LMFDB - Embedded newform 63.7.m.d.10.2

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			10.2
Root			$-2.75320 - 4.76869i$ of defining polynomial
Character	$\chi$	$=$	63.10
Dual form			63.7.m.d.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25320 - 3.90266i) q^{2} +(21.8461 - 37.8386i) q^{4} +(-53.9244 + 31.1333i) q^{5} +(218.833 - 264.124i) q^{7} -485.305 q^{8} +O(q^{10})$	\(q+(-2.25320 - 3.90266i) q^{2} +(21.8461 - 37.8386i) q^{4} +(-53.9244 + 31.1333i) q^{5} +(218.833 - 264.124i) q^{7} -485.305 q^{8} +(243.005 + 140.299i) q^{10} +(9.71675 - 16.8299i) q^{11} -1642.65i q^{13} +(-1523.86 - 258.906i) q^{14} +(-304.661 - 527.689i) q^{16} +(186.054 + 107.418i) q^{17} +(-8237.53 + 4755.94i) q^{19} +2720.57i q^{20} -87.5753 q^{22} +(-7223.90 - 12512.2i) q^{23} +(-5873.94 + 10174.0i) q^{25} +(-6410.70 + 3701.22i) q^{26} +(-5213.43 - 14050.4i) q^{28} -43016.4 q^{29} +(-7799.62 - 4503.11i) q^{31} +(-16902.7 + 29276.3i) q^{32} -968.141i q^{34} +(-3577.38 + 21055.7i) q^{35} +(16564.6 + 28690.7i) q^{37} +(37121.7 + 21432.2i) q^{38} +(26169.8 - 15109.1i) q^{40} -73712.4i q^{41} +4761.19 q^{43} +(-424.547 - 735.337i) q^{44} +(-32553.9 + 56384.9i) q^{46} +(63760.5 - 36812.2i) q^{47} +(-21873.6 - 115598. i) q^{49} +52940.7 q^{50} +(-62155.6 - 35885.5i) q^{52} +(119317. - 206663. i) q^{53} +1210.06i q^{55} +(-106201. + 128181. i) q^{56} +(96924.8 + 167879. i) q^{58} +(282811. + 163281. i) q^{59} +(350517. - 202371. i) q^{61} +40585.7i q^{62} +113344. q^{64} +(51141.0 + 88578.8i) q^{65} +(-109982. + 190494. i) q^{67} +(8129.12 - 4693.35i) q^{68} +(90233.8 - 33481.4i) q^{70} -350228. q^{71} +(-174606. - 100809. i) q^{73} +(74646.7 - 129292. i) q^{74} +415596. i q^{76} +(-2318.83 - 6249.36i) q^{77} +(-197745. - 342505. i) q^{79} +(32857.4 + 18970.2i) q^{80} +(-287675. + 166089. i) q^{82} +13229.0i q^{83} -13377.1 q^{85} +(-10727.9 - 18581.3i) q^{86} +(-4715.59 + 8167.65i) q^{88} +(199460. - 115158. i) q^{89} +(-433862. - 359465. i) q^{91} -631258. q^{92} +(-287331. - 165891. i) q^{94} +(296136. - 512922. i) q^{95} +662517. i q^{97} +(-401853. + 345831. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.25320	−	3.90266i	−0.281650	−	0.487833i	0.690141	−	0.723675i	$-0.257549\pi$
$2$	−2.25320	−	3.90266i	−0.281650	−	0.487833i	−0.971791	+	0.235842i	$0.924215\pi$
$3$		0			0
$3$		0			0
$4$	21.8461	−	37.8386i	0.341346	−	0.591229i
$5$	−53.9244	+	31.1333i	−0.431395	+	0.249066i	−0.699941	−	0.714201i	$-0.746790\pi$
$5$	−53.9244	+	31.1333i	−0.431395	+	0.249066i	0.268546	+	0.963267i	$0.413457\pi$
$6$		0			0
$7$	218.833	−	264.124i	0.637996	−	0.770040i
$7$	218.833	−	264.124i	0.637996	−	0.770040i
$8$	−485.305			−0.947862
$9$		0			0
$10$	243.005	+	140.299i	0.243005	+	0.140299i
$11$	9.71675	−	16.8299i	0.00730034	−	0.0126446i	−0.862352	−	0.506309i	$-0.831010\pi$
$11$	9.71675	−	16.8299i	0.00730034	−	0.0126446i	0.869652	+	0.493664i	$0.164343\pi$
$12$		0			0
$13$		−	1642.65i		−	0.747678i	−0.927494	−	0.373839i	$-0.878041\pi$
$13$		−	1642.65i		−	0.747678i	0.927494	−	0.373839i	$-0.121959\pi$
$14$	−1523.86	−	258.906i	−0.555343	−	0.0943533i
$15$		0			0
$16$	−304.661	−	527.689i	−0.0743802	−	0.128830i
$17$	186.054	+	107.418i	0.0378697	+	0.0218641i	0.518815	−	0.854886i	$-0.326373\pi$
$17$	186.054	+	107.418i	0.0378697	+	0.0218641i	−0.480946	+	0.876750i	$0.659707\pi$
$18$		0			0
$19$	−8237.53	+	4755.94i	−1.20098	+	0.693387i	−0.960773	−	0.277335i	$-0.910549\pi$
$19$	−8237.53	+	4755.94i	−1.20098	+	0.693387i	−0.240208	+	0.970722i	$0.577215\pi$
$20$			2720.57i			0.340071i
$21$		0			0
$22$	−87.5753			−0.00822458
$23$	−7223.90	−	12512.2i	−0.593729	−	1.02837i	−0.993725	−	0.111852i	$-0.964322\pi$
$23$	−7223.90	−	12512.2i	−0.593729	−	1.02837i	0.399996	−	0.916517i	$-0.369012\pi$
$24$		0			0
$25$	−5873.94	+	10174.0i	−0.375932	+	0.651134i
$26$	−6410.70	+	3701.22i	−0.364742	+	0.210584i
$27$		0			0
$28$	−5213.43	−	14050.4i	−0.237492	−	0.640051i
$29$	−43016.4			−1.76376			−0.881882	−	0.471471i	$-0.843723\pi$
$29$	−43016.4			−1.76376			−0.881882	+	0.471471i	$0.843723\pi$
$30$		0			0
$31$	−7799.62	−	4503.11i	−0.261811	−	0.151157i	0.363349	−	0.931653i	$-0.381633\pi$
$31$	−7799.62	−	4503.11i	−0.261811	−	0.151157i	−0.625161	+	0.780496i	$0.714967\pi$
$32$	−16902.7	+	29276.3i	−0.515829	+	0.893443i
$33$		0			0
$34$		−	968.141i		−	0.0246321i
$35$	−3577.38	+	21055.7i	−0.0834375	+	0.491094i
$36$		0			0
$37$	16564.6	+	28690.7i	0.327020	+	0.566416i	0.981919	−	0.189301i	$-0.0606221\pi$
$37$	16564.6	+	28690.7i	0.327020	+	0.566416i	−0.654899	+	0.755717i	$0.727289\pi$
$38$	37121.7	+	21432.2i	0.676514	+	0.390585i
$39$		0			0
$40$	26169.8	−	15109.1i	0.408903	−	0.236080i
$41$		−	73712.4i		−	1.06952i	−0.845004	−	0.534760i	$-0.820402\pi$
$41$		−	73712.4i		−	1.06952i	0.845004	−	0.534760i	$-0.179598\pi$
$42$		0			0
$43$	4761.19			0.0598839			0.0299420	−	0.999552i	$-0.490468\pi$
$43$	4761.19			0.0598839			0.0299420	+	0.999552i	$0.490468\pi$
$44$	−424.547	−	735.337i	−0.00498388	−	0.00863234i
$45$		0			0
$46$	−32553.9	+	56384.9i	−0.334448	+	0.579281i
$47$	63760.5	−	36812.2i	0.614127	−	0.354567i	−0.160452	−	0.987044i	$-0.551295\pi$
$47$	63760.5	−	36812.2i	0.614127	−	0.354567i	0.774579	+	0.632477i	$0.217962\pi$
$48$		0			0
$49$	−21873.6	−	115598.i	−0.185922	−	0.982564i
$50$	52940.7			0.423526
$51$		0			0
$52$	−62155.6	−	35885.5i	−0.442049	−	0.255217i
$53$	119317.	−	206663.i	0.801447	−	1.38815i	−0.117216	−	0.993106i	$-0.537397\pi$
$53$	119317.	−	206663.i	0.801447	−	1.38815i	0.918664	−	0.395041i	$-0.129270\pi$
$54$		0			0
$55$			1210.06i			0.00727307i
$56$	−106201.	+	128181.i	−0.604732	+	0.729891i
$57$		0			0
$58$	96924.8	+	167879.i	0.496765	+	0.860422i
$59$	282811.	+	163281.i	1.37702	+	0.795023i	0.991800	−	0.127801i	$-0.0407919\pi$
$59$	282811.	+	163281.i	1.37702	+	0.795023i	0.385221	+	0.922824i	$0.374125\pi$
$60$		0			0
$61$	350517.	−	202371.i	1.54426	−	0.891578i	0.545696	−	0.837983i	$-0.316265\pi$
$61$	350517.	−	202371.i	1.54426	−	0.891578i	0.998563	−	0.0535954i	$-0.0170681\pi$
$62$			40585.7i			0.170294i
$63$		0			0
$64$	113344.			0.432374
$65$	51141.0	+	88578.8i	0.186221	+	0.322545i
$66$		0			0
$67$	−109982.	+	190494.i	−0.365676	+	0.633369i	−0.988884	−	0.148687i	$-0.952495\pi$
$67$	−109982.	+	190494.i	−0.365676	+	0.633369i	0.623209	+	0.782056i	$0.285829\pi$
$68$	8129.12	−	4693.35i	0.0258533	−	0.0149264i
$69$		0			0
$70$	90233.8	−	33481.4i	0.263072	−	0.0976134i
$71$	−350228.			−0.978535			−0.489267	−	0.872134i	$-0.662736\pi$
$71$	−350228.			−0.978535			−0.489267	+	0.872134i	$0.662736\pi$
$72$		0			0
$73$	−174606.	−	100809.i	−0.448838	−	0.259137i	0.258501	−	0.966011i	$-0.416771\pi$
$73$	−174606.	−	100809.i	−0.448838	−	0.259137i	−0.707339	+	0.706874i	$0.750105\pi$
$74$	74646.7	−	129292.i	0.184211	−	0.319063i
$75$		0			0
$76$			415596.i			0.946739i
$77$	−2318.83	−	6249.36i	−0.00507923	−	0.0136887i
$78$		0			0
$79$	−197745.	−	342505.i	−0.401074	−	0.694681i	0.592782	−	0.805363i	$-0.298030\pi$
$79$	−197745.	−	342505.i	−0.401074	−	0.694681i	−0.993856	+	0.110682i	$0.964696\pi$
$80$	32857.4	+	18970.2i	0.0641745	+	0.0370512i
$81$		0			0
$82$	−287675.	+	166089.i	−0.521747	+	0.301231i
$83$			13229.0i			0.0231362i	0.999933	+	0.0115681i	$0.00368232\pi$
$83$			13229.0i			0.0231362i	−0.999933	+	0.0115681i	$0.996318\pi$
$84$		0			0
$85$	−13377.1			−0.0217824
$86$	−10727.9	−	18581.3i	−0.0168663	−	0.0292134i
$87$		0			0
$88$	−4715.59	+	8167.65i	−0.00691972	+	0.0119853i
$89$	199460.	−	115158.i	0.282934	−	0.163352i	−0.351817	−	0.936069i	$-0.614436\pi$
$89$	199460.	−	115158.i	0.282934	−	0.163352i	0.634751	+	0.772717i	$0.281103\pi$
$90$		0			0
$91$	−433862.	−	359465.i	−0.575742	−	0.477015i
$92$	−631258.			−0.810668
$93$		0			0
$94$	−287331.	−	165891.i	−0.345939	−	0.199728i
$95$	296136.	−	512922.i	0.345398	−	0.598247i
$96$		0			0
$97$			662517.i			0.725909i	0.931807	+	0.362954i	$0.118232\pi$
$97$			662517.i			0.725909i	−0.931807	+	0.362954i	$0.881768\pi$
$98$	−401853.	+	345831.i	−0.426962	+	0.367439i
$99$		0			0
$100$	256646.	+	444524.i	0.256646	+	0.444524i
$101$	−1.62606e6	−	938803.i	−1.57823	−	0.911193i	−0.995106	−	0.0988126i	$-0.968496\pi$
$101$	−1.62606e6	−	938803.i	−1.57823	−	0.911193i	−0.583127	−	0.812381i	$-0.698171\pi$
$102$		0			0
$103$	782887.	−	452000.i	0.716452	−	0.413644i	−0.0969931	−	0.995285i	$-0.530922\pi$
$103$	782887.	−	452000.i	0.716452	−	0.413644i	0.813446	+	0.581641i	$0.197589\pi$
$104$			797186.i			0.708696i
$105$		0			0
$106$	−1.07538e6			−0.902912
$107$	423106.	+	732842.i	0.345381	+	0.598217i	0.985423	−	0.170123i	$-0.0544164\pi$
$107$	423106.	+	732842.i	0.345381	+	0.598217i	−0.640042	+	0.768340i	$0.721083\pi$
$108$		0			0
$109$	847674.	−	1.46821e6i	0.654560	−	1.13373i	−0.327444	−	0.944871i	$-0.606187\pi$
$109$	847674.	−	1.46821e6i	0.654560	−	1.13373i	0.982004	−	0.188861i	$-0.0604794\pi$
$110$	4722.44	−	2726.50i	0.00354804	−	0.00204846i
$111$		0			0
$112$	−206045.	−	35007.3i	−0.146659	−	0.0249175i
$113$	152753.			0.105866			0.0529328	−	0.998598i	$-0.483143\pi$
$113$	152753.			0.105866			0.0529328	+	0.998598i	$0.483143\pi$
$114$		0			0
$115$	779089.	+	449807.i	0.512264	+	0.295756i
$116$	−939743.	+	1.62768e6i	−0.602054	+	1.04279i
$117$		0			0
$118$		−	1.47162e6i		−	0.895675i
$119$	69086.3	−	25634.6i	0.0409969	−	0.0152120i
$120$		0			0
$121$	885592.	+	1.53389e6i	0.499893	+	0.865841i
$122$	−1.57957e6	−	911968.i	−0.869883	−	0.502227i
$123$		0			0
$124$	−340783.	+	196751.i	−0.178737	+	0.103194i
$125$		−	1.70441e6i		−	0.872660i
$126$		0			0
$127$	−2.82114e6			−1.37725			−0.688627	−	0.725116i	$-0.741786\pi$
$127$	−2.82114e6			−1.37725			−0.688627	+	0.725116i	$0.741786\pi$
$128$	826385.	+	1.43134e6i	0.394051	+	0.682517i
$129$		0			0
$130$	230462.	−	399172.i	0.104899	−	0.181690i
$131$	3.86131e6	−	2.22933e6i	1.71759	−	0.991654i	0.794333	−	0.607482i	$-0.207820\pi$
$131$	3.86131e6	−	2.22933e6i	1.71759	−	0.991654i	0.923262	−	0.384171i	$-0.125513\pi$
$132$		0			0
$133$	−546484.	+	3.21648e6i	−0.232286	+	1.36718i
$134$	991245.			0.411971
$135$		0			0
$136$	−90292.9	−	52130.6i	−0.0358952	−	0.0207241i
$137$	649623.	−	1.12518e6i	0.252639	−	0.437583i	−0.711613	−	0.702572i	$-0.752035\pi$
$137$	649623.	−	1.12518e6i	0.252639	−	0.437583i	0.964252	+	0.264989i	$0.0853682\pi$
$138$		0			0
$139$			119566.i			0.0445207i	0.999752	+	0.0222603i	$0.00708627\pi$
$139$			119566.i			0.0445207i	−0.999752	+	0.0222603i	$0.992914\pi$
$140$	718566.	+	595349.i	0.261868	+	0.216964i
$141$		0			0
$142$	789136.	+	1.36682e6i	0.275605	+	0.477361i
$143$	−27645.6	−	15961.2i	−0.00945406	−	0.00545830i
$144$		0			0
$145$	2.31963e6	−	1.33924e6i	0.760879	−	0.439293i
$146$			908570.i			0.291944i
$147$		0			0
$148$	1.44749e6			0.446509
$149$	3.12914e6	+	5.41983e6i	0.945946	+	1.63843i	0.753845	+	0.657052i	$0.228197\pi$
$149$	3.12914e6	+	5.41983e6i	0.945946	+	1.63843i	0.192101	+	0.981375i	$0.438470\pi$
$150$		0			0
$151$	753969.	−	1.30591e6i	0.218989	−	0.379300i	−0.735510	−	0.677514i	$-0.763057\pi$
$151$	753969.	−	1.30591e6i	0.218989	−	0.379300i	0.954499	+	0.298213i	$0.0963907\pi$
$152$	3.99772e6	−	2.30808e6i	1.13836	−	0.657235i
$153$		0			0
$154$	−19164.3	+	23130.7i	−0.00524725	+	0.00633325i
$155$	560786.			0.150592
$156$		0			0
$157$	2.14761e6	+	1.23992e6i	0.554954	+	0.320403i	0.751118	−	0.660169i	$-0.229515\pi$
$157$	2.14761e6	+	1.23992e6i	0.554954	+	0.320403i	−0.196164	+	0.980571i	$0.562848\pi$
$158$	−891121.	+	1.54347e6i	−0.225925	+	0.391314i
$159$		0			0
$160$		−	2.10494e6i		−	0.513902i
$161$	−4.88558e6	−	830066.i	−1.17068	−	0.198900i
$162$		0			0
$163$	−3.29510e6	−	5.70727e6i	−0.760861	−	1.31785i	−0.942407	−	0.334468i	$-0.891444\pi$
$163$	−3.29510e6	−	5.70727e6i	−0.760861	−	1.31785i	0.181546	−	0.983382i	$-0.441890\pi$
$164$	−2.78918e6	−	1.61033e6i	−0.632331	−	0.365076i
$165$		0			0
$166$	51628.2	−	29807.5i	0.0112866	−	0.00651631i
$167$		−	5.45006e6i		−	1.17018i	−0.810969	−	0.585089i	$-0.801059\pi$
$167$		−	5.45006e6i		−	1.17018i	0.810969	−	0.585089i	$-0.198941\pi$
$168$		0			0
$169$	2.12851e6			0.440978
$170$	30141.4	+	52206.4i	0.00613502	+	0.0106262i
$171$		0			0
$172$	104014.	−	180157.i	0.0204411	−	0.0354051i
$173$	−2.39148e6	+	1.38072e6i	−0.461879	+	0.266666i	−0.712834	−	0.701333i	$-0.752589\pi$
$173$	−2.39148e6	+	1.38072e6i	−0.461879	+	0.266666i	0.250955	+	0.967999i	$0.419255\pi$
$174$		0			0
$175$	1.40177e6	+	3.77784e6i	0.261556	+	0.704903i
$176$	−11841.3			−0.00217200
$177$		0			0
$178$	−898847.	−	518949.i	−0.159377	−	0.0920164i
$179$	−743863.	+	1.28841e6i	−0.129698	+	0.224644i	−0.923560	−	0.383455i	$-0.874734\pi$
$179$	−743863.	+	1.28841e6i	−0.129698	+	0.224644i	0.793861	+	0.608099i	$0.208068\pi$
$180$		0			0
$181$		−	6.01679e6i		−	1.01468i	−0.861746	−	0.507340i	$-0.830629\pi$
$181$		−	6.01679e6i		−	1.01468i	0.861746	−	0.507340i	$-0.169371\pi$
$182$	−425291.	+	2.50317e6i	−0.0705459	+	0.415217i
$183$		0			0
$184$	3.50580e6	+	6.07222e6i	0.562773	+	0.974752i
$185$	−1.78647e6	−	1.03142e6i	−0.282150	−	0.162899i
$186$		0			0
$187$	3615.68	−	2087.51i	0.000552923	−	0.000319230i
$188$		−	3.21682e6i		−	0.484120i
$189$		0			0
$190$	−2.66902e6			−0.389126
$191$	3.20172e6	+	5.54554e6i	0.459498	+	0.795874i	0.998934	−	0.0461527i	$-0.0146961\pi$
$191$	3.20172e6	+	5.54554e6i	0.459498	+	0.795874i	−0.539437	+	0.842026i	$0.681363\pi$
$192$		0			0
$193$	−4.92592e6	+	8.53194e6i	−0.685197	+	1.18680i	0.288178	+	0.957577i	$0.406951\pi$
$193$	−4.92592e6	+	8.53194e6i	−0.685197	+	1.18680i	−0.973375	+	0.229219i	$0.926383\pi$
$194$	2.58558e6	−	1.49279e6i	0.354122	−	0.204453i
$195$		0			0
$196$	−4.85191e6	−	1.69770e6i	−0.644384	−	0.225472i
$197$	−2.38883e6			−0.312454			−0.156227	−	0.987721i	$-0.549933\pi$
$197$	−2.38883e6			−0.312454			−0.156227	+	0.987721i	$0.549933\pi$
$198$		0			0
$199$	−1.36103e7	−	7.85789e6i	−1.72706	−	0.997118i	−0.901464	−	0.432854i	$-0.857507\pi$
$199$	−1.36103e7	−	7.85789e6i	−1.72706	−	0.997118i	−0.825594	−	0.564264i	$-0.809160\pi$
$200$	2.85066e6	−	4.93748e6i	0.356332	−	0.617185i
$201$		0			0
$202$			8.46126e6i			1.02655i
$203$	−9.41339e6	+	1.13617e7i	−1.12527	+	1.35817i
$204$		0			0
$205$	2.29491e6	+	3.97490e6i	0.266381	+	0.461386i
$206$	−3.52801e6	−	2.03690e6i	−0.403578	−	0.233006i
$207$		0			0
$208$	−866808.	+	500452.i	−0.0963236	+	0.0556125i
$209$			184849.i			0.0202478i
$210$		0			0
$211$	1.46740e6			0.156207			0.0781034	−	0.996945i	$-0.475114\pi$
$211$	1.46740e6			0.156207			0.0781034	+	0.996945i	$0.475114\pi$
$212$	−5.21324e6	−	9.02959e6i	−0.547142	−	0.947677i
$213$		0			0
$214$	1.90669e6	−	3.30248e6i	0.194553	−	0.336976i
$215$	−256744.	+	148231.i	−0.0258336	+	0.0149151i
$216$		0			0
$217$	−2.89619e6	+	1.07464e6i	−0.283431	+	0.105168i
$218$	−7.63993e6			−0.737429
$219$		0			0
$220$	45786.9	+	26435.1i	0.00430005	+	0.00248263i
$221$	176450.	−	305621.i	0.0163473	−	0.0283143i
$222$		0			0
$223$		−	3.63341e6i		−	0.327642i	−0.986490	−	0.163821i	$-0.947618\pi$
$223$		−	3.63341e6i		−	0.327642i	0.986490	−	0.163821i	$-0.0523820\pi$
$224$	4.03371e6	+	1.08710e7i	0.358889	+	0.967222i
$225$		0			0
$226$	−344184.	−	596144.i	−0.0298171	−	0.0516447i
$227$	−5.14121e6	−	2.96828e6i	−0.439529	−	0.253762i	0.263869	−	0.964559i	$-0.415001\pi$
$227$	−5.14121e6	−	2.96828e6i	−0.439529	−	0.253762i	−0.703398	+	0.710796i	$0.748335\pi$
$228$		0			0
$229$	1.05964e7	−	6.11784e6i	0.882373	−	0.509438i	0.0109329	−	0.999940i	$-0.496520\pi$
$229$	1.05964e7	−	6.11784e6i	0.882373	−	0.509438i	0.871440	+	0.490502i	$0.163187\pi$
$230$		−	4.05403e6i		−	0.333199i
$231$		0			0
$232$	2.08761e7			1.67180
$233$	6.06046e6	+	1.04970e7i	0.479113	+	0.829848i	0.999713	−	0.0239524i	$-0.00762503\pi$
$233$	6.06046e6	+	1.04970e7i	0.479113	+	0.829848i	−0.520600	+	0.853801i	$0.674292\pi$
$234$		0			0
$235$	−2.29216e6	+	3.97015e6i	−0.176621	+	0.305917i
$236$	1.23567e7	−	7.13413e6i	0.940081	−	0.542756i
$237$		0			0
$238$	−255709.	−	211861.i	−0.0189677	−	0.0157152i
$239$	−1.19016e7			−0.871790			−0.435895	−	0.899998i	$-0.643568\pi$
$239$	−1.19016e7			−0.871790			−0.435895	+	0.899998i	$0.643568\pi$
$240$		0			0
$241$	−8.62117e6	−	4.97743e6i	−0.615907	−	0.355594i	0.159367	−	0.987219i	$-0.449055\pi$
$241$	−8.62117e6	−	4.97743e6i	−0.615907	−	0.355594i	−0.775274	+	0.631625i	$0.782388\pi$
$242$	3.99084e6	−	6.91233e6i	0.281590	−	0.487729i
$243$		0			0
$244$		−	1.76841e7i		−	1.21735i
$245$	4.77845e6	+	5.55254e6i	0.324929	+	0.377566i
$246$		0			0
$247$	7.81234e6	+	1.35314e7i	0.518430	+	0.897947i
$248$	3.78520e6	+	2.18539e6i	0.248161	+	0.143276i
$249$		0			0
$250$	−6.65175e6	+	3.84039e6i	−0.425712	+	0.245785i
$251$		−	4.57737e6i		−	0.289464i	−0.989471	−	0.144732i	$-0.953768\pi$
$251$		−	4.57737e6i		−	0.289464i	0.989471	−	0.144732i	$-0.0462320\pi$
$252$		0			0
$253$	−280772.			−0.0173377
$254$	6.35661e6	+	1.10100e7i	0.387904	+	0.671870i
$255$		0			0
$256$	7.35104e6	−	1.27324e7i	0.438156	−	0.758909i
$257$	3.50429e6	−	2.02320e6i	0.206443	−	0.119190i	−0.393214	−	0.919447i	$-0.628637\pi$
$257$	3.50429e6	−	2.02320e6i	0.206443	−	0.119190i	0.599657	+	0.800257i	$0.295304\pi$
$258$		0			0
$259$	1.12028e7	+	1.90336e6i	0.644801	+	0.109552i
$260$	4.46893e6			0.254263
$261$		0			0
$262$	−1.74006e7	−	1.00463e7i	−0.967523	−	0.558600i
$263$	1.48379e7	−	2.56999e7i	0.815651	−	1.41275i	−0.0932094	−	0.995647i	$-0.529713\pi$
$263$	1.48379e7	−	2.56999e7i	0.815651	−	1.41275i	0.908860	−	0.417102i	$-0.136954\pi$
$264$		0			0
$265$			1.48589e7i			0.798453i
$266$	1.37842e7	−	5.11464e6i	0.732379	−	0.271751i
$267$		0			0
$268$	4.80535e6	+	8.32312e6i	0.249644	+	0.432396i
$269$	1.77285e7	+	1.02355e7i	0.910783	+	0.525841i	0.880683	−	0.473706i	$-0.157084\pi$
$269$	1.77285e7	+	1.02355e7i	0.910783	+	0.525841i	0.0300997	+	0.999547i	$0.490418\pi$
$270$		0			0
$271$	2.19287e6	−	1.26606e6i	0.110181	−	0.0636128i	−0.443897	−	0.896078i	$-0.646404\pi$
$271$	2.19287e6	−	1.26606e6i	0.110181	−	0.0636128i	0.554078	+	0.832465i	$0.313071\pi$
$272$		−	130905.i		−	0.00650502i
$273$		0			0
$274$	−5.85494e6			−0.284623
$275$	114151.	+	197716.i	0.00548887	+	0.00950700i
$276$		0			0
$277$	−1.52864e7	+	2.64769e7i	−0.719229	+	1.24574i	0.242077	+	0.970257i	$0.422171\pi$
$277$	−1.52864e7	+	2.64769e7i	−0.719229	+	1.24574i	−0.961306	+	0.275484i	$0.911162\pi$
$278$	466624.	−	269405.i	0.0217186	−	0.0125393i
$279$		0			0
$280$	1.73612e6	−	1.02184e7i	0.0790872	−	0.465490i
$281$	2.27089e7			1.02348			0.511738	−	0.859142i	$-0.329002\pi$
$281$	2.27089e7			1.02348			0.511738	+	0.859142i	$0.329002\pi$
$282$		0			0
$283$	3.54922e7	+	2.04914e7i	1.56593	+	0.904092i	0.996636	+	0.0819595i	$0.0261178\pi$
$283$	3.54922e7	+	2.04914e7i	1.56593	+	0.904092i	0.569297	+	0.822132i	$0.307216\pi$
$284$	−7.65114e6	+	1.32522e7i	−0.334019	+	0.578538i
$285$		0			0
$286$			143855.i			0.00614934i
$287$	−1.94692e7	−	1.61307e7i	−0.823573	−	0.682349i
$288$		0			0
$289$	−1.20457e7	−	2.08638e7i	−0.499044	−	0.864369i
$290$	−1.04532e7	−	6.03517e6i	−0.428604	−	0.247454i
$291$		0			0
$292$	−7.62892e6	+	4.40456e6i	−0.306418	+	0.176911i
$293$			2.94333e7i			1.17014i	0.810984	+	0.585069i	$0.198932\pi$
$293$			2.94333e7i			1.17014i	−0.810984	+	0.585069i	$0.801068\pi$
$294$		0			0
$295$	−2.03339e7			−0.792053
$296$	−8.03887e6	−	1.39237e7i	−0.309970	−	0.536884i
$297$		0			0
$298$	1.41012e7	−	2.44240e7i	0.532853	−	0.922928i
$299$	−2.05531e7	+	1.18663e7i	−0.768889	+	0.443918i
$300$		0			0
$301$	1.04190e6	−	1.25754e6i	0.0382057	−	0.0461130i
$302$	−6.79538e6			−0.246714
$303$		0			0
$304$	5.01931e6	+	2.89790e6i	0.178658	+	0.103148i
$305$	−1.26010e7	+	2.18255e7i	−0.444124	+	0.769245i
$306$		0			0
$307$		−	4.67295e6i		−	0.161501i	−0.996734	−	0.0807506i	$-0.974268\pi$
$307$		−	4.67295e6i		−	0.161501i	0.996734	−	0.0807506i	$-0.0257317\pi$
$308$	−287125.	−	48782.8i	−0.00982694	−	0.00166961i
$309$		0			0
$310$	−1.26357e6	−	2.18856e6i	−0.0424143	−	0.0734638i
$311$	−2.77399e7	−	1.60156e7i	−0.922196	−	0.532430i	−0.0378610	−	0.999283i	$-0.512054\pi$
$311$	−2.77399e7	−	1.60156e7i	−0.922196	−	0.532430i	−0.884335	+	0.466853i	$0.845388\pi$
$312$		0			0
$313$	1.88804e7	−	1.09006e7i	0.615714	−	0.355483i	−0.159484	−	0.987200i	$-0.550983\pi$
$313$	1.88804e7	−	1.09006e7i	0.615714	−	0.355483i	0.775199	+	0.631718i	$0.217650\pi$
$314$		−	1.11752e7i		−	0.360966i
$315$		0			0
$316$	−1.72799e7			−0.547620
$317$	5.26241e6	+	9.11476e6i	0.165199	+	0.286133i	0.936726	−	0.350064i	$-0.113840\pi$
$317$	5.26241e6	+	9.11476e6i	0.165199	+	0.286133i	−0.771527	+	0.636196i	$0.780507\pi$
$318$		0			0
$319$	−417980.	+	723962.i	−0.0128761	+	0.0223020i
$320$	−6.11202e6	+	3.52878e6i	−0.186524	+	0.107690i
$321$		0			0
$322$	7.76875e6	+	2.09371e7i	0.232693	+	0.627117i
$323$	−2.04350e6			−0.0606410
$324$		0			0
$325$	1.67122e7	+	9.64882e6i	0.486838	+	0.281076i
$326$	−1.48490e7	+	2.57193e7i	−0.428594	+	0.742346i
$327$		0			0
$328$			3.57730e7i			1.01376i
$329$	4.22992e6	−	2.48964e7i	0.118780	−	0.699114i
$330$		0			0
$331$	−2.03472e7	−	3.52425e7i	−0.561076	−	0.971812i	−0.997403	−	0.0720239i	$-0.977054\pi$
$331$	−2.03472e7	−	3.52425e7i	−0.561076	−	0.971812i	0.436327	−	0.899788i	$-0.356279\pi$
$332$	500566.	+	289002.i	0.0136788	+	0.00789744i
$333$		0			0
$334$	−2.12698e7	+	1.22801e7i	−0.570852	+	0.329581i
$335$		−	1.36964e7i		−	0.364310i
$336$		0			0
$337$	−4.05258e7			−1.05887			−0.529434	−	0.848351i	$-0.677596\pi$
$337$	−4.05258e7			−1.05887			−0.529434	+	0.848351i	$0.677596\pi$
$338$	−4.79598e6	−	8.30688e6i	−0.124202	−	0.215123i
$339$		0			0
$340$	−292238.	+	506172.i	−0.00743533	+	0.0128784i
$341$	−151574.	+	87511.3i	−0.00382262	+	0.00220699i
$342$		0			0
$343$	−3.53187e7	−	1.95192e7i	−0.875231	−	0.483704i
$344$	−2.31063e6			−0.0567617
$345$		0			0
$346$	1.07770e7	+	6.22209e6i	0.260177	+	0.150213i
$347$	−8.26775e6	+	1.43202e7i	−0.197879	+	0.342736i	−0.947840	−	0.318745i	$-0.896738\pi$
$347$	−8.26775e6	+	1.43202e7i	−0.197879	+	0.342736i	0.749962	+	0.661481i	$0.230072\pi$
$348$		0			0
$349$		−	5.07209e6i		−	0.119319i	−0.998219	−	0.0596597i	$-0.980998\pi$
$349$		−	5.07209e6i		−	0.119319i	0.998219	−	0.0596597i	$-0.0190015\pi$
$350$	1.15852e7	−	1.39829e7i	0.270208	−	0.326132i
$351$		0			0
$352$	328479.	+	568942.i	0.00753146	+	0.0130449i
$353$	3.94332e7	+	2.27668e7i	0.896475	+	0.517580i	0.876055	−	0.482211i	$-0.160166\pi$
$353$	3.94332e7	+	2.27668e7i	0.896475	+	0.517580i	0.0204200	+	0.999791i	$0.493500\pi$
$354$		0			0
$355$	1.88858e7	−	1.09037e7i	0.422135	−	0.243720i
$356$		−	1.00630e7i		−	0.223038i
$357$		0			0
$358$	6.70430e6			0.146118
$359$	−2.00085e7	−	3.46558e7i	−0.432446	−	0.749018i	0.564638	−	0.825339i	$-0.309016\pi$
$359$	−2.00085e7	−	3.46558e7i	−0.432446	−	0.749018i	−0.997083	+	0.0763210i	$0.975683\pi$
$360$		0			0
$361$	2.17150e7	−	3.76114e7i	0.461570	−	0.799463i
$362$	−2.34815e7	+	1.35570e7i	−0.494994	+	0.285785i
$363$		0			0
$364$	−2.30799e7	+	8.56383e6i	−0.478552	+	0.177568i
$365$	1.25540e7			0.258169
$366$		0			0
$367$	1.53736e7	+	8.87597e6i	0.311013	+	0.179563i	0.647380	−	0.762168i	$-0.275865\pi$
$367$	1.53736e7	+	8.87597e6i	0.311013	+	0.179563i	−0.336367	+	0.941731i	$0.609198\pi$
$368$	−4.40169e6	+	7.62395e6i	−0.0883234	+	0.152981i
$369$		0			0
$370$			9.29598e6i			0.183523i
$371$	−2.84742e7	−	7.67391e7i	−0.557609	−	1.50278i
$372$		0			0
$373$	2.69790e6	+	4.67291e6i	0.0519876	+	0.0900452i	0.890848	−	0.454301i	$-0.150111\pi$
$373$	2.69790e6	+	4.67291e6i	0.0519876	+	0.0900452i	−0.838860	+	0.544346i	$0.816778\pi$
$374$	−16293.7	−	9407.18i	−0.000311462	−	0.000179823i
$375$		0			0
$376$	−3.09433e7	+	1.78651e7i	−0.582108	+	0.336080i
$377$			7.06609e7i			1.31873i
$378$		0			0
$379$	3.47845e7			0.638951			0.319475	−	0.947595i	$-0.396493\pi$
$379$	3.47845e7			0.638951			0.319475	+	0.947595i	$0.396493\pi$
$380$	−1.29388e7	−	2.24107e7i	−0.235801	−	0.408418i
$381$		0			0
$382$	1.44283e7	−	2.49905e7i	0.258836	−	0.448316i
$383$	4.90000e7	−	2.82902e7i	0.872168	−	0.503546i	0.00409994	−	0.999992i	$-0.498695\pi$
$383$	4.90000e7	−	2.82902e7i	0.872168	−	0.503546i	0.868068	+	0.496445i	$0.165362\pi$
$384$		0			0
$385$	319605.	+	264800.i	0.00560055	+	0.00464019i
$386$	4.43964e7			0.771944
$387$		0			0
$388$	2.50688e7	+	1.44735e7i	0.429178	+	0.247786i
$389$	−1.30039e7	+	2.25234e7i	−0.220915	+	0.382636i	−0.955086	−	0.296329i	$-0.904238\pi$
$389$	−1.30039e7	+	2.25234e7i	−0.220915	+	0.382636i	0.734171	+	0.678964i	$0.237571\pi$
$390$		0			0
$391$		−	3.10392e6i		−	0.0519254i
$392$	1.06154e7	+	5.61002e7i	0.176229	+	0.931336i
$393$		0			0
$394$	5.38252e6	+	9.32280e6i	0.0880029	+	0.152425i
$395$	2.13266e7	+	1.23129e7i	0.346043	+	0.199788i
$396$		0			0
$397$	−1.18039e7	+	6.81496e6i	−0.188648	+	0.108916i	−0.591350	−	0.806415i	$-0.701405\pi$
$397$	−1.18039e7	+	6.81496e6i	−0.188648	+	0.108916i	0.402701	+	0.915331i	$0.368071\pi$
$398$			7.08217e7i			1.12335i
$399$		0			0
$400$	7.15825e6			0.111848
$401$	−2.00929e7	−	3.48019e7i	−0.311609	−	0.539722i	0.667102	−	0.744966i	$-0.267535\pi$
$401$	−2.00929e7	−	3.48019e7i	−0.311609	−	0.539722i	−0.978711	+	0.205244i	$0.934201\pi$
$402$		0			0
$403$	−7.39703e6	+	1.28120e7i	−0.113017	+	0.195751i
$404$	−7.10461e7	+	4.10185e7i	−1.07745	+	0.622064i
$405$		0			0
$406$	6.55510e7	+	1.11372e7i	0.979493	+	0.166417i
$407$	643815.			0.00954944
$408$		0			0
$409$	6.55577e6	+	3.78497e6i	0.0958194	+	0.0553214i	0.547144	−	0.837038i	$-0.315715\pi$
$409$	6.55577e6	+	3.78497e6i	0.0958194	+	0.0553214i	−0.451325	+	0.892360i	$0.649048\pi$
$410$	1.03418e7	−	1.79125e7i	0.150053	−	0.259899i
$411$		0			0
$412$		−	3.94978e7i		−	0.564783i
$413$	1.05015e8	−	3.89659e7i	1.49073	−	0.553139i
$414$		0			0
$415$	−411860.	−	713363.i	−0.00576243	−	0.00998082i
$416$	4.80907e7	+	2.77652e7i	0.668008	+	0.385674i
$417$		0			0
$418$	721404.	−	416503.i	0.00987756	−	0.00570281i
$419$		−	3.12413e7i		−	0.424705i	−0.977193	−	0.212353i	$-0.931887\pi$
$419$		−	3.12413e7i		−	0.424705i	0.977193	−	0.212353i	$-0.0681125\pi$
$420$		0			0
$421$	5.98978e7			0.802721			0.401361	−	0.915920i	$-0.368537\pi$
$421$	5.98978e7			0.802721			0.401361	+	0.915920i	$0.368537\pi$
$422$	−3.30634e6	−	5.72675e6i	−0.0439957	−	0.0762029i
$423$		0			0
$424$	−5.79052e7	+	1.00295e8i	−0.759661	+	1.31577i
$425$	−2.18574e6	+	1.26194e6i	−0.0284729	+	0.0164388i
$426$		0			0
$427$	2.32536e7	−	1.36865e8i	0.298680	−	1.75796i
$428$	3.69730e7			0.471577
$429$		0			0
$430$	1.15699e6	+	667991.i	0.0145521	+	0.00840166i
$431$	4.81510e7	−	8.33999e7i	0.601414	−	1.04168i	−0.391194	−	0.920308i	$-0.627938\pi$
$431$	4.81510e7	−	8.33999e7i	0.601414	−	1.04168i	0.992607	−	0.121371i	$-0.0387290\pi$
$432$		0			0
$433$			1.11186e8i			1.36958i	0.728741	+	0.684790i	$0.240106\pi$
$433$			1.11186e8i			1.36958i	−0.728741	+	0.684790i	$0.759894\pi$
$434$	1.07197e7	+	8.88148e6i	0.131133	+	0.108647i
$435$		0			0
$436$	−3.70368e7	−	6.41497e7i	−0.446863	−	0.773989i
$437$	1.19014e8	+	6.87129e7i	1.42611	+	0.823368i
$438$		0			0
$439$	−7.90517e7	+	4.56405e7i	−0.934367	+	0.539457i	−0.888190	−	0.459476i	$-0.848037\pi$
$439$	−7.90517e7	+	4.56405e7i	−0.934367	+	0.539457i	−0.0461770	+	0.998933i	$0.514704\pi$
$440$		−	587247.i		−	0.00689386i
$441$		0			0
$442$	−1.59031e6			−0.0184169
$443$	−5.31635e7	−	9.20820e7i	−0.611509	−	1.05916i	−0.990986	−	0.133963i	$-0.957230\pi$
$443$	−5.31635e7	−	9.20820e7i	−0.611509	−	1.05916i	0.379477	−	0.925201i	$-0.376104\pi$
$444$		0			0
$445$	−7.17049e6	+	1.24197e7i	−0.0813709	+	0.140939i
$446$	−1.41800e7	+	8.18681e6i	−0.159835	+	0.0922806i
$447$		0			0
$448$	2.48034e7	−	2.99369e7i	0.275853	−	0.332945i
$449$	−7.74221e7			−0.855315			−0.427657	−	0.903941i	$-0.640661\pi$
$449$	−7.74221e7			−0.855315			−0.427657	+	0.903941i	$0.640661\pi$
$450$		0			0
$451$	−1.24057e6	−	716245.i	−0.0135236	−	0.00780786i
$452$	3.33707e6	−	5.77997e6i	0.0361368	−	0.0625907i
$453$		0			0
$454$			2.67525e7i			0.285889i
$455$	3.45871e7	+	5.87638e6i	0.367180	+	0.0623844i
$456$		0			0
$457$	−9.50468e6	−	1.64626e7i	−0.0995838	−	0.172484i	0.811929	−	0.583757i	$-0.198418\pi$
$457$	−9.50468e6	−	1.64626e7i	−0.0995838	−	0.172484i	−0.911512	+	0.411272i	$0.865084\pi$
$458$	−4.77517e7	−	2.75695e7i	−0.497042	−	0.286967i
$459$		0			0
$460$	3.40402e7	−	1.96531e7i	0.349718	−	0.201910i
$461$		−	1.05709e8i		−	1.07897i	−0.841996	−	0.539483i	$-0.818620\pi$
$461$		−	1.05709e8i		−	1.07897i	0.841996	−	0.539483i	$-0.181380\pi$
$462$		0			0
$463$	−2.82212e7			−0.284336			−0.142168	−	0.989843i	$-0.545407\pi$
$463$	−2.82212e7			−0.284336			−0.142168	+	0.989843i	$0.545407\pi$
$464$	1.31054e7	+	2.26993e7i	0.131189	+	0.227226i
$465$		0			0
$466$	2.73109e7	−	4.73039e7i	0.269885	−	0.467454i
$467$	−1.49701e8	+	8.64297e7i	−1.46985	+	0.848619i	−0.999428	−	0.0338227i	$-0.989232\pi$
$467$	−1.49701e8	+	8.64297e7i	−1.46985	+	0.848619i	−0.470423	+	0.882441i	$0.655899\pi$
$468$		0			0
$469$	2.62464e7	+	7.07351e7i	0.254420	+	0.685672i
$470$	2.06589e7			0.198982
$471$		0			0
$472$	−1.37250e8	−	7.92412e7i	−1.30523	−	0.753572i
$473$	46263.3	−	80130.4i	0.000437173	−	0.000757206i
$474$		0			0
$475$		−	1.11744e8i		−	1.04267i
$476$	539292.	−	3.17415e6i	0.00500038	−	0.0294311i
$477$		0			0
$478$	2.68167e7	+	4.64480e7i	0.245540	+	0.425288i
$479$	2.41808e7	+	1.39608e7i	0.220021	+	0.127029i	0.605960	−	0.795495i	$-0.292789\pi$
$479$	2.41808e7	+	1.39608e7i	0.220021	+	0.127029i	−0.385939	+	0.922524i	$0.626122\pi$
$480$		0			0
$481$	4.71287e7	−	2.72098e7i	0.423497	−	0.244506i
$482$			4.48607e7i			0.400613i
$483$		0			0
$484$	7.73871e7			0.682546
$485$	−2.06263e7	−	3.57258e7i	−0.180799	−	0.313153i
$486$		0			0
$487$	−2.68794e7	+	4.65566e7i	−0.232720	+	0.403082i	−0.958608	−	0.284731i	$-0.908096\pi$
$487$	−2.68794e7	+	4.65566e7i	−0.232720	+	0.403082i	0.725888	+	0.687813i	$0.241429\pi$
$488$	−1.70108e8	+	9.82119e7i	−1.46374	+	0.845093i
$489$		0			0
$490$	1.09029e7	−	3.11597e7i	0.0926728	−	0.264853i
$491$	−9.34867e7			−0.789779			−0.394889	−	0.918729i	$-0.629217\pi$
$491$	−9.34867e7			−0.789779			−0.394889	+	0.918729i	$0.629217\pi$
$492$		0			0
$493$	−8.00337e6	−	4.62075e6i	−0.0667932	−	0.0385631i
$494$	3.52056e7	−	6.09778e7i	0.292032	−	0.505814i
$495$		0			0
$496$			5.48770e6i			0.0449723i
$497$	−7.66414e7	+	9.25036e7i	−0.624301	+	0.753511i
$498$		0			0
$499$	−2.51376e6	−	4.35396e6i	−0.0202312	−	0.0350415i	0.855733	−	0.517418i	$-0.173107\pi$
$499$	−2.51376e6	−	4.35396e6i	−0.0202312	−	0.0350415i	−0.875964	+	0.482377i	$0.839774\pi$
$500$	−6.44927e7	−	3.72349e7i	−0.515941	−	0.297879i
$501$		0			0
$502$	−1.78639e7	+	1.03137e7i	−0.141210	+	0.0815277i
$503$			1.45016e8i			1.13949i	0.821820	+	0.569747i	$0.192959\pi$
$503$			1.45016e8i			1.13949i	−0.821820	+	0.569747i	$0.807041\pi$
$504$		0			0
$505$	1.16912e8			0.907789
$506$	632635.	+	1.09576e6i	0.00488317	+	0.00845790i
$507$		0			0
$508$	−6.16311e7	+	1.06748e8i	−0.470120	+	0.814272i
$509$	−1.14421e7	+	6.60609e6i	−0.0867665	+	0.0500946i	−0.542755	−	0.839891i	$-0.682619\pi$
$509$	−1.14421e7	+	6.60609e6i	−0.0867665	+	0.0500946i	0.455989	+	0.889985i	$0.349286\pi$
$510$		0			0
$511$	−6.48353e7	+	2.40573e7i	−0.485903	+	0.180295i
$512$	3.95237e7			0.294474
$513$		0			0
$514$	−1.57918e7	−	9.11737e6i	−0.116290	−	0.0671399i
$515$	−2.81445e7	+	4.87476e7i	−0.206049	+	0.356888i
$516$		0			0
$517$		−	1.43078e6i		−	0.0103538i
$518$	−1.78139e7	−	4.80092e7i	−0.128165	−	0.345410i
$519$		0			0
$520$	−2.48190e7	−	4.29878e7i	−0.176512	−	0.305728i
$521$	6.70170e7	+	3.86923e7i	0.473884	+	0.273597i	0.717864	−	0.696183i	$-0.245120\pi$
$521$	6.70170e7	+	3.86923e7i	0.473884	+	0.273597i	−0.243980	+	0.969780i	$0.578453\pi$
$522$		0			0
$523$	−1.16424e8	+	6.72177e7i	−0.813840	+	0.469871i	−0.848288	−	0.529536i	$-0.822366\pi$
$523$	−1.16424e8	+	6.72177e7i	−0.813840	+	0.469871i	0.0344475	+	0.999407i	$0.489033\pi$
$524$		−	1.94809e8i		−	1.35399i
$525$		0			0
$526$	−1.33731e8			−0.918913
$527$	−967433.	−	1.67564e6i	−0.00660981	−	0.0114485i
$528$		0			0
$529$	−3.03516e7	+	5.25705e7i	−0.205029	+	0.355120i
$530$	5.79893e7	−	3.34802e7i	0.389512	−	0.224885i
$531$		0			0
$532$	1.09769e8	+	9.09459e7i	0.729027	+	0.604016i
$533$	−1.21084e8			−0.799657
$534$		0			0
$535$	−4.56315e7	−	2.63453e7i	−0.297991	−	0.172045i
$536$	5.33747e7	−	9.24478e7i	0.346610	−	0.600347i
$537$		0			0
$538$		−	9.22511e7i		−	0.592413i
$539$	−2.15804e6	−	755104.i	−0.0137814	−	0.00482215i
$540$		0			0
$541$	7.51469e7	+	1.30158e8i	0.474590	+	0.822015i	0.999577	−	0.0290960i	$-0.00926284\pi$
$541$	7.51469e7	+	1.30158e8i	0.474590	+	0.822015i	−0.524986	+	0.851111i	$0.675930\pi$
$542$	−9.88197e6	−	5.70536e6i	−0.0620649	−	0.0358332i
$543$		0			0
$544$	−6.28962e6	+	3.63132e6i	−0.0390686	+	0.0225563i
$545$			1.05563e8i			0.652115i
$546$		0			0
$547$	−6.65431e7			−0.406576			−0.203288	−	0.979119i	$-0.565163\pi$
$547$	−6.65431e7			−0.406576			−0.203288	+	0.979119i	$0.565163\pi$
$548$	−2.83835e7	−	4.91617e7i	−0.172474	−	0.298735i
$549$		0			0
$550$	514412.	−	890988.i	0.00309188	−	0.00535530i
$551$	3.54349e8	−	2.04583e8i	2.11825	−	1.22297i
$552$		0			0
$553$	−1.33737e8	−	2.27220e7i	−0.790816	−	0.134360i
$554$	1.37774e8			0.810284
$555$		0			0
$556$	4.52420e6	+	2.61205e6i	0.0263219	+	0.0151969i
$557$	−1.26843e8	+	2.19698e8i	−0.734007	+	1.27134i	0.221151	+	0.975240i	$0.429019\pi$
$557$	−1.26843e8	+	2.19698e8i	−0.734007	+	1.27134i	−0.955158	+	0.296097i	$0.904315\pi$
$558$		0			0
$559$		−	7.82096e6i		−	0.0447739i
$560$	1.22007e7	−	4.52710e6i	0.0694740	−	0.0257784i
$561$		0			0
$562$	−5.11678e7	−	8.86252e7i	−0.288262	−	0.499285i
$563$	−1.43519e8	−	8.28606e7i	−0.804236	−	0.464326i	0.0407139	−	0.999171i	$-0.487037\pi$
$563$	−1.43519e8	−	8.28606e7i	−0.804236	−	0.464326i	−0.844950	+	0.534845i	$0.820370\pi$
$564$		0			0
$565$	−8.23711e6	+	4.75570e6i	−0.0456699	+	0.0263675i
$566$		−	1.84685e8i		−	1.01855i
$567$		0			0
$568$	1.69968e8			0.927516
$569$	8.19891e7	+	1.42009e8i	0.445061	+	0.770868i	0.998056	−	0.0623160i	$-0.0198487\pi$
$569$	8.19891e7	+	1.42009e8i	0.445061	+	0.770868i	−0.552996	+	0.833184i	$0.686515\pi$
$570$		0			0
$571$	1.70285e8	−	2.94942e8i	0.914677	−	1.58427i	0.107305	−	0.994226i	$-0.465778\pi$
$571$	1.70285e8	−	2.94942e8i	0.914677	−	1.58427i	0.807373	−	0.590042i	$-0.200889\pi$
$572$	−1.20790e6	+	697382.i	−0.00645421	+	0.00372634i
$573$		0			0
$574$	−1.90846e7	+	1.12327e8i	−0.100913	+	0.593950i
$575$	1.69731e8			0.892808
$576$		0			0
$577$	2.37115e8	+	1.36899e8i	1.23433	+	0.712642i	0.967930	−	0.251220i	$-0.0808317\pi$
$577$	2.37115e8	+	1.36899e8i	1.23433	+	0.712642i	0.266402	+	0.963862i	$0.414165\pi$
$578$	−5.42829e7	+	9.40207e7i	−0.281112	+	0.486900i
$579$		0			0
$580$		−	1.17029e8i		−	0.599804i
$581$	3.49408e6	+	2.89493e6i	0.0178158	+	0.0147608i
$582$		0			0
$583$	−2.31875e6	−	4.01619e6i	−0.0117017	−	0.0202679i
$584$	8.47371e7	+	4.89230e7i	0.425437	+	0.245626i
$585$		0			0
$586$	1.14868e8	−	6.63193e7i	0.570831	−	0.329570i
$587$			2.96429e8i			1.46557i	0.680460	+	0.732785i	$0.261780\pi$
$587$			2.96429e8i			1.46557i	−0.680460	+	0.732785i	$0.738220\pi$
$588$		0			0
$589$	8.56661e7			0.419241
$590$	4.58164e7	+	7.93563e7i	0.223082	+	0.386390i
$591$		0			0
$592$	1.00932e7	−	1.74819e7i	0.0486477	−	0.0842603i
$593$	1.12529e8	−	6.49684e7i	0.539633	−	0.311557i	−0.205297	−	0.978700i	$-0.565816\pi$
$593$	1.12529e8	−	6.49684e7i	0.539633	−	0.311557i	0.744930	+	0.667142i	$0.232483\pi$
$594$		0			0
$595$	−2.92735e6	+	3.53321e6i	−0.0138971	+	0.0167733i
$596$	2.73439e8			1.29158
$597$		0			0
$598$	9.26206e7	+	5.34745e7i	0.433116	+	0.250060i
$599$	−3.82426e7	+	6.62382e7i	−0.177937	+	0.308197i	−0.941174	−	0.337923i	$-0.890276\pi$
$599$	−3.82426e7	+	6.62382e7i	−0.177937	+	0.308197i	0.763237	+	0.646119i	$0.223609\pi$
$600$		0			0
$601$			1.12466e8i			0.518080i	0.965867	+	0.259040i	$0.0834061\pi$
$601$			1.12466e8i			0.518080i	−0.965867	+	0.259040i	$0.916594\pi$
$602$	−7.25539e6	−	1.23270e6i	−0.0332561	−	0.00565025i
$603$		0			0
$604$	−3.29426e7	−	5.70583e7i	−0.149502	−	0.258945i
$605$	−9.55100e7	−	5.51427e7i	−0.431303	−	0.249013i
$606$		0			0
$607$	−4.03159e6	+	2.32764e6i	−0.0180264	+	0.0104076i	−0.508986	−	0.860775i	$-0.669980\pi$
$607$	−4.03159e6	+	2.32764e6i	−0.0180264	+	0.0104076i	0.490960	+	0.871182i	$0.336646\pi$
$608$		−	3.21553e8i		−	1.43068i
$609$		0			0
$610$	1.13570e8			0.500351
$611$	−6.04695e7	−	1.04736e8i	−0.265102	−	0.459170i
$612$		0			0
$613$	1.02768e8	−	1.78000e8i	0.446147	−	0.772749i	−0.551984	−	0.833854i	$-0.686129\pi$
$613$	1.02768e8	−	1.78000e8i	0.446147	−	0.772749i	0.998131	+	0.0611054i	$0.0194626\pi$
$614$	−1.82369e7	+	1.05291e7i	−0.0787856	+	0.0454869i
$615$		0			0
$616$	1.12534e6	+	3.03285e6i	0.00481441	+	0.0129750i
$617$	−1.85696e8			−0.790583			−0.395292	−	0.918556i	$-0.629356\pi$
$617$	−1.85696e8			−0.790583			−0.395292	+	0.918556i	$0.629356\pi$
$618$		0			0
$619$	7.59648e7	+	4.38583e7i	0.320288	+	0.184918i	0.651521	−	0.758631i	$-0.274131\pi$
$619$	7.59648e7	+	4.38583e7i	0.320288	+	0.184918i	−0.331233	+	0.943549i	$0.607465\pi$
$620$	1.22510e7	−	2.12194e7i	0.0514040	−	0.0890344i
$621$		0			0
$622$			1.44346e8i			0.599837i
$623$	1.32323e7	−	7.78824e7i	0.0547232	−	0.322088i
$624$		0			0
$625$	−3.87164e7	−	6.70588e7i	−0.158582	−	0.274673i
$626$	−8.50830e7	−	4.91227e7i	−0.346832	−	0.200244i
$627$		0			0
$628$	9.38340e7	−	5.41751e7i	0.378862	−	0.218736i
$629$			7.11735e6i			0.0286000i
$630$		0			0
$631$	−4.15732e8			−1.65472			−0.827362	−	0.561670i	$-0.810159\pi$
$631$	−4.15732e8			−1.65472			−0.827362	+	0.561670i	$0.810159\pi$
$632$	9.59668e7	+	1.66219e8i	0.380163	+	0.658462i
$633$		0			0
$634$	2.37146e7	−	4.10748e7i	0.0930566	−	0.161179i
$635$	1.52128e8	−	8.78313e7i	0.594140	−	0.343027i
$636$		0			0
$637$	−1.89886e8	+	3.59306e7i	−0.734642	+	0.139010i
$638$	3.76718e6			0.0145062
$639$		0			0
$640$	−8.91246e7	−	5.14561e7i	−0.339983	−	0.196289i
$641$	8.98600e7	−	1.55642e8i	0.341187	−	0.590953i	−0.643466	−	0.765474i	$-0.722504\pi$
$641$	8.98600e7	−	1.55642e8i	0.341187	−	0.590953i	0.984653	+	0.174521i	$0.0558378\pi$
$642$		0			0
$643$		−	8.10561e7i		−	0.304897i	−0.988311	−	0.152448i	$-0.951284\pi$
$643$		−	8.10561e7i		−	0.304897i	0.988311	−	0.152448i	$-0.0487158\pi$
$644$	−1.38140e8	+	1.66730e8i	−0.517203	+	0.624247i
$645$		0			0
$646$	4.60442e6	+	7.97508e6i	0.0170796	+	0.0295827i
$647$	−9.06246e7	−	5.23221e7i	−0.334606	−	0.193185i	0.323278	−	0.946304i	$-0.395215\pi$
$647$	−9.06246e7	−	5.23221e7i	−0.334606	−	0.193185i	−0.657884	+	0.753119i	$0.728548\pi$
$648$		0			0
$649$	5.49601e6	−	3.17312e6i	0.0201054	−	0.0116079i
$650$		−	8.69630e7i		−	0.316661i
$651$		0			0
$652$	−2.87941e8			−1.03887
$653$	2.36179e8	+	4.09074e8i	0.848206	+	1.46914i	0.882808	+	0.469734i	$0.155650\pi$
$653$	2.36179e8	+	4.09074e8i	0.848206	+	1.46914i	−0.0346020	+	0.999401i	$0.511016\pi$
$654$		0			0
$655$	−1.38812e8	+	2.40430e8i	−0.493975	+	0.855589i
$656$	−3.88972e7	+	2.24573e7i	−0.137787	+	0.0795511i
$657$		0			0
$658$	−1.06693e8	+	3.95886e7i	−0.374506	+	0.138961i
$659$	−1.73758e8			−0.607141			−0.303570	−	0.952809i	$-0.598179\pi$
$659$	−1.73758e8			−0.607141			−0.303570	+	0.952809i	$0.598179\pi$
$660$		0			0
$661$	−1.91974e7	−	1.10836e7i	−0.0664720	−	0.0383776i	0.466396	−	0.884576i	$-0.345552\pi$
$661$	−1.91974e7	−	1.10836e7i	−0.0664720	−	0.0383776i	−0.532868	+	0.846199i	$0.678886\pi$
$662$	−9.16930e7	+	1.58817e8i	−0.316055	+	0.547423i
$663$		0			0
$664$		−	6.42008e6i		−	0.0219299i
$665$	−7.06707e7	−	1.90460e8i	−0.240311	−	0.647649i
$666$		0			0
$667$	3.10746e8	+	5.38229e8i	1.04720	+	1.81380i
$668$	−2.06223e8	−	1.19063e8i	−0.691843	−	0.399436i
$669$		0			0
$670$	−5.34523e7	+	3.08607e7i	−0.177722	+	0.102608i
$671$		−	7.86557e6i		−	0.0260353i
$672$		0			0
$673$	−4.00045e8			−1.31239			−0.656195	−	0.754591i	$-0.727835\pi$
$673$	−4.00045e8			−1.31239			−0.656195	+	0.754591i	$0.727835\pi$
$674$	9.13128e7	+	1.58158e8i	0.298230	+	0.516550i
$675$		0			0
$676$	4.64998e7	−	8.05401e7i	0.150526	−	0.260719i
$677$	2.51224e8	−	1.45044e8i	0.809646	−	0.467449i	−0.0371872	−	0.999308i	$-0.511840\pi$
$677$	2.51224e8	−	1.45044e8i	0.809646	−	0.467449i	0.846833	+	0.531859i	$0.178506\pi$
$678$		0			0
$679$	1.74987e8	+	1.44980e8i	0.558979	+	0.463127i
$680$	6.49199e6			0.0206467
$681$		0			0
$682$	683054.	+	394362.i	0.00215329	+	0.00124320i
$683$	5.77014e7	−	9.99417e7i	0.181102	−	0.313678i	−0.761154	−	0.648571i	$-0.775367\pi$
$683$	5.77014e7	−	9.99417e7i	0.181102	−	0.313678i	0.942256	+	0.334893i	$0.108700\pi$
$684$		0			0
$685$			8.08996e7i			0.251695i
$686$	3.40341e6	+	1.81818e8i	0.0105425	+	0.563202i
$687$		0			0
$688$	−1.45055e6	−	2.51243e6i	−0.00445418	−	0.00771487i
$689$	−3.39475e8	−	1.95996e8i	−1.03789	−	0.599224i
$690$		0			0
$691$	3.59314e8	−	2.07450e8i	1.08903	−	0.628752i	0.155712	−	0.987802i	$-0.450233\pi$
$691$	3.59314e8	−	2.07450e8i	1.08903	−	0.628752i	0.933318	+	0.359051i	$0.116899\pi$
$692$			1.20654e8i			0.364101i
$693$		0			0
$694$	7.45157e7			0.222930
$695$	−3.72246e6	−	6.44750e6i	−0.0110886	−	0.0192060i
$696$		0			0
$697$	7.91806e6	−	1.37145e7i	0.0233841	−	0.0405024i
$698$	−1.97947e7	+	1.14285e7i	−0.0582079	+	0.0336063i
$699$		0			0
$700$	1.73572e8	+	2.94900e7i	0.506040	+	0.0859768i
$701$	−5.13427e8			−1.49047			−0.745237	−	0.666800i	$-0.767664\pi$
$701$	−5.13427e8			−1.49047			−0.745237	+	0.666800i	$0.767664\pi$
$702$		0			0
$703$	−2.72902e8	−	1.57560e8i	−0.785491	−	0.453503i
$704$	1.10134e6	−	1.90757e6i	0.00315648	−	0.00546718i
$705$		0			0
$706$		−	2.05193e8i		−	0.583107i
$707$	−6.03794e8	+	2.24039e8i	−1.70856	+	0.633965i
$708$		0			0
$709$	−1.64200e8	−	2.84402e8i	−0.460716	−	0.797984i	0.538281	−	0.842766i	$-0.319074\pi$
$709$	−1.64200e8	−	2.84402e8i	−0.460716	−	0.797984i	−0.998997	+	0.0447818i	$0.985741\pi$
$710$	−8.51073e7	−	4.91367e7i	−0.237789	−	0.137288i
$711$		0			0
$712$	−9.67989e7	+	5.58869e7i	−0.268182	+	0.154835i
$713$			1.30120e8i			0.358985i
$714$		0			0
$715$	1.98770e6			0.00543791
$716$	3.25011e7	+	5.62935e7i	0.0885439	+	0.153363i
$717$		0			0
$718$	−9.01665e7	+	1.56173e8i	−0.243597	+	0.421923i
$719$	−9.79686e7	+	5.65622e7i	−0.263573	+	0.152174i	−0.625963	−	0.779853i	$-0.715294\pi$
$719$	−9.79686e7	+	5.65622e7i	−0.263573	+	0.152174i	0.362391	+	0.932026i	$0.381961\pi$
$720$		0			0
$721$	5.19373e7	−	3.05691e8i	0.138571	−	0.815600i
$722$	−1.95713e8			−0.520006
$723$		0			0
$724$	−2.27667e8	−	1.31444e8i	−0.599907	−	0.346357i
$725$	2.52676e8	−	4.37648e8i	0.663055	−	1.14845i
$726$		0			0
$727$		−	9.97740e7i		−	0.259666i	−0.991536	−	0.129833i	$-0.958556\pi$
$727$		−	9.97740e7i		−	0.259666i	0.991536	−	0.129833i	$-0.0414440\pi$
$728$	2.10556e8	+	1.74450e8i	0.545724	+	0.452145i
$729$		0			0
$730$	−2.82867e7	−	4.89940e7i	−0.0727133	−	0.125943i
$731$	885838.	+	511439.i	0.00226779	+	0.00130931i
$732$		0			0
$733$	3.13962e8	−	1.81266e8i	0.797197	−	0.460262i	−0.0452931	−	0.998974i	$-0.514422\pi$
$733$	3.13962e8	−	1.81266e8i	0.797197	−	0.460262i	0.842490	+	0.538712i	$0.181089\pi$
$734$		−	7.99975e7i		−	0.202296i
$735$		0			0
$736$	4.88414e8			1.22505
$737$	2.13733e6	+	3.70197e6i	0.00533912	+	0.00924762i
$738$		0			0
$739$	1.02140e8	−	1.76912e8i	0.253083	−	0.438352i	−0.711290	−	0.702899i	$-0.751889\pi$
$739$	1.02140e8	−	1.76912e8i	0.253083	−	0.438352i	0.964373	+	0.264546i	$0.0852221\pi$
$740$	−7.80549e7	+	4.50650e7i	−0.192622	+	0.111210i
$741$		0			0
$742$	−2.35329e8	+	2.84034e8i	−0.576054	+	0.695278i
$743$	−2.63900e8			−0.643389			−0.321695	−	0.946844i	$-0.604252\pi$
$743$	−2.63900e8			−0.643389			−0.321695	+	0.946844i	$0.604252\pi$
$744$		0			0
$745$	−3.37474e8	−	1.94841e8i	−0.816153	−	0.471206i
$746$	1.21579e7	−	2.10580e7i	0.0292847	−	0.0507226i
$747$		0			0
$748$		−	182416.i		−	0.000435872i
$749$	2.86150e8	+	4.86172e7i	0.681002	+	0.115703i
$750$		0			0
$751$	3.68938e8	+	6.39019e8i	0.871031	+	1.50867i	0.860932	+	0.508721i	$0.169881\pi$
$751$	3.68938e8	+	6.39019e8i	0.871031	+	1.50867i	0.0100992	+	0.999949i	$0.496785\pi$
$752$	−3.88508e7	−	2.24305e7i	−0.0913579	−	0.0527455i
$753$		0			0
$754$	2.75766e8	−	1.59213e8i	0.643318	−	0.371420i
$755$			9.38940e7i			0.218171i
$756$		0			0
$757$	−1.43307e8			−0.330355			−0.165177	−	0.986264i	$-0.552820\pi$
$757$	−1.43307e8			−0.330355			−0.165177	+	0.986264i	$0.552820\pi$
$758$	−7.83765e7	−	1.35752e8i	−0.179961	−	0.311701i
$759$		0			0
$760$	−1.43716e8	+	2.48924e8i	−0.327390	+	0.567056i
$761$	6.67428e8	−	3.85340e8i	1.51444	−	0.874360i	0.514578	−	0.857443i	$-0.327948\pi$
$761$	6.67428e8	−	3.85340e8i	1.51444	−	0.874360i	0.999857	−	0.0169164i	$-0.00538490\pi$
$762$		0			0
$763$	−2.02291e8	−	5.45184e8i	−0.455411	−	1.22735i
$764$	2.79781e8			0.627391
$765$		0			0
$766$	−2.20814e8	−	1.27487e8i	−0.491293	−	0.283648i
$767$	2.68213e8	−	4.64559e8i	0.594421	−	1.02957i
$768$		0			0
$769$			6.97335e8i			1.53343i	0.641990	+	0.766713i	$0.278109\pi$
$769$			6.97335e8i			1.53343i	−0.641990	+	0.766713i	$0.721891\pi$
$770$	313290.	−	1.84396e6i	0.000686238	−	0.00403904i
$771$		0			0
$772$	2.15225e8	+	3.72780e8i	0.467779	+	0.810216i
$773$	7.04415e8	+	4.06694e8i	1.52507	+	0.880500i	0.999558	+	0.0297144i	$0.00945977\pi$
$773$	7.04415e8	+	4.06694e8i	1.52507	+	0.880500i	0.525513	+	0.850786i	$0.323874\pi$
$774$		0			0
$775$	9.16290e7	−	5.29021e7i	0.196847	−	0.113649i
$776$		−	3.21523e8i		−	0.688061i
$777$		0			0
$778$	1.17202e8			0.248883
$779$	3.50572e8	+	6.07208e8i	0.741591	+	1.28447i
$780$		0			0
$781$	−3.40308e6	+	5.89431e6i	−0.00714364	+	0.0123731i
$782$	−1.21135e7	+	6.99375e6i	−0.0253309	+	0.0146248i
$783$		0			0
$784$	−5.43356e7	+	4.67606e7i	−0.112755	+	0.0970358i
$785$	−1.54411e8			−0.319206
$786$		0			0
$787$	3.22928e8	+	1.86443e8i	0.662494	+	0.382491i	0.793227	−	0.608927i	$-0.208400\pi$
$787$	3.22928e8	+	1.86443e8i	0.662494	+	0.382491i	−0.130733	+	0.991418i	$0.541733\pi$
$788$	−5.21867e7	+	9.03900e7i	−0.106655	+	0.184732i
$789$		0			0
$790$		−	1.10974e8i		−	0.225081i
$791$	3.34273e7	−	4.03457e7i	0.0675418	−	0.0815207i
$792$		0			0
$793$	−3.32425e8	−	5.75777e8i	−0.666614	−	1.15461i
$794$	5.31930e7	+	3.07110e7i	0.106266	+	0.0613525i
$795$		0			0
$796$	−5.94663e8	+	3.43329e8i	−1.17905	+	0.680724i
$797$		−	4.15047e8i		−	0.819827i	−0.912124	−	0.409913i	$-0.865559\pi$
$797$		−	4.15047e8i		−	0.819827i	0.912124	−	0.409913i	$-0.134441\pi$
$798$		0			0
$799$	1.58172e7			0.0310091
$800$	−1.98571e8	−	3.43935e8i	−0.387834	−	0.671748i
$801$		0			0
$802$	−9.05468e7	+	1.56832e8i	−0.175530	+	0.304026i
$803$	−3.39320e6	+	1.95906e6i	−0.00655334	+	0.00378357i
$804$		0			0
$805$	2.89295e8	−	1.07343e8i	0.554566	−	0.205773i
$806$	6.66681e7			0.127325
$807$		0			0
$808$	7.89133e8	+	4.55606e8i	1.49595	+	0.863686i
$809$	−1.17384e8	+	2.03314e8i	−0.221698	+	0.383992i	−0.955324	−	0.295562i	$-0.904493\pi$
$809$	−1.17384e8	+	2.03314e8i	−0.221698	+	0.383992i	0.733626	+	0.679554i	$0.237827\pi$
$810$		0			0
$811$			8.08164e7i			0.151508i	0.997127	+	0.0757542i	$0.0241364\pi$
$811$			8.08164e7i			0.151508i	−0.997127	+	0.0757542i	$0.975864\pi$
$812$	2.24263e8	+	6.04398e8i	0.418880	+	1.12890i
$813$		0			0
$814$	−1.45065e6	−	2.51259e6i	−0.00268961	−	0.00465853i
$815$	3.55372e8	+	2.05174e8i	0.656463	+	0.379009i
$816$		0			0
$817$	−3.92204e7	+	2.26439e7i	−0.0719194	+	0.0415227i
$818$		−	3.41133e7i		−	0.0623252i
$819$		0			0
$820$	2.00539e8			0.363713
$821$	−3.22564e7	−	5.58697e7i	−0.0582890	−	0.100959i	0.835408	−	0.549630i	$-0.185231\pi$
$821$	−3.22564e7	−	5.58697e7i	−0.0582890	−	0.100959i	−0.893697	+	0.448670i	$0.851898\pi$
$822$		0			0
$823$	7.83609e7	−	1.35725e8i	0.140572	−	0.243478i	−0.787140	−	0.616774i	$-0.788439\pi$
$823$	7.83609e7	−	1.35725e8i	0.140572	−	0.243478i	0.927712	+	0.373296i	$0.121772\pi$
$824$	−3.79939e8	+	2.19358e8i	−0.679098	+	0.392077i
$825$		0			0
$826$	−3.88690e8	−	3.22039e8i	−0.689705	−	0.571437i
$827$	6.46564e8			1.14313			0.571565	−	0.820557i	$-0.306337\pi$
$827$	6.46564e8			1.14313			0.571565	+	0.820557i	$0.306337\pi$
$828$		0			0
$829$	−8.11604e8	−	4.68580e8i	−1.42456	−	0.822470i	−0.427875	−	0.903838i	$-0.640738\pi$
$829$	−8.11604e8	−	4.68580e8i	−1.42456	−	0.822470i	−0.996684	+	0.0813680i	$0.974071\pi$
$830$	−1.85601e6	+	3.21470e6i	−0.00324598	+	0.00562221i
$831$		0			0
$832$		−	1.86185e8i		−	0.323277i
$833$	8.34764e6	−	2.38570e7i	0.0144420	−	0.0412744i
$834$		0			0
$835$	1.69678e8	+	2.93891e8i	0.291452	+	0.504809i
$836$	6.99444e6	+	4.03824e6i	0.0119711	+	0.00691152i
$837$		0			0
$838$	−1.21924e8	+	7.03931e7i	−0.207185	+	0.119618i
$839$			7.25284e8i			1.22807i	0.789280	+	0.614034i	$0.210454\pi$
$839$			7.25284e8i			1.22807i	−0.789280	+	0.614034i	$0.789546\pi$
$840$		0			0
$841$	1.25559e9			2.11086
$842$	−1.34962e8	−	2.33761e8i	−0.226087	−	0.391594i
$843$		0			0
$844$	3.20570e7	−	5.55243e7i	0.0533206	−	0.0923540i
$845$	−1.14779e8	+	6.62676e7i	−0.190236	+	0.109833i
$846$		0			0
$847$	5.98933e8	+	1.01759e8i	0.985662	+	0.167465i
$848$	−1.45405e8			−0.238447
$849$		0			0
$850$	9.84983e6	+	5.68680e6i	0.0160388	+	0.00926001i
$851$	2.39322e8	−	4.14517e8i	0.388323	−	0.672595i
$852$		0			0
$853$			1.38063e8i			0.222449i	0.993795	+	0.111224i	$0.0354772\pi$
$853$			1.38063e8i			0.222449i	−0.993795	+	0.111224i	$0.964523\pi$
$854$	−5.86535e8	+	2.17635e8i	−0.941716	+	0.349425i
$855$		0			0
$856$	−2.05336e8	−	3.55652e8i	−0.327373	−	0.567027i
$857$	−6.12238e8	−	3.53476e8i	−0.972698	−	0.561588i	−0.0726405	−	0.997358i	$-0.523143\pi$
$857$	−6.12238e8	−	3.53476e8i	−0.972698	−	0.561588i	−0.900058	+	0.435771i	$0.856476\pi$
$858$		0			0
$859$	2.85515e8	−	1.64842e8i	0.450453	−	0.260069i	−0.257569	−	0.966260i	$-0.582921\pi$
$859$	2.85515e8	−	1.64842e8i	0.450453	−	0.260069i	0.708021	+	0.706191i	$0.249588\pi$
$860$			1.29531e7i			0.0203648i
$861$		0			0
$862$	−4.33976e8			−0.677554
$863$	−4.84152e8	−	8.38576e8i	−0.753268	−	1.30470i	−0.946231	−	0.323493i	$-0.895143\pi$
$863$	−4.84152e8	−	8.38576e8i	−0.753268	−	1.30470i	0.192962	−	0.981206i	$-0.438190\pi$
$864$		0			0
$865$	8.59726e7	−	1.48909e8i	0.132835	−	0.230077i
$866$	4.33922e8	−	2.50525e8i	0.668126	−	0.385743i
$867$		0			0
$868$	−2.26078e7	+	1.33065e8i	−0.0345700	+	0.203471i
$869$	−7.68577e6			−0.0117119
$870$		0			0
$871$	3.12915e8	+	1.80661e8i	0.473556	+	0.273408i
$872$	−4.11381e8	+	7.12532e8i	−0.620433	+	1.07462i
$873$		0			0
$874$		−	6.19296e8i		−	0.927608i
$875$	−4.50176e8	−	3.72981e8i	−0.671983	−	0.556753i
$876$		0			0
$877$	−1.33382e8	−	2.31025e8i	−0.197742	−	0.342500i	0.750054	−	0.661377i	$-0.230028\pi$
$877$	−1.33382e8	−	2.31025e8i	−0.197742	−	0.342500i	−0.947796	+	0.318877i	$0.896694\pi$
$878$	3.56239e8	+	2.05675e8i	0.526330	+	0.303877i
$879$		0			0
$880$	638534.	−	368657.i	0.000936992	−	0.000540972i
$881$		−	6.08909e8i		−	0.890481i	−0.895411	−	0.445241i	$-0.853118\pi$
$881$		−	6.08909e8i		−	0.890481i	0.895411	−	0.445241i	$-0.146882\pi$
$882$		0			0
$883$	−6.56488e8			−0.953553			−0.476777	−	0.879025i	$-0.658195\pi$
$883$	−6.56488e8			−0.953553			−0.476777	+	0.879025i	$0.658195\pi$
$884$	−7.70952e6	−	1.33533e7i	−0.0111602	−	0.0193300i
$885$		0			0
$886$	−2.39577e8	+	4.14959e8i	−0.344464	+	0.596628i
$887$	6.04195e7	−	3.48832e7i	0.0865778	−	0.0499857i	−0.456086	−	0.889936i	$-0.650749\pi$
$887$	6.04195e7	−	3.48832e7i	0.0865778	−	0.0499857i	0.542664	+	0.839950i	$0.317416\pi$
$888$		0			0
$889$	−6.17358e8	+	7.45130e8i	−0.878682	+	1.06054i
$890$	6.46263e7			0.0916726
$891$		0			0
$892$	−1.37483e8	−	7.93760e7i	−0.193711	−	0.111839i
$893$	−3.50153e8	+	6.06482e8i	−0.491703	+	0.851655i
$894$		0			0
$895$		−	9.26355e7i		−	0.129214i
$896$	5.58891e8	+	9.49562e7i	0.776968	+	0.132008i
$897$		0			0
$898$	1.74448e8	+	3.02152e8i	0.240900	+	0.417251i
$899$	3.35512e8	+	1.93708e8i	0.461773	+	0.266605i
$900$		0			0
$901$	4.43988e7	−	2.56337e7i	0.0607011	−	0.0350458i
$902$			6.45539e6i			0.00879635i
$903$		0			0
$904$	−7.41319e7			−0.100346
$905$	1.87322e8	+	3.24451e8i	0.252722	+	0.437728i
$906$		0			0
$907$	−4.31361e8	+	7.47140e8i	−0.578122	+	1.00134i	0.417573	+	0.908643i	$0.362881\pi$
$907$	−4.31361e8	+	7.47140e8i	−0.578122	+	1.00134i	−0.995695	+	0.0926927i	$0.970453\pi$
$908$	−2.24631e8	+	1.29691e8i	−0.300063	+	0.173241i
$909$		0			0
$910$	−5.49982e7	−	1.48222e8i	−0.0729834	−	0.196693i
$911$	1.41296e8			0.186885			0.0934425	−	0.995625i	$-0.470213\pi$
$911$	1.41296e8			0.186885			0.0934425	+	0.995625i	$0.470213\pi$
$912$		0			0
$913$	222642.	+	128542.i	0.000292547	+	0.000168902i
$914$	−4.28319e7	+	7.41871e7i	−0.0560956	+	0.0971605i
$915$		0			0
$916$		−	5.34605e8i		−	0.695579i
$917$	2.56162e8	−	1.50771e9i	0.332206	−	1.95529i
$918$		0			0
$919$	−5.59845e8	−	9.69681e8i	−0.721309	−	1.24934i	−0.960475	−	0.278366i	$-0.910207\pi$
$919$	−5.59845e8	−	9.69681e8i	−0.721309	−	1.24934i	0.239166	−	0.970979i	$-0.423126\pi$
$920$	−3.78096e8	−	2.18294e8i	−0.485555	−	0.280335i
$921$		0			0
$922$	−4.12546e8	+	2.38183e8i	−0.526356	+	0.303892i
$923$			5.75302e8i			0.731629i
$924$		0			0
$925$	−3.89197e8			−0.491750
$926$	6.35881e7	+	1.10138e8i	0.0800834	+	0.138709i
$927$		0			0
$928$	7.27094e8	−	1.25936e9i	0.909801	−	1.57582i
$929$	−1.14228e9	+	6.59494e8i	−1.42470	+	0.822553i	−0.996696	−	0.0812225i	$-0.974118\pi$
$929$	−1.14228e9	+	6.59494e8i	−1.42470	+	0.822553i	−0.428007	+	0.903775i	$0.640784\pi$
$930$		0			0
$931$	7.29960e8	+	8.48210e8i	0.904586	+	1.05112i
$932$	5.29591e8			0.654173
$933$		0			0
$934$	6.74612e8	+	3.89488e8i	0.827968	+	0.478028i
$935$	−129982.	+	225136.i	−0.000159019	+	0.000275429i
$936$		0			0
$937$		−	1.04041e6i		−	0.00126469i	−1.00000		0.000632345i	$-0.999799\pi$
$937$		−	1.04041e6i		−	0.00126469i	1.00000		0.000632345i	$-0.000201282\pi$
$938$	2.16917e8	−	2.61811e8i	0.262836	−	0.317234i
$939$		0			0
$940$	1.00150e8	+	1.73465e8i	0.120578	+	0.208847i
$941$	−5.93842e8	−	3.42855e8i	−0.712692	−	0.411473i	0.0993650	−	0.995051i	$-0.468319\pi$
$941$	−5.93842e8	−	3.42855e8i	−0.712692	−	0.411473i	−0.812057	+	0.583578i	$0.801652\pi$
$942$		0			0
$943$	−9.22302e8	+	5.32491e8i	−1.09986	+	0.635005i
$944$		−	1.98982e8i		−	0.236536i
$945$		0			0
$946$	−416963.			−0.000492520
$947$	2.67038e8	+	4.62523e8i	0.314429	+	0.544608i	0.979316	−	0.202337i	$-0.0648535\pi$
$947$	2.67038e8	+	4.62523e8i	0.314429	+	0.544608i	−0.664887	+	0.746944i	$0.731520\pi$
$948$		0			0
$949$	−1.65593e8	+	2.86816e8i	−0.193751	+	0.335586i
$950$	−4.36101e8	+	2.51783e8i	−0.508647	+	0.293667i
$951$		0			0
$952$	−3.35280e7	+	1.24406e7i	−0.0388594	+	0.0144189i
$953$	−8.66817e8			−1.00150			−0.500748	−	0.865593i	$-0.666942\pi$
$953$	−8.66817e8			−1.00150			−0.500748	+	0.865593i	$0.666942\pi$
$954$		0			0
$955$	−3.45302e8	−	1.99360e8i	−0.396450	−	0.228891i
$956$	−2.60004e8	+	4.50340e8i	−0.297582	+	0.515427i
$957$		0			0
$958$		−	1.25826e8i		−	0.143112i
$959$	−1.55028e8	−	4.17807e8i	−0.175774	−	0.473718i
$960$		0			0
$961$	−4.03196e8	−	6.98356e8i	−0.454303	−	0.786876i
$962$	−2.12381e8	−	1.22618e8i	−0.238556	−	0.137730i
$963$		0			0
$964$	−3.76679e8	+	2.17475e8i	−0.420475	+	0.242761i
$965$		−	6.13440e8i		−	0.682637i
$966$		0			0
$967$	1.71422e8			0.189577			0.0947886	−	0.995497i	$-0.469782\pi$
$967$	1.71422e8			0.189577			0.0947886	+	0.995497i	$0.469782\pi$
$968$	−4.29782e8	−	7.44405e8i	−0.473830	−	0.820698i
$969$		0			0
$970$	−9.29506e7	+	1.60995e8i	−0.101844	+	0.176400i
$971$	−9.77273e8	+	5.64229e8i	−1.06748	+	0.616308i	−0.927491	−	0.373846i	$-0.878039\pi$
$971$	−9.77273e8	+	5.64229e8i	−1.06748	+	0.616308i	−0.139985	+	0.990154i	$0.544706\pi$
$972$		0			0
$973$	3.15801e7	+	2.61648e7i	0.0342827	+	0.0284040i
$974$	2.42259e8			0.262183
$975$		0			0
$976$	−2.13578e8	−	1.23309e8i	−0.229725	−	0.132632i
$977$	−2.09709e8	+	3.63227e8i	−0.224871	+	0.389488i	−0.956281	−	0.292450i	$-0.905529\pi$
$977$	−2.09709e8	+	3.63227e8i	−0.224871	+	0.389488i	0.731410	+	0.681938i	$0.238863\pi$
$978$		0			0
$979$		−	4.47585e6i		−	0.00477010i
$980$	3.14491e8	−	5.95086e7i	0.334141	−	0.0632268i
$981$		0			0
$982$	2.10645e8	+	3.64847e8i	0.222442	+	0.385280i
$983$	5.99335e8	+	3.46026e8i	0.630971	+	0.364291i	0.781128	−	0.624371i	$-0.214645\pi$
$983$	5.99335e8	+	3.46026e8i	0.630971	+	0.364291i	−0.150157	+	0.988662i	$0.547978\pi$
$984$		0			0
$985$	1.28816e8	−	7.43720e7i	0.134791	−	0.0778217i
$986$			4.16459e7i			0.0434452i
$987$		0			0
$988$	6.82678e8			0.707856
$989$	−3.43944e7	−	5.95728e7i	−0.0355548	−	0.0615828i
$990$		0			0
$991$	4.13436e8	−	7.16091e8i	0.424802	−	0.735779i	−0.571600	−	0.820533i	$-0.693677\pi$
$991$	4.13436e8	−	7.16091e8i	0.424802	−	0.735779i	0.996402	+	0.0847535i	$0.0270103\pi$
$992$	2.63669e8	−	1.52230e8i	0.270100	−	0.155942i
$993$		0			0
$994$	5.33699e8	+	9.06761e7i	0.543422	+	0.0923280i
$995$	9.78566e8			0.993393
$996$		0			0
$997$	1.48696e9	+	8.58496e8i	1.50042	+	0.866269i	1.00000		0.000486585i	$0.000154885\pi$
$997$	1.48696e9	+	8.58496e8i	1.50042	+	0.866269i	0.500421	+	0.865782i	$0.333178\pi$
$998$	−1.13280e7	+	1.96207e7i	−0.0113963	+	0.0197389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.d.10.2		8
3.2	odd	2		21.7.f.a.10.3	✓	8
7.3	odd	6		441.7.d.c.244.6		8
7.4	even	3		441.7.d.c.244.5		8
7.5	odd	6	inner	63.7.m.d.19.2		8
12.11	even	2		336.7.bh.d.241.4		8
21.2	odd	6		147.7.f.d.19.3		8
21.5	even	6		21.7.f.a.19.3	yes	8
21.11	odd	6		147.7.d.b.97.4		8
21.17	even	6		147.7.d.b.97.3		8
21.20	even	2		147.7.f.d.31.3		8
84.47	odd	6		336.7.bh.d.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.3	✓	8	3.2	odd	2
21.7.f.a.19.3	yes	8	21.5	even	6
63.7.m.d.10.2		8	1.1	even	1	trivial
63.7.m.d.19.2		8	7.5	odd	6	inner
147.7.d.b.97.3		8	21.17	even	6
147.7.d.b.97.4		8	21.11	odd	6
147.7.f.d.19.3		8	21.2	odd	6
147.7.f.d.31.3		8	21.20	even	2
336.7.bh.d.145.4		8	84.47	odd	6
336.7.bh.d.241.4		8	12.11	even	2
441.7.d.c.244.5		8	7.4	even	3
441.7.d.c.244.6		8	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-2.25320 - 3.90266i) q^{2} +(21.8461 - 37.8386i) q^{4} +(-53.9244 + 31.1333i) q^{5} +(218.833 - 264.124i) q^{7} -485.305 q^{8} +O(q^{10})\)	\(q+(-2.25320 - 3.90266i) q^{2} +(21.8461 - 37.8386i) q^{4} +(-53.9244 + 31.1333i) q^{5} +(218.833 - 264.124i) q^{7} -485.305 q^{8} +(243.005 + 140.299i) q^{10} +(9.71675 - 16.8299i) q^{11} -1642.65i q^{13} +(-1523.86 - 258.906i) q^{14} +(-304.661 - 527.689i) q^{16} +(186.054 + 107.418i) q^{17} +(-8237.53 + 4755.94i) q^{19} +2720.57i q^{20} -87.5753 q^{22} +(-7223.90 - 12512.2i) q^{23} +(-5873.94 + 10174.0i) q^{25} +(-6410.70 + 3701.22i) q^{26} +(-5213.43 - 14050.4i) q^{28} -43016.4 q^{29} +(-7799.62 - 4503.11i) q^{31} +(-16902.7 + 29276.3i) q^{32} -968.141i q^{34} +(-3577.38 + 21055.7i) q^{35} +(16564.6 + 28690.7i) q^{37} +(37121.7 + 21432.2i) q^{38} +(26169.8 - 15109.1i) q^{40} -73712.4i q^{41} +4761.19 q^{43} +(-424.547 - 735.337i) q^{44} +(-32553.9 + 56384.9i) q^{46} +(63760.5 - 36812.2i) q^{47} +(-21873.6 - 115598. i) q^{49} +52940.7 q^{50} +(-62155.6 - 35885.5i) q^{52} +(119317. - 206663. i) q^{53} +1210.06i q^{55} +(-106201. + 128181. i) q^{56} +(96924.8 + 167879. i) q^{58} +(282811. + 163281. i) q^{59} +(350517. - 202371. i) q^{61} +40585.7i q^{62} +113344. q^{64} +(51141.0 + 88578.8i) q^{65} +(-109982. + 190494. i) q^{67} +(8129.12 - 4693.35i) q^{68} +(90233.8 - 33481.4i) q^{70} -350228. q^{71} +(-174606. - 100809. i) q^{73} +(74646.7 - 129292. i) q^{74} +415596. i q^{76} +(-2318.83 - 6249.36i) q^{77} +(-197745. - 342505. i) q^{79} +(32857.4 + 18970.2i) q^{80} +(-287675. + 166089. i) q^{82} +13229.0i q^{83} -13377.1 q^{85} +(-10727.9 - 18581.3i) q^{86} +(-4715.59 + 8167.65i) q^{88} +(199460. - 115158. i) q^{89} +(-433862. - 359465. i) q^{91} -631258. q^{92} +(-287331. - 165891. i) q^{94} +(296136. - 512922. i) q^{95} +662517. i q^{97} +(-401853. + 345831. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8}+O(q^{10}) \) 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

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Representations

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Database

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