LMFDB - Embedded newform 74.8.c.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.47");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	74.47
Dual form			74.8.c.a.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(-33.0633 - 57.2674i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(102.843 + 178.129i) q^{5} +529.013 q^{6} +(87.2990 + 151.206i) q^{7} +512.000 q^{8} +(-1092.87 + 1892.90i) q^{9} -1645.48 q^{10} -5682.10 q^{11} +(-2116.05 + 3665.11i) q^{12} +(-6239.48 - 10807.1i) q^{13} -1396.78 q^{14} +(6800.64 - 11779.1i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10150.4 + 17581.0i) q^{17} +(-8742.95 - 15143.2i) q^{18} +(29257.4 + 50675.4i) q^{19} +(6581.93 - 11400.2i) q^{20} +(5772.80 - 9998.77i) q^{21} +(22728.4 - 39366.8i) q^{22} +65697.1 q^{23} +(-16928.4 - 29320.9i) q^{24} +(17909.3 - 31019.8i) q^{25} +99831.7 q^{26} -83.4648 q^{27} +(5587.14 - 9677.21i) q^{28} +177274. q^{29} +(54405.1 + 94232.4i) q^{30} -95681.2 q^{31} +(-16384.0 - 28377.9i) q^{32} +(187869. + 325399. i) q^{33} +(-81203.3 - 140648. i) q^{34} +(-17956.1 + 31100.9i) q^{35} +139887. q^{36} +(274975. - 138999. i) q^{37} -468119. q^{38} +(-412596. + 714638. i) q^{39} +(52655.4 + 91201.9i) q^{40} +(244216. + 422995. i) q^{41} +(46182.4 + 79990.2i) q^{42} +761147. q^{43} +(181827. + 314934. i) q^{44} -449574. q^{45} +(-262788. + 455163. i) q^{46} -423371. q^{47} +270855. q^{48} +(396529. - 686809. i) q^{49} +(143274. + 248158. i) q^{50} +1.34243e6 q^{51} +(-399327. + 691655. i) q^{52} +(-327136. + 566616. i) q^{53} +(333.859 - 578.261i) q^{54} +(-584363. - 1.01215e6i) q^{55} +(44697.1 + 77417.7i) q^{56} +(1.93470e6 - 3.35099e6i) q^{57} +(-709094. + 1.22819e6i) q^{58} +(-91051.3 + 157706. i) q^{59} -870482. q^{60} +(1.23526e6 + 2.13954e6i) q^{61} +(382725. - 662898. i) q^{62} -381626. q^{63} +262144. q^{64} +(1.28337e6 - 2.22286e6i) q^{65} -3.00591e6 q^{66} +(-1.13014e6 - 1.95746e6i) q^{67} +1.29925e6 q^{68} +(-2.17217e6 - 3.76230e6i) q^{69} +(-143649. - 248807. i) q^{70} +(1.36480e6 + 2.36390e6i) q^{71} +(-559549. + 969167. i) q^{72} +4.27107e6 q^{73} +(-136883. + 2.46108e6i) q^{74} -2.36856e6 q^{75} +(1.87248e6 - 3.24322e6i) q^{76} +(-496042. - 859170. i) q^{77} +(-3.30077e6 - 5.71710e6i) q^{78} +(-756160. - 1.30971e6i) q^{79} -842487. q^{80} +(2.39286e6 + 4.14456e6i) q^{81} -3.90746e6 q^{82} +(-3.15145e6 + 5.45848e6i) q^{83} -738918. q^{84} -4.17558e6 q^{85} +(-3.04459e6 + 5.27338e6i) q^{86} +(-5.86126e6 - 1.01520e7i) q^{87} -2.90924e6 q^{88} +(550715. - 953866. i) q^{89} +(1.79830e6 - 3.11474e6i) q^{90} +(1.08940e6 - 1.88690e6i) q^{91} +(-2.10231e6 - 3.64130e6i) q^{92} +(3.16354e6 + 5.47941e6i) q^{93} +(1.69349e6 - 2.93320e6i) q^{94} +(-6.01782e6 + 1.04232e7i) q^{95} +(-1.08342e6 + 1.87654e6i) q^{96} -203177. q^{97} +(3.17223e6 + 5.49447e6i) q^{98} +(6.20980e6 - 1.07557e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 88 q^{2} + 40 q^{3} - 704 q^{4} + 475 q^{5} - 640 q^{6} - 588 q^{7} + 11264 q^{8} - 8369 q^{9} - 7600 q^{10} - 4904 q^{11} + 2560 q^{12} - 2612 q^{13} + 9408 q^{14} - 3688 q^{15} - 45056 q^{16} + 24651 q^{17}+ \cdots + 13715284 q^{99}+O(q^{100}) $ 22 * q - 88 * q^2 + 40 * q^3 - 704 * q^4 + 475 * q^5 - 640 * q^6 - 588 * q^7 + 11264 * q^8 - 8369 * q^9 - 7600 * q^10 - 4904 * q^11 + 2560 * q^12 - 2612 * q^13 + 9408 * q^14 - 3688 * q^15 - 45056 * q^16 + 24651 * q^17 - 66952 * q^18 + 82536 * q^19 + 30400 * q^20 + 50810 * q^21 + 19616 * q^22 + 118832 * q^23 + 20480 * q^24 - 256572 * q^25 + 41792 * q^26 - 363800 * q^27 - 37632 * q^28 - 372170 * q^29 - 29504 * q^30 + 42808 * q^31 - 360448 * q^32 - 170612 * q^33 + 197208 * q^34 + 347316 * q^35 + 1071232 * q^36 - 605757 * q^37 - 1320576 * q^38 + 928324 * q^39 + 243200 * q^40 - 171689 * q^41 + 406480 * q^42 - 794528 * q^43 + 156928 * q^44 - 2199730 * q^45 - 475328 * q^46 - 517424 * q^47 - 327680 * q^48 - 1990061 * q^49 - 2052576 * q^50 + 1046736 * q^51 - 167168 * q^52 - 2880196 * q^53 + 1455200 * q^54 + 120328 * q^55 - 301056 * q^56 - 1881606 * q^57 + 1488680 * q^58 + 2657756 * q^59 + 472064 * q^60 + 1449979 * q^61 - 171232 * q^62 + 7031672 * q^63 + 5767168 * q^64 + 3463904 * q^65 + 2729792 * q^66 + 1415120 * q^67 - 3155328 * q^68 - 7425740 * q^69 + 2778528 * q^70 + 718320 * q^71 - 4284928 * q^72 + 21142228 * q^73 + 2481504 * q^74 - 38086392 * q^75 + 5282304 * q^76 + 3057932 * q^77 + 7426592 * q^78 + 8331416 * q^79 - 3891200 * q^80 + 8804005 * q^81 + 2747024 * q^82 - 1747036 * q^83 - 6503680 * q^84 - 4638522 * q^85 + 3178112 * q^86 + 3200432 * q^87 - 2510848 * q^88 + 16909895 * q^89 + 8798920 * q^90 + 13361368 * q^91 - 3802624 * q^92 + 15700724 * q^93 + 2069696 * q^94 - 32197184 * q^95 + 1310720 * q^96 - 72528842 * q^97 - 15920488 * q^98 + 13715284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$	−33.0633	−	57.2674i	−0.707005	−	1.22457i	−0.965963	−	0.258680i	$-0.916713\pi$
$3$	−33.0633	−	57.2674i	−0.707005	−	1.22457i	0.258958	−	0.965888i	$-0.416621\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	102.843	+	178.129i	0.367941	+	0.637292i	0.989243	−	0.146278i	$-0.0467295\pi$
$5$	102.843	+	178.129i	0.367941	+	0.637292i	−0.621303	+	0.783571i	$0.713396\pi$
$6$	529.013			0.999856
$7$	87.2990	+	151.206i	0.0961981	+	0.166620i	0.910108	−	0.414371i	$-0.135998\pi$
$7$	87.2990	+	151.206i	0.0961981	+	0.166620i	−0.813910	+	0.580991i	$0.802665\pi$
$8$	512.000			0.353553
$9$	−1092.87	+	1892.90i	−0.499711	+	0.865526i
$10$	−1645.48			−0.520347
$11$	−5682.10			−1.28717			−0.643583	−	0.765376i	$-0.722553\pi$
$11$	−5682.10			−1.28717			−0.643583	+	0.765376i	$0.722553\pi$
$12$	−2116.05	+	3665.11i	−0.353502	+	0.612284i
$13$	−6239.48	−	10807.1i	−0.787675	−	1.36429i	−0.927388	−	0.374101i	$-0.877951\pi$
$13$	−6239.48	−	10807.1i	−0.787675	−	1.36429i	0.139713	−	0.990192i	$-0.455382\pi$
$14$	−1396.78			−0.136045
$15$	6800.64	−	11779.1i	0.520272	−	0.901138i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−10150.4	+	17581.0i	−0.501086	+	0.867907i	0.498913	+	0.866652i	$0.333733\pi$
$17$	−10150.4	+	17581.0i	−0.501086	+	0.867907i	−0.999999	+	0.00125471i	$0.999601\pi$
$18$	−8742.95	−	15143.2i	−0.353349	−	0.612019i
$19$	29257.4	+	50675.4i	0.978586	+	1.69496i	0.667556	+	0.744560i	$0.267340\pi$
$19$	29257.4	+	50675.4i	0.978586	+	1.69496i	0.311030	+	0.950400i	$0.399326\pi$
$20$	6581.93	−	11400.2i	0.183970	−	0.318646i
$21$	5772.80	−	9998.77i	0.136025	−	0.235602i
$22$	22728.4	−	39366.8i	0.455082	−	0.788225i
$23$	65697.1			1.12590			0.562949	−	0.826492i	$-0.309667\pi$
$23$	65697.1			1.12590			0.562949	+	0.826492i	$0.309667\pi$
$24$	−16928.4	−	29320.9i	−0.249964	−	0.432950i
$25$	17909.3	−	31019.8i	0.229239	−	0.397053i
$26$	99831.7			1.11394
$27$	−83.4648			−0.000816075
$28$	5587.14	−	9677.21i	0.0480990	−	0.0833100i
$29$	177274.			1.34974			0.674871	−	0.737936i	$-0.264199\pi$
$29$	177274.			1.34974			0.674871	+	0.737936i	$0.264199\pi$
$30$	54405.1	+	94232.4i	0.367888	+	0.637200i
$31$	−95681.2			−0.576847			−0.288423	−	0.957503i	$-0.593131\pi$
$31$	−95681.2			−0.576847			−0.288423	+	0.957503i	$0.593131\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$	187869.	+	325399.i	0.910033	+	1.57622i
$34$	−81203.3	−	140648.i	−0.354321	−	0.613703i
$35$	−17956.1	+	31100.9i	−0.0707904	+	0.122613i
$36$	139887.			0.499711
$37$	274975.	−	138999.i	0.892456	−	0.451135i
$37$	274975.	−	138999.i	0.892456	−	0.451135i
$38$	−468119.			−1.38393
$39$	−412596.	+	714638.i	−1.11378	+	1.92912i
$40$	52655.4	+	91201.9i	0.130087	+	0.225317i
$41$	244216.	+	422995.i	0.553389	+	0.958498i	0.998027	+	0.0627876i	$0.0199991\pi$
$41$	244216.	+	422995.i	0.553389	+	0.958498i	−0.444638	+	0.895710i	$0.646668\pi$
$42$	46182.4	+	79990.2i	0.0961842	+	0.166596i
$43$	761147.			1.45992			0.729959	−	0.683490i	$-0.239539\pi$
$43$	761147.			1.45992			0.729959	+	0.683490i	$0.239539\pi$
$44$	181827.	+	314934.i	0.321792	+	0.557360i
$45$	−449574.			−0.735457
$46$	−262788.	+	455163.i	−0.398065	+	0.689469i
$47$	−423371.			−0.594811			−0.297406	−	0.954751i	$-0.596121\pi$
$47$	−423371.			−0.594811			−0.297406	+	0.954751i	$0.596121\pi$
$48$	270855.			0.353502
$49$	396529.	−	686809.i	0.481492	−	0.833968i
$50$	143274.	+	248158.i	0.162096	+	0.280759i
$51$	1.34243e6			1.41708
$52$	−399327.	+	691655.i	−0.393837	+	0.682146i
$53$	−327136.	+	566616.i	−0.301830	+	0.522785i	−0.976551	−	0.215288i	$-0.930931\pi$
$53$	−327136.	+	566616.i	−0.301830	+	0.522785i	0.674720	+	0.738073i	$0.264264\pi$
$54$	333.859	−	578.261i	0.000288526	−	0.000499742i
$55$	−584363.	−	1.01215e6i	−0.473601	−	0.820302i
$56$	44697.1	+	77417.7i	0.0340111	+	0.0589090i
$57$	1.93470e6	−	3.35099e6i	1.38373	−	2.39669i
$58$	−709094.	+	1.22819e6i	−0.477206	+	0.826545i
$59$	−91051.3	+	157706.i	−0.0577171	+	0.0999689i	−0.893440	−	0.449182i	$-0.851715\pi$
$59$	−91051.3	+	157706.i	−0.0577171	+	0.0999689i	0.835723	+	0.549151i	$0.185049\pi$
$60$	−870482.			−0.520272
$61$	1.23526e6	+	2.13954e6i	0.696794	+	1.20688i	0.969572	+	0.244806i	$0.0787241\pi$
$61$	1.23526e6	+	2.13954e6i	0.696794	+	1.20688i	−0.272778	+	0.962077i	$0.587943\pi$
$62$	382725.	−	662898.i	0.203946	−	0.353245i
$63$	−381626.			−0.192285
$64$	262144.			0.125000
$65$	1.28337e6	−	2.22286e6i	0.579636	−	1.00396i
$66$	−3.00591e6			−1.28698
$67$	−1.13014e6	−	1.95746e6i	−0.459060	−	0.795116i	0.539851	−	0.841760i	$-0.318480\pi$
$67$	−1.13014e6	−	1.95746e6i	−0.459060	−	0.795116i	−0.998912	+	0.0466448i	$0.985147\pi$
$68$	1.29925e6			0.501086
$69$	−2.17217e6	−	3.76230e6i	−0.796015	−	1.37874i
$70$	−143649.	−	248807.i	−0.0500564	−	0.0867002i
$71$	1.36480e6	+	2.36390e6i	0.452548	+	0.783836i	0.998544	−	0.0539518i	$-0.0171817\pi$
$71$	1.36480e6	+	2.36390e6i	0.452548	+	0.783836i	−0.545995	+	0.837788i	$0.683848\pi$
$72$	−559549.	+	969167.i	−0.176675	+	0.306010i
$73$	4.27107e6			1.28501			0.642505	−	0.766281i	$-0.277895\pi$
$73$	4.27107e6			1.28501			0.642505	+	0.766281i	$0.277895\pi$
$74$	−136883.	+	2.46108e6i	−0.0392679	+	0.706016i
$75$	−2.36856e6			−0.648292
$76$	1.87248e6	−	3.24322e6i	0.489293	−	0.847480i
$77$	−496042.	−	859170.i	−0.123823	−	0.214468i
$78$	−3.30077e6	−	5.71710e6i	−0.787561	−	1.36410i
$79$	−756160.	−	1.30971e6i	−0.172551	−	0.298868i	0.766760	−	0.641934i	$-0.221868\pi$
$79$	−756160.	−	1.30971e6i	−0.172551	−	0.298868i	−0.939311	+	0.343066i	$0.888534\pi$
$80$	−842487.			−0.183970
$81$	2.39286e6	+	4.14456e6i	0.500288	+	0.866525i
$82$	−3.90746e6			−0.782610
$83$	−3.15145e6	+	5.45848e6i	−0.604975	+	1.04785i	0.387080	+	0.922046i	$0.373484\pi$
$83$	−3.15145e6	+	5.45848e6i	−0.604975	+	1.04785i	−0.992055	+	0.125802i	$0.959850\pi$
$84$	−738918.			−0.136025
$85$	−4.17558e6			−0.737481
$86$	−3.04459e6	+	5.27338e6i	−0.516159	+	0.894014i
$87$	−5.86126e6	−	1.01520e7i	−0.954274	−	1.65285i
$88$	−2.90924e6			−0.455082
$89$	550715.	−	953866.i	0.0828060	−	0.143424i	−0.821648	−	0.569995i	$-0.806945\pi$
$89$	550715.	−	953866.i	0.0828060	−	0.143424i	0.904454	+	0.426571i	$0.140278\pi$
$90$	1.79830e6	−	3.11474e6i	0.260023	−	0.450374i
$91$	1.08940e6	−	1.88690e6i	0.151546	−	0.262485i
$92$	−2.10231e6	−	3.64130e6i	−0.281474	−	0.487528i
$93$	3.16354e6	+	5.47941e6i	0.407833	+	0.706388i
$94$	1.69349e6	−	2.93320e6i	0.210297	−	0.364246i
$95$	−6.01782e6	+	1.04232e7i	−0.720123	+	1.24729i
$96$	−1.08342e6	+	1.87654e6i	−0.124982	+	0.216475i
$97$	−203177.			−0.0226034			−0.0113017	−	0.999936i	$-0.503598\pi$
$97$	−203177.			−0.0226034			−0.0113017	+	0.999936i	$0.503598\pi$
$98$	3.17223e6	+	5.49447e6i	0.340466	+	0.589705i
$99$	6.20980e6	−	1.07557e7i	0.643212	−	1.11408i
$100$	−2.29239e6			−0.229239
$101$	7.19482e6			0.694856			0.347428	−	0.937707i	$-0.387055\pi$
$101$	7.19482e6			0.694856			0.347428	+	0.937707i	$0.387055\pi$
$102$	−5.36970e6	+	9.30060e6i	−0.501014	+	0.867782i
$103$	−1.48628e7			−1.34020			−0.670101	−	0.742270i	$-0.733749\pi$
$103$	−1.48628e7			−1.34020			−0.670101	+	0.742270i	$0.733749\pi$
$104$	−3.19462e6	−	5.53324e6i	−0.278485	−	0.482350i
$105$	2.37476e6			0.200197
$106$	−2.61709e6	−	4.53293e6i	−0.213426	−	0.369665i
$107$	1.25379e7	+	2.17163e7i	0.989425	+	1.71373i	0.620327	+	0.784343i	$0.287000\pi$
$107$	1.25379e7	+	2.17163e7i	0.989425	+	1.71373i	0.369097	+	0.929391i	$0.379667\pi$
$108$	2670.87	+	4626.09i	0.000204019	+	0.000353371i
$109$	−163897.	+	283879.i	−0.0121221	+	0.0209962i	−0.872023	−	0.489465i	$-0.837192\pi$
$109$	−163897.	+	283879.i	−0.0121221	+	0.0209962i	0.859901	+	0.510461i	$0.170525\pi$
$110$	9.34980e6			0.669773
$111$	−1.70517e7	−	1.11513e7i	−1.18342	−	0.773918i
$112$	−715154.			−0.0480990
$113$	9.09328e6	−	1.57500e7i	0.592852	−	1.02685i	−0.400994	−	0.916081i	$-0.631335\pi$
$113$	9.09328e6	−	1.57500e7i	0.592852	−	1.02685i	0.993846	−	0.110769i	$-0.0353314\pi$
$114$	1.54776e7	+	2.68080e7i	0.978444	+	1.69472i
$115$	6.75646e6	+	1.17025e7i	0.414264	+	0.717526i
$116$	−5.67275e6	−	9.82550e6i	−0.337436	−	0.584456i
$117$	2.72757e7			1.57444
$118$	−728411.	−	1.26164e6i	−0.0408121	−	0.0706887i
$119$	−3.54448e6			−0.192814
$120$	3.48193e6	−	6.03088e6i	0.183944	−	0.318600i
$121$	1.27991e7			0.656798
$122$	−1.97642e7			−0.985415
$123$	1.61492e7	−	2.79712e7i	0.782498	−	1.35533i
$124$	3.06180e6	+	5.30319e6i	0.144212	+	0.249782i
$125$	2.34365e7			1.07327
$126$	1.52650e6	−	2.64398e6i	0.0679830	−	0.117750i
$127$	−6.52628e6	+	1.13039e7i	−0.282718	+	0.489681i	−0.972053	−	0.234761i	$-0.924569\pi$
$127$	−6.52628e6	+	1.13039e7i	−0.282718	+	0.489681i	0.689336	+	0.724442i	$0.257903\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$	−2.51660e7	−	4.35889e7i	−1.03217	−	1.78777i
$130$	1.02670e7	+	1.77829e7i	0.409864	+	0.709906i
$131$	5.33799e6	−	9.24567e6i	0.207457	−	0.359326i	−0.743456	−	0.668785i	$-0.766815\pi$
$131$	5.33799e6	−	9.24567e6i	0.207457	−	0.359326i	0.950913	+	0.309459i	$0.100148\pi$
$132$	1.20236e7	−	2.08256e7i	0.455016	−	0.788112i
$133$	−5.10829e6	+	8.84782e6i	−0.188276	+	0.326104i
$134$	1.80822e7			0.649209
$135$	−8583.73	−	14867.5i	−0.000300267	−	0.000520078i
$136$	−5.19701e6	+	9.00149e6i	−0.177161	+	0.306851i
$137$	−2.48718e7			−0.826391			−0.413195	−	0.910642i	$-0.635587\pi$
$137$	−2.48718e7			−0.826391			−0.413195	+	0.910642i	$0.635587\pi$
$138$	3.47547e7			1.12574
$139$	−1.98302e7	+	3.43469e7i	−0.626290	+	1.08477i	0.362000	+	0.932178i	$0.382094\pi$
$139$	−1.98302e7	+	3.43469e7i	−0.626290	+	1.08477i	−0.988290	+	0.152587i	$0.951239\pi$
$140$	2.29838e6			0.0707904
$141$	1.39981e7	+	2.42454e7i	0.420534	+	0.728387i
$142$	−2.18368e7			−0.640000
$143$	3.54534e7	+	6.14071e7i	1.01387	+	1.75607i
$144$	−4.47639e6	−	7.75334e6i	−0.124928	−	0.216381i
$145$	1.82313e7	+	3.15775e7i	0.496626	+	0.860181i
$146$	−1.70843e7	+	2.95909e7i	−0.454320	+	0.786905i
$147$	−5.24423e7			−1.36167
$148$	−1.65033e7	−	1.07927e7i	−0.418461	−	0.273661i
$149$	−1.90913e7			−0.472806			−0.236403	−	0.971655i	$-0.575969\pi$
$149$	−1.90913e7			−0.472806			−0.236403	+	0.971655i	$0.575969\pi$
$150$	9.47426e6	−	1.64099e7i	0.229206	−	0.396996i
$151$	−4.46190e6	−	7.72824e6i	−0.105463	−	0.182668i	0.808464	−	0.588545i	$-0.200299\pi$
$151$	−4.46190e6	−	7.72824e6i	−0.105463	−	0.182668i	−0.913927	+	0.405878i	$0.866966\pi$
$152$	1.49798e7	+	2.59458e7i	0.345982	+	0.599259i
$153$	−2.21861e7	−	3.84275e7i	−0.500797	−	0.867406i
$154$	7.93668e6			0.175112
$155$	−9.84010e6	−	1.70436e7i	−0.212246	−	0.367620i
$156$	5.28123e7			1.11378
$157$	−3.82479e6	+	6.62473e6i	−0.0788785	+	0.136622i	−0.902766	−	0.430131i	$-0.858467\pi$
$157$	−3.82479e6	+	6.62473e6i	−0.0788785	+	0.136622i	0.823888	+	0.566753i	$0.191801\pi$
$158$	1.20986e7			0.244025
$159$	4.32648e7			0.853582
$160$	3.36995e6	−	5.83692e6i	0.0650434	−	0.112658i
$161$	5.73530e6	+	9.93382e6i	0.108309	+	0.187597i
$162$	−3.82858e7			−0.707515
$163$	2.95512e7	−	5.11841e7i	0.534463	−	0.925718i	−0.464726	−	0.885455i	$-0.653847\pi$
$163$	2.95512e7	−	5.11841e7i	0.534463	−	0.925718i	0.999189	−	0.0402630i	$-0.0128196\pi$
$164$	1.56298e7	−	2.70717e7i	0.276695	−	0.479249i
$165$	−3.86420e7	+	6.69298e7i	−0.669677	+	1.15991i
$166$	−2.52116e7	−	4.36678e7i	−0.427782	−	0.740940i
$167$	−3.17445e6	−	5.49831e6i	−0.0527425	−	0.0913527i	0.838449	−	0.544980i	$-0.183463\pi$
$167$	−3.17445e6	−	5.49831e6i	−0.0527425	−	0.0913527i	−0.891191	+	0.453628i	$0.850130\pi$
$168$	2.95567e6	−	5.11937e6i	0.0480921	−	0.0832979i
$169$	−4.64880e7	+	8.05197e7i	−0.740863	+	1.28321i
$170$	1.67023e7	−	2.89293e7i	0.260739	−	0.451613i
$171$	−1.27898e8			−1.95604
$172$	−2.43567e7	−	4.21870e7i	−0.364980	−	0.632163i
$173$	−7.37844e6	+	1.27798e7i	−0.108344	+	0.187657i	−0.915099	−	0.403228i	$-0.867888\pi$
$173$	−7.37844e6	+	1.27798e7i	−0.108344	+	0.187657i	0.806756	+	0.590885i	$0.201221\pi$
$174$	9.37801e7			1.34955
$175$	6.25386e6			0.0882094
$176$	1.16369e7	−	2.01558e7i	0.160896	−	0.278680i
$177$	1.20418e7			0.163225
$178$	4.40572e6	+	7.63093e6i	0.0585527	+	0.101416i
$179$	6.93955e7			0.904370			0.452185	−	0.891924i	$-0.350645\pi$
$179$	6.93955e7			0.904370			0.452185	+	0.891924i	$0.350645\pi$
$180$	1.43864e7	+	2.49179e7i	0.183864	+	0.318462i
$181$	5.13734e7	+	8.89814e7i	0.643967	+	1.11538i	0.984539	+	0.175165i	$0.0560458\pi$
$181$	5.13734e7	+	8.89814e7i	0.643967	+	1.11538i	−0.340573	+	0.940218i	$0.610621\pi$
$182$	8.71521e6	+	1.50952e7i	0.107159	+	0.185605i
$183$	8.16837e7	−	1.41480e8i	0.985273	−	1.70654i
$184$	3.36369e7			0.398065
$185$	5.30389e7	+	3.46858e7i	0.615876	+	0.402764i
$186$	−5.06166e7			−0.576764
$187$	5.76757e7	−	9.98972e7i	0.644982	−	1.11714i
$188$	1.35479e7	+	2.34656e7i	0.148703	+	0.257561i
$189$	−7286.39	−	12620.4i	−7.85048e−5	−	0.000135974i
$190$	−4.81426e7	−	8.33854e7i	−0.509204	−	0.881967i
$191$	−1.41972e8			−1.47430			−0.737152	−	0.675727i	$-0.763830\pi$
$191$	−1.41972e8			−1.47430			−0.737152	+	0.675727i	$0.763830\pi$
$192$	−8.66736e6	−	1.50123e7i	−0.0883756	−	0.153071i
$193$	−1.04565e8			−1.04698			−0.523488	−	0.852033i	$-0.675370\pi$
$193$	−1.04565e8			−1.04698			−0.523488	+	0.852033i	$0.675370\pi$
$194$	812707.	−	1.40765e6i	0.00799149	−	0.0138417i
$195$	−1.69730e8			−1.63922
$196$	−5.07557e7			−0.481492
$197$	6.87121e7	−	1.19013e8i	0.640326	−	1.10908i	−0.345034	−	0.938590i	$-0.612133\pi$
$197$	6.87121e7	−	1.19013e8i	0.640326	−	1.10908i	0.985360	−	0.170487i	$-0.0545342\pi$
$198$	4.96784e7	+	8.60454e7i	0.454820	+	0.787771i
$199$	−8.23840e7			−0.741066			−0.370533	−	0.928819i	$-0.620825\pi$
$199$	−8.23840e7			−0.741066			−0.370533	+	0.928819i	$0.620825\pi$
$200$	9.16956e6	−	1.58821e7i	0.0810482	−	0.140380i
$201$	−7.47323e7	+	1.29440e8i	−0.649115	+	1.12430i
$202$	−2.87793e7	+	4.98472e7i	−0.245669	+	0.425511i
$203$	1.54758e7	+	2.68049e7i	0.129843	+	0.224894i
$204$	−4.29576e7	−	7.44048e7i	−0.354270	−	0.613614i
$205$	−5.02316e7	+	8.70037e7i	−0.407229	+	0.705341i
$206$	5.94512e7	−	1.02973e8i	0.473833	−	0.820703i
$207$	−7.17983e7	+	1.24358e8i	−0.562624	+	0.974493i
$208$	5.11138e7			0.393837
$209$	−1.66244e8	−	2.87943e8i	−1.25960	−	2.18170i
$210$	−9.49903e6	+	1.64528e7i	−0.0707802	+	0.122595i
$211$	−1.95531e8			−1.43294			−0.716468	−	0.697620i	$-0.754243\pi$
$211$	−1.95531e8			−1.43294			−0.716468	+	0.697620i	$0.754243\pi$
$212$	4.18734e7			0.301830
$213$	9.02497e7	−	1.56317e8i	0.639907	−	1.10835i
$214$	−2.00607e8			−1.39926
$215$	7.82783e7	+	1.35582e8i	0.537164	+	0.930395i
$216$	−42734.0			−0.000288526
$217$	−8.35287e6	−	1.44676e7i	−0.0554915	−	0.0961142i
$218$	−1.31118e6	−	2.27103e6i	−0.00857165	−	0.0148465i
$219$	−1.41216e8	−	2.44593e8i	−0.908509	−	1.57358i
$220$	−3.73992e7	+	6.47773e7i	−0.236801	+	0.410151i
$221$	2.53333e8			1.57877
$222$	1.45465e8	−	7.35325e7i	0.892327	−	0.451070i
$223$	1.42945e8			0.863181			0.431590	−	0.902070i	$-0.357953\pi$
$223$	1.42945e8			0.863181			0.431590	+	0.902070i	$0.357953\pi$
$224$	2.86061e6	−	4.95473e6i	0.0170056	−	0.0294545i
$225$	3.91450e7	+	6.78012e7i	0.229107	+	0.396824i
$226$	7.27463e7	+	1.26000e8i	0.419210	+	0.726092i
$227$	9.98211e7	+	1.72895e8i	0.566411	+	0.981053i	0.996917	+	0.0784648i	$0.0250018\pi$
$227$	9.98211e7	+	1.72895e8i	0.566411	+	0.981053i	−0.430506	+	0.902588i	$0.641665\pi$
$228$	−2.47641e8			−1.38373
$229$	−1.15473e8	−	2.00004e8i	−0.635411	−	1.10056i	−0.986428	−	0.164194i	$-0.947498\pi$
$229$	−1.15473e8	−	2.00004e8i	−0.635411	−	1.10056i	0.351017	−	0.936369i	$-0.385836\pi$
$230$	−1.08103e8			−0.585858
$231$	−3.28016e7	+	5.68141e7i	−0.175087	+	0.303259i
$232$	9.07640e7			0.477206
$233$	2.27221e8			1.17680			0.588399	−	0.808571i	$-0.299758\pi$
$233$	2.27221e8			1.17680			0.588399	+	0.808571i	$0.299758\pi$
$234$	−1.09103e8	+	1.88972e8i	−0.556649	+	0.964144i
$235$	−4.35406e7	−	7.54146e7i	−0.218855	−	0.379069i
$236$	1.16546e7			0.0577171
$237$	−5.00023e7	+	8.66066e7i	−0.243989	+	0.422602i
$238$	1.41779e7	−	2.45569e7i	0.0681701	−	0.118074i
$239$	1.64265e6	−	2.84516e6i	0.00778311	−	0.0134807i	−0.862108	−	0.506725i	$-0.830856\pi$
$239$	1.64265e6	−	2.84516e6i	0.00778311	−	0.0134807i	0.869891	+	0.493244i	$0.164189\pi$
$240$	2.78554e7	+	4.82470e7i	0.130068	+	0.225284i
$241$	1.64801e8	+	2.85444e8i	0.758405	+	1.31360i	0.943664	+	0.330906i	$0.107354\pi$
$241$	1.64801e8	+	2.85444e8i	0.758405	+	1.31360i	−0.185259	+	0.982690i	$0.559312\pi$
$242$	−5.11966e7	+	8.86750e7i	−0.232213	+	0.402205i
$243$	1.58141e8	−	2.73908e8i	0.707005	−	1.22457i
$244$	7.90567e7	−	1.36930e8i	0.348397	−	0.603441i
$245$	1.63120e8			0.708642
$246$	1.29194e8	+	2.23770e8i	0.553309	+	0.958360i
$247$	3.65103e8	−	6.32376e8i	1.54161	−	2.67015i
$248$	−4.89888e7			−0.203946
$249$	4.16790e8			1.71088
$250$	−9.37461e7	+	1.62373e8i	−0.379457	+	0.657239i
$251$	2.97593e8			1.18786			0.593929	−	0.804518i	$-0.297576\pi$
$251$	2.97593e8			1.18786			0.593929	+	0.804518i	$0.297576\pi$
$252$	1.22120e7	+	2.11518e7i	0.0480713	+	0.0832619i
$253$	−3.73298e8			−1.44922
$254$	−5.22103e7	−	9.04308e7i	−0.199912	−	0.346257i
$255$	1.38059e8	+	2.39125e8i	0.521402	+	0.903095i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−8.76073e7	+	1.51740e8i	−0.321940	+	0.557616i	−0.980888	−	0.194572i	$-0.937668\pi$
$257$	−8.76073e7	+	1.51740e8i	−0.321940	+	0.557616i	0.658949	+	0.752188i	$0.271001\pi$
$258$	4.02657e8			1.45971
$259$	4.50226e7	+	2.94434e7i	0.161021	+	0.105303i
$260$	−1.64271e8			−0.579636
$261$	−1.93737e8	+	3.35562e8i	−0.674482	+	1.16824i
$262$	4.27039e7	+	7.39654e7i	0.146694	+	0.254082i
$263$	4.22487e7	+	7.31770e7i	0.143208	+	0.248044i	0.928703	−	0.370824i	$-0.120925\pi$
$263$	4.22487e7	+	7.31770e7i	0.143208	+	0.248044i	−0.785495	+	0.618868i	$0.787591\pi$
$264$	9.61891e7	+	1.66604e8i	0.321745	+	0.557279i
$265$	−1.34574e8			−0.444223
$266$	−4.08663e7	−	7.07826e7i	−0.133131	−	0.230590i
$267$	−7.28339e7			−0.234177
$268$	−7.23288e7	+	1.25277e8i	−0.229530	+	0.397558i
$269$	2.13687e8			0.669338			0.334669	−	0.942336i	$-0.391376\pi$
$269$	2.13687e8			0.669338			0.334669	+	0.942336i	$0.391376\pi$
$270$	137340.			0.000424642
$271$	−1.70568e8	+	2.95432e8i	−0.520601	+	0.901707i	0.479112	+	0.877754i	$0.340959\pi$
$271$	−1.70568e8	+	2.95432e8i	−0.520601	+	0.901707i	−0.999713	+	0.0239537i	$0.992375\pi$
$272$	−4.15761e7	−	7.20119e7i	−0.125272	−	0.216977i
$273$	−1.44077e8			−0.428574
$274$	9.94872e7	−	1.72317e8i	0.292173	−	0.506059i
$275$	−1.01762e8	+	1.76258e8i	−0.295069	+	0.511074i
$276$	−1.39019e8	+	2.40787e8i	−0.398008	+	0.689369i
$277$	2.50203e7	+	4.33364e7i	0.0707315	+	0.122511i	0.899222	−	0.437492i	$-0.144133\pi$
$277$	2.50203e7	+	4.33364e7i	0.0707315	+	0.122511i	−0.828491	+	0.560003i	$0.810800\pi$
$278$	−1.58642e8	−	2.74775e8i	−0.442854	−	0.767045i
$279$	1.04567e8	−	1.81115e8i	0.288257	−	0.499276i
$280$	−9.19353e6	+	1.59237e7i	−0.0250282	+	0.0433501i
$281$	−1.90644e8	+	3.30205e8i	−0.512568	+	0.887793i	0.487326	+	0.873220i	$0.337972\pi$
$281$	−1.90644e8	+	3.30205e8i	−0.512568	+	0.887793i	−0.999894	+	0.0145732i	$0.995361\pi$
$282$	−2.23969e8			−0.594725
$283$	1.17189e8	+	2.02978e8i	0.307352	+	0.532349i	0.977782	−	0.209623i	$-0.0672238\pi$
$283$	1.17189e8	+	2.02978e8i	0.307352	+	0.532349i	−0.670430	+	0.741972i	$0.733890\pi$
$284$	8.73472e7	−	1.51290e8i	0.226274	−	0.391918i
$285$	7.95878e8			2.03652
$286$	−5.67254e8			−1.43383
$287$	−4.26396e7	+	7.38540e7i	−0.106470	+	0.184411i
$288$	7.16223e7			0.176675
$289$	−892401.	−	1.54568e6i	−0.00217479	−	0.00376685i
$290$	−2.91700e8			−0.702335
$291$	6.71770e6	+	1.16354e7i	0.0159807	+	0.0276794i
$292$	−1.36674e8	−	2.36727e8i	−0.321253	−	0.556426i
$293$	2.52263e8	+	4.36932e8i	0.585891	+	1.01479i	0.994764	+	0.102201i	$0.0325886\pi$
$293$	2.52263e8	+	4.36932e8i	0.585891	+	1.01479i	−0.408873	+	0.912591i	$0.634078\pi$
$294$	2.09769e8	−	3.63331e8i	0.481422	−	0.833848i
$295$	−3.74558e7			−0.0849459
$296$	1.40787e8	−	7.11677e7i	0.315531	−	0.159500i
$297$	474255.			0.00105042
$298$	7.63651e7	−	1.32268e8i	0.167162	−	0.289534i
$299$	−4.09916e8	−	7.09996e8i	−0.886841	−	1.53605i
$300$	7.57940e7	+	1.31279e8i	0.162073	+	0.280719i
$301$	6.64474e7	+	1.15090e8i	0.140441	+	0.243252i
$302$	7.13905e7			0.149147
$303$	−2.37885e8	−	4.12028e8i	−0.491267	−	0.850899i
$304$	−2.39677e8			−0.489293
$305$	−2.54075e8	+	4.40071e8i	−0.512758	+	0.888123i
$306$	3.54978e8			0.708234
$307$	−1.90308e8			−0.375381			−0.187691	−	0.982228i	$-0.560100\pi$
$307$	−1.90308e8			−0.375381			−0.187691	+	0.982228i	$0.560100\pi$
$308$	−3.17467e7	+	5.49869e7i	−0.0619115	+	0.107234i
$309$	4.91414e8	+	8.51154e8i	0.947530	+	1.64117i
$310$	1.57442e8			0.300161
$311$	3.02378e8	−	5.23735e8i	0.570019	−	0.987302i	−0.426544	−	0.904467i	$-0.640269\pi$
$311$	3.02378e8	−	5.23735e8i	0.570019	−	0.987302i	0.996563	−	0.0828351i	$-0.0263975\pi$
$312$	−2.11249e8	+	3.65895e8i	−0.393781	+	0.682048i
$313$	2.37570e7	−	4.11484e7i	0.0437912	−	0.0758486i	−0.843299	−	0.537445i	$-0.819390\pi$
$313$	2.37570e7	−	4.11484e7i	0.0437912	−	0.0758486i	0.887090	+	0.461596i	$0.152723\pi$
$314$	−3.05983e7	−	5.29978e7i	−0.0557755	−	0.0966060i
$315$	−3.92474e7	−	6.79785e7i	−0.0707496	−	0.122542i
$316$	−4.83942e7	+	8.38212e7i	−0.0862757	+	0.149434i
$317$	5.49685e8	−	9.52083e8i	0.969185	−	1.67868i	0.271261	−	0.962506i	$-0.412559\pi$
$317$	5.49685e8	−	9.52083e8i	0.969185	−	1.67868i	0.697924	−	0.716172i	$-0.254107\pi$
$318$	−1.73059e8	+	2.99747e8i	−0.301787	+	0.522710i
$319$	−1.00729e9			−1.73734
$320$	2.69596e7	+	4.66954e7i	0.0459926	+	0.0796616i
$321$	8.29092e8	−	1.43603e9i	1.39906	−	2.42324i
$322$	−9.17647e7			−0.153172
$323$	−1.18790e9			−1.96142
$324$	1.53143e8	−	2.65252e8i	0.250144	−	0.433262i
$325$	−4.46979e8			−0.722263
$326$	2.36409e8	+	4.09473e8i	0.377923	+	0.654581i
$327$	2.16760e7			0.0342816
$328$	1.25039e8	+	2.16573e8i	0.195653	+	0.338880i
$329$	−3.69599e7	−	6.40165e7i	−0.0572197	−	0.0991074i
$330$	−3.09136e8	−	5.35439e8i	−0.473533	−	0.820183i
$331$	−6.01124e7	+	1.04118e8i	−0.0911100	+	0.157807i	−0.907978	−	0.419017i	$-0.862375\pi$
$331$	−6.01124e7	+	1.04118e8i	−0.0911100	+	0.157807i	0.816868	+	0.576824i	$0.195708\pi$
$332$	4.03386e8			0.604975
$333$	−3.73987e7	+	6.72409e8i	−0.0555011	+	0.997881i
$334$	5.07912e7			0.0745892
$335$	2.32453e8	−	4.02620e8i	0.337814	−	0.585111i
$336$	2.36454e7	+	4.09550e7i	0.0340062	+	0.0589005i
$337$	−4.60562e8	−	7.97718e8i	−0.655517	−	1.13539i	−0.981764	−	0.190104i	$-0.939117\pi$
$337$	−4.60562e8	−	7.97718e8i	−0.655517	−	1.13539i	0.326247	−	0.945285i	$-0.394216\pi$
$338$	−3.71904e8	−	6.44157e8i	−0.523869	−	0.907368i
$339$	−1.20262e9			−1.67660
$340$	1.33619e8	+	2.31434e8i	0.184370	+	0.319338i
$341$	5.43670e8			0.742498
$342$	5.11593e8	−	8.86105e8i	0.691565	−	1.19783i
$343$	2.82256e8			0.377670
$344$	3.89707e8			0.516159
$345$	4.46783e8	−	7.73850e8i	0.585773	−	1.01459i
$346$	−5.90275e7	−	1.02239e8i	−0.0766105	−	0.132693i
$347$	8.20647e8			1.05439			0.527197	−	0.849743i	$-0.323243\pi$
$347$	8.20647e8			1.05439			0.527197	+	0.849743i	$0.323243\pi$
$348$	−3.75120e8	+	6.49727e8i	−0.477137	+	0.826426i
$349$	2.85785e8	−	4.94993e8i	0.359873	−	0.623319i	−0.628066	−	0.778160i	$-0.716153\pi$
$349$	2.85785e8	−	4.94993e8i	0.359873	−	0.623319i	0.987939	+	0.154841i	$0.0494865\pi$
$350$	−2.50154e7	+	4.33280e7i	−0.0311867	+	0.0540170i
$351$	520777.	+	902012.i	0.000642801	+	0.00111336i
$352$	9.30956e7	+	1.61246e8i	0.113771	+	0.197056i
$353$	3.99070e8	−	6.91209e8i	0.482878	−	0.836369i	−0.516929	−	0.856028i	$-0.672925\pi$
$353$	3.99070e8	−	6.91209e8i	0.482878	−	0.836369i	0.999807	+	0.0196593i	$0.00625814\pi$
$354$	−4.81674e7	+	8.34284e7i	−0.0577087	+	0.0999545i
$355$	−2.80719e8	+	4.86220e8i	−0.333022	+	0.576811i
$356$	−7.04915e7			−0.0828060
$357$	1.17193e8	+	2.02983e8i	0.136320	+	0.236114i
$358$	−2.77582e8	+	4.80786e8i	−0.319743	+	0.553811i
$359$	−9.18116e8			−1.04729			−0.523645	−	0.851936i	$-0.675428\pi$
$359$	−9.18116e8			−1.04729			−0.523645	+	0.851936i	$0.675428\pi$
$360$	−2.30182e8			−0.260023
$361$	−1.26506e9	+	2.19115e9i	−1.41526	+	2.45130i
$362$	−8.21975e8			−0.910706
$363$	−4.23182e8	−	7.32973e8i	−0.464359	−	0.804294i
$364$	−1.39443e8			−0.151546
$365$	4.39248e8	+	7.60800e8i	0.472808	+	0.818928i
$366$	6.53470e8	+	1.13184e9i	0.696693	+	1.20671i
$367$	−1.25225e8	−	2.16896e8i	−0.132239	−	0.229045i	0.792300	−	0.610132i	$-0.208883\pi$
$367$	−1.25225e8	−	2.16896e8i	−0.132239	−	0.229045i	−0.924539	+	0.381086i	$0.875550\pi$
$368$	−1.34548e8	+	2.33043e8i	−0.140737	+	0.243764i
$369$	−1.06758e9			−1.10614
$370$	−4.52466e8	+	2.28721e8i	−0.464387	+	0.234747i
$371$	−1.14235e8			−0.116142
$372$	2.02466e8	−	3.50682e8i	0.203917	−	0.353194i
$373$	8.92411e8	+	1.54570e9i	0.890398	+	1.54221i	0.839399	+	0.543516i	$0.182907\pi$
$373$	8.92411e8	+	1.54570e9i	0.890398	+	1.54221i	0.0509994	+	0.998699i	$0.483759\pi$
$374$	4.61406e8	+	7.99178e8i	0.456071	+	0.789938i
$375$	−7.74889e8	−	1.34215e9i	−0.758805	−	1.31429i
$376$	−2.16766e8			−0.210297
$377$	−1.10610e9	−	1.91581e9i	−1.06316	−	1.84144i
$378$	116582.			0.000111023
$379$	−2.24696e8	+	3.89184e8i	−0.212011	+	0.367213i	−0.952344	−	0.305027i	$-0.901334\pi$
$379$	−2.24696e8	+	3.89184e8i	−0.212011	+	0.367213i	0.740333	+	0.672240i	$0.234668\pi$
$380$	7.70282e8			0.720123
$381$	8.63123e8			0.799531
$382$	5.67889e8	−	9.83613e8i	0.521245	−	0.902823i
$383$	4.14759e8	+	7.18384e8i	0.377225	+	0.653372i	0.990657	−	0.136375i	$-0.0435451\pi$
$383$	4.14759e8	+	7.18384e8i	0.377225	+	0.653372i	−0.613433	+	0.789747i	$0.710212\pi$
$384$	1.38678e8			0.124982
$385$	1.02029e8	−	1.76719e8i	0.0911191	−	0.157823i
$386$	4.18261e8	−	7.24450e8i	0.370162	−	0.641140i
$387$	−8.31833e8	+	1.44078e9i	−0.729538	+	1.26360i
$388$	6.50166e6	+	1.12612e7i	0.00565084	+	0.00978754i
$389$	6.35425e8	+	1.10059e9i	0.547319	+	0.947984i	0.998457	+	0.0555301i	$0.0176849\pi$
$389$	6.35425e8	+	1.10059e9i	0.547319	+	0.947984i	−0.451138	+	0.892454i	$0.648982\pi$
$390$	6.78920e8	−	1.17592e9i	0.579552	−	1.00381i
$391$	−6.66853e8	+	1.15502e9i	−0.564172	+	0.977174i
$392$	2.03023e8	−	3.51646e8i	0.170233	−	0.294852i
$393$	−7.05967e8			−0.586693
$394$	5.49697e8	+	9.52102e8i	0.452779	+	0.784236i
$395$	1.55531e8	−	2.69387e8i	0.126978	−	0.219931i
$396$	−7.94854e8			−0.643212
$397$	−9.52444e8			−0.763963			−0.381982	−	0.924170i	$-0.624758\pi$
$397$	−9.52444e8			−0.763963			−0.381982	+	0.924170i	$0.624758\pi$
$398$	3.29536e8	−	5.70773e8i	0.262007	−	0.453809i
$399$	6.75589e8			0.532448
$400$	7.33565e7	+	1.27057e8i	0.0573097	+	0.0992634i
$401$	−7.29454e8			−0.564928			−0.282464	−	0.959278i	$-0.591152\pi$
$401$	−7.29454e8			−0.564928			−0.282464	+	0.959278i	$0.591152\pi$
$402$	−5.97858e8	−	1.03552e9i	−0.458994	−	0.795001i
$403$	5.97001e8	+	1.03404e9i	0.454368	+	0.786988i
$404$	−2.30234e8	−	3.98777e8i	−0.173714	−	0.300882i
$405$	−4.92177e8	+	8.52475e8i	−0.368153	+	0.637660i
$406$	−2.47613e8			−0.183625
$407$	−1.56243e9	+	7.89809e8i	−1.14874	+	0.580686i
$408$	6.87322e8			0.501014
$409$	5.49737e8	−	9.52173e8i	0.397304	−	0.688152i	−0.596088	−	0.802919i	$-0.703279\pi$
$409$	5.49737e8	−	9.52173e8i	0.397304	−	0.688152i	0.993392	+	0.114768i	$0.0366124\pi$
$410$	−4.01853e8	−	6.96030e8i	−0.287954	−	0.498752i
$411$	8.22345e8	+	1.42434e9i	0.584262	+	1.01197i
$412$	4.75610e8	+	8.23780e8i	0.335051	+	0.580325i
$413$	−3.17948e7			−0.0222091
$414$	−5.74387e8	−	9.94867e8i	−0.397835	−	0.689071i
$415$	−1.29641e9			−0.890380
$416$	−2.04455e8	+	3.54127e8i	−0.139243	+	0.241175i
$417$	2.62261e9			1.77116
$418$	2.65990e9			1.78135
$419$	5.02986e7	−	8.71197e7i	0.0334046	−	0.0578585i	−0.848840	−	0.528650i	$-0.822698\pi$
$419$	5.02986e7	−	8.71197e7i	0.0334046	−	0.0578585i	0.882244	+	0.470792i	$0.156032\pi$
$420$	−7.59922e7	−	1.31622e8i	−0.0500492	−	0.0866877i
$421$	−2.50820e8			−0.163823			−0.0819116	−	0.996640i	$-0.526103\pi$
$421$	−2.50820e8			−0.163823			−0.0819116	+	0.996640i	$0.526103\pi$
$422$	7.82124e8	−	1.35468e9i	0.506620	−	0.877491i
$423$	4.62689e8	−	8.01402e8i	0.297234	−	0.514824i
$424$	−1.67494e8	+	2.90107e8i	−0.106713	+	0.184832i
$425$	3.63573e8	+	6.29728e8i	0.229737	+	0.397916i
$426$	7.21998e8	+	1.25054e9i	0.452483	+	0.783723i
$427$	−2.15674e8	+	3.73559e8i	−0.134060	+	0.232199i
$428$	8.02428e8	−	1.38985e9i	0.494712	−	0.856867i
$429$	2.34442e9	−	4.06065e9i	1.43362	−	2.48310i
$430$	−1.25245e9			−0.759664
$431$	5.20141e8	+	9.00910e8i	0.312932	+	0.542015i	0.978996	−	0.203880i	$-0.0653554\pi$
$431$	5.20141e8	+	9.00910e8i	0.312932	+	0.542015i	−0.666064	+	0.745895i	$0.732022\pi$
$432$	170936.	−	296070.i	0.000102009	−	0.000176685i
$433$	2.78932e9			1.65117			0.825584	−	0.564279i	$-0.190846\pi$
$433$	2.78932e9			1.65117			0.825584	+	0.564279i	$0.190846\pi$
$434$	1.33646e8			0.0784769
$435$	1.20557e9	−	2.08811e9i	0.702233	−	1.21630i
$436$	2.09789e7			0.0121221
$437$	1.92213e9	+	3.32923e9i	1.10179	+	1.90835i
$438$	2.25945e9			1.28483
$439$	−9.89247e8	−	1.71343e9i	−0.558057	−	0.966584i	−0.997659	−	0.0683906i	$-0.978214\pi$
$439$	−9.89247e8	−	1.71343e9i	−0.558057	−	0.966584i	0.439601	−	0.898193i	$-0.355120\pi$
$440$	−2.99194e8	−	5.18219e8i	−0.167443	−	0.290020i
$441$	8.66709e8	+	1.50118e9i	0.481214	+	0.833487i
$442$	−1.01333e9	+	1.75514e9i	−0.558180	+	0.966796i
$443$	−3.63514e7			−0.0198659			−0.00993296	−	0.999951i	$-0.503162\pi$
$443$	−3.63514e7			−0.0198659			−0.00993296	+	0.999951i	$0.503162\pi$
$444$	−7.24127e7	+	1.30194e9i	−0.0392622	+	0.705914i
$445$	2.26548e8			0.121871
$446$	−5.71780e8	+	9.90351e8i	−0.305180	+	0.528588i
$447$	6.31222e8	+	1.09331e9i	0.334276	+	0.578984i
$448$	2.28849e7	+	3.96378e7i	0.0120248	+	0.0208275i
$449$	1.43180e8	+	2.47996e8i	0.0746485	+	0.129295i	0.900933	−	0.433957i	$-0.142883\pi$
$449$	1.43180e8	+	2.47996e8i	0.0746485	+	0.129295i	−0.826285	+	0.563252i	$0.809550\pi$
$450$	−6.26320e8			−0.324006
$451$	−1.38766e9	−	2.40350e9i	−0.712304	−	1.23375i
$452$	−1.16394e9			−0.592852
$453$	−2.95051e8	+	5.11043e8i	−0.149126	+	0.258294i
$454$	−1.59714e9			−0.801026
$455$	4.48148e8			0.223039
$456$	9.90565e8	−	1.71571e9i	0.489222	−	0.847358i
$457$	4.09367e8	+	7.09044e8i	0.200635	+	0.347510i	0.948733	−	0.316078i	$-0.102366\pi$
$457$	4.09367e8	+	7.09044e8i	0.200635	+	0.347510i	−0.748098	+	0.663588i	$0.769033\pi$
$458$	1.84756e9			0.898606
$459$	847202.	−	1.46740e6i	0.000408924	−	0.000708277i
$460$	4.32414e8	−	7.48963e8i	0.207132	−	0.358763i
$461$	−3.51653e7	+	6.09081e7i	−0.0167171	+	0.0289549i	−0.874263	−	0.485453i	$-0.838655\pi$
$461$	−3.51653e7	+	6.09081e7i	−0.0167171	+	0.0289549i	0.857546	+	0.514408i	$0.171988\pi$
$462$	−2.62413e8	−	4.54513e8i	−0.123805	−	0.214437i
$463$	−4.79035e8	−	8.29713e8i	−0.224302	−	0.388503i	0.731808	−	0.681511i	$-0.238677\pi$
$463$	−4.79035e8	−	8.29713e8i	−0.224302	−	0.388503i	−0.956110	+	0.293008i	$0.905344\pi$
$464$	−3.63056e8	+	6.28832e8i	−0.168718	+	0.292228i
$465$	−6.50693e8	+	1.12703e9i	−0.300117	+	0.519818i
$466$	−9.08882e8	+	1.57423e9i	−0.416061	+	0.720639i
$467$	−1.12248e9			−0.510000			−0.255000	−	0.966941i	$-0.582075\pi$
$467$	−1.12248e9			−0.510000			−0.255000	+	0.966941i	$0.582075\pi$
$468$	−8.72824e8	−	1.51178e9i	−0.393610	−	0.681753i
$469$	1.97320e8	−	3.41768e8i	0.0883214	−	0.152977i
$470$	6.96650e8			0.309508
$471$	5.05841e8			0.223070
$472$	−4.66183e7	+	8.07452e7i	−0.0204061	+	0.0353443i
$473$	−4.32491e9			−1.87916
$474$	−4.00019e8	−	6.92853e8i	−0.172527	−	0.298825i
$475$	2.09592e9			0.897320
$476$	1.13424e8	+	1.96455e8i	0.0482035	+	0.0834909i
$477$	−7.15033e8	−	1.23847e9i	−0.301656	−	0.522484i
$478$	1.31412e7	+	2.27613e7i	0.00550349	+	0.00953232i
$479$	−1.25400e9	+	2.17200e9i	−0.521344	+	0.902995i	0.478347	+	0.878171i	$0.341236\pi$
$479$	−1.25400e9	+	2.17200e9i	−0.521344	+	0.902995i	−0.999692	+	0.0248243i	$0.992097\pi$
$480$	−4.45687e8			−0.183944
$481$	−3.21788e9	−	2.10439e9i	−1.31845	−	0.862223i
$482$	−2.63682e9			−1.07255
$483$	3.79256e8	−	6.56891e8i	0.153150	−	0.265264i
$484$	−4.09572e8	−	7.09400e8i	−0.164200	−	0.284402i
$485$	−2.08952e7	−	3.61916e7i	−0.00831670	−	0.0144050i
$486$	1.26513e9	+	2.19126e9i	0.499928	+	0.865900i
$487$	−1.85017e9			−0.725874			−0.362937	−	0.931814i	$-0.618226\pi$
$487$	−1.85017e9			−0.725874			−0.362937	+	0.931814i	$0.618226\pi$
$488$	6.32454e8	+	1.09544e9i	0.246354	+	0.426697i
$489$	−3.90824e9			−1.51147
$490$	−6.52482e8	+	1.13013e9i	−0.250543	+	0.433953i
$491$	1.44884e9			0.552375			0.276188	−	0.961104i	$-0.410929\pi$
$491$	1.44884e9			0.552375			0.276188	+	0.961104i	$0.410929\pi$
$492$	−2.06710e9			−0.782498
$493$	−1.79940e9	+	3.11665e9i	−0.676337	+	1.17145i
$494$	2.92082e9	+	5.05901e9i	1.09009	+	1.88808i
$495$	2.55453e9			0.946656
$496$	1.95955e8	−	3.39404e8i	0.0721058	−	0.124891i
$497$	−2.38291e8	+	4.12733e8i	−0.0870685	+	0.150807i
$498$	−1.66716e9	+	2.88761e9i	−0.604888	+	1.04770i
$499$	−1.86563e9	−	3.23137e9i	−0.672163	−	1.16422i	−0.977290	−	0.211908i	$-0.932032\pi$
$499$	−1.86563e9	−	3.23137e9i	−0.672163	−	1.16422i	0.305127	−	0.952312i	$-0.401301\pi$
$500$	−7.49968e8	−	1.29898e9i	−0.268317	−	0.464738i
$501$	−2.09916e8	+	3.63585e8i	−0.0745784	+	0.129174i
$502$	−1.19037e9	+	2.06178e9i	−0.419971	+	0.727411i
$503$	2.63972e9	−	4.57213e9i	0.924847	−	1.60188i	0.133039	−	0.991111i	$-0.457526\pi$
$503$	2.63972e9	−	4.57213e9i	0.924847	−	1.60188i	0.791807	−	0.610771i	$-0.209140\pi$
$504$	−1.95392e8			−0.0679830
$505$	7.39934e8	+	1.28160e9i	0.255666	+	0.442827i
$506$	1.49319e9	−	2.58628e9i	0.512376	−	0.887461i
$507$	6.14820e9			2.09517
$508$	8.35364e8			0.282718
$509$	5.86626e8	−	1.01607e9i	0.197174	−	0.341515i	−0.750437	−	0.660942i	$-0.770157\pi$
$509$	5.86626e8	−	1.01607e9i	0.197174	−	0.341515i	0.947611	+	0.319427i	$0.103490\pi$
$510$	−2.20894e9			−0.737374
$511$	3.72860e8	+	6.45813e8i	0.123616	+	0.214108i
$512$	1.34218e8			0.0441942
$513$	−2.44197e6	−	4.22961e6i	−0.000798599	−	0.00138321i
$514$	−7.00859e8	−	1.21392e9i	−0.227646	−	0.394294i
$515$	−1.52853e9	−	2.64749e9i	−0.493115	−	0.854101i
$516$	−1.61063e9	+	2.78969e9i	−0.516085	+	0.893885i
$517$	2.40564e9			0.765621
$518$	−3.84080e8	+	1.94152e8i	−0.121414	+	0.0613745i
$519$	9.75823e8			0.306398
$520$	6.57085e8	−	1.13811e9i	0.204932	−	0.354953i
$521$	−1.03976e9	−	1.80091e9i	−0.322106	−	0.557904i	0.658816	−	0.752304i	$-0.271057\pi$
$521$	−1.03976e9	−	1.80091e9i	−0.322106	−	0.557904i	−0.980922	+	0.194400i	$0.937724\pi$
$522$	−1.54989e9	−	2.68449e9i	−0.476931	−	0.826068i
$523$	2.29797e9	+	3.98020e9i	0.702406	+	1.21660i	0.967620	+	0.252413i	$0.0812241\pi$
$523$	2.29797e9	+	3.98020e9i	0.702406	+	1.21660i	−0.265214	+	0.964190i	$0.585443\pi$
$524$	−6.83263e8			−0.207457
$525$	−2.06773e8	−	3.58142e8i	−0.0623644	−	0.108018i
$526$	−6.75980e8			−0.202527
$527$	9.71203e8	−	1.68217e9i	0.289050	−	0.500649i
$528$	−1.53903e9			−0.455016
$529$	9.11286e8			0.267646
$530$	5.38296e8	−	9.32356e8i	0.157056	−	0.272030i
$531$	−1.99014e8	−	3.44703e8i	−0.0576838	−	0.0999112i
$532$	6.53862e8			0.188276
$533$	3.04756e9	−	5.27853e9i	0.871781	−	1.50997i
$534$	2.91335e8	−	5.04608e8i	0.0827940	−	0.143403i
$535$	−2.57887e9	+	4.46673e9i	−0.728100	+	1.26111i
$536$	−5.78631e8	−	1.00222e9i	−0.162302	−	0.281116i
$537$	−2.29445e9	−	3.97410e9i	−0.639394	−	1.10746i
$538$	−8.54748e8	+	1.48047e9i	−0.236647	+	0.409884i
$539$	−2.25312e9	+	3.90252e9i	−0.619760	+	1.07346i
$540$	−549359.	+	951518.i	−0.000150134	+	0.000260039i
$541$	−5.95661e9			−1.61737			−0.808684	−	0.588244i	$-0.799820\pi$
$541$	−5.95661e9			−1.61737			−0.808684	+	0.588244i	$0.799820\pi$
$542$	−1.36454e9	−	2.36346e9i	−0.368121	−	0.637603i
$543$	3.39715e9	−	5.88404e9i	0.910575	−	1.57716i
$544$	6.65217e8			0.177161
$545$	−6.74226e7			−0.0178409
$546$	5.76308e8	−	9.98195e8i	0.151524	−	0.262447i
$547$	6.55369e9			1.71210			0.856052	−	0.516890i	$-0.172910\pi$
$547$	6.55369e9			1.71210			0.856052	+	0.516890i	$0.172910\pi$
$548$	7.95898e8	+	1.37854e9i	0.206598	+	0.357838i
$549$	−5.39991e9			−1.39278
$550$	−8.14100e8	−	1.41006e9i	−0.208645	−	0.361384i
$551$	5.18657e9	+	8.98340e9i	1.32084	+	2.28776i
$552$	−1.11215e9	−	1.92630e9i	−0.281434	−	0.487458i
$553$	1.32024e8	−	2.28672e8i	0.0331982	−	0.0575010i
$554$	−4.00325e8			−0.100029
$555$	2.32722e8	−	4.18423e9i	0.0577847	−	1.03894i
$556$	2.53826e9			0.626290
$557$	−6.06102e8	+	1.04980e9i	−0.148611	+	0.257403i	−0.930715	−	0.365746i	$-0.880814\pi$
$557$	−6.06102e8	+	1.04980e9i	−0.148611	+	0.257403i	0.782103	+	0.623149i	$0.214147\pi$
$558$	8.36536e8	+	1.44892e9i	0.203828	+	0.353041i
$559$	−4.74916e9	−	8.22579e9i	−1.14994	−	1.99176i
$560$	−7.35483e7	−	1.27389e8i	−0.0176976	−	0.0306531i
$561$	−7.62781e9			−1.82402
$562$	−1.52515e9	−	2.64164e9i	−0.362440	−	0.627765i
$563$	2.22115e9			0.524563			0.262282	−	0.964991i	$-0.415525\pi$
$563$	2.22115e9			0.524563			0.262282	+	0.964991i	$0.415525\pi$
$564$	8.95877e8	−	1.55170e9i	0.210267	−	0.364193i
$565$	3.74071e9			0.872538
$566$	−1.87503e9			−0.434661
$567$	−4.17789e8	+	7.23632e8i	−0.0962535	+	0.166716i
$568$	6.98778e8	+	1.21032e9i	0.160000	+	0.277128i
$569$	−5.04048e9			−1.14704			−0.573520	−	0.819192i	$-0.694423\pi$
$569$	−5.04048e9			−1.14704			−0.573520	+	0.819192i	$0.694423\pi$
$570$	−3.18351e9	+	5.51400e9i	−0.720019	+	1.24711i
$571$	−1.59482e9	+	2.76231e9i	−0.358497	+	0.620935i	−0.987710	−	0.156298i	$-0.950044\pi$
$571$	−1.59482e9	+	2.76231e9i	−0.358497	+	0.620935i	0.629213	+	0.777233i	$0.283377\pi$
$572$	2.26902e9	−	3.93005e9i	0.506934	−	0.878036i
$573$	4.69408e9	+	8.13038e9i	1.04234	+	1.80539i
$574$	−3.41117e8	−	5.90832e8i	−0.0752856	−	0.130398i
$575$	1.17659e9	−	2.03791e9i	0.258100	−	0.447042i
$576$	−2.86489e8	+	4.96214e8i	−0.0624639	+	0.108191i
$577$	4.53197e9	−	7.84960e9i	0.982136	−	1.70111i	0.328106	−	0.944641i	$-0.393590\pi$
$577$	4.53197e9	−	7.84960e9i	0.982136	−	1.70111i	0.654030	−	0.756469i	$-0.273077\pi$
$578$	1.42784e7			0.00307562
$579$	3.45728e9	+	5.98818e9i	0.740217	+	1.28209i
$580$	1.16680e9	−	2.02096e9i	0.248313	−	0.430090i
$581$	−1.10048e9			−0.232790
$582$	−1.07483e8			−0.0226001
$583$	1.85882e9	−	3.21957e9i	0.388506	−	0.672912i
$584$	2.18679e9			0.454320
$585$	2.80511e9	+	4.85859e9i	0.579301	+	1.00338i
$586$	−4.03621e9			−0.828575
$587$	1.43883e8	+	2.49212e8i	0.0293613	+	0.0508553i	0.880333	−	0.474357i	$-0.157319\pi$
$587$	1.43883e8	+	2.49212e8i	0.0293613	+	0.0508553i	−0.850971	+	0.525212i	$0.823986\pi$
$588$	1.67815e9	+	2.90665e9i	0.340417	+	0.589620i
$589$	−2.79939e9	−	4.84868e9i	−0.564494	−	0.977732i
$590$	1.49823e8	−	2.59502e8i	0.0300329	−	0.0520185i
$591$	−9.08740e9			−1.81085
$592$	−7.00839e7	+	1.26007e9i	−0.0138833	+	0.249614i
$593$	−6.45832e9			−1.27183			−0.635913	−	0.771761i	$-0.719376\pi$
$593$	−6.45832e9			−1.27183			−0.635913	+	0.771761i	$0.719376\pi$
$594$	−1.89702e6	+	3.28574e6i	−0.000371381	+	0.000643251i
$595$	−3.64524e8	−	6.31374e8i	−0.0709442	−	0.122879i
$596$	6.10921e8	+	1.05815e9i	0.118202	+	0.204731i
$597$	2.72389e9	+	4.71792e9i	0.523937	+	0.907486i
$598$	6.55866e9			1.25418
$599$	2.16097e9	+	3.74292e9i	0.410824	+	0.711568i	0.994980	−	0.100073i	$-0.0319077\pi$
$599$	2.16097e9	+	3.74292e9i	0.410824	+	0.711568i	−0.584156	+	0.811641i	$0.698574\pi$
$600$	−1.21270e9			−0.229206
$601$	2.83309e9	−	4.90706e9i	0.532354	−	0.922064i	−0.466933	−	0.884293i	$-0.654641\pi$
$601$	2.83309e9	−	4.90706e9i	0.532354	−	0.922064i	0.999286	−	0.0377708i	$-0.0120257\pi$
$602$	−1.06316e9			−0.198614
$603$	4.94037e9			0.917590
$604$	−2.85562e8	+	4.94608e8i	−0.0527316	+	0.0913338i
$605$	1.31630e9	+	2.27989e9i	0.241663	+	0.418573i
$606$	3.80615e9			0.694756
$607$	−3.16656e8	+	5.48463e8i	−0.0574681	+	0.0995376i	−0.893328	−	0.449405i	$-0.851636\pi$
$607$	−3.16656e8	+	5.48463e8i	−0.0574681	+	0.0995376i	0.835860	+	0.548942i	$0.184969\pi$
$608$	9.58708e8	−	1.66053e9i	0.172991	−	0.299629i
$609$	1.02336e9	−	1.77252e9i	0.183599	−	0.318002i
$610$	−2.03260e9	−	3.52057e9i	−0.362575	−	0.627998i
$611$	2.64162e9	+	4.57542e9i	0.468518	+	0.811496i
$612$	−1.41991e9	+	2.45936e9i	−0.250399	+	0.433703i
$613$	1.99594e9	−	3.45707e9i	0.349974	−	0.606172i	−0.636271	−	0.771466i	$-0.719524\pi$
$613$	1.99594e9	−	3.45707e9i	0.349974	−	0.606172i	0.986244	+	0.165294i	$0.0528572\pi$
$614$	7.61232e8	−	1.31849e9i	0.132717	−	0.229873i
$615$	6.64330e9			1.15165
$616$	−2.53974e8	−	4.39895e8i	−0.0437780	−	0.0758258i
$617$	1.33468e9	−	2.31173e9i	0.228759	−	0.396222i	−0.728682	−	0.684853i	$-0.759867\pi$
$617$	1.33468e9	−	2.31173e9i	0.228759	−	0.396222i	0.957441	+	0.288630i	$0.0931999\pi$
$618$	−7.86262e9			−1.34001
$619$	−5.70698e9			−0.967139			−0.483569	−	0.875306i	$-0.660660\pi$
$619$	−5.70698e9			−0.967139			−0.483569	+	0.875306i	$0.660660\pi$
$620$	−6.29766e8	+	1.09079e9i	−0.106123	+	0.183810i
$621$	−5.48339e6			−0.000918817
$622$	2.41903e9	+	4.18988e9i	0.403064	+	0.698128i
$623$	1.92307e8			0.0318631
$624$	−1.68999e9	−	2.92716e9i	−0.278445	−	0.482281i
$625$	1.01111e9	+	1.75129e9i	0.165660	+	0.286932i
$626$	1.90056e8	+	3.29187e8i	0.0309651	+	0.0536331i
$627$	−1.09932e10	+	1.90407e10i	−1.78109	+	3.08494i
$628$	4.89573e8			0.0788785
$629$	−3.47354e8	+	6.24524e9i	−0.0556538	+	1.00063i
$630$	6.27958e8			0.100055
$631$	5.21371e9	−	9.03041e9i	0.826121	−	1.43088i	−0.0749377	−	0.997188i	$-0.523876\pi$
$631$	5.21371e9	−	9.03041e9i	0.826121	−	1.43088i	0.901059	−	0.433696i	$-0.142791\pi$
$632$	−3.87154e8	−	6.70570e8i	−0.0610062	−	0.105666i
$633$	6.46491e9	+	1.11975e10i	1.01309	+	1.75473i
$634$	4.39748e9	+	7.61666e9i	0.685317	+	1.18700i
$635$	−2.68472e9			−0.416094
$636$	−1.38447e9	−	2.39798e9i	−0.213395	−	0.369612i
$637$	−9.89655e9			−1.51704
$638$	4.02915e9	−	6.97869e9i	0.614244	−	1.06390i
$639$	−5.96619e9			−0.904574
$640$	−4.31353e8			−0.0650434
$641$	2.30437e9	−	3.99129e9i	0.345581	−	0.598563i	−0.639878	−	0.768476i	$-0.721015\pi$
$641$	2.30437e9	−	3.99129e9i	0.345581	−	0.598563i	0.985459	+	0.169913i	$0.0543486\pi$
$642$	6.63274e9	+	1.14882e10i	0.989282	+	1.71349i
$643$	4.40952e9			0.654113			0.327057	−	0.945005i	$-0.393943\pi$
$643$	4.40952e9			0.654113			0.327057	+	0.945005i	$0.393943\pi$
$644$	3.67059e8	−	6.35765e8i	0.0541546	−	0.0937985i
$645$	5.17628e9	−	8.96559e9i	0.759555	−	1.31559i
$646$	4.75160e9	−	8.23002e9i	0.693468	−	1.20112i
$647$	5.97464e9	+	1.03484e10i	0.867255	+	1.50213i	0.864791	+	0.502132i	$0.167451\pi$
$647$	5.97464e9	+	1.03484e10i	0.867255	+	1.50213i	0.00246394	+	0.999997i	$0.499216\pi$
$648$	1.22515e9	+	2.12202e9i	0.176879	+	0.306363i
$649$	5.17363e8	−	8.96099e8i	0.0742915	−	0.128677i
$650$	1.78792e9	−	3.09676e9i	0.255358	−	0.442294i
$651$	−5.52348e8	+	9.56694e8i	−0.0784656	+	0.135906i
$652$	−3.78255e9			−0.534463
$653$	−1.84460e9	−	3.19495e9i	−0.259243	−	0.449022i	0.706796	−	0.707417i	$-0.250140\pi$
$653$	−1.84460e9	−	3.19495e9i	−0.259243	−	0.449022i	−0.966039	+	0.258395i	$0.916806\pi$
$654$	−8.67039e7	+	1.50176e8i	−0.0121204	+	0.0209931i
$655$	2.19589e9			0.305328
$656$	−2.00062e9			−0.276695
$657$	−4.66772e9	+	8.08473e9i	−0.642135	+	1.11221i
$658$	5.91359e8			0.0809208
$659$	3.59404e9	+	6.22507e9i	0.489198	+	0.847316i	0.999923	−	0.0124287i	$-0.00395627\pi$
$659$	3.59404e9	+	6.22507e9i	0.489198	+	0.847316i	−0.510725	+	0.859744i	$0.670623\pi$
$660$	4.94617e9			0.669677
$661$	4.20354e9	+	7.28075e9i	0.566122	+	0.980553i	0.996944	+	0.0781157i	$0.0248904\pi$
$661$	4.20354e9	+	7.28075e9i	0.566122	+	0.980553i	−0.430822	+	0.902437i	$0.641776\pi$
$662$	−4.80899e8	−	8.32941e8i	−0.0644245	−	0.111586i
$663$	−8.37605e9	−	1.45077e10i	−1.11620	−	1.93331i
$664$	−1.61354e9	+	2.79474e9i	−0.213891	+	0.370470i
$665$	−2.10140e9			−0.277098
$666$	−4.50899e9	−	2.94874e9i	−0.591452	−	0.386791i
$667$	1.16464e10			1.51967
$668$	−2.03165e8	+	3.51892e8i	−0.0263712	+	0.0456763i
$669$	−4.72624e9	−	8.18608e9i	−0.610273	−	1.05702i
$670$	1.85962e9	+	3.22096e9i	0.238871	+	0.413736i
$671$	−7.01888e9	−	1.21571e10i	−0.896890	−	1.55346i
$672$	−3.78326e8			−0.0480921
$673$	1.38835e9	+	2.40469e9i	0.175568	+	0.304092i	0.940358	−	0.340187i	$-0.110491\pi$
$673$	1.38835e9	+	2.40469e9i	0.175568	+	0.304092i	−0.764790	+	0.644280i	$0.777157\pi$
$674$	7.36900e9			0.927041
$675$	−1.49479e6	+	2.58906e6i	−0.000187076	+	0.000324025i
$676$	5.95047e9			0.740863
$677$	−6.79466e8			−0.0841603			−0.0420801	−	0.999114i	$-0.513398\pi$
$677$	−6.79466e8			−0.0841603			−0.0420801	+	0.999114i	$0.513398\pi$
$678$	4.81047e9	−	8.33198e9i	0.592766	−	1.02670i
$679$	−1.77371e7	−	3.07216e7i	−0.00217440	−	0.00376617i
$680$	−2.13790e9			−0.260739
$681$	6.60083e9	−	1.14330e10i	0.800910	−	1.38722i
$682$	−2.17468e9	+	3.76666e9i	−0.262513	+	0.454685i
$683$	−7.55881e9	+	1.30922e10i	−0.907781	+	1.57232i	−0.0906398	+	0.995884i	$0.528891\pi$
$683$	−7.55881e9	+	1.30922e10i	−0.907781	+	1.57232i	−0.817141	+	0.576438i	$0.804442\pi$
$684$	4.09274e9	+	7.08884e9i	0.489010	+	0.846991i
$685$	−2.55788e9	−	4.43038e9i	−0.304063	−	0.526652i
$686$	−1.12902e9	+	1.95552e9i	−0.133527	+	0.231275i
$687$	−7.63581e9	+	1.32256e10i	−0.898477	+	1.55621i
$688$	−1.55883e9	+	2.69997e9i	−0.182490	+	0.316082i
$689$	8.16464e9			0.950976
$690$	3.57426e9	+	6.19080e9i	0.414204	+	0.717423i
$691$	3.67767e9	−	6.36992e9i	0.424033	−	0.734447i	−0.572296	−	0.820047i	$-0.693947\pi$
$691$	3.67767e9	−	6.36992e9i	0.424033	−	0.734447i	0.996330	+	0.0855996i	$0.0272806\pi$
$692$	9.44440e8			0.108344
$693$	2.16844e9			0.247503
$694$	−3.28259e9	+	5.68561e9i	−0.372785	+	0.645682i
$695$	−8.15756e9			−0.921750
$696$	−3.00096e9	−	5.19782e9i	−0.337387	−	0.584371i
$697$	−9.91557e9			−1.10918
$698$	2.28628e9	+	3.95995e9i	0.254469	+	0.440753i
$699$	−7.51267e9	−	1.30123e10i	−0.832002	−	1.44107i
$700$	−2.00123e8	−	3.46624e8i	−0.0220523	−	0.0381958i
$701$	5.90179e9	−	1.02222e10i	0.647099	−	1.12081i	−0.336713	−	0.941607i	$-0.609315\pi$
$701$	5.90179e9	−	1.02222e10i	0.647099	−	1.12081i	0.983812	−	0.179201i	$-0.0573513\pi$
$702$	−8.33243e6			−0.000909058
$703$	1.50889e10	+	9.86768e9i	1.63800	+	1.07120i
$704$	−1.48953e9			−0.160896
$705$	−2.87920e9	+	4.98692e9i	−0.309464	+	0.536007i
$706$	3.19256e9	+	5.52967e9i	0.341446	+	0.591402i
$707$	6.28101e8	+	1.08790e9i	0.0668438	+	0.115777i
$708$	−3.85339e8	−	6.67427e8i	−0.0408062	−	0.0706785i
$709$	8.55548e9			0.901535			0.450767	−	0.892641i	$-0.351150\pi$
$709$	8.55548e9			0.901535			0.450767	+	0.892641i	$0.351150\pi$
$710$	−2.24575e9	−	3.88976e9i	−0.235482	−	0.407867i
$711$	3.30553e9			0.344904
$712$	2.81966e8	−	4.88379e8i	0.0292763	−	0.0507081i
$713$	−6.28598e9			−0.649470
$714$	−1.87508e9			−0.192786
$715$	−7.29224e9	+	1.26305e10i	−0.746088	+	1.29226i
$716$	−2.22066e9	−	3.84629e9i	−0.226092	−	0.391604i
$717$	−2.17246e8			−0.0220108
$718$	3.67246e9	−	6.36090e9i	0.370273	−	0.641332i
$719$	5.48147e8	−	9.49419e8i	0.0549979	−	0.0952592i	−0.837216	−	0.546873i	$-0.815818\pi$
$719$	5.48147e8	−	9.49419e8i	0.0549979	−	0.0952592i	0.892214	+	0.451614i	$0.149151\pi$
$720$	9.20728e8	−	1.59475e9i	0.0919321	−	0.159231i
$721$	−1.29751e9	−	2.24735e9i	−0.128925	−	0.223304i
$722$	−1.01205e10	−	1.75292e10i	−1.00074	−	1.73333i
$723$	1.08978e10	−	1.88755e10i	1.07239	−	1.85744i
$724$	3.28790e9	−	5.69481e9i	0.321983	−	0.557691i
$725$	3.17484e9	−	5.49899e9i	0.309413	−	0.535920i
$726$	6.77092e9			0.656703
$727$	−4.04479e9	−	7.00578e9i	−0.390414	−	0.676217i	0.602090	−	0.798428i	$-0.294335\pi$
$727$	−4.04479e9	−	7.00578e9i	−0.390414	−	0.676217i	−0.992504	+	0.122211i	$0.961001\pi$
$728$	5.57774e8	−	9.66092e8i	0.0535794	−	0.0928023i
$729$	−1.04483e10			−0.998845
$730$	−7.02797e9			−0.668652
$731$	−7.72595e9	+	1.33817e10i	−0.731545	+	1.26707i
$732$	−1.04555e10			−0.985273
$733$	−6.38475e9	−	1.10587e10i	−0.598798	−	1.03715i	−0.992999	−	0.118124i	$-0.962312\pi$
$733$	−6.38475e9	−	1.10587e10i	−0.598798	−	1.03715i	0.394201	−	0.919024i	$-0.371021\pi$
$734$	2.00360e9			0.187015
$735$	−5.39331e9	−	9.34148e9i	−0.501013	−	0.867781i
$736$	−1.07638e9	−	1.86435e9i	−0.0995162	−	0.172367i
$737$	6.42156e9	+	1.11225e10i	0.590887	+	1.02345i
$738$	4.27034e9	−	7.39644e9i	0.391079	−	0.677369i
$739$	−1.90123e10			−1.73292			−0.866459	−	0.499247i	$-0.833610\pi$
$739$	−1.90123e10			−1.73292			−0.866459	+	0.499247i	$0.833610\pi$
$740$	2.25238e8	−	4.04966e9i	0.0204329	−	0.367373i
$741$	−4.82861e10			−4.35971
$742$	4.56938e8	−	7.91441e8i	0.0410624	−	0.0711221i
$743$	7.78857e9	+	1.34902e10i	0.696621	+	1.20658i	0.969631	+	0.244572i	$0.0786476\pi$
$743$	7.78857e9	+	1.34902e10i	0.696621	+	1.20658i	−0.273010	+	0.962011i	$0.588019\pi$
$744$	1.61973e9	+	2.80546e9i	0.144191	+	0.249746i
$745$	−1.96340e9	−	3.40071e9i	−0.173965	−	0.301316i
$746$	−1.42786e10			−1.25921
$747$	−6.88825e9	−	1.19308e10i	−0.604626	−	1.04724i
$748$	−7.38249e9			−0.644982
$749$	−2.18910e9	+	3.79163e9i	−0.190361	+	0.329716i
$750$	1.23982e10			1.07311
$751$	6.04137e9			0.520470			0.260235	−	0.965545i	$-0.416200\pi$
$751$	6.04137e9			0.520470			0.260235	+	0.965545i	$0.416200\pi$
$752$	8.67065e8	−	1.50180e9i	0.0743514	−	0.128780i
$753$	−9.83941e9	−	1.70424e10i	−0.839821	−	1.45461i
$754$	1.76975e10			1.50353
$755$	9.17748e8	−	1.58959e9i	0.0776084	−	0.134422i
$756$	−466329.	+	807706.i	−3.92524e−5	+	6.79872e-5i
$757$	1.80052e9	−	3.11859e9i	0.150856	−	0.261290i	−0.780686	−	0.624923i	$-0.785130\pi$
$757$	1.80052e9	−	3.11859e9i	0.150856	−	0.261290i	0.931542	+	0.363633i	$0.118464\pi$
$758$	−1.79757e9	−	3.11347e9i	−0.149914	−	0.259659i
$759$	1.23425e10	+	2.13778e10i	1.02460	+	1.77467i
$760$	−3.08113e9	+	5.33667e9i	−0.254602	+	0.440984i
$761$	−5.92131e9	+	1.02560e10i	−0.487048	+	0.843591i	−0.999889	−	0.0148920i	$-0.995260\pi$
$761$	−5.92131e9	+	1.02560e10i	−0.487048	+	0.843591i	0.512841	+	0.858483i	$0.328593\pi$
$762$	−3.45249e9	+	5.97989e9i	−0.282677	+	0.489611i
$763$	−5.72323e7			−0.00466451
$764$	4.54311e9	+	7.86891e9i	0.368576	+	0.638392i
$765$	4.56336e9	−	7.90397e9i	0.368527	−	0.638308i
$766$	−6.63615e9			−0.533476
$767$	2.27245e9			0.181849
$768$	−5.54711e8	+	9.60787e8i	−0.0441878	+	0.0765355i
$769$	2.27682e10			1.80546			0.902729	−	0.430210i	$-0.141561\pi$
$769$	2.27682e10			1.80546			0.902729	+	0.430210i	$0.141561\pi$
$770$	8.16229e8	+	1.41375e9i	0.0644309	+	0.111598i
$771$	1.15864e10			0.910451
$772$	3.34609e9	+	5.79560e9i	0.261744	+	0.453354i
$773$	1.09428e10	+	1.89535e10i	0.852117	+	1.47591i	0.879294	+	0.476280i	$0.158015\pi$
$773$	1.09428e10	+	1.89535e10i	0.852117	+	1.47591i	−0.0271763	+	0.999631i	$0.508652\pi$
$774$	−6.65467e9	−	1.15262e10i	−0.515861	−	0.893498i
$775$	−1.71358e9	+	2.96801e9i	−0.132236	+	0.229039i
$776$	−1.04027e8			−0.00799149
$777$	1.97549e8	−	3.55182e9i	0.0151078	−	0.271630i
$778$	−1.01668e10			−0.774026
$779$	−1.42903e10	+	2.47515e10i	−1.08308	+	1.87594i
$780$	5.43136e9	+	9.40739e9i	0.409805	+	0.709803i
$781$	−7.75494e9	−	1.34319e10i	−0.582505	−	1.00893i
$782$	−5.33482e9	−	9.24018e9i	−0.398930	−	0.690967i
$783$	−1.47961e7			−0.00110149
$784$	1.62418e9	+	2.81317e9i	0.120373	+	0.208492i
$785$	−1.57341e9			−0.116091
$786$	2.82387e9	−	4.89109e9i	0.207427	−	0.359274i
$787$	1.03415e10			0.756263			0.378131	−	0.925752i	$-0.376567\pi$
$787$	1.03415e10			0.756263			0.378131	+	0.925752i	$0.376567\pi$
$788$	−8.79515e9			−0.640326
$789$	2.79377e9	−	4.83895e9i	0.202498	−	0.350737i
$790$	1.24425e9	+	2.15510e9i	0.0897867	+	0.155515i
$791$	3.17534e9			0.228125
$792$	3.17942e9	−	5.50691e9i	0.227410	−	0.393885i
$793$	1.54148e10	−	2.66992e10i	1.09769	−	1.90126i
$794$	3.80977e9	−	6.59872e9i	0.270102	−	0.467830i
$795$	4.44947e9	+	7.70670e9i	0.314068	+	0.543981i
$796$	2.63629e9	+	4.56618e9i	0.185267	+	0.320891i
$797$	−7.23480e9	+	1.25310e10i	−0.506201	+	0.876765i	0.493774	+	0.869590i	$0.335617\pi$
$797$	−7.23480e9	+	1.25310e10i	−0.506201	+	0.876765i	−0.999974	+	0.00717472i	$0.997716\pi$
$798$	−2.70236e9	+	4.68062e9i	−0.188249	+	0.326057i
$799$	4.29739e9	−	7.44331e9i	0.298052	−	0.516241i
$800$	−1.17370e9			−0.0810482
$801$	1.20372e9	+	2.08490e9i	0.0827582	+	0.143341i
$802$	2.91782e9	−	5.05381e9i	0.199732	−	0.345946i
$803$	−2.42687e10			−1.65402
$804$	9.56573e9			0.649115
$805$	−1.17967e9	+	2.04324e9i	−0.0797028	+	0.138049i
$806$	−9.55202e9			−0.642573
$807$	−7.06521e9	−	1.22373e10i	−0.473225	−	0.819649i
$808$	3.68375e9			0.245669
$809$	−8.54214e9	−	1.47954e10i	−0.567214	−	0.982443i	−0.996840	−	0.0794360i	$-0.974688\pi$
$809$	−8.54214e9	−	1.47954e10i	−0.567214	−	0.982443i	0.429626	−	0.903007i	$-0.358645\pi$
$810$	−3.93741e9	−	6.81980e9i	−0.260324	−	0.450894i
$811$	6.49416e9	+	1.12482e10i	0.427514	+	0.740476i	0.996652	−	0.0817667i	$-0.0260562\pi$
$811$	6.49416e9	+	1.12482e10i	0.427514	+	0.740476i	−0.569138	+	0.822242i	$0.692723\pi$
$812$	9.90452e8	−	1.71551e9i	0.0649213	−	0.112447i
$813$	2.25582e10			1.47227
$814$	7.77781e8	−	1.39841e10i	0.0505443	−	0.908760i
$815$	1.21565e10			0.786604
$816$	−2.74929e9	+	4.76191e9i	−0.177135	+	0.306807i
$817$	2.22692e10	+	3.85714e10i	1.42866	+	2.47450i
$818$	4.39790e9	+	7.61738e9i	0.280937	+	0.486597i
$819$	2.38115e9	+	4.12427e9i	0.151458	+	0.262333i
$820$	6.42965e9			0.407229
$821$	−7.95300e9	−	1.37750e10i	−0.501568	−	0.868741i	−0.999998	−	0.00181136i	$-0.999423\pi$
$821$	−7.95300e9	−	1.37750e10i	−0.501568	−	0.868741i	0.498430	−	0.866930i	$-0.333910\pi$
$822$	−1.31575e10			−0.826271
$823$	1.19682e10	−	2.07296e10i	0.748395	−	1.29626i	−0.200197	−	0.979756i	$-0.564158\pi$
$823$	1.19682e10	−	2.07296e10i	0.748395	−	1.29626i	0.948592	−	0.316503i	$-0.102509\pi$
$824$	−7.60976e9			−0.473833
$825$	1.34584e10			0.834460
$826$	1.27179e8	−	2.20281e8i	0.00785210	−	0.0136002i
$827$	−2.37341e9	−	4.11087e9i	−0.145916	−	0.252735i	0.783798	−	0.621016i	$-0.213280\pi$
$827$	−2.37341e9	−	4.11087e9i	−0.145916	−	0.252735i	−0.929714	+	0.368281i	$0.879946\pi$
$828$	9.19019e9			0.562624
$829$	−1.15292e10	+	1.99691e10i	−0.702840	+	1.21736i	0.264625	+	0.964351i	$0.414752\pi$
$829$	−1.15292e10	+	1.99691e10i	−0.702840	+	1.21736i	−0.967465	+	0.253004i	$0.918581\pi$
$830$	5.18566e9	−	8.98182e9i	0.314797	−	0.545244i
$831$	1.65451e9	−	2.86569e9i	0.100015	−	0.173231i
$832$	−1.63564e9	−	2.83302e9i	−0.0984593	−	0.170537i
$833$	8.04987e9	+	1.39428e10i	0.482538	+	0.835780i
$834$	−1.04904e10	+	1.81700e10i	−0.626199	+	1.08461i
$835$	6.52937e8	−	1.13092e9i	0.0388123	−	0.0672248i
$836$	−1.06396e10	+	1.84283e10i	−0.629801	+	1.09085i
$837$	7.98600e6			0.000470750
$838$	4.02389e8	+	6.96958e8i	0.0236207	+	0.0409122i
$839$	3.10277e9	−	5.37416e9i	0.181377	−	0.314155i	−0.760972	−	0.648784i	$-0.775278\pi$
$839$	3.10277e9	−	5.37416e9i	0.181377	−	0.314155i	0.942350	+	0.334629i	$0.108611\pi$
$840$	1.21588e9			0.0707802
$841$	1.41760e10			0.821805
$842$	1.00328e9	−	1.73773e9i	0.0579202	−	0.100321i
$843$	2.52133e10			1.44955
$844$	6.25699e9	+	1.08374e10i	0.358234	+	0.620480i
$845$	−1.91238e10			−1.09038
$846$	3.70152e9	+	6.41121e9i	0.210176	+	0.364036i
$847$	1.11735e9	+	1.93531e9i	0.0631827	+	0.109436i
$848$	−1.33995e9	−	2.32086e9i	−0.0754575	−	0.130696i
$849$	7.74935e9	−	1.34223e10i	0.434598	−	0.752747i
$850$	−5.81717e9			−0.324897
$851$	1.80650e10	−	9.13186e9i	1.00481	−	0.507932i
$852$	−1.15520e10			−0.639907
$853$	−9.63221e9	+	1.66835e10i	−0.531379	+	0.920375i	0.467950	+	0.883755i	$0.344993\pi$
$853$	−9.63221e9	+	1.66835e10i	−0.531379	+	0.920375i	−0.999329	+	0.0366204i	$0.988341\pi$
$854$	−1.72539e9	−	2.98847e9i	−0.0947950	−	0.164190i
$855$	−1.31534e10	−	2.27823e10i	−0.719708	−	1.24657i
$856$	6.41942e9	+	1.11188e10i	0.349814	+	0.605896i
$857$	−5.42608e9			−0.294479			−0.147239	−	0.989101i	$-0.547039\pi$
$857$	−5.42608e9			−0.294479			−0.147239	+	0.989101i	$0.547039\pi$
$858$	1.87553e10	+	3.24852e10i	1.01372	+	1.75582i
$859$	−4.57327e9			−0.246179			−0.123089	−	0.992396i	$-0.539280\pi$
$859$	−4.57327e9			−0.246179			−0.123089	+	0.992396i	$0.539280\pi$
$860$	5.00981e9	−	8.67725e9i	0.268582	−	0.465198i
$861$	5.63924e9			0.301099
$862$	−8.32225e9			−0.442553
$863$	2.71067e9	−	4.69503e9i	0.143562	−	0.248657i	−0.785274	−	0.619149i	$-0.787478\pi$
$863$	2.71067e9	−	4.69503e9i	0.143562	−	0.248657i	0.928836	+	0.370492i	$0.120811\pi$
$864$	1.36749e6	+	2.36856e6i	7.21315e−5	+	0.000124935i
$865$	−3.03527e9			−0.159456
$866$	−1.11573e10	+	1.93250e10i	−0.583776	+	1.01113i
$867$	−5.90115e7	+	1.02211e8i	−0.00307518	+	0.00532636i
$868$	−5.34584e8	+	9.25926e8i	−0.0277458	+	0.0480571i
$869$	4.29658e9	+	7.44189e9i	0.222103	+	0.384693i
$870$	9.64459e9	+	1.67049e10i	0.496554	+	0.860056i
$871$	−1.41030e10	+	2.44270e10i	−0.723180	+	1.25258i
$872$	−8.39155e7	+	1.45346e8i	−0.00428582	+	0.00742327i
$873$	2.22046e8	−	3.84594e8i	0.0112952	−	0.0195638i
$874$	−3.07541e10			−1.55816
$875$	2.04598e9	+	3.54375e9i	0.103246	+	0.178828i
$876$	−9.03782e9	+	1.56540e10i	−0.454254	+	0.786792i
$877$	2.34576e10			1.17431			0.587157	−	0.809473i	$-0.300247\pi$
$877$	2.34576e10			1.17431			0.587157	+	0.809473i	$0.300247\pi$
$878$	1.58279e10			0.789212
$879$	1.66813e10	−	2.88929e10i	0.828455	−	1.43493i
$880$	4.78710e9			0.236801
$881$	−6.52963e9	−	1.13096e10i	−0.321716	−	0.557228i	0.659126	−	0.752032i	$-0.270926\pi$
$881$	−6.52963e9	−	1.13096e10i	−0.321716	−	0.557228i	−0.980842	+	0.194804i	$0.937593\pi$
$882$	−1.38673e10			−0.680539
$883$	4.44035e9	+	7.69091e9i	0.217048	+	0.375937i	0.953904	−	0.300112i	$-0.0970240\pi$
$883$	4.44035e9	+	7.69091e9i	0.217048	+	0.375937i	−0.736857	+	0.676049i	$0.763691\pi$
$884$	−8.10667e9	−	1.40412e10i	−0.394693	−	0.683628i
$885$	1.23842e9	+	2.14500e9i	0.0600572	+	0.104022i
$886$	1.45406e8	−	2.51850e8i	0.00702366	−	0.0121653i
$887$	−3.97795e9			−0.191393			−0.0956966	−	0.995411i	$-0.530508\pi$
$887$	−3.97795e9			−0.191393			−0.0956966	+	0.995411i	$0.530508\pi$
$888$	−8.73048e9	−	5.70946e9i	−0.418401	−	0.273621i
$889$	−2.27895e9			−0.108788
$890$	−9.06191e8	+	1.56957e9i	−0.0430878	+	0.0746303i
$891$	−1.35965e10	−	2.35498e10i	−0.643955	−	1.11536i
$892$	−4.57424e9	−	7.92281e9i	−0.215795	−	0.373768i
$893$	−1.23868e10	−	2.14545e10i	−0.582074	−	1.00818i
$894$	−1.00995e10			−0.472738
$895$	7.13682e9	+	1.23613e10i	0.332755	+	0.576348i
$896$	−3.66159e8			−0.0170056
$897$	−2.71064e10	+	4.69496e10i	−1.25400	+	2.17199i
$898$	−2.29089e9			−0.105569
$899$	−1.69617e10			−0.778595
$900$	2.50528e9	−	4.33927e9i	0.114553	−	0.198412i
$901$	−6.64113e9	−	1.15028e10i	−0.302486	−	0.523921i
$902$	2.22026e10			1.00735
$903$	4.39394e9	−	7.61053e9i	0.198585	−	0.343960i
$904$	4.65576e9	−	8.06402e9i	0.209605	−	0.363046i
$905$	−1.05668e10	+	1.83022e10i	−0.473883	+	0.820790i
$906$	−2.36041e9	−	4.08834e9i	−0.105448	−	0.182641i
$907$	3.17776e9	+	5.50404e9i	0.141415	+	0.244938i	0.928030	−	0.372506i	$-0.121501\pi$
$907$	3.17776e9	+	5.50404e9i	0.141415	+	0.244938i	−0.786615	+	0.617444i	$0.788168\pi$
$908$	6.38855e9	−	1.10653e10i	0.283205	−	0.490526i
$909$	−7.86299e9	+	1.36191e10i	−0.347228	+	0.601416i
$910$	−1.79259e9	+	3.10486e9i	−0.0788563	+	0.136583i
$911$	1.98980e10			0.871956			0.435978	−	0.899957i	$-0.356403\pi$
$911$	1.98980e10			0.871956			0.435978	+	0.899957i	$0.356403\pi$
$912$	7.92452e9	+	1.37257e10i	0.345932	+	0.599172i
$913$	1.79069e10	−	3.10156e10i	0.778704	−	1.34875i
$914$	−6.54987e9			−0.283740
$915$	3.36023e10			1.45009
$916$	−7.39024e9	+	1.28003e10i	−0.317705	+	0.550282i
$917$	1.86401e9			0.0798279
$918$	6.77761e6	+	1.17392e7i	0.000289153	+	0.000500827i
$919$	3.28479e10			1.39606			0.698030	−	0.716069i	$-0.254060\pi$
$919$	3.28479e10			1.39606			0.698030	+	0.716069i	$0.254060\pi$
$920$	3.45931e9	+	5.99170e9i	0.146464	+	0.253684i
$921$	6.29222e9	+	1.08984e10i	0.265396	+	0.459680i
$922$	−2.81322e8	−	4.87264e8i	−0.0118208	−	0.0204742i
$923$	1.70313e10	−	2.94991e10i	0.712921	−	1.23482i
$924$	4.19861e9			0.175087
$925$	6.12868e8	−	1.10190e10i	0.0254607	−	0.457770i
$926$	7.66456e9			0.317211
$927$	1.62431e10	−	2.81339e10i	0.669715	−	1.15998i
$928$	−2.90445e9	−	5.03065e9i	−0.119302	−	0.206636i
$929$	−7.58708e8	−	1.31412e9i	−0.0310470	−	0.0537750i	0.850084	−	0.526646i	$-0.176551\pi$
$929$	−7.58708e8	−	1.31412e9i	−0.0310470	−	0.0537750i	−0.881131	+	0.472871i	$0.843217\pi$
$930$	−5.20555e9	−	9.01627e9i	−0.212215	−	0.367567i
$931$	4.64057e10			1.88472
$932$	−7.27106e9	−	1.25938e10i	−0.294199	−	0.509568i
$933$	−3.99905e10			−1.61202
$934$	4.48993e9	−	7.77678e9i	0.180312	−	0.312310i
$935$	2.37261e10			0.949260
$936$	1.39652e10			0.556649
$937$	−1.48859e10	+	2.57831e10i	−0.591133	+	1.02387i	0.402947	+	0.915223i	$0.367986\pi$
$937$	−1.48859e10	+	2.57831e10i	−0.591133	+	1.02387i	−0.994080	+	0.108650i	$0.965347\pi$
$938$	1.57856e9	+	2.73414e9i	0.0624527	+	0.108171i
$939$	−3.14195e9			−0.123842
$940$	−2.78660e9	+	4.82653e9i	−0.109428	+	0.189534i
$941$	2.21399e9	−	3.83474e9i	0.0866187	−	0.150028i	−0.819461	−	0.573135i	$-0.805727\pi$
$941$	2.21399e9	−	3.83474e9i	0.0866187	−	0.150028i	0.906080	+	0.423107i	$0.139060\pi$
$942$	−2.02336e9	+	3.50457e9i	−0.0788671	+	0.136602i
$943$	1.60443e10	+	2.77895e10i	0.623060	+	1.07917i
$944$	−3.72946e8	−	6.45962e8i	−0.0144293	−	0.0249922i
$945$	1.49870e6	−	2.59583e6i	5.77703e−5	−	0.000100061i
$946$	1.72997e10	−	2.99639e10i	0.664383	−	1.15075i
$947$	−1.18430e8	+	2.05127e8i	−0.00453146	+	0.00784871i	−0.868282	−	0.496071i	$-0.834776\pi$
$947$	−1.18430e8	+	2.05127e8i	−0.00453146	+	0.00784871i	0.863751	+	0.503919i	$0.168109\pi$
$948$	6.40030e9			0.243989
$949$	−2.66493e10	−	4.61579e10i	−1.01217	−	1.75313i
$950$	−8.38368e9	+	1.45210e10i	−0.317250	+	0.549494i
$951$	−7.26977e10			−2.74087
$952$	−1.81478e9			−0.0681701
$953$	1.67505e9	−	2.90127e9i	0.0626906	−	0.108583i	−0.832977	−	0.553308i	$-0.813365\pi$
$953$	1.67505e9	−	2.90127e9i	0.0626906	−	0.108583i	0.895667	+	0.444725i	$0.146699\pi$
$954$	1.14405e10			0.426606
$955$	−1.46008e10	−	2.52893e10i	−0.542457	−	0.939563i
$956$	−2.10260e8			−0.00778311
$957$	3.33043e10	+	5.76847e10i	1.22831	+	2.12750i
$958$	−1.00320e10	−	1.73760e10i	−0.368646	−	0.638514i
$959$	−2.17128e9	−	3.76078e9i	−0.0794972	−	0.137693i
$960$	1.78275e9	−	3.08781e9i	0.0650340	−	0.112642i
$961$	−1.83577e10			−0.667248
$962$	2.74512e10	−	1.38765e10i	0.994142	−	0.502538i
$963$	−5.48093e10			−1.97771
$964$	1.05473e10	−	1.82684e10i	0.379202	−	0.656798i
$965$	−1.07538e10	−	1.86261e10i	−0.385226	−	0.667230i
$966$	3.03405e9	+	5.25513e9i	0.108294	+	0.187570i
$967$	−2.05488e10	−	3.55915e10i	−0.730790	−	1.26577i	−0.956546	−	0.291582i	$-0.905818\pi$
$967$	−2.05488e10	−	3.55915e10i	−0.730790	−	1.26577i	0.225755	−	0.974184i	$-0.427515\pi$
$968$	6.55316e9			0.232213
$969$	3.92760e10	+	6.80280e10i	1.38674	+	2.40190i
$970$	3.34324e8			0.0117616
$971$	−2.07609e10	+	3.59590e10i	−0.727745	+	1.26049i	0.230089	+	0.973170i	$0.426098\pi$
$971$	−2.07609e10	+	3.59590e10i	−0.727745	+	1.26049i	−0.957834	+	0.287322i	$0.907235\pi$
$972$	−2.02420e10			−0.707005
$973$	−6.92463e9			−0.240991
$974$	7.40069e9	−	1.28184e10i	0.256635	−	0.444505i
$975$	1.47786e10	+	2.55973e10i	0.510643	+	0.884460i
$976$	−1.01193e10			−0.348397
$977$	2.79759e10	−	4.84557e10i	0.959739	−	1.66232i	0.236609	−	0.971605i	$-0.423964\pi$
$977$	2.79759e10	−	4.84557e10i	0.959739	−	1.66232i	0.723130	−	0.690712i	$-0.242703\pi$
$978$	1.56330e10	−	2.70771e10i	0.534386	−	0.925584i
$979$	−3.12922e9	+	5.41997e9i	−0.106585	+	0.184611i
$980$	−5.21985e9	−	9.04105e9i	−0.177161	−	0.306851i
$981$	−3.58237e8	−	6.20484e8i	−0.0121151	−	0.0209840i
$982$	−5.79535e9	+	1.00378e10i	−0.195294	+	0.338259i
$983$	−2.41878e10	+	4.18945e10i	−0.812194	+	1.40676i	0.0991319	+	0.995074i	$0.468393\pi$
$983$	−2.41878e10	+	4.18945e10i	−0.812194	+	1.40676i	−0.911326	+	0.411686i	$0.864940\pi$
$984$	8.26839e9	−	1.43213e10i	0.276655	−	0.479180i
$985$	2.82661e10			0.942409
$986$	−1.43952e10	−	2.49332e10i	−0.478243	−	0.828341i
$987$	−2.44404e9	+	4.23320e9i	−0.0809092	+	0.140139i
$988$	−4.67331e10			−1.54161
$989$	5.00051e10			1.64372
$990$	−1.02181e10	+	1.76983e10i	−0.334693	+	0.579706i
$991$	−3.30034e9			−0.107721			−0.0538606	−	0.998548i	$-0.517153\pi$
$991$	−3.30034e9			−0.107721			−0.0538606	+	0.998548i	$0.517153\pi$
$992$	1.56764e9	+	2.71523e9i	0.0509865	+	0.0883113i
$993$	7.95006e9			0.257661
$994$	−1.90633e9	−	3.30186e9i	−0.0615667	−	0.106637i
$995$	−8.47259e9	−	1.46749e10i	−0.272669	−	0.472276i
$996$	−1.33373e10	−	2.31009e10i	−0.427720	−	0.740833i
$997$	1.15607e10	−	2.00238e10i	0.369447	−	0.639901i	−0.620032	−	0.784576i	$-0.712880\pi$
$997$	1.15607e10	−	2.00238e10i	0.369447	−	0.639901i	0.989479	+	0.144675i	$0.0462138\pi$
$998$	2.98501e10			0.950581
$999$	−2.29507e7	+	1.16015e7i	−0.000728310	+	0.000368160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.c.a.47.2	✓	22
37.26	even	3	inner	74.8.c.a.63.2	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.c.a.47.2	✓	22	1.1	even	1	trivial
74.8.c.a.63.2	yes	22	37.26	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-33.0633 - 57.2674i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(102.843 + 178.129i) q^{5} +529.013 q^{6} +(87.2990 + 151.206i) q^{7} +512.000 q^{8} +(-1092.87 + 1892.90i) q^{9} -1645.48 q^{10} -5682.10 q^{11} +(-2116.05 + 3665.11i) q^{12} +(-6239.48 - 10807.1i) q^{13} -1396.78 q^{14} +(6800.64 - 11779.1i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10150.4 + 17581.0i) q^{17} +(-8742.95 - 15143.2i) q^{18} +(29257.4 + 50675.4i) q^{19} +(6581.93 - 11400.2i) q^{20} +(5772.80 - 9998.77i) q^{21} +(22728.4 - 39366.8i) q^{22} +65697.1 q^{23} +(-16928.4 - 29320.9i) q^{24} +(17909.3 - 31019.8i) q^{25} +99831.7 q^{26} -83.4648 q^{27} +(5587.14 - 9677.21i) q^{28} +177274. q^{29} +(54405.1 + 94232.4i) q^{30} -95681.2 q^{31} +(-16384.0 - 28377.9i) q^{32} +(187869. + 325399. i) q^{33} +(-81203.3 - 140648. i) q^{34} +(-17956.1 + 31100.9i) q^{35} +139887. q^{36} +(274975. - 138999. i) q^{37} -468119. q^{38} +(-412596. + 714638. i) q^{39} +(52655.4 + 91201.9i) q^{40} +(244216. + 422995. i) q^{41} +(46182.4 + 79990.2i) q^{42} +761147. q^{43} +(181827. + 314934. i) q^{44} -449574. q^{45} +(-262788. + 455163. i) q^{46} -423371. q^{47} +270855. q^{48} +(396529. - 686809. i) q^{49} +(143274. + 248158. i) q^{50} +1.34243e6 q^{51} +(-399327. + 691655. i) q^{52} +(-327136. + 566616. i) q^{53} +(333.859 - 578.261i) q^{54} +(-584363. - 1.01215e6i) q^{55} +(44697.1 + 77417.7i) q^{56} +(1.93470e6 - 3.35099e6i) q^{57} +(-709094. + 1.22819e6i) q^{58} +(-91051.3 + 157706. i) q^{59} -870482. q^{60} +(1.23526e6 + 2.13954e6i) q^{61} +(382725. - 662898. i) q^{62} -381626. q^{63} +262144. q^{64} +(1.28337e6 - 2.22286e6i) q^{65} -3.00591e6 q^{66} +(-1.13014e6 - 1.95746e6i) q^{67} +1.29925e6 q^{68} +(-2.17217e6 - 3.76230e6i) q^{69} +(-143649. - 248807. i) q^{70} +(1.36480e6 + 2.36390e6i) q^{71} +(-559549. + 969167. i) q^{72} +4.27107e6 q^{73} +(-136883. + 2.46108e6i) q^{74} -2.36856e6 q^{75} +(1.87248e6 - 3.24322e6i) q^{76} +(-496042. - 859170. i) q^{77} +(-3.30077e6 - 5.71710e6i) q^{78} +(-756160. - 1.30971e6i) q^{79} -842487. q^{80} +(2.39286e6 + 4.14456e6i) q^{81} -3.90746e6 q^{82} +(-3.15145e6 + 5.45848e6i) q^{83} -738918. q^{84} -4.17558e6 q^{85} +(-3.04459e6 + 5.27338e6i) q^{86} +(-5.86126e6 - 1.01520e7i) q^{87} -2.90924e6 q^{88} +(550715. - 953866. i) q^{89} +(1.79830e6 - 3.11474e6i) q^{90} +(1.08940e6 - 1.88690e6i) q^{91} +(-2.10231e6 - 3.64130e6i) q^{92} +(3.16354e6 + 5.47941e6i) q^{93} +(1.69349e6 - 2.93320e6i) q^{94} +(-6.01782e6 + 1.04232e7i) q^{95} +(-1.08342e6 + 1.87654e6i) q^{96} -203177. q^{97} +(3.17223e6 + 5.49447e6i) q^{98} +(6.20980e6 - 1.07557e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 88 q^{2} + 40 q^{3} - 704 q^{4} + 475 q^{5} - 640 q^{6} - 588 q^{7} + 11264 q^{8} - 8369 q^{9} - 7600 q^{10} - 4904 q^{11} + 2560 q^{12} - 2612 q^{13} + 9408 q^{14} - 3688 q^{15} - 45056 q^{16} + 24651 q^{17}+ \cdots + 13715284 q^{99}+O(q^{100}) \) 22 * q - 88 * q^2 + 40 * q^3 - 704 * q^4 + 475 * q^5 - 640 * q^6 - 588 * q^7 + 11264 * q^8 - 8369 * q^9 - 7600 * q^10 - 4904 * q^11 + 2560 * q^12 - 2612 * q^13 + 9408 * q^14 - 3688 * q^15 - 45056 * q^16 + 24651 * q^17 - 66952 * q^18 + 82536 * q^19 + 30400 * q^20 + 50810 * q^21 + 19616 * q^22 + 118832 * q^23 + 20480 * q^24 - 256572 * q^25 + 41792 * q^26 - 363800 * q^27 - 37632 * q^28 - 372170 * q^29 - 29504 * q^30 + 42808 * q^31 - 360448 * q^32 - 170612 * q^33 + 197208 * q^34 + 347316 * q^35 + 1071232 * q^36 - 605757 * q^37 - 1320576 * q^38 + 928324 * q^39 + 243200 * q^40 - 171689 * q^41 + 406480 * q^42 - 794528 * q^43 + 156928 * q^44 - 2199730 * q^45 - 475328 * q^46 - 517424 * q^47 - 327680 * q^48 - 1990061 * q^49 - 2052576 * q^50 + 1046736 * q^51 - 167168 * q^52 - 2880196 * q^53 + 1455200 * q^54 + 120328 * q^55 - 301056 * q^56 - 1881606 * q^57 + 1488680 * q^58 + 2657756 * q^59 + 472064 * q^60 + 1449979 * q^61 - 171232 * q^62 + 7031672 * q^63 + 5767168 * q^64 + 3463904 * q^65 + 2729792 * q^66 + 1415120 * q^67 - 3155328 * q^68 - 7425740 * q^69 + 2778528 * q^70 + 718320 * q^71 - 4284928 * q^72 + 21142228 * q^73 + 2481504 * q^74 - 38086392 * q^75 + 5282304 * q^76 + 3057932 * q^77 + 7426592 * q^78 + 8331416 * q^79 - 3891200 * q^80 + 8804005 * q^81 + 2747024 * q^82 - 1747036 * q^83 - 6503680 * q^84 - 4638522 * q^85 + 3178112 * q^86 + 3200432 * q^87 - 2510848 * q^88 + 16909895 * q^89 + 8798920 * q^90 + 13361368 * q^91 - 3802624 * q^92 + 15700724 * q^93 + 2069696 * q^94 - 32197184 * q^95 + 1310720 * q^96 - 72528842 * q^97 - 15920488 * q^98 + 13715284 * q^99

Introduction

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