LMFDB - Embedded newform 91.8.u.a.30.8

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			30.8
Character	$\chi$	$=$	91.30
Dual form			91.8.u.a.88.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.6734 + 9.04906i) q^{2} -13.5023 q^{3} +(99.7708 - 172.808i) q^{4} +(-99.0313 - 57.1757i) q^{5} +(211.628 - 122.183i) q^{6} +(-118.523 - 899.720i) q^{7} +1294.77i q^{8} -2004.69 q^{9} +O(q^{10})$	\(q+(-15.6734 + 9.04906i) q^{2} -13.5023 q^{3} +(99.7708 - 172.808i) q^{4} +(-99.0313 - 57.1757i) q^{5} +(211.628 - 122.183i) q^{6} +(-118.523 - 899.720i) q^{7} +1294.77i q^{8} -2004.69 q^{9} +2069.55 q^{10} -8666.81i q^{11} +(-1347.14 + 2333.31i) q^{12} +(-4996.73 - 6146.65i) q^{13} +(9999.27 + 13029.2i) q^{14} +(1337.15 + 772.005i) q^{15} +(1054.23 + 1825.99i) q^{16} +(5012.30 - 8681.55i) q^{17} +(31420.3 - 18140.5i) q^{18} +5821.11i q^{19} +(-19760.9 + 11408.9i) q^{20} +(1600.34 + 12148.3i) q^{21} +(78426.4 + 135839. i) q^{22} +(26044.0 + 45109.5i) q^{23} -17482.4i q^{24} +(-32524.4 - 56333.9i) q^{25} +(133937. + 51123.3i) q^{26} +56597.5 q^{27} +(-167304. - 69284.0i) q^{28} +(22181.6 - 38419.7i) q^{29} -27943.7 q^{30} +(112628. - 65025.8i) q^{31} +(-176574. - 101945. i) q^{32} +117022. i q^{33} +181426. i q^{34} +(-39704.6 + 95877.0i) q^{35} +(-200009. + 346426. i) q^{36} +(-40017.8 + 23104.3i) q^{37} +(-52675.5 - 91236.7i) q^{38} +(67467.4 + 82994.0i) q^{39} +(74029.3 - 128223. i) q^{40} +(-301107. - 173844. i) q^{41} +(-135013. - 175924. i) q^{42} +(-20362.9 - 35269.7i) q^{43} +(-1.49770e6 - 864695. i) q^{44} +(198527. + 114619. i) q^{45} +(-816396. - 471347. i) q^{46} +(-689415. - 398034. i) q^{47} +(-14234.6 - 24655.1i) q^{48} +(-795448. + 213275. i) q^{49} +(1.01954e6 + 588630. i) q^{50} +(-67677.6 + 117221. i) q^{51} +(-1.56072e6 + 250219. i) q^{52} +(-638576. - 1.10605e6i) q^{53} +(-887077. + 512154. i) q^{54} +(-495531. + 858285. i) q^{55} +(1.16493e6 - 153460. i) q^{56} -78598.4i q^{57} +802890. i q^{58} +(-1.32826e6 - 766873. i) q^{59} +(266817. - 154047. i) q^{60} +1.58207e6 q^{61} +(-1.17684e6 + 2.03835e6i) q^{62} +(237602. + 1.80366e6i) q^{63} +3.42013e6 q^{64} +(143393. + 894402. i) q^{65} +(-1.05894e6 - 1.83414e6i) q^{66} +3.75023e6i q^{67} +(-1.00016e6 - 1.73233e6i) q^{68} +(-351654. - 609083. i) q^{69} +(-245289. - 1.86201e6i) q^{70} +(-594956. + 343498. i) q^{71} -2.59561e6i q^{72} +(5.09930e6 - 2.94409e6i) q^{73} +(418144. - 724246. i) q^{74} +(439155. + 760638. i) q^{75} +(1.00593e6 + 580776. i) q^{76} +(-7.79770e6 + 1.02722e6i) q^{77} +(-1.80846e6 - 690284. i) q^{78} +(-1.90701e6 + 3.30304e6i) q^{79} -241107. i q^{80} +3.62005e6 q^{81} +6.29250e6 q^{82} -3.45779e6i q^{83} +(2.25899e6 + 935495. i) q^{84} +(-992748. + 573163. i) q^{85} +(638314. + 368531. i) q^{86} +(-299503. + 518755. i) q^{87} +1.12215e7 q^{88} +(6.56768e6 - 3.79185e6i) q^{89} -4.14879e6 q^{90} +(-4.93803e6 + 5.22417e6i) q^{91} +1.03937e7 q^{92} +(-1.52074e6 + 878000. i) q^{93} +1.44073e7 q^{94} +(332826. - 576471. i) q^{95} +(2.38415e6 + 1.37649e6i) q^{96} +(-5.86233e6 + 3.38462e6i) q^{97} +(1.05374e7 - 1.05408e7i) q^{98} +1.73742e7i 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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−15.6734	+	9.04906i	−1.38535	+	0.799831i	−0.992787	−	0.119895i	$-0.961744\pi$
$2$	−15.6734	+	9.04906i	−1.38535	+	0.799831i	−0.392561	+	0.919726i	$0.628411\pi$
$3$	−13.5023			−0.288725			−0.144362	−	0.989525i	$-0.546113\pi$
$3$	−13.5023			−0.288725			−0.144362	+	0.989525i	$0.546113\pi$
$4$	99.7708	−	172.808i	0.779459	−	1.35006i
$5$	−99.0313	−	57.1757i	−0.354305	−	0.204558i	0.312275	−	0.949992i	$-0.398909\pi$
$5$	−99.0313	−	57.1757i	−0.354305	−	0.204558i	−0.666580	+	0.745434i	$0.732242\pi$
$6$	211.628	−	122.183i	0.399984	−	0.230931i
$7$	−118.523	−	899.720i	−0.130605	−	0.991434i
$7$	−118.523	−	899.720i	−0.130605	−	0.991434i
$8$			1294.77i			0.894081i
$9$	−2004.69			−0.916638
$10$	2069.55			0.654448
$11$		−	8666.81i		−	1.96329i	−0.190712	−	0.981646i	$-0.561080\pi$
$11$		−	8666.81i		−	1.96329i	0.190712	−	0.981646i	$-0.438920\pi$
$12$	−1347.14	+	2333.31i	−0.225049	+	0.389797i
$13$	−4996.73	−	6146.65i	−0.630788	−	0.775955i
$13$	−4996.73	−	6146.65i	−0.630788	−	0.775955i
$14$	9999.27	+	13029.2i	0.973913	+	1.26902i
$15$	1337.15	+	772.005i	0.102297	+	0.0590610i
$16$	1054.23	+	1825.99i	0.0643454	+	0.111449i
$17$	5012.30	−	8681.55i	0.247437	−	0.428574i	−0.715377	−	0.698739i	$-0.753745\pi$
$17$	5012.30	−	8681.55i	0.247437	−	0.428574i	0.962814	+	0.270165i	$0.0870782\pi$
$18$	31420.3	−	18140.5i	1.26986	−	0.733156i
$19$			5821.11i			0.194701i	0.995250	+	0.0973504i	$0.0310368\pi$
$19$			5821.11i			0.194701i	−0.995250	+	0.0973504i	$0.968963\pi$
$20$	−19760.9	+	11408.9i	−0.552333	+	0.318889i
$21$	1600.34	+	12148.3i	0.0377089	+	0.286252i
$22$	78426.4	+	135839.i	1.57030	+	2.71984i
$23$	26044.0	+	45109.5i	0.446334	+	0.773073i	0.998144	−	0.0608968i	$-0.0193961\pi$
$23$	26044.0	+	45109.5i	0.446334	+	0.773073i	−0.551810	+	0.833970i	$0.686063\pi$
$24$		−	17482.4i		−	0.258143i
$25$	−32524.4	−	56333.9i	−0.416312	−	0.721073i
$26$	133937.	+	51123.3i	1.49449	+	0.570443i
$27$	56597.5			0.553381
$28$	−167304.	−	69284.0i	−1.44030	−	0.596458i
$29$	22181.6	−	38419.7i	0.168888	−	0.292523i	−0.769141	−	0.639079i	$-0.779316\pi$
$29$	22181.6	−	38419.7i	0.168888	−	0.292523i	0.938029	+	0.346556i	$0.112649\pi$
$30$	−27943.7			−0.188955
$31$	112628.	−	65025.8i	0.679017	−	0.392031i	−0.120468	−	0.992717i	$-0.538439\pi$
$31$	112628.	−	65025.8i	0.679017	−	0.392031i	0.799485	+	0.600687i	$0.205106\pi$
$32$	−176574.	−	101945.i	−0.952579	−	0.549972i
$33$			117022.i			0.566851i
$34$			181426.i			0.791633i
$35$	−39704.6	+	95877.0i	−0.156532	+	0.377987i
$36$	−200009.	+	346426.i	−0.714482	+	1.23752i
$37$	−40017.8	+	23104.3i	−0.129881	+	0.0749870i	−0.563533	−	0.826094i	$-0.690558\pi$
$37$	−40017.8	+	23104.3i	−0.129881	+	0.0749870i	0.433652	+	0.901081i	$0.357225\pi$
$38$	−52675.5	−	91236.7i	−0.155728	−	0.269728i
$39$	67467.4	+	82994.0i	0.182124	+	0.224037i
$40$	74029.3	−	128223.i	0.182892	−	0.316778i
$41$	−301107.	−	173844.i	−0.682303	−	0.393928i	0.118419	−	0.992964i	$-0.462217\pi$
$41$	−301107.	−	173844.i	−0.682303	−	0.393928i	−0.800722	+	0.599036i	$0.795551\pi$
$42$	−135013.	−	175924.i	−0.281193	−	0.366397i
$43$	−20362.9	−	35269.7i	−0.0390572	−	0.0676490i	0.845836	−	0.533443i	$-0.179102\pi$
$43$	−20362.9	−	35269.7i	−0.0390572	−	0.0676490i	−0.884893	+	0.465794i	$0.845769\pi$
$44$	−1.49770e6	−	864695.i	−2.65057	−	1.53031i
$45$	198527.	+	114619.i	0.324769	+	0.187506i
$46$	−816396.	−	471347.i	−1.23666	−	0.713983i
$47$	−689415.	−	398034.i	−0.968586	−	0.559213i	−0.0697810	−	0.997562i	$-0.522230\pi$
$47$	−689415.	−	398034.i	−0.968586	−	0.559213i	−0.898805	+	0.438349i	$0.855563\pi$
$48$	−14234.6	−	24655.1i	−0.0185781	−	0.0321782i
$49$	−795448.	+	213275.i	−0.965885	+	0.258973i
$50$	1.01954e6	+	588630.i	1.15347	+	0.665958i
$51$	−67677.6	+	117221.i	−0.0714413	+	0.123740i
$52$	−1.56072e6	+	250219.i	−1.53926	+	0.246779i
$53$	−638576.	−	1.10605e6i	−0.589179	−	1.02049i	−0.994340	−	0.106243i	$-0.966118\pi$
$53$	−638576.	−	1.10605e6i	−0.589179	−	1.02049i	0.405161	−	0.914245i	$-0.367215\pi$
$54$	−887077.	+	512154.i	−0.766625	+	0.442611i
$55$	−495531.	+	858285.i	−0.401607	+	0.695604i
$56$	1.16493e6	−	153460.i	0.886423	−	0.116771i
$57$		−	78598.4i		−	0.0562150i
$58$			802890.i			0.540329i
$59$	−1.32826e6	−	766873.i	−0.841980	−	0.486118i	0.0159566	−	0.999873i	$-0.494921\pi$
$59$	−1.32826e6	−	766873.i	−0.841980	−	0.486118i	−0.857937	+	0.513755i	$0.828254\pi$
$60$	266817.	−	154047.i	0.159472	−	0.0920713i
$61$	1.58207e6			0.892423			0.446211	−	0.894928i	$-0.352773\pi$
$61$	1.58207e6			0.892423			0.446211	+	0.894928i	$0.352773\pi$
$62$	−1.17684e6	+	2.03835e6i	−0.627116	+	1.08620i
$63$	237602.	+	1.80366e6i	0.119717	+	0.908787i
$64$	3.42013e6			1.63085
$65$	143393.	+	894402.i	0.0647637	+	0.403958i
$66$	−1.05894e6	−	1.83414e6i	−0.453385	−	0.785286i
$67$			3.75023e6i			1.52334i	0.647966	+	0.761670i	$0.275620\pi$
$67$			3.75023e6i			1.52334i	−0.647966	+	0.761670i	$0.724380\pi$
$68$	−1.00016e6	−	1.73233e6i	−0.385735	−	0.668112i
$69$	−351654.	−	609083.i	−0.128868	−	0.223205i
$70$	−245289.	−	1.86201e6i	−0.0854741	−	0.648842i
$71$	−594956.	+	343498.i	−0.197279	+	0.113899i	−0.595386	−	0.803440i	$-0.703001\pi$
$71$	−594956.	+	343498.i	−0.197279	+	0.113899i	0.398107	+	0.917339i	$0.369667\pi$
$72$		−	2.59561e6i		−	0.819549i
$73$	5.09930e6	−	2.94409e6i	1.53420	−	0.885769i	0.535035	−	0.844830i	$-0.320299\pi$
$73$	5.09930e6	−	2.94409e6i	1.53420	−	0.885769i	0.999162	−	0.0409387i	$-0.0130348\pi$
$74$	418144.	−	724246.i	0.119954	−	0.207766i
$75$	439155.	+	760638.i	0.120200	+	0.208192i
$76$	1.00593e6	+	580776.i	0.262858	+	0.151761i
$77$	−7.79770e6	+	1.02722e6i	−1.94648	+	0.256416i
$78$	−1.80846e6	−	690284.i	−0.431498	−	0.164701i
$79$	−1.90701e6	+	3.30304e6i	−0.435170	+	0.753736i	−0.997309	−	0.0733063i	$-0.976645\pi$
$79$	−1.90701e6	+	3.30304e6i	−0.435170	+	0.753736i	0.562140	+	0.827042i	$0.309978\pi$
$80$		−	241107.i		−	0.0526495i
$81$	3.62005e6			0.756863
$82$	6.29250e6			1.26030
$83$		−	3.45779e6i		−	0.663781i	−0.943318	−	0.331890i	$-0.892314\pi$
$83$		−	3.45779e6i		−	0.663781i	0.943318	−	0.331890i	$-0.107686\pi$
$84$	2.25899e6	+	935495.i	0.415850	+	0.172212i
$85$	−992748.	+	573163.i	−0.175337	+	0.101231i
$86$	638314.	+	368531.i	0.108216	+	0.0624783i
$87$	−299503.	+	518755.i	−0.0487623	+	0.0844588i
$88$	1.12215e7			1.75534
$89$	6.56768e6	−	3.79185e6i	0.987522	−	0.570146i	0.0829894	−	0.996550i	$-0.473553\pi$
$89$	6.56768e6	−	3.79185e6i	0.987522	−	0.570146i	0.904533	+	0.426404i	$0.140220\pi$
$90$	−4.14879e6			−0.599892
$91$	−4.93803e6	+	5.22417e6i	−0.686924	+	0.726729i
$92$	1.03937e7			1.39160
$93$	−1.52074e6	+	878000.i	−0.196049	+	0.113189i
$94$	1.44073e7			1.78910
$95$	332826.	−	576471.i	0.0398276	−	0.0689835i
$96$	2.38415e6	+	1.37649e6i	0.275033	+	0.158790i
$97$	−5.86233e6	+	3.38462e6i	−0.652182	+	0.376538i	−0.789292	−	0.614018i	$-0.789552\pi$
$97$	−5.86233e6	+	3.38462e6i	−0.652182	+	0.376538i	0.137109	+	0.990556i	$0.456219\pi$
$98$	1.05374e7	−	1.05408e7i	1.13095	−	1.13131i
$99$			1.73742e7i			1.79963i
$100$	−1.29799e7			−1.29799
$101$	−1.23240e7			−1.19022			−0.595110	−	0.803644i	$-0.702892\pi$
$101$	−1.23240e7			−1.19022			−0.595110	+	0.803644i	$0.702892\pi$
$102$		−	2.44967e6i		−	0.228564i
$103$	−7.45596e6	+	1.29141e7i	−0.672316	+	1.16448i	0.304930	+	0.952375i	$0.401367\pi$
$103$	−7.45596e6	+	1.29141e7i	−0.672316	+	1.16448i	−0.977246	+	0.212110i	$0.931966\pi$
$104$	7.95848e6	−	6.46960e6i	0.693767	−	0.563976i
$105$	536105.	−	1.29456e6i	0.0451947	−	0.109134i
$106$	2.00174e7	+	1.15570e7i	1.63244	+	0.942487i
$107$	−2.94103e6	−	5.09402e6i	−0.232090	−	0.401992i	0.726333	−	0.687343i	$-0.241223\pi$
$107$	−2.94103e6	−	5.09402e6i	−0.232090	−	0.401992i	−0.958423	+	0.285351i	$0.907890\pi$
$108$	5.64678e6	−	9.78051e6i	0.431338	−	0.747099i
$109$	1.69213e7	−	9.76949e6i	1.25153	−	0.722569i	0.280114	−	0.959967i	$-0.409628\pi$
$109$	1.69213e7	−	9.76949e6i	1.25153	−	0.722569i	0.971412	+	0.237398i	$0.0762945\pi$
$110$		−	1.79364e7i		−	1.28487i
$111$	540333.	−	311961.i	0.0375000	−	0.0216506i
$112$	1.51793e6	−	1.16494e6i	0.102091	−	0.0783501i
$113$	1.18477e6	+	2.05208e6i	0.0772428	+	0.133789i	0.902059	−	0.431612i	$-0.142055\pi$
$113$	1.18477e6	+	2.05208e6i	0.0772428	+	0.133789i	−0.824817	+	0.565400i	$0.808722\pi$
$114$	711242.	+	1.23191e6i	0.0449625	+	0.0778773i
$115$		−	5.95633e6i		−	0.365205i
$116$	−4.42615e6	−	7.66632e6i	−0.263283	−	0.456020i
$117$	1.00169e7	+	1.23221e7i	0.578205	+	0.711270i
$118$	2.77579e7			1.55525
$119$	−8.40503e6	−	3.48070e6i	−0.457220	−	0.189344i
$120$	−999568.	+	1.73130e6i	−0.0528053	+	0.0914615i
$121$	−5.56264e7			−2.85452
$122$	−2.47964e7	+	1.43162e7i	−1.23632	+	0.713787i
$123$	4.06564e6	+	2.34730e6i	0.196998	+	0.113737i
$124$		−	2.59507e7i		−	1.22229i
$125$			1.63721e7i			0.749756i
$126$	−2.00454e7	−	2.61194e7i	−0.892726	−	1.16323i
$127$	−1.98379e6	+	3.43602e6i	−0.0859374	+	0.148848i	−0.905790	−	0.423726i	$-0.860722\pi$
$127$	−1.98379e6	+	3.43602e6i	−0.0859374	+	0.148848i	0.819853	+	0.572574i	$0.194055\pi$
$128$	−3.10038e7	+	1.79000e7i	−1.30671	+	0.754430i
$129$	274947.	+	476222.i	0.0112768	+	0.0195320i
$130$	−1.03409e7	−	1.27208e7i	−0.412818	−	0.507822i
$131$	4.00110e6	−	6.93012e6i	0.155500	−	0.269334i	−0.777741	−	0.628585i	$-0.783634\pi$
$131$	4.00110e6	−	6.93012e6i	0.155500	−	0.269334i	0.933241	+	0.359251i	$0.116968\pi$
$132$	2.02224e7	+	1.16754e7i	0.765285	+	0.441837i
$133$	5.23736e6	−	689935.i	0.193033	−	0.0254289i
$134$	−3.39361e7	−	5.87790e7i	−1.21841	−	2.11036i
$135$	−5.60492e6	−	3.23600e6i	−0.196066	−	0.113199i
$136$	1.12406e7	+	6.48976e6i	0.383180	+	0.221229i
$137$	7.52433e6	+	4.34417e6i	0.250003	+	0.144340i	0.619766	−	0.784787i	$-0.287228\pi$
$137$	7.52433e6	+	4.34417e6i	0.250003	+	0.144340i	−0.369762	+	0.929126i	$0.620561\pi$
$138$	1.10232e7	+	6.36427e6i	0.357053	+	0.206145i
$139$	−7.76121e6	−	1.34428e7i	−0.245119	−	0.424559i	0.717046	−	0.697026i	$-0.245494\pi$
$139$	−7.76121e6	−	1.34428e7i	−0.245119	−	0.424559i	−0.962165	+	0.272467i	$0.912161\pi$
$140$	1.26070e7	+	1.64270e7i	0.388295	+	0.505953i
$141$	9.30870e6	+	5.37438e6i	0.279655	+	0.161459i
$142$	6.21667e6	−	1.07676e7i	0.182200	−	0.315580i
$143$	−5.32718e7	+	4.33057e7i	−1.52343	+	1.23842i
$144$	−2.11341e6	−	3.66053e6i	−0.0589814	−	0.102159i
$145$	−4.39334e6	+	2.53650e6i	−0.119676	+	0.0690950i
$146$	−5.32824e7	+	9.22878e7i	−1.41693	+	2.45420i
$147$	1.07404e7	−	2.87971e6i	0.278875	−	0.0747718i
$148$			9.22053e6i			0.233797i
$149$		−	3.65751e6i		−	0.0905802i	−0.998974	−	0.0452901i	$-0.985579\pi$
$149$		−	3.65751e6i		−	0.0905802i	0.998974	−	0.0452901i	$-0.0144212\pi$
$150$	−1.37661e7	−	7.94787e6i	−0.333037	−	0.192279i
$151$	6.31027e7	−	3.64324e7i	1.49152	−	0.861129i	0.491566	−	0.870840i	$-0.336425\pi$
$151$	6.31027e7	−	3.64324e7i	1.49152	−	0.861129i	0.999953	+	0.00971152i	$0.00309132\pi$
$152$	−7.53698e6			−0.174078
$153$	−1.00481e7	+	1.74038e7i	−0.226811	+	0.392847i
$154$	1.12921e8	−	8.66618e7i	2.49146	−	1.91208i
$155$	−1.48716e7			−0.320772
$156$	2.10733e7	−	3.37853e6i	0.444423	−	0.0712512i
$157$	4.71661e7	+	8.16941e7i	0.972705	+	1.68477i	0.687309	+	0.726365i	$0.258792\pi$
$157$	4.71661e7	+	8.16941e7i	0.972705	+	1.68477i	0.285396	+	0.958410i	$0.407875\pi$
$158$		−	6.90266e7i		−	1.39225i
$159$	8.62226e6	+	1.49342e7i	0.170111	+	0.294640i
$160$	1.16575e7	+	2.01914e7i	0.225002	+	0.389715i
$161$	3.74991e7	−	2.87788e7i	0.708158	−	0.543478i
$162$	−5.67386e7	+	3.27581e7i	−1.04852	+	0.605363i
$163$		−	2.55243e7i		−	0.461634i	−0.972997	−	0.230817i	$-0.925860\pi$
$163$		−	2.55243e7i		−	0.461634i	0.972997	−	0.230817i	$-0.0741399\pi$
$164$	−6.00833e7	+	3.46891e7i	−1.06365	+	0.614101i
$165$	6.69082e6	−	1.15888e7i	0.115954	−	0.200838i
$166$	3.12897e7	+	5.41953e7i	0.530913	+	0.919568i
$167$	7.81594e7	+	4.51253e7i	1.29859	+	0.749743i	0.980161	−	0.198202i	$-0.0635102\pi$
$167$	7.81594e7	+	4.51253e7i	1.29859	+	0.749743i	0.318433	+	0.947946i	$0.396844\pi$
$168$	−1.57292e7	+	2.07206e6i	−0.255932	+	0.0337148i
$169$	−1.28140e7	+	6.14262e7i	−0.204212	+	0.978927i
$170$	1.03732e7	−	1.79669e7i	0.161935	−	0.280479i
$171$		−	1.16695e7i		−	0.178470i
$172$	−8.12651e6			−0.121774
$173$	−1.08777e8			−1.59727			−0.798633	−	0.601818i	$-0.794443\pi$
$173$	−1.08777e8			−1.59727			−0.798633	+	0.601818i	$0.794443\pi$
$174$		−	1.08409e7i		−	0.156006i
$175$	−4.68298e7	+	3.59397e7i	−0.660525	+	0.506922i
$176$	1.58255e7	−	9.13685e6i	0.218808	−	0.126329i
$177$	1.79346e7	+	1.03546e7i	0.243101	+	0.140354i
$178$	−6.86253e7	+	1.18863e8i	−0.912041	+	1.57970i
$179$	5.37213e7			0.700101			0.350051	−	0.936731i	$-0.386164\pi$
$179$	5.37213e7			0.700101			0.350051	+	0.936731i	$0.386164\pi$
$180$	3.96143e7	−	2.28714e7i	0.506289	−	0.292306i
$181$	−9.94113e6			−0.124612			−0.0623061	−	0.998057i	$-0.519846\pi$
$181$	−9.94113e6			−0.124612			−0.0623061	+	0.998057i	$0.519846\pi$
$182$	3.01220e7	−	1.26565e8i	0.370369	−	1.55620i
$183$	−2.13616e7			−0.257665
$184$	−5.84063e7	+	3.37209e7i	−0.691190	+	0.399059i
$185$	5.28401e6			0.0613568
$186$	1.58901e7	−	2.75225e7i	0.181064	−	0.313612i
$187$	−7.52413e7	−	4.34406e7i	−0.841416	−	0.485792i
$188$	−1.37567e8	+	7.94243e7i	−1.50995	+	0.871768i
$189$	−6.70811e6	−	5.09219e7i	−0.0722743	−	0.548641i
$190$			1.20470e7i			0.127422i
$191$	8.23839e6			0.0855511			0.0427756	−	0.999085i	$-0.486380\pi$
$191$	8.23839e6			0.0855511			0.0427756	+	0.999085i	$0.486380\pi$
$192$	−4.61797e7			−0.470866
$193$			1.30073e8i			1.30238i	0.758915	+	0.651189i	$0.225730\pi$
$193$			1.30073e8i			1.30238i	−0.758915	+	0.651189i	$0.774270\pi$
$194$	6.12552e7	−	1.06097e8i	0.602333	−	1.04327i
$195$	−1.93614e6	−	1.20765e7i	−0.0186989	−	0.116633i
$196$	−4.25068e7	+	1.58738e8i	−0.403239	+	1.50586i
$197$	−9.12710e7	−	5.26953e7i	−0.850552	−	0.491066i	0.0102851	−	0.999947i	$-0.496726\pi$
$197$	−9.12710e7	−	5.26953e7i	−0.850552	−	0.491066i	−0.860837	+	0.508881i	$0.830059\pi$
$198$	−1.57220e8	−	2.72314e8i	−1.43940	−	2.49311i
$199$	−1.53950e7	+	2.66650e7i	−0.138483	+	0.239859i	−0.926922	−	0.375253i	$-0.877556\pi$
$199$	−1.53950e7	+	2.66650e7i	−0.138483	+	0.239859i	0.788440	+	0.615112i	$0.210889\pi$
$200$	7.29393e7	−	4.21115e7i	0.644698	−	0.372217i
$201$		−	5.06369e7i		−	0.439826i
$202$	1.93159e8	−	1.11521e8i	1.64887	−	0.951975i
$203$	−3.71960e7	−	1.54036e7i	−0.312075	−	0.129237i
$204$	1.35045e7	+	2.33905e7i	0.111371	+	0.192901i
$205$	1.98793e7	+	3.44320e7i	0.161162	+	0.279141i
$206$		−	2.69878e8i		−	2.15096i
$207$	−5.22100e7	−	9.04304e7i	−0.409127	−	0.708628i
$208$	5.95598e6	−	1.56040e7i	0.0458914	−	0.120230i
$209$	5.04504e7			0.382255
$210$	3.31197e6	+	2.51415e7i	0.0246785	+	0.187337i
$211$	1.16372e8	−	2.01562e8i	0.852822	−	1.47713i	−0.0258288	−	0.999666i	$-0.508222\pi$
$211$	1.16372e8	−	2.01562e8i	0.852822	−	1.47713i	0.878651	−	0.477465i	$-0.158444\pi$
$212$	−2.54845e8			−1.83696
$213$	8.03329e6	−	4.63802e6i	0.0569593	−	0.0328855i
$214$	9.21921e7	+	5.32271e7i	0.643051	+	0.371266i
$215$			4.65706e6i			0.0319579i
$216$			7.32807e7i			0.494768i
$217$	−7.18540e7	−	9.36266e7i	−0.477356	−	0.622000i
$218$	−1.76809e8	+	3.06243e8i	−1.15587	+	2.00202i
$219$	−6.88525e7	+	3.97520e7i	−0.442961	+	0.255743i
$220$	9.88791e7	+	1.71264e8i	0.626073	+	1.08439i
$221$	−7.84075e7	+	1.25705e7i	−0.488635	+	0.0783394i
$222$	−5.64591e6	+	9.77900e6i	−0.0346337	+	0.0599873i
$223$	2.10118e8	+	1.21312e8i	1.26881	+	0.732547i	0.974762	−	0.223245i	$-0.0716649\pi$
$223$	2.10118e8	+	1.21312e8i	1.26881	+	0.732547i	0.294046	+	0.955791i	$0.404998\pi$
$224$	−7.07937e7	+	1.70950e8i	−0.420849	+	1.01625i
$225$	6.52012e7	+	1.12932e8i	0.381607	+	0.660963i
$226$	−3.71387e7	−	2.14420e7i	−0.214016	−	0.123562i
$227$	2.11809e8	+	1.22288e8i	1.20186	+	0.693894i	0.960969	−	0.276658i	$-0.0892268\pi$
$227$	2.11809e8	+	1.22288e8i	1.20186	+	0.693894i	0.240892	+	0.970552i	$0.422560\pi$
$228$	−1.35824e7	−	7.84183e6i	−0.0758938	−	0.0438173i
$229$	1.75151e8	+	1.01123e8i	0.963803	+	0.556452i	0.897341	−	0.441337i	$-0.145496\pi$
$229$	1.75151e8	+	1.01123e8i	0.963803	+	0.556452i	0.0664616	+	0.997789i	$0.478829\pi$
$230$	5.38992e7	+	9.33561e7i	0.292102	+	0.505936i
$231$	1.05287e8	−	1.38698e7i	0.561996	−	0.0740336i
$232$	4.97446e7	+	2.87200e7i	0.261540	+	0.151000i
$233$	5.27787e7	−	9.14155e7i	0.273346	−	0.473450i	−0.696370	−	0.717683i	$-0.745203\pi$
$233$	5.27787e7	−	9.14155e7i	0.273346	−	0.473450i	0.969717	+	0.244233i	$0.0785361\pi$
$234$	−2.68502e8	−	1.02486e8i	−1.36991	−	0.522890i
$235$	4.55158e7	+	7.88356e7i	0.228783	+	0.396264i
$236$	−2.65044e8	+	1.53023e8i	−1.31258	+	0.757818i
$237$	2.57491e7	−	4.45987e7i	0.125644	−	0.217622i
$238$	1.63233e8	−	2.15032e7i	0.784852	−	0.103391i
$239$			9.42115e7i			0.446387i	0.974774	+	0.223193i	$0.0716481\pi$
$239$			9.42115e7i			0.446387i	−0.974774	+	0.223193i	$0.928352\pi$
$240$			3.25550e6i			0.0152012i
$241$	−1.68304e8	−	9.71706e7i	−0.774525	−	0.447172i	0.0599611	−	0.998201i	$-0.480902\pi$
$241$	−1.68304e8	−	9.71706e7i	−0.774525	−	0.447172i	−0.834487	+	0.551028i	$0.814236\pi$
$242$	8.71857e8	−	5.03367e8i	3.95450	−	2.28313i
$243$	−1.72658e8			−0.771906
$244$	1.57844e8	−	2.73394e8i	0.695607	−	1.20483i
$245$	9.09683e7	+	2.43594e7i	0.395193	+	0.105824i
$246$	−8.49633e7			−0.363880
$247$	3.57803e7	−	2.90865e7i	0.151079	−	0.122815i
$248$	8.41934e7	+	1.45827e8i	0.350507	+	0.607096i
$249$			4.66881e7i			0.191650i
$250$	−1.48152e8	−	2.56607e8i	−0.599678	−	1.03867i
$251$	−1.77879e8	−	3.08095e8i	−0.710014	−	1.22978i	−0.964852	−	0.262796i	$-0.915355\pi$
$251$	−1.77879e8	−	3.08095e8i	−0.710014	−	1.22978i	0.254838	−	0.966984i	$-0.417978\pi$
$252$	3.35392e8	+	1.38893e8i	1.32023	+	0.546736i
$253$	3.90955e8	−	2.25718e8i	1.51777	−	0.876284i
$254$		−	7.18056e7i		−	0.274942i
$255$	1.34044e7	−	7.73903e6i	0.0506240	−	0.0292278i
$256$	1.05068e8	−	1.81984e8i	0.391410	−	0.677942i
$257$	1.51173e8	+	2.61840e8i	0.555532	+	0.962210i	0.997862	+	0.0653575i	$0.0208188\pi$
$257$	1.51173e8	+	2.61840e8i	0.555532	+	0.962210i	−0.442330	+	0.896853i	$0.645848\pi$
$258$	−8.61872e6	−	4.97602e6i	−0.0312445	−	0.0180390i
$259$	2.55304e7	+	3.32664e7i	0.0913079	+	0.118975i
$260$	1.68866e8	+	6.44557e7i	0.595849	+	0.227434i
$261$	−4.44672e7	+	7.70194e7i	−0.154810	+	0.268138i
$262$			1.44825e8i			0.497495i
$263$	−1.87889e8			−0.636877			−0.318438	−	0.947944i	$-0.603158\pi$
$263$	−1.87889e8			−0.636877			−0.318438	+	0.947944i	$0.603158\pi$
$264$	−1.51516e8			−0.506811
$265$			1.46044e8i			0.482085i
$266$	−7.58441e7	+	5.82068e7i	−0.247079	+	0.189622i
$267$	−8.86789e7	+	5.11988e7i	−0.285122	+	0.164615i
$268$	6.48071e8	+	3.74164e8i	2.05660	+	1.18738i
$269$	2.41423e7	−	4.18157e7i	0.0756216	−	0.130980i	−0.825735	−	0.564058i	$-0.809239\pi$
$269$	2.41423e7	−	4.18157e7i	0.0756216	−	0.130980i	0.901356	+	0.433078i	$0.142573\pi$
$270$	1.17131e8			0.362159
$271$	−5.33741e7	+	3.08155e7i	−0.162906	+	0.0940540i	−0.579237	−	0.815159i	$-0.696649\pi$
$271$	−5.33741e7	+	3.08155e7i	−0.162906	+	0.0940540i	0.416330	+	0.909213i	$0.363316\pi$
$272$	2.11365e7			0.0636858
$273$	6.66749e7	−	7.05384e7i	0.198332	−	0.209825i
$274$	−1.57243e8			−0.461789
$275$	−4.88235e8	+	2.81883e8i	−1.41568	+	0.817342i
$276$	−1.40339e8			−0.401788
$277$	3.60051e7	−	6.23627e7i	0.101785	−	0.176297i	−0.810635	−	0.585552i	$-0.800878\pi$
$277$	3.60051e7	−	6.23627e7i	0.101785	−	0.176297i	0.912420	+	0.409254i	$0.134211\pi$
$278$	2.43290e8	+	1.40463e8i	0.679151	+	0.392108i
$279$	−2.25784e8	+	1.30356e8i	−0.622413	+	0.359350i
$280$	−1.24139e8	−	5.14083e7i	−0.337951	−	0.139952i
$281$			2.40001e7i			0.0645270i	0.999479	+	0.0322635i	$0.0102716\pi$
$281$			2.40001e7i			0.0645270i	−0.999479	+	0.0322635i	$0.989728\pi$
$282$	−1.94532e8			−0.516559
$283$	5.14870e7			0.135035			0.0675173	−	0.997718i	$-0.478492\pi$
$283$	5.14870e7			0.135035			0.0675173	+	0.997718i	$0.478492\pi$
$284$			1.37084e8i			0.355119i
$285$	−4.49392e6	+	7.78370e6i	−0.0114992	+	0.0199172i
$286$	4.43076e8	−	1.16081e9i	1.11995	−	2.93413i
$287$	−1.20723e8	+	2.91516e8i	−0.301441	+	0.727907i
$288$	3.53975e8	+	2.04367e8i	0.873170	+	0.504125i
$289$	1.54923e8	+	2.68335e8i	0.377549	+	0.653935i
$290$	4.59058e7	−	7.95112e7i	0.110529	−	0.191441i
$291$	7.91550e7	−	4.57002e7i	0.188301	−	0.108716i
$292$		−	1.17493e9i		−	2.76168i
$293$	−6.21044e8	+	3.58560e8i	−1.44240	+	0.832770i	−0.998010	−	0.0630624i	$-0.979913\pi$
$293$	−6.21044e8	+	3.58560e8i	−1.44240	+	0.832770i	−0.444391	+	0.895833i	$0.646580\pi$
$294$	−1.42280e8	+	1.42325e8i	−0.326534	+	0.326638i
$295$	8.76930e7	+	1.51889e8i	0.198879	+	0.344468i
$296$	−2.99147e7	−	5.18137e7i	−0.0670445	−	0.116124i
$297$		−	4.90520e8i		−	1.08645i
$298$	3.30970e7	+	5.73257e7i	0.0724489	+	0.125485i
$299$	1.47137e8	−	3.85483e8i	0.318327	−	0.833980i
$300$	1.75259e8			0.374763
$301$	−2.93193e7	+	2.25012e7i	−0.0619685	+	0.0475579i
$302$	−6.59357e8	+	1.14204e9i	−1.37752	+	2.38593i
$303$	1.66403e8			0.343646
$304$	−1.06293e7	+	6.13681e6i	−0.0216993	+	0.0125281i
$305$	−1.56674e8	−	9.04559e7i	−0.316190	−	0.182552i
$306$		−	3.63703e8i		−	0.725641i
$307$			2.84935e8i			0.562032i	0.959703	+	0.281016i	$0.0906714\pi$
$307$			2.84935e8i			0.562032i	−0.959703	+	0.281016i	$0.909329\pi$
$308$	−6.00471e8	+	1.44999e9i	−1.17102	+	2.82773i
$309$	1.00673e8	−	1.74370e8i	0.194114	−	0.336216i
$310$	2.33089e8	−	1.34574e8i	0.444381	−	0.256563i
$311$	−4.11311e8	−	7.12412e8i	−0.775370	−	1.34298i	−0.934586	−	0.355737i	$-0.884230\pi$
$311$	−4.11311e8	−	7.12412e8i	−0.775370	−	1.34298i	0.159216	−	0.987244i	$-0.449103\pi$
$312$	−1.07458e8	+	8.73546e7i	−0.200308	+	0.162834i
$313$	−3.62468e8	+	6.27813e8i	−0.668136	+	1.15725i	0.310289	+	0.950642i	$0.399574\pi$
$313$	−3.62468e8	+	6.27813e8i	−0.668136	+	1.15725i	−0.978425	+	0.206603i	$0.933759\pi$
$314$	−1.47851e9	−	8.53617e8i	−2.69507	−	1.55600i
$315$	7.95954e7	−	1.92203e8i	0.143483	−	0.346477i
$316$	3.80528e8	+	6.59094e8i	0.678394	+	1.17501i
$317$	−9.72778e7	−	5.61633e7i	−0.171517	−	0.0990252i	0.411784	−	0.911281i	$-0.364906\pi$
$317$	−9.72778e7	−	5.61633e7i	−0.171517	−	0.0990252i	−0.583301	+	0.812256i	$0.698239\pi$
$318$	−2.70281e8	−	1.56047e8i	−0.471325	−	0.272119i
$319$	−3.32976e8	−	1.92244e8i	−0.574309	−	0.331577i
$320$	−3.38700e8	−	1.95549e8i	−0.577817	−	0.333603i
$321$	3.97108e7	+	6.87811e7i	0.0670102	+	0.116065i
$322$	−3.27318e8	+	7.90393e8i	−0.546354	+	1.31931i
$323$	5.05362e7	+	2.91771e7i	0.0834438	+	0.0481763i
$324$	3.61176e8	−	6.25575e8i	0.589944	−	1.02181i
$325$	−1.83749e8	+	4.81401e8i	−0.296916	+	0.777884i
$326$	2.30971e8	+	4.00054e8i	0.369229	+	0.639524i
$327$	−2.28476e8	+	1.31911e8i	−0.361347	+	0.208624i
$328$	2.25088e8	−	3.89863e8i	0.352203	−	0.610034i
$329$	−2.76407e8	+	6.67456e8i	−0.427921	+	1.03333i
$330$			2.42182e8i			0.370974i
$331$		−	3.27005e8i		−	0.495628i	−0.968808	−	0.247814i	$-0.920288\pi$
$331$		−	3.27005e8i		−	0.495628i	0.968808	−	0.247814i	$-0.0797122\pi$
$332$	−5.97533e8	−	3.44986e8i	−0.896146	−	0.517390i
$333$	8.02231e7	−	4.63168e7i	0.119054	−	0.0687360i
$334$	−1.63337e9			−2.39867
$335$	2.14422e8	−	3.71390e8i	0.311611	−	0.539727i
$336$	−2.04955e7	+	1.57294e7i	−0.0294762	+	0.0226216i
$337$	3.07390e8			0.437508			0.218754	−	0.975780i	$-0.429801\pi$
$337$	3.07390e8			0.437508			0.218754	+	0.975780i	$0.429801\pi$
$338$	−3.55010e8	−	1.07871e9i	−0.500071	−	1.51949i
$339$	−1.59971e7	−	2.77078e7i	−0.0223019	−	0.0386281i
$340$			2.28740e8i			0.315621i
$341$	−5.63566e8	−	9.76126e8i	−0.769670	−	1.33311i
$342$	1.05598e8	+	1.82901e8i	0.142746	+	0.247243i
$343$	2.86167e8	+	6.90402e8i	0.382904	+	0.923788i
$344$	4.56660e7	−	2.63653e7i	0.0604837	−	0.0349203i
$345$			8.04243e7i			0.105444i
$346$	1.70491e9	−	9.84333e8i	2.21277	−	1.27754i
$347$	1.37493e8	−	2.38146e8i	0.176656	−	0.305978i	−0.764077	−	0.645125i	$-0.776805\pi$
$347$	1.37493e8	−	2.38146e8i	0.176656	−	0.305978i	0.940733	+	0.339148i	$0.110139\pi$
$348$	5.97633e7	+	1.03513e8i	0.0760164	+	0.131664i
$349$	−7.66218e8	−	4.42376e8i	−0.964858	−	0.557061i	−0.0671930	−	0.997740i	$-0.521404\pi$
$349$	−7.66218e8	−	4.42376e8i	−0.964858	−	0.557061i	−0.897665	+	0.440679i	$0.854738\pi$
$350$	4.08763e8	−	9.87063e8i	0.509605	−	1.23057i
$351$	−2.82802e8	−	3.47885e8i	−0.349066	−	0.429399i
$352$	−8.83536e8	+	1.53033e9i	−1.07975	+	1.87019i
$353$			4.40424e8i			0.532917i	0.963846	+	0.266459i	$0.0858535\pi$
$353$			4.40424e8i			0.532917i	−0.963846	+	0.266459i	$0.914146\pi$
$354$	−3.74796e8			−0.449039
$355$	7.85590e7			0.0931959
$356$		−	1.51326e9i		−	1.77762i
$357$	1.13487e8	+	4.69975e7i	0.132011	+	0.0546683i
$358$	−8.41997e8	+	4.86127e8i	−0.969884	+	0.559963i
$359$	9.72525e8	+	5.61487e8i	1.10935	+	0.640486i	0.938662	−	0.344839i	$-0.112066\pi$
$359$	9.72525e8	+	5.61487e8i	1.10935	+	0.640486i	0.170692	+	0.985324i	$0.445400\pi$
$360$	−1.48406e8	+	2.57046e8i	−0.167645	+	0.290370i
$361$	8.59986e8			0.962092
$362$	1.55812e8	−	8.99578e7i	0.172631	−	0.0996688i
$363$	7.51086e8			0.824169
$364$	4.10108e8	+	1.37455e9i	0.445701	+	1.49385i
$365$	−6.73321e8			−0.724765
$366$	3.34809e8	−	1.93302e8i	0.356955	−	0.206088i
$367$	−1.31015e9			−1.38353			−0.691767	−	0.722121i	$-0.743167\pi$
$367$	−1.31015e9			−1.38353			−0.691767	+	0.722121i	$0.743167\pi$
$368$	−5.49129e7	+	9.51120e7i	−0.0574390	+	0.0994873i
$369$	6.03625e8	+	3.48503e8i	0.625425	+	0.361089i
$370$	−8.28186e7	+	4.78153e7i	−0.0850006	+	0.0490751i
$371$	−9.19446e8	+	7.05632e8i	−0.934797	+	0.717413i
$372$			3.50395e8i			0.352905i
$373$	1.71864e9			1.71476			0.857379	−	0.514685i	$-0.172091\pi$
$373$	1.71864e9			1.71476			0.857379	+	0.514685i	$0.172091\pi$
$374$	1.57239e9			1.55421
$375$		−	2.21062e8i		−	0.216473i
$376$	5.15362e8	−	8.92632e8i	0.499982	−	0.865995i
$377$	−3.46987e8	+	5.56300e7i	−0.333518	+	0.0534706i
$378$	5.65934e8	+	7.37418e8i	0.538945	+	0.702251i
$379$	−7.34905e8	−	4.24298e8i	−0.693416	−	0.400344i	0.111474	−	0.993767i	$-0.464443\pi$
$379$	−7.34905e8	−	4.24298e8i	−0.693416	−	0.400344i	−0.804891	+	0.593423i	$0.797776\pi$
$380$	−6.64126e7	−	1.15030e8i	−0.0620881	−	0.107540i
$381$	2.67857e7	−	4.63943e7i	0.0248122	−	0.0429761i
$382$	−1.29124e8	+	7.45497e7i	−0.118518	+	0.0684265i
$383$		−	1.19745e9i		−	1.08909i	−0.838732	−	0.544544i	$-0.816703\pi$
$383$		−	1.19745e9i		−	1.08909i	0.838732	−	0.544544i	$-0.183297\pi$
$384$	4.18623e8	−	2.41692e8i	0.377280	−	0.217823i
$385$	8.30948e8	+	3.44113e8i	0.742098	+	0.307318i
$386$	−1.17704e9	−	2.03869e9i	−1.04168	−	1.80425i
$387$	4.08213e7	+	7.07046e7i	0.0358013	+	0.0620097i
$388$			1.35074e9i			1.17398i
$389$	9.33418e8	+	1.61673e9i	0.803993	+	1.39256i	0.916969	+	0.398959i	$0.130629\pi$
$389$	9.33418e8	+	1.61673e9i	0.803993	+	1.39256i	−0.112975	+	0.993598i	$0.536038\pi$
$390$	1.39627e8	+	1.71760e8i	0.119191	+	0.146621i
$391$	5.22160e8			0.441759
$392$	−2.76142e8	−	1.02992e9i	−0.231543	−	0.863580i
$393$	−5.40242e7	+	9.35727e7i	−0.0448967	+	0.0777634i
$394$	1.90737e9			1.57108
$395$	3.77708e8	−	2.18070e8i	0.308366	−	0.178035i
$396$	3.00241e9	+	1.73344e9i	2.42961	+	1.40274i
$397$		−	5.66348e8i		−	0.454273i	−0.973863	−	0.227136i	$-0.927064\pi$
$397$		−	5.66348e8i		−	0.454273i	0.973863	−	0.227136i	$-0.0729363\pi$
$398$		−	5.57242e8i		−	0.443050i
$399$	−7.07165e7	+	9.31573e6i	−0.0557335	+	0.00734195i
$400$	6.85766e7	−	1.18778e8i	0.0535755	−	0.0927955i
$401$	2.16175e9	−	1.24809e9i	1.67417	−	0.966584i	0.708912	−	0.705297i	$-0.249186\pi$
$401$	2.16175e9	−	1.24809e9i	1.67417	−	0.966584i	0.965261	−	0.261287i	$-0.0841469\pi$
$402$	4.58216e8	+	7.93653e8i	0.351786	+	0.609312i
$403$	−9.62462e8	−	3.67368e8i	−0.732514	−	0.279598i
$404$	−1.22958e9	+	2.12969e9i	−0.927728	+	1.60687i
$405$	−3.58498e8	−	2.06979e8i	−0.268160	−	0.154823i
$406$	7.22376e8	−	9.51610e7i	0.535701	−	0.0705696i
$407$	2.00240e8	+	3.46826e8i	0.147221	+	0.254995i
$408$	−1.51774e8	−	8.76268e7i	−0.110634	−	0.0638744i
$409$	−1.36552e9	−	7.88381e8i	−0.986882	−	0.569776i	−0.0825410	−	0.996588i	$-0.526304\pi$
$409$	−1.36552e9	−	7.88381e8i	−0.986882	−	0.569776i	−0.904341	+	0.426811i	$0.859637\pi$
$410$	−6.23154e8	−	3.59778e8i	−0.446531	−	0.257805i
$411$	−1.01596e8	−	5.86564e7i	−0.0721822	−	0.0416744i
$412$	1.48777e9	+	2.57690e9i	1.04809	+	1.81534i
$413$	−5.32541e8	+	1.28596e9i	−0.371987	+	0.898258i
$414$	1.63662e9	+	9.44903e8i	1.13357	+	0.654464i
$415$	−1.97701e8	+	3.42429e8i	−0.135782	+	0.235181i
$416$	2.55671e8	+	1.59473e9i	0.174123	+	1.08607i
$417$	1.04794e8	+	1.81509e8i	0.0707720	+	0.122581i
$418$	−7.90731e8	+	4.56529e8i	−0.529556	+	0.305739i
$419$	1.01067e9	−	1.75054e9i	0.671215	−	1.16258i	−0.306345	−	0.951920i	$-0.599106\pi$
$419$	1.01067e9	−	1.75054e9i	0.671215	−	1.16258i	0.977560	−	0.210657i	$-0.0675604\pi$
$420$	−1.70223e8	−	2.21803e8i	−0.112111	−	0.146081i
$421$		−	1.62154e9i		−	1.05911i	−0.848276	−	0.529554i	$-0.822359\pi$
$421$		−	1.62154e9i		−	1.05911i	0.848276	−	0.529554i	$-0.177641\pi$
$422$			4.21221e9i			2.72845i
$423$	1.38206e9	+	7.97933e8i	0.887843	+	0.512596i
$424$	1.43207e9	−	8.26808e8i	0.912399	−	0.526774i
$425$	−6.52087e8			−0.412045
$426$	−8.39394e7	+	1.45387e8i	−0.0526056	+	0.0911156i
$427$	−1.87511e8	−	1.42342e9i	−0.116555	−	0.884779i
$428$	−1.17372e9			−0.723619
$429$	7.19293e8	−	5.84727e8i	0.439851	−	0.357563i
$430$	−4.21420e7	−	7.29921e7i	−0.0255609	−	0.0442728i
$431$		−	1.28540e9i		−	0.773333i	−0.922220	−	0.386667i	$-0.873626\pi$
$431$		−	1.28540e9i		−	0.773333i	0.922220	−	0.386667i	$-0.126374\pi$
$432$	5.96670e7	+	1.03346e8i	0.0356075	+	0.0616740i
$433$	−9.21902e8	−	1.59678e9i	−0.545729	−	0.945231i	−0.998561	−	0.0536345i	$-0.982919\pi$
$433$	−9.21902e8	−	1.59678e9i	−0.545729	−	0.945231i	0.452831	−	0.891596i	$-0.350414\pi$
$434$	1.97343e9	+	8.17238e8i	1.15880	+	0.479882i
$435$	5.93204e7	−	3.42486e7i	0.0345534	−	0.0199494i
$436$		−	3.89884e9i		−	2.25285i
$437$	−2.62587e8	+	1.51605e8i	−0.150518	+	0.0869016i
$438$	7.19436e8	−	1.24610e9i	0.409103	−	0.708587i
$439$	−1.35857e9	−	2.35311e9i	−0.766400	−	1.32744i	−0.939503	−	0.342540i	$-0.888713\pi$
$439$	−1.35857e9	−	2.35311e9i	−0.766400	−	1.32744i	0.173103	−	0.984904i	$-0.444621\pi$
$440$	−1.11128e9	−	6.41598e8i	−0.621927	−	0.359070i
$441$	1.59462e9	−	4.27550e8i	0.885367	−	0.237384i
$442$	1.11516e9	−	9.06537e8i	0.614271	−	0.499353i
$443$	−1.22669e9	+	2.12468e9i	−0.670380	+	1.16113i	0.307417	+	0.951575i	$0.400535\pi$
$443$	−1.22669e9	+	2.12468e9i	−0.670380	+	1.16113i	−0.977797	+	0.209557i	$0.932798\pi$
$444$		−	1.24499e8i		−	0.0675031i
$445$	−8.67207e8			−0.466512
$446$	−4.39102e9			−2.34365
$447$			4.93849e7i			0.0261528i
$448$	−4.05365e8	−	3.07716e9i	−0.212997	−	1.61688i
$449$	2.12348e9	−	1.22599e9i	1.10710	−	0.639183i	0.169022	−	0.985612i	$-0.445939\pi$
$449$	2.12348e9	−	1.22599e9i	1.10710	−	0.639183i	0.938076	+	0.346429i	$0.112606\pi$
$450$	−2.04385e9	−	1.18002e9i	−1.05732	−	0.610443i
$451$	−1.50667e9	+	2.60964e9i	−0.773395	+	1.33956i
$452$	4.72820e8			0.240831
$453$	−8.52033e8	+	4.91922e8i	−0.430638	+	0.248629i
$454$	−4.42636e9			−2.21999
$455$	7.87715e8	−	2.35021e8i	0.392039	−	0.116968i
$456$	1.01767e8			0.0502608
$457$	9.77817e8	−	5.64543e8i	0.479237	−	0.276688i	−0.240861	−	0.970560i	$-0.577430\pi$
$457$	9.77817e8	−	5.64543e8i	0.479237	−	0.276688i	0.720099	+	0.693872i	$0.244097\pi$
$458$	−3.66029e9			−1.78027
$459$	2.83683e8	−	4.91354e8i	0.136927	−	0.237165i
$460$	−1.02930e9	−	5.94268e8i	−0.493050	−	0.284662i
$461$	−2.75687e7	+	1.59168e7i	−0.0131058	+	0.00756662i	−0.506539	−	0.862217i	$-0.669075\pi$
$461$	−2.75687e7	+	1.59168e7i	−0.0131058	+	0.00756662i	0.493433	+	0.869784i	$0.335742\pi$
$462$	−1.52470e9	+	1.17014e9i	−0.719345	+	0.552064i
$463$		−	1.66347e9i		−	0.778899i	−0.921048	−	0.389449i	$-0.872665\pi$
$463$		−	1.66347e9i		−	0.778899i	0.921048	−	0.389449i	$-0.127335\pi$
$464$	9.35385e7			0.0434688
$465$	2.00801e8			0.0926149
$466$			1.91039e9i			0.874524i
$467$	5.53421e8	−	9.58553e8i	0.251447	−	0.435519i	−0.712478	−	0.701695i	$-0.752427\pi$
$467$	5.53421e8	−	9.58553e8i	0.251447	−	0.435519i	0.963924	+	0.266176i	$0.0857603\pi$
$468$	3.12875e9	−	5.01610e8i	1.41095	−	0.226207i
$469$	3.37416e9	−	4.44489e8i	1.51029	−	0.198956i
$470$	−1.42678e9	−	8.23749e8i	−0.633889	−	0.365976i
$471$	−6.36852e8	−	1.10306e9i	−0.280844	−	0.486436i
$472$	9.92923e8	−	1.71979e9i	0.434629	−	0.752799i
$473$	−3.05675e8	+	1.76482e8i	−0.132815	+	0.0766807i
$474$			9.32020e8i			0.401977i
$475$	3.27925e8	−	1.89328e8i	0.140394	−	0.0810563i
$476$	−1.44007e9	+	1.10519e9i	−0.612011	+	0.469690i
$477$	1.28015e9	+	2.21728e9i	0.540064	+	0.935418i
$478$	−8.52525e8	−	1.47662e9i	−0.357034	−	0.618401i
$479$		−	8.53876e7i		−	0.0354993i	−0.999842	−	0.0177497i	$-0.994350\pi$
$479$		−	8.53876e7i		−	0.0354993i	0.999842	−	0.0177497i	$-0.00565019\pi$
$480$	−1.57404e8	−	2.72631e8i	−0.0649637	−	0.112520i
$481$	3.41972e8	+	1.30529e8i	0.140114	+	0.0534811i
$482$	3.51721e9			1.43065
$483$	−5.06325e8	+	3.88580e8i	−0.204463	+	0.156916i
$484$	−5.54989e9	+	9.61270e9i	−2.22498	+	3.85378i
$485$	7.74072e8			0.308095
$486$	2.70614e9	−	1.56239e9i	1.06936	−	0.617394i
$487$	−1.95227e7	−	1.12714e7i	−0.00765927	−	0.00442208i	0.496165	−	0.868228i	$-0.334741\pi$
$487$	−1.95227e7	−	1.12714e7i	−0.00765927	−	0.00442208i	−0.503825	+	0.863806i	$0.668074\pi$
$488$			2.04841e9i			0.797898i
$489$			3.44638e8i			0.133285i
$490$	−1.64621e9	+	4.41382e8i	−0.632121	+	0.169484i
$491$	−2.47875e8	+	4.29332e8i	−0.0945034	+	0.163685i	−0.909401	−	0.415920i	$-0.863460\pi$
$491$	−2.47875e8	+	4.29332e8i	−0.0945034	+	0.163685i	0.814898	+	0.579605i	$0.196793\pi$
$492$	8.11265e8	−	4.68384e8i	0.307103	−	0.177306i
$493$	−2.22361e8	−	3.85141e8i	−0.0835787	−	0.144762i
$494$	−2.97594e8	+	7.79662e8i	−0.111066	+	0.290979i
$495$	9.93385e8	−	1.72059e9i	0.368128	−	0.637617i
$496$	2.37473e8	+	1.37105e8i	0.0873832	+	0.0504507i
$497$	3.79568e8	+	4.94581e8i	0.138689	+	0.180713i
$498$	−4.22484e8	−	7.31763e8i	−0.153288	−	0.265502i
$499$	−2.19698e9	−	1.26842e9i	−0.791541	−	0.456996i	0.0489639	−	0.998801i	$-0.484408\pi$
$499$	−2.19698e9	−	1.26842e9i	−0.791541	−	0.456996i	−0.840505	+	0.541804i	$0.817741\pi$
$500$	2.82924e9	+	1.63346e9i	1.01222	+	0.584405i
$501$	−1.05533e9	−	6.09297e8i	−0.374936	−	0.216470i
$502$	5.57595e9	+	3.21927e9i	1.96723	+	1.13578i
$503$	2.75029e8	+	4.76363e8i	0.0963585	+	0.166898i	0.910175	−	0.414224i	$-0.135947\pi$
$503$	2.75029e8	+	4.76363e8i	0.0963585	+	0.166898i	−0.813816	+	0.581122i	$0.802614\pi$
$504$	−2.33532e9	+	3.07639e8i	−0.812529	+	0.107037i
$505$	1.22046e9	+	7.04634e8i	0.421701	+	0.243469i
$506$	−4.08507e9	+	7.07555e9i	−1.40176	+	2.42792i
$507$	1.73019e8	−	8.29396e8i	0.0589610	−	0.282640i
$508$	3.95848e8	+	6.85629e8i	0.133969	+	0.232042i
$509$	4.70736e9	−	2.71779e9i	1.58221	−	0.913491i	0.587677	−	0.809096i	$-0.300043\pi$
$509$	4.70736e9	−	2.71779e9i	1.58221	−	0.913491i	0.994536	−	0.104395i	$-0.0332907\pi$
$510$	−1.40062e8	+	2.42594e8i	−0.0467546	+	0.0809814i
$511$	−3.25324e9	−	4.23900e9i	−1.07856	−	1.40537i
$512$		−	7.79332e8i		−	0.256612i
$513$			3.29460e8i			0.107744i
$514$	−4.73881e9	−	2.73595e9i	−1.53921	−	0.888664i
$515$	1.47675e9	−	8.52600e8i	0.476410	−	0.275055i
$516$	1.09727e8			0.0351592
$517$	−3.44968e9	+	5.97503e9i	−1.09790	+	1.90162i
$518$	−7.01178e8	−	2.90372e8i	−0.221653	−	0.0917911i
$519$	1.46875e9			0.461170
$520$	−1.15804e9	+	1.85661e8i	−0.361171	+	0.0579040i
$521$	−2.09053e9	−	3.62090e9i	−0.647625	−	1.12172i	−0.983689	−	0.179880i	$-0.942429\pi$
$521$	−2.09053e9	−	3.62090e9i	−0.647625	−	1.12172i	0.336064	−	0.941839i	$-0.390904\pi$
$522$		−	1.60954e9i		−	0.495286i
$523$	2.51227e9	+	4.35137e9i	0.767909	+	1.33006i	0.938695	+	0.344750i	$0.112036\pi$
$523$	2.51227e9	+	4.35137e9i	0.767909	+	1.33006i	−0.170786	+	0.985308i	$0.554631\pi$
$524$	−7.98387e8	−	1.38285e9i	−0.242412	−	0.419870i
$525$	6.32311e8	−	4.85269e8i	0.190710	−	0.146361i
$526$	2.94486e9	−	1.70021e9i	0.882296	−	0.509394i
$527$		−	1.30371e9i		−	0.388012i
$528$	−2.13681e8	+	1.23369e8i	−0.0631752	+	0.0364742i
$529$	3.45836e8	−	5.99005e8i	0.101572	−	0.175928i
$530$	−1.32156e9	−	2.28901e9i	−0.385587	−	0.667856i
$531$	2.66275e9	+	1.53734e9i	0.771791	+	0.445594i
$532$	4.03309e8	−	9.73894e8i	0.116131	−	0.280428i
$533$	4.35990e8	+	2.71945e9i	0.124719	+	0.777921i
$534$	9.26601e8	−	1.60492e9i	0.263329	−	0.456099i
$535$			6.72623e8i			0.189904i
$536$	−4.85568e9			−1.36199
$537$	−7.25362e8			−0.202137
$538$			8.73860e8i			0.241938i
$539$	1.84841e9	+	6.89399e9i	0.508439	+	1.89631i
$540$	−1.11842e9	+	6.45717e8i	−0.305650	+	0.176467i
$541$	−3.04550e9	−	1.75832e9i	−0.826930	−	0.477428i	0.0258703	−	0.999665i	$-0.491764\pi$
$541$	−3.04550e9	−	1.75832e9i	−0.826930	−	0.477428i	−0.852800	+	0.522237i	$0.825098\pi$
$542$	5.57703e8	−	9.65970e8i	0.150455	−	0.260595i
$543$	1.34228e8			0.0359786
$544$	−1.77008e9	+	1.02196e9i	−0.471407	+	0.272167i
$545$	−2.23431e9			−0.591229
$546$	−4.06717e8	+	1.70892e9i	−0.106935	+	0.449312i
$547$	1.27665e9			0.333516			0.166758	−	0.985998i	$-0.446670\pi$
$547$	1.27665e9			0.333516			0.166758	+	0.985998i	$0.446670\pi$
$548$	1.50142e9	−	8.66844e8i	0.389735	−	0.225014i
$549$	−3.17155e9			−0.818028
$550$	5.10154e9	−	8.83613e9i	1.30747	−	2.26461i
$551$	2.23645e8	+	1.29121e8i	0.0569546	+	0.0328827i
$552$	7.88621e8	−	4.55311e8i	0.199564	−	0.115218i
$553$	3.19784e9	+	1.32429e9i	0.804115	+	0.333001i
$554$			1.30325e9i			0.325644i
$555$	−7.13464e7			−0.0177152
$556$	−3.09737e9			−0.764243
$557$			3.93991e9i			0.966035i	0.875611	+	0.483017i	$0.160459\pi$
$557$			3.93991e9i			0.966035i	−0.875611	+	0.483017i	$0.839541\pi$
$558$	2.35921e9	−	4.08626e9i	0.574839	−	0.995650i
$559$	−1.15042e8	+	3.01397e8i	−0.0278558	+	0.0729788i
$560$	−2.16928e8	+	2.85767e7i	−0.0521985	+	0.00687628i
$561$	1.01593e9	+	5.86549e8i	0.242938	+	0.140260i
$562$	−2.17178e8	−	3.76164e8i	−0.0516107	−	0.0893923i
$563$	2.34779e9	−	4.06649e9i	0.554472	−	0.960373i	−0.443473	−	0.896288i	$-0.646254\pi$
$563$	2.34779e9	−	4.06649e9i	0.554472	−	0.960373i	0.997944	−	0.0640855i	$-0.0204130\pi$
$564$	1.85747e9	−	1.07241e9i	0.435959	−	0.251701i
$565$		−	2.70960e8i		−	0.0632026i
$566$	−8.06977e8	+	4.65909e8i	−0.187070	+	0.108005i
$567$	−4.29060e8	−	3.25703e9i	−0.0988501	−	0.750380i
$568$	−4.44750e8	−	7.70330e8i	−0.101835	−	0.176383i
$569$	9.60964e8	+	1.66444e9i	0.218683	+	0.378769i	0.954405	−	0.298513i	$-0.0964907\pi$
$569$	9.60964e8	+	1.66444e9i	0.218683	+	0.378769i	−0.735723	+	0.677283i	$0.763157\pi$
$570$		−	1.62663e8i		−	0.0367898i
$571$	4.31844e8	+	7.47975e8i	0.0970734	+	0.168136i	0.910472	−	0.413571i	$-0.135719\pi$
$571$	4.31844e8	+	7.47975e8i	0.0970734	+	0.168136i	−0.813399	+	0.581707i	$0.802385\pi$
$572$	2.16860e9	+	1.35264e10i	0.484499	+	3.02202i
$573$	−1.11237e8			−0.0247007
$574$	−7.45806e8	−	5.66148e9i	−0.164602	−	1.24951i
$575$	1.69413e9	−	2.93432e9i	0.371628	−	0.643679i
$576$	−6.85630e9			−1.49490
$577$	−3.73036e9	+	2.15372e9i	−0.808417	+	0.466740i	−0.846406	−	0.532539i	$-0.821238\pi$
$577$	−3.73036e9	+	2.15372e9i	−0.808417	+	0.466740i	0.0379890	+	0.999278i	$0.487905\pi$
$578$	−4.85635e9	−	2.80382e9i	−1.04607	−	0.603952i
$579$		−	1.75629e9i		−	0.376029i
$580$			1.01227e9i			0.215427i
$581$	−3.11104e9	+	4.09827e8i	−0.658095	+	0.0866931i
$582$	−8.27087e8	+	1.43256e9i	−0.173908	+	0.301218i
$583$	−9.58589e9	+	5.53442e9i	−2.00352	+	1.15673i
$584$	3.81191e9	+	6.60242e9i	0.791949	+	1.37170i
$585$	−2.87458e8	−	1.79300e9i	−0.0593648	−	0.370283i
$586$	6.48926e9	−	1.12397e10i	1.33215	−	2.30735i
$587$	1.82393e9	+	1.05304e9i	0.372198	+	0.214888i	0.674418	−	0.738350i	$-0.264395\pi$
$587$	1.82393e9	+	1.05304e9i	0.372198	+	0.214888i	−0.302220	+	0.953238i	$0.597728\pi$
$588$	5.73940e8	−	2.14334e9i	0.116425	−	0.434780i
$589$	3.78522e8	+	6.55620e8i	0.0763287	+	0.132205i
$590$	−2.74890e9	−	1.58708e9i	−0.551032	−	0.318139i
$591$	1.23237e9	+	7.11509e8i	0.245575	+	0.141783i
$592$	−8.43762e7	−	4.87146e7i	−0.0167145	−	0.00965014i
$593$	−1.45363e9	−	8.39256e8i	−0.286262	−	0.165273i	0.349993	−	0.936752i	$-0.386184\pi$
$593$	−1.45363e9	−	8.39256e8i	−0.286262	−	0.165273i	−0.636255	+	0.771479i	$0.719517\pi$
$594$	4.43874e9	+	7.68813e9i	0.868975	+	1.50511i
$595$	6.33350e8	+	8.25262e8i	0.123263	+	0.160614i
$596$	−6.32047e8	−	3.64913e8i	−0.122289	−	0.0706036i
$597$	2.07869e8	−	3.60039e8i	0.0399833	−	0.0692532i
$598$	1.18211e9	+	7.37329e9i	0.226049	+	1.40996i
$599$	−5.92347e8	−	1.02598e9i	−0.112611	−	0.195049i	0.804211	−	0.594344i	$-0.202588\pi$
$599$	−5.92347e8	−	1.02598e9i	−0.112611	−	0.195049i	−0.916822	+	0.399295i	$0.869255\pi$
$600$	−9.84850e8	+	5.68603e8i	−0.186140	+	0.107468i
$601$	−1.58670e9	+	2.74824e9i	−0.298149	+	0.516410i	−0.975713	−	0.219055i	$-0.929703\pi$
$601$	−1.58670e9	+	2.74824e9i	−0.298149	+	0.516410i	0.677563	+	0.735464i	$0.263036\pi$
$602$	2.55919e8	−	6.17983e8i	0.0478097	−	0.115449i
$603$		−	7.51805e9i		−	1.39635i
$604$		−	1.45395e10i		−	2.68486i
$605$	5.50876e9	+	3.18048e9i	1.01137	+	0.583914i
$606$	−2.60810e9	+	1.50579e9i	−0.476069	+	0.274859i
$607$	−1.21952e9			−0.221325			−0.110662	−	0.993858i	$-0.535297\pi$
$607$	−1.21952e9			−0.221325			−0.110662	+	0.993858i	$0.535297\pi$
$608$	5.93432e8	−	1.02785e9i	0.107080	−	0.185468i
$609$	5.02232e8	+	2.07984e8i	0.0901039	+	0.0373139i
$610$	3.27416e9			0.584044
$611$	9.98243e8	+	6.22645e9i	0.177048	+	1.10432i
$612$	2.00501e9	+	3.47278e9i	0.353579	+	0.612417i
$613$		−	6.37486e9i		−	1.11779i	−0.829240	−	0.558893i	$-0.811226\pi$
$613$		−	6.37486e9i		−	1.11779i	0.829240	−	0.558893i	$-0.188774\pi$
$614$	−2.57839e9	−	4.46590e9i	−0.449531	−	0.778610i
$615$	−2.68417e8	−	4.64912e8i	−0.0465315	−	0.0805949i
$616$	−1.33001e9	−	1.00962e10i	−0.229256	−	1.74031i
$617$	−5.47325e9	+	3.15998e9i	−0.938095	+	0.541610i	−0.889363	−	0.457202i	$-0.848852\pi$
$617$	−5.47325e9	+	3.15998e9i	−0.938095	+	0.541610i	−0.0487326	+	0.998812i	$0.515518\pi$
$618$			3.64397e9i			0.621034i
$619$	−7.94071e9	+	4.58457e9i	−1.34568	+	0.776929i	−0.987634	−	0.156774i	$-0.949891\pi$
$619$	−7.94071e9	+	4.58457e9i	−1.34568	+	0.776929i	−0.358047	+	0.933704i	$0.616557\pi$
$620$	−1.48375e9	+	2.56993e9i	−0.250029	+	0.433063i
$621$	1.47402e9	+	2.55308e9i	0.246993	+	0.427804i
$622$	1.28933e10	+	7.44395e9i	2.14831	+	1.24033i
$623$	−4.19002e9	−	5.45965e9i	−0.694238	−	0.904600i
$624$	−8.04196e7	+	2.10690e8i	−0.0132500	+	0.0347134i
$625$	−1.60488e9	+	2.77973e9i	−0.262943	+	0.455431i
$626$		−	1.31200e10i		−	2.13758i
$627$	−6.81198e8			−0.110366
$628$	1.88232e10			3.03274
$629$			4.63222e8i			0.0742184i
$630$	4.91727e8	+	3.73275e9i	0.0783488	+	0.594753i
$631$	4.03057e9	−	2.32705e9i	0.638651	−	0.368725i	−0.145444	−	0.989366i	$-0.546461\pi$
$631$	4.03057e9	−	2.32705e9i	0.638651	−	0.368725i	0.784095	+	0.620641i	$0.213128\pi$
$632$	−4.27667e9	−	2.46914e9i	−0.673901	−	0.389077i
$633$	−1.57129e9	+	2.72155e9i	−0.246231	+	0.426484i
$634$	2.03290e9			0.316814
$635$	3.92914e8	−	2.26849e8i	0.0608961	−	0.0351584i
$636$	3.44100e9			0.530377
$637$	5.28556e9	+	3.82366e9i	0.810220	+	0.586126i
$638$	6.95850e9			1.06082
$639$	1.19270e9	−	6.88606e8i	0.180833	−	0.104404i
$640$	4.09379e9			0.617299
$641$	−4.21203e9	+	7.29546e9i	−0.631668	+	1.09408i	0.355543	+	0.934660i	$0.384296\pi$
$641$	−4.21203e9	+	7.29546e9i	−0.631668	+	1.09408i	−0.987211	+	0.159421i	$0.949037\pi$
$642$	−1.24481e9	−	7.18690e8i	−0.185665	−	0.107194i
$643$	−7.83981e9	+	4.52632e9i	−1.16297	+	0.671439i	−0.952013	−	0.306057i	$-0.900990\pi$
$643$	−7.83981e9	+	4.52632e9i	−1.16297	+	0.671439i	−0.210954	+	0.977496i	$0.567657\pi$
$644$	−1.23189e9	−	9.35143e9i	−0.181749	−	1.37968i
$645$		−	6.28812e7i		−	0.00922703i
$646$	−1.05610e9			−0.154132
$647$	−2.87821e9			−0.417789			−0.208895	−	0.977938i	$-0.566987\pi$
$647$	−2.87821e9			−0.417789			−0.208895	+	0.977938i	$0.566987\pi$
$648$			4.68713e9i			0.676697i
$649$	−6.64634e9	+	1.15118e10i	−0.954391	+	1.65305i
$650$	−1.47625e9	−	9.20795e9i	−0.210844	−	1.31512i
$651$	9.70196e8	+	1.26418e9i	0.137824	+	0.179587i
$652$	−4.41081e9	−	2.54658e9i	−0.623235	−	0.359825i
$653$	5.53624e8	+	9.58905e8i	0.0778070	+	0.134766i	0.902304	−	0.431101i	$-0.141875\pi$
$653$	5.53624e8	+	9.58905e8i	0.0778070	+	0.134766i	−0.824496	+	0.565867i	$0.808542\pi$
$654$	2.38734e9	−	4.13499e9i	0.333727	−	0.578032i
$655$	−7.92469e8	+	4.57532e8i	−0.110189	+	0.0636176i
$656$		−	7.33090e8i		−	0.101390i
$657$	−1.02225e10	+	5.90197e9i	−1.40630	+	0.811929i
$658$	−1.70760e9	−	1.29625e10i	−0.233666	−	1.77378i
$659$	−1.47024e9	−	2.54653e9i	−0.200119	−	0.346617i	0.748447	−	0.663194i	$-0.230800\pi$
$659$	−1.47024e9	−	2.54653e9i	−0.200119	−	0.346617i	−0.948567	+	0.316577i	$0.897466\pi$
$660$	−1.33510e9	−	2.31246e9i	−0.180763	−	0.313090i
$661$		−	8.81378e9i		−	1.18702i	−0.804827	−	0.593509i	$-0.797742\pi$
$661$		−	8.81378e9i		−	1.18702i	0.804827	−	0.593509i	$-0.202258\pi$
$662$	2.95908e9	+	5.12528e9i	0.396419	+	0.686618i
$663$	1.05868e9	−	1.69731e8i	0.141081	−	0.0226185i
$664$	4.47703e9			0.593474
$665$	−5.58110e8	−	2.31125e8i	−0.0735943	−	0.0304769i
$666$	−8.38247e8	+	1.45189e9i	−0.109954	+	0.190446i
$667$	2.31079e9			0.301523
$668$	1.55960e10	−	9.00438e9i	2.02440	−	1.16879i
$669$	−2.83708e9	−	1.63799e9i	−0.366336	−	0.211504i
$670$			7.76128e9i			0.996946i
$671$		−	1.37115e10i		−	1.75209i
$672$	9.55879e8	−	2.30822e9i	0.121510	−	0.293416i
$673$	6.48825e9	−	1.12380e10i	0.820494	−	1.42114i	−0.0848216	−	0.996396i	$-0.527032\pi$
$673$	6.48825e9	−	1.12380e10i	0.820494	−	1.42114i	0.905315	−	0.424740i	$-0.139635\pi$
$674$	−4.81786e9	+	2.78159e9i	−0.606100	+	0.349932i
$675$	−1.84080e9	−	3.18836e9i	−0.230379	−	0.399028i
$676$	9.33648e9	+	8.34290e9i	1.16244	+	1.03873i
$677$	1.92200e8	−	3.32901e8i	0.0238064	−	0.0412339i	−0.853877	−	0.520475i	$-0.825755\pi$
$677$	1.92200e8	−	3.32901e8i	0.0238064	−	0.0412339i	0.877683	+	0.479241i	$0.159088\pi$
$678$	5.01459e8	+	2.89517e8i	0.0617918	+	0.0356755i
$679$	3.74003e9	+	4.87330e9i	0.458491	+	0.597418i
$680$	−7.42114e8	−	1.28538e9i	−0.0905085	−	0.156765i
$681$	−2.85991e9	−	1.65117e9i	−0.347007	−	0.200344i
$682$	1.76660e10	+	1.01995e10i	2.13252	+	1.23121i
$683$	1.65303e9	+	9.54376e8i	0.198522	+	0.114617i	0.595966	−	0.803010i	$-0.296769\pi$
$683$	1.65303e9	+	9.54376e8i	0.198522	+	0.114617i	−0.397444	+	0.917626i	$0.630103\pi$
$684$	−2.01658e9	−	1.16428e9i	−0.240946	−	0.139110i
$685$	−4.96763e8	−	8.60418e8i	−0.0590516	−	0.102280i
$686$	−1.07327e10	−	8.23142e9i	−1.26933	−	0.973510i
$687$	−2.36494e9	−	1.36540e9i	−0.278274	−	0.160661i
$688$	4.29346e7	−	7.43650e7i	0.00502630	−	0.00870580i
$689$	−3.60769e9	+	9.45171e9i	−0.420205	+	1.10089i
$690$	−7.27764e8	−	1.26052e9i	−0.0843371	−	0.146076i
$691$	−8.26737e9	+	4.77317e9i	−0.953223	+	0.550343i	−0.894081	−	0.447906i	$-0.852170\pi$
$691$	−8.26737e9	+	4.77317e9i	−0.953223	+	0.550343i	−0.0591421	+	0.998250i	$0.518837\pi$
$692$	−1.08528e10	+	1.87976e10i	−1.24500	+	2.15641i
$693$	1.56319e10	−	2.05925e9i	1.78421	−	0.235040i
$694$			4.97674e9i			0.565181i
$695$			1.77501e9i			0.200565i
$696$	−6.71667e8	−	3.87787e8i	−0.0755130	−	0.0435975i
$697$	−3.01847e9	+	1.74272e9i	−0.337654	+	0.194945i
$698$	1.60123e10			1.78222
$699$	−7.12636e8	+	1.23432e9i	−0.0789219	+	0.136697i
$700$	1.53842e9	+	1.16783e10i	0.169524	+	1.28688i
$701$	1.05278e10			1.15432			0.577160	−	0.816631i	$-0.304161\pi$
$701$	1.05278e10			1.15432			0.577160	+	0.816631i	$0.304161\pi$
$702$	7.58051e9	+	2.89345e9i	0.827025	+	0.315672i
$703$	−1.34492e8	−	2.32948e8i	−0.0146000	−	0.0252880i
$704$		−	2.96416e10i		−	3.20183i
$705$	−6.14568e8	−	1.06446e9i	−0.0660554	−	0.114411i
$706$	−3.98542e9	−	6.90295e9i	−0.426244	−	0.738276i
$707$	1.46068e9	+	1.10882e10i	0.155449	+	1.18003i
$708$	3.57871e9	−	2.06617e9i	0.378974	−	0.218801i
$709$			1.79424e10i			1.89069i	0.326077	+	0.945343i	$0.394273\pi$
$709$			1.79424e10i			1.89069i	−0.326077	+	0.945343i	$0.605727\pi$
$710$	−1.23129e9	+	7.10885e8i	−0.129109	+	0.0745410i
$711$	3.82296e9	−	6.62156e9i	0.398893	−	0.690903i
$712$	4.90957e9	+	8.50362e9i	0.509757	+	0.882925i
$713$	5.86656e9	+	3.38706e9i	0.606136	+	0.349953i
$714$	−2.20402e9	+	2.90343e8i	−0.226606	+	0.0298516i
$715$	7.75161e9	−	1.24276e9i	0.793087	−	0.127150i
$716$	5.35982e9	−	9.28347e9i	0.545701	−	0.945181i
$717$		−	1.27207e9i		−	0.128883i
$718$	−2.03237e10			−2.04912
$719$	−9.64628e9			−0.967851			−0.483926	−	0.875109i	$-0.660790\pi$
$719$	−9.64628e9			−0.967851			−0.483926	+	0.875109i	$0.660790\pi$
$720$			4.83343e8i			0.0482605i
$721$	1.25028e10	+	5.17765e9i	1.24232	+	0.514469i
$722$	−1.34789e10	+	7.78207e9i	−1.33283	+	0.769511i
$723$	2.27250e9	+	1.31203e9i	0.223625	+	0.129110i
$724$	−9.91835e8	+	1.71791e9i	−0.0971302	+	0.168234i
$725$	−2.88577e9			−0.281241
$726$	−1.17721e10	+	6.79662e9i	−1.14176	+	0.659196i
$727$	−2.53364e9			−0.244554			−0.122277	−	0.992496i	$-0.539020\pi$
$727$	−2.53364e9			−0.244554			−0.122277	+	0.992496i	$0.539020\pi$
$728$	−6.76409e9	−	6.39360e9i	−0.649755	−	0.614166i
$729$	−5.58577e9			−0.533995
$730$	1.05532e10	−	6.09292e9i	1.00405	−	0.579689i
$731$	−4.08260e8			−0.0386568
$732$	−2.13126e9	+	3.69145e9i	−0.200839	+	0.347863i
$733$	1.79589e10	+	1.03686e10i	1.68429	+	0.972423i	0.958755	+	0.284232i	$0.0917387\pi$
$733$	1.79589e10	+	1.03686e10i	1.68429	+	0.972423i	0.725530	+	0.688190i	$0.241595\pi$
$734$	2.05345e10	−	1.18556e10i	1.91668	−	1.10659i
$735$	−1.22828e9	−	3.28908e8i	−0.114102	−	0.0305541i
$736$		−	1.06202e10i		−	0.981884i
$737$	3.25026e10			2.99076
$738$	−1.26145e10			−1.15524
$739$			1.59773e10i			1.45629i	0.685421	+	0.728147i	$0.259618\pi$
$739$			1.59773e10i			1.45629i	−0.685421	+	0.728147i	$0.740382\pi$
$740$	5.27190e8	−	9.13120e8i	0.0478252	−	0.0828356i
$741$	−4.83117e8	+	3.92735e8i	−0.0436203	+	0.0354597i
$742$	8.02556e9	−	1.93798e10i	0.721210	−	1.74155i
$743$	−1.46596e10	−	8.46373e9i	−1.31118	−	0.757008i	−0.328886	−	0.944370i	$-0.606673\pi$
$743$	−1.46596e10	−	8.46373e9i	−1.31118	−	0.757008i	−0.982291	+	0.187361i	$0.940007\pi$
$744$	−1.13681e9	−	1.96901e9i	−0.101200	−	0.175284i
$745$	−2.09121e8	+	3.62208e8i	−0.0185289	+	0.0320930i
$746$	−2.69369e10	+	1.55520e10i	−2.37554	+	1.37152i
$747$			6.93178e9i			0.608447i
$748$	−1.50138e10	+	8.66821e9i	−1.31170	+	0.757310i
$749$	−4.23461e9	+	3.24986e9i	−0.368237	+	0.282604i
$750$	2.00040e9	+	3.46479e9i	0.173142	+	0.299891i
$751$	−5.54208e9	−	9.59917e9i	−0.477456	−	0.826978i	0.522210	−	0.852817i	$-0.325108\pi$
$751$	−5.54208e9	−	9.59917e9i	−0.477456	−	0.826978i	−0.999666	+	0.0258390i	$0.991774\pi$
$752$		−	1.67848e9i		−	0.143931i
$753$	2.40178e9	+	4.16000e9i	0.204998	+	0.355068i
$754$	4.93508e9	−	4.01182e9i	0.419271	−	0.340833i
$755$	−8.33219e9			−0.704604
$756$	−9.46899e9	−	3.92130e9i	−0.797035	−	0.330068i
$757$	3.67458e9	−	6.36456e9i	0.307873	−	0.533252i	−0.670023	−	0.742340i	$-0.733716\pi$
$757$	3.67458e9	−	6.36456e9i	0.307873	−	0.533252i	0.977897	+	0.209087i	$0.0670493\pi$
$758$	1.53580e10			1.28083
$759$	−5.27880e9	+	3.04772e9i	−0.438217	+	0.253005i
$760$	7.46397e8	+	4.30932e8i	0.0616769	+	0.0356092i
$761$		−	7.23283e9i		−	0.594925i	−0.954734	−	0.297462i	$-0.903860\pi$
$761$		−	7.23283e9i		−	0.594925i	0.954734	−	0.297462i	$-0.0961403\pi$
$762$			9.69542e8i			0.0793824i
$763$	−1.07954e10	−	1.40665e10i	−0.879835	−	1.14644i
$764$	8.21951e8	−	1.42366e9i	0.0666836	−	0.115499i
$765$	1.99015e9	−	1.14901e9i	0.160720	−	0.0927919i
$766$	1.08358e10	+	1.87682e10i	0.871086	+	1.50877i
$767$	1.92327e9	+	1.19962e10i	0.153906	+	0.959976i
$768$	−1.41867e9	+	2.45720e9i	−0.113010	+	0.195739i
$769$	1.83141e10	+	1.05737e10i	1.45226	+	0.838463i	0.998609	−	0.0527173i	$-0.0167882\pi$
$769$	1.83141e10	+	1.05737e10i	1.45226	+	0.838463i	0.453650	+	0.891180i	$0.350122\pi$
$770$	−1.61377e10	+	2.12587e9i	−1.27387	+	0.167811i
$771$	−2.04119e9	−	3.53545e9i	−0.160396	−	0.277814i
$772$	2.24777e10	+	1.29775e10i	1.75829	+	1.01515i
$773$	−1.54491e10	−	8.91952e9i	−1.20302	−	0.694565i	−0.241797	−	0.970327i	$-0.577737\pi$
$773$	−1.54491e10	−	8.91952e9i	−1.20302	−	0.694565i	−0.961226	+	0.275762i	$0.911070\pi$
$774$	−1.27962e9	−	7.38789e8i	−0.0991945	−	0.0572700i
$775$	−7.32631e9	−	4.22985e9i	−0.565366	−	0.326414i
$776$	−4.38229e9	−	7.59036e9i	−0.336655	−	0.583104i
$777$	−3.44720e8	−	4.49173e8i	−0.0263628	−	0.0343511i
$778$	−2.92597e10	−	1.68931e10i	−2.22762	−	1.28612i
$779$	1.01196e9	−	1.75277e9i	0.0766980	−	0.132845i
$780$	−2.28009e9	−	8.70301e8i	−0.172036	−	0.0656657i
$781$	2.97703e9	+	5.15637e9i	0.223617	+	0.387316i
$782$	−8.18404e9	+	4.72506e9i	−0.611990	+	0.353332i
$783$	1.25542e9	−	2.17446e9i	0.0934596	−	0.161877i
$784$	−1.22803e9	−	1.22764e9i	−0.0910126	−	0.0909836i
$785$		−	1.07870e10i		−	0.795899i
$786$		−	1.95547e9i		−	0.143639i
$787$	−1.52107e10	−	8.78188e9i	−1.11234	−	0.642208i	−0.172903	−	0.984939i	$-0.555315\pi$
$787$	−1.52107e10	−	8.78188e9i	−1.11234	−	0.642208i	−0.939434	+	0.342731i	$0.888648\pi$
$788$	−1.82124e10	+	1.05149e10i	−1.32594	+	0.765533i
$789$	2.53693e9			0.183882
$790$	−3.94665e9	+	6.83579e9i	−0.284796	+	0.493281i
$791$	1.70587e9	−	1.30918e9i	0.122554	−	0.0940547i
$792$	−2.24956e10			−1.60901
$793$	−7.90516e9	−	9.72441e9i	−0.562930	−	0.692480i
$794$	5.12492e9	+	8.87661e9i	0.363341	+	0.629326i
$795$		−	1.97194e9i		−	0.139190i
$796$	3.07195e9	+	5.32077e9i	0.215883	+	0.373920i
$797$	−2.51144e8	−	4.34994e8i	−0.0175719	−	0.0304354i	0.857106	−	0.515141i	$-0.172260\pi$
$797$	−2.51144e8	−	4.34994e8i	−0.0175719	−	0.0304354i	−0.874678	+	0.484705i	$0.838927\pi$
$798$	1.02407e9	−	7.85927e8i	0.0713379	−	0.0547485i
$799$	−6.91110e9	+	3.99013e9i	−0.479329	+	0.276741i
$800$			1.32628e10i			0.915839i
$801$	−1.31661e10	+	7.60147e9i	−0.905200	+	0.522618i
$802$	−2.25880e10	+	3.91236e10i	−1.54621	+	2.67811i
$803$	−2.55158e10	−	4.41947e10i	−1.73902	−	3.01208i
$804$	−8.75046e9	−	5.05208e9i	−0.593793	−	0.342826i
$805$	−5.35903e9	+	7.05963e8i	−0.362077	+	0.0476976i
$806$	1.84094e10	−	2.95145e9i	1.23842	−	0.198547i
$807$	−3.25977e8	+	5.64609e8i	−0.0218338	+	0.0378173i
$808$		−	1.59567e10i		−	1.06415i
$809$	−3.87684e9			−0.257429			−0.128715	−	0.991682i	$-0.541085\pi$
$809$	−3.87684e9			−0.257429			−0.128715	+	0.991682i	$0.541085\pi$
$810$	7.49186e9			0.495327
$811$		−	5.44574e9i		−	0.358496i	−0.983804	−	0.179248i	$-0.942634\pi$
$811$		−	5.44574e9i		−	0.358496i	0.983804	−	0.179248i	$-0.0573664\pi$
$812$	−6.37294e9	+	4.89093e9i	−0.417728	+	0.320587i
$813$	7.20674e8	−	4.16081e8i	0.0470351	−	0.0271557i
$814$	−6.27690e9	−	3.62397e9i	−0.407906	−	0.235505i
$815$	−1.45937e9	+	2.52771e9i	−0.0944310	+	0.163559i
$816$	−2.85392e8			−0.0183877
$817$	2.05308e8	−	1.18535e8i	0.0131713	−	0.00760447i
$818$	2.85364e10			1.82290
$819$	9.89921e9	−	1.04728e10i	0.629661	−	0.666147i
$820$	7.93351e9			0.502478
$821$	1.11991e10	−	6.46581e9i	0.706289	−	0.407776i	−0.103396	−	0.994640i	$-0.532971\pi$
$821$	1.11991e10	−	6.46581e9i	0.706289	−	0.407776i	0.809686	+	0.586864i	$0.199638\pi$
$822$	2.12314e9			0.133330
$823$	−1.55851e9	+	2.69942e9i	−0.0974564	+	0.168799i	−0.910631	−	0.413220i	$-0.864404\pi$
$823$	−1.55851e9	+	2.69942e9i	−0.0974564	+	0.168799i	0.813175	+	0.582020i	$0.197737\pi$
$824$	−1.67208e10	−	9.65374e9i	−1.04114	−	0.601105i
$825$	6.59230e9	−	3.80607e9i	0.408741	−	0.235987i
$826$	−3.28995e9	−	2.49743e10i	−0.203123	−	1.54193i
$827$		−	2.20970e10i		−	1.35852i	−0.733900	−	0.679258i	$-0.762302\pi$
$827$		−	2.20970e10i		−	1.35852i	0.733900	−	0.679258i	$-0.237698\pi$
$828$	−2.08361e10			−1.27559
$829$	2.67611e10			1.63141			0.815706	−	0.578466i	$-0.196348\pi$
$829$	2.67611e10			1.63141			0.815706	+	0.578466i	$0.196348\pi$
$830$		−	7.15605e9i		−	0.434410i
$831$	−4.86153e8	+	8.42042e8i	−0.0293880	+	0.0509014i
$832$	−1.70895e10	−	2.10223e10i	−1.02872	−	1.26546i
$833$	−2.13546e9	+	7.97472e9i	−0.128007	+	0.478033i
$834$	−3.28497e9	−	1.89658e9i	−0.196088	−	0.113211i
$835$	−5.16015e9	−	8.93764e9i	−0.306732	−	0.531276i
$836$	5.03348e9	−	8.71824e9i	0.297952	−	0.516068i
$837$	6.37447e9	−	3.68030e9i	0.375755	−	0.216942i
$838$			3.65825e10i			2.14743i
$839$	−2.49139e10	+	1.43841e10i	−1.45638	+	0.840843i	−0.998831	−	0.0483397i	$-0.984607\pi$
$839$	−2.49139e10	+	1.43841e10i	−1.45638	+	0.840843i	−0.457552	+	0.889183i	$0.651274\pi$
$840$	1.67616e9	+	6.94131e8i	0.0975748	+	0.0404077i
$841$	7.64089e9	+	1.32344e10i	0.442953	+	0.767218i
$842$	1.46734e10	+	2.54151e10i	0.847108	+	1.46723i
$843$		−	3.24057e8i		−	0.0186305i
$844$	−2.32210e10	−	4.02199e10i	−1.32948	−	2.30273i
$845$	4.78107e9	−	5.35047e9i	0.272601	−	0.305065i
$846$	−2.88822e10			−1.63996
$847$	6.59301e9	+	5.00482e10i	0.372814	+	2.83006i
$848$	1.34642e9	−	2.33206e9i	0.0758219	−	0.131327i
$849$	−6.95194e8			−0.0389878
$850$	1.02204e10	−	5.90077e9i	0.570825	−	0.329566i
$851$	−2.08444e9	−	1.20345e9i	−0.115941	−	0.0669385i
$852$		−	1.85096e9i		−	0.102532i
$853$			2.34444e8i			0.0129335i	0.999979	+	0.00646677i	$0.00205845\pi$
$853$			2.34444e8i			0.0129335i	−0.999979	+	0.00646677i	$0.997942\pi$
$854$	1.58195e10	+	2.06130e10i	0.869142	+	1.13250i
$855$	−6.67212e8	+	1.15564e9i	−0.0365075	+	0.0632329i
$856$	6.59557e9	−	3.80796e9i	0.359413	−	0.207507i
$857$	−8.01119e9	−	1.38758e10i	−0.434775	−	0.753052i	0.562502	−	0.826796i	$-0.309839\pi$
$857$	−8.01119e9	−	1.38758e10i	−0.434775	−	0.753052i	−0.997277	+	0.0737435i	$0.976505\pi$
$858$	−5.98256e9	+	1.56736e10i	−0.323356	+	0.847156i
$859$	6.78405e9	−	1.17503e10i	0.365185	−	0.632519i	−0.623621	−	0.781727i	$-0.714339\pi$
$859$	6.78405e9	−	1.17503e10i	0.365185	−	0.632519i	0.988806	+	0.149208i	$0.0476723\pi$
$860$	8.04779e8	+	4.64639e8i	0.0431451	+	0.0249099i
$861$	1.63004e9	−	3.93615e9i	0.0870336	−	0.210165i
$862$	1.16316e10	+	2.01466e10i	0.618536	+	1.07134i
$863$	1.73546e10	+	1.00197e10i	0.919130	+	0.530660i	0.883358	−	0.468700i	$-0.155277\pi$
$863$	1.73546e10	+	1.00197e10i	0.919130	+	0.530660i	0.0357728	+	0.999360i	$0.488611\pi$
$864$	−9.99363e9	−	5.76982e9i	−0.527139	−	0.304344i
$865$	1.07724e10	+	6.21943e9i	0.565920	+	0.326734i
$866$	2.88987e10	+	1.66847e10i	1.51205	+	0.872982i
$867$	−2.09182e9	−	3.62314e9i	−0.109008	−	0.188807i
$868$	−2.33484e10	+	3.07576e9i	−1.21182	+	0.159637i
$869$	2.86268e10	+	1.65277e10i	1.47980	+	0.854365i
$870$	−6.19835e8	+	1.07359e9i	−0.0319124	+	0.0552738i
$871$	2.30514e10	−	1.87389e10i	1.18204	−	0.960905i
$872$	1.26492e10	+	2.19091e10i	0.646035	+	1.11897i
$873$	1.17521e10	−	6.78510e9i	0.597815	−	0.345149i
$874$	2.74376e9	−	4.75233e9i	0.139013	−	0.240778i
$875$	1.47303e10	−	1.94047e9i	0.743334	−	0.0979219i
$876$			1.58644e10i			0.797366i
$877$			8.92659e9i			0.446876i	0.974718	+	0.223438i	$0.0717280\pi$
$877$			8.92659e9i			0.446876i	−0.974718	+	0.223438i	$0.928272\pi$
$878$	4.25868e10	+	2.45875e10i	2.12346	+	1.22598i
$879$	8.38554e9	−	4.84139e9i	0.416457	−	0.240441i
$880$	−2.08962e9			−0.103366
$881$	−6.61599e9	+	1.14592e10i	−0.325971	+	0.564599i	−0.981708	−	0.190391i	$-0.939025\pi$
$881$	−6.61599e9	+	1.14592e10i	−0.325971	+	0.564599i	0.655737	+	0.754989i	$0.272358\pi$
$882$	−2.11243e10	+	2.11310e10i	−1.03667	+	1.03700i
$883$	2.62856e10			1.28486			0.642430	−	0.766344i	$-0.277926\pi$
$883$	2.62856e10			1.28486			0.642430	+	0.766344i	$0.277926\pi$
$884$	−5.65049e9	+	1.48036e10i	−0.275108	+	0.720750i
$885$	−1.18406e9	−	2.05085e9i	−0.0574212	−	0.0994564i
$886$		−	4.44014e10i		−	2.14476i
$887$	1.08166e10	+	1.87349e10i	0.520424	+	0.901401i	0.999718	+	0.0237465i	$0.00755946\pi$
$887$	1.08166e10	+	1.87349e10i	0.520424	+	0.901401i	−0.479294	+	0.877654i	$0.659107\pi$
$888$	4.03917e8	+	6.99606e8i	0.0193574	+	0.0335280i
$889$	3.32658e9	+	1.37760e9i	0.158797	+	0.0657610i
$890$	1.35921e10	−	7.84741e9i	0.646282	−	0.373131i
$891$		−	3.13743e10i		−	1.48594i
$892$	4.19273e10	−	2.42067e10i	1.97797	−	1.14198i
$893$	2.31700e9	−	4.01316e9i	0.108879	−	0.188584i
$894$	−4.46886e8	−	7.74030e8i	−0.0209178	−	0.0362307i
$895$	−5.32009e9	−	3.07155e9i	−0.248049	−	0.143211i
$896$	1.97797e10	+	2.57731e10i	0.918631	+	1.19699i
$897$	−1.98670e9	+	5.20491e9i	−0.0919090	+	0.240791i
$898$	−2.21881e10	+	3.84310e10i	−1.02248	+	1.77098i
$899$		−	5.76951e9i		−	0.264838i
$900$	2.60207e10			1.18979
$901$	−1.28029e10			−0.583140
$902$		−	5.45359e10i		−	2.47434i
$903$	3.95879e8	−	3.03819e8i	0.0178918	−	0.0137312i
$904$	−2.65696e9	+	1.53400e9i	−0.119618	+	0.0690614i
$905$	9.84483e8	+	5.68391e8i	0.0441508	+	0.0254904i
$906$	8.90285e9	−	1.54202e10i	0.397723	−	0.688876i
$907$	1.41739e10			0.630758			0.315379	−	0.948966i	$-0.397868\pi$
$907$	1.41739e10			0.630758			0.315379	+	0.948966i	$0.397868\pi$
$908$	4.22647e10	−	2.44015e10i	1.87360	−	1.08173i
$909$	2.47058e10			1.09100
$910$	−1.02195e10	+	1.08117e10i	−0.449556	+	0.475606i
$911$	−3.14067e9			−0.137629			−0.0688143	−	0.997629i	$-0.521922\pi$
$911$	−3.14067e9			−0.137629			−0.0688143	+	0.997629i	$0.521922\pi$
$912$	1.43520e8	−	8.28612e7i	0.00626513	−	0.00361717i
$913$	−2.99680e10			−1.30320
$914$	−1.02172e10	+	1.76966e10i	−0.442607	+	0.766618i
$915$	2.11546e9	+	1.22136e9i	0.0912918	+	0.0527074i
$916$	3.49499e10	−	2.01783e10i	1.50249	−	0.867463i
$917$	−6.70938e9	−	2.77849e9i	−0.287336	−	0.118992i
$918$			1.02683e10i			0.438074i
$919$	−1.39211e10			−0.591654			−0.295827	−	0.955241i	$-0.595595\pi$
$919$	−1.39211e10			−0.591654			−0.295827	+	0.955241i	$0.595595\pi$
$920$	7.71207e9			0.326523
$921$		−	3.84728e9i		−	0.162273i
$922$	2.88064e8	−	4.98941e8i	0.0121040	−	0.0209648i
$923$	5.08419e9	+	1.94062e9i	0.212822	+	0.0812333i
$924$	8.10776e9	−	1.95783e10i	0.338103	−	0.816436i
$925$	2.60311e9	+	1.50290e9i	0.108142	+	0.0624360i
$926$	1.50528e10	+	2.60722e10i	0.622988	+	1.07905i
$927$	1.49469e10	−	2.58887e10i	0.616270	−	1.06741i
$928$	−7.83337e9	+	4.52260e9i	−0.321759	+	0.185768i
$929$			7.51741e9i			0.307619i	0.988101	+	0.153810i	$0.0491542\pi$
$929$			7.51741e9i			0.307619i	−0.988101	+	0.153810i	$0.950846\pi$
$930$	−3.14724e9	+	1.81706e9i	−0.128304	+	0.0740762i
$931$	−1.24150e9	−	4.63038e9i	−0.0504222	−	0.188059i
$932$	−1.05316e10	−	1.82412e10i	−0.426125	−	0.738070i
$933$	5.55365e9	+	9.61921e9i	0.223869	+	0.387752i
$934$			2.00317e10i			0.804460i
$935$	4.96750e9	+	8.60396e9i	0.198745	+	0.344237i
$936$	−1.59543e10	+	1.29695e10i	−0.635933	+	0.516962i
$937$	−3.12561e10			−1.24121			−0.620606	−	0.784122i	$-0.713113\pi$
$937$	−3.12561e10			−1.24121			−0.620606	+	0.784122i	$0.713113\pi$
$938$	−4.88624e10	+	3.74996e10i	−1.93315	+	1.48360i
$939$	4.89416e9	−	8.47694e9i	0.192907	−	0.334125i
$940$	1.81646e10			0.713309
$941$	−8.50105e8	+	4.90808e8i	−0.0332590	+	0.0192021i	−0.516537	−	0.856265i	$-0.672779\pi$
$941$	−8.50105e8	+	4.90808e8i	−0.0332590	+	0.0192021i	0.483278	+	0.875467i	$0.339446\pi$
$942$	1.99633e10	+	1.15258e10i	0.778134	+	0.449256i
$943$		−	1.81104e10i		−	0.703293i
$944$		−	3.23386e9i		−	0.125118i
$945$	−2.24718e9	+	5.42640e9i	−0.0866218	+	0.209171i
$946$	3.19399e9	−	5.53215e9i	0.122663	−	0.212459i
$947$	4.40835e10	−	2.54516e10i	1.68675	−	0.973846i	0.729770	−	0.683693i	$-0.239627\pi$
$947$	4.40835e10	−	2.54516e10i	1.68675	−	0.973846i	0.956980	−	0.290153i	$-0.0937063\pi$
$948$	−5.13801e9	−	8.89930e9i	−0.195869	−	0.339255i
$949$	−4.35761e10	−	1.66328e10i	−1.65507	−	0.631734i
$950$	−3.42648e9	+	5.93483e9i	−0.129663	+	0.224582i
$951$	1.31348e9	+	7.58335e8i	0.0495211	+	0.0285910i
$952$	4.50669e9	−	1.08826e10i	0.169289	−	0.408792i
$953$	−3.98869e9	−	6.90861e9i	−0.149281	−	0.258563i	0.781681	−	0.623679i	$-0.214363\pi$
$953$	−3.98869e9	−	6.90861e9i	−0.149281	−	0.258563i	−0.930962	+	0.365116i	$0.881029\pi$
$954$	−4.01285e10	−	2.31682e10i	−1.49635	−	0.863920i
$955$	−8.15859e8	−	4.71036e8i	−0.0303112	−	0.0175002i
$956$	1.62805e10	+	9.39955e9i	0.602650	+	0.347940i
$957$	4.49595e9	+	2.59574e9i	0.165817	+	0.0957346i
$958$	7.72677e8	+	1.33832e9i	0.0283935	+	0.0491789i
$959$	3.01673e9	−	7.28467e9i	0.110452	−	0.266713i
$960$	4.57324e9	+	2.64036e9i	0.166830	+	0.0963194i
$961$	−5.29959e9	+	9.17916e9i	−0.192624	+	0.333635i
$962$	−6.54103e9	+	1.04868e9i	−0.236883	+	0.0379777i
$963$	5.89585e9	+	1.02119e10i	0.212743	+	0.368481i
$964$	−3.35837e10	+	1.93896e10i	−1.20742	+	0.697106i
$965$	7.43703e9	−	1.28813e10i	0.266412	−	0.461439i
$966$	4.41955e9	−	1.06721e10i	0.157746	−	0.380918i
$967$			7.32842e9i			0.260626i	0.991473	+	0.130313i	$0.0415982\pi$
$967$			7.32842e9i			0.260626i	−0.991473	+	0.130313i	$0.958402\pi$
$968$		−	7.20233e10i		−	2.55217i
$969$	−6.82356e8	−	3.93959e8i	−0.0240923	−	0.0139097i
$970$	−1.21324e10	+	7.00462e9i	−0.426819	+	0.246424i
$971$	−2.20454e10			−0.772772			−0.386386	−	0.922337i	$-0.626277\pi$
$971$	−2.20454e10			−0.772772			−0.386386	+	0.922337i	$0.626277\pi$
$972$	−1.72262e10	+	2.98367e10i	−0.601669	+	1.04212i
$973$	−1.11749e10	+	8.57620e9i	−0.388909	+	0.298469i
$974$	4.07982e8			0.0141477
$975$	2.48104e9	−	6.50003e9i	0.0857269	−	0.224594i
$976$	1.66787e9	+	2.88884e9i	0.0574233	+	0.0994600i
$977$		−	1.86789e10i		−	0.640795i	−0.947283	−	0.320398i	$-0.896183\pi$
$977$		−	1.86789e10i		−	0.640795i	0.947283	−	0.320398i	$-0.103817\pi$
$978$	−3.11865e9	−	5.40166e9i	−0.106606	−	0.184646i
$979$	−3.28632e10	−	5.69208e10i	−1.11936	−	1.93879i
$980$	1.32855e10	−	1.32897e10i	0.450906	−	0.451050i
$981$	−3.39218e10	+	1.95848e10i	−1.14720	+	0.662334i
$982$		−	8.97214e9i		−	0.302347i
$983$	1.05374e10	−	6.08377e9i	0.353831	−	0.204285i	−0.312540	−	0.949905i	$-0.601180\pi$
$983$	1.05374e10	−	6.08377e9i	0.353831	−	0.204285i	0.666371	+	0.745620i	$0.267847\pi$
$984$	−3.03921e9	+	5.26406e9i	−0.101690	+	0.176132i
$985$	6.02579e9	+	1.04370e10i	0.200903	+	0.347975i
$986$	6.97033e9	+	4.02432e9i	0.231571	+	0.133698i
$987$	3.73214e9	−	9.01221e9i	0.123551	−	0.298347i
$988$	−1.45655e9	−	9.08510e9i	−0.0480481	−	0.299696i
$989$	1.06066e9	−	1.83712e9i	0.0348651	−	0.0603881i
$990$			3.59568e10i			1.17776i
$991$	−1.31475e10			−0.429126			−0.214563	−	0.976710i	$-0.568833\pi$
$991$	−1.31475e10			−0.429126			−0.214563	+	0.976710i	$0.568833\pi$
$992$	−2.65162e10			−0.862423
$993$			4.41532e9i			0.143100i
$994$	−1.04246e10	−	4.31705e9i	−0.336673	−	0.139423i
$995$	3.04918e9	−	1.76044e9i	0.0981301	−	0.0566554i
$996$	8.06809e9	+	4.65811e9i	0.258740	+	0.149383i
$997$	−3.91501e9	+	6.78100e9i	−0.125112	+	0.216701i	−0.921777	−	0.387721i	$-0.873262\pi$
$997$	−3.91501e9	+	6.78100e9i	−0.125112	+	0.216701i	0.796665	+	0.604422i	$0.206596\pi$
$998$	4.59122e10			1.46208
$999$	−2.26491e9	+	1.30764e9i	−0.0718739	+	0.0414964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.u.a.30.8	yes	126
7.4	even	3		91.8.k.a.4.8	✓	126
13.10	even	6		91.8.k.a.23.56	yes	126
91.88	even	6	inner	91.8.u.a.88.8	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.k.a.4.8	✓	126	7.4	even	3
91.8.k.a.23.56	yes	126	13.10	even	6
91.8.u.a.30.8	yes	126	1.1	even	1	trivial
91.8.u.a.88.8	yes	126	91.88	even	6	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.6734 + 9.04906i) q^{2} -13.5023 q^{3} +(99.7708 - 172.808i) q^{4} +(-99.0313 - 57.1757i) q^{5} +(211.628 - 122.183i) q^{6} +(-118.523 - 899.720i) q^{7} +1294.77i q^{8} -2004.69 q^{9} +O(q^{10})\)	\(q+(-15.6734 + 9.04906i) q^{2} -13.5023 q^{3} +(99.7708 - 172.808i) q^{4} +(-99.0313 - 57.1757i) q^{5} +(211.628 - 122.183i) q^{6} +(-118.523 - 899.720i) q^{7} +1294.77i q^{8} -2004.69 q^{9} +2069.55 q^{10} -8666.81i q^{11} +(-1347.14 + 2333.31i) q^{12} +(-4996.73 - 6146.65i) q^{13} +(9999.27 + 13029.2i) q^{14} +(1337.15 + 772.005i) q^{15} +(1054.23 + 1825.99i) q^{16} +(5012.30 - 8681.55i) q^{17} +(31420.3 - 18140.5i) q^{18} +5821.11i q^{19} +(-19760.9 + 11408.9i) q^{20} +(1600.34 + 12148.3i) q^{21} +(78426.4 + 135839. i) q^{22} +(26044.0 + 45109.5i) q^{23} -17482.4i q^{24} +(-32524.4 - 56333.9i) q^{25} +(133937. + 51123.3i) q^{26} +56597.5 q^{27} +(-167304. - 69284.0i) q^{28} +(22181.6 - 38419.7i) q^{29} -27943.7 q^{30} +(112628. - 65025.8i) q^{31} +(-176574. - 101945. i) q^{32} +117022. i q^{33} +181426. i q^{34} +(-39704.6 + 95877.0i) q^{35} +(-200009. + 346426. i) q^{36} +(-40017.8 + 23104.3i) q^{37} +(-52675.5 - 91236.7i) q^{38} +(67467.4 + 82994.0i) q^{39} +(74029.3 - 128223. i) q^{40} +(-301107. - 173844. i) q^{41} +(-135013. - 175924. i) q^{42} +(-20362.9 - 35269.7i) q^{43} +(-1.49770e6 - 864695. i) q^{44} +(198527. + 114619. i) q^{45} +(-816396. - 471347. i) q^{46} +(-689415. - 398034. i) q^{47} +(-14234.6 - 24655.1i) q^{48} +(-795448. + 213275. i) q^{49} +(1.01954e6 + 588630. i) q^{50} +(-67677.6 + 117221. i) q^{51} +(-1.56072e6 + 250219. i) q^{52} +(-638576. - 1.10605e6i) q^{53} +(-887077. + 512154. i) q^{54} +(-495531. + 858285. i) q^{55} +(1.16493e6 - 153460. i) q^{56} -78598.4i q^{57} +802890. i q^{58} +(-1.32826e6 - 766873. i) q^{59} +(266817. - 154047. i) q^{60} +1.58207e6 q^{61} +(-1.17684e6 + 2.03835e6i) q^{62} +(237602. + 1.80366e6i) q^{63} +3.42013e6 q^{64} +(143393. + 894402. i) q^{65} +(-1.05894e6 - 1.83414e6i) q^{66} +3.75023e6i q^{67} +(-1.00016e6 - 1.73233e6i) q^{68} +(-351654. - 609083. i) q^{69} +(-245289. - 1.86201e6i) q^{70} +(-594956. + 343498. i) q^{71} -2.59561e6i q^{72} +(5.09930e6 - 2.94409e6i) q^{73} +(418144. - 724246. i) q^{74} +(439155. + 760638. i) q^{75} +(1.00593e6 + 580776. i) q^{76} +(-7.79770e6 + 1.02722e6i) q^{77} +(-1.80846e6 - 690284. i) q^{78} +(-1.90701e6 + 3.30304e6i) q^{79} -241107. i q^{80} +3.62005e6 q^{81} +6.29250e6 q^{82} -3.45779e6i q^{83} +(2.25899e6 + 935495. i) q^{84} +(-992748. + 573163. i) q^{85} +(638314. + 368531. i) q^{86} +(-299503. + 518755. i) q^{87} +1.12215e7 q^{88} +(6.56768e6 - 3.79185e6i) q^{89} -4.14879e6 q^{90} +(-4.93803e6 + 5.22417e6i) q^{91} +1.03937e7 q^{92} +(-1.52074e6 + 878000. i) q^{93} +1.44073e7 q^{94} +(332826. - 576471. i) q^{95} +(2.38415e6 + 1.37649e6i) q^{96} +(-5.86233e6 + 3.38462e6i) q^{97} +(1.05374e7 - 1.05408e7i) q^{98} +1.73742e7i 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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