0
$985$	−13.2874	+	29.0954i	−0.423372	+	0.927056i
$986$		0			0
$987$	−2.02379	+	14.0758i	−0.0644180	+	0.448037i
$988$		0			0
$989$	−4.31576	−	1.26722i	−0.137233	−	0.0402953i
$990$		0			0
$991$	2.68209	−	18.6544i	0.0851995	−	0.592576i	−0.901837	−	0.432077i	$-0.857781\pi$
$991$	2.68209	−	18.6544i	0.0851995	−	0.592576i	0.987036	−	0.160498i	$-0.0513102\pi$
$992$		0			0
$993$	29.5364	+	18.9819i	0.937310	+	0.602373i
$994$		0			0
$995$	−15.1794	−	33.2383i	−0.481220	−	1.05372i
$996$		0			0
$997$	−17.2203	+	11.0668i	−0.545374	+	0.350490i	−0.784137	−	0.620587i	$-0.786894\pi$
$997$	−17.2203	+	11.0668i	−0.545374	+	0.350490i	0.238764	+	0.971078i	$0.423258\pi$
$998$		0			0
$999$	3.81039	−	1.11883i	0.120555	−	0.0353983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.241.4	✓	60
67.62	even	11	inner	804.2.q.b.397.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.241.4	✓	60	1.1	even	1	trivial
804.2.q.b.397.4	yes	60	67.62	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-4.86843 - 1.42950i) q^{11} +(-1.52774 - 0.981818i) q^{13} +(-1.09898 + 1.26829i) q^{15} +(-0.741435 - 5.15679i) q^{17} +(-5.41739 + 6.25200i) q^{19} +(2.54000 - 0.745811i) q^{21} +(-1.76573 + 3.86640i) q^{23} +(-1.83702 - 1.18058i) q^{25} +(0.959493 - 0.281733i) q^{27} -5.92850 q^{29} +(5.48491 - 3.52494i) q^{31} +(3.32273 - 3.83464i) q^{33} +(-1.84551 - 4.04109i) q^{35} +3.97126 q^{37} +(1.52774 - 0.981818i) q^{39} +(-0.509333 - 3.54249i) q^{41} +(0.150600 + 1.04744i) q^{43} +(-0.697146 - 1.52654i) q^{45} +(-2.23155 + 4.88641i) q^{47} +(-0.00111521 + 0.00775643i) q^{49} +(4.99879 + 1.46778i) q^{51} +(-0.275366 + 1.91521i) q^{53} +(-7.16333 - 4.60359i) q^{55} +(-3.43656 - 7.52501i) q^{57} +(-0.666382 + 0.428258i) q^{59} +(0.419761 - 0.123253i) q^{61} +(-0.376740 + 2.62029i) q^{63} +(-1.99578 - 2.30325i) q^{65} +(-1.49365 - 8.04792i) q^{67} +(-2.78350 - 3.21232i) q^{69} +(0.458922 - 3.19187i) q^{71} +(6.68618 - 1.96324i) q^{73} +(1.83702 - 1.18058i) q^{75} +(5.57983 + 12.2181i) q^{77} +(-9.05517 - 5.81941i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-16.4522 - 4.83081i) q^{83} +(1.24427 - 8.65408i) q^{85} +(2.46279 - 5.39276i) q^{87} +(4.61371 + 10.1026i) q^{89} +(0.684170 + 4.75851i) q^{91} +(0.927882 + 6.45356i) q^{93} +(-11.6791 + 7.50571i) q^{95} +11.4218 q^{97} +(2.10780 + 4.61543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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