LMFDB - Embedded newform 16.8.e.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,8,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, 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:	$4.99816040775$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	16.5
Dual form			16.8.e.a.13.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3129 + 0.135147i) q^{2} +(26.1364 - 26.1364i) q^{3} +(127.963 + 3.05781i) q^{4} +(-31.6175 - 31.6175i) q^{5} +(299.211 - 292.146i) q^{6} -444.381i q^{7} +(1447.22 + 51.8865i) q^{8} +820.775i q^{9} +O(q^{10})$	\(q+(11.3129 + 0.135147i) q^{2} +(26.1364 - 26.1364i) q^{3} +(127.963 + 3.05781i) q^{4} +(-31.6175 - 31.6175i) q^{5} +(299.211 - 292.146i) q^{6} -444.381i q^{7} +(1447.22 + 51.8865i) q^{8} +820.775i q^{9} +(-353.412 - 361.958i) q^{10} +(472.948 + 472.948i) q^{11} +(3424.43 - 3264.59i) q^{12} +(-2745.87 + 2745.87i) q^{13} +(60.0567 - 5027.24i) q^{14} -1652.73 q^{15} +(16365.3 + 782.575i) q^{16} -27961.3 q^{17} +(-110.925 + 9285.35i) q^{18} +(-35750.5 + 35750.5i) q^{19} +(-3949.20 - 4142.56i) q^{20} +(-11614.5 - 11614.5i) q^{21} +(5286.49 + 5414.33i) q^{22} +18979.1i q^{23} +(39181.4 - 36469.1i) q^{24} -76125.7i q^{25} +(-31434.8 + 30692.6i) q^{26} +(78612.5 + 78612.5i) q^{27} +(1358.83 - 56864.5i) q^{28} +(101443. - 101443. i) q^{29} +(-18697.2 - 223.362i) q^{30} +212249. q^{31} +(185033. + 11064.9i) q^{32} +24722.3 q^{33} +(-316324. - 3778.89i) q^{34} +(-14050.2 + 14050.2i) q^{35} +(-2509.77 + 105029. i) q^{36} +(-306569. - 306569. i) q^{37} +(-409274. + 399611. i) q^{38} +143534. i q^{39} +(-44117.1 - 47398.1i) q^{40} +152195. i q^{41} +(-129824. - 132964. i) q^{42} +(-3511.39 - 3511.39i) q^{43} +(59073.8 + 61966.2i) q^{44} +(25950.8 - 25950.8i) q^{45} +(-2564.96 + 214708. i) q^{46} +530864. q^{47} +(448184. - 407277. i) q^{48} +626069. q^{49} +(10288.2 - 861202. i) q^{50} +(-730809. + 730809. i) q^{51} +(-359767. + 342974. i) q^{52} +(-1.04981e6 - 1.04981e6i) q^{53} +(878711. + 899959. i) q^{54} -29906.8i q^{55} +(23057.4 - 643119. i) q^{56} +1.86878e6i q^{57} +(1.16133e6 - 1.13391e6i) q^{58} +(-1.13322e6 - 1.13322e6i) q^{59} +(-211490. - 5053.75i) q^{60} +(195148. - 195148. i) q^{61} +(2.40115e6 + 28684.8i) q^{62} +364737. q^{63} +(2.09177e6 + 150183. i) q^{64} +173635. q^{65} +(279681. + 3341.15i) q^{66} +(-1.52689e6 + 1.52689e6i) q^{67} +(-3.57803e6 - 85500.3i) q^{68} +(496045. + 496045. i) q^{69} +(-160847. + 157050. i) q^{70} -4.95086e6i q^{71} +(-42587.2 + 1.18785e6i) q^{72} +5.65272e6i q^{73} +(-3.42676e6 - 3.50962e6i) q^{74} +(-1.98965e6 - 1.98965e6i) q^{75} +(-4.68408e6 + 4.46545e6i) q^{76} +(210169. - 210169. i) q^{77} +(-19398.2 + 1.62379e6i) q^{78} +5.88689e6 q^{79} +(-492686. - 542172. i) q^{80} +2.31426e6 q^{81} +(-20568.7 + 1.72177e6i) q^{82} +(-1.38794e6 + 1.38794e6i) q^{83} +(-1.45072e6 - 1.52175e6i) q^{84} +(884066. + 884066. i) q^{85} +(-39249.5 - 40198.6i) q^{86} -5.30273e6i q^{87} +(659922. + 709001. i) q^{88} -2.76039e6i q^{89} +(297086. - 290072. i) q^{90} +(1.22021e6 + 1.22021e6i) q^{91} +(-58034.4 + 2.42863e6i) q^{92} +(5.54742e6 - 5.54742e6i) q^{93} +(6.00561e6 + 71744.6i) q^{94} +2.26068e6 q^{95} +(5.12530e6 - 4.54691e6i) q^{96} +4.24399e6 q^{97} +(7.08265e6 + 84611.2i) q^{98} +(-388184. + 388184. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) $ 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	11.3129	+	0.135147i	0.999929	+	0.0119454i
$2$	11.3129	+	0.135147i	0.999929	+	0.0119454i
$3$	26.1364	−	26.1364i	0.558884	−	0.558884i	−0.370106	−	0.928990i	$-0.620679\pi$
$3$	26.1364	−	26.1364i	0.558884	−	0.558884i	0.928990	+	0.370106i	$0.120679\pi$
$4$	127.963	+	3.05781i	0.999715	+	0.0238891i
$5$	−31.6175	−	31.6175i	−0.113118	−	0.113118i	0.648282	−	0.761400i	$-0.275488\pi$
$5$	−31.6175	−	31.6175i	−0.113118	−	0.113118i	−0.761400	+	0.648282i	$0.775488\pi$
$6$	299.211	−	292.146i	0.565520	−	0.552168i
$7$		−	444.381i		−	0.489680i	−0.969563	−	0.244840i	$-0.921265\pi$
$7$		−	444.381i		−	0.489680i	0.969563	−	0.244840i	$-0.0787354\pi$
$8$	1447.22	+	51.8865i	0.999358	+	0.0358294i
$9$			820.775i			0.375297i
$10$	−353.412	−	361.958i	−0.111759	−	0.114461i
$11$	472.948	+	472.948i	0.107137	+	0.107137i	0.758643	−	0.651506i	$-0.225863\pi$
$11$	472.948	+	472.948i	0.107137	+	0.107137i	−0.651506	+	0.758643i	$0.725863\pi$
$12$	3424.43	−	3264.59i	0.572076	−	0.545373i
$13$	−2745.87	+	2745.87i	−0.346639	+	0.346639i	−0.858856	−	0.512217i	$-0.828824\pi$
$13$	−2745.87	+	2745.87i	−0.346639	+	0.346639i	0.512217	+	0.858856i	$0.328824\pi$
$14$	60.0567	−	5027.24i	0.00584943	−	0.489645i
$15$	−1652.73			−0.126440
$16$	16365.3	+	782.575i	0.998859	+	0.0477646i
$17$	−27961.3			−1.38034			−0.690170	−	0.723647i	$-0.742464\pi$
$17$	−27961.3			−1.38034			−0.690170	+	0.723647i	$0.742464\pi$
$18$	−110.925	+	9285.35i	−0.00448308	+	0.375271i
$19$	−35750.5	+	35750.5i	−1.19576	+	1.19576i	−0.220340	+	0.975423i	$0.570717\pi$
$19$	−35750.5	+	35750.5i	−1.19576	+	1.19576i	−0.975423	+	0.220340i	$0.929283\pi$
$20$	−3949.20	−	4142.56i	−0.110384	−	0.115788i
$21$	−11614.5	−	11614.5i	−0.273674	−	0.273674i
$22$	5286.49	+	5414.33i	0.105849	+	0.108409i
$23$			18979.1i			0.325258i	0.986687	+	0.162629i	$0.0519973\pi$
$23$			18979.1i			0.325258i	−0.986687	+	0.162629i	$0.948003\pi$
$24$	39181.4	−	36469.1i	0.578550	−	0.538501i
$25$		−	76125.7i		−	0.974409i
$26$	−31434.8	+	30692.6i	−0.350755	+	0.342474i
$27$	78612.5	+	78612.5i	0.768632	+	0.768632i
$28$	1358.83	−	56864.5i	0.0116980	−	0.489540i
$29$	101443.	−	101443.i	0.772380	−	0.772380i	−0.206142	−	0.978522i	$-0.566091\pi$
$29$	101443.	−	101443.i	0.772380	−	0.772380i	0.978522	+	0.206142i	$0.0660910\pi$
$30$	−18697.2	−	223.362i	−0.126431	−	0.00151038i
$31$	212249.			1.27962			0.639808	−	0.768535i	$-0.279014\pi$
$31$	212249.			1.27962			0.639808	+	0.768535i	$0.279014\pi$
$32$	185033.	+	11064.9i	0.998217	+	0.0596930i
$33$	24722.3			0.119754
$34$	−316324.	−	3778.89i	−1.38024	−	0.0164887i
$35$	−14050.2	+	14050.2i	−0.0553917	+	0.0553917i
$36$	−2509.77	+	105029.i	−0.00896552	+	0.375190i
$37$	−306569.	−	306569.i	−0.995000	−	0.995000i	0.00498797	−	0.999988i	$-0.498412\pi$
$37$	−306569.	−	306569.i	−0.995000	−	0.995000i	−0.999988	+	0.00498797i	$0.998412\pi$
$38$	−409274.	+	399611.i	−1.20996	+	1.18139i
$39$			143534.i			0.387462i
$40$	−44117.1	−	47398.1i	−0.108993	−	0.117098i
$41$			152195.i			0.344871i	0.985021	+	0.172436i	$0.0551637\pi$
$41$			152195.i			0.344871i	−0.985021	+	0.172436i	$0.944836\pi$
$42$	−129824.	−	132964.i	−0.270386	−	0.276924i
$43$	−3511.39	−	3511.39i	−0.00673503	−	0.00673503i	0.703731	−	0.710466i	$-0.251516\pi$
$43$	−3511.39	−	3511.39i	−0.00673503	−	0.00673503i	−0.710466	+	0.703731i	$0.751516\pi$
$44$	59073.8	+	61966.2i	0.104547	+	0.109666i
$45$	25950.8	−	25950.8i	0.0424529	−	0.0424529i
$46$	−2564.96	+	214708.i	−0.00388534	+	0.325235i
$47$	530864.			0.745831			0.372916	−	0.927865i	$-0.378358\pi$
$47$	530864.			0.745831			0.372916	+	0.927865i	$0.378358\pi$
$48$	448184.	−	407277.i	0.584941	−	0.531551i
$49$	626069.			0.760213
$50$	10288.2	−	861202.i	0.0116397	−	0.974339i
$51$	−730809.	+	730809.i	−0.771450	+	0.771450i
$52$	−359767.	+	342974.i	−0.354821	+	0.338259i
$53$	−1.04981e6	−	1.04981e6i	−0.968602	−	0.968602i	0.0309199	−	0.999522i	$-0.490156\pi$
$53$	−1.04981e6	−	1.04981e6i	−0.968602	−	0.968602i	−0.999522	+	0.0309199i	$0.990156\pi$
$54$	878711.	+	899959.i	0.759395	+	0.777758i
$55$		−	29906.8i		−	0.0242382i
$56$	23057.4	−	643119.i	0.0175450	−	0.489366i
$57$			1.86878e6i			1.33659i
$58$	1.16133e6	−	1.13391e6i	0.781551	−	0.763098i
$59$	−1.13322e6	−	1.13322e6i	−0.718343	−	0.718343i	0.249923	−	0.968266i	$-0.419595\pi$
$59$	−1.13322e6	−	1.13322e6i	−0.718343	−	0.718343i	−0.968266	+	0.249923i	$0.919595\pi$
$60$	−211490.	−	5053.75i	−0.126404	−	0.00302054i
$61$	195148.	−	195148.i	0.110080	−	0.110080i	−0.649921	−	0.760002i	$-0.725198\pi$
$61$	195148.	−	195148.i	0.110080	−	0.110080i	0.760002	+	0.649921i	$0.225198\pi$
$62$	2.40115e6	+	28684.8i	1.27952	+	0.0152855i
$63$	364737.			0.183776
$64$	2.09177e6	+	150183.i	0.997433	+	0.0716128i
$65$	173635.			0.0784223
$66$	279681.	+	3341.15i	0.119746	+	0.00143051i
$67$	−1.52689e6	+	1.52689e6i	−0.620221	+	0.620221i	−0.945588	−	0.325367i	$-0.894512\pi$
$67$	−1.52689e6	+	1.52689e6i	−0.620221	+	0.620221i	0.325367	+	0.945588i	$0.394512\pi$
$68$	−3.57803e6	−	85500.3i	−1.37995	−	0.0329751i
$69$	496045.	+	496045.i	0.181781	+	0.181781i
$70$	−160847.	+	157050.i	−0.0560494	+	0.0547260i
$71$		−	4.95086e6i		−	1.64164i	−0.571190	−	0.820818i	$-0.693518\pi$
$71$		−	4.95086e6i		−	1.64164i	0.571190	−	0.820818i	$-0.306482\pi$
$72$	−42587.2	+	1.18785e6i	−0.0134467	+	0.375056i
$73$			5.65272e6i			1.70070i	0.526218	+	0.850350i	$0.323610\pi$
$73$			5.65272e6i			1.70070i	−0.526218	+	0.850350i	$0.676390\pi$
$74$	−3.42676e6	−	3.50962e6i	−0.983043	−	1.00681i
$75$	−1.98965e6	−	1.98965e6i	−0.544581	−	0.544581i
$76$	−4.68408e6	+	4.46545e6i	−1.22399	+	1.16686i
$77$	210169.	−	210169.i	0.0524628	−	0.0524628i
$78$	−19398.2	+	1.62379e6i	−0.00462839	+	0.387434i
$79$	5.88689e6			1.34336			0.671678	−	0.740843i	$-0.265574\pi$
$79$	5.88689e6			1.34336			0.671678	+	0.740843i	$0.265574\pi$
$80$	−492686.	−	542172.i	−0.107586	−	0.118392i
$81$	2.31426e6			0.483855
$82$	−20568.7	+	1.72177e6i	−0.00411963	+	0.344847i
$83$	−1.38794e6	+	1.38794e6i	−0.266439	+	0.266439i	−0.827664	−	0.561225i	$-0.810330\pi$
$83$	−1.38794e6	+	1.38794e6i	−0.266439	+	0.266439i	0.561225	+	0.827664i	$0.310330\pi$
$84$	−1.45072e6	−	1.52175e6i	−0.267058	−	0.280134i
$85$	884066.	+	884066.i	0.156142	+	0.156142i
$86$	−39249.5	−	40198.6i	−0.00665410	−	0.00681500i
$87$		−	5.30273e6i		−	0.863341i
$88$	659922.	+	709001.i	0.103229	+	0.110907i
$89$		−	2.76039e6i		−	0.415054i	−0.978229	−	0.207527i	$-0.933458\pi$
$89$		−	2.76039e6i		−	0.415054i	0.978229	−	0.207527i	$-0.0665415\pi$
$90$	297086.	−	290072.i	0.0429570	−	0.0419428i
$91$	1.22021e6	+	1.22021e6i	0.169742	+	0.169742i
$92$	−58034.4	+	2.42863e6i	−0.00777012	+	0.325165i
$93$	5.54742e6	−	5.54742e6i	0.715156	−	0.715156i
$94$	6.00561e6	+	71744.6i	0.745778	+	0.00890926i
$95$	2.26068e6			0.270525
$96$	5.12530e6	−	4.54691e6i	0.591249	−	0.524526i
$97$	4.24399e6			0.472143			0.236072	−	0.971736i	$-0.424140\pi$
$97$	4.24399e6			0.472143			0.236072	+	0.971736i	$0.424140\pi$
$98$	7.08265e6	+	84611.2i	0.760159	+	0.00908107i
$99$	−388184.	+	388184.i	−0.0402082	+	0.0402082i
$100$	232778.	−	9.74131e6i	0.0232778	−	0.974131i
$101$	−8.86731e6	−	8.86731e6i	−0.856381	−	0.856381i	0.134529	−	0.990910i	$-0.457048\pi$
$101$	−8.86731e6	−	8.86731e6i	−0.856381	−	0.856381i	−0.990910	+	0.134529i	$0.957048\pi$
$102$	−8.36633e6	+	8.16880e6i	−0.780611	+	0.762180i
$103$			1.83335e7i			1.65316i	0.562817	+	0.826581i	$0.309717\pi$
$103$			1.83335e7i			1.65316i	−0.562817	+	0.826581i	$0.690283\pi$
$104$	−4.11636e6	+	3.83141e6i	−0.358836	+	0.333997i
$105$			734444.i			0.0619150i
$106$	−1.17345e7	−	1.20183e7i	−0.956962	−	0.980103i
$107$	3.00093e6	+	3.00093e6i	0.236817	+	0.236817i	0.815531	−	0.578714i	$-0.196445\pi$
$107$	3.00093e6	+	3.00093e6i	0.236817	+	0.236817i	−0.578714	+	0.815531i	$0.696445\pi$
$108$	9.81914e6	+	1.02999e7i	0.750050	+	0.786774i
$109$	−9.62142e6	+	9.62142e6i	−0.711617	+	0.711617i	−0.966873	−	0.255256i	$-0.917840\pi$
$109$	−9.62142e6	+	9.62142e6i	−0.711617	+	0.711617i	0.255256	+	0.966873i	$0.417840\pi$
$110$	4041.81	−	338333.i	0.000289536	−	0.0242365i
$111$	−1.60253e7			−1.11218
$112$	347762.	−	7.27243e6i	0.0233894	−	0.489121i
$113$	−1.64461e7			−1.07223			−0.536115	−	0.844145i	$-0.680109\pi$
$113$	−1.64461e7			−1.07223			−0.536115	+	0.844145i	$0.680109\pi$
$114$	−252560.	+	2.11414e7i	−0.0159661	+	1.33649i
$115$	600070.	−	600070.i	0.0367925	−	0.0367925i
$116$	1.32912e7	−	1.26709e7i	0.790611	−	0.753708i
$117$	−2.25374e6	−	2.25374e6i	−0.130093	−	0.130093i
$118$	−1.26668e7	−	1.29731e7i	−0.709711	−	0.726873i
$119$			1.24255e7i			0.675925i
$120$	−2.39188e6	−	85754.7i	−0.126359	−	0.00453027i
$121$		−	1.90398e7i		−	0.977043i
$122$	2.23406e6	−	2.18132e6i	0.111387	−	0.108757i
$123$	3.97783e6	+	3.97783e6i	0.192743	+	0.192743i
$124$	2.71601e7	+	649016.i	1.27925	+	0.0305689i
$125$	−4.87702e6	+	4.87702e6i	−0.223341	+	0.223341i
$126$	4.12623e6	+	49293.1i	0.183762	+	0.00219528i
$127$	−1.93456e6			−0.0838050			−0.0419025	−	0.999122i	$-0.513342\pi$
$127$	−1.93456e6			−0.0838050			−0.0419025	+	0.999122i	$0.513342\pi$
$128$	2.36437e7	+	1.98170e6i	0.996506	+	0.0835225i
$129$	−183550.			−0.00752820
$130$	1.96431e6	+	23466.2i	0.0784167	+	0.000936787i
$131$	1.83661e7	−	1.83661e7i	0.713783	−	0.713783i	−0.253541	−	0.967325i	$-0.581595\pi$
$131$	1.83661e7	−	1.83661e7i	0.713783	−	0.713783i	0.967325	+	0.253541i	$0.0815954\pi$
$132$	3.16355e6	+	75596.1i	0.119720	+	0.00286082i
$133$	1.58869e7	+	1.58869e7i	0.585541	+	0.585541i
$134$	−1.74799e7	+	1.70672e7i	−0.627586	+	0.612768i
$135$		−	4.97105e6i		−	0.173892i
$136$	−4.04663e7	−	1.45082e6i	−1.37945	−	0.0494568i
$137$		−	2.81962e7i		−	0.936848i	−0.883504	−	0.468424i	$-0.844822\pi$
$137$		−	2.81962e7i		−	0.936848i	0.883504	−	0.468424i	$-0.155178\pi$
$138$	5.54467e6	+	5.67875e6i	0.179597	+	0.183940i
$139$	1.79690e7	+	1.79690e7i	0.567508	+	0.567508i	0.931430	−	0.363921i	$-0.118562\pi$
$139$	1.79690e7	+	1.79690e7i	0.567508	+	0.567508i	−0.363921	+	0.931430i	$0.618562\pi$
$140$	−1.84088e6	+	1.75495e6i	−0.0566991	+	0.0540526i
$141$	1.38749e7	−	1.38749e7i	0.416833	−	0.416833i
$142$	669094.	−	5.60086e7i	0.0196100	−	1.64152i
$143$	−2.59730e6			−0.0742756
$144$	−642319.	+	1.34322e7i	−0.0179259	+	0.374869i
$145$	−6.41477e6			−0.174740
$146$	−763948.	+	6.39487e7i	−0.0203156	+	1.70058i
$147$	1.63632e7	−	1.63632e7i	0.424871	−	0.424871i
$148$	−3.82923e7	−	4.01671e7i	−0.970946	−	1.01849i
$149$	4.93177e7	+	4.93177e7i	1.22138	+	1.22138i	0.967142	+	0.254238i	$0.0818246\pi$
$149$	4.93177e7	+	4.93177e7i	1.22138	+	1.22138i	0.254238	+	0.967142i	$0.418175\pi$
$150$	−2.22398e7	−	2.27776e7i	−0.538037	−	0.551048i
$151$		−	9.71762e6i		−	0.229689i	−0.993383	−	0.114845i	$-0.963363\pi$
$151$		−	9.71762e6i		−	0.229689i	0.993383	−	0.114845i	$-0.0366370\pi$
$152$	−5.35941e7	+	4.98841e7i	−1.23784	+	1.15215i
$153$		−	2.29500e7i		−	0.518038i
$154$	2.40602e6	−	2.34922e6i	0.0530857	−	0.0518323i
$155$	−6.71077e6	−	6.71077e6i	−0.144748	−	0.144748i
$156$	−438900.	+	1.83671e7i	−0.00925613	+	0.387351i
$157$	2.31520e6	−	2.31520e6i	0.0477463	−	0.0477463i	−0.682831	−	0.730577i	$-0.739251\pi$
$157$	2.31520e6	−	2.31520e6i	0.0477463	−	0.0477463i	0.730577	+	0.682831i	$0.239251\pi$
$158$	6.65978e7	+	795595.i	1.34326	+	0.0160469i
$159$	−5.48766e7			−1.08267
$160$	−5.50044e6	−	6.20013e6i	−0.106164	−	0.119669i
$161$	8.43394e6			0.159272
$162$	2.61810e7	+	312765.i	0.483820	+	0.00577984i
$163$	−138818.	+	138818.i	−0.00251067	+	0.00251067i	−0.708361	−	0.705850i	$-0.750565\pi$
$163$	−138818.	+	138818.i	−0.00251067	+	0.00251067i	0.705850	+	0.708361i	$0.250565\pi$
$164$	−465383.	+	1.94754e7i	−0.00823867	+	0.344773i
$165$	−781657.	−	781657.i	−0.0135464	−	0.0135464i
$166$	−1.58892e7	+	1.55141e7i	−0.269603	+	0.263237i
$167$		−	3.12063e7i		−	0.518483i	−0.965813	−	0.259242i	$-0.916527\pi$
$167$		−	3.12063e7i		−	0.518483i	0.965813	−	0.259242i	$-0.0834726\pi$
$168$	−1.62062e7	−	1.74115e7i	−0.263693	−	0.283304i
$169$			4.76690e7i			0.759683i
$170$	9.88187e6	+	1.01208e7i	0.154265	+	0.157996i
$171$	−2.93432e7	−	2.93432e7i	−0.448767	−	0.448767i
$172$	−438593.	−	460067.i	−0.00657222	−	0.00689400i
$173$	−7.27617e7	+	7.27617e7i	−1.06842	+	1.06842i	−0.0709376	+	0.997481i	$0.522599\pi$
$173$	−7.27617e7	+	7.27617e7i	−1.06842	+	1.06842i	−0.997481	+	0.0709376i	$0.977401\pi$
$174$	716648.	−	5.99893e7i	0.0103130	−	0.863280i
$175$	−3.38288e7			−0.477148
$176$	7.36981e6	+	8.11005e6i	0.101897	+	0.112132i
$177$	−5.92366e7			−0.802941
$178$	373058.	−	3.12280e7i	0.00495799	−	0.415025i
$179$	2.54298e7	−	2.54298e7i	0.331404	−	0.331404i	−0.521715	−	0.853120i	$-0.674708\pi$
$179$	2.54298e7	−	2.54298e7i	0.331404	−	0.331404i	0.853120	+	0.521715i	$0.174708\pi$
$180$	3.40011e6	−	3.24141e6i	0.0434550	−	0.0414266i
$181$	5.86540e7	+	5.86540e7i	0.735229	+	0.735229i	0.971651	−	0.236422i	$-0.0759747\pi$
$181$	5.86540e7	+	5.86540e7i	0.735229	+	0.735229i	−0.236422	+	0.971651i	$0.575975\pi$
$182$	1.36392e7	+	1.39690e7i	0.167702	+	0.171758i
$183$		−	1.02009e7i		−	0.123044i
$184$	−984759.	+	2.74670e7i	−0.0116538	+	0.325049i
$185$			1.93859e7i			0.225105i
$186$	6.35072e7	−	6.20077e7i	0.723648	−	0.706563i
$187$	−1.32242e7	−	1.32242e7i	−0.147885	−	0.147885i
$188$	6.79312e7	+	1.62328e6i	0.745618	+	0.0178173i
$189$	3.49339e7	−	3.49339e7i	0.376384	−	0.376384i
$190$	2.55749e7	+	305524.i	0.270506	+	0.00323153i
$191$	6.38182e7			0.662716			0.331358	−	0.943505i	$-0.392493\pi$
$191$	6.38182e7			0.662716			0.331358	+	0.943505i	$0.392493\pi$
$192$	5.85966e7	−	5.07461e7i	0.597472	−	0.517426i
$193$	1.17325e8			1.17474			0.587368	−	0.809320i	$-0.300164\pi$
$193$	1.17325e8			1.17474			0.587368	+	0.809320i	$0.300164\pi$
$194$	4.80119e7	+	573563.i	0.472109	+	0.00563995i
$195$	4.53819e6	−	4.53819e6i	0.0438290	−	0.0438290i
$196$	8.01139e7	+	1.91440e6i	0.759997	+	0.0181608i
$197$	−1.18253e8	−	1.18253e8i	−1.10200	−	1.10200i	−0.994169	−	0.107831i	$-0.965609\pi$
$197$	−1.18253e8	−	1.18253e8i	−1.10200	−	1.10200i	−0.107831	−	0.994169i	$-0.534391\pi$
$198$	−4.44395e6	+	4.33902e6i	−0.0406856	+	0.0397250i
$199$			8.85319e7i			0.796368i	0.917305	+	0.398184i	$0.130360\pi$
$199$			8.85319e7i			0.796368i	−0.917305	+	0.398184i	$0.869640\pi$
$200$	3.94990e6	−	1.10171e8i	0.0349125	−	0.973783i
$201$			7.98150e7i			0.693264i
$202$	−9.91166e7	−	1.01513e8i	−0.846090	−	0.866550i
$203$	−4.50795e7	−	4.50795e7i	−0.378219	−	0.378219i
$204$	−9.57515e7	+	9.12821e7i	−0.789660	+	0.752801i
$205$	4.81202e6	−	4.81202e6i	0.0390112	−	0.0390112i
$206$	−2.47772e6	+	2.07405e8i	−0.0197477	+	1.65304i
$207$	−1.55776e7			−0.122068
$208$	−4.70858e7	+	4.27881e7i	−0.362800	+	0.329686i
$209$	−3.38163e7			−0.256220
$210$	−99257.9	+	8.30869e6i	−0.000739601	+	0.0619106i
$211$	−1.36911e8	+	1.36911e8i	−1.00334	+	1.00334i	−0.00334674	+	0.999994i	$0.501065\pi$
$211$	−1.36911e8	+	1.36911e8i	−1.00334	+	1.00334i	−0.999994	+	0.00334674i	$0.998935\pi$
$212$	−1.31127e8	−	1.37548e8i	−0.945186	−	0.991465i
$213$	−1.29398e8	−	1.29398e8i	−0.917484	−	0.917484i
$214$	3.35436e7	+	3.43547e7i	0.233971	+	0.239629i
$215$			222043.i			0.00152371i
$216$	1.09691e8	+	1.17849e8i	0.740599	+	0.795678i
$217$		−	9.43194e7i		−	0.626602i
$218$	−1.10146e8	+	1.07546e8i	−0.720067	+	0.703066i
$219$	1.47742e8	+	1.47742e8i	0.950494	+	0.950494i
$220$	91449.3	−	3.82698e6i	0.000579030	−	0.0242313i
$221$	7.67780e7	−	7.67780e7i	0.478480	−	0.478480i
$222$	−1.81292e8	−	2.16576e6i	−1.11210	−	0.0132854i
$223$	1.81255e8			1.09452			0.547260	−	0.836963i	$-0.315671\pi$
$223$	1.81255e8			1.09452			0.547260	+	0.836963i	$0.315671\pi$
$224$	4.91704e6	−	8.22253e7i	0.0292305	−	0.488807i
$225$	6.24821e7			0.365693
$226$	−1.86053e8	−	2.22264e6i	−1.07215	−	0.0128082i
$227$	−7.92186e6	+	7.92186e6i	−0.0449507	+	0.0449507i	−0.729225	−	0.684274i	$-0.760119\pi$
$227$	−7.92186e6	+	7.92186e6i	−0.0449507	+	0.0449507i	0.684274	+	0.729225i	$0.260119\pi$
$228$	−5.71438e6	+	2.39136e8i	−0.0319299	+	1.33620i
$229$	−5.36324e7	−	5.36324e7i	−0.295123	−	0.295123i	0.543977	−	0.839100i	$-0.316918\pi$
$229$	−5.36324e7	−	5.36324e7i	−0.295123	−	0.295123i	−0.839100	+	0.543977i	$0.816918\pi$
$230$	6.86963e6	−	6.70744e6i	0.0372294	−	0.0363504i
$231$		−	1.09861e7i		−	0.0586412i
$232$	1.52075e8	−	1.41548e8i	0.799557	−	0.744210i
$233$			5.85746e7i			0.303364i	0.988429	+	0.151682i	$0.0484689\pi$
$233$			5.85746e7i			0.303364i	−0.988429	+	0.151682i	$0.951531\pi$
$234$	−2.51917e7	−	2.58009e7i	−0.128529	−	0.131637i
$235$	−1.67846e7	−	1.67846e7i	−0.0843670	−	0.0843670i
$236$	−1.41546e8	−	1.48476e8i	−0.700977	−	0.735299i
$237$	1.53862e8	−	1.53862e8i	0.750780	−	0.750780i
$238$	−1.67927e6	+	1.40568e8i	−0.00807421	+	0.675877i
$239$	3.59343e8			1.70261			0.851307	−	0.524668i	$-0.175811\pi$
$239$	3.59343e8			1.70261			0.851307	+	0.524668i	$0.175811\pi$
$240$	−2.70475e7	−	1.29339e6i	−0.126295	−	0.00603935i
$241$	8.75574e7			0.402933			0.201467	−	0.979495i	$-0.435429\pi$
$241$	8.75574e7			0.402933			0.201467	+	0.979495i	$0.435429\pi$
$242$	2.57317e6	−	2.15396e8i	0.0116712	−	0.976974i
$243$	−1.11439e8	+	1.11439e8i	−0.498213	+	0.498213i
$244$	2.55685e7	−	2.43751e7i	0.112679	−	0.107419i
$245$	−1.97947e7	−	1.97947e7i	−0.0859939	−	0.0859939i
$246$	4.44633e7	+	4.55384e7i	0.190427	+	0.195032i
$247$		−	1.96332e8i		−	0.828996i
$248$	3.07172e8	+	1.10129e7i	1.27879	+	0.0458479i
$249$			7.25516e7i			0.297817i
$250$	−5.58323e7	+	5.45141e7i	−0.225993	+	0.220658i
$251$	−4.91876e7	−	4.91876e7i	−0.196335	−	0.196335i	0.602092	−	0.798427i	$-0.294334\pi$
$251$	−4.91876e7	−	4.91876e7i	−0.196335	−	0.196335i	−0.798427	+	0.602092i	$0.794334\pi$
$252$	4.66730e7	+	1.11530e6i	0.183723	+	0.00439024i
$253$	−8.97611e6	+	8.97611e6i	−0.0348471	+	0.0348471i
$254$	−2.18855e7	−	261450.i	−0.0837990	−	0.00100109i
$255$	4.62126e7			0.174530
$256$	2.67211e8	+	2.56142e7i	0.995437	+	0.0954202i
$257$	−3.42669e8			−1.25924			−0.629621	−	0.776903i	$-0.716790\pi$
$257$	−3.42669e8			−1.25924			−0.629621	+	0.776903i	$0.716790\pi$
$258$	−2.07649e6	−	24806.3i	−0.00752767	−	8.99275e-5i
$259$	−1.36234e8	+	1.36234e8i	−0.487231	+	0.487231i
$260$	2.22189e7	+	530941.i	0.0783999	+	0.00187344i
$261$	8.32622e7	+	8.32622e7i	0.289872	+	0.289872i
$262$	2.10255e8	−	2.05291e8i	0.722259	−	0.705206i
$263$		−	6.78208e7i		−	0.229889i	−0.993372	−	0.114944i	$-0.963331\pi$
$263$		−	6.78208e7i		−	0.229889i	0.993372	−	0.114944i	$-0.0366690\pi$
$264$	3.57788e7	+	1.28276e6i	0.119677	+	0.00429072i
$265$			6.63847e7i			0.219133i
$266$	1.77579e8	+	1.81874e8i	0.578505	+	0.592494i
$267$	−7.21466e7	−	7.21466e7i	−0.231967	−	0.231967i
$268$	−2.00055e8	+	1.90718e8i	−0.634861	+	0.605228i
$269$	−2.80613e8	+	2.80613e8i	−0.878972	+	0.878972i	−0.993428	−	0.114456i	$-0.963487\pi$
$269$	−2.80613e8	+	2.80613e8i	−0.878972	+	0.878972i	0.114456	+	0.993428i	$0.463487\pi$
$270$	671823.	−	5.62371e7i	0.00207722	−	0.173880i
$271$	−5.33255e8			−1.62758			−0.813789	−	0.581160i	$-0.802599\pi$
$271$	−5.33255e8			−1.62758			−0.813789	+	0.581160i	$0.802599\pi$
$272$	−4.57595e8	−	2.18818e7i	−1.37877	−	0.0659314i
$273$	6.37839e7			0.189732
$274$	3.81063e6	−	3.18981e8i	0.0111910	−	0.936781i
$275$	3.60035e7	−	3.60035e7i	0.104395	−	0.104395i
$276$	6.19588e7	+	6.49925e7i	0.177387	+	0.186072i
$277$	−1.22860e8	−	1.22860e8i	−0.347321	−	0.347321i	0.511790	−	0.859111i	$-0.328983\pi$
$277$	−1.22860e8	−	1.22860e8i	−0.347321	−	0.347321i	−0.859111	+	0.511790i	$0.828983\pi$
$278$	2.00853e8	+	2.05710e8i	0.560689	+	0.574247i
$279$			1.74209e8i			0.480236i
$280$	−2.10628e7	+	1.96048e7i	−0.0573408	+	0.0533715i
$281$			2.85601e8i			0.767869i	0.923360	+	0.383934i	$0.125431\pi$
$281$			2.85601e8i			0.767869i	−0.923360	+	0.383934i	$0.874569\pi$
$282$	1.58840e8	−	1.55090e8i	0.421783	−	0.411824i
$283$	−1.08062e8	−	1.08062e8i	−0.283413	−	0.283413i	0.551055	−	0.834469i	$-0.314225\pi$
$283$	−1.08062e8	−	1.08062e8i	−0.283413	−	0.283413i	−0.834469	+	0.551055i	$0.814225\pi$
$284$	1.51388e7	−	6.33530e8i	0.0392172	−	1.64117i
$285$	5.90862e7	−	5.90862e7i	0.151192	−	0.151192i
$286$	−2.93830e7	−	351017.i	−0.0742703	−	0.000887253i
$287$	6.76326e7			0.168877
$288$	−9.08181e6	+	1.51871e8i	−0.0224026	+	0.374628i
$289$	3.71496e8			0.905341
$290$	−7.25696e7	−	866936.i	−0.174728	−	0.00208734i
$291$	1.10923e8	−	1.10923e8i	0.263873	−	0.263873i
$292$	−1.72849e7	+	7.23342e8i	−0.0406282	+	1.70021i
$293$	9.71864e7	+	9.71864e7i	0.225719	+	0.225719i	0.810902	−	0.585182i	$-0.198977\pi$
$293$	9.71864e7	+	9.71864e7i	0.225719	+	0.225719i	−0.585182	+	0.810902i	$0.698977\pi$
$294$	1.87327e8	−	1.82904e8i	0.429916	−	0.419766i
$295$			7.16591e7i			0.162515i
$296$	−4.27768e8	−	4.59582e8i	−0.958710	−	1.03001i
$297$			7.43592e7i			0.164698i
$298$	5.51261e8	+	5.64591e8i	1.20670	+	1.23588i
$299$	−5.21140e7	−	5.21140e7i	−0.112747	−	0.112747i
$300$	−2.48519e8	−	2.60687e8i	−0.531416	−	0.557436i
$301$	−1.56040e6	+	1.56040e6i	−0.00329801	+	0.00329801i
$302$	1.31331e6	−	1.09934e8i	0.00274373	−	0.229673i
$303$	−4.63519e8			−0.957235
$304$	−6.13046e8	+	5.57091e8i	−1.25151	+	1.13728i
$305$	−1.23402e7			−0.0249041
$306$	3.10162e6	−	2.59631e8i	0.00618818	−	0.518001i
$307$	2.96897e8	−	2.96897e8i	0.585628	−	0.585628i	−0.350816	−	0.936444i	$-0.614096\pi$
$307$	2.96897e8	−	2.96897e8i	0.585628	−	0.585628i	0.936444	+	0.350816i	$0.114096\pi$
$308$	2.75366e7	−	2.62513e7i	0.0537011	−	0.0511945i
$309$	4.79173e8	+	4.79173e8i	0.923926	+	0.923926i
$310$	−7.50114e7	−	7.68252e7i	−0.143008	−	0.146466i
$311$		−	3.68775e8i		−	0.695185i	−0.937646	−	0.347592i	$-0.886999\pi$
$311$		−	3.68775e8i		−	0.695185i	0.937646	−	0.347592i	$-0.113001\pi$
$312$	−7.44749e6	+	2.07726e8i	−0.0138825	+	0.387213i
$313$		−	6.25781e8i		−	1.15350i	−0.816921	−	0.576750i	$-0.804321\pi$
$313$		−	6.25781e8i		−	1.15350i	0.816921	−	0.576750i	$-0.195679\pi$
$314$	2.65045e7	−	2.58787e7i	0.0483133	−	0.0471726i
$315$	−1.15321e7	−	1.15321e7i	−0.0207883	−	0.0207883i
$316$	7.53307e8	+	1.80010e7i	1.34297	+	0.0320916i
$317$	−2.24146e8	+	2.24146e8i	−0.395206	+	0.395206i	−0.876538	−	0.481332i	$-0.840153\pi$
$317$	−2.24146e8	+	2.24146e8i	−0.395206	+	0.395206i	0.481332	+	0.876538i	$0.340153\pi$
$318$	−6.20813e8	−	7.41640e6i	−1.08260	−	0.0129330i
$319$	9.59548e7			0.165501
$320$	−6.13880e7	−	7.08848e7i	−0.104727	−	0.120928i
$321$	1.56867e8			0.264706
$322$	9.54123e7	+	1.13982e6i	0.159261	+	0.00190257i
$323$	9.99632e8	−	9.99632e8i	1.65056	−	1.65056i
$324$	2.96141e8	+	7.07657e6i	0.483717	+	0.0115589i
$325$	2.09031e8	+	2.09031e8i	0.337768	+	0.337768i
$326$	−1.58920e6	+	1.55168e6i	−0.00254048	+	0.00248050i
$327$			5.02939e8i			0.795423i
$328$	−7.89688e6	+	2.20260e8i	−0.0123565	+	0.344650i
$329$		−	2.35906e8i		−	0.365219i
$330$	−8.73717e6	−	8.94845e6i	−0.0133836	−	0.0137072i
$331$	−3.22910e7	−	3.22910e7i	−0.0489421	−	0.0489421i	0.682212	−	0.731154i	$-0.261018\pi$
$331$	−3.22910e7	−	3.22910e7i	−0.0489421	−	0.0489421i	−0.731154	+	0.682212i	$0.761018\pi$
$332$	−1.81850e8	+	1.73362e8i	−0.272728	+	0.259998i
$333$	2.51625e8	−	2.51625e8i	0.373421	−	0.373421i
$334$	4.21744e6	−	3.53034e8i	0.00619350	−	0.518446i
$335$	9.65530e7			0.140317
$336$	−1.80986e8	−	1.99164e8i	−0.260290	−	0.286434i
$337$	3.19389e7			0.0454586			0.0227293	−	0.999742i	$-0.492764\pi$
$337$	3.19389e7			0.0454586			0.0227293	+	0.999742i	$0.492764\pi$
$338$	−6.44231e6	+	5.39274e8i	−0.00907473	+	0.759629i
$339$	−4.29842e8	+	4.29842e8i	−0.599252	+	0.599252i
$340$	1.10425e8	+	1.15831e8i	0.152367	+	0.159827i
$341$	1.00383e8	+	1.00383e8i	0.137094	+	0.137094i
$342$	−3.27991e8	−	3.35922e8i	−0.443374	−	0.454095i
$343$		−	6.44180e8i		−	0.861941i
$344$	−4.89958e6	−	5.26397e6i	−0.00648940	−	0.00697202i
$345$		−	3.13674e7i		−	0.0411255i
$346$	−8.32979e8	+	8.13312e8i	−1.08110	+	1.05558i
$347$	1.02043e9	+	1.02043e9i	1.31109	+	1.31109i	0.920616	+	0.390470i	$0.127687\pi$
$347$	1.02043e9	+	1.02043e9i	1.31109	+	1.31109i	0.390470	+	0.920616i	$0.372313\pi$
$348$	1.62147e7	−	6.78556e8i	0.0206245	−	0.863095i
$349$	−3.51725e8	+	3.51725e8i	−0.442908	+	0.442908i	−0.892988	−	0.450080i	$-0.851395\pi$
$349$	−3.51725e8	+	3.51725e8i	−0.442908	+	0.442908i	0.450080	+	0.892988i	$0.351395\pi$
$350$	−3.82702e8	−	4.57186e6i	−0.477114	−	0.00569974i
$351$	−4.31719e8			−0.532876
$352$	8.22779e7	+	9.27442e7i	0.100550	+	0.113341i
$353$	−1.60258e9			−1.93914			−0.969569	−	0.244817i	$-0.921272\pi$
$353$	−1.60258e9			−1.93914			−0.969569	+	0.244817i	$0.921272\pi$
$354$	−6.70138e8	−	8.00564e6i	−0.802884	−	0.00959146i
$355$	−1.56534e8	+	1.56534e8i	−0.185699	+	0.185699i
$356$	8.44073e6	−	3.53229e8i	0.00991528	−	0.414936i
$357$	3.24757e8	+	3.24757e8i	0.377764	+	0.377764i
$358$	2.91122e8	−	2.84248e8i	0.335339	−	0.327422i
$359$			1.56087e9i			1.78048i	0.455494	+	0.890239i	$0.349463\pi$
$359$			1.56087e9i			1.78048i	−0.455494	+	0.890239i	$0.650537\pi$
$360$	3.89032e7	−	3.62102e7i	0.0439467	−	0.0409046i
$361$		−	1.66233e9i		−	1.85970i
$362$	6.55620e8	+	6.71474e8i	0.726394	+	0.743959i
$363$	−4.97633e8	−	4.97633e8i	−0.546054	−	0.546054i
$364$	1.52411e8	+	1.59874e8i	0.165639	+	0.173749i
$365$	1.78725e8	−	1.78725e8i	0.192380	−	0.192380i
$366$	1.37863e6	−	1.15402e8i	0.00146981	−	0.123035i
$367$	−1.38962e9			−1.46745			−0.733726	−	0.679445i	$-0.762221\pi$
$367$	−1.38962e9			−1.46745			−0.733726	+	0.679445i	$0.762221\pi$
$368$	−1.48526e7	+	3.10598e8i	−0.0155358	+	0.324886i
$369$	−1.24918e8			−0.129429
$370$	−2.61995e6	+	2.19311e8i	−0.00268897	+	0.225089i
$371$	−4.66516e8	+	4.66516e8i	−0.474305	+	0.474305i
$372$	7.26831e8	−	6.92905e8i	0.732037	−	0.697868i
$373$	−8.64637e8	−	8.64637e8i	−0.862686	−	0.862686i	0.128963	−	0.991649i	$-0.458835\pi$
$373$	−8.64637e8	−	8.64637e8i	−0.862686	−	0.862686i	−0.991649	+	0.128963i	$0.958835\pi$
$374$	−1.47817e8	−	1.51392e8i	−0.146108	−	0.149641i
$375$			2.54935e8i			0.249644i
$376$	7.68279e8	+	2.75447e7i	0.745352	+	0.0267227i
$377$			5.57100e8i			0.535474i
$378$	3.99925e8	−	3.90482e8i	0.380853	−	0.371861i
$379$	8.63314e8	+	8.63314e8i	0.814576	+	0.814576i	0.985316	−	0.170740i	$-0.0546159\pi$
$379$	8.63314e8	+	8.63314e8i	0.814576	+	0.814576i	−0.170740	+	0.985316i	$0.554616\pi$
$380$	2.89285e8	+	6.91274e6i	0.270448	+	0.00646260i
$381$	−5.05626e7	+	5.05626e7i	−0.0468373	+	0.0468373i
$382$	7.21969e8	+	8.62483e6i	0.662669	+	0.00791642i
$383$	1.30181e9			1.18400			0.592000	−	0.805938i	$-0.298338\pi$
$383$	1.30181e9			1.18400			0.592000	+	0.805938i	$0.298338\pi$
$384$	6.69755e8	−	5.66166e8i	0.603611	−	0.510252i
$385$	−1.32900e7			−0.0118690
$386$	1.32729e9	+	1.58561e7i	1.17465	+	0.0140327i
$387$	2.88206e6	−	2.88206e6i	0.00252764	−	0.00252764i
$388$	5.43076e8	+	1.29773e7i	0.472008	+	0.0112791i
$389$	1.66899e8	+	1.66899e8i	0.143758	+	0.143758i	0.775323	−	0.631565i	$-0.217587\pi$
$389$	1.66899e8	+	1.66899e8i	0.143758	+	0.143758i	−0.631565	+	0.775323i	$0.717587\pi$
$390$	5.19534e7	−	5.07267e7i	0.0443494	−	0.0433023i
$391$		−	5.30680e8i		−	0.448966i
$392$	9.06062e8	+	3.24845e7i	0.759725	+	0.0272380i
$393$		−	9.60046e8i		−	0.797844i
$394$	−1.32181e9	−	1.35377e9i	−1.08876	−	1.11509i
$395$	−1.86129e8	−	1.86129e8i	−0.151958	−	0.151958i
$396$	−5.08603e7	+	4.84863e7i	−0.0411572	+	0.0392361i
$397$	5.54114e8	−	5.54114e8i	0.444460	−	0.444460i	−0.449048	−	0.893508i	$-0.648237\pi$
$397$	5.54114e8	−	5.54114e8i	0.444460	−	0.444460i	0.893508	+	0.449048i	$0.148237\pi$
$398$	−1.19648e7	+	1.00155e9i	−0.00951295	+	0.796312i
$399$	8.30452e8			0.654499
$400$	5.95741e7	−	1.24582e9i	0.0465422	−	0.973296i
$401$	2.46956e8			0.191256			0.0956278	−	0.995417i	$-0.469514\pi$
$401$	2.46956e8			0.191256			0.0956278	+	0.995417i	$0.469514\pi$
$402$	−1.07868e7	+	9.02940e8i	−0.00828132	+	0.693214i
$403$	−5.82807e8	+	5.82807e8i	−0.443565	+	0.443565i
$404$	−1.10758e9	−	1.16181e9i	−0.835678	−	0.876595i
$405$	−7.31711e7	−	7.31711e7i	−0.0547327	−	0.0547327i
$406$	−5.03888e8	−	5.16072e8i	−0.373674	−	0.382710i
$407$		−	2.89983e8i		−	0.213202i
$408$	−1.09556e9	+	1.01973e9i	−0.798596	+	0.743314i
$409$			1.36724e9i			0.988129i	0.869425	+	0.494064i	$0.164489\pi$
$409$			1.36724e9i			0.988129i	−0.869425	+	0.494064i	$0.835511\pi$
$410$	5.50883e7	−	5.37876e7i	0.0394744	−	0.0385424i
$411$	−7.36948e8	−	7.36948e8i	−0.523589	−	0.523589i
$412$	−5.60604e7	+	2.34602e9i	−0.0394926	+	1.65269i
$413$	−5.03581e8	+	5.03581e8i	−0.351758	+	0.351758i
$414$	−1.76227e8	−	2.10526e6i	−0.122060	−	0.00145816i
$415$	8.77664e7			0.0602782
$416$	−5.38459e8	+	4.77694e8i	−0.366713	+	0.325329i
$417$	9.39291e8			0.634343
$418$	−3.82560e8	−	4.57017e6i	−0.256202	−	0.00306066i
$419$	1.12255e9	−	1.12255e9i	0.745518	−	0.745518i	−0.228116	−	0.973634i	$-0.573256\pi$
$419$	1.12255e9	−	1.12255e9i	0.745518	−	0.745518i	0.973634	+	0.228116i	$0.0732565\pi$
$420$	−2.24579e6	+	9.39820e7i	−0.00147910	+	0.0618974i
$421$	−4.86053e8	−	4.86053e8i	−0.317465	−	0.317465i	0.530328	−	0.847793i	$-0.322069\pi$
$421$	−4.86053e8	−	4.86053e8i	−0.317465	−	0.317465i	−0.847793	+	0.530328i	$0.822069\pi$
$422$	−1.56736e9	+	1.53035e9i	−1.01525	+	0.991284i
$423$			4.35720e8i			0.279908i
$424$	−1.46484e9	−	1.57378e9i	−0.933276	−	1.00268i
$425$			2.12857e9i			1.34502i
$426$	−1.44638e9	−	1.48135e9i	−0.906459	−	0.928378i
$427$	−8.67200e7	−	8.67200e7i	−0.0539041	−	0.0539041i
$428$	3.74833e8	+	3.93185e8i	0.231092	+	0.242406i
$429$	−6.78842e7	+	6.78842e7i	−0.0415114	+	0.0415114i
$430$	−30008.4	+	2.51195e6i	−1.82013e−5	+	0.00152360i
$431$	−4.27527e8			−0.257213			−0.128607	−	0.991696i	$-0.541050\pi$
$431$	−4.27527e8			−0.257213			−0.128607	+	0.991696i	$0.541050\pi$
$432$	1.22500e9	+	1.34804e9i	0.731041	+	0.804468i
$433$	1.84114e9			1.08988			0.544941	−	0.838474i	$-0.316552\pi$
$433$	1.84114e9			1.08988			0.544941	+	0.838474i	$0.316552\pi$
$434$	1.27470e7	−	1.06703e9i	0.00748502	−	0.626557i
$435$	−1.67659e8	+	1.67659e8i	−0.0976595	+	0.0976595i
$436$	−1.26061e9	+	1.20177e9i	−0.728414	+	0.694414i
$437$	−6.78512e8	−	6.78512e8i	−0.388931	−	0.388931i
$438$	1.65142e9	+	1.69136e9i	0.939072	+	0.961780i
$439$		−	2.42084e9i		−	1.36565i	−0.730582	−	0.682825i	$-0.760751\pi$
$439$		−	2.42084e9i		−	1.36565i	0.730582	−	0.682825i	$-0.239249\pi$
$440$	1.55176e6	−	4.32819e7i	0.000868442	−	0.0242227i
$441$			5.13862e8i			0.285306i
$442$	8.78958e8	−	8.58206e8i	0.484162	−	0.472730i
$443$	−8.89890e8	−	8.89890e8i	−0.486321	−	0.486321i	0.420822	−	0.907143i	$-0.361742\pi$
$443$	−8.89890e8	−	8.89890e8i	−0.486321	−	0.486321i	−0.907143	+	0.420822i	$0.861742\pi$
$444$	−2.05065e9	−	4.90022e7i	−1.11186	−	0.0265690i
$445$	−8.72764e7	+	8.72764e7i	−0.0469501	+	0.0469501i
$446$	2.05052e9	+	2.44961e7i	1.09444	+	0.0130745i
$447$	2.57797e9			1.36522
$448$	6.67385e7	−	9.29542e8i	0.0350674	−	0.488423i
$449$	5.46373e8			0.284857			0.142429	−	0.989805i	$-0.454509\pi$
$449$	5.46373e8			0.284857			0.142429	+	0.989805i	$0.454509\pi$
$450$	7.06853e8	+	8.44426e6i	0.365667	+	0.00436835i
$451$	−7.19803e7	+	7.19803e7i	−0.0369484	+	0.0369484i
$452$	−2.10450e9	−	5.02890e7i	−1.07192	−	0.0256146i
$453$	−2.53984e8	−	2.53984e8i	−0.128370	−	0.128370i
$454$	−9.06899e7	+	8.85486e7i	−0.0454845	+	0.0444106i
$455$		−	7.71599e7i		−	0.0384018i
$456$	−9.69647e7	+	2.70455e9i	−0.0478891	+	1.33573i
$457$			2.28521e9i			1.12000i	0.828492	+	0.560001i	$0.189199\pi$
$457$			2.28521e9i			1.12000i	−0.828492	+	0.560001i	$0.810801\pi$
$458$	−5.99489e8	−	6.13986e8i	−0.291576	−	0.298627i
$459$	−2.19811e9	−	2.19811e9i	−1.06097	−	1.06097i
$460$	7.86220e7	−	7.49522e7i	0.0376610	−	0.0359031i
$461$	1.51466e9	−	1.51466e9i	0.720051	−	0.720051i	−0.248564	−	0.968615i	$-0.579959\pi$
$461$	1.51466e9	−	1.51466e9i	0.720051	−	0.720051i	0.968615	+	0.248564i	$0.0799587\pi$
$462$	1.48474e6	−	1.24285e8i	0.000700493	−	0.0586370i
$463$	−1.19373e9			−0.558950			−0.279475	−	0.960153i	$-0.590160\pi$
$463$	−1.19373e9			−0.558950			−0.279475	+	0.960153i	$0.590160\pi$
$464$	1.73954e9	−	1.58076e9i	0.808390	−	0.734606i
$465$	−3.50791e8			−0.161794
$466$	−7.91618e6	+	6.62649e8i	−0.00362381	+	0.303342i
$467$	−1.65047e9	+	1.65047e9i	−0.749890	+	0.749890i	−0.974458	−	0.224568i	$-0.927903\pi$
$467$	−1.65047e9	+	1.65047e9i	−0.749890	+	0.749890i	0.224568	+	0.974458i	$0.427903\pi$
$468$	−2.81505e8	−	2.95288e8i	−0.126948	−	0.133163i
$469$	6.78522e8	+	6.78522e8i	0.303710	+	0.303710i
$470$	−1.87614e8	−	1.92151e8i	−0.0833532	−	0.0853688i
$471$		−	1.21022e8i		−	0.0533693i
$472$	−1.58122e9	−	1.69882e9i	−0.692144	−	0.743620i
$473$		−	3.32141e6i		−	0.00144314i
$474$	1.76142e9	−	1.71983e9i	0.759695	−	0.741758i
$475$	2.72153e9	+	2.72153e9i	1.16516	+	1.16516i
$476$	−3.79947e7	+	1.59001e9i	−0.0161473	+	0.675732i
$477$	8.61658e8	−	8.61658e8i	0.363514	−	0.363514i
$478$	4.06521e9	+	4.85641e7i	1.70249	+	0.0203384i
$479$	1.06104e9			0.441121			0.220560	−	0.975373i	$-0.429211\pi$
$479$	1.06104e9			0.441121			0.220560	+	0.975373i	$0.429211\pi$
$480$	−3.05811e8	−	1.82874e7i	−0.126214	−	0.00754757i
$481$	1.68360e9			0.689811
$482$	9.90528e8	+	1.18331e7i	0.402904	+	0.00481320i
$483$	2.20433e8	−	2.20433e8i	0.0890147	−	0.0890147i
$484$	5.82201e7	−	2.43640e9i	0.0233407	−	0.976765i
$485$	−1.34184e8	−	1.34184e8i	−0.0534079	−	0.0534079i
$486$	−1.27576e9	+	1.24564e9i	−0.504129	+	0.492226i
$487$			3.68998e8i			0.144768i	0.997377	+	0.0723839i	$0.0230607\pi$
$487$			3.68998e8i			0.144768i	−0.997377	+	0.0723839i	$0.976939\pi$
$488$	2.92548e8	−	2.72297e8i	0.113954	−	0.106065i
$489$			7.25642e6i			0.00280635i
$490$	−2.21260e8	−	2.26611e8i	−0.0849605	−	0.0870150i
$491$	−2.47495e9	−	2.47495e9i	−0.943587	−	0.943587i	0.0549047	−	0.998492i	$-0.482515\pi$
$491$	−2.47495e9	−	2.47495e9i	−0.943587	−	0.943587i	−0.998492	+	0.0549047i	$0.982515\pi$
$492$	4.96854e8	+	5.21181e8i	0.188084	+	0.197293i
$493$	−2.83649e9	+	2.83649e9i	−1.06615	+	1.06615i
$494$	2.65337e7	−	2.22109e9i	0.00990270	−	0.828937i
$495$	2.45468e7			0.00909654
$496$	3.47352e9	+	1.66101e8i	1.27815	+	0.0611203i
$497$	−2.20007e9			−0.803876
$498$	−9.80513e6	+	8.20770e8i	−0.00355755	+	0.297796i
$499$	−3.63023e9	+	3.63023e9i	−1.30792	+	1.30792i	−0.385010	+	0.922912i	$0.625802\pi$
$499$	−3.63023e9	+	3.63023e9i	−1.30792	+	1.30792i	−0.922912	+	0.385010i	$0.874198\pi$
$500$	−6.38993e8	+	6.09167e8i	−0.228613	+	0.217942i
$501$	−8.15621e8	−	8.15621e8i	−0.289772	−	0.289772i
$502$	−5.49807e8	−	5.63102e8i	−0.193976	−	0.198666i
$503$		−	4.36481e9i		−	1.52925i	−0.644478	−	0.764623i	$-0.722925\pi$
$503$		−	4.36481e9i		−	1.52925i	0.644478	−	0.764623i	$-0.277075\pi$
$504$	5.27856e8	+	1.89249e7i	0.183658	+	0.00658457i
$505$			5.60724e8i			0.193744i
$506$	−1.02759e8	+	1.00333e8i	−0.0352609	+	0.0344283i
$507$	1.24590e9	+	1.24590e9i	0.424575	+	0.424575i
$508$	−2.47553e8	−	5.91552e6i	−0.0837811	−	0.00200203i
$509$	1.15247e9	−	1.15247e9i	0.387361	−	0.387361i	−0.486384	−	0.873745i	$-0.661684\pi$
$509$	1.15247e9	−	1.15247e9i	0.387361	−	0.387361i	0.873745	+	0.486384i	$0.161684\pi$
$510$	5.22799e8	+	6.24550e6i	0.174518	+	0.00208483i
$511$	2.51196e9			0.832798
$512$	3.01947e9	+	3.25883e8i	0.994226	+	0.107304i
$513$	−5.62088e9			−1.83820
$514$	−3.87658e9	−	4.63107e7i	−1.25915	−	0.0150422i
$515$	5.79660e8	−	5.79660e8i	0.187003	−	0.187003i
$516$	−2.34877e7	−	561262.i	−0.00752605	−	0.000179842i
$517$	2.51071e8	+	2.51071e8i	0.0799060	+	0.0799060i
$518$	−1.55961e9	+	1.52279e9i	−0.493017	+	0.481376i
$519$			3.80346e9i			1.19424i
$520$	2.51288e8	+	9.00930e6i	0.0783719	+	0.00280983i
$521$		−	1.98502e9i		−	0.614942i	−0.951558	−	0.307471i	$-0.900517\pi$
$521$		−	1.98502e9i		−	0.614942i	0.951558	−	0.307471i	$-0.0994827\pi$
$522$	9.30685e8	+	9.53190e8i	0.286389	+	0.293314i
$523$	1.50861e9	+	1.50861e9i	0.461128	+	0.461128i	0.899025	−	0.437897i	$-0.144277\pi$
$523$	1.50861e9	+	1.50861e9i	0.461128	+	0.461128i	−0.437897	+	0.899025i	$0.644277\pi$
$524$	2.40634e9	−	2.29402e9i	0.730631	−	0.696528i
$525$	−8.84164e8	+	8.84164e8i	−0.266671	+	0.266671i
$526$	9.16577e6	−	7.67250e8i	0.00274612	−	0.229872i
$527$	−5.93476e9			−1.76631
$528$	4.04588e8	+	1.93471e7i	0.119617	+	0.00572001i
$529$	3.04462e9			0.894207
$530$	−8.97169e6	+	7.51004e8i	−0.00261763	+	0.219117i
$531$	9.30118e8	−	9.30118e8i	0.269592	−	0.269592i
$532$	1.98436e9	+	2.08152e9i	0.571386	+	0.599362i
$533$	−4.17907e8	−	4.17907e8i	−0.119546	−	0.119546i
$534$	−8.06437e8	−	8.25938e8i	−0.229180	−	0.234722i
$535$		−	1.89763e8i		−	0.0535765i
$536$	−2.28898e9	+	2.13053e9i	−0.642045	+	0.597601i
$537$		−	1.32929e9i		−	0.370433i
$538$	−3.21247e9	+	3.13662e9i	−0.889409	+	0.868409i
$539$	2.96098e8	+	2.96098e8i	0.0814469	+	0.0814469i
$540$	1.52005e7	−	6.36113e8i	0.00415413	−	0.173843i
$541$	−1.15791e9	+	1.15791e9i	−0.314401	+	0.314401i	−0.846612	−	0.532211i	$-0.821361\pi$
$541$	−1.15791e9	+	1.15791e9i	−0.314401	+	0.314401i	0.532211	+	0.846612i	$0.321361\pi$
$542$	−6.03266e9	−	7.20677e7i	−1.62746	−	0.0194421i
$543$	3.06601e9			0.821815
$544$	−5.17377e9	−	3.09390e8i	−1.37788	−	0.0823967i
$545$	6.08410e8			0.160994
$546$	7.21581e8	+	8.62019e6i	0.189719	+	0.00226643i
$547$	3.28878e9	−	3.28878e9i	0.859170	−	0.859170i	−0.132070	−	0.991240i	$-0.542162\pi$
$547$	3.28878e9	−	3.28878e9i	0.859170	−	0.859170i	0.991240	+	0.132070i	$0.0421624\pi$
$548$	8.62187e7	−	3.60809e9i	0.0223805	−	0.936580i
$549$	1.60173e8	+	1.60173e8i	0.0413128	+	0.0413128i
$550$	4.12169e8	−	4.02438e8i	0.105635	−	0.103141i
$551$			7.25331e9i			1.84717i
$552$	6.92151e8	+	7.43627e8i	0.175151	+	0.188178i
$553$		−	2.61602e9i		−	0.657815i
$554$	−1.37330e9	−	1.40650e9i	−0.343147	−	0.351445i
$555$	5.06678e8	+	5.06678e8i	0.125808	+	0.125808i
$556$	2.24443e9	+	2.35432e9i	0.553789	+	0.580904i
$557$	5.44038e9	−	5.44038e9i	1.33394	−	1.33394i	0.432127	−	0.901813i	$-0.357763\pi$
$557$	5.44038e9	−	5.44038e9i	1.33394	−	1.33394i	0.901813	−	0.432127i	$-0.142237\pi$
$558$	−2.35438e7	+	1.97080e9i	−0.00573662	+	0.480202i
$559$	1.92836e7			0.00466925
$560$	−2.40931e8	+	2.18940e8i	−0.0579742	+	0.0526827i
$561$	−6.91268e8			−0.165301
$562$	−3.85981e7	+	3.23097e9i	−0.00917251	+	0.767814i
$563$	1.87595e9	−	1.87595e9i	0.443039	−	0.443039i	−0.449993	−	0.893032i	$-0.648574\pi$
$563$	1.87595e9	−	1.87595e9i	0.443039	−	0.443039i	0.893032	+	0.449993i	$0.148574\pi$
$564$	1.81790e9	−	1.73305e9i	0.426672	−	0.406756i
$565$	5.19984e8	+	5.19984e8i	0.121289	+	0.121289i
$566$	−1.20789e9	−	1.23710e9i	−0.280008	−	0.286779i
$567$		−	1.02841e9i		−	0.236934i
$568$	2.56883e8	−	7.16501e9i	0.0588189	−	1.64058i
$569$		−	6.48062e9i		−	1.47477i	−0.675474	−	0.737384i	$-0.736061\pi$
$569$		−	6.48062e9i		−	1.47477i	0.675474	−	0.737384i	$-0.263939\pi$
$570$	6.76421e8	−	6.60451e8i	0.152987	−	0.149375i
$571$	5.86197e9	+	5.86197e9i	1.31770	+	1.31770i	0.915592	+	0.402109i	$0.131723\pi$
$571$	5.86197e9	+	5.86197e9i	1.31770	+	1.31770i	0.402109	+	0.915592i	$0.368277\pi$
$572$	−3.32360e8	−	7.94205e6i	−0.0742544	−	0.00177438i
$573$	1.66798e9	−	1.66798e9i	0.370381	−	0.370381i
$574$	7.65121e8	+	9.14034e6i	0.168865	+	0.00201730i
$575$	1.44479e9			0.316934
$576$	−1.23266e8	+	1.71687e9i	−0.0268761	+	0.374334i
$577$	5.29442e9			1.14737			0.573685	−	0.819076i	$-0.305513\pi$
$577$	5.29442e9			1.14737			0.573685	+	0.819076i	$0.305513\pi$
$578$	4.20270e9	+	5.02066e7i	0.905276	+	0.0108147i
$579$	3.06646e9	−	3.06646e9i	0.656541	−	0.656541i
$580$	−8.20856e8	−	1.96151e7i	−0.174690	−	0.00417439i
$581$	6.16775e8	+	6.16775e8i	0.130470	+	0.130470i
$582$	1.26985e9	−	1.23987e9i	0.267007	−	0.260702i
$583$		−	9.93011e8i		−	0.207546i
$584$	−2.93300e8	+	8.18076e9i	−0.0609351	+	1.69961i
$585$			1.42515e8i			0.0294317i
$586$	1.08633e9	+	1.11259e9i	0.223007	+	0.228400i
$587$	−3.58100e9	−	3.58100e9i	−0.730754	−	0.730754i	0.240015	−	0.970769i	$-0.422847\pi$
$587$	−3.58100e9	−	3.58100e9i	−0.730754	−	0.730754i	−0.970769	+	0.240015i	$0.922847\pi$
$588$	2.14393e9	−	2.04385e9i	0.434900	−	0.414600i
$589$	−7.58801e9	+	7.58801e9i	−1.53012	+	1.53012i
$590$	−9.68450e6	+	8.10672e8i	−0.00194131	+	0.162504i
$591$	−6.18144e9			−1.23178
$592$	−4.77719e9	−	5.25702e9i	−0.946338	−	1.04139i
$593$	−3.63519e9			−0.715873			−0.357937	−	0.933746i	$-0.616520\pi$
$593$	−3.63519e9			−0.715873			−0.357937	+	0.933746i	$0.616520\pi$
$594$	−1.00494e7	+	8.41218e8i	−0.00196738	+	0.164686i
$595$	3.92862e8	−	3.92862e8i	0.0764594	−	0.0764594i
$596$	6.16006e9	+	6.46166e9i	1.19185	+	1.25021i
$597$	2.31391e9	+	2.31391e9i	0.445078	+	0.445078i
$598$	−5.82517e8	−	5.96603e8i	−0.111392	−	0.114086i
$599$			5.93543e9i			1.12839i	0.825643	+	0.564194i	$0.190813\pi$
$599$			5.93543e9i			1.12839i	−0.825643	+	0.564194i	$0.809187\pi$
$600$	−2.77624e9	−	2.98271e9i	−0.524720	−	0.563744i
$601$		−	4.68669e9i		−	0.880654i	−0.897838	−	0.440327i	$-0.854863\pi$
$601$		−	4.68669e9i		−	0.880654i	0.897838	−	0.440327i	$-0.145137\pi$
$602$	−1.78635e7	+	1.74417e7i	−0.00333717	+	0.00325838i
$603$	−1.25324e9	−	1.25324e9i	−0.232767	−	0.232767i
$604$	2.97146e7	−	1.24350e9i	0.00548707	−	0.229624i
$605$	−6.01991e8	+	6.01991e8i	−0.110521	+	0.110521i
$606$	−5.24375e9	−	6.26432e7i	−0.957167	−	0.0114346i
$607$	−8.28661e9			−1.50389			−0.751945	−	0.659225i	$-0.770884\pi$
$607$	−8.28661e9			−1.50389			−0.751945	+	0.659225i	$0.770884\pi$
$608$	−7.01062e9	+	6.21946e9i	−1.26501	+	1.12225i
$609$	−2.35643e9			−0.422761
$610$	−1.39603e8	−	1.66774e6i	−0.0249024	−	0.000297490i
$611$	−1.45768e9	+	1.45768e9i	−0.258534	+	0.258534i
$612$	7.01765e7	−	2.93676e9i	0.0123755	−	0.517890i
$613$	−1.45115e9	−	1.45115e9i	−0.254448	−	0.254448i	0.568343	−	0.822792i	$-0.307585\pi$
$613$	−1.45115e9	−	1.45115e9i	−0.254448	−	0.254448i	−0.822792	+	0.568343i	$0.807585\pi$
$614$	3.39889e9	−	3.31864e9i	0.592582	−	0.578591i
$615$		−	2.51538e8i		−	0.0436055i
$616$	3.15067e8	−	2.93257e8i	0.0543088	−	0.0505494i
$617$			6.51159e9i			1.11606i	0.829820	+	0.558032i	$0.188443\pi$
$617$			6.51159e9i			1.11606i	−0.829820	+	0.558032i	$0.811557\pi$
$618$	5.35607e9	+	5.48559e9i	0.912824	+	0.934897i
$619$	−1.88997e9	−	1.88997e9i	−0.320285	−	0.320285i	0.528591	−	0.848877i	$-0.322720\pi$
$619$	−1.88997e9	−	1.88997e9i	−0.320285	−	0.320285i	−0.848877	+	0.528591i	$0.822720\pi$
$620$	−8.38213e8	−	8.79254e8i	−0.141248	−	0.148164i
$621$	−1.49199e9	+	1.49199e9i	−0.250003	+	0.250003i
$622$	4.98388e7	−	4.17191e9i	0.00830427	−	0.695135i
$623$	−1.22666e9			−0.203244
$624$	−1.12326e8	+	2.34898e9i	−0.0185070	+	0.387020i
$625$	−5.63892e9			−0.923881
$626$	8.45724e7	−	7.07940e9i	0.0137790	−	1.15342i
$627$	−8.83836e8	+	8.83836e8i	−0.143198	+	0.143198i
$628$	3.03341e8	−	2.89182e8i	0.0488733	−	0.0465921i
$629$	8.57209e9	+	8.57209e9i	1.37344	+	1.37344i
$630$	−1.28903e8	−	1.32020e8i	−0.0205385	−	0.0210352i
$631$		−	1.09010e10i		−	1.72728i	−0.504109	−	0.863640i	$-0.668179\pi$
$631$		−	1.09010e10i		−	1.72728i	0.504109	−	0.863640i	$-0.331821\pi$
$632$	8.51965e9	+	3.05450e8i	1.34249	+	0.0481317i
$633$			7.15671e9i			1.12150i
$634$	−2.56603e9	+	2.50545e9i	−0.399899	+	0.390457i
$635$	6.11660e7	+	6.11660e7i	0.00947986	+	0.00947986i
$636$	−7.02220e9	−	1.67802e8i	−1.08236	−	0.0258641i
$637$	−1.71910e9	+	1.71910e9i	−0.263520	+	0.263520i
$638$	1.08553e9	+	1.29680e7i	0.165489	+	0.00197697i
$639$	4.06355e9			0.616101
$640$	−6.84896e8	−	8.10209e8i	−0.103275	−	0.122171i
$641$	5.40291e9			0.810261			0.405130	−	0.914259i	$-0.367226\pi$
$641$	5.40291e9			0.810261			0.405130	+	0.914259i	$0.367226\pi$
$642$	1.77462e9	+	2.12001e7i	0.264687	+	0.00316202i
$643$	4.85998e9	−	4.85998e9i	0.720935	−	0.720935i	−0.247861	−	0.968796i	$-0.579727\pi$
$643$	4.85998e9	−	4.85998e9i	0.720935	−	0.720935i	0.968796	+	0.247861i	$0.0797275\pi$
$644$	1.07924e9	+	2.57894e7i	0.159227	+	0.00380487i
$645$	5.80340e6	+	5.80340e6i	0.000851576	+	0.000851576i
$646$	1.14438e10	−	1.11736e10i	1.67016	−	1.63073i
$647$			7.65726e8i			0.111150i	0.998455	+	0.0555749i	$0.0176992\pi$
$647$			7.65726e8i			0.111150i	−0.998455	+	0.0555749i	$0.982301\pi$
$648$	3.34926e9	+	1.20079e8i	0.483544	+	0.0173362i
$649$		−	1.07191e9i		−	0.153922i
$650$	2.33650e9	+	2.39300e9i	0.333709	+	0.341779i
$651$	−2.46517e9	−	2.46517e9i	−0.350198	−	0.350198i
$652$	−1.81881e7	+	1.73392e7i	−0.00256993	+	0.00244998i
$653$	−3.14536e8	+	3.14536e8i	−0.0442053	+	0.0442053i	−0.728864	−	0.684659i	$-0.759951\pi$
$653$	−3.14536e8	+	3.14536e8i	−0.0442053	+	0.0442053i	0.684659	+	0.728864i	$0.259951\pi$
$654$	−6.79707e7	+	5.68970e9i	−0.00950166	+	0.795366i
$655$	−1.16138e9			−0.161484
$656$	−1.19104e8	+	2.49072e9i	−0.0164726	+	0.344478i
$657$	−4.63961e9			−0.638268
$658$	3.18819e7	−	2.66878e9i	0.00436269	−	0.365193i
$659$	−5.32575e9	+	5.32575e9i	−0.724906	+	0.724906i	−0.969600	−	0.244694i	$-0.921312\pi$
$659$	−5.32575e9	+	5.32575e9i	−0.724906	+	0.724906i	0.244694	+	0.969600i	$0.421312\pi$
$660$	−9.76334e7	−	1.02414e8i	−0.0132189	−	0.0138661i
$661$	−9.68609e8	−	9.68609e8i	−0.130450	−	0.130450i	0.638867	−	0.769317i	$-0.279403\pi$
$661$	−9.68609e8	−	9.68609e8i	−0.130450	−	0.130450i	−0.769317	+	0.638867i	$0.779403\pi$
$662$	−3.60940e8	−	3.69668e8i	−0.0483540	−	0.0495233i
$663$		−	4.01340e9i		−	0.534830i
$664$	−2.08068e9	+	1.93665e9i	−0.275814	+	0.256722i
$665$		−	1.00460e9i		−	0.132471i
$666$	2.88061e9	−	2.81260e9i	0.377855	−	0.368933i
$667$	1.92530e9	+	1.92530e9i	0.251222	+	0.251222i
$668$	9.54229e7	−	3.99327e9i	0.0123861	−	0.518335i
$669$	4.73736e9	−	4.73736e9i	0.611709	−	0.611709i
$670$	1.09229e9	+	1.30488e7i	0.140307	+	0.00167614i
$671$	1.84590e8			0.0235873
$672$	−2.02056e9	−	2.27759e9i	−0.256850	−	0.289523i
$673$	2.59657e9			0.328358			0.164179	−	0.986431i	$-0.447503\pi$
$673$	2.59657e9			0.328358			0.164179	+	0.986431i	$0.447503\pi$
$674$	3.61322e8	+	4.31645e6i	0.0454553	+	0.000543022i
$675$	5.98443e9	−	5.98443e9i	0.748961	−	0.748961i
$676$	−1.45763e8	+	6.09989e9i	−0.0181482	+	0.759466i
$677$	1.50540e9	+	1.50540e9i	0.186462	+	0.186462i	0.794165	−	0.607703i	$-0.207909\pi$
$677$	1.50540e9	+	1.50540e9i	0.186462	+	0.186462i	−0.607703	+	0.794165i	$0.707909\pi$
$678$	−4.92085e9	+	4.80467e9i	−0.606368	+	0.592051i
$679$		−	1.88595e9i		−	0.231199i
$680$	1.23357e9	+	1.32531e9i	0.150447	+	0.161636i
$681$			4.14098e8i			0.0502445i
$682$	1.12205e9	+	1.14918e9i	0.135446	+	0.138722i
$683$	−1.82787e9	−	1.82787e9i	−0.219520	−	0.219520i	0.588776	−	0.808296i	$-0.299610\pi$
$683$	−1.82787e9	−	1.82787e9i	−0.219520	−	0.219520i	−0.808296	+	0.588776i	$0.799610\pi$
$684$	−3.66513e9	−	3.84458e9i	−0.437918	−	0.459359i
$685$	−8.91493e8	+	8.91493e8i	−0.105974	+	0.105974i
$686$	8.70589e7	−	7.28754e9i	0.0102962	−	0.861880i
$687$	−2.80352e9			−0.329879
$688$	−5.47170e7	−	6.02129e7i	−0.00640565	−	0.00704904i
$689$	5.76528e9			0.671511
$690$	4.23920e6	−	3.54856e8i	0.000491261	−	0.0411226i
$691$	−1.02776e10	+	1.02776e10i	−1.18501	+	1.18501i	−0.206576	+	0.978431i	$0.566232\pi$
$691$	−1.02776e10	+	1.02776e10i	−1.18501	+	1.18501i	−0.978431	+	0.206576i	$0.933768\pi$
$692$	−9.53333e9	+	9.08835e9i	−1.09364	+	1.04259i
$693$	1.72501e8	+	1.72501e8i	0.0196891	+	0.0196891i
$694$	1.14061e10	+	1.16820e10i	1.29533	+	1.32665i
$695$		−	1.13627e9i		−	0.128391i
$696$	2.75141e8	−	7.67425e9i	0.0309330	−	0.862787i
$697$		−	4.25557e9i		−	0.476040i
$698$	−4.02656e9	+	3.93149e9i	−0.448167	+	0.437586i
$699$	1.53093e9	+	1.53093e9i	0.169545	+	0.169545i
$700$	−4.32885e9	−	1.03442e8i	−0.477012	−	0.0113987i
$701$	4.74719e9	−	4.74719e9i	0.520503	−	0.520503i	−0.397220	−	0.917723i	$-0.630025\pi$
$701$	4.74719e9	−	4.74719e9i	0.520503	−	0.520503i	0.917723	+	0.397220i	$0.130025\pi$
$702$	−4.88399e9	−	5.83454e7i	−0.532837	−	0.00636542i
$703$	2.19201e10			2.37957
$704$	9.18268e8	+	1.06033e9i	0.0991894	+	0.114534i
$705$	−8.77377e8			−0.0943028
$706$	−1.81299e10	−	2.16584e8i	−1.93900	−	0.0231638i
$707$	−3.94046e9	+	3.94046e9i	−0.419353	+	0.419353i
$708$	−7.58012e9	−	1.81134e8i	−0.802712	−	0.0191816i
$709$	−6.91565e9	−	6.91565e9i	−0.728738	−	0.728738i	0.241630	−	0.970368i	$-0.422318\pi$
$709$	−6.91565e9	−	6.91565e9i	−0.728738	−	0.728738i	−0.970368	+	0.241630i	$0.922318\pi$
$710$	−1.79201e9	+	1.74970e9i	−0.187904	+	0.183467i
$711$			4.83181e9i			0.504158i
$712$	1.43227e8	−	3.99490e9i	0.0148712	−	0.414788i
$713$			4.02829e9i			0.416205i
$714$	3.63006e9	+	3.71784e9i	0.373224	+	0.382249i
$715$	8.21201e7	+	8.21201e7i	0.00840192	+	0.00840192i
$716$	3.33185e9	−	3.17633e9i	0.339226	−	0.323393i
$717$	9.39193e9	−	9.39193e9i	0.951564	−	0.951564i
$718$	−2.10947e8	+	1.76580e10i	−0.0212685	+	1.78035i
$719$	3.93170e9			0.394484			0.197242	−	0.980355i	$-0.436802\pi$
$719$	3.93170e9			0.394484			0.197242	+	0.980355i	$0.436802\pi$
$720$	4.45002e8	−	4.04385e8i	0.0444322	−	0.0403767i
$721$	8.14707e9			0.809521
$722$	2.24659e8	−	1.88058e10i	0.0222149	−	1.85957i
$723$	2.28844e9	−	2.28844e9i	0.225193	−	0.225193i
$724$	7.32621e9	+	7.68492e9i	0.717455	+	0.752583i
$725$	−7.72245e9	−	7.72245e9i	−0.752613	−	0.752613i
$726$	−5.56241e9	−	5.69692e9i	−0.539492	−	0.552538i
$727$		−	4.34879e9i		−	0.419757i	−0.977727	−	0.209879i	$-0.932693\pi$
$727$		−	4.34879e9i		−	0.419757i	0.977727	−	0.209879i	$-0.0673069\pi$
$728$	1.70261e9	+	1.82923e9i	0.163551	+	0.175715i
$729$			1.08865e10i			1.04074i
$730$	2.04605e9	−	1.99774e9i	0.194664	−	0.190068i
$731$	9.81831e7	+	9.81831e7i	0.00929664	+	0.00929664i
$732$	3.11925e7	−	1.30535e9i	0.00293942	−	0.123009i
$733$	−1.06119e10	+	1.06119e10i	−0.995242	+	0.995242i	−0.999989	−	0.00474700i	$-0.998489\pi$
$733$	−1.06119e10	+	1.06119e10i	−0.995242	+	0.995242i	0.00474700	+	0.999989i	$0.498489\pi$
$734$	−1.57206e10	−	1.87803e8i	−1.46735	−	0.0175293i
$735$	−1.03473e9			−0.0961212
$736$	−2.10002e8	+	3.51176e9i	−0.0194156	+	0.324678i
$737$	−1.44428e9			−0.132897
$738$	−1.41318e9	−	1.68823e7i	−0.129420	−	0.00154609i
$739$	4.83454e8	−	4.83454e8i	0.0440656	−	0.0440656i	−0.684731	−	0.728796i	$-0.740080\pi$
$739$	4.83454e8	−	4.83454e8i	0.0440656	−	0.0440656i	0.728796	+	0.684731i	$0.240080\pi$
$740$	−5.92784e7	+	2.48069e9i	−0.00537756	+	0.225041i
$741$	−5.13143e9	−	5.13143e9i	−0.463313	−	0.463313i
$742$	−5.34070e9	+	5.21460e9i	−0.479937	+	0.468605i
$743$			1.78064e10i			1.59263i	0.604882	+	0.796315i	$0.293220\pi$
$743$			1.78064e10i			1.59263i	−0.604882	+	0.796315i	$0.706780\pi$
$744$	8.31621e9	−	7.74053e9i	0.740321	−	0.689074i
$745$		−	3.11860e9i		−	0.276320i
$746$	−9.66470e9	−	9.89840e9i	−0.852319	−	0.872930i
$747$	−1.13919e9	−	1.13919e9i	−0.0999939	−	0.0999939i
$748$	−1.65178e9	−	1.73266e9i	−0.144310	−	0.151376i
$749$	1.33355e9	−	1.33355e9i	0.115964	−	0.115964i
$750$	−3.44537e7	+	2.88406e9i	−0.00298210	+	0.249626i
$751$	−5.00764e9			−0.431413			−0.215706	−	0.976458i	$-0.569205\pi$
$751$	−5.00764e9			−0.431413			−0.215706	+	0.976458i	$0.569205\pi$
$752$	8.68775e9	+	4.15441e8i	0.744980	+	0.0356243i
$753$	−2.57118e9			−0.219457
$754$	−7.52903e7	+	6.30241e9i	−0.00639646	+	0.535436i
$755$	−3.07246e8	+	3.07246e8i	−0.0259820	+	0.0259820i
$756$	4.57708e9	−	4.36344e9i	0.385268	−	0.367285i
$757$	−1.30164e10	−	1.30164e10i	−1.09058	−	1.09058i	−0.995467	−	0.0951093i	$-0.969680\pi$
$757$	−1.30164e10	−	1.30164e10i	−1.09058	−	1.09058i	−0.0951093	−	0.995467i	$-0.530320\pi$
$758$	9.64991e9	+	9.88326e9i	0.804787	+	0.824248i
$759$			4.69207e8i			0.0389509i
$760$	3.27172e9	+	1.17299e8i	0.270351	+	0.00969275i
$761$			2.52192e9i			0.207436i	0.994607	+	0.103718i	$0.0330740\pi$
$761$			2.52192e9i			0.207436i	−0.994607	+	0.103718i	$0.966926\pi$
$762$	−5.78843e8	+	5.65176e8i	−0.0473934	+	0.0462744i
$763$	4.27558e9	+	4.27558e9i	0.348465	+	0.348465i
$764$	8.16639e9	+	1.95144e8i	0.662527	+	0.0158317i
$765$	−7.25619e8	+	7.25619e8i	−0.0585995	+	0.0585995i
$766$	1.47272e10	+	1.75936e8i	1.18392	+	0.0141434i
$767$	6.22333e9			0.498012
$768$	7.65339e9	−	6.31447e9i	0.609663	−	0.503005i
$769$	7.13864e8			0.0566074			0.0283037	−	0.999599i	$-0.490989\pi$
$769$	7.13864e8			0.0566074			0.0283037	+	0.999599i	$0.490989\pi$
$770$	−1.50349e8	−	1.79611e6i	−0.0118681	−	0.000141780i
$771$	−8.95614e9	+	8.95614e9i	−0.703770	+	0.703770i
$772$	1.50133e10	+	3.58758e8i	1.17440	+	0.0280634i
$773$	−1.12518e9	−	1.12518e9i	−0.0876182	−	0.0876182i	0.661939	−	0.749557i	$-0.269734\pi$
$773$	−1.12518e9	−	1.12518e9i	−0.0876182	−	0.0876182i	−0.749557	+	0.661939i	$0.769734\pi$
$774$	3.29940e7	−	3.22150e7i	0.00255765	−	0.00249727i
$775$		−	1.61576e10i		−	1.24687i
$776$	6.14201e9	+	2.20206e8i	0.471840	+	0.0169166i
$777$			7.12132e9i			0.544612i
$778$	1.86556e9	+	1.91067e9i	0.142030	+	0.145465i
$779$	−5.44106e9	−	5.44106e9i	−0.412384	−	0.412384i
$780$	5.94599e8	−	5.66845e8i	0.0448635	−	0.0427694i
$781$	2.34150e9	−	2.34150e9i	0.175880	−	0.175880i
$782$	7.17198e7	−	6.00353e9i	0.00536309	−	0.448934i
$783$	1.59494e10			1.18735
$784$	1.02458e10	+	4.89946e8i	0.759346	+	0.0363113i
$785$	−1.46402e8			−0.0108019
$786$	1.29747e8	−	1.08609e10i	0.00953058	−	0.797787i
$787$	−2.58350e9	+	2.58350e9i	−0.188928	+	0.188928i	−0.795233	−	0.606304i	$-0.792651\pi$
$787$	−2.58350e9	+	2.58350e9i	−0.188928	+	0.188928i	0.606304	+	0.795233i	$0.292651\pi$
$788$	−1.47705e10	−	1.54937e10i	−1.07536	−	1.12801i
$789$	−1.77259e9	−	1.77259e9i	−0.128481	−	0.128481i
$790$	−2.08050e9	−	2.13081e9i	−0.150132	−	0.153762i
$791$			7.30833e9i			0.525050i
$792$	−5.81931e8	+	5.41648e8i	−0.0416230	+	0.0387417i
$793$			1.07170e9i			0.0763162i
$794$	6.34353e9	−	6.19375e9i	0.449737	−	0.439119i
$795$	1.73506e9	+	1.73506e9i	0.122470	+	0.122470i
$796$	−2.70714e8	+	1.13288e10i	−0.0190245	+	0.796141i
$797$	7.04397e9	−	7.04397e9i	0.492848	−	0.492848i	−0.416354	−	0.909202i	$-0.636692\pi$
$797$	7.04397e9	−	7.04397e9i	0.492848	−	0.492848i	0.909202	+	0.416354i	$0.136692\pi$
$798$	9.39482e9	+	1.12233e8i	0.654453	+	0.00781826i
$799$	−1.48436e10			−1.02950
$800$	8.42324e8	−	1.40858e10i	0.0581654	−	0.972671i
$801$	2.26566e9			0.155769
$802$	2.79379e9	+	3.33753e7i	0.191242	+	0.00228463i
$803$	−2.67344e9	+	2.67344e9i	−0.182208	+	0.182208i
$804$	−2.44059e8	+	1.02134e10i	−0.0165615	+	0.693066i
$805$	−2.66660e8	−	2.66660e8i	−0.0180166	−	0.0180166i
$806$	−6.67200e9	+	6.51447e9i	−0.448832	+	0.438234i
$807$			1.46684e10i			0.982487i
$808$	−1.23729e10	−	1.32931e10i	−0.825147	−	0.886515i
$809$		−	9.20718e9i		−	0.611374i	−0.952132	−	0.305687i	$-0.901114\pi$
$809$		−	9.20718e9i		−	0.611374i	0.952132	−	0.305687i	$-0.0988861\pi$
$810$	−8.17889e8	−	8.37666e8i	−0.0540750	−	0.0553826i
$811$	4.75890e9	+	4.75890e9i	0.313280	+	0.313280i	0.846179	−	0.532899i	$-0.178897\pi$
$811$	4.75890e9	+	4.75890e9i	0.313280	+	0.313280i	−0.532899	+	0.846179i	$0.678897\pi$
$812$	−5.63069e9	−	5.90638e9i	−0.369076	−	0.387146i
$813$	−1.39374e10	+	1.39374e10i	−0.909628	+	0.909628i
$814$	3.91903e7	−	3.28055e9i	0.00254679	−	0.213187i
$815$	8.77816e6			0.000568005
$816$	−1.25318e10	+	1.13880e10i	−0.807418	+	0.733722i
$817$	2.51068e8			0.0161070
$818$	−1.84778e8	+	1.54675e10i	−0.0118036	+	0.988058i
$819$	−1.00152e9	+	1.00152e9i	−0.0637038	+	0.0637038i
$820$	6.30477e8	−	6.01049e8i	0.0399320	−	0.0380681i
$821$	1.09380e10	+	1.09380e10i	0.689824	+	0.689824i	0.962193	−	0.272369i	$-0.0878072\pi$
$821$	1.09380e10	+	1.09380e10i	0.689824	+	0.689824i	−0.272369	+	0.962193i	$0.587807\pi$
$822$	−8.23743e9	−	8.43662e9i	−0.517297	−	0.529806i
$823$		−	9.52649e9i		−	0.595708i	−0.954611	−	0.297854i	$-0.903729\pi$
$823$		−	9.52649e9i		−	0.595708i	0.954611	−	0.297854i	$-0.0962708\pi$
$824$	−9.51263e8	+	2.65327e10i	−0.0592319	+	1.65210i
$825$		−	1.88200e9i		−	0.116689i
$826$	−5.76502e9	+	5.62891e9i	−0.355935	+	0.347531i
$827$	−8.59630e9	−	8.59630e9i	−0.528497	−	0.528497i	0.391627	−	0.920124i	$-0.371912\pi$
$827$	−8.59630e9	−	8.59630e9i	−0.528497	−	0.528497i	−0.920124	+	0.391627i	$0.871912\pi$
$828$	−1.99336e9	−	4.76332e7i	−0.122034	−	0.00291611i
$829$	5.18213e9	−	5.18213e9i	0.315913	−	0.315913i	−0.531282	−	0.847195i	$-0.678290\pi$
$829$	5.18213e9	−	5.18213e9i	0.315913	−	0.315913i	0.847195	+	0.531282i	$0.178290\pi$
$830$	9.92893e8	+	1.18614e7i	0.0602739	+	0.000720048i
$831$	−6.42223e9			−0.388224
$832$	−6.15609e9	+	5.33133e9i	−0.370573	+	0.320925i
$833$	−1.75057e10			−1.04935
$834$	1.06261e10	+	1.26942e8i	0.634297	+	0.00757749i
$835$	−9.86664e8	+	9.86664e8i	−0.0586498	+	0.0586498i
$836$	−4.32725e9	−	1.03404e8i	−0.256147	−	0.00612088i
$837$	1.66854e10	+	1.66854e10i	0.983553	+	0.983553i
$838$	1.28511e10	−	1.25476e10i	0.754371	−	0.736559i
$839$		−	2.06657e10i		−	1.20805i	−0.796967	−	0.604023i	$-0.793563\pi$
$839$		−	2.06657e10i		−	1.20805i	0.796967	−	0.604023i	$-0.206437\pi$
$840$	−3.81078e7	+	1.06291e9i	−0.00221838	+	0.0618753i
$841$		−	3.33164e9i		−	0.193140i
$842$	−5.43298e9	−	5.56435e9i	−0.313650	−	0.321235i
$843$	7.46458e9	+	7.46458e9i	0.429150	+	0.429150i
$844$	−1.79382e10	+	1.71009e10i	−1.02702	+	0.979086i
$845$	1.50717e9	−	1.50717e9i	0.0859339	−	0.0859339i
$846$	−5.88862e7	+	4.92926e9i	−0.00334362	+	0.279889i
$847$	−8.46093e9			−0.478439
$848$	−1.63589e10	−	1.80020e10i	−0.921232	−	1.01376i
$849$	−5.64870e9			−0.316790
$850$	−2.87670e8	+	2.40803e10i	−0.0160668	+	1.34492i
$851$	5.81841e9	−	5.81841e9i	0.323631	−	0.323631i
$852$	−1.61625e10	−	1.69539e10i	−0.895304	−	0.939140i
$853$	9.45572e9	+	9.45572e9i	0.521643	+	0.521643i	0.918067	−	0.396425i	$-0.129749\pi$
$853$	9.45572e9	+	9.45572e9i	0.521643	+	0.521643i	−0.396425	+	0.918067i	$0.629749\pi$
$854$	−9.69335e8	−	9.92775e8i	−0.0532564	−	0.0545442i
$855$			1.85551e9i			0.101527i
$856$	4.18731e9	+	4.49872e9i	0.228179	+	0.245149i
$857$		−	2.40277e9i		−	0.130401i	−0.997872	−	0.0652003i	$-0.979231\pi$
$857$		−	2.40277e9i		−	0.130401i	0.997872	−	0.0652003i	$-0.0207686\pi$
$858$	−7.77141e8	+	7.58792e8i	−0.0420044	+	0.0410126i
$859$	−1.06835e10	−	1.06835e10i	−0.575094	−	0.575094i	0.358454	−	0.933547i	$-0.383304\pi$
$859$	−1.06835e10	−	1.06835e10i	−0.575094	−	0.575094i	−0.933547	+	0.358454i	$0.883304\pi$
$860$	−678964.	+	2.84133e7i	−3.64000e−5	+	0.00152327i
$861$	1.76767e9	−	1.76767e9i	0.0943824	−	0.0943824i
$862$	−4.83657e9	−	5.77790e7i	−0.257195	−	0.00307252i
$863$	9.86567e8			0.0522503			0.0261252	−	0.999659i	$-0.491683\pi$
$863$	9.86567e8			0.0522503			0.0261252	+	0.999659i	$0.491683\pi$
$864$	1.36761e10	+	1.54158e10i	0.721379	+	0.813143i
$865$	4.60108e9			0.241715
$866$	2.08286e10	+	2.48825e8i	1.08980	+	0.0130191i
$867$	9.70958e9	−	9.70958e9i	0.505980	−	0.505980i
$868$	2.88410e8	−	1.20694e10i	0.0149690	−	0.626423i
$869$	2.78419e9	+	2.78419e9i	0.143923	+	0.143923i
$870$	−1.91937e9	+	1.87405e9i	−0.0988191	+	0.0964860i
$871$		−	8.38528e9i		−	0.429986i
$872$	−1.44236e10	+	1.34251e10i	−0.736657	+	0.685664i
$873$			3.48337e9i			0.177194i
$874$	−7.58424e9	−	7.76764e9i	−0.384257	−	0.393549i
$875$	2.16725e9	+	2.16725e9i	0.109366	+	0.109366i
$876$	1.84538e10	+	1.93573e10i	0.927516	+	0.972929i
$877$	5.68260e9	−	5.68260e9i	0.284478	−	0.284478i	−0.550414	−	0.834892i	$-0.685530\pi$
$877$	5.68260e9	−	5.68260e9i	0.284478	−	0.284478i	0.834892	+	0.550414i	$0.185530\pi$
$878$	3.27169e8	−	2.73867e10i	0.0163133	−	1.36555i
$879$	5.08021e9			0.252302
$880$	2.34043e7	−	4.89434e8i	0.00115773	−	0.0242106i
$881$	3.09124e10			1.52306			0.761530	−	0.648130i	$-0.224449\pi$
$881$	3.09124e10			1.52306			0.761530	+	0.648130i	$0.224449\pi$
$882$	−6.94468e7	+	5.81326e9i	−0.00340810	+	0.285286i
$883$	2.37413e10	−	2.37413e10i	1.16049	−	1.16049i	0.176121	−	0.984369i	$-0.443645\pi$
$883$	2.37413e10	−	2.37413e10i	1.16049	−	1.16049i	0.984369	−	0.176121i	$-0.0563550\pi$
$884$	1.00596e10	−	9.59001e9i	0.489774	−	0.466913i
$885$	1.87291e9	+	1.87291e9i	0.0908272	+	0.0908272i
$886$	−9.94698e9	−	1.01875e10i	−0.480477	−	0.492096i
$887$		−	1.05637e10i		−	0.508256i	−0.967171	−	0.254128i	$-0.918211\pi$
$887$		−	1.05637e10i		−	0.508256i	0.967171	−	0.254128i	$-0.0817885\pi$
$888$	−2.31922e10	−	8.31495e8i	−1.11146	−	0.0398487i
$889$			8.59683e8i			0.0410376i
$890$	−9.99145e8	+	9.75554e8i	−0.0475076	+	0.0463859i
$891$	1.09452e9	+	1.09452e9i	0.0518386	+	0.0518386i
$892$	2.31940e10	+	5.54243e8i	1.09421	+	0.0261471i
$893$	−1.89787e10	+	1.89787e10i	−0.891837	+	0.891837i
$894$	2.91644e10	+	3.48405e8i	1.36512	+	0.0163081i
$895$	−1.60805e9			−0.0749756
$896$	8.80631e8	−	1.05068e10i	0.0408993	−	0.487969i
$897$	−2.72415e9			−0.126025
$898$	6.18106e9	+	7.38406e7i	0.284837	+	0.00340274i
$899$	2.15312e10	−	2.15312e10i	0.988349	−	0.988349i
$900$	7.99542e9	+	1.91058e8i	0.365589	+	0.00873608i
$901$	2.93541e10	+	2.93541e10i	1.33700	+	1.33700i
$902$	−8.24034e8	+	8.04578e8i	−0.0373871	+	0.0365044i
$903$			8.15663e7i			0.00368641i
$904$	−2.38012e10	−	8.53331e8i	−1.07154	−	0.0384174i
$905$		−	3.70898e9i		−	0.166335i
$906$	−2.83897e9	−	2.90762e9i	−0.126827	−	0.129894i
$907$	2.15527e9	+	2.15527e9i	0.0959127	+	0.0959127i	0.753435	−	0.657522i	$-0.228395\pi$
$907$	2.15527e9	+	2.15527e9i	0.0959127	+	0.0959127i	−0.657522	+	0.753435i	$0.728395\pi$
$908$	−1.03793e9	+	9.89486e8i	−0.0460117	+	0.0438641i
$909$	7.27807e9	−	7.27807e9i	0.321397	−	0.321397i
$910$	1.04279e7	−	8.72903e8i	0.000458726	−	0.0383991i
$911$	−3.54892e10			−1.55519			−0.777593	−	0.628769i	$-0.783559\pi$
$911$	−3.54892e10			−1.55519			−0.777593	+	0.628769i	$0.783559\pi$
$912$	−1.46246e9	+	3.05832e10i	−0.0638415	+	1.33506i
$913$	−1.31285e9			−0.0570909
$914$	−3.08839e8	+	2.58523e10i	−0.0133789	+	1.11992i
$915$	−3.22528e8	+	3.22528e8i	−0.0139185	+	0.0139185i
$916$	−6.69899e9	−	7.02698e9i	−0.287988	−	0.302089i
$917$	−8.16153e9	−	8.16153e9i	−0.349525	−	0.349525i
$918$	−2.45699e10	−	2.51640e10i	−1.04822	−	1.07357i
$919$			3.38803e10i			1.43993i	0.694008	+	0.719967i	$0.255843\pi$
$919$			3.38803e10i			1.43993i	−0.694008	+	0.719967i	$0.744157\pi$
$920$	8.99572e8	−	8.37301e8i	0.0380872	−	0.0354507i
$921$		−	1.55197e10i		−	0.654596i
$922$	1.73400e10	−	1.69306e10i	0.728601	−	0.711398i
$923$	1.35944e10	+	1.35944e10i	0.569055	+	0.569055i
$924$	3.35935e7	−	1.40582e9i	0.00140089	−	0.0586245i
$925$	−2.33378e10	+	2.33378e10i	−0.969536	+	0.969536i
$926$	−1.35046e10	−	1.61329e8i	−0.558910	−	0.00667689i
$927$	−1.50477e10			−0.620428
$928$	1.98929e10	−	1.76479e10i	0.817108	−	0.724897i
$929$	−3.61327e10			−1.47858			−0.739292	−	0.673385i	$-0.764840\pi$
$929$	−3.61327e10			−1.47858			−0.739292	+	0.673385i	$0.764840\pi$
$930$	−3.96846e9	−	4.74083e7i	−0.161783	−	0.00193270i
$931$	−2.23823e10	+	2.23823e10i	−0.909035	+	0.909035i
$932$	−1.79110e8	+	7.49541e9i	−0.00724709	+	0.303277i
$933$	−9.63846e9	−	9.63846e9i	−0.388528	−	0.388528i
$934$	−1.88946e10	+	1.84485e10i	−0.758795	+	0.740879i
$935$			8.36234e8i			0.0334570i
$936$	−3.14473e9	−	3.37860e9i	−0.125348	−	0.134670i
$937$		−	1.21837e10i		−	0.483827i	−0.970298	−	0.241913i	$-0.922225\pi$
$937$		−	1.21837e10i		−	0.483827i	0.970298	−	0.241913i	$-0.0777750\pi$
$938$	7.58436e9	+	7.76776e9i	0.300060	+	0.307316i
$939$	−1.63557e10	−	1.63557e10i	−0.644672	−	0.644672i
$940$	−2.09649e9	−	2.19914e9i	−0.0823275	−	0.0863584i
$941$	−1.36613e9	+	1.36613e9i	−0.0534474	+	0.0534474i	−0.733325	−	0.679878i	$-0.762033\pi$
$941$	−1.36613e9	+	1.36613e9i	−0.0534474	+	0.0534474i	0.679878	+	0.733325i	$0.262033\pi$
$942$	1.63558e7	−	1.36911e9i	0.000637519	−	0.0533655i
$943$	−2.88852e9			−0.112172
$944$	−1.76586e10	−	1.94323e10i	−0.683212	−	0.751835i
$945$	−2.20904e9			−0.0851516
$946$	448878.	−	3.75748e7i	1.72389e−5	−	0.00144304i
$947$	−1.52257e9	+	1.52257e9i	−0.0582577	+	0.0582577i	−0.735635	−	0.677378i	$-0.763116\pi$
$947$	−1.52257e9	+	1.52257e9i	−0.0582577	+	0.0582577i	0.677378	+	0.735635i	$0.263116\pi$
$948$	2.01592e10	−	1.92183e10i	0.768501	−	0.732630i
$949$	−1.55216e10	−	1.55216e10i	−0.589529	−	0.589529i
$950$	3.04206e10	+	3.11563e10i	1.15116	+	1.17900i
$951$			1.17167e10i			0.441749i
$952$	−6.44715e8	+	1.79825e10i	−0.0242180	+	0.675491i
$953$			2.06035e10i			0.771108i	0.922685	+	0.385554i	$0.125990\pi$
$953$			2.06035e10i			0.771108i	−0.922685	+	0.385554i	$0.874010\pi$
$954$	9.86431e9	−	9.63141e9i	0.367830	−	0.359145i
$955$	−2.01777e9	−	2.01777e9i	−0.0749652	−	0.0749652i
$956$	4.59827e10	+	1.09880e9i	1.70213	+	0.0406740i
$957$	2.50792e9	−	2.50792e9i	0.0924956	−	0.0924956i
$958$	1.20034e10	+	1.43396e8i	0.441089	+	0.00526937i
$959$	−1.25299e10			−0.458756
$960$	−3.45714e9	−	2.48213e8i	−0.126115	−	0.00905471i
$961$	1.75370e10			0.637415
$962$	1.90464e10	+	2.27533e8i	0.689762	+	0.00824008i
$963$	−2.46309e9	+	2.46309e9i	−0.0888766	+	0.0888766i
$964$	1.12041e10	+	2.67734e8i	0.402818	+	0.00962572i
$965$	−3.70952e9	−	3.70952e9i	−0.132884	−	0.132884i
$966$	2.52353e9	−	2.46395e9i	0.0900717	−	0.0879450i
$967$			4.60290e10i			1.63696i	0.574533	+	0.818481i	$0.305184\pi$
$967$			4.60290e10i			1.63696i	−0.574533	+	0.818481i	$0.694816\pi$
$968$	9.87910e8	−	2.75549e10i	0.0350069	−	0.976416i
$969$		−	5.22536e10i		−	1.84494i
$970$	−1.49988e9	−	1.53615e9i	−0.0527661	−	0.0540421i
$971$	1.76045e10	+	1.76045e10i	0.617100	+	0.617100i	0.944787	−	0.327686i	$-0.106269\pi$
$971$	1.76045e10	+	1.76045e10i	0.617100	+	0.617100i	−0.327686	+	0.944787i	$0.606269\pi$
$972$	−1.46009e10	+	1.39194e10i	−0.509973	+	0.486169i
$973$	7.98509e9	−	7.98509e9i	0.277897	−	0.277897i
$974$	−4.98689e7	+	4.17443e9i	−0.00172931	+	0.144758i
$975$	1.09266e10			0.377546
$976$	3.34637e9	−	3.04094e9i	0.115213	−	0.104697i
$977$	−2.25205e10			−0.772587			−0.386294	−	0.922376i	$-0.626245\pi$
$977$	−2.25205e10			−0.772587			−0.386294	+	0.922376i	$0.626245\pi$
$978$	−980683.	+	8.20912e7i	−3.35230e−5	+	0.00280615i
$979$	1.30552e9	−	1.30552e9i	0.0444676	−	0.0444676i
$980$	−2.47247e9	−	2.59353e9i	−0.0839150	−	0.0880237i
$981$	−7.89702e9	−	7.89702e9i	−0.267068	−	0.267068i
$982$	−2.76644e10	−	2.83334e10i	−0.932248	−	0.954791i
$983$			2.50806e10i			0.842173i	0.907020	+	0.421087i	$0.138351\pi$
$983$			2.50806e10i			0.842173i	−0.907020	+	0.421087i	$0.861649\pi$
$984$	5.55042e9	+	5.96322e9i	0.185713	+	0.199525i
$985$			7.47775e9i			0.249312i
$986$	−3.24723e10	+	3.17056e10i	−1.07881	+	1.05334i
$987$	−6.16573e9	−	6.16573e9i	−0.204115	−	0.204115i
$988$	6.00347e8	−	2.51234e10i	0.0198040	−	0.828760i
$989$	6.66430e7	−	6.66430e7i	0.00219062	−	0.00219062i
$990$	2.77695e8	+	3.31742e6i	0.00909589	+	0.000108662i
$991$	−2.15255e10			−0.702580			−0.351290	−	0.936267i	$-0.614257\pi$
$991$	−2.15255e10			−0.702580			−0.351290	+	0.936267i	$0.614257\pi$
$992$	3.92731e10	+	2.34852e9i	1.27733	+	0.0763841i
$993$	−1.68794e9			−0.0547060
$994$	−2.48892e10	−	2.97333e8i	−0.803819	−	0.00960263i
$995$	2.79915e9	−	2.79915e9i	0.0900837	−	0.0900837i
$996$	−2.21849e8	+	9.28396e9i	−0.00711459	+	0.297732i
$997$	2.61314e9	+	2.61314e9i	0.0835084	+	0.0835084i	0.747627	−	0.664119i	$-0.231193\pi$
$997$	2.61314e9	+	2.61314e9i	0.0835084	+	0.0835084i	−0.664119	+	0.747627i	$0.731193\pi$
$998$	−4.15590e10	+	4.05778e10i	−1.32345	+	1.29221i
$999$		−	4.82004e10i		−	1.52958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.8.e.a.5.13	✓	26
4.3	odd	2		64.8.e.a.49.4		26
8.3	odd	2		128.8.e.a.97.10		26
8.5	even	2		128.8.e.b.97.4		26
16.3	odd	4		64.8.e.a.17.4		26
16.5	even	4		128.8.e.b.33.4		26
16.11	odd	4		128.8.e.a.33.10		26
16.13	even	4	inner	16.8.e.a.13.13	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.13	✓	26	1.1	even	1	trivial
16.8.e.a.13.13	yes	26	16.13	even	4	inner
64.8.e.a.17.4		26	16.3	odd	4
64.8.e.a.49.4		26	4.3	odd	2
128.8.e.a.33.10		26	16.11	odd	4
128.8.e.a.97.10		26	8.3	odd	2
128.8.e.b.33.4		26	16.5	even	4
128.8.e.b.97.4		26	8.5	even	2

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.3129 + 0.135147i) q^{2} +(26.1364 - 26.1364i) q^{3} +(127.963 + 3.05781i) q^{4} +(-31.6175 - 31.6175i) q^{5} +(299.211 - 292.146i) q^{6} -444.381i q^{7} +(1447.22 + 51.8865i) q^{8} +820.775i q^{9} +O(q^{10})\)	\(q+(11.3129 + 0.135147i) q^{2} +(26.1364 - 26.1364i) q^{3} +(127.963 + 3.05781i) q^{4} +(-31.6175 - 31.6175i) q^{5} +(299.211 - 292.146i) q^{6} -444.381i q^{7} +(1447.22 + 51.8865i) q^{8} +820.775i q^{9} +(-353.412 - 361.958i) q^{10} +(472.948 + 472.948i) q^{11} +(3424.43 - 3264.59i) q^{12} +(-2745.87 + 2745.87i) q^{13} +(60.0567 - 5027.24i) q^{14} -1652.73 q^{15} +(16365.3 + 782.575i) q^{16} -27961.3 q^{17} +(-110.925 + 9285.35i) q^{18} +(-35750.5 + 35750.5i) q^{19} +(-3949.20 - 4142.56i) q^{20} +(-11614.5 - 11614.5i) q^{21} +(5286.49 + 5414.33i) q^{22} +18979.1i q^{23} +(39181.4 - 36469.1i) q^{24} -76125.7i q^{25} +(-31434.8 + 30692.6i) q^{26} +(78612.5 + 78612.5i) q^{27} +(1358.83 - 56864.5i) q^{28} +(101443. - 101443. i) q^{29} +(-18697.2 - 223.362i) q^{30} +212249. q^{31} +(185033. + 11064.9i) q^{32} +24722.3 q^{33} +(-316324. - 3778.89i) q^{34} +(-14050.2 + 14050.2i) q^{35} +(-2509.77 + 105029. i) q^{36} +(-306569. - 306569. i) q^{37} +(-409274. + 399611. i) q^{38} +143534. i q^{39} +(-44117.1 - 47398.1i) q^{40} +152195. i q^{41} +(-129824. - 132964. i) q^{42} +(-3511.39 - 3511.39i) q^{43} +(59073.8 + 61966.2i) q^{44} +(25950.8 - 25950.8i) q^{45} +(-2564.96 + 214708. i) q^{46} +530864. q^{47} +(448184. - 407277. i) q^{48} +626069. q^{49} +(10288.2 - 861202. i) q^{50} +(-730809. + 730809. i) q^{51} +(-359767. + 342974. i) q^{52} +(-1.04981e6 - 1.04981e6i) q^{53} +(878711. + 899959. i) q^{54} -29906.8i q^{55} +(23057.4 - 643119. i) q^{56} +1.86878e6i q^{57} +(1.16133e6 - 1.13391e6i) q^{58} +(-1.13322e6 - 1.13322e6i) q^{59} +(-211490. - 5053.75i) q^{60} +(195148. - 195148. i) q^{61} +(2.40115e6 + 28684.8i) q^{62} +364737. q^{63} +(2.09177e6 + 150183. i) q^{64} +173635. q^{65} +(279681. + 3341.15i) q^{66} +(-1.52689e6 + 1.52689e6i) q^{67} +(-3.57803e6 - 85500.3i) q^{68} +(496045. + 496045. i) q^{69} +(-160847. + 157050. i) q^{70} -4.95086e6i q^{71} +(-42587.2 + 1.18785e6i) q^{72} +5.65272e6i q^{73} +(-3.42676e6 - 3.50962e6i) q^{74} +(-1.98965e6 - 1.98965e6i) q^{75} +(-4.68408e6 + 4.46545e6i) q^{76} +(210169. - 210169. i) q^{77} +(-19398.2 + 1.62379e6i) q^{78} +5.88689e6 q^{79} +(-492686. - 542172. i) q^{80} +2.31426e6 q^{81} +(-20568.7 + 1.72177e6i) q^{82} +(-1.38794e6 + 1.38794e6i) q^{83} +(-1.45072e6 - 1.52175e6i) q^{84} +(884066. + 884066. i) q^{85} +(-39249.5 - 40198.6i) q^{86} -5.30273e6i q^{87} +(659922. + 709001. i) q^{88} -2.76039e6i q^{89} +(297086. - 290072. i) q^{90} +(1.22021e6 + 1.22021e6i) q^{91} +(-58034.4 + 2.42863e6i) q^{92} +(5.54742e6 - 5.54742e6i) q^{93} +(6.00561e6 + 71744.6i) q^{94} +2.26068e6 q^{95} +(5.12530e6 - 4.54691e6i) q^{96} +4.24399e6 q^{97} +(7.08265e6 + 84611.2i) q^{98} +(-388184. + 388184. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8	\( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^3 - 184 * q^4 - 2 * q^5 - 176 * q^6 - 1004 * q^8 + 12972 * q^10 + 1202 * q^11 - 27356 * q^12 - 2 * q^13 + 22268 * q^14 - 27004 * q^15 + 13336 * q^16 - 4 * q^17 - 29346 * q^18 + 60582 * q^19 + 46204 * q^20 + 4372 * q^21 - 44348 * q^22 - 59216 * q^24 - 35960 * q^26 - 233672 * q^27 + 220312 * q^28 - 51690 * q^29 + 27636 * q^30 + 357488 * q^31 - 248632 * q^32 - 4 * q^33 + 924660 * q^34 - 252004 * q^35 - 1015508 * q^36 + 415574 * q^37 - 5472 * q^38 - 1121976 * q^40 + 124600 * q^42 + 569754 * q^43 - 758620 * q^44 + 151874 * q^45 + 2335660 * q^46 - 2076464 * q^47 + 4141288 * q^48 - 1647090 * q^49 - 787194 * q^50 + 2609508 * q^51 + 410324 * q^52 + 907814 * q^53 - 7404512 * q^54 - 4093160 * q^56 - 1860712 * q^58 - 4865142 * q^59 + 5147328 * q^60 + 2279886 * q^61 + 6274096 * q^62 + 8295108 * q^63 + 10452224 * q^64 - 1426892 * q^65 + 10937812 * q^66 - 5564458 * q^67 - 7403760 * q^68 - 4786076 * q^69 - 22140800 * q^70 - 25293948 * q^72 - 13177044 * q^74 + 6212566 * q^75 + 17814260 * q^76 + 7604308 * q^77 + 37993916 * q^78 - 9598912 * q^79 + 40047272 * q^80 - 5314414 * q^81 + 22858240 * q^82 + 4531198 * q^83 - 30159704 * q^84 + 7377748 * q^85 - 54129468 * q^86 - 59216392 * q^88 - 33515304 * q^90 + 2587652 * q^91 + 21810936 * q^92 - 14504144 * q^93 + 77196112 * q^94 - 4900620 * q^95 + 116940464 * q^96 - 4 * q^97 + 21823866 * q^98 + 18815006 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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