LMFDB - Embedded newform 43.8.c.a.6.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, 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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.12
Character	$\chi$	$=$	43.6
Dual form			43.8.c.a.36.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06697 q^{2} +(-34.1249 + 59.1060i) q^{3} -126.862 q^{4} +(-137.791 + 238.662i) q^{5} +(-36.4102 + 63.0644i) q^{6} +(809.683 + 1402.41i) q^{7} -271.930 q^{8} +(-1235.52 - 2139.98i) q^{9} +O(q^{10})$	\(q+1.06697 q^{2} +(-34.1249 + 59.1060i) q^{3} -126.862 q^{4} +(-137.791 + 238.662i) q^{5} +(-36.4102 + 63.0644i) q^{6} +(809.683 + 1402.41i) q^{7} -271.930 q^{8} +(-1235.52 - 2139.98i) q^{9} +(-147.019 + 254.645i) q^{10} -5266.36 q^{11} +(4329.14 - 7498.29i) q^{12} +(-2052.05 - 3554.26i) q^{13} +(863.908 + 1496.33i) q^{14} +(-9404.24 - 16288.6i) q^{15} +15948.1 q^{16} +(10939.8 + 18948.3i) q^{17} +(-1318.26 - 2283.29i) q^{18} +(24646.3 - 42688.6i) q^{19} +(17480.4 - 30277.0i) q^{20} -110521. q^{21} -5619.05 q^{22} +(-9044.27 + 15665.1i) q^{23} +(9279.57 - 16072.7i) q^{24} +(1089.54 + 1887.14i) q^{25} +(-2189.48 - 3792.29i) q^{26} +19385.1 q^{27} +(-102718. - 177912. i) q^{28} +(40294.4 + 69792.0i) q^{29} +(-10034.0 - 17379.5i) q^{30} +(-103550. + 179354. i) q^{31} +51823.2 q^{32} +(179714. - 311274. i) q^{33} +(11672.5 + 20217.3i) q^{34} -446270. q^{35} +(156740. + 271481. i) q^{36} +(106496. - 184456. i) q^{37} +(26296.8 - 45547.4i) q^{38} +280104. q^{39} +(37469.6 - 64899.2i) q^{40} +320915. q^{41} -117923. q^{42} +(211602. + 476490. i) q^{43} +668099. q^{44} +680974. q^{45} +(-9649.97 + 16714.2i) q^{46} -1.30803e6 q^{47} +(-544229. + 942631. i) q^{48} +(-899402. + 1.55781e6i) q^{49} +(1162.51 + 2013.52i) q^{50} -1.49328e6 q^{51} +(260327. + 450899. i) q^{52} +(852523. - 1.47661e6i) q^{53} +20683.4 q^{54} +(725659. - 1.25688e6i) q^{55} +(-220177. - 381358. i) q^{56} +(1.68210e6 + 2.91348e6i) q^{57} +(42992.9 + 74466.0i) q^{58} -857042. q^{59} +(1.19304e6 + 2.06640e6i) q^{60} +(225398. + 390401. i) q^{61} +(-110485. + 191366. i) q^{62} +(2.00075e6 - 3.46541e6i) q^{63} -1.98607e6 q^{64} +1.13102e6 q^{65} +(191750. - 332120. i) q^{66} +(1.15072e6 - 1.99310e6i) q^{67} +(-1.38784e6 - 2.40381e6i) q^{68} +(-617270. - 1.06914e6i) q^{69} -476157. q^{70} +(477019. + 826220. i) q^{71} +(335974. + 581923. i) q^{72} +(-1.86404e6 - 3.22861e6i) q^{73} +(113628. - 196809. i) q^{74} -148722. q^{75} +(-3.12666e6 + 5.41554e6i) q^{76} +(-4.26408e6 - 7.38561e6i) q^{77} +298863. q^{78} +(-999456. - 1.73111e6i) q^{79} +(-2.19752e6 + 3.80621e6i) q^{80} +(2.04056e6 - 3.53435e6i) q^{81} +342407. q^{82} +(-666631. + 1.15464e6i) q^{83} +1.40209e7 q^{84} -6.02965e6 q^{85} +(225774. + 508401. i) q^{86} -5.50017e6 q^{87} +1.43208e6 q^{88} +(-3.76862e6 + 6.52745e6i) q^{89} +726579. q^{90} +(3.32303e6 - 5.75565e6i) q^{91} +(1.14737e6 - 1.98730e6i) q^{92} +(-7.06728e6 - 1.22409e7i) q^{93} -1.39563e6 q^{94} +(6.79208e6 + 1.17642e7i) q^{95} +(-1.76846e6 + 3.06306e6i) q^{96} +917821. q^{97} +(-959636. + 1.66214e6i) q^{98} +(6.50667e6 + 1.12699e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9}+O(q^{10}) $ 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99}+O(q^{100}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9 + 1667 * q^10 - 4594 * q^11 - 8448 * q^12 + 2972 * q^13 - 15928 * q^14 - 2485 * q^15 + 185846 * q^16 + 25298 * q^17 + 13249 * q^18 + 3269 * q^19 + 2705 * q^20 - 85260 * q^21 + 150968 * q^22 - 19120 * q^23 - 55070 * q^24 - 296876 * q^25 - 139545 * q^26 - 274154 * q^27 - 118970 * q^28 - 231057 * q^29 + 240447 * q^30 - 177637 * q^31 + 1254274 * q^32 - 344986 * q^33 + 104923 * q^34 - 518850 * q^35 + 816168 * q^36 + 885140 * q^37 + 200956 * q^38 - 59884 * q^39 + 160425 * q^40 + 2202852 * q^41 - 349786 * q^42 + 1009342 * q^43 - 1012518 * q^44 + 775768 * q^45 - 1277532 * q^46 - 2784982 * q^47 - 2238049 * q^48 - 1241240 * q^49 - 5126146 * q^50 - 2477574 * q^51 - 268404 * q^52 - 398258 * q^53 + 6491644 * q^54 - 2551752 * q^55 - 4471819 * q^56 + 2094777 * q^57 - 2294852 * q^58 + 5664766 * q^59 + 1374965 * q^60 + 2652290 * q^61 - 5621243 * q^62 - 3210173 * q^63 + 5395148 * q^64 + 22093214 * q^65 - 284525 * q^66 + 5696184 * q^67 + 2422800 * q^68 + 4199245 * q^69 - 8874170 * q^70 - 16652990 * q^71 + 5916954 * q^72 + 108058 * q^73 + 8260200 * q^74 - 3594466 * q^75 - 7386456 * q^76 - 8874183 * q^77 - 27627308 * q^78 - 7378370 * q^79 + 7523523 * q^80 - 14862361 * q^81 + 7898428 * q^82 + 18099816 * q^83 + 47917640 * q^84 + 5843026 * q^85 + 14578342 * q^86 - 24244628 * q^87 + 23110740 * q^88 - 20405960 * q^89 + 32640076 * q^90 + 10283016 * q^91 - 27186571 * q^92 - 19267997 * q^93 - 52636002 * q^94 + 1708621 * q^95 + 8113092 * q^96 + 53505940 * q^97 - 3752059 * q^98 + 10929650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.06697			0.0943077			0.0471539	−	0.998888i	$-0.484985\pi$
$2$	1.06697			0.0943077			0.0471539	+	0.998888i	$0.484985\pi$
$3$	−34.1249	+	59.1060i	−0.729704	+	1.26388i	0.227304	+	0.973824i	$0.427009\pi$
$3$	−34.1249	+	59.1060i	−0.729704	+	1.26388i	−0.957008	+	0.290061i	$0.906324\pi$
$4$	−126.862			−0.991106
$5$	−137.791	+	238.662i	−0.492978	+	0.853862i	−0.999967	−	0.00808983i	$-0.997425\pi$
$5$	−137.791	+	238.662i	−0.492978	+	0.853862i	0.506990	+	0.861952i	$0.330758\pi$
$6$	−36.4102	+	63.0644i	−0.0688168	+	0.119194i
$7$	809.683	+	1402.41i	0.892220	+	1.54537i	0.837208	+	0.546885i	$0.184186\pi$
$7$	809.683	+	1402.41i	0.892220	+	1.54537i	0.0550124	+	0.998486i	$0.482480\pi$
$8$	−271.930			−0.187777
$9$	−1235.52	−	2139.98i	−0.564937	−	0.978499i
$10$	−147.019	+	254.645i	−0.0464916	+	0.0805258i
$11$	−5266.36			−1.19299			−0.596494	−	0.802617i	$-0.703440\pi$
$11$	−5266.36			−1.19299			−0.596494	+	0.802617i	$0.703440\pi$
$12$	4329.14	−	7498.29i	0.723214	−	1.25264i
$13$	−2052.05	−	3554.26i	−0.259052	−	0.448691i	0.706936	−	0.707277i	$-0.250077\pi$
$13$	−2052.05	−	3554.26i	−0.259052	−	0.448691i	−0.965988	+	0.258586i	$0.916743\pi$
$14$	863.908	+	1496.33i	0.0841433	+	0.145740i
$15$	−9404.24	−	16288.6i	−0.719456	−	1.24613i
$16$	15948.1			0.973397
$17$	10939.8	+	18948.3i	0.540056	+	0.935404i	0.998900	+	0.0468874i	$0.0149302\pi$
$17$	10939.8	+	18948.3i	0.540056	+	0.935404i	−0.458844	+	0.888517i	$0.651736\pi$
$18$	−1318.26	−	2283.29i	−0.0532779	−	0.0922800i
$19$	24646.3	−	42688.6i	0.824353	−	1.42782i	−0.0780596	−	0.996949i	$-0.524872\pi$
$19$	24646.3	−	42688.6i	0.824353	−	1.42782i	0.902413	−	0.430873i	$-0.141794\pi$
$20$	17480.4	−	30277.0i	0.488593	−	0.846268i
$21$	−110521.			−2.60423
$22$	−5619.05			−0.112508
$23$	−9044.27	+	15665.1i	−0.154998	+	0.268464i	−0.933058	−	0.359725i	$-0.882870\pi$
$23$	−9044.27	+	15665.1i	−0.154998	+	0.268464i	0.778060	+	0.628190i	$0.216204\pi$
$24$	9279.57	−	16072.7i	0.137021	−	0.237328i
$25$	1089.54	+	1887.14i	0.0139461	+	0.0241554i
$26$	−2189.48	−	3792.29i	−0.0244306	−	0.0423150i
$27$	19385.1			0.189538
$28$	−102718.	−	177912.i	−0.884285	−	1.53163i
$29$	40294.4	+	69792.0i	0.306798	+	0.531389i	0.977660	−	0.210193i	$-0.0674092\pi$
$29$	40294.4	+	69792.0i	0.306798	+	0.531389i	−0.670862	+	0.741582i	$0.734076\pi$
$30$	−10034.0	−	17379.5i	−0.0678503	−	0.117520i
$31$	−103550.	+	179354.i	−0.624289	+	1.08130i	0.364389	+	0.931247i	$0.381278\pi$
$31$	−103550.	+	179354.i	−0.624289	+	1.08130i	−0.988678	+	0.150053i	$0.952056\pi$
$32$	51823.2			0.279576
$33$	179714.	−	311274.i	0.870529	−	1.50780i
$34$	11672.5	+	20217.3i	0.0509314	+	0.0882158i
$35$	−446270.			−1.75938
$36$	156740.	+	271481.i	0.559912	+	0.969796i
$37$	106496.	−	184456.i	0.345642	−	0.598669i	−0.639828	−	0.768518i	$-0.720995\pi$
$37$	106496.	−	184456.i	0.345642	−	0.598669i	0.985470	+	0.169849i	$0.0543279\pi$
$38$	26296.8	−	45547.4i	0.0777429	−	0.134655i
$39$	280104.			0.756125
$40$	37469.6	−	64899.2i	0.0925697	−	0.160335i
$41$	320915.			0.727187			0.363594	−	0.931558i	$-0.381550\pi$
$41$	320915.			0.727187			0.363594	+	0.931558i	$0.381550\pi$
$42$	−117923.			−0.245599
$43$	211602.	+	476490.i	0.405865	+	0.913933i
$43$	211602.	+	476490.i	0.405865	+	0.913933i
$44$	668099.			1.18238
$45$	680974.			1.11400
$46$	−9649.97	+	16714.2i	−0.0146175	+	0.0253183i
$47$	−1.30803e6			−1.83770			−0.918852	−	0.394603i	$-0.870882\pi$
$47$	−1.30803e6			−1.83770			−0.918852	+	0.394603i	$0.870882\pi$
$48$	−544229.	+	942631.i	−0.710292	+	1.23026i
$49$	−899402.	+	1.55781e6i	−1.09211	+	1.89160i
$50$	1162.51	+	2013.52i	0.00131523	+	0.00227804i
$51$	−1.49328e6			−1.57632
$52$	260327.	+	450899.i	0.256748	+	0.444700i
$53$	852523.	−	1.47661e6i	0.786576	−	1.36239i	−0.141477	−	0.989941i	$-0.545185\pi$
$53$	852523.	−	1.47661e6i	0.786576	−	1.36239i	0.928053	−	0.372448i	$-0.121481\pi$
$54$	20683.4			0.0178749
$55$	725659.	−	1.25688e6i	0.588117	−	1.01865i
$56$	−220177.	−	381358.i	−0.167538	−	0.290185i
$57$	1.68210e6	+	2.91348e6i	1.20307	+	2.08377i
$58$	42992.9	+	74466.0i	0.0289334	+	0.0501141i
$59$	−857042.			−0.543275			−0.271638	−	0.962400i	$-0.587565\pi$
$59$	−857042.			−0.543275			−0.271638	+	0.962400i	$0.587565\pi$
$60$	1.19304e6	+	2.06640e6i	0.713057	+	1.23505i
$61$	225398.	+	390401.i	0.127144	+	0.220220i	0.922569	−	0.385832i	$-0.126086\pi$
$61$	225398.	+	390401.i	0.127144	+	0.220220i	−0.795425	+	0.606052i	$0.792752\pi$
$62$	−110485.	+	191366.i	−0.0588753	+	0.101975i
$63$	2.00075e6	−	3.46541e6i	1.00810	−	1.74607i
$64$	−1.98607e6			−0.947031
$65$	1.13102e6			0.510827
$66$	191750.	−	332120.i	0.0820976	−	0.142197i
$67$	1.15072e6	−	1.99310e6i	0.467420	−	0.809595i	−0.531887	−	0.846815i	$-0.678517\pi$
$67$	1.15072e6	−	1.99310e6i	0.467420	−	0.809595i	0.999307	+	0.0372204i	$0.0118504\pi$
$68$	−1.38784e6	−	2.40381e6i	−0.535253	−	0.927085i
$69$	−617270.	−	1.06914e6i	−0.226205	−	0.391799i
$70$	−476157.			−0.165923
$71$	477019.	+	826220.i	0.158173	+	0.273963i	0.934210	−	0.356724i	$-0.116106\pi$
$71$	477019.	+	826220.i	0.158173	+	0.273963i	−0.776037	+	0.630687i	$0.782773\pi$
$72$	335974.	+	581923.i	0.106082	+	0.183739i
$73$	−1.86404e6	−	3.22861e6i	−0.560822	−	0.971373i	−0.997425	−	0.0717181i	$-0.977152\pi$
$73$	−1.86404e6	−	3.22861e6i	−0.560822	−	0.971373i	0.436603	−	0.899654i	$-0.356182\pi$
$74$	113628.	−	196809.i	0.0325967	−	0.0564591i
$75$	−148722.			−0.0407061
$76$	−3.12666e6	+	5.41554e6i	−0.817021	+	1.41512i
$77$	−4.26408e6	−	7.38561e6i	−1.06441	−	1.84361i
$78$	298863.			0.0713084
$79$	−999456.	−	1.73111e6i	−0.228070	−	0.395029i	0.729166	−	0.684337i	$-0.239908\pi$
$79$	−999456.	−	1.73111e6i	−0.228070	−	0.395029i	−0.957236	+	0.289308i	$0.906575\pi$
$80$	−2.19752e6	+	3.80621e6i	−0.479863	+	0.831147i
$81$	2.04056e6	−	3.53435e6i	0.426630	−	0.738945i
$82$	342407.			0.0685794
$83$	−666631.	+	1.15464e6i	−0.127971	+	0.221652i	−0.922890	−	0.385063i	$-0.874180\pi$
$83$	−666631.	+	1.15464e6i	−0.127971	+	0.221652i	0.794919	+	0.606715i	$0.207513\pi$
$84$	1.40209e7			2.58107
$85$	−6.02965e6			−1.06494
$86$	225774.	+	508401.i	0.0382762	+	0.0861910i
$87$	−5.50017e6			−0.895486
$88$	1.43208e6			0.224015
$89$	−3.76862e6	+	6.52745e6i	−0.566654	+	0.981473i	0.430240	+	0.902715i	$0.358429\pi$
$89$	−3.76862e6	+	6.52745e6i	−0.566654	+	0.981473i	−0.996894	+	0.0787587i	$0.974904\pi$
$90$	726579.			0.105059
$91$	3.32303e6	−	5.75565e6i	0.462263	−	0.800662i
$92$	1.14737e6	−	1.98730e6i	0.153619	−	0.266077i
$93$	−7.06728e6	−	1.22409e7i	−0.911092	−	1.57806i
$94$	−1.39563e6			−0.173310
$95$	6.79208e6	+	1.17642e7i	0.812775	+	1.40777i
$96$	−1.76846e6	+	3.06306e6i	−0.204008	+	0.353351i
$97$	917821.			0.102107			0.0510537	−	0.998696i	$-0.483742\pi$
$97$	917821.			0.102107			0.0510537	+	0.998696i	$0.483742\pi$
$98$	−959636.	+	1.66214e6i	−0.102995	+	0.178392i
$99$	6.50667e6	+	1.12699e7i	0.673963	+	1.16734i
$100$	−138221.	−	239405.i	−0.0138221	−	0.0239405i
$101$	7.30351e6	+	1.26501e7i	0.705354	+	1.22171i	0.966564	+	0.256426i	$0.0825451\pi$
$101$	7.30351e6	+	1.26501e7i	0.705354	+	1.22171i	−0.261210	+	0.965282i	$0.584122\pi$
$102$	−1.59328e6			−0.148660
$103$	−7.76916e6	−	1.34566e7i	−0.700557	−	1.21340i	−0.968271	−	0.249902i	$-0.919602\pi$
$103$	−7.76916e6	−	1.34566e7i	−0.700557	−	1.21340i	0.267714	−	0.963498i	$-0.413732\pi$
$104$	558014.	+	966509.i	0.0486439	+	0.0842537i
$105$	1.52289e7	−	2.63772e7i	1.28383	−	2.22365i
$106$	909617.	−	1.57550e6i	0.0741802	−	0.128484i
$107$	−9.98194e6			−0.787720			−0.393860	−	0.919170i	$-0.628860\pi$
$107$	−9.98194e6			−0.787720			−0.393860	+	0.919170i	$0.628860\pi$
$108$	−2.45923e6			−0.187852
$109$	−2.90563e6	+	5.03270e6i	−0.214906	+	0.372228i	−0.953243	−	0.302204i	$-0.902278\pi$
$109$	−2.90563e6	+	5.03270e6i	−0.214906	+	0.372228i	0.738338	+	0.674431i	$0.235611\pi$
$110$	774257.	−	1.34105e6i	0.0554640	−	0.0960664i
$111$	7.26831e6	+	1.25891e7i	0.504432	+	0.873703i
$112$	1.29129e7	+	2.23659e7i	0.868485	+	1.50426i
$113$	9.20119e6			0.599887			0.299943	−	0.953957i	$-0.403032\pi$
$113$	9.20119e6			0.599887			0.299943	+	0.953957i	$0.403032\pi$
$114$	1.79475e6	+	3.10860e6i	0.113459	+	0.196516i
$115$	−2.49245e6	−	4.31704e6i	−0.152821	−	0.264694i
$116$	−5.11181e6	−	8.85392e6i	−0.304069	−	0.526663i
$117$	−5.07069e6	+	8.78269e6i	−0.292696	+	0.506964i
$118$	−914438.			−0.0512351
$119$	−1.77156e7	+	3.06843e7i	−0.963697	+	1.66917i
$120$	2.55729e6	+	4.42936e6i	0.135097	+	0.233995i
$121$	8.24739e6			0.423221
$122$	240493.	+	416546.i	0.0119907	+	0.0207684i
$123$	−1.09512e7	+	1.89680e7i	−0.530632	+	0.919081i
$124$	1.31366e7	−	2.27532e7i	0.618736	−	1.07168i
$125$	−2.21304e7			−1.01346
$126$	2.13474e6	−	3.69749e6i	0.0950712	−	0.164668i
$127$	5.29514e6			0.229385			0.114692	−	0.993401i	$-0.463412\pi$
$127$	5.29514e6			0.229385			0.114692	+	0.993401i	$0.463412\pi$
$128$	−8.75245e6			−0.368888
$129$	−3.53844e7	−	3.75319e6i	−1.45127	−	0.153935i
$130$	1.20677e6			0.0481750
$131$	8.55422e6			0.332454			0.166227	−	0.986088i	$-0.446842\pi$
$131$	8.55422e6			0.332454			0.166227	+	0.986088i	$0.446842\pi$
$132$	−2.27988e7	+	3.94887e7i	−0.862786	+	1.49439i
$133$	7.98226e7			2.94202
$134$	1.22778e6	−	2.12658e6i	0.0440813	−	0.0763511i
$135$	−2.67111e6	+	4.62649e6i	−0.0934379	+	0.161839i
$136$	−2.97486e6	−	5.15261e6i	−0.101410	−	0.175647i
$137$	−4.24699e7			−1.41111			−0.705553	−	0.708657i	$-0.749301\pi$
$137$	−4.24699e7			−1.41111			−0.705553	+	0.708657i	$0.749301\pi$
$138$	−658608.	−	1.14074e6i	−0.0213329	−	0.0369497i
$139$	−163376.	+	282975.i	−0.00515983	+	0.00893709i	−0.868594	−	0.495525i	$-0.834976\pi$
$139$	−163376.	+	282975.i	−0.00515983	+	0.00893709i	0.863434	+	0.504462i	$0.168309\pi$
$140$	5.66145e7			1.74373
$141$	4.46364e7	−	7.73125e7i	1.34098	−	2.32265i
$142$	508965.	+	881553.i	0.0149169	+	0.0258368i
$143$	1.08069e7	+	1.87180e7i	0.309046	+	0.535283i
$144$	−1.97042e7	−	3.41287e7i	−0.549908	−	0.952468i
$145$	−2.22089e7			−0.604977
$146$	−1.98888e6	−	3.44483e6i	−0.0528899	−	0.0916080i
$147$	−6.13840e7	−	1.06320e8i	−1.59384	−	2.76061i
$148$	−1.35102e7	+	2.34004e7i	−0.342568	+	0.593344i
$149$	1.58275e7	−	2.74140e7i	0.391977	−	0.678924i	−0.600733	−	0.799449i	$-0.705125\pi$
$149$	1.58275e7	−	2.74140e7i	0.391977	−	0.678924i	0.992710	+	0.120526i	$0.0384580\pi$
$150$	−158682.			−0.00383890
$151$	1.05303e7			0.248899			0.124449	−	0.992226i	$-0.460284\pi$
$151$	1.05303e7			0.248899			0.124449	+	0.992226i	$0.460284\pi$
$152$	−6.70205e6	+	1.16083e7i	−0.154794	+	0.268112i
$153$	2.70326e7	−	4.68219e7i	0.610194	−	1.05689i
$154$	−4.54965e6	−	7.88023e6i	−0.100382	−	0.173867i
$155$	−2.85367e7	−	4.94270e7i	−0.615521	−	1.06611i
$156$	−3.55345e7			−0.749400
$157$	−1.50222e7	−	2.60191e7i	−0.309802	−	0.536592i	0.668517	−	0.743697i	$-0.266929\pi$
$157$	−1.50222e7	−	2.60191e7i	−0.309802	−	0.536592i	−0.978319	+	0.207105i	$0.933596\pi$
$158$	−1.06639e6	−	1.84704e6i	−0.0215088	−	0.0372543i
$159$	5.81845e7	+	1.00779e8i	1.14794	+	1.98828i
$160$	−7.14079e6	+	1.23682e7i	−0.137825	+	0.238719i
$161$	−2.92920e7			−0.553169
$162$	2.17721e6	−	3.77105e6i	0.0402345	−	0.0696882i
$163$	4.99682e7	+	8.65474e7i	0.903726	+	1.56530i	0.822618	+	0.568594i	$0.192512\pi$
$163$	4.99682e7	+	8.65474e7i	0.903726	+	1.56530i	0.0811078	+	0.996705i	$0.474154\pi$
$164$	−4.07118e7			−0.720720
$165$	4.95261e7	+	8.57817e7i	0.858302	+	1.48662i
$166$	−711275.	+	1.23196e6i	−0.0120687	+	0.0209035i
$167$	−2.48793e7	+	4.30922e7i	−0.413362	+	0.715963i	−0.995255	−	0.0973019i	$-0.968979\pi$
$167$	−2.48793e7	+	4.30922e7i	−0.413362	+	0.715963i	0.581893	+	0.813265i	$0.302312\pi$
$168$	3.00541e7			0.489013
$169$	2.29524e7	−	3.97548e7i	0.365784	−	0.633557i
$170$	−6.43346e6			−0.100432
$171$	−1.21803e8			−1.86283
$172$	−2.68442e7	−	6.04483e7i	−0.402255	−	0.905805i
$173$	8.59617e7			1.26225			0.631123	−	0.775683i	$-0.282594\pi$
$173$	8.59617e7			1.26225			0.631123	+	0.775683i	$0.282594\pi$
$174$	−5.86852e6			−0.0844513
$175$	−1.76436e6	+	3.05597e6i	−0.0248860	+	0.0431038i
$176$	−8.39887e7			−1.16125
$177$	2.92465e7	−	5.06564e7i	0.396430	−	0.686638i
$178$	−4.02101e6	+	6.96460e6i	−0.0534399	+	0.0925605i
$179$	2.59768e7	+	4.49932e7i	0.338532	+	0.586355i	0.984157	−	0.177300i	$-0.0567362\pi$
$179$	2.59768e7	+	4.49932e7i	0.338532	+	0.586355i	−0.645624	+	0.763655i	$0.723403\pi$
$180$	−8.63895e7			−1.10410
$181$	2.96123e7	+	5.12901e7i	0.371191	+	0.642922i	0.989749	−	0.142817i	$-0.0456161\pi$
$181$	2.96123e7	+	5.12901e7i	0.371191	+	0.642922i	−0.618558	+	0.785739i	$0.712283\pi$
$182$	3.54557e6	−	6.14111e6i	0.0435949	−	0.0755087i
$183$	−3.07667e7			−0.371110
$184$	2.45941e6	−	4.25982e6i	0.0291050	−	0.0504114i
$185$	2.93484e7	+	5.08329e7i	0.340787	+	0.590261i
$186$	−7.54058e6	−	1.30607e7i	−0.0859230	−	0.148823i
$187$	−5.76130e7	−	9.97886e7i	−0.644280	−	1.11593i
$188$	1.65939e8			1.82136
$189$	1.56958e7	+	2.71860e7i	0.169109	+	0.292906i
$190$	7.24695e6	+	1.25521e7i	0.0766510	+	0.132763i
$191$	−2.23079e7	+	3.86385e7i	−0.231655	+	0.401239i	−0.958295	−	0.285779i	$-0.907748\pi$
$191$	−2.23079e7	+	3.86385e7i	−0.231655	+	0.401239i	0.726640	+	0.687018i	$0.241081\pi$
$192$	6.77744e7	−	1.17389e8i	0.691053	−	1.19694i
$193$	−6.12264e7			−0.613039			−0.306519	−	0.951864i	$-0.599164\pi$
$193$	−6.12264e7			−0.613039			−0.306519	+	0.951864i	$0.599164\pi$
$194$	979288.			0.00962951
$195$	−3.85960e7	+	6.68502e7i	−0.372753	+	0.645627i
$196$	1.14100e8	−	1.97626e8i	1.08240	−	1.87477i
$197$	1.11748e7	+	1.93554e7i	0.104138	+	0.180372i	0.913386	−	0.407095i	$-0.133458\pi$
$197$	1.11748e7	+	1.93554e7i	0.104138	+	0.180372i	−0.809248	+	0.587468i	$0.800125\pi$
$198$	6.94243e6	+	1.20246e7i	0.0635599	+	0.110089i
$199$	1.93204e8			1.73792			0.868960	−	0.494882i	$-0.164789\pi$
$199$	1.93204e8			1.73792			0.868960	+	0.494882i	$0.164789\pi$
$200$	−296278.	−	513169.i	−0.00261875	−	0.00453581i
$201$	7.85362e7	+	1.36029e8i	0.682156	+	1.18153i
$202$	7.79263e6	+	1.34972e7i	0.0665203	+	0.115217i
$203$	−6.52514e7	+	1.13019e8i	−0.547462	+	0.948232i
$204$	1.89440e8			1.56230
$205$	−4.42193e7	+	7.65901e7i	−0.358487	+	0.620918i
$206$	−8.28946e6	−	1.43578e7i	−0.0660680	−	0.114433i
$207$	4.46974e7			0.350256
$208$	−3.27264e7	−	5.66838e7i	−0.252160	−	0.436755i
$209$	−1.29796e8	+	2.24813e8i	−0.983444	+	1.70337i
$210$	1.62488e7	−	2.81437e7i	0.121075	−	0.209708i
$211$	−9.83960e7			−0.721089			−0.360544	−	0.932742i	$-0.617409\pi$
$211$	−9.83960e7			−0.721089			−0.360544	+	0.932742i	$0.617409\pi$
$212$	−1.08152e8	+	1.87325e8i	−0.779580	+	1.35027i
$213$	−6.51128e7			−0.461677
$214$	−1.06504e7			−0.0742881
$215$	−1.42877e8	−	1.51549e7i	−0.980455	−	0.103996i
$216$	−5.27140e6			−0.0355908
$217$	−3.35372e8			−2.22801
$218$	−3.10022e6	+	5.36974e6i	−0.0202673	+	0.0351039i
$219$	2.54441e8			1.63694
$220$	−9.20583e7	+	1.59450e8i	−0.582886	+	1.00959i
$221$	4.48981e7	−	7.77659e7i	0.279805	−	0.484636i
$222$	7.75507e6	+	1.34322e7i	0.0475719	+	0.0823969i
$223$	1.79338e8			1.08294			0.541470	−	0.840720i	$-0.317868\pi$
$223$	1.79338e8			1.08294			0.541470	+	0.840720i	$0.317868\pi$
$224$	4.19604e7	+	7.26775e7i	0.249443	+	0.432048i
$225$	2.69229e6	−	4.66318e6i	0.0157573	−	0.0272925i
$226$	9.81740e6			0.0565740
$227$	−1.42048e8	+	2.46034e8i	−0.806016	+	1.39606i	0.109588	+	0.993977i	$0.465047\pi$
$227$	−1.42048e8	+	2.46034e8i	−0.806016	+	1.39606i	−0.915603	+	0.402083i	$0.868286\pi$
$228$	−2.13394e8	−	3.69609e8i	−1.19237	−	2.06524i
$229$	−7.89572e7	−	1.36758e8i	−0.434478	−	0.752537i	0.562775	−	0.826610i	$-0.309734\pi$
$229$	−7.89572e7	−	1.36758e8i	−0.434478	−	0.752537i	−0.997253	+	0.0740726i	$0.976400\pi$
$230$	−2.65937e6	−	4.60616e6i	−0.0144122	−	0.0249627i
$231$	5.82046e8			3.10681
$232$	−1.09573e7	−	1.89785e7i	−0.0576094	−	0.0997825i
$233$	−1.64453e8	−	2.84841e8i	−0.851718	−	1.47522i	−0.879657	−	0.475608i	$-0.842228\pi$
$233$	−1.64453e8	−	2.84841e8i	−0.851718	−	1.47522i	0.0279396	−	0.999610i	$-0.491105\pi$
$234$	−5.41027e6	+	9.37087e6i	−0.0276035	+	0.0478106i
$235$	1.80235e8	−	3.12177e8i	0.905947	−	1.56915i
$236$	1.08726e8			0.538444
$237$	1.36425e8			0.665695
$238$	−1.89020e7	+	3.27392e7i	−0.0908841	+	0.157416i
$239$	−1.01923e8	+	1.76535e8i	−0.482924	+	0.836449i	−0.999808	−	0.0196068i	$-0.993759\pi$
$239$	−1.01923e8	+	1.76535e8i	−0.482924	+	0.836449i	0.516884	+	0.856056i	$0.327092\pi$
$240$	−1.49980e8	−	2.59773e8i	−0.700316	−	1.21298i
$241$	6.96083e6	+	1.20565e7i	0.0320333	+	0.0554833i	0.881598	−	0.472002i	$-0.156468\pi$
$241$	6.96083e6	+	1.20565e7i	0.0320333	+	0.0554833i	−0.849564	+	0.527485i	$0.823135\pi$
$242$	8.79972e6			0.0399131
$243$	1.60465e8	+	2.77934e8i	0.717396	+	1.24257i
$244$	−2.85944e7	−	4.95269e7i	−0.126013	−	0.218261i
$245$	−2.47860e8	−	4.29306e8i	−1.07678	−	1.86503i
$246$	−1.16846e7	+	2.02383e7i	−0.0500427	+	0.0866764i
$247$	−2.02302e8			−0.854201
$248$	2.81584e7	−	4.87718e7i	0.117227	−	0.203043i
$249$	−4.54974e7	−	7.88038e7i	−0.186762	−	0.323482i
$250$	−2.36125e7			−0.0955767
$251$	−1.46626e8	−	2.53964e8i	−0.585266	−	1.01371i	−0.994842	−	0.101435i	$-0.967657\pi$
$251$	−1.46626e8	−	2.53964e8i	−0.585266	−	1.01371i	0.409576	−	0.912276i	$-0.365677\pi$
$252$	−2.53819e8	+	4.39627e8i	−0.999130	+	1.73054i
$253$	4.76304e7	−	8.24983e7i	0.184911	−	0.320275i
$254$	5.64976e6			0.0216328
$255$	2.05761e8	−	3.56389e8i	0.777092	−	1.34596i
$256$	2.44878e8			0.912242
$257$	−1.09871e8			−0.403753			−0.201877	−	0.979411i	$-0.564704\pi$
$257$	−1.09871e8			−0.403753			−0.201877	+	0.979411i	$0.564704\pi$
$258$	−3.77541e7	−	4.00455e6i	−0.136866	−	0.0145173i
$259$	3.44911e8			1.23355
$260$	−1.43483e8			−0.506284
$261$	9.95688e7	−	1.72458e8i	0.346642	−	0.600402i
$262$	9.12710e6			0.0313530
$263$	3.92613e7	−	6.80026e7i	0.133082	−	0.230505i	−0.791781	−	0.610805i	$-0.790846\pi$
$263$	3.92613e7	−	6.80026e7i	0.133082	−	0.230505i	0.924863	+	0.380300i	$0.124179\pi$
$264$	−4.88696e7	+	8.46446e7i	−0.163465	+	0.283130i
$265$	2.34941e8	+	4.06929e8i	0.775529	+	1.34325i
$266$	8.51684e7			0.277455
$267$	−2.57208e8	−	4.45497e8i	−0.826979	−	1.43237i
$268$	−1.45982e8	+	2.52848e8i	−0.463263	+	0.802394i
$269$	−5.16651e8			−1.61832			−0.809161	−	0.587588i	$-0.800078\pi$
$269$	−5.16651e8			−1.61832			−0.809161	+	0.587588i	$0.800078\pi$
$270$	−2.84999e6	+	4.93633e6i	−0.00881192	+	0.0152627i
$271$	1.12609e7	+	1.95045e7i	0.0343701	+	0.0595307i	0.882699	−	0.469939i	$-0.155724\pi$
$271$	1.12609e7	+	1.95045e7i	0.0343701	+	0.0595307i	−0.848329	+	0.529470i	$0.822391\pi$
$272$	1.74470e8	+	3.02190e8i	0.525689	+	0.910520i
$273$	2.26796e8	+	3.92822e8i	0.674630	+	1.16849i
$274$	−4.53142e7			−0.133078
$275$	−5.73791e6	−	9.93835e6i	−0.0166375	−	0.0288171i
$276$	7.83078e7	+	1.35633e8i	0.224194	+	0.388315i
$277$	2.49964e8	−	4.32950e8i	0.706639	−	1.22394i	−0.259457	−	0.965755i	$-0.583544\pi$
$277$	2.49964e8	−	4.32950e8i	0.706639	−	1.22394i	0.966097	−	0.258181i	$-0.0831230\pi$
$278$	−174317.	+	301926.i	−0.000486612	+	0.000842837i
$279$	5.11752e8			1.41073
$280$	1.21354e8			0.330370
$281$	−2.61548e8	+	4.53015e8i	−0.703201	+	1.21798i	0.264136	+	0.964485i	$0.414913\pi$
$281$	−2.61548e8	+	4.53015e8i	−0.703201	+	1.21798i	−0.967337	+	0.253494i	$0.918420\pi$
$282$	4.76257e7	−	8.24902e7i	0.126465	−	0.219043i
$283$	−2.05694e8	−	3.56273e8i	−0.539473	−	0.934395i	−0.998932	−	0.0461963i	$-0.985290\pi$
$283$	−2.05694e8	−	3.56273e8i	−0.539473	−	0.934395i	0.459459	−	0.888199i	$-0.348043\pi$
$284$	−6.05153e7	−	1.04816e8i	−0.156766	−	0.271526i
$285$	−9.27117e8			−2.37234
$286$	1.15306e7	+	1.99716e7i	0.0291454	+	0.0504814i
$287$	2.59839e8	+	4.50055e8i	0.648811	+	1.12377i
$288$	−6.40284e7	−	1.10900e8i	−0.157942	−	0.273564i
$289$	−3.41896e7	+	5.92181e7i	−0.0833204	+	0.144315i
$290$	−2.36962e7			−0.0570540
$291$	−3.13205e7	+	5.42488e7i	−0.0745082	+	0.129052i
$292$	2.36475e8	+	4.09587e8i	0.555834	+	0.962733i
$293$	1.96961e8			0.457450			0.228725	−	0.973491i	$-0.426544\pi$
$293$	1.96961e8			0.457450			0.228725	+	0.973491i	$0.426544\pi$
$294$	−6.54949e7	−	1.13441e8i	−0.150311	−	0.260347i
$295$	1.18093e8	−	2.04543e8i	0.267823	−	0.463882i
$296$	−2.89594e7	+	5.01591e7i	−0.0649035	+	0.112416i
$297$	−1.02089e8			−0.226116
$298$	1.68875e7	−	2.92500e7i	0.0369665	−	0.0640278i
$299$	7.42373e7			0.160610
$300$	1.88671e7			0.0403441
$301$	−4.96905e8	+	6.82560e8i	−1.05025	+	1.44264i
$302$	1.12355e7			0.0234731
$303$	−9.96926e8			−2.05880
$304$	3.93062e8	−	6.80803e8i	0.802423	−	1.38984i
$305$	−1.24232e8			−0.250717
$306$	2.88430e7	−	4.99576e7i	0.0575461	−	0.0996727i
$307$	−5.64180e7	+	9.77189e7i	−0.111284	+	0.192750i	−0.916288	−	0.400519i	$-0.868830\pi$
$307$	−5.64180e7	+	9.77189e7i	−0.111284	+	0.192750i	0.805004	+	0.593269i	$0.202163\pi$
$308$	5.40948e8	+	9.36950e8i	1.05494	+	1.82721i
$309$	1.06049e9			2.04480
$310$	−3.04478e7	−	5.27371e7i	−0.0580484	−	0.100543i
$311$	−3.80010e8	+	6.58197e8i	−0.716364	+	1.24078i	0.246067	+	0.969253i	$0.420862\pi$
$311$	−3.80010e8	+	6.58197e8i	−0.716364	+	1.24078i	−0.962431	+	0.271526i	$0.912472\pi$
$312$	−7.61687e7			−0.141983
$313$	2.47025e8	−	4.27860e8i	0.455341	−	0.788673i	−0.543367	−	0.839495i	$-0.682851\pi$
$313$	2.47025e8	−	4.27860e8i	0.455341	−	0.788673i	0.998708	+	0.0508221i	$0.0161842\pi$
$314$	−1.60282e7	−	2.77617e7i	−0.0292167	−	0.0506048i
$315$	5.51373e8	+	9.55007e8i	0.993937	+	1.72155i
$316$	1.26792e8	+	2.19611e8i	0.226042	+	0.391516i
$317$	6.71071e8			1.18321			0.591604	−	0.806229i	$-0.298495\pi$
$317$	6.71071e8			1.18321			0.591604	+	0.806229i	$0.298495\pi$
$318$	6.20811e7	+	1.07528e8i	0.108259	+	0.187510i
$319$	−2.12205e8	−	3.67550e8i	−0.366006	−	0.633941i
$320$	2.73663e8	−	4.73999e8i	0.466865	−	0.808634i
$321$	3.40633e8	−	5.89993e8i	0.574802	−	0.995587i
$322$	−3.12537e7			−0.0521682
$323$	1.07850e9			1.78079
$324$	−2.58868e8	+	4.48373e8i	−0.422836	+	0.732373i
$325$	4.47158e6	−	7.74501e6i	0.00722553	−	0.0125150i
$326$	5.33146e7	+	9.23435e7i	0.0852284	+	0.147620i
$327$	−1.98309e8	−	3.43481e8i	−0.313635	−	0.543232i
$328$	−8.72663e7			−0.136549
$329$	−1.05909e9	−	1.83440e9i	−1.63964	−	2.83993i
$330$	5.28429e7	+	9.15266e7i	0.0809446	+	0.140200i
$331$	−2.62756e7	−	4.55106e7i	−0.0398248	−	0.0689786i	0.845426	−	0.534093i	$-0.179347\pi$
$331$	−2.62756e7	−	4.55106e7i	−0.0398248	−	0.0689786i	−0.885251	+	0.465114i	$0.846013\pi$
$332$	8.45698e7	−	1.46479e8i	0.126833	−	0.219681i
$333$	−5.26309e8			−0.781063
$334$	−2.65454e7	+	4.59781e7i	−0.0389832	+	0.0675209i
$335$	3.17118e8	+	5.49265e8i	0.460855	+	0.798224i
$336$	−1.76261e9			−2.53495
$337$	6.12192e8	+	1.06035e9i	0.871331	+	1.50919i	0.860621	+	0.509247i	$0.170076\pi$
$337$	6.12192e8	+	1.06035e9i	0.871331	+	1.50919i	0.0107101	+	0.999943i	$0.496591\pi$
$338$	2.44896e7	−	4.24171e7i	0.0344963	−	0.0597493i
$339$	−3.13990e8	+	5.43846e8i	−0.437740	+	0.758188i
$340$	7.64931e8			1.05547
$341$	5.45333e8	−	9.44545e8i	0.744769	−	1.28998i
$342$	−1.29961e8			−0.175679
$343$	−1.57931e9			−2.11318
$344$	−5.75410e7	−	1.29572e8i	−0.0762119	−	0.171615i
$345$	3.40218e8			0.446057
$346$	9.17186e7			0.119040
$347$	−2.27280e8	+	3.93661e8i	−0.292017	+	0.505789i	−0.974287	−	0.225312i	$-0.927660\pi$
$347$	−2.27280e8	+	3.93661e8i	−0.292017	+	0.505789i	0.682269	+	0.731101i	$0.260993\pi$
$348$	6.97760e8			0.887521
$349$	−4.30121e8	+	7.44992e8i	−0.541629	+	0.938129i	0.457182	+	0.889373i	$0.348859\pi$
$349$	−4.30121e8	+	7.44992e8i	−0.541629	+	0.938129i	−0.998811	+	0.0487555i	$0.984474\pi$
$350$	−1.88252e6	+	3.26063e6i	−0.00234694	+	0.00406502i
$351$	−3.97793e7	−	6.88998e7i	−0.0491001	−	0.0850439i
$352$	−2.72920e8			−0.333531
$353$	−8.40081e7	−	1.45506e8i	−0.101651	−	0.176064i	0.810714	−	0.585442i	$-0.199079\pi$
$353$	−8.40081e7	−	1.45506e8i	−0.101651	−	0.176064i	−0.912365	+	0.409378i	$0.865746\pi$
$354$	3.12051e7	−	5.40488e7i	0.0373865	−	0.0647552i
$355$	−2.62916e8			−0.311902
$356$	4.78094e8	−	8.28083e8i	0.561614	−	0.972744i
$357$	−1.20908e9	−	2.09419e9i	−1.40643	−	2.43600i
$358$	2.77165e7	+	4.80064e7i	0.0319262	+	0.0552979i
$359$	8.64724e7	+	1.49775e8i	0.0986387	+	0.170847i	0.911121	−	0.412138i	$-0.135218\pi$
$359$	8.64724e7	+	1.49775e8i	0.0986387	+	0.170847i	−0.812483	+	0.582985i	$0.801885\pi$
$360$	−1.85177e8			−0.209184
$361$	−7.67940e8	−	1.33011e9i	−0.859116	−	1.48803i
$362$	3.15955e7	+	5.47250e7i	0.0350062	+	0.0606325i
$363$	−2.81441e8	+	4.87471e8i	−0.308827	+	0.534903i
$364$	−4.21564e8	+	7.30171e8i	−0.458151	+	0.793541i
$365$	1.02739e9			1.10589
$366$	−3.28272e7			−0.0349985
$367$	−9.32651e8	+	1.61540e9i	−0.984890	+	1.70588i	−0.342467	+	0.939530i	$0.611263\pi$
$367$	−9.32651e8	+	1.61540e9i	−0.984890	+	1.70588i	−0.642423	+	0.766350i	$0.722071\pi$
$368$	−1.44239e8	+	2.49830e8i	−0.150875	+	0.261323i
$369$	−3.96495e8	−	6.86750e8i	−0.410815	−	0.711552i
$370$	3.13139e7	+	5.42372e7i	0.0321389	+	0.0556662i
$371$	2.76109e9			2.80720
$372$	8.96567e8	+	1.55290e9i	0.902989	+	1.56402i
$373$	−4.34342e8	−	7.52302e8i	−0.433362	−	0.750604i	0.563799	−	0.825912i	$-0.309339\pi$
$373$	−4.34342e8	−	7.52302e8i	−0.433362	−	0.750604i	−0.997160	+	0.0753078i	$0.976006\pi$
$374$	−6.14714e7	−	1.06472e8i	−0.0607606	−	0.105240i
$375$	7.55198e8	−	1.30804e9i	0.739523	−	1.28089i
$376$	3.55692e8			0.345078
$377$	1.65373e8	−	2.86434e8i	0.158953	−	0.275315i
$378$	1.67470e7	+	2.90066e7i	0.0159483	+	0.0276233i
$379$	−2.32925e8			−0.219775			−0.109888	−	0.993944i	$-0.535049\pi$
$379$	−2.32925e8			−0.219775			−0.109888	+	0.993944i	$0.535049\pi$
$380$	−8.61655e8	−	1.49243e9i	−0.805546	−	1.39525i
$381$	−1.80696e8	+	3.12975e8i	−0.167383	+	0.289916i
$382$	−2.38019e7	+	4.12261e7i	−0.0218469	+	0.0378400i
$383$	−1.79379e9			−1.63146			−0.815728	−	0.578436i	$-0.803663\pi$
$383$	−1.79379e9			−1.63146			−0.815728	+	0.578436i	$0.803663\pi$
$384$	2.98676e8	−	5.17322e8i	0.269179	−	0.466232i
$385$	2.35022e9			2.09892
$386$	−6.53267e7			−0.0578143
$387$	7.58240e8	−	1.04154e9i	0.664995	−	0.913452i
$388$	−1.16436e8			−0.101199
$389$	3.67857e8			0.316852			0.158426	−	0.987371i	$-0.449358\pi$
$389$	3.67857e8			0.316852			0.158426	+	0.987371i	$0.449358\pi$
$390$	−4.11808e7	+	7.13272e7i	−0.0351535	+	0.0608876i
$391$	−3.95770e8			−0.334830
$392$	2.44574e8	−	4.23615e8i	0.205074	−	0.355198i
$393$	−2.91912e8	+	5.05606e8i	−0.242593	+	0.420183i
$394$	1.19232e7	+	2.06516e7i	0.00982102	+	0.0170105i
$395$	5.50866e8			0.449734
$396$	−8.25447e8	−	1.42972e9i	−0.667969	−	1.15696i
$397$	1.07879e9	−	1.86851e9i	0.865304	−	1.49875i	−0.00144163	−	0.999999i	$-0.500459\pi$
$397$	1.07879e9	−	1.86851e9i	0.865304	−	1.49875i	0.866745	−	0.498751i	$-0.166208\pi$
$398$	2.06143e8			0.163899
$399$	−2.72394e9	+	4.71800e9i	−2.14680	+	3.71837i
$400$	1.73761e7	+	3.00963e7i	0.0135751	+	0.0235128i
$401$	5.27599e7	+	9.13828e7i	0.0408600	+	0.0707716i	0.885732	−	0.464197i	$-0.153657\pi$
$401$	5.27599e7	+	9.13828e7i	0.0408600	+	0.0707716i	−0.844872	+	0.534968i	$0.820324\pi$
$402$	8.37958e7	+	1.45139e8i	0.0643326	+	0.111427i
$403$	8.49963e8			0.646893
$404$	−9.26535e8	−	1.60481e9i	−0.699080	−	1.21084i
$405$	5.62343e8	+	9.74006e8i	0.420638	+	0.728566i
$406$	−6.96213e7	+	1.20588e8i	−0.0516299	+	0.0894256i
$407$	−5.60845e8	+	9.71412e8i	−0.412347	+	0.714205i
$408$	4.06067e8			0.295997
$409$	−8.50530e8			−0.614693			−0.307346	−	0.951598i	$-0.599441\pi$
$409$	−8.50530e8			−0.614693			−0.307346	+	0.951598i	$0.599441\pi$
$410$	−4.71807e7	+	8.17194e7i	−0.0338081	+	0.0585574i
$411$	1.44928e9	−	2.51023e9i	1.02969	−	1.78348i
$412$	9.85607e8	+	1.70712e9i	0.694326	+	1.20261i
$413$	−6.93933e8	−	1.20193e9i	−0.484721	−	0.839562i
$414$	4.76908e7			0.0330319
$415$	−1.83712e8	−	3.18199e8i	−0.126174	−	0.218539i
$416$	−1.06344e8	−	1.84193e8i	−0.0724246	−	0.125443i
$417$	−1.11504e7	−	1.93130e7i	−0.00753030	−	0.0130429i
$418$	−1.38489e8	+	2.39869e8i	−0.0927464	+	0.160641i
$419$	3.30092e8			0.219223			0.109611	−	0.993975i	$-0.465039\pi$
$419$	3.30092e8			0.219223			0.109611	+	0.993975i	$0.465039\pi$
$420$	−1.93196e9	+	3.34626e9i	−1.27241	+	2.20387i
$421$	2.57161e8	+	4.45417e8i	0.167965	+	0.290924i	0.937704	−	0.347435i	$-0.112947\pi$
$421$	2.57161e8	+	4.45417e8i	0.167965	+	0.290924i	−0.769739	+	0.638358i	$0.779614\pi$
$422$	−1.04986e8			−0.0680043
$423$	1.61609e9	+	2.79915e9i	1.03819	+	1.79819i
$424$	−2.31826e8	+	4.01535e8i	−0.147701	+	0.255825i
$425$	−2.38387e7	+	4.12898e7i	−0.0150633	+	0.0260905i
$426$	−6.94735e7			−0.0435397
$427$	−3.65002e8	+	6.32202e8i	−0.226881	+	0.392969i
$428$	1.26632e9			0.780714
$429$	−1.47513e9			−0.902048
$430$	−1.52446e8	−	1.61698e7i	−0.0924645	−	0.00980765i
$431$	−1.48066e9			−0.890808			−0.445404	−	0.895330i	$-0.646940\pi$
$431$	−1.48066e9			−0.890808			−0.445404	+	0.895330i	$0.646940\pi$
$432$	3.09157e8			0.184496
$433$	−1.50821e9	+	2.61229e9i	−0.892798	+	1.54637i	−0.0562918	+	0.998414i	$0.517928\pi$
$433$	−1.50821e9	+	2.61229e9i	−0.892798	+	1.54637i	−0.836506	+	0.547957i	$0.815406\pi$
$434$	−3.57832e8			−0.210119
$435$	7.57876e8	−	1.31268e9i	0.441454	−	0.764622i
$436$	3.68613e8	−	6.38457e8i	0.212994	−	0.368917i
$437$	4.45815e8	+	7.72174e8i	0.255546	+	0.442619i
$438$	2.71481e8			0.154376
$439$	7.35485e8	+	1.27390e9i	0.414905	+	0.718636i	0.995418	−	0.0956146i	$-0.0304816\pi$
$439$	7.35485e8	+	1.27390e9i	0.414905	+	0.718636i	−0.580514	+	0.814250i	$0.697148\pi$
$440$	−1.97328e8	+	3.41783e8i	−0.110435	+	0.191278i
$441$	4.44491e9			2.46790
$442$	4.79050e7	−	8.29739e7i	0.0263878	−	0.0457050i
$443$	4.33757e8	+	7.51289e8i	0.237047	+	0.410577i	0.959865	−	0.280461i	$-0.0904873\pi$
$443$	4.33757e8	+	7.51289e8i	0.237047	+	0.410577i	−0.722819	+	0.691037i	$0.757154\pi$
$444$	−9.22069e8	−	1.59707e9i	−0.499946	−	0.865932i
$445$	−1.03857e9	−	1.79885e9i	−0.558695	−	0.967689i
$446$	1.91348e8			0.102130
$447$	1.08022e9	+	1.87100e9i	0.572054	+	0.990827i
$448$	−1.60809e9	−	2.78529e9i	−0.844960	−	1.46351i
$449$	−3.20067e7	+	5.54372e7i	−0.0166870	+	0.0289028i	−0.874248	−	0.485479i	$-0.838645\pi$
$449$	−3.20067e7	+	5.54372e7i	−0.0166870	+	0.0289028i	0.857561	+	0.514382i	$0.171979\pi$
$450$	2.87259e6	−	4.97547e6i	0.00148604	−	0.00257389i
$451$	−1.69005e9			−0.867526
$452$	−1.16728e9			−0.594552
$453$	−3.59346e8	+	6.22406e8i	−0.181622	+	0.314579i
$454$	−1.51561e8	+	2.62511e8i	−0.0760135	+	0.131659i
$455$	9.15769e8	+	1.58616e9i	0.455770	+	0.789417i
$456$	−4.57413e8	−	7.92263e8i	−0.225908	−	0.391284i
$457$	−1.07344e8			−0.0526102			−0.0263051	−	0.999654i	$-0.508374\pi$
$457$	−1.07344e8			−0.0526102			−0.0263051	+	0.999654i	$0.508374\pi$
$458$	−8.42450e7	−	1.45917e8i	−0.0409746	−	0.0709701i
$459$	2.12070e8	+	3.67316e8i	0.102361	+	0.177294i
$460$	3.16196e8	+	5.47667e8i	0.151462	+	0.262340i
$461$	6.03940e8	−	1.04606e9i	0.287105	−	0.497280i	−0.686012	−	0.727590i	$-0.740640\pi$
$461$	6.03940e8	−	1.04606e9i	0.287105	−	0.497280i	0.973117	+	0.230309i	$0.0739738\pi$
$462$	6.21025e8			0.292997
$463$	4.72300e8	−	8.18048e8i	0.221149	−	0.383041i	−0.734008	−	0.679141i	$-0.762353\pi$
$463$	4.72300e8	−	8.18048e8i	0.221149	−	0.383041i	0.955157	+	0.296099i	$0.0956860\pi$
$464$	6.42621e8	+	1.11305e9i	0.298636	+	0.517253i
$465$	3.89525e9			1.79659
$466$	−1.75466e8	−	3.03917e8i	−0.0803236	−	0.139124i
$467$	−1.28467e9	+	2.22511e9i	−0.583689	+	1.01098i	0.411349	+	0.911478i	$0.365058\pi$
$467$	−1.28467e9	+	2.22511e9i	−0.583689	+	1.01098i	−0.995038	+	0.0995004i	$0.968276\pi$
$468$	6.43276e8	−	1.11419e9i	0.290093	−	0.502455i
$469$	3.72687e9			1.66817
$470$	1.92306e8	−	3.33083e8i	0.0854378	−	0.147983i
$471$	2.05052e9			0.904254
$472$	2.33055e8			0.102014
$473$	−1.11438e9	−	2.50937e9i	−0.484192	−	1.09031i
$474$	1.45562e8			0.0627802
$475$	1.07412e8			0.0459860
$476$	2.24742e9	−	3.89265e9i	0.955126	−	1.65433i
$477$	−4.21322e9			−1.77746
$478$	−1.08749e8	+	1.88358e8i	−0.0455435	+	0.0788836i
$479$	−4.86382e8	+	8.42438e8i	−0.202210	+	0.350238i	−0.949240	−	0.314552i	$-0.898146\pi$
$479$	−4.86382e8	+	8.42438e8i	−0.202210	+	0.350238i	0.747030	+	0.664790i	$0.231479\pi$
$480$	−4.87358e8	−	8.44128e8i	−0.201142	−	0.348389i
$481$	−8.74139e8			−0.358157
$482$	7.42700e6	+	1.28639e7i	0.00302099	+	0.00523250i
$483$	9.99586e8	−	1.73133e9i	0.403650	−	0.699142i
$484$	−1.04628e9			−0.419457
$485$	−1.26468e8	+	2.19049e8i	−0.0503366	+	0.0871856i
$486$	1.71212e8	+	2.96547e8i	0.0676560	+	0.117184i
$487$	4.02585e8	+	6.97298e8i	0.157945	+	0.273569i	0.934128	−	0.356939i	$-0.116180\pi$
$487$	4.02585e8	+	6.97298e8i	0.157945	+	0.273569i	−0.776182	+	0.630508i	$0.782846\pi$
$488$	−6.12924e7	−	1.06162e8i	−0.0238747	−	0.0413522i
$489$	−6.82063e9			−2.63781
$490$	−2.64459e8	−	4.58057e8i	−0.101548	−	0.175887i
$491$	−7.30700e8	−	1.26561e9i	−0.278582	−	0.482519i	0.692450	−	0.721466i	$-0.256531\pi$
$491$	−7.30700e8	−	1.26561e9i	−0.278582	−	0.482519i	−0.971033	+	0.238947i	$0.923198\pi$
$492$	1.38928e9	−	2.40631e9i	0.525912	−	0.910907i
$493$	−8.81627e8	+	1.52702e9i	−0.331376	+	0.573959i
$494$	−2.15850e8			−0.0805578
$495$	−3.58626e9			−1.32899
$496$	−1.65143e9	+	2.86037e9i	−0.607681	+	1.05253i
$497$	−7.72468e8	+	1.33795e9i	−0.282249	+	0.488870i
$498$	−4.85444e7	−	8.40813e7i	−0.0176131	−	0.0305068i
$499$	−1.45764e9	−	2.52470e9i	−0.525167	−	0.909615i	−0.999570	−	0.0293080i	$-0.990670\pi$
$499$	−1.45764e9	−	2.52470e9i	−0.525167	−	0.909615i	0.474404	−	0.880307i	$-0.342664\pi$
$500$	2.80750e9			1.00444
$501$	−1.69800e9	−	2.94103e9i	−0.603263	−	1.04488i
$502$	−1.56446e8	−	2.70972e8i	−0.0551951	−	0.0956008i
$503$	−1.35884e9	−	2.35359e9i	−0.476082	−	0.824598i	0.523543	−	0.851999i	$-0.324610\pi$
$503$	−1.35884e9	−	2.35359e9i	−0.476082	−	0.824598i	−0.999625	+	0.0274016i	$0.991277\pi$
$504$	−5.44064e8	+	9.42347e8i	−0.189297	+	0.327872i
$505$	−4.02544e9			−1.39089
$506$	5.08202e7	−	8.80232e7i	0.0174385	−	0.0302044i
$507$	1.56650e9	+	2.71325e9i	0.533829	+	0.924618i
$508$	−6.71750e8			−0.227345
$509$	8.58414e8	+	1.48682e9i	0.288526	+	0.499741i	0.973458	−	0.228866i	$-0.0735016\pi$
$509$	8.58414e8	+	1.48682e9i	0.288526	+	0.499741i	−0.684932	+	0.728607i	$0.740168\pi$
$510$	2.19541e8	−	3.80256e8i	0.0732858	−	0.126935i
$511$	3.01856e9	−	5.22831e9i	1.00075	−	1.73336i
$512$	1.38159e9			0.454919
$513$	4.77771e8	−	8.27524e8i	0.156246	−	0.270626i
$514$	−1.17229e8			−0.0380771
$515$	4.28209e9			1.38144
$516$	4.48892e9	+	4.76136e8i	1.43836	+	0.152566i
$517$	6.88856e9			2.19236
$518$	3.68010e8			0.116334
$519$	−2.93343e9	+	5.08086e9i	−0.921066	+	1.59533i
$520$	−3.07558e8			−0.0959214
$521$	−1.63498e9	+	2.83188e9i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335729\pi$
$521$	−1.63498e9	+	2.83188e9i	−0.506502	+	0.877288i	−0.999972	+	0.00752457i	$0.997605\pi$
$522$	1.06237e8	−	1.84008e8i	0.0326911	−	0.0566226i
$523$	1.57385e9	+	2.72598e9i	0.481068	+	0.833235i	0.999764	−	0.0217243i	$-0.00691560\pi$
$523$	1.57385e9	+	2.72598e9i	0.481068	+	0.833235i	−0.518696	+	0.854959i	$0.673582\pi$
$524$	−1.08520e9			−0.329497
$525$	−1.20417e8	−	2.08569e8i	−0.0363188	−	0.0629060i
$526$	4.18907e7	−	7.25568e7i	0.0125507	−	0.0217384i
$527$	−4.53128e9			−1.34860
$528$	2.86610e9	−	4.96424e9i	0.847370	−	1.46769i
$529$	1.53882e9	+	2.66531e9i	0.451951	+	0.782802i
$530$	2.50675e8	+	4.34182e8i	0.0731384	+	0.126679i
$531$	1.05889e9	+	1.83405e9i	0.306916	+	0.531594i
$532$	−1.01264e10			−2.91585
$533$	−6.58534e8	−	1.14061e9i	−0.188379	−	0.326282i
$534$	−2.74433e8	−	4.75332e8i	−0.0779906	−	0.135084i
$535$	1.37543e9	−	2.38231e9i	0.388328	−	0.672604i
$536$	−3.12914e8	+	5.41984e8i	−0.0877706	+	0.152023i
$537$	−3.54582e9			−0.988114
$538$	−5.51252e8			−0.152620
$539$	4.73658e9	−	8.20399e9i	1.30288	−	2.25665i
$540$	3.38861e8	−	5.86924e8i	0.0926069	−	0.160400i
$541$	−1.26882e8	−	2.19766e8i	−0.0344516	−	0.0596719i	0.848286	−	0.529539i	$-0.177635\pi$
$541$	−1.26882e8	−	2.19766e8i	−0.0344516	−	0.0596719i	−0.882737	+	0.469867i	$0.844302\pi$
$542$	1.20150e7	+	2.08107e7i	0.00324137	+	0.00561421i
$543$	−4.04207e9			−1.08344
$544$	5.66936e8	+	9.81962e8i	0.150986	+	0.261516i
$545$	−8.00743e8	−	1.38693e9i	−0.211887	−	0.367000i
$546$	2.41984e8	+	4.19129e8i	0.0636228	+	0.110198i
$547$	−2.52000e9	+	4.36477e9i	−0.658333	+	1.14027i	0.322714	+	0.946496i	$0.395405\pi$
$547$	−2.52000e9	+	4.36477e9i	−0.658333	+	1.14027i	−0.981047	+	0.193769i	$0.937929\pi$
$548$	5.38780e9			1.39856
$549$	5.56966e8	−	9.64693e8i	0.143657	−	0.248820i
$550$	−6.12218e6	−	1.06039e7i	−0.00156905	−	0.00271767i
$551$	3.97243e9			1.01164
$552$	1.67854e8	+	2.90732e8i	0.0424761	+	0.0735708i
$553$	1.61848e9	−	2.80330e9i	0.406978	−	0.704906i
$554$	2.66704e8	−	4.61945e8i	0.0666416	−	0.115427i
$555$	−4.00604e9			−0.994696
$556$	2.07261e7	−	3.58986e7i	0.00511394	−	0.00885761i
$557$	−3.14277e9			−0.770583			−0.385291	−	0.922795i	$-0.625899\pi$
$557$	−3.14277e9			−0.770583			−0.385291	+	0.922795i	$0.625899\pi$
$558$	5.46024e8			0.133043
$559$	1.25935e9	−	1.72987e9i	0.304934	−	0.418864i
$560$	−7.11717e9			−1.71257
$561$	7.86415e9			1.88054
$562$	−2.79064e8	+	4.83353e8i	−0.0663173	+	0.114865i
$563$	6.90710e9			1.63123			0.815617	−	0.578592i	$-0.196398\pi$
$563$	6.90710e9			1.63123			0.815617	+	0.578592i	$0.196398\pi$
$564$	−5.66264e9	+	9.80799e9i	−1.32905	+	2.30199i
$565$	−1.26785e9	+	2.19597e9i	−0.295731	+	0.512221i
$566$	−2.19470e8	−	3.80133e8i	−0.0508765	−	0.0881207i
$567$	6.60882e9			1.52259
$568$	−1.29716e8	−	2.24674e8i	−0.0297011	−	0.0514438i
$569$	1.83276e9	−	3.17444e9i	0.417075	−	0.722394i	−0.578569	−	0.815633i	$-0.696389\pi$
$569$	1.83276e9	−	3.17444e9i	0.417075	−	0.722394i	0.995644	+	0.0932389i	$0.0297220\pi$
$570$	−9.89206e8			−0.223730
$571$	1.50869e9	−	2.61312e9i	0.339135	−	0.587399i	−0.645135	−	0.764068i	$-0.723199\pi$
$571$	1.50869e9	−	2.61312e9i	0.339135	−	0.587399i	0.984270	+	0.176669i	$0.0565323\pi$
$572$	−1.37097e9	−	2.37460e9i	−0.306297	−	0.530522i
$573$	−1.52251e9	−	2.63707e9i	−0.338080	−	0.585572i
$574$	2.77241e8	+	4.80195e8i	0.0611879	+	0.105981i
$575$	−3.94163e7			−0.00864647
$576$	2.45382e9	+	4.25014e9i	0.535012	+	0.926669i
$577$	1.67205e9	+	2.89608e9i	0.362355	+	0.627618i	0.988348	−	0.152211i	$-0.0486393\pi$
$577$	1.67205e9	+	2.89608e9i	0.362355	+	0.627618i	−0.625993	+	0.779829i	$0.715306\pi$
$578$	−3.64793e7	+	6.31840e7i	−0.00785776	+	0.0136100i
$579$	2.08934e9	−	3.61885e9i	0.447337	−	0.774810i
$580$	2.81746e9			0.599597
$581$	−2.15904e9			−0.456714
$582$	−3.34181e7	+	5.78818e7i	−0.00702670	+	0.0121706i
$583$	−4.48969e9	+	7.77638e9i	−0.938376	+	1.62531i
$584$	5.06888e8	+	8.77956e8i	0.105309	+	0.182401i
$585$	−1.39739e9	−	2.42036e9i	−0.288585	−	0.499844i
$586$	2.10152e8			0.0431411
$587$	1.33703e9	+	2.31580e9i	0.272839	+	0.472572i	0.969588	−	0.244744i	$-0.0787039\pi$
$587$	1.33703e9	+	2.31580e9i	0.272839	+	0.472572i	−0.696748	+	0.717316i	$0.745371\pi$
$588$	7.78727e9	+	1.34880e10i	1.57966	+	2.73606i
$589$	5.10425e9	+	8.84083e9i	1.02927	+	1.78275i
$590$	1.26002e8	−	2.18241e8i	0.0252577	−	0.0437477i
$591$	−1.52536e9			−0.303960
$592$	1.69841e9	−	2.94173e9i	0.336447	−	0.582743i
$593$	−1.20225e9	−	2.08236e9i	−0.236757	−	0.410076i	0.723025	−	0.690822i	$-0.242751\pi$
$593$	−1.20225e9	−	2.08236e9i	−0.236757	−	0.410076i	−0.959782	+	0.280746i	$0.909418\pi$
$594$	−1.08926e8			−0.0213245
$595$	−4.88211e9	−	8.45606e9i	−0.950162	−	1.64573i
$596$	−2.00790e9	+	3.47779e9i	−0.388491	+	0.672886i
$597$	−6.59306e9	+	1.14195e10i	−1.26817	+	2.19653i
$598$	7.92090e7			0.0151468
$599$	−1.35789e9	+	2.35194e9i	−0.258149	+	0.447128i	−0.965746	−	0.259489i	$-0.916446\pi$
$599$	−1.35789e9	+	2.35194e9i	−0.258149	+	0.447128i	0.707597	+	0.706616i	$0.249779\pi$
$600$	4.04418e7			0.00764366
$601$	2.43163e8			0.0456916			0.0228458	−	0.999739i	$-0.492727\pi$
$601$	2.43163e8			0.0456916			0.0228458	+	0.999739i	$0.492727\pi$
$602$	−5.30183e8	+	7.28271e8i	−0.0990462	+	0.136052i
$603$	−5.68692e9			−1.05625
$604$	−1.33589e9			−0.246685
$605$	−1.13642e9	+	1.96834e9i	−0.208639	+	0.361373i
$606$	−1.06369e9			−0.194161
$607$	4.70172e9	−	8.14362e9i	0.853289	−	1.47794i	−0.0249335	−	0.999689i	$-0.507937\pi$
$607$	4.70172e9	−	8.14362e9i	0.853289	−	1.47794i	0.878223	−	0.478251i	$-0.158729\pi$
$608$	1.27725e9	−	2.21226e9i	0.230469	−	0.399184i
$609$	−4.45340e9	−	7.71351e9i	−0.798970	−	1.38386i
$610$	−1.32552e8			−0.0236445
$611$	2.68415e9	+	4.64908e9i	0.476060	+	0.824561i
$612$	−3.42940e9	+	5.93990e9i	−0.604767	+	1.04749i
$613$	−1.94475e9			−0.340998			−0.170499	−	0.985358i	$-0.554538\pi$
$613$	−1.94475e9			−0.340998			−0.170499	+	0.985358i	$0.554538\pi$
$614$	−6.01964e7	+	1.04263e8i	−0.0104950	+	0.0181778i
$615$	−3.01796e9	−	5.22726e9i	−0.523179	−	0.906173i
$616$	1.15953e9	+	2.00837e9i	0.199871	+	0.346187i
$617$	3.63635e9	+	6.29834e9i	0.623257	+	1.07951i	0.988875	+	0.148748i	$0.0475242\pi$
$617$	3.63635e9	+	6.29834e9i	0.623257	+	1.07951i	−0.365618	+	0.930765i	$0.619142\pi$
$618$	1.13151e9			0.192840
$619$	1.51342e9	+	2.62132e9i	0.256473	+	0.444224i	0.965295	−	0.261163i	$-0.0841062\pi$
$619$	1.51342e9	+	2.62132e9i	0.256473	+	0.444224i	−0.708821	+	0.705388i	$0.750773\pi$
$620$	3.62021e9	+	6.27039e9i	0.610046	+	1.05663i
$621$	−1.75325e8	+	3.03671e8i	−0.0293780	+	0.0508842i
$622$	−4.05459e8	+	7.02276e8i	−0.0675587	+	0.117015i
$623$	−1.22056e10			−2.02232
$624$	4.46714e9			0.736010
$625$	2.96426e9	−	5.13425e9i	0.485665	−	0.841196i
$626$	2.63569e8	−	4.56514e8i	0.0429421	−	0.0743780i
$627$	−8.85855e9	−	1.53435e10i	−1.43525	−	2.48592i
$628$	1.90573e9	+	3.30083e9i	0.307046	+	0.531820i
$629$	4.66017e9			0.746663
$630$	5.88299e8	+	1.01896e9i	0.0937360	+	0.162355i
$631$	9.22860e8	+	1.59844e9i	0.146229	+	0.253276i	0.929831	−	0.367987i	$-0.119953\pi$
$631$	9.22860e8	+	1.59844e9i	0.146229	+	0.253276i	−0.783602	+	0.621263i	$0.786620\pi$
$632$	2.71782e8	+	4.70740e8i	0.0428263	+	0.0741773i
$633$	3.35775e9	−	5.81580e9i	0.526182	−	0.911373i
$634$	7.16013e8			0.111586
$635$	−7.29625e8	+	1.26375e9i	−0.113082	+	0.195863i
$636$	−7.38138e9	−	1.27849e10i	−1.13773	−	1.97060i
$637$	7.38248e9			1.13166
$638$	−2.26416e8	−	3.92165e8i	−0.0345172	−	0.0597855i
$639$	1.17873e9	−	2.04162e9i	0.178715	−	0.309543i
$640$	1.20601e9	−	2.08887e9i	0.181854	−	0.314980i
$641$	9.91409e9			1.48679			0.743395	−	0.668853i	$-0.233214\pi$
$641$	9.91409e9			1.48679			0.743395	+	0.668853i	$0.233214\pi$
$642$	3.63445e8	−	6.29505e8i	0.0542083	−	0.0938916i
$643$	−3.77540e8			−0.0560048			−0.0280024	−	0.999608i	$-0.508915\pi$
$643$	−3.77540e8			−0.0560048			−0.0280024	+	0.999608i	$0.508915\pi$
$644$	3.71603e9			0.548250
$645$	5.77141e9	−	7.92774e9i	0.846882	−	1.16330i
$646$	1.15073e9			0.167942
$647$	−1.10827e10			−1.60872			−0.804360	−	0.594142i	$-0.797492\pi$
$647$	−1.10827e10			−1.60872			−0.804360	+	0.594142i	$0.797492\pi$
$648$	−5.54888e8	+	9.61095e8i	−0.0801112	+	0.138757i
$649$	4.51349e9			0.648121
$650$	4.77105e6	−	8.26369e6i	0.000681423	−	0.00118026i
$651$	1.14445e10	−	1.98225e10i	1.62579	−	2.81595i
$652$	−6.33904e9	−	1.09795e10i	−0.895688	−	1.55138i
$653$	1.10289e9			0.155002			0.0775009	−	0.996992i	$-0.475306\pi$
$653$	1.10289e9			0.155002			0.0775009	+	0.996992i	$0.475306\pi$
$654$	−2.11590e8	−	3.66484e8i	−0.0295782	−	0.0512310i
$655$	−1.17870e9	+	2.04157e9i	−0.163892	+	0.283870i
$656$	5.11799e9			0.707842
$657$	−4.60610e9	+	7.97800e9i	−0.633658	+	1.09753i
$658$	−1.13002e9	−	1.95725e9i	−0.154630	−	0.267828i
$659$	−2.46752e8	−	4.27387e8i	−0.0335863	−	0.0581731i	0.848744	−	0.528804i	$-0.177360\pi$
$659$	−2.46752e8	−	4.27387e8i	−0.0335863	−	0.0581731i	−0.882330	+	0.470631i	$0.844026\pi$
$660$	−6.28296e9	−	1.08824e10i	−0.850669	−	1.47340i
$661$	1.33545e9			0.179855			0.0899274	−	0.995948i	$-0.471336\pi$
$661$	1.33545e9			0.179855			0.0899274	+	0.995948i	$0.471336\pi$
$662$	−2.80352e7	−	4.85584e7i	−0.00375579	−	0.00650522i
$663$	3.06429e9	+	5.30750e9i	0.408350	+	0.707282i
$664$	1.81277e8	−	3.13980e8i	0.0240300	−	0.0416212i
$665$	−1.09989e10	+	1.90506e10i	−1.45035	+	2.51208i
$666$	−5.61556e8			−0.0736602
$667$	−1.45773e9			−0.190212
$668$	3.15622e9	−	5.46674e9i	0.409685	−	0.709595i
$669$	−6.11987e9	+	1.05999e10i	−0.790226	+	1.36871i
$670$	3.38356e8	+	5.86049e8i	0.0434622	+	0.0752787i
$671$	−1.18703e9	−	2.05599e9i	−0.151681	−	0.262720i
$672$	−5.72757e9			−0.728078
$673$	−1.61310e9	−	2.79398e9i	−0.203990	−	0.353322i	0.745820	−	0.666147i	$-0.232058\pi$
$673$	−1.61310e9	−	2.79398e9i	−0.203990	−	0.353322i	−0.949811	+	0.312826i	$0.898724\pi$
$674$	6.53191e8	+	1.13136e9i	0.0821732	+	0.142328i
$675$	2.11209e7	+	3.65824e7i	0.00264331	+	0.00457835i
$676$	−2.91178e9	+	5.04335e9i	−0.362531	+	0.627922i
$677$	−1.31320e10			−1.62657			−0.813283	−	0.581869i	$-0.802322\pi$
$677$	−1.31320e10			−1.62657			−0.813283	+	0.581869i	$0.802322\pi$
$678$	−3.35018e8	+	5.80267e8i	−0.0412823	+	0.0715030i
$679$	7.43144e8	+	1.28716e9i	0.0911022	+	0.157794i
$680$	1.63964e9			0.199971
$681$	−9.69472e9	−	1.67917e10i	−1.17631	−	2.03742i
$682$	5.81854e8	−	1.00780e9i	0.0702375	−	0.121655i
$683$	−4.10774e9	+	7.11481e9i	−0.493322	+	0.854458i	−0.999970	−	0.00769445i	$-0.997551\pi$
$683$	−4.10774e9	+	7.11481e9i	−0.493322	+	0.854458i	0.506649	+	0.862153i	$0.330884\pi$
$684$	1.54522e10			1.84626
$685$	5.85199e9	−	1.01359e10i	0.695644	−	1.20489i
$686$	−1.68507e9			−0.199289
$687$	1.07776e10			1.26816
$688$	3.37467e9	+	7.59913e9i	0.395067	+	0.889620i
$689$	−6.99769e9			−0.815056
$690$	3.63002e8			0.0420666
$691$	3.55741e9	−	6.16161e9i	0.410167	−	0.710429i	−0.584741	−	0.811220i	$-0.698804\pi$
$691$	3.55741e9	−	6.16161e9i	0.410167	−	0.710429i	0.994908	+	0.100791i	$0.0321372\pi$
$692$	−1.09052e10			−1.25102
$693$	−1.05367e10	+	1.82501e10i	−1.20265	+	2.08304i
$694$	−2.42501e8	+	4.20024e8i	−0.0275395	+	0.0476998i
$695$	−4.50235e7	−	7.79831e7i	−0.00508736	−	0.00881157i
$696$	1.49566e9			0.168151
$697$	3.51075e9	+	6.08079e9i	0.392722	+	0.680214i
$698$	−4.58927e8	+	7.94884e8i	−0.0510798	+	0.0884728i
$699$	2.24477e10			2.48601
$700$	2.23830e8	−	3.87685e8i	0.0246646	−	0.0427204i
$701$	−3.67644e9	−	6.36779e9i	−0.403102	−	0.698193i	0.590997	−	0.806674i	$-0.298735\pi$
$701$	−3.67644e9	−	6.36779e9i	−0.403102	−	0.698193i	−0.994099	+	0.108481i	$0.965401\pi$
$702$	−4.24434e7	−	7.35141e7i	−0.00463052	−	0.00802030i
$703$	−5.24944e9	−	9.09230e9i	−0.569862	−	0.987029i
$704$	1.04594e10			1.12980
$705$	1.23010e10	+	2.13060e10i	1.32215	+	2.29002i
$706$	−8.96341e7	−	1.55251e8i	−0.00958643	−	0.0166042i
$707$	−1.18271e10	+	2.04851e10i	−1.25866	+	2.18007i
$708$	−3.71025e9	+	6.42635e9i	−0.392905	+	0.680531i
$709$	−8.89392e9			−0.937198			−0.468599	−	0.883411i	$-0.655241\pi$
$709$	−8.89392e9			−0.937198			−0.468599	+	0.883411i	$0.655241\pi$
$710$	−2.80524e8			−0.0294148
$711$	−2.46969e9	+	4.27762e9i	−0.257690	+	0.446333i
$712$	1.02480e9	−	1.77501e9i	0.106404	−	0.184298i
$713$	−1.87307e9	−	3.24426e9i	−0.193527	−	0.335199i
$714$	−1.29006e9	−	2.23444e9i	−0.132637	−	0.229734i
$715$	−5.95637e9			−0.609411
$716$	−3.29546e9	−	5.70790e9i	−0.335522	−	0.581140i
$717$	−6.95621e9	−	1.20485e10i	−0.704783	−	1.22072i
$718$	9.22635e7	+	1.59805e8i	0.00930239	+	0.0161122i
$719$	1.82888e9	−	3.16772e9i	0.183499	−	0.317830i	−0.759570	−	0.650425i	$-0.774591\pi$
$719$	1.82888e9	−	3.16772e9i	0.183499	−	0.317830i	0.943070	+	0.332595i	$0.107924\pi$
$720$	1.08603e10			1.08437
$721$	1.25811e10	−	2.17911e10i	1.25010	−	2.16524i
$722$	−8.19369e8	−	1.41919e9i	−0.0810213	−	0.140333i
$723$	−9.50150e8			−0.0934993
$724$	−3.75667e9	−	6.50674e9i	−0.367890	−	0.637204i
$725$	−8.78047e7	+	1.52082e8i	−0.00855726	+	0.0148216i
$726$	−3.00289e8	+	5.20117e8i	−0.0291247	+	0.0504455i
$727$	−2.56078e9			−0.247173			−0.123587	−	0.992334i	$-0.539440\pi$
$727$	−2.56078e9			−0.247173			−0.123587	+	0.992334i	$0.539440\pi$
$728$	−9.03629e8	+	1.56513e9i	−0.0868022	+	0.150346i
$729$	−1.29780e10			−1.24069
$730$	1.09620e9			0.104294
$731$	−6.71379e9	+	9.22222e9i	−0.635707	+	0.873222i
$732$	3.90312e9			0.367809
$733$	9.19221e9			0.862097			0.431048	−	0.902329i	$-0.358144\pi$
$733$	9.19221e9			0.862097			0.431048	+	0.902329i	$0.358144\pi$
$734$	−9.95111e8	+	1.72358e9i	−0.0928828	+	0.160878i
$735$	3.38328e10			3.14291
$736$	−4.68703e8	+	8.11818e8i	−0.0433337	+	0.0750561i
$737$	−6.06010e9	+	1.04964e10i	−0.557626	+	0.965837i
$738$	−4.23049e8	−	7.32742e8i	−0.0387430	−	0.0671048i
$739$	−2.83666e9			−0.258554			−0.129277	−	0.991609i	$-0.541266\pi$
$739$	−2.83666e9			−0.258554			−0.129277	+	0.991609i	$0.541266\pi$
$740$	−3.72318e9	−	6.44874e9i	−0.337756	−	0.585011i
$741$	6.90352e9	−	1.19572e10i	0.623314	−	1.07961i
$742$	2.94601e9			0.264740
$743$	9.98471e9	−	1.72940e10i	0.893048	−	1.54680i	0.0568450	−	0.998383i	$-0.481896\pi$
$743$	9.98471e9	−	1.72940e10i	0.893048	−	1.54680i	0.836203	−	0.548421i	$-0.184771\pi$
$744$	1.92180e9	+	3.32866e9i	0.171082	+	0.296323i
$745$	4.36179e9	+	7.55484e9i	0.386472	+	0.669389i
$746$	−4.63430e8	−	8.02684e8i	−0.0408694	−	0.0707878i
$747$	3.29453e9			0.289182
$748$	7.30888e9	+	1.26593e10i	0.638550	+	1.10600i
$749$	−8.08221e9	−	1.39988e10i	−0.702819	−	1.21732i
$750$	8.05774e8	−	1.39564e9i	0.0697427	−	0.120798i
$751$	−9.87324e9	+	1.71010e10i	−0.850589	+	1.47326i	0.0300878	+	0.999547i	$0.490421\pi$
$751$	−9.87324e9	+	1.71010e10i	−0.850589	+	1.47326i	−0.880677	+	0.473717i	$0.842912\pi$
$752$	−2.08607e10			−1.78882
$753$	2.00144e10			1.70829
$754$	1.76448e8	−	3.05616e8i	0.0149905	−	0.0259643i
$755$	−1.45099e9	+	2.51319e9i	−0.122701	+	0.212525i
$756$	−1.99120e9	−	3.44886e9i	−0.167605	−	0.290301i
$757$	2.06577e8	+	3.57801e8i	0.0173080	+	0.0299783i	0.874550	−	0.484936i	$-0.161157\pi$
$757$	2.06577e8	+	3.57801e8i	0.0173080	+	0.0299783i	−0.857242	+	0.514914i	$0.827824\pi$
$758$	−2.48524e8			−0.0207265
$759$	3.25076e9	+	5.63049e9i	0.269860	+	0.467412i
$760$	−1.84697e9	−	3.19905e9i	−0.152620	−	0.264346i
$761$	1.13816e10	+	1.97134e10i	0.936172	+	1.62150i	0.772531	+	0.634977i	$0.218990\pi$
$761$	1.13816e10	+	1.97134e10i	0.936172	+	1.62150i	0.163640	+	0.986520i	$0.447676\pi$
$762$	−1.92797e8	+	3.33935e8i	−0.0157855	+	0.0273413i
$763$	−9.41057e9			−0.766973
$764$	2.83002e9	−	4.90174e9i	0.229595	−	0.397670i
$765$	7.44973e9	+	1.29033e10i	0.601624	+	1.04204i
$766$	−1.91392e9			−0.153859
$767$	1.75870e9	+	3.04615e9i	0.140737	+	0.243763i
$768$	−8.35644e9	+	1.44738e10i	−0.665667	+	1.15297i
$769$	−1.11923e10	+	1.93857e10i	−0.887519	+	1.53723i	−0.0447206	+	0.999000i	$0.514240\pi$
$769$	−1.11923e10	+	1.93857e10i	−0.887519	+	1.53723i	−0.842799	+	0.538229i	$0.819094\pi$
$770$	2.50761e9			0.197944
$771$	3.74933e9	−	6.49402e9i	0.294620	−	0.510298i
$772$	7.76727e9			0.607586
$773$	9.59556e9			0.747209			0.373604	−	0.927588i	$-0.378122\pi$
$773$	9.59556e9			0.747209			0.373604	+	0.927588i	$0.378122\pi$
$774$	8.09020e8	−	1.11129e9i	0.0627142	−	0.0861456i
$775$	−4.51288e8			−0.0348256
$776$	−2.49583e8			−0.0191734
$777$	−1.17701e10	+	2.03863e10i	−0.900130	+	1.55907i
$778$	3.92493e8			0.0298816
$779$	7.90935e9	−	1.36994e10i	0.599459	−	1.03829i
$780$	4.89635e9	−	8.48072e9i	0.369437	−	0.639884i
$781$	−2.51215e9	−	4.35117e9i	−0.188698	−	0.326835i
$782$	−4.22275e8			−0.0315771
$783$	7.81113e8	+	1.35293e9i	0.0581497	+	0.100718i
$784$	−1.43438e10	+	2.48442e10i	−1.06306	+	1.84127i
$785$	8.27970e9			0.610901
$786$	−3.11461e8	+	5.39467e8i	−0.0228784	+	0.0396265i
$787$	−2.43416e9	−	4.21608e9i	−0.178007	−	0.308317i	0.763191	−	0.646173i	$-0.223632\pi$
$787$	−2.43416e9	−	4.21608e9i	−0.178007	−	0.308317i	−0.941198	+	0.337856i	$0.890298\pi$
$788$	−1.41766e9	−	2.45545e9i	−0.103212	−	0.178768i
$789$	2.67958e9	+	4.64116e9i	0.194221	+	0.336401i
$790$	5.87757e8			0.0424134
$791$	7.45005e9	+	1.29039e10i	0.535231	+	0.927048i
$792$	−1.76936e9	−	3.06462e9i	−0.126555	−	0.219199i
$793$	9.25057e8	−	1.60225e9i	0.0658738	−	0.114097i
$794$	1.15103e9	−	1.99365e9i	0.0816048	−	0.141344i
$795$	−3.20693e10			−2.26363
$796$	−2.45101e10			−1.72246
$797$	−6.54920e8	+	1.13435e9i	−0.0458231	+	0.0793679i	−0.888027	−	0.459791i	$-0.847924\pi$
$797$	−6.54920e8	+	1.13435e9i	−0.0458231	+	0.0793679i	0.842204	+	0.539159i	$0.181258\pi$
$798$	−2.90636e9	+	5.03397e9i	−0.202460	+	0.350671i
$799$	−1.43096e10	−	2.47850e10i	−0.992462	−	1.71899i
$800$	5.64634e7	+	9.77975e7i	0.00389899	+	0.00675325i
$801$	1.86248e10			1.28049
$802$	5.62932e7	+	9.75027e7i	0.00385342	+	0.00667431i
$803$	9.81671e9	+	1.70030e10i	0.669054	+	1.15884i
$804$	−9.96323e9	−	1.72568e10i	−0.676089	−	1.17102i
$805$	4.03618e9	−	6.99088e9i	0.272700	−	0.472331i
$806$	9.06885e8			0.0610070
$807$	1.76307e10	−	3.05372e10i	1.18090	−	2.04537i
$808$	−1.98604e9	−	3.43993e9i	−0.132449	−	0.229408i
$809$	1.78668e10			1.18639			0.593193	−	0.805061i	$-0.297867\pi$
$809$	1.78668e10			1.18639			0.593193	+	0.805061i	$0.297867\pi$
$810$	6.00003e8	+	1.03924e9i	0.0396694	+	0.0687095i
$811$	−7.27059e9	+	1.25930e10i	−0.478627	+	0.829006i	−0.999700	−	0.0245065i	$-0.992199\pi$
$811$	−7.27059e9	+	1.25930e10i	−0.478627	+	0.829006i	0.521073	+	0.853512i	$0.325532\pi$
$812$	8.27790e9	−	1.43377e10i	0.542593	−	0.939798i
$813$	−1.53711e9			−0.100320
$814$	−5.98405e8	+	1.03647e9i	−0.0388875	+	0.0673551i
$815$	−2.75407e10			−1.78207
$816$	−2.38150e10			−1.53439
$817$	2.55559e10	+	2.71070e9i	1.63951	+	0.173902i
$818$	−9.07491e8			−0.0579703
$819$	−1.64226e10			−1.04460
$820$	5.60973e9	−	9.71634e9i	0.355299	−	0.615395i
$821$	2.00644e9			0.126539			0.0632697	−	0.997996i	$-0.479847\pi$
$821$	2.00644e9			0.126539			0.0632697	+	0.997996i	$0.479847\pi$
$822$	1.54634e9	−	2.67834e9i	0.0971077	−	0.168196i
$823$	9.28091e9	−	1.60750e10i	0.580351	−	1.00520i	−0.415086	−	0.909782i	$-0.636249\pi$
$823$	9.28091e9	−	1.60750e10i	0.580351	−	1.00520i	0.995437	−	0.0954160i	$-0.0304181\pi$
$824$	2.11266e9	+	3.65924e9i	0.131548	+	0.227848i
$825$	7.83222e8			0.0485619
$826$	−7.40405e8	−	1.28242e9i	−0.0457130	−	0.0791772i
$827$	−4.21686e9	+	7.30381e9i	−0.259251	+	0.449035i	−0.966041	−	0.258387i	$-0.916809\pi$
$827$	−4.21686e9	+	7.30381e9i	−0.259251	+	0.449035i	0.706791	+	0.707423i	$0.250142\pi$
$828$	−5.67038e9			−0.347141
$829$	6.62105e9	−	1.14680e10i	0.403632	−	0.699111i	−0.590529	−	0.807016i	$-0.701081\pi$
$829$	6.62105e9	−	1.14680e10i	0.403632	−	0.699111i	0.994161	+	0.107905i	$0.0344142\pi$
$830$	−1.96015e8	−	3.39508e8i	−0.0118992	−	0.0206100i
$831$	1.70600e10	+	2.95487e10i	1.03128	+	1.78622i
$832$	4.07552e9	+	7.05900e9i	0.245330	+	0.424924i
$833$	−3.93572e10			−2.35921
$834$	−1.18971e7	−	2.06064e7i	−0.000710166	−	0.00123004i
$835$	−6.85630e9	−	1.18755e10i	−0.407556	−	0.705908i
$836$	1.64661e10	−	2.85202e10i	0.974697	−	1.68822i
$837$	−2.00734e9	+	3.47681e9i	−0.118326	+	0.204947i
$838$	3.52198e8			0.0206744
$839$	−8.72818e9			−0.510219			−0.255110	−	0.966912i	$-0.582112\pi$
$839$	−8.72818e9			−0.510219			−0.255110	+	0.966912i	$0.582112\pi$
$840$	−4.14119e9	+	7.17275e9i	−0.241073	+	0.417550i
$841$	5.37766e9	−	9.31438e9i	0.311751	−	0.539968i
$842$	2.74384e8	+	4.75246e8i	0.0158404	+	0.0274364i
$843$	−1.78506e10	−	3.09181e10i	−1.02626	−	1.77753i
$844$	1.24827e10			0.714676
$845$	6.32529e9	+	1.09557e10i	0.360647	+	0.624659i
$846$	1.72432e9	+	2.98662e9i	0.0979090	+	0.169583i
$847$	6.67777e9	+	1.15662e10i	0.377607	+	0.654034i
$848$	1.35962e10	−	2.35492e10i	0.765651	−	1.32615i
$849$	2.80772e10			1.57462
$850$	−2.54352e7	+	4.40550e7i	−0.00142059	+	0.00246053i
$851$	1.92635e9	+	3.33654e9i	0.107148	+	0.185585i
$852$	8.26032e9			0.457571
$853$	5.97137e8	+	1.03427e9i	0.0329422	+	0.0570575i	0.882026	−	0.471200i	$-0.156179\pi$
$853$	5.97137e8	+	1.03427e9i	0.0329422	+	0.0570575i	−0.849084	+	0.528257i	$0.822846\pi$
$854$	−3.89446e8	+	6.74541e8i	−0.0213966	+	0.0370600i
$855$	1.67835e10	−	2.90698e10i	0.918333	−	1.59060i
$856$	2.71439e9			0.147915
$857$	8.91648e9	−	1.54438e10i	0.483905	−	0.838149i	−0.515924	−	0.856635i	$-0.672551\pi$
$857$	8.91648e9	−	1.54438e10i	0.483905	−	0.838149i	0.999829	+	0.0184858i	$0.00588456\pi$
$858$	−1.57392e9			−0.0850702
$859$	−2.12376e10			−1.14322			−0.571610	−	0.820525i	$-0.693681\pi$
$859$	−2.12376e10			−1.14322			−0.571610	+	0.820525i	$0.693681\pi$
$860$	1.81256e10	+	1.92257e9i	0.971735	+	0.103071i
$861$	−3.54680e10			−1.89376
$862$	−1.57982e9			−0.0840101
$863$	−1.76231e10	+	3.05241e10i	−0.933351	+	1.61661i	−0.155803	+	0.987788i	$0.549796\pi$
$863$	−1.76231e10	+	3.05241e10i	−0.933351	+	1.61661i	−0.777548	+	0.628823i	$0.783537\pi$
$864$	1.00460e9			0.0529902
$865$	−1.18448e10	+	2.05158e10i	−0.622259	+	1.07778i
$866$	−1.60921e9	+	2.78724e9i	−0.0841978	+	0.145835i
$867$	−2.33343e9	−	4.04162e9i	−0.121599	−	0.210615i
$868$	4.25458e10			2.20820
$869$	5.26349e9	+	9.11664e9i	0.272085	+	0.471265i
$870$	8.08632e8	−	1.40059e9i	0.0416326	−	0.0721097i
$871$	−9.44533e9			−0.484344
$872$	7.90128e8	−	1.36854e9i	0.0403543	−	0.0698957i
$873$	−1.13398e9	−	1.96412e9i	−0.0576842	−	0.0999119i
$874$	4.75671e8	+	8.23887e8i	0.0241000	+	0.0417424i
$875$	−1.79186e10	−	3.10360e10i	−0.904226	−	1.56616i
$876$	−3.22787e10			−1.62238
$877$	−1.36544e10	−	2.36501e10i	−0.683555	−	1.18395i	−0.973888	−	0.227027i	$-0.927099\pi$
$877$	−1.36544e10	−	2.36501e10i	−0.683555	−	1.18395i	0.290333	−	0.956926i	$-0.406234\pi$
$878$	7.84741e8	+	1.35921e9i	0.0391287	+	0.0677729i
$879$	−6.72127e9	+	1.16416e10i	−0.333803	+	0.578164i
$880$	1.15729e10	−	2.00449e10i	0.572471	−	0.991549i
$881$	2.10808e10			1.03866			0.519328	−	0.854575i	$-0.326182\pi$
$881$	2.10808e10			1.03866			0.519328	+	0.854575i	$0.326182\pi$
$882$	4.74258e9			0.232742
$883$	8.64518e8	−	1.49739e9i	0.0422582	−	0.0731934i	−0.844123	−	0.536150i	$-0.819878\pi$
$883$	8.64518e8	−	1.49739e9i	0.0422582	−	0.0731934i	0.886381	+	0.462957i	$0.153211\pi$
$884$	−5.69585e9	+	9.86550e9i	−0.277316	+	0.480326i
$885$	8.05982e9	+	1.39600e10i	0.390863	+	0.676994i
$886$	4.62806e8	+	8.01603e8i	0.0223553	+	0.0387206i
$887$	3.01514e10			1.45069			0.725344	−	0.688386i	$-0.241681\pi$
$887$	3.01514e10			1.45069			0.725344	+	0.688386i	$0.241681\pi$
$888$	−1.97647e9	−	3.42335e9i	−0.0947207	−	0.164061i
$889$	4.28739e9	+	7.42597e9i	0.204662	+	0.354485i
$890$	−1.10812e9	−	1.91932e9i	−0.0526893	−	0.0912606i
$891$	−1.07463e10	+	1.86132e10i	−0.508965	+	0.881553i
$892$	−2.27510e10			−1.07331
$893$	−3.22380e10	+	5.58379e10i	−1.51492	+	2.62391i
$894$	1.15257e9	+	1.99630e9i	0.0539492	+	0.0934427i
$895$	−1.43175e10			−0.667556
$896$	−7.08671e9	−	1.22745e10i	−0.329129	−	0.570069i
$897$	−2.53334e9	+	4.38787e9i	−0.117198	+	0.202993i
$898$	−3.41502e7	+	5.91499e7i	−0.00157371	+	0.00272575i
$899$	−1.66900e10			−0.766121
$900$	−3.41548e8	+	5.91578e8i	−0.0156172	+	0.0270497i
$901$	3.73058e10			1.69918
$902$	−1.80324e9			−0.0818144
$903$	−2.33866e10	−	5.26624e10i	−1.05696	−	2.38009i
$904$	−2.50208e9			−0.112645
$905$	−1.63213e10			−0.731956
$906$	−3.83412e8	+	6.64089e8i	−0.0171284	+	0.0296673i
$907$	−8.29103e9			−0.368963			−0.184482	−	0.982836i	$-0.559061\pi$
$907$	−8.29103e9			−0.368963			−0.184482	+	0.982836i	$0.559061\pi$
$908$	1.80204e10	−	3.12122e10i	0.798847	−	1.38364i
$909$	1.80472e10	−	3.12587e10i	0.796960	−	1.38038i
$910$	9.77098e8	+	1.69238e9i	0.0429827	+	0.0744482i
$911$	3.30863e10			1.44989			0.724943	−	0.688809i	$-0.241866\pi$
$911$	3.30863e10			1.44989			0.724943	+	0.688809i	$0.241866\pi$
$912$	2.68264e10	+	4.64647e10i	1.17106	+	2.02834i
$913$	3.51072e9	−	6.08074e9i	0.152668	−	0.264429i
$914$	−1.14533e8			−0.00496155
$915$	4.23939e9	−	7.34284e9i	0.182949	−	0.316877i
$916$	1.00166e10	+	1.73493e10i	0.430613	+	0.745844i
$917$	6.92621e9	+	1.19966e10i	0.296622	+	0.513764i
$918$	2.26272e8	+	3.91915e8i	0.00965344	+	0.0167202i
$919$	5.54457e7			0.00235648			0.00117824	−	0.999999i	$-0.499625\pi$
$919$	5.54457e7			0.00235648			0.00117824	+	0.999999i	$0.499625\pi$
$920$	6.77770e8	+	1.17393e9i	0.0286962	+	0.0497034i
$921$	−3.85052e9	−	6.66929e9i	−0.162409	−	0.281301i
$922$	6.44386e8	−	1.11611e9i	0.0270762	−	0.0468974i
$923$	1.95773e9	−	3.39090e9i	0.0819498	−	0.141941i
$924$	−7.38392e10			−3.07918
$925$	4.64125e8			0.0192814
$926$	5.03930e8	−	8.72833e8i	0.0208561	−	0.0361237i
$927$	−1.91978e10	+	3.32516e10i	−0.791541	+	1.37099i
$928$	2.08819e9	+	3.61684e9i	0.0857731	+	0.148563i
$929$	4.77507e9	+	8.27066e9i	0.195400	+	0.338443i	0.947032	−	0.321140i	$-0.104066\pi$
$929$	4.77507e9	+	8.27066e9i	0.195400	+	0.338443i	−0.751632	+	0.659583i	$0.770733\pi$
$930$	4.15611e9			0.169433
$931$	4.43338e10	+	7.67884e10i	1.80057	+	3.11869i
$932$	2.08627e10	+	3.61353e10i	0.844142	+	1.46210i
$933$	−2.59356e10	−	4.49218e10i	−1.04547	−	1.81080i
$934$	−1.37070e9	+	2.37412e9i	−0.0550464	+	0.0953431i
$935$	3.17543e10			1.27046
$936$	1.37887e9	−	2.38827e9i	0.0549614	−	0.0951960i
$937$	−3.49171e8	−	6.04782e8i	−0.0138659	−	0.0240165i	0.859009	−	0.511960i	$-0.171080\pi$
$937$	−3.49171e8	−	6.04782e8i	−0.0138659	−	0.0240165i	−0.872875	+	0.487944i	$0.837747\pi$
$938$	3.97646e9			0.157321
$939$	1.68594e10	+	2.92014e10i	0.664528	+	1.15100i
$940$	−2.28649e10	+	3.96032e10i	−0.897889	+	1.55519i
$941$	2.05461e10	−	3.55870e10i	0.803834	−	1.39228i	−0.113241	−	0.993568i	$-0.536123\pi$
$941$	2.05461e10	−	3.55870e10i	0.803834	−	1.39228i	0.917075	−	0.398714i	$-0.130544\pi$
$942$	2.18784e9			0.0852782
$943$	−2.90244e9	+	5.02717e9i	−0.112713	+	0.195224i
$944$	−1.36682e10			−0.528823
$945$	−8.65100e9			−0.333469
$946$	−1.18901e9	−	2.67742e9i	−0.0456630	−	0.102825i
$947$	1.33659e10			0.511414			0.255707	−	0.966754i	$-0.417692\pi$
$947$	1.33659e10			0.511414			0.255707	+	0.966754i	$0.417692\pi$
$948$	−1.73071e10			−0.659775
$949$	−7.65022e9	+	1.32506e10i	−0.290564	+	0.503272i
$950$	1.14606e8			0.00433684
$951$	−2.29002e10	+	3.96644e10i	−0.863392	+	1.49544i
$952$	4.81739e9	−	8.34396e9i	0.180960	−	0.313432i
$953$	−5.17716e9	−	8.96710e9i	−0.193761	−	0.335604i	0.752733	−	0.658326i	$-0.228735\pi$
$953$	−5.17716e9	−	8.96710e9i	−0.193761	−	0.335604i	−0.946494	+	0.322723i	$0.895402\pi$
$954$	−4.49539e9			−0.167628
$955$	−6.14768e9	−	1.06481e10i	−0.228402	−	0.395604i
$956$	1.29301e10	−	2.23956e10i	0.478629	−	0.829009i
$957$	2.89659e10			1.06830
$958$	−5.18955e8	+	8.98856e8i	−0.0190700	+	0.0330302i
$959$	−3.43872e10	−	5.95604e10i	−1.25902	−	2.18068i
$960$	1.86775e10	+	3.23503e10i	0.681347	+	1.18013i
$961$	−7.68902e9	−	1.33178e10i	−0.279473	−	0.484061i
$962$	−9.32681e8			−0.0337769
$963$	1.23328e10	+	2.13611e10i	0.445012	+	0.770783i
$964$	−8.83062e8	−	1.52951e9i	−0.0317484	−	0.0549898i
$965$	8.43647e9	−	1.46124e10i	0.302214	−	0.523451i
$966$	1.06653e9	−	1.84728e9i	0.0380673	−	0.0659346i
$967$	4.19293e10			1.49116			0.745581	−	0.666414i	$-0.232172\pi$
$967$	4.19293e10			1.49116			0.745581	+	0.666414i	$0.232172\pi$
$968$	−2.24271e9			−0.0794711
$969$	−3.68037e10	+	6.37459e10i	−1.29945	+	2.25071i
$970$	−1.34937e8	+	2.33719e8i	−0.00474714	+	0.00822228i
$971$	−2.50981e10	−	4.34712e10i	−0.879778	−	1.52382i	−0.851584	−	0.524218i	$-0.824358\pi$
$971$	−2.50981e10	−	4.34712e10i	−0.879778	−	1.52382i	−0.0281943	−	0.999602i	$-0.508976\pi$
$972$	−2.03569e10	−	3.52591e10i	−0.711016	−	1.23152i
$973$	−5.29130e8			−0.0184148
$974$	4.29546e8	+	7.43996e8i	0.0148955	+	0.0257997i
$975$	3.05185e8	+	5.28595e8i	0.0105450	+	0.0182645i
$976$	3.59468e9	+	6.22617e9i	0.123762	+	0.214361i
$977$	4.27680e9	−	7.40763e9i	0.146719	−	0.254126i	−0.783294	−	0.621652i	$-0.786462\pi$
$977$	4.27680e9	−	7.40763e9i	0.146719	−	0.254126i	0.930013	+	0.367526i	$0.119795\pi$
$978$	−7.27741e9			−0.248766
$979$	1.98469e10	−	3.43759e10i	0.676012	−	1.17089i
$980$	3.14439e10	+	5.44624e10i	1.06720	+	1.84844i
$981$	1.43598e10			0.485632
$982$	−7.79635e8	−	1.35037e9i	−0.0262725	−	0.0455053i
$983$	1.32484e10	−	2.29469e10i	0.444862	−	0.770524i	−0.553180	−	0.833062i	$-0.686586\pi$
$983$	1.32484e10	−	2.29469e10i	0.444862	−	0.770524i	0.998043	+	0.0625373i	$0.0199192\pi$
$984$	2.97795e9	−	5.15796e9i	0.0996403	−	0.172582i
$985$	−6.15919e9			−0.205351
$986$	−9.40669e8	+	1.62929e9i	−0.0312513	+	0.0541288i
$987$	1.44565e11			4.78580
$988$	2.56643e10			0.846604
$989$	−9.37808e9	−	9.94726e8i	−0.308267	−	0.0326976i
$990$	−3.82643e9			−0.125334
$991$	4.78422e9			0.156154			0.0780770	−	0.996947i	$-0.475122\pi$
$991$	4.78422e9			0.156154			0.0780770	+	0.996947i	$0.475122\pi$
$992$	−5.36631e9	+	9.29472e9i	−0.174536	+	0.302305i
$993$	3.58660e9			0.116241
$994$	−8.24200e8	+	1.42756e9i	−0.0266183	+	0.0461043i
$995$	−2.66218e10	+	4.61104e10i	−0.856756	+	1.48394i
$996$	5.77187e9	+	9.99717e9i	0.185101	+	0.320604i
$997$	−6.97369e9			−0.222859			−0.111429	−	0.993772i	$-0.535543\pi$
$997$	−6.97369e9			−0.222859			−0.111429	+	0.993772i	$0.535543\pi$
$998$	−1.55525e9	−	2.69378e9i	−0.0495273	−	0.0857838i
$999$	2.06444e9	−	3.57571e9i	0.0655122	−	0.113470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.c.a.6.12	✓	50
43.36	even	3	inner	43.8.c.a.36.12	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.c.a.6.12	✓	50	1.1	even	1	trivial
43.8.c.a.36.12	yes	50	43.36	even	3	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.06697 q^{2} +(-34.1249 + 59.1060i) q^{3} -126.862 q^{4} +(-137.791 + 238.662i) q^{5} +(-36.4102 + 63.0644i) q^{6} +(809.683 + 1402.41i) q^{7} -271.930 q^{8} +(-1235.52 - 2139.98i) q^{9} +O(q^{10})\)	\(q+1.06697 q^{2} +(-34.1249 + 59.1060i) q^{3} -126.862 q^{4} +(-137.791 + 238.662i) q^{5} +(-36.4102 + 63.0644i) q^{6} +(809.683 + 1402.41i) q^{7} -271.930 q^{8} +(-1235.52 - 2139.98i) q^{9} +(-147.019 + 254.645i) q^{10} -5266.36 q^{11} +(4329.14 - 7498.29i) q^{12} +(-2052.05 - 3554.26i) q^{13} +(863.908 + 1496.33i) q^{14} +(-9404.24 - 16288.6i) q^{15} +15948.1 q^{16} +(10939.8 + 18948.3i) q^{17} +(-1318.26 - 2283.29i) q^{18} +(24646.3 - 42688.6i) q^{19} +(17480.4 - 30277.0i) q^{20} -110521. q^{21} -5619.05 q^{22} +(-9044.27 + 15665.1i) q^{23} +(9279.57 - 16072.7i) q^{24} +(1089.54 + 1887.14i) q^{25} +(-2189.48 - 3792.29i) q^{26} +19385.1 q^{27} +(-102718. - 177912. i) q^{28} +(40294.4 + 69792.0i) q^{29} +(-10034.0 - 17379.5i) q^{30} +(-103550. + 179354. i) q^{31} +51823.2 q^{32} +(179714. - 311274. i) q^{33} +(11672.5 + 20217.3i) q^{34} -446270. q^{35} +(156740. + 271481. i) q^{36} +(106496. - 184456. i) q^{37} +(26296.8 - 45547.4i) q^{38} +280104. q^{39} +(37469.6 - 64899.2i) q^{40} +320915. q^{41} -117923. q^{42} +(211602. + 476490. i) q^{43} +668099. q^{44} +680974. q^{45} +(-9649.97 + 16714.2i) q^{46} -1.30803e6 q^{47} +(-544229. + 942631. i) q^{48} +(-899402. + 1.55781e6i) q^{49} +(1162.51 + 2013.52i) q^{50} -1.49328e6 q^{51} +(260327. + 450899. i) q^{52} +(852523. - 1.47661e6i) q^{53} +20683.4 q^{54} +(725659. - 1.25688e6i) q^{55} +(-220177. - 381358. i) q^{56} +(1.68210e6 + 2.91348e6i) q^{57} +(42992.9 + 74466.0i) q^{58} -857042. q^{59} +(1.19304e6 + 2.06640e6i) q^{60} +(225398. + 390401. i) q^{61} +(-110485. + 191366. i) q^{62} +(2.00075e6 - 3.46541e6i) q^{63} -1.98607e6 q^{64} +1.13102e6 q^{65} +(191750. - 332120. i) q^{66} +(1.15072e6 - 1.99310e6i) q^{67} +(-1.38784e6 - 2.40381e6i) q^{68} +(-617270. - 1.06914e6i) q^{69} -476157. q^{70} +(477019. + 826220. i) q^{71} +(335974. + 581923. i) q^{72} +(-1.86404e6 - 3.22861e6i) q^{73} +(113628. - 196809. i) q^{74} -148722. q^{75} +(-3.12666e6 + 5.41554e6i) q^{76} +(-4.26408e6 - 7.38561e6i) q^{77} +298863. q^{78} +(-999456. - 1.73111e6i) q^{79} +(-2.19752e6 + 3.80621e6i) q^{80} +(2.04056e6 - 3.53435e6i) q^{81} +342407. q^{82} +(-666631. + 1.15464e6i) q^{83} +1.40209e7 q^{84} -6.02965e6 q^{85} +(225774. + 508401. i) q^{86} -5.50017e6 q^{87} +1.43208e6 q^{88} +(-3.76862e6 + 6.52745e6i) q^{89} +726579. q^{90} +(3.32303e6 - 5.75565e6i) q^{91} +(1.14737e6 - 1.98730e6i) q^{92} +(-7.06728e6 - 1.22409e7i) q^{93} -1.39563e6 q^{94} +(6.79208e6 + 1.17642e7i) q^{95} +(-1.76846e6 + 3.06306e6i) q^{96} +917821. q^{97} +(-959636. + 1.66214e6i) q^{98} +(6.50667e6 + 1.12699e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9}+O(q^{10}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9	\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99}+O(q^{100}) \) 50 * q + 26 * q^2 - 2 * q^3 + 3014 * q^4 - 249 * q^5 - 1281 * q^6 - 687 * q^7 + 5496 * q^8 - 13389 * q^9 + 1667 * q^10 - 4594 * q^11 - 8448 * q^12 + 2972 * q^13 - 15928 * q^14 - 2485 * q^15 + 185846 * q^16 + 25298 * q^17 + 13249 * q^18 + 3269 * q^19 + 2705 * q^20 - 85260 * q^21 + 150968 * q^22 - 19120 * q^23 - 55070 * q^24 - 296876 * q^25 - 139545 * q^26 - 274154 * q^27 - 118970 * q^28 - 231057 * q^29 + 240447 * q^30 - 177637 * q^31 + 1254274 * q^32 - 344986 * q^33 + 104923 * q^34 - 518850 * q^35 + 816168 * q^36 + 885140 * q^37 + 200956 * q^38 - 59884 * q^39 + 160425 * q^40 + 2202852 * q^41 - 349786 * q^42 + 1009342 * q^43 - 1012518 * q^44 + 775768 * q^45 - 1277532 * q^46 - 2784982 * q^47 - 2238049 * q^48 - 1241240 * q^49 - 5126146 * q^50 - 2477574 * q^51 - 268404 * q^52 - 398258 * q^53 + 6491644 * q^54 - 2551752 * q^55 - 4471819 * q^56 + 2094777 * q^57 - 2294852 * q^58 + 5664766 * q^59 + 1374965 * q^60 + 2652290 * q^61 - 5621243 * q^62 - 3210173 * q^63 + 5395148 * q^64 + 22093214 * q^65 - 284525 * q^66 + 5696184 * q^67 + 2422800 * q^68 + 4199245 * q^69 - 8874170 * q^70 - 16652990 * q^71 + 5916954 * q^72 + 108058 * q^73 + 8260200 * q^74 - 3594466 * q^75 - 7386456 * q^76 - 8874183 * q^77 - 27627308 * q^78 - 7378370 * q^79 + 7523523 * q^80 - 14862361 * q^81 + 7898428 * q^82 + 18099816 * q^83 + 47917640 * q^84 + 5843026 * q^85 + 14578342 * q^86 - 24244628 * q^87 + 23110740 * q^88 - 20405960 * q^89 + 32640076 * q^90 + 10283016 * q^91 - 27186571 * q^92 - 19267997 * q^93 - 52636002 * q^94 + 1708621 * q^95 + 8113092 * q^96 + 53505940 * q^97 - 3752059 * q^98 + 10929650 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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