LMFDB - Embedded newform 91.8.u.a.88.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(30,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("91.30");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.14
Character	$\chi$	$=$	91.88
Dual form			91.8.u.a.30.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.2351 - 6.48656i) q^{2} +29.5960 q^{3} +(20.1509 + 34.9025i) q^{4} +(-169.575 + 97.9040i) q^{5} +(-332.513 - 191.977i) q^{6} +(-849.576 - 319.005i) q^{7} +1137.72i q^{8} -1311.07 q^{9} +O(q^{10})$	\(q+(-11.2351 - 6.48656i) q^{2} +29.5960 q^{3} +(20.1509 + 34.9025i) q^{4} +(-169.575 + 97.9040i) q^{5} +(-332.513 - 191.977i) q^{6} +(-849.576 - 319.005i) q^{7} +1137.72i q^{8} -1311.07 q^{9} +2540.24 q^{10} -1409.19i q^{11} +(596.388 + 1032.97i) q^{12} +(-4992.18 - 6150.33i) q^{13} +(7475.78 + 9094.86i) q^{14} +(-5018.74 + 2897.57i) q^{15} +(9959.20 - 17249.8i) q^{16} +(13919.5 + 24109.4i) q^{17} +(14730.0 + 8504.36i) q^{18} -28631.1i q^{19} +(-6834.18 - 3945.72i) q^{20} +(-25144.1 - 9441.29i) q^{21} +(-9140.80 + 15832.3i) q^{22} +(-19772.8 + 34247.5i) q^{23} +33672.0i q^{24} +(-19892.1 + 34454.1i) q^{25} +(16192.9 + 101481. i) q^{26} -103529. q^{27} +(-5985.69 - 36080.5i) q^{28} +(26531.8 + 45954.4i) q^{29} +75181.1 q^{30} +(109726. + 63350.3i) q^{31} +(-97666.8 + 56387.9i) q^{32} -41706.5i q^{33} -361160. i q^{34} +(175298. - 29081.7i) q^{35} +(-26419.4 - 45759.7i) q^{36} +(105471. + 60893.6i) q^{37} +(-185717. + 321672. i) q^{38} +(-147749. - 182026. i) q^{39} +(-111387. - 192928. i) q^{40} +(706833. - 408090. i) q^{41} +(221254. + 269172. i) q^{42} +(185384. - 321095. i) q^{43} +(49184.2 - 28396.5i) q^{44} +(222325. - 128359. i) q^{45} +(444296. - 256515. i) q^{46} +(269159. - 155399. i) q^{47} +(294753. - 510527. i) q^{48} +(620014. + 542038. i) q^{49} +(446978. - 258063. i) q^{50} +(411964. + 713542. i) q^{51} +(114065. - 298175. i) q^{52} +(-6012.55 + 10414.0i) q^{53} +(1.16316e6 + 671548. i) q^{54} +(137966. + 238963. i) q^{55} +(362938. - 966578. i) q^{56} -847367. i q^{57} -688400. i q^{58} +(1.20991e6 - 698543. i) q^{59} +(-202265. - 116778. i) q^{60} +438128. q^{61} +(-821851. - 1.42349e6i) q^{62} +(1.11386e6 + 418239. i) q^{63} -1.08650e6 q^{64} +(1.44869e6 + 554186. i) q^{65} +(-270532. + 468575. i) q^{66} +402085. i q^{67} +(-560984. + 971653. i) q^{68} +(-585196. + 1.01359e6i) q^{69} +(-2.15813e6 - 810350. i) q^{70} +(-1.91043e6 - 1.10299e6i) q^{71} -1.49163e6i q^{72} +(2.70969e6 + 1.56444e6i) q^{73} +(-789980. - 1.36828e6i) q^{74} +(-588727. + 1.01971e6i) q^{75} +(999295. - 576943. i) q^{76} +(-449539. + 1.19721e6i) q^{77} +(479247. + 3.00345e6i) q^{78} +(106615. + 184662. i) q^{79} +3.90018e6i q^{80} -196734. q^{81} -1.05884e7 q^{82} +4.29541e6i q^{83} +(-177153. - 1.06784e6i) q^{84} +(-4.72081e6 - 2.72556e6i) q^{85} +(-4.16560e6 + 2.40501e6i) q^{86} +(785235. + 1.36007e6i) q^{87} +1.60326e6 q^{88} +(409637. + 236504. i) q^{89} -3.33045e6 q^{90} +(2.27925e6 + 6.81771e6i) q^{91} -1.59376e6 q^{92} +(3.24745e6 + 1.87492e6i) q^{93} -4.03203e6 q^{94} +(2.80310e6 + 4.85511e6i) q^{95} +(-2.89055e6 + 1.66886e6i) q^{96} +(-8.76318e6 - 5.05942e6i) q^{97} +(-3.44993e6 - 1.01116e7i) q^{98} +1.84755e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) $ 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.2351	−	6.48656i	−0.993048	−	0.573336i	−0.0868638	−	0.996220i	$-0.527685\pi$
$2$	−11.2351	−	6.48656i	−0.993048	−	0.573336i	−0.906184	+	0.422884i	$0.861018\pi$
$3$	29.5960			0.632862			0.316431	−	0.948615i	$-0.397515\pi$
$3$	29.5960			0.632862			0.316431	+	0.948615i	$0.397515\pi$
$4$	20.1509	+	34.9025i	0.157429	+	0.272675i
$5$	−169.575	+	97.9040i	−0.606689	+	0.350272i	−0.771669	−	0.636025i	$-0.780578\pi$
$5$	−169.575	+	97.9040i	−0.606689	+	0.350272i	0.164979	+	0.986297i	$0.447244\pi$
$6$	−332.513	−	191.977i	−0.628463	−	0.362843i
$7$	−849.576	−	319.005i	−0.936179	−	0.351524i
$7$	−849.576	−	319.005i	−0.936179	−	0.351524i
$8$			1137.72i			0.785633i
$9$	−1311.07			−0.599485
$10$	2540.24			0.803295
$11$		−	1409.19i		−	0.319224i	−0.987180	−	0.159612i	$-0.948976\pi$
$11$		−	1409.19i		−	0.319224i	0.987180	−	0.159612i	$-0.0510243\pi$
$12$	596.388	+	1032.97i	0.0996310	+	0.172566i
$13$	−4992.18	−	6150.33i	−0.630215	−	0.776420i
$13$	−4992.18	−	6150.33i	−0.630215	−	0.776420i
$14$	7475.78	+	9094.86i	0.728129	+	0.885825i
$15$	−5018.74	+	2897.57i	−0.383951	+	0.221674i
$16$	9959.20	−	17249.8i	0.607861	−	1.05285i
$17$	13919.5	+	24109.4i	0.687154	+	1.19019i	0.972755	+	0.231837i	$0.0744735\pi$
$17$	13919.5	+	24109.4i	0.687154	+	1.19019i	−0.285601	+	0.958349i	$0.592193\pi$
$18$	14730.0	+	8504.36i	0.595317	+	0.343707i
$19$		−	28631.1i		−	0.957636i	−0.877914	−	0.478818i	$-0.841065\pi$
$19$		−	28631.1i		−	0.957636i	0.877914	−	0.478818i	$-0.158935\pi$
$20$	−6834.18	−	3945.72i	−0.191021	−	0.110286i
$21$	−25144.1	−	9441.29i	−0.592472	−	0.222466i
$22$	−9140.80	+	15832.3i	−0.183023	+	0.317005i
$23$	−19772.8	+	34247.5i	−0.338860	+	0.586923i	−0.984219	−	0.176957i	$-0.943375\pi$
$23$	−19772.8	+	34247.5i	−0.338860	+	0.586923i	0.645359	+	0.763880i	$0.276708\pi$
$24$			33672.0i			0.497198i
$25$	−19892.1	+	34454.1i	−0.254619	+	0.441013i
$26$	16192.9	+	101481.i	0.180684	+	1.13235i
$27$	−103529.			−1.01225
$28$	−5985.69	−	36080.5i	−0.0515301	−	0.310613i
$29$	26531.8	+	45954.4i	0.202010	+	0.349892i	0.949176	−	0.314746i	$-0.101919\pi$
$29$	26531.8	+	45954.4i	0.202010	+	0.349892i	−0.747166	+	0.664638i	$0.768586\pi$
$30$	75181.1			0.508375
$31$	109726.	+	63350.3i	0.661520	+	0.381929i	0.792856	−	0.609409i	$-0.208593\pi$
$31$	109726.	+	63350.3i	0.661520	+	0.381929i	−0.131336	+	0.991338i	$0.541927\pi$
$32$	−97666.8	+	56387.9i	−0.526892	+	0.304201i
$33$		−	41706.5i		−	0.202025i
$34$		−	361160.i		−	1.57588i
$35$	175298.	−	29081.7i	0.691099	−	0.114652i
$36$	−26419.4	−	45759.7i	−0.0943765	−	0.163465i
$37$	105471.	+	60893.6i	0.342315	+	0.197636i	0.661295	−	0.750126i	$-0.270007\pi$
$37$	105471.	+	60893.6i	0.342315	+	0.197636i	−0.318980	+	0.947761i	$0.603340\pi$
$38$	−185717.	+	321672.i	−0.549047	+	0.950978i
$39$	−147749.	−	182026.i	−0.398840	−	0.491367i
$40$	−111387.	−	192928.i	−0.275185	−	0.476635i
$41$	706833.	−	408090.i	1.60167	−	0.924725i	0.610517	−	0.792003i	$-0.290962\pi$
$41$	706833.	−	408090.i	1.60167	−	0.924725i	0.991153	−	0.132721i	$-0.0423715\pi$
$42$	221254.	+	269172.i	0.460806	+	0.560605i
$43$	185384.	−	321095.i	0.355577	−	0.615877i	−0.631640	−	0.775262i	$-0.717618\pi$
$43$	185384.	−	321095.i	0.355577	−	0.615877i	0.987216	+	0.159385i	$0.0509512\pi$
$44$	49184.2	−	28396.5i	0.0870445	−	0.0502552i
$45$	222325.	−	128359.i	0.363701	−	0.209983i
$46$	444296.	−	256515.i	0.673008	−	0.388562i
$47$	269159.	−	155399.i	0.378153	−	0.218327i	−0.298862	−	0.954296i	$-0.596607\pi$
$47$	269159.	−	155399.i	0.378153	−	0.218327i	0.677014	+	0.735970i	$0.263274\pi$
$48$	294753.	−	510527.i	0.384693	−	0.666307i
$49$	620014.	+	542038.i	0.752862	+	0.658178i
$50$	446978.	−	258063.i	0.505697	−	0.291965i
$51$	411964.	+	713542.i	0.434874	+	0.753223i
$52$	114065.	−	298175.i	0.112496	−	0.294075i
$53$	−6012.55	+	10414.0i	−0.00554745	+	0.00960846i	−0.868786	−	0.495188i	$-0.835099\pi$
$53$	−6012.55	+	10414.0i	−0.00554745	+	0.00960846i	0.863238	+	0.504797i	$0.168432\pi$
$54$	1.16316e6	+	671548.i	1.00522	+	0.580362i
$55$	137966.	+	238963.i	0.111815	+	0.193670i
$56$	362938.	−	966578.i	0.276169	−	0.735493i
$57$		−	847367.i		−	0.606052i
$58$		−	688400.i		−	0.463279i
$59$	1.20991e6	−	698543.i	0.766959	−	0.442804i	−0.0648299	−	0.997896i	$-0.520650\pi$
$59$	1.20991e6	−	698543.i	0.766959	−	0.442804i	0.831789	+	0.555093i	$0.187317\pi$
$60$	−202265.	−	116778.i	−0.120890	−	0.0697959i
$61$	438128.			0.247142			0.123571	−	0.992336i	$-0.460565\pi$
$61$	438128.			0.247142			0.123571	+	0.992336i	$0.460565\pi$
$62$	−821851.	−	1.42349e6i	−0.437947	−	0.758547i
$63$	1.11386e6	+	418239.i	0.561225	+	0.210733i
$64$	−1.08650e6			−0.518084
$65$	1.44869e6	+	554186.i	0.654303	+	0.250299i
$66$	−270532.	+	468575.i	−0.115828	+	0.200620i
$67$			402085.i			0.163326i	0.996660	+	0.0816631i	$0.0260231\pi$
$67$			402085.i			0.163326i	−0.996660	+	0.0816631i	$0.973977\pi$
$68$	−560984.	+	971653.i	−0.216356	+	0.374740i
$69$	−585196.	+	1.01359e6i	−0.214452	+	0.371441i
$70$	−2.15813e6	−	810350.i	−0.752028	−	0.282377i
$71$	−1.91043e6	−	1.10299e6i	−0.633472	−	0.365735i	0.148623	−	0.988894i	$-0.452516\pi$
$71$	−1.91043e6	−	1.10299e6i	−0.633472	−	0.365735i	−0.782096	+	0.623158i	$0.785849\pi$
$72$		−	1.49163e6i		−	0.470975i
$73$	2.70969e6	+	1.56444e6i	0.815249	+	0.470684i	0.848775	−	0.528754i	$-0.177340\pi$
$73$	2.70969e6	+	1.56444e6i	0.815249	+	0.470684i	−0.0335265	+	0.999438i	$0.510674\pi$
$74$	−789980.	−	1.36828e6i	−0.226623	−	0.392523i
$75$	−588727.	+	1.01971e6i	−0.161139	+	0.279100i
$76$	999295.	−	576943.i	0.261124	−	0.150760i
$77$	−449539.	+	1.19721e6i	−0.112215	+	0.298851i
$78$	479247.	+	3.00345e6i	0.114348	+	0.716620i
$79$	106615.	+	184662.i	0.0243289	+	0.0421389i	0.877934	−	0.478783i	$-0.158922\pi$
$79$	106615.	+	184662.i	0.0243289	+	0.0421389i	−0.853605	+	0.520921i	$0.825588\pi$
$80$			3.90018e6i			0.851667i
$81$	−196734.			−0.0411322
$82$	−1.05884e7			−2.12071
$83$			4.29541e6i			0.824576i	0.911053	+	0.412288i	$0.135270\pi$
$83$			4.29541e6i			0.824576i	−0.911053	+	0.412288i	$0.864730\pi$
$84$	−177153.	−	1.06784e6i	−0.0326115	−	0.196575i
$85$	−4.72081e6	−	2.72556e6i	−0.833777	−	0.481382i
$86$	−4.16560e6	+	2.40501e6i	−0.706209	+	0.407730i
$87$	785235.	+	1.36007e6i	0.127845	+	0.221433i
$88$	1.60326e6			0.250793
$89$	409637.	+	236504.i	0.0615934	+	0.0355610i	0.530480	−	0.847697i	$-0.322012\pi$
$89$	409637.	+	236504.i	0.0615934	+	0.0355610i	−0.468887	+	0.883258i	$0.655345\pi$
$90$	−3.33045e6			−0.481563
$91$	2.27925e6	+	6.81771e6i	0.317064	+	0.948404i
$92$	−1.59376e6			−0.213386
$93$	3.24745e6	+	1.87492e6i	0.418651	+	0.241708i
$94$	−4.03203e6			−0.500698
$95$	2.80310e6	+	4.85511e6i	0.335433	+	0.580987i
$96$	−2.89055e6	+	1.66886e6i	−0.333450	+	0.192518i
$97$	−8.76318e6	−	5.05942e6i	−0.974901	−	0.562859i	−0.0741740	−	0.997245i	$-0.523632\pi$
$97$	−8.76318e6	−	5.05942e6i	−0.974901	−	0.562859i	−0.900727	+	0.434386i	$0.856965\pi$
$98$	−3.44993e6	−	1.01116e7i	−0.370271	−	1.08525i
$99$			1.84755e6i			0.191370i
$100$	−1.60338e6			−0.160338
$101$	−482349.			−0.0465840			−0.0232920	−	0.999729i	$-0.507415\pi$
$101$	−482349.			−0.0465840			−0.0232920	+	0.999729i	$0.507415\pi$
$102$		−	1.06889e7i		−	0.997316i
$103$	−4.08420e6	−	7.07404e6i	−0.368279	−	0.637877i	0.621018	−	0.783796i	$-0.286719\pi$
$103$	−4.08420e6	−	7.07404e6i	−0.368279	−	0.637877i	−0.989297	+	0.145919i	$0.953386\pi$
$104$	6.99735e6	−	5.67970e6i	0.609982	−	0.495118i
$105$	5.18814e6	−	860702.i	0.437370	−	0.0725588i
$106$	135103.	−	78001.5i	0.0110178	−	0.00636110i
$107$	−4.99989e6	+	8.66007e6i	−0.394564	+	0.683405i	−0.993045	−	0.117732i	$-0.962438\pi$
$107$	−4.99989e6	+	8.66007e6i	−0.394564	+	0.683405i	0.598482	+	0.801137i	$0.295771\pi$
$108$	−2.08621e6	−	3.61342e6i	−0.159358	−	0.276017i
$109$	2.03538e7	+	1.17513e7i	1.50540	+	0.869145i	0.999980	+	0.00627315i	$0.00199682\pi$
$109$	2.03538e7	+	1.17513e7i	1.50540	+	0.869145i	0.505423	+	0.862872i	$0.331337\pi$
$110$		−	3.57969e6i		−	0.256431i
$111$	3.12152e6	+	1.80221e6i	0.216638	+	0.125076i
$112$	−1.39639e7	+	1.14780e7i	−0.939167	+	0.771975i
$113$	−6.62537e6	+	1.14755e7i	−0.431952	+	0.748163i	−0.997041	−	0.0768669i	$-0.975508\pi$
$113$	−6.62537e6	+	1.14755e7i	−0.431952	+	0.748163i	0.565089	+	0.825030i	$0.308842\pi$
$114$	−5.49650e6	+	9.52021e6i	−0.347471	+	0.601838i
$115$		−	7.74334e6i		−	0.474773i
$116$	−1.06928e6	+	1.85205e6i	−0.0636046	+	0.110166i
$117$	6.54512e6	+	8.06354e6i	0.377805	+	0.465453i
$118$	−1.81246e7			−1.01550
$119$	−4.13470e6	−	2.49231e7i	−0.224921	−	1.35578i
$120$	−3.29662e6	−	5.70991e6i	−0.174154	−	0.301644i
$121$	1.75014e7			0.898096
$122$	−4.92240e6	−	2.84195e6i	−0.245424	−	0.141696i
$123$	2.09194e7	−	1.20778e7i	1.01364	−	0.585223i
$124$			5.10627e6i			0.240507i
$125$		−	2.30876e7i		−	1.05729i
$126$	−9.80130e6	−	1.19240e7i	−0.436503	−	0.531039i
$127$	8.46183e6	+	1.46563e7i	0.366565	+	0.634910i	0.989026	−	0.147741i	$-0.0472003\pi$
$127$	8.46183e6	+	1.46563e7i	0.366565	+	0.634910i	−0.622461	+	0.782651i	$0.713867\pi$
$128$	2.47082e7	+	1.42653e7i	1.04137	+	0.601238i
$129$	5.48664e6	−	9.50314e6i	0.225031	−	0.389765i
$130$	−1.26814e7	−	1.56233e7i	−0.506249	−	0.623695i
$131$	−1.01154e7	−	1.75204e7i	−0.393128	−	0.680918i	0.599732	−	0.800201i	$-0.295274\pi$
$131$	−1.01154e7	−	1.75204e7i	−0.393128	−	0.680918i	−0.992860	+	0.119283i	$0.961941\pi$
$132$	1.45566e6	−	840425.i	0.0550872	−	0.0318046i
$133$	−9.13346e6	+	2.43243e7i	−0.336632	+	0.896518i
$134$	2.60815e6	−	4.51744e6i	0.0936408	−	0.162191i
$135$	1.75559e7	−	1.01359e7i	0.614123	−	0.354564i
$136$	−2.74297e7	+	1.58365e7i	−0.935049	+	0.539851i
$137$	4.91778e7	−	2.83928e7i	1.63398	−	0.943379i	0.651131	−	0.758965i	$-0.274295\pi$
$137$	4.91778e7	−	2.83928e7i	1.63398	−	0.943379i	0.982849	−	0.184413i	$-0.0590385\pi$
$138$	1.31494e7	−	7.59182e6i	0.425922	−	0.245906i
$139$	−2.46464e7	+	4.26888e7i	−0.778398	+	1.34823i	0.154466	+	0.987998i	$0.450634\pi$
$139$	−2.46464e7	+	4.26888e7i	−0.778398	+	1.34823i	−0.932864	+	0.360227i	$0.882699\pi$
$140$	4.54745e6	+	5.53232e6i	0.140062	+	0.170396i
$141$	7.96605e6	−	4.59920e6i	0.239319	−	0.138171i
$142$	1.43092e7	+	2.47843e7i	0.419379	+	0.726385i
$143$	−8.66700e6	+	7.03494e6i	−0.247852	+	0.201180i
$144$	−1.30572e7	+	2.26158e7i	−0.364404	+	0.631166i
$145$	−8.99823e6	−	5.19513e6i	−0.245115	−	0.141517i
$146$	−2.02957e7	−	3.51532e7i	−0.539721	−	0.934824i
$147$	1.83500e7	+	1.60422e7i	0.476458	+	0.416536i
$148$			4.90825e6i			0.124455i
$149$			2.28850e7i			0.566760i	0.959008	+	0.283380i	$0.0914558\pi$
$149$			2.28850e7i			0.566760i	−0.959008	+	0.283380i	$0.908544\pi$
$150$	1.32288e7	−	7.63763e6i	0.320037	−	0.184773i
$151$	−5.09654e7	−	2.94249e7i	−1.20464	−	0.695497i	−0.243054	−	0.970013i	$-0.578149\pi$
$151$	−5.09654e7	−	2.94249e7i	−1.20464	−	0.695497i	−0.961583	+	0.274516i	$0.911482\pi$
$152$	3.25741e7			0.752350
$153$	−1.82496e7	−	3.16092e7i	−0.411939	−	0.713499i
$154$	1.28164e7	−	1.05348e7i	0.282777	−	0.232436i
$155$	−2.48090e7			−0.535116
$156$	3.37586e6	−	8.82479e6i	0.0711948	−	0.186109i
$157$	−3.99089e7	+	6.91243e7i	−0.823041	+	1.42555i	0.0803665	+	0.996765i	$0.474391\pi$
$157$	−3.99089e7	+	6.91243e7i	−0.823041	+	1.42555i	−0.903407	+	0.428783i	$0.858942\pi$
$158$		−	2.76626e6i		−	0.0557946i
$159$	−177948.	+	308214.i	−0.00351077	+	0.00608083i
$160$	1.10412e7	−	1.91239e7i	0.213107	−	0.369111i
$161$	2.77236e7	−	2.27882e7i	0.523551	−	0.430347i
$162$	2.21032e6	+	1.27613e6i	0.0408463	+	0.0235826i
$163$			6.05947e7i			1.09592i	0.836505	+	0.547959i	$0.184595\pi$
$163$			6.05947e7i			1.09592i	−0.836505	+	0.547959i	$0.815405\pi$
$164$	2.84867e7	+	1.64468e7i	0.504299	+	0.291157i
$165$	4.08323e6	+	7.07237e6i	0.0707637	+	0.122566i
$166$	2.78624e7	−	4.82591e7i	0.472760	−	0.818844i
$167$	−1.95419e7	+	1.12825e7i	−0.324683	+	0.187456i	−0.653478	−	0.756946i	$-0.726691\pi$
$167$	−1.95419e7	+	1.12825e7i	−0.324683	+	0.187456i	0.328795	+	0.944401i	$0.393357\pi$
$168$	1.07415e7	−	2.86069e7i	0.174777	−	0.465466i
$169$	−1.29047e7	+	6.14072e7i	−0.205657	+	0.978624i
$170$	3.53590e7	+	6.12436e7i	0.551987	+	0.956070i
$171$			3.75375e7i			0.574088i
$172$	1.49427e7			0.223913
$173$	4.03708e7			0.592797			0.296399	−	0.955064i	$-0.404214\pi$
$173$	4.03708e7			0.592797			0.296399	+	0.955064i	$0.404214\pi$
$174$		−	2.03739e7i		−	0.293192i
$175$	2.78909e7	−	2.29257e7i	0.393395	−	0.323362i
$176$	−2.43083e7	−	1.40344e7i	−0.336094	−	0.194044i
$177$	3.58086e7	−	2.06741e7i	0.485379	−	0.280234i
$178$	−3.06820e6	−	5.31427e6i	−0.0407768	−	0.0706275i
$179$	7.40698e7			0.965286			0.482643	−	0.875817i	$-0.339677\pi$
$179$	7.40698e7			0.965286			0.482643	+	0.875817i	$0.339677\pi$
$180$	8.96012e6	+	5.17313e6i	0.114514	+	0.0661149i
$181$	3.20709e7			0.402009			0.201005	−	0.979590i	$-0.435579\pi$
$181$	3.20709e7			0.402009			0.201005	+	0.979590i	$0.435579\pi$
$182$	1.86160e7	−	9.13818e7i	0.228895	−	1.12359i
$183$	1.29669e7			0.156407
$184$	−3.89640e7	−	2.24959e7i	−0.461106	−	0.266220i
$185$	−2.38469e7			−0.276905
$186$	−2.43235e7	−	4.21296e7i	−0.277160	−	0.480056i
$187$	3.39747e7	−	1.96153e7i	0.379936	−	0.219356i
$188$	1.08476e7	+	6.26288e6i	0.119065	+	0.0687419i
$189$	8.79558e7	+	3.30263e7i	0.947651	+	0.355831i
$190$		−	7.27299e7i		−	0.769264i
$191$	−4.34097e7			−0.450785			−0.225393	−	0.974268i	$-0.572366\pi$
$191$	−4.34097e7			−0.450785			−0.225393	+	0.974268i	$0.572366\pi$
$192$	−3.21561e7			−0.327876
$193$		−	1.79032e8i		−	1.79258i	−0.443467	−	0.896291i	$-0.646252\pi$
$193$		−	1.79032e8i		−	1.79258i	0.443467	−	0.896291i	$-0.353748\pi$
$194$	6.56365e7	+	1.13686e8i	0.645415	+	1.11789i
$195$	4.28755e7	+	1.64017e7i	0.414084	+	0.158405i
$196$	−6.42458e6	+	3.25626e7i	−0.0609465	+	0.308903i
$197$	−2.83431e7	+	1.63639e7i	−0.264128	+	0.152495i	−0.626216	−	0.779649i	$-0.715397\pi$
$197$	−2.83431e7	+	1.63639e7i	−0.264128	+	0.152495i	0.362088	+	0.932144i	$0.382064\pi$
$198$	1.19843e7	−	2.07574e7i	0.109719	−	0.190040i
$199$	3.55715e7	+	6.16117e7i	0.319975	+	0.554214i	0.980483	−	0.196606i	$-0.0629920\pi$
$199$	3.55715e7	+	6.16117e7i	0.319975	+	0.554214i	−0.660507	+	0.750820i	$0.729659\pi$
$200$	−3.91991e7	−	2.26316e7i	−0.346474	−	0.200037i
$201$			1.19001e7i			0.103363i
$202$	5.41921e6	+	3.12878e6i	0.0462601	+	0.0267083i
$203$	−7.88106e6	−	4.75055e7i	−0.0661224	−	0.398573i
$204$	−1.66029e7	+	2.87571e7i	−0.136924	+	0.237159i
$205$	−7.99073e7	+	1.38404e8i	−0.647811	+	1.12204i
$206$			1.05970e8i			0.844590i
$207$	2.59236e7	−	4.49010e7i	0.203142	−	0.351852i
$208$	−1.55810e8	+	2.48620e7i	−1.20054	+	0.191564i
$209$	−4.03467e7			−0.305700
$210$	−6.38720e7	−	2.39832e7i	−0.475930	−	0.178706i
$211$	4.57668e7	+	7.92705e7i	0.335400	+	0.580929i	0.983561	−	0.180574i	$-0.0577954\pi$
$211$	4.57668e7	+	7.92705e7i	0.335400	+	0.580929i	−0.648162	+	0.761502i	$0.724462\pi$
$212$	−484634.			−0.00349332
$213$	−5.65413e7	−	3.26441e7i	−0.400901	−	0.231460i
$214$	1.12348e8	−	6.48642e7i	0.783642	−	0.452436i
$215$			7.25995e7i			0.498194i
$216$		−	1.17787e8i		−	0.795260i
$217$	−7.30114e7	−	8.88240e7i	−0.485044	−	0.590094i
$218$	−1.52451e8	−	2.64052e8i	−0.996625	−	1.72620i
$219$	8.01962e7	+	4.63013e7i	0.515940	+	0.297878i
$220$	−5.56027e6	+	9.63067e6i	−0.0352060	+	0.0609785i
$221$	7.87917e7	−	2.05968e8i	0.491029	−	1.28359i
$222$	−2.33803e7	−	4.04958e7i	−0.143421	−	0.248413i
$223$	−1.29447e8	+	7.47364e7i	−0.781675	+	0.451300i	−0.837023	−	0.547167i	$-0.815706\pi$
$223$	−1.29447e8	+	7.47364e7i	−0.781675	+	0.451300i	0.0553488	+	0.998467i	$0.482373\pi$
$224$	1.00963e8	−	1.67496e7i	0.600200	−	0.0995719i
$225$	2.60800e7	−	4.51719e7i	0.152640	−	0.264381i
$226$	1.48873e8	−	8.59517e7i	0.857898	−	0.495308i
$227$	−2.83211e7	+	1.63512e7i	−0.160701	+	0.0927810i	−0.578194	−	0.815899i	$-0.696242\pi$
$227$	−2.83211e7	+	1.63512e7i	−0.160701	+	0.0927810i	0.417493	+	0.908680i	$0.362909\pi$
$228$	2.95752e7	−	1.70752e7i	0.165255	−	0.0954102i
$229$	−1.83099e8	+	1.05712e8i	−1.00754	+	0.581703i	−0.910470	−	0.413574i	$-0.864280\pi$
$229$	−1.83099e8	+	1.05712e8i	−1.00754	+	0.581703i	−0.0970692	+	0.995278i	$0.530947\pi$
$230$	−5.02276e7	+	8.69968e7i	−0.272205	+	0.471472i
$231$	−1.33046e7	+	3.54328e7i	−0.0710165	+	0.189131i
$232$	−5.22831e7	+	3.01857e7i	−0.274887	+	0.158706i
$233$	1.92857e7	+	3.34039e7i	0.0998827	+	0.173002i	0.911636	−	0.410999i	$-0.134820\pi$
$233$	1.92857e7	+	3.34039e7i	0.0998827	+	0.173002i	−0.811753	+	0.584001i	$0.801487\pi$
$234$	−2.12302e7	−	1.33050e8i	−0.108317	−	0.678826i
$235$	−3.04284e7	+	5.27036e7i	−0.152947	+	0.264913i
$236$	4.87618e7	+	2.81526e7i	0.241483	+	0.139421i
$237$	3.15538e6	+	5.46528e6i	0.0153969	+	0.0266681i
$238$	−1.15212e8	+	3.06833e8i	−0.553959	+	1.47531i
$239$			3.37514e8i			1.59919i	0.600542	+	0.799593i	$0.294952\pi$
$239$			3.37514e8i			1.59919i	−0.600542	+	0.799593i	$0.705048\pi$
$240$			1.15430e8i			0.538988i
$241$	1.94431e8	−	1.12255e8i	0.894758	−	0.516589i	0.0192619	−	0.999814i	$-0.493868\pi$
$241$	1.94431e8	−	1.12255e8i	0.894758	−	0.516589i	0.875496	+	0.483226i	$0.160535\pi$
$242$	−1.96629e8	−	1.13524e8i	−0.891852	−	0.514911i
$243$	2.20596e8			0.986223
$244$	8.82870e6	+	1.52918e7i	0.0389074	+	0.0673896i
$245$	−1.58207e8	−	3.12140e7i	−0.687295	−	0.135603i
$246$	−3.13375e8			−1.34212
$247$	−1.76091e8	+	1.42932e8i	−0.743528	+	0.603517i
$248$	−7.20748e7	+	1.24837e8i	−0.300056	+	0.519712i
$249$			1.27127e8i			0.521843i
$250$	−1.49759e8	+	2.59390e8i	−0.606182	+	1.04994i
$251$	−1.32035e8	+	2.28691e8i	−0.527024	+	0.912832i	0.472480	+	0.881341i	$0.343359\pi$
$251$	−1.32035e8	+	2.28691e8i	−0.527024	+	0.912832i	−0.999504	+	0.0314909i	$0.989974\pi$
$252$	7.84768e6	+	4.73042e7i	0.0308915	+	0.186208i
$253$	4.82612e7	+	2.78636e7i	0.187360	+	0.108172i
$254$		−	2.19553e8i		−	0.840661i
$255$	−1.39717e8	−	8.06658e7i	−0.527666	−	0.304648i
$256$	−1.15530e8	−	2.00103e8i	−0.430381	−	0.745442i
$257$	2.05800e8	−	3.56456e8i	0.756275	−	1.30991i	−0.188463	−	0.982080i	$-0.560350\pi$
$257$	2.05800e8	−	3.56456e8i	0.756275	−	1.30991i	0.944738	−	0.327827i	$-0.106316\pi$
$258$	−1.23285e8	+	7.11789e7i	−0.446933	+	0.258037i
$259$	−7.01800e7	−	8.53794e7i	−0.250995	−	0.305354i
$260$	9.85002e6	+	6.17302e7i	0.0347561	+	0.217817i
$261$	−3.47851e7	−	6.02496e7i	−0.121102	−	0.209755i
$262$			2.62457e8i			0.901579i
$263$	2.85209e8			0.966759			0.483379	−	0.875411i	$-0.339409\pi$
$263$	2.85209e8			0.966759			0.483379	+	0.875411i	$0.339409\pi$
$264$	4.74502e7			0.158717
$265$		−	2.35461e6i		−	0.00777246i
$266$	2.60396e8	−	2.14040e8i	0.848298	−	0.697282i
$267$	1.21236e7	+	6.99959e6i	0.0389802	+	0.0225052i
$268$	−1.40337e7	+	8.10238e6i	−0.0445350	+	0.0257123i
$269$	9.51111e7	+	1.64737e8i	0.297919	+	0.516011i	0.975660	−	0.219290i	$-0.0703741\pi$
$269$	9.51111e7	+	1.64737e8i	0.297919	+	0.516011i	−0.677741	+	0.735301i	$0.737041\pi$
$270$	−2.62989e8			−0.813139
$271$	1.09772e7	+	6.33769e6i	0.0335042	+	0.0193437i	0.516659	−	0.856192i	$-0.327176\pi$
$271$	1.09772e7	+	6.33769e6i	0.0335042	+	0.0193437i	−0.483154	+	0.875535i	$0.660509\pi$
$272$	5.54510e8			1.67078
$273$	6.74568e7	+	2.01777e8i	0.200658	+	0.600209i
$274$	−7.36686e8			−2.16349
$275$	4.85525e7	+	2.80318e7i	0.140782	+	0.0812805i
$276$	−4.71690e7			−0.135044
$277$	−1.35813e8	−	2.35234e8i	−0.383938	−	0.665000i	0.607684	−	0.794179i	$-0.292099\pi$
$277$	−1.35813e8	−	2.35234e8i	−0.383938	−	0.665000i	−0.991621	+	0.129180i	$0.958766\pi$
$278$	5.53808e8	−	3.19741e8i	1.54597	−	0.892568i
$279$	−1.43859e8	−	8.30569e7i	−0.396572	−	0.228961i
$280$	3.30867e7	+	1.99440e8i	0.0900743	+	0.542950i
$281$		−	5.08053e8i		−	1.36596i	−0.730438	−	0.682979i	$-0.760684\pi$
$281$		−	5.08053e8i		−	1.36596i	0.730438	−	0.682979i	$-0.239316\pi$
$282$	−1.19332e8			−0.316873
$283$	1.89172e8			0.496140			0.248070	−	0.968742i	$-0.420204\pi$
$283$	1.89172e8			0.496140			0.248070	+	0.968742i	$0.420204\pi$
$284$		−	8.89051e7i		−	0.230310i
$285$	8.29606e7	+	1.43692e8i	0.212283	+	0.367685i
$286$	1.43007e8	−	2.28190e7i	0.361473	−	0.0576786i
$287$	−7.30691e8	+	1.21220e8i	−1.82451	+	0.302683i
$288$	1.28048e8	−	7.39288e7i	0.315864	−	0.182364i
$289$	−1.82338e8	+	3.15819e8i	−0.444361	+	0.769655i
$290$	6.73971e7	+	1.16735e8i	0.162274	+	0.281066i
$291$	−2.59355e8	−	1.49739e8i	−0.616978	−	0.356212i
$292$			1.26100e8i			0.296398i
$293$	3.58120e8	+	2.06761e8i	0.831748	+	0.480210i	0.854451	−	0.519532i	$-0.173894\pi$
$293$	3.58120e8	+	2.06761e8i	0.831748	+	0.480210i	−0.0227027	+	0.999742i	$0.507227\pi$
$294$	−1.02104e8	−	2.99263e8i	−0.234330	−	0.686811i
$295$	−1.36780e8	+	2.36911e8i	−0.310204	+	0.537289i
$296$	−6.92797e7	+	1.19996e8i	−0.155269	+	0.268934i
$297$			1.45892e8i			0.323136i
$298$	1.48445e8	−	2.57114e8i	0.324944	−	0.562820i
$299$	3.09343e8	−	4.93604e7i	0.669254	−	0.106790i
$300$	−4.74536e7			−0.101472
$301$	−2.59929e8	+	2.13656e8i	−0.549379	+	0.451577i
$302$	3.81732e8	+	6.61180e8i	0.797507	+	1.38132i
$303$	−1.42756e7			−0.0294812
$304$	−4.93882e8	−	2.85143e8i	−1.00824	−	0.582110i
$305$	−7.42955e7	+	4.28945e7i	−0.149938	+	0.0865670i
$306$			4.73508e8i			0.944717i
$307$		−	6.23298e8i		−	1.22945i	−0.788741	−	0.614726i	$-0.789267\pi$
$307$		−	6.23298e8i		−	1.22945i	0.788741	−	0.614726i	$-0.210733\pi$
$308$	−5.08444e7	+	8.43498e6i	−0.0991552	+	0.0164496i
$309$	−1.20876e8	−	2.09364e8i	−0.233070	−	0.403688i
$310$	2.78730e8	+	1.60925e8i	0.531396	+	0.306802i
$311$	5.04938e8	−	8.74578e8i	0.951868	−	1.64868i	0.210489	−	0.977596i	$-0.432494\pi$
$311$	5.04938e8	−	8.74578e8i	0.951868	−	1.64868i	0.741379	−	0.671087i	$-0.234172\pi$
$312$	2.07094e8	−	1.68097e8i	0.386034	−	0.313342i
$313$	4.50920e8	+	7.81016e8i	0.831178	+	1.43964i	0.897104	+	0.441819i	$0.145667\pi$
$313$	4.50920e8	+	7.81016e8i	0.831178	+	1.43964i	−0.0659258	+	0.997825i	$0.521000\pi$
$314$	8.96758e8	−	5.17744e8i	1.63464	−	0.943759i
$315$	−2.29829e8	+	3.81282e7i	−0.414303	+	0.0687321i
$316$	−4.29678e6	+	7.44224e6i	−0.00766017	+	0.0132678i
$317$	5.99444e8	−	3.46089e8i	1.05692	−	0.610212i	0.132340	−	0.991204i	$-0.457751\pi$
$317$	5.99444e8	−	3.46089e8i	1.05692	−	0.610212i	0.924578	+	0.380992i	$0.124418\pi$
$318$	3.99850e6	−	2.30854e6i	0.00697272	−	0.00402570i
$319$	6.47585e7	−	3.73883e7i	0.111694	−	0.0644865i
$320$	1.84243e8	−	1.06373e8i	0.314316	−	0.181470i
$321$	−1.47977e8	+	2.56304e8i	−0.249705	+	0.432501i
$322$	−4.59293e8	+	7.61958e7i	−0.766645	+	0.127185i
$323$	6.90277e8	−	3.98532e8i	1.13976	−	0.658043i
$324$	−3.96438e6	−	6.86651e6i	−0.00647542	−	0.0112158i
$325$	3.11209e8	−	4.96583e7i	0.502876	−	0.0802417i
$326$	3.93051e8	−	6.80784e8i	0.628329	−	1.08830i
$327$	6.02392e8	+	3.47791e8i	0.952713	+	0.550049i
$328$	4.64291e8	+	8.04176e8i	0.726494	+	1.25833i
$329$	−2.78244e8	+	4.61602e7i	−0.430765	+	0.0714631i
$330$		−	1.05945e8i		−	0.162286i
$331$		−	1.20050e9i		−	1.81955i	−0.415097	−	0.909777i	$-0.636252\pi$
$331$		−	1.20050e9i		−	1.81955i	0.415097	−	0.909777i	$-0.363748\pi$
$332$	−1.49920e8	+	8.65565e7i	−0.224842	+	0.129812i
$333$	−1.38280e8	−	7.98360e7i	−0.205213	−	0.118480i
$334$	2.92739e8			0.429901
$335$	−3.93657e7	−	6.81834e7i	−0.0572086	−	0.0990882i
$336$	−4.13276e8	+	3.39704e8i	−0.594364	+	0.488554i
$337$	−2.16506e8			−0.308152			−0.154076	−	0.988059i	$-0.549240\pi$
$337$	−2.16506e8			−0.308152			−0.154076	+	0.988059i	$0.549240\pi$
$338$	5.43307e8	−	6.06206e8i	0.765308	−	0.853910i
$339$	−1.96085e8	+	3.39629e8i	−0.273366	+	0.473484i
$340$		−	2.19690e8i		−	0.303134i
$341$	8.92726e7	−	1.54625e8i	0.121921	−	0.211173i
$342$	2.43489e8	−	4.21736e8i	0.329146	−	0.570097i
$343$	−3.53836e8	−	6.58290e8i	−0.473449	−	0.880821i
$344$	3.65316e8	+	2.10915e8i	0.483853	+	0.279353i
$345$		−	2.29172e8i		−	0.300466i
$346$	−4.53568e8	−	2.61868e8i	−0.588676	−	0.339872i
$347$	2.92394e8	+	5.06441e8i	0.375678	+	0.650693i	0.990428	−	0.138029i	$-0.0440766\pi$
$347$	2.92394e8	+	5.06441e8i	0.375678	+	0.650693i	−0.614751	+	0.788722i	$0.710743\pi$
$348$	−3.16465e7	+	5.48133e7i	−0.0402530	+	0.0697202i
$349$	1.30350e9	−	7.52576e8i	1.64143	−	0.947680i	0.661103	−	0.750295i	$-0.270088\pi$
$349$	1.30350e9	−	7.52576e8i	1.64143	−	0.947680i	0.980326	−	0.197385i	$-0.0632449\pi$
$350$	−4.62065e8	+	7.66556e7i	−0.576056	+	0.0955665i
$351$	5.16837e8	+	6.36739e8i	0.637938	+	0.785935i
$352$	7.94614e7	+	1.37631e8i	0.0971084	+	0.168197i
$353$			1.21753e9i			1.47322i	0.676318	+	0.736610i	$0.263575\pi$
$353$			1.21753e9i			1.47322i	−0.676318	+	0.736610i	$0.736425\pi$
$354$	−5.36416e8			−0.642673
$355$	4.31948e8			0.512428
$356$			1.90631e7i			0.0223933i
$357$	−1.22371e8	−	7.37626e8i	−0.142344	−	0.858020i
$358$	−8.32179e8	−	4.80459e8i	−0.958575	−	0.553433i
$359$	2.22143e8	−	1.28254e8i	0.253397	−	0.146299i	−0.367922	−	0.929857i	$-0.619931\pi$
$359$	2.22143e8	−	1.28254e8i	0.253397	−	0.146299i	0.621319	+	0.783558i	$0.286597\pi$
$360$	1.46037e8	+	2.52943e8i	0.164970	+	0.285736i
$361$	7.41324e7			0.0829340
$362$	−3.60318e8	−	2.08030e8i	−0.399214	−	0.230487i
$363$	5.17971e8			0.568371
$364$	−1.92026e8	+	2.16935e8i	−0.208691	+	0.235762i
$365$	−6.12661e8			−0.659470
$366$	−1.45683e8	−	8.41104e7i	−0.155320	−	0.0896738i
$367$	9.19621e8			0.971130			0.485565	−	0.874200i	$-0.338614\pi$
$367$	9.19621e8			0.971130			0.485565	+	0.874200i	$0.338614\pi$
$368$	3.93842e8	+	6.82155e8i	0.411960	+	0.713535i
$369$	−9.26710e8	+	5.35036e8i	−0.960178	+	0.554359i
$370$	2.67921e8	+	1.54684e8i	0.274980	+	0.158760i
$371$	8.43025e6	−	6.92948e6i	0.00857100	−	0.00704518i
$372$			1.51125e8i			0.152208i
$373$	−1.10869e9			−1.10619			−0.553096	−	0.833117i	$-0.686554\pi$
$373$	−1.10869e9			−1.10619			−0.553096	+	0.833117i	$0.686554\pi$
$374$	−5.08944e8			−0.503059
$375$		−	6.83301e8i		−	0.669118i
$376$	1.76801e8	+	3.06228e8i	0.171525	+	0.297089i
$377$	1.50183e8	−	3.92592e8i	0.144353	−	0.377352i
$378$	−7.73961e8	−	9.41584e8i	−0.737052	−	0.896680i
$379$	−1.17899e9	+	6.80691e8i	−1.11243	+	0.642262i	−0.939458	−	0.342664i	$-0.888671\pi$
$379$	−1.17899e9	+	6.80691e8i	−1.11243	+	0.642262i	−0.172973	+	0.984927i	$0.555337\pi$
$380$	−1.12970e8	+	1.95670e8i	−0.105614	+	0.182929i
$381$	2.50437e8	+	4.33769e8i	0.231985	+	0.401810i
$382$	4.87710e8	+	2.81579e8i	0.447651	+	0.258452i
$383$			1.03623e9i			0.942455i	0.882012	+	0.471227i	$0.156189\pi$
$383$			1.03623e9i			0.942455i	−0.882012	+	0.471227i	$0.843811\pi$
$384$	7.31266e8	+	4.22197e8i	0.659046	+	0.380501i
$385$	−4.09816e7	−	2.47029e8i	−0.0365996	−	0.220615i
$386$	−1.16130e9	+	2.01143e9i	−1.02775	+	1.78012i
$387$	−2.43053e8	+	4.20979e8i	−0.213163	+	0.369209i
$388$		−	4.07808e8i		−	0.354442i
$389$	−3.85665e8	+	6.67991e8i	−0.332190	+	0.575370i	−0.982941	−	0.183921i	$-0.941121\pi$
$389$	−3.85665e8	+	6.67991e8i	−0.332190	+	0.575370i	0.650751	+	0.759291i	$0.274454\pi$
$390$	−3.75318e8	−	4.62389e8i	−0.320386	−	0.394713i
$391$	−1.10091e9			−0.931396
$392$	−6.16687e8	+	7.05402e8i	−0.517087	+	0.591474i
$393$	−2.99376e8	−	5.18535e8i	−0.248796	−	0.430928i
$394$	4.24581e8			0.349723
$395$	−3.61584e7	−	2.08761e7i	−0.0295202	−	0.0170435i
$396$	−6.44842e7	+	3.72300e7i	−0.0521819	+	0.0301272i
$397$			1.39621e9i			1.11991i	0.828524	+	0.559954i	$0.189181\pi$
$397$			1.39621e9i			1.11991i	−0.828524	+	0.559954i	$0.810819\pi$
$398$		−	9.22947e8i		−	0.733814i
$399$	−2.70314e8	+	7.19902e8i	−0.213041	+	0.567373i
$400$	3.96219e8	+	6.86271e8i	0.309546	+	0.536149i
$401$	−1.13477e9	−	6.55160e8i	−0.878826	−	0.507390i	−0.00855491	−	0.999963i	$-0.502723\pi$
$401$	−1.13477e9	−	6.55160e8i	−0.878826	−	0.507390i	−0.870271	+	0.492573i	$0.836056\pi$
$402$	7.71908e7	−	1.33698e8i	0.0592618	−	0.102644i
$403$	−1.58147e8	−	9.91107e8i	−0.120363	−	0.754315i
$404$	−9.71978e6	−	1.68352e7i	−0.00733368	−	0.0127023i
$405$	3.33612e7	−	1.92611e7i	0.0249545	−	0.0144075i
$406$	−2.19603e8	+	5.84847e8i	−0.162854	+	0.433712i
$407$	8.58107e7	−	1.48628e8i	0.0630901	−	0.109275i
$408$	−8.11810e8	+	4.68699e8i	−0.591757	+	0.341651i
$409$	−1.36414e9	+	7.87586e8i	−0.985887	+	0.569202i	−0.904042	−	0.427443i	$-0.859414\pi$
$409$	−1.36414e9	+	7.87586e8i	−0.985887	+	0.569202i	−0.0818446	+	0.996645i	$0.526081\pi$
$410$	1.79553e9	−	1.03665e9i	1.28661	−	0.742827i
$411$	1.45547e9	−	8.40314e8i	1.03408	−	0.597029i
$412$	1.64601e8	−	2.85097e8i	0.115956	−	0.200841i
$413$	−1.25075e9	+	2.07497e8i	−0.873667	+	0.144940i
$414$	−5.82506e8	+	3.36310e8i	−0.403459	+	0.232937i
$415$	−4.20538e8	−	7.28392e8i	−0.288826	−	0.500262i
$416$	8.34375e8	+	3.19184e8i	0.568244	+	0.217378i
$417$	−7.29436e8	+	1.26342e9i	−0.492619	+	0.853241i
$418$	4.53297e8	+	2.61711e8i	0.303575	+	0.175269i
$419$	−3.91998e8	−	6.78960e8i	−0.260336	−	0.450916i	0.705995	−	0.708217i	$-0.250500\pi$
$419$	−3.91998e8	−	6.78960e8i	−0.260336	−	0.450916i	−0.966331	+	0.257301i	$0.917167\pi$
$420$	1.34587e8	+	1.63735e8i	0.0886399	+	0.107837i
$421$		−	1.89594e9i		−	1.23833i	−0.785259	−	0.619167i	$-0.787470\pi$
$421$		−	1.89594e9i		−	1.23833i	0.785259	−	0.619167i	$-0.212530\pi$
$422$		−	1.18748e9i		−	0.769187i
$423$	−3.52888e8	+	2.03740e8i	−0.226697	+	0.130884i
$424$	−1.18482e7	−	6.84059e6i	−0.00754872	−	0.00435826i
$425$	−1.10756e9			−0.699849
$426$	4.23496e8	+	7.33517e8i	0.265409	+	0.459702i
$427$	−3.72223e8	−	1.39765e8i	−0.231369	−	0.0868763i
$428$	−4.03010e8			−0.248464
$429$	−2.56509e8	+	2.08206e8i	−0.156856	+	0.127319i
$430$	4.70921e8	−	8.15659e8i	0.285633	−	0.494731i
$431$		−	1.70102e9i		−	1.02338i	−0.859169	−	0.511692i	$-0.829019\pi$
$431$		−	1.70102e9i		−	1.02338i	0.859169	−	0.511692i	$-0.170981\pi$
$432$	−1.03107e9	+	1.78586e9i	−0.615310	+	1.06575i
$433$	5.64942e8	−	9.78509e8i	0.334423	−	0.579238i	−0.648951	−	0.760831i	$-0.724792\pi$
$433$	5.64942e8	−	9.78509e8i	0.334423	−	0.579238i	0.983374	+	0.181592i	$0.0581251\pi$
$434$	2.44125e8	+	1.47153e9i	0.143350	+	0.864085i
$435$	−2.66312e8	−	1.53755e8i	−0.155124	−	0.0895608i
$436$			9.47197e8i			0.547315i
$437$	9.80542e8	+	5.66116e8i	0.562058	+	0.324504i
$438$	−6.00672e8	−	1.04040e9i	−0.341569	−	0.591615i
$439$	−4.36795e8	+	7.56552e8i	−0.246407	+	0.426789i	−0.962526	−	0.271189i	$-0.912583\pi$
$439$	−4.36795e8	+	7.56552e8i	−0.246407	+	0.426789i	0.716120	+	0.697978i	$0.245917\pi$
$440$	−2.71873e8	+	1.56966e8i	−0.152153	+	0.0878458i
$441$	−8.12885e8	−	7.10652e8i	−0.451330	−	0.394568i
$442$	−2.22125e9	+	1.80298e9i	−1.22355	+	0.993144i
$443$	−1.07806e9	−	1.86725e9i	−0.589155	−	1.02045i	−0.994343	−	0.106214i	$-0.966127\pi$
$443$	−1.07806e9	−	1.86725e9i	−0.589155	−	1.02045i	0.405188	−	0.914233i	$-0.367206\pi$
$444$			1.45265e8i			0.0787626i
$445$	−9.26188e7			−0.0498241
$446$	1.93913e9			1.03499
$447$			6.77306e8i			0.358681i
$448$	9.23064e8	+	3.46599e8i	0.485019	+	0.182119i
$449$	3.10413e9	+	1.79217e9i	1.61837	+	0.934366i	0.987342	+	0.158607i	$0.0507002\pi$
$449$	3.10413e9	+	1.79217e9i	1.61837	+	0.934366i	0.631028	+	0.775760i	$0.282633\pi$
$450$	−5.86021e8	+	3.38339e8i	−0.303158	+	0.175028i
$451$	−5.75077e8	−	9.96062e8i	−0.295194	−	0.511292i
$452$	−5.34030e8			−0.272007
$453$	−1.50837e9	−	8.70860e8i	−0.762369	−	0.440154i
$454$	4.24252e8			0.212779
$455$	−1.05398e9	−	9.32963e8i	−0.524559	−	0.464328i
$456$	9.64065e8			0.476134
$457$	2.93689e9	+	1.69561e9i	1.43940	+	0.831036i	0.997808	−	0.0661815i	$-0.0210816\pi$
$457$	2.93689e9	+	1.69561e9i	1.43940	+	0.831036i	0.441589	+	0.897217i	$0.354415\pi$
$458$	2.74284e9			1.33405
$459$	−1.44108e9	−	2.49602e9i	−0.695574	−	1.20477i
$460$	2.70262e8	−	1.56036e8i	0.129459	−	0.0747431i
$461$	−3.49975e8	−	2.02058e8i	−0.166373	−	0.0960557i	0.414501	−	0.910049i	$-0.363956\pi$
$461$	−3.49975e8	−	2.02058e8i	−0.166373	−	0.0960557i	−0.580875	+	0.813993i	$0.697289\pi$
$462$	3.79315e8	−	3.11789e8i	0.178959	−	0.147100i
$463$		−	3.11474e9i		−	1.45844i	−0.684280	−	0.729220i	$-0.739883\pi$
$463$		−	3.11474e9i		−	1.45844i	0.684280	−	0.729220i	$-0.260117\pi$
$464$	1.05694e9			0.491177
$465$	−7.34248e8			−0.338655
$466$		−	5.00392e8i		−	0.229066i
$467$	6.29274e7	+	1.08993e8i	0.0285911	+	0.0495212i	0.879967	−	0.475035i	$-0.157565\pi$
$467$	6.29274e7	+	1.08993e8i	0.0285911	+	0.0495212i	−0.851376	+	0.524556i	$0.824231\pi$
$468$	−1.49547e8	+	3.90929e8i	−0.0674400	+	0.176294i
$469$	1.28267e8	−	3.41601e8i	0.0574130	−	0.152903i
$470$	6.83730e8	−	3.94752e8i	0.303768	−	0.175381i
$471$	−1.18115e9	+	2.04581e9i	−0.520872	+	0.902176i
$472$	7.94746e8	+	1.37654e9i	0.347881	+	0.602548i
$473$	−4.52484e8	−	2.61242e8i	−0.196603	−	0.113509i
$474$		−	8.18702e7i		−	0.0353103i
$475$	9.86459e8	+	5.69533e8i	0.422330	+	0.243832i
$476$	7.86561e8	−	6.46536e8i	0.334278	−	0.274769i
$477$	7.88290e6	−	1.36536e7i	0.00332561	−	0.00576013i
$478$	2.18931e9	−	3.79199e9i	0.916872	−	1.58807i
$479$		−	2.06945e9i		−	0.860363i	−0.902743	−	0.430181i	$-0.858450\pi$
$479$		−	2.06945e9i		−	0.860363i	0.902743	−	0.430181i	$-0.141550\pi$
$480$	3.26776e8	−	5.65993e8i	0.134867	−	0.233597i
$481$	−1.52014e8	−	9.52672e8i	−0.0622838	−	0.390333i
$482$	−2.91259e9			−1.18472
$483$	8.20509e8	−	6.74440e8i	0.331336	−	0.272351i
$484$	3.52669e8	+	6.10840e8i	0.141387	+	0.244889i
$485$	1.98135e9			0.788616
$486$	−2.47840e9	−	1.43091e9i	−0.979366	−	0.565438i
$487$	−2.74952e9	+	1.58743e9i	−1.07871	+	0.622794i	−0.930548	−	0.366169i	$-0.880669\pi$
$487$	−2.74952e9	+	1.58743e9i	−1.07871	+	0.622794i	−0.148162	+	0.988963i	$0.547336\pi$
$488$			4.98467e8i			0.194163i
$489$			1.79336e9i			0.693565i
$490$	1.57499e9	+	1.37691e9i	0.604771	+	0.528711i
$491$	1.00811e8	+	1.74609e8i	0.0384345	+	0.0665705i	0.884603	−	0.466345i	$-0.154430\pi$
$491$	1.00811e8	+	1.74609e8i	0.0384345	+	0.0665705i	−0.846168	+	0.532916i	$0.821096\pi$
$492$	8.43093e8	+	4.86760e8i	0.319152	+	0.184263i
$493$	−7.38620e8	+	1.27933e9i	−0.277624	+	0.480859i
$494$	2.90552e9	−	4.63622e8i	1.08438	−	0.173029i
$495$	−1.80883e8	−	3.13299e8i	−0.0670316	−	0.116102i
$496$	2.18556e9	−	1.26184e9i	0.804225	−	0.464320i
$497$	1.27120e9	+	1.54651e9i	0.464479	+	0.565074i
$498$	8.24617e8	−	1.42828e9i	0.299192	−	0.518215i
$499$	3.64146e9	−	2.10240e9i	1.31197	−	0.757466i	0.329547	−	0.944139i	$-0.393104\pi$
$499$	3.64146e9	−	2.10240e9i	1.31197	−	0.757466i	0.982422	+	0.186673i	$0.0597705\pi$
$500$	8.05813e8	−	4.65236e8i	0.288296	−	0.166448i
$501$	−5.78363e8	+	3.33918e8i	−0.205479	+	0.118634i
$502$	2.96684e9	−	1.71290e9i	1.04672	−	0.604324i
$503$	−6.54069e8	+	1.13288e9i	−0.229158	+	0.396914i	−0.957559	−	0.288238i	$-0.906931\pi$
$503$	−6.54069e8	+	1.13288e9i	−0.229158	+	0.396914i	0.728401	+	0.685151i	$0.240264\pi$
$504$	−4.75839e8	+	1.26726e9i	−0.165559	+	0.440917i
$505$	8.17942e7	−	4.72239e7i	0.0282620	−	0.0163171i
$506$	−3.61478e8	−	6.26099e8i	−0.124038	−	0.214840i
$507$	−3.81928e8	+	1.81741e9i	−0.130153	+	0.619334i
$508$	−3.41028e8	+	5.90677e8i	−0.115416	+	0.199907i
$509$	2.31310e9	+	1.33547e9i	0.777469	+	0.448872i	0.835532	−	0.549441i	$-0.185159\pi$
$509$	2.31310e9	+	1.33547e9i	0.777469	+	0.448872i	−0.0580637	+	0.998313i	$0.518493\pi$
$510$	1.04649e9	+	1.81257e9i	0.349332	+	0.605061i
$511$	−1.80302e9	−	2.19352e9i	−0.597762	−	0.727224i
$512$		−	6.54361e8i		−	0.215463i
$513$			2.96415e9i			0.969370i
$514$	−4.62435e9	+	2.66987e9i	−1.50203	+	0.867200i
$515$	1.38515e9	+	7.99719e8i	0.446861	+	0.257995i
$516$	4.42244e8			0.141706
$517$	−2.18987e8	−	3.79297e8i	−0.0696951	−	0.120715i
$518$	2.34658e8	+	1.41447e9i	0.0741789	+	0.447136i
$519$	1.19482e9			0.375159
$520$	−6.30508e8	+	1.64820e9i	−0.196643	+	0.514042i
$521$	2.20185e9	−	3.81372e9i	0.682113	−	1.18145i	−0.292222	−	0.956351i	$-0.594394\pi$
$521$	2.20185e9	−	3.81372e9i	0.682113	−	1.18145i	0.974335	−	0.225104i	$-0.0722722\pi$
$522$			9.02543e8i			0.277729i
$523$	−4.56915e8	+	7.91400e8i	−0.139662	+	0.241902i	−0.927369	−	0.374148i	$-0.877935\pi$
$523$	−4.56915e8	+	7.91400e8i	−0.139662	+	0.241902i	0.787706	+	0.616051i	$0.211268\pi$
$524$	4.07670e8	−	7.06106e8i	0.123780	−	0.214393i
$525$	8.25460e8	−	6.78510e8i	0.248965	−	0.204644i
$526$	−3.20434e9	−	1.85003e9i	−0.960038	−	0.554278i
$527$			3.52723e9i			1.04978i
$528$	−7.19430e8	−	4.15363e8i	−0.212701	−	0.122803i
$529$	9.20487e8	+	1.59433e9i	0.270348	+	0.468256i
$530$	−1.52733e7	+	2.64542e7i	−0.00445624	+	0.00771843i
$531$	−1.58629e9	+	9.15842e8i	−0.459780	+	0.265454i
$532$	−1.03302e9	+	1.71377e8i	−0.297454	+	0.0493470i
$533$	−6.03853e9	−	2.31000e9i	−1.72737	−	0.660794i
$534$	−9.08065e7	−	1.57281e8i	−0.0258061	−	0.0446975i
$535$		−	1.95804e9i		−	0.552819i
$536$	−4.57459e8			−0.128314
$537$	2.19217e9			0.610893
$538$		−	2.46778e9i		−	0.683232i
$539$	7.63835e8	−	8.73719e8i	0.210106	−	0.240332i
$540$	7.07537e8	+	4.08497e8i	0.193362	+	0.111638i
$541$	−4.69763e9	+	2.71218e9i	−1.27552	+	0.736424i	−0.976022	−	0.217672i	$-0.930154\pi$
$541$	−4.69763e9	+	2.71218e9i	−1.27552	+	0.736424i	−0.299501	+	0.954096i	$0.596820\pi$
$542$	−8.22197e7	−	1.42409e8i	−0.0221809	−	0.0384184i
$543$	9.49171e8			0.254417
$544$	−2.71895e9	−	1.56979e9i	−0.724112	−	0.418066i
$545$	−4.60199e9			−1.21775
$546$	5.50959e8	−	2.70454e9i	0.144859	−	0.711081i
$547$	2.01407e9			0.526162			0.263081	−	0.964774i	$-0.415261\pi$
$547$	2.01407e9			0.526162			0.263081	+	0.964774i	$0.415261\pi$
$548$	1.98196e9	+	1.14428e9i	0.514472	+	0.297031i
$549$	−5.74419e8			−0.148158
$550$	−3.63660e8	−	6.29877e8i	−0.0932021	−	0.161431i
$551$	1.31572e9	−	7.59633e8i	0.335069	−	0.193452i
$552$	−1.15318e9	−	6.65788e8i	−0.291817	−	0.168480i
$553$	−3.16692e7	−	1.90895e8i	−0.00796340	−	0.0480018i
$554$			3.52383e9i			0.880502i
$555$	−7.05774e8			−0.175243
$556$	−1.98659e9			−0.490171
$557$			5.87888e9i			1.44146i	0.693218	+	0.720728i	$0.256192\pi$
$557$			5.87888e9i			1.44146i	−0.693218	+	0.720728i	$0.743808\pi$
$558$	1.07751e9	+	1.86630e9i	0.262543	+	0.454738i
$559$	−2.90031e9	+	4.62790e8i	−0.702269	+	0.112058i
$560$	1.24418e9	−	3.31350e9i	0.299381	−	0.797313i
$561$	1.00552e9	−	5.80536e8i	0.240447	−	0.138822i
$562$	−3.29552e9	+	5.70801e9i	−0.783153	+	1.35646i
$563$	4.23170e9	+	7.32951e9i	0.999390	+	1.73099i	0.529934	+	0.848039i	$0.322217\pi$
$563$	4.23170e9	+	7.32951e9i	0.999390	+	1.73099i	0.469456	+	0.882956i	$0.344450\pi$
$564$	3.21047e8	+	1.85357e8i	0.0753515	+	0.0435042i
$565$		−	2.59460e9i		−	0.605203i
$566$	−2.12536e9	−	1.22708e9i	−0.492691	−	0.284455i
$567$	1.67141e8	+	6.27592e7i	0.0385071	+	0.0144590i
$568$	1.25489e9	−	2.17354e9i	0.287334	−	0.497677i
$569$	−5.49187e8	+	9.51219e8i	−0.124976	+	0.216465i	−0.921724	−	0.387847i	$-0.873219\pi$
$569$	−5.49187e8	+	9.51219e8i	−0.124976	+	0.216465i	0.796747	+	0.604312i	$0.206552\pi$
$570$		−	2.15252e9i		−	0.486838i
$571$	4.25975e9	−	7.37810e9i	0.957541	−	1.65851i	0.229099	−	0.973403i	$-0.426422\pi$
$571$	4.25975e9	−	7.37810e9i	0.957541	−	1.65851i	0.728442	−	0.685107i	$-0.240245\pi$
$572$	−4.20185e8	−	1.60739e8i	−0.0938760	−	0.0359116i
$573$	−1.28475e9			−0.285285
$574$	8.99565e9	+	3.37775e9i	1.98537	+	0.745481i
$575$	−7.86644e8	−	1.36251e9i	−0.172560	−	0.298883i
$576$	1.42448e9			0.310583
$577$	3.74509e9	+	2.16223e9i	0.811609	+	0.468583i	0.847514	−	0.530773i	$-0.178098\pi$
$577$	3.74509e9	+	2.16223e9i	0.811609	+	0.468583i	−0.0359054	+	0.999355i	$0.511432\pi$
$578$	4.09716e9	−	2.36550e9i	0.882543	−	0.509536i
$579$		−	5.29862e9i		−	1.13446i
$580$		−	4.18747e8i		−	0.0891157i
$581$	1.37026e9	−	3.64927e9i	0.289858	−	0.771951i
$582$	1.94258e9	+	3.36465e9i	0.408459	+	0.707472i
$583$	1.46754e7	+	8.47283e6i	0.00306725	+	0.00177088i
$584$	−1.77989e9	+	3.08287e9i	−0.369785	+	0.640486i
$585$	−1.89934e9	−	7.26579e8i	−0.392245	−	0.150051i
$586$	−2.68233e9	−	4.64593e9i	−0.550644	−	0.953743i
$587$	5.22761e9	−	3.01816e9i	1.06677	−	0.615898i	0.139471	−	0.990226i	$-0.455460\pi$
$587$	5.22761e9	−	3.01816e9i	1.06677	−	0.615898i	0.927296	+	0.374328i	$0.122127\pi$
$588$	−1.90142e8	+	9.63724e8i	−0.0385707	+	0.195493i
$589$	1.81379e9	−	3.14157e9i	0.365749	−	0.633495i
$590$	3.07347e9	−	1.77447e9i	0.616094	−	0.355702i
$591$	−8.38843e8	+	4.84306e8i	−0.167157	+	0.0965081i
$592$	2.10081e9	−	1.21290e9i	0.416160	−	0.240270i
$593$	6.48872e8	−	3.74626e8i	0.127781	−	0.0737746i	−0.434747	−	0.900553i	$-0.643162\pi$
$593$	6.48872e8	−	3.74626e8i	0.127781	−	0.0737746i	0.562528	+	0.826778i	$0.309829\pi$
$594$	9.46340e8	−	1.63911e9i	0.185266	−	0.320889i
$595$	3.14122e9	+	3.82153e9i	0.611348	+	0.743752i
$596$	−7.98743e8	+	4.61155e8i	−0.154542	+	0.0892246i
$597$	1.05278e9	+	1.82346e9i	0.202500	+	0.350741i
$598$	−3.79566e9	−	1.45200e9i	−0.725827	−	0.277660i
$599$	2.28092e9	−	3.95067e9i	0.433627	−	0.751064i	−0.563555	−	0.826078i	$-0.690567\pi$
$599$	2.28092e9	−	3.95067e9i	0.433627	−	0.751064i	0.997182	+	0.0750142i	$0.0239002\pi$
$600$	−1.16014e9	−	6.69806e8i	−0.219271	−	0.126596i
$601$	1.28677e9	+	2.22875e9i	0.241792	+	0.418795i	0.961225	−	0.275767i	$-0.0889317\pi$
$601$	1.28677e9	+	2.22875e9i	0.241792	+	0.418795i	−0.719433	+	0.694562i	$0.755598\pi$
$602$	4.30621e9	−	7.14391e8i	0.804465	−	0.133459i
$603$		−	5.27163e8i		−	0.0979116i
$604$		−	2.37176e9i		−	0.437966i
$605$	−2.96779e9	+	1.71345e9i	−0.544865	+	0.314578i
$606$	1.60387e8	+	9.25997e7i	0.0292763	+	0.0169027i
$607$	−8.58245e9			−1.55758			−0.778791	−	0.627283i	$-0.784167\pi$
$607$	−8.58245e9			−1.55758			−0.778791	+	0.627283i	$0.784167\pi$
$608$	1.61445e9	+	2.79631e9i	0.291314	+	0.504571i
$609$	−2.33248e8	−	1.40597e9i	−0.0418464	−	0.252242i
$610$	1.11295e9			0.198528
$611$	−2.29945e9	−	8.79638e8i	−0.407831	−	0.156013i
$612$	7.35492e8	−	1.27391e9i	0.129702	−	0.224651i
$613$			2.03428e9i			0.356698i	0.983967	+	0.178349i	$0.0570755\pi$
$613$			2.03428e9i			0.356698i	−0.983967	+	0.178349i	$0.942924\pi$
$614$	−4.04306e9	+	7.00278e9i	−0.704889	+	1.22090i
$615$	−2.36494e9	+	4.09620e9i	−0.409975	+	0.710097i
$616$	−1.36209e9	−	5.11449e8i	−0.234787	−	0.0881597i
$617$	1.01113e9	+	5.83774e8i	0.173303	+	0.100057i	0.584143	−	0.811651i	$-0.301431\pi$
$617$	1.01113e9	+	5.83774e8i	0.173303	+	0.100057i	−0.410839	+	0.911708i	$0.634764\pi$
$618$			3.13628e9i			0.534509i
$619$	3.53921e9	+	2.04337e9i	0.599777	+	0.346281i	0.768954	−	0.639304i	$-0.220778\pi$
$619$	3.53921e9	+	2.04337e9i	0.599777	+	0.346281i	−0.169177	+	0.985586i	$0.554111\pi$
$620$	−4.99924e8	−	8.65894e8i	−0.0842429	−	0.145913i
$621$	2.04706e9	−	3.54561e9i	0.343012	−	0.594115i
$622$	−1.13460e10	+	6.55062e9i	−1.89050	+	1.09148i
$623$	−2.72572e8	−	3.31604e8i	−0.0451619	−	0.0549430i
$624$	−4.61137e9	+	7.35816e8i	−0.759774	+	0.121234i
$625$	7.06296e8	+	1.22334e9i	0.115720	+	0.200432i
$626$		−	1.16997e10i		−	1.90618i
$627$	−1.19410e9			−0.193466
$628$	−3.21681e9			−0.518283
$629$			3.39044e9i			0.543224i
$630$	2.82947e9	+	1.06243e9i	0.450830	+	0.169281i
$631$	5.46254e9	+	3.15380e9i	0.865550	+	0.499725i	0.865867	−	0.500275i	$-0.166768\pi$
$631$	5.46254e9	+	3.15380e9i	0.865550	+	0.499725i	−0.000317139		1.00000i	$0.500101\pi$
$632$	−2.10094e8	+	1.21298e8i	−0.0331057	+	0.0191136i
$633$	1.35452e9	+	2.34609e9i	0.212262	+	0.367648i
$634$	−8.97972e9			−1.39943
$635$	−2.86983e9	−	1.65689e9i	−0.444782	−	0.256795i
$636$	−1.43433e7			−0.00221079
$637$	2.38488e8	−	6.51925e9i	0.0365576	−	0.999332i
$638$	−9.70087e8			−0.147890
$639$	2.50472e9	+	1.44610e9i	0.379757	+	0.219253i
$640$	−5.58652e9			−0.842387
$641$	−2.46420e8	−	4.26811e8i	−0.0369549	−	0.0640078i	0.846956	−	0.531662i	$-0.178432\pi$
$641$	−2.46420e8	−	4.26811e8i	−0.0369549	−	0.0640078i	−0.883911	+	0.467655i	$0.845099\pi$
$642$	3.32506e9	−	1.91972e9i	0.495937	−	0.286329i
$643$	7.81673e6	+	4.51299e6i	0.00115954	+	0.000669462i	0.500580	−	0.865690i	$-0.333120\pi$
$643$	7.81673e6	+	4.51299e6i	0.00115954	+	0.000669462i	−0.499420	+	0.866360i	$0.666454\pi$
$644$	1.35402e9	+	5.08418e8i	0.199767	+	0.0750102i
$645$			2.14866e9i			0.315288i
$646$	−1.03404e10			−1.50912
$647$	4.80500e9			0.697474			0.348737	−	0.937221i	$-0.386611\pi$
$647$	4.80500e9			0.697474			0.348737	+	0.937221i	$0.386611\pi$
$648$		−	2.23828e8i		−	0.0323149i
$649$	−9.84381e8	−	1.70500e9i	−0.141354	−	0.244832i
$650$	−3.81857e9	−	1.46077e9i	−0.545385	−	0.208633i
$651$	−2.16085e9	−	2.62884e9i	−0.306966	−	0.373448i
$652$	−2.11490e9	+	1.22104e9i	−0.298830	+	0.172529i
$653$	−3.82329e9	+	6.62213e9i	−0.537329	+	0.930682i	0.461717	+	0.887027i	$0.347233\pi$
$653$	−3.82329e9	+	6.62213e9i	−0.537329	+	0.930682i	−0.999047	+	0.0436547i	$0.986100\pi$
$654$	−4.51194e9	−	7.81491e9i	−0.630726	−	1.09245i
$655$	3.43064e9	+	1.98068e9i	0.477013	+	0.275404i
$656$		−	1.62570e10i		−	2.24842i
$657$	−3.55261e9	−	2.05110e9i	−0.488730	−	0.282168i
$658$	3.42551e9	+	1.28624e9i	0.468743	+	0.176007i
$659$	3.39063e9	−	5.87275e9i	0.461511	−	0.799360i	−0.537526	−	0.843247i	$-0.680641\pi$
$659$	3.39063e9	−	5.87275e9i	0.461511	−	0.799360i	0.999037	+	0.0438870i	$0.0139742\pi$
$660$	−1.64562e8	+	2.85030e8i	−0.0222805	+	0.0385910i
$661$			6.69595e9i			0.901793i	0.892576	+	0.450897i	$0.148896\pi$
$661$			6.69595e9i			0.901793i	−0.892576	+	0.450897i	$0.851104\pi$
$662$	−7.78713e9	+	1.34877e10i	−1.04322	+	1.80690i
$663$	2.33192e9	−	6.09585e9i	0.310754	−	0.812338i
$664$	−4.88696e9			−0.647815
$665$	−8.32640e8	−	5.01899e9i	−0.109795	−	0.661821i
$666$	1.03572e9	+	1.79392e9i	0.135857	+	0.235312i
$667$	−2.09843e9			−0.273813
$668$	−7.87575e8	−	4.54707e8i	−0.102229	−	0.0590220i
$669$	−3.83113e9	+	2.21190e9i	−0.494692	+	0.285611i
$670$			1.02139e9i			0.131199i
$671$		−	6.17407e8i		−	0.0788937i
$672$	2.98812e9	−	4.95722e8i	0.379844	−	0.0630153i
$673$	5.23175e9	+	9.06166e9i	0.661598	+	1.14592i	0.980196	+	0.198032i	$0.0634549\pi$
$673$	5.23175e9	+	9.06166e9i	0.661598	+	1.14592i	−0.318597	+	0.947890i	$0.603212\pi$
$674$	2.43246e9	+	1.40438e9i	0.306010	+	0.176675i
$675$	2.05941e9	−	3.56701e9i	0.257739	−	0.446417i
$676$	−2.40330e9	+	7.87007e8i	−0.299223	+	0.0979863i
$677$	7.36168e9	+	1.27508e10i	0.911835	+	1.57935i	0.811470	+	0.584394i	$0.198668\pi$
$677$	7.36168e9	+	1.27508e10i	0.911835	+	1.57935i	0.100366	+	0.994951i	$0.467999\pi$
$678$	4.40604e9	−	2.54383e9i	0.542931	−	0.313462i
$679$	5.83100e9	+	7.09386e9i	0.714823	+	0.869638i
$680$	3.10092e9	−	5.37095e9i	0.378189	−	0.655043i
$681$	−8.38193e8	+	4.83931e8i	−0.101702	+	0.0587176i
$682$	−2.00597e9	+	1.15814e9i	−0.242147	+	0.139803i
$683$	−6.03669e9	+	3.48529e9i	−0.724981	+	0.418568i	−0.816583	−	0.577228i	$-0.804134\pi$
$683$	−6.03669e9	+	3.48529e9i	−0.724981	+	0.418568i	0.0916023	+	0.995796i	$0.470801\pi$
$684$	−1.31015e9	+	7.56416e8i	−0.156540	+	0.0903783i
$685$	−5.55954e9	+	9.62940e9i	−0.660879	+	1.14468i
$686$	−2.94669e8	+	9.69110e9i	−0.0348498	+	1.14614i
$687$	−5.41901e9	+	3.12867e9i	−0.637634	+	0.368138i
$688$	−3.69256e9	−	6.39570e9i	−0.432283	−	0.748735i
$689$	9.40656e7	−	1.50096e7i	0.0109563	−	0.00174825i
$690$	−1.48654e9	+	2.57476e9i	−0.172268	+	0.298377i
$691$	−4.51736e8	−	2.60810e8i	−0.0520849	−	0.0300712i	0.473731	−	0.880669i	$-0.342907\pi$
$691$	−4.51736e8	−	2.60810e8i	−0.0520849	−	0.0300712i	−0.525816	+	0.850598i	$0.676240\pi$
$692$	8.13510e8	+	1.40904e9i	0.0933236	+	0.161641i
$693$	5.89379e8	−	1.56964e9i	0.0672711	−	0.179157i
$694$		−	7.58653e9i		−	0.861559i
$695$		−	9.65193e9i		−	1.09061i
$696$	−1.54737e9	+	8.93377e8i	−0.173965	+	0.100439i
$697$	1.96776e10	+	1.13609e10i	2.20119	+	1.27086i
$698$	−1.95265e10			−2.17336
$699$	5.70781e8	+	9.88622e8i	0.0632120	+	0.109486i
$700$	1.36219e9	+	5.11486e8i	0.150105	+	0.0563625i
$701$	−3.51467e9			−0.385365			−0.192682	−	0.981261i	$-0.561719\pi$
$701$	−3.51467e9			−0.385365			−0.192682	+	0.981261i	$0.561719\pi$
$702$	−1.67644e9	−	1.05063e10i	−0.182898	−	1.14622i
$703$	1.74345e9	−	3.01974e9i	0.189263	−	0.327813i
$704$			1.53109e9i			0.165385i
$705$	−9.00561e8	+	1.55982e9i	−0.0967946	+	0.167653i
$706$	7.89757e9	−	1.36790e10i	0.844651	−	1.46298i
$707$	4.09792e8	+	1.53872e8i	0.0436109	+	0.0163754i
$708$	1.44316e9	+	8.33206e8i	0.152826	+	0.0882340i
$709$		−	4.16357e9i		−	0.438737i	−0.975642	−	0.219368i	$-0.929600\pi$
$709$		−	4.16357e9i		−	0.438737i	0.975642	−	0.219368i	$-0.0703997\pi$
$710$	−4.85296e9	−	2.80186e9i	−0.508865	−	0.293793i
$711$	−1.39780e8	−	2.42106e8i	−0.0145848	−	0.0252617i
$712$	−2.69075e8	+	4.66052e8i	−0.0279379	+	0.0483898i
$713$	−4.33917e9	+	2.50522e9i	−0.448326	+	0.258841i
$714$	−3.40982e9	+	9.08104e9i	−0.350580	+	0.933666i
$715$	7.80955e8	−	2.04148e9i	0.0799014	−	0.208869i
$716$	1.49258e9	+	2.58522e9i	0.151964	+	0.263210i
$717$			9.98908e9i			1.01207i
$718$	−3.32771e9			−0.335514
$719$	6.15335e8			0.0617391			0.0308696	−	0.999523i	$-0.490172\pi$
$719$	6.15335e8			0.0617391			0.0308696	+	0.999523i	$0.490172\pi$
$720$		−	5.11343e9i		−	0.510562i
$721$	1.21318e9	+	7.31281e9i	0.120546	+	0.726626i
$722$	−8.32881e8	−	4.80864e8i	−0.0823574	−	0.0475491i
$723$	5.75438e9	−	3.32229e9i	0.566258	−	0.326929i
$724$	6.46259e8	+	1.11935e9i	0.0632880	+	0.109618i
$725$	−2.11109e9			−0.205742
$726$	−5.81943e9	−	3.35985e9i	−0.564420	−	0.325868i
$727$	−1.82239e9			−0.175902			−0.0879508	−	0.996125i	$-0.528032\pi$
$727$	−1.82239e9			−0.175902			−0.0879508	+	0.996125i	$0.528032\pi$
$728$	−7.75663e9	+	2.59315e9i	−0.745098	+	0.249096i
$729$	6.95902e9			0.665276
$730$	6.88328e9	+	3.97406e9i	0.654885	+	0.378098i
$731$	1.03219e10			0.977344
$732$	2.61295e8	+	4.52575e8i	0.0246230	+	0.0426483i
$733$	−8.62199e9	+	4.97791e9i	−0.808618	+	0.466856i	−0.846476	−	0.532427i	$-0.821280\pi$
$733$	−8.62199e9	+	4.97791e9i	−0.808618	+	0.466856i	0.0378575	+	0.999283i	$0.487947\pi$
$734$	−1.03320e10	−	5.96518e9i	−0.964379	−	0.556784i
$735$	−4.68229e9	−	9.23812e8i	−0.434963	−	0.0858179i
$736$		−	4.45978e9i		−	0.412327i
$737$	5.66614e8			0.0521376
$738$	1.38822e10			1.27134
$739$			1.57397e10i			1.43463i	0.696750	+	0.717315i	$0.254629\pi$
$739$			1.57397e10i			1.43463i	−0.696750	+	0.717315i	$0.745371\pi$
$740$	−4.80537e8	−	8.32315e8i	−0.0435930	−	0.0755052i
$741$	−5.21159e9	+	4.23021e9i	−0.470551	+	0.381943i
$742$	−1.39663e8	+	2.31698e7i	−0.0125507	+	0.00208213i
$743$	1.68665e10	−	9.73788e9i	1.50857	−	0.870971i	0.508615	−	0.860994i	$-0.330158\pi$
$743$	1.68665e10	−	9.73788e9i	1.50857	−	0.870971i	0.999950	−	0.00997664i	$-0.00317571\pi$
$744$	−2.13313e9	+	3.69469e9i	−0.189894	+	0.328906i
$745$	−2.24054e9	−	3.88072e9i	−0.198520	−	0.343847i
$746$	1.24562e10	+	7.19161e9i	1.09850	+	0.634220i
$747$		−	5.63160e9i		−	0.494321i
$748$	1.36924e9	+	7.90534e8i	0.119626	+	0.0690661i
$749$	7.01039e9	−	5.76239e9i	0.609615	−	0.501091i
$750$	−4.43227e9	+	7.67692e9i	−0.383630	+	0.664466i
$751$	6.27638e9	−	1.08710e10i	0.540716	−	0.936548i	−0.458147	−	0.888876i	$-0.651487\pi$
$751$	6.27638e9	−	1.08710e10i	0.540716	−	0.936548i	0.998863	−	0.0476713i	$-0.0151800\pi$
$752$		−	6.19061e9i		−	0.530849i
$753$	−3.90771e9	+	6.76835e9i	−0.333534	+	0.577697i
$754$	−4.23389e9	+	3.43662e9i	−0.359699	+	0.291965i
$755$	1.15233e10			0.974453
$756$	6.19693e8	+	3.73539e9i	0.0521615	+	0.314419i
$757$	6.76255e9	+	1.17131e10i	0.566597	+	0.981376i	0.996899	+	0.0786904i	$0.0250739\pi$
$757$	6.76255e9	+	1.17131e10i	0.566597	+	0.981376i	−0.430302	+	0.902685i	$0.641593\pi$
$758$	1.76614e10			1.47293
$759$	1.42834e9	+	8.24653e8i	0.118573	+	0.0684581i
$760$	−5.52375e9	+	3.18914e9i	−0.456443	+	0.263527i
$761$			2.12944e10i			1.75153i	0.482734	+	0.875767i	$0.339644\pi$
$761$			2.12944e10i			1.75153i	−0.482734	+	0.875767i	$0.660356\pi$
$762$		−	6.49789e9i		−	0.532023i
$763$	−1.35434e10	−	1.64766e10i	−1.10380	−	1.34286i
$764$	−8.74746e8	−	1.51510e9i	−0.0709668	−	0.122918i
$765$	6.18933e9	+	3.57341e9i	0.499837	+	0.288581i
$766$	6.72157e9	−	1.16421e10i	0.540343	−	0.935902i
$767$	−1.03364e10	−	3.95411e9i	−0.827151	−	0.316421i
$768$	−3.41922e9	−	5.92226e9i	−0.272372	−	0.471762i
$769$	1.54303e10	−	8.90867e9i	1.22358	−	0.706433i	0.257898	−	0.966172i	$-0.416970\pi$
$769$	1.54303e10	−	8.90867e9i	1.22358	−	0.706433i	0.965679	+	0.259739i	$0.0836367\pi$
$770$	−1.14194e9	+	3.04121e9i	−0.0901416	+	0.240065i
$771$	6.09087e9	−	1.05497e10i	0.478618	−	0.828991i
$772$	6.24864e9	−	3.60765e9i	0.488793	−	0.282205i
$773$	−5.34320e9	+	3.08490e9i	−0.416076	+	0.240222i	−0.693397	−	0.720556i	$-0.743887\pi$
$773$	−5.34320e9	+	3.08490e9i	−0.416076	+	0.240222i	0.277321	+	0.960777i	$0.410553\pi$
$774$	5.46142e9	−	3.15315e9i	0.423362	−	0.244428i
$775$	−4.36536e9	+	2.52034e9i	−0.336871	+	0.194493i
$776$	5.75620e9	−	9.97003e9i	0.442201	−	0.765914i
$777$	−2.07705e9	−	2.52689e9i	−0.158845	−	0.193247i
$778$	8.66593e9	−	5.00328e9i	0.659761	−	0.380913i
$779$	−1.16841e10	−	2.02374e10i	−0.885549	−	1.53382i
$780$	2.91522e8	+	1.82697e9i	0.0219958	+	0.137848i
$781$	−1.55432e9	+	2.69217e9i	−0.116752	+	0.202220i
$782$	1.23688e10	+	7.14114e9i	0.924920	+	0.534003i
$783$	−2.74681e9	−	4.75762e9i	−0.204486	−	0.354179i
$784$	1.55249e10	−	5.29689e9i	1.15060	−	0.392568i
$785$		−	1.56290e10i		−	1.15315i
$786$			7.76769e9i			0.570575i
$787$	1.16462e9	−	6.72391e8i	0.0851669	−	0.0491711i	−0.456812	−	0.889563i	$-0.651009\pi$
$787$	1.16462e9	−	6.72391e8i	0.0851669	−	0.0491711i	0.541979	+	0.840392i	$0.317675\pi$
$788$	−1.14228e9	−	6.59495e8i	−0.0831631	−	0.0480142i
$789$	8.44106e9			0.611825
$790$	2.70828e8	+	4.69087e8i	0.0195433	+	0.0338500i
$791$	9.28949e9	−	7.63576e9i	0.667381	−	0.548573i
$792$	−2.10200e9			−0.150347
$793$	−2.18722e9	−	2.69464e9i	−0.155753	−	0.191886i
$794$	9.05657e9	−	1.56864e10i	0.642084	−	1.11212i
$795$		−	6.96872e7i		−	0.00491890i
$796$	−1.43360e9	+	2.48307e9i	−0.100747	+	0.174499i
$797$	4.31078e8	−	7.46650e8i	0.0301614	−	0.0522411i	−0.850551	−	0.525893i	$-0.823731\pi$
$797$	4.31078e8	−	7.46650e8i	0.0301614	−	0.0522411i	0.880712	+	0.473652i	$0.157065\pi$
$798$	7.70669e9	−	6.33473e9i	0.536856	−	0.441284i
$799$	7.49316e9	+	4.32618e9i	0.519698	+	0.300048i
$800$		−	4.48670e9i		−	0.309822i
$801$	−5.37065e8	−	3.10074e8i	−0.0369243	−	0.0213183i
$802$	8.49947e9	+	1.47215e10i	0.581811	+	1.00773i
$803$	2.20460e9	−	3.81848e9i	0.150254	−	0.260247i
$804$	−4.15343e8	+	2.39799e8i	−0.0281845	+	0.0162724i
$805$	−2.47017e9	+	6.57855e9i	−0.166894	+	0.444472i
$806$	−4.65209e9	+	1.21610e10i	−0.312950	+	0.818079i
$807$	2.81491e9	+	4.87557e9i	0.188542	+	0.326564i
$808$		−	5.48777e8i		−	0.0365979i
$809$	−1.07919e10			−0.716603			−0.358301	−	0.933606i	$-0.616644\pi$
$809$	−1.07919e10			−0.716603			−0.358301	+	0.933606i	$0.616644\pi$
$810$	−4.99753e8			−0.0330413
$811$			2.64989e10i			1.74443i	0.489118	+	0.872217i	$0.337319\pi$
$811$			2.64989e10i			1.74443i	−0.489118	+	0.872217i	$0.662681\pi$
$812$	1.49925e9	−	1.23235e9i	0.0982714	−	0.0807769i
$813$	3.24882e8	+	1.87571e8i	0.0212036	+	0.0122419i
$814$	−1.92818e9	+	1.11323e9i	−0.125303	+	0.0723436i
$815$	−5.93246e9	−	1.02753e10i	−0.383869	−	0.664881i
$816$	1.64113e10			1.05737
$817$	−9.19330e9	−	5.30775e9i	−0.589786	−	0.340513i
$818$	2.04349e10			1.30538
$819$	−2.98827e9	−	8.93852e9i	−0.190075	−	0.568554i
$820$	−6.44083e9			−0.407937
$821$	−2.41372e10	−	1.39356e10i	−1.52225	−	0.878870i	−0.999654	−	0.0262868i	$-0.991632\pi$
$821$	−2.41372e10	−	1.39356e10i	−1.52225	−	0.878870i	−0.522592	−	0.852583i	$-0.675035\pi$
$822$	−2.18030e10			−1.36919
$823$	−3.02943e8	−	5.24713e8i	−0.0189436	−	0.0328112i	0.856398	−	0.516316i	$-0.172697\pi$
$823$	−3.02943e8	−	5.24713e8i	−0.0189436	−	0.0328112i	−0.875342	+	0.483505i	$0.839364\pi$
$824$	8.04826e9	−	4.64667e9i	0.501137	−	0.289332i
$825$	1.43696e9	+	8.29630e8i	0.0890956	+	0.0514393i
$826$	1.53982e10	+	5.78183e9i	0.950692	+	0.356973i
$827$		−	2.46013e9i		−	0.151247i	−0.997136	−	0.0756237i	$-0.975905\pi$
$827$		−	2.46013e9i		−	0.151247i	0.997136	−	0.0756237i	$-0.0240948\pi$
$828$	2.08954e9			0.127922
$829$	−7.20646e9			−0.439320			−0.219660	−	0.975576i	$-0.570495\pi$
$829$	−7.20646e9			−0.439320			−0.219660	+	0.975576i	$0.570495\pi$
$830$			1.09114e10i			0.662378i
$831$	−4.01951e9	−	6.96200e9i	−0.242980	−	0.420853i
$832$	5.42401e9	+	6.68234e9i	0.326504	+	0.402251i
$833$	−4.43787e9	+	2.24931e10i	−0.266022	+	1.34832i
$834$	1.63905e10	−	9.46307e9i	0.978388	−	0.564873i
$835$	2.20921e9	−	3.82646e9i	0.131321	−	0.227455i
$836$	−8.13024e8	−	1.40820e9i	−0.0481262	−	0.0833570i
$837$	−1.13598e10	−	6.55860e9i	−0.669627	−	0.386609i
$838$			1.01709e10i			0.597041i
$839$	6.16115e8	+	3.55714e8i	0.0360160	+	0.0207938i	0.517900	−	0.855441i	$-0.326714\pi$
$839$	6.16115e8	+	3.55714e8i	0.0360160	+	0.0207938i	−0.481884	+	0.876235i	$0.660047\pi$
$840$	9.79237e8	+	5.90264e9i	0.0570046	+	0.343613i
$841$	7.21707e9	−	1.25003e10i	0.418384	−	0.724662i
$842$	−1.22981e10	+	2.13010e10i	−0.709982	+	1.22972i
$843$		−	1.50364e10i		−	0.864463i
$844$	−1.84449e9	+	3.19475e9i	−0.105603	+	0.182910i
$845$	−3.82370e9	−	1.16765e10i	−0.218015	−	0.665757i
$846$	5.28629e9			0.300161
$847$	−1.48687e10	−	5.58302e9i	−0.840779	−	0.315702i
$848$	1.19760e8	+	2.07431e8i	0.00674416	+	0.0116812i
$849$	5.59875e9			0.313989
$850$	1.24435e10	+	7.18423e9i	0.694984	+	0.401249i
$851$	−4.17090e9	+	2.40807e9i	−0.231994	+	0.133942i
$852$		−	2.63124e9i		−	0.145754i
$853$			1.62300e9i			0.0895360i	0.998997	+	0.0447680i	$0.0142549\pi$
$853$			1.62300e9i			0.0895360i	−0.998997	+	0.0447680i	$0.985745\pi$
$854$	3.27535e9	+	3.98472e9i	0.179951	+	0.218925i
$855$	−3.67507e9	−	6.36541e9i	−0.201087	−	0.348293i
$856$	−9.85272e9	−	5.68847e9i	−0.536905	−	0.309982i
$857$	−9.34896e9	+	1.61929e10i	−0.507376	+	0.878802i	0.492587	+	0.870263i	$0.336051\pi$
$857$	−9.34896e9	+	1.61929e10i	−0.507376	+	0.878802i	−0.999964	+	0.00853851i	$0.997282\pi$
$858$	4.23243e9	−	6.75351e8i	0.228762	−	0.0365026i
$859$	−8.17037e9	−	1.41515e10i	−0.439810	−	0.761774i	0.557864	−	0.829932i	$-0.311621\pi$
$859$	−8.17037e9	−	1.41515e10i	−0.439810	−	0.761774i	−0.997675	+	0.0681584i	$0.978288\pi$
$860$	−2.53390e9	+	1.46295e9i	−0.135845	+	0.0784304i
$861$	−2.16255e10	+	3.58763e9i	−1.15467	+	0.191557i
$862$	−1.10338e10	+	1.91110e10i	−0.586743	+	1.01627i
$863$	−8.78876e9	+	5.07419e9i	−0.465468	+	0.268738i	−0.714341	−	0.699798i	$-0.753273\pi$
$863$	−8.78876e9	+	5.07419e9i	−0.465468	+	0.268738i	0.248873	+	0.968536i	$0.419940\pi$
$864$	1.01114e10	−	5.83779e9i	0.533349	−	0.307929i
$865$	−6.84587e9	+	3.95246e9i	−0.359644	+	0.207640i
$866$	−1.26943e10	+	7.32907e9i	−0.664197	+	0.383474i
$867$	−5.39649e9	+	9.34700e9i	−0.281219	+	0.487086i
$868$	1.62893e9	−	4.33816e9i	0.0845439	−	0.225158i
$869$	2.60225e8	−	1.50241e8i	0.0134518	−	0.00776638i
$870$	1.99469e9	+	3.45490e9i	0.102697	+	0.177876i
$871$	2.47296e9	−	2.00728e9i	0.126810	−	0.102931i
$872$	−1.33696e10	+	2.31569e10i	−0.682829	+	1.18269i
$873$	1.14892e10	+	6.63328e9i	0.584439	+	0.337426i
$874$	−7.34430e9	−	1.27207e10i	−0.372100	−	0.644497i
$875$	−7.36505e9	+	1.96146e10i	−0.371662	+	0.989811i
$876$			3.73206e9i			0.187579i
$877$		−	9.90994e9i		−	0.496104i	−0.968747	−	0.248052i	$-0.920210\pi$
$877$		−	9.90994e9i		−	0.496104i	0.968747	−	0.248052i	$-0.0797904\pi$
$878$	9.81484e9	−	5.66660e9i	0.489387	−	0.282548i
$879$	1.05989e10	+	6.11930e9i	0.526382	+	0.303907i
$880$	5.49610e9			0.271873
$881$	−1.64804e9	−	2.85448e9i	−0.0811990	−	0.140641i	0.822566	−	0.568669i	$-0.192542\pi$
$881$	−1.64804e9	−	2.85448e9i	−0.0811990	−	0.140641i	−0.903765	+	0.428029i	$0.859208\pi$
$882$	4.52312e9	+	1.32570e10i	0.221972	+	0.650589i
$883$	7.19423e9			0.351659			0.175830	−	0.984421i	$-0.443739\pi$
$883$	7.19423e9			0.351659			0.175830	+	0.984421i	$0.443739\pi$
$884$	8.77653e9	−	1.40043e9i	0.427307	−	0.0681834i
$885$	−4.04816e9	+	7.01162e9i	−0.196316	+	0.340030i
$886$			2.79716e10i			1.35114i
$887$	1.12739e10	−	1.95269e10i	0.542425	−	0.939508i	−0.456339	−	0.889806i	$-0.650840\pi$
$887$	1.12739e10	−	1.95269e10i	0.542425	−	0.939508i	0.998764	−	0.0497020i	$-0.0158271\pi$
$888$	−2.05041e9	+	3.55141e9i	−0.0982640	+	0.170198i
$889$	−2.51352e9	−	1.51510e10i	−0.119985	−	0.723245i
$890$	1.04058e9	+	6.00778e8i	0.0494777	+	0.0285660i
$891$			2.77236e8i			0.0131304i
$892$	−5.21697e9	−	3.01202e9i	−0.246117	−	0.142096i
$893$	−4.44925e9	−	7.70633e9i	−0.209077	−	0.362132i
$894$	4.39339e9	−	7.60957e9i	0.205645	−	0.356187i
$895$	−1.25604e10	+	7.25174e9i	−0.585628	+	0.338113i
$896$	−1.64408e10	−	2.00015e10i	−0.763563	−	0.928934i
$897$	9.15532e9	−	1.46087e9i	0.423545	−	0.0675833i
$898$	−2.32501e10	−	4.02703e10i	−1.07141	−	1.85574i
$899$			6.72318e9i			0.308614i
$900$	2.10215e9			0.0961201
$901$	−3.34768e8			−0.0152478
$902$			1.49211e10i			0.676983i
$903$	−7.69287e9	+	6.32337e9i	−0.347681	+	0.285786i
$904$	−1.30559e10	−	7.53780e9i	−0.587782	−	0.339356i
$905$	−5.43841e9	+	3.13987e9i	−0.243895	+	0.140813i
$906$	1.12978e10	+	1.95683e10i	0.504712	+	0.874188i
$907$	6.46972e9			0.287912			0.143956	−	0.989584i	$-0.454018\pi$
$907$	6.46972e9			0.287912			0.143956	+	0.989584i	$0.454018\pi$
$908$	−1.14139e9	−	6.58984e8i	−0.0505982	−	0.0292129i
$909$	6.32395e8			0.0279264
$910$	5.78985e9	+	1.73186e10i	0.254696	+	0.761848i
$911$	−3.68079e10			−1.61297			−0.806487	−	0.591252i	$-0.798634\pi$
$911$	−3.68079e10			−1.61297			−0.806487	+	0.591252i	$0.798634\pi$
$912$	−1.46169e10	−	8.43910e9i	−0.638079	−	0.368395i
$913$	6.05305e9			0.263225
$914$	−2.19974e10	−	3.81006e10i	−0.952926	−	1.65052i
$915$	−2.19885e9	+	1.26951e9i	−0.0948904	+	0.0547850i
$916$	−7.37924e9	−	4.26041e9i	−0.317232	−	0.183154i
$917$	3.00471e9	+	1.81118e10i	0.128680	+	0.775655i
$918$			3.73906e10i			1.59519i
$919$	−6.02386e9			−0.256018			−0.128009	−	0.991773i	$-0.540859\pi$
$919$	−6.02386e9			−0.256018			−0.128009	+	0.991773i	$0.540859\pi$
$920$	8.80974e9			0.372997
$921$		−	1.84472e10i		−	0.778073i
$922$	2.62133e9	+	4.54027e9i	0.110144	+	0.190776i
$923$	2.75348e9	+	1.72561e10i	0.115259	+	0.722333i
$924$	−1.50479e9	+	2.49642e8i	−0.0627516	+	0.0104104i
$925$	−4.19607e9	+	2.42260e9i	−0.174320	+	0.100644i
$926$	−2.02040e10	+	3.49943e10i	−0.836176	+	1.44830i
$927$	5.35469e9	+	9.27459e9i	0.220778	+	0.382398i
$928$	−5.18254e9	−	2.99214e9i	−0.212875	−	0.122904i
$929$			7.85055e8i			0.0321251i	0.999871	+	0.0160626i	$0.00511310\pi$
$929$			7.85055e8i			0.0321251i	−0.999871	+	0.0160626i	$0.994887\pi$
$930$	8.24931e9	+	4.76274e9i	0.336300	+	0.194163i
$931$	1.55191e10	−	1.77517e10i	0.630295	−	0.720968i
$932$	−7.77251e8	+	1.34624e9i	−0.0314489	+	0.0544711i
$933$	1.49442e10	−	2.58840e10i	0.602401	−	1.04339i
$934$		−	1.63273e9i		−	0.0655692i
$935$	−3.84084e9	+	6.65252e9i	−0.153669	+	0.266162i
$936$	−9.17404e9	+	7.44651e9i	−0.365675	+	0.296816i
$937$	−1.18628e10			−0.471084			−0.235542	−	0.971864i	$-0.575687\pi$
$937$	−1.18628e10			−0.471084			−0.235542	+	0.971864i	$0.575687\pi$
$938$	−3.65691e9	+	3.00590e9i	−0.144678	+	0.118923i
$939$	1.33454e10	+	2.31150e10i	0.526022	+	0.911096i
$940$	−2.45265e9			−0.0963135
$941$	−2.13078e10	−	1.23020e10i	−0.833631	−	0.481297i	0.0214630	−	0.999770i	$-0.493168\pi$
$941$	−2.13078e10	−	1.23020e10i	−0.833631	−	0.481297i	−0.855094	+	0.518472i	$0.826501\pi$
$942$	2.65405e10	−	1.53232e10i	1.03450	−	0.597269i
$943$			3.22763e10i			1.25341i
$944$		−	2.78277e10i		−	1.07665i
$945$	−1.81485e10	+	3.01080e9i	−0.699567	+	0.116057i
$946$	3.38912e9	+	5.87013e9i	0.130157	+	0.225439i
$947$	−1.27202e10	−	7.34404e9i	−0.486710	−	0.281002i	0.236498	−	0.971632i	$-0.424000\pi$
$947$	−1.27202e10	−	7.34404e9i	−0.486710	−	0.281002i	−0.723209	+	0.690630i	$0.757334\pi$
$948$	−1.27168e8	+	2.20261e8i	−0.00484783	+	0.00839669i
$949$	−3.90545e9	−	2.44755e10i	−0.148333	−	0.929608i
$950$	−7.38861e9	−	1.27975e10i	−0.279596	−	0.484274i
$951$	1.77412e10	−	1.02429e10i	0.668884	−	0.386180i
$952$	2.83555e10	−	4.70412e9i	1.06514	−	0.176705i
$953$	−1.96765e10	+	3.40806e10i	−0.736414	+	1.27551i	0.217686	+	0.976019i	$0.430149\pi$
$953$	−1.96765e10	+	3.40806e10i	−0.736414	+	1.27551i	−0.954100	+	0.299488i	$0.903184\pi$
$954$	−1.77130e8	+	1.02266e8i	−0.00660498	+	0.00381339i
$955$	7.36118e9	−	4.24998e9i	0.273486	−	0.157897i
$956$	−1.17801e10	+	6.80122e9i	−0.436059	+	0.251759i
$957$	1.91659e9	−	1.10655e9i	0.0706868	−	0.0408111i
$958$	−1.34236e10	+	2.32504e10i	−0.493277	+	0.854381i
$959$	−5.08377e10	+	8.43387e9i	−1.86132	+	0.308789i
$960$	5.45286e9	−	3.14821e9i	0.198919	−	0.114846i
$961$	−5.72979e9	−	9.92429e9i	−0.208261	−	0.360718i
$962$	−4.47168e9	+	1.16894e10i	−0.161942	+	0.423329i
$963$	6.55523e9	−	1.13540e10i	0.236535	−	0.409691i
$964$	7.83593e9	+	4.52407e9i	0.281722	+	0.162652i
$965$	1.75279e10	+	3.03592e10i	0.627891	+	1.08754i
$966$	−1.35933e10	+	2.25509e9i	−0.485181	+	0.0804905i
$967$		−	4.25353e9i		−	0.151272i	−0.997136	−	0.0756358i	$-0.975901\pi$
$967$		−	4.25353e9i		−	0.151272i	0.997136	−	0.0756358i	$-0.0240986\pi$
$968$			1.99116e10i			0.705574i
$969$	2.04295e10	−	1.17950e10i	0.721314	−	0.416451i
$970$	−2.22606e10	−	1.28522e10i	−0.783133	−	0.452142i
$971$	1.25698e10			0.440617			0.220309	−	0.975430i	$-0.429294\pi$
$971$	1.25698e10			0.440617			0.220309	+	0.975430i	$0.429294\pi$
$972$	4.44521e9	+	7.69933e9i	0.155260	+	0.268919i
$973$	3.45570e10	−	2.84051e10i	1.20265	−	0.988555i
$974$	4.11880e10			1.42828
$975$	9.21057e9	−	1.46969e9i	0.318251	−	0.0507820i
$976$	4.36341e9	−	7.55764e9i	0.150228	−	0.260203i
$977$			6.31979e9i			0.216806i	0.994107	+	0.108403i	$0.0345737\pi$
$977$			6.31979e9i			0.216806i	−0.994107	+	0.108403i	$0.965426\pi$
$978$	1.16328e10	−	2.01485e10i	0.397646	−	0.688743i
$979$	3.33279e8	−	5.77257e8i	0.0113519	−	0.0196621i
$980$	−2.09856e9	−	6.15079e9i	−0.0712247	−	0.208756i
$981$	−2.66853e10	−	1.54068e10i	−0.902467	−	0.521040i
$982$		−	2.61566e9i		−	0.0881436i
$983$	−2.37969e10	−	1.37391e10i	−0.799066	−	0.461341i	0.0440784	−	0.999028i	$-0.485965\pi$
$983$	−2.37969e10	−	1.37391e10i	−0.799066	−	0.461341i	−0.843145	+	0.537687i	$0.819298\pi$
$984$	1.37412e10	+	2.38004e10i	0.459771	+	0.796347i
$985$	3.20418e9	−	5.54980e9i	0.106829	−	0.185034i
$986$	1.65969e10	−	9.58221e9i	0.551388	−	0.318344i
$987$	−8.23493e9	+	1.36616e9i	−0.272615	+	0.0452263i
$988$	−8.53706e9	−	3.26579e9i	−0.281617	−	0.107731i
$989$	7.33112e9	+	1.26979e10i	0.240981	+	0.417392i
$990$			4.69323e9i			0.153727i
$991$	3.04511e10			0.993907			0.496953	−	0.867777i	$-0.334452\pi$
$991$	3.04511e10			0.993907			0.496953	+	0.867777i	$0.334452\pi$
$992$	−1.42888e10			−0.464733
$993$		−	3.55301e10i		−	1.15153i
$994$	−4.25044e9	−	2.56208e10i	−0.137272	−	0.827448i
$995$	−1.20641e10	−	6.96519e9i	−0.388251	−	0.224157i
$996$	−4.43705e9	+	2.56173e9i	−0.142294	+	0.0821534i
$997$	1.61430e10	+	2.79605e10i	0.515882	+	0.893534i	0.999830	+	0.0184375i	$0.00586918\pi$
$997$	1.61430e10	+	2.79605e10i	0.515882	+	0.893534i	−0.483948	+	0.875097i	$0.660797\pi$
$998$	−5.45493e10			−1.73713
$999$	−1.09193e10	−	6.30426e9i	−0.346510	−	0.200058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.u.a.88.14	yes	126
7.2	even	3		91.8.k.a.23.50	yes	126
13.4	even	6		91.8.k.a.4.14	✓	126
91.30	even	6	inner	91.8.u.a.30.14	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.k.a.4.14	✓	126	13.4	even	6
91.8.k.a.23.50	yes	126	7.2	even	3
91.8.u.a.30.14	yes	126	91.30	even	6	inner
91.8.u.a.88.14	yes	126	1.1	even	1	trivial

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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.2351 - 6.48656i) q^{2} +29.5960 q^{3} +(20.1509 + 34.9025i) q^{4} +(-169.575 + 97.9040i) q^{5} +(-332.513 - 191.977i) q^{6} +(-849.576 - 319.005i) q^{7} +1137.72i q^{8} -1311.07 q^{9} +O(q^{10})\)	\(q+(-11.2351 - 6.48656i) q^{2} +29.5960 q^{3} +(20.1509 + 34.9025i) q^{4} +(-169.575 + 97.9040i) q^{5} +(-332.513 - 191.977i) q^{6} +(-849.576 - 319.005i) q^{7} +1137.72i q^{8} -1311.07 q^{9} +2540.24 q^{10} -1409.19i q^{11} +(596.388 + 1032.97i) q^{12} +(-4992.18 - 6150.33i) q^{13} +(7475.78 + 9094.86i) q^{14} +(-5018.74 + 2897.57i) q^{15} +(9959.20 - 17249.8i) q^{16} +(13919.5 + 24109.4i) q^{17} +(14730.0 + 8504.36i) q^{18} -28631.1i q^{19} +(-6834.18 - 3945.72i) q^{20} +(-25144.1 - 9441.29i) q^{21} +(-9140.80 + 15832.3i) q^{22} +(-19772.8 + 34247.5i) q^{23} +33672.0i q^{24} +(-19892.1 + 34454.1i) q^{25} +(16192.9 + 101481. i) q^{26} -103529. q^{27} +(-5985.69 - 36080.5i) q^{28} +(26531.8 + 45954.4i) q^{29} +75181.1 q^{30} +(109726. + 63350.3i) q^{31} +(-97666.8 + 56387.9i) q^{32} -41706.5i q^{33} -361160. i q^{34} +(175298. - 29081.7i) q^{35} +(-26419.4 - 45759.7i) q^{36} +(105471. + 60893.6i) q^{37} +(-185717. + 321672. i) q^{38} +(-147749. - 182026. i) q^{39} +(-111387. - 192928. i) q^{40} +(706833. - 408090. i) q^{41} +(221254. + 269172. i) q^{42} +(185384. - 321095. i) q^{43} +(49184.2 - 28396.5i) q^{44} +(222325. - 128359. i) q^{45} +(444296. - 256515. i) q^{46} +(269159. - 155399. i) q^{47} +(294753. - 510527. i) q^{48} +(620014. + 542038. i) q^{49} +(446978. - 258063. i) q^{50} +(411964. + 713542. i) q^{51} +(114065. - 298175. i) q^{52} +(-6012.55 + 10414.0i) q^{53} +(1.16316e6 + 671548. i) q^{54} +(137966. + 238963. i) q^{55} +(362938. - 966578. i) q^{56} -847367. i q^{57} -688400. i q^{58} +(1.20991e6 - 698543. i) q^{59} +(-202265. - 116778. i) q^{60} +438128. q^{61} +(-821851. - 1.42349e6i) q^{62} +(1.11386e6 + 418239. i) q^{63} -1.08650e6 q^{64} +(1.44869e6 + 554186. i) q^{65} +(-270532. + 468575. i) q^{66} +402085. i q^{67} +(-560984. + 971653. i) q^{68} +(-585196. + 1.01359e6i) q^{69} +(-2.15813e6 - 810350. i) q^{70} +(-1.91043e6 - 1.10299e6i) q^{71} -1.49163e6i q^{72} +(2.70969e6 + 1.56444e6i) q^{73} +(-789980. - 1.36828e6i) q^{74} +(-588727. + 1.01971e6i) q^{75} +(999295. - 576943. i) q^{76} +(-449539. + 1.19721e6i) q^{77} +(479247. + 3.00345e6i) q^{78} +(106615. + 184662. i) q^{79} +3.90018e6i q^{80} -196734. q^{81} -1.05884e7 q^{82} +4.29541e6i q^{83} +(-177153. - 1.06784e6i) q^{84} +(-4.72081e6 - 2.72556e6i) q^{85} +(-4.16560e6 + 2.40501e6i) q^{86} +(785235. + 1.36007e6i) q^{87} +1.60326e6 q^{88} +(409637. + 236504. i) q^{89} -3.33045e6 q^{90} +(2.27925e6 + 6.81771e6i) q^{91} -1.59376e6 q^{92} +(3.24745e6 + 1.87492e6i) q^{93} -4.03203e6 q^{94} +(2.80310e6 + 4.85511e6i) q^{95} +(-2.89055e6 + 1.66886e6i) q^{96} +(-8.76318e6 - 5.05942e6i) q^{97} +(-3.44993e6 - 1.01116e7i) q^{98} +1.84755e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Introduction

L-functions

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