LMFDB - Embedded newform 68.7.c.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,7,Mod(35,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("68.35");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	68.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.6436776861$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	68.35
Dual form			68.7.c.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.60885 - 2.47090i) q^{2} +43.5409i q^{3} +(51.7893 + 37.6014i) q^{4} -9.10522 q^{5} +(107.585 - 331.296i) q^{6} -262.967i q^{7} +(-301.148 - 414.070i) q^{8} -1166.81 q^{9} +O(q^{10})$	\(q+(-7.60885 - 2.47090i) q^{2} +43.5409i q^{3} +(51.7893 + 37.6014i) q^{4} -9.10522 q^{5} +(107.585 - 331.296i) q^{6} -262.967i q^{7} +(-301.148 - 414.070i) q^{8} -1166.81 q^{9} +(69.2803 + 22.4981i) q^{10} -1819.86i q^{11} +(-1637.20 + 2254.95i) q^{12} +580.321 q^{13} +(-649.764 + 2000.87i) q^{14} -396.450i q^{15} +(1268.27 + 3894.70i) q^{16} +1191.58 q^{17} +(8878.10 + 2883.07i) q^{18} -1133.69i q^{19} +(-471.553 - 342.369i) q^{20} +11449.8 q^{21} +(-4496.69 + 13847.1i) q^{22} -13760.4i q^{23} +(18029.0 - 13112.3i) q^{24} -15542.1 q^{25} +(-4415.58 - 1433.92i) q^{26} -19062.7i q^{27} +(9887.92 - 13618.9i) q^{28} +32409.0 q^{29} +(-979.587 + 3016.53i) q^{30} -28669.7i q^{31} +(-26.6211 - 32768.0i) q^{32} +79238.4 q^{33} +(-9066.54 - 2944.27i) q^{34} +2394.37i q^{35} +(-60428.4 - 43873.8i) q^{36} +50561.2 q^{37} +(-2801.22 + 8626.05i) q^{38} +25267.7i q^{39} +(2742.02 + 3770.20i) q^{40} -52955.8 q^{41} +(-87119.9 - 28291.3i) q^{42} +59950.8i q^{43} +(68429.4 - 94249.4i) q^{44} +10624.1 q^{45} +(-34000.5 + 104701. i) q^{46} +35763.0i q^{47} +(-169579. + 55221.4i) q^{48} +48497.6 q^{49} +(118258. + 38403.0i) q^{50} +51882.4i q^{51} +(30054.4 + 21820.9i) q^{52} +171930. q^{53} +(-47102.1 + 145045. i) q^{54} +16570.2i q^{55} +(-108887. + 79191.8i) q^{56} +49361.7 q^{57} +(-246596. - 80079.5i) q^{58} -134207. i q^{59} +(14907.1 - 20531.9i) q^{60} -139218. q^{61} +(-70839.9 + 218143. i) q^{62} +306832. i q^{63} +(-80763.9 + 249393. i) q^{64} -5283.95 q^{65} +(-602914. - 195790. i) q^{66} -150545. i q^{67} +(61711.0 + 44805.0i) q^{68} +599140. q^{69} +(5916.24 - 18218.4i) q^{70} -527493. i q^{71} +(351383. + 483142. i) q^{72} -628763. q^{73} +(-384713. - 124932. i) q^{74} -676717. i q^{75} +(42628.2 - 58712.8i) q^{76} -478563. q^{77} +(62434.0 - 192258. i) q^{78} +110212. i q^{79} +(-11547.8 - 35462.1i) q^{80} -20597.1 q^{81} +(402933. + 130848. i) q^{82} -1.04758e6i q^{83} +(592977. + 430529. i) q^{84} -10849.6 q^{85} +(148133. - 456157. i) q^{86} +1.41112e6i q^{87} +(-753550. + 548047. i) q^{88} +887788. q^{89} +(-80837.1 - 26251.0i) q^{90} -152605. i q^{91} +(517410. - 712641. i) q^{92} +1.24830e6 q^{93} +(88366.9 - 272116. i) q^{94} +10322.5i q^{95} +(1.42675e6 - 1159.11i) q^{96} +1.57949e6 q^{97} +(-369011. - 119833. i) q^{98} +2.12344e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9}+O(q^{10}) $ 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9} - 1710 q^{10} - 6234 q^{12} - 5040 q^{13} + 9040 q^{14} - 1230 q^{16} - 6974 q^{18} + 1046 q^{20} - 35488 q^{21} - 13254 q^{22} + 22838 q^{24} + 173856 q^{25} + 44744 q^{26} + 42864 q^{28} - 83536 q^{29} - 95104 q^{30} - 53050 q^{32} + 9072 q^{33} + 24174 q^{36} + 62640 q^{37} + 399840 q^{38} - 58218 q^{40} + 70448 q^{41} - 90520 q^{42} - 356746 q^{44} - 103808 q^{45} - 177084 q^{46} + 808886 q^{48} - 758880 q^{49} - 560506 q^{50} - 85800 q^{52} + 744784 q^{53} - 263596 q^{54} - 701896 q^{56} - 125008 q^{57} - 351534 q^{58} - 64960 q^{60} + 196560 q^{61} + 1428016 q^{62} - 60246 q^{64} - 708656 q^{65} + 1089052 q^{66} + 428496 q^{69} - 1132824 q^{70} - 1043230 q^{72} - 454272 q^{73} - 1135082 q^{74} + 850224 q^{76} - 549200 q^{77} + 703076 q^{78} + 1608910 q^{80} + 3871872 q^{81} - 328536 q^{82} + 2825208 q^{84} + 3243644 q^{86} + 691398 q^{88} - 1729776 q^{89} + 214114 q^{90} + 1469284 q^{92} - 6618704 q^{93} - 551136 q^{94} - 5148618 q^{96} + 4548720 q^{97} - 2942042 q^{98}+O(q^{100}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9 - 1710 * q^10 - 6234 * q^12 - 5040 * q^13 + 9040 * q^14 - 1230 * q^16 - 6974 * q^18 + 1046 * q^20 - 35488 * q^21 - 13254 * q^22 + 22838 * q^24 + 173856 * q^25 + 44744 * q^26 + 42864 * q^28 - 83536 * q^29 - 95104 * q^30 - 53050 * q^32 + 9072 * q^33 + 24174 * q^36 + 62640 * q^37 + 399840 * q^38 - 58218 * q^40 + 70448 * q^41 - 90520 * q^42 - 356746 * q^44 - 103808 * q^45 - 177084 * q^46 + 808886 * q^48 - 758880 * q^49 - 560506 * q^50 - 85800 * q^52 + 744784 * q^53 - 263596 * q^54 - 701896 * q^56 - 125008 * q^57 - 351534 * q^58 - 64960 * q^60 + 196560 * q^61 + 1428016 * q^62 - 60246 * q^64 - 708656 * q^65 + 1089052 * q^66 + 428496 * q^69 - 1132824 * q^70 - 1043230 * q^72 - 454272 * q^73 - 1135082 * q^74 + 850224 * q^76 - 549200 * q^77 + 703076 * q^78 + 1608910 * q^80 + 3871872 * q^81 - 328536 * q^82 + 2825208 * q^84 + 3243644 * q^86 + 691398 * q^88 - 1729776 * q^89 + 214114 * q^90 + 1469284 * q^92 - 6618704 * q^93 - 551136 * q^94 - 5148618 * q^96 + 4548720 * q^97 - 2942042 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−7.60885	−	2.47090i	−0.951107	−	0.308862i
$2$	−7.60885	−	2.47090i	−0.951107	−	0.308862i
$3$			43.5409i			1.61263i	0.591489	+	0.806313i	$0.298540\pi$
$3$			43.5409i			1.61263i	−0.591489	+	0.806313i	$0.701460\pi$
$4$	51.7893	+	37.6014i	0.809208	+	0.587522i
$5$	−9.10522			−0.0728418			−0.0364209	−	0.999337i	$-0.511596\pi$
$5$	−9.10522			−0.0728418			−0.0364209	+	0.999337i	$0.511596\pi$
$6$	107.585	−	331.296i	0.498080	−	1.53378i
$7$		−	262.967i		−	0.766666i	−0.923610	−	0.383333i	$-0.874776\pi$
$7$		−	262.967i		−	0.766666i	0.923610	−	0.383333i	$-0.125224\pi$
$8$	−301.148	−	414.070i	−0.588180	−	0.808730i
$9$	−1166.81			−1.60056
$10$	69.2803	+	22.4981i	0.0692803	+	0.0224981i
$11$		−	1819.86i		−	1.36729i	−0.729815	−	0.683644i	$-0.760394\pi$
$11$		−	1819.86i		−	1.36729i	0.729815	−	0.683644i	$-0.239606\pi$
$12$	−1637.20	+	2254.95i	−0.947454	+	1.30495i
$13$	580.321			0.264143			0.132071	−	0.991240i	$-0.457837\pi$
$13$	580.321			0.264143			0.132071	+	0.991240i	$0.457837\pi$
$14$	−649.764	+	2000.87i	−0.236794	+	0.729181i
$15$		−	396.450i		−	0.117467i
$16$	1268.27	+	3894.70i	0.309635	+	0.950855i
$17$	1191.58			0.242536
$17$	1191.58			0.242536
$18$	8878.10	+	2883.07i	1.52231	+	0.494354i
$19$		−	1133.69i		−	0.165284i	−0.996579	−	0.0826422i	$-0.973664\pi$
$19$		−	1133.69i		−	0.165284i	0.996579	−	0.0826422i	$-0.0263359\pi$
$20$	−471.553	−	342.369i	−0.0589441	−	0.0427962i
$21$	11449.8			1.23635
$22$	−4496.69	+	13847.1i	−0.422304	+	1.30044i
$23$		−	13760.4i		−	1.13096i	−0.824762	−	0.565480i	$-0.808691\pi$
$23$		−	13760.4i		−	1.13096i	0.824762	−	0.565480i	$-0.191309\pi$
$24$	18029.0	−	13112.3i	1.30418	−	0.948514i
$25$	−15542.1			−0.994694
$26$	−4415.58	−	1433.92i	−0.251228	−	0.0815837i
$27$		−	19062.7i		−	0.968487i
$28$	9887.92	−	13618.9i	0.450434	−	0.620392i
$29$	32409.0			1.32884			0.664419	−	0.747360i	$-0.268679\pi$
$29$	32409.0			1.32884			0.664419	+	0.747360i	$0.268679\pi$
$30$	−979.587	+	3016.53i	−0.0362810	+	0.111723i
$31$		−	28669.7i		−	0.962360i	−0.876622	−	0.481180i	$-0.840208\pi$
$31$		−	28669.7i		−	0.962360i	0.876622	−	0.481180i	$-0.159792\pi$
$32$	−26.6211	−	32768.0i	−0.000812411	−	1.00000i
$33$	79238.4			2.20493
$34$	−9066.54	−	2944.27i	−0.230677	−	0.0749101i
$35$			2394.37i			0.0558453i
$36$	−60428.4	−	43873.8i	−1.29519	−	0.940368i
$37$	50561.2			0.998189			0.499094	−	0.866548i	$-0.333666\pi$
$37$	50561.2			0.998189			0.499094	+	0.866548i	$0.333666\pi$
$38$	−2801.22	+	8626.05i	−0.0510502	+	0.157203i
$39$			25267.7i			0.425963i
$40$	2742.02	+	3770.20i	0.0428440	+	0.0589093i
$41$	−52955.8			−0.768355			−0.384177	−	0.923259i	$-0.625515\pi$
$41$	−52955.8			−0.768355			−0.384177	+	0.923259i	$0.625515\pi$
$42$	−87119.9	−	28291.3i	−1.17590	−	0.381861i
$43$			59950.8i			0.754032i	0.926207	+	0.377016i	$0.123050\pi$
$43$			59950.8i			0.754032i	−0.926207	+	0.377016i	$0.876950\pi$
$44$	68429.4	−	94249.4i	0.803313	−	1.10642i
$45$	10624.1			0.116588
$46$	−34000.5	+	104701.i	−0.349311	+	1.07566i
$47$			35763.0i			0.344462i	0.985057	+	0.172231i	$0.0550975\pi$
$47$			35763.0i			0.344462i	−0.985057	+	0.172231i	$0.944902\pi$
$48$	−169579.	+	55221.4i	−1.53337	+	0.499326i
$49$	48497.6			0.412223
$50$	118258.	+	38403.0i	0.946060	+	0.307224i
$51$			51882.4i			0.391119i
$52$	30054.4	+	21820.9i	0.213746	+	0.155190i
$53$	171930.			1.15484			0.577422	−	0.816446i	$-0.304059\pi$
$53$	171930.			1.15484			0.577422	+	0.816446i	$0.304059\pi$
$54$	−47102.1	+	145045.i	−0.299129	+	0.921134i
$55$			16570.2i			0.0995957i
$56$	−108887.	+	79191.8i	−0.620026	+	0.450937i
$57$	49361.7			0.266542
$58$	−246596.	−	80079.5i	−1.26387	−	0.410428i
$59$		−	134207.i		−	0.653459i	−0.945118	−	0.326729i	$-0.894053\pi$
$59$		−	134207.i		−	0.653459i	0.945118	−	0.326729i	$-0.105947\pi$
$60$	14907.1	−	20531.9i	0.0690142	−	0.0950549i
$61$	−139218.			−0.613348			−0.306674	−	0.951815i	$-0.599216\pi$
$61$	−139218.			−0.613348			−0.306674	+	0.951815i	$0.599216\pi$
$62$	−70839.9	+	218143.i	−0.297237	+	0.915307i
$63$			306832.i			1.22710i
$64$	−80763.9	+	249393.i	−0.308090	+	0.951357i
$65$	−5283.95			−0.0192406
$66$	−602914.	−	195790.i	−2.09712	−	0.681019i
$67$		−	150545.i		−	0.500544i	−0.968176	−	0.250272i	$-0.919480\pi$
$67$		−	150545.i		−	0.500544i	0.968176	−	0.250272i	$-0.0805200\pi$
$68$	61711.0	+	44805.0i	0.196262	+	0.142495i
$69$	599140.			1.82382
$70$	5916.24	−	18218.4i	0.0172485	−	0.0531149i
$71$		−	527493.i		−	1.47381i	−0.675996	−	0.736905i	$-0.736286\pi$
$71$		−	527493.i		−	1.47381i	0.675996	−	0.736905i	$-0.263714\pi$
$72$	351383.	+	483142.i	0.941419	+	1.29443i
$73$	−628763.			−1.61629			−0.808143	−	0.588986i	$-0.799527\pi$
$73$	−628763.			−1.61629			−0.808143	+	0.588986i	$0.799527\pi$
$74$	−384713.	−	124932.i	−0.949384	−	0.308303i
$75$		−	676717.i		−	1.60407i
$76$	42628.2	−	58712.8i	0.0971083	−	0.133749i
$77$	−478563.			−1.04825
$78$	62434.0	−	192258.i	0.131564	−	0.405137i
$79$			110212.i			0.223536i	0.993734	+	0.111768i	$0.0356513\pi$
$79$			110212.i			0.223536i	−0.993734	+	0.111768i	$0.964349\pi$
$80$	−11547.8	−	35462.1i	−0.0225544	−	0.0692620i
$81$	−20597.1			−0.0387571
$82$	402933.	+	130848.i	0.730787	+	0.237316i
$83$		−	1.04758e6i		−	1.83212i	−0.401036	−	0.916062i	$-0.631350\pi$
$83$		−	1.04758e6i		−	1.83212i	0.401036	−	0.916062i	$-0.368650\pi$
$84$	592977.	+	430529.i	1.00046	+	0.726381i
$85$	−10849.6			−0.0176667
$86$	148133.	−	456157.i	0.232892	−	0.717165i
$87$			1.41112e6i			2.14292i
$88$	−753550.	+	548047.i	−1.10577	+	0.804211i
$89$	887788.			1.25933			0.629664	−	0.776867i	$-0.283192\pi$
$89$	887788.			1.25933			0.629664	+	0.776867i	$0.283192\pi$
$90$	−80837.1	−	26251.0i	−0.110888	−	0.0360096i
$91$		−	152605.i		−	0.202509i
$92$	517410.	−	712641.i	0.664464	−	0.915182i
$93$	1.24830e6			1.55193
$94$	88366.9	−	272116.i	0.106391	−	0.327620i
$95$			10322.5i			0.0120396i
$96$	1.42675e6	−	1159.11i	1.61263	−	0.00131012i
$97$	1.57949e6			1.73062			0.865310	−	0.501237i	$-0.167121\pi$
$97$	1.57949e6			1.73062			0.865310	+	0.501237i	$0.167121\pi$
$98$	−369011.	−	119833.i	−0.392068	−	0.127320i
$99$			2.12344e6i			2.18843i
$100$	−804914.	−	584405.i	−0.804914	−	0.584405i
$101$	−1.92176e6			−1.86524			−0.932621	−	0.360858i	$-0.882484\pi$
$101$	−1.92176e6			−1.86524			−0.932621	+	0.360858i	$0.882484\pi$
$102$	128196.	−	394765.i	0.120802	−	0.371996i
$103$			919453.i			0.841430i	0.907193	+	0.420715i	$0.138221\pi$
$103$			919453.i			0.841430i	−0.907193	+	0.420715i	$0.861779\pi$
$104$	−174763.	−	240294.i	−0.155363	−	0.213620i
$105$	−104253.			−0.0900577
$106$	−1.30819e6	−	424821.i	−1.09838	−	0.356688i
$107$		−	1.75394e6i		−	1.43173i	−0.698236	−	0.715867i	$-0.746032\pi$
$107$		−	1.75394e6i		−	1.43173i	0.698236	−	0.715867i	$-0.253968\pi$
$108$	716786.	−	987245.i	0.569008	−	0.783707i
$109$	−2.07634e6			−1.60331			−0.801656	−	0.597785i	$-0.796048\pi$
$109$	−2.07634e6			−1.60331			−0.801656	+	0.597785i	$0.796048\pi$
$110$	40943.4	−	126081.i	0.0307614	−	0.0947262i
$111$			2.20148e6i			1.60971i
$112$	1.02418e6	−	333511.i	0.728989	−	0.237387i
$113$	864678.			0.599265			0.299633	−	0.954055i	$-0.403136\pi$
$113$	864678.			0.599265			0.299633	+	0.954055i	$0.403136\pi$
$114$	−375586.	−	121968.i	−0.253510	−	0.0823249i
$115$			125291.i			0.0823811i
$116$	1.67844e6	+	1.21863e6i	1.07531	+	0.780722i
$117$	−677126.			−0.422777
$118$	−331611.	+	1.02116e6i	−0.201829	+	0.621509i
$119$		−	313345.i		−	0.185944i
$120$	−164158.	+	119390.i	−0.0949988	+	0.0690914i
$121$	−1.54033e6			−0.869478
$122$	1.05929e6	+	343995.i	0.583359	+	0.189440i
$123$		−	2.30574e6i		−	1.23907i
$124$	1.07802e6	−	1.48478e6i	0.565408	−	0.778749i
$125$	283783.			0.145297
$126$	758152.	−	2.33464e6i	0.379005	−	1.16710i
$127$		−	1.05320e6i		−	0.514163i	−0.966390	−	0.257082i	$-0.917239\pi$
$127$		−	1.05320e6i		−	0.514163i	0.966390	−	0.257082i	$-0.0827609\pi$
$128$	1.23074e6	−	1.69803e6i	0.586865	−	0.809685i
$129$	−2.61031e6			−1.21597
$130$	40204.8	+	13056.1i	0.0182999	+	0.00594270i
$131$		−	1.12509e6i		−	0.500465i	−0.968186	−	0.250232i	$-0.919493\pi$
$131$		−	1.12509e6i		−	0.500465i	0.968186	−	0.250232i	$-0.0805070\pi$
$132$	4.10370e6	+	2.97948e6i	1.78424	+	1.29544i
$133$	−298121.			−0.126718
$134$	−371982.	+	1.14547e6i	−0.154599	+	0.476070i
$135$			173570.i			0.0705463i
$136$	−358841.	−	493396.i	−0.142654	−	0.196146i
$137$	1.07464e6			0.417927			0.208963	−	0.977923i	$-0.432991\pi$
$137$	1.07464e6			0.417927			0.208963	+	0.977923i	$0.432991\pi$
$138$	−4.55877e6	−	1.48041e6i	−1.73464	−	0.563308i
$139$			782104.i			0.291219i	0.989342	+	0.145610i	$0.0465144\pi$
$139$			782104.i			0.291219i	−0.989342	+	0.145610i	$0.953486\pi$
$140$	−90031.7	+	124003.i	−0.0328104	+	0.0451905i
$141$	−1.55716e6			−0.555488
$142$	−1.30338e6	+	4.01362e6i	−0.455205	+	1.40175i
$143$		−	1.05610e6i		−	0.361159i
$144$	−1.47983e6	−	4.54439e6i	−0.495591	−	1.52191i
$145$	−295092.			−0.0967950
$146$	4.78417e6	+	1.55361e6i	1.53726	+	0.499210i
$147$			2.11163e6i			0.664762i
$148$	2.61853e6	+	1.90118e6i	0.807742	+	0.586458i
$149$	2.10374e6			0.635965			0.317982	−	0.948097i	$-0.396995\pi$
$149$	2.10374e6			0.635965			0.317982	+	0.948097i	$0.396995\pi$
$150$	−1.67210e6	+	5.14904e6i	−0.495437	+	1.52564i
$151$		−	3.34842e6i		−	0.972545i	−0.873807	−	0.486272i	$-0.838356\pi$
$151$		−	3.34842e6i		−	0.972545i	0.873807	−	0.486272i	$-0.161644\pi$
$152$	−469425.	+	341407.i	−0.133671	+	0.0972169i
$153$	−1.39035e6			−0.388194
$154$	3.64131e6	+	1.18248e6i	0.997001	+	0.323766i
$155$			261044.i			0.0701000i
$156$	−950103.	+	1.30860e6i	−0.250263	+	0.344693i
$157$	−3.39697e6			−0.877794			−0.438897	−	0.898537i	$-0.644631\pi$
$157$	−3.39697e6			−0.877794			−0.438897	+	0.898537i	$0.644631\pi$
$158$	272322.	−	838585.i	0.0690418	−	0.212606i
$159$			7.48597e6i			1.86233i
$160$	242.391	+	298360.i	5.91775e−5	+	0.0728417i
$161$	−3.61852e6			−0.867069
$162$	156720.	+	50893.4i	0.0368621	+	0.0119706i
$163$		−	6.73032e6i		−	1.55408i	−0.629452	−	0.777039i	$-0.716721\pi$
$163$		−	6.73032e6i		−	1.55408i	0.629452	−	0.777039i	$-0.283279\pi$
$164$	−2.74254e6	−	1.99121e6i	−0.621759	−	0.451426i
$165$	−721483.			−0.160611
$166$	−2.58848e6	+	7.97092e6i	−0.565874	+	1.74255i
$167$			7.21479e6i			1.54908i	0.632524	+	0.774541i	$0.282019\pi$
$167$			7.21479e6i			1.54908i	−0.632524	+	0.774541i	$0.717981\pi$
$168$	−3.44808e6	−	4.74102e6i	−0.727194	−	0.999871i
$169$	−4.49004e6			−0.930229
$170$	82552.8	+	26808.2i	0.0168029	+	0.00545659i
$171$			1.32280e6i			0.264548i
$172$	−2.25424e6	+	3.10481e6i	−0.443011	+	0.610169i
$173$	1.40326e6			0.271019			0.135510	−	0.990776i	$-0.456733\pi$
$173$	1.40326e6			0.271019			0.135510	+	0.990776i	$0.456733\pi$
$174$	3.48674e6	−	1.07370e7i	0.661868	−	2.03815i
$175$			4.08705e6i			0.762598i
$176$	7.08782e6	−	2.30807e6i	1.30009	−	0.423360i
$177$	5.84348e6			1.05379
$178$	−6.75505e6	−	2.19363e6i	−1.19776	−	0.388959i
$179$			3.57496e6i			0.623322i	0.950193	+	0.311661i	$0.100885\pi$
$179$			3.57496e6i			0.623322i	−0.950193	+	0.311661i	$0.899115\pi$
$180$	550214.	+	399481.i	0.0943439	+	0.0684980i
$181$	858162.			0.144722			0.0723608	−	0.997379i	$-0.476947\pi$
$181$	858162.			0.144722			0.0723608	+	0.997379i	$0.476947\pi$
$182$	−377072.	+	1.16115e6i	−0.0625475	+	0.192608i
$183$		−	6.06170e6i		−	0.989101i
$184$	−5.69776e6	+	4.14391e6i	−0.914642	+	0.665207i
$185$	−460371.			−0.0727098
$186$	−9.49816e6	−	3.08443e6i	−1.47605	−	0.479332i
$187$		−	2.16851e6i		−	0.331616i
$188$	−1.34474e6	+	1.85214e6i	−0.202379	+	0.278741i
$189$	−5.01286e6			−0.742506
$190$	25505.8	−	78542.1i	0.00371858	−	0.0114510i
$191$		−	9.16860e6i		−	1.31584i	−0.753088	−	0.657920i	$-0.771436\pi$
$191$		−	9.16860e6i		−	1.31584i	0.753088	−	0.657920i	$-0.228564\pi$
$192$	−1.08588e7	−	3.51653e6i	−1.53418	−	0.496834i
$193$	1.35878e7			1.89007			0.945037	−	0.326964i	$-0.106026\pi$
$193$	1.35878e7			1.89007			0.945037	+	0.326964i	$0.106026\pi$
$194$	−1.20181e7	−	3.90276e6i	−1.64600	−	0.534524i
$195$		−	230068.i		−	0.0310279i
$196$	2.51166e6	+	1.82358e6i	0.333574	+	0.242190i
$197$	1.17057e7			1.53108			0.765541	−	0.643387i	$-0.222471\pi$
$197$	1.17057e7			1.53108			0.765541	+	0.643387i	$0.222471\pi$
$198$	5.24680e6	−	1.61569e7i	0.675925	−	2.08143i
$199$			7.43521e6i			0.943483i	0.881737	+	0.471742i	$0.156374\pi$
$199$			7.43521e6i			0.943483i	−0.881737	+	0.471742i	$0.843626\pi$
$200$	4.68047e6	+	6.43551e6i	0.585059	+	0.804439i
$201$	6.55487e6			0.807190
$202$	1.46224e7	+	4.74848e6i	1.77404	+	0.576103i
$203$		−	8.52249e6i		−	1.01878i
$204$	−1.95085e6	+	2.68695e6i	−0.229791	+	0.316497i
$205$	482174.			0.0559683
$206$	2.27188e6	−	6.99598e6i	0.259886	−	0.800290i
$207$			1.60558e7i			1.81017i
$208$	736001.	+	2.26018e6i	0.0817878	+	0.251161i
$209$	−2.06315e6			−0.225992
$210$	793246.	+	257599.i	0.0856544	+	0.0278154i
$211$			1.07306e7i			1.14230i	0.820847	+	0.571148i	$0.193502\pi$
$211$			1.07306e7i			1.14230i	−0.820847	+	0.571148i	$0.806498\pi$
$212$	8.90412e6	+	6.46480e6i	0.934509	+	0.678496i
$213$	2.29675e7			2.37671
$214$	−4.33380e6	+	1.33454e7i	−0.442209	+	1.36173i
$215$		−	545866.i		−	0.0549250i
$216$	−7.89330e6	+	5.74070e6i	−0.783245	+	0.569644i
$217$	−7.53916e6			−0.737809
$218$	1.57985e7	+	5.13042e6i	1.52492	+	0.495203i
$219$		−	2.73769e7i		−	2.60647i
$220$	−623065.	+	858161.i	−0.0585147	+	0.0805936i
$221$	691498.			0.0640640
$222$	5.43964e6	−	1.67508e7i	0.497178	−	1.53100i
$223$			360785.i			0.0325338i	0.999868	+	0.0162669i	$0.00517814\pi$
$223$			360785.i			0.0325338i	−0.999868	+	0.0162669i	$0.994822\pi$
$224$	−8.61688e6	+	7000.46i	−0.766666	+	0.000622848i
$225$	1.81347e7			1.59207
$226$	−6.57921e6	−	2.13653e6i	−0.569965	−	0.185091i
$227$			919317.i			0.0785937i	0.999228	+	0.0392968i	$0.0125118\pi$
$227$			919317.i			0.0785937i	−0.999228	+	0.0392968i	$0.987488\pi$
$228$	2.55641e6	+	1.85607e6i	0.215688	+	0.156599i
$229$	−3.21590e6			−0.267791			−0.133895	−	0.990995i	$-0.542749\pi$
$229$	−3.21590e6			−0.267791			−0.133895	+	0.990995i	$0.542749\pi$
$230$	309582.	−	953324.i	0.0254444	−	0.0783532i
$231$		−	2.08371e7i		−	1.69044i
$232$	−9.75992e6	−	1.34196e7i	−0.781596	−	1.07467i
$233$	−5.17769e6			−0.409325			−0.204662	−	0.978833i	$-0.565610\pi$
$233$	−5.17769e6			−0.409325			−0.204662	+	0.978833i	$0.565610\pi$
$234$	5.15215e6	+	1.67311e6i	0.402106	+	0.130580i
$235$		−	325630.i		−	0.0250912i
$236$	5.04636e6	−	6.95047e6i	0.383922	−	0.528784i
$237$	−4.79872e6			−0.360480
$238$	−774244.	+	2.38420e6i	−0.0574311	+	0.176852i
$239$		−	2.09637e6i		−	0.153559i	−0.997048	−	0.0767793i	$-0.975536\pi$
$239$		−	2.09637e6i		−	0.153559i	0.997048	−	0.0767793i	$-0.0244637\pi$
$240$	1.54405e6	−	502803.i	0.111694	−	0.0363718i
$241$	−1.39934e7			−0.999708			−0.499854	−	0.866110i	$-0.666613\pi$
$241$	−1.39934e7			−0.999708			−0.499854	+	0.866110i	$0.666613\pi$
$242$	1.17202e7	+	3.80601e6i	0.826967	+	0.268549i
$243$		−	1.47935e7i		−	1.03099i
$244$	−7.21002e6	−	5.23481e6i	−0.496326	−	0.360356i
$245$	−441581.			−0.0300270
$246$	−5.69726e6	+	1.75441e7i	−0.382702	+	1.17849i
$247$		−	657902.i		−	0.0436587i
$248$	−1.18712e7	+	8.63381e6i	−0.778290	+	0.566040i
$249$	4.56128e7			2.95453
$250$	−2.15927e6	−	701200.i	−0.138193	−	0.0448768i
$251$		−	2.86712e7i		−	1.81311i	−0.422086	−	0.906556i	$-0.638702\pi$
$251$		−	2.86712e7i		−	1.81311i	0.422086	−	0.906556i	$-0.361298\pi$
$252$	−1.15373e7	+	1.58906e7i	−0.720948	+	0.992978i
$253$	−2.50420e7			−1.54635
$254$	−2.60236e6	+	8.01367e6i	−0.158806	+	0.489024i
$255$		−	472401.i		−	0.0284898i
$256$	−1.35602e7	+	9.87903e6i	−0.808252	+	0.588836i
$257$	−296498.			−0.0174672			−0.00873358	−	0.999962i	$-0.502780\pi$
$257$	−296498.			−0.0174672			−0.00873358	+	0.999962i	$0.502780\pi$
$258$	1.98615e7	+	6.44983e6i	1.15652	+	0.375568i
$259$		−	1.32959e7i		−	0.765278i
$260$	−273652.	−	198684.i	−0.0155697	−	0.0113043i
$261$	−3.78153e7			−2.12689
$262$	−2.77999e6	+	8.56065e6i	−0.154575	+	0.475995i
$263$			350290.i			0.0192558i	0.999954	+	0.00962788i	$0.00306470\pi$
$263$			350290.i			0.0192558i	−0.999954	+	0.00962788i	$0.996935\pi$
$264$	−2.38625e7	−	3.28103e7i	−1.29689	−	1.78319i
$265$	−1.56546e6			−0.0841208
$266$	2.26836e6	+	736628.i	0.120522	+	0.0391384i
$267$			3.86551e7i			2.03083i
$268$	5.66071e6	−	7.79662e6i	0.294081	−	0.405044i
$269$	−2.69210e7			−1.38304			−0.691518	−	0.722359i	$-0.743058\pi$
$269$	−2.69210e7			−1.38304			−0.691518	+	0.722359i	$0.743058\pi$
$270$	428875.	−	1.32067e6i	0.0217891	−	0.0670971i
$271$			2.21766e7i			1.11426i	0.830425	+	0.557131i	$0.188098\pi$
$271$			2.21766e7i			1.11426i	−0.830425	+	0.557131i	$0.811902\pi$
$272$	1.51124e6	+	4.64084e6i	0.0750975	+	0.230616i
$273$	6.64457e6			0.326572
$274$	−8.17676e6	−	2.65532e6i	−0.397493	−	0.129082i
$275$			2.82845e7i			1.36003i
$276$	3.10290e7	+	2.25285e7i	1.47585	+	1.07153i
$277$	2.54382e7			1.19687			0.598436	−	0.801171i	$-0.295789\pi$
$277$	2.54382e7			1.19687			0.598436	+	0.801171i	$0.295789\pi$
$278$	1.93250e6	−	5.95092e6i	0.0899468	−	0.276981i
$279$			3.34521e7i			1.54032i
$280$	991436.	−	721059.i	0.0451638	−	0.0328471i
$281$	−1.65477e7			−0.745793			−0.372897	−	0.927873i	$-0.621635\pi$
$281$	−1.65477e7			−0.745793			−0.372897	+	0.927873i	$0.621635\pi$
$282$	1.18482e7	+	3.84758e6i	0.528328	+	0.171569i
$283$			1.73629e7i			0.766062i	0.923736	+	0.383031i	$0.125120\pi$
$283$			1.73629e7i			0.766062i	−0.923736	+	0.383031i	$0.874880\pi$
$284$	1.98345e7	−	2.73185e7i	0.865897	−	1.19262i
$285$	−449449.			−0.0194154
$286$	−2.60953e6	+	8.03574e6i	−0.111549	+	0.343501i
$287$			1.39256e7i			0.589072i
$288$	31061.8	+	3.82341e7i	0.00130032	+	1.60056i
$289$	1.41986e6			0.0588235
$290$	2.24531e6	+	729142.i	0.0920623	+	0.0298963i
$291$			6.87725e7i			2.79084i
$292$	−3.25632e7	−	2.36424e7i	−1.30791	−	0.949604i
$293$	−3.03577e7			−1.20689			−0.603443	−	0.797406i	$-0.706205\pi$
$293$	−3.03577e7			−1.20689			−0.603443	+	0.797406i	$0.706205\pi$
$294$	5.21763e6	−	1.60671e7i	0.205320	−	0.632259i
$295$			1.22198e6i			0.0475991i
$296$	−1.52264e7	−	2.09359e7i	−0.587114	−	0.807265i
$297$	−3.46915e7			−1.32420
$298$	−1.60070e7	−	5.19813e6i	−0.604870	−	0.196426i
$299$		−	7.98545e6i		−	0.298735i
$300$	2.54455e7	−	3.50467e7i	0.942427	−	1.29803i
$301$	1.57651e7			0.578091
$302$	−8.27362e6	+	2.54777e7i	−0.300383	+	0.924994i
$303$		−	8.36752e7i		−	3.00794i
$304$	4.41537e6	−	1.43781e6i	0.157162	−	0.0511779i
$305$	1.26761e6			0.0446774
$306$	1.05789e7	+	3.43541e6i	0.369214	+	0.119899i
$307$			3.49708e7i			1.20862i	0.796748	+	0.604311i	$0.206552\pi$
$307$			3.49708e7i			1.20862i	−0.796748	+	0.604311i	$0.793448\pi$
$308$	−2.47844e7	−	1.79946e7i	−0.848256	−	0.615873i
$309$	−4.00338e7			−1.35691
$310$	645013.	−	1.98624e6i	0.0216513	−	0.0666726i
$311$			2.46184e7i			0.818425i	0.912439	+	0.409212i	$0.134197\pi$
$311$			2.46184e7i			0.818425i	−0.912439	+	0.409212i	$0.865803\pi$
$312$	1.04626e7	−	7.60932e6i	0.344490	−	0.250543i
$313$	1.96963e6			0.0642321			0.0321161	−	0.999484i	$-0.489775\pi$
$313$	1.96963e6			0.0642321			0.0321161	+	0.999484i	$0.489775\pi$
$314$	2.58470e7	+	8.39357e6i	0.834876	+	0.271118i
$315$		−	2.79378e6i		−	0.0893841i
$316$	−4.14412e6	+	5.70779e6i	−0.131332	+	0.180887i
$317$	2.71893e7			0.853534			0.426767	−	0.904362i	$-0.359652\pi$
$317$	2.71893e7			0.853534			0.426767	+	0.904362i	$0.359652\pi$
$318$	1.84971e7	−	5.69597e7i	0.575204	−	1.77128i
$319$		−	5.89800e7i		−	1.81691i
$320$	735373.	−	2.27077e6i	0.0224418	−	0.0692985i
$321$	7.63680e7			2.30885
$322$	2.75328e7	+	8.94100e6i	0.824675	+	0.267805i
$323$		−	1.35087e6i		−	0.0400874i
$324$	−1.06671e6	−	774481.i	−0.0313626	−	0.0227707i
$325$	−9.01941e6			−0.262741
$326$	−1.66300e7	+	5.12100e7i	−0.479997	+	1.47809i
$327$		−	9.04056e7i		−	2.58554i
$328$	1.59475e7	+	2.19274e7i	0.451931	+	0.621392i
$329$	9.40448e6			0.264087
$330$	5.48966e6	+	1.78271e6i	0.152758	+	0.0496066i
$331$			1.51602e6i			0.0418044i	0.999782	+	0.0209022i	$0.00665386\pi$
$331$			1.51602e6i			0.0418044i	−0.999782	+	0.0209022i	$0.993346\pi$
$332$	3.93907e7	−	5.42537e7i	1.07641	−	1.48257i
$333$	−5.89955e7			−1.59767
$334$	1.78270e7	−	5.48963e7i	0.478453	−	1.47334i
$335$			1.37075e6i			0.0364605i
$336$	1.45214e7	+	4.45936e7i	0.382816	+	1.17559i
$337$	−1.32399e7			−0.345934			−0.172967	−	0.984928i	$-0.555335\pi$
$337$	−1.32399e7			−0.345934			−0.172967	+	0.984928i	$0.555335\pi$
$338$	3.41640e7	+	1.10944e7i	0.884747	+	0.287313i
$339$			3.76489e7i			0.966391i
$340$	−561892.	−	407960.i	−0.0142961	−	0.0103796i
$341$	−5.21748e7			−1.31582
$342$	3.26850e6	−	1.00650e7i	0.0817091	−	0.251614i
$343$		−	4.36910e7i		−	1.08270i
$344$	2.48238e7	−	1.80541e7i	0.609809	−	0.443506i
$345$	−5.45530e6			−0.132850
$346$	−1.06772e7	−	3.46732e6i	−0.257768	−	0.0837076i
$347$			3.66538e7i			0.877265i	0.898666	+	0.438633i	$0.144537\pi$
$347$			3.66538e7i			0.877265i	−0.898666	+	0.438633i	$0.855463\pi$
$348$	−5.30601e7	+	7.30809e7i	−1.25901	+	1.73407i
$349$	−1.61135e7			−0.379066			−0.189533	−	0.981874i	$-0.560697\pi$
$349$	−1.61135e7			−0.379066			−0.189533	+	0.981874i	$0.560697\pi$
$350$	1.00987e7	−	3.10978e7i	0.235538	−	0.725312i
$351$		−	1.10625e7i		−	0.255819i
$352$	−5.96332e7	+	48446.7i	−1.36729	+	0.00111080i
$353$	−3.40346e7			−0.773743			−0.386871	−	0.922134i	$-0.626444\pi$
$353$	−3.40346e7			−0.773743			−0.386871	+	0.922134i	$0.626444\pi$
$354$	−4.44622e7	−	1.44387e7i	−1.00226	−	0.325475i
$355$			4.80294e6i			0.107355i
$356$	4.59779e7	+	3.33821e7i	1.01906	+	0.739884i
$357$	1.36433e7			0.299858
$358$	8.83337e6	−	2.72014e7i	0.192521	−	0.592846i
$359$			6.54554e7i			1.41469i	0.706868	+	0.707346i	$0.250108\pi$
$359$			6.54554e7i			1.41469i	−0.706868	+	0.707346i	$0.749892\pi$
$360$	−3.19942e6	−	4.39911e6i	−0.0685747	−	0.0942882i
$361$	4.57606e7			0.972681
$362$	−6.52963e6	−	2.12043e6i	−0.137646	−	0.0446991i
$363$		−	6.70675e7i		−	1.40214i
$364$	5.73817e6	−	7.90331e6i	0.118979	−	0.163872i
$365$	5.72503e6			0.117733
$366$	−1.49778e7	+	4.61226e7i	−0.305496	+	0.940741i
$367$		−	3.69957e7i		−	0.748434i	−0.927341	−	0.374217i	$-0.877912\pi$
$367$		−	3.69957e7i		−	0.748434i	0.927341	−	0.374217i	$-0.122088\pi$
$368$	5.35926e7	−	1.74518e7i	1.07538	−	0.350185i
$369$	6.17894e7			1.22980
$370$	3.50290e6	+	1.13753e6i	0.0691548	+	0.0224573i
$371$		−	4.52117e7i		−	0.885380i
$372$	6.46488e7	+	4.69380e7i	1.25583	+	0.911792i
$373$	−4.33721e7			−0.835765			−0.417882	−	0.908501i	$-0.637228\pi$
$373$	−4.33721e7			−0.835765			−0.417882	+	0.908501i	$0.637228\pi$
$374$	−5.35816e6	+	1.64998e7i	−0.102424	+	0.315402i
$375$			1.23562e7i			0.234310i
$376$	1.48084e7	−	1.07700e7i	0.278577	−	0.202605i
$377$	1.88077e7			0.351003
$378$	3.81421e7	+	1.23863e7i	0.706203	+	0.229332i
$379$			7.78719e7i			1.43042i	0.698911	+	0.715209i	$0.253669\pi$
$379$			7.78719e7i			1.43042i	−0.698911	+	0.715209i	$0.746331\pi$
$380$	−388139.	+	534593.i	−0.00707354	+	0.00974255i
$381$	4.58574e7			0.829153
$382$	−2.26547e7	+	6.97626e7i	−0.406414	+	1.25150i
$383$			8.30546e7i			1.47832i	0.673532	+	0.739158i	$0.264776\pi$
$383$			8.30546e7i			1.47832i	−0.673532	+	0.739158i	$0.735224\pi$
$384$	7.39339e7	+	5.35877e7i	1.30572	+	0.946394i
$385$	4.35742e6			0.0763567
$386$	−1.03388e8	−	3.35742e7i	−1.79766	−	0.583773i
$387$		−	6.99513e7i		−	1.20688i
$388$	8.18007e7	+	5.93911e7i	1.40043	+	1.01678i
$389$	4.69089e7			0.796906			0.398453	−	0.917189i	$-0.369547\pi$
$389$	4.69089e7			0.796906			0.398453	+	0.917189i	$0.369547\pi$
$390$	−568476.	+	1.75056e6i	−0.00958336	+	0.0295109i
$391$		−	1.63966e7i		−	0.274298i
$392$	−1.46050e7	−	2.00814e7i	−0.242461	−	0.333377i
$393$	4.89875e7			0.807063
$394$	−8.90669e7	−	2.89236e7i	−1.45622	−	0.472894i
$395$		−	1.00350e6i		−	0.0162827i
$396$	−7.98442e7	+	1.09971e8i	−1.28575	+	1.77090i
$397$	9.54296e7			1.52515			0.762573	−	0.646902i	$-0.223936\pi$
$397$	9.54296e7			1.52515			0.762573	+	0.646902i	$0.223936\pi$
$398$	1.83717e7	−	5.65734e7i	0.291407	−	0.897353i
$399$		−	1.29805e7i		−	0.204349i
$400$	−1.97115e7	−	6.05319e7i	−0.307992	−	0.945810i
$401$	−7.26890e7			−1.12729			−0.563645	−	0.826017i	$-0.690601\pi$
$401$	−7.26890e7			−1.12729			−0.563645	+	0.826017i	$0.690601\pi$
$402$	−4.98750e7	−	1.61964e7i	−0.767724	−	0.249311i
$403$		−	1.66376e7i		−	0.254200i
$404$	−9.95266e7	−	7.22609e7i	−1.50937	−	1.09587i
$405$	187541.			0.00282314
$406$	−2.10582e7	+	6.48464e7i	−0.314662	+	0.968964i
$407$		−	9.20144e7i		−	1.36481i
$408$	2.14829e7	−	1.56243e7i	0.316310	−	0.230048i
$409$	3.97207e7			0.580560			0.290280	−	0.956942i	$-0.406252\pi$
$409$	3.97207e7			0.580560			0.290280	+	0.956942i	$0.406252\pi$
$410$	−3.66879e6	−	1.19140e6i	−0.0532319	−	0.0172865i
$411$			4.67907e7i			0.673960i
$412$	−3.45727e7	+	4.76178e7i	−0.494359	+	0.680892i
$413$	−3.52919e7			−0.500985
$414$	3.96722e7	−	1.22166e8i	0.559095	−	1.72167i
$415$			9.53849e6i			0.133455i
$416$	−15448.8	−	1.90160e7i	−0.000214592	−	0.264143i
$417$	−3.40535e7			−0.469628
$418$	1.56982e7	+	5.09784e6i	0.214942	+	0.0698003i
$419$			7.87941e7i			1.07115i	0.844486	+	0.535577i	$0.179906\pi$
$419$			7.87941e7i			1.07115i	−0.844486	+	0.535577i	$0.820094\pi$
$420$	−5.39919e6	−	3.92006e6i	−0.0728754	−	0.0529109i
$421$	−8.24857e7			−1.10543			−0.552717	−	0.833369i	$-0.686409\pi$
$421$	−8.24857e7			−1.10543			−0.552717	+	0.833369i	$0.686409\pi$
$422$	2.65143e7	−	8.16479e7i	0.352812	−	1.08644i
$423$		−	4.17287e7i		−	0.551333i
$424$	−5.17763e7	−	7.11909e7i	−0.679255	−	0.933957i
$425$	−1.85196e7			−0.241249
$426$	−1.74757e8	−	5.67505e7i	−2.26050	−	0.734075i
$427$			3.66098e7i			0.470233i
$428$	6.59505e7	−	9.08352e7i	0.841176	−	1.15857i
$429$	4.59838e7			0.582415
$430$	−1.34878e6	+	4.15341e6i	−0.0169643	+	0.0522396i
$431$			5.65989e7i			0.706930i	0.935448	+	0.353465i	$0.114997\pi$
$431$			5.65989e7i			0.706930i	−0.935448	+	0.353465i	$0.885003\pi$
$432$	7.42437e7	−	2.41766e7i	0.920891	−	0.299877i
$433$	8.93042e7			1.10004			0.550020	−	0.835152i	$-0.314620\pi$
$433$	8.93042e7			1.10004			0.550020	+	0.835152i	$0.314620\pi$
$434$	5.73644e7	+	1.86285e7i	0.701735	+	0.227881i
$435$		−	1.28486e7i		−	0.156094i
$436$	−1.07532e8	−	7.80732e7i	−1.29741	−	0.941982i
$437$	−1.56000e7			−0.186930
$438$	−6.76456e7	+	2.08307e8i	−0.805040	+	2.47903i
$439$			3.65018e7i			0.431440i	0.976455	+	0.215720i	$0.0692098\pi$
$439$			3.65018e7i			0.431440i	−0.976455	+	0.215720i	$0.930790\pi$
$440$	6.86124e6	−	4.99009e6i	0.0805461	−	0.0585802i
$441$	−5.65876e7			−0.659789
$442$	−5.26151e6	−	1.70862e6i	−0.0609317	−	0.0197870i
$443$		−	1.38784e8i		−	1.59635i	−0.602427	−	0.798174i	$-0.705799\pi$
$443$		−	1.38784e8i		−	1.59635i	0.602427	−	0.798174i	$-0.294201\pi$
$444$	−8.27789e7	+	1.14013e8i	−0.945738	+	1.30259i
$445$	−8.08350e6			−0.0917317
$446$	891464.	−	2.74516e6i	0.0100485	−	0.0309431i
$447$			9.15987e7i			1.02557i
$448$	6.55819e7	+	2.12382e7i	0.729374	+	0.236202i
$449$	9.74112e7			1.07614			0.538072	−	0.842899i	$-0.319153\pi$
$449$	9.74112e7			1.07614			0.538072	+	0.842899i	$0.319153\pi$
$450$	−1.37984e8	−	4.48090e7i	−1.51423	−	0.491731i
$451$			9.63722e7i			1.05056i
$452$	4.47811e7	+	3.25131e7i	0.484930	+	0.352082i
$453$	1.45793e8			1.56835
$454$	2.27154e6	−	6.99495e6i	0.0242746	−	0.0747510i
$455$			1.38950e6i			0.0147511i
$456$	−1.48652e7	−	2.04392e7i	−0.156775	−	0.215561i
$457$	1.54098e8			1.61454			0.807272	−	0.590180i	$-0.200943\pi$
$457$	1.54098e8			1.61454			0.807272	+	0.590180i	$0.200943\pi$
$458$	2.44693e7	+	7.94616e6i	0.254698	+	0.0827106i
$459$		−	2.27147e7i		−	0.234893i
$460$	−4.71113e6	+	6.48875e6i	−0.0484007	+	0.0666634i
$461$	−1.71026e8			−1.74566			−0.872831	−	0.488022i	$-0.837718\pi$
$461$	−1.71026e8			−1.74566			−0.872831	+	0.488022i	$0.837718\pi$
$462$	−5.14863e7	+	1.58546e8i	−0.522114	+	1.60779i
$463$			5.67174e7i			0.571444i	0.958313	+	0.285722i	$0.0922333\pi$
$463$			5.67174e7i			0.571444i	−0.958313	+	0.285722i	$0.907767\pi$
$464$	4.11033e7	+	1.26224e8i	0.411455	+	1.26353i
$465$	−1.13661e7			−0.113045
$466$	3.93963e7	+	1.27935e7i	0.389311	+	0.126425i
$467$			1.02160e8i			1.00307i	0.865137	+	0.501535i	$0.167231\pi$
$467$			1.02160e8i			1.00307i	−0.865137	+	0.501535i	$0.832769\pi$
$468$	−3.50679e7	−	2.54609e7i	−0.342115	−	0.248391i
$469$	−3.95883e7			−0.383750
$470$	−804600.	+	2.47767e6i	−0.00774973	+	0.0238644i
$471$		−	1.47907e8i		−	1.41555i
$472$	−5.55710e7	+	4.04161e7i	−0.528472	+	0.384351i
$473$	1.09102e8			1.03098
$474$	3.65128e7	+	1.18572e7i	0.342855	+	0.111339i
$475$			1.76199e7i			0.164407i
$476$	1.17822e7	−	1.62279e7i	0.109246	−	0.150467i
$477$	−2.00610e8			−1.84840
$478$	−5.17992e6	+	1.59510e7i	−0.0474285	+	0.146051i
$479$			1.66044e8i			1.51083i	0.655246	+	0.755416i	$0.272565\pi$
$479$			1.66044e8i			1.51083i	−0.655246	+	0.755416i	$0.727435\pi$
$480$	−1.29909e7	+	10553.9i	−0.117467	+	9.54312e-5i
$481$	2.93418e7			0.263664
$482$	1.06474e8	+	3.45764e7i	0.950829	+	0.308772i
$483$		−	1.57554e8i		−	1.39826i
$484$	−7.97728e7	−	5.79187e7i	−0.703589	−	0.510838i
$485$	−1.43816e7			−0.126061
$486$	−3.65534e7	+	1.12562e8i	−0.318433	+	0.980579i
$487$		−	1.62480e8i		−	1.40673i	−0.710827	−	0.703367i	$-0.751679\pi$
$487$		−	1.62480e8i		−	1.40673i	0.710827	−	0.703367i	$-0.248321\pi$
$488$	4.19253e7	+	5.76461e7i	0.360759	+	0.496033i
$489$	2.93044e8			2.50615
$490$	3.35993e6	+	1.09110e6i	0.0285589	+	0.00927423i
$491$		−	1.67898e8i		−	1.41841i	−0.705004	−	0.709203i	$-0.749055\pi$
$491$		−	1.67898e8i		−	1.41841i	0.705004	−	0.709203i	$-0.250945\pi$
$492$	8.66993e7	−	1.19413e8i	0.727981	−	1.00266i
$493$	3.86179e7			0.322291
$494$	−1.62561e6	+	5.00588e6i	−0.0134845	+	0.0415241i
$495$		−	1.93343e7i		−	0.159409i
$496$	1.11660e8	−	3.63607e7i	0.915065	−	0.297980i
$497$	−1.38713e8			−1.12992
$498$	−3.47061e8	−	1.12705e8i	−2.81008	−	0.912544i
$499$		−	2.38335e7i		−	0.191816i	−0.995390	−	0.0959082i	$-0.969424\pi$
$499$		−	2.38335e7i		−	0.191816i	0.995390	−	0.0959082i	$-0.0305755\pi$
$500$	1.46969e7	+	1.06707e7i	0.117576	+	0.0853653i
$501$	−3.14139e8			−2.49809
$502$	−7.08436e7	+	2.18155e8i	−0.560002	+	1.72446i
$503$			7.21900e7i			0.567249i	0.958935	+	0.283624i	$0.0915368\pi$
$503$			7.21900e7i			0.567249i	−0.958935	+	0.283624i	$0.908463\pi$
$504$	1.27050e8	−	9.24020e7i	0.992392	−	0.721755i
$505$	1.74980e7			0.135867
$506$	1.90541e8	+	6.18763e7i	1.47074	+	0.477609i
$507$		−	1.95500e8i		−	1.50011i
$508$	3.96019e7	−	5.45446e7i	0.302082	−	0.416065i
$509$	−1.49391e8			−1.13285			−0.566423	−	0.824115i	$-0.691673\pi$
$509$	−1.49391e8			−1.13285			−0.566423	+	0.824115i	$0.691673\pi$
$510$	−1.16725e6	+	3.59443e6i	−0.00879944	+	0.0270969i
$511$			1.65344e8i			1.23915i
$512$	1.27588e8	−	4.16622e7i	0.950604	−	0.310407i
$513$	−2.16111e7			−0.160076
$514$	2.25601e6	+	732617.i	0.0166131	+	0.00539495i
$515$		−	8.37182e6i		−	0.0612912i
$516$	−1.35186e8	−	9.81516e7i	−0.983975	−	0.714411i
$517$	6.50838e7			0.470979
$518$	−3.28529e7	+	1.01167e8i	−0.236365	+	0.727861i
$519$			6.10993e7i			0.437053i
$520$	1.59125e6	+	2.18793e6i	0.0113169	+	0.0155605i
$521$	9.17303e7			0.648634			0.324317	−	0.945948i	$-0.394866\pi$
$521$	9.17303e7			0.648634			0.324317	+	0.945948i	$0.394866\pi$
$522$	2.87731e8	+	9.34377e7i	2.02290	+	0.656917i
$523$		−	4.60766e7i		−	0.322089i	−0.986947	−	0.161044i	$-0.948514\pi$
$523$		−	4.60766e7i		−	0.322089i	0.986947	−	0.161044i	$-0.0514862\pi$
$524$	4.23050e7	−	5.82677e7i	0.294034	−	0.404980i
$525$	−1.77954e8			−1.22979
$526$	865532.	−	2.66531e6i	0.00594738	−	0.0183143i
$527$		−	3.41621e7i		−	0.233407i
$528$	1.00495e8	+	3.08610e8i	0.682722	+	2.09657i
$529$	−4.13124e7			−0.279070
$530$	1.19113e7	+	3.86809e6i	0.0800079	+	0.0259818i
$531$			1.56594e8i			1.04590i
$532$	−1.54395e7	−	1.12098e7i	−0.102541	−	0.0744497i
$533$	−3.07314e7			−0.202955
$534$	9.55128e7	−	2.94121e8i	0.627246	−	1.93153i
$535$			1.59700e7i			0.104290i
$536$	−6.23362e7	+	4.53363e7i	−0.404805	+	0.294410i
$537$	−1.55657e8			−1.00519
$538$	2.04838e8	+	6.65190e7i	1.31542	+	0.427168i
$539$		−	8.82589e7i		−	0.563628i
$540$	−6.52649e6	+	8.98909e6i	−0.0414475	+	0.0570866i
$541$	2.38822e8			1.50828			0.754140	−	0.656714i	$-0.228054\pi$
$541$	2.38822e8			1.50828			0.754140	+	0.656714i	$0.228054\pi$
$542$	5.47962e7	−	1.68739e8i	0.344154	−	1.05978i
$543$			3.73652e7i			0.233382i
$544$	−31721.1	−	3.90456e7i	−0.000197039	−	0.242536i
$545$	1.89055e7			0.116788
$546$	−5.05575e7	−	1.64181e7i	−0.310605	−	0.100866i
$547$		−	1.98215e8i		−	1.21108i	−0.795813	−	0.605542i	$-0.792956\pi$
$547$		−	1.98215e8i		−	1.21108i	0.795813	−	0.605542i	$-0.207044\pi$
$548$	5.56547e7	+	4.04079e7i	0.338190	+	0.245541i
$549$	1.62442e8			0.981703
$550$	6.98881e7	−	2.15212e8i	0.420063	−	1.29354i
$551$		−	3.67417e7i		−	0.219636i
$552$	−1.80430e8	−	2.48086e8i	−1.07273	−	1.47498i
$553$	2.89820e7			0.171377
$554$	−1.93556e8	−	6.28553e7i	−1.13835	−	0.369669i
$555$		−	2.00450e7i		−	0.117254i
$556$	−2.94082e7	+	4.05047e7i	−0.171098	+	0.235657i
$557$	−1.81523e8			−1.05043			−0.525213	−	0.850971i	$-0.676014\pi$
$557$	−1.81523e8			−1.05043			−0.525213	+	0.850971i	$0.676014\pi$
$558$	8.26568e7	−	2.54532e8i	0.475747	−	1.46501i
$559$			3.47908e7i			0.199172i
$560$	−9.32536e6	+	3.03669e6i	−0.0531008	+	0.0172917i
$561$	9.44187e7			0.534773
$562$	1.25909e8	+	4.08877e7i	0.709329	+	0.230348i
$563$		−	4.87909e7i		−	0.273409i	−0.990612	−	0.136705i	$-0.956349\pi$
$563$		−	4.87909e7i		−	0.273409i	0.990612	−	0.136705i	$-0.0436511\pi$
$564$	−8.06440e7	−	5.85513e7i	−0.449505	−	0.326362i
$565$	−7.87309e6			−0.0436515
$566$	4.29021e7	−	1.32112e8i	0.236608	−	0.728607i
$567$			5.41635e6i			0.0297138i
$568$	−2.18419e8	+	1.58853e8i	−1.19192	+	0.866865i
$569$	1.01654e8			0.551806			0.275903	−	0.961186i	$-0.411023\pi$
$569$	1.01654e8			0.551806			0.275903	+	0.961186i	$0.411023\pi$
$570$	3.41980e6	+	1.11054e6i	0.0184661	+	0.00599669i
$571$			1.76389e7i			0.0947463i	0.998877	+	0.0473732i	$0.0150850\pi$
$571$			1.76389e7i			0.0947463i	−0.998877	+	0.0473732i	$0.984915\pi$
$572$	3.97110e7	−	5.46949e7i	0.212189	−	0.292253i
$573$	3.99209e8			2.12196
$574$	3.44088e7	−	1.05958e8i	0.181942	−	0.560270i
$575$			2.13865e8i			1.12496i
$576$	9.42362e7	−	2.90994e8i	0.493117	−	1.52271i
$577$	9.31440e7			0.484872			0.242436	−	0.970167i	$-0.422054\pi$
$577$	9.31440e7			0.484872			0.242436	+	0.970167i	$0.422054\pi$
$578$	−1.08035e7	−	3.50832e6i	−0.0559475	−	0.0181684i
$579$			5.91627e8i			3.04798i
$580$	−1.52826e7	−	1.10959e7i	−0.0783272	−	0.0568692i
$581$	−2.75480e8			−1.40463
$582$	1.69930e8	−	5.23280e8i	0.861987	−	2.65439i
$583$		−	3.12888e8i		−	1.57900i
$584$	1.89351e8	+	2.60352e8i	0.950667	+	1.30714i
$585$	6.16538e6			0.0307959
$586$	2.30988e8	+	7.50109e7i	1.14788	+	0.372762i
$587$		−	1.79888e8i		−	0.889379i	−0.895685	−	0.444689i	$-0.853314\pi$
$587$		−	1.79888e8i		−	0.889379i	0.895685	−	0.444689i	$-0.146686\pi$
$588$	−7.94003e7	+	1.09360e8i	−0.390562	+	0.537930i
$589$	−3.25024e7			−0.159063
$590$	3.01939e6	−	9.29788e6i	0.0147016	−	0.0452718i
$591$			5.09677e8i			2.46906i
$592$	6.41251e7	+	1.96921e8i	0.309074	+	0.949133i
$593$	−3.78328e8			−1.81428			−0.907141	−	0.420826i	$-0.861740\pi$
$593$	−3.78328e8			−1.81428			−0.907141	+	0.420826i	$0.861740\pi$
$594$	2.63963e8	+	8.57193e7i	1.25946	+	0.408996i
$595$			2.85308e6i			0.0135445i
$596$	1.08951e8	+	7.91036e7i	0.514628	+	0.373643i
$597$	−3.23736e8			−1.52149
$598$	−1.97312e7	+	6.07601e7i	−0.0922679	+	0.284129i
$599$			2.70374e8i			1.25801i	0.777400	+	0.629006i	$0.216538\pi$
$599$			2.70374e8i			1.25801i	−0.777400	+	0.629006i	$0.783462\pi$
$600$	−2.80208e8	+	2.03792e8i	−1.29726	+	0.943481i
$601$	−1.32070e8			−0.608386			−0.304193	−	0.952610i	$-0.598387\pi$
$601$	−1.32070e8			−0.608386			−0.304193	+	0.952610i	$0.598387\pi$
$602$	−1.19954e8	−	3.89539e7i	−0.549826	−	0.178551i
$603$			1.75658e8i			0.801152i
$604$	1.25906e8	−	1.73413e8i	0.571392	−	0.786991i
$605$	1.40251e7			0.0633343
$606$	−2.06753e8	+	6.36672e8i	−0.929039	+	2.86087i
$607$			161700.i			0.000723008i	1.00000		0.000361504i	$0.000115070\pi$
$607$			161700.i			0.000723008i	−1.00000		0.000361504i	$0.999885\pi$
$608$	−3.71486e7	+	30180.0i	−0.165284	+	0.000134279i
$609$	3.71077e8			1.64291
$610$	−9.64509e6	−	3.13215e6i	−0.0424929	−	0.0137992i
$611$			2.07541e7i			0.0909870i
$612$	−7.20051e7	−	5.22790e7i	−0.314130	−	0.228073i
$613$	−9.72083e6			−0.0422009			−0.0211005	−	0.999777i	$-0.506717\pi$
$613$	−9.72083e6			−0.0422009			−0.0211005	+	0.999777i	$0.506717\pi$
$614$	8.64094e7	−	2.66088e8i	0.373298	−	1.14953i
$615$			2.09943e7i			0.0902560i
$616$	1.44118e8	+	1.98158e8i	0.616562	+	0.847755i
$617$	−2.03009e8			−0.864291			−0.432145	−	0.901804i	$-0.642243\pi$
$617$	−2.03009e8			−0.864291			−0.432145	+	0.901804i	$0.642243\pi$
$618$	3.04612e8	+	9.89196e7i	1.29057	+	0.419099i
$619$		−	4.09936e8i		−	1.72840i	−0.503149	−	0.864200i	$-0.667825\pi$
$619$		−	4.09936e8i		−	1.72840i	0.503149	−	0.864200i	$-0.332175\pi$
$620$	−9.81561e6	+	1.35193e7i	−0.0411853	+	0.0567255i
$621$	−2.62311e8			−1.09532
$622$	6.08296e7	−	1.87318e8i	0.252781	−	0.778409i
$623$		−	2.33458e8i		−	0.965485i
$624$	−9.84103e7	+	3.20462e7i	−0.405030	+	0.131893i
$625$	2.40261e8			0.984110
$626$	−1.49866e7	−	4.86676e6i	−0.0610916	−	0.0198389i
$627$		−	8.98315e7i		−	0.364440i
$628$	−1.75927e8	−	1.27731e8i	−0.710318	−	0.515724i
$629$	6.02476e7			0.242096
$630$	−6.90314e6	+	2.12574e7i	−0.0276074	+	0.0850138i
$631$		−	2.54420e8i		−	1.01266i	−0.862340	−	0.506330i	$-0.831002\pi$
$631$		−	2.54420e8i		−	1.01266i	0.862340	−	0.506330i	$-0.168998\pi$
$632$	4.56354e7	−	3.31901e7i	0.180780	−	0.131479i
$633$	−4.67222e8			−1.84210
$634$	−2.06880e8	−	6.71821e7i	−0.811802	−	0.263625i
$635$			9.58964e6i			0.0374525i
$636$	−2.81483e8	+	3.87693e8i	−1.09416	+	1.50701i
$637$	2.81442e7			0.108886
$638$	−1.45734e8	+	4.48770e8i	−0.561174	+	1.72807i
$639$			6.15485e8i			2.35893i
$640$	−1.12062e7	+	1.54610e7i	−0.0427483	+	0.0589789i
$641$	−4.27649e8			−1.62373			−0.811863	−	0.583847i	$-0.801547\pi$
$641$	−4.27649e8			−1.62373			−0.811863	+	0.583847i	$0.801547\pi$
$642$	−5.81073e8	−	1.88698e8i	−2.19597	−	0.713118i
$643$			1.09850e8i			0.413208i	0.978425	+	0.206604i	$0.0662412\pi$
$643$			1.09850e8i			0.413208i	−0.978425	+	0.206604i	$0.933759\pi$
$644$	−1.87401e8	−	1.36062e8i	−0.701639	−	0.509422i
$645$	2.37675e7			0.0885736
$646$	−3.33788e6	+	1.02786e7i	−0.0123815	+	0.0381274i
$647$		−	2.89318e8i		−	1.06822i	−0.845414	−	0.534112i	$-0.820646\pi$
$647$		−	2.89318e8i		−	1.06822i	0.845414	−	0.534112i	$-0.179354\pi$
$648$	6.20278e6	+	8.52864e6i	0.0227961	+	0.0313440i
$649$	−2.44238e8			−0.893467
$650$	6.86274e7	+	2.22861e7i	0.249895	+	0.0811509i
$651$		−	3.28262e8i		−	1.18981i
$652$	2.53070e8	−	3.48559e8i	0.913056	−	1.25757i
$653$	−3.16769e8			−1.13764			−0.568818	−	0.822464i	$-0.692599\pi$
$653$	−3.16769e8			−1.13764			−0.568818	+	0.822464i	$0.692599\pi$
$654$	−2.23383e8	+	6.87883e8i	−0.798578	+	2.45913i
$655$			1.02442e7i			0.0364547i
$656$	−6.71620e7	−	2.06247e8i	−0.237910	−	0.730594i
$657$	7.33648e8			2.58697
$658$	−7.15573e7	−	2.32375e7i	−0.251175	−	0.0815666i
$659$			1.19463e8i			0.417422i	0.977977	+	0.208711i	$0.0669269\pi$
$659$			1.19463e8i			0.417422i	−0.977977	+	0.208711i	$0.933073\pi$
$660$	−3.73651e7	−	2.71288e7i	−0.129967	−	0.0943624i
$661$	5.04458e7			0.174671			0.0873356	−	0.996179i	$-0.472165\pi$
$661$	5.04458e7			0.174671			0.0873356	+	0.996179i	$0.472165\pi$
$662$	3.74594e6	−	1.15352e7i	0.0129118	−	0.0397604i
$663$			3.01085e7i			0.103311i
$664$	−4.33773e8	+	3.15478e8i	−1.48169	+	1.07762i
$665$	2.71446e6			0.00923036
$666$	4.48888e8	+	1.45772e8i	1.51955	+	0.493459i
$667$		−	4.45961e8i		−	1.50286i
$668$	−2.71286e8	+	3.73649e8i	−0.910120	+	1.25353i
$669$	−1.57089e7			−0.0524648
$670$	3.38697e6	−	1.04298e7i	0.0112613	−	0.0346778i
$671$			2.53358e8i			0.838624i
$672$	−304806.	−	3.75187e8i	−0.00100442	−	1.23635i
$673$	1.72008e8			0.564292			0.282146	−	0.959371i	$-0.408954\pi$
$673$	1.72008e8			0.564292			0.282146	+	0.959371i	$0.408954\pi$
$674$	1.00740e8	+	3.27144e7i	0.329021	+	0.106846i
$675$			2.96275e8i			0.963348i
$676$	−2.32536e8	−	1.68832e8i	−0.752748	−	0.546530i
$677$	2.10440e8			0.678208			0.339104	−	0.940749i	$-0.389876\pi$
$677$	2.10440e8			0.678208			0.339104	+	0.940749i	$0.389876\pi$
$678$	9.30266e7	−	2.86465e8i	0.298482	−	0.919141i
$679$		−	4.15353e8i		−	1.32681i
$680$	3.26733e6	+	4.49248e6i	0.0103912	+	0.0142876i
$681$	−4.00279e7			−0.126742
$682$	3.96990e8	+	1.28919e8i	1.25149	+	0.406409i
$683$		−	1.06406e7i		−	0.0333968i	−0.999861	−	0.0166984i	$-0.994684\pi$
$683$		−	1.06406e7i		−	0.0333968i	0.999861	−	0.0166984i	$-0.00531552\pi$
$684$	−4.97391e7	+	6.85068e7i	−0.155428	+	0.214075i
$685$	−9.78481e6			−0.0304425
$686$	−1.07956e8	+	3.32438e8i	−0.334407	+	1.02977i
$687$		−	1.40023e8i		−	0.431847i
$688$	−2.33491e8	+	7.60336e7i	−0.716976	+	0.233475i
$689$	9.97744e7			0.305043
$690$	4.15086e7	+	1.34795e7i	0.126354	+	0.0410324i
$691$		−	2.48386e8i		−	0.752823i	−0.926453	−	0.376411i	$-0.877158\pi$
$691$		−	2.48386e8i		−	0.752823i	0.926453	−	0.376411i	$-0.122842\pi$
$692$	7.26739e7	+	5.27646e7i	0.219311	+	0.159230i
$693$	5.58392e8			1.67780
$694$	9.05679e7	−	2.78894e8i	0.270954	−	0.834373i
$695$		−	7.12123e6i		−	0.0212129i
$696$	5.84302e8	−	4.24956e8i	1.73305	−	1.26042i
$697$	−6.31009e7			−0.186353
$698$	1.22606e8	+	3.98149e7i	0.360532	+	0.117079i
$699$		−	2.25441e8i		−	0.660088i
$700$	−1.53679e8	+	2.11666e8i	−0.448044	+	0.617101i
$701$	6.25347e8			1.81538			0.907689	−	0.419643i	$-0.137845\pi$
$701$	6.25347e8			1.81538			0.907689	+	0.419643i	$0.137845\pi$
$702$	−2.73343e7	+	8.41730e7i	−0.0790128	+	0.243311i
$703$		−	5.73206e7i		−	0.164985i
$704$	4.53860e8	+	1.46979e8i	1.30078	+	0.421248i
$705$	1.41782e7			0.0404627
$706$	2.58964e8	+	8.40961e7i	0.735912	+	0.238980i
$707$			5.05359e8i			1.43002i
$708$	3.02630e8	+	2.19723e8i	0.852731	+	0.619122i
$709$	5.13509e8			1.44082			0.720409	−	0.693549i	$-0.243954\pi$
$709$	5.13509e8			1.44082			0.720409	+	0.693549i	$0.243954\pi$
$710$	1.18676e7	−	3.65449e7i	0.0331579	−	0.102106i
$711$		−	1.28596e8i		−	0.357783i
$712$	−2.67355e8	−	3.67606e8i	−0.740711	−	1.01846i
$713$	−3.94506e8			−1.08839
$714$	−1.03810e8	−	3.37113e7i	−0.285197	−	0.0926149i
$715$			9.61606e6i			0.0263075i
$716$	−1.34424e8	+	1.85145e8i	−0.366216	+	0.504397i
$717$	9.12778e7			0.247633
$718$	1.61734e8	−	4.98040e8i	0.436945	−	1.34552i
$719$		−	2.09864e8i		−	0.564614i	−0.959324	−	0.282307i	$-0.908900\pi$
$719$		−	2.09864e8i		−	0.564614i	0.959324	−	0.282307i	$-0.0910998\pi$
$720$	1.34741e7	+	4.13776e7i	0.0360997	+	0.110858i
$721$	2.41785e8			0.645096
$722$	−3.48186e8	−	1.13070e8i	−0.925123	−	0.300425i
$723$		−	6.09287e8i		−	1.61216i
$724$	4.44436e7	+	3.22681e7i	0.117110	+	0.0850272i
$725$	−5.03704e8			−1.32179
$726$	−1.65717e8	+	5.10307e8i	−0.433070	+	1.33359i
$727$			4.11970e8i			1.07217i	0.844165	+	0.536083i	$0.180097\pi$
$727$			4.11970e8i			1.07217i	−0.844165	+	0.536083i	$0.819903\pi$
$728$	−6.31892e7	+	4.59567e7i	−0.163775	+	0.119112i
$729$	6.29109e8			1.62384
$730$	−4.35609e7	−	1.41460e7i	−0.111977	−	0.0363634i
$731$			7.14361e7i			0.182880i
$732$	2.27928e8	−	3.13931e8i	0.581119	−	0.800389i
$733$	1.04418e8			0.265133			0.132566	−	0.991174i	$-0.457678\pi$
$733$	1.04418e8			0.265133			0.132566	+	0.991174i	$0.457678\pi$
$734$	−9.14128e7	+	2.81495e8i	−0.231163	+	0.711841i
$735$		−	1.92269e7i		−	0.0484224i
$736$	−4.50900e8	+	366317.i	−1.13096	+	0.000918804i
$737$	−2.73971e8			−0.684388
$738$	−4.70147e8	−	1.52675e8i	−1.16967	−	0.379840i
$739$		−	1.28487e8i		−	0.318365i	−0.987249	−	0.159182i	$-0.949114\pi$
$739$		−	1.28487e8i		−	0.318365i	0.987249	−	0.159182i	$-0.0508858\pi$
$740$	−2.38423e7	−	1.73106e7i	−0.0588374	−	0.0427186i
$741$	2.86457e7			0.0704051
$742$	−1.11714e8	+	3.44009e8i	−0.273460	+	0.842090i
$743$		−	5.74784e7i		−	0.140132i	−0.997542	−	0.0700661i	$-0.977679\pi$
$743$		−	5.74784e7i		−	0.140132i	0.997542	−	0.0700661i	$-0.0223210\pi$
$744$	−3.75924e8	−	5.16885e8i	−0.912812	−	1.25509i
$745$	−1.91550e7			−0.0463248
$746$	3.30012e8	+	1.07168e8i	0.794901	+	0.258136i
$747$			1.22233e9i			2.93243i
$748$	8.15389e7	−	1.12305e8i	0.194832	−	0.268346i
$749$	−4.61227e8			−1.09766
$750$	3.05309e7	−	9.40164e7i	0.0723695	−	0.222854i
$751$			3.89920e7i			0.0920567i	0.998940	+	0.0460283i	$0.0146565\pi$
$751$			3.89920e7i			0.0920567i	−0.998940	+	0.0460283i	$0.985344\pi$
$752$	−1.39286e8	+	4.53570e7i	−0.327533	+	0.106657i
$753$	1.24837e9			2.92387
$754$	−1.43105e8	−	4.64718e7i	−0.333841	−	0.108412i
$755$			3.04881e7i			0.0708419i
$756$	−2.59613e8	−	1.88491e8i	−0.600842	−	0.436239i
$757$	1.84924e8			0.426290			0.213145	−	0.977021i	$-0.431629\pi$
$757$	1.84924e8			0.426290			0.213145	+	0.977021i	$0.431629\pi$
$758$	1.92414e8	−	5.92516e8i	0.441802	−	1.36048i
$759$		−	1.09035e9i		−	2.49368i
$760$	4.27422e6	−	3.10859e6i	0.00973680	−	0.00708145i
$761$	6.50180e8			1.47530			0.737648	−	0.675185i	$-0.235936\pi$
$761$	6.50180e8			1.47530			0.737648	+	0.675185i	$0.235936\pi$
$762$	−3.48922e8	−	1.13309e8i	−0.788613	−	0.256094i
$763$			5.46007e8i			1.22921i
$764$	3.44753e8	−	4.74836e8i	0.773085	−	1.06479i
$765$	1.26594e7			0.0282767
$766$	2.05220e8	−	6.31950e8i	0.456596	−	1.40604i
$767$		−	7.78830e7i		−	0.172606i
$768$	−4.30142e8	−	5.90425e8i	−0.949573	−	1.30341i
$769$	−2.84439e8			−0.625475			−0.312737	−	0.949840i	$-0.601246\pi$
$769$	−2.84439e8			−0.625475			−0.312737	+	0.949840i	$0.601246\pi$
$770$	−3.31550e7	−	1.07667e7i	−0.0726233	−	0.0235837i
$771$		−	1.29098e7i		−	0.0281680i
$772$	7.03705e8	+	5.10922e8i	1.52946	+	1.11046i
$773$	4.38619e8			0.949617			0.474809	−	0.880089i	$-0.342517\pi$
$773$	4.38619e8			0.949617			0.474809	+	0.880089i	$0.342517\pi$
$774$	−1.72843e8	+	5.32250e8i	−0.372759	+	1.14787i
$775$			4.45587e8i			0.957254i
$776$	−4.75660e8	−	6.54020e8i	−1.01792	−	1.39961i
$777$	5.78916e8			1.23411
$778$	−3.56923e8	−	1.15907e8i	−0.757942	−	0.246134i
$779$			6.00352e7i			0.126997i
$780$	8.65089e6	−	1.19151e7i	0.0182296	−	0.0251080i
$781$	−9.59964e8			−2.01512
$782$	−4.05143e7	+	1.24759e8i	−0.0847204	+	0.260887i
$783$		−	6.17805e8i		−	1.28696i
$784$	6.15078e7	+	1.88884e8i	0.127639	+	0.391964i
$785$	3.09302e7			0.0639401
$786$	−3.72739e8	−	1.21043e8i	−0.767603	−	0.249271i
$787$			4.67758e8i			0.959615i	0.877374	+	0.479807i	$0.159293\pi$
$787$			4.67758e8i			0.959615i	−0.877374	+	0.479807i	$0.840707\pi$
$788$	6.06230e8	+	4.40151e8i	1.23896	+	0.899545i
$789$	−1.52520e7			−0.0310524
$790$	−2.47955e6	+	7.63550e6i	−0.00502912	+	0.0154866i
$791$		−	2.27381e8i		−	0.459437i
$792$	8.79251e8	−	6.39468e8i	1.76985	−	1.28719i
$793$	−8.07914e7			−0.162011
$794$	−7.26110e8	−	2.35797e8i	−1.45058	−	0.471061i
$795$		−	6.81614e7i		−	0.135656i
$796$	−2.79575e8	+	3.85065e8i	−0.554317	+	0.763474i
$797$	3.40075e8			0.671737			0.335869	−	0.941909i	$-0.390970\pi$
$797$	3.40075e8			0.671737			0.335869	+	0.941909i	$0.390970\pi$
$798$	−3.20735e7	+	9.87666e7i	−0.0631157	+	0.194358i
$799$			4.26144e7i			0.0835442i
$800$	413748.	+	5.09283e8i	0.000808101	+	0.994694i
$801$	−1.03588e9			−2.01564
$802$	5.53080e8	+	1.79607e8i	1.07217	+	0.348177i
$803$			1.14426e9i			2.20993i
$804$	3.39472e8	+	2.46472e8i	0.653185	+	0.474242i
$805$	3.29474e7			0.0631588
$806$	−4.11099e7	+	1.26593e8i	−0.0785129	+	0.241772i
$807$		−	1.17216e9i		−	2.23032i
$808$	5.78734e8	+	7.95743e8i	1.09710	+	1.50848i
$809$	−9.53044e8			−1.79998			−0.899990	−	0.435911i	$-0.856426\pi$
$809$	−9.53044e8			−1.79998			−0.899990	+	0.435911i	$0.856426\pi$
$810$	−1.42697e6	−	463396.i	−0.00268510	−	0.000871961i
$811$		−	8.69141e8i		−	1.62940i	−0.579883	−	0.814700i	$-0.696902\pi$
$811$		−	8.69141e8i		−	1.62940i	0.579883	−	0.814700i	$-0.303098\pi$
$812$	3.20458e8	−	4.41374e8i	0.598554	−	0.824401i
$813$	−9.65590e8			−1.79689
$814$	−2.27358e8	+	7.00124e8i	−0.421539	+	1.29808i
$815$			6.12811e7i			0.113202i
$816$	−2.02067e8	+	6.58006e7i	−0.371898	+	0.121104i
$817$	6.79654e7			0.124630
$818$	−3.02229e8	−	9.81459e7i	−0.552175	−	0.179313i
$819$			1.78061e8i			0.324129i
$820$	2.49715e7	+	1.81304e7i	0.0452900	+	0.0328826i
$821$	8.03772e8			1.45246			0.726228	−	0.687453i	$-0.241271\pi$
$821$	8.03772e8			1.45246			0.726228	+	0.687453i	$0.241271\pi$
$822$	1.15615e8	−	3.56024e8i	0.208161	−	0.641008i
$823$			5.42307e8i			0.972849i	0.873723	+	0.486424i	$0.161699\pi$
$823$			5.42307e8i			0.972849i	−0.873723	+	0.486424i	$0.838301\pi$
$824$	3.80718e8	−	2.76891e8i	0.680490	−	0.494912i
$825$	−1.23153e9			−2.19323
$826$	2.68531e8	+	8.72027e7i	0.476490	+	0.154735i
$827$		−	8.46333e7i		−	0.149632i	−0.997197	−	0.0748160i	$-0.976163\pi$
$827$		−	8.46333e7i		−	0.149632i	0.997197	−	0.0748160i	$-0.0238369\pi$
$828$	−6.03720e8	+	8.31518e8i	−1.06352	+	1.46481i
$829$	4.04550e8			0.710081			0.355041	−	0.934851i	$-0.384467\pi$
$829$	4.04550e8			0.710081			0.355041	+	0.934851i	$0.384467\pi$
$830$	2.35687e7	−	7.25770e7i	0.0412193	−	0.126930i
$831$			1.10760e9i			1.93011i
$832$	−4.68690e7	+	1.44728e8i	−0.0813796	+	0.251294i
$833$	5.77887e7			0.0999787
$834$	2.59108e8	+	8.41429e7i	0.446667	+	0.145051i
$835$		−	6.56923e7i		−	0.112838i
$836$	−1.06849e8	−	7.75774e7i	−0.182874	−	0.132775i
$837$	−5.46522e8			−0.932033
$838$	1.94692e8	−	5.99533e8i	0.330839	−	1.01878i
$839$		−	1.65369e8i		−	0.280006i	−0.990151	−	0.140003i	$-0.955289\pi$
$839$		−	1.65369e8i		−	0.280006i	0.990151	−	0.140003i	$-0.0447113\pi$
$840$	3.13956e7	+	4.31680e7i	0.0529701	+	0.0728324i
$841$	4.55523e8			0.765812
$842$	6.27622e8	+	2.03814e8i	1.05139	+	0.341427i
$843$		−	7.20502e8i		−	1.20269i
$844$	−4.03488e8	+	5.55733e8i	−0.671124	+	0.924355i
$845$	4.08828e7			0.0677595
$846$	−1.03108e8	+	3.17508e8i	−0.170286	+	0.524377i
$847$			4.05056e8i			0.666600i
$848$	2.18052e8	+	6.69615e8i	0.357580	+	1.09809i
$849$	−7.55998e8			−1.23537
$850$	1.40913e8	+	4.57601e7i	0.229453	+	0.0745127i
$851$		−	6.95742e8i		−	1.12891i
$852$	1.18947e9	+	8.63612e8i	1.92325	+	1.39637i
$853$	7.38497e8			1.18988			0.594938	−	0.803771i	$-0.297176\pi$
$853$	7.38497e8			1.18988			0.594938	+	0.803771i	$0.297176\pi$
$854$	9.04591e7	−	2.78558e8i	0.145237	−	0.447242i
$855$		−	1.20444e7i		−	0.0192702i
$856$	−7.26252e8	+	5.28194e8i	−1.15789	+	0.842117i
$857$	7.73520e8			1.22893			0.614467	−	0.788942i	$-0.289371\pi$
$857$	7.73520e8			1.22893			0.614467	+	0.788942i	$0.289371\pi$
$858$	−3.49884e8	−	1.13621e8i	−0.553939	−	0.179886i
$859$			6.91609e8i			1.09114i	0.838065	+	0.545571i	$0.183687\pi$
$859$			6.91609e8i			1.09114i	−0.838065	+	0.545571i	$0.816313\pi$
$860$	2.05253e7	−	2.82700e7i	0.0322697	−	0.0444458i
$861$	−6.06333e8			−0.949953
$862$	1.39850e8	−	4.30653e8i	0.218344	−	0.672366i
$863$		−	2.96236e8i		−	0.460899i	−0.973084	−	0.230449i	$-0.925980\pi$
$863$		−	2.96236e8i		−	0.460899i	0.973084	−	0.230449i	$-0.0740196\pi$
$864$	−6.24647e8	+	507471.i	−0.968487	+	0.000786810i
$865$	−1.27770e7			−0.0197415
$866$	−6.79503e8	−	2.20662e8i	−1.04625	−	0.339761i
$867$			6.18219e7i			0.0948604i
$868$	−3.90448e8	−	2.83483e8i	−0.597041	−	0.433479i
$869$	2.00570e8			0.305638
$870$	−3.17475e7	+	9.77628e7i	−0.0482116	+	0.148462i
$871$		−	8.73645e7i		−	0.132215i
$872$	6.25284e8	+	8.59749e8i	0.943036	+	1.29665i
$873$	−1.84297e9			−2.76997
$874$	1.18698e8	+	3.85459e7i	0.177790	+	0.0577357i
$875$		−	7.46255e7i		−	0.111394i
$876$	1.02941e9	−	1.41783e9i	1.53136	−	2.10917i
$877$	−1.05271e9			−1.56067			−0.780335	−	0.625362i	$-0.784951\pi$
$877$	−1.05271e9			−1.56067			−0.780335	+	0.625362i	$0.784951\pi$
$878$	9.01922e7	−	2.77737e8i	0.133256	−	0.410345i
$879$		−	1.32180e9i		−	1.94626i
$880$	−6.45362e7	+	2.10155e7i	−0.0947011	+	0.0308383i
$881$	5.01300e8			0.733111			0.366555	−	0.930396i	$-0.380537\pi$
$881$	5.01300e8			0.733111			0.366555	+	0.930396i	$0.380537\pi$
$882$	4.30567e8	+	1.39822e8i	0.627530	+	0.203784i
$883$			1.06087e9i			1.54092i	0.637487	+	0.770461i	$0.279974\pi$
$883$			1.06087e9i			1.54092i	−0.637487	+	0.770461i	$0.720026\pi$
$884$	3.58122e7	+	2.60013e7i	0.0518411	+	0.0376390i
$885$	−5.32062e7			−0.0767596
$886$	−3.42921e8	+	1.05599e9i	−0.493052	+	1.51830i
$887$			4.75244e8i			0.680998i	0.940245	+	0.340499i	$0.110596\pi$
$887$			4.75244e8i			0.680998i	−0.940245	+	0.340499i	$0.889404\pi$
$888$	9.11568e8	−	6.62972e8i	1.30182	−	0.946796i
$889$	−2.76957e8			−0.394191
$890$	6.15062e7	+	1.99735e7i	0.0872467	+	0.0283325i
$891$			3.74839e7i			0.0529921i
$892$	−1.35660e7	+	1.86848e7i	−0.0191143	+	0.0263266i
$893$	4.05441e7			0.0569342
$894$	2.26331e8	−	6.96961e8i	0.316761	−	0.975430i
$895$		−	3.25508e7i		−	0.0454039i
$896$	−4.46526e8	−	3.23645e8i	−0.620758	−	0.449929i
$897$	3.47694e8			0.481748
$898$	−7.41188e8	−	2.40693e8i	−1.02353	−	0.332380i
$899$		−	9.29156e8i		−	1.27882i
$900$	9.39184e8	+	6.81891e8i	1.28832	+	0.935378i
$901$	2.04867e8			0.280091
$902$	2.38126e8	−	7.33282e8i	0.324479	−	0.999197i
$903$			6.86425e8i			0.932245i
$904$	−2.60396e8	−	3.58037e8i	−0.352476	−	0.484644i
$905$	−7.81375e6			−0.0105418
$906$	−1.10932e9	−	3.60241e8i	−1.49167	−	0.484405i
$907$			8.35125e8i			1.11926i	0.828744	+	0.559628i	$0.189056\pi$
$907$			8.35125e8i			1.11926i	−0.828744	+	0.559628i	$0.810944\pi$
$908$	−3.45676e7	+	4.76108e7i	−0.0461755	+	0.0635986i
$909$	2.24233e9			2.98544
$910$	3.43332e6	−	1.05725e7i	0.00455607	−	0.0140299i
$911$			2.29793e8i			0.303935i	0.988385	+	0.151968i	$0.0485610\pi$
$911$			2.29793e8i			0.303935i	−0.988385	+	0.151968i	$0.951439\pi$
$912$	6.26038e7	+	1.92249e8i	0.0825308	+	0.253443i
$913$	−1.90646e9			−2.50504
$914$	−1.17251e9	−	3.80762e8i	−1.53560	−	0.498672i
$915$			5.51931e7i			0.0720479i
$916$	−1.66549e8	−	1.20922e8i	−0.216699	−	0.157333i
$917$	−2.95861e8			−0.383689
$918$	−5.61258e7	+	1.72833e8i	−0.0725495	+	0.223408i
$919$		−	5.44854e8i		−	0.701994i	−0.936377	−	0.350997i	$-0.885843\pi$
$919$		−	5.44854e8i		−	0.701994i	0.936377	−	0.350997i	$-0.114157\pi$
$920$	5.18794e7	−	3.77312e7i	0.0666241	−	0.0484549i
$921$	−1.52266e9			−1.94906
$922$	1.30131e9	+	4.22589e8i	1.66031	+	0.539169i
$923$		−	3.06115e8i		−	0.389296i
$924$	7.83503e8	−	1.07914e9i	0.993173	−	1.36792i
$925$	−7.85828e8			−0.992892
$926$	1.40143e8	−	4.31554e8i	0.176497	−	0.543504i
$927$		−	1.07283e9i		−	1.34676i
$928$	−862764.	−	1.06198e9i	−0.00107956	−	1.32884i
$929$	1.00814e9			1.25740			0.628698	−	0.777650i	$-0.283588\pi$
$929$	1.00814e9			1.25740			0.628698	+	0.777650i	$0.283588\pi$
$930$	8.64828e7	+	2.80844e7i	0.107518	+	0.0349154i
$931$		−	5.49811e7i		−	0.0681340i
$932$	−2.68149e8	−	1.94688e8i	−0.331229	−	0.240487i
$933$	−1.07191e9			−1.31981
$934$	2.52428e8	−	7.77323e8i	0.309811	−	0.954027i
$935$			1.97447e7i			0.0241555i
$936$	2.03915e8	+	2.80377e8i	0.248669	+	0.341913i
$937$	−3.84890e8			−0.467862			−0.233931	−	0.972253i	$-0.575159\pi$
$937$	−3.84890e8			−0.467862			−0.233931	+	0.972253i	$0.575159\pi$
$938$	3.01222e8	+	9.78187e7i	0.364987	+	0.118526i
$939$			8.57596e7i			0.103582i
$940$	1.22442e7	−	1.68642e7i	0.0147416	−	0.0203040i
$941$	−2.97126e8			−0.356593			−0.178296	−	0.983977i	$-0.557059\pi$
$941$	−2.97126e8			−0.356593			−0.178296	+	0.983977i	$0.557059\pi$
$942$	−3.65464e8	+	1.12540e9i	−0.437212	+	1.34634i
$943$			7.28692e8i			0.868978i
$944$	5.22696e8	−	1.70210e8i	0.621345	−	0.202334i
$945$	4.56432e7			0.0540855
$946$	−8.30143e8	−	2.69581e8i	−0.980572	−	0.318431i
$947$			6.06724e8i			0.714400i	0.934028	+	0.357200i	$0.116268\pi$
$947$			6.06724e8i			0.714400i	−0.934028	+	0.357200i	$0.883732\pi$
$948$	−2.48523e8	−	1.80439e8i	−0.291703	−	0.211790i
$949$	−3.64885e8			−0.426930
$950$	4.35369e7	−	1.34067e8i	0.0507793	−	0.156369i
$951$			1.18385e9i			1.37643i
$952$	−1.29747e8	+	9.43632e7i	−0.150378	+	0.109368i
$953$	4.71825e8			0.545133			0.272567	−	0.962137i	$-0.412128\pi$
$953$	4.71825e8			0.545133			0.272567	+	0.962137i	$0.412128\pi$
$954$	1.52641e9	+	4.95686e8i	1.75803	+	0.570902i
$955$			8.34822e7i			0.0958481i
$956$	7.88265e7	−	1.08570e8i	0.0902191	−	0.124261i
$957$	2.56804e9			2.92999
$958$	4.10277e8	−	1.26340e9i	0.466639	−	1.43696i
$959$		−	2.82594e8i		−	0.320410i
$960$	9.88716e7	+	3.20188e7i	0.111753	+	0.0361902i
$961$	6.55542e7			0.0738635
$962$	−2.23257e8	−	7.25006e7i	−0.250773	−	0.0814360i
$963$			2.04651e9i			2.29158i
$964$	−7.24710e8	−	5.26173e8i	−0.808972	−	0.587351i
$965$	−1.23720e8			−0.137676
$966$	−3.89300e8	+	1.19880e9i	−0.431869	+	1.32989i
$967$			1.27333e9i			1.40819i	0.710106	+	0.704095i	$0.248647\pi$
$967$			1.27333e9i			1.40819i	−0.710106	+	0.704095i	$0.751353\pi$
$968$	4.63868e8	+	6.37806e8i	0.511409	+	0.703173i
$969$	5.88183e7			0.0646460
$970$	1.09428e8	+	3.55355e7i	0.119898	+	0.0389356i
$971$			7.13645e8i			0.779516i	0.920917	+	0.389758i	$0.127441\pi$
$971$			7.13645e8i			0.779516i	−0.920917	+	0.389758i	$0.872559\pi$
$972$	5.56258e8	−	7.66147e8i	0.605728	−	0.834283i
$973$	2.05667e8			0.223268
$974$	−4.01471e8	+	1.23628e9i	−0.434487	+	1.33795i
$975$		−	3.92713e8i		−	0.423703i
$976$	−1.76566e8	−	5.42214e8i	−0.189914	−	0.583205i
$977$	−2.62269e8			−0.281231			−0.140615	−	0.990064i	$-0.544908\pi$
$977$	−2.62269e8			−0.281231			−0.140615	+	0.990064i	$0.544908\pi$
$978$	−2.22973e9	−	7.24083e8i	−2.38362	−	0.774055i
$979$		−	1.61565e9i		−	1.72187i
$980$	−2.28692e7	−	1.66041e7i	−0.0242981	−	0.0176416i
$981$	2.42269e9			2.56621
$982$	−4.14859e8	+	1.27751e9i	−0.438092	+	1.34906i
$983$			1.02993e9i			1.08429i	0.840284	+	0.542146i	$0.182388\pi$
$983$			1.02993e9i			1.08429i	−0.840284	+	0.542146i	$0.817612\pi$
$984$	−9.54739e8	+	6.94370e8i	−1.00207	+	0.728795i
$985$	−1.06583e8			−0.111527
$986$	−2.93838e8	−	9.54209e7i	−0.306533	−	0.0995435i
$987$			4.09480e8i			0.425874i
$988$	2.47381e7	−	3.40723e7i	0.0256504	−	0.0353289i
$989$	8.24947e8			0.852780
$990$	−4.77732e7	+	1.47112e8i	−0.0492356	+	0.151615i
$991$		−	4.32656e8i		−	0.444551i	−0.974984	−	0.222276i	$-0.928652\pi$
$991$		−	4.32656e8i		−	0.444551i	0.974984	−	0.222276i	$-0.0713485\pi$
$992$	−9.39447e8	+	763218.i	−0.962360	+	0.000781832i
$993$	−6.60090e7			−0.0674148
$994$	1.05545e9	+	3.42746e8i	1.07468	+	0.348990i
$995$		−	6.76993e7i		−	0.0687250i
$996$	2.36226e9	+	1.71511e9i	2.39083	+	1.73585i
$997$	1.82860e8			0.184516			0.0922579	−	0.995735i	$-0.470592\pi$
$997$	1.82860e8			0.184516			0.0922579	+	0.995735i	$0.470592\pi$
$998$	−5.88901e7	+	1.81345e8i	−0.0592449	+	0.182438i
$999$		−	9.63835e8i		−	0.966732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.7.c.a.35.5	✓	48
4.3	odd	2	inner	68.7.c.a.35.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.7.c.a.35.5	✓	48	1.1	even	1	trivial
68.7.c.a.35.6	yes	48	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	68.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.60885 - 2.47090i) q^{2} +43.5409i q^{3} +(51.7893 + 37.6014i) q^{4} -9.10522 q^{5} +(107.585 - 331.296i) q^{6} -262.967i q^{7} +(-301.148 - 414.070i) q^{8} -1166.81 q^{9} +O(q^{10})\)	\(q+(-7.60885 - 2.47090i) q^{2} +43.5409i q^{3} +(51.7893 + 37.6014i) q^{4} -9.10522 q^{5} +(107.585 - 331.296i) q^{6} -262.967i q^{7} +(-301.148 - 414.070i) q^{8} -1166.81 q^{9} +(69.2803 + 22.4981i) q^{10} -1819.86i q^{11} +(-1637.20 + 2254.95i) q^{12} +580.321 q^{13} +(-649.764 + 2000.87i) q^{14} -396.450i q^{15} +(1268.27 + 3894.70i) q^{16} +1191.58 q^{17} +(8878.10 + 2883.07i) q^{18} -1133.69i q^{19} +(-471.553 - 342.369i) q^{20} +11449.8 q^{21} +(-4496.69 + 13847.1i) q^{22} -13760.4i q^{23} +(18029.0 - 13112.3i) q^{24} -15542.1 q^{25} +(-4415.58 - 1433.92i) q^{26} -19062.7i q^{27} +(9887.92 - 13618.9i) q^{28} +32409.0 q^{29} +(-979.587 + 3016.53i) q^{30} -28669.7i q^{31} +(-26.6211 - 32768.0i) q^{32} +79238.4 q^{33} +(-9066.54 - 2944.27i) q^{34} +2394.37i q^{35} +(-60428.4 - 43873.8i) q^{36} +50561.2 q^{37} +(-2801.22 + 8626.05i) q^{38} +25267.7i q^{39} +(2742.02 + 3770.20i) q^{40} -52955.8 q^{41} +(-87119.9 - 28291.3i) q^{42} +59950.8i q^{43} +(68429.4 - 94249.4i) q^{44} +10624.1 q^{45} +(-34000.5 + 104701. i) q^{46} +35763.0i q^{47} +(-169579. + 55221.4i) q^{48} +48497.6 q^{49} +(118258. + 38403.0i) q^{50} +51882.4i q^{51} +(30054.4 + 21820.9i) q^{52} +171930. q^{53} +(-47102.1 + 145045. i) q^{54} +16570.2i q^{55} +(-108887. + 79191.8i) q^{56} +49361.7 q^{57} +(-246596. - 80079.5i) q^{58} -134207. i q^{59} +(14907.1 - 20531.9i) q^{60} -139218. q^{61} +(-70839.9 + 218143. i) q^{62} +306832. i q^{63} +(-80763.9 + 249393. i) q^{64} -5283.95 q^{65} +(-602914. - 195790. i) q^{66} -150545. i q^{67} +(61711.0 + 44805.0i) q^{68} +599140. q^{69} +(5916.24 - 18218.4i) q^{70} -527493. i q^{71} +(351383. + 483142. i) q^{72} -628763. q^{73} +(-384713. - 124932. i) q^{74} -676717. i q^{75} +(42628.2 - 58712.8i) q^{76} -478563. q^{77} +(62434.0 - 192258. i) q^{78} +110212. i q^{79} +(-11547.8 - 35462.1i) q^{80} -20597.1 q^{81} +(402933. + 130848. i) q^{82} -1.04758e6i q^{83} +(592977. + 430529. i) q^{84} -10849.6 q^{85} +(148133. - 456157. i) q^{86} +1.41112e6i q^{87} +(-753550. + 548047. i) q^{88} +887788. q^{89} +(-80837.1 - 26251.0i) q^{90} -152605. i q^{91} +(517410. - 712641. i) q^{92} +1.24830e6 q^{93} +(88366.9 - 272116. i) q^{94} +10322.5i q^{95} +(1.42675e6 - 1159.11i) q^{96} +1.57949e6 q^{97} +(-369011. - 119833. i) q^{98} +2.12344e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9}+O(q^{10}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9	\( 48 q - 10 q^{2} + 90 q^{4} - 510 q^{6} + 1406 q^{8} - 11664 q^{9} - 1710 q^{10} - 6234 q^{12} - 5040 q^{13} + 9040 q^{14} - 1230 q^{16} - 6974 q^{18} + 1046 q^{20} - 35488 q^{21} - 13254 q^{22} + 22838 q^{24} + 173856 q^{25} + 44744 q^{26} + 42864 q^{28} - 83536 q^{29} - 95104 q^{30} - 53050 q^{32} + 9072 q^{33} + 24174 q^{36} + 62640 q^{37} + 399840 q^{38} - 58218 q^{40} + 70448 q^{41} - 90520 q^{42} - 356746 q^{44} - 103808 q^{45} - 177084 q^{46} + 808886 q^{48} - 758880 q^{49} - 560506 q^{50} - 85800 q^{52} + 744784 q^{53} - 263596 q^{54} - 701896 q^{56} - 125008 q^{57} - 351534 q^{58} - 64960 q^{60} + 196560 q^{61} + 1428016 q^{62} - 60246 q^{64} - 708656 q^{65} + 1089052 q^{66} + 428496 q^{69} - 1132824 q^{70} - 1043230 q^{72} - 454272 q^{73} - 1135082 q^{74} + 850224 q^{76} - 549200 q^{77} + 703076 q^{78} + 1608910 q^{80} + 3871872 q^{81} - 328536 q^{82} + 2825208 q^{84} + 3243644 q^{86} + 691398 q^{88} - 1729776 q^{89} + 214114 q^{90} + 1469284 q^{92} - 6618704 q^{93} - 551136 q^{94} - 5148618 q^{96} + 4548720 q^{97} - 2942042 q^{98}+O(q^{100}) \) 48 * q - 10 * q^2 + 90 * q^4 - 510 * q^6 + 1406 * q^8 - 11664 * q^9 - 1710 * q^10 - 6234 * q^12 - 5040 * q^13 + 9040 * q^14 - 1230 * q^16 - 6974 * q^18 + 1046 * q^20 - 35488 * q^21 - 13254 * q^22 + 22838 * q^24 + 173856 * q^25 + 44744 * q^26 + 42864 * q^28 - 83536 * q^29 - 95104 * q^30 - 53050 * q^32 + 9072 * q^33 + 24174 * q^36 + 62640 * q^37 + 399840 * q^38 - 58218 * q^40 + 70448 * q^41 - 90520 * q^42 - 356746 * q^44 - 103808 * q^45 - 177084 * q^46 + 808886 * q^48 - 758880 * q^49 - 560506 * q^50 - 85800 * q^52 + 744784 * q^53 - 263596 * q^54 - 701896 * q^56 - 125008 * q^57 - 351534 * q^58 - 64960 * q^60 + 196560 * q^61 + 1428016 * q^62 - 60246 * q^64 - 708656 * q^65 + 1089052 * q^66 + 428496 * q^69 - 1132824 * q^70 - 1043230 * q^72 - 454272 * q^73 - 1135082 * q^74 + 850224 * q^76 - 549200 * q^77 + 703076 * q^78 + 1608910 * q^80 + 3871872 * q^81 - 328536 * q^82 + 2825208 * q^84 + 3243644 * q^86 + 691398 * q^88 - 1729776 * q^89 + 214114 * q^90 + 1469284 * q^92 - 6618704 * q^93 - 551136 * q^94 - 5148618 * q^96 + 4548720 * q^97 - 2942042 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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