LMFDB - Embedded newform 76.7.j.a.53.8

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			53.8
Character	$\chi$	$=$	76.53
Dual form			76.7.j.a.33.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30.7547 - 5.42288i) q^{3} +(-106.252 + 89.1559i) q^{5} +(-115.766 + 200.512i) q^{7} +(231.408 - 84.2256i) q^{9} +O(q^{10})$	\(q+(30.7547 - 5.42288i) q^{3} +(-106.252 + 89.1559i) q^{5} +(-115.766 + 200.512i) q^{7} +(231.408 - 84.2256i) q^{9} +(-1120.76 - 1941.22i) q^{11} +(-4192.44 - 739.240i) q^{13} +(-2784.26 + 3318.15i) q^{15} +(3106.86 + 1130.80i) q^{17} +(4419.48 - 5245.39i) q^{19} +(-2472.99 + 6794.48i) q^{21} +(-5695.37 - 4778.98i) q^{23} +(627.432 - 3558.35i) q^{25} +(-13055.8 + 7537.79i) q^{27} +(14107.7 + 38760.5i) q^{29} +(-39912.0 - 23043.2i) q^{31} +(-44995.7 - 53623.8i) q^{33} +(-5576.52 - 31626.0i) q^{35} +62972.2i q^{37} -132946. q^{39} +(-60966.8 + 10750.1i) q^{41} +(105402. - 88442.6i) q^{43} +(-17078.3 + 29580.5i) q^{45} +(-72086.3 + 26237.3i) q^{47} +(32021.1 + 55462.1i) q^{49} +(101683. + 17929.4i) q^{51} +(21190.6 - 25254.0i) q^{53} +(292154. + 106335. i) q^{55} +(107475. - 185287. i) q^{57} +(-58629.8 + 161084. i) q^{59} +(-73364.7 - 61560.3i) q^{61} +(-9900.86 + 56150.6i) q^{63} +(511362. - 295235. i) q^{65} +(144648. + 397418. i) q^{67} +(-201075. - 116091. i) q^{69} +(-209882. - 250128. i) q^{71} +(19599.9 + 111156. i) q^{73} -112838. i q^{75} +518984. q^{77} +(591695. - 104332. i) q^{79} +(-498174. + 418018. i) q^{81} +(159557. - 276360. i) q^{83} +(-430928. + 156845. i) q^{85} +(644070. + 1.11556e6i) q^{87} +(-488777. - 86184.6i) q^{89} +(633568. - 755057. i) q^{91} +(-1.35244e6 - 492249. i) q^{93} +(-1920.23 + 951355. i) q^{95} +(474540. - 1.30379e6i) q^{97} +(-422854. - 354817. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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
$3$	30.7547	−	5.42288i	1.13906	−	0.200848i	0.427867	−	0.903842i	$-0.359265\pi$
$3$	30.7547	−	5.42288i	1.13906	−	0.200848i	0.711196	+	0.702994i	$0.248154\pi$
$4$		0			0
$5$	−106.252	+	89.1559i	−0.850015	+	0.713247i	−0.959793	−	0.280709i	$-0.909430\pi$
$5$	−106.252	+	89.1559i	−0.850015	+	0.713247i	0.109778	+	0.993956i	$0.464986\pi$
$6$		0			0
$7$	−115.766	+	200.512i	−0.337510	+	0.584584i	−0.983964	−	0.178369i	$-0.942918\pi$
$7$	−115.766	+	200.512i	−0.337510	+	0.584584i	0.646454	+	0.762953i	$0.276251\pi$
$8$		0			0
$9$	231.408	−	84.2256i	0.317432	−	0.115536i
$10$		0			0
$11$	−1120.76	−	1941.22i	−0.842046	−	1.45847i	−0.888162	−	0.459530i	$-0.848018\pi$
$11$	−1120.76	−	1941.22i	−0.842046	−	1.45847i	0.0461160	−	0.998936i	$-0.485316\pi$
$12$		0			0
$13$	−4192.44	−	739.240i	−1.90826	−	0.336477i	−0.911123	−	0.412135i	$-0.864783\pi$
$13$	−4192.44	−	739.240i	−1.90826	−	0.336477i	−0.997134	+	0.0756581i	$0.975894\pi$
$14$		0			0
$15$	−2784.26	+	3318.15i	−0.824967	+	0.983157i
$16$		0			0
$17$	3106.86	+	1130.80i	0.632375	+	0.230166i	0.638265	−	0.769817i	$-0.279652\pi$
$17$	3106.86	+	1130.80i	0.632375	+	0.230166i	−0.00588950	+	0.999983i	$0.501875\pi$
$18$		0			0
$19$	4419.48	−	5245.39i	0.644332	−	0.764745i
$19$	4419.48	−	5245.39i	0.644332	−	0.764745i
$20$		0			0
$21$	−2472.99	+	6794.48i	−0.267033	+	0.733666i
$22$		0			0
$23$	−5695.37	−	4778.98i	−0.468099	−	0.392782i	0.378001	−	0.925805i	$-0.376611\pi$
$23$	−5695.37	−	4778.98i	−0.468099	−	0.392782i	−0.846101	+	0.533023i	$0.821056\pi$
$24$		0			0
$25$	627.432	−	3558.35i	0.0401557	−	0.227734i
$26$		0			0
$27$	−13055.8	+	7537.79i	−0.663305	+	0.382959i
$28$		0			0
$29$	14107.7	+	38760.5i	0.578443	+	1.58926i	0.790804	+	0.612069i	$0.209663\pi$
$29$	14107.7	+	38760.5i	0.578443	+	1.58926i	−0.212361	+	0.977191i	$0.568115\pi$
$30$		0			0
$31$	−39912.0	−	23043.2i	−1.33973	−	0.773496i	−0.352967	−	0.935636i	$-0.614827\pi$
$31$	−39912.0	−	23043.2i	−1.33973	−	0.773496i	−0.986768	+	0.162140i	$0.948160\pi$
$32$		0			0
$33$	−44995.7	−	53623.8i	−1.25207	−	1.49216i
$34$		0			0
$35$	−5576.52	−	31626.0i	−0.130065	−	0.737633i
$36$		0			0
$37$			62972.2i			1.24321i	0.783332	+	0.621604i	$0.213518\pi$
$37$			62972.2i			1.24321i	−0.783332	+	0.621604i	$0.786482\pi$
$38$		0			0
$39$	−132946.			−2.24120
$40$		0			0
$41$	−60966.8	+	10750.1i	−0.884590	+	0.155977i	−0.597445	−	0.801910i	$-0.703817\pi$
$41$	−60966.8	+	10750.1i	−0.884590	+	0.155977i	−0.287145	+	0.957887i	$0.592706\pi$
$42$		0			0
$43$	105402.	−	88442.6i	1.32569	−	1.11239i	0.340628	−	0.940198i	$-0.389360\pi$
$43$	105402.	−	88442.6i	1.32569	−	1.11239i	0.985064	−	0.172190i	$-0.0550842\pi$
$44$		0			0
$45$	−17078.3	+	29580.5i	−0.187416	+	0.324615i
$46$		0			0
$47$	−72086.3	+	26237.3i	−0.694320	+	0.252712i	−0.664984	−	0.746858i	$-0.731561\pi$
$47$	−72086.3	+	26237.3i	−0.694320	+	0.252712i	−0.0293359	+	0.999570i	$0.509339\pi$
$48$		0			0
$49$	32021.1	+	55462.1i	0.272174	+	0.471420i
$50$		0			0
$51$	101683.	+	17929.4i	0.766544	+	0.135162i
$52$		0			0
$53$	21190.6	−	25254.0i	0.142337	−	0.169630i	−0.690166	−	0.723651i	$-0.742463\pi$
$53$	21190.6	−	25254.0i	0.142337	−	0.169630i	0.832503	+	0.554021i	$0.186907\pi$
$54$		0			0
$55$	292154.	+	106335.i	1.75600	+	0.639131i
$56$		0			0
$57$	107475.	−	185287.i	0.580338	−	1.00051i
$58$		0			0
$59$	−58629.8	+	161084.i	−0.285471	+	0.784325i	0.711214	+	0.702975i	$0.248145\pi$
$59$	−58629.8	+	161084.i	−0.285471	+	0.784325i	−0.996686	+	0.0813503i	$0.974077\pi$
$60$		0			0
$61$	−73364.7	−	61560.3i	−0.323220	−	0.271213i	0.466711	−	0.884410i	$-0.345439\pi$
$61$	−73364.7	−	61560.3i	−0.323220	−	0.271213i	−0.789930	+	0.613197i	$0.789883\pi$
$62$		0			0
$63$	−9900.86	+	56150.6i	−0.0395960	+	0.224560i
$64$		0			0
$65$	511362.	−	295235.i	1.86204	−	1.07505i
$66$		0			0
$67$	144648.	+	397418.i	0.480938	+	1.32137i	0.908690	+	0.417471i	$0.137084\pi$
$67$	144648.	+	397418.i	0.480938	+	1.32137i	−0.427752	+	0.903896i	$0.640694\pi$
$68$		0			0
$69$	−201075.	−	116091.i	−0.612084	−	0.353387i
$70$		0			0
$71$	−209882.	−	250128.i	−0.586409	−	0.698855i	0.388503	−	0.921448i	$-0.372992\pi$
$71$	−209882.	−	250128.i	−0.586409	−	0.698855i	−0.974911	+	0.222593i	$0.928548\pi$
$72$		0			0
$73$	19599.9	+	111156.i	0.0503831	+	0.285737i	0.999581	−	0.0289428i	$-0.00921407\pi$
$73$	19599.9	+	111156.i	0.0503831	+	0.285737i	−0.949198	+	0.314680i	$0.898103\pi$
$74$		0			0
$75$		−	112838.i		−	0.267469i
$76$		0			0
$77$	518984.			1.13679
$78$		0			0
$79$	591695.	−	104332.i	1.20010	−	0.211610i	0.462357	−	0.886694i	$-0.347004\pi$
$79$	591695.	−	104332.i	1.20010	−	0.211610i	0.737740	+	0.675084i	$0.235893\pi$
$80$		0			0
$81$	−498174.	+	418018.i	−0.937403	+	0.786574i
$82$		0			0
$83$	159557.	−	276360.i	0.279049	−	0.483327i	−0.692100	−	0.721802i	$-0.743314\pi$
$83$	159557.	−	276360.i	0.279049	−	0.483327i	0.971149	+	0.238475i	$0.0766475\pi$
$84$		0			0
$85$	−430928.	+	156845.i	−0.701694	+	0.255396i
$86$		0			0
$87$	644070.	+	1.11556e6i	0.978083	+	1.69409i
$88$		0			0
$89$	−488777.	−	86184.6i	−0.693331	−	0.122253i	−0.184132	−	0.982902i	$-0.558947\pi$
$89$	−488777.	−	86184.6i	−0.693331	−	0.122253i	−0.509199	+	0.860649i	$0.670058\pi$
$90$		0			0
$91$	633568.	−	755057.i	0.840754	−	1.00197i
$92$		0			0
$93$	−1.35244e6	−	492249.i	−1.68140	−	0.611978i
$94$		0			0
$95$	−1920.23	+	951355.i	−0.00223966	+	1.10961i
$96$		0			0
$97$	474540.	−	1.30379e6i	0.519945	−	1.42854i	−0.350636	−	0.936512i	$-0.614035\pi$
$97$	474540.	−	1.30379e6i	0.519945	−	1.42854i	0.870581	−	0.492025i	$-0.163743\pi$
$98$		0			0
$99$	−422854.	−	354817.i	−0.435798	−	0.365678i
$100$		0			0
$101$	−95210.6	+	539966.i	−0.0924105	+	0.524086i	0.903100	+	0.429431i	$0.141286\pi$
$101$	−95210.6	+	539966.i	−0.0924105	+	0.524086i	−0.995510	+	0.0946550i	$0.969825\pi$
$102$		0			0
$103$	52164.0	−	30116.9i	0.0477374	−	0.0275612i	−0.475941	−	0.879477i	$-0.657893\pi$
$103$	52164.0	−	30116.9i	0.0477374	−	0.0275612i	0.523679	+	0.851916i	$0.324559\pi$
$104$		0			0
$105$	−343008.	−	942408.i	−0.296303	−	0.814087i
$106$		0			0
$107$	330370.	+	190739.i	0.269680	+	0.155700i	0.628742	−	0.777614i	$-0.283570\pi$
$107$	330370.	+	190739.i	0.269680	+	0.155700i	−0.359062	+	0.933314i	$0.616903\pi$
$108$		0			0
$109$	−328292.	−	391244.i	−0.253502	−	0.302112i	0.624253	−	0.781223i	$-0.285404\pi$
$109$	−328292.	−	391244.i	−0.253502	−	0.302112i	−0.877754	+	0.479111i	$0.840959\pi$
$110$		0			0
$111$	341491.	+	1.93669e6i	0.249695	+	1.41609i
$112$		0			0
$113$		−	363681.i		−	0.252049i	−0.992027	−	0.126025i	$-0.959778\pi$
$113$		−	363681.i		−	0.252049i	0.992027	−	0.126025i	$-0.0402218\pi$
$114$		0			0
$115$	1.03122e6			0.678042
$116$		0			0
$117$	−1.03243e6	+	182045.i	−0.644617	+	0.113663i
$118$		0			0
$119$	−586408.	+	492055.i	−0.347984	+	0.291993i
$120$		0			0
$121$	−1.62644e6	+	2.81708e6i	−0.918083	+	1.59017i
$122$		0			0
$123$	−1.81672e6	+	661232.i	−0.976276	+	0.355335i
$124$		0			0
$125$	−833028.	−	1.44285e6i	−0.426510	−	0.738737i
$126$		0			0
$127$	−1.88131e6	−	331725.i	−0.918435	−	0.161945i	−0.305604	−	0.952159i	$-0.598858\pi$
$127$	−1.88131e6	−	331725.i	−0.918435	−	0.161945i	−0.612831	+	0.790214i	$0.709969\pi$
$128$		0			0
$129$	2.76199e6	−	3.29161e6i	1.28663	−	1.53334i
$130$		0			0
$131$	−2.44333e6	−	889299.i	−1.08685	−	0.395580i	−0.264394	−	0.964415i	$-0.585172\pi$
$131$	−2.44333e6	−	889299.i	−1.08685	−	0.395580i	−0.822452	+	0.568835i	$0.807394\pi$
$132$		0			0
$133$	540141.	+	1.49340e6i	0.229589	+	0.634775i
$134$		0			0
$135$	715168.	−	1.96491e6i	0.290675	−	0.798622i
$136$		0			0
$137$	−3.41368e6	−	2.86442e6i	−1.32758	−	1.11397i	−0.984636	−	0.174618i	$-0.944131\pi$
$137$	−3.41368e6	−	2.86442e6i	−1.32758	−	1.11397i	−0.342946	−	0.939355i	$-0.611425\pi$
$138$		0			0
$139$	382392.	−	2.16865e6i	0.142385	−	0.807506i	−0.827045	−	0.562136i	$-0.809980\pi$
$139$	382392.	−	2.16865e6i	0.142385	−	0.807506i	0.969430	−	0.245369i	$-0.0789093\pi$
$140$		0			0
$141$	−2.07471e6	+	1.19784e6i	−0.740117	+	0.427307i
$142$		0			0
$143$	3.26371e6	+	8.96696e6i	1.11610	+	3.06646i
$144$		0			0
$145$	−4.95469e6	−	2.86059e6i	−1.62522	−	0.938322i
$146$		0			0
$147$	1.28556e6	+	1.53207e6i	0.404707	+	0.482312i
$148$		0			0
$149$	−18448.4	−	104626.i	−0.00557700	−	0.0316288i	0.981892	−	0.189440i	$-0.0606673\pi$
$149$	−18448.4	−	104626.i	−0.00557700	−	0.0316288i	−0.987469	+	0.157811i	$0.949556\pi$
$150$		0			0
$151$		−	2.39836e6i		−	0.696600i	−0.937383	−	0.348300i	$-0.886759\pi$
$151$		−	2.39836e6i		−	0.696600i	0.937383	−	0.348300i	$-0.113241\pi$
$152$		0			0
$153$	814195.			0.227329
$154$		0			0
$155$	6.29517e6	−	1.11001e6i	1.69049	−	0.298079i
$156$		0			0
$157$	−360178.	+	302225.i	−0.0930718	+	0.0780965i	−0.688136	−	0.725581i	$-0.741571\pi$
$157$	−360178.	+	302225.i	−0.0930718	+	0.0780965i	0.595065	+	0.803678i	$0.297126\pi$
$158$		0			0
$159$	514762.	−	891594.i	0.128060	−	0.221807i
$160$		0			0
$161$	1.61757e6	−	588748.i	0.387602	−	0.141076i
$162$		0			0
$163$	1.90491e6	+	3.29940e6i	0.439857	+	0.761855i	0.997678	−	0.0681062i	$-0.0216957\pi$
$163$	1.90491e6	+	3.29940e6i	0.439857	+	0.761855i	−0.557821	+	0.829961i	$0.688362\pi$
$164$		0			0
$165$	9.56176e6	+	1.68600e6i	2.12856	+	0.375323i
$166$		0			0
$167$	1.44676e6	−	1.72418e6i	0.310632	−	0.370197i	−0.588030	−	0.808839i	$-0.700096\pi$
$167$	1.44676e6	−	1.72418e6i	0.310632	−	0.370197i	0.898662	+	0.438643i	$0.144541\pi$
$168$		0			0
$169$	1.24944e7	+	4.54757e6i	2.58853	+	0.942149i
$170$		0			0
$171$	580906.	−	1.58606e6i	0.116176	−	0.317198i
$172$		0			0
$173$	−14081.9	+	38689.6i	−0.00271970	+	0.00747232i	−0.941045	−	0.338281i	$-0.890154\pi$
$173$	−14081.9	+	38689.6i	−0.00271970	+	0.00747232i	0.938325	+	0.345754i	$0.112377\pi$
$174$		0			0
$175$	640857.	+	537743.i	0.119577	+	0.100337i
$176$		0			0
$177$	−929601.	+	5.27203e6i	−0.167640	+	0.950732i
$178$		0			0
$179$	−6.04873e6	+	3.49223e6i	−1.05464	+	0.608898i	−0.923945	−	0.382525i	$-0.875055\pi$
$179$	−6.04873e6	+	3.49223e6i	−1.05464	+	0.608898i	−0.130696	+	0.991422i	$0.541721\pi$
$180$		0			0
$181$	60444.4	+	166070.i	0.0101934	+	0.0280062i	0.944685	−	0.327979i	$-0.106368\pi$
$181$	60444.4	+	166070.i	0.0101934	+	0.0280062i	−0.934492	+	0.355985i	$0.884145\pi$
$182$		0			0
$183$	−2.59014e6	−	1.49542e6i	−0.422640	−	0.244011i
$184$		0			0
$185$	−5.61434e6	−	6.69091e6i	−0.886714	−	1.05674i
$186$		0			0
$187$	−1.28692e6	−	7.29846e6i	−0.196800	−	1.11611i
$188$		0			0
$189$		−	3.49047e6i		−	0.517010i
$190$		0			0
$191$	−178176.			−0.0255711			−0.0127856	−	0.999918i	$-0.504070\pi$
$191$	−178176.			−0.0255711			−0.0127856	+	0.999918i	$0.504070\pi$
$192$		0			0
$193$	−1.87604e6	+	330796.i	−0.260957	+	0.0460138i	−0.302596	−	0.953119i	$-0.597853\pi$
$193$	−1.87604e6	+	330796.i	−0.260957	+	0.0460138i	0.0416386	+	0.999133i	$0.486742\pi$
$194$		0			0
$195$	1.41258e7	−	1.18529e7i	1.90506	−	1.59853i
$196$		0			0
$197$	−5.73043e6	+	9.92540e6i	−0.749529	+	1.29822i	0.198520	+	0.980097i	$0.436387\pi$
$197$	−5.73043e6	+	9.92540e6i	−0.749529	+	1.29822i	−0.948049	+	0.318126i	$0.896947\pi$
$198$		0			0
$199$	431664.	−	157113.i	0.0547756	−	0.0199367i	−0.314487	−	0.949262i	$-0.601833\pi$
$199$	431664.	−	157113.i	0.0547756	−	0.0199367i	0.369263	+	0.929325i	$0.379610\pi$
$200$		0			0
$201$	6.60377e6	+	1.14381e7i	0.813212	+	1.40853i
$202$		0			0
$203$	−9.40513e6	−	1.65838e6i	−1.12429	−	0.198242i
$204$		0			0
$205$	5.51940e6	−	6.57777e6i	0.640665	−	0.763514i
$206$		0			0
$207$	−1.72047e6	−	626198.i	−0.193970	−	0.0705994i
$208$		0			0
$209$	−1.51356e7	−	2.70033e6i	−1.65791	−	0.295786i
$210$		0			0
$211$	−2.85287e6	+	7.83820e6i	−0.303693	+	0.834390i	0.690157	+	0.723659i	$0.257541\pi$
$211$	−2.85287e6	+	7.83820e6i	−0.303693	+	0.834390i	−0.993850	+	0.110731i	$0.964681\pi$
$212$		0			0
$213$	−7.81127e6	−	6.55444e6i	−0.808319	−	0.678261i
$214$		0			0
$215$	−3.31396e6	+	1.87944e7i	−0.333451	+	1.89109i
$216$		0			0
$217$	9.24090e6	−	5.33523e6i	0.904347	−	0.522125i
$218$		0			0
$219$	1.20558e6	+	3.31229e6i	0.114779	+	0.315353i
$220$		0			0
$221$	−1.21894e7	−	7.03755e6i	−1.12929	−	0.651995i
$222$		0			0
$223$	3.37743e6	+	4.02506e6i	0.304559	+	0.362960i	0.896517	−	0.443009i	$-0.146089\pi$
$223$	3.37743e6	+	4.02506e6i	0.304559	+	0.362960i	−0.591958	+	0.805969i	$0.701645\pi$
$224$		0			0
$225$	−154511.	−	876275.i	−0.0135648	−	0.0769295i
$226$		0			0
$227$		−	1.57724e6i		−	0.134841i	−0.997725	−	0.0674203i	$-0.978523\pi$
$227$		−	1.57724e6i		−	0.134841i	0.997725	−	0.0674203i	$-0.0214768\pi$
$228$		0			0
$229$	1.00376e7			0.835844			0.417922	−	0.908483i	$-0.362758\pi$
$229$	1.00376e7			0.835844			0.417922	+	0.908483i	$0.362758\pi$
$230$		0			0
$231$	1.59612e7	−	2.81439e6i	1.29488	−	0.228322i
$232$		0			0
$233$	−1.60492e7	+	1.34669e7i	−1.26878	+	1.06463i	−0.274088	+	0.961705i	$0.588376\pi$
$233$	−1.60492e7	+	1.34669e7i	−1.26878	+	1.06463i	−0.994689	+	0.102926i	$0.967180\pi$
$234$		0			0
$235$	5.32010e6	−	9.21468e6i	0.409936	−	0.710030i
$236$		0			0
$237$	1.76316e7	−	6.41738e6i	1.32448	−	0.482073i
$238$		0			0
$239$	−7.68175e6	−	1.33052e7i	−0.562687	−	0.974602i	−0.997261	−	0.0739659i	$-0.976434\pi$
$239$	−7.68175e6	−	1.33052e7i	−0.562687	−	0.974602i	0.434574	−	0.900636i	$-0.356899\pi$
$240$		0			0
$241$	−4.08730e6	−	720701.i	−0.292002	−	0.0514878i	0.0257284	−	0.999669i	$-0.491809\pi$
$241$	−4.08730e6	−	720701.i	−0.292002	−	0.0514878i	−0.317730	+	0.948181i	$0.602921\pi$
$242$		0			0
$243$	−5.99004e6	+	7.13865e6i	−0.417456	+	0.497505i
$244$		0			0
$245$	−8.34707e6	−	3.03809e6i	−0.567591	−	0.206586i
$246$		0			0
$247$	−2.24060e7	+	1.87239e7i	−1.48687	+	1.24253i
$248$		0			0
$249$	3.40844e6	−	9.36462e6i	0.220779	−	0.606586i
$250$		0			0
$251$	−1.07888e7	−	9.05289e6i	−0.682264	−	0.572487i	0.234403	−	0.972140i	$-0.424686\pi$
$251$	−1.07888e7	−	9.05289e6i	−0.682264	−	0.572487i	−0.916667	+	0.399652i	$0.869131\pi$
$252$		0			0
$253$	−2.89389e6	+	1.64121e7i	−0.178698	+	1.01345i
$254$		0			0
$255$	−1.24025e7	+	7.16059e6i	−0.747978	+	0.431845i
$256$		0			0
$257$	−4.13899e6	−	1.13718e7i	−0.243835	−	0.669930i	−0.999881	−	0.0154122i	$-0.995094\pi$
$257$	−4.13899e6	−	1.13718e7i	−0.243835	−	0.669930i	0.756047	−	0.654518i	$-0.227128\pi$
$258$		0			0
$259$	−1.26267e7	−	7.29002e6i	−0.726759	−	0.419594i
$260$		0			0
$261$	6.52925e6	+	7.78126e6i	0.367233	+	0.437651i
$262$		0			0
$263$	1.09206e6	+	6.19337e6i	0.0600314	+	0.340455i	1.00000		0.000806953i	$-0.000256861\pi$
$263$	1.09206e6	+	6.19337e6i	0.0600314	+	0.340455i	−0.939968	+	0.341262i	$0.889146\pi$
$264$		0			0
$265$			4.57256e6i			0.245709i
$266$		0			0
$267$	−1.54996e7			−0.814302
$268$		0			0
$269$	1.61378e7	−	2.84552e6i	0.829061	−	0.146186i	0.257015	−	0.966407i	$-0.417261\pi$
$269$	1.61378e7	−	2.84552e6i	0.829061	−	0.146186i	0.572046	+	0.820222i	$0.306150\pi$
$270$		0			0
$271$	1.83117e7	−	1.53654e7i	0.920072	−	0.772032i	−0.0539363	−	0.998544i	$-0.517177\pi$
$271$	1.83117e7	−	1.53654e7i	0.920072	−	0.772032i	0.974008	+	0.226512i	$0.0727323\pi$
$272$		0			0
$273$	1.53906e7	−	2.66573e7i	0.756428	−	1.31017i
$274$		0			0
$275$	−7.61073e6	+	2.77008e6i	−0.365956	+	0.133197i
$276$		0			0
$277$	712466.	+	1.23403e6i	0.0335216	+	0.0580611i	0.882299	−	0.470688i	$-0.155994\pi$
$277$	712466.	+	1.23403e6i	0.0335216	+	0.0580611i	−0.848778	+	0.528750i	$0.822661\pi$
$278$		0			0
$279$	−1.11768e7	−	1.97077e6i	−0.514641	−	0.0907451i
$280$		0			0
$281$	−1.90244e7	+	2.26724e7i	−0.857417	+	1.02183i	0.142072	+	0.989856i	$0.454624\pi$
$281$	−1.90244e7	+	2.26724e7i	−0.857417	+	1.02183i	−0.999489	+	0.0319734i	$0.989821\pi$
$282$		0			0
$283$	1.15304e7	+	4.19671e6i	0.508725	+	0.185161i	0.583614	−	0.812031i	$-0.301638\pi$
$283$	1.15304e7	+	4.19671e6i	0.508725	+	0.185161i	−0.0748889	+	0.997192i	$0.523860\pi$
$284$		0			0
$285$	5.10003e6	+	2.92690e7i	0.220312	+	1.26437i
$286$		0			0
$287$	4.90235e6	−	1.34691e7i	0.207376	−	0.569761i
$288$		0			0
$289$	−1.01166e7	−	8.48883e6i	−0.419122	−	0.351685i
$290$		0			0
$291$	7.52404e6	−	4.26709e7i	0.305332	−	1.73162i
$292$		0			0
$293$	−1.66602e7	+	9.61875e6i	−0.662333	+	0.382398i	−0.793165	−	0.609006i	$-0.791568\pi$
$293$	−1.66602e7	+	9.61875e6i	−0.662333	+	0.382398i	0.130832	+	0.991405i	$0.458235\pi$
$294$		0			0
$295$	−8.13207e6	−	2.23427e7i	−0.316763	−	0.870300i
$296$		0			0
$297$	2.92650e7	+	1.68962e7i	1.11707	+	0.644939i
$298$		0			0
$299$	2.03447e7	+	2.42458e7i	0.761092	+	0.907034i
$300$		0			0
$301$	5.53190e6	+	3.13730e7i	0.202850	+	1.15042i
$302$		0			0
$303$			1.71228e7i			0.615527i
$304$		0			0
$305$	1.32836e7			0.468184
$306$		0			0
$307$	1.72205e6	−	303643.i	0.0595154	−	0.0104942i	−0.143811	−	0.989605i	$-0.545936\pi$
$307$	1.72205e6	−	303643.i	0.0595154	−	0.0104942i	0.203327	+	0.979111i	$0.434825\pi$
$308$		0			0
$309$	1.44097e6	−	1.20911e6i	0.0488403	−	0.0409819i
$310$		0			0
$311$	−1.11411e7	+	1.92970e7i	−0.370381	+	0.641518i	−0.989624	−	0.143681i	$-0.954106\pi$
$311$	−1.11411e7	+	1.92970e7i	−0.370381	+	0.641518i	0.619243	+	0.785199i	$0.287439\pi$
$312$		0			0
$313$	3.47632e7	−	1.26528e7i	1.13367	−	0.412623i	0.294047	−	0.955791i	$-0.404998\pi$
$313$	3.47632e7	−	1.26528e7i	1.13367	−	0.412623i	0.839624	+	0.543168i	$0.182775\pi$
$314$		0			0
$315$	−3.95417e6	−	6.84883e6i	−0.126510	−	0.219121i
$316$		0			0
$317$	6.04932e7	+	1.06666e7i	1.89902	+	0.334848i	0.995583	−	0.0938820i	$-0.0299276\pi$
$317$	6.04932e7	+	1.06666e7i	1.89902	+	0.334848i	0.903433	+	0.428730i	$0.141039\pi$
$318$		0			0
$319$	5.94312e7	−	7.08274e7i	1.83081	−	2.18187i
$320$		0			0
$321$	1.11948e7	+	4.07457e6i	0.338455	+	0.123188i
$322$		0			0
$323$	1.96622e7	−	1.12991e7i	0.583478	−	0.335303i
$324$		0			0
$325$	−5.26094e6	+	1.44543e7i	−0.153255	+	0.421064i
$326$		0			0
$327$	−1.22182e7	−	1.02523e7i	−0.349433	−	0.293209i
$328$		0			0
$329$	3.08424e6	−	1.74916e7i	0.0866084	−	0.491181i
$330$		0			0
$331$	−8.33281e6	+	4.81095e6i	−0.229778	+	0.132662i	−0.610469	−	0.792040i	$-0.709019\pi$
$331$	−8.33281e6	+	4.81095e6i	−0.229778	+	0.132662i	0.380692	+	0.924702i	$0.375686\pi$
$332$		0			0
$333$	5.30387e6	+	1.45723e7i	0.143635	+	0.394634i
$334$		0			0
$335$	−5.08014e7	−	2.93302e7i	−1.35127	−	0.780154i
$336$		0			0
$337$	3.31311e6	+	3.94841e6i	0.0865657	+	0.103165i	0.807589	−	0.589746i	$-0.200772\pi$
$337$	3.31311e6	+	3.94841e6i	0.0865657	+	0.103165i	−0.721023	+	0.692911i	$0.756328\pi$
$338$		0			0
$339$	−1.97220e6	−	1.11849e7i	−0.0506234	−	0.287100i
$340$		0			0
$341$			1.03304e8i			2.60528i
$342$		0			0
$343$	−4.20672e7			−1.04247
$344$		0			0
$345$	3.17148e7	−	5.59217e6i	0.772333	−	0.136183i
$346$		0			0
$347$	−4.38380e7	+	3.67845e7i	−1.04921	+	0.880392i	−0.993010	−	0.118028i	$-0.962343\pi$
$347$	−4.38380e7	+	3.67845e7i	−1.04921	+	0.880392i	−0.0561999	+	0.998420i	$0.517898\pi$
$348$		0			0
$349$	3.03475e7	−	5.25633e7i	0.713914	−	1.23654i	−0.249462	−	0.968384i	$-0.580254\pi$
$349$	3.03475e7	−	5.25633e7i	0.713914	−	1.23654i	0.963377	−	0.268151i	$-0.0864127\pi$
$350$		0			0
$351$	6.03080e7	−	2.19503e7i	1.39461	−	0.507598i
$352$		0			0
$353$	8.84405e6	+	1.53183e7i	0.201061	+	0.348247i	0.948870	−	0.315666i	$-0.102228\pi$
$353$	8.84405e6	+	1.53183e7i	0.201061	+	0.348247i	−0.747810	+	0.663913i	$0.768895\pi$
$354$		0			0
$355$	4.46007e7	+	7.86431e6i	0.996912	+	0.175783i
$356$		0			0
$357$	−1.53665e7	+	1.83130e7i	−0.337730	+	0.402490i
$358$		0			0
$359$	−3.44613e7	−	1.25429e7i	−0.744814	−	0.271090i	−0.0583922	−	0.998294i	$-0.518597\pi$
$359$	−3.44613e7	−	1.25429e7i	−0.744814	−	0.271090i	−0.686422	+	0.727204i	$0.740820\pi$
$360$		0			0
$361$	−7.98233e6	−	4.63637e7i	−0.169671	−	0.985501i
$362$		0			0
$363$	−3.47440e7	+	9.54583e7i	−0.726373	+	1.99569i
$364$		0			0
$365$	−1.19928e7	−	1.00631e7i	−0.246627	−	0.206945i
$366$		0			0
$367$	−1.08334e6	+	6.14395e6i	−0.0219163	+	0.124294i	−0.993803	−	0.111155i	$-0.964545\pi$
$367$	−1.08334e6	+	6.14395e6i	−0.0219163	+	0.124294i	0.971887	+	0.235449i	$0.0756560\pi$
$368$		0			0
$369$	−1.32028e7	+	7.62263e6i	−0.262776	+	0.151714i
$370$		0			0
$371$	2.61059e6	+	7.17253e6i	0.0511230	+	0.140459i
$372$		0			0
$373$	1.33445e7	+	7.70447e6i	0.257144	+	0.148462i	0.623031	−	0.782197i	$-0.285901\pi$
$373$	1.33445e7	+	7.70447e6i	0.257144	+	0.148462i	−0.365887	+	0.930659i	$0.619234\pi$
$374$		0			0
$375$	−3.34439e7	−	3.98569e7i	−0.634195	−	0.755805i
$376$		0			0
$377$	−3.04922e7	−	1.72930e8i	−0.569069	−	3.22735i
$378$		0			0
$379$			2.24242e7i			0.411906i	0.978562	+	0.205953i	$0.0660294\pi$
$379$			2.24242e7i			0.411906i	−0.978562	+	0.205953i	$0.933971\pi$
$380$		0			0
$381$	−5.96579e7			−1.07868
$382$		0			0
$383$	−3.52076e7	+	6.20805e6i	−0.626671	+	0.110499i	−0.477960	−	0.878382i	$-0.658624\pi$
$383$	−3.52076e7	+	6.20805e6i	−0.626671	+	0.110499i	−0.148711	+	0.988881i	$0.547512\pi$
$384$		0			0
$385$	−5.51431e7	+	4.62705e7i	−0.966293	+	0.810816i
$386$		0			0
$387$	1.69417e7	−	2.93439e7i	0.292297	−	0.506272i
$388$		0			0
$389$	−8.91698e7	+	3.24552e7i	−1.51485	+	0.551360i	−0.959855	−	0.280496i	$-0.909501\pi$
$389$	−8.91698e7	+	3.24552e7i	−1.51485	+	0.551360i	−0.554993	+	0.831855i	$0.687279\pi$
$390$		0			0
$391$	−1.22906e7	−	2.12880e7i	−0.205610	−	0.356126i
$392$		0			0
$393$	−7.99664e7	−	1.41002e7i	−1.31744	−	0.232300i
$394$		0			0
$395$	−5.35669e7	+	6.38385e7i	−0.869171	+	1.03584i
$396$		0			0
$397$	−3.34086e7	−	1.21597e7i	−0.533932	−	0.194335i	0.0609609	−	0.998140i	$-0.480583\pi$
$397$	−3.34086e7	−	1.21597e7i	−0.533932	−	0.194335i	−0.594893	+	0.803805i	$0.702806\pi$
$398$		0			0
$399$	2.47104e7	+	4.29998e7i	0.389010	+	0.676937i
$400$		0			0
$401$	6.54420e6	−	1.79801e7i	0.101490	−	0.278842i	−0.878547	−	0.477656i	$-0.841487\pi$
$401$	6.54420e6	−	1.79801e7i	0.101490	−	0.278842i	0.980037	+	0.198814i	$0.0637089\pi$
$402$		0			0
$403$	1.50294e8	+	1.26112e8i	2.29629	+	1.92682i
$404$		0			0
$405$	1.56632e7	−	8.88304e7i	0.235784	−	1.33720i
$406$		0			0
$407$	1.22243e8	−	7.05769e7i	1.81318	−	1.04684i
$408$		0			0
$409$	9.41827e6	+	2.58765e7i	0.137658	+	0.378212i	0.989297	−	0.145917i	$-0.0466132\pi$
$409$	9.41827e6	+	2.58765e7i	0.137658	+	0.378212i	−0.851639	+	0.524129i	$0.824391\pi$
$410$		0			0
$411$	−1.20520e8	−	6.95824e7i	−1.73594	−	1.00224i
$412$		0			0
$413$	−2.55120e7	−	3.04040e7i	−0.362155	−	0.431599i
$414$		0			0
$415$	7.68595e6	+	4.35892e7i	0.107536	+	0.609866i
$416$		0			0
$417$		−	6.87699e7i		−	0.948398i
$418$		0			0
$419$	6.50283e7			0.884016			0.442008	−	0.897011i	$-0.354266\pi$
$419$	6.50283e7			0.884016			0.442008	+	0.897011i	$0.354266\pi$
$420$		0			0
$421$	−1.10360e8	+	1.94595e7i	−1.47899	+	0.260787i	−0.854176	−	0.519983i	$-0.825938\pi$
$421$	−1.10360e8	+	1.94595e7i	−1.47899	+	0.260787i	−0.624818	+	0.780770i	$0.714827\pi$
$422$		0			0
$423$	−1.44715e7	+	1.21430e7i	−0.191202	+	0.160438i
$424$		0			0
$425$	5.97314e6	−	1.03458e7i	0.0778101	−	0.134771i
$426$		0			0
$427$	2.08367e7	−	7.58395e6i	0.267637	−	0.0974118i
$428$		0			0
$429$	1.49001e8	+	2.58077e8i	1.88720	+	3.26872i
$430$		0			0
$431$	1.16110e8	+	2.04733e7i	1.45023	+	0.255715i	0.842615	−	0.538517i	$-0.181015\pi$
$431$	1.16110e8	+	2.04733e7i	1.45023	+	0.255715i	0.607615	+	0.794232i	$0.292126\pi$
$432$		0			0
$433$	6.68524e7	−	7.96716e7i	0.823481	−	0.981386i	−0.176515	−	0.984298i	$-0.556482\pi$
$433$	6.68524e7	−	7.96716e7i	0.823481	−	0.981386i	0.999996	+	0.00291165i	$0.000926808\pi$
$434$		0			0
$435$	−1.67893e8	−	6.11079e7i	−2.03969	−	0.742386i
$436$		0			0
$437$	−5.02381e7	+	8.75382e6i	−0.601990	+	0.104895i
$438$		0			0
$439$	−3.49377e7	+	9.59907e7i	−0.412954	+	1.13458i	0.542659	+	0.839953i	$0.317418\pi$
$439$	−3.49377e7	+	9.59907e7i	−0.412954	+	1.13458i	−0.955612	+	0.294627i	$0.904804\pi$
$440$		0			0
$441$	1.20813e7	+	1.01374e7i	0.140863	+	0.118198i
$442$		0			0
$443$	7.00928e6	−	3.97516e7i	0.0806236	−	0.457239i	−0.917592	−	0.397524i	$-0.869870\pi$
$443$	7.00928e6	−	3.97516e7i	0.0806236	−	0.457239i	0.998215	−	0.0597154i	$-0.0190193\pi$
$444$		0			0
$445$	5.96173e7	−	3.44201e7i	0.676538	−	0.390600i
$446$		0			0
$447$	−1.13475e6	−	3.11771e6i	−0.0127051	−	0.0349070i
$448$		0			0
$449$	−4.01042e7	−	2.31542e7i	−0.443048	−	0.255794i	0.261842	−	0.965111i	$-0.415670\pi$
$449$	−4.01042e7	−	2.31542e7i	−0.443048	−	0.255794i	−0.704890	+	0.709317i	$0.749003\pi$
$450$		0			0
$451$	8.91977e7	+	1.06302e8i	0.972353	+	1.15880i
$452$		0			0
$453$	−1.30060e7	−	7.37608e7i	−0.139910	−	0.793471i
$454$		0			0
$455$			1.36713e8i			1.45136i
$456$		0			0
$457$	−7.83699e7			−0.821109			−0.410554	−	0.911836i	$-0.634665\pi$
$457$	−7.83699e7			−0.821109			−0.410554	+	0.911836i	$0.634665\pi$
$458$		0			0
$459$	−4.90864e7	+	8.65526e6i	−0.507602	+	0.0895039i
$460$		0			0
$461$	2.91251e6	−	2.44389e6i	0.0297279	−	0.0249447i	−0.627803	−	0.778373i	$-0.716046\pi$
$461$	2.91251e6	−	2.44389e6i	0.0297279	−	0.0249447i	0.657531	+	0.753428i	$0.271601\pi$
$462$		0			0
$463$	7.41177e7	−	1.28376e8i	0.746756	−	1.29342i	−0.202614	−	0.979259i	$-0.564944\pi$
$463$	7.41177e7	−	1.28376e8i	0.746756	−	1.29342i	0.949370	−	0.314161i	$-0.101723\pi$
$464$		0			0
$465$	1.87587e8	−	6.82759e7i	1.86570	−	0.679061i
$466$		0			0
$467$	−4.22060e7	−	7.31030e7i	−0.414404	−	0.717768i	0.580962	−	0.813931i	$-0.302677\pi$
$467$	−4.22060e7	−	7.31030e7i	−0.414404	−	0.717768i	−0.995366	+	0.0961624i	$0.969343\pi$
$468$		0			0
$469$	−9.64326e7	−	1.70037e7i	−0.934771	−	0.164825i
$470$		0			0
$471$	−9.43823e6	+	1.12480e7i	−0.0903291	+	0.107650i
$472$		0			0
$473$	−2.89817e8	−	1.05485e8i	−2.73867	−	0.996796i
$474$		0			0
$475$	−1.58920e7	−	1.90172e7i	−0.148285	−	0.177445i
$476$		0			0
$477$	2.77665e6	−	7.62877e6i	0.0255838	−	0.0702910i
$478$		0			0
$479$	4.11826e7	+	3.45563e7i	0.374720	+	0.314428i	0.810625	−	0.585565i	$-0.199127\pi$
$479$	4.11826e7	+	3.45563e7i	0.374720	+	0.314428i	−0.435905	+	0.899993i	$0.643572\pi$
$480$		0			0
$481$	4.65516e7	−	2.64007e8i	0.418311	−	2.37236i
$482$		0			0
$483$	4.65552e7	−	2.68787e7i	0.413168	−	0.238543i
$484$		0			0
$485$	6.58196e7	+	1.80838e8i	0.576939	+	1.58513i
$486$		0			0
$487$	−6.41443e7	−	3.70337e7i	−0.555356	−	0.320635i	0.195924	−	0.980619i	$-0.437230\pi$
$487$	−6.41443e7	−	3.70337e7i	−0.555356	−	0.320635i	−0.751279	+	0.659984i	$0.770563\pi$
$488$		0			0
$489$	7.64772e7	+	9.11420e7i	0.654042	+	0.779457i
$490$		0			0
$491$	2.43790e7	+	1.38260e8i	0.205955	+	1.16803i	0.895930	+	0.444194i	$0.146510\pi$
$491$	2.43790e7	+	1.38260e8i	0.205955	+	1.16803i	−0.689976	+	0.723832i	$0.742379\pi$
$492$		0			0
$493$			1.36376e8i			1.13815i
$494$		0			0
$495$	7.65630e7			0.631253
$496$		0			0
$497$	7.44508e7	−	1.31277e7i	0.606458	−	0.106935i
$498$		0			0
$499$	−3.65572e7	+	3.06751e7i	−0.294219	+	0.246879i	−0.777933	−	0.628347i	$-0.783732\pi$
$499$	−3.65572e7	+	3.06751e7i	−0.294219	+	0.246879i	0.483714	+	0.875226i	$0.339287\pi$
$500$		0			0
$501$	3.51446e7	−	6.08721e7i	0.279476	−	0.484067i
$502$		0			0
$503$	1.50135e8	−	5.46446e7i	1.17971	−	0.429381i	0.323614	−	0.946189i	$-0.395102\pi$
$503$	1.50135e8	−	5.46446e7i	1.17971	−	0.429381i	0.856101	+	0.516808i	$0.172880\pi$
$504$		0			0
$505$	−3.80249e7	−	6.58610e7i	−0.295253	−	0.511393i
$506$		0			0
$507$	4.08921e8	+	7.21038e7i	3.13773	+	0.553267i
$508$		0			0
$509$	−6.33822e7	+	7.55360e7i	−0.480633	+	0.572796i	−0.950810	−	0.309776i	$-0.899746\pi$
$509$	−6.33822e7	+	7.55360e7i	−0.480633	+	0.572796i	0.470176	+	0.882573i	$0.344190\pi$
$510$		0			0
$511$	−2.45572e7	−	8.93810e6i	−0.184042	−	0.0669857i
$512$		0			0
$513$	−1.81613e7	+	1.01796e8i	−0.134523	+	0.754013i
$514$		0			0
$515$	−2.85742e6	+	7.85070e6i	−0.0209196	+	0.0574760i
$516$		0			0
$517$	1.31724e8	+	1.10530e8i	0.953220	+	0.799847i
$518$		0			0
$519$	−223274.	+	1.26625e6i	−0.00159712	+	0.00905769i
$520$		0			0
$521$	−1.88197e6	+	1.08656e6i	−0.0133076	+	0.00768316i	−0.506639	−	0.862158i	$-0.669112\pi$
$521$	−1.88197e6	+	1.08656e6i	−0.0133076	+	0.00768316i	0.493331	+	0.869841i	$0.335779\pi$
$522$		0			0
$523$	−672461.	−	1.84757e6i	−0.00470069	−	0.0129151i	0.937320	−	0.348470i	$-0.113299\pi$
$523$	−672461.	−	1.84757e6i	−0.00470069	−	0.0129151i	−0.942021	+	0.335555i	$0.891076\pi$
$524$		0			0
$525$	2.26255e7	+	1.30628e7i	0.156358	+	0.0902733i
$526$		0			0
$527$	−9.79437e7	−	1.16725e8i	−0.669183	−	0.797501i
$528$		0			0
$529$	−1.61076e7	−	9.13508e7i	−0.108809	−	0.617086i
$530$		0			0
$531$			4.22142e7i			0.281952i
$532$		0			0
$533$	2.63547e8			1.74051
$534$		0			0
$535$	−5.21080e7	+	9.18804e6i	−0.340285	+	0.0600014i
$536$		0			0
$537$	−1.67089e8	+	1.40204e8i	−1.07901	+	0.905395i
$538$		0			0
$539$	7.17760e7	−	1.24320e8i	0.458367	−	0.793915i
$540$		0			0
$541$	−4.44468e6	+	1.61773e6i	−0.0280704	+	0.0102168i	−0.356017	−	0.934479i	$-0.615866\pi$
$541$	−4.44468e6	+	1.61773e6i	−0.0280704	+	0.0102168i	0.327947	+	0.944696i	$0.393643\pi$
$542$		0			0
$543$	2.75952e6	+	4.77964e6i	0.0172359	+	0.0298535i
$544$		0			0
$545$	6.97633e7	+	1.23012e7i	0.430961	+	0.0759900i
$546$		0			0
$547$	1.39243e8	−	1.65944e8i	0.850770	−	1.01391i	−0.148916	−	0.988850i	$-0.547578\pi$
$547$	1.39243e8	−	1.65944e8i	0.850770	−	1.01391i	0.999686	−	0.0250587i	$-0.00797726\pi$
$548$		0			0
$549$	−2.21621e7	−	8.06636e6i	−0.133935	−	0.0487484i
$550$		0			0
$551$	2.65662e8	+	9.73008e7i	1.58809	+	0.581650i
$552$		0			0
$553$	−4.75782e7	+	1.30720e8i	−0.281341	+	0.772978i
$554$		0			0
$555$	−2.08951e8	−	1.75331e8i	−1.22227	−	1.02560i
$556$		0			0
$557$	4.31430e7	−	2.44676e8i	0.249658	−	1.41588i	−0.559764	−	0.828652i	$-0.689108\pi$
$557$	4.31430e7	−	2.44676e8i	0.249658	−	1.41588i	0.809422	−	0.587227i	$-0.199781\pi$
$558$		0			0
$559$	−5.07271e8	+	2.92873e8i	−2.90405	+	1.67666i
$560$		0			0
$561$	−7.91574e7	−	2.17483e8i	−0.448335	−	1.23179i
$562$		0			0
$563$	−1.14447e8	−	6.60758e7i	−0.641324	−	0.370269i	0.143800	−	0.989607i	$-0.454068\pi$
$563$	−1.14447e8	−	6.60758e7i	−0.641324	−	0.370269i	−0.785125	+	0.619338i	$0.787401\pi$
$564$		0			0
$565$	3.24243e7	+	3.86418e7i	0.179773	+	0.214246i
$566$		0			0
$567$	−2.61462e7	−	1.48282e8i	−0.143436	−	0.813467i
$568$		0			0
$569$			2.09761e8i			1.13864i	0.822115	+	0.569321i	$0.192794\pi$
$569$			2.09761e8i			1.13864i	−0.822115	+	0.569321i	$0.807206\pi$
$570$		0			0
$571$	−3.35596e8			−1.80264			−0.901320	−	0.433155i	$-0.857400\pi$
$571$	−3.35596e8			−1.80264			−0.901320	+	0.433155i	$0.857400\pi$
$572$		0			0
$573$	−5.47976e6	+	966229.i	−0.0291271	+	0.00513589i
$574$		0			0
$575$	−2.05787e7	+	1.72676e7i	−0.108247	+	0.0908298i
$576$		0			0
$577$	6.89575e6	−	1.19438e7i	0.0358967	−	0.0621749i	−0.847519	−	0.530765i	$-0.821905\pi$
$577$	6.89575e6	−	1.19438e7i	0.0358967	−	0.0621749i	0.883416	+	0.468590i	$0.155238\pi$
$578$		0			0
$579$	−5.59031e7	+	2.03471e7i	−0.288005	+	0.104825i
$580$		0			0
$581$	3.69424e7	+	6.39861e7i	0.188363	+	0.326255i
$582$		0			0
$583$	−7.27733e7	−	1.28319e7i	−0.367254	−	0.0647567i
$584$		0			0
$585$	9.34669e7	−	1.11390e8i	0.466864	−	0.556387i
$586$		0			0
$587$	3.36919e6	+	1.22629e6i	0.0166576	+	0.00606286i	0.350335	−	0.936624i	$-0.386068\pi$
$587$	3.36919e6	+	1.22629e6i	0.0166576	+	0.00606286i	−0.333678	+	0.942687i	$0.608290\pi$
$588$		0			0
$589$	−2.97261e8	+	1.07515e8i	−1.45476	+	0.526167i
$590$		0			0
$591$	−1.22413e8	+	3.36328e8i	−0.593016	+	1.62930i
$592$		0			0
$593$	−1.34438e8	−	1.12807e8i	−0.644698	−	0.540966i	0.260759	−	0.965404i	$-0.416027\pi$
$593$	−1.34438e8	−	1.12807e8i	−0.644698	−	0.540966i	−0.905457	+	0.424438i	$0.860472\pi$
$594$		0			0
$595$	1.84374e7	−	1.04564e8i	0.0875282	−	0.496397i
$596$		0			0
$597$	1.24237e7	−	7.17283e6i	0.0583886	−	0.0337107i
$598$		0			0
$599$	5.78797e7	+	1.59023e8i	0.269306	+	0.739912i	0.998455	+	0.0555577i	$0.0176937\pi$
$599$	5.78797e7	+	1.59023e8i	0.269306	+	0.739912i	−0.729149	+	0.684354i	$0.760084\pi$
$600$		0			0
$601$	−3.05762e8	−	1.76532e8i	−1.40851	−	0.813203i	−0.413265	−	0.910611i	$-0.635612\pi$
$601$	−3.05762e8	−	1.76532e8i	−1.40851	−	0.813203i	−0.995245	+	0.0974078i	$0.968945\pi$
$602$		0			0
$603$	6.69456e7	+	7.97827e7i	0.305331	+	0.363879i
$604$		0			0
$605$	−7.83467e7	−	4.44326e8i	−0.353798	−	2.00649i
$606$		0			0
$607$			2.21709e8i			0.991328i	0.868514	+	0.495664i	$0.165075\pi$
$607$			2.21709e8i			0.991328i	−0.868514	+	0.495664i	$0.834925\pi$
$608$		0			0
$609$	−2.98245e8			−1.32045
$610$		0			0
$611$	3.21613e8	−	5.67091e7i	1.40997	−	0.248616i
$612$		0			0
$613$	−2.06308e8	+	1.73113e8i	−0.895644	+	0.751534i	−0.969334	−	0.245747i	$-0.920967\pi$
$613$	−2.06308e8	+	1.73113e8i	−0.895644	+	0.751534i	0.0736903	+	0.997281i	$0.476522\pi$
$614$		0			0
$615$	1.34077e8	−	2.32228e8i	0.576407	−	0.998367i
$616$		0			0
$617$	2.75456e8	−	1.00258e8i	1.17273	−	0.426837i	0.319099	−	0.947721i	$-0.396620\pi$
$617$	2.75456e8	−	1.00258e8i	1.17273	−	0.426837i	0.853627	+	0.520884i	$0.174398\pi$
$618$		0			0
$619$	9.02254e7	+	1.56275e8i	0.380415	+	0.658897i	0.991121	−	0.132959i	$-0.0424480\pi$
$619$	9.02254e7	+	1.56275e8i	0.380415	+	0.658897i	−0.610707	+	0.791857i	$0.709115\pi$
$620$		0			0
$621$	1.10381e8	+	1.94631e7i	0.460912	+	0.0812713i
$622$		0			0
$623$	7.38647e7	−	8.80285e7i	0.305473	−	0.364049i
$624$		0			0
$625$	2.70201e8	+	9.83452e7i	1.10674	+	0.402822i
$626$		0			0
$627$	−4.80136e8	−	969114.i	−1.94788	−	0.00393163i
$628$		0			0
$629$	−7.12092e7	+	1.95646e8i	−0.286144	+	0.786173i
$630$		0			0
$631$	−2.35457e8	−	1.97572e8i	−0.937181	−	0.786388i	0.0399113	−	0.999203i	$-0.487292\pi$
$631$	−2.35457e8	−	1.97572e8i	−0.937181	−	0.786388i	−0.977093	+	0.212815i	$0.931737\pi$
$632$		0			0
$633$	−4.52336e7	+	2.56532e8i	−0.178340	+	1.01142i
$634$		0			0
$635$	2.29468e8	−	1.32483e8i	0.896190	−	0.517416i
$636$		0			0
$637$	−9.32465e7	−	2.56193e8i	−0.360757	−	0.991171i
$638$		0			0
$639$	−6.96355e7	−	4.02041e7i	−0.266888	−	0.154088i
$640$		0			0
$641$	1.07173e8	+	1.27724e8i	0.406924	+	0.484953i	0.930118	−	0.367260i	$-0.119704\pi$
$641$	1.07173e8	+	1.27724e8i	0.406924	+	0.484953i	−0.523194	+	0.852213i	$0.675260\pi$
$642$		0			0
$643$	2.21625e7	+	1.25690e8i	0.0833654	+	0.472789i	0.997697	+	0.0678233i	$0.0216054\pi$
$643$	2.21625e7	+	1.25690e8i	0.0833654	+	0.472789i	−0.914332	+	0.404966i	$0.867283\pi$
$644$		0			0
$645$			5.95987e8i			2.22105i
$646$		0			0
$647$	−4.10357e8			−1.51513			−0.757564	−	0.652761i	$-0.773611\pi$
$647$	−4.10357e8			−1.51513			−0.757564	+	0.652761i	$0.773611\pi$
$648$		0			0
$649$	3.78409e8	−	6.67238e7i	1.38429	−	0.244088i
$650$		0			0
$651$	2.55269e8	−	2.14196e8i	0.925240	−	0.776369i
$652$		0			0
$653$	3.50457e7	−	6.07010e7i	0.125862	−	0.218000i	−0.796207	−	0.605024i	$-0.793164\pi$
$653$	3.50457e7	−	6.07010e7i	0.125862	−	0.218000i	0.922070	+	0.387024i	$0.126497\pi$
$654$		0			0
$655$	3.38894e8	−	1.23347e8i	1.20598	−	0.438941i
$656$		0			0
$657$	1.38978e7	+	2.40717e7i	0.0490060	+	0.0848809i
$658$		0			0
$659$	1.13629e8	+	2.00359e7i	0.397039	+	0.0700087i	0.368603	−	0.929587i	$-0.379836\pi$
$659$	1.13629e8	+	2.00359e7i	0.397039	+	0.0700087i	0.0284360	+	0.999596i	$0.490947\pi$
$660$		0			0
$661$	1.75209e7	−	2.08806e7i	0.0606668	−	0.0722999i	−0.734858	−	0.678221i	$-0.762751\pi$
$661$	1.75209e7	−	2.08806e7i	0.0606668	−	0.0722999i	0.795524	+	0.605922i	$0.207195\pi$
$662$		0			0
$663$	−4.13045e8	−	1.50336e8i	−1.41728	−	0.515849i
$664$		0			0
$665$	−1.90536e8	−	1.10519e8i	−0.647906	−	0.375815i
$666$		0			0
$667$	1.04887e8	−	2.88175e8i	0.353464	−	0.971134i
$668$		0			0
$669$	1.25699e8	+	1.05474e8i	0.419812	+	0.352264i
$670$		0			0
$671$	−3.72775e7	+	2.11411e8i	−0.123390	+	0.699779i
$672$		0			0
$673$	2.03986e8	−	1.17771e8i	0.669198	−	0.386361i	−0.126575	−	0.991957i	$-0.540398\pi$
$673$	2.03986e8	−	1.17771e8i	0.669198	−	0.386361i	0.795773	+	0.605596i	$0.207065\pi$
$674$		0			0
$675$	1.86304e7	+	5.11866e7i	0.0605775	+	0.166435i
$676$		0			0
$677$	−7.41515e7	−	4.28114e7i	−0.238976	−	0.137973i	0.375730	−	0.926729i	$-0.377392\pi$
$677$	−7.41515e7	−	4.28114e7i	−0.238976	−	0.137973i	−0.614706	+	0.788756i	$0.710725\pi$
$678$		0			0
$679$	2.06490e8	+	2.46085e8i	0.659613	+	0.786096i
$680$		0			0
$681$	−8.55319e6	−	4.85076e7i	−0.0270824	−	0.153592i
$682$		0			0
$683$		−	3.63470e8i		−	1.14079i	−0.821370	−	0.570396i	$-0.806790\pi$
$683$		−	3.63470e8i		−	1.14079i	0.821370	−	0.570396i	$-0.193210\pi$
$684$		0			0
$685$	6.18090e8			1.92300
$686$		0			0
$687$	3.08705e8	−	5.44330e7i	0.952079	−	0.167877i
$688$		0			0
$689$	−1.07509e8	+	9.02110e7i	−0.328691	+	0.275805i
$690$		0			0
$691$	5.32571e7	−	9.22441e7i	0.161415	−	0.279579i	−0.773961	−	0.633233i	$-0.781728\pi$
$691$	5.32571e7	−	9.22441e7i	0.161415	−	0.279579i	0.935376	+	0.353654i	$0.115061\pi$
$692$		0			0
$693$	1.20097e8	−	4.37118e7i	0.360855	−	0.131340i
$694$		0			0
$695$	1.52718e8	+	2.64516e8i	0.454922	+	0.787948i
$696$		0			0
$697$	−2.01572e8	−	3.55425e7i	−0.595293	−	0.104966i
$698$		0			0
$699$	−4.20559e8	+	5.01202e8i	−1.23139	+	1.46751i
$700$		0			0
$701$	4.74955e8	+	1.72869e8i	1.37879	+	0.501839i	0.921811	−	0.387639i	$-0.126709\pi$
$701$	4.74955e8	+	1.72869e8i	1.37879	+	0.501839i	0.456979	+	0.889477i	$0.348931\pi$
$702$		0			0
$703$	3.30314e8	+	2.78304e8i	0.950737	+	0.801039i
$704$		0			0
$705$	1.13648e8	−	3.12245e8i	0.324335	−	0.891104i
$706$		0			0
$707$	−9.72477e7	−	8.16005e7i	−0.275183	−	0.230906i
$708$		0			0
$709$	−1.09730e8	+	6.22308e8i	−0.307883	+	1.74609i	0.301732	+	0.953393i	$0.402435\pi$
$709$	−1.09730e8	+	6.22308e8i	−0.307883	+	1.74609i	−0.609615	+	0.792698i	$0.708676\pi$
$710$		0			0
$711$	1.28135e8	−	7.39790e7i	0.356501	−	0.205826i
$712$		0			0
$713$	1.17191e8	+	3.21978e8i	0.323314	+	0.888297i
$714$		0			0
$715$	−1.14623e9	−	6.61777e8i	−3.13584	−	1.81048i
$716$		0			0
$717$	−3.08402e8	−	3.67540e8i	−0.836682	−	0.997119i
$718$		0			0
$719$	3.50252e7	+	1.98638e8i	0.0942311	+	0.534411i	0.994980	+	0.100071i	$0.0319071\pi$
$719$	3.50252e7	+	1.98638e8i	0.0942311	+	0.534411i	−0.900749	+	0.434340i	$0.856982\pi$
$720$		0			0
$721$			1.39460e7i			0.0372087i
$722$		0			0
$723$	−1.29612e8			−0.342949
$724$		0			0
$725$	1.46775e8	−	2.58803e7i	0.385157	−	0.0679135i
$726$		0			0
$727$	4.38951e8	−	3.68323e8i	1.14238	−	0.958574i	0.142870	−	0.989741i	$-0.454367\pi$
$727$	4.38951e8	−	3.68323e8i	1.14238	−	0.958574i	0.999514	+	0.0311670i	$0.00992236\pi$
$728$		0			0
$729$	9.15320e7	−	1.58538e8i	0.236260	−	0.409214i
$730$		0			0
$731$	4.27480e8	−	1.55590e8i	1.09437	−	0.398318i
$732$		0			0
$733$	2.29498e8	+	3.97502e8i	0.582728	+	1.00932i	0.995154	+	0.0983242i	$0.0313482\pi$
$733$	2.29498e8	+	3.97502e8i	0.582728	+	1.00932i	−0.412426	+	0.910991i	$0.635318\pi$
$734$		0			0
$735$	−2.73187e8	−	4.81702e7i	−0.688015	−	0.121316i
$736$		0			0
$737$	6.09359e8	−	7.26206e8i	1.52220	−	1.81408i
$738$		0			0
$739$	1.12106e8	+	4.08031e7i	0.277776	+	0.101102i	0.477152	−	0.878821i	$-0.341669\pi$
$739$	1.12106e8	+	4.08031e7i	0.277776	+	0.101102i	−0.199376	+	0.979923i	$0.563891\pi$
$740$		0			0
$741$	−5.87552e8	+	6.97354e8i	−1.44408	+	1.71395i
$742$		0			0
$743$	5.59629e7	−	1.53757e8i	0.136437	−	0.374859i	−0.852592	−	0.522577i	$-0.824971\pi$
$743$	5.59629e7	−	1.53757e8i	0.136437	−	0.374859i	0.989029	+	0.147718i	$0.0471929\pi$
$744$		0			0
$745$	1.12882e7	+	9.47196e6i	0.0272997	+	0.0229071i
$746$		0			0
$747$	1.36461e7	−	7.73906e7i	0.0327375	−	0.185664i
$748$		0			0
$749$	−7.64911e7	+	4.41622e7i	−0.182039	+	0.105101i
$750$		0			0
$751$	−5.01623e7	−	1.37820e8i	−0.118429	−	0.325381i	0.866288	−	0.499545i	$-0.166500\pi$
$751$	−5.01623e7	−	1.37820e8i	−0.118429	−	0.325381i	−0.984716	+	0.174165i	$0.944277\pi$
$752$		0			0
$753$	−3.80899e8	−	2.19912e8i	−0.892124	−	0.515068i
$754$		0			0
$755$	2.13828e8	+	2.54830e8i	0.496848	+	0.592120i
$756$		0			0
$757$	2.16196e7	+	1.22611e8i	0.0498380	+	0.282646i	0.999534	−	0.0305281i	$-0.00971892\pi$
$757$	2.16196e7	+	1.22611e8i	0.0498380	+	0.282646i	−0.949696	+	0.313174i	$0.898608\pi$
$758$		0			0
$759$			5.20441e8i			1.19027i
$760$		0			0
$761$	1.03814e8			0.235561			0.117780	−	0.993040i	$-0.462422\pi$
$761$	1.03814e8			0.235561			0.117780	+	0.993040i	$0.462422\pi$
$762$		0			0
$763$	1.16454e8	−	2.05340e7i	0.262169	−	0.0462275i
$764$		0			0
$765$	−8.65097e7	+	7.25903e7i	−0.193233	+	0.162142i
$766$		0			0
$767$	3.64882e8	−	6.31993e8i	0.808660	−	1.40064i
$768$		0			0
$769$	4.61175e8	−	1.67854e8i	1.01411	−	0.369108i	0.219103	−	0.975702i	$-0.429687\pi$
$769$	4.61175e8	−	1.67854e8i	1.01411	−	0.369108i	0.795012	+	0.606594i	$0.207465\pi$
$770$		0			0
$771$	−1.88961e8	−	3.27291e8i	−0.412297	−	0.714119i
$772$		0			0
$773$	6.60111e8	+	1.16395e8i	1.42915	+	0.251998i	0.834066	−	0.551664i	$-0.186007\pi$
$773$	6.60111e8	+	1.16395e8i	1.42915	+	0.251998i	0.595086	+	0.803662i	$0.297118\pi$
$774$		0			0
$775$	−1.07038e8	+	1.27563e8i	−0.229949	+	0.274043i
$776$		0			0
$777$	−4.27863e8	−	1.55729e8i	−0.912098	−	0.331977i
$778$		0			0
$779$	−2.13053e8	+	3.67305e8i	−0.450687	+	0.776987i
$780$		0			0
$781$	−2.50325e8	+	6.87761e8i	−0.525473	+	1.44372i
$782$		0			0
$783$	−4.76356e8	−	3.99710e8i	−0.992307	−	0.832644i
$784$		0			0
$785$	1.13244e7	−	6.42240e7i	0.0234103	−	0.132766i
$786$		0			0
$787$	−7.30966e8	+	4.22023e8i	−1.49959	+	0.865789i	−1.00000		0.000472187i	$-0.999850\pi$
$787$	−7.30966e8	+	4.22023e8i	−1.49959	+	0.865789i	−0.499591	+	0.866261i	$0.666516\pi$
$788$		0			0
$789$	6.71718e7	+	1.84553e8i	0.136759	+	0.375742i
$790$		0			0
$791$	7.29225e7	+	4.21018e7i	0.147344	+	0.0850690i
$792$		0			0
$793$	2.62069e8	+	3.12322e8i	0.525529	+	0.626301i
$794$		0			0
$795$	2.47964e7	+	1.40628e8i	0.0493501	+	0.279878i
$796$		0			0
$797$		−	7.25651e8i		−	1.43335i	−0.697406	−	0.716676i	$-0.745663\pi$
$797$		−	7.25651e8i		−	1.43335i	0.697406	−	0.716676i	$-0.254337\pi$
$798$		0			0
$799$	−2.53631e8			−0.497236
$800$		0			0
$801$	−1.20366e8	+	2.12237e7i	−0.234210	+	0.0412976i
$802$		0			0
$803$	1.93812e8	−	1.62628e8i	0.374313	−	0.314085i
$804$		0			0
$805$	−1.19380e8	+	2.06772e8i	−0.228846	+	0.396373i
$806$		0			0
$807$	4.80881e8	−	1.75026e8i	0.914991	−	0.333030i
$808$		0			0
$809$	3.71224e8	+	6.42979e8i	0.701117	+	1.21437i	0.968075	+	0.250662i	$0.0806483\pi$
$809$	3.71224e8	+	6.42979e8i	0.701117	+	1.21437i	−0.266958	+	0.963708i	$0.586018\pi$
$810$		0			0
$811$	9.44875e7	+	1.66607e7i	0.177138	+	0.0312342i	0.261514	−	0.965200i	$-0.415778\pi$
$811$	9.44875e7	+	1.66607e7i	0.177138	+	0.0312342i	−0.0843754	+	0.996434i	$0.526890\pi$
$812$		0			0
$813$	4.79848e8	−	5.71860e8i	0.892959	−	1.06419i
$814$		0			0
$815$	−4.96562e8	−	1.80734e8i	−0.917277	−	0.333861i
$816$		0			0
$817$	1.90487e6	−	9.43744e8i	0.00349300	−	1.73056i
$818$		0			0
$819$	8.30175e7	−	2.28089e8i	0.151119	−	0.415195i
$820$		0			0
$821$	−8.45806e8	−	7.09715e8i	−1.52841	−	1.28249i	−0.808698	−	0.588224i	$-0.799827\pi$
$821$	−8.45806e8	−	7.09715e8i	−1.52841	−	1.28249i	−0.719717	−	0.694268i	$-0.755728\pi$
$822$		0			0
$823$	1.80858e7	−	1.02570e8i	0.0324443	−	0.184001i	−0.964279	−	0.264889i	$-0.914665\pi$
$823$	1.80858e7	−	1.02570e8i	0.0324443	−	0.184001i	0.996723	+	0.0808885i	$0.0257758\pi$
$824$		0			0
$825$	−2.19044e8	+	1.26465e8i	−0.390094	+	0.225221i
$826$		0			0
$827$	2.88605e8	+	7.92936e8i	0.510256	+	1.40192i	0.880972	+	0.473169i	$0.156890\pi$
$827$	2.88605e8	+	7.92936e8i	0.510256	+	1.40192i	−0.370716	+	0.928746i	$0.620888\pi$
$828$		0			0
$829$	4.30475e8	+	2.48535e8i	0.755586	+	0.436238i	0.827709	−	0.561158i	$-0.189644\pi$
$829$	4.30475e8	+	2.48535e8i	0.755586	+	0.436238i	−0.0721228	+	0.997396i	$0.522977\pi$
$830$		0			0
$831$	2.86036e7	+	3.40885e7i	0.0498446	+	0.0594025i
$832$		0			0
$833$	3.67681e7	+	2.08523e8i	0.0636117	+	0.360760i
$834$		0			0
$835$			3.12184e8i			0.536230i
$836$		0			0
$837$	6.94780e8			1.18487
$838$		0			0
$839$	−6.58297e8	+	1.16075e8i	−1.11464	+	0.196542i	−0.700488	−	0.713665i	$-0.747034\pi$
$839$	−6.58297e8	+	1.16075e8i	−1.11464	+	0.196542i	−0.414155	+	0.910206i	$0.635923\pi$
$840$		0			0
$841$	−8.47687e8	+	7.11294e8i	−1.42511	+	1.19581i
$842$		0			0
$843$	−4.62140e8	+	8.00450e8i	−0.771420	+	1.33614i
$844$		0			0
$845$	−1.73299e9	+	6.30757e8i	−2.87228	+	1.04542i
$846$		0			0
$847$	−3.76572e8	−	6.52242e8i	−0.619724	−	1.07339i
$848$		0			0
$849$	3.77371e8	+	6.65407e7i	0.616659	+	0.108734i
$850$		0			0
$851$	3.00943e8	−	3.58649e8i	0.488309	−	0.581944i
$852$		0			0
$853$	−6.99999e8	−	2.54779e8i	−1.12785	−	0.410503i	−0.290337	−	0.956924i	$-0.593767\pi$
$853$	−6.99999e8	−	2.54779e8i	−1.12785	−	0.410503i	−0.837510	+	0.546422i	$0.815990\pi$
$854$		0			0
$855$	7.96841e7	+	2.20313e8i	0.127489	+	0.352486i
$856$		0			0
$857$	−1.75306e8	+	4.81650e8i	−0.278519	+	0.765225i	0.719012	+	0.694998i	$0.244595\pi$
$857$	−1.75306e8	+	4.81650e8i	−0.278519	+	0.765225i	−0.997531	+	0.0702273i	$0.977628\pi$
$858$		0			0
$859$	−1.26644e8	−	1.06267e8i	−0.199804	−	0.167656i	0.537396	−	0.843330i	$-0.319408\pi$
$859$	−1.26644e8	−	1.06267e8i	−0.199804	−	0.167656i	−0.737200	+	0.675674i	$0.763852\pi$
$860$		0			0
$861$	7.77289e7	−	4.40823e8i	0.121779	−	0.690644i
$862$		0			0
$863$	−7.48032e8	+	4.31876e8i	−1.16382	+	0.671934i	−0.952218	−	0.305420i	$-0.901203\pi$
$863$	−7.48032e8	+	4.31876e8i	−1.16382	+	0.671934i	−0.211607	+	0.977355i	$0.567870\pi$
$864$		0			0
$865$	−1.95318e6	−	5.36632e6i	−0.00301783	−	0.00829141i
$866$		0			0
$867$	−3.57167e8	−	2.06210e8i	−0.548042	−	0.316412i
$868$		0			0
$869$	−8.65680e8	−	1.03168e9i	−1.31916	−	1.57212i
$870$		0			0
$871$	−3.12642e8	−	1.77308e9i	−0.473144	−	2.68333i
$872$		0			0
$873$		−	3.41675e8i		−	0.513536i
$874$		0			0
$875$	3.85744e8			0.575805
$876$		0			0
$877$	1.12910e9	−	1.99091e8i	1.67391	−	0.295156i	0.745446	−	0.666567i	$-0.232237\pi$
$877$	1.12910e9	−	1.99091e8i	1.67391	−	0.295156i	0.928469	+	0.371410i	$0.121126\pi$
$878$		0			0
$879$	−4.60217e8	+	3.86168e8i	−0.677636	+	0.568604i
$880$		0			0
$881$	−5.05684e8	+	8.75871e8i	−0.739523	+	1.28089i	0.213187	+	0.977011i	$0.431616\pi$
$881$	−5.05684e8	+	8.75871e8i	−0.739523	+	1.28089i	−0.952710	+	0.303880i	$0.901718\pi$
$882$		0			0
$883$	−5.17621e8	+	1.88398e8i	−0.751847	+	0.273650i	−0.689383	−	0.724397i	$-0.742118\pi$
$883$	−5.17621e8	+	1.88398e8i	−0.751847	+	0.273650i	−0.0624642	+	0.998047i	$0.519896\pi$
$884$		0			0
$885$	−3.71261e8	−	6.43043e8i	−0.535611	−	0.927705i
$886$		0			0
$887$	1.82853e8	+	3.22419e7i	0.262018	+	0.0462008i	0.303114	−	0.952954i	$-0.401974\pi$
$887$	1.82853e8	+	3.22419e7i	0.262018	+	0.0462008i	−0.0410959	+	0.999155i	$0.513085\pi$
$888$		0			0
$889$	2.84306e8	−	3.38823e8i	0.404651	−	0.482244i
$890$		0			0
$891$	1.36980e9	+	4.98566e8i	1.93653	+	0.704839i
$892$		0			0
$893$	−1.80959e8	+	4.94076e8i	−0.254113	+	0.693808i
$894$		0			0
$895$	3.31335e8	−	9.10336e8i	0.462167	−	1.26979i
$896$		0			0
$897$	7.57176e8	+	6.35346e8i	1.04911	+	0.880305i
$898$		0			0
$899$	3.30101e8	−	1.87210e9i	0.454326	−	2.57661i
$900$		0			0
$901$	9.43937e7	−	5.44982e7i	0.129053	−	0.0745089i
$902$		0			0
$903$	3.40264e8	+	9.34868e8i	0.462118	+	1.26966i
$904$		0			0
$905$	−2.12284e7	−	1.22562e7i	−0.0286399	−	0.0165353i
$906$		0			0
$907$	1.00143e8	+	1.19345e8i	0.134214	+	0.159950i	0.828965	−	0.559300i	$-0.188930\pi$
$907$	1.00143e8	+	1.19345e8i	0.134214	+	0.159950i	−0.694751	+	0.719250i	$0.744486\pi$
$908$		0			0
$909$	2.34465e7	+	1.32972e8i	0.0312167	+	0.177038i
$910$		0			0
$911$			7.10309e8i			0.939490i	0.882802	+	0.469745i	$0.155654\pi$
$911$			7.10309e8i			0.939490i	−0.882802	+	0.469745i	$0.844346\pi$
$912$		0			0
$913$	−7.15300e8			−0.939888
$914$		0			0
$915$	4.08533e8	−	7.20354e7i	0.533291	−	0.0940336i
$916$		0			0
$917$	4.61169e8	−	3.86967e8i	0.598070	−	0.501841i
$918$		0			0
$919$	−4.44877e8	+	7.70549e8i	−0.573183	+	0.992782i	0.423054	+	0.906105i	$0.360958\pi$
$919$	−4.44877e8	+	7.70549e8i	−0.573183	+	0.992782i	−0.996236	+	0.0866771i	$0.972375\pi$
$920$		0			0
$921$	5.13144e7	−	1.86769e7i	0.0656841	−	0.0239071i
$922$		0			0
$923$	6.95013e8	+	1.20380e9i	0.883869	+	1.53091i
$924$		0			0
$925$	2.24077e8	+	3.95108e7i	0.283121	+	0.0499218i
$926$		0			0
$927$	9.53454e6	−	1.13628e7i	0.0119691	−	0.0142642i
$928$		0			0
$929$	−5.91031e8	−	2.15118e8i	−0.737162	−	0.268305i	−0.0539687	−	0.998543i	$-0.517187\pi$
$929$	−5.91031e8	−	2.15118e8i	−0.737162	−	0.268305i	−0.683193	+	0.730238i	$0.739409\pi$
$930$		0			0
$931$	4.32437e8	+	7.71505e7i	0.535887	+	0.0956070i
$932$		0			0
$933$	−2.37997e8	+	6.53891e8i	−0.293040	+	0.805120i
$934$		0			0
$935$	7.87438e8	+	6.60739e8i	0.963344	+	0.808342i
$936$		0			0
$937$	−1.25394e8	+	7.11142e8i	−0.152425	+	0.864446i	0.808677	+	0.588253i	$0.200184\pi$
$937$	−1.25394e8	+	7.11142e8i	−0.152425	+	0.864446i	−0.961102	+	0.276193i	$0.910927\pi$
$938$		0			0
$939$	1.00052e9	−	5.77650e8i	1.20845	−	0.697698i
$940$		0			0
$941$	−3.99044e8	−	1.09636e9i	−0.478908	−	1.31579i	−0.910422	−	0.413682i	$-0.864243\pi$
$941$	−3.99044e8	−	1.09636e9i	−0.478908	−	1.31579i	0.431514	−	0.902106i	$-0.357980\pi$
$942$		0			0
$943$	3.98603e8	+	2.30133e8i	0.475341	+	0.274438i
$944$		0			0
$945$	3.11196e8	+	3.70869e8i	0.368756	+	0.439466i
$946$		0			0
$947$	1.71779e8	+	9.74209e8i	0.202265	+	1.14710i	0.901686	+	0.432392i	$0.142330\pi$
$947$	1.71779e8	+	9.74209e8i	0.202265	+	1.14710i	−0.699421	+	0.714710i	$0.746559\pi$
$948$		0			0
$949$		−	4.80506e8i		−	0.562212i
$950$		0			0
$951$	1.91829e9			2.23035
$952$		0			0
$953$	−2.15405e8	+	3.79817e7i	−0.248872	+	0.0438829i	−0.296693	−	0.954973i	$-0.595884\pi$
$953$	−2.15405e8	+	3.79817e7i	−0.248872	+	0.0438829i	0.0478202	+	0.998856i	$0.484773\pi$
$954$		0			0
$955$	1.89316e7	−	1.58855e7i	0.0217358	−	0.0182385i
$956$		0			0
$957$	1.44370e9	−	2.50056e9i	1.64718	−	2.85300i
$958$		0			0
$959$	9.69539e8	−	3.52883e8i	1.09928	−	0.400106i
$960$		0			0
$961$	6.18228e8	+	1.07080e9i	0.696593	+	1.20653i
$962$		0			0
$963$	9.25154e7	+	1.63130e7i	0.103594	+	0.0182664i
$964$		0			0
$965$	1.69840e8	−	2.02408e8i	0.188999	−	0.225240i
$966$		0			0
$967$	2.03203e8	+	7.39600e7i	0.224725	+	0.0817932i	0.451929	−	0.892054i	$-0.350736\pi$
$967$	2.03203e8	+	7.39600e7i	0.224725	+	0.0817932i	−0.227204	+	0.973847i	$0.572958\pi$
$968$		0			0
$969$	5.43431e8	−	4.54127e8i	0.597274	−	0.499121i
$970$		0			0
$971$	−4.97294e8	+	1.36630e9i	−0.543194	+	1.49241i	0.299540	+	0.954084i	$0.403167\pi$
$971$	−4.97294e8	+	1.36630e9i	−0.543194	+	1.49241i	−0.842734	+	0.538330i	$0.819055\pi$
$972$		0			0
$973$	3.90574e8	+	3.27730e8i	0.423998	+	0.355777i
$974$		0			0
$975$	−8.34146e7	+	4.73068e8i	−0.0899971	+	0.510399i
$976$		0			0
$977$	8.59978e7	−	4.96508e7i	0.0922154	−	0.0532406i	−0.453183	−	0.891417i	$-0.649712\pi$
$977$	8.59978e7	−	4.96508e7i	0.0922154	−	0.0532406i	0.545399	+	0.838177i	$0.316378\pi$
$978$		0			0
$979$	3.80500e8	+	1.04542e9i	0.405515	+	1.11414i
$980$		0			0
$981$	−1.08922e8	−	6.28862e7i	−0.115374	−	0.0666114i
$982$		0			0
$983$	−8.06131e8	−	9.60710e8i	−0.848682	−	1.01142i	−0.999738	−	0.0228950i	$-0.992712\pi$
$983$	−8.06131e8	−	9.60710e8i	−0.848682	−	1.01142i	0.151056	−	0.988525i	$-0.451733\pi$
$984$		0			0
$985$	−2.76039e8	−	1.56549e9i	−0.288843	−	1.63811i
$986$		0			0
$987$		−	5.54674e8i		−	0.576881i
$988$		0			0
$989$	−1.02297e9			−1.05748
$990$		0			0
$991$	−1.08673e9	+	1.91619e8i	−1.11660	+	0.196887i	−0.701349	−	0.712818i	$-0.747418\pi$
$991$	−1.08673e9	+	1.91619e8i	−1.11660	+	0.196887i	−0.415254	+	0.909705i	$0.636307\pi$
$992$		0			0
$993$	−2.30184e8	+	1.93147e8i	−0.235086	+	0.197261i
$994$		0			0
$995$	−3.18576e7	+	5.51790e7i	−0.0323403	+	0.0560150i
$996$		0			0
$997$	1.84117e8	−	6.70130e7i	0.185784	−	0.0676198i	−0.247453	−	0.968900i	$-0.579594\pi$
$997$	1.84117e8	−	6.70130e7i	0.185784	−	0.0676198i	0.433237	+	0.901280i	$0.357371\pi$
$998$		0			0
$999$	−4.74671e8	−	8.22154e8i	−0.476098	−	0.824626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.53.8	yes	60
19.14	odd	18	inner	76.7.j.a.33.8	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.8	✓	60	19.14	odd	18	inner
76.7.j.a.53.8	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(30.7547 - 5.42288i) q^{3} +(-106.252 + 89.1559i) q^{5} +(-115.766 + 200.512i) q^{7} +(231.408 - 84.2256i) q^{9} +O(q^{10})\)	\(q+(30.7547 - 5.42288i) q^{3} +(-106.252 + 89.1559i) q^{5} +(-115.766 + 200.512i) q^{7} +(231.408 - 84.2256i) q^{9} +(-1120.76 - 1941.22i) q^{11} +(-4192.44 - 739.240i) q^{13} +(-2784.26 + 3318.15i) q^{15} +(3106.86 + 1130.80i) q^{17} +(4419.48 - 5245.39i) q^{19} +(-2472.99 + 6794.48i) q^{21} +(-5695.37 - 4778.98i) q^{23} +(627.432 - 3558.35i) q^{25} +(-13055.8 + 7537.79i) q^{27} +(14107.7 + 38760.5i) q^{29} +(-39912.0 - 23043.2i) q^{31} +(-44995.7 - 53623.8i) q^{33} +(-5576.52 - 31626.0i) q^{35} +62972.2i q^{37} -132946. q^{39} +(-60966.8 + 10750.1i) q^{41} +(105402. - 88442.6i) q^{43} +(-17078.3 + 29580.5i) q^{45} +(-72086.3 + 26237.3i) q^{47} +(32021.1 + 55462.1i) q^{49} +(101683. + 17929.4i) q^{51} +(21190.6 - 25254.0i) q^{53} +(292154. + 106335. i) q^{55} +(107475. - 185287. i) q^{57} +(-58629.8 + 161084. i) q^{59} +(-73364.7 - 61560.3i) q^{61} +(-9900.86 + 56150.6i) q^{63} +(511362. - 295235. i) q^{65} +(144648. + 397418. i) q^{67} +(-201075. - 116091. i) q^{69} +(-209882. - 250128. i) q^{71} +(19599.9 + 111156. i) q^{73} -112838. i q^{75} +518984. q^{77} +(591695. - 104332. i) q^{79} +(-498174. + 418018. i) q^{81} +(159557. - 276360. i) q^{83} +(-430928. + 156845. i) q^{85} +(644070. + 1.11556e6i) q^{87} +(-488777. - 86184.6i) q^{89} +(633568. - 755057. i) q^{91} +(-1.35244e6 - 492249. i) q^{93} +(-1920.23 + 951355. i) q^{95} +(474540. - 1.30379e6i) q^{97} +(-422854. - 354817. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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