LMFDB - Embedded newform 150.6.g.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, 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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 67300 x^{18} - 605415 x^{17} + 1505002471 x^{16} - 12026298320 x^{15} + \cdots + 45\!\cdots\!05 $ x^20 - 10x^19 + 67300x^18 - 605415x^17 + 1505002471x^16 - 12026298320x^15 + 15161344295580x^14 - 105918997871590x^13 + 72521519492275041x^12 - 433752716999522710x^11 + 150954604904063839080x^10 - 750799480917962811625x^9 + 100084099910299358028076x^8 - 395836369710607771806480x^7 + 22144208384329171616972475x^6 - 65050346450081546072582845x^5 + 865137734840778899106150416x^4 - 1622318535480468844324766865x^3 + 11299132807307021058314145735x^2 - 10498749516125580450644510315*x + 45940690246932155189634577205
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.4
Root			$0.500000 - 3.46508i$ of defining polynomial
Character	$\chi$	$=$	150.91
Dual form			150.6.g.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(32.6761 - 45.3572i) q^{5} +(11.1246 - 34.2380i) q^{6} -9.31479 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(32.6761 - 45.3572i) q^{5} +(11.1246 - 34.2380i) q^{6} -9.31479 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(212.383 - 69.9528i) q^{10} +(429.968 + 312.390i) q^{11} +(116.498 - 84.6411i) q^{12} +(-16.2317 + 11.7930i) q^{13} +(-30.1433 - 21.9004i) q^{14} +(-479.112 - 153.546i) q^{15} +(-207.108 + 150.473i) q^{16} +(504.620 - 1553.06i) q^{17} -324.000 q^{18} +(734.424 - 2260.32i) q^{19} +(851.755 + 272.971i) q^{20} +(25.9059 + 79.7301i) q^{21} +(656.933 + 2021.83i) q^{22} +(-1792.53 - 1302.35i) q^{23} +576.000 q^{24} +(-989.546 - 2964.19i) q^{25} -80.2539 q^{26} +(589.773 + 428.495i) q^{27} +(-46.0549 - 141.742i) q^{28} +(2008.32 + 6180.97i) q^{29} +(-1189.43 - 1623.35i) q^{30} +(1311.67 - 4036.91i) q^{31} -1024.00 q^{32} +(1478.10 - 4549.12i) q^{33} +(5284.45 - 3839.38i) q^{34} +(-304.371 + 422.493i) q^{35} +(-1048.49 - 761.770i) q^{36} +(9258.59 - 6726.76i) q^{37} +(7690.99 - 5587.83i) q^{38} +(146.085 + 106.137i) q^{39} +(2114.55 + 2885.95i) q^{40} +(13150.7 - 9554.53i) q^{41} +(-103.623 + 318.920i) q^{42} -1306.33 q^{43} +(-2627.73 + 8087.33i) q^{44} +(18.2061 + 4528.00i) q^{45} +(-2738.75 - 8428.99i) q^{46} +(656.489 + 2020.46i) q^{47} +(1863.98 + 1354.26i) q^{48} -16720.2 q^{49} +(3766.99 - 11918.9i) q^{50} -14696.9 q^{51} +(-259.707 - 188.688i) q^{52} +(-2380.28 - 7325.75i) q^{53} +(901.094 + 2773.28i) q^{54} +(28218.8 - 9294.46i) q^{55} +(184.220 - 566.969i) q^{56} -21389.8 q^{57} +(-8033.28 + 24723.9i) q^{58} +(5155.76 - 3745.88i) q^{59} +(-32.3664 - 8049.78i) q^{60} +(35602.1 + 25866.5i) q^{61} +(13736.0 - 9979.80i) q^{62} +(610.402 - 443.483i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(4.50960 + 1121.57i) q^{65} +(15478.9 - 11246.1i) q^{66} +(-13867.1 + 42678.4i) q^{67} +26127.8 q^{68} +(-6162.18 + 18965.2i) q^{69} +(-1978.31 + 651.596i) q^{70} +(-15890.7 - 48906.5i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(-42845.6 - 31129.1i) q^{73} +45777.0 q^{74} +(-22619.9 + 16713.9i) q^{75} +38026.3 q^{76} +(-4005.07 - 2909.85i) q^{77} +(223.198 + 686.934i) q^{78} +(31598.7 + 97250.9i) q^{79} +(57.5403 + 14310.7i) q^{80} +(2027.46 - 6239.88i) q^{81} +65020.6 q^{82} +(-27294.5 + 84003.8i) q^{83} +(-1085.16 + 788.414i) q^{84} +(-53953.5 - 73636.1i) q^{85} +(-4227.39 - 3071.38i) q^{86} +(47320.7 - 34380.5i) q^{87} +(-27518.0 + 19993.0i) q^{88} +(-19284.7 - 14011.1i) q^{89} +(-10587.1 + 14695.7i) q^{90} +(151.195 - 109.849i) q^{91} +(10955.0 - 33716.0i) q^{92} -38201.9 q^{93} +(-2625.95 + 8081.86i) q^{94} +(-78523.8 - 107170. i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-30663.2 - 94371.6i) q^{97} +(-54107.8 - 39311.6i) q^{98} -43049.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	32.6761	−	45.3572i	0.584528	−	0.811374i
$5$	32.6761	−	45.3572i	0.584528	−	0.811374i
$6$	11.1246	−	34.2380i	0.126156	−	0.388267i
$7$	−9.31479			−0.0718502			−0.0359251	−	0.999354i	$-0.511438\pi$
$7$	−9.31479			−0.0718502			−0.0359251	+	0.999354i	$0.511438\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	212.383	−	69.9528i	0.671615	−	0.221210i
$11$	429.968	+	312.390i	1.07141	+	0.778423i	0.976165	−	0.217031i	$-0.0696371\pi$
$11$	429.968	+	312.390i	1.07141	+	0.778423i	0.0952432	+	0.995454i	$0.469637\pi$
$12$	116.498	−	84.6411i	0.233543	−	0.169679i
$13$	−16.2317	+	11.7930i	−0.0266382	+	0.0193538i	−0.601025	−	0.799230i	$-0.705241\pi$
$13$	−16.2317	+	11.7930i	−0.0266382	+	0.0193538i	0.574386	+	0.818584i	$0.305241\pi$
$14$	−30.1433	−	21.9004i	−0.0411027	−	0.0298629i
$15$	−479.112	−	153.546i	−0.549806	−	0.176202i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	504.620	−	1553.06i	0.423489	−	1.30337i	−0.480944	−	0.876751i	$-0.659706\pi$
$17$	504.620	−	1553.06i	0.423489	−	1.30337i	0.904433	−	0.426615i	$-0.140294\pi$
$18$	−324.000			−0.235702
$19$	734.424	−	2260.32i	0.466727	−	1.43644i	−0.390071	−	0.920785i	$-0.627549\pi$
$19$	734.424	−	2260.32i	0.466727	−	1.43644i	0.856798	−	0.515653i	$-0.172451\pi$
$20$	851.755	+	272.971i	0.476146	+	0.152595i
$21$	25.9059	+	79.7301i	0.0128189	+	0.0394524i
$22$	656.933	+	2021.83i	0.289377	+	0.890612i
$23$	−1792.53	−	1302.35i	−0.706557	−	0.513344i	0.175504	−	0.984479i	$-0.443845\pi$
$23$	−1792.53	−	1302.35i	−0.706557	−	0.513344i	−0.882061	+	0.471135i	$0.843845\pi$
$24$	576.000			0.204124
$25$	−989.546	−	2964.19i	−0.316655	−	0.948541i
$26$	−80.2539			−0.0232827
$27$	589.773	+	428.495i	0.155695	+	0.113119i
$28$	−46.0549	−	141.742i	−0.0111015	−	0.0341668i
$29$	2008.32	+	6180.97i	0.443443	+	1.36478i	0.884182	+	0.467142i	$0.154716\pi$
$29$	2008.32	+	6180.97i	0.443443	+	1.36478i	−0.440739	+	0.897635i	$0.645284\pi$
$30$	−1189.43	−	1623.35i	−0.241288	−	0.329312i
$31$	1311.67	−	4036.91i	0.245144	−	0.754475i	−0.750469	−	0.660906i	$-0.770172\pi$
$31$	1311.67	−	4036.91i	0.245144	−	0.754475i	0.995613	−	0.0935695i	$-0.0298277\pi$
$32$	−1024.00			−0.176777
$33$	1478.10	−	4549.12i	0.236276	−	0.727182i
$34$	5284.45	−	3839.38i	0.783976	−	0.569592i
$35$	−304.371	+	422.493i	−0.0419984	+	0.0582974i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	9258.59	−	6726.76i	1.11184	−	0.807796i	0.128884	−	0.991660i	$-0.458860\pi$
$37$	9258.59	−	6726.76i	1.11184	−	0.807796i	0.982952	+	0.183864i	$0.0588605\pi$
$38$	7690.99	−	5587.83i	0.864019	−	0.627746i
$39$	146.085	+	106.137i	0.0153796	+	0.0111739i
$40$	2114.55	+	2885.95i	0.208962	+	0.285193i
$41$	13150.7	−	9554.53i	1.22177	−	0.887666i	0.225522	−	0.974238i	$-0.427591\pi$
$41$	13150.7	−	9554.53i	1.22177	−	0.887666i	0.996246	+	0.0865715i	$0.0275911\pi$
$42$	−103.623	+	318.920i	−0.00906431	+	0.0278971i
$43$	−1306.33			−0.107742			−0.0538708	−	0.998548i	$-0.517156\pi$
$43$	−1306.33			−0.107742			−0.0538708	+	0.998548i	$0.517156\pi$
$44$	−2627.73	+	8087.33i	−0.204621	+	0.629758i
$45$	18.2061	+	4528.00i	0.00134025	+	0.333331i
$46$	−2738.75	−	8428.99i	−0.190835	−	0.587329i
$47$	656.489	+	2020.46i	0.0433493	+	0.133416i	0.970389	−	0.241548i	$-0.0776552\pi$
$47$	656.489	+	2020.46i	0.0433493	+	0.133416i	−0.927039	+	0.374964i	$0.877655\pi$
$48$	1863.98	+	1354.26i	0.116772	+	0.0848395i
$49$	−16720.2			−0.994838
$50$	3766.99	−	11918.9i	0.213093	−	0.674234i
$51$	−14696.9			−0.791224
$52$	−259.707	−	188.688i	−0.0133191	−	0.00967690i
$53$	−2380.28	−	7325.75i	−0.116396	−	0.358231i	0.875840	−	0.482602i	$-0.160308\pi$
$53$	−2380.28	−	7325.75i	−0.116396	−	0.358231i	−0.992236	+	0.124372i	$0.960308\pi$
$54$	901.094	+	2773.28i	0.0420519	+	0.129422i
$55$	28218.8	−	9294.46i	1.25786	−	0.414302i
$56$	184.220	−	566.969i	0.00784993	−	0.0241596i
$57$	−21389.8			−0.872007
$58$	−8033.28	+	24723.9i	−0.313562	+	0.965044i
$59$	5155.76	−	3745.88i	0.192825	−	0.140095i	−0.487184	−	0.873299i	$-0.661976\pi$
$59$	5155.76	−	3745.88i	0.192825	−	0.140095i	0.680009	+	0.733204i	$0.261976\pi$
$60$	−32.3664	−	8049.78i	−0.00116069	−	0.288673i
$61$	35602.1	+	25866.5i	1.22504	+	0.890046i	0.996509	−	0.0834892i	$-0.0266064\pi$
$61$	35602.1	+	25866.5i	1.22504	+	0.890046i	0.228535	+	0.973536i	$0.426606\pi$
$62$	13736.0	−	9979.80i	0.453818	−	0.329718i
$63$	610.402	−	443.483i	0.0193760	−	0.0140775i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	4.50960	+	1121.57i	0.000132390	+	0.0329264i
$66$	15478.9	−	11246.1i	0.437400	−	0.317790i
$67$	−13867.1	+	42678.4i	−0.377396	+	1.16151i	0.564452	+	0.825466i	$0.309088\pi$
$67$	−13867.1	+	42678.4i	−0.377396	+	1.16151i	−0.941848	+	0.336040i	$0.890912\pi$
$68$	26127.8			0.685220
$69$	−6162.18	+	18965.2i	−0.155816	+	0.479552i
$70$	−1978.31	+	651.596i	−0.0482557	+	0.0158940i
$71$	−15890.7	−	48906.5i	−0.374108	−	1.15139i	−0.944079	−	0.329720i	$-0.893046\pi$
$71$	−15890.7	−	48906.5i	−0.374108	−	1.15139i	0.569971	−	0.821665i	$-0.306954\pi$
$72$	−1601.94	−	4930.28i	−0.0364180	−	0.112083i
$73$	−42845.6	−	31129.1i	−0.941020	−	0.683691i	0.00764569	−	0.999971i	$-0.497566\pi$
$73$	−42845.6	−	31129.1i	−0.941020	−	0.683691i	−0.948666	+	0.316279i	$0.897566\pi$
$74$	45777.0			0.971780
$75$	−22619.9	+	16713.9i	−0.464342	+	0.343103i
$76$	38026.3			0.755180
$77$	−4005.07	−	2909.85i	−0.0769809	−	0.0559299i
$78$	223.198	+	686.934i	0.00415388	+	0.0127843i
$79$	31598.7	+	97250.9i	0.569642	+	1.75318i	0.653739	+	0.756720i	$0.273199\pi$
$79$	31598.7	+	97250.9i	0.569642	+	1.75318i	−0.0840970	+	0.996458i	$0.526801\pi$
$80$	57.5403	+	14310.7i	0.00100519	+	0.249998i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	65020.6			1.06786
$83$	−27294.5	+	84003.8i	−0.434891	+	1.33846i	0.458308	+	0.888793i	$0.348456\pi$
$83$	−27294.5	+	84003.8i	−0.434891	+	1.33846i	−0.893199	+	0.449662i	$0.851544\pi$
$84$	−1085.16	+	788.414i	−0.0167801	+	0.0121915i
$85$	−53953.5	−	73636.1i	−0.809976	−	1.10546i
$86$	−4227.39	−	3071.38i	−0.0616348	−	0.0447803i
$87$	47320.7	−	34380.5i	0.670274	−	0.486983i
$88$	−27518.0	+	19993.0i	−0.378800	+	0.275214i
$89$	−19284.7	−	14011.1i	−0.258070	−	0.187499i	0.451226	−	0.892410i	$-0.350987\pi$
$89$	−19284.7	−	14011.1i	−0.258070	−	0.187499i	−0.709296	+	0.704911i	$0.750987\pi$
$90$	−10587.1	+	14695.7i	−0.137774	+	0.191243i
$91$	151.195	−	109.849i	0.00191396	−	0.00139057i
$92$	10955.0	−	33716.0i	0.134940	−	0.415304i
$93$	−38201.9			−0.458013
$94$	−2625.95	+	8081.86i	−0.0306526	+	0.0943390i
$95$	−78523.8	−	107170.i	−0.892673	−	1.21833i
$96$	2847.90	+	8764.94i	0.0315389	+	0.0970668i
$97$	−30663.2	−	94371.6i	−0.330894	−	1.01839i	−0.968710	−	0.248197i	$-0.920162\pi$
$97$	−30663.2	−	94371.6i	−0.330894	−	1.01839i	0.637816	−	0.770189i	$-0.279838\pi$
$98$	−54107.8	−	39311.6i	−0.569108	−	0.413481i
$99$	−43049.1			−0.441444
$100$	40213.2	−	29713.6i	0.402132	−	0.297136i
$101$	−4889.11			−0.0476899			−0.0238449	−	0.999716i	$-0.507591\pi$
$101$	−4889.11			−0.0476899			−0.0238449	+	0.999716i	$0.507591\pi$
$102$	−47560.1	−	34554.4i	−0.452629	−	0.328854i
$103$	43329.0	+	133353.i	0.402426	+	1.23854i	0.923026	+	0.384738i	$0.125708\pi$
$103$	43329.0	+	133353.i	0.402426	+	1.23854i	−0.520600	+	0.853801i	$0.674292\pi$
$104$	−396.797	−	1221.22i	−0.00359737	−	0.0110716i
$105$	4462.83	+	1430.25i	0.0395037	+	0.0126601i
$106$	9521.13	−	29303.0i	0.0823045	−	0.253307i
$107$	35240.0			0.297561			0.148780	−	0.988870i	$-0.452465\pi$
$107$	35240.0			0.297561			0.148780	+	0.988870i	$0.452465\pi$
$108$	−3604.37	+	11093.1i	−0.0297352	+	0.0915155i
$109$	−87425.9	+	63518.6i	−0.704813	+	0.512076i	−0.881496	−	0.472191i	$-0.843463\pi$
$109$	−87425.9	+	63518.6i	−0.704813	+	0.512076i	0.176683	+	0.984268i	$0.443463\pi$
$110$	113171.	+	36269.0i	0.891768	+	0.285794i
$111$	−83327.3	−	60540.9i	−0.641919	−	0.466381i
$112$	1929.17	−	1401.63i	0.0145320	−	0.0105581i
$113$	−65864.7	+	47853.5i	−0.485240	+	0.352547i	−0.803351	−	0.595506i	$-0.796952\pi$
$113$	−65864.7	+	47853.5i	−0.485240	+	0.352547i	0.318111	+	0.948053i	$0.396952\pi$
$114$	−69218.9	−	50290.5i	−0.498841	−	0.362430i
$115$	−117644.	+	38748.5i	−0.829516	+	0.273218i
$116$	−84125.6	+	61120.8i	−0.580475	+	0.421740i
$117$	502.196	−	1545.60i	0.00339163	−	0.0104384i
$118$	25491.5			0.168535
$119$	−4700.44	+	14466.5i	−0.0304278	+	0.0936472i
$120$	18821.4	−	26125.7i	0.119316	−	0.165621i
$121$	37517.6	+	115467.i	0.232955	+	0.716962i
$122$	54395.2	+	167411.i	0.330873	+	1.01832i
$123$	−118356.	−	85990.8i	−0.705388	−	0.512494i
$124$	67914.6			0.396651
$125$	−166782.	−	51975.1i	−0.954715	−	0.297523i
$126$	3017.99			0.0169353
$127$	151292.	+	109920.i	0.832351	+	0.604739i	0.920224	−	0.391393i	$-0.128007\pi$
$127$	151292.	+	109920.i	0.832351	+	0.604739i	−0.0878722	+	0.996132i	$0.528007\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	3633.12	+	11181.6i	0.0192223	+	0.0591601i
$130$	−2622.38	+	3640.09i	−0.0136094	+	0.0188909i
$131$	−47651.9	+	146658.i	−0.242606	+	0.746666i	0.753415	+	0.657546i	$0.228405\pi$
$131$	−47651.9	+	146658.i	−0.242606	+	0.746666i	−0.996021	+	0.0891198i	$0.971595\pi$
$132$	76531.7			0.382302
$133$	−6841.01	+	21054.5i	−0.0335344	+	0.103208i
$134$	−145218.	+	105507.i	−0.698647	+	0.507597i
$135$	38706.8	−	12748.9i	0.182790	−	0.0602058i
$136$	84551.3	+	61430.1i	0.391988	+	0.284796i
$137$	−152325.	+	110671.i	−0.693379	+	0.503770i	−0.877769	−	0.479084i	$-0.840969\pi$
$137$	−152325.	+	110671.i	−0.693379	+	0.503770i	0.184390	+	0.982853i	$0.440969\pi$
$138$	−64531.2	+	46884.6i	−0.288451	+	0.209572i
$139$	166130.	+	120701.i	0.729310	+	0.529874i	0.889345	−	0.457237i	$-0.151161\pi$
$139$	166130.	+	120701.i	0.729310	+	0.529874i	−0.160035	+	0.987111i	$0.551161\pi$
$140$	−7933.92	−	2542.67i	−0.0342112	−	0.0109640i
$141$	15468.4	−	11238.4i	0.0655235	−	0.0476056i
$142$	63562.7	−	195626.i	0.264534	−	0.814152i
$143$	−10663.1			−0.0436058
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	345976.	+	110878.i	1.36655	+	0.437952i
$146$	−65462.2	−	201472.i	−0.254161	−	0.782227i
$147$	46501.5	+	143117.i	0.177490	+	0.546258i
$148$	148137.	+	107628.i	0.555918	+	0.403898i
$149$	−215765.			−0.796186			−0.398093	−	0.917345i	$-0.630328\pi$
$149$	−215765.			−0.796186			−0.398093	+	0.917345i	$0.630328\pi$
$150$	−112496.	+	904.661i	−0.408235	+	0.00328290i
$151$	−123419.			−0.440492			−0.220246	−	0.975444i	$-0.570686\pi$
$151$	−123419.			−0.440492			−0.220246	+	0.975444i	$0.570686\pi$
$152$	123056.	+	89405.3i	0.432009	+	0.313873i
$153$	40874.3	+	125798.i	0.141163	+	0.434455i
$154$	−6119.20	−	18833.0i	−0.0207918	−	0.0639907i
$155$	−140243.	−	191404.i	−0.468868	−	0.639915i
$156$	−892.793	+	2747.73i	−0.00293724	+	0.00903989i
$157$	418998.			1.35664			0.678318	−	0.734769i	$-0.262709\pi$
$157$	418998.			1.35664			0.678318	+	0.734769i	$0.262709\pi$
$158$	−126395.	+	389004.i	−0.402798	+	1.23968i
$159$	−56084.9	+	40748.1i	−0.175935	+	0.127825i
$160$	−33460.3	+	46445.7i	−0.103331	+	0.143432i
$161$	16697.1	+	12131.1i	0.0507663	+	0.0368839i
$162$	21231.8	−	15425.8i	0.0635624	−	0.0461808i
$163$	255445.	−	185592.i	0.753059	−	0.547129i	−0.143714	−	0.989619i	$-0.545905\pi$
$163$	255445.	−	185592.i	0.753059	−	0.547129i	0.896774	+	0.442490i	$0.145905\pi$
$164$	210411.	+	152873.i	0.610884	+	0.443833i
$165$	−158037.	−	215690.i	−0.451907	−	0.616766i
$166$	−285832.	+	207669.i	−0.805082	+	0.584927i
$167$	191658.	−	589863.i	0.531785	−	1.63667i	−0.218710	−	0.975790i	$-0.570185\pi$
$167$	191658.	−	589863.i	0.531785	−	1.63667i	0.750495	−	0.660876i	$-0.229815\pi$
$168$	−5365.32			−0.0146664
$169$	−114611.	+	352738.i	−0.308682	+	0.950025i
$170$	−1468.16	−	365144.i	−0.00389630	−	0.969040i
$171$	59488.3	+	183086.i	0.155576	+	0.478813i
$172$	−6458.87	−	19878.4i	−0.0166470	−	0.0512342i
$173$	−540156.	−	392447.i	−1.37216	−	0.996931i	−0.997565	−	0.0697419i	$-0.977782\pi$
$173$	−540156.	−	392447.i	−1.37216	−	0.996931i	−0.374593	−	0.927189i	$-0.622218\pi$
$174$	233966.			0.585841
$175$	9217.42	+	27610.8i	0.0227517	+	0.0681529i
$176$	−136056.			−0.331083
$177$	−46401.8	−	33712.9i	−0.111327	−	0.0808841i
$178$	−29464.3	−	90681.9i	−0.0697022	−	0.214521i
$179$	16770.1	+	51613.0i	0.0391203	+	0.120400i	0.968709	−	0.248197i	$-0.0798382\pi$
$179$	16770.1	+	51613.0i	0.0391203	+	0.120400i	−0.929589	+	0.368597i	$0.879838\pi$
$180$	−68812.1	+	22664.7i	−0.158301	+	0.0521397i
$181$	−112978.	+	347710.i	−0.256329	+	0.788898i	0.737236	+	0.675635i	$0.236130\pi$
$181$	−112978.	+	347710.i	−0.256329	+	0.788898i	−0.993565	+	0.113263i	$0.963870\pi$
$182$	747.548			0.00167286
$183$	122389.	−	376676.i	0.270157	−	0.831457i
$184$	114722.	−	83350.5i	0.249806	−	0.181495i
$185$	−2572.29	−	639748.i	−0.00552574	−	1.37429i
$186$	−123624.	−	89818.2i	−0.262012	−	0.190363i
$187$	702132.	−	510129.i	1.46830	−	1.06678i
$188$	−27499.4	+	19979.4i	−0.0567450	+	0.0412277i
$189$	−5493.62	−	3991.35i	−0.0111867	−	0.00812765i
$190$	−2136.76	−	531430.i	−0.00429410	−	1.06798i
$191$	−146243.	+	106251.i	−0.290062	+	0.210742i	−0.723294	−	0.690540i	$-0.757373\pi$
$191$	−146243.	+	106251.i	−0.290062	+	0.210742i	0.433232	+	0.901282i	$0.357373\pi$
$192$	−11391.6	+	35059.7i	−0.0223014	+	0.0686366i
$193$	−133830.			−0.258618			−0.129309	−	0.991604i	$-0.541276\pi$
$193$	−133830.			−0.258618			−0.129309	+	0.991604i	$0.541276\pi$
$194$	122653.	−	377487.i	0.233977	−	0.720107i
$195$	9587.57	−	3157.86i	0.0180560	−	0.00594712i
$196$	−82669.4	−	254430.i	−0.153711	−	0.473073i
$197$	102474.	+	315382.i	0.188125	+	0.578990i	0.999988	−	0.00485792i	$-0.00154633\pi$
$197$	102474.	+	315382.i	0.188125	+	0.578990i	−0.811863	+	0.583848i	$0.801546\pi$
$198$	−139310.	−	101214.i	−0.252533	−	0.183476i
$199$	420392.			0.752527			0.376264	−	0.926513i	$-0.377209\pi$
$199$	420392.			0.752527			0.376264	+	0.926513i	$0.377209\pi$
$200$	199994.	−	1608.29i	0.353542	−	0.00284308i
$201$	403873.			0.705106
$202$	−15821.5	−	11495.0i	−0.0272815	−	0.0198212i
$203$	−18707.1	−	57574.5i	−0.0318615	−	0.0980596i
$204$	−72665.3	−	223641.i	−0.122251	−	0.376249i
$205$	−3653.62	−	908683.i	−0.00607209	−	1.51018i
$206$	−173316.	+	533412.i	−0.284558	+	0.875779i
$207$	179471.			0.291118
$208$	1587.19	−	4884.86i	0.00254372	−	0.00782878i
$209$	1.02188e6	−	742441.i	1.61821	−	1.17570i
$210$	11079.3	+	15121.1i	0.0173366	+	0.0236612i
$211$	909789.	+	661000.i	1.40681	+	1.02211i	0.993777	+	0.111388i	$0.0355296\pi$
$211$	909789.	+	661000.i	1.40681	+	1.02211i	0.413030	+	0.910717i	$0.364470\pi$
$212$	99706.5	−	72441.0i	0.152365	−	0.110699i
$213$	−374421.	+	272033.i	−0.565472	+	0.410840i
$214$	114039.	+	82854.1i	0.170223	+	0.123674i
$215$	−42685.9	+	59251.6i	−0.0629779	+	0.0874187i
$216$	−37745.5	+	27423.7i	−0.0550466	+	0.0399937i
$217$	−12218.0	+	37603.0i	−0.0176136	+	0.0542092i
$218$	−432257.			−0.616029
$219$	−147290.	+	453312.i	−0.207522	+	0.638686i
$220$	280954.	+	383449.i	0.391363	+	0.534135i
$221$	10124.4	+	31159.8i	0.0139441	+	0.0429155i
$222$	−127313.	−	391829.i	−0.173376	−	0.533597i
$223$	90158.2	+	65503.8i	0.121407	+	0.0882073i	0.646832	−	0.762633i	$-0.276094\pi$
$223$	90158.2	+	65503.8i	0.121407	+	0.0882073i	−0.525425	+	0.850840i	$0.676094\pi$
$224$	9538.35			0.0127014
$225$	205972.	+	147132.i	0.271239	+	0.193754i
$226$	−325653.			−0.424115
$227$	415277.	+	301716.i	0.534900	+	0.388628i	0.822188	−	0.569217i	$-0.192753\pi$
$227$	415277.	+	301716.i	0.534900	+	0.388628i	−0.287287	+	0.957844i	$0.592753\pi$
$228$	−105757.	−	325487.i	−0.134732	−	0.414664i
$229$	77266.3	+	237801.i	0.0973647	+	0.299658i	0.987863	−	0.155329i	$-0.0496439\pi$
$229$	77266.3	+	237801.i	0.0973647	+	0.299658i	−0.890498	+	0.454987i	$0.849644\pi$
$230$	−471807.	−	151205.i	−0.588091	−	0.188472i
$231$	−13768.2	+	42374.2i	−0.0169765	+	0.0522482i
$232$	−415940.			−0.507353
$233$	432593.	−	1.33139e6i	0.522024	−	1.60662i	−0.248104	−	0.968733i	$-0.579807\pi$
$233$	432593.	−	1.33139e6i	0.522024	−	1.60662i	0.770127	−	0.637890i	$-0.220193\pi$
$234$	5259.07	−	3820.93i	0.00627869	−	0.00456173i
$235$	113094.	+	36244.4i	0.133589	+	0.0428126i
$236$	82492.2	+	59934.1i	0.0964123	+	0.0700477i
$237$	744539.	−	540939.i	0.861027	−	0.625573i
$238$	−49223.6	+	35763.0i	−0.0563289	+	0.0409253i
$239$	733561.	+	532963.i	0.830695	+	0.603535i	0.919756	−	0.392491i	$-0.128387\pi$
$239$	733561.	+	532963.i	0.830695	+	0.603535i	−0.0890611	+	0.996026i	$0.528387\pi$
$240$	122333.	−	40292.8i	0.137093	−	0.0451543i
$241$	−341334.	+	247993.i	−0.378561	+	0.275041i	−0.760752	−	0.649042i	$-0.775170\pi$
$241$	−341334.	+	247993.i	−0.378561	+	0.275041i	0.382191	+	0.924083i	$0.375170\pi$
$242$	−150071.	+	461870.i	−0.164724	+	0.506968i
$243$	−59049.0			−0.0641500
$244$	−217581.	+	669645.i	−0.233963	+	0.720063i
$245$	−546352.	+	758383.i	−0.581510	+	0.807185i
$246$	−180832.	−	556544.i	−0.190519	−	0.586357i
$247$	14735.1	+	45349.9i	0.0153678	+	0.0472971i
$248$	219776.	+	159677.i	0.226909	+	0.164859i
$249$	794942.			0.812526
$250$	−417516.	−	560322.i	−0.422497	−	0.567006i
$251$	−607154.			−0.608296			−0.304148	−	0.952625i	$-0.598372\pi$
$251$	−607154.			−0.608296			−0.304148	+	0.952625i	$0.598372\pi$
$252$	9766.43	+	7095.73i	0.00968801	+	0.00703875i
$253$	−363890.	−	1.11994e6i	−0.357412	−	1.10000i
$254$	231154.	+	711418.i	0.224810	+	0.691895i
$255$	−480236.	+	666609.i	−0.462492	+	0.641978i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	451858.			0.426745			0.213373	−	0.976971i	$-0.431555\pi$
$257$	451858.			0.426745			0.213373	+	0.976971i	$0.431555\pi$
$258$	−14532.5	+	44726.3i	−0.0135922	+	0.0418325i
$259$	−86241.9	+	62658.4i	−0.0798857	+	0.0580403i
$260$	−17044.6	+	5613.98i	−0.0156370	+	0.00515036i
$261$	−425886.	−	309424.i	−0.386983	−	0.281160i
$262$	−499017.	+	362557.i	−0.449120	+	0.326305i
$263$	−1.03887e6	+	754785.i	−0.926132	+	0.672874i	−0.945043	−	0.326947i	$-0.893980\pi$
$263$	−1.03887e6	+	754785.i	−0.926132	+	0.672874i	0.0189106	+	0.999821i	$0.493980\pi$
$264$	247662.	+	179937.i	0.218700	+	0.158895i
$265$	−410054.	−	131414.i	−0.358696	−	0.114955i
$266$	−71640.0	+	52049.5i	−0.0620799	+	0.0451037i
$267$	−66294.8	+	204034.i	−0.0569116	+	0.175156i
$268$	−717996.			−0.610640
$269$	2853.96	−	8783.59i	0.00240474	−	0.00740101i	−0.949847	−	0.312715i	$-0.898761\pi$
$269$	2853.96	−	8783.59i	0.00240474	−	0.00740101i	0.952252	+	0.305314i	$0.0987615\pi$
$270$	155232.	+	49748.9i	0.129590	+	0.0415312i
$271$	451381.	+	1.38921e6i	0.373353	+	1.14906i	0.944583	+	0.328273i	$0.106467\pi$
$271$	451381.	+	1.38921e6i	0.373353	+	1.14906i	−0.571229	+	0.820790i	$0.693533\pi$
$272$	129183.	+	397584.i	0.105872	+	0.325842i
$273$	−1360.75	−	988.645i	−0.00110503	−	0.000802849i
$274$	−753138.			−0.606036
$275$	500511.	−	1.58363e6i	0.399100	−	1.26277i
$276$	−319060.			−0.252115
$277$	−1.09416e6	−	794956.i	−0.856806	−	0.622506i	0.0702079	−	0.997532i	$-0.477634\pi$
$277$	−1.09416e6	−	794956.i	−0.856806	−	0.622506i	−0.927014	+	0.375026i	$0.877634\pi$
$278$	253825.	+	781192.i	0.196980	+	0.606241i
$279$	106245.	+	326990.i	0.0817146	+	0.251492i
$280$	−19696.6	−	26882.0i	−0.0150140	−	0.0204912i
$281$	−664722.	+	2.04580e6i	−0.502197	+	1.54560i	0.303236	+	0.952916i	$0.401933\pi$
$281$	−664722.	+	2.04580e6i	−0.502197	+	1.54560i	−0.805433	+	0.592687i	$0.798067\pi$
$282$	76479.9			0.0572697
$283$	146206.	−	449977.i	0.108518	−	0.333983i	−0.882022	−	0.471208i	$-0.843818\pi$
$283$	146206.	−	449977.i	0.108518	−	0.333983i	0.990540	+	0.137225i	$0.0438182\pi$
$284$	665637.	−	483614.i	0.489713	−	0.355798i
$285$	−698935.	+	970182.i	−0.509712	+	0.707523i
$286$	−34506.6	−	25070.5i	−0.0249452	−	0.0181238i
$287$	−122496.	+	88998.5i	−0.0877843	+	0.0637790i
$288$	67103.1	−	48753.3i	0.0476718	−	0.0346356i
$289$	−1.00867e6	−	732842.i	−0.710403	−	0.516138i
$290$	858910.	+	1.17225e6i	0.599726	+	0.818510i
$291$	−722496.	+	524924.i	−0.500153	+	0.363382i
$292$	261849.	−	805888.i	0.179719	−	0.553118i
$293$	−631131.			−0.429487			−0.214744	−	0.976670i	$-0.568892\pi$
$293$	−631131.			−0.429487			−0.214744	+	0.976670i	$0.568892\pi$
$294$	−186006.	+	572468.i	−0.125504	+	0.386263i
$295$	−1432.41	−	356251.i	−0.000958323	−	0.238342i
$296$	226334.	+	696584.i	0.150148	+	0.462109i
$297$	119726.	+	368479.i	0.0787585	+	0.242394i
$298$	−698229.	−	507293.i	−0.455467	−	0.330916i
$299$	44454.5			0.0287566
$300$	−366173.	−	261567.i	−0.234900	−	0.167795i
$301$	12168.2			0.00774126
$302$	−399391.	−	290174.i	−0.251989	−	0.183080i
$303$	13597.4	+	41848.3i	0.00850840	+	0.0261862i
$304$	188013.	+	578643.i	0.116682	+	0.359109i
$305$	2.33657e6	−	769598.i	1.43823	−	0.473712i
$306$	−163497.	+	503192.i	−0.0998174	+	0.307206i
$307$	−1.76308e6			−1.06764			−0.533822	−	0.845597i	$-0.679245\pi$
$307$	−1.76308e6			−1.06764			−0.533822	+	0.845597i	$0.679245\pi$
$308$	24476.8	−	75331.8i	0.0147020	−	0.0452482i
$309$	1.02093e6	−	741750.i	0.608275	−	0.441938i
$310$	−3816.23	−	949127.i	−0.00225544	−	0.560945i
$311$	314632.	+	228593.i	0.184460	+	0.134018i	0.676183	−	0.736734i	$-0.263633\pi$
$311$	314632.	+	228593.i	0.184460	+	0.134018i	−0.491723	+	0.870752i	$0.663633\pi$
$312$	−9349.45	+	6792.77i	−0.00543750	+	0.00395058i
$313$	−1.43490e6	+	1.04252e6i	−0.827870	+	0.601482i	−0.918956	−	0.394361i	$-0.870966\pi$
$313$	−1.43490e6	+	1.04252e6i	−0.827870	+	0.601482i	0.0910862	+	0.995843i	$0.470966\pi$
$314$	1.35591e6	+	985124.i	0.776079	+	0.563854i
$315$	−169.586	−	42177.4i	−9.62973e−5	−	0.0239499i
$316$	−1.32363e6	+	961670.i	−0.745671	+	0.541762i
$317$	806243.	−	2.48136e6i	0.450627	−	1.38689i	−0.425565	−	0.904928i	$-0.639925\pi$
$317$	806243.	−	2.48136e6i	0.450627	−	1.38689i	0.876193	−	0.481961i	$-0.160075\pi$
$318$	−277299.			−0.153773
$319$	−1.06736e6	+	3.28500e6i	−0.587267	+	1.80742i
$320$	−217480.	+	71631.7i	−0.118726	+	0.0391048i
$321$	−98007.7	−	301637.i	−0.0530882	−	0.163389i
$322$	25510.9	+	78514.3i	0.0137115	+	0.0421997i
$323$	−3.13982e6	−	2.28121e6i	−1.67455	−	1.21663i
$324$	104976.			0.0555556
$325$	51018.7	+	36444.1i	0.0267930	+	0.0191390i
$326$	1.26299e6			0.658198
$327$	786833.	+	571667.i	0.406924	+	0.295647i
$328$	321479.	+	989412.i	0.164994	+	0.507800i
$329$	−6115.06	−	18820.2i	−0.00311466	−	0.00958594i
$330$	−4300.45	−	1.06955e6i	−0.00217385	−	0.540652i
$331$	−994903.	+	3.06200e6i	−0.499127	+	1.53615i	0.311298	+	0.950312i	$0.399236\pi$
$331$	−994903.	+	3.06200e6i	−0.499127	+	1.53615i	−0.810425	+	0.585842i	$0.800764\pi$
$332$	−1.41323e6			−0.703668
$333$	−286454.	+	881614.i	−0.141561	+	0.435680i
$334$	2.00707e6	−	1.45822e6i	0.984456	−	0.715249i
$335$	1.48265e6	+	2.02353e6i	0.721817	+	0.985142i
$336$	−17362.5	−	12614.6i	−0.00839006	−	0.00609574i
$337$	1.88900e6	−	1.37244e6i	0.906061	−	0.658292i	−0.0339545	−	0.999423i	$-0.510810\pi$
$337$	1.88900e6	−	1.37244e6i	0.906061	−	0.658292i	0.940016	+	0.341131i	$0.110810\pi$
$338$	−1.20023e6	+	872016.i	−0.571441	+	0.415176i
$339$	592782.	+	430681.i	0.280153	+	0.203543i
$340$	853753.	−	1.18508e6i	0.400530	−	0.555970i
$341$	1.82507e6	−	1.32599e6i	0.849950	−	0.617525i
$342$	−237953.	+	732345.i	−0.110009	+	0.338572i
$343$	312299.			0.143330
$344$	25835.5	−	79513.5i	0.0117712	−	0.0362280i
$345$	658854.	+	899209.i	0.298017	+	0.406736i
$346$	−825285.	−	2.53997e6i	−0.370607	−	1.14061i
$347$	845031.	+	2.60074e6i	0.376746	+	1.15951i	0.942293	+	0.334790i	$0.108665\pi$
$347$	845031.	+	2.60074e6i	0.376746	+	1.15951i	−0.565547	+	0.824716i	$0.691335\pi$
$348$	757131.	+	550088.i	0.335137	+	0.243491i
$349$	573338.			0.251969			0.125984	−	0.992032i	$-0.459791\pi$
$349$	573338.			0.251969			0.125984	+	0.992032i	$0.459791\pi$
$350$	−35088.7	+	111022.i	−0.0153108	+	0.0484439i
$351$	−14626.3			−0.00633674
$352$	−440288.	−	319888.i	−0.189400	−	0.137607i
$353$	−982201.	−	3.02290e6i	−0.419531	−	1.29118i	−0.908135	−	0.418677i	$-0.862494\pi$
$353$	−982201.	−	3.02290e6i	−0.419531	−	1.29118i	0.488605	−	0.872505i	$-0.337506\pi$
$354$	−70895.7	−	218195.i	−0.0300685	−	0.0925413i
$355$	−2.73751e6	−	877316.i	−1.15288	−	0.369475i
$356$	117857.	−	362728.i	0.0492869	−	0.151690i
$357$	136898.			0.0568496
$358$	−67080.3	+	206452.i	−0.0276622	+	0.0851356i
$359$	−1.55605e6	+	1.13054e6i	−0.637217	+	0.462965i	−0.858893	−	0.512155i	$-0.828847\pi$
$359$	−1.55605e6	+	1.13054e6i	−0.637217	+	0.462965i	0.221676	+	0.975120i	$0.428847\pi$
$360$	−275969.	−	88442.5i	−0.112229	−	0.0359670i
$361$	−2.56648e6	−	1.86466e6i	−1.03650	−	0.753063i
$362$	−1.18312e6	+	859587.i	−0.474523	+	0.344761i
$363$	884002.	−	642265.i	0.352117	−	0.255828i
$364$	2419.12	+	1757.59i	0.000956981	+	0.000695287i
$365$	−2.81196e6	+	926176.i	−1.10478	+	0.363883i
$366$	1.28168e6	−	931193.i	0.500122	−	0.363360i
$367$	952126.	−	2.93034e6i	0.369002	−	1.13567i	−0.578434	−	0.815729i	$-0.696336\pi$
$367$	952126.	−	2.93034e6i	0.369002	−	1.13567i	0.947437	−	0.319944i	$-0.103664\pi$
$368$	567217.			0.218338
$369$	−406872.	+	1.25222e6i	−0.155558	+	0.478758i
$370$	1.49581e6	−	2.07632e6i	0.568032	−	0.788477i
$371$	22171.8	+	68237.9i	0.00836309	+	0.0257389i
$372$	−188881.	−	581315.i	−0.0707669	−	0.217798i
$373$	1.68529e6	+	1.22444e6i	0.627195	+	0.455684i	0.855427	−	0.517923i	$-0.173294\pi$
$373$	1.68529e6	+	1.22444e6i	0.627195	+	0.455684i	−0.228232	+	0.973607i	$0.573294\pi$
$374$	3.47153e6			1.28334
$375$	18964.3	+	1.57212e6i	0.00696399	+	0.577308i
$376$	−135964.			−0.0495970
$377$	−105491.	−	76643.5i	−0.0382262	−	0.0277729i
$378$	−8393.50	−	25832.5i	−0.00302144	−	0.00929903i
$379$	−706444.	−	2.17421e6i	−0.252627	−	0.777506i	−0.994288	−	0.106731i	$-0.965962\pi$
$379$	−706444.	−	2.17421e6i	−0.252627	−	0.777506i	0.741661	−	0.670775i	$-0.234038\pi$
$380$	1.24255e6	−	1.72477e6i	0.441424	−	0.612733i
$381$	520096.	−	1.60069e6i	0.183557	−	0.564930i
$382$	−723063.			−0.253523
$383$	−622403.	+	1.91556e6i	−0.216808	+	0.667266i	0.782212	+	0.623012i	$0.214091\pi$
$383$	−622403.	+	1.91556e6i	−0.216808	+	0.667266i	−0.999020	+	0.0442541i	$0.985909\pi$
$384$	−119294.	+	86672.5i	−0.0412850	+	0.0299953i
$385$	−262853.	+	86576.0i	−0.0903775	+	0.0297677i
$386$	−433082.	−	314652.i	−0.147946	−	0.107489i
$387$	85604.6	−	62195.4i	0.0290549	−	0.0211096i
$388$	1.28444e6	−	933198.i	0.433145	−	0.314698i
$389$	−4.44570e6	−	3.22999e6i	−1.48959	−	1.08225i	−0.974307	−	0.225226i	$-0.927688\pi$
$389$	−4.44570e6	−	3.22999e6i	−1.48959	−	1.08225i	−0.515280	−	0.857022i	$-0.672312\pi$
$390$	38450.6	+	12322.7i	0.0128009	+	0.00410245i
$391$	−2.92718e6	+	2.12672e6i	−0.968295	+	0.703507i
$392$	330678.	−	1.01772e6i	0.108690	−	0.334513i
$393$	1.38784e6			0.453272
$394$	−409895.	+	1.26153e6i	−0.133025	+	0.409408i
$395$	5.44355e6	+	1.74455e6i	1.75545	+	0.562588i
$396$	−212846.	−	655074.i	−0.0682069	−	0.209919i
$397$	−1.34379e6	−	4.13575e6i	−0.427911	−	1.31698i	−0.900179	−	0.435521i	$-0.856564\pi$
$397$	−1.34379e6	−	4.13575e6i	−0.427911	−	1.31698i	0.472267	−	0.881455i	$-0.343436\pi$
$398$	1.36042e6	+	988402.i	0.430492	+	0.312770i
$399$	199242.			0.0626539
$400$	650974.	+	465008.i	0.203429	+	0.145315i
$401$	2.44788e6			0.760201			0.380101	−	0.924945i	$-0.375889\pi$
$401$	2.44788e6			0.760201			0.380101	+	0.924945i	$0.375889\pi$
$402$	1.30696e6	+	949562.i	0.403364	+	0.293061i
$403$	26316.7	+	80994.4i	0.00807177	+	0.0248423i
$404$	−24173.1	−	74397.1i	−0.00736849	−	0.0226779i
$405$	−216774.	−	295855.i	−0.0656704	−	0.0896275i
$406$	74828.4	−	230298.i	0.0225295	−	0.0693386i
$407$	6.08228e6			1.82004
$408$	290661.	−	894564.i	0.0864444	−	0.266049i
$409$	−2.79031e6	+	2.02728e6i	−0.824792	+	0.599246i	−0.918081	−	0.396393i	$-0.870262\pi$
$409$	−2.79031e6	+	2.02728e6i	−0.824792	+	0.599246i	0.0932894	+	0.995639i	$0.470262\pi$
$410$	2.12462e6	−	2.94915e6i	0.624196	−	0.866437i
$411$	1.37093e6	+	996038.i	0.400323	+	0.290852i
$412$	−1.81499e6	+	1.31867e6i	−0.526782	+	0.382729i
$413$	−48024.8	+	34892.1i	−0.0138545	+	0.0100659i
$414$	580781.	+	421962.i	0.166537	+	0.120996i
$415$	2.91830e6	+	3.98292e6i	0.831782	+	1.13522i
$416$	16621.2	−	12076.0i	0.00470902	−	0.00342130i
$417$	571105.	−	1.75768e6i	0.160833	−	0.494994i
$418$	5.05247e6			1.41437
$419$	2.08892e6	−	6.42904e6i	0.581282	−	1.78900i	−0.0324314	−	0.999474i	$-0.510325\pi$
$419$	2.08892e6	−	6.42904e6i	0.581282	−	1.78900i	0.613714	−	0.789529i	$-0.289675\pi$
$420$	301.486	+	74982.0i	8.33959e−5	+	0.0207412i
$421$	−684595.	−	2.10697e6i	−0.188247	−	0.579365i	0.811742	−	0.584016i	$-0.198520\pi$
$421$	−684595.	−	2.10697e6i	−0.188247	−	0.579365i	−0.999989	+	0.00465096i	$0.998520\pi$
$422$	1.39003e6	+	4.27808e6i	0.379966	+	1.16941i
$423$	−139215.	−	101146.i	−0.0378300	−	0.0274851i
$424$	492976.			0.133171
$425$	−5.10292e6	+	41036.1i	−1.37040	+	0.0110203i
$426$	−1.85124e6			−0.494241
$427$	−331627.	−	240941.i	−0.0880197	−	0.0639500i
$428$	174236.	+	536243.i	0.0459757	+	0.141499i
$429$	29655.8	+	91271.2i	0.00777976	+	0.0239437i
$430$	−277443.	+	91381.8i	−0.0723608	+	0.0238335i
$431$	661195.	−	2.03495e6i	0.171450	−	0.527668i	−0.828004	−	0.560722i	$-0.810523\pi$
$431$	661195.	−	2.03495e6i	0.171450	−	0.527668i	0.999454	+	0.0330545i	$0.0105235\pi$
$432$	−186624.			−0.0481125
$433$	902296.	−	2.77698e6i	0.231275	−	0.711792i	−0.766318	−	0.642461i	$-0.777913\pi$
$433$	902296.	−	2.77698e6i	0.231275	−	0.711792i	0.997594	−	0.0693314i	$-0.0220866\pi$
$434$	−127948.	+	92959.7i	−0.0326069	+	0.0236903i
$435$	−13147.0	−	3.26975e6i	−0.00333121	−	0.828498i
$436$	−1.39881e6	−	1.01630e6i	−0.352406	−	0.256038i
$437$	−4.26022e6	+	3.09523e6i	−1.06716	+	0.775334i
$438$	−1.54244e6	+	1.12065e6i	−0.384170	+	0.279116i
$439$	−1.54517e6	−	1.12263e6i	−0.382663	−	0.278021i	0.379780	−	0.925077i	$-0.376000\pi$
$439$	−1.54517e6	−	1.12263e6i	−0.382663	−	0.278021i	−0.762442	+	0.647056i	$0.776000\pi$
$440$	7645.24	+	1.90143e6i	0.00188261	+	0.468219i
$441$	1.09568e6	−	796060.i	0.268280	−	0.194917i
$442$	−40497.7	+	124639.i	−0.00985996	+	0.0303458i
$443$	−1.80102e6			−0.436024			−0.218012	−	0.975946i	$-0.569957\pi$
$443$	−1.80102e6			−0.436024			−0.218012	+	0.975946i	$0.569957\pi$
$444$	509251.	−	1.56731e6i	0.122596	−	0.377310i
$445$	−1.26565e6	+	416869.i	−0.302980	+	0.0997929i
$446$	137750.	+	423949.i	0.0327909	+	0.100920i
$447$	600075.	+	1.84684e6i	0.142048	+	0.437180i
$448$	30866.7	+	22426.0i	0.00726601	+	0.00527906i
$449$	−6.04868e6			−1.41594			−0.707969	−	0.706243i	$-0.750389\pi$
$449$	−6.04868e6			−1.41594			−0.707969	+	0.706243i	$0.750389\pi$
$450$	320613.	+	960398.i	0.0746363	+	0.223573i
$451$	8.63912e6			1.99999
$452$	−1.05383e6	−	765656.i	−0.242620	−	0.176274i
$453$	343246.	+	1.05640e6i	0.0785887	+	0.241871i
$454$	634486.	+	1.95275e6i	0.144472	+	0.444638i
$455$	−42.0060	−	10447.2i	−9.51224e−6	−	0.00236577i
$456$	423028.	−	1.30195e6i	0.0952702	−	0.293212i
$457$	3.02342e6			0.677185			0.338593	−	0.940933i	$-0.390049\pi$
$457$	3.02342e6			0.677185			0.338593	+	0.940933i	$0.390049\pi$
$458$	−309065.	+	951205.i	−0.0688472	+	0.211890i
$459$	963092.	−	699727.i	0.213371	−	0.155023i
$460$	−1.17130e6	−	1.59859e6i	−0.258090	−	0.352244i
$461$	6.47703e6	+	4.70584e6i	1.41946	+	1.03130i	0.991860	+	0.127333i	$0.0406416\pi$
$461$	6.47703e6	+	4.70584e6i	1.41946	+	1.03130i	0.427602	+	0.903967i	$0.359358\pi$
$462$	−144182.	+	104755.i	−0.0314273	+	0.0228333i
$463$	−474161.	+	344498.i	−0.102795	+	0.0746852i	−0.637996	−	0.770040i	$-0.720236\pi$
$463$	−474161.	+	344498.i	−0.102795	+	0.0746852i	0.535200	+	0.844725i	$0.320236\pi$
$464$	−1.34601e6	−	977933.i	−0.290237	−	0.210870i
$465$	−1.24829e6	+	1.73273e6i	−0.267721	+	0.371620i
$466$	4.53018e6	−	3.29137e6i	0.966386	−	0.702120i
$467$	−1.77774e6	+	5.47131e6i	−0.377203	+	1.16091i	0.564778	+	0.825243i	$0.308962\pi$
$467$	−1.77774e6	+	5.47131e6i	−0.377203	+	1.16091i	−0.941980	+	0.335668i	$0.891038\pi$
$468$	26002.2			0.00548777
$469$	129169.	−	397541.i	0.0271160	−	0.0834545i
$470$	280764.	+	383189.i	0.0586269	+	0.0800145i
$471$	−1.16530e6	−	3.58642e6i	−0.242039	−	0.744919i
$472$	126037.	+	387901.i	0.0260401	+	0.0801431i
$473$	−561683.	−	408086.i	−0.115435	−	0.0838686i
$474$	3.68120e6			0.752565
$475$	−7.42678e6	+	59723.9i	−1.51031	+	0.0121455i
$476$	−243375.			−0.0492332
$477$	504764.	+	366733.i	0.101576	+	0.0737995i
$478$	1.12078e6	+	3.44941e6i	0.224363	+	0.690518i
$479$	−560029.	−	1.72359e6i	−0.111525	−	0.343238i	0.879682	−	0.475563i	$-0.157756\pi$
$479$	−560029.	−	1.72359e6i	−0.111525	−	0.343238i	−0.991206	+	0.132325i	$0.957756\pi$
$480$	490611.	+	157231.i	0.0971928	+	0.0311484i
$481$	−70953.8	+	218373.i	−0.0139834	+	0.0430365i
$482$	−1.68765e6			−0.330875
$483$	57399.4	−	176657.i	0.0111954	−	0.0344559i
$484$	−1.57156e6	+	1.14180e6i	−0.304942	+	0.221553i
$485$	−5.28238e6	−	1.69290e6i	−1.01971	−	0.326796i
$486$	−191087.	−	138833.i	−0.0366978	−	0.0266625i
$487$	1.00847e6	−	732696.i	0.192682	−	0.139991i	−0.487262	−	0.873256i	$-0.662004\pi$
$487$	1.00847e6	−	732696.i	0.192682	−	0.139991i	0.679943	+	0.733265i	$0.262004\pi$
$488$	−2.27854e6	+	1.65545e6i	−0.433118	+	0.314679i
$489$	−2.29901e6	−	1.67033e6i	−0.434779	−	0.315885i
$490$	−3.55110e6	+	1.16963e6i	−0.668147	+	0.220068i
$491$	−4.97697e6	+	3.61598e6i	−0.931668	+	0.676896i	−0.946401	−	0.322995i	$-0.895310\pi$
$491$	−4.97697e6	+	3.61598e6i	−0.931668	+	0.676896i	0.0147326	+	0.999891i	$0.495310\pi$
$492$	723329.	−	2.22618e6i	0.134717	−	0.414617i
$493$	1.06129e7			1.96660
$494$	−58940.4	+	181400.i	−0.0108666	+	0.0334441i
$495$	−1.40668e6	+	1.95258e6i	−0.258036	+	0.358176i
$496$	335788.	+	1.03345e6i	0.0612860	+	0.188619i
$497$	148018.	+	455554.i	0.0268797	+	0.0827273i
$498$	2.57249e6	+	1.86902e6i	0.464814	+	0.337707i
$499$	−1.94327e6			−0.349367			−0.174683	−	0.984625i	$-0.555890\pi$
$499$	−1.94327e6			−0.349367			−0.174683	+	0.984625i	$0.555890\pi$
$500$	−33714.3	−	2.79488e6i	−0.00603099	−	0.499964i
$501$	−5.58197e6			−0.993558
$502$	−1.96479e6	−	1.42751e6i	−0.347982	−	0.252824i
$503$	−1.15491e6	−	3.55445e6i	−0.203530	−	0.626402i	−0.999771	−	0.0214212i	$-0.993181\pi$
$503$	−1.15491e6	−	3.55445e6i	−0.203530	−	0.626402i	0.796240	−	0.604980i	$-0.206819\pi$
$504$	14921.8	+	45924.5i	0.00261664	+	0.00805320i
$505$	−159757.	+	221756.i	−0.0278760	+	0.0386943i
$506$	1.45556e6	−	4.47976e6i	0.252729	−	0.777819i
$507$	3.33801e6			0.576724
$508$	−924615.	+	2.84567e6i	−0.158965	+	0.489244i
$509$	4.96037e6	−	3.60392e6i	0.848632	−	0.616568i	−0.0761362	−	0.997097i	$-0.524258\pi$
$509$	4.96037e6	−	3.60392e6i	0.848632	−	0.616568i	0.924769	+	0.380530i	$0.124258\pi$
$510$	−3.12137e6	+	1.02809e6i	−0.531398	+	0.175027i
$511$	399098.	+	289962.i	0.0676125	+	0.0491234i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	1.40168e6	−	1.01838e6i	0.235156	−	0.170851i
$514$	1.46224e6	+	1.06238e6i	0.244125	+	0.177367i
$515$	7.46433e6	+	2.39217e6i	1.24015	+	0.397442i
$516$	−152186.	+	110570.i	−0.0251623	+	0.0182815i
$517$	−348904.	+	1.07382e6i	−0.0574090	+	0.176687i
$518$	−426403.			−0.0698226
$519$	−1.85689e6	+	5.71493e6i	−0.302600	+	0.931306i
$520$	−68356.6	−	21907.0i	−0.0110859	−	0.00355282i
$521$	−355165.	−	1.09308e6i	−0.0573239	−	0.176425i	0.918295	−	0.395897i	$-0.129566\pi$
$521$	−355165.	−	1.09308e6i	−0.0573239	−	0.176425i	−0.975619	+	0.219473i	$0.929566\pi$
$522$	−650696.	−	2.00264e6i	−0.104521	−	0.321681i
$523$	7.83004e6	+	5.68885e6i	1.25173	+	0.909433i	0.998321	−	0.0579274i	$-0.0184492\pi$
$523$	7.83004e6	+	5.68885e6i	1.25173	+	0.909433i	0.253406	+	0.967360i	$0.418449\pi$
$524$	−2.46728e6			−0.392545
$525$	210700.	−	155687.i	0.0333631	−	0.0246520i
$526$	−5.13647e6			−0.809469
$527$	−5.60768e6	−	4.07422e6i	−0.879542	−	0.639025i
$528$	378394.	+	1.16458e6i	0.0590689	+	0.181795i
$529$	−471885.	−	1.45231e6i	−0.0733157	−	0.225643i
$530$	−1.01799e6	−	1.38936e6i	−0.157418	−	0.214845i
$531$	−159515.	+	490938.i	−0.0245508	+	0.0755597i
$532$	−354208.			−0.0542599
$533$	−100781.	+	310172.i	−0.0153660	+	0.0472917i
$534$	−694248.	+	504401.i	−0.105357	+	0.0765460i
$535$	1.15150e6	−	1.59838e6i	0.173933	−	0.241433i
$536$	−2.32348e6	−	1.68811e6i	−0.349323	−	0.253798i
$537$	395141.	−	287087.i	0.0591312	−	0.0429613i
$538$	29887.1	−	21714.2i	0.00445172	−	0.00323436i
$539$	−7.18917e6	−	5.22324e6i	−1.06588	−	0.774405i
$540$	385376.	+	525964.i	0.0568722	+	0.0776197i
$541$	6.22585e6	−	4.52335e6i	0.914546	−	0.664457i	−0.0276143	−	0.999619i	$-0.508791\pi$
$541$	6.22585e6	−	4.52335e6i	0.914546	−	0.664457i	0.942161	+	0.335162i	$0.108791\pi$
$542$	−1.80552e6	+	5.55683e6i	−0.264001	+	0.812511i
$543$	3.29044e6			0.478910
$544$	−516731.	+	1.59034e6i	−0.0748630	+	0.230405i
$545$	24289.3	+	6.04093e6i	0.00350286	+	0.871189i
$546$	−2079.05	−	6398.64i	−0.000298457	−	0.000918558i
$547$	3.68732e6	+	1.13484e7i	0.526917	+	1.62169i	0.760493	+	0.649346i	$0.224957\pi$
$547$	3.68732e6	+	1.13484e7i	0.526917	+	1.62169i	−0.233575	+	0.972339i	$0.575043\pi$
$548$	−2.43721e6	−	1.77073e6i	−0.346690	−	0.251885i
$549$	−3.56454e6			−0.504746
$550$	5.34303e6	−	3.94797e6i	0.753149	−	0.556503i
$551$	1.54460e7			2.16739
$552$	−1.03250e6	−	750154.i	−0.144225	−	0.104786i
$553$	−294336.	−	905872.i	−0.0409289	−	0.125966i
$554$	−1.67173e6	−	5.14506e6i	−0.231415	−	0.712224i
$555$	−5.46877e6	+	1.80125e6i	−0.753629	+	0.248223i
$556$	−1.01530e6	+	3.12477e6i	−0.139286	+	0.428677i
$557$	−5.28094e6			−0.721229			−0.360614	−	0.932715i	$-0.617433\pi$
$557$	−5.28094e6			−0.721229			−0.360614	+	0.932715i	$0.617433\pi$
$558$	−424982.	+	1.30796e6i	−0.0577810	+	0.177832i
$559$	21204.0	−	15405.6i	0.00287004	−	0.00208521i
$560$	−535.976	−	133301.i	−7.22229e−5	−	0.0179624i
$561$	−6.31919e6	−	4.59116e6i	−0.847724	−	0.615907i
$562$	−6.96105e6	+	5.05750e6i	−0.929682	+	0.675453i
$563$	720370.	−	523380.i	0.0957822	−	0.0695898i	−0.538863	−	0.842393i	$-0.681146\pi$
$563$	720370.	−	523380.i	0.0957822	−	0.0695898i	0.634646	+	0.772803i	$0.281146\pi$
$564$	247494.	+	179815.i	0.0327618	+	0.0238028i
$565$	18299.0	+	4.55110e6i	0.00241160	+	0.599785i
$566$	1.53109e6	−	1.11240e6i	0.200891	−	0.145956i
$567$	−18885.4	+	58123.2i	−0.00246699	+	0.00759263i
$568$	3.29109e6			0.428025
$569$	−2.95510e6	+	9.09485e6i	−0.382641	+	1.17765i	0.555537	+	0.831492i	$0.312513\pi$
$569$	−2.95510e6	+	9.09485e6i	−0.382641	+	1.17765i	−0.938177	+	0.346155i	$0.887487\pi$
$570$	−4.54284e6	+	1.49628e6i	−0.585652	+	0.192897i
$571$	−2.27721e6	−	7.00854e6i	−0.292290	−	0.899575i	−0.984118	−	0.177514i	$-0.943195\pi$
$571$	−2.27721e6	−	7.00854e6i	−0.292290	−	0.899575i	0.691829	−	0.722062i	$-0.256805\pi$
$572$	−52721.4	−	162260.i	−0.00673747	−	0.0207358i
$573$	1.31618e6	+	956263.i	0.167467	+	0.121672i
$574$	−605653.			−0.0767263
$575$	−2.08662e6	+	6.60214e6i	−0.263193	+	0.832751i
$576$	331776.			0.0416667
$577$	1.91663e6	+	1.39251e6i	0.239661	+	0.174124i	0.701132	−	0.713031i	$-0.252678\pi$
$577$	1.91663e6	+	1.39251e6i	0.239661	+	0.174124i	−0.461471	+	0.887155i	$0.652678\pi$
$578$	−1.54111e6	−	4.74306e6i	−0.191873	−	0.590525i
$579$	372201.	+	1.14552e6i	0.0461404	+	0.142005i
$580$	23372.4	+	5.81289e6i	0.00288491	+	0.717500i
$581$	254243.	−	782479.i	0.0312470	−	0.0961683i
$582$	−3.57222e6			−0.437150
$583$	1.26505e6	−	3.89342e6i	0.154147	−	0.474417i
$584$	2.74212e6	−	1.99227e6i	0.332701	−	0.241721i
$585$	−53694.3	−	73282.4i	−0.00648692	−	0.00885339i
$586$	−2.04238e6	−	1.48388e6i	−0.245693	−	0.178507i
$587$	1.43553e6	−	1.04297e6i	0.171956	−	0.124933i	−0.498479	−	0.866902i	$-0.666108\pi$
$587$	1.43553e6	−	1.04297e6i	0.171956	−	0.124933i	0.670434	+	0.741969i	$0.266108\pi$
$588$	−1.94788e6	+	1.41522e6i	−0.232337	+	0.168803i
$589$	−8.16141e6	−	5.92961e6i	−0.969342	−	0.704268i
$590$	832962.	−	1.15622e6i	0.0985133	−	0.136745i
$591$	2.41452e6	−	1.75425e6i	0.284356	−	0.206597i
$592$	−905336.	+	2.78634e6i	−0.106171	+	0.326760i
$593$	1.58403e6			0.184980			0.0924902	−	0.995714i	$-0.470517\pi$
$593$	1.58403e6			0.184980			0.0924902	+	0.995714i	$0.470517\pi$
$594$	−478904.	+	1.47392e6i	−0.0556907	+	0.171398i
$595$	502566.	+	685906.i	0.0581970	+	0.0794277i
$596$	−1.06680e6	−	3.28327e6i	−0.123018	−	0.378609i
$597$	−1.16918e6	−	3.59835e6i	−0.134259	−	0.413207i
$598$	143858.	+	104519.i	0.0164505	+	0.0119520i
$599$	−2.10454e6			−0.239657			−0.119829	−	0.992795i	$-0.538235\pi$
$599$	−2.10454e6			−0.239657			−0.119829	+	0.992795i	$0.538235\pi$
$600$	−569979.	−	1.70737e6i	−0.0646369	−	0.193620i
$601$	1.86299e6			0.210390			0.105195	−	0.994452i	$-0.466453\pi$
$601$	1.86299e6			0.210390			0.105195	+	0.994452i	$0.466453\pi$
$602$	39377.2	+	28609.2i	0.00442847	+	0.00321747i
$603$	−1.12323e6	−	3.45695e6i	−0.125799	−	0.387169i
$604$	−610215.	−	1.87805e6i	−0.0680598	−	0.209466i
$605$	6.46320e6	+	2.07133e6i	0.717893	+	0.230070i
$606$	−54389.4	+	167393.i	−0.00601634	+	0.0185164i
$607$	982689.			0.108254			0.0541271	−	0.998534i	$-0.482762\pi$
$607$	982689.			0.108254			0.0541271	+	0.998534i	$0.482762\pi$
$608$	−752050.	+	2.31457e6i	−0.0825064	+	0.253929i
$609$	−440782.	+	320247.i	−0.0481594	+	0.0349898i
$610$	9.37073e6	+	3.00313e6i	1.01964	+	0.326776i
$611$	−34483.3	−	25053.6i	−0.00373685	−	0.00271498i
$612$	−1.71216e6	+	1.24396e6i	−0.184785	+	0.134254i
$613$	−4.02214e6	+	2.92225e6i	−0.432320	+	0.314099i	−0.782576	−	0.622555i	$-0.786095\pi$
$613$	−4.02214e6	+	2.92225e6i	−0.432320	+	0.314099i	0.350256	+	0.936654i	$0.386095\pi$
$614$	−5.70545e6	−	4.14525e6i	−0.610758	−	0.443742i
$615$	−7.76772e6	+	2.55846e6i	−0.828143	+	0.272766i
$616$	256324.	−	186231.i	0.0272169	−	0.0197742i
$617$	−4.97555e6	+	1.53132e7i	−0.526173	+	1.61939i	0.235813	+	0.971799i	$0.424225\pi$
$617$	−4.97555e6	+	1.53132e7i	−0.526173	+	1.61939i	−0.761985	+	0.647594i	$0.775775\pi$
$618$	5.04776e6			0.531652
$619$	−4.78421e6	+	1.47243e7i	−0.501862	+	1.54457i	0.304122	+	0.952633i	$0.401637\pi$
$619$	−4.78421e6	+	1.47243e7i	−0.501862	+	1.54457i	−0.805983	+	0.591938i	$0.798363\pi$
$620$	2.21918e6	−	3.08041e6i	0.231854	−	0.321832i
$621$	−499136.	−	1.53618e6i	−0.0519386	−	0.159851i
$622$	480715.	+	1.47949e6i	0.0498209	+	0.153333i
$623$	179633.	+	130511.i	0.0185424	+	0.0134718i
$624$	−46226.2			−0.00475255
$625$	−7.80722e6	+	5.86641e6i	−0.799459	+	0.600720i
$626$	−7.09455e6			−0.723585
$627$	−9.19695e6	−	6.68197e6i	−0.934275	−	0.678791i
$628$	2.07164e6	+	6.37586e6i	0.209612	+	0.645119i
$629$	−5.77500e6	−	1.77736e7i	−0.582003	−	1.79122i
$630$	98616.2	−	136888.i	0.00989913	−	0.0137408i
$631$	1.97292e6	−	6.07202e6i	0.197258	−	0.607099i	−0.802684	−	0.596404i	$-0.796596\pi$
$631$	1.97292e6	−	6.07202e6i	0.197258	−	0.607099i	0.999943	−	0.0106950i	$-0.00340440\pi$
$632$	−6.54436e6			−0.651740
$633$	3.12758e6	−	9.62569e6i	0.310241	−	0.954822i
$634$	8.44308e6	−	6.13426e6i	0.834215	−	0.606093i
$635$	9.92930e6	−	3.27042e6i	0.977201	−	0.321862i
$636$	−897359.	−	651969.i	−0.0879677	−	0.0639123i
$637$	271398.	−	197182.i	0.0265007	−	0.0192539i
$638$	−1.11776e7	+	8.12098e6i	−1.08717	+	0.789872i
$639$	3.36979e6	+	2.44830e6i	0.326476	+	0.237198i
$640$	−872197.	−	279522.i	−0.0841715	−	0.0269753i
$641$	5.71630e6	−	4.15314e6i	0.549503	−	0.399238i	−0.278099	−	0.960552i	$-0.589704\pi$
$641$	5.71630e6	−	4.15314e6i	0.549503	−	0.399238i	0.827602	+	0.561315i	$0.189704\pi$
$642$	392031.	−	1.20655e6i	0.0375390	−	0.115533i
$643$	−1.88621e6			−0.179913			−0.0899564	−	0.995946i	$-0.528673\pi$
$643$	−1.88621e6			−0.179913			−0.0899564	+	0.995946i	$0.528673\pi$
$644$	−102043.	+	314057.i	−0.00969550	+	0.0298397i
$645$	625881.	+	200582.i	0.0592369	+	0.0189843i
$646$	−4.79722e6	−	1.47643e7i	−0.452281	−	1.39198i
$647$	2.08263e6	+	6.40968e6i	0.195592	+	0.601971i	0.999969	+	0.00785166i	$0.00249929\pi$
$647$	2.08263e6	+	6.40968e6i	0.195592	+	0.601971i	−0.804377	+	0.594119i	$0.797501\pi$
$648$	339709.	+	246813.i	0.0317812	+	0.0230904i
$649$	3.38699e6			0.315647
$650$	79414.9	+	237888.i	0.00737257	+	0.0220845i
$651$	355843.			0.0329084
$652$	4.08713e6	+	2.96947e6i	0.376530	+	0.273565i
$653$	787357.	+	2.42323e6i	0.0722584	+	0.222389i	0.980663	−	0.195703i	$-0.0626990\pi$
$653$	787357.	+	2.42323e6i	0.0722584	+	0.222389i	−0.908405	+	0.418092i	$0.862699\pi$
$654$	1.20217e6	+	3.69991e6i	0.109906	+	0.338257i
$655$	5.09489e6	+	6.95355e6i	0.464015	+	0.633291i
$656$	−1.28592e6	+	3.95765e6i	−0.116668	+	0.359069i
$657$	4.28977e6			0.387722
$658$	24460.2	−	75280.8i	0.00220240	−	0.00677828i
$659$	1.07276e7	−	7.79406e6i	0.962253	−	0.699118i	0.00857998	−	0.999963i	$-0.497269\pi$
$659$	1.07276e7	−	7.79406e6i	0.962253	−	0.699118i	0.953673	+	0.300846i	$0.0972689\pi$
$660$	2.50076e6	−	3.47126e6i	0.223466	−	0.310190i
$661$	1.55946e7	+	1.13301e7i	1.38826	+	1.00863i	0.996054	+	0.0887480i	$0.0282866\pi$
$661$	1.55946e7	+	1.13301e7i	1.38826	+	1.00863i	0.392202	+	0.919879i	$0.371713\pi$
$662$	−1.04188e7	+	7.56967e6i	−0.923998	+	0.671324i
$663$	238555.	−	173320.i	0.0210768	−	0.0153132i
$664$	−4.57331e6	−	3.32270e6i	−0.402541	−	0.292463i
$665$	731433.	+	998266.i	0.0641388	+	0.0875371i
$666$	−2.99978e6	+	2.17947e6i	−0.262062	+	0.190399i
$667$	4.44982e6	−	1.36951e7i	0.387282	−	1.19193i
$668$	9.92350e6			0.860446
$669$	309936.	−	953886.i	0.0267736	−	0.0824008i
$670$	40345.4	+	1.00342e7i	0.00347222	+	0.863568i
$671$	7.22736e6	+	2.22435e7i	0.619689	+	1.90721i
$672$	−26527.6	−	81643.6i	−0.00226608	−	0.00697427i
$673$	1.63524e7	+	1.18807e7i	1.39169	+	1.01112i	0.995677	+	0.0928810i	$0.0296076\pi$
$673$	1.63524e7	+	1.18807e7i	1.39169	+	1.01112i	0.396016	+	0.918243i	$0.370392\pi$
$674$	9.33974e6			0.791926
$675$	686534.	−	2.17222e6i	0.0579966	−	0.183503i
$676$	−5.93425e6			−0.499458
$677$	1.44853e6	+	1.05242e6i	0.121466	+	0.0882504i	0.646860	−	0.762609i	$-0.276082\pi$
$677$	1.44853e6	+	1.05242e6i	0.121466	+	0.0882504i	−0.525394	+	0.850859i	$0.676082\pi$
$678$	905690.	+	2.78743e6i	0.0756668	+	0.232879i
$679$	285621.	+	879052.i	0.0237748	+	0.0731712i
$680$	5.54910e6	−	1.82771e6i	0.460204	−	0.151578i
$681$	1.42759e6	−	4.39368e6i	0.117961	−	0.363045i
$682$	9.02364e6			0.742884
$683$	2.96361e6	−	9.12106e6i	0.243091	−	0.748159i	−0.752853	−	0.658189i	$-0.771323\pi$
$683$	2.96361e6	−	9.12106e6i	0.243091	−	0.748159i	0.995944	−	0.0899699i	$-0.0286771\pi$
$684$	−2.49188e6	+	1.81046e6i	−0.203651	+	0.147961i
$685$	42320.1	+	1.05253e7i	0.00344604	+	0.857057i
$686$	1.01062e6	+	734260.i	0.0819933	+	0.0595716i
$687$	1.82057e6	−	1.32272e6i	0.147169	−	0.106924i
$688$	270553.	−	196568.i	0.0217912	−	0.0158322i
$689$	125029.	+	90838.6i	0.0100337	+	0.00728992i
$690$	17928.5	+	4.45896e6i	0.00143358	+	0.356542i
$691$	−1.18070e7	+	8.57830e6i	−0.940687	+	0.683449i	−0.948586	−	0.316519i	$-0.897486\pi$
$691$	−1.18070e7	+	8.57830e6i	−0.940687	+	0.683449i	0.00789864	+	0.999969i	$0.497486\pi$
$692$	3.30114e6	−	1.01599e7i	0.262059	−	0.806534i
$693$	400993.			0.0317179
$694$	−3.38012e6	+	1.04030e7i	−0.266400	+	0.819895i
$695$	1.09031e7	−	3.59117e6i	0.856228	−	0.282016i
$696$	1.15679e6	+	3.56024e6i	0.0905175	+	0.278584i
$697$	−8.20268e6	−	2.52452e7i	−0.639549	−	1.96833i
$698$	1.85536e6	+	1.34800e6i	0.144142	+	0.104725i
$699$	−1.25991e7			−0.975320
$700$	−374578.	+	276776.i	−0.0288933	+	0.0213493i
$701$	8.01122e6			0.615749			0.307875	−	0.951427i	$-0.400382\pi$
$701$	8.01122e6			0.615749			0.307875	+	0.951427i	$0.400382\pi$
$702$	−47331.6	−	34388.4i	−0.00362500	−	0.00263372i
$703$	−8.40493e6	−	2.58677e7i	−0.641425	−	1.97410i
$704$	−672700.	−	2.07036e6i	−0.0511552	−	0.157439i
$705$	−4297.53	−	1.06883e6i	−0.000325647	−	0.0809909i
$706$	3.92880e6	−	1.20916e7i	0.296653	−	0.913004i
$707$	45541.0			0.00342653
$708$	283583.	−	872778.i	0.0212616	−	0.0654366i
$709$	1.67830e7	−	1.21936e7i	1.25387	−	0.910993i	0.255435	−	0.966826i	$-0.417781\pi$
$709$	1.67830e7	−	1.21936e7i	1.25387	−	0.910993i	0.998440	+	0.0558328i	$0.0177814\pi$
$710$	−6.79606e6	−	9.27532e6i	−0.505954	−	0.690530i
$711$	−6.70085e6	−	4.86845e6i	−0.497114	−	0.361174i
$712$	1.23422e6	−	896712.i	0.0912414	−	0.0662908i
$713$	−7.60869e6	+	5.52804e6i	−0.560514	+	0.407237i
$714$	443012.	+	321867.i	0.0325215	+	0.0236282i
$715$	−348429.	+	483650.i	−0.0254888	+	0.0353806i
$716$	−702474.	+	510377.i	−0.0512091	+	0.0372056i
$717$	2.52176e6	−	7.76117e6i	0.183192	−	0.563806i
$718$	−7.69353e6			−0.556948
$719$	−2.61097e6	+	8.03575e6i	−0.188356	+	0.579701i	−0.999990	−	0.00446553i	$-0.998579\pi$
$719$	−2.61097e6	+	8.03575e6i	−0.188356	+	0.579701i	0.811634	+	0.584167i	$0.198579\pi$
$720$	−685113.	−	935047.i	−0.0492528	−	0.0672206i
$721$	−403601.	−	1.24216e6i	−0.0289144	−	0.0889893i
$722$	−3.92124e6	−	1.20683e7i	−0.279950	−	0.861597i
$723$	3.07200e6	+	2.23194e6i	0.218563	+	0.158795i
$724$	−5.84967e6			−0.414748
$725$	1.63343e7	−	1.20694e7i	1.15413	−	0.852788i
$726$	4.37075e6			0.307761
$727$	−1.71296e7	−	1.24454e7i	−1.20202	−	0.873318i	−0.207537	−	0.978227i	$-0.566545\pi$
$727$	−1.71296e7	−	1.24454e7i	−1.20202	−	0.873318i	−0.994482	+	0.104909i	$0.966545\pi$
$728$	3696.08	+	11375.4i	0.000258472	+	0.000795494i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	−1.12773e7	−	3.61414e6i	−0.783242	−	0.251014i
$731$	−659203.	+	2.02882e6i	−0.0456274	+	0.140427i
$732$	6.33696e6			0.437123
$733$	−1.87091e6	+	5.75807e6i	−0.128615	+	0.395837i	−0.994542	−	0.104333i	$-0.966729\pi$
$733$	−1.87091e6	+	5.75807e6i	−0.128615	+	0.395837i	0.865927	+	0.500170i	$0.166729\pi$
$734$	9.97079e6	−	7.24420e6i	0.683108	−	0.496307i
$735$	8.01087e6	+	2.56733e6i	0.546967	+	0.175292i
$736$	1.83555e6	+	1.33361e6i	0.124903	+	0.0907473i
$737$	−1.92947e7	+	1.40184e7i	−1.30849	+	0.950673i
$738$	−4.26082e6	+	3.09567e6i	−0.287974	+	0.209225i
$739$	1.86675e7	+	1.35627e7i	1.25740	+	0.913556i	0.998627	−	0.0523817i	$-0.0166812\pi$
$739$	1.86675e7	+	1.35627e7i	1.25740	+	0.913556i	0.258775	+	0.965938i	$0.416681\pi$
$740$	9.72226e6	−	3.20223e6i	0.652662	−	0.214968i
$741$	347193.	−	252250.i	0.0232287	−	0.0168766i
$742$	−88687.3	+	272952.i	−0.00591360	+	0.0182002i
$743$	4.89569e6			0.325344			0.162672	−	0.986680i	$-0.447989\pi$
$743$	4.89569e6			0.325344			0.162672	+	0.986680i	$0.447989\pi$
$744$	755523.	−	2.32526e6i	0.0500398	−	0.154007i
$745$	−7.05035e6	+	9.78648e6i	−0.465393	+	0.646005i
$746$	2.57490e6	+	7.92471e6i	0.169400	+	0.521359i
$747$	−2.21085e6	−	6.80431e6i	−0.144964	−	0.446152i
$748$	1.12341e7	+	8.16206e6i	0.734150	+	0.533391i
$749$	−328253.			−0.0213798
$750$	−3.63491e6	+	5.13208e6i	−0.235961	+	0.333150i
$751$	673661.			0.0435854			0.0217927	−	0.999763i	$-0.493063\pi$
$751$	673661.			0.0435854			0.0217927	+	0.999763i	$0.493063\pi$
$752$	−439990.	−	319671.i	−0.0283725	−	0.0206138i
$753$	1.68859e6	+	5.19694e6i	0.108527	+	0.334011i
$754$	−161175.	−	496047.i	−0.0103245	−	0.0317757i
$755$	−4.03284e6	+	5.59792e6i	−0.257480	+	0.357404i
$756$	33574.0	−	103330.i	0.00213648	−	0.00657541i
$757$	1.84904e7			1.17275			0.586376	−	0.810039i	$-0.300554\pi$
$757$	1.84904e7			1.17275			0.586376	+	0.810039i	$0.300554\pi$
$758$	2.82578e6	−	8.69685e6i	0.178634	−	0.549780i
$759$	−8.57410e6	+	6.22945e6i	−0.540237	+	0.392505i
$760$	8.07615e6	−	2.66005e6i	0.507190	−	0.167054i
$761$	−1.17263e7	−	8.51965e6i	−0.734005	−	0.533286i	0.156823	−	0.987627i	$-0.449875\pi$
$761$	−1.17263e7	−	8.51965e6i	−0.734005	−	0.533286i	−0.890828	+	0.454341i	$0.849875\pi$
$762$	5.44651e6	−	3.95712e6i	0.339806	−	0.246884i
$763$	814354.	−	591663.i	0.0506409	−	0.0367928i
$764$	−2.33988e6	−	1.70002e6i	−0.145031	−	0.105371i
$765$	7.04145e6	+	2.25665e6i	0.435019	+	0.139415i
$766$	−6.51789e6	+	4.73553e6i	−0.401361	+	0.291606i
$767$	−39511.5	+	121604.i	−0.00242513	+	0.00746378i
$768$	−589824.			−0.0360844
$769$	3.53807e6	−	1.08891e7i	0.215750	−	0.664010i	−0.783350	−	0.621581i	$-0.786491\pi$
$769$	3.53807e6	−	1.08891e7i	0.215750	−	0.664010i	0.999100	−	0.0424285i	$-0.0135095\pi$
$770$	−1.05416e6	−	337838.i	−0.0640738	−	0.0205344i
$771$	−1.25669e6	−	3.86768e6i	−0.0761361	−	0.234323i
$772$	−661690.	−	2.03647e6i	−0.0399587	−	0.122980i
$773$	−1.00751e7	−	7.31998e6i	−0.606457	−	0.440617i	0.241708	−	0.970349i	$-0.422293\pi$
$773$	−1.00751e7	−	7.31998e6i	−0.606457	−	0.440617i	−0.848165	+	0.529732i	$0.822293\pi$
$774$	423252.			0.0253949
$775$	−1.32641e7	+	106666.i	−0.793277	+	0.00637929i
$776$	6.35061e6			0.378583
$777$	776177.	+	563926.i	0.0461220	+	0.0335096i
$778$	−6.79242e6	−	2.09049e7i	−0.402324	−	1.23822i
$779$	−1.19382e7	−	3.67419e7i	−0.704846	−	2.16929i
$780$	95456.5	+	130280.i	0.00561783	+	0.00766726i
$781$	8.44542e6	−	2.59923e7i	0.495443	−	1.52482i
$782$	−1.44728e7			−0.846321
$783$	−1.46407e6	+	4.50593e6i	−0.0853407	+	0.262652i
$784$	3.46290e6	−	2.51594e6i	0.201210	−	0.146188i
$785$	1.36912e7	−	1.90046e7i	0.792991	−	1.10074i
$786$	4.49116e6	+	3.26302e6i	0.259300	+	0.188392i
$787$	−1.36691e7	+	9.93117e6i	−0.786688	+	0.571562i	−0.906979	−	0.421177i	$-0.861617\pi$
$787$	−1.36691e7	+	9.93117e6i	−0.786688	+	0.571562i	0.120291	+	0.992739i	$0.461617\pi$
$788$	−4.29248e6	+	3.11867e6i	−0.246259	+	0.178918i
$789$	9.34985e6	+	6.79307e6i	0.534703	+	0.388484i
$790$	1.35140e7	+	1.84440e7i	0.770401	+	1.05145i
$791$	613516.	−	445745.i	0.0348646	−	0.0253306i
$792$	851386.	−	2.62030e6i	0.0482296	−	0.148435i
$793$	−882926.			−0.0498588
$794$	5.37514e6	−	1.65430e7i	0.302579	−	0.931243i
$795$	15581.9	+	3.87534e6i	0.000874385	+	0.217466i
$796$	2.07853e6	+	6.39707e6i	0.116272	+	0.357848i
$797$	8.63983e6	+	2.65907e7i	0.481792	+	1.48280i	0.836574	+	0.547854i	$0.184555\pi$
$797$	8.63983e6	+	2.65907e7i	0.481792	+	1.48280i	−0.354782	+	0.934949i	$0.615445\pi$
$798$	644760.	+	468445.i	0.0358419	+	0.0260406i
$799$	3.46918e6			0.192247
$800$	1.01330e6	+	3.03533e6i	0.0559772	+	0.167680i
$801$	1.93081e6			0.106331
$802$	7.92150e6	+	5.75530e6i	0.434882	+	0.315960i
$803$	−8.69781e6	−	2.67691e7i	−0.476015	−	1.46502i
$804$	1.99686e6	+	6.14569e6i	0.108945	+	0.335298i
$805$	1.09583e6	−	360934.i	0.0596009	−	0.0196308i
$806$	−105267.	+	323978.i	−0.00570760	+	0.0175662i
$807$	−83120.5			−0.00449287
$808$	96692.3	−	297588.i	0.00521031	−	0.0160357i
$809$	485734.	−	352907.i	0.0260932	−	0.0189578i	−0.574662	−	0.818391i	$-0.694867\pi$
$809$	485734.	−	352907.i	0.0260932	−	0.0189578i	0.600755	+	0.799433i	$0.294867\pi$
$810$	−5898.78	−	1.46707e6i	−0.000315900	−	0.0785668i
$811$	−2.53053e7	−	1.83854e7i	−1.35101	−	0.981570i	−0.998960	−	0.0455903i	$-0.985483\pi$
$811$	−2.53053e7	−	1.83854e7i	−1.35101	−	0.981570i	−0.352055	−	0.935979i	$-0.614517\pi$
$812$	783613.	−	569328.i	0.0417072	−	0.0303021i
$813$	1.06356e7	−	7.72720e6i	0.564332	−	0.410011i
$814$	1.96827e7	+	1.43003e7i	1.04117	+	0.756457i
$815$	−70969.6	−	1.76507e7i	−0.00374264	−	0.930825i
$816$	3.04385e6	−	2.21148e6i	0.160028	−	0.116267i
$817$	−959403.	+	2.95274e6i	−0.0502859	+	0.154764i
$818$	−1.37961e7			−0.720894
$819$	−4677.85	+	14396.9i	−0.000243689	+	0.000749999i
$820$	1.38093e7	−	4.54837e6i	0.717193	−	0.236223i
$821$	9.61384e6	+	2.95884e7i	0.497782	+	1.53202i	0.812576	+	0.582855i	$0.198065\pi$
$821$	9.61384e6	+	2.95884e7i	0.497782	+	1.53202i	−0.314794	+	0.949160i	$0.601935\pi$
$822$	2.09459e6	+	6.44649e6i	0.108123	+	0.332770i
$823$	−6.52032e6	−	4.73729e6i	−0.335559	−	0.243798i	0.407226	−	0.913327i	$-0.366496\pi$
$823$	−6.52032e6	−	4.73729e6i	−0.335559	−	0.243798i	−0.742786	+	0.669529i	$0.766496\pi$
$824$	−8.97380e6			−0.460424
$825$	−1.49471e7	+	120200.i	−0.764579	+	0.00614851i
$826$	−237448.			−0.0121093
$827$	5.62763e6	+	4.08871e6i	0.286129	+	0.207885i	0.721586	−	0.692325i	$-0.243413\pi$
$827$	5.62763e6	+	4.08871e6i	0.286129	+	0.207885i	−0.435457	+	0.900209i	$0.643413\pi$
$828$	887354.	+	2.73099e6i	0.0449802	+	0.138435i
$829$	6.24189e6	+	1.92106e7i	0.315449	+	0.970853i	0.975569	+	0.219693i	$0.0705055\pi$
$829$	6.24189e6	+	1.92106e7i	0.315449	+	0.970853i	−0.660120	+	0.751160i	$0.729494\pi$
$830$	79411.8	+	1.97503e7i	0.00400119	+	0.995128i
$831$	−3.76140e6	+	1.15764e7i	−0.188950	+	0.581528i
$832$	82179.9			0.00411583
$833$	−8.43737e6	+	2.59676e7i	−0.421303	+	1.29664i
$834$	5.98069e6	−	4.34523e6i	0.297739	−	0.216320i
$835$	−2.04919e7	−	2.79675e7i	−1.01710	−	1.38815i
$836$	1.63501e7	+	1.18791e7i	0.809106	+	0.587850i
$837$	2.50339e6	−	1.81882e6i	0.123514	−	0.0897378i
$838$	2.18755e7	−	1.58935e7i	1.07609	−	0.781823i
$839$	−1.30586e6	−	948762.i	−0.0640459	−	0.0465320i	0.555302	−	0.831649i	$-0.312603\pi$
$839$	−1.30586e6	−	948762.i	−0.0640459	−	0.0465320i	−0.619348	+	0.785117i	$0.712603\pi$
$840$	−175318.	+	243356.i	−0.00857290	+	0.0118999i
$841$	−1.75772e7	+	1.27706e7i	−0.856960	+	0.622618i
$842$	2.73838e6	−	8.42787e6i	0.133111	−	0.409673i
$843$	1.93598e7			0.938277
$844$	−5.56014e6	+	1.71123e7i	−0.268676	+	0.826900i
$845$	1.22541e7	+	1.67245e7i	0.590393	+	0.805773i
$846$	−212702.	−	654630.i	−0.0102175	−	0.0314463i
$847$	−349469.	−	1.07555e6i	−0.0167379	−	0.0515139i
$848$	1.59530e6	+	1.15906e6i	0.0761823	+	0.0553497i
$849$	−4.25821e6			−0.202748
$850$	−1.66099e7	−	1.18649e7i	−0.788531	−	0.563269i
$851$	−2.53569e7			−1.20025
$852$	−5.99074e6	−	4.35253e6i	−0.282736	−	0.205420i
$853$	−5.59575e6	−	1.72219e7i	−0.263321	−	0.810419i	−0.992075	−	0.125644i	$-0.959900\pi$
$853$	−5.59575e6	−	1.72219e7i	−0.263321	−	0.810419i	0.728754	−	0.684775i	$-0.240100\pi$
$854$	−506680.	−	1.55940e6i	−0.0237733	−	0.0731667i
$855$	1.02481e7	+	3.28432e6i	0.479434	+	0.153649i
$856$	−696944.	+	2.14497e6i	−0.0325097	+	0.100055i
$857$	−2.63697e7			−1.22646			−0.613230	−	0.789904i	$-0.710130\pi$
$857$	−2.63697e7			−1.22646			−0.613230	+	0.789904i	$0.710130\pi$
$858$	−118623.	+	365085.i	−0.00550112	+	0.0169307i
$859$	7.05159e6	−	5.12328e6i	0.326065	−	0.236900i	−0.412694	−	0.910870i	$-0.635412\pi$
$859$	7.05159e6	−	5.12328e6i	0.326065	−	0.236900i	0.738759	+	0.673970i	$0.235412\pi$
$860$	−1.11268e6	−	356591.i	−0.0513007	−	0.0164409i
$861$	1.10246e6	+	800987.i	0.0506823	+	0.0368228i
$862$	6.92413e6	−	5.03067e6i	0.317393	−	0.230599i
$863$	−2.91447e7	+	2.11749e7i	−1.33209	+	0.967819i	−0.332393	+	0.943141i	$0.607856\pi$
$863$	−2.91447e7	+	2.11749e7i	−1.33209	+	0.967819i	−0.999695	+	0.0246775i	$0.992144\pi$
$864$	−603928.	−	438779.i	−0.0275233	−	0.0199969i
$865$	−3.54505e7	+	1.16763e7i	−1.61095	+	0.530599i
$866$	9.44897e6	−	6.86508e6i	0.428144	−	0.311065i
$867$	−3.46750e6	+	1.06719e7i	−0.156664	+	0.482162i
$868$	−632610.			−0.0284995
$869$	−1.67938e7	+	5.16860e7i	−0.754396	+	2.32179i
$870$	7.64510e6	−	1.06120e7i	0.342440	−	0.475336i
$871$	−278221.	−	856277.i	−0.0124264	−	0.0382445i
$872$	−2.13720e6	−	6.57762e6i	−0.0951817	−	0.292939i
$873$	6.50246e6	+	4.72432e6i	0.288763	+	0.209799i
$874$	−2.10637e7			−0.932729
$875$	1.55354e6	+	484137.i	0.0685965	+	0.0213771i
$876$	−7.62625e6			−0.335777
$877$	−8.41781e6	−	6.11589e6i	−0.369573	−	0.268510i	0.387461	−	0.921886i	$-0.373352\pi$
$877$	−8.41781e6	−	6.11589e6i	−0.369573	−	0.268510i	−0.757034	+	0.653376i	$0.773352\pi$
$878$	−2.36082e6	−	7.26584e6i	−0.103354	−	0.318090i
$879$	1.75527e6	+	5.40217e6i	0.0766253	+	0.235828i
$880$	−4.44579e6	+	6.17113e6i	−0.193527	+	0.268632i
$881$	−9.18708e6	+	2.82749e7i	−0.398784	+	1.22733i	0.527191	+	0.849747i	$0.323245\pi$
$881$	−9.18708e6	+	2.82749e7i	−0.398784	+	1.22733i	−0.925975	+	0.377584i	$0.876755\pi$
$882$	5.41736e6			0.234485
$883$	−9.55997e6	+	2.94226e7i	−0.412624	+	1.26993i	0.501734	+	0.865022i	$0.332695\pi$
$883$	−9.55997e6	+	2.94226e7i	−0.412624	+	1.26993i	−0.914359	+	0.404905i	$0.867305\pi$
$884$	−424098.	+	308125.i	−0.0182530	+	0.0132616i
$885$	−3.04535e6	+	1.00305e6i	−0.130701	+	0.0430491i
$886$	−5.82823e6	−	4.23446e6i	−0.249432	−	0.181223i
$887$	−7.57797e6	+	5.50572e6i	−0.323403	+	0.234966i	−0.737626	−	0.675209i	$-0.764053\pi$
$887$	−7.57797e6	+	5.50572e6i	−0.323403	+	0.234966i	0.414223	+	0.910175i	$0.364053\pi$
$888$	5.33295e6	−	3.87461e6i	0.226953	−	0.164891i
$889$	−1.40925e6	−	1.02388e6i	−0.0598046	−	0.0434506i
$890$	−5.07586e6	−	1.62671e6i	−0.214800	−	0.0688391i
$891$	2.82102e6	−	2.04959e6i	0.119045	−	0.0864915i
$892$	−550998.	+	1.69580e6i	−0.0231866	+	0.0713612i
$893$	5.04905e6			0.211875
$894$	−2.40030e6	+	7.38736e6i	−0.100443	+	0.309133i
$895$	2.88900e6	+	925867.i	0.120556	+	0.0386359i
$896$	47160.2	+	145144.i	0.00196248	+	0.00603990i
$897$	−123635.	−	380508.i	−0.00513049	−	0.0157900i
$898$	−1.95739e7	−	1.42213e7i	−0.810004	−	0.588502i
$899$	2.75863e7			1.13840
$900$	−1.22050e6	+	3.86172e6i	−0.0502265	+	0.158918i
$901$	−1.25785e7			−0.516198
$902$	2.79568e7	+	2.03118e7i	1.14412	+	0.831251i
$903$	−33841.7	−	104154.i	−0.00138113	−	0.00425067i
$904$	−1.61012e6	−	4.95543e6i	−0.0655294	−	0.201679i
$905$	1.20795e7	+	1.64862e7i	0.490260	+	0.669111i
$906$	−1.37298e6	+	4.22561e6i	−0.0555706	+	0.171029i
$907$	3.70534e7			1.49558			0.747790	−	0.663935i	$-0.231115\pi$
$907$	3.70534e7			1.49558			0.747790	+	0.663935i	$0.231115\pi$
$908$	−2.53795e6	+	7.81099e6i	−0.102157	+	0.314407i
$909$	320385.	−	232773.i	0.0128606	−	0.00934380i
$910$	24426.9	−	33906.7i	0.000977835	−	0.00135732i
$911$	6.06940e6	+	4.40968e6i	0.242298	+	0.176040i	0.702307	−	0.711875i	$-0.252154\pi$
$911$	6.06940e6	+	4.40968e6i	0.242298	+	0.176040i	−0.460008	+	0.887915i	$0.652154\pi$
$912$	4.43001e6	−	3.21859e6i	0.176367	−	0.128138i
$913$	−3.79778e7	+	2.75925e7i	−1.50783	+	1.09550i
$914$	9.78398e6	+	7.10848e6i	0.387391	+	0.281456i
$915$	−1.30857e7	−	1.78595e7i	−0.516708	−	0.705208i
$916$	−3.23657e6	+	2.35151e6i	−0.127452	+	0.0925993i
$917$	443868.	−	1.36608e6i	0.0174313	−	0.0536481i
$918$	4.76179e6			0.186493
$919$	7.32335e6	−	2.25389e7i	0.286036	−	0.880329i	−0.700050	−	0.714094i	$-0.746839\pi$
$919$	7.32335e6	−	2.25389e7i	0.286036	−	0.880329i	0.986086	−	0.166235i	$-0.0531610\pi$
$920$	−31872.9	−	7.92704e6i	−0.00124151	−	0.308774i
$921$	4.90340e6	+	1.50911e7i	0.190480	+	0.586236i
$922$	9.89603e6	+	3.04568e7i	0.383384	+	1.17993i
$923$	834687.	+	606436.i	0.0322492	+	0.0234304i
$924$	−712877.			−0.0274685
$925$	−2.91012e7	−	2.07878e7i	−1.11830	−	0.798829i
$926$	−2.34438e6			−0.0898464
$927$	−9.18838e6	−	6.67575e6i	−0.351188	−	0.255153i
$928$	−2.05652e6	−	6.32932e6i	−0.0783904	−	0.241261i
$929$	8.22394e6	+	2.53107e7i	0.312637	+	0.962198i	0.976716	+	0.214536i	$0.0688238\pi$
$929$	8.22394e6	+	2.53107e7i	0.312637	+	0.962198i	−0.664079	+	0.747662i	$0.731176\pi$
$930$	−8.11345e6	+	2.67233e6i	−0.307608	+	0.101317i
$931$	−1.22797e7	+	3.77932e7i	−0.464317	+	1.42902i
$932$	2.23984e7			0.844652
$933$	1.08161e6	−	3.32885e6i	0.0406786	−	0.125196i
$934$	−1.86167e7	+	1.35258e7i	−0.698289	+	0.507337i
$935$	−195071.	−	4.85158e7i	−0.00729734	−	1.81490i
$936$	84145.0	+	61135.0i	0.00313934	+	0.00228087i
$937$	3.86893e7	−	2.81094e7i	1.43960	−	1.04593i	0.451472	−	0.892285i	$-0.350899\pi$
$937$	3.86893e7	−	2.81094e7i	1.43960	−	1.04593i	0.988126	−	0.153644i	$-0.0491010\pi$
$938$	1.35267e6	−	982775.i	0.0501979	−	0.0364709i
$939$	1.29141e7	+	9.38267e6i	0.477971	+	0.347266i
$940$	7640.06	+	1.90014e6i	0.000282018	+	0.0701401i
$941$	−4.37207e6	+	3.17649e6i	−0.160958	+	0.116943i	−0.665349	−	0.746533i	$-0.731717\pi$
$941$	−4.37207e6	+	3.17649e6i	−0.160958	+	0.116943i	0.504391	+	0.863476i	$0.331717\pi$
$942$	4.66120e6	−	1.43457e7i	0.171147	−	0.526737i
$943$	−3.60164e7			−1.31893
$944$	−504147.	+	1.55161e6i	−0.0184131	+	0.0566698i
$945$	−360546.	+	118753.i	−0.0131335	+	0.00432580i
$946$	−858175.	−	2.64119e6i	−0.0311780	−	0.0959559i
$947$	4.48092e6	+	1.37908e7i	0.162365	+	0.499707i	0.998832	−	0.0483089i	$-0.0153832\pi$
$947$	4.48092e6	+	1.37908e7i	0.162365	+	0.499707i	−0.836468	+	0.548016i	$0.815383\pi$
$948$	1.19126e7	+	8.65503e6i	0.430513	+	0.312786i
$949$	1.06256e6			0.0382991
$950$	−2.41740e7	−	1.72681e7i	−0.869039	−	0.620778i
$951$	−2.34815e7			−0.841927
$952$	−787578.	−	572209.i	−0.0281644	−	0.0204627i
$953$	−7.08261e6	−	2.17980e7i	−0.252616	−	0.777473i	−0.994290	−	0.106712i	$-0.965968\pi$
$953$	−7.08261e6	−	2.17980e7i	−0.252616	−	0.777473i	0.741674	−	0.670761i	$-0.234032\pi$
$954$	771211.	+	2.37354e6i	0.0274348	+	0.0844357i
$955$	40630.1	+	1.01050e7i	0.00144158	+	0.358533i
$956$	−4.48313e6	+	1.37976e7i	−0.158649	+	0.488270i
$957$	3.10865e7			1.09722
$958$	2.24012e6	−	6.89437e6i	0.0788600	−	0.242706i
$959$	1.41888e6	−	1.03088e6i	0.0498195	−	0.0361960i
$960$	1.21798e6	+	1.66231e6i	0.0426542	+	0.0582147i
$961$	8.58530e6	+	6.23758e6i	0.299879	+	0.217875i
$962$	−743038.	+	539849.i	−0.0258865	+	0.0188076i
$963$	−2.30929e6	+	1.67780e6i	−0.0802439	+	0.0583006i
$964$	−5.46134e6	−	3.96789e6i	−0.189281	−	0.137520i
$965$	−4.37303e6	+	6.07014e6i	−0.151170	+	0.209836i
$966$	601095.	−	436721.i	0.0207253	−	0.0150578i
$967$	−5.39604e6	+	1.66073e7i	−0.185571	+	0.571128i	−0.999958	−	0.00919444i	$-0.997073\pi$
$967$	−5.39604e6	+	1.66073e7i	−0.185571	+	0.571128i	0.814387	+	0.580322i	$0.197073\pi$
$968$	−7.77021e6			−0.266529
$969$	−1.07937e7	+	3.32197e7i	−0.369286	+	1.13654i
$970$	−1.31139e7	−	1.78980e7i	−0.447510	−	0.610765i
$971$	4.94664e6	+	1.52242e7i	0.168369	+	0.518187i	0.999269	−	0.0382354i	$-0.0121737\pi$
$971$	4.94664e6	+	1.52242e7i	0.168369	+	0.518187i	−0.830900	+	0.556422i	$0.812174\pi$
$972$	−291954.	−	898543.i	−0.00991172	−	0.0305052i
$973$	−1.54747e6	−	1.12430e6i	−0.0524011	−	0.0380716i
$974$	4.98614e6			0.168410
$975$	170052.	−	538052.i	0.00572890	−	0.0181264i
$976$	−1.12657e7			−0.378559
$977$	1.64625e7	+	1.19607e7i	0.551772	+	0.400886i	0.828438	−	0.560080i	$-0.189230\pi$
$977$	1.64625e7	+	1.19607e7i	0.551772	+	0.400886i	−0.276667	+	0.960966i	$0.589230\pi$
$978$	−3.51257e6	−	1.08106e7i	−0.117430	−	0.361412i
$979$	−3.91486e6	−	1.20487e7i	−0.130545	−	0.401775i
$980$	−1.42415e7	−	4.56413e6i	−0.473688	−	0.151808i
$981$	2.70489e6	−	8.32480e6i	0.0897382	−	0.276186i
$982$	−2.46075e7			−0.814308
$983$	1.03293e7	−	3.17904e7i	0.340948	−	1.04933i	−0.622770	−	0.782405i	$-0.713993\pi$
$983$	1.03293e7	−	3.17904e7i	0.340948	−	1.04933i	0.963717	−	0.266924i	$-0.0860074\pi$
$984$	7.57480e6	−	5.50341e6i	0.249392	−	0.181194i
$985$	1.76533e7	+	5.65753e6i	0.579742	+	0.185796i
$986$	3.43440e7	+	2.49524e7i	1.12502	+	0.817371i
$987$	−144085.	+	104684.i	−0.00470788	+	0.00342047i
$988$	−617231.	+	448445.i	−0.0201166	+	0.0146156i
$989$	2.34165e6	+	1.70131e6i	0.0761256	+	0.0553085i
$990$	−9.14290e6	+	3.01140e6i	−0.296480	+	0.0976520i
$991$	2.43928e7	−	1.77224e7i	0.789002	−	0.573243i	−0.118665	−	0.992934i	$-0.537862\pi$
$991$	2.43928e7	−	1.77224e7i	0.789002	−	0.573243i	0.907667	+	0.419691i	$0.137862\pi$
$992$	−1.34315e6	+	4.13380e6i	−0.0433357	+	0.133374i
$993$	2.89762e7			0.932541
$994$	−592074.	+	1.82222e6i	−0.0190068	+	0.0584970i
$995$	1.37368e7	−	1.90678e7i	0.439873	−	0.610581i
$996$	3.93041e6	+	1.20966e7i	0.125542	+	0.386379i
$997$	2.29402e6	+	7.06026e6i	0.0730902	+	0.224948i	0.980927	−	0.194374i	$-0.0622676\pi$
$997$	2.29402e6	+	7.06026e6i	0.0730902	+	0.224948i	−0.907837	+	0.419323i	$0.862268\pi$
$998$	−6.28855e6	−	4.56890e6i	−0.199859	−	0.145206i
$999$	8.34286e6			0.264485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.91.4	yes	20
25.11	even	5	inner	150.6.g.a.61.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.61.4	✓	20	25.11	even	5	inner
150.6.g.a.91.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(32.6761 - 45.3572i) q^{5} +(11.1246 - 34.2380i) q^{6} -9.31479 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(32.6761 - 45.3572i) q^{5} +(11.1246 - 34.2380i) q^{6} -9.31479 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(212.383 - 69.9528i) q^{10} +(429.968 + 312.390i) q^{11} +(116.498 - 84.6411i) q^{12} +(-16.2317 + 11.7930i) q^{13} +(-30.1433 - 21.9004i) q^{14} +(-479.112 - 153.546i) q^{15} +(-207.108 + 150.473i) q^{16} +(504.620 - 1553.06i) q^{17} -324.000 q^{18} +(734.424 - 2260.32i) q^{19} +(851.755 + 272.971i) q^{20} +(25.9059 + 79.7301i) q^{21} +(656.933 + 2021.83i) q^{22} +(-1792.53 - 1302.35i) q^{23} +576.000 q^{24} +(-989.546 - 2964.19i) q^{25} -80.2539 q^{26} +(589.773 + 428.495i) q^{27} +(-46.0549 - 141.742i) q^{28} +(2008.32 + 6180.97i) q^{29} +(-1189.43 - 1623.35i) q^{30} +(1311.67 - 4036.91i) q^{31} -1024.00 q^{32} +(1478.10 - 4549.12i) q^{33} +(5284.45 - 3839.38i) q^{34} +(-304.371 + 422.493i) q^{35} +(-1048.49 - 761.770i) q^{36} +(9258.59 - 6726.76i) q^{37} +(7690.99 - 5587.83i) q^{38} +(146.085 + 106.137i) q^{39} +(2114.55 + 2885.95i) q^{40} +(13150.7 - 9554.53i) q^{41} +(-103.623 + 318.920i) q^{42} -1306.33 q^{43} +(-2627.73 + 8087.33i) q^{44} +(18.2061 + 4528.00i) q^{45} +(-2738.75 - 8428.99i) q^{46} +(656.489 + 2020.46i) q^{47} +(1863.98 + 1354.26i) q^{48} -16720.2 q^{49} +(3766.99 - 11918.9i) q^{50} -14696.9 q^{51} +(-259.707 - 188.688i) q^{52} +(-2380.28 - 7325.75i) q^{53} +(901.094 + 2773.28i) q^{54} +(28218.8 - 9294.46i) q^{55} +(184.220 - 566.969i) q^{56} -21389.8 q^{57} +(-8033.28 + 24723.9i) q^{58} +(5155.76 - 3745.88i) q^{59} +(-32.3664 - 8049.78i) q^{60} +(35602.1 + 25866.5i) q^{61} +(13736.0 - 9979.80i) q^{62} +(610.402 - 443.483i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(4.50960 + 1121.57i) q^{65} +(15478.9 - 11246.1i) q^{66} +(-13867.1 + 42678.4i) q^{67} +26127.8 q^{68} +(-6162.18 + 18965.2i) q^{69} +(-1978.31 + 651.596i) q^{70} +(-15890.7 - 48906.5i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(-42845.6 - 31129.1i) q^{73} +45777.0 q^{74} +(-22619.9 + 16713.9i) q^{75} +38026.3 q^{76} +(-4005.07 - 2909.85i) q^{77} +(223.198 + 686.934i) q^{78} +(31598.7 + 97250.9i) q^{79} +(57.5403 + 14310.7i) q^{80} +(2027.46 - 6239.88i) q^{81} +65020.6 q^{82} +(-27294.5 + 84003.8i) q^{83} +(-1085.16 + 788.414i) q^{84} +(-53953.5 - 73636.1i) q^{85} +(-4227.39 - 3071.38i) q^{86} +(47320.7 - 34380.5i) q^{87} +(-27518.0 + 19993.0i) q^{88} +(-19284.7 - 14011.1i) q^{89} +(-10587.1 + 14695.7i) q^{90} +(151.195 - 109.849i) q^{91} +(10955.0 - 33716.0i) q^{92} -38201.9 q^{93} +(-2625.95 + 8081.86i) q^{94} +(-78523.8 - 107170. i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-30663.2 - 94371.6i) q^{97} +(-54107.8 - 39311.6i) q^{98} -43049.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Introduction

L-functions

Modular forms

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Database

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