LMFDB - Embedded newform 76.7.j.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	76.53
Dual form			76.7.j.a.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.55244 - 0.626392i) q^{3} +(-10.1242 + 8.49522i) q^{5} +(110.999 - 192.257i) q^{7} +(-672.808 + 244.882i) q^{9} +O(q^{10})$	\(q+(3.55244 - 0.626392i) q^{3} +(-10.1242 + 8.49522i) q^{5} +(110.999 - 192.257i) q^{7} +(-672.808 + 244.882i) q^{9} +(-245.534 - 425.277i) q^{11} +(1550.95 + 273.474i) q^{13} +(-30.6444 + 36.5205i) q^{15} +(-7565.82 - 2753.73i) q^{17} +(305.082 - 6852.21i) q^{19} +(273.891 - 752.510i) q^{21} +(-4764.38 - 3997.79i) q^{23} +(-2682.92 + 15215.6i) q^{25} +(-4514.09 + 2606.21i) q^{27} +(-12693.0 - 34873.8i) q^{29} +(-35759.6 - 20645.8i) q^{31} +(-1138.63 - 1356.97i) q^{33} +(509.481 + 2889.41i) q^{35} -73991.1i q^{37} +5680.96 q^{39} +(-64009.4 + 11286.6i) q^{41} +(-57910.4 + 48592.6i) q^{43} +(4731.33 - 8194.90i) q^{45} +(80803.1 - 29409.9i) q^{47} +(34182.7 + 59206.2i) q^{49} +(-28602.1 - 5043.32i) q^{51} +(-1911.87 + 2278.48i) q^{53} +(6098.65 + 2219.73i) q^{55} +(-3208.38 - 24533.2i) q^{57} +(66931.9 - 183894. i) q^{59} +(255234. + 214167. i) q^{61} +(-27601.1 + 156534. i) q^{63} +(-18025.3 + 10406.9i) q^{65} +(115279. + 316726. i) q^{67} +(-19429.4 - 11217.5i) q^{69} +(416036. + 495812. i) q^{71} +(-65628.3 - 372197. i) q^{73} +55733.1i q^{75} -109016. q^{77} +(303328. - 53484.9i) q^{79} +(385437. - 323420. i) q^{81} +(-391211. + 677597. i) q^{83} +(99991.6 - 36394.0i) q^{85} +(-66935.9 - 115936. i) q^{87} +(-103944. - 18328.2i) q^{89} +(224732. - 267825. i) q^{91} +(-139966. - 50943.6i) q^{93} +(55122.3 + 71965.0i) q^{95} +(-164328. + 451487. i) q^{97} +(269340. + 226003. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.55244	−	0.626392i	0.131572	−	0.0231997i	−0.107474	−	0.994208i	$-0.534276\pi$
$3$	3.55244	−	0.626392i	0.131572	−	0.0231997i	0.239046	+	0.971008i	$0.423165\pi$
$4$		0			0
$5$	−10.1242	+	8.49522i	−0.0809937	+	0.0679618i	−0.682386	−	0.730992i	$-0.739057\pi$
$5$	−10.1242	+	8.49522i	−0.0809937	+	0.0679618i	0.601392	+	0.798954i	$0.294613\pi$
$6$		0			0
$7$	110.999	−	192.257i	0.323614	−	0.560515i	−0.657617	−	0.753352i	$-0.728436\pi$
$7$	110.999	−	192.257i	0.323614	−	0.560515i	0.981231	+	0.192837i	$0.0617689\pi$
$8$		0			0
$9$	−672.808	+	244.882i	−0.922920	+	0.335915i
$10$		0			0
$11$	−245.534	−	425.277i	−0.184473	−	0.319517i	0.758926	−	0.651177i	$-0.225725\pi$
$11$	−245.534	−	425.277i	−0.184473	−	0.319517i	−0.943399	+	0.331660i	$0.892391\pi$
$12$		0			0
$13$	1550.95	+	273.474i	0.705939	+	0.124476i	0.515081	−	0.857142i	$-0.327762\pi$
$13$	1550.95	+	273.474i	0.705939	+	0.124476i	0.190858	+	0.981618i	$0.438873\pi$
$14$		0			0
$15$	−30.6444	+	36.5205i	−0.00907981	+	0.0108209i
$16$		0			0
$17$	−7565.82	−	2753.73i	−1.53996	−	0.560499i	−0.573924	−	0.818909i	$-0.694580\pi$
$17$	−7565.82	−	2753.73i	−1.53996	−	0.560499i	−0.966036	+	0.258409i	$0.916802\pi$
$18$		0			0
$19$	305.082	−	6852.21i	0.0444791	−	0.999010i
$19$	305.082	−	6852.21i	0.0444791	−	0.999010i
$20$		0			0
$21$	273.891	−	752.510i	0.0295747	−	0.0812558i
$22$		0			0
$23$	−4764.38	−	3997.79i	−0.391582	−	0.328576i	0.425647	−	0.904889i	$-0.360046\pi$
$23$	−4764.38	−	3997.79i	−0.391582	−	0.328576i	−0.817229	+	0.576313i	$0.804491\pi$
$24$		0			0
$25$	−2682.92	+	15215.6i	−0.171707	+	0.973799i
$26$		0			0
$27$	−4514.09	+	2606.21i	−0.229340	+	0.132409i
$28$		0			0
$29$	−12693.0	−	34873.8i	−0.520440	−	1.42990i	−0.870032	−	0.492996i	$-0.835902\pi$
$29$	−12693.0	−	34873.8i	−0.520440	−	1.42990i	0.349592	−	0.936902i	$-0.386320\pi$
$30$		0			0
$31$	−35759.6	−	20645.8i	−1.20035	−	0.693022i	−0.239717	−	0.970843i	$-0.577055\pi$
$31$	−35759.6	−	20645.8i	−1.20035	−	0.693022i	−0.960633	+	0.277821i	$0.910388\pi$
$32$		0			0
$33$	−1138.63	−	1356.97i	−0.0316842	−	0.0377597i
$34$		0			0
$35$	509.481	+	2889.41i	0.0118829	+	0.0673916i
$36$		0			0
$37$		−	73991.1i		−	1.46074i	−0.683050	−	0.730372i	$-0.739347\pi$
$37$		−	73991.1i		−	1.46074i	0.683050	−	0.730372i	$-0.260653\pi$
$38$		0			0
$39$	5680.96			0.0957696
$40$		0			0
$41$	−64009.4	+	11286.6i	−0.928736	+	0.163761i	−0.617499	−	0.786571i	$-0.711854\pi$
$41$	−64009.4	+	11286.6i	−0.928736	+	0.163761i	−0.311236	+	0.950333i	$0.600743\pi$
$42$		0			0
$43$	−57910.4	+	48592.6i	−0.728369	+	0.611174i	−0.929686	−	0.368352i	$-0.879922\pi$
$43$	−57910.4	+	48592.6i	−0.728369	+	0.611174i	0.201318	+	0.979526i	$0.435478\pi$
$44$		0			0
$45$	4731.33	−	8194.90i	0.0519213	−	0.0899303i
$46$		0			0
$47$	80803.1	−	29409.9i	0.778277	−	0.283270i	0.0778231	−	0.996967i	$-0.475203\pi$
$47$	80803.1	−	29409.9i	0.778277	−	0.283270i	0.700454	+	0.713697i	$0.252981\pi$
$48$		0			0
$49$	34182.7	+	59206.2i	0.290548	+	0.503245i
$50$		0			0
$51$	−28602.1	−	5043.32i	−0.215619	−	0.0380194i
$52$		0			0
$53$	−1911.87	+	2278.48i	−0.0128420	+	0.0153045i	−0.772427	−	0.635103i	$-0.780958\pi$
$53$	−1911.87	+	2278.48i	−0.0128420	+	0.0153045i	0.759585	+	0.650408i	$0.225402\pi$
$54$		0			0
$55$	6098.65	+	2219.73i	0.0366561	+	0.0133417i
$56$		0			0
$57$	−3208.38	−	24533.2i	−0.0173245	−	0.132474i
$58$		0			0
$59$	66931.9	−	183894.i	0.325894	−	0.895388i	−0.663244	−	0.748403i	$-0.730821\pi$
$59$	66931.9	−	183894.i	0.325894	−	0.895388i	0.989139	−	0.146985i	$-0.0469568\pi$
$60$		0			0
$61$	255234.	+	214167.i	1.12447	+	0.943544i	0.998822	−	0.0485305i	$-0.0154538\pi$
$61$	255234.	+	214167.i	1.12447	+	0.943544i	0.125650	+	0.992075i	$0.459898\pi$
$62$		0			0
$63$	−27601.1	+	156534.i	−0.110384	+	0.626017i
$64$		0			0
$65$	−18025.3	+	10406.9i	−0.0656362	+	0.0378951i
$66$		0			0
$67$	115279.	+	316726.i	0.383288	+	1.05308i	0.969963	+	0.243253i	$0.0782147\pi$
$67$	115279.	+	316726.i	0.383288	+	1.05308i	−0.586674	+	0.809823i	$0.699563\pi$
$68$		0			0
$69$	−19429.4	−	11217.5i	−0.0591441	−	0.0341468i
$70$		0			0
$71$	416036.	+	495812.i	1.16240	+	1.38529i	0.908406	+	0.418089i	$0.137300\pi$
$71$	416036.	+	495812.i	1.16240	+	1.38529i	0.253994	+	0.967206i	$0.418256\pi$
$72$		0			0
$73$	−65628.3	−	372197.i	−0.168703	−	0.956762i	−0.945164	−	0.326596i	$-0.894098\pi$
$73$	−65628.3	−	372197.i	−0.168703	−	0.956762i	0.776461	−	0.630165i	$-0.217013\pi$
$74$		0			0
$75$			55733.1i			0.132108i
$76$		0			0
$77$	−109016.			−0.238792
$78$		0			0
$79$	303328.	−	53484.9i	0.615220	−	0.108480i	0.142651	−	0.989773i	$-0.454438\pi$
$79$	303328.	−	53484.9i	0.615220	−	0.108480i	0.472570	+	0.881293i	$0.343326\pi$
$80$		0			0
$81$	385437.	−	323420.i	0.725268	−	0.608572i
$82$		0			0
$83$	−391211.	+	677597.i	−0.684190	+	1.18505i	0.289501	+	0.957178i	$0.406511\pi$
$83$	−391211.	+	677597.i	−0.684190	+	1.18505i	−0.973691	+	0.227874i	$0.926823\pi$
$84$		0			0
$85$	99991.6	−	36394.0i	0.162820	−	0.0592615i
$86$		0			0
$87$	−66935.9	−	115936.i	−0.101649	−	0.176060i
$88$		0			0
$89$	−103944.	−	18328.2i	−0.147445	−	0.0259986i	0.0994382	−	0.995044i	$-0.468295\pi$
$89$	−103944.	−	18328.2i	−0.147445	−	0.0259986i	−0.246884	+	0.969045i	$0.579407\pi$
$90$		0			0
$91$	224732.	−	267825.i	0.298222	−	0.355407i
$92$		0			0
$93$	−139966.	−	50943.6i	−0.174010	−	0.0633346i
$94$		0			0
$95$	55122.3	+	71965.0i	0.0642920	+	0.0839364i
$96$		0			0
$97$	−164328.	+	451487.i	−0.180051	+	0.494687i	−0.996581	−	0.0826159i	$-0.973673\pi$
$97$	−164328.	+	451487.i	−0.180051	+	0.494687i	0.816530	+	0.577303i	$0.195895\pi$
$98$		0			0
$99$	269340.	+	226003.i	0.277584	+	0.232921i
$100$		0			0
$101$	159947.	−	907103.i	0.155243	−	0.880425i	−0.803321	−	0.595547i	$-0.796936\pi$
$101$	159947.	−	907103.i	0.155243	−	0.880425i	0.958564	−	0.284879i	$-0.0919533\pi$
$102$		0			0
$103$	−950614.	+	548837.i	−0.869947	+	0.502264i	−0.867331	−	0.497733i	$-0.834166\pi$
$103$	−950614.	+	548837.i	−0.869947	+	0.502264i	−0.00261628	+	0.999997i	$0.500833\pi$
$104$		0			0
$105$	3619.81	+	9945.34i	0.00312693	+	0.00859116i
$106$		0			0
$107$	−359996.	−	207844.i	−0.293864	−	0.169663i	0.345819	−	0.938301i	$-0.387601\pi$
$107$	−359996.	−	207844.i	−0.293864	−	0.169663i	−0.639683	+	0.768639i	$0.720934\pi$
$108$		0			0
$109$	−1.09863e6	−	1.30930e6i	−0.848348	−	1.01102i	−0.999746	−	0.0225485i	$-0.992822\pi$
$109$	−1.09863e6	−	1.30930e6i	−0.848348	−	1.01102i	0.151398	−	0.988473i	$-0.451622\pi$
$110$		0			0
$111$	−46347.4	−	262849.i	−0.0338888	−	0.192193i
$112$		0			0
$113$		−	1.52260e6i		−	1.05524i	−0.849481	−	0.527619i	$-0.823085\pi$
$113$		−	1.52260e6i		−	1.05524i	0.849481	−	0.527619i	$-0.176915\pi$
$114$		0			0
$115$	82197.6			0.0540463
$116$		0			0
$117$	−1.11046e6	+	195804.i	−0.693338	+	0.122254i
$118$		0			0
$119$	−1.36923e6	+	1.14892e6i	−0.812520	+	0.681785i
$120$		0			0
$121$	765207.	−	1.32538e6i	0.431939	−	0.748141i
$122$		0			0
$123$	−220320.	+	80189.9i	−0.118396	+	0.0430928i
$124$		0			0
$125$	−205349.	−	355675.i	−0.105139	−	0.182106i
$126$		0			0
$127$	1.63595e6	+	288461.i	0.798652	+	0.140824i	0.558058	−	0.829802i	$-0.311547\pi$
$127$	1.63595e6	+	288461.i	0.798652	+	0.140824i	0.240594	+	0.970626i	$0.422658\pi$
$128$		0			0
$129$	−175285.	+	208897.i	−0.0816539	+	0.0973113i
$130$		0			0
$131$	21290.1	+	7748.95i	0.00947028	+	0.00344690i	0.346751	−	0.937957i	$-0.387285\pi$
$131$	21290.1	+	7748.95i	0.00947028	+	0.00344690i	−0.337281	+	0.941404i	$0.609507\pi$
$132$		0			0
$133$	−1.28352e6	−	819246.i	−0.545566	−	0.348225i
$134$		0			0
$135$	23561.3	−	64734.1i	0.00957630	−	0.0263107i
$136$		0			0
$137$	−3.33810e6	−	2.80100e6i	−1.29819	−	1.08931i	−0.990455	−	0.137835i	$-0.955986\pi$
$137$	−3.33810e6	−	2.80100e6i	−1.29819	−	1.08931i	−0.307731	−	0.951473i	$-0.599570\pi$
$138$		0			0
$139$	−210259.	+	1.19244e6i	−0.0782907	+	0.444009i	0.920313	+	0.391183i	$0.127934\pi$
$139$	−210259.	+	1.19244e6i	−0.0782907	+	0.444009i	−0.998604	+	0.0528259i	$0.983177\pi$
$140$		0			0
$141$	268626.	−	155091.i	0.0958277	−	0.0553261i
$142$		0			0
$143$	−264508.	−	726729.i	−0.0904545	−	0.248522i
$144$		0			0
$145$	424767.	+	245240.i	0.139331	+	0.0804427i
$146$		0			0
$147$	158519.	+	188915.i	0.0499032	+	0.0594723i
$148$		0			0
$149$	389070.	+	2.20653e6i	0.117617	+	0.667038i	0.985421	+	0.170132i	$0.0544195\pi$
$149$	389070.	+	2.20653e6i	0.117617	+	0.667038i	−0.867804	+	0.496906i	$0.834469\pi$
$150$		0			0
$151$			3.78577e6i			1.09957i	0.835306	+	0.549785i	$0.185290\pi$
$151$			3.78577e6i			1.09957i	−0.835306	+	0.549785i	$0.814710\pi$
$152$		0			0
$153$	5.76469e6			1.60954
$154$		0			0
$155$	537429.	−	94763.2i	0.144320	−	0.0254475i
$156$		0			0
$157$	2.82569e6	−	2.37103e6i	0.730172	−	0.612687i	−0.200006	−	0.979795i	$-0.564096\pi$
$157$	2.82569e6	−	2.37103e6i	0.730172	−	0.612687i	0.930179	+	0.367107i	$0.119652\pi$
$158$		0			0
$159$	−5364.60	+	9291.76i	−0.00133458	+	0.00231157i
$160$		0			0
$161$	−1.29744e6	+	472231.i	−0.310893	+	0.113156i
$162$		0			0
$163$	1.39955e6	+	2.42409e6i	0.323166	+	0.559741i	0.981140	−	0.193301i	$-0.0619193\pi$
$163$	1.39955e6	+	2.42409e6i	0.323166	+	0.559741i	−0.657973	+	0.753041i	$0.728586\pi$
$164$		0			0
$165$	23055.5	+	4065.31i	0.00513244	+	0.000904987i
$166$		0			0
$167$	254695.	−	303534.i	0.0546853	−	0.0651714i	−0.738008	−	0.674792i	$-0.764234\pi$
$167$	254695.	−	303534.i	0.0546853	−	0.0651714i	0.792694	+	0.609620i	$0.208678\pi$
$168$		0			0
$169$	−2.20506e6	−	802578.i	−0.456837	−	0.166275i
$170$		0			0
$171$	1.47272e6	+	4.68494e6i	0.294532	+	0.936947i
$172$		0			0
$173$	−1.13559e6	+	3.12001e6i	−0.219323	+	0.602584i	−0.999743	−	0.0226712i	$-0.992783\pi$
$173$	−1.13559e6	+	3.12001e6i	−0.219323	+	0.602584i	0.780420	+	0.625255i	$0.215005\pi$
$174$		0			0
$175$	2.62750e6	+	2.20473e6i	0.490262	+	0.411379i
$176$		0			0
$177$	122582.	−	695198.i	0.0221059	−	0.125369i
$178$		0			0
$179$	7.62765e6	−	4.40383e6i	1.32994	−	0.767841i	0.344649	−	0.938732i	$-0.387998\pi$
$179$	7.62765e6	−	4.40383e6i	1.32994	−	0.767841i	0.985290	+	0.170891i	$0.0546646\pi$
$180$		0			0
$181$	1.36553e6	+	3.75175e6i	0.230284	+	0.632700i	0.999984	−	0.00570578i	$-0.00181622\pi$
$181$	1.36553e6	+	3.75175e6i	0.230284	+	0.632700i	−0.769700	+	0.638406i	$0.779594\pi$
$182$		0			0
$183$	1.04086e6	+	600938.i	0.169839	+	0.0980566i
$184$		0			0
$185$	628571.	+	749101.i	0.0992748	+	0.118311i
$186$		0			0
$187$	686565.	+	3.89370e6i	0.104992	+	0.595440i
$188$		0			0
$189$			1.15715e6i			0.171398i
$190$		0			0
$191$	−1.27729e7			−1.83311			−0.916554	−	0.399911i	$-0.869041\pi$
$191$	−1.27729e7			−1.83311			−0.916554	+	0.399911i	$0.869041\pi$
$192$		0			0
$193$	8.43536e6	−	1.48738e6i	1.17336	−	0.206895i	0.447209	−	0.894429i	$-0.352418\pi$
$193$	8.43536e6	−	1.48738e6i	1.17336	−	0.206895i	0.726152	+	0.687534i	$0.241307\pi$
$194$		0			0
$195$	−57515.2	+	48261.0i	−0.00775673	+	0.00650867i
$196$		0			0
$197$	1.69481e6	−	2.93549e6i	0.221677	−	0.383956i	−0.733640	−	0.679538i	$-0.762180\pi$
$197$	1.69481e6	−	2.93549e6i	0.221677	−	0.383956i	0.955317	+	0.295582i	$0.0955135\pi$
$198$		0			0
$199$	3.85541e6	−	1.40326e6i	0.489229	−	0.178065i	−0.0856145	−	0.996328i	$-0.527285\pi$
$199$	3.85541e6	−	1.40326e6i	0.489229	−	0.178065i	0.574843	+	0.818264i	$0.305063\pi$
$200$		0			0
$201$	607917.	+	1.05294e6i	0.0748611	+	0.129663i
$202$		0			0
$203$	−8.11364e6	−	1.43065e6i	−0.969901	−	0.171020i
$204$		0			0
$205$	552163.	−	658042.i	0.0640922	−	0.0763822i
$206$		0			0
$207$	4.18450e6	+	1.52303e6i	0.471772	+	0.171711i
$208$		0			0
$209$	−2.98899e6	+	1.55270e6i	−0.327406	+	0.170079i
$210$		0			0
$211$	3.00360e6	−	8.25231e6i	0.319738	−	0.878473i	−0.670850	−	0.741593i	$-0.734070\pi$
$211$	3.00360e6	−	8.25231e6i	0.319738	−	0.878473i	0.990588	−	0.136879i	$-0.0437073\pi$
$212$		0			0
$213$	1.78852e6	+	1.50074e6i	0.185078	+	0.155299i
$214$		0			0
$215$	173492.	−	983924.i	0.0174568	−	0.0990025i
$216$		0			0
$217$	−7.93859e6	+	4.58335e6i	−0.776899	+	0.448543i
$218$		0			0
$219$	−466282.	−	1.28110e6i	−0.0443931	−	0.121969i
$220$		0			0
$221$	−1.09811e7	−	6.33995e6i	−1.01735	−	0.587367i
$222$		0			0
$223$	−3.84800e6	−	4.58587e6i	−0.346993	−	0.413530i	0.564116	−	0.825695i	$-0.309217\pi$
$223$	−3.84800e6	−	4.58587e6i	−0.346993	−	0.413530i	−0.911109	+	0.412166i	$0.864773\pi$
$224$		0			0
$225$	−1.92094e6	−	1.08942e7i	−0.168642	−	0.956417i
$226$		0			0
$227$			6.57369e6i			0.561994i	0.959709	+	0.280997i	$0.0906650\pi$
$227$			6.57369e6i			0.561994i	−0.959709	+	0.280997i	$0.909335\pi$
$228$		0			0
$229$	277192.			0.0230821			0.0115410	−	0.999933i	$-0.496326\pi$
$229$	277192.			0.0230821			0.0115410	+	0.999933i	$0.496326\pi$
$230$		0			0
$231$	−387275.	+	68287.0i	−0.0314183	+	0.00553990i
$232$		0			0
$233$	−8.81884e6	+	7.39989e6i	−0.697178	+	0.585002i	−0.920969	−	0.389635i	$-0.872601\pi$
$233$	−8.81884e6	+	7.39989e6i	−0.697178	+	0.585002i	0.223791	+	0.974637i	$0.428157\pi$
$234$		0			0
$235$	−568224.	+	984192.i	−0.0437840	+	0.0758362i
$236$		0			0
$237$	1.04405e6	−	380004.i	0.0784291	−	0.0285458i
$238$		0			0
$239$	−2.07572e6	−	3.59525e6i	−0.152046	−	0.263351i	0.779934	−	0.625862i	$-0.215253\pi$
$239$	−2.07572e6	−	3.59525e6i	−0.152046	−	0.263351i	−0.931979	+	0.362511i	$0.881919\pi$
$240$		0			0
$241$	5.59558e6	+	986651.i	0.399755	+	0.0704876i	0.369911	−	0.929067i	$-0.379388\pi$
$241$	5.59558e6	+	986651.i	0.399755	+	0.0704876i	0.0298434	+	0.999555i	$0.490499\pi$
$242$		0			0
$243$	3.60916e6	−	4.30123e6i	0.251528	−	0.299760i
$244$		0			0
$245$	−849044.	−	309027.i	−0.0577340	−	0.0210135i
$246$		0			0
$247$	2.34707e6	−	1.05440e7i	0.155752	−	0.699704i
$248$		0			0
$249$	−965313.	+	2.65218e6i	−0.0625274	+	0.171793i
$250$		0			0
$251$	−2.15904e7	−	1.81165e7i	−1.36534	−	1.14565i	−0.974293	−	0.225283i	$-0.927669\pi$
$251$	−2.15904e7	−	1.81165e7i	−1.36534	−	1.14565i	−0.391045	−	0.920372i	$-0.627886\pi$
$252$		0			0
$253$	−530351.	+	3.00777e6i	−0.0327493	+	0.185730i
$254$		0			0
$255$	332418.	−	191921.i	0.0200476	−	0.0115745i
$256$		0			0
$257$	−3.68345e6	−	1.01202e7i	−0.216998	−	0.596197i	0.782657	−	0.622453i	$-0.213864\pi$
$257$	−3.68345e6	−	1.01202e7i	−0.216998	−	0.596197i	−0.999655	+	0.0262557i	$0.991642\pi$
$258$		0			0
$259$	−1.42253e7	−	8.21297e6i	−0.818769	−	0.472717i
$260$		0			0
$261$	1.70799e7	+	2.03551e7i	0.960649	+	1.14486i
$262$		0			0
$263$	−2.84522e6	−	1.61360e7i	−0.156404	−	0.887012i	−0.957491	−	0.288464i	$-0.906855\pi$
$263$	−2.84522e6	−	1.61360e7i	−0.156404	−	0.887012i	0.801087	−	0.598549i	$-0.204256\pi$
$264$		0			0
$265$		−	39309.6i		−	0.00211233i
$266$		0			0
$267$	−380737.			−0.0200028
$268$		0			0
$269$	−2.27929e7	+	4.01900e6i	−1.17096	+	0.206472i	−0.725109	−	0.688634i	$-0.758211\pi$
$269$	−2.27929e7	+	4.01900e6i	−1.17096	+	0.206472i	−0.445853	+	0.895106i	$0.647099\pi$
$270$		0			0
$271$	−5.17676e6	+	4.34381e6i	−0.260106	+	0.218255i	−0.763509	−	0.645797i	$-0.776525\pi$
$271$	−5.17676e6	+	4.34381e6i	−0.260106	+	0.218255i	0.503404	+	0.864051i	$0.332081\pi$
$272$		0			0
$273$	630583.	−	1.09220e6i	0.0309923	−	0.0536803i
$274$		0			0
$275$	7.12959e6	−	2.59496e6i	0.342820	−	0.124776i
$276$		0			0
$277$	9.73007e6	+	1.68530e7i	0.457801	+	0.792934i	0.998844	−	0.0480601i	$-0.0153039\pi$
$277$	9.73007e6	+	1.68530e7i	0.457801	+	0.792934i	−0.541044	+	0.840995i	$0.681971\pi$
$278$		0			0
$279$	2.91152e7	+	5.13379e6i	1.34062	+	0.236388i
$280$		0			0
$281$	1.31255e7	−	1.56424e7i	0.591558	−	0.704992i	−0.384346	−	0.923189i	$-0.625573\pi$
$281$	1.31255e7	−	1.56424e7i	0.591558	−	0.704992i	0.975905	+	0.218197i	$0.0700176\pi$
$282$		0			0
$283$	−1.14851e7	−	4.18023e6i	−0.506728	−	0.184434i	0.0759894	−	0.997109i	$-0.475788\pi$
$283$	−1.14851e7	−	4.18023e6i	−0.506728	−	0.184434i	−0.582718	+	0.812675i	$0.698011\pi$
$284$		0			0
$285$	240897.	+	221123.i	0.0104063	+	0.00955213i
$286$		0			0
$287$	−4.93509e6	+	1.35590e7i	−0.208761	+	0.573566i
$288$		0			0
$289$	3.11682e7	+	2.61532e7i	1.29127	+	1.08351i
$290$		0			0
$291$	−300958.	+	1.70682e6i	−0.0122131	+	0.0692641i
$292$		0			0
$293$	−2.90286e7	+	1.67597e7i	−1.15405	+	0.666289i	−0.949870	−	0.312645i	$-0.898785\pi$
$293$	−2.90286e7	+	1.67597e7i	−1.15405	+	0.666289i	−0.204176	+	0.978934i	$0.565452\pi$
$294$		0			0
$295$	884587.	+	2.43038e6i	0.0344567	+	0.0946691i
$296$		0			0
$297$	2.21672e6	+	1.27983e6i	0.0846140	+	0.0488519i
$298$		0			0
$299$	−6.29601e6	−	7.50329e6i	−0.235533	−	0.280697i
$300$		0			0
$301$	2.91423e6	+	1.65274e7i	0.106862	+	0.606046i
$302$		0			0
$303$		−	3.32262e6i		−	0.119441i
$304$		0			0
$305$	−4.40343e6			−0.155200
$306$		0			0
$307$	4.91685e7	−	8.66974e6i	1.69931	−	0.299634i	0.761856	−	0.647747i	$-0.224288\pi$
$307$	4.91685e7	−	8.66974e6i	1.69931	−	0.299634i	0.937453	+	0.348113i	$0.113177\pi$
$308$		0			0
$309$	−3.03322e6	+	2.54517e6i	−0.102808	+	0.0862664i
$310$		0			0
$311$	1.35355e7	−	2.34441e7i	0.449979	−	0.779386i	−0.548405	−	0.836213i	$-0.684765\pi$
$311$	1.35355e7	−	2.34441e7i	0.449979	−	0.779386i	0.998384	+	0.0568267i	$0.0180982\pi$
$312$		0			0
$313$	4.36900e7	−	1.59019e7i	1.42478	−	0.518579i	0.489352	−	0.872086i	$-0.337233\pi$
$313$	4.36900e7	−	1.59019e7i	1.42478	−	0.518579i	0.935432	+	0.353508i	$0.115011\pi$
$314$		0			0
$315$	−1.05035e6	−	1.81926e6i	−0.0336049	−	0.0582053i
$316$		0			0
$317$	3.85635e6	+	679978.i	0.121059	+	0.0213460i	0.233850	−	0.972273i	$-0.424868\pi$
$317$	3.85635e6	+	679978.i	0.121059	+	0.0213460i	−0.112790	+	0.993619i	$0.535979\pi$
$318$		0			0
$319$	−1.17144e7	+	1.39607e7i	−0.360869	+	0.430067i
$320$		0			0
$321$	−1.40906e6	−	512855.i	−0.0426004	−	0.0155053i
$322$		0			0
$323$	−2.11774e7	+	5.10025e7i	−0.628441	+	1.51350i
$324$		0			0
$325$	−8.32215e6	+	2.28649e7i	−0.242429	+	0.666069i
$326$		0			0
$327$	−4.72297e6	−	3.96305e6i	−0.135074	−	0.113341i
$328$		0			0
$329$	3.31484e6	−	1.87994e7i	0.0930841	−	0.527906i
$330$		0			0
$331$	1.57682e7	−	9.10376e6i	0.434808	−	0.251037i	−0.266585	−	0.963811i	$-0.585895\pi$
$331$	1.57682e7	−	9.10376e6i	0.434808	−	0.251037i	0.701393	+	0.712775i	$0.252562\pi$
$332$		0			0
$333$	1.81191e7	+	4.97818e7i	0.490686	+	1.34815i
$334$		0			0
$335$	−3.85777e6	−	2.22728e6i	−0.102613	−	0.0592436i
$336$		0			0
$337$	1.11531e7	+	1.32918e7i	0.291412	+	0.347291i	0.891810	−	0.452410i	$-0.149436\pi$
$337$	1.11531e7	+	1.32918e7i	0.291412	+	0.347291i	−0.600398	+	0.799701i	$0.704991\pi$
$338$		0			0
$339$	−953743.	−	5.40895e6i	−0.0244812	−	0.138840i
$340$		0			0
$341$			2.02770e7i			0.511376i
$342$		0			0
$343$	4.12950e7			1.02333
$344$		0			0
$345$	292002.	−	51487.9i	0.00711098	−	0.00125386i
$346$		0			0
$347$	1.92198e7	−	1.61273e7i	0.460003	−	0.385989i	−0.383129	−	0.923695i	$-0.625153\pi$
$347$	1.92198e7	−	1.61273e7i	0.460003	−	0.385989i	0.843132	+	0.537706i	$0.180709\pi$
$348$		0			0
$349$	−5.12064e6	+	8.86921e6i	−0.120461	+	0.208645i	−0.919950	−	0.392036i	$-0.871771\pi$
$349$	−5.12064e6	+	8.86921e6i	−0.120461	+	0.208645i	0.799488	+	0.600682i	$0.205104\pi$
$350$		0			0
$351$	−7.71386e6	+	2.80761e6i	−0.178382	+	0.0649256i
$352$		0			0
$353$	−2.30444e6	−	3.99141e6i	−0.0523892	−	0.0907408i	0.838642	−	0.544684i	$-0.183350\pi$
$353$	−2.30444e6	−	3.99141e6i	−0.0523892	−	0.0907408i	−0.891031	+	0.453943i	$0.850017\pi$
$354$		0			0
$355$	−8.42407e6	−	1.48539e6i	−0.188294	−	0.0332013i
$356$		0			0
$357$	−4.14443e6	+	4.93913e6i	−0.0910877	+	0.108554i
$358$		0			0
$359$	−6.11571e7	−	2.22593e7i	−1.32179	−	0.481093i	−0.417760	−	0.908557i	$-0.637185\pi$
$359$	−6.11571e7	−	2.22593e7i	−1.32179	−	0.481093i	−0.904032	+	0.427464i	$0.859407\pi$
$360$		0			0
$361$	−4.68597e7	−	4.18098e6i	−0.996043	−	0.0888702i
$362$		0			0
$363$	1.88815e6	−	5.18765e6i	0.0394745	−	0.108455i
$364$		0			0
$365$	3.82633e6	+	3.21067e6i	0.0786871	+	0.0660263i
$366$		0			0
$367$	1.34590e7	−	7.63297e7i	0.272279	−	1.54417i	−0.475196	−	0.879880i	$-0.657623\pi$
$367$	1.34590e7	−	7.63297e7i	0.272279	−	1.54417i	0.747475	−	0.664290i	$-0.231266\pi$
$368$		0			0
$369$	4.03022e7	−	2.32685e7i	0.802139	−	0.463115i
$370$		0			0
$371$	225837.	+	620481.i	0.00442255	+	0.0121509i
$372$		0			0
$373$	−6.68390e7	−	3.85895e7i	−1.28796	−	0.743605i	−0.309672	−	0.950843i	$-0.600219\pi$
$373$	−6.68390e7	−	3.85895e7i	−1.28796	−	0.743605i	−0.978291	+	0.207238i	$0.933553\pi$
$374$		0			0
$375$	−952284.	−	1.13489e6i	−0.0180581	−	0.0215208i
$376$		0			0
$377$	−1.01491e7	−	5.75586e7i	−0.189411	−	1.07420i
$378$		0			0
$379$			9.13267e7i			1.67757i	0.544464	+	0.838784i	$0.316733\pi$
$379$			9.13267e7i			1.67757i	−0.544464	+	0.838784i	$0.683267\pi$
$380$		0			0
$381$	5.99229e6			0.108347
$382$		0			0
$383$	−4.35265e7	+	7.67490e6i	−0.774743	+	0.136608i	−0.547022	−	0.837118i	$-0.684239\pi$
$383$	−4.35265e7	+	7.67490e6i	−0.774743	+	0.136608i	−0.227721	+	0.973726i	$0.573127\pi$
$384$		0			0
$385$	1.10371e6	−	926119.i	0.0193406	−	0.0162287i
$386$		0			0
$387$	2.70631e7	−	4.68747e7i	0.466923	−	0.808734i
$388$		0			0
$389$	1.47665e7	−	5.37458e6i	0.250859	−	0.0913052i	−0.213530	−	0.976936i	$-0.568496\pi$
$389$	1.47665e7	−	5.37458e6i	0.250859	−	0.0913052i	0.464389	+	0.885631i	$0.346274\pi$
$390$		0			0
$391$	2.50376e7	+	4.33664e7i	0.418853	+	0.725475i
$392$		0			0
$393$	80485.6	+	14191.8i	0.00132599	+	0.000233808i
$394$		0			0
$395$	−2.61659e6	+	3.11833e6i	−0.0424565	+	0.0505977i
$396$		0			0
$397$	−5.52133e7	−	2.00960e7i	−0.882414	−	0.321172i	−0.139230	−	0.990260i	$-0.544463\pi$
$397$	−5.52133e7	−	2.00960e7i	−0.882414	−	0.321172i	−0.743183	+	0.669088i	$0.766685\pi$
$398$		0			0
$399$	−5.07280e6	−	2.10634e6i	−0.0798600	−	0.0331596i
$400$		0			0
$401$	−8.51186e6	+	2.33861e7i	−0.132005	+	0.362682i	−0.988032	−	0.154250i	$-0.950704\pi$
$401$	−8.51186e6	+	2.33861e7i	−0.132005	+	0.362682i	0.856026	+	0.516932i	$0.172926\pi$
$402$		0			0
$403$	−4.98152e7	−	4.17999e7i	−0.761109	−	0.638646i
$404$		0			0
$405$	−1.15472e6	+	6.54875e6i	−0.0173825	+	0.0985810i
$406$		0			0
$407$	−3.14667e7	+	1.81673e7i	−0.466732	+	0.269468i
$408$		0			0
$409$	−1.02283e7	−	2.81021e7i	−0.149498	−	0.410742i	0.842227	−	0.539123i	$-0.181244\pi$
$409$	−1.02283e7	−	2.81021e7i	−0.149498	−	0.410742i	−0.991725	+	0.128381i	$0.959022\pi$
$410$		0			0
$411$	−1.36129e7	−	7.85942e6i	−0.196077	−	0.113205i
$412$		0			0
$413$	−2.79254e7	−	3.32802e7i	−0.396415	−	0.472428i
$414$		0			0
$415$	−1.79564e6	−	1.01836e7i	−0.0251232	−	0.142480i
$416$		0			0
$417$			4.36777e6i			0.0602354i
$418$		0			0
$419$	−1.15655e8			−1.57225			−0.786126	−	0.618066i	$-0.787916\pi$
$419$	−1.15655e8			−1.57225			−0.786126	+	0.618066i	$0.787916\pi$
$420$		0			0
$421$	2.23326e7	−	3.93784e6i	0.299291	−	0.0527730i	−0.0219864	−	0.999758i	$-0.506999\pi$
$421$	2.23326e7	−	3.93784e6i	0.299291	−	0.0527730i	0.321277	+	0.946985i	$0.395888\pi$
$422$		0			0
$423$	−4.71630e7	+	3.95745e7i	−0.623133	+	0.522870i
$424$		0			0
$425$	6.21982e7	−	1.07731e8i	0.810236	−	1.40337i
$426$		0			0
$427$	6.95058e7	−	2.52980e7i	0.892765	−	0.324940i
$428$		0			0
$429$	−1.39487e6	−	2.41598e6i	−0.0176669	−	0.0306000i
$430$		0			0
$431$	1.28628e8	+	2.26806e7i	1.60658	+	0.283284i	0.903747	−	0.428067i	$-0.140805\pi$
$431$	1.28628e8	+	2.26806e7i	1.60658	+	0.283284i	0.702837	+	0.711351i	$0.251916\pi$
$432$		0			0
$433$	6.94573e7	−	8.27760e7i	0.855568	−	1.01963i	−0.143981	−	0.989580i	$-0.545990\pi$
$433$	6.94573e7	−	8.27760e7i	0.855568	−	1.01963i	0.999549	−	0.0300453i	$-0.00956516\pi$
$434$		0			0
$435$	1.66258e6	+	605129.i	0.0201983	+	0.00735157i
$436$		0			0
$437$	−2.88472e7	+	3.14269e7i	−0.345668	+	0.376579i
$438$		0			0
$439$	−4.65750e7	+	1.27964e8i	−0.550502	+	1.51249i	0.282525	+	0.959260i	$0.408828\pi$
$439$	−4.65750e7	+	1.27964e8i	−0.550502	+	1.51249i	−0.833027	+	0.553232i	$0.813394\pi$
$440$		0			0
$441$	−3.74970e7	−	3.14637e7i	−0.437201	−	0.366855i
$442$		0			0
$443$	−6.78118e6	+	3.84580e7i	−0.0779999	+	0.442359i	0.920649	+	0.390392i	$0.127660\pi$
$443$	−6.78118e6	+	3.84580e7i	−0.0779999	+	0.442359i	−0.998649	+	0.0519677i	$0.983451\pi$
$444$		0			0
$445$	1.20806e6	−	697472.i	0.0137091	−	0.00791493i
$446$		0			0
$447$	2.76430e6	+	7.59486e6i	0.0309502	+	0.0850349i
$448$		0			0
$449$	−1.02605e8	−	5.92389e7i	−1.13352	−	0.654437i	−0.188701	−	0.982035i	$-0.560428\pi$
$449$	−1.02605e8	−	5.92389e7i	−1.13352	−	0.654437i	−0.944817	+	0.327597i	$0.893761\pi$
$450$		0			0
$451$	2.05164e7	+	2.44505e7i	0.223651	+	0.266537i
$452$		0			0
$453$	2.37137e6	+	1.34487e7i	0.0255097	+	0.144673i
$454$		0			0
$455$			4.62066e6i			0.0490535i
$456$		0			0
$457$	1.94324e7			0.203600			0.101800	−	0.994805i	$-0.467540\pi$
$457$	1.94324e7			0.203600			0.101800	+	0.994805i	$0.467540\pi$
$458$		0			0
$459$	4.13296e7	−	7.28753e6i	0.427389	−	0.0753603i
$460$		0			0
$461$	−7.72179e7	+	6.47935e7i	−0.788162	+	0.661346i	−0.945290	−	0.326232i	$-0.894221\pi$
$461$	−7.72179e7	+	6.47935e7i	−0.788162	+	0.661346i	0.157128	+	0.987578i	$0.449777\pi$
$462$		0			0
$463$	1.70251e7	−	2.94883e7i	0.171532	−	0.297103i	−0.767423	−	0.641141i	$-0.778462\pi$
$463$	1.70251e7	−	2.94883e7i	0.171532	−	0.297103i	0.938956	+	0.344038i	$0.111795\pi$
$464$		0			0
$465$	1.84983e6	−	673282.i	0.0183981	−	0.00669635i
$466$		0			0
$467$	7.75086e7	+	1.34249e8i	0.761026	+	1.31814i	0.942322	+	0.334707i	$0.108637\pi$
$467$	7.75086e7	+	1.34249e8i	0.761026	+	1.31814i	−0.181296	+	0.983429i	$0.558029\pi$
$468$		0			0
$469$	7.36887e7	+	1.29933e7i	0.714303	+	0.125951i
$470$		0			0
$471$	8.55290e6	−	1.01930e7i	0.0818561	−	0.0975523i
$472$		0			0
$473$	3.48843e7	+	1.26968e7i	0.329645	+	0.119981i
$474$		0			0
$475$	1.03442e8	+	2.30260e7i	0.965198	+	0.214851i
$476$		0			0
$477$	728365.	−	2.00117e6i	0.00671110	−	0.0184386i
$478$		0			0
$479$	9.95642e7	+	8.35443e7i	0.905934	+	0.760169i	0.971341	−	0.237690i	$-0.0763901\pi$
$479$	9.95642e7	+	8.35443e7i	0.905934	+	0.760169i	−0.0654069	+	0.997859i	$0.520835\pi$
$480$		0			0
$481$	2.02346e7	−	1.14756e8i	0.181828	−	1.03120i
$482$		0			0
$483$	−4.31330e6	+	2.49028e6i	−0.0382796	+	0.0221008i
$484$		0			0
$485$	−2.17179e6	−	5.96696e6i	−0.0190368	−	0.0523031i
$486$		0			0
$487$	−1.66544e8	−	9.61541e7i	−1.44192	−	0.832494i	−0.443944	−	0.896055i	$-0.646421\pi$
$487$	−1.66544e8	−	9.61541e7i	−1.44192	−	0.832494i	−0.997978	+	0.0635607i	$0.979754\pi$
$488$		0			0
$489$	6.49026e6	+	7.73479e6i	0.0555055	+	0.0661488i
$490$		0			0
$491$	−1.14352e7	−	6.48521e7i	−0.0966047	−	0.547873i	−0.994244	−	0.107141i	$-0.965830\pi$
$491$	−1.14352e7	−	6.48521e7i	−0.0966047	−	0.547873i	0.897639	−	0.440731i	$-0.145281\pi$
$492$		0			0
$493$			2.98802e8i			2.49369i
$494$		0			0
$495$	−4.64680e6			−0.0383123
$496$		0			0
$497$	1.41503e8	−	2.49508e7i	1.15265	−	0.203243i
$498$		0			0
$499$	−1.21017e8	+	1.01546e8i	−0.973972	+	0.817259i	−0.983169	−	0.182698i	$-0.941517\pi$
$499$	−1.21017e8	+	1.01546e8i	−0.973972	+	0.817259i	0.00919739	+	0.999958i	$0.497072\pi$
$500$		0			0
$501$	714658.	−	1.23782e6i	0.00568310	−	0.00984342i
$502$		0			0
$503$	2.36136e8	−	8.59465e7i	1.85549	−	0.675343i	0.873378	−	0.487044i	$-0.161925\pi$
$503$	2.36136e8	−	8.59465e7i	1.85549	−	0.675343i	0.982112	−	0.188299i	$-0.0602974\pi$
$504$		0			0
$505$	6.08671e6	+	1.05425e7i	0.0472616	+	0.0818595i
$506$		0			0
$507$	−8.33610e6	−	1.46988e6i	−0.0639645	−	0.0112787i
$508$		0			0
$509$	2.30870e7	−	2.75140e7i	0.175071	−	0.208641i	−0.671373	−	0.741120i	$-0.734295\pi$
$509$	2.30870e7	−	2.75140e7i	0.175071	−	0.208641i	0.846443	+	0.532479i	$0.178739\pi$
$510$		0			0
$511$	−7.88420e7	−	2.86961e7i	−0.590874	−	0.215061i
$512$		0			0
$513$	1.64812e7	+	3.17266e7i	0.122077	+	0.235002i
$514$		0			0
$515$	4.96173e6	−	1.36322e7i	0.0363255	−	0.0998034i
$516$		0			0
$517$	−3.23472e7	−	2.71425e7i	−0.234081	−	0.196417i
$518$		0			0
$519$	−2.07977e6	+	1.17950e7i	−0.0148770	+	0.0843714i
$520$		0			0
$521$	5.00335e7	−	2.88868e7i	0.353792	−	0.204262i	−0.312562	−	0.949897i	$-0.601187\pi$
$521$	5.00335e7	−	2.88868e7i	0.353792	−	0.204262i	0.666354	+	0.745636i	$0.267854\pi$
$522$		0			0
$523$	3.67288e7	+	1.00912e8i	0.256745	+	0.705401i	0.999363	+	0.0356856i	$0.0113615\pi$
$523$	3.67288e7	+	1.00912e8i	0.256745	+	0.705401i	−0.742618	+	0.669715i	$0.766416\pi$
$524$		0			0
$525$	1.07151e7	+	6.18635e6i	0.0740486	+	0.0427520i
$526$		0			0
$527$	2.13698e8	+	2.54675e8i	1.46005	+	1.74002i
$528$		0			0
$529$	−1.89892e7	−	1.07693e8i	−0.128274	−	0.727479i
$530$		0			0
$531$			1.40116e8i			0.935844i
$532$		0			0
$533$	−1.02362e8			−0.676015
$534$		0			0
$535$	5.41036e6	−	953993.i	0.0353317	−	0.00622994i
$536$		0			0
$537$	2.43383e7	−	2.04222e7i	0.157169	−	0.131880i
$538$		0			0
$539$	1.67860e7	−	2.90742e7i	0.107197	−	0.185670i
$540$		0			0
$541$	3.67571e6	−	1.33785e6i	0.0232140	−	0.00844919i	−0.330387	−	0.943846i	$-0.607179\pi$
$541$	3.67571e6	−	1.33785e6i	0.0232140	−	0.00844919i	0.353601	+	0.935396i	$0.384957\pi$
$542$		0			0
$543$	7.20102e6	+	1.24725e7i	0.0449774	+	0.0779031i
$544$		0			0
$545$	2.22456e7	+	3.92250e6i	0.137422	+	0.0242311i
$546$		0			0
$547$	1.02447e8	−	1.22092e8i	0.625948	−	0.745976i	−0.356133	−	0.934435i	$-0.615905\pi$
$547$	1.02447e8	−	1.22092e8i	0.625948	−	0.745976i	0.982081	+	0.188459i	$0.0603494\pi$
$548$		0			0
$549$	−2.24169e8	−	8.15909e7i	−1.35475	−	0.493088i
$550$		0			0
$551$	−2.42835e8	+	7.63359e7i	−1.45163	+	0.456325i
$552$		0			0
$553$	2.33864e7	−	6.42536e7i	0.138289	−	0.379946i
$554$		0			0
$555$	2.70219e6	+	2.26741e6i	0.0158066	+	0.0132633i
$556$		0			0
$557$	4.28092e7	−	2.42783e8i	0.247726	−	1.40492i	−0.566349	−	0.824165i	$-0.691645\pi$
$557$	4.28092e7	−	2.42783e8i	0.247726	−	1.40492i	0.814075	−	0.580759i	$-0.197244\pi$
$558$		0			0
$559$	−1.03105e8	+	5.95276e7i	−0.590260	+	0.340787i
$560$		0			0
$561$	4.87796e6	+	1.34021e7i	0.0276280	+	0.0759074i
$562$		0			0
$563$	−1.25335e8	−	7.23624e7i	−0.702342	−	0.405497i	0.105877	−	0.994379i	$-0.466235\pi$
$563$	−1.25335e8	−	7.23624e7i	−0.702342	−	0.405497i	−0.808219	+	0.588882i	$0.799568\pi$
$564$		0			0
$565$	1.29348e7	+	1.54151e7i	0.0717158	+	0.0854676i
$566$		0			0
$567$	−1.93964e7	−	1.10002e8i	−0.106407	−	0.603466i
$568$		0			0
$569$			1.41826e8i			0.769873i	0.922943	+	0.384936i	$0.125777\pi$
$569$			1.41826e8i			0.769873i	−0.922943	+	0.384936i	$0.874223\pi$
$570$		0			0
$571$	−1.41023e8			−0.757500			−0.378750	−	0.925499i	$-0.623646\pi$
$571$	−1.41023e8			−0.757500			−0.378750	+	0.925499i	$0.623646\pi$
$572$		0			0
$573$	−4.53749e7	+	8.00081e6i	−0.241186	+	0.0425275i
$574$		0			0
$575$	7.36112e7	−	6.17671e7i	0.387204	−	0.324903i
$576$		0			0
$577$	1.77807e8	−	3.07971e8i	0.925596	−	1.60318i	0.134996	−	0.990846i	$-0.456898\pi$
$577$	1.77807e8	−	3.07971e8i	0.925596	−	1.60318i	0.790600	−	0.612333i	$-0.209769\pi$
$578$		0			0
$579$	2.90345e7	−	1.05677e7i	0.149582	−	0.0544432i
$580$		0			0
$581$	8.68484e7	+	1.50426e8i	0.442826	+	0.766998i
$582$		0			0
$583$	1.43841e6	+	253631.i	0.00725903	+	0.00127996i
$584$		0			0
$585$	9.57913e6	−	1.14160e7i	0.0478474	−	0.0570223i
$586$		0			0
$587$	−1.43344e8	−	5.21729e7i	−0.708704	−	0.257947i	−0.0375812	−	0.999294i	$-0.511965\pi$
$587$	−1.43344e8	−	5.21729e7i	−0.708704	−	0.257947i	−0.671122	+	0.741347i	$0.734188\pi$
$588$		0			0
$589$	−1.52379e8	+	2.38734e8i	−0.745727	+	1.16834i
$590$		0			0
$591$	4.18194e6	−	1.14898e7i	0.0202589	−	0.0556607i
$592$		0			0
$593$	−9.95521e7	−	8.35342e7i	−0.477405	−	0.400590i	0.372082	−	0.928200i	$-0.378644\pi$
$593$	−9.95521e7	−	8.35342e7i	−0.477405	−	0.400590i	−0.849487	+	0.527610i	$0.823088\pi$
$594$		0			0
$595$	4.10203e6	−	2.32638e7i	0.0194737	−	0.110441i
$596$		0			0
$597$	1.28172e7	−	7.39999e6i	0.0602377	−	0.0347783i
$598$		0			0
$599$	−5.20947e6	−	1.43129e7i	−0.0242389	−	0.0665959i	0.926983	−	0.375103i	$-0.122393\pi$
$599$	−5.20947e6	−	1.43129e7i	−0.0242389	−	0.0665959i	−0.951222	+	0.308507i	$0.900171\pi$
$600$		0			0
$601$	−2.23384e8	−	1.28971e8i	−1.02903	−	0.594112i	−0.112325	−	0.993671i	$-0.535830\pi$
$601$	−2.23384e8	−	1.28971e8i	−1.02903	−	0.594112i	−0.916707	+	0.399559i	$0.869163\pi$
$602$		0			0
$603$	−1.55121e8	−	1.84866e8i	−0.707489	−	0.843152i
$604$		0			0
$605$	3.51226e6	+	1.99190e7i	0.0158606	+	0.0899501i
$606$		0			0
$607$		−	2.13026e8i		−	0.952505i	−0.879309	−	0.476252i	$-0.841995\pi$
$607$		−	2.13026e8i		−	0.952505i	0.879309	−	0.476252i	$-0.158005\pi$
$608$		0			0
$609$	−2.97194e7			−0.131579
$610$		0			0
$611$	1.33364e8	−	2.35157e7i	0.584677	−	0.103094i
$612$		0			0
$613$	−1.80944e8	+	1.51830e8i	−0.785528	+	0.659136i	−0.944634	−	0.328125i	$-0.893583\pi$
$613$	−1.80944e8	+	1.51830e8i	−0.785528	+	0.659136i	0.159106	+	0.987261i	$0.449139\pi$
$614$		0			0
$615$	1.54933e6	−	2.68353e6i	0.00666070	−	0.0115367i
$616$		0			0
$617$	4.04199e8	−	1.47117e8i	1.72084	−	0.626334i	0.722927	−	0.690925i	$-0.242796\pi$
$617$	4.04199e8	−	1.47117e8i	1.72084	−	0.626334i	0.997912	+	0.0645904i	$0.0205741\pi$
$618$		0			0
$619$	−7.54619e7	−	1.30704e8i	−0.318168	−	0.551082i	0.661938	−	0.749558i	$-0.269734\pi$
$619$	−7.54619e7	−	1.30704e8i	−0.318168	−	0.551082i	−0.980106	+	0.198476i	$0.936401\pi$
$620$		0			0
$621$	3.19259e7	+	5.62940e6i	0.133312	+	0.0235065i
$622$		0			0
$623$	−1.50615e7	+	1.79496e7i	−0.0622879	+	0.0742319i
$624$		0			0
$625$	−2.21752e8	−	8.07111e7i	−0.908296	−	0.330593i
$626$		0			0
$627$	−9.64563e6	+	7.38817e6i	−0.0391316	+	0.0299733i
$628$		0			0
$629$	−2.03752e8	+	5.59803e8i	−0.818746	+	2.24949i
$630$		0			0
$631$	3.10002e7	+	2.60123e7i	0.123389	+	0.103536i	0.702394	−	0.711788i	$-0.252114\pi$
$631$	3.10002e7	+	2.60123e7i	0.123389	+	0.103536i	−0.579005	+	0.815324i	$0.696559\pi$
$632$		0			0
$633$	5.50092e6	−	3.11973e7i	0.0216883	−	0.123000i
$634$		0			0
$635$	−1.90132e7	+	1.09773e7i	−0.0742564	+	0.0428720i
$636$		0			0
$637$	3.68243e7	+	1.01174e8i	0.142468	+	0.391426i
$638$		0			0
$639$	−4.01328e8	−	2.31707e8i	−1.53814	−	0.888048i
$640$		0			0
$641$	2.33042e7	+	2.77729e7i	0.0884832	+	0.105450i	0.808469	−	0.588538i	$-0.200296\pi$
$641$	2.33042e7	+	2.77729e7i	0.0884832	+	0.105450i	−0.719986	+	0.693988i	$0.755852\pi$
$642$		0			0
$643$	−4.06300e7	−	2.30424e8i	−0.152832	−	0.866752i	−0.960741	−	0.277446i	$-0.910512\pi$
$643$	−4.06300e7	−	2.30424e8i	−0.152832	−	0.866752i	0.807910	−	0.589306i	$-0.200599\pi$
$644$		0			0
$645$		−	3.60401e6i		−	0.0134309i
$646$		0			0
$647$	4.73795e8			1.74936			0.874678	−	0.484705i	$-0.161073\pi$
$647$	4.73795e8			1.74936			0.874678	+	0.484705i	$0.161073\pi$
$648$		0			0
$649$	−9.46398e7	+	1.66875e7i	−0.346210	+	0.0610462i
$650$		0			0
$651$	−2.53304e7	+	2.12548e7i	−0.0918121	+	0.0770395i
$652$		0			0
$653$	6.53796e7	−	1.13241e8i	0.234802	−	0.406690i	−0.724413	−	0.689366i	$-0.757889\pi$
$653$	6.53796e7	−	1.13241e8i	0.234802	−	0.406690i	0.959215	+	0.282677i	$0.0912224\pi$
$654$		0			0
$655$	−281374.	+	102412.i	−0.00100129	+	0.000364440i
$656$		0			0
$657$	1.35300e8	+	2.34346e8i	0.477090	+	0.826344i
$658$		0			0
$659$	5.17209e8	+	9.11979e7i	1.80721	+	0.318661i	0.972655	−	0.232256i	$-0.0746108\pi$
$659$	5.17209e8	+	9.11979e7i	1.80721	+	0.318661i	0.834560	+	0.550917i	$0.185722\pi$
$660$		0			0
$661$	327961.	−	390849.i	0.00113558	−	0.00135333i	−0.765476	−	0.643464i	$-0.777497\pi$
$661$	327961.	−	390849.i	0.00113558	−	0.00135333i	0.766612	+	0.642111i	$0.221941\pi$
$662$		0			0
$663$	−4.29811e7	−	1.56438e7i	−0.147481	−	0.0536788i
$664$		0			0
$665$	1.99543e7	−	2.60957e6i	0.0678534	−	0.00887367i
$666$		0			0
$667$	−7.89436e7	+	2.16896e8i	−0.266035	+	0.730926i
$668$		0			0
$669$	−1.65423e7	−	1.38807e7i	−0.0552483	−	0.0463588i
$670$		0			0
$671$	2.84116e7	−	1.61130e8i	0.0940433	−	0.533346i
$672$		0			0
$673$	4.32803e6	−	2.49879e6i	0.0141986	−	0.00819756i	−0.492884	−	0.870095i	$-0.664057\pi$
$673$	4.32803e6	−	2.49879e6i	0.0141986	−	0.00819756i	0.507082	+	0.861898i	$0.330724\pi$
$674$		0			0
$675$	−2.75442e7	−	7.56769e7i	−0.0895608	−	0.246066i
$676$		0			0
$677$	−4.83889e7	−	2.79373e7i	−0.155948	−	0.0900365i	0.419995	−	0.907526i	$-0.362032\pi$
$677$	−4.83889e7	−	2.79373e7i	−0.155948	−	0.0900365i	−0.575943	+	0.817490i	$0.695365\pi$
$678$		0			0
$679$	6.85612e7	+	8.17080e7i	0.219012	+	0.261009i
$680$		0			0
$681$	4.11770e6	+	2.33526e7i	0.0130381	+	0.0739426i
$682$		0			0
$683$			6.36127e8i			1.99656i	0.0586497	+	0.998279i	$0.481320\pi$
$683$			6.36127e8i			1.99656i	−0.0586497	+	0.998279i	$0.518680\pi$
$684$		0			0
$685$	5.75907e7			0.179176
$686$		0			0
$687$	984711.	−	173631.i	0.00303696	−	0.000535497i
$688$		0			0
$689$	−3.58832e6	+	3.01096e6i	−0.0109707	+	0.00920550i
$690$		0			0
$691$	2.45296e8	−	4.24866e8i	0.743459	−	1.28771i	−0.207453	−	0.978245i	$-0.566517\pi$
$691$	2.45296e8	−	4.24866e8i	0.743459	−	1.28771i	0.950911	−	0.309463i	$-0.100149\pi$
$692$		0			0
$693$	7.33472e7	−	2.66962e7i	0.220386	−	0.0802139i
$694$		0			0
$695$	−8.00132e6	−	1.38587e7i	−0.0238346	−	0.0412827i
$696$		0			0
$697$	5.15364e8	+	9.08726e7i	1.52200	+	0.268370i
$698$		0			0
$699$	−2.66932e7	+	3.18117e7i	−0.0781573	+	0.0931442i
$700$		0			0
$701$	1.46423e8	+	5.32937e7i	0.425065	+	0.154711i	0.545690	−	0.837987i	$-0.316268\pi$
$701$	1.46423e8	+	5.32937e7i	0.425065	+	0.154711i	−0.120625	+	0.992698i	$0.538490\pi$
$702$		0			0
$703$	−5.07002e8	−	2.25734e7i	−1.45930	−	0.0649726i
$704$		0			0
$705$	−1.40209e6	+	3.85222e6i	−0.00400138	+	0.0109937i
$706$		0			0
$707$	−1.56643e8	−	1.31439e8i	−0.443253	−	0.371933i
$708$		0			0
$709$	−5.61310e7	+	3.18335e8i	−0.157494	+	0.893193i	0.798976	+	0.601363i	$0.205375\pi$
$709$	−5.61310e7	+	3.18335e8i	−0.157494	+	0.893193i	−0.956470	+	0.291830i	$0.905736\pi$
$710$		0			0
$711$	−1.90984e8	+	1.10265e8i	−0.531359	+	0.306780i
$712$		0			0
$713$	8.78346e7	+	2.41324e8i	0.242324	+	0.665781i
$714$		0			0
$715$	8.85166e6	+	5.11051e6i	0.0242162	+	0.0139812i
$716$		0			0
$717$	−9.62589e6	−	1.14717e7i	−0.0261146	−	0.0311222i
$718$		0			0
$719$	2.28045e7	+	1.29331e8i	0.0613528	+	0.347949i	0.999995	+	0.00305749i	$0.000973231\pi$
$719$	2.28045e7	+	1.29331e8i	0.0613528	+	0.347949i	−0.938643	+	0.344892i	$0.887916\pi$
$720$		0			0
$721$			2.43683e8i			0.650158i
$722$		0			0
$723$	2.04960e7			0.0542318
$724$		0			0
$725$	5.64680e8	−	9.95683e7i	1.48180	−	0.261281i
$726$		0			0
$727$	1.56144e8	−	1.31020e8i	0.406370	−	0.340985i	−0.416579	−	0.909099i	$-0.636771\pi$
$727$	1.56144e8	−	1.31020e8i	0.406370	−	0.340985i	0.822950	+	0.568114i	$0.192327\pi$
$728$		0			0
$729$	−1.73272e8	+	3.00116e8i	−0.447245	+	0.774652i
$730$		0			0
$731$	5.71951e8	−	2.08173e8i	1.46422	−	0.532933i
$732$		0			0
$733$	3.54135e8	+	6.13380e8i	0.899202	+	1.55746i	0.828516	+	0.559965i	$0.189185\pi$
$733$	3.54135e8	+	6.13380e8i	0.899202	+	1.55746i	0.0706857	+	0.997499i	$0.477481\pi$
$734$		0			0
$735$	−3.20975e6	−	565966.i	−0.00808368	−	0.00142537i
$736$		0			0
$737$	1.06392e8	−	1.26792e8i	0.265769	−	0.316731i
$738$		0			0
$739$	−1.67304e8	−	6.08938e7i	−0.414547	−	0.150883i	0.126323	−	0.991989i	$-0.459683\pi$
$739$	−1.67304e8	−	6.08938e7i	−0.414547	−	0.150883i	−0.540870	+	0.841106i	$0.681905\pi$
$740$		0			0
$741$	1.73316e6	−	3.89271e7i	0.00425975	−	0.0956748i
$742$		0			0
$743$	−5.78472e7	+	1.58934e8i	−0.141031	+	0.387480i	−0.990019	−	0.140932i	$-0.954990\pi$
$743$	−5.78472e7	+	1.58934e8i	−0.141031	+	0.387480i	0.848988	+	0.528412i	$0.177212\pi$
$744$		0			0
$745$	−2.26840e7	−	1.90341e7i	−0.0548593	−	0.0460324i
$746$		0			0
$747$	9.72785e7	−	5.51694e8i	0.233375	−	1.32354i
$748$		0			0
$749$	−7.99188e7	+	4.61412e7i	−0.190197	+	0.109810i
$750$		0			0
$751$	1.70297e8	+	4.67888e8i	0.402057	+	1.10464i	0.961268	+	0.275617i	$0.0888822\pi$
$751$	1.70297e8	+	4.67888e8i	0.402057	+	1.10464i	−0.559210	+	0.829026i	$0.688896\pi$
$752$		0			0
$753$	−8.80468e7	−	5.08339e7i	−0.206219	−	0.119061i
$754$		0			0
$755$	−3.21609e7	−	3.83279e7i	−0.0747288	−	0.0890583i
$756$		0			0
$757$	−8.93862e7	−	5.06934e8i	−0.206055	−	1.16860i	−0.895771	−	0.444516i	$-0.853376\pi$
$757$	−8.93862e7	−	5.06934e8i	−0.206055	−	1.16860i	0.689716	−	0.724080i	$-0.257735\pi$
$758$		0			0
$759$			1.10171e7i			0.0251967i
$760$		0			0
$761$	−4.75349e8			−1.07860			−0.539298	−	0.842115i	$-0.681310\pi$
$761$	−4.75349e8			−1.07860			−0.539298	+	0.842115i	$0.681310\pi$
$762$		0			0
$763$	−3.73670e8	+	6.58881e7i	−0.841230	+	0.148331i
$764$		0			0
$765$	−5.83629e7	+	4.89723e7i	−0.130363	+	0.109387i
$766$		0			0
$767$	1.54098e8	−	2.66906e8i	0.341516	−	0.591523i
$768$		0			0
$769$	−1.51595e8	+	5.51762e7i	−0.333355	+	0.121331i	−0.503274	−	0.864127i	$-0.667871\pi$
$769$	−1.51595e8	+	5.51762e7i	−0.333355	+	0.121331i	0.169919	+	0.985458i	$0.445649\pi$
$770$		0			0
$771$	−1.94245e7	−	3.36442e7i	−0.0423825	−	0.0734086i
$772$		0			0
$773$	−3.86435e8	−	6.81389e7i	−0.836638	−	0.147522i	−0.261115	−	0.965308i	$-0.584090\pi$
$773$	−3.86435e8	−	6.81389e7i	−0.836638	−	0.147522i	−0.575523	+	0.817786i	$0.695201\pi$
$774$		0			0
$775$	4.10079e8	−	4.88713e8i	0.880972	−	1.04990i
$776$		0			0
$777$	−5.56790e7	−	2.02655e7i	−0.118694	−	0.0432011i
$778$		0			0
$779$	5.78099e7	+	4.42049e8i	0.122290	+	0.935101i
$780$		0			0
$781$	1.08707e8	−	2.98669e8i	0.228193	−	0.626956i
$782$		0			0
$783$	1.48186e8	+	1.24343e8i	0.308689	+	0.259021i
$784$		0			0
$785$	−8.46541e6	+	4.80097e7i	−0.0175000	+	0.0992476i
$786$		0			0
$787$	2.89964e8	−	1.67411e8i	0.594868	−	0.343447i	−0.172152	−	0.985070i	$-0.555072\pi$
$787$	2.89964e8	−	1.67411e8i	0.594868	−	0.343447i	0.767020	+	0.641623i	$0.221739\pi$
$788$		0			0
$789$	−2.02150e7	−	5.55401e7i	−0.0411568	−	0.113077i
$790$		0			0
$791$	−2.92730e8	−	1.69008e8i	−0.591477	−	0.341489i
$792$		0			0
$793$	3.37285e8	+	4.01961e8i	0.676360	+	0.806054i
$794$		0			0
$795$	−24623.2	−	139645.i	−4.90054e−5	−	0.000277923i
$796$		0			0
$797$			2.89140e8i			0.571127i	0.958360	+	0.285563i	$0.0921807\pi$
$797$			2.89140e8i			0.571127i	−0.958360	+	0.285563i	$0.907819\pi$
$798$		0			0
$799$	−6.92329e8			−1.35729
$800$		0			0
$801$	7.44229e7	−	1.31228e7i	0.144814	−	0.0255345i
$802$		0			0
$803$	−1.42173e8	+	1.19297e8i	−0.274580	+	0.230400i
$804$		0			0
$805$	9.12389e6	−	1.58030e7i	0.0174901	−	0.0302938i
$806$		0			0
$807$	−7.84530e7	+	2.85546e7i	−0.149276	+	0.0543319i
$808$		0			0
$809$	−2.16516e8	−	3.75017e8i	−0.408926	−	0.708280i	0.585844	−	0.810424i	$-0.300763\pi$
$809$	−2.16516e8	−	3.75017e8i	−0.408926	−	0.708280i	−0.994770	+	0.102144i	$0.967430\pi$
$810$		0			0
$811$	−3.92109e8	−	6.91395e7i	−0.735097	−	0.129617i	−0.206448	−	0.978458i	$-0.566190\pi$
$811$	−3.92109e8	−	6.91395e7i	−0.735097	−	0.129617i	−0.528650	+	0.848840i	$0.677301\pi$
$812$		0			0
$813$	−1.56692e7	+	1.86738e7i	−0.0291592	+	0.0347506i
$814$		0			0
$815$	−3.47626e7	−	1.26525e7i	−0.0642154	−	0.0233725i
$816$		0			0
$817$	3.15299e8	+	4.11639e8i	0.578172	+	0.754832i
$818$		0			0
$819$	−8.56158e7	+	2.35227e8i	−0.155848	+	0.428190i
$820$		0			0
$821$	−3.68012e7	−	3.08799e7i	−0.0665017	−	0.0558015i	0.608931	−	0.793223i	$-0.291599\pi$
$821$	−3.68012e7	−	3.08799e7i	−0.0665017	−	0.0558015i	−0.675433	+	0.737422i	$0.736043\pi$
$822$		0			0
$823$	9.35848e7	−	5.30746e8i	0.167883	−	0.952110i	−0.778160	−	0.628067i	$-0.783847\pi$
$823$	9.35848e7	−	5.30746e8i	0.167883	−	0.952110i	0.946042	−	0.324043i	$-0.105042\pi$
$824$		0			0
$825$	2.37020e7	−	1.36844e7i	0.0422108	−	0.0243704i
$826$		0			0
$827$	−2.30362e8	−	6.32914e8i	−0.407281	−	1.11900i	−0.958614	−	0.284710i	$-0.908103\pi$
$827$	−2.30362e8	−	6.32914e8i	−0.407281	−	1.11900i	0.551333	−	0.834286i	$-0.314120\pi$
$828$		0			0
$829$	−8.20283e8	−	4.73590e8i	−1.43979	−	0.831265i	−0.441958	−	0.897036i	$-0.645716\pi$
$829$	−8.20283e8	−	4.73590e8i	−1.43979	−	0.831265i	−0.997835	+	0.0657714i	$0.979049\pi$
$830$		0			0
$831$	4.51221e7	+	5.37744e7i	0.0786296	+	0.0937071i
$832$		0			0
$833$	−9.55823e7	−	5.42074e8i	−0.165365	−	0.937829i
$834$		0			0
$835$			5.23673e6i			0.00899499i
$836$		0			0
$837$	2.15230e8			0.367050
$838$		0			0
$839$	6.61530e8	−	1.16646e8i	1.12012	−	0.197507i	0.417225	−	0.908803i	$-0.363003\pi$
$839$	6.61530e8	−	1.16646e8i	1.12012	−	0.197507i	0.702892	+	0.711296i	$0.251892\pi$
$840$		0			0
$841$	−5.99407e8	+	5.02962e8i	−1.00771	+	0.845565i
$842$		0			0
$843$	3.68294e7	−	6.37904e7i	0.0614769	−	0.106481i
$844$		0			0
$845$	2.91426e7	−	1.06070e7i	0.0483013	−	0.0175802i
$846$		0			0
$847$	−1.69875e8	−	2.94232e8i	−0.279563	−	0.484217i
$848$		0			0
$849$	−4.34186e7	−	7.65587e6i	−0.0709501	−	0.0125104i
$850$		0			0
$851$	−2.95800e8	+	3.52521e8i	−0.479966	+	0.572001i
$852$		0			0
$853$	−4.54576e8	−	1.65452e8i	−0.732419	−	0.266579i	−0.0512306	−	0.998687i	$-0.516314\pi$
$853$	−4.54576e8	−	1.65452e8i	−0.732419	−	0.266579i	−0.681188	+	0.732108i	$0.738537\pi$
$854$		0			0
$855$	−5.47097e7	−	3.49202e7i	−0.0875319	−	0.0558699i
$856$		0			0
$857$	2.59194e8	−	7.12129e8i	0.411796	−	1.13140i	−0.544439	−	0.838800i	$-0.683257\pi$
$857$	2.59194e8	−	7.12129e8i	0.411796	−	1.13140i	0.956235	−	0.292600i	$-0.0945203\pi$
$858$		0			0
$859$	−2.55332e8	−	2.14249e8i	−0.402834	−	0.338017i	0.418754	−	0.908100i	$-0.362467\pi$
$859$	−2.55332e8	−	2.14249e8i	−0.402834	−	0.338017i	−0.821588	+	0.570082i	$0.806911\pi$
$860$		0			0
$861$	−9.03835e6	+	5.12590e7i	−0.0141605	+	0.0803084i
$862$		0			0
$863$	−1.20580e8	+	6.96168e7i	−0.187604	+	0.108313i	−0.590860	−	0.806774i	$-0.701212\pi$
$863$	−1.20580e8	+	6.96168e7i	−0.187604	+	0.108313i	0.403256	+	0.915087i	$0.367878\pi$
$864$		0			0
$865$	−1.50082e7	−	4.12347e7i	−0.0231889	−	0.0637111i
$866$		0			0
$867$	1.27105e8	+	7.33842e7i	0.195032	+	0.112602i
$868$		0			0
$869$	−9.72230e7	−	1.15866e8i	−0.148153	−	0.176562i
$870$		0			0
$871$	9.21753e7	+	5.22752e8i	0.139495	+	0.791118i
$872$		0			0
$873$		−	3.44006e8i		−	0.517038i
$874$		0			0
$875$	−9.11746e7			−0.136097
$876$		0			0
$877$	8.93530e7	−	1.57553e7i	0.132468	−	0.0233576i	−0.107021	−	0.994257i	$-0.534131\pi$
$877$	8.93530e7	−	1.57553e7i	0.132468	−	0.0233576i	0.239489	+	0.970899i	$0.423020\pi$
$878$		0			0
$879$	−9.26243e7	+	7.77210e7i	−0.136382	+	0.114438i
$880$		0			0
$881$	1.73752e8	−	3.00947e8i	0.254099	−	0.440112i	−0.710552	−	0.703645i	$-0.751555\pi$
$881$	1.73752e8	−	3.00947e8i	0.254099	−	0.440112i	0.964650	+	0.263533i	$0.0848879\pi$
$882$		0			0
$883$	3.17941e8	−	1.15721e8i	0.461812	−	0.168086i	−0.100628	−	0.994924i	$-0.532085\pi$
$883$	3.17941e8	−	1.15721e8i	0.461812	−	0.168086i	0.562440	+	0.826838i	$0.309863\pi$
$884$		0			0
$885$	4.66481e6	+	8.07970e6i	0.00672984	+	0.0116564i
$886$		0			0
$887$	−1.54467e8	−	2.72367e7i	−0.221343	−	0.0390287i	0.0618769	−	0.998084i	$-0.480291\pi$
$887$	−1.54467e8	−	2.72367e7i	−0.221343	−	0.0390287i	−0.283220	+	0.959055i	$0.591402\pi$
$888$		0			0
$889$	2.37048e8	−	2.82502e8i	0.337389	−	0.402084i
$890$		0			0
$891$	−2.32181e8	−	8.45069e7i	−0.328241	−	0.119470i
$892$		0			0
$893$	−1.76871e8	−	5.62652e8i	−0.248372	−	0.790106i
$894$		0			0
$895$	−3.98125e7	+	1.09384e8i	−0.0555329	+	0.152575i
$896$		0			0
$897$	−2.70662e7	−	2.27112e7i	−0.0375016	−	0.0314676i
$898$		0			0
$899$	−2.66100e8	+	1.50913e9i	−0.366241	+	2.07705i
$900$		0			0
$901$	2.07392e7	−	1.19738e7i	0.0283543	−	0.0163703i
$902$		0			0
$903$	2.07053e7	+	5.68873e7i	0.0281201	+	0.0772595i
$904$		0			0
$905$	−4.56968e7	−	2.63831e7i	−0.0616510	−	0.0355942i
$906$		0			0
$907$	1.11594e8	+	1.32992e8i	0.149561	+	0.178240i	0.835623	−	0.549303i	$-0.185107\pi$
$907$	1.11594e8	+	1.32992e8i	0.149561	+	0.178240i	−0.686062	+	0.727543i	$0.740662\pi$
$908$		0			0
$909$	1.14520e8	+	6.49475e8i	0.152472	+	0.864710i
$910$		0			0
$911$			1.03648e9i			1.37091i	0.728117	+	0.685453i	$0.240396\pi$
$911$			1.03648e9i			1.37091i	−0.728117	+	0.685453i	$0.759604\pi$
$912$		0			0
$913$	3.84222e8			0.504858
$914$		0			0
$915$	−1.56429e7	+	2.75827e6i	−0.0204200	+	0.00360059i
$916$		0			0
$917$	3.85297e6	−	3.23303e6i	0.00499675	−	0.00419277i
$918$		0			0
$919$	−7.07678e7	+	1.22573e8i	−0.0911778	+	0.157925i	−0.908007	−	0.418955i	$-0.862396\pi$
$919$	−7.07678e7	+	1.22573e8i	−0.0911778	+	0.157925i	0.816829	+	0.576880i	$0.195730\pi$
$920$		0			0
$921$	1.69238e8	−	6.15975e7i	0.216630	−	0.0788469i
$922$		0			0
$923$	5.09658e8	+	8.82754e8i	0.648148	+	1.12262i
$924$		0			0
$925$	1.12582e9	+	1.98512e8i	1.42247	+	0.250820i
$926$		0			0
$927$	5.05181e8	−	6.02051e8i	0.634173	−	0.755778i
$928$		0			0
$929$	−3.39692e8	−	1.23638e8i	−0.423680	−	0.154207i	0.121376	−	0.992607i	$-0.461269\pi$
$929$	−3.39692e8	−	1.23638e8i	−0.423680	−	0.154207i	−0.545056	+	0.838400i	$0.683492\pi$
$930$		0			0
$931$	4.16122e8	−	2.16165e8i	0.515670	−	0.267877i
$932$		0			0
$933$	3.33988e7	−	9.17624e7i	0.0411231	−	0.112985i
$934$		0			0
$935$	−4.00288e7	−	3.35881e7i	−0.0489709	−	0.0410914i
$936$		0			0
$937$	7.28327e7	−	4.13055e8i	0.0885335	−	0.502098i	−0.908005	−	0.418960i	$-0.862395\pi$
$937$	7.28327e7	−	4.13055e8i	0.0885335	−	0.502098i	0.996538	−	0.0831380i	$-0.0264942\pi$
$938$		0			0
$939$	1.45245e8	−	8.38575e7i	0.175431	−	0.101285i
$940$		0			0
$941$	−1.51052e8	−	4.15013e8i	−0.181284	−	0.498073i	0.815450	−	0.578827i	$-0.196489\pi$
$941$	−1.51052e8	−	4.15013e8i	−0.181284	−	0.498073i	−0.996734	+	0.0807540i	$0.974267\pi$
$942$		0			0
$943$	3.50086e8	+	2.02122e8i	0.417484	+	0.241035i
$944$		0			0
$945$	−9.83027e6	−	1.17153e7i	−0.0116485	−	0.0138821i
$946$		0			0
$947$	1.33011e7	+	7.54342e7i	0.0156616	+	0.0888216i	0.991637	−	0.129061i	$-0.0411962\pi$
$947$	1.33011e7	+	7.54342e7i	0.0156616	+	0.0888216i	−0.975975	+	0.217882i	$0.930085\pi$
$948$		0			0
$949$		−	5.95205e8i		−	0.696415i
$950$		0			0
$951$	1.41254e7			0.0164232
$952$		0			0
$953$	−1.28182e9	+	2.26020e8i	−1.48098	+	0.261136i	−0.854969	−	0.518679i	$-0.826424\pi$
$953$	−1.28182e9	+	2.26020e8i	−1.48098	+	0.261136i	−0.626009	+	0.779816i	$0.715313\pi$
$954$		0			0
$955$	1.29315e8	−	1.08508e8i	0.148470	−	0.124581i
$956$		0			0
$957$	−3.28700e7	+	5.69325e7i	−0.0375028	+	0.0649568i
$958$		0			0
$959$	−9.09037e8	+	3.30862e8i	−1.03068	+	0.375138i
$960$		0			0
$961$	4.08748e8	+	7.07972e8i	0.460559	+	0.797712i
$962$		0			0
$963$	2.93106e8	+	5.16825e7i	0.328205	+	0.0578715i
$964$		0			0
$965$	−7.27658e7	+	8.67189e7i	−0.0809739	+	0.0965009i
$966$		0			0
$967$	1.59375e9	+	5.80079e8i	1.76255	+	0.641516i	0.999985	−	0.00539588i	$-0.00171757\pi$
$967$	1.59375e9	+	5.80079e8i	1.76255	+	0.641516i	0.762565	+	0.646912i	$0.223940\pi$
$968$		0			0
$969$	−4.32839e7	+	1.94449e8i	−0.0475724	+	0.213714i
$970$		0			0
$971$	1.09518e8	−	3.00899e8i	0.119627	−	0.328673i	−0.865398	−	0.501086i	$-0.832934\pi$
$971$	1.09518e8	−	3.00899e8i	0.119627	−	0.328673i	0.985025	+	0.172413i	$0.0551564\pi$
$972$		0			0
$973$	2.05916e8	+	1.72784e8i	0.223538	+	0.187570i
$974$		0			0
$975$	−1.52416e7	+	8.64392e7i	−0.0164443	+	0.0932603i
$976$		0			0
$977$	−1.11787e8	+	6.45403e7i	−0.119869	+	0.0692066i	−0.558736	−	0.829346i	$-0.688713\pi$
$977$	−1.11787e8	+	6.45403e7i	−0.119869	+	0.0692066i	0.438867	+	0.898552i	$0.355380\pi$
$978$		0			0
$979$	1.77273e7	+	4.87053e7i	0.0188927	+	0.0519073i
$980$		0			0
$981$	1.05980e9	+	6.11873e8i	1.12257	+	0.648119i
$982$		0			0
$983$	3.11750e8	+	3.71529e8i	0.328205	+	0.391140i	0.904762	−	0.425917i	$-0.140048\pi$
$983$	3.11750e8	+	3.71529e8i	0.328205	+	0.391140i	−0.576557	+	0.817057i	$0.695604\pi$
$984$		0			0
$985$	7.77907e6	+	4.41173e7i	0.00813989	+	0.0461636i
$986$		0			0
$987$		−	6.88603e7i		−	0.0716172i
$988$		0			0
$989$	4.70170e8			0.486033
$990$		0			0
$991$	1.75131e8	−	3.08803e7i	0.179946	−	0.0317293i	−0.0829492	−	0.996554i	$-0.526434\pi$
$991$	1.75131e8	−	3.08803e7i	0.179946	−	0.0317293i	0.262895	+	0.964825i	$0.415323\pi$
$992$		0			0
$993$	5.03131e7	−	4.22177e7i	0.0513846	−	0.0431168i
$994$		0			0
$995$	−2.71121e7	+	4.69595e7i	−0.0275228	+	0.0476710i
$996$		0			0
$997$	9.22672e8	−	3.35825e8i	0.931026	−	0.338866i	0.168410	−	0.985717i	$-0.446137\pi$
$997$	9.22672e8	−	3.35825e8i	0.931026	−	0.338866i	0.762616	+	0.646851i	$0.223915\pi$
$998$		0			0
$999$	1.92836e8	+	3.34003e8i	0.193416	+	0.335007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.53.5	yes	60
19.14	odd	18	inner	76.7.j.a.33.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.5	✓	60	19.14	odd	18	inner
76.7.j.a.53.5	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)

\(f(q)\)	\(=\)	\(q+(3.55244 - 0.626392i) q^{3} +(-10.1242 + 8.49522i) q^{5} +(110.999 - 192.257i) q^{7} +(-672.808 + 244.882i) q^{9} +O(q^{10})\)	\(q+(3.55244 - 0.626392i) q^{3} +(-10.1242 + 8.49522i) q^{5} +(110.999 - 192.257i) q^{7} +(-672.808 + 244.882i) q^{9} +(-245.534 - 425.277i) q^{11} +(1550.95 + 273.474i) q^{13} +(-30.6444 + 36.5205i) q^{15} +(-7565.82 - 2753.73i) q^{17} +(305.082 - 6852.21i) q^{19} +(273.891 - 752.510i) q^{21} +(-4764.38 - 3997.79i) q^{23} +(-2682.92 + 15215.6i) q^{25} +(-4514.09 + 2606.21i) q^{27} +(-12693.0 - 34873.8i) q^{29} +(-35759.6 - 20645.8i) q^{31} +(-1138.63 - 1356.97i) q^{33} +(509.481 + 2889.41i) q^{35} -73991.1i q^{37} +5680.96 q^{39} +(-64009.4 + 11286.6i) q^{41} +(-57910.4 + 48592.6i) q^{43} +(4731.33 - 8194.90i) q^{45} +(80803.1 - 29409.9i) q^{47} +(34182.7 + 59206.2i) q^{49} +(-28602.1 - 5043.32i) q^{51} +(-1911.87 + 2278.48i) q^{53} +(6098.65 + 2219.73i) q^{55} +(-3208.38 - 24533.2i) q^{57} +(66931.9 - 183894. i) q^{59} +(255234. + 214167. i) q^{61} +(-27601.1 + 156534. i) q^{63} +(-18025.3 + 10406.9i) q^{65} +(115279. + 316726. i) q^{67} +(-19429.4 - 11217.5i) q^{69} +(416036. + 495812. i) q^{71} +(-65628.3 - 372197. i) q^{73} +55733.1i q^{75} -109016. q^{77} +(303328. - 53484.9i) q^{79} +(385437. - 323420. i) q^{81} +(-391211. + 677597. i) q^{83} +(99991.6 - 36394.0i) q^{85} +(-66935.9 - 115936. i) q^{87} +(-103944. - 18328.2i) q^{89} +(224732. - 267825. i) q^{91} +(-139966. - 50943.6i) q^{93} +(55122.3 + 71965.0i) q^{95} +(-164328. + 451487. i) q^{97} +(269340. + 226003. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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