LMFDB - Embedded newform 76.7.j.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	76.53
Dual form			76.7.j.a.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.3521 + 3.94128i) q^{3} +(18.7591 - 15.7407i) q^{5} +(52.4083 - 90.7739i) q^{7} +(-200.954 + 73.1411i) q^{9} +O(q^{10})$	\(q+(-22.3521 + 3.94128i) q^{3} +(18.7591 - 15.7407i) q^{5} +(52.4083 - 90.7739i) q^{7} +(-200.954 + 73.1411i) q^{9} +(-640.572 - 1109.50i) q^{11} +(888.307 + 156.633i) q^{13} +(-357.266 + 425.772i) q^{15} +(3790.43 + 1379.60i) q^{17} +(983.265 + 6788.16i) q^{19} +(-813.671 + 2235.54i) q^{21} +(12200.4 + 10237.4i) q^{23} +(-2609.12 + 14797.1i) q^{25} +(18532.8 - 10699.9i) q^{27} +(9849.35 + 27060.9i) q^{29} +(137.856 + 79.5910i) q^{31} +(18691.0 + 22275.0i) q^{33} +(-445.715 - 2527.78i) q^{35} +11354.4i q^{37} -20472.9 q^{39} +(-9891.18 + 1744.08i) q^{41} +(50656.4 - 42505.7i) q^{43} +(-2618.41 + 4535.21i) q^{45} +(54790.0 - 19941.9i) q^{47} +(53331.2 + 92372.4i) q^{49} +(-90161.3 - 15897.9i) q^{51} +(-78739.2 + 93837.7i) q^{53} +(-29480.9 - 10730.2i) q^{55} +(-48732.0 - 147854. i) q^{57} +(20944.3 - 57543.9i) q^{59} +(104145. + 87388.2i) q^{61} +(-3892.34 + 22074.5i) q^{63} +(19129.3 - 11044.3i) q^{65} +(-76833.7 - 211099. i) q^{67} +(-313054. - 180742. i) q^{69} +(-144170. - 171815. i) q^{71} +(-44412.7 - 251877. i) q^{73} -341028. i q^{75} -134285. q^{77} +(-281936. + 49712.9i) q^{79} +(-252651. + 211999. i) q^{81} +(80835.5 - 140011. i) q^{83} +(92820.7 - 33784.0i) q^{85} +(-326808. - 566048. i) q^{87} +(592488. + 104472. i) q^{89} +(60772.9 - 72426.3i) q^{91} +(-3395.05 - 1235.70i) q^{93} +(125296. + 111862. i) q^{95} +(-281608. + 773712. i) q^{97} +(209875. + 176106. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−22.3521	+	3.94128i	−0.827855	+	0.145973i	−0.571492	−	0.820607i	$-0.693635\pi$
$3$	−22.3521	+	3.94128i	−0.827855	+	0.145973i	−0.256363	+	0.966581i	$0.582524\pi$
$4$		0			0
$5$	18.7591	−	15.7407i	0.150072	−	0.125926i	−0.564660	−	0.825323i	$-0.690993\pi$
$5$	18.7591	−	15.7407i	0.150072	−	0.125926i	0.714733	+	0.699398i	$0.246548\pi$
$6$		0			0
$7$	52.4083	−	90.7739i	0.152794	−	0.264647i	−0.779460	−	0.626452i	$-0.784506\pi$
$7$	52.4083	−	90.7739i	0.152794	−	0.264647i	0.932254	+	0.361806i	$0.117840\pi$
$8$		0			0
$9$	−200.954	+	73.1411i	−0.275656	+	0.100331i
$10$		0			0
$11$	−640.572	−	1109.50i	−0.481271	−	0.833586i	0.518498	−	0.855079i	$-0.326491\pi$
$11$	−640.572	−	1109.50i	−0.481271	−	0.833586i	−0.999769	+	0.0214931i	$0.993158\pi$
$12$		0			0
$13$	888.307	+	156.633i	0.404327	+	0.0712938i	0.372114	−	0.928187i	$-0.378633\pi$
$13$	888.307	+	156.633i	0.404327	+	0.0712938i	0.0322138	+	0.999481i	$0.489744\pi$
$14$		0			0
$15$	−357.266	+	425.772i	−0.105856	+	0.126155i
$16$		0			0
$17$	3790.43	+	1379.60i	0.771509	+	0.280806i	0.697628	−	0.716461i	$-0.254239\pi$
$17$	3790.43	+	1379.60i	0.771509	+	0.280806i	0.0738818	+	0.997267i	$0.476461\pi$
$18$		0			0
$19$	983.265	+	6788.16i	0.143354	+	0.989671i
$19$	983.265	+	6788.16i	0.143354	+	0.989671i
$20$		0			0
$21$	−813.671	+	2235.54i	−0.0878599	+	0.241393i
$22$		0			0
$23$	12200.4	+	10237.4i	1.00275	+	0.841406i	0.987363	−	0.158475i	$-0.0506579\pi$
$23$	12200.4	+	10237.4i	1.00275	+	0.841406i	0.0153860	+	0.999882i	$0.495102\pi$
$24$		0			0
$25$	−2609.12	+	14797.1i	−0.166984	+	0.947012i
$26$		0			0
$27$	18532.8	−	10699.9i	0.941562	−	0.543611i
$28$		0			0
$29$	9849.35	+	27060.9i	0.403844	+	1.10955i	0.960371	+	0.278723i	$0.0899112\pi$
$29$	9849.35	+	27060.9i	0.403844	+	1.10955i	−0.556527	+	0.830829i	$0.687867\pi$
$30$		0			0
$31$	137.856	+	79.5910i	0.00462743	+	0.00267165i	0.502312	−	0.864686i	$-0.332483\pi$
$31$	137.856	+	79.5910i	0.00462743	+	0.00267165i	−0.497685	+	0.867358i	$0.665816\pi$
$32$		0			0
$33$	18691.0	+	22275.0i	0.520104	+	0.619836i
$34$		0			0
$35$	−445.715	−	2527.78i	−0.0103957	−	0.0589569i
$36$		0			0
$37$			11354.4i			0.224160i	0.993699	+	0.112080i	$0.0357513\pi$
$37$			11354.4i			0.224160i	−0.993699	+	0.112080i	$0.964249\pi$
$38$		0			0
$39$	−20472.9			−0.345132
$40$		0			0
$41$	−9891.18	+	1744.08i	−0.143515	+	0.0253055i	−0.244944	−	0.969537i	$-0.578770\pi$
$41$	−9891.18	+	1744.08i	−0.143515	+	0.0253055i	0.101429	+	0.994843i	$0.467658\pi$
$42$		0			0
$43$	50656.4	−	42505.7i	0.637131	−	0.534616i	−0.266005	−	0.963972i	$-0.585704\pi$
$43$	50656.4	−	42505.7i	0.637131	−	0.534616i	0.903136	+	0.429356i	$0.141259\pi$
$44$		0			0
$45$	−2618.41	+	4535.21i	−0.0287342	+	0.0497691i
$46$		0			0
$47$	54790.0	−	19941.9i	0.527725	−	0.192076i	−0.0643970	−	0.997924i	$-0.520512\pi$
$47$	54790.0	−	19941.9i	0.527725	−	0.192076i	0.592122	+	0.805848i	$0.298290\pi$
$48$		0			0
$49$	53331.2	+	92372.4i	0.453308	+	0.785152i
$50$		0			0
$51$	−90161.3	−	15897.9i	−0.679688	−	0.119847i
$52$		0			0
$53$	−78739.2	+	93837.7i	−0.528887	+	0.630303i	−0.962658	−	0.270720i	$-0.912738\pi$
$53$	−78739.2	+	93837.7i	−0.528887	+	0.630303i	0.433771	+	0.901023i	$0.357183\pi$
$54$		0			0
$55$	−29480.9	−	10730.2i	−0.177195	−	0.0644938i
$56$		0			0
$57$	−48732.0	−	147854.i	−0.263142	−	0.798379i
$58$		0			0
$59$	20944.3	−	57543.9i	0.101979	−	0.280184i	−0.878202	−	0.478290i	$-0.841257\pi$
$59$	20944.3	−	57543.9i	0.101979	−	0.280184i	0.980181	+	0.198106i	$0.0634790\pi$
$60$		0			0
$61$	104145.	+	87388.2i	0.458828	+	0.385002i	0.842700	−	0.538384i	$-0.180965\pi$
$61$	104145.	+	87388.2i	0.458828	+	0.385002i	−0.383872	+	0.923387i	$0.625409\pi$
$62$		0			0
$63$	−3892.34	+	22074.5i	−0.0155664	+	0.0882816i
$64$		0			0
$65$	19129.3	−	11044.3i	0.0696561	−	0.0402160i
$66$		0			0
$67$	−76833.7	−	211099.i	−0.255463	−	0.701878i	−0.999433	−	0.0336654i	$-0.989282\pi$
$67$	−76833.7	−	211099.i	−0.255463	−	0.701878i	0.743971	−	0.668212i	$-0.232940\pi$
$68$		0			0
$69$	−313054.	−	180742.i	−0.952954	−	0.550188i
$70$		0			0
$71$	−144170.	−	171815.i	−0.402809	−	0.480049i	0.526065	−	0.850444i	$-0.323667\pi$
$71$	−144170.	−	171815.i	−0.402809	−	0.480049i	−0.928874	+	0.370395i	$0.879222\pi$
$72$		0			0
$73$	−44412.7	−	251877.i	−0.114167	−	0.647471i	−0.987159	−	0.159738i	$-0.948935\pi$
$73$	−44412.7	−	251877.i	−0.114167	−	0.647471i	0.872993	−	0.487733i	$-0.162176\pi$
$74$		0			0
$75$		−	341028.i		−	0.808364i
$76$		0			0
$77$	−134285.			−0.294141
$78$		0			0
$79$	−281936.	+	49712.9i	−0.571832	+	0.100829i	−0.452085	−	0.891975i	$-0.649320\pi$
$79$	−281936.	+	49712.9i	−0.571832	+	0.100829i	−0.119747	+	0.992804i	$0.538208\pi$
$80$		0			0
$81$	−252651.	+	211999.i	−0.475407	+	0.398914i
$82$		0			0
$83$	80835.5	−	140011.i	0.141373	−	0.244866i	−0.786641	−	0.617411i	$-0.788181\pi$
$83$	80835.5	−	140011.i	0.141373	−	0.244866i	0.928014	+	0.372545i	$0.121515\pi$
$84$		0			0
$85$	92820.7	−	33784.0i	0.151143	−	0.0550116i
$86$		0			0
$87$	−326808.	−	566048.i	−0.496289	−	0.859598i
$88$		0			0
$89$	592488.	+	104472.i	0.840445	+	0.148193i	0.577269	−	0.816554i	$-0.304119\pi$
$89$	592488.	+	104472.i	0.840445	+	0.148193i	0.263177	+	0.964748i	$0.415230\pi$
$90$		0			0
$91$	60772.9	−	72426.3i	0.0806465	−	0.0961107i
$92$		0			0
$93$	−3395.05	−	1235.70i	−0.00422083	−	0.00153626i
$94$		0			0
$95$	125296.	+	111862.i	0.146139	+	0.130470i
$96$		0			0
$97$	−281608.	+	773712.i	−0.308553	+	0.847742i	0.684386	+	0.729120i	$0.260070\pi$
$97$	−281608.	+	773712.i	−0.308553	+	0.847742i	−0.992939	+	0.118623i	$0.962152\pi$
$98$		0			0
$99$	209875.	+	176106.i	0.216300	+	0.181497i
$100$		0			0
$101$	21594.4	−	122468.i	0.0209593	−	0.118866i	−0.972533	−	0.232765i	$-0.925223\pi$
$101$	21594.4	−	122468.i	0.0209593	−	0.118866i	0.993492	+	0.113899i	$0.0363339\pi$
$102$		0			0
$103$	−344797.	+	199069.i	−0.315538	+	0.182176i	−0.649402	−	0.760445i	$-0.724981\pi$
$103$	−344797.	+	199069.i	−0.315538	+	0.182176i	0.333864	+	0.942621i	$0.391647\pi$
$104$		0			0
$105$	19925.3	+	54744.4i	0.0172123	+	0.0472903i
$106$		0			0
$107$	1.77988e6	+	1.02762e6i	1.45291	+	0.838841i	0.998646	−	0.0520236i	$-0.0165671\pi$
$107$	1.77988e6	+	1.02762e6i	1.45291	+	0.838841i	0.454269	+	0.890865i	$0.349900\pi$
$108$		0			0
$109$	1.19922e6	+	1.42918e6i	0.926021	+	1.10359i	0.994374	+	0.105928i	$0.0337812\pi$
$109$	1.19922e6	+	1.42918e6i	0.926021	+	1.10359i	−0.0683529	+	0.997661i	$0.521774\pi$
$110$		0			0
$111$	−44750.8	−	253794.i	−0.0327214	−	0.185572i
$112$		0			0
$113$			1.42151e6i			0.985178i	0.870262	+	0.492589i	$0.163949\pi$
$113$			1.42151e6i			0.985178i	−0.870262	+	0.492589i	$0.836051\pi$
$114$		0			0
$115$	390013.			0.256440
$116$		0			0
$117$	−189965.	+	33495.9i	−0.118608	+	0.0209139i
$118$		0			0
$119$	323882.	−	271769.i	0.192197	−	0.161272i
$120$		0			0
$121$	65116.5	−	112785.i	0.0367566	−	0.0636642i
$122$		0			0
$123$	214215.	−	77967.7i	0.115115	−	0.0418986i
$124$		0			0
$125$	375286.	+	650014.i	0.192146	+	0.332807i
$126$		0			0
$127$	−336708.	−	59370.8i	−0.164378	−	0.0289842i	0.0908536	−	0.995864i	$-0.471040\pi$
$127$	−336708.	−	59370.8i	−0.164378	−	0.0289842i	−0.255231	+	0.966880i	$0.582152\pi$
$128$		0			0
$129$	−964749.	+	1.14974e6i	−0.449412	+	0.535589i
$130$		0			0
$131$	−870595.	−	316871.i	−0.387260	−	0.140951i	0.141051	−	0.990002i	$-0.454952\pi$
$131$	−870595.	−	316871.i	−0.387260	−	0.140951i	−0.528310	+	0.849051i	$0.677174\pi$
$132$		0			0
$133$	667719.	+	266501.i	0.283817	+	0.113278i
$134$		0			0
$135$	179233.	−	492439.i	0.0728479	−	0.200148i
$136$		0			0
$137$	1.69953e6	+	1.42607e6i	0.660948	+	0.554601i	0.910371	−	0.413794i	$-0.135797\pi$
$137$	1.69953e6	+	1.42607e6i	0.660948	+	0.554601i	−0.249423	+	0.968395i	$0.580241\pi$
$138$		0			0
$139$	851269.	−	4.82779e6i	0.316973	−	1.79764i	−0.243962	−	0.969785i	$-0.578447\pi$
$139$	851269.	−	4.82779e6i	0.316973	−	1.79764i	0.560935	−	0.827860i	$-0.310442\pi$
$140$		0			0
$141$	−1.14608e6	+	661687.i	−0.408842	+	0.236045i
$142$		0			0
$143$	−395240.	−	1.08591e6i	−0.135162	−	0.371353i
$144$		0			0
$145$	610722.	+	352601.i	0.200327	+	0.115659i
$146$		0			0
$147$	−1.55613e6	−	1.85452e6i	−0.489885	−	0.583822i
$148$		0			0
$149$	266232.	+	1.50988e6i	0.0804825	+	0.456439i	0.998240	+	0.0592983i	$0.0188863\pi$
$149$	266232.	+	1.50988e6i	0.0804825	+	0.456439i	−0.917758	+	0.397140i	$0.870003\pi$
$150$		0			0
$151$			2.16379e6i			0.628470i	0.949345	+	0.314235i	$0.101748\pi$
$151$			2.16379e6i			0.628470i	−0.949345	+	0.314235i	$0.898252\pi$
$152$		0			0
$153$	−862605.			−0.240845
$154$		0			0
$155$	3838.86	−	676.895i	0.00103088	−	0.000181772i
$156$		0			0
$157$	−2.14957e6	+	1.80370e6i	−0.555460	+	0.466086i	−0.876785	−	0.480883i	$-0.840316\pi$
$157$	−2.14957e6	+	1.80370e6i	−0.555460	+	0.466086i	0.321325	+	0.946969i	$0.395872\pi$
$158$		0			0
$159$	1.39014e6	−	2.40780e6i	0.345835	−	0.599003i
$160$		0			0
$161$	1.56869e6	−	570957.i	0.375890	−	0.136813i
$162$		0			0
$163$	−2.46435e6	−	4.26838e6i	−0.569036	−	0.985599i	−0.996662	−	0.0816430i	$-0.973983\pi$
$163$	−2.46435e6	−	4.26838e6i	−0.569036	−	0.985599i	0.427626	−	0.903956i	$-0.359350\pi$
$164$		0			0
$165$	701250.	+	123649.i	0.156106	+	0.0275258i
$166$		0			0
$167$	−2.29747e6	+	2.73802e6i	−0.493288	+	0.587877i	−0.954050	−	0.299646i	$-0.903131\pi$
$167$	−2.29747e6	+	2.73802e6i	−0.493288	+	0.587877i	0.460763	+	0.887523i	$0.347576\pi$
$168$		0			0
$169$	−3.77116e6	−	1.37259e6i	−0.781295	−	0.284368i
$170$		0			0
$171$	−694084.	−	1.29219e6i	−0.138811	−	0.258427i
$172$		0			0
$173$	−1.35598e6	+	3.72551e6i	−0.261887	+	0.719528i	0.737154	+	0.675725i	$0.236169\pi$
$173$	−1.35598e6	+	3.72551e6i	−0.261887	+	0.719528i	−0.999040	+	0.0438025i	$0.986053\pi$
$174$		0			0
$175$	1.20645e6	+	1.01233e6i	0.225110	+	0.188889i
$176$		0			0
$177$	−241352.	+	1.36877e6i	−0.0435242	+	0.246838i
$178$		0			0
$179$	9.20655e6	−	5.31540e6i	1.60523	−	0.926781i	0.614815	−	0.788672i	$-0.289231\pi$
$179$	9.20655e6	−	5.31540e6i	1.60523	−	0.926781i	0.990417	−	0.138109i	$-0.0441025\pi$
$180$		0			0
$181$	−2.39305e6	−	6.57485e6i	−0.403568	−	1.10879i	−0.960511	−	0.278242i	$-0.910248\pi$
$181$	−2.39305e6	−	6.57485e6i	−0.403568	−	1.10879i	0.556943	−	0.830551i	$-0.311974\pi$
$182$		0			0
$183$	−2.67229e6	−	1.54284e6i	−0.436043	−	0.251750i
$184$		0			0
$185$	178726.	+	212998.i	0.0282276	+	0.0336403i
$186$		0			0
$187$	−897367.	−	5.08922e6i	−0.137229	−	0.778263i
$188$		0			0
$189$		−	2.24305e6i		−	0.332242i
$190$		0			0
$191$	−7.12480e6			−1.02252			−0.511261	−	0.859426i	$-0.670821\pi$
$191$	−7.12480e6			−1.02252			−0.511261	+	0.859426i	$0.670821\pi$
$192$		0			0
$193$	−1.16095e7	+	2.04707e6i	−1.61489	+	0.284749i	−0.906859	−	0.421434i	$-0.861527\pi$
$193$	−1.16095e7	+	2.04707e6i	−1.61489	+	0.284749i	−0.708030	+	0.706182i	$0.750416\pi$
$194$		0			0
$195$	−384051.	+	322257.i	−0.0517947	+	0.0434609i
$196$		0			0
$197$	4.52728e6	−	7.84148e6i	0.592160	−	1.02565i	−0.401781	−	0.915736i	$-0.631609\pi$
$197$	4.52728e6	−	7.84148e6i	0.592160	−	1.02565i	0.993941	−	0.109915i	$-0.0350579\pi$
$198$		0			0
$199$	−1.85279e6	+	674359.i	−0.235107	+	0.0855721i	−0.456887	−	0.889525i	$-0.651036\pi$
$199$	−1.85279e6	+	674359.i	−0.235107	+	0.0855721i	0.221780	+	0.975097i	$0.428813\pi$
$200$		0			0
$201$	2.54939e6	+	4.41568e6i	0.313941	+	0.543763i
$202$		0			0
$203$	2.97261e6	+	524151.i	0.355345	+	0.0626568i
$204$		0			0
$205$	−158096.	+	188412.i	−0.0183510	+	0.0218699i
$206$		0			0
$207$	−3.20050e6	−	1.16489e6i	−0.360833	−	0.131333i
$208$		0			0
$209$	6.90163e6	−	5.43924e6i	0.755984	−	0.595798i
$210$		0			0
$211$	−1.78055e6	+	4.89203e6i	−0.189543	+	0.520765i	−0.997669	−	0.0682453i	$-0.978260\pi$
$211$	−1.78055e6	+	4.89203e6i	−0.189543	+	0.520765i	0.808126	+	0.589010i	$0.200482\pi$
$212$		0			0
$213$	3.89966e6	+	3.27221e6i	0.403542	+	0.338612i
$214$		0			0
$215$	281195.	−	1.59473e6i	0.0282938	−	0.160462i
$216$		0			0
$217$	14449.6	−	8342.47i	0.00141409	−	0.000816423i
$218$		0			0
$219$	1.98544e6	+	5.45494e6i	0.189027	+	0.519347i
$220$		0			0
$221$	3.15097e6	+	1.81921e6i	0.291923	+	0.168542i
$222$		0			0
$223$	4.66590e6	+	5.56060e6i	0.420747	+	0.501426i	0.934229	−	0.356674i	$-0.116089\pi$
$223$	4.66590e6	+	5.56060e6i	0.420747	+	0.501426i	−0.513482	+	0.858100i	$0.671645\pi$
$224$		0			0
$225$	−557961.	−	3.16436e6i	−0.0489843	−	0.277804i
$226$		0			0
$227$			2.02331e7i			1.72976i	0.501980	+	0.864879i	$0.332605\pi$
$227$			2.02331e7i			1.72976i	−0.501980	+	0.864879i	$0.667395\pi$
$228$		0			0
$229$	5.10117e6			0.424779			0.212390	−	0.977185i	$-0.431875\pi$
$229$	5.10117e6			0.424779			0.212390	+	0.977185i	$0.431875\pi$
$230$		0			0
$231$	3.00155e6	−	529255.i	0.243506	−	0.0429367i
$232$		0			0
$233$	−3.53458e6	+	2.96587e6i	−0.279428	+	0.234468i	−0.771721	−	0.635962i	$-0.780604\pi$
$233$	−3.53458e6	+	2.96587e6i	−0.279428	+	0.234468i	0.492292	+	0.870430i	$0.336159\pi$
$234$		0			0
$235$	713909.	−	1.23653e6i	0.0550097	−	0.0952796i
$236$		0			0
$237$	6.10592e6	−	2.22237e6i	0.458676	−	0.166944i
$238$		0			0
$239$	9.04934e6	+	1.56739e7i	0.662862	+	1.14811i	0.979860	+	0.199685i	$0.0639919\pi$
$239$	9.04934e6	+	1.56739e7i	0.662862	+	1.14811i	−0.316998	+	0.948426i	$0.602675\pi$
$240$		0			0
$241$	3.36108e6	+	592649.i	0.240120	+	0.0423396i	0.292413	−	0.956292i	$-0.405542\pi$
$241$	3.36108e6	+	592649.i	0.240120	+	0.0423396i	−0.0522931	+	0.998632i	$0.516653\pi$
$242$		0			0
$243$	−5.21605e6	+	6.21624e6i	−0.363515	+	0.433221i
$244$		0			0
$245$	2.45445e6	+	893347.i	0.166900	+	0.0607466i
$246$		0			0
$247$	−189804.	+	6.18398e6i	−0.0125955	+	0.410372i
$248$		0			0
$249$	−1.25502e6	+	3.44814e6i	−0.0812929	+	0.223350i
$250$		0			0
$251$	1.74609e7	+	1.46515e7i	1.10420	+	0.926531i	0.997700	−	0.0677821i	$-0.0215923\pi$
$251$	1.74609e7	+	1.46515e7i	1.10420	+	0.926531i	0.106496	+	0.994313i	$0.466037\pi$
$252$		0			0
$253$	3.54315e6	−	2.00942e7i	0.218790	−	1.24082i
$254$		0			0
$255$	−1.94159e6	+	1.12097e6i	−0.117094	+	0.0676045i
$256$		0			0
$257$	1.04493e6	+	2.87093e6i	0.0615587	+	0.169131i	0.966659	−	0.256067i	$-0.0824267\pi$
$257$	1.04493e6	+	2.87093e6i	0.0615587	+	0.169131i	−0.905100	+	0.425198i	$0.860204\pi$
$258$		0			0
$259$	1.03068e6	+	595065.i	0.0593233	+	0.0342503i
$260$		0			0
$261$	−3.95853e6	−	4.71759e6i	−0.222644	−	0.265337i
$262$		0			0
$263$	−216164.	−	1.22593e6i	−0.0118827	−	0.0673904i	0.978290	−	0.207242i	$-0.0664487\pi$
$263$	−216164.	−	1.22593e6i	−0.0118827	−	0.0673904i	−0.990173	+	0.139851i	$0.955338\pi$
$264$		0			0
$265$			2.99972e6i			0.161192i
$266$		0			0
$267$	−1.36551e7			−0.717399
$268$		0			0
$269$	1.11262e7	−	1.96185e6i	0.571598	−	0.100788i	0.119624	−	0.992819i	$-0.461831\pi$
$269$	1.11262e7	−	1.96185e6i	0.571598	−	0.100788i	0.451974	+	0.892031i	$0.350720\pi$
$270$		0			0
$271$	−1.44698e7	+	1.21416e7i	−0.727036	+	0.610055i	−0.929322	−	0.369271i	$-0.879607\pi$
$271$	−1.44698e7	+	1.21416e7i	−0.727036	+	0.610055i	0.202286	+	0.979326i	$0.435163\pi$
$272$		0			0
$273$	−1.07295e6	+	1.85840e6i	−0.0527340	+	0.0913380i
$274$		0			0
$275$	1.80887e7	−	6.58375e6i	0.869780	−	0.316574i
$276$		0			0
$277$	−1.51701e7	−	2.62754e7i	−0.713756	−	1.23626i	−0.963437	−	0.267933i	$-0.913659\pi$
$277$	−1.51701e7	−	2.62754e7i	−0.713756	−	1.23626i	0.249682	−	0.968328i	$-0.419674\pi$
$278$		0			0
$279$	−33524.0	−	5911.18i	−0.00154363	−	0.000272183i
$280$		0			0
$281$	6.44671e6	−	7.68289e6i	0.290549	−	0.346263i	−0.600949	−	0.799287i	$-0.705211\pi$
$281$	6.44671e6	−	7.68289e6i	0.290549	−	0.346263i	0.891498	+	0.453025i	$0.149655\pi$
$282$		0			0
$283$	−2.08703e7	−	7.59616e6i	−0.920807	−	0.335146i	−0.162248	−	0.986750i	$-0.551874\pi$
$283$	−2.08703e7	−	7.59616e6i	−0.920807	−	0.335146i	−0.758560	+	0.651604i	$0.774097\pi$
$284$		0			0
$285$	−3.24150e6	−	2.00653e6i	−0.140027	−	0.0866783i
$286$		0			0
$287$	−360063.	+	989265.i	−0.0152312	+	0.0418473i
$288$		0			0
$289$	−6.02643e6	−	5.05677e6i	−0.249670	−	0.209498i
$290$		0			0
$291$	3.24512e6	−	1.84040e7i	0.131690	−	0.746848i
$292$		0			0
$293$	−4.10372e6	+	2.36928e6i	−0.163145	+	0.0941920i	−0.579350	−	0.815079i	$-0.696693\pi$
$293$	−4.10372e6	+	2.36928e6i	−0.163145	+	0.0941920i	0.416204	+	0.909271i	$0.363360\pi$
$294$		0			0
$295$	−512887.	−	1.40915e6i	−0.0199782	−	0.0548896i
$296$		0			0
$297$	−2.37431e7	−	1.37081e7i	−0.906293	−	0.523248i
$298$		0			0
$299$	9.23424e6	+	1.10049e7i	0.345452	+	0.411693i
$300$		0			0
$301$	−1.20360e6	−	6.82593e6i	−0.0441348	−	0.250301i
$302$		0			0
$303$			2.82252e6i			0.101463i
$304$		0			0
$305$	3.32922e6			0.117339
$306$		0			0
$307$	−1.32608e7	+	2.33824e6i	−0.458306	+	0.0808118i	−0.398035	−	0.917370i	$-0.630308\pi$
$307$	−1.32608e7	+	2.33824e6i	−0.458306	+	0.0808118i	−0.0602713	+	0.998182i	$0.519197\pi$
$308$		0			0
$309$	6.92235e6	−	5.80854e6i	0.234627	−	0.196875i
$310$		0			0
$311$	1.18544e6	−	2.05324e6i	0.0394092	−	0.0682588i	−0.845648	−	0.533741i	$-0.820786\pi$
$311$	1.18544e6	−	2.05324e6i	0.0394092	−	0.0682588i	0.885057	+	0.465482i	$0.154119\pi$
$312$		0			0
$313$	−1.52088e7	+	5.53556e6i	−0.495978	+	0.180521i	−0.577884	−	0.816119i	$-0.696122\pi$
$313$	−1.52088e7	+	5.53556e6i	−0.495978	+	0.180521i	0.0819059	+	0.996640i	$0.473899\pi$
$314$		0			0
$315$	274453.	+	475366.i	0.00878083	+	0.0152088i
$316$		0			0
$317$	3.49698e7	+	6.16612e6i	1.09778	+	0.193568i	0.693065	−	0.720875i	$-0.256260\pi$
$317$	3.49698e7	+	6.16612e6i	1.09778	+	0.193568i	0.404715	+	0.914443i	$0.367371\pi$
$318$		0			0
$319$	2.37149e7	−	2.82623e7i	0.730549	−	0.870634i
$320$		0			0
$321$	−4.38342e7	−	1.59544e7i	−1.32525	−	0.482352i
$322$		0			0
$323$	−5.63796e6	+	2.70865e7i	−0.167307	+	0.803796i
$324$		0			0
$325$	−4.63540e6	+	1.27357e7i	−0.135032	+	0.370998i
$326$		0			0
$327$	−3.24380e7	−	2.72187e7i	−0.927706	−	0.778438i
$328$		0			0
$329$	1.06125e6	−	6.01863e6i	0.0298008	−	0.169009i
$330$		0			0
$331$	−1.93544e7	+	1.11743e7i	−0.533698	+	0.308131i	−0.742521	−	0.669823i	$-0.766370\pi$
$331$	−1.93544e7	+	1.11743e7i	−0.533698	+	0.308131i	0.208823	+	0.977953i	$0.433037\pi$
$332$		0			0
$333$	−830473.	−	2.28171e6i	−0.0224902	−	0.0617913i
$334$		0			0
$335$	−4.76417e6	−	2.75060e6i	−0.126722	−	0.0731632i
$336$		0			0
$337$	1.10666e7	+	1.31887e7i	0.289152	+	0.344597i	0.890992	−	0.454019i	$-0.150010\pi$
$337$	1.10666e7	+	1.31887e7i	0.289152	+	0.344597i	−0.601840	+	0.798616i	$0.705566\pi$
$338$		0			0
$339$	−5.60257e6	−	3.17737e7i	−0.143810	−	0.815585i
$340$		0			0
$341$		−	203935.i		−	0.00514314i
$342$		0			0
$343$	2.35116e7			0.582639
$344$		0			0
$345$	−8.71760e6	+	1.53715e6i	−0.212295	+	0.0374333i
$346$		0			0
$347$	−1.20826e7	+	1.01385e7i	−0.289183	+	0.242653i	−0.775825	−	0.630948i	$-0.782666\pi$
$347$	−1.20826e7	+	1.01385e7i	−0.289183	+	0.242653i	0.486642	+	0.873602i	$0.338222\pi$
$348$		0			0
$349$	3.88662e7	−	6.73182e7i	0.914314	−	1.58364i	0.106412	−	0.994322i	$-0.466064\pi$
$349$	3.88662e7	−	6.73182e7i	0.914314	−	1.58364i	0.807902	−	0.589317i	$-0.200603\pi$
$350$		0			0
$351$	1.81387e7	−	6.60196e6i	0.419455	−	0.152669i
$352$		0			0
$353$	2.60725e7	+	4.51589e7i	0.592733	+	1.02664i	0.993863	+	0.110622i	$0.0352843\pi$
$353$	2.60725e7	+	4.51589e7i	0.592733	+	1.02664i	−0.401130	+	0.916021i	$0.631382\pi$
$354$		0			0
$355$	−5.40898e6	−	953748.i	−0.120901	−	0.0213181i
$356$		0			0
$357$	−6.16832e6	+	7.35111e6i	−0.135570	+	0.161565i
$358$		0			0
$359$	1.36460e7	+	4.96675e6i	0.294933	+	0.107347i	0.485249	−	0.874376i	$-0.338729\pi$
$359$	1.36460e7	+	4.96675e6i	0.294933	+	0.107347i	−0.190316	+	0.981723i	$0.560951\pi$
$360$		0			0
$361$	−4.51123e7	+	1.33491e7i	−0.958899	+	0.283747i
$362$		0			0
$363$	−1.01097e6	+	2.77763e6i	−0.0211358	+	0.0580703i
$364$		0			0
$365$	−4.79787e6	−	4.02589e6i	−0.0986665	−	0.0827910i
$366$		0			0
$367$	−5.71293e6	+	3.23996e7i	−0.115574	+	0.655453i	0.870890	+	0.491478i	$0.163543\pi$
$367$	−5.71293e6	+	3.23996e7i	−0.115574	+	0.655453i	−0.986464	+	0.163976i	$0.947568\pi$
$368$		0			0
$369$	1.86010e6	−	1.07393e6i	0.0370218	−	0.0213746i
$370$		0			0
$371$	4.39142e6	+	1.20653e7i	0.0859971	+	0.236275i
$372$		0			0
$373$	−7.66559e7	−	4.42573e7i	−1.47713	−	0.852822i	−0.477464	−	0.878651i	$-0.658444\pi$
$373$	−7.66559e7	−	4.42573e7i	−1.47713	−	0.852822i	−0.999666	+	0.0258297i	$0.991777\pi$
$374$		0			0
$375$	−1.09503e7	−	1.30501e7i	−0.207650	−	0.247468i
$376$		0			0
$377$	4.51064e6	+	2.55811e7i	0.0841810	+	0.477414i
$378$		0			0
$379$			2.67715e7i			0.491762i	0.969300	+	0.245881i	$0.0790773\pi$
$379$			2.67715e7i			0.491762i	−0.969300	+	0.245881i	$0.920923\pi$
$380$		0			0
$381$	7.76013e6			0.140312
$382$		0			0
$383$	6.67464e7	−	1.17692e7i	1.18804	−	0.209484i	0.455519	−	0.890226i	$-0.349454\pi$
$383$	6.67464e7	−	1.17692e7i	1.18804	−	0.209484i	0.732523	+	0.680742i	$0.238343\pi$
$384$		0			0
$385$	−2.51906e6	+	2.11374e6i	−0.0441425	+	0.0370399i
$386$		0			0
$387$	−7.07066e6	+	1.22467e7i	−0.121991	+	0.211294i
$388$		0			0
$389$	1.06521e8	−	3.87704e7i	1.80961	−	0.658645i	0.812479	−	0.582990i	$-0.198117\pi$
$389$	1.06521e8	−	3.87704e7i	1.80961	−	0.658645i	0.997134	−	0.0756554i	$-0.0241049\pi$
$390$		0			0
$391$	3.21214e7	+	5.56358e7i	0.537358	+	0.930731i
$392$		0			0
$393$	2.07085e7	+	3.65147e6i	0.341170	+	0.0601575i
$394$		0			0
$395$	−4.50633e6	+	5.37043e6i	−0.0731192	+	0.0871401i
$396$		0			0
$397$	3.16678e7	+	1.15261e7i	0.506111	+	0.184209i	0.582441	−	0.812873i	$-0.302098\pi$
$397$	3.16678e7	+	1.15261e7i	0.506111	+	0.184209i	−0.0763293	+	0.997083i	$0.524320\pi$
$398$		0			0
$399$	−1.59753e7	−	3.32519e6i	−0.251495	−	0.0523478i
$400$		0			0
$401$	−1.26989e7	+	3.48899e7i	−0.196939	+	0.541086i	−0.998374	−	0.0569953i	$-0.981848\pi$
$401$	−1.26989e7	+	3.48899e7i	−0.196939	+	0.541086i	0.801435	+	0.598082i	$0.204070\pi$
$402$		0			0
$403$	109992.	+	92294.0i	0.00168052	+	0.00141013i
$404$		0			0
$405$	−1.40247e6	+	7.95381e6i	−0.0211120	+	0.119732i
$406$		0			0
$407$	1.25977e7	−	7.27330e6i	0.186857	−	0.107882i
$408$		0			0
$409$	3.85403e7	+	1.05889e8i	0.563308	+	1.54767i	0.814756	+	0.579804i	$0.196871\pi$
$409$	3.85403e7	+	1.05889e8i	0.563308	+	1.54767i	−0.251448	+	0.967871i	$0.580907\pi$
$410$		0			0
$411$	−4.36086e7	−	2.51774e7i	−0.628126	−	0.362649i
$412$		0			0
$413$	−4.12583e6	−	4.91697e6i	−0.0585681	−	0.0697987i
$414$		0			0
$415$	−687479.	−	3.89889e6i	−0.00961867	−	0.0545502i
$416$		0			0
$417$			1.11266e8i			1.53446i
$418$		0			0
$419$	−1.99699e6			−0.0271478			−0.0135739	−	0.999908i	$-0.504321\pi$
$419$	−1.99699e6			−0.0271478			−0.0135739	+	0.999908i	$0.504321\pi$
$420$		0			0
$421$	8.16969e7	−	1.44054e7i	1.09486	−	0.193054i	0.403083	−	0.915163i	$-0.367939\pi$
$421$	8.16969e7	−	1.44054e7i	1.09486	−	0.193054i	0.691778	+	0.722110i	$0.256827\pi$
$422$		0			0
$423$	−9.55168e6	+	8.01481e6i	−0.126200	+	0.105894i
$424$		0			0
$425$	−3.03037e7	+	5.24876e7i	−0.394757	+	0.683738i
$426$		0			0
$427$	1.33907e7	−	4.87380e6i	0.171996	−	0.0626014i
$428$		0			0
$429$	1.31143e7	+	2.27147e7i	0.166102	+	0.287697i
$430$		0			0
$431$	5.56575e7	+	9.81392e6i	0.695172	+	0.122578i	0.510059	−	0.860140i	$-0.329624\pi$
$431$	5.56575e7	+	9.81392e6i	0.695172	+	0.122578i	0.185113	+	0.982717i	$0.440735\pi$
$432$		0			0
$433$	7.17836e7	−	8.55483e7i	0.884222	−	1.05377i	−0.113959	−	0.993485i	$-0.536353\pi$
$433$	7.17836e7	−	8.55483e7i	0.884222	−	1.05377i	0.998181	−	0.0602895i	$-0.0192024\pi$
$434$		0			0
$435$	−1.50406e7	−	5.47433e6i	−0.182725	−	0.0665064i
$436$		0			0
$437$	−5.74967e7	+	9.28846e7i	−0.688968	+	1.11301i
$438$		0			0
$439$	−1.46101e7	+	4.01410e7i	−0.172687	+	0.474455i	−0.995599	−	0.0937145i	$-0.970126\pi$
$439$	−1.46101e7	+	4.01410e7i	−0.172687	+	0.474455i	0.822912	+	0.568169i	$0.192348\pi$
$440$		0			0
$441$	−1.74733e7	−	1.46619e7i	−0.203732	−	0.170952i
$442$		0			0
$443$	−116875.	+	662829.i	−0.00134434	+	0.00762412i	−0.985473	−	0.169835i	$-0.945677\pi$
$443$	−116875.	+	662829.i	−0.00134434	+	0.00762412i	0.984128	+	0.177459i	$0.0567877\pi$
$444$		0			0
$445$	1.27590e7	−	7.36639e6i	0.144789	−	0.0835940i
$446$		0			0
$447$	−1.19017e7	−	3.26996e7i	−0.133256	−	0.366117i
$448$		0			0
$449$	−1.20818e8	−	6.97542e7i	−1.33472	−	0.770604i	−0.348705	−	0.937232i	$-0.613379\pi$
$449$	−1.20818e8	−	6.97542e7i	−1.33472	−	0.770604i	−0.986020	+	0.166629i	$0.946712\pi$
$450$		0			0
$451$	8.27107e6	+	9.85708e6i	0.0901638	+	0.107453i
$452$		0			0
$453$	−8.52810e6	−	4.83653e7i	−0.0917398	−	0.520282i
$454$		0			0
$455$		−	2.31526e6i		−	0.0245790i
$456$		0			0
$457$	−1.28827e8			−1.34976			−0.674881	−	0.737927i	$-0.735805\pi$
$457$	−1.28827e8			−1.34976			−0.674881	+	0.737927i	$0.735805\pi$
$458$		0			0
$459$	8.50086e7	−	1.49893e7i	0.879073	−	0.155004i
$460$		0			0
$461$	6.31301e7	−	5.29724e7i	0.644367	−	0.540688i	−0.260989	−	0.965342i	$-0.584049\pi$
$461$	6.31301e7	−	5.29724e7i	0.644367	−	0.540688i	0.905356	+	0.424653i	$0.139604\pi$
$462$		0			0
$463$	7.85774e7	−	1.36100e8i	0.791689	−	1.37125i	−0.133232	−	0.991085i	$-0.542535\pi$
$463$	7.85774e7	−	1.36100e8i	0.791689	−	1.37125i	0.924921	−	0.380160i	$-0.124131\pi$
$464$		0			0
$465$	−83138.8	+	30260.0i	−0.000826884	+	0.000300961i
$466$		0			0
$467$	1.62009e7	+	2.80607e7i	0.159070	+	0.275517i	0.934533	−	0.355875i	$-0.115817\pi$
$467$	1.62009e7	+	2.80607e7i	0.159070	+	0.275517i	−0.775464	+	0.631392i	$0.782484\pi$
$468$		0			0
$469$	−2.31890e7	−	4.08885e6i	−0.224783	−	0.0396353i
$470$		0			0
$471$	4.09385e7	−	4.87886e7i	0.391804	−	0.466934i
$472$		0			0
$473$	−7.96092e7	−	2.89754e7i	−0.752281	−	0.273808i
$474$		0			0
$475$	−1.03010e8	−	3.16168e6i	−0.961168	−	0.0295011i
$476$		0			0
$477$	8.95952e6	−	2.46161e7i	0.0825524	−	0.226811i
$478$		0			0
$479$	−1.58596e8	−	1.33078e8i	−1.44307	−	1.21088i	−0.937451	−	0.348117i	$-0.886821\pi$
$479$	−1.58596e8	−	1.33078e8i	−1.44307	−	1.21088i	−0.505615	−	0.862759i	$-0.668734\pi$
$480$		0			0
$481$	−1.77847e6	+	1.00862e7i	−0.0159813	+	0.0906342i
$482$		0			0
$483$	−3.28133e7	+	1.89447e7i	−0.291211	+	0.168131i
$484$		0			0
$485$	6.89607e6	+	1.89468e7i	0.0604473	+	0.166078i
$486$		0			0
$487$	−1.89176e8	−	1.09221e8i	−1.63786	−	0.945622i	−0.981567	−	0.191120i	$-0.938788\pi$
$487$	−1.89176e8	−	1.09221e8i	−1.63786	−	0.945622i	−0.656298	−	0.754502i	$-0.727879\pi$
$488$		0			0
$489$	7.19062e7	+	8.56945e7i	0.614950	+	0.732869i
$490$		0			0
$491$	−3.50193e7	−	1.98604e8i	−0.295844	−	1.67781i	−0.663752	−	0.747953i	$-0.731037\pi$
$491$	−3.50193e7	−	1.98604e8i	−0.295844	−	1.67781i	0.367908	−	0.929862i	$-0.380074\pi$
$492$		0			0
$493$			1.16160e8i			0.969432i
$494$		0			0
$495$	6.70910e6			0.0553158
$496$		0			0
$497$	−2.31520e7	+	4.08232e6i	−0.188590	+	0.0332535i
$498$		0			0
$499$	−5.07184e7	+	4.25578e7i	−0.408191	+	0.342513i	−0.823650	−	0.567099i	$-0.808066\pi$
$499$	−5.07184e7	+	4.25578e7i	−0.408191	+	0.342513i	0.415458	+	0.909612i	$0.363621\pi$
$500$		0			0
$501$	4.05620e7	−	7.02554e7i	0.322556	−	0.558684i
$502$		0			0
$503$	8.00541e7	−	2.91373e7i	0.629042	−	0.228952i	−0.00777246	−	0.999970i	$-0.502474\pi$
$503$	8.00541e7	−	2.91373e7i	0.629042	−	0.228952i	0.636814	+	0.771017i	$0.280252\pi$
$504$		0			0
$505$	−1.52264e6	−	2.63729e6i	−0.0118229	−	0.0204778i
$506$		0			0
$507$	8.97031e7	+	1.58171e7i	0.688309	+	0.121367i
$508$		0			0
$509$	5.06448e7	−	6.03561e7i	0.384045	−	0.457687i	−0.539042	−	0.842279i	$-0.681214\pi$
$509$	5.06448e7	−	6.03561e7i	0.384045	−	0.457687i	0.923086	+	0.384592i	$0.125658\pi$
$510$		0			0
$511$	−2.51915e7	−	9.16894e6i	−0.188795	−	0.0687158i
$512$		0			0
$513$	9.08552e7	+	1.15282e8i	0.672973	+	0.853908i
$514$		0			0
$515$	−3.33458e6	+	9.16169e6i	−0.0244129	+	0.0670740i
$516$		0			0
$517$	−5.72226e7	−	4.80154e7i	−0.414091	−	0.347464i
$518$		0			0
$519$	1.56256e7	−	8.86172e7i	0.111772	−	0.633893i
$520$		0			0
$521$	−1.86468e8	+	1.07657e8i	−1.31853	+	0.761254i	−0.983492	−	0.180951i	$-0.942083\pi$
$521$	−1.86468e8	+	1.07657e8i	−1.31853	+	0.761254i	−0.335038	+	0.942205i	$0.608749\pi$
$522$		0			0
$523$	−380949.	−	1.04665e6i	−0.00266294	−	0.00731638i	0.938354	−	0.345676i	$-0.112350\pi$
$523$	−380949.	−	1.04665e6i	−0.00266294	−	0.00731638i	−0.941017	+	0.338359i	$0.890128\pi$
$524$		0			0
$525$	−3.09565e7	−	1.78727e7i	−0.213931	−	0.123513i
$526$		0			0
$527$	412728.	+	491870.i	0.00281989	+	0.00336061i
$528$		0			0
$529$	1.83406e7	+	1.04015e8i	0.123893	+	0.702631i
$530$		0			0
$531$			1.30955e7i			0.0874661i
$532$		0			0
$533$	−9.05959e6			−0.0598311
$534$		0			0
$535$	4.95643e7	−	8.73953e6i	0.323674	−	0.0570725i
$536$		0			0
$537$	−1.84836e8	+	1.55096e8i	−1.19361	+	1.00156i
$538$		0			0
$539$	6.83249e7	−	1.18342e8i	0.436328	−	0.755742i
$540$		0			0
$541$	1.58744e8	−	5.77780e7i	1.00255	−	0.364898i	0.211981	−	0.977274i	$-0.432008\pi$
$541$	1.58744e8	−	5.77780e7i	1.00255	−	0.364898i	0.790567	+	0.612376i	$0.209786\pi$
$542$		0			0
$543$	7.94030e7	+	1.37530e8i	0.495950	+	0.859010i
$544$		0			0
$545$	4.49926e7	+	7.93341e6i	0.277940	+	0.0490084i
$546$		0			0
$547$	8.93491e7	−	1.06482e8i	0.545919	−	0.650601i	−0.420585	−	0.907253i	$-0.638175\pi$
$547$	8.93491e7	−	1.06482e8i	0.545919	−	0.650601i	0.966504	+	0.256652i	$0.0826195\pi$
$548$		0			0
$549$	−2.73200e7	−	9.94368e6i	−0.165107	−	0.0600939i
$550$		0			0
$551$	−1.74009e8	+	9.34670e7i	−1.04020	+	0.558732i
$552$		0			0
$553$	−1.02631e7	+	2.81978e7i	−0.0606883	+	0.166740i
$554$		0			0
$555$	−4.83439e6	−	4.05653e6i	−0.0282789	−	0.0237288i
$556$		0			0
$557$	2.10504e7	−	1.19383e8i	0.121814	−	0.690839i	−0.861336	−	0.508036i	$-0.830372\pi$
$557$	2.10504e7	−	1.19383e8i	0.121814	−	0.690839i	0.983150	−	0.182803i	$-0.0585171\pi$
$558$		0			0
$559$	5.16562e7	−	2.98237e7i	0.295724	−	0.170736i
$560$		0			0
$561$	4.01161e7	+	1.10218e8i	0.227211	+	0.624258i
$562$		0			0
$563$	−8.92878e7	−	5.15504e7i	−0.500342	−	0.288873i	0.228513	−	0.973541i	$-0.426614\pi$
$563$	−8.92878e7	−	5.15504e7i	−0.500342	−	0.288873i	−0.728855	+	0.684668i	$0.759947\pi$
$564$		0			0
$565$	2.23756e7	+	2.66662e7i	0.124059	+	0.147848i
$566$		0			0
$567$	6.00298e6	+	3.40446e7i	0.0329320	+	0.186767i
$568$		0			0
$569$			1.31472e8i			0.713668i	0.934168	+	0.356834i	$0.116144\pi$
$569$			1.31472e8i			0.713668i	−0.934168	+	0.356834i	$0.883856\pi$
$570$		0			0
$571$	2.44773e8			1.31479			0.657393	−	0.753548i	$-0.271659\pi$
$571$	2.44773e8			1.31479			0.657393	+	0.753548i	$0.271659\pi$
$572$		0			0
$573$	1.59254e8	−	2.80808e7i	0.846500	−	0.149261i
$574$		0			0
$575$	−1.83316e8	+	1.53820e8i	−0.964264	+	0.809114i
$576$		0			0
$577$	−1.11594e7	+	1.93286e7i	−0.0580915	+	0.100617i	−0.893609	−	0.448847i	$-0.851835\pi$
$577$	−1.11594e7	+	1.93286e7i	−0.0580915	+	0.100617i	0.835517	+	0.549464i	$0.185168\pi$
$578$		0			0
$579$	2.51429e8	−	9.15127e7i	1.29533	−	0.471461i
$580$		0			0
$581$	−8.47291e6	−	1.46755e7i	−0.0432020	−	0.0748281i
$582$		0			0
$583$	1.54551e8	+	2.72516e7i	0.779950	+	0.137526i
$584$		0			0
$585$	−3.03631e6	+	3.61853e6i	−0.0151663	+	0.0180744i
$586$		0			0
$587$	−2.74807e8	−	1.00022e8i	−1.35867	−	0.494515i	−0.443027	−	0.896508i	$-0.646095\pi$
$587$	−2.74807e8	−	1.00022e8i	−1.35867	−	0.494515i	−0.915643	+	0.401993i	$0.868318\pi$
$588$		0			0
$589$	−404728.	+	1.01405e6i	−0.00198069	+	0.00496263i
$590$		0			0
$591$	−7.02888e7	+	1.93117e8i	−0.340505	+	0.935530i
$592$		0			0
$593$	4.10615e7	+	3.44547e7i	0.196911	+	0.165228i	0.735912	−	0.677077i	$-0.236754\pi$
$593$	4.10615e7	+	3.44547e7i	0.196911	+	0.165228i	−0.539001	+	0.842305i	$0.681198\pi$
$594$		0			0
$595$	1.79788e6	−	1.01963e7i	0.00853510	−	0.0484050i
$596$		0			0
$597$	3.87558e7	−	2.23757e7i	0.182144	−	0.105161i
$598$		0			0
$599$	−3.23675e7	−	8.89288e7i	−0.150601	−	0.413773i	0.841335	−	0.540514i	$-0.181770\pi$
$599$	−3.23675e7	−	8.89288e7i	−0.150601	−	0.413773i	−0.991936	+	0.126741i	$0.959548\pi$
$600$		0			0
$601$	−2.60582e8	−	1.50447e8i	−1.20039	−	0.693043i	−0.239745	−	0.970836i	$-0.577064\pi$
$601$	−2.60582e8	−	1.50447e8i	−1.20039	−	0.693043i	−0.960641	+	0.277792i	$0.910397\pi$
$602$		0			0
$603$	3.08800e7	+	3.68014e7i	0.140840	+	0.167846i
$604$		0			0
$605$	−553794.	−	3.14072e6i	−0.00250082	−	0.0141828i
$606$		0			0
$607$			4.18081e8i			1.86937i	0.355480	+	0.934684i	$0.384317\pi$
$607$			4.18081e8i			1.86937i	−0.355480	+	0.934684i	$0.615683\pi$
$608$		0			0
$609$	−6.85099e7			−0.303320
$610$		0			0
$611$	5.17939e7	−	9.13267e6i	0.227068	−	0.0400382i
$612$		0			0
$613$	2.01021e8	−	1.68677e8i	0.872692	−	0.732275i	−0.0919713	−	0.995762i	$-0.529317\pi$
$613$	2.01021e8	−	1.68677e8i	0.872692	−	0.732275i	0.964663	+	0.263486i	$0.0848724\pi$
$614$		0			0
$615$	2.79120e6	−	4.83449e6i	0.0119995	−	0.0207838i
$616$		0			0
$617$	9.29803e7	−	3.38421e7i	0.395854	−	0.144079i	−0.136420	−	0.990651i	$-0.543560\pi$
$617$	9.29803e7	−	3.38421e7i	0.395854	−	0.144079i	0.532274	+	0.846572i	$0.321337\pi$
$618$		0			0
$619$	1.57788e8	+	2.73297e8i	0.665276	+	1.15229i	0.979211	+	0.202847i	$0.0650193\pi$
$619$	1.57788e8	+	2.73297e8i	0.665276	+	1.15229i	−0.313935	+	0.949444i	$0.601647\pi$
$620$		0			0
$621$	3.35647e8	+	5.91836e7i	1.40155	+	0.247131i
$622$		0			0
$623$	4.05346e7	−	4.83073e7i	0.167634	−	0.199778i
$624$		0			0
$625$	−2.03341e8	−	7.40099e7i	−0.832883	−	0.303145i
$626$		0			0
$627$	−1.32828e8	+	1.48780e8i	−0.538875	+	0.603588i
$628$		0			0
$629$	−1.56645e7	+	4.30380e7i	−0.0629457	+	0.172942i
$630$		0			0
$631$	3.02761e8	+	2.54047e8i	1.20507	+	1.01117i	0.999471	+	0.0325368i	$0.0103586\pi$
$631$	3.02761e8	+	2.54047e8i	1.20507	+	1.01117i	0.205599	+	0.978636i	$0.434086\pi$
$632$		0			0
$633$	2.05182e7	−	1.16365e8i	0.0808964	−	0.458786i
$634$		0			0
$635$	−7.25087e6	+	4.18629e6i	−0.0283184	+	0.0163496i
$636$		0			0
$637$	3.29060e7	+	9.04085e7i	0.127308	+	0.349777i
$638$		0			0
$639$	4.15382e7	+	2.39821e7i	0.159201	+	0.0919145i
$640$		0			0
$641$	1.25192e8	+	1.49198e8i	0.475339	+	0.566487i	0.949426	−	0.313991i	$-0.101666\pi$
$641$	1.25192e8	+	1.49198e8i	0.475339	+	0.566487i	−0.474087	+	0.880478i	$0.657222\pi$
$642$		0			0
$643$	−3.88242e7	−	2.20183e8i	−0.146039	−	0.828230i	−0.966527	−	0.256566i	$-0.917409\pi$
$643$	−3.88242e7	−	2.20183e8i	−0.146039	−	0.828230i	0.820487	−	0.571665i	$-0.193702\pi$
$644$		0			0
$645$			3.67539e7i			0.136970i
$646$		0			0
$647$	−3.64508e8			−1.34584			−0.672922	−	0.739713i	$-0.734961\pi$
$647$	−3.64508e8			−1.34584			−0.672922	+	0.739713i	$0.734961\pi$
$648$		0			0
$649$	−7.72614e7	+	1.36233e7i	−0.282637	+	0.0498365i
$650$		0			0
$651$	−290098.	+	243421.i	−0.00105148	+	0.000882299i
$652$		0			0
$653$	2.39299e8	−	4.14478e8i	0.859411	−	1.48854i	−0.0130805	−	0.999914i	$-0.504164\pi$
$653$	2.39299e8	−	4.14478e8i	0.859411	−	1.48854i	0.872492	−	0.488629i	$-0.162503\pi$
$654$		0			0
$655$	−2.13193e7	+	7.75959e6i	−0.0758663	+	0.0276131i
$656$		0			0
$657$	2.73475e7	+	4.73672e7i	0.0964320	+	0.167025i
$658$		0			0
$659$	−5.33416e7	−	9.40557e6i	−0.186385	−	0.0328646i	0.0796766	−	0.996821i	$-0.474611\pi$
$659$	−5.33416e7	−	9.40557e6i	−0.186385	−	0.0328646i	−0.266061	+	0.963956i	$0.585722\pi$
$660$		0			0
$661$	−7.50670e7	+	8.94614e7i	−0.259923	+	0.309764i	−0.880185	−	0.474630i	$-0.842582\pi$
$661$	−7.50670e7	+	8.94614e7i	−0.259923	+	0.309764i	0.620262	+	0.784395i	$0.287026\pi$
$662$		0			0
$663$	−7.76009e7	−	2.82444e7i	−0.266272	−	0.0969152i
$664$		0			0
$665$	1.67207e7	−	5.51106e6i	0.0568577	−	0.0187400i
$666$		0			0
$667$	−1.56866e8	+	4.30986e8i	−0.528630	+	1.45240i
$668$		0			0
$669$	−1.26208e8	−	1.05901e8i	−0.421512	−	0.353691i
$670$		0			0
$671$	3.02450e7	−	1.71528e8i	0.100112	−	0.567763i
$672$		0			0
$673$	2.03113e8	−	1.17267e8i	0.666336	−	0.384709i	−0.128351	−	0.991729i	$-0.540968\pi$
$673$	2.03113e8	−	1.17267e8i	0.666336	−	0.384709i	0.794687	+	0.607020i	$0.207635\pi$
$674$		0			0
$675$	1.09973e8	+	3.02148e8i	0.357580	+	0.982444i
$676$		0			0
$677$	−3.82940e8	−	2.21090e8i	−1.23414	−	0.712531i	−0.266250	−	0.963904i	$-0.585785\pi$
$677$	−3.82940e8	−	2.21090e8i	−1.23414	−	0.712531i	−0.967890	+	0.251373i	$0.919118\pi$
$678$		0			0
$679$	5.54742e7	+	6.61116e7i	0.177207	+	0.211188i
$680$		0			0
$681$	−7.97444e7	−	4.52253e8i	−0.252498	−	1.43199i
$682$		0			0
$683$			1.10403e8i			0.346511i	0.984877	+	0.173256i	$0.0554287\pi$
$683$			1.10403e8i			0.346511i	−0.984877	+	0.173256i	$0.944571\pi$
$684$		0			0
$685$	5.43290e7			0.169029
$686$		0			0
$687$	−1.14022e8	+	2.01051e7i	−0.351656	+	0.0620064i
$688$		0			0
$689$	−8.46426e7	+	7.10236e7i	−0.258780	+	0.217143i
$690$		0			0
$691$	1.00292e8	−	1.73711e8i	0.303971	−	0.526494i	−0.673060	−	0.739587i	$-0.735021\pi$
$691$	1.00292e8	−	1.73711e8i	0.303971	−	0.526494i	0.977032	+	0.213094i	$0.0683540\pi$
$692$		0			0
$693$	2.69851e7	−	9.82177e6i	0.0810819	−	0.0295114i
$694$		0			0
$695$	−6.00238e7	−	1.03964e8i	−0.178801	−	0.309692i
$696$		0			0
$697$	−3.98979e7	−	7.03508e6i	−0.117829	−	0.0207764i
$698$		0			0
$699$	6.73160e7	−	8.02241e7i	0.197100	−	0.234895i
$700$		0			0
$701$	−3.20949e8	−	1.16816e8i	−0.931713	−	0.339116i	−0.168825	−	0.985646i	$-0.553997\pi$
$701$	−3.20949e8	−	1.16816e8i	−0.931713	−	0.339116i	−0.762888	+	0.646530i	$0.776219\pi$
$702$		0			0
$703$	−7.70754e7	+	1.11644e7i	−0.221845	+	0.0321343i
$704$		0			0
$705$	−1.10839e7	+	3.04527e7i	−0.0316318	+	0.0869076i
$706$		0			0
$707$	−9.98516e6	−	8.37854e6i	−0.0282551	−	0.0237088i
$708$		0			0
$709$	1.22651e8	−	6.95586e8i	0.344136	−	1.95170i	0.0395243	−	0.999219i	$-0.487416\pi$
$709$	1.22651e8	−	6.95586e8i	0.344136	−	1.95170i	0.304612	−	0.952476i	$-0.401473\pi$
$710$		0			0
$711$	5.30199e7	−	3.06111e7i	0.147513	−	0.0851667i
$712$		0			0
$713$	867097.	+	2.38233e6i	0.00239221	+	0.00657254i
$714$		0			0
$715$	−2.45074e7	−	1.41493e7i	−0.0670469	−	0.0387096i
$716$		0			0
$717$	−2.64047e8	−	3.14679e8i	−0.716348	−	0.853710i
$718$		0			0
$719$	−8.44936e7	−	4.79187e8i	−0.227320	−	1.28919i	−0.858201	−	0.513314i	$-0.828417\pi$
$719$	−8.44936e7	−	4.79187e8i	−0.227320	−	1.28919i	0.630881	−	0.775880i	$-0.282694\pi$
$720$		0			0
$721$			4.17314e7i			0.111342i
$722$		0			0
$723$	−7.74630e7			−0.204965
$724$		0			0
$725$	−4.26120e8	+	7.51364e7i	−1.11819	+	0.197168i
$726$		0			0
$727$	−3.31397e8	+	2.78075e8i	−0.862473	+	0.723701i	−0.962499	−	0.271284i	$-0.912552\pi$
$727$	−3.31397e8	+	2.78075e8i	−0.862473	+	0.723701i	0.100027	+	0.994985i	$0.468107\pi$
$728$		0			0
$729$	2.12306e8	−	3.67725e8i	0.547999	−	0.949163i
$730$		0			0
$731$	2.50650e8	−	9.12292e7i	0.641676	−	0.233551i
$732$		0			0
$733$	1.00067e8	+	1.73322e8i	0.254086	+	0.440090i	0.964647	−	0.263546i	$-0.0848920\pi$
$733$	1.00067e8	+	1.73322e8i	0.254086	+	0.440090i	−0.710561	+	0.703636i	$0.751559\pi$
$734$		0			0
$735$	−5.83830e7	−	1.02945e7i	−0.147036	−	0.0259265i
$736$		0			0
$737$	−1.84997e8	+	2.20471e8i	−0.462129	+	0.550743i
$738$		0			0
$739$	−1.10116e8	−	4.00789e7i	−0.272845	−	0.0993076i	0.201974	−	0.979391i	$-0.435264\pi$
$739$	−1.10116e8	−	4.00789e7i	−0.272845	−	0.0993076i	−0.474819	+	0.880083i	$0.657487\pi$
$740$		0			0
$741$	−2.01303e7	−	1.38973e8i	−0.0494760	−	0.341567i
$742$		0			0
$743$	−2.92492e7	+	8.03614e7i	−0.0713094	+	0.195921i	−0.970227	−	0.242196i	$-0.922132\pi$
$743$	−2.92492e7	+	8.03614e7i	−0.0713094	+	0.195921i	0.898918	+	0.438117i	$0.144354\pi$
$744$		0			0
$745$	2.87608e7	+	2.41332e7i	0.0695556	+	0.0583641i
$746$		0			0
$747$	−6.00361e6	+	3.40482e7i	−0.0144029	+	0.0816830i
$748$		0			0
$749$	1.86561e8	−	1.07711e8i	0.443993	−	0.256340i
$750$		0			0
$751$	−9.65304e7	−	2.65215e8i	−0.227900	−	0.626150i	0.772056	−	0.635555i	$-0.219229\pi$
$751$	−9.65304e7	−	2.65215e8i	−0.227900	−	0.626150i	−0.999956	+	0.00940468i	$0.997006\pi$
$752$		0			0
$753$	−4.48034e8	−	2.58673e8i	−1.04936	−	0.605850i
$754$		0			0
$755$	3.40596e7	+	4.05907e7i	0.0791405	+	0.0943160i
$756$		0			0
$757$	7.47591e7	+	4.23980e8i	0.172336	+	0.977367i	0.941174	+	0.337923i	$0.109724\pi$
$757$	7.47591e7	+	4.23980e8i	0.172336	+	0.977367i	−0.768837	+	0.639444i	$0.779164\pi$
$758$		0			0
$759$			4.63112e8i			1.05916i
$760$		0			0
$761$	−3.40445e8			−0.772491			−0.386245	−	0.922396i	$-0.626228\pi$
$761$	−3.40445e8			−0.772491			−0.386245	+	0.922396i	$0.626228\pi$
$762$		0			0
$763$	1.92582e8	−	3.39573e7i	0.433552	−	0.0764469i
$764$		0			0
$765$	−1.61817e7	+	1.35780e7i	−0.0361442	+	0.0303286i
$766$		0			0
$767$	2.76182e7	−	4.78361e7i	0.0612081	−	0.106016i
$768$		0			0
$769$	7.81923e8	−	2.84597e8i	1.71943	−	0.625822i	0.721641	−	0.692268i	$-0.243388\pi$
$769$	7.81923e8	−	2.84597e8i	1.71943	−	0.625822i	0.997790	+	0.0664461i	$0.0211660\pi$
$770$		0			0
$771$	−3.46716e7	−	6.00530e7i	−0.0756503	−	0.131030i
$772$		0			0
$773$	6.35678e8	+	1.12087e8i	1.37625	+	0.242671i	0.812350	−	0.583170i	$-0.198188\pi$
$773$	6.35678e8	+	1.12087e8i	1.37625	+	0.242671i	0.563904	+	0.825840i	$0.309299\pi$
$774$		0			0
$775$	−1.53740e6	+	1.83220e6i	−0.00330279	+	0.00393611i
$776$		0			0
$777$	−2.53832e7	−	9.23874e6i	−0.0541108	−	0.0196947i
$778$		0			0
$779$	−2.15648e7	−	6.54280e7i	−0.0456176	−	0.138405i
$780$		0			0
$781$	−9.82779e7	+	2.70016e8i	−0.206302	+	0.566809i
$782$		0			0
$783$	4.72084e8	+	3.96126e8i	0.983409	+	0.825178i
$784$		0			0
$785$	−1.19323e7	+	6.76715e7i	−0.0246670	+	0.139893i
$786$		0			0
$787$	−2.91010e8	+	1.68015e8i	−0.597013	+	0.344686i	−0.767866	−	0.640611i	$-0.778681\pi$
$787$	−2.91010e8	+	1.68015e8i	−0.597013	+	0.344686i	0.170853	+	0.985297i	$0.445348\pi$
$788$		0			0
$789$	9.66345e6	+	2.65501e7i	0.0196744	+	0.0540549i
$790$		0			0
$791$	1.29036e8	+	7.44990e7i	0.260724	+	0.150529i
$792$		0			0
$793$	7.88252e7	+	9.39402e7i	0.158068	+	0.188379i
$794$		0			0
$795$	−1.18227e7	−	6.70499e7i	−0.0235297	−	0.133443i
$796$		0			0
$797$			7.63309e8i			1.50774i	0.657025	+	0.753869i	$0.271814\pi$
$797$			7.63309e8i			1.50774i	−0.657025	+	0.753869i	$0.728186\pi$
$798$		0			0
$799$	2.35189e8			0.461081
$800$		0			0
$801$	−1.26704e8	+	2.23413e7i	−0.246543	+	0.0434721i
$802$		0			0
$803$	−2.51009e8	+	2.10621e8i	−0.484777	+	0.406777i
$804$		0			0
$805$	2.04399e7	−	3.54030e7i	0.0391824	−	0.0678660i
$806$		0			0
$807$	−2.40962e8	+	8.77031e7i	−0.458488	+	0.166876i
$808$		0			0
$809$	1.30314e8	+	2.25711e8i	0.246120	+	0.426292i	0.962446	−	0.271474i	$-0.0875111\pi$
$809$	1.30314e8	+	2.25711e8i	0.246120	+	0.426292i	−0.716326	+	0.697766i	$0.754178\pi$
$810$		0			0
$811$	3.12984e8	+	5.51875e7i	0.586759	+	0.103461i	0.459143	−	0.888362i	$-0.348156\pi$
$811$	3.12984e8	+	5.51875e7i	0.586759	+	0.103461i	0.127616	+	0.991824i	$0.459268\pi$
$812$		0			0
$813$	2.75578e8	−	3.28420e8i	0.512828	−	0.611165i
$814$		0			0
$815$	−1.13416e8	−	4.12801e7i	−0.209509	−	0.0762550i
$816$		0			0
$817$	3.38344e8	+	3.02069e8i	0.620430	+	0.553911i
$818$		0			0
$819$	−6.91518e6	+	1.89993e7i	−0.0125879	+	0.0345849i
$820$		0			0
$821$	5.04693e7	+	4.23488e7i	0.0912006	+	0.0765264i	0.687248	−	0.726423i	$-0.258819\pi$
$821$	5.04693e7	+	4.23488e7i	0.0912006	+	0.0765264i	−0.596047	+	0.802949i	$0.703263\pi$
$822$		0			0
$823$	6.29851e7	−	3.57206e8i	0.112990	−	0.640795i	−0.874736	−	0.484599i	$-0.838966\pi$
$823$	6.29851e7	−	3.57206e8i	0.112990	−	0.640795i	0.987726	−	0.156197i	$-0.0499233\pi$
$824$		0			0
$825$	−3.78372e8	+	2.18453e8i	−0.673841	+	0.389042i
$826$		0			0
$827$	−2.33223e8	−	6.40774e8i	−0.412339	−	1.13289i	−0.955944	−	0.293550i	$-0.905163\pi$
$827$	−2.33223e8	−	6.40774e8i	−0.412339	−	1.13289i	0.543605	−	0.839341i	$-0.317059\pi$
$828$		0			0
$829$	3.50067e8	+	2.02111e8i	0.614451	+	0.354754i	0.774706	−	0.632322i	$-0.217898\pi$
$829$	3.50067e8	+	2.02111e8i	0.614451	+	0.354754i	−0.160254	+	0.987076i	$0.551231\pi$
$830$		0			0
$831$	4.42643e8	+	5.27521e8i	0.771347	+	0.919256i
$832$		0			0
$833$	7.47109e7	+	4.23707e8i	0.129256	+	0.733044i
$834$		0			0
$835$			8.75264e7i			0.150342i
$836$		0			0
$837$	3.40646e6			0.00580935
$838$		0			0
$839$	7.18496e8	−	1.26690e8i	1.21657	−	0.214515i	0.471724	−	0.881746i	$-0.343632\pi$
$839$	7.18496e8	−	1.26690e8i	1.21657	−	0.214515i	0.744851	+	0.667231i	$0.232521\pi$
$840$		0			0
$841$	−1.79620e8	+	1.50719e8i	−0.301972	+	0.253385i
$842$		0			0
$843$	−1.13817e8	+	1.97137e8i	−0.189987	+	0.329068i
$844$		0			0
$845$	−9.23489e7	+	3.36123e7i	−0.153060	+	0.0557093i
$846$		0			0
$847$	−6.82529e6	−	1.18218e7i	−0.0112324	−	0.0194550i
$848$		0			0
$849$	4.96433e8	+	8.75345e7i	0.811217	+	0.143040i
$850$		0			0
$851$	−1.16239e8	+	1.38529e8i	−0.188610	+	0.224777i
$852$		0			0
$853$	−1.01559e9	−	3.69645e8i	−1.63633	−	0.595576i	−0.649941	−	0.759985i	$-0.725206\pi$
$853$	−1.01559e9	−	3.69645e8i	−1.63633	−	0.595576i	−0.986392	+	0.164409i	$0.947428\pi$
$854$		0			0
$855$	−3.33603e7	−	1.33148e7i	−0.0533742	−	0.0213028i
$856$		0			0
$857$	−4.94621e7	+	1.35896e8i	−0.0785833	+	0.215906i	−0.972763	−	0.231803i	$-0.925538\pi$
$857$	−4.94621e7	+	1.35896e8i	−0.0785833	+	0.215906i	0.894179	+	0.447709i	$0.147760\pi$
$858$		0			0
$859$	−9.29468e7	−	7.79917e7i	−0.146641	−	0.123046i	0.566516	−	0.824051i	$-0.308291\pi$
$859$	−9.29468e7	−	7.79917e7i	−0.146641	−	0.123046i	−0.713157	+	0.701004i	$0.752735\pi$
$860$		0			0
$861$	4.14920e6	−	2.35313e7i	0.00650061	−	0.0368668i
$862$		0			0
$863$	6.55569e8	−	3.78493e8i	1.01997	−	0.588878i	0.105873	−	0.994380i	$-0.466236\pi$
$863$	6.55569e8	−	3.78493e8i	1.01997	−	0.588878i	0.914094	+	0.405501i	$0.132903\pi$
$864$		0			0
$865$	3.32054e7	+	9.12311e7i	0.0513051	+	0.140960i
$866$		0			0
$867$	1.54633e8	+	8.92776e7i	0.237272	+	0.136989i
$868$		0			0
$869$	2.35757e8	+	2.80964e8i	0.359256	+	0.428145i
$870$		0			0
$871$	−3.51870e7	−	1.99555e8i	−0.0532510	−	0.302001i
$872$		0			0
$873$		−	1.76077e8i		−	0.264643i
$874$		0			0
$875$	7.86724e7			0.117435
$876$		0			0
$877$	−2.15375e8	+	3.79764e7i	−0.319298	+	0.0563008i	−0.331000	−	0.943631i	$-0.607386\pi$
$877$	−2.15375e8	+	3.79764e7i	−0.319298	+	0.0563008i	0.0117024	+	0.999932i	$0.496275\pi$
$878$		0			0
$879$	8.23886e7	−	6.91323e7i	0.121311	−	0.101792i
$880$		0			0
$881$	2.84674e8	−	4.93070e8i	0.416313	−	0.721075i	−0.579252	−	0.815148i	$-0.696655\pi$
$881$	2.84674e8	−	4.93070e8i	0.416313	−	0.721075i	0.995565	+	0.0940731i	$0.0299888\pi$
$882$		0			0
$883$	−1.72552e8	+	6.28038e7i	−0.250633	+	0.0912228i	−0.464281	−	0.885688i	$-0.653687\pi$
$883$	−1.72552e8	+	6.28038e7i	−0.250633	+	0.0912228i	0.213649	+	0.976911i	$0.431465\pi$
$884$		0			0
$885$	1.70179e7	+	2.94759e7i	0.0245515	+	0.0425244i
$886$		0			0
$887$	−1.07085e9	−	1.88819e8i	−1.53446	−	0.270567i	−0.658364	−	0.752700i	$-0.728751\pi$
$887$	−1.07085e9	−	1.88819e8i	−1.53446	−	0.270567i	−0.876098	+	0.482132i	$0.839862\pi$
$888$		0			0
$889$	−2.30356e7	+	2.74528e7i	−0.0327865	+	0.0390734i
$890$		0			0
$891$	3.97055e8	+	1.44516e8i	0.561328	+	0.204307i
$892$		0			0
$893$	1.89242e8	+	3.52315e8i	0.265744	+	0.494740i
$894$		0			0
$895$	8.90379e7	−	2.44630e8i	0.124195	−	0.341224i
$896$		0			0
$897$	−2.49778e8	−	2.09589e8i	−0.346080	−	0.290396i
$898$		0			0
$899$	−796013.	+	4.51442e6i	−0.00109557	+	0.00621330i
$900$		0			0
$901$	−4.27914e8	+	2.47056e8i	−0.585035	+	0.337770i
$902$		0			0
$903$	5.38058e7	+	1.47830e8i	0.0730744	+	0.200770i
$904$		0			0
$905$	−1.48384e8	−	8.56697e7i	−0.200190	−	0.115580i
$906$		0			0
$907$	3.78029e6	+	4.50517e6i	0.00506644	+	0.00603795i	0.768572	−	0.639764i	$-0.220968\pi$
$907$	3.78029e6	+	4.50517e6i	0.00506644	+	0.00603795i	−0.763505	+	0.645802i	$0.776523\pi$
$908$		0			0
$909$	4.61797e6	+	2.61898e7i	0.00614836	+	0.0348691i
$910$		0			0
$911$		−	2.88580e8i		−	0.381690i	−0.981620	−	0.190845i	$-0.938877\pi$
$911$		−	2.88580e8i		−	0.381690i	0.981620	−	0.190845i	$-0.0611227\pi$
$912$		0			0
$913$	−2.07124e8			−0.272156
$914$		0			0
$915$	−7.44150e7	+	1.31214e7i	−0.0971398	+	0.0171284i
$916$		0			0
$917$	−7.43900e7	+	6.24206e7i	−0.0964732	+	0.0809506i
$918$		0			0
$919$	3.28411e8	−	5.68825e8i	0.423128	−	0.732878i	−0.573116	−	0.819474i	$-0.694266\pi$
$919$	3.28411e8	−	5.68825e8i	0.423128	−	0.732878i	0.996244	+	0.0865959i	$0.0275989\pi$
$920$		0			0
$921$	2.87192e8	−	1.04529e8i	0.367615	−	0.133801i
$922$		0			0
$923$	−1.01155e8	−	1.75206e8i	−0.128642	−	0.222815i
$924$		0			0
$925$	−1.68012e8	−	2.96250e7i	−0.212282	−	0.0374311i
$926$		0			0
$927$	5.47281e7	−	6.52224e7i	0.0687023	−	0.0818762i
$928$		0			0
$929$	1.06978e9	+	3.89369e8i	1.33428	+	0.485640i	0.908008	−	0.418953i	$-0.137603\pi$
$929$	1.06978e9	+	3.89369e8i	1.33428	+	0.485640i	0.426277	+	0.904593i	$0.359825\pi$
$930$		0			0
$931$	−5.74600e8	+	4.52847e8i	−0.712059	+	0.561181i
$932$		0			0
$933$	−1.84047e7	+	5.05664e7i	−0.0226612	+	0.0622611i
$934$		0			0
$935$	−9.69417e7	−	8.13438e7i	−0.118598	−	0.0995152i
$936$		0			0
$937$	−8.73267e6	+	4.95254e7i	−0.0106152	+	0.0602018i	−0.989655	−	0.143466i	$-0.954175\pi$
$937$	−8.73267e6	+	4.95254e7i	−0.0106152	+	0.0602018i	0.979040	+	0.203668i	$0.0652863\pi$
$938$		0			0
$939$	3.18132e8	−	1.83674e8i	0.384247	−	0.221845i
$940$		0			0
$941$	2.83983e8	+	7.80237e8i	0.340819	+	0.936392i	0.985158	+	0.171652i	$0.0549105\pi$
$941$	2.83983e8	+	7.80237e8i	0.340819	+	0.936392i	−0.644339	+	0.764740i	$0.722867\pi$
$942$		0			0
$943$	−1.38532e8	−	7.99813e7i	−0.165201	−	0.0953791i
$944$		0			0
$945$	−3.53073e7	−	4.20776e7i	−0.0418378	−	0.0498603i
$946$		0			0
$947$	−1.10259e8	−	6.25308e8i	−0.129826	−	0.736281i	−0.978324	−	0.207082i	$-0.933603\pi$
$947$	−1.10259e8	−	6.25308e8i	−0.129826	−	0.736281i	0.848497	−	0.529200i	$-0.177508\pi$
$948$		0			0
$949$		−	2.30701e8i		−	0.269930i
$950$		0			0
$951$	−8.05951e8			−0.937059
$952$		0			0
$953$	−1.96583e8	+	3.46628e7i	−0.227126	+	0.0400484i	−0.286053	−	0.958214i	$-0.592343\pi$
$953$	−1.96583e8	+	3.46628e7i	−0.227126	+	0.0400484i	0.0589269	+	0.998262i	$0.481232\pi$
$954$		0			0
$955$	−1.33655e8	+	1.12149e8i	−0.153452	+	0.128762i
$956$		0			0
$957$	−4.18688e8	+	7.25189e8i	−0.477699	+	0.827399i
$958$		0			0
$959$	2.18520e8	−	7.95347e7i	0.247762	−	0.0901781i
$960$		0			0
$961$	−4.43739e8	−	7.68579e8i	−0.499986	−	0.866001i
$962$		0			0
$963$	−4.32835e8	−	7.63205e7i	−0.484667	−	0.0854599i
$964$		0			0
$965$	−1.85561e8	+	2.21143e8i	−0.206493	+	0.246089i
$966$		0			0
$967$	−1.71156e8	−	6.22956e7i	−0.189283	−	0.0688934i	0.245639	−	0.969361i	$-0.421002\pi$
$967$	−1.71156e8	−	6.22956e7i	−0.189283	−	0.0688934i	−0.434923	+	0.900468i	$0.643224\pi$
$968$		0			0
$969$	1.92647e7	−	6.27661e8i	0.0211735	−	0.689849i
$970$		0			0
$971$	7.29126e7	−	2.00326e8i	0.0796425	−	0.218816i	−0.893480	−	0.449102i	$-0.851744\pi$
$971$	7.29126e7	−	2.00326e8i	0.0796425	−	0.218816i	0.973123	+	0.230286i	$0.0739662\pi$
$972$		0			0
$973$	−3.93624e8	−	3.30289e8i	−0.427310	−	0.358555i
$974$		0			0
$975$	5.34162e7	−	3.02938e8i	0.0576314	−	0.326844i
$976$		0			0
$977$	−2.03764e8	+	1.17643e8i	−0.218496	+	0.126149i	−0.605254	−	0.796033i	$-0.706928\pi$
$977$	−2.03764e8	+	1.17643e8i	−0.218496	+	0.126149i	0.386758	+	0.922181i	$0.373595\pi$
$978$		0			0
$979$	−2.63619e8	−	7.24288e8i	−0.280950	−	0.771904i
$980$		0			0
$981$	−3.45520e8	−	1.99486e8i	−0.365988	−	0.211303i
$982$		0			0
$983$	−4.28049e8	−	5.10128e8i	−0.450643	−	0.537055i	0.492116	−	0.870529i	$-0.336223\pi$
$983$	−4.28049e8	−	5.10128e8i	−0.450643	−	0.537055i	−0.942759	+	0.333474i	$0.891779\pi$
$984$		0			0
$985$	−3.85030e7	−	2.18361e8i	−0.0402890	−	0.228490i
$986$		0			0
$987$			1.38712e8i			0.144265i
$988$		0			0
$989$	1.05318e9			1.08871
$990$		0			0
$991$	4.12878e8	−	7.28015e7i	0.424229	−	0.0748031i	0.0425422	−	0.999095i	$-0.486454\pi$
$991$	4.12878e8	−	7.28015e7i	0.424229	−	0.0748031i	0.381687	+	0.924292i	$0.375343\pi$
$992$		0			0
$993$	3.88570e8	−	3.26049e8i	0.396846	−	0.332993i
$994$		0			0
$995$	−2.41416e7	+	4.18145e7i	−0.0245074	+	0.0424481i
$996$		0			0
$997$	−7.77634e8	+	2.83036e8i	−0.784675	+	0.285598i	−0.703121	−	0.711071i	$-0.748211\pi$
$997$	−7.77634e8	+	2.83036e8i	−0.784675	+	0.285598i	−0.0815542	+	0.996669i	$0.525988\pi$
$998$		0			0
$999$	1.21491e8	+	2.10428e8i	0.121856	+	0.211061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.53.4	yes	60
19.14	odd	18	inner	76.7.j.a.33.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.4	✓	60	19.14	odd	18	inner
76.7.j.a.53.4	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-22.3521 + 3.94128i) q^{3} +(18.7591 - 15.7407i) q^{5} +(52.4083 - 90.7739i) q^{7} +(-200.954 + 73.1411i) q^{9} +O(q^{10})\)	\(q+(-22.3521 + 3.94128i) q^{3} +(18.7591 - 15.7407i) q^{5} +(52.4083 - 90.7739i) q^{7} +(-200.954 + 73.1411i) q^{9} +(-640.572 - 1109.50i) q^{11} +(888.307 + 156.633i) q^{13} +(-357.266 + 425.772i) q^{15} +(3790.43 + 1379.60i) q^{17} +(983.265 + 6788.16i) q^{19} +(-813.671 + 2235.54i) q^{21} +(12200.4 + 10237.4i) q^{23} +(-2609.12 + 14797.1i) q^{25} +(18532.8 - 10699.9i) q^{27} +(9849.35 + 27060.9i) q^{29} +(137.856 + 79.5910i) q^{31} +(18691.0 + 22275.0i) q^{33} +(-445.715 - 2527.78i) q^{35} +11354.4i q^{37} -20472.9 q^{39} +(-9891.18 + 1744.08i) q^{41} +(50656.4 - 42505.7i) q^{43} +(-2618.41 + 4535.21i) q^{45} +(54790.0 - 19941.9i) q^{47} +(53331.2 + 92372.4i) q^{49} +(-90161.3 - 15897.9i) q^{51} +(-78739.2 + 93837.7i) q^{53} +(-29480.9 - 10730.2i) q^{55} +(-48732.0 - 147854. i) q^{57} +(20944.3 - 57543.9i) q^{59} +(104145. + 87388.2i) q^{61} +(-3892.34 + 22074.5i) q^{63} +(19129.3 - 11044.3i) q^{65} +(-76833.7 - 211099. i) q^{67} +(-313054. - 180742. i) q^{69} +(-144170. - 171815. i) q^{71} +(-44412.7 - 251877. i) q^{73} -341028. i q^{75} -134285. q^{77} +(-281936. + 49712.9i) q^{79} +(-252651. + 211999. i) q^{81} +(80835.5 - 140011. i) q^{83} +(92820.7 - 33784.0i) q^{85} +(-326808. - 566048. i) q^{87} +(592488. + 104472. i) q^{89} +(60772.9 - 72426.3i) q^{91} +(-3395.05 - 1235.70i) q^{93} +(125296. + 111862. i) q^{95} +(-281608. + 773712. i) q^{97} +(209875. + 176106. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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