LMFDB - Embedded newform 63.7.m.d.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,7,Mod(10,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("63.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, degree $2$, 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:	$14.4934072681$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$7.29767 - 12.6399i$ of defining polynomial
Character	$\chi$	$=$	63.19
Dual form			63.7.m.d.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.79767 - 13.5060i) q^{2} +(-89.6073 - 155.204i) q^{4} +(-22.3721 - 12.9165i) q^{5} +(-203.121 + 276.389i) q^{7} -1796.81 q^{8} +O(q^{10})$	\(q+(7.79767 - 13.5060i) q^{2} +(-89.6073 - 155.204i) q^{4} +(-22.3721 - 12.9165i) q^{5} +(-203.121 + 276.389i) q^{7} -1796.81 q^{8} +(-348.901 + 201.438i) q^{10} +(311.967 + 540.343i) q^{11} -3257.26i q^{13} +(2149.03 + 4898.53i) q^{14} +(-8276.07 + 14334.6i) q^{16} +(-275.246 + 158.913i) q^{17} +(-5196.73 - 3000.33i) q^{19} +4629.67i q^{20} +9730.47 q^{22} +(-21.0083 + 36.3874i) q^{23} +(-7478.83 - 12953.7i) q^{25} +(-43992.4 - 25399.0i) q^{26} +(61097.9 + 6758.77i) q^{28} +24273.4 q^{29} +(-17547.8 + 10131.2i) q^{31} +(71570.2 + 123963. i) q^{32} +4956.62i q^{34} +(8114.24 - 3559.79i) q^{35} +(8688.57 - 15049.0i) q^{37} +(-81044.8 + 46791.2i) q^{38} +(40198.5 + 23208.6i) q^{40} -100535. i q^{41} -67873.7 q^{43} +(55909.1 - 96837.4i) q^{44} +(327.631 + 567.474i) q^{46} +(-57039.5 - 32931.8i) q^{47} +(-35132.9 - 112281. i) q^{49} -233270. q^{50} +(-505541. + 291874. i) q^{52} +(49611.0 + 85928.8i) q^{53} -16118.2i q^{55} +(364970. - 496619. i) q^{56} +(189276. - 327835. i) q^{58} +(-87190.7 + 50339.6i) q^{59} +(-201092. - 116101. i) q^{61} +315999. i q^{62} +1.17299e6 q^{64} +(-42072.6 + 72871.8i) q^{65} +(-20544.0 - 35583.3i) q^{67} +(49328.1 + 28479.6i) q^{68} +(15193.8 - 137349. i) q^{70} +400361. q^{71} +(479106. - 276612. i) q^{73} +(-135501. - 234695. i) q^{74} +1.07541e6i q^{76} +(-212712. - 23530.6i) q^{77} +(5240.77 - 9077.28i) q^{79} +(370306. - 213797. i) q^{80} +(-1.35782e6 - 783939. i) q^{82} -712797. i q^{83} +8210.45 q^{85} +(-529257. + 916700. i) q^{86} +(-560546. - 970895. i) q^{88} +(164942. + 95229.2i) q^{89} +(900271. + 661617. i) q^{91} +7529.99 q^{92} +(-889550. + 513582. i) q^{94} +(77507.9 + 134248. i) q^{95} +1.07270e6i q^{97} +(-1.79041e6 - 401025. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8	$ 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8} - 3411 q^{10} + 314 q^{11} + 5360 q^{14} - 12721 q^{16} + 5532 q^{17} - 18234 q^{19} + 86106 q^{22} - 3928 q^{23} - 17038 q^{25} - 12366 q^{26} + 85037 q^{28} + 8300 q^{29} - 89508 q^{31} + 186207 q^{32} + 25860 q^{35} + 64706 q^{37} + 77136 q^{38} + 221823 q^{40} + 45740 q^{43} - 92529 q^{44} - 111504 q^{46} - 483276 q^{47} - 310684 q^{49} - 967216 q^{50} - 1673988 q^{52} + 540974 q^{53} + 241885 q^{56} + 539799 q^{58} + 181770 q^{59} + 418224 q^{61} + 2378626 q^{64} + 414204 q^{65} - 1158902 q^{67} + 821250 q^{68} + 1087917 q^{70} - 1442344 q^{71} - 378666 q^{73} + 432940 q^{74} - 1065994 q^{77} + 611452 q^{79} + 2094945 q^{80} - 1561266 q^{82} - 275112 q^{85} - 816224 q^{86} - 366441 q^{88} + 989196 q^{89} + 304446 q^{91} - 678720 q^{92} - 716148 q^{94} + 591792 q^{95} - 3509629 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8 - 3411 * q^10 + 314 * q^11 + 5360 * q^14 - 12721 * q^16 + 5532 * q^17 - 18234 * q^19 + 86106 * q^22 - 3928 * q^23 - 17038 * q^25 - 12366 * q^26 + 85037 * q^28 + 8300 * q^29 - 89508 * q^31 + 186207 * q^32 + 25860 * q^35 + 64706 * q^37 + 77136 * q^38 + 221823 * q^40 + 45740 * q^43 - 92529 * q^44 - 111504 * q^46 - 483276 * q^47 - 310684 * q^49 - 967216 * q^50 - 1673988 * q^52 + 540974 * q^53 + 241885 * q^56 + 539799 * q^58 + 181770 * q^59 + 418224 * q^61 + 2378626 * q^64 + 414204 * q^65 - 1158902 * q^67 + 821250 * q^68 + 1087917 * q^70 - 1442344 * q^71 - 378666 * q^73 + 432940 * q^74 - 1065994 * q^77 + 611452 * q^79 + 2094945 * q^80 - 1561266 * q^82 - 275112 * q^85 - 816224 * q^86 - 366441 * q^88 + 989196 * q^89 + 304446 * q^91 - 678720 * q^92 - 716148 * q^94 + 591792 * q^95 - 3509629 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	7.79767	−	13.5060i	0.974709	−	1.68825i	0.293816	−	0.955862i	$-0.405075\pi$
$2$	7.79767	−	13.5060i	0.974709	−	1.68825i	0.680893	−	0.732383i	$-0.261592\pi$
$3$		0			0
$3$		0			0
$4$	−89.6073	−	155.204i	−1.40011	−	2.42507i
$5$	−22.3721	−	12.9165i	−0.178977	−	0.103332i	0.407835	−	0.913056i	$-0.366284\pi$
$5$	−22.3721	−	12.9165i	−0.178977	−	0.103332i	−0.586812	+	0.809723i	$0.699617\pi$
$6$		0			0
$7$	−203.121	+	276.389i	−0.592189	+	0.805799i
$7$	−203.121	+	276.389i	−0.592189	+	0.805799i
$8$	−1796.81			−3.50940
$9$		0			0
$10$	−348.901	+	201.438i	−0.348901	+	0.201438i
$11$	311.967	+	540.343i	0.234386	+	0.405968i	0.959094	−	0.283088i	$-0.0913588\pi$
$11$	311.967	+	540.343i	0.234386	+	0.405968i	−0.724708	+	0.689056i	$0.758025\pi$
$12$		0			0
$13$		−	3257.26i		−	1.48259i	−0.671177	−	0.741297i	$-0.734211\pi$
$13$		−	3257.26i		−	1.48259i	0.671177	−	0.741297i	$-0.265789\pi$
$14$	2149.03	+	4898.53i	0.783175	+	1.78518i
$15$		0			0
$16$	−8276.07	+	14334.6i	−2.02053	+	3.49965i
$17$	−275.246	+	158.913i	−0.0560240	+	0.0323455i	−0.527750	−	0.849400i	$-0.676964\pi$
$17$	−275.246	+	158.913i	−0.0560240	+	0.0323455i	0.471726	+	0.881745i	$0.343631\pi$
$18$		0			0
$19$	−5196.73	−	3000.33i	−0.757651	−	0.437430i	0.0708006	−	0.997490i	$-0.477445\pi$
$19$	−5196.73	−	3000.33i	−0.757651	−	0.437430i	−0.828452	+	0.560060i	$0.810778\pi$
$20$			4629.67i			0.578709i
$21$		0			0
$22$	9730.47			0.913831
$23$	−21.0083	+	36.3874i	−0.00172666	+	0.00299067i	−0.866887	−	0.498504i	$-0.833883\pi$
$23$	−21.0083	+	36.3874i	−0.00172666	+	0.00299067i	0.865161	+	0.501495i	$0.167216\pi$
$24$		0			0
$25$	−7478.83	−	12953.7i	−0.478645	−	0.829037i
$26$	−43992.4	−	25399.0i	−2.50298	−	1.44510i
$27$		0			0
$28$	61097.9	+	6758.77i	2.78325	+	0.307888i
$29$	24273.4			0.995260			0.497630	−	0.867389i	$-0.334204\pi$
$29$	24273.4			0.995260			0.497630	+	0.867389i	$0.334204\pi$
$30$		0			0
$31$	−17547.8	+	10131.2i	−0.589030	+	0.340076i	−0.764714	−	0.644370i	$-0.777120\pi$
$31$	−17547.8	+	10131.2i	−0.589030	+	0.340076i	0.175684	+	0.984447i	$0.443786\pi$
$32$	71570.2	+	123963.i	2.18415	+	3.78306i
$33$		0			0
$34$			4956.62i			0.126110i
$35$	8114.24	−	3559.79i	0.189253	−	0.0830272i
$36$		0			0
$37$	8688.57	−	15049.0i	0.171531	−	0.297101i	−0.767424	−	0.641140i	$-0.778462\pi$
$37$	8688.57	−	15049.0i	0.171531	−	0.297101i	0.938955	+	0.344039i	$0.111795\pi$
$38$	−81044.8	+	46791.2i	−1.47698	+	0.852734i
$39$		0			0
$40$	40198.5	+	23208.6i	0.628101	+	0.362634i
$41$		−	100535.i		−	1.45870i	−0.684141	−	0.729350i	$-0.739823\pi$
$41$		−	100535.i		−	1.45870i	0.684141	−	0.729350i	$-0.260177\pi$
$42$		0			0
$43$	−67873.7			−0.853682			−0.426841	−	0.904327i	$-0.640374\pi$
$43$	−67873.7			−0.853682			−0.426841	+	0.904327i	$0.640374\pi$
$44$	55909.1	−	96837.4i	0.656333	−	1.13680i
$45$		0			0
$46$	327.631	+	567.474i	0.00336598	+	0.00583006i
$47$	−57039.5	−	32931.8i	−0.549392	−	0.317191i	0.199485	−	0.979901i	$-0.436073\pi$
$47$	−57039.5	−	32931.8i	−0.549392	−	0.317191i	−0.748877	+	0.662709i	$0.769406\pi$
$48$		0			0
$49$	−35132.9	−	112281.i	−0.298624	−	0.954371i
$50$	−233270.			−1.86616
$51$		0			0
$52$	−505541.	+	291874.i	−3.59539	+	2.07580i
$53$	49611.0	+	85928.8i	0.333235	+	0.577180i	0.983144	−	0.182832i	$-0.0585264\pi$
$53$	49611.0	+	85928.8i	0.333235	+	0.577180i	−0.649909	+	0.760012i	$0.725193\pi$
$54$		0			0
$55$		−	16118.2i		−	0.0968785i
$56$	364970.	−	496619.i	2.07823	−	2.82787i
$57$		0			0
$58$	189276.	−	327835.i	0.970088	−	1.68024i
$59$	−87190.7	+	50339.6i	−0.424536	+	0.245106i	−0.697016	−	0.717055i	$-0.745489\pi$
$59$	−87190.7	+	50339.6i	−0.424536	+	0.245106i	0.272480	+	0.962161i	$0.412156\pi$
$60$		0			0
$61$	−201092.	−	116101.i	−0.885943	−	0.511499i	−0.0133295	−	0.999911i	$-0.504243\pi$
$61$	−201092.	−	116101.i	−0.885943	−	0.511499i	−0.872613	+	0.488412i	$0.837576\pi$
$62$			315999.i			1.32590i
$63$		0			0
$64$	1.17299e6			4.47458
$65$	−42072.6	+	72871.8i	−0.153200	+	0.265350i
$66$		0			0
$67$	−20544.0	−	35583.3i	−0.0683063	−	0.118310i	0.829850	−	0.557987i	$-0.188426\pi$
$67$	−20544.0	−	35583.3i	−0.0683063	−	0.118310i	−0.898156	+	0.439677i	$0.855093\pi$
$68$	49328.1	+	28479.6i	0.156880	+	0.0905747i
$69$		0			0
$70$	15193.8	−	137349.i	0.0442967	−	0.400433i
$71$	400361.			1.11861			0.559303	−	0.828963i	$-0.311069\pi$
$71$	400361.			1.11861			0.559303	+	0.828963i	$0.311069\pi$
$72$		0			0
$73$	479106.	−	276612.i	1.23158	−	0.711054i	0.264223	−	0.964462i	$-0.414885\pi$
$73$	479106.	−	276612.i	1.23158	−	0.711054i	0.967360	+	0.253407i	$0.0815513\pi$
$74$	−135501.	−	234695.i	−0.334386	−	0.579173i
$75$		0			0
$76$			1.07541e6i			2.44981i
$77$	−212712.	−	23530.6i	−0.465929	−	0.0515420i
$78$		0			0
$79$	5240.77	−	9077.28i	0.0106295	−	0.0184109i	−0.860662	−	0.509177i	$-0.829950\pi$
$79$	5240.77	−	9077.28i	0.0106295	−	0.0184109i	0.871291	+	0.490766i	$0.163283\pi$
$80$	370306.	−	213797.i	0.723255	−	0.417571i
$81$		0			0
$82$	−1.35782e6	−	783939.i	−2.46264	−	1.42181i
$83$		−	712797.i		−	1.24661i	−0.781978	−	0.623306i	$-0.785789\pi$
$83$		−	712797.i		−	1.24661i	0.781978	−	0.623306i	$-0.214211\pi$
$84$		0			0
$85$	8210.45			0.0133693
$86$	−529257.	+	916700.i	−0.832091	+	1.44122i
$87$		0			0
$88$	−560546.	−	970895.i	−0.822552	−	1.42470i
$89$	164942.	+	95229.2i	0.233970	+	0.135083i	0.612402	−	0.790546i	$-0.290203\pi$
$89$	164942.	+	95229.2i	0.233970	+	0.135083i	−0.378432	+	0.925629i	$0.623537\pi$
$90$		0			0
$91$	900271.	+	661617.i	1.19467	+	0.877976i
$92$	7529.99			0.00967009
$93$		0			0
$94$	−889550.	+	513582.i	−1.07099	+	0.618339i
$95$	77507.9	+	134248.i	0.0904014	+	0.156580i
$96$		0			0
$97$			1.07270e6i			1.17533i	0.809103	+	0.587667i	$0.199954\pi$
$97$			1.07270e6i			1.17533i	−0.809103	+	0.587667i	$0.800046\pi$
$98$	−1.79041e6	−	401025.i	−1.90228	−	0.426082i
$99$		0			0
$100$	−1.34031e6	+	2.32149e6i	−1.34031	+	2.32149i
$101$	461204.	−	266276.i	0.447640	−	0.258445i	−0.259193	−	0.965826i	$-0.583456\pi$
$101$	461204.	−	266276.i	0.447640	−	0.258445i	0.706833	+	0.707380i	$0.250123\pi$
$102$		0			0
$103$	904654.	+	522302.i	0.827886	+	0.477980i	0.853128	−	0.521701i	$-0.174702\pi$
$103$	904654.	+	522302.i	0.827886	+	0.477980i	−0.0252420	+	0.999681i	$0.508036\pi$
$104$			5.85268e6i			5.20301i
$105$		0			0
$106$	1.54740e6			1.29923
$107$	179422.	−	310767.i	0.146461	−	0.253679i	−0.783456	−	0.621448i	$-0.786545\pi$
$107$	179422.	−	310767.i	0.146461	−	0.253679i	0.929917	+	0.367769i	$0.119878\pi$
$108$		0			0
$109$	−376187.	−	651575.i	−0.290485	−	0.503136i	0.683439	−	0.730007i	$-0.260483\pi$
$109$	−376187.	−	651575.i	−0.290485	−	0.503136i	−0.973925	+	0.226872i	$0.927150\pi$
$110$	−217691.	−	125684.i	−0.163555	−	0.0944283i
$111$		0			0
$112$	−2.28088e6	−	5.19907e6i	−1.62348	−	3.70059i
$113$	2.37249e6			1.64425			0.822126	−	0.569306i	$-0.192788\pi$
$113$	2.37249e6			1.64425			0.822126	+	0.569306i	$0.192788\pi$
$114$		0			0
$115$	940.000	−	542.709i	0.000618065	−	0.000356840i
$116$	−2.17507e6	−	3.76734e6i	−1.39348	−	2.41357i
$117$		0			0
$118$			1.57013e6i			0.955627i
$119$	11986.3	−	108354.i	0.00711285	−	0.0642987i
$120$		0			0
$121$	691133.	−	1.19708e6i	0.390127	−	0.675719i
$122$	−3.13610e6	+	1.81063e6i	−1.72707	+	0.997126i
$123$		0			0
$124$	3.14482e6	+	1.81566e6i	1.64942	+	0.952291i
$125$			790045.i			0.404503i
$126$		0			0
$127$	−1.06403e6			−0.519447			−0.259724	−	0.965683i	$-0.583631\pi$
$127$	−1.06403e6			−0.519447			−0.259724	+	0.965683i	$0.583631\pi$
$128$	4.56606e6	−	7.90865e6i	2.17727	−	3.77114i
$129$		0			0
$130$	656136.	+	1.13646e6i	0.298651	+	0.517278i
$131$	565054.	+	326234.i	0.251348	+	0.145116i	0.620382	−	0.784300i	$-0.286978\pi$
$131$	565054.	+	326234.i	0.251348	+	0.145116i	−0.369033	+	0.929416i	$0.620311\pi$
$132$		0			0
$133$	1.88482e6	−	826889.i	0.801153	−	0.351473i
$134$	−640782.			−0.266315
$135$		0			0
$136$	494565.	−	285537.i	0.196610	−	0.113513i
$137$	2.29875e6	+	3.98155e6i	0.893985	+	1.54843i	0.835056	+	0.550165i	$0.185435\pi$
$137$	2.29875e6	+	3.98155e6i	0.893985	+	1.54843i	0.0589291	+	0.998262i	$0.481231\pi$
$138$		0			0
$139$			1.96781e6i			0.732720i	0.930473	+	0.366360i	$0.119396\pi$
$139$			1.96781e6i			0.732720i	−0.930473	+	0.366360i	$0.880604\pi$
$140$	−1.27959e6	−	940382.i	−0.466323	−	0.342705i
$141$		0			0
$142$	3.12189e6	−	5.40726e6i	1.09031	−	1.88848i
$143$	1.76004e6	−	1.01616e6i	0.601886	−	0.347499i
$144$		0			0
$145$	−543047.	−	313528.i	−0.178129	−	0.102843i
$146$		−	8.62772e6i		−	2.77228i
$147$		0			0
$148$	−3.11424e6			−0.960653
$149$	−1.55562e6	+	2.69442e6i	−0.470268	+	0.814529i	−0.999422	−	0.0339975i	$-0.989176\pi$
$149$	−1.55562e6	+	2.69442e6i	−0.470268	+	0.814529i	0.529154	+	0.848526i	$0.322510\pi$
$150$		0			0
$151$	869607.	+	1.50620e6i	0.252576	+	0.437475i	0.964234	−	0.265051i	$-0.0853889\pi$
$151$	869607.	+	1.50620e6i	0.252576	+	0.437475i	−0.711658	+	0.702526i	$0.752056\pi$
$152$	9.33754e6	+	5.39103e6i	2.65890	+	1.53512i
$153$		0			0
$154$	−1.97646e6	+	2.68940e6i	−0.541161	+	0.736364i
$155$	523441.			0.140564
$156$		0			0
$157$	−735252.	+	424498.i	−0.189993	+	0.109692i	−0.591979	−	0.805953i	$-0.701653\pi$
$157$	−735252.	+	424498.i	−0.189993	+	0.109692i	0.401986	+	0.915646i	$0.368320\pi$
$158$	−81731.6	−	141563.i	−0.0207214	−	0.0358905i
$159$		0			0
$160$		−	3.69776e6i		−	0.902773i
$161$	−5789.87	−	13197.5i	−0.00138737	−	0.00316238i
$162$		0			0
$163$	−671609.	+	1.16326e6i	−0.155079	+	0.268605i	−0.933088	−	0.359648i	$-0.882897\pi$
$163$	−671609.	+	1.16326e6i	−0.155079	+	0.268605i	0.778009	+	0.628254i	$0.216230\pi$
$164$	−1.56035e7	+	9.00868e6i	−3.53745	+	2.04235i
$165$		0			0
$166$	−9.62701e6	−	5.55815e6i	−2.10459	−	1.21508i
$167$		−	6.60321e6i		−	1.41777i	−0.705324	−	0.708885i	$-0.749199\pi$
$167$		−	6.60321e6i		−	1.41777i	0.705324	−	0.708885i	$-0.250801\pi$
$168$		0			0
$169$	−5.78293e6			−1.19809
$170$	64022.4	−	110890.i	0.0130312	−	0.0225707i
$171$		0			0
$172$	6.08198e6	+	1.05343e7i	1.19525	+	2.07024i
$173$	−8.15811e6	−	4.71008e6i	−1.57562	−	0.909684i	−0.995460	−	0.0951797i	$-0.969657\pi$
$173$	−8.15811e6	−	4.71008e6i	−1.57562	−	0.909684i	−0.580158	−	0.814504i	$-0.697009\pi$
$174$		0			0
$175$	5.09937e6	+	564102.i	0.951486	+	0.105255i
$176$	−1.03275e7			−1.89433
$177$		0			0
$178$	2.57232e6	−	1.48513e6i	0.456106	−	0.263333i
$179$	−1.50382e6	−	2.60470e6i	−0.262203	−	0.454149i	0.704624	−	0.709581i	$-0.251116\pi$
$179$	−1.50382e6	−	2.60470e6i	−0.262203	−	0.454149i	−0.966827	+	0.255432i	$0.917782\pi$
$180$		0			0
$181$		−	8.77281e6i		−	1.47946i	−0.672904	−	0.739730i	$-0.734953\pi$
$181$		−	8.77281e6i		−	1.47946i	0.672904	−	0.739730i	$-0.265047\pi$
$182$	1.59558e7	−	6.99995e6i	2.64670	−	1.16113i
$183$		0			0
$184$	37747.9	−	65381.3i	0.00605954	−	0.0104954i
$185$	−388763.	+	224453.i	−0.0614002	+	0.0354494i
$186$		0			0
$187$	−171736.	−	99151.6i	−0.0262625	−	0.0151626i
$188$			1.18037e7i			1.77642i
$189$		0			0
$190$	2.41752e6			0.352460
$191$	720715.	−	1.24831e6i	0.103434	−	0.179153i	−0.809663	−	0.586895i	$-0.800350\pi$
$191$	720715.	−	1.24831e6i	0.103434	−	0.179153i	0.913097	+	0.407742i	$0.133684\pi$
$192$		0			0
$193$	−851094.	−	1.47414e6i	−0.118387	−	0.205053i	0.800741	−	0.599010i	$-0.204439\pi$
$193$	−851094.	−	1.47414e6i	−0.118387	−	0.205053i	−0.919129	+	0.393957i	$0.871106\pi$
$194$	1.44878e7	+	8.36453e6i	1.98425	+	1.14561i
$195$		0			0
$196$	−1.42783e7	+	1.55140e7i	−1.89631	+	2.06041i
$197$	−6.42619e6			−0.840534			−0.420267	−	0.907401i	$-0.638064\pi$
$197$	−6.42619e6			−0.840534			−0.420267	+	0.907401i	$0.638064\pi$
$198$		0			0
$199$	−5.77106e6	+	3.33192e6i	−0.732312	+	0.422801i	−0.819267	−	0.573412i	$-0.805620\pi$
$199$	−5.77106e6	+	3.33192e6i	−0.732312	+	0.422801i	0.0869554	+	0.996212i	$0.472286\pi$
$200$	1.34380e7	+	2.32754e7i	1.67975	+	2.90942i
$201$		0			0
$202$		−	8.30534e6i		−	1.00764i
$203$	−4.93043e6	+	6.70890e6i	−0.589382	+	0.801979i
$204$		0			0
$205$	−1.29857e6	+	2.24918e6i	−0.150731	+	0.261074i
$206$	1.41084e7	−	8.14548e6i	1.61390	−	0.931783i
$207$		0			0
$208$	4.66914e7	+	2.69573e7i	5.18856	+	2.99562i
$209$		−	3.74402e6i		−	0.410109i
$210$		0			0
$211$	1.06742e6			0.113629			0.0568144	−	0.998385i	$-0.481906\pi$
$211$	1.06742e6			0.113629			0.0568144	+	0.998385i	$0.481906\pi$
$212$	8.89102e6	−	1.53997e7i	0.933134	−	1.61624i
$213$		0			0
$214$	−2.79814e6	−	4.84652e6i	−0.285515	−	0.494526i
$215$	1.51848e6	+	876694.i	0.152789	+	0.0882130i
$216$		0			0
$217$	764162.	−	6.90788e6i	0.0747836	−	0.676029i
$218$	−1.17335e7			−1.13255
$219$		0			0
$220$	−2.50161e6	+	1.44431e6i	−0.234937	+	0.135641i
$221$	517622.	+	896548.i	0.0479552	+	0.0830609i
$222$		0			0
$223$		−	1.67396e7i		−	1.50949i	−0.656016	−	0.754747i	$-0.727760\pi$
$223$		−	1.67396e7i		−	1.50949i	0.656016	−	0.754747i	$-0.272240\pi$
$224$	−4.87995e7	−	5.39829e6i	−4.34181	−	0.480299i
$225$		0			0
$226$	1.84999e7	−	3.20427e7i	1.60267	−	2.77590i
$227$	−1.64212e7	+	9.48080e6i	−1.40387	+	0.810527i	−0.994788	−	0.101969i	$-0.967486\pi$
$227$	−1.64212e7	+	9.48080e6i	−1.40387	+	0.810527i	−0.409086	+	0.912496i	$0.634153\pi$
$228$		0			0
$229$	−3.68706e6	−	2.12872e6i	−0.307025	−	0.177261i	0.338569	−	0.940941i	$-0.390057\pi$
$229$	−3.68706e6	−	2.12872e6i	−0.307025	−	0.177261i	−0.645594	+	0.763680i	$0.723390\pi$
$230$		−	16927.5i		−	0.00139126i
$231$		0			0
$232$	−4.36147e7			−3.49276
$233$	6.08975e6	−	1.05478e7i	0.481429	−	0.833859i	−0.518344	−	0.855172i	$-0.673451\pi$
$233$	6.08975e6	−	1.05478e7i	0.481429	−	0.833859i	0.999773	+	0.0213134i	$0.00678477\pi$
$234$		0			0
$235$	850730.	+	1.47351e6i	0.0655523	+	0.113540i
$236$	1.56259e7	+	9.02159e6i	1.18880	+	0.686352i
$237$		0			0
$238$	−1.36995e6	−	1.00679e6i	−0.101619	−	0.0746808i
$239$	1.03799e7			0.760328			0.380164	−	0.924919i	$-0.375868\pi$
$239$	1.03799e7			0.760328			0.380164	+	0.924919i	$0.375868\pi$
$240$		0			0
$241$	−9.70985e6	+	5.60598e6i	−0.693683	+	0.400498i	−0.804990	−	0.593288i	$-0.797830\pi$
$241$	−9.70985e6	+	5.60598e6i	−0.693683	+	0.400498i	0.111307	+	0.993786i	$0.464496\pi$
$242$	−1.07785e7	−	1.86688e7i	−0.760520	−	1.31726i
$243$		0			0
$244$			4.16139e7i			2.86463i
$245$	−664283.	+	2.96575e6i	−0.0451705	+	0.201668i
$246$		0			0
$247$	−9.77286e6	+	1.69271e7i	−0.648531	+	1.12329i
$248$	3.15300e7	−	1.82039e7i	2.06714	−	1.19346i
$249$		0			0
$250$	1.06703e7	+	6.16051e6i	0.682900	+	0.394272i
$251$			2.63644e7i			1.66724i	0.552341	+	0.833618i	$0.313735\pi$
$251$			2.63644e7i			1.66724i	−0.552341	+	0.833618i	$0.686265\pi$
$252$		0			0
$253$	−26215.6			−0.00161882
$254$	−8.29693e6	+	1.43707e7i	−0.506310	+	0.876954i
$255$		0			0
$256$	−3.36737e7	−	5.83246e7i	−2.00711	−	3.47642i
$257$	−2.22833e7	−	1.28653e7i	−1.31274	−	0.757913i	−0.330194	−	0.943913i	$-0.607114\pi$
$257$	−2.22833e7	−	1.28653e7i	−1.31274	−	0.757913i	−0.982550	+	0.186000i	$0.940447\pi$
$258$		0			0
$259$	2.39456e6	+	5.45820e6i	0.137825	+	0.314159i
$260$	1.50800e7			0.857990
$261$		0			0
$262$	8.81221e6	−	5.08773e6i	0.489983	−	0.282892i
$263$	8.45919e6	+	1.46517e7i	0.465009	+	0.805420i	0.999202	−	0.0399431i	$-0.0127177\pi$
$263$	8.45919e6	+	1.46517e7i	0.465009	+	0.805420i	−0.534193	+	0.845363i	$0.679384\pi$
$264$		0			0
$265$		−	2.56321e6i		−	0.137736i
$266$	3.52930e6	−	3.19042e7i	0.187518	−	1.69513i
$267$		0			0
$268$	−3.68179e6	+	6.37705e6i	−0.191273	+	0.331295i
$269$	2.28580e7	−	1.31971e7i	1.17431	−	0.677987i	0.219617	−	0.975586i	$-0.429519\pi$
$269$	2.28580e7	−	1.31971e7i	1.17431	−	0.677987i	0.954691	+	0.297599i	$0.0961859\pi$
$270$		0			0
$271$	5.51435e6	+	3.18371e6i	0.277068	+	0.159965i	0.632095	−	0.774891i	$-0.282195\pi$
$271$	5.51435e6	+	3.18371e6i	0.277068	+	0.159965i	−0.355027	+	0.934856i	$0.615528\pi$
$272$		−	5.26071e6i		−	0.261419i
$273$		0			0
$274$	7.16996e7			3.48550
$275$	4.66630e6	−	8.08227e6i	0.224375	−	0.388629i
$276$		0			0
$277$	1.72556e7	+	2.98876e7i	0.811878	+	1.40621i	0.911548	+	0.411194i	$0.134888\pi$
$277$	1.72556e7	+	2.98876e7i	0.811878	+	1.40621i	−0.0996696	+	0.995021i	$0.531779\pi$
$278$	2.65771e7	+	1.53443e7i	1.23701	+	0.714189i
$279$		0			0
$280$	−1.45797e7	+	6.39627e6i	−0.664165	+	0.291375i
$281$	−4.02256e7			−1.81294			−0.906470	−	0.422270i	$-0.861233\pi$
$281$	−4.02256e7			−1.81294			−0.906470	+	0.422270i	$0.861233\pi$
$282$		0			0
$283$	−2.53348e6	+	1.46270e6i	−0.111778	+	0.0645352i	−0.554847	−	0.831953i	$-0.687223\pi$
$283$	−2.53348e6	+	1.46270e6i	−0.111778	+	0.0645352i	0.443069	+	0.896488i	$0.353890\pi$
$284$	−3.58753e7	−	6.21378e7i	−1.56618	−	2.71270i
$285$		0			0
$286$		−	3.16947e7i		−	1.35484i
$287$	2.77868e7	+	2.04208e7i	1.17542	+	0.863826i
$288$		0			0
$289$	−1.20183e7	+	2.08163e7i	−0.497908	+	0.862401i
$290$	−8.46900e6	+	4.88958e6i	−0.347247	+	0.200483i
$291$		0			0
$292$	−8.58629e7	−	4.95730e7i	−3.44871	−	1.99111i
$293$		−	1.16741e7i		−	0.464109i	−0.972703	−	0.232054i	$-0.925455\pi$
$293$		−	1.16741e7i		−	0.464109i	0.972703	−	0.232054i	$-0.0745448\pi$
$294$		0			0
$295$	2.60086e6			0.101309
$296$	−1.56117e7	+	2.70403e7i	−0.601971	+	1.04264i
$297$		0			0
$298$	2.42605e7	+	4.20204e7i	0.916749	+	1.58786i
$299$	118523.	+	68429.5i	0.00443394	+	0.00255994i
$300$		0			0
$301$	1.37866e7	−	1.87596e7i	0.505541	−	0.687896i
$302$	2.71236e7			0.984753
$303$		0			0
$304$	8.60170e7	−	4.96619e7i	3.06171	−	1.76768i
$305$	2.99924e6	+	5.19483e6i	0.105709	+	0.183093i
$306$		0			0
$307$		−	3.20193e7i		−	1.10661i	−0.832977	−	0.553307i	$-0.813366\pi$
$307$		−	3.20193e7i		−	1.10661i	0.832977	−	0.553307i	$-0.186634\pi$
$308$	1.54085e7	+	3.51224e7i	0.527361	+	1.20208i
$309$		0			0
$310$	4.08162e6	−	7.06958e6i	0.137009	−	0.237306i
$311$	−2.10086e6	+	1.21293e6i	−0.0698418	+	0.0403232i	−0.534514	−	0.845159i	$-0.679505\pi$
$311$	−2.10086e6	+	1.21293e6i	−0.0698418	+	0.0403232i	0.464672	+	0.885483i	$0.346172\pi$
$312$		0			0
$313$	2.43110e7	+	1.40359e7i	0.792810	+	0.457729i	0.840951	−	0.541112i	$-0.181996\pi$
$313$	2.43110e7	+	1.40359e7i	0.792810	+	0.457729i	−0.0481409	+	0.998841i	$0.515330\pi$
$314$			1.32404e7i			0.427673i
$315$		0			0
$316$	−1.87845e6			−0.0595302
$317$	3.84108e6	−	6.65294e6i	0.120580	−	0.208851i	−0.799417	−	0.600777i	$-0.794858\pi$
$317$	3.84108e6	−	6.65294e6i	0.120580	−	0.208851i	0.919997	+	0.391927i	$0.128191\pi$
$318$		0			0
$319$	7.57251e6	+	1.31160e7i	0.233275	+	0.404044i
$320$	−2.62422e7	−	1.51509e7i	−0.800847	−	0.462369i
$321$		0			0
$322$	−223392.	−	24712.1i	−0.00669115	−	0.000740188i
$323$	1.90717e6			0.0565955
$324$		0			0
$325$	−4.21936e7	+	2.43605e7i	−1.22913	+	0.709636i
$326$	1.04740e7	+	1.81414e7i	0.302314	+	0.523624i
$327$		0			0
$328$			1.80642e8i			5.11916i
$329$	2.06879e7	−	9.07597e6i	0.580936	−	0.254862i
$330$		0			0
$331$	2.56402e7	−	4.44102e7i	0.707031	−	1.22461i	−0.258923	−	0.965898i	$-0.583368\pi$
$331$	2.56402e7	−	4.44102e7i	0.707031	−	1.22461i	0.965954	−	0.258715i	$-0.0832990\pi$
$332$	−1.10629e8	+	6.38718e7i	−3.02312	+	1.74540i
$333$		0			0
$334$	−8.91827e7	−	5.14896e7i	−2.39354	−	1.38191i
$335$			1.06143e6i			0.0282330i
$336$		0			0
$337$	1.62829e7			0.425443			0.212721	−	0.977113i	$-0.431767\pi$
$337$	1.62829e7			0.425443			0.212721	+	0.977113i	$0.431767\pi$
$338$	−4.50934e7	+	7.81041e7i	−1.16778	+	2.02266i
$339$		0			0
$340$	−735716.	−	1.27430e6i	−0.0187186	−	0.0324216i
$341$	−1.09487e7	−	6.32122e6i	−0.276120	−	0.159418i
$342$		0			0
$343$	3.81694e7	+	1.30962e7i	0.945873	+	0.324537i
$344$	1.21956e8			2.99591
$345$		0			0
$346$	−1.27228e8	+	7.34554e7i	−3.07154	+	1.77335i
$347$	3.79000e7	+	6.56447e7i	0.907091	+	1.57113i	0.818086	+	0.575096i	$0.195035\pi$
$347$	3.79000e7	+	6.56447e7i	0.907091	+	1.57113i	0.0890043	+	0.996031i	$0.471632\pi$
$348$		0			0
$349$		−	2.89740e7i		−	0.681605i	−0.940135	−	0.340802i	$-0.889301\pi$
$349$		−	2.89740e7i		−	0.681605i	0.940135	−	0.340802i	$-0.110699\pi$
$350$	4.73819e7	−	6.44732e7i	1.10512	−	1.50375i
$351$		0			0
$352$	−4.46551e7	+	7.73449e7i	−1.02387	+	1.77339i
$353$	−5.10415e7	+	2.94688e7i	−1.16038	+	0.669945i	−0.951395	−	0.307974i	$-0.900349\pi$
$353$	−5.10415e7	+	2.94688e7i	−1.16038	+	0.669945i	−0.208984	+	0.977919i	$0.567016\pi$
$354$		0			0
$355$	−8.95693e6	−	5.17129e6i	−0.200205	−	0.115588i
$356$		−	3.41329e7i		−	0.756525i
$357$		0			0
$358$	−4.69053e7			−1.02229
$359$	3.87579e7	−	6.71306e7i	0.837677	−	1.45090i	−0.0541559	−	0.998532i	$-0.517247\pi$
$359$	3.87579e7	−	6.71306e7i	0.837677	−	1.45090i	0.891832	−	0.452366i	$-0.149420\pi$
$360$		0			0
$361$	−5.51894e6	−	9.55909e6i	−0.117310	−	0.203187i
$362$	−1.18485e8	−	6.84075e7i	−2.49769	−	1.44204i
$363$		0			0
$364$	2.20151e7	−	1.99012e8i	0.456474	−	4.12643i
$365$	−1.42915e7			−0.293900
$366$		0			0
$367$	−3.58541e7	+	2.07004e7i	−0.725338	+	0.418774i	−0.816714	−	0.577042i	$-0.804207\pi$
$367$	−3.58541e7	+	2.07004e7i	−0.725338	+	0.418774i	0.0913764	+	0.995816i	$0.470873\pi$
$368$	−347732.	−	602290.i	−0.00697753	−	0.0120854i
$369$		0			0
$370$			7.00083e6i			0.138212i
$371$	−3.38268e7	−	3.74199e6i	−0.662429	−	0.0732791i
$372$		0			0
$373$	2.39688e7	−	4.15152e7i	0.461871	−	0.799983i	−0.537184	−	0.843465i	$-0.680512\pi$
$373$	2.39688e7	−	4.15152e7i	0.461871	−	0.799983i	0.999054	+	0.0434819i	$0.0138451\pi$
$374$	−2.67827e6	+	1.54630e6i	−0.0511965	+	0.0295583i
$375$		0			0
$376$	1.02489e8	+	5.91722e7i	1.92803	+	1.11315i
$377$		−	7.90647e7i		−	1.47557i
$378$		0			0
$379$	−1.73029e7			−0.317835			−0.158917	−	0.987292i	$-0.550800\pi$
$379$	−1.73029e7			−0.317835			−0.158917	+	0.987292i	$0.550800\pi$
$380$	1.38905e7	−	2.40591e7i	0.253145	−	0.438459i
$381$		0			0
$382$	−1.12398e7	−	1.94679e7i	−0.201636	−	0.349244i
$383$	5.60339e7	+	3.23512e7i	0.997365	+	0.575829i	0.907468	−	0.420122i	$-0.138013\pi$
$383$	5.60339e7	+	3.23512e7i	0.997365	+	0.575829i	0.0898976	+	0.995951i	$0.471346\pi$
$384$		0			0
$385$	4.45489e6	+	3.27394e6i	0.0780646	+	0.0573704i
$386$	−2.65462e7			−0.461573
$387$		0			0
$388$	1.66487e8	−	9.61214e7i	2.85027	−	1.64560i
$389$	−3.97139e7	−	6.87865e7i	−0.674673	−	1.16857i	−0.976564	−	0.215226i	$-0.930951\pi$
$389$	−3.97139e7	−	6.87865e7i	−0.674673	−	1.16857i	0.301891	−	0.953342i	$-0.402382\pi$
$390$		0			0
$391$		−	13354.0i		−	0.000223399i
$392$	6.31271e7	+	2.01747e8i	1.04799	+	3.34927i
$393$		0			0
$394$	−5.01093e7	+	8.67919e7i	−0.819276	+	1.41903i
$395$	−234494.	+	135385.i	−0.00380488	+	0.00219675i
$396$		0			0
$397$	−2.19165e7	−	1.26535e7i	−0.350267	−	0.202227i	0.314536	−	0.949246i	$-0.398151\pi$
$397$	−2.19165e7	−	1.26535e7i	−0.350267	−	0.202227i	−0.664803	+	0.747019i	$0.731484\pi$
$398$			1.03925e8i			1.64843i
$399$		0			0
$400$	2.47581e8			3.86846
$401$	5.65920e6	−	9.80202e6i	0.0877651	−	0.152014i	−0.818801	−	0.574077i	$-0.805361\pi$
$401$	5.65920e6	−	9.80202e6i	0.0877651	−	0.152014i	0.906566	+	0.422064i	$0.138694\pi$
$402$		0			0
$403$	3.30000e7	+	5.71577e7i	0.504195	+	0.873292i
$404$	−8.26546e7	−	4.77206e7i	−1.25350	−	0.723706i
$405$		0			0
$406$	5.21643e7	+	1.18904e8i	0.779462	+	1.77672i
$407$	1.08422e7			0.160818
$408$		0			0
$409$	−3.32964e7	+	1.92237e7i	−0.486661	+	0.280974i	−0.723188	−	0.690651i	$-0.757324\pi$
$409$	−3.32964e7	+	1.92237e7i	−0.486661	+	0.280974i	0.236527	+	0.971625i	$0.423991\pi$
$410$	2.02516e7	+	3.50768e7i	0.293838	+	0.508942i
$411$		0			0
$412$		−	1.87208e8i		−	2.67691i
$413$	3.79694e6	−	3.43236e7i	0.0538994	−	0.487240i
$414$		0			0
$415$	−9.20688e6	+	1.59468e7i	−0.128815	+	0.223115i
$416$	4.03780e8	−	2.33123e8i	5.60874	−	3.23821i
$417$		0			0
$418$	−5.05666e7	−	2.91947e7i	−0.692365	−	0.399737i
$419$		−	5.55673e7i		−	0.755401i	−0.925928	−	0.377701i	$-0.876715\pi$
$419$		−	5.55673e7i		−	0.755401i	0.925928	−	0.377701i	$-0.123285\pi$
$420$		0			0
$421$	−9.27660e7			−1.24320			−0.621602	−	0.783333i	$-0.713518\pi$
$421$	−9.27660e7			−1.24320			−0.621602	+	0.783333i	$0.713518\pi$
$422$	8.32339e6	−	1.44165e7i	0.110755	−	0.191833i
$423$		0			0
$424$	−8.91416e7	−	1.54398e8i	−1.16945	−	2.02555i
$425$	4.11703e6	+	2.37697e6i	0.0536312	+	0.0309640i
$426$		0			0
$427$	7.29349e7	−	3.19972e7i	0.936811	−	0.410988i
$428$	−6.43099e7			−0.820251
$429$		0			0
$430$	2.36812e7	−	1.36723e7i	0.297850	−	0.171964i
$431$	6.58699e7	+	1.14090e8i	0.822726	+	1.42500i	0.903645	+	0.428282i	$0.140881\pi$
$431$	6.58699e7	+	1.14090e8i	0.822726	+	1.42500i	−0.0809190	+	0.996721i	$0.525785\pi$
$432$		0			0
$433$		−	9.64602e7i		−	1.18819i	−0.804396	−	0.594093i	$-0.797511\pi$
$433$		−	9.64602e7i		−	1.18819i	0.804396	−	0.594093i	$-0.202489\pi$
$434$	−8.73388e7	−	6.41861e7i	−1.06841	−	0.785184i
$435$		0			0
$436$	−6.74182e7	+	1.16772e8i	−0.813426	+	1.40889i
$437$	218349.	−	126064.i	0.00261641	−	0.00151059i
$438$		0			0
$439$	−8.41958e7	−	4.86105e7i	−0.995169	−	0.574561i	−0.0883535	−	0.996089i	$-0.528161\pi$
$439$	−8.41958e7	−	4.86105e7i	−0.995169	−	0.574561i	−0.906815	+	0.421528i	$0.861494\pi$
$440$			2.89613e7i			0.339985i
$441$		0			0
$442$	1.61450e7			0.186970
$443$	−8.31985e7	+	1.44104e8i	−0.956983	+	1.65754i	−0.227219	+	0.973844i	$0.572963\pi$
$443$	−8.31985e7	+	1.44104e8i	−0.956983	+	1.65754i	−0.729764	+	0.683699i	$0.760370\pi$
$444$		0			0
$445$	−2.46006e6	−	4.26096e6i	−0.0279168	−	0.0483534i
$446$	−2.26085e8	−	1.30530e8i	−2.54840	−	1.47132i
$447$		0			0
$448$	−2.38258e8	+	3.24200e8i	−2.64980	+	3.60562i
$449$	1.03969e8			1.14859			0.574294	−	0.818649i	$-0.305277\pi$
$449$	1.03969e8			1.14859			0.574294	+	0.818649i	$0.305277\pi$
$450$		0			0
$451$	5.43234e7	−	3.13637e7i	0.592185	−	0.341898i
$452$	−2.12592e8	−	3.68220e8i	−2.30214	−	3.98742i
$453$		0			0
$454$			2.95713e8i			3.16011i
$455$	−1.15952e7	−	2.64302e7i	−0.123096	−	0.280586i
$456$		0			0
$457$	3.54494e7	−	6.14002e7i	0.371416	−	0.643311i	−0.618368	−	0.785889i	$-0.712206\pi$
$457$	3.54494e7	−	6.14002e7i	0.371416	−	0.643311i	0.989784	+	0.142578i	$0.0455391\pi$
$458$	−5.75009e7	+	3.31982e7i	−0.598520	+	0.345556i
$459$		0			0
$460$	−168462.	−	97261.4i	−0.00173072	−	0.000999234i
$461$		−	2.94715e7i		−	0.300815i	−0.988624	−	0.150408i	$-0.951941\pi$
$461$		−	2.94715e7i		−	0.300815i	0.988624	−	0.150408i	$-0.0480586\pi$
$462$		0			0
$463$	−7.67219e7			−0.772994			−0.386497	−	0.922291i	$-0.626315\pi$
$463$	−7.67219e7			−0.772994			−0.386497	+	0.922291i	$0.626315\pi$
$464$	−2.00888e8	+	3.47949e8i	−2.01095	+	3.48306i
$465$		0			0
$466$	−9.49717e7	−	1.64496e8i	−0.938505	−	1.62554i
$467$	1.69532e8	+	9.78791e7i	1.66456	+	0.961035i	0.970494	+	0.241126i	$0.0775166\pi$
$467$	1.69532e8	+	9.78791e7i	1.66456	+	0.961035i	0.694068	+	0.719910i	$0.255817\pi$
$468$		0			0
$469$	1.40078e7	+	1.54956e6i	0.135784	+	0.0150207i
$470$	2.65348e7			0.255578
$471$		0			0
$472$	1.56665e8	−	9.04507e7i	1.48986	−	0.860174i
$473$	−2.11744e7	−	3.66751e7i	−0.200091	−	0.346568i
$474$		0			0
$475$			8.97559e7i			0.837495i
$476$	−1.78910e7	+	7.84895e6i	−0.165888	+	0.0727764i
$477$		0			0
$478$	8.09393e7	−	1.40191e8i	0.741098	−	1.28362i
$479$	2.78233e7	−	1.60638e7i	0.253164	−	0.146164i	−0.368048	−	0.929807i	$-0.619974\pi$
$479$	2.78233e7	−	1.60638e7i	0.253164	−	0.146164i	0.621212	+	0.783642i	$0.286640\pi$
$480$		0			0
$481$	−4.90186e7	−	2.83009e7i	−0.440480	−	0.254311i
$482$			1.74854e8i			1.56148i
$483$		0			0
$484$	−2.47722e8			−2.18489
$485$	1.38555e7	−	2.39985e7i	0.121450	−	0.210358i
$486$		0			0
$487$	8.66229e7	+	1.50035e8i	0.749973	+	1.29899i	0.947835	+	0.318762i	$0.103267\pi$
$487$	8.66229e7	+	1.50035e8i	0.749973	+	1.29899i	−0.197862	+	0.980230i	$0.563400\pi$
$488$	3.61325e8	+	2.08611e8i	3.10912	+	1.79505i
$489$		0			0
$490$	3.48755e7	+	3.20978e7i	0.296437	+	0.272826i
$491$	−2.27726e7			−0.192383			−0.0961917	−	0.995363i	$-0.530666\pi$
$491$	−2.27726e7			−0.192383			−0.0961917	+	0.995363i	$0.530666\pi$
$492$		0			0
$493$	−6.68115e6	+	3.85737e6i	−0.0557584	+	0.0321922i
$494$	1.52411e8	+	2.63984e8i	1.26426	+	2.18976i
$495$		0			0
$496$		−	3.35387e8i		−	2.74853i
$497$	−8.13217e7	+	1.10656e8i	−0.662426	+	0.901372i
$498$		0			0
$499$	7.15586e7	−	1.23943e8i	0.575917	−	0.997518i	−0.420024	−	0.907513i	$-0.637978\pi$
$499$	7.15586e7	−	1.23943e8i	0.575917	−	0.997518i	0.995941	−	0.0900050i	$-0.0286883\pi$
$500$	1.22618e8	−	7.07938e7i	0.980947	−	0.566350i
$501$		0			0
$502$	3.56077e8	+	2.05581e8i	2.81470	+	1.62507i
$503$		−	1.94323e8i		−	1.52693i	−0.645848	−	0.763466i	$-0.723496\pi$
$503$		−	1.94323e8i		−	1.52693i	0.645848	−	0.763466i	$-0.276504\pi$
$504$		0			0
$505$	−1.37575e7			−0.106823
$506$	−204421.	+	354067.i	−0.00157788	+	0.00273296i
$507$		0			0
$508$	9.53446e7	+	1.65142e8i	0.727286	+	1.25970i
$509$	1.45925e7	+	8.42496e6i	0.110656	+	0.0638873i	0.554307	−	0.832313i	$-0.312984\pi$
$509$	1.45925e7	+	8.42496e6i	0.110656	+	0.0638873i	−0.443651	+	0.896200i	$0.646317\pi$
$510$		0			0
$511$	−2.08639e7	+	1.88606e8i	−0.156363	+	1.41349i
$512$	−4.65851e8			−3.47086
$513$		0			0
$514$	−3.47515e8	+	2.00638e8i	−2.55909	+	1.47749i
$515$	−1.34927e7	−	2.33700e7i	−0.0987817	−	0.171095i
$516$		0			0
$517$		−	4.10946e7i		−	0.297381i
$518$	9.23902e7	+	1.02204e7i	0.664717	+	0.0735322i
$519$		0			0
$520$	7.55964e7	−	1.30937e8i	0.537640	−	0.931219i
$521$	−5.01224e7	+	2.89382e7i	−0.354421	+	0.204625i	−0.666631	−	0.745388i	$-0.732264\pi$
$521$	−5.01224e7	+	2.89382e7i	−0.354421	+	0.204625i	0.312210	+	0.950013i	$0.398931\pi$
$522$		0			0
$523$	2.20396e8	+	1.27246e8i	1.54063	+	0.889483i	0.998799	+	0.0489961i	$0.0156022\pi$
$523$	2.20396e8	+	1.27246e8i	1.54063	+	0.889483i	0.541831	+	0.840487i	$0.317731\pi$
$524$		−	1.16932e8i		−	0.812716i
$525$		0			0
$526$	2.63848e8			1.81299
$527$	3.21997e6	−	5.57715e6i	0.0219999	−	0.0381049i
$528$		0			0
$529$	7.40171e7	+	1.28201e8i	0.499994	+	0.866015i
$530$	−3.46186e7	−	1.99871e7i	−0.232532	−	0.134252i
$531$		0			0
$532$	−2.97231e8	−	2.18438e8i	−1.97405	−	1.45075i
$533$	−3.27469e8			−2.16266
$534$		0			0
$535$	−8.02808e6	+	4.63501e6i	−0.0524264	+	0.0302684i
$536$	3.69137e7	+	6.39364e7i	0.239714	+	0.415197i
$537$		0			0
$538$		−	4.11626e8i		−	2.64336i
$539$	4.97099e7	−	5.40117e7i	0.317451	−	0.344923i
$540$		0			0
$541$	3.10487e7	−	5.37779e7i	0.196088	−	0.339635i	−0.751168	−	0.660111i	$-0.770509\pi$
$541$	3.10487e7	−	5.37779e7i	0.196088	−	0.339635i	0.947257	+	0.320476i	$0.103843\pi$
$542$	8.59981e7	−	4.96510e7i	0.540121	−	0.311839i
$543$		0			0
$544$	−3.93988e7	−	2.27469e7i	−0.244730	−	0.141295i
$545$			1.94362e7i			0.120066i
$546$		0			0
$547$	7.72887e6			0.0472230			0.0236115	−	0.999721i	$-0.492484\pi$
$547$	7.72887e6			0.0472230			0.0236115	+	0.999721i	$0.492484\pi$
$548$	4.11970e8	−	7.13553e8i	2.50336	−	4.33595i
$549$		0			0
$550$	−7.27725e7	−	1.26046e8i	−0.437401	−	0.757600i
$551$	−1.26142e8	−	7.28282e7i	−0.754060	−	0.435357i
$552$		0			0
$553$	1.44435e6	+	3.29228e6i	0.00854078	+	0.0194680i
$554$	5.38214e8			3.16538
$555$		0			0
$556$	3.05412e8	−	1.76330e8i	1.77690	−	1.02589i
$557$	1.26683e7	+	2.19422e7i	0.0733083	+	0.126974i	0.900349	−	0.435168i	$-0.143311\pi$
$557$	1.26683e7	+	2.19422e7i	0.0733083	+	0.126974i	−0.827041	+	0.562142i	$0.809978\pi$
$558$		0			0
$559$			2.21082e8i			1.26566i
$560$	−1.61259e7	+	1.45775e8i	−0.0918249	+	0.830079i
$561$		0			0
$562$	−3.13666e8	+	5.43285e8i	−1.76709	+	3.06069i
$563$	−6.59556e7	+	3.80795e7i	−0.369596	+	0.213386i	−0.673282	−	0.739386i	$-0.735116\pi$
$563$	−6.59556e7	+	3.80795e7i	−0.369596	+	0.213386i	0.303686	+	0.952772i	$0.401783\pi$
$564$		0			0
$565$	−5.30775e7	−	3.06443e7i	−0.294283	−	0.169904i
$566$			4.56227e7i			0.251612i
$567$		0			0
$568$	−7.19374e8			−3.92563
$569$	−2.66483e7	+	4.61562e7i	−0.144655	+	0.250549i	−0.929244	−	0.369466i	$-0.879540\pi$
$569$	−2.66483e7	+	4.61562e7i	−0.144655	+	0.250549i	0.784589	+	0.620016i	$0.212874\pi$
$570$		0			0
$571$	−2.05691e7	−	3.56267e7i	−0.110486	−	0.191367i	0.805480	−	0.592622i	$-0.201907\pi$
$571$	−2.05691e7	−	3.56267e7i	−0.110486	−	0.191367i	−0.915966	+	0.401255i	$0.868574\pi$
$572$	−3.15425e8	−	1.82110e8i	−1.68542	−	0.973076i
$573$		0			0
$574$	4.92474e8	−	2.16053e8i	2.60404	−	1.14242i
$575$	628469.			0.00330583
$576$		0			0
$577$	−7.59861e7	+	4.38706e7i	−0.395555	+	0.228374i	−0.684564	−	0.728953i	$-0.740007\pi$
$577$	−7.59861e7	+	4.38706e7i	−0.395555	+	0.228374i	0.289009	+	0.957326i	$0.406674\pi$
$578$	1.87429e8	+	3.24637e8i	0.970630	+	1.68118i
$579$		0			0
$580$			1.12378e8i			0.575965i
$581$	1.97009e8	+	1.44784e8i	1.00452	+	0.738230i
$582$		0			0
$583$	−3.09540e7	+	5.36140e7i	−0.156211	+	0.270565i
$584$	−8.60864e8	+	4.97020e8i	−4.32211	+	2.49537i
$585$		0			0
$586$	−1.57670e8	−	9.10307e7i	−0.783530	−	0.452371i
$587$			4.55880e7i			0.225391i	0.993630	+	0.112695i	$0.0359485\pi$
$587$			4.55880e7i			0.225391i	−0.993630	+	0.112695i	$0.964052\pi$
$588$		0			0
$589$	1.21588e8			0.595039
$590$	2.02806e7	−	3.51270e7i	0.0987473	−	0.171035i
$591$		0			0
$592$	1.43814e8	+	2.49094e8i	0.693166	+	1.20060i
$593$	1.25860e8	+	7.26654e7i	0.603565	+	0.348468i	0.770443	−	0.637509i	$-0.220035\pi$
$593$	1.25860e8	+	7.26654e7i	0.603565	+	0.348468i	−0.166878	+	0.985978i	$0.553369\pi$
$594$		0			0
$595$	−1.66771e6	+	2.26928e6i	−0.00791718	+	0.0107730i
$596$	5.57581e8			2.63372
$597$		0			0
$598$	1.84841e6	−	1.06718e6i	0.00864361	−	0.00499039i
$599$	2.81542e7	+	4.87645e7i	0.130998	+	0.226894i	0.924061	−	0.382244i	$-0.124849\pi$
$599$	2.81542e7	+	4.87645e7i	0.130998	+	0.226894i	−0.793064	+	0.609139i	$0.791515\pi$
$600$		0			0
$601$		−	2.39440e8i		−	1.10299i	−0.834177	−	0.551497i	$-0.814057\pi$
$601$		−	2.39440e8i		−	1.10299i	0.834177	−	0.551497i	$-0.185943\pi$
$602$	−1.45863e8	−	3.32482e8i	−0.668582	−	1.52398i
$603$		0			0
$604$	1.55846e8	−	2.69934e8i	0.707271	−	1.22503i
$605$	−3.09242e7	+	1.78541e7i	−0.139647	+	0.0806254i
$606$		0			0
$607$	−2.54893e8	−	1.47163e8i	−1.13970	−	0.658008i	−0.193347	−	0.981130i	$-0.561934\pi$
$607$	−2.54893e8	−	1.47163e8i	−1.13970	−	0.658008i	−0.946357	+	0.323122i	$0.895268\pi$
$608$		−	8.58938e8i		−	3.82165i
$609$		0			0
$610$	9.35483e7			0.412141
$611$	−1.07267e8	+	1.85792e8i	−0.470266	+	0.814525i
$612$		0			0
$613$	−1.10391e8	−	1.91204e8i	−0.479241	−	0.830070i	0.520475	−	0.853877i	$-0.325755\pi$
$613$	−1.10391e8	−	1.91204e8i	−0.479241	−	0.830070i	−0.999717	+	0.0238066i	$0.992421\pi$
$614$	−4.32451e8	−	2.49676e8i	−1.86824	−	1.07863i
$615$		0			0
$616$	3.82203e8	+	4.22801e7i	1.63513	+	0.180881i
$617$	−3.86786e8			−1.64670			−0.823352	−	0.567531i	$-0.807899\pi$
$617$	−3.86786e8			−1.64670			−0.823352	+	0.567531i	$0.807899\pi$
$618$		0			0
$619$	1.13096e8	−	6.52959e7i	0.476842	−	0.275305i	−0.242257	−	0.970212i	$-0.577888\pi$
$619$	1.13096e8	−	6.52959e7i	0.476842	−	0.275305i	0.719100	+	0.694907i	$0.244554\pi$
$620$	−4.69042e7	−	8.12404e7i	−0.196805	−	0.340876i
$621$		0			0
$622$			3.78321e7i			0.157213i
$623$	−5.98234e7	+	2.62451e7i	−0.247404	+	0.108538i
$624$		0			0
$625$	−1.06652e8	+	1.84727e8i	−0.436847	+	0.756641i
$626$	3.79138e8	−	2.18895e8i	1.54552	−	0.892305i
$627$		0			0
$628$	1.31768e8	+	7.60762e7i	0.532023	+	0.307164i
$629$			5.52292e6i			0.0221930i
$630$		0			0
$631$	−1.10414e8			−0.439475			−0.219738	−	0.975559i	$-0.570520\pi$
$631$	−1.10414e8			−0.439475			−0.219738	+	0.975559i	$0.570520\pi$
$632$	−9.41667e6	+	1.63102e7i	−0.0373032	+	0.0646111i
$633$		0			0
$634$	−5.99029e7	−	1.03755e8i	−0.235061	−	0.407137i
$635$	2.38045e7	+	1.37436e7i	0.0929691	+	0.0536757i
$636$		0			0
$637$	−3.65728e8	+	1.14437e8i	−1.41494	+	0.442739i
$638$	2.36192e8			0.909499
$639$		0			0
$640$	−2.04305e8	+	1.17956e8i	−0.779362	+	0.449965i
$641$	−2.56393e7	−	4.44085e7i	−0.0973491	−	0.168614i	0.813238	−	0.581932i	$-0.197703\pi$
$641$	−2.56393e7	−	4.44085e7i	−0.0973491	−	0.168614i	−0.910587	+	0.413318i	$0.864370\pi$
$642$		0			0
$643$		−	2.95342e8i		−	1.11094i	−0.831535	−	0.555472i	$-0.812537\pi$
$643$		−	2.95342e8i		−	1.11094i	0.831535	−	0.555472i	$-0.187463\pi$
$644$	−1.52950e6	+	2.08121e6i	−0.00572652	+	0.00779215i
$645$		0			0
$646$	1.48715e7	−	2.57582e7i	0.0551642	−	0.0955472i
$647$	2.54170e8	−	1.46745e8i	0.938449	−	0.541814i	0.0489752	−	0.998800i	$-0.484404\pi$
$647$	2.54170e8	−	1.46745e8i	0.938449	−	0.541814i	0.889474	+	0.456986i	$0.151071\pi$
$648$		0			0
$649$	−5.44013e7	−	3.14086e7i	−0.199010	−	0.114899i
$650$			7.59820e8i			2.76675i
$651$		0			0
$652$	2.40724e8			0.868515
$653$	1.58530e8	−	2.74583e8i	0.569342	−	0.986129i	−0.427289	−	0.904115i	$-0.640531\pi$
$653$	1.58530e8	−	2.74583e8i	0.569342	−	0.986129i	0.996631	−	0.0820143i	$-0.0261353\pi$
$654$		0			0
$655$	−8.42764e6	−	1.45971e7i	−0.0299904	−	0.0519449i
$656$	1.44113e9	+	8.32035e8i	5.10494	+	2.94734i
$657$		0			0
$658$	3.87377e7	−	3.50181e8i	0.135974	−	1.22918i
$659$	−1.86604e8			−0.652026			−0.326013	−	0.945365i	$-0.605705\pi$
$659$	−1.86604e8			−0.652026			−0.326013	+	0.945365i	$0.605705\pi$
$660$		0			0
$661$	2.56295e8	−	1.47972e8i	0.887433	−	0.512359i	0.0143307	−	0.999897i	$-0.495438\pi$
$661$	2.56295e8	−	1.47972e8i	0.887433	−	0.512359i	0.873102	+	0.487538i	$0.162105\pi$
$662$	−3.99868e8	−	6.92592e8i	−1.37830	−	2.38728i
$663$		0			0
$664$			1.28076e9i			4.37486i
$665$	−5.28480e7	−	5.84615e6i	−0.179707	−	0.0198795i
$666$		0			0
$667$	−509942.	+	883246.i	−0.00171848	+	0.00297649i
$668$	−1.02485e9	+	5.91696e8i	−3.43819	+	1.98504i
$669$		0			0
$670$	1.43356e7	+	8.27669e6i	0.0476643	+	0.0275190i
$671$		−	1.44878e8i		−	0.479552i
$672$		0			0
$673$	1.17111e8			0.384197			0.192098	−	0.981376i	$-0.438471\pi$
$673$	1.17111e8			0.384197			0.192098	+	0.981376i	$0.438471\pi$
$674$	1.26968e8	−	2.19916e8i	0.414683	−	0.718252i
$675$		0			0
$676$	5.18193e8	+	8.97537e8i	1.67746	+	2.90544i
$677$	8.12613e7	+	4.69162e7i	0.261889	+	0.151202i	0.625196	−	0.780468i	$-0.285019\pi$
$677$	8.12613e7	+	4.69162e7i	0.261889	+	0.151202i	−0.363307	+	0.931670i	$0.618352\pi$
$678$		0			0
$679$	−2.96482e8	−	2.17887e8i	−0.947084	−	0.696020i
$680$	−1.47526e7			−0.0469183
$681$		0			0
$682$	−1.70748e8	+	9.85815e7i	−0.538274	+	0.310772i
$683$	−1.47967e8	−	2.56287e8i	−0.464412	−	0.804385i	0.534763	−	0.845002i	$-0.320401\pi$
$683$	−1.47967e8	−	2.56287e8i	−0.464412	−	0.804385i	−0.999175	+	0.0406170i	$0.987068\pi$
$684$		0			0
$685$		−	1.18768e8i		−	0.369510i
$686$	4.74509e8	−	4.13394e8i	1.46985	−	1.28054i
$687$		0			0
$688$	5.61728e8	−	9.72941e8i	1.72489	−	2.98759i
$689$	2.79892e8	−	1.61596e8i	0.855723	−	0.494052i
$690$		0			0
$691$	−9.29926e6	−	5.36893e6i	−0.0281848	−	0.0162725i	0.485841	−	0.874047i	$-0.338513\pi$
$691$	−9.29926e6	−	5.36893e6i	−0.0281848	−	0.0162725i	−0.514026	+	0.857774i	$0.671847\pi$
$692$			1.68823e9i			5.09464i
$693$		0			0
$694$	1.18213e9			3.53660
$695$	2.54173e7	−	4.40240e7i	0.0757137	−	0.131140i
$696$		0			0
$697$	1.59764e7	+	2.76719e7i	0.0471824	+	0.0817222i
$698$	−3.91322e8	−	2.25930e8i	−1.15072	−	0.664366i
$699$		0			0
$700$	−3.69390e8	−	8.41992e8i	−1.07694	−	2.45479i
$701$	−1.38696e8			−0.402634			−0.201317	−	0.979526i	$-0.564522\pi$
$701$	−1.38696e8			−0.402634			−0.201317	+	0.979526i	$0.564522\pi$
$702$		0			0
$703$	−9.03043e7	+	5.21372e7i	−0.259922	+	0.150066i
$704$	3.65933e8	+	6.33815e8i	1.04878	+	1.81654i
$705$		0			0
$706$			9.19153e8i			2.61200i
$707$	−2.00843e7	+	1.81558e8i	−0.0568327	+	0.513757i
$708$		0			0
$709$	−1.68784e8	+	2.92343e8i	−0.473580	+	0.820264i	−0.999543	−	0.0302432i	$-0.990372\pi$
$709$	−1.68784e8	+	2.92343e8i	−0.473580	+	0.820264i	0.525963	+	0.850508i	$0.323705\pi$
$710$	−1.39686e8	+	8.06480e7i	−0.390282	+	0.225330i
$711$		0			0
$712$	−2.96369e8	−	1.71109e8i	−0.821094	−	0.474059i
$713$		−	851358.i		−	0.00234879i
$714$		0			0
$715$	−5.25011e7			−0.143632
$716$	−2.69507e8	+	4.66800e8i	−0.734229	+	1.27172i
$717$		0			0
$718$	−6.04442e8	−	1.04692e9i	−1.63298	−	2.82841i
$719$	9.78596e7	+	5.64993e7i	0.263279	+	0.152004i	0.625830	−	0.779960i	$-0.284761\pi$
$719$	9.78596e7	+	5.64993e7i	0.263279	+	0.152004i	−0.362550	+	0.931964i	$0.618094\pi$
$720$		0			0
$721$	−3.28113e8	+	1.43946e8i	−0.875421	+	0.384055i
$722$	−1.72140e8			−0.457372
$723$		0			0
$724$	−1.36158e9	+	7.86108e8i	−3.58779	+	2.07141i
$725$	−1.81536e8	−	3.14430e8i	−0.476376	−	0.825107i
$726$		0			0
$727$			4.17662e8i			1.08698i	0.839415	+	0.543490i	$0.182898\pi$
$727$			4.17662e8i			1.08698i	−0.839415	+	0.543490i	$0.817102\pi$
$728$	−1.61762e9	−	1.18880e9i	−4.19258	−	3.08117i
$729$		0			0
$730$	−1.11440e8	+	1.93020e8i	−0.286467	+	0.496175i
$731$	1.86820e7	−	1.07860e7i	0.0478267	−	0.0276128i
$732$		0			0
$733$	6.34509e8	+	3.66334e8i	1.61111	+	0.930177i	0.989113	+	0.147159i	$0.0470130\pi$
$733$	6.34509e8	+	3.66334e8i	1.61111	+	0.930177i	0.622000	+	0.783017i	$0.286320\pi$
$734$			6.45658e8i			1.63273i
$735$		0			0
$736$	−6.01427e6			−0.0150851
$737$	1.28181e7	−	2.22016e7i	0.0320201	−	0.0554604i
$738$		0			0
$739$	−2.93464e8	−	5.08295e8i	−0.727146	−	1.25945i	−0.958084	−	0.286486i	$-0.907513\pi$
$739$	−2.93464e8	−	5.08295e8i	−0.727146	−	1.25945i	0.230938	−	0.972968i	$-0.425820\pi$
$740$	6.96721e7	+	4.02252e7i	0.171935	+	0.0992665i
$741$		0			0
$742$	−3.14309e8	+	4.27685e8i	−0.769388	+	1.04692i
$743$	3.73015e8			0.909411			0.454705	−	0.890642i	$-0.349745\pi$
$743$	3.73015e8			0.909411			0.454705	+	0.890642i	$0.349745\pi$
$744$		0			0
$745$	6.96052e7	−	4.01866e7i	0.168334	−	0.0971879i
$746$	−3.73802e8	−	6.47444e8i	−0.900379	−	1.55950i
$747$		0			0
$748$			3.55388e7i			0.0849177i
$749$	4.94484e7	+	1.12713e8i	0.117681	+	0.268244i
$750$		0			0
$751$	2.73909e8	−	4.74424e8i	0.646675	−	1.12007i	−0.337236	−	0.941420i	$-0.609492\pi$
$751$	2.73909e8	−	4.74424e8i	0.646675	−	1.12007i	0.983912	−	0.178655i	$-0.0571745\pi$
$752$	9.44126e8	−	5.45091e8i	2.22012	−	1.28179i
$753$		0			0
$754$	−1.06785e9	−	6.16521e8i	−2.49112	−	1.43825i
$755$		−	4.49293e7i		−	0.104397i
$756$		0			0
$757$	4.01667e8			0.925931			0.462966	−	0.886376i	$-0.346785\pi$
$757$	4.01667e8			0.925931			0.462966	+	0.886376i	$0.346785\pi$
$758$	−1.34922e8	+	2.33692e8i	−0.309796	+	0.536583i
$759$		0			0
$760$	−1.39267e8	−	2.41218e8i	−0.317254	−	0.549501i
$761$	9.49273e7	+	5.48063e7i	0.215396	+	0.124359i	0.603816	−	0.797123i	$-0.293646\pi$
$761$	9.49273e7	+	5.48063e7i	0.215396	+	0.124359i	−0.388421	+	0.921482i	$0.626979\pi$
$762$		0			0
$763$	2.56500e8	+	2.83745e7i	0.577448	+	0.0638784i
$764$	−2.58325e8			−0.579278
$765$		0			0
$766$	8.73867e8	−	5.04527e8i	1.94428	−	1.12253i
$767$	1.63969e8	+	2.84003e8i	0.363393	+	0.629414i
$768$		0			0
$769$		−	2.51373e8i		−	0.552763i	−0.961048	−	0.276381i	$-0.910865\pi$
$769$		−	2.51373e8i		−	0.552763i	0.961048	−	0.276381i	$-0.0891353\pi$
$770$	7.89554e7	−	3.46384e7i	0.172946	−	0.0758728i
$771$		0			0
$772$	−1.52528e8	+	2.64187e8i	−0.331512	+	0.574195i
$773$	5.00828e8	−	2.89153e8i	1.08430	−	0.626022i	0.152248	−	0.988342i	$-0.451349\pi$
$773$	5.00828e8	−	2.89153e8i	1.08430	−	0.626022i	0.932054	+	0.362321i	$0.118015\pi$
$774$		0			0
$775$	2.62474e8	+	1.51539e8i	0.563872	+	0.325552i
$776$		−	1.92743e9i		−	4.12471i
$777$		0			0
$778$	−1.23870e9			−2.63044
$779$	−3.01639e8	+	5.22453e8i	−0.638079	+	1.10519i
$780$		0			0
$781$	1.24900e8	+	2.16333e8i	0.262185	+	0.454118i
$782$	−180358.	−	104130.i	−0.000377152	−	0.000217749i
$783$		0			0
$784$	1.90026e9	+	4.25629e8i	3.94334	+	0.883249i
$785$	2.19322e7			0.0453391
$786$		0			0
$787$	5.03438e8	−	2.90660e8i	1.03281	−	0.596296i	0.115025	−	0.993363i	$-0.463305\pi$
$787$	5.03438e8	−	2.90660e8i	1.03281	−	0.596296i	0.917790	+	0.397067i	$0.129972\pi$
$788$	5.75834e8	+	9.97374e8i	1.17684	+	2.03835i
$789$		0			0
$790$			4.22276e6i			0.00856476i
$791$	−4.81901e8	+	6.55729e8i	−0.973708	+	1.32494i
$792$		0			0
$793$	−3.78170e8	+	6.55009e8i	−0.758346	+	1.31349i
$794$	−3.41795e8	+	1.97335e8i	−0.682817	+	0.394224i
$795$		0			0
$796$	1.03426e9	+	5.97129e8i	2.05064	+	1.18394i
$797$			2.88172e8i			0.569215i	0.958644	+	0.284607i	$0.0918632\pi$
$797$			2.88172e8i			0.569215i	−0.958644	+	0.284607i	$0.908137\pi$
$798$		0			0
$799$	2.09332e7			0.0410388
$800$	1.07052e9	−	1.85420e9i	2.09086	−	3.62148i
$801$		0			0
$802$	−8.82572e7	−	1.52866e8i	−0.171091	−	0.296338i
$803$	2.98931e8	+	1.72588e8i	0.577331	+	0.333322i
$804$		0			0
$805$	−40934.7	+	370041.i	−7.84700e−5	+	0.000709353i
$806$	1.02929e9			1.96577
$807$		0			0
$808$	−8.28697e8	+	4.78449e8i	−1.57095	+	0.906987i
$809$	2.68679e7	+	4.65365e7i	0.0507444	+	0.0878918i	0.890282	−	0.455410i	$-0.150507\pi$
$809$	2.68679e7	+	4.65365e7i	0.0507444	+	0.0878918i	−0.839537	+	0.543302i	$0.817174\pi$
$810$		0			0
$811$			1.37731e8i			0.258208i	0.991631	+	0.129104i	$0.0412101\pi$
$811$			1.37731e8i			0.258208i	−0.991631	+	0.129104i	$0.958790\pi$
$812$	1.48305e9	+	1.64058e8i	2.77006	+	0.306429i
$813$		0			0
$814$	8.45439e7	−	1.46434e8i	0.156750	−	0.271500i
$815$	3.00506e7	−	1.73497e7i	0.0555112	−	0.0320494i
$816$		0			0
$817$	3.52721e8	+	2.03644e8i	0.646793	+	0.373426i
$818$			5.99599e8i			1.09547i
$819$		0			0
$820$	4.65444e8			0.844162
$821$	2.27200e8	−	3.93522e8i	0.410563	−	0.711115i	−0.584389	−	0.811474i	$-0.698666\pi$
$821$	2.27200e8	−	3.93522e8i	0.410563	−	0.711115i	0.994951	+	0.100359i	$0.0319990\pi$
$822$		0			0
$823$	−1.19151e8	−	2.06376e8i	−0.213747	−	0.370220i	0.739137	−	0.673555i	$-0.235233\pi$
$823$	−1.19151e8	−	2.06376e8i	−0.213747	−	0.370220i	−0.952884	+	0.303335i	$0.901900\pi$
$824$	−1.62549e9	−	9.38478e8i	−2.90538	−	1.67742i
$825$		0			0
$826$	−4.33966e8	−	3.18925e8i	−0.770044	−	0.565912i
$827$	−1.39387e8			−0.246437			−0.123218	−	0.992380i	$-0.539322\pi$
$827$	−1.39387e8			−0.246437			−0.123218	+	0.992380i	$0.539322\pi$
$828$		0			0
$829$	6.84951e8	−	3.95457e8i	1.20225	−	0.694121i	0.241198	−	0.970476i	$-0.422460\pi$
$829$	6.84951e8	−	3.95457e8i	1.20225	−	0.694121i	0.961056	+	0.276355i	$0.0891264\pi$
$830$	1.43584e8	+	2.48695e8i	0.251115	+	0.434944i
$831$		0			0
$832$		−	3.82072e9i		−	6.63399i
$833$	2.75131e7	+	2.53217e7i	0.0475997	+	0.0438085i
$834$		0			0
$835$	−8.52907e7	+	1.47728e8i	−0.146502	+	0.253748i
$836$	−5.81089e8	+	3.35492e8i	−0.994544	+	0.574200i
$837$		0			0
$838$	−7.50490e8	−	4.33296e8i	−1.27530	−	0.736296i
$839$		−	8.67968e8i		−	1.46966i	−0.678250	−	0.734832i	$-0.737261\pi$
$839$		−	8.67968e8i		−	1.46966i	0.678250	−	0.734832i	$-0.262739\pi$
$840$		0			0
$841$	−5.62593e6			−0.00945816
$842$	−7.23359e8	+	1.25289e9i	−1.21176	+	2.09883i
$843$		0			0
$844$	−9.56487e7	−	1.65668e8i	−0.159093	−	0.275558i
$845$	1.29376e8	+	7.46955e7i	0.214430	+	0.123801i
$846$		0			0
$847$	1.90476e8	+	4.34173e8i	0.313465	+	0.714517i
$848$	−1.64234e9			−2.69324
$849$		0			0
$850$	6.42065e7	−	3.70697e7i	0.104550	−	0.0603618i
$851$	365064.	+	632309.i	0.000592352	+	0.00102598i
$852$		0			0
$853$			7.06613e8i			1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$853$			7.06613e8i			1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$854$	1.36569e8	−	1.23456e9i	0.219270	−	1.98216i
$855$		0			0
$856$	−3.22387e8	+	5.58390e8i	−0.513991	+	0.890259i
$857$	4.82285e8	−	2.78447e8i	0.766233	−	0.442385i	−0.0652960	−	0.997866i	$-0.520799\pi$
$857$	4.82285e8	−	2.78447e8i	0.766233	−	0.442385i	0.831529	+	0.555481i	$0.187466\pi$
$858$		0			0
$859$	2.54250e8	+	1.46791e8i	0.401127	+	0.231591i	0.686970	−	0.726686i	$-0.258940\pi$
$859$	2.54250e8	+	1.46791e8i	0.401127	+	0.231591i	−0.285843	+	0.958276i	$0.592274\pi$
$860$		−	3.14233e8i		−	0.494033i
$861$		0			0
$862$	2.05453e9			3.20767
$863$	4.51752e8	−	7.82458e8i	0.702859	−	1.21739i	−0.264600	−	0.964358i	$-0.585240\pi$
$863$	4.51752e8	−	7.82458e8i	0.702859	−	1.21739i	0.967459	−	0.253029i	$-0.0814267\pi$
$864$		0			0
$865$	1.21676e8	+	2.10749e8i	0.188000	+	0.325625i
$866$	−1.30279e9	−	7.52165e8i	−2.00595	−	1.15813i
$867$		0			0
$868$	−1.14061e9	+	5.00395e8i	−1.74412	+	0.765162i
$869$	6.53980e6			0.00996564
$870$		0			0
$871$	−1.15904e8	+	6.69172e7i	−0.175406	+	0.101271i
$872$	6.75937e8	+	1.17076e9i	1.01943	+	1.76570i
$873$		0			0
$874$		−	3.93201e6i		−	0.00588953i
$875$	−2.18360e8	−	1.60474e8i	−0.325948	−	0.239542i
$876$		0			0
$877$	−8.98625e7	+	1.55646e8i	−0.133223	+	0.230749i	−0.924917	−	0.380168i	$-0.875866\pi$
$877$	−8.98625e7	+	1.55646e8i	−0.133223	+	0.230749i	0.791694	+	0.610918i	$0.209199\pi$
$878$	−1.31306e9	+	7.58097e8i	−1.94000	+	1.12006i
$879$		0			0
$880$	2.31047e8	+	1.33395e8i	0.339041	+	0.195746i
$881$			1.07737e9i			1.57556i	0.615954	+	0.787782i	$0.288771\pi$
$881$			1.07737e9i			1.57556i	−0.615954	+	0.787782i	$0.711229\pi$
$882$		0			0
$883$	−1.25270e9			−1.81955			−0.909775	−	0.415102i	$-0.863746\pi$
$883$	−1.25270e9			−1.81955			−0.909775	+	0.415102i	$0.863746\pi$
$884$	9.27654e7	−	1.60674e8i	0.134286	−	0.232589i
$885$		0			0
$886$	1.29751e9	+	2.24735e9i	1.86556	+	3.23124i
$887$	−3.29604e8	−	1.90297e8i	−0.472304	−	0.272685i	0.244900	−	0.969548i	$-0.421245\pi$
$887$	−3.29604e8	−	1.90297e8i	−0.472304	−	0.272685i	−0.717204	+	0.696864i	$0.754578\pi$
$888$		0			0
$889$	2.16126e8	−	2.94085e8i	0.307611	−	0.418570i
$890$	−7.67311e7			−0.108843
$891$		0			0
$892$	−2.59807e9	+	1.49999e9i	−3.66063	+	2.11346i
$893$	1.97613e8	+	3.42275e8i	0.277498	+	0.480641i
$894$		0			0
$895$			7.76969e7i			0.108376i
$896$	1.25840e9	+	2.86842e9i	1.74943	+	3.98767i
$897$		0			0
$898$	8.10714e8	−	1.40420e9i	1.11954	−	1.93910i
$899$	−4.25944e8	+	2.45919e8i	−0.586237	+	0.338464i
$900$		0			0
$901$	−2.73105e7	−	1.57677e7i	−0.0373383	−	0.0215573i
$902$		−	9.78254e8i		−	1.33301i
$903$		0			0
$904$	−4.26291e9			−5.77033
$905$	−1.13314e8	+	1.96266e8i	−0.152876	+	0.264789i
$906$		0			0
$907$	−3.32531e8	−	5.75961e8i	−0.445667	−	0.771918i	0.552431	−	0.833558i	$-0.313700\pi$
$907$	−3.32531e8	−	5.75961e8i	−0.445667	−	0.771918i	−0.998098	+	0.0616405i	$0.980367\pi$
$908$	2.94292e9	+	1.69910e9i	3.93117	+	2.26966i
$909$		0			0
$910$	−4.47380e8	−	4.94900e7i	−0.593680	−	0.0656740i
$911$	9.53125e8			1.26065			0.630325	−	0.776331i	$-0.282922\pi$
$911$	9.53125e8			1.26065			0.630325	+	0.776331i	$0.282922\pi$
$912$		0			0
$913$	3.85155e8	−	2.22369e8i	0.506085	−	0.292188i
$914$	−5.52846e8	−	9.57557e8i	−0.724045	−	1.25408i
$915$		0			0
$916$			7.62997e8i			0.992742i
$917$	−2.04942e8	+	8.99099e7i	−0.265780	+	0.116600i
$918$		0			0
$919$	6.24861e8	−	1.08229e9i	0.805076	−	1.39443i	−0.111164	−	0.993802i	$-0.535458\pi$
$919$	6.24861e8	−	1.08229e9i	0.805076	−	1.39443i	0.916240	−	0.400630i	$-0.131209\pi$
$920$	−1.68900e6	+	975146.i	−0.00216904	+	0.00125229i
$921$		0			0
$922$	−3.98041e8	−	2.29809e8i	−0.507850	−	0.293207i
$923$		−	1.30408e9i		−	1.65844i
$924$		0			0
$925$	−2.59921e8			−0.328410
$926$	−5.98252e8	+	1.03620e9i	−0.753444	+	1.30500i
$927$		0			0
$928$	1.73725e9	+	3.00901e9i	2.17380	+	3.76512i
$929$	9.03228e8	+	5.21479e8i	1.12655	+	0.650414i	0.943065	−	0.332609i	$-0.107929\pi$
$929$	9.03228e8	+	5.21479e8i	1.12655	+	0.650414i	0.183485	+	0.983023i	$0.441262\pi$
$930$		0			0
$931$	−1.54304e8	+	6.88903e8i	−0.191217	+	0.853707i
$932$	−2.18274e9			−2.69622
$933$		0			0
$934$	2.64390e9	−	1.52646e9i	3.24493	−	1.87346i
$935$	2.56139e6	+	4.43646e6i	0.00313358	+	0.00542752i
$936$		0			0
$937$			4.82808e8i			0.586889i	0.955976	+	0.293444i	$0.0948015\pi$
$937$			4.82808e8i			0.586889i	−0.955976	+	0.293444i	$0.905198\pi$
$938$	1.30156e8	−	1.77105e8i	0.157709	−	0.214597i
$939$		0			0
$940$	1.52463e8	−	2.64074e8i	0.183561	−	0.317938i
$941$	4.90467e8	−	2.83172e8i	0.588629	−	0.339845i	−0.175926	−	0.984403i	$-0.556292\pi$
$941$	4.90467e8	−	2.83172e8i	0.588629	−	0.339845i	0.764555	+	0.644558i	$0.222959\pi$
$942$		0			0
$943$	3.65821e6	+	2.11207e6i	0.00436248	+	0.00251868i
$944$		−	1.66646e9i		−	1.98097i
$945$		0			0
$946$	−6.60443e8			−0.780121
$947$	−1.09258e7	+	1.89240e7i	−0.0128648	+	0.0222824i	−0.872386	−	0.488817i	$-0.837428\pi$
$947$	−1.09258e7	+	1.89240e7i	−0.0128648	+	0.0222824i	0.859521	+	0.511100i	$0.170762\pi$
$948$		0			0
$949$	−9.00998e8	−	1.56057e9i	−1.05421	−	1.82594i
$950$	1.21224e9	+	6.99887e8i	1.41390	+	0.816313i
$951$		0			0
$952$	−2.15371e7	+	1.94691e8i	−0.0249618	+	0.225650i
$953$	−1.05425e9			−1.21805			−0.609023	−	0.793152i	$-0.708438\pi$
$953$	−1.05425e9			−1.21805			−0.609023	+	0.793152i	$0.708438\pi$
$954$		0			0
$955$	−3.22478e7	+	1.86183e7i	−0.0370246	+	0.0213762i
$956$	−9.30118e8	−	1.61101e9i	−1.06455	−	1.84385i
$957$		0			0
$958$		−	5.01041e8i		−	0.569871i
$959$	−1.56738e9	−	1.73387e8i	−1.77713	−	0.196589i
$960$		0			0
$961$	−2.38469e8	+	4.13040e8i	−0.268696	+	0.465395i
$962$	−7.64462e8	+	4.41362e8i	−0.858679	+	0.495758i
$963$		0			0
$964$	1.74015e9	+	1.00467e9i	1.94247	+	1.12149i
$965$			4.39728e7i			0.0489330i
$966$		0			0
$967$	−7.18604e8			−0.794713			−0.397356	−	0.917664i	$-0.630072\pi$
$967$	−7.18604e8			−0.794713			−0.397356	+	0.917664i	$0.630072\pi$
$968$	−1.24184e9	+	2.15092e9i	−1.36911	+	2.37137i
$969$		0			0
$970$	−2.16082e8	−	3.74264e8i	−0.236757	−	0.410075i
$971$	−5.48150e8	−	3.16475e8i	−0.598745	−	0.345686i	0.169803	−	0.985478i	$-0.445687\pi$
$971$	−5.48150e8	−	3.16475e8i	−0.598745	−	0.345686i	−0.768548	+	0.639792i	$0.779020\pi$
$972$		0			0
$973$	−5.43881e8	−	3.99703e8i	−0.590425	−	0.433909i
$974$	2.70183e9			2.92402
$975$		0			0
$976$	3.32851e9	−	1.92171e9i	3.58014	−	2.06699i
$977$	6.59658e8	+	1.14256e9i	0.707351	+	1.22517i	0.965836	+	0.259153i	$0.0834434\pi$
$977$	6.59658e8	+	1.14256e9i	0.707351	+	1.22517i	−0.258485	+	0.966015i	$0.583223\pi$
$978$		0			0
$979$			1.18834e8i			0.126646i
$980$	5.19823e8	−	1.62653e8i	0.552302	−	0.172816i
$981$		0			0
$982$	−1.77573e8	+	3.07566e8i	−0.187518	+	0.324790i
$983$	6.44167e7	−	3.71910e7i	0.0678169	−	0.0391541i	−0.465708	−	0.884938i	$-0.654200\pi$
$983$	6.44167e7	−	3.71910e7i	0.0678169	−	0.0391541i	0.533525	+	0.845784i	$0.320867\pi$
$984$		0			0
$985$	1.43768e8	+	8.30042e7i	0.150436	+	0.0868544i
$986$			1.20314e8i			0.125512i
$987$		0			0
$988$	3.50288e9			3.63207
$989$	1.42591e6	−	2.46975e6i	0.00147402	−	0.00255308i
$990$		0			0
$991$	−7.98815e8	−	1.38359e9i	−0.820777	−	1.42163i	−0.905105	−	0.425189i	$-0.860208\pi$
$991$	−7.98815e8	−	1.38359e9i	−0.820777	−	1.42163i	0.0843276	−	0.996438i	$-0.473126\pi$
$992$	−2.51180e9	−	1.45019e9i	−2.57306	−	1.48555i
$993$		0			0
$994$	8.60389e8	+	1.96118e9i	0.876064	+	1.99691i
$995$	1.72148e8			0.174756
$996$		0			0
$997$	−1.13154e9	+	6.53297e8i	−1.14179	+	0.659212i	−0.946873	−	0.321608i	$-0.895777\pi$
$997$	−1.13154e9	+	6.53297e8i	−1.14179	+	0.659212i	−0.194916	+	0.980820i	$0.562443\pi$
$998$	−1.11598e9	−	1.93293e9i	−1.12270	−	1.94458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.d.19.4		8
3.2	odd	2		21.7.f.a.19.1	yes	8
7.2	even	3		441.7.d.c.244.2		8
7.3	odd	6	inner	63.7.m.d.10.4		8
7.5	odd	6		441.7.d.c.244.1		8
12.11	even	2		336.7.bh.d.145.3		8
21.2	odd	6		147.7.d.b.97.7		8
21.5	even	6		147.7.d.b.97.8		8
21.11	odd	6		147.7.f.d.31.1		8
21.17	even	6		21.7.f.a.10.1	✓	8
21.20	even	2		147.7.f.d.19.1		8
84.59	odd	6		336.7.bh.d.241.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.1	✓	8	21.17	even	6
21.7.f.a.19.1	yes	8	3.2	odd	2
63.7.m.d.10.4		8	7.3	odd	6	inner
63.7.m.d.19.4		8	1.1	even	1	trivial
147.7.d.b.97.7		8	21.2	odd	6
147.7.d.b.97.8		8	21.5	even	6
147.7.f.d.19.1		8	21.20	even	2
147.7.f.d.31.1		8	21.11	odd	6
336.7.bh.d.145.3		8	12.11	even	2
336.7.bh.d.241.3		8	84.59	odd	6
441.7.d.c.244.1		8	7.5	odd	6
441.7.d.c.244.2		8	7.2	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.79767 - 13.5060i) q^{2} +(-89.6073 - 155.204i) q^{4} +(-22.3721 - 12.9165i) q^{5} +(-203.121 + 276.389i) q^{7} -1796.81 q^{8} +O(q^{10})\)	\(q+(7.79767 - 13.5060i) q^{2} +(-89.6073 - 155.204i) q^{4} +(-22.3721 - 12.9165i) q^{5} +(-203.121 + 276.389i) q^{7} -1796.81 q^{8} +(-348.901 + 201.438i) q^{10} +(311.967 + 540.343i) q^{11} -3257.26i q^{13} +(2149.03 + 4898.53i) q^{14} +(-8276.07 + 14334.6i) q^{16} +(-275.246 + 158.913i) q^{17} +(-5196.73 - 3000.33i) q^{19} +4629.67i q^{20} +9730.47 q^{22} +(-21.0083 + 36.3874i) q^{23} +(-7478.83 - 12953.7i) q^{25} +(-43992.4 - 25399.0i) q^{26} +(61097.9 + 6758.77i) q^{28} +24273.4 q^{29} +(-17547.8 + 10131.2i) q^{31} +(71570.2 + 123963. i) q^{32} +4956.62i q^{34} +(8114.24 - 3559.79i) q^{35} +(8688.57 - 15049.0i) q^{37} +(-81044.8 + 46791.2i) q^{38} +(40198.5 + 23208.6i) q^{40} -100535. i q^{41} -67873.7 q^{43} +(55909.1 - 96837.4i) q^{44} +(327.631 + 567.474i) q^{46} +(-57039.5 - 32931.8i) q^{47} +(-35132.9 - 112281. i) q^{49} -233270. q^{50} +(-505541. + 291874. i) q^{52} +(49611.0 + 85928.8i) q^{53} -16118.2i q^{55} +(364970. - 496619. i) q^{56} +(189276. - 327835. i) q^{58} +(-87190.7 + 50339.6i) q^{59} +(-201092. - 116101. i) q^{61} +315999. i q^{62} +1.17299e6 q^{64} +(-42072.6 + 72871.8i) q^{65} +(-20544.0 - 35583.3i) q^{67} +(49328.1 + 28479.6i) q^{68} +(15193.8 - 137349. i) q^{70} +400361. q^{71} +(479106. - 276612. i) q^{73} +(-135501. - 234695. i) q^{74} +1.07541e6i q^{76} +(-212712. - 23530.6i) q^{77} +(5240.77 - 9077.28i) q^{79} +(370306. - 213797. i) q^{80} +(-1.35782e6 - 783939. i) q^{82} -712797. i q^{83} +8210.45 q^{85} +(-529257. + 916700. i) q^{86} +(-560546. - 970895. i) q^{88} +(164942. + 95229.2i) q^{89} +(900271. + 661617. i) q^{91} +7529.99 q^{92} +(-889550. + 513582. i) q^{94} +(77507.9 + 134248. i) q^{95} +1.07270e6i q^{97} +(-1.79041e6 - 401025. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8	\( 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8} - 3411 q^{10} + 314 q^{11} + 5360 q^{14} - 12721 q^{16} + 5532 q^{17} - 18234 q^{19} + 86106 q^{22} - 3928 q^{23} - 17038 q^{25} - 12366 q^{26} + 85037 q^{28} + 8300 q^{29} - 89508 q^{31} + 186207 q^{32} + 25860 q^{35} + 64706 q^{37} + 77136 q^{38} + 221823 q^{40} + 45740 q^{43} - 92529 q^{44} - 111504 q^{46} - 483276 q^{47} - 310684 q^{49} - 967216 q^{50} - 1673988 q^{52} + 540974 q^{53} + 241885 q^{56} + 539799 q^{58} + 181770 q^{59} + 418224 q^{61} + 2378626 q^{64} + 414204 q^{65} - 1158902 q^{67} + 821250 q^{68} + 1087917 q^{70} - 1442344 q^{71} - 378666 q^{73} + 432940 q^{74} - 1065994 q^{77} + 611452 q^{79} + 2094945 q^{80} - 1561266 q^{82} - 275112 q^{85} - 816224 q^{86} - 366441 q^{88} + 989196 q^{89} + 304446 q^{91} - 678720 q^{92} - 716148 q^{94} + 591792 q^{95} - 3509629 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8 - 3411 * q^10 + 314 * q^11 + 5360 * q^14 - 12721 * q^16 + 5532 * q^17 - 18234 * q^19 + 86106 * q^22 - 3928 * q^23 - 17038 * q^25 - 12366 * q^26 + 85037 * q^28 + 8300 * q^29 - 89508 * q^31 + 186207 * q^32 + 25860 * q^35 + 64706 * q^37 + 77136 * q^38 + 221823 * q^40 + 45740 * q^43 - 92529 * q^44 - 111504 * q^46 - 483276 * q^47 - 310684 * q^49 - 967216 * q^50 - 1673988 * q^52 + 540974 * q^53 + 241885 * q^56 + 539799 * q^58 + 181770 * q^59 + 418224 * q^61 + 2378626 * q^64 + 414204 * q^65 - 1158902 * q^67 + 821250 * q^68 + 1087917 * q^70 - 1442344 * q^71 - 378666 * q^73 + 432940 * q^74 - 1065994 * q^77 + 611452 * q^79 + 2094945 * q^80 - 1561266 * q^82 - 275112 * q^85 - 816224 * q^86 - 366441 * q^88 + 989196 * q^89 + 304446 * q^91 - 678720 * q^92 - 716148 * q^94 + 591792 * q^95 - 3509629 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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