LMFDB - Embedded newform 414.3.k.a.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.6
Character	$\chi$	$=$	414.35
Dual form			414.3.k.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.466986 - 1.59041i) q^{5} +(-2.89002 - 3.33526i) q^{7} +(-2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.466986 - 1.59041i) q^{5} +(-2.89002 - 3.33526i) q^{7} +(-2.79964 + 0.402527i) q^{8} +(1.53508 - 1.77157i) q^{10} +(3.30050 - 5.13568i) q^{11} +(9.84315 - 11.3596i) q^{13} +(1.75834 - 5.98837i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(9.94871 - 4.54342i) q^{17} +(3.47127 - 7.60102i) q^{19} +(3.28136 + 0.471788i) q^{20} +8.63349 q^{22} +(10.5665 + 20.4291i) q^{23} +(18.7200 - 12.0306i) q^{25} +(21.0406 + 3.02518i) q^{26} +(8.46883 - 2.48667i) q^{28} +(1.37521 - 0.628036i) q^{29} +(-7.81855 - 54.3792i) q^{31} +(1.59372 - 5.42771i) q^{32} +(13.0120 + 8.36228i) q^{34} +(-3.95482 + 6.15383i) q^{35} +(-9.31847 - 2.73615i) q^{37} +(11.6971 - 1.68179i) q^{38} +(1.94757 + 4.26459i) q^{40} +(7.76093 + 26.4313i) q^{41} +(0.461419 - 3.20924i) q^{43} +(6.60100 + 10.2714i) q^{44} +(-16.2258 + 28.1908i) q^{46} +16.5698i q^{47} +(4.20168 - 29.2233i) q^{49} +(28.6260 + 13.0730i) q^{50} +(12.4881 + 27.3452i) q^{52} +(19.7900 - 17.1482i) q^{53} +(-9.70911 - 2.85085i) q^{55} +(9.43354 + 8.17421i) q^{56} +(1.79864 + 1.15592i) q^{58} +(39.3240 + 34.0745i) q^{59} +(-7.43111 - 51.6845i) q^{61} +(58.7177 - 50.8792i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-22.6630 - 10.3499i) q^{65} +(-72.0417 + 46.2984i) q^{67} +21.8741i q^{68} -10.3451 q^{70} +(13.0536 + 20.3119i) q^{71} +(-17.4408 + 38.1901i) q^{73} +(-3.86950 - 13.1783i) q^{74} +(10.9442 + 12.6303i) q^{76} +(-26.6673 + 3.83419i) q^{77} +(11.1321 - 12.8471i) q^{79} +(-3.58456 + 5.57768i) q^{80} +(-25.5118 + 29.4422i) q^{82} +(21.5848 - 73.5110i) q^{83} +(-11.8718 - 13.7008i) q^{85} +(4.17087 - 1.90477i) q^{86} +(-7.17296 + 15.7066i) q^{88} +(-81.9773 - 11.7865i) q^{89} -66.3341 q^{91} +(-45.9449 + 2.25018i) q^{92} +(-19.7133 + 12.6690i) q^{94} +(-13.7097 - 1.97116i) q^{95} +(130.934 - 38.4456i) q^{97} +(37.9799 - 17.3448i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 - 16 * q^7	$ 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.764582	+	1.18971i	0.382291	+	0.594856i
$2$	0.764582	+	1.18971i	0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	+	1.81926i	−0.207708	+	0.454816i
$5$	−0.466986	−	1.59041i	−0.0933971	−	0.318081i	0.899522	−	0.436876i	$-0.143915\pi$
$5$	−0.466986	−	1.59041i	−0.0933971	−	0.318081i	−0.992919	+	0.118795i	$0.962097\pi$
$6$		0			0
$7$	−2.89002	−	3.33526i	−0.412860	−	0.476466i	0.510789	−	0.859706i	$-0.329353\pi$
$7$	−2.89002	−	3.33526i	−0.412860	−	0.476466i	−0.923649	+	0.383241i	$0.874808\pi$
$8$	−2.79964	+	0.402527i	−0.349955	+	0.0503159i
$9$		0			0
$10$	1.53508	−	1.77157i	0.153508	−	0.177157i
$11$	3.30050	−	5.13568i	0.300046	−	0.466880i	−0.658193	−	0.752849i	$-0.728679\pi$
$11$	3.30050	−	5.13568i	0.300046	−	0.466880i	0.958239	+	0.285969i	$0.0923154\pi$
$12$		0			0
$13$	9.84315	−	11.3596i	0.757166	−	0.873816i	−0.238077	−	0.971246i	$-0.576517\pi$
$13$	9.84315	−	11.3596i	0.757166	−	0.873816i	0.995242	+	0.0974306i	$0.0310624\pi$
$14$	1.75834	−	5.98837i	0.125596	−	0.427741i
$15$		0			0
$16$	−2.61944	−	3.02300i	−0.163715	−	0.188937i
$17$	9.94871	−	4.54342i	0.585218	−	0.267260i	−0.100726	−	0.994914i	$-0.532117\pi$
$17$	9.94871	−	4.54342i	0.585218	−	0.267260i	0.685944	+	0.727654i	$0.259389\pi$
$18$		0			0
$19$	3.47127	−	7.60102i	0.182698	−	0.400053i	−0.796018	−	0.605274i	$-0.793064\pi$
$19$	3.47127	−	7.60102i	0.182698	−	0.400053i	0.978716	+	0.205220i	$0.0657910\pi$
$20$	3.28136	+	0.471788i	0.164068	+	0.0235894i
$21$		0			0
$22$	8.63349			0.392431
$23$	10.5665	+	20.4291i	0.459414	+	0.888222i
$23$	10.5665	+	20.4291i	0.459414	+	0.888222i
$24$		0			0
$25$	18.7200	−	12.0306i	0.748801	−	0.481225i
$26$	21.0406	+	3.02518i	0.809252	+	0.116353i
$27$		0			0
$28$	8.46883	−	2.48667i	0.302458	−	0.0888098i
$29$	1.37521	−	0.628036i	0.0474209	−	0.0216564i	−0.391563	−	0.920151i	$-0.628066\pi$
$29$	1.37521	−	0.628036i	0.0474209	−	0.0216564i	0.438984	+	0.898495i	$0.355338\pi$
$30$		0			0
$31$	−7.81855	−	54.3792i	−0.252211	−	1.75417i	−0.584875	−	0.811123i	$-0.698856\pi$
$31$	−7.81855	−	54.3792i	−0.252211	−	1.75417i	0.332664	−	0.943046i	$-0.392053\pi$
$32$	1.59372	−	5.42771i	0.0498038	−	0.169616i
$33$		0			0
$34$	13.0120	+	8.36228i	0.382705	+	0.245949i
$35$	−3.95482	+	6.15383i	−0.112995	+	0.175824i
$36$		0			0
$37$	−9.31847	−	2.73615i	−0.251851	−	0.0739500i	0.153370	−	0.988169i	$-0.450987\pi$
$37$	−9.31847	−	2.73615i	−0.251851	−	0.0739500i	−0.405221	+	0.914219i	$0.632805\pi$
$38$	11.6971	−	1.68179i	0.307818	−	0.0442576i
$39$		0			0
$40$	1.94757	+	4.26459i	0.0486893	+	0.106615i
$41$	7.76093	+	26.4313i	0.189291	+	0.644666i	0.998376	+	0.0569738i	$0.0181451\pi$
$41$	7.76093	+	26.4313i	0.189291	+	0.644666i	−0.809085	+	0.587692i	$0.800037\pi$
$42$		0			0
$43$	0.461419	−	3.20924i	0.0107307	−	0.0746335i	−0.983752	−	0.179530i	$-0.942542\pi$
$43$	0.461419	−	3.20924i	0.0107307	−	0.0746335i	0.994483	+	0.104897i	$0.0334513\pi$
$44$	6.60100	+	10.2714i	0.150023	+	0.233440i
$45$		0			0
$46$	−16.2258	+	28.1908i	−0.352735	+	0.612844i
$47$			16.5698i			0.352549i	0.984341	+	0.176274i	$0.0564046\pi$
$47$			16.5698i			0.352549i	−0.984341	+	0.176274i	$0.943595\pi$
$48$		0			0
$49$	4.20168	−	29.2233i	0.0857486	−	0.596394i
$50$	28.6260	+	13.0730i	0.572519	+	0.261461i
$51$		0			0
$52$	12.4881	+	27.3452i	0.240156	+	0.525869i
$53$	19.7900	−	17.1482i	0.373397	−	0.323550i	−0.447865	−	0.894101i	$-0.647816\pi$
$53$	19.7900	−	17.1482i	0.373397	−	0.323550i	0.821262	+	0.570551i	$0.193270\pi$
$54$		0			0
$55$	−9.70911	−	2.85085i	−0.176529	−	0.0518337i
$56$	9.43354	+	8.17421i	0.168456	+	0.145968i
$57$		0			0
$58$	1.79864	+	1.15592i	0.0310110	+	0.0199296i
$59$	39.3240	+	34.0745i	0.666509	+	0.577533i	0.921010	−	0.389539i	$-0.127366\pi$
$59$	39.3240	+	34.0745i	0.666509	+	0.577533i	−0.254501	+	0.967073i	$0.581911\pi$
$60$		0			0
$61$	−7.43111	−	51.6845i	−0.121821	−	0.847287i	−0.955490	−	0.295022i	$-0.904673\pi$
$61$	−7.43111	−	51.6845i	−0.121821	−	0.847287i	0.833669	−	0.552265i	$-0.186236\pi$
$62$	58.7177	−	50.8792i	0.947060	−	0.820632i
$63$		0			0
$64$	7.67594	−	2.25386i	0.119937	−	0.0352166i
$65$	−22.6630	−	10.3499i	−0.348662	−	0.159228i
$66$		0			0
$67$	−72.0417	+	46.2984i	−1.07525	+	0.691021i	−0.953455	−	0.301534i	$-0.902501\pi$
$67$	−72.0417	+	46.2984i	−1.07525	+	0.691021i	−0.121795	+	0.992555i	$0.538865\pi$
$68$			21.8741i			0.321679i
$69$		0			0
$70$	−10.3451			−0.147787
$71$	13.0536	+	20.3119i	0.183854	+	0.286082i	0.920930	−	0.389727i	$-0.127431\pi$
$71$	13.0536	+	20.3119i	0.183854	+	0.286082i	−0.737076	+	0.675809i	$0.763794\pi$
$72$		0			0
$73$	−17.4408	+	38.1901i	−0.238915	+	0.523152i	−0.990669	−	0.136293i	$-0.956481\pi$
$73$	−17.4408	+	38.1901i	−0.238915	+	0.523152i	0.751753	+	0.659444i	$0.229208\pi$
$74$	−3.86950	−	13.1783i	−0.0522906	−	0.178085i
$75$		0			0
$76$	10.9442	+	12.6303i	0.144003	+	0.166188i
$77$	−26.6673	+	3.83419i	−0.346329	+	0.0497946i
$78$		0			0
$79$	11.1321	−	12.8471i	0.140913	−	0.162622i	−0.680906	−	0.732370i	$-0.738414\pi$
$79$	11.1321	−	12.8471i	0.140913	−	0.162622i	0.821819	+	0.569749i	$0.192959\pi$
$80$	−3.58456	+	5.57768i	−0.0448070	+	0.0697210i
$81$		0			0
$82$	−25.5118	+	29.4422i	−0.311119	+	0.359051i
$83$	21.5848	−	73.5110i	0.260058	−	0.885675i	−0.721160	−	0.692769i	$-0.756391\pi$
$83$	21.5848	−	73.5110i	0.260058	−	0.885675i	0.981217	−	0.192906i	$-0.0617912\pi$
$84$		0			0
$85$	−11.8718	−	13.7008i	−0.139668	−	0.161186i
$86$	4.17087	−	1.90477i	0.0484985	−	0.0221485i
$87$		0			0
$88$	−7.17296	+	15.7066i	−0.0815109	+	0.178484i
$89$	−81.9773	−	11.7865i	−0.921093	−	0.132433i	−0.334575	−	0.942369i	$-0.608593\pi$
$89$	−81.9773	−	11.7865i	−0.921093	−	0.132433i	−0.586518	+	0.809936i	$0.699502\pi$
$90$		0			0
$91$	−66.3341			−0.728947
$92$	−45.9449	+	2.25018i	−0.499401	+	0.0244585i
$93$		0			0
$94$	−19.7133	+	12.6690i	−0.209716	+	0.134776i
$95$	−13.7097	−	1.97116i	−0.144313	−	0.0207491i
$96$		0			0
$97$	130.934	−	38.4456i	1.34983	−	0.396346i	0.474664	−	0.880167i	$-0.342570\pi$
$97$	130.934	−	38.4456i	1.34983	−	0.396346i	0.875167	+	0.483821i	$0.160752\pi$
$98$	37.9799	−	17.3448i	0.387550	−	0.176988i
$99$		0			0
$100$	6.33373	+	44.0521i	0.0633373	+	0.440521i
$101$	−19.4662	+	66.2956i	−0.192734	+	0.656392i	0.805250	+	0.592935i	$0.202031\pi$
$101$	−19.4662	+	66.2956i	−0.192734	+	0.656392i	−0.997985	+	0.0634574i	$0.979787\pi$
$102$		0			0
$103$	−60.7327	−	39.0305i	−0.589637	−	0.378937i	0.211535	−	0.977370i	$-0.432154\pi$
$103$	−60.7327	−	39.0305i	−0.589637	−	0.378937i	−0.801173	+	0.598433i	$0.795790\pi$
$104$	−22.9847	+	35.7649i	−0.221007	+	0.343893i
$105$		0			0
$106$	35.5325	+	10.4333i	0.335212	+	0.0984271i
$107$	−201.019	+	28.9021i	−1.87868	+	0.270114i	−0.984209	−	0.177011i	$-0.943357\pi$
$107$	−201.019	+	28.9021i	−1.87868	+	0.270114i	−0.894472	+	0.447124i	$0.852448\pi$
$108$		0			0
$109$	11.6714	+	25.5569i	0.107077	+	0.234467i	0.955585	−	0.294717i	$-0.0952254\pi$
$109$	11.6714	+	25.5569i	0.107077	+	0.234467i	−0.848507	+	0.529184i	$0.822498\pi$
$110$	−4.03172	−	13.7308i	−0.0366520	−	0.124825i
$111$		0			0
$112$	−2.51224	+	17.4730i	−0.0224308	+	0.156009i
$113$	12.6915	+	19.7484i	0.112314	+	0.174764i	0.892860	−	0.450334i	$-0.148695\pi$
$113$	12.6915	+	19.7484i	0.112314	+	0.174764i	−0.780546	+	0.625098i	$0.785059\pi$
$114$		0			0
$115$	27.5562	−	26.3452i	0.239619	−	0.229089i
$116$			3.02366i			0.0260660i
$117$		0			0
$118$	−10.4724	+	72.8370i	−0.0887490	+	0.617263i
$119$	−43.9055	−	20.0509i	−0.368953	−	0.168495i
$120$		0			0
$121$	34.7833	+	76.1648i	0.287465	+	0.629461i
$122$	55.8080	−	48.3579i	0.457443	−	0.396376i
$123$		0			0
$124$	105.426	+	30.9559i	0.850210	+	0.249644i
$125$	−59.1929	−	51.2909i	−0.473543	−	0.410327i
$126$		0			0
$127$	−7.15226	−	4.59648i	−0.0563170	−	0.0361927i	0.512179	−	0.858879i	$-0.328838\pi$
$127$	−7.15226	−	4.59648i	−0.0563170	−	0.0361927i	−0.568496	+	0.822686i	$0.692475\pi$
$128$	8.55033	+	7.40890i	0.0667995	+	0.0578821i
$129$		0			0
$130$	−5.01438	−	34.8758i	−0.0385721	−	0.268275i
$131$	−25.5878	+	22.1720i	−0.195327	+	0.169252i	−0.747033	−	0.664787i	$-0.768522\pi$
$131$	−25.5878	+	22.1720i	−0.195327	+	0.169252i	0.551706	+	0.834039i	$0.313977\pi$
$132$		0			0
$133$	−35.3834	+	10.3895i	−0.266041	+	0.0781165i
$134$	−110.164	−	50.3100i	−0.822116	−	0.375448i
$135$		0			0
$136$	−26.0239	+	16.7246i	−0.191352	+	0.122975i
$137$		−	137.106i		−	1.00077i	−0.865802	−	0.500386i	$-0.833191\pi$
$137$		−	137.106i		−	1.00077i	0.865802	−	0.500386i	$-0.166809\pi$
$138$		0			0
$139$	71.0800			0.511367			0.255684	−	0.966761i	$-0.417699\pi$
$139$	71.0800			0.511367			0.255684	+	0.966761i	$0.417699\pi$
$140$	−7.90965	−	12.3077i	−0.0564975	−	0.0879118i
$141$		0			0
$142$	−14.1847	+	31.0601i	−0.0998922	+	0.218733i
$143$	−25.8520	−	88.0437i	−0.180783	−	0.615690i
$144$		0			0
$145$	−1.64104	−	1.89386i	−0.0113175	−	0.0130611i
$146$	−58.7701	+	8.44987i	−0.402535	+	0.0578758i
$147$		0			0
$148$	12.7198	−	14.6795i	0.0859449	−	0.0991857i
$149$	−28.3394	+	44.0969i	−0.190197	+	0.295953i	−0.923235	−	0.384235i	$-0.874465\pi$
$149$	−28.3394	+	44.0969i	−0.190197	+	0.295953i	0.733038	+	0.680188i	$0.238102\pi$
$150$		0			0
$151$	−30.6294	+	35.3483i	−0.202844	+	0.234094i	−0.848053	−	0.529912i	$-0.822225\pi$
$151$	−30.6294	+	35.3483i	−0.202844	+	0.234094i	0.645209	+	0.764006i	$0.276770\pi$
$152$	−6.65868	+	22.6774i	−0.0438071	+	0.149193i
$153$		0			0
$154$	−24.9509	−	28.7949i	−0.162019	−	0.186980i
$155$	−82.8340	+	37.8290i	−0.534413	+	0.244058i
$156$		0			0
$157$	−1.15755	+	2.53468i	−0.00737293	+	0.0161445i	−0.913283	−	0.407326i	$-0.866461\pi$
$157$	−1.15755	+	2.53468i	−0.00737293	+	0.0161445i	0.905910	+	0.423471i	$0.139188\pi$
$158$	23.7958	+	3.42132i	0.150606	+	0.0216539i
$159$		0			0
$160$	−9.37652			−0.0586032
$161$	37.5989	−	94.2826i	0.233534	−	0.585606i
$162$		0			0
$163$	−108.262	+	69.5755i	−0.664182	+	0.426844i	−0.828824	−	0.559510i	$-0.810989\pi$
$163$	−108.262	+	69.5755i	−0.664182	+	0.426844i	0.164642	+	0.986353i	$0.447353\pi$
$164$	−54.5335	−	7.84074i	−0.332521	−	0.0478094i
$165$		0			0
$166$	103.960	−	30.5255i	0.626266	−	0.183888i
$167$	−114.194	+	52.1505i	−0.683794	+	0.312278i	−0.726852	−	0.686794i	$-0.759017\pi$
$167$	−114.194	+	52.1505i	−0.683794	+	0.312278i	0.0430575	+	0.999073i	$0.486290\pi$
$168$		0			0
$169$	−8.10174	−	56.3489i	−0.0479393	−	0.333425i
$170$	7.22303	−	24.5994i	0.0424884	−	0.144702i
$171$		0			0
$172$	5.45510	+	3.50578i	0.0317157	+	0.0203824i
$173$	95.4196	−	148.476i	0.551558	−	0.858242i	−0.447797	−	0.894135i	$-0.647791\pi$
$173$	95.4196	−	148.476i	0.551558	−	0.858242i	0.999356	+	0.0358935i	$0.0114277\pi$
$174$		0			0
$175$	−94.2265	−	27.6674i	−0.538437	−	0.158099i
$176$	−24.1706	+	3.47521i	−0.137333	+	0.0197455i
$177$		0			0
$178$	−48.6557	−	106.541i	−0.273347	−	0.598546i
$179$	54.2932	+	184.906i	0.303314	+	1.03299i	0.960272	+	0.279066i	$0.0900248\pi$
$179$	54.2932	+	184.906i	0.303314	+	1.03299i	−0.656958	+	0.753927i	$0.728157\pi$
$180$		0			0
$181$	−32.5747	+	226.562i	−0.179971	+	1.25172i	0.676855	+	0.736117i	$0.263343\pi$
$181$	−32.5747	+	226.562i	−0.179971	+	1.25172i	−0.856825	+	0.515607i	$0.827567\pi$
$182$	−50.7179	−	78.9185i	−0.278670	−	0.433618i
$183$		0			0
$184$	−37.8057	−	52.9408i	−0.205466	−	0.287722i
$185$			16.0979i			0.0870157i
$186$		0			0
$187$	9.50216	−	66.0890i	0.0508137	−	0.353417i
$188$	−30.1448	−	13.7667i	−0.160345	−	0.0732270i
$189$		0			0
$190$	−8.13710	−	17.8178i	−0.0428268	−	0.0937777i
$191$	−36.7654	+	31.8574i	−0.192489	+	0.166793i	−0.745773	−	0.666200i	$-0.767920\pi$
$191$	−36.7654	+	31.8574i	−0.192489	+	0.166793i	0.553284	+	0.832992i	$0.313374\pi$
$192$		0			0
$193$	329.092	+	96.6301i	1.70514	+	0.500674i	0.981816	−	0.189835i	$-0.0607954\pi$
$193$	329.092	+	96.6301i	1.70514	+	0.500674i	0.723323	+	0.690509i	$0.242614\pi$
$194$	145.849	+	126.378i	0.751797	+	0.651435i
$195$		0			0
$196$	49.6741	+	31.9236i	0.253439	+	0.162875i
$197$	−160.824	−	139.355i	−0.816365	−	0.707385i	0.142947	−	0.989730i	$-0.454342\pi$
$197$	−160.824	−	139.355i	−0.816365	−	0.707385i	−0.959313	+	0.282346i	$0.908888\pi$
$198$		0			0
$199$	1.81726	+	12.6393i	0.00913195	+	0.0635141i	0.993878	−	0.110485i	$-0.0352403\pi$
$199$	1.81726	+	12.6393i	0.00913195	+	0.0635141i	−0.984746	+	0.173999i	$0.944331\pi$
$200$	−47.5666	+	41.2167i	−0.237833	+	0.206084i
$201$		0			0
$202$	−93.7562	+	27.5293i	−0.464139	+	0.136284i
$203$	−6.06904	−	2.77164i	−0.0298967	−	0.0136534i
$204$		0			0
$205$	38.4123	−	24.6861i	0.187377	−	0.120420i
$206$		−	102.096i		−	0.495613i
$207$		0			0
$208$	−60.1236			−0.289056
$209$	−27.5795	−	42.9145i	−0.131959	−	0.205332i
$210$		0			0
$211$	−62.8344	+	137.588i	−0.297793	+	0.652077i	−0.998090	−	0.0617753i	$-0.980324\pi$
$211$	−62.8344	+	137.588i	−0.297793	+	0.652077i	0.700297	+	0.713852i	$0.253051\pi$
$212$	14.7549	+	50.2505i	0.0695985	+	0.237031i
$213$		0			0
$214$	−188.081	−	217.057i	−0.878881	−	1.01428i
$215$	−5.31948	+	0.764826i	−0.0247418	+	0.00355733i
$216$		0			0
$217$	−158.773	+	183.234i	−0.731673	+	0.844396i
$218$	−21.4816	+	33.4260i	−0.0985393	+	0.153330i
$219$		0			0
$220$	13.2531	−	15.2949i	0.0602413	−	0.0695221i
$221$	46.3152	−	157.735i	0.209571	−	0.713733i
$222$		0			0
$223$	−58.7911	−	67.8485i	−0.263637	−	0.304253i	0.608462	−	0.793583i	$-0.291787\pi$
$223$	−58.7911	−	67.8485i	−0.263637	−	0.304253i	−0.872099	+	0.489330i	$0.837241\pi$
$224$	−22.7087	+	10.3707i	−0.101378	+	0.0462979i
$225$		0			0
$226$	−13.7912	+	30.1985i	−0.0610229	+	0.133621i
$227$	387.071	+	55.6524i	1.70516	+	0.245165i	0.924877	−	0.380266i	$-0.124168\pi$
$227$	387.071	+	55.6524i	1.70516	+	0.245165i	0.780280	+	0.625431i	$0.215077\pi$
$228$		0			0
$229$	332.316			1.45116			0.725581	−	0.688136i	$-0.241571\pi$
$229$	332.316			1.45116			0.725581	+	0.688136i	$0.241571\pi$
$230$	52.4121	+	12.6409i	0.227879	+	0.0549604i
$231$		0			0
$232$	−3.59728	+	2.31183i	−0.0155055	+	0.00996479i
$233$	456.270	+	65.6017i	1.95824	+	0.281552i	0.999990	−	0.00438210i	$-0.00139487\pi$
$233$	456.270	+	65.6017i	1.95824	+	0.281552i	0.958249	+	0.285934i	$0.0923040\pi$
$234$		0			0
$235$	26.3527	−	7.73786i	0.112139	−	0.0329271i
$236$	−94.6621	+	43.2307i	−0.401110	+	0.183181i
$237$		0			0
$238$	−9.71444	−	67.5654i	−0.0408170	−	0.283888i
$239$	−59.6369	+	203.105i	−0.249527	+	0.849810i	0.735517	+	0.677506i	$0.236939\pi$
$239$	−59.6369	+	203.105i	−0.249527	+	0.849810i	−0.985044	+	0.172304i	$0.944879\pi$
$240$		0			0
$241$	−131.445	−	84.4747i	−0.545415	−	0.350517i	0.238738	−	0.971084i	$-0.423266\pi$
$241$	−131.445	−	84.4747i	−0.545415	−	0.350517i	−0.784154	+	0.620567i	$0.786903\pi$
$242$	−64.0195	+	99.6163i	−0.264544	+	0.411638i
$243$		0			0
$244$	100.202	+	29.4219i	0.410663	+	0.120581i
$245$	−48.4391	+	6.96449i	−0.197711	+	0.0284265i
$246$		0			0
$247$	−52.1763	−	114.250i	−0.211240	−	0.462551i
$248$	43.7782	+	149.095i	0.176525	+	0.601189i
$249$		0			0
$250$	15.7637	−	109.639i	0.0630546	−	0.438554i
$251$	68.4626	+	106.530i	0.272759	+	0.424422i	0.950428	−	0.310946i	$-0.100646\pi$
$251$	68.4626	+	106.530i	0.272759	+	0.424422i	−0.677668	+	0.735368i	$0.737009\pi$
$252$		0			0
$253$	139.792	+	13.1600i	0.552539	+	0.0520159i
$254$		−	12.0235i		−	0.0473367i
$255$		0			0
$256$	−2.27704	+	15.8371i	−0.00889468	+	0.0618638i
$257$	224.618	+	102.580i	0.874000	+	0.399142i	0.801336	−	0.598214i	$-0.204123\pi$
$257$	224.618	+	102.580i	0.874000	+	0.399142i	0.0726635	+	0.997357i	$0.476850\pi$
$258$		0			0
$259$	17.8048	+	38.9871i	0.0687444	+	0.150529i
$260$	37.6582	−	32.6310i	0.144839	−	0.125504i
$261$		0			0
$262$	−45.9423	−	13.4899i	−0.175352	−	0.0514880i
$263$	377.211	+	326.855i	1.43426	+	1.24280i	0.923788	+	0.382904i	$0.125076\pi$
$263$	377.211	+	326.855i	1.43426	+	1.24280i	0.510476	+	0.859892i	$0.329469\pi$
$264$		0			0
$265$	−36.5142	−	23.4663i	−0.137790	−	0.0885520i
$266$	−39.4140	−	34.1524i	−0.148173	−	0.128393i
$267$		0			0
$268$	−24.3746	−	169.529i	−0.0909500	−	0.632571i
$269$	150.325	−	130.257i	0.558829	−	0.484228i	−0.329045	−	0.944314i	$-0.606727\pi$
$269$	150.325	−	130.257i	0.558829	−	0.484228i	0.887874	+	0.460086i	$0.152181\pi$
$270$		0			0
$271$	−303.086	+	88.9942i	−1.11840	+	0.328392i	−0.788139	−	0.615498i	$-0.788955\pi$
$271$	−303.086	+	88.9942i	−1.11840	+	0.328392i	−0.330261	+	0.943890i	$0.607137\pi$
$272$	−39.7948	−	18.1737i	−0.146305	−	0.0668150i
$273$		0			0
$274$	163.116	−	104.829i	0.595316	−	0.382586i
$275$		−	135.847i		−	0.493990i
$276$		0			0
$277$	214.433			0.774125			0.387062	−	0.922054i	$-0.373490\pi$
$277$	214.433			0.774125			0.387062	+	0.922054i	$0.373490\pi$
$278$	54.3465	+	84.5648i	0.195491	+	0.304190i
$279$		0			0
$280$	8.59499	−	18.8204i	0.0306964	−	0.0672157i
$281$	14.3211	+	48.7732i	0.0509648	+	0.173570i	0.981043	−	0.193793i	$-0.0620789\pi$
$281$	14.3211	+	48.7732i	0.0509648	+	0.173570i	−0.930078	+	0.367363i	$0.880261\pi$
$282$		0			0
$283$	−193.212	−	222.979i	−0.682730	−	0.787912i	0.303582	−	0.952805i	$-0.401817\pi$
$283$	−193.212	−	222.979i	−0.682730	−	0.787912i	−0.986311	+	0.164893i	$0.947272\pi$
$284$	−47.7980	+	6.87231i	−0.168303	+	0.0241983i
$285$		0			0
$286$	84.9807	−	98.0730i	0.297135	−	0.342913i
$287$	65.7260	−	102.272i	0.229011	−	0.356347i
$288$		0			0
$289$	−110.921	+	128.009i	−0.383808	+	0.442939i
$290$	0.998438	−	3.40037i	0.00344289	−	0.0117254i
$291$		0			0
$292$	−54.9874	−	63.4589i	−0.188313	−	0.217325i
$293$	118.733	−	54.2237i	0.405233	−	0.185064i	−0.202362	−	0.979311i	$-0.564862\pi$
$293$	118.733	−	54.2237i	0.405233	−	0.185064i	0.607595	+	0.794247i	$0.292134\pi$
$294$		0			0
$295$	35.8285	−	78.4535i	0.121453	−	0.265944i
$296$	27.1897	+	3.90929i	0.0918572	+	0.0132071i
$297$		0			0
$298$	−74.1304			−0.248760
$299$	336.075	+	81.0553i	1.12400	+	0.271088i
$300$		0			0
$301$	−12.0372	+	7.73582i	−0.0399906	+	0.0257004i
$302$	−65.4730	−	9.41359i	−0.216798	−	0.0311708i
$303$		0			0
$304$	−32.0706	+	9.41679i	−0.105496	+	0.0309763i
$305$	−78.7292	+	35.9544i	−0.258128	+	0.117883i
$306$		0			0
$307$	66.2443	+	460.739i	0.215779	+	1.50078i	0.753383	+	0.657582i	$0.228421\pi$
$307$	66.2443	+	460.739i	0.215779	+	1.50078i	−0.537604	+	0.843198i	$0.680670\pi$
$308$	15.1806	−	51.7005i	0.0492878	−	0.167859i
$309$		0			0
$310$	−108.339	−	69.6252i	−0.349481	−	0.224598i
$311$	−112.265	+	174.688i	−0.360981	+	0.561697i	−0.973479	−	0.228775i	$-0.926528\pi$
$311$	−112.265	+	174.688i	−0.360981	+	0.561697i	0.612499	+	0.790472i	$0.290165\pi$
$312$		0			0
$313$	315.047	+	92.5060i	1.00654	+	0.295546i	0.743137	−	0.669140i	$-0.233337\pi$
$313$	315.047	+	92.5060i	1.00654	+	0.295546i	0.263402	+	0.964686i	$0.415155\pi$
$314$	−3.90058	+	0.560819i	−0.0124222	+	0.00178605i
$315$		0			0
$316$	14.1234	+	30.9260i	0.0446944	+	0.0978671i
$317$	27.4178	+	93.3764i	0.0864914	+	0.294563i	0.991368	−	0.131112i	$-0.0418549\pi$
$317$	27.4178	+	93.3764i	0.0864914	+	0.294563i	−0.904876	+	0.425675i	$0.860037\pi$
$318$		0			0
$319$	1.31348	−	9.13546i	0.00411750	−	0.0286378i
$320$	−7.16911	−	11.1554i	−0.0224035	−	0.0348605i
$321$		0			0
$322$	140.917	−	27.3549i	0.437629	−	0.0849530i
$323$		−	91.3917i		−	0.282947i
$324$		0			0
$325$	47.6009	−	331.071i	0.146464	−	1.01868i
$326$	−165.550	−	75.6040i	−0.507821	−	0.231914i
$327$		0			0
$328$	−32.3671	−	70.8741i	−0.0986802	−	0.216080i
$329$	55.2646	−	47.8870i	0.167977	−	0.145553i
$330$		0			0
$331$	289.525	+	85.0122i	0.874698	+	0.256834i	0.688112	−	0.725604i	$-0.258440\pi$
$331$	289.525	+	85.0122i	0.874698	+	0.256834i	0.186586	+	0.982439i	$0.440258\pi$
$332$	115.803	+	100.344i	0.348803	+	0.302240i
$333$		0			0
$334$	−149.354	−	95.9843i	−0.447169	−	0.287378i
$335$	107.276	+	92.9550i	0.320226	+	0.277478i
$336$		0			0
$337$	−55.7521	−	387.764i	−0.165436	−	1.15064i	−0.888172	−	0.459511i	$-0.848025\pi$
$337$	−55.7521	−	387.764i	−0.165436	−	1.15064i	0.722736	−	0.691124i	$-0.242884\pi$
$338$	60.8445	−	52.7221i	0.180013	−	0.155982i
$339$		0			0
$340$	34.7888	−	10.2149i	0.102320	−	0.0300439i
$341$	−305.080	−	139.325i	−0.894662	−	0.408578i
$342$		0			0
$343$	−291.528	+	187.354i	−0.849936	+	0.546220i
$344$			9.17045i			0.0266583i
$345$		0			0
$346$	249.600			0.721386
$347$	−54.0436	−	84.0936i	−0.155745	−	0.242345i	0.754608	−	0.656175i	$-0.227827\pi$
$347$	−54.0436	−	84.0936i	−0.155745	−	0.242345i	−0.910354	+	0.413831i	$0.864190\pi$
$348$		0			0
$349$	254.880	−	558.110i	0.730316	−	1.59917i	−0.0685420	−	0.997648i	$-0.521835\pi$
$349$	254.880	−	558.110i	0.730316	−	1.59917i	0.798858	−	0.601520i	$-0.205438\pi$
$350$	−39.1276	−	133.256i	−0.111793	−	0.380732i
$351$		0			0
$352$	−22.6149	−	26.0990i	−0.0642469	−	0.0741449i
$353$	234.679	−	33.7418i	0.664814	−	0.0955858i	0.198357	−	0.980130i	$-0.436439\pi$
$353$	234.679	−	33.7418i	0.664814	−	0.0955858i	0.466457	+	0.884544i	$0.345530\pi$
$354$		0			0
$355$	26.2083	−	30.2459i	0.0738261	−	0.0851998i
$356$	89.5520	−	139.346i	0.251551	−	0.391420i
$357$		0			0
$358$	−178.473	+	205.969i	−0.498528	+	0.575332i
$359$	71.1206	−	242.215i	0.198108	−	0.674692i	−0.799180	−	0.601092i	$-0.794733\pi$
$359$	71.1206	−	242.215i	0.198108	−	0.674692i	0.997288	−	0.0736009i	$-0.0234491\pi$
$360$		0			0
$361$	190.679	+	220.055i	0.528197	+	0.609571i
$362$	−294.449	+	134.471i	−0.813396	+	0.371466i
$363$		0			0
$364$	55.1124	−	120.679i	0.151408	−	0.331537i
$365$	68.8824	+	9.90379i	0.188719	+	0.0271337i
$366$		0			0
$367$	−42.6382			−0.116180			−0.0580902	−	0.998311i	$-0.518501\pi$
$367$	−42.6382			−0.116180			−0.0580902	+	0.998311i	$0.518501\pi$
$368$	34.0788	−	85.4555i	0.0926053	−	0.232216i
$369$		0			0
$370$	−19.1519	+	12.3082i	−0.0517618	+	0.0332653i
$371$	−114.387	−	16.4464i	−0.308321	−	0.0443299i
$372$		0			0
$373$	513.996	−	150.923i	1.37801	−	0.404619i	0.492932	−	0.870068i	$-0.335925\pi$
$373$	513.996	−	150.923i	1.37801	−	0.404619i	0.885075	+	0.465449i	$0.154107\pi$
$374$	85.8920	−	39.2256i	0.229658	−	0.104881i
$375$		0			0
$376$	−6.66979	−	46.3894i	−0.0177388	−	0.123376i
$377$	6.40214	−	21.8037i	0.0169818	−	0.0578347i
$378$		0			0
$379$	−239.951	−	154.207i	−0.633115	−	0.406879i	0.184346	−	0.982861i	$-0.440983\pi$
$379$	−239.951	−	154.207i	−0.633115	−	0.406879i	−0.817462	+	0.575983i	$0.804620\pi$
$380$	14.9765	−	23.3039i	0.0394119	−	0.0613262i
$381$		0			0
$382$	−66.0112	−	19.3827i	−0.172804	−	0.0507399i
$383$	−418.962	+	60.2377i	−1.09390	+	0.157279i	−0.665563	−	0.746342i	$-0.731808\pi$
$383$	−418.962	+	60.2377i	−1.09390	+	0.157279i	−0.428334	+	0.903621i	$0.640899\pi$
$384$		0			0
$385$	18.5512	+	40.6214i	0.0481849	+	0.105510i
$386$	136.656	+	465.406i	0.354030	+	1.20572i
$387$		0			0
$388$	−38.8409	+	270.144i	−0.100105	+	0.696248i
$389$	−411.908	−	640.942i	−1.05889	−	1.64766i	−0.699762	−	0.714376i	$-0.746711\pi$
$389$	−411.908	−	640.942i	−1.05889	−	1.64766i	−0.359128	−	0.933288i	$-0.616926\pi$
$390$		0			0
$391$	197.941	+	155.235i	0.506244	+	0.397021i
$392$			83.5060i			0.213026i
$393$		0			0
$394$	42.8290	−	297.882i	0.108703	−	0.756047i
$395$	−25.6307	−	11.7051i	−0.0648878	−	0.0296333i
$396$		0			0
$397$	187.248	+	410.016i	0.471657	+	1.03279i	0.984674	+	0.174407i	$0.0558007\pi$
$397$	187.248	+	410.016i	0.471657	+	1.03279i	−0.513016	+	0.858379i	$0.671472\pi$
$398$	−13.6477	+	11.8258i	−0.0342907	+	0.0297131i
$399$		0			0
$400$	−85.4046	−	25.0770i	−0.213511	−	0.0626926i
$401$	26.7842	+	23.2087i	0.0667936	+	0.0578770i	0.687618	−	0.726073i	$-0.258656\pi$
$401$	26.7842	+	23.2087i	0.0667936	+	0.0578770i	−0.620824	+	0.783950i	$0.713202\pi$
$402$		0			0
$403$	−694.686	−	446.448i	−1.72379	−	1.10781i
$404$	−104.436	−	90.4945i	−0.258505	−	0.223996i
$405$		0			0
$406$	−1.34283	−	9.33955i	−0.00330745	−	0.0230038i
$407$	−44.8076	+	38.8260i	−0.110092	+	0.0953957i
$408$		0			0
$409$	−86.0133	+	25.2558i	−0.210301	+	0.0617501i	−0.385186	−	0.922839i	$-0.625863\pi$
$409$	−86.0133	+	25.2558i	−0.210301	+	0.0617501i	0.174885	+	0.984589i	$0.444045\pi$
$410$	58.7387	+	26.8250i	0.143265	+	0.0654269i
$411$		0			0
$412$	121.465	−	78.0610i	0.294819	−	0.189468i
$413$		−	229.632i		−	0.556009i
$414$		0			0
$415$	−126.992			−0.306005
$416$	−45.9694	−	71.5298i	−0.110503	−	0.171947i
$417$		0			0
$418$	29.9691	−	65.6233i	0.0716965	−	0.156993i
$419$	29.0410	+	98.9046i	0.0693103	+	0.236049i	0.986862	−	0.161568i	$-0.0516553\pi$
$419$	29.0410	+	98.9046i	0.0693103	+	0.236049i	−0.917551	+	0.397618i	$0.869837\pi$
$420$		0			0
$421$	62.5740	+	72.2143i	0.148632	+	0.171530i	0.825183	−	0.564865i	$-0.191072\pi$
$421$	62.5740	+	72.2143i	0.148632	+	0.171530i	−0.676551	+	0.736395i	$0.736526\pi$
$422$	−211.732	+	30.4425i	−0.501735	+	0.0721387i
$423$		0			0
$424$	−48.5023	+	55.9747i	−0.114392	+	0.132016i
$425$	131.580	−	204.742i	0.309600	−	0.481746i
$426$		0			0
$427$	−150.905	+	174.154i	−0.353408	+	0.407854i
$428$	114.432	−	389.719i	0.267364	−	0.910559i
$429$		0			0
$430$	−4.97710	−	5.74388i	−0.0115746	−	0.0133579i
$431$	−167.992	+	76.7193i	−0.389772	+	0.178003i	−0.600655	−	0.799508i	$-0.705093\pi$
$431$	−167.992	+	76.7193i	−0.389772	+	0.178003i	0.210883	+	0.977511i	$0.432366\pi$
$432$		0			0
$433$	−330.586	+	723.882i	−0.763478	+	1.67178i	−0.0229693	+	0.999736i	$0.507312\pi$
$433$	−330.586	+	723.882i	−0.763478	+	1.67178i	−0.740508	+	0.672047i	$0.765415\pi$
$434$	−339.391	−	48.7970i	−0.782006	−	0.112436i
$435$		0			0
$436$	−56.1917			−0.128880
$437$	191.961	−	9.40142i	0.439270	−	0.0215135i
$438$		0			0
$439$	128.711	−	82.7173i	0.293191	−	0.188422i	−0.385774	−	0.922593i	$-0.626065\pi$
$439$	128.711	−	82.7173i	0.293191	−	0.188422i	0.678964	+	0.734171i	$0.262429\pi$
$440$	28.3295	+	4.07317i	0.0643853	+	0.00925721i
$441$		0			0
$442$	223.071	−	65.4996i	0.504686	−	0.148189i
$443$	−62.6117	+	28.5938i	−0.141336	+	0.0645458i	−0.484827	−	0.874610i	$-0.661118\pi$
$443$	−62.6117	+	28.5938i	−0.141336	+	0.0645458i	0.343492	+	0.939156i	$0.388390\pi$
$444$		0			0
$445$	19.5368	+	135.881i	0.0439029	+	0.305351i
$446$	35.7696	−	121.820i	0.0802009	−	0.273139i
$447$		0			0
$448$	−29.7008	−	19.0876i	−0.0662965	−	0.0426062i
$449$	−355.313	+	552.878i	−0.791343	+	1.23135i	0.177608	+	0.984101i	$0.443164\pi$
$449$	−355.313	+	552.878i	−0.791343	+	1.23135i	−0.968951	+	0.247253i	$0.920472\pi$
$450$		0			0
$451$	161.358	+	47.3789i	0.357778	+	0.105053i
$452$	−46.4719	+	6.68166i	−0.102814	+	0.0147824i
$453$		0			0
$454$	229.737	+	503.053i	0.506028	+	1.10805i
$455$	30.9771	+	105.498i	0.0680815	+	0.231864i
$456$		0			0
$457$	−36.4466	+	253.492i	−0.0797520	+	0.554687i	0.910296	+	0.413958i	$0.135854\pi$
$457$	−36.4466	+	253.492i	−0.0797520	+	0.554687i	−0.990048	+	0.140729i	$0.955055\pi$
$458$	254.083	+	395.361i	0.554766	+	0.863233i
$459$		0			0
$460$	25.0343	+	72.0204i	0.0544225	+	0.156566i
$461$			363.811i			0.789178i	0.918858	+	0.394589i	$0.129113\pi$
$461$			363.811i			0.789178i	−0.918858	+	0.394589i	$0.870887\pi$
$462$		0			0
$463$	50.5132	−	351.327i	0.109100	−	0.758805i	−0.859671	−	0.510848i	$-0.829332\pi$
$463$	50.5132	−	351.327i	0.109100	−	0.758805i	0.968771	−	0.247957i	$-0.0797593\pi$
$464$	−5.50083	−	2.51214i	−0.0118552	−	0.00541411i
$465$		0			0
$466$	270.808	+	592.988i	0.581134	+	1.27251i
$467$	−476.802	+	413.152i	−1.02099	+	0.884693i	−0.993374	−	0.114925i	$-0.963337\pi$
$467$	−476.802	+	413.152i	−1.02099	+	0.884693i	−0.0276162	+	0.999619i	$0.508792\pi$
$468$		0			0
$469$	362.619	+	106.475i	0.773175	+	0.227025i
$470$	29.3546	+	25.4359i	0.0624567	+	0.0541190i
$471$		0			0
$472$	−123.809	−	79.5672i	−0.262307	−	0.168575i
$473$	−14.9587	−	12.9618i	−0.0316252	−	0.0274034i
$474$		0			0
$475$	−26.4628	−	184.053i	−0.0557111	−	0.387479i
$476$	72.9559	−	63.2167i	0.153269	−	0.132808i
$477$		0			0
$478$	−287.233	+	84.3393i	−0.600907	+	0.176442i
$479$	−381.078	−	174.032i	−0.795569	−	0.363324i	−0.0241959	−	0.999707i	$-0.507703\pi$
$479$	−381.078	−	174.032i	−0.795569	−	0.363324i	−0.771373	+	0.636383i	$0.780430\pi$
$480$		0			0
$481$	−122.805	+	78.9218i	−0.255311	+	0.164079i
$482$		−	220.970i		−	0.458443i
$483$		0			0
$484$	−167.463			−0.345998
$485$	−122.288	−	190.284i	−0.252141	−	0.392338i
$486$		0			0
$487$	−197.822	+	433.170i	−0.406206	+	0.889466i	0.590398	+	0.807113i	$0.298971\pi$
$487$	−197.822	+	433.170i	−0.406206	+	0.889466i	−0.996603	+	0.0823536i	$0.973756\pi$
$488$	41.6088	+	141.707i	0.0852640	+	0.290382i
$489$		0			0
$490$	−45.3214	−	52.3037i	−0.0924926	−	0.106742i
$491$	−587.003	+	84.3983i	−1.19553	+	0.171891i	−0.711195	−	0.702995i	$-0.751846\pi$
$491$	−587.003	+	84.3983i	−1.19553	+	0.171891i	−0.484330	+	0.874885i	$0.660937\pi$
$492$		0			0
$493$	10.8281	−	12.4963i	0.0219637	−	0.0253475i
$494$	96.0318	−	149.428i	0.194396	−	0.302487i
$495$		0			0
$496$	−143.908	+	166.079i	−0.290137	+	0.334836i
$497$	30.0200	−	102.239i	0.0604025	−	0.205712i
$498$		0			0
$499$	−569.028	−	656.693i	−1.14034	−	1.31602i	−0.941896	−	0.335905i	$-0.890958\pi$
$499$	−569.028	−	656.693i	−1.14034	−	1.31602i	−0.198440	−	0.980113i	$-0.563588\pi$
$500$	142.491	−	65.0734i	0.284982	−	0.130147i
$501$		0			0
$502$	−74.3946	+	162.902i	−0.148196	+	0.324505i
$503$	624.990	+	89.8599i	1.24252	+	0.178648i	0.732053	−	0.681247i	$-0.238562\pi$
$503$	624.990	+	89.8599i	1.24252	+	0.178648i	0.510471	+	0.859895i	$0.329471\pi$
$504$		0			0
$505$	114.527			0.226787
$506$	91.2260	+	176.374i	0.180288	+	0.348566i
$507$		0			0
$508$	14.3045	−	9.19296i	0.0281585	−	0.0180964i
$509$	−922.141	−	132.584i	−1.81167	−	0.260479i	−0.848467	−	0.529248i	$-0.822474\pi$
$509$	−922.141	−	132.584i	−1.81167	−	0.260479i	−0.963205	+	0.268769i	$0.913383\pi$
$510$		0			0
$511$	177.778	−	52.2004i	0.347902	−	0.102153i
$512$	−20.5826	+	9.39977i	−0.0402004	+	0.0183589i
$513$		0			0
$514$	49.6986	+	345.661i	0.0966898	+	0.672492i
$515$	−33.7131	+	114.816i	−0.0654624	+	0.222944i
$516$		0			0
$517$	85.0972	+	54.6886i	0.164598	+	0.105781i
$518$	−32.7702	+	50.9914i	−0.0632628	+	0.0984389i
$519$		0			0
$520$	67.6143	+	19.8534i	0.130028	+	0.0381795i
$521$	−581.929	+	83.6688i	−1.11695	+	0.160593i	−0.675972	−	0.736927i	$-0.736276\pi$
$521$	−581.929	+	83.6688i	−1.11695	+	0.160593i	−0.440974	+	0.897520i	$0.645367\pi$
$522$		0			0
$523$	−37.5428	−	82.2072i	−0.0717835	−	0.157184i	0.870339	−	0.492454i	$-0.163900\pi$
$523$	−37.5428	−	82.2072i	−0.0717835	−	0.157184i	−0.942122	+	0.335270i	$0.891173\pi$
$524$	−19.0776	−	64.9722i	−0.0364075	−	0.123993i
$525$		0			0
$526$	−100.455	+	698.681i	−0.190979	+	1.32829i
$527$	−324.852	−	505.480i	−0.616418	−	0.959165i
$528$		0			0
$529$	−305.697	+	431.729i	−0.577877	+	0.816124i
$530$		−	61.3833i		−	0.115818i
$531$		0			0
$532$	10.4963	−	73.0036i	0.0197300	−	0.137225i
$533$	376.641	+	172.006i	0.706644	+	0.322713i
$534$		0			0
$535$	139.839	+	306.205i	0.261382	+	0.572346i
$536$	183.054	−	158.618i	0.341519	−	0.295928i
$537$		0			0
$538$	269.904	+	79.2511i	0.501681	+	0.147307i
$539$	−136.214	−	118.030i	−0.252716	−	0.218980i
$540$		0			0
$541$	−789.973	−	507.685i	−1.46021	−	0.938419i	−0.998684	−	0.0512913i	$-0.983666\pi$
$541$	−789.973	−	507.685i	−1.46021	−	0.938419i	−0.461524	−	0.887128i	$-0.652697\pi$
$542$	−337.612	−	292.542i	−0.622900	−	0.539746i
$543$		0			0
$544$	−8.80494	−	61.2397i	−0.0161855	−	0.112573i
$545$	35.1955	−	30.4971i	0.0645789	−	0.0559579i
$546$		0			0
$547$	−569.388	+	167.187i	−1.04093	+	0.305644i	−0.757147	−	0.653245i	$-0.773407\pi$
$547$	−569.388	+	167.187i	−1.04093	+	0.305644i	−0.283782	+	0.958889i	$0.591589\pi$
$548$	249.432	+	113.912i	0.455167	+	0.207868i
$549$		0			0
$550$	161.619	−	103.866i	0.293853	−	0.188848i
$551$		−	12.6331i		−	0.0229275i
$552$		0			0
$553$	−75.0205			−0.135661
$554$	163.951	+	255.113i	0.295941	+	0.460493i
$555$		0			0
$556$	−59.0554	+	129.313i	−0.106215	+	0.232578i
$557$	−88.1153	−	300.093i	−0.158196	−	0.538767i	0.841803	−	0.539785i	$-0.181494\pi$
$557$	−88.1153	−	300.093i	−0.158196	−	0.538767i	−0.999999	+	0.00101745i	$0.999676\pi$
$558$		0			0
$559$	−31.9139	−	36.8306i	−0.0570911	−	0.0658866i
$560$	28.9624	−	4.16417i	0.0517186	−	0.00743602i
$561$		0			0
$562$	−47.0764	+	54.3291i	−0.0837659	+	0.0966710i
$563$	213.193	−	331.734i	0.378672	−	0.589226i	−0.598643	−	0.801016i	$-0.704293\pi$
$563$	213.193	−	331.734i	0.378672	−	0.589226i	0.977315	+	0.211790i	$0.0679294\pi$
$564$		0			0
$565$	25.4812	−	29.4068i	0.0450994	−	0.0520475i
$566$	117.554	−	400.353i	0.207693	−	0.707337i
$567$		0			0
$568$	−44.7215	−	51.6114i	−0.0787351	−	0.0908651i
$569$	479.740	−	219.090i	0.843128	−	0.385044i	0.0534540	−	0.998570i	$-0.482977\pi$
$569$	479.740	−	219.090i	0.843128	−	0.385044i	0.789674	+	0.613527i	$0.210250\pi$
$570$		0			0
$571$	−59.5974	+	130.500i	−0.104374	+	0.228547i	−0.954612	−	0.297851i	$-0.903730\pi$
$571$	−59.5974	+	130.500i	−0.104374	+	0.228547i	0.850239	+	0.526397i	$0.176458\pi$
$572$	181.653	+	26.1178i	0.317576	+	0.0456605i
$573$		0			0
$574$	171.927			0.299524
$575$	443.581	+	255.311i	0.771444	+	0.444020i
$576$		0			0
$577$	−92.7031	+	59.5767i	−0.160664	+	0.103253i	−0.618502	−	0.785783i	$-0.712260\pi$
$577$	−92.7031	+	59.5767i	−0.160664	+	0.103253i	0.457838	+	0.889036i	$0.348624\pi$
$578$	−237.102	−	34.0901i	−0.410211	−	0.0589795i
$579$		0			0
$580$	4.80885	−	1.41200i	0.00829111	−	0.00243449i
$581$	−307.559	+	140.457i	−0.529361	+	0.241751i
$582$		0			0
$583$	−22.7505	−	158.233i	−0.0390231	−	0.271411i
$584$	33.4554	−	113.939i	0.0572867	−	0.195101i
$585$		0			0
$586$	155.292	+	99.8001i	0.265003	+	0.170307i
$587$	−211.253	+	328.716i	−0.359885	+	0.559992i	−0.973233	−	0.229821i	$-0.926186\pi$
$587$	−211.253	+	328.716i	−0.359885	+	0.559992i	0.613348	+	0.789813i	$0.289822\pi$
$588$		0			0
$589$	−440.478	−	129.336i	−0.747840	−	0.219586i
$590$	120.731	−	17.3585i	0.204629	−	0.0294212i
$591$		0			0
$592$	16.1378	+	35.3369i	0.0272598	+	0.0596907i
$593$	258.171	+	879.250i	0.435364	+	1.48271i	0.826793	+	0.562506i	$0.190163\pi$
$593$	258.171	+	879.250i	0.435364	+	1.48271i	−0.391429	+	0.920208i	$0.628019\pi$
$594$		0			0
$595$	−11.3860	+	79.1911i	−0.0191361	+	0.133094i
$596$	−56.6788	−	88.1939i	−0.0950986	−	0.147976i
$597$		0			0
$598$	160.524	+	461.805i	0.268435	+	0.772250i
$599$		−	413.440i		−	0.690216i	−0.938563	−	0.345108i	$-0.887842\pi$
$599$		−	413.440i		−	0.690216i	0.938563	−	0.345108i	$-0.112158\pi$
$600$		0			0
$601$	66.0856	−	459.635i	0.109959	−	0.764784i	−0.857995	−	0.513658i	$-0.828290\pi$
$601$	66.0856	−	459.635i	0.109959	−	0.764784i	0.967954	−	0.251126i	$-0.0808009\pi$
$602$	−18.4068	−	8.40610i	−0.0305761	−	0.0139636i
$603$		0			0
$604$	−38.8600	−	85.0914i	−0.0643377	−	0.140880i
$605$	104.890	−	90.8875i	0.173372	−	0.150227i
$606$		0			0
$607$	593.511	+	174.270i	0.977777	+	0.287101i	0.731306	−	0.682049i	$-0.238911\pi$
$607$	593.511	+	174.270i	0.977777	+	0.287101i	0.246471	+	0.969150i	$0.420729\pi$
$608$	−35.7239	−	30.9549i	−0.0587564	−	0.0509127i
$609$		0			0
$610$	−102.970	−	66.1750i	−0.168804	−	0.108484i
$611$	188.226	+	163.099i	0.308063	+	0.266938i
$612$		0			0
$613$	−117.042	−	814.048i	−0.190934	−	1.32797i	−0.829543	−	0.558443i	$-0.811399\pi$
$613$	−117.042	−	814.048i	−0.190934	−	1.32797i	0.638609	−	0.769531i	$-0.279510\pi$
$614$	−497.498	+	431.084i	−0.810257	+	0.702092i
$615$		0			0
$616$	73.1156	−	21.4687i	0.118694	−	0.0348517i
$617$	−971.971	−	443.884i	−1.57532	−	0.719424i	−0.579868	−	0.814710i	$-0.696896\pi$
$617$	−971.971	−	443.884i	−1.57532	−	0.719424i	−0.995450	+	0.0952867i	$0.969623\pi$
$618$		0			0
$619$	739.808	−	475.446i	1.19517	−	0.768087i	0.217053	−	0.976160i	$-0.430355\pi$
$619$	739.808	−	475.446i	1.19517	−	0.768087i	0.978113	+	0.208073i	$0.0667190\pi$
$620$		−	182.126i		−	0.293752i
$621$		0			0
$622$	−293.664			−0.472129
$623$	197.605	+	307.479i	0.317182	+	0.493545i
$624$		0			0
$625$	177.170	−	387.947i	0.283471	−	0.620716i
$626$	130.823	+	445.543i	0.208983	+	0.711730i
$627$		0			0
$628$	−3.64952	−	4.21178i	−0.00581134	−	0.00670665i
$629$	−105.138	+	15.1166i	−0.167151	+	0.0240327i
$630$		0			0
$631$	−298.744	+	344.769i	−0.473446	+	0.546385i	−0.941367	−	0.337385i	$-0.890458\pi$
$631$	−298.744	+	344.769i	−0.473446	+	0.546385i	0.467921	+	0.883770i	$0.345003\pi$
$632$	−25.9945	+	40.4483i	−0.0411306	+	0.0640004i
$633$		0			0
$634$	−90.1279	+	104.013i	−0.142158	+	0.164059i
$635$	−3.97027	+	13.5215i	−0.00625239	+	0.0212937i
$636$		0			0
$637$	−290.608	−	335.379i	−0.456213	−	0.526498i
$638$	11.8728	−	5.42214i	0.0186095	−	0.00849866i
$639$		0			0
$640$	7.79029	−	17.0584i	0.0121723	−	0.0266537i
$641$	465.473	+	66.9249i	0.726167	+	0.104407i	0.495478	−	0.868621i	$-0.334993\pi$
$641$	465.473	+	66.9249i	0.726167	+	0.104407i	0.230689	+	0.973028i	$0.425902\pi$
$642$		0			0
$643$	817.503			1.27139			0.635694	−	0.771941i	$-0.280714\pi$
$643$	817.503			1.27139			0.635694	+	0.771941i	$0.280714\pi$
$644$	140.287	+	146.735i	0.217836	+	0.227850i
$645$		0			0
$646$	108.730	−	69.8764i	0.168312	−	0.108168i
$647$	−30.1466	−	4.33442i	−0.0465944	−	0.00669926i	0.118978	−	0.992897i	$-0.462038\pi$
$647$	−30.1466	−	4.33442i	−0.0465944	−	0.00669926i	−0.165573	+	0.986198i	$0.552947\pi$
$648$		0			0
$649$	304.785	−	89.4929i	0.469622	−	0.137893i
$650$	430.274	−	196.500i	0.661960	−	0.302307i
$651$		0			0
$652$	−36.6292	−	254.762i	−0.0561798	−	0.390739i
$653$	55.9023	−	190.386i	0.0856084	−	0.291556i	−0.905550	−	0.424240i	$-0.860541\pi$
$653$	55.9023	−	190.386i	0.0856084	−	0.291556i	0.991158	+	0.132684i	$0.0423596\pi$
$654$		0			0
$655$	47.2116	+	30.3411i	0.0720789	+	0.0463223i
$656$	59.5725	−	92.6966i	0.0908117	−	0.141306i
$657$		0			0
$658$	99.2260	+	29.1354i	0.150799	+	0.0442787i
$659$	−293.342	+	42.1762i	−0.445132	+	0.0640003i	−0.361236	−	0.932474i	$-0.617645\pi$
$659$	−293.342	+	42.1762i	−0.445132	+	0.0640003i	−0.0838954	+	0.996475i	$0.526736\pi$
$660$		0			0
$661$	−9.65393	−	21.1391i	−0.0146050	−	0.0319806i	0.902189	−	0.431341i	$-0.141959\pi$
$661$	−9.65393	−	21.1391i	−0.0146050	−	0.0319806i	−0.916794	+	0.399361i	$0.869232\pi$
$662$	120.225	+	409.450i	0.181609	+	0.618505i
$663$		0			0
$664$	−30.8394	+	214.493i	−0.0464448	+	0.323031i
$665$	33.0471	+	51.4223i	0.0496949	+	0.0773267i
$666$		0			0
$667$	27.3614	+	21.4581i	0.0410216	+	0.0321711i
$668$		−	251.077i		−	0.375863i
$669$		0			0
$670$	−28.5686	+	198.699i	−0.0426397	+	0.296566i
$671$	−289.962	−	132.421i	−0.432133	−	0.197349i
$672$		0			0
$673$	80.7094	+	176.729i	0.119925	+	0.262599i	0.960068	−	0.279765i	$-0.0902566\pi$
$673$	80.7094	+	176.729i	0.119925	+	0.262599i	−0.840144	+	0.542364i	$0.817529\pi$
$674$	418.701	−	362.806i	0.621218	−	0.538288i
$675$		0			0
$676$	109.245	+	32.0771i	0.161604	+	0.0474514i
$677$	619.613	+	536.898i	0.915233	+	0.793054i	0.978778	−	0.204925i	$-0.0656950\pi$
$677$	619.613	+	536.898i	0.915233	+	0.793054i	−0.0635444	+	0.997979i	$0.520240\pi$
$678$		0			0
$679$	−506.626	−	325.589i	−0.746136	−	0.479513i
$680$	38.7517	+	33.5785i	0.0569878	+	0.0493802i
$681$		0			0
$682$	−67.5014	−	469.482i	−0.0989756	−	0.688391i
$683$	510.817	−	442.625i	0.747902	−	0.648061i	−0.195125	−	0.980778i	$-0.562511\pi$
$683$	510.817	−	442.625i	0.747902	−	0.648061i	0.943026	+	0.332718i	$0.107966\pi$
$684$		0			0
$685$	−218.054	+	64.0265i	−0.318327	+	0.0934693i
$686$	−445.794	−	203.587i	−0.649845	−	0.296774i
$687$		0			0
$688$	−10.9102	+	7.01156i	−0.0158578	+	0.0101912i
$689$		−	393.599i		−	0.571261i
$690$		0			0
$691$	539.950			0.781404			0.390702	−	0.920517i	$-0.372232\pi$
$691$	539.950			0.781404			0.390702	+	0.920517i	$0.372232\pi$
$692$	190.839	+	296.952i	0.275779	+	0.429121i
$693$		0			0
$694$	58.7263	−	128.593i	0.0846201	−	0.185292i
$695$	−33.1934	−	113.046i	−0.0477602	−	0.162656i
$696$		0			0
$697$	197.300	+	227.696i	0.283070	+	0.326680i
$698$	858.867	−	123.486i	1.23047	−	0.176915i
$699$		0			0
$700$	128.620	−	148.436i	0.183744	−	0.212051i
$701$	−609.963	+	949.121i	−0.870132	+	1.35395i	0.0643443	+	0.997928i	$0.479504\pi$
$701$	−609.963	+	949.121i	−0.870132	+	1.35395i	−0.934477	+	0.356025i	$0.884132\pi$
$702$		0			0
$703$	−53.1444	+	61.3319i	−0.0755966	+	0.0872432i
$704$	13.7594	−	46.8601i	0.0195445	−	0.0665626i
$705$		0			0
$706$	219.575	+	253.403i	0.311012	+	0.358927i
$707$	277.371	−	126.671i	0.392321	−	0.179167i
$708$		0			0
$709$	299.494	−	655.799i	0.422417	−	0.924964i	−0.572080	−	0.820198i	$-0.693863\pi$
$709$	299.494	−	655.799i	0.422417	−	0.924964i	0.994497	−	0.104766i	$-0.0334094\pi$
$710$	56.0223	+	8.05479i	0.0789047	+	0.0113448i
$711$		0			0
$712$	234.251			0.329004
$713$	1028.30	−	734.326i	1.44222	−	1.02991i
$714$		0			0
$715$	−127.953	+	82.2303i	−0.178955	+	0.115007i
$716$	−381.501	−	54.8516i	−0.532823	−	0.0766083i
$717$		0			0
$718$	342.543	−	100.580i	0.477080	−	0.140083i
$719$	−792.680	+	362.005i	−1.10248	+	0.503484i	−0.881686	−	0.471838i	$-0.843591\pi$
$719$	−792.680	+	362.005i	−1.10248	+	0.503484i	−0.220790	+	0.975321i	$0.570864\pi$
$720$		0			0
$721$	45.3416	+	315.358i	0.0628872	+	0.437390i
$722$	−116.013	+	395.103i	−0.160683	+	0.547235i
$723$		0			0
$724$	−385.112	−	247.496i	−0.531923	−	0.341846i
$725$	18.1882	−	28.3015i	0.0250872	−	0.0390365i
$726$		0			0
$727$	1022.30	+	300.175i	1.40619	+	0.412896i	0.894807	−	0.446454i	$-0.147313\pi$
$727$	1022.30	+	300.175i	1.40619	+	0.412896i	0.511388	+	0.859350i	$0.329131\pi$
$728$	185.712	−	26.7013i	0.255098	−	0.0366776i
$729$		0			0
$730$	40.8835	+	89.5224i	0.0560048	+	0.122633i
$731$	−9.99042	−	34.0242i	−0.0136668	−	0.0465448i
$732$		0			0
$733$	90.7171	−	630.952i	0.123761	−	0.860780i	−0.829473	−	0.558547i	$-0.811359\pi$
$733$	90.7171	−	630.952i	0.123761	−	0.860780i	0.953234	−	0.302233i	$-0.0977319\pi$
$734$	−32.6004	−	50.7272i	−0.0444147	−	0.0691107i
$735$		0			0
$736$	127.723	−	24.7938i	0.173537	−	0.0336872i
$737$			522.791i			0.709351i
$738$		0			0
$739$	170.226	−	1183.95i	0.230346	−	1.60209i	−0.466266	−	0.884645i	$-0.654401\pi$
$739$	170.226	−	1183.95i	0.230346	−	1.60209i	0.696612	−	0.717448i	$-0.254690\pi$
$740$	−29.2863	−	13.3746i	−0.0395761	−	0.0180738i
$741$		0			0
$742$	−67.8919	−	148.662i	−0.0914985	−	0.200354i
$743$	58.6876	−	50.8531i	0.0789873	−	0.0684429i	−0.614472	−	0.788938i	$-0.710631\pi$
$743$	58.6876	−	50.8531i	0.0789873	−	0.0684429i	0.693460	+	0.720495i	$0.256086\pi$
$744$		0			0
$745$	83.3662	+	24.4785i	0.111901	+	0.0328571i
$746$	572.547	+	496.115i	0.767489	+	0.665033i
$747$		0			0
$748$	112.339	+	72.1956i	0.150185	+	0.0965182i
$749$	677.344	+	586.922i	0.904332	+	0.783608i
$750$		0			0
$751$	−133.856	−	930.989i	−0.178237	−	1.23967i	−0.860840	−	0.508876i	$-0.830061\pi$
$751$	−133.856	−	930.989i	−0.178237	−	1.23967i	0.682603	−	0.730789i	$-0.260848\pi$
$752$	50.0905	−	43.4036i	0.0666096	−	0.0577176i
$753$		0			0
$754$	30.8350	−	9.05399i	0.0408953	−	0.0120079i
$755$	70.5216	+	32.2062i	0.0934061	+	0.0426572i
$756$		0			0
$757$	925.953	−	595.074i	1.22319	−	0.786095i	0.240372	−	0.970681i	$-0.422731\pi$
$757$	925.953	−	595.074i	1.22319	−	0.786095i	0.982816	+	0.184586i	$0.0590943\pi$
$758$		−	403.376i		−	0.532158i
$759$		0			0
$760$	39.1758			0.0515471
$761$	409.481	+	637.166i	0.538083	+	0.837274i	0.998734	−	0.0503076i	$-0.0160202\pi$
$761$	409.481	+	637.166i	0.538083	+	0.837274i	−0.460650	+	0.887582i	$0.652384\pi$
$762$		0			0
$763$	51.5082	−	112.787i	0.0675075	−	0.147821i
$764$	−27.4112	−	93.3540i	−0.0358785	−	0.122191i
$765$		0			0
$766$	−391.996	−	452.388i	−0.511745	−	0.590585i
$767$	774.145	−	111.305i	1.00932	−	0.145118i
$768$		0			0
$769$	−808.885	+	933.503i	−1.05187	+	1.21392i	−0.0756464	+	0.997135i	$0.524102\pi$
$769$	−808.885	+	933.503i	−1.05187	+	1.21392i	−0.976220	+	0.216783i	$0.930443\pi$
$770$	−34.1439	+	53.1290i	−0.0443428	+	0.0689987i
$771$		0			0
$772$	−449.215	+	518.422i	−0.581885	+	0.671531i
$773$	342.549	−	1166.62i	0.443143	−	1.50921i	−0.371051	−	0.928612i	$-0.621003\pi$
$773$	342.549	−	1166.62i	0.443143	−	1.50921i	0.814194	−	0.580593i	$-0.197179\pi$
$774$		0			0
$775$	−800.580	−	923.918i	−1.03301	−	1.19215i
$776$	−351.091	+	160.338i	−0.452437	+	0.206621i
$777$		0			0
$778$	447.599	−	980.104i	0.575319	−	1.25977i
$779$	227.845	+	32.7592i	0.292484	+	0.0420528i
$780$		0			0
$781$	147.399			0.188731
$782$	−33.3427	+	354.183i	−0.0426378	+	0.452920i
$783$		0			0
$784$	−99.3481	+	63.8472i	−0.126720	+	0.0814377i
$785$	4.57173	+	0.657316i	0.00582386	+	0.000837345i
$786$		0			0
$787$	179.349	−	52.6615i	0.227889	−	0.0669143i	−0.165794	−	0.986160i	$-0.553019\pi$
$787$	179.349	−	52.6615i	0.227889	−	0.0669143i	0.393683	+	0.919246i	$0.371201\pi$
$788$	387.141	−	176.801i	0.491295	−	0.224367i
$789$		0			0
$790$	−5.67100	−	39.4427i	−0.00717848	−	0.0499274i
$791$	29.1872	−	99.4025i	0.0368991	−	0.125667i
$792$		0			0
$793$	−660.261	−	424.324i	−0.832612	−	0.535087i
$794$	−344.634	+	536.262i	−0.434048	+	0.675393i
$795$		0			0
$796$	−24.5041	−	7.19505i	−0.0307840	−	0.00903900i
$797$	−731.841	+	105.223i	−0.918245	+	0.132024i	−0.585202	−	0.810888i	$-0.698985\pi$
$797$	−731.841	+	105.223i	−0.918245	+	0.132024i	−0.333044	+	0.942911i	$0.608076\pi$
$798$		0			0
$799$	75.2836	+	164.848i	0.0942223	+	0.206318i
$800$	−35.4643	−	120.780i	−0.0443304	−	0.150975i
$801$		0			0
$802$	−7.13291	+	49.6105i	−0.00889390	+	0.0618584i
$803$	138.569	+	215.617i	0.172564	+	0.268514i
$804$		0			0
$805$	−167.506	−	15.7690i	−0.208082	−	0.0195888i
$806$		−	1167.82i		−	1.44891i
$807$		0			0
$808$	27.8124	−	193.439i	0.0344213	−	0.239405i
$809$	366.884	+	167.550i	0.453504	+	0.207108i	0.629053	−	0.777362i	$-0.283443\pi$
$809$	366.884	+	167.550i	0.453504	+	0.207108i	−0.175549	+	0.984471i	$0.556170\pi$
$810$		0			0
$811$	402.872	+	882.166i	0.496759	+	1.08775i	0.977509	+	0.210893i	$0.0676373\pi$
$811$	402.872	+	882.166i	0.496759	+	1.08775i	−0.480750	+	0.876858i	$0.659635\pi$
$812$	10.0847	−	8.73843i	0.0124196	−	0.0107616i
$813$		0			0
$814$	−80.4509	−	23.6225i	−0.0988340	−	0.0290203i
$815$	161.210	+	139.689i	0.197804	+	0.171398i
$816$		0			0
$817$	−22.7918	−	14.6474i	−0.0278969	−	0.0179283i
$818$	−95.8113	−	83.0210i	−0.117129	−	0.101493i
$819$		0			0
$820$	12.9964	+	90.3920i	0.0158493	+	0.110234i
$821$	−742.886	+	643.714i	−0.904855	+	0.784061i	−0.976979	−	0.213334i	$-0.931568\pi$
$821$	−742.886	+	643.714i	−0.904855	+	0.784061i	0.0721244	+	0.997396i	$0.477022\pi$
$822$		0			0
$823$	−942.191	+	276.652i	−1.14482	+	0.336151i	−0.798518	−	0.601971i	$-0.794382\pi$
$823$	−942.191	+	276.652i	−1.14482	+	0.336151i	−0.346306	+	0.938121i	$0.612564\pi$
$824$	185.740	+	84.8247i	0.225413	+	0.102943i
$825$		0			0
$826$	273.196	−	175.572i	0.330745	−	0.212557i
$827$		−	7.98290i		−	0.00965284i	−0.999988	−	0.00482642i	$-0.998464\pi$
$827$		−	7.98290i		−	0.00965284i	0.999988	−	0.00482642i	$-0.00153630\pi$
$828$		0			0
$829$	702.949			0.847948			0.423974	−	0.905674i	$-0.360635\pi$
$829$	702.949			0.847948			0.423974	+	0.905674i	$0.360635\pi$
$830$	−97.0959	−	151.084i	−0.116983	−	0.182029i
$831$		0			0
$832$	49.9525	−	109.381i	0.0600391	−	0.131467i
$833$	−90.9726	−	309.824i	−0.109211	−	0.371938i
$834$		0			0
$835$	136.267	+	157.261i	0.163194	+	0.188336i
$836$	100.987	−	14.5197i	0.120797	−	0.0173680i
$837$		0			0
$838$	−95.4637	+	110.171i	−0.113919	+	0.131469i
$839$	570.531	−	887.764i	0.680013	−	1.05812i	−0.314059	−	0.949403i	$-0.601689\pi$
$839$	570.531	−	887.764i	0.680013	−	1.05812i	0.994073	−	0.108718i	$-0.0346746\pi$
$840$		0			0
$841$	−549.241	+	633.858i	−0.653081	+	0.753696i
$842$	−38.0713	+	129.659i	−0.0452153	+	0.153989i
$843$		0			0
$844$	−198.104	−	228.625i	−0.234721	−	0.270882i
$845$	−85.8343	+	39.1992i	−0.101579	+	0.0463896i
$846$		0			0
$847$	153.505	−	336.129i	0.181234	−	0.396847i
$848$	−103.678	−	14.9066i	−0.122262	−	0.0175786i
$849$		0			0
$850$	344.188			0.404927
$851$	−42.5668	−	219.280i	−0.0500197	−	0.257673i
$852$		0			0
$853$	−663.464	+	426.383i	−0.777801	+	0.499862i	−0.868303	−	0.496034i	$-0.834789\pi$
$853$	−663.464	+	426.383i	−0.777801	+	0.499862i	0.0905020	+	0.995896i	$0.471153\pi$
$854$	−322.572	−	46.3789i	−0.377719	−	0.0543078i
$855$		0			0
$856$	551.146	−	161.831i	0.643862	−	0.189055i
$857$	989.262	−	451.781i	1.15433	−	0.527165i	0.256083	−	0.966655i	$-0.417568\pi$
$857$	989.262	−	451.781i	1.15433	−	0.527165i	0.898248	+	0.439489i	$0.144841\pi$
$858$		0			0
$859$	174.998	+	1217.14i	0.203723	+	1.41693i	0.793111	+	0.609077i	$0.208460\pi$
$859$	174.998	+	1217.14i	0.203723	+	1.41693i	−0.589388	+	0.807850i	$0.700631\pi$
$860$	3.02816	−	10.3130i	0.00352112	−	0.0119918i
$861$		0			0
$862$	−219.717	−	141.204i	−0.254892	−	0.163809i
$863$	607.431	−	945.181i	0.703860	−	1.09523i	−0.286684	−	0.958025i	$-0.592553\pi$
$863$	607.431	−	945.181i	0.703860	−	1.09523i	0.990543	−	0.137202i	$-0.0438108\pi$
$864$		0			0
$865$	−280.697	−	82.4200i	−0.324505	−	0.0952832i
$866$	−1113.97	+	160.165i	−1.28634	+	0.184948i
$867$		0			0
$868$	−201.437	−	441.086i	−0.232071	−	0.508164i
$869$	−29.2372	−	99.5729i	−0.0336447	−	0.114583i
$870$		0			0
$871$	−183.186	+	1274.09i	−0.210317	+	1.46279i
$872$	−42.9632	−	66.8520i	−0.0492697	−	0.0766651i
$873$		0			0
$874$	157.955	+	221.190i	0.180727	+	0.253078i
$875$			345.655i			0.395035i
$876$		0			0
$877$	−6.31863	+	43.9470i	−0.00720482	+	0.0501107i	−0.993107	−	0.117214i	$-0.962604\pi$
$877$	−6.31863	+	43.9470i	−0.00720482	+	0.0501107i	0.985902	+	0.167325i	$0.0535128\pi$
$878$	196.820	+	89.8845i	0.224168	+	0.102374i
$879$		0			0
$880$	16.8143	+	36.8183i	0.0191072	+	0.0418390i
$881$	−724.872	+	628.105i	−0.822783	+	0.712946i	−0.960727	−	0.277494i	$-0.910496\pi$
$881$	−724.872	+	628.105i	−0.822783	+	0.712946i	0.137944	+	0.990440i	$0.455951\pi$
$882$		0			0
$883$	310.627	+	91.2082i	0.351785	+	0.103294i	0.452851	−	0.891586i	$-0.350407\pi$
$883$	310.627	+	91.2082i	0.351785	+	0.103294i	−0.101065	+	0.994880i	$0.532225\pi$
$884$	248.482	+	215.311i	0.281088	+	0.243564i
$885$		0			0
$886$	−81.8901	−	52.6276i	−0.0924268	−	0.0593991i
$887$	966.581	+	837.547i	1.08972	+	0.944247i	0.998668	−	0.0515994i	$-0.0164319\pi$
$887$	966.581	+	837.547i	1.08972	+	0.944247i	0.0910511	+	0.995846i	$0.470977\pi$
$888$		0			0
$889$	5.33972	+	37.1385i	0.00600643	+	0.0417756i
$890$	−146.722	+	127.136i	−0.164856	+	0.142849i
$891$		0			0
$892$	172.280	−	50.5859i	0.193139	−	0.0567106i
$893$	125.947	+	57.5182i	0.141038	+	0.0644101i
$894$		0			0
$895$	268.721	−	172.697i	0.300247	−	0.192957i
$896$		−	49.9294i		−	0.0557248i
$897$		0			0
$898$	−929.432			−1.03500
$899$	−44.9043	−	69.8724i	−0.0499491	−	0.0777224i
$900$		0			0
$901$	118.974	−	260.517i	0.132047	−	0.289142i
$902$	67.0039	+	228.194i	0.0742837	+	0.252987i
$903$		0			0
$904$	−43.4808	−	50.1796i	−0.0480983	−	0.0555084i
$905$	375.538	−	53.9942i	0.414959	−	0.0596621i
$906$		0			0
$907$	−671.226	+	774.637i	−0.740051	+	0.854065i	−0.993565	−	0.113267i	$-0.963868\pi$
$907$	−671.226	+	774.637i	−0.740051	+	0.854065i	0.253513	+	0.967332i	$0.418414\pi$
$908$	−422.836	+	657.946i	−0.465679	+	0.724610i
$909$		0			0
$910$	−101.828	+	117.516i	−0.111899	+	0.129138i
$911$	−408.102	+	1389.87i	−0.447971	+	1.52565i	0.358015	+	0.933716i	$0.383454\pi$
$911$	−408.102	+	1389.87i	−0.447971	+	1.52565i	−0.805986	+	0.591934i	$0.798365\pi$
$912$		0			0
$913$	−306.288	−	353.476i	−0.335475	−	0.387158i
$914$	−329.449	+	150.454i	−0.360447	+	0.164611i
$915$		0			0
$916$	−276.098	+	604.571i	−0.301417	+	0.660012i
$917$	147.899	+	21.2646i	0.161285	+	0.0231893i
$918$		0			0
$919$	1788.88			1.94655			0.973277	−	0.229633i	$-0.0737525\pi$
$919$	1788.88			1.94655			0.973277	+	0.229633i	$0.0737525\pi$
$920$	−66.5427	+	84.8491i	−0.0723290	+	0.0922273i
$921$		0			0
$922$	−432.830	+	278.163i	−0.469447	+	0.301695i
$923$	359.224	+	51.6485i	0.389191	+	0.0559573i
$924$		0			0
$925$	−207.360	+	60.8863i	−0.224173	+	0.0658230i
$926$	456.599	−	208.522i	0.493088	−	0.225186i
$927$		0			0
$928$	−1.21710	−	8.46514i	−0.00131153	−	0.00912192i
$929$	41.4313	−	141.102i	0.0445977	−	0.151886i	−0.934184	−	0.356792i	$-0.883871\pi$
$929$	41.4313	−	141.102i	0.0445977	−	0.151886i	0.978782	+	0.204906i	$0.0656888\pi$
$930$		0			0
$931$	−207.542	−	133.379i	−0.222923	−	0.143264i
$932$	−498.429	+	775.571i	−0.534796	+	0.832158i
$933$		0			0
$934$	−856.086	−	251.370i	−0.916580	−	0.269132i
$935$	−109.546	+	15.7503i	−0.117161	+	0.0168452i
$936$		0			0
$937$	216.244	+	473.508i	0.230783	+	0.505345i	0.989226	−	0.146395i	$-0.0467669\pi$
$937$	216.244	+	473.508i	0.230783	+	0.505345i	−0.758443	+	0.651739i	$0.774040\pi$
$938$	150.578	+	512.821i	0.160531	+	0.546718i
$939$		0			0
$940$	−7.81743	+	54.3714i	−0.00831641	+	0.0578419i
$941$	−643.175	−	1000.80i	−0.683501	−	1.06355i	−0.993612	−	0.112848i	$-0.964003\pi$
$941$	−643.175	−	1000.80i	−0.683501	−	1.06355i	0.310111	−	0.950700i	$-0.399634\pi$
$942$		0			0
$943$	−457.962	+	437.836i	−0.485644	+	0.464301i
$944$		−	208.133i		−	0.220480i
$945$		0			0
$946$	3.98366	−	27.7069i	0.00421105	−	0.0292885i
$947$	−775.233	−	354.037i	−0.818620	−	0.373851i	−0.0383270	−	0.999265i	$-0.512203\pi$
$947$	−775.233	−	354.037i	−0.818620	−	0.373851i	−0.780293	+	0.625414i	$0.784930\pi$
$948$		0			0
$949$	262.151	+	574.031i	0.276240	+	0.604880i
$950$	198.737	−	172.206i	0.209197	−	0.181270i
$951$		0			0
$952$	130.990	+	38.4623i	0.137595	+	0.0404015i
$953$	625.284	+	541.811i	0.656121	+	0.568532i	0.918006	−	0.396567i	$-0.129798\pi$
$953$	625.284	+	541.811i	0.656121	+	0.568532i	−0.261884	+	0.965099i	$0.584344\pi$
$954$		0			0
$955$	67.8351	+	43.5950i	0.0710315	+	0.0456492i
$956$	−319.953	−	277.241i	−0.334679	−	0.290001i
$957$		0			0
$958$	−84.3166	−	586.435i	−0.0880131	−	0.612145i
$959$	−457.284	+	396.239i	−0.476834	+	0.413179i
$960$		0			0
$961$	−1973.90	+	579.589i	−2.05401	+	0.603110i
$962$	−187.788	−	85.7601i	−0.195206	−	0.0891477i
$963$		0			0
$964$	262.890	−	168.949i	0.272708	−	0.175259i
$965$		−	568.515i		−	0.589135i
$966$		0			0
$967$	1672.71			1.72980			0.864898	−	0.501948i	$-0.167383\pi$
$967$	1672.71			1.72980			0.864898	+	0.501948i	$0.167383\pi$
$968$	−128.039	−	199.233i	−0.132272	−	0.205819i
$969$		0			0
$970$	132.884	−	290.976i	0.136994	−	0.299975i
$971$	−480.136	−	1635.19i	−0.494475	−	1.68403i	−0.707280	−	0.706934i	$-0.750078\pi$
$971$	−480.136	−	1635.19i	−0.494475	−	1.68403i	0.212804	−	0.977095i	$-0.431740\pi$
$972$		0			0
$973$	−205.423	−	237.070i	−0.211123	−	0.243649i
$974$	−666.599	+	95.8424i	−0.684393	+	0.0984009i
$975$		0			0
$976$	−136.777	+	157.849i	−0.140140	+	0.161730i
$977$	−197.289	+	306.987i	−0.201933	+	0.314214i	−0.927420	−	0.374022i	$-0.877978\pi$
$977$	−197.289	+	306.987i	−0.201933	+	0.314214i	0.725487	+	0.688236i	$0.241615\pi$
$978$		0			0
$979$	−331.098	+	382.108i	−0.338200	+	0.390304i
$980$	27.5744	−	93.9098i	0.0281372	−	0.0958264i
$981$		0			0
$982$	−549.221	−	633.835i	−0.559288	−	0.645453i
$983$	482.049	−	220.144i	0.490385	−	0.223952i	−0.154846	−	0.987939i	$-0.549488\pi$
$983$	482.049	−	220.144i	0.490385	−	0.223952i	0.645232	+	0.763987i	$0.276761\pi$
$984$		0			0
$985$	−146.528	+	320.852i	−0.148760	+	0.325738i
$986$	23.1460	+	3.32789i	0.0234746	+	0.00337514i
$987$		0			0
$988$	251.201			0.254252
$989$	70.4376	−	24.4842i	0.0712210	−	0.0247565i
$990$		0			0
$991$	0.218341	−	0.140319i	0.000220324	−	0.000141594i	−0.540531	−	0.841324i	$-0.681776\pi$
$991$	0.218341	−	0.140319i	0.000220324	−	0.000141594i	0.540751	+	0.841183i	$0.318140\pi$
$992$	−307.615	−	44.2284i	−0.310096	−	0.0445851i
$993$		0			0
$994$	144.588	−	42.4548i	0.145460	−	0.0427110i
$995$	19.2530	−	8.79256i	0.0193498	−	0.00883674i
$996$		0			0
$997$	−137.051	−	953.213i	−0.137464	−	0.956081i	−0.935463	−	0.353423i	$-0.885017\pi$
$997$	−137.051	−	953.213i	−0.137464	−	0.956081i	0.798000	−	0.602658i	$-0.205892\pi$
$998$	346.208	−	1179.07i	0.346901	−	1.18144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.a.35.6	yes	80
3.2	odd	2	inner	414.3.k.a.35.3	✓	80
23.2	even	11	inner	414.3.k.a.71.3	yes	80
69.2	odd	22	inner	414.3.k.a.71.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.35.3	✓	80	3.2	odd	2	inner
414.3.k.a.35.6	yes	80	1.1	even	1	trivial
414.3.k.a.71.3	yes	80	23.2	even	11	inner
414.3.k.a.71.6	yes	80	69.2	odd	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.466986 - 1.59041i) q^{5} +(-2.89002 - 3.33526i) q^{7} +(-2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.466986 - 1.59041i) q^{5} +(-2.89002 - 3.33526i) q^{7} +(-2.79964 + 0.402527i) q^{8} +(1.53508 - 1.77157i) q^{10} +(3.30050 - 5.13568i) q^{11} +(9.84315 - 11.3596i) q^{13} +(1.75834 - 5.98837i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(9.94871 - 4.54342i) q^{17} +(3.47127 - 7.60102i) q^{19} +(3.28136 + 0.471788i) q^{20} +8.63349 q^{22} +(10.5665 + 20.4291i) q^{23} +(18.7200 - 12.0306i) q^{25} +(21.0406 + 3.02518i) q^{26} +(8.46883 - 2.48667i) q^{28} +(1.37521 - 0.628036i) q^{29} +(-7.81855 - 54.3792i) q^{31} +(1.59372 - 5.42771i) q^{32} +(13.0120 + 8.36228i) q^{34} +(-3.95482 + 6.15383i) q^{35} +(-9.31847 - 2.73615i) q^{37} +(11.6971 - 1.68179i) q^{38} +(1.94757 + 4.26459i) q^{40} +(7.76093 + 26.4313i) q^{41} +(0.461419 - 3.20924i) q^{43} +(6.60100 + 10.2714i) q^{44} +(-16.2258 + 28.1908i) q^{46} +16.5698i q^{47} +(4.20168 - 29.2233i) q^{49} +(28.6260 + 13.0730i) q^{50} +(12.4881 + 27.3452i) q^{52} +(19.7900 - 17.1482i) q^{53} +(-9.70911 - 2.85085i) q^{55} +(9.43354 + 8.17421i) q^{56} +(1.79864 + 1.15592i) q^{58} +(39.3240 + 34.0745i) q^{59} +(-7.43111 - 51.6845i) q^{61} +(58.7177 - 50.8792i) q^{62} +(7.67594 - 2.25386i) q^{64} +(-22.6630 - 10.3499i) q^{65} +(-72.0417 + 46.2984i) q^{67} +21.8741i q^{68} -10.3451 q^{70} +(13.0536 + 20.3119i) q^{71} +(-17.4408 + 38.1901i) q^{73} +(-3.86950 - 13.1783i) q^{74} +(10.9442 + 12.6303i) q^{76} +(-26.6673 + 3.83419i) q^{77} +(11.1321 - 12.8471i) q^{79} +(-3.58456 + 5.57768i) q^{80} +(-25.5118 + 29.4422i) q^{82} +(21.5848 - 73.5110i) q^{83} +(-11.8718 - 13.7008i) q^{85} +(4.17087 - 1.90477i) q^{86} +(-7.17296 + 15.7066i) q^{88} +(-81.9773 - 11.7865i) q^{89} -66.3341 q^{91} +(-45.9449 + 2.25018i) q^{92} +(-19.7133 + 12.6690i) q^{94} +(-13.7097 - 1.97116i) q^{95} +(130.934 - 38.4456i) q^{97} +(37.9799 - 17.3448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 - 16 * q^7	\( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Introduction

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