LMFDB - Embedded newform 60.7.l.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.95256 + 0.869892i) q^{2} +(26.9945 + 0.547129i) q^{3} +(62.4866 - 13.8357i) q^{4} +(-116.176 - 46.1326i) q^{5} +(-215.151 + 19.1312i) q^{6} +(371.962 + 371.962i) q^{7} +(-484.893 + 164.386i) q^{8} +(728.401 + 29.5389i) q^{9} +O(q^{10})$	\(q+(-7.95256 + 0.869892i) q^{2} +(26.9945 + 0.547129i) q^{3} +(62.4866 - 13.8357i) q^{4} +(-116.176 - 46.1326i) q^{5} +(-215.151 + 19.1312i) q^{6} +(371.962 + 371.962i) q^{7} +(-484.893 + 164.386i) q^{8} +(728.401 + 29.5389i) q^{9} +(964.025 + 265.812i) q^{10} -569.699 q^{11} +(1694.36 - 339.300i) q^{12} +(-819.948 - 819.948i) q^{13} +(-3281.62 - 2634.49i) q^{14} +(-3110.86 - 1308.89i) q^{15} +(3713.14 - 1729.10i) q^{16} +(3518.63 + 3518.63i) q^{17} +(-5818.35 + 398.720i) q^{18} +1210.25 q^{19} +(-7897.70 - 1275.29i) q^{20} +(9837.41 + 10244.4i) q^{21} +(4530.57 - 495.576i) q^{22} +(10792.2 + 10792.2i) q^{23} +(-13179.4 + 4172.22i) q^{24} +(11368.6 + 10719.0i) q^{25} +(7233.95 + 5807.42i) q^{26} +(19646.6 + 1195.92i) q^{27} +(28389.0 + 18096.3i) q^{28} +20856.1 q^{29} +(25877.9 + 7702.91i) q^{30} +37575.1i q^{31} +(-28024.9 + 16980.8i) q^{32} +(-15378.7 - 311.699i) q^{33} +(-31043.0 - 24921.3i) q^{34} +(-26053.4 - 60372.6i) q^{35} +(45924.0 - 8232.19i) q^{36} +(-36838.4 + 36838.4i) q^{37} +(-9624.58 + 1052.79i) q^{38} +(-21685.4 - 22582.7i) q^{39} +(63916.3 + 3271.71i) q^{40} +76619.8i q^{41} +(-87144.2 - 72912.0i) q^{42} +(90895.3 - 90895.3i) q^{43} +(-35598.5 + 7882.21i) q^{44} +(-83259.8 - 37034.8i) q^{45} +(-95213.5 - 76437.5i) q^{46} +(17525.1 - 17525.1i) q^{47} +(101180. - 44644.4i) q^{48} +159063. i q^{49} +(-99733.6 - 75353.9i) q^{50} +(93058.4 + 96908.7i) q^{51} +(-62580.3 - 39891.1i) q^{52} +(148904. - 148904. i) q^{53} +(-157281. + 7579.85i) q^{54} +(66185.1 + 26281.7i) q^{55} +(-241507. - 119216. i) q^{56} +(32670.0 + 662.162i) q^{57} +(-165859. + 18142.5i) q^{58} -192836. i q^{59} +(-212496. - 38746.9i) q^{60} -277312. q^{61} +(-32686.2 - 298818. i) q^{62} +(259951. + 281925. i) q^{63} +(208098. - 159419. i) q^{64} +(57431.6 + 133084. i) q^{65} +(122571. - 10899.0i) q^{66} +(95247.8 + 95247.8i) q^{67} +(268550. + 171184. i) q^{68} +(285424. + 297234. i) q^{69} +(259709. + 457453. i) q^{70} -183408. q^{71} +(-358052. + 105416. i) q^{72} +(-67928.2 - 67928.2i) q^{73} +(260914. - 325005. i) q^{74} +(301024. + 295573. i) q^{75} +(75624.3 - 16744.7i) q^{76} +(-211907. - 211907. i) q^{77} +(192099. + 160726. i) q^{78} -790523. q^{79} +(-511145. + 29581.8i) q^{80} +(529696. + 43032.4i) q^{81} +(-66651.0 - 609324. i) q^{82} +(-500605. - 500605. i) q^{83} +(756446. + 504032. i) q^{84} +(-246456. - 571103. i) q^{85} +(-643782. + 801920. i) q^{86} +(562998. + 11411.0i) q^{87} +(276243. - 93650.6i) q^{88} -399264. q^{89} +(694345. + 222094. i) q^{90} -609979. i q^{91} +(823684. + 525048. i) q^{92} +(-20558.4 + 1.01432e6i) q^{93} +(-124124. + 154614. i) q^{94} +(-140601. - 55832.0i) q^{95} +(-765807. + 443054. i) q^{96} +(913843. - 913843. i) q^{97} +(-138368. - 1.26496e6i) q^{98} +(-414969. - 16828.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−7.95256	+	0.869892i	−0.994071	+	0.108736i
$2$	−7.95256	+	0.869892i	−0.994071	+	0.108736i
$3$	26.9945	+	0.547129i	0.999795	+	0.0202640i
$3$	26.9945	+	0.547129i	0.999795	+	0.0202640i
$4$	62.4866	−	13.8357i	0.976353	−	0.216183i
$5$	−116.176	−	46.1326i	−0.929405	−	0.369061i
$5$	−116.176	−	46.1326i	−0.929405	−	0.369061i
$6$	−215.151	+	19.1312i	−0.996070	+	0.0885703i
$7$	371.962	+	371.962i	1.08444	+	1.08444i	0.996090	+	0.0883489i	$0.0281591\pi$
$7$	371.962	+	371.962i	1.08444	+	1.08444i	0.0883489	+	0.996090i	$0.471841\pi$
$8$	−484.893	+	164.386i	−0.947057	+	0.321067i
$9$	728.401	+	29.5389i	0.999179	+	0.0405198i
$10$	964.025	+	265.812i	0.964025	+	0.265812i
$11$	−569.699			−0.428023			−0.214012	−	0.976831i	$-0.568653\pi$
$11$	−569.699			−0.428023			−0.214012	+	0.976831i	$0.568653\pi$
$12$	1694.36	−	339.300i	0.980533	−	0.196354i
$13$	−819.948	−	819.948i	−0.373212	−	0.373212i	0.495433	−	0.868646i	$-0.335009\pi$
$13$	−819.948	−	819.948i	−0.373212	−	0.373212i	−0.868646	+	0.495433i	$0.835009\pi$
$14$	−3281.62	−	2634.49i	−1.19593	−	0.960090i
$15$	−3110.86	−	1308.89i	−0.921736	−	0.387819i
$16$	3713.14	−	1729.10i	0.906529	−	0.422143i
$17$	3518.63	+	3518.63i	0.716188	+	0.716188i	0.967822	−	0.251634i	$-0.0809680\pi$
$17$	3518.63	+	3518.63i	0.716188	+	0.716188i	−0.251634	+	0.967822i	$0.580968\pi$
$18$	−5818.35	+	398.720i	−0.997660	+	0.0683677i
$19$	1210.25			0.176447			0.0882234	−	0.996101i	$-0.471881\pi$
$19$	1210.25			0.176447			0.0882234	+	0.996101i	$0.471881\pi$
$20$	−7897.70	−	1275.29i	−0.987212	−	0.159412i
$21$	9837.41	+	10244.4i	1.06224	+	1.10619i
$22$	4530.57	−	495.576i	0.425485	−	0.0465417i
$23$	10792.2	+	10792.2i	0.887004	+	0.887004i	0.994234	−	0.107230i	$-0.0341982\pi$
$23$	10792.2	+	10792.2i	0.887004	+	0.887004i	−0.107230	+	0.994234i	$0.534198\pi$
$24$	−13179.4	+	4172.22i	−0.953368	+	0.301810i
$25$	11368.6	+	10719.0i	0.727588	+	0.686014i
$26$	7233.95	+	5807.42i	0.411581	+	0.330418i
$27$	19646.6	+	1195.92i	0.998152	+	0.0607588i
$28$	28389.0	+	18096.3i	1.29323	+	0.824357i
$29$	20856.1			0.855142			0.427571	−	0.903982i	$-0.359369\pi$
$29$	20856.1			0.855142			0.427571	+	0.903982i	$0.359369\pi$
$30$	25877.9	+	7702.91i	0.958440	+	0.285293i
$31$			37575.1i			1.26129i	0.776072	+	0.630644i	$0.217209\pi$
$31$			37575.1i			1.26129i	−0.776072	+	0.630644i	$0.782791\pi$
$32$	−28024.9	+	16980.8i	−0.855252	+	0.518212i
$33$	−15378.7	−	311.699i	−0.427935	−	0.00867348i
$34$	−31043.0	−	24921.3i	−0.789817	−	0.634066i
$35$	−26053.4	−	60372.6i	−0.607659	−	1.40811i
$36$	45924.0	−	8232.19i	0.984311	−	0.176444i
$37$	−36838.4	+	36838.4i	−0.727269	+	0.727269i	−0.970075	−	0.242806i	$-0.921932\pi$
$37$	−36838.4	+	36838.4i	−0.727269	+	0.727269i	0.242806	+	0.970075i	$0.421932\pi$
$38$	−9624.58	+	1052.79i	−0.175401	+	0.0191862i
$39$	−21685.4	−	22582.7i	−0.365573	−	0.380699i
$40$	63916.3	+	3271.71i	0.998692	+	0.0511204i
$41$			76619.8i			1.11170i	0.831281	+	0.555852i	$0.187608\pi$
$41$			76619.8i			1.11170i	−0.831281	+	0.555852i	$0.812392\pi$
$42$	−87144.2	−	72912.0i	−1.17623	−	0.984128i
$43$	90895.3	−	90895.3i	1.14324	−	1.14324i	0.155382	−	0.987854i	$-0.450339\pi$
$43$	90895.3	−	90895.3i	1.14324	−	1.14324i	0.987854	−	0.155382i	$-0.0496610\pi$
$44$	−35598.5	+	7882.21i	−0.417902	+	0.0925315i
$45$	−83259.8	−	37034.8i	−0.913688	−	0.406417i
$46$	−95213.5	−	76437.5i	−0.978194	−	0.785295i
$47$	17525.1	−	17525.1i	0.168797	−	0.168797i	−0.617653	−	0.786451i	$-0.711916\pi$
$47$	17525.1	−	17525.1i	0.168797	−	0.168797i	0.786451	+	0.617653i	$0.211916\pi$
$48$	101180.	−	44644.4i	0.914898	−	0.403686i
$49$			159063.i			1.35201i
$50$	−99733.6	−	75353.9i	−0.797869	−	0.602831i
$51$	93058.4	+	96908.7i	0.701528	+	0.730554i
$52$	−62580.3	−	39891.1i	−0.445069	−	0.283705i
$53$	148904.	−	148904.i	1.00018	−	1.00018i	0.000179023	−	1.00000i	$-0.499943\pi$
$53$	148904.	−	148904.i	1.00018	−	1.00018i	1.00000		0.000179023i	$-5.69848e-5\pi$
$54$	−157281.	+	7579.85i	−0.998841	+	0.0481370i
$55$	66185.1	+	26281.7i	0.397807	+	0.157967i
$56$	−241507.	−	119216.i	−1.37520	−	0.678847i
$57$	32670.0	+	662.162i	0.176411	+	0.00357553i
$58$	−165859.	+	18142.5i	−0.850072	+	0.0929852i
$59$		−	192836.i		−	0.938927i	−0.882952	−	0.469464i	$-0.844447\pi$
$59$		−	192836.i		−	0.938927i	0.882952	−	0.469464i	$-0.155553\pi$
$60$	−212496.	−	38746.9i	−0.983779	−	0.179384i
$61$	−277312.			−1.22174			−0.610871	−	0.791730i	$-0.709181\pi$
$61$	−277312.			−1.22174			−0.610871	+	0.791730i	$0.709181\pi$
$62$	−32686.2	−	298818.i	−0.137148	−	1.25381i
$63$	259951.	+	281925.i	1.03961	+	1.12749i
$64$	208098.	−	159419.i	0.793832	−	0.608137i
$65$	57431.6	+	133084.i	0.209127	+	0.484604i
$66$	122571.	−	10899.0i	0.426341	−	0.0379101i
$67$	95247.8	+	95247.8i	0.316687	+	0.316687i	0.847493	−	0.530806i	$-0.178111\pi$
$67$	95247.8	+	95247.8i	0.316687	+	0.316687i	−0.530806	+	0.847493i	$0.678111\pi$
$68$	268550.	+	171184.i	0.854080	+	0.544424i
$69$	285424.	+	297234.i	0.868847	+	0.904796i
$70$	259709.	+	457453.i	0.757168	+	1.33368i
$71$	−183408.			−0.512440			−0.256220	−	0.966619i	$-0.582477\pi$
$71$	−183408.			−0.512440			−0.256220	+	0.966619i	$0.582477\pi$
$72$	−358052.	+	105416.i	−0.959288	+	0.282429i
$73$	−67928.2	−	67928.2i	−0.174615	−	0.174615i	0.614389	−	0.789004i	$-0.289403\pi$
$73$	−67928.2	−	67928.2i	−0.174615	−	0.174615i	−0.789004	+	0.614389i	$0.789403\pi$
$74$	260914.	−	325005.i	0.643876	−	0.802037i
$75$	301024.	+	295573.i	0.713537	+	0.700617i
$76$	75624.3	−	16744.7i	0.172274	−	0.0381449i
$77$	−211907.	−	211907.i	−0.464165	−	0.464165i
$78$	192099.	+	160726.i	0.404801	+	0.338690i
$79$	−790523.			−1.60337			−0.801684	−	0.597748i	$-0.796062\pi$
$79$	−790523.			−1.60337			−0.801684	+	0.597748i	$0.796062\pi$
$80$	−511145.	+	29581.8i	−0.998330	+	0.0577770i
$81$	529696.	+	43032.4i	0.996716	+	0.0809730i
$82$	−66651.0	−	609324.i	−0.120883	−	1.10511i
$83$	−500605.	−	500605.i	−0.875510	−	0.875510i	0.117556	−	0.993066i	$-0.462494\pi$
$83$	−500605.	−	500605.i	−0.875510	−	0.875510i	−0.993066	+	0.117556i	$0.962494\pi$
$84$	756446.	+	504032.i	1.27626	+	0.850394i
$85$	−246456.	−	571103.i	−0.401312	−	0.929946i
$86$	−643782.	+	801920.i	−1.01215	+	1.26077i
$87$	562998.	+	11411.0i	0.854967	+	0.0173286i
$88$	276243.	−	93650.6i	0.405362	−	0.137424i
$89$	−399264.			−0.566357			−0.283178	−	0.959067i	$-0.591389\pi$
$89$	−399264.			−0.566357			−0.283178	+	0.959067i	$0.591389\pi$
$90$	694345.	+	222094.i	0.952462	+	0.304656i
$91$		−	609979.i		−	0.809452i
$92$	823684.	+	525048.i	1.05778	+	0.674273i
$93$	−20558.4	+	1.01432e6i	−0.0255588	+	1.26103i
$94$	−124124.	+	154614.i	−0.149442	+	0.186151i
$95$	−140601.	−	55832.0i	−0.163991	−	0.0651196i
$96$	−765807.	+	443054.i	−0.865577	+	0.500775i
$97$	913843.	−	913843.i	1.00128	−	1.00128i	0.00128293	−	0.999999i	$-0.499592\pi$
$97$	913843.	−	913843.i	1.00128	−	1.00128i	0.999999	−	0.00128293i	$-0.000408371\pi$
$98$	−138368.	−	1.26496e6i	−0.147013	−	1.34400i
$99$	−414969.	−	16828.3i	−0.427672	−	0.0173434i
$100$	858688.	+	512499.i	0.858688	+	0.512499i
$101$			1.21566e6i			1.17990i	0.807438	+	0.589952i	$0.200853\pi$
$101$			1.21566e6i			1.17990i	−0.807438	+	0.589952i	$0.799147\pi$
$102$	−824353.	−	689722.i	−0.776806	−	0.649940i
$103$	529852.	−	529852.i	0.484890	−	0.484890i	−0.421799	−	0.906689i	$-0.638601\pi$
$103$	529852.	−	529852.i	0.484890	−	0.484890i	0.906689	+	0.421799i	$0.138601\pi$
$104$	532375.	+	262799.i	0.473279	+	0.233627i
$105$	−670265.	−	1.64398e6i	−0.579000	−	1.42013i
$106$	−1.05464e6	+	1.31370e6i	−0.885493	+	1.10300i
$107$	−538521.	+	538521.i	−0.439593	+	0.439593i	−0.891875	−	0.452282i	$-0.850610\pi$
$107$	−538521.	+	538521.i	−0.439593	+	0.439593i	0.452282	+	0.891875i	$0.350610\pi$
$108$	1.24420e6	−	197097.i	0.987684	−	0.156462i
$109$			1.22351e6i			0.944773i	0.881391	+	0.472387i	$0.156607\pi$
$109$			1.22351e6i			0.944773i	−0.881391	+	0.472387i	$0.843393\pi$
$110$	−549204.	−	151433.i	−0.412625	−	0.113774i
$111$	−1.01459e6	+	974276.i	−0.741857	+	0.712382i
$112$	2.02431e6	+	737991.i	1.44086	+	0.525288i
$113$	1.26193e6	−	1.26193e6i	0.874580	−	0.874580i	−0.118387	−	0.992968i	$-0.537772\pi$
$113$	1.26193e6	−	1.26193e6i	0.874580	−	0.874580i	0.992968	+	0.118387i	$0.0377724\pi$
$114$	−260386.	+	23153.5i	−0.175753	+	0.0156279i
$115$	−755917.	−	1.75166e6i	−0.497028	−	1.15174i
$116$	1.30322e6	−	288559.i	0.834921	−	0.184868i
$117$	−573031.	−	621471.i	−0.357783	−	0.388028i
$118$	167746.	+	1.53354e6i	0.102096	+	0.933360i
$119$			2.61760e6i			1.55332i
$120$	1.72360e6	+	123288.i	0.997452	+	0.0713475i
$121$	−1.44700e6			−0.816796
$122$	2.20534e6	−	241232.i	1.21450	−	0.132848i
$123$	−41920.9	+	2.06831e6i	−0.0225276	+	1.11148i
$124$	519879.	+	2.34794e6i	0.272670	+	1.23146i
$125$	−826256.	−	1.76975e6i	−0.423043	−	0.906110i
$126$	−2.31252e6	−	2.01590e6i	−1.15604	−	1.00776i
$127$	−273003.	−	273003.i	−0.133277	−	0.133277i	0.637321	−	0.770598i	$-0.280043\pi$
$127$	−273003.	−	273003.i	−0.133277	−	0.133277i	−0.770598	+	0.637321i	$0.780043\pi$
$128$	−1.51624e6	+	1.44882e6i	−0.722999	+	0.690850i
$129$	2.50340e6	−	2.40394e6i	1.16617	−	1.11984i
$130$	−572498.	−	1.00840e6i	−0.260582	−	0.458990i
$131$	1.63515e6			0.727351			0.363675	−	0.931526i	$-0.381522\pi$
$131$	1.63515e6			0.727351			0.363675	+	0.931526i	$0.381522\pi$
$132$	−965275.	+	193299.i	−0.419691	+	0.0840442i
$133$	450167.	+	450167.i	0.191346	+	0.191346i
$134$	−840320.	−	674609.i	−0.349245	−	0.280374i
$135$	−2.22729e6	−	1.04529e6i	−0.905264	−	0.424849i
$136$	−2.28457e6	−	1.12775e6i	−0.908215	−	0.448326i
$137$	−2.38860e6	−	2.38860e6i	−0.928928	−	0.928928i	0.0687086	−	0.997637i	$-0.478112\pi$
$137$	−2.38860e6	−	2.38860e6i	−0.928928	−	0.928928i	−0.997637	+	0.0687086i	$0.978112\pi$
$138$	−2.52842e6	−	2.11548e6i	−0.962080	−	0.804956i
$139$	−382208.			−0.142317			−0.0711583	−	0.997465i	$-0.522670\pi$
$139$	−382208.			−0.142317			−0.0711583	+	0.997465i	$0.522670\pi$
$140$	−2.46329e6	−	3.41201e6i	−0.897699	−	1.24344i
$141$	482668.	−	463491.i	0.172183	−	0.165342i
$142$	1.45856e6	−	159545.i	0.509401	−	0.0557209i
$143$	467123.	+	467123.i	0.159744	+	0.159744i
$144$	2.75573e6	−	1.14979e6i	0.922890	−	0.385064i
$145$	−2.42297e6	−	962145.i	−0.794774	−	0.315600i
$146$	599293.	+	481113.i	0.192567	+	0.154593i
$147$	−87028.0	+	4.29382e6i	−0.0273973	+	1.35174i
$148$	−1.79222e6	+	2.81159e6i	−0.552848	+	0.867295i
$149$	442061.			0.133636			0.0668180	−	0.997765i	$-0.478715\pi$
$149$	442061.			0.133636			0.0668180	+	0.997765i	$0.478715\pi$
$150$	−2.65103e6	−	2.08871e6i	−0.785489	−	0.618876i
$151$		−	5.30769e6i		−	1.54161i	−0.637071	−	0.770805i	$-0.719854\pi$
$151$		−	5.30769e6i		−	1.54161i	0.637071	−	0.770805i	$-0.280146\pi$
$152$	−586841.	+	198948.i	−0.167105	+	0.0566512i
$153$	2.45904e6	+	2.66691e6i	0.686580	+	0.744620i
$154$	1.86954e6	+	1.50086e6i	0.511884	+	0.410941i
$155$	1.73344e6	−	4.36531e6i	0.465492	−	1.17225i
$156$	−1.66750e6	−	1.11108e6i	−0.439229	−	0.292665i
$157$	−5.10852e6	+	5.10852e6i	−1.32007	+	1.32007i	−0.406349	+	0.913718i	$0.633198\pi$
$157$	−5.10852e6	+	5.10852e6i	−1.32007	+	1.32007i	−0.913718	+	0.406349i	$0.866802\pi$
$158$	6.28668e6	−	687669.i	1.59386	−	0.174345i
$159$	4.10104e6	−	3.93810e6i	1.02024	−	0.979706i
$160$	4.03918e6	−	679892.i	0.986128	−	0.165989i
$161$			8.02857e6i			1.92380i
$162$	−4.24987e6	+	118561.i	−0.999611	+	0.0278866i
$163$	1.98755e6	−	1.98755e6i	0.458939	−	0.458939i	−0.439368	−	0.898307i	$-0.644798\pi$
$163$	1.98755e6	−	1.98755e6i	0.458939	−	0.458939i	0.898307	+	0.439368i	$0.144798\pi$
$164$	1.06009e6	+	4.78771e6i	0.240332	+	1.08542i
$165$	1.77225e6	+	745672.i	0.394524	+	0.165995i
$166$	4.41657e6	+	3.54562e6i	0.965518	+	0.775119i
$167$	−1.51470e6	+	1.51470e6i	−0.325220	+	0.325220i	−0.850765	−	0.525546i	$-0.823861\pi$
$167$	−1.51470e6	+	1.51470e6i	−0.325220	+	0.325220i	0.525546	+	0.850765i	$0.323861\pi$
$168$	−6.45414e6	−	3.35032e6i	−1.36116	−	0.706575i
$169$		−	3.48218e6i		−	0.721425i
$170$	2.45675e6	+	4.32734e6i	0.500051	+	0.880795i
$171$	881547.	+	35749.4i	0.176302	+	0.00714958i
$172$	4.42213e6	−	6.93734e6i	0.869053	−	1.36335i
$173$	−2.13598e6	+	2.13598e6i	−0.412534	+	0.412534i	−0.882620	−	0.470087i	$-0.844223\pi$
$173$	−2.13598e6	+	2.13598e6i	−0.412534	+	0.412534i	0.470087	+	0.882620i	$0.344223\pi$
$174$	−4.48721e6	+	399001.i	−0.851782	+	0.0757402i
$175$	241622.	+	8.21573e6i	0.0450841	+	1.53296i
$176$	−2.11537e6	+	985064.i	−0.388016	+	0.180687i
$177$	105506.	−	5.20550e6i	0.0190265	−	0.938735i
$178$	3.17517e6	−	347316.i	0.562999	−	0.0615836i
$179$		−	3.29925e6i		−	0.575249i	−0.957743	−	0.287624i	$-0.907135\pi$
$179$		−	3.29925e6i		−	0.575249i	0.957743	−	0.287624i	$-0.0928655\pi$
$180$	−5.71502e6	−	1.16221e6i	−0.979942	−	0.199282i
$181$	−3.89681e6			−0.657164			−0.328582	−	0.944475i	$-0.606571\pi$
$181$	−3.89681e6			−0.657164			−0.328582	+	0.944475i	$0.606571\pi$
$182$	530616.	+	4.85090e6i	0.0880169	+	0.804652i
$183$	−7.48589e6	−	151726.i	−1.22149	−	0.0247574i
$184$	−7.00714e6	−	3.45897e6i	−1.12483	−	0.555255i
$185$	5.97917e6	−	2.58027e6i	0.944334	−	0.407521i
$186$	−718855.	−	8.08431e6i	−0.111713	−	1.25633i
$187$	−2.00456e6	−	2.00456e6i	−0.306545	−	0.306545i
$188$	852609.	−	1.33755e6i	0.128315	−	0.201297i
$189$	6.86297e6	+	7.75265e6i	1.01655	+	1.14832i
$190$	1.16671e6	+	321699.i	0.170099	+	0.0469018i
$191$	8.18028e6			1.17400			0.587000	−	0.809587i	$-0.300309\pi$
$191$	8.18028e6			1.17400			0.587000	+	0.809587i	$0.300309\pi$
$192$	5.70472e6	−	4.18958e6i	0.805992	−	0.591926i
$193$	6.56530e6	+	6.56530e6i	0.913235	+	0.913235i	0.996525	−	0.0832902i	$-0.0265428\pi$
$193$	6.56530e6	+	6.56530e6i	0.913235	+	0.913235i	−0.0832902	+	0.996525i	$0.526543\pi$
$194$	−6.47245e6	+	8.06234e6i	−0.886469	+	1.10422i
$195$	1.47752e6	+	3.62396e6i	0.199264	+	0.488742i
$196$	2.20076e6	+	9.93931e6i	0.292283	+	1.32004i
$197$	7.17332e6	+	7.17332e6i	0.938256	+	0.938256i	0.998202	−	0.0599458i	$-0.0190928\pi$
$197$	7.17332e6	+	7.17332e6i	0.938256	+	0.938256i	−0.0599458	+	0.998202i	$0.519093\pi$
$198$	3.31471e6	−	227150.i	0.427022	−	0.0292630i
$199$	2.14496e6			0.272183			0.136091	−	0.990696i	$-0.456546\pi$
$199$	2.14496e6			0.272183			0.136091	+	0.990696i	$0.456546\pi$
$200$	−7.27459e6	−	3.32872e6i	−0.909323	−	0.416090i
$201$	2.51905e6	+	2.62328e6i	0.310205	+	0.323040i
$202$	−1.05749e6	−	9.66758e6i	−0.128299	−	1.17291i
$203$	7.75767e6	+	7.75767e6i	0.927349	+	0.927349i
$204$	7.15570e6	+	4.76796e6i	0.842872	+	0.561619i
$205$	3.53467e6	−	8.90136e6i	0.410287	−	1.03322i
$206$	−3.75277e6	+	4.67460e6i	−0.429289	+	0.534740i
$207$	7.54225e6	+	8.17982e6i	0.850334	+	0.922217i
$208$	−4.46235e6	−	1.62682e6i	−0.495877	−	0.180779i
$209$	−689477.			−0.0755233
$210$	6.76041e6	+	1.24908e7i	0.729987	+	1.34875i
$211$		−	5.06414e6i		−	0.539086i	−0.962988	−	0.269543i	$-0.913127\pi$
$211$		−	5.06414e6i		−	0.539086i	0.962988	−	0.269543i	$-0.0868726\pi$
$212$	7.24429e6	−	1.13647e7i	0.760305	−	1.19275i
$213$	−4.95100e6	−	100348.i	−0.512335	−	0.0103841i
$214$	3.81417e6	−	4.75108e6i	0.389187	−	0.484787i
$215$	−1.47531e7	+	6.36658e6i	−1.48445	+	0.640606i
$216$	−9.72311e6	+	2.64974e6i	−0.964814	+	0.262932i
$217$	−1.39765e7	+	1.39765e7i	−1.36779	+	1.36779i
$218$	−1.06432e6	−	9.73003e6i	−0.102731	−	0.939171i
$219$	−1.79652e6	−	1.87085e6i	−0.171041	−	0.178117i
$220$	4.49931e6	+	726533.i	0.422550	+	0.0682319i
$221$		−	5.77019e6i		−	0.534580i
$222$	7.22105e6	−	8.63058e6i	0.659996	−	0.788825i
$223$	5.97945e6	−	5.97945e6i	0.539196	−	0.539196i	−0.384097	−	0.923293i	$-0.625487\pi$
$223$	5.97945e6	−	5.97945e6i	0.539196	−	0.539196i	0.923293	+	0.384097i	$0.125487\pi$
$224$	−1.67404e7	−	4.10799e6i	−1.48944	−	0.365499i
$225$	7.96425e6	+	8.14353e6i	0.699193	+	0.714933i
$226$	−8.93783e6	+	1.11333e7i	−0.774296	+	0.964493i
$227$	5.24471e6	−	5.24471e6i	0.448378	−	0.448378i	−0.446437	−	0.894815i	$-0.647307\pi$
$227$	5.24471e6	−	5.24471e6i	0.448378	−	0.448378i	0.894815	+	0.446437i	$0.147307\pi$
$228$	2.05060e6	−	410638.i	0.173012	−	0.0346461i
$229$		−	1.42606e7i		−	1.18749i	−0.804653	−	0.593746i	$-0.797648\pi$
$229$		−	1.42606e7i		−	1.18749i	0.804653	−	0.593746i	$-0.202352\pi$
$230$	7.53523e6	+	1.32726e7i	0.619317	+	1.09087i
$231$	−5.60436e6	−	5.83624e6i	−0.454664	−	0.473475i
$232$	−1.01130e7	+	3.42845e6i	−0.809868	+	0.274558i
$233$	−5.75974e6	+	5.75974e6i	−0.455339	+	0.455339i	−0.897122	−	0.441783i	$-0.854346\pi$
$233$	−5.75974e6	+	5.75974e6i	−0.455339	+	0.455339i	0.441783	+	0.897122i	$0.354346\pi$
$234$	5.09768e6	+	4.44382e6i	0.397855	+	0.346823i
$235$	−2.84446e6	+	1.22751e6i	−0.219178	+	0.0945847i
$236$	−2.66803e6	−	1.20497e7i	−0.202981	−	0.916724i
$237$	−2.13397e7	−	432518.i	−1.60304	−	0.0324907i
$238$	−2.27703e6	−	2.08166e7i	−0.168903	−	1.54411i
$239$		−	6.55628e6i		−	0.480246i	−0.970742	−	0.240123i	$-0.922812\pi$
$239$		−	6.55628e6i		−	0.480246i	0.970742	−	0.240123i	$-0.0771877\pi$
$240$	−1.38143e7	+	518883.i	−0.999295	+	0.0375349i
$241$	1.76003e7			1.25739			0.628693	−	0.777654i	$-0.283590\pi$
$241$	1.76003e7			1.25739			0.628693	+	0.777654i	$0.283590\pi$
$242$	1.15074e7	−	1.25874e6i	0.811953	−	0.0888155i
$243$	1.42753e7	+	1.45145e6i	0.994871	+	0.101154i
$244$	−1.73283e7	+	3.83682e6i	−1.19285	+	0.264120i
$245$	7.33800e6	−	1.84793e7i	0.498976	−	1.25657i
$246$	−1.46583e6	−	1.64848e7i	−0.0984640	−	1.10734i
$247$	−992341.	−	992341.i	−0.0658522	−	0.0658522i
$248$	−6.17682e6	−	1.82199e7i	−0.404958	−	1.19451i
$249$	−1.32397e7	−	1.37875e7i	−0.857589	−	0.893071i
$250$	8.11034e6	+	1.33553e7i	0.519062	+	0.854737i
$251$	−3.49880e6			−0.221257			−0.110629	−	0.993862i	$-0.535286\pi$
$251$	−3.49880e6			−0.221257			−0.110629	+	0.993862i	$0.535286\pi$
$252$	2.01441e7	+	1.40199e7i	1.25877	+	0.876081i
$253$	−6.14829e6	−	6.14829e6i	−0.379658	−	0.379658i
$254$	2.40856e6	+	1.93359e6i	0.146979	+	0.117995i
$255$	−6.34047e6	−	1.55515e7i	−0.382385	−	0.937887i
$256$	1.07977e7	−	1.28408e7i	0.643591	−	0.765370i
$257$	−1.67503e7	−	1.67503e7i	−0.986787	−	0.986787i	0.0131271	−	0.999914i	$-0.495821\pi$
$257$	−1.67503e7	−	1.67503e7i	−0.986787	−	0.986787i	−0.999914	+	0.0131271i	$0.995821\pi$
$258$	−1.78173e7	+	2.12952e7i	−1.03749	+	1.24000i
$259$	−2.74050e7			−1.57736
$260$	5.43003e6	+	7.52137e6i	0.308945	+	0.427934i
$261$	1.51916e7	+	616065.i	0.854440	+	0.0346502i
$262$	−1.30036e7	+	1.42240e6i	−0.723038	+	0.0790896i
$263$	−8.87284e6	−	8.87284e6i	−0.487748	−	0.487748i	0.419847	−	0.907595i	$-0.362084\pi$
$263$	−8.87284e6	−	8.87284e6i	−0.487748	−	0.487748i	−0.907595	+	0.419847i	$0.862084\pi$
$264$	7.50827e6	−	2.37691e6i	0.408064	−	0.129182i
$265$	−2.41683e7	+	1.04297e7i	−1.29870	+	0.560445i
$266$	−3.97158e6	−	3.18839e6i	−0.211017	−	0.169405i
$267$	−1.07779e7	−	218449.i	−0.566240	−	0.0114767i
$268$	7.26953e6	+	4.63389e6i	0.377661	+	0.240736i
$269$	−8.87613e6			−0.456002			−0.228001	−	0.973661i	$-0.573219\pi$
$269$	−8.87613e6			−0.456002			−0.228001	+	0.973661i	$0.573219\pi$
$270$	1.86220e7	+	6.37521e6i	0.946093	+	0.323894i
$271$			3.04047e7i			1.52768i	0.645405	+	0.763841i	$0.276689\pi$
$271$			3.04047e7i			1.52768i	−0.645405	+	0.763841i	$0.723311\pi$
$272$	1.91492e7	+	6.98113e6i	0.951579	+	0.346912i
$273$	333737.	−	1.64661e7i	0.0164028	−	0.809286i
$274$	2.10733e7	+	1.69177e7i	1.02443	+	0.822412i
$275$	−6.47666e6	−	6.10659e6i	−0.311425	−	0.293630i
$276$	2.19476e7	+	1.46241e7i	1.04390	+	0.695570i
$277$	1.40311e7	−	1.40311e7i	0.660163	−	0.660163i	−0.295256	−	0.955418i	$-0.595405\pi$
$277$	1.40311e7	−	1.40311e7i	0.660163	−	0.660163i	0.955418	+	0.295256i	$0.0954048\pi$
$278$	3.03954e6	−	332480.i	0.141473	−	0.0154750i
$279$	−1.10993e6	+	2.73697e7i	−0.0511071	+	1.26025i
$280$	2.25575e7	+	2.49914e7i	1.02758	+	1.13846i
$281$		−	5.59049e6i		−	0.251960i	−0.992033	−	0.125980i	$-0.959793\pi$
$281$		−	5.59049e6i		−	0.251960i	0.992033	−	0.125980i	$-0.0402075\pi$
$282$	−3.43526e6	+	4.10581e6i	−0.153184	+	0.183085i
$283$	2.84026e7	−	2.84026e7i	1.25314	−	1.25314i	0.298834	−	0.954305i	$-0.403402\pi$
$283$	2.84026e7	−	2.84026e7i	1.25314	−	1.25314i	0.954305	−	0.298834i	$-0.0965976\pi$
$284$	−1.14605e7	+	2.53758e6i	−0.500322	+	0.110781i
$285$	−3.76491e6	−	1.58408e6i	−0.162637	−	0.0684294i
$286$	−4.12117e6	−	3.30848e6i	−0.176166	−	0.141426i
$287$	−2.84997e7	+	2.84997e7i	−1.20558	+	1.20558i
$288$	−2.09150e7	+	1.15410e7i	−0.875547	+	0.483132i
$289$			623966.i			0.0258504i
$290$	2.01058e7	+	5.54380e6i	0.824378	+	0.227307i
$291$	2.51687e7	−	2.41687e7i	1.02137	−	0.980786i
$292$	−5.18444e6	−	3.30476e6i	−0.208235	−	0.132737i
$293$	−2.37345e7	+	2.37345e7i	−0.943577	+	0.943577i	−0.998491	−	0.0549143i	$-0.982511\pi$
$293$	−2.37345e7	+	2.37345e7i	−0.943577	+	0.943577i	0.0549143	+	0.998491i	$0.482511\pi$
$294$	−3.04306e6	−	3.42226e7i	−0.119748	−	1.34670i
$295$	−8.89603e6	+	2.24028e7i	−0.346521	+	0.872644i
$296$	1.18069e7	−	2.39184e7i	0.455263	−	0.922267i
$297$	−1.11927e7	−	681312.i	−0.427232	−	0.0260062i
$298$	−3.51552e6	+	384546.i	−0.132844	+	0.0145311i
$299$		−	1.76980e7i		−	0.662082i
$300$	2.28994e7	+	1.43045e7i	0.848126	+	0.529795i
$301$	6.76193e7			2.47954
$302$	4.61711e6	+	4.22097e7i	0.167629	+	1.53247i
$303$	−665121.	+	3.28160e7i	−0.0239096	+	1.17966i
$304$	4.49383e6	−	2.09264e6i	0.159954	−	0.0744857i
$305$	3.22169e7	+	1.27931e7i	1.13549	+	0.450897i
$306$	−2.18756e7	−	1.90697e7i	−0.763476	−	0.665548i
$307$	1.83724e7	+	1.83724e7i	0.634967	+	0.634967i	0.949310	−	0.314343i	$-0.101784\pi$
$307$	1.83724e7	+	1.83724e7i	0.634967	+	0.634967i	−0.314343	+	0.949310i	$0.601784\pi$
$308$	−1.61732e7	−	1.03094e7i	−0.553533	−	0.352844i
$309$	1.45930e7	−	1.40132e7i	0.494616	−	0.474964i
$310$	−9.98792e6	+	3.62233e7i	−0.335266	+	1.21591i
$311$	−944633.			−0.0314038			−0.0157019	−	0.999877i	$-0.504998\pi$
$311$	−944633.			−0.0314038			−0.0157019	+	0.999877i	$0.504998\pi$
$312$	1.42274e7	+	7.38539e6i	0.468448	+	0.243170i
$313$	1.80438e7	+	1.80438e7i	0.588431	+	0.588431i	0.937206	−	0.348775i	$-0.113402\pi$
$313$	1.80438e7	+	1.80438e7i	0.588431	+	0.588431i	−0.348775	+	0.937206i	$0.613402\pi$
$314$	3.61820e7	−	4.50697e7i	1.16870	−	1.45578i
$315$	−1.71940e7	−	4.47451e7i	−0.550104	−	1.43157i
$316$	−4.93971e7	+	1.09375e7i	−1.56545	+	0.346622i
$317$	6.26817e6	+	6.26817e6i	0.196772	+	0.196772i	0.798615	−	0.601843i	$-0.205567\pi$
$317$	6.26817e6	+	6.26817e6i	0.196772	+	0.196772i	−0.601843	+	0.798615i	$0.705567\pi$
$318$	−2.91881e7	+	3.48855e7i	−0.907662	+	1.08483i
$319$	−1.18817e7			−0.366021
$320$	−3.15304e7	+	8.92053e6i	−0.962231	+	0.272233i
$321$	−1.48317e7	+	1.42424e7i	−0.448411	+	0.430595i
$322$	−6.98399e6	−	6.38477e7i	−0.209188	−	1.91240i
$323$	4.25842e6	+	4.25842e6i	0.126369	+	0.126369i
$324$	3.36943e7	−	4.63979e6i	0.990652	−	0.136415i
$325$	−532629.	−	1.81106e7i	−0.0155158	−	0.527574i
$326$	−1.40772e7	+	1.75351e7i	−0.406315	+	0.506122i
$327$	−669417.	+	3.30280e7i	−0.0191449	+	0.944579i
$328$	−1.25952e7	−	3.71524e7i	−0.356932	−	1.05285i
$329$	1.30373e7			0.366101
$330$	−1.47426e7	−	4.38834e6i	−0.410235	−	0.122112i
$331$		−	1.14208e7i		−	0.314929i	−0.987525	−	0.157464i	$-0.949668\pi$
$331$		−	1.14208e7i		−	0.314929i	0.987525	−	0.157464i	$-0.0503319\pi$
$332$	−3.82073e7	−	2.43549e7i	−1.04408	−	0.665536i
$333$	−2.79213e7	+	2.57449e7i	−0.756141	+	0.697203i
$334$	1.07281e7	−	1.33634e7i	0.287928	−	0.358655i
$335$	−6.67144e6	−	1.54595e7i	−0.177454	−	0.411208i
$336$	5.42413e7	+	2.10292e7i	1.42992	+	0.554377i
$337$	1.15685e7	−	1.15685e7i	0.302263	−	0.302263i	−0.539635	−	0.841899i	$-0.681438\pi$
$337$	1.15685e7	−	1.15685e7i	0.302263	−	0.302263i	0.841899	+	0.539635i	$0.181438\pi$
$338$	3.02912e6	+	2.76923e7i	0.0784452	+	0.717147i
$339$	3.47555e7	−	3.33747e7i	0.892123	−	0.856678i
$340$	−2.33018e7	−	3.22764e7i	−0.592861	−	0.821198i
$341$		−	2.14065e7i		−	0.539861i
$342$	−7.04166e6	+	482551.i	−0.176034	+	0.0120633i
$343$	−1.54045e7	+	1.54045e7i	−0.381737	+	0.381737i
$344$	−2.91326e7	+	5.90164e7i	−0.715654	+	1.44977i
$345$	−1.94472e7	−	4.76987e7i	−0.473586	−	1.16158i
$346$	1.51285e7	−	1.88446e7i	0.365230	−	0.454945i
$347$	−9.48089e6	+	9.48089e6i	−0.226914	+	0.226914i	−0.811402	−	0.584488i	$-0.801295\pi$
$347$	−9.48089e6	+	9.48089e6i	−0.226914	+	0.226914i	0.584488	+	0.811402i	$0.301295\pi$
$348$	3.53377e7	−	7.07647e6i	0.838495	−	0.167911i
$349$			2.11996e7i			0.498714i	0.968412	+	0.249357i	$0.0802192\pi$
$349$			2.11996e7i			0.498714i	−0.968412	+	0.249357i	$0.919781\pi$
$350$	−9.06832e6	−	6.51260e7i	−0.211506	−	1.51897i
$351$	−1.51286e7	−	1.70898e7i	−0.349847	−	0.395199i
$352$	1.59657e7	−	9.67393e6i	0.366068	−	0.221807i
$353$	−1.24693e7	+	1.24693e7i	−0.283478	+	0.283478i	−0.834494	−	0.551016i	$-0.814240\pi$
$353$	−1.24693e7	+	1.24693e7i	−0.283478	+	0.283478i	0.551016	+	0.834494i	$0.314240\pi$
$354$	3.68918e6	+	4.14889e7i	0.0831611	+	0.935237i
$355$	2.13075e7	+	8.46109e6i	0.476264	+	0.189122i
$356$	−2.49486e7	+	5.52411e6i	−0.552964	+	0.122437i
$357$	−1.43216e6	+	7.06606e7i	−0.0314766	+	1.55300i
$358$	2.86999e6	+	2.62375e7i	0.0625505	+	0.571838i
$359$		−	1.27731e7i		−	0.276067i	−0.990428	−	0.138033i	$-0.955922\pi$
$359$		−	1.27731e7i		−	0.276067i	0.990428	−	0.138033i	$-0.0440782\pi$
$360$	4.64601e7	+	4.27113e6i	0.995801	+	0.0915452i
$361$	−4.55812e7			−0.968867
$362$	3.09897e7	−	3.38981e6i	0.653267	−	0.0714577i
$363$	−3.90611e7	−	791698.i	−0.816628	−	0.0165516i
$364$	−8.43952e6	−	3.81155e7i	−0.174990	−	0.790311i
$365$	4.75789e6	+	1.10253e7i	0.0978445	+	0.226732i
$366$	5.96640e7	−	5.30531e6i	1.21694	−	0.108210i
$367$	4.35861e7	+	4.35861e7i	0.881759	+	0.881759i	0.993713	−	0.111954i	$-0.0357109\pi$
$367$	4.35861e7	+	4.35861e7i	0.881759	+	0.881759i	−0.111954	+	0.993713i	$0.535711\pi$
$368$	5.87336e7	+	2.14122e7i	1.17854	+	0.429653i
$369$	−2.26327e6	+	5.58100e7i	−0.0450460	+	1.11079i
$370$	−4.53052e7	+	2.57210e7i	−0.894423	+	0.507788i
$371$	1.10773e8			2.16927
$372$	1.27492e7	+	6.36657e7i	0.247659	+	1.23674i
$373$	−9.60146e6	−	9.60146e6i	−0.185017	−	0.185017i	0.608521	−	0.793538i	$-0.291763\pi$
$373$	−9.60146e6	−	9.60146e6i	−0.185017	−	0.185017i	−0.793538	+	0.608521i	$0.791763\pi$
$374$	1.76851e7	+	1.41976e7i	0.338060	+	0.271395i
$375$	−2.13360e7	−	4.82254e7i	−0.404595	−	0.914496i
$376$	−5.61690e6	+	1.13787e7i	−0.105665	+	0.214056i
$377$	−1.71009e7	−	1.71009e7i	−0.319150	−	0.319150i
$378$	−6.13222e7	−	5.56834e7i	−1.13538	−	1.03098i
$379$	−4.08005e7			−0.749459			−0.374729	−	0.927134i	$-0.622264\pi$
$379$	−4.08005e7			−0.749459			−0.374729	+	0.927134i	$0.622264\pi$
$380$	−9.55818e6	−	1.54342e6i	−0.174190	−	0.0281277i
$381$	−7.22021e6	−	7.51894e6i	−0.130549	−	0.135951i
$382$	−6.50542e7	+	7.11596e6i	−1.16704	+	0.127657i
$383$	−3.36403e7	−	3.36403e7i	−0.598775	−	0.598775i	0.341211	−	0.939987i	$-0.389163\pi$
$383$	−3.36403e7	−	3.36403e7i	−0.598775	−	0.598775i	−0.939987	+	0.341211i	$0.889163\pi$
$384$	−4.17227e7	+	3.82804e7i	−0.736850	+	0.676057i
$385$	1.48426e7	+	3.43942e7i	0.260092	+	0.602702i
$386$	−5.79221e7	−	4.64999e7i	−1.00712	−	0.808518i
$387$	6.88932e7	−	6.35233e7i	1.18862	−	1.09597i
$388$	4.44592e7	−	6.97466e7i	0.761144	−	1.19407i
$389$	2.08701e7			0.354549			0.177275	−	0.984161i	$-0.443272\pi$
$389$	2.08701e7			0.354549			0.177275	+	0.984161i	$0.443272\pi$
$390$	−1.49025e7	−	2.75345e7i	−0.251227	−	0.464177i
$391$			7.59474e7i			1.27052i
$392$	−2.61478e7	−	7.71286e7i	−0.434087	−	1.28043i
$393$	4.41400e7	+	894639.i	0.727202	+	0.0147391i
$394$	−6.32863e7	−	5.08063e7i	−1.03472	−	0.830670i
$395$	9.18395e7	+	3.64689e7i	1.49018	+	0.591740i
$396$	−2.61628e7	+	4.68987e6i	−0.421308	+	0.0755223i
$397$	−1.75113e7	+	1.75113e7i	−0.279864	+	0.279864i	−0.833055	−	0.553191i	$-0.813410\pi$
$397$	−1.75113e7	+	1.75113e7i	−0.279864	+	0.279864i	0.553191	+	0.833055i	$0.313410\pi$
$398$	−1.70579e7	+	1.86588e6i	−0.270569	+	0.0295962i
$399$	1.19057e7	+	1.23983e7i	0.187429	+	0.195184i
$400$	6.07473e7	+	2.01438e7i	0.949176	+	0.314746i
$401$			2.72336e7i			0.422349i	0.977448	+	0.211175i	$0.0677288\pi$
$401$			2.72336e7i			0.422349i	−0.977448	+	0.211175i	$0.932271\pi$
$402$	−2.23149e7	−	1.86705e7i	−0.343492	−	0.287394i
$403$	3.08096e7	−	3.08096e7i	0.470729	−	0.470729i
$404$	1.68195e7	+	7.59622e7i	0.255076	+	1.15200i
$405$	−5.95526e7	−	2.94356e7i	−0.896469	−	0.443106i
$406$	−6.84417e7	−	5.49451e7i	−1.02269	−	0.821014i
$407$	2.09868e7	−	2.09868e7i	0.311288	−	0.311288i
$408$	−6.10538e7	−	3.16928e7i	−0.898943	−	0.466638i
$409$		−	8.01778e7i		−	1.17188i	−0.810354	−	0.585941i	$-0.800725\pi$
$409$		−	8.01778e7i		−	1.17188i	0.810354	−	0.585941i	$-0.199275\pi$
$410$	−2.03665e7	+	7.38634e7i	−0.295505	+	1.07171i
$411$	−6.31721e7	−	6.57859e7i	−0.909914	−	0.947561i
$412$	2.57777e7	−	4.04395e7i	0.368598	−	0.578249i
$413$	7.17277e7	−	7.17277e7i	1.01821	−	1.01821i
$414$	−6.70958e7	−	5.84896e7i	−0.945571	−	0.824286i
$415$	3.50639e7	+	8.12524e7i	0.490587	+	1.13682i
$416$	3.69023e7	+	9.05559e6i	0.512594	+	0.125787i
$417$	−1.03175e7	−	209117.i	−0.142287	−	0.00288391i
$418$	5.48311e6	−	599771.i	0.0750755	−	0.00821214i
$419$			8.59169e7i			1.16798i	0.811760	+	0.583992i	$0.198510\pi$
$419$			8.59169e7i			1.16798i	−0.811760	+	0.583992i	$0.801490\pi$
$420$	−6.46282e7	−	9.34530e7i	−0.872317	−	1.26138i
$421$	−1.08132e8			−1.44913			−0.724566	−	0.689205i	$-0.757960\pi$
$421$	−1.08132e8			−1.44913			−0.724566	+	0.689205i	$0.757960\pi$
$422$	4.40525e6	+	4.02729e7i	0.0586183	+	0.535890i
$423$	1.32829e7	−	1.22476e7i	0.175498	−	0.161819i
$424$	−4.77246e7	+	9.66800e7i	−0.626102	+	1.26835i
$425$	2.28566e6	+	7.77179e7i	0.0297746	+	1.01240i
$426$	3.94604e7	−	3.50881e6i	0.510426	−	0.0453869i
$427$	−1.03150e8	−	1.03150e8i	−1.32490	−	1.32490i
$428$	−2.61995e7	+	4.11012e7i	−0.334165	+	0.524231i
$429$	1.23542e7	+	1.28653e7i	0.156474	+	0.162948i
$430$	1.11786e8	−	6.34642e7i	1.40600	−	0.798222i
$431$	−9.91535e7			−1.23844			−0.619222	−	0.785216i	$-0.712552\pi$
$431$	−9.91535e7			−1.23844			−0.619222	+	0.785216i	$0.712552\pi$
$432$	7.50186e7	−	2.95303e7i	0.930503	−	0.366283i
$433$	4.20914e7	+	4.20914e7i	0.518477	+	0.518477i	0.917110	−	0.398633i	$-0.130515\pi$
$433$	4.20914e7	+	4.20914e7i	0.518477	+	0.518477i	−0.398633	+	0.917110i	$0.630515\pi$
$434$	9.89910e7	−	1.23307e8i	1.21095	−	1.50841i
$435$	−6.48803e7	−	2.72983e7i	−0.788215	−	0.331640i
$436$	1.69282e7	+	7.64529e7i	0.204244	+	0.922432i
$437$	1.30612e7	+	1.30612e7i	0.156509	+	0.156509i
$438$	1.59144e7	+	1.33153e7i	0.189394	+	0.158463i
$439$	6.26785e7			0.740841			0.370421	−	0.928864i	$-0.379214\pi$
$439$	6.26785e7			0.740841			0.370421	+	0.928864i	$0.379214\pi$
$440$	−3.64131e7	−	1.86389e6i	−0.427463	−	0.0218807i
$441$	−4.69855e6	+	1.15862e8i	−0.0547833	+	1.35090i
$442$	5.01944e6	+	4.58878e7i	0.0581284	+	0.531411i
$443$	2.21315e7	+	2.21315e7i	0.254566	+	0.254566i	0.822840	−	0.568274i	$-0.192388\pi$
$443$	2.21315e7	+	2.21315e7i	0.254566	+	0.254566i	−0.568274	+	0.822840i	$0.692388\pi$
$444$	−4.99182e7	+	7.49167e7i	−0.570309	+	0.855914i
$445$	4.63847e7	+	1.84191e7i	0.526375	+	0.209020i
$446$	−4.23505e7	+	5.27535e7i	−0.477369	+	0.594629i
$447$	1.19332e7	+	241865.i	0.133609	+	0.00270801i
$448$	1.36703e8	+	1.81067e7i	1.52035	+	0.201375i
$449$	−2.21265e7			−0.244441			−0.122220	−	0.992503i	$-0.539001\pi$
$449$	−2.21265e7			−0.244441			−0.122220	+	0.992503i	$0.539001\pi$
$450$	−7.04202e7	−	5.78339e7i	−0.772787	−	0.634666i
$451$		−	4.36502e7i		−	0.475835i
$452$	6.13939e7	−	9.63134e7i	0.664829	−	1.04297i
$453$	2.90399e6	−	1.43278e8i	0.0312392	−	1.54129i
$454$	−3.71466e7	+	4.62712e7i	−0.396964	+	0.494474i
$455$	−2.81399e7	+	7.08648e7i	−0.298737	+	0.752309i
$456$	−1.59503e7	+	5.04942e6i	−0.168219	+	0.0532534i
$457$	5.38780e7	−	5.38780e7i	0.564499	−	0.564499i	−0.366083	−	0.930582i	$-0.619301\pi$
$457$	5.38780e7	−	5.38780e7i	0.564499	−	0.564499i	0.930582	+	0.366083i	$0.119301\pi$
$458$	1.24052e7	+	1.13408e8i	0.129124	+	1.18045i
$459$	6.49213e7	+	7.33373e7i	0.671350	+	0.758380i
$460$	−7.14702e7	−	9.89965e7i	−0.734262	−	1.01706i
$461$		−	2.33159e7i		−	0.237985i	−0.992895	−	0.118993i	$-0.962034\pi$
$461$		−	2.33159e7i		−	0.237985i	0.992895	−	0.118993i	$-0.0379665\pi$
$462$	4.96459e7	+	4.15379e7i	0.503452	+	0.421229i
$463$	1.24534e7	−	1.24534e7i	0.125471	−	0.125471i	−0.641583	−	0.767054i	$-0.721722\pi$
$463$	1.24534e7	−	1.24534e7i	0.125471	−	0.125471i	0.767054	+	0.641583i	$0.221722\pi$
$464$	7.74416e7	−	3.60622e7i	0.775212	−	0.360992i
$465$	4.91815e7	−	1.16891e8i	0.489151	−	1.16257i
$466$	4.07943e7	−	5.08150e7i	0.403127	−	0.502151i
$467$	5.58941e6	−	5.58941e6i	0.0548801	−	0.0548801i	−0.679134	−	0.734014i	$-0.737645\pi$
$467$	5.58941e6	−	5.58941e6i	0.0548801	−	0.0548801i	0.734014	+	0.679134i	$0.237645\pi$
$468$	−4.44052e7	−	3.09053e7i	−0.433208	−	0.301506i
$469$			7.08572e7i			0.686856i
$470$	2.15530e7	−	1.22362e7i	0.207593	−	0.117856i
$471$	−1.40697e8	+	1.35107e8i	−1.34655	+	1.29305i
$472$	3.16996e7	+	9.35048e7i	0.301458	+	0.889217i
$473$	−5.17830e7	+	5.17830e7i	−0.489332	+	0.489332i
$474$	1.70082e8	−	1.51236e7i	1.59707	−	0.142011i
$475$	1.37588e7	+	1.29726e7i	0.128381	+	0.121045i
$476$	3.62164e7	+	1.63565e8i	0.335803	+	1.51659i
$477$	1.12860e8	−	1.04063e8i	1.03988	−	0.958831i
$478$	5.70325e6	+	5.21392e7i	0.0522202	+	0.477398i
$479$		−	1.61719e8i		−	1.47148i	−0.677262	−	0.735742i	$-0.736834\pi$
$479$		−	1.61719e8i		−	1.47148i	0.677262	−	0.735742i	$-0.263166\pi$
$480$	1.09407e8	−	1.61434e7i	0.989289	−	0.145972i
$481$	6.04111e7			0.542852
$482$	−1.39967e8	+	1.53103e7i	−1.24993	+	0.136724i
$483$	−4.39266e6	+	2.16727e8i	−0.0389840	+	1.92341i
$484$	−9.04183e7	+	2.00204e7i	−0.797481	+	0.176578i
$485$	−1.48324e8	+	6.40083e7i	−1.30013	+	0.561063i
$486$	−1.14788e8	+	875249.i	−0.999971	+	0.00762470i
$487$	−1.18183e8	−	1.18183e8i	−1.02322	−	1.02322i	−0.999724	−	0.0234953i	$-0.992521\pi$
$487$	−1.18183e8	−	1.18183e8i	−1.02322	−	1.02322i	−0.0234953	−	0.999724i	$-0.507479\pi$
$488$	1.34467e8	−	4.55863e7i	1.15706	−	0.392261i
$489$	5.47403e7	−	5.25654e7i	0.468145	−	0.449545i
$490$	−4.22809e7	+	1.53341e8i	−0.359382	+	1.30337i
$491$	4.52341e7			0.382139			0.191070	−	0.981576i	$-0.438804\pi$
$491$	4.52341e7			0.382139			0.191070	+	0.981576i	$0.438804\pi$
$492$	2.59971e7	+	1.29822e8i	0.218288	+	1.09006i
$493$	7.33848e7	+	7.33848e7i	0.612443	+	0.612443i
$494$	8.75488e6	+	7.02843e6i	0.0726222	+	0.0583012i
$495$	4.74330e7	+	2.10987e7i	0.391079	+	0.173956i
$496$	6.49709e7	+	1.39522e8i	0.532444	+	1.14340i
$497$	−6.82208e7	−	6.82208e7i	−0.555710	−	0.555710i
$498$	1.17283e8	+	9.81286e7i	0.949613	+	0.794525i
$499$	−3.80446e6			−0.0306191			−0.0153095	−	0.999883i	$-0.504873\pi$
$499$	−3.80446e6			−0.0306191			−0.0153095	+	0.999883i	$0.504873\pi$
$500$	−7.61156e7	−	9.91535e7i	−0.608925	−	0.793228i
$501$	−4.17172e7	+	4.00597e7i	−0.331743	+	0.318563i
$502$	2.78244e7	−	3.04357e6i	0.219945	−	0.0240587i
$503$	−1.22064e6	−	1.22064e6i	−0.00959145	−	0.00959145i	0.702295	−	0.711886i	$-0.252159\pi$
$503$	−1.22064e6	−	1.22064e6i	−0.00959145	−	0.00959145i	−0.711886	+	0.702295i	$0.752159\pi$
$504$	−1.72393e8	−	9.39713e7i	−1.34657	−	0.734013i
$505$	5.60814e7	−	1.41230e8i	0.435456	−	1.09661i
$506$	5.42430e7	+	4.35463e7i	0.418690	+	0.336124i
$507$	1.90520e6	−	9.39996e7i	0.0146190	−	0.721277i
$508$	−2.08362e7	−	1.32818e7i	−0.158938	−	0.101313i
$509$	−7.54703e7			−0.572299			−0.286149	−	0.958185i	$-0.592375\pi$
$509$	−7.54703e7			−0.572299			−0.286149	+	0.958185i	$0.592375\pi$
$510$	6.39511e7	+	1.18158e8i	0.482100	+	0.890747i
$511$		−	5.05334e7i		−	0.378718i
$512$	−7.46991e7	+	1.11510e8i	−0.556551	+	0.830813i
$513$	2.37773e7	+	1.44736e6i	0.176121	+	0.0107207i
$514$	1.47779e8	+	1.18637e8i	1.08824	+	0.873636i
$515$	−8.59994e7	+	3.71124e7i	−0.629613	+	0.271705i
$516$	1.23169e8	−	1.84850e8i	0.896502	−	1.34546i
$517$	−9.98401e6	+	9.98401e6i	−0.0722492	+	0.0722492i
$518$	2.17940e8	−	2.38394e7i	1.56800	−	0.171516i
$519$	−5.88283e7	+	5.64910e7i	−0.420808	+	0.404089i
$520$	−4.97254e7	−	5.50907e7i	−0.353646	−	0.391803i
$521$		−	1.27914e8i		−	0.904489i	−0.891894	−	0.452245i	$-0.850623\pi$
$521$		−	1.27914e8i		−	0.904489i	0.891894	−	0.452245i	$-0.149377\pi$
$522$	−1.21348e8	+	8.31574e6i	−0.853142	+	0.0584641i
$523$	4.78006e7	−	4.78006e7i	0.334140	−	0.334140i	−0.520017	−	0.854156i	$-0.674074\pi$
$523$	4.78006e7	−	4.78006e7i	0.334140	−	0.334140i	0.854156	+	0.520017i	$0.174074\pi$
$524$	1.02175e8	−	2.26235e7i	0.710151	−	0.157241i
$525$	2.02740e6	+	2.21911e8i	0.0140108	+	1.53356i
$526$	7.82802e7	+	6.28434e7i	0.537892	+	0.431820i
$527$	−1.32213e8	+	1.32213e8i	−0.903320	+	0.903320i
$528$	−5.76423e7	+	2.54339e7i	−0.391597	+	0.172787i
$529$			8.49063e7i			0.573552i
$530$	1.83127e8	−	1.03966e8i	1.23006	−	0.698337i
$531$	5.69616e6	−	1.40462e8i	0.0380451	−	0.938156i
$532$	3.43578e7	+	2.19010e7i	0.228187	+	0.145455i
$533$	6.28242e7	−	6.28242e7i	0.414902	−	0.414902i
$534$	8.59021e7	−	7.63839e6i	0.564131	−	0.0501624i
$535$	8.74064e7	−	3.77196e7i	0.570797	−	0.246324i
$536$	−6.18424e7	−	3.05276e7i	−0.401599	−	0.198243i
$537$	1.80511e6	−	8.90614e7i	0.0116569	−	0.575131i
$538$	7.05880e7	−	7.72127e6i	0.453298	−	0.0495841i
$539$		−	9.06180e7i		−	0.578693i
$540$	−1.53638e8	−	3.45002e7i	−0.975703	−	0.219099i
$541$	−2.40902e8			−1.52142			−0.760709	−	0.649093i	$-0.775149\pi$
$541$	−2.40902e8			−1.52142			−0.760709	+	0.649093i	$0.775149\pi$
$542$	−2.64488e7	−	2.41795e8i	−0.166115	−	1.51862i
$543$	−1.05192e8	−	2.13206e6i	−0.657029	−	0.0133168i
$544$	−1.58358e8	−	3.88601e7i	−0.983659	−	0.241384i
$545$	5.64437e7	−	1.42142e8i	0.348679	−	0.878077i
$546$	1.16696e7	+	1.31238e8i	0.0716934	+	0.806271i
$547$	−9.70708e7	−	9.70708e7i	−0.593098	−	0.593098i	0.345369	−	0.938467i	$-0.387754\pi$
$547$	−9.70708e7	−	9.70708e7i	−0.593098	−	0.593098i	−0.938467	+	0.345369i	$0.887754\pi$
$548$	−1.82304e8	−	1.16207e8i	−1.10778	−	0.706143i
$549$	−2.01995e8	−	8.19150e6i	−1.22074	−	0.0495047i
$550$	5.68181e7	+	4.29290e7i	0.341506	+	0.258026i
$551$	2.52410e7			0.150887
$552$	−1.87261e8	−	9.72067e7i	−1.11335	−	0.577935i
$553$	−2.94045e8	−	2.94045e8i	−1.73875	−	1.73875i
$554$	−9.93774e7	+	1.23788e8i	−0.584465	+	0.728032i
$555$	1.62816e8	−	6.63816e7i	0.952398	−	0.388301i
$556$	−2.38829e7	+	5.28814e6i	−0.138951	+	0.0307665i
$557$	2.06116e8	+	2.06116e8i	1.19274	+	1.19274i	0.976295	+	0.216446i	$0.0694465\pi$
$557$	2.06116e8	+	2.06116e8i	1.19274	+	1.19274i	0.216446	+	0.976295i	$0.430553\pi$
$558$	−1.49819e7	−	2.18625e8i	−0.0862314	−	1.25834i
$559$	−1.49059e8			−0.853340
$560$	−2.01130e8	−	1.79123e8i	−1.14528	−	1.01997i
$561$	−5.30153e7	−	5.52088e7i	−0.300270	−	0.312694i
$562$	4.86313e6	+	4.44588e7i	0.0273972	+	0.250466i
$563$	−1.69673e8	−	1.69673e8i	−0.950797	−	0.950797i	0.0480477	−	0.998845i	$-0.484700\pi$
$563$	−1.69673e8	−	1.69673e8i	−0.950797	−	0.950797i	−0.998845	+	0.0480477i	$0.984700\pi$
$564$	2.37475e7	−	3.56400e7i	0.132367	−	0.198656i
$565$	−2.04822e8	+	8.83894e7i	−1.13561	+	0.490066i
$566$	−2.01167e8	+	2.50581e8i	−1.10945	+	1.38197i
$567$	1.81021e8	+	2.13033e8i	0.993067	+	1.16869i
$568$	8.89332e7	−	3.01497e7i	0.485310	−	0.164527i
$569$	9.55295e7			0.518562			0.259281	−	0.965802i	$-0.416514\pi$
$569$	9.55295e7			0.518562			0.259281	+	0.965802i	$0.416514\pi$
$570$	3.13187e7	+	9.32244e6i	0.169114	+	0.0503390i
$571$			6.87591e7i			0.369336i	0.982801	+	0.184668i	$0.0591211\pi$
$571$			6.87591e7i			0.369336i	−0.982801	+	0.184668i	$0.940879\pi$
$572$	3.56519e7	+	2.27259e7i	0.190500	+	0.121432i
$573$	2.20822e8	+	4.47567e6i	1.17376	+	0.0237900i
$574$	2.01854e8	−	2.51437e8i	1.06734	−	1.32952i
$575$	7.01047e6	+	2.38373e8i	0.0368760	+	1.25387i
$576$	1.56288e8	−	1.09974e8i	0.817822	−	0.575472i
$577$	5.07259e7	−	5.07259e7i	0.264060	−	0.264060i	−0.562641	−	0.826701i	$-0.690215\pi$
$577$	5.07259e7	−	5.07259e7i	0.264060	−	0.264060i	0.826701	+	0.562641i	$0.190215\pi$
$578$	−542783.	−	4.96213e6i	−0.00281088	−	0.0256971i
$579$	1.73635e8	+	1.80819e8i	0.894542	+	0.931553i
$580$	−1.64715e8	−	2.65976e7i	−0.844207	−	0.136320i
$581$		−	3.72413e8i		−	1.89887i
$582$	−1.79131e8	+	2.14097e8i	−0.908663	+	1.08603i
$583$	−8.48302e7	+	8.48302e7i	−0.428100	+	0.428100i
$584$	4.41043e7	+	2.17714e7i	0.221433	+	0.109307i
$585$	3.79021e7	+	9.86352e7i	0.189320	+	0.492679i
$586$	1.68104e8	−	2.09397e8i	0.835381	−	1.04058i
$587$	2.38300e8	−	2.38300e8i	1.17818	−	1.17818i	0.197967	−	0.980209i	$-0.436566\pi$
$587$	2.38300e8	−	2.38300e8i	1.17818	−	1.17818i	0.980209	−	0.197967i	$-0.0634338\pi$
$588$	5.39701e7	+	2.69510e8i	0.265474	+	1.32569i
$589$			4.54752e7i			0.222550i
$590$	5.12582e7	−	1.85899e8i	0.249579	−	0.905149i
$591$	1.89715e8	+	1.97564e8i	0.919050	+	0.957076i
$592$	−7.30891e7	+	2.00483e8i	−0.352279	+	0.966302i
$593$	−1.61520e8	+	1.61520e8i	−0.774571	+	0.774571i	−0.978902	−	0.204331i	$-0.934498\pi$
$593$	−1.61520e8	+	1.61520e8i	−0.774571	+	0.774571i	0.204331	+	0.978902i	$0.434498\pi$
$594$	8.96031e7	−	4.31823e6i	0.427527	−	0.0206038i
$595$	1.20757e8	−	3.04101e8i	0.573271	−	1.44367i
$596$	2.76229e7	−	6.11625e6i	0.130476	−	0.0288899i
$597$	5.79021e7	+	1.17357e6i	0.272127	+	0.00551552i
$598$	1.53954e7	+	1.40745e8i	0.0719924	+	0.658156i
$599$			1.98463e8i			0.923421i	0.887031	+	0.461711i	$0.152764\pi$
$599$			1.98463e8i			0.923421i	−0.887031	+	0.461711i	$0.847236\pi$
$600$	−1.94552e8	−	9.38371e7i	−0.900705	−	0.434431i
$601$	−9.06782e7			−0.417714			−0.208857	−	0.977946i	$-0.566974\pi$
$601$	−9.06782e7			−0.417714			−0.208857	+	0.977946i	$0.566974\pi$
$602$	−5.37747e8	+	5.88215e7i	−2.46484	+	0.269616i
$603$	6.65651e7	+	7.21921e7i	0.303595	+	0.329259i
$604$	−7.34358e7	−	3.31659e8i	−0.333271	−	1.50515i
$605$	1.68107e8	+	6.67541e7i	0.759135	+	0.301448i
$606$	−2.32569e7	−	2.61550e8i	−0.104504	−	1.17527i
$607$	5.44346e7	+	5.44346e7i	0.243393	+	0.243393i	0.818252	−	0.574859i	$-0.194943\pi$
$607$	5.44346e7	+	5.44346e7i	0.243393	+	0.243393i	−0.574859	+	0.818252i	$0.694943\pi$
$608$	−3.39171e7	+	2.05510e7i	−0.150907	+	0.0914370i
$609$	2.05170e8	+	2.13659e8i	0.908367	+	0.945951i
$610$	−2.67336e8	−	7.37130e7i	−1.17779	−	0.324754i
$611$	−2.87393e7			−0.125995
$612$	1.90556e8	+	1.32624e8i	0.831319	+	0.578584i
$613$	7.82046e7	+	7.82046e7i	0.339508	+	0.339508i	0.856182	−	0.516674i	$-0.172830\pi$
$613$	7.82046e7	+	7.82046e7i	0.339508	+	0.339508i	−0.516674	+	0.856182i	$0.672830\pi$
$614$	−1.62090e8	−	1.30126e8i	−0.700246	−	0.562158i
$615$	1.00287e8	−	2.38353e8i	0.431140	−	1.02470i
$616$	1.37587e8	+	6.79175e7i	0.588618	+	0.290562i
$617$	2.34604e8	+	2.34604e8i	0.998803	+	0.998803i	0.999999	−	0.00119580i	$-0.000380636\pi$
$617$	2.34604e8	+	2.34604e8i	0.998803	+	0.998803i	−0.00119580	+	0.999999i	$0.500381\pi$
$618$	−1.03862e8	+	1.24135e8i	−0.440037	+	0.525931i
$619$	−2.14980e7			−0.0906414			−0.0453207	−	0.998972i	$-0.514431\pi$
$619$	−2.14980e7			−0.0906414			−0.0453207	+	0.998972i	$0.514431\pi$
$620$	4.79192e7	−	2.96756e8i	0.201064	−	1.24516i
$621$	1.99123e8	+	2.24936e8i	0.831472	+	0.939258i
$622$	7.51226e6	−	821729.i	0.0312176	−	0.00341474i
$623$	−1.48511e8	−	1.48511e8i	−0.614179	−	0.614179i
$624$	−1.19569e8	−	4.63565e7i	−0.492112	−	0.190790i
$625$	1.43478e7	+	2.43719e8i	0.0587686	+	0.998272i
$626$	−1.59191e8	−	1.27799e8i	−0.648926	−	0.520958i
$627$	−1.86121e7	−	377233.i	−0.0755078	−	0.00153041i
$628$	−2.48534e8	+	3.89894e8i	−1.00347	+	1.57423i
$629$	−2.59241e8			−1.04172
$630$	1.75660e8	+	3.40881e8i	0.702506	+	1.36327i
$631$			5.04047e7i			0.200624i	0.994956	+	0.100312i	$0.0319841\pi$
$631$			5.04047e7i			0.200624i	−0.994956	+	0.100312i	$0.968016\pi$
$632$	3.83319e8	−	1.29951e8i	1.51848	−	0.514788i
$633$	2.77074e6	−	1.36704e8i	0.0109241	−	0.538975i
$634$	−5.53007e7	−	4.43954e7i	−0.217001	−	0.174209i
$635$	1.91220e7	+	4.43107e7i	0.0746813	+	0.173056i
$636$	2.01774e8	−	3.02820e8i	0.784319	−	1.17710i
$637$	1.30423e8	−	1.30423e8i	0.504588	−	0.504588i
$638$	9.44898e7	−	1.03358e7i	0.363850	−	0.0397998i
$639$	−1.33595e8	−	5.41767e6i	−0.512019	−	0.0207639i
$640$	2.42988e8	−	9.83692e7i	0.926924	−	0.375249i
$641$			2.54315e8i			0.965603i	0.875730	+	0.482801i	$0.160381\pi$
$641$			2.54315e8i			0.965603i	−0.875730	+	0.482801i	$0.839619\pi$
$642$	1.05561e8	−	1.26166e8i	0.398931	−	0.476801i
$643$	1.58822e7	−	1.58822e7i	0.0597418	−	0.0597418i	−0.676605	−	0.736346i	$-0.736549\pi$
$643$	1.58822e7	−	1.58822e7i	0.0597418	−	0.0597418i	0.736346	+	0.676605i	$0.236549\pi$
$644$	1.11081e8	+	5.01678e8i	0.415894	+	1.87831i
$645$	−4.01734e8	+	1.63791e8i	−1.49713	+	0.610394i
$646$	−3.75697e7	−	3.01610e7i	−0.139361	−	0.111879i
$647$	2.14950e8	−	2.14950e8i	0.793643	−	0.793643i	−0.188442	−	0.982084i	$-0.560344\pi$
$647$	2.14950e8	−	2.14950e8i	0.793643	−	0.793643i	0.982084	+	0.188442i	$0.0603436\pi$
$648$	−2.63920e8	+	6.62086e7i	−0.969944	+	0.243327i
$649$			1.09858e8i			0.401883i
$650$	1.99900e7	+	1.43563e8i	0.0727903	+	0.522759i
$651$	−3.84935e8	+	3.69641e8i	−1.39523	+	1.33979i
$652$	9.66960e7	−	1.51694e8i	0.348872	−	0.547302i
$653$	1.95844e7	−	1.95844e7i	0.0703350	−	0.0703350i	−0.671064	−	0.741399i	$-0.734163\pi$
$653$	1.95844e7	−	1.95844e7i	0.0703350	−	0.0703350i	0.741399	+	0.671064i	$0.234163\pi$
$654$	−2.34072e7	−	2.63239e8i	−0.0836788	−	0.941060i
$655$	−1.89965e8	−	7.54338e7i	−0.676004	−	0.268437i
$656$	1.32483e8	+	2.84500e8i	0.469298	+	1.00779i
$657$	−4.74724e7	−	5.14855e7i	−0.167396	−	0.181547i
$658$	−1.03680e8	+	1.13411e7i	−0.363930	+	0.0398085i
$659$		−	3.28041e8i		−	1.14623i	−0.819475	−	0.573114i	$-0.805735\pi$
$659$		−	3.28041e8i		−	1.14623i	0.819475	−	0.573114i	$-0.194265\pi$
$660$	1.21059e8	+	2.20741e7i	0.421080	+	0.0767804i
$661$	1.42932e8			0.494908			0.247454	−	0.968900i	$-0.420406\pi$
$661$	1.42932e8			0.494908			0.247454	+	0.968900i	$0.420406\pi$
$662$	9.93485e6	+	9.08245e7i	0.0342442	+	0.313061i
$663$	3.15704e6	−	1.55763e8i	0.0108328	−	0.534471i
$664$	3.25032e8	+	1.60447e8i	1.11025	+	0.548060i
$665$	−3.15311e7	−	7.30658e7i	−0.107219	−	0.248456i
$666$	1.99650e8	−	2.29027e8i	0.675846	−	0.775289i
$667$	2.25082e8	+	2.25082e8i	0.758515	+	0.758515i
$668$	−7.36914e7	+	1.15605e8i	−0.247222	+	0.387836i
$669$	1.64684e8	−	1.58141e8i	0.550012	−	0.528159i
$670$	6.65032e7	+	1.17139e8i	0.221115	+	0.389474i
$671$	1.57984e8			0.522934
$672$	−4.49651e8	−	1.20052e8i	−1.48173	−	0.395606i
$673$	−3.15523e7	−	3.15523e7i	−0.103511	−	0.103511i	0.653455	−	0.756966i	$-0.273319\pi$
$673$	−3.15523e7	−	3.15523e7i	−0.103511	−	0.103511i	−0.756966	+	0.653455i	$0.773319\pi$
$674$	−8.19356e7	+	1.02062e8i	−0.267604	+	0.333338i
$675$	2.10535e8	+	2.24188e8i	0.684562	+	0.728954i
$676$	−4.81786e7	−	2.17590e8i	−0.155960	−	0.704365i
$677$	2.49885e8	+	2.49885e8i	0.805329	+	0.805329i	0.983923	−	0.178594i	$-0.0571548\pi$
$677$	2.49885e8	+	2.49885e8i	0.805329	+	0.805329i	−0.178594	+	0.983923i	$0.557155\pi$
$678$	−2.47363e8	+	2.95648e8i	−0.793681	+	0.948605i
$679$	6.79831e8			2.17166
$680$	2.13386e8	+	2.36410e8i	0.678640	+	0.751863i
$681$	1.44448e8	−	1.38709e8i	0.457372	−	0.439200i
$682$	1.86213e7	+	1.70236e8i	0.0587026	+	0.536660i
$683$	−2.12135e8	−	2.12135e8i	−0.665809	−	0.665809i	0.290934	−	0.956743i	$-0.406034\pi$
$683$	−2.12135e8	−	2.12135e8i	−0.665809	−	0.665809i	−0.956743	+	0.290934i	$0.906034\pi$
$684$	5.55795e7	−	9.96300e6i	0.173679	−	0.0311331i
$685$	1.67305e8	+	3.87690e8i	0.520520	+	1.20618i
$686$	1.09105e8	−	1.35905e8i	0.337965	−	0.420983i
$687$	7.80238e6	−	3.84957e8i	0.0240634	−	1.18725i
$688$	1.80341e8	−	4.94674e8i	0.553769	−	1.51899i
$689$	−2.44186e8			−0.746558
$690$	1.96148e8	+	3.62410e8i	0.597084	+	1.10320i
$691$			1.18268e8i			0.358455i	0.983808	+	0.179228i	$0.0573598\pi$
$691$			1.18268e8i			0.358455i	−0.983808	+	0.179228i	$0.942640\pi$
$692$	−1.03917e8	+	1.63023e8i	−0.313595	+	0.491961i
$693$	−1.48094e8	−	1.60612e8i	−0.444976	−	0.482591i
$694$	6.71501e7	−	8.36448e7i	0.200895	−	0.250242i
$695$	4.44033e7	+	1.76323e7i	0.132270	+	0.0525235i
$696$	−2.74870e8	+	8.70160e7i	−0.815266	+	0.258090i
$697$	−2.69597e8	+	2.69597e8i	−0.796190	+	0.796190i
$698$	−1.84414e7	−	1.68591e8i	−0.0542284	−	0.495757i
$699$	−1.58632e8	+	1.52330e8i	−0.464473	+	0.446019i
$700$	1.28769e8	+	5.10030e8i	0.375420	+	1.48697i
$701$		−	6.44161e8i		−	1.87000i	−0.354654	−	0.934998i	$-0.615401\pi$
$701$		−	6.44161e8i		−	1.87000i	0.354654	−	0.934998i	$-0.384599\pi$
$702$	1.35178e8	+	1.22747e8i	0.390745	+	0.354814i
$703$	−4.45836e7	+	4.45836e7i	−0.128324	+	0.128324i
$704$	−1.18553e8	+	9.08211e7i	−0.339779	+	0.260297i
$705$	−7.74563e7	+	3.15796e7i	−0.221049	+	0.0901238i
$706$	8.83163e7	−	1.10010e8i	0.250973	−	0.312622i
$707$	−4.52178e8	+	4.52178e8i	−1.27953	+	1.27953i
$708$	−6.54293e7	−	3.26734e8i	−0.184362	−	0.920649i
$709$		−	3.28361e8i		−	0.921324i	−0.887576	−	0.460662i	$-0.847612\pi$
$709$		−	3.28361e8i		−	0.921324i	0.887576	−	0.460662i	$-0.152388\pi$
$710$	−1.76810e8	−	4.87521e7i	−0.494005	−	0.136213i
$711$	−5.75818e8	−	2.33512e7i	−1.60205	−	0.0649681i
$712$	1.93600e8	−	6.56335e7i	0.536372	−	0.181838i
$713$	−4.05517e8	+	4.05517e8i	−1.11877	+	1.11877i
$714$	−5.00777e7	−	5.63179e8i	−0.137578	−	1.54722i
$715$	−3.27187e7	−	7.58180e7i	−0.0895114	−	0.207422i
$716$	−4.56475e7	−	2.06159e8i	−0.124359	−	0.561646i
$717$	3.58713e6	−	1.76983e8i	0.00973172	−	0.480147i
$718$	1.11113e7	+	1.01579e8i	0.0300185	+	0.274430i
$719$			9.33471e7i			0.251139i	0.992085	+	0.125570i	$0.0400758\pi$
$719$			9.33471e7i			0.251139i	−0.992085	+	0.125570i	$0.959924\pi$
$720$	−3.73192e8	+	6.44878e6i	−0.999851	+	0.0172775i
$721$	3.94170e8			1.05167
$722$	3.62487e8	−	3.96507e7i	0.963122	−	0.105351i
$723$	4.75110e8	+	9.62962e6i	1.25713	+	0.0254797i
$724$	−2.43498e8	+	5.39153e7i	−0.641624	+	0.142068i
$725$	2.37104e8	+	2.23556e8i	0.622191	+	0.586640i
$726$	3.11325e8	−	2.76829e7i	0.813586	−	0.0723439i
$727$	−2.29502e8	−	2.29502e8i	−0.597287	−	0.597287i	0.342303	−	0.939590i	$-0.388793\pi$
$727$	−2.29502e8	−	2.29502e8i	−0.597287	−	0.597287i	−0.939590	+	0.342303i	$0.888793\pi$
$728$	1.00272e8	+	2.95775e8i	0.259888	+	0.766597i
$729$	3.84560e8	+	4.69915e7i	0.992617	+	0.121293i
$730$	−4.74283e7	−	8.35406e7i	−0.121918	−	0.214748i
$731$	6.39654e8			1.63754
$732$	−4.69867e8	+	9.40920e7i	−1.19796	+	0.239894i
$733$	−3.70893e8	−	3.70893e8i	−0.941753	−	0.941753i	0.0566417	−	0.998395i	$-0.481961\pi$
$733$	−3.70893e8	−	3.70893e8i	−0.941753	−	0.941753i	−0.998395	+	0.0566417i	$0.981961\pi$
$734$	−3.84537e8	−	3.08706e8i	−0.972410	−	0.780652i
$735$	2.08196e8	−	4.94823e8i	0.524336	−	1.24620i
$736$	−4.85709e8	−	1.19190e8i	−1.21827	−	0.298955i
$737$	−5.42626e7	−	5.42626e7i	−0.135549	−	0.135549i
$738$	−3.05499e7	−	4.45801e8i	−0.0760047	−	1.10910i
$739$	−4.66919e8			−1.15693			−0.578467	−	0.815706i	$-0.696349\pi$
$739$	−4.66919e8			−1.15693			−0.578467	+	0.815706i	$0.696349\pi$
$740$	3.37918e8	−	2.43959e8i	0.833904	−	0.602034i
$741$	−2.62448e7	−	2.73306e7i	−0.0645042	−	0.0671731i
$742$	−8.80930e8	+	9.63606e7i	−2.15640	+	0.235878i
$743$	3.44315e8	+	3.44315e8i	0.839440	+	0.839440i	0.988785	−	0.149345i	$-0.0477165\pi$
$743$	3.44315e8	+	3.44315e8i	0.839440	+	0.839440i	−0.149345	+	0.988785i	$0.547716\pi$
$744$	−1.56771e8	−	4.95215e8i	−0.380669	−	1.20247i
$745$	−5.13568e7	−	2.03934e7i	−0.124202	−	0.0493199i
$746$	8.47084e7	+	6.80040e7i	0.204038	+	0.163801i
$747$	−3.49854e8	−	3.79429e8i	−0.839315	−	0.910266i
$748$	−1.52993e8	−	9.75235e7i	−0.365566	−	0.233026i
$749$	−4.00619e8			−0.953424
$750$	2.11627e8	+	3.64955e8i	0.501635	+	0.865080i
$751$		−	4.51792e8i		−	1.06664i	−0.845913	−	0.533321i	$-0.820944\pi$
$751$		−	4.51792e8i		−	1.06664i	0.845913	−	0.533321i	$-0.179056\pi$
$752$	3.47706e7	−	9.53756e7i	0.0817633	−	0.224277i
$753$	−9.44481e7	−	1.91429e6i	−0.221212	−	0.00448357i
$754$	1.50872e8	+	1.21120e8i	0.351961	+	0.282554i
$755$	−2.44857e8	+	6.16624e8i	−0.568948	+	1.43278i
$756$	5.36107e8	+	3.89482e8i	1.24076	+	0.901409i
$757$	1.51684e8	−	1.51684e8i	0.349664	−	0.349664i	−0.510320	−	0.859984i	$-0.670473\pi$
$757$	1.51684e8	−	1.51684e8i	0.349664	−	0.349664i	0.859984	+	0.510320i	$0.170473\pi$
$758$	3.24469e8	−	3.54920e7i	0.745015	−	0.0814935i
$759$	−1.62606e8	−	1.69334e8i	−0.371887	−	0.387274i
$760$	7.73547e7	+	3.95958e6i	0.176216	+	0.00902004i
$761$		−	9.64031e6i		−	0.0218744i	−0.999940	−	0.0109372i	$-0.996519\pi$
$761$		−	9.64031e6i		−	0.0218744i	0.999940	−	0.0109372i	$-0.00348149\pi$
$762$	6.39598e7	+	5.35141e7i	0.144558	+	0.120949i
$763$	−4.55099e8	+	4.55099e8i	−1.02455	+	1.02455i
$764$	5.11158e8	−	1.13180e8i	1.14624	−	0.253799i
$765$	−1.62649e8	−	4.23272e8i	−0.363301	−	0.945443i
$766$	2.96790e8	+	2.38263e8i	0.660334	+	0.530116i
$767$	−1.58115e8	+	1.58115e8i	−0.350419	+	0.350419i
$768$	2.98503e8	−	3.40722e8i	0.658968	−	0.752171i
$769$			5.96272e7i			0.131119i	0.997849	+	0.0655595i	$0.0208832\pi$
$769$			5.96272e7i			0.131119i	−0.997849	+	0.0655595i	$0.979117\pi$
$770$	−1.47956e8	−	2.60611e8i	−0.324086	−	0.570847i
$771$	−4.43001e8	−	4.61330e8i	−0.966588	−	1.00658i
$772$	5.01079e8	+	3.19407e8i	1.08907	+	0.694213i
$773$	6.02561e8	−	6.02561e8i	1.30456	−	1.30456i	0.379271	−	0.925286i	$-0.376175\pi$
$773$	6.02561e8	−	6.02561e8i	1.30456	−	1.30456i	0.925286	−	0.379271i	$-0.123825\pi$
$774$	−4.92619e8	+	5.65103e8i	−1.06240	+	1.21872i
$775$	−4.02766e8	+	4.27174e8i	−0.865262	+	0.917699i
$776$	−2.92893e8	+	5.93339e8i	−0.626792	+	1.26975i
$777$	−7.39782e8	−	1.49941e7i	−1.57703	−	0.0319636i
$778$	−1.65971e8	+	1.81548e7i	−0.352447	+	0.0385524i
$779$			9.27290e7i			0.196157i
$780$	1.42465e8	+	2.06006e8i	0.300210	+	0.434107i
$781$	1.04487e8			0.219336
$782$	−6.60660e7	−	6.03976e8i	−0.138152	−	1.26299i
$783$	4.09752e8	+	2.49421e7i	0.853563	+	0.0519575i
$784$	2.75035e8	+	5.90624e8i	0.570743	+	1.22564i
$785$	8.29155e8	−	3.57816e8i	1.71406	−	0.739692i
$786$	−3.51805e8	+	3.12824e7i	−0.724492	+	0.0644217i
$787$	6.82103e8	+	6.82103e8i	1.39935	+	1.39935i	0.801928	+	0.597421i	$0.203808\pi$
$787$	6.82103e8	+	6.82103e8i	1.39935	+	1.39935i	0.597421	+	0.801928i	$0.296192\pi$
$788$	5.47484e8	+	3.48988e8i	1.11890	+	0.713233i
$789$	−2.34663e8	−	2.44372e8i	−0.477764	−	0.497531i
$790$	−7.62084e8	−	2.10131e8i	−1.54569	−	0.426195i
$791$	9.38781e8			1.89686
$792$	2.03982e8	−	6.00553e7i	0.410598	−	0.120886i
$793$	2.27381e8	+	2.27381e8i	0.455969	+	0.455969i
$794$	1.24027e8	−	1.54493e8i	0.247773	−	0.308636i
$795$	−6.58116e8	+	2.68320e8i	−1.30979	+	0.534013i
$796$	1.34031e8	−	2.96771e7i	0.265746	−	0.0588414i
$797$	−4.00276e8	−	4.00276e8i	−0.790651	−	0.790651i	0.190949	−	0.981600i	$-0.438844\pi$
$797$	−4.00276e8	−	4.00276e8i	−0.790651	−	0.790651i	−0.981600	+	0.190949i	$0.938844\pi$
$798$	−1.05466e8	−	8.82417e7i	−0.207541	−	0.173646i
$799$	1.23328e8			0.241781
$800$	−5.00619e8	−	1.07351e8i	−0.977772	−	0.209670i
$801$	−2.90824e8	−	1.17938e7i	−0.565892	−	0.0229486i
$802$	−2.36903e7	−	2.16577e8i	−0.0459247	−	0.419845i
$803$	3.86986e7	+	3.86986e7i	0.0747392	+	0.0747392i
$804$	1.93702e8	+	1.29067e8i	0.372705	+	0.248339i
$805$	3.70379e8	−	9.32724e8i	0.710000	−	1.78799i
$806$	−2.18214e8	+	2.71816e8i	−0.416752	+	0.519123i
$807$	−2.39606e8	−	4.85639e6i	−0.455908	−	0.00924044i
$808$	−1.99837e8	−	5.89463e8i	−0.378828	−	1.11744i
$809$	−7.61996e8			−1.43915			−0.719577	−	0.694413i	$-0.755664\pi$
$809$	−7.61996e8			−1.43915			−0.719577	+	0.694413i	$0.755664\pi$
$810$	4.99201e8	+	1.82284e8i	0.939336	+	0.342999i
$811$			2.57850e8i			0.483398i	0.970351	+	0.241699i	$0.0777046\pi$
$811$			2.57850e8i			0.483398i	−0.970351	+	0.241699i	$0.922295\pi$
$812$	5.92084e8	+	3.77417e8i	1.10590	+	0.704942i
$813$	−1.66353e7	+	8.20758e8i	−0.0309570	+	1.52737i
$814$	−1.48642e8	+	1.85155e8i	−0.275594	+	0.343291i
$815$	−3.22596e8	+	1.39214e8i	−0.595917	+	0.257164i
$816$	5.13104e8	+	1.98929e8i	0.944354	+	0.366124i
$817$	1.10006e8	−	1.10006e8i	0.201721	−	0.201721i
$818$	6.97460e7	+	6.37619e8i	0.127426	+	1.16493i
$819$	1.80181e7	−	4.44310e8i	0.0327988	−	0.808787i
$820$	9.77127e7	−	6.05120e8i	0.177219	−	1.09749i
$821$		−	2.73749e7i		−	0.0494678i	−0.999694	−	0.0247339i	$-0.992126\pi$
$821$		−	2.73749e7i		−	0.0494678i	0.999694	−	0.0247339i	$-0.00787385\pi$
$822$	5.59607e8	+	4.68214e8i	1.00755	+	0.843002i
$823$	3.09407e8	−	3.09407e8i	0.555048	−	0.555048i	−0.372845	−	0.927894i	$-0.621618\pi$
$823$	3.09407e8	−	3.09407e8i	0.555048	−	0.555048i	0.927894	+	0.372845i	$0.121618\pi$
$824$	−1.69821e8	+	3.44022e8i	−0.303536	+	0.614900i
$825$	−1.71493e8	−	1.68388e8i	−0.305410	−	0.299880i
$826$	−5.08024e8	+	6.32815e8i	−0.901455	+	1.12289i
$827$	−2.17090e8	+	2.17090e8i	−0.383816	+	0.383816i	−0.872475	−	0.488659i	$-0.837486\pi$
$827$	−2.17090e8	+	2.17090e8i	−0.383816	+	0.383816i	0.488659	+	0.872475i	$0.337486\pi$
$828$	5.84463e8	+	4.06777e8i	1.02959	+	0.716581i
$829$		−	5.70382e7i		−	0.100116i	−0.998746	−	0.0500578i	$-0.984059\pi$
$829$		−	5.70382e7i		−	0.100116i	0.998746	−	0.0500578i	$-0.0159406\pi$
$830$	−3.49529e8	−	6.15663e8i	−0.611292	−	1.07673i
$831$	3.86438e8	−	3.71084e8i	0.673405	−	0.646650i
$832$	−3.01345e8	−	3.99142e7i	−0.523232	−	0.0693038i
$833$	−5.59684e8	+	5.59684e8i	−0.968296	+	0.968296i
$834$	8.22326e7	−	7.31210e6i	0.141757	−	0.0126050i
$835$	2.45848e8	−	1.06094e8i	0.422287	−	0.182235i
$836$	−4.30831e7	+	9.53943e6i	−0.0737374	+	0.0163269i
$837$	−4.49366e7	+	7.38223e8i	−0.0766344	+	1.25896i
$838$	−7.47384e7	−	6.83260e8i	−0.127002	−	1.16106i
$839$		−	6.15831e8i		−	1.04274i	−0.853331	−	0.521370i	$-0.825421\pi$
$839$		−	6.15831e8i		−	1.04274i	0.853331	−	0.521370i	$-0.174579\pi$
$840$	5.95254e8	+	6.86972e8i	1.00430	+	1.15905i
$841$	−1.59848e8			−0.268731
$842$	8.59927e8	−	9.40632e7i	1.44054	−	0.157574i
$843$	3.05872e6	−	1.50912e8i	0.00510572	−	0.251908i
$844$	−7.00661e7	−	3.16441e8i	−0.116541	−	0.526338i
$845$	−1.60642e8	+	4.04545e8i	−0.266250	+	0.670496i
$846$	−9.49794e7	+	1.08955e8i	−0.156862	+	0.179943i
$847$	−5.38231e8	−	5.38231e8i	−0.885765	−	0.885765i
$848$	2.95432e8	−	8.10370e8i	0.484473	−	1.32891i
$849$	7.82253e8	−	7.51174e8i	1.27828	−	1.22749i
$850$	−8.57831e7	−	6.16068e8i	−0.139683	−	1.00316i
$851$	−7.95132e8			−1.29018
$852$	−3.10759e8	+	6.22303e7i	−0.502464	+	0.100620i
$853$	5.37667e8	+	5.37667e8i	0.866296	+	0.866296i	0.992060	−	0.125764i	$-0.0401382\pi$
$853$	5.37667e8	+	5.37667e8i	0.866296	+	0.866296i	−0.125764	+	0.992060i	$0.540138\pi$
$854$	9.10034e8	+	7.30576e8i	1.46111	+	1.17298i
$855$	−1.00765e8	−	4.48213e7i	−0.161217	−	0.0717110i
$856$	1.72600e8	−	3.49650e8i	0.275181	−	0.557459i
$857$	−4.39584e8	−	4.39584e8i	−0.698392	−	0.698392i	0.265672	−	0.964064i	$-0.414406\pi$
$857$	−4.39584e8	−	4.39584e8i	−0.698392	−	0.698392i	−0.964064	+	0.265672i	$0.914406\pi$
$858$	−1.09439e8	−	9.15655e7i	−0.173264	−	0.144967i
$859$	1.12077e6			0.00176823			0.000884113	−	1.00000i	$-0.499719\pi$
$859$	1.12077e6			0.00176823			0.000884113		1.00000i	$0.499719\pi$
$860$	−8.33782e8	+	6.01946e8i	−1.31086	+	0.946372i
$861$	−7.84927e8	+	7.53741e8i	−1.22976	+	1.18090i
$862$	7.88525e8	−	8.62528e7i	1.23110	−	0.134664i
$863$	−7.87715e8	−	7.87715e8i	−1.22557	−	1.22557i	−0.965625	−	0.259941i	$-0.916297\pi$
$863$	−7.87715e8	−	7.87715e8i	−1.22557	−	1.22557i	−0.259941	−	0.965625i	$-0.583703\pi$
$864$	−5.70902e8	+	3.00100e8i	−0.885158	+	0.465291i
$865$	3.46688e8	−	1.49611e8i	0.535661	−	0.231161i
$866$	−3.71350e8	−	2.98120e8i	−0.571780	−	0.459026i
$867$	−341390.	+	1.68436e7i	−0.000523833	+	0.0258451i
$868$	−6.79969e8	+	1.06672e9i	−1.03975	+	1.63114i
$869$	4.50360e8			0.686278
$870$	5.39711e8	+	1.60652e8i	0.819603	+	0.243966i
$871$		−	1.56196e8i		−	0.236383i
$872$	−2.01128e8	−	5.93271e8i	−0.303335	−	0.894754i
$873$	6.92638e8	−	6.38651e8i	1.04103	−	0.959888i
$874$	−1.15232e8	−	9.25084e7i	−0.172599	−	0.138563i
$875$	3.50943e8	−	9.65615e8i	0.523856	−	1.44138i
$876$	−1.38143e8	−	9.20468e7i	−0.205502	−	0.136929i
$877$	1.00192e8	−	1.00192e8i	0.148536	−	0.148536i	−0.628928	−	0.777464i	$-0.716506\pi$
$877$	1.00192e8	−	1.00192e8i	0.148536	−	0.148536i	0.777464	+	0.628928i	$0.216506\pi$
$878$	−4.98455e8	+	5.45235e7i	−0.736449	+	0.0805565i
$879$	−6.53686e8	+	6.27714e8i	−0.962504	+	0.924262i
$880$	2.91199e8	−	1.68527e7i	0.427308	−	0.0247299i
$881$			1.01988e9i			1.49150i	0.666228	+	0.745748i	$0.267908\pi$
$881$			1.01988e9i			1.49150i	−0.666228	+	0.745748i	$0.732092\pi$
$882$	−6.34217e7	−	9.25485e8i	−0.0924341	−	1.34885i
$883$	−4.29193e8	+	4.29193e8i	−0.623405	+	0.623405i	−0.946400	−	0.322996i	$-0.895310\pi$
$883$	−4.29193e8	+	4.29193e8i	−0.623405	+	0.623405i	0.322996	+	0.946400i	$0.395310\pi$
$884$	−7.98348e7	−	3.60559e8i	−0.115567	−	0.521939i
$885$	−2.52401e8	+	5.99885e8i	−0.364134	+	0.865443i
$886$	−1.95255e8	−	1.56750e8i	−0.280737	−	0.225376i
$887$	5.53654e6	−	5.53654e6i	0.00793355	−	0.00793355i	−0.703129	−	0.711062i	$-0.748214\pi$
$887$	5.53654e6	−	5.53654e6i	0.00793355	−	0.00793355i	0.711062	+	0.703129i	$0.248214\pi$
$888$	3.31808e8	−	6.39204e8i	0.473858	−	0.912852i
$889$		−	2.03094e8i		−	0.289062i
$890$	−3.84900e8	−	1.06129e8i	−0.545982	−	0.150545i
$891$	−3.01767e8	−	2.45155e7i	−0.426618	−	0.0346583i
$892$	2.90905e8	−	4.56366e8i	0.409880	−	0.643011i
$893$	2.12097e7	−	2.12097e7i	0.0297838	−	0.0297838i
$894$	−9.51100e7	+	8.45715e6i	−0.133111	+	0.0118362i
$895$	−1.52203e8	+	3.83292e8i	−0.212302	+	0.534639i
$896$	−1.10289e9	−	2.50783e7i	−1.53323	−	0.0348637i
$897$	9.68311e6	−	4.77749e8i	0.0134165	−	0.661946i
$898$	1.75963e8	−	1.92477e7i	0.242992	−	0.0265796i
$899$			7.83668e8i			1.07858i
$900$	6.10330e8	+	3.98670e8i	0.837216	+	0.546872i
$901$	1.04787e9			1.43263
$902$	3.79710e7	+	3.47131e8i	0.0517407	+	0.473014i
$903$	1.82535e9	+	3.69965e7i	2.47903	+	0.0502455i
$904$	−4.04457e8	+	8.19344e8i	−0.547478	+	1.10908i
$905$	4.52715e8	+	1.79770e8i	0.610772	+	0.242534i
$906$	1.01542e8	+	1.14195e9i	0.136541	+	1.53555i
$907$	9.14446e8	+	9.14446e8i	1.22556	+	1.22556i	0.965625	+	0.259940i	$0.0837028\pi$
$907$	9.14446e8	+	9.14446e8i	1.22556	+	1.22556i	0.259940	+	0.965625i	$0.416297\pi$
$908$	2.55160e8	−	4.00288e8i	0.340843	−	0.534707i
$909$	−3.59091e7	+	8.85485e8i	−0.0478094	+	1.17893i
$910$	1.62140e8	−	5.88035e8i	0.215162	−	0.780332i
$911$	1.03770e9			1.37251			0.686255	−	0.727361i	$-0.259254\pi$
$911$	1.03770e9			1.37251			0.686255	+	0.727361i	$0.259254\pi$
$912$	1.22453e8	−	5.40309e7i	0.161431	−	0.0712291i
$913$	2.85194e8	+	2.85194e8i	0.374738	+	0.374738i
$914$	−3.81600e8	+	4.75337e8i	−0.499770	+	0.622533i
$915$	8.62679e8	+	3.62971e8i	1.12612	+	0.473814i
$916$	−1.97306e8	−	8.91095e8i	−0.256716	−	1.15941i
$917$	6.08215e8	+	6.08215e8i	0.788767	+	0.788767i
$918$	−5.80086e8	−	5.26745e8i	−0.749833	−	0.680883i
$919$	1.16193e9			1.49704			0.748521	−	0.663111i	$-0.230764\pi$
$919$	1.16193e9			1.49704			0.748521	+	0.663111i	$0.230764\pi$
$920$	6.54487e8	+	7.25105e8i	0.840500	+	0.931188i
$921$	4.85901e8	+	5.06005e8i	0.621970	+	0.647704i
$922$	2.02823e7	+	1.85421e8i	0.0258777	+	0.236574i
$923$	1.50385e8	+	1.50385e8i	0.191249	+	0.191249i
$924$	−4.30946e8	−	2.87146e8i	−0.546270	−	0.363988i
$925$	−8.13669e8	+	2.39298e7i	−1.02807	+	0.0302352i
$926$	−8.82032e7	+	1.09869e8i	−0.111084	+	0.138371i
$927$	4.01596e8	−	3.70294e8i	0.504139	−	0.464844i
$928$	−5.84489e8	+	3.54152e8i	−0.731362	+	0.443145i
$929$	1.15806e9			1.44439			0.722193	−	0.691692i	$-0.243134\pi$
$929$	1.15806e9			1.44439			0.722193	+	0.691692i	$0.243134\pi$
$930$	−2.89437e8	+	9.72363e8i	−0.359837	+	1.20887i
$931$			1.92506e8i			0.238559i
$932$	−2.80216e8	+	4.39597e8i	−0.346135	+	0.543009i
$933$	−2.54999e7	−	516836.i	−0.0313973	−	0.000636368i
$934$	−3.95879e7	+	4.93123e7i	−0.0485872	+	0.0605222i
$935$	1.40405e8	+	3.25357e8i	0.171771	+	0.398038i
$936$	3.80020e8	+	2.07149e8i	0.463424	+	0.252612i
$937$	−1.04343e9	+	1.04343e9i	−1.26836	+	1.26836i	−0.321430	+	0.946933i	$0.604164\pi$
$937$	−1.04343e9	+	1.04343e9i	−1.26836	+	1.26836i	−0.946933	+	0.321430i	$0.895836\pi$
$938$	−6.16381e7	−	5.63497e8i	−0.0746863	−	0.682783i
$939$	4.77211e8	+	4.96956e8i	0.576386	+	0.600234i
$940$	−1.60757e8	+	1.16058e8i	−0.193547	+	0.139731i
$941$		−	2.33517e8i		−	0.280253i	−0.990134	−	0.140126i	$-0.955249\pi$
$941$		−	2.33517e8i		−	0.280253i	0.990134	−	0.140126i	$-0.0447509\pi$
$942$	1.00137e9	−	1.19684e9i	1.19796	−	1.43180i
$943$	−8.26895e8	+	8.26895e8i	−0.986087	+	0.986087i
$944$	−3.33432e8	−	7.16028e8i	−0.396361	−	0.851165i
$945$	−4.39661e8	−	1.21728e9i	−0.520981	−	1.44243i
$946$	3.66762e8	−	4.56853e8i	0.433222	−	0.539639i
$947$	−3.43317e8	+	3.43317e8i	−0.404245	+	0.404245i	−0.879726	−	0.475481i	$-0.842274\pi$
$947$	−3.43317e8	+	3.43317e8i	−0.404245	+	0.404245i	0.475481	+	0.879726i	$0.342274\pi$
$948$	−1.33943e9	+	2.68224e8i	−1.57215	+	0.314828i
$949$			1.11395e8i			0.130337i
$950$	−1.20702e8	−	9.11970e7i	−0.140781	−	0.106368i
$951$	1.65776e8	+	1.72635e8i	0.192744	+	0.200719i
$952$	−4.30297e8	−	1.26925e9i	−0.498721	−	1.47109i
$953$	1.24773e8	−	1.24773e8i	0.144159	−	0.144159i	−0.631344	−	0.775503i	$-0.717496\pi$
$953$	1.24773e8	−	1.24773e8i	0.144159	−	0.144159i	0.775503	+	0.631344i	$0.217496\pi$
$954$	−8.07003e8	+	9.25745e8i	−0.929459	+	1.06622i
$955$	−9.50349e8	−	3.77378e8i	−1.09112	−	0.433277i
$956$	−9.07110e7	−	4.09679e8i	−0.103821	−	0.468889i
$957$	−3.20739e8	−	6.50081e6i	−0.365946	−	0.00741706i
$958$	1.40678e8	+	1.28608e9i	0.160004	+	1.46276i
$959$		−	1.77694e9i		−	2.01473i
$960$	−8.56027e8	+	2.23554e8i	−0.967550	+	0.252678i
$961$	−5.24381e8			−0.590849
$962$	−4.80423e8	+	5.25511e7i	−0.539633	+	0.0590278i
$963$	−4.08167e8	+	3.76352e8i	−0.457045	+	0.421420i
$964$	1.09978e9	−	2.43513e8i	1.22765	−	0.271826i
$965$	−4.59853e8	−	1.06560e9i	−0.511726	−	1.18580i
$966$	−1.53596e8	−	1.72736e9i	−0.170392	−	1.91624i
$967$	5.71660e8	+	5.71660e8i	0.632205	+	0.632205i	0.948621	−	0.316416i	$-0.102479\pi$
$967$	5.71660e8	+	5.71660e8i	0.632205	+	0.632205i	−0.316416	+	0.948621i	$0.602479\pi$
$968$	7.01642e8	−	2.37868e8i	0.773552	−	0.262246i
$969$	1.12624e8	+	1.17284e8i	0.123782	+	0.128904i
$970$	1.12388e9	−	6.38057e8i	1.23141	−	0.699108i
$971$	−1.63809e9			−1.78928			−0.894642	−	0.446784i	$-0.852569\pi$
$971$	−1.63809e9			−1.78928			−0.894642	+	0.446784i	$0.852569\pi$
$972$	9.12097e8	−	1.06814e8i	0.993213	−	0.116313i
$973$	−1.42167e8	−	1.42167e8i	−0.154334	−	0.154334i
$974$	1.04267e9	+	8.37053e8i	1.12841	+	0.905891i
$975$	−4.46917e6	−	4.89178e8i	−0.00482184	−	0.527780i
$976$	−1.02970e9	+	4.79499e8i	−1.10754	+	0.515749i
$977$	−5.99601e8	−	5.99601e8i	−0.642952	−	0.642952i	0.308328	−	0.951280i	$-0.400231\pi$
$977$	−5.99601e8	−	5.99601e8i	−0.642952	−	0.642952i	−0.951280	+	0.308328i	$0.900231\pi$
$978$	−3.89599e8	+	4.65648e8i	−0.416487	+	0.497784i
$979$	2.27460e8			0.242414
$980$	2.02852e8	−	1.25623e9i	0.215527	−	1.33472i
$981$	−3.61411e7	+	8.91205e8i	−0.0382820	+	0.943997i
$982$	−3.59727e8	+	3.93488e7i	−0.379874	+	0.0415525i
$983$	−9.11274e7	−	9.11274e7i	−0.0959375	−	0.0959375i	0.657509	−	0.753447i	$-0.271610\pi$
$983$	−9.11274e7	−	9.11274e7i	−0.0959375	−	0.0959375i	−0.753447	+	0.657509i	$0.771610\pi$
$984$	−3.19674e8	−	1.00980e9i	−0.335523	−	1.05986i
$985$	−5.02441e8	−	1.16429e9i	−0.525746	−	1.21829i
$986$	−6.47434e8	−	5.19761e8i	−0.675406	−	0.542216i
$987$	3.51936e8	+	7.13310e6i	0.366026	+	0.00741869i
$988$	−7.57377e7	−	4.82782e7i	−0.0785311	−	0.0500588i
$989$	1.96192e9			2.02811
$990$	−3.95568e8	−	1.26527e8i	−0.407676	−	0.130400i
$991$		−	1.19599e9i		−	1.22887i	−0.788966	−	0.614437i	$-0.789383\pi$
$991$		−	1.19599e9i		−	1.22887i	0.788966	−	0.614437i	$-0.210617\pi$
$992$	−6.38054e8	−	1.05304e9i	−0.653616	−	1.07872i
$993$	6.24864e6	−	3.08298e8i	0.00638172	−	0.314864i
$994$	6.01875e8	+	4.83186e8i	0.612840	+	0.491989i
$995$	−2.49192e8	−	9.89527e7i	−0.252968	−	0.100452i
$996$	−1.01806e9	−	6.78350e8i	−1.03038	−	0.686556i
$997$	−1.32271e9	+	1.32271e9i	−1.33469	+	1.33469i	−0.433571	+	0.901120i	$0.642747\pi$
$997$	−1.32271e9	+	1.32271e9i	−1.33469	+	1.33469i	−0.901120	+	0.433571i	$0.857253\pi$
$998$	3.02552e7	−	3.30947e6i	0.0304375	−	0.00332941i
$999$	−7.67805e8	+	6.79694e8i	−0.770113	+	0.681737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.2	✓	136
3.2	odd	2	inner	60.7.l.a.23.67	yes	136
4.3	odd	2	inner	60.7.l.a.23.36	yes	136
5.2	odd	4	inner	60.7.l.a.47.33	yes	136
12.11	even	2	inner	60.7.l.a.23.33	yes	136
15.2	even	4	inner	60.7.l.a.47.36	yes	136
20.7	even	4	inner	60.7.l.a.47.67	yes	136
60.47	odd	4	inner	60.7.l.a.47.2	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.2	✓	136	1.1	even	1	trivial
60.7.l.a.23.33	yes	136	12.11	even	2	inner
60.7.l.a.23.36	yes	136	4.3	odd	2	inner
60.7.l.a.23.67	yes	136	3.2	odd	2	inner
60.7.l.a.47.2	yes	136	60.47	odd	4	inner
60.7.l.a.47.33	yes	136	5.2	odd	4	inner
60.7.l.a.47.36	yes	136	15.2	even	4	inner
60.7.l.a.47.67	yes	136	20.7	even	4	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.95256 + 0.869892i) q^{2} +(26.9945 + 0.547129i) q^{3} +(62.4866 - 13.8357i) q^{4} +(-116.176 - 46.1326i) q^{5} +(-215.151 + 19.1312i) q^{6} +(371.962 + 371.962i) q^{7} +(-484.893 + 164.386i) q^{8} +(728.401 + 29.5389i) q^{9} +O(q^{10})\)	\(q+(-7.95256 + 0.869892i) q^{2} +(26.9945 + 0.547129i) q^{3} +(62.4866 - 13.8357i) q^{4} +(-116.176 - 46.1326i) q^{5} +(-215.151 + 19.1312i) q^{6} +(371.962 + 371.962i) q^{7} +(-484.893 + 164.386i) q^{8} +(728.401 + 29.5389i) q^{9} +(964.025 + 265.812i) q^{10} -569.699 q^{11} +(1694.36 - 339.300i) q^{12} +(-819.948 - 819.948i) q^{13} +(-3281.62 - 2634.49i) q^{14} +(-3110.86 - 1308.89i) q^{15} +(3713.14 - 1729.10i) q^{16} +(3518.63 + 3518.63i) q^{17} +(-5818.35 + 398.720i) q^{18} +1210.25 q^{19} +(-7897.70 - 1275.29i) q^{20} +(9837.41 + 10244.4i) q^{21} +(4530.57 - 495.576i) q^{22} +(10792.2 + 10792.2i) q^{23} +(-13179.4 + 4172.22i) q^{24} +(11368.6 + 10719.0i) q^{25} +(7233.95 + 5807.42i) q^{26} +(19646.6 + 1195.92i) q^{27} +(28389.0 + 18096.3i) q^{28} +20856.1 q^{29} +(25877.9 + 7702.91i) q^{30} +37575.1i q^{31} +(-28024.9 + 16980.8i) q^{32} +(-15378.7 - 311.699i) q^{33} +(-31043.0 - 24921.3i) q^{34} +(-26053.4 - 60372.6i) q^{35} +(45924.0 - 8232.19i) q^{36} +(-36838.4 + 36838.4i) q^{37} +(-9624.58 + 1052.79i) q^{38} +(-21685.4 - 22582.7i) q^{39} +(63916.3 + 3271.71i) q^{40} +76619.8i q^{41} +(-87144.2 - 72912.0i) q^{42} +(90895.3 - 90895.3i) q^{43} +(-35598.5 + 7882.21i) q^{44} +(-83259.8 - 37034.8i) q^{45} +(-95213.5 - 76437.5i) q^{46} +(17525.1 - 17525.1i) q^{47} +(101180. - 44644.4i) q^{48} +159063. i q^{49} +(-99733.6 - 75353.9i) q^{50} +(93058.4 + 96908.7i) q^{51} +(-62580.3 - 39891.1i) q^{52} +(148904. - 148904. i) q^{53} +(-157281. + 7579.85i) q^{54} +(66185.1 + 26281.7i) q^{55} +(-241507. - 119216. i) q^{56} +(32670.0 + 662.162i) q^{57} +(-165859. + 18142.5i) q^{58} -192836. i q^{59} +(-212496. - 38746.9i) q^{60} -277312. q^{61} +(-32686.2 - 298818. i) q^{62} +(259951. + 281925. i) q^{63} +(208098. - 159419. i) q^{64} +(57431.6 + 133084. i) q^{65} +(122571. - 10899.0i) q^{66} +(95247.8 + 95247.8i) q^{67} +(268550. + 171184. i) q^{68} +(285424. + 297234. i) q^{69} +(259709. + 457453. i) q^{70} -183408. q^{71} +(-358052. + 105416. i) q^{72} +(-67928.2 - 67928.2i) q^{73} +(260914. - 325005. i) q^{74} +(301024. + 295573. i) q^{75} +(75624.3 - 16744.7i) q^{76} +(-211907. - 211907. i) q^{77} +(192099. + 160726. i) q^{78} -790523. q^{79} +(-511145. + 29581.8i) q^{80} +(529696. + 43032.4i) q^{81} +(-66651.0 - 609324. i) q^{82} +(-500605. - 500605. i) q^{83} +(756446. + 504032. i) q^{84} +(-246456. - 571103. i) q^{85} +(-643782. + 801920. i) q^{86} +(562998. + 11411.0i) q^{87} +(276243. - 93650.6i) q^{88} -399264. q^{89} +(694345. + 222094. i) q^{90} -609979. i q^{91} +(823684. + 525048. i) q^{92} +(-20558.4 + 1.01432e6i) q^{93} +(-124124. + 154614. i) q^{94} +(-140601. - 55832.0i) q^{95} +(-765807. + 443054. i) q^{96} +(913843. - 913843. i) q^{97} +(-138368. - 1.26496e6i) q^{98} +(-414969. - 16828.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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