LMFDB - Embedded newform 76.7.j.a.21.3

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			21.3
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.9376 + 21.3772i) q^{3} +(-219.363 + 79.8415i) q^{5} +(237.710 + 411.726i) q^{7} +(-8.63778 - 48.9873i) q^{9} +O(q^{10})$	\(q+(-17.9376 + 21.3772i) q^{3} +(-219.363 + 79.8415i) q^{5} +(237.710 + 411.726i) q^{7} +(-8.63778 - 48.9873i) q^{9} +(-834.519 + 1445.43i) q^{11} +(-1316.39 - 1568.81i) q^{13} +(2228.05 - 6121.53i) q^{15} +(1052.70 - 5970.18i) q^{17} +(-2047.17 + 6546.37i) q^{19} +(-13065.5 - 2303.80i) q^{21} +(10179.9 + 3705.18i) q^{23} +(29775.9 - 24984.9i) q^{25} +(-16415.8 - 9477.66i) q^{27} +(-5406.79 + 953.363i) q^{29} +(18400.7 - 10623.7i) q^{31} +(-15930.0 - 43767.2i) q^{33} +(-85017.5 - 71338.2i) q^{35} -4155.35i q^{37} +57149.7 q^{39} +(-68681.9 + 81851.9i) q^{41} +(71716.5 - 26102.7i) q^{43} +(5806.03 + 10056.3i) q^{45} +(-4631.63 - 26267.3i) q^{47} +(-54187.6 + 93855.7i) q^{49} +(108743. + 129595. i) q^{51} +(-79871.9 + 219446. i) q^{53} +(67657.1 - 383702. i) q^{55} +(-103222. - 161189. i) q^{57} +(-66154.1 - 11664.8i) q^{59} +(75603.3 + 27517.3i) q^{61} +(18116.1 - 15201.2i) q^{63} +(414023. + 239036. i) q^{65} +(316105. - 55737.8i) q^{67} +(-261810. + 151156. i) q^{69} +(-25259.6 - 69400.2i) q^{71} +(194909. + 163548. i) q^{73} +1.08470e6i q^{75} -793494. q^{77} +(-627085. + 747331. i) q^{79} +(531142. - 193320. i) q^{81} +(-70734.7 - 122516. i) q^{83} +(245744. + 1.39369e6i) q^{85} +(76604.7 - 132683. i) q^{87} +(-672124. - 801007. i) q^{89} +(333002. - 914915. i) q^{91} +(-102961. + 583920. i) q^{93} +(-73598.2 - 1.59948e6i) q^{95} +(468378. + 82587.7i) q^{97} +(78016.1 + 28395.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−17.9376	+	21.3772i	−0.664356	+	0.791749i	−0.988004	−	0.154429i	$-0.950646\pi$
$3$	−17.9376	+	21.3772i	−0.664356	+	0.791749i	0.323648	+	0.946178i	$0.395091\pi$
$4$		0			0
$5$	−219.363	+	79.8415i	−1.75490	+	0.638732i	−0.999856	−	0.0169409i	$-0.994607\pi$
$5$	−219.363	+	79.8415i	−1.75490	+	0.638732i	−0.755045	+	0.655673i	$0.772385\pi$
$6$		0			0
$7$	237.710	+	411.726i	0.693032	+	1.20037i	0.970840	+	0.239730i	$0.0770590\pi$
$7$	237.710	+	411.726i	0.693032	+	1.20037i	−0.277807	+	0.960637i	$0.589608\pi$
$8$		0			0
$9$	−8.63778	−	48.9873i	−0.0118488	−	0.0671980i
$10$		0			0
$11$	−834.519	+	1445.43i	−0.626986	+	1.08597i	0.361167	+	0.932501i	$0.382378\pi$
$11$	−834.519	+	1445.43i	−0.626986	+	1.08597i	−0.988153	+	0.153471i	$0.950955\pi$
$12$		0			0
$13$	−1316.39	−	1568.81i	−0.599176	−	0.714071i	0.378165	−	0.925738i	$-0.376555\pi$
$13$	−1316.39	−	1568.81i	−0.599176	−	0.714071i	−0.977342	+	0.211667i	$0.932111\pi$
$14$		0			0
$15$	2228.05	−	6121.53i	0.660164	−	1.81379i
$16$		0			0
$17$	1052.70	−	5970.18i	0.214269	−	1.21518i	−0.667901	−	0.744250i	$-0.732807\pi$
$17$	1052.70	−	5970.18i	0.214269	−	1.21518i	0.882170	−	0.470931i	$-0.156082\pi$
$18$		0			0
$19$	−2047.17	+	6546.37i	−0.298465	+	0.954420i
$19$	−2047.17	+	6546.37i	−0.298465	+	0.954420i
$20$		0			0
$21$	−13065.5	−	2303.80i	−1.41081	−	0.248764i
$22$		0			0
$23$	10179.9	+	3705.18i	0.836681	+	0.304527i	0.724598	−	0.689172i	$-0.242025\pi$
$23$	10179.9	+	3705.18i	0.836681	+	0.304527i	0.112083	+	0.993699i	$0.464248\pi$
$24$		0			0
$25$	29775.9	−	24984.9i	1.90566	−	1.59904i
$26$		0			0
$27$	−16415.8	−	9477.66i	−0.834009	−	0.481515i
$28$		0			0
$29$	−5406.79	+	953.363i	−0.221690	+	0.0390899i	−0.283390	−	0.959005i	$-0.591459\pi$
$29$	−5406.79	+	953.363i	−0.221690	+	0.0390899i	0.0616999	+	0.998095i	$0.480348\pi$
$30$		0			0
$31$	18400.7	−	10623.7i	0.617661	−	0.356607i	−0.158297	−	0.987392i	$-0.550600\pi$
$31$	18400.7	−	10623.7i	0.617661	−	0.356607i	0.775958	+	0.630785i	$0.217267\pi$
$32$		0			0
$33$	−15930.0	−	43767.2i	−0.443275	−	1.21789i
$34$		0			0
$35$	−85017.5	−	71338.2i	−1.98292	−	1.66386i
$36$		0			0
$37$		−	4155.35i		−	0.0820355i	−0.999158	−	0.0410178i	$-0.986940\pi$
$37$		−	4155.35i		−	0.0820355i	0.999158	−	0.0410178i	$-0.0130600\pi$
$38$		0			0
$39$	57149.7			0.963431
$40$		0			0
$41$	−68681.9	+	81851.9i	−0.996530	+	1.18762i	−0.0143081	+	0.999898i	$0.504555\pi$
$41$	−68681.9	+	81851.9i	−0.996530	+	1.18762i	−0.982222	+	0.187721i	$0.939890\pi$
$42$		0			0
$43$	71716.5	−	26102.7i	0.902015	−	0.328307i	0.150955	−	0.988541i	$-0.451765\pi$
$43$	71716.5	−	26102.7i	0.902015	−	0.328307i	0.751060	+	0.660234i	$0.229543\pi$
$44$		0			0
$45$	5806.03	+	10056.3i	0.0637150	+	0.110358i
$46$		0			0
$47$	−4631.63	−	26267.3i	−0.0446109	−	0.253001i	0.954344	−	0.298710i	$-0.0965563\pi$
$47$	−4631.63	−	26267.3i	−0.0446109	−	0.253001i	−0.998955	+	0.0457092i	$0.985445\pi$
$48$		0			0
$49$	−54187.6	+	93855.7i	−0.460587	+	0.797761i
$50$		0			0
$51$	108743.	+	129595.i	0.819767	+	0.976960i
$52$		0			0
$53$	−79871.9	+	219446.i	−0.536496	+	1.47401i	0.314715	+	0.949186i	$0.398091\pi$
$53$	−79871.9	+	219446.i	−0.536496	+	1.47401i	−0.851211	+	0.524824i	$0.824131\pi$
$54$		0			0
$55$	67657.1	−	383702.i	0.406654	−	2.30625i
$56$		0			0
$57$	−103222.	−	161189.i	−0.557374	−	0.870384i
$58$		0			0
$59$	−66154.1	−	11664.8i	−0.322107	−	0.0567962i	0.0102566	−	0.999947i	$-0.496735\pi$
$59$	−66154.1	−	11664.8i	−0.322107	−	0.0567962i	−0.332364	+	0.943151i	$0.607846\pi$
$60$		0			0
$61$	75603.3	+	27517.3i	0.333082	+	0.121232i	0.503147	−	0.864201i	$-0.332175\pi$
$61$	75603.3	+	27517.3i	0.333082	+	0.121232i	−0.170065	+	0.985433i	$0.554398\pi$
$62$		0			0
$63$	18116.1	−	15201.2i	0.0724506	−	0.0607933i
$64$		0			0
$65$	414023.	+	239036.i	1.50760	+	0.870411i
$66$		0			0
$67$	316105.	−	55737.8i	1.05101	−	0.185321i	0.378646	−	0.925542i	$-0.376390\pi$
$67$	316105.	−	55737.8i	1.05101	−	0.185321i	0.672364	+	0.740220i	$0.265279\pi$
$68$		0			0
$69$	−261810.	+	151156.i	−0.796963	+	0.460127i
$70$		0			0
$71$	−25259.6	−	69400.2i	−0.0705751	−	0.193903i	0.899390	−	0.437147i	$-0.144011\pi$
$71$	−25259.6	−	69400.2i	−0.0705751	−	0.193903i	−0.969965	+	0.243243i	$0.921789\pi$
$72$		0			0
$73$	194909.	+	163548.i	0.501030	+	0.420414i	0.857959	−	0.513717i	$-0.171732\pi$
$73$	194909.	+	163548.i	0.501030	+	0.420414i	−0.356930	+	0.934131i	$0.616176\pi$
$74$		0			0
$75$			1.08470e6i			2.57113i
$76$		0			0
$77$	−793494.			−1.73809
$78$		0			0
$79$	−627085.	+	747331.i	−1.27188	+	1.51576i	−0.524409	+	0.851466i	$0.675714\pi$
$79$	−627085.	+	747331.i	−1.27188	+	1.51576i	−0.747468	+	0.664298i	$0.768731\pi$
$80$		0			0
$81$	531142.	−	193320.i	0.999437	−	0.363765i
$82$		0			0
$83$	−70734.7	−	122516.i	−0.123708	−	0.214269i	0.797519	−	0.603294i	$-0.206145\pi$
$83$	−70734.7	−	122516.i	−0.123708	−	0.214269i	−0.921227	+	0.389025i	$0.872812\pi$
$84$		0			0
$85$	245744.	+	1.39369e6i	0.400154	+	2.26938i
$86$		0			0
$87$	76604.7	−	132683.i	0.116332	−	0.201492i
$88$		0			0
$89$	−672124.	−	801007.i	−0.953410	−	1.13623i	−0.990582	−	0.136921i	$-0.956279\pi$
$89$	−672124.	−	801007.i	−0.953410	−	1.13623i	0.0371721	−	0.999309i	$-0.488165\pi$
$90$		0			0
$91$	333002.	−	914915.i	0.441898	−	1.21411i
$92$		0			0
$93$	−102961.	+	583920.i	−0.128004	+	0.725946i
$94$		0			0
$95$	−73598.2	−	1.59948e6i	−0.0858413	−	1.86555i
$96$		0			0
$97$	468378.	+	82587.7i	0.513194	+	0.0904900i	0.424247	−	0.905546i	$-0.360539\pi$
$97$	468378.	+	82587.7i	0.513194	+	0.0904900i	0.0889469	+	0.996036i	$0.471650\pi$
$98$		0			0
$99$	78016.1	+	28395.5i	0.0804042	+	0.0292647i
$100$		0			0
$101$	986348.	−	827644.i	0.957340	−	0.803303i	−0.0231787	−	0.999731i	$-0.507379\pi$
$101$	986348.	−	827644.i	0.957340	−	0.803303i	0.980518	+	0.196428i	$0.0629342\pi$
$102$		0			0
$103$	−964243.	−	556706.i	−0.882419	−	0.509465i	−0.0109640	−	0.999940i	$-0.503490\pi$
$103$	−964243.	−	556706.i	−0.882419	−	0.509465i	−0.871455	+	0.490475i	$0.836823\pi$
$104$		0			0
$105$	3.05002e6	−	537801.i	2.63472	−	0.464573i
$106$		0			0
$107$	−1.01746e6	+	587433.i	−0.830554	+	0.479521i	−0.854042	−	0.520204i	$-0.825856\pi$
$107$	−1.01746e6	+	587433.i	−0.830554	+	0.479521i	0.0234883	+	0.999724i	$0.492523\pi$
$108$		0			0
$109$	−842402.	−	2.31448e6i	−0.650489	−	1.78720i	−0.615929	−	0.787802i	$-0.711219\pi$
$109$	−842402.	−	2.31448e6i	−0.650489	−	1.78720i	−0.0345604	−	0.999403i	$-0.511003\pi$
$110$		0			0
$111$	88829.7	+	74537.0i	0.0649515	+	0.0545008i
$112$		0			0
$113$			828780.i			0.574386i	0.957873	+	0.287193i	$0.0927221\pi$
$113$			828780.i			0.574386i	−0.957873	+	0.287193i	$0.907278\pi$
$114$		0			0
$115$	−2.52892e6			−1.66280
$116$		0			0
$117$	−65481.2	+	78037.5i	−0.0408846	+	0.0487243i
$118$		0			0
$119$	2.70832e6	−	985747.i	1.60716	−	0.584958i
$120$		0			0
$121$	−507063.	−	878259.i	−0.286224	−	0.495754i
$122$		0			0
$123$	−517776.	−	2.93645e6i	−0.278245	−	1.57800i
$124$		0			0
$125$	−2.71313e6	+	4.69927e6i	−1.38912	+	2.40603i
$126$		0			0
$127$	−79457.8	−	94694.2i	−0.0387905	−	0.0462287i	0.746300	−	0.665609i	$-0.231828\pi$
$127$	−79457.8	−	94694.2i	−0.0387905	−	0.0462287i	−0.785091	+	0.619381i	$0.787384\pi$
$128$		0			0
$129$	−728420.	+	2.00132e6i	−0.339323	+	0.932282i
$130$		0			0
$131$	338184.	−	1.91794e6i	0.150432	−	0.853141i	−0.812412	−	0.583083i	$-0.801846\pi$
$131$	338184.	−	1.91794e6i	0.150432	−	0.853141i	0.962844	−	0.270058i	$-0.0870428\pi$
$132$		0			0
$133$	−3.18194e6	+	713263.i	−1.35250	+	0.303176i
$134$		0			0
$135$	4.35772e6	+	768384.i	1.77116	+	0.312304i
$136$		0			0
$137$	−3.91290e6	−	1.42418e6i	−1.52173	−	0.553864i	−0.560149	−	0.828392i	$-0.689256\pi$
$137$	−3.91290e6	−	1.42418e6i	−1.52173	−	0.553864i	−0.961579	+	0.274528i	$0.911478\pi$
$138$		0			0
$139$	3.26139e6	−	2.73663e6i	1.21439	−	1.01899i	0.215291	−	0.976550i	$-0.430930\pi$
$139$	3.26139e6	−	2.73663e6i	1.21439	−	1.01899i	0.999099	−	0.0424437i	$-0.0135143\pi$
$140$		0			0
$141$	644602.	+	372161.i	0.229951	+	0.132762i
$142$		0			0
$143$	3.36616e6	−	593545.i	1.15114	−	0.202976i
$144$		0			0
$145$	1.10993e6	−	640819.i	0.364076	−	0.210199i
$146$		0			0
$147$	−1.03438e6	−	2.84193e6i	−0.325632	−	0.894666i
$148$		0			0
$149$	1.81013e6	+	1.51888e6i	0.547205	+	0.459159i	0.873993	−	0.485938i	$-0.161522\pi$
$149$	1.81013e6	+	1.51888e6i	0.547205	+	0.459159i	−0.326788	+	0.945098i	$0.605966\pi$
$150$		0			0
$151$		−	301196.i		−	0.0874819i	−0.999043	−	0.0437410i	$-0.986072\pi$
$151$		−	301196.i		−	0.0874819i	0.999043	−	0.0437410i	$-0.0139276\pi$
$152$		0			0
$153$	−301556.			−0.0841965
$154$		0			0
$155$	−3.18823e6	+	3.79958e6i	−0.856159	+	1.02033i
$156$		0			0
$157$	−4.53222e6	+	1.64959e6i	−1.17115	+	0.426263i	−0.853067	−	0.521801i	$-0.825260\pi$
$157$	−4.53222e6	+	1.64959e6i	−1.17115	+	0.426263i	−0.318080	+	0.948064i	$0.603038\pi$
$158$		0			0
$159$	−3.25844e6	−	5.64378e6i	−0.810621	−	1.40404i
$160$		0			0
$161$	894346.	+	5.07209e6i	0.214303	+	1.21537i
$162$		0			0
$163$	−999424.	+	1.73105e6i	−0.230774	+	0.399713i	−0.958036	−	0.286647i	$-0.907459\pi$
$163$	−999424.	+	1.73105e6i	−0.230774	+	0.399713i	0.727262	+	0.686360i	$0.240793\pi$
$164$		0			0
$165$	6.98888e6	+	8.32902e6i	1.55581	+	1.85414i
$166$		0			0
$167$	−884529.	+	2.43022e6i	−0.189916	+	0.521791i	−0.997707	−	0.0676782i	$-0.978441\pi$
$167$	−884529.	+	2.43022e6i	−0.189916	+	0.521791i	0.807791	+	0.589469i	$0.200663\pi$
$168$		0			0
$169$	109876.	−	623138.i	0.0227637	−	0.129099i
$170$		0			0
$171$	338372.	+	43739.4i	0.0676716	+	0.00874752i
$172$		0			0
$173$	2.22846e6	+	392938.i	0.430394	+	0.0758901i	0.384649	−	0.923063i	$-0.374323\pi$
$173$	2.22846e6	+	392938.i	0.430394	+	0.0758901i	0.0457455	+	0.998953i	$0.485434\pi$
$174$		0			0
$175$	1.73650e7	+	6.32033e6i	3.24011	+	1.17930i
$176$		0			0
$177$	1.43601e6	−	1.20495e6i	0.258962	−	0.217295i
$178$		0			0
$179$	−9.43993e6	−	5.45015e6i	−1.64592	−	0.950274i	−0.978669	−	0.205445i	$-0.934136\pi$
$179$	−9.43993e6	−	5.45015e6i	−1.64592	−	0.950274i	−0.667255	−	0.744829i	$-0.732531\pi$
$180$		0			0
$181$	−5.02175e6	+	885470.i	−0.846875	+	0.149327i	−0.580215	−	0.814463i	$-0.697031\pi$
$181$	−5.02175e6	+	885470.i	−0.846875	+	0.149327i	−0.266661	+	0.963790i	$0.585920\pi$
$182$		0			0
$183$	−1.94439e6	+	1.12259e6i	−0.317270	+	0.183176i
$184$		0			0
$185$	331769.	+	911528.i	0.0523987	+	0.143964i
$186$		0			0
$187$	7.75098e6	+	6.50384e6i	1.18531	+	0.994592i
$188$		0			0
$189$		−	9.01174e6i		−	1.33482i
$190$		0			0
$191$	−5.13661e6			−0.737186			−0.368593	−	0.929591i	$-0.620160\pi$
$191$	−5.13661e6			−0.737186			−0.368593	+	0.929591i	$0.620160\pi$
$192$		0			0
$193$	−1.02807e6	+	1.22521e6i	−0.143005	+	0.170427i	−0.832793	−	0.553585i	$-0.813259\pi$
$193$	−1.02807e6	+	1.22521e6i	−0.143005	+	0.170427i	0.689788	+	0.724012i	$0.257704\pi$
$194$		0			0
$195$	−1.25365e7	+	4.56292e6i	−1.69073	+	0.615374i
$196$		0			0
$197$	4.87896e6	+	8.45061e6i	0.638158	+	1.10532i	0.985837	+	0.167709i	$0.0536369\pi$
$197$	4.87896e6	+	8.45061e6i	0.638158	+	1.10532i	−0.347678	+	0.937614i	$0.613030\pi$
$198$		0			0
$199$	−55087.4	−	312416.i	−0.00699025	−	0.0396437i	0.981113	−	0.193435i	$-0.0619628\pi$
$199$	−55087.4	−	312416.i	−0.00699025	−	0.0396437i	−0.988103	+	0.153791i	$0.950852\pi$
$200$		0			0
$201$	−4.47865e6	+	7.75725e6i	−0.551517	+	0.955255i
$202$		0			0
$203$	−1.67777e6	−	1.99949e6i	−0.200560	−	0.239018i
$204$		0			0
$205$	8.53107e6	−	2.34389e7i	0.990243	−	2.72067i
$206$		0			0
$207$	93575.1	−	530691.i	0.0105499	−	0.0598316i
$208$		0			0
$209$	−7.75391e6	−	8.42211e6i	−0.849340	−	0.922534i
$210$		0			0
$211$	8.79053e6	+	1.55001e6i	0.935767	+	0.165001i	0.620682	−	0.784063i	$-0.286856\pi$
$211$	8.79053e6	+	1.55001e6i	0.935767	+	0.165001i	0.315085	+	0.949063i	$0.397967\pi$
$212$		0			0
$213$	1.93668e6	+	704894.i	0.200410	+	0.0729432i
$214$		0			0
$215$	−1.36479e7	+	1.14519e7i	−1.37325	+	1.15229i
$216$		0			0
$217$	8.74809e6	+	5.05071e6i	0.856118	+	0.494280i
$218$		0			0
$219$	−6.99240e6	+	1.23295e6i	−0.665724	+	0.117385i
$220$		0			0
$221$	−1.07519e7	+	6.20760e6i	−0.996110	+	0.575104i
$222$		0			0
$223$	3.34531e6	+	9.19115e6i	0.301662	+	0.828811i	0.994212	+	0.107440i	$0.0342654\pi$
$223$	3.34531e6	+	9.19115e6i	0.301662	+	0.828811i	−0.692549	+	0.721371i	$0.743512\pi$
$224$		0			0
$225$	−1.48114e6	−	1.24283e6i	−0.130032	−	0.109110i
$226$		0			0
$227$		−	1.08691e7i		−	0.929216i	−0.885516	−	0.464608i	$-0.846195\pi$
$227$		−	1.08691e7i		−	0.929216i	0.885516	−	0.464608i	$-0.153805\pi$
$228$		0			0
$229$	1.76006e7			1.46562			0.732810	−	0.680433i	$-0.238208\pi$
$229$	1.76006e7			1.46562			0.732810	+	0.680433i	$0.238208\pi$
$230$		0			0
$231$	1.42334e7	−	1.69627e7i	1.15471	−	1.37613i
$232$		0			0
$233$	−247290.	+	90006.1i	−0.0195496	+	0.00711548i	−0.351776	−	0.936084i	$-0.614422\pi$
$233$	−247290.	+	90006.1i	−0.0195496	+	0.00711548i	0.332227	+	0.943200i	$0.392200\pi$
$234$		0			0
$235$	3.11323e6	+	5.39227e6i	0.239887	+	0.415497i
$236$		0			0
$237$	−4.72744e6	−	2.68107e7i	−0.355125	−	2.01401i
$238$		0			0
$239$	3.99043e6	−	6.91163e6i	0.292298	−	0.506275i	−0.682055	−	0.731301i	$-0.738913\pi$
$239$	3.99043e6	−	6.91163e6i	0.292298	−	0.506275i	0.974353	+	0.225026i	$0.0722467\pi$
$240$		0			0
$241$	−5.61329e6	−	6.68966e6i	−0.401021	−	0.477918i	0.527310	−	0.849673i	$-0.323201\pi$
$241$	−5.61329e6	−	6.68966e6i	−0.401021	−	0.477918i	−0.928331	+	0.371755i	$0.878756\pi$
$242$		0			0
$243$	−668595.	+	1.83695e6i	−0.0465955	+	0.128020i
$244$		0			0
$245$	4.39316e6	−	2.49149e7i	0.298730	−	1.69418i
$246$		0			0
$247$	1.29649e7	−	5.40594e6i	0.860357	−	0.358741i
$248$		0			0
$249$	3.88786e6	+	685535.i	0.251833	+	0.0444050i
$250$		0			0
$251$	−1.67177e7	−	6.08476e6i	−1.05720	−	0.384788i	−0.245823	−	0.969315i	$-0.579058\pi$
$251$	−1.67177e7	−	6.08476e6i	−1.05720	−	0.384788i	−0.811375	+	0.584526i	$0.801280\pi$
$252$		0			0
$253$	−1.38509e7	+	1.16223e7i	−0.855296	+	0.717678i
$254$		0			0
$255$	−3.42012e7	−	1.97461e7i	−2.06263	−	1.19086i
$256$		0			0
$257$	1.77317e6	−	312658.i	0.104460	−	0.0184192i	−0.121174	−	0.992631i	$-0.538666\pi$
$257$	1.77317e6	−	312658.i	0.104460	−	0.0184192i	0.225634	+	0.974212i	$0.427555\pi$
$258$		0			0
$259$	1.71086e6	−	987767.i	0.0984727	−	0.0568533i
$260$		0			0
$261$	93405.4	+	256629.i	0.00525352	+	0.0144339i
$262$		0			0
$263$	1.04812e7	+	8.79476e6i	0.576160	+	0.483456i	0.883684	−	0.468085i	$-0.155056\pi$
$263$	1.04812e7	+	8.79476e6i	0.576160	+	0.483456i	−0.307523	+	0.951541i	$0.599500\pi$
$264$		0			0
$265$		−	5.45154e7i		−	2.92942i
$266$		0			0
$267$	2.91796e7			1.53301
$268$		0			0
$269$	−2.38443e6	+	2.84165e6i	−0.122498	+	0.145987i	−0.823808	−	0.566869i	$-0.808154\pi$
$269$	−2.38443e6	+	2.84165e6i	−0.122498	+	0.145987i	0.701310	+	0.712856i	$0.252599\pi$
$270$		0			0
$271$	−1.32697e7	+	4.82977e6i	−0.666734	+	0.242671i	−0.653141	−	0.757236i	$-0.726549\pi$
$271$	−1.32697e7	+	4.82977e6i	−0.666734	+	0.242671i	−0.0135928	+	0.999908i	$0.504327\pi$
$272$		0			0
$273$	1.35851e7	+	2.35300e7i	0.667689	+	1.15647i
$274$		0			0
$275$	1.12654e7	+	6.38893e7i	0.541688	+	3.07206i
$276$		0			0
$277$	−1.81769e7	+	3.14833e7i	−0.855224	+	1.48129i	0.0212128	+	0.999775i	$0.493247\pi$
$277$	−1.81769e7	+	3.14833e7i	−0.855224	+	1.48129i	−0.876437	+	0.481517i	$0.840086\pi$
$278$		0			0
$279$	−679367.	−	809638.i	−0.0312818	−	0.0372802i
$280$		0			0
$281$	−8.90848e6	+	2.44759e7i	−0.401499	+	1.10311i	0.560045	+	0.828462i	$0.310784\pi$
$281$	−8.90848e6	+	2.44759e7i	−0.401499	+	1.10311i	−0.961545	+	0.274648i	$0.911439\pi$
$282$		0			0
$283$	−407420.	+	2.31059e6i	−0.0179756	+	0.101945i	−0.992476	−	0.122443i	$-0.960927\pi$
$283$	−407420.	+	2.31059e6i	−0.0179756	+	0.101945i	0.974500	+	0.224388i	$0.0720382\pi$
$284$		0			0
$285$	3.55126e7	+	2.71175e7i	1.53408	+	1.17143i
$286$		0			0
$287$	−5.00269e7	−	8.82109e6i	−2.11621	−	0.373144i
$288$		0			0
$289$	−1.18530e7	−	4.31415e6i	−0.491061	−	0.178732i
$290$		0			0
$291$	−1.01671e7	+	8.53120e6i	−0.412589	+	0.346203i
$292$		0			0
$293$	−1.97198e7	−	1.13852e7i	−0.783970	−	0.452625i	0.0538654	−	0.998548i	$-0.482846\pi$
$293$	−1.97198e7	−	1.13852e7i	−0.783970	−	0.452625i	−0.837835	+	0.545923i	$0.816179\pi$
$294$		0			0
$295$	1.54431e7	−	2.72303e6i	0.601545	−	0.106069i
$296$		0			0
$297$	2.73986e7	−	1.58186e7i	1.04582	−	0.603807i
$298$		0			0
$299$	−7.58799e6	−	2.08478e7i	−0.283866	−	0.779915i
$300$		0			0
$301$	2.77949e7	+	2.33227e7i	1.01921	+	0.855222i
$302$		0			0
$303$			3.59313e7i			1.29165i
$304$		0			0
$305$	−1.87816e7			−0.661961
$306$		0			0
$307$	1.27658e6	−	1.52136e6i	0.0441196	−	0.0525797i	−0.743533	−	0.668699i	$-0.766852\pi$
$307$	1.27658e6	−	1.52136e6i	0.0441196	−	0.0525797i	0.787653	+	0.616119i	$0.211296\pi$
$308$		0			0
$309$	2.91971e7	−	1.06269e7i	0.989609	−	0.360188i
$310$		0			0
$311$	1.05718e7	+	1.83109e7i	0.351453	+	0.608734i	0.986504	−	0.163736i	$-0.0523545\pi$
$311$	1.05718e7	+	1.83109e7i	0.351453	+	0.608734i	−0.635051	+	0.772470i	$0.719021\pi$
$312$		0			0
$313$	−9.47118e6	−	5.37137e7i	−0.308867	−	1.75167i	−0.604722	−	0.796437i	$-0.706716\pi$
$313$	−9.47118e6	−	5.37137e7i	−0.308867	−	1.75167i	0.295855	−	0.955233i	$-0.404395\pi$
$314$		0			0
$315$	−2.76030e6	+	4.78098e6i	−0.0883131	+	0.152963i
$316$		0			0
$317$	833655.	+	993512.i	0.0261703	+	0.0311886i	0.778971	−	0.627060i	$-0.215742\pi$
$317$	833655.	+	993512.i	0.0261703	+	0.0311886i	−0.752801	+	0.658249i	$0.771298\pi$
$318$		0			0
$319$	3.13405e6	−	8.61073e6i	0.0965459	−	0.265258i
$320$		0			0
$321$	5.69319e6	−	3.22877e7i	0.172124	−	0.976162i
$322$		0			0
$323$	3.69280e7	+	1.91134e7i	1.09584	+	0.567192i
$324$		0			0
$325$	−7.83934e7	−	1.38229e7i	−2.28365	−	0.402669i
$326$		0			0
$327$	6.45878e7	+	2.35081e7i	1.84717	+	0.672316i
$328$		0			0
$329$	9.71394e6	−	8.15097e6i	0.272777	−	0.228887i
$330$		0			0
$331$	2.85732e7	+	1.64968e7i	0.787908	+	0.454899i	0.839225	−	0.543784i	$-0.183009\pi$
$331$	2.85732e7	+	1.64968e7i	0.787908	+	0.454899i	−0.0513178	+	0.998682i	$0.516342\pi$
$332$		0			0
$333$	−203559.	+	35893.0i	−0.00551262	+	0.000972024i
$334$		0			0
$335$	−6.48914e7	+	3.74651e7i	−1.72605	+	0.996535i
$336$		0			0
$337$	1.32013e7	+	3.62702e7i	0.344926	+	0.947676i	0.983943	+	0.178484i	$0.0571191\pi$
$337$	1.32013e7	+	3.62702e7i	0.344926	+	0.947676i	−0.639017	+	0.769193i	$0.720659\pi$
$338$		0			0
$339$	−1.77170e7	−	1.48663e7i	−0.454769	−	0.381597i
$340$		0			0
$341$			3.54626e7i			0.894351i
$342$		0			0
$343$	4.40891e6			0.109257
$344$		0			0
$345$	4.53628e7	−	5.40612e7i	1.10469	−	1.31652i
$346$		0			0
$347$	2.76867e7	−	1.00771e7i	0.662648	−	0.241184i	0.0112688	−	0.999937i	$-0.496413\pi$
$347$	2.76867e7	−	1.00771e7i	0.662648	−	0.241184i	0.651379	+	0.758752i	$0.274191\pi$
$348$		0			0
$349$	7.71907e6	+	1.33698e7i	0.181589	+	0.314521i	0.942422	−	0.334427i	$-0.108543\pi$
$349$	7.71907e6	+	1.33698e7i	0.181589	+	0.314521i	−0.760833	+	0.648948i	$0.775209\pi$
$350$		0			0
$351$	6.74091e6	+	3.82296e7i	0.155882	+	0.884053i
$352$		0			0
$353$	3.51265e6	−	6.08409e6i	0.0798566	−	0.138316i	−0.823331	−	0.567561i	$-0.807887\pi$
$353$	3.51265e6	−	6.08409e6i	0.0798566	−	0.138316i	0.903188	+	0.429245i	$0.141220\pi$
$354$		0			0
$355$	1.10820e7	+	1.32070e7i	0.247705	+	0.295203i
$356$		0			0
$357$	−2.75082e7	+	7.55782e7i	−0.604586	+	1.66109i
$358$		0			0
$359$	−1.87787e6	+	1.06499e7i	−0.0405866	+	0.230178i	−0.998353	−	0.0573694i	$-0.981729\pi$
$359$	−1.87787e6	+	1.06499e7i	−0.0405866	+	0.230178i	0.957766	+	0.287547i	$0.0928398\pi$
$360$		0			0
$361$	−3.86640e7	−	2.68031e7i	−0.821837	−	0.569723i
$362$		0			0
$363$	2.78702e7	+	4.91427e6i	0.582667	+	0.102740i
$364$		0			0
$365$	−5.58137e7	−	2.03145e7i	−1.14779	−	0.417761i
$366$		0			0
$367$	−3.04955e6	+	2.55888e6i	−0.0616933	+	0.0517668i	−0.673113	−	0.739540i	$-0.735043\pi$
$367$	−3.04955e6	+	2.55888e6i	−0.0616933	+	0.0517668i	0.611420	+	0.791307i	$0.290599\pi$
$368$		0			0
$369$	4.60296e6	+	2.65752e6i	0.0916133	+	0.0528929i
$370$		0			0
$371$	−1.09338e8	+	1.92792e7i	−2.14116	+	0.377545i
$372$		0			0
$373$	−7.42616e7	+	4.28749e7i	−1.43099	+	0.826185i	−0.997197	−	0.0748259i	$-0.976160\pi$
$373$	−7.42616e7	+	4.28749e7i	−1.43099	+	0.826185i	−0.433797	+	0.901011i	$0.642827\pi$
$374$		0			0
$375$	−5.17904e7	−	1.42293e8i	−0.982099	−	2.69829i
$376$		0			0
$377$	8.61310e6	+	7.22725e6i	0.160744	+	0.134880i
$378$		0			0
$379$		−	7.67724e6i		−	0.141022i	−0.997511	−	0.0705111i	$-0.977537\pi$
$379$		−	7.67724e6i		−	0.141022i	0.997511	−	0.0705111i	$-0.0224630\pi$
$380$		0			0
$381$	3.44958e6			0.0623722
$382$		0			0
$383$	−6.26225e7	+	7.46305e7i	−1.11464	+	1.32837i	−0.175639	+	0.984455i	$0.556199\pi$
$383$	−6.26225e7	+	7.46305e7i	−1.11464	+	1.32837i	−0.938999	+	0.343919i	$0.888245\pi$
$384$		0			0
$385$	1.74063e8	−	6.33538e7i	3.05017	−	1.11017i
$386$		0			0
$387$	−1.89817e6	−	3.28773e6i	−0.0327493	−	0.0567235i
$388$		0			0
$389$	−1.41730e7	−	8.03789e7i	−0.240775	−	1.36550i	−0.830103	−	0.557611i	$-0.811718\pi$
$389$	−1.41730e7	−	8.03789e7i	−0.240775	−	1.36550i	0.589327	−	0.807894i	$-0.299393\pi$
$390$		0			0
$391$	3.28370e7	−	5.68754e7i	0.549331	−	0.951469i
$392$		0			0
$393$	3.49340e7	+	4.16327e7i	0.575533	+	0.685894i
$394$		0			0
$395$	7.78911e7	−	2.14004e8i	1.26385	−	3.47241i
$396$		0			0
$397$	1.69975e6	−	9.63975e6i	0.0271652	−	0.154062i	−0.968208	−	0.250147i	$-0.919521\pi$
$397$	1.69975e6	−	9.63975e6i	0.0271652	−	0.154062i	0.995373	+	0.0960853i	$0.0306322\pi$
$398$		0			0
$399$	4.18289e7	−	8.08153e7i	0.658503	−	1.27226i
$400$		0			0
$401$	1.01203e8	+	1.78448e7i	1.56950	+	0.276745i	0.889662	−	0.456619i	$-0.150940\pi$
$401$	1.01203e8	+	1.78448e7i	1.56950	+	0.276745i	0.679836	+	0.733364i	$0.262051\pi$
$402$		0			0
$403$	−4.08891e7	−	1.48824e7i	−0.624731	−	0.227383i
$404$		0			0
$405$	−1.01078e8	+	8.48143e7i	−1.52157	+	1.27674i
$406$		0			0
$407$	6.00626e6	+	3.46771e6i	0.0890883	+	0.0514352i
$408$		0			0
$409$	−3.16219e7	+	5.57579e6i	−0.462187	+	0.0814961i	−0.399893	−	0.916562i	$-0.630953\pi$
$409$	−3.16219e7	+	5.57579e6i	−0.462187	+	0.0814961i	−0.0622940	+	0.998058i	$0.519842\pi$
$410$		0			0
$411$	1.00633e8	−	5.81005e7i	1.44949	−	0.836863i
$412$		0			0
$413$	−1.09228e7	−	3.00102e7i	−0.155055	−	0.426009i
$414$		0			0
$415$	2.52984e7	+	2.12279e7i	0.353956	+	0.297004i
$416$		0			0
$417$			1.18808e8i			1.63847i
$418$		0			0
$419$	−9.81970e7			−1.33492			−0.667462	−	0.744644i	$-0.732619\pi$
$419$	−9.81970e7			−1.33492			−0.667462	+	0.744644i	$0.732619\pi$
$420$		0			0
$421$	−1.07398e7	+	1.27993e7i	−0.143930	+	0.171529i	−0.833193	−	0.552982i	$-0.813490\pi$
$421$	−1.07398e7	+	1.27993e7i	−0.143930	+	0.171529i	0.689263	+	0.724511i	$0.257934\pi$
$422$		0			0
$423$	−1.24676e6	+	453783.i	−0.0164726	+	0.00599552i
$424$		0			0
$425$	−1.17819e8	−	2.04069e8i	−1.53479	−	2.65834i
$426$		0			0
$427$	6.64206e6	+	3.76690e7i	0.0853137	+	0.483838i
$428$		0			0
$429$	−4.76925e7	+	8.26059e7i	−0.604058	+	1.04626i
$430$		0			0
$431$	6.04114e7	+	7.19955e7i	0.754548	+	0.899236i	0.997490	−	0.0708052i	$-0.0225569\pi$
$431$	6.04114e7	+	7.19955e7i	0.754548	+	0.899236i	−0.242942	+	0.970041i	$0.578112\pi$
$432$		0			0
$433$	3.99391e7	−	1.09732e8i	0.491966	−	1.35167i	−0.406912	−	0.913467i	$-0.633395\pi$
$433$	3.99391e7	−	1.09732e8i	0.491966	−	1.35167i	0.898878	−	0.438198i	$-0.144383\pi$
$434$		0			0
$435$	−6.21058e6	+	3.52220e7i	−0.0754509	+	0.427903i
$436$		0			0
$437$	−4.50955e7	+	5.90563e7i	−0.540367	+	0.707655i
$438$		0			0
$439$	−1.05869e8	−	1.86675e7i	−1.25134	−	0.220644i	−0.491568	−	0.870839i	$-0.663576\pi$
$439$	−1.05869e8	−	1.86675e7i	−1.25134	−	0.220644i	−0.759768	+	0.650195i	$0.774687\pi$
$440$		0			0
$441$	5.06580e6	+	1.84380e6i	0.0590653	+	0.0214980i
$442$		0			0
$443$	9.73840e7	−	8.17149e7i	1.12015	−	0.939918i	0.121539	−	0.992587i	$-0.461217\pi$
$443$	9.73840e7	−	8.17149e7i	1.12015	−	0.939918i	0.998612	+	0.0526684i	$0.0167726\pi$
$444$		0			0
$445$	2.11393e8	+	1.22048e8i	2.39889	+	1.38500i
$446$		0			0
$447$	−6.49386e7	+	1.14504e7i	−0.727077	+	0.128203i
$448$		0			0
$449$	3.10031e7	−	1.78996e7i	0.342504	−	0.197745i	−0.318875	−	0.947797i	$-0.603305\pi$
$449$	3.10031e7	−	1.78996e7i	0.342504	−	0.197745i	0.661379	+	0.750052i	$0.269972\pi$
$450$		0			0
$451$	−6.09948e7	−	1.67582e8i	−0.664910	−	1.82683i
$452$		0			0
$453$	6.43873e6	+	5.40274e6i	0.0692637	+	0.0581191i
$454$		0			0
$455$			2.27286e8i			2.41289i
$456$		0			0
$457$	−1.08481e7			−0.113659			−0.0568296	−	0.998384i	$-0.518099\pi$
$457$	−1.08481e7			−0.113659			−0.0568296	+	0.998384i	$0.518099\pi$
$458$		0			0
$459$	−7.38644e7	+	8.80281e7i	−0.763830	+	0.910298i
$460$		0			0
$461$	4.47211e7	−	1.62772e7i	0.456467	−	0.166141i	−0.103545	−	0.994625i	$-0.533019\pi$
$461$	4.47211e7	−	1.62772e7i	0.456467	−	0.166141i	0.560012	+	0.828484i	$0.310796\pi$
$462$		0			0
$463$	−3.74522e7	−	6.48692e7i	−0.377342	−	0.653575i	0.613333	−	0.789824i	$-0.289828\pi$
$463$	−3.74522e7	−	6.48692e7i	−0.377342	−	0.653575i	−0.990675	+	0.136250i	$0.956495\pi$
$464$		0			0
$465$	−2.40353e7	−	1.36311e8i	−0.239051	−	1.35572i
$466$		0			0
$467$	−3.75058e7	+	6.49619e7i	−0.368254	+	0.637835i	−0.989293	−	0.145945i	$-0.953378\pi$
$467$	−3.75058e7	+	6.49619e7i	−0.368254	+	0.637835i	0.621039	+	0.783780i	$0.286711\pi$
$468$		0			0
$469$	9.80900e7	+	1.16899e8i	0.950838	+	1.13316i
$470$		0			0
$471$	4.60334e7	−	1.26476e8i	0.440566	−	1.21044i
$472$		0			0
$473$	−2.21192e7	+	1.25444e8i	−0.209019	+	1.18541i
$474$		0			0
$475$	1.02604e8	+	2.46072e8i	0.957380	+	2.29605i
$476$		0			0
$477$	1.14400e7	+	2.01718e6i	0.105407	+	0.0185862i
$478$		0			0
$479$	−4.42922e7	−	1.61210e7i	−0.403014	−	0.146685i	0.132557	−	0.991175i	$-0.457681\pi$
$479$	−4.42922e7	−	1.61210e7i	−0.403014	−	0.146685i	−0.535571	+	0.844490i	$0.679904\pi$
$480$		0			0
$481$	−6.51896e6	+	5.47006e6i	−0.0585792	+	0.0491537i
$482$		0			0
$483$	−1.24470e8	−	7.18625e7i	−1.10464	−	0.637766i
$484$		0			0
$485$	−1.09339e8	+	1.92794e7i	−0.958404	+	0.168992i
$486$		0			0
$487$	5.01725e7	−	2.89671e7i	0.434389	−	0.250794i	−0.266826	−	0.963745i	$-0.585975\pi$
$487$	5.01725e7	−	2.89671e7i	0.434389	−	0.250794i	0.701215	+	0.712950i	$0.252641\pi$
$488$		0			0
$489$	−1.90778e7	−	5.24159e7i	−0.163156	−	0.448266i
$490$		0			0
$491$	1.30635e8	+	1.09616e8i	1.10361	+	0.926037i	0.997662	−	0.0683352i	$-0.0217687\pi$
$491$	1.30635e8	+	1.09616e8i	1.10361	+	0.926037i	0.105945	+	0.994372i	$0.466213\pi$
$492$		0			0
$493$			3.32831e7i			0.277769i
$494$		0			0
$495$	−1.93810e7			−0.159794
$496$		0			0
$497$	2.25694e7	−	2.68971e7i	0.183844	−	0.219097i
$498$		0			0
$499$	7.36123e7	−	2.67927e7i	0.592446	−	0.215633i	−0.0283591	−	0.999598i	$-0.509028\pi$
$499$	7.36123e7	−	2.67927e7i	0.592446	−	0.215633i	0.620805	+	0.783965i	$0.286806\pi$
$500$		0			0
$501$	−3.60851e7	−	6.25011e7i	−0.286955	−	0.497021i
$502$		0			0
$503$	−6.54690e6	−	3.71293e7i	−0.0514436	−	0.291751i	0.948222	−	0.317608i	$-0.102880\pi$
$503$	−6.54690e6	−	3.71293e7i	−0.0514436	−	0.291751i	−0.999666	+	0.0258569i	$0.991769\pi$
$504$		0			0
$505$	−1.50288e8	+	2.60306e8i	−1.16694	+	2.02120i
$506$		0			0
$507$	1.13500e7	+	1.35264e7i	0.0870910	+	0.103791i
$508$		0			0
$509$	−6.60891e7	+	1.81578e8i	−0.501160	+	1.37693i	0.388983	+	0.921245i	$0.372827\pi$
$509$	−6.60891e7	+	1.81578e8i	−0.501160	+	1.37693i	−0.890143	+	0.455681i	$0.849396\pi$
$510$		0			0
$511$	−2.10051e7	+	1.19126e8i	−0.157421	+	0.892780i
$512$		0			0
$513$	9.56503e7	−	8.80614e7i	0.708491	−	0.652279i
$514$		0			0
$515$	2.55967e8	+	4.51339e7i	1.87397	+	0.330432i
$516$		0			0
$517$	4.18327e7	+	1.52259e7i	0.302722	+	0.110182i
$518$		0			0
$519$	−4.83731e7	+	4.05899e7i	−0.346021	+	0.290346i
$520$		0			0
$521$	−5.17397e7	−	2.98719e7i	−0.365857	−	0.211227i	0.305790	−	0.952099i	$-0.401079\pi$
$521$	−5.17397e7	−	2.98719e7i	−0.365857	−	0.211227i	−0.671647	+	0.740872i	$0.734413\pi$
$522$		0			0
$523$	4.61403e7	−	8.13578e6i	0.322534	−	0.0568714i	−0.0100371	−	0.999950i	$-0.503195\pi$
$523$	4.61403e7	−	8.13578e6i	0.322534	−	0.0568714i	0.332571	+	0.943078i	$0.392084\pi$
$524$		0			0
$525$	−4.46597e8	+	2.57843e8i	−3.08630	+	1.78188i
$526$		0			0
$527$	−4.40548e7	−	1.21039e8i	−0.300996	−	0.826980i
$528$		0			0
$529$	−2.35000e7	−	1.97188e7i	−0.158745	−	0.133203i
$530$		0			0
$531$			3.34147e6i			0.0223179i
$532$		0			0
$533$	2.18822e8			1.44514
$534$		0			0
$535$	1.76292e8	−	2.10097e8i	1.15126	−	1.37201i
$536$		0			0
$537$	2.85839e8	−	1.04037e8i	1.84586	−	0.671837i
$538$		0			0
$539$	−9.04412e7	−	1.56649e8i	−0.577564	−	1.00037i
$540$		0			0
$541$	−1.43059e7	−	8.11327e7i	−0.0903490	−	0.512394i	−0.996074	−	0.0885280i	$-0.971784\pi$
$541$	−1.43059e7	−	8.11327e7i	−0.0903490	−	0.512394i	0.905725	−	0.423866i	$-0.139327\pi$
$542$		0			0
$543$	7.11493e7	−	1.23234e8i	0.444397	−	0.769719i
$544$		0			0
$545$	3.69583e8	+	4.40452e8i	2.28309	+	2.72088i
$546$		0			0
$547$	3.26395e7	−	8.96762e7i	0.199426	−	0.547917i	−0.799158	−	0.601121i	$-0.794721\pi$
$547$	3.26395e7	−	8.96762e7i	0.199426	−	0.547917i	0.998584	+	0.0532035i	$0.0169432\pi$
$548$		0			0
$549$	694956.	−	3.94129e6i	0.00419991	−	0.0238189i
$550$		0			0
$551$	4.82758e6	−	3.73466e7i	0.0288585	−	0.223252i
$552$		0			0
$553$	−4.56760e8	−	8.05391e7i	−2.70093	−	0.476246i
$554$		0			0
$555$	−2.54371e7	−	9.25834e6i	−0.148795	−	0.0541569i
$556$		0			0
$557$	1.17621e8	−	9.86954e7i	0.680641	−	0.571125i	−0.235553	−	0.971862i	$-0.575690\pi$
$557$	1.17621e8	−	9.86954e7i	0.680641	−	0.571125i	0.916194	+	0.400736i	$0.131246\pi$
$558$		0			0
$559$	−1.35357e8	−	7.81485e7i	−0.774900	−	0.447389i
$560$		0			0
$561$	−2.78068e8	+	4.90309e7i	−1.57493	+	0.277703i
$562$		0			0
$563$	7.77768e7	−	4.49045e7i	0.435838	−	0.251631i	−0.265993	−	0.963975i	$-0.585700\pi$
$563$	7.77768e7	−	4.49045e7i	0.435838	−	0.251631i	0.701831	+	0.712344i	$0.252366\pi$
$564$		0			0
$565$	−6.61710e7	−	1.81803e8i	−0.366879	−	1.00799i
$566$		0			0
$567$	2.05853e8	+	1.72731e8i	1.12929	+	0.947590i
$568$		0			0
$569$		−	2.05159e8i		−	1.11366i	−0.830625	−	0.556832i	$-0.812017\pi$
$569$		−	2.05159e8i		−	1.11366i	0.830625	−	0.556832i	$-0.187983\pi$
$570$		0			0
$571$	−3.28636e8			−1.76525			−0.882627	−	0.470074i	$-0.844227\pi$
$571$	−3.28636e8			−1.76525			−0.882627	+	0.470074i	$0.844227\pi$
$572$		0			0
$573$	9.21386e7	−	1.09806e8i	0.489754	−	0.583666i
$574$		0			0
$575$	3.95689e8	−	1.44019e8i	2.08138	−	0.757559i
$576$		0			0
$577$	1.03130e8	+	1.78627e8i	0.536857	+	0.929864i	0.999071	+	0.0430953i	$0.0137219\pi$
$577$	1.03130e8	+	1.78627e8i	0.536857	+	0.929864i	−0.462214	+	0.886768i	$0.652945\pi$
$578$		0			0
$579$	−7.75038e6	−	4.39546e7i	−0.0399289	−	0.226448i
$580$		0			0
$581$	3.36287e7	−	5.82466e7i	0.171467	−	0.296990i
$582$		0			0
$583$	−2.50539e8	−	2.98581e8i	−1.26436	−	1.50680i
$584$		0			0
$585$	8.13351e6	−	2.23466e7i	0.0406266	−	0.111621i
$586$		0			0
$587$	3.56975e7	−	2.02450e8i	0.176491	−	1.00093i	−0.759917	−	0.650020i	$-0.774761\pi$
$587$	3.56975e7	−	2.02450e8i	0.176491	−	1.00093i	0.936409	−	0.350912i	$-0.114128\pi$
$588$		0			0
$589$	3.18770e7	+	1.42207e8i	0.156002	+	0.695943i
$590$		0			0
$591$	−2.68167e8	−	4.72851e7i	−1.29910	−	0.229067i
$592$		0			0
$593$	−1.42224e8	−	5.17655e7i	−0.682041	−	0.248243i	−0.0223172	−	0.999751i	$-0.507104\pi$
$593$	−1.42224e8	−	5.17655e7i	−0.682041	−	0.248243i	−0.659723	+	0.751508i	$0.729327\pi$
$594$		0			0
$595$	−5.15400e8	+	4.32472e8i	−2.44677	+	2.05309i
$596$		0			0
$597$	7.66672e6	+	4.42638e6i	0.0360318	+	0.0208030i
$598$		0			0
$599$	−1.18766e8	+	2.09417e7i	−0.552603	+	0.0974388i	−0.442975	−	0.896534i	$-0.646077\pi$
$599$	−1.18766e8	+	2.09417e7i	−0.552603	+	0.0974388i	−0.109628	+	0.993973i	$0.534966\pi$
$600$		0			0
$601$	4.08184e7	−	2.35665e7i	0.188032	−	0.108561i	−0.403029	−	0.915187i	$-0.632043\pi$
$601$	4.08184e7	−	2.35665e7i	0.188032	−	0.108561i	0.591061	+	0.806627i	$0.298709\pi$
$602$		0			0
$603$	−5.46089e6	−	1.50037e7i	−0.0249064	−	0.0684299i
$604$		0			0
$605$	1.81352e8	+	1.52173e8i	0.818948	+	0.687179i
$606$		0			0
$607$			1.46093e7i			0.0653227i	0.999466	+	0.0326613i	$0.0103983\pi$
$607$			1.46093e7i			0.0653227i	−0.999466	+	0.0326613i	$0.989602\pi$
$608$		0			0
$609$	7.28388e7			0.322486
$610$		0			0
$611$	−3.51114e7	+	4.18442e7i	−0.153931	+	0.183447i
$612$		0			0
$613$	−3.11804e8	+	1.13487e8i	−1.35363	+	0.492682i	−0.914080	−	0.405535i	$-0.867085\pi$
$613$	−3.11804e8	+	1.13487e8i	−1.35363	+	0.492682i	−0.439553	+	0.898217i	$0.644863\pi$
$614$		0			0
$615$	3.48032e8	+	6.02808e8i	1.49621	+	2.59152i
$616$		0			0
$617$	5.74622e6	+	3.25884e7i	0.0244640	+	0.138742i	0.994593	−	0.103846i	$-0.0331149\pi$
$617$	5.74622e6	+	3.25884e7i	0.0244640	+	0.138742i	−0.970129	+	0.242588i	$0.922004\pi$
$618$		0			0
$619$	−4.79058e7	+	8.29753e7i	−0.201984	+	0.349846i	−0.949167	−	0.314772i	$-0.898072\pi$
$619$	−4.79058e7	+	8.29753e7i	−0.201984	+	0.349846i	0.747184	+	0.664617i	$0.231405\pi$
$620$		0			0
$621$	−1.31995e8	−	1.57305e8i	−0.551165	−	0.656853i
$622$		0			0
$623$	1.70024e8	−	4.67138e8i	0.703149	−	1.93189i
$624$		0			0
$625$	1.14499e8	−	6.49354e8i	0.468986	−	2.65975i
$626$		0			0
$627$	3.19128e8	−	1.46843e7i	1.29468	−	0.0595732i
$628$		0			0
$629$	−2.48082e7	−	4.37435e6i	−0.0996880	−	0.0175777i
$630$		0			0
$631$	3.62276e8	+	1.31858e8i	1.44195	+	0.524828i	0.940332	−	0.340259i	$-0.110515\pi$
$631$	3.62276e8	+	1.31858e8i	1.44195	+	0.524828i	0.501622	+	0.865087i	$0.332737\pi$
$632$		0			0
$633$	−1.90816e8	+	1.60114e8i	−0.752321	+	0.631273i
$634$		0			0
$635$	2.49906e7	+	1.44283e7i	0.0976013	+	0.0563501i
$636$		0			0
$637$	2.18574e8	−	3.85405e7i	0.845630	−	0.149107i
$638$		0			0
$639$	−3.18154e6	+	1.83686e6i	−0.0121937	+	0.00704003i
$640$		0			0
$641$	−1.41062e8	−	3.87565e8i	−0.535594	−	1.47153i	−0.852323	−	0.523016i	$-0.824807\pi$
$641$	−1.41062e8	−	3.87565e8i	−0.535594	−	1.47153i	0.316729	−	0.948516i	$-0.397416\pi$
$642$		0			0
$643$	1.01061e8	+	8.48005e7i	0.380147	+	0.318982i	0.812760	−	0.582598i	$-0.197964\pi$
$643$	1.01061e8	+	8.48005e7i	0.380147	+	0.318982i	−0.432613	+	0.901580i	$0.642408\pi$
$644$		0			0
$645$		−	4.97173e8i		−	1.85280i
$646$		0			0
$647$	−304768.			−0.00112527			−0.000562634	−	1.00000i	$-0.500179\pi$
$647$	−304768.			−0.00112527			−0.000562634		1.00000i	$0.500179\pi$
$648$		0			0
$649$	7.20674e7	−	8.58866e7i	0.263636	−	0.314189i
$650$		0			0
$651$	−2.64890e8	+	9.64120e7i	−0.960113	+	0.349453i
$652$		0			0
$653$	7.74153e7	+	1.34087e8i	0.278027	+	0.481557i	0.970894	−	0.239508i	$-0.0769861\pi$
$653$	7.74153e7	+	1.34087e8i	0.278027	+	0.481557i	−0.692867	+	0.721065i	$0.743653\pi$
$654$		0			0
$655$	7.89461e7	+	4.47725e8i	0.280936	+	1.59326i
$656$		0			0
$657$	6.32820e6	−	1.09608e7i	0.0223143	−	0.0386496i
$658$		0			0
$659$	−2.02888e8	−	2.41793e8i	−0.708926	−	0.844865i	0.284580	−	0.958652i	$-0.408146\pi$
$659$	−2.02888e8	−	2.41793e8i	−0.708926	−	0.844865i	−0.993505	+	0.113788i	$0.963702\pi$
$660$		0			0
$661$	2.02408e7	−	5.56111e7i	0.0700847	−	0.192556i	−0.899705	−	0.436498i	$-0.856218\pi$
$661$	2.02408e7	−	5.56111e7i	0.0700847	−	0.192556i	0.969790	+	0.243942i	$0.0784407\pi$
$662$		0			0
$663$	6.01618e7	−	3.41195e8i	0.206434	−	1.17074i
$664$		0			0
$665$	6.41052e8	−	4.10514e8i	2.17986	−	1.39593i
$666$		0			0
$667$	−5.85730e7	−	1.03280e7i	−0.197388	−	0.0348048i
$668$		0			0
$669$	−2.56488e8	−	9.33540e7i	−0.856621	−	0.311785i
$670$		0			0
$671$	−1.02867e8	+	8.63154e7i	−0.340492	+	0.285707i
$672$		0			0
$673$	−4.56556e8	−	2.63593e8i	−1.49778	−	0.864746i	−0.497787	−	0.867299i	$-0.665854\pi$
$673$	−4.56556e8	−	2.63593e8i	−1.49778	−	0.864746i	−0.999997	+	0.00255313i	$0.999187\pi$
$674$		0			0
$675$	−7.25593e8	+	1.27942e8i	−2.35929	+	0.416007i
$676$		0			0
$677$	−1.74788e8	+	1.00914e8i	−0.563309	+	0.325226i	−0.754472	−	0.656332i	$-0.772107\pi$
$677$	−1.74788e8	+	1.00914e8i	−0.563309	+	0.325226i	0.191164	+	0.981558i	$0.438774\pi$
$678$		0			0
$679$	7.73347e7	+	2.12475e8i	0.247039	+	0.678734i
$680$		0			0
$681$	2.32351e8	+	1.94966e8i	0.735706	+	0.617330i
$682$		0			0
$683$			3.24259e8i			1.01772i	0.860848	+	0.508862i	$0.169934\pi$
$683$			3.24259e8i			1.01772i	−0.860848	+	0.508862i	$0.830066\pi$
$684$		0			0
$685$	9.72053e8			3.02425
$686$		0			0
$687$	−3.15713e8	+	3.76252e8i	−0.973694	+	1.16040i
$688$		0			0
$689$	4.49413e8	−	1.63573e8i	1.37400	−	0.500096i
$690$		0			0
$691$	6.18703e7	+	1.07162e8i	0.187520	+	0.324794i	0.944423	−	0.328733i	$-0.106622\pi$
$691$	6.18703e7	+	1.07162e8i	0.187520	+	0.324794i	−0.756903	+	0.653528i	$0.773288\pi$
$692$		0			0
$693$	6.85403e6	+	3.88711e7i	0.0205943	+	0.116796i
$694$		0			0
$695$	−4.96930e8	+	8.60708e8i	−1.48027	+	2.56390i
$696$		0			0
$697$	4.16369e8	+	4.96209e8i	1.22965	+	1.46543i
$698$		0			0
$699$	2.51171e6	−	6.90086e6i	0.00735423	−	0.0202056i
$700$		0			0
$701$	−1.10634e6	+	6.27435e6i	−0.00321169	+	0.0182144i	−0.986371	−	0.164534i	$-0.947388\pi$
$701$	−1.10634e6	+	6.27435e6i	−0.00321169	+	0.0182144i	0.983160	+	0.182748i	$0.0584992\pi$
$702$		0			0
$703$	2.72024e7	+	8.50672e6i	0.0782964	+	0.0244848i
$704$		0			0
$705$	−1.71116e8	−	3.01723e7i	−0.488340	−	0.0861075i
$706$		0			0
$707$	5.75227e8	+	2.09366e8i	1.62773	+	0.592444i
$708$		0			0
$709$	−4.58812e8	+	3.84989e8i	−1.28735	+	1.08021i	−0.295161	+	0.955448i	$0.595373\pi$
$709$	−4.58812e8	+	3.84989e8i	−1.28735	+	1.08021i	−0.992186	+	0.124765i	$0.960182\pi$
$710$		0			0
$711$	4.20264e7	+	2.42639e7i	0.116926	+	0.0675075i
$712$		0			0
$713$	2.26681e8	−	3.99699e7i	0.625382	−	0.110272i
$714$		0			0
$715$	−6.91021e8	+	3.98961e8i	−1.89048	+	1.09147i
$716$		0			0
$717$	7.61726e7	+	2.09282e8i	0.206653	+	0.567774i
$718$		0			0
$719$	−1.17519e8	−	9.86099e7i	−0.316170	−	0.265298i	0.470867	−	0.882204i	$-0.343941\pi$
$719$	−1.17519e8	−	9.86099e7i	−0.316170	−	0.265298i	−0.787036	+	0.616906i	$0.788386\pi$
$720$		0			0
$721$		−	5.29339e8i		−	1.41230i
$722$		0			0
$723$	2.43695e8			0.644811
$724$		0			0
$725$	−1.37172e8	+	1.63476e8i	−0.359958	+	0.428982i
$726$		0			0
$727$	2.94890e7	−	1.07331e7i	0.0767462	−	0.0279333i	−0.303362	−	0.952875i	$-0.598109\pi$
$727$	2.94890e7	−	1.07331e7i	0.0767462	−	0.0279333i	0.380108	+	0.924942i	$0.375887\pi$
$728$		0			0
$729$	1.78750e8	+	3.09604e8i	0.461386	+	0.799143i
$730$		0			0
$731$	−8.03415e7	−	4.55639e8i	−0.205678	−	1.16646i
$732$		0			0
$733$	−3.33980e8	+	5.78470e8i	−0.848025	+	1.46882i	0.0349432	+	0.999389i	$0.488875\pi$
$733$	−3.33980e8	+	5.78470e8i	−0.848025	+	1.46882i	−0.882968	+	0.469433i	$0.844458\pi$
$734$		0			0
$735$	4.53808e8	+	5.40827e8i	1.14290	+	1.36206i
$736$		0			0
$737$	−1.83230e8	+	5.03422e8i	−0.457715	+	1.25756i
$738$		0			0
$739$	3.92470e7	−	2.22581e8i	0.0972464	−	0.551511i	−0.896789	−	0.442457i	$-0.854107\pi$
$739$	3.92470e7	−	2.22581e8i	0.0972464	−	0.551511i	0.994036	−	0.109054i	$-0.0347821\pi$
$740$		0			0
$741$	−1.16996e8	+	3.74123e8i	−0.287551	+	0.919518i
$742$		0			0
$743$	−3.26176e8	−	5.75137e7i	−0.795217	−	0.140218i	−0.238743	−	0.971083i	$-0.576735\pi$
$743$	−3.26176e8	−	5.75137e7i	−0.795217	−	0.140218i	−0.556475	+	0.830865i	$0.687846\pi$
$744$		0			0
$745$	−5.18343e8	−	1.88662e8i	−1.25357	−	0.456262i
$746$		0			0
$747$	−5.39074e6	+	4.52337e6i	−0.0129326	+	0.0108518i
$748$		0			0
$749$	−4.83723e8	−	2.79278e8i	−1.15120	−	0.664646i
$750$		0			0
$751$	4.49946e8	−	7.93377e7i	1.06228	−	0.187309i	0.384915	−	0.922952i	$-0.374231\pi$
$751$	4.49946e8	−	7.93377e7i	1.06228	−	0.187309i	0.677370	+	0.735643i	$0.263120\pi$
$752$		0			0
$753$	4.29951e8	−	2.48233e8i	1.00701	−	0.581398i
$754$		0			0
$755$	2.40479e7	+	6.60712e7i	0.0558775	+	0.153522i
$756$		0			0
$757$	−1.32401e8	−	1.11097e8i	−0.305213	−	0.256104i	0.477297	−	0.878742i	$-0.341617\pi$
$757$	−1.32401e8	−	1.11097e8i	−0.305213	−	0.256104i	−0.782510	+	0.622638i	$0.786061\pi$
$758$		0			0
$759$		−	5.04570e8i		−	1.15397i
$760$		0			0
$761$	−1.24966e8			−0.283556			−0.141778	−	0.989898i	$-0.545282\pi$
$761$	−1.24966e8			−0.283556			−0.141778	+	0.989898i	$0.545282\pi$
$762$		0			0
$763$	7.52684e8	−	8.97014e8i	1.69449	−	2.01942i
$764$		0			0
$765$	6.61502e7	−	2.40767e7i	0.147757	−	0.0537790i
$766$		0			0
$767$	6.87848e7	+	1.19139e8i	0.152443	+	0.264038i
$768$		0			0
$769$	−3.43239e7	−	1.94660e8i	−0.0754775	−	0.428054i	−0.999008	−	0.0445292i	$-0.985821\pi$
$769$	−3.43239e7	−	1.94660e8i	−0.0754775	−	0.428054i	0.923531	−	0.383525i	$-0.125290\pi$
$770$		0			0
$771$	−2.51227e7	+	4.35138e7i	−0.0548155	+	0.0949432i
$772$		0			0
$773$	−2.31783e8	−	2.76229e8i	−0.501815	−	0.598040i	0.454366	−	0.890815i	$-0.349866\pi$
$773$	−2.31783e8	−	2.76229e8i	−0.501815	−	0.598040i	−0.956181	+	0.292775i	$0.905421\pi$
$774$		0			0
$775$	2.82467e8	−	7.76071e8i	0.606823	−	1.66723i
$776$		0			0
$777$	−9.57309e6	+	5.42917e7i	−0.0204075	+	0.115736i
$778$		0			0
$779$	−3.95229e8	−	6.17182e8i	−0.836058	−	1.30557i
$780$		0			0
$781$	1.21393e8	+	2.14048e7i	0.254823	+	0.0449322i
$782$		0			0
$783$	9.77924e7	+	3.55935e7i	0.203714	+	0.0741457i
$784$		0			0
$785$	8.62493e8	−	7.23718e8i	1.78298	−	1.49610i
$786$		0			0
$787$	2.35995e8	+	1.36252e8i	0.484148	+	0.279523i	0.722143	−	0.691743i	$-0.243157\pi$
$787$	2.35995e8	+	1.36252e8i	0.484148	+	0.279523i	−0.237996	+	0.971266i	$0.576490\pi$
$788$		0			0
$789$	−3.76015e8	+	6.63016e7i	−0.765551	+	0.134987i
$790$		0			0
$791$	−3.41230e8	+	1.97009e8i	−0.689474	+	0.398068i
$792$		0			0
$793$	−5.63539e7	−	1.54831e8i	−0.113007	−	0.310483i
$794$		0			0
$795$	1.16539e9	+	9.77876e8i	2.31936	+	1.94618i
$796$		0			0
$797$			7.70374e8i			1.52169i	0.648933	+	0.760845i	$0.275215\pi$
$797$			7.70374e8i			1.52169i	−0.648933	+	0.760845i	$0.724785\pi$
$798$		0			0
$799$	−1.61696e8			−0.317001
$800$		0			0
$801$	−3.34335e7	+	3.98445e7i	−0.0650555	+	0.0775302i
$802$		0			0
$803$	−3.99052e8	+	1.45243e8i	−0.770696	+	0.280511i
$804$		0			0
$805$	−6.01149e8	−	1.04122e9i	−1.15238	−	1.99598i
$806$		0			0
$807$	−1.79756e7	−	1.01945e8i	−0.0342030	−	0.193975i
$808$		0			0
$809$	−9.72899e7	+	1.68511e8i	−0.183748	+	0.318260i	−0.943154	−	0.332356i	$-0.892156\pi$
$809$	−9.72899e7	+	1.68511e8i	−0.183748	+	0.318260i	0.759406	+	0.650617i	$0.225490\pi$
$810$		0			0
$811$	5.52328e8	+	6.58239e8i	1.03546	+	1.23402i	0.971741	+	0.236049i	$0.0758527\pi$
$811$	5.52328e8	+	6.58239e8i	1.03546	+	1.23402i	0.0637222	+	0.997968i	$0.479703\pi$
$812$		0			0
$813$	1.34779e8	−	3.70303e8i	0.250814	−	0.689106i
$814$		0			0
$815$	8.10265e7	−	4.59524e8i	0.149677	−	0.848859i
$816$		0			0
$817$	2.40616e7	+	5.22920e8i	0.0441222	+	0.958890i
$818$		0			0
$819$	−4.76956e7	−	8.41002e6i	−0.0868214	−	0.0153090i
$820$		0			0
$821$	9.77704e8	+	3.55855e8i	1.76676	+	0.643049i	0.999999	+	0.00111835i	$0.000355981\pi$
$821$	9.77704e8	+	3.55855e8i	1.76676	+	0.643049i	0.766763	+	0.641931i	$0.221866\pi$
$822$		0			0
$823$	−7.89255e8	+	6.62263e8i	−1.41585	+	1.18804i	−0.462333	+	0.886706i	$0.652987\pi$
$823$	−7.89255e8	+	6.62263e8i	−1.41585	+	1.18804i	−0.953519	+	0.301334i	$0.902568\pi$
$824$		0			0
$825$	−1.56785e9	−	9.05199e8i	−2.79218	−	1.61206i
$826$		0			0
$827$	9.04309e8	−	1.59454e8i	1.59882	−	0.281916i	0.697999	−	0.716099i	$-0.254074\pi$
$827$	9.04309e8	−	1.59454e8i	1.59882	−	0.281916i	0.900825	+	0.434183i	$0.142963\pi$
$828$		0			0
$829$	−4.43551e8	+	2.56084e8i	−0.778538	+	0.449489i	−0.835912	−	0.548864i	$-0.815061\pi$
$829$	−4.43551e8	+	2.56084e8i	−0.778538	+	0.449489i	0.0573740	+	0.998353i	$0.481727\pi$
$830$		0			0
$831$	−3.46975e8	−	9.53306e8i	−0.604637	−	1.66123i
$832$		0			0
$833$	5.03293e8	+	4.22313e8i	0.870734	+	0.730633i
$834$		0			0
$835$		−	6.03722e8i		−	1.03700i
$836$		0			0
$837$	−4.02750e8			−0.686846
$838$		0			0
$839$	−2.10746e8	+	2.51158e8i	−0.356840	+	0.425266i	−0.914363	−	0.404896i	$-0.867308\pi$
$839$	−2.10746e8	+	2.51158e8i	−0.356840	+	0.425266i	0.557522	+	0.830162i	$0.311752\pi$
$840$		0			0
$841$	−5.30627e8	+	1.93132e8i	−0.892074	+	0.324688i
$842$		0			0
$843$	−3.63429e8	−	6.29477e8i	−0.606648	−	1.05074i
$844$		0			0
$845$	2.56496e7	+	1.45466e8i	0.0425118	+	0.241097i
$846$		0			0
$847$	2.41068e8	−	4.17542e8i	0.396725	−	0.687147i
$848$		0			0
$849$	−4.20859e7	−	5.01560e7i	−0.0687723	−	0.0819596i
$850$		0			0
$851$	1.53963e7	−	4.23010e7i	0.0249820	−	0.0686376i
$852$		0			0
$853$	−5.02193e7	+	2.84808e8i	−0.0809140	+	0.458886i	0.917250	+	0.398313i	$0.130404\pi$
$853$	−5.02193e7	+	2.84808e8i	−0.0809140	+	0.458886i	−0.998164	+	0.0605735i	$0.980707\pi$
$854$		0			0
$855$	−7.77184e7	+	1.74213e7i	−0.124344	+	0.0278730i
$856$		0			0
$857$	1.07936e9	+	1.90320e8i	1.71484	+	0.302372i	0.942839	−	0.333250i	$-0.108145\pi$
$857$	1.07936e9	+	1.90320e8i	1.71484	+	0.302372i	0.772000	+	0.635622i	$0.219256\pi$
$858$		0			0
$859$	−3.98440e8	−	1.45020e8i	−0.628614	−	0.228797i	0.00801401	−	0.999968i	$-0.497449\pi$
$859$	−3.98440e8	−	1.45020e8i	−0.628614	−	0.228797i	−0.636628	+	0.771171i	$0.719671\pi$
$860$		0			0
$861$	1.08593e9	−	9.11206e8i	1.70135	−	1.42760i
$862$		0			0
$863$	5.18311e8	+	2.99247e8i	0.806413	+	0.465583i	0.845709	−	0.533645i	$-0.179178\pi$
$863$	5.18311e8	+	2.99247e8i	0.806413	+	0.465583i	−0.0392955	+	0.999228i	$0.512511\pi$
$864$		0			0
$865$	−5.20214e8	+	9.17277e7i	−0.803773	+	0.141727i
$866$		0			0
$867$	3.04839e8	−	1.75999e8i	0.467750	−	0.270055i
$868$		0			0
$869$	−5.56899e8	−	1.53007e9i	−0.848628	−	2.33159i
$870$		0			0
$871$	−5.03560e8	−	4.22537e8i	−0.762073	−	0.639455i
$872$		0			0
$873$		−	2.36580e7i		−	0.0355578i
$874$		0			0
$875$	−2.57975e9			−3.85082
$876$		0			0
$877$	−4.66957e8	+	5.56497e8i	−0.692273	+	0.825019i	−0.991629	−	0.129122i	$-0.958784\pi$
$877$	−4.66957e8	+	5.56497e8i	−0.692273	+	0.825019i	0.299355	+	0.954142i	$0.403228\pi$
$878$		0			0
$879$	5.97110e8	−	2.17330e8i	0.879201	−	0.320003i
$880$		0			0
$881$	−5.17441e7	−	8.96234e7i	−0.0756717	−	0.131067i	0.825706	−	0.564100i	$-0.190777\pi$
$881$	−5.17441e7	−	8.96234e7i	−0.0756717	−	0.131067i	−0.901378	+	0.433033i	$0.857443\pi$
$882$		0			0
$883$	7.77340e7	+	4.40852e8i	0.112909	+	0.640339i	0.987764	+	0.155955i	$0.0498454\pi$
$883$	7.77340e7	+	4.40852e8i	0.112909	+	0.640339i	−0.874855	+	0.484385i	$0.839044\pi$
$884$		0			0
$885$	−2.18801e8	+	3.78975e8i	−0.315660	+	0.546739i
$886$		0			0
$887$	−2.43397e8	−	2.90069e8i	−0.348774	−	0.415653i	0.562927	−	0.826507i	$-0.309675\pi$
$887$	−2.43397e8	−	2.90069e8i	−0.348774	−	0.415653i	−0.911701	+	0.410853i	$0.865231\pi$
$888$		0			0
$889$	2.01001e7	−	5.52246e7i	0.0286084	−	0.0786009i
$890$		0			0
$891$	−1.63818e8	+	9.29057e8i	−0.231594	+	1.31344i
$892$		0			0
$893$	1.81437e8	+	2.34534e7i	0.254784	+	0.0329345i
$894$		0			0
$895$	2.50592e9	+	4.41861e8i	3.49540	+	0.616334i
$896$		0			0
$897$	5.81779e8	+	2.11750e8i	0.806085	+	0.293391i
$898$		0			0
$899$	−8.93608e7	+	7.49826e7i	−0.122989	+	0.103200i
$900$		0			0
$901$	1.22605e9	+	7.07862e8i	1.67623	+	0.967775i
$902$		0			0
$903$	−9.97148e8	+	1.75824e8i	−1.35424	+	0.238789i
$904$		0			0
$905$	1.03089e9	−	5.95183e8i	1.39080	−	0.802981i
$906$		0			0
$907$	−3.36881e8	−	9.25574e8i	−0.451497	−	1.24048i	−0.931670	−	0.363305i	$-0.881648\pi$
$907$	−3.36881e8	−	9.25574e8i	−0.451497	−	1.24048i	0.480173	−	0.877174i	$-0.340574\pi$
$908$		0			0
$909$	−4.90639e7	−	4.11695e7i	−0.0653237	−	0.0548131i
$910$		0			0
$911$			1.18132e9i			1.56247i	0.624237	+	0.781235i	$0.285410\pi$
$911$			1.18132e9i			1.56247i	−0.624237	+	0.781235i	$0.714590\pi$
$912$		0			0
$913$	2.36118e8			0.310253
$914$		0			0
$915$	3.36896e8	−	4.01498e8i	0.439778	−	0.524107i
$916$		0			0
$917$	8.70055e8	−	3.16674e8i	1.12834	−	0.410681i
$918$		0			0
$919$	−6.56357e7	−	1.13684e8i	−0.0845656	−	0.146472i	0.820640	−	0.571445i	$-0.193617\pi$
$919$	−6.56357e7	−	1.13684e8i	−0.0845656	−	0.146472i	−0.905206	+	0.424973i	$0.860284\pi$
$920$		0			0
$921$	9.62380e6	+	5.45793e7i	0.0123188	+	0.0698633i
$922$		0			0
$923$	−7.56244e7	+	1.30985e8i	−0.0961738	+	0.166578i
$924$		0			0
$925$	−1.03821e8	−	1.23729e8i	−0.131178	−	0.156332i
$926$		0			0
$927$	−1.89426e7	+	5.20444e7i	−0.0237794	+	0.0653333i
$928$		0			0
$929$	−1.39752e8	+	7.92571e8i	−0.174305	+	0.988533i	0.764638	+	0.644460i	$0.222918\pi$
$929$	−1.39752e8	+	7.92571e8i	−0.174305	+	0.988533i	−0.938943	+	0.344073i	$0.888193\pi$
$930$		0			0
$931$	−5.03483e8	−	5.46871e8i	−0.623930	−	0.677698i
$932$		0			0
$933$	−5.81068e8	−	1.02458e8i	−0.715454	−	0.126154i
$934$		0			0
$935$	−2.21955e9	−	8.07851e8i	−2.71538	−	0.988317i
$936$		0			0
$937$	−1.19334e9	+	1.00133e9i	−1.45059	+	1.21719i	−0.518442	+	0.855113i	$0.673488\pi$
$937$	−1.19334e9	+	1.00133e9i	−1.45059	+	1.21719i	−0.932148	+	0.362077i	$0.882068\pi$
$938$		0			0
$939$	1.31814e9	+	7.61028e8i	1.59208	+	0.919187i
$940$		0			0
$941$	2.29273e8	−	4.04270e7i	0.275159	−	0.0485180i	−0.0343658	−	0.999409i	$-0.510941\pi$
$941$	2.29273e8	−	4.04270e7i	0.275159	−	0.0485180i	0.309525	+	0.950891i	$0.399830\pi$
$942$		0			0
$943$	−1.00245e9	+	5.78765e8i	−1.19544	+	0.690188i
$944$		0			0
$945$	7.19511e8	+	1.97684e9i	0.852593	+	2.34248i
$946$		0			0
$947$	1.09674e9	+	9.20276e8i	1.29138	+	1.08360i	0.991566	+	0.129601i	$0.0413696\pi$
$947$	1.09674e9	+	9.20276e8i	1.29138	+	1.08360i	0.299816	+	0.953997i	$0.403075\pi$
$948$		0			0
$949$		−	5.21069e8i		−	0.609672i
$950$		0			0
$951$	−3.61923e7			−0.0420799
$952$		0			0
$953$	−7.09684e8	+	8.45768e8i	−0.819948	+	0.977176i	−0.999979	−	0.00648496i	$-0.997936\pi$
$953$	−7.09684e8	+	8.45768e8i	−0.819948	+	0.977176i	0.180031	+	0.983661i	$0.442380\pi$
$954$		0			0
$955$	1.12678e9	−	4.10115e8i	1.29369	−	0.470864i
$956$		0			0
$957$	1.27856e8	+	2.21453e8i	0.145877	+	0.252666i
$958$		0			0
$959$	−3.43764e8	−	1.94958e9i	−0.389767	−	2.21048i
$960$		0			0
$961$	−2.18027e8	+	3.77633e8i	−0.245663	+	0.425501i
$962$		0			0
$963$	3.75654e7	+	4.47687e7i	0.0420639	+	0.0501298i
$964$		0			0
$965$	1.27698e8	−	3.50848e8i	0.142103	−	0.390424i
$966$		0			0
$967$	−1.46787e8	+	8.32473e8i	−0.162334	+	0.920642i	0.789437	+	0.613832i	$0.210373\pi$
$967$	−1.46787e8	+	8.32473e8i	−0.162334	+	0.920642i	−0.951771	+	0.306810i	$0.900738\pi$
$968$		0			0
$969$	−1.07099e9	+	4.46568e8i	−1.17710	+	0.490813i
$970$		0			0
$971$	−4.75751e8	−	8.38877e7i	−0.519663	−	0.0916306i	−0.0923364	−	0.995728i	$-0.529434\pi$
$971$	−4.75751e8	−	8.38877e7i	−0.519663	−	0.0916306i	−0.427327	+	0.904097i	$0.640545\pi$
$972$		0			0
$973$	1.90201e9	+	6.92273e8i	2.06478	+	0.751518i
$974$		0			0
$975$	1.70168e9	−	1.42788e9i	1.83597	−	1.54056i
$976$		0			0
$977$	−4.03570e8	−	2.33001e8i	−0.432749	−	0.249847i	0.267768	−	0.963483i	$-0.413714\pi$
$977$	−4.03570e8	−	2.33001e8i	−0.432749	−	0.249847i	−0.700517	+	0.713636i	$0.747047\pi$
$978$		0			0
$979$	1.71870e9	−	3.03053e8i	1.83169	−	0.322976i
$980$		0			0
$981$	−1.06104e8	+	6.12590e7i	−0.112389	+	0.0648878i
$982$		0			0
$983$	3.91501e8	+	1.07564e9i	0.412166	+	1.13242i	0.956036	+	0.293248i	$0.0947362\pi$
$983$	3.91501e8	+	1.07564e9i	0.412166	+	1.13242i	−0.543870	+	0.839169i	$0.683042\pi$
$984$		0			0
$985$	−1.74497e9	−	1.46420e9i	−1.82591	−	1.53212i
$986$		0			0
$987$			3.53866e8i			0.368033i
$988$		0			0
$989$	8.26782e8			0.854678
$990$		0			0
$991$	−4.19536e8	+	4.99984e8i	−0.431071	+	0.513730i	−0.937231	−	0.348710i	$-0.886620\pi$
$991$	−4.19536e8	+	4.99984e8i	−0.431071	+	0.513730i	0.506160	+	0.862439i	$0.331064\pi$
$992$		0			0
$993$	−8.65190e8	+	3.14903e8i	−0.883616	+	0.321610i
$994$		0			0
$995$	3.70279e7	+	6.41342e7i	0.0375889	+	0.0651059i
$996$		0			0
$997$	2.76114e8	+	1.56592e9i	0.278614	+	1.58010i	0.727244	+	0.686379i	$0.240801\pi$
$997$	2.76114e8	+	1.56592e9i	0.278614	+	1.58010i	−0.448630	+	0.893718i	$0.648088\pi$
$998$		0			0
$999$	−3.93830e7	+	6.82133e7i	−0.0395013	+	0.0684183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.3	✓	60
19.10	odd	18	inner	76.7.j.a.29.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.3	✓	60	1.1	even	1	trivial
76.7.j.a.29.3	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)

\(f(q)\)	\(=\)	\(q+(-17.9376 + 21.3772i) q^{3} +(-219.363 + 79.8415i) q^{5} +(237.710 + 411.726i) q^{7} +(-8.63778 - 48.9873i) q^{9} +O(q^{10})\)	\(q+(-17.9376 + 21.3772i) q^{3} +(-219.363 + 79.8415i) q^{5} +(237.710 + 411.726i) q^{7} +(-8.63778 - 48.9873i) q^{9} +(-834.519 + 1445.43i) q^{11} +(-1316.39 - 1568.81i) q^{13} +(2228.05 - 6121.53i) q^{15} +(1052.70 - 5970.18i) q^{17} +(-2047.17 + 6546.37i) q^{19} +(-13065.5 - 2303.80i) q^{21} +(10179.9 + 3705.18i) q^{23} +(29775.9 - 24984.9i) q^{25} +(-16415.8 - 9477.66i) q^{27} +(-5406.79 + 953.363i) q^{29} +(18400.7 - 10623.7i) q^{31} +(-15930.0 - 43767.2i) q^{33} +(-85017.5 - 71338.2i) q^{35} -4155.35i q^{37} +57149.7 q^{39} +(-68681.9 + 81851.9i) q^{41} +(71716.5 - 26102.7i) q^{43} +(5806.03 + 10056.3i) q^{45} +(-4631.63 - 26267.3i) q^{47} +(-54187.6 + 93855.7i) q^{49} +(108743. + 129595. i) q^{51} +(-79871.9 + 219446. i) q^{53} +(67657.1 - 383702. i) q^{55} +(-103222. - 161189. i) q^{57} +(-66154.1 - 11664.8i) q^{59} +(75603.3 + 27517.3i) q^{61} +(18116.1 - 15201.2i) q^{63} +(414023. + 239036. i) q^{65} +(316105. - 55737.8i) q^{67} +(-261810. + 151156. i) q^{69} +(-25259.6 - 69400.2i) q^{71} +(194909. + 163548. i) q^{73} +1.08470e6i q^{75} -793494. q^{77} +(-627085. + 747331. i) q^{79} +(531142. - 193320. i) q^{81} +(-70734.7 - 122516. i) q^{83} +(245744. + 1.39369e6i) q^{85} +(76604.7 - 132683. i) q^{87} +(-672124. - 801007. i) q^{89} +(333002. - 914915. i) q^{91} +(-102961. + 583920. i) q^{93} +(-73598.2 - 1.59948e6i) q^{95} +(468378. + 82587.7i) q^{97} +(78016.1 + 28395.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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