LMFDB - Embedded newform 804.2.y.b.121.6

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			121.6
Character	$\chi$	$=$	804.121
Dual form			804.2.y.b.505.6

$q$-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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{26}{33}\right)$	$1$

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	0.0745429	−	0.997218i	$-0.476250\pi$
$5$	2.26427	−	1.45516i	1.01261	−	0.650765i	0.938067	+	0.346453i	$0.112614\pi$
$6$		0			0
$7$	−0.275857	−	0.110437i	−0.104264	−	0.0417411i	0.318944	−	0.947774i	$-0.396672\pi$
$7$	−0.275857	−	0.110437i	−0.104264	−	0.0417411i	−0.423208	+	0.906032i	$0.639096\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	−0.141549	−	2.97147i	−0.0426785	−	0.895933i	−0.914123	−	0.405438i	$-0.867119\pi$
$11$	−0.141549	−	2.97147i	−0.0426785	−	0.895933i	0.871444	−	0.490495i	$-0.163184\pi$
$12$		0			0
$13$	−2.35877	+	0.225236i	−0.654206	+	0.0624691i	−0.416881	−	0.908961i	$-0.636877\pi$
$13$	−2.35877	+	0.225236i	−0.654206	+	0.0624691i	−0.237325	+	0.971430i	$0.576271\pi$
$14$		0			0
$15$	0.383046	−	2.66414i	0.0989020	−	0.687878i
$16$		0			0
$17$	−1.55999	−	6.43038i	−0.378354	−	1.55960i	−0.769119	−	0.639106i	$-0.779304\pi$
$17$	−1.55999	−	6.43038i	−0.378354	−	1.55960i	0.390764	−	0.920491i	$-0.372211\pi$
$18$		0			0
$19$	−0.0392194	+	0.0157011i	−0.00899754	+	0.00360207i	−0.376157	−	0.926556i	$-0.622755\pi$
$19$	−0.0392194	+	0.0157011i	−0.00899754	+	0.00360207i	0.367159	+	0.930158i	$0.380330\pi$
$20$		0			0
$21$	−0.264111	+	0.136158i	−0.0576337	+	0.0297122i
$22$		0			0
$23$	6.70108	+	1.29153i	1.39727	+	0.269302i	0.831622	−	0.555343i	$-0.187413\pi$
$23$	6.70108	+	1.29153i	1.39727	+	0.269302i	0.565651	+	0.824645i	$0.308625\pi$
$24$		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	0.0428465	+	0.999082i	$0.486357\pi$
$29$	−4.54404	+	7.87051i	−0.843807	+	1.46152i	−0.886653	+	0.462435i	$0.846976\pi$
$30$		0			0
$31$	6.70820	+	0.640555i	1.20483	+	0.115047i	0.678089	−	0.734980i	$-0.262809\pi$
$31$	6.70820	+	0.640555i	1.20483	+	0.115047i	0.526739	+	0.850027i	$0.323415\pi$
$32$		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	−0.994339	−	0.106256i	$-0.966114\pi$
$37$	−3.58390	−	6.20750i	−0.589190	−	1.02051i	0.405149	−	0.914251i	$-0.367220\pi$
$38$		0			0
$39$	−1.37445	+	1.93014i	−0.220088	+	0.309070i
$40$		0			0
$41$	−1.14105	+	1.08799i	−0.178203	+	0.169916i	−0.773931	−	0.633270i	$-0.781712\pi$
$41$	−1.14105	+	1.08799i	−0.178203	+	0.169916i	0.595728	+	0.803186i	$0.296864\pi$
$42$		0			0
$43$	−0.0911731	−	0.0267708i	−0.0139038	−	0.00408252i	0.274773	−	0.961509i	$-0.411397\pi$
$43$	−0.0911731	−	0.0267708i	−0.0139038	−	0.00408252i	−0.288677	+	0.957427i	$0.593215\pi$
$44$		0			0
$45$	−1.76258	−	2.03413i	−0.262750	−	0.303230i
$46$		0			0
$47$	1.33349	+	3.85286i	0.194509	+	0.561997i	0.999511	−	0.0312755i	$-0.00995692\pi$
$47$	1.33349	+	3.85286i	0.194509	+	0.561997i	−0.805002	+	0.593272i	$0.797836\pi$
$48$		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	0.483143	−	0.875541i	$-0.339495\pi$
$53$	9.92237	−	2.91347i	1.36294	−	0.400196i	0.879799	+	0.475346i	$0.157677\pi$
$54$		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	0.954810	−	0.297218i	$-0.0960587\pi$
$59$	0.805907	+	1.76469i	0.104920	+	0.229743i	−0.849890	+	0.526961i	$0.823331\pi$
$60$		0			0
$61$	−0.0570785	+	1.19823i	−0.00730816	+	0.153417i	0.992263	+	0.124150i	$0.0396204\pi$
$61$	−0.0570785	+	1.19823i	−0.00730816	+	0.153417i	−0.999572	+	0.0292672i	$0.990683\pi$
$62$		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	−0.704654	−	0.709551i	$-0.748898\pi$
$71$	2.07959	−	8.57221i	0.246802	−	1.01733i	0.951457	−	0.307783i	$-0.0995870\pi$
$72$		0			0
$73$	−0.527712	+	11.0780i	−0.0617640	+	1.29659i	0.729021	+	0.684492i	$0.239976\pi$
$73$	−0.527712	+	11.0780i	−0.0617640	+	1.29659i	−0.790785	+	0.612094i	$0.790327\pi$
$74$		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	0.811775	−	0.583970i	$-0.198501\pi$
$79$	−0.0496144	−	0.0696736i	−0.00558205	−	0.00783889i	−0.817358	+	0.576131i	$0.804562\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	5.57384	+	2.87352i	0.611809	+	0.315409i	0.736138	−	0.676832i	$-0.236647\pi$
$83$	5.57384	+	2.87352i	0.611809	+	0.315409i	−0.124329	+	0.992241i	$0.539678\pi$
$84$		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	0.872047	−	0.489422i	$-0.162792\pi$
$89$	2.48587	+	2.86885i	0.263502	+	0.304097i	−0.608546	+	0.793519i	$0.708247\pi$
$90$		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	−0.965417	−	0.260710i	$-0.916043\pi$
$97$	−6.97782	−	12.0859i	−0.708490	−	1.22714i	0.256927	−	0.966431i	$-0.417290\pi$
$98$		0			0
$99$	−2.92108	+	0.562993i	−0.293580	+	0.0565829i
$100$		0			0
$101$	7.14022	+	5.61513i	0.710479	+	0.558727i	0.906671	−	0.421839i	$-0.138615\pi$
$101$	7.14022	+	5.61513i	0.710479	+	0.558727i	−0.196192	+	0.980565i	$0.562858\pi$
$102$		0			0
$103$	−10.9460	−	1.04521i	−1.07854	−	0.102988i	−0.459369	−	0.888246i	$-0.651924\pi$
$103$	−10.9460	−	1.04521i	−1.07854	−	0.102988i	−0.619169	+	0.785258i	$0.712530\pi$
$104$		0			0
$105$	−0.399885	+	0.692621i	−0.0390248	+	0.0675929i
$106$		0			0
$107$	15.0236	+	9.65507i	1.45238	+	0.933391i	0.999117	+	0.0420157i	$0.0133780\pi$
$107$	15.0236	+	9.65507i	1.45238	+	0.933391i	0.453267	+	0.891375i	$0.350258\pi$
$108$		0			0
$109$	−1.58087	+	3.46162i	−0.151420	+	0.331563i	−0.970107	−	0.242676i	$-0.921975\pi$
$109$	−1.58087	+	3.46162i	−0.151420	+	0.331563i	0.818688	+	0.574239i	$0.194702\pi$
$110$		0			0
$111$	−7.03827	−	1.35652i	−0.668043	−	0.128755i
$112$		0			0
$113$	2.63705	−	1.35949i	0.248072	−	0.127890i	−0.329707	−	0.944083i	$-0.606950\pi$
$113$	2.63705	−	1.35949i	0.248072	−	0.127890i	0.577779	+	0.816193i	$0.303920\pi$
$114$		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	−0.0561840	−	0.998420i	$-0.517893\pi$
$127$	−8.85591	−	3.54537i	−0.785835	−	0.314601i	−0.729651	+	0.683819i	$0.760318\pi$
$128$		0			0
$129$	−0.0799378	+	0.0513729i	−0.00703813	+	0.00452313i
$130$		0			0
$131$	−9.30270	+	10.7359i	−0.812781	+	0.937999i	−0.999009	−	0.0445073i	$-0.985828\pi$
$131$	−9.30270	+	10.7359i	−0.812781	+	0.937999i	0.186228	+	0.982507i	$0.440374\pi$
$132$		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	−0.0420631	+	0.999115i	$0.513393\pi$
$137$	−11.9976	+	13.8459i	−1.02502	+	1.18294i	−0.982959	+	0.183824i	$0.941152\pi$
$138$		0			0
$139$	11.7475	−	7.54968i	0.996413	−	0.640356i	0.0625707	−	0.998041i	$-0.480070\pi$
$139$	11.7475	−	7.54968i	0.996413	−	0.640356i	0.933842	+	0.357685i	$0.116434\pi$
$140$		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	−0.991928	−	0.126801i	$-0.959529\pi$
$149$	−0.0543944	+	0.378321i	−0.00445616	+	0.0309933i	0.987472	+	0.157794i	$0.0504382\pi$
$150$		0			0
$151$	−0.358180	−	1.47644i	−0.0291483	−	0.120151i	0.955379	−	0.295383i	$-0.0954474\pi$
$151$	−0.358180	−	1.47644i	−0.0291483	−	0.120151i	−0.984527	+	0.175233i	$0.943932\pi$
$152$		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	0.646391	−	0.763006i	$-0.276277\pi$
$157$	12.0651	+	2.32536i	0.962900	+	0.185584i	0.316508	+	0.948590i	$0.397489\pi$
$158$		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	0.183723	+	0.982978i	$0.441185\pi$
$163$	−9.69566	+	16.7934i	−0.759422	+	1.31536i	−0.943146	+	0.332380i	$0.892148\pi$
$164$		0			0
$165$	−7.97064	−	0.761104i	−0.620514	−	0.0592519i
$166$		0			0
$167$	12.0511	+	9.47713i	0.932546	+	0.733362i	0.963933	−	0.266145i	$-0.0857501\pi$
$167$	12.0511	+	9.47713i	0.932546	+	0.733362i	−0.0313873	+	0.999507i	$0.509993\pi$
$168$		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	−0.992958	−	0.118471i	$-0.962201\pi$
$173$	−7.31617	+	10.2741i	−0.556238	+	0.781127i	0.436719	+	0.899598i	$0.356140\pi$
$174$		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	0.828918	−	0.559371i	$-0.188957\pi$
$179$	2.10417	+	2.42834i	0.157273	+	0.181503i	−0.671644	+	0.740874i	$0.734412\pi$
$180$		0			0
$181$	−2.57303	−	7.43429i	−0.191252	−	0.552586i	0.808082	−	0.589070i	$-0.200506\pi$
$181$	−2.57303	−	7.43429i	−0.191252	−	0.552586i	−0.999334	+	0.0364834i	$0.988384\pi$
$182$		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	−0.963858	−	0.266415i	$-0.914161\pi$
$191$	−0.573925	+	1.65825i	−0.0415277	+	0.119987i	0.922331	+	0.386401i	$0.126282\pi$
$192$		0			0
$193$	−0.218531	−	0.478517i	−0.0157302	−	0.0344444i	0.901604	−	0.432563i	$-0.142391\pi$
$193$	−0.218531	−	0.478517i	−0.0157302	−	0.0344444i	−0.917334	+	0.398118i	$0.869663\pi$
$194$		0			0
$195$	−0.303459	+	6.37038i	−0.0217311	+	0.456192i
$196$		0			0
$197$	−2.94312	+	12.1317i	−0.209689	+	0.864349i	0.765582	+	0.643338i	$0.222451\pi$
$197$	−2.94312	+	12.1317i	−0.209689	+	0.864349i	−0.975271	+	0.221011i	$0.929064\pi$
$198$		0			0
$199$	5.46650	−	4.29891i	0.387510	−	0.304741i	−0.405331	−	0.914170i	$-0.632844\pi$
$199$	5.46650	−	4.29891i	0.387510	−	0.304741i	0.792841	+	0.609429i	$0.208601\pi$
$200$		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	0.383592	+	0.923503i	$0.374687\pi$
$211$	−7.10028	+	20.5149i	−0.488803	+	1.41230i	−0.872395	+	0.488801i	$0.837434\pi$
$212$		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	0.995880	+	0.0906790i	$0.0289037\pi$
$223$	14.0955	+	16.2671i	0.943908	+	1.08933i	−0.0519725	+	0.998649i	$0.516551\pi$
$224$		0			0
$225$	−2.15346	−	0.632313i	−0.143564	−	0.0421542i
$226$		0			0
$227$	6.74633	−	6.43261i	0.447770	−	0.426947i	−0.432345	−	0.901708i	$-0.642314\pi$
$227$	6.74633	−	6.43261i	0.447770	−	0.426947i	0.880115	+	0.474761i	$0.157465\pi$
$228$		0			0
$229$	4.59014	−	6.44595i	0.303325	−	0.425961i	−0.634577	−	0.772859i	$-0.718826\pi$
$229$	4.59014	−	6.44595i	0.303325	−	0.425961i	0.937903	+	0.346899i	$0.112765\pi$
$230$		0			0
$231$	0.441976	+	0.765524i	0.0290799	+	0.0503678i
$232$		0			0
$233$	19.4646	−	3.75149i	1.27517	−	0.245768i	0.493654	−	0.869658i	$-0.335661\pi$
$233$	19.4646	−	3.75149i	1.27517	−	0.245768i	0.781512	+	0.623890i	$0.214449\pi$
$234$		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	−0.490386	−	0.871505i	$-0.663144\pi$
$239$	7.87749	−	13.6442i	0.509553	−	0.882571i	0.999939	−	0.0110656i	$-0.00352237\pi$
$240$		0			0
$241$	−5.97485	−	3.83980i	−0.384874	−	0.247344i	0.333869	−	0.942620i	$-0.391646\pi$
$241$	−5.97485	−	3.83980i	−0.384874	−	0.247344i	−0.718743	+	0.695276i	$0.755282\pi$
$242$		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	0.914383	+	0.404851i	$0.132677\pi$
$251$	4.54948	+	18.7532i	0.287160	+	1.18369i	−0.627222	+	0.778840i	$0.715808\pi$
$252$		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	−0.683986	−	0.729495i	$-0.739755\pi$
$257$	−1.16130	−	24.3787i	−0.0724401	−	1.52070i	0.611546	−	0.791209i	$-0.290548\pi$
$258$		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	0.143298	−	0.989680i	$-0.454229\pi$
$263$	17.8888	−	11.4964i	1.10307	−	0.708900i	0.959772	+	0.280780i	$0.0905930\pi$
$264$		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	−0.999818	−	0.0190749i	$-0.993928\pi$
$271$	−13.8059	+	15.9329i	−0.838648	+	0.967852i	0.161170	+	0.986927i	$0.448473\pi$
$272$		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	−0.919668	−	0.392697i	$-0.871542\pi$
$277$	−2.46135	−	17.1191i	−0.147888	−	1.02859i	0.771780	−	0.635890i	$-0.219367\pi$
$278$		0			0
$279$	−0.320641	−	6.73108i	−0.0191963	−	0.402979i
$280$		0			0
$281$	−30.9658	+	2.95687i	−1.84726	+	0.176392i	−0.959087	−	0.283112i	$-0.908633\pi$
$281$	−30.9658	+	2.95687i	−1.84726	+	0.176392i	−0.888175	+	0.459505i	$0.848027\pi$
$282$		0			0
$283$	−3.61930	+	25.1728i	−0.215145	+	1.49637i	0.540478	+	0.841358i	$0.318243\pi$
$283$	−3.61930	+	25.1728i	−0.215145	+	1.49637i	−0.755623	+	0.655007i	$0.772666\pi$
$284$		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	−0.990356	−	0.138546i	$-0.955757\pi$
$293$	−4.05857	+	8.88703i	−0.237104	+	0.519186i	0.753252	+	0.657732i	$0.228484\pi$
$294$		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	−0.585980	−	0.810325i	$-0.699290\pi$
$307$	6.50803	−	9.13926i	0.371433	−	0.521605i	0.957413	+	0.288720i	$0.0932298\pi$
$308$		0			0
$309$	−7.95800	+	7.58794i	−0.452715	+	0.431663i
$310$		0			0
$311$	−11.4158	−	3.35197i	−0.647328	−	0.190073i	−0.0584447	−	0.998291i	$-0.518614\pi$
$311$	−11.4158	−	3.35197i	−0.647328	−	0.190073i	−0.588884	+	0.808218i	$0.700432\pi$
$312$		0			0
$313$	21.2257	+	24.4957i	1.19974	+	1.38458i	0.903010	+	0.429620i	$0.141352\pi$
$313$	21.2257	+	24.4957i	1.19974	+	1.38458i	0.296735	+	0.954960i	$0.404102\pi$
$314$		0			0
$315$	0.261579	+	0.755783i	0.0147383	+	0.0425835i
$316$		0			0
$317$	−18.3447	−	17.4916i	−1.03034	−	0.982426i	−0.0304847	−	0.999535i	$-0.509705\pi$
$317$	−18.3447	−	17.4916i	−1.03034	−	0.982426i	−0.999854	+	0.0171096i	$0.994554\pi$
$318$		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	−0.934137	−	0.356915i	$-0.883828\pi$
$331$	1.08624	−	4.47755i	0.0597052	−	0.246108i	0.993842	+	0.110807i	$0.0353436\pi$
$332$		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	−0.834247	−	0.551391i	$-0.814097\pi$
$337$	−9.08847	+	7.14725i	−0.495080	+	0.389336i	0.339167	+	0.940726i	$0.389855\pi$
$338$		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	0.416792	−	0.909002i	$-0.363154\pi$
$347$	−10.7769	−	15.1341i	−0.578535	−	0.812439i	−0.995327	+	0.0965630i	$0.969215\pi$
$348$		0			0
$349$	8.64492	−	2.53838i	0.462752	−	0.135876i	−0.0420424	−	0.999116i	$-0.513386\pi$
$349$	8.64492	−	2.53838i	0.462752	−	0.135876i	0.504794	+	0.863240i	$0.331568\pi$
$350$		0			0
$351$	2.10610	+	1.08577i	0.112415	+	0.0579541i
$352$		0			0
$353$	−1.51712	−	1.44657i	−0.0807480	−	0.0769930i	0.648630	−	0.761104i	$-0.275342\pi$
$353$	−1.51712	−	1.44657i	−0.0807480	−	0.0769930i	−0.729378	+	0.684111i	$0.760191\pi$
$354$		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	0.638930	−	0.769265i	$-0.279377\pi$
$359$	14.4101	+	4.23118i	0.760535	+	0.223313i	0.121606	+	0.992578i	$0.461196\pi$
$360$		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	−0.584751	−	0.811213i	$-0.698808\pi$
$367$	−15.8262	+	3.05024i	−0.826119	+	0.159221i	−0.241367	+	0.970434i	$0.577596\pi$
$368$		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	0.348715	−	0.937229i	$-0.386618\pi$
$373$	19.0432	−	32.9839i	0.986022	−	1.70784i	0.637306	−	0.770611i	$-0.280049\pi$
$374$		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	−0.237375	−	0.971418i	$-0.576287\pi$
$379$	−15.9401	−	3.07219i	−0.818786	−	0.157808i	−0.581411	+	0.813610i	$0.697499\pi$
$380$		0			0
$381$	−8.47880	+	4.37113i	−0.434382	+	0.223940i
$382$		0			0
$383$	18.7714	−	7.51492i	0.959172	−	0.383995i	0.161356	−	0.986896i	$-0.448413\pi$
$383$	18.7714	−	7.51492i	0.959172	−	0.383995i	0.797815	+	0.602902i	$0.205989\pi$
$384$		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	−0.428084	−	0.903739i	$-0.640811\pi$
$389$	−13.3604	+	1.27576i	−0.677398	+	0.0646837i	−0.249314	+	0.968423i	$0.580205\pi$
$390$		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	0.197712	−	0.980260i	$-0.436649\pi$
$397$	23.3424	−	15.0012i	1.17152	−	0.752891i	0.973809	+	0.227369i	$0.0730125\pi$
$398$		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	0.0303985	−	0.999538i	$-0.490322\pi$
$409$	−12.8898	−	5.16031i	−0.637361	−	0.255161i	−0.667760	+	0.744377i	$0.732747\pi$
$410$		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	0.923035	−	0.384717i	$-0.125701\pi$
$419$	−1.50817	−	6.21674i	−0.0736787	−	0.303708i	−0.996713	+	0.0810091i	$0.974186\pi$
$420$		0			0
$421$	−10.9904	+	4.39989i	−0.535639	+	0.214437i	−0.623680	−	0.781679i	$-0.714363\pi$
$421$	−10.9904	+	4.39989i	−0.535639	+	0.214437i	0.0880417	+	0.996117i	$0.471939\pi$
$422$		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	−0.281864	−	0.959454i	$-0.590953\pi$
$431$	14.3244	−	24.8105i	0.689980	−	1.19508i	0.971844	−	0.235626i	$-0.0757140\pi$
$432$		0			0
$433$	21.0509	+	2.01012i	1.01164	+	0.0966002i	0.587692	−	0.809085i	$-0.300037\pi$
$433$	21.0509	+	2.01012i	1.01164	+	0.0966002i	0.423951	+	0.905685i	$0.360643\pi$
$434$		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	−0.795675	−	0.605723i	$-0.792884\pi$
$439$	−19.3266	−	33.4747i	−0.922409	−	1.59766i	−0.126734	−	0.991937i	$-0.540449\pi$
$440$		0			0
$441$	−4.00918	+	5.63011i	−0.190913	+	0.268100i
$442$		0			0
$443$	8.00732	−	7.63496i	0.380439	−	0.362748i	−0.475598	−	0.879663i	$-0.657768\pi$
$443$	8.00732	−	7.63496i	0.380439	−	0.362748i	0.856037	+	0.516915i	$0.172920\pi$
$444$		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	−0.894094	−	0.447879i	$-0.852180\pi$
$449$	−9.91990	−	28.6617i	−0.468149	−	1.35263i	0.425945	−	0.904749i	$-0.359942\pi$
$450$		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	0.659104	−	0.752052i	$-0.270936\pi$
$457$	−5.71117	−	8.02021i	−0.267157	−	0.375170i	−0.926261	+	0.376882i	$0.876996\pi$
$458$		0			0
$459$	−2.16418	+	6.25298i	−0.101015	+	0.291864i
$460$		0			0
$461$	−0.144120	−	0.315578i	−0.00671232	−	0.0146979i	0.906246	−	0.422750i	$-0.138935\pi$
$461$	−0.144120	−	0.315578i	−0.00671232	−	0.0146979i	−0.912958	+	0.408052i	$0.866208\pi$
$462$		0			0
$463$	1.06877	−	22.4362i	0.0496699	−	1.04270i	−0.827181	−	0.561936i	$-0.810057\pi$
$463$	1.06877	−	22.4362i	0.0496699	−	1.04270i	0.876851	−	0.480763i	$-0.159640\pi$
$464$		0			0
$465$	4.27607	−	17.6262i	0.198298	−	0.817396i
$466$		0			0
$467$	−4.61756	+	3.63129i	−0.213675	+	0.168036i	−0.719260	−	0.694741i	$-0.755519\pi$
$467$	−4.61756	+	3.63129i	−0.213675	+	0.168036i	0.505585	+	0.862777i	$0.331277\pi$
$468$		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	−0.849413	−	0.527729i	$-0.823044\pi$
$479$	3.16234	−	9.13697i	0.144491	−	0.417479i	0.993904	+	0.110250i	$0.0351651\pi$
$480$		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	0.518843	−	0.854870i	$-0.326363\pi$
$487$	−6.84929	−	6.53078i	−0.310371	−	0.295938i	−0.829214	+	0.558932i	$0.811211\pi$
$488$		0			0
$489$	6.34228	+	18.3248i	0.286808	+	0.828676i
$490$		0			0
$491$	−6.32110	−	7.29494i	−0.285267	−	0.329216i	0.594972	−	0.803747i	$-0.297163\pi$
$491$	−6.32110	−	7.29494i	−0.285267	−	0.329216i	−0.880239	+	0.474531i	$0.842618\pi$
$492$		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	0.740196	−	0.672391i	$-0.234733\pi$
$499$	−4.74041	−	8.21064i	−0.212210	−	0.367559i	−0.952406	+	0.304833i	$0.901399\pi$
$500$		0			0
$501$	15.0542	−	2.90145i	0.672570	−	0.129627i
$502$		0			0
$503$	−21.2390	−	16.7025i	−0.946999	−	0.744728i	0.0199229	−	0.999802i	$-0.493658\pi$
$503$	−21.2390	−	16.7025i	−0.946999	−	0.744728i	−0.966922	+	0.255073i	$0.917900\pi$
$504$		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	0.787696	−	0.616064i	$-0.211274\pi$
$509$	12.5107	+	8.04012i	0.554526	+	0.356372i	−0.233171	+	0.972436i	$0.574910\pi$
$510$		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	−0.992499	−	0.122251i	$-0.960989\pi$
$521$	−0.131499	+	0.914597i	−0.00576109	+	0.0400692i	0.986738	+	0.162320i	$0.0518978\pi$
$522$		0			0
$523$	−43.9974	+	4.20124i	−1.92387	+	0.183707i	−0.986401	−	0.164357i	$-0.947445\pi$
$523$	−43.9974	+	4.20124i	−1.92387	+	0.183707i	−0.937471	+	0.348064i	$0.886839\pi$
$524$		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	−0.642649	−	0.766161i	$-0.722165\pi$
$541$	−4.94705	+	3.17928i	−0.212690	+	0.136688i	0.429959	+	0.902849i	$0.358528\pi$
$542$		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	0.995271	+	0.0971354i	$0.0309680\pi$
$547$	0.321351	+	6.74599i	0.0137400	+	0.288438i	−0.981531	+	0.191302i	$0.938729\pi$
$548$		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	−0.677541	−	0.735485i	$-0.736955\pi$
$557$	−11.1265	+	5.73612i	−0.471446	+	0.243047i	0.206096	+	0.978532i	$0.433924\pi$
$558$		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	0.947932	−	0.318474i	$-0.103170\pi$
$563$	24.9620	+	16.0421i	1.05202	+	0.676094i	0.104091	+	0.994568i	$0.466807\pi$
$564$		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	0.520250	−	0.854014i	$-0.325839\pi$
$569$	−4.46152	−	3.50858i	−0.187037	−	0.147087i	−0.707287	+	0.706927i	$0.750081\pi$
$570$		0			0
$571$	−33.7473	+	6.50425i	−1.41228	+	0.272194i	−0.837645	−	0.546216i	$-0.816068\pi$
$571$	−33.7473	+	6.50425i	−1.41228	+	0.272194i	−0.574634	+	0.818410i	$0.694856\pi$
$572$		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	−0.905893	−	0.423506i	$-0.860799\pi$
$577$	−12.6343	+	12.0467i	−0.525971	+	0.501513i	0.379922	+	0.925018i	$0.375951\pi$
$578$		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	0.428786	−	0.903406i	$-0.358942\pi$
$587$	−1.41461	−	0.729281i	−0.0583871	−	0.0301006i	−0.487173	+	0.873306i	$0.661972\pi$
$588$		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	−0.903524	−	0.428537i	$-0.859029\pi$
$593$	1.74353	−	5.03759i	0.0715980	−	0.206869i	0.975122	+	0.221668i	$0.0711502\pi$
$594$		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	−0.921245	−	0.388982i	$-0.872827\pi$
$599$	1.85595	−	7.65034i	0.0758322	−	0.312584i	0.997077	+	0.0763978i	$0.0243419\pi$
$600$		0			0
$601$	−13.2581	+	10.4263i	−0.540808	+	0.425296i	−0.850836	−	0.525431i	$-0.823904\pi$
$601$	−13.2581	+	10.4263i	−0.540808	+	0.425296i	0.310028	+	0.950727i	$0.399662\pi$
$602$		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	0.776624	+	0.629964i	$0.216930\pi$
$607$	−4.98495	+	20.5483i	−0.202333	+	0.834028i	−0.978957	+	0.204064i	$0.934585\pi$
$608$		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	0.397350	+	0.917667i	$0.369930\pi$
$613$	−11.9400	+	34.4984i	−0.482252	+	1.39338i	−0.879602	+	0.475710i	$0.842191\pi$
$614$		0			0
$615$	2.46149	+	3.45668i	0.0992568	+	0.139387i
$616$		0			0
$617$	−35.8824	+	10.5360i	−1.44457	+	0.424165i	−0.907743	−	0.419526i	$-0.862196\pi$
$617$	−35.8824	+	10.5360i	−1.44457	+	0.424165i	−0.536829	+	0.843691i	$0.680378\pi$
$618$		0			0
$619$	−4.39433	−	2.26543i	−0.176623	−	0.0910555i	0.367648	−	0.929965i	$-0.380163\pi$
$619$	−4.39433	−	2.26543i	−0.176623	−	0.0910555i	−0.544271	+	0.838910i	$0.683194\pi$
$620$		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	0.0989835	+	0.995089i	$0.468441\pi$
$631$	−21.9484	+	30.8222i	−0.873751	+	1.22701i	−0.972734	+	0.231922i	$0.925498\pi$
$632$		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	−0.787195	−	0.616705i	$-0.788467\pi$
$641$	3.55679	−	6.16053i	0.140485	−	0.243326i	0.927679	+	0.373378i	$0.121801\pi$
$642$		0			0
$643$	−9.32470	−	5.99262i	−0.367730	−	0.236326i	0.343705	−	0.939078i	$-0.388318\pi$
$643$	−9.32470	−	5.99262i	−0.367730	−	0.236326i	−0.711435	+	0.702752i	$0.751954\pi$
$644$		0			0
$645$	−0.106245	+	0.232644i	−0.00418338	+	0.00916034i
$646$		0			0
$647$	−6.59795	−	1.27165i	−0.259392	−	0.0499937i	0.0578971	−	0.998323i	$-0.481560\pi$
$647$	−6.59795	−	1.27165i	−0.259392	−	0.0499937i	−0.317289	+	0.948329i	$0.602773\pi$
$648$		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	0.969017	+	0.246993i	$0.0794426\pi$
$653$	5.64483	+	23.2683i	0.220899	+	0.910559i	−0.748118	+	0.663566i	$0.769042\pi$
$654$		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	1.00000		2.16420e-5i	$6.88887e-6\pi$
$659$	0.116293	+	2.44129i	0.00453013	+	0.0950992i	−0.995470	+	0.0950776i	$0.969690\pi$
$660$		0			0
$661$	−6.57117	−	45.7035i	−0.255589	−	1.77766i	−0.563371	−	0.826204i	$-0.690496\pi$
$661$	−6.57117	−	45.7035i	−0.255589	−	1.77766i	0.307782	−	0.951457i	$-0.400413\pi$
$662$		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	0.0673997	−	0.997726i	$-0.478530\pi$
$673$	27.1195	−	31.2975i	1.04538	−	1.20643i	0.977979	−	0.208705i	$-0.0669248\pi$
$674$		0			0
$675$	−1.88809	+	1.21340i	−0.0726726	+	0.0467038i
$676$		0			0
$677$	38.0618	+	15.2377i	1.46284	+	0.585631i	0.960311	−	0.278932i	$-0.0899804\pi$
$677$	38.0618	+	15.2377i	1.46284	+	0.585631i	0.502525	+	0.864563i	$0.332405\pi$
$678$		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	−0.454115	−	0.890943i	$-0.650044\pi$
$683$	−19.1149	+	1.82525i	−0.731411	+	0.0698413i	−0.277296	+	0.960784i	$0.589438\pi$
$684$		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	−0.536823	−	0.843695i	$-0.680376\pi$
$691$	−4.23109	+	2.18128i	−0.160958	+	0.0829798i	0.375865	+	0.926674i	$0.377346\pi$
$692$		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	0.328228	−	0.944598i	$-0.393549\pi$
$701$	12.4905	+	1.19269i	0.471758	+	0.0450475i	0.143530	+	0.989646i	$0.454155\pi$
$702$		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	−0.771617	−	0.636088i	$-0.780552\pi$
$709$	2.17964	−	3.06088i	0.0818582	−	0.114954i	0.853475	+	0.521134i	$0.174491\pi$
$710$		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	0.562951	−	0.826490i	$-0.309666\pi$
$719$	−6.32323	−	6.02919i	−0.235817	−	0.224851i	−0.798768	+	0.601639i	$0.794514\pi$
$720$		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	−0.783491	−	0.621403i	$-0.786563\pi$
$727$	5.83749	−	16.8663i	0.216501	−	0.625538i	0.999991	−	0.00413415i	$-0.00131594\pi$
$728$		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	0.558732	+	0.829348i	$0.311288\pi$
$733$	−8.60731	+	35.4798i	−0.317918	+	1.31048i	−0.876650	+	0.481128i	$0.840227\pi$
$734$		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	−0.998650	−	0.0519388i	$-0.983460\pi$
$739$	−32.1761	+	25.3035i	−1.18362	+	0.930806i	−0.184966	+	0.982745i	$0.559218\pi$
$740$		0			0
$741$	0.0235997	−	0.0972791i	0.000866955	−	0.00357364i
$742$		0			0
$743$	1.55407	−	32.6240i	0.0570134	−	1.19686i	−0.771255	−	0.636527i	$-0.780371\pi$
$743$	1.55407	−	32.6240i	0.0570134	−	1.19686i	0.828268	−	0.560332i	$-0.189326\pi$
$744$		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	0.231359	−	0.972868i	$-0.425683\pi$
$751$	26.0880	−	7.66011i	0.951963	−	0.279522i	0.720604	+	0.693347i	$0.243865\pi$
$752$		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	0.771217	+	0.636572i	$0.219648\pi$
$757$	15.3664	+	44.3984i	0.558502	+	1.61369i	−0.212715	+	0.977114i	$0.568231\pi$
$758$		0			0
$759$	−13.2947	−	15.3429i	−0.482566	−	0.556911i
$760$		0			0
$761$	−34.9199	−	10.2534i	−1.26585	−	0.371686i	−0.421179	−	0.906977i	$-0.638384\pi$
$761$	−34.9199	−	10.2534i	−1.26585	−	0.371686i	−0.844668	+	0.535291i	$0.820202\pi$
$762$		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	0.123813	−	0.992306i	$-0.460488\pi$
$769$	16.8482	−	3.24722i	0.607560	−	0.117098i	0.483747	+	0.875208i	$0.339276\pi$
$770$		0			0
$771$	−19.1847	−	15.0870i	−0.690921	−	0.543346i
$772$		0			0
$773$	0.392881	+	0.0375156i	0.0141309	+	0.00134934i	0.102119	−	0.994772i	$-0.467438\pi$
$773$	0.392881	+	0.0375156i	0.0141309	+	0.00134934i	−0.0879882	+	0.996122i	$0.528044\pi$
$774$		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	0.986419	−	0.164248i	$-0.0525197\pi$
$787$	0.964821	+	3.97704i	0.0343921	+	0.141766i	−0.952027	+	0.306014i	$0.901005\pi$
$788$		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	0.848008	−	0.529984i	$-0.177802\pi$
$797$	30.9417	+	12.3872i	1.09601	+	0.438776i	0.248002	+	0.968760i	$0.420226\pi$
$798$		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	−0.920082	−	0.391726i	$-0.871878\pi$
$809$	−26.9062	+	17.2915i	−0.945971	+	0.607938i	−0.0258889	+	0.999665i	$0.508242\pi$
$810$		0			0
$811$	4.82014	+	1.92969i	0.169258	+	0.0677607i	0.454744	−	0.890622i	$-0.349731\pi$
$811$	4.82014	+	1.92969i	0.169258	+	0.0677607i	−0.285486	+	0.958383i	$0.592155\pi$
$812$		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	0.997179	−	0.0750613i	$-0.0239152\pi$
$821$	2.19070	+	9.03018i	0.0764559	+	0.315155i	−0.920723	+	0.390217i	$0.872400\pi$
$822$		0			0
$823$	40.0054	−	16.0157i	1.39450	−	0.558274i	0.451861	−	0.892088i	$-0.350760\pi$
$823$	40.0054	−	16.0157i	1.39450	−	0.558274i	0.942639	+	0.333815i	$0.108336\pi$
$824$		0			0
$825$	−5.93445	+	3.05942i	−0.206611	+	0.106515i
$826$		0			0
$827$	15.3488	+	2.95824i	0.533730	+	0.102868i	0.448993	−	0.893535i	$-0.351783\pi$
$827$	15.3488	+	2.95824i	0.533730	+	0.102868i	0.0847369	+	0.996403i	$0.472995\pi$
$828$		0			0
$829$	9.25526	−	20.2662i	0.321448	−	0.703874i	−0.678067	−	0.735000i	$-0.737182\pi$
$829$	9.25526	−	20.2662i	0.321448	−	0.703874i	0.999515	+	0.0311263i	$0.00990939\pi$
$830$		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	−0.355807	−	0.934559i	$-0.615794\pi$
$839$	−9.81311	+	1.89132i	−0.338786	+	0.0652957i	0.0170208	+	0.999855i	$0.494582\pi$
$840$		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	0.678346	−	0.734743i	$-0.262697\pi$
$853$	−0.680129	−	0.648502i	−0.0232872	−	0.0222043i	−0.701633	+	0.712538i	$0.747546\pi$
$854$		0			0
$855$	0.101065	+	0.0521028i	0.00345636	+	0.00178188i
$856$		0			0
$857$	46.8810	−	13.7655i	1.60142	−	0.470221i	0.645482	−	0.763775i	$-0.276656\pi$
$857$	46.8810	−	13.7655i	1.60142	−	0.470221i	0.955942	+	0.293554i	$0.0948382\pi$
$858$		0			0
$859$	28.3454	+	39.8056i	0.967133	+	1.35815i	0.933447	+	0.358716i	$0.116785\pi$
$859$	28.3454	+	39.8056i	0.967133	+	1.35815i	0.0336861	+	0.999432i	$0.489275\pi$
$860$		0			0
$861$	0.153225	−	0.442714i	0.00522189	−	0.0150877i
$862$		0			0
$863$	11.5298	+	25.2467i	0.392479	+	0.859408i	0.997978	+	0.0635623i	$0.0202462\pi$
$863$	11.5298	+	25.2467i	0.392479	+	0.859408i	−0.605499	+	0.795846i	$0.707027\pi$
$864$		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	−0.877371	−	0.479813i	$-0.840705\pi$
$877$	1.23303	−	25.8844i	0.0416363	−	0.874054i	0.919007	−	0.394241i	$-0.128992\pi$
$878$		0			0
$879$	4.05857	+	8.88703i	0.136892	+	0.299752i
$880$		0			0
$881$	8.83422	−	25.5248i	0.297632	−	0.859952i	−0.692699	−	0.721227i	$-0.743578\pi$
$881$	8.83422	−	25.5248i	0.297632	−	0.859952i	0.990331	−	0.138725i	$-0.0443004\pi$
$882$		0			0
$883$	6.51293	+	9.14614i	0.219178	+	0.307792i	0.909495	−	0.415715i	$-0.136469\pi$
$883$	6.51293	+	9.14614i	0.219178	+	0.307792i	−0.690317	+	0.723507i	$0.742529\pi$
$884$		0			0
$885$	5.01008	−	1.47109i	0.168412	−	0.0494503i
$886$		0			0
$887$	−6.26679	−	3.23076i	−0.210418	−	0.108478i	0.349796	−	0.936826i	$-0.386251\pi$
$887$	−6.26679	−	3.23076i	−0.210418	−	0.108478i	−0.560214	+	0.828348i	$0.689281\pi$
$888$		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	−0.0878310	−	0.996135i	$-0.527994\pi$
$907$	−10.9201	−	1.04274i	−0.362595	−	0.0346236i	−0.274764	+	0.961512i	$0.588600\pi$
$908$		0			0
$909$	4.54182	−	7.86666i	0.150643	−	0.260921i
$910$		0			0
$911$	−42.0802	−	27.0433i	−1.39418	−	0.895985i	−0.394442	−	0.918921i	$-0.629062\pi$
$911$	−42.0802	−	27.0433i	−1.39418	−	0.895985i	−0.999737	+	0.0229362i	$0.992699\pi$
$912$		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	0.0179806	−	0.999838i	$-0.494276\pi$
$919$	21.8559	−	8.74980i	0.720961	−	0.288629i	0.702981	+	0.711209i	$0.251852\pi$
$920$		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	0.720301	+	0.693662i	$0.244004\pi$
$929$	6.84583	+	47.6138i	0.224604	+	1.56216i	−0.495696	+	0.868496i	$0.665087\pi$
$930$		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	−0.911076	−	0.412238i	$-0.864747\pi$
$941$	−11.4535	+	13.2181i	−0.373375	+	0.430898i	0.537701	+	0.843135i	$0.319293\pi$
$942$		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	−0.987212	−	0.159413i	$-0.949040\pi$
$947$	−2.61268	−	18.1716i	−0.0849008	−	0.590498i	0.902311	−	0.431085i	$-0.141869\pi$
$948$		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	−0.787848	−	0.615870i	$-0.788805\pi$
$953$	4.37120	−	30.4024i	0.141597	−	0.984830i	0.929445	−	0.368960i	$-0.120286\pi$
$954$		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	−0.980640	−	0.195822i	$-0.937263\pi$
$967$	−9.97372	+	17.2750i	−0.320733	+	0.555526i	0.659906	+	0.751348i	$0.270596\pi$
$968$		0			0
$969$	0.278269	+	0.0265714i	0.00893928	+	0.000853597i
$970$		0			0
$971$	29.9158	+	23.5261i	0.960045	+	0.754987i	0.969531	−	0.244968i	$-0.0787773\pi$
$971$	29.9158	+	23.5261i	0.960045	+	0.754987i	−0.00948664	+	0.999955i	$0.503020\pi$
$972$		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	0.0959395	−	0.995387i	$-0.469414\pi$
$977$	31.4196	−	44.1227i	1.00520	−	1.41161i	0.909263	−	0.416222i	$-0.136646\pi$
$978$		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	0.964393	+	0.264475i	$0.0851987\pi$
$983$	34.1410	+	39.4008i	1.08893	+	1.25669i	0.124536	+	0.992215i	$0.460256\pi$
$984$		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	−0.795111	−	0.606464i	$-0.792587\pi$
$991$	−35.7653	+	10.5016i	−1.13612	+	0.333595i	−0.341011	+	0.940059i	$0.610769\pi$
$992$		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	0.881875	−	0.471483i	$-0.156281\pi$
$997$	−1.64044	−	3.59206i	−0.0519532	−	0.113762i	−0.933828	+	0.357721i	$0.883554\pi$
$998$		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.121.6	✓	120
67.36	even	33	inner	804.2.y.b.505.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.6	✓	120	1.1	even	1	trivial
804.2.y.b.505.6	yes	120	67.36	even	33	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.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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