LMFDB - Embedded newform 91.8.c.a.64.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(64,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("91.64");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.c (of order $2$, degree $1$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.15
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.0195i q^{2} -52.4283 q^{3} +6.57091 q^{4} -215.435i q^{5} +577.733i q^{6} +343.000i q^{7} -1482.90i q^{8} +561.727 q^{9} +O(q^{10})$	\(q-11.0195i q^{2} -52.4283 q^{3} +6.57091 q^{4} -215.435i q^{5} +577.733i q^{6} +343.000i q^{7} -1482.90i q^{8} +561.727 q^{9} -2373.98 q^{10} +188.689i q^{11} -344.502 q^{12} +(-5927.83 - 5254.46i) q^{13} +3779.68 q^{14} +11294.9i q^{15} -15499.7 q^{16} -25297.8 q^{17} -6189.94i q^{18} +13463.9i q^{19} -1415.60i q^{20} -17982.9i q^{21} +2079.26 q^{22} -7182.76 q^{23} +77746.1i q^{24} +31712.9 q^{25} +(-57901.4 + 65321.7i) q^{26} +85210.3 q^{27} +2253.82i q^{28} -45214.5 q^{29} +124464. q^{30} +59368.7i q^{31} -19012.2i q^{32} -9892.67i q^{33} +278768. i q^{34} +73894.1 q^{35} +3691.06 q^{36} +600810. i q^{37} +148365. q^{38} +(310786. + 275482. i) q^{39} -319469. q^{40} +214124. i q^{41} -198162. q^{42} +828867. q^{43} +1239.86i q^{44} -121015. i q^{45} +79150.3i q^{46} -933473. i q^{47} +812625. q^{48} -117649. q^{49} -349459. i q^{50} +1.32632e6 q^{51} +(-38951.2 - 34526.6i) q^{52} +937937. q^{53} -938974. i q^{54} +40650.3 q^{55} +508636. q^{56} -705888. i q^{57} +498241. i q^{58} +1.50528e6i q^{59} +74217.6i q^{60} -1.40949e6 q^{61} +654212. q^{62} +192672. i q^{63} -2.19347e6 q^{64} +(-1.13199e6 + 1.27706e6i) q^{65} -109012. q^{66} +2.46831e6i q^{67} -166229. q^{68} +376580. q^{69} -814275. i q^{70} +704227. i q^{71} -832986. i q^{72} +4.16803e6i q^{73} +6.62062e6 q^{74} -1.66265e6 q^{75} +88469.8i q^{76} -64720.5 q^{77} +(3.03567e6 - 3.42470e6i) q^{78} -6.10710e6 q^{79} +3.33918e6i q^{80} -5.69593e6 q^{81} +2.35953e6 q^{82} -2.40146e6i q^{83} -118164. i q^{84} +5.45002e6i q^{85} -9.13369e6i q^{86} +2.37052e6 q^{87} +279808. q^{88} +2.61372e6i q^{89} -1.33353e6 q^{90} +(1.80228e6 - 2.03325e6i) q^{91} -47197.2 q^{92} -3.11260e6i q^{93} -1.02864e7 q^{94} +2.90058e6 q^{95} +996780. i q^{96} +595405. i q^{97} +1.29643e6i q^{98} +105992. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) $ 50 * q - 3328 * q^4 + 40514 * q^9	$ 50 q - 3328 q^{4} + 40514 q^{9} + 5320 q^{10} + 8700 q^{12} + 17044 q^{13} + 10976 q^{14} + 228808 q^{16} + 33664 q^{17} + 70228 q^{22} - 75042 q^{23} - 664772 q^{25} + 78276 q^{26} - 661404 q^{27} + 135778 q^{29} + 994888 q^{30} + 372498 q^{35} - 3549604 q^{36} + 338468 q^{38} - 973080 q^{39} + 79316 q^{40} + 296352 q^{42} - 53618 q^{43} + 1400384 q^{48} - 5882450 q^{49} - 2182360 q^{51} - 6982340 q^{52} + 2841746 q^{53} + 6871356 q^{55} - 2107392 q^{56} + 1773716 q^{61} - 6969608 q^{62} - 9449120 q^{64} - 7901430 q^{65} - 11755548 q^{66} + 11829980 q^{68} + 3564460 q^{69} + 45595884 q^{74} - 7220964 q^{75} + 186592 q^{77} - 8093012 q^{78} - 21257822 q^{79} + 53034530 q^{81} + 10907568 q^{82} + 14135000 q^{87} - 51594780 q^{88} - 61226356 q^{90} - 8096858 q^{91} - 11200212 q^{92} + 80667028 q^{94} + 30430066 q^{95}+O(q^{100}) $ 50 * q - 3328 * q^4 + 40514 * q^9 + 5320 * q^10 + 8700 * q^12 + 17044 * q^13 + 10976 * q^14 + 228808 * q^16 + 33664 * q^17 + 70228 * q^22 - 75042 * q^23 - 664772 * q^25 + 78276 * q^26 - 661404 * q^27 + 135778 * q^29 + 994888 * q^30 + 372498 * q^35 - 3549604 * q^36 + 338468 * q^38 - 973080 * q^39 + 79316 * q^40 + 296352 * q^42 - 53618 * q^43 + 1400384 * q^48 - 5882450 * q^49 - 2182360 * q^51 - 6982340 * q^52 + 2841746 * q^53 + 6871356 * q^55 - 2107392 * q^56 + 1773716 * q^61 - 6969608 * q^62 - 9449120 * q^64 - 7901430 * q^65 - 11755548 * q^66 + 11829980 * q^68 + 3564460 * q^69 + 45595884 * q^74 - 7220964 * q^75 + 186592 * q^77 - 8093012 * q^78 - 21257822 * q^79 + 53034530 * q^81 + 10907568 * q^82 + 14135000 * q^87 - 51594780 * q^88 - 61226356 * q^90 - 8096858 * q^91 - 11200212 * q^92 + 80667028 * q^94 + 30430066 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	11.0195i		−	0.973994i	−0.873404	−	0.486997i	$-0.838092\pi$
$2$		−	11.0195i		−	0.973994i	0.873404	−	0.486997i	$-0.161908\pi$
$3$	−52.4283			−1.12109			−0.560546	−	0.828123i	$-0.689409\pi$
$3$	−52.4283			−1.12109			−0.560546	+	0.828123i	$0.689409\pi$
$4$	6.57091			0.0513352
$5$		−	215.435i		−	0.770763i	−0.922757	−	0.385381i	$-0.874070\pi$
$5$		−	215.435i		−	0.770763i	0.922757	−	0.385381i	$-0.125930\pi$
$6$			577.733i			1.09194i
$7$			343.000i			0.377964i
$7$			343.000i			0.377964i
$8$		−	1482.90i		−	1.02399i
$9$	561.727			0.256848
$10$	−2373.98			−0.750719
$11$			188.689i			0.0427438i	0.999772	+	0.0213719i	$0.00680341\pi$
$11$			188.689i			0.0427438i	−0.999772	+	0.0213719i	$0.993197\pi$
$12$	−344.502			−0.0575515
$13$	−5927.83	−	5254.46i	−0.748332	−	0.663325i
$13$	−5927.83	−	5254.46i	−0.748332	−	0.663325i
$14$	3779.68			0.368135
$15$			11294.9i			0.864096i
$16$	−15499.7			−0.946029
$17$	−25297.8			−1.24885			−0.624426	−	0.781084i	$-0.714667\pi$
$17$	−25297.8			−1.24885			−0.624426	+	0.781084i	$0.714667\pi$
$18$		−	6189.94i		−	0.250169i
$19$			13463.9i			0.450331i	0.974320	+	0.225166i	$0.0722923\pi$
$19$			13463.9i			0.450331i	−0.974320	+	0.225166i	$0.927708\pi$
$20$		−	1415.60i		−	0.0395673i
$21$		−	17982.9i		−	0.423733i
$22$	2079.26			0.0416322
$23$	−7182.76			−0.123096			−0.0615480	−	0.998104i	$-0.519604\pi$
$23$	−7182.76			−0.123096			−0.0615480	+	0.998104i	$0.519604\pi$
$24$			77746.1i			1.14799i
$25$	31712.9			0.405925
$26$	−57901.4	+	65321.7i	−0.646074	+	0.728871i
$27$	85210.3			0.833142
$28$			2253.82i			0.0194029i
$29$	−45214.5			−0.344259			−0.172129	−	0.985074i	$-0.555065\pi$
$29$	−45214.5			−0.344259			−0.172129	+	0.985074i	$0.555065\pi$
$30$	124464.			0.841625
$31$			59368.7i			0.357925i	0.983856	+	0.178962i	$0.0572740\pi$
$31$			59368.7i			0.357925i	−0.983856	+	0.178962i	$0.942726\pi$
$32$		−	19012.2i		−	0.102567i
$33$		−	9892.67i		−	0.0479198i
$34$			278768.i			1.21637i
$35$	73894.1			0.291321
$36$	3691.06			0.0131854
$37$			600810.i			1.94998i	0.222239	+	0.974992i	$0.428663\pi$
$37$			600810.i			1.94998i	−0.222239	+	0.974992i	$0.571337\pi$
$38$	148365.			0.438620
$39$	310786.	+	275482.i	0.838949	+	0.743648i
$40$	−319469.			−0.789257
$41$			214124.i			0.485201i	0.970126	+	0.242600i	$0.0780004\pi$
$41$			214124.i			0.485201i	−0.970126	+	0.242600i	$0.922000\pi$
$42$	−198162.			−0.412714
$43$	828867.			1.58981			0.794905	−	0.606734i	$-0.207521\pi$
$43$	828867.			1.58981			0.794905	+	0.606734i	$0.207521\pi$
$44$			1239.86i			0.00219426i
$45$		−	121015.i		−	0.197969i
$46$			79150.3i			0.119895i
$47$		−	933473.i		−	1.31147i	−0.754990	−	0.655736i	$-0.772358\pi$
$47$		−	933473.i		−	1.31147i	0.754990	−	0.655736i	$-0.227642\pi$
$48$	812625.			1.06059
$49$	−117649.			−0.142857
$50$		−	349459.i		−	0.395368i
$51$	1.32632e6			1.40008
$52$	−38951.2	−	34526.6i	−0.0384158	−	0.0340519i
$53$	937937.			0.865382			0.432691	−	0.901542i	$-0.357564\pi$
$53$	937937.			0.865382			0.432691	+	0.901542i	$0.357564\pi$
$54$		−	938974.i		−	0.811475i
$55$	40650.3			0.0329453
$56$	508636.			0.387034
$57$		−	705888.i		−	0.504863i
$58$			498241.i			0.335306i
$59$			1.50528e6i			0.954193i	0.878851	+	0.477096i	$0.158311\pi$
$59$			1.50528e6i			0.954193i	−0.878851	+	0.477096i	$0.841689\pi$
$60$			74217.6i			0.0443586i
$61$	−1.40949e6			−0.795076			−0.397538	−	0.917586i	$-0.630135\pi$
$61$	−1.40949e6			−0.795076			−0.397538	+	0.917586i	$0.630135\pi$
$62$	654212.			0.348616
$63$			192672.i			0.0970794i
$64$	−2.19347e6			−1.04593
$65$	−1.13199e6	+	1.27706e6i	−0.511266	+	0.576786i
$66$	−109012.			−0.0466736
$67$			2.46831e6i			1.00263i	0.865266	+	0.501313i	$0.167149\pi$
$67$			2.46831e6i			1.00263i	−0.865266	+	0.501313i	$0.832851\pi$
$68$	−166229.			−0.0641101
$69$	376580.			0.138002
$70$		−	814275.i		−	0.283745i
$71$			704227.i			0.233512i	0.993161	+	0.116756i	$0.0372495\pi$
$71$			704227.i			0.233512i	−0.993161	+	0.116756i	$0.962750\pi$
$72$		−	832986.i		−	0.263011i
$73$			4.16803e6i			1.25401i	0.779016	+	0.627004i	$0.215719\pi$
$73$			4.16803e6i			1.25401i	−0.779016	+	0.627004i	$0.784281\pi$
$74$	6.62062e6			1.89927
$75$	−1.66265e6			−0.455079
$76$			88469.8i			0.0231179i
$77$	−64720.5			−0.0161556
$78$	3.03567e6	−	3.42470e6i	0.724309	−	0.817131i
$79$	−6.10710e6			−1.39361			−0.696804	−	0.717262i	$-0.745395\pi$
$79$	−6.10710e6			−1.39361			−0.696804	+	0.717262i	$0.745395\pi$
$80$			3.33918e6i			0.729164i
$81$	−5.69593e6			−1.19088
$82$	2.35953e6			0.472583
$83$		−	2.40146e6i		−	0.461000i	−0.973072	−	0.230500i	$-0.925964\pi$
$83$		−	2.40146e6i		−	0.461000i	0.973072	−	0.230500i	$-0.0740362\pi$
$84$		−	118164.i		−	0.0217524i
$85$			5.45002e6i			0.962569i
$86$		−	9.13369e6i		−	1.54847i
$87$	2.37052e6			0.385946
$88$	279808.			0.0437694
$89$			2.61372e6i			0.393001i	0.980504	+	0.196501i	$0.0629578\pi$
$89$			2.61372e6i			0.393001i	−0.980504	+	0.196501i	$0.937042\pi$
$90$	−1.33353e6			−0.192821
$91$	1.80228e6	−	2.03325e6i	0.250713	−	0.282843i
$92$	−47197.2			−0.00631916
$93$		−	3.11260e6i		−	0.401266i
$94$	−1.02864e7			−1.27737
$95$	2.90058e6			0.347099
$96$			996780.i			0.114987i
$97$			595405.i			0.0662387i	0.999451	+	0.0331193i	$0.0105441\pi$
$97$			595405.i			0.0662387i	−0.999451	+	0.0331193i	$0.989456\pi$
$98$			1.29643e6i			0.139142i
$99$			105992.i			0.0109787i
$100$	208382.			0.0208382
$101$	−7.46452e6			−0.720903			−0.360451	−	0.932778i	$-0.617377\pi$
$101$	−7.46452e6			−0.720903			−0.360451	+	0.932778i	$0.617377\pi$
$102$		−	1.46154e7i		−	1.36367i
$103$	−1.39761e7			−1.26025			−0.630124	−	0.776494i	$-0.716996\pi$
$103$	−1.39761e7			−1.26025			−0.630124	+	0.776494i	$0.716996\pi$
$104$	−7.79185e6	+	8.79040e6i	−0.679241	+	0.766287i
$105$	−3.87414e6			−0.326598
$106$		−	1.03356e7i		−	0.842877i
$107$	−2.08566e7			−1.64589			−0.822944	−	0.568122i	$-0.807670\pi$
$107$	−2.08566e7			−1.64589			−0.822944	+	0.568122i	$0.807670\pi$
$108$	559909.			0.0427695
$109$		−	4.20261e6i		−	0.310833i	−0.987849	−	0.155416i	$-0.950328\pi$
$109$		−	4.20261e6i		−	0.310833i	0.987849	−	0.155416i	$-0.0496719\pi$
$110$		−	447945.i		−	0.0320886i
$111$		−	3.14994e7i		−	2.18611i
$112$		−	5.31641e6i		−	0.357566i
$113$	1.78284e7			1.16235			0.581177	−	0.813777i	$-0.302592\pi$
$113$	1.78284e7			1.16235			0.581177	+	0.813777i	$0.302592\pi$
$114$	−7.77852e6			−0.491734
$115$			1.54742e6i			0.0948778i
$116$	−297100.			−0.0176726
$117$	−3.32982e6	−	2.95157e6i	−0.192208	−	0.170374i
$118$	1.65874e7			0.929378
$119$		−	8.67713e6i		−	0.472022i
$120$	1.67492e7			0.884830
$121$	1.94516e7			0.998173
$122$			1.55319e7i			0.774399i
$123$		−	1.12261e7i		−	0.543955i
$124$			390106.i			0.0183741i
$125$		−	2.36629e7i		−	1.08363i
$126$	2.12315e6			0.0945548
$127$	2.67669e7			1.15954			0.579769	−	0.814781i	$-0.303143\pi$
$127$	2.67669e7			1.15954			0.579769	+	0.814781i	$0.303143\pi$
$128$			2.17374e7i			0.916162i
$129$	−4.34561e7			−1.78232
$130$	1.40726e7	+	1.24740e7i	0.561786	+	0.497970i
$131$	9.83599e6			0.382269			0.191134	−	0.981564i	$-0.438783\pi$
$131$	9.83599e6			0.382269			0.191134	+	0.981564i	$0.438783\pi$
$132$		−	65003.8i		−	0.00245997i
$133$	−4.61811e6			−0.170209
$134$	2.71996e7			0.976551
$135$		−	1.83573e7i		−	0.642155i
$136$			3.75141e7i			1.27882i
$137$		−	3.51295e7i		−	1.16721i	−0.812036	−	0.583607i	$-0.801641\pi$
$137$		−	3.51295e7i		−	1.16721i	0.812036	−	0.583607i	$-0.198359\pi$
$138$		−	4.14972e6i		−	0.134413i
$139$	−4.02464e7			−1.27109			−0.635543	−	0.772066i	$-0.719224\pi$
$139$	−4.02464e7			−1.27109			−0.635543	+	0.772066i	$0.719224\pi$
$140$	485552.			0.0149550
$141$			4.89404e7i			1.47028i
$142$	7.76023e6			0.227439
$143$	991461.	−	1.11852e6i	0.0283530	−	0.0319866i
$144$	−8.70662e6			−0.242986
$145$			9.74077e6i			0.265342i
$146$	4.59295e7			1.22140
$147$	6.16814e6			0.160156
$148$			3.94787e6i			0.100103i
$149$			4.86830e7i			1.20566i	0.797869	+	0.602831i	$0.205961\pi$
$149$			4.86830e7i			1.20566i	−0.797869	+	0.602831i	$0.794039\pi$
$150$			1.83216e7i			0.443244i
$151$			2.83831e7i			0.670874i	0.942063	+	0.335437i	$0.108884\pi$
$151$			2.83831e7i			0.670874i	−0.942063	+	0.335437i	$0.891116\pi$
$152$	1.99656e7			0.461137
$153$	−1.42104e7			−0.320765
$154$			713187.i			0.0157355i
$155$	1.27901e7			0.275875
$156$	2.04215e6	+	1.81017e6i	0.0430676	+	0.0381754i
$157$	1.01529e7			0.209383			0.104691	−	0.994505i	$-0.466614\pi$
$157$	1.01529e7			0.209383			0.104691	+	0.994505i	$0.466614\pi$
$158$			6.72971e7i			1.35737i
$159$	−4.91744e7			−0.970173
$160$	−4.09590e6			−0.0790550
$161$		−	2.46369e6i		−	0.0465259i
$162$			6.27662e7i			1.15991i
$163$		−	5.82222e7i		−	1.05301i	−0.850173	−	0.526504i	$-0.823502\pi$
$163$		−	5.82222e7i		−	1.05301i	0.850173	−	0.526504i	$-0.176498\pi$
$164$			1.40699e6i			0.0249079i
$165$	−2.13122e6			−0.0369348
$166$	−2.64628e7			−0.449012
$167$		−	1.62048e7i		−	0.269238i	−0.990897	−	0.134619i	$-0.957019\pi$
$167$		−	1.62048e7i		−	0.269238i	0.990897	−	0.134619i	$-0.0429810\pi$
$168$	−2.66669e7			−0.433900
$169$	7.52986e6	+	6.22951e7i	0.120001	+	0.992774i
$170$	6.00564e7			0.937536
$171$			7.56301e6i			0.115667i
$172$	5.44641e6			0.0816133
$173$	−9.37382e7			−1.37643			−0.688217	−	0.725505i	$-0.741606\pi$
$173$	−9.37382e7			−1.37643			−0.688217	+	0.725505i	$0.741606\pi$
$174$		−	2.61219e7i		−	0.375909i
$175$			1.08775e7i			0.153425i
$176$		−	2.92464e6i		−	0.0404369i
$177$		−	7.89194e7i		−	1.06974i
$178$	2.88018e7			0.382781
$179$	2.51335e7			0.327542			0.163771	−	0.986498i	$-0.447634\pi$
$179$	2.51335e7			0.327542			0.163771	+	0.986498i	$0.447634\pi$
$180$		−	795182.i		−	0.0101628i
$181$	−9.51739e7			−1.19301			−0.596503	−	0.802611i	$-0.703444\pi$
$181$	−9.51739e7			−1.19301			−0.596503	+	0.802611i	$0.703444\pi$
$182$	−2.24053e7	−	1.98602e7i	−0.275487	−	0.244193i
$183$	7.38973e7			0.891354
$184$			1.06513e7i			0.126050i
$185$	1.29435e8			1.50298
$186$	−3.42992e7			−0.390831
$187$		−	4.77342e6i		−	0.0533807i
$188$		−	6.13377e6i		−	0.0673248i
$189$			2.92271e7i			0.314898i
$190$		−	3.19630e7i		−	0.338072i
$191$	5.85259e7			0.607759			0.303879	−	0.952710i	$-0.401718\pi$
$191$	5.85259e7			0.607759			0.303879	+	0.952710i	$0.401718\pi$
$192$	1.15000e8			1.17258
$193$			5.43152e7i			0.543840i	0.962320	+	0.271920i	$0.0876586\pi$
$193$			5.43152e7i			0.543840i	−0.962320	+	0.271920i	$0.912341\pi$
$194$	6.56106e6			0.0645161
$195$	5.93485e7	−	6.69541e7i	0.573176	−	0.646631i
$196$	−773061.			−0.00733360
$197$		−	1.13008e7i		−	0.105312i	−0.998613	−	0.0526559i	$-0.983231\pi$
$197$		−	1.13008e7i		−	0.105312i	0.998613	−	0.0526559i	$-0.0167687\pi$
$198$	1.16798e6			0.0106932
$199$	−1.68898e8			−1.51929			−0.759644	−	0.650339i	$-0.774627\pi$
$199$	−1.68898e8			−1.51929			−0.759644	+	0.650339i	$0.774627\pi$
$200$		−	4.70271e7i		−	0.415665i
$201$		−	1.29410e8i		−	1.12404i
$202$			8.22551e7i			0.702155i
$203$		−	1.55086e7i		−	0.130117i
$204$	8.71512e6			0.0718733
$205$	4.61297e7			0.373975
$206$			1.54010e8i			1.22747i
$207$	−4.03475e6			−0.0316170
$208$	9.18799e7	+	8.14428e7i	0.707944	+	0.627525i
$209$	−2.54049e6			−0.0192489
$210$			4.26911e7i			0.318104i
$211$	−5.47331e6			−0.0401108			−0.0200554	−	0.999799i	$-0.506384\pi$
$211$	−5.47331e6			−0.0401108			−0.0200554	+	0.999799i	$0.506384\pi$
$212$	6.16310e6			0.0444246
$213$		−	3.69214e7i		−	0.261788i
$214$			2.29829e8i			1.60309i
$215$		−	1.78567e8i		−	1.22537i
$216$		−	1.26359e8i		−	0.853133i
$217$	−2.03635e7			−0.135283
$218$	−4.63106e7			−0.302749
$219$		−	2.18523e8i		−	1.40586i
$220$	267109.			0.00169126
$221$	1.49961e8	+	1.32926e8i	0.934555	+	0.828394i
$222$	−3.47108e8			−2.12926
$223$		−	1.40402e8i		−	0.847827i	−0.905703	−	0.423913i	$-0.860656\pi$
$223$		−	1.40402e8i		−	0.847827i	0.905703	−	0.423913i	$-0.139344\pi$
$224$	6.52120e6			0.0387668
$225$	1.78140e7			0.104261
$226$		−	1.96460e8i		−	1.13213i
$227$			1.69503e8i			0.961804i	0.876774	+	0.480902i	$0.159691\pi$
$227$			1.69503e8i			0.961804i	−0.876774	+	0.480902i	$0.840309\pi$
$228$		−	4.63832e6i		−	0.0259173i
$229$		−	1.10956e7i		−	0.0610560i	−0.999534	−	0.0305280i	$-0.990281\pi$
$229$		−	1.10956e7i		−	0.0610560i	0.999534	−	0.0305280i	$-0.00971888\pi$
$230$	1.70517e7			0.0924104
$231$	3.39319e6			0.0181120
$232$			6.70487e7i			0.352519i
$233$	6.10383e6			0.0316123			0.0158062	−	0.999875i	$-0.494969\pi$
$233$	6.10383e6			0.0316123			0.0158062	+	0.999875i	$0.494969\pi$
$234$	−3.25248e7	+	3.66929e7i	−0.165943	+	0.187209i
$235$	−2.01103e8			−1.01083
$236$			9.89108e6i			0.0489837i
$237$	3.20185e8			1.56236
$238$	−9.56176e7			−0.459746
$239$		−	1.07162e8i		−	0.507747i	−0.967237	−	0.253874i	$-0.918295\pi$
$239$		−	1.07162e8i		−	0.507747i	0.967237	−	0.253874i	$-0.0817047\pi$
$240$		−	1.75068e8i		−	0.817461i
$241$		−	1.35355e8i		−	0.622894i	−0.950264	−	0.311447i	$-0.899186\pi$
$241$		−	1.35355e8i		−	0.622894i	0.950264	−	0.311447i	$-0.100814\pi$
$242$		−	2.14346e8i		−	0.972215i
$243$	1.12273e8			0.501941
$244$	−9.26165e6			−0.0408154
$245$			2.53457e7i			0.110109i
$246$	−1.23706e8			−0.529809
$247$	7.07453e7	−	7.98115e7i	0.298716	−	0.336997i
$248$	8.80380e7			0.366513
$249$			1.25904e8i			0.516824i
$250$	−2.60753e8			−1.05545
$251$	−4.57153e8			−1.82475			−0.912376	−	0.409354i	$-0.865754\pi$
$251$	−4.57153e8			−1.82475			−0.912376	+	0.409354i	$0.865754\pi$
$252$			1.26603e6i			0.00498360i
$253$		−	1.35531e6i		−	0.00526159i
$254$		−	2.94958e8i		−	1.12938i
$255$		−	2.85735e8i		−	1.07913i
$256$	−4.12298e7			−0.153593
$257$	1.77558e8			0.652492			0.326246	−	0.945285i	$-0.394216\pi$
$257$	1.77558e8			0.652492			0.326246	+	0.945285i	$0.394216\pi$
$258$			4.78864e8i			1.73597i
$259$	−2.06078e8			−0.737025
$260$	−7.43822e6	+	8.39145e6i	−0.0262460	+	0.0296095i
$261$	−2.53982e7			−0.0884221
$262$		−	1.08388e8i		−	0.372327i
$263$	−3.39688e8			−1.15142			−0.575712	−	0.817653i	$-0.695275\pi$
$263$	−3.39688e8			−1.15142			−0.575712	+	0.817653i	$0.695275\pi$
$264$	−1.46699e7			−0.0490696
$265$		−	2.02064e8i		−	0.667004i
$266$			5.08892e7i			0.165783i
$267$		−	1.37033e8i		−	0.440591i
$268$			1.62191e7i			0.0514700i
$269$	−7.36492e6			−0.0230693			−0.0115347	−	0.999933i	$-0.503672\pi$
$269$	−7.36492e6			−0.0230693			−0.0115347	+	0.999933i	$0.503672\pi$
$270$	−2.02288e8			−0.625455
$271$			4.25358e8i			1.29826i	0.760677	+	0.649130i	$0.224867\pi$
$271$			4.25358e8i			1.29826i	−0.760677	+	0.649130i	$0.775133\pi$
$272$	3.92109e8			1.18145
$273$	−9.44904e7	+	1.06600e8i	−0.281073	+	0.317093i
$274$	−3.87110e8			−1.13686
$275$			5.98388e6i			0.0173508i
$276$	2.47447e6			0.00708436
$277$	−6.10873e8			−1.72692			−0.863459	−	0.504418i	$-0.831707\pi$
$277$	−6.10873e8			−1.72692			−0.863459	+	0.504418i	$0.831707\pi$
$278$			4.43494e8i			1.23803i
$279$			3.33490e7i			0.0919322i
$280$		−	1.09578e8i		−	0.298311i
$281$			3.91910e8i			1.05369i	0.849960	+	0.526847i	$0.176626\pi$
$281$			3.91910e8i			1.05369i	−0.849960	+	0.526847i	$0.823374\pi$
$282$	5.39298e8			1.43205
$283$	−4.40412e8			−1.15507			−0.577533	−	0.816367i	$-0.695984\pi$
$283$	−4.40412e8			−1.15507			−0.577533	+	0.816367i	$0.695984\pi$
$284$			4.62741e6i			0.0119874i
$285$	−1.52073e8			−0.389130
$286$	−1.23255e7	−	1.09254e7i	−0.0311547	−	0.0276157i
$287$	−7.34445e7			−0.183389
$288$		−	1.06797e7i		−	0.0263442i
$289$	2.29638e8			0.559631
$290$	1.07338e8			0.258441
$291$		−	3.12161e7i		−	0.0742597i
$292$			2.73877e7i			0.0643748i
$293$			1.27254e7i			0.0295552i	0.999891	+	0.0147776i	$0.00470403\pi$
$293$			1.27254e7i			0.0295552i	−0.999891	+	0.0147776i	$0.995296\pi$
$294$		−	6.79697e7i		−	0.155991i
$295$	3.24290e8			0.735456
$296$	8.90943e8			1.99677
$297$			1.60783e7i			0.0356117i
$298$	5.36462e8			1.17431
$299$	4.25782e7	+	3.77415e7i	0.0921166	+	0.0816526i
$300$	−1.09251e7			−0.0233616
$301$			2.84301e8i			0.600892i
$302$	3.12767e8			0.653427
$303$	3.91352e8			0.808199
$304$		−	2.08687e8i		−	0.426027i
$305$			3.03654e8i			0.612815i
$306$			1.56592e8i			0.312423i
$307$			7.01418e7i			0.138354i	0.997604	+	0.0691772i	$0.0220374\pi$
$307$			7.01418e7i			0.138354i	−0.997604	+	0.0691772i	$0.977963\pi$
$308$	−425273.			−0.000829354
$309$	7.32744e8			1.41285
$310$		−	1.40940e8i		−	0.268701i
$311$	−5.80662e8			−1.09462			−0.547309	−	0.836931i	$-0.684348\pi$
$311$	−5.80662e8			−1.09462			−0.547309	+	0.836931i	$0.684348\pi$
$312$	4.08513e8	−	4.60866e8i	0.761492	−	0.859079i
$313$	4.90795e8			0.904680			0.452340	−	0.891846i	$-0.350589\pi$
$313$	4.90795e8			0.904680			0.452340	+	0.891846i	$0.350589\pi$
$314$		−	1.11880e8i		−	0.203938i
$315$	4.15083e7			0.0748252
$316$	−4.01292e7			−0.0715411
$317$		−	3.79217e8i		−	0.668622i	−0.942463	−	0.334311i	$-0.891496\pi$
$317$		−	3.79217e8i		−	0.668622i	0.942463	−	0.334311i	$-0.108504\pi$
$318$			5.41877e8i			0.944943i
$319$		−	8.53150e6i		−	0.0147149i
$320$			4.72550e8i			0.806163i
$321$	1.09348e9			1.84519
$322$	−2.71486e7			−0.0453160
$323$		−	3.40606e8i		−	0.562397i
$324$	−3.74274e7			−0.0611340
$325$	−1.87989e8	−	1.66634e8i	−0.303766	−	0.269260i
$326$	−6.41578e8			−1.02562
$327$			2.20336e8i			0.348472i
$328$	3.17525e8			0.496843
$329$	3.20181e8			0.495690
$330$			2.34850e7i			0.0359743i
$331$			5.49951e8i			0.833539i	0.909012	+	0.416770i	$0.136838\pi$
$331$			5.49951e8i			0.833539i	−0.909012	+	0.416770i	$0.863162\pi$
$332$		−	1.57797e7i		−	0.0236656i
$333$			3.37491e8i			0.500850i
$334$	−1.78568e8			−0.262236
$335$	5.31761e8			0.772786
$336$			2.78731e8i			0.400864i
$337$	−1.22873e9			−1.74885			−0.874426	−	0.485159i	$-0.838762\pi$
$337$	−1.22873e9			−1.74885			−0.874426	+	0.485159i	$0.838762\pi$
$338$	6.86460e8	−	8.29752e7i	0.966956	−	0.116880i
$339$	−9.34715e8			−1.30311
$340$			3.58116e7i			0.0494137i
$341$	−1.12022e7			−0.0152991
$342$	8.33405e7			0.112659
$343$		−	4.03536e7i		−	0.0539949i
$344$		−	1.22913e9i		−	1.62796i
$345$		−	8.11284e7i		−	0.106367i
$346$			1.03295e9i			1.34064i
$347$	4.01729e8			0.516155			0.258077	−	0.966124i	$-0.416911\pi$
$347$	4.01729e8			0.516155			0.258077	+	0.966124i	$0.416911\pi$
$348$	1.55765e7			0.0198126
$349$		−	1.07924e9i		−	1.35903i	−0.733661	−	0.679515i	$-0.762190\pi$
$349$		−	1.07924e9i		−	1.35903i	0.733661	−	0.679515i	$-0.237810\pi$
$350$	1.19865e8			0.149435
$351$	−5.05112e8	−	4.47734e8i	−0.623467	−	0.552644i
$352$	3.58741e6			0.00438411
$353$			1.64172e9i			1.98650i	0.116008	+	0.993248i	$0.462990\pi$
$353$			1.64172e9i			1.98650i	−0.116008	+	0.993248i	$0.537010\pi$
$354$	−8.69652e8			−1.04192
$355$	1.51715e8			0.179982
$356$			1.71745e7i			0.0201748i
$357$			4.54927e8i			0.529180i
$358$		−	2.76958e8i		−	0.319024i
$359$			8.46989e6i			0.00966156i	0.999988	+	0.00483078i	$0.00153769\pi$
$359$			8.46989e6i			0.00966156i	−0.999988	+	0.00483078i	$0.998462\pi$
$360$	−1.79454e8			−0.202719
$361$	7.12596e8			0.797202
$362$			1.04877e9i			1.16198i
$363$	−1.01981e9			−1.11904
$364$	1.18426e7	−	1.33603e7i	0.0128704	−	0.0145198i
$365$	8.97938e8			0.966543
$366$		−	8.14311e8i		−	0.868173i
$367$	−1.36487e8			−0.144132			−0.0720661	−	0.997400i	$-0.522959\pi$
$367$	−1.36487e8			−0.144132			−0.0720661	+	0.997400i	$0.522959\pi$
$368$	1.11331e8			0.116452
$369$			1.20279e8i			0.124623i
$370$		−	1.42631e9i		−	1.46389i
$371$			3.21712e8i			0.327084i
$372$		−	2.04526e7i		−	0.0205991i
$373$	6.03899e8			0.602536			0.301268	−	0.953539i	$-0.402590\pi$
$373$	6.03899e8			0.602536			0.301268	+	0.953539i	$0.402590\pi$
$374$	−5.26007e7			−0.0519925
$375$			1.24061e9i			1.21485i
$376$	−1.38425e9			−1.34294
$377$	2.68024e8	+	2.37578e8i	0.257620	+	0.228355i
$378$	3.22068e8			0.306709
$379$		−	1.88952e9i		−	1.78285i	−0.453168	−	0.891425i	$-0.649706\pi$
$379$		−	1.88952e9i		−	1.78285i	0.453168	−	0.891425i	$-0.350294\pi$
$380$	1.90595e7			0.0178184
$381$	−1.40334e9			−1.29995
$382$		−	6.44925e8i		−	0.591954i
$383$		−	1.29017e9i		−	1.17341i	−0.809801	−	0.586705i	$-0.800425\pi$
$383$		−	1.29017e9i		−	1.17341i	0.809801	−	0.586705i	$-0.199575\pi$
$384$		−	1.13965e9i		−	1.02710i
$385$			1.39430e7i			0.0124522i
$386$	5.98526e8			0.529697
$387$	4.65597e8			0.408340
$388$			3.91235e6i			0.00340038i
$389$	−1.07384e9			−0.924946			−0.462473	−	0.886633i	$-0.653038\pi$
$389$	−1.07384e9			−0.924946			−0.462473	+	0.886633i	$0.653038\pi$
$390$	−7.37800e8	−	6.53990e8i	−0.629815	−	0.558271i
$391$	1.81708e8			0.153729
$392$			1.74462e8i			0.146285i
$393$	−5.15684e8			−0.428558
$394$	−1.24529e8			−0.102573
$395$			1.31568e9i			1.07414i
$396$			696463.i			0.000563592i
$397$			2.29145e9i			1.83799i	0.394269	+	0.918995i	$0.370998\pi$
$397$			2.29145e9i			1.83799i	−0.394269	+	0.918995i	$0.629002\pi$
$398$			1.86117e9i			1.47978i
$399$	2.42119e8			0.190820
$400$	−4.91541e8			−0.384017
$401$			1.14126e9i			0.883854i	0.897051	+	0.441927i	$0.145705\pi$
$401$			1.14126e9i			0.883854i	−0.897051	+	0.441927i	$0.854295\pi$
$402$	−1.42603e9			−1.09480
$403$	3.11950e8	−	3.51928e8i	0.237420	−	0.267846i
$404$	−4.90487e7			−0.0370077
$405$			1.22710e9i			0.917884i
$406$	−1.70897e8			−0.126734
$407$	−1.13367e8			−0.0833498
$408$		−	1.96680e9i		−	1.43367i
$409$		−	1.27878e9i		−	0.924198i	−0.886828	−	0.462099i	$-0.847097\pi$
$409$		−	1.27878e9i		−	0.924198i	0.886828	−	0.462099i	$-0.152903\pi$
$410$		−	5.08326e8i		−	0.364249i
$411$			1.84178e9i			1.30855i
$412$	−9.18358e7			−0.0646951
$413$	−5.16312e8			−0.360651
$414$			4.44608e7i			0.0307947i
$415$	−5.17357e8			−0.355322
$416$	−9.98991e7	+	1.12701e8i	−0.0680354	+	0.0767543i
$417$	2.11005e9			1.42500
$418$			2.79949e7i			0.0187483i
$419$	1.86693e9			1.23988			0.619939	−	0.784650i	$-0.287157\pi$
$419$	1.86693e9			1.23988			0.619939	+	0.784650i	$0.287157\pi$
$420$	−2.54566e7			−0.0167660
$421$		−	1.11376e9i		−	0.727452i	−0.931506	−	0.363726i	$-0.881504\pi$
$421$		−	1.11376e9i		−	0.727452i	0.931506	−	0.363726i	$-0.118496\pi$
$422$			6.03131e7i			0.0390677i
$423$		−	5.24357e8i		−	0.336849i
$424$		−	1.39087e9i		−	0.886147i
$425$	−8.02264e8			−0.506940
$426$	−4.06855e8			−0.254980
$427$		−	4.83456e8i		−	0.300510i
$428$	−1.37047e8			−0.0844921
$429$	−5.19806e7	+	5.86421e7i	−0.0317864	+	0.0358599i
$430$	−1.96771e9			−1.19350
$431$			7.59689e8i			0.457052i	0.973538	+	0.228526i	$0.0733905\pi$
$431$			7.59689e8i			0.457052i	−0.973538	+	0.228526i	$0.926609\pi$
$432$	−1.32074e9			−0.788177
$433$	1.65704e9			0.980901			0.490451	−	0.871469i	$-0.336832\pi$
$433$	1.65704e9			0.980901			0.490451	+	0.871469i	$0.336832\pi$
$434$			2.24395e8i			0.131765i
$435$		−	5.10692e8i		−	0.297473i
$436$		−	2.76150e7i		−	0.0159567i
$437$		−	9.67077e7i		−	0.0554340i
$438$	−2.40801e9			−1.36930
$439$	4.17796e8			0.235689			0.117844	−	0.993032i	$-0.462402\pi$
$439$	4.17796e8			0.235689			0.117844	+	0.993032i	$0.462402\pi$
$440$		−	6.02804e7i		−	0.0337359i
$441$	−6.60866e7			−0.0366926
$442$	1.46478e9	−	1.65249e9i	0.806851	−	0.910252i
$443$	2.90882e9			1.58966			0.794829	−	0.606834i	$-0.207561\pi$
$443$	2.90882e9			1.58966			0.794829	+	0.606834i	$0.207561\pi$
$444$		−	2.06980e8i		−	0.112225i
$445$	5.63086e8			0.302911
$446$	−1.54716e9			−0.825778
$447$		−	2.55237e9i		−	1.35166i
$448$		−	7.52361e8i		−	0.395324i
$449$		−	9.72196e8i		−	0.506864i	−0.967353	−	0.253432i	$-0.918441\pi$
$449$		−	9.72196e8i		−	0.506864i	0.967353	−	0.253432i	$-0.0815595\pi$
$450$		−	1.96301e8i		−	0.101550i
$451$	−4.04029e7			−0.0207393
$452$	1.17149e8			0.0596698
$453$		−	1.48808e9i		−	0.752111i
$454$	1.86784e9			0.936792
$455$	−4.38032e8	−	3.88274e8i	−0.218005	−	0.193240i
$456$	−1.04676e9			−0.516977
$457$		−	1.83907e9i		−	0.901346i	−0.892689	−	0.450673i	$-0.851184\pi$
$457$		−	1.83907e9i		−	0.901346i	0.892689	−	0.450673i	$-0.148816\pi$
$458$	−1.22268e8			−0.0594682
$459$	−2.15563e9			−1.04047
$460$			1.01679e7i			0.00487057i
$461$			6.95445e8i			0.330605i	0.986243	+	0.165303i	$0.0528601\pi$
$461$			6.95445e8i			0.330605i	−0.986243	+	0.165303i	$0.947140\pi$
$462$		−	3.73912e7i		−	0.0176410i
$463$			1.88032e9i			0.880439i	0.897890	+	0.440219i	$0.145099\pi$
$463$			1.88032e9i			0.880439i	−0.897890	+	0.440219i	$0.854901\pi$
$464$	7.00813e8			0.325679
$465$	−6.70562e8			−0.309281
$466$		−	6.72610e7i		−	0.0307902i
$467$	1.92023e9			0.872458			0.436229	−	0.899836i	$-0.356314\pi$
$467$	1.92023e9			0.872458			0.436229	+	0.899836i	$0.356314\pi$
$468$	−2.18800e7	−	1.93945e7i	−0.00986702	−	0.00874617i
$469$	−8.46632e8			−0.378957
$470$			2.21605e9i			0.984547i
$471$	−5.32299e8			−0.234738
$472$	2.23219e9			0.977088
$473$			1.56398e8i			0.0679545i
$474$		−	3.52827e9i		−	1.52173i
$475$			4.26978e8i			0.182801i
$476$		−	5.70167e7i		−	0.0242313i
$477$	5.26864e8			0.222272
$478$	−1.18087e9			−0.494543
$479$			3.41748e9i			1.42080i	0.703800	+	0.710398i	$0.251485\pi$
$479$			3.41748e9i			1.42080i	−0.703800	+	0.710398i	$0.748515\pi$
$480$	2.14741e8			0.0886279
$481$	3.15693e9	−	3.56150e9i	1.29347	−	1.45924i
$482$	−1.49154e9			−0.606695
$483$			1.29167e8i			0.0521598i
$484$	1.27814e8			0.0512414
$485$	1.28271e8			0.0510543
$486$		−	1.23719e9i		−	0.488888i
$487$			7.56195e8i			0.296676i	0.988937	+	0.148338i	$0.0473924\pi$
$487$			7.56195e8i			0.296676i	−0.988937	+	0.148338i	$0.952608\pi$
$488$			2.09014e9i			0.814153i
$489$			3.05249e9i			1.18052i
$490$	2.79296e8			0.107246
$491$	−3.02905e9			−1.15484			−0.577419	−	0.816448i	$-0.695940\pi$
$491$	−3.02905e9			−1.15484			−0.577419	+	0.816448i	$0.695940\pi$
$492$		−	7.37660e7i		−	0.0279240i
$493$	1.14383e9			0.429928
$494$	−8.79482e8	−	7.79577e8i	−0.328233	−	0.290948i
$495$	2.28343e7			0.00846195
$496$		−	9.20200e8i		−	0.338607i
$497$	−2.41550e8			−0.0882591
$498$	1.38740e9			0.503383
$499$		−	4.11621e9i		−	1.48302i	−0.670944	−	0.741508i	$-0.734111\pi$
$499$		−	4.11621e9i		−	1.48302i	0.670944	−	0.741508i	$-0.265889\pi$
$500$		−	1.55487e8i		−	0.0556286i
$501$			8.49589e8i			0.301840i
$502$			5.03759e9i			1.77730i
$503$	1.77391e9			0.621504			0.310752	−	0.950491i	$-0.399419\pi$
$503$	1.77391e9			0.621504			0.310752	+	0.950491i	$0.399419\pi$
$504$	2.85714e8			0.0994088
$505$			1.60812e9i			0.555645i
$506$	−1.49348e7			−0.00512476
$507$	−3.94778e8	−	3.26603e9i	−0.134532	−	1.11299i
$508$	1.75883e8			0.0595252
$509$			2.54763e9i			0.856296i	0.903709	+	0.428148i	$0.140834\pi$
$509$			2.54763e9i			0.856296i	−0.903709	+	0.428148i	$0.859166\pi$
$510$	−3.14866e9			−1.05106
$511$	−1.42963e9			−0.473971
$512$			3.23672e9i			1.06576i
$513$			1.14726e9i			0.375190i
$514$		−	1.95660e9i		−	0.635523i
$515$			3.01094e9i			0.971353i
$516$	−2.85546e8			−0.0914960
$517$	1.76137e8			0.0560574
$518$			2.27087e9i			0.717858i
$519$	4.91454e9			1.54311
$520$	1.89376e9	+	1.67863e9i	0.590626	+	0.523534i
$521$	3.89811e9			1.20760			0.603798	−	0.797137i	$-0.293653\pi$
$521$	3.89811e9			1.20760			0.603798	+	0.797137i	$0.293653\pi$
$522$			2.79875e8i			0.0861227i
$523$	2.46430e9			0.753247			0.376623	−	0.926367i	$-0.377085\pi$
$523$	2.46430e9			0.753247			0.376623	+	0.926367i	$0.377085\pi$
$524$	6.46314e7			0.0196238
$525$		−	5.70289e8i		−	0.172004i
$526$			3.74319e9i			1.12148i
$527$		−	1.50189e9i		−	0.446995i
$528$			1.53334e8i			0.0453335i
$529$	−3.35323e9			−0.984847
$530$	−2.22664e9			−0.649658
$531$			8.45558e8i			0.245083i
$532$	−3.03452e7			−0.00873773
$533$	1.12510e9	−	1.26929e9i	0.321846	−	0.363091i
$534$	−1.51003e9			−0.429133
$535$			4.49324e9i			1.26859i
$536$	3.66027e9			1.02668
$537$	−1.31770e9			−0.367204
$538$			8.11576e7i			0.0224694i
$539$		−	2.21991e7i		−	0.00610626i
$540$		−	1.20624e8i		−	0.0329652i
$541$			4.43248e9i			1.20353i	0.798674	+	0.601764i	$0.205535\pi$
$541$			4.43248e9i			1.20353i	−0.798674	+	0.601764i	$0.794465\pi$
$542$	4.68723e9			1.26450
$543$	4.98980e9			1.33747
$544$			4.80967e8i			0.128091i
$545$	−9.05389e8			−0.239578
$546$	1.17467e9	+	1.04124e9i	0.308847	+	0.273763i
$547$	−9.04260e8			−0.236232			−0.118116	−	0.993000i	$-0.537685\pi$
$547$	−9.04260e8			−0.236232			−0.118116	+	0.993000i	$0.537685\pi$
$548$		−	2.30833e8i		−	0.0599192i
$549$	−7.91750e8			−0.204214
$550$	6.59393e7			0.0168995
$551$		−	6.08762e8i		−	0.155030i
$552$		−	5.58431e8i		−	0.141313i
$553$		−	2.09474e9i		−	0.526734i
$554$			6.73151e9i			1.68201i
$555$	−6.78608e9			−1.68497
$556$	−2.64455e8			−0.0652515
$557$			5.85207e9i			1.43488i	0.696619	+	0.717441i	$0.254687\pi$
$557$			5.85207e9i			1.43488i	−0.696619	+	0.717441i	$0.745313\pi$
$558$	3.67489e8			0.0895415
$559$	−4.91338e9	−	4.35525e9i	−1.18971	−	1.05456i
$560$	−1.14534e9			−0.275598
$561$			2.50262e8i			0.0598447i
$562$	4.31865e9			1.02629
$563$	1.67322e9			0.395161			0.197580	−	0.980287i	$-0.436692\pi$
$563$	1.67322e9			0.395161			0.197580	+	0.980287i	$0.436692\pi$
$564$			3.21583e8i			0.0754773i
$565$		−	3.84087e9i		−	0.895900i
$566$			4.85311e9i			1.12503i
$567$		−	1.95370e9i		−	0.450109i
$568$	1.04430e9			0.239115
$569$	−3.61607e9			−0.822893			−0.411447	−	0.911434i	$-0.634976\pi$
$569$	−3.61607e9			−0.822893			−0.411447	+	0.911434i	$0.634976\pi$
$570$			1.67576e9i			0.379010i
$571$	−3.80048e9			−0.854303			−0.427152	−	0.904180i	$-0.640483\pi$
$571$	−3.80048e9			−0.854303			−0.427152	+	0.904180i	$0.640483\pi$
$572$	6.51480e6	−	7.34969e6i	0.00145551	−	0.00164204i
$573$	−3.06841e9			−0.681354
$574$			8.09320e8i			0.178619i
$575$	−2.27786e8			−0.0499677
$576$	−1.23213e9			−0.268645
$577$		−	2.62544e8i		−	0.0568967i	−0.999595	−	0.0284484i	$-0.990943\pi$
$577$		−	2.62544e8i		−	0.0568967i	0.999595	−	0.0284484i	$-0.00905661\pi$
$578$		−	2.53050e9i		−	0.545077i
$579$		−	2.84765e9i		−	0.609695i
$580$			6.40057e7i			0.0136214i
$581$	8.23699e8			0.174242
$582$	−3.43985e8			−0.0723285
$583$			1.76979e8i			0.0369897i
$584$	6.18078e9			1.28410
$585$	−6.35871e8	+	7.17359e8i	−0.131318	+	0.148146i
$586$	1.40227e8			0.0287866
$587$		−	7.86055e9i		−	1.60406i	−0.597286	−	0.802029i	$-0.703754\pi$
$587$		−	7.86055e9i		−	1.60406i	0.597286	−	0.802029i	$-0.296246\pi$
$588$	4.05303e7			0.00822165
$589$	−7.99332e8			−0.161185
$590$		−	3.57351e9i		−	0.716330i
$591$			5.92482e8i			0.118064i
$592$		−	9.31240e9i		−	1.84474i
$593$		−	5.77722e9i		−	1.13770i	−0.822442	−	0.568849i	$-0.807389\pi$
$593$		−	5.77722e9i		−	1.13770i	0.822442	−	0.568849i	$-0.192611\pi$
$594$	1.77175e8			0.0346856
$595$	−1.86936e9			−0.363817
$596$			3.19892e8i			0.0618929i
$597$	8.85506e9			1.70326
$598$	4.15892e8	−	4.69190e8i	0.0795291	−	0.0897210i
$599$	3.23193e9			0.614424			0.307212	−	0.951641i	$-0.400604\pi$
$599$	3.23193e9			0.614424			0.307212	+	0.951641i	$0.400604\pi$
$600$			2.46555e9i			0.465998i
$601$	−7.59301e9			−1.42677			−0.713384	−	0.700773i	$-0.752839\pi$
$601$	−7.59301e9			−1.42677			−0.713384	+	0.700773i	$0.752839\pi$
$602$	3.13285e9			0.585265
$603$			1.38652e9i			0.257522i
$604$			1.86503e8i			0.0344394i
$605$		−	4.19054e9i		−	0.769355i
$606$		−	4.31250e9i		−	0.787181i
$607$	−9.37915e8			−0.170217			−0.0851085	−	0.996372i	$-0.527124\pi$
$607$	−9.37915e8			−0.170217			−0.0851085	+	0.996372i	$0.527124\pi$
$608$	2.55978e8			0.0461892
$609$			8.13088e8i			0.145874i
$610$	3.34611e9			0.596878
$611$	−4.90489e9	+	5.53347e9i	−0.869932	+	0.981417i
$612$	−9.33754e7			−0.0164666
$613$			5.68052e9i			0.996039i	0.867166	+	0.498020i	$0.165939\pi$
$613$			5.68052e9i			0.996039i	−0.867166	+	0.498020i	$0.834061\pi$
$614$	7.72927e8			0.134756
$615$	−2.41850e9			−0.419260
$616$			9.59742e7i			0.0165433i
$617$			1.17598e9i			0.201559i	0.994909	+	0.100780i	$0.0321337\pi$
$617$			1.17598e9i			0.201559i	−0.994909	+	0.100780i	$0.967866\pi$
$618$		−	8.07446e9i		−	1.37611i
$619$		−	8.89106e9i		−	1.50673i	−0.657601	−	0.753367i	$-0.728429\pi$
$619$		−	8.89106e9i		−	1.50673i	0.657601	−	0.753367i	$-0.271571\pi$
$620$	8.40424e7			0.0141621
$621$	−6.12045e8			−0.102556
$622$			6.39860e9i			1.06615i
$623$	−8.96506e8			−0.148541
$624$	−4.81711e9	−	4.26991e9i	−0.793670	−	0.703513i
$625$	−2.62024e9			−0.429301
$626$		−	5.40831e9i		−	0.881153i
$627$	1.33194e8			0.0215798
$628$	6.67138e7			0.0107487
$629$		−	1.51992e10i		−	2.43524i
$630$		−	4.57400e8i		−	0.0728793i
$631$			8.52732e8i			0.135117i	0.997715	+	0.0675585i	$0.0215209\pi$
$631$			8.52732e8i			0.135117i	−0.997715	+	0.0675585i	$0.978479\pi$
$632$			9.05624e9i			1.42705i
$633$	2.86957e8			0.0449680
$634$	−4.17878e9			−0.651234
$635$		−	5.76652e9i		−	0.893730i
$636$	−3.23121e8			−0.0498041
$637$	6.97403e8	+	6.18182e8i	0.106905	+	0.0947607i
$638$	−9.40128e7			−0.0143323
$639$			3.95583e8i			0.0599770i
$640$	4.68299e9			0.706144
$641$	3.79841e9			0.569637			0.284819	−	0.958581i	$-0.408067\pi$
$641$	3.79841e9			0.569637			0.284819	+	0.958581i	$0.408067\pi$
$642$		−	1.20496e10i		−	1.79721i
$643$			4.25448e9i			0.631114i	0.948907	+	0.315557i	$0.102191\pi$
$643$			4.25448e9i			0.631114i	−0.948907	+	0.315557i	$0.897809\pi$
$644$		−	1.61887e7i		−	0.00238842i
$645$			9.36195e9i			1.37375i
$646$	−3.75330e9			−0.547772
$647$	6.35498e9			0.922464			0.461232	−	0.887280i	$-0.347408\pi$
$647$	6.35498e9			0.922464			0.461232	+	0.887280i	$0.347408\pi$
$648$			8.44651e9i			1.21945i
$649$	−2.84031e8			−0.0407859
$650$	−1.83622e9	+	2.07154e9i	−0.262258	+	0.295867i
$651$	1.06762e9			0.151664
$652$		−	3.82573e8i		−	0.0540564i
$653$	−5.17809e9			−0.727735			−0.363868	−	0.931451i	$-0.618544\pi$
$653$	−5.17809e9			−0.727735			−0.363868	+	0.931451i	$0.618544\pi$
$654$	2.42799e9			0.339410
$655$		−	2.11901e9i		−	0.294638i
$656$		−	3.31886e9i		−	0.459014i
$657$			2.34129e9i			0.322090i
$658$		−	3.52823e9i		−	0.482799i
$659$	−1.08713e10			−1.47973			−0.739866	−	0.672754i	$-0.765111\pi$
$659$	−1.08713e10			−1.47973			−0.739866	+	0.672754i	$0.765111\pi$
$660$	−1.40041e7			−0.00189606
$661$			7.64680e9i			1.02985i	0.857235	+	0.514926i	$0.172181\pi$
$661$			7.64680e9i			1.02985i	−0.857235	+	0.514926i	$0.827819\pi$
$662$	6.06018e9			0.811863
$663$	−7.86219e9	−	6.96909e9i	−1.04772	−	0.928707i
$664$	−3.56112e9			−0.472062
$665$			9.94901e8i			0.131191i
$666$	3.71898e9			0.487825
$667$	3.24765e8			0.0423768
$668$		−	1.06480e8i		−	0.0138214i
$669$			7.36105e9i			0.950492i
$670$		−	5.85973e9i		−	0.752689i
$671$		−	2.65957e8i		−	0.0339846i
$672$	−3.41895e8			−0.0434611
$673$	2.43269e9			0.307633			0.153817	−	0.988099i	$-0.450844\pi$
$673$	2.43269e9			0.307633			0.153817	+	0.988099i	$0.450844\pi$
$674$			1.35400e10i			1.70337i
$675$	2.70226e9			0.338193
$676$	4.94780e7	+	4.09335e8i	0.00616026	+	0.0509643i
$677$	9.84568e9			1.21951			0.609755	−	0.792590i	$-0.291268\pi$
$677$	9.84568e9			1.21951			0.609755	+	0.792590i	$0.291268\pi$
$678$			1.03001e10i			1.26922i
$679$	−2.04224e8			−0.0250359
$680$	8.08184e9			0.985665
$681$		−	8.88675e9i		−	1.07827i
$682$			1.23443e8i			0.0149012i
$683$		−	1.41153e10i		−	1.69519i	−0.530642	−	0.847596i	$-0.678049\pi$
$683$		−	1.41153e10i		−	1.69519i	0.530642	−	0.847596i	$-0.321951\pi$
$684$			4.96959e7i			0.00593778i
$685$	−7.56812e9			−0.899645
$686$	−4.44676e8			−0.0525907
$687$			5.81726e8i			0.0684494i
$688$	−1.28472e10			−1.50401
$689$	−5.55993e9	−	4.92835e9i	−0.647593	−	0.574029i
$690$	−8.93993e8			−0.103601
$691$			1.63592e10i			1.88621i	0.332494	+	0.943105i	$0.392110\pi$
$691$			1.63592e10i			1.88621i	−0.332494	+	0.943105i	$0.607890\pi$
$692$	−6.15945e8			−0.0706596
$693$	−3.63552e7			−0.00414955
$694$		−	4.42684e9i		−	0.502732i
$695$			8.67046e9i			0.979705i
$696$		−	3.51525e9i		−	0.395206i
$697$		−	5.41685e9i		−	0.605944i
$698$	−1.18927e10			−1.32369
$699$	−3.20013e8			−0.0354403
$700$			7.14751e7i			0.00787611i
$701$	−9.71693e9			−1.06541			−0.532704	−	0.846302i	$-0.678824\pi$
$701$	−9.71693e9			−1.06541			−0.532704	+	0.846302i	$0.678824\pi$
$702$	−4.93380e9	+	5.56608e9i	−0.538272	+	0.607253i
$703$	−8.08923e9			−0.878139
$704$		−	4.13885e8i		−	0.0447070i
$705$	1.05435e10			1.13324
$706$	1.80909e10			1.93484
$707$		−	2.56033e9i		−	0.272476i
$708$		−	5.18573e8i		−	0.0549153i
$709$			1.34682e10i			1.41922i	0.704597	+	0.709608i	$0.251128\pi$
$709$			1.34682e10i			1.41922i	−0.704597	+	0.709608i	$0.748872\pi$
$710$		−	1.67182e9i		−	0.175302i
$711$	−3.43052e9			−0.357945
$712$	3.87589e9			0.402431
$713$		−	4.26431e8i		−	0.0440591i
$714$	5.01307e9			0.515418
$715$	−2.40968e8	−	2.13595e8i	−0.0246540	−	0.0218535i
$716$	1.65150e8			0.0168144
$717$			5.61831e9i			0.569231i
$718$	9.33338e7			0.00941030
$719$	5.72532e9			0.574445			0.287223	−	0.957864i	$-0.407268\pi$
$719$	5.72532e9			0.574445			0.287223	+	0.957864i	$0.407268\pi$
$720$			1.87571e9i			0.187284i
$721$		−	4.79381e9i		−	0.476329i
$722$		−	7.85244e9i		−	0.776470i
$723$			7.09642e9i			0.698321i
$724$	−6.25379e8			−0.0612432
$725$	−1.43388e9			−0.139743
$726$			1.12378e10i			1.08994i
$727$	6.07450e9			0.586327			0.293164	−	0.956062i	$-0.405292\pi$
$727$	6.07450e9			0.586327			0.293164	+	0.956062i	$0.405292\pi$
$728$	−3.01511e9	−	2.67260e9i	−0.289629	−	0.256729i
$729$	6.57072e9			0.628155
$730$		−	9.89481e9i		−	0.941407i
$731$	−2.09685e10			−1.98544
$732$	4.85573e8			0.0457578
$733$		−	1.81386e9i		−	0.170114i	−0.996376	−	0.0850571i	$-0.972893\pi$
$733$		−	1.81386e9i		−	0.170114i	0.996376	−	0.0850571i	$-0.0271073\pi$
$734$			1.50402e9i			0.140384i
$735$		−	1.32883e9i		−	0.123442i
$736$			1.36560e8i			0.0126256i
$737$	−4.65745e8			−0.0428560
$738$	1.32541e9			0.121382
$739$		−	6.99992e9i		−	0.638025i	−0.947751	−	0.319012i	$-0.896649\pi$
$739$		−	6.99992e9i		−	0.638025i	0.947751	−	0.319012i	$-0.103351\pi$
$740$	8.50508e8			0.0771556
$741$	−3.70906e9	+	4.18438e9i	−0.334888	+	0.377805i
$742$	3.54510e9			0.318578
$743$		−	1.25412e10i		−	1.12171i	−0.827915	−	0.560854i	$-0.810473\pi$
$743$		−	1.25412e10i		−	1.12171i	0.827915	−	0.560854i	$-0.189527\pi$
$744$	−4.61568e9			−0.410895
$745$	1.04880e10			0.929279
$746$		−	6.65465e9i		−	0.586867i
$747$		−	1.34896e9i		−	0.118407i
$748$		−	3.13657e7i		−	0.00274031i
$749$		−	7.15382e9i		−	0.622088i
$750$	1.36708e10			1.18326
$751$	−1.13095e10			−0.974325			−0.487163	−	0.873311i	$-0.661968\pi$
$751$	−1.13095e10			−0.974325			−0.487163	+	0.873311i	$0.661968\pi$
$752$			1.44686e10i			1.24069i
$753$	2.39678e10			2.04571
$754$	2.61798e9	−	2.95349e9i	0.222417	−	0.250920i
$755$	6.11471e9			0.517084
$756$			1.92049e8i			0.0161654i
$757$	−7.02878e9			−0.588904			−0.294452	−	0.955666i	$-0.595137\pi$
$757$	−7.02878e9			−0.588904			−0.294452	+	0.955666i	$0.595137\pi$
$758$	−2.08216e10			−1.73649
$759$			7.10566e7i			0.00589873i
$760$		−	4.30128e9i		−	0.355427i
$761$			1.63919e10i			1.34829i	0.738600	+	0.674144i	$0.235487\pi$
$761$			1.63919e10i			1.34829i	−0.738600	+	0.674144i	$0.764513\pi$
$762$			1.54641e10i			1.26614i
$763$	1.44150e9			0.117484
$764$	3.84568e8			0.0311994
$765$			3.06142e9i			0.247234i
$766$	−1.42170e10			−1.14289
$767$	7.90945e9	−	8.92307e9i	0.632940	−	0.714053i
$768$	2.16161e9			0.172192
$769$			1.27685e10i			1.01251i	0.862385	+	0.506253i	$0.168970\pi$
$769$			1.27685e10i			1.01251i	−0.862385	+	0.506253i	$0.831030\pi$
$770$	1.53645e8			0.0121283
$771$	−9.30908e9			−0.731504
$772$			3.56900e8i			0.0279181i
$773$			3.90491e9i			0.304077i	0.988375	+	0.152038i	$0.0485837\pi$
$773$			3.90491e9i			0.304077i	−0.988375	+	0.152038i	$0.951416\pi$
$774$		−	5.13064e9i		−	0.397720i
$775$			1.88275e9i			0.145290i
$776$	8.82928e8			0.0678280
$777$	1.08043e10			0.826273
$778$			1.18332e10i			0.900893i
$779$	−2.88293e9			−0.218501
$780$	3.89973e8	−	4.39950e8i	0.0294241	−	0.0331949i
$781$	−1.32880e8			−0.00998118
$782$		−	2.00233e9i		−	0.149731i
$783$	−3.85274e9			−0.286816
$784$	1.82353e9			0.135147
$785$		−	2.18729e9i		−	0.161385i
$786$			5.68258e9i			0.417413i
$787$		−	2.34336e10i		−	1.71367i	−0.515587	−	0.856837i	$-0.672426\pi$
$787$		−	2.34336e10i		−	1.71367i	0.515587	−	0.856837i	$-0.327574\pi$
$788$		−	7.42565e7i		−	0.00540621i
$789$	1.78093e10			1.29085
$790$	1.44981e10			1.04621
$791$			6.11515e9i			0.439329i
$792$	1.57176e8			0.0112421
$793$	8.35524e9	+	7.40612e9i	0.594981	+	0.527394i
$794$	2.52506e10			1.79019
$795$			1.05939e10i			0.747774i
$796$	−1.10982e9			−0.0779930
$797$	9.95467e9			0.696503			0.348251	−	0.937401i	$-0.386776\pi$
$797$	9.95467e9			0.696503			0.348251	+	0.937401i	$0.386776\pi$
$798$		−	2.66803e9i		−	0.185858i
$799$			2.36148e10i			1.63784i
$800$		−	6.02933e8i		−	0.0416346i
$801$			1.46820e9i			0.100942i
$802$	1.25761e10			0.860869
$803$	−7.86463e8			−0.0536011
$804$		−	8.50338e8i		−	0.0577026i
$805$	−5.30764e8			−0.0358604
$806$	−3.87806e9	−	3.43753e9i	−0.260881	−	0.231246i
$807$	3.86130e8			0.0258628
$808$			1.10691e10i			0.738201i
$809$	1.38449e10			0.919330			0.459665	−	0.888092i	$-0.347970\pi$
$809$	1.38449e10			0.919330			0.459665	+	0.888092i	$0.347970\pi$
$810$	1.35220e10			0.894014
$811$		−	1.68945e10i		−	1.11217i	−0.831125	−	0.556086i	$-0.812302\pi$
$811$		−	1.68945e10i		−	1.11217i	0.831125	−	0.556086i	$-0.187698\pi$
$812$		−	1.01905e8i		−	0.00667961i
$813$		−	2.23008e10i		−	1.45547i
$814$			1.24924e9i			0.0811822i
$815$	−1.25431e10			−0.811620
$816$	−2.05576e10			−1.32452
$817$			1.11598e10i			0.715941i
$818$	−1.40915e10			−0.900163
$819$	1.01239e9	−	1.14213e9i	0.0643952	−	0.0726476i
$820$	3.03114e8			0.0191981
$821$		−	6.90678e9i		−	0.435587i	−0.975995	−	0.217793i	$-0.930114\pi$
$821$		−	6.90678e9i		−	0.435587i	0.975995	−	0.217793i	$-0.0698859\pi$
$822$	2.02955e10			1.27452
$823$	−1.28512e10			−0.803606			−0.401803	−	0.915726i	$-0.631616\pi$
$823$	−1.28512e10			−0.803606			−0.401803	+	0.915726i	$0.631616\pi$
$824$			2.07252e10i			1.29049i
$825$		−	3.13725e8i		−	0.0194518i
$826$			5.68950e9i			0.351272i
$827$		−	9.88087e9i		−	0.607471i	−0.952756	−	0.303736i	$-0.901766\pi$
$827$		−	9.88087e9i		−	0.607471i	0.952756	−	0.303736i	$-0.0982340\pi$
$828$	−2.65120e7			−0.00162306
$829$	−3.08689e9			−0.188183			−0.0940915	−	0.995564i	$-0.529995\pi$
$829$	−3.08689e9			−0.188183			−0.0940915	+	0.995564i	$0.529995\pi$
$830$			5.70101e9i			0.346081i
$831$	3.20270e10			1.93604
$832$	1.30025e10	+	1.15255e10i	0.782702	+	0.693791i
$833$	2.97626e9			0.178407
$834$		−	2.32516e10i		−	1.38795i
$835$	−3.49107e9			−0.207518
$836$	−1.66933e7			−0.000988146
$837$			5.05882e9i			0.298202i
$838$		−	2.05726e10i		−	1.20763i
$839$		−	1.07257e10i		−	0.626988i	−0.949590	−	0.313494i	$-0.898500\pi$
$839$		−	1.07257e10i		−	0.626988i	0.949590	−	0.313494i	$-0.101500\pi$
$840$			5.74498e9i			0.334434i
$841$	−1.52055e10			−0.881486
$842$	−1.22731e10			−0.708534
$843$		−	2.05472e10i		−	1.18129i
$844$	−3.59647e7			−0.00205910
$845$	1.34205e10	−	1.62219e9i	0.765193	−	0.0924920i
$846$	−5.77814e9			−0.328089
$847$			6.67189e9i			0.377274i
$848$	−1.45378e10			−0.818677
$849$	2.30901e10			1.29494
$850$			8.84054e9i			0.493756i
$851$		−	4.31547e9i		−	0.240035i
$852$		−	2.42607e8i		−	0.0134390i
$853$			1.34773e10i			0.743500i	0.928333	+	0.371750i	$0.121242\pi$
$853$			1.34773e10i			0.743500i	−0.928333	+	0.371750i	$0.878758\pi$
$854$	−5.32744e9			−0.292695
$855$	1.62934e9			0.0891516
$856$			3.09283e10i			1.68538i
$857$	4.13671e9			0.224503			0.112252	−	0.993680i	$-0.464194\pi$
$857$	4.13671e9			0.224503			0.112252	+	0.993680i	$0.464194\pi$
$858$	6.46206e8	+	5.72800e8i	0.0349273	+	0.0309597i
$859$	−1.99593e10			−1.07441			−0.537203	−	0.843453i	$-0.680519\pi$
$859$	−1.99593e10			−1.07441			−0.537203	+	0.843453i	$0.680519\pi$
$860$		−	1.17335e9i		−	0.0629045i
$861$	3.85057e9			0.205596
$862$	8.37138e9			0.445166
$863$		−	2.38249e10i		−	1.26181i	−0.775861	−	0.630904i	$-0.782684\pi$
$863$		−	2.38249e10i		−	1.26181i	0.775861	−	0.630904i	$-0.217316\pi$
$864$		−	1.62004e9i		−	0.0854530i
$865$			2.01945e10i			1.06090i
$866$		−	1.82597e10i		−	0.955392i
$867$	−1.20395e10			−0.627398
$868$	−1.33806e8			−0.00694477
$869$		−	1.15235e9i		−	0.0595681i
$870$	−5.62757e9			−0.289737
$871$	1.29697e10	−	1.46318e10i	0.665066	−	0.750296i
$872$	−6.23206e9			−0.318291
$873$			3.34455e8i			0.0170133i
$874$	−1.06567e9			−0.0539924
$875$	8.11637e9			0.409575
$876$		−	1.43589e9i		−	0.0721701i
$877$			2.74053e10i			1.37194i	0.727629	+	0.685971i	$0.240622\pi$
$877$			2.74053e10i			1.37194i	−0.727629	+	0.685971i	$0.759378\pi$
$878$		−	4.60390e9i		−	0.229559i
$879$		−	6.67170e8i		−	0.0331341i
$880$	−6.30069e8			−0.0311673
$881$	−1.74710e10			−0.860797			−0.430399	−	0.902639i	$-0.641627\pi$
$881$	−1.74710e10			−0.860797			−0.430399	+	0.902639i	$0.641627\pi$
$882$			7.28240e8i			0.0357384i
$883$	−1.44809e10			−0.707838			−0.353919	−	0.935276i	$-0.615151\pi$
$883$	−1.44809e10			−0.707838			−0.353919	+	0.935276i	$0.615151\pi$
$884$	9.85379e8	+	8.73445e8i	0.0479756	+	0.0425258i
$885$	−1.70020e10			−0.824515
$886$		−	3.20537e10i		−	1.54832i
$887$	−2.04319e10			−0.983049			−0.491524	−	0.870864i	$-0.663560\pi$
$887$	−2.04319e10			−0.983049			−0.491524	+	0.870864i	$0.663560\pi$
$888$	−4.67106e10			−2.23857
$889$			9.18105e9i			0.438265i
$890$		−	6.20492e9i		−	0.295033i
$891$		−	1.07476e9i		−	0.0509026i
$892$		−	9.22571e8i		−	0.0435234i
$893$	1.25682e10			0.590597
$894$	−2.81258e10			−1.31651
$895$		−	5.41462e9i		−	0.252457i
$896$	−7.45592e9			−0.346277
$897$	−2.23230e9	−	1.97872e9i	−0.103271	−	0.0915401i
$898$	−1.07131e10			−0.493683
$899$		−	2.68433e9i		−	0.123219i
$900$	1.17054e8			0.00535226
$901$	−2.37277e10			−1.08073
$902$			4.45219e8i			0.0202000i
$903$		−	1.49054e10i		−	0.673655i
$904$		−	2.64378e10i		−	1.19025i
$905$			2.05038e10i			0.919525i
$906$	−1.63979e10			−0.732552
$907$	−2.83647e10			−1.26227			−0.631136	−	0.775672i	$-0.717411\pi$
$907$	−2.83647e10			−1.26227			−0.631136	+	0.775672i	$0.717411\pi$
$908$			1.11379e9i			0.0493744i
$909$	−4.19302e9			−0.185163
$910$	−4.27858e9	+	4.82689e9i	−0.188215	+	0.212335i
$911$	−1.66106e10			−0.727897			−0.363948	−	0.931419i	$-0.618572\pi$
$911$	−1.66106e10			−0.727897			−0.363948	+	0.931419i	$0.618572\pi$
$912$			1.09411e10i			0.477615i
$913$	4.53129e8			0.0197049
$914$	−2.02656e10			−0.877906
$915$		−	1.59201e10i		−	0.687022i
$916$		−	7.29085e7i		−	0.00313432i
$917$			3.37374e9i			0.144484i
$918$			2.37539e10i			1.01341i
$919$	8.81367e9			0.374587			0.187293	−	0.982304i	$-0.440029\pi$
$919$	8.81367e9			0.374587			0.187293	+	0.982304i	$0.440029\pi$
$920$	2.29467e9			0.0971543
$921$		−	3.67742e9i		−	0.155108i
$922$	7.66345e9			0.322007
$923$	3.70033e9	−	4.17454e9i	0.154894	−	0.174744i
$924$	2.22963e7			0.000929782
$925$			1.90534e10i			0.791547i
$926$	2.07202e10			0.857542
$927$	−7.85076e9			−0.323692
$928$			8.59629e8i			0.0353096i
$929$		−	1.83643e10i		−	0.751484i	−0.926724	−	0.375742i	$-0.877388\pi$
$929$		−	1.83643e10i		−	0.751484i	0.926724	−	0.375742i	$-0.122612\pi$
$930$			7.38925e9i			0.301238i
$931$		−	1.58401e9i		−	0.0643330i
$932$	4.01077e7			0.00162283
$933$	3.04431e10			1.22717
$934$		−	2.11600e10i		−	0.849769i
$935$	−1.02836e9			−0.0411439
$936$	−4.37689e9	+	4.93780e9i	−0.174462	+	0.196819i
$937$	4.29852e10			1.70699			0.853494	−	0.521103i	$-0.174479\pi$
$937$	4.29852e10			1.70699			0.853494	+	0.521103i	$0.174479\pi$
$938$			9.32945e9i			0.369102i
$939$	−2.57315e10			−1.01423
$940$	−1.32143e9			−0.0518914
$941$		−	5.23951e9i		−	0.204987i	−0.994734	−	0.102494i	$-0.967318\pi$
$941$		−	5.23951e9i		−	0.204987i	0.994734	−	0.102494i	$-0.0326821\pi$
$942$			5.86566e9i			0.228633i
$943$		−	1.53800e9i		−	0.0597262i
$944$		−	2.33315e10i		−	0.902695i
$945$	6.29654e9			0.242712
$946$	1.72343e9			0.0661873
$947$		−	4.65738e10i		−	1.78204i	−0.453966	−	0.891019i	$-0.649991\pi$
$947$		−	4.65738e10i		−	1.78204i	0.453966	−	0.891019i	$-0.350009\pi$
$948$	2.10391e9			0.0802042
$949$	2.19007e10	−	2.47074e10i	0.831815	−	0.938414i
$950$	4.70508e9			0.178047
$951$			1.98817e10i			0.749587i
$952$	−1.28673e10			−0.483348
$953$	−5.70083e8			−0.0213360			−0.0106680	−	0.999943i	$-0.503396\pi$
$953$	−5.70083e8			−0.0213360			−0.0106680	+	0.999943i	$0.503396\pi$
$954$		−	5.80577e9i		−	0.216491i
$955$		−	1.26085e10i		−	0.468438i
$956$		−	7.04151e8i		−	0.0260653i
$957$			4.47292e8i			0.0164968i
$958$	3.76589e10			1.38385
$959$	1.20494e10			0.441165
$960$		−	2.47750e10i		−	0.903784i
$961$	2.39880e10			0.871890
$962$	−3.92459e10	−	3.47878e10i	−1.42129	−	1.25984i
$963$	−1.17157e10			−0.422743
$964$		−	8.89404e8i		−	0.0319764i
$965$	1.17014e10			0.419171
$966$	1.42335e9			0.0508034
$967$			3.67106e10i			1.30556i	0.757546	+	0.652782i	$0.226398\pi$
$967$			3.67106e10i			1.30556i	−0.757546	+	0.652782i	$0.773602\pi$
$968$		−	2.88448e10i		−	1.02212i
$969$			1.78574e10i			0.630499i
$970$		−	1.41348e9i		−	0.0497266i
$971$	1.79289e10			0.628471			0.314236	−	0.949345i	$-0.398252\pi$
$971$	1.79289e10			0.628471			0.314236	+	0.949345i	$0.398252\pi$
$972$	7.37735e8			0.0257673
$973$		−	1.38045e10i		−	0.480425i
$974$	8.33289e9			0.288961
$975$	9.85592e9	+	8.73633e9i	0.340550	+	0.301865i
$976$	2.18468e10			0.752165
$977$			4.89033e10i			1.67767i	0.544384	+	0.838836i	$0.316763\pi$
$977$			4.89033e10i			1.67767i	−0.544384	+	0.838836i	$0.683237\pi$
$978$	3.36369e10			1.14982
$979$	−4.93181e8			−0.0167984
$980$			1.66544e8i			0.00565247i
$981$		−	2.36072e9i		−	0.0798368i
$982$			3.33786e10i			1.12481i
$983$			1.08703e10i			0.365011i	0.983205	+	0.182505i	$0.0584207\pi$
$983$			1.08703e10i			0.365011i	−0.983205	+	0.182505i	$0.941579\pi$
$984$	−1.66473e10			−0.557007
$985$	−2.43458e9			−0.0811705
$986$		−	1.26044e10i		−	0.418747i
$987$	−1.67866e10			−0.555714
$988$	4.64861e8	−	5.24434e8i	0.0153346	−	0.0172998i
$989$	−5.95355e9			−0.195699
$990$		−	2.51623e8i		−	0.00824189i
$991$	4.02699e10			1.31438			0.657192	−	0.753723i	$-0.271744\pi$
$991$	4.02699e10			1.31438			0.657192	+	0.753723i	$0.271744\pi$
$992$	1.12873e9			0.0367113
$993$		−	2.88330e10i		−	0.934475i
$994$			2.66176e9i			0.0859639i
$995$			3.63866e10i			1.17101i
$996$			8.27305e8i			0.0265313i
$997$	1.93735e10			0.619122			0.309561	−	0.950880i	$-0.399818\pi$
$997$	1.93735e10			0.619122			0.309561	+	0.950880i	$0.399818\pi$
$998$	−4.53586e10			−1.44445
$999$			5.11952e10i			1.62461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.15	✓	50
13.12	even	2	inner	91.8.c.a.64.36	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.15	✓	50	1.1	even	1	trivial
91.8.c.a.64.36	yes	50	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.0195i q^{2} -52.4283 q^{3} +6.57091 q^{4} -215.435i q^{5} +577.733i q^{6} +343.000i q^{7} -1482.90i q^{8} +561.727 q^{9} +O(q^{10})\)	\(q-11.0195i q^{2} -52.4283 q^{3} +6.57091 q^{4} -215.435i q^{5} +577.733i q^{6} +343.000i q^{7} -1482.90i q^{8} +561.727 q^{9} -2373.98 q^{10} +188.689i q^{11} -344.502 q^{12} +(-5927.83 - 5254.46i) q^{13} +3779.68 q^{14} +11294.9i q^{15} -15499.7 q^{16} -25297.8 q^{17} -6189.94i q^{18} +13463.9i q^{19} -1415.60i q^{20} -17982.9i q^{21} +2079.26 q^{22} -7182.76 q^{23} +77746.1i q^{24} +31712.9 q^{25} +(-57901.4 + 65321.7i) q^{26} +85210.3 q^{27} +2253.82i q^{28} -45214.5 q^{29} +124464. q^{30} +59368.7i q^{31} -19012.2i q^{32} -9892.67i q^{33} +278768. i q^{34} +73894.1 q^{35} +3691.06 q^{36} +600810. i q^{37} +148365. q^{38} +(310786. + 275482. i) q^{39} -319469. q^{40} +214124. i q^{41} -198162. q^{42} +828867. q^{43} +1239.86i q^{44} -121015. i q^{45} +79150.3i q^{46} -933473. i q^{47} +812625. q^{48} -117649. q^{49} -349459. i q^{50} +1.32632e6 q^{51} +(-38951.2 - 34526.6i) q^{52} +937937. q^{53} -938974. i q^{54} +40650.3 q^{55} +508636. q^{56} -705888. i q^{57} +498241. i q^{58} +1.50528e6i q^{59} +74217.6i q^{60} -1.40949e6 q^{61} +654212. q^{62} +192672. i q^{63} -2.19347e6 q^{64} +(-1.13199e6 + 1.27706e6i) q^{65} -109012. q^{66} +2.46831e6i q^{67} -166229. q^{68} +376580. q^{69} -814275. i q^{70} +704227. i q^{71} -832986. i q^{72} +4.16803e6i q^{73} +6.62062e6 q^{74} -1.66265e6 q^{75} +88469.8i q^{76} -64720.5 q^{77} +(3.03567e6 - 3.42470e6i) q^{78} -6.10710e6 q^{79} +3.33918e6i q^{80} -5.69593e6 q^{81} +2.35953e6 q^{82} -2.40146e6i q^{83} -118164. i q^{84} +5.45002e6i q^{85} -9.13369e6i q^{86} +2.37052e6 q^{87} +279808. q^{88} +2.61372e6i q^{89} -1.33353e6 q^{90} +(1.80228e6 - 2.03325e6i) q^{91} -47197.2 q^{92} -3.11260e6i q^{93} -1.02864e7 q^{94} +2.90058e6 q^{95} +996780. i q^{96} +595405. i q^{97} +1.29643e6i q^{98} +105992. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 50 * q - 3328 * q^4 + 40514 * q^9	\( 50 q - 3328 q^{4} + 40514 q^{9} + 5320 q^{10} + 8700 q^{12} + 17044 q^{13} + 10976 q^{14} + 228808 q^{16} + 33664 q^{17} + 70228 q^{22} - 75042 q^{23} - 664772 q^{25} + 78276 q^{26} - 661404 q^{27} + 135778 q^{29} + 994888 q^{30} + 372498 q^{35} - 3549604 q^{36} + 338468 q^{38} - 973080 q^{39} + 79316 q^{40} + 296352 q^{42} - 53618 q^{43} + 1400384 q^{48} - 5882450 q^{49} - 2182360 q^{51} - 6982340 q^{52} + 2841746 q^{53} + 6871356 q^{55} - 2107392 q^{56} + 1773716 q^{61} - 6969608 q^{62} - 9449120 q^{64} - 7901430 q^{65} - 11755548 q^{66} + 11829980 q^{68} + 3564460 q^{69} + 45595884 q^{74} - 7220964 q^{75} + 186592 q^{77} - 8093012 q^{78} - 21257822 q^{79} + 53034530 q^{81} + 10907568 q^{82} + 14135000 q^{87} - 51594780 q^{88} - 61226356 q^{90} - 8096858 q^{91} - 11200212 q^{92} + 80667028 q^{94} + 30430066 q^{95}+O(q^{100}) \) 50 * q - 3328 * q^4 + 40514 * q^9 + 5320 * q^10 + 8700 * q^12 + 17044 * q^13 + 10976 * q^14 + 228808 * q^16 + 33664 * q^17 + 70228 * q^22 - 75042 * q^23 - 664772 * q^25 + 78276 * q^26 - 661404 * q^27 + 135778 * q^29 + 994888 * q^30 + 372498 * q^35 - 3549604 * q^36 + 338468 * q^38 - 973080 * q^39 + 79316 * q^40 + 296352 * q^42 - 53618 * q^43 + 1400384 * q^48 - 5882450 * q^49 - 2182360 * q^51 - 6982340 * q^52 + 2841746 * q^53 + 6871356 * q^55 - 2107392 * q^56 + 1773716 * q^61 - 6969608 * q^62 - 9449120 * q^64 - 7901430 * q^65 - 11755548 * q^66 + 11829980 * q^68 + 3564460 * q^69 + 45595884 * q^74 - 7220964 * q^75 + 186592 * q^77 - 8093012 * q^78 - 21257822 * q^79 + 53034530 * q^81 + 10907568 * q^82 + 14135000 * q^87 - 51594780 * q^88 - 61226356 * q^90 - 8096858 * q^91 - 11200212 * q^92 + 80667028 * q^94 + 30430066 * q^95

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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