LMFDB - Embedded newform 76.7.j.a.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.40108 + 6.43676i) q^{3} +(-171.496 + 62.4193i) q^{5} +(-231.676 - 401.275i) q^{7} +(114.329 + 648.394i) q^{9} +O(q^{10})$	\(q+(-5.40108 + 6.43676i) q^{3} +(-171.496 + 62.4193i) q^{5} +(-231.676 - 401.275i) q^{7} +(114.329 + 648.394i) q^{9} +(1086.88 - 1882.53i) q^{11} +(1386.12 + 1651.91i) q^{13} +(524.484 - 1441.01i) q^{15} +(-485.784 + 2755.02i) q^{17} +(6636.26 + 1733.75i) q^{19} +(3834.22 + 676.076i) q^{21} +(-2564.65 - 933.456i) q^{23} +(13545.1 - 11365.7i) q^{25} +(-10095.9 - 5828.86i) q^{27} +(33032.7 - 5824.55i) q^{29} +(20009.7 - 11552.6i) q^{31} +(6247.08 + 17163.7i) q^{33} +(64778.8 + 54355.9i) q^{35} +25431.6i q^{37} -18119.5 q^{39} +(65806.9 - 78425.6i) q^{41} +(9100.52 - 3312.32i) q^{43} +(-60079.3 - 104060. i) q^{45} +(-22458.5 - 127368. i) q^{47} +(-48523.5 + 84045.1i) q^{49} +(-15109.6 - 18007.0i) q^{51} +(-27025.9 + 74253.0i) q^{53} +(-68889.0 + 390689. i) q^{55} +(-47002.7 + 33351.9i) q^{57} +(327590. + 57763.0i) q^{59} +(-319883. - 116428. i) q^{61} +(233697. - 196095. i) q^{63} +(-340825. - 196775. i) q^{65} +(-195646. + 34497.6i) q^{67} +(19860.3 - 11466.4i) q^{69} +(-77343.5 - 212499. i) q^{71} +(317454. + 266375. i) q^{73} +148574. i q^{75} -1.00722e6 q^{77} +(-312513. + 372438. i) q^{79} +(-358978. + 130657. i) q^{81} +(-269443. - 466689. i) q^{83} +(-88656.5 - 502796. i) q^{85} +(-140921. + 244082. i) q^{87} +(500639. + 596638. i) q^{89} +(341741. - 938925. i) q^{91} +(-33712.7 + 191194. i) q^{93} +(-1.24631e6 + 116901. i) q^{95} +(1.61652e6 + 285036. i) q^{97} +(1.34489e6 + 489499. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

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
$3$	−5.40108	+	6.43676i	−0.200040	+	0.238398i	−0.856734	−	0.515759i	$-0.827510\pi$
$3$	−5.40108	+	6.43676i	−0.200040	+	0.238398i	0.656694	+	0.754157i	$0.271954\pi$
$4$		0			0
$5$	−171.496	+	62.4193i	−1.37197	+	0.499355i	−0.919733	−	0.392546i	$-0.871595\pi$
$5$	−171.496	+	62.4193i	−1.37197	+	0.499355i	−0.452233	+	0.891900i	$0.649372\pi$
$6$		0			0
$7$	−231.676	−	401.275i	−0.675442	−	1.16990i	−0.976340	−	0.216243i	$-0.930620\pi$
$7$	−231.676	−	401.275i	−0.675442	−	1.16990i	0.300898	−	0.953656i	$-0.402714\pi$
$8$		0			0
$9$	114.329	+	648.394i	0.156830	+	0.889429i
$10$		0			0
$11$	1086.88	−	1882.53i	0.816590	−	1.41438i	−0.0915899	−	0.995797i	$-0.529195\pi$
$11$	1086.88	−	1882.53i	0.816590	−	1.41438i	0.908180	−	0.418579i	$-0.137472\pi$
$12$		0			0
$13$	1386.12	+	1651.91i	0.630915	+	0.751895i	0.982906	−	0.184108i	$-0.0589398\pi$
$13$	1386.12	+	1651.91i	0.630915	+	0.751895i	−0.351991	+	0.936003i	$0.614495\pi$
$14$		0			0
$15$	524.484	−	1441.01i	0.155403	−	0.426965i
$16$		0			0
$17$	−485.784	+	2755.02i	−0.0988773	+	0.560761i	0.894613	+	0.446842i	$0.147451\pi$
$17$	−485.784	+	2755.02i	−0.0988773	+	0.560761i	−0.993490	+	0.113919i	$0.963660\pi$
$18$		0			0
$19$	6636.26	+	1733.75i	0.967526	+	0.252770i
$19$	6636.26	+	1733.75i	0.967526	+	0.252770i
$20$		0			0
$21$	3834.22	+	676.076i	0.414018	+	0.0730025i
$22$		0			0
$23$	−2564.65	−	933.456i	−0.210787	−	0.0767203i	0.234468	−	0.972124i	$-0.424665\pi$
$23$	−2564.65	−	933.456i	−0.210787	−	0.0767203i	−0.445256	+	0.895403i	$0.646887\pi$
$24$		0			0
$25$	13545.1	−	11365.7i	0.866889	−	0.727406i
$26$		0			0
$27$	−10095.9	−	5828.86i	−0.512924	−	0.296137i
$28$		0			0
$29$	33032.7	−	5824.55i	1.35441	−	0.238819i	0.551129	−	0.834420i	$-0.314197\pi$
$29$	33032.7	−	5824.55i	1.35441	−	0.238819i	0.803280	+	0.595601i	$0.203086\pi$
$30$		0			0
$31$	20009.7	−	11552.6i	0.671670	−	0.387789i	−0.125039	−	0.992152i	$-0.539906\pi$
$31$	20009.7	−	11552.6i	0.671670	−	0.387789i	0.796709	+	0.604363i	$0.206572\pi$
$32$		0			0
$33$	6247.08	+	17163.7i	0.173834	+	0.477606i
$34$		0			0
$35$	64778.8	+	54355.9i	1.51088	+	1.26778i
$36$		0			0
$37$			25431.6i			0.502075i	0.967977	+	0.251037i	$0.0807717\pi$
$37$			25431.6i			0.502075i	−0.967977	+	0.251037i	$0.919228\pi$
$38$		0			0
$39$	−18119.5			−0.305459
$40$		0			0
$41$	65806.9	−	78425.6i	0.954816	−	1.13791i	−0.0355409	−	0.999368i	$-0.511315\pi$
$41$	65806.9	−	78425.6i	0.954816	−	1.13791i	0.990357	−	0.138537i	$-0.0442401\pi$
$42$		0			0
$43$	9100.52	−	3312.32i	0.114462	−	0.0416607i	−0.284154	−	0.958779i	$-0.591713\pi$
$43$	9100.52	−	3312.32i	0.114462	−	0.0416607i	0.398616	+	0.917118i	$0.369491\pi$
$44$		0			0
$45$	−60079.3	−	104060.i	−0.659306	−	1.14195i
$46$		0			0
$47$	−22458.5	−	127368.i	−0.216315	−	1.22678i	−0.878610	−	0.477540i	$-0.841529\pi$
$47$	−22458.5	−	127368.i	−0.216315	−	1.22678i	0.662295	−	0.749243i	$-0.269583\pi$
$48$		0			0
$49$	−48523.5	+	84045.1i	−0.412443	+	0.714372i
$50$		0			0
$51$	−15109.6	−	18007.0i	−0.113905	−	0.135747i
$52$		0			0
$53$	−27025.9	+	74253.0i	−0.181532	+	0.498754i	−0.996764	−	0.0803793i	$-0.974387\pi$
$53$	−27025.9	+	74253.0i	−0.181532	+	0.498754i	0.815233	+	0.579134i	$0.196609\pi$
$54$		0			0
$55$	−68889.0	+	390689.i	−0.414059	+	2.34824i
$56$		0			0
$57$	−47002.7	+	33351.9i	−0.253804	+	0.180093i
$58$		0			0
$59$	327590.	+	57763.0i	1.59505	+	0.281251i	0.899400	−	0.437127i	$-0.144004\pi$
$59$	327590.	+	57763.0i	1.59505	+	0.281251i	0.695653	+	0.718378i	$0.255115\pi$
$60$		0			0
$61$	−319883.	−	116428.i	−1.40929	−	0.512941i	−0.478371	−	0.878158i	$-0.658773\pi$
$61$	−319883.	−	116428.i	−1.40929	−	0.512941i	−0.930922	+	0.365217i	$0.880995\pi$
$62$		0			0
$63$	233697.	−	196095.i	0.934613	−	0.784233i
$64$		0			0
$65$	−340825.	−	196775.i	−1.24106	−	0.716523i
$66$		0			0
$67$	−195646.	+	34497.6i	−0.650498	+	0.114700i	−0.489154	−	0.872198i	$-0.662694\pi$
$67$	−195646.	+	34497.6i	−0.650498	+	0.114700i	−0.161345	+	0.986898i	$0.551583\pi$
$68$		0			0
$69$	19860.3	−	11466.4i	0.0604559	−	0.0349043i
$70$		0			0
$71$	−77343.5	−	212499.i	−0.216097	−	0.593721i	0.783521	−	0.621365i	$-0.213422\pi$
$71$	−77343.5	−	212499.i	−0.216097	−	0.593721i	−0.999618	+	0.0276440i	$0.991200\pi$
$72$		0			0
$73$	317454.	+	266375.i	0.816041	+	0.684740i	0.952041	−	0.305969i	$-0.0989804\pi$
$73$	317454.	+	266375.i	0.816041	+	0.684740i	−0.136000	+	0.990709i	$0.543425\pi$
$74$		0			0
$75$			148574.i			0.352175i
$76$		0			0
$77$	−1.00722e6			−2.20624
$78$		0			0
$79$	−312513.	+	372438.i	−0.633850	+	0.755393i	−0.983385	−	0.181530i	$-0.941895\pi$
$79$	−312513.	+	372438.i	−0.633850	+	0.755393i	0.349535	+	0.936923i	$0.386340\pi$
$80$		0			0
$81$	−358978.	+	130657.i	−0.675480	+	0.245854i
$82$		0			0
$83$	−269443.	−	466689.i	−0.471229	−	0.816193i	0.528229	−	0.849102i	$-0.322856\pi$
$83$	−269443.	−	466689.i	−0.471229	−	0.816193i	−0.999458	+	0.0329086i	$0.989523\pi$
$84$		0			0
$85$	−88656.5	−	502796.i	−0.144362	−	0.818719i
$86$		0			0
$87$	−140921.	+	244082.i	−0.214002	+	0.370662i
$88$		0			0
$89$	500639.	+	596638.i	0.710158	+	0.846333i	0.993635	−	0.112646i	$-0.0359326\pi$
$89$	500639.	+	596638.i	0.710158	+	0.846333i	−0.283478	+	0.958979i	$0.591488\pi$
$90$		0			0
$91$	341741.	−	938925.i	0.453495	−	1.24597i
$92$		0			0
$93$	−33712.7	+	191194.i	−0.0419126	+	0.237698i
$94$		0			0
$95$	−1.24631e6	+	116901.i	−1.45363	+	0.136347i
$96$		0			0
$97$	1.61652e6	+	285036.i	1.77119	+	0.312309i	0.961554	−	0.274616i	$-0.0885509\pi$
$97$	1.61652e6	+	285036.i	1.77119	+	0.312309i	0.809641	+	0.586926i	$0.199662\pi$
$98$		0			0
$99$	1.34489e6	+	489499.i	1.38605	+	0.504482i
$100$		0			0
$101$	724184.	−	607662.i	0.702886	−	0.589791i	−0.219707	−	0.975566i	$-0.570510\pi$
$101$	724184.	−	607662.i	0.702886	−	0.589791i	0.922593	+	0.385775i	$0.126066\pi$
$102$		0			0
$103$	1.37963e6	+	796531.i	1.26256	+	0.728939i	0.973569	−	0.228393i	$-0.0733470\pi$
$103$	1.37963e6	+	796531.i	1.26256	+	0.728939i	0.288991	+	0.957332i	$0.406680\pi$
$104$		0			0
$105$	−699752.	+	123385.i	−0.604472	+	0.106585i
$106$		0			0
$107$	975256.	−	563064.i	0.796099	−	0.459628i	−0.0460061	−	0.998941i	$-0.514649\pi$
$107$	975256.	−	563064.i	0.796099	−	0.459628i	0.842105	+	0.539313i	$0.181316\pi$
$108$		0			0
$109$	−525068.	−	1.44261e6i	−0.405449	−	1.11396i	−0.959556	−	0.281517i	$-0.909162\pi$
$109$	−525068.	−	1.44261e6i	−0.405449	−	1.11396i	0.554107	−	0.832445i	$-0.313060\pi$
$110$		0			0
$111$	−163697.	−	137358.i	−0.119694	−	0.100435i
$112$		0			0
$113$			1.33600e6i			0.925913i	0.886381	+	0.462957i	$0.153211\pi$
$113$			1.33600e6i			0.925913i	−0.886381	+	0.462957i	$0.846789\pi$
$114$		0			0
$115$	498092.			0.327504
$116$		0			0
$117$	−912616.	+	1.08761e6i	−0.569811	+	0.679074i
$118$		0			0
$119$	1.21807e6	−	443340.i	0.722819	−	0.263085i
$120$		0			0
$121$	−1.47684e6	−	2.55797e6i	−0.833640	−	1.44391i
$122$		0			0
$123$	149378.	+	847166.i	0.0802735	+	0.455253i
$124$		0			0
$125$	−187697.	+	325100.i	−0.0961007	+	0.166451i
$126$		0			0
$127$	2.09732e6	+	2.49948e6i	1.02389	+	1.22022i	0.975181	+	0.221410i	$0.0710658\pi$
$127$	2.09732e6	+	2.49948e6i	1.02389	+	1.22022i	0.0487077	+	0.998813i	$0.484490\pi$
$128$		0			0
$129$	−27832.1	+	76467.9i	−0.0129651	+	0.0356213i
$130$		0			0
$131$	299588.	−	1.69905e6i	0.133263	−	0.755774i	−0.842790	−	0.538243i	$-0.819088\pi$
$131$	299588.	−	1.69905e6i	0.133263	−	0.755774i	0.976053	−	0.217531i	$-0.0698005\pi$
$132$		0			0
$133$	−841756.	−	3.06464e6i	−0.357792	−	1.30264i
$134$		0			0
$135$	2.09523e6	+	369446.i	0.851591	+	0.150159i
$136$		0			0
$137$	1.78560e6	+	649906.i	0.694421	+	0.252748i	0.665027	−	0.746819i	$-0.268420\pi$
$137$	1.78560e6	+	649906.i	0.694421	+	0.252748i	0.0293939	+	0.999568i	$0.490642\pi$
$138$		0			0
$139$	910158.	−	763714.i	0.338901	−	0.284372i	−0.457414	−	0.889254i	$-0.651224\pi$
$139$	910158.	−	763714.i	0.338901	−	0.284372i	0.796315	+	0.604882i	$0.206780\pi$
$140$		0			0
$141$	941139.	+	543367.i	0.335735	+	0.193837i
$142$		0			0
$143$	4.61633e6	−	813984.i	1.57866	−	0.278360i
$144$		0			0
$145$	−5.30140e6	+	3.06076e6i	−1.73895	+	1.00398i
$146$		0			0
$147$	−278899.	−	766268.i	−0.0878000	−	0.241229i
$148$		0			0
$149$	−2.56069e6	−	2.14867e6i	−0.774102	−	0.649549i	0.167654	−	0.985846i	$-0.446381\pi$
$149$	−2.56069e6	−	2.14867e6i	−0.774102	−	0.649549i	−0.941756	+	0.336297i	$0.890825\pi$
$150$		0			0
$151$			752425.i			0.218541i	0.994012	+	0.109270i	$0.0348514\pi$
$151$			752425.i			0.218541i	−0.994012	+	0.109270i	$0.965149\pi$
$152$		0			0
$153$	−1.84188e6			−0.514264
$154$		0			0
$155$	−2.71047e6	+	3.23021e6i	−0.727863	+	0.867434i
$156$		0			0
$157$	908339.	−	330608.i	0.234719	−	0.0854309i	−0.221983	−	0.975051i	$-0.571253\pi$
$157$	908339.	−	330608.i	0.234719	−	0.0854309i	0.456702	+	0.889620i	$0.349031\pi$
$158$		0			0
$159$	−331980.	−	575006.i	−0.0825887	−	0.143048i
$160$		0			0
$161$	219596.	+	1.24539e6i	0.0526195	+	0.298420i
$162$		0			0
$163$	−3.28850e6	+	5.69586e6i	−0.759339	+	1.31521i	0.183850	+	0.982954i	$0.441144\pi$
$163$	−3.28850e6	+	5.69586e6i	−0.759339	+	1.31521i	−0.943188	+	0.332259i	$0.892189\pi$
$164$		0			0
$165$	−2.14270e6	−	2.55356e6i	−0.476989	−	0.568454i
$166$		0			0
$167$	1.60361e6	−	4.40588e6i	0.344309	−	0.945982i	−0.639819	−	0.768525i	$-0.720991\pi$
$167$	1.60361e6	−	4.40588e6i	0.344309	−	0.945982i	0.984129	−	0.177457i	$-0.0567869\pi$
$168$		0			0
$169$	30677.6	−	173981.i	0.00635568	−	0.0360448i
$170$		0			0
$171$	−365432.	+	4.50113e6i	−0.0730833	+	0.900188i
$172$		0			0
$173$	−8.87745e6	−	1.56533e6i	−1.71455	−	0.302321i	−0.771810	−	0.635853i	$-0.780649\pi$
$173$	−8.87745e6	−	1.56533e6i	−1.71455	−	0.302321i	−0.942739	+	0.333531i	$0.891760\pi$
$174$		0			0
$175$	−7.69888e6	−	2.80216e6i	−1.43653	−	0.522852i
$176$		0			0
$177$	−2.14115e6	+	1.79664e6i	−0.386124	+	0.323997i
$178$		0			0
$179$	−3.40806e6	−	1.96765e6i	−0.594222	−	0.343074i	0.172543	−	0.985002i	$-0.444802\pi$
$179$	−3.40806e6	−	1.96765e6i	−0.594222	−	0.343074i	−0.766765	+	0.641928i	$0.778135\pi$
$180$		0			0
$181$	7.74051e6	−	1.36486e6i	1.30537	−	0.230172i	0.522652	−	0.852546i	$-0.324943\pi$
$181$	7.74051e6	−	1.36486e6i	1.30537	−	0.230172i	0.782720	+	0.622374i	$0.213832\pi$
$182$		0			0
$183$	2.47713e6	−	1.43017e6i	0.404200	−	0.233365i
$184$		0			0
$185$	−1.58742e6	−	4.36141e6i	−0.250713	−	0.688829i
$186$		0			0
$187$	4.65843e6	+	3.90888e6i	0.712384	+	0.597761i
$188$		0			0
$189$			5.40164e6i			0.800093i
$190$		0			0
$191$	−5.07908e6			−0.728929			−0.364464	−	0.931217i	$-0.618748\pi$
$191$	−5.07908e6			−0.728929			−0.364464	+	0.931217i	$0.618748\pi$
$192$		0			0
$193$	3.72206e6	−	4.43578e6i	0.517740	−	0.617019i	−0.442305	−	0.896865i	$-0.645839\pi$
$193$	3.72206e6	−	4.43578e6i	0.517740	−	0.617019i	0.960045	+	0.279846i	$0.0902835\pi$
$194$		0			0
$195$	3.10742e6	−	1.13101e6i	0.419079	−	0.152532i
$196$		0			0
$197$	3.31687e6	+	5.74499e6i	0.433841	+	0.751434i	0.997200	−	0.0747777i	$-0.0238247\pi$
$197$	3.31687e6	+	5.74499e6i	0.433841	+	0.751434i	−0.563360	+	0.826212i	$0.690491\pi$
$198$		0			0
$199$	1.25900e6	+	7.14016e6i	0.159760	+	0.906043i	0.954304	+	0.298837i	$0.0965986\pi$
$199$	1.25900e6	+	7.14016e6i	0.159760	+	0.906043i	−0.794545	+	0.607206i	$0.792290\pi$
$200$		0			0
$201$	834646.	−	1.44565e6i	0.102781	−	0.178022i
$202$		0			0
$203$	−9.99015e6	−	1.19058e7i	−1.19422	−	1.42321i
$204$		0			0
$205$	−6.39032e6	+	1.75573e7i	−0.741756	+	2.03796i
$206$		0			0
$207$	312033.	−	1.76962e6i	0.0351794	−	0.199513i
$208$		0			0
$209$	1.04767e7	−	1.06086e7i	1.14758	−	1.16204i
$210$		0			0
$211$	1.58838e6	+	280075.i	0.169086	+	0.0298145i	0.257550	−	0.966265i	$-0.417085\pi$
$211$	1.58838e6	+	280075.i	0.169086	+	0.0298145i	−0.0884640	+	0.996079i	$0.528196\pi$
$212$		0			0
$213$	1.78555e6	+	649886.i	0.184770	+	0.0672509i
$214$		0			0
$215$	−1.35395e6	+	1.13610e6i	−0.136234	+	0.114314i
$216$		0			0
$217$	−9.27156e6	−	5.35294e6i	−0.907347	−	0.523857i
$218$		0			0
$219$	−3.42919e6	+	604658.i	−0.326482	+	0.0575676i
$220$		0			0
$221$	−5.22440e6	+	3.01631e6i	−0.484016	+	0.279447i
$222$		0			0
$223$	−547787.	−	1.50503e6i	−0.0493966	−	0.135716i	0.912541	−	0.408985i	$-0.134117\pi$
$223$	−547787.	−	1.50503e6i	−0.0493966	−	0.135716i	−0.961938	+	0.273269i	$0.911895\pi$
$224$		0			0
$225$	8.91807e6	+	7.48315e6i	0.782931	+	0.656957i
$226$		0			0
$227$		−	1.97069e7i		−	1.68477i	−0.538874	−	0.842387i	$-0.681150\pi$
$227$		−	1.97069e7i		−	1.68477i	0.538874	−	0.842387i	$-0.318850\pi$
$228$		0			0
$229$	1.33655e7			1.11296			0.556481	−	0.830861i	$-0.312151\pi$
$229$	1.33655e7			1.11296			0.556481	+	0.830861i	$0.312151\pi$
$230$		0			0
$231$	5.44008e6	−	6.48323e6i	0.441336	−	0.525963i
$232$		0			0
$233$	1.18913e7	−	4.32808e6i	0.940074	−	0.342159i	0.173879	−	0.984767i	$-0.444370\pi$
$233$	1.18913e7	−	4.32808e6i	0.940074	−	0.342159i	0.766195	+	0.642608i	$0.222148\pi$
$234$		0			0
$235$	1.18018e7	+	2.04413e7i	0.909376	+	1.57509i
$236$		0			0
$237$	−709388.	−	4.02314e6i	−0.0532892	−	0.302218i
$238$		0			0
$239$	−1.71521e6	+	2.97084e6i	−0.125639	+	0.217613i	−0.921983	−	0.387231i	$-0.873431\pi$
$239$	−1.71521e6	+	2.97084e6i	−0.125639	+	0.217613i	0.796344	+	0.604845i	$0.206765\pi$
$240$		0			0
$241$	1.07674e7	+	1.28320e7i	0.769234	+	0.916737i	0.998394	−	0.0566517i	$-0.0180425\pi$
$241$	1.07674e7	+	1.28320e7i	0.769234	+	0.916737i	−0.229160	+	0.973389i	$0.573598\pi$
$242$		0			0
$243$	4.00451e6	−	1.10023e7i	0.279081	−	0.766769i
$244$		0			0
$245$	3.07553e6	−	1.74422e7i	0.209132	−	1.18605i
$246$		0			0
$247$	6.33465e6	+	1.33657e7i	0.420370	+	0.886954i
$248$		0			0
$249$	4.45925e6	+	786285.i	0.288844	+	0.0509310i
$250$		0			0
$251$	7.98248e6	+	2.90539e6i	0.504797	+	0.183731i	0.581850	−	0.813296i	$-0.302329\pi$
$251$	7.98248e6	+	2.90539e6i	0.504797	+	0.183731i	−0.0770533	+	0.997027i	$0.524551\pi$
$252$		0			0
$253$	−4.54474e6	+	3.81349e6i	−0.280638	+	0.235484i
$254$		0			0
$255$	3.71522e6	+	2.14498e6i	0.224060	+	0.129361i
$256$		0			0
$257$	−1.91422e7	+	3.37528e6i	−1.12770	+	0.198843i	−0.706218	−	0.707995i	$-0.749600\pi$
$257$	−1.91422e7	+	3.37528e6i	−1.12770	+	0.198843i	−0.421479	+	0.906838i	$0.638489\pi$
$258$		0			0
$259$	1.02051e7	−	5.89190e6i	0.587377	−	0.339122i
$260$		0			0
$261$	7.55321e6	+	2.07523e7i	0.424825	+	1.16720i
$262$		0			0
$263$	9.98309e6	+	8.37681e6i	0.548779	+	0.460481i	0.874527	−	0.484976i	$-0.161172\pi$
$263$	9.98309e6	+	8.37681e6i	0.548779	+	0.460481i	−0.325748	+	0.945457i	$0.605616\pi$
$264$		0			0
$265$		−	1.44210e7i		−	0.774922i
$266$		0			0
$267$	−6.54441e6			−0.343824
$268$		0			0
$269$	5.35050e6	−	6.37647e6i	0.274876	−	0.327585i	−0.610891	−	0.791715i	$-0.709189\pi$
$269$	5.35050e6	−	6.37647e6i	0.274876	−	0.327585i	0.885767	+	0.464130i	$0.153633\pi$
$270$		0			0
$271$	−2.86500e7	+	1.04277e7i	−1.43952	+	0.523941i	−0.939643	−	0.342158i	$-0.888842\pi$
$271$	−2.86500e7	+	1.04277e7i	−1.43952	+	0.523941i	−0.499873	+	0.866099i	$0.666620\pi$
$272$		0			0
$273$	4.19786e6	+	7.27091e6i	0.206320	+	0.357356i
$274$		0			0
$275$	−6.67440e6	−	3.78524e7i	−0.320933	−	1.82010i
$276$		0			0
$277$	1.04028e7	−	1.80183e7i	0.489455	−	0.847761i	−0.510471	−	0.859895i	$-0.670529\pi$
$277$	1.04028e7	−	1.80183e7i	0.489455	−	0.847761i	0.999926	+	0.0121338i	$0.00386239\pi$
$278$		0			0
$279$	9.77834e6	+	1.16534e7i	0.450249	+	0.536586i
$280$		0			0
$281$	1.26893e6	−	3.48636e6i	0.0571898	−	0.157128i	−0.907808	−	0.419387i	$-0.862245\pi$
$281$	1.26893e6	−	3.48636e6i	0.0571898	−	0.157128i	0.964998	+	0.262259i	$0.0844674\pi$
$282$		0			0
$283$	872798.	−	4.94988e6i	0.0385083	−	0.218391i	−0.959481	−	0.281773i	$-0.909077\pi$
$283$	872798.	−	4.94988e6i	0.0385083	−	0.218391i	0.997989	+	0.0633817i	$0.0201885\pi$
$284$		0			0
$285$	5.97896e6	−	8.65359e6i	0.258280	−	0.373819i
$286$		0			0
$287$	−4.67162e7	−	8.23732e6i	−1.97616	−	0.348450i
$288$		0			0
$289$	1.53278e7	+	5.57885e6i	0.635017	+	0.231127i
$290$		0			0
$291$	−1.05657e7	+	8.86565e6i	−0.428764	+	0.359776i
$292$		0			0
$293$	−1.92074e7	−	1.10894e7i	−0.763601	−	0.440865i	0.0669863	−	0.997754i	$-0.478662\pi$
$293$	−1.92074e7	−	1.10894e7i	−0.763601	−	0.440865i	−0.830587	+	0.556889i	$0.811995\pi$
$294$		0			0
$295$	−5.97859e7	+	1.05419e7i	−2.32880	+	0.410630i
$296$		0			0
$297$	−2.19461e7	+	1.26706e7i	−0.837698	+	0.483645i
$298$		0			0
$299$	−2.01292e6	−	5.53046e6i	−0.0753032	−	0.206894i
$300$		0			0
$301$	−3.43753e6	−	2.88443e6i	−0.126051	−	0.105769i
$302$		0			0
$303$			7.94343e6i			0.285549i
$304$		0			0
$305$	6.21259e7			2.18964
$306$		0			0
$307$	−5.65862e6	+	6.74367e6i	−0.195567	+	0.233067i	−0.854912	−	0.518773i	$-0.826389\pi$
$307$	−5.65862e6	+	6.74367e6i	−0.195567	+	0.233067i	0.659345	+	0.751840i	$0.270834\pi$
$308$		0			0
$309$	−1.25786e7	+	4.57823e6i	−0.426341	+	0.155175i
$310$		0			0
$311$	−7.43597e6	−	1.28795e7i	−0.247205	−	0.428171i	0.715545	−	0.698567i	$-0.246179\pi$
$311$	−7.43597e6	−	1.28795e7i	−0.247205	−	0.428171i	−0.962749	+	0.270396i	$0.912845\pi$
$312$		0			0
$313$	6.93840e6	+	3.93496e7i	0.226270	+	1.28324i	0.860243	+	0.509885i	$0.170312\pi$
$313$	6.93840e6	+	3.93496e7i	0.226270	+	1.28324i	−0.633973	+	0.773355i	$0.718577\pi$
$314$		0			0
$315$	−2.78379e7	+	4.82167e7i	−0.890646	+	1.54264i
$316$		0			0
$317$	1.42528e7	+	1.69859e7i	0.447428	+	0.533224i	0.941866	−	0.335989i	$-0.109070\pi$
$317$	1.42528e7	+	1.69859e7i	0.447428	+	0.533224i	−0.494438	+	0.869213i	$0.664626\pi$
$318$		0			0
$319$	2.49377e7	−	6.85158e7i	0.768218	−	2.11066i
$320$		0			0
$321$	−1.64313e6	+	9.31864e6i	−0.0496771	+	0.281733i
$322$		0			0
$323$	−8.00030e6	+	1.74408e7i	−0.237410	+	0.517558i
$324$		0			0
$325$	3.75504e7	+	6.62114e6i	1.09387	+	0.192878i
$326$		0			0
$327$	1.21217e7	+	4.41194e6i	0.346673	+	0.126179i
$328$		0			0
$329$	−4.59067e7	+	3.85203e7i	−1.28910	+	1.08169i
$330$		0			0
$331$	−2.59299e7	−	1.49707e7i	−0.715019	−	0.412816i	0.0978978	−	0.995196i	$-0.468788\pi$
$331$	−2.59299e7	−	1.49707e7i	−0.715019	−	0.412816i	−0.812917	+	0.582380i	$0.802121\pi$
$332$		0			0
$333$	−1.64897e7	+	2.90758e6i	−0.446560	+	0.0787406i
$334$		0			0
$335$	3.13991e7	−	1.81283e7i	0.835185	−	0.482194i
$336$		0			0
$337$	−1.46456e7	−	4.02384e7i	−0.382663	−	1.05136i	−0.970230	−	0.242184i	$-0.922136\pi$
$337$	−1.46456e7	−	4.02384e7i	−0.382663	−	1.05136i	0.587567	−	0.809176i	$-0.300086\pi$
$338$		0			0
$339$	−8.59949e6	−	7.21583e6i	−0.220736	−	0.185220i
$340$		0			0
$341$		−	5.02253e7i		−	1.26666i
$342$		0			0
$343$	−9.54603e6			−0.236560
$344$		0			0
$345$	−2.69024e6	+	3.20610e6i	−0.0655138	+	0.0780764i
$346$		0			0
$347$	−2.62466e7	+	9.55296e6i	−0.628180	+	0.228639i	−0.636439	−	0.771327i	$-0.719593\pi$
$347$	−2.62466e7	+	9.55296e6i	−0.628180	+	0.228639i	0.00825916	+	0.999966i	$0.497371\pi$
$348$		0			0
$349$	−3.55905e7	−	6.16445e7i	−0.837255	−	1.45017i	−0.892181	−	0.451678i	$-0.850826\pi$
$349$	−3.55905e7	−	6.16445e7i	−0.837255	−	1.45017i	0.0549261	−	0.998490i	$-0.482508\pi$
$350$		0			0
$351$	−4.36533e6	−	2.47570e7i	−0.100948	−	0.572502i
$352$		0			0
$353$	−1.65379e7	+	2.86444e7i	−0.375972	+	0.651202i	−0.990472	−	0.137715i	$-0.956024\pi$
$353$	−1.65379e7	+	2.86444e7i	−0.375972	+	0.651202i	0.614500	+	0.788916i	$0.289358\pi$
$354$		0			0
$355$	2.65281e7	+	3.16150e7i	0.592955	+	0.706656i
$356$		0			0
$357$	−3.72520e6	+	1.02349e7i	−0.0818738	+	0.224947i
$358$		0			0
$359$	−551323.	+	3.12671e6i	−0.0119158	+	0.0675778i	−0.990186	−	0.139757i	$-0.955368\pi$
$359$	−551323.	+	3.12671e6i	−0.0119158	+	0.0675778i	0.978270	+	0.207335i	$0.0664790\pi$
$360$		0			0
$361$	4.10341e7	+	2.30112e7i	0.872215	+	0.489123i
$362$		0			0
$363$	2.44416e7	+	4.30971e6i	0.510986	+	0.0901007i
$364$		0			0
$365$	−7.10689e7	−	2.58670e7i	−1.46151	−	0.531945i
$366$		0			0
$367$	−2.32664e7	+	1.95228e7i	−0.470686	+	0.394952i	−0.847045	−	0.531522i	$-0.821620\pi$
$367$	−2.32664e7	+	1.95228e7i	−0.470686	+	0.394952i	0.376359	+	0.926474i	$0.377176\pi$
$368$		0			0
$369$	5.83743e7	+	3.37024e7i	1.16183	+	0.670783i
$370$		0			0
$371$	3.60572e7	−	6.35785e6i	0.706106	−	0.124506i
$372$		0			0
$373$	−7.56533e7	+	4.36784e7i	−1.45781	+	0.841667i	−0.998903	−	0.0468167i	$-0.985092\pi$
$373$	−7.56533e7	+	4.36784e7i	−1.45781	+	0.841667i	−0.458907	+	0.888484i	$0.651759\pi$
$374$		0			0
$375$	−1.07883e6	−	2.96405e6i	−0.0204577	−	0.0562072i
$376$		0			0
$377$	5.54089e7	+	4.64936e7i	1.03408	+	0.867699i
$378$		0			0
$379$			7.25393e7i			1.33247i	0.745744	+	0.666233i	$0.232094\pi$
$379$			7.25393e7i			1.33247i	−0.745744	+	0.666233i	$0.767906\pi$
$380$		0			0
$381$	−2.74164e7			−0.495718
$382$		0			0
$383$	6.00371e7	−	7.15495e7i	1.06862	−	1.27353i	0.108456	−	0.994101i	$-0.465409\pi$
$383$	6.00371e7	−	7.15495e7i	1.06862	−	1.27353i	0.960166	−	0.279432i	$-0.0901461\pi$
$384$		0			0
$385$	1.72734e8	−	6.28700e7i	3.02688	−	1.10169i
$386$		0			0
$387$	3.18814e6	+	5.52203e6i	0.0550053	+	0.0952721i
$388$		0			0
$389$	−1.48894e7	−	8.44418e7i	−0.252946	−	1.43453i	−0.801291	−	0.598275i	$-0.795853\pi$
$389$	−1.48894e7	−	8.44418e7i	−0.252946	−	1.43453i	0.548345	−	0.836252i	$-0.315258\pi$
$390$		0			0
$391$	3.81755e6	−	6.61220e6i	0.0638638	−	0.110615i
$392$		0			0
$393$	9.31827e6	+	1.11051e7i	0.153517	+	0.182955i
$394$		0			0
$395$	3.03473e7	−	8.33784e7i	0.492411	−	1.35289i
$396$		0			0
$397$	−8.69178e6	+	4.92935e7i	−0.138911	+	0.787804i	0.833145	+	0.553055i	$0.186538\pi$
$397$	−8.69178e6	+	4.92935e7i	−0.138911	+	0.787804i	−0.972056	+	0.234749i	$0.924573\pi$
$398$		0			0
$399$	2.42727e7	+	1.11342e7i	0.382120	+	0.175283i
$400$		0			0
$401$	−3.31739e7	−	5.84945e6i	−0.514474	−	0.0907156i	−0.0896173	−	0.995976i	$-0.528564\pi$
$401$	−3.31739e7	−	5.84945e6i	−0.514474	−	0.0907156i	−0.424857	+	0.905261i	$0.639676\pi$
$402$		0			0
$403$	4.68198e7	+	1.70410e7i	0.715342	+	0.260363i
$404$		0			0
$405$	5.34076e7	−	4.48143e7i	0.803966	−	0.674607i
$406$		0			0
$407$	4.78759e7	+	2.76411e7i	0.710123	+	0.409990i
$408$		0			0
$409$	5.35348e7	−	9.43963e6i	0.782467	−	0.137970i	0.231876	−	0.972745i	$-0.425514\pi$
$409$	5.35348e7	−	9.43963e6i	0.782467	−	0.137970i	0.550591	+	0.834775i	$0.314402\pi$
$410$		0			0
$411$	−1.38275e7	+	7.98329e6i	−0.199167	+	0.114989i
$412$		0			0
$413$	−5.27161e7	−	1.44836e8i	−0.748330	−	2.05602i
$414$		0			0
$415$	7.53387e7	+	6.32167e7i	1.05408	+	0.884478i
$416$		0			0
$417$			9.98335e6i			0.137679i
$418$		0			0
$419$	−1.13680e8			−1.54541			−0.772705	−	0.634766i	$-0.781097\pi$
$419$	−1.13680e8			−1.54541			−0.772705	+	0.634766i	$0.781097\pi$
$420$		0			0
$421$	−6.74297e7	+	8.03595e7i	−0.903659	+	1.07694i	0.0930323	+	0.995663i	$0.470344\pi$
$421$	−6.74297e7	+	8.03595e7i	−0.903659	+	1.07694i	−0.996692	+	0.0812761i	$0.974100\pi$
$422$		0			0
$423$	8.00172e7	−	2.91239e7i	1.05721	−	0.384794i
$424$		0			0
$425$	2.47328e7	+	4.28384e7i	0.322185	+	0.558041i
$426$		0			0
$427$	2.73897e7	+	1.55335e8i	0.351806	+	1.99519i
$428$		0			0
$429$	−1.96938e7	+	3.41106e7i	−0.249435	+	0.432034i
$430$		0			0
$431$	3.58278e6	+	4.26980e6i	0.0447496	+	0.0533305i	0.787955	−	0.615733i	$-0.211140\pi$
$431$	3.58278e6	+	4.26980e6i	0.0447496	+	0.0533305i	−0.743205	+	0.669063i	$0.766695\pi$
$432$		0			0
$433$	−2.10401e7	+	5.78072e7i	−0.259170	+	0.712063i	0.740049	+	0.672553i	$0.234802\pi$
$433$	−2.10401e7	+	5.78072e7i	−0.259170	+	0.712063i	−0.999219	+	0.0395106i	$0.987420\pi$
$434$		0			0
$435$	8.93189e6	−	5.06553e7i	0.108511	−	0.615399i
$436$		0			0
$437$	−1.54013e7	−	1.06411e7i	−0.184550	−	0.127510i
$438$		0			0
$439$	−3.45283e7	−	6.08827e6i	−0.408114	−	0.0719615i	−0.0341774	−	0.999416i	$-0.510881\pi$
$439$	−3.45283e7	−	6.08827e6i	−0.408114	−	0.0719615i	−0.373937	+	0.927454i	$0.621992\pi$
$440$		0			0
$441$	−6.00420e7	−	2.18535e7i	−0.700066	−	0.254803i
$442$		0			0
$443$	1.47329e7	−	1.23623e7i	0.169463	−	0.142197i	−0.554112	−	0.832442i	$-0.686942\pi$
$443$	1.47329e7	−	1.23623e7i	0.169463	−	0.142197i	0.723575	+	0.690246i	$0.242498\pi$
$444$		0			0
$445$	−1.23099e8	−	7.10713e7i	−1.39693	−	0.806519i
$446$		0			0
$447$	2.76610e7	−	4.87738e6i	0.309703	−	0.0546090i
$448$		0			0
$449$	−1.81312e7	+	1.04681e7i	−0.200303	+	0.115645i	−0.596797	−	0.802392i	$-0.703560\pi$
$449$	−1.81312e7	+	1.04681e7i	−0.200303	+	0.115645i	0.396494	+	0.918037i	$0.370227\pi$
$450$		0			0
$451$	−7.61146e7	−	2.09123e8i	−0.829733	−	2.27967i
$452$		0			0
$453$	−4.84318e6	−	4.06391e6i	−0.0520998	−	0.0437169i
$454$		0			0
$455$			1.82353e8i			1.93588i
$456$		0			0
$457$	2.99217e7			0.313500			0.156750	−	0.987638i	$-0.449898\pi$
$457$	2.99217e7			0.313500			0.156750	+	0.987638i	$0.449898\pi$
$458$		0			0
$459$	2.09630e7	−	2.49828e7i	0.216779	−	0.258347i
$460$		0			0
$461$	1.41202e8	−	5.13932e7i	1.44124	−	0.524569i	0.501111	−	0.865383i	$-0.332925\pi$
$461$	1.41202e8	−	5.13932e7i	1.44124	−	0.524569i	0.940131	+	0.340814i	$0.110702\pi$
$462$		0			0
$463$	−6.51473e7	−	1.12838e8i	−0.656377	−	1.13688i	−0.981547	−	0.191223i	$-0.938755\pi$
$463$	−6.51473e7	−	1.12838e8i	−0.656377	−	1.13688i	0.325169	−	0.945656i	$-0.394579\pi$
$464$		0			0
$465$	−6.15263e6	−	3.48933e7i	−0.0611930	−	0.347043i
$466$		0			0
$467$	−3.13227e7	+	5.42525e7i	−0.307545	+	0.532683i	−0.977825	−	0.209425i	$-0.932841\pi$
$467$	−3.13227e7	+	5.42525e7i	−0.307545	+	0.532683i	0.670280	+	0.742108i	$0.266174\pi$
$468$		0			0
$469$	5.91696e7	+	7.05156e7i	0.573561	+	0.683544i
$470$		0			0
$471$	−2.77797e6	+	7.63240e6i	−0.0265867	+	0.0730463i
$472$		0			0
$473$	3.65564e6	−	2.07321e7i	0.0345445	−	0.195912i
$474$		0			0
$475$	1.09594e8	−	5.19421e7i	1.02260	−	0.484662i
$476$		0			0
$477$	−5.12351e7	−	9.03413e6i	−0.472076	−	0.0832398i
$478$		0			0
$479$	1.48258e8	+	5.39615e7i	1.34900	+	0.490995i	0.912635	−	0.408776i	$-0.134044\pi$
$479$	1.48258e8	+	5.39615e7i	1.34900	+	0.490995i	0.436363	+	0.899771i	$0.356266\pi$
$480$		0			0
$481$	−4.20108e7	+	3.52512e7i	−0.377508	+	0.316766i
$482$		0			0
$483$	−9.20234e6	−	5.31297e6i	−0.0816689	−	0.0471516i
$484$		0			0
$485$	−2.95018e8	+	5.20197e7i	−2.58597	+	0.455976i
$486$		0			0
$487$	−1.40113e8	+	8.08943e7i	−1.21309	+	0.700376i	−0.963430	−	0.267959i	$-0.913651\pi$
$487$	−1.40113e8	+	8.08943e7i	−1.21309	+	0.700376i	−0.249656	+	0.968335i	$0.580317\pi$
$488$		0			0
$489$	−1.89014e7	−	5.19311e7i	−0.161647	−	0.444121i
$490$		0			0
$491$	9.80524e7	+	8.22757e7i	0.828350	+	0.695068i	0.954911	−	0.296891i	$-0.0959497\pi$
$491$	9.80524e7	+	8.22757e7i	0.828350	+	0.695068i	−0.126562	+	0.991959i	$0.540394\pi$
$492$		0			0
$493$			9.38351e7i			0.783113i
$494$		0			0
$495$	−2.61196e8			−2.15353
$496$		0			0
$497$	−6.73521e7	+	8.02671e7i	−0.548633	+	0.653836i
$498$		0			0
$499$	1.94923e8	−	7.09463e7i	1.56878	−	0.570989i	0.596054	−	0.802945i	$-0.296735\pi$
$499$	1.94923e8	−	7.09463e7i	1.56878	−	0.570989i	0.972726	+	0.231955i	$0.0745124\pi$
$500$		0			0
$501$	1.96983e7	+	3.41185e7i	0.156645	+	0.271317i
$502$		0			0
$503$	−1.84588e7	−	1.04685e8i	−0.145044	−	0.822586i	−0.967332	−	0.253514i	$-0.918414\pi$
$503$	−1.84588e7	−	1.04685e8i	−0.145044	−	0.822586i	0.822288	−	0.569072i	$-0.192697\pi$
$504$		0			0
$505$	−8.62645e7	+	1.49415e8i	−0.669820	+	1.16016i
$506$		0			0
$507$	954185.	+	1.13715e6i	0.00732164	+	0.00872559i
$508$		0			0
$509$	1.63812e7	−	4.50070e7i	0.124220	−	0.341292i	−0.861958	−	0.506979i	$-0.830762\pi$
$509$	1.63812e7	−	4.50070e7i	0.124220	−	0.341292i	0.986178	+	0.165687i	$0.0529842\pi$
$510$		0			0
$511$	3.33433e7	−	1.89099e8i	0.249888	−	1.41719i
$512$		0			0
$513$	−5.68932e7	−	5.61856e7i	−0.421413	−	0.416172i
$514$		0			0
$515$	−2.86320e8	−	5.04859e7i	−2.09619	−	0.369614i
$516$		0			0
$517$	−2.64185e8	−	9.61555e7i	−1.91177	−	0.695829i
$518$		0			0
$519$	5.80235e7	−	4.86875e7i	0.415052	−	0.348270i
$520$		0			0
$521$	7.48231e7	+	4.31991e7i	0.529081	+	0.305465i	0.740642	−	0.671900i	$-0.234521\pi$
$521$	7.48231e7	+	4.31991e7i	0.529081	+	0.305465i	−0.211561	+	0.977365i	$0.567855\pi$
$522$		0			0
$523$	−2.63326e7	+	4.64315e6i	−0.184072	+	0.0324569i	−0.264924	−	0.964269i	$-0.585347\pi$
$523$	−2.63326e7	+	4.64315e6i	−0.184072	+	0.0324569i	0.0808520	+	0.996726i	$0.474236\pi$
$524$		0			0
$525$	5.96191e7	−	3.44211e7i	0.412010	−	0.237874i
$526$		0			0
$527$	2.21073e7	+	6.07392e7i	0.151044	+	0.414989i
$528$		0			0
$529$	−1.07696e8	−	9.03677e7i	−0.727499	−	0.610444i
$530$		0			0
$531$			2.19012e8i			1.46280i
$532$		0			0
$533$	2.20768e8			1.45799
$534$		0			0
$535$	−1.32106e8	+	1.57438e8i	−0.862703	+	1.02813i
$536$		0			0
$537$	3.10725e7	−	1.13095e7i	0.200656	−	0.0730330i
$538$		0			0
$539$	1.05479e8	+	1.82694e8i	0.673593	+	1.16670i
$540$		0			0
$541$	−2.97616e7	−	1.68786e8i	−0.187960	−	1.06597i	−0.922094	−	0.386967i	$-0.873523\pi$
$541$	−2.97616e7	−	1.68786e8i	−0.187960	−	1.06597i	0.734134	−	0.679005i	$-0.237588\pi$
$542$		0			0
$543$	−3.30219e7	+	5.71956e7i	−0.206254	+	0.357242i
$544$		0			0
$545$	1.80094e8	+	2.14628e8i	1.11252	+	1.32585i
$546$		0			0
$547$	8.20893e7	−	2.25539e8i	0.501562	−	1.37803i	−0.388187	−	0.921581i	$-0.626899\pi$
$547$	8.20893e7	−	2.25539e8i	0.501562	−	1.37803i	0.889749	−	0.456450i	$-0.150879\pi$
$548$		0			0
$549$	3.89191e7	−	2.20721e8i	0.235205	−	1.33391i
$550$		0			0
$551$	2.29312e8	+	1.86171e7i	1.37079	+	0.111290i
$552$		0			0
$553$	2.21852e8	+	3.91185e7i	1.31186	+	0.231317i
$554$		0			0
$555$	3.66471e7	+	1.33385e7i	0.214369	+	0.0780238i
$556$		0			0
$557$	−2.14287e8	+	1.79808e8i	−1.24002	+	1.04050i	−0.242502	+	0.970151i	$0.577968\pi$
$557$	−2.14287e8	+	1.79808e8i	−1.24002	+	1.04050i	−0.997522	+	0.0703526i	$0.977588\pi$
$558$		0			0
$559$	1.80861e7	+	1.04420e7i	0.103540	+	0.0597789i
$560$		0			0
$561$	−5.03211e7	+	8.87296e6i	−0.285011	+	0.0502551i
$562$		0			0
$563$	6.12767e6	−	3.53781e6i	0.0343376	−	0.0198248i	−0.482733	−	0.875768i	$-0.660356\pi$
$563$	6.12767e6	−	3.53781e6i	0.0343376	−	0.0198248i	0.517071	+	0.855943i	$0.327022\pi$
$564$		0			0
$565$	−8.33920e7	−	2.29118e8i	−0.462359	−	1.27032i
$566$		0			0
$567$	1.35596e8	+	1.13779e8i	0.743872	+	0.624183i
$568$		0			0
$569$		−	2.78067e8i		−	1.50943i	−0.656052	−	0.754715i	$-0.727775\pi$
$569$		−	2.78067e8i		−	1.50943i	0.656052	−	0.754715i	$-0.272225\pi$
$570$		0			0
$571$	3.43184e8			1.84340			0.921698	−	0.387908i	$-0.126802\pi$
$571$	3.43184e8			1.84340			0.921698	+	0.387908i	$0.126802\pi$
$572$		0			0
$573$	2.74325e7	−	3.26928e7i	0.145815	−	0.173776i
$574$		0			0
$575$	−4.53480e7	+	1.65053e7i	−0.238536	+	0.0868201i
$576$		0			0
$577$	−9.28861e7	−	1.60883e8i	−0.483530	−	0.837498i	0.516292	−	0.856413i	$-0.327312\pi$
$577$	−9.28861e7	−	1.60883e8i	−0.483530	−	0.837498i	−0.999821	+	0.0189151i	$0.993979\pi$
$578$		0			0
$579$	8.44889e6	+	4.79160e7i	0.0435275	+	0.246857i
$580$		0			0
$581$	−1.24847e8	+	2.16242e8i	−0.636576	+	1.10258i
$582$		0			0
$583$	1.10410e8	+	1.31581e8i	0.557189	+	0.664032i
$584$		0			0
$585$	8.86216e7	−	2.43486e8i	0.442662	−	1.21620i
$586$		0			0
$587$	−2.81050e7	+	1.59391e8i	−0.138953	+	0.788043i	0.833072	+	0.553165i	$0.186580\pi$
$587$	−2.81050e7	+	1.59391e8i	−0.138953	+	0.788043i	−0.972025	+	0.234878i	$0.924531\pi$
$588$		0			0
$589$	1.52819e8	−	4.19744e7i	0.747879	−	0.205418i
$590$		0			0
$591$	−5.48939e7	−	9.67927e6i	−0.265926	−	0.0468900i
$592$		0			0
$593$	1.79147e8	+	6.52041e7i	0.859102	+	0.312688i	0.733746	−	0.679424i	$-0.237770\pi$
$593$	1.79147e8	+	6.52041e7i	0.859102	+	0.312688i	0.125356	+	0.992112i	$0.459993\pi$
$594$		0			0
$595$	−1.81220e8	+	1.52062e8i	−0.860310	+	0.721886i
$596$		0			0
$597$	−5.27595e7	−	3.04607e7i	−0.247958	−	0.143158i
$598$		0			0
$599$	−2.07969e8	+	3.66706e7i	−0.967652	+	0.170623i	−0.635073	−	0.772452i	$-0.719030\pi$
$599$	−2.07969e8	+	3.66706e7i	−0.967652	+	0.170623i	−0.332579	+	0.943075i	$0.607919\pi$
$600$		0			0
$601$	−2.18161e8	+	1.25955e8i	−1.00497	+	0.580220i	−0.909715	−	0.415232i	$-0.863700\pi$
$601$	−2.18161e8	+	1.25955e8i	−1.00497	+	0.580220i	−0.0952559	+	0.995453i	$0.530367\pi$
$602$		0			0
$603$	−4.47361e7	−	1.22911e8i	−0.204036	−	0.560584i
$604$		0			0
$605$	4.12939e8	+	3.46497e8i	1.86475	+	1.56471i
$606$		0			0
$607$		−	2.41074e8i		−	1.07792i	−0.842333	−	0.538958i	$-0.818818\pi$
$607$		−	2.41074e8i		−	1.07792i	0.842333	−	0.538958i	$-0.181182\pi$
$608$		0			0
$609$	1.30592e8			0.578184
$610$		0			0
$611$	1.79271e8	−	2.13647e8i	0.785936	−	0.936642i
$612$		0			0
$613$	6.82552e7	−	2.48429e7i	0.296316	−	0.107850i	−0.189585	−	0.981864i	$-0.560714\pi$
$613$	6.82552e7	−	2.48429e7i	0.296316	−	0.107850i	0.485900	+	0.874014i	$0.338492\pi$
$614$		0			0
$615$	−7.84973e7	−	1.35961e8i	−0.337465	−	0.584507i
$616$		0			0
$617$	−6.50171e6	−	3.68730e7i	−0.0276804	−	0.156983i	0.967835	−	0.251587i	$-0.0809526\pi$
$617$	−6.50171e6	−	3.68730e7i	−0.0276804	−	0.156983i	−0.995515	+	0.0946041i	$0.969841\pi$
$618$		0			0
$619$	8.85809e7	−	1.53427e8i	0.373481	−	0.646888i	−0.616618	−	0.787263i	$-0.711498\pi$
$619$	8.85809e7	−	1.53427e8i	0.373481	−	0.646888i	0.990098	+	0.140375i	$0.0448309\pi$
$620$		0			0
$621$	2.04514e7	+	2.43731e7i	0.0853982	+	0.101774i
$622$		0			0
$623$	1.23430e8	−	3.39121e8i	0.510454	−	1.40246i
$624$		0			0
$625$	−3.60789e7	+	2.04614e8i	−0.147779	+	0.838098i
$626$		0			0
$627$	1.16997e7	+	1.24734e8i	0.0474650	+	0.506036i
$628$		0			0
$629$	−7.00645e7	−	1.23543e7i	−0.281544	−	0.0496438i
$630$		0			0
$631$	1.51754e8	+	5.52341e7i	0.604023	+	0.219846i	0.625886	−	0.779915i	$-0.284738\pi$
$631$	1.51754e8	+	5.52341e7i	0.604023	+	0.219846i	−0.0218631	+	0.999761i	$0.506960\pi$
$632$		0			0
$633$	−1.03818e7	+	8.71134e6i	−0.0409317	+	0.0343458i
$634$		0			0
$635$	−5.15697e8	−	2.97738e8i	−2.01406	−	1.16282i
$636$		0			0
$637$	−2.06094e8	+	3.63400e7i	−0.797348	+	0.140594i
$638$		0			0
$639$	1.28941e8	−	7.44440e7i	0.494183	−	0.285316i
$640$		0			0
$641$	1.21713e8	+	3.34405e8i	0.462130	+	1.26969i	0.923880	+	0.382681i	$0.124999\pi$
$641$	1.21713e8	+	3.34405e8i	0.462130	+	1.26969i	−0.461751	+	0.887010i	$0.652778\pi$
$642$		0			0
$643$	2.52639e7	+	2.11989e7i	0.0950315	+	0.0797409i	0.689066	−	0.724699i	$-0.258021\pi$
$643$	2.52639e7	+	2.11989e7i	0.0950315	+	0.0797409i	−0.594034	+	0.804440i	$0.702466\pi$
$644$		0			0
$645$		−	1.48512e7i		−	0.0553454i
$646$		0			0
$647$	1.16530e7			0.0430253			0.0215127	−	0.999769i	$-0.493152\pi$
$647$	1.16530e7			0.0430253			0.0215127	+	0.999769i	$0.493152\pi$
$648$		0			0
$649$	4.64793e8	−	5.53919e8i	1.70030	−	2.02634i
$650$		0			0
$651$	8.45320e7	−	3.07671e7i	0.306393	−	0.111518i
$652$		0			0
$653$	1.84807e8	+	3.20096e8i	0.663712	+	1.14958i	0.979633	+	0.200798i	$0.0643534\pi$
$653$	1.84807e8	+	3.20096e8i	0.663712	+	1.14958i	−0.315921	+	0.948786i	$0.602313\pi$
$654$		0			0
$655$	5.46754e7	+	3.10080e8i	0.194566	+	1.10344i
$656$		0			0
$657$	−1.36422e8	+	2.36290e8i	−0.481048	+	0.833199i
$658$		0			0
$659$	7.92065e6	+	9.43947e6i	0.0276761	+	0.0329831i	0.779705	−	0.626147i	$-0.215369\pi$
$659$	7.92065e6	+	9.43947e6i	0.0276761	+	0.0329831i	−0.752029	+	0.659130i	$0.770925\pi$
$660$		0			0
$661$	2.58043e7	−	7.08968e7i	0.0893487	−	0.245483i	−0.886968	−	0.461832i	$-0.847192\pi$
$661$	2.58043e7	−	7.08968e7i	0.0893487	−	0.245483i	0.976316	+	0.216348i	$0.0694146\pi$
$662$		0			0
$663$	8.80217e6	−	4.99196e7i	0.0302029	−	0.171289i
$664$		0			0
$665$	3.35650e8	+	4.73030e8i	1.14136	+	1.60851i
$666$		0			0
$667$	−9.01542e7	−	1.58966e7i	−0.303815	−	0.0535707i
$668$		0			0
$669$	1.26462e7	+	4.60283e6i	0.0422358	+	0.0153726i
$670$		0			0
$671$	−5.66854e8	+	4.75647e8i	−1.87631	+	1.57441i
$672$		0			0
$673$	3.03644e8	+	1.75309e8i	0.996138	+	0.575120i	0.907103	−	0.420908i	$-0.138289\pi$
$673$	3.03644e8	+	1.75309e8i	0.996138	+	0.575120i	0.0890345	+	0.996029i	$0.471622\pi$
$674$		0			0
$675$	−2.02999e8	+	3.57943e7i	−0.660060	+	0.116386i
$676$		0			0
$677$	−1.36763e8	+	7.89604e7i	−0.440762	+	0.254474i	−0.703921	−	0.710279i	$-0.748569\pi$
$677$	−1.36763e8	+	7.89604e7i	−0.440762	+	0.254474i	0.263159	+	0.964752i	$0.415236\pi$
$678$		0			0
$679$	−2.60132e8	−	7.14706e8i	−0.830968	−	2.28307i
$680$		0			0
$681$	1.26849e8	+	1.06439e8i	0.401647	+	0.337022i
$682$		0			0
$683$		−	3.47943e8i		−	1.09206i	−0.837766	−	0.546029i	$-0.816139\pi$
$683$		−	3.47943e8i		−	1.09206i	0.837766	−	0.546029i	$-0.183861\pi$
$684$		0			0
$685$	−3.46789e8			−1.07893
$686$		0			0
$687$	−7.21884e7	+	8.60307e7i	−0.222637	+	0.265328i
$688$		0			0
$689$	−1.60121e8	+	5.82792e7i	−0.489542	+	0.178179i
$690$		0			0
$691$	−3.53336e7	−	6.11996e7i	−0.107091	−	0.185488i	0.807499	−	0.589868i	$-0.200820\pi$
$691$	−3.53336e7	−	6.11996e7i	−0.107091	−	0.185488i	−0.914591	+	0.404381i	$0.867487\pi$
$692$		0			0
$693$	−1.15155e8	−	6.53075e8i	−0.346005	−	1.96229i
$694$		0			0
$695$	−1.08418e8	+	1.87785e8i	−0.322958	+	0.559380i
$696$		0			0
$697$	1.84096e8	+	2.19397e8i	0.543683	+	0.647936i
$698$		0			0
$699$	−3.63671e7	+	9.99179e7i	−0.106482	+	0.292558i
$700$		0			0
$701$	6.63733e7	−	3.76421e8i	0.192681	−	1.09275i	−0.723002	−	0.690846i	$-0.757238\pi$
$701$	6.63733e7	−	3.76421e8i	0.192681	−	1.09275i	0.915683	−	0.401902i	$-0.131651\pi$
$702$		0			0
$703$	−4.40920e7	+	1.68771e8i	−0.126909	+	0.485771i
$704$		0			0
$705$	−1.95318e8	−	3.44398e7i	−0.557410	−	0.0982864i
$706$		0			0
$707$	−4.11616e8	−	1.49816e8i	−1.16475	−	0.423936i
$708$		0			0
$709$	−1.95701e8	+	1.64213e8i	−0.549104	+	0.460753i	−0.874638	−	0.484777i	$-0.838901\pi$
$709$	−1.95701e8	+	1.64213e8i	−0.549104	+	0.460753i	0.325533	+	0.945531i	$0.394456\pi$
$710$		0			0
$711$	−2.77216e8	−	1.60051e8i	−0.771276	−	0.445296i
$712$		0			0
$713$	−6.21018e7	+	1.09502e7i	−0.171331	+	0.0302102i
$714$		0			0
$715$	−7.40872e8	+	4.27743e8i	−2.02687	+	1.17021i
$716$		0			0
$717$	−9.85855e6	−	2.70861e7i	−0.0267458	−	0.0734835i
$718$		0			0
$719$	2.72428e8	+	2.28594e8i	0.732934	+	0.615004i	0.930930	−	0.365199i	$-0.118999\pi$
$719$	2.72428e8	+	2.28594e8i	0.732934	+	0.615004i	−0.197996	+	0.980203i	$0.563443\pi$
$720$		0			0
$721$		−	7.38150e8i		−	1.96942i
$722$		0			0
$723$	−1.40752e8			−0.372426
$724$		0			0
$725$	3.81232e8	−	4.54335e8i	1.00040	−	1.19224i
$726$		0			0
$727$	−1.63373e8	+	5.94631e7i	−0.425185	+	0.154755i	−0.545745	−	0.837951i	$-0.683753\pi$
$727$	−1.63373e8	+	5.94631e7i	−0.425185	+	0.154755i	0.120560	+	0.992706i	$0.461531\pi$
$728$		0			0
$729$	−9.00543e7	−	1.55979e8i	−0.232446	−	0.402608i
$730$		0			0
$731$	4.70461e6	+	2.66812e7i	0.0120440	+	0.0683050i
$732$		0			0
$733$	−1.50930e8	+	2.61418e8i	−0.383233	+	0.663779i	−0.991522	−	0.129936i	$-0.958523\pi$
$733$	−1.50930e8	+	2.61418e8i	−0.383233	+	0.663779i	0.608289	+	0.793716i	$0.291856\pi$
$734$		0			0
$735$	9.56599e7	+	1.14003e8i	0.240917	+	0.287114i
$736$		0			0
$737$	−1.47701e8	+	4.05805e8i	−0.368961	+	1.01371i
$738$		0			0
$739$	−3.97913e7	+	2.25668e8i	−0.0985950	+	0.559160i	0.894991	+	0.446084i	$0.147182\pi$
$739$	−3.97913e7	+	2.25668e8i	−0.0985950	+	0.559160i	−0.993586	+	0.113076i	$0.963930\pi$
$740$		0			0
$741$	−1.20246e8	−	3.14147e7i	−0.295539	−	0.0772107i
$742$		0			0
$743$	8.70593e7	+	1.53509e7i	0.212250	+	0.0374255i	0.278762	−	0.960360i	$-0.410076\pi$
$743$	8.70593e7	+	1.53509e7i	0.212250	+	0.0374255i	−0.0665118	+	0.997786i	$0.521187\pi$
$744$		0			0
$745$	5.73266e8	+	2.08652e8i	1.38640	+	0.504607i
$746$		0			0
$747$	2.71793e8	−	2.28061e8i	0.652043	−	0.547129i
$748$		0			0
$749$	−4.51888e8	−	2.60897e8i	−1.07544	−	0.620904i
$750$		0			0
$751$	−2.72402e7	+	4.80318e6i	−0.0643118	+	0.0113399i	−0.205711	−	0.978613i	$-0.565951\pi$
$751$	−2.72402e7	+	4.80318e6i	−0.0643118	+	0.0113399i	0.141400	+	0.989953i	$0.454840\pi$
$752$		0			0
$753$	−6.18153e7	+	3.56891e7i	−0.144781	+	0.0835893i
$754$		0			0
$755$	−4.69659e7	−	1.29038e8i	−0.109129	−	0.299830i
$756$		0			0
$757$	2.59138e8	+	2.17443e8i	0.597370	+	0.501253i	0.890599	−	0.454789i	$-0.150285\pi$
$757$	2.59138e8	+	2.17443e8i	0.597370	+	0.501253i	−0.293229	+	0.956042i	$0.594730\pi$
$758$		0			0
$759$		−	4.98503e7i		−	0.114010i
$760$		0			0
$761$	3.77273e8			0.856055			0.428027	−	0.903766i	$-0.359209\pi$
$761$	3.77273e8			0.856055			0.428027	+	0.903766i	$0.359209\pi$
$762$		0			0
$763$	−4.57239e8	+	5.44917e8i	−1.02937	+	1.22675i
$764$		0			0
$765$	3.15874e8	−	1.14969e8i	0.705552	−	0.256800i
$766$		0			0
$767$	3.58660e8	+	6.21217e8i	0.794871	+	1.37676i
$768$		0			0
$769$	4.09569e7	+	2.32278e8i	0.0900632	+	0.510774i	0.996149	+	0.0876794i	$0.0279451\pi$
$769$	4.09569e7	+	2.32278e8i	0.0900632	+	0.510774i	−0.906086	+	0.423095i	$0.860944\pi$
$770$		0			0
$771$	8.16626e7	−	1.41444e8i	0.178181	−	0.308618i
$772$		0			0
$773$	1.77059e8	+	2.11010e8i	0.383335	+	0.456841i	0.922864	−	0.385126i	$-0.125842\pi$
$773$	1.77059e8	+	2.11010e8i	0.383335	+	0.456841i	−0.539529	+	0.841967i	$0.681398\pi$
$774$		0			0
$775$	1.39731e8	−	3.83907e8i	0.300183	−	0.824747i
$776$		0			0
$777$	−1.71937e7	+	9.75103e7i	−0.0366527	+	0.207868i
$778$		0			0
$779$	5.72682e8	−	4.06360e8i	1.21144	−	0.859605i
$780$		0			0
$781$	−4.84101e8	−	8.53600e7i	−1.01621	−	0.179185i
$782$		0			0
$783$	−3.67445e8	−	1.33739e8i	−0.765432	−	0.278595i
$784$		0			0
$785$	−1.35140e8	+	1.13396e8i	−0.279366	+	0.234416i
$786$		0			0
$787$	1.95858e7	+	1.13078e7i	0.0401806	+	0.0231983i	0.519956	−	0.854193i	$-0.325948\pi$
$787$	1.95858e7	+	1.13078e7i	0.0401806	+	0.0231983i	−0.479775	+	0.877391i	$0.659282\pi$
$788$		0			0
$789$	−1.07839e8	+	1.90149e7i	−0.219556	+	0.0387136i
$790$		0			0
$791$	5.36103e8	−	3.09519e8i	1.08323	−	0.625400i
$792$		0			0
$793$	−2.51067e8	−	6.89802e8i	−0.503466	−	1.38326i
$794$		0			0
$795$	9.28246e7	+	7.78891e7i	0.184740	+	0.155016i
$796$		0			0
$797$			8.29891e8i			1.63925i	0.572898	+	0.819627i	$0.305819\pi$
$797$			8.29891e8i			1.63925i	−0.572898	+	0.819627i	$0.694181\pi$
$798$		0			0
$799$	3.61812e8			0.709321
$800$		0			0
$801$	−3.29619e8	+	3.92825e8i	−0.641379	+	0.764366i
$802$		0			0
$803$	8.46496e8	−	3.08099e8i	1.63485	−	0.595037i
$804$		0			0
$805$	−1.15396e8	−	1.99872e8i	−0.221210	−	0.383146i
$806$		0			0
$807$	1.21454e7	+	6.88797e7i	0.0231094	+	0.131060i
$808$		0			0
$809$	−8.98480e7	+	1.55621e8i	−0.169693	+	0.293916i	−0.938312	−	0.345790i	$-0.887611\pi$
$809$	−8.98480e7	+	1.55621e8i	−0.169693	+	0.293916i	0.768619	+	0.639707i	$0.220944\pi$
$810$		0			0
$811$	−1.69809e8	−	2.02370e8i	−0.318345	−	0.379388i	0.583014	−	0.812462i	$-0.301873\pi$
$811$	−1.69809e8	−	2.02370e8i	−0.318345	−	0.379388i	−0.901358	+	0.433074i	$0.857429\pi$
$812$		0			0
$813$	8.76200e7	−	2.40734e8i	0.163054	−	0.447988i
$814$		0			0
$815$	2.08433e8	−	1.18208e9i	0.385029	−	2.18361i
$816$		0			0
$817$	6.61362e7	−	6.20341e6i	0.121275	−	0.0113753i
$818$		0			0
$819$	6.47864e8	+	1.14236e8i	1.17932	+	0.207946i
$820$		0			0
$821$	6.95585e7	+	2.53172e7i	0.125696	+	0.0457495i	0.404102	−	0.914714i	$-0.367584\pi$
$821$	6.95585e7	+	2.53172e7i	0.125696	+	0.0457495i	−0.278406	+	0.960463i	$0.589806\pi$
$822$		0			0
$823$	2.46053e8	−	2.06463e8i	0.441397	−	0.370376i	−0.394835	−	0.918752i	$-0.629198\pi$
$823$	2.46053e8	−	2.06463e8i	0.441397	−	0.370376i	0.836232	+	0.548376i	$0.184754\pi$
$824$		0			0
$825$	2.79696e8	+	1.61482e8i	0.498109	+	0.287583i
$826$		0			0
$827$	−6.55477e8	+	1.15578e8i	−1.15889	+	0.204343i	−0.719852	−	0.694127i	$-0.755791\pi$
$827$	−6.55477e8	+	1.15578e8i	−1.15889	+	0.204343i	−0.439035	+	0.898470i	$0.644679\pi$
$828$		0			0
$829$	4.39711e8	−	2.53867e8i	0.771798	−	0.445598i	−0.0617178	−	0.998094i	$-0.519658\pi$
$829$	4.39711e8	−	2.53867e8i	0.771798	−	0.445598i	0.833516	+	0.552496i	$0.186325\pi$
$830$		0			0
$831$	5.97926e7	+	1.64279e8i	0.104194	+	0.286272i
$832$		0			0
$833$	−2.07974e8	−	1.74511e8i	−0.359810	−	0.301917i
$834$		0			0
$835$			8.55685e8i			1.46979i
$836$		0			0
$837$	−2.69354e8			−0.459354
$838$		0			0
$839$	−2.64898e8	+	3.15693e8i	−0.448531	+	0.534538i	−0.942173	−	0.335127i	$-0.891221\pi$
$839$	−2.64898e8	+	3.15693e8i	−0.448531	+	0.534538i	0.493642	+	0.869665i	$0.335665\pi$
$840$		0			0
$841$	4.98282e8	−	1.81360e8i	0.837697	−	0.304897i
$842$		0			0
$843$	1.55872e7	+	2.69979e7i	0.0260188	+	0.0450658i
$844$		0			0
$845$	5.59872e6	+	3.17519e7i	0.00927938	+	0.0526260i
$846$		0			0
$847$	−6.84300e8	+	1.18524e9i	−1.12615	+	1.95055i
$848$		0			0
$849$	2.71472e7	+	3.23527e7i	0.0443610	+	0.0528674i
$850$		0			0
$851$	2.37393e7	−	6.52232e7i	0.0385194	−	0.105831i
$852$		0			0
$853$	1.45602e8	−	8.25747e8i	0.234595	−	1.33045i	−0.608870	−	0.793270i	$-0.708377\pi$
$853$	1.45602e8	−	8.25747e8i	0.234595	−	1.33045i	0.843465	−	0.537184i	$-0.180512\pi$
$854$		0			0
$855$	−2.18288e8	−	7.94734e8i	−0.349245	−	1.27152i
$856$		0			0
$857$	−1.04242e9	−	1.83807e8i	−1.65615	−	0.292024i	−0.734085	−	0.679058i	$-0.762388\pi$
$857$	−1.04242e9	−	1.83807e8i	−1.65615	−	0.292024i	−0.922065	+	0.387034i	$0.873500\pi$
$858$		0			0
$859$	4.30723e8	+	1.56770e8i	0.679546	+	0.247335i	0.658653	−	0.752447i	$-0.271127\pi$
$859$	4.30723e8	+	1.56770e8i	0.679546	+	0.247335i	0.0208935	+	0.999782i	$0.493349\pi$
$860$		0			0
$861$	3.05340e8	−	2.56210e8i	0.478381	−	0.401409i
$862$		0			0
$863$	6.17144e8	+	3.56308e8i	0.960184	+	0.554362i	0.896230	−	0.443591i	$-0.146296\pi$
$863$	6.17144e8	+	3.56308e8i	0.960184	+	0.554362i	0.0639541	+	0.997953i	$0.479629\pi$
$864$		0			0
$865$	1.62015e9	−	2.85676e8i	2.50327	−	0.441394i
$866$		0			0
$867$	−1.18696e8	+	6.85293e7i	−0.182129	+	0.105152i
$868$		0			0
$869$	3.61463e8	+	9.93113e8i	0.550814	+	1.51335i
$870$		0			0
$871$	−3.28176e8	−	2.75372e8i	−0.496652	−	0.416740i
$872$		0			0
$873$			1.08073e9i			1.62433i
$874$		0			0
$875$	1.73940e8			0.259642
$876$		0			0
$877$	3.00824e6	−	3.58508e6i	0.00445978	−	0.00531495i	−0.763810	−	0.645441i	$-0.776674\pi$
$877$	3.00824e6	−	3.58508e6i	0.00445978	−	0.00531495i	0.768270	+	0.640126i	$0.221118\pi$
$878$		0			0
$879$	1.75121e8	−	6.37387e7i	0.257852	−	0.0938506i
$880$		0			0
$881$	6.06346e7	+	1.05022e8i	0.0886733	+	0.153587i	0.906951	−	0.421237i	$-0.138404\pi$
$881$	6.06346e7	+	1.05022e8i	0.0886733	+	0.153587i	−0.818277	+	0.574824i	$0.805071\pi$
$882$		0			0
$883$	2.09067e7	+	1.18568e8i	0.0303671	+	0.172221i	0.996219	−	0.0868728i	$-0.0276874\pi$
$883$	2.09067e7	+	1.18568e8i	0.0303671	+	0.172221i	−0.965852	+	0.259093i	$0.916576\pi$
$884$		0			0
$885$	2.55053e8	−	4.41765e8i	0.367960	−	0.637325i
$886$		0			0
$887$	−5.07972e7	−	6.05378e7i	−0.0727895	−	0.0867472i	0.728421	−	0.685130i	$-0.240255\pi$
$887$	−5.07972e7	−	6.05378e7i	−0.0727895	−	0.0867472i	−0.801210	+	0.598383i	$0.795810\pi$
$888$		0			0
$889$	5.17083e8	−	1.42067e9i	0.735961	−	2.02204i
$890$		0			0
$891$	−1.44200e8	+	8.17796e8i	−0.203859	+	1.15614i
$892$		0			0
$893$	7.17842e7	−	8.84187e8i	0.100803	−	1.24162i
$894$		0			0
$895$	7.07287e8	+	1.24714e8i	0.986567	+	0.173958i
$896$		0			0
$897$	4.64702e7	+	1.69138e7i	0.0643869	+	0.0234349i
$898$		0			0
$899$	5.93686e8	−	4.98161e8i	0.817104	−	0.685632i
$900$		0			0
$901$	−1.91440e8	−	1.10528e8i	−0.261733	−	0.151111i
$902$		0			0
$903$	3.71327e7	−	6.54750e6i	0.0504306	−	0.00889227i
$904$		0			0
$905$	−1.24227e9	+	7.17225e8i	−1.67599	+	0.967631i
$906$		0			0
$907$	−3.06982e8	−	8.43426e8i	−0.411425	−	1.13038i	−0.956433	−	0.291951i	$-0.905696\pi$
$907$	−3.06982e8	−	8.43426e8i	−0.411425	−	1.13038i	0.545008	−	0.838431i	$-0.316527\pi$
$908$		0			0
$909$	4.76800e8	+	4.00083e8i	0.634811	+	0.532670i
$910$		0			0
$911$		−	8.43849e7i		−	0.111612i	−0.998442	−	0.0558058i	$-0.982227\pi$
$911$		−	8.43849e7i		−	0.111612i	0.998442	−	0.0558058i	$-0.0177728\pi$
$912$		0			0
$913$	−1.17141e9			−1.53921
$914$		0			0
$915$	−3.35547e8	+	3.99889e8i	−0.438016	+	0.522007i
$916$		0			0
$917$	−7.51194e8	+	2.73412e8i	−0.974191	+	0.354576i
$918$		0			0
$919$	−4.94401e8	−	8.56327e8i	−0.636990	−	1.10330i	−0.986090	−	0.166213i	$-0.946846\pi$
$919$	−4.94401e8	−	8.56327e8i	−0.636990	−	1.10330i	0.349100	−	0.937085i	$-0.386487\pi$
$920$		0			0
$921$	−1.28448e7	−	7.28463e7i	−0.0164417	−	0.0932456i
$922$		0			0
$923$	2.43823e8	−	4.22314e8i	0.310077	−	0.537070i
$924$		0			0
$925$	2.89049e8	+	3.44475e8i	0.365213	+	0.435243i
$926$		0			0
$927$	−3.58734e8	+	9.85613e8i	−0.450332	+	1.23728i
$928$		0			0
$929$	6.74501e7	−	3.82528e8i	0.0841270	−	0.477108i	−0.913415	−	0.407030i	$-0.866564\pi$
$929$	6.74501e7	−	3.82528e8i	0.0841270	−	0.477108i	0.997542	−	0.0700774i	$-0.0223246\pi$
$930$		0			0
$931$	−4.67727e8	+	4.73618e8i	−0.579621	+	0.586920i
$932$		0			0
$933$	1.23064e8	+	2.16996e7i	0.151526	+	0.0267181i
$934$		0			0
$935$	−1.04289e9	−	3.79581e8i	−1.27586	−	0.464376i
$936$		0			0
$937$	−6.59431e8	+	5.53328e8i	−0.801586	+	0.672611i	−0.948584	−	0.316526i	$-0.897484\pi$
$937$	−6.59431e8	+	5.53328e8i	−0.801586	+	0.672611i	0.146997	+	0.989137i	$0.453039\pi$
$938$		0			0
$939$	−2.90759e8	−	1.67870e8i	−0.351185	−	0.202757i
$940$		0			0
$941$	−9.41622e8	+	1.66033e8i	−1.13008	+	0.199263i	−0.707261	−	0.706953i	$-0.750069\pi$
$941$	−9.41622e8	+	1.66033e8i	−1.13008	+	0.199263i	−0.422815	+	0.906216i	$0.638958\pi$
$942$		0			0
$943$	−2.41979e8	+	1.39706e8i	−0.288564	+	0.166602i
$944$		0			0
$945$	−3.37167e8	−	9.26358e8i	−0.399530	−	1.09770i
$946$		0			0
$947$	1.65393e7	+	1.38782e7i	0.0194746	+	0.0163411i	0.652473	−	0.757812i	$-0.273732\pi$
$947$	1.65393e7	+	1.38782e7i	0.0194746	+	0.0163411i	−0.632998	+	0.774153i	$0.718176\pi$
$948$		0			0
$949$			8.93634e8i			1.04559i
$950$		0			0
$951$	−1.86315e8			−0.216623
$952$		0			0
$953$	−6.78958e8	+	8.09150e8i	−0.784448	+	0.934868i	−0.999125	−	0.0418167i	$-0.986685\pi$
$953$	−6.78958e8	+	8.09150e8i	−0.784448	+	0.934868i	0.214678	+	0.976685i	$0.431130\pi$
$954$		0			0
$955$	8.71041e8	−	3.17033e8i	1.00007	−	0.363994i
$956$		0			0
$957$	3.06329e8	+	5.30577e8i	0.349504	+	0.605359i
$958$		0			0
$959$	−1.52891e8	−	8.67085e8i	−0.173350	−	0.983119i
$960$		0			0
$961$	−1.76826e8	+	3.06272e8i	−0.199240	+	0.345094i
$962$		0			0
$963$	4.76588e8	+	5.67975e8i	0.533659	+	0.635990i
$964$		0			0
$965$	−3.61439e8	+	9.93046e8i	−0.402210	+	1.10506i
$966$		0			0
$967$	−2.18166e8	+	1.23728e9i	−0.241272	+	1.36832i	0.587722	+	0.809063i	$0.300025\pi$
$967$	−2.18166e8	+	1.23728e9i	−0.241272	+	1.36832i	−0.828994	+	0.559258i	$0.811086\pi$
$968$		0			0
$969$	−6.90520e7	−	1.45695e8i	−0.0758935	−	0.160130i
$970$		0			0
$971$	1.17684e9	+	2.07508e8i	1.28546	+	0.226661i	0.774296	−	0.632823i	$-0.218104\pi$
$971$	1.17684e9	+	2.07508e8i	1.28546	+	0.226661i	0.511162	+	0.859484i	$0.329215\pi$
$972$		0			0
$973$	−5.17322e8	−	1.88290e8i	−0.561594	−	0.204403i
$974$		0			0
$975$	−2.45431e8	+	2.05941e8i	−0.264799	+	0.222193i
$976$		0			0
$977$	−6.23816e8	−	3.60160e8i	−0.668918	−	0.386200i	0.126749	−	0.991935i	$-0.459546\pi$
$977$	−6.23816e8	−	3.60160e8i	−0.668918	−	0.386200i	−0.795666	+	0.605735i	$0.792879\pi$
$978$		0			0
$979$	1.66733e9	−	2.93995e8i	1.77694	−	0.313323i
$980$		0			0
$981$	8.75351e8	−	5.05384e8i	0.927204	−	0.535321i
$982$		0			0
$983$	−2.23052e8	−	6.12831e8i	−0.234826	−	0.645179i	−0.999999	−	0.00135422i	$-0.999569\pi$
$983$	−2.23052e8	−	6.12831e8i	−0.234826	−	0.645179i	0.765173	−	0.643824i	$-0.222653\pi$
$984$		0			0
$985$	−9.27428e8	−	7.78205e8i	−0.970446	−	0.814301i
$986$		0			0
$987$		−	5.03541e8i		−	0.523701i
$988$		0			0
$989$	−2.64315e7			−0.0273233
$990$		0			0
$991$	3.96581e8	−	4.72627e8i	0.407484	−	0.485621i	−0.522802	−	0.852454i	$-0.675113\pi$
$991$	3.96581e8	−	4.72627e8i	0.407484	−	0.485621i	0.930287	+	0.366833i	$0.119558\pi$
$992$		0			0
$993$	2.36412e8	−	8.60470e7i	0.241447	−	0.0878796i
$994$		0			0
$995$	−6.61597e8	−	1.14592e9i	−0.671621	−	1.16328i
$996$		0			0
$997$	1.74286e8	+	9.88424e8i	0.175864	+	0.997373i	0.937142	+	0.348948i	$0.113461\pi$
$997$	1.74286e8	+	9.88424e8i	0.175864	+	0.997373i	−0.761278	+	0.648425i	$0.775428\pi$
$998$		0			0
$999$	1.48237e8	−	2.56755e8i	0.148683	−	0.257526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.5	✓	60
19.10	odd	18	inner	76.7.j.a.29.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.5	✓	60	1.1	even	1	trivial
76.7.j.a.29.5	yes	60	19.10	odd	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.40108 + 6.43676i) q^{3} +(-171.496 + 62.4193i) q^{5} +(-231.676 - 401.275i) q^{7} +(114.329 + 648.394i) q^{9} +O(q^{10})\)	\(q+(-5.40108 + 6.43676i) q^{3} +(-171.496 + 62.4193i) q^{5} +(-231.676 - 401.275i) q^{7} +(114.329 + 648.394i) q^{9} +(1086.88 - 1882.53i) q^{11} +(1386.12 + 1651.91i) q^{13} +(524.484 - 1441.01i) q^{15} +(-485.784 + 2755.02i) q^{17} +(6636.26 + 1733.75i) q^{19} +(3834.22 + 676.076i) q^{21} +(-2564.65 - 933.456i) q^{23} +(13545.1 - 11365.7i) q^{25} +(-10095.9 - 5828.86i) q^{27} +(33032.7 - 5824.55i) q^{29} +(20009.7 - 11552.6i) q^{31} +(6247.08 + 17163.7i) q^{33} +(64778.8 + 54355.9i) q^{35} +25431.6i q^{37} -18119.5 q^{39} +(65806.9 - 78425.6i) q^{41} +(9100.52 - 3312.32i) q^{43} +(-60079.3 - 104060. i) q^{45} +(-22458.5 - 127368. i) q^{47} +(-48523.5 + 84045.1i) q^{49} +(-15109.6 - 18007.0i) q^{51} +(-27025.9 + 74253.0i) q^{53} +(-68889.0 + 390689. i) q^{55} +(-47002.7 + 33351.9i) q^{57} +(327590. + 57763.0i) q^{59} +(-319883. - 116428. i) q^{61} +(233697. - 196095. i) q^{63} +(-340825. - 196775. i) q^{65} +(-195646. + 34497.6i) q^{67} +(19860.3 - 11466.4i) q^{69} +(-77343.5 - 212499. i) q^{71} +(317454. + 266375. i) q^{73} +148574. i q^{75} -1.00722e6 q^{77} +(-312513. + 372438. i) q^{79} +(-358978. + 130657. i) q^{81} +(-269443. - 466689. i) q^{83} +(-88656.5 - 502796. i) q^{85} +(-140921. + 244082. i) q^{87} +(500639. + 596638. i) q^{89} +(341741. - 938925. i) q^{91} +(-33712.7 + 191194. i) q^{93} +(-1.24631e6 + 116901. i) q^{95} +(1.61652e6 + 285036. i) q^{97} +(1.34489e6 + 489499. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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