LMFDB - Embedded newform 62.6.g.a.41.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	62.41
Dual form			62.6.g.a.59.3

$q$-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} +(-1.45953 - 13.8865i) q^{3} +(4.94427 + 15.2169i) q^{4} +(5.22891 + 9.05674i) q^{5} +(-27.9260 + 48.3693i) q^{6} +(206.500 + 43.8929i) q^{7} +(19.7771 - 60.8676i) q^{8} +(46.9845 - 9.98686i) q^{9} +(4.37256 - 41.6021i) q^{10} +(47.5180 - 52.7741i) q^{11} +(204.094 - 90.8683i) q^{12} +(-86.1960 - 38.3769i) q^{13} +(-565.049 - 627.551i) q^{14} +(118.135 - 85.8300i) q^{15} +(-207.108 + 150.473i) q^{16} +(-710.614 - 789.217i) q^{17} +(-175.526 - 78.1490i) q^{18} +(600.575 - 267.393i) q^{19} +(-111.962 + 124.347i) q^{20} +(308.127 - 2931.63i) q^{21} +(-277.851 + 59.0590i) q^{22} +(648.408 - 1995.60i) q^{23} +(-874.105 - 185.797i) q^{24} +(1507.82 - 2611.62i) q^{25} +(188.707 + 326.849i) q^{26} +(-1255.76 - 3864.82i) q^{27} +(353.077 + 3359.31i) q^{28} +(915.255 + 664.972i) q^{29} -584.091 q^{30} +(2603.59 + 4674.45i) q^{31} +1024.00 q^{32} +(-802.203 - 582.834i) q^{33} +(444.035 + 4224.71i) q^{34} +(682.243 + 2099.73i) q^{35} +(384.273 + 665.581i) q^{36} +(-818.711 + 1418.05i) q^{37} +(-2572.18 - 546.734i) q^{38} +(-407.116 + 1252.98i) q^{39} +(654.675 - 139.155i) q^{40} +(430.444 - 4095.40i) q^{41} +(-7889.79 + 8762.50i) q^{42} +(2500.40 - 1113.25i) q^{43} +(1038.00 + 462.147i) q^{44} +(336.126 + 373.306i) q^{45} +(-6790.22 + 4933.38i) q^{46} +(-15813.0 + 11488.8i) q^{47} +(2391.83 + 2656.40i) q^{48} +(25361.7 + 11291.7i) q^{49} +(-11019.7 + 4906.28i) q^{50} +(-9922.32 + 11019.8i) q^{51} +(157.802 - 1501.38i) q^{52} +(24528.2 - 5213.63i) q^{53} +(-5023.03 + 15459.3i) q^{54} +(726.429 + 154.407i) q^{55} +(6755.62 - 11701.1i) q^{56} +(-4589.72 - 7949.63i) q^{57} +(-1398.39 - 4303.79i) q^{58} +(974.136 + 9268.28i) q^{59} +(1890.16 + 1373.28i) q^{60} +18976.2 q^{61} +(2564.88 - 21248.2i) q^{62} +10140.6 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-103.141 - 981.324i) q^{65} +(1225.66 + 3772.18i) q^{66} +(-29882.5 - 51758.0i) q^{67} +(8495.97 - 14715.4i) q^{68} +(-28658.3 - 6091.50i) q^{69} +(2728.97 - 8398.91i) q^{70} +(-30449.3 + 6472.19i) q^{71} +(321.340 - 3057.35i) q^{72} +(-1476.08 + 1639.35i) q^{73} +(5983.44 - 2664.00i) q^{74} +(-38467.0 - 17126.6i) q^{75} +(7038.30 + 7816.83i) q^{76} +(12128.9 - 8812.14i) q^{77} +(4263.38 - 3097.53i) q^{78} +(52297.2 + 58081.9i) q^{79} +(-2445.75 - 1088.92i) q^{80} +(-41173.0 + 18331.4i) q^{81} +(-11021.8 + 12241.0i) q^{82} +(7034.74 - 66931.1i) q^{83} +(46133.8 - 9806.04i) q^{84} +(3431.99 - 10562.6i) q^{85} +(-10708.9 - 2276.24i) q^{86} +(7898.30 - 13680.3i) q^{87} +(-2272.46 - 3936.02i) q^{88} +(-26391.1 - 81223.4i) q^{89} +(-210.032 - 1998.32i) q^{90} +(-16115.0 - 11708.2i) q^{91} +33572.7 q^{92} +(61111.8 - 42977.4i) q^{93} +78183.9 q^{94} +(5562.06 + 4041.08i) q^{95} +(-1494.56 - 14219.8i) q^{96} +(49213.5 + 151464. i) q^{97} +(-55523.6 - 96169.6i) q^{98} +(1705.56 - 2954.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) $ 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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
$3$	−1.45953	−	13.8865i	−0.0936291	−	0.890821i	−0.936018	−	0.351951i	$-0.885518\pi$
$3$	−1.45953	−	13.8865i	−0.0936291	−	0.890821i	0.842389	−	0.538870i	$-0.181148\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	5.22891	+	9.05674i	0.0935376	+	0.162012i	0.908997	−	0.416802i	$-0.136849\pi$
$5$	5.22891	+	9.05674i	0.0935376	+	0.162012i	−0.815460	+	0.578814i	$0.803516\pi$
$6$	−27.9260	+	48.3693i	−0.316688	+	0.548519i
$7$	206.500	+	43.8929i	1.59285	+	0.338571i	0.917130	−	0.398588i	$-0.130500\pi$
$7$	206.500	+	43.8929i	1.59285	+	0.338571i	0.675719	+	0.737159i	$0.263833\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	46.9845	−	9.98686i	0.193352	−	0.0410982i
$10$	4.37256	−	41.6021i	0.0138273	−	0.131558i
$11$	47.5180	−	52.7741i	0.118407	−	0.131504i	−0.681027	−	0.732258i	$-0.738466\pi$
$11$	47.5180	−	52.7741i	0.118407	−	0.131504i	0.799434	+	0.600754i	$0.205133\pi$
$12$	204.094	−	90.8683i	0.409144	−	0.182163i
$13$	−86.1960	−	38.3769i	−0.141458	−	0.0629813i	0.334787	−	0.942294i	$-0.391336\pi$
$13$	−86.1960	−	38.3769i	−0.141458	−	0.0629813i	−0.476245	+	0.879313i	$0.658002\pi$
$14$	−565.049	−	627.551i	−0.770489	−	0.855714i
$15$	118.135	−	85.8300i	0.135566	−	0.0984943i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−710.614	−	789.217i	−0.596364	−	0.662329i	0.367095	−	0.930183i	$-0.380352\pi$
$17$	−710.614	−	789.217i	−0.596364	−	0.662329i	−0.963460	+	0.267854i	$0.913686\pi$
$18$	−175.526	−	78.1490i	−0.127691	−	0.0568515i
$19$	600.575	−	267.393i	0.381666	−	0.169929i	−0.206931	−	0.978356i	$-0.566347\pi$
$19$	600.575	−	267.393i	0.381666	−	0.169929i	0.588596	+	0.808427i	$0.299681\pi$
$20$	−111.962	+	124.347i	−0.0625889	+	0.0695120i
$21$	308.127	−	2931.63i	0.152469	−	1.45064i
$22$	−277.851	+	59.0590i	−0.122393	+	0.0260153i
$23$	648.408	−	1995.60i	0.255581	−	0.786598i	−0.738133	−	0.674655i	$-0.764293\pi$
$23$	648.408	−	1995.60i	0.255581	−	0.786598i	0.993715	−	0.111943i	$-0.0357075\pi$
$24$	−874.105	−	185.797i	−0.309767	−	0.0658431i
$25$	1507.82	−	2611.62i	0.482501	−	0.835717i
$26$	188.707	+	326.849i	0.0547462	+	0.0948231i
$27$	−1255.76	−	3864.82i	−0.331510	−	1.02028i
$28$	353.077	+	3359.31i	0.0851089	+	0.809757i
$29$	915.255	+	664.972i	0.202091	+	0.146828i	0.684228	−	0.729268i	$-0.260139\pi$
$29$	915.255	+	664.972i	0.202091	+	0.146828i	−0.482137	+	0.876096i	$0.660139\pi$
$30$	−584.091			−0.118489
$31$	2603.59	+	4674.45i	0.486596	+	0.873627i
$31$	2603.59	+	4674.45i	0.486596	+	0.873627i
$32$	1024.00			0.176777
$33$	−802.203	−	582.834i	−0.128233	−	0.0931666i
$34$	444.035	+	4224.71i	0.0658749	+	0.626758i
$35$	682.243	+	2099.73i	0.0941389	+	0.289730i
$36$	384.273	+	665.581i	0.0494179	+	0.0855942i
$37$	−818.711	+	1418.05i	−0.0983165	+	0.170289i	−0.910988	−	0.412433i	$-0.864679\pi$
$37$	−818.711	+	1418.05i	−0.0983165	+	0.170289i	0.812671	+	0.582722i	$0.198012\pi$
$38$	−2572.18	−	546.734i	−0.288963	−	0.0614210i
$39$	−407.116	+	1252.98i	−0.0428605	+	0.131911i
$40$	654.675	−	139.155i	0.0646957	−	0.0137515i
$41$	430.444	−	4095.40i	0.0399905	−	0.380484i	−0.956161	−	0.292840i	$-0.905400\pi$
$41$	430.444	−	4095.40i	0.0399905	−	0.380484i	0.996152	−	0.0876440i	$-0.0279338\pi$
$42$	−7889.79	+	8762.50i	−0.690148	+	0.766487i
$43$	2500.40	−	1113.25i	0.206224	−	0.0918167i	−0.301026	−	0.953616i	$-0.597329\pi$
$43$	2500.40	−	1113.25i	0.206224	−	0.0918167i	0.507249	+	0.861799i	$0.330662\pi$
$44$	1038.00	+	462.147i	0.0808287	+	0.0359873i
$45$	336.126	+	373.306i	0.0247441	+	0.0274811i
$46$	−6790.22	+	4933.38i	−0.473139	+	0.343756i
$47$	−15813.0	+	11488.8i	−1.04417	+	0.758632i	−0.971095	−	0.238694i	$-0.923281\pi$
$47$	−15813.0	+	11488.8i	−1.04417	+	0.758632i	−0.0730732	+	0.997327i	$0.523281\pi$
$48$	2391.83	+	2656.40i	0.149840	+	0.166414i
$49$	25361.7	+	11291.7i	1.50899	+	0.671847i
$50$	−11019.7	+	4906.28i	−0.623367	+	0.277541i
$51$	−9922.32	+	11019.8i	−0.534180	+	0.593267i
$52$	157.802	−	1501.38i	0.00809288	−	0.0769986i
$53$	24528.2	−	5213.63i	1.19943	−	0.254947i	0.435468	−	0.900204i	$-0.356583\pi$
$53$	24528.2	−	5213.63i	1.19943	−	0.254947i	0.763966	+	0.645257i	$0.223250\pi$
$54$	−5023.03	+	15459.3i	−0.234413	+	0.721448i
$55$	726.429	+	154.407i	0.0323807	+	0.00688273i
$56$	6755.62	−	11701.1i	0.287869	−	0.498604i
$57$	−4589.72	−	7949.63i	−0.187111	−	0.324086i
$58$	−1398.39	−	4303.79i	−0.0545829	−	0.167989i
$59$	974.136	+	9268.28i	0.0364325	+	0.346632i	0.997520	+	0.0703873i	$0.0224235\pi$
$59$	974.136	+	9268.28i	0.0364325	+	0.346632i	−0.961087	+	0.276245i	$0.910910\pi$
$60$	1890.16	+	1373.28i	0.0677829	+	0.0492472i
$61$	18976.2			0.652958			0.326479	−	0.945204i	$-0.394138\pi$
$61$	18976.2			0.652958			0.326479	+	0.945204i	$0.394138\pi$
$62$	2564.88	−	21248.2i	0.0847398	−	0.702011i
$63$	10140.6			0.321895
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−103.141	−	981.324i	−0.00302796	−	0.0288091i
$66$	1225.66	+	3772.18i	0.0346345	+	0.106594i
$67$	−29882.5	−	51758.0i	−0.813260	−	1.40861i	−0.910570	−	0.413354i	$-0.864357\pi$
$67$	−29882.5	−	51758.0i	−0.813260	−	1.40861i	0.0973098	−	0.995254i	$-0.468976\pi$
$68$	8495.97	−	14715.4i	0.222813	−	0.385924i
$69$	−28658.3	−	6091.50i	−0.724648	−	0.154029i
$70$	2728.97	−	8398.91i	0.0665662	−	0.204870i
$71$	−30449.3	+	6472.19i	−0.716854	+	0.152372i	−0.551877	−	0.833925i	$-0.686088\pi$
$71$	−30449.3	+	6472.19i	−0.716854	+	0.152372i	−0.164977	+	0.986297i	$0.552755\pi$
$72$	321.340	−	3057.35i	0.00730522	−	0.0695046i
$73$	−1476.08	+	1639.35i	−0.0324193	+	0.0360052i	−0.759136	−	0.650932i	$-0.774378\pi$
$73$	−1476.08	+	1639.35i	−0.0324193	+	0.0360052i	0.726717	+	0.686937i	$0.241045\pi$
$74$	5983.44	−	2664.00i	0.127020	−	0.0565529i
$75$	−38467.0	−	17126.6i	−0.789650	−	0.351575i
$76$	7038.30	+	7816.83i	0.139776	+	0.155237i
$77$	12128.9	−	8812.14i	0.233127	−	0.169377i
$78$	4263.38	−	3097.53i	0.0793446	−	0.0576472i
$79$	52297.2	+	58081.9i	0.942781	+	1.04706i	0.998817	+	0.0486352i	$0.0154872\pi$
$79$	52297.2	+	58081.9i	0.942781	+	1.04706i	−0.0560360	+	0.998429i	$0.517846\pi$
$80$	−2445.75	−	1088.92i	−0.0427254	−	0.0190226i
$81$	−41173.0	+	18331.4i	−0.697268	+	0.310444i
$82$	−11021.8	+	12241.0i	−0.181017	+	0.201039i
$83$	7034.74	−	66931.1i	0.112086	−	1.06643i	−0.783454	−	0.621450i	$-0.786544\pi$
$83$	7034.74	−	66931.1i	0.112086	−	1.06643i	0.895540	−	0.444981i	$-0.146790\pi$
$84$	46133.8	−	9806.04i	0.713380	−	0.151634i
$85$	3431.99	−	10562.6i	0.0515228	−	0.158571i
$86$	−10708.9	−	2276.24i	−0.156134	−	0.0331873i
$87$	7898.30	−	13680.3i	0.111876	−	0.193774i
$88$	−2272.46	−	3936.02i	−0.0312817	−	0.0541815i
$89$	−26391.1	−	81223.4i	−0.353168	−	1.08694i	−0.957064	−	0.289877i	$-0.906386\pi$
$89$	−26391.1	−	81223.4i	−0.353168	−	1.08694i	0.603895	−	0.797064i	$-0.293614\pi$
$90$	−210.032	−	1998.32i	−0.00273325	−	0.0260052i
$91$	−16115.0	−	11708.2i	−0.203998	−	0.148213i
$92$	33572.7			0.413539
$93$	61111.8	−	42977.4i	0.732686	−	0.515267i
$94$	78183.9			0.912636
$95$	5562.06	+	4041.08i	0.0632306	+	0.0459397i
$96$	−1494.56	−	14219.8i	−0.0165514	−	0.157476i
$97$	49213.5	+	151464.i	0.531074	+	1.63448i	0.751983	+	0.659183i	$0.229098\pi$
$97$	49213.5	+	151464.i	0.531074	+	1.63448i	−0.220909	+	0.975294i	$0.570902\pi$
$98$	−55523.6	−	96169.6i	−0.583999	−	1.01152i
$99$	1705.56	−	2954.12i	0.0174896	−	0.0302928i
$100$	47195.8	+	10031.8i	0.471958	+	0.100318i
$101$	−39832.9	+	122593.i	−0.388542	+	1.19581i	0.545335	+	0.838218i	$0.316402\pi$
$101$	−39832.9	+	122593.i	−0.388542	+	1.19581i	−0.933878	+	0.357592i	$0.883598\pi$
$102$	58018.5	−	12332.2i	0.552161	−	0.117366i
$103$	−17028.0	+	162011.i	−0.158151	+	1.50471i	0.571339	+	0.820714i	$0.306424\pi$
$103$	−17028.0	+	162011.i	−0.158151	+	1.50471i	−0.729490	+	0.683991i	$0.760243\pi$
$104$	−4040.62	+	4487.56i	−0.0366323	+	0.0406843i
$105$	28162.2	−	12538.6i	0.249283	−	0.110988i
$106$	−91632.9	−	40797.6i	−0.792113	−	0.352671i
$107$	−73049.6	−	81129.8i	−0.616820	−	0.685048i	0.351091	−	0.936341i	$-0.385811\pi$
$107$	−73049.6	−	81129.8i	−0.616820	−	0.685048i	−0.967911	+	0.251293i	$0.919144\pi$
$108$	52601.8	−	38217.5i	0.433952	−	0.315284i
$109$	−93990.5	+	68288.1i	−0.757736	+	0.550527i	−0.898215	−	0.439557i	$-0.855136\pi$
$109$	−93990.5	+	68288.1i	−0.757736	+	0.550527i	0.140479	+	0.990084i	$0.455136\pi$
$110$	−1987.74	−	2207.61i	−0.0156631	−	0.0173956i
$111$	20886.7	+	9299.37i	0.160902	+	0.0716384i
$112$	−49372.5	+	21982.1i	−0.371912	+	0.165586i
$113$	−6762.46	+	7510.47i	−0.0498206	+	0.0553313i	−0.767540	−	0.641001i	$-0.778519\pi$
$113$	−6762.46	+	7510.47i	−0.0498206	+	0.0553313i	0.717719	+	0.696332i	$0.245186\pi$
$114$	−3838.05	+	36516.6i	−0.0276598	+	0.263165i
$115$	21464.1	−	4562.33i	0.151345	−	0.0321693i
$116$	−5593.54	+	17215.2i	−0.0385960	+	0.118786i
$117$	−4433.14	−	942.293i	−0.0299397	−	0.00636387i
$118$	18638.7	−	32283.1i	0.123228	−	0.213437i
$119$	−112101.	−	194164.i	−0.725673	−	1.25690i
$120$	−2887.90	−	8888.06i	−0.0183075	−	0.0563448i
$121$	16307.3	+	155153.i	0.101255	+	0.963380i
$122$	−61408.3	−	44615.8i	−0.373532	−	0.271387i
$123$	−57499.2			−0.342688
$124$	−58257.7	+	62730.4i	−0.340251	+	0.366373i
$125$	64217.7			0.367603
$126$	−32815.8	−	23842.1i	−0.184144	−	0.133788i
$127$	10969.3	+	104366.i	0.0603491	+	0.574183i	0.982357	+	0.187013i	$0.0598807\pi$
$127$	10969.3	+	104366.i	0.0603491	+	0.574183i	−0.922008	+	0.387170i	$0.873453\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−19108.6	−	33097.1i	−0.101101	−	0.175112i
$130$	−1973.46	+	3418.13i	−0.0102416	+	0.0177391i
$131$	−125347.	−	26643.3i	−0.638168	−	0.135647i	−0.122546	−	0.992463i	$-0.539106\pi$
$131$	−125347.	−	26643.3i	−0.638168	−	0.135647i	−0.515622	+	0.856816i	$0.672439\pi$
$132$	4902.63	−	15088.7i	0.0244903	−	0.0753734i
$133$	135755.	−	28855.7i	0.665469	−	0.141450i
$134$	−24988.6	+	237750.i	−0.120221	+	1.14382i
$135$	28436.5	−	31581.9i	0.134289	−	0.149143i
$136$	−62091.6	+	27645.0i	−0.287863	+	0.128165i
$137$	356130.	+	158559.i	1.62109	+	0.721756i	0.998167	−	0.0605274i	$-0.0192783\pi$
$137$	356130.	+	158559.i	1.62109	+	0.721756i	0.622923	+	0.782283i	$0.285945\pi$
$138$	78418.1	+	87092.1i	0.350525	+	0.389297i
$139$	−268364.	+	194978.i	−1.17811	+	0.855950i	−0.991958	−	0.126570i	$-0.959603\pi$
$139$	−268364.	+	194978.i	−1.17811	+	0.855950i	−0.186157	+	0.982520i	$0.559603\pi$
$140$	−28578.2	+	20763.3i	−0.123229	+	0.0895314i
$141$	182620.	+	202820.i	0.773570	+	0.859137i
$142$	113753.	+	50646.0i	0.473414	+	0.210778i
$143$	−6121.17	+	2725.32i	−0.0250319	+	0.0111449i
$144$	−8228.13	+	9138.26i	−0.0330670	+	0.0367246i
$145$	−1236.69	+	11766.3i	−0.00488473	+	0.0464751i
$146$	8631.06	−	1834.59i	0.0335106	−	0.00712289i
$147$	119787.	−	368666.i	0.457210	−	1.40715i
$148$	−25626.3	−	5447.03i	−0.0961681	−	0.0204412i
$149$	13095.6	−	22682.2i	0.0483236	−	0.0836989i	−0.840852	−	0.541265i	$-0.817945\pi$
$149$	13095.6	−	22682.2i	0.0483236	−	0.0836989i	0.889175	+	0.457566i	$0.151279\pi$
$150$	84214.7	+	145864.i	0.305604	+	0.529323i
$151$	−22656.3	−	69728.8i	−0.0808622	−	0.248868i	0.902450	−	0.430795i	$-0.141767\pi$
$151$	−22656.3	−	69728.8i	−0.0808622	−	0.248868i	−0.983312	+	0.181926i	$0.941767\pi$
$152$	−4397.96	−	41843.8i	−0.0154398	−	0.146900i
$153$	−41269.6	−	29984.2i	−0.142529	−	0.103553i
$154$	−59968.4			−0.203761
$155$	−28721.3	+	48022.3i	−0.0960229	+	0.160551i
$156$	−21079.3			−0.0693497
$157$	129331.	+	93964.2i	0.418747	+	0.304238i	0.777134	−	0.629336i	$-0.216673\pi$
$157$	129331.	+	93964.2i	0.418747	+	0.304238i	−0.358386	+	0.933573i	$0.616673\pi$
$158$	−32678.5	−	310915.i	−0.104140	−	0.990830i
$159$	−108199.	−	333002.i	−0.339414	−	1.04461i
$160$	5354.41	+	9274.10i	0.0165353	+	0.0286399i
$161$	221489.	−	383630.i	0.673421	−	1.16640i
$162$	176338.	+	37481.8i	0.527909	+	0.112210i
$163$	55459.1	−	170686.i	0.163495	−	0.503186i	−0.835427	−	0.549601i	$-0.814780\pi$
$163$	55459.1	−	170686.i	0.163495	−	0.503186i	0.998922	+	0.0464154i	$0.0147798\pi$
$164$	64447.6	−	13698.8i	0.187110	−	0.0397715i
$165$	1083.93	−	10312.9i	0.00309951	−	0.0294898i
$166$	−180129.	+	200054.i	−0.507358	+	0.563478i
$167$	−226658.	+	100915.i	−0.628898	+	0.280003i	−0.696331	−	0.717721i	$-0.745186\pi$
$167$	−226658.	+	100915.i	−0.628898	+	0.280003i	0.0674337	+	0.997724i	$0.478519\pi$
$168$	−172347.	−	76734.0i	−0.471120	−	0.209756i
$169$	−242487.	−	269309.i	−0.653087	−	0.725326i
$170$	−35940.3	+	26112.2i	−0.0953805	+	0.0692980i
$171$	25547.3	−	18561.2i	0.0668120	−	0.0485418i
$172$	29302.9	+	32544.1i	0.0755247	+	0.0838787i
$173$	302838.	+	134832.i	0.769300	+	0.342514i	0.753575	−	0.657362i	$-0.228328\pi$
$173$	302838.	+	134832.i	0.769300	+	0.342514i	0.0157248	+	0.999876i	$0.494994\pi$
$174$	−57723.7	+	25700.2i	−0.144538	+	0.0643523i
$175$	425995.	−	473116.i	1.05150	−	1.16781i
$176$	−1900.30	+	18080.1i	−0.00462424	+	0.0439967i
$177$	127282.	−	27054.7i	0.305376	−	0.0649097i
$178$	−105564.	+	324893.i	−0.249728	+	0.768583i
$179$	−768976.	−	163451.i	−1.79382	−	0.381289i	−0.813955	−	0.580928i	$-0.802690\pi$
$179$	−768976.	−	163451.i	−1.79382	−	0.381289i	−0.979870	+	0.199639i	$0.936023\pi$
$180$	−4018.66	+	6960.53i	−0.00924486	+	0.0160126i
$181$	−22990.0	−	39819.8i	−0.0521606	−	0.0903448i	0.838766	−	0.544492i	$-0.183277\pi$
$181$	−22990.0	−	39819.8i	−0.0521606	−	0.0903448i	−0.890927	+	0.454147i	$0.849944\pi$
$182$	24621.5	+	75777.2i	0.0550981	+	0.169574i
$183$	−27696.4	−	263514.i	−0.0611358	−	0.581669i
$184$	−108643.	−	78934.1i	−0.236570	−	0.171878i
$185$	−17123.9			−0.0367852
$186$	−298808.	−	4604.73i	−0.633300	−	0.00975937i
$187$	−75417.1			−0.157712
$188$	−253008.	−	183821.i	−0.522084	−	0.379316i
$189$	−89675.4	−	853204.i	−0.182608	−	1.73739i
$190$	−8498.08	−	26154.4i	−0.0170780	−	0.0525606i
$191$	182809.	+	316634.i	0.362588	+	0.628021i	0.988386	−	0.151964i	$-0.0485599\pi$
$191$	182809.	+	316634.i	0.362588	+	0.628021i	−0.625798	+	0.779985i	$0.715227\pi$
$192$	−28596.3	+	49530.2i	−0.0559830	+	0.0969654i
$193$	352679.	+	74964.3i	0.681533	+	0.144864i	0.535653	−	0.844438i	$-0.320065\pi$
$193$	352679.	+	74964.3i	0.681533	+	0.144864i	0.145880	+	0.989302i	$0.453399\pi$
$194$	196854.	−	605854.i	0.375526	−	1.15575i
$195$	−13476.6	+	2864.55i	−0.0253802	+	0.00539473i
$196$	−46430.4	+	441755.i	−0.0863300	+	0.821375i
$197$	191152.	−	212296.i	0.350924	−	0.389741i	−0.541678	−	0.840586i	$-0.682211\pi$
$197$	191152.	−	212296.i	0.350924	−	0.389741i	0.892602	+	0.450845i	$0.148877\pi$
$198$	−12464.9	+	5549.72i	−0.0225956	+	0.0100602i
$199$	670729.	+	298628.i	1.20064	+	0.534561i	0.906909	−	0.421326i	$-0.138435\pi$
$199$	670729.	+	298628.i	1.20064	+	0.534561i	0.293734	+	0.955887i	$0.405102\pi$
$200$	−129143.	−	143427.i	−0.228294	−	0.253546i
$201$	−675124.	+	490506.i	−1.17867	+	0.856356i
$202$	417135.	−	303067.i	0.719281	−	0.522588i
$203$	159813.	+	177490.i	0.272189	+	0.302297i
$204$	−216747.	−	96501.8i	−0.364651	−	0.162353i
$205$	39341.8	−	17516.1i	0.0653836	−	0.0291107i
$206$	436015.	−	484243.i	0.715868	−	0.795052i
$207$	10535.4	−	100238.i	0.0170893	−	0.162594i
$208$	23626.6	−	5021.99i	0.0378654	−	0.00804855i
$209$	14426.7	−	44400.8i	0.0228455	−	0.0703113i
$210$	−120615.	−	25637.5i	−0.188735	−	0.0401168i
$211$	−487682.	+	844691.i	−0.754103	+	1.30615i	0.191715	+	0.981451i	$0.438595\pi$
$211$	−487682.	+	844691.i	−0.754103	+	1.30615i	−0.945819	+	0.324695i	$0.894738\pi$
$212$	200609.	+	347466.i	0.306557	+	0.530973i
$213$	134318.	+	413388.i	0.202855	+	0.624322i
$214$	45645.9	+	434292.i	0.0681345	+	0.648257i
$215$	23156.8	+	16824.4i	0.0341651	+	0.0248224i
$216$	−260078.			−0.379288
$217$	332467.	+	1.07955e6i	0.479291	+	1.55630i
$218$	464715.			0.662285
$219$	24919.3	+	18105.0i	0.0351096	+	0.0255086i
$220$	1242.06	+	11817.4i	0.00173016	+	0.0164614i
$221$	30964.4	+	95298.5i	0.0426463	+	0.131252i
$222$	−45726.7	−	79201.0i	−0.0622713	−	0.107857i
$223$	−15310.9	+	26519.2i	−0.0206176	+	0.0357107i	−0.876150	−	0.482038i	$-0.839897\pi$
$223$	−15310.9	+	26519.2i	−0.0206176	+	0.0357107i	0.855533	+	0.517749i	$0.173230\pi$
$224$	211456.	+	44946.3i	0.281579	+	0.0598514i
$225$	44762.2	−	137764.i	0.0589461	−	0.181417i
$226$	39542.0	−	8404.90i	0.0514976	−	0.0109462i
$227$	−159055.	+	1.51330e6i	−0.204872	+	1.94922i	0.0955686	+	0.995423i	$0.469533\pi$
$227$	−159055.	+	1.51330e6i	−0.204872	+	1.94922i	−0.300440	+	0.953801i	$0.597134\pi$
$228$	98275.9	−	109146.i	0.125202	−	0.139051i
$229$	−743508.	+	331031.i	−0.936908	+	0.417138i	−0.817644	−	0.575724i	$-0.804720\pi$
$229$	−743508.	+	331031.i	−0.936908	+	0.417138i	−0.119264	+	0.992863i	$0.538054\pi$
$230$	−80185.8	−	35701.0i	−0.0999489	−	0.0445001i
$231$	−140072.	−	155566.i	−0.172712	−	0.191816i
$232$	58576.3	−	42558.2i	0.0714500	−	0.0519115i
$233$	−127225.	+	92434.6i	−0.153527	+	0.111544i	−0.661897	−	0.749595i	$-0.730248\pi$
$233$	−127225.	+	92434.6i	−0.153527	+	0.111544i	0.508370	+	0.861139i	$0.330248\pi$
$234$	12130.5	+	13472.3i	0.0144823	+	0.0160843i
$235$	−186736.	−	83140.4i	−0.220576	−	0.0982070i
$236$	−136218.	+	60648.2i	−0.159204	+	0.0708824i
$237$	730227.	−	810999.i	0.844475	−	0.937884i
$238$	−93741.7	+	891893.i	−0.107273	+	1.02063i
$239$	−1.07831e6	+	229202.i	−1.22109	+	0.259552i	−0.772984	−	0.634426i	$-0.781236\pi$
$239$	−1.07831e6	+	229202.i	−1.22109	+	0.259552i	−0.448111	+	0.893978i	$0.647903\pi$
$240$	−11551.6	+	35552.2i	−0.0129454	+	0.0398418i
$241$	540281.	+	114840.i	0.599207	+	0.127365i	0.497522	−	0.867451i	$-0.334243\pi$
$241$	540281.	+	114840.i	0.599207	+	0.127365i	0.101685	+	0.994817i	$0.467577\pi$
$242$	312016.	−	540427.i	0.342482	−	0.593197i
$243$	−179089.	−	310191.i	−0.194560	−	0.336987i
$244$	93823.6	+	288759.i	0.100888	+	0.310500i
$245$	30347.5	+	288737.i	0.0323004	+	0.307318i
$246$	186071.	+	135189.i	0.196038	+	0.142430i
$247$	−62028.9			−0.0646922
$248$	336014.	−	66027.6i	0.346919	−	0.0681705i
$249$	−939708.			−0.960494
$250$	−207813.	−	150985.i	−0.210292	−	0.152786i
$251$	−59412.5	−	565272.i	−0.0595242	−	0.566335i	−0.983119	−	0.182966i	$-0.941430\pi$
$251$	−59412.5	−	565272.i	−0.0595242	−	0.566335i	0.923595	−	0.383369i	$-0.125236\pi$
$252$	50138.1	+	154309.i	0.0497355	+	0.153070i
$253$	−74504.6	−	129046.i	−0.0731782	−	0.126748i
$254$	209882.	−	363527.i	0.204123	−	0.353551i
$255$	−151687.	−	32242.0i	−0.146082	−	0.0310507i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	1.02562e6	−	218002.i	0.968618	−	0.205886i	0.303671	−	0.952777i	$-0.401788\pi$
$257$	1.02562e6	−	218002.i	0.968618	−	0.205886i	0.664947	+	0.746891i	$0.268454\pi$
$258$	−15979.1	+	152031.i	−0.0149453	+	0.142195i
$259$	−231306.	+	256891.i	−0.214258	+	0.237958i
$260$	14422.8	−	6421.43i	0.0132317	−	0.00589112i
$261$	49643.8	+	22102.8i	0.0451090	+	0.0200838i
$262$	342989.	+	380927.i	0.308693	+	0.342838i
$263$	−639671.	+	464748.i	−0.570253	+	0.414313i	−0.835197	−	0.549951i	$-0.814646\pi$
$263$	−639671.	+	464748.i	−0.570253	+	0.414313i	0.264944	+	0.964264i	$0.414646\pi$
$264$	−51341.0	+	37301.4i	−0.0453372	+	0.0329394i
$265$	175474.	+	194884.i	0.153497	+	0.170475i
$266$	−507157.	−	225801.i	−0.439479	−	0.195669i
$267$	−1.08939e6	+	485028.i	−0.935203	+	0.416379i
$268$	639849.	−	710624.i	0.544177	−	0.604370i
$269$	−45192.3	+	429976.i	−0.0380788	+	0.362296i	0.958846	+	0.283928i	$0.0916376\pi$
$269$	−45192.3	+	429976.i	−0.0380788	+	0.362296i	−0.996924	+	0.0783681i	$0.975029\pi$
$270$	−166276.	+	35343.0i	−0.138810	+	0.0295049i
$271$	400841.	−	1.23366e6i	0.331550	−	1.02041i	−0.636846	−	0.770991i	$-0.719761\pi$
$271$	400841.	−	1.23366e6i	0.331550	−	1.02041i	0.968397	−	0.249416i	$-0.0802385\pi$
$272$	265930.	+	56525.2i	0.217944	+	0.0463254i
$273$	−139066.	+	240870.i	−0.112931	+	0.195603i
$274$	−779665.	−	1.35042e6i	−0.627382	−	1.08666i
$275$	−66177.2	−	203672.i	−0.0527687	−	0.162405i
$276$	−49000.4	−	466208.i	−0.0387193	−	0.368389i
$277$	−1.75782e6	−	1.27713e6i	−1.37650	−	1.00008i	−0.997198	−	0.0748093i	$-0.976165\pi$
$277$	−1.75782e6	−	1.27713e6i	−1.37650	−	1.00008i	−0.379299	−	0.925274i	$-0.623835\pi$
$278$	1.32687e6			1.02971
$279$	169012.	+	193625.i	0.129989	+	0.148919i
$280$	141298.			0.107706
$281$	1.18445e6	+	860551.i	0.894849	+	0.650146i	0.937138	−	0.348960i	$-0.113465\pi$
$281$	1.18445e6	+	860551.i	0.894849	+	0.650146i	−0.0422887	+	0.999105i	$0.513465\pi$
$282$	−114112.	−	1.08570e6i	−0.0854493	−	0.812996i
$283$	17910.6	+	55123.0i	0.0132936	+	0.0409135i	0.957483	−	0.288489i	$-0.0931528\pi$
$283$	17910.6	+	55123.0i	0.0132936	+	0.0409135i	−0.944190	+	0.329402i	$0.893153\pi$
$284$	−249036.	−	431343.i	−0.183217	−	0.317342i
$285$	47998.5	−	83135.8i	0.0350038	−	0.0606284i
$286$	26216.1	+	5572.41i	0.0189519	+	0.00402836i
$287$	268646.	−	826807.i	0.192520	−	0.592515i
$288$	48112.1	−	10226.5i	0.0341801	−	0.00726520i
$289$	30524.6	−	290422.i	0.0214983	−	0.204543i
$290$	31666.3	−	35168.9i	0.0221107	−	0.0245564i
$291$	2.03147e6	−	904471.i	1.40630	−	0.626126i
$292$	−32244.1	−	14356.0i	−0.0221306	−	0.00985316i
$293$	−1.06815e6	−	1.18631e6i	−0.726884	−	0.807287i	0.260526	−	0.965467i	$-0.416104\pi$
$293$	−1.06815e6	−	1.18631e6i	−0.726884	−	0.807287i	−0.987410	+	0.158180i	$0.949437\pi$
$294$	−1.25442e6	+	911392.i	−0.846401	+	0.614946i
$295$	−78846.8	+	57285.5i	−0.0527508	+	0.0383257i
$296$	70121.6	+	77877.9i	0.0465181	+	0.0516636i
$297$	−263633.	−	117377.i	−0.173424	−	0.0772134i
$298$	−95707.3	+	42611.6i	−0.0624316	+	0.0277963i
$299$	−132475.	+	147128.i	−0.0856951	+	0.0951741i
$300$	70422.7	−	670027.i	0.0451762	−	0.429822i
$301$	565196.	−	120136.i	0.359570	−	0.0764289i
$302$	−90625.0	+	278915.i	−0.0571782	+	0.175977i
$303$	1.76053e6	+	374212.i	1.10163	+	0.234159i
$304$	−84148.6	+	145750.i	−0.0522232	+	0.0904532i
$305$	99225.0	+	171863.i	0.0610761	+	0.105787i
$306$	63054.4	+	194062.i	0.0384957	+	0.118477i
$307$	−1769.09	−	16831.7i	−0.00107128	−	0.0101926i	0.993973	−	0.109623i	$-0.0349645\pi$
$307$	−1769.09	−	16831.7i	−0.00107128	−	0.0101926i	−0.995044	+	0.0994308i	$0.968298\pi$
$308$	194062.	+	140994.i	0.116564	+	0.0846885i
$309$	2.27462e6			1.35523
$310$	205851.	−	87875.8i	0.121660	−	0.0519356i
$311$	2.50992e6			1.47149			0.735747	−	0.677256i	$-0.236831\pi$
$311$	2.50992e6			1.47149			0.735747	+	0.677256i	$0.236831\pi$
$312$	68214.1	+	49560.4i	0.0396723	+	0.0288236i
$313$	−116729.	−	1.11060e6i	−0.0673471	−	0.640765i	−0.975177	−	0.221426i	$-0.928929\pi$
$313$	−116729.	−	1.11060e6i	−0.0673471	−	0.640765i	0.907830	−	0.419338i	$-0.137738\pi$
$314$	−197600.	−	608149.i	−0.113100	−	0.348085i
$315$	53024.5	+	91841.2i	0.0301093	+	0.0521508i
$316$	−625255.	+	1.08297e6i	−0.352241	+	0.610099i
$317$	−1.76811e6	−	375823.i	−0.988236	−	0.210056i	−0.314685	−	0.949196i	$-0.601899\pi$
$317$	−1.76811e6	−	375823.i	−0.988236	−	0.210056i	−0.673552	+	0.739140i	$0.735232\pi$
$318$	−432796.	+	1.33201e6i	−0.240002	+	0.738651i
$319$	78584.4	−	16703.6i	0.0432374	−	0.00919039i
$320$	4477.50	−	42600.6i	0.00244434	−	0.0232563i
$321$	−1.01999e6	+	1.13282e6i	−0.552503	+	0.613617i
$322$	−1.61872e6	+	720700.i	−0.870026	+	0.387360i
$323$	−637808.	−	283971.i	−0.340160	−	0.151449i
$324$	−482517.	−	535890.i	−0.255358	−	0.283604i
$325$	−230194.	+	167245.i	−0.120888	+	0.0878306i
$326$	−580776.	+	421958.i	−0.302667	+	0.219900i
$327$	1.08547e6	+	1.20553e6i	0.561367	+	0.623461i
$328$	−240764.	−	107195.i	−0.123568	−	0.0550162i
$329$	−3.76967e6	+	1.67836e6i	−1.92005	+	0.854863i
$330$	−27754.8	+	30824.9i	−0.0140299	+	0.0155818i
$331$	324243.	−	3.08497e6i	0.162667	−	1.54768i	−0.543364	−	0.839497i	$-0.682850\pi$
$331$	324243.	−	3.08497e6i	0.162667	−	1.54768i	0.706032	−	0.708180i	$-0.250484\pi$
$332$	1.05327e6	−	223879.i	0.524436	−	0.111472i
$333$	−24304.9	+	74802.7i	−0.0120111	+	0.0369664i
$334$	970745.	+	206338.i	0.476145	+	0.101208i
$335$	312506.	−	541276.i	0.152141	−	0.263516i
$336$	377315.	+	653530.i	0.182329	+	0.315804i
$337$	−584071.	−	1.79759e6i	−0.280150	−	0.862214i	−0.987811	−	0.155661i	$-0.950249\pi$
$337$	−584071.	−	1.79759e6i	−0.280150	−	0.862214i	0.707660	−	0.706553i	$-0.249751\pi$
$338$	151520.	+	1.44162e6i	0.0721406	+	0.686372i
$339$	114164.	+	82945.3i	0.0539550	+	0.0392006i
$340$	177699.			0.0833656
$341$	370407.	+	84718.1i	0.172502	+	0.0394539i
$342$	−126313.			−0.0583959
$343$	1.87101e6	+	1.35937e6i	0.858700	+	0.623882i
$344$	−18310.2	−	174210.i	−0.00834253	−	0.0793739i
$345$	−94682.4	−	291402.i	−0.0428274	−	0.131809i
$346$	−662996.	−	1.14834e6i	−0.297729	−	0.515681i
$347$	−12517.4	+	21680.8i	−0.00558072	+	0.00966610i	−0.868802	−	0.495159i	$-0.835110\pi$
$347$	−12517.4	+	21680.8i	−0.00558072	+	0.00966610i	0.863222	+	0.504825i	$0.168443\pi$
$348$	247223.	+	52548.8i	0.109431	+	0.0232603i
$349$	733916.	−	2.25876e6i	0.322539	−	0.992674i	−0.650000	−	0.759934i	$-0.725231\pi$
$349$	733916.	−	2.25876e6i	0.322539	−	0.992674i	0.972539	−	0.232739i	$-0.0747689\pi$
$350$	−2.49091e6	+	529460.i	−1.08690	+	0.231027i
$351$	−40078.8	+	381324.i	−0.0173639	+	0.165206i
$352$	48658.4	−	54040.7i	0.0209315	−	0.0232468i
$353$	−822749.	+	366311.i	−0.351423	+	0.156464i	−0.574854	−	0.818256i	$-0.694941\pi$
$353$	−822749.	+	366311.i	−0.351423	+	0.156464i	0.223430	+	0.974720i	$0.428274\pi$
$354$	−475504.	−	211708.i	−0.201672	−	0.0897903i
$355$	−217833.	−	241928.i	−0.0917389	−	0.101886i
$356$	1.10548e6	−	803181.i	0.462304	−	0.335883i
$357$	−2.53265e6	+	1.84008e6i	−1.05173	+	0.764127i
$358$	2.10416e6	+	2.33691e6i	0.867704	+	0.963683i
$359$	−1.12753e6	−	502007.i	−0.461732	−	0.205576i	0.162668	−	0.986681i	$-0.447990\pi$
$359$	−1.12753e6	−	502007.i	−0.461732	−	0.205576i	−0.624400	+	0.781104i	$0.714657\pi$
$360$	29369.8	−	13076.3i	0.0119439	−	0.00531776i
$361$	−1.36764e6	+	1.51892e6i	−0.552338	+	0.613433i
$362$	−19224.9	+	182912.i	−0.00771067	+	0.0733621i
$363$	2.13074e6	−	452903.i	0.848719	−	0.180401i
$364$	98486.1	−	303109.i	0.0389602	−	0.119907i
$365$	−22565.5	−	4796.45i	−0.00886570	−	0.00188446i
$366$	−529931.	+	917867.i	−0.206784	+	0.358160i
$367$	1.83202e6	+	3.17314e6i	0.710009	+	1.22977i	0.964853	+	0.262790i	$0.0846427\pi$
$367$	1.83202e6	+	3.17314e6i	0.710009	+	1.22977i	−0.254844	+	0.966982i	$0.582024\pi$
$368$	165992.	+	510872.i	0.0638953	+	0.196650i
$369$	−20676.0	−	196719.i	−0.00790499	−	0.0752109i
$370$	55414.0	+	40260.6i	0.0210434	+	0.0152889i
$371$	5.29391e6			1.99683
$372$	956136.	+	717440.i	0.358230	+	0.268800i
$373$	958083.			0.356559			0.178279	−	0.983980i	$-0.442947\pi$
$373$	958083.			0.356559			0.178279	+	0.983980i	$0.442947\pi$
$374$	244055.	+	177316.i	0.0902212	+	0.0655496i
$375$	−93727.8	−	891760.i	−0.0344184	−	0.327469i
$376$	386563.	+	1.18972e6i	0.141010	+	0.433984i
$377$	−53371.8	−	92442.6i	−0.0193401	−	0.0334980i
$378$	−1.71581e6	+	2.97187e6i	−0.617645	+	1.06979i
$379$	72394.5	+	15387.9i	0.0258886	+	0.00550278i	0.220838	−	0.975311i	$-0.429121\pi$
$379$	72394.5	+	15387.9i	0.0258886	+	0.00550278i	−0.194949	+	0.980813i	$0.562454\pi$
$380$	−33992.3	+	104618.i	−0.0120760	+	0.0371660i
$381$	1.43327e6	−	304652.i	0.505844	−	0.107521i
$382$	152870.	−	1.45446e6i	0.0535998	−	0.509968i
$383$	−2.87486e6	+	3.19285e6i	−1.00143	+	1.11220i	−0.00774543	+	0.999970i	$0.502465\pi$
$383$	−2.87486e6	+	3.19285e6i	−1.00143	+	1.11220i	−0.993682	+	0.112228i	$0.964201\pi$
$384$	208992.	−	93049.2i	0.0723271	−	0.0322021i
$385$	143230.	+	63770.1i	0.0492473	+	0.0219263i
$386$	−965043.	−	1.07179e6i	−0.329669	−	0.366135i
$387$	106362.	−	77276.7i	0.0361002	−	0.0262283i
$388$	−2.06148e6	+	1.49775e6i	−0.695185	+	0.505081i
$389$	−2.59483e6	−	2.88185e6i	−0.869431	−	0.965601i	0.130234	−	0.991483i	$-0.458427\pi$
$389$	−2.59483e6	−	2.88185e6i	−0.869431	−	0.965601i	−0.999665	+	0.0258820i	$0.991761\pi$
$390$	50346.3	+	22415.6i	0.0167612	+	0.00746259i
$391$	−2.03573e6	+	906363.i	−0.673406	+	0.299820i
$392$	1.18888e6	−	1.32039e6i	0.390772	−	0.433996i
$393$	−187035.	+	1.77952e6i	−0.0610859	+	0.581194i
$394$	−1.11772e6	+	237578.i	−0.362737	+	0.0771021i
$395$	−252575.	+	777347.i	−0.0814514	+	0.250682i
$396$	53385.3	+	11347.4i	0.0171074	+	0.00363629i
$397$	2.69482e6	−	4.66756e6i	0.858130	−	1.48632i	−0.0155805	−	0.999879i	$-0.504960\pi$
$397$	2.69482e6	−	4.66756e6i	0.858130	−	1.48632i	0.873711	−	0.486446i	$-0.161707\pi$
$398$	−1.46841e6	−	2.54336e6i	−0.464664	−	0.804822i
$399$	−598845.	−	1.84305e6i	−0.188314	−	0.579570i
$400$	80696.2	+	767773.i	0.0252176	+	0.239929i
$401$	183697.	+	133464.i	0.0570481	+	0.0414479i	0.615944	−	0.787790i	$-0.288775\pi$
$401$	183697.	+	133464.i	0.0570481	+	0.0414479i	−0.558896	+	0.829238i	$0.688775\pi$
$402$	3.33800e6			1.03020
$403$	−45028.4	−	502837.i	−0.0138110	−	0.154228i
$404$	−2.06243e6			−0.628675
$405$	−381312.	−	277040.i	−0.115516	−	0.0839275i
$406$	−99860.7	−	950111.i	−0.0300663	−	0.286061i
$407$	35932.7	+	110590.i	0.0107524	+	0.0330924i
$408$	474517.	+	821888.i	0.141124	+	0.244434i
$409$	−2.01674e6	+	3.49310e6i	−0.596132	+	1.03253i	0.397254	+	0.917709i	$0.369963\pi$
$409$	−2.01674e6	+	3.49310e6i	−0.596132	+	1.03253i	−0.993386	+	0.114822i	$0.963370\pi$
$410$	−168495.	−	35814.8i	−0.0495026	−	0.0105221i
$411$	1.68205e6	−	5.17683e6i	0.491174	−	1.51168i
$412$	−2.54950e6	+	541912.i	−0.739966	+	0.157285i
$413$	−205653.	+	1.95666e6i	−0.0593280	+	0.564468i
$414$	−269766.	+	299605.i	−0.0773546	+	0.0859110i
$415$	642962.	−	286265.i	0.183259	−	0.0815921i
$416$	−88264.7	−	39298.0i	−0.0250065	−	0.0111336i
$417$	3.09925e6	+	3.44207e6i	0.872804	+	0.969347i
$418$	−151078.	+	109765.i	−0.0422923	+	0.0307271i
$419$	−4.85616e6	+	3.52820e6i	−1.35132	+	0.981790i	−0.352373	+	0.935860i	$0.614625\pi$
$419$	−4.85616e6	+	3.52820e6i	−1.35132	+	0.981790i	−0.998945	+	0.0459303i	$0.985375\pi$
$420$	330040.	+	366547.i	0.0912943	+	0.101393i
$421$	−3.84378e6	−	1.71136e6i	−1.05695	−	0.470584i	−0.196703	−	0.980463i	$-0.563023\pi$
$421$	−3.84378e6	−	1.71136e6i	−1.05695	−	0.470584i	−0.860246	+	0.509879i	$0.829690\pi$
$422$	3.56416e6	−	1.58687e6i	0.974263	−	0.433770i
$423$	−628230.	+	697720.i	−0.170713	+	0.189596i
$424$	167755.	−	1.59608e6i	0.0453170	−	0.431163i
$425$	−3.13261e6	+	665856.i	−0.841266	+	0.178817i
$426$	537272.	−	1.65355e6i	0.143440	−	0.441462i
$427$	3.91859e6	+	832921.i	1.04006	+	0.221072i
$428$	873368.	−	1.51272e6i	0.230456	−	0.399161i
$429$	46779.3	+	81024.1i	0.0122719	+	0.0212555i
$430$	−35380.4	−	108890.i	−0.00922767	−	0.0283998i
$431$	633118.	+	6.02372e6i	0.164169	+	1.56197i	0.697828	+	0.716265i	$0.254150\pi$
$431$	633118.	+	6.02372e6i	0.164169	+	1.56197i	−0.533659	+	0.845700i	$0.679183\pi$
$432$	841629.	+	611479.i	0.216976	+	0.157642i
$433$	6.13212e6			1.57178			0.785889	−	0.618368i	$-0.212206\pi$
$433$	6.13212e6			1.57178			0.785889	+	0.618368i	$0.212206\pi$
$434$	1.46229e6	−	4.27518e6i	0.372658	−	1.08951i
$435$	165198.			0.0418583
$436$	−1.50385e6	−	1.09261e6i	−0.378868	−	0.275264i
$437$	−144191.	−	1.37188e6i	−0.0361189	−	0.343648i
$438$	−38073.4	−	117178.i	−0.00948278	−	0.0291850i
$439$	−2.36410e6	−	4.09474e6i	−0.585470	−	1.01406i	−0.994817	−	0.101685i	$-0.967577\pi$
$439$	−2.36410e6	−	4.09474e6i	−0.585470	−	1.01406i	0.409346	−	0.912379i	$-0.365757\pi$
$440$	23765.0	−	41162.2i	0.00585203	−	0.0101360i
$441$	1.30437e6	+	277253.i	0.319378	+	0.0678860i
$442$	123857.	−	381194.i	0.0301555	−	0.0928091i
$443$	128046.	−	27217.1i	0.0309997	−	0.00658919i	−0.192386	−	0.981319i	$-0.561622\pi$
$443$	128046.	−	27217.1i	0.0309997	−	0.00658919i	0.223385	+	0.974730i	$0.428289\pi$
$444$	−38237.9	+	363810.i	−0.00920528	+	0.0875824i
$445$	597622.	−	663727.i	0.143063	−	0.158887i
$446$	111897.	−	49819.9i	0.0266368	−	0.0118595i
$447$	−334091.	−	148747.i	−0.0790853	−	0.0352110i
$448$	−578610.	−	642612.i	−0.136204	−	0.151270i
$449$	295230.	−	214497.i	0.0691106	−	0.0502118i	−0.552694	−	0.833385i	$-0.686400\pi$
$449$	295230.	−	214497.i	0.0691106	−	0.0502118i	0.621804	+	0.783173i	$0.286400\pi$
$450$	−468756.	+	340571.i	−0.109123	+	0.0792823i
$451$	−195677.	−	217322.i	−0.0453001	−	0.0503108i
$452$	−147722.	−	65769.9i	−0.0340093	−	0.0151419i
$453$	−935223.	+	416388.i	−0.214126	+	0.0953351i
$454$	4.07270e6	−	4.52320e6i	0.927349	−	1.02993i
$455$	21774.5	−	207171.i	0.00493083	−	0.0469137i
$456$	−574646.	+	122145.i	−0.129416	+	0.0275083i
$457$	1.75706e6	−	5.40768e6i	0.393547	−	1.21121i	−0.536541	−	0.843874i	$-0.680269\pi$
$457$	1.75706e6	−	5.40768e6i	0.393547	−	1.21121i	0.930087	−	0.367338i	$-0.119731\pi$
$458$	3.18434e6	+	676853.i	0.709343	+	0.150776i
$459$	−2.15782e6	+	3.73746e6i	−0.478062	+	0.828028i
$460$	175549.	+	304059.i	0.0386815	+	0.0669982i
$461$	−141425.	−	435260.i	−0.0309937	−	0.0953887i	0.934363	−	0.356323i	$-0.115970\pi$
$461$	−141425.	−	435260.i	−0.0309937	−	0.0953887i	−0.965357	+	0.260934i	$0.915970\pi$
$462$	87525.9	+	832753.i	0.0190779	+	0.181514i
$463$	−2.01709e6	−	1.46550e6i	−0.437293	−	0.317712i	0.347265	−	0.937767i	$-0.387110\pi$
$463$	−2.01709e6	−	1.46550e6i	−0.437293	−	0.317712i	−0.784559	+	0.620055i	$0.787110\pi$
$464$	−289617.			−0.0624496
$465$	708783.	+	328749.i	0.152013	+	0.0705069i
$466$	629037.			0.134187
$467$	6.38726e6	+	4.64061e6i	1.35526	+	0.984653i	0.998731	+	0.0503681i	$0.0160395\pi$
$467$	6.38726e6	+	4.64061e6i	1.35526	+	0.984653i	0.356528	+	0.934285i	$0.383961\pi$
$468$	−7579.87	−	72117.6i	−0.00159973	−	0.0152204i
$469$	−3.89892e6	−	1.19996e7i	−0.818488	−	2.51905i
$470$	408817.	+	708091.i	0.0853658	+	0.147858i
$471$	1.11607e6	−	1.93310e6i	0.231814	−	0.401514i
$472$	583404.	+	124006.i	0.120535	+	0.0256206i
$473$	60063.3	−	184856.i	0.0123440	−	0.0379909i
$474$	−4.26984e6	+	907581.i	−0.872902	+	0.185541i
$475$	207229.	−	1.97165e6i	0.0421421	−	0.400955i
$476$	2.40032e6	−	2.66583e6i	0.485570	−	0.539280i
$477$	1.10038e6	−	489920.i	0.221435	−	0.0985891i
$478$	4.02837e6	+	1.79355e6i	0.806418	+	0.359040i
$479$	−20359.4	−	22611.4i	−0.00405439	−	0.00450286i	0.741114	−	0.671379i	$-0.234298\pi$
$479$	−20359.4	−	22611.4i	−0.00405439	−	0.00450286i	−0.745169	+	0.666876i	$0.767631\pi$
$480$	120970.	−	87889.9i	0.0239649	−	0.0174115i
$481$	124990.	−	90810.6i	0.0246327	−	0.0178967i
$482$	−1.47838e6	−	1.64191e6i	−0.289847	−	0.321908i
$483$	−5.65055e6	−	2.51579e6i	−1.10211	−	0.490689i
$484$	−2.28033e6	+	1.01527e6i	−0.442470	+	0.197000i
$485$	−1.11443e6	+	1.23770e6i	−0.215129	+	0.238925i
$486$	−149759.	+	1.42486e6i	−0.0287609	+	0.273642i
$487$	−9.44797e6	+	2.00823e6i	−1.80516	+	0.383699i	−0.982712	−	0.185139i	$-0.940726\pi$
$487$	−9.44797e6	+	2.00823e6i	−1.80516	+	0.383699i	−0.822450	+	0.568838i	$0.807393\pi$
$488$	375294.	−	1.15504e6i	0.0713383	−	0.219557i
$489$	−2.45118e6	−	521014.i	−0.463556	−	0.0985319i
$490$	580656.	−	1.00573e6i	0.109252	−	0.189230i
$491$	4.23383e6	+	7.33321e6i	0.792555	+	1.37275i	0.924380	+	0.381473i	$0.124583\pi$
$491$	4.23383e6	+	7.33321e6i	0.792555	+	1.37275i	−0.131824	+	0.991273i	$0.542084\pi$
$492$	−284291.	−	874959.i	−0.0529482	−	0.162958i
$493$	−125586.	−	1.19487e6i	−0.0232715	−	0.221414i
$494$	200730.	+	145839.i	0.0370079	+	0.0268878i
$495$	35672.9			0.00654373
$496$	−1.24260e6	−	576346.i	−0.226792	−	0.105191i
$497$	−6.57185e6			−1.19343
$498$	3.04096e6	+	2.20939e6i	0.549461	+	0.399207i
$499$	−480393.	−	4.57063e6i	−0.0863665	−	0.821722i	−0.948869	−	0.315670i	$-0.897771\pi$
$499$	−480393.	−	4.57063e6i	−0.0863665	−	0.821722i	0.862503	−	0.506053i	$-0.168896\pi$
$500$	317510.	+	977194.i	0.0567978	+	0.174806i
$501$	1.73217e6	+	3.00020e6i	0.308316	+	0.534019i
$502$	−1.13677e6	+	1.96895e6i	−0.201333	+	0.348718i
$503$	8.37932e6	+	1.78108e6i	1.47669	+	0.313880i	0.874715	−	0.484637i	$-0.161048\pi$
$503$	8.37932e6	+	1.78108e6i	1.47669	+	0.313880i	0.601973	+	0.798517i	$0.294382\pi$
$504$	200552.	−	617237.i	0.0351683	−	0.108237i
$505$	−1.31858e6	+	280272.i	−0.230079	+	0.0489048i
$506$	−62302.8	+	592772.i	−0.0108176	+	0.102923i
$507$	−3.38584e6	+	3.76036e6i	−0.584988	+	0.649695i
$508$	−1.53390e6	+	682934.i	−0.263716	+	0.117414i
$509$	3.47888e6	+	1.54890e6i	0.595175	+	0.264989i	0.682139	−	0.731222i	$-0.261050\pi$
$509$	3.47888e6	+	1.54890e6i	0.595175	+	0.264989i	−0.0869640	+	0.996211i	$0.527717\pi$
$510$	415063.	+	460975.i	0.0706625	+	0.0784786i
$511$	−376767.	+	273737.i	−0.0638293	+	0.0463747i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−1.78760e6	−	1.98533e6i	−0.299901	−	0.333074i
$514$	−3.83152e6	−	1.70590e6i	−0.639681	−	0.284804i
$515$	−1.55633e6	+	692923.i	−0.258573	+	0.115124i
$516$	409157.	−	454414.i	0.0676496	−	0.0751325i
$517$	−145091.	+	1.38044e6i	−0.0238733	+	0.227139i
$518$	1.35251e6	−	287485.i	0.221471	−	0.0470750i
$519$	1.43035e6	−	4.40216e6i	0.233090	−	0.717378i
$520$	−61770.7	−	13129.8i	−0.0100178	−	0.00212936i
$521$	−5.17324e6	+	8.96032e6i	−0.834965	+	1.44620i	0.0590931	+	0.998252i	$0.481179\pi$
$521$	−5.17324e6	+	8.96032e6i	−0.834965	+	1.44620i	−0.894059	+	0.447950i	$0.852154\pi$
$522$	−108684.	−	188246.i	−0.0174578	−	0.0302377i
$523$	1.16686e6	+	3.59124e6i	0.186538	+	0.574104i	0.999971	−	0.00755377i	$-0.00240446\pi$
$523$	1.16686e6	+	3.59124e6i	0.186538	+	0.574104i	−0.813434	+	0.581657i	$0.802404\pi$
$524$	−214320.	−	2.03912e6i	−0.0340985	−	0.324425i
$525$	−7.19169e6	−	5.22507e6i	−1.13876	−	0.827358i
$526$	3.16271e6			0.498419
$527$	1.83900e6	−	5.37653e6i	0.288440	−	0.843287i
$528$	253844.			0.0396261
$529$	1.64514e6	+	1.19527e6i	0.255602	+	0.185706i
$530$	−109647.	−	1.04322e6i	−0.0169554	−	0.161320i
$531$	138330.	+	425737.i	0.0212903	+	0.0655247i
$532$	1.11031e6	+	1.92311e6i	0.170084	+	0.294594i
$533$	−194272.	+	336488.i	−0.0296204	+	0.0513041i
$534$	4.66572e6	+	991728.i	0.708052	+	0.150501i
$535$	352802.	−	1.08581e6i	0.0532901	−	0.164010i
$536$	−3.74137e6	+	795253.i	−0.562496	+	0.119562i
$537$	−1.14742e6	+	1.09170e7i	−0.171706	+	1.63368i
$538$	1.15718e6	−	1.28518e6i	0.172363	−	0.191429i
$539$	1.80105e6	−	801877.i	0.267026	−	0.118887i
$540$	621176.	+	276565.i	0.0916706	+	0.0408144i
$541$	5.62387e6	+	6.24594e6i	0.826118	+	0.917497i	0.997708	−	0.0676719i	$-0.0215571\pi$
$541$	5.62387e6	+	6.24594e6i	0.826118	+	0.917497i	−0.171590	+	0.985168i	$0.554890\pi$
$542$	−4.19766e6	+	3.04978e6i	−0.613775	+	0.445934i
$543$	−519404.	+	377369.i	−0.0755973	+	0.0549246i
$544$	−727669.	−	808158.i	−0.105423	−	0.117084i
$545$	−1.10994e6	−	494175.i	−0.160069	−	0.0712672i
$546$	1.01635e6	−	452507.i	0.145902	−	0.0649596i
$547$	852687.	−	947005.i	0.121849	−	0.135327i	−0.679134	−	0.734015i	$-0.737644\pi$
$547$	852687.	−	947005.i	0.121849	−	0.135327i	0.800982	+	0.598688i	$0.204311\pi$
$548$	−651978.	+	6.20315e6i	−0.0927431	+	0.882391i
$549$	891588.	−	189513.i	0.126251	−	0.0268354i
$550$	−264709.	+	814690.i	−0.0373131	+	0.114838i
$551$	727488.	+	154632.i	0.102081	+	0.0216981i
$552$	−937552.	+	1.62389e6i	−0.130963	+	0.226834i
$553$	8.24998e6	+	1.42894e7i	1.14720	+	1.98701i
$554$	2.68571e6	+	8.26577e6i	0.371779	+	1.14422i
$555$	24992.9	+	237791.i	0.00344416	+	0.0327690i
$556$	−4.29383e6	−	3.11965e6i	−0.589057	−	0.427975i
$557$	1.12184e7			1.53212			0.766060	−	0.642769i	$-0.222215\pi$
$557$	1.12184e7			1.53212			0.766060	+	0.642769i	$0.222215\pi$
$558$	−91693.8	−	1.02395e6i	−0.0124668	−	0.139218i
$559$	−258248.			−0.0349548
$560$	−457251.	−	332212.i	−0.0616147	−	0.0447657i
$561$	110074.	+	1.04728e6i	0.0147665	+	0.140494i
$562$	−1.80967e6	−	5.56960e6i	−0.241690	−	0.743847i
$563$	7.06066e6	+	1.22294e7i	0.938803	+	1.62605i	0.767708	+	0.640800i	$0.221397\pi$
$563$	7.06066e6	+	1.22294e7i	0.938803	+	1.62605i	0.171095	+	0.985255i	$0.445270\pi$
$564$	−2.18337e6	+	3.78170e6i	−0.289021	+	0.500598i
$565$	−103381.	−	21974.2i	−0.0136244	−	0.00289596i
$566$	71642.2	−	220492.i	0.00940000	−	0.0289302i
$567$	−9.30683e6	+	1.97823e6i	−1.21575	+	0.258416i
$568$	−208251.	+	1.98137e6i	−0.0270842	+	0.257689i
$569$	5.18964e6	−	5.76368e6i	0.671981	−	0.746310i	−0.306675	−	0.951814i	$-0.599217\pi$
$569$	5.18964e6	−	5.76368e6i	0.671981	−	0.746310i	0.978656	+	0.205504i	$0.0658833\pi$
$570$	−350790.	+	156182.i	−0.0452231	+	0.0201346i
$571$	7.89989e6	+	3.51726e6i	1.01398	+	0.451455i	0.845343	−	0.534223i	$-0.179396\pi$
$571$	7.89989e6	+	3.51726e6i	1.01398	+	0.451455i	0.168640	+	0.985678i	$0.446062\pi$
$572$	−71735.7	−	79670.5i	−0.00916737	−	0.0101814i
$573$	4.13013e6	−	3.00072e6i	0.525506	−	0.381802i
$574$	−2.81329e6	+	2.04398e6i	−0.356398	+	0.258938i
$575$	−4.23405e6	−	4.70239e6i	−0.534055	−	0.593128i
$576$	−179738.	−	80024.6i	−0.0225727	−	0.0100500i
$577$	−602838.	+	268401.i	−0.0753808	+	0.0335617i	−0.444081	−	0.895987i	$-0.646470\pi$
$577$	−602838.	+	268401.i	−0.0753808	+	0.0335617i	0.368700	+	0.929548i	$0.379803\pi$
$578$	−781602.	+	868057.i	−0.0973119	+	0.108076i
$579$	526247.	−	5.00690e6i	0.0652369	−	0.620687i
$580$	−185161.	+	39357.2i	−0.0228549	+	0.00485797i
$581$	4.39047e6	−	1.35125e7i	0.539599	−	1.66072i
$582$	−8.70053e6	−	1.84935e6i	−1.06473	−	0.226315i
$583$	890387.	−	1.54219e6i	0.108494	−	0.187918i
$584$	70591.0	+	122267.i	0.00856480	+	0.0148347i
$585$	−14646.4	−	45077.0i	−0.00176946	−	0.00544584i
$586$	667449.	+	6.35035e6i	0.0802923	+	0.763930i
$587$	−6.08939e6	−	4.42420e6i	−0.729421	−	0.529956i	0.159959	−	0.987124i	$-0.448864\pi$
$587$	−6.08939e6	−	4.42420e6i	−0.729421	−	0.529956i	−0.889380	+	0.457168i	$0.848864\pi$
$588$	6.20221e6			0.739781
$589$	2.81357e6	+	2.11117e6i	0.334171	+	0.250747i
$590$	389840.			0.0461059
$591$	−3.22704e6	−	2.34458e6i	−0.380046	−	0.276120i
$592$	−43816.3	−	416884.i	−0.00513844	−	0.0488890i
$593$	−2.64644e6	−	8.14492e6i	−0.309048	−	0.951152i	−0.978136	−	0.207968i	$-0.933315\pi$
$593$	−2.64644e6	−	8.14492e6i	−0.309048	−	0.951152i	0.669088	−	0.743184i	$-0.266685\pi$
$594$	577166.	+	999680.i	0.0671173	+	0.116251i
$595$	1.17233e6	−	2.03053e6i	0.135755	−	0.235135i
$596$	409901.	+	87127.2i	0.0472676	+	0.0100470i
$597$	3.16795e6	−	9.74995e6i	0.363783	−	1.11961i
$598$	774618.	−	164650.i	0.0885798	−	0.0188282i
$599$	806001.	−	7.66859e6i	0.0917843	−	0.873270i	−0.847654	−	0.530550i	$-0.821985\pi$
$599$	806001.	−	7.66859e6i	0.0917843	−	0.873270i	0.939438	−	0.342719i	$-0.111348\pi$
$600$	−1.80322e6	+	2.00268e6i	−0.204489	+	0.227108i
$601$	−8.06354e6	+	3.59012e6i	−0.910625	+	0.405437i	−0.807931	−	0.589276i	$-0.799413\pi$
$601$	−8.06354e6	+	3.59012e6i	−0.910625	+	0.405437i	−0.102694	+	0.994713i	$0.532746\pi$
$602$	−2.11147e6	−	940087.i	−0.237462	−	0.105725i
$603$	−1.92091e6	−	2.13339e6i	−0.215137	−	0.238934i
$604$	949038.	−	689516.i	0.105850	−	0.0769046i
$605$	−1.31991e6	+	958974.i	−0.146608	+	0.106517i
$606$	−4.81737e6	−	5.35023e6i	−0.532878	−	0.591821i
$607$	−9.10110e6	−	4.05207e6i	−1.00259	−	0.446381i	−0.161263	−	0.986911i	$-0.551557\pi$
$607$	−9.10110e6	−	4.05207e6i	−1.00259	−	0.446381i	−0.841324	+	0.540531i	$0.818223\pi$
$608$	614989.	−	273811.i	0.0674696	−	0.0300394i
$609$	2.23146e6	−	2.47829e6i	0.243807	−	0.270776i
$610$	82974.7	−	789451.i	0.00902861	−	0.0859015i
$611$	1.80393e6	−	383436.i	0.195486	−	0.0415518i
$612$	252218.	−	776246.i	0.0272206	−	0.0837762i
$613$	1.35188e7	+	2.87351e6i	1.45307	+	0.308860i	0.865743	−	0.500488i	$-0.166846\pi$
$613$	1.35188e7	+	2.87351e6i	1.45307	+	0.308860i	0.587329	+	0.809348i	$0.300180\pi$
$614$	−33848.9	+	58628.0i	−0.00362346	+	0.00627602i
$615$	−300658.	−	520755.i	−0.0320542	−	0.0555195i
$616$	−296500.	−	912534.i	−0.0314828	−	0.0968941i
$617$	1.19649e6	+	1.13839e7i	0.126531	+	1.20386i	0.854943	+	0.518723i	$0.173592\pi$
$617$	1.19649e6	+	1.13839e7i	0.126531	+	1.20386i	−0.728412	+	0.685140i	$0.759741\pi$
$618$	−7.36084e6	−	5.34796e6i	−0.775275	−	0.563270i
$619$	−1.52683e7			−1.60164			−0.800819	−	0.598906i	$-0.795602\pi$
$619$	−1.52683e7			−1.60164			−0.800819	+	0.598906i	$0.795602\pi$
$620$	−872757.	−	199614.i	−0.0911831	−	0.0208550i
$621$	−8.52686e6			−0.887279
$622$	−8.12227e6	−	5.90117e6i	−0.841785	−	0.611593i
$623$	−1.88462e6	−	1.79310e7i	−0.194538	−	1.85091i
$624$	−104222.	−	320762.i	−0.0107151	−	0.0329778i
$625$	−4.37614e6	−	7.57970e6i	−0.448117	−	0.776161i
$626$	−2.23344e6	+	3.86844e6i	−0.227792	+	0.394548i
$627$	−637629.	−	135532.i	−0.0647738	−	0.0137681i
$628$	−790398.	+	2.43260e6i	−0.0799736	+	0.246134i
$629$	1.70094e6	−	361545.i	0.171420	−	0.0364364i
$630$	44340.6	−	421873.i	0.00445092	−	0.0423477i
$631$	−2.90775e6	+	3.22939e6i	−0.290726	+	0.322884i	−0.870760	−	0.491708i	$-0.836373\pi$
$631$	−2.90775e6	+	3.22939e6i	−0.290726	+	0.322884i	0.580034	+	0.814592i	$0.303039\pi$
$632$	4.56959e6	−	2.03451e6i	0.455077	−	0.202613i
$633$	1.24416e7	+	5.53936e6i	1.23415	+	0.549478i
$634$	4.83811e6	+	5.37326e6i	0.478027	+	0.530903i
$635$	−887860.	+	645068.i	−0.0873796	+	0.0634850i
$636$	4.53230e6	−	3.29291e6i	0.444299	−	0.322802i
$637$	−1.75273e6	−	1.94661e6i	−0.171146	−	0.190077i
$638$	−293577.	−	130709.i	−0.0285542	−	0.0127132i
$639$	−1.36601e6	+	608185.i	−0.132343	+	0.0589228i
$640$	−114649.	+	127331.i	−0.0110643	+	0.0122881i
$641$	−2.11299e6	+	2.01037e7i	−0.203120	+	1.93255i	0.133775	+	0.991012i	$0.457290\pi$
$641$	−2.11299e6	+	2.01037e7i	−0.203120	+	1.93255i	−0.336894	+	0.941542i	$0.609376\pi$
$642$	5.96418e6	−	1.26773e6i	0.571101	−	0.121391i
$643$	4.55402e6	−	1.40158e7i	0.434378	−	1.33688i	−0.459345	−	0.888258i	$-0.651916\pi$
$643$	4.55402e6	−	1.40158e7i	0.434378	−	1.33688i	0.893723	−	0.448620i	$-0.148084\pi$
$644$	6.93276e6	+	1.47360e6i	0.658705	+	0.140012i
$645$	199834.	−	346123.i	0.0189134	−	0.0327591i
$646$	1.39634e6	+	2.41853e6i	0.131646	+	0.228018i
$647$	−4.49197e6	−	1.38249e7i	−0.421868	−	1.29838i	−0.905962	−	0.423360i	$-0.860851\pi$
$647$	−4.49197e6	−	1.38249e7i	−0.421868	−	1.29838i	0.484094	−	0.875016i	$-0.339149\pi$
$648$	301506.	+	2.86864e6i	0.0282071	+	0.268373i
$649$	535414.	+	389001.i	0.0498974	+	0.0362526i
$650$	1.13814e6			0.105660
$651$	1.45060e7	−	6.19245e6i	1.34151	−	0.572677i
$652$	2.87151e6			0.264540
$653$	−5.57609e6	−	4.05126e6i	−0.511737	−	0.371799i	0.301745	−	0.953389i	$-0.402431\pi$
$653$	−5.57609e6	−	4.05126e6i	−0.511737	−	0.371799i	−0.813482	+	0.581590i	$0.802431\pi$
$654$	−678266.	−	6.45327e6i	−0.0620091	−	0.589978i
$655$	−414126.	−	1.27455e6i	−0.0377163	−	0.116079i
$656$	527099.	+	912962.i	0.0478225	+	0.0828311i
$657$	−52980.9	+	91765.7i	−0.00478858	+	0.00829406i
$658$	1.61450e7	+	3.43172e6i	1.45369	+	0.308992i
$659$	3.39845e6	−	1.04594e7i	0.304837	−	0.938192i	−0.674901	−	0.737908i	$-0.735814\pi$
$659$	3.39845e6	−	1.04594e7i	0.304837	−	0.938192i	0.979738	−	0.200284i	$-0.0641863\pi$
$660$	162290.	−	34495.8i	0.0145021	−	0.00308253i
$661$	−171733.	+	1.63393e6i	−0.0152880	+	0.145455i	−0.999503	−	0.0315208i	$-0.989965\pi$
$661$	−171733.	+	1.63393e6i	−0.0152880	+	0.145455i	0.984215	+	0.176976i	$0.0566316\pi$
$662$	−8.30246e6	+	9.22082e6i	−0.736312	+	0.817757i
$663$	1.27817e6	−	569079.i	0.112929	−	0.0502792i
$664$	−3.93481e6	−	1.75189e6i	−0.346341	−	0.154201i
$665$	971191.	+	1.07862e6i	0.0851629	+	0.0945830i
$666$	254524.	−	184922.i	0.0222353	−	0.0161549i
$667$	1.92047e6	−	1.39531e6i	0.167145	−	0.121438i
$668$	−2.65627e6	−	2.95008e6i	−0.230319	−	0.255796i
$669$	390606.	+	173909.i	0.0337422	+	0.0150230i
$670$	−2.28391e6	+	1.01686e6i	−0.196558	+	0.0875133i
$671$	901712.	−	1.00145e6i	0.0773146	−	0.0858666i
$672$	315522.	−	3.00199e6i	0.0269529	−	0.256440i
$673$	1.46647e7	−	3.11708e6i	1.24806	−	0.265284i	0.463927	−	0.885873i	$-0.346440\pi$
$673$	1.46647e7	−	3.11708e6i	1.24806	−	0.265284i	0.784136	+	0.620589i	$0.213107\pi$
$674$	−2.33629e6	+	7.19035e6i	−0.198096	+	0.609677i
$675$	−1.19869e7	−	2.54789e6i	−1.01262	−	0.215239i
$676$	2.89912e6	−	5.02143e6i	0.244006	−	0.422630i
$677$	−6.82796e6	−	1.18264e7i	−0.572558	−	0.991699i	−0.996302	−	0.0859174i	$-0.972618\pi$
$677$	−6.82796e6	−	1.18264e7i	−0.572558	−	0.991699i	0.423745	−	0.905782i	$-0.360715\pi$
$678$	−174428.	−	536833.i	−0.0145727	−	0.0448503i
$679$	3.51441e6	+	3.34373e7i	0.292535	+	2.78328i
$680$	−575045.	−	417795.i	−0.0476902	−	0.0346490i
$681$	2.12467e7			1.75559
$682$	−999479.	−	1.14503e6i	−0.0822835	−	0.0942664i
$683$	6.42623e6			0.527114			0.263557	−	0.964644i	$-0.415104\pi$
$683$	6.42623e6			0.527114			0.263557	+	0.964644i	$0.415104\pi$
$684$	408757.	+	296979.i	0.0334060	+	0.0242709i
$685$	426142.	+	4.05447e6i	0.0346999	+	0.330147i
$686$	−2.85865e6	−	8.79803e6i	−0.231927	−	0.713798i
$687$	5.68205e6	+	9.84160e6i	0.459318	+	0.795561i
$688$	−350340.	+	606806.i	−0.0282175	+	0.0488741i
$689$	−2.31432e6	−	491923.i	−0.185727	−	0.0394775i
$690$	−378729.	+	1.16561e6i	−0.0302835	+	0.0932031i
$691$	−1.91760e7	+	4.07599e6i	−1.52779	+	0.324742i	−0.893752	−	0.448560i	$-0.851937\pi$
$691$	−1.91760e7	+	4.07599e6i	−1.52779	+	0.324742i	−0.634038	+	0.773302i	$0.718604\pi$
$692$	−554415.	+	5.27491e6i	−0.0440119	+	0.418745i
$693$	481863.	−	535163.i	0.0381145	−	0.0423305i
$694$	91481.7	−	40730.3i	0.00721001	−	0.00321010i
$695$	−3.16912e6	−	1.41098e6i	−0.248872	−	0.110805i
$696$	−676479.	−	751307.i	−0.0529336	−	0.0587887i
$697$	−3.53804e6	+	2.57054e6i	−0.275855	+	0.200420i
$698$	−7.68566e6	+	5.58396e6i	−0.597094	+	0.433814i
$699$	1.46929e6	+	1.63181e6i	0.113740	+	0.126321i
$700$	9.30560e6	+	4.14312e6i	0.717793	+	0.319582i
$701$	−7.65554e6	+	3.40847e6i	−0.588411	+	0.261977i	−0.679273	−	0.733886i	$-0.737705\pi$
$701$	−7.65554e6	+	3.40847e6i	−0.588411	+	0.261977i	0.0908616	+	0.995864i	$0.471038\pi$
$702$	1.02625e6	−	1.13976e6i	0.0785974	−	0.0872913i
$703$	−112521.	+	1.07056e6i	−0.00858705	+	0.0817003i
$704$	−284519.	+	60476.4i	−0.0216361	+	0.00459890i
$705$	−881983.	+	2.71447e6i	−0.0668325	+	0.205689i
$706$	3.52372e6	+	748990.i	0.266066	+	0.0565541i
$707$	−1.36064e7	+	2.35671e7i	−1.02376	+	1.77320i
$708$	1.04101e6	+	1.80308e6i	0.0780497	+	0.135186i
$709$	−7.24750e6	−	2.23055e7i	−0.541468	−	1.66647i	−0.729243	−	0.684254i	$-0.760128\pi$
$709$	−7.24750e6	−	2.23055e7i	−0.541468	−	1.66647i	0.187776	−	0.982212i	$-0.439872\pi$
$710$	136116.	+	1.29505e6i	0.0101336	+	0.0964144i
$711$	3.03721e6	+	2.20666e6i	0.225321	+	0.163705i
$712$	−5.46581e6			−0.404068
$713$	1.10165e7	−	2.16477e6i	0.811558	−	0.159473i
$714$	1.25221e7			0.919247
$715$	−56689.6	−	41187.4i	−0.00414704	−	0.00301300i
$716$	−1.31481e6	−	1.25096e7i	−0.0958474	−	0.911927i
$717$	4.75665e6	+	1.46395e7i	0.345544	+	1.06348i
$718$	2.46846e6	+	4.27550e6i	0.178696	+	0.309511i
$719$	−4.56217e6	+	7.90191e6i	−0.329116	+	0.570046i	−0.982337	−	0.187122i	$-0.940084\pi$
$719$	−4.56217e6	+	7.90191e6i	−0.329116	+	0.570046i	0.653220	+	0.757168i	$0.273418\pi$
$720$	−125787.	−	26736.9i	−0.00904284	−	0.00192211i
$721$	−1.06274e7	+	3.27078e7i	−0.761360	+	2.34322i
$722$	7.99698e6	−	1.69981e6i	0.570930	−	0.121355i
$723$	806175.	−	7.67024e6i	0.0573566	−	0.545712i
$724$	492266.	−	546717.i	0.0349022	−	0.0387629i
$725$	3.11669e6	−	1.38764e6i	0.220216	−	0.0980463i
$726$	−7.96006e6	−	3.54405e6i	−0.560499	−	0.249550i
$727$	8.11076e6	+	9.00792e6i	0.569149	+	0.632104i	0.957163	−	0.289550i	$-0.0935055\pi$
$727$	8.11076e6	+	9.00792e6i	0.569149	+	0.632104i	−0.388014	+	0.921653i	$0.626839\pi$
$728$	−1.03136e6	+	749326.i	−0.0721243	+	0.0524014i
$729$	−1.29063e7	+	9.37700e6i	−0.899465	+	0.653499i
$730$	61746.4	+	68576.3i	0.00428849	+	0.00476285i
$731$	−2.65542e6	−	1.18227e6i	−0.183797	−	0.0818318i
$732$	3.87293e6	−	1.72434e6i	0.267154	−	0.118945i
$733$	−553898.	+	615166.i	−0.0380776	+	0.0422895i	−0.761883	−	0.647715i	$-0.775725\pi$
$733$	−553898.	+	615166.i	−0.0380776	+	0.0422895i	0.723805	+	0.690004i	$0.242391\pi$
$734$	1.53198e6	−	1.45758e7i	0.104958	−	0.998604i
$735$	3.96527e6	−	842843.i	0.270741	−	0.0575478i
$736$	663970.	−	2.04349e6i	0.0451808	−	0.139052i
$737$	−4.15144e6	−	882415.i	−0.281533	−	0.0598417i
$738$	−395606.	+	685209.i	−0.0267375	+	0.0463108i
$739$	7.79743e6	+	1.35056e7i	0.525219	+	0.909706i	0.999569	+	0.0293698i	$0.00935003\pi$
$739$	7.79743e6	+	1.35056e7i	0.525219	+	0.909706i	−0.474349	+	0.880337i	$0.657317\pi$
$740$	−84665.1	−	260572.i	−0.00568362	−	0.0174924i
$741$	90533.2	+	861366.i	0.00605707	+	0.0576291i
$742$	−1.71315e7	−	1.24467e7i	−1.14231	−	0.829938i
$743$	−9.05757e6			−0.601921			−0.300960	−	0.953637i	$-0.597307\pi$
$743$	−9.05757e6			−0.601921			−0.300960	+	0.953637i	$0.597307\pi$
$744$	−1.40732e6	−	4.56970e6i	−0.0932094	−	0.302660i
$745$	273903.			0.0180803
$746$	−3.10042e6	−	2.25259e6i	−0.203973	−	0.148195i
$747$	−337908.	−	3.21498e6i	−0.0221563	−	0.210803i
$748$	−372883.	−	1.14762e6i	−0.0243679	−	0.0749967i
$749$	−1.15237e7	−	1.99597e7i	−0.750564	−	1.30002i
$750$	−1.79334e6	+	3.10616e6i	−0.116415	+	0.201637i
$751$	−5.09733e6	−	1.08347e6i	−0.329794	−	0.0700999i	0.0400389	−	0.999198i	$-0.487252\pi$
$751$	−5.09733e6	−	1.08347e6i	−0.329794	−	0.0700999i	−0.369833	+	0.929098i	$0.620585\pi$
$752$	1.54625e6	−	4.75887e6i	0.0997092	−	0.306873i
$753$	−7.76295e6	+	1.65007e6i	−0.498930	+	0.106051i
$754$	−44630.9	+	424635.i	−0.00285896	+	0.0272012i
$755$	513048.	−	569798.i	0.0327560	−	0.0363792i
$756$	1.25397e7	−	5.58306e6i	0.797966	−	0.355277i
$757$	2.03962e7	+	9.08096e6i	1.29363	+	0.575959i	0.934045	−	0.357154i	$-0.116253\pi$
$757$	2.03962e7	+	9.08096e6i	1.29363	+	0.575959i	0.359581	+	0.933114i	$0.382920\pi$
$758$	−198094.	−	220006.i	−0.0125227	−	0.0139079i
$759$	−1.68326e6	+	1.22296e6i	−0.106059	+	0.0770561i
$760$	355972.	−	258629.i	0.0223554	−	0.0162421i
$761$	1.02532e7	+	1.13873e7i	0.641796	+	0.712787i	0.973008	−	0.230769i	$-0.0741243\pi$
$761$	1.02532e7	+	1.13873e7i	0.641796	+	0.712787i	−0.331212	+	0.943556i	$0.607458\pi$
$762$	−5.35445e6	−	2.38396e6i	−0.334062	−	0.148734i
$763$	−2.24064e7	+	9.97597e6i	−1.39335	+	0.620360i
$764$	−3.91433e6	+	4.34731e6i	−0.242619	+	0.269455i
$765$	55763.4	−	530553.i	0.00344505	−	0.0327775i
$766$	1.68101e7	−	3.57310e6i	1.03514	−	0.220025i
$767$	271722.	−	836273.i	0.0166777	−	0.0513286i
$768$	−895084.	−	190256.i	−0.0547596	−	0.0116395i
$769$	−1.71276e6	+	2.96659e6i	−0.104443	+	0.180901i	−0.913511	−	0.406815i	$-0.866639\pi$
$769$	−1.71276e6	+	2.96659e6i	−0.104443	+	0.180901i	0.809067	+	0.587716i	$0.199973\pi$
$770$	−313570.	−	543118.i	−0.0190593	−	0.0330117i
$771$	−4.52421e6	−	1.39241e7i	−0.274098	−	0.843588i
$772$	603018.	+	5.73733e6i	0.0364156	+	0.346471i
$773$	−1.36726e7	−	9.93373e6i	−0.823005	−	0.597948i	0.0945667	−	0.995519i	$-0.469853\pi$
$773$	−1.36726e7	−	9.93373e6i	−0.823005	−	0.597948i	−0.917572	+	0.397570i	$0.869853\pi$
$774$	−525884.			−0.0315528
$775$	1.61336e7	+	248624.i	0.964888	+	0.0148693i
$776$	1.01925e7			0.607614
$777$	3.90493e6	+	2.83710e6i	0.232039	+	0.168586i
$778$	1.62141e6	+	1.54267e7i	0.0960382	+	0.913742i
$779$	−836569.	−	2.57469e6i	−0.0493922	−	0.152013i
$780$	−110222.	−	190910.i	−0.00648681	−	0.0112355i
$781$	−1.10532e6	+	1.91448e6i	−0.0648428	+	0.112311i
$782$	8.71873e6	+	1.85322e6i	0.509843	+	0.108370i
$783$	1.42066e6	−	4.37234e6i	0.0828106	−	0.254865i
$784$	−6.95171e6	+	1.47763e6i	−0.403926	+	0.0858571i
$785$	−174751.	+	1.66264e6i	−0.0101215	+	0.0962997i
$786$	4.78915e6	−	5.31890e6i	0.276505	−	0.307090i
$787$	−1.83336e7	+	8.16263e6i	−1.05514	+	0.469778i	−0.859627	−	0.510923i	$-0.829304\pi$
$787$	−1.83336e7	+	8.16263e6i	−1.05514	+	0.469778i	−0.195513	+	0.980701i	$0.562637\pi$
$788$	4.17559e6	+	1.85909e6i	0.239553	+	0.106656i
$789$	7.38736e6	+	8.20449e6i	0.422471	+	0.469201i
$790$	2.64500e6	−	1.92171e6i	0.150785	−	0.109552i
$791$	−1.72610e6	+	1.25409e6i	−0.0980902	+	0.0712667i
$792$	−146079.	−	162237.i	−0.00827514	−	0.00919047i
$793$	−1.63567e6	−	728249.i	−0.0923664	−	0.0411242i
$794$	−1.96947e7	+	8.76865e6i	−1.10866	+	0.493607i
$795$	2.45015e6	−	2.72117e6i	0.137491	−	0.152699i
$796$	−1.22792e6	+	1.16829e7i	−0.0686892	+	0.653534i
$797$	1.70068e7	−	3.61492e6i	0.948370	−	0.201582i	0.292338	−	0.956315i	$-0.405567\pi$
$797$	1.70068e7	−	3.61492e6i	0.948370	−	0.201582i	0.656032	+	0.754733i	$0.272233\pi$
$798$	−2.39538e6	+	7.37222e6i	−0.133158	+	0.409818i
$799$	2.03041e7	+	4.31578e6i	1.12517	+	0.239162i
$800$	1.54400e6	−	2.67429e6i	0.0852950	−	0.147735i
$801$	−2.05114e6	−	3.55267e6i	−0.112957	−	0.195647i
$802$	−280664.	−	863795.i	−0.0154082	−	0.0474214i
$803$	16375.0	+	155798.i	0.000896174	+	0.00852653i
$804$	−1.08020e7	−	7.84810e6i	−0.589337	−	0.428178i
$805$	4.63258e6			0.251961
$806$	−1.03652e6	+	1.73308e6i	−0.0562007	+	0.0939683i
$807$	6.03683e6			0.326306
$808$	6.67417e6	+	4.84907e6i	0.359641	+	0.261294i
$809$	−1.58507e6	−	1.50809e7i	−0.0851484	−	0.810133i	−0.950867	−	0.309601i	$-0.899804\pi$
$809$	−1.58507e6	−	1.50809e7i	−0.0851484	−	0.810133i	0.865718	−	0.500532i	$-0.166862\pi$
$810$	582593.	+	1.79304e6i	0.0311999	+	0.0960234i
$811$	−1.09140e7	−	1.89036e7i	−0.582683	−	1.00924i	−0.995160	−	0.0982689i	$-0.968669\pi$
$811$	−1.09140e7	−	1.89036e7i	−0.582683	−	1.00924i	0.412477	−	0.910968i	$-0.364664\pi$
$812$	−1.91069e6	+	3.30941e6i	−0.101695	+	0.176141i
$813$	−1.77163e7	−	3.76572e6i	−0.940042	−	0.199812i
$814$	143731.	−	442358.i	0.00760308	−	0.0233999i
$815$	1.83585e6	−	390221.i	0.0968150	−	0.0205787i
$816$	396805.	−	3.77534e6i	0.0208618	−	0.198487i
$817$	1.20400e6	−	1.33718e6i	0.0631062	−	0.0700866i
$818$	1.47391e7	−	6.56227e6i	0.770172	−	0.342903i
$819$	−874083.	−	389167.i	−0.0455348	−	0.0202734i
$820$	461057.	+	512055.i	0.0239453	+	0.0265939i
$821$	2.81832e7	−	2.04763e7i	1.45926	−	1.06022i	0.475706	−	0.879604i	$-0.342193\pi$
$821$	2.81832e7	−	2.04763e7i	1.45926	−	1.06022i	0.983555	−	0.180611i	$-0.0578075\pi$
$822$	−1.76147e7	+	1.27978e7i	−0.909276	+	0.660628i
$823$	2.02757e6	+	2.25184e6i	0.104346	+	0.115888i	0.793055	−	0.609149i	$-0.208489\pi$
$823$	2.02757e6	+	2.25184e6i	0.104346	+	0.115888i	−0.688709	+	0.725038i	$0.741822\pi$
$824$	9.52446e6	+	4.24056e6i	0.488678	+	0.217573i
$825$	−2.73171e6	+	1.21624e6i	−0.139733	+	0.0622133i
$826$	5.26588e6	−	5.84835e6i	0.268547	−	0.298252i
$827$	2.07257e6	−	1.97192e7i	0.105377	−	1.00259i	−0.806250	−	0.591576i	$-0.798506\pi$
$827$	2.07257e6	−	1.97192e7i	0.105377	−	1.00259i	0.911627	−	0.411019i	$-0.134827\pi$
$828$	1.57740e6	−	335286.i	0.0799585	−	0.0169957i
$829$	−2.46332e6	+	7.58133e6i	−0.124490	+	0.383141i	−0.993808	−	0.111112i	$-0.964559\pi$
$829$	−2.46332e6	+	7.58133e6i	−0.124490	+	0.383141i	0.869318	+	0.494254i	$0.164559\pi$
$830$	−2.75372e6	−	585321.i	−0.138747	−	0.0294916i
$831$	−1.51693e7	+	2.62740e7i	−0.762015	+	1.31985i
$832$	193236.	+	334694.i	0.00967784	+	0.0167625i
$833$	−9.11072e6	−	2.80399e7i	−0.454925	−	1.40012i
$834$	−1.93660e6	−	1.84256e7i	−0.0964108	−	0.917287i
$835$	−2.09913e6	−	1.52511e6i	−0.104189	−	0.0756981i
$836$	746972.			0.0369648
$837$	1.47964e7	−	1.59324e7i	0.730034	−	0.786081i
$838$	2.40102e7			1.18110
$839$	7.38130e6	+	5.36283e6i	0.362016	+	0.263020i	0.753893	−	0.656998i	$-0.228174\pi$
$839$	7.38130e6	+	5.36283e6i	0.362016	+	0.263020i	−0.391876	+	0.920018i	$0.628174\pi$
$840$	−206229.	−	1.96214e6i	−0.0100845	−	0.0959471i
$841$	−5.94279e6	−	1.82900e7i	−0.289735	−	0.891711i
$842$	8.41509e6	+	1.45754e7i	0.409052	+	0.708499i
$843$	1.02213e7	−	1.77039e7i	0.495380	−	0.858023i
$844$	−1.52648e7	−	3.24464e6i	−0.737625	−	0.156787i
$845$	1.17112e6	−	3.60433e6i	0.0564233	−	0.173653i
$846$	3.67343e6	−	780812.i	0.176460	−	0.0375077i
$847$	−3.44268e6	+	3.27549e7i	−0.164888	+	1.56880i
$848$	−4.29549e6	+	4.77062e6i	−0.205127	+	0.227817i
$849$	739326.	−	329169.i	0.0352020	−	0.0156729i
$850$	1.17029e7	+	5.21044e6i	0.555577	+	0.247359i
$851$	2.29899e6	+	2.55329e6i	0.108821	+	0.120858i
$852$	−5.62638e6	+	4.08780e6i	−0.265540	+	0.192926i
$853$	1.80015e6	−	1.30788e6i	0.0847102	−	0.0615455i	−0.544624	−	0.838680i	$-0.683328\pi$
$853$	1.80015e6	−	1.30788e6i	0.0847102	−	0.0615455i	0.629334	+	0.777135i	$0.283328\pi$
$854$	−1.07225e7	−	1.19085e7i	−0.503097	−	0.558745i
$855$	301689.	+	134320.i	0.0141138	+	0.00628386i
$856$	−6.38289e6	+	2.84185e6i	−0.297737	+	0.132561i
$857$	−5.30539e6	+	5.89224e6i	−0.246755	+	0.274049i	−0.853780	−	0.520633i	$-0.825696\pi$
$857$	−5.30539e6	+	5.89224e6i	−0.246755	+	0.274049i	0.607026	+	0.794682i	$0.292363\pi$
$858$	39118.1	−	372184.i	0.00181409	−	0.0172600i
$859$	−4.02943e6	+	856481.i	−0.186320	+	0.0396036i	−0.300127	−	0.953899i	$-0.597029\pi$
$859$	−4.02943e6	+	856481.i	−0.186320	+	0.0396036i	0.113806	+	0.993503i	$0.463696\pi$
$860$	−141522.	+	435559.i	−0.00652495	+	0.0200817i
$861$	−1.18736e7	−	2.52380e6i	−0.545850	−	0.116024i
$862$	1.21138e7	−	2.09817e7i	0.555280	−	0.961773i
$863$	−2.14215e7	−	3.71032e7i	−0.979092	−	1.69584i	−0.665712	−	0.746208i	$-0.731872\pi$
$863$	−2.14215e7	−	3.71032e7i	−0.979092	−	1.69584i	−0.313379	−	0.949628i	$-0.601461\pi$
$864$	−1.28590e6	−	3.95758e6i	−0.0586032	−	0.180362i
$865$	362374.	+	3.44775e6i	0.0164671	+	0.156674i
$866$	−1.98440e7	−	1.44175e7i	−0.899154	−	0.653273i
$867$	−4.07750e6			−0.184224
$868$	−1.47836e7	+	1.03967e7i	−0.666012	+	0.468378i
$869$	5.55028e6			0.249325
$870$	−534592.	−	388404.i	−0.0239455	−	0.0173975i
$871$	589438.	+	5.60813e6i	0.0263265	+	0.250480i
$872$	2.29767e6	+	7.07152e6i	0.102329	+	0.314935i
$873$	3.82492e6	+	6.62495e6i	0.169858	+	0.294203i
$874$	−2.75888e6	+	4.77852e6i	−0.122167	+	0.211600i
$875$	1.32609e7	+	2.81870e6i	0.585537	+	0.124460i
$876$	−152293.	+	468711.i	−0.00670534	+	0.0206369i
$877$	1.94786e7	−	4.14031e6i	0.855183	−	0.181775i	0.240597	−	0.970625i	$-0.422657\pi$
$877$	1.94786e7	−	4.14031e6i	0.855183	−	0.181775i	0.614585	+	0.788850i	$0.289323\pi$
$878$	−1.97693e6	+	1.88092e7i	−0.0865475	+	0.823444i
$879$	−1.49147e7	+	1.65644e7i	−0.651090	+	0.723109i
$880$	−173684.	+	77328.9i	−0.00756052	+	0.00336616i
$881$	5.35056e6	+	2.38222e6i	0.232252	+	0.103405i	0.519563	−	0.854432i	$-0.326095\pi$
$881$	5.35056e6	+	2.38222e6i	0.232252	+	0.103405i	−0.287311	+	0.957837i	$0.592761\pi$
$882$	−3.56918e6	−	3.96398e6i	−0.154489	−	0.171577i
$883$	9.24708e6	−	6.71840e6i	0.399120	−	0.289977i	−0.370063	−	0.929007i	$-0.620664\pi$
$883$	9.24708e6	−	6.71840e6i	0.399120	−	0.289977i	0.769182	+	0.639029i	$0.220664\pi$
$884$	−1.29705e6	+	942364.i	−0.0558248	+	0.0405591i
$885$	910576.	+	1.01130e6i	0.0390803	+	0.0434031i
$886$	−478358.	−	212978.i	−0.0204724	−	0.00911489i
$887$	3.20089e7	−	1.42513e7i	1.36604	−	0.608198i	0.412909	−	0.910772i	$-0.364513\pi$
$887$	3.20089e7	−	1.42513e7i	1.36604	−	0.608198i	0.953126	+	0.302574i	$0.0978460\pi$
$888$	979109.	−	1.08741e6i	0.0416676	−	0.0462766i
$889$	−2.31577e6	+	2.20331e7i	−0.0982746	+	0.935020i
$890$	−3.49446e6	+	742771.i	−0.147879	+	0.0314326i
$891$	−989035.	+	3.04394e6i	−0.0417366	+	0.128452i
$892$	−479241.	−	101866.i	−0.0201670	−	0.00428663i
$893$	−6.42487e6	+	1.11282e7i	−0.269610	+	0.466978i
$894$	731416.	+	1.26685e6i	0.0306070	+	0.0530128i
$895$	−2.54057e6	−	7.81908e6i	−0.106017	−	0.326286i
$896$	361551.	+	3.43993e6i	0.0150453	+	0.143146i
$897$	2.23645e6	+	1.62488e6i	0.0928066	+	0.0674279i
$898$	−1.45970e6			−0.0604049
$899$	−725423.	+	6.00963e6i	−0.0299359	+	0.247998i
$900$	2.31766e6			0.0953768
$901$	−2.15448e7	−	1.56532e7i	−0.884158	−	0.642378i
$902$	122271.	+	1.16333e6i	0.00500389	+	0.0476088i
$903$	−2.49320e6	−	7.67327e6i	−0.101751	−	0.313156i
$904$	323403.	+	560150.i	0.0131620	+	0.0227973i
$905$	240425.	−	416429.i	0.00975795	−	0.0169013i
$906$	4.00543e6	+	851381.i	0.162117	+	0.0344591i
$907$	4.89616e6	−	1.50688e7i	0.197623	−	0.608221i	−0.802313	−	0.596904i	$-0.796397\pi$
$907$	4.89616e6	−	1.50688e7i	0.197623	−	0.608221i	0.999936	−	0.0113176i	$-0.00360259\pi$
$908$	−2.38142e7	+	5.06187e6i	−0.958565	+	0.203749i
$909$	−647208.	+	6.15778e6i	−0.0259797	+	0.247181i
$910$	−557551.	+	619223.i	−0.0223193	+	0.0247881i
$911$	3.67074e7	−	1.63432e7i	1.46541	−	0.652440i	0.489772	−	0.871850i	$-0.337080\pi$
$911$	3.67074e7	−	1.63432e7i	1.46541	−	0.652440i	0.975633	+	0.219410i	$0.0704132\pi$
$912$	2.14677e6	+	955806.i	0.0854672	+	0.0380524i
$913$	−3.19795e6	−	3.55168e6i	−0.126968	−	0.141012i
$914$	−1.84002e7	+	1.33685e7i	−0.728545	+	0.529319i
$915$	2.24175e6	−	1.62873e6i	0.0885187	−	0.0643126i
$916$	−8.71338e6	−	9.67719e6i	−0.343121	−	0.381075i
$917$	−2.47146e7	−	1.10037e7i	−0.970579	−	0.432130i
$918$	1.57702e7	−	7.02133e6i	0.617632	−	0.274987i
$919$	3.37349e7	−	3.74664e7i	1.31762	−	1.46337i	0.528795	−	0.848750i	$-0.322644\pi$
$919$	3.37349e7	−	3.74664e7i	1.31762	−	1.46337i	0.788826	−	0.614617i	$-0.210689\pi$
$920$	146799.	−	1.39670e6i	0.00571811	−	0.0544042i
$921$	−231152.	+	49133.0i	−0.00897944	+	0.00190864i
$922$	−565699.	+	1.74104e6i	−0.0219158	+	0.0674500i
$923$	2.87299e6	+	610672.i	0.111002	+	0.0235941i
$924$	1.67468e6	−	2.90063e6i	0.0645286	−	0.111767i
$925$	2.46893e6	+	4.27632e6i	0.0948757	+	0.164330i
$926$	3.08184e6	+	9.48493e6i	0.118109	+	0.363502i
$927$	817928.	+	7.78206e6i	0.0312619	+	0.297437i
$928$	937221.	+	680931.i	0.0357250	+	0.0259557i
$929$	−1.25354e7			−0.476539			−0.238270	−	0.971199i	$-0.576580\pi$
$929$	−1.25354e7			−0.476539			−0.238270	+	0.971199i	$0.576580\pi$
$930$	−1.52074e6	−	2.73030e6i	−0.0576562	−	0.103515i
$931$	1.82509e7			0.690097
$932$	−2.03561e6	−	1.47895e6i	−0.0767633	−	0.0557718i
$933$	−3.66331e6	−	3.48541e7i	−0.137775	−	1.31084i
$934$	−9.75886e6	−	3.00347e7i	−0.366043	−	1.12656i
$935$	−394350.	−	683034.i	−0.0147520	−	0.0255513i
$936$	−145030.	+	251199.i	−0.00541088	+	0.00937191i
$937$	1.82954e7	+	3.88880e6i	0.680758	+	0.144700i	0.535296	−	0.844664i	$-0.320200\pi$
$937$	1.82954e7	+	3.88880e6i	0.680758	+	0.144700i	0.145461	+	0.989364i	$0.453533\pi$
$938$	−1.55957e7	+	4.79986e7i	−0.578758	+	1.78124i
$939$	−1.52521e7	+	3.24193e6i	−0.564501	+	0.119988i
$940$	341864.	−	3.25262e6i	0.0126193	−	0.120064i
$941$	−2.10659e7	+	2.33960e7i	−0.775542	+	0.861327i	−0.993406	−	0.114653i	$-0.963425\pi$
$941$	−2.10659e7	+	2.33960e7i	−0.775542	+	0.861327i	0.217864	+	0.975979i	$0.430091\pi$
$942$	−8.15667e6	+	3.63158e6i	−0.299492	+	0.133343i
$943$	−7.89366e6	−	3.51448e6i	−0.289067	−	0.128701i
$944$	−1.59638e6	−	1.77296e6i	−0.0583050	−	0.0647543i
$945$	7.25834e6	−	5.27350e6i	0.264398	−	0.192096i
$946$	−628991.	+	456989.i	−0.0228516	+	0.0166027i
$947$	1.39875e7	+	1.55347e7i	0.506832	+	0.562894i	0.941204	−	0.337840i	$-0.109696\pi$
$947$	1.39875e7	+	1.55347e7i	0.506832	+	0.562894i	−0.434371	+	0.900734i	$0.643029\pi$
$948$	1.59513e7	+	7.10199e6i	0.576469	+	0.256661i
$949$	190146.	−	84658.3i	0.00685364	−	0.00305144i
$950$	−5.30624e6	+	5.89317e6i	−0.190756	+	0.211856i
$951$	−2.63826e6	+	2.51014e7i	−0.0945948	+	0.900009i
$952$	−1.40353e7	+	2.98330e6i	−0.501915	+	0.106685i
$953$	1.81511e6	−	5.58632e6i	0.0647395	−	0.199248i	−0.913455	−	0.406941i	$-0.866596\pi$
$953$	1.81511e6	−	5.58632e6i	0.0647395	−	0.199248i	0.978194	+	0.207693i	$0.0665955\pi$
$954$	−4.71277e6	−	1.00173e6i	−0.167651	−	0.0356352i
$955$	−1.91178e6	+	3.31130e6i	−0.0678312	+	0.117487i
$956$	−8.81921e6	−	1.52753e7i	−0.312094	−	0.540562i
$957$	−346652.	−	1.06688e6i	−0.0122353	−	0.0376563i
$958$	12721.8	+	121040.i	0.000447852	+	0.00426103i
$959$	6.65812e7	+	4.83740e7i	2.33779	+	1.69850i
$960$	−598109.			−0.0209461
$961$	−1.50718e7	+	2.43407e7i	−0.526448	+	0.850207i
$962$	−617985.			−0.0215298
$963$	−4.24243e6	−	3.08231e6i	−0.147418	−	0.107105i
$964$	923783.	+	8.78921e6i	0.0320168	+	0.304619i
$965$	1.16520e6	+	3.58611e6i	0.0402792	+	0.123967i
$966$	1.23706e7	+	2.14265e7i	0.426528	+	0.738769i
$967$	6.65720e6	−	1.15306e7i	0.228942	−	0.396539i	−0.728553	−	0.684990i	$-0.759807\pi$
$967$	6.65720e6	−	1.15306e7i	0.228942	−	0.396539i	0.957495	+	0.288450i	$0.0931401\pi$
$968$	9.76632e6	+	2.07590e6i	0.334998	+	0.0712061i
$969$	−3.01246e6	+	9.27141e6i	−0.103065	+	0.317202i
$970$	6.51640e6	−	1.38510e6i	0.222371	−	0.0472664i
$971$	−1.38507e6	+	1.31781e7i	−0.0471437	+	0.448542i	0.945333	+	0.326107i	$0.105737\pi$
$971$	−1.38507e6	+	1.31781e7i	−0.0471437	+	0.448542i	−0.992477	+	0.122435i	$0.960930\pi$
$972$	3.83468e6	−	4.25885e6i	0.130186	−	0.144586i
$973$	−6.39753e7	+	2.84836e7i	−2.16636	+	0.964525i
$974$	3.52959e7	+	1.57147e7i	1.19214	+	0.530775i
$975$	2.65843e6	+	2.95249e6i	0.0895600	+	0.0994665i
$976$	−3.93013e6	+	2.85541e6i	−0.132063	+	0.0959497i
$977$	1.19455e7	−	8.67895e6i	0.400377	−	0.290891i	−0.369317	−	0.929303i	$-0.620408\pi$
$977$	1.19455e7	−	8.67895e6i	0.400377	−	0.290891i	0.769695	+	0.638412i	$0.220408\pi$
$978$	6.70720e6	+	7.44910e6i	0.224230	+	0.249033i
$979$	−5.54054e6	−	2.46681e6i	−0.184755	−	0.0822580i
$980$	−4.24364e6	+	1.88939e6i	−0.141148	+	0.0628430i
$981$	−3.73411e6	+	4.14715e6i	−0.123884	+	0.137587i
$982$	3.54045e6	−	3.36851e7i	0.117160	−	1.11470i
$983$	−3.24600e7	+	6.89959e6i	−1.07143	+	0.227740i	−0.709673	−	0.704532i	$-0.751157\pi$
$983$	−3.24600e7	+	6.89959e6i	−1.07143	+	0.227740i	−0.361759	+	0.932271i	$0.617824\pi$
$984$	−1.13717e6	+	3.49984e6i	−0.0374400	+	0.115229i
$985$	2.92222e6	+	621138.i	0.0959672	+	0.0203985i
$986$	−2.40291e6	+	4.16196e6i	−0.0787128	+	0.136334i
$987$	2.88086e7	+	4.98979e7i	0.941302	+	1.63038i
$988$	−306688.	−	943888.i	−0.00999549	−	0.0307630i
$989$	−600316.	−	5.71163e6i	−0.0195159	−	0.185682i
$990$	−115440.	−	83872.1i	−0.00374342	−	0.00271975i
$991$	−3.53171e6			−0.114236			−0.0571178	−	0.998367i	$-0.518191\pi$
$991$	−3.53171e6			−0.114236			−0.0571178	+	0.998367i	$0.518191\pi$
$992$	2.66608e6	+	4.78663e6i	0.0860189	+	0.154437i
$993$	−4.33127e7			−1.39393
$994$	2.12670e7	+	1.54513e7i	0.682715	+	0.496021i
$995$	802588.	+	7.63611e6i	0.0257001	+	0.244520i
$996$	−4.64617e6	−	1.42994e7i	−0.148404	−	0.456742i
$997$	−8.55983e6	−	1.48261e7i	−0.272727	−	0.472376i	0.696832	−	0.717234i	$-0.254592\pi$
$997$	−8.55983e6	−	1.48261e7i	−0.272727	−	0.472376i	−0.969559	+	0.244858i	$0.921259\pi$
$998$	−9.19162e6	+	1.59204e7i	−0.292123	+	0.505972i
$999$	6.50861e6	+	1.38345e6i	0.206336	+	0.0438580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.a.41.3	✓	56
31.28	even	15	inner	62.6.g.a.59.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.a.41.3	✓	56	1.1	even	1	trivial
62.6.g.a.59.3	yes	56	31.28	even	15	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(-1.45953 - 13.8865i) q^{3} +(4.94427 + 15.2169i) q^{4} +(5.22891 + 9.05674i) q^{5} +(-27.9260 + 48.3693i) q^{6} +(206.500 + 43.8929i) q^{7} +(19.7771 - 60.8676i) q^{8} +(46.9845 - 9.98686i) q^{9} +(4.37256 - 41.6021i) q^{10} +(47.5180 - 52.7741i) q^{11} +(204.094 - 90.8683i) q^{12} +(-86.1960 - 38.3769i) q^{13} +(-565.049 - 627.551i) q^{14} +(118.135 - 85.8300i) q^{15} +(-207.108 + 150.473i) q^{16} +(-710.614 - 789.217i) q^{17} +(-175.526 - 78.1490i) q^{18} +(600.575 - 267.393i) q^{19} +(-111.962 + 124.347i) q^{20} +(308.127 - 2931.63i) q^{21} +(-277.851 + 59.0590i) q^{22} +(648.408 - 1995.60i) q^{23} +(-874.105 - 185.797i) q^{24} +(1507.82 - 2611.62i) q^{25} +(188.707 + 326.849i) q^{26} +(-1255.76 - 3864.82i) q^{27} +(353.077 + 3359.31i) q^{28} +(915.255 + 664.972i) q^{29} -584.091 q^{30} +(2603.59 + 4674.45i) q^{31} +1024.00 q^{32} +(-802.203 - 582.834i) q^{33} +(444.035 + 4224.71i) q^{34} +(682.243 + 2099.73i) q^{35} +(384.273 + 665.581i) q^{36} +(-818.711 + 1418.05i) q^{37} +(-2572.18 - 546.734i) q^{38} +(-407.116 + 1252.98i) q^{39} +(654.675 - 139.155i) q^{40} +(430.444 - 4095.40i) q^{41} +(-7889.79 + 8762.50i) q^{42} +(2500.40 - 1113.25i) q^{43} +(1038.00 + 462.147i) q^{44} +(336.126 + 373.306i) q^{45} +(-6790.22 + 4933.38i) q^{46} +(-15813.0 + 11488.8i) q^{47} +(2391.83 + 2656.40i) q^{48} +(25361.7 + 11291.7i) q^{49} +(-11019.7 + 4906.28i) q^{50} +(-9922.32 + 11019.8i) q^{51} +(157.802 - 1501.38i) q^{52} +(24528.2 - 5213.63i) q^{53} +(-5023.03 + 15459.3i) q^{54} +(726.429 + 154.407i) q^{55} +(6755.62 - 11701.1i) q^{56} +(-4589.72 - 7949.63i) q^{57} +(-1398.39 - 4303.79i) q^{58} +(974.136 + 9268.28i) q^{59} +(1890.16 + 1373.28i) q^{60} +18976.2 q^{61} +(2564.88 - 21248.2i) q^{62} +10140.6 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-103.141 - 981.324i) q^{65} +(1225.66 + 3772.18i) q^{66} +(-29882.5 - 51758.0i) q^{67} +(8495.97 - 14715.4i) q^{68} +(-28658.3 - 6091.50i) q^{69} +(2728.97 - 8398.91i) q^{70} +(-30449.3 + 6472.19i) q^{71} +(321.340 - 3057.35i) q^{72} +(-1476.08 + 1639.35i) q^{73} +(5983.44 - 2664.00i) q^{74} +(-38467.0 - 17126.6i) q^{75} +(7038.30 + 7816.83i) q^{76} +(12128.9 - 8812.14i) q^{77} +(4263.38 - 3097.53i) q^{78} +(52297.2 + 58081.9i) q^{79} +(-2445.75 - 1088.92i) q^{80} +(-41173.0 + 18331.4i) q^{81} +(-11021.8 + 12241.0i) q^{82} +(7034.74 - 66931.1i) q^{83} +(46133.8 - 9806.04i) q^{84} +(3431.99 - 10562.6i) q^{85} +(-10708.9 - 2276.24i) q^{86} +(7898.30 - 13680.3i) q^{87} +(-2272.46 - 3936.02i) q^{88} +(-26391.1 - 81223.4i) q^{89} +(-210.032 - 1998.32i) q^{90} +(-16115.0 - 11708.2i) q^{91} +33572.7 q^{92} +(61111.8 - 42977.4i) q^{93} +78183.9 q^{94} +(5562.06 + 4041.08i) q^{95} +(-1494.56 - 14219.8i) q^{96} +(49213.5 + 151464. i) q^{97} +(-55523.6 - 96169.6i) q^{98} +(1705.56 - 2954.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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