LMFDB - Embedded newform 91.8.c.a.64.3

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			64.3
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.4516i q^{2} -67.6652 q^{3} -290.269 q^{4} +268.414i q^{5} +1383.86i q^{6} -343.000i q^{7} +3318.67i q^{8} +2391.58 q^{9} +O(q^{10})$	\(q-20.4516i q^{2} -67.6652 q^{3} -290.269 q^{4} +268.414i q^{5} +1383.86i q^{6} -343.000i q^{7} +3318.67i q^{8} +2391.58 q^{9} +5489.50 q^{10} +4031.07i q^{11} +19641.1 q^{12} +(-3009.06 - 7327.62i) q^{13} -7014.91 q^{14} -18162.3i q^{15} +30717.8 q^{16} +3670.35 q^{17} -48911.8i q^{18} +49826.2i q^{19} -77912.3i q^{20} +23209.2i q^{21} +82442.0 q^{22} -46382.0 q^{23} -224559. i q^{24} +6078.93 q^{25} +(-149862. + 61540.2i) q^{26} -13843.2 q^{27} +99562.4i q^{28} -83198.9 q^{29} -371449. q^{30} -188525. i q^{31} -203439. i q^{32} -272764. i q^{33} -75064.7i q^{34} +92066.0 q^{35} -694203. q^{36} +497724. i q^{37} +1.01903e6 q^{38} +(203609. + 495825. i) q^{39} -890778. q^{40} -652718. i q^{41} +474666. q^{42} +150546. q^{43} -1.17010e6i q^{44} +641935. i q^{45} +948588. i q^{46} +360426. i q^{47} -2.07853e6 q^{48} -117649. q^{49} -124324. i q^{50} -248355. q^{51} +(873438. + 2.12698e6i) q^{52} -524455. q^{53} +283117. i q^{54} -1.08200e6 q^{55} +1.13830e6 q^{56} -3.37150e6i q^{57} +1.70155e6i q^{58} -1.52938e6i q^{59} +5.27196e6i q^{60} -2.72450e6 q^{61} -3.85563e6 q^{62} -820313. i q^{63} -228780. q^{64} +(1.96684e6 - 807674. i) q^{65} -5.57846e6 q^{66} -1.22199e6i q^{67} -1.06539e6 q^{68} +3.13845e6 q^{69} -1.88290e6i q^{70} -2.61312e6i q^{71} +7.93688e6i q^{72} -4.01722e6i q^{73} +1.01793e7 q^{74} -411332. q^{75} -1.44630e7i q^{76} +1.38266e6 q^{77} +(1.01404e7 - 4.16413e6i) q^{78} +7.40505e6 q^{79} +8.24508e6i q^{80} -4.29369e6 q^{81} -1.33492e7 q^{82} -1.71703e6i q^{83} -6.73691e6i q^{84} +985175. i q^{85} -3.07892e6i q^{86} +5.62967e6 q^{87} -1.33778e7 q^{88} -1.29971e6i q^{89} +1.31286e7 q^{90} +(-2.51338e6 + 1.03211e6i) q^{91} +1.34633e7 q^{92} +1.27566e7i q^{93} +7.37131e6 q^{94} -1.33741e7 q^{95} +1.37657e7i q^{96} -5.54671e6i q^{97} +2.40611e6i q^{98} +9.64065e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	20.4516i		−	1.80769i	−0.427864	−	0.903843i	$-0.640734\pi$
$2$		−	20.4516i		−	1.80769i	0.427864	−	0.903843i	$-0.359266\pi$
$3$	−67.6652			−1.44691			−0.723454	−	0.690372i	$-0.757447\pi$
$3$	−67.6652			−1.44691			−0.723454	+	0.690372i	$0.757447\pi$
$4$	−290.269			−2.26773
$5$			268.414i			0.960307i	0.877184	+	0.480154i	$0.159419\pi$
$5$			268.414i			0.960307i	−0.877184	+	0.480154i	$0.840581\pi$
$6$			1383.86i			2.61556i
$7$		−	343.000i		−	0.377964i
$7$		−	343.000i		−	0.377964i
$8$			3318.67i			2.29166i
$9$	2391.58			1.09355
$10$	5489.50			1.73593
$11$			4031.07i			0.913159i	0.889683	+	0.456579i	$0.150926\pi$
$11$			4031.07i			0.913159i	−0.889683	+	0.456579i	$0.849074\pi$
$12$	19641.1			3.28120
$13$	−3009.06	−	7327.62i	−0.379865	−	0.925042i
$13$	−3009.06	−	7327.62i	−0.379865	−	0.925042i
$14$	−7014.91			−0.683241
$15$		−	18162.3i		−	1.38948i
$16$	30717.8			1.87486
$17$	3670.35			0.181191			0.0905955	−	0.995888i	$-0.471123\pi$
$17$	3670.35			0.181191			0.0905955	+	0.995888i	$0.471123\pi$
$18$		−	48911.8i		−	1.97679i
$19$			49826.2i			1.66656i	0.552853	+	0.833279i	$0.313539\pi$
$19$			49826.2i			1.66656i	−0.552853	+	0.833279i	$0.686461\pi$
$20$		−	77912.3i		−	2.17772i
$21$			23209.2i			0.546880i
$22$	82442.0			1.65070
$23$	−46382.0			−0.794881			−0.397441	−	0.917628i	$-0.630102\pi$
$23$	−46382.0			−0.794881			−0.397441	+	0.917628i	$0.630102\pi$
$24$		−	224559.i		−	3.31582i
$25$	6078.93			0.0778103
$26$	−149862.	+	61540.2i	−1.67219	+	0.686676i
$27$	−13843.2			−0.135352
$28$			99562.4i			0.857121i
$29$	−83198.9			−0.633468			−0.316734	−	0.948514i	$-0.602586\pi$
$29$	−83198.9			−0.633468			−0.316734	+	0.948514i	$0.602586\pi$
$30$	−371449.			−2.51174
$31$		−	188525.i		−	1.13659i	−0.822827	−	0.568293i	$-0.807604\pi$
$31$		−	188525.i		−	1.13659i	0.822827	−	0.568293i	$-0.192396\pi$
$32$		−	203439.i		−	1.09751i
$33$		−	272764.i		−	1.32126i
$34$		−	75064.7i		−	0.327537i
$35$	92066.0			0.362962
$36$	−694203.			−2.47986
$37$			497724.i			1.61541i	0.589588	+	0.807704i	$0.299290\pi$
$37$			497724.i			1.61541i	−0.589588	+	0.807704i	$0.700710\pi$
$38$	1.01903e6			3.01261
$39$	203609.	+	495825.i	0.549630	+	1.33845i
$40$	−890778.			−2.20069
$41$		−	652718.i		−	1.47905i	−0.673130	−	0.739524i	$-0.735051\pi$
$41$		−	652718.i		−	1.47905i	0.673130	−	0.739524i	$-0.264949\pi$
$42$	474666.			0.988588
$43$	150546.			0.288756			0.144378	−	0.989523i	$-0.453882\pi$
$43$	150546.			0.288756			0.144378	+	0.989523i	$0.453882\pi$
$44$		−	1.17010e6i		−	2.07080i
$45$			641935.i			1.05014i
$46$			948588.i			1.43690i
$47$			360426.i			0.506377i	0.967417	+	0.253188i	$0.0814793\pi$
$47$			360426.i			0.506377i	−0.967417	+	0.253188i	$0.918521\pi$
$48$	−2.07853e6			−2.71276
$49$	−117649.			−0.142857
$50$		−	124324.i		−	0.140657i
$51$	−248355.			−0.262167
$52$	873438.	+	2.12698e6i	0.861430	+	2.09774i
$53$	−524455.			−0.483885			−0.241943	−	0.970291i	$-0.577785\pi$
$53$	−524455.			−0.483885			−0.241943	+	0.970291i	$0.577785\pi$
$54$			283117.i			0.244674i
$55$	−1.08200e6			−0.876913
$56$	1.13830e6			0.866164
$57$		−	3.37150e6i		−	2.41136i
$58$			1.70155e6i			1.14511i
$59$		−	1.52938e6i		−	0.969469i	−0.874661	−	0.484734i	$-0.838916\pi$
$59$		−	1.52938e6i		−	0.969469i	0.874661	−	0.484734i	$-0.161084\pi$
$60$			5.27196e6i			3.15096i
$61$	−2.72450e6			−1.53686			−0.768428	−	0.639936i	$-0.778961\pi$
$61$	−2.72450e6			−1.53686			−0.768428	+	0.639936i	$0.778961\pi$
$62$	−3.85563e6			−2.05459
$63$		−	820313.i		−	0.413321i
$64$	−228780.			−0.109091
$65$	1.96684e6	−	807674.i	0.888324	−	0.364787i
$66$	−5.57846e6			−2.38842
$67$		−	1.22199e6i		−	0.496369i	−0.968713	−	0.248185i	$-0.920166\pi$
$67$		−	1.22199e6i		−	0.496369i	0.968713	−	0.248185i	$-0.0798340\pi$
$68$	−1.06539e6			−0.410892
$69$	3.13845e6			1.15012
$70$		−	1.88290e6i		−	0.656121i
$71$		−	2.61312e6i		−	0.866472i	−0.901280	−	0.433236i	$-0.857372\pi$
$71$		−	2.61312e6i		−	0.866472i	0.901280	−	0.433236i	$-0.142628\pi$
$72$			7.93688e6i			2.50603i
$73$		−	4.01722e6i		−	1.20864i	−0.796743	−	0.604318i	$-0.793446\pi$
$73$		−	4.01722e6i		−	1.20864i	0.796743	−	0.604318i	$-0.206554\pi$
$74$	1.01793e7			2.92015
$75$	−411332.			−0.112584
$76$		−	1.44630e7i		−	3.77930i
$77$	1.38266e6			0.345142
$78$	1.01404e7	−	4.16413e6i	2.41950	−	0.993558i
$79$	7.40505e6			1.68979			0.844895	−	0.534932i	$-0.179663\pi$
$79$	7.40505e6			1.68979			0.844895	+	0.534932i	$0.179663\pi$
$80$			8.24508e6i			1.80045i
$81$	−4.29369e6			−0.897704
$82$	−1.33492e7			−2.67366
$83$		−	1.71703e6i		−	0.329612i	−0.986326	−	0.164806i	$-0.947300\pi$
$83$		−	1.71703e6i		−	0.329612i	0.986326	−	0.164806i	$-0.0526999\pi$
$84$		−	6.73691e6i		−	1.24018i
$85$			985175.i			0.173999i
$86$		−	3.07892e6i		−	0.521979i
$87$	5.62967e6			0.916571
$88$	−1.33778e7			−2.09264
$89$		−	1.29971e6i		−	0.195425i	−0.995215	−	0.0977127i	$-0.968847\pi$
$89$		−	1.29971e6i		−	0.195425i	0.995215	−	0.0977127i	$-0.0311526\pi$
$90$	1.31286e7			1.89832
$91$	−2.51338e6	+	1.03211e6i	−0.349633	+	0.143575i
$92$	1.34633e7			1.80258
$93$			1.27566e7i			1.64454i
$94$	7.37131e6			0.915371
$95$	−1.33741e7			−1.60041
$96$			1.37657e7i			1.58800i
$97$		−	5.54671e6i		−	0.617070i	−0.951213	−	0.308535i	$-0.900161\pi$
$97$		−	5.54671e6i		−	0.617070i	0.951213	−	0.308535i	$-0.0998386\pi$
$98$			2.40611e6i			0.258241i
$99$			9.64065e6i			0.998581i
$100$	−1.76453e6			−0.176453
$101$	−8.89656e6			−0.859206			−0.429603	−	0.903018i	$-0.641347\pi$
$101$	−8.89656e6			−0.859206			−0.429603	+	0.903018i	$0.641347\pi$
$102$			5.07927e6i			0.473916i
$103$	1.94148e7			1.75066			0.875332	−	0.483522i	$-0.160643\pi$
$103$	1.94148e7			1.75066			0.875332	+	0.483522i	$0.160643\pi$
$104$	2.43180e7	−	9.98608e6i	2.11988	−	0.870519i
$105$	−6.22967e6			−0.525173
$106$			1.07260e7i			0.874713i
$107$	1.02274e7			0.807089			0.403545	−	0.914960i	$-0.367778\pi$
$107$	1.02274e7			0.807089			0.403545	+	0.914960i	$0.367778\pi$
$108$	4.01827e6			0.306942
$109$		−	4.74097e6i		−	0.350650i	−0.984511	−	0.175325i	$-0.943902\pi$
$109$		−	4.74097e6i		−	0.350650i	0.984511	−	0.175325i	$-0.0560977\pi$
$110$			2.21286e7i			1.58518i
$111$		−	3.36786e7i		−	2.33735i
$112$		−	1.05362e7i		−	0.708632i
$113$	8.63044e6			0.562676			0.281338	−	0.959609i	$-0.409222\pi$
$113$	8.63044e6			0.562676			0.281338	+	0.959609i	$0.409222\pi$
$114$	−6.89527e7			−4.35898
$115$		−	1.24496e7i		−	0.763330i
$116$	2.41501e7			1.43653
$117$	−7.19642e6	−	1.75246e7i	−0.415400	−	1.01158i
$118$	−3.12783e7			−1.75249
$119$		−	1.25893e6i		−	0.0684838i
$120$	6.02747e7			3.18420
$121$	3.23762e6			0.166141
$122$			5.57206e7i			2.77815i
$123$			4.41663e7i			2.14005i
$124$			5.47229e7i			2.57747i
$125$			2.26015e7i			1.03503i
$126$	−1.67767e7			−0.747155
$127$	4.20838e7			1.82306			0.911531	−	0.411231i	$-0.134901\pi$
$127$	4.20838e7			1.82306			0.911531	+	0.411231i	$0.134901\pi$
$128$		−	2.13612e7i		−	0.900309i
$129$	−1.01867e7			−0.417803
$130$	−1.65182e7	−	4.02250e7i	−0.659420	−	1.60581i
$131$	3.28307e7			1.27594			0.637970	−	0.770061i	$-0.279774\pi$
$131$	3.28307e7			1.27594			0.637970	+	0.770061i	$0.279774\pi$
$132$			7.91749e7i			2.99625i
$133$	1.70904e7			0.629900
$134$	−2.49916e7			−0.897280
$135$		−	3.71572e6i		−	0.129979i
$136$			1.21807e7i			0.415227i
$137$			4.86626e7i			1.61686i	0.588590	+	0.808432i	$0.299683\pi$
$137$			4.86626e7i			1.61686i	−0.588590	+	0.808432i	$0.700317\pi$
$138$		−	6.41864e7i		−	2.07906i
$139$	−4.19124e7			−1.32370			−0.661852	−	0.749634i	$-0.730229\pi$
$139$	−4.19124e7			−1.32370			−0.661852	+	0.749634i	$0.730229\pi$
$140$	−2.67239e7			−0.823099
$141$		−	2.43883e7i		−	0.732681i
$142$	−5.34425e7			−1.56631
$143$	2.95382e7	−	1.21297e7i	0.844710	−	0.346877i
$144$	7.34642e7			2.05025
$145$		−	2.23318e7i		−	0.608324i
$146$	−8.21587e7			−2.18483
$147$	7.96075e6			0.206701
$148$		−	1.44474e8i		−	3.66331i
$149$			1.11660e7i			0.276533i	0.990395	+	0.138267i	$0.0441531\pi$
$149$			1.11660e7i			0.276533i	−0.990395	+	0.138267i	$0.955847\pi$
$150$			8.41241e6i			0.203517i
$151$		−	5.41762e7i		−	1.28053i	−0.768155	−	0.640264i	$-0.778825\pi$
$151$		−	5.41762e7i		−	1.28053i	0.768155	−	0.640264i	$-0.221175\pi$
$152$	−1.65357e8			−3.81918
$153$	8.77796e6			0.198141
$154$		−	2.82776e7i		−	0.623908i
$155$	5.06026e7			1.09147
$156$	−5.91014e7	−	1.43923e8i	−1.24641	−	3.03524i
$157$	6.26778e7			1.29260			0.646301	−	0.763083i	$-0.276315\pi$
$157$	6.26778e7			1.29260			0.646301	+	0.763083i	$0.276315\pi$
$158$		−	1.51445e8i		−	3.05461i
$159$	3.54874e7			0.700138
$160$	5.46058e7			1.05395
$161$			1.59090e7i			0.300437i
$162$			8.78129e7i			1.62277i
$163$		−	1.96612e7i		−	0.355593i	−0.984067	−	0.177796i	$-0.943103\pi$
$163$		−	1.96612e7i		−	0.355593i	0.984067	−	0.177796i	$-0.0568969\pi$
$164$			1.89464e8i			3.35408i
$165$	7.32135e7			1.26881
$166$	−3.51160e7			−0.595836
$167$		−	1.05116e8i		−	1.74647i	−0.487303	−	0.873233i	$-0.662019\pi$
$167$		−	1.05116e8i		−	1.74647i	0.487303	−	0.873233i	$-0.337981\pi$
$168$	−7.70236e7			−1.25326
$169$	−4.46396e7	+	4.40985e7i	−0.711405	+	0.702782i
$170$	2.01484e7			0.314536
$171$			1.19164e8i			1.82246i
$172$	−4.36989e7			−0.654819
$173$	−6.36120e7			−0.934066			−0.467033	−	0.884240i	$-0.654677\pi$
$173$	−6.36120e7			−0.934066			−0.467033	+	0.884240i	$0.654677\pi$
$174$		−	1.15136e8i		−	1.65687i
$175$		−	2.08507e6i		−	0.0294095i
$176$			1.23826e8i			1.71205i
$177$			1.03486e8i			1.40273i
$178$	−2.65812e7			−0.353268
$179$	−2.22004e7			−0.289318			−0.144659	−	0.989482i	$-0.546209\pi$
$179$	−2.22004e7			−0.289318			−0.144659	+	0.989482i	$0.546209\pi$
$180$		−	1.86334e8i		−	2.38143i
$181$	−1.56041e7			−0.195598			−0.0977991	−	0.995206i	$-0.531180\pi$
$181$	−1.56041e7			−0.195598			−0.0977991	+	0.995206i	$0.531180\pi$
$182$	2.11083e7	+	5.14026e7i	0.259539	+	0.632027i
$183$	1.84354e8			2.22369
$184$		−	1.53927e8i		−	1.82159i
$185$	−1.33596e8			−1.55129
$186$	2.60892e8			2.97280
$187$			1.47955e7i			0.165456i
$188$		−	1.04621e8i		−	1.14833i
$189$			4.74823e6i			0.0511582i
$190$			2.73521e8i			2.89303i
$191$	−8.47751e7			−0.880342			−0.440171	−	0.897914i	$-0.645082\pi$
$191$	−8.47751e7			−0.880342			−0.440171	+	0.897914i	$0.645082\pi$
$192$	1.54804e7			0.157844
$193$		−	2.41523e7i		−	0.241829i	−0.992663	−	0.120915i	$-0.961417\pi$
$193$		−	2.41523e7i		−	0.241829i	0.992663	−	0.120915i	$-0.0385827\pi$
$194$	−1.13439e8			−1.11547
$195$	−1.33086e8	+	5.46514e7i	−1.28532	+	0.527813i
$196$	3.41499e7			0.323961
$197$			9.47899e7i			0.883345i	0.897176	+	0.441672i	$0.145615\pi$
$197$			9.47899e7i			0.883345i	−0.897176	+	0.441672i	$0.854385\pi$
$198$	1.97167e8			1.80512
$199$	1.51915e8			1.36651			0.683257	−	0.730178i	$-0.260563\pi$
$199$	1.51915e8			1.36651			0.683257	+	0.730178i	$0.260563\pi$
$200$			2.01740e7i			0.178314i
$201$			8.26860e7i			0.718201i
$202$			1.81949e8i			1.55317i
$203$			2.85372e7i			0.239428i
$204$	7.20899e7			0.594524
$205$	1.75199e8			1.42034
$206$		−	3.97064e8i		−	3.16465i
$207$	−1.10927e8			−0.869239
$208$	−9.24316e7	−	2.25088e8i	−0.712195	−	1.73433i
$209$	−2.00853e8			−1.52183
$210$			1.27407e8i			0.949348i
$211$	−5.28202e7			−0.387089			−0.193545	−	0.981091i	$-0.561998\pi$
$211$	−5.28202e7			−0.387089			−0.193545	+	0.981091i	$0.561998\pi$
$212$	1.52233e8			1.09732
$213$			1.76817e8i			1.25371i
$214$		−	2.09167e8i		−	1.45896i
$215$			4.04087e7i			0.277294i
$216$		−	4.59412e7i		−	0.310180i
$217$	−6.46639e7			−0.429589
$218$	−9.69606e7			−0.633866
$219$			2.71826e8i			1.74879i
$220$	3.14070e8			1.98860
$221$	−1.10443e7	−	2.68950e7i	−0.0688281	−	0.167609i
$222$	−6.88782e8			−4.22519
$223$			2.17916e8i			1.31590i	0.753062	+	0.657949i	$0.228576\pi$
$223$			2.17916e8i			1.31590i	−0.753062	+	0.657949i	$0.771424\pi$
$224$	−6.97795e7			−0.414820
$225$	1.45383e7			0.0850891
$226$		−	1.76506e8i		−	1.01714i
$227$			1.61829e8i			0.918260i	0.888369	+	0.459130i	$0.151839\pi$
$227$			1.61829e8i			0.918260i	−0.888369	+	0.459130i	$0.848161\pi$
$228$			9.78644e8i			5.46830i
$229$		−	2.58522e8i		−	1.42257i	−0.702903	−	0.711286i	$-0.748113\pi$
$229$		−	2.58522e8i		−	1.42257i	0.702903	−	0.711286i	$-0.251887\pi$
$230$	−2.54614e8			−1.37986
$231$	−9.35579e7			−0.499388
$232$		−	2.76110e8i		−	1.45169i
$233$	1.89235e8			0.980065			0.490032	−	0.871704i	$-0.336985\pi$
$233$	1.89235e8			0.980065			0.490032	+	0.871704i	$0.336985\pi$
$234$	−3.58407e8	+	1.47179e8i	−1.82861	+	0.750912i
$235$	−9.67435e7			−0.486277
$236$			4.43932e8i			2.19849i
$237$	−5.01064e8			−2.44497
$238$	−2.57472e7			−0.123797
$239$			6.88046e7i			0.326005i	0.986626	+	0.163003i	$0.0521179\pi$
$239$			6.88046e7i			0.326005i	−0.986626	+	0.163003i	$0.947882\pi$
$240$		−	5.57905e8i		−	2.60508i
$241$		−	3.75221e8i		−	1.72674i	−0.504570	−	0.863371i	$-0.668349\pi$
$241$		−	3.75221e8i		−	1.72674i	0.504570	−	0.863371i	$-0.331651\pi$
$242$		−	6.62146e7i		−	0.300331i
$243$	3.20809e8			1.43425
$244$	7.90840e8			3.48517
$245$		−	3.15786e7i		−	0.137187i
$246$	9.03274e8			3.86854
$247$	3.65108e8	−	1.49930e8i	1.54164	−	0.633067i
$248$	6.25651e8			2.60466
$249$			1.16183e8i			0.476919i
$250$	4.62238e8			1.87101
$251$	3.98262e8			1.58968			0.794842	−	0.606816i	$-0.207554\pi$
$251$	3.98262e8			1.58968			0.794842	+	0.606816i	$0.207554\pi$
$252$			2.38112e8i			0.937301i
$253$		−	1.86969e8i		−	0.725853i
$254$		−	8.60682e8i		−	3.29552i
$255$		−	6.66621e7i		−	0.251761i
$256$	−4.66156e8			−1.73657
$257$	−1.54942e8			−0.569380			−0.284690	−	0.958620i	$-0.591891\pi$
$257$	−1.54942e8			−0.569380			−0.284690	+	0.958620i	$0.591891\pi$
$258$			2.08336e8i			0.755257i
$259$	1.70719e8			0.610567
$260$	−5.70912e8	+	2.34443e8i	−2.01448	+	0.827238i
$261$	−1.98977e8			−0.692726
$262$		−	6.71441e8i		−	2.30650i
$263$	−2.19882e8			−0.745323			−0.372661	−	0.927967i	$-0.621555\pi$
$263$	−2.19882e8			−0.745323			−0.372661	+	0.927967i	$0.621555\pi$
$264$	9.05212e8			3.02787
$265$		−	1.40771e8i		−	0.464679i
$266$		−	3.49526e8i		−	1.13866i
$267$			8.79451e7i			0.282763i
$268$			3.54705e8i			1.12563i
$269$	1.41976e8			0.444715			0.222357	−	0.974965i	$-0.428625\pi$
$269$	1.41976e8			0.444715			0.222357	+	0.974965i	$0.428625\pi$
$270$	−7.59925e7			−0.234962
$271$			1.84610e8i			0.563461i	0.959494	+	0.281730i	$0.0909083\pi$
$271$			1.84610e8i			0.563461i	−0.959494	+	0.281730i	$0.909092\pi$
$272$	1.12745e8			0.339709
$273$	1.70068e8	−	6.98378e7i	0.505887	−	0.207741i
$274$	9.95229e8			2.92278
$275$			2.45046e7i			0.0710531i
$276$	−9.10996e8			−2.60816
$277$	1.72685e8			0.488176			0.244088	−	0.969753i	$-0.421512\pi$
$277$	1.72685e8			0.488176			0.244088	+	0.969753i	$0.421512\pi$
$278$			8.57178e8i			2.39284i
$279$		−	4.50872e8i		−	1.24291i
$280$			3.05537e8i			0.831784i
$281$		−	2.93020e8i		−	0.787817i	−0.919150	−	0.393908i	$-0.871123\pi$
$281$		−	2.93020e8i		−	0.787817i	0.919150	−	0.393908i	$-0.128877\pi$
$282$	−4.98781e8			−1.32446
$283$	6.75121e7			0.177064			0.0885318	−	0.996073i	$-0.471783\pi$
$283$	6.75121e7			0.177064			0.0885318	+	0.996073i	$0.471783\pi$
$284$			7.58508e8i			1.96492i
$285$	9.04959e8			2.31564
$286$	−2.48073e8	−	6.04104e8i	−0.627045	−	1.52697i
$287$	−2.23882e8			−0.559028
$288$		−	4.86541e8i		−	1.20018i
$289$	−3.96867e8			−0.967170
$290$	−4.56721e8			−1.09966
$291$			3.75319e8i			0.892843i
$292$			1.16607e9i			2.74086i
$293$		−	7.04402e8i		−	1.63600i	−0.575216	−	0.818002i	$-0.695082\pi$
$293$		−	7.04402e8i		−	1.63600i	0.575216	−	0.818002i	$-0.304918\pi$
$294$		−	1.62810e8i		−	0.373651i
$295$	4.10507e8			0.930988
$296$	−1.65178e9			−3.70196
$297$		−	5.58031e7i		−	0.123598i
$298$	2.28364e8			0.499885
$299$	1.39566e8	+	3.39870e8i	0.301947	+	0.735299i
$300$	1.19397e8			0.255311
$301$		−	5.16374e7i		−	0.109139i
$302$	−1.10799e9			−2.31479
$303$	6.01988e8			1.24319
$304$			1.53055e9i			3.12457i
$305$		−	7.31295e8i		−	1.47585i
$306$		−	1.79524e8i		−	0.358176i
$307$			2.46121e7i			0.0485473i	0.999705	+	0.0242736i	$0.00772730\pi$
$307$			2.46121e7i			0.0485473i	−0.999705	+	0.0242736i	$0.992273\pi$
$308$	−4.01343e8			−0.782687
$309$	−1.31371e9			−2.53305
$310$		−	1.03491e9i		−	1.97304i
$311$	2.86963e8			0.540959			0.270479	−	0.962726i	$-0.412818\pi$
$311$	2.86963e8			0.540959			0.270479	+	0.962726i	$0.412818\pi$
$312$	−1.64548e9	+	6.75711e8i	−3.06727	+	1.25956i
$313$	−5.74357e8			−1.05871			−0.529355	−	0.848401i	$-0.677566\pi$
$313$	−5.74357e8			−1.05871			−0.529355	+	0.848401i	$0.677566\pi$
$314$		−	1.28186e9i		−	2.33662i
$315$	2.20184e8			0.396915
$316$	−2.14946e9			−3.83199
$317$			2.35184e8i			0.414667i	0.978270	+	0.207334i	$0.0664785\pi$
$317$			2.35184e8i			0.414667i	−0.978270	+	0.207334i	$0.933521\pi$
$318$		−	7.25774e8i		−	1.26563i
$319$		−	3.35381e8i		−	0.578457i
$320$		−	6.14077e7i		−	0.104761i
$321$	−6.92039e8			−1.16778
$322$	3.25366e8			0.543096
$323$			1.82880e8i			0.301965i
$324$	1.24633e9			2.03575
$325$	−1.82919e7	−	4.45441e7i	−0.0295574	−	0.0719778i
$326$	−4.02103e8			−0.642800
$327$			3.20799e8i			0.507359i
$328$	2.16616e9			3.38947
$329$	1.23626e8			0.191393
$330$		−	1.49734e9i		−	2.29362i
$331$		−	7.11738e8i		−	1.07875i	−0.842064	−	0.539377i	$-0.818660\pi$
$331$		−	7.11738e8i		−	1.07875i	0.842064	−	0.539377i	$-0.181340\pi$
$332$			4.98400e8i			0.747471i
$333$			1.19035e9i			1.76652i
$334$	−2.14979e9			−3.15706
$335$	3.27998e8			0.476667
$336$			7.12934e8i			1.02533i
$337$	1.76464e8			0.251161			0.125580	−	0.992083i	$-0.459921\pi$
$337$	1.76464e8			0.251161			0.125580	+	0.992083i	$0.459921\pi$
$338$	9.01887e8	+	9.12953e8i	1.27041	+	1.28600i
$339$	−5.83980e8			−0.814141
$340$		−	2.85966e8i		−	0.394583i
$341$	7.59956e8			1.03788
$342$	2.43709e9			3.29443
$343$			4.03536e7i			0.0539949i
$344$			4.99614e8i			0.661728i
$345$			8.42404e8i			1.10447i
$346$			1.30097e9i			1.68850i
$347$	9.86378e8			1.26733			0.633666	−	0.773607i	$-0.281549\pi$
$347$	9.86378e8			1.26733			0.633666	+	0.773607i	$0.281549\pi$
$348$	−1.63412e9			−2.07853
$349$			7.96457e8i			1.00294i	0.865176	+	0.501468i	$0.167207\pi$
$349$			7.96457e8i			1.00294i	−0.865176	+	0.501468i	$0.832793\pi$
$350$	−4.26431e7			−0.0531632
$351$	4.16551e7	+	1.01438e8i	0.0514155	+	0.125206i
$352$	8.20077e8			1.00220
$353$		−	3.75710e8i		−	0.454612i	−0.973823	−	0.227306i	$-0.927008\pi$
$353$		−	3.75710e8i		−	0.454612i	0.973823	−	0.227306i	$-0.0729917\pi$
$354$	2.11646e9			2.53570
$355$	7.01397e8			0.832080
$356$			3.77265e8i			0.443172i
$357$			8.51859e7i			0.0990898i
$358$			4.54035e8i			0.522996i
$359$			1.16514e9i			1.32907i	0.747259	+	0.664533i	$0.231369\pi$
$359$			1.16514e9i			1.32907i	−0.747259	+	0.664533i	$0.768631\pi$
$360$	−2.13037e9			−2.40656
$361$	−1.58878e9			−1.77742
$362$			3.19130e8i			0.353580i
$363$	−2.19074e8			−0.240391
$364$	7.29556e8	−	2.99589e8i	0.792873	−	0.325590i
$365$	1.07828e9			1.16066
$366$		−	3.77035e9i		−	4.01973i
$367$	1.82277e8			0.192487			0.0962435	−	0.995358i	$-0.469317\pi$
$367$	1.82277e8			0.192487			0.0962435	+	0.995358i	$0.469317\pi$
$368$	−1.42475e9			−1.49029
$369$		−	1.56103e9i		−	1.61741i
$370$			2.73226e9i			2.80424i
$371$			1.79888e8i			0.182892i
$372$		−	3.70284e9i		−	3.72936i
$373$	4.65622e8			0.464572			0.232286	−	0.972648i	$-0.425379\pi$
$373$	4.65622e8			0.464572			0.232286	+	0.972648i	$0.425379\pi$
$374$	3.02591e8			0.299093
$375$		−	1.52934e9i		−	1.49759i
$376$	−1.19614e9			−1.16044
$377$	2.50351e8	+	6.09650e8i	0.240632	+	0.585984i
$378$	9.71091e7			0.0924780
$379$		−	1.96360e9i		−	1.85275i	−0.376605	−	0.926374i	$-0.622909\pi$
$379$		−	1.96360e9i		−	1.85275i	0.376605	−	0.926374i	$-0.377091\pi$
$380$	3.88208e9			3.62929
$381$	−2.84761e9			−2.63781
$382$			1.73379e9i			1.59138i
$383$		−	9.36181e8i		−	0.851460i	−0.904850	−	0.425730i	$-0.860017\pi$
$383$		−	9.36181e8i		−	0.851460i	0.904850	−	0.425730i	$-0.139983\pi$
$384$			1.44541e9i			1.30267i
$385$			3.71125e8i			0.331442i
$386$	−4.93955e8			−0.437151
$387$	3.60044e8			0.315767
$388$			1.61004e9i			1.39935i
$389$	2.07406e9			1.78648			0.893241	−	0.449578i	$-0.148426\pi$
$389$	2.07406e9			1.78648			0.893241	+	0.449578i	$0.148426\pi$
$390$	1.11771e9	+	2.72184e9i	0.954121	+	2.32346i
$391$	−1.70238e8			−0.144025
$392$		−	3.90438e8i		−	0.327379i
$393$	−2.22149e9			−1.84617
$394$	1.93861e9			1.59681
$395$			1.98762e9i			1.62272i
$396$		−	2.79838e9i		−	2.26451i
$397$		−	1.65387e9i		−	1.32658i	−0.748361	−	0.663292i	$-0.769159\pi$
$397$		−	1.65387e9i		−	1.32658i	0.748361	−	0.663292i	$-0.230841\pi$
$398$		−	3.10690e9i		−	2.47023i
$399$	−1.15643e9			−0.911407
$400$	1.86731e8			0.145884
$401$		−	1.37590e9i		−	1.06557i	−0.846250	−	0.532786i	$-0.821145\pi$
$401$		−	1.37590e9i		−	1.06557i	0.846250	−	0.532786i	$-0.178855\pi$
$402$	1.69106e9			1.29828
$403$	−1.38144e9	+	5.67282e8i	−1.05139	+	0.431749i
$404$	2.58240e9			1.94845
$405$		−	1.15249e9i		−	0.862071i
$406$	5.83633e8			0.432811
$407$	−2.00636e9			−1.47512
$408$		−	8.24210e8i		−	0.600796i
$409$		−	4.95527e8i		−	0.358126i	−0.983838	−	0.179063i	$-0.942693\pi$
$409$		−	4.95527e8i		−	0.358126i	0.983838	−	0.179063i	$-0.0573066\pi$
$410$		−	3.58310e9i		−	2.56753i
$411$		−	3.29277e9i		−	2.33945i
$412$	−5.63552e9			−3.97003
$413$	−5.24578e8			−0.366425
$414$			2.26863e9i			1.57131i
$415$	4.60874e8			0.316529
$416$	−1.49072e9	+	6.12160e8i	−1.01524	+	0.416906i
$417$	2.83601e9			1.91528
$418$			4.10777e9i			2.75099i
$419$	−1.13825e9			−0.755943			−0.377971	−	0.925817i	$-0.623378\pi$
$419$	−1.13825e9			−0.755943			−0.377971	+	0.925817i	$0.623378\pi$
$420$	1.80828e9			1.19095
$421$		−	8.79136e8i		−	0.574207i	−0.957899	−	0.287104i	$-0.907308\pi$
$421$		−	8.79136e8i		−	0.574207i	0.957899	−	0.287104i	$-0.0926924\pi$
$422$			1.08026e9i			0.699736i
$423$			8.61990e8i			0.553746i
$424$		−	1.74049e9i		−	1.10890i
$425$	2.23118e7			0.0140985
$426$	3.61620e9			2.26631
$427$			9.34505e8i			0.580877i
$428$	−2.96870e9			−1.83026
$429$	−1.99871e9	+	8.20762e8i	−1.22222	+	0.501899i
$430$	8.26424e8			0.501260
$431$			1.93447e9i			1.16383i	0.813249	+	0.581916i	$0.197697\pi$
$431$			1.93447e9i			1.16383i	−0.813249	+	0.581916i	$0.802303\pi$
$432$	−4.25234e8			−0.253767
$433$	1.02671e9			0.607773			0.303886	−	0.952708i	$-0.401716\pi$
$433$	1.02671e9			0.607773			0.303886	+	0.952708i	$0.401716\pi$
$434$			1.32248e9i			0.776562i
$435$			1.51108e9i			0.880189i
$436$			1.37616e9i			0.795180i
$437$		−	2.31104e9i		−	1.32472i
$438$	5.55928e9			3.16125
$439$	−1.02647e9			−0.579058			−0.289529	−	0.957169i	$-0.593499\pi$
$439$	−1.02647e9			−0.579058			−0.289529	+	0.957169i	$0.593499\pi$
$440$		−	3.59079e9i		−	2.00958i
$441$	−2.81367e8			−0.156221
$442$	−5.50046e8	+	2.25874e8i	−0.302985	+	0.124420i
$443$	−3.02506e9			−1.65318			−0.826591	−	0.562803i	$-0.809723\pi$
$443$	−3.02506e9			−1.65318			−0.826591	+	0.562803i	$0.809723\pi$
$444$			9.77586e9i			5.30047i
$445$	3.48860e8			0.187668
$446$	4.45674e9			2.37873
$447$		−	7.55552e8i		−	0.400118i
$448$			7.84715e7i			0.0412324i
$449$		−	4.95366e8i		−	0.258264i	−0.991627	−	0.129132i	$-0.958781\pi$
$449$		−	4.95366e8i		−	0.258264i	0.991627	−	0.129132i	$-0.0412191\pi$
$450$		−	2.97331e8i		−	0.153814i
$451$	2.63116e9			1.35061
$452$	−2.50515e9			−1.27600
$453$			3.66585e9i			1.85281i
$454$	3.30966e9			1.65993
$455$	−2.77032e8	−	6.74625e8i	−0.137876	−	0.335755i
$456$	1.11889e10			5.52600
$457$			1.07590e9i			0.527308i	0.964617	+	0.263654i	$0.0849276\pi$
$457$			1.07590e9i			0.527308i	−0.964617	+	0.263654i	$0.915072\pi$
$458$	−5.28721e9			−2.57156
$459$	−5.08096e7			−0.0245246
$460$			3.61373e9i			1.73103i
$461$			1.09855e9i			0.522237i	0.965307	+	0.261118i	$0.0840913\pi$
$461$			1.09855e9i			0.522237i	−0.965307	+	0.261118i	$0.915909\pi$
$462$			1.91341e9i			0.902737i
$463$		−	1.05477e9i		−	0.493884i	−0.969030	−	0.246942i	$-0.920574\pi$
$463$		−	1.05477e9i		−	0.493884i	0.969030	−	0.246942i	$-0.0794257\pi$
$464$	−2.55569e9			−1.18767
$465$	−3.42404e9			−1.57926
$466$		−	3.87016e9i		−	1.77165i
$467$	−5.45292e8			−0.247754			−0.123877	−	0.992298i	$-0.539533\pi$
$467$	−5.45292e8			−0.247754			−0.123877	+	0.992298i	$0.539533\pi$
$468$	2.08890e9	+	5.08686e9i	0.942013	+	2.29398i
$469$	−4.19142e8			−0.187610
$470$			1.97856e9i			0.879037i
$471$	−4.24111e9			−1.87028
$472$	5.07551e9			2.22169
$473$			6.06863e8i			0.263680i
$474$			1.02476e10i			4.41974i
$475$			3.02890e8i			0.129675i
$476$			3.65429e8i			0.155303i
$477$	−1.25428e9			−0.529151
$478$	1.40717e9			0.589315
$479$			3.83715e9i			1.59527i	0.603139	+	0.797636i	$0.293916\pi$
$479$			3.83715e9i			1.59527i	−0.603139	+	0.797636i	$0.706084\pi$
$480$	−3.69492e9			−1.52497
$481$	3.64713e9	−	1.49768e9i	1.49432	−	0.613637i
$482$	−7.67388e9			−3.12141
$483$		−	1.07649e9i		−	0.434705i
$484$	−9.39782e8			−0.376763
$485$	1.48881e9			0.592576
$486$		−	6.56106e9i		−	2.59267i
$487$			1.23905e9i			0.486112i	0.970012	+	0.243056i	$0.0781498\pi$
$487$			1.23905e9i			0.486112i	−0.970012	+	0.243056i	$0.921850\pi$
$488$		−	9.04174e9i		−	3.52194i
$489$			1.33038e9i			0.514510i
$490$	−6.45835e8			−0.247991
$491$	1.02058e9			0.389099			0.194549	−	0.980893i	$-0.437676\pi$
$491$	1.02058e9			0.389099			0.194549	+	0.980893i	$0.437676\pi$
$492$		−	1.28201e10i		−	4.85305i
$493$	−3.05370e8			−0.114779
$494$	−3.06632e9	−	7.46705e9i	−1.14439	−	2.78679i
$495$	−2.58769e9			−0.958944
$496$		−	5.79106e9i		−	2.13094i
$497$	−8.96299e8			−0.327496
$498$	2.37613e9			0.862120
$499$			1.71893e9i			0.619309i	0.950849	+	0.309655i	$0.100213\pi$
$499$			1.71893e9i			0.619309i	−0.950849	+	0.309655i	$0.899787\pi$
$500$		−	6.56052e9i		−	2.34716i
$501$			7.11268e9i			2.52698i
$502$		−	8.14511e9i		−	2.87365i
$503$	5.00341e9			1.75298			0.876492	−	0.481416i	$-0.159877\pi$
$503$	5.00341e9			1.75298			0.876492	+	0.481416i	$0.159877\pi$
$504$	2.72235e9			0.947190
$505$		−	2.38796e9i		−	0.825102i
$506$	−3.82383e9			−1.31211
$507$	3.02055e9	−	2.98394e9i	1.02934	−	1.01686i
$508$	−1.22156e10			−4.13421
$509$		−	2.06978e9i		−	0.695683i	−0.937553	−	0.347841i	$-0.886915\pi$
$509$		−	2.06978e9i		−	0.695683i	0.937553	−	0.347841i	$-0.113085\pi$
$510$	−1.36335e9			−0.455105
$511$	−1.37791e9			−0.456821
$512$			6.79941e9i			2.23886i
$513$		−	6.89757e8i		−	0.225572i
$514$			3.16881e9i			1.02926i
$515$			5.21121e9i			1.68117i
$516$	2.95690e9			0.947464
$517$	−1.45290e9			−0.462403
$518$		−	3.49149e9i		−	1.10371i
$519$	4.30432e9			1.35151
$520$	2.68040e9	+	6.52728e9i	0.835966	+	2.03573i
$521$	2.54969e8			0.0789869			0.0394935	−	0.999220i	$-0.487426\pi$
$521$	2.54969e8			0.0789869			0.0394935	+	0.999220i	$0.487426\pi$
$522$			4.06941e9i			1.25223i
$523$	−7.31235e7			−0.0223512			−0.0111756	−	0.999938i	$-0.503557\pi$
$523$	−7.31235e7			−0.0223512			−0.0111756	+	0.999938i	$0.503557\pi$
$524$	−9.52973e9			−2.89349
$525$			1.41087e8i			0.0425529i
$526$			4.49694e9i			1.34731i
$527$		−	6.91952e8i		−	0.205939i
$528$		−	8.37869e9i		−	2.47718i
$529$	−1.25353e9			−0.368164
$530$	−2.87900e9			−0.839993
$531$		−	3.65764e9i		−	1.06016i
$532$	−4.96082e9			−1.42844
$533$	−4.78288e9	+	1.96407e9i	−1.36818	+	0.561839i
$534$	1.79862e9			0.511146
$535$			2.74517e9i			0.775053i
$536$	4.05537e9			1.13751
$537$	1.50220e9			0.418617
$538$		−	2.90364e9i		−	0.803905i
$539$		−	4.74252e8i		−	0.130451i
$540$			1.07856e9i			0.294758i
$541$			6.31339e9i			1.71424i	0.515115	+	0.857121i	$0.327749\pi$
$541$			6.31339e9i			1.71424i	−0.515115	+	0.857121i	$0.672251\pi$
$542$	3.77558e9			1.01856
$543$	1.05586e9			0.283013
$544$		−	7.46693e8i		−	0.198859i
$545$	1.27254e9			0.336732
$546$	−1.42830e9	−	3.47817e9i	−0.375530	−	0.914485i
$547$	−2.51513e9			−0.657059			−0.328529	−	0.944494i	$-0.606553\pi$
$547$	−2.51513e9			−0.657059			−0.328529	+	0.944494i	$0.606553\pi$
$548$		−	1.41253e10i		−	3.66661i
$549$	−6.51588e9			−1.68062
$550$	5.01159e8			0.128442
$551$		−	4.14549e9i		−	1.05571i
$552$			1.04155e10i			2.63568i
$553$		−	2.53993e9i		−	0.638681i
$554$		−	3.53169e9i		−	0.882468i
$555$	9.03980e9			2.24457
$556$	1.21659e10			3.00180
$557$			7.23785e9i			1.77466i	0.461130	+	0.887332i	$0.347444\pi$
$557$			7.23785e9i			1.77466i	−0.461130	+	0.887332i	$0.652556\pi$
$558$	−9.22108e9			−2.24679
$559$	−4.53003e8	−	1.10315e9i	−0.109688	−	0.267111i
$560$	2.82806e9			0.680504
$561$		−	1.00114e9i		−	0.239400i
$562$	−5.99274e9			−1.42413
$563$	−8.15630e9			−1.92626			−0.963128	−	0.269044i	$-0.913292\pi$
$563$	−8.15630e9			−1.92626			−0.963128	+	0.269044i	$0.913292\pi$
$564$			7.07918e9i			1.66152i
$565$			2.31653e9i			0.540341i
$566$		−	1.38073e9i		−	0.320075i
$567$			1.47274e9i			0.339300i
$568$	8.67208e9			1.98566
$569$	3.49260e8			0.0794797			0.0397398	−	0.999210i	$-0.487347\pi$
$569$	3.49260e8			0.0794797			0.0397398	+	0.999210i	$0.487347\pi$
$570$		−	1.85079e10i		−	4.18596i
$571$	8.33646e9			1.87394			0.936969	−	0.349413i	$-0.113619\pi$
$571$	8.33646e9			1.87394			0.936969	+	0.349413i	$0.113619\pi$
$572$	−8.57403e9	+	3.52089e9i	−1.91557	+	0.786623i
$573$	5.73633e9			1.27378
$574$			4.57876e9i			1.01055i
$575$	−2.81953e8			−0.0618500
$576$	−5.47146e8			−0.119296
$577$			6.57645e8i			0.142520i	0.997458	+	0.0712600i	$0.0227020\pi$
$577$			6.57645e8i			0.142520i	−0.997458	+	0.0712600i	$0.977298\pi$
$578$			8.11658e9i			1.74834i
$579$			1.63427e9i			0.349905i
$580$			6.48222e9i			1.37951i
$581$	−5.88940e8			−0.124582
$582$	7.67589e9			1.61398
$583$		−	2.11412e9i		−	0.441864i
$584$	1.33318e10			2.76978
$585$	4.70386e9	−	1.93162e9i	0.971423	−	0.398911i
$586$	−1.44062e10			−2.95738
$587$		−	6.55135e9i		−	1.33690i	−0.743759	−	0.668448i	$-0.766959\pi$
$587$		−	6.55135e9i		−	1.33690i	0.743759	−	0.668448i	$-0.233041\pi$
$588$	−2.31076e9			−0.468742
$589$	9.39347e9			1.89418
$590$		−	8.39555e9i		−	1.68293i
$591$		−	6.41398e9i		−	1.27812i
$592$			1.52890e10i			3.02867i
$593$		−	7.57440e9i		−	1.49161i	−0.666162	−	0.745807i	$-0.732064\pi$
$593$		−	7.57440e9i		−	1.49161i	0.666162	−	0.745807i	$-0.267936\pi$
$594$	−1.14126e9			−0.223426
$595$	3.37915e8			0.0657655
$596$		−	3.24116e9i		−	0.627102i
$597$	−1.02793e10			−1.97722
$598$	6.95090e9	−	2.85436e9i	1.32919	−	0.545826i
$599$	4.41843e9			0.839990			0.419995	−	0.907526i	$-0.362032\pi$
$599$	4.41843e9			0.839990			0.419995	+	0.907526i	$0.362032\pi$
$600$		−	1.36508e9i		−	0.258005i
$601$	1.35958e9			0.255472			0.127736	−	0.991808i	$-0.459229\pi$
$601$	1.35958e9			0.255472			0.127736	+	0.991808i	$0.459229\pi$
$602$	−1.05607e9			−0.197290
$603$		−	2.92249e9i		−	0.542802i
$604$			1.57257e10i			2.90389i
$605$			8.69023e8i			0.159547i
$606$		−	1.23116e10i		−	2.24730i
$607$	4.58070e9			0.831325			0.415663	−	0.909519i	$-0.363550\pi$
$607$	4.58070e9			0.831325			0.415663	+	0.909519i	$0.363550\pi$
$608$	1.01366e10			1.82907
$609$		−	1.93098e9i		−	0.346431i
$610$	−1.49562e10			−2.66788
$611$	2.64107e9	−	1.08454e9i	0.468420	−	0.192355i
$612$	−2.54797e9			−0.449329
$613$		−	6.60952e9i		−	1.15893i	−0.814996	−	0.579467i	$-0.803261\pi$
$613$		−	6.60952e9i		−	1.15893i	0.814996	−	0.579467i	$-0.196739\pi$
$614$	5.03358e8			0.0877582
$615$	−1.18549e10			−2.05510
$616$			4.58859e9i			0.790945i
$617$			7.12469e9i			1.22115i	0.791959	+	0.610574i	$0.209061\pi$
$617$			7.12469e9i			1.22115i	−0.791959	+	0.610574i	$0.790939\pi$
$618$			2.68675e10i			4.57896i
$619$			2.66019e9i			0.450812i	0.974265	+	0.225406i	$0.0723708\pi$
$619$			2.66019e9i			0.450812i	−0.974265	+	0.225406i	$0.927629\pi$
$620$	−1.46884e10			−2.47516
$621$	6.42078e8			0.107589
$622$		−	5.86885e9i		−	0.977883i
$623$	−4.45800e8			−0.0738638
$624$	6.25441e9	+	1.52307e10i	1.03048	+	2.50942i
$625$	−5.59165e9			−0.916135
$626$			1.17465e10i			1.91381i
$627$	1.35908e10			2.20195
$628$	−1.81934e10			−2.93127
$629$			1.82682e9i			0.292697i
$630$		−	4.50311e9i		−	0.717499i
$631$		−	8.46847e9i		−	1.34184i	−0.741528	−	0.670922i	$-0.765898\pi$
$631$		−	8.46847e9i		−	1.34184i	0.741528	−	0.670922i	$-0.234102\pi$
$632$			2.45749e10i			3.87242i
$633$	3.57409e9			0.560083
$634$	4.80989e9			0.749588
$635$			1.12959e10i			1.75070i
$636$	−1.03009e10			−1.58772
$637$	3.54013e8	+	8.62088e8i	0.0542664	+	0.132149i
$638$	−6.85909e9			−1.04567
$639$		−	6.24949e9i		−	0.947527i
$640$	5.73366e9			0.864573
$641$	2.04426e9			0.306573			0.153287	−	0.988182i	$-0.451014\pi$
$641$	2.04426e9			0.306573			0.153287	+	0.988182i	$0.451014\pi$
$642$			1.41533e10i			2.11099i
$643$			6.20243e9i			0.920076i	0.887899	+	0.460038i	$0.152164\pi$
$643$			6.20243e9i			0.920076i	−0.887899	+	0.460038i	$0.847836\pi$
$644$		−	4.61790e9i		−	0.681309i
$645$		−	2.73427e9i		−	0.401219i
$646$	3.74019e9			0.545859
$647$	7.98319e9			1.15881			0.579404	−	0.815040i	$-0.303285\pi$
$647$	7.98319e9			1.15881			0.579404	+	0.815040i	$0.303285\pi$
$648$		−	1.42493e10i		−	2.05723i
$649$	6.16505e9			0.885279
$650$	−9.11000e8	+	3.74098e8i	−0.130113	+	0.0534305i
$651$	4.37550e9			0.621576
$652$			5.70704e9i			0.806388i
$653$	3.88376e9			0.545829			0.272914	−	0.962038i	$-0.412012\pi$
$653$	3.88376e9			0.545829			0.272914	+	0.962038i	$0.412012\pi$
$654$	6.56086e9			0.917146
$655$			8.81221e9i			1.22529i
$656$		−	2.00501e10i		−	2.77302i
$657$		−	9.60751e9i		−	1.32170i
$658$		−	2.52836e9i		−	0.345978i
$659$	−4.01427e9			−0.546397			−0.273198	−	0.961958i	$-0.588082\pi$
$659$	−4.01427e9			−0.546397			−0.273198	+	0.961958i	$0.588082\pi$
$660$	−2.12516e10			−2.87732
$661$		−	9.05632e9i		−	1.21968i	−0.792524	−	0.609841i	$-0.791233\pi$
$661$		−	9.05632e9i		−	1.21968i	0.792524	−	0.609841i	$-0.208767\pi$
$662$	−1.45562e10			−1.95005
$663$	7.47316e8	+	1.81986e9i	0.0995880	+	0.242515i
$664$	5.69824e9			0.755358
$665$			4.58730e9i			0.604897i
$666$	2.43446e10			3.19332
$667$	3.85893e9			0.503532
$668$			3.05119e10i			3.96051i
$669$		−	1.47453e10i		−	1.90399i
$670$		−	6.70810e9i		−	0.861664i
$671$		−	1.09827e10i		−	1.40339i
$672$	4.72165e9			0.600207
$673$	1.82378e9			0.230632			0.115316	−	0.993329i	$-0.463212\pi$
$673$	1.82378e9			0.230632			0.115316	+	0.993329i	$0.463212\pi$
$674$		−	3.60898e9i		−	0.454019i
$675$	−8.41521e7			−0.0105318
$676$	1.29575e10	−	1.28004e10i	1.61327	−	1.59372i
$677$	5.99874e9			0.743019			0.371509	−	0.928429i	$-0.378840\pi$
$677$	5.99874e9			0.743019			0.371509	+	0.928429i	$0.378840\pi$
$678$			1.19434e10i			1.47171i
$679$	−1.90252e9			−0.233230
$680$	−3.26947e9			−0.398746
$681$		−	1.09502e10i		−	1.32864i
$682$		−	1.55423e10i		−	1.87617i
$683$			1.00738e10i			1.20982i	0.796294	+	0.604909i	$0.206791\pi$
$683$			1.00738e10i			1.20982i	−0.796294	+	0.604909i	$0.793209\pi$
$684$		−	3.45895e10i		−	4.13284i
$685$	−1.30617e10			−1.55269
$686$	8.25297e8			0.0976059
$687$			1.74930e10i			2.05833i
$688$	4.62445e9			0.541378
$689$	1.57812e9	+	3.84301e9i	0.183811	+	0.447614i
$690$	1.72285e10			1.99653
$691$		−	6.71764e8i		−	0.0774540i	−0.999250	−	0.0387270i	$-0.987670\pi$
$691$		−	6.71764e8i		−	0.0774540i	0.999250	−	0.0387270i	$-0.0123303\pi$
$692$	1.84646e10			2.11821
$693$	3.30674e9			0.377428
$694$		−	2.01731e10i		−	2.29094i
$695$		−	1.12499e10i		−	1.27116i
$696$			1.86830e10i			2.10046i
$697$		−	2.39571e9i		−	0.267990i
$698$	1.62888e10			1.81299
$699$	−1.28046e10			−1.41806
$700$			6.05233e8i			0.0666928i
$701$	−1.25607e10			−1.37721			−0.688607	−	0.725135i	$-0.741777\pi$
$701$	−1.25607e10			−1.37721			−0.688607	+	0.725135i	$0.741777\pi$
$702$	2.07457e9	−	8.51916e8i	0.226334	−	0.0929430i
$703$	−2.47997e10			−2.69217
$704$		−	9.22228e8i		−	0.0996172i
$705$	6.54617e9			0.703599
$706$	−7.68387e9			−0.821795
$707$			3.05152e9i			0.324749i
$708$		−	3.00388e10i		−	3.18102i
$709$		−	7.68892e9i		−	0.810221i	−0.914268	−	0.405111i	$-0.867233\pi$
$709$		−	7.68892e9i		−	0.810221i	0.914268	−	0.405111i	$-0.132767\pi$
$710$		−	1.43447e10i		−	1.50414i
$711$	1.77098e10			1.84786
$712$	4.31330e9			0.447847
$713$			8.74415e9i			0.903450i
$714$	1.74219e9			0.179123
$715$	3.25579e9	+	7.92846e9i	0.333108	+	0.811181i
$716$	6.44410e9			0.656095
$717$		−	4.65568e9i		−	0.471700i
$718$	2.38290e10			2.40253
$719$	−2.77418e9			−0.278346			−0.139173	−	0.990268i	$-0.544444\pi$
$719$	−2.77418e9			−0.278346			−0.139173	+	0.990268i	$0.544444\pi$
$720$			1.97188e10i			1.96887i
$721$		−	6.65928e9i		−	0.661689i
$722$			3.24932e10i			3.21301i
$723$			2.53894e10i			2.49844i
$724$	4.52940e9			0.443564
$725$	−5.05760e8			−0.0492903
$726$			4.48043e9i			0.434552i
$727$	−6.41610e9			−0.619299			−0.309650	−	0.950851i	$-0.600212\pi$
$727$	−6.41610e9			−0.619299			−0.309650	+	0.950851i	$0.600212\pi$
$728$	−3.42523e9	−	8.34107e9i	−0.329025	−	0.801238i
$729$	−1.23173e10			−1.17752
$730$		−	2.20525e10i		−	2.09811i
$731$	5.52558e8			0.0523199
$732$	−5.35124e10			−5.04273
$733$			1.03049e10i			0.966453i	0.875495	+	0.483227i	$0.160535\pi$
$733$			1.03049e10i			0.966453i	−0.875495	+	0.483227i	$0.839465\pi$
$734$		−	3.72787e9i		−	0.347956i
$735$			2.13678e9i			0.198497i
$736$			9.43590e9i			0.872391i
$737$	4.92592e9			0.453264
$738$	−3.19256e10			−2.92376
$739$		−	1.63037e10i		−	1.48604i	−0.669271	−	0.743018i	$-0.733393\pi$
$739$		−	1.63037e10i		−	1.48604i	0.669271	−	0.743018i	$-0.266607\pi$
$740$	3.87788e10			3.51790
$741$	−2.47051e10	+	1.01451e10i	−2.23061	+	0.915990i
$742$	3.67900e9			0.330610
$743$		−	1.94647e9i		−	0.174095i	−0.996204	−	0.0870474i	$-0.972257\pi$
$743$		−	1.94647e9i		−	0.174095i	0.996204	−	0.0870474i	$-0.0277432\pi$
$744$	−4.23348e10			−3.76871
$745$	−2.99712e9			−0.265557
$746$		−	9.52274e9i		−	0.839800i
$747$		−	4.10641e9i		−	0.360446i
$748$		−	4.29467e9i		−	0.375210i
$749$		−	3.50799e9i		−	0.305051i
$750$	−3.12774e10			−2.70718
$751$	1.89166e10			1.62969			0.814843	−	0.579682i	$-0.196823\pi$
$751$	1.89166e10			1.62969			0.814843	+	0.579682i	$0.196823\pi$
$752$			1.10715e10i			0.949388i
$753$	−2.69485e10			−2.30013
$754$	1.24683e10	−	5.12008e9i	1.05928	−	0.434988i
$755$	1.45417e10			1.22970
$756$		−	1.37827e9i		−	0.116013i
$757$	1.78185e10			1.49292			0.746458	−	0.665432i	$-0.231753\pi$
$757$	1.78185e10			1.49292			0.746458	+	0.665432i	$0.231753\pi$
$758$	−4.01589e10			−3.34919
$759$			1.26513e10i			1.05024i
$760$		−	4.43841e10i		−	3.66758i
$761$			2.61584e9i			0.215162i	0.994196	+	0.107581i	$0.0343105\pi$
$761$			2.61584e9i			0.215162i	−0.994196	+	0.107581i	$0.965690\pi$
$762$			5.82382e10i			4.76832i
$763$	−1.62615e9			−0.132533
$764$	2.46076e10			1.99638
$765$			2.35613e9i			0.190276i
$766$	−1.91464e10			−1.53917
$767$	−1.12067e10	+	4.60200e9i	−0.896799	+	0.368267i
$768$	3.15426e10			2.51265
$769$		−	1.25351e10i		−	0.993999i	−0.867751	−	0.497000i	$-0.834435\pi$
$769$		−	1.25351e10i		−	0.993999i	0.867751	−	0.497000i	$-0.165565\pi$
$770$	7.59011e9			0.599143
$771$	1.04842e10			0.823842
$772$			7.01068e9i			0.548403i
$773$			7.95742e9i			0.619647i	0.950794	+	0.309823i	$0.100270\pi$
$773$			7.95742e9i			0.619647i	−0.950794	+	0.309823i	$0.899730\pi$
$774$		−	7.36349e9i		−	0.570808i
$775$		−	1.14603e9i		−	0.0884380i
$776$	1.84077e10			1.41411
$777$	−1.15518e10			−0.883434
$778$		−	4.24180e10i		−	3.22940i
$779$	3.25225e10			2.46492
$780$	3.86309e10	−	1.58636e10i	2.91477	−	1.19694i
$781$	1.05337e10			0.791227
$782$			3.48166e9i			0.260353i
$783$	1.15174e9			0.0857412
$784$	−3.61392e9			−0.267838
$785$			1.68236e10i			1.24129i
$786$			4.54332e10i			3.33729i
$787$		−	1.63863e10i		−	1.19831i	−0.800634	−	0.599154i	$-0.795504\pi$
$787$		−	1.63863e10i		−	1.19831i	0.800634	−	0.599154i	$-0.204496\pi$
$788$		−	2.75146e10i		−	2.00319i
$789$	1.48784e10			1.07841
$790$	4.06500e10			2.93336
$791$		−	2.96024e9i		−	0.212671i
$792$	−3.19942e10			−2.28840
$793$	8.19820e9	+	1.99641e10i	0.583798	+	1.42166i
$794$	−3.38244e10			−2.39805
$795$			9.52530e9i			0.672348i
$796$	−4.40962e10			−3.09888
$797$	−1.39133e10			−0.973480			−0.486740	−	0.873547i	$-0.661814\pi$
$797$	−1.39133e10			−0.973480			−0.486740	+	0.873547i	$0.661814\pi$
$798$			2.36508e10i			1.64754i
$799$			1.32289e9i			0.0917510i
$800$		−	1.23669e9i		−	0.0853977i
$801$		−	3.10836e9i		−	0.213706i
$802$	−2.81395e10			−1.92622
$803$	1.61937e10			1.10368
$804$		−	2.40012e10i		−	1.62868i
$805$	−4.27021e9			−0.288512
$806$	1.16018e10	+	2.82526e10i	0.780466	+	1.90058i
$807$	−9.60683e9			−0.643462
$808$		−	2.95248e10i		−	1.96900i
$809$	−1.99244e9			−0.132301			−0.0661507	−	0.997810i	$-0.521072\pi$
$809$	−1.99244e9			−0.132301			−0.0661507	+	0.997810i	$0.521072\pi$
$810$	−2.35702e10			−1.55835
$811$		−	1.49649e10i		−	0.985147i	−0.870271	−	0.492573i	$-0.836056\pi$
$811$		−	1.49649e10i		−	0.985147i	0.870271	−	0.492573i	$-0.163944\pi$
$812$		−	8.28348e9i		−	0.542959i
$813$		−	1.24917e10i		−	0.815276i
$814$			4.10333e10i			2.66656i
$815$	5.27734e9			0.341478
$816$	−7.62893e9			−0.491528
$817$			7.50115e9i			0.481228i
$818$	−1.01343e10			−0.647379
$819$	−6.01095e9	+	2.46837e9i	−0.382340	+	0.157006i
$820$	−5.08548e10			−3.22095
$821$		−	3.29123e9i		−	0.207567i	−0.994600	−	0.103783i	$-0.966905\pi$
$821$		−	3.29123e9i		−	0.207567i	0.994600	−	0.103783i	$-0.0330949\pi$
$822$	−6.73424e10			−4.22900
$823$	2.98129e10			1.86425			0.932126	−	0.362135i	$-0.117952\pi$
$823$	2.98129e10			1.86425			0.932126	+	0.362135i	$0.117952\pi$
$824$			6.44314e10i			4.01192i
$825$		−	1.65811e9i		−	0.102807i
$826$			1.07285e10i			0.662381i
$827$			1.69994e10i			1.04512i	0.852604	+	0.522558i	$0.175022\pi$
$827$			1.69994e10i			1.04512i	−0.852604	+	0.522558i	$0.824978\pi$
$828$	3.21986e10			1.97120
$829$	−2.57091e10			−1.56728			−0.783638	−	0.621218i	$-0.786638\pi$
$829$	−2.57091e10			−1.56728			−0.783638	+	0.621218i	$0.786638\pi$
$830$		−	9.42562e9i		−	0.572185i
$831$	−1.16848e10			−0.706346
$832$	6.88412e8	+	1.67641e9i	0.0414397	+	0.100914i
$833$	−4.31814e8			−0.0258844
$834$		−	5.80011e10i		−	3.46222i
$835$	2.82145e10			1.67714
$836$	5.83015e10			3.45110
$837$			2.60979e9i			0.153839i
$838$			2.32791e10i			1.36651i
$839$			1.05802e10i			0.618483i	0.950984	+	0.309241i	$0.100075\pi$
$839$			1.05802e10i			0.618483i	−0.950984	+	0.309241i	$0.899925\pi$
$840$		−	2.06742e10i		−	1.20352i
$841$	−1.03278e10			−0.598718
$842$	−1.79798e10			−1.03799
$843$			1.98273e10i			1.13990i
$844$	1.53321e10			0.877814
$845$	−1.18367e10	−	1.19819e10i	−0.674886	−	0.683168i
$846$	1.76291e10			1.00100
$847$		−	1.11050e9i		−	0.0627955i
$848$	−1.61101e10			−0.907220
$849$	−4.56822e9			−0.256195
$850$		−	4.56313e8i		−	0.0254857i
$851$		−	2.30854e10i		−	1.28406i
$852$		−	5.13246e10i		−	2.84307i
$853$		−	1.61507e10i		−	0.890985i	−0.895286	−	0.445492i	$-0.853029\pi$
$853$		−	1.61507e10i		−	0.890985i	0.895286	−	0.445492i	$-0.146971\pi$
$854$	1.91122e10			1.05004
$855$	−3.19852e10			−1.75012
$856$			3.39413e10i			1.84957i
$857$	−6.24763e9			−0.339064			−0.169532	−	0.985525i	$-0.554226\pi$
$857$	−6.24763e9			−0.339064			−0.169532	+	0.985525i	$0.554226\pi$
$858$	1.67859e10	+	4.08768e10i	0.907276	+	2.20939i
$859$	2.00450e10			1.07902			0.539511	−	0.841979i	$-0.318609\pi$
$859$	2.00450e10			1.07902			0.539511	+	0.841979i	$0.318609\pi$
$860$		−	1.17294e10i		−	0.628828i
$861$	1.51491e10			0.808862
$862$	3.95630e10			2.10384
$863$			5.69418e9i			0.301574i	0.988566	+	0.150787i	$0.0481807\pi$
$863$			5.69418e9i			0.301574i	−0.988566	+	0.150787i	$0.951819\pi$
$864$			2.81625e9i			0.148550i
$865$		−	1.70743e10i		−	0.896990i
$866$		−	2.09979e10i		−	1.09866i
$867$	2.68541e10			1.39941
$868$	1.87699e10			0.974191
$869$			2.98503e10i			1.54305i
$870$	3.09041e10			1.59111
$871$	−8.95426e9	+	3.67703e9i	−0.459162	+	0.188553i
$872$	1.57337e10			0.803570
$873$		−	1.32654e10i		−	0.674794i
$874$	−4.72646e10			−2.39467
$875$	7.75232e9			0.391204
$876$		−	7.89027e10i		−	3.96577i
$877$		−	1.11010e10i		−	0.555731i	−0.960620	−	0.277865i	$-0.910373\pi$
$877$		−	1.11010e10i		−	0.555731i	0.960620	−	0.277865i	$-0.0896269\pi$
$878$			2.09931e10i			1.04676i
$879$			4.76636e10i			2.36715i
$880$	−3.32365e10			−1.64409
$881$	−2.93592e9			−0.144653			−0.0723267	−	0.997381i	$-0.523042\pi$
$881$	−2.93592e9			−0.144653			−0.0723267	+	0.997381i	$0.523042\pi$
$882$			5.75442e9i			0.282398i
$883$	−3.19399e10			−1.56124			−0.780622	−	0.625003i	$-0.785098\pi$
$883$	−3.19399e10			−1.56124			−0.780622	+	0.625003i	$0.785098\pi$
$884$	3.20583e9	+	7.80679e9i	0.156084	+	0.380093i
$885$	−2.77771e10			−1.34705
$886$			6.18674e10i			2.98843i
$887$	−8.99151e9			−0.432613			−0.216307	−	0.976325i	$-0.569401\pi$
$887$	−8.99151e9			−0.432613			−0.216307	+	0.976325i	$0.569401\pi$
$888$	1.11768e11			5.35640
$889$		−	1.44347e10i		−	0.689053i
$890$		−	7.13475e9i		−	0.339245i
$891$		−	1.73082e10i		−	0.819746i
$892$		−	6.32543e10i		−	2.98410i
$893$	−1.79587e10			−0.843907
$894$	−1.54523e10			−0.723288
$895$		−	5.95890e9i		−	0.277834i
$896$	−7.32691e9			−0.340285
$897$	−9.44379e9	−	2.29974e10i	−0.436891	−	1.06391i
$898$	−1.01310e10			−0.466860
$899$			1.56850e10i			0.719990i
$900$	−4.22001e9			−0.192959
$901$	−1.92494e9			−0.0876757
$902$		−	5.38114e10i		−	2.44147i
$903$			3.49405e9i			0.157915i
$904$			2.86416e10i			1.28946i
$905$		−	4.18837e9i		−	0.187834i
$906$	7.49725e10			3.34930
$907$	1.55959e10			0.694042			0.347021	−	0.937857i	$-0.387193\pi$
$907$	1.55959e10			0.694042			0.347021	+	0.937857i	$0.387193\pi$
$908$		−	4.69739e10i		−	2.08236i
$909$	−2.12769e10			−0.939581
$910$	−1.37972e10	+	5.66576e9i	−0.606940	+	0.249237i
$911$	5.54009e9			0.242774			0.121387	−	0.992605i	$-0.461266\pi$
$911$	5.54009e9			0.242774			0.121387	+	0.992605i	$0.461266\pi$
$912$		−	1.03565e11i		−	4.52097i
$913$	6.92146e9			0.300988
$914$	2.20038e10			0.953206
$915$			4.94833e10i			2.13543i
$916$			7.50411e10i			3.22601i
$917$		−	1.12609e10i		−	0.482260i
$918$			1.03914e9i			0.0443327i
$919$	−1.88609e10			−0.801603			−0.400801	−	0.916165i	$-0.631268\pi$
$919$	−1.88609e10			−0.801603			−0.400801	+	0.916165i	$0.631268\pi$
$920$	4.13161e10			1.74929
$921$		−	1.66539e9i		−	0.0702435i
$922$	2.24672e10			0.944040
$923$	−1.91479e10	+	7.86303e9i	−0.801523	+	0.329142i
$924$	2.71570e10			1.13248
$925$			3.02563e9i			0.125695i
$926$	−2.15718e10			−0.892787
$927$	4.64321e10			1.91443
$928$			1.69259e10i			0.695238i
$929$		−	2.50856e10i		−	1.02653i	−0.858231	−	0.513263i	$-0.828437\pi$
$929$		−	2.50856e10i		−	1.02653i	0.858231	−	0.513263i	$-0.171563\pi$
$930$			7.00272e10i			2.85480i
$931$		−	5.86201e9i		−	0.238080i
$932$	−5.49290e10			−2.22252
$933$	−1.94174e10			−0.782718
$934$			1.11521e10i			0.447861i
$935$	−3.97131e9			−0.158889
$936$	5.81585e10	−	2.38826e10i	2.31818	−	0.951953i
$937$	7.59883e8			0.0301757			0.0150879	−	0.999886i	$-0.495197\pi$
$937$	7.59883e8			0.0301757			0.0150879	+	0.999886i	$0.495197\pi$
$938$			8.57213e9i			0.339140i
$939$	3.88640e10			1.53186
$940$	2.80817e10			1.10275
$941$		−	1.15563e10i		−	0.452123i	−0.974113	−	0.226061i	$-0.927415\pi$
$941$		−	1.15563e10i		−	0.452123i	0.974113	−	0.226061i	$-0.0725850\pi$
$942$			8.67375e10i			3.38087i
$943$			3.02744e10i			1.17567i
$944$		−	4.69792e10i		−	1.81762i
$945$	−1.27449e9			−0.0491276
$946$	1.24113e10			0.476650
$947$		−	1.47140e9i		−	0.0562996i	−0.999604	−	0.0281498i	$-0.991038\pi$
$947$		−	1.47140e9i		−	0.0562996i	0.999604	−	0.0281498i	$-0.00896154\pi$
$948$	1.45444e11			5.54454
$949$	−2.94367e10	+	1.20880e10i	−1.11804	+	0.459118i
$950$	6.19460e9			0.234412
$951$		−	1.59137e10i		−	0.599985i
$952$	4.17798e9			0.156941
$953$	−3.85642e10			−1.44331			−0.721653	−	0.692255i	$-0.756618\pi$
$953$	−3.85642e10			−1.44331			−0.721653	+	0.692255i	$0.756618\pi$
$954$			2.56520e10i			0.956538i
$955$		−	2.27548e10i		−	0.845399i
$956$		−	1.99719e10i		−	0.739291i
$957$			2.26936e10i			0.836974i
$958$	7.84760e10			2.88375
$959$	1.66913e10			0.611117
$960$			4.15517e9i			0.151579i
$961$	−8.02889e9			−0.291826
$962$	−3.06300e10	−	7.45898e10i	−1.10926	−	2.70126i
$963$	2.44597e10			0.882589
$964$			1.08915e11i			3.91578i
$965$	6.48283e9			0.232230
$966$	−2.20160e10			−0.785810
$967$		−	2.73331e10i		−	0.972067i	−0.873940	−	0.486034i	$-0.838443\pi$
$967$		−	2.73331e10i		−	0.972067i	0.873940	−	0.486034i	$-0.161557\pi$
$968$			1.07446e10i			0.380738i
$969$		−	1.23746e10i		−	0.436916i
$970$		−	3.04487e10i		−	1.07119i
$971$	1.31321e10			0.460327			0.230163	−	0.973152i	$-0.426074\pi$
$971$	1.31321e10			0.460327			0.230163	+	0.973152i	$0.426074\pi$
$972$	−9.31209e10			−3.25248
$973$			1.43760e10i			0.500313i
$974$	2.53405e10			0.878737
$975$	1.23772e9	+	3.01409e9i	0.0427669	+	0.104145i
$976$	−8.36907e10			−2.88140
$977$			5.67512e10i			1.94690i	0.228898	+	0.973450i	$0.426488\pi$
$977$			5.67512e10i			1.94690i	−0.228898	+	0.973450i	$0.573512\pi$
$978$	2.72084e10			0.930073
$979$	5.23922e9			0.178454
$980$			9.16631e9i			0.311102i
$981$		−	1.13384e10i		−	0.383452i
$982$		−	2.08724e10i		−	0.703369i
$983$		−	2.70777e10i		−	0.909231i	−0.890688	−	0.454615i	$-0.849777\pi$
$983$		−	2.70777e10i		−	0.909231i	0.890688	−	0.454615i	$-0.150223\pi$
$984$	−1.46574e11			−4.90425
$985$	−2.54429e10			−0.848282
$986$			6.24531e9i			0.207484i
$987$	−8.36520e9			−0.276928
$988$	−1.05980e11	+	4.35201e10i	−3.49601	+	1.43562i
$989$	−6.98264e9			−0.229526
$990$			5.29224e10i			1.73347i
$991$	1.75371e10			0.572402			0.286201	−	0.958170i	$-0.407607\pi$
$991$	1.75371e10			0.572402			0.286201	+	0.958170i	$0.407607\pi$
$992$	−3.83532e10			−1.24741
$993$			4.81599e10i			1.56086i
$994$			1.83308e10i			0.592010i
$995$			4.07760e10i			1.31227i
$996$		−	3.37243e10i		−	1.08152i
$997$	1.86815e10			0.597008			0.298504	−	0.954408i	$-0.403512\pi$
$997$	1.86815e10			0.597008			0.298504	+	0.954408i	$0.403512\pi$
$998$	3.51550e10			1.11952
$999$		−	6.89011e9i		−	0.218649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.3	✓	50
13.12	even	2	inner	91.8.c.a.64.48	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.3	✓	50	1.1	even	1	trivial
91.8.c.a.64.48	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)

\(f(q)\)	\(=\)	\(q-20.4516i q^{2} -67.6652 q^{3} -290.269 q^{4} +268.414i q^{5} +1383.86i q^{6} -343.000i q^{7} +3318.67i q^{8} +2391.58 q^{9} +O(q^{10})\)	\(q-20.4516i q^{2} -67.6652 q^{3} -290.269 q^{4} +268.414i q^{5} +1383.86i q^{6} -343.000i q^{7} +3318.67i q^{8} +2391.58 q^{9} +5489.50 q^{10} +4031.07i q^{11} +19641.1 q^{12} +(-3009.06 - 7327.62i) q^{13} -7014.91 q^{14} -18162.3i q^{15} +30717.8 q^{16} +3670.35 q^{17} -48911.8i q^{18} +49826.2i q^{19} -77912.3i q^{20} +23209.2i q^{21} +82442.0 q^{22} -46382.0 q^{23} -224559. i q^{24} +6078.93 q^{25} +(-149862. + 61540.2i) q^{26} -13843.2 q^{27} +99562.4i q^{28} -83198.9 q^{29} -371449. q^{30} -188525. i q^{31} -203439. i q^{32} -272764. i q^{33} -75064.7i q^{34} +92066.0 q^{35} -694203. q^{36} +497724. i q^{37} +1.01903e6 q^{38} +(203609. + 495825. i) q^{39} -890778. q^{40} -652718. i q^{41} +474666. q^{42} +150546. q^{43} -1.17010e6i q^{44} +641935. i q^{45} +948588. i q^{46} +360426. i q^{47} -2.07853e6 q^{48} -117649. q^{49} -124324. i q^{50} -248355. q^{51} +(873438. + 2.12698e6i) q^{52} -524455. q^{53} +283117. i q^{54} -1.08200e6 q^{55} +1.13830e6 q^{56} -3.37150e6i q^{57} +1.70155e6i q^{58} -1.52938e6i q^{59} +5.27196e6i q^{60} -2.72450e6 q^{61} -3.85563e6 q^{62} -820313. i q^{63} -228780. q^{64} +(1.96684e6 - 807674. i) q^{65} -5.57846e6 q^{66} -1.22199e6i q^{67} -1.06539e6 q^{68} +3.13845e6 q^{69} -1.88290e6i q^{70} -2.61312e6i q^{71} +7.93688e6i q^{72} -4.01722e6i q^{73} +1.01793e7 q^{74} -411332. q^{75} -1.44630e7i q^{76} +1.38266e6 q^{77} +(1.01404e7 - 4.16413e6i) q^{78} +7.40505e6 q^{79} +8.24508e6i q^{80} -4.29369e6 q^{81} -1.33492e7 q^{82} -1.71703e6i q^{83} -6.73691e6i q^{84} +985175. i q^{85} -3.07892e6i q^{86} +5.62967e6 q^{87} -1.33778e7 q^{88} -1.29971e6i q^{89} +1.31286e7 q^{90} +(-2.51338e6 + 1.03211e6i) q^{91} +1.34633e7 q^{92} +1.27566e7i q^{93} +7.37131e6 q^{94} -1.33741e7 q^{95} +1.37657e7i q^{96} -5.54671e6i q^{97} +2.40611e6i q^{98} +9.64065e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 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

Varieties

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Database

Properties

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