LMFDB - Embedded newform 76.7.j.a.13.4

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			13.4
Character	$\chi$	$=$	76.13
Dual form			76.7.j.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.46108 + 17.7517i) q^{3} +(14.8495 + 84.2156i) q^{5} +(158.113 - 273.859i) q^{7} +(285.070 + 239.202i) q^{9} +O(q^{10})$	\(q+(-6.46108 + 17.7517i) q^{3} +(14.8495 + 84.2156i) q^{5} +(158.113 - 273.859i) q^{7} +(285.070 + 239.202i) q^{9} +(1056.82 + 1830.46i) q^{11} +(-564.897 - 1552.04i) q^{13} +(-1590.91 - 280.520i) q^{15} +(-3148.54 + 2641.94i) q^{17} +(-6565.47 - 1985.07i) q^{19} +(3839.88 + 4576.19i) q^{21} +(-3598.68 + 20409.1i) q^{23} +(7810.94 - 2842.95i) q^{25} +(-18014.6 + 10400.7i) q^{27} +(-8792.59 + 10478.6i) q^{29} +(-18710.1 - 10802.3i) q^{31} +(-39321.8 + 6933.50i) q^{33} +(25411.1 + 9248.89i) q^{35} +80621.8i q^{37} +31201.2 q^{39} +(-19334.7 + 53121.7i) q^{41} +(-22123.2 - 125467. i) q^{43} +(-15911.4 + 27559.4i) q^{45} +(115198. + 96662.9i) q^{47} +(8825.22 + 15285.7i) q^{49} +(-26555.8 - 72961.5i) q^{51} +(37281.2 + 6573.68i) q^{53} +(-138460. + 116182. i) q^{55} +(77658.3 - 103722. i) q^{57} +(-256993. - 306273. i) q^{59} +(11158.6 - 63283.6i) q^{61} +(110581. - 40248.2i) q^{63} +(122318. - 70620.1i) q^{65} +(145521. - 173425. i) q^{67} +(-339045. - 195748. i) q^{69} +(257237. - 45357.8i) q^{71} +(514628. + 187309. i) q^{73} +157026. i q^{75} +668384. q^{77} +(185999. - 511029. i) q^{79} +(-21128.3 - 119825. i) q^{81} +(-244399. + 423311. i) q^{83} +(-269246. - 225925. i) q^{85} +(-129203. - 223786. i) q^{87} +(31040.2 + 85282.2i) q^{89} +(-514358. - 90695.2i) q^{91} +(312647. - 262342. i) q^{93} +(69679.8 - 582392. i) q^{95} +(726988. + 866390. i) q^{97} +(-136583. + 774602. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	−6.46108	+	17.7517i	−0.239299	+	0.657469i	0.760666	+	0.649143i	$0.224872\pi$
$3$	−6.46108	+	17.7517i	−0.239299	+	0.657469i	−0.999965	+	0.00832580i	$0.997350\pi$
$4$		0			0
$5$	14.8495	+	84.2156i	0.118796	+	0.673725i	0.984801	+	0.173689i	$0.0555687\pi$
$5$	14.8495	+	84.2156i	0.118796	+	0.673725i	−0.866005	+	0.500036i	$0.833320\pi$
$6$		0			0
$7$	158.113	−	273.859i	0.460970	−	0.798424i	−0.538039	−	0.842920i	$-0.680835\pi$
$7$	158.113	−	273.859i	0.460970	−	0.798424i	0.999010	+	0.0444960i	$0.0141682\pi$
$8$		0			0
$9$	285.070	+	239.202i	0.391043	+	0.328124i
$10$		0			0
$11$	1056.82	+	1830.46i	0.794001	+	1.37525i	0.923472	+	0.383667i	$0.125339\pi$
$11$	1056.82	+	1830.46i	0.794001	+	1.37525i	−0.129471	+	0.991583i	$0.541328\pi$
$12$		0			0
$13$	−564.897	−	1552.04i	−0.257122	−	0.706436i	−0.999342	−	0.0362800i	$-0.988449\pi$
$13$	−564.897	−	1552.04i	−0.257122	−	0.706436i	0.742220	−	0.670157i	$-0.233773\pi$
$14$		0			0
$15$	−1590.91	−	280.520i	−0.471381	−	0.0831172i
$16$		0			0
$17$	−3148.54	+	2641.94i	−0.640859	+	0.537744i	−0.904282	−	0.426936i	$-0.859593\pi$
$17$	−3148.54	+	2641.94i	−0.640859	+	0.537744i	0.263423	+	0.964680i	$0.415148\pi$
$18$		0			0
$19$	−6565.47	−	1985.07i	−0.957205	−	0.289411i
$19$	−6565.47	−	1985.07i	−0.957205	−	0.289411i
$20$		0			0
$21$	3839.88	+	4576.19i	0.414629	+	0.494136i
$22$		0			0
$23$	−3598.68	+	20409.1i	−0.295774	+	1.67742i	0.368266	+	0.929721i	$0.379952\pi$
$23$	−3598.68	+	20409.1i	−0.295774	+	1.67742i	−0.664040	+	0.747697i	$0.731159\pi$
$24$		0			0
$25$	7810.94	−	2842.95i	0.499900	−	0.181949i
$26$		0			0
$27$	−18014.6	+	10400.7i	−0.915234	+	0.528411i
$28$		0			0
$29$	−8792.59	+	10478.6i	−0.360515	+	0.429645i	−0.915564	−	0.402173i	$-0.868255\pi$
$29$	−8792.59	+	10478.6i	−0.360515	+	0.429645i	0.555049	+	0.831818i	$0.312699\pi$
$30$		0			0
$31$	−18710.1	−	10802.3i	−0.628047	−	0.362603i	0.151948	−	0.988388i	$-0.451445\pi$
$31$	−18710.1	−	10802.3i	−0.628047	−	0.362603i	−0.779995	+	0.625785i	$0.784779\pi$
$32$		0			0
$33$	−39321.8	+	6933.50i	−1.09419	+	0.192935i
$34$		0			0
$35$	25411.1	+	9248.89i	0.592679	+	0.215718i
$36$		0			0
$37$			80621.8i			1.59165i	0.605528	+	0.795824i	$0.292962\pi$
$37$			80621.8i			1.59165i	−0.605528	+	0.795824i	$0.707038\pi$
$38$		0			0
$39$	31201.2			0.525989
$40$		0			0
$41$	−19334.7	+	53121.7i	−0.280535	+	0.770762i	0.716765	+	0.697315i	$0.245622\pi$
$41$	−19334.7	+	53121.7i	−0.280535	+	0.770762i	−0.997299	+	0.0734471i	$0.976600\pi$
$42$		0			0
$43$	−22123.2	−	125467.i	−0.278255	−	1.57806i	−0.728430	−	0.685120i	$-0.759750\pi$
$43$	−22123.2	−	125467.i	−0.278255	−	1.57806i	0.450176	−	0.892940i	$-0.351361\pi$
$44$		0			0
$45$	−15911.4	+	27559.4i	−0.174611	+	0.302435i
$46$		0			0
$47$	115198.	+	96662.9i	1.10957	+	0.931036i	0.998031	−	0.0627246i	$-0.0199790\pi$
$47$	115198.	+	96662.9i	1.10957	+	0.931036i	0.111535	+	0.993761i	$0.464423\pi$
$48$		0			0
$49$	8825.22	+	15285.7i	0.0750131	+	0.129926i
$50$		0			0
$51$	−26555.8	−	72961.5i	−0.200193	−	0.550026i
$52$		0			0
$53$	37281.2	+	6573.68i	0.250416	+	0.0441551i	0.297447	−	0.954738i	$-0.403865\pi$
$53$	37281.2	+	6573.68i	0.250416	+	0.0441551i	−0.0470309	+	0.998893i	$0.514976\pi$
$54$		0			0
$55$	−138460.	+	116182.i	−0.832216	+	0.698312i
$56$		0			0
$57$	77658.3	−	103722.i	0.419337	−	0.560077i
$58$		0			0
$59$	−256993.	−	306273.i	−1.25131	−	1.49126i	−0.801333	−	0.598219i	$-0.795875\pi$
$59$	−256993.	−	306273.i	−1.25131	−	1.49126i	−0.449980	−	0.893038i	$-0.648569\pi$
$60$		0			0
$61$	11158.6	−	63283.6i	0.0491610	−	0.278806i	−0.950311	−	0.311303i	$-0.899235\pi$
$61$	11158.6	−	63283.6i	0.0491610	−	0.278806i	0.999472	+	0.0324968i	$0.0103459\pi$
$62$		0			0
$63$	110581.	−	40248.2i	0.442241	−	0.160963i
$64$		0			0
$65$	122318.	−	70620.1i	0.445399	−	0.257151i
$66$		0			0
$67$	145521.	−	173425.i	0.483839	−	0.576616i	−0.467801	−	0.883834i	$-0.654954\pi$
$67$	145521.	−	173425.i	0.483839	−	0.576616i	0.951639	+	0.307218i	$0.0993980\pi$
$68$		0			0
$69$	−339045.	−	195748.i	−1.03207	−	0.595867i
$70$		0			0
$71$	257237.	−	45357.8i	0.718717	−	0.126729i	0.197684	−	0.980266i	$-0.436658\pi$
$71$	257237.	−	45357.8i	0.718717	−	0.126729i	0.521033	+	0.853537i	$0.325547\pi$
$72$		0			0
$73$	514628.	+	187309.i	1.32289	+	0.481494i	0.904384	−	0.426719i	$-0.140331\pi$
$73$	514628.	+	187309.i	1.32289	+	0.481494i	0.418509	+	0.908213i	$0.362553\pi$
$74$		0			0
$75$			157026.i			0.372209i
$76$		0			0
$77$	668384.			1.46404
$78$		0			0
$79$	185999.	−	511029.i	0.377251	−	1.03649i	−0.595240	−	0.803548i	$-0.702943\pi$
$79$	185999.	−	511029.i	0.377251	−	1.03649i	0.972491	−	0.232941i	$-0.0748348\pi$
$80$		0			0
$81$	−21128.3	−	119825.i	−0.0397567	−	0.225471i
$82$		0			0
$83$	−244399.	+	423311.i	−0.427430	+	0.740330i	−0.996644	−	0.0818590i	$-0.973914\pi$
$83$	−244399.	+	423311.i	−0.427430	+	0.740330i	0.569214	+	0.822189i	$0.307248\pi$
$84$		0			0
$85$	−269246.	−	225925.i	−0.438423	−	0.367880i
$86$		0			0
$87$	−129203.	−	223786.i	−0.196207	−	0.339841i
$88$		0			0
$89$	31040.2	+	85282.2i	0.0440305	+	0.120973i	0.959759	−	0.280824i	$-0.0906079\pi$
$89$	31040.2	+	85282.2i	0.0440305	+	0.120973i	−0.915729	+	0.401797i	$0.868386\pi$
$90$		0			0
$91$	−514358.	−	90695.2i	−0.682561	−	0.120354i
$92$		0			0
$93$	312647.	−	262342.i	0.388691	−	0.326151i
$94$		0			0
$95$	69679.8	−	582392.i	0.0812711	−	0.679273i
$96$		0			0
$97$	726988.	+	866390.i	0.796548	+	0.949289i	0.999553	−	0.0298887i	$-0.00951529\pi$
$97$	726988.	+	866390.i	0.796548	+	0.949289i	−0.203005	+	0.979178i	$0.565071\pi$
$98$		0			0
$99$	−136583.	+	774602.i	−0.140764	+	0.798313i
$100$		0			0
$101$	−980185.	+	356758.i	−0.951357	+	0.346266i	−0.770641	−	0.637269i	$-0.780064\pi$
$101$	−980185.	+	356758.i	−0.951357	+	0.346266i	−0.180716	+	0.983535i	$0.557842\pi$
$102$		0			0
$103$	−675320.	+	389896.i	−0.618014	+	0.356810i	−0.776095	−	0.630616i	$-0.782802\pi$
$103$	−675320.	+	389896.i	−0.618014	+	0.356810i	0.158082	+	0.987426i	$0.449469\pi$
$104$		0			0
$105$	−328366.	+	391332.i	−0.283655	+	0.338047i
$106$		0			0
$107$	−912201.	−	526660.i	−0.744628	−	0.429911i	0.0791216	−	0.996865i	$-0.474788\pi$
$107$	−912201.	−	526660.i	−0.744628	−	0.429911i	−0.823750	+	0.566954i	$0.808122\pi$
$108$		0			0
$109$	1.88349e6	−	332111.i	1.45440	−	0.256450i	0.610103	−	0.792322i	$-0.291128\pi$
$109$	1.88349e6	−	332111.i	1.45440	−	0.256450i	0.844299	+	0.535872i	$0.180017\pi$
$110$		0			0
$111$	−1.43117e6	−	520903.i	−1.04646	−	0.380880i
$112$		0			0
$113$			1.05013e6i			0.727791i	0.931440	+	0.363896i	$0.118553\pi$
$113$			1.05013e6i			0.727791i	−0.931440	+	0.363896i	$0.881447\pi$
$114$		0			0
$115$	−1.77221e6			−1.16525
$116$		0			0
$117$	210217.	−	577565.i	0.131253	−	0.360615i
$118$		0			0
$119$	225695.	+	1.27998e6i	0.133931	+	0.759561i
$120$		0			0
$121$	−1.34794e6	+	2.33469e6i	−0.760875	+	1.31787i
$122$		0			0
$123$	−818076.	−	686447.i	−0.439621	−	0.368886i
$124$		0			0
$125$	1.02349e6	+	1.77274e6i	0.524028	+	0.907644i
$126$		0			0
$127$	975660.	+	2.68060e6i	0.476307	+	1.30864i	0.912606	+	0.408841i	$0.134067\pi$
$127$	975660.	+	2.68060e6i	0.476307	+	1.30864i	−0.436298	+	0.899802i	$0.643711\pi$
$128$		0			0
$129$	2.37018e6	+	417927.i	1.10411	+	0.194685i
$130$		0			0
$131$	1.69776e6	−	1.42459e6i	0.755199	−	0.633687i	−0.181673	−	0.983359i	$-0.558151\pi$
$131$	1.69776e6	−	1.42459e6i	0.755199	−	0.633687i	0.936872	+	0.349672i	$0.113707\pi$
$132$		0			0
$133$	−1.58171e6	+	1.48415e6i	−0.672315	+	0.630846i
$134$		0			0
$135$	−1.14341e6	−	1.36266e6i	−0.464729	−	0.553843i
$136$		0			0
$137$	501818.	−	2.84595e6i	0.195157	−	1.10679i	−0.717038	−	0.697034i	$-0.754502\pi$
$137$	501818.	−	2.84595e6i	0.195157	−	1.10679i	0.912195	−	0.409757i	$-0.134386\pi$
$138$		0			0
$139$	17695.1	−	6440.48i	0.00658883	−	0.00239814i	−0.338724	−	0.940886i	$-0.609995\pi$
$139$	17695.1	−	6440.48i	0.00658883	−	0.00239814i	0.345312	+	0.938488i	$0.387773\pi$
$140$		0			0
$141$	−2.46023e6	+	1.42042e6i	−0.877645	+	0.506709i
$142$		0			0
$143$	2.24395e6	−	2.67424e6i	0.767372	−	0.914518i
$144$		0			0
$145$	−1.01303e6	−	584871.i	−0.332290	−	0.191848i
$146$		0			0
$147$	−328367.	+	57900.0i	−0.103373	+	0.0182275i
$148$		0			0
$149$	1.65206e6	+	601299.i	0.499420	+	0.181774i	0.579433	−	0.815020i	$-0.303274\pi$
$149$	1.65206e6	+	601299.i	0.499420	+	0.181774i	−0.0800130	+	0.996794i	$0.525496\pi$
$150$		0			0
$151$		−	916961.i		−	0.266330i	−0.991094	−	0.133165i	$-0.957486\pi$
$151$		−	916961.i		−	0.266330i	0.991094	−	0.133165i	$-0.0425140\pi$
$152$		0			0
$153$	−1.52951e6			−0.427050
$154$		0			0
$155$	631887.	−	1.73609e6i	0.169685	−	0.466206i
$156$		0			0
$157$	188582.	+	1.06950e6i	0.0487307	+	0.276365i	0.999430	−	0.0337476i	$-0.0107442\pi$
$157$	188582.	+	1.06950e6i	0.0487307	+	0.276365i	−0.950700	+	0.310113i	$0.899633\pi$
$158$		0			0
$159$	−357571.	+	619330.i	−0.0889550	+	0.154075i
$160$		0			0
$161$	5.02024e6	+	4.21248e6i	1.20295	+	1.00939i
$162$		0			0
$163$	−2.17156e6	−	3.76126e6i	−0.501429	−	0.868501i	−0.999999	−	0.00165139i	$-0.999474\pi$
$163$	−2.17156e6	−	3.76126e6i	−0.501429	−	0.868501i	0.498569	−	0.866850i	$-0.333859\pi$
$164$		0			0
$165$	−1.16782e6	−	3.20855e6i	−0.259970	−	0.714262i
$166$		0			0
$167$	−4.77676e6	−	842271.i	−1.02561	−	0.180843i	−0.364558	−	0.931181i	$-0.618780\pi$
$167$	−4.77676e6	−	842271.i	−1.02561	−	0.180843i	−0.661055	+	0.750337i	$0.729891\pi$
$168$		0			0
$169$	1.60783e6	−	1.34913e6i	0.333104	−	0.279507i
$170$		0			0
$171$	−1.39679e6	−	2.13636e6i	−0.279346	−	0.427254i
$172$		0			0
$173$	1.75642e6	+	2.09322e6i	0.339227	+	0.404275i	0.908508	−	0.417868i	$-0.137223\pi$
$173$	1.75642e6	+	2.09322e6i	0.339227	+	0.404275i	−0.569281	+	0.822143i	$0.692778\pi$
$174$		0			0
$175$	456441.	−	2.58861e6i	0.0851668	−	0.483005i
$176$		0			0
$177$	7.09731e6	−	2.58321e6i	1.27989	−	0.465843i
$178$		0			0
$179$	9.23024e6	−	5.32908e6i	1.60936	−	0.929166i	0.619850	−	0.784720i	$-0.287193\pi$
$179$	9.23024e6	−	5.32908e6i	1.60936	−	0.929166i	0.989513	−	0.144446i	$-0.0461399\pi$
$180$		0			0
$181$	3.42901e6	−	4.08653e6i	0.578272	−	0.689158i	−0.395034	−	0.918666i	$-0.629267\pi$
$181$	3.42901e6	−	4.08653e6i	0.578272	−	0.689158i	0.973307	+	0.229508i	$0.0737117\pi$
$182$		0			0
$183$	1.05129e6	+	606964.i	0.171542	+	0.0990398i
$184$		0			0
$185$	−6.78961e6	+	1.19719e6i	−1.07233	+	0.189081i
$186$		0			0
$187$	−8.16338e6	−	2.97123e6i	−1.24837	−	0.454371i
$188$		0			0
$189$			6.57794e6i			0.974326i
$190$		0			0
$191$	1.39908e6			0.200790			0.100395	−	0.994948i	$-0.467989\pi$
$191$	1.39908e6			0.200790			0.100395	+	0.994948i	$0.467989\pi$
$192$		0			0
$193$	1.71827e6	−	4.72090e6i	0.239012	−	0.656679i	−0.760957	−	0.648802i	$-0.775270\pi$
$193$	1.71827e6	−	4.72090e6i	0.239012	−	0.656679i	0.999969	−	0.00787697i	$-0.00250734\pi$
$194$		0			0
$195$	463321.	+	2.62762e6i	0.0624853	+	0.354372i
$196$		0			0
$197$	2.82302e6	−	4.88962e6i	0.369246	−	0.639552i	−0.620202	−	0.784442i	$-0.712949\pi$
$197$	2.82302e6	−	4.88962e6i	0.369246	−	0.639552i	0.989448	+	0.144890i	$0.0462827\pi$
$198$		0			0
$199$	6.47260e6	+	5.43115e6i	0.821333	+	0.689180i	0.953284	−	0.302076i	$-0.0976797\pi$
$199$	6.47260e6	+	5.43115e6i	0.821333	+	0.689180i	−0.131951	+	0.991256i	$0.542124\pi$
$200$		0			0
$201$	2.13836e6	+	3.70375e6i	0.263325	+	0.456093i
$202$		0			0
$203$	1.47944e6	+	4.06473e6i	0.176852	+	0.485897i
$204$		0			0
$205$	−4.76079e6	−	839455.i	−0.552608	−	0.0974397i
$206$		0			0
$207$	−5.90779e6	+	4.95723e6i	−0.666061	+	0.558892i
$208$		0			0
$209$	−3.30491e6	−	1.41157e7i	−0.362010	−	1.54619i
$210$		0			0
$211$	−2.61206e6	−	3.11294e6i	−0.278059	−	0.331377i	0.608882	−	0.793261i	$-0.291618\pi$
$211$	−2.61206e6	−	3.11294e6i	−0.278059	−	0.331377i	−0.886941	+	0.461883i	$0.847174\pi$
$212$		0			0
$213$	−856850.	+	4.85944e6i	−0.0886678	+	0.502860i
$214$		0			0
$215$	1.02377e7	−	3.72623e6i	1.03012	−	0.374934i
$216$		0			0
$217$	−5.91663e6	+	3.41597e6i	−0.579022	+	0.334298i
$218$		0			0
$219$	−6.65010e6	+	7.92529e6i	−0.633135	+	0.754541i
$220$		0			0
$221$	5.87899e6	+	3.39424e6i	0.544661	+	0.314460i
$222$		0			0
$223$	6.26097e6	−	1.10398e6i	0.564582	−	0.0995510i	0.115930	−	0.993257i	$-0.463015\pi$
$223$	6.26097e6	−	1.10398e6i	0.564582	−	0.0995510i	0.448652	+	0.893706i	$0.351904\pi$
$224$		0			0
$225$	2.90671e6	+	1.05795e6i	0.255184	+	0.0928795i
$226$		0			0
$227$			8.58670e6i			0.734089i	0.930203	+	0.367044i	$0.119630\pi$
$227$			8.58670e6i			0.734089i	−0.930203	+	0.367044i	$0.880370\pi$
$228$		0			0
$229$	−1.48641e7			−1.23775			−0.618875	−	0.785490i	$-0.712411\pi$
$229$	−1.48641e7			−1.23775			−0.618875	+	0.785490i	$0.712411\pi$
$230$		0			0
$231$	−4.31848e6	+	1.18649e7i	−0.350344	+	0.962563i
$232$		0			0
$233$	596824.	+	3.38475e6i	0.0471822	+	0.267584i	0.999268	−	0.0382464i	$-0.0121772\pi$
$233$	596824.	+	3.38475e6i	0.0471822	+	0.267584i	−0.952086	+	0.305830i	$0.901066\pi$
$234$		0			0
$235$	−6.42989e6	+	1.11369e7i	−0.495450	+	0.858145i
$236$		0			0
$237$	7.86986e6	+	6.60360e6i	0.591183	+	0.496062i
$238$		0			0
$239$	−239616.	−	415026.i	−0.0175518	−	0.0304006i	0.857116	−	0.515123i	$-0.172254\pi$
$239$	−239616.	−	415026.i	−0.0175518	−	0.0304006i	−0.874668	+	0.484723i	$0.838921\pi$
$240$		0			0
$241$	−6.52378e6	−	1.79239e7i	−0.466067	−	1.28051i	−0.920854	−	0.389908i	$-0.872507\pi$
$241$	−6.52378e6	−	1.79239e7i	−0.466067	−	1.28051i	0.454787	−	0.890600i	$-0.349716\pi$
$242$		0			0
$243$	−1.26703e7	−	2.23411e6i	−0.883012	−	0.155699i
$244$		0			0
$245$	−1.15625e6	+	970206.i	−0.0786234	+	0.0659729i
$246$		0			0
$247$	627906.	+	1.13112e7i	0.0416681	+	0.750618i
$248$		0			0
$249$	−5.93540e6	−	7.07353e6i	−0.384461	−	0.458182i
$250$		0			0
$251$	1.10638e6	−	6.27458e6i	0.0699652	−	0.396792i	−0.929634	−	0.368484i	$-0.879877\pi$
$251$	1.10638e6	−	6.27458e6i	0.0699652	−	0.396792i	0.999599	−	0.0283083i	$-0.00901200\pi$
$252$		0			0
$253$	−4.11612e7	+	1.49815e7i	−2.54171	+	0.925108i
$254$		0			0
$255$	5.75016e6	−	3.31986e6i	0.346784	−	0.200216i
$256$		0			0
$257$	−42353.2	+	50474.5i	−0.00249509	+	0.00297353i	−0.767291	−	0.641300i	$-0.778396\pi$
$257$	−42353.2	+	50474.5i	−0.00249509	+	0.00297353i	0.764795	+	0.644273i	$0.222840\pi$
$258$		0			0
$259$	2.20790e7	+	1.27473e7i	1.27081	+	0.733702i
$260$		0			0
$261$	−5.01301e6	+	883930.i	−0.281953	+	0.0497160i
$262$		0			0
$263$	−9.61921e6	−	3.50111e6i	−0.528776	−	0.192459i	0.0638155	−	0.997962i	$-0.479673\pi$
$263$	−9.61921e6	−	3.50111e6i	−0.528776	−	0.192459i	−0.592592	+	0.805503i	$0.701895\pi$
$264$		0			0
$265$			3.23727e6i			0.173957i
$266$		0			0
$267$	−1.71445e6			−0.0900724
$268$		0			0
$269$	1.25798e7	−	3.45626e7i	0.646273	−	1.77562i	0.0152150	−	0.999884i	$-0.495157\pi$
$269$	1.25798e7	−	3.45626e7i	0.646273	−	1.77562i	0.631058	−	0.775736i	$-0.282621\pi$
$270$		0			0
$271$	2.11420e6	+	1.19902e7i	0.106228	+	0.602448i	0.990723	+	0.135898i	$0.0433921\pi$
$271$	2.11420e6	+	1.19902e7i	0.106228	+	0.602448i	−0.884495	+	0.466550i	$0.845497\pi$
$272$		0			0
$273$	4.93330e6	−	8.54473e6i	0.242465	−	0.419962i
$274$		0			0
$275$	1.34586e7	+	1.12931e7i	0.647146	+	0.543020i
$276$		0			0
$277$	1.35623e7	+	2.34906e7i	0.638107	+	1.10523i	0.985848	+	0.167644i	$0.0536158\pi$
$277$	1.35623e7	+	2.34906e7i	0.638107	+	1.10523i	−0.347740	+	0.937591i	$0.613051\pi$
$278$		0			0
$279$	−2.74977e6	−	7.55493e6i	−0.126615	−	0.347871i
$280$		0			0
$281$	3.38876e7	+	5.97529e6i	1.52729	+	0.269302i	0.873293	−	0.487195i	$-0.161980\pi$
$281$	3.38876e7	+	5.97529e6i	1.52729	+	0.269302i	0.653997	+	0.756497i	$0.273091\pi$
$282$		0			0
$283$	1.03999e7	−	8.72653e6i	0.458848	−	0.385019i	−0.383859	−	0.923392i	$-0.625405\pi$
$283$	1.03999e7	−	8.72653e6i	0.458848	−	0.385019i	0.842707	+	0.538373i	$0.180961\pi$
$284$		0			0
$285$	9.88822e6	+	4.99981e6i	0.427153	+	0.215983i
$286$		0			0
$287$	1.14908e7	+	1.36942e7i	0.486077	+	0.579284i
$288$		0			0
$289$	−1.25799e6	+	7.13439e6i	−0.0521173	+	0.295572i
$290$		0			0
$291$	−2.00770e7	+	7.30743e6i	−0.814741	+	0.296542i
$292$		0			0
$293$	−8.21376e6	+	4.74222e6i	−0.326542	+	0.188529i	−0.654305	−	0.756231i	$-0.727039\pi$
$293$	−8.21376e6	+	4.74222e6i	−0.326542	+	0.188529i	0.327763	+	0.944760i	$0.393705\pi$
$294$		0			0
$295$	2.19767e7	−	2.61908e7i	0.856046	−	1.02020i
$296$		0			0
$297$	−3.80761e7	−	2.19833e7i	−1.45339	−	0.839117i
$298$		0			0
$299$	3.37087e7	−	5.94376e6i	1.26104	−	0.222355i
$300$		0			0
$301$	−3.78582e7	−	1.37793e7i	−1.38823	−	0.505273i
$302$		0			0
$303$		−	1.97049e7i		−	0.708349i
$304$		0			0
$305$	5.49517e6			0.193678
$306$		0			0
$307$	9.24642e6	−	2.54043e7i	0.319564	−	0.877996i	−0.671062	−	0.741401i	$-0.734162\pi$
$307$	9.24642e6	−	2.54043e7i	0.319564	−	0.877996i	0.990627	−	0.136595i	$-0.0436160\pi$
$308$		0			0
$309$	−2.55801e6	−	1.45072e7i	−0.0867016	−	0.491709i
$310$		0			0
$311$	7.38779e6	−	1.27960e7i	0.245603	−	0.425397i	−0.716698	−	0.697384i	$-0.754347\pi$
$311$	7.38779e6	−	1.27960e7i	0.245603	−	0.425397i	0.962301	+	0.271987i	$0.0876807\pi$
$312$		0			0
$313$	−2.13125e7	−	1.78833e7i	−0.695027	−	0.583197i	0.225327	−	0.974283i	$-0.427655\pi$
$313$	−2.13125e7	−	1.78833e7i	−0.695027	−	0.583197i	−0.920354	+	0.391086i	$0.872099\pi$
$314$		0			0
$315$	5.03160e6	+	8.71498e6i	0.160981	+	0.278827i
$316$		0			0
$317$	1.19178e6	+	3.27439e6i	0.0374127	+	0.102790i	0.956992	−	0.290113i	$-0.0936929\pi$
$317$	1.19178e6	+	3.27439e6i	0.0374127	+	0.102790i	−0.919580	+	0.392903i	$0.871471\pi$
$318$		0			0
$319$	−2.84728e7	−	5.02052e6i	−0.877118	−	0.154659i
$320$		0			0
$321$	1.52429e7	−	1.27903e7i	0.460842	−	0.386692i
$322$		0			0
$323$	2.59161e7	−	1.10955e7i	0.769062	−	0.329260i
$324$		0			0
$325$	−8.82475e6	−	1.05169e7i	−0.257070	−	0.306365i
$326$		0			0
$327$	−6.27388e6	+	3.55809e7i	−0.179429	+	1.01759i
$328$		0			0
$329$	4.46864e7	−	1.62645e7i	1.25484	−	0.456724i
$330$		0			0
$331$	−3.01166e7	+	1.73878e7i	−0.830465	+	0.479469i	−0.854012	−	0.520253i	$-0.825837\pi$
$331$	−3.01166e7	+	1.73878e7i	−0.830465	+	0.479469i	0.0235468	+	0.999723i	$0.492504\pi$
$332$		0			0
$333$	−1.92849e7	+	2.29829e7i	−0.522258	+	0.622403i
$334$		0			0
$335$	1.67660e7	+	9.67984e6i	0.445959	+	0.257474i
$336$		0			0
$337$	8.80905e6	−	1.55327e6i	0.230165	−	0.0405843i	−0.0573760	−	0.998353i	$-0.518273\pi$
$337$	8.80905e6	−	1.55327e6i	0.230165	−	0.0405843i	0.287541	+	0.957768i	$0.407162\pi$
$338$		0			0
$339$	−1.86415e7	−	6.78496e6i	−0.478500	−	0.174160i
$340$		0			0
$341$		−	4.56642e7i		−	1.15163i
$342$		0			0
$343$	4.27851e7			1.06026
$344$		0			0
$345$	1.14504e7	−	3.14596e7i	0.278844	−	0.766119i
$346$		0			0
$347$	−2.41103e6	−	1.36736e7i	−0.0577050	−	0.327261i	0.942266	−	0.334865i	$-0.108691\pi$
$347$	−2.41103e6	−	1.36736e7i	−0.0577050	−	0.327261i	−0.999971	+	0.00760381i	$0.997580\pi$
$348$		0			0
$349$	3.84028e6	−	6.65157e6i	0.0903414	−	0.156476i	−0.817313	−	0.576193i	$-0.804537\pi$
$349$	3.84028e6	−	6.65157e6i	0.0903414	−	0.156476i	0.907655	+	0.419717i	$0.137871\pi$
$350$		0			0
$351$	2.63187e7	+	2.20840e7i	0.608615	+	0.510689i
$352$		0			0
$353$	9.53676e6	+	1.65182e7i	0.216809	+	0.375524i	0.953831	−	0.300345i	$-0.0971019\pi$
$353$	9.53676e6	+	1.65182e7i	0.216809	+	0.375524i	−0.737022	+	0.675869i	$0.763769\pi$
$354$		0			0
$355$	7.63966e6	+	2.09898e7i	0.170761	+	0.469162i
$356$		0			0
$357$	−2.41800e7	−	4.26359e6i	−0.531437	−	0.0937067i
$358$		0			0
$359$	−1.01184e7	+	8.49035e6i	−0.218690	+	0.183503i	−0.745551	−	0.666449i	$-0.767813\pi$
$359$	−1.01184e7	+	8.49035e6i	−0.218690	+	0.183503i	0.526861	+	0.849952i	$0.323369\pi$
$360$		0			0
$361$	3.91649e7	+	2.60658e7i	0.832483	+	0.554051i
$362$		0			0
$363$	−3.27356e7	−	3.90128e7i	−0.684385	−	0.815618i
$364$		0			0
$365$	−8.13240e6	+	4.61212e7i	−0.167240	+	0.948466i
$366$		0			0
$367$	−2.62719e7	+	9.56220e6i	−0.531489	+	0.193446i	−0.593803	−	0.804611i	$-0.702374\pi$
$367$	−2.62719e7	+	9.56220e6i	−0.531489	+	0.193446i	0.0623143	+	0.998057i	$0.480152\pi$
$368$		0			0
$369$	−1.82186e7	+	1.05185e7i	−0.362607	+	0.209351i
$370$		0			0
$371$	7.69490e6	−	9.17042e6i	0.150689	−	0.179584i
$372$		0			0
$373$	1.79774e7	+	1.03792e7i	0.346417	+	0.200004i	0.663106	−	0.748525i	$-0.269238\pi$
$373$	1.79774e7	+	1.03792e7i	0.346417	+	0.200004i	−0.316689	+	0.948529i	$0.602571\pi$
$374$		0			0
$375$	−3.80820e7	+	6.71488e6i	−0.722147	+	0.127334i
$376$		0			0
$377$	2.12301e7	+	7.72713e6i	0.396213	+	0.144210i
$378$		0			0
$379$			9.88087e7i			1.81500i	0.420047	+	0.907502i	$0.362014\pi$
$379$			9.88087e7i			1.81500i	−0.420047	+	0.907502i	$0.637986\pi$
$380$		0			0
$381$	−5.38890e7			−0.974372
$382$		0			0
$383$	1.10104e7	−	3.02508e7i	0.195978	−	0.538444i	−0.802312	−	0.596905i	$-0.796397\pi$
$383$	1.10104e7	−	3.02508e7i	0.195978	−	0.538444i	0.998290	+	0.0584606i	$0.0186192\pi$
$384$		0			0
$385$	9.92515e6	+	5.62883e7i	0.173922	+	0.986362i
$386$		0			0
$387$	2.37053e7	−	4.10588e7i	0.408990	−	0.708391i
$388$		0			0
$389$	3.14527e7	+	2.63919e7i	0.534329	+	0.448355i	0.869593	−	0.493769i	$-0.164381\pi$
$389$	3.14527e7	+	2.63919e7i	0.534329	+	0.448355i	−0.335264	+	0.942124i	$0.608826\pi$
$390$		0			0
$391$	−4.25891e7	−	7.37665e7i	−0.712472	−	1.23404i
$392$		0			0
$393$	1.43194e7	+	3.93424e7i	0.235911	+	0.648161i
$394$		0			0
$395$	4.57986e7	+	8.07553e6i	0.743124	+	0.131033i
$396$		0			0
$397$	−4.97081e7	+	4.17100e7i	−0.794429	+	0.666605i	−0.946837	−	0.321712i	$-0.895742\pi$
$397$	−4.97081e7	+	4.17100e7i	−0.794429	+	0.666605i	0.152408	+	0.988318i	$0.451297\pi$
$398$		0			0
$399$	−1.61266e7	−	3.76673e7i	−0.253877	−	0.592987i
$400$		0			0
$401$	−5.50684e7	−	6.56280e7i	−0.854022	−	1.01778i	−0.999596	−	0.0284368i	$-0.990947\pi$
$401$	−5.50684e7	−	6.56280e7i	−0.854022	−	1.01778i	0.145573	−	0.989347i	$-0.453497\pi$
$402$		0			0
$403$	−6.19632e6	+	3.51411e7i	−0.0946715	+	0.536908i
$404$		0			0
$405$	9.77737e6	−	3.55867e6i	0.147183	−	0.0535701i
$406$		0			0
$407$	−1.47575e8	+	8.52023e7i	−2.18891	+	1.26377i
$408$		0			0
$409$	5.56615e7	−	6.63348e7i	0.813551	−	0.969552i	−0.186366	−	0.982480i	$-0.559671\pi$
$409$	5.56615e7	−	6.63348e7i	0.813551	−	0.969552i	0.999916	+	0.0129283i	$0.00411531\pi$
$410$		0			0
$411$	4.72781e7	+	2.72960e7i	0.680980	+	0.393164i
$412$		0			0
$413$	−1.24510e8	+	2.19544e7i	−1.76747	+	0.311653i
$414$		0			0
$415$	−3.92786e7	−	1.42962e7i	−0.549556	−	0.200022i
$416$		0			0
$417$			355730.i			0.00490582i
$418$		0			0
$419$	1.29690e8			1.76306			0.881528	−	0.472132i	$-0.156516\pi$
$419$	1.29690e8			1.76306			0.881528	+	0.472132i	$0.156516\pi$
$420$		0			0
$421$	−3.47640e7	+	9.55134e7i	−0.465890	+	1.28002i	0.455101	+	0.890440i	$0.349603\pi$
$421$	−3.47640e7	+	9.55134e7i	−0.465890	+	1.28002i	−0.920991	+	0.389583i	$0.872619\pi$
$422$		0			0
$423$	9.71764e6	+	5.51115e7i	0.128393	+	0.728150i
$424$		0			0
$425$	−1.70821e7	+	2.95871e7i	−0.222523	+	0.385422i
$426$		0			0
$427$	−1.55665e7	−	1.30618e7i	−0.199943	−	0.167772i
$428$		0			0
$429$	3.29739e7	+	5.71124e7i	0.417636	+	0.723367i
$430$		0			0
$431$	1.47861e7	+	4.06245e7i	0.184681	+	0.507407i	0.997137	−	0.0756154i	$-0.0240921\pi$
$431$	1.47861e7	+	4.06245e7i	0.184681	+	0.507407i	−0.812456	+	0.583023i	$0.801870\pi$
$432$		0			0
$433$	3.24880e7	+	5.72850e6i	0.400183	+	0.0705631i	0.370118	−	0.928985i	$-0.379317\pi$
$433$	3.24880e7	+	5.72850e6i	0.400183	+	0.0705631i	0.0300653	+	0.999548i	$0.490428\pi$
$434$		0			0
$435$	1.69277e7	−	1.42040e7i	0.205651	−	0.172561i
$436$		0			0
$437$	6.41406e7	−	1.26852e8i	0.768579	−	1.52003i
$438$		0			0
$439$	−1.05303e8	−	1.25495e8i	−1.24465	−	1.48332i	−0.814073	−	0.580762i	$-0.802755\pi$
$439$	−1.05303e8	−	1.25495e8i	−1.24465	−	1.48332i	−0.430577	−	0.902554i	$-0.641690\pi$
$440$		0			0
$441$	−1.14057e6	+	6.46852e6i	−0.0132987	+	0.0754204i
$442$		0			0
$443$	−7.03031e7	+	2.55882e7i	−0.808655	+	0.294326i	−0.713068	−	0.701095i	$-0.752695\pi$
$443$	−7.03031e7	+	2.55882e7i	−0.808655	+	0.294326i	−0.0955867	+	0.995421i	$0.530473\pi$
$444$		0			0
$445$	−6.72116e6	+	3.88046e6i	−0.0762718	+	0.0440355i
$446$		0			0
$447$	−2.13481e7	+	2.54417e7i	−0.239022	+	0.284855i
$448$		0			0
$449$	−768127.	−	443478.i	−0.00848582	−	0.00489929i	0.495751	−	0.868465i	$-0.334893\pi$
$449$	−768127.	−	443478.i	−0.00848582	−	0.00489929i	−0.504237	+	0.863565i	$0.668226\pi$
$450$		0			0
$451$	−1.17670e8	+	2.07484e7i	−1.28274	+	0.226181i
$452$		0			0
$453$	1.62776e7	+	5.92455e6i	0.175104	+	0.0637325i
$454$		0			0
$455$		−	4.46638e7i		−	0.474156i
$456$		0			0
$457$	1.42404e8			1.49201			0.746006	−	0.665939i	$-0.231969\pi$
$457$	1.42404e8			1.49201			0.746006	+	0.665939i	$0.231969\pi$
$458$		0			0
$459$	2.92415e7	−	8.03404e7i	0.302386	−	0.830799i
$460$		0			0
$461$	2.47112e7	+	1.40144e8i	0.252227	+	1.43045i	0.803092	+	0.595855i	$0.203187\pi$
$461$	2.47112e7	+	1.40144e8i	0.252227	+	1.43045i	−0.550865	+	0.834594i	$0.685702\pi$
$462$		0			0
$463$	8.65865e7	−	1.49972e8i	0.872383	−	1.51101i	0.0128590	−	0.999917i	$-0.495907\pi$
$463$	8.65865e7	−	1.49972e8i	0.872383	−	1.51101i	0.859524	−	0.511095i	$-0.170760\pi$
$464$		0			0
$465$	2.67359e7	+	2.24341e7i	0.265911	+	0.223126i
$466$		0			0
$467$	4.36976e7	+	7.56865e7i	0.429049	+	0.743135i	0.996789	−	0.0800729i	$-0.0255153\pi$
$467$	4.36976e7	+	7.56865e7i	0.429049	+	0.743135i	−0.567740	+	0.823208i	$0.692182\pi$
$468$		0			0
$469$	−2.44853e7	−	6.72729e7i	−0.237349	−	0.652111i
$470$		0			0
$471$	−2.02039e7	−	3.56250e6i	−0.193363	−	0.0340951i
$472$		0			0
$473$	2.06282e8	−	1.73091e8i	1.94929	−	1.63565i
$474$		0			0
$475$	−5.69259e7	+	3.16006e6i	−0.531165	+	0.0294859i
$476$		0			0
$477$	9.05532e6	+	1.07917e7i	0.0834351	+	0.0994341i
$478$		0			0
$479$	1.18667e7	−	6.72995e7i	0.107975	−	0.612358i	−0.882015	−	0.471222i	$-0.843813\pi$
$479$	1.18667e7	−	6.72995e7i	0.107975	−	0.612358i	0.989990	−	0.141137i	$-0.0450757\pi$
$480$		0			0
$481$	1.25128e8	−	4.55430e7i	1.12440	−	0.409248i
$482$		0			0
$483$	−1.07215e8	+	6.19004e7i	−0.951509	+	0.549354i
$484$		0			0
$485$	−6.21682e7	+	7.40892e7i	−0.544933	+	0.649426i
$486$		0			0
$487$	1.70798e8	+	9.86105e7i	1.47876	+	0.853761i	0.999711	−	0.0240293i	$-0.00764950\pi$
$487$	1.70798e8	+	9.86105e7i	1.47876	+	0.853761i	0.479046	+	0.877790i	$0.340983\pi$
$488$		0			0
$489$	8.07993e7	−	1.42471e7i	0.691004	−	0.121843i
$490$		0			0
$491$	−9.62337e7	−	3.50262e7i	−0.812985	−	0.295903i	−0.0981290	−	0.995174i	$-0.531286\pi$
$491$	−9.62337e7	−	3.50262e7i	−0.812985	−	0.295903i	−0.714856	+	0.699271i	$0.753508\pi$
$492$		0			0
$493$		−	5.62217e7i		−	0.469206i
$494$		0			0
$495$	−6.72617e7			−0.554565
$496$		0			0
$497$	2.82507e7	−	7.76183e7i	0.230123	−	0.632259i
$498$		0			0
$499$	−1.39047e7	−	7.88577e7i	−0.111908	−	0.634662i	−0.988235	−	0.152945i	$-0.951124\pi$
$499$	−1.39047e7	−	7.88577e7i	−0.111908	−	0.634662i	0.876327	−	0.481717i	$-0.159987\pi$
$500$		0			0
$501$	4.58147e7	−	7.93534e7i	0.364327	−	0.631034i
$502$		0			0
$503$	−3.24467e7	−	2.72261e7i	−0.254957	−	0.213934i	0.506346	−	0.862330i	$-0.330996\pi$
$503$	−3.24467e7	−	2.72261e7i	−0.254957	−	0.213934i	−0.761303	+	0.648396i	$0.775440\pi$
$504$		0			0
$505$	−4.45998e7	−	7.72491e7i	−0.346305	−	0.599818i
$506$		0			0
$507$	1.35610e7	+	3.72584e7i	0.104056	+	0.285891i
$508$		0			0
$509$	−1.51160e8	−	2.66535e7i	−1.14626	−	0.202116i	−0.431917	−	0.901913i	$-0.642163\pi$
$509$	−1.51160e8	−	2.66535e7i	−1.14626	−	0.202116i	−0.714342	+	0.699797i	$0.753274\pi$
$510$		0			0
$511$	1.32666e8	−	1.11320e8i	0.994251	−	0.834275i
$512$		0			0
$513$	1.38920e8	−	3.25254e7i	1.02899	−	0.240919i
$514$		0			0
$515$	−4.28635e7	−	5.10827e7i	−0.313809	−	0.373984i
$516$		0			0
$517$	−5.51940e7	+	3.13021e8i	−0.399411	+	2.26517i
$518$		0			0
$519$	−4.85065e7	+	1.76549e7i	−0.346975	+	0.126289i
$520$		0			0
$521$	−1.75590e8	+	1.01377e8i	−1.24162	+	0.716848i	−0.969423	−	0.245394i	$-0.921083\pi$
$521$	−1.75590e8	+	1.01377e8i	−1.24162	+	0.716848i	−0.272194	+	0.962242i	$0.587749\pi$
$522$		0			0
$523$	1.26023e8	−	1.50188e8i	0.880937	−	1.04986i	−0.117449	−	0.993079i	$-0.537472\pi$
$523$	1.26023e8	−	1.50188e8i	0.880937	−	1.04986i	0.998387	−	0.0567812i	$-0.0180838\pi$
$524$		0			0
$525$	4.30029e7	+	2.48278e7i	0.297181	+	0.171577i
$526$		0			0
$527$	8.74486e7	−	1.54196e7i	0.597477	−	0.105351i
$528$		0			0
$529$	−2.64474e8	−	9.62608e7i	−1.78656	−	0.650253i
$530$		0			0
$531$		−	1.48783e8i		−	0.993732i
$532$		0			0
$533$	9.33692e7			0.616626
$534$		0			0
$535$	3.08072e7	−	8.46422e7i	0.201183	−	0.552746i
$536$		0			0
$537$	3.49628e7	+	1.98284e8i	0.225779	+	1.28045i
$538$		0			0
$539$	−1.86532e7	+	3.23084e7i	−0.119121	+	0.206324i
$540$		0			0
$541$	2.01059e8	+	1.68708e8i	1.26979	+	1.06548i	0.994567	+	0.104096i	$0.0331951\pi$
$541$	2.01059e8	+	1.68708e8i	1.26979	+	1.06548i	0.275220	+	0.961381i	$0.411249\pi$
$542$		0			0
$543$	5.03876e7	+	8.72740e7i	0.314720	+	0.545111i
$544$		0			0
$545$	5.59378e7	+	1.53688e8i	0.345554	+	0.949402i
$546$		0			0
$547$	−1.72857e7	−	3.04793e6i	−0.105615	−	0.0186227i	0.120591	−	0.992702i	$-0.461521\pi$
$547$	−1.72857e7	−	3.04793e6i	−0.105615	−	0.0186227i	−0.226206	+	0.974080i	$0.572632\pi$
$548$		0			0
$549$	1.83186e7	−	1.53711e7i	0.110707	−	0.0928941i
$550$		0			0
$551$	7.85282e7	−	5.13431e7i	0.469430	−	0.306921i
$552$		0			0
$553$	−1.10541e8	−	1.31738e8i	−0.653656	−	0.778996i
$554$		0			0
$555$	2.26161e7	−	1.28262e8i	0.132293	−	0.750273i
$556$		0			0
$557$	−3.20571e8	+	1.16678e8i	−1.85506	+	0.675187i	−0.872682	+	0.488289i	$0.837621\pi$
$557$	−3.20571e8	+	1.16678e8i	−1.85506	+	0.675187i	−0.982379	+	0.186898i	$0.940157\pi$
$558$		0			0
$559$	−1.82232e8	+	1.05212e8i	−1.04325	+	0.602323i
$560$		0			0
$561$	1.05488e8	−	1.25716e8i	0.597470	−	0.712037i
$562$		0			0
$563$	−1.79978e8	−	1.03911e8i	−1.00854	−	0.582284i	−0.0977796	−	0.995208i	$-0.531174\pi$
$563$	−1.79978e8	−	1.03911e8i	−1.00854	−	0.582284i	−0.910765	+	0.412924i	$0.864507\pi$
$564$		0			0
$565$	−8.84371e7	+	1.55938e7i	−0.490331	+	0.0864586i
$566$		0			0
$567$	−3.61558e7	−	1.31596e7i	−0.198348	−	0.0721929i
$568$		0			0
$569$		−	2.55512e8i		−	1.38699i	−0.720460	−	0.693497i	$-0.756069\pi$
$569$		−	2.55512e8i		−	1.38699i	0.720460	−	0.693497i	$-0.243931\pi$
$570$		0			0
$571$	3.74820e7			0.201333			0.100666	−	0.994920i	$-0.467903\pi$
$571$	3.74820e7			0.201333			0.100666	+	0.994920i	$0.467903\pi$
$572$		0			0
$573$	−9.03956e6	+	2.48360e7i	−0.0480489	+	0.132013i
$574$		0			0
$575$	2.99131e7	+	1.69645e8i	0.157347	+	0.892357i
$576$		0			0
$577$	−1.33663e7	+	2.31510e7i	−0.0695796	+	0.120515i	−0.898716	−	0.438530i	$-0.855499\pi$
$577$	−1.33663e7	+	2.31510e7i	−0.0695796	+	0.120515i	0.829137	+	0.559046i	$0.188832\pi$
$578$		0			0
$579$	7.27020e7	+	6.10042e7i	0.374551	+	0.314285i
$580$		0			0
$581$	7.72852e7	+	1.33862e8i	0.394065	+	0.682540i
$582$		0			0
$583$	2.73665e7	+	7.51888e7i	0.138106	+	0.379444i
$584$		0			0
$585$	5.17616e7	+	9.12697e6i	0.258547	+	0.0455889i
$586$		0			0
$587$	−2.36258e8	+	1.98244e8i	−1.16808	+	0.980137i	−0.999984	−	0.00563384i	$-0.998207\pi$
$587$	−2.36258e8	+	1.98244e8i	−1.16808	+	0.980137i	−0.168097	+	0.985770i	$0.553762\pi$
$588$		0			0
$589$	1.01398e8	+	1.08063e8i	0.496229	+	0.528849i
$590$		0			0
$591$	6.85591e7	+	8.17055e7i	0.332126	+	0.395812i
$592$		0			0
$593$	−2.27212e7	+	1.28858e8i	−0.108960	+	0.617942i	0.880605	+	0.473852i	$0.157137\pi$
$593$	−2.27212e7	+	1.28858e8i	−0.108960	+	0.617942i	−0.989565	+	0.144090i	$0.953974\pi$
$594$		0			0
$595$	−1.04443e8	+	3.80141e7i	−0.495824	+	0.180465i
$596$		0			0
$597$	−1.38232e8	+	7.98083e7i	−0.649659	+	0.375081i
$598$		0			0
$599$	−8.86014e6	+	1.05591e7i	−0.0412249	+	0.0491300i	−0.786263	−	0.617892i	$-0.787987\pi$
$599$	−8.86014e6	+	1.05591e7i	−0.0412249	+	0.0491300i	0.745038	+	0.667022i	$0.232431\pi$
$600$		0			0
$601$	3.21114e8	+	1.85396e8i	1.47923	+	0.854035i	0.999724	−	0.0235017i	$-0.00748151\pi$
$601$	3.21114e8	+	1.85396e8i	1.47923	+	0.854035i	0.479509	+	0.877537i	$0.340815\pi$
$602$		0			0
$603$	8.29673e7	−	1.46294e7i	0.378403	−	0.0667227i
$604$		0			0
$605$	−2.16634e8	−	7.88483e7i	−0.978273	−	0.356062i
$606$		0			0
$607$			3.99628e8i			1.78686i	0.449205	+	0.893429i	$0.351707\pi$
$607$			3.99628e8i			1.78686i	−0.449205	+	0.893429i	$0.648293\pi$
$608$		0			0
$609$	−8.17146e7			−0.361783
$610$		0			0
$611$	8.49497e7	−	2.33397e8i	0.372424	−	1.02323i
$612$		0			0
$613$	549889.	+	3.11858e6i	0.00238723	+	0.0135386i	0.985978	−	0.166875i	$-0.0533676\pi$
$613$	549889.	+	3.11858e6i	0.00238723	+	0.0135386i	−0.983591	+	0.180413i	$0.942256\pi$
$614$		0			0
$615$	4.56615e7	−	7.90881e7i	0.196302	−	0.340005i
$616$		0			0
$617$	1.19824e8	+	1.00545e8i	0.510140	+	0.428058i	0.861178	−	0.508303i	$-0.169727\pi$
$617$	1.19824e8	+	1.00545e8i	0.510140	+	0.428058i	−0.351038	+	0.936361i	$0.614171\pi$
$618$		0			0
$619$	8.21674e7	+	1.42318e8i	0.346440	+	0.600051i	0.985614	−	0.169011i	$-0.0540572\pi$
$619$	8.21674e7	+	1.42318e8i	0.346440	+	0.600051i	−0.639175	+	0.769062i	$0.720724\pi$
$620$		0			0
$621$	−1.47441e8	−	4.05091e8i	−0.615663	−	1.69152i
$622$		0			0
$623$	2.82632e7	+	4.98356e6i	0.116884	+	0.0206099i
$624$		0			0
$625$	−3.46014e7	+	2.90340e7i	−0.141727	+	0.118923i
$626$		0			0
$627$	2.71930e8	+	3.25348e7i	1.10320	+	0.131991i
$628$		0			0
$629$	−2.12998e8	−	2.53841e8i	−0.855899	−	1.02002i
$630$		0			0
$631$	−4.57583e7	+	2.59508e8i	−0.182130	+	1.03291i	0.747458	+	0.664309i	$0.231274\pi$
$631$	−4.57583e7	+	2.59508e8i	−0.182130	+	1.03291i	−0.929588	+	0.368601i	$0.879837\pi$
$632$		0			0
$633$	7.21366e7	−	2.62556e7i	0.284410	−	0.103517i
$634$		0			0
$635$	−2.11260e8	+	1.21971e8i	−0.825082	+	0.476361i
$636$		0			0
$637$	1.87387e7	−	2.23320e7i	0.0724973	−	0.0863989i
$638$		0			0
$639$	8.41802e7	+	4.86015e7i	0.322632	+	0.186272i
$640$		0			0
$641$	−4.28444e8	+	7.55462e7i	−1.62675	+	0.286839i	−0.911274	−	0.411801i	$-0.864900\pi$
$641$	−4.28444e8	+	7.55462e7i	−1.62675	+	0.286839i	−0.715473	+	0.698641i	$0.753789\pi$
$642$		0			0
$643$	−1.47603e8	−	5.37233e7i	−0.555218	−	0.202083i	0.0491454	−	0.998792i	$-0.484350\pi$
$643$	−1.47603e8	−	5.37233e7i	−0.555218	−	0.202083i	−0.604363	+	0.796709i	$0.706572\pi$
$644$		0			0
$645$			2.05812e8i			0.766995i
$646$		0			0
$647$	−2.40563e8			−0.888211			−0.444106	−	0.895974i	$-0.646479\pi$
$647$	−2.40563e8			−0.888211			−0.444106	+	0.895974i	$0.646479\pi$
$648$		0			0
$649$	2.89025e8	−	7.94090e8i	1.05731	−	2.90493i
$650$		0			0
$651$	−2.24113e7	−	1.27101e8i	−0.0812314	−	0.460686i
$652$		0			0
$653$	−8.22465e6	+	1.42455e7i	−0.0295378	+	0.0511609i	−0.880416	−	0.474201i	$-0.842737\pi$
$653$	−8.22465e6	+	1.42455e7i	−0.0295378	+	0.0511609i	0.850879	+	0.525362i	$0.176070\pi$
$654$		0			0
$655$	1.45183e8	+	1.21823e8i	0.516645	+	0.433517i
$656$		0			0
$657$	1.01900e8	+	1.76497e8i	0.359319	+	0.622358i
$658$		0			0
$659$	5.04313e7	+	1.38559e8i	0.176215	+	0.484148i	0.996085	−	0.0884026i	$-0.0281762\pi$
$659$	5.04313e7	+	1.38559e8i	0.176215	+	0.484148i	−0.819869	+	0.572551i	$0.805954\pi$
$660$		0			0
$661$	−2.31319e8	−	4.07878e7i	−0.800954	−	0.141230i	−0.241835	−	0.970317i	$-0.577749\pi$
$661$	−2.31319e8	−	4.07878e7i	−0.800954	−	0.141230i	−0.559119	+	0.829088i	$0.688860\pi$
$662$		0			0
$663$	−9.82380e7	+	8.24315e7i	−0.337085	+	0.282848i
$664$		0			0
$665$	−1.48476e8	−	1.11166e8i	−0.504884	−	0.378014i
$666$		0			0
$667$	−1.82218e8	−	2.17158e8i	−0.614063	−	0.731811i
$668$		0			0
$669$	−2.08552e7	+	1.18275e8i	−0.0696522	+	0.395018i
$670$		0			0
$671$	1.27631e8	−	4.64537e7i	0.422461	−	0.153763i
$672$		0			0
$673$	2.69322e8	−	1.55493e8i	0.883540	−	0.510112i	0.0117163	−	0.999931i	$-0.496270\pi$
$673$	2.69322e8	−	1.55493e8i	0.883540	−	0.510112i	0.871824	+	0.489819i	$0.162937\pi$
$674$		0			0
$675$	−1.11142e8	+	1.32454e8i	−0.361382	+	0.430678i
$676$		0			0
$677$	−2.27046e8	−	1.31085e8i	−0.731724	−	0.422461i	0.0873284	−	0.996180i	$-0.472167\pi$
$677$	−2.27046e8	−	1.31085e8i	−0.731724	−	0.422461i	−0.819053	+	0.573718i	$0.805500\pi$
$678$		0			0
$679$	3.52215e8	−	6.21050e7i	1.12512	−	0.198389i
$680$		0			0
$681$	−1.52428e8	−	5.54793e7i	−0.482641	−	0.175667i
$682$		0			0
$683$			5.83239e8i			1.83056i	0.402817	+	0.915281i	$0.368031\pi$
$683$			5.83239e8i			1.83056i	−0.402817	+	0.915281i	$0.631969\pi$
$684$		0			0
$685$	2.47125e8			0.768856
$686$		0			0
$687$	9.60382e7	−	2.63863e8i	0.296192	−	0.813782i
$688$		0			0
$689$	−1.08574e7	−	6.15754e7i	−0.0331947	−	0.188256i
$690$		0			0
$691$	2.61641e8	−	4.53176e8i	0.792998	−	1.37351i	−0.131104	−	0.991369i	$-0.541852\pi$
$691$	2.61641e8	−	4.53176e8i	0.792998	−	1.37351i	0.924103	−	0.382144i	$-0.124814\pi$
$692$		0			0
$693$	1.90536e8	+	1.59879e8i	0.572504	+	0.480388i
$694$		0			0
$695$	805152.	+	1.39456e6i	0.00239841	+	0.00415417i
$696$		0			0
$697$	−7.94681e7	−	2.18337e8i	−0.234690	−	0.644805i
$698$		0			0
$699$	−6.39412e7	−	1.12746e7i	−0.187219	−	0.0330117i
$700$		0			0
$701$	3.50124e8	−	2.93789e8i	1.01641	−	0.852866i	0.0272347	−	0.999629i	$-0.491330\pi$
$701$	3.50124e8	−	2.93789e8i	1.01641	−	0.852866i	0.989172	+	0.146763i	$0.0468854\pi$
$702$		0			0
$703$	1.60040e8	−	5.29320e8i	0.460640	−	1.52353i
$704$		0			0
$705$	−1.56154e8	−	1.86098e8i	−0.445643	−	0.531097i
$706$		0			0
$707$	−5.72782e7	+	3.24841e8i	−0.162081	+	0.919205i
$708$		0			0
$709$	−7.37349e7	+	2.68373e7i	−0.206888	+	0.0753010i	−0.443385	−	0.896331i	$-0.646223\pi$
$709$	−7.37349e7	+	2.68373e7i	−0.206888	+	0.0753010i	0.236498	+	0.971632i	$0.424000\pi$
$710$		0			0
$711$	1.75262e8	−	1.01188e8i	0.487618	−	0.281526i
$712$		0			0
$713$	2.87798e8	−	3.42984e8i	0.793997	−	0.946249i
$714$		0			0
$715$	2.58534e8	+	1.49265e8i	0.707294	+	0.408356i
$716$		0			0
$717$	8.91558e6	−	1.57206e6i	0.0241876	−	0.00426492i
$718$		0			0
$719$	2.45667e6	+	894155.i	0.00660937	+	0.00240561i	0.345323	−	0.938484i	$-0.387769\pi$
$719$	2.45667e6	+	894155.i	0.00660937	+	0.00240561i	−0.338713	+	0.940890i	$0.609992\pi$
$720$		0			0
$721$			2.46590e8i			0.657916i
$722$		0			0
$723$	3.60331e8			0.953424
$724$		0			0
$725$	−3.88883e7	+	1.06845e8i	−0.102048	+	0.280375i
$726$		0			0
$727$	5.85140e7	+	3.31849e8i	0.152285	+	0.863650i	0.961226	+	0.275761i	$0.0889298\pi$
$727$	5.85140e7	+	3.31849e8i	0.152285	+	0.863650i	−0.808941	+	0.587889i	$0.799959\pi$
$728$		0			0
$729$	1.65873e8	−	2.87300e8i	0.428146	−	0.741571i
$730$		0			0
$731$	4.01131e8	+	3.36589e8i	1.02691	+	0.861683i
$732$		0			0
$733$	−2.20880e7	−	3.82576e7i	−0.0560848	−	0.0971418i	0.836620	−	0.547784i	$-0.184528\pi$
$733$	−2.20880e7	−	3.82576e7i	−0.0560848	−	0.0971418i	−0.892705	+	0.450642i	$0.851195\pi$
$734$		0			0
$735$	−9.75217e6	−	2.67939e7i	−0.0245606	−	0.0674797i
$736$		0			0
$737$	4.71235e8	+	8.30915e7i	1.17716	+	0.207565i
$738$		0			0
$739$	−1.83323e7	+	1.53826e7i	−0.0454238	+	0.0381151i	−0.665217	−	0.746650i	$-0.731661\pi$
$739$	−1.83323e7	+	1.53826e7i	−0.0454238	+	0.0381151i	0.619793	+	0.784765i	$0.287217\pi$
$740$		0			0
$741$	−2.04850e8	−	6.19364e7i	−0.503480	−	0.152227i
$742$		0			0
$743$	−2.81994e8	−	3.36067e8i	−0.687501	−	0.819331i	0.303550	−	0.952815i	$-0.401828\pi$
$743$	−2.81994e8	−	3.36067e8i	−0.687501	−	0.819331i	−0.991051	+	0.133484i	$0.957383\pi$
$744$		0			0
$745$	−2.61066e7	+	1.48058e8i	−0.0631366	+	0.358066i
$746$		0			0
$747$	−1.70928e8	+	6.22127e7i	−0.410064	+	0.149251i
$748$		0			0
$749$	−2.88461e8	+	1.66543e8i	−0.686502	+	0.396352i
$750$		0			0
$751$	−7.60231e7	+	9.06008e7i	−0.179484	+	0.213901i	−0.848284	−	0.529542i	$-0.822364\pi$
$751$	−7.60231e7	+	9.06008e7i	−0.179484	+	0.213901i	0.668800	+	0.743443i	$0.266808\pi$
$752$		0			0
$753$	1.04236e8	+	6.01806e7i	0.244136	+	0.140952i
$754$		0			0
$755$	7.72224e7	−	1.36164e7i	0.179433	−	0.0316389i
$756$		0			0
$757$	−6.53304e8	−	2.37783e8i	−1.50601	−	0.548142i	−0.548400	−	0.836216i	$-0.684763\pi$
$757$	−6.53304e8	−	2.37783e8i	−1.50601	−	0.548142i	−0.957608	+	0.288073i	$0.906985\pi$
$758$		0			0
$759$		−	8.27477e8i		−	1.89248i
$760$		0			0
$761$	−5.47446e8			−1.24219			−0.621094	−	0.783736i	$-0.713311\pi$
$761$	−5.47446e8			−1.24219			−0.621094	+	0.783736i	$0.713311\pi$
$762$		0			0
$763$	2.06853e8	−	5.68323e8i	0.465680	−	1.27945i
$764$		0			0
$765$	−2.27125e7	−	1.28809e8i	−0.0507318	−	0.287714i
$766$		0			0
$767$	−3.30173e8	+	5.71877e8i	−0.731738	+	1.26741i
$768$		0			0
$769$	8.84758e7	+	7.42400e7i	0.194556	+	0.163252i	0.734862	−	0.678217i	$-0.237247\pi$
$769$	8.84758e7	+	7.42400e7i	0.194556	+	0.163252i	−0.540306	+	0.841469i	$0.681691\pi$
$770$		0			0
$771$	−622360.	−	1.07796e6i	−0.00135793	−	0.00235201i
$772$		0			0
$773$	−1.14554e8	−	3.14734e8i	−0.248011	−	0.681406i	−0.999759	−	0.0219546i	$-0.993011\pi$
$773$	−1.14554e8	−	3.14734e8i	−0.248011	−	0.681406i	0.751748	−	0.659451i	$-0.229211\pi$
$774$		0			0
$775$	−1.76854e8	−	3.11842e7i	−0.379936	−	0.0669930i
$776$		0			0
$777$	−3.68941e8	+	3.09578e8i	−0.786490	+	0.659944i
$778$		0			0
$779$	2.32392e8	−	3.10388e8i	0.491596	−	0.656588i
$780$		0			0
$781$	3.54877e8	+	4.22926e8i	0.744946	+	0.887792i
$782$		0			0
$783$	4.94097e7	−	2.80217e8i	0.102927	−	0.583725i
$784$		0			0
$785$	−8.72686e7	+	3.17632e7i	−0.180405	+	0.0656621i
$786$		0			0
$787$	−1.99623e7	+	1.15253e7i	−0.0409532	+	0.0236443i	−0.520337	−	0.853961i	$-0.674194\pi$
$787$	−1.99623e7	+	1.15253e7i	−0.0409532	+	0.0236443i	0.479384	+	0.877605i	$0.340860\pi$
$788$		0			0
$789$	1.24301e8	−	1.48136e8i	0.253071	−	0.301599i
$790$		0			0
$791$	2.87587e8	+	1.66039e8i	0.581086	+	0.335490i
$792$		0			0
$793$	−1.04522e8	+	1.84301e7i	−0.209599	+	0.0369579i
$794$		0			0
$795$	−5.74670e7	−	2.09163e7i	−0.114371	−	0.0416278i
$796$		0			0
$797$			3.10590e8i			0.613496i	0.951791	+	0.306748i	$0.0992409\pi$
$797$			3.10590e8i			0.613496i	−0.951791	+	0.306748i	$0.900759\pi$
$798$		0			0
$799$	−6.18084e8			−1.21173
$800$		0			0
$801$	−1.15511e7	+	3.17363e7i	−0.0224763	+	0.0617531i
$802$		0			0
$803$	2.01005e8	+	1.13996e9i	0.388204	+	2.20162i
$804$		0			0
$805$	−2.80208e8	+	4.85335e8i	−0.537148	+	0.930367i
$806$		0			0
$807$	5.32265e8	+	4.46624e8i	1.01276	+	0.849809i
$808$		0			0
$809$	−1.25973e8	−	2.18191e8i	−0.237920	−	0.412089i	0.722197	−	0.691687i	$-0.243132\pi$
$809$	−1.25973e8	−	2.18191e8i	−0.237920	−	0.412089i	−0.960117	+	0.279598i	$0.909799\pi$
$810$		0			0
$811$	1.18397e8	+	3.25292e8i	0.221961	+	0.609833i	0.999827	−	0.0185974i	$-0.00592007\pi$
$811$	1.18397e8	+	3.25292e8i	0.221961	+	0.609833i	−0.777866	+	0.628430i	$0.783698\pi$
$812$		0			0
$813$	−2.26507e8	−	3.99392e7i	−0.421511	−	0.0743238i
$814$		0			0
$815$	2.84510e8	−	2.38732e8i	0.525563	−	0.441000i
$816$		0			0
$817$	−1.03811e8	+	8.67665e8i	−0.190361	+	1.59106i
$818$		0			0
$819$	−1.24934e8	−	1.48890e8i	−0.227420	−	0.271028i
$820$		0			0
$821$	5.67713e7	−	3.21966e8i	0.102589	−	0.581809i	−0.889567	−	0.456804i	$-0.848994\pi$
$821$	5.67713e7	−	3.21966e8i	0.102589	−	0.581809i	0.992156	−	0.125005i	$-0.0398948\pi$
$822$		0			0
$823$	−4.28297e7	+	1.55887e7i	−0.0768326	+	0.0279648i	−0.380151	−	0.924925i	$-0.624128\pi$
$823$	−4.28297e7	+	1.55887e7i	−0.0768326	+	0.0279648i	0.303318	+	0.952889i	$0.401906\pi$
$824$		0			0
$825$	−2.87429e8	+	1.65947e8i	−0.511880	+	0.295534i
$826$		0			0
$827$	2.72245e8	−	3.24449e8i	0.481330	−	0.573627i	−0.469660	−	0.882847i	$-0.655624\pi$
$827$	2.72245e8	−	3.24449e8i	0.481330	−	0.573627i	0.950990	+	0.309220i	$0.100068\pi$
$828$		0			0
$829$	−2.01591e8	−	1.16389e8i	−0.353840	−	0.204290i	0.312535	−	0.949906i	$-0.398822\pi$
$829$	−2.01591e8	−	1.16389e8i	−0.353840	−	0.204290i	−0.666375	+	0.745616i	$0.732155\pi$
$830$		0			0
$831$	−5.04624e8	+	8.89788e7i	−0.879356	+	0.155054i
$832$		0			0
$833$	−6.81704e7	−	2.48120e7i	−0.117940	−	0.0429266i
$834$		0			0
$835$		−	4.14785e8i		−	0.712465i
$836$		0			0
$837$	4.49407e8			0.766414
$838$		0			0
$839$	−1.18352e8	+	3.25168e8i	−0.200396	+	0.550582i	−0.998661	−	0.0517228i	$-0.983529\pi$
$839$	−1.18352e8	+	3.25168e8i	−0.200396	+	0.550582i	0.798266	+	0.602305i	$0.205751\pi$
$840$		0			0
$841$	7.07985e7	+	4.01519e8i	0.119024	+	0.675021i
$842$		0			0
$843$	−3.25022e8	+	5.62954e8i	−0.542537	+	0.939702i
$844$		0			0
$845$	1.37493e8	+	1.15370e8i	0.227882	+	0.191216i
$846$		0			0
$847$	4.26252e8	+	7.38290e8i	0.701481	+	1.21500i
$848$		0			0
$849$	8.77160e7	+	2.40998e8i	0.143336	+	0.393813i
$850$		0			0
$851$	−1.64542e9	−	2.90132e8i	−2.66986	−	0.470768i
$852$		0			0
$853$	9.44338e8	−	7.92394e8i	1.52153	−	1.27672i	0.685430	−	0.728139i	$-0.259614\pi$
$853$	9.44338e8	−	7.92394e8i	1.52153	−	1.27672i	0.836100	−	0.548577i	$-0.184830\pi$
$854$		0			0
$855$	1.59173e8	−	1.49355e8i	0.254666	−	0.238958i
$856$		0			0
$857$	−1.88466e8	−	2.24605e8i	−0.299426	−	0.356843i	0.595263	−	0.803531i	$-0.297048\pi$
$857$	−1.88466e8	−	2.24605e8i	−0.299426	−	0.356843i	−0.894690	+	0.446688i	$0.852603\pi$
$858$		0			0
$859$	9.62360e7	−	5.45781e8i	0.151830	−	0.861072i	−0.809797	−	0.586711i	$-0.800423\pi$
$859$	9.62360e7	−	5.45781e8i	0.151830	−	0.861072i	0.961627	−	0.274361i	$-0.0884663\pi$
$860$		0			0
$861$	−3.17338e8	+	1.15502e8i	−0.497179	+	0.180958i
$862$		0			0
$863$	−1.02124e9	+	5.89616e8i	−1.58890	+	0.917353i	−0.595414	+	0.803419i	$0.703012\pi$
$863$	−1.02124e9	+	5.89616e8i	−1.58890	+	0.917353i	−0.993488	+	0.113934i	$0.963655\pi$
$864$		0			0
$865$	−1.50200e8	+	1.79001e8i	−0.232071	+	0.276572i
$866$		0			0
$867$	−1.18519e8	−	6.84272e7i	−0.181858	−	0.104996i
$868$		0			0
$869$	1.13198e9	−	1.99599e8i	1.72497	−	0.304158i
$870$		0			0
$871$	−3.51367e8	−	1.27887e8i	−0.531748	−	0.193541i
$872$		0			0
$873$			4.20879e8i			0.632579i
$874$		0			0
$875$	6.47309e8			0.966246
$876$		0			0
$877$	−1.81018e8	+	4.97344e8i	−0.268364	+	0.737323i	0.730174	+	0.683261i	$0.239439\pi$
$877$	−1.81018e8	+	4.97344e8i	−0.268364	+	0.737323i	−0.998538	+	0.0540616i	$0.982783\pi$
$878$		0			0
$879$	−3.11125e7	−	1.76448e8i	−0.0458108	−	0.259806i
$880$		0			0
$881$	3.14368e8	−	5.44501e8i	0.459738	−	0.796290i	−0.539209	−	0.842172i	$-0.681277\pi$
$881$	3.14368e8	−	5.44501e8i	0.459738	−	0.796290i	0.998947	+	0.0458824i	$0.0146100\pi$
$882$		0			0
$883$	−8.14783e8	−	6.83684e8i	−1.18348	−	0.993055i	−0.999950	−	0.0100403i	$-0.996804\pi$
$883$	−8.14783e8	−	6.83684e8i	−1.18348	−	0.993055i	−0.183527	−	0.983015i	$-0.558752\pi$
$884$		0			0
$885$	3.22938e8	+	5.59345e8i	0.465896	+	0.806956i
$886$		0			0
$887$	2.29528e8	+	6.30622e8i	0.328900	+	0.903646i	0.988391	+	0.151933i	$0.0485498\pi$
$887$	2.29528e8	+	6.30622e8i	0.328900	+	0.903646i	−0.659491	+	0.751713i	$0.729228\pi$
$888$		0			0
$889$	8.88372e8	+	1.56644e8i	1.26442	+	0.222951i
$890$		0			0
$891$	1.97005e8	−	1.65307e8i	0.278513	−	0.233700i
$892$		0			0
$893$	−5.64449e8	−	8.63314e8i	−0.792630	−	1.21231i
$894$		0			0
$895$	5.85856e8	+	6.98196e8i	0.817188	+	0.973886i
$896$		0			0
$897$	−1.12283e8	+	6.36789e8i	−0.155574	+	0.882304i
$898$		0			0
$899$	2.77704e8	−	1.01076e8i	0.382211	−	0.139113i
$900$		0			0
$901$	−1.34749e8	+	7.77971e7i	−0.184225	+	0.106363i
$902$		0			0
$903$	4.89210e8	−	5.83017e8i	0.664403	−	0.791805i
$904$		0			0
$905$	3.95068e8	+	2.28093e8i	0.532999	+	0.307727i
$906$		0			0
$907$	−5.54899e8	+	9.78437e7i	−0.743690	+	0.131133i	−0.532639	−	0.846342i	$-0.678800\pi$
$907$	−5.54899e8	+	9.78437e7i	−0.743690	+	0.131133i	−0.211051	+	0.977475i	$0.567689\pi$
$908$		0			0
$909$	−3.64759e8	−	1.32761e8i	−0.485640	−	0.176758i
$910$		0			0
$911$		−	1.45828e8i		−	0.192879i	−0.995339	−	0.0964394i	$-0.969255\pi$
$911$		−	1.45828e8i		−	0.192879i	0.995339	−	0.0964394i	$-0.0307454\pi$
$912$		0			0
$913$	−1.03314e9			−1.35752
$914$		0			0
$915$	−3.55047e7	+	9.75483e7i	−0.0463471	+	0.127338i
$916$		0			0
$917$	−1.21699e8	−	6.90192e8i	−0.157827	−	0.895080i
$918$		0			0
$919$	4.70066e8	−	8.14178e8i	0.605636	−	1.04899i	−0.386314	−	0.922367i	$-0.626252\pi$
$919$	4.70066e8	−	8.14178e8i	0.605636	−	1.04899i	0.991951	−	0.126626i	$-0.0404148\pi$
$920$		0			0
$921$	3.91227e8	+	3.28279e8i	0.500784	+	0.420207i
$922$		0			0
$923$	−2.15709e8	−	3.73619e8i	−0.274324	−	0.475143i
$924$		0			0
$925$	2.29204e8	+	6.29732e8i	0.289598	+	0.795665i
$926$		0			0
$927$	−2.85778e8	−	5.03904e7i	−0.358748	−	0.0632570i
$928$		0			0
$929$	3.36327e8	−	2.82212e8i	0.419483	−	0.351988i	−0.408483	−	0.912766i	$-0.633942\pi$
$929$	3.36327e8	−	2.82212e8i	0.419483	−	0.351988i	0.827966	+	0.560778i	$0.189498\pi$
$930$		0			0
$931$	−2.75985e7	−	1.17877e8i	−0.0342008	−	0.146076i
$932$		0			0
$933$	1.79418e8	+	2.13822e8i	0.220913	+	0.263273i
$934$		0			0
$935$	1.29002e8	−	7.31605e8i	0.157819	−	0.895038i
$936$		0			0
$937$	3.51181e8	−	1.27819e8i	0.426886	−	0.155374i	−0.119637	−	0.992818i	$-0.538173\pi$
$937$	3.51181e8	−	1.27819e8i	0.426886	−	0.155374i	0.546523	+	0.837444i	$0.315951\pi$
$938$		0			0
$939$	4.55160e8	−	2.62787e8i	0.549753	−	0.317400i
$940$		0			0
$941$	−2.52212e8	+	3.00574e8i	−0.302689	+	0.360730i	−0.895853	−	0.444351i	$-0.853434\pi$
$941$	−2.52212e8	+	3.00574e8i	−0.302689	+	0.360730i	0.593164	+	0.805082i	$0.297879\pi$
$942$		0			0
$943$	−1.01459e9	−	5.85773e8i	−1.20992	−	0.698545i
$944$		0			0
$945$	−5.53965e8	+	9.76790e7i	−0.656428	+	0.115746i
$946$		0			0
$947$	1.01806e9	+	3.70542e8i	1.19873	+	0.436303i	0.862782	−	0.505577i	$-0.168720\pi$
$947$	1.01806e9	+	3.70542e8i	1.19873	+	0.436303i	0.335951	+	0.941880i	$0.390942\pi$
$948$		0			0
$949$		−	9.04534e8i		−	1.05834i
$950$		0			0
$951$	−6.58261e7			−0.0765343
$952$		0			0
$953$	8.94360e7	−	2.45723e8i	0.103332	−	0.283902i	−0.877243	−	0.480046i	$-0.840620\pi$
$953$	8.94360e7	−	2.45723e8i	0.103332	−	0.283902i	0.980575	+	0.196145i	$0.0628422\pi$
$954$		0			0
$955$	2.07756e7	+	1.17824e8i	0.0238530	+	0.135277i
$956$		0			0
$957$	2.73087e8	−	4.73001e8i	0.311577	−	0.539668i
$958$		0			0
$959$	−7.00046e8	−	5.87409e8i	−0.793727	−	0.666016i
$960$		0			0
$961$	−2.10372e8	−	3.64375e8i	−0.237038	−	0.410562i
$962$		0			0
$963$	−1.34063e8	−	3.68336e8i	−0.150117	−	0.412444i
$964$		0			0
$965$	4.23089e8	+	7.46020e7i	0.470814	+	0.0830173i
$966$		0			0
$967$	−8.48787e8	+	7.12217e8i	−0.938684	+	0.787649i	−0.977356	−	0.211603i	$-0.932132\pi$
$967$	−8.48787e8	+	7.12217e8i	−0.938684	+	0.787649i	0.0386721	+	0.999252i	$0.487687\pi$
$968$		0			0
$969$	2.95179e7	+	5.31742e8i	0.0324425	+	0.584426i
$970$		0			0
$971$	−1.96220e8	−	2.33845e8i	−0.214331	−	0.255430i	0.648158	−	0.761506i	$-0.275540\pi$
$971$	−1.96220e8	−	2.33845e8i	−0.214331	−	0.255430i	−0.862489	+	0.506077i	$0.831095\pi$
$972$		0			0
$973$	1.03403e6	−	5.86429e6i	0.00112252	−	0.00636615i
$974$		0			0
$975$	2.43710e8	−	8.87033e7i	0.262942	−	0.0957031i
$976$		0			0
$977$	5.80818e8	−	3.35335e8i	0.622811	−	0.359580i	−0.155152	−	0.987891i	$-0.549587\pi$
$977$	5.80818e8	−	3.35335e8i	0.622811	−	0.359580i	0.777963	+	0.628311i	$0.216253\pi$
$978$		0			0
$979$	−1.23302e8	+	1.46945e8i	−0.131408	+	0.156606i
$980$		0			0
$981$	6.16370e8	+	3.55861e8i	0.652881	+	0.376941i
$982$		0			0
$983$	2.62188e8	−	4.62308e7i	0.276027	−	0.0486711i	−0.0339208	−	0.999425i	$-0.510799\pi$
$983$	2.62188e8	−	4.62308e7i	0.276027	−	0.0486711i	0.309948	+	0.950753i	$0.399688\pi$
$984$		0			0
$985$	4.53702e8	+	1.65134e8i	0.474747	+	0.172794i
$986$		0			0
$987$			8.98344e8i			0.934311i
$988$		0			0
$989$	2.64028e9			2.72937
$990$		0			0
$991$	4.24563e8	−	1.16648e9i	0.436235	−	1.19855i	−0.505688	−	0.862717i	$-0.668761\pi$
$991$	4.24563e8	−	1.16648e9i	0.436235	−	1.19855i	0.941923	−	0.335830i	$-0.109017\pi$
$992$		0			0
$993$	−1.14077e8	−	6.46963e8i	−0.116507	−	0.660742i
$994$		0			0
$995$	−3.61273e8	+	6.25743e8i	−0.366747	+	0.635224i
$996$		0			0
$997$	3.22734e8	+	2.70806e8i	0.325656	+	0.273258i	0.790927	−	0.611910i	$-0.209599\pi$
$997$	3.22734e8	+	2.70806e8i	0.325656	+	0.273258i	−0.465271	+	0.885168i	$0.654043\pi$
$998$		0			0
$999$	−8.38524e8	−	1.45237e9i	−0.841044	−	1.45673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.13.4	✓	60
19.3	odd	18	inner	76.7.j.a.41.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.13.4	✓	60	1.1	even	1	trivial
76.7.j.a.41.4	yes	60	19.3	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-6.46108 + 17.7517i) q^{3} +(14.8495 + 84.2156i) q^{5} +(158.113 - 273.859i) q^{7} +(285.070 + 239.202i) q^{9} +O(q^{10})\)	\(q+(-6.46108 + 17.7517i) q^{3} +(14.8495 + 84.2156i) q^{5} +(158.113 - 273.859i) q^{7} +(285.070 + 239.202i) q^{9} +(1056.82 + 1830.46i) q^{11} +(-564.897 - 1552.04i) q^{13} +(-1590.91 - 280.520i) q^{15} +(-3148.54 + 2641.94i) q^{17} +(-6565.47 - 1985.07i) q^{19} +(3839.88 + 4576.19i) q^{21} +(-3598.68 + 20409.1i) q^{23} +(7810.94 - 2842.95i) q^{25} +(-18014.6 + 10400.7i) q^{27} +(-8792.59 + 10478.6i) q^{29} +(-18710.1 - 10802.3i) q^{31} +(-39321.8 + 6933.50i) q^{33} +(25411.1 + 9248.89i) q^{35} +80621.8i q^{37} +31201.2 q^{39} +(-19334.7 + 53121.7i) q^{41} +(-22123.2 - 125467. i) q^{43} +(-15911.4 + 27559.4i) q^{45} +(115198. + 96662.9i) q^{47} +(8825.22 + 15285.7i) q^{49} +(-26555.8 - 72961.5i) q^{51} +(37281.2 + 6573.68i) q^{53} +(-138460. + 116182. i) q^{55} +(77658.3 - 103722. i) q^{57} +(-256993. - 306273. i) q^{59} +(11158.6 - 63283.6i) q^{61} +(110581. - 40248.2i) q^{63} +(122318. - 70620.1i) q^{65} +(145521. - 173425. i) q^{67} +(-339045. - 195748. i) q^{69} +(257237. - 45357.8i) q^{71} +(514628. + 187309. i) q^{73} +157026. i q^{75} +668384. q^{77} +(185999. - 511029. i) q^{79} +(-21128.3 - 119825. i) q^{81} +(-244399. + 423311. i) q^{83} +(-269246. - 225925. i) q^{85} +(-129203. - 223786. i) q^{87} +(31040.2 + 85282.2i) q^{89} +(-514358. - 90695.2i) q^{91} +(312647. - 262342. i) q^{93} +(69679.8 - 582392. i) q^{95} +(726988. + 866390. i) q^{97} +(-136583. + 774602. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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