LMFDB - Embedded newform 804.2.y.b.505.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			505.6
Character	$\chi$	$=$	804.505
Dual form			804.2.y.b.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(2.26427 + 1.45516i) q^{5} +(-0.275857 + 0.110437i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(2.26427 + 1.45516i) q^{5} +(-0.275857 + 0.110437i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.141549 + 2.97147i) q^{11} +(-2.35877 - 0.225236i) q^{13} +(0.383046 + 2.66414i) q^{15} +(-1.55999 + 6.43038i) q^{17} +(-0.0392194 - 0.0157011i) q^{19} +(-0.264111 - 0.136158i) q^{21} +(6.70108 - 1.29153i) q^{23} +(0.932347 + 2.04156i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-4.54404 - 7.87051i) q^{29} +(6.70820 - 0.640555i) q^{31} +(-2.33838 + 1.83893i) q^{33} +(-0.785317 - 0.151357i) q^{35} +(-3.58390 + 6.20750i) q^{37} +(-1.37445 - 1.93014i) q^{39} +(-1.14105 - 1.08799i) q^{41} +(-0.0911731 + 0.0267708i) q^{43} +(-1.76258 + 2.03413i) q^{45} +(1.33349 - 3.85286i) q^{47} +(-5.00224 + 4.76962i) q^{49} +(-5.88134 + 3.03204i) q^{51} +(9.92237 + 2.91347i) q^{53} +(-4.64446 + 6.52223i) q^{55} +(-0.0138171 - 0.0399220i) q^{57} +(0.805907 - 1.76469i) q^{59} +(-0.0570785 - 1.19823i) q^{61} +(-0.0700539 - 0.288766i) q^{63} +(-5.01314 - 3.94237i) q^{65} +(8.13460 + 0.910133i) q^{67} +(5.36435 + 4.21857i) q^{69} +(2.07959 + 8.57221i) q^{71} +(-0.527712 - 11.0780i) q^{73} +(-0.932347 + 2.04156i) q^{75} +(-0.289112 - 0.835335i) q^{77} +(-0.0496144 + 0.0696736i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(5.57384 - 2.87352i) q^{83} +(-12.8894 + 12.2901i) q^{85} +(2.97242 - 8.58824i) q^{87} +(2.48587 - 2.86885i) q^{89} +(0.675559 - 0.198362i) q^{91} +(4.87703 + 4.65024i) q^{93} +(-0.0659556 - 0.0926216i) q^{95} +(-6.97782 + 12.0859i) q^{97} +(-2.92108 - 0.562993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{7}{33}\right)$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	2.26427	+	1.45516i	1.01261	+	0.650765i	0.938067	−	0.346453i	$-0.112614\pi$
$5$	2.26427	+	1.45516i	1.01261	+	0.650765i	0.0745429	+	0.997218i	$0.476250\pi$
$6$		0			0
$7$	−0.275857	+	0.110437i	−0.104264	+	0.0417411i	−0.423208	−	0.906032i	$-0.639096\pi$
$7$	−0.275857	+	0.110437i	−0.104264	+	0.0417411i	0.318944	+	0.947774i	$0.396672\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−0.141549	+	2.97147i	−0.0426785	+	0.895933i	0.871444	+	0.490495i	$0.163184\pi$
$11$	−0.141549	+	2.97147i	−0.0426785	+	0.895933i	−0.914123	+	0.405438i	$0.867119\pi$
$12$		0			0
$13$	−2.35877	−	0.225236i	−0.654206	−	0.0624691i	−0.237325	−	0.971430i	$-0.576271\pi$
$13$	−2.35877	−	0.225236i	−0.654206	−	0.0624691i	−0.416881	+	0.908961i	$0.636877\pi$
$14$		0			0
$15$	0.383046	+	2.66414i	0.0989020	+	0.687878i
$16$		0			0
$17$	−1.55999	+	6.43038i	−0.378354	+	1.55960i	0.390764	+	0.920491i	$0.372211\pi$
$17$	−1.55999	+	6.43038i	−0.378354	+	1.55960i	−0.769119	+	0.639106i	$0.779304\pi$
$18$		0			0
$19$	−0.0392194	−	0.0157011i	−0.00899754	−	0.00360207i	0.367159	−	0.930158i	$-0.380330\pi$
$19$	−0.0392194	−	0.0157011i	−0.00899754	−	0.00360207i	−0.376157	+	0.926556i	$0.622755\pi$
$20$		0			0
$21$	−0.264111	−	0.136158i	−0.0576337	−	0.0297122i
$22$		0			0
$23$	6.70108	−	1.29153i	1.39727	−	0.269302i	0.565651	−	0.824645i	$-0.308625\pi$
$23$	6.70108	−	1.29153i	1.39727	−	0.269302i	0.831622	+	0.555343i	$0.187413\pi$
$24$		0			0
$25$	0.932347	+	2.04156i	0.186469	+	0.408311i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−4.54404	−	7.87051i	−0.843807	−	1.46152i	−0.886653	−	0.462435i	$-0.846976\pi$
$29$	−4.54404	−	7.87051i	−0.843807	−	1.46152i	0.0428465	−	0.999082i	$-0.486357\pi$
$30$		0			0
$31$	6.70820	−	0.640555i	1.20483	−	0.115047i	0.526739	−	0.850027i	$-0.323415\pi$
$31$	6.70820	−	0.640555i	1.20483	−	0.115047i	0.678089	+	0.734980i	$0.262809\pi$
$32$		0			0
$33$	−2.33838	+	1.83893i	−0.407060	+	0.320116i
$34$		0			0
$35$	−0.785317	−	0.151357i	−0.132743	−	0.0255841i
$36$		0			0
$37$	−3.58390	+	6.20750i	−0.589190	+	1.02051i	0.405149	+	0.914251i	$0.367220\pi$
$37$	−3.58390	+	6.20750i	−0.589190	+	1.02051i	−0.994339	+	0.106256i	$0.966114\pi$
$38$		0			0
$39$	−1.37445	−	1.93014i	−0.220088	−	0.309070i
$40$		0			0
$41$	−1.14105	−	1.08799i	−0.178203	−	0.169916i	0.595728	−	0.803186i	$-0.296864\pi$
$41$	−1.14105	−	1.08799i	−0.178203	−	0.169916i	−0.773931	+	0.633270i	$0.781712\pi$
$42$		0			0
$43$	−0.0911731	+	0.0267708i	−0.0139038	+	0.00408252i	−0.288677	−	0.957427i	$-0.593215\pi$
$43$	−0.0911731	+	0.0267708i	−0.0139038	+	0.00408252i	0.274773	+	0.961509i	$0.411397\pi$
$44$		0			0
$45$	−1.76258	+	2.03413i	−0.262750	+	0.303230i
$46$		0			0
$47$	1.33349	−	3.85286i	0.194509	−	0.561997i	−0.805002	−	0.593272i	$-0.797836\pi$
$47$	1.33349	−	3.85286i	0.194509	−	0.561997i	0.999511	+	0.0312755i	$0.00995692\pi$
$48$		0			0
$49$	−5.00224	+	4.76962i	−0.714605	+	0.681375i
$50$		0			0
$51$	−5.88134	+	3.03204i	−0.823552	+	0.424571i
$52$		0			0
$53$	9.92237	+	2.91347i	1.36294	+	0.400196i	0.879799	−	0.475346i	$-0.157677\pi$
$53$	9.92237	+	2.91347i	1.36294	+	0.400196i	0.483143	+	0.875541i	$0.339495\pi$
$54$		0			0
$55$	−4.64446	+	6.52223i	−0.626258	+	0.879457i
$56$		0			0
$57$	−0.0138171	−	0.0399220i	−0.00183013	−	0.00528780i
$58$		0			0
$59$	0.805907	−	1.76469i	0.104920	−	0.229743i	−0.849890	−	0.526961i	$-0.823331\pi$
$59$	0.805907	−	1.76469i	0.104920	−	0.229743i	0.954810	+	0.297218i	$0.0960587\pi$
$60$		0			0
$61$	−0.0570785	−	1.19823i	−0.00730816	−	0.153417i	−0.999572	−	0.0292672i	$-0.990683\pi$
$61$	−0.0570785	−	1.19823i	−0.00730816	−	0.153417i	0.992263	−	0.124150i	$-0.0396204\pi$
$62$		0			0
$63$	−0.0700539	−	0.288766i	−0.00882597	−	0.0363811i
$64$		0			0
$65$	−5.01314	−	3.94237i	−0.621803	−	0.488991i
$66$		0			0
$67$	8.13460	+	0.910133i	0.993799	+	0.111190i
$67$	8.13460	+	0.910133i	0.993799	+	0.111190i
$68$		0			0
$69$	5.36435	+	4.21857i	0.645792	+	0.507856i
$70$		0			0
$71$	2.07959	+	8.57221i	0.246802	+	1.01733i	0.951457	+	0.307783i	$0.0995870\pi$
$71$	2.07959	+	8.57221i	0.246802	+	1.01733i	−0.704654	+	0.709551i	$0.748898\pi$
$72$		0			0
$73$	−0.527712	−	11.0780i	−0.0617640	−	1.29659i	−0.790785	−	0.612094i	$-0.790327\pi$
$73$	−0.527712	−	11.0780i	−0.0617640	−	1.29659i	0.729021	−	0.684492i	$-0.239976\pi$
$74$		0			0
$75$	−0.932347	+	2.04156i	−0.107658	+	0.235738i
$76$		0			0
$77$	−0.289112	−	0.835335i	−0.0329474	−	0.0951952i
$78$		0			0
$79$	−0.0496144	+	0.0696736i	−0.00558205	+	0.00783889i	−0.817358	−	0.576131i	$-0.804562\pi$
$79$	−0.0496144	+	0.0696736i	−0.00558205	+	0.00783889i	0.811775	+	0.583970i	$0.198501\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	5.57384	−	2.87352i	0.611809	−	0.315409i	−0.124329	−	0.992241i	$-0.539678\pi$
$83$	5.57384	−	2.87352i	0.611809	−	0.315409i	0.736138	+	0.676832i	$0.236647\pi$
$84$		0			0
$85$	−12.8894	+	12.2901i	−1.39806	+	1.33304i
$86$		0			0
$87$	2.97242	−	8.58824i	0.318677	−	0.920756i
$88$		0			0
$89$	2.48587	−	2.86885i	0.263502	−	0.304097i	−0.608546	−	0.793519i	$-0.708247\pi$
$89$	2.48587	−	2.86885i	0.263502	−	0.304097i	0.872047	+	0.489422i	$0.162792\pi$
$90$		0			0
$91$	0.675559	−	0.198362i	0.0708178	−	0.0207940i
$92$		0			0
$93$	4.87703	+	4.65024i	0.505725	+	0.482208i
$94$		0			0
$95$	−0.0659556	−	0.0926216i	−0.00676690	−	0.00950278i
$96$		0			0
$97$	−6.97782	+	12.0859i	−0.708490	+	1.22714i	0.256927	+	0.966431i	$0.417290\pi$
$97$	−6.97782	+	12.0859i	−0.708490	+	1.22714i	−0.965417	+	0.260710i	$0.916043\pi$
$98$		0			0
$99$	−2.92108	−	0.562993i	−0.293580	−	0.0565829i
$100$		0			0
$101$	7.14022	−	5.61513i	0.710479	−	0.558727i	−0.196192	−	0.980565i	$-0.562858\pi$
$101$	7.14022	−	5.61513i	0.710479	−	0.558727i	0.906671	+	0.421839i	$0.138615\pi$
$102$		0			0
$103$	−10.9460	+	1.04521i	−1.07854	+	0.102988i	−0.619169	−	0.785258i	$-0.712530\pi$
$103$	−10.9460	+	1.04521i	−1.07854	+	0.102988i	−0.459369	+	0.888246i	$0.651924\pi$
$104$		0			0
$105$	−0.399885	−	0.692621i	−0.0390248	−	0.0675929i
$106$		0			0
$107$	15.0236	−	9.65507i	1.45238	−	0.933391i	0.453267	−	0.891375i	$-0.350258\pi$
$107$	15.0236	−	9.65507i	1.45238	−	0.933391i	0.999117	−	0.0420157i	$-0.0133780\pi$
$108$		0			0
$109$	−1.58087	−	3.46162i	−0.151420	−	0.331563i	0.818688	−	0.574239i	$-0.194702\pi$
$109$	−1.58087	−	3.46162i	−0.151420	−	0.331563i	−0.970107	+	0.242676i	$0.921975\pi$
$110$		0			0
$111$	−7.03827	+	1.35652i	−0.668043	+	0.128755i
$112$		0			0
$113$	2.63705	+	1.35949i	0.248072	+	0.127890i	0.577779	−	0.816193i	$-0.303920\pi$
$113$	2.63705	+	1.35949i	0.248072	+	0.127890i	−0.329707	+	0.944083i	$0.606950\pi$
$114$		0			0
$115$	17.0524	+	6.82675i	1.59014	+	0.636598i
$116$		0			0
$117$	0.558631	−	2.30271i	0.0516455	−	0.212886i
$118$		0			0
$119$	−0.279814	−	1.94615i	−0.0256505	−	0.178403i
$120$		0			0
$121$	2.14058	+	0.204401i	0.194598	+	0.0185819i
$122$		0			0
$123$	0.0750186	−	1.57483i	0.00676419	−	0.141998i
$124$		0			0
$125$	1.05553	−	7.34138i	0.0944095	−	0.656633i
$126$		0			0
$127$	−8.85591	+	3.54537i	−0.785835	+	0.314601i	−0.729651	−	0.683819i	$-0.760318\pi$
$127$	−8.85591	+	3.54537i	−0.785835	+	0.314601i	−0.0561840	+	0.998420i	$0.517893\pi$
$128$		0			0
$129$	−0.0799378	−	0.0513729i	−0.00703813	−	0.00452313i
$130$		0			0
$131$	−9.30270	−	10.7359i	−0.812781	−	0.937999i	0.186228	−	0.982507i	$-0.440374\pi$
$131$	−9.30270	−	10.7359i	−0.812781	−	0.937999i	−0.999009	+	0.0445073i	$0.985828\pi$
$132$		0			0
$133$	0.0125529			0.00108848
$134$		0			0
$135$	−2.69154			−0.231651
$136$		0			0
$137$	−11.9976	−	13.8459i	−1.02502	−	1.18294i	−0.982959	−	0.183824i	$-0.941152\pi$
$137$	−11.9976	−	13.8459i	−1.02502	−	1.18294i	−0.0420631	−	0.999115i	$-0.513393\pi$
$138$		0			0
$139$	11.7475	+	7.54968i	0.996413	+	0.640356i	0.933842	−	0.357685i	$-0.116434\pi$
$139$	11.7475	+	7.54968i	0.996413	+	0.640356i	0.0625707	+	0.998041i	$0.480070\pi$
$140$		0			0
$141$	3.78504	−	1.51530i	0.318758	−	0.127611i
$142$		0			0
$143$	1.00316	−	6.97715i	0.0838887	−	0.583458i
$144$		0			0
$145$	1.16390	−	24.4332i	0.0966564	−	2.02907i
$146$		0			0
$147$	−6.88041	−	0.656999i	−0.567487	−	0.0541884i
$148$		0			0
$149$	−0.0543944	−	0.378321i	−0.00445616	−	0.0309933i	0.987472	−	0.157794i	$-0.0504382\pi$
$149$	−0.0543944	−	0.378321i	−0.00445616	−	0.0309933i	−0.991928	+	0.126801i	$0.959529\pi$
$150$		0			0
$151$	−0.358180	+	1.47644i	−0.0291483	+	0.120151i	−0.984527	−	0.175233i	$-0.943932\pi$
$151$	−0.358180	+	1.47644i	−0.0291483	+	0.120151i	0.955379	+	0.295383i	$0.0954474\pi$
$152$		0			0
$153$	−6.14292	−	2.45925i	−0.496626	−	0.198819i
$154$		0			0
$155$	16.1212	+	8.31108i	1.29489	+	0.667562i
$156$		0			0
$157$	12.0651	−	2.32536i	0.962900	−	0.185584i	0.316508	−	0.948590i	$-0.397489\pi$
$157$	12.0651	−	2.32536i	0.962900	−	0.185584i	0.646391	+	0.763006i	$0.276277\pi$
$158$		0			0
$159$	4.29592	+	9.40674i	0.340688	+	0.746003i
$160$		0			0
$161$	−1.70591	+	1.09632i	−0.134445	+	0.0864023i
$162$		0			0
$163$	−9.69566	−	16.7934i	−0.759422	−	1.31536i	−0.943146	−	0.332380i	$-0.892148\pi$
$163$	−9.69566	−	16.7934i	−0.759422	−	1.31536i	0.183723	−	0.982978i	$-0.441185\pi$
$164$		0			0
$165$	−7.97064	+	0.761104i	−0.620514	+	0.0592519i
$166$		0			0
$167$	12.0511	−	9.47713i	0.932546	−	0.733362i	−0.0313873	−	0.999507i	$-0.509993\pi$
$167$	12.0511	−	9.47713i	0.932546	−	0.733362i	0.963933	+	0.266145i	$0.0857501\pi$
$168$		0			0
$169$	−7.25199	−	1.39771i	−0.557846	−	0.107516i
$170$		0			0
$171$	0.0211228	−	0.0365857i	0.00161530	−	0.00279778i
$172$		0			0
$173$	−7.31617	−	10.2741i	−0.556238	−	0.781127i	0.436719	−	0.899598i	$-0.356140\pi$
$173$	−7.31617	−	10.2741i	−0.556238	−	0.781127i	−0.992958	+	0.118471i	$0.962201\pi$
$174$		0			0
$175$	−0.482657	−	0.460213i	−0.0364855	−	0.0347888i
$176$		0			0
$177$	1.86142	−	0.546562i	0.139913	−	0.0410821i
$178$		0			0
$179$	2.10417	−	2.42834i	0.157273	−	0.181503i	−0.671644	−	0.740874i	$-0.734412\pi$
$179$	2.10417	−	2.42834i	0.157273	−	0.181503i	0.828918	+	0.559371i	$0.188957\pi$
$180$		0			0
$181$	−2.57303	+	7.43429i	−0.191252	+	0.552586i	−0.999334	−	0.0364834i	$-0.988384\pi$
$181$	−2.57303	+	7.43429i	−0.191252	+	0.552586i	0.808082	+	0.589070i	$0.200506\pi$
$182$		0			0
$183$	0.868180	−	0.827808i	0.0641777	−	0.0611933i
$184$		0			0
$185$	−17.1478	+	8.84030i	−1.26073	+	0.649952i
$186$		0			0
$187$	−18.8869	−	5.54569i	−1.38115	−	0.405541i
$188$		0			0
$189$	0.172359	−	0.242045i	0.0125373	−	0.0176062i
$190$		0			0
$191$	−0.573925	−	1.65825i	−0.0415277	−	0.119987i	0.922331	−	0.386401i	$-0.126282\pi$
$191$	−0.573925	−	1.65825i	−0.0415277	−	0.119987i	−0.963858	+	0.266415i	$0.914161\pi$
$192$		0			0
$193$	−0.218531	+	0.478517i	−0.0157302	+	0.0344444i	−0.917334	−	0.398118i	$-0.869663\pi$
$193$	−0.218531	+	0.478517i	−0.0157302	+	0.0344444i	0.901604	+	0.432563i	$0.142391\pi$
$194$		0			0
$195$	−0.303459	−	6.37038i	−0.0217311	−	0.456192i
$196$		0			0
$197$	−2.94312	−	12.1317i	−0.209689	−	0.864349i	−0.975271	−	0.221011i	$-0.929064\pi$
$197$	−2.94312	−	12.1317i	−0.209689	−	0.864349i	0.765582	−	0.643338i	$-0.222451\pi$
$198$		0			0
$199$	5.46650	+	4.29891i	0.387510	+	0.304741i	0.792841	−	0.609429i	$-0.208601\pi$
$199$	5.46650	+	4.29891i	0.387510	+	0.304741i	−0.405331	+	0.914170i	$0.632844\pi$
$200$		0			0
$201$	4.63920	+	6.74373i	0.327224	+	0.475666i
$202$		0			0
$203$	2.12270	+	1.66931i	0.148984	+	0.117163i
$204$		0			0
$205$	−1.00045	−	4.12391i	−0.0698745	−	0.288026i
$206$		0			0
$207$	0.324718	+	6.81668i	0.0225695	+	0.473792i
$208$		0			0
$209$	0.0522067	−	0.114317i	0.00361122	−	0.00790746i
$210$		0			0
$211$	−7.10028	−	20.5149i	−0.488803	−	1.41230i	−0.872395	−	0.488801i	$-0.837434\pi$
$211$	−7.10028	−	20.5149i	−0.488803	−	1.41230i	0.383592	−	0.923503i	$-0.374687\pi$
$212$		0			0
$213$	−5.11660	+	7.18525i	−0.350583	+	0.492326i
$214$		0			0
$215$	−0.245396	−	0.0720547i	−0.0167359	−	0.00491409i
$216$		0			0
$217$	−1.77976	+	0.917532i	−0.120818	+	0.0622862i
$218$		0			0
$219$	8.02664	−	7.65339i	0.542390	−	0.517168i
$220$		0			0
$221$	5.12802	−	14.8164i	0.344948	−	0.996662i
$222$		0			0
$223$	14.0955	−	16.2671i	0.943908	−	1.08933i	−0.0519725	−	0.998649i	$-0.516551\pi$
$223$	14.0955	−	16.2671i	0.943908	−	1.08933i	0.995880	−	0.0906790i	$-0.0289037\pi$
$224$		0			0
$225$	−2.15346	+	0.632313i	−0.143564	+	0.0421542i
$226$		0			0
$227$	6.74633	+	6.43261i	0.447770	+	0.426947i	0.880115	−	0.474761i	$-0.157465\pi$
$227$	6.74633	+	6.43261i	0.447770	+	0.426947i	−0.432345	+	0.901708i	$0.642314\pi$
$228$		0			0
$229$	4.59014	+	6.44595i	0.303325	+	0.425961i	0.937903	−	0.346899i	$-0.112765\pi$
$229$	4.59014	+	6.44595i	0.303325	+	0.425961i	−0.634577	+	0.772859i	$0.718826\pi$
$230$		0			0
$231$	0.441976	−	0.765524i	0.0290799	−	0.0503678i
$232$		0			0
$233$	19.4646	+	3.75149i	1.27517	+	0.245768i	0.781512	−	0.623890i	$-0.214449\pi$
$233$	19.4646	+	3.75149i	1.27517	+	0.245768i	0.493654	+	0.869658i	$0.335661\pi$
$234$		0			0
$235$	8.62587	−	6.78346i	0.562690	−	0.442504i
$236$		0			0
$237$	−0.0851463	+	0.00813048i	−0.00553085	+	0.000528132i
$238$		0			0
$239$	7.87749	+	13.6442i	0.509553	+	0.882571i	0.999939	+	0.0110656i	$0.00352237\pi$
$239$	7.87749	+	13.6442i	0.509553	+	0.882571i	−0.490386	+	0.871505i	$0.663144\pi$
$240$		0			0
$241$	−5.97485	+	3.83980i	−0.384874	+	0.247344i	−0.718743	−	0.695276i	$-0.755282\pi$
$241$	−5.97485	+	3.83980i	−0.384874	+	0.247344i	0.333869	+	0.942620i	$0.391646\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−18.2669	+	3.52066i	−1.16703	+	0.224927i
$246$		0			0
$247$	0.0889732	+	0.0458688i	0.00566123	+	0.00291856i
$248$		0			0
$249$	5.82175	+	2.33068i	0.368938	+	0.147701i
$250$		0			0
$251$	4.54948	−	18.7532i	0.287160	−	1.18369i	−0.627222	−	0.778840i	$-0.715808\pi$
$251$	4.54948	−	18.7532i	0.287160	−	1.18369i	0.914383	−	0.404851i	$-0.132677\pi$
$252$		0			0
$253$	2.88921	+	20.0949i	0.181643	+	1.26336i
$254$		0			0
$255$	−17.7290	−	1.69291i	−1.11023	−	0.106014i
$256$		0			0
$257$	−1.16130	+	24.3787i	−0.0724401	+	1.52070i	0.611546	+	0.791209i	$0.290548\pi$
$257$	−1.16130	+	24.3787i	−0.0724401	+	1.52070i	−0.683986	+	0.729495i	$0.739755\pi$
$258$		0			0
$259$	0.303110	−	2.10818i	0.0188344	−	0.130996i
$260$		0			0
$261$	8.43708	−	3.37770i	0.522242	−	0.209074i
$262$		0			0
$263$	17.8888	+	11.4964i	1.10307	+	0.708900i	0.959772	−	0.280780i	$-0.0905930\pi$
$263$	17.8888	+	11.4964i	1.10307	+	0.708900i	0.143298	+	0.989680i	$0.454229\pi$
$264$		0			0
$265$	18.2273	+	21.0355i	1.11970	+	1.29220i
$266$		0			0
$267$	3.79603			0.232313
$268$		0			0
$269$	−6.01851			−0.366955			−0.183478	−	0.983024i	$-0.558735\pi$
$269$	−6.01851			−0.366955			−0.183478	+	0.983024i	$0.558735\pi$
$270$		0			0
$271$	−13.8059	−	15.9329i	−0.838648	−	0.967852i	0.161170	−	0.986927i	$-0.448473\pi$
$271$	−13.8059	−	15.9329i	−0.838648	−	0.967852i	−0.999818	+	0.0190749i	$0.993928\pi$
$272$		0			0
$273$	0.592309	+	0.380654i	0.0358482	+	0.0230382i
$274$		0			0
$275$	−6.19840	+	2.48146i	−0.373777	+	0.149638i
$276$		0			0
$277$	−2.46135	+	17.1191i	−0.147888	+	1.02859i	0.771780	+	0.635890i	$0.219367\pi$
$277$	−2.46135	+	17.1191i	−0.147888	+	1.02859i	−0.919668	+	0.392697i	$0.871542\pi$
$278$		0			0
$279$	−0.320641	+	6.73108i	−0.0191963	+	0.402979i
$280$		0			0
$281$	−30.9658	−	2.95687i	−1.84726	−	0.176392i	−0.888175	−	0.459505i	$-0.848027\pi$
$281$	−30.9658	−	2.95687i	−1.84726	−	0.176392i	−0.959087	+	0.283112i	$0.908633\pi$
$282$		0			0
$283$	−3.61930	−	25.1728i	−0.215145	−	1.49637i	−0.755623	−	0.655007i	$-0.772666\pi$
$283$	−3.61930	−	25.1728i	−0.215145	−	1.49637i	0.540478	−	0.841358i	$-0.318243\pi$
$284$		0			0
$285$	0.0268071	−	0.110500i	0.00158791	−	0.00654547i
$286$		0			0
$287$	0.434922	+	0.174116i	0.0256726	+	0.0102778i
$288$		0			0
$289$	−23.8060	−	12.2729i	−1.40035	−	0.721933i
$290$		0			0
$291$	−13.7034	+	2.64112i	−0.803310	+	0.154825i
$292$		0			0
$293$	−4.05857	−	8.88703i	−0.237104	−	0.519186i	0.753252	−	0.657732i	$-0.228484\pi$
$293$	−4.05857	−	8.88703i	−0.237104	−	0.519186i	−0.990356	+	0.138546i	$0.955757\pi$
$294$		0			0
$295$	4.39269	−	2.82301i	0.255752	−	0.164362i
$296$		0			0
$297$	−1.48742	−	2.57629i	−0.0863089	−	0.149491i
$298$		0			0
$299$	−16.0972	+	1.53710i	−0.930927	+	0.0888927i
$300$		0			0
$301$	0.0221943	−	0.0174538i	0.00127926	−	0.00100602i
$302$		0			0
$303$	8.91949	+	1.71909i	0.512411	+	0.0987592i
$304$		0			0
$305$	1.61436	−	2.79616i	0.0924382	−	0.160108i
$306$		0			0
$307$	6.50803	+	9.13926i	0.371433	+	0.521605i	0.957413	−	0.288720i	$-0.0932298\pi$
$307$	6.50803	+	9.13926i	0.371433	+	0.521605i	−0.585980	+	0.810325i	$0.699290\pi$
$308$		0			0
$309$	−7.95800	−	7.58794i	−0.452715	−	0.431663i
$310$		0			0
$311$	−11.4158	+	3.35197i	−0.647328	+	0.190073i	−0.588884	−	0.808218i	$-0.700432\pi$
$311$	−11.4158	+	3.35197i	−0.647328	+	0.190073i	−0.0584447	+	0.998291i	$0.518614\pi$
$312$		0			0
$313$	21.2257	−	24.4957i	1.19974	−	1.38458i	0.296735	−	0.954960i	$-0.404102\pi$
$313$	21.2257	−	24.4957i	1.19974	−	1.38458i	0.903010	−	0.429620i	$-0.141352\pi$
$314$		0			0
$315$	0.261579	−	0.755783i	0.0147383	−	0.0425835i
$316$		0			0
$317$	−18.3447	+	17.4916i	−1.03034	+	0.982426i	−0.999854	−	0.0171096i	$-0.994554\pi$
$317$	−18.3447	+	17.4916i	−1.03034	+	0.982426i	−0.0304847	+	0.999535i	$0.509705\pi$
$318$		0			0
$319$	24.0302	−	12.3884i	1.34543	−	0.693619i
$320$		0			0
$321$	17.1352	+	5.03134i	0.956392	+	0.280822i
$322$		0			0
$323$	0.162146	−	0.227702i	0.00902204	−	0.0126697i
$324$		0			0
$325$	−1.73936	−	5.02556i	−0.0964826	−	0.278768i
$326$		0			0
$327$	1.58087	−	3.46162i	0.0874223	−	0.191428i
$328$		0			0
$329$	0.0576444	+	1.21010i	0.00317804	+	0.0667152i
$330$		0			0
$331$	1.08624	+	4.47755i	0.0597052	+	0.246108i	0.993842	−	0.110807i	$-0.0353436\pi$
$331$	1.08624	+	4.47755i	0.0597052	+	0.246108i	−0.934137	+	0.356915i	$0.883828\pi$
$332$		0			0
$333$	−5.63428	−	4.43084i	−0.308756	−	0.242809i
$334$		0			0
$335$	17.0945	+	13.8979i	0.933972	+	0.759322i
$336$		0			0
$337$	−9.08847	−	7.14725i	−0.495080	−	0.389336i	0.339167	−	0.940726i	$-0.389855\pi$
$337$	−9.08847	−	7.14725i	−0.495080	−	0.389336i	−0.834247	+	0.551391i	$0.814097\pi$
$338$		0			0
$339$	0.699462	+	2.88322i	0.0379896	+	0.156595i
$340$		0			0
$341$	0.953855	+	20.0239i	0.0516542	+	1.08435i
$342$		0			0
$343$	1.71722	−	3.76020i	0.0927214	−	0.203032i
$344$		0			0
$345$	6.00763	+	17.3579i	0.323440	+	0.934519i
$346$		0			0
$347$	−10.7769	+	15.1341i	−0.578535	+	0.812439i	−0.995327	−	0.0965630i	$-0.969215\pi$
$347$	−10.7769	+	15.1341i	−0.578535	+	0.812439i	0.416792	+	0.909002i	$0.363154\pi$
$348$		0			0
$349$	8.64492	+	2.53838i	0.462752	+	0.135876i	0.504794	−	0.863240i	$-0.331568\pi$
$349$	8.64492	+	2.53838i	0.462752	+	0.135876i	−0.0420424	+	0.999116i	$0.513386\pi$
$350$		0			0
$351$	2.10610	−	1.08577i	0.112415	−	0.0579541i
$352$		0			0
$353$	−1.51712	+	1.44657i	−0.0807480	+	0.0769930i	−0.729378	−	0.684111i	$-0.760191\pi$
$353$	−1.51712	+	1.44657i	−0.0807480	+	0.0769930i	0.648630	+	0.761104i	$0.275342\pi$
$354$		0			0
$355$	−7.76514	+	22.4359i	−0.412131	+	1.19077i
$356$		0			0
$357$	1.28756	−	1.48593i	0.0681450	−	0.0786435i
$358$		0			0
$359$	14.4101	−	4.23118i	0.760535	−	0.223313i	0.121606	−	0.992578i	$-0.461196\pi$
$359$	14.4101	−	4.23118i	0.760535	−	0.223313i	0.638930	+	0.769265i	$0.279377\pi$
$360$		0			0
$361$	−13.7497	−	13.1103i	−0.723666	−	0.690014i
$362$		0			0
$363$	1.24731	+	1.75160i	0.0654666	+	0.0919349i
$364$		0			0
$365$	14.9254	−	25.8515i	0.781230	−	1.35313i
$366$		0			0
$367$	−15.8262	−	3.05024i	−0.826119	−	0.159221i	−0.241367	−	0.970434i	$-0.577596\pi$
$367$	−15.8262	−	3.05024i	−0.826119	−	0.159221i	−0.584751	+	0.811213i	$0.698808\pi$
$368$		0			0
$369$	1.23931	−	0.974601i	0.0645157	−	0.0507357i
$370$		0			0
$371$	−3.05891	+	0.292091i	−0.158811	+	0.0151646i
$372$		0			0
$373$	19.0432	+	32.9839i	0.986022	+	1.70784i	0.637306	+	0.770611i	$0.280049\pi$
$373$	19.0432	+	32.9839i	0.986022	+	1.70784i	0.348715	+	0.937229i	$0.386618\pi$
$374$		0			0
$375$	6.23947	−	4.00986i	0.322205	−	0.207068i
$376$		0			0
$377$	8.94564	+	19.5882i	0.460724	+	1.00884i
$378$		0			0
$379$	−15.9401	+	3.07219i	−0.818786	+	0.157808i	−0.581411	−	0.813610i	$-0.697499\pi$
$379$	−15.9401	+	3.07219i	−0.818786	+	0.157808i	−0.237375	+	0.971418i	$0.576287\pi$
$380$		0			0
$381$	−8.47880	−	4.37113i	−0.434382	−	0.223940i
$382$		0			0
$383$	18.7714	+	7.51492i	0.959172	+	0.383995i	0.797815	−	0.602902i	$-0.205989\pi$
$383$	18.7714	+	7.51492i	0.959172	+	0.383995i	0.161356	+	0.986896i	$0.448413\pi$
$384$		0			0
$385$	0.560915	−	2.31212i	0.0285869	−	0.117837i
$386$		0			0
$387$	−0.0135231	−	0.0940550i	−0.000687416	−	0.00478108i
$388$		0			0
$389$	−13.3604	−	1.27576i	−0.677398	−	0.0646837i	−0.249314	−	0.968423i	$-0.580205\pi$
$389$	−13.3604	−	1.27576i	−0.677398	−	0.0646837i	−0.428084	+	0.903739i	$0.640811\pi$
$390$		0			0
$391$	−2.14863	+	45.1053i	−0.108661	+	2.28107i
$392$		0			0
$393$	2.02167	−	14.0610i	0.101980	−	0.709285i
$394$		0			0
$395$	−0.213726	+	0.0855630i	−0.0107537	+	0.00430514i
$396$		0			0
$397$	23.3424	+	15.0012i	1.17152	+	0.752891i	0.973809	−	0.227369i	$-0.0730125\pi$
$397$	23.3424	+	15.0012i	1.17152	+	0.752891i	0.197712	+	0.980260i	$0.436649\pi$
$398$		0			0
$399$	0.00822042	+	0.00948687i	0.000411536	+	0.000474937i
$400$		0			0
$401$	14.9125			0.744694			0.372347	−	0.928094i	$-0.378553\pi$
$401$	14.9125			0.744694			0.372347	+	0.928094i	$0.378553\pi$
$402$		0			0
$403$	−15.9674			−0.795392
$404$		0			0
$405$	−1.76258	−	2.03413i	−0.0875834	−	0.101077i
$406$		0			0
$407$	−17.9381	−	11.5281i	−0.889160	−	0.571428i
$408$		0			0
$409$	−12.8898	+	5.16031i	−0.637361	+	0.255161i	−0.667760	−	0.744377i	$-0.732747\pi$
$409$	−12.8898	+	5.16031i	−0.637361	+	0.255161i	0.0303985	+	0.999538i	$0.490322\pi$
$410$		0			0
$411$	2.60732	−	18.1343i	0.128610	−	0.894501i
$412$		0			0
$413$	−0.0274289	+	0.575804i	−0.00134969	+	0.0283335i
$414$		0			0
$415$	16.8021	+	1.60440i	0.824782	+	0.0787571i
$416$		0			0
$417$	1.98733	+	13.8222i	0.0973200	+	0.676875i
$418$		0			0
$419$	−1.50817	+	6.21674i	−0.0736787	+	0.303708i	−0.996713	−	0.0810091i	$-0.974186\pi$
$419$	−1.50817	+	6.21674i	−0.0736787	+	0.303708i	0.923035	+	0.384717i	$0.125701\pi$
$420$		0			0
$421$	−10.9904	−	4.39989i	−0.535639	−	0.214437i	0.0880417	−	0.996117i	$-0.471939\pi$
$421$	−10.9904	−	4.39989i	−0.535639	−	0.214437i	−0.623680	+	0.781679i	$0.714363\pi$
$422$		0			0
$423$	3.62387	+	1.86823i	0.176198	+	0.0908366i
$424$		0			0
$425$	−14.5824	+	2.81053i	−0.707352	+	0.136331i
$426$		0			0
$427$	0.148074	+	0.324236i	0.00716578	+	0.0156909i
$428$		0			0
$429$	5.92991	−	3.81092i	0.286299	−	0.183993i
$430$		0			0
$431$	14.3244	+	24.8105i	0.689980	+	1.19508i	0.971844	+	0.235626i	$0.0757140\pi$
$431$	14.3244	+	24.8105i	0.689980	+	1.19508i	−0.281864	+	0.959454i	$0.590953\pi$
$432$		0			0
$433$	21.0509	−	2.01012i	1.01164	−	0.0966002i	0.423951	−	0.905685i	$-0.360643\pi$
$433$	21.0509	−	2.01012i	1.01164	−	0.0966002i	0.587692	+	0.809085i	$0.300037\pi$
$434$		0			0
$435$	19.2276	−	15.1207i	0.921891	−	0.724983i
$436$		0			0
$437$	−0.283091	−	0.0545612i	−0.0135421	−	0.00261002i
$438$		0			0
$439$	−19.3266	+	33.4747i	−0.922409	+	1.59766i	−0.126734	+	0.991937i	$0.540449\pi$
$439$	−19.3266	+	33.4747i	−0.922409	+	1.59766i	−0.795675	+	0.605723i	$0.792884\pi$
$440$		0			0
$441$	−4.00918	−	5.63011i	−0.190913	−	0.268100i
$442$		0			0
$443$	8.00732	+	7.63496i	0.380439	+	0.362748i	0.856037	−	0.516915i	$-0.172920\pi$
$443$	8.00732	+	7.63496i	0.380439	+	0.362748i	−0.475598	+	0.879663i	$0.657768\pi$
$444$		0			0
$445$	9.80328	−	2.87850i	0.464720	−	0.136454i
$446$		0			0
$447$	0.250295	−	0.288856i	0.0118386	−	0.0136624i
$448$		0			0
$449$	−9.91990	+	28.6617i	−0.468149	+	1.35263i	0.425945	+	0.904749i	$0.359942\pi$
$449$	−9.91990	+	28.6617i	−0.468149	+	1.35263i	−0.894094	+	0.447879i	$0.852180\pi$
$450$		0			0
$451$	3.39445	−	3.23660i	0.159838	−	0.152406i
$452$		0			0
$453$	−1.35038	+	0.696167i	−0.0634462	+	0.0327088i
$454$		0			0
$455$	1.81829	+	0.533899i	0.0852429	+	0.0250296i
$456$		0			0
$457$	−5.71117	+	8.02021i	−0.267157	+	0.375170i	−0.926261	−	0.376882i	$-0.876996\pi$
$457$	−5.71117	+	8.02021i	−0.267157	+	0.375170i	0.659104	+	0.752052i	$0.270936\pi$
$458$		0			0
$459$	−2.16418	−	6.25298i	−0.101015	−	0.291864i
$460$		0			0
$461$	−0.144120	+	0.315578i	−0.00671232	+	0.0146979i	−0.912958	−	0.408052i	$-0.866208\pi$
$461$	−0.144120	+	0.315578i	−0.00671232	+	0.0146979i	0.906246	+	0.422750i	$0.138935\pi$
$462$		0			0
$463$	1.06877	+	22.4362i	0.0496699	+	1.04270i	0.876851	+	0.480763i	$0.159640\pi$
$463$	1.06877	+	22.4362i	0.0496699	+	1.04270i	−0.827181	+	0.561936i	$0.810057\pi$
$464$		0			0
$465$	4.27607	+	17.6262i	0.198298	+	0.817396i
$466$		0			0
$467$	−4.61756	−	3.63129i	−0.213675	−	0.168036i	0.505585	−	0.862777i	$-0.331277\pi$
$467$	−4.61756	−	3.63129i	−0.213675	−	0.168036i	−0.719260	+	0.694741i	$0.755519\pi$
$468$		0			0
$469$	−2.34450	+	0.647290i	−0.108259	+	0.0298891i
$470$		0			0
$471$	9.65835	+	7.59541i	0.445033	+	0.349978i
$472$		0			0
$473$	−0.0666434	−	0.274708i	−0.00306427	−	0.0126311i
$474$		0			0
$475$	−0.00451147	−	0.0947073i	−0.000207000	−	0.00434547i
$476$		0			0
$477$	−4.29592	+	9.40674i	−0.196696	+	0.430705i
$478$		0			0
$479$	3.16234	+	9.13697i	0.144491	+	0.417479i	0.993904	−	0.110250i	$-0.0351651\pi$
$479$	3.16234	+	9.13697i	0.144491	+	0.417479i	−0.849413	+	0.527729i	$0.823044\pi$
$480$		0			0
$481$	9.85176	−	13.8349i	0.449202	−	0.630816i
$482$		0			0
$483$	−1.94568	−	0.571303i	−0.0885315	−	0.0259952i
$484$		0			0
$485$	−33.3865	+	17.2120i	−1.51600	+	0.781555i
$486$		0			0
$487$	−6.84929	+	6.53078i	−0.310371	+	0.295938i	−0.829214	−	0.558932i	$-0.811211\pi$
$487$	−6.84929	+	6.53078i	−0.310371	+	0.295938i	0.518843	+	0.854870i	$0.326363\pi$
$488$		0			0
$489$	6.34228	−	18.3248i	0.286808	−	0.828676i
$490$		0			0
$491$	−6.32110	+	7.29494i	−0.285267	+	0.329216i	−0.880239	−	0.474531i	$-0.842618\pi$
$491$	−6.32110	+	7.29494i	−0.285267	+	0.329216i	0.594972	+	0.803747i	$0.297163\pi$
$492$		0			0
$493$	57.6990	−	16.9420i	2.59863	−	0.763028i
$494$		0			0
$495$	−5.79487	−	5.52539i	−0.260460	−	0.248348i
$496$		0			0
$497$	−1.52036	−	2.13504i	−0.0681973	−	0.0957698i
$498$		0			0
$499$	−4.74041	+	8.21064i	−0.212210	+	0.367559i	−0.952406	−	0.304833i	$-0.901399\pi$
$499$	−4.74041	+	8.21064i	−0.212210	+	0.367559i	0.740196	+	0.672391i	$0.234733\pi$
$500$		0			0
$501$	15.0542	+	2.90145i	0.672570	+	0.129627i
$502$		0			0
$503$	−21.2390	+	16.7025i	−0.946999	+	0.744728i	−0.966922	−	0.255073i	$-0.917900\pi$
$503$	−21.2390	+	16.7025i	−0.946999	+	0.744728i	0.0199229	+	0.999802i	$0.493658\pi$
$504$		0			0
$505$	24.3383	−	2.32402i	1.08304	−	0.103418i
$506$		0			0
$507$	−3.69273	−	6.39599i	−0.164000	−	0.284056i
$508$		0			0
$509$	12.5107	−	8.04012i	0.554526	−	0.356372i	−0.233171	−	0.972436i	$-0.574910\pi$
$509$	12.5107	−	8.04012i	0.554526	−	0.356372i	0.787696	+	0.616064i	$0.211274\pi$
$510$		0			0
$511$	1.36899	+	2.99768i	0.0605607	+	0.132609i
$512$		0			0
$513$	0.0414821	−	0.00799501i	0.00183148	−	0.000352988i
$514$		0			0
$515$	−26.3055	−	13.5614i	−1.15916	−	0.597588i
$516$		0			0
$517$	11.2599	+	4.50779i	0.495210	+	0.198252i
$518$		0			0
$519$	2.97359	−	12.2573i	0.130526	−	0.538036i
$520$		0			0
$521$	−0.131499	−	0.914597i	−0.00576109	−	0.0400692i	0.986738	−	0.162320i	$-0.0518978\pi$
$521$	−0.131499	−	0.914597i	−0.00576109	−	0.0400692i	−0.992499	+	0.122251i	$0.960989\pi$
$522$		0			0
$523$	−43.9974	−	4.20124i	−1.92387	−	0.183707i	−0.937471	−	0.348064i	$-0.886839\pi$
$523$	−43.9974	−	4.20124i	−1.92387	−	0.183707i	−0.986401	+	0.164357i	$0.947445\pi$
$524$		0			0
$525$	0.0317323	−	0.666143i	0.00138491	−	0.0290729i
$526$		0			0
$527$	−6.34573	+	44.1355i	−0.276424	+	1.92257i
$528$		0			0
$529$	21.8840	−	8.76103i	0.951478	−	0.380915i
$530$		0			0
$531$	1.63204	+	1.04885i	0.0708243	+	0.0455160i
$532$		0			0
$533$	2.44643	+	2.82333i	0.105967	+	0.122292i
$534$		0			0
$535$	48.0670			2.07812
$536$		0			0
$537$	3.21316			0.138658
$538$		0			0
$539$	−13.4647	−	15.5391i	−0.579968	−	0.669318i
$540$		0			0
$541$	−4.94705	−	3.17928i	−0.212690	−	0.136688i	0.429959	−	0.902849i	$-0.358528\pi$
$541$	−4.94705	−	3.17928i	−0.212690	−	0.136688i	−0.642649	+	0.766161i	$0.722165\pi$
$542$		0			0
$543$	−7.30344	+	2.92385i	−0.313420	+	0.125475i
$544$		0			0
$545$	1.45769	−	10.1384i	0.0624405	−	0.434283i
$546$		0			0
$547$	0.321351	−	6.74599i	0.0137400	−	0.288438i	−0.981531	−	0.191302i	$-0.938729\pi$
$547$	0.321351	−	6.74599i	0.0137400	−	0.288438i	0.995271	−	0.0971354i	$-0.0309680\pi$
$548$		0			0
$549$	1.19415	+	0.114028i	0.0509652	+	0.00486659i
$550$		0			0
$551$	0.0546390	+	0.380023i	0.00232770	+	0.0161895i
$552$		0			0
$553$	0.00599197	−	0.0246992i	0.000254804	−	0.00105032i
$554$		0			0
$555$	−17.9105	−	7.17027i	−0.760257	−	0.304361i
$556$		0			0
$557$	−11.1265	−	5.73612i	−0.471446	−	0.243047i	0.206096	−	0.978532i	$-0.433924\pi$
$557$	−11.1265	−	5.73612i	−0.471446	−	0.243047i	−0.677541	+	0.735485i	$0.736955\pi$
$558$		0			0
$559$	0.221086	−	0.0426109i	0.00935096	−	0.00180225i
$560$		0			0
$561$	−8.17713	−	17.9054i	−0.345239	−	0.755967i
$562$		0			0
$563$	24.9620	−	16.0421i	1.05202	−	0.676094i	0.104091	−	0.994568i	$-0.466807\pi$
$563$	24.9620	−	16.0421i	1.05202	−	0.676094i	0.947932	+	0.318474i	$0.103170\pi$
$564$		0			0
$565$	3.99270	+	6.91556i	0.167974	+	0.290940i
$566$		0			0
$567$	0.295797	−	0.0282452i	0.0124223	−	0.00118619i
$568$		0			0
$569$	−4.46152	+	3.50858i	−0.187037	+	0.147087i	−0.707287	−	0.706927i	$-0.750081\pi$
$569$	−4.46152	+	3.50858i	−0.187037	+	0.147087i	0.520250	+	0.854014i	$0.325839\pi$
$570$		0			0
$571$	−33.7473	−	6.50425i	−1.41228	−	0.272194i	−0.574634	−	0.818410i	$-0.694856\pi$
$571$	−33.7473	−	6.50425i	−1.41228	−	0.272194i	−0.837645	+	0.546216i	$0.816068\pi$
$572$		0			0
$573$	0.877378	−	1.51966i	0.0366530	−	0.0634849i
$574$		0			0
$575$	8.88446	+	12.4765i	0.370508	+	0.520305i
$576$		0			0
$577$	−12.6343	−	12.0467i	−0.525971	−	0.501513i	0.379922	−	0.925018i	$-0.375951\pi$
$577$	−12.6343	−	12.0467i	−0.525971	−	0.501513i	−0.905893	+	0.423506i	$0.860799\pi$
$578$		0			0
$579$	−0.504746	+	0.148207i	−0.0209765	+	0.00615927i
$580$		0			0
$581$	−1.22024	+	1.40824i	−0.0506243	+	0.0584235i
$582$		0			0
$583$	−10.0618	+	29.0716i	−0.416717	+	1.20402i
$584$		0			0
$585$	4.61569	−	4.40105i	0.190835	−	0.181961i
$586$		0			0
$587$	−1.41461	+	0.729281i	−0.0583871	+	0.0301006i	−0.487173	−	0.873306i	$-0.661972\pi$
$587$	−1.41461	+	0.729281i	−0.0583871	+	0.0301006i	0.428786	+	0.903406i	$0.358942\pi$
$588$		0			0
$589$	−0.273149	−	0.0802037i	−0.0112549	−	0.00330473i
$590$		0			0
$591$	7.24121	−	10.1689i	0.297863	−	0.418291i
$592$		0			0
$593$	1.74353	+	5.03759i	0.0715980	+	0.206869i	0.975122	−	0.221668i	$-0.0711502\pi$
$593$	1.74353	+	5.03759i	0.0715980	+	0.206869i	−0.903524	+	0.428537i	$0.859029\pi$
$594$		0			0
$595$	2.19838	−	4.81377i	0.0901246	−	0.197345i
$596$		0			0
$597$	0.330902	+	6.94649i	0.0135429	+	0.284301i
$598$		0			0
$599$	1.85595	+	7.65034i	0.0758322	+	0.312584i	0.997077	−	0.0763978i	$-0.0243419\pi$
$599$	1.85595	+	7.65034i	0.0758322	+	0.312584i	−0.921245	+	0.388982i	$0.872827\pi$
$600$		0			0
$601$	−13.2581	−	10.4263i	−0.540808	−	0.425296i	0.310028	−	0.950727i	$-0.399662\pi$
$601$	−13.2581	−	10.4263i	−0.540808	−	0.425296i	−0.850836	+	0.525431i	$0.823904\pi$
$602$		0			0
$603$	−2.05854	+	7.92227i	−0.0838304	+	0.322620i
$604$		0			0
$605$	4.54941	+	3.57769i	0.184960	+	0.145454i
$606$		0			0
$607$	−4.98495	−	20.5483i	−0.202333	−	0.834028i	−0.978957	−	0.204064i	$-0.934585\pi$
$607$	−4.98495	−	20.5483i	−0.202333	−	0.834028i	0.776624	−	0.629964i	$-0.216930\pi$
$608$		0			0
$609$	0.128493	+	2.69739i	0.00520679	+	0.109304i
$610$		0			0
$611$	−4.01319	+	8.78767i	−0.162356	+	0.355511i
$612$		0			0
$613$	−11.9400	−	34.4984i	−0.482252	−	1.39338i	−0.879602	−	0.475710i	$-0.842191\pi$
$613$	−11.9400	−	34.4984i	−0.482252	−	1.39338i	0.397350	−	0.917667i	$-0.369930\pi$
$614$		0			0
$615$	2.46149	−	3.45668i	0.0992568	−	0.139387i
$616$		0			0
$617$	−35.8824	−	10.5360i	−1.44457	−	0.424165i	−0.536829	−	0.843691i	$-0.680378\pi$
$617$	−35.8824	−	10.5360i	−1.44457	−	0.424165i	−0.907743	+	0.419526i	$0.862196\pi$
$618$		0			0
$619$	−4.39433	+	2.26543i	−0.176623	+	0.0910555i	−0.544271	−	0.838910i	$-0.683194\pi$
$619$	−4.39433	+	2.26543i	−0.176623	+	0.0910555i	0.367648	+	0.929965i	$0.380163\pi$
$620$		0			0
$621$	−4.93906	+	4.70938i	−0.198198	+	0.188981i
$622$		0			0
$623$	−0.368920	+	1.06592i	−0.0147805	+	0.0427053i
$624$		0			0
$625$	20.4216	−	23.5678i	0.816864	−	0.942712i
$626$		0			0
$627$	0.120583	−	0.0354064i	0.00481562	−	0.00141399i
$628$		0			0
$629$	−34.3257	−	32.7295i	−1.36866	−	1.30501i
$630$		0			0
$631$	−21.9484	−	30.8222i	−0.873751	−	1.22701i	−0.972734	−	0.231922i	$-0.925498\pi$
$631$	−21.9484	−	30.8222i	−0.873751	−	1.22701i	0.0989835	−	0.995089i	$-0.468441\pi$
$632$		0			0
$633$	10.8544	−	18.8004i	0.431425	−	0.747250i
$634$		0			0
$635$	−25.2112	−	4.85906i	−1.00048	−	0.192826i
$636$		0			0
$637$	12.8734	−	10.1238i	0.510064	−	0.401119i
$638$		0			0
$639$	−8.78091	+	0.838475i	−0.347367	+	0.0331696i
$640$		0			0
$641$	3.55679	+	6.16053i	0.140485	+	0.243326i	0.927679	−	0.373378i	$-0.121801\pi$
$641$	3.55679	+	6.16053i	0.140485	+	0.243326i	−0.787195	+	0.616705i	$0.788467\pi$
$642$		0			0
$643$	−9.32470	+	5.99262i	−0.367730	+	0.236326i	−0.711435	−	0.702752i	$-0.751954\pi$
$643$	−9.32470	+	5.99262i	−0.367730	+	0.236326i	0.343705	+	0.939078i	$0.388318\pi$
$644$		0			0
$645$	−0.106245	−	0.232644i	−0.00418338	−	0.00916034i
$646$		0			0
$647$	−6.59795	+	1.27165i	−0.259392	+	0.0499937i	−0.317289	−	0.948329i	$-0.602773\pi$
$647$	−6.59795	+	1.27165i	−0.259392	+	0.0499937i	0.0578971	+	0.998323i	$0.481560\pi$
$648$		0			0
$649$	5.12965	+	2.64452i	0.201356	+	0.103806i
$650$		0			0
$651$	−1.85892	−	0.744200i	−0.0728569	−	0.0291675i
$652$		0			0
$653$	5.64483	−	23.2683i	0.220899	−	0.910559i	−0.748118	−	0.663566i	$-0.769042\pi$
$653$	5.64483	−	23.2683i	0.220899	−	0.910559i	0.969017	−	0.246993i	$-0.0794426\pi$
$654$		0			0
$655$	−5.44140	−	37.8458i	−0.212613	−	1.47876i
$656$		0			0
$657$	11.0404	+	1.05423i	0.430726	+	0.0411294i
$658$		0			0
$659$	0.116293	−	2.44129i	0.00453013	−	0.0950992i	−0.995470	−	0.0950776i	$-0.969690\pi$
$659$	0.116293	−	2.44129i	0.00453013	−	0.0950992i	1.00000		2.16420e-5i	$-6.88887e-6\pi$
$660$		0			0
$661$	−6.57117	+	45.7035i	−0.255589	+	1.77766i	0.307782	+	0.951457i	$0.400413\pi$
$661$	−6.57117	+	45.7035i	−0.255589	+	1.77766i	−0.563371	+	0.826204i	$0.690496\pi$
$662$		0			0
$663$	14.5557	−	5.82721i	0.565295	−	0.226310i
$664$		0			0
$665$	0.0284232	+	0.0182665i	0.00110220	+	0.000708343i
$666$		0			0
$667$	−40.6150	−	46.8722i	−1.57262	−	1.81490i
$668$		0			0
$669$	21.5245			0.832185
$670$		0			0
$671$	3.56857			0.137763
$672$		0			0
$673$	27.1195	+	31.2975i	1.04538	+	1.20643i	0.977979	+	0.208705i	$0.0669248\pi$
$673$	27.1195	+	31.2975i	1.04538	+	1.20643i	0.0673997	+	0.997726i	$0.478530\pi$
$674$		0			0
$675$	−1.88809	−	1.21340i	−0.0726726	−	0.0467038i
$676$		0			0
$677$	38.0618	−	15.2377i	1.46284	−	0.585631i	0.502525	−	0.864563i	$-0.332405\pi$
$677$	38.0618	−	15.2377i	1.46284	−	0.585631i	0.960311	+	0.278932i	$0.0899804\pi$
$678$		0			0
$679$	0.590153	−	4.10460i	0.0226480	−	0.157520i
$680$		0			0
$681$	−0.443538	+	9.31100i	−0.0169964	+	0.356798i
$682$		0			0
$683$	−19.1149	−	1.82525i	−0.731411	−	0.0698413i	−0.277296	−	0.960784i	$-0.589438\pi$
$683$	−19.1149	−	1.82525i	−0.731411	−	0.0698413i	−0.454115	+	0.890943i	$0.650044\pi$
$684$		0			0
$685$	−7.01771	−	48.8092i	−0.268133	−	1.86490i
$686$		0			0
$687$	−1.86562	+	7.69020i	−0.0711779	+	0.293399i
$688$		0			0
$689$	−22.7484	−	9.10709i	−0.866645	−	0.346952i
$690$		0			0
$691$	−4.23109	−	2.18128i	−0.160958	−	0.0829798i	0.375865	−	0.926674i	$-0.377346\pi$
$691$	−4.23109	−	2.18128i	−0.160958	−	0.0829798i	−0.536823	+	0.843695i	$0.680376\pi$
$692$		0			0
$693$	0.867977	−	0.167289i	0.0329717	−	0.00635478i
$694$		0			0
$695$	15.6136	+	34.1890i	0.592257	+	1.29686i
$696$		0			0
$697$	8.77624	−	5.64015i	0.332424	−	0.213636i
$698$		0			0
$699$	9.91139	+	17.1670i	0.374883	+	0.649317i
$700$		0			0
$701$	12.4905	−	1.19269i	0.471758	−	0.0450475i	0.143530	−	0.989646i	$-0.454155\pi$
$701$	12.4905	−	1.19269i	0.471758	−	0.0450475i	0.328228	+	0.944598i	$0.393549\pi$
$702$		0			0
$703$	0.238023	−	0.187183i	0.00897720	−	0.00705975i
$704$		0			0
$705$	10.7753	+	2.07678i	0.405823	+	0.0782159i
$706$		0			0
$707$	−1.34957	+	2.33752i	−0.0507557	+	0.0879114i
$708$		0			0
$709$	2.17964	+	3.06088i	0.0818582	+	0.114954i	0.853475	−	0.521134i	$-0.174491\pi$
$709$	2.17964	+	3.06088i	0.0818582	+	0.114954i	−0.771617	+	0.636088i	$0.780552\pi$
$710$		0			0
$711$	−0.0619036	−	0.0590249i	−0.00232157	−	0.00221361i
$712$		0			0
$713$	44.1249	−	12.9562i	1.65249	−	0.485215i
$714$		0			0
$715$	12.4243	−	14.3384i	0.464641	−	0.536224i
$716$		0			0
$717$	−5.15295	+	14.8885i	−0.192440	+	0.556020i
$718$		0			0
$719$	−6.32323	+	6.02919i	−0.235817	+	0.224851i	−0.798768	−	0.601639i	$-0.794514\pi$
$719$	−6.32323	+	6.02919i	−0.235817	+	0.224851i	0.562951	+	0.826490i	$0.309666\pi$
$720$		0			0
$721$	2.90409	−	1.49716i	0.108154	−	0.0557573i
$722$		0			0
$723$	−6.81463	−	2.00095i	−0.253439	−	0.0744163i
$724$		0			0
$725$	11.8315	−	16.6149i	0.439409	−	0.617064i
$726$		0			0
$727$	5.83749	+	16.8663i	0.216501	+	0.625538i	0.999991	+	0.00413415i	$0.00131594\pi$
$727$	5.83749	+	16.8663i	0.216501	+	0.625538i	−0.783491	+	0.621403i	$0.786563\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−0.0299173	−	0.628040i	−0.00110653	−	0.0232289i
$732$		0			0
$733$	−8.60731	−	35.4798i	−0.317918	−	1.31048i	−0.876650	−	0.481128i	$-0.840227\pi$
$733$	−8.60731	−	35.4798i	−0.317918	−	1.31048i	0.558732	−	0.829348i	$-0.311288\pi$
$734$		0			0
$735$	−14.6230	−	11.4997i	−0.539379	−	0.424172i
$736$		0			0
$737$	−3.85588	+	24.0429i	−0.142033	+	0.885632i
$738$		0			0
$739$	−32.1761	−	25.3035i	−1.18362	−	0.930806i	−0.184966	−	0.982745i	$-0.559218\pi$
$739$	−32.1761	−	25.3035i	−1.18362	−	0.930806i	−0.998650	+	0.0519388i	$0.983460\pi$
$740$		0			0
$741$	0.0235997	+	0.0972791i	0.000866955	+	0.00357364i
$742$		0			0
$743$	1.55407	+	32.6240i	0.0570134	+	1.19686i	0.828268	+	0.560332i	$0.189326\pi$
$743$	1.55407	+	32.6240i	0.0570134	+	1.19686i	−0.771255	+	0.636527i	$0.780371\pi$
$744$		0			0
$745$	0.427353	−	0.935772i	0.0156570	−	0.0342840i
$746$		0			0
$747$	2.05103	+	5.92606i	0.0750432	+	0.216823i
$748$		0			0
$749$	−3.07809	+	4.32257i	−0.112471	+	0.157943i
$750$		0			0
$751$	26.0880	+	7.66011i	0.951963	+	0.279522i	0.720604	−	0.693347i	$-0.243865\pi$
$751$	26.0880	+	7.66011i	0.951963	+	0.279522i	0.231359	+	0.972868i	$0.425683\pi$
$752$		0			0
$753$	17.1520	−	8.84247i	0.625053	−	0.322237i
$754$		0			0
$755$	−2.95946	+	2.82184i	−0.107706	+	0.102697i
$756$		0			0
$757$	15.3664	−	44.3984i	0.558502	−	1.61369i	−0.212715	−	0.977114i	$-0.568231\pi$
$757$	15.3664	−	44.3984i	0.558502	−	1.61369i	0.771217	−	0.636572i	$-0.219648\pi$
$758$		0			0
$759$	−13.2947	+	15.3429i	−0.482566	+	0.556911i
$760$		0			0
$761$	−34.9199	+	10.2534i	−1.26585	+	0.371686i	−0.844668	−	0.535291i	$-0.820202\pi$
$761$	−34.9199	+	10.2534i	−1.26585	+	0.371686i	−0.421179	+	0.906977i	$0.638384\pi$
$762$		0			0
$763$	0.818384	+	0.780328i	0.0296275	+	0.0282498i
$764$		0			0
$765$	−10.3306	−	14.5073i	−0.373504	−	0.524513i
$766$		0			0
$767$	−2.29842	+	3.98098i	−0.0829912	+	0.143745i
$768$		0			0
$769$	16.8482	+	3.24722i	0.607560	+	0.117098i	0.483747	−	0.875208i	$-0.339276\pi$
$769$	16.8482	+	3.24722i	0.607560	+	0.117098i	0.123813	+	0.992306i	$0.460488\pi$
$770$		0			0
$771$	−19.1847	+	15.0870i	−0.690921	+	0.543346i
$772$		0			0
$773$	0.392881	−	0.0375156i	0.0141309	−	0.00134934i	−0.0879882	−	0.996122i	$-0.528044\pi$
$773$	0.392881	−	0.0375156i	0.0141309	−	0.00134934i	0.102119	+	0.994772i	$0.467438\pi$
$774$		0			0
$775$	7.56209	+	13.0979i	0.271638	+	0.470492i
$776$		0			0
$777$	1.79175	−	1.15149i	0.0642787	−	0.0413094i
$778$		0			0
$779$	0.0276687	+	0.0605861i	0.000991336	+	0.00217072i
$780$		0			0
$781$	−25.7664	+	4.96607i	−0.921996	+	0.177700i
$782$		0			0
$783$	8.07781	+	4.16440i	0.288677	+	0.148823i
$784$		0			0
$785$	30.7024	+	12.2914i	1.09581	+	0.438698i
$786$		0			0
$787$	0.964821	−	3.97704i	0.0343921	−	0.141766i	−0.952027	−	0.306014i	$-0.901005\pi$
$787$	0.964821	−	3.97704i	0.0343921	−	0.141766i	0.986419	+	0.164248i	$0.0525197\pi$
$788$		0			0
$789$	3.02625	+	21.0480i	0.107737	+	0.749329i
$790$		0			0
$791$	−0.877586	−	0.0837993i	−0.0312034	−	0.00297956i
$792$		0			0
$793$	−0.135248	+	2.83920i	−0.00480279	+	0.100823i
$794$		0			0
$795$	−3.96118	+	27.5506i	−0.140488	+	0.977119i
$796$		0			0
$797$	30.9417	−	12.3872i	1.09601	−	0.438776i	0.248002	−	0.968760i	$-0.420226\pi$
$797$	30.9417	−	12.3872i	1.09601	−	0.438776i	0.848008	+	0.529984i	$0.177802\pi$
$798$		0			0
$799$	22.6951	+	14.5853i	0.802895	+	0.515989i
$800$		0			0
$801$	2.48587	+	2.86885i	0.0878339	+	0.101366i
$802$		0			0
$803$	32.9928			1.16429
$804$		0			0
$805$	−5.45796			−0.192368
$806$		0			0
$807$	−3.94129	−	4.54849i	−0.138740	−	0.160114i
$808$		0			0
$809$	−26.9062	−	17.2915i	−0.945971	−	0.607938i	−0.0258889	−	0.999665i	$-0.508242\pi$
$809$	−26.9062	−	17.2915i	−0.945971	−	0.607938i	−0.920082	+	0.391726i	$0.871878\pi$
$810$		0			0
$811$	4.82014	−	1.92969i	0.169258	−	0.0677607i	−0.285486	−	0.958383i	$-0.592155\pi$
$811$	4.82014	−	1.92969i	0.169258	−	0.0677607i	0.454744	+	0.890622i	$0.349731\pi$
$812$		0			0
$813$	3.00031	−	20.8676i	0.105225	−	0.731859i
$814$		0			0
$815$	2.48342	−	52.1333i	0.0869903	−	1.82615i
$816$		0			0
$817$	0.00399608		0.000381580i	0.000139805		1.33498e-5i
$818$		0			0
$819$	0.100201	+	0.696913i	0.00350130	+	0.0243521i
$820$		0			0
$821$	2.19070	−	9.03018i	0.0764559	−	0.315155i	−0.920723	−	0.390217i	$-0.872400\pi$
$821$	2.19070	−	9.03018i	0.0764559	−	0.315155i	0.997179	+	0.0750613i	$0.0239152\pi$
$822$		0			0
$823$	40.0054	+	16.0157i	1.39450	+	0.558274i	0.942639	−	0.333815i	$-0.108336\pi$
$823$	40.0054	+	16.0157i	1.39450	+	0.558274i	0.451861	+	0.892088i	$0.350760\pi$
$824$		0			0
$825$	−5.93445	−	3.05942i	−0.206611	−	0.106515i
$826$		0			0
$827$	15.3488	−	2.95824i	0.533730	−	0.102868i	0.0847369	−	0.996403i	$-0.472995\pi$
$827$	15.3488	−	2.95824i	0.533730	−	0.102868i	0.448993	+	0.893535i	$0.351783\pi$
$828$		0			0
$829$	9.25526	+	20.2662i	0.321448	+	0.703874i	0.999515	−	0.0311263i	$-0.00990939\pi$
$829$	9.25526	+	20.2662i	0.321448	+	0.703874i	−0.678067	+	0.735000i	$0.737182\pi$
$830$		0			0
$831$	−14.5496	+	9.35046i	−0.504720	+	0.324364i
$832$		0			0
$833$	−22.8670	−	39.6069i	−0.792296	−	1.37230i
$834$		0			0
$835$	41.0777	−	3.92244i	1.42155	−	0.135742i
$836$		0			0
$837$	−5.29698	+	4.16559i	−0.183091	+	0.143984i
$838$		0			0
$839$	−9.81311	−	1.89132i	−0.338786	−	0.0652957i	0.0170208	−	0.999855i	$-0.494582\pi$
$839$	−9.81311	−	1.89132i	−0.338786	−	0.0652957i	−0.355807	+	0.934559i	$0.615794\pi$
$840$		0			0
$841$	−26.7966	+	46.4130i	−0.924020	+	1.60045i
$842$		0			0
$843$	−18.0436	−	25.3387i	−0.621455	−	0.872711i
$844$		0			0
$845$	−14.3866	−	13.7176i	−0.494913	−	0.471898i
$846$		0			0
$847$	−0.613068	+	0.180013i	−0.0210653	+	0.00618532i
$848$		0			0
$849$	16.6542	−	19.2199i	0.571570	−	0.659626i
$850$		0			0
$851$	−15.9989	+	46.2257i	−0.548434	+	1.58460i
$852$		0			0
$853$	−0.680129	+	0.648502i	−0.0232872	+	0.0222043i	−0.701633	−	0.712538i	$-0.747546\pi$
$853$	−0.680129	+	0.648502i	−0.0232872	+	0.0222043i	0.678346	+	0.734743i	$0.262697\pi$
$854$		0			0
$855$	0.101065	−	0.0521028i	0.00345636	−	0.00178188i
$856$		0			0
$857$	46.8810	+	13.7655i	1.60142	+	0.470221i	0.955942	−	0.293554i	$-0.0948382\pi$
$857$	46.8810	+	13.7655i	1.60142	+	0.470221i	0.645482	+	0.763775i	$0.276656\pi$
$858$		0			0
$859$	28.3454	−	39.8056i	0.967133	−	1.35815i	0.0336861	−	0.999432i	$-0.489275\pi$
$859$	28.3454	−	39.8056i	0.967133	−	1.35815i	0.933447	−	0.358716i	$-0.116785\pi$
$860$		0			0
$861$	0.153225	+	0.442714i	0.00522189	+	0.0150877i
$862$		0			0
$863$	11.5298	−	25.2467i	0.392479	−	0.859408i	−0.605499	−	0.795846i	$-0.707027\pi$
$863$	11.5298	−	25.2467i	0.392479	−	0.859408i	0.997978	−	0.0635623i	$-0.0202462\pi$
$864$		0			0
$865$	−1.61531	−	33.9095i	−0.0549222	−	1.15296i
$866$		0			0
$867$	−6.31443	−	26.0284i	−0.214449	−	0.883971i
$868$		0			0
$869$	−0.200010	−	0.157290i	−0.00678489	−	0.00533569i
$870$		0			0
$871$	−18.9827	−	3.97900i	−0.643203	−	0.134823i
$872$		0			0
$873$	−10.9699	−	8.62680i	−0.371274	−	0.291973i
$874$		0			0
$875$	0.519581	+	2.14174i	0.0175650	+	0.0724041i
$876$		0			0
$877$	1.23303	+	25.8844i	0.0416363	+	0.874054i	0.919007	+	0.394241i	$0.128992\pi$
$877$	1.23303	+	25.8844i	0.0416363	+	0.874054i	−0.877371	+	0.479813i	$0.840705\pi$
$878$		0			0
$879$	4.05857	−	8.88703i	0.136892	−	0.299752i
$880$		0			0
$881$	8.83422	+	25.5248i	0.297632	+	0.859952i	0.990331	+	0.138725i	$0.0443004\pi$
$881$	8.83422	+	25.5248i	0.297632	+	0.859952i	−0.692699	+	0.721227i	$0.743578\pi$
$882$		0			0
$883$	6.51293	−	9.14614i	0.219178	−	0.307792i	−0.690317	−	0.723507i	$-0.742529\pi$
$883$	6.51293	−	9.14614i	0.219178	−	0.307792i	0.909495	+	0.415715i	$0.136469\pi$
$884$		0			0
$885$	5.01008	+	1.47109i	0.168412	+	0.0494503i
$886$		0			0
$887$	−6.26679	+	3.23076i	−0.210418	+	0.108478i	−0.560214	−	0.828348i	$-0.689281\pi$
$887$	−6.26679	+	3.23076i	−0.210418	+	0.108478i	0.349796	+	0.936826i	$0.386251\pi$
$888$		0			0
$889$	2.05143	−	1.95603i	0.0688028	−	0.0656033i
$890$		0			0
$891$	0.972975	−	2.81123i	0.0325959	−	0.0941797i
$892$		0			0
$893$	−0.112792	+	0.130169i	−0.00377446	+	0.00435595i
$894$		0			0
$895$	8.29802	−	2.43652i	0.277372	−	0.0814439i
$896$		0			0
$897$	−11.7031	−	11.1589i	−0.390755	−	0.372585i
$898$		0			0
$899$	−35.5238	−	49.8862i	−1.18478	−	1.66380i
$900$		0			0
$901$	−34.2136	+	59.2596i	−1.13982	+	1.97422i
$902$		0			0
$903$	0.0277249	+	0.00534353i	0.000922626	+	0.000177822i
$904$		0			0
$905$	−16.6441	+	13.0890i	−0.553267	+	0.435094i
$906$		0			0
$907$	−10.9201	+	1.04274i	−0.362595	+	0.0346236i	−0.274764	−	0.961512i	$-0.588600\pi$
$907$	−10.9201	+	1.04274i	−0.362595	+	0.0346236i	−0.0878310	+	0.996135i	$0.527994\pi$
$908$		0			0
$909$	4.54182	+	7.86666i	0.150643	+	0.260921i
$910$		0			0
$911$	−42.0802	+	27.0433i	−1.39418	+	0.895985i	−0.999737	−	0.0229362i	$-0.992699\pi$
$911$	−42.0802	+	27.0433i	−1.39418	+	0.895985i	−0.394442	+	0.918921i	$0.629062\pi$
$912$		0			0
$913$	7.74961	+	16.9693i	0.256474	+	0.561601i
$914$		0			0
$915$	3.17038	−	0.611041i	0.104810	−	0.0202004i
$916$		0			0
$917$	3.75186	+	1.93422i	0.123897	+	0.0638734i
$918$		0			0
$919$	21.8559	+	8.74980i	0.720961	+	0.288629i	0.702981	−	0.711209i	$-0.251852\pi$
$919$	21.8559	+	8.74980i	0.720961	+	0.288629i	0.0179806	+	0.999838i	$0.494276\pi$
$920$		0			0
$921$	−2.64513	+	10.9034i	−0.0871601	+	0.359279i
$922$		0			0
$923$	−2.97453	−	20.6883i	−0.0979077	−	0.680963i
$924$		0			0
$925$	−16.0144	−	1.52919i	−0.526550	−	0.0502794i
$926$		0			0
$927$	0.523199	−	10.9833i	0.0171841	−	0.360739i
$928$		0			0
$929$	6.84583	−	47.6138i	0.224604	−	1.56216i	−0.495696	−	0.868496i	$-0.665087\pi$
$929$	6.84583	−	47.6138i	0.224604	−	1.56216i	0.720301	−	0.693662i	$-0.244004\pi$
$930$		0			0
$931$	0.271073	−	0.108521i	0.00888405	−	0.00355664i
$932$		0			0
$933$	−10.0090	−	6.43238i	−0.327679	−	0.210587i
$934$		0			0
$935$	−34.6951	−	40.0403i	−1.13465	−	1.30946i
$936$		0			0
$937$	−51.5491			−1.68404			−0.842018	−	0.539450i	$-0.818632\pi$
$937$	−51.5491			−1.68404			−0.842018	+	0.539450i	$0.818632\pi$
$938$		0			0
$939$	32.4125			1.05774
$940$		0			0
$941$	−11.4535	−	13.2181i	−0.373375	−	0.430898i	0.537701	−	0.843135i	$-0.319293\pi$
$941$	−11.4535	−	13.2181i	−0.373375	−	0.430898i	−0.911076	+	0.412238i	$0.864747\pi$
$942$		0			0
$943$	−9.05146	−	5.81702i	−0.294756	−	0.189428i
$944$		0			0
$945$	0.742480	−	0.297244i	0.0241529	−	0.00966936i
$946$		0			0
$947$	−2.61268	+	18.1716i	−0.0849008	+	0.590498i	0.902311	+	0.431085i	$0.141869\pi$
$947$	−2.61268	+	18.1716i	−0.0849008	+	0.590498i	−0.987212	+	0.159413i	$0.949040\pi$
$948$		0			0
$949$	−1.25041	+	26.2494i	−0.0405902	+	0.852093i
$950$		0			0
$951$	−25.2325	−	2.40941i	−0.818218	−	0.0781304i
$952$		0			0
$953$	4.37120	+	30.4024i	0.141597	+	0.984830i	0.929445	+	0.368960i	$0.120286\pi$
$953$	4.37120	+	30.4024i	0.141597	+	0.984830i	−0.787848	+	0.615870i	$0.788805\pi$
$954$		0			0
$955$	1.11349	−	4.58986i	0.0360316	−	0.148524i
$956$		0			0
$957$	25.0990	+	10.0481i	0.811335	+	0.324809i
$958$		0			0
$959$	4.83872	+	2.49453i	0.156250	+	0.0805527i
$960$		0			0
$961$	14.1498	−	2.72715i	0.456445	−	0.0879725i
$962$		0			0
$963$	7.41871	+	16.2447i	0.239065	+	0.523479i
$964$		0			0
$965$	−1.19113	+	0.765492i	−0.0383438	+	0.0246421i
$966$		0			0
$967$	−9.97372	−	17.2750i	−0.320733	−	0.555526i	0.659906	−	0.751348i	$-0.270596\pi$
$967$	−9.97372	−	17.2750i	−0.320733	−	0.555526i	−0.980640	+	0.195822i	$0.937263\pi$
$968$		0			0
$969$	0.278269	−	0.0265714i	0.00893928	−	0.000853597i
$970$		0			0
$971$	29.9158	−	23.5261i	0.960045	−	0.754987i	−0.00948664	−	0.999955i	$-0.503020\pi$
$971$	29.9158	−	23.5261i	0.960045	−	0.754987i	0.969531	+	0.244968i	$0.0787773\pi$
$972$		0			0
$973$	−4.07441	−	0.785277i	−0.130619	−	0.0251748i
$974$		0			0
$975$	2.65903	−	4.60557i	0.0851570	−	0.147496i
$976$		0			0
$977$	31.4196	+	44.1227i	1.00520	+	1.41161i	0.909263	+	0.416222i	$0.136646\pi$
$977$	31.4196	+	44.1227i	1.00520	+	1.41161i	0.0959395	+	0.995387i	$0.469414\pi$
$978$		0			0
$979$	8.17282	+	7.79277i	0.261205	+	0.249058i
$980$		0			0
$981$	3.65137	−	1.07214i	0.116579	−	0.0342307i
$982$		0			0
$983$	34.1410	−	39.4008i	1.08893	−	1.25669i	0.124536	−	0.992215i	$-0.460256\pi$
$983$	34.1410	−	39.4008i	1.08893	−	1.25669i	0.964393	−	0.264475i	$-0.0851987\pi$
$984$		0			0
$985$	10.9895	−	31.7521i	0.350155	−	1.01171i
$986$		0			0
$987$	−0.876787	+	0.836015i	−0.0279084	+	0.0266106i
$988$		0			0
$989$	−0.576383	+	0.297146i	−0.0183279	+	0.00944870i
$990$		0			0
$991$	−35.7653	−	10.5016i	−1.13612	−	0.333595i	−0.341011	−	0.940059i	$-0.610769\pi$
$991$	−35.7653	−	10.5016i	−1.13612	−	0.333595i	−0.795111	+	0.606464i	$0.792587\pi$
$992$		0			0
$993$	−2.67257	+	3.75309i	−0.0848113	+	0.119101i
$994$		0			0
$995$	6.12204	+	17.6885i	0.194082	+	0.560762i
$996$		0			0
$997$	−1.64044	+	3.59206i	−0.0519532	+	0.113762i	−0.933828	−	0.357721i	$-0.883554\pi$
$997$	−1.64044	+	3.59206i	−0.0519532	+	0.113762i	0.881875	+	0.471483i	$0.156281\pi$
$998$		0			0
$999$	−0.341058	−	7.15969i	−0.0107906	−	0.226522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.505.6	yes	120
67.54	even	33	inner	804.2.y.b.121.6	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.6	✓	120	67.54	even	33	inner
804.2.y.b.505.6	yes	120	1.1	even	1	trivial

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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(2.26427 + 1.45516i) q^{5} +(-0.275857 + 0.110437i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(2.26427 + 1.45516i) q^{5} +(-0.275857 + 0.110437i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.141549 + 2.97147i) q^{11} +(-2.35877 - 0.225236i) q^{13} +(0.383046 + 2.66414i) q^{15} +(-1.55999 + 6.43038i) q^{17} +(-0.0392194 - 0.0157011i) q^{19} +(-0.264111 - 0.136158i) q^{21} +(6.70108 - 1.29153i) q^{23} +(0.932347 + 2.04156i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-4.54404 - 7.87051i) q^{29} +(6.70820 - 0.640555i) q^{31} +(-2.33838 + 1.83893i) q^{33} +(-0.785317 - 0.151357i) q^{35} +(-3.58390 + 6.20750i) q^{37} +(-1.37445 - 1.93014i) q^{39} +(-1.14105 - 1.08799i) q^{41} +(-0.0911731 + 0.0267708i) q^{43} +(-1.76258 + 2.03413i) q^{45} +(1.33349 - 3.85286i) q^{47} +(-5.00224 + 4.76962i) q^{49} +(-5.88134 + 3.03204i) q^{51} +(9.92237 + 2.91347i) q^{53} +(-4.64446 + 6.52223i) q^{55} +(-0.0138171 - 0.0399220i) q^{57} +(0.805907 - 1.76469i) q^{59} +(-0.0570785 - 1.19823i) q^{61} +(-0.0700539 - 0.288766i) q^{63} +(-5.01314 - 3.94237i) q^{65} +(8.13460 + 0.910133i) q^{67} +(5.36435 + 4.21857i) q^{69} +(2.07959 + 8.57221i) q^{71} +(-0.527712 - 11.0780i) q^{73} +(-0.932347 + 2.04156i) q^{75} +(-0.289112 - 0.835335i) q^{77} +(-0.0496144 + 0.0696736i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(5.57384 - 2.87352i) q^{83} +(-12.8894 + 12.2901i) q^{85} +(2.97242 - 8.58824i) q^{87} +(2.48587 - 2.86885i) q^{89} +(0.675559 - 0.198362i) q^{91} +(4.87703 + 4.65024i) q^{93} +(-0.0659556 - 0.0926216i) q^{95} +(-6.97782 + 12.0859i) q^{97} +(-2.92108 - 0.562993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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