LMFDB - Embedded newform 96.8.n.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,8,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, 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:	$29.9889624465$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	96.13
Dual form			96.8.n.a.37.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.68559 + 7.24987i) q^{2} +(10.3325 - 24.9447i) q^{3} +(22.8788 - 125.939i) q^{4} +(-438.852 + 181.778i) q^{5} +(91.1027 + 291.569i) q^{6} +(343.163 - 343.163i) q^{7} +(714.323 + 1259.72i) q^{8} +(-515.481 - 515.481i) q^{9} +O(q^{10})$	\(q+(-8.68559 + 7.24987i) q^{2} +(10.3325 - 24.9447i) q^{3} +(22.8788 - 125.939i) q^{4} +(-438.852 + 181.778i) q^{5} +(91.1027 + 291.569i) q^{6} +(343.163 - 343.163i) q^{7} +(714.323 + 1259.72i) q^{8} +(-515.481 - 515.481i) q^{9} +(2493.81 - 4760.47i) q^{10} +(-1260.75 - 3043.71i) q^{11} +(-2905.12 - 1871.96i) q^{12} +(-4398.91 - 1822.09i) q^{13} +(-492.685 + 5468.45i) q^{14} +12825.3i q^{15} +(-15337.1 - 5762.66i) q^{16} -8123.12i q^{17} +(8214.42 + 740.085i) q^{18} +(-51460.1 - 21315.5i) q^{19} +(12852.5 + 59427.3i) q^{20} +(-5014.39 - 12105.8i) q^{21} +(33016.8 + 17296.2i) q^{22} +(66934.5 + 66934.5i) q^{23} +(38804.1 - 4802.61i) q^{24} +(104305. - 104305. i) q^{25} +(51417.1 - 16065.6i) q^{26} +(-18184.7 + 7532.36i) q^{27} +(-35366.3 - 51068.6i) q^{28} +(1848.24 - 4462.06i) q^{29} +(-92981.4 - 111395. i) q^{30} -29713.1 q^{31} +(174990. - 61140.0i) q^{32} -88951.3 q^{33} +(58891.5 + 70554.1i) q^{34} +(-88218.0 + 212977. i) q^{35} +(-76712.6 + 53125.4i) q^{36} +(252492. - 104586. i) q^{37} +(601496. - 187942. i) q^{38} +(-90903.2 + 90903.2i) q^{39} +(-542472. - 422982. i) q^{40} +(266179. + 266179. i) q^{41} +(131319. + 68792.4i) q^{42} +(300494. + 725457. i) q^{43} +(-412166. + 89140.3i) q^{44} +(319923. + 132516. i) q^{45} +(-1.06663e6 - 96099.1i) q^{46} +1.26208e6i q^{47} +(-302218. + 323038. i) q^{48} +588022. i q^{49} +(-149752. + 1.66214e6i) q^{50} +(-202629. - 83931.8i) q^{51} +(-330114. + 512306. i) q^{52} +(23261.9 + 56159.2i) q^{53} +(103336. - 197260. i) q^{54} +(1.10656e6 + 1.10656e6i) q^{55} +(677418. + 187160. i) q^{56} +(-1.06342e6 + 1.06342e6i) q^{57} +(16296.2 + 52155.1i) q^{58} +(-1.84342e6 + 763568. i) q^{59} +(1.61520e6 + 293427. i) q^{60} +(384123. - 927356. i) q^{61} +(258075. - 215416. i) q^{62} -353788. q^{63} +(-1.07664e6 + 1.79969e6i) q^{64} +2.26169e6 q^{65} +(772594. - 644885. i) q^{66} +(1.24941e6 - 3.01634e6i) q^{67} +(-1.02302e6 - 185847. i) q^{68} +(2.36126e6 - 978067. i) q^{69} +(-777830. - 2.48940e6i) q^{70} +(946955. - 946955. i) q^{71} +(281142. - 1.01758e6i) q^{72} +(2.03632e6 + 2.03632e6i) q^{73} +(-1.43481e6 + 2.73892e6i) q^{74} +(-1.52413e6 - 3.67958e6i) q^{75} +(-3.86179e6 + 5.99315e6i) q^{76} +(-1.47713e6 - 611847. i) q^{77} +(130511. - 1.44858e6i) q^{78} -2.22455e6i q^{79} +(7.77825e6 - 259004. i) q^{80} +531441. i q^{81} +(-4.24168e6 - 382157. i) q^{82} +(1.43309e6 + 593606. i) q^{83} +(-1.63931e6 + 354540. i) q^{84} +(1.47661e6 + 3.56484e6i) q^{85} +(-7.86944e6 - 4.12248e6i) q^{86} +(-92208.0 - 92208.0i) q^{87} +(2.93365e6 - 3.76238e6i) q^{88} +(-6.58908e6 + 6.58908e6i) q^{89} +(-3.73944e6 + 1.16842e6i) q^{90} +(-2.13482e6 + 884270. i) q^{91} +(9.96103e6 - 6.89827e6i) q^{92} +(-307009. + 741185. i) q^{93} +(-9.14989e6 - 1.09619e7i) q^{94} +2.64580e7 q^{95} +(282957. - 4.99682e6i) q^{96} -1.35708e6 q^{97} +(-4.26308e6 - 5.10731e6i) q^{98} +(-919085. + 2.21887e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q+O(q^{10}) $ 224 * q	$ 224 q + 13000 q^{10} - 30672 q^{12} + 52384 q^{14} + 21112 q^{16} - 40824 q^{18} - 164000 q^{20} + 511464 q^{22} + 286832 q^{23} - 81864 q^{24} + 727960 q^{26} + 390920 q^{28} + 1429968 q^{31} - 1071320 q^{32} + 403160 q^{34} - 1633008 q^{35} + 1244920 q^{38} - 4089528 q^{40} - 732368 q^{43} + 3370472 q^{44} + 2715808 q^{46} + 2317416 q^{50} - 2993328 q^{51} - 8882216 q^{52} + 3631264 q^{53} + 157464 q^{54} + 4191008 q^{55} + 10737272 q^{56} + 7269664 q^{58} + 3671872 q^{59} - 2168208 q^{60} + 4559776 q^{61} - 10347504 q^{62} - 4000752 q^{63} - 22412520 q^{64} - 3757104 q^{66} + 776272 q^{67} + 17922136 q^{68} - 9580896 q^{69} - 1696200 q^{70} + 24697408 q^{71} - 21862880 q^{74} - 11260512 q^{75} + 5188008 q^{76} + 23828896 q^{77} - 14742648 q^{78} + 69474376 q^{80} - 6997080 q^{82} - 39909568 q^{86} - 37691824 q^{88} + 3406992 q^{91} - 684560 q^{92} + 50770592 q^{94} + 54100440 q^{96} - 52426160 q^{98}+O(q^{100}) $ 224 * q + 13000 * q^10 - 30672 * q^12 + 52384 * q^14 + 21112 * q^16 - 40824 * q^18 - 164000 * q^20 + 511464 * q^22 + 286832 * q^23 - 81864 * q^24 + 727960 * q^26 + 390920 * q^28 + 1429968 * q^31 - 1071320 * q^32 + 403160 * q^34 - 1633008 * q^35 + 1244920 * q^38 - 4089528 * q^40 - 732368 * q^43 + 3370472 * q^44 + 2715808 * q^46 + 2317416 * q^50 - 2993328 * q^51 - 8882216 * q^52 + 3631264 * q^53 + 157464 * q^54 + 4191008 * q^55 + 10737272 * q^56 + 7269664 * q^58 + 3671872 * q^59 - 2168208 * q^60 + 4559776 * q^61 - 10347504 * q^62 - 4000752 * q^63 - 22412520 * q^64 - 3757104 * q^66 + 776272 * q^67 + 17922136 * q^68 - 9580896 * q^69 - 1696200 * q^70 + 24697408 * q^71 - 21862880 * q^74 - 11260512 * q^75 + 5188008 * q^76 + 23828896 * q^77 - 14742648 * q^78 + 69474376 * q^80 - 6997080 * q^82 - 39909568 * q^86 - 37691824 * q^88 + 3406992 * q^91 - 684560 * q^92 + 50770592 * q^94 + 54100440 * q^96 - 52426160 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−8.68559	+	7.24987i	−0.767705	+	0.640804i
$2$	−8.68559	+	7.24987i	−0.767705	+	0.640804i
$3$	10.3325	−	24.9447i	0.220942	−	0.533402i
$3$	10.3325	−	24.9447i	0.220942	−	0.533402i
$4$	22.8788	−	125.939i	0.178741	−	0.983896i
$5$	−438.852	+	181.778i	−1.57008	+	0.650350i	−0.986804	−	0.161922i	$-0.948231\pi$
$5$	−438.852	+	181.778i	−1.57008	+	0.650350i	−0.583280	+	0.812271i	$0.698231\pi$
$6$	91.1027	+	291.569i	0.172188	+	0.551076i
$7$	343.163	−	343.163i	0.378144	−	0.378144i	−0.492288	−	0.870432i	$-0.663839\pi$
$7$	343.163	−	343.163i	0.378144	−	0.378144i	0.870432	+	0.492288i	$0.163839\pi$
$8$	714.323	+	1259.72i	0.493264	+	0.869879i
$9$	−515.481	−	515.481i	−0.235702	−	0.235702i
$10$	2493.81	−	4760.47i	0.788613	−	1.50539i
$11$	−1260.75	−	3043.71i	−0.285597	−	0.689492i	0.714350	−	0.699789i	$-0.246722\pi$
$11$	−1260.75	−	3043.71i	−0.285597	−	0.689492i	−0.999947	+	0.0102965i	$0.996722\pi$
$12$	−2905.12	−	1871.96i	−0.485321	−	0.312725i
$13$	−4398.91	−	1822.09i	−0.555321	−	0.230021i	0.0873317	−	0.996179i	$-0.472166\pi$
$13$	−4398.91	−	1822.09i	−0.555321	−	0.230021i	−0.642652	+	0.766158i	$0.722166\pi$
$14$	−492.685	+	5468.45i	−0.0479867	+	0.532619i
$15$			12825.3i			0.981175i
$16$	−15337.1	−	5762.66i	−0.936103	−	0.351725i
$17$		−	8123.12i		−	0.401007i	−0.979693	−	0.200503i	$-0.935742\pi$
$17$		−	8123.12i		−	0.401007i	0.979693	−	0.200503i	$-0.0642578\pi$
$18$	8214.42	+	740.085i	0.331989	+	0.0299108i
$19$	−51460.1	−	21315.5i	−1.72121	−	0.712947i	−0.999791	−	0.0204451i	$-0.993492\pi$
$19$	−51460.1	−	21315.5i	−1.72121	−	0.712947i	−0.721416	−	0.692502i	$-0.756508\pi$
$20$	12852.5	+	59427.3i	0.359239	+	1.66104i
$21$	−5014.39	−	12105.8i	−0.118155	−	0.285251i
$22$	33016.8	+	17296.2i	0.661083	+	0.346315i
$23$	66934.5	+	66934.5i	1.14710	+	1.14710i	0.987120	+	0.159985i	$0.0511445\pi$
$23$	66934.5	+	66934.5i	1.14710	+	1.14710i	0.159985	+	0.987120i	$0.448856\pi$
$24$	38804.1	−	4802.61i	0.572979	−	0.0709150i
$25$	104305.	−	104305.i	1.33510	−	1.33510i
$26$	51417.1	−	16065.6i	0.573721	−	0.179263i
$27$	−18184.7	+	7532.36i	−0.177801	+	0.0736475i
$28$	−35366.3	−	51068.6i	−0.304464	−	0.439644i
$29$	1848.24	−	4462.06i	0.0140723	−	0.0339736i	−0.916687	−	0.399606i	$-0.869147\pi$
$29$	1848.24	−	4462.06i	0.0140723	−	0.0339736i	0.930760	+	0.365632i	$0.119147\pi$
$30$	−92981.4	−	111395.i	−0.628741	−	0.753253i
$31$	−29713.1			−0.179135			−0.0895677	−	0.995981i	$-0.528549\pi$
$31$	−29713.1			−0.179135			−0.0895677	+	0.995981i	$0.528549\pi$
$32$	174990.	−	61140.0i	0.944038	−	0.329838i
$33$	−88951.3			−0.430877
$34$	58891.5	+	70554.1i	0.256967	+	0.307855i
$35$	−88218.0	+	212977.i	−0.347791	+	0.839643i
$36$	−76712.6	+	53125.4i	−0.274036	+	0.189777i
$37$	252492.	−	104586.i	0.819486	−	0.339442i	0.0667543	−	0.997769i	$-0.478736\pi$
$37$	252492.	−	104586.i	0.819486	−	0.339442i	0.752732	+	0.658327i	$0.228736\pi$
$38$	601496.	−	187942.i	1.77824	−	0.555623i
$39$	−90903.2	+	90903.2i	−0.245388	+	0.245388i
$40$	−542472.	−	422982.i	−1.34019	−	1.04499i
$41$	266179.	+	266179.i	0.603156	+	0.603156i	0.941149	−	0.337993i	$-0.109748\pi$
$41$	266179.	+	266179.i	0.603156	+	0.603156i	−0.337993	+	0.941149i	$0.609748\pi$
$42$	131319.	+	68792.4i	0.273498	+	0.143274i
$43$	300494.	+	725457.i	0.576364	+	1.39146i	0.896055	+	0.443943i	$0.146421\pi$
$43$	300494.	+	725457.i	0.576364	+	1.39146i	−0.319691	+	0.947522i	$0.603579\pi$
$44$	−412166.	+	89140.3i	−0.729436	+	0.157757i
$45$	319923.	+	132516.i	0.523361	+	0.216783i
$46$	−1.06663e6	−	96099.1i	−1.61571	−	0.145568i
$47$			1.26208e6i			1.77314i	0.462593	+	0.886571i	$0.346919\pi$
$47$			1.26208e6i			1.77314i	−0.462593	+	0.886571i	$0.653081\pi$
$48$	−302218.	+	323038.i	−0.394436	+	0.421609i
$49$			588022.i			0.714015i
$50$	−149752.	+	1.66214e6i	−0.169425	+	1.88050i
$51$	−202629.	−	83931.8i	−0.213898	−	0.0885994i
$52$	−330114.	+	512306.i	−0.325576	+	0.505264i
$53$	23261.9	+	56159.2i	0.0214625	+	0.0518150i	0.934247	−	0.356625i	$-0.116073\pi$
$53$	23261.9	+	56159.2i	0.0214625	+	0.0518150i	−0.912785	+	0.408440i	$0.866073\pi$
$54$	103336.	−	197260.i	0.0893048	−	0.170475i
$55$	1.10656e6	+	1.10656e6i	0.896822	+	0.896822i
$56$	677418.	+	187160.i	0.515464	+	0.142415i
$57$	−1.06342e6	+	1.06342e6i	−0.760575	+	0.760575i
$58$	16296.2	+	52155.1i	0.0109670	+	0.0350993i
$59$	−1.84342e6	+	763568.i	−1.16853	+	0.484023i	−0.880708	−	0.473660i	$-0.842933\pi$
$59$	−1.84342e6	+	763568.i	−1.16853	+	0.484023i	−0.287826	+	0.957683i	$0.592933\pi$
$60$	1.61520e6	+	293427.i	0.965375	+	0.175376i
$61$	384123.	−	927356.i	0.216679	−	0.523109i	−0.777743	−	0.628582i	$-0.783636\pi$
$61$	384123.	−	927356.i	0.216679	−	0.523109i	0.994422	+	0.105473i	$0.0336357\pi$
$62$	258075.	−	215416.i	0.137523	−	0.114791i
$63$	−353788.			−0.178259
$64$	−1.07664e6	+	1.79969e6i	−0.513380	+	0.858161i
$65$	2.26169e6			1.02149
$66$	772594.	−	644885.i	0.330786	−	0.276108i
$67$	1.24941e6	−	3.01634e6i	0.507507	−	1.22523i	−0.437807	−	0.899069i	$-0.644245\pi$
$67$	1.24941e6	−	3.01634e6i	0.507507	−	1.22523i	0.945314	−	0.326162i	$-0.105755\pi$
$68$	−1.02302e6	−	185847.i	−0.394549	−	0.0716762i
$69$	2.36126e6	−	978067.i	0.865312	−	0.358424i
$70$	−777830.	−	2.48940e6i	−0.271045	−	0.867464i
$71$	946955.	−	946955.i	0.313997	−	0.313997i	−0.532459	−	0.846456i	$-0.678732\pi$
$71$	946955.	−	946955.i	0.313997	−	0.313997i	0.846456	+	0.532459i	$0.178732\pi$
$72$	281142.	−	1.01758e6i	0.0887690	−	0.321296i
$73$	2.03632e6	+	2.03632e6i	0.612656	+	0.612656i	0.943637	−	0.330981i	$-0.107380\pi$
$73$	2.03632e6	+	2.03632e6i	0.612656	+	0.612656i	−0.330981	+	0.943637i	$0.607380\pi$
$74$	−1.43481e6	+	2.73892e6i	−0.411607	+	0.785721i
$75$	−1.52413e6	−	3.67958e6i	−0.417165	−	1.00712i
$76$	−3.86179e6	+	5.99315e6i	−1.00912	+	1.56606i
$77$	−1.47713e6	−	611847.i	−0.368724	−	0.152730i
$78$	130511.	−	1.44858e6i	0.0311399	−	0.345631i
$79$		−	2.22455e6i		−	0.507630i	−0.967253	−	0.253815i	$-0.918315\pi$
$79$		−	2.22455e6i		−	0.507630i	0.967253	−	0.253815i	$-0.0816854\pi$
$80$	7.77825e6	−	259004.i	1.69850	−	0.0565576i
$81$			531441.i			0.111111i
$82$	−4.24168e6	−	382157.i	−0.849550	−	0.0765409i
$83$	1.43309e6	+	593606.i	0.275107	+	0.113953i	0.515971	−	0.856606i	$-0.327431\pi$
$83$	1.43309e6	+	593606.i	0.275107	+	0.113953i	−0.240865	+	0.970559i	$0.577431\pi$
$84$	−1.63931e6	+	354540.i	−0.301776	+	0.0652660i
$85$	1.47661e6	+	3.56484e6i	0.260795	+	0.629614i
$86$	−7.86944e6	−	4.12248e6i	−1.33413	−	0.698898i
$87$	−92208.0	−	92208.0i	−0.0150124	−	0.0150124i
$88$	2.93365e6	−	3.76238e6i	0.458900	−	0.588537i
$89$	−6.58908e6	+	6.58908e6i	−0.990740	+	0.990740i	−0.999958	−	0.00921764i	$-0.997066\pi$
$89$	−6.58908e6	+	6.58908e6i	−0.990740	+	0.990740i	0.00921764	+	0.999958i	$0.497066\pi$
$90$	−3.73944e6	+	1.16842e6i	−0.540702	+	0.168946i
$91$	−2.13482e6	+	884270.i	−0.296972	+	0.123010i
$92$	9.96103e6	−	6.89827e6i	1.33367	−	0.923597i
$93$	−307009.	+	741185.i	−0.0395786	+	0.0955512i
$94$	−9.14989e6	−	1.09619e7i	−1.13624	−	1.36125i
$95$	2.64580e7			3.16610
$96$	282957.	−	4.99682e6i	0.0326416	−	0.576427i
$97$	−1.35708e6			−0.150975			−0.0754876	−	0.997147i	$-0.524051\pi$
$97$	−1.35708e6			−0.150975			−0.0754876	+	0.997147i	$0.524051\pi$
$98$	−4.26308e6	−	5.10731e6i	−0.457543	−	0.548152i
$99$	−919085.	+	2.21887e6i	−0.0951990	+	0.229831i
$100$	−1.07496e7	−	1.55224e7i	−1.07496	−	1.55224i
$101$	1.72927e7	−	7.16287e6i	1.67008	−	0.691771i	0.671305	−	0.741181i	$-0.265734\pi$
$101$	1.72927e7	−	7.16287e6i	1.67008	−	0.691771i	0.998779	+	0.0494103i	$0.0157342\pi$
$102$	2.36845e6	−	740038.i	0.220985	−	0.0690484i
$103$	−1.96321e6	+	1.96321e6i	−0.177026	+	0.177026i	−0.790058	−	0.613032i	$-0.789950\pi$
$103$	−1.96321e6	+	1.96321e6i	−0.177026	+	0.177026i	0.613032	+	0.790058i	$0.289950\pi$
$104$	−846923.	−	6.84296e6i	−0.0738291	−	0.596523i
$105$	4.40115e6	+	4.40115e6i	0.371025	+	0.371025i
$106$	−609190.	−	319130.i	−0.0496801	−	0.0260254i
$107$	4.72770e6	+	1.14137e7i	0.373084	+	0.900705i	0.993224	+	0.116214i	$0.0370758\pi$
$107$	4.72770e6	+	1.14137e7i	0.373084	+	0.900705i	−0.620140	+	0.784491i	$0.712924\pi$
$108$	532571.	+	2.46249e6i	0.0406812	+	0.188101i
$109$	4.59461e6	+	1.90315e6i	0.339826	+	0.140760i	0.546069	−	0.837740i	$-0.316124\pi$
$109$	4.59461e6	+	1.90315e6i	0.339826	+	0.140760i	−0.206243	+	0.978501i	$0.566124\pi$
$110$	−1.76336e7	−	1.58871e6i	−1.26318	−	0.113807i
$111$		−	7.37898e6i		−	0.512113i
$112$	−7.24066e6	+	3.28560e6i	−0.486984	+	0.220979i
$113$			1.28425e7i			0.837289i	0.908150	+	0.418645i	$0.137495\pi$
$113$			1.28425e7i			0.837289i	−0.908150	+	0.418645i	$0.862505\pi$
$114$	1.52677e6	−	1.69461e7i	0.0965175	−	1.07128i
$115$	−4.15416e7	−	1.72071e7i	−2.54707	−	1.05503i
$116$	−519660.	−	334852.i	−0.0309112	−	0.0199182i
$117$	1.32830e6	+	3.20681e6i	0.0766738	+	0.185107i
$118$	1.04754e7	−	1.99966e7i	0.586926	−	1.12039i
$119$	−2.78755e6	−	2.78755e6i	−0.151638	−	0.151638i
$120$	−1.61562e7	+	9.16138e6i	−0.853504	+	0.483979i
$121$	6.10481e6	−	6.10481e6i	0.313273	−	0.313273i
$122$	3.38687e6	+	1.08395e7i	0.168865	+	0.540442i
$123$	9.39003e6	−	3.88948e6i	0.454987	−	0.188462i
$124$	−679800.	+	3.74202e6i	−0.0320188	+	0.176251i
$125$	−1.26125e7	+	3.04493e7i	−0.577586	+	1.39442i
$126$	3.07285e6	−	2.56491e6i	0.136850	−	0.114229i
$127$	1.06282e7			0.460413			0.230206	−	0.973142i	$-0.426060\pi$
$127$	1.06282e7			0.460413			0.230206	+	0.973142i	$0.426060\pi$
$128$	−3.69632e6	−	2.34369e7i	−0.155788	−	0.987790i
$129$	2.12012e7			0.869553
$130$	−1.96441e7	+	1.63969e7i	−0.784206	+	0.654577i
$131$	3.15629e6	−	7.61997e6i	0.122667	−	0.296144i	−0.850603	−	0.525809i	$-0.823763\pi$
$131$	3.15629e6	−	7.61997e6i	0.122667	−	0.296144i	0.973270	+	0.229664i	$0.0737628\pi$
$132$	−2.03510e6	+	1.12024e7i	−0.0770153	+	0.423938i
$133$	−2.49739e7	+	1.03445e7i	−0.920460	+	0.381267i
$134$	1.10162e7	+	3.52567e7i	0.395517	+	1.26583i
$135$	6.61117e6	−	6.61117e6i	0.231265	−	0.231265i
$136$	1.02329e7	−	5.80253e6i	0.348827	−	0.197802i
$137$	−3.70950e7	−	3.70950e7i	−1.23252	−	1.23252i	−0.962993	−	0.269525i	$-0.913133\pi$
$137$	−3.70950e7	−	3.70950e7i	−1.23252	−	1.23252i	−0.269525	−	0.962993i	$-0.586867\pi$
$138$	−1.34181e7	+	2.56139e7i	−0.434624	+	0.829659i
$139$	1.46632e7	+	3.54002e7i	0.463103	+	1.11803i	0.967116	+	0.254334i	$0.0818563\pi$
$139$	1.46632e7	+	3.54002e7i	0.463103	+	1.11803i	−0.504013	+	0.863696i	$0.668144\pi$
$140$	2.48037e7	+	1.59827e7i	0.763957	+	0.492269i
$141$	3.14822e7	+	1.30404e7i	0.945797	+	0.391762i
$142$	−1.35956e6	+	1.50902e7i	−0.0398464	+	0.442267i
$143$			1.56862e7i			0.448583i
$144$	4.93545e6	+	1.08765e7i	0.137739	+	0.303544i
$145$			2.29415e6i			0.0624934i
$146$	−3.24498e7	−	2.92359e6i	−0.862932	−	0.0777465i
$147$	1.46681e7	+	6.07571e6i	0.380857	+	0.157756i
$148$	−7.39466e6	−	3.41913e7i	−0.187500	−	0.866962i
$149$	−1.41711e7	−	3.42121e7i	−0.350956	−	0.847282i	−0.996503	−	0.0835614i	$-0.973371\pi$
$149$	−1.41711e7	−	3.42121e7i	−0.350956	−	0.847282i	0.645547	−	0.763721i	$-0.276629\pi$
$150$	3.99144e7	+	2.09095e7i	0.965629	+	0.505854i
$151$	−2.57740e7	−	2.57740e7i	−0.609203	−	0.609203i	0.333535	−	0.942738i	$-0.391758\pi$
$151$	−2.57740e7	−	2.57740e7i	−0.609203	−	0.609203i	−0.942738	+	0.333535i	$0.891758\pi$
$152$	−9.90762e6	−	8.00515e7i	−0.228832	−	1.84891i
$153$	−4.18731e6	+	4.18731e6i	−0.0945182	+	0.0945182i
$154$	1.72656e7	−	5.39475e6i	0.380941	−	0.119028i
$155$	1.30396e7	−	5.40119e6i	0.281258	−	0.116501i
$156$	9.36847e6	+	1.35280e7i	0.197575	+	0.285297i
$157$	−3.19125e7	+	7.70436e7i	−0.658130	+	1.58887i	0.142558	+	0.989786i	$0.454467\pi$
$157$	−3.19125e7	+	7.70436e7i	−0.658130	+	1.58887i	−0.800689	+	0.599081i	$0.795533\pi$
$158$	1.61277e7	+	1.93215e7i	0.325291	+	0.389710i
$159$	1.64123e6			0.0323802
$160$	−6.56809e7	+	5.86409e7i	−1.26771	+	1.13183i
$161$	4.59389e7			0.867540
$162$	−3.85288e6	−	4.61588e6i	−0.0712004	−	0.0853005i
$163$	3.44384e7	−	8.31416e7i	0.622854	−	1.50370i	−0.225484	−	0.974247i	$-0.572396\pi$
$163$	3.44384e7	−	8.31416e7i	0.622854	−	1.50370i	0.848338	−	0.529456i	$-0.177604\pi$
$164$	3.96120e7	−	2.74323e7i	0.701251	−	0.485634i
$165$	3.90364e7	−	1.61694e7i	0.676513	−	0.280221i
$166$	−1.67508e7	+	5.23391e6i	−0.284222	+	0.0888072i
$167$	2.20456e7	−	2.20456e7i	0.366280	−	0.366280i	−0.499838	−	0.866119i	$-0.666607\pi$
$167$	2.20456e7	−	2.20456e7i	0.366280	−	0.366280i	0.866119	+	0.499838i	$0.166607\pi$
$168$	1.16680e7	−	1.49642e7i	0.189852	−	0.243484i
$169$	−2.83395e7	−	2.83395e7i	−0.451636	−	0.451636i
$170$	−3.86698e7	−	2.02576e7i	−0.603672	−	0.316239i
$171$	1.55390e7	+	3.75144e7i	0.237649	+	0.573736i
$172$	9.82381e7	−	2.12463e7i	1.47208	−	0.318370i
$173$	1.74256e7	+	7.21794e6i	0.255875	+	0.105987i	0.506934	−	0.861985i	$-0.330779\pi$
$173$	1.74256e7	+	7.21794e6i	0.255875	+	0.105987i	−0.251059	+	0.967972i	$0.580779\pi$
$174$	1.46938e6	+	132385.i	0.0211451	+	0.00190509i
$175$		−	7.15869e7i		−	1.00972i
$176$	1.79635e6	+	5.39470e7i	0.0248369	+	0.745887i
$177$			5.38731e7i			0.730240i
$178$	9.46006e6	−	1.05000e8i	0.125726	−	1.39547i
$179$	−4.27196e7	−	1.76950e7i	−0.556726	−	0.230604i	0.0865369	−	0.996249i	$-0.472420\pi$
$179$	−4.27196e7	−	1.76950e7i	−0.556726	−	0.230604i	−0.643263	+	0.765645i	$0.722420\pi$
$180$	2.40084e7	−	3.72588e7i	0.306838	−	0.476185i
$181$	5.92514e7	+	1.43045e8i	0.742717	+	1.79308i	0.594454	+	0.804129i	$0.297368\pi$
$181$	5.92514e7	+	1.43045e8i	0.742717	+	1.79308i	0.148262	+	0.988948i	$0.452632\pi$
$182$	1.21313e7	−	2.31575e7i	0.149162	−	0.284736i
$183$	−1.91637e7	−	1.91637e7i	−0.231154	−	0.231154i
$184$	−3.65059e7	+	1.32132e8i	−0.432017	+	1.56367i
$185$	−9.17951e7	+	9.17951e7i	−1.06591	+	1.06591i
$186$	−2.70694e6	−	8.66340e6i	−0.0308449	−	0.0987172i
$187$	−2.47244e7	+	1.02412e7i	−0.276491	+	0.114526i
$188$	1.58944e8	+	2.88748e7i	1.74459	+	0.316933i
$189$	−3.65549e6	+	8.82514e6i	−0.0393849	+	0.0950835i
$190$	−2.29804e8	+	1.91817e8i	−2.43063	+	2.02885i
$191$	−2.01242e7			−0.208979			−0.104489	−	0.994526i	$-0.533321\pi$
$191$	−2.01242e7			−0.208979			−0.104489	+	0.994526i	$0.533321\pi$
$192$	3.37686e7	+	4.54517e7i	0.344317	+	0.463442i
$193$	1.66130e8			1.66340			0.831699	−	0.555226i	$-0.187368\pi$
$193$	1.66130e8			1.66340			0.831699	+	0.555226i	$0.187368\pi$
$194$	1.17871e7	−	9.83869e6i	0.115904	−	0.0967456i
$195$	2.33688e7	−	5.64172e7i	0.225691	−	0.544867i
$196$	7.40547e7	+	1.34532e7i	0.702516	+	0.127624i
$197$	−8.38345e7	+	3.47254e7i	−0.781252	+	0.323605i	−0.737421	−	0.675434i	$-0.763956\pi$
$197$	−8.38345e7	+	3.47254e7i	−0.781252	+	0.323605i	−0.0438314	+	0.999039i	$0.513956\pi$
$198$	−8.10370e6	−	2.59354e7i	−0.0741917	−	0.237446i
$199$	−1.99535e7	+	1.99535e7i	−0.179487	+	0.179487i	−0.791132	−	0.611645i	$-0.790508\pi$
$199$	−1.99535e7	+	1.99535e7i	−0.179487	+	0.179487i	0.611645	+	0.791132i	$0.290508\pi$
$200$	2.05902e8	+	5.68874e7i	1.81993	+	0.502819i
$201$	−6.23323e7	−	6.23323e7i	−0.541411	−	0.541411i
$202$	−9.82674e7	+	1.87584e8i	−0.838841	+	1.60127i
$203$	−896963.	−	2.16546e6i	−0.00752555	−	0.0181683i
$204$	−1.52062e7	+	2.35986e7i	−0.125405	+	0.194617i
$205$	−1.65198e8	−	6.84274e7i	−1.33927	−	0.554743i
$206$	2.81862e6	−	3.12847e7i	0.0224647	−	0.249343i
$207$		−	6.90069e7i		−	0.540750i
$208$	5.69666e7	+	5.32950e7i	0.438933	+	0.410644i
$209$			1.83503e8i			1.39037i
$210$	−7.01343e7	−	6.31881e6i	−0.522592	−	0.0470834i
$211$	−1.78205e8	−	7.38149e7i	−1.30596	−	0.540948i	−0.382260	−	0.924055i	$-0.624854\pi$
$211$	−1.78205e8	−	7.38149e7i	−1.30596	−	0.540948i	−0.923704	+	0.383107i	$0.874854\pi$
$212$	7.60483e6	−	1.64472e6i	0.0548168	−	0.0118554i
$213$	−1.38372e7	−	3.34059e7i	−0.0981114	−	0.236862i
$214$	−1.23811e8	−	6.48593e7i	−0.863594	−	0.452402i
$215$	−2.63745e8	−	2.63745e8i	−1.80988	−	1.80988i
$216$	−2.24784e7	−	1.75271e7i	−0.151767	−	0.118337i
$217$	−1.01964e7	+	1.01964e7i	−0.0677389	+	0.0677389i
$218$	−5.37045e7	+	1.67804e7i	−0.351086	+	0.109699i
$219$	7.18358e7	−	2.97554e7i	0.462154	−	0.191430i
$220$	1.64676e8	−	1.14042e8i	1.04268	−	0.722081i
$221$	−1.48011e7	+	3.57329e7i	−0.0922401	+	0.222687i
$222$	5.34966e7	+	6.40907e7i	0.328164	+	0.393151i
$223$	2.07057e8			1.25033			0.625164	−	0.780494i	$-0.285032\pi$
$223$	2.07057e8			1.25033			0.625164	+	0.780494i	$0.285032\pi$
$224$	3.90692e7	−	8.10311e7i	0.232256	−	0.481708i
$225$	−1.07534e8			−0.629372
$226$	−9.31065e7	−	1.11545e8i	−0.536538	−	0.642791i
$227$	−6.68937e7	+	1.61496e8i	−0.379573	+	0.916369i	0.612473	+	0.790491i	$0.290175\pi$
$227$	−6.68937e7	+	1.61496e8i	−0.379573	+	0.916369i	−0.992046	+	0.125878i	$0.959825\pi$
$228$	1.09596e8	+	1.58255e8i	0.612381	+	0.884273i
$229$	5.15479e7	−	2.13519e7i	0.283653	−	0.117493i	−0.236321	−	0.971675i	$-0.575942\pi$
$229$	5.15479e7	−	2.13519e7i	0.283653	−	0.117493i	0.519974	+	0.854182i	$0.325942\pi$
$230$	4.85562e8	−	1.51717e8i	2.63146	−	0.822219i
$231$	−3.05248e7	+	3.05248e7i	−0.162933	+	0.162933i
$232$	6.94119e6	−	859080.i	0.0364944	−	0.00451675i
$233$	2.02845e8	+	2.02845e8i	1.05056	+	1.05056i	0.998652	+	0.0519033i	$0.0165288\pi$
$233$	2.02845e8	+	2.02845e8i	1.05056	+	1.05056i	0.0519033	+	0.998652i	$0.483471\pi$
$234$	−3.47860e7	−	1.82230e7i	−0.177480	−	0.0929745i
$235$	−2.29418e8	−	5.53865e8i	−1.15316	−	2.78398i
$236$	5.39876e7	+	2.49627e8i	0.267363	+	1.23623i
$237$	−5.54908e7	−	2.29850e7i	−0.270771	−	0.112157i
$238$	4.44209e7	+	4.00214e6i	0.213584	+	0.0192430i
$239$		−	1.41448e8i		−	0.670197i	−0.942183	−	0.335099i	$-0.891230\pi$
$239$		−	1.41448e8i		−	0.670197i	0.942183	−	0.335099i	$-0.108770\pi$
$240$	7.39076e7	−	1.96703e8i	0.345104	−	0.918482i
$241$			8.26883e7i			0.380526i	0.981733	+	0.190263i	$0.0609341\pi$
$241$			8.26883e7i			0.380526i	−0.981733	+	0.190263i	$0.939066\pi$
$242$	−8.76478e6	+	9.72829e7i	−0.0397546	+	0.441248i
$243$	1.32567e7	+	5.49109e6i	0.0592669	+	0.0245492i
$244$	−1.08002e8	−	6.95928e7i	−0.475955	−	0.306690i
$245$	−1.06890e8	−	2.58054e8i	−0.464359	−	1.12106i
$246$	−5.33597e7	+	1.01859e8i	−0.228529	+	0.436241i
$247$	1.87530e8	+	1.87530e8i	0.791829	+	0.791829i
$248$	−2.12247e7	−	3.74301e7i	−0.0883611	−	0.155826i
$249$	2.96147e7	−	2.96147e7i	0.121565	−	0.121565i
$250$	−1.11206e8	−	3.55909e8i	−0.450132	−	1.44062i
$251$	−1.13528e8	+	4.70247e7i	−0.453152	+	0.187702i	−0.597573	−	0.801815i	$-0.703868\pi$
$251$	−1.13528e8	+	4.70247e7i	−0.453152	+	0.187702i	0.144421	+	0.989516i	$0.453868\pi$
$252$	−8.09424e6	+	4.45555e7i	−0.0318621	+	0.175388i
$253$	1.19342e8	−	2.88117e8i	0.463310	−	1.11853i
$254$	−9.23123e7	+	7.70532e7i	−0.353461	+	0.295034i
$255$	1.04181e8			0.393458
$256$	2.02019e8	+	1.76765e8i	0.752579	+	0.658501i
$257$	−2.93803e8			−1.07967			−0.539835	−	0.841771i	$-0.681513\pi$
$257$	−2.93803e8			−1.07967			−0.539835	+	0.841771i	$0.681513\pi$
$258$	−1.84145e8	+	1.53706e8i	−0.667560	+	0.557213i
$259$	5.07560e7	−	1.22536e8i	0.181526	−	0.438242i
$260$	5.17447e7	−	2.84834e8i	0.182583	−	1.00504i
$261$	−3.25284e6	+	1.34737e6i	−0.0113245	+	0.00469078i
$262$	2.78295e7	+	8.90666e7i	0.0955985	+	0.305957i
$263$	−3.27543e7	+	3.27543e7i	−0.111026	+	0.111026i	−0.760437	−	0.649412i	$-0.775015\pi$
$263$	−3.27543e7	+	3.27543e7i	−0.111026	+	0.111026i	0.649412	+	0.760437i	$0.275015\pi$
$264$	−6.35399e7	−	1.12054e8i	−0.212536	−	0.374811i
$265$	−2.04171e7	−	2.04171e7i	−0.0673958	−	0.0673958i
$266$	1.41916e8	−	2.70905e8i	0.462324	−	0.882535i
$267$	9.62816e7	+	2.32444e8i	0.309566	+	0.747359i
$268$	−3.51289e8	−	2.26359e8i	−1.11479	−	0.718333i
$269$	3.61939e8	+	1.49920e8i	1.13371	+	0.469599i	0.869041	−	0.494740i	$-0.164737\pi$
$269$	3.61939e8	+	1.49920e8i	1.13371	+	0.469599i	0.264671	+	0.964339i	$0.414737\pi$
$270$	−9.49178e6	+	1.05352e8i	−0.0293477	+	0.325739i
$271$			5.71070e8i			1.74300i	0.490396	+	0.871499i	$0.336852\pi$
$271$			5.71070e8i			1.74300i	−0.490396	+	0.871499i	$0.663148\pi$
$272$	−4.68108e7	+	1.24585e8i	−0.141044	+	0.375384i
$273$			6.23891e7i			0.185584i
$274$	5.91126e8	+	5.32580e7i	1.73601	+	0.156408i
$275$	−4.48975e8	−	1.85972e8i	−1.30184	−	0.539240i
$276$	−6.91536e7	−	3.19751e8i	−0.197985	−	0.915442i
$277$	−1.16332e8	−	2.80850e8i	−0.328866	−	0.793953i	−0.998677	−	0.0514215i	$-0.983625\pi$
$277$	−1.16332e8	−	2.80850e8i	−0.328866	−	0.793953i	0.669811	−	0.742532i	$-0.266375\pi$
$278$	−3.84005e8	−	2.01165e8i	−1.07196	−	0.561559i
$279$	1.53165e7	+	1.53165e7i	0.0422226	+	0.0422226i
$280$	−3.31308e8	+	4.10045e7i	−0.901941	+	0.111629i
$281$	−3.51339e8	+	3.51339e8i	−0.944615	+	0.944615i	−0.998545	−	0.0539298i	$-0.982825\pi$
$281$	−3.51339e8	+	3.51339e8i	−0.944615	+	0.944615i	0.0539298	+	0.998545i	$0.482825\pi$
$282$	−3.67982e8	+	1.14979e8i	−0.977136	+	0.305313i
$283$	−3.77294e8	+	1.56280e8i	−0.989525	+	0.409875i	−0.817946	−	0.575295i	$-0.804887\pi$
$283$	−3.77294e8	+	1.56280e8i	−0.989525	+	0.409875i	−0.171580	+	0.985170i	$0.554887\pi$
$284$	−9.75931e7	−	1.40924e8i	−0.252816	−	0.365064i
$285$	2.73376e8	−	6.59989e8i	0.699526	−	1.68881i
$286$	−1.13723e8	−	1.36244e8i	−0.287453	−	0.344379i
$287$	1.82685e8			0.456159
$288$	−1.21721e8	−	5.86877e7i	−0.300255	−	0.144768i
$289$	3.44354e8			0.839194
$290$	−1.66323e7	−	1.99261e7i	−0.0400460	−	0.0479765i
$291$	−1.40220e7	+	3.38521e7i	−0.0333568	+	0.0805305i
$292$	3.03041e8	−	2.09863e8i	0.712297	−	0.493284i
$293$	−5.30183e7	+	2.19609e7i	−0.123137	+	0.0510051i	−0.443401	−	0.896323i	$-0.646228\pi$
$293$	−5.30183e7	+	2.19609e7i	−0.123137	+	0.0510051i	0.320264	+	0.947328i	$0.396228\pi$
$294$	−1.71449e8	+	5.35704e7i	−0.393476	+	0.122945i
$295$	6.70186e8	−	6.70186e8i	1.51991	−	1.51991i
$296$	3.12110e8	+	2.43361e8i	0.699497	+	0.545419i
$297$	4.58527e7	+	4.58527e7i	0.101559	+	0.101559i
$298$	3.71118e8	+	1.94414e8i	0.812372	+	0.425569i
$299$	−1.72479e8	−	4.16400e8i	−0.373152	−	0.900869i
$300$	−4.98271e8	+	1.07763e8i	−1.06547	+	0.230433i
$301$	3.52068e8	+	1.45831e8i	0.744122	+	0.308225i
$302$	4.10720e8	+	3.70041e7i	0.858067	+	0.0773082i
$303$		−	5.05372e8i		−	1.04367i
$304$	6.66416e8	+	6.23465e8i	1.36047	+	1.27278i
$305$			4.76797e8i			0.962241i
$306$	6.01180e6	−	6.67267e7i	0.0119944	−	0.133130i
$307$	2.03277e8	+	8.42002e7i	0.400963	+	0.166084i	0.574046	−	0.818823i	$-0.305373\pi$
$307$	2.03277e8	+	8.42002e7i	0.400963	+	0.166084i	−0.173083	+	0.984907i	$0.555373\pi$
$308$	−1.10850e8	+	1.72030e8i	−0.216177	+	0.335487i
$309$	2.86870e7	+	6.92566e7i	0.0553135	+	0.133539i
$310$	−7.40989e7	+	1.41448e8i	−0.141269	+	0.269669i
$311$	1.26395e8	+	1.26395e8i	0.238269	+	0.238269i	0.816133	−	0.577864i	$-0.196114\pi$
$311$	1.26395e8	+	1.26395e8i	0.238269	+	0.238269i	−0.577864	+	0.816133i	$0.696114\pi$
$312$	−1.79447e8	−	4.95783e7i	−0.334499	−	0.0924167i
$313$	7.37674e7	−	7.37674e7i	0.135975	−	0.135975i	−0.635843	−	0.771818i	$-0.719347\pi$
$313$	7.37674e7	−	7.37674e7i	0.135975	−	0.135975i	0.771818	+	0.635843i	$0.219347\pi$
$314$	−2.81377e8	−	9.00530e8i	−0.512903	−	1.64151i
$315$	1.55260e8	−	6.43109e7i	0.279881	−	0.115930i
$316$	−2.80157e8	−	5.08950e7i	−0.499455	−	0.0907341i
$317$	1.08398e8	−	2.61696e8i	0.191123	−	0.461412i	−0.799049	−	0.601266i	$-0.794663\pi$
$317$	1.08398e8	−	2.61696e8i	0.191123	−	0.461412i	0.990172	+	0.139854i	$0.0446632\pi$
$318$	−1.42550e7	+	1.18987e7i	−0.0248584	+	0.0207494i
$319$	−1.59114e7			−0.0274436
$320$	1.45338e8	−	9.85508e8i	0.247945	−	1.68126i
$321$	3.33560e8			0.562868
$322$	−3.99006e8	+	3.33051e8i	−0.666015	+	0.555923i
$323$	−1.73148e8	+	4.18017e8i	−0.285897	+	0.690215i
$324$	6.69290e7	+	1.21587e7i	0.109322	+	0.0198601i
$325$	−6.48880e8	+	2.68775e8i	−1.04851	+	0.434307i
$326$	3.03648e8	+	9.71808e8i	0.485411	+	1.55353i
$327$	9.49473e7	−	9.49473e7i	0.150164	−	0.150164i
$328$	−1.45173e8	+	5.25448e8i	−0.227158	+	0.822188i
$329$	4.33098e8	+	4.33098e8i	0.670502	+	0.670502i
$330$	−2.21828e8	+	4.23450e8i	−0.339795	+	0.648639i
$331$	1.03518e8	+	2.49914e8i	0.156898	+	0.378784i	0.982708	−	0.185164i	$-0.0592817\pi$
$331$	1.03518e8	+	2.49914e8i	0.156898	+	0.378784i	−0.825810	+	0.563948i	$0.809282\pi$
$332$	1.07545e8	−	1.66901e8i	0.161291	−	0.250308i
$333$	−1.84067e8	−	7.62429e7i	−0.273162	−	0.113147i
$334$	−3.16512e7	+	3.51306e8i	−0.0464812	+	0.515909i
$335$			1.55084e9i			2.25377i
$336$	7.14468e6	+	2.14565e8i	0.0102753	+	0.308582i
$337$			6.02673e8i			0.857782i	0.903356	+	0.428891i	$0.141096\pi$
$337$			6.02673e8i			0.857782i	−0.903356	+	0.428891i	$0.858904\pi$
$338$	4.51602e8	+	4.06875e7i	0.636133	+	0.0573129i
$339$	3.20353e8	+	1.32695e8i	0.446612	+	0.184993i
$340$	4.82735e8	−	1.04403e8i	0.666089	−	0.144057i
$341$	3.74607e7	+	9.04380e7i	0.0511605	+	0.123512i
$342$	−4.06940e8	−	2.13179e8i	−0.550096	−	0.288173i
$343$	4.84396e8	+	4.84396e8i	0.648144	+	0.648144i
$344$	−6.99223e8	+	8.96750e8i	−0.926107	+	1.18773i
$345$	−8.58453e8	+	8.58453e8i	−1.12551	+	1.12551i
$346$	−2.03681e8	+	6.36416e7i	−0.264353	+	0.0825990i
$347$	2.61628e8	−	1.08370e8i	0.336149	−	0.139237i	−0.208223	−	0.978081i	$-0.566768\pi$
$347$	2.61628e8	−	1.08370e8i	0.336149	−	0.139237i	0.544372	+	0.838844i	$0.316768\pi$
$348$	−1.37222e7	+	9.50295e6i	−0.0174540	+	0.0120873i
$349$	5.05164e8	−	1.21957e9i	0.636126	−	1.53574i	−0.195675	−	0.980669i	$-0.562690\pi$
$349$	5.05164e8	−	1.21957e9i	0.636126	−	1.53574i	0.831801	−	0.555075i	$-0.187310\pi$
$350$	5.18996e8	+	6.21774e8i	0.647032	+	0.775166i
$351$	9.37177e7			0.115677
$352$	−4.06711e8	−	4.55538e8i	−0.497035	−	0.556706i
$353$	−1.33882e9			−1.61999			−0.809994	−	0.586438i	$-0.800530\pi$
$353$	−1.33882e9			−1.61999			−0.809994	+	0.586438i	$0.800530\pi$
$354$	−3.90573e8	−	4.67919e8i	−0.467941	−	0.560608i
$355$	−2.43437e8	+	5.87709e8i	−0.288793	+	0.697209i
$356$	6.79070e8	+	9.80570e8i	0.797700	+	1.15187i
$357$	−9.83370e7	+	4.07325e7i	−0.114387	+	0.0473808i
$358$	4.99332e8	−	1.56020e8i	0.575173	−	0.179717i
$359$	2.66352e8	−	2.66352e8i	0.303826	−	0.303826i	−0.538683	−	0.842509i	$-0.681078\pi$
$359$	2.66352e8	−	2.66352e8i	0.303826	−	0.303826i	0.842509	+	0.538683i	$0.181078\pi$
$360$	6.15948e7	+	4.97673e8i	0.0695801	+	0.562192i
$361$	1.56173e9	+	1.56173e9i	1.74715	+	1.74715i
$362$	−1.55169e9	−	8.12869e8i	−1.71920	−	0.900618i
$363$	−8.92052e7	−	2.15360e8i	−0.0978852	−	0.236316i
$364$	6.25217e7	+	2.89087e8i	0.0679479	+	0.314177i
$365$	−1.26380e9	−	5.23485e8i	−1.36036	−	0.563480i
$366$	3.05383e8	+	2.75137e7i	0.325582	+	0.0293336i
$367$		−	2.51023e8i		−	0.265083i	−0.991177	−	0.132542i	$-0.957686\pi$
$367$		−	2.51023e8i		−	0.265083i	0.991177	−	0.132542i	$-0.0423139\pi$
$368$	−6.40862e8	−	1.41230e9i	−0.670343	−	1.47727i
$369$		−	2.74420e8i		−	0.284330i
$370$	1.31792e8	−	1.46280e9i	0.135264	−	1.50134i
$371$	2.72544e7	+	1.12891e7i	0.0277094	+	0.0114776i
$372$	8.63199e7	+	5.56217e7i	0.0869382	+	0.0560201i
$373$	5.38697e8	+	1.30053e9i	0.537482	+	1.29760i	0.926475	+	0.376356i	$0.122823\pi$
$373$	5.38697e8	+	1.30053e9i	0.537482	+	1.29760i	−0.388993	+	0.921241i	$0.627177\pi$
$374$	1.40499e8	−	2.68200e8i	0.138874	−	0.265099i
$375$	6.29232e8	+	6.29232e8i	0.616171	+	0.616171i
$376$	−1.58986e9	+	9.01531e8i	−1.54242	+	0.874628i
$377$	−1.62605e7	+	1.62605e7i	−0.0156293	+	0.0156293i
$378$	−3.22310e7	−	1.03153e8i	−0.0306939	−	0.0982341i
$379$	7.83269e7	−	3.24441e7i	0.0739050	−	0.0306124i	−0.345425	−	0.938446i	$-0.612265\pi$
$379$	7.83269e7	−	3.24441e7i	0.0739050	−	0.0306124i	0.419330	+	0.907834i	$0.362265\pi$
$380$	6.05329e8	−	3.33209e9i	0.565912	−	3.11512i
$381$	1.09816e8	−	2.65118e8i	0.101725	−	0.245585i
$382$	1.74791e8	−	1.45898e8i	0.160434	−	0.133915i
$383$	9.00075e8			0.818621			0.409311	−	0.912395i	$-0.365769\pi$
$383$	9.00075e8			0.818621			0.409311	+	0.912395i	$0.365769\pi$
$384$	−6.22819e8	−	1.49957e8i	−0.561310	−	0.135147i
$385$	7.59461e8			0.678255
$386$	−1.44293e9	+	1.20442e9i	−1.27700	+	1.06591i
$387$	2.19060e8	−	5.28858e8i	0.192121	−	0.463822i
$388$	−3.10485e7	+	1.70909e8i	−0.0269854	+	0.148544i
$389$	−4.43167e8	+	1.83566e8i	−0.381719	+	0.158113i	−0.565288	−	0.824894i	$-0.691235\pi$
$389$	−4.43167e8	+	1.83566e8i	−0.381719	+	0.158113i	0.183569	+	0.983007i	$0.441235\pi$
$390$	2.06046e8	+	6.59437e8i	0.175889	+	0.562921i
$391$	5.43717e8	−	5.43717e8i	0.459996	−	0.459996i
$392$	−7.40743e8	+	4.20038e8i	−0.621107	+	0.352198i
$393$	−1.57466e8	−	1.57466e8i	−0.130862	−	0.130862i
$394$	4.76397e8	−	9.09400e8i	0.392403	−	0.749063i
$395$	4.04375e8	+	9.76247e8i	0.330137	+	0.797021i
$396$	2.58414e8	+	1.66513e8i	0.209114	+	0.134746i
$397$	8.02055e8	+	3.32222e8i	0.643335	+	0.266478i	0.680407	−	0.732834i	$-0.261803\pi$
$397$	8.02055e8	+	3.32222e8i	0.643335	+	0.266478i	−0.0370716	+	0.999313i	$0.511803\pi$
$398$	2.86476e7	−	3.17968e8i	0.0227771	−	0.252809i
$399$			7.29851e8i			0.575213i
$400$	−2.20080e9	+	9.98661e8i	−1.71938	+	0.780204i
$401$		−	1.92186e9i		−	1.48839i	−0.667963	−	0.744194i	$-0.732834\pi$
$401$		−	1.92186e9i		−	1.48839i	0.667963	−	0.744194i	$-0.267166\pi$
$402$	9.93294e8	+	8.94916e7i	0.762582	+	0.0687055i
$403$	1.30705e8	+	5.41399e7i	0.0994776	+	0.0412050i
$404$	−5.06446e8	−	2.34170e9i	−0.382119	−	1.76684i
$405$	−9.66044e7	−	2.33224e8i	−0.0722611	−	0.174454i
$406$	2.34899e7	+	1.23054e7i	0.0174197	+	0.00912548i
$407$	−6.36657e8	−	6.36657e8i	−0.468086	−	0.468086i
$408$	−3.90122e7	−	3.15210e8i	−0.0284374	−	0.229768i
$409$	8.78577e8	−	8.78577e8i	0.634963	−	0.634963i	−0.314346	−	0.949309i	$-0.601785\pi$
$409$	8.78577e8	−	8.78577e8i	0.634963	−	0.634963i	0.949309	+	0.314346i	$0.101785\pi$
$410$	1.93093e9	−	6.03334e8i	1.38364	−	0.432329i
$411$	−1.30861e9	+	5.42043e8i	−0.929744	+	0.385112i
$412$	2.02329e8	+	2.92160e8i	0.142533	+	0.205817i
$413$	−3.70564e8	+	8.94620e8i	−0.258844	+	0.624904i
$414$	5.00291e8	+	5.99366e8i	0.346515	+	0.415136i
$415$	−7.36820e8			−0.506049
$416$	−8.81170e8	−	4.98984e7i	−0.600113	−	0.0339829i
$417$	1.03456e9			0.698679
$418$	−1.33037e9	−	1.59383e9i	−0.890957	−	1.06740i
$419$	−1.05991e9	+	2.55884e9i	−0.703913	+	1.69940i	0.0107657	+	0.999942i	$0.496573\pi$
$419$	−1.05991e9	+	2.55884e9i	−0.703913	+	1.69940i	−0.714678	+	0.699453i	$0.753427\pi$
$420$	6.54968e8	−	4.53582e8i	0.431368	−	0.298733i
$421$	9.70971e8	−	4.02189e8i	0.634189	−	0.262690i	−0.0423428	−	0.999103i	$-0.513482\pi$
$421$	9.70971e8	−	4.02189e8i	0.634189	−	0.262690i	0.676532	+	0.736413i	$0.263482\pi$
$422$	2.08296e9	−	6.50837e8i	1.34924	−	0.421579i
$423$	6.50577e8	−	6.50577e8i	0.417933	−	0.417933i
$424$	−5.41284e7	+	6.94193e7i	−0.0344861	+	0.0442283i
$425$	−8.47279e8	−	8.47279e8i	−0.535384	−	0.535384i
$426$	3.62373e8	+	1.89832e8i	0.227102	+	0.118970i
$427$	−1.86417e8	−	4.50051e8i	−0.115875	−	0.279746i
$428$	1.54559e9	−	3.34269e8i	0.952886	−	0.206084i
$429$	3.91289e8	+	1.62077e8i	0.239275	+	0.0991109i
$430$	4.20289e9	+	3.78663e8i	2.54923	+	0.229675i
$431$			2.30413e9i			1.38624i	0.720825	+	0.693118i	$0.243763\pi$
$431$			2.30413e9i			1.38624i	−0.720825	+	0.693118i	$0.756237\pi$
$432$	3.22308e8	−	1.07324e7i	0.192343	−	0.00640475i
$433$		−	1.80964e9i		−	1.07124i	−0.844460	−	0.535618i	$-0.820079\pi$
$433$		−	1.80964e9i		−	1.07124i	0.844460	−	0.535618i	$-0.179921\pi$
$434$	1.46392e7	−	1.62484e8i	0.00859612	−	0.0954109i
$435$	5.72270e7	+	2.37042e7i	0.0333341	+	0.0138074i
$436$	3.44800e8	−	5.35098e8i	0.199234	−	0.309194i
$437$	−2.01772e9	−	4.87120e9i	−1.15658	−	2.79223i
$438$	−4.08214e8	+	7.79243e8i	−0.232128	+	0.443112i
$439$	−1.04966e9	−	1.04966e9i	−0.592138	−	0.592138i	0.346071	−	0.938208i	$-0.387516\pi$
$439$	−1.04966e9	−	1.04966e9i	−0.592138	−	0.592138i	−0.938208	+	0.346071i	$0.887516\pi$
$440$	−6.03515e8	+	2.18440e9i	−0.337757	+	1.22250i
$441$	3.03114e8	−	3.03114e8i	0.168295	−	0.168295i
$442$	−1.30503e8	−	4.17667e8i	−0.0718857	−	0.230066i
$443$	−4.25920e8	+	1.76422e8i	−0.232763	+	0.0964137i	−0.496017	−	0.868313i	$-0.665205\pi$
$443$	−4.25920e8	+	1.76422e8i	−0.232763	+	0.0964137i	0.263253	+	0.964727i	$0.415205\pi$
$444$	−9.29299e8	−	1.68822e8i	−0.503866	−	0.0915354i
$445$	1.69388e9	−	4.08938e9i	0.911217	−	2.19987i
$446$	−1.79842e9	+	1.50114e9i	−0.959882	+	0.801215i
$447$	−9.99835e8			−0.529483
$448$	2.48126e8	+	9.87049e8i	0.130377	+	0.518640i
$449$	−1.21446e9			−0.633173			−0.316587	−	0.948564i	$-0.602537\pi$
$449$	−1.21446e9			−0.633173			−0.316587	+	0.948564i	$0.602537\pi$
$450$	9.33997e8	−	7.79608e8i	0.483172	−	0.403304i
$451$	4.74587e8	−	1.14576e9i	0.243612	−	0.588131i
$452$	1.61737e9	+	2.93822e8i	0.823806	+	0.149658i
$453$	−9.09233e8	+	3.76617e8i	−0.459549	+	0.190351i
$454$	−5.89812e8	−	1.88766e9i	−0.295813	−	0.946733i
$455$	7.76127e8	−	7.76127e8i	0.386271	−	0.386271i
$456$	−2.09923e9	−	5.79985e8i	−1.03677	−	0.286444i
$457$	−3.67725e8	−	3.67725e8i	−0.180226	−	0.180226i	0.611229	−	0.791454i	$-0.290676\pi$
$457$	−3.67725e8	−	3.67725e8i	−0.180226	−	0.180226i	−0.791454	+	0.611229i	$0.790676\pi$
$458$	−2.92926e8	+	5.59169e8i	−0.142472	+	0.271966i
$459$	6.11862e7	+	1.47717e8i	0.0295331	+	0.0712993i
$460$	−3.11746e9	+	4.83801e9i	−1.49330	+	2.31747i
$461$	4.39153e7	+	1.81903e7i	0.0208767	+	0.00864742i	0.393097	−	0.919497i	$-0.371404\pi$
$461$	4.39153e7	+	1.81903e7i	0.0208767	+	0.00864742i	−0.372221	+	0.928144i	$0.621404\pi$
$462$	4.38249e7	−	4.86426e8i	0.0206764	−	0.229493i
$463$		−	1.03331e9i		−	0.483834i	−0.970297	−	0.241917i	$-0.922224\pi$
$463$		−	1.03331e9i		−	0.483834i	0.970297	−	0.241917i	$-0.0777762\pi$
$464$	−5.40601e7	+	5.77843e7i	−0.0251225	+	0.0268533i
$465$		−	3.81078e8i		−	0.175763i
$466$	−3.23243e9	−	2.91228e8i	−1.47972	−	0.133316i
$467$	−1.53249e9	−	6.34780e8i	−0.696289	−	0.288412i	0.00632841	−	0.999980i	$-0.497986\pi$
$467$	−1.53249e9	−	6.34780e8i	−0.696289	−	0.288412i	−0.702618	+	0.711567i	$0.747986\pi$
$468$	4.34251e8	−	9.39169e7i	0.195831	−	0.0423529i
$469$	−6.06344e8	−	1.46384e9i	−0.271403	−	0.655224i
$470$	6.00808e9	+	3.14739e9i	2.66927	+	1.39832i
$471$	1.59210e9	+	1.59210e9i	0.702096	+	0.702096i
$472$	−2.27868e9	−	1.77675e9i	−0.997438	−	0.777733i
$473$	1.82924e9	−	1.82924e9i	0.794796	−	0.794796i
$474$	6.48609e8	−	2.02662e8i	0.279743	−	0.0874076i
$475$	−7.59083e9	+	3.14423e9i	−3.24984	+	1.34613i
$476$	−4.14837e8	+	2.87285e8i	−0.176300	+	0.122092i
$477$	1.69579e7	−	4.09401e7i	0.00715416	−	0.0172717i
$478$	1.02548e9	+	1.22855e9i	0.429465	+	0.514514i
$479$	4.55536e9			1.89386			0.946932	−	0.321435i	$-0.104165\pi$
$479$	4.55536e9			1.89386			0.946932	+	0.321435i	$0.104165\pi$
$480$	7.84137e8	+	2.24430e9i	0.323629	+	0.926266i
$481$	−1.30126e9			−0.533157
$482$	−5.99479e8	−	7.18196e8i	−0.243843	−	0.292132i
$483$	4.74661e8	−	1.14593e9i	0.191676	−	0.462748i
$484$	−6.29161e8	−	9.08502e8i	−0.252234	−	0.364223i
$485$	5.95559e8	−	2.46689e8i	0.237044	−	0.0981867i
$486$	−1.54952e8	+	4.84157e7i	−0.0612307	+	0.0191320i
$487$	−3.30380e9	+	3.30380e9i	−1.29617	+	1.29617i	−0.365266	+	0.930903i	$0.619022\pi$
$487$	−3.30380e9	+	3.30380e9i	−1.29617	+	1.29617i	−0.930903	+	0.365266i	$0.880978\pi$
$488$	1.44260e9	−	1.78544e8i	0.561921	−	0.0695465i
$489$	−1.71811e9	−	1.71811e9i	−0.664463	−	0.664463i
$490$	2.79926e9	+	1.46642e9i	1.07487	+	0.563082i
$491$	9.41342e7	+	2.27260e8i	0.0358891	+	0.0866439i	0.940808	−	0.338941i	$-0.110069\pi$
$491$	9.41342e7	+	2.27260e8i	0.0358891	+	0.0866439i	−0.904919	+	0.425584i	$0.860069\pi$
$492$	−2.75003e8	−	1.27156e9i	−0.104102	−	0.481346i
$493$	−3.62458e7	−	1.50135e7i	−0.0136237	−	0.00564310i
$494$	−2.98837e9	−	2.69240e8i	−1.11530	−	0.100484i
$495$		−	1.14082e9i		−	0.422766i
$496$	4.55713e8	+	1.71226e8i	0.167689	+	0.0630064i
$497$		−	6.49919e8i		−	0.237472i
$498$	−4.25184e7	+	4.71924e8i	−0.0154267	+	0.171226i
$499$	−1.57221e9	−	6.51229e8i	−0.566444	−	0.234629i	0.0810359	−	0.996711i	$-0.474177\pi$
$499$	−1.57221e9	−	6.51229e8i	−0.566444	−	0.234629i	−0.647480	+	0.762082i	$0.724177\pi$
$500$	3.54619e9	+	2.28505e9i	1.26872	+	0.817524i
$501$	−3.22136e8	−	7.77706e8i	−0.114448	−	0.276301i
$502$	6.45131e8	−	1.23150e9i	0.227607	−	0.434481i
$503$	2.44943e9	+	2.44943e9i	0.858176	+	0.858176i	0.991123	−	0.132947i	$-0.0424441\pi$
$503$	2.44943e9	+	2.44943e9i	0.858176	+	0.858176i	−0.132947	+	0.991123i	$0.542444\pi$
$504$	−2.52719e8	−	4.45673e8i	−0.0879286	−	0.155064i
$505$	−6.28688e9	+	6.28688e9i	−2.17228	+	2.17228i
$506$	1.05226e9	+	3.36768e9i	0.361072	+	1.15559i
$507$	−9.99737e8	+	4.14105e8i	−0.340689	+	0.141118i
$508$	2.43161e8	−	1.33850e9i	0.0822946	−	0.452999i
$509$	−8.58312e8	+	2.07215e9i	−0.288491	+	0.696480i	−0.999981	−	0.00621718i	$-0.998021\pi$
$509$	−8.58312e8	+	2.07215e9i	−0.288491	+	0.696480i	0.711489	+	0.702697i	$0.248021\pi$
$510$	−9.04874e8	+	7.55299e8i	−0.302059	+	0.252129i
$511$	1.39758e9			0.463344
$512$	−3.03618e9	−	7.06976e7i	−0.999729	−	0.0232788i
$513$	1.09634e9			0.358539
$514$	2.55185e9	−	2.13004e9i	0.828867	−	0.691856i
$515$	5.04690e8	−	1.21843e9i	0.162817	−	0.393074i
$516$	4.85058e8	−	2.67005e9i	0.155425	−	0.855550i
$517$	3.84140e9	−	1.59116e9i	1.22257	−	0.506404i
$518$	4.47523e8	+	1.43227e9i	0.141469	+	0.452762i
$519$	3.60099e8	−	3.60099e8i	0.113067	−	0.113067i
$520$	1.61558e9	+	2.84909e9i	0.503867	+	0.888576i
$521$	4.11990e9	+	4.11990e9i	1.27630	+	1.27630i	0.942720	+	0.333585i	$0.108258\pi$
$521$	4.11990e9	+	4.11990e9i	1.27630	+	1.27630i	0.333585	+	0.942720i	$0.391742\pi$
$522$	1.84846e7	−	3.52854e7i	0.00568804	−	0.0108579i
$523$	2.21440e8	+	5.34603e8i	0.0676862	+	0.163409i	0.954103	−	0.299480i	$-0.0968130\pi$
$523$	2.21440e8	+	5.34603e8i	0.0676862	+	0.163409i	−0.886417	+	0.462888i	$0.846813\pi$
$524$	−8.87437e8	−	5.71836e8i	−0.269450	−	0.173625i
$525$	−1.78572e9	−	7.39668e8i	−0.538586	−	0.223090i
$526$	4.70259e7	−	5.21954e8i	0.0140892	−	0.156380i
$527$			2.41363e8i			0.0718345i
$528$	1.36426e9	+	5.12596e8i	0.403345	+	0.151550i
$529$			5.55564e9i			1.63170i
$530$	3.25355e8	+	2.93131e7i	0.0949275	+	0.00855257i
$531$	1.34385e9	+	5.56641e8i	0.389511	+	0.161341i
$532$	7.31402e8	+	3.38185e9i	0.210603	+	0.973785i
$533$	−6.85895e8	−	1.65590e9i	−0.196206	−	0.473684i
$534$	−2.52145e9	−	1.32089e9i	−0.716566	−	0.375380i
$535$	−4.14952e9	−	4.14952e9i	−1.17155	−	1.17155i
$536$	4.69222e9	−	5.80736e8i	1.31614	−	0.162893i
$537$	−8.82797e8	+	8.82797e8i	−0.246009	+	0.246009i
$538$	−4.23056e9	+	1.32187e9i	−1.17128	+	0.365974i
$539$	1.78977e9	−	7.41347e8i	0.492307	−	0.203920i
$540$	−6.81347e8	−	9.83859e8i	−0.186204	−	0.268878i
$541$	−9.79146e8	+	2.36387e9i	−0.265862	+	0.641849i	−0.999280	−	0.0379293i	$-0.987924\pi$
$541$	−9.79146e8	+	2.36387e9i	−0.265862	+	0.641849i	0.733418	+	0.679778i	$0.237924\pi$
$542$	−4.14019e9	−	4.96008e9i	−1.11692	−	1.33811i
$543$	4.18044e9			1.12053
$544$	−4.96648e8	−	1.42147e9i	−0.132267	−	0.378565i
$545$	−2.36231e9			−0.625098
$546$	−4.52313e8	−	5.41886e8i	−0.118923	−	0.142473i
$547$	3.59235e8	−	8.67269e8i	0.0938474	−	0.226568i	−0.869984	−	0.493080i	$-0.835871\pi$
$547$	3.59235e8	−	8.67269e8i	0.0938474	−	0.226568i	0.963832	+	0.266512i	$0.0858711\pi$
$548$	−5.52039e9	+	3.82301e9i	−1.43297	+	0.992369i
$549$	−6.76042e8	+	2.80026e8i	−0.174370	+	0.0722262i
$550$	5.24788e9	−	1.63974e9i	1.34498	−	0.420248i
$551$	−1.90222e8	+	1.90222e8i	−0.0484428	+	0.0484428i
$552$	2.91880e9	+	2.27587e9i	0.738613	+	0.575919i
$553$	−7.63382e8	−	7.63382e8i	−0.191957	−	0.191957i
$554$	3.04653e9	+	1.59596e9i	0.761241	+	0.398783i
$555$	1.34134e9	+	3.23828e9i	0.333052	+	0.804060i
$556$	4.79373e9	−	1.03675e9i	1.18280	−	0.255808i
$557$	4.73591e9	+	1.96168e9i	1.16121	+	0.480989i	0.878277	−	0.478152i	$-0.158693\pi$
$557$	4.73591e9	+	1.96168e9i	1.16121	+	0.480989i	0.282932	+	0.959140i	$0.408693\pi$
$558$	−2.44076e8	−	2.19902e7i	−0.0594709	−	0.00535808i
$559$		−	3.73875e9i		−	0.905285i
$560$	2.58032e9	−	2.75808e9i	0.620892	−	0.663666i
$561$			7.22562e8i			0.172785i
$562$	5.04424e8	−	5.59875e9i	0.119872	−	1.33050i
$563$	−5.21770e9	−	2.16124e9i	−1.23225	−	0.510415i	−0.330967	−	0.943642i	$-0.607375\pi$
$563$	−5.21770e9	−	2.16124e9i	−1.23225	−	0.510415i	−0.901285	+	0.433227i	$0.857375\pi$
$564$	2.36256e9	−	3.66648e9i	0.554506	−	0.860543i
$565$	−2.33449e9	−	5.63596e9i	−0.544531	−	1.31461i
$566$	2.14401e9	−	4.09271e9i	0.497014	−	0.948754i
$567$	1.82371e8	+	1.82371e8i	0.0420160	+	0.0420160i
$568$	1.86933e9	+	5.16466e8i	0.428023	+	0.118256i
$569$	−2.33905e9	+	2.33905e9i	−0.532287	+	0.532287i	−0.921253	−	0.388965i	$-0.872833\pi$
$569$	−2.33905e9	+	2.33905e9i	−0.532287	+	0.532287i	0.388965	+	0.921253i	$0.372833\pi$
$570$	2.41040e9	+	7.71434e9i	0.545164	+	1.74476i
$571$	−4.63710e9	+	1.92075e9i	−1.04237	+	0.431762i	−0.837161	−	0.546957i	$-0.815786\pi$
$571$	−4.63710e9	+	1.92075e9i	−1.04237	+	0.431762i	−0.205205	+	0.978719i	$0.565786\pi$
$572$	1.97550e9	+	3.58882e8i	0.441359	+	0.0801800i
$573$	−2.07933e8	+	5.01994e8i	−0.0461723	+	0.111470i
$574$	−1.58673e9	+	1.32444e9i	−0.350196	+	0.292309i
$575$	1.39632e10			3.06300
$576$	1.48269e9	−	3.72722e8i	0.323275	−	0.0812656i
$577$	3.60059e9			0.780295			0.390147	−	0.920752i	$-0.372424\pi$
$577$	3.60059e9			0.780295			0.390147	+	0.920752i	$0.372424\pi$
$578$	−2.99091e9	+	2.49652e9i	−0.644253	+	0.537759i
$579$	1.71653e9	−	4.14406e9i	0.367515	−	0.887260i
$580$	2.88923e8	+	5.24875e7i	0.0614870	+	0.0111701i
$581$	6.95487e8	−	2.88080e8i	0.147120	−	0.0609393i
$582$	−1.23634e8	−	3.95683e8i	−0.0259961	−	0.0831989i
$583$	1.41605e8	−	1.41605e8i	0.0295964	−	0.0295964i
$584$	−1.11060e9	+	4.01979e9i	−0.230736	+	0.835139i
$585$	−1.16586e9	−	1.16586e9i	−0.240768	−	0.240768i
$586$	3.01281e8	−	5.75119e8i	0.0618487	−	0.118064i
$587$	−3.26740e9	−	7.88820e9i	−0.666759	−	1.60970i	−0.786999	−	0.616954i	$-0.788366\pi$
$587$	−3.26740e9	−	7.88820e9i	−0.666759	−	1.60970i	0.120240	−	0.992745i	$-0.461634\pi$
$588$	1.10075e9	−	1.70827e9i	0.223290	−	0.346526i
$589$	1.52904e9	+	6.33348e8i	0.308329	+	0.127714i
$590$	−9.62198e8	+	1.06797e10i	−0.192878	+	2.14081i
$591$			2.45003e9i			0.488220i
$592$	−4.47519e9	+	1.49017e8i	−0.886514	+	0.0295196i
$593$		−	3.74206e9i		−	0.736918i	−0.929644	−	0.368459i	$-0.879886\pi$
$593$		−	3.74206e9i		−	0.736918i	0.929644	−	0.368459i	$-0.120114\pi$
$594$	−7.30683e8	−	6.58315e7i	−0.143046	−	0.0128879i
$595$	1.73004e9	+	7.16605e8i	0.336702	+	0.139467i
$596$	−4.63285e9	+	1.00196e9i	−0.896368	+	0.193860i
$597$	2.91566e8	+	7.03904e8i	0.0560825	+	0.135395i
$598$	4.51692e9	+	2.36623e9i	0.863751	+	0.452484i
$599$	−3.85889e9	−	3.85889e9i	−0.733615	−	0.733615i	0.237719	−	0.971334i	$-0.423600\pi$
$599$	−3.85889e9	−	3.85889e9i	−0.733615	−	0.733615i	−0.971334	+	0.237719i	$0.923600\pi$
$600$	3.54651e9	−	4.54838e9i	0.670305	−	0.859662i
$601$	−3.51053e9	+	3.51053e9i	−0.659647	+	0.659647i	−0.955297	−	0.295649i	$-0.904464\pi$
$601$	−3.51053e9	+	3.51053e9i	−0.659647	+	0.659647i	0.295649	+	0.955297i	$0.404464\pi$
$602$	−4.11518e9	+	1.28582e9i	−0.768778	+	0.240210i
$603$	−2.19891e9	+	9.10818e8i	−0.408410	+	0.169169i
$604$	−3.83562e9	+	2.65626e9i	−0.708281	+	0.490503i
$605$	−1.56938e9	+	3.78882e9i	−0.288128	+	0.695602i
$606$	3.66388e9	+	4.38945e9i	0.668786	+	0.801228i
$607$	−5.18429e9			−0.940869			−0.470435	−	0.882435i	$-0.655903\pi$
$607$	−5.18429e9			−0.940869			−0.470435	+	0.882435i	$0.655903\pi$
$608$	−1.03083e10	−	5.83730e8i	−1.86004	−	0.105329i
$609$	−6.32847e7			−0.0113537
$610$	−3.45671e9	−	4.14126e9i	−0.616608	−	0.738717i
$611$	2.29962e9	−	5.55177e9i	0.407860	−	0.984662i
$612$	4.31544e8	+	6.23146e8i	0.0761018	+	0.109890i
$613$	−2.49553e9	+	1.03368e9i	−0.437573	+	0.181249i	−0.590585	−	0.806976i	$-0.701103\pi$
$613$	−2.49553e9	+	1.03368e9i	−0.437573	+	0.181249i	0.153012	+	0.988224i	$0.451103\pi$
$614$	−2.37602e9	+	7.42405e8i	−0.414249	+	0.129435i
$615$	−3.41381e9	+	3.41381e9i	−0.591802	+	0.591802i
$616$	−2.84392e8	−	2.29783e9i	−0.0490213	−	0.396082i
$617$	3.57705e9	+	3.57705e9i	0.613094	+	0.613094i	0.943751	−	0.330657i	$-0.107270\pi$
$617$	3.57705e9	+	3.57705e9i	0.613094	+	0.613094i	−0.330657	+	0.943751i	$0.607270\pi$
$618$	−7.51265e8	−	3.93557e8i	−0.128036	−	0.0670731i
$619$	3.01183e9	+	7.27120e9i	0.510403	+	1.23222i	0.943650	+	0.330946i	$0.107368\pi$
$619$	3.01183e9	+	7.27120e9i	0.510403	+	1.23222i	−0.433247	+	0.901275i	$0.642632\pi$
$620$	−3.81888e8	−	1.76577e9i	−0.0643524	−	0.297552i
$621$	−1.72136e9	−	7.13011e8i	−0.288437	−	0.119475i
$622$	−2.01416e9	−	1.81467e8i	−0.335604	−	0.0302365i
$623$			4.52225e9i			0.749284i
$624$	1.91804e9	−	8.70349e8i	0.316017	−	0.143399i
$625$		−	4.13126e9i		−	0.676866i
$626$	−1.05909e8	+	1.17552e9i	−0.0172553	+	0.191522i
$627$	4.57744e9	+	1.89604e9i	0.741628	+	0.307193i
$628$	8.97265e9	+	5.78168e9i	1.44565	+	0.931527i
$629$	−8.49562e8	−	2.05102e9i	−0.136119	−	0.328619i
$630$	−8.82281e8	+	1.68419e9i	−0.140577	+	0.268349i
$631$	7.41514e8	+	7.41514e8i	0.117494	+	0.117494i	0.763409	−	0.645915i	$-0.223524\pi$
$631$	7.41514e8	+	7.41514e8i	0.117494	+	0.117494i	−0.645915	+	0.763409i	$0.723524\pi$
$632$	2.80231e9	−	1.58905e9i	0.441577	−	0.250396i
$633$	−3.68259e9	+	3.68259e9i	−0.577086	+	0.577086i
$634$	9.55760e8	+	3.05885e9i	0.148949	+	0.476701i
$635$	−4.66421e9	+	1.93198e9i	−0.722887	+	0.299429i
$636$	3.75494e7	−	2.06694e8i	0.00578766	−	0.0318588i
$637$	1.07143e9	−	2.58666e9i	0.164239	−	0.396507i
$638$	1.38200e8	−	1.15355e8i	0.0210686	−	0.0175860i
$639$	−9.76275e8			−0.148020
$640$	5.88245e9	+	9.61340e9i	0.887010	+	1.44960i
$641$	5.84385e9			0.876388			0.438194	−	0.898880i	$-0.355618\pi$
$641$	5.84385e9			0.876388			0.438194	+	0.898880i	$0.355618\pi$
$642$	−2.89717e9	+	2.41827e9i	−0.432117	+	0.360688i
$643$	4.96016e9	−	1.19749e10i	0.735796	−	1.77637i	0.113574	−	0.993530i	$-0.463770\pi$
$643$	4.96016e9	−	1.19749e10i	0.735796	−	1.77637i	0.622223	−	0.782840i	$-0.286230\pi$
$644$	1.05103e9	−	5.78548e9i	0.155065	−	0.853570i
$645$	−9.30418e9	+	3.85392e9i	−1.36527	+	0.565514i
$646$	−1.52667e9	−	4.88602e9i	−0.222809	−	0.713085i
$647$	2.13196e9	−	2.13196e9i	0.309467	−	0.309467i	−0.535236	−	0.844703i	$-0.679777\pi$
$647$	2.13196e9	−	2.13196e9i	0.309467	−	0.309467i	0.844703	+	0.535236i	$0.179777\pi$
$648$	−6.69467e8	+	3.79621e8i	−0.0966533	+	0.0548072i
$649$	4.64816e9	+	4.64816e9i	0.667460	+	0.667460i
$650$	3.68732e9	−	7.03876e9i	0.526640	−	1.00531i
$651$	1.48993e8	+	3.59701e8i	0.0211657	+	0.0510985i
$652$	−9.68284e9	−	6.23931e9i	−1.36816	−	0.881597i
$653$	1.72577e9	+	7.14837e8i	0.242542	+	0.100464i	0.500643	−	0.865654i	$-0.333097\pi$
$653$	1.72577e9	+	7.14837e8i	0.242542	+	0.100464i	−0.258101	+	0.966118i	$0.583097\pi$
$654$	−1.36317e8	+	1.51303e9i	−0.0190559	+	0.211507i
$655$			3.91778e9i			0.544748i
$656$	−2.54852e9	−	5.61631e9i	−0.352472	−	0.776761i
$657$		−	2.09937e9i		−	0.288809i
$658$	−6.90161e9	−	6.21806e8i	−0.944408	−	0.0850872i
$659$	6.21723e9	+	2.57526e9i	0.846249	+	0.350528i	0.763314	−	0.646027i	$-0.223571\pi$
$659$	6.21723e9	+	2.57526e9i	0.846249	+	0.350528i	0.0829347	+	0.996555i	$0.473571\pi$
$660$	−1.14325e9	−	5.28613e9i	−0.154788	−	0.715705i
$661$	1.33406e9	+	3.22070e9i	0.179667	+	0.433756i	0.987897	−	0.155112i	$-0.0495739\pi$
$661$	1.33406e9	+	3.22070e9i	0.179667	+	0.433756i	−0.808229	+	0.588868i	$0.799574\pi$
$662$	−2.71095e9	−	1.42016e9i	−0.363177	−	0.190254i
$663$	7.38417e8	+	7.38417e8i	0.0984021	+	0.0984021i
$664$	2.75913e8	+	2.22932e9i	0.0365750	+	0.295518i
$665$	9.07941e9	−	9.07941e9i	1.19724	−	1.19724i
$666$	2.15148e9	−	6.72245e8i	0.282213	−	0.0881795i
$667$	4.22377e8	−	1.74954e8i	0.0551138	−	0.0228289i
$668$	−2.27201e9	−	3.28077e9i	−0.294913	−	0.425851i
$669$	2.13941e9	−	5.16500e9i	0.276250	−	0.666927i
$670$	−1.12434e10	−	1.34699e10i	−1.44423	−	1.73023i
$671$	−3.30689e9			−0.422562
$672$	−1.61762e9	−	1.81182e9i	−0.205629	−	0.230315i
$673$	1.05619e10			1.33563			0.667817	−	0.744325i	$-0.267229\pi$
$673$	1.05619e10			1.33563			0.667817	+	0.744325i	$0.267229\pi$
$674$	−4.36930e9	−	5.23457e9i	−0.549670	−	0.658523i
$675$	−1.11109e9	+	2.68241e9i	−0.139055	+	0.335708i
$676$	−4.21741e9	+	2.92066e9i	−0.525088	+	0.363637i
$677$	−5.57544e9	+	2.30942e9i	−0.690588	+	0.286051i	−0.700245	−	0.713902i	$-0.746926\pi$
$677$	−5.57544e9	+	2.30942e9i	−0.690588	+	0.286051i	0.00965708	+	0.999953i	$0.496926\pi$
$678$	−3.74448e9	+	1.16999e9i	−0.461410	+	0.144171i
$679$	−4.65701e8	+	4.65701e8i	−0.0570904	+	0.0570904i
$680$	−3.43593e9	+	4.40656e9i	−0.419047	+	0.537426i
$681$	3.33729e9	+	3.33729e9i	0.404930	+	0.404930i
$682$	−9.81032e8	−	5.13922e8i	−0.118423	−	0.0620372i
$683$	5.77084e9	+	1.39320e10i	0.693053	+	1.67318i	0.738536	+	0.674214i	$0.235517\pi$
$683$	5.77084e9	+	1.39320e10i	0.693053	+	1.67318i	−0.0454830	+	0.998965i	$0.514483\pi$
$684$	5.08003e9	−	1.09867e9i	0.606974	−	0.131272i
$685$	2.30223e10	+	9.53614e9i	2.73673	+	1.13359i
$686$	−7.71908e9	−	6.95456e8i	−0.912916	−	0.0822499i
$687$		−	1.50647e9i		−	0.177260i
$688$	−4.28154e8	−	1.28581e10i	−0.0501234	−	1.50528i
$689$		−	2.89425e8i		−	0.0337108i
$690$	1.23250e9	−	1.36798e10i	0.142828	−	1.58529i
$691$	7.22485e9	+	2.99263e9i	0.833020	+	0.345048i	0.758098	−	0.652141i	$-0.226129\pi$
$691$	7.22485e9	+	2.99263e9i	0.833020	+	0.345048i	0.0749227	+	0.997189i	$0.476129\pi$
$692$	1.30770e9	−	2.02943e9i	0.150015	−	0.232810i
$693$	4.46037e8	+	1.07683e9i	0.0509101	+	0.122908i
$694$	−1.48673e9	+	2.83803e9i	−0.168839	+	0.322299i
$695$	−1.28700e10	−	1.28700e10i	−1.45422	−	1.45422i
$696$	5.02899e7	−	1.82023e8i	0.00565391	−	0.0204641i
$697$	2.16220e9	−	2.16220e9i	0.241870	−	0.241870i
$698$	4.45410e9	+	1.42551e10i	0.495754	+	1.58663i
$699$	7.15581e9	−	2.96403e9i	0.792481	−	0.328256i
$700$	−9.01556e9	−	1.63782e9i	−0.993459	−	0.180478i
$701$	−1.16234e9	+	2.80614e9i	−0.127444	+	0.307677i	−0.974703	−	0.223502i	$-0.928251\pi$
$701$	−1.16234e9	+	2.80614e9i	−0.127444	+	0.307677i	0.847259	+	0.531180i	$0.178251\pi$
$702$	−8.13993e8	+	6.79441e8i	−0.0888057	+	0.0741262i
$703$	−1.52226e10			−1.65251
$704$	6.83512e9	+	1.00801e9i	0.738315	+	0.108884i
$705$	−1.61865e10			−1.73976
$706$	1.16285e10	−	9.70630e9i	1.24367	−	1.03810i
$707$	3.47618e9	−	8.39224e9i	0.369943	−	0.893120i
$708$	6.78471e9	+	1.23255e9i	0.718480	+	0.130524i
$709$	−1.73332e9	+	7.17967e8i	−0.182649	+	0.0756558i	−0.472134	−	0.881527i	$-0.656516\pi$
$709$	−1.73332e9	+	7.17967e8i	−0.182649	+	0.0756558i	0.289485	+	0.957183i	$0.406516\pi$
$710$	−2.14642e9	−	6.86948e9i	−0.225066	−	0.720310i
$711$	−1.14671e9	+	1.14671e9i	−0.119649	+	0.119649i
$712$	−1.30071e10	−	3.59366e9i	−1.35052	−	0.373128i
$713$	−1.98883e9	−	1.98883e9i	−0.205487	−	0.205487i
$714$	5.58809e8	−	1.06672e9i	0.0574539	−	0.109674i
$715$	−2.85142e9	−	6.88393e9i	−0.291736	−	0.704312i
$716$	−3.20587e9	+	4.97521e9i	−0.326400	+	0.506543i
$717$	−3.52837e9	−	1.46150e9i	−0.357485	−	0.148075i
$718$	−3.82406e8	+	4.24444e9i	−0.0385558	+	0.427942i
$719$		−	3.92109e9i		−	0.393419i	−0.980462	−	0.196709i	$-0.936974\pi$
$719$		−	3.92109e9i		−	0.393419i	0.980462	−	0.196709i	$-0.0630256\pi$
$720$	−4.14305e9	−	3.87602e9i	−0.413672	−	0.387011i
$721$			1.34740e9i			0.133883i
$722$	−2.48869e10	−	2.24220e9i	−2.46088	−	0.221715i
$723$	2.06264e9	+	8.54373e8i	0.202973	+	0.0840743i
$724$	1.93706e10	−	4.18933e9i	1.89696	−	0.410260i
$725$	−2.72633e8	−	6.58194e8i	−0.0265702	−	0.0641462i
$726$	2.33613e9	+	1.22381e9i	0.226579	+	0.118696i
$727$	−9.05406e9	−	9.05406e9i	−0.873922	−	0.873922i	0.118975	−	0.992897i	$-0.462039\pi$
$727$	−9.05406e9	−	9.05406e9i	−0.873922	−	0.873922i	−0.992897	+	0.118975i	$0.962039\pi$
$728$	−2.63888e9	−	2.05762e9i	−0.253490	−	0.197654i
$729$	2.73948e8	−	2.73948e8i	0.0261891	−	0.0261891i
$730$	1.47721e10	−	4.61564e9i	1.40544	−	0.439139i
$731$	5.89298e9	−	2.44095e9i	0.557987	−	0.231126i
$732$	−2.85190e9	+	1.97501e9i	−0.268748	+	0.186115i
$733$	−3.51375e9	+	8.48294e9i	−0.329539	+	0.795578i	0.669087	+	0.743184i	$0.266685\pi$
$733$	−3.51375e9	+	8.48294e9i	−0.329539	+	0.795578i	−0.998626	+	0.0523939i	$0.983315\pi$
$734$	1.81989e9	+	2.18028e9i	0.169867	+	0.203506i
$735$	−7.54153e9			−0.700574
$736$	1.58053e10	+	7.62052e9i	1.46127	+	0.704551i
$737$	−1.07561e10			−0.989730
$738$	1.98951e9	+	2.38350e9i	0.182200	+	0.218282i
$739$	1.32632e9	−	3.20201e9i	0.120890	−	0.291855i	−0.851837	−	0.523807i	$-0.824511\pi$
$739$	1.32632e9	−	3.20201e9i	0.120890	−	0.291855i	0.972727	+	0.231952i	$0.0745113\pi$
$740$	9.46040e9	+	1.36607e10i	0.858219	+	1.23926i
$741$	6.61553e9	−	2.74024e9i	0.597311	−	0.247415i
$742$	−3.18565e8	+	9.95379e7i	−0.0286276	+	0.00894489i
$743$	9.61505e9	−	9.61505e9i	0.859985	−	0.859985i	−0.131351	−	0.991336i	$-0.541932\pi$
$743$	9.61505e9	−	9.61505e9i	0.859985	−	0.859985i	0.991336	+	0.131351i	$0.0419315\pi$
$744$	−1.15299e9	+	1.42700e8i	−0.102641	+	0.0127034i
$745$	1.24380e10	+	1.24380e10i	1.10206	+	1.10206i
$746$	−1.41076e10	−	7.39038e9i	−1.24413	−	0.651750i
$747$	−4.32739e8	−	1.04472e9i	−0.0379843	−	0.0917022i
$748$	7.24098e8	+	3.34807e9i	0.0632618	+	0.292509i
$749$	5.53912e9	+	2.29438e9i	0.481676	+	0.199517i
$750$	−1.00271e10	−	9.03400e8i	−0.867882	−	0.0781926i
$751$		−	3.21763e7i		−	0.00277202i	−0.999999	−	0.00138601i	$-0.999559\pi$
$751$		−	3.21763e7i		−	0.00277202i	0.999999	−	0.00138601i	$-0.000441180\pi$
$752$	7.27292e9	−	1.93566e10i	0.623658	−	1.65984i
$753$			3.31780e9i			0.283183i
$754$	2.33455e7	−	2.59119e8i	0.00198337	−	0.0220140i
$755$	1.59961e10	+	6.62579e9i	1.35269	+	0.560304i
$756$	1.02779e9	+	6.62277e8i	0.0865126	+	0.0557459i
$757$	9.07634e9	+	2.19122e10i	0.760458	+	1.83591i	0.484700	+	0.874680i	$0.338929\pi$
$757$	9.07634e9	+	2.19122e10i	0.760458	+	1.83591i	0.275757	+	0.961227i	$0.411071\pi$
$758$	−4.45100e8	+	8.49655e8i	−0.0371206	+	0.0708599i
$759$	−5.95391e9	−	5.95391e9i	−0.494261	−	0.494261i
$760$	1.88996e10	+	3.33297e10i	1.56173	+	2.75413i
$761$	−6.01450e9	+	6.01450e9i	−0.494713	+	0.494713i	−0.909787	−	0.415074i	$-0.863756\pi$
$761$	−6.01450e9	+	6.01450e9i	−0.494713	+	0.494713i	0.415074	+	0.909787i	$0.363756\pi$
$762$	9.68260e8	+	3.09886e9i	0.0792774	+	0.253723i
$763$	2.22979e9	−	9.23610e8i	0.181731	−	0.0752753i
$764$	−4.60419e8	+	2.53442e9i	−0.0373531	+	0.205614i
$765$	1.07645e9	−	2.59877e9i	0.0869315	−	0.209871i
$766$	−7.81768e9	+	6.52543e9i	−0.628459	+	0.524576i
$767$	9.50032e9			0.760247
$768$	6.49671e9	−	3.21290e9i	0.517523	−	0.255937i
$769$	5.15334e9			0.408646			0.204323	−	0.978904i	$-0.434501\pi$
$769$	5.15334e9			0.408646			0.204323	+	0.978904i	$0.434501\pi$
$770$	−6.59637e9	+	5.50599e9i	−0.520700	+	0.434629i
$771$	−3.03571e9	+	7.32885e9i	−0.238545	+	0.575898i
$772$	3.80085e9	−	2.09221e10i	0.297317	−	1.63661i
$773$	−2.11156e10	+	8.74637e9i	−1.64428	+	0.681082i	−0.996720	−	0.0809331i	$-0.974210\pi$
$773$	−2.11156e10	+	8.74637e9i	−1.64428	+	0.681082i	−0.647559	+	0.762016i	$0.724210\pi$
$774$	1.93149e9	+	6.18160e9i	0.149726	+	0.479190i
$775$	−3.09921e9	+	3.09921e9i	−0.239164	+	0.239164i
$776$	−9.69397e8	−	1.70955e9i	−0.0744707	−	0.131330i
$777$	−2.53219e9	−	2.53219e9i	−0.193652	−	0.193652i
$778$	2.51834e9	−	4.80728e9i	0.191728	−	0.365991i
$779$	−8.02385e9	−	1.93713e10i	−0.608138	−	1.46817i
$780$	−6.57046e9	−	4.23379e9i	−0.495752	−	0.319447i
$781$	−4.07613e9	−	1.68839e9i	−0.306175	−	0.126822i
$782$	−7.80625e8	+	8.66438e9i	−0.0583739	+	0.647909i
$783$			9.50629e7i			0.00707693i
$784$	3.38857e9	−	9.01856e9i	0.251137	−	0.668392i
$785$		−	3.96117e10i		−	2.92267i
$786$	2.50929e9	+	2.26077e8i	0.184320	+	0.0166064i
$787$	−2.50749e9	−	1.03863e9i	−0.183369	−	0.0759541i	0.289110	−	0.957296i	$-0.406641\pi$
$787$	−2.50749e9	−	1.03863e9i	−0.183369	−	0.0759541i	−0.472479	+	0.881342i	$0.656641\pi$
$788$	2.45524e9	+	1.13525e10i	0.178752	+	0.826512i
$789$	4.78615e8	+	1.15548e9i	0.0346910	+	0.0837515i
$790$	−1.05899e10	−	5.54761e9i	−0.764182	−	0.400324i
$791$	4.40707e9	+	4.40707e9i	0.316616	+	0.316616i
$792$	−3.45167e9	+	4.27199e8i	−0.246883	+	0.0305557i
$793$	−3.37945e9	+	3.37945e9i	−0.240652	+	0.240652i
$794$	−9.37489e9	+	2.92925e9i	−0.664652	+	0.207675i
$795$	−7.20257e8	+	2.98340e8i	−0.0508396	+	0.0210585i
$796$	2.05641e9	+	2.96943e9i	0.144515	+	0.208678i
$797$	−5.88255e9	+	1.42017e10i	−0.411587	+	0.993658i	0.573125	+	0.819468i	$0.305731\pi$
$797$	−5.88255e9	+	1.42017e10i	−0.411587	+	0.993658i	−0.984712	+	0.174190i	$0.944269\pi$
$798$	−5.29132e9	−	6.33918e9i	−0.368599	−	0.441594i
$799$	1.02520e10			0.711042
$800$	1.18751e10	−	2.46295e10i	0.820017	−	1.70075i
$801$	6.79309e9			0.467039
$802$	1.39332e10	+	1.66925e10i	0.953765	+	1.14264i
$803$	3.63070e9	−	8.76528e9i	0.247449	−	0.597394i
$804$	−9.27614e9	+	6.42396e9i	−0.629464	+	0.435920i
$805$	−2.01603e10	+	8.35069e9i	−1.36211	+	0.564205i
$806$	−1.52776e9	+	4.77359e8i	−0.102774	+	0.0321124i
$807$	7.47944e9	−	7.47944e9i	0.500970	−	0.500970i
$808$	2.13758e10	+	1.66674e10i	1.42555	+	1.11155i
$809$	8.63057e9	+	8.63057e9i	0.573086	+	0.573086i	0.932989	−	0.359904i	$-0.117190\pi$
$809$	8.63057e9	+	8.63057e9i	0.573086	+	0.573086i	−0.359904	+	0.932989i	$0.617190\pi$
$810$	2.52991e9	+	1.32532e9i	0.167266	+	0.0876237i
$811$	−5.96897e9	−	1.44104e10i	−0.392940	−	0.948641i	−0.989296	−	0.145921i	$-0.953385\pi$
$811$	−5.96897e9	−	1.44104e10i	−0.392940	−	0.948641i	0.596356	−	0.802720i	$-0.296615\pi$
$812$	−2.93237e8	+	6.34192e7i	−0.0192208	+	0.00415695i
$813$	1.42452e10	+	5.90056e9i	0.929719	+	0.385102i
$814$	1.01454e10	+	9.14060e8i	0.659303	+	0.0594004i
$815$			4.27470e10i			2.76601i
$816$	2.62408e9	+	2.45495e9i	0.169068	+	0.158171i
$817$		−	4.37373e10i		−	2.80592i
$818$	−1.26139e9	+	1.40005e10i	−0.0805773	+	0.894351i
$819$	1.55628e9	+	6.44633e8i	0.0989907	+	0.0410033i
$820$	−1.23972e10	+	1.92393e10i	−0.785191	+	1.21854i
$821$	7.94020e9	+	1.91693e10i	0.500761	+	1.20894i	0.949070	+	0.315065i	$0.102026\pi$
$821$	7.94020e9	+	1.91693e10i	0.500761	+	1.20894i	−0.448309	+	0.893878i	$0.647974\pi$
$822$	7.43629e9	−	1.41952e10i	0.466987	−	0.891436i
$823$	−1.07483e10	−	1.07483e10i	−0.672112	−	0.672112i	0.286091	−	0.958203i	$-0.407644\pi$
$823$	−1.07483e10	−	1.07483e10i	−0.672112	−	0.672112i	−0.958203	+	0.286091i	$0.907644\pi$
$824$	−3.87547e9	−	1.07073e9i	−0.241312	−	0.0666707i
$825$	−9.27803e9	+	9.27803e9i	−0.575264	+	0.575264i
$826$	−3.26731e9	−	1.04568e10i	−0.201725	−	0.645610i
$827$	−2.15779e10	+	8.93784e9i	−1.32660	+	0.549495i	−0.929683	−	0.368361i	$-0.879919\pi$
$827$	−2.15779e10	+	8.93784e9i	−1.32660	+	0.549495i	−0.396914	+	0.917856i	$0.629919\pi$
$828$	−8.69065e9	−	1.57880e9i	−0.532042	−	0.0966541i
$829$	−3.54530e9	+	8.55911e9i	−0.216128	+	0.521780i	−0.994343	−	0.106218i	$-0.966126\pi$
$829$	−3.54530e9	+	8.55911e9i	−0.216128	+	0.521780i	0.778214	+	0.627999i	$0.216126\pi$
$830$	6.39971e9	−	5.34185e9i	0.388496	−	0.324278i
$831$	−8.20772e9			−0.496157
$832$	8.01524e9	−	5.95497e9i	0.482486	−	0.358466i
$833$	4.77657e9			0.286325
$834$	−8.98572e9	+	7.50039e9i	−0.536379	+	0.447716i
$835$	−5.66732e9	+	1.36821e10i	−0.336880	+	0.813301i
$836$	2.31102e10	+	4.19834e9i	1.36798	+	0.248517i
$837$	5.40324e8	−	2.23809e8i	0.0318504	−	0.0131929i
$838$	−9.34535e9	−	2.99092e10i	−0.548582	−	1.75570i
$839$	2.22955e9	−	2.22955e9i	0.130332	−	0.130332i	−0.638932	−	0.769264i	$-0.720623\pi$
$839$	2.22955e9	−	2.22955e9i	0.130332	−	0.130332i	0.769264	+	0.638932i	$0.220623\pi$
$840$	−2.40037e9	+	8.68806e9i	−0.139734	+	0.505761i
$841$	1.21810e10	+	1.21810e10i	0.706151	+	0.706151i
$842$	−5.51763e9	+	1.05327e10i	−0.318537	+	0.608059i
$843$	5.13388e9	+	1.23943e10i	0.295154	+	0.712565i
$844$	−1.33733e10	+	2.07541e10i	−0.765666	+	1.18824i
$845$	1.75883e10	+	7.28532e9i	1.00283	+	0.415384i
$846$	−9.34044e8	+	1.03672e10i	−0.0530361	+	0.588663i
$847$		−	4.18988e9i		−	0.236924i
$848$	−3.31444e7	−	9.95371e8i	−0.00186648	−	0.0560531i
$849$			1.10262e10i			0.618374i
$850$	1.35018e10	+	1.21645e9i	0.754093	+	0.0679406i
$851$	2.39008e10	+	9.90005e9i	1.32941	+	0.550660i
$852$	−4.52368e9	+	9.78350e8i	−0.250584	+	0.0541945i
$853$	−2.84455e9	−	6.86735e9i	−0.156925	−	0.378850i	0.825789	−	0.563978i	$-0.190730\pi$
$853$	−2.84455e9	−	6.86735e9i	−0.156925	−	0.378850i	−0.982714	+	0.185128i	$0.940730\pi$
$854$	4.88195e9	+	2.55745e9i	0.268220	+	0.140509i
$855$	−1.36386e10	−	1.36386e10i	−0.746258	−	0.746258i
$856$	−1.10009e10	+	1.41086e10i	−0.599476	+	0.768824i
$857$	−1.67440e10	+	1.67440e10i	−0.908711	+	0.908711i	−0.996168	−	0.0874576i	$-0.972126\pi$
$857$	−1.67440e10	+	1.67440e10i	−0.908711	+	0.908711i	0.0874576	+	0.996168i	$0.472126\pi$
$858$	−4.57361e9	+	1.42906e9i	−0.247203	+	0.0772404i
$859$	−1.01860e10	+	4.21918e9i	−0.548312	+	0.227118i	−0.639602	−	0.768706i	$-0.720901\pi$
$859$	−1.01860e10	+	4.21918e9i	−0.548312	+	0.227118i	0.0912901	+	0.995824i	$0.470901\pi$
$860$	−3.92498e10	+	2.71815e10i	−2.10423	+	1.45723i
$861$	1.88759e9	−	4.55703e9i	0.100785	−	0.243316i
$862$	−1.67047e10	−	2.00127e10i	−0.888305	−	1.06422i
$863$	−2.44724e10			−1.29610			−0.648050	−	0.761598i	$-0.724415\pi$
$863$	−2.44724e10			−1.29610			−0.648050	+	0.761598i	$0.724415\pi$
$864$	−2.72162e9	+	2.42990e9i	−0.143559	+	0.128171i
$865$	−8.95934e9			−0.470673
$866$	1.31197e10	+	1.57178e10i	0.686453	+	0.822393i
$867$	3.55802e9	−	8.58981e9i	0.185413	−	0.447628i
$868$	1.05084e9	+	1.51740e9i	0.0545404	+	0.0787558i
$869$	−6.77089e9	+	2.80459e9i	−0.350007	+	0.144978i
$870$	−6.68903e8	+	2.09003e8i	−0.0344386	+	0.0107606i
$871$	−1.09921e10	+	1.09921e10i	−0.563659	+	0.563659i
$872$	8.84601e8	+	7.14739e9i	0.0451793	+	0.365040i
$873$	6.99551e8	+	6.99551e8i	0.0355852	+	0.0355852i
$874$	5.28406e10	+	2.76810e10i	2.67718	+	1.40247i
$875$	6.12092e9	+	1.47772e10i	0.308879	+	0.745700i
$876$	−2.10383e9	−	9.72768e9i	−0.105742	−	0.488928i
$877$	−3.63338e9	−	1.50499e9i	−0.181891	−	0.0753419i	0.289879	−	0.957063i	$-0.406385\pi$
$877$	−3.63338e9	−	1.50499e9i	−0.181891	−	0.0753419i	−0.471770	+	0.881721i	$0.656385\pi$
$878$	1.67268e10	+	1.50702e9i	0.834031	+	0.0751427i
$879$			1.54944e9i			0.0769508i
$880$	−1.05947e10	−	2.33482e10i	−0.524084	−	1.15495i
$881$		−	1.05469e10i		−	0.519647i	−0.965656	−	0.259823i	$-0.916336\pi$
$881$		−	1.05469e10i		−	0.519647i	0.965656	−	0.259823i	$-0.0836644\pi$
$882$	−4.35186e8	+	4.83026e9i	−0.0213567	+	0.237045i
$883$	−1.94819e10	−	8.06969e9i	−0.952292	−	0.394452i	−0.148200	−	0.988957i	$-0.547348\pi$
$883$	−1.94819e10	−	8.06969e9i	−0.952292	−	0.394452i	−0.804092	+	0.594505i	$0.797348\pi$
$884$	4.16153e9	+	2.68155e9i	0.202614	+	0.130558i
$885$	−9.79296e9	−	2.36423e10i	−0.474911	−	1.14654i
$886$	2.42033e9	−	4.62019e9i	0.116911	−	0.223173i
$887$	2.78446e10	+	2.78446e10i	1.33970	+	1.33970i	0.896344	+	0.443360i	$0.146214\pi$
$887$	2.78446e10	+	2.78446e10i	1.33970	+	1.33970i	0.443360	+	0.896344i	$0.353786\pi$
$888$	9.29544e9	−	5.27097e9i	0.445476	−	0.252607i
$889$	3.64721e9	−	3.64721e9i	0.174102	−	0.174102i
$890$	1.49352e10	+	4.77990e10i	0.710141	+	2.27276i
$891$	1.61755e9	−	6.70013e8i	0.0766102	−	0.0317330i
$892$	4.73723e9	−	2.60765e10i	0.223485	−	1.23019i
$893$	2.69018e10	−	6.49466e10i	1.26416	−	3.05194i
$894$	8.68415e9	−	7.24867e9i	0.406487	−	0.339295i
$895$	2.19641e10			1.02408
$896$	−9.31110e9	−	6.77422e9i	−0.432437	−	0.314616i
$897$	−1.21691e10			−0.562971
$898$	1.05483e10	−	8.80471e9i	0.486090	−	0.405740i
$899$	−5.49170e7	+	1.32581e8i	−0.00252086	+	0.00608588i
$900$	−2.46025e9	+	1.35427e10i	−0.112494	+	0.619237i
$901$	4.56188e8	−	1.88959e8i	0.0207782	−	0.00860660i
$902$	4.18450e9	+	1.33922e10i	0.189855	+	0.607618i
$903$	7.27546e9	−	7.27546e9i	0.328816	−	0.328816i
$904$	−1.61780e10	+	9.17371e9i	−0.728341	+	0.413005i
$905$	−5.20051e10	−	5.20051e10i	−2.33225	−	2.33225i
$906$	5.16680e9	−	9.86295e9i	0.230820	−	0.440614i
$907$	4.35075e9	+	1.05036e10i	0.193615	+	0.467428i	0.990637	−	0.136522i	$-0.0435926\pi$
$907$	4.35075e9	+	1.05036e10i	0.193615	+	0.467428i	−0.797022	+	0.603950i	$0.793593\pi$
$908$	1.88081e10	+	1.21193e10i	0.833767	+	0.537253i
$909$	−1.26064e10	−	5.22173e9i	−0.556694	−	0.230590i
$910$	−1.11430e9	+	1.23679e10i	−0.0490181	+	0.544067i
$911$		−	1.47351e10i		−	0.645710i	−0.946448	−	0.322855i	$-0.895357\pi$
$911$		−	1.47351e10i		−	0.645710i	0.946448	−	0.322855i	$-0.104643\pi$
$912$	2.24379e10	−	1.01817e10i	0.979490	−	0.444464i
$913$		−	5.11031e9i		−	0.222228i
$914$	5.85986e9	+	5.27949e8i	0.253849	+	0.0228708i
$915$	1.18936e10	+	4.92648e9i	0.513261	+	0.212600i
$916$	−1.50967e9	−	6.98039e9i	−0.0649004	−	0.300086i
$917$	−1.53177e9	−	3.69801e9i	−0.0655994	−	0.158371i
$918$	−1.60236e9	−	8.39414e8i	−0.0683616	−	0.0358118i
$919$	−2.18966e10	−	2.18966e10i	−0.930622	−	0.930622i	0.0671229	−	0.997745i	$-0.478618\pi$
$919$	−2.18966e10	−	2.18966e10i	−0.930622	−	0.930622i	−0.997745	+	0.0671229i	$0.978618\pi$
$920$	−7.99800e9	−	6.46222e10i	−0.338629	−	2.73605i
$921$	4.20071e9	−	4.20071e9i	0.177180	−	0.177180i
$922$	−5.13307e8	+	1.60386e8i	−0.0215685	+	0.00673922i
$923$	−5.89101e9	+	2.44014e9i	−0.246595	+	0.102143i
$924$	3.14588e9	+	4.54262e9i	0.131187	+	0.189432i
$925$	1.54273e10	−	3.72449e10i	0.640906	−	1.54728i
$926$	7.49135e9	+	8.97489e9i	0.310043	+	0.371442i
$927$	2.02400e9			0.0834509
$928$	5.06147e7	−	8.93819e8i	0.00207902	−	0.0367140i
$929$	1.05089e10			0.430035			0.215017	−	0.976610i	$-0.431019\pi$
$929$	1.05089e10			0.430035			0.215017	+	0.976610i	$0.431019\pi$
$930$	2.76276e9	+	3.30988e9i	0.112630	+	0.134934i
$931$	1.25340e10	−	3.02597e10i	0.509055	−	1.22897i
$932$	3.01869e10	−	2.09052e10i	1.22141	−	0.845860i
$933$	4.45885e9	−	1.84692e9i	0.179737	−	0.0744495i
$934$	1.79127e10	−	5.59695e9i	0.719360	−	0.224769i
$935$	8.98873e9	−	8.98873e9i	0.359632	−	0.359632i
$936$	−3.09084e9	+	3.96399e9i	−0.123200	+	0.158004i
$937$	−6.85803e8	−	6.85803e8i	−0.0272340	−	0.0272340i	0.693359	−	0.720593i	$-0.256130\pi$
$937$	−6.85803e8	−	6.85803e8i	−0.0272340	−	0.0272340i	−0.720593	+	0.693359i	$0.756130\pi$
$938$	1.58791e10	+	8.31843e9i	0.628227	+	0.329103i
$939$	−1.07791e9	−	2.60231e9i	−0.0424867	−	0.102572i
$940$	−7.50018e10	+	1.62209e10i	−2.94526	+	0.636981i
$941$	3.73820e9	+	1.54841e9i	0.146251	+	0.0605792i	0.454608	−	0.890691i	$-0.349779\pi$
$941$	3.73820e9	+	1.54841e9i	0.146251	+	0.0605792i	−0.308357	+	0.951271i	$0.599779\pi$
$942$	−2.53708e10	−	2.28580e9i	−0.988908	−	0.0890965i
$943$			3.56331e10i			1.38377i
$944$	3.26729e10	−	1.08796e9i	1.26411	−	0.0420930i
$945$		−	4.53742e9i		−	0.174903i
$946$	−2.62627e9	+	2.91497e10i	−0.100860	+	1.11948i
$947$	−4.15817e10	−	1.72237e10i	−1.59102	−	0.659024i	−0.600914	−	0.799313i	$-0.705197\pi$
$947$	−4.15817e10	−	1.72237e10i	−1.59102	−	0.659024i	−0.990111	+	0.140289i	$0.955197\pi$
$948$	−4.16427e9	+	6.46257e9i	−0.158749	+	0.246363i
$949$	−5.24725e9	−	1.26680e10i	−0.199297	−	0.481145i
$950$	4.31356e10	−	8.23420e10i	1.63231	−	3.11594i
$951$	−5.40792e9	−	5.40792e9i	−0.203891	−	0.203891i
$952$	1.52032e9	−	5.50275e9i	0.0571092	−	0.206705i
$953$	8.97049e8	−	8.97049e8i	0.0335731	−	0.0335731i	−0.690121	−	0.723694i	$-0.742443\pi$
$953$	8.97049e8	−	8.97049e8i	0.0335731	−	0.0335731i	0.723694	+	0.690121i	$0.242443\pi$
$954$	1.49521e8	+	4.78531e8i	0.00557547	+	0.0178440i
$955$	8.83155e9	−	3.65815e9i	0.328114	−	0.135909i
$956$	−1.78137e10	−	3.23615e9i	−0.659405	−	0.119792i
$957$	−1.64404e8	+	3.96906e8i	−0.00606345	+	0.0146385i
$958$	−3.95660e10	+	3.30258e10i	−1.45393	+	1.21359i
$959$	−2.54592e10			−0.932138
$960$	−2.30815e10	−	1.38081e10i	−0.842007	−	0.503716i
$961$	−2.66297e10			−0.967911
$962$	1.13022e10	−	9.43393e9i	0.409307	−	0.341649i
$963$	3.44650e9	−	8.32058e9i	0.124361	−	0.300235i
$964$	1.04137e10	+	1.89181e9i	0.374398	+	0.0680155i
$965$	−7.29062e10	+	3.01987e10i	−2.61167	+	1.08179i
$966$	4.18516e9	+	1.33943e10i	0.149380	+	0.478081i
$967$	−1.32406e10	+	1.32406e10i	−0.470885	+	0.470885i	−0.902201	−	0.431316i	$-0.858050\pi$
$967$	−1.32406e10	+	1.32406e10i	−0.470885	+	0.470885i	0.431316	+	0.902201i	$0.358050\pi$
$968$	1.20511e10	+	3.32954e9i	0.427036	+	0.117983i
$969$	8.63827e9	+	8.63827e9i	0.304996	+	0.304996i
$970$	−3.38432e9	+	6.46036e9i	−0.119061	+	0.227277i
$971$	4.45379e9	+	1.07524e10i	0.156121	+	0.376910i	0.982515	−	0.186182i	$-0.0596114\pi$
$971$	4.45379e9	+	1.07524e10i	0.156121	+	0.376910i	−0.826394	+	0.563093i	$0.809611\pi$
$972$	9.94837e8	−	1.54390e9i	0.0347472	−	0.0539245i
$973$	1.71799e10	+	7.11614e9i	0.597896	+	0.247657i
$974$	4.74332e9	−	5.26475e10i	0.164485	−	1.82567i
$975$			1.89632e10i			0.655234i
$976$	−1.12354e10	+	1.20094e10i	−0.386824	+	0.413473i
$977$		−	3.06809e10i		−	1.05253i	−0.850319	−	0.526267i	$-0.823591\pi$
$977$		−	3.06809e10i		−	1.05253i	0.850319	−	0.526267i	$-0.176409\pi$
$978$	2.73789e10	+	2.46673e9i	0.935902	+	0.0843209i
$979$	2.83624e10	+	1.17481e10i	0.966060	+	0.400155i
$980$	−3.49445e10	+	7.55756e9i	−1.18601	+	0.256502i
$981$	−1.38740e9	−	3.34947e9i	−0.0469201	−	0.113275i
$982$	−2.46522e9	−	1.29143e9i	−0.0830739	−	0.0435191i
$983$	−3.48635e10	−	3.48635e10i	−1.17067	−	1.17067i	−0.982050	−	0.188619i	$-0.939599\pi$
$983$	−3.48635e10	−	3.48635e10i	−1.17067	−	1.17067i	−0.188619	−	0.982050i	$-0.560401\pi$
$984$	1.16072e10	+	9.05047e9i	0.388368	+	0.302823i
$985$	3.04786e10	−	3.04786e10i	1.01617	−	1.01617i
$986$	4.23662e8	−	1.32376e8i	0.0140751	−	0.00439786i
$987$	1.52785e10	−	6.32855e9i	0.505790	−	0.209505i
$988$	2.79077e10	−	1.93268e10i	0.920609	−	0.637545i
$989$	−2.84447e10	+	6.86716e10i	−0.935006	+	2.25730i
$990$	8.27082e9	+	9.90871e9i	0.270910	+	0.324559i
$991$	3.84102e10			1.25369			0.626843	−	0.779145i	$-0.284347\pi$
$991$	3.84102e10			1.25369			0.626843	+	0.779145i	$0.284347\pi$
$992$	−5.19950e9	+	1.81666e9i	−0.169111	+	0.0590857i
$993$	7.30362e9			0.236710
$994$	4.71183e9	+	5.64493e9i	0.152173	+	0.182308i
$995$	5.12951e9	−	1.23837e10i	0.165080	−	0.398539i
$996$	−3.05209e9	−	4.40719e9i	−0.0978790	−	0.141336i
$997$	−5.36573e9	+	2.22256e9i	−0.171473	+	0.0710264i	−0.466769	−	0.884380i	$-0.654582\pi$
$997$	−5.36573e9	+	2.22256e9i	−0.171473	+	0.0710264i	0.295296	+	0.955406i	$0.404582\pi$
$998$	1.83768e10	−	5.74198e9i	0.585213	−	0.182854i
$999$	−3.80372e9	+	3.80372e9i	−0.120706	+	0.120706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.8.n.a.13.14	✓	224
32.5	even	8	inner	96.8.n.a.37.14	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.8.n.a.13.14	✓	224	1.1	even	1	trivial
96.8.n.a.37.14	yes	224	32.5	even	8	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.68559 + 7.24987i) q^{2} +(10.3325 - 24.9447i) q^{3} +(22.8788 - 125.939i) q^{4} +(-438.852 + 181.778i) q^{5} +(91.1027 + 291.569i) q^{6} +(343.163 - 343.163i) q^{7} +(714.323 + 1259.72i) q^{8} +(-515.481 - 515.481i) q^{9} +O(q^{10})\)	\(q+(-8.68559 + 7.24987i) q^{2} +(10.3325 - 24.9447i) q^{3} +(22.8788 - 125.939i) q^{4} +(-438.852 + 181.778i) q^{5} +(91.1027 + 291.569i) q^{6} +(343.163 - 343.163i) q^{7} +(714.323 + 1259.72i) q^{8} +(-515.481 - 515.481i) q^{9} +(2493.81 - 4760.47i) q^{10} +(-1260.75 - 3043.71i) q^{11} +(-2905.12 - 1871.96i) q^{12} +(-4398.91 - 1822.09i) q^{13} +(-492.685 + 5468.45i) q^{14} +12825.3i q^{15} +(-15337.1 - 5762.66i) q^{16} -8123.12i q^{17} +(8214.42 + 740.085i) q^{18} +(-51460.1 - 21315.5i) q^{19} +(12852.5 + 59427.3i) q^{20} +(-5014.39 - 12105.8i) q^{21} +(33016.8 + 17296.2i) q^{22} +(66934.5 + 66934.5i) q^{23} +(38804.1 - 4802.61i) q^{24} +(104305. - 104305. i) q^{25} +(51417.1 - 16065.6i) q^{26} +(-18184.7 + 7532.36i) q^{27} +(-35366.3 - 51068.6i) q^{28} +(1848.24 - 4462.06i) q^{29} +(-92981.4 - 111395. i) q^{30} -29713.1 q^{31} +(174990. - 61140.0i) q^{32} -88951.3 q^{33} +(58891.5 + 70554.1i) q^{34} +(-88218.0 + 212977. i) q^{35} +(-76712.6 + 53125.4i) q^{36} +(252492. - 104586. i) q^{37} +(601496. - 187942. i) q^{38} +(-90903.2 + 90903.2i) q^{39} +(-542472. - 422982. i) q^{40} +(266179. + 266179. i) q^{41} +(131319. + 68792.4i) q^{42} +(300494. + 725457. i) q^{43} +(-412166. + 89140.3i) q^{44} +(319923. + 132516. i) q^{45} +(-1.06663e6 - 96099.1i) q^{46} +1.26208e6i q^{47} +(-302218. + 323038. i) q^{48} +588022. i q^{49} +(-149752. + 1.66214e6i) q^{50} +(-202629. - 83931.8i) q^{51} +(-330114. + 512306. i) q^{52} +(23261.9 + 56159.2i) q^{53} +(103336. - 197260. i) q^{54} +(1.10656e6 + 1.10656e6i) q^{55} +(677418. + 187160. i) q^{56} +(-1.06342e6 + 1.06342e6i) q^{57} +(16296.2 + 52155.1i) q^{58} +(-1.84342e6 + 763568. i) q^{59} +(1.61520e6 + 293427. i) q^{60} +(384123. - 927356. i) q^{61} +(258075. - 215416. i) q^{62} -353788. q^{63} +(-1.07664e6 + 1.79969e6i) q^{64} +2.26169e6 q^{65} +(772594. - 644885. i) q^{66} +(1.24941e6 - 3.01634e6i) q^{67} +(-1.02302e6 - 185847. i) q^{68} +(2.36126e6 - 978067. i) q^{69} +(-777830. - 2.48940e6i) q^{70} +(946955. - 946955. i) q^{71} +(281142. - 1.01758e6i) q^{72} +(2.03632e6 + 2.03632e6i) q^{73} +(-1.43481e6 + 2.73892e6i) q^{74} +(-1.52413e6 - 3.67958e6i) q^{75} +(-3.86179e6 + 5.99315e6i) q^{76} +(-1.47713e6 - 611847. i) q^{77} +(130511. - 1.44858e6i) q^{78} -2.22455e6i q^{79} +(7.77825e6 - 259004. i) q^{80} +531441. i q^{81} +(-4.24168e6 - 382157. i) q^{82} +(1.43309e6 + 593606. i) q^{83} +(-1.63931e6 + 354540. i) q^{84} +(1.47661e6 + 3.56484e6i) q^{85} +(-7.86944e6 - 4.12248e6i) q^{86} +(-92208.0 - 92208.0i) q^{87} +(2.93365e6 - 3.76238e6i) q^{88} +(-6.58908e6 + 6.58908e6i) q^{89} +(-3.73944e6 + 1.16842e6i) q^{90} +(-2.13482e6 + 884270. i) q^{91} +(9.96103e6 - 6.89827e6i) q^{92} +(-307009. + 741185. i) q^{93} +(-9.14989e6 - 1.09619e7i) q^{94} +2.64580e7 q^{95} +(282957. - 4.99682e6i) q^{96} -1.35708e6 q^{97} +(-4.26308e6 - 5.10731e6i) q^{98} +(-919085. + 2.21887e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q+O(q^{10}) \) 224 * q	\( 224 q + 13000 q^{10} - 30672 q^{12} + 52384 q^{14} + 21112 q^{16} - 40824 q^{18} - 164000 q^{20} + 511464 q^{22} + 286832 q^{23} - 81864 q^{24} + 727960 q^{26} + 390920 q^{28} + 1429968 q^{31} - 1071320 q^{32} + 403160 q^{34} - 1633008 q^{35} + 1244920 q^{38} - 4089528 q^{40} - 732368 q^{43} + 3370472 q^{44} + 2715808 q^{46} + 2317416 q^{50} - 2993328 q^{51} - 8882216 q^{52} + 3631264 q^{53} + 157464 q^{54} + 4191008 q^{55} + 10737272 q^{56} + 7269664 q^{58} + 3671872 q^{59} - 2168208 q^{60} + 4559776 q^{61} - 10347504 q^{62} - 4000752 q^{63} - 22412520 q^{64} - 3757104 q^{66} + 776272 q^{67} + 17922136 q^{68} - 9580896 q^{69} - 1696200 q^{70} + 24697408 q^{71} - 21862880 q^{74} - 11260512 q^{75} + 5188008 q^{76} + 23828896 q^{77} - 14742648 q^{78} + 69474376 q^{80} - 6997080 q^{82} - 39909568 q^{86} - 37691824 q^{88} + 3406992 q^{91} - 684560 q^{92} + 50770592 q^{94} + 54100440 q^{96} - 52426160 q^{98}+O(q^{100}) \) 224 * q + 13000 * q^10 - 30672 * q^12 + 52384 * q^14 + 21112 * q^16 - 40824 * q^18 - 164000 * q^20 + 511464 * q^22 + 286832 * q^23 - 81864 * q^24 + 727960 * q^26 + 390920 * q^28 + 1429968 * q^31 - 1071320 * q^32 + 403160 * q^34 - 1633008 * q^35 + 1244920 * q^38 - 4089528 * q^40 - 732368 * q^43 + 3370472 * q^44 + 2715808 * q^46 + 2317416 * q^50 - 2993328 * q^51 - 8882216 * q^52 + 3631264 * q^53 + 157464 * q^54 + 4191008 * q^55 + 10737272 * q^56 + 7269664 * q^58 + 3671872 * q^59 - 2168208 * q^60 + 4559776 * q^61 - 10347504 * q^62 - 4000752 * q^63 - 22412520 * q^64 - 3757104 * q^66 + 776272 * q^67 + 17922136 * q^68 - 9580896 * q^69 - 1696200 * q^70 + 24697408 * q^71 - 21862880 * q^74 - 11260512 * q^75 + 5188008 * q^76 + 23828896 * q^77 - 14742648 * q^78 + 69474376 * q^80 - 6997080 * q^82 - 39909568 * q^86 - 37691824 * q^88 + 3406992 * q^91 - 684560 * q^92 + 50770592 * q^94 + 54100440 * q^96 - 52426160 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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