LMFDB - Embedded newform 76.7.j.a.21.8

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			21.8
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(18.3534 - 21.8727i) q^{3} +(-6.18195 + 2.25005i) q^{5} +(237.753 + 411.801i) q^{7} +(-14.9788 - 84.9490i) q^{9} +O(q^{10})$	\(q+(18.3534 - 21.8727i) q^{3} +(-6.18195 + 2.25005i) q^{5} +(237.753 + 411.801i) q^{7} +(-14.9788 - 84.9490i) q^{9} +(-392.040 + 679.033i) q^{11} +(2328.74 + 2775.28i) q^{13} +(-64.2450 + 176.512i) q^{15} +(1030.34 - 5843.34i) q^{17} +(6818.69 - 742.507i) q^{19} +(13370.7 + 2357.62i) q^{21} +(-18733.7 - 6818.51i) q^{23} +(-11936.3 + 10015.7i) q^{25} +(15893.3 + 9176.00i) q^{27} +(36753.1 - 6480.56i) q^{29} +(37495.3 - 21647.9i) q^{31} +(7657.02 + 21037.5i) q^{33} +(-2396.35 - 2010.78i) q^{35} +49844.0i q^{37} +103443. q^{39} +(-41007.6 + 48871.0i) q^{41} +(33920.9 - 12346.2i) q^{43} +(283.738 + 491.448i) q^{45} +(12181.4 + 69084.1i) q^{47} +(-54228.6 + 93926.7i) q^{49} +(-108899. - 129781. i) q^{51} +(58673.4 - 161204. i) q^{53} +(895.716 - 5079.86i) q^{55} +(108905. - 162771. i) q^{57} +(-371365. - 65481.6i) q^{59} +(-85938.1 - 31278.9i) q^{61} +(31420.8 - 26365.2i) q^{63} +(-20640.6 - 11916.9i) q^{65} +(104964. - 18508.0i) q^{67} +(-492965. + 284614. i) q^{69} +(37743.4 + 103699. i) q^{71} +(-492480. - 413239. i) q^{73} +444901. i q^{75} -372835. q^{77} +(-43700.8 + 52080.6i) q^{79} +(551490. - 200726. i) q^{81} +(184974. + 320385. i) q^{83} +(6778.29 + 38441.6i) q^{85} +(532795. - 922828. i) q^{87} +(33813.4 + 40297.3i) q^{89} +(-589197. + 1.61881e6i) q^{91} +(214666. - 1.21743e6i) q^{93} +(-40482.2 + 19932.5i) q^{95} +(-891260. - 157153. i) q^{97} +(63555.4 + 23132.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	18.3534	−	21.8727i	0.679754	−	0.810099i	−0.310322	−	0.950631i	$-0.600437\pi$
$3$	18.3534	−	21.8727i	0.679754	−	0.810099i	0.990076	+	0.140532i	$0.0448814\pi$
$4$		0			0
$5$	−6.18195	+	2.25005i	−0.0494556	+	0.0180004i	−0.366630	−	0.930367i	$-0.619488\pi$
$5$	−6.18195	+	2.25005i	−0.0494556	+	0.0180004i	0.317174	+	0.948367i	$0.397266\pi$
$6$		0			0
$7$	237.753	+	411.801i	0.693158	+	1.20058i	0.970798	+	0.239899i	$0.0771145\pi$
$7$	237.753	+	411.801i	0.693158	+	1.20058i	−0.277640	+	0.960685i	$0.589552\pi$
$8$		0			0
$9$	−14.9788	−	84.9490i	−0.0205470	−	0.116528i
$10$		0			0
$11$	−392.040	+	679.033i	−0.294545	+	0.510167i	−0.974879	−	0.222735i	$-0.928501\pi$
$11$	−392.040	+	679.033i	−0.294545	+	0.510167i	0.680334	+	0.732902i	$0.261835\pi$
$12$		0			0
$13$	2328.74	+	2775.28i	1.05996	+	1.26321i	0.963452	+	0.267881i	$0.0863234\pi$
$13$	2328.74	+	2775.28i	1.05996	+	1.26321i	0.0965095	+	0.995332i	$0.469232\pi$
$14$		0			0
$15$	−64.2450	+	176.512i	−0.0190356	+	0.0522998i
$16$		0			0
$17$	1030.34	−	5843.34i	0.209717	−	1.18936i	−0.680126	−	0.733095i	$-0.738075\pi$
$17$	1030.34	−	5843.34i	0.209717	−	1.18936i	0.889843	−	0.456268i	$-0.150814\pi$
$18$		0			0
$19$	6818.69	−	742.507i	0.994123	−	0.108253i
$19$	6818.69	−	742.507i	0.994123	−	0.108253i
$20$		0			0
$21$	13370.7	+	2357.62i	1.44377	+	0.254575i
$22$		0			0
$23$	−18733.7	−	6818.51i	−1.53971	−	0.560410i	−0.573737	−	0.819039i	$-0.694507\pi$
$23$	−18733.7	−	6818.51i	−1.53971	−	0.560410i	−0.965977	+	0.258629i	$0.916729\pi$
$24$		0			0
$25$	−11936.3	+	10015.7i	−0.763923	+	0.641007i
$26$		0			0
$27$	15893.3	+	9176.00i	0.807464	+	0.466189i
$28$		0			0
$29$	36753.1	−	6480.56i	1.50695	−	0.265716i	0.641662	−	0.766987i	$-0.278245\pi$
$29$	36753.1	−	6480.56i	1.50695	−	0.265716i	0.865290	+	0.501271i	$0.167134\pi$
$30$		0			0
$31$	37495.3	−	21647.9i	1.25861	−	0.726659i	0.285807	−	0.958287i	$-0.407739\pi$
$31$	37495.3	−	21647.9i	1.25861	−	0.726659i	0.972804	+	0.231628i	$0.0744052\pi$
$32$		0			0
$33$	7657.02	+	21037.5i	0.213068	+	0.585399i
$34$		0			0
$35$	−2396.35	−	2010.78i	−0.0558915	−	0.0468986i
$36$		0			0
$37$			49844.0i			0.984029i	0.870587	+	0.492014i	$0.163739\pi$
$37$			49844.0i			0.984029i	−0.870587	+	0.492014i	$0.836261\pi$
$38$		0			0
$39$	103443.			1.74384
$40$		0			0
$41$	−41007.6	+	48871.0i	−0.594994	+	0.709087i	−0.976558	−	0.215256i	$-0.930941\pi$
$41$	−41007.6	+	48871.0i	−0.594994	+	0.709087i	0.381563	+	0.924343i	$0.375386\pi$
$42$		0			0
$43$	33920.9	−	12346.2i	0.426641	−	0.155284i	−0.119770	−	0.992802i	$-0.538216\pi$
$43$	33920.9	−	12346.2i	0.426641	−	0.155284i	0.546411	+	0.837517i	$0.315994\pi$
$44$		0			0
$45$	283.738	+	491.448i	0.00311372	+	0.00539312i
$46$		0			0
$47$	12181.4	+	69084.1i	0.117329	+	0.665403i	0.985571	+	0.169263i	$0.0541387\pi$
$47$	12181.4	+	69084.1i	0.117329	+	0.665403i	−0.868242	+	0.496140i	$0.834750\pi$
$48$		0			0
$49$	−54228.6	+	93926.7i	−0.460936	+	0.798364i
$50$		0			0
$51$	−108899.	−	129781.i	−0.820946	−	0.978365i
$52$		0			0
$53$	58673.4	−	161204.i	0.394106	−	1.08280i	−0.571002	−	0.820948i	$-0.693445\pi$
$53$	58673.4	−	161204.i	0.394106	−	1.08280i	0.965109	−	0.261850i	$-0.0843325\pi$
$54$		0			0
$55$	895.716	−	5079.86i	0.00538372	−	0.0305326i
$56$		0			0
$57$	108905.	−	162771.i	0.588063	−	0.878924i
$58$		0			0
$59$	−371365.	−	65481.6i	−1.80819	−	0.318833i	−0.835248	−	0.549874i	$-0.814676\pi$
$59$	−371365.	−	65481.6i	−1.80819	−	0.318833i	−0.972944	+	0.231041i	$0.925787\pi$
$60$		0			0
$61$	−85938.1	−	31278.9i	−0.378614	−	0.137804i	0.145701	−	0.989329i	$-0.453456\pi$
$61$	−85938.1	−	31278.9i	−0.378614	−	0.137804i	−0.524315	+	0.851525i	$0.675678\pi$
$62$		0			0
$63$	31420.8	−	26365.2i	0.125660	−	0.105441i
$64$		0			0
$65$	−20640.6	−	11916.9i	−0.0751594	−	0.0433933i
$66$		0			0
$67$	104964.	−	18508.0i	0.348993	−	0.0615370i	0.00359617	−	0.999994i	$-0.498855\pi$
$67$	104964.	−	18508.0i	0.348993	−	0.0615370i	0.345397	+	0.938457i	$0.387744\pi$
$68$		0			0
$69$	−492965.	+	284614.i	−1.50061	+	0.866380i
$70$		0			0
$71$	37743.4	+	103699.i	0.105455	+	0.289735i	0.981186	−	0.193064i	$-0.0618425\pi$
$71$	37743.4	+	103699.i	0.105455	+	0.289735i	−0.875731	+	0.482799i	$0.839620\pi$
$72$		0			0
$73$	−492480.	−	413239.i	−1.26596	−	1.06227i	−0.995021	−	0.0996693i	$-0.968222\pi$
$73$	−492480.	−	413239.i	−1.26596	−	1.06227i	−0.270939	−	0.962597i	$-0.587334\pi$
$74$		0			0
$75$			444901.i			1.05458i
$76$		0			0
$77$	−372835.			−0.816665
$78$		0			0
$79$	−43700.8	+	52080.6i	−0.0886356	+	0.105632i	−0.808539	−	0.588442i	$-0.799741\pi$
$79$	−43700.8	+	52080.6i	−0.0886356	+	0.105632i	0.719904	+	0.694074i	$0.244186\pi$
$80$		0			0
$81$	551490.	−	200726.i	1.03773	−	0.377701i
$82$		0			0
$83$	184974.	+	320385.i	0.323502	+	0.560322i	0.981208	−	0.192953i	$-0.0618065\pi$
$83$	184974.	+	320385.i	0.323502	+	0.560322i	−0.657706	+	0.753275i	$0.728473\pi$
$84$		0			0
$85$	6778.29	+	38441.6i	0.0110373	+	0.0625957i
$86$		0			0
$87$	532795.	−	922828.i	0.809100	−	1.40140i
$88$		0			0
$89$	33813.4	+	40297.3i	0.0479644	+	0.0571618i	0.789493	−	0.613759i	$-0.210343\pi$
$89$	33813.4	+	40297.3i	0.0479644	+	0.0571618i	−0.741529	+	0.670921i	$0.765899\pi$
$90$		0			0
$91$	−589197.	+	1.61881e6i	−0.781873	+	2.14818i
$92$		0			0
$93$	214666.	−	1.21743e6i	0.266880	−	1.51355i
$94$		0			0
$95$	−40482.2	+	19932.5i	−0.0472164	+	0.0232483i
$96$		0			0
$97$	−891260.	−	157153.i	−0.976538	−	0.172190i	−0.337467	−	0.941338i	$-0.609570\pi$
$97$	−891260.	−	157153.i	−0.976538	−	0.172190i	−0.639071	+	0.769148i	$0.720681\pi$
$98$		0			0
$99$	63555.4	+	23132.3i	0.0655009	+	0.0238404i
$100$		0			0
$101$	−410766.	+	344673.i	−0.398685	+	0.334536i	−0.819985	−	0.572385i	$-0.806018\pi$
$101$	−410766.	+	344673.i	−0.398685	+	0.334536i	0.421300	+	0.906921i	$0.361574\pi$
$102$		0			0
$103$	996344.	+	575240.i	0.911796	+	0.526426i	0.881009	−	0.473100i	$-0.156865\pi$
$103$	996344.	+	575240.i	0.911796	+	0.526426i	0.0307876	+	0.999526i	$0.490198\pi$
$104$		0			0
$105$	−87962.1	+	15510.1i	−0.0759850	+	0.0133982i
$106$		0			0
$107$	1.40683e6	−	812231.i	1.14839	−	0.663023i	0.199895	−	0.979817i	$-0.435940\pi$
$107$	1.40683e6	−	812231.i	1.14839	−	0.663023i	0.948494	+	0.316795i	$0.102607\pi$
$108$		0			0
$109$	−650653.	−	1.78765e6i	−0.502424	−	1.38040i	−0.888901	−	0.458099i	$-0.848531\pi$
$109$	−650653.	−	1.78765e6i	−0.502424	−	1.38040i	0.386478	−	0.922299i	$-0.373692\pi$
$110$		0			0
$111$	1.09022e6	+	914805.i	0.797161	+	0.668897i
$112$		0			0
$113$			456664.i			0.316491i	0.987400	+	0.158246i	$0.0505838\pi$
$113$			456664.i			0.316491i	−0.987400	+	0.158246i	$0.949416\pi$
$114$		0			0
$115$	131153.			0.0862351
$116$		0			0
$117$	200875.	−	239394.i	0.125421	−	0.149471i
$118$		0			0
$119$	2.65126e6	−	964979.i	1.57330	−	0.572634i
$120$		0			0
$121$	578390.	+	1.00180e6i	0.326486	+	0.565491i
$122$		0			0
$123$	316312.	+	1.79389e6i	0.169981	+	0.964009i
$124$		0			0
$125$	102650.	−	177795.i	0.0525567	−	0.0910309i
$126$		0			0
$127$	−438701.	−	522823.i	−0.214169	−	0.255237i	0.648255	−	0.761424i	$-0.275499\pi$
$127$	−438701.	−	522823.i	−0.214169	−	0.255237i	−0.862424	+	0.506187i	$0.831055\pi$
$128$		0			0
$129$	352518.	−	968535.i	0.164215	−	0.451176i
$130$		0			0
$131$	−541898.	+	3.07326e6i	−0.241048	+	1.36705i	0.588446	+	0.808536i	$0.299740\pi$
$131$	−541898.	+	3.07326e6i	−0.241048	+	1.36705i	−0.829494	+	0.558515i	$0.811371\pi$
$132$		0			0
$133$	1.92693e6	+	2.63141e6i	0.819051	+	1.11849i
$134$		0			0
$135$	−118898.	−	20964.9i	−0.0483252	−	0.00852104i
$136$		0			0
$137$	−1.16260e6	−	423153.i	−0.452137	−	0.164564i	0.105907	−	0.994376i	$-0.466226\pi$
$137$	−1.16260e6	−	423153.i	−0.452137	−	0.164564i	−0.558043	+	0.829812i	$0.688448\pi$
$138$		0			0
$139$	2.62458e6	−	2.20228e6i	0.977272	−	0.820029i	−0.00640341	−	0.999979i	$-0.502038\pi$
$139$	2.62458e6	−	2.20228e6i	0.977272	−	0.820029i	0.983676	+	0.179951i	$0.0575938\pi$
$140$		0			0
$141$	1.73462e6	+	1.00149e6i	0.618797	+	0.357263i
$142$		0			0
$143$	−2.79746e6	+	493268.i	−0.956656	+	0.168684i
$144$		0			0
$145$	−212624.	+	122759.i	−0.0697443	+	0.0402669i
$146$		0			0
$147$	1.05915e6	+	2.91000e6i	0.333431	+	0.916094i
$148$		0			0
$149$	−4.45056e6	−	3.73446e6i	−1.34541	−	1.12894i	−0.980200	−	0.198012i	$-0.936551\pi$
$149$	−4.45056e6	−	3.73446e6i	−1.34541	−	1.12894i	−0.365214	−	0.930924i	$-0.619004\pi$
$150$		0			0
$151$			2.34183e6i			0.680182i	0.940393	+	0.340091i	$0.110458\pi$
$151$			2.34183e6i			0.680182i	−0.940393	+	0.340091i	$0.889542\pi$
$152$		0			0
$153$	−511819.			−0.142903
$154$		0			0
$155$	−183085.	+	218193.i	−0.0491653	+	0.0585929i
$156$		0			0
$157$	−1.27175e6	+	462879.i	−0.328627	+	0.119610i	−0.501064	−	0.865410i	$-0.667058\pi$
$157$	−1.27175e6	+	462879.i	−0.328627	+	0.119610i	0.172438	+	0.985020i	$0.444836\pi$
$158$		0			0
$159$	−2.44910e6	−	4.24197e6i	−0.609279	−	1.05530i
$160$		0			0
$161$	−1.64613e6	−	9.33567e6i	−0.394445	−	2.23701i
$162$		0			0
$163$	1.29851e6	−	2.24908e6i	0.299835	−	0.519329i	−0.676263	−	0.736660i	$-0.736402\pi$
$163$	1.29851e6	−	2.24908e6i	0.299835	−	0.519329i	0.976098	+	0.217331i	$0.0697352\pi$
$164$		0			0
$165$	−94670.7	−	112824.i	−0.0210748	−	0.0251160i
$166$		0			0
$167$	2.30069e6	−	6.32110e6i	0.493980	−	1.35720i	−0.403029	−	0.915187i	$-0.632043\pi$
$167$	2.30069e6	−	6.32110e6i	0.493980	−	1.35720i	0.897009	−	0.442012i	$-0.145735\pi$
$168$		0			0
$169$	−1.44100e6	+	8.17230e6i	−0.298540	+	1.69311i
$170$		0			0
$171$	−165211.	−	568119.i	−0.0330408	−	0.113619i
$172$		0			0
$173$	−71303.0	−	12572.6i	−0.0137711	−	0.00242822i	0.166758	−	0.985998i	$-0.446670\pi$
$173$	−71303.0	−	12572.6i	−0.0137711	−	0.00242822i	−0.180529	+	0.983570i	$0.557781\pi$
$174$		0			0
$175$	−6.96238e6	−	2.53410e6i	−1.29910	−	0.472835i
$176$		0			0
$177$	−8.24804e6	+	6.92093e6i	−1.48741	+	1.24809i
$178$		0			0
$179$	−2.93846e6	−	1.69652e6i	−0.512343	−	0.295801i	0.221453	−	0.975171i	$-0.428920\pi$
$179$	−2.93846e6	−	1.69652e6i	−0.512343	−	0.295801i	−0.733796	+	0.679370i	$0.762253\pi$
$180$		0			0
$181$	−5.92700e6	+	1.04509e6i	−0.999537	+	0.176245i	−0.649395	−	0.760451i	$-0.724978\pi$
$181$	−5.92700e6	+	1.04509e6i	−0.999537	+	0.176245i	−0.350142	+	0.936697i	$0.613867\pi$
$182$		0			0
$183$	−2.26141e6	+	1.30562e6i	−0.368999	+	0.213042i
$184$		0			0
$185$	−112151.	−	308133.i	−0.0177129	−	0.0486658i
$186$		0			0
$187$	3.56388e6	+	2.99045e6i	0.545003	+	0.457312i
$188$		0			0
$189$			8.72650e6i			1.29257i
$190$		0			0
$191$	8.23262e6			1.18151			0.590756	−	0.806851i	$-0.298830\pi$
$191$	8.23262e6			1.18151			0.590756	+	0.806851i	$0.298830\pi$
$192$		0			0
$193$	6.83521e6	−	8.14588e6i	0.950779	−	1.13309i	−0.0402148	−	0.999191i	$-0.512804\pi$
$193$	6.83521e6	−	8.14588e6i	0.950779	−	1.13309i	0.990994	−	0.133904i	$-0.0427513\pi$
$194$		0			0
$195$	−639479.	+	232751.i	−0.0862427	+	0.0313898i
$196$		0			0
$197$	−7.35895e6	−	1.27461e7i	−0.962536	−	1.66716i	−0.716095	−	0.698003i	$-0.754072\pi$
$197$	−7.35895e6	−	1.27461e7i	−0.962536	−	1.66716i	−0.246441	−	0.969158i	$-0.579261\pi$
$198$		0			0
$199$	62091.5	+	352139.i	0.00787904	+	0.0446842i	0.988494	−	0.151261i	$-0.0483335\pi$
$199$	62091.5	+	352139.i	0.00787904	+	0.0446842i	−0.980615	+	0.195946i	$0.937222\pi$
$200$		0			0
$201$	1.52163e6	−	2.63553e6i	0.187379	−	0.324549i
$202$		0			0
$203$	1.14069e7	+	1.35942e7i	1.36357	+	1.62504i
$204$		0			0
$205$	143545.	−	394387.i	0.0166620	−	0.0457784i
$206$		0			0
$207$	−298617.	+	1.69354e6i	−0.0336669	+	0.190935i
$208$		0			0
$209$	−2.16901e6	+	4.92121e6i	−0.237587	+	0.539055i
$210$		0			0
$211$	−7.03121e6	−	1.23979e6i	−0.748484	−	0.131978i	−0.213621	−	0.976917i	$-0.568526\pi$
$211$	−7.03121e6	−	1.23979e6i	−0.748484	−	0.131978i	−0.534863	+	0.844939i	$0.679637\pi$
$212$		0			0
$213$	2.96090e6	+	1.07768e6i	0.306397	+	0.111519i
$214$		0			0
$215$	−181918.	+	152647.i	−0.0183046	+	0.0153594i
$216$		0			0
$217$	1.78292e7	+	1.02937e7i	1.74483	+	1.00738i
$218$		0			0
$219$	−1.80773e7	+	3.18752e6i	−1.72108	+	0.303473i
$220$		0			0
$221$	1.86163e7	−	1.07481e7i	1.72471	−	0.995762i
$222$		0			0
$223$	−1.43991e6	−	3.95612e6i	−0.129844	−	0.356743i	0.857686	−	0.514173i	$-0.171901\pi$
$223$	−1.43991e6	−	3.95612e6i	−0.129844	−	0.356743i	−0.987530	+	0.157431i	$0.949679\pi$
$224$		0			0
$225$	1.02962e6	+	863952.i	0.0903917	+	0.0758476i
$226$		0			0
$227$		−	3.02821e6i		−	0.258886i	−0.991587	−	0.129443i	$-0.958681\pi$
$227$		−	3.02821e6i		−	0.258886i	0.991587	−	0.129443i	$-0.0413189\pi$
$228$		0			0
$229$	−8.92393e6			−0.743104			−0.371552	−	0.928412i	$-0.621174\pi$
$229$	−8.92393e6			−0.743104			−0.371552	+	0.928412i	$0.621174\pi$
$230$		0			0
$231$	−6.84277e6	+	8.15489e6i	−0.555131	+	0.661580i
$232$		0			0
$233$	9.64294e6	−	3.50974e6i	0.762328	−	0.277465i	0.0685440	−	0.997648i	$-0.478165\pi$
$233$	9.64294e6	−	3.50974e6i	0.762328	−	0.277465i	0.693784	+	0.720184i	$0.255942\pi$
$234$		0			0
$235$	−230747.	−	399666.i	−0.0177801	−	0.0307960i
$236$		0			0
$237$	337085.	+	1.91171e6i	0.0253218	+	0.143607i
$238$		0			0
$239$	1.16435e7	−	2.01672e7i	0.852887	−	1.47724i	−0.0257050	−	0.999670i	$-0.508183\pi$
$239$	1.16435e7	−	2.01672e7i	0.852887	−	1.47724i	0.878592	−	0.477574i	$-0.158484\pi$
$240$		0			0
$241$	−2.47086e6	−	2.94466e6i	−0.176521	−	0.210370i	0.670528	−	0.741884i	$-0.266068\pi$
$241$	−2.47086e6	−	2.94466e6i	−0.176521	−	0.210370i	−0.847049	+	0.531514i	$0.821623\pi$
$242$		0			0
$243$	1.15552e6	−	3.17477e6i	0.0805303	−	0.221255i
$244$		0			0
$245$	123899.	−	702668.i	0.00842501	−	0.0477806i
$246$		0			0
$247$	1.79396e7	+	1.71947e7i	1.19048	+	1.14105i
$248$		0			0
$249$	1.04026e7	+	1.83425e6i	0.673817	+	0.118812i
$250$		0			0
$251$	1.12273e7	+	4.08641e6i	0.709995	+	0.258417i	0.671672	−	0.740848i	$-0.265576\pi$
$251$	1.12273e7	+	4.08641e6i	0.709995	+	0.258417i	0.0383225	+	0.999265i	$0.487799\pi$
$252$		0			0
$253$	1.19743e7	−	1.00477e7i	0.739418	−	0.620446i
$254$		0			0
$255$	965224.	+	557273.i	0.0582114	+	0.0336083i
$256$		0			0
$257$	−6.44601e6	+	1.13661e6i	−0.379745	+	0.0669592i	−0.360262	−	0.932851i	$-0.617313\pi$
$257$	−6.44601e6	+	1.13661e6i	−0.379745	+	0.0669592i	−0.0194821	+	0.999810i	$0.506202\pi$
$258$		0			0
$259$	−2.05258e7	+	1.18506e7i	−1.18141	+	0.682087i
$260$		0			0
$261$	−1.10103e6	−	3.02506e6i	−0.0619269	−	0.170143i
$262$		0			0
$263$	−1.19563e7	−	1.00325e7i	−0.657246	−	0.551495i	0.252014	−	0.967724i	$-0.418907\pi$
$263$	−1.19563e7	−	1.00325e7i	−0.657246	−	0.551495i	−0.909260	+	0.416229i	$0.863351\pi$
$264$		0			0
$265$			1.12857e6i			0.0606445i
$266$		0			0
$267$	1.50200e6			0.0789107
$268$		0			0
$269$	3.96152e6	−	4.72115e6i	0.203519	−	0.242544i	−0.654625	−	0.755954i	$-0.727173\pi$
$269$	3.96152e6	−	4.72115e6i	0.203519	−	0.242544i	0.858144	+	0.513410i	$0.171618\pi$
$270$		0			0
$271$	2.76962e7	−	1.00806e7i	1.39159	−	0.506499i	0.465922	−	0.884826i	$-0.345723\pi$
$271$	2.76962e7	−	1.00806e7i	1.39159	−	0.506499i	0.925672	+	0.378327i	$0.123500\pi$
$272$		0			0
$273$	2.45939e7	+	4.25978e7i	1.20876	+	2.09363i
$274$		0			0
$275$	−2.12151e6	−	1.20317e7i	−0.102011	−	0.578534i
$276$		0			0
$277$	−1.74603e7	+	3.02421e7i	−0.821508	+	1.42289i	0.0830517	+	0.996545i	$0.473533\pi$
$277$	−1.74603e7	+	3.02421e7i	−0.821508	+	1.42289i	−0.904559	+	0.426348i	$0.859800\pi$
$278$		0			0
$279$	−2.40060e6	−	2.86093e6i	−0.110537	−	0.131733i
$280$		0			0
$281$	591062.	−	1.62393e6i	0.0266388	−	0.0731895i	−0.925660	−	0.378355i	$-0.876490\pi$
$281$	591062.	−	1.62393e6i	0.0266388	−	0.0731895i	0.952299	+	0.305166i	$0.0987119\pi$
$282$		0			0
$283$	−1.75578e6	+	9.95751e6i	−0.0774658	+	0.439331i	0.921264	+	0.388939i	$0.127158\pi$
$283$	−1.75578e6	+	9.95751e6i	−0.0774658	+	0.439331i	−0.998730	+	0.0503920i	$0.983953\pi$
$284$		0			0
$285$	−307006.	+	1.25128e6i	−0.0132621	+	0.0540531i
$286$		0			0
$287$	−2.98748e7	−	5.26773e6i	−1.26374	−	0.222832i
$288$		0			0
$289$	−1.04011e7	−	3.78570e6i	−0.430911	−	0.156839i
$290$		0			0
$291$	−1.97950e7	+	1.66099e7i	−0.803296	+	0.674046i
$292$		0			0
$293$	−4.52660e6	−	2.61343e6i	−0.179957	−	0.103898i	0.407315	−	0.913288i	$-0.366465\pi$
$293$	−4.52660e6	−	2.61343e6i	−0.179957	−	0.103898i	−0.587273	+	0.809389i	$0.699798\pi$
$294$		0			0
$295$	2.44310e6	−	430784.i	0.0951644	−	0.0167800i
$296$		0			0
$297$	−1.24616e7	+	7.19472e6i	−0.475669	+	0.274628i
$298$		0			0
$299$	−2.47026e7	−	6.78698e7i	−0.924120	−	2.53900i
$300$		0			0
$301$	1.31490e7	+	1.10333e7i	0.482161	+	0.404582i
$302$		0			0
$303$			1.53105e7i			0.550377i
$304$		0			0
$305$	601645.			0.0212051
$306$		0			0
$307$	4.77913e6	−	5.69555e6i	0.165171	−	0.196843i	−0.677110	−	0.735882i	$-0.736768\pi$
$307$	4.77913e6	−	5.69555e6i	0.165171	−	0.196843i	0.842281	+	0.539039i	$0.181212\pi$
$308$		0			0
$309$	3.08683e7	−	1.12351e7i	1.04625	−	0.380805i
$310$		0			0
$311$	−1.50696e7	−	2.61013e7i	−0.500979	−	0.867721i	−0.999999	−	0.00113090i	$-0.999640\pi$
$311$	−1.50696e7	−	2.61013e7i	−0.500979	−	0.867721i	0.499020	−	0.866590i	$-0.333693\pi$
$312$		0			0
$313$	145431.	+	824778.i	0.00474267	+	0.0268970i	0.987087	−	0.160183i	$-0.0512086\pi$
$313$	145431.	+	824778.i	0.00474267	+	0.0268970i	−0.982345	+	0.187080i	$0.940097\pi$
$314$		0			0
$315$	−134919.	+	233687.i	−0.00431660	+	0.00747656i
$316$		0			0
$317$	−4.33024e6	−	5.16058e6i	−0.135936	−	0.162002i	0.693782	−	0.720185i	$-0.255943\pi$
$317$	−4.33024e6	−	5.16058e6i	−0.135936	−	0.162002i	−0.829718	+	0.558183i	$0.811499\pi$
$318$		0			0
$319$	−1.00081e7	+	2.74972e7i	−0.308306	+	0.847063i
$320$		0			0
$321$	8.05430e6	−	4.56782e7i	0.243508	−	1.38100i
$322$		0			0
$323$	2.68684e6	−	4.06090e7i	0.0797322	−	1.20508i
$324$		0			0
$325$	−5.55929e7	−	9.80253e6i	−1.61946	−	0.285554i
$326$		0			0
$327$	−5.10424e7	−	1.85779e7i	−1.45978	−	0.531317i
$328$		0			0
$329$	−2.55527e7	+	2.14413e7i	−0.717546	+	0.602092i
$330$		0			0
$331$	−4.15027e7	−	2.39616e7i	−1.14444	−	0.660742i	−0.196912	−	0.980421i	$-0.563091\pi$
$331$	−4.15027e7	−	2.39616e7i	−1.14444	−	0.660742i	−0.947526	+	0.319680i	$0.896425\pi$
$332$		0			0
$333$	4.23420e6	−	746604.i	0.114667	−	0.0202189i
$334$		0			0
$335$	−607241.	+	350591.i	−0.0161520	+	0.00932536i
$336$		0			0
$337$	2.27842e7	+	6.25991e7i	0.595311	+	1.63560i	0.760496	+	0.649342i	$0.224956\pi$
$337$	2.27842e7	+	6.25991e7i	0.595311	+	1.63560i	−0.165185	+	0.986263i	$0.552822\pi$
$338$		0			0
$339$	9.98847e6	+	8.38132e6i	0.256389	+	0.215136i
$340$		0			0
$341$			3.39474e7i			0.856136i
$342$		0			0
$343$	4.37074e6			0.108311
$344$		0			0
$345$	2.40709e6	−	2.86866e6i	0.0586187	−	0.0698590i
$346$		0			0
$347$	−5.68533e6	+	2.06929e6i	−0.136072	+	0.0495260i	−0.409158	−	0.912463i	$-0.634178\pi$
$347$	−5.68533e6	+	2.06929e6i	−0.136072	+	0.0495260i	0.273087	+	0.961989i	$0.411955\pi$
$348$		0			0
$349$	−6.65650e6	−	1.15294e7i	−0.156592	−	0.271225i	0.777046	−	0.629444i	$-0.216717\pi$
$349$	−6.65650e6	−	1.15294e7i	−0.156592	−	0.271225i	−0.933638	+	0.358219i	$0.883384\pi$
$350$		0			0
$351$	1.15453e7	+	6.54768e7i	0.266984	+	1.51414i
$352$		0			0
$353$	−1.12852e7	+	1.95466e7i	−0.256558	+	0.444372i	−0.965318	−	0.261078i	$-0.915922\pi$
$353$	−1.12852e7	+	1.95466e7i	−0.256558	+	0.444372i	0.708759	+	0.705450i	$0.249255\pi$
$354$		0			0
$355$	−466656.	−	556140.i	−0.0104307	−	0.0124308i
$356$		0			0
$357$	2.75528e7	−	7.57007e7i	0.605565	−	1.66378i
$358$		0			0
$359$	4.90389e6	−	2.78114e7i	0.105988	−	0.601089i	−0.884833	−	0.465909i	$-0.845727\pi$
$359$	4.90389e6	−	2.78114e7i	0.105988	−	0.601089i	0.990821	−	0.135180i	$-0.0431614\pi$
$360$		0			0
$361$	4.59432e7	−	1.01259e7i	0.976563	−	0.215234i
$362$		0			0
$363$	3.25275e7	+	5.73547e6i	0.680034	+	0.119908i
$364$		0			0
$365$	3.97430e6	+	1.44653e6i	0.0817300	+	0.0297473i
$366$		0			0
$367$	−2.53010e6	+	2.12301e6i	−0.0511847	+	0.0429491i	−0.668021	−	0.744142i	$-0.732858\pi$
$367$	−2.53010e6	+	2.12301e6i	−0.0511847	+	0.0429491i	0.616836	+	0.787091i	$0.288414\pi$
$368$		0			0
$369$	4.76578e6	+	2.75153e6i	0.0948539	+	0.0547639i
$370$		0			0
$371$	8.03336e7	−	1.41650e7i	1.57317	−	0.277392i
$372$		0			0
$373$	−4.59816e7	+	2.65475e7i	−0.886048	+	0.511560i	−0.872648	−	0.488350i	$-0.837599\pi$
$373$	−4.59816e7	+	2.65475e7i	−0.886048	+	0.511560i	−0.0134005	+	0.999910i	$0.504266\pi$
$374$		0			0
$375$	−2.00488e6	−	5.50835e6i	−0.0380184	−	0.104455i
$376$		0			0
$377$	1.03574e8	+	8.69085e7i	1.93297	+	1.62195i
$378$		0			0
$379$		−	2.14091e7i		−	0.393262i	−0.980478	−	0.196631i	$-0.937000\pi$
$379$		−	2.14091e7i		−	0.393262i	0.980478	−	0.196631i	$-0.0630001\pi$
$380$		0			0
$381$	−1.94872e7			−0.352350
$382$		0			0
$383$	−2.66465e7	+	3.17561e7i	−0.474291	+	0.565238i	−0.949150	−	0.314824i	$-0.898054\pi$
$383$	−2.66465e7	+	3.17561e7i	−0.474291	+	0.565238i	0.474859	+	0.880062i	$0.342499\pi$
$384$		0			0
$385$	2.30485e6	−	838896.i	0.0403887	−	0.0147003i
$386$		0			0
$387$	−1.55689e6	−	2.69662e6i	−0.0268612	−	0.0465250i
$388$		0			0
$389$	−1.19474e7	−	6.77573e7i	−0.202967	−	1.15109i	−0.900606	−	0.434636i	$-0.856877\pi$
$389$	−1.19474e7	−	6.77573e7i	−0.202967	−	1.15109i	0.697639	−	0.716449i	$-0.254234\pi$
$390$		0			0
$391$	−5.91449e7	+	1.02442e8i	−0.989435	+	1.71375i
$392$		0			0
$393$	5.72747e7	+	6.82573e7i	0.943594	+	1.12453i
$394$		0			0
$395$	152973.	−	420289.i	0.00248212	−	0.00681956i
$396$		0			0
$397$	1.06558e7	−	6.04319e7i	0.170300	−	0.965817i	−0.773131	−	0.634246i	$-0.781310\pi$
$397$	1.06558e7	−	6.04319e7i	0.170300	−	0.965817i	0.943431	−	0.331570i	$-0.107578\pi$
$398$		0			0
$399$	9.29216e7	+	6.14803e6i	1.46284	+	0.0967870i
$400$		0			0
$401$	−1.79468e7	−	3.16450e6i	−0.278325	−	0.0490763i	0.0327430	−	0.999464i	$-0.489576\pi$
$401$	−1.79468e7	−	3.16450e6i	−0.278325	−	0.0490763i	−0.311068	+	0.950388i	$0.600687\pi$
$402$		0			0
$403$	1.47396e8	+	5.36476e7i	2.25200	+	0.819663i
$404$		0			0
$405$	−2.95764e6	+	2.48176e6i	−0.0445226	+	0.0373589i
$406$		0			0
$407$	−3.38457e7	−	1.95408e7i	−0.502019	−	0.289841i
$408$		0			0
$409$	−7.04487e7	+	1.24220e7i	−1.02968	+	0.181561i	−0.662870	−	0.748735i	$-0.730662\pi$
$409$	−7.04487e7	+	1.24220e7i	−1.02968	+	0.181561i	−0.366811	+	0.930295i	$0.619551\pi$
$410$		0			0
$411$	−3.05932e7	+	1.76630e7i	−0.440655	+	0.254412i
$412$		0			0
$413$	−6.13277e7	−	1.68497e8i	−0.870576	−	2.39189i
$414$		0			0
$415$	−1.86438e6	−	1.56440e6i	−0.0260850	−	0.0218879i
$416$		0			0
$417$		−	9.78259e7i		−	1.34910i
$418$		0			0
$419$	9.51816e7			1.29393			0.646965	−	0.762520i	$-0.276038\pi$
$419$	9.51816e7			1.29393			0.646965	+	0.762520i	$0.276038\pi$
$420$		0			0
$421$	−1.83274e7	+	2.18417e7i	−0.245614	+	0.292712i	−0.874741	−	0.484591i	$-0.838968\pi$
$421$	−1.83274e7	+	2.18417e7i	−0.245614	+	0.292712i	0.629126	+	0.777303i	$0.283413\pi$
$422$		0			0
$423$	5.68617e6	−	2.06959e6i	0.0751274	−	0.0273441i
$424$		0			0
$425$	4.62269e7	+	8.00674e7i	0.602183	+	1.04301i
$426$		0			0
$427$	−7.55138e6	−	4.28260e7i	−0.0969936	−	0.550078i
$428$		0			0
$429$	−4.05537e7	+	7.02411e7i	−0.513640	+	0.889650i
$430$		0			0
$431$	4.31461e7	+	5.14195e7i	0.538902	+	0.642239i	0.964941	−	0.262466i	$-0.0845358\pi$
$431$	4.31461e7	+	5.14195e7i	0.538902	+	0.642239i	−0.426039	+	0.904705i	$0.640091\pi$
$432$		0			0
$433$	4.99981e7	−	1.37369e8i	0.615871	−	1.69209i	−0.101002	−	0.994886i	$-0.532205\pi$
$433$	4.99981e7	−	1.37369e8i	0.615871	−	1.69209i	0.716873	−	0.697204i	$-0.245573\pi$
$434$		0			0
$435$	−1.21731e6	+	6.90369e6i	−0.0147888	+	0.0838714i
$436$		0			0
$437$	−1.32802e8	−	3.25834e7i	−1.59133	−	0.390438i
$438$		0			0
$439$	1.55389e8	+	2.73992e7i	1.83665	+	0.323851i	0.981045	−	0.193781i	$-0.0620750\pi$
$439$	1.55389e8	+	2.73992e7i	1.83665	+	0.323851i	0.855604	+	0.517631i	$0.173186\pi$
$440$		0			0
$441$	8.79126e6	+	3.19976e6i	0.102503	+	0.0373079i
$442$		0			0
$443$	1.43554e7	−	1.20456e7i	0.165121	−	0.138553i	−0.556483	−	0.830859i	$-0.687850\pi$
$443$	1.43554e7	−	1.20456e7i	0.165121	−	0.138553i	0.721604	+	0.692306i	$0.243405\pi$
$444$		0			0
$445$	−299704.	−	173034.i	−0.00340105	−	0.00196359i
$446$		0			0
$447$	−1.63365e8	+	2.88057e7i	−1.82910	+	0.322520i
$448$		0			0
$449$	−1.83755e7	+	1.06091e7i	−0.203002	+	0.117203i	−0.598055	−	0.801455i	$-0.704060\pi$
$449$	−1.83755e7	+	1.06091e7i	−0.203002	+	0.117203i	0.395053	+	0.918658i	$0.370726\pi$
$450$		0			0
$451$	−1.71084e7	−	4.70048e7i	−0.186500	−	0.512405i
$452$		0			0
$453$	5.12221e7	+	4.29805e7i	0.551014	+	0.462356i
$454$		0			0
$455$		−	1.13331e7i		−	0.120314i
$456$		0			0
$457$	−9.00487e7			−0.943472			−0.471736	−	0.881740i	$-0.656372\pi$
$457$	−9.00487e7			−0.943472			−0.471736	+	0.881740i	$0.656372\pi$
$458$		0			0
$459$	6.99940e7	−	8.34156e7i	0.723807	−	0.862600i
$460$		0			0
$461$	6.13607e7	−	2.23335e7i	0.626308	−	0.227957i	−0.00931573	−	0.999957i	$-0.502965\pi$
$461$	6.13607e7	−	2.23335e7i	0.626308	−	0.227957i	0.635623	+	0.771999i	$0.280743\pi$
$462$		0			0
$463$	2.61841e7	+	4.53522e7i	0.263812	+	0.456936i	0.967252	−	0.253819i	$-0.0816868\pi$
$463$	2.61841e7	+	4.53522e7i	0.263812	+	0.456936i	−0.703440	+	0.710755i	$0.748354\pi$
$464$		0			0
$465$	1.41223e6	+	8.00913e6i	0.0140458	+	0.0796575i
$466$		0			0
$467$	−8.92229e7	+	1.54539e8i	−0.876044	+	1.51735i	−0.0203966	+	0.999792i	$0.506493\pi$
$467$	−8.92229e7	+	1.54539e8i	−0.876044	+	1.51735i	−0.855647	+	0.517560i	$0.826840\pi$
$468$		0			0
$469$	3.25772e7	+	3.88240e7i	0.315788	+	0.376341i
$470$		0			0
$471$	−1.32165e7	+	3.63120e7i	−0.126489	+	0.347526i
$472$		0			0
$473$	−4.91487e6	+	2.78736e7i	−0.0464439	+	0.263396i
$474$		0			0
$475$	−7.39531e7	+	7.71570e7i	−0.690042	+	0.719937i
$476$		0			0
$477$	−1.45730e7	−	2.56960e6i	−0.134274	−	0.0236762i
$478$		0			0
$479$	2.54778e7	+	9.27316e6i	0.231822	+	0.0843764i	0.455319	−	0.890328i	$-0.349525\pi$
$479$	2.54778e7	+	9.27316e6i	0.231822	+	0.0843764i	−0.223497	+	0.974705i	$0.571747\pi$
$480$		0			0
$481$	−1.38331e8	+	1.16074e8i	−1.24304	+	1.04303i
$482$		0			0
$483$	−2.34408e8	−	1.35336e8i	−2.08033	−	1.20108i
$484$		0			0
$485$	5.86333e6	−	1.03386e6i	0.0513948	−	0.00906229i
$486$		0			0
$487$	−1.48998e7	+	8.60240e6i	−0.129001	+	0.0744788i	−0.563112	−	0.826381i	$-0.690396\pi$
$487$	−1.48998e7	+	8.60240e6i	−0.129001	+	0.0744788i	0.434111	+	0.900860i	$0.357063\pi$
$488$		0			0
$489$	−2.53615e7	−	6.96800e7i	−0.216894	−	0.595912i
$490$		0			0
$491$	1.14300e8	+	9.59091e7i	0.965610	+	0.810243i	0.981857	−	0.189625i	$-0.0607273\pi$
$491$	1.14300e8	+	9.59091e7i	0.965610	+	0.810243i	−0.0162469	+	0.999868i	$0.505172\pi$
$492$		0			0
$493$		−	2.21438e8i		−	1.84804i
$494$		0			0
$495$	−444945.			−0.00366852
$496$		0			0
$497$	−3.37298e7	+	4.01976e7i	−0.274754	+	0.327439i
$498$		0			0
$499$	−3.27668e7	+	1.19261e7i	−0.263713	+	0.0959838i	−0.470493	−	0.882404i	$-0.655924\pi$
$499$	−3.27668e7	+	1.19261e7i	−0.263713	+	0.0959838i	0.206780	+	0.978388i	$0.433702\pi$
$500$		0			0
$501$	−9.60340e7	−	1.66336e8i	−0.763681	−	1.32273i
$502$		0			0
$503$	1.14247e6	+	6.47929e6i	0.00897722	+	0.0509124i	0.988967	−	0.148134i	$-0.0473267\pi$
$503$	1.14247e6	+	6.47929e6i	0.00897722	+	0.0509124i	−0.979990	+	0.199046i	$0.936216\pi$
$504$		0			0
$505$	1.76380e6	−	3.05500e6i	0.0136954	−	0.0237212i
$506$		0			0
$507$	1.52303e8	+	1.81508e8i	1.16865	+	1.39274i
$508$		0			0
$509$	3.14749e7	−	8.64764e7i	0.238677	−	0.655759i	−0.761296	−	0.648404i	$-0.775437\pi$
$509$	3.14749e7	−	8.64764e7i	0.238677	−	0.655759i	0.999973	−	0.00735492i	$-0.00234116\pi$
$510$		0			0
$511$	5.30837e7	−	3.01052e8i	0.397831	−	2.25621i
$512$		0			0
$513$	1.15185e8	+	5.07675e7i	0.853185	+	0.376039i
$514$		0			0
$515$	−7.45367e6	−	1.31428e6i	−0.0545693	−	0.00962204i
$516$		0			0
$517$	−5.16860e7	−	1.88122e7i	−0.374025	−	0.136134i
$518$		0			0
$519$	−1.58365e6	+	1.32884e6i	−0.0113281	+	0.00950538i
$520$		0			0
$521$	−6.78516e7	−	3.91742e7i	−0.479786	−	0.277004i	0.240542	−	0.970639i	$-0.422675\pi$
$521$	−6.78516e7	−	3.91742e7i	−0.479786	−	0.277004i	−0.720327	+	0.693634i	$0.756008\pi$
$522$		0			0
$523$	−1.26434e8	+	2.22938e7i	−0.883812	+	0.155840i	−0.597090	−	0.802174i	$-0.703677\pi$
$523$	−1.26434e8	+	2.22938e7i	−0.883812	+	0.155840i	−0.286722	+	0.958014i	$0.592566\pi$
$524$		0			0
$525$	−1.83210e8	+	1.05777e8i	−1.26611	+	0.730990i
$526$		0			0
$527$	−8.78633e7	−	2.41402e8i	−0.600310	−	1.64934i
$528$		0			0
$529$	1.91057e8	+	1.60316e8i	1.29062	+	1.08296i
$530$		0			0
$531$			3.25279e7i			0.217256i
$532$		0			0
$533$	−2.31126e8			−1.52640
$534$		0			0
$535$	−6.86937e6	+	8.18660e6i	−0.0448596	+	0.0534616i
$536$		0			0
$537$	−9.10380e7	+	3.31351e7i	−0.587895	+	0.213976i
$538$		0			0
$539$	−4.25195e7	−	7.36460e7i	−0.271533	−	0.470309i
$540$		0			0
$541$	1.82739e6	+	1.03636e7i	0.0115409	+	0.0654516i	0.990034	−	0.140826i	$-0.0449760\pi$
$541$	1.82739e6	+	1.03636e7i	0.0115409	+	0.0654516i	−0.978493	+	0.206278i	$0.933865\pi$
$542$		0			0
$543$	−8.59214e7	+	1.48820e8i	−0.536663	+	0.929528i
$544$		0			0
$545$	8.04461e6	+	9.58720e6i	0.0496953	+	0.0592246i
$546$		0			0
$547$	9.74540e7	−	2.67753e8i	0.595440	−	1.63596i	−0.164810	−	0.986325i	$-0.552701\pi$
$547$	9.74540e7	−	2.67753e8i	0.595440	−	1.63596i	0.760249	−	0.649631i	$-0.225077\pi$
$548$		0			0
$549$	−1.36986e6	+	7.76888e6i	−0.00827866	+	0.0469506i
$550$		0			0
$551$	2.45796e8	−	7.14783e7i	1.46933	−	0.427287i
$552$		0			0
$553$	−3.18368e7	−	5.61369e6i	−0.188258	−	0.0331950i
$554$		0			0
$555$	−8.79806e6	−	3.20223e6i	−0.0514645	−	0.0187315i
$556$		0			0
$557$	−1.13371e8	+	9.51296e7i	−0.656049	+	0.550491i	−0.908900	−	0.417015i	$-0.863076\pi$
$557$	−1.13371e8	+	9.51296e7i	−0.656049	+	0.550491i	0.252851	+	0.967505i	$0.418632\pi$
$558$		0			0
$559$	1.13257e8	+	6.53890e7i	0.648380	+	0.374342i
$560$		0			0
$561$	1.30818e8	−	2.30668e7i	0.740936	−	0.130647i
$562$		0			0
$563$	−7.69337e7	+	4.44177e7i	−0.431113	+	0.248903i	−0.699821	−	0.714318i	$-0.746737\pi$
$563$	−7.69337e7	+	4.44177e7i	−0.431113	+	0.248903i	0.268707	+	0.963222i	$0.413404\pi$
$564$		0			0
$565$	−1.02752e6	−	2.82308e6i	−0.00569696	−	0.0156523i
$566$		0			0
$567$	2.13778e8	+	1.79381e8i	1.17277	+	0.984071i
$568$		0			0
$569$			2.93025e8i			1.59063i	0.606199	+	0.795313i	$0.292694\pi$
$569$			2.93025e8i			1.59063i	−0.606199	+	0.795313i	$0.707306\pi$
$570$		0			0
$571$	1.75400e8			0.942152			0.471076	−	0.882093i	$-0.343866\pi$
$571$	1.75400e8			0.942152			0.471076	+	0.882093i	$0.343866\pi$
$572$		0			0
$573$	1.51096e8	−	1.80069e8i	0.803137	−	0.957141i
$574$		0			0
$575$	2.91903e8	−	1.06244e8i	1.53545	−	0.558858i
$576$		0			0
$577$	5.52522e7	+	9.56996e7i	0.287622	+	0.498176i	0.973242	−	0.229784i	$-0.0738020\pi$
$577$	5.52522e7	+	9.56996e7i	0.287622	+	0.498176i	−0.685620	+	0.727960i	$0.740469\pi$
$578$		0			0
$579$	−5.27233e7	−	2.99009e8i	−0.271623	−	1.54045i
$580$		0			0
$581$	−8.79564e7	+	1.52345e8i	−0.448476	+	0.776783i
$582$		0			0
$583$	8.64603e7	+	1.03039e8i	0.436326	+	0.519993i
$584$		0			0
$585$	−703155.	+	1.93190e6i	−0.00351223	+	0.00964979i
$586$		0			0
$587$	−7.00699e7	+	3.97386e8i	−0.346431	+	1.96471i	−0.103751	+	0.994603i	$0.533084\pi$
$587$	−7.00699e7	+	3.97386e8i	−0.346431	+	1.96471i	−0.242680	+	0.970106i	$0.578027\pi$
$588$		0			0
$589$	2.39595e8	−	1.75451e8i	1.17255	−	0.858638i
$590$		0			0
$591$	−4.13852e8	−	7.29733e7i	−2.00485	−	0.353510i
$592$		0			0
$593$	1.84627e8	+	6.71988e7i	0.885384	+	0.322253i	0.744380	−	0.667756i	$-0.232745\pi$
$593$	1.84627e8	+	6.71988e7i	0.885384	+	0.322253i	0.141003	+	0.990009i	$0.454967\pi$
$594$		0			0
$595$	−1.42187e7	+	1.19309e7i	−0.0675008	+	0.0566399i
$596$		0			0
$597$	8.84180e6	+	5.10481e6i	0.0415545	+	0.0239915i
$598$		0			0
$599$	1.93089e8	−	3.40468e7i	0.898416	−	0.158415i	0.294677	−	0.955597i	$-0.404788\pi$
$599$	1.93089e8	−	3.40468e7i	0.898416	−	0.158415i	0.603739	+	0.797182i	$0.293677\pi$
$600$		0			0
$601$	−2.16637e7	+	1.25075e7i	−0.0997951	+	0.0576167i	−0.549067	−	0.835778i	$-0.685017\pi$
$601$	−2.16637e7	+	1.25075e7i	−0.0997951	+	0.0576167i	0.449272	+	0.893395i	$0.351683\pi$
$602$		0			0
$603$	−3.14448e6	−	8.63938e6i	−0.0143416	−	0.0394031i
$604$		0			0
$605$	−5.82968e6	−	4.89169e6i	−0.0263256	−	0.0220898i
$606$		0			0
$607$			6.45363e7i			0.288561i	0.989537	+	0.144281i	$0.0460868\pi$
$607$			6.45363e7i			0.288561i	−0.989537	+	0.144281i	$0.953913\pi$
$608$		0			0
$609$	5.06695e8			2.24334
$610$		0			0
$611$	−1.63361e8	+	1.94685e8i	−0.716182	+	0.853513i
$612$		0			0
$613$	3.17129e8	−	1.15425e8i	1.37675	−	0.501095i	0.455557	−	0.890207i	$-0.349440\pi$
$613$	3.17129e8	−	1.15425e8i	1.37675	−	0.501095i	0.921191	+	0.389111i	$0.127218\pi$
$614$		0			0
$615$	−5.99176e6	−	1.03780e7i	−0.0257590	−	0.0446159i
$616$		0			0
$617$	4.70028e7	+	2.66566e8i	0.200110	+	1.13488i	0.904952	+	0.425514i	$0.139907\pi$
$617$	4.70028e7	+	2.66566e8i	0.200110	+	1.13488i	−0.704842	+	0.709364i	$0.748982\pi$
$618$		0			0
$619$	−9.47734e7	+	1.64152e8i	−0.399590	+	0.692110i	−0.993675	−	0.112292i	$-0.964181\pi$
$619$	−9.47734e7	+	1.64152e8i	−0.399590	+	0.692110i	0.594085	+	0.804402i	$0.297514\pi$
$620$		0			0
$621$	−2.35174e8	−	2.80269e8i	−0.982006	−	1.17031i
$622$		0			0
$623$	−8.55519e6	+	2.35052e7i	−0.0353806	+	0.0972075i
$624$		0			0
$625$	4.20426e7	−	2.38436e8i	0.172207	−	0.976632i
$626$		0			0
$627$	6.78313e7	+	1.37763e8i	0.275187	+	0.558893i
$628$		0			0
$629$	2.91256e8	+	5.13562e7i	1.17037	+	0.206367i
$630$		0			0
$631$	−3.05577e8	−	1.11221e8i	−1.21628	−	0.442688i	−0.347399	−	0.937717i	$-0.612935\pi$
$631$	−3.05577e8	−	1.11221e8i	−1.21628	−	0.442688i	−0.868876	+	0.495029i	$0.835157\pi$
$632$		0			0
$633$	−1.56164e8	+	1.31037e8i	−0.615700	+	0.516634i
$634$		0			0
$635$	3.88840e6	+	2.24497e6i	0.0151862	+	0.00876778i
$636$		0			0
$637$	−3.86957e8	+	6.82310e7i	−1.49708	+	0.263975i
$638$		0			0
$639$	8.24380e6	−	4.75956e6i	0.0315955	−	0.0182416i
$640$		0			0
$641$	−5.15373e7	−	1.41598e8i	−0.195681	−	0.537628i	0.802582	−	0.596541i	$-0.203459\pi$
$641$	−5.15373e7	−	1.41598e8i	−0.195681	−	0.537628i	−0.998263	+	0.0589129i	$0.981237\pi$
$642$		0			0
$643$	−1.10409e8	−	9.26442e7i	−0.415310	−	0.348486i	0.411066	−	0.911606i	$-0.365157\pi$
$643$	−1.10409e8	−	9.26442e7i	−0.415310	−	0.348486i	−0.826375	+	0.563120i	$0.809601\pi$
$644$		0			0
$645$			6.78062e6i			0.0252691i
$646$		0			0
$647$	−2.94811e8			−1.08851			−0.544254	−	0.838921i	$-0.683187\pi$
$647$	−2.94811e8			−1.08851			−0.544254	+	0.838921i	$0.683187\pi$
$648$		0			0
$649$	1.90054e8	−	2.26497e8i	0.695252	−	0.828569i
$650$		0			0
$651$	5.52378e8	−	2.01049e8i	2.00213	−	0.728717i
$652$		0			0
$653$	1.19233e8	+	2.06518e8i	0.428212	+	0.741685i	0.996714	−	0.0809969i	$-0.0258104\pi$
$653$	1.19233e8	+	2.06518e8i	0.428212	+	0.741685i	−0.568503	+	0.822682i	$0.692477\pi$
$654$		0			0
$655$	−3.56498e6	−	2.02180e7i	−0.0126863	−	0.0719474i
$656$		0			0
$657$	−2.77275e7	+	4.80255e7i	−0.0977721	+	0.169346i
$658$		0			0
$659$	2.78180e8	+	3.31522e8i	0.972007	+	1.15839i	0.987357	+	0.158511i	$0.0506692\pi$
$659$	2.78180e8	+	3.31522e8i	0.972007	+	1.15839i	−0.0153503	+	0.999882i	$0.504886\pi$
$660$		0			0
$661$	7.89371e7	−	2.16878e8i	0.273324	−	0.750950i	−0.724756	−	0.689006i	$-0.758048\pi$
$661$	7.89371e7	−	2.16878e8i	0.273324	−	0.750950i	0.998080	−	0.0619446i	$-0.0197302\pi$
$662$		0			0
$663$	1.06581e8	−	6.04452e8i	0.365713	−	2.07406i
$664$		0			0
$665$	−1.78330e7	−	1.19316e7i	−0.0606400	−	0.0405725i
$666$		0			0
$667$	−7.32709e8	−	1.29196e8i	−2.46919	−	0.435384i
$668$		0			0
$669$	−1.12958e8	−	4.11134e7i	−0.377259	−	0.137311i
$670$		0			0
$671$	5.49306e7	−	4.60922e7i	0.181822	−	0.152567i
$672$		0			0
$673$	−1.56261e8	−	9.02176e7i	−0.512633	−	0.295969i	0.221282	−	0.975210i	$-0.428976\pi$
$673$	−1.56261e8	−	9.02176e7i	−0.512633	−	0.295969i	−0.733915	+	0.679241i	$0.762309\pi$
$674$		0			0
$675$	−2.81612e8	+	4.96557e7i	−0.915670	+	0.161457i
$676$		0			0
$677$	−2.89799e8	+	1.67316e8i	−0.933966	+	0.539226i	−0.888064	−	0.459720i	$-0.847950\pi$
$677$	−2.89799e8	+	1.67316e8i	−0.933966	+	0.539226i	−0.0459025	+	0.998946i	$0.514616\pi$
$678$		0			0
$679$	−1.47184e8	−	4.04385e8i	−0.470166	−	1.29177i
$680$		0			0
$681$	−6.62350e7	−	5.55777e7i	−0.209723	−	0.175978i
$682$		0			0
$683$			2.75139e8i			0.863555i	0.901980	+	0.431777i	$0.142113\pi$
$683$			2.75139e8i			0.863555i	−0.901980	+	0.431777i	$0.857887\pi$
$684$		0			0
$685$	8.13927e6			0.0253229
$686$		0			0
$687$	−1.63784e8	+	1.95190e8i	−0.505128	+	0.601988i
$688$		0			0
$689$	5.84020e8	−	2.12566e8i	1.78554	−	0.649884i
$690$		0			0
$691$	1.09629e8	+	1.89884e8i	0.332271	+	0.575511i	0.982957	−	0.183837i	$-0.0588517\pi$
$691$	1.09629e8	+	1.89884e8i	0.332271	+	0.575511i	−0.650686	+	0.759347i	$0.725518\pi$
$692$		0			0
$693$	5.58462e6	+	3.16719e7i	0.0167801	+	0.0951645i
$694$		0			0
$695$	−1.12698e7	+	1.95199e7i	−0.0335708	+	0.0581463i
$696$		0			0
$697$	2.43318e8	+	2.89975e8i	0.718581	+	0.856372i
$698$		0			0
$699$	1.00213e8	−	2.75332e8i	0.293421	−	0.806168i
$700$		0			0
$701$	2.25968e6	−	1.28153e7i	0.00655982	−	0.0372026i	−0.981352	−	0.192219i	$-0.938432\pi$
$701$	2.25968e6	−	1.28153e7i	0.00655982	−	0.0372026i	0.987912	+	0.155016i	$0.0495429\pi$
$702$		0			0
$703$	3.70096e7	+	3.39871e8i	0.106524	+	0.978246i
$704$		0			0
$705$	−1.29768e7	−	2.28815e6i	−0.0370339	−	0.00653007i
$706$		0			0
$707$	−2.39597e8	−	8.72063e7i	−0.677991	−	0.246769i
$708$		0			0
$709$	−4.10775e8	+	3.44681e8i	−1.15256	+	0.967117i	−0.999776	−	0.0211421i	$-0.993270\pi$
$709$	−4.10775e8	+	3.44681e8i	−1.15256	+	0.967117i	−0.152788	+	0.988259i	$0.548825\pi$
$710$		0			0
$711$	5.07878e6	+	2.93223e6i	0.0141303	+	0.00815811i
$712$		0			0
$713$	−8.50032e8	+	1.49884e8i	−2.34513	+	0.413509i
$714$		0			0
$715$	1.61839e7	−	9.34378e6i	0.0442757	−	0.0255626i
$716$		0			0
$717$	−2.27413e8	−	6.24811e8i	−0.616960	−	1.69508i
$718$		0			0
$719$	5.90486e7	+	4.95476e7i	0.158863	+	0.133302i	0.718754	−	0.695264i	$-0.244713\pi$
$719$	5.90486e7	+	4.95476e7i	0.158863	+	0.133302i	−0.559891	+	0.828566i	$0.689157\pi$
$720$		0			0
$721$			5.47060e8i			1.45958i
$722$		0			0
$723$	−1.09756e8			−0.290412
$724$		0			0
$725$	−3.73788e8	+	4.45463e8i	−0.980869	+	1.16895i
$726$		0			0
$727$	−4.08335e8	+	1.48622e8i	−1.06271	+	0.386794i	−0.813445	−	0.581643i	$-0.802410\pi$
$727$	−4.08335e8	+	1.48622e8i	−1.06271	+	0.386794i	−0.249262	+	0.968436i	$0.580188\pi$
$728$		0			0
$729$	1.65686e8	+	2.86977e8i	0.427664	+	0.740737i
$730$		0			0
$731$	−3.71930e7	−	2.10932e8i	−0.0952159	−	0.539996i
$732$		0			0
$733$	3.86622e8	−	6.69649e8i	0.981691	−	1.70034i	0.325882	−	0.945410i	$-0.394339\pi$
$733$	3.86622e8	−	6.69649e8i	0.981691	−	1.70034i	0.655808	−	0.754928i	$-0.272328\pi$
$734$		0			0
$735$	−1.30953e7	−	1.56063e7i	−0.0329801	−	0.0393041i
$736$		0			0
$737$	−2.85826e7	+	7.85301e7i	−0.0714002	+	0.196170i
$738$		0			0
$739$	5.85604e6	−	3.32113e7i	0.0145101	−	0.0822909i	−0.976693	−	0.214642i	$-0.931142\pi$
$739$	5.85604e6	−	3.32113e7i	0.0145101	−	0.0822909i	0.991203	+	0.132351i	$0.0422526\pi$
$740$		0			0
$741$	7.05345e8	−	7.68071e7i	1.73359	−	0.188776i
$742$		0			0
$743$	−5.09805e8	−	8.98924e7i	−1.24290	−	0.219158i	−0.486745	−	0.873544i	$-0.661816\pi$
$743$	−5.09805e8	−	8.98924e7i	−1.24290	−	0.219158i	−0.756160	+	0.654387i	$0.772927\pi$
$744$		0			0
$745$	3.59159e7	+	1.30723e7i	0.0868595	+	0.0316143i
$746$		0			0
$747$	2.44457e7	−	2.05123e7i	0.0586462	−	0.0492100i
$748$		0			0
$749$	6.68954e8	+	3.86221e8i	1.59203	+	0.919159i
$750$		0			0
$751$	1.66657e8	−	2.93860e7i	0.393462	−	0.0693779i	0.0265828	−	0.999647i	$-0.491537\pi$
$751$	1.66657e8	−	2.93860e7i	0.393462	−	0.0693779i	0.366879	+	0.930269i	$0.380426\pi$
$752$		0			0
$753$	2.95440e8	−	1.70572e8i	0.691965	−	0.399506i
$754$		0			0
$755$	−5.26923e6	−	1.44771e7i	−0.0122435	−	0.0336388i
$756$		0			0
$757$	1.44452e8	+	1.21209e8i	0.332993	+	0.279414i	0.793918	−	0.608025i	$-0.208038\pi$
$757$	1.44452e8	+	1.21209e8i	0.332993	+	0.279414i	−0.460925	+	0.887439i	$0.652482\pi$
$758$		0			0
$759$		−	4.46319e8i		−	1.02075i
$760$		0			0
$761$	−5.74977e8			−1.30466			−0.652329	−	0.757936i	$-0.726208\pi$
$761$	−5.74977e8			−1.30466			−0.652329	+	0.757936i	$0.726208\pi$
$762$		0			0
$763$	5.81462e8	−	6.92960e8i	1.30902	−	1.56004i
$764$		0			0
$765$	3.16404e6	−	1.15162e6i	0.00706737	−	0.00257231i
$766$		0			0
$767$	−6.83080e8	−	1.18313e9i	−1.51386	−	2.62208i
$768$		0			0
$769$	−6.90248e7	−	3.91459e8i	−0.151784	−	0.860810i	−0.961667	−	0.274219i	$-0.911581\pi$
$769$	−6.90248e7	−	3.91459e8i	−0.151784	−	0.860810i	0.809883	−	0.586591i	$-0.199530\pi$
$770$		0			0
$771$	−9.34453e7	+	1.61852e8i	−0.203889	+	0.353146i
$772$		0			0
$773$	1.26247e8	+	1.50455e8i	0.273326	+	0.325737i	0.885194	−	0.465223i	$-0.154026\pi$
$773$	1.26247e8	+	1.50455e8i	0.273326	+	0.325737i	−0.611867	+	0.790960i	$0.709581\pi$
$774$		0			0
$775$	−2.30735e8	+	6.33939e8i	−0.495687	+	1.36189i
$776$		0			0
$777$	−1.17513e8	+	6.66452e8i	−0.250510	+	1.42071i
$778$		0			0
$779$	−2.43331e8	+	3.63684e8i	−0.514737	+	0.769329i
$780$		0			0
$781$	−8.52121e7	−	1.50252e7i	−0.178874	−	0.0315404i
$782$		0			0
$783$	6.43593e8	+	2.34249e8i	1.34068	+	0.487969i
$784$		0			0
$785$	6.82040e6	−	5.72299e6i	0.0140994	−	0.0118308i
$786$		0			0
$787$	8.73592e7	+	5.04369e7i	0.179219	+	0.103472i	0.586926	−	0.809641i	$-0.300338\pi$
$787$	8.73592e7	+	5.04369e7i	0.179219	+	0.103472i	−0.407707	+	0.913113i	$0.633671\pi$
$788$		0			0
$789$	−4.38875e8	+	7.73854e7i	−0.893531	+	0.157554i
$790$		0			0
$791$	−1.88055e8	+	1.08573e8i	−0.379975	+	0.219378i
$792$		0			0
$793$	−1.13319e8	−	3.11343e8i	−0.227240	−	0.624337i
$794$		0			0
$795$	2.46849e7	+	2.07131e7i	0.0491281	+	0.0412234i
$796$		0			0
$797$			1.47186e8i			0.290731i	0.989378	+	0.145365i	$0.0464357\pi$
$797$			1.47186e8i			0.290731i	−0.989378	+	0.145365i	$0.953564\pi$
$798$		0			0
$799$	4.16233e8			0.816012
$800$		0			0
$801$	2.91673e6	−	3.47602e6i	0.00567543	−	0.00676371i
$802$		0			0
$803$	4.73675e8	−	1.72403e8i	0.914815	−	0.332966i
$804$		0			0
$805$	3.11820e7	+	5.40088e7i	0.0597746	+	0.103533i
$806$		0			0
$807$	−3.05571e7	−	1.73298e8i	−0.0581422	−	0.329741i
$808$		0			0
$809$	−5.41156e7	+	9.37311e7i	−0.102206	+	0.177026i	−0.912593	−	0.408868i	$-0.865923\pi$
$809$	−5.41156e7	+	9.37311e7i	−0.102206	+	0.177026i	0.810387	+	0.585895i	$0.199257\pi$
$810$		0			0
$811$	6.45191e7	+	7.68909e7i	0.120956	+	0.144149i	0.823124	−	0.567862i	$-0.192229\pi$
$811$	6.45191e7	+	7.68909e7i	0.120956	+	0.144149i	−0.702169	+	0.712011i	$0.747785\pi$
$812$		0			0
$813$	2.87829e8	−	7.90803e8i	0.535627	−	1.47162i
$814$		0			0
$815$	−2.96678e6	+	1.68254e7i	−0.00548040	+	0.0310809i
$816$		0			0
$817$	2.22129e8	−	1.09371e8i	0.407323	−	0.200557i
$818$		0			0
$819$	1.46341e8	+	2.58039e7i	0.266388	+	0.0469715i
$820$		0			0
$821$	2.91553e8	+	1.06116e8i	0.526851	+	0.191758i	0.591732	−	0.806135i	$-0.298445\pi$
$821$	2.91553e8	+	1.06116e8i	0.526851	+	0.191758i	−0.0648810	+	0.997893i	$0.520667\pi$
$822$		0			0
$823$	−2.80769e7	+	2.35593e7i	−0.0503673	+	0.0422632i	−0.667624	−	0.744499i	$-0.732689\pi$
$823$	−2.80769e7	+	2.35593e7i	−0.0503673	+	0.0422632i	0.617256	+	0.786762i	$0.288244\pi$
$824$		0			0
$825$	−3.02102e8	−	1.74419e8i	−0.538012	−	0.310621i
$826$		0			0
$827$	−3.45171e8	+	6.08629e7i	−0.610264	+	0.107606i	−0.470235	−	0.882541i	$-0.655831\pi$
$827$	−3.45171e8	+	6.08629e7i	−0.610264	+	0.107606i	−0.140029	+	0.990147i	$0.544720\pi$
$828$		0			0
$829$	−1.07799e8	+	6.22379e7i	−0.189213	+	0.109242i	−0.591614	−	0.806221i	$-0.701509\pi$
$829$	−1.07799e8	+	6.22379e7i	−0.189213	+	0.109242i	0.402401	+	0.915464i	$0.368176\pi$
$830$		0			0
$831$	3.41021e8	+	9.36946e8i	0.594261	+	1.63272i
$832$		0			0
$833$	4.92972e8	+	4.13653e8i	0.852879	+	0.715650i
$834$		0			0
$835$			4.42534e7i			0.0760130i
$836$		0			0
$837$	7.94565e8			1.35504
$838$		0			0
$839$	3.86952e8	−	4.61151e8i	0.655196	−	0.780832i	−0.331492	−	0.943458i	$-0.607552\pi$
$839$	3.86952e8	−	4.61151e8i	0.655196	−	0.780832i	0.986688	+	0.162626i	$0.0519964\pi$
$840$		0			0
$841$	7.49839e8	−	2.72919e8i	1.26061	−	0.458824i
$842$		0			0
$843$	−2.46717e7	−	4.27327e7i	−0.0411829	−	0.0713309i
$844$		0			0
$845$	−9.47989e6	−	5.37631e7i	−0.0157121	−	0.0891075i
$846$		0			0
$847$	−2.75028e8	+	4.76363e8i	−0.452613	+	0.783949i
$848$		0			0
$849$	1.85573e8	+	2.21157e8i	0.303244	+	0.361392i
$850$		0			0
$851$	3.39862e8	−	9.33763e8i	0.551460	−	1.51512i
$852$		0			0
$853$	−2.05953e8	+	1.16802e9i	−0.331835	+	1.88193i	0.124654	+	0.992200i	$0.460218\pi$
$853$	−2.05953e8	+	1.16802e9i	−0.331835	+	1.88193i	−0.456489	+	0.889729i	$0.650893\pi$
$854$		0			0
$855$	2.29962e6	+	3.14035e6i	0.00367924	+	0.00502435i
$856$		0			0
$857$	1.19677e9	+	2.11023e8i	1.90137	+	0.335264i	0.996000	−	0.0893505i	$-0.0284791\pi$
$857$	1.19677e9	+	2.11023e8i	1.90137	+	0.335264i	0.905374	+	0.424614i	$0.139590\pi$
$858$		0			0
$859$	−4.72106e8	−	1.71833e8i	−0.744835	−	0.271098i	−0.0584042	−	0.998293i	$-0.518601\pi$
$859$	−4.72106e8	−	1.71833e8i	−0.744835	−	0.271098i	−0.686431	+	0.727195i	$0.740823\pi$
$860$		0			0
$861$	−6.63522e8	+	5.56761e8i	−1.03955	+	0.872286i
$862$		0			0
$863$	3.33199e8	+	1.92373e8i	0.518408	+	0.299303i	0.736283	−	0.676674i	$-0.236579\pi$
$863$	3.33199e8	+	1.92373e8i	0.518408	+	0.299303i	−0.217875	+	0.975977i	$0.569913\pi$
$864$		0			0
$865$	469081.	−	82711.6i	0.000724769	−	0.000127796i
$866$		0			0
$867$	−2.73699e8	+	1.58020e8i	−0.419968	+	0.242469i
$868$		0			0
$869$	−1.82320e7	−	5.00919e7i	−0.0277827	−	0.0763323i
$870$		0			0
$871$	2.95799e8	+	2.48205e8i	0.447654	+	0.375626i
$872$		0			0
$873$			7.80656e7i			0.117332i
$874$		0			0
$875$	9.76213e7			0.145720
$876$		0			0
$877$	1.62300e8	−	1.93421e8i	0.240613	−	0.286751i	−0.632201	−	0.774804i	$-0.717848\pi$
$877$	1.62300e8	−	1.93421e8i	0.240613	−	0.286751i	0.872814	+	0.488053i	$0.162293\pi$
$878$		0			0
$879$	−1.40241e8	+	5.10436e7i	−0.206495	+	0.0751579i
$880$		0			0
$881$	−3.68608e8	−	6.38449e8i	−0.539061	−	0.933680i	−0.998955	−	0.0457066i	$-0.985446\pi$
$881$	−3.68608e8	−	6.38449e8i	−0.539061	−	0.933680i	0.459894	−	0.887974i	$-0.347887\pi$
$882$		0			0
$883$	1.86853e7	+	1.05970e8i	0.0271406	+	0.153922i	0.995366	−	0.0961562i	$-0.0306548\pi$
$883$	1.86853e7	+	1.05970e8i	0.0271406	+	0.153922i	−0.968226	+	0.250078i	$0.919544\pi$
$884$		0			0
$885$	3.54166e7	−	6.13434e7i	0.0510948	−	0.0884989i
$886$		0			0
$887$	6.59416e8	+	7.85861e8i	0.944906	+	1.12609i	0.991877	+	0.127198i	$0.0405985\pi$
$887$	6.59416e8	+	7.85861e8i	0.944906	+	1.12609i	−0.0469716	+	0.998896i	$0.514957\pi$
$888$		0			0
$889$	1.10996e8	−	3.04960e8i	0.157981	−	0.434048i
$890$		0			0
$891$	−7.99065e7	+	4.53172e8i	−0.112966	+	0.640664i
$892$		0			0
$893$	1.34357e8	+	4.62019e8i	0.188671	+	0.648792i
$894$		0			0
$895$	2.19827e7	+	3.87614e6i	0.0306628	+	0.00540667i
$896$		0			0
$897$	−1.93787e9	−	7.05326e8i	−2.68502	−	0.977266i
$898$		0			0
$899$	1.23778e9	−	1.03862e9i	1.70358	−	1.42947i
$900$		0			0
$901$	−8.81515e8	−	5.08943e8i	−1.20519	−	0.695816i
$902$		0			0
$903$	4.82656e8	−	8.51052e7i	0.655502	−	0.115583i
$904$		0			0
$905$	3.42889e7	−	1.97967e7i	0.0462603	−	0.0267084i
$906$		0			0
$907$	−1.11784e8	−	3.07123e8i	−0.149815	−	0.411614i	0.841971	−	0.539523i	$-0.181396\pi$
$907$	−1.11784e8	−	3.07123e8i	−0.149815	−	0.411614i	−0.991786	+	0.127909i	$0.959173\pi$
$908$		0			0
$909$	3.54324e7	+	2.97313e7i	0.0471747	+	0.0395843i
$910$		0			0
$911$			1.16712e9i			1.54369i	0.635808	+	0.771847i	$0.280667\pi$
$911$			1.16712e9i			1.54369i	−0.635808	+	0.771847i	$0.719333\pi$
$912$		0			0
$913$	−2.90069e8			−0.381144
$914$		0			0
$915$	1.10422e7	−	1.31596e7i	0.0144143	−	0.0171782i
$916$		0			0
$917$	−1.39441e9	+	5.07523e8i	−1.80835	+	0.658184i
$918$		0			0
$919$	1.49765e8	+	2.59400e8i	0.192958	+	0.334214i	0.946229	−	0.323497i	$-0.104858\pi$
$919$	1.49765e8	+	2.59400e8i	0.192958	+	0.334214i	−0.753271	+	0.657710i	$0.771525\pi$
$920$		0			0
$921$	−3.68638e7	−	2.09065e8i	−0.0471869	−	0.267610i
$922$		0			0
$923$	−1.99900e8	+	3.46237e8i	−0.254219	+	0.440320i
$924$		0			0
$925$	−4.99225e8	−	5.94953e8i	−0.630770	−	0.751722i
$926$		0			0
$927$	3.39420e7	−	9.32548e7i	0.0426087	−	0.117066i
$928$		0			0
$929$	2.29793e8	−	1.30322e9i	0.286609	−	1.62544i	−0.412871	−	0.910790i	$-0.635474\pi$
$929$	2.29793e8	−	1.30322e9i	0.286609	−	1.62544i	0.699480	−	0.714652i	$-0.253415\pi$
$930$		0			0
$931$	−3.00027e8	+	6.80723e8i	−0.371802	+	0.843570i
$932$		0			0
$933$	−8.47481e8	−	1.49434e8i	−1.04348	−	0.183994i
$934$		0			0
$935$	−2.87604e7	−	1.04679e7i	−0.0351853	−	0.0128064i
$936$		0			0
$937$	−6.00960e8	+	5.04265e8i	−0.730511	+	0.612971i	−0.930271	−	0.366874i	$-0.880428\pi$
$937$	−6.00960e8	+	5.04265e8i	−0.730511	+	0.612971i	0.199760	+	0.979845i	$0.435984\pi$
$938$		0			0
$939$	2.07092e7	+	1.19565e7i	0.0250131	+	0.0144413i
$940$		0			0
$941$	3.22620e8	−	5.68867e7i	0.387189	−	0.0682718i	0.0233345	−	0.999728i	$-0.492572\pi$
$941$	3.22620e8	−	5.68867e7i	0.387189	−	0.0682718i	0.363854	+	0.931456i	$0.381461\pi$
$942$		0			0
$943$	1.10145e9	−	6.35923e8i	1.31350	−	0.758350i
$944$		0			0
$945$	−1.96350e7	−	5.39468e7i	−0.0232668	−	0.0639249i
$946$		0			0
$947$	−1.21104e9	−	1.01619e9i	−1.42597	−	1.19653i	−0.948048	−	0.318128i	$-0.896946\pi$
$947$	−1.21104e9	−	1.01619e9i	−1.42597	−	1.19653i	−0.477921	−	0.878403i	$-0.658610\pi$
$948$		0			0
$949$		−	2.32909e9i		−	2.72514i
$950$		0			0
$951$	−1.92350e8			−0.223641
$952$		0			0
$953$	−3.08169e8	+	3.67261e8i	−0.356049	+	0.424323i	−0.914103	−	0.405482i	$-0.867104\pi$
$953$	−3.08169e8	+	3.67261e8i	−0.356049	+	0.424323i	0.558054	+	0.829805i	$0.311548\pi$
$954$		0			0
$955$	−5.08937e7	+	1.85238e7i	−0.0584324	+	0.0212676i
$956$		0			0
$957$	4.17753e8	+	7.23570e8i	0.476633	+	0.825553i
$958$		0			0
$959$	−1.02158e8	−	5.79367e8i	−0.115829	−	0.656897i
$960$		0			0
$961$	4.93512e8	−	8.54788e8i	0.556068	−	0.963138i
$962$		0			0
$963$	−9.00708e7	−	1.07342e8i	−0.100857	−	0.120196i
$964$		0			0
$965$	−2.39263e7	+	6.57370e7i	−0.0266253	+	0.0731523i
$966$		0			0
$967$	−2.85028e7	+	1.61647e8i	−0.0315215	+	0.178768i	−0.996504	−	0.0835477i	$-0.973375\pi$
$967$	−2.85028e7	+	1.61647e8i	−0.0315215	+	0.178768i	0.964982	+	0.262315i	$0.0844860\pi$
$968$		0			0
$969$	−8.38914e8	−	8.04079e8i	−0.922033	−	0.883746i
$970$		0			0
$971$	7.27718e8	+	1.28316e8i	0.794887	+	0.140160i	0.556323	−	0.830966i	$-0.312212\pi$
$971$	7.27718e8	+	1.28316e8i	0.794887	+	0.140160i	0.238565	+	0.971127i	$0.423323\pi$
$972$		0			0
$973$	1.53090e9	+	5.57204e8i	1.66192	+	0.604889i
$974$		0			0
$975$	−1.23472e9	+	1.03606e9i	−1.33216	+	1.11781i
$976$		0			0
$977$	−3.55559e8	−	2.05282e8i	−0.381266	−	0.220124i	0.297103	−	0.954845i	$-0.403980\pi$
$977$	−3.55559e8	−	2.05282e8i	−0.381266	−	0.220124i	−0.678369	+	0.734721i	$0.737313\pi$
$978$		0			0
$979$	−4.06194e7	+	7.16229e6i	−0.0432898	+	0.00763315i
$980$		0			0
$981$	−1.42113e8	+	8.20492e7i	−0.150532	+	0.0869096i
$982$		0			0
$983$	−4.05317e8	−	1.11360e9i	−0.426712	−	1.17238i	−0.947796	−	0.318876i	$-0.896695\pi$
$983$	−4.05317e8	−	1.11360e9i	−0.426712	−	1.17238i	0.521085	−	0.853505i	$-0.325528\pi$
$984$		0			0
$985$	7.41719e7	+	6.22376e7i	0.0776123	+	0.0651245i
$986$		0			0
$987$			9.52426e8i			0.990557i
$988$		0			0
$989$	−7.19647e8			−0.743928
$990$		0			0
$991$	−1.20450e9	+	1.43547e9i	−1.23762	+	1.47494i	−0.411532	+	0.911395i	$0.635006\pi$
$991$	−1.20450e9	+	1.43547e9i	−1.23762	+	1.47494i	−0.826088	+	0.563542i	$0.809438\pi$
$992$		0			0
$993$	−1.28582e9	+	4.67999e8i	−1.31320	+	0.477966i
$994$		0			0
$995$	−1.17618e6	−	2.03720e6i	−0.00119400	−	0.00206806i
$996$		0			0
$997$	2.02983e8	+	1.15117e9i	0.204821	+	1.16160i	0.897721	+	0.440564i	$0.145221\pi$
$997$	2.02983e8	+	1.15117e9i	0.204821	+	1.16160i	−0.692900	+	0.721033i	$0.743667\pi$
$998$		0			0
$999$	−4.57369e8	+	7.92186e8i	−0.458744	+	0.794568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.8	✓	60
19.10	odd	18	inner	76.7.j.a.29.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.8	✓	60	1.1	even	1	trivial
76.7.j.a.29.8	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)

\(f(q)\)	\(=\)	\(q+(18.3534 - 21.8727i) q^{3} +(-6.18195 + 2.25005i) q^{5} +(237.753 + 411.801i) q^{7} +(-14.9788 - 84.9490i) q^{9} +O(q^{10})\)	\(q+(18.3534 - 21.8727i) q^{3} +(-6.18195 + 2.25005i) q^{5} +(237.753 + 411.801i) q^{7} +(-14.9788 - 84.9490i) q^{9} +(-392.040 + 679.033i) q^{11} +(2328.74 + 2775.28i) q^{13} +(-64.2450 + 176.512i) q^{15} +(1030.34 - 5843.34i) q^{17} +(6818.69 - 742.507i) q^{19} +(13370.7 + 2357.62i) q^{21} +(-18733.7 - 6818.51i) q^{23} +(-11936.3 + 10015.7i) q^{25} +(15893.3 + 9176.00i) q^{27} +(36753.1 - 6480.56i) q^{29} +(37495.3 - 21647.9i) q^{31} +(7657.02 + 21037.5i) q^{33} +(-2396.35 - 2010.78i) q^{35} +49844.0i q^{37} +103443. q^{39} +(-41007.6 + 48871.0i) q^{41} +(33920.9 - 12346.2i) q^{43} +(283.738 + 491.448i) q^{45} +(12181.4 + 69084.1i) q^{47} +(-54228.6 + 93926.7i) q^{49} +(-108899. - 129781. i) q^{51} +(58673.4 - 161204. i) q^{53} +(895.716 - 5079.86i) q^{55} +(108905. - 162771. i) q^{57} +(-371365. - 65481.6i) q^{59} +(-85938.1 - 31278.9i) q^{61} +(31420.8 - 26365.2i) q^{63} +(-20640.6 - 11916.9i) q^{65} +(104964. - 18508.0i) q^{67} +(-492965. + 284614. i) q^{69} +(37743.4 + 103699. i) q^{71} +(-492480. - 413239. i) q^{73} +444901. i q^{75} -372835. q^{77} +(-43700.8 + 52080.6i) q^{79} +(551490. - 200726. i) q^{81} +(184974. + 320385. i) q^{83} +(6778.29 + 38441.6i) q^{85} +(532795. - 922828. i) q^{87} +(33813.4 + 40297.3i) q^{89} +(-589197. + 1.61881e6i) q^{91} +(214666. - 1.21743e6i) q^{93} +(-40482.2 + 19932.5i) q^{95} +(-891260. - 157153. i) q^{97} +(63555.4 + 23132.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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