LMFDB - Embedded newform 91.8.c.a.64.20

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			64.20
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.39578i q^{2} -84.2461 q^{3} +108.677 q^{4} -187.956i q^{5} +370.327i q^{6} -343.000i q^{7} -1040.38i q^{8} +4910.40 q^{9} +O(q^{10})$	\(q-4.39578i q^{2} -84.2461 q^{3} +108.677 q^{4} -187.956i q^{5} +370.327i q^{6} -343.000i q^{7} -1040.38i q^{8} +4910.40 q^{9} -826.214 q^{10} +7998.43i q^{11} -9155.62 q^{12} +(-7483.05 + 2598.56i) q^{13} -1507.75 q^{14} +15834.6i q^{15} +9337.39 q^{16} +18701.7 q^{17} -21585.0i q^{18} +1178.29i q^{19} -20426.6i q^{20} +28896.4i q^{21} +35159.3 q^{22} -31565.2 q^{23} +87647.9i q^{24} +42797.4 q^{25} +(11422.7 + 32893.8i) q^{26} -229436. q^{27} -37276.3i q^{28} +182544. q^{29} +69605.3 q^{30} -7920.65i q^{31} -174214. i q^{32} -673836. i q^{33} -82208.7i q^{34} -64469.0 q^{35} +533648. q^{36} -503488. i q^{37} +5179.50 q^{38} +(630417. - 218918. i) q^{39} -195546. q^{40} +261868. i q^{41} +127022. q^{42} -126751. q^{43} +869247. i q^{44} -922940. i q^{45} +138753. i q^{46} -1.17246e6i q^{47} -786638. q^{48} -117649. q^{49} -188128. i q^{50} -1.57555e6 q^{51} +(-813236. + 282404. i) q^{52} +379603. q^{53} +1.00855e6i q^{54} +1.50336e6 q^{55} -356850. q^{56} -99266.3i q^{57} -802423. i q^{58} -1.12588e6i q^{59} +1.72086e6i q^{60} +1.68205e6 q^{61} -34817.4 q^{62} -1.68427e6i q^{63} +429381. q^{64} +(488416. + 1.40649e6i) q^{65} -2.96204e6 q^{66} +4.44669e6i q^{67} +2.03245e6 q^{68} +2.65924e6 q^{69} +283392. i q^{70} -3.80157e6i q^{71} -5.10868e6i q^{72} +1.04985e6i q^{73} -2.21322e6 q^{74} -3.60551e6 q^{75} +128053. i q^{76} +2.74346e6 q^{77} +(-962317. - 2.77117e6i) q^{78} +3.47810e6 q^{79} -1.75502e6i q^{80} +8.59000e6 q^{81} +1.15111e6 q^{82} -1.89214e6i q^{83} +3.14038e6i q^{84} -3.51511e6i q^{85} +557170. i q^{86} -1.53786e7 q^{87} +8.32141e6 q^{88} -9.24930e6i q^{89} -4.05704e6 q^{90} +(891306. + 2.56669e6i) q^{91} -3.43041e6 q^{92} +667284. i q^{93} -5.15386e6 q^{94} +221467. q^{95} +1.46768e7i q^{96} -1.90475e6i q^{97} +517159. i q^{98} +3.92755e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	4.39578i		−	0.388536i	−0.980949	−	0.194268i	$-0.937767\pi$
$2$		−	4.39578i		−	0.388536i	0.980949	−	0.194268i	$-0.0622331\pi$
$3$	−84.2461			−1.80146			−0.900731	−	0.434377i	$-0.856969\pi$
$3$	−84.2461			−1.80146			−0.900731	+	0.434377i	$0.856969\pi$
$4$	108.677			0.849040
$5$		−	187.956i		−	0.672453i	−0.941781	−	0.336227i	$-0.890849\pi$
$5$		−	187.956i		−	0.672453i	0.941781	−	0.336227i	$-0.109151\pi$
$6$			370.327i			0.699932i
$7$		−	343.000i		−	0.377964i
$7$		−	343.000i		−	0.377964i
$8$		−	1040.38i		−	0.718418i
$9$	4910.40			2.24527
$10$	−826.214			−0.261272
$11$			7998.43i			1.81188i	0.423401	+	0.905942i	$0.360836\pi$
$11$			7998.43i			1.81188i	−0.423401	+	0.905942i	$0.639164\pi$
$12$	−9155.62			−1.52951
$13$	−7483.05	+	2598.56i	−0.944663	+	0.328043i
$13$	−7483.05	+	2598.56i	−0.944663	+	0.328043i
$14$	−1507.75			−0.146853
$15$			15834.6i			1.21140i
$16$	9337.39			0.569909
$17$	18701.7			0.923232			0.461616	−	0.887080i	$-0.347270\pi$
$17$	18701.7			0.923232			0.461616	+	0.887080i	$0.347270\pi$
$18$		−	21585.0i		−	0.872366i
$19$			1178.29i			0.0394107i	0.999806	+	0.0197054i	$0.00627282\pi$
$19$			1178.29i			0.0394107i	−0.999806	+	0.0197054i	$0.993727\pi$
$20$		−	20426.6i		−	0.570940i
$21$			28896.4i			0.680889i
$22$	35159.3			0.703982
$23$	−31565.2			−0.540954			−0.270477	−	0.962726i	$-0.587181\pi$
$23$	−31565.2			−0.540954			−0.270477	+	0.962726i	$0.587181\pi$
$24$			87647.9i			1.29420i
$25$	42797.4			0.547807
$26$	11422.7	+	32893.8i	0.127456	+	0.367035i
$27$	−229436.			−2.24330
$28$		−	37276.3i		−	0.320907i
$29$	182544.			1.38987			0.694936	−	0.719072i	$-0.255433\pi$
$29$	182544.			1.38987			0.694936	+	0.719072i	$0.255433\pi$
$30$	69605.3			0.470672
$31$		−	7920.65i		−	0.0477524i	−0.999715	−	0.0238762i	$-0.992399\pi$
$31$		−	7920.65i		−	0.0477524i	0.999715	−	0.0238762i	$-0.00760075\pi$
$32$		−	174214.i		−	0.939848i
$33$		−	673836.i		−	3.26404i
$34$		−	82208.7i		−	0.358709i
$35$	−64469.0			−0.254163
$36$	533648.			1.90632
$37$		−	503488.i		−	1.63412i	−0.576554	−	0.817059i	$-0.695603\pi$
$37$		−	503488.i		−	1.63412i	0.576554	−	0.817059i	$-0.304397\pi$
$38$	5179.50			0.0153125
$39$	630417.	−	218918.i	1.70177	−	0.590957i
$40$	−195546.			−0.483102
$41$			261868.i			0.593388i	0.954973	+	0.296694i	$0.0958842\pi$
$41$			261868.i			0.593388i	−0.954973	+	0.296694i	$0.904116\pi$
$42$	127022.			0.264550
$43$	−126751.			−0.243115			−0.121558	−	0.992584i	$-0.538789\pi$
$43$	−126751.			−0.243115			−0.121558	+	0.992584i	$0.538789\pi$
$44$			869247.i			1.53836i
$45$		−	922940.i		−	1.50984i
$46$			138753.i			0.210180i
$47$		−	1.17246e6i		−	1.64723i	−0.567149	−	0.823615i	$-0.691954\pi$
$47$		−	1.17246e6i		−	1.64723i	0.567149	−	0.823615i	$-0.308046\pi$
$48$	−786638.			−1.02667
$49$	−117649.			−0.142857
$50$		−	188128.i		−	0.212842i
$51$	−1.57555e6			−1.66317
$52$	−813236.	+	282404.i	−0.802057	+	0.278522i
$53$	379603.			0.350239			0.175119	−	0.984547i	$-0.443969\pi$
$53$	379603.			0.350239			0.175119	+	0.984547i	$0.443969\pi$
$54$			1.00855e6i			0.871602i
$55$	1.50336e6			1.21841
$56$	−356850.			−0.271536
$57$		−	99266.3i		−	0.0709970i
$58$		−	802423.i		−	0.540015i
$59$		−	1.12588e6i		−	0.713691i	−0.934163	−	0.356845i	$-0.883852\pi$
$59$		−	1.12588e6i		−	0.713691i	0.934163	−	0.356845i	$-0.116148\pi$
$60$			1.72086e6i			1.02853i
$61$	1.68205e6			0.948822			0.474411	−	0.880303i	$-0.342661\pi$
$61$	1.68205e6			0.948822			0.474411	+	0.880303i	$0.342661\pi$
$62$	−34817.4			−0.0185535
$63$		−	1.68427e6i		−	0.848631i
$64$	429381.			0.204745
$65$	488416.	+	1.40649e6i	0.220594	+	0.635241i
$66$	−2.96204e6			−1.26820
$67$			4.44669e6i			1.80624i	0.429390	+	0.903119i	$0.358729\pi$
$67$			4.44669e6i			1.80624i	−0.429390	+	0.903119i	$0.641271\pi$
$68$	2.03245e6			0.783861
$69$	2.65924e6			0.974509
$70$			283392.i			0.0987515i
$71$		−	3.80157e6i		−	1.26055i	−0.776373	−	0.630273i	$-0.782943\pi$
$71$		−	3.80157e6i		−	1.26055i	0.776373	−	0.630273i	$-0.217057\pi$
$72$		−	5.10868e6i		−	1.61304i
$73$			1.04985e6i			0.315861i	0.987450	+	0.157931i	$0.0504822\pi$
$73$			1.04985e6i			0.315861i	−0.987450	+	0.157931i	$0.949518\pi$
$74$	−2.21322e6			−0.634913
$75$	−3.60551e6			−0.986853
$76$			128053.i			0.0334613i
$77$	2.74346e6			0.684828
$78$	−962317.	−	2.77117e6i	−0.229608	−	0.661200i
$79$	3.47810e6			0.793684			0.396842	−	0.917887i	$-0.370106\pi$
$79$	3.47810e6			0.793684			0.396842	+	0.917887i	$0.370106\pi$
$80$		−	1.75502e6i		−	0.383237i
$81$	8.59000e6			1.79595
$82$	1.15111e6			0.230552
$83$		−	1.89214e6i		−	0.363229i	−0.983370	−	0.181614i	$-0.941868\pi$
$83$		−	1.89214e6i		−	0.363229i	0.983370	−	0.181614i	$-0.0581322\pi$
$84$			3.14038e6i			0.578102i
$85$		−	3.51511e6i		−	0.620830i
$86$			557170.i			0.0944589i
$87$	−1.53786e7			−2.50380
$88$	8.32141e6			1.30169
$89$		−	9.24930e6i		−	1.39073i	−0.718655	−	0.695367i	$-0.755242\pi$
$89$		−	9.24930e6i		−	1.39073i	0.718655	−	0.695367i	$-0.244758\pi$
$90$	−4.05704e6			−0.586625
$91$	891306.	+	2.56669e6i	0.123989	+	0.357049i
$92$	−3.43041e6			−0.459292
$93$			667284.i			0.0860241i
$94$	−5.15386e6			−0.640008
$95$	221467.			0.0265019
$96$			1.46768e7i			1.69310i
$97$		−	1.90475e6i		−	0.211903i	−0.994371	−	0.105951i	$-0.966211\pi$
$97$		−	1.90475e6i		−	0.211903i	0.994371	−	0.105951i	$-0.0337888\pi$
$98$			517159.i			0.0555051i
$99$			3.92755e7i			4.06816i
$100$	4.65110e6			0.465110
$101$	−1.38799e7			−1.34049			−0.670244	−	0.742141i	$-0.733810\pi$
$101$	−1.38799e7			−1.34049			−0.670244	+	0.742141i	$0.733810\pi$
$102$			6.92576e6i			0.646200i
$103$	1.12727e7			1.01648			0.508240	−	0.861215i	$-0.330296\pi$
$103$	1.12727e7			1.01648			0.508240	+	0.861215i	$0.330296\pi$
$104$	2.70349e6	+	7.78521e6i	0.235672	+	0.678663i
$105$	5.43126e6			0.457866
$106$		−	1.66865e6i		−	0.136080i
$107$	−4.64832e6			−0.366820			−0.183410	−	0.983036i	$-0.558714\pi$
$107$	−4.64832e6			−0.366820			−0.183410	+	0.983036i	$0.558714\pi$
$108$	−2.49344e7			−1.90465
$109$			382358.i			0.0282799i	0.999900	+	0.0141399i	$0.00450103\pi$
$109$			382358.i			0.0282799i	−0.999900	+	0.0141399i	$0.995499\pi$
$110$		−	6.60842e6i		−	0.473395i
$111$			4.24169e7i			2.94380i
$112$		−	3.20273e6i		−	0.215405i
$113$	2.90777e7			1.89577			0.947884	−	0.318614i	$-0.103218\pi$
$113$	2.90777e7			1.89577			0.947884	+	0.318614i	$0.103218\pi$
$114$	−436353.			−0.0275848
$115$			5.93287e6i			0.363766i
$116$	1.98384e7			1.18006
$117$	−3.67447e7	+	1.27600e7i	−2.12102	+	0.736544i
$118$	−4.94912e6			−0.277294
$119$		−	6.41470e6i		−	0.348949i
$120$	1.64740e7			0.870291
$121$	−4.44878e7			−2.28293
$122$		−	7.39393e6i		−	0.368651i
$123$		−	2.20613e7i		−	1.06897i
$124$		−	860794.i		−	0.0405437i
$125$		−	2.27281e7i		−	1.04083i
$126$	−7.40366e6			−0.329723
$127$	2.04037e6			0.0883887			0.0441943	−	0.999023i	$-0.485928\pi$
$127$	2.04037e6			0.0883887			0.0441943	+	0.999023i	$0.485928\pi$
$128$		−	2.41868e7i		−	1.01940i
$129$	1.06783e7			0.437963
$130$	6.18260e6	−	2.14697e6i	0.246814	−	0.0857085i
$131$	−2.52314e7			−0.980598			−0.490299	−	0.871554i	$-0.663112\pi$
$131$	−2.52314e7			−0.980598			−0.490299	+	0.871554i	$0.663112\pi$
$132$		−	7.32306e7i		−	2.77130i
$133$	404153.			0.0148959
$134$	1.95467e7			0.701788
$135$			4.31239e7i			1.50851i
$136$		−	1.94569e7i		−	0.663266i
$137$			1.84953e7i			0.614524i	0.951625	+	0.307262i	$0.0994128\pi$
$137$			1.84953e7i			0.614524i	−0.951625	+	0.307262i	$0.900587\pi$
$138$		−	1.16894e7i		−	0.378631i
$139$	3.83026e7			1.20970			0.604849	−	0.796340i	$-0.293233\pi$
$139$	3.83026e7			1.20970			0.604849	+	0.796340i	$0.293233\pi$
$140$	−7.00631e6			−0.215795
$141$			9.87749e7i			2.96742i
$142$	−1.67109e7			−0.489767
$143$	−2.07844e7	−	5.98527e7i	−0.594376	−	1.71162i
$144$	4.58503e7			1.27960
$145$		−	3.43103e7i		−	0.934624i
$146$	4.61490e6			0.122723
$147$	9.91146e6			0.257352
$148$		−	5.47177e7i		−	1.38743i
$149$		−	5.50094e7i		−	1.36234i	−0.732126	−	0.681169i	$-0.761472\pi$
$149$		−	5.50094e7i		−	1.36234i	0.732126	−	0.681169i	$-0.238528\pi$
$150$			1.58490e7i			0.383428i
$151$			3.16353e7i			0.747743i	0.927481	+	0.373872i	$0.121970\pi$
$151$			3.16353e7i			0.747743i	−0.927481	+	0.373872i	$0.878030\pi$
$152$	1.22587e6			0.0283134
$153$	9.18330e7			2.07290
$154$		−	1.20597e7i		−	0.266080i
$155$	−1.48874e6			−0.0321112
$156$	6.85119e7	−	2.37914e7i	1.44487	−	0.501747i
$157$	6.86137e6			0.141502			0.0707509	−	0.997494i	$-0.477460\pi$
$157$	6.86137e6			0.141502			0.0707509	+	0.997494i	$0.477460\pi$
$158$		−	1.52890e7i		−	0.308374i
$159$	−3.19801e7			−0.630942
$160$	−3.27446e7			−0.632004
$161$			1.08268e7i			0.204461i
$162$		−	3.77597e7i		−	0.697792i
$163$			2.33452e7i			0.422223i	0.977462	+	0.211111i	$0.0677083\pi$
$163$			2.33452e7i			0.422223i	−0.977462	+	0.211111i	$0.932292\pi$
$164$			2.84591e7i			0.503810i
$165$	−1.26652e8			−2.19491
$166$	−8.31743e6			−0.141127
$167$			2.10687e7i			0.350050i	0.984564	+	0.175025i	$0.0560006\pi$
$167$			2.10687e7i			0.350050i	−0.984564	+	0.175025i	$0.943999\pi$
$168$	3.00632e7			0.489163
$169$	4.92435e7	−	3.88903e7i	0.784775	−	0.619780i
$170$	−1.54517e7			−0.241215
$171$			5.78587e6i			0.0884876i
$172$	−1.37749e7			−0.206415
$173$	8.20532e7			1.20485			0.602427	−	0.798174i	$-0.294201\pi$
$173$	8.20532e7			1.20485			0.602427	+	0.798174i	$0.294201\pi$
$174$			6.76010e7i			0.972816i
$175$		−	1.46795e7i		−	0.207052i
$176$			7.46845e7i			1.03261i
$177$			9.48510e7i			1.28569i
$178$	−4.06579e7			−0.540349
$179$	−5.76515e7			−0.751319			−0.375660	−	0.926758i	$-0.622584\pi$
$179$	−5.76515e7			−0.751319			−0.375660	+	0.926758i	$0.622584\pi$
$180$		−	1.00303e8i		−	1.28191i
$181$	7.97976e7			1.00026			0.500132	−	0.865949i	$-0.333285\pi$
$181$	7.97976e7			1.00026			0.500132	+	0.865949i	$0.333285\pi$
$182$	1.12826e7	−	3.91798e6i	0.138726	−	0.0481740i
$183$	−1.41706e8			−1.70927
$184$			3.28398e7i			0.388631i
$185$	−9.46338e7			−1.09887
$186$	2.93323e6			0.0334234
$187$			1.49585e8i			1.67279i
$188$		−	1.27419e8i		−	1.39856i
$189$			7.86964e7i			0.847888i
$190$		−	973520.i		−	0.0102969i
$191$	1.55835e8			1.61826			0.809128	−	0.587633i	$-0.199940\pi$
$191$	1.55835e8			1.61826			0.809128	+	0.587633i	$0.199940\pi$
$192$	−3.61737e7			−0.368840
$193$		−	1.54188e8i		−	1.54383i	−0.635723	−	0.771917i	$-0.719298\pi$
$193$		−	1.54188e8i		−	1.54383i	0.635723	−	0.771917i	$-0.280702\pi$
$194$	−8.37285e6			−0.0823318
$195$	−4.11471e7	−	1.18491e8i	−0.397391	−	1.14436i
$196$	−1.27858e7			−0.121291
$197$		−	1.90806e7i		−	0.177812i	−0.996040	−	0.0889060i	$-0.971663\pi$
$197$		−	1.90806e7i		−	0.177812i	0.996040	−	0.0889060i	$-0.0283371\pi$
$198$	1.72646e8			1.58063
$199$	1.89345e8			1.70321			0.851605	−	0.524183i	$-0.175629\pi$
$199$	1.89345e8			1.70321			0.851605	+	0.524183i	$0.175629\pi$
$200$		−	4.45256e7i		−	0.393554i
$201$		−	3.74616e8i		−	3.25387i
$202$			6.10131e7i			0.520827i
$203$		−	6.26126e7i		−	0.525322i
$204$	−1.71226e8			−1.41210
$205$	4.92198e7			0.399026
$206$		−	4.95524e7i		−	0.394939i
$207$	−1.54997e8			−1.21459
$208$	−6.98722e7	+	2.42638e7i	−0.538372	+	0.186955i
$209$	−9.42447e6			−0.0714077
$210$		−	2.38746e7i		−	0.177897i
$211$	−8.15112e6			−0.0597349			−0.0298675	−	0.999554i	$-0.509509\pi$
$211$	−8.15112e6			−0.0597349			−0.0298675	+	0.999554i	$0.509509\pi$
$212$	4.12542e7			0.297367
$213$			3.20267e8i			2.27083i
$214$			2.04330e7i			0.142523i
$215$			2.38237e7i			0.163484i
$216$			2.38700e8i			1.61163i
$217$	−2.71678e6			−0.0180487
$218$	1.68076e6			0.0109877
$219$		−	8.84455e7i		−	0.569012i
$220$	1.63380e8			1.03448
$221$	−1.39946e8	+	4.85976e7i	−0.872143	+	0.302860i
$222$	1.86455e8			1.14377
$223$			1.13810e8i			0.687248i	0.939107	+	0.343624i	$0.111654\pi$
$223$			1.13810e8i			0.687248i	−0.939107	+	0.343624i	$0.888346\pi$
$224$	−5.97553e7			−0.355229
$225$	2.10152e8			1.22997
$226$		−	1.27819e8i		−	0.736574i
$227$			1.23924e7i			0.0703177i	0.999382	+	0.0351588i	$0.0111937\pi$
$227$			1.23924e7i			0.0703177i	−0.999382	+	0.0351588i	$0.988806\pi$
$228$		−	1.07880e7i		−	0.0602793i
$229$			3.54652e8i			1.95155i	0.218786	+	0.975773i	$0.429790\pi$
$229$			3.54652e8i			1.95155i	−0.218786	+	0.975773i	$0.570210\pi$
$230$	2.60796e7			0.141336
$231$	−2.31126e8			−1.23369
$232$		−	1.89915e8i		−	0.998509i
$233$	−3.82071e7			−0.197879			−0.0989393	−	0.995093i	$-0.531545\pi$
$233$	−3.82071e7			−0.197879			−0.0989393	+	0.995093i	$0.531545\pi$
$234$	5.60900e7	+	1.61522e8i	0.286174	+	0.824092i
$235$	−2.20371e8			−1.10769
$236$		−	1.22357e8i		−	0.605952i
$237$	−2.93016e8			−1.42979
$238$	−2.81976e7			−0.135579
$239$			2.91236e8i			1.37992i	0.723849	+	0.689958i	$0.242371\pi$
$239$			2.91236e8i			1.37992i	−0.723849	+	0.689958i	$0.757629\pi$
$240$			1.47854e8i			0.690387i
$241$		−	2.82230e8i		−	1.29880i	−0.760445	−	0.649402i	$-0.775019\pi$
$241$		−	2.82230e8i		−	1.29880i	0.760445	−	0.649402i	$-0.224981\pi$
$242$			1.95558e8i			0.886998i
$243$	−2.21898e8			−0.992045
$244$	1.82801e8			0.805588
$245$			2.21129e7i			0.0960647i
$246$	−9.69768e7			−0.415332
$247$	−3.06186e6	−	8.81720e6i	−0.0129284	−	0.0372299i
$248$	−8.24049e6			−0.0343062
$249$			1.59405e8i			0.654343i
$250$	−9.99078e7			−0.404399
$251$	−8.45121e6			−0.0337335			−0.0168667	−	0.999858i	$-0.505369\pi$
$251$	−8.45121e6			−0.0337335			−0.0168667	+	0.999858i	$0.505369\pi$
$252$		−	1.83041e8i		−	0.720522i
$253$		−	2.52472e8i		−	0.980146i
$254$		−	8.96903e6i		−	0.0343421i
$255$			2.96134e8i			1.11840i
$256$	−5.13591e7			−0.191328
$257$	5.16978e7			0.189979			0.0949896	−	0.995478i	$-0.469718\pi$
$257$	5.16978e7			0.189979			0.0949896	+	0.995478i	$0.469718\pi$
$258$		−	4.69394e7i		−	0.170164i
$259$	−1.72696e8			−0.617638
$260$	5.30796e7	+	1.52853e8i	0.187293	+	0.539345i
$261$	8.96364e8			3.12063
$262$			1.10911e8i			0.380997i
$263$	1.16236e8			0.394001			0.197000	−	0.980403i	$-0.436880\pi$
$263$	1.16236e8			0.394001			0.197000	+	0.980403i	$0.436880\pi$
$264$	−7.01046e8			−2.34495
$265$		−	7.13488e7i		−	0.235519i
$266$		−	1.77657e6i		−	0.00578757i
$267$			7.79217e8i			2.50535i
$268$			4.83254e8i			1.53357i
$269$	7.00228e7			0.219334			0.109667	−	0.993968i	$-0.465022\pi$
$269$	7.00228e7			0.219334			0.109667	+	0.993968i	$0.465022\pi$
$270$	1.89563e8			0.586112
$271$			3.52584e8i			1.07614i	0.842900	+	0.538071i	$0.180847\pi$
$271$			3.52584e8i			1.07614i	−0.842900	+	0.538071i	$0.819153\pi$
$272$	1.74626e8			0.526158
$273$	−7.50890e7	−	2.16233e8i	−0.223361	−	0.643210i
$274$	8.13011e7			0.238764
$275$			3.42312e8i			0.992563i
$276$	2.88999e8			0.827397
$277$	6.72294e7			0.190055			0.0950277	−	0.995475i	$-0.469706\pi$
$277$	6.72294e7			0.190055			0.0950277	+	0.995475i	$0.469706\pi$
$278$		−	1.68370e8i		−	0.470011i
$279$		−	3.88935e7i		−	0.107217i
$280$			6.70723e7i			0.182596i
$281$		−	4.62581e8i		−	1.24370i	−0.783137	−	0.621849i	$-0.786382\pi$
$281$		−	4.62581e8i		−	1.24370i	0.783137	−	0.621849i	$-0.213618\pi$
$282$	4.34192e8			1.15295
$283$	−9.43018e7			−0.247325			−0.123662	−	0.992324i	$-0.539464\pi$
$283$	−9.43018e7			−0.247325			−0.123662	+	0.992324i	$0.539464\pi$
$284$		−	4.13144e8i		−	1.07025i
$285$	−1.86577e7			−0.0477421
$286$	−2.63099e8	+	9.13636e7i	−0.665025	+	0.230936i
$287$	8.98207e7			0.224280
$288$		−	8.55459e8i		−	2.11021i
$289$	−6.05834e7			−0.147643
$290$	−1.50821e8			−0.363135
$291$			1.60468e8i			0.381735i
$292$			1.14094e8i			0.268179i
$293$			2.98883e7i			0.0694167i	0.999397	+	0.0347083i	$0.0110502\pi$
$293$			2.98883e7i			0.0694167i	−0.999397	+	0.0347083i	$0.988950\pi$
$294$		−	4.35686e7i		−	0.0999903i
$295$	−2.11616e8			−0.479924
$296$	−5.23819e8			−1.17398
$297$		−	1.83512e9i		−	4.06460i
$298$	−2.41809e8			−0.529317
$299$	2.36204e8	−	8.20239e7i	0.511019	−	0.177456i
$300$	−3.91837e8			−0.837878
$301$			4.34756e7i			0.0918889i
$302$	1.39062e8			0.290525
$303$	1.16933e9			2.41484
$304$			1.10022e7i			0.0224605i
$305$		−	3.16152e8i		−	0.638038i
$306$		−	4.03678e8i		−	0.805396i
$307$		−	2.37632e8i		−	0.468729i	−0.972149	−	0.234364i	$-0.924699\pi$
$307$		−	2.37632e8i		−	0.468729i	0.972149	−	0.234364i	$-0.0753008\pi$
$308$	2.98152e8			0.581446
$309$	−9.49683e8			−1.83115
$310$			6.54416e6i			0.0124764i
$311$	−6.25103e8			−1.17839			−0.589196	−	0.807990i	$-0.700556\pi$
$311$	−6.25103e8			−1.17839			−0.589196	+	0.807990i	$0.700556\pi$
$312$	−2.27758e8	−	6.55874e8i	−0.424554	−	1.22259i
$313$	9.68662e8			1.78553			0.892765	−	0.450523i	$-0.148763\pi$
$313$	9.68662e8			1.78553			0.892765	+	0.450523i	$0.148763\pi$
$314$		−	3.01611e7i		−	0.0549785i
$315$	−3.16569e8			−0.570665
$316$	3.77990e8			0.673870
$317$		−	1.10049e8i		−	0.194035i	−0.995283	−	0.0970174i	$-0.969070\pi$
$317$		−	1.10049e8i		−	0.194035i	0.995283	−	0.0970174i	$-0.0309303\pi$
$318$			1.40577e8i			0.245143i
$319$			1.46007e9i			2.51829i
$320$		−	8.07049e7i		−	0.137681i
$321$	3.91603e8			0.660813
$322$	4.75924e7			0.0794405
$323$			2.20361e7i			0.0363853i
$324$	9.33536e8			1.52484
$325$	−3.20255e8	+	1.11212e8i	−0.517493	+	0.179704i
$326$	1.02620e8			0.164049
$327$		−	3.22121e7i		−	0.0509451i
$328$	2.72442e8			0.426301
$329$	−4.02153e8			−0.622595
$330$			5.56733e8i			0.852803i
$331$			1.10906e9i			1.68096i	0.541842	+	0.840480i	$0.317727\pi$
$331$			1.10906e9i			1.68096i	−0.541842	+	0.840480i	$0.682273\pi$
$332$		−	2.05632e8i		−	0.308396i
$333$		−	2.47233e9i		−	3.66903i
$334$	9.26133e7			0.136007
$335$	8.35784e8			1.21461
$336$			2.69817e8i			0.388045i
$337$	8.27317e7			0.117752			0.0588758	−	0.998265i	$-0.481248\pi$
$337$	8.27317e7			0.117752			0.0588758	+	0.998265i	$0.481248\pi$
$338$	−1.70953e8	−	2.16463e8i	−0.240807	−	0.304913i
$339$	−2.44968e9			−3.41516
$340$		−	3.82012e8i		−	0.527110i
$341$	6.33528e7			0.0865218
$342$	2.54334e7			0.0343806
$343$			4.03536e7i			0.0539949i
$344$			1.31869e8i			0.174658i
$345$		−	4.99821e8i		−	0.655311i
$346$		−	3.60688e8i		−	0.468128i
$347$	−5.61394e8			−0.721298			−0.360649	−	0.932702i	$-0.617445\pi$
$347$	−5.61394e8			−0.721298			−0.360649	+	0.932702i	$0.617445\pi$
$348$	−1.67130e9			−2.12583
$349$			9.70689e8i			1.22234i	0.791500	+	0.611169i	$0.209300\pi$
$349$			9.70689e8i			1.22234i	−0.791500	+	0.611169i	$0.790700\pi$
$350$	−6.45279e7			−0.0804469
$351$	1.71688e9	−	5.96202e8i	2.11916	−	0.735899i
$352$	1.39344e9			1.70290
$353$			7.52870e8i			0.910979i	0.890241	+	0.455489i	$0.150536\pi$
$353$			7.52870e8i			0.910979i	−0.890241	+	0.455489i	$0.849464\pi$
$354$	4.16944e8			0.499535
$355$	−7.14530e8			−0.847659
$356$		−	1.00519e9i		−	1.18079i
$357$			5.40413e8i			0.628618i
$358$			2.53423e8i			0.291914i
$359$		−	7.12777e8i		−	0.813061i	−0.913637	−	0.406531i	$-0.866738\pi$
$359$		−	7.12777e8i		−	0.813061i	0.913637	−	0.406531i	$-0.133262\pi$
$360$	−9.60209e8			−1.08469
$361$	8.92483e8			0.998447
$362$		−	3.50772e8i		−	0.388638i
$363$	3.74792e9			4.11260
$364$	9.68646e7	+	2.78940e8i	0.105271	+	0.303149i
$365$	1.97326e8			0.212402
$366$			6.22909e8i			0.664111i
$367$	−9.85076e8			−1.04025			−0.520126	−	0.854090i	$-0.674115\pi$
$367$	−9.85076e8			−1.04025			−0.520126	+	0.854090i	$0.674115\pi$
$368$	−2.94736e8			−0.308295
$369$			1.28588e9i			1.33231i
$370$			4.15989e8i			0.426949i
$371$		−	1.30204e8i		−	0.132378i
$372$			7.25185e7i			0.0730379i
$373$	−1.75407e9			−1.75011			−0.875055	−	0.484024i	$-0.839175\pi$
$373$	−1.75407e9			−1.75011			−0.875055	+	0.484024i	$0.839175\pi$
$374$	6.57541e8			0.649938
$375$			1.91476e9i			1.87501i
$376$	−1.21980e9			−1.18340
$377$	−1.36599e9	+	4.74352e8i	−1.31296	+	0.455938i
$378$	3.45932e8			0.329435
$379$		−	3.77429e8i		−	0.356121i	−0.984020	−	0.178061i	$-0.943018\pi$
$379$		−	3.77429e8i		−	0.356121i	0.984020	−	0.178061i	$-0.0569823\pi$
$380$	2.40684e7			0.0225012
$381$	−1.71893e8			−0.159229
$382$		−	6.85014e8i		−	0.628750i
$383$		−	1.80137e9i		−	1.63835i	−0.573543	−	0.819175i	$-0.694432\pi$
$383$		−	1.80137e9i		−	1.63835i	0.573543	−	0.819175i	$-0.305568\pi$
$384$			2.03764e9i			1.83641i
$385$		−	5.15651e8i		−	0.460515i
$386$	−6.77777e8			−0.599834
$387$	−6.22398e8			−0.545858
$388$		−	2.07003e8i		−	0.179914i
$389$	1.31017e9			1.12851			0.564254	−	0.825601i	$-0.309164\pi$
$389$	1.31017e9			1.12851			0.564254	+	0.825601i	$0.309164\pi$
$390$	−5.20860e8	+	1.80874e8i	−0.444626	+	0.154401i
$391$	−5.90323e8			−0.499426
$392$			1.22400e8i			0.102631i
$393$	2.12564e9			1.76651
$394$	−8.38742e7			−0.0690863
$395$		−	6.53732e8i		−	0.533715i
$396$			4.26835e9i			3.45403i
$397$			1.20398e9i			0.965724i	0.875696	+	0.482862i	$0.160403\pi$
$397$			1.20398e9i			0.965724i	−0.875696	+	0.482862i	$0.839597\pi$
$398$		−	8.32319e8i		−	0.661758i
$399$	−3.40483e7			−0.0268343
$400$	3.99616e8			0.312200
$401$		−	1.80885e9i		−	1.40087i	−0.713718	−	0.700433i	$-0.752990\pi$
$401$		−	1.80885e9i		−	1.40087i	0.713718	−	0.700433i	$-0.247010\pi$
$402$	−1.64673e9			−1.26424
$403$	2.05823e7	+	5.92706e7i	0.0156648	+	0.0451099i
$404$	−1.50843e9			−1.13813
$405$		−	1.61454e9i		−	1.20770i
$406$	−2.75231e8			−0.204106
$407$	4.02712e9			2.96083
$408$			1.63917e9i			1.19485i
$409$		−	1.46638e8i		−	0.105977i	−0.998595	−	0.0529887i	$-0.983125\pi$
$409$		−	1.46638e8i		−	0.105977i	0.998595	−	0.0529887i	$-0.0168747\pi$
$410$		−	2.16359e8i		−	0.155036i
$411$		−	1.55815e9i		−	1.10704i
$412$	1.22509e9			0.863032
$413$	−3.86177e8			−0.269750
$414$			6.81334e8i			0.471910i
$415$	−3.55640e8			−0.244254
$416$	4.52705e8	+	1.30365e9i	0.308311	+	0.887839i
$417$	−3.22685e9			−2.17923
$418$			4.14279e7i			0.0277444i
$419$	1.67385e9			1.11165			0.555824	−	0.831300i	$-0.312403\pi$
$419$	1.67385e9			1.11165			0.555824	+	0.831300i	$0.312403\pi$
$420$	5.90254e8			0.388746
$421$		−	3.84267e8i		−	0.250984i	−0.992095	−	0.125492i	$-0.959949\pi$
$421$		−	3.84267e8i		−	0.250984i	0.992095	−	0.125492i	$-0.0400509\pi$
$422$			3.58305e7i			0.0232092i
$423$		−	5.75723e9i		−	3.69847i
$424$		−	3.94932e8i		−	0.251618i
$425$	8.00386e8			0.505753
$426$	1.40782e9			0.882297
$427$		−	5.76944e8i		−	0.358621i
$428$	−5.05166e8			−0.311445
$429$	1.75100e9	+	5.04235e9i	1.07075	+	3.08342i
$430$	1.04724e8			0.0635192
$431$		−	2.10651e9i		−	1.26734i	−0.773604	−	0.633669i	$-0.781548\pi$
$431$		−	2.10651e9i		−	1.26734i	0.773604	−	0.633669i	$-0.218452\pi$
$432$	−2.14233e9			−1.27848
$433$	−2.66957e9			−1.58028			−0.790138	−	0.612929i	$-0.789991\pi$
$433$	−2.66957e9			−1.58028			−0.790138	+	0.612929i	$0.789991\pi$
$434$			1.19424e7i			0.00701256i
$435$			2.89051e9i			1.68369i
$436$			4.15536e7i			0.0240107i
$437$		−	3.71929e7i		−	0.0213194i
$438$	−3.88787e8			−0.221081
$439$	−1.84724e9			−1.04207			−0.521035	−	0.853536i	$-0.674454\pi$
$439$	−1.84724e9			−1.04207			−0.521035	+	0.853536i	$0.674454\pi$
$440$		−	1.56406e9i		−	0.875326i
$441$	−5.77703e8			−0.320752
$442$	2.13624e8	+	6.15172e8i	0.117672	+	0.338859i
$443$	1.47385e9			0.805453			0.402727	−	0.915320i	$-0.368062\pi$
$443$	1.47385e9			0.805453			0.402727	+	0.915320i	$0.368062\pi$
$444$			4.60975e9i			2.49941i
$445$	−1.73846e9			−0.935203
$446$	5.00283e8			0.267020
$447$			4.63433e9i			2.45420i
$448$		−	1.47278e8i		−	0.0773863i
$449$		−	2.89813e9i		−	1.51097i	−0.655166	−	0.755485i	$-0.727401\pi$
$449$		−	2.89813e9i		−	1.51097i	0.655166	−	0.755485i	$-0.272599\pi$
$450$		−	9.23783e8i		−	0.477888i
$451$	−2.09453e9			−1.07515
$452$	3.16008e9			1.60958
$453$		−	2.66515e9i		−	1.34703i
$454$	5.44742e7			0.0273209
$455$	4.82425e8	−	1.67527e8i	0.240099	−	0.0833766i
$456$	−1.03275e8			−0.0510055
$457$		−	1.14745e9i		−	0.562376i	−0.959653	−	0.281188i	$-0.909272\pi$
$457$		−	1.14745e9i		−	0.562376i	0.959653	−	0.281188i	$-0.0907284\pi$
$458$	1.55897e9			0.758245
$459$	−4.29084e9			−2.07109
$460$			6.44767e8i			0.308852i
$461$			2.80018e9i			1.33117i	0.746324	+	0.665583i	$0.231817\pi$
$461$			2.80018e9i			1.33117i	−0.746324	+	0.665583i	$0.768183\pi$
$462$			1.01598e9i			0.479333i
$463$		−	3.99259e8i		−	0.186948i	−0.995622	−	0.0934742i	$-0.970203\pi$
$463$		−	3.99259e8i		−	0.186948i	0.995622	−	0.0934742i	$-0.0297973\pi$
$464$	1.70449e9			0.792101
$465$	1.25420e8			0.0578472
$466$			1.67950e8i			0.0768828i
$467$	−8.00802e8			−0.363845			−0.181922	−	0.983313i	$-0.558232\pi$
$467$	−8.00802e8			−0.363845			−0.181922	+	0.983313i	$0.558232\pi$
$468$	−3.99331e9	+	1.38672e9i	−1.80083	+	0.625356i
$469$	1.52521e9			0.682694
$470$			9.68701e8i			0.430375i
$471$	−5.78043e8			−0.254910
$472$	−1.17134e9			−0.512728
$473$		−	1.01381e9i		−	0.440497i
$474$			1.28804e9i			0.555525i
$475$			5.04278e7i			0.0215895i
$476$		−	6.97131e8i		−	0.296272i
$477$	1.86400e9			0.786379
$478$	1.28021e9			0.536147
$479$			1.01534e9i			0.422123i	0.977473	+	0.211061i	$0.0676920\pi$
$479$			1.01534e9i			0.422123i	−0.977473	+	0.211061i	$0.932308\pi$
$480$	2.75860e9			1.13853
$481$	1.30834e9	+	3.76763e9i	0.536061	+	1.54369i
$482$	−1.24062e9			−0.504632
$483$		−	9.12119e8i		−	0.368330i
$484$	−4.83480e9			−1.93830
$485$	−3.58010e8			−0.142495
$486$			9.75414e8i			0.385445i
$487$		−	1.43153e9i		−	0.561628i	−0.959762	−	0.280814i	$-0.909396\pi$
$487$		−	1.43153e9i		−	0.561628i	0.959762	−	0.280814i	$-0.0906044\pi$
$488$		−	1.74997e9i		−	0.681651i
$489$		−	1.96674e9i		−	0.760618i
$490$	9.72033e7			0.0373246
$491$	−3.09965e9			−1.18175			−0.590877	−	0.806762i	$-0.701218\pi$
$491$	−3.09965e9			−1.18175			−0.590877	+	0.806762i	$0.701218\pi$
$492$		−	2.39756e9i		−	0.907595i
$493$	3.41389e9			1.28317
$494$	−3.87585e7	+	1.34592e7i	−0.0144651	+	0.00502315i
$495$	7.38208e9			2.73565
$496$		−	7.39582e7i		−	0.0272145i
$497$	−1.30394e9			−0.476442
$498$	7.00711e8			0.254235
$499$		−	2.64781e9i		−	0.953969i	−0.878912	−	0.476985i	$-0.841730\pi$
$499$		−	2.64781e9i		−	0.953969i	0.878912	−	0.476985i	$-0.158270\pi$
$500$		−	2.47003e9i		−	0.883704i
$501$		−	1.77495e9i		−	0.630601i
$502$			3.71496e7i			0.0131066i
$503$	1.29576e9			0.453979			0.226989	−	0.973897i	$-0.427112\pi$
$503$	1.29576e9			0.453979			0.226989	+	0.973897i	$0.427112\pi$
$504$	−1.75228e9			−0.609672
$505$			2.60882e9i			0.901415i
$506$	−1.10981e9			−0.380822
$507$	−4.14857e9	+	3.27635e9i	−1.41374	+	1.11651i
$508$	2.21742e8			0.0750455
$509$			1.40051e9i			0.470731i	0.971907	+	0.235366i	$0.0756287\pi$
$509$			1.40051e9i			0.470731i	−0.971907	+	0.235366i	$0.924371\pi$
$510$	1.30174e9			0.434539
$511$	3.60098e8			0.119384
$512$		−	2.87015e9i		−	0.945061i
$513$		−	2.70342e8i		−	0.0884101i
$514$		−	2.27252e8i		−	0.0738137i
$515$		−	2.11878e9i		−	0.683535i
$516$	1.16048e9			0.371848
$517$	9.37782e9			2.98459
$518$			7.59135e8i			0.239975i
$519$	−6.91266e9			−2.17050
$520$	1.46328e9	−	5.08138e8i	0.456369	−	0.158478i
$521$	9.25237e7			0.0286629			0.0143315	−	0.999897i	$-0.495438\pi$
$521$	9.25237e7			0.0286629			0.0143315	+	0.999897i	$0.495438\pi$
$522$		−	3.94022e9i		−	1.21248i
$523$	−1.83856e9			−0.561981			−0.280991	−	0.959711i	$-0.590663\pi$
$523$	−1.83856e9			−0.561981			−0.280991	+	0.959711i	$0.590663\pi$
$524$	−2.74207e9			−0.832567
$525$			1.23669e9i			0.372996i
$526$		−	5.10949e8i		−	0.153083i
$527$		−	1.48130e8i		−	0.0440865i
$528$		−	6.29187e9i		−	1.86021i
$529$	−2.40847e9			−0.707369
$530$	−3.13634e8			−0.0915076
$531$		−	5.52852e9i		−	1.60243i
$532$	4.39222e7			0.0126472
$533$	−6.80480e8	−	1.95957e9i	−0.194657	−	0.560552i
$534$	3.42526e9			0.973419
$535$			8.73682e8i			0.246669i
$536$	4.62625e9			1.29763
$537$	4.85691e9			1.35347
$538$		−	3.07805e8i		−	0.0852192i
$539$		−	9.41008e8i		−	0.258841i
$540$			4.68658e9i			1.28079i
$541$		−	2.03654e9i		−	0.552971i	−0.961018	−	0.276485i	$-0.910830\pi$
$541$		−	2.03654e9i		−	0.552971i	0.961018	−	0.276485i	$-0.0891698\pi$
$542$	1.54988e9			0.418119
$543$	−6.72263e9			−1.80194
$544$		−	3.25810e9i		−	0.867698i
$545$	7.18666e7			0.0190169
$546$	−9.50513e8	+	3.30075e8i	−0.249910	+	0.0867837i
$547$	−1.84441e8			−0.0481840			−0.0240920	−	0.999710i	$-0.507669\pi$
$547$	−1.84441e8			−0.0481840			−0.0240920	+	0.999710i	$0.507669\pi$
$548$			2.01001e9i			0.521756i
$549$	8.25954e9			2.13036
$550$	1.50473e9			0.385646
$551$			2.15090e8i			0.0547759i
$552$		−	2.76662e9i		−	0.700104i
$553$		−	1.19299e9i		−	0.299984i
$554$		−	2.95526e8i		−	0.0738432i
$555$	7.97253e9			1.97957
$556$	4.16262e9			1.02708
$557$			2.24904e9i			0.551447i	0.961237	+	0.275723i	$0.0889174\pi$
$557$			2.24904e9i			0.551447i	−0.961237	+	0.275723i	$0.911083\pi$
$558$	−1.70967e8			−0.0416575
$559$	9.48485e8	−	3.29370e8i	0.229662	−	0.0797523i
$560$	−6.01973e8			−0.144850
$561$		−	1.26019e10i		−	3.01347i
$562$	−2.03340e9			−0.483221
$563$	5.05532e9			1.19390			0.596952	−	0.802277i	$-0.296378\pi$
$563$	5.05532e9			1.19390			0.596952	+	0.802277i	$0.296378\pi$
$564$			1.07346e10i			2.51946i
$565$		−	5.46534e9i		−	1.27482i
$566$			4.14530e8i			0.0960944i
$567$		−	2.94637e9i		−	0.678807i
$568$	−3.95508e9			−0.905599
$569$	−4.96681e9			−1.13028			−0.565138	−	0.824997i	$-0.691177\pi$
$569$	−4.96681e9			−1.13028			−0.565138	+	0.824997i	$0.691177\pi$
$570$			8.20152e7i			0.0185495i
$571$	6.96990e9			1.56675			0.783376	−	0.621548i	$-0.213496\pi$
$571$	6.96990e9			1.56675			0.783376	+	0.621548i	$0.213496\pi$
$572$	−2.25879e9	−	6.50461e9i	−0.504649	−	1.45323i
$573$	−1.31284e10			−2.91523
$574$		−	3.94832e8i		−	0.0871406i
$575$	−1.35091e9			−0.296338
$576$	2.10843e9			0.459707
$577$			8.26709e9i			1.79158i	0.444473	+	0.895792i	$0.353391\pi$
$577$			8.26709e9i			1.79158i	−0.444473	+	0.895792i	$0.646609\pi$
$578$			2.66311e8i			0.0573644i
$579$			1.29897e10i			2.78116i
$580$		−	3.72875e9i		−	0.793533i
$581$	−6.49004e8			−0.137288
$582$	7.05380e8			0.148318
$583$			3.03623e9i			0.634592i
$584$	1.09224e9			0.226920
$585$	2.39832e9	+	6.90641e9i	0.495291	+	1.42629i
$586$	1.31382e8			0.0269709
$587$		−	7.23081e9i		−	1.47555i	−0.675048	−	0.737774i	$-0.735877\pi$
$587$		−	7.23081e9i		−	1.47555i	0.675048	−	0.737774i	$-0.264123\pi$
$588$	1.07715e9			0.218502
$589$	9.33282e6			0.00188196
$590$			9.30218e8i			0.186467i
$591$			1.60747e9i			0.320322i
$592$		−	4.70127e9i		−	0.931299i
$593$		−	2.48971e8i		−	0.0490295i	−0.999699	−	0.0245147i	$-0.992196\pi$
$593$		−	2.48971e8i		−	0.0490295i	0.999699	−	0.0245147i	$-0.00780406\pi$
$594$	−8.06680e9			−1.57924
$595$	−1.20568e9			−0.234652
$596$		−	5.97826e9i		−	1.15668i
$597$	−1.59516e10			−3.06827
$598$	−3.60559e8	−	1.03830e9i	−0.0689481	−	0.198549i
$599$	−6.81902e9			−1.29637			−0.648184	−	0.761484i	$-0.724471\pi$
$599$	−6.81902e9			−1.29637			−0.648184	+	0.761484i	$0.724471\pi$
$600$			3.75110e9i			0.708973i
$601$	−1.47546e9			−0.277246			−0.138623	−	0.990345i	$-0.544268\pi$
$601$	−1.47546e9			−0.277246			−0.138623	+	0.990345i	$0.544268\pi$
$602$	1.91109e8			0.0357021
$603$			2.18350e10i			4.05549i
$604$			3.43803e9i			0.634864i
$605$			8.36176e9i			1.53516i
$606$		−	5.14012e9i		−	0.938250i
$607$	−5.48425e9			−0.995306			−0.497653	−	0.867376i	$-0.665805\pi$
$607$	−5.48425e9			−0.995306			−0.497653	+	0.867376i	$0.665805\pi$
$608$	2.05274e8			0.0370401
$609$			5.27487e9i			0.946348i
$610$	−1.38974e9			−0.247901
$611$	3.04670e9	+	8.77355e9i	0.540363	+	1.55608i
$612$	9.98015e9			1.75998
$613$			8.09588e9i			1.41955i	0.704426	+	0.709777i	$0.251204\pi$
$613$			8.09588e9i			1.41955i	−0.704426	+	0.709777i	$0.748796\pi$
$614$	−1.04458e9			−0.182118
$615$	−4.14657e9			−0.718830
$616$		−	2.85424e9i		−	0.491993i
$617$			2.13548e9i			0.366013i	0.983112	+	0.183007i	$0.0585830\pi$
$617$			2.13548e9i			0.366013i	−0.983112	+	0.183007i	$0.941417\pi$
$618$			4.17460e9i			0.711467i
$619$			3.33065e9i			0.564432i	0.959351	+	0.282216i	$0.0910695\pi$
$619$			3.33065e9i			0.564432i	−0.959351	+	0.282216i	$0.908931\pi$
$620$	−1.61792e8			−0.0272637
$621$	7.24217e9			1.21352
$622$			2.74781e9i			0.457847i
$623$	−3.17251e9			−0.525648
$624$	5.88645e9	−	2.04413e9i	0.969857	−	0.336792i
$625$	−9.28350e8			−0.152101
$626$		−	4.25802e9i		−	0.693742i
$627$	7.93975e8			0.128638
$628$	7.45674e8			0.120141
$629$		−	9.41611e9i		−	1.50867i
$630$			1.39157e9i			0.221723i
$631$			8.93580e9i			1.41589i	0.706266	+	0.707947i	$0.250378\pi$
$631$			8.93580e9i			1.41589i	−0.706266	+	0.707947i	$0.749622\pi$
$632$		−	3.61855e9i		−	0.570197i
$633$	6.86699e8			0.107610
$634$	−4.83752e8			−0.0753894
$635$		−	3.83501e8i		−	0.0594372i
$636$	−3.47550e9			−0.535695
$637$	8.80373e8	−	3.05718e8i	0.134952	−	0.0468633i
$638$	6.41813e9			0.978444
$639$		−	1.86672e10i		−	2.83026i
$640$	−4.54607e9			−0.685498
$641$	−3.05170e9			−0.457656			−0.228828	−	0.973467i	$-0.573489\pi$
$641$	−3.05170e9			−0.457656			−0.228828	+	0.973467i	$0.573489\pi$
$642$		−	1.72140e9i		−	0.256749i
$643$		−	2.87131e9i		−	0.425934i	−0.977059	−	0.212967i	$-0.931687\pi$
$643$		−	2.87131e9i		−	0.425934i	0.977059	−	0.212967i	$-0.0683126\pi$
$644$			1.17663e9i			0.173596i
$645$		−	2.00705e9i		−	0.294510i
$646$	9.68657e7			0.0141370
$647$	1.45477e9			0.211168			0.105584	−	0.994410i	$-0.466329\pi$
$647$	1.45477e9			0.211168			0.105584	+	0.994410i	$0.466329\pi$
$648$		−	8.93686e9i		−	1.29025i
$649$	9.00528e9			1.29313
$650$	4.88862e8	+	1.40777e9i	0.0698215	+	0.201064i
$651$	2.28878e8			0.0325141
$652$			2.53709e9i			0.358484i
$653$	1.57506e9			0.221361			0.110681	−	0.993856i	$-0.464697\pi$
$653$	1.57506e9			0.221361			0.110681	+	0.993856i	$0.464697\pi$
$654$	−1.41597e8			−0.0197940
$655$			4.74239e9i			0.659406i
$656$			2.44516e9i			0.338177i
$657$			5.15517e9i			0.709192i
$658$			1.76777e9i			0.241900i
$659$	1.15694e10			1.57475			0.787374	−	0.616476i	$-0.211440\pi$
$659$	1.15694e10			1.57475			0.787374	+	0.616476i	$0.211440\pi$
$660$	−1.37642e10			−1.86357
$661$		−	5.97525e9i		−	0.804732i	−0.915479	−	0.402366i	$-0.868188\pi$
$661$		−	5.97525e9i		−	0.804732i	0.915479	−	0.402366i	$-0.131812\pi$
$662$	4.87519e9			0.653113
$663$	1.17899e10	−	4.09416e9i	1.57113	−	0.545591i
$664$	−1.96855e9			−0.260950
$665$		−	7.59632e7i		−	0.0100168i
$666$	−1.08678e10			−1.42555
$667$	−5.76203e9			−0.751857
$668$			2.28968e9i			0.297206i
$669$		−	9.58804e9i		−	1.23805i
$670$		−	3.67392e9i		−	0.471919i
$671$			1.34538e10i			1.71916i
$672$	5.03415e9			0.639932
$673$	−1.05117e10			−1.32930			−0.664648	−	0.747157i	$-0.731418\pi$
$673$	−1.05117e10			−1.32930			−0.664648	+	0.747157i	$0.731418\pi$
$674$		−	3.63670e8i		−	0.0457507i
$675$	−9.81925e9			−1.22890
$676$	5.35164e9	−	4.22649e9i	0.666306	−	0.526218i
$677$	−7.80842e9			−0.967170			−0.483585	−	0.875297i	$-0.660666\pi$
$677$	−7.80842e9			−0.967170			−0.483585	+	0.875297i	$0.660666\pi$
$678$			1.07683e10i			1.32691i
$679$	−6.53329e8			−0.0800917
$680$	−3.65705e9			−0.446016
$681$		−	1.04401e9i		−	0.126675i
$682$		−	2.78485e8i		−	0.0336168i
$683$			6.90087e9i			0.828765i	0.910103	+	0.414383i	$0.136002\pi$
$683$			6.90087e9i			0.828765i	−0.910103	+	0.414383i	$0.863998\pi$
$684$			6.28792e8i			0.0751295i
$685$	3.47631e9			0.413239
$686$	1.77386e8			0.0209789
$687$		−	2.98781e10i		−	3.51564i
$688$	−1.18352e9			−0.138554
$689$	−2.84059e9	+	9.86421e8i	−0.330858	+	0.114893i
$690$	−2.19710e9			−0.254612
$691$			7.32682e9i			0.844778i	0.906415	+	0.422389i	$0.138808\pi$
$691$			7.32682e9i			0.844778i	−0.906415	+	0.422389i	$0.861192\pi$
$692$	8.91731e9			1.02297
$693$	1.34715e10			1.53762
$694$			2.46777e9i			0.280250i
$695$		−	7.19923e9i		−	0.813465i
$696$			1.59996e10i			1.79878i
$697$			4.89739e9i			0.547835i
$698$	4.26693e9			0.474922
$699$	3.21880e9			0.356471
$700$		−	1.59533e9i		−	0.175795i
$701$	−1.96507e9			−0.215459			−0.107729	−	0.994180i	$-0.534358\pi$
$701$	−1.96507e9			−0.215459			−0.107729	+	0.994180i	$0.534358\pi$
$702$	−2.62077e9	−	7.54701e9i	−0.285923	−	0.823370i
$703$	5.93255e8			0.0644018
$704$			3.43438e9i			0.370974i
$705$	1.85654e10			1.99545
$706$	3.30945e9			0.353948
$707$			4.76082e9i			0.506657i
$708$			1.03081e10i			1.09160i
$709$		−	2.01835e9i		−	0.212684i	−0.994330	−	0.106342i	$-0.966086\pi$
$709$		−	2.01835e9i		−	0.212684i	0.994330	−	0.106342i	$-0.0339138\pi$
$710$			3.14091e9i			0.329346i
$711$	1.70789e10			1.78203
$712$	−9.62279e9			−0.999128
$713$			2.50017e8i			0.0258318i
$714$	2.37554e9			0.244241
$715$	−1.12497e10	+	3.90656e9i	−1.15098	+	0.399690i
$716$	−6.26539e9			−0.637900
$717$		−	2.45355e10i		−	2.48587i
$718$	−3.13321e9			−0.315903
$719$	−9.48745e9			−0.951915			−0.475958	−	0.879468i	$-0.657898\pi$
$719$	−9.48745e9			−0.951915			−0.475958	+	0.879468i	$0.657898\pi$
$720$		−	8.61786e9i		−	0.860470i
$721$		−	3.86655e9i		−	0.384193i
$722$		−	3.92316e9i		−	0.387932i
$723$			2.37768e10i			2.33975i
$724$	8.67217e9			0.849264
$725$	7.81241e9			0.761381
$726$		−	1.64750e10i		−	1.59789i
$727$	1.52418e10			1.47118			0.735591	−	0.677426i	$-0.236904\pi$
$727$	1.52418e10			1.47118			0.735591	+	0.677426i	$0.236904\pi$
$728$	2.67033e9	−	9.27297e8i	0.256510	−	0.0890757i
$729$	−9.23026e7			−0.00882404
$730$		−	8.67399e8i		−	0.0825257i
$731$	−2.37047e9			−0.224452
$732$	−1.54002e10			−1.45124
$733$			1.50315e10i			1.40973i	0.709339	+	0.704867i	$0.248994\pi$
$733$			1.50315e10i			1.40973i	−0.709339	+	0.704867i	$0.751006\pi$
$734$			4.33018e9i			0.404175i
$735$		−	1.86292e9i		−	0.173057i
$736$			5.49908e9i			0.508415i
$737$	−3.55666e10			−3.27270
$738$	5.65243e9			0.517652
$739$		−	1.51674e10i		−	1.38247i	−0.722628	−	0.691237i	$-0.757066\pi$
$739$		−	1.51674e10i		−	1.38247i	0.722628	−	0.691237i	$-0.242934\pi$
$740$	−1.02845e10			−0.932983
$741$	2.57949e8	+	7.42814e8i	0.0232901	+	0.0670682i
$742$	−5.72347e8			−0.0514335
$743$			4.66700e9i			0.417423i	0.977977	+	0.208712i	$0.0669270\pi$
$743$			4.66700e9i			0.417423i	−0.977977	+	0.208712i	$0.933073\pi$
$744$	6.94229e8			0.0618012
$745$	−1.03394e10			−0.916109
$746$			7.71049e9i			0.679980i
$747$		−	9.29116e9i		−	0.815545i
$748$			1.62564e10i			1.42027i
$749$			1.59437e9i			0.138645i
$750$	8.41684e9			0.728509
$751$	3.42853e9			0.295371			0.147686	−	0.989034i	$-0.452818\pi$
$751$	3.42853e9			0.295371			0.147686	+	0.989034i	$0.452818\pi$
$752$		−	1.09477e10i		−	0.938772i
$753$	7.11981e8			0.0607695
$754$	2.08515e9	+	6.00457e9i	0.177148	+	0.510132i
$755$	5.94605e9			0.502822
$756$			8.55250e9i			0.719891i
$757$	−5.99029e8			−0.0501894			−0.0250947	−	0.999685i	$-0.507989\pi$
$757$	−5.99029e8			−0.0501894			−0.0250947	+	0.999685i	$0.507989\pi$
$758$	−1.65909e9			−0.138366
$759$			2.12697e10i			1.76570i
$760$		−	2.30410e8i		−	0.0190394i
$761$			1.32096e10i			1.08653i	0.839560	+	0.543267i	$0.182813\pi$
$761$			1.32096e10i			1.08653i	−0.839560	+	0.543267i	$0.817187\pi$
$762$			7.55605e8i			0.0618661i
$763$	1.31149e8			0.0106888
$764$	1.69357e10			1.37396
$765$		−	1.72606e10i		−	1.39393i
$766$	−7.91842e9			−0.636557
$767$	2.92567e9	+	8.42501e9i	0.234121	+	0.674197i
$768$	4.32681e9			0.344670
$769$		−	3.08943e9i		−	0.244983i	−0.992470	−	0.122492i	$-0.960912\pi$
$769$		−	3.08943e9i		−	0.244983i	0.992470	−	0.122492i	$-0.0390885\pi$
$770$	−2.26669e9			−0.178926
$771$	−4.35533e9			−0.342240
$772$		−	1.67567e10i		−	1.31078i
$773$			3.64515e9i			0.283849i	0.989877	+	0.141924i	$0.0453290\pi$
$773$			3.64515e9i			0.283849i	−0.989877	+	0.141924i	$0.954671\pi$
$774$			2.73592e9i			0.212085i
$775$		−	3.38983e8i		−	0.0261591i
$776$	−1.98166e9			−0.152235
$777$	1.45490e10			1.11265
$778$		−	5.75922e9i		−	0.438465i
$779$	−3.08556e8			−0.0233859
$780$	−4.47175e9	−	1.28773e10i	−0.337401	−	0.971610i
$781$	3.04066e10			2.28397
$782$			2.59493e9i			0.194045i
$783$	−4.18821e10			−3.11790
$784$	−1.09853e9			−0.0814156
$785$		−	1.28964e9i		−	0.0951534i
$786$		−	9.34385e9i		−	0.686352i
$787$		−	1.17696e10i		−	0.860697i	−0.902663	−	0.430348i	$-0.858391\pi$
$787$		−	1.17696e10i		−	0.860697i	0.902663	−	0.430348i	$-0.141609\pi$
$788$		−	2.07363e9i		−	0.150969i
$789$	−9.79246e9			−0.709777
$790$	−2.87366e9			−0.207367
$791$		−	9.97365e9i		−	0.716533i
$792$	4.08614e10			2.92264
$793$	−1.25869e10	+	4.37091e9i	−0.896317	+	0.311255i
$794$	5.29244e9			0.375218
$795$			6.01086e9i			0.424279i
$796$	2.05775e10			1.44609
$797$	1.51754e10			1.06179			0.530893	−	0.847439i	$-0.321857\pi$
$797$	1.51754e10			1.06179			0.530893	+	0.847439i	$0.321857\pi$
$798$			1.49669e8i			0.0104261i
$799$		−	2.19270e10i		−	1.52078i
$800$		−	7.45590e9i		−	0.514855i
$801$		−	4.54177e10i		−	3.12257i
$802$	−7.95129e9			−0.544286
$803$	−8.39714e9			−0.572304
$804$		−	4.07122e10i		−	2.76267i
$805$	2.03497e9			0.137491
$806$	2.60540e8	−	9.04752e7i	0.0175268	−	0.00608635i
$807$	−5.89914e9			−0.395122
$808$			1.44404e10i			0.963030i
$809$	1.25468e10			0.833133			0.416567	−	0.909105i	$-0.363233\pi$
$809$	1.25468e10			0.833133			0.416567	+	0.909105i	$0.363233\pi$
$810$	−7.09718e9			−0.469233
$811$			2.59859e10i			1.71067i	0.518078	+	0.855334i	$0.326648\pi$
$811$			2.59859e10i			1.71067i	−0.518078	+	0.855334i	$0.673352\pi$
$812$		−	6.80456e9i		−	0.446020i
$813$		−	2.97038e10i		−	1.93863i
$814$		−	1.77023e10i		−	1.15039i
$815$	4.38789e9			0.283925
$816$	−1.47115e10			−0.947855
$817$		−	1.49350e8i		−	0.00958135i
$818$	−6.44586e8			−0.0411760
$819$	4.37667e9	+	1.26034e10i	0.278388	+	0.801670i
$820$	5.34906e9			0.338789
$821$		−	1.17467e10i		−	0.740821i	−0.928868	−	0.370411i	$-0.879217\pi$
$821$		−	1.17467e10i		−	0.740821i	0.928868	−	0.370411i	$-0.120783\pi$
$822$	−6.84930e9			−0.430125
$823$	−6.05330e9			−0.378523			−0.189262	−	0.981927i	$-0.560609\pi$
$823$	−6.05330e9			−0.378523			−0.189262	+	0.981927i	$0.560609\pi$
$824$		−	1.17279e10i		−	0.730258i
$825$		−	2.88385e10i		−	1.78806i
$826$			1.69755e9i			0.104807i
$827$			2.10722e10i			1.29551i	0.761849	+	0.647755i	$0.224292\pi$
$827$			2.10722e10i			1.29551i	−0.761849	+	0.647755i	$0.775708\pi$
$828$	−1.68447e10			−1.03123
$829$	2.76563e10			1.68598			0.842990	−	0.537929i	$-0.180793\pi$
$829$	2.76563e10			1.68598			0.842990	+	0.537929i	$0.180793\pi$
$830$			1.56331e9i			0.0949014i
$831$	−5.66381e9			−0.342377
$832$	−3.21308e9	+	1.11577e9i	−0.193415	+	0.0671652i
$833$	−2.20024e9			−0.131890
$834$			1.41845e10i			0.846707i
$835$	3.95999e9			0.235392
$836$	−1.02422e9			−0.0606280
$837$			1.81728e9i			0.107123i
$838$		−	7.35786e9i		−	0.431914i
$839$		−	1.44817e9i		−	0.0846549i	−0.999104	−	0.0423275i	$-0.986523\pi$
$839$		−	1.44817e9i		−	0.0846549i	0.999104	−	0.0423275i	$-0.0134773\pi$
$840$		−	5.65058e9i		−	0.328939i
$841$	1.60725e10			0.931744
$842$	−1.68915e9			−0.0975161
$843$			3.89706e10i			2.24048i
$844$	−8.85840e8			−0.0507174
$845$	−7.30968e9	−	9.25563e9i	−0.416773	−	0.527725i
$846$	−2.53075e10			−1.43699
$847$			1.52593e10i			0.862865i
$848$	3.54450e9			0.199604
$849$	7.94455e9			0.445546
$850$		−	3.51832e9i		−	0.196503i
$851$			1.58927e10i			0.883983i
$852$			3.48057e10i			1.92802i
$853$		−	1.28853e10i		−	0.710839i	−0.934707	−	0.355420i	$-0.884338\pi$
$853$		−	1.28853e10i		−	0.710839i	0.934707	−	0.355420i	$-0.115662\pi$
$854$	−2.53612e9			−0.139337
$855$	1.08749e9			0.0595038
$856$			4.83602e9i			0.263530i
$857$	−2.09568e10			−1.13735			−0.568673	−	0.822563i	$-0.692543\pi$
$857$	−2.09568e10			−1.13735			−0.568673	+	0.822563i	$0.692543\pi$
$858$	2.21651e10	−	7.69703e9i	1.19802	−	0.416023i
$859$	−2.01276e10			−1.08347			−0.541733	−	0.840551i	$-0.682232\pi$
$859$	−2.01276e10			−1.08347			−0.541733	+	0.840551i	$0.682232\pi$
$860$			2.58909e9i			0.138804i
$861$	−7.56704e9			−0.404031
$862$	−9.25974e9			−0.492406
$863$			8.78522e9i			0.465281i	0.972563	+	0.232640i	$0.0747365\pi$
$863$			8.78522e9i			0.465281i	−0.972563	+	0.232640i	$0.925264\pi$
$864$			3.99708e10i			2.10836i
$865$		−	1.54224e10i		−	0.810207i
$866$			1.17348e10i			0.613994i
$867$	5.10391e9			0.265972
$868$	−2.95252e8			−0.0153241
$869$			2.78194e10i			1.43806i
$870$	1.27060e10			0.654173
$871$	−1.15550e10	−	3.32748e10i	−0.592524	−	1.70629i
$872$	3.97797e8			0.0203168
$873$		−	9.35307e9i		−	0.475778i
$874$	−1.63492e8			−0.00828335
$875$	−7.79575e9			−0.393396
$876$		−	9.61201e9i		−	0.483114i
$877$			2.78197e10i			1.39269i	0.717708	+	0.696344i	$0.245191\pi$
$877$			2.78197e10i			1.39269i	−0.717708	+	0.696344i	$0.754809\pi$
$878$			8.12004e9i			0.404881i
$879$		−	2.51797e9i		−	0.125052i
$880$	1.40374e10			0.694382
$881$	−1.26692e10			−0.624214			−0.312107	−	0.950047i	$-0.601035\pi$
$881$	−1.26692e10			−0.624214			−0.312107	+	0.950047i	$0.601035\pi$
$882$			2.53946e9i			0.124624i
$883$	−6.02563e9			−0.294537			−0.147269	−	0.989097i	$-0.547048\pi$
$883$	−6.02563e9			−0.294537			−0.147269	+	0.989097i	$0.547048\pi$
$884$	−1.52089e10	+	5.28145e9i	−0.740484	+	0.257140i
$885$	1.78278e10			0.864564
$886$		−	6.47872e9i		−	0.312947i
$887$	3.56381e10			1.71468			0.857339	−	0.514753i	$-0.172116\pi$
$887$	3.56381e10			1.71468			0.857339	+	0.514753i	$0.172116\pi$
$888$	4.41297e10			2.11488
$889$		−	6.99848e8i		−	0.0334078i
$890$			7.64190e9i			0.363360i
$891$			6.87065e10i			3.25406i
$892$			1.23685e10i			0.583501i
$893$	1.38149e9			0.0649186
$894$	2.03715e10			0.953545
$895$			1.08360e10i			0.505227i
$896$	−8.29608e9			−0.385296
$897$	−1.98992e10	+	6.91019e9i	−0.920582	+	0.319681i
$898$	−1.27395e10			−0.587065
$899$		−	1.44587e9i		−	0.0663697i
$900$	2.28387e10			1.04430
$901$	7.09924e9			0.323352
$902$			9.20710e9i			0.417734i
$903$		−	3.66265e9i		−	0.165534i
$904$		−	3.02519e10i		−	1.36195i
$905$		−	1.49985e10i		−	0.672631i
$906$	−1.17154e10			−0.523369
$907$	−3.69484e10			−1.64426			−0.822130	−	0.569300i	$-0.807214\pi$
$907$	−3.69484e10			−1.64426			−0.822130	+	0.569300i	$0.807214\pi$
$908$			1.34677e9i			0.0597025i
$909$	−6.81560e10			−3.00975
$910$	−7.36410e8	−	2.12063e9i	−0.0323948	−	0.0932869i
$911$	−2.50912e10			−1.09953			−0.549764	−	0.835320i	$-0.685282\pi$
$911$	−2.50912e10			−1.09953			−0.549764	+	0.835320i	$0.685282\pi$
$912$		−	9.26888e8i		−	0.0404618i
$913$	1.51342e10			0.658128
$914$	−5.04393e9			−0.218503
$915$			2.66346e10i			1.14940i
$916$			3.85426e10i			1.65694i
$917$			8.65436e9i			0.370631i
$918$			1.88616e10i			0.804691i
$919$	2.62631e9			0.111620			0.0558100	−	0.998441i	$-0.482226\pi$
$919$	2.62631e9			0.111620			0.0558100	+	0.998441i	$0.482226\pi$
$920$	6.17244e9			0.261336
$921$			2.00196e10i			0.844397i
$922$	1.23090e10			0.517205
$923$	9.87861e9	+	2.84473e10i	0.413514	+	1.19079i
$924$	−2.51181e10			−1.04745
$925$		−	2.15480e10i		−	0.895181i
$926$	−1.75506e9			−0.0726361
$927$	5.53536e10			2.28227
$928$		−	3.18017e10i		−	1.30627i
$929$			3.79291e9i			0.155209i	0.996984	+	0.0776046i	$0.0247272\pi$
$929$			3.79291e9i			0.155209i	−0.996984	+	0.0776046i	$0.975273\pi$
$930$		−	5.51319e8i		−	0.0224757i
$931$		−	1.38625e8i		−	0.00563011i
$932$	−4.15224e9			−0.168007
$933$	5.26624e10			2.12283
$934$			3.52015e9i			0.141367i
$935$	2.81154e10			1.12487
$936$	1.32752e10	+	3.82285e10i	0.529147	+	1.52378i
$937$	2.80388e10			1.11345			0.556725	−	0.830697i	$-0.312058\pi$
$937$	2.80388e10			1.11345			0.556725	+	0.830697i	$0.312058\pi$
$938$		−	6.70451e9i		−	0.265251i
$939$	−8.16059e10			−3.21656
$940$	−2.39493e10			−0.940469
$941$			1.68655e10i			0.659835i	0.944010	+	0.329918i	$0.107021\pi$
$941$			1.68655e10i			0.659835i	−0.944010	+	0.329918i	$0.892979\pi$
$942$			2.54095e9i			0.0990417i
$943$		−	8.26590e9i		−	0.320996i
$944$		−	1.05128e10i		−	0.406739i
$945$	1.47915e10			0.570165
$946$	−4.45648e9			−0.171149
$947$		−	6.04371e9i		−	0.231248i	−0.993293	−	0.115624i	$-0.963113\pi$
$947$		−	6.04371e9i		−	0.231248i	0.993293	−	0.115624i	$-0.0368868\pi$
$948$	−3.18442e10			−1.21395
$949$	−2.72809e9	−	7.85606e9i	−0.103616	−	0.298382i
$950$	2.21669e8			0.00838828
$951$			9.27122e9i			0.349546i
$952$	−6.67373e9			−0.250691
$953$	−3.04958e10			−1.14134			−0.570669	−	0.821180i	$-0.693316\pi$
$953$	−3.04958e10			−1.14134			−0.570669	+	0.821180i	$0.693316\pi$
$954$		−	8.19374e9i		−	0.305536i
$955$		−	2.92901e10i		−	1.08820i
$956$			3.16507e10i			1.17160i
$957$		−	1.23005e11i		−	4.53660i
$958$	4.46323e9			0.164010
$959$	6.34388e9			0.232268
$960$			6.79907e9i			0.248028i
$961$	2.74499e10			0.997720
$962$	1.65617e10	−	5.75119e9i	0.599779	−	0.208279i
$963$	−2.28251e10			−0.823609
$964$		−	3.06720e10i		−	1.10274i
$965$	−2.89807e10			−1.03816
$966$	−4.00947e9			−0.143109
$967$		−	1.84504e9i		−	0.0656167i	−0.999462	−	0.0328083i	$-0.989555\pi$
$967$		−	1.84504e9i		−	0.0656167i	0.999462	−	0.0328083i	$-0.0104451\pi$
$968$			4.62842e10i			1.64009i
$969$		−	1.85645e9i		−	0.0655467i
$970$			1.57373e9i			0.0553642i
$971$	−4.29594e10			−1.50588			−0.752942	−	0.658087i	$-0.771366\pi$
$971$	−4.29594e10			−1.50588			−0.752942	+	0.658087i	$0.771366\pi$
$972$	−2.41152e10			−0.842286
$973$		−	1.31378e10i		−	0.457223i
$974$	−6.29268e9			−0.218212
$975$	2.69802e10	−	9.36914e9i	0.932244	−	0.323730i
$976$	1.57060e10			0.540743
$977$		−	1.80973e10i		−	0.620845i	−0.950599	−	0.310422i	$-0.899530\pi$
$977$		−	1.80973e10i		−	0.620845i	0.950599	−	0.310422i	$-0.100470\pi$
$978$	−8.64537e9			−0.295527
$979$	7.39799e10			2.51985
$980$			2.40316e9i			0.0815628i
$981$			1.87753e9i			0.0634958i
$982$			1.36254e10i			0.459154i
$983$			2.14808e10i			0.721295i	0.932702	+	0.360648i	$0.117444\pi$
$983$			2.14808e10i			0.721295i	−0.932702	+	0.360648i	$0.882556\pi$
$984$	−2.29522e10			−0.767965
$985$	−3.58633e9			−0.119570
$986$		−	1.50067e10i		−	0.498559i
$987$	3.38798e10			1.12158
$988$	−3.32754e8	−	9.58228e8i	−0.0109767	−	0.0316096i
$989$	4.00092e9			0.131514
$990$		−	3.24500e10i		−	1.06290i
$991$	3.63540e10			1.18657			0.593286	−	0.804991i	$-0.297830\pi$
$991$	3.63540e10			1.18657			0.593286	+	0.804991i	$0.297830\pi$
$992$	−1.37989e9			−0.0448800
$993$		−	9.34340e10i		−	3.02819i
$994$			5.73183e9i			0.185115i
$995$		−	3.55886e10i		−	1.14533i
$996$			1.73237e10i			0.555563i
$997$	−3.09328e9			−0.0988522			−0.0494261	−	0.998778i	$-0.515739\pi$
$997$	−3.09328e9			−0.0988522			−0.0494261	+	0.998778i	$0.515739\pi$
$998$	−1.16392e10			−0.370651
$999$			1.15518e11i			3.66582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.20	✓	50
13.12	even	2	inner	91.8.c.a.64.31	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.20	✓	50	1.1	even	1	trivial
91.8.c.a.64.31	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)

\(f(q)\)	\(=\)	\(q-4.39578i q^{2} -84.2461 q^{3} +108.677 q^{4} -187.956i q^{5} +370.327i q^{6} -343.000i q^{7} -1040.38i q^{8} +4910.40 q^{9} +O(q^{10})\)	\(q-4.39578i q^{2} -84.2461 q^{3} +108.677 q^{4} -187.956i q^{5} +370.327i q^{6} -343.000i q^{7} -1040.38i q^{8} +4910.40 q^{9} -826.214 q^{10} +7998.43i q^{11} -9155.62 q^{12} +(-7483.05 + 2598.56i) q^{13} -1507.75 q^{14} +15834.6i q^{15} +9337.39 q^{16} +18701.7 q^{17} -21585.0i q^{18} +1178.29i q^{19} -20426.6i q^{20} +28896.4i q^{21} +35159.3 q^{22} -31565.2 q^{23} +87647.9i q^{24} +42797.4 q^{25} +(11422.7 + 32893.8i) q^{26} -229436. q^{27} -37276.3i q^{28} +182544. q^{29} +69605.3 q^{30} -7920.65i q^{31} -174214. i q^{32} -673836. i q^{33} -82208.7i q^{34} -64469.0 q^{35} +533648. q^{36} -503488. i q^{37} +5179.50 q^{38} +(630417. - 218918. i) q^{39} -195546. q^{40} +261868. i q^{41} +127022. q^{42} -126751. q^{43} +869247. i q^{44} -922940. i q^{45} +138753. i q^{46} -1.17246e6i q^{47} -786638. q^{48} -117649. q^{49} -188128. i q^{50} -1.57555e6 q^{51} +(-813236. + 282404. i) q^{52} +379603. q^{53} +1.00855e6i q^{54} +1.50336e6 q^{55} -356850. q^{56} -99266.3i q^{57} -802423. i q^{58} -1.12588e6i q^{59} +1.72086e6i q^{60} +1.68205e6 q^{61} -34817.4 q^{62} -1.68427e6i q^{63} +429381. q^{64} +(488416. + 1.40649e6i) q^{65} -2.96204e6 q^{66} +4.44669e6i q^{67} +2.03245e6 q^{68} +2.65924e6 q^{69} +283392. i q^{70} -3.80157e6i q^{71} -5.10868e6i q^{72} +1.04985e6i q^{73} -2.21322e6 q^{74} -3.60551e6 q^{75} +128053. i q^{76} +2.74346e6 q^{77} +(-962317. - 2.77117e6i) q^{78} +3.47810e6 q^{79} -1.75502e6i q^{80} +8.59000e6 q^{81} +1.15111e6 q^{82} -1.89214e6i q^{83} +3.14038e6i q^{84} -3.51511e6i q^{85} +557170. i q^{86} -1.53786e7 q^{87} +8.32141e6 q^{88} -9.24930e6i q^{89} -4.05704e6 q^{90} +(891306. + 2.56669e6i) q^{91} -3.43041e6 q^{92} +667284. i q^{93} -5.15386e6 q^{94} +221467. q^{95} +1.46768e7i q^{96} -1.90475e6i q^{97} +517159. i q^{98} +3.92755e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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