LMFDB - Embedded newform 72.8.l.b.11.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,8,Mod(11,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$22.4917218349$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.24
Character	$\chi$	$=$	72.11
Dual form			72.8.l.b.59.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.61467 + 9.17857i) q^{2} +(11.3508 + 45.3669i) q^{3} +(-40.4922 - 121.426i) q^{4} +(233.289 + 404.068i) q^{5} +(-491.485 - 195.904i) q^{6} +(-414.838 - 239.507i) q^{7} +(1382.36 + 431.535i) q^{8} +(-1929.32 + 1029.90i) q^{9} +O(q^{10})$	\(q+(-6.61467 + 9.17857i) q^{2} +(11.3508 + 45.3669i) q^{3} +(-40.4922 - 121.426i) q^{4} +(233.289 + 404.068i) q^{5} +(-491.485 - 195.904i) q^{6} +(-414.838 - 239.507i) q^{7} +(1382.36 + 431.535i) q^{8} +(-1929.32 + 1029.90i) q^{9} +(-5251.90 - 531.521i) q^{10} +(1233.61 + 712.228i) q^{11} +(5049.13 - 3215.29i) q^{12} +(-1900.02 + 1096.97i) q^{13} +(4942.34 - 2223.36i) q^{14} +(-15683.3 + 15170.1i) q^{15} +(-13104.8 + 9833.66i) q^{16} +31080.9i q^{17} +(3308.80 - 24520.8i) q^{18} -33328.0 q^{19} +(39618.2 - 44689.1i) q^{20} +(6156.95 - 21538.5i) q^{21} +(-14697.2 + 6611.66i) q^{22} +(-3438.06 - 5954.89i) q^{23} +(-3886.53 + 67611.9i) q^{24} +(-69785.0 + 120871. i) q^{25} +(2499.32 - 24695.5i) q^{26} +(-68622.7 - 75837.2i) q^{27} +(-12284.7 + 60070.4i) q^{28} +(23764.9 - 41162.1i) q^{29} +(-35499.7 - 244296. i) q^{30} +(232212. - 134068. i) q^{31} +(-3575.20 - 185329. i) q^{32} +(-18309.1 + 64049.7i) q^{33} +(-285278. - 205590. i) q^{34} -223497. i q^{35} +(203180. + 192567. i) q^{36} -393519. i q^{37} +(220454. - 305903. i) q^{38} +(-71333.0 - 73746.4i) q^{39} +(148120. + 659242. i) q^{40} +(-4714.14 + 2721.71i) q^{41} +(156966. + 198982. i) q^{42} +(68730.4 - 119045. i) q^{43} +(36531.5 - 178633. i) q^{44} +(-866239. - 539312. i) q^{45} +(77399.0 + 7833.20i) q^{46} +(-351478. + 608777. i) q^{47} +(-594872. - 482903. i) q^{48} +(-297045. - 514497. i) q^{49} +(-647819. - 1.44005e6i) q^{50} +(-1.41004e6 + 352792. i) q^{51} +(210138. + 186293. i) q^{52} -1.23451e6 q^{53} +(1.14999e6 - 128221. i) q^{54} +664619. i q^{55} +(-470101. - 510102. i) q^{56} +(-378299. - 1.51199e6i) q^{57} +(220612. + 490402. i) q^{58} +(824388. - 475961. i) q^{59} +(2.47710e6 + 1.29010e6i) q^{60} +(2.31942e6 + 1.33912e6i) q^{61} +(-305457. + 3.01819e6i) q^{62} +(1.04702e6 + 34843.2i) q^{63} +(1.72471e6 + 1.19308e6i) q^{64} +(-886505. - 511824. i) q^{65} +(-466776. - 591719. i) q^{66} +(1.49709e6 + 2.59304e6i) q^{67} +(3.77404e6 - 1.25853e6i) q^{68} +(231131. - 223567. i) q^{69} +(2.05138e6 + 1.47836e6i) q^{70} +1.61523e6 q^{71} +(-3.11146e6 + 591128. i) q^{72} -6.62481e6 q^{73} +(3.61195e6 + 2.60300e6i) q^{74} +(-6.27567e6 - 1.79395e6i) q^{75} +(1.34953e6 + 4.04690e6i) q^{76} +(-341166. - 590918. i) q^{77} +(1.14873e6 - 166927. i) q^{78} +(3.97194e6 + 2.29320e6i) q^{79} +(-7.03066e6 - 3.00113e6i) q^{80} +(2.66158e6 - 3.97401e6i) q^{81} +(6201.09 - 61272.3i) q^{82} +(-3.12548e6 - 1.80450e6i) q^{83} +(-2.86465e6 + 124525. i) q^{84} +(-1.25588e7 + 7.25082e6i) q^{85} +(638030. + 1.41829e6i) q^{86} +(2.13715e6 + 610921. i) q^{87} +(1.39795e6 + 1.51691e6i) q^{88} +1.06718e7i q^{89} +(1.06800e7 - 4.38346e6i) q^{90} +1.05093e6 q^{91} +(-583867. + 658598. i) q^{92} +(8.71803e6 + 9.01298e6i) q^{93} +(-3.26279e6 - 7.25293e6i) q^{94} +(-7.77506e6 - 1.34668e7i) q^{95} +(8.36724e6 - 2.26583e6i) q^{96} +(-14967.7 + 25924.8i) q^{97} +(6.68720e6 + 676781. i) q^{98} +(-3.11356e6 - 103614. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) $ 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−6.61467	+	9.17857i	−0.584660	+	0.811278i
$2$	−6.61467	+	9.17857i	−0.584660	+	0.811278i
$3$	11.3508	+	45.3669i	0.242718	+	0.970097i
$3$	11.3508	+	45.3669i	0.242718	+	0.970097i
$4$	−40.4922	−	121.426i	−0.316346	−	0.948644i
$5$	233.289	+	404.068i	0.834640	+	1.44564i	0.894323	+	0.447421i	$0.147658\pi$
$5$	233.289	+	404.068i	0.834640	+	1.44564i	−0.0596832	+	0.998217i	$0.519009\pi$
$6$	−491.485	−	195.904i	−0.928926	−	0.370265i
$7$	−414.838	−	239.507i	−0.457125	−	0.263921i	0.253710	−	0.967280i	$-0.418349\pi$
$7$	−414.838	−	239.507i	−0.457125	−	0.263921i	−0.710835	+	0.703359i	$0.751683\pi$
$8$	1382.36	+	431.535i	0.954569	+	0.297990i
$9$	−1929.32	+	1029.90i	−0.882176	+	0.470919i
$10$	−5251.90	−	531.521i	−1.66080	−	0.168082i
$11$	1233.61	+	712.228i	0.279451	+	0.161341i	0.633175	−	0.774009i	$-0.281751\pi$
$11$	1233.61	+	712.228i	0.279451	+	0.161341i	−0.353724	+	0.935350i	$0.615085\pi$
$12$	5049.13	−	3215.29i	0.843494	−	0.537139i
$13$	−1900.02	+	1096.97i	−0.239859	+	0.138482i	−0.615112	−	0.788440i	$-0.710889\pi$
$13$	−1900.02	+	1096.97i	−0.239859	+	0.138482i	0.375253	+	0.926922i	$0.377556\pi$
$14$	4942.34	−	2223.36i	0.481376	−	0.216551i
$15$	−15683.3	+	15170.1i	−1.19983	+	1.16056i
$16$	−13104.8	+	9833.66i	−0.799851	+	0.600199i
$17$			31080.9i			1.53434i	0.641443	+	0.767171i	$0.278336\pi$
$17$			31080.9i			1.53434i	−0.641443	+	0.767171i	$0.721664\pi$
$18$	3308.80	−	24520.8i	0.133726	−	0.991018i
$19$	−33328.0			−1.11474			−0.557368	−	0.830266i	$-0.688189\pi$
$19$	−33328.0			−1.11474			−0.557368	+	0.830266i	$0.688189\pi$
$20$	39618.2	−	44689.1i	1.10736	−	1.24910i
$21$	6156.95	−	21538.5i	0.145077	−	0.507514i
$22$	−14697.2	+	6611.66i	−0.294276	+	0.132383i
$23$	−3438.06	−	5954.89i	−0.0589204	−	0.102053i	0.835061	−	0.550158i	$-0.185432\pi$
$23$	−3438.06	−	5954.89i	−0.0589204	−	0.102053i	−0.893981	+	0.448105i	$0.852099\pi$
$24$	−3886.53	+	67611.9i	−0.0573882	+	0.998352i
$25$	−69785.0	+	120871.i	−0.893248	+	1.54715i
$26$	2499.32	−	24695.5i	0.0278879	−	0.275557i
$27$	−68622.7	−	75837.2i	−0.670957	−	0.741496i
$28$	−12284.7	+	60070.4i	−0.105758	+	0.517139i
$29$	23764.9	−	41162.1i	0.180944	−	0.313404i	−0.761258	−	0.648449i	$-0.775418\pi$
$29$	23764.9	−	41162.1i	0.180944	−	0.313404i	0.942202	+	0.335045i	$0.108751\pi$
$30$	−35499.7	−	244296.i	−0.240049	−	1.65193i
$31$	232212.	−	134068.i	1.39997	−	0.808273i	0.405581	−	0.914059i	$-0.367069\pi$
$31$	232212.	−	134068.i	1.39997	−	0.808273i	0.994389	+	0.105786i	$0.0337358\pi$
$32$	−3575.20	−	185329.i	−0.0192875	−	0.999814i
$33$	−18309.1	+	64049.7i	−0.0886887	+	0.310255i
$34$	−285278.	−	205590.i	−1.24478	−	0.897068i
$35$		−	223497.i		−	0.881117i
$36$	203180.	+	192567.i	0.725807	+	0.687898i
$37$		−	393519.i		−	1.27720i	−0.769537	−	0.638602i	$-0.779513\pi$
$37$		−	393519.i		−	1.27720i	0.769537	−	0.638602i	$-0.220487\pi$
$38$	220454.	−	305903.i	0.651741	−	0.904361i
$39$	−71333.0	−	73746.4i	−0.192559	−	0.199074i
$40$	148120.	+	659242.i	0.365936	+	1.62868i
$41$	−4714.14	+	2721.71i	−0.0106822	+	0.00616735i	−0.505332	−	0.862925i	$-0.668630\pi$
$41$	−4714.14	+	2721.71i	−0.0106822	+	0.00616735i	0.494649	+	0.869093i	$0.335296\pi$
$42$	156966.	+	198982.i	0.326914	+	0.414421i
$43$	68730.4	−	119045.i	0.131829	−	0.228334i	−0.792553	−	0.609803i	$-0.791249\pi$
$43$	68730.4	−	119045.i	0.131829	−	0.228334i	0.924381	+	0.381469i	$0.124582\pi$
$44$	36531.5	−	178633.i	0.0646521	−	0.316139i
$45$	−866239.	−	539312.i	−1.41708	−	0.882260i
$46$	77399.0	+	7833.20i	0.117242	+	0.0118655i
$47$	−351478.	+	608777.i	−0.493805	+	0.855295i	−0.999975	−	0.00713876i	$-0.997728\pi$
$47$	−351478.	+	608777.i	−0.493805	+	0.855295i	0.506170	+	0.862434i	$0.331061\pi$
$48$	−594872.	−	482903.i	−0.776389	−	0.630254i
$49$	−297045.	−	514497.i	−0.360691	−	0.624736i
$50$	−647819.	−	1.44005e6i	−0.732924	−	1.62923i
$51$	−1.41004e6	+	352792.i	−1.48846	+	0.372412i
$52$	210138.	+	186293.i	0.207249	+	0.183732i
$53$	−1.23451e6			−1.13901			−0.569506	−	0.821987i	$-0.692865\pi$
$53$	−1.23451e6			−1.13901			−0.569506	+	0.821987i	$0.692865\pi$
$54$	1.14999e6	−	128221.i	0.993842	−	0.110810i
$55$			664619.i			0.538646i
$56$	−470101.	−	510102.i	−0.357711	−	0.388150i
$57$	−378299.	−	1.51199e6i	−0.270566	−	1.08140i
$58$	220612.	+	490402.i	0.148467	+	0.330030i
$59$	824388.	−	475961.i	0.522576	−	0.301710i	−0.215412	−	0.976523i	$-0.569109\pi$
$59$	824388.	−	475961.i	0.522576	−	0.301710i	0.737988	+	0.674814i	$0.235776\pi$
$60$	2.47710e6	+	1.29010e6i	1.48052	+	0.771070i
$61$	2.31942e6	+	1.33912e6i	1.30835	+	0.755378i	0.981821	−	0.189809i	$-0.0607868\pi$
$61$	2.31942e6	+	1.33912e6i	1.30835	+	0.755378i	0.326531	+	0.945186i	$0.394120\pi$
$62$	−305457.	+	3.01819e6i	−0.162772	+	1.60833i
$63$	1.04702e6	+	34843.2i	0.527550	+	0.0175560i
$64$	1.72471e6	+	1.19308e6i	0.822404	+	0.568904i
$65$	−886505.	−	511824.i	−0.400391	−	0.231166i
$66$	−466776.	−	591719.i	−0.199850	−	0.253345i
$67$	1.49709e6	+	2.59304e6i	0.608117	+	1.05329i	0.991551	+	0.129721i	$0.0414080\pi$
$67$	1.49709e6	+	2.59304e6i	0.608117	+	1.05329i	−0.383434	+	0.923568i	$0.625259\pi$
$68$	3.77404e6	−	1.25853e6i	1.45554	−	0.485382i
$69$	231131.	−	223567.i	0.0847004	−	0.0819286i
$70$	2.05138e6	+	1.47836e6i	0.714831	+	0.515154i
$71$	1.61523e6			0.535588			0.267794	−	0.963476i	$-0.413705\pi$
$71$	1.61523e6			0.535588			0.267794	+	0.963476i	$0.413705\pi$
$72$	−3.11146e6	+	591128.i	−0.982427	+	0.186646i
$73$	−6.62481e6			−1.99317			−0.996583	−	0.0826023i	$-0.973677\pi$
$73$	−6.62481e6			−1.99317			−0.996583	+	0.0826023i	$0.973677\pi$
$74$	3.61195e6	+	2.60300e6i	1.03617	+	0.746730i
$75$	−6.27567e6	−	1.79395e6i	−1.71769	−	0.491016i
$76$	1.34953e6	+	4.04690e6i	0.352642	+	1.05749i
$77$	−341166.	−	590918.i	−0.0851626	−	0.147506i
$78$	1.14873e6	−	166927.i	0.274086	−	0.0398287i
$79$	3.97194e6	+	2.29320e6i	0.906375	+	0.523296i	0.879263	−	0.476336i	$-0.158036\pi$
$79$	3.97194e6	+	2.29320e6i	0.906375	+	0.523296i	0.0271121	+	0.999632i	$0.491369\pi$
$80$	−7.03066e6	−	3.00113e6i	−1.53526	−	0.655346i
$81$	2.66158e6	−	3.97401e6i	0.556470	−	0.830868i
$82$	6201.09	−	61272.3i	0.00124199	−	0.0122720i
$83$	−3.12548e6	−	1.80450e6i	−0.599989	−	0.346404i	0.169048	−	0.985608i	$-0.445931\pi$
$83$	−3.12548e6	−	1.80450e6i	−0.599989	−	0.346404i	−0.769037	+	0.639204i	$0.779264\pi$
$84$	−2.86465e6	+	124525.i	−0.527344	+	0.0229235i
$85$	−1.25588e7	+	7.25082e6i	−2.21810	+	1.28062i
$86$	638030.	+	1.41829e6i	0.108167	+	0.240447i
$87$	2.13715e6	+	610921.i	0.347950	+	0.0994643i
$88$	1.39795e6	+	1.51691e6i	0.218677	+	0.237284i
$89$			1.06718e7i			1.60462i	0.596910	+	0.802308i	$0.296395\pi$
$89$			1.06718e7i			1.60462i	−0.596910	+	0.802308i	$0.703605\pi$
$90$	1.06800e7	−	4.38346e6i	1.54427	−	0.633823i
$91$	1.05093e6			0.146194
$92$	−583867.	+	658598.i	−0.0781729	+	0.0881786i
$93$	8.71803e6	+	9.01298e6i	1.12390	+	1.16192i
$94$	−3.26279e6	−	7.25293e6i	−0.405175	−	0.900670i
$95$	−7.77506e6	−	1.34668e7i	−0.930403	−	1.61150i
$96$	8.36724e6	−	2.26583e6i	0.965235	−	0.261383i
$97$	−14967.7	+	25924.8i	−0.00166515	+	0.00288412i	−0.866857	−	0.498557i	$-0.833863\pi$
$97$	−14967.7	+	25924.8i	−0.00166515	+	0.00288412i	0.865192	+	0.501441i	$0.167197\pi$
$98$	6.68720e6	+	676781.i	0.717716	+	0.0726368i
$99$	−3.11356e6	−	103614.i	−0.322503	−	0.0107324i
$100$	1.75027e7	+	3.57940e6i	1.75027	+	0.357940i
$101$	−984584.	+	1.70535e6i	−0.0950885	+	0.164698i	−0.909646	−	0.415385i	$-0.863647\pi$
$101$	−984584.	+	1.70535e6i	−0.0950885	+	0.164698i	0.814557	+	0.580083i	$0.196980\pi$
$102$	6.08885e6	−	1.52758e7i	0.568113	−	1.42529i
$103$	−8.91455e6	+	5.14682e6i	−0.803839	+	0.464097i	−0.844812	−	0.535064i	$-0.820288\pi$
$103$	−8.91455e6	+	5.14682e6i	−0.803839	+	0.464097i	0.0409729	+	0.999160i	$0.486954\pi$
$104$	−3.09990e6	+	696494.i	−0.270228	+	0.0607156i
$105$	1.01394e7	−	2.53687e6i	0.854769	−	0.213863i
$106$	8.16586e6	−	1.13310e7i	0.665935	−	0.924056i
$107$		−	1.58340e7i		−	1.24953i	−0.780812	−	0.624766i	$-0.785194\pi$
$107$		−	1.58340e7i		−	1.24953i	0.780812	−	0.624766i	$-0.214806\pi$
$108$	−6.42995e6	+	1.14034e7i	−0.491161	+	0.871069i
$109$			1.34071e7i			0.991616i	0.868432	+	0.495808i	$0.165128\pi$
$109$			1.34071e7i			0.991616i	−0.868432	+	0.495808i	$0.834872\pi$
$110$	−6.10026e6	−	4.39624e6i	−0.436992	−	0.314925i
$111$	1.78528e7	−	4.46675e6i	1.23901	−	0.310000i
$112$	7.79157e6	−	940694.i	0.524037	−	0.0632681i
$113$	−1.42714e7	+	8.23957e6i	−0.930445	+	0.537193i	−0.886952	−	0.461861i	$-0.847182\pi$
$113$	−1.42714e7	+	8.23957e6i	−0.930445	+	0.537193i	−0.0434926	+	0.999054i	$0.513849\pi$
$114$	1.63802e7	+	6.52907e6i	1.03551	+	0.412748i
$115$	1.60412e6	−	2.77842e6i	0.0983547	−	0.170355i
$116$	−5.96046e6	−	1.21895e6i	−0.354549	−	0.0725073i
$117$	2.53596e6	−	4.07324e6i	0.146384	−	0.235120i
$118$	−1.08442e6	+	1.07150e7i	−0.0607590	+	0.600353i
$119$	7.44407e6	−	1.28935e7i	0.404945	−	0.701386i
$120$	−2.82265e7	+	1.42027e7i	−1.49115	+	0.750302i
$121$	−8.72905e6	−	1.51192e7i	−0.447938	−	0.775852i
$122$	−2.76334e7	+	1.24311e7i	−1.37776	+	0.619799i
$123$	−176985.	−	182973.i	−0.00857568	−	0.00886581i
$124$	−2.56821e7	−	2.27680e7i	−1.20964	−	1.07238i
$125$	−2.86689e7			−1.31288
$126$	−7.24552e6	+	9.37969e6i	−0.322680	+	0.417726i
$127$		−	3.26737e7i		−	1.41542i	−0.706503	−	0.707710i	$-0.749728\pi$
$127$		−	3.26737e7i		−	1.41542i	0.706503	−	0.707710i	$-0.250272\pi$
$128$	−2.23591e7	+	7.93852e6i	−0.942366	+	0.334584i
$129$	6.18083e6	+	1.76684e6i	0.253503	+	0.0724658i
$130$	1.05618e7	−	4.75130e6i	0.421633	−	0.189675i
$131$	−2.24482e7	+	1.29605e7i	−0.872434	+	0.503700i	−0.868156	−	0.496291i	$-0.834695\pi$
$131$	−2.24482e7	+	1.29605e7i	−0.872434	+	0.503700i	−0.00427770	+	0.999991i	$0.501362\pi$
$132$	8.51870e6	−	370305.i	0.322377	−	0.0140136i
$133$	1.38257e7	+	7.98228e6i	0.509573	+	0.294202i
$134$	−3.37032e7	−	3.41095e6i	−1.21005	−	0.122464i
$135$	1.46345e7	−	4.54202e7i	0.511928	−	1.58884i
$136$	−1.34125e7	+	4.29651e7i	−0.457218	+	1.46463i
$137$	4.17766e7	+	2.41197e7i	1.38807	+	0.801402i	0.993098	−	0.117291i	$-0.0374210\pi$
$137$	4.17766e7	+	2.41197e7i	1.38807	+	0.801402i	0.394972	+	0.918693i	$0.370754\pi$
$138$	523171.	+	3.60027e6i	0.0169460	+	0.116616i
$139$	1.06990e7	+	1.85312e7i	0.337903	+	0.585265i	0.984038	−	0.177958i	$-0.0569491\pi$
$139$	1.06990e7	+	1.85312e7i	0.337903	+	0.585265i	−0.646135	+	0.763223i	$0.723616\pi$
$140$	−2.71384e7	+	9.04989e6i	−0.835866	+	0.278737i
$141$	−3.16079e7	−	9.03537e6i	−0.949574	−	0.271443i
$142$	−1.06842e7	+	1.48255e7i	−0.313137	+	0.434511i
$143$	−3.12518e6			−0.0893715
$144$	1.51556e7	−	3.24689e7i	0.422964	−	0.906146i
$145$	2.21764e7			0.604091
$146$	4.38209e7	−	6.08063e7i	1.16532	−	1.61701i
$147$	1.99694e7	−	1.93160e7i	0.518508	−	0.501540i
$148$	−4.77837e7	+	1.59345e7i	−1.21161	+	0.404038i
$149$	−5.24015e6	−	9.07621e6i	−0.129775	−	0.224777i	0.793814	−	0.608160i	$-0.208092\pi$
$149$	−5.24015e6	−	9.07621e6i	−0.129775	−	0.224777i	−0.923589	+	0.383383i	$0.874759\pi$
$150$	5.79774e7	−	4.57353e7i	1.40262	−	1.10645i
$151$	7.06415e7	+	4.07849e7i	1.66971	+	0.964006i	0.967794	+	0.251745i	$0.0810043\pi$
$151$	7.06415e7	+	4.07849e7i	1.66971	+	0.964006i	0.701914	+	0.712262i	$0.252329\pi$
$152$	−4.60714e7	−	1.43822e7i	−1.06409	−	0.332180i
$153$	−3.20102e7	−	5.99649e7i	−0.722551	−	1.35356i
$154$	7.68048e6	+	777307.i	0.169459	+	0.0171502i
$155$	1.08345e8	+	6.25530e7i	2.33694	+	1.34923i
$156$	−6.06633e6	+	1.16479e7i	−0.127935	+	0.245646i
$157$	−5.97385e7	+	3.44900e7i	−1.23199	+	0.711287i	−0.967443	−	0.253087i	$-0.918554\pi$
$157$	−5.97385e7	+	3.44900e7i	−1.23199	+	0.711287i	−0.264542	+	0.964374i	$0.585221\pi$
$158$	−4.73214e7	+	2.12880e7i	−0.954460	+	0.429373i
$159$	−1.40126e7	−	5.60059e7i	−0.276458	−	1.10495i
$160$	7.40517e7	−	4.46799e7i	1.42927	−	0.862367i
$161$			3.29375e6i			0.0622014i
$162$	1.88703e7	+	5.07163e7i	0.348719	+	0.937227i
$163$	−7.61305e7			−1.37690			−0.688450	−	0.725284i	$-0.741709\pi$
$163$	−7.61305e7			−1.37690			−0.688450	+	0.725284i	$0.741709\pi$
$164$	521374.	+	462213.i	0.00922987	+	0.00818256i
$165$	−3.01518e7	+	7.54395e6i	−0.522539	+	0.130739i
$166$	3.72367e7	−	1.67513e7i	0.631820	−	0.284230i
$167$	3.62935e7	+	6.28621e7i	0.603005	+	1.04444i	0.992363	+	0.123349i	$0.0393634\pi$
$167$	3.62935e7	+	6.28621e7i	0.603005	+	1.04444i	−0.389359	+	0.921086i	$0.627303\pi$
$168$	1.78058e7	−	2.71171e7i	0.289720	−	0.441226i
$169$	−2.89676e7	+	5.01733e7i	−0.461645	+	0.799593i
$170$	1.65201e7	−	1.63234e8i	0.257895	−	2.54823i
$171$	6.43004e7	−	3.43245e7i	0.983393	−	0.524950i
$172$	−1.72382e7	−	3.52531e6i	−0.258311	−	0.0528260i
$173$	−1.53623e7	+	2.66084e7i	−0.225578	+	0.390712i	−0.956493	−	0.291757i	$-0.905760\pi$
$173$	−1.53623e7	+	2.66084e7i	−0.225578	+	0.390712i	0.730915	+	0.682469i	$0.239094\pi$
$174$	−1.97439e7	+	1.55749e7i	−0.284126	+	0.224132i
$175$	5.78989e7	−	3.34279e7i	0.816652	−	0.471494i
$176$	−2.31700e7	+	2.79737e6i	−0.320355	+	0.0386772i
$177$	3.09503e7	+	3.19975e7i	0.419526	+	0.433720i
$178$	−9.79515e7	−	7.05902e7i	−1.30179	−	0.938155i
$179$			2.74657e7i			0.357936i	0.983855	+	0.178968i	$0.0572759\pi$
$179$			2.74657e7i			0.357936i	−0.983855	+	0.178968i	$0.942724\pi$
$180$	−3.04108e7	+	1.27022e8i	−0.388664	+	1.62340i
$181$		−	2.32233e7i		−	0.291105i	−0.989351	−	0.145552i	$-0.953504\pi$
$181$		−	2.32233e7i		−	0.291105i	0.989351	−	0.145552i	$-0.0464959\pi$
$182$	−6.95156e6	+	9.64604e6i	−0.0854737	+	0.118604i
$183$	−3.44244e7	+	1.20425e8i	−0.415229	+	1.45257i
$184$	−2.18290e6	−	9.71547e6i	−0.0258328	−	0.114974i
$185$	1.59009e8	−	9.18037e7i	1.84638	−	1.06601i
$186$	−1.40393e8	+	2.04011e7i	−1.59974	+	0.232466i
$187$	−2.21367e7	+	3.83418e7i	−0.247552	+	0.428773i
$188$	8.81538e7	+	1.80279e7i	0.967584	+	0.197876i
$189$	1.03038e7	+	4.78957e7i	0.111015	+	0.516036i
$190$	1.75035e8	+	1.77145e7i	1.85135	+	0.187366i
$191$	6.04104e7	−	1.04634e8i	0.627328	−	1.08656i	−0.360757	−	0.932660i	$-0.617482\pi$
$191$	6.04104e7	−	1.04634e8i	0.627328	−	1.08656i	0.988086	−	0.153905i	$-0.0491850\pi$
$192$	−3.45495e7	+	9.17870e7i	−0.352280	+	0.935895i
$193$	8.94073e7	+	1.54858e8i	0.895205	+	1.55054i	0.833551	+	0.552443i	$0.186304\pi$
$193$	8.94073e7	+	1.54858e8i	0.895205	+	1.55054i	0.0616543	+	0.998098i	$0.480362\pi$
$194$	−138946.	−	308866.i	−0.00136628	−	0.00303713i
$195$	1.31574e7	−	4.60276e7i	0.127071	−	0.444526i
$196$	−5.04455e7	+	5.69022e7i	−0.478549	+	0.539800i
$197$	1.20361e7			0.112164			0.0560819	−	0.998426i	$-0.482139\pi$
$197$	1.20361e7			0.112164			0.0560819	+	0.998426i	$0.482139\pi$
$198$	2.15462e7	−	2.78927e7i	0.197262	−	0.255365i
$199$		−	1.12811e7i		−	0.101476i	−0.998712	−	0.0507381i	$-0.983843\pi$
$199$		−	1.12811e7i		−	0.101476i	0.998712	−	0.0507381i	$-0.0161574\pi$
$200$	−1.48628e8	+	1.36973e8i	−1.31370	+	1.21068i
$201$	−1.00645e8	+	9.73516e7i	−0.874192	+	0.845584i
$202$	−9.13997e6	−	2.03174e7i	−0.0780216	−	0.173436i
$203$	−1.97172e7	+	1.13837e7i	−0.165428	+	0.0955098i
$204$	9.99341e7	+	1.56931e8i	0.824154	+	1.29421i
$205$	−2.19951e6	−	1.26989e6i	−0.0178315	−	0.0102950i
$206$	1.17264e7	−	1.15867e8i	0.0934608	−	0.923476i
$207$	1.27661e7	+	7.94803e6i	0.100037	+	0.0622821i
$208$	1.41120e7	−	3.30597e7i	0.108734	−	0.254728i
$209$	−4.11139e7	−	2.37371e7i	−0.311513	−	0.179852i
$210$	−4.37838e7	+	1.09845e8i	−0.326247	+	0.818492i
$211$	−6.44901e7	−	1.11700e8i	−0.472612	−	0.818587i	0.526897	−	0.849929i	$-0.323355\pi$
$211$	−6.44901e7	−	1.11700e8i	−0.472612	−	0.818587i	−0.999509	+	0.0313418i	$0.990022\pi$
$212$	4.99880e7	+	1.49902e8i	0.360321	+	1.08052i
$213$	1.83342e7	+	7.32782e7i	0.129997	+	0.519573i
$214$	1.45334e8	+	1.04737e8i	1.01372	+	0.730552i
$215$	6.41362e7			0.440117
$216$	−6.21352e7	−	1.34448e8i	−0.419517	−	0.907748i
$217$	−1.28440e8			−0.853282
$218$	−1.23058e8	−	8.86838e7i	−0.804476	−	0.579758i
$219$	−7.51968e7	−	3.00547e8i	−0.483776	−	1.93356i
$220$	8.07024e7	−	2.69119e7i	0.510984	−	0.170398i
$221$	−3.40949e7	−	5.90541e7i	−0.212479	−	0.368025i
$222$	−7.70919e7	+	1.93409e8i	−0.472904	+	1.18643i
$223$	−7.67410e7	−	4.43065e7i	−0.463405	−	0.267547i	0.250070	−	0.968228i	$-0.419546\pi$
$223$	−7.67410e7	−	4.43065e7i	−0.463405	−	0.267547i	−0.713475	+	0.700681i	$0.752880\pi$
$224$	−4.29045e7	+	7.77378e7i	−0.255055	+	0.462130i
$225$	1.01523e7	−	3.05071e8i	0.0594189	−	1.78551i
$226$	1.87729e7	−	1.85493e8i	0.108181	−	1.06892i
$227$	2.39949e8	+	1.38534e8i	1.36153	+	0.786081i	0.989828	−	0.142270i	$-0.0454401\pi$
$227$	2.39949e8	+	1.38534e8i	1.36153	+	0.786081i	0.371705	+	0.928351i	$0.378773\pi$
$228$	−1.68277e8	+	1.07159e8i	−0.940272	+	0.598767i
$229$	−9.59667e7	+	5.54064e7i	−0.528076	+	0.304885i	−0.740233	−	0.672351i	$-0.765285\pi$
$229$	−9.59667e7	+	5.54064e7i	−0.528076	+	0.304885i	0.212157	+	0.977236i	$0.431951\pi$
$230$	1.48912e7	+	3.31019e7i	0.0807015	+	0.179393i
$231$	2.29356e7	−	2.21851e7i	0.122425	−	0.118418i
$232$	5.06147e7	−	4.66455e7i	0.266114	−	0.245246i
$233$			1.38383e8i			0.716701i	0.933587	+	0.358350i	$0.116661\pi$
$233$			1.38383e8i			0.716701i	−0.933587	+	0.358350i	$0.883339\pi$
$234$	2.06120e7	+	5.02197e7i	0.105163	+	0.256223i
$235$	−3.27984e8			−1.64860
$236$	−9.11756e7	−	8.08298e7i	−0.451530	−	0.400295i
$237$	−5.89509e7	+	2.06224e8i	−0.287655	+	1.00628i
$238$	6.91039e7	+	1.53612e8i	0.332264	+	0.738595i
$239$	1.96610e7	+	3.40539e7i	0.0931566	+	0.161352i	0.908838	−	0.417150i	$-0.136971\pi$
$239$	1.96610e7	+	3.40539e7i	0.0931566	+	0.161352i	−0.815681	+	0.578502i	$0.803638\pi$
$240$	5.63488e7	−	3.53025e8i	0.263115	−	1.64841i
$241$	−1.29531e8	+	2.24355e8i	−0.596095	+	1.03247i	0.397296	+	0.917690i	$0.369949\pi$
$241$	−1.29531e8	+	2.24355e8i	−0.596095	+	1.03247i	−0.993391	+	0.114777i	$0.963385\pi$
$242$	1.96512e8	+	1.98881e7i	0.891323	+	0.0902068i
$243$	2.10500e8	+	7.56395e7i	0.941087	+	0.338164i
$244$	6.86858e7	−	3.35863e8i	0.302693	−	1.48012i
$245$	1.38595e8	−	2.40053e8i	0.602095	−	1.04286i
$246$	2.85012e6	−	414164.i	0.0122065	−	0.00177378i
$247$	6.33237e7	−	3.65600e7i	0.267379	−	0.154371i
$248$	3.78856e8	−	8.51226e7i	1.57723	−	0.354376i
$249$	4.63879e7	−	1.62276e8i	0.190417	−	0.666126i
$250$	1.89635e8	−	2.63139e8i	0.767589	−	1.06511i
$251$		−	4.03440e6i		−	0.0161035i	−0.999968	−	0.00805176i	$-0.997437\pi$
$251$		−	4.03440e6i		−	0.0161035i	0.999968	−	0.00805176i	$-0.00256298\pi$
$252$	−3.81654e7	−	1.28547e8i	−0.150234	−	0.506011i
$253$		−	9.79472e6i		−	0.0380251i
$254$	2.99898e8	+	2.16126e8i	1.14830	+	0.827539i
$255$	−4.71500e8	−	4.87452e8i	−1.78070	−	1.84095i
$256$	7.50339e7	−	2.57735e8i	0.279523	−	0.960139i
$257$	1.55556e8	−	8.98100e7i	0.571636	−	0.330034i	−0.186167	−	0.982518i	$-0.559606\pi$
$257$	1.55556e8	−	8.98100e7i	0.571636	−	0.330034i	0.757802	+	0.652484i	$0.226273\pi$
$258$	−5.71012e7	+	4.50441e7i	−0.207003	+	0.163294i
$259$	−9.42505e7	+	1.63247e8i	−0.337081	+	0.583842i
$260$	−2.62524e7	+	1.28370e8i	−0.0926322	+	0.452957i
$261$	−3.45731e6	+	1.03890e8i	−0.0120364	+	0.361687i
$262$	2.95289e7	−	2.91772e8i	0.101436	−	1.00228i
$263$	−2.01149e8	+	3.48401e8i	−0.681826	+	1.18096i	0.292597	+	0.956236i	$0.405481\pi$
$263$	−2.01149e8	+	3.48401e8i	−0.681826	+	1.18096i	−0.974423	+	0.224721i	$0.927853\pi$
$264$	−5.29495e7	+	8.06389e7i	−0.177112	+	0.269731i
$265$	−2.87997e8	−	4.98826e8i	−0.950665	−	1.64660i
$266$	−1.64718e8	+	7.41001e7i	−0.536607	+	0.241398i
$267$	−4.84145e8	+	1.21133e8i	−1.55663	+	0.389469i
$268$	2.54243e8	−	2.86785e8i	0.806821	−	0.910090i
$269$	3.05475e8			0.956847			0.478424	−	0.878129i	$-0.341208\pi$
$269$	3.05475e8			0.956847			0.478424	+	0.878129i	$0.341208\pi$
$270$	3.20091e8	+	4.34763e8i	0.989691	+	1.34425i
$271$		−	3.65176e8i		−	1.11458i	−0.830319	−	0.557289i	$-0.811842\pi$
$271$		−	3.65176e8i		−	1.11458i	0.830319	−	0.557289i	$-0.188158\pi$
$272$	−3.05639e8	−	4.07307e8i	−0.920910	−	1.22724i
$273$	1.19289e7	+	4.76775e7i	0.0354838	+	0.141822i
$274$	−4.97723e8	+	2.23905e8i	−1.46171	+	0.657563i
$275$	−1.72176e8	+	9.94056e7i	−0.499237	+	0.288235i
$276$	−3.65059e7	−	1.90126e7i	−0.104516	−	0.0544328i
$277$	−3.90947e7	−	2.25713e7i	−0.110519	−	0.0638084i	0.443721	−	0.896165i	$-0.353658\pi$
$277$	−3.90947e7	−	2.25713e7i	−0.110519	−	0.0638084i	−0.554241	+	0.832356i	$0.686991\pi$
$278$	−2.40861e8	−	2.43764e7i	−0.672371	−	0.0680476i
$279$	−3.09935e8	+	4.97815e8i	−0.854389	+	1.37231i
$280$	9.64468e7	−	3.08954e8i	0.262564	−	0.841087i
$281$	−3.19998e8	−	1.84751e8i	−0.860351	−	0.496724i	0.00377898	−	0.999993i	$-0.498797\pi$
$281$	−3.19998e8	−	1.84751e8i	−0.860351	−	0.496724i	−0.864130	+	0.503269i	$0.832130\pi$
$282$	2.92008e8	−	2.30349e8i	0.775394	−	0.611667i
$283$	9.19053e7	+	1.59185e8i	0.241039	+	0.417493i	0.961011	−	0.276511i	$-0.0891783\pi$
$283$	9.19053e7	+	1.59185e8i	0.241039	+	0.417493i	−0.719971	+	0.694004i	$0.755845\pi$
$284$	−6.54044e7	−	1.96132e8i	−0.169431	−	0.508083i
$285$	5.22694e8	−	5.05589e8i	1.33749	−	1.29372i
$286$	2.06721e7	−	2.86847e7i	0.0522520	−	0.0725052i
$287$	2.60747e6			0.00651078
$288$	1.97768e8	+	3.53877e8i	0.487847	+	0.872929i
$289$	−5.55682e8			−1.35420
$290$	−1.46690e8	+	2.03547e8i	−0.353188	+	0.490086i
$291$	−1.34602e6	−	384771.i	−0.00320204	−	0.000915329i
$292$	2.68253e8	+	8.04427e8i	0.630529	+	1.89080i
$293$	7.64559e7	+	1.32426e8i	0.177572	+	0.307564i	0.941048	−	0.338272i	$-0.109842\pi$
$293$	7.64559e7	+	1.32426e8i	0.177572	+	0.307564i	−0.763476	+	0.645836i	$0.776509\pi$
$294$	4.52014e7	+	3.11060e8i	0.103738	+	0.713885i
$295$	3.84641e8	+	2.22073e8i	0.872326	+	0.503638i
$296$	1.69818e8	−	5.43987e8i	0.380594	−	1.21918i
$297$	−3.06407e7	−	1.42429e8i	−0.0678658	−	0.315464i
$298$	1.17968e8	+	1.19391e7i	0.258231	+	0.0261344i
$299$	1.30647e7	+	7.54292e6i	0.0282651	+	0.0163189i
$300$	3.62829e7	+	8.34673e8i	0.0775850	+	1.78481i
$301$	−5.70239e7	+	3.29228e7i	−0.120524	+	0.0695847i
$302$	−8.41617e8	+	3.78609e8i	−1.75829	+	0.790982i
$303$	−8.85423e7	−	2.53105e7i	−0.182853	−	0.0522699i
$304$	4.36755e8	−	3.27736e8i	0.891622	−	0.669063i
$305$			1.24960e9i			2.52187i
$306$	7.62129e8	+	1.02840e8i	1.52056	+	0.205182i
$307$	1.20175e8			0.237045			0.118522	−	0.992951i	$-0.462184\pi$
$307$	1.20175e8			0.237045			0.118522	+	0.992951i	$0.462184\pi$
$308$	−5.79384e7	+	6.53542e7i	−0.112990	+	0.127452i
$309$	−3.34682e8	−	3.46005e8i	−0.645325	−	0.667157i
$310$	−1.29081e9	+	5.80684e8i	−2.46092	+	1.10707i
$311$	3.68292e8	+	6.37901e8i	0.694274	+	1.20252i	0.970425	+	0.241404i	$0.0776078\pi$
$311$	3.68292e8	+	6.37901e8i	0.694274	+	1.20252i	−0.276151	+	0.961114i	$0.589059\pi$
$312$	−6.67840e7	−	1.32727e8i	−0.124489	−	0.247411i
$313$	1.45989e8	−	2.52860e8i	0.269100	−	0.466095i	−0.699530	−	0.714604i	$-0.746607\pi$
$313$	1.45989e8	−	2.52860e8i	0.269100	−	0.466095i	0.968630	+	0.248509i	$0.0799404\pi$
$314$	7.85814e7	−	7.76454e8i	0.143241	−	1.41534i
$315$	2.30180e8	+	4.31197e8i	0.414935	+	0.777300i
$316$	1.17622e8	−	5.75156e8i	0.209694	−	1.02537i
$317$	2.26084e8	−	3.91588e8i	0.398622	−	0.690434i	−0.594934	−	0.803775i	$-0.702822\pi$
$317$	2.26084e8	−	3.91588e8i	0.398622	−	0.690434i	0.993556	+	0.113341i	$0.0361551\pi$
$318$	6.06743e8	+	2.41844e8i	1.05806	+	0.421737i
$319$	5.86335e7	−	3.38521e7i	0.101130	−	0.0583873i
$320$	−7.97298e7	+	9.75231e8i	−0.136018	+	1.66373i
$321$	7.18341e8	−	1.79728e8i	1.21217	−	0.303284i
$322$	−3.02319e7	−	2.17871e7i	−0.0504626	−	0.0363667i
$323$		−	1.03586e9i		−	1.71038i
$324$	−5.90324e8	−	1.62269e8i	−0.964235	−	0.265051i
$325$		−	3.06209e8i		−	0.494797i
$326$	5.03579e8	−	6.98769e8i	0.805018	−	1.11705i
$327$	−6.08241e8	+	1.52182e8i	−0.961963	+	0.240683i
$328$	−7.69117e6	+	1.72808e6i	−0.0120347	+	0.00270399i
$329$	2.91612e8	−	1.68362e8i	0.451461	−	0.260651i
$330$	1.30201e8	−	3.26651e8i	0.199442	−	0.500363i
$331$	1.68574e8	−	2.91978e8i	0.255500	−	0.442540i	−0.709531	−	0.704674i	$-0.751093\pi$
$331$	1.68574e8	−	2.91978e8i	0.255500	−	0.442540i	0.965031	+	0.262135i	$0.0844265\pi$
$332$	−9.25560e7	+	4.52584e8i	−0.138810	+	0.678760i
$333$	4.05286e8	+	7.59225e8i	0.601460	+	1.12672i
$334$	−8.17054e8	−	8.26903e7i	−1.19988	−	0.121434i
$335$	−6.98510e8	+	1.20986e9i	−1.01512	+	1.75823i
$336$	1.31117e8	+	3.42802e8i	0.188569	+	0.493010i
$337$	2.36112e8	+	4.08958e8i	0.336057	+	0.582069i	0.983687	−	0.179886i	$-0.0575730\pi$
$337$	2.36112e8	+	4.08958e8i	0.336057	+	0.582069i	−0.647630	+	0.761955i	$0.724240\pi$
$338$	−2.68908e8	−	5.97760e8i	−0.378787	−	0.842013i
$339$	−5.35795e8	−	5.53922e8i	−0.746964	−	0.772236i
$340$	1.38898e9	+	1.23137e9i	1.91654	+	1.69907i
$341$	3.81947e8			0.521630
$342$	−1.10276e8	+	8.17231e8i	−0.149069	+	1.10472i
$343$			6.79065e8i			0.908619i
$344$	1.46382e8	−	1.34903e8i	0.193881	−	0.178677i
$345$	1.44256e8	+	4.12369e7i	0.189134	+	0.0540653i
$346$	−1.42610e8	−	3.17010e8i	−0.185090	−	0.411440i
$347$	6.95453e8	−	4.01520e8i	0.893541	−	0.515886i	0.0184422	−	0.999830i	$-0.494129\pi$
$347$	6.95453e8	−	4.01520e8i	0.893541	−	0.515886i	0.875099	+	0.483944i	$0.160796\pi$
$348$	−1.23560e7	−	2.84244e8i	−0.0157163	−	0.361546i
$349$	7.39064e7	+	4.26699e7i	0.0930664	+	0.0537319i	0.545811	−	0.837908i	$-0.316222\pi$
$349$	7.39064e7	+	4.26699e7i	0.0930664	+	0.0537319i	−0.452744	+	0.891640i	$0.649555\pi$
$350$	−7.61615e7	+	7.52543e8i	−0.0949505	+	0.938196i
$351$	2.13576e8	+	6.88144e7i	0.263619	+	0.0849385i
$352$	1.27586e8	−	2.31171e8i	0.155921	−	0.282511i
$353$	3.61272e8	+	2.08580e8i	0.437142	+	0.252384i	0.702385	−	0.711798i	$-0.252119\pi$
$353$	3.61272e8	+	2.08580e8i	0.437142	+	0.252384i	−0.265243	+	0.964182i	$0.585452\pi$
$354$	−4.98417e8	+	7.24272e7i	−0.597148	+	0.0867741i
$355$	3.76816e8	+	6.52665e8i	0.447023	+	0.774267i
$356$	1.29583e9	−	4.32124e8i	1.52221	−	0.507613i
$357$	6.69435e8	+	1.91363e8i	0.778699	+	0.222597i
$358$	−2.52096e8	−	1.81677e8i	−0.290386	−	0.209271i
$359$	−8.40341e8			−0.958573			−0.479287	−	0.877659i	$-0.659105\pi$
$359$	−8.40341e8			−0.958573			−0.479287	+	0.877659i	$0.659105\pi$
$360$	−9.64725e8	−	1.11934e9i	−1.08980	−	1.26445i
$361$	2.16884e8			0.242634
$362$	2.13157e8	+	1.53615e8i	0.236167	+	0.170197i
$363$	5.86828e8	−	5.67625e8i	0.643929	−	0.622856i
$364$	−4.25545e7	−	1.27611e8i	−0.0462478	−	0.138686i
$365$	−1.54549e9	−	2.67688e9i	−1.66358	−	2.88140i
$366$	−8.77622e8	−	1.11254e9i	−0.935673	−	1.18613i
$367$	6.83101e8	+	3.94388e8i	0.721362	+	0.416479i	0.815254	−	0.579104i	$-0.196597\pi$
$367$	6.83101e8	+	3.94388e8i	0.721362	+	0.416479i	−0.0938915	+	0.995582i	$0.529931\pi$
$368$	1.03613e8	+	4.42287e7i	0.108380	+	0.0462634i
$369$	6.29199e6	−	1.01061e7i	0.00651923	−	0.0104711i
$370$	−2.09164e8	+	2.06672e9i	−0.214674	+	2.12118i
$371$	5.12120e8	+	2.95673e8i	0.520671	+	0.300609i
$372$	7.41401e8	−	1.42355e9i	0.746712	−	1.43375i
$373$	−1.08598e9	+	6.26993e8i	−1.08353	+	0.625579i	−0.931848	−	0.362850i	$-0.881804\pi$
$373$	−1.08598e9	+	6.26993e8i	−1.08353	+	0.625579i	−0.151687	+	0.988429i	$0.548470\pi$
$374$	−2.05496e8	−	4.56801e8i	−0.203120	−	0.451520i
$375$	−3.25414e8	−	1.30062e9i	−0.318659	−	1.27362i
$376$	−7.48579e8	+	6.89877e8i	−0.726240	+	0.669290i
$377$			1.04278e8i			0.100230i
$378$	−5.07770e8	−	2.22240e8i	−0.483555	−	0.211642i
$379$	9.12602e8			0.861081			0.430541	−	0.902571i	$-0.358323\pi$
$379$	9.12602e8			0.861081			0.430541	+	0.902571i	$0.358323\pi$
$380$	−1.32040e9	+	1.48940e9i	−1.23442	+	1.39241i
$381$	1.48231e9	−	3.70872e8i	1.37309	−	0.343547i
$382$	5.60794e8	+	1.24660e9i	0.514733	+	1.14421i
$383$	−1.31385e8	−	2.27565e8i	−0.119495	−	0.206971i	0.800073	−	0.599903i	$-0.204794\pi$
$383$	−1.31385e8	−	2.27565e8i	−0.119495	−	0.206971i	−0.919568	+	0.392932i	$0.871461\pi$
$384$	−6.13940e8	−	9.24256e8i	−0.553308	−	0.832977i
$385$	1.59181e8	−	2.75709e8i	0.142160	−	0.246229i
$386$	−2.01277e9	−	2.03704e8i	−1.78131	−	0.180278i
$387$	−9.99885e6	+	3.00461e8i	−0.00876924	+	0.263511i
$388$	3.75403e6	+	767720.i	0.00326277	+	0.000667255i
$389$	7.44300e8	−	1.28917e9i	0.641098	−	1.11041i	−0.344090	−	0.938937i	$-0.611813\pi$
$389$	7.44300e8	−	1.28917e9i	0.641098	−	1.11041i	0.985188	−	0.171477i	$-0.0548541\pi$
$390$	3.35436e8	+	4.25224e8i	0.286341	+	0.362987i
$391$	1.85083e8	−	1.06858e8i	0.156584	−	0.0904040i
$392$	−1.88600e8	−	8.39407e8i	−0.158140	−	0.703835i
$393$	−8.42783e8	−	8.71296e8i	−0.700393	−	0.724089i
$394$	−7.96146e7	+	1.10474e8i	−0.0655777	+	0.0909961i
$395$			2.13991e9i			1.74705i
$396$	1.13493e8	+	3.82264e8i	0.0918413	+	0.309336i
$397$			1.04753e9i			0.840231i	0.907471	+	0.420116i	$0.138010\pi$
$397$			1.04753e9i			0.840231i	−0.907471	+	0.420116i	$0.861990\pi$
$398$	1.03544e8	+	7.46205e7i	0.0823254	+	0.0593291i
$399$	−2.05199e8	+	7.17835e8i	−0.161722	+	0.565743i
$400$	−2.74090e8	−	2.27023e9i	−0.214133	−	1.77362i
$401$	8.85768e8	−	5.11399e8i	0.685985	−	0.396054i	−0.116121	−	0.993235i	$-0.537046\pi$
$401$	8.85768e8	−	5.11399e8i	0.685985	−	0.396054i	0.802106	+	0.597181i	$0.203713\pi$
$402$	−2.27813e8	−	1.56773e9i	−0.174899	−	1.20359i
$403$	−2.94138e8	+	5.09461e8i	−0.223863	+	0.387743i
$404$	2.46942e8	+	5.05011e7i	0.186321	+	0.0381036i
$405$	2.22669e9	+	1.48366e8i	1.66559	+	0.110979i
$406$	2.59364e7	−	2.56275e8i	0.0192340	−	0.190049i
$407$	2.80275e8	−	4.85451e8i	0.206065	−	0.356915i
$408$	−2.10144e9	−	1.20797e8i	−1.53181	−	0.0880531i
$409$	8.14094e8	+	1.41005e9i	0.588360	+	1.01907i	0.994447	+	0.105235i	$0.0335596\pi$
$409$	8.14094e8	+	1.41005e9i	0.588360	+	1.01907i	−0.406087	+	0.913834i	$0.633107\pi$
$410$	2.62048e7	−	1.17885e7i	0.0187775	−	0.00844724i
$411$	−6.20042e8	+	2.16905e9i	−0.440529	+	1.54108i
$412$	9.85929e8	+	8.74056e8i	0.694553	+	0.615742i
$413$	−4.55983e8			−0.318510
$414$	−1.57395e8	+	6.46005e7i	−0.109016	+	0.0447440i
$415$		−	1.68388e9i		−	1.15649i
$416$	2.10094e8	+	3.48207e8i	0.143083	+	0.237143i
$417$	−7.19264e8	+	6.95726e8i	−0.485749	+	0.469853i
$418$	4.89828e8	−	2.20354e8i	0.328040	−	0.147572i
$419$	−4.35891e8	+	2.51662e8i	−0.289487	+	0.167135i	−0.637710	−	0.770276i	$-0.720118\pi$
$419$	−4.35891e8	+	2.51662e8i	−0.289487	+	0.167135i	0.348224	+	0.937411i	$0.386785\pi$
$420$	−7.18608e8	−	1.12846e9i	−0.473282	−	0.743217i
$421$	−3.12767e8	−	1.80576e8i	−0.204284	−	0.117943i	0.394368	−	0.918952i	$-0.370963\pi$
$421$	−3.12767e8	−	1.80576e8i	−0.204284	−	0.117943i	−0.598652	+	0.801009i	$0.704297\pi$
$422$	1.45183e9	+	1.46933e8i	0.940419	+	0.0951755i
$423$	5.11327e7	−	1.53651e9i	0.0328479	−	0.987063i
$424$	−1.70654e9	−	5.32734e8i	−1.08727	−	0.339414i
$425$	−3.75678e9	−	2.16898e9i	−2.37386	−	1.37055i
$426$	−7.93863e8	−	3.16430e8i	−0.497522	−	0.198310i
$427$	−6.41455e8	−	1.11103e9i	−0.398720	−	0.690604i
$428$	−1.92267e9	+	6.41154e8i	−1.18536	+	0.395284i
$429$	−3.54733e7	−	1.41780e8i	−0.0216921	−	0.0866991i
$430$	−4.24240e8	+	5.88678e8i	−0.257319	+	0.357058i
$431$	−1.87221e8			−0.112638			−0.0563188	−	0.998413i	$-0.517936\pi$
$431$	−1.87221e8			−0.112638			−0.0563188	+	0.998413i	$0.517936\pi$
$432$	1.64504e9	+	3.19015e8i	0.981711	+	0.190379i
$433$	2.55056e9			1.50983			0.754915	−	0.655823i	$-0.227678\pi$
$433$	2.55056e9			1.50983			0.754915	+	0.655823i	$0.227678\pi$
$434$	8.49591e8	−	1.17890e9i	0.498880	−	0.692249i
$435$	2.51719e8	+	1.00607e9i	0.146624	+	0.586027i
$436$	1.62798e9	−	5.42885e8i	0.940690	−	0.313693i
$437$	1.14584e8	+	1.98465e8i	0.0656807	+	0.113762i
$438$	3.25600e9	+	1.29782e9i	1.85150	+	0.738000i
$439$	1.02962e9	+	5.94453e8i	0.580834	+	0.335345i	0.761465	−	0.648206i	$-0.224481\pi$
$439$	1.02962e9	+	5.94453e8i	0.580834	+	0.335345i	−0.180631	+	0.983551i	$0.557814\pi$
$440$	−2.86807e8	+	9.18746e8i	−0.160511	+	0.514175i
$441$	1.10297e9	+	6.86702e8i	0.612393	+	0.381270i
$442$	7.67559e8	+	7.76812e7i	0.422799	+	0.0427896i
$443$	−2.83740e9	−	1.63818e9i	−1.55063	−	0.895256i	−0.998090	−	0.0617693i	$-0.980326\pi$
$443$	−2.83740e9	−	1.63818e9i	−1.55063	−	0.895256i	−0.552539	−	0.833487i	$-0.686341\pi$
$444$	−1.26528e9	−	1.98693e9i	−0.686035	−	1.07731i
$445$	−4.31212e9	+	2.48960e9i	−2.31970	+	1.33928i
$446$	9.14287e8	−	4.11300e8i	0.487989	−	0.219526i
$447$	3.52280e8	−	3.40752e8i	0.186557	−	0.180452i
$448$	−4.29723e8	−	9.08012e8i	−0.225796	−	0.477110i
$449$		−	1.73533e9i		−	0.904731i	−0.891833	−	0.452366i	$-0.850580\pi$
$449$		−	1.73533e9i		−	0.904731i	0.891833	−	0.452366i	$-0.149420\pi$
$450$	2.73296e9	+	2.11113e9i	1.41380	+	1.09212i
$451$	−7.75391e6			−0.00398018
$452$	1.57838e9	+	1.39928e9i	0.803947	+	0.712722i
$453$	−1.04845e9	+	3.66773e9i	−0.529912	+	1.85376i
$454$	−2.85873e9	+	1.28603e9i	−1.43376	+	0.644992i
$455$	2.45170e8	+	4.24648e8i	0.122019	+	0.211343i
$456$	1.29530e8	−	2.25337e9i	0.0639726	−	1.11290i
$457$	4.53465e8	−	7.85425e8i	0.222248	−	0.384944i	−0.733243	−	0.679967i	$-0.761994\pi$
$457$	4.53465e8	−	7.85425e8i	0.222248	−	0.384944i	0.955490	+	0.295023i	$0.0953273\pi$
$458$	1.26237e8	−	1.24733e9i	0.0613984	−	0.606671i
$459$	2.35708e9	−	2.13285e9i	1.13771	−	1.02948i
$460$	−4.02328e8	−	8.22783e7i	−0.192721	−	0.0394124i
$461$	−2.85867e8	+	4.95136e8i	−0.135897	+	0.235381i	−0.925940	−	0.377671i	$-0.876725\pi$
$461$	−2.85867e8	+	4.95136e8i	−0.135897	+	0.235381i	0.790043	+	0.613052i	$0.210058\pi$
$462$	5.19154e7	+	3.57263e8i	0.0244934	+	0.168555i
$463$	1.22165e9	−	7.05322e8i	0.572024	−	0.330258i	−0.185933	−	0.982562i	$-0.559531\pi$
$463$	1.22165e9	−	7.05322e8i	0.572024	−	0.330258i	0.757957	+	0.652304i	$0.226197\pi$
$464$	9.33399e7	+	7.73115e8i	0.0433765	+	0.359278i
$465$	−1.60804e9	+	5.62531e9i	−0.741671	+	2.59454i
$466$	−1.27016e9	−	9.15360e8i	−0.581444	−	0.419026i
$467$			2.09937e9i			0.953850i	0.878944	+	0.476925i	$0.158249\pi$
$467$			2.09937e9i			0.953850i	−0.878944	+	0.476925i	$0.841751\pi$
$468$	−5.97286e8	−	1.42998e8i	−0.269353	−	0.0644867i
$469$		−	1.43425e9i		−	0.641979i
$470$	2.16950e9	−	3.01042e9i	0.963869	−	1.33747i
$471$	−2.24279e9	−	2.31866e9i	−0.989042	−	1.02250i
$472$	1.34500e9	−	3.02198e8i	0.588742	−	0.132280i
$473$	1.69574e8	−	9.79034e7i	0.0736791	−	0.0425387i
$474$	−1.50290e9	−	1.90519e9i	−0.648197	−	0.821702i
$475$	2.32579e9	−	4.02839e9i	0.995735	−	1.72466i
$476$	−1.86704e9	−	3.81820e8i	−0.793468	−	0.162269i
$477$	2.38176e9	−	1.27142e9i	1.00481	−	0.536383i
$478$	−4.42617e8	−	4.47953e7i	−0.185366	−	0.0187601i
$479$	−2.18601e9	+	3.78629e9i	−0.908822	+	1.57413i	−0.0931184	+	0.995655i	$0.529684\pi$
$479$	−2.18601e9	+	3.78629e9i	−0.908822	+	1.57413i	−0.815703	+	0.578470i	$0.803650\pi$
$480$	2.86754e9	+	2.85235e9i	1.18349	+	1.17722i
$481$	4.31681e8	+	7.47693e8i	0.176870	+	0.306348i
$482$	−1.20245e9	−	2.67295e9i	−0.489105	−	1.08724i
$483$	−1.49427e8	+	3.73866e7i	−0.0603414	+	0.0150974i
$484$	−1.48241e9	+	1.67215e9i	−0.594304	+	0.670371i
$485$	−1.39672e7			−0.00555920
$486$	−2.08665e9	+	1.43176e9i	−0.824561	+	0.565773i
$487$		−	4.23873e9i		−	1.66297i	−0.555547	−	0.831485i	$-0.687491\pi$
$487$		−	4.23873e9i		−	1.66297i	0.555547	−	0.831485i	$-0.312509\pi$
$488$	2.62840e9	+	2.85206e9i	1.02382	+	1.11094i
$489$	−8.64141e8	−	3.45381e9i	−0.334198	−	1.33573i
$490$	1.28658e9	+	2.85997e9i	0.494028	+	1.09818i
$491$	1.45551e9	−	8.40338e8i	0.554919	−	0.320382i	−0.196185	−	0.980567i	$-0.562855\pi$
$491$	1.45551e9	−	8.40338e8i	0.554919	−	0.320382i	0.751103	+	0.660184i	$0.229522\pi$
$492$	−1.50512e7	+	2.88996e7i	−0.00569762	+	0.0109399i
$493$	1.27935e9	+	7.38635e8i	0.480868	+	0.277629i
$494$	−8.32975e7	+	8.23053e8i	−0.0310876	+	0.307173i
$495$	−6.84492e8	−	1.28226e9i	−0.253659	−	0.475181i
$496$	−1.72471e9	+	4.04042e9i	−0.634643	+	1.48676i
$497$	−6.70059e8	−	3.86859e8i	−0.244831	−	0.141353i
$498$	1.18262e9	+	1.49918e9i	0.429084	+	0.543939i
$499$	−2.12466e9	−	3.68002e9i	−0.765486	−	1.32586i	−0.939989	−	0.341204i	$-0.889165\pi$
$499$	−2.12466e9	−	3.68002e9i	−0.765486	−	1.32586i	0.174503	−	0.984657i	$-0.444168\pi$
$500$	1.16087e9	+	3.48116e9i	0.415324	+	1.24546i
$501$	−2.43990e9	+	2.36006e9i	−0.866843	+	0.838476i
$502$	3.70300e7	+	2.66862e7i	0.0130644	+	0.00941508i
$503$	3.28522e9			1.15100			0.575501	−	0.817801i	$-0.304807\pi$
$503$	3.28522e9			1.15100			0.575501	+	0.817801i	$0.304807\pi$
$504$	1.43233e9	+	4.99993e8i	0.498352	+	0.173963i
$505$	−9.18770e8			−0.317459
$506$	8.99015e7	+	6.47889e7i	0.0308489	+	0.0222317i
$507$	−2.60501e9	−	7.44663e8i	−0.887732	−	0.253765i
$508$	−3.96745e9	+	1.32303e9i	−1.34273	+	0.447762i
$509$	−5.40960e7	−	9.36970e7i	−0.0181825	−	0.0314930i	0.856791	−	0.515664i	$-0.172455\pi$
$509$	−5.40960e7	−	9.36970e7i	−0.0181825	−	0.0314930i	−0.874973	+	0.484171i	$0.839121\pi$
$510$	7.59293e9	−	1.10336e9i	2.53462	−	0.368317i
$511$	2.74822e9	+	1.58668e9i	0.911125	+	0.526039i
$512$	1.86932e9	+	2.39354e9i	0.615514	+	0.788126i
$513$	2.28706e9	+	2.52750e9i	0.747940	+	0.826572i
$514$	−2.04621e8	+	2.02184e9i	−0.0664630	+	0.656714i
$515$	−4.15933e9	−	2.40139e9i	−1.34183	−	0.774707i
$516$	−3.57346e7	−	8.22060e8i	−0.0114503	−	0.263408i
$517$	−8.67176e8	+	5.00664e8i	−0.275988	+	0.159342i
$518$	−8.74934e8	−	1.94491e9i	−0.276580	−	0.614815i
$519$	−1.38151e9	−	3.94917e8i	−0.433780	−	0.123999i
$520$	−1.00460e9	−	1.09009e9i	−0.313316	−	0.339976i
$521$		−	6.28790e8i		−	0.194793i	−0.995246	−	0.0973965i	$-0.968949\pi$
$521$		−	6.28790e8i		−	0.194793i	0.995246	−	0.0973965i	$-0.0310515\pi$
$522$	−9.30695e8	−	7.18933e8i	−0.286392	−	0.221229i
$523$	−1.95751e9			−0.598339			−0.299169	−	0.954200i	$-0.596710\pi$
$523$	−1.95751e9			−0.598339			−0.299169	+	0.954200i	$0.596710\pi$
$524$	2.48273e9	+	2.20101e9i	0.753823	+	0.668286i
$525$	2.17372e9	+	2.24726e9i	0.655611	+	0.677791i
$526$	−1.86728e9	−	4.15082e9i	−0.559449	−	1.24361i
$527$	4.16694e9	+	7.21735e9i	1.24017	+	2.14803i
$528$	−3.89906e8	−	1.01940e9i	−0.115277	−	0.301388i
$529$	1.67877e9	−	2.90772e9i	0.493057	−	0.853999i
$530$	6.48351e9	+	6.56167e8i	1.89167	+	0.191447i
$531$	−1.10032e9	+	1.76732e9i	−0.318924	+	0.512253i
$532$	4.09425e8	−	2.00203e9i	0.117892	−	0.576473i
$533$	5.97130e6	−	1.03426e7i	0.00170814	−	0.00295858i
$534$	2.09064e9	−	5.24501e9i	0.594133	−	1.49057i
$535$	6.39802e9	−	3.69390e9i	1.80637	−	1.04291i
$536$	9.50538e8	+	4.23057e9i	0.266620	+	1.18665i
$537$	−1.24604e9	+	3.11758e8i	−0.347233	+	0.0868774i
$538$	−2.02062e9	+	2.80382e9i	−0.559430	+	0.776270i
$539$		−	8.46254e8i		−	0.232777i
$540$	−6.10780e9	+	6.21559e7i	−1.66919	+	0.0169865i
$541$			1.54528e9i			0.419582i	0.977746	+	0.209791i	$0.0672784\pi$
$541$			1.54528e9i			0.419582i	−0.977746	+	0.209791i	$0.932722\pi$
$542$	3.35180e9	+	2.41552e9i	0.904232	+	0.651649i
$543$	1.05357e9	−	2.63603e8i	0.282400	−	0.0706562i
$544$	5.76020e9	−	1.11120e8i	1.53406	−	0.0295936i
$545$	−5.41740e9	+	3.12774e9i	−1.43352	+	0.827642i
$546$	−5.16517e8	−	2.05881e8i	−0.135803	−	0.0541305i
$547$	−1.31045e9	+	2.26976e9i	−0.342345	+	0.592959i	−0.984868	−	0.173307i	$-0.944555\pi$
$547$	−1.31045e9	+	2.26976e9i	−0.342345	+	0.592959i	0.642523	+	0.766267i	$0.277888\pi$
$548$	1.23715e9	−	6.04945e9i	0.321136	−	1.57030i
$549$	−5.85406e9	−	1.94814e8i	−1.50992	−	0.0502477i
$550$	2.26484e8	−	2.23786e9i	0.0580454	−	0.573540i
$551$	−7.92038e8	+	1.37185e9i	−0.201704	+	0.349362i
$552$	4.15983e8	−	2.09310e8i	0.105266	−	0.0529667i
$553$	−1.09847e9	−	1.90261e9i	−0.276218	−	0.478423i
$554$	4.65771e8	−	2.09531e8i	0.116383	−	0.0523558i
$555$	5.96973e9	+	6.17170e9i	1.48228	+	1.53242i
$556$	1.81696e9	−	2.04951e9i	0.448314	−	0.505696i
$557$	−5.39310e9			−1.32235			−0.661173	−	0.750233i	$-0.729941\pi$
$557$	−5.39310e9			−1.32235			−0.661173	+	0.750233i	$0.729941\pi$
$558$	−2.51911e9	−	6.13764e9i	−0.613801	−	1.49548i
$559$			3.01582e8i			0.0730238i
$560$	2.19779e9	+	2.92887e9i	0.528845	+	0.704762i
$561$	−1.99072e9	−	5.69063e8i	−0.476036	−	0.136079i
$562$	3.81243e9	−	1.71506e9i	0.905994	−	0.407570i
$563$	1.03355e9	−	5.96723e8i	0.244092	−	0.140927i	−0.372964	−	0.927846i	$-0.621658\pi$
$563$	1.03355e9	−	5.96723e8i	0.244092	−	0.140927i	0.617056	+	0.786919i	$0.288325\pi$
$564$	1.82742e8	+	4.20390e9i	0.0428905	+	0.986678i
$565$	−6.65870e9	−	3.84440e9i	−1.55317	−	0.896725i
$566$	−2.06901e9	−	2.09395e8i	−0.479629	−	0.0485410i
$567$	−2.05593e9	+	1.01110e9i	−0.473660	+	0.232946i
$568$	2.23284e9	+	6.97030e8i	0.511256	+	0.159600i
$569$	6.45822e8	+	3.72865e8i	0.146967	+	0.0848514i	0.571680	−	0.820476i	$-0.306292\pi$
$569$	6.45822e8	+	3.72865e8i	0.146967	+	0.0848514i	−0.424713	+	0.905328i	$0.639625\pi$
$570$	1.18313e9	+	8.14189e9i	0.267591	+	1.84146i
$571$	3.80534e9	+	6.59104e9i	0.855395	+	1.48159i	0.876278	+	0.481806i	$0.160019\pi$
$571$	3.80534e9	+	6.59104e9i	0.855395	+	1.48159i	−0.0208826	+	0.999782i	$0.506648\pi$
$572$	1.26546e8	+	3.79480e8i	0.0282723	+	0.0847818i
$573$	5.43263e9	+	1.55296e9i	1.20634	+	0.344841i
$574$	−1.72476e7	+	2.39328e7i	−0.00380659	+	0.00528205i
$575$	9.59699e8			0.210522
$576$	−4.55626e9	−	5.25551e8i	−0.993413	−	0.114587i
$577$	−1.44823e9			−0.313851			−0.156926	−	0.987610i	$-0.550158\pi$
$577$	−1.44823e9			−0.313851			−0.156926	+	0.987610i	$0.550158\pi$
$578$	3.67565e9	−	5.10036e9i	0.791748	−	1.09864i
$579$	−6.01059e9	+	5.81390e9i	−1.28689	+	1.24478i
$580$	−8.97971e8	−	2.69280e9i	−0.191102	−	0.573068i
$581$	8.64378e8	+	1.49715e9i	0.182847	+	0.316700i
$582$	1.24351e7	−	9.80943e6i	0.00261469	−	0.00206259i
$583$	−1.52291e9	−	8.79251e8i	−0.318298	−	0.183769i
$584$	−9.15789e9	−	2.85884e9i	−1.90261	−	0.593943i
$585$	2.23748e9	+	7.44598e7i	0.462076	+	0.0153772i
$586$	−1.72121e9	−	1.74196e8i	−0.353339	−	0.0357598i
$587$	−3.88669e9	−	2.24398e9i	−0.793133	−	0.457916i	0.0479311	−	0.998851i	$-0.484737\pi$
$587$	−3.88669e9	−	2.24398e9i	−0.793133	−	0.457916i	−0.841064	+	0.540935i	$0.818071\pi$
$588$	−3.15407e9	−	1.64267e9i	−0.639810	−	0.333220i
$589$	−7.73916e9	+	4.46821e9i	−1.56060	+	0.901010i
$590$	−4.58259e9	+	2.06152e9i	−0.918605	+	0.413243i
$591$	1.36619e8	+	5.46039e8i	0.0272241	+	0.108810i
$592$	3.86973e9	+	5.15698e9i	0.766576	+	1.02157i
$593$		−	1.78409e9i		−	0.351338i	−0.984449	−	0.175669i	$-0.943791\pi$
$593$		−	1.78409e9i		−	0.351338i	0.984449	−	0.175669i	$-0.0562088\pi$
$594$	1.50997e9	+	6.60882e8i	0.295608	+	0.129381i
$595$	6.94648e9			1.35193
$596$	−8.89906e8	+	1.00381e9i	−0.172180	+	0.194218i
$597$	5.11787e8	−	1.28049e8i	0.0984417	−	0.0246301i
$598$	−1.55652e8	+	7.00215e7i	−0.0297647	+	0.0133899i
$599$	−3.84639e9	−	6.66214e9i	−0.731238	−	1.26654i	−0.956354	−	0.292210i	$-0.905609\pi$
$599$	−3.84639e9	−	6.66214e9i	−0.731238	−	1.26654i	0.225116	−	0.974332i	$-0.427724\pi$
$600$	−7.90110e9	−	5.18806e9i	−1.49334	−	0.980564i
$601$	−4.57084e8	+	7.91692e8i	−0.0858885	+	0.148763i	−0.905769	−	0.423771i	$-0.860706\pi$
$601$	−4.57084e8	+	7.91692e8i	−0.0858885	+	0.148763i	0.819881	+	0.572534i	$0.194040\pi$
$602$	7.50106e7	−	7.41171e8i	0.0140131	−	0.138462i
$603$	−5.55894e9	−	3.46095e9i	−1.03248	−	0.642813i
$604$	2.09193e9	−	1.02292e10i	0.386294	−	1.88892i
$605$	4.07278e9	−	7.05426e9i	0.747734	−	1.29511i
$606$	8.17992e8	−	6.45271e8i	0.149312	−	0.117784i
$607$	4.29797e9	−	2.48143e9i	0.780015	−	0.450342i	−0.0564207	−	0.998407i	$-0.517969\pi$
$607$	4.29797e9	−	2.48143e9i	0.780015	−	0.450342i	0.836436	+	0.548065i	$0.184635\pi$
$608$	1.19154e8	+	6.17666e9i	0.0215004	+	1.11453i
$609$	−7.40250e8	−	7.65294e8i	−0.132806	−	0.137299i
$610$	−1.14696e10	−	8.26573e9i	−2.04594	−	1.47444i
$611$		−	1.54225e9i		−	0.273533i
$612$	−5.98516e9	+	6.31500e9i	−1.05547	+	1.11364i
$613$		−	6.01027e9i		−	1.05386i	−0.849909	−	0.526929i	$-0.823343\pi$
$613$		−	6.01027e9i		−	1.05386i	0.849909	−	0.526929i	$-0.176657\pi$
$614$	−7.94920e8	+	1.10304e9i	−0.138591	+	0.192309i
$615$	3.26448e7	−	1.14200e8i	0.00565916	−	0.0197971i
$616$	−2.16614e8	−	9.64088e8i	−0.0373383	−	0.166182i
$617$	1.60585e9	−	9.27135e8i	0.275236	−	0.158908i	−0.356029	−	0.934475i	$-0.615869\pi$
$617$	1.60585e9	−	9.27135e8i	0.275236	−	0.158908i	0.631265	+	0.775567i	$0.282536\pi$
$618$	5.38965e9	−	7.83193e8i	0.918546	−	0.133478i
$619$	−5.72987e8	+	9.92442e8i	−0.0971018	+	0.168185i	−0.910484	−	0.413545i	$-0.864291\pi$
$619$	−5.72987e8	+	9.92442e8i	−0.0971018	+	0.168185i	0.813382	+	0.581730i	$0.197624\pi$
$620$	3.20846e9	−	1.56889e10i	0.540662	−	2.64375i
$621$	−2.15673e8	+	6.69373e8i	−0.0361389	+	0.112163i
$622$	−8.29114e9	−	8.39109e8i	−1.38149	−	0.139814i
$623$	2.55596e9	−	4.42705e9i	0.423492	−	0.733510i
$624$	1.66000e9	+	2.64964e8i	0.273503	+	0.0436557i
$625$	−1.23618e9	−	2.14112e9i	−0.202535	−	0.350802i
$626$	1.35522e9	+	3.01255e9i	0.220801	+	0.490822i
$627$	6.10206e8	−	2.13465e9i	0.0988644	−	0.345852i
$628$	6.60695e9	+	5.85725e9i	1.06449	+	0.943703i
$629$	1.22309e10			1.95967
$630$	−5.48033e9	−	7.39507e8i	−0.873203	−	0.117829i
$631$			6.97491e8i			0.110519i	0.998472	+	0.0552593i	$0.0175986\pi$
$631$			6.97491e8i			0.110519i	−0.998472	+	0.0552593i	$0.982401\pi$
$632$	4.50107e9	+	4.88407e9i	0.709261	+	0.769613i
$633$	4.33548e9	−	4.19360e9i	0.679398	−	0.657165i
$634$	2.09875e9	+	4.66535e9i	0.327076	+	0.727063i
$635$	1.32024e10	−	7.62241e9i	2.04619	−	1.18137i
$636$	−6.23319e9	+	3.96931e9i	−0.960750	+	0.611807i
$637$	1.12878e9	+	6.51701e8i	0.173030	+	0.0998988i
$638$	−7.71279e7	+	7.62092e8i	−0.0117582	+	0.116181i
$639$	−3.11630e9	+	1.66353e9i	−0.472483	+	0.252219i
$640$	−8.42384e9	−	7.18264e9i	−1.27022	−	1.08306i
$641$	8.99406e9	+	5.19272e9i	1.34882	+	0.778739i	0.988082	−	0.153930i	$-0.0491930\pi$
$641$	8.99406e9	+	5.19272e9i	1.34882	+	0.778739i	0.360734	+	0.932669i	$0.382526\pi$
$642$	−3.10194e9	+	7.78218e9i	−0.462659	+	1.16072i
$643$	2.98030e8	+	5.16203e8i	0.0442101	+	0.0765741i	0.887284	−	0.461224i	$-0.152590\pi$
$643$	2.98030e8	+	5.16203e8i	0.0442101	+	0.0765741i	−0.843074	+	0.537798i	$0.819256\pi$
$644$	3.99948e8	−	1.33371e8i	0.0590070	−	0.0196771i
$645$	7.27996e8	+	2.90966e9i	0.106824	+	0.426957i
$646$	9.50774e9	+	6.85190e9i	1.38760	+	0.999993i
$647$	1.59184e9			0.231065			0.115532	−	0.993304i	$-0.463143\pi$
$647$	1.59184e9			0.231065			0.115532	+	0.993304i	$0.463143\pi$
$648$	5.39420e9	−	4.34497e9i	0.778779	−	0.627298i
$649$	1.35597e9			0.194712
$650$	2.81056e9	+	2.02547e9i	0.401418	+	0.289288i
$651$	−1.45790e9	−	5.82695e9i	−0.207107	−	0.827766i
$652$	3.08270e9	+	9.24426e9i	0.435576	+	1.30619i
$653$	−5.58747e9	−	9.67778e9i	−0.785270	−	1.36013i	−0.928838	−	0.370487i	$-0.879191\pi$
$653$	−5.58747e9	−	9.67778e9i	−0.785270	−	1.36013i	0.143568	−	0.989641i	$-0.454143\pi$
$654$	2.62651e9	−	6.58941e9i	0.367161	−	0.921138i
$655$	−1.04738e10	−	6.04708e9i	−1.45634	−	0.840816i
$656$	3.50133e7	−	8.20246e7i	0.00484250	−	0.0113444i
$657$	1.27814e10	−	6.82289e9i	1.75832	−	0.938620i
$658$	−3.83594e8	+	3.79025e9i	−0.0524905	+	0.518653i
$659$	4.23220e8	+	2.44346e8i	0.0576060	+	0.0332588i	0.528526	−	0.848917i	$-0.322745\pi$
$659$	4.23220e8	+	2.44346e8i	0.0576060	+	0.0332588i	−0.470920	+	0.882176i	$0.656078\pi$
$660$	2.13695e9	+	3.35575e9i	0.289328	+	0.454345i
$661$	1.03964e10	−	6.00239e9i	1.40017	−	0.808386i	0.405757	−	0.913981i	$-0.367008\pi$
$661$	1.03964e10	−	6.00239e9i	1.40017	−	0.808386i	0.994409	+	0.105595i	$0.0336747\pi$
$662$	1.56488e9	+	3.47860e9i	0.209642	+	0.466017i
$663$	2.29210e9	−	2.21709e9i	0.305447	−	0.295452i
$664$	−3.54185e9	−	3.84323e9i	−0.469506	−	0.509457i
$665$			7.44871e9i			0.982212i
$666$	−9.64943e9	−	1.30208e9i	−1.26573	−	0.170796i
$667$	−3.26821e8			−0.0426451
$668$	6.16352e9	−	6.95241e9i	0.800039	−	0.902439i
$669$	1.13898e9	−	3.98442e9i	0.147070	−	0.514486i
$670$	−6.48432e9	−	1.44141e10i	−0.832919	−	1.85151i
$671$	1.90751e9	+	3.30391e9i	0.243747	+	0.422181i
$672$	−4.01373e9	−	1.06406e9i	−0.510218	−	0.135261i
$673$	−7.06491e9	+	1.22368e10i	−0.893417	+	1.54744i	−0.0576652	+	0.998336i	$0.518366\pi$
$673$	−7.06491e9	+	1.22368e10i	−0.893417	+	1.54744i	−0.835752	+	0.549107i	$0.814968\pi$
$674$	−5.31545e9	−	5.37953e8i	−0.668699	−	0.0676760i
$675$	1.39554e10	−	3.00221e9i	1.74654	−	0.375732i
$676$	7.26532e9	+	1.48580e9i	0.904569	+	0.184989i
$677$	−2.64104e9	+	4.57441e9i	−0.327125	+	0.566598i	−0.981940	−	0.189192i	$-0.939413\pi$
$677$	−2.64104e9	+	4.57441e9i	−0.327125	+	0.566598i	0.654815	+	0.755789i	$0.272747\pi$
$678$	8.62832e9	−	1.25382e9i	1.06322	−	0.154501i
$679$	1.24183e7	−	7.16971e6i	0.00152236	−	0.000878937i
$680$	−2.04898e10	+	4.60371e9i	−2.49895	+	0.561471i
$681$	−3.56128e9	+	1.24582e10i	−0.432107	+	1.51161i
$682$	−2.52645e9	+	3.50573e9i	−0.304976	+	0.423187i
$683$			7.16005e9i			0.859891i	0.902855	+	0.429946i	$0.141467\pi$
$683$			7.16005e9i			0.859891i	−0.902855	+	0.429946i	$0.858533\pi$
$684$	−6.77157e9	−	6.41789e9i	−0.809083	−	0.766824i
$685$			2.25075e10i			2.67553i
$686$	−6.23284e9	−	4.49179e9i	−0.737143	−	0.531233i
$687$	−3.60292e9	−	3.72481e9i	−0.423941	−	0.438284i
$688$	2.69948e8	+	2.23592e9i	0.0316024	+	0.261756i
$689$	2.34558e9	−	1.35422e9i	0.273202	−	0.157733i
$690$	−1.33270e9	+	1.05130e9i	−0.154441	+	0.121830i
$691$	−1.13687e9	+	1.96911e9i	−0.131080	+	0.227037i	−0.924093	−	0.382167i	$-0.875178\pi$
$691$	−1.13687e9	+	1.96911e9i	−0.131080	+	0.227037i	0.793013	+	0.609204i	$0.208511\pi$
$692$	3.85301e9	+	7.87963e8i	0.442007	+	0.0903929i
$693$	1.26681e9	+	7.88701e8i	0.144592	+	0.0900215i
$694$	−9.14815e8	+	9.03919e9i	−0.103890	+	1.02653i
$695$	−4.99192e9	+	8.64627e9i	−0.564055	+	0.976971i
$696$	2.69068e9	+	1.76677e9i	0.302503	+	0.198631i
$697$	−8.45932e7	−	1.46520e8i	−0.00946282	−	0.0163901i
$698$	−8.80515e8	+	3.96108e8i	−0.0980038	+	0.0440879i
$699$	−6.27803e9	+	1.57076e9i	−0.695269	+	0.173956i
$700$	−6.40349e9	−	5.67688e9i	−0.705624	−	0.625557i
$701$	−5.73222e9			−0.628506			−0.314253	−	0.949339i	$-0.601754\pi$
$701$	−5.73222e9			−0.628506			−0.314253	+	0.949339i	$0.601754\pi$
$702$	−2.04435e9	+	1.50513e9i	−0.223036	+	0.164208i
$703$			1.31152e10i			1.42374i
$704$	1.27788e9	+	2.70018e9i	0.138034	+	0.291668i
$705$	−3.72287e9	−	1.48796e10i	−0.400144	−	1.59930i
$706$	−4.30416e9	+	1.93627e9i	−0.460333	+	0.207085i
$707$	8.16885e8	−	4.71629e8i	0.0869346	−	0.0501917i
$708$	2.63209e9	−	5.05384e9i	0.278730	−	0.535186i
$709$	1.47007e9	+	8.48746e8i	0.154909	+	0.0894367i	0.575451	−	0.817836i	$-0.304827\pi$
$709$	1.47007e9	+	8.48746e8i	0.154909	+	0.0894367i	−0.420542	+	0.907273i	$0.638160\pi$
$710$	−8.48304e9	−	8.58530e8i	−0.889503	−	0.0900225i
$711$	−1.00249e10	−	3.33613e8i	−1.04601	−	0.0348097i
$712$	−4.60524e9	+	1.47523e10i	−0.478159	+	1.53172i
$713$	−1.59672e9	−	9.21865e8i	−0.164974	−	0.0952476i
$714$	−6.18454e9	+	4.87865e9i	−0.635863	+	0.501598i
$715$	−7.29071e8	−	1.26279e9i	−0.0745931	−	0.129199i
$716$	3.33507e9	−	1.11215e9i	0.339554	−	0.113232i
$717$	−1.32175e9	+	1.27850e9i	−0.133916	+	0.129534i
$718$	5.55858e9	−	7.71313e9i	0.560439	−	0.777670i
$719$	−1.59659e10			−1.60192			−0.800962	−	0.598715i	$-0.795678\pi$
$719$	−1.59659e10			−1.60192			−0.800962	+	0.598715i	$0.795678\pi$
$720$	1.66553e10	−	1.45074e9i	1.66298	−	0.144852i
$721$	4.93078e9			0.489940
$722$	−1.43462e9	+	1.99069e9i	−0.141859	+	0.196844i
$723$	−1.16486e10	−	3.32984e9i	−1.14628	−	0.327672i
$724$	−2.81992e9	+	9.40363e8i	−0.276155	+	0.0920896i
$725$	3.31687e9	+	5.74499e9i	0.323255	+	0.559894i
$726$	1.32830e9	+	9.14089e9i	0.128831	+	0.886565i
$727$	7.82483e8	+	4.51767e8i	0.0755274	+	0.0436058i	0.537288	−	0.843399i	$-0.319449\pi$
$727$	7.82483e8	+	4.51767e8i	0.0755274	+	0.0436058i	−0.461761	+	0.887005i	$0.652782\pi$
$728$	1.45277e9	+	4.53514e8i	0.139552	+	0.0435643i
$729$	−1.04219e9	+	1.04083e10i	−0.0996329	+	0.995024i
$730$	3.47928e10	+	3.52122e9i	3.31024	+	0.335014i
$731$	3.70001e9	+	2.13620e9i	0.350342	+	0.202270i
$732$	1.60167e10	−	6.96240e8i	1.50933	−	0.0656100i
$733$	1.37445e10	−	7.93542e9i	1.28904	−	0.744228i	0.310557	−	0.950555i	$-0.399484\pi$
$733$	1.37445e10	−	7.93542e9i	1.28904	−	0.744228i	0.978483	+	0.206327i	$0.0661510\pi$
$734$	−8.13841e9	+	3.66114e9i	−0.759632	+	0.341727i
$735$	1.24636e10	+	3.56282e9i	1.15781	+	0.330970i
$736$	−1.09132e9	+	6.58463e8i	−0.100898	+	0.0608778i
$737$			4.26508e9i			0.392456i
$738$	5.11405e7	+	1.24600e8i	0.00468347	+	0.0114110i
$739$	−8.28207e9			−0.754890			−0.377445	−	0.926032i	$-0.623197\pi$
$739$	−8.28207e9			−0.754890			−0.377445	+	0.926032i	$0.623197\pi$
$740$	−1.75860e10	−	1.55905e10i	−1.59535	−	1.41433i
$741$	2.37739e9	+	2.45782e9i	0.214653	+	0.221915i
$742$	−6.10136e9	+	2.74475e9i	−0.548293	+	0.246655i
$743$	2.16543e9	+	3.75064e9i	0.193680	+	0.335463i	0.946467	−	0.322801i	$-0.104624\pi$
$743$	2.16543e9	+	3.75064e9i	0.193680	+	0.335463i	−0.752787	+	0.658264i	$0.771291\pi$
$744$	8.16207e9	+	1.62213e10i	0.726599	+	1.44405i
$745$	2.44494e9	−	4.23476e9i	0.216631	−	0.375216i
$746$	1.42853e9	−	1.41151e10i	0.125980	−	1.24480i
$747$	7.88850e9	+	2.62517e8i	0.692425	+	0.0230428i
$748$	5.55207e9	+	1.13543e9i	0.485065	+	0.0991984i
$749$	−3.79235e9	+	6.56854e9i	−0.329778	+	0.571193i
$750$	1.40903e10	+	5.61633e9i	1.21957	+	0.486114i
$751$	1.05813e10	−	6.10914e9i	0.911593	−	0.526309i	0.0306500	−	0.999530i	$-0.490242\pi$
$751$	1.05813e10	−	6.10914e9i	0.911593	−	0.526309i	0.880944	+	0.473221i	$0.156909\pi$
$752$	−1.38048e9	−	1.14342e10i	−0.118377	−	0.980490i
$753$	1.83028e8	−	4.57936e7i	0.0156220	−	0.00390861i
$754$	−9.57124e8	−	6.89765e8i	−0.0813146	−	0.0586005i
$755$			3.80586e10i			3.21839i
$756$	5.39858e9	−	3.19056e9i	0.454416	−	0.268559i
$757$		−	1.47780e10i		−	1.23817i	−0.785324	−	0.619085i	$-0.787504\pi$
$757$		−	1.47780e10i		−	1.23817i	0.785324	−	0.619085i	$-0.212496\pi$
$758$	−6.03656e9	+	8.37638e9i	−0.503440	+	0.698577i
$759$	4.44357e8	−	1.11178e8i	0.0368880	−	0.00922936i
$760$	−4.93656e9	−	2.19712e10i	−0.407922	−	1.81554i
$761$	1.56824e10	−	9.05423e9i	1.28993	−	0.744741i	0.311287	−	0.950316i	$-0.399240\pi$
$761$	1.56824e10	−	9.05423e9i	1.28993	−	0.744741i	0.978641	+	0.205575i	$0.0659065\pi$
$762$	−6.40089e9	+	1.60586e10i	−0.524081	+	1.31482i
$763$	3.21110e9	−	5.56178e9i	0.261708	−	0.453292i
$764$	−1.51515e10	−	3.09856e9i	−1.22922	−	0.251381i
$765$	1.67623e10	−	2.69235e10i	1.35369	−	2.17428i
$766$	2.95778e9	+	2.99344e8i	0.237775	+	0.0240641i
$767$	−1.04423e9	+	1.80867e9i	−0.0835630	+	0.144735i
$768$	1.25444e10	+	4.78562e8i	0.999273	+	0.0381218i
$769$	−2.87863e9	−	4.98594e9i	−0.228267	−	0.395371i	0.729027	−	0.684485i	$-0.239973\pi$
$769$	−2.87863e9	−	4.98594e9i	−0.228267	−	0.395371i	−0.957295	+	0.289114i	$0.906639\pi$
$770$	1.47769e9	+	3.28478e9i	0.116645	+	0.259291i
$771$	5.84008e9	+	6.03766e9i	0.458911	+	0.474437i
$772$	1.51836e10	−	1.71270e10i	1.18772	−	1.33974i
$773$	1.64149e10			1.27823			0.639117	−	0.769109i	$-0.279300\pi$
$773$	1.64149e10			1.27823			0.639117	+	0.769109i	$0.279300\pi$
$774$	−2.69166e9	−	2.07922e9i	−0.208654	−	0.161179i
$775$			3.74236e10i			2.88795i
$776$	−3.18782e7	+	2.93784e7i	−0.00244894	+	0.00225690i
$777$	−8.47582e9	−	2.42288e9i	−0.648199	−	0.185293i
$778$	6.90939e9	+	1.53590e10i	0.526031	+	1.16932i
$779$	1.57113e8	−	9.07092e7i	0.0119078	−	0.00687496i
$780$	−6.12174e9	+	2.66110e8i	−0.461896	+	0.0200784i
$781$	1.99258e9	+	1.15041e9i	0.149670	+	0.0864123i
$782$	−2.43463e8	+	2.40563e9i	−0.0182058	+	0.179889i
$783$	−4.75243e9	+	1.02239e9i	−0.353793	+	0.0761114i
$784$	8.95208e9	+	3.82132e9i	0.663465	+	0.283209i
$785$	−2.78727e10	−	1.60923e10i	−2.05653	−	1.18734i
$786$	1.35720e10	−	1.97220e9i	0.996929	−	0.144868i
$787$	−6.90250e9	−	1.19555e10i	−0.504772	−	0.874290i	−0.999985	−	0.00551864i	$-0.998243\pi$
$787$	−6.90250e9	−	1.19555e10i	−0.504772	−	0.874290i	0.495213	−	0.868772i	$-0.335090\pi$
$788$	−4.87367e8	−	1.46150e9i	−0.0354825	−	0.106404i
$789$	−1.80891e10	−	5.17091e9i	−1.31113	−	0.374798i
$790$	−1.96413e10	−	1.41548e10i	−1.41735	−	1.02143i
$791$	7.89372e9			0.567106
$792$	−4.25936e9	−	1.48684e9i	−0.304654	−	0.106347i
$793$	−5.87591e9			−0.418426
$794$	−9.61481e9	−	6.92905e9i	−0.681662	−	0.491250i
$795$	1.93612e10	−	1.87276e10i	1.36662	−	1.32190i
$796$	−1.36982e9	+	4.56795e8i	−0.0962648	+	0.0321015i
$797$	−4.42997e9	−	7.67294e9i	−0.309954	−	0.536856i	0.668398	−	0.743804i	$-0.266980\pi$
$797$	−4.42997e9	−	7.67294e9i	−0.309954	−	0.536856i	−0.978352	+	0.206948i	$0.933647\pi$
$798$	−5.23138e9	−	6.63168e9i	−0.364423	−	0.461969i
$799$	−1.89213e10	−	1.09242e10i	−1.31231	−	0.757665i
$800$	2.26505e10	+	1.25011e10i	1.56409	+	0.863241i
$801$	−1.09909e10	−	2.05892e10i	−0.755645	−	1.41555i
$802$	−1.16516e9	+	1.15128e10i	−0.0797582	+	0.788082i
$803$	−8.17246e9	−	4.71837e9i	−0.556991	−	0.321579i
$804$	1.58964e10	+	8.27900e9i	1.07870	+	0.561800i
$805$	−1.33090e9	+	7.68395e8i	−0.0899207	+	0.0519158i
$806$	−2.73050e9	−	6.06968e9i	−0.183683	−	0.408313i
$807$	3.46738e9	+	1.38585e10i	0.232244	+	0.928235i
$808$	−2.09697e9	+	1.93253e9i	−0.139847	+	0.128880i
$809$			1.38102e10i			0.917020i	0.888689	+	0.458510i	$0.151617\pi$
$809$			1.38102e10i			0.917020i	−0.888689	+	0.458510i	$0.848383\pi$
$810$	−1.60906e10	+	1.94564e10i	−1.06384	+	1.28637i
$811$	−1.46452e10			−0.964102			−0.482051	−	0.876143i	$-0.660108\pi$
$811$	−1.46452e10			−0.964102			−0.482051	+	0.876143i	$0.660108\pi$
$812$	2.18068e9	+	1.93323e9i	0.142937	+	0.126718i
$813$	1.65669e10	−	4.14504e9i	1.08125	−	0.270528i
$814$	2.60182e9	+	5.78363e9i	0.169080	+	0.375850i
$815$	−1.77604e10	−	3.07619e10i	−1.14922	−	1.99050i
$816$	1.50091e10	−	1.84891e10i	0.967025	−	1.19125i
$817$	−2.29065e9	+	3.96752e9i	−0.146954	+	0.254532i
$818$	−1.83272e10	−	1.85482e9i	−1.17074	−	0.118485i
$819$	−2.02758e9	+	1.08235e9i	−0.128969	+	0.0688455i
$820$	−6.51350e7	+	3.18500e8i	−0.00412540	+	0.0201726i
$821$	1.85995e9	−	3.22153e9i	0.117301	−	0.203171i	−0.801396	−	0.598133i	$-0.795909\pi$
$821$	1.85995e9	−	3.22153e9i	0.117301	−	0.203171i	0.918697	+	0.394963i	$0.129243\pi$
$822$	−1.58074e10	−	2.00387e10i	−0.992682	−	1.25840i
$823$	−2.42120e10	+	1.39788e10i	−1.51402	+	0.874120i	−0.514156	+	0.857697i	$0.671895\pi$
$823$	−2.42120e10	+	1.39788e10i	−1.51402	+	0.874120i	−0.999865	+	0.0164238i	$0.994772\pi$
$824$	−1.45442e10	+	3.26783e9i	−0.905616	+	0.203476i
$825$	−6.46406e9	−	6.68275e9i	−0.400789	−	0.414349i
$826$	3.01618e9	−	4.18527e9i	0.186220	−	0.258401i
$827$		−	8.11129e9i		−	0.498678i	−0.968416	−	0.249339i	$-0.919787\pi$
$827$		−	8.11129e9i		−	0.498678i	0.968416	−	0.249339i	$-0.0802134\pi$
$828$	4.48175e8	−	1.87197e9i	0.0274373	−	0.114602i
$829$		−	6.85479e9i		−	0.417882i	−0.977928	−	0.208941i	$-0.932998\pi$
$829$		−	6.85479e9i		−	0.417882i	0.977928	−	0.208941i	$-0.0670016\pi$
$830$	1.54556e10	+	1.11383e10i	0.938236	+	0.676154i
$831$	5.80237e8	−	2.02981e9i	0.0350753	−	0.122702i
$832$	−4.58574e9	−	3.74906e8i	−0.276044	−	0.0225679i
$833$	1.59910e10	−	9.23241e9i	0.958557	−	0.553423i
$834$	−1.62807e9	−	1.12038e10i	−0.0971836	−	0.668782i
$835$	−1.69337e10	+	2.93301e10i	−1.00658	+	1.74345i
$836$	−1.21752e9	+	5.95349e9i	−0.0720700	+	0.352411i
$837$	−2.61023e10	−	8.41021e9i	−1.53865	−	0.495756i
$838$	5.73380e8	−	5.66551e9i	0.0336580	−	0.332571i
$839$	6.91080e9	−	1.19699e10i	0.403981	−	0.699716i	−0.590221	−	0.807242i	$-0.700959\pi$
$839$	6.91080e9	−	1.19699e10i	0.403981	−	0.699716i	0.994202	+	0.107525i	$0.0342927\pi$
$840$	1.51110e10	+	8.68627e8i	0.879665	+	0.0505657i
$841$	7.49539e9	+	1.29824e10i	0.434519	+	0.752609i
$842$	3.72628e9	−	1.67630e9i	0.215121	−	0.0967743i
$843$	4.74936e9	−	1.66144e10i	0.273048	−	0.955187i
$844$	−1.09520e10	+	1.23538e10i	−0.627039	+	0.707297i
$845$	−2.70312e10			−1.54123
$846$	1.37648e10	+	1.06329e10i	0.781578	+	0.603745i
$847$			8.36266e9i			0.472882i
$848$	1.61779e10	−	1.21397e10i	0.911040	−	0.683634i
$849$	−6.17853e9	+	5.97633e9i	−0.346504	+	0.335164i
$850$	4.47580e10	−	2.01348e10i	2.49979	−	1.12456i
$851$	−2.34337e9	+	1.35294e9i	−0.130343	+	0.0752534i
$852$	8.15552e9	−	5.19345e9i	0.451765	−	0.287685i
$853$	1.48652e10	+	8.58244e9i	0.820068	+	0.473466i	0.850440	−	0.526072i	$-0.176336\pi$
$853$	1.48652e10	+	8.58244e9i	0.820068	+	0.473466i	−0.0303721	+	0.999539i	$0.509669\pi$
$854$	1.44407e10	+	1.46148e9i	0.793388	+	0.0802952i
$855$	2.88700e10	+	1.79742e10i	1.57967	+	0.983486i
$856$	6.83293e9	−	2.18884e10i	0.372348	−	1.19277i
$857$	7.43999e9	+	4.29548e9i	0.403775	+	0.233120i	0.688112	−	0.725605i	$-0.258440\pi$
$857$	7.43999e9	+	4.29548e9i	0.403775	+	0.233120i	−0.284336	+	0.958725i	$0.591773\pi$
$858$	1.53598e9	+	6.12234e8i	0.0830196	+	0.0330912i
$859$	−5.18682e9	−	8.98384e9i	−0.279206	−	0.483600i	0.691981	−	0.721915i	$-0.256738\pi$
$859$	−5.18682e9	−	8.98384e9i	−0.279206	−	0.483600i	−0.971188	+	0.238316i	$0.923405\pi$
$860$	−2.59702e9	−	7.78783e9i	−0.139229	−	0.417515i
$861$	2.95968e7	+	1.18293e8i	0.00158028	+	0.00631608i
$862$	1.23840e9	−	1.71842e9i	0.0658547	−	0.0913804i
$863$	1.91261e10			1.01295			0.506476	−	0.862254i	$-0.330948\pi$
$863$	1.91261e10			1.01295			0.506476	+	0.862254i	$0.330948\pi$
$864$	−1.38095e10	+	1.29889e10i	−0.728417	+	0.685134i
$865$	−1.43355e10			−0.753104
$866$	−1.68711e10	+	2.34105e10i	−0.882737	+	1.22489i
$867$	−6.30742e9	−	2.52096e10i	−0.328689	−	1.31371i
$868$	5.20084e9	+	1.55961e10i	0.269932	+	0.809461i
$869$	3.26656e9	+	5.65785e9i	0.168858	+	0.292471i
$870$	−1.08994e10	−	4.34443e9i	−0.561156	−	0.223674i
$871$	−5.68900e9	−	3.28455e9i	−0.291724	−	0.168427i
$872$	−5.78565e9	+	1.85335e10i	−0.295491	+	0.946566i
$873$	2.17749e6	−	6.54324e7i	0.000110766	−	0.00332846i
$874$	−2.57955e9	−	2.61065e8i	−0.130694	−	0.0132269i
$875$	1.18929e10	+	6.86638e9i	0.600151	+	0.346497i
$876$	−3.34495e10	+	2.13007e10i	−1.68122	+	1.07061i
$877$	−2.17091e10	+	1.25338e10i	−1.08678	+	0.627455i	−0.932719	−	0.360605i	$-0.882570\pi$
$877$	−2.17091e10	+	1.25338e10i	−1.08678	+	0.627455i	−0.154066	+	0.988061i	$0.549237\pi$
$878$	−1.22668e10	+	5.51835e9i	−0.611648	+	0.275156i
$879$	−5.13991e9	+	4.97170e9i	−0.255267	+	0.246913i
$880$	−6.53564e9	−	8.70968e9i	−0.323295	−	0.430837i
$881$			1.59664e10i			0.786669i	0.919395	+	0.393335i	$0.128679\pi$
$881$			1.59664e10i			0.786669i	−0.919395	+	0.393335i	$0.871321\pi$
$882$	−1.35988e10	+	5.58142e9i	−0.667358	+	0.273908i
$883$	−1.20485e10			−0.588939			−0.294469	−	0.955661i	$-0.595143\pi$
$883$	−1.20485e10			−0.588939			−0.294469	+	0.955661i	$0.595143\pi$
$884$	−5.79015e9	+	6.53126e9i	−0.281908	+	0.317990i
$885$	−5.70879e9	+	1.99707e10i	−0.276849	+	0.968483i
$886$	3.38046e10	−	1.52073e10i	1.63289	−	0.734572i
$887$	1.63725e9	+	2.83580e9i	0.0787738	+	0.136440i	0.902721	−	0.430226i	$-0.141566\pi$
$887$	1.63725e9	+	2.83580e9i	0.0787738	+	0.136440i	−0.823947	+	0.566666i	$0.808233\pi$
$888$	2.66066e10	+	1.52942e9i	1.27510	+	0.0732964i
$889$	−7.82556e9	+	1.35543e10i	−0.373559	+	0.647024i
$890$	5.67226e9	−	5.60470e10i	0.269706	−	2.66494i
$891$	6.11377e9	−	3.00675e9i	0.289559	−	0.142405i
$892$	−2.27256e9	+	1.11125e10i	−0.107211	+	0.524244i
$893$	1.17141e10	−	2.02893e10i	0.550462	−	0.953428i
$894$	7.97396e8	+	5.48739e9i	0.0373244	+	0.256853i
$895$	−1.10980e10	+	6.40745e9i	−0.517446	+	0.298748i
$896$	1.11767e10	+	2.06196e9i	0.519083	+	0.0957638i
$897$	−1.93905e8	+	6.78325e8i	−0.00897045	+	0.0313808i
$898$	1.59278e10	+	1.14786e10i	0.733989	+	0.528960i
$899$		−	1.27444e10i		−	0.585008i
$900$	−3.74547e10	+	1.11202e10i	−1.71261	+	0.508470i
$901$		−	3.83696e10i		−	1.74763i
$902$	5.12896e7	−	7.11698e7i	0.00232705	−	0.00322904i
$903$	−2.14087e9	−	2.21330e9i	−0.0967573	−	0.100031i
$904$	−2.32839e10	+	5.23149e9i	−1.04825	+	0.235524i
$905$	9.38380e9	−	5.41774e9i	0.420832	−	0.242967i
$906$	−2.67293e10	−	3.38841e10i	−1.19410	−	1.51373i
$907$	3.39562e9	−	5.88139e9i	0.151110	−	0.261730i	−0.780526	−	0.625124i	$-0.785049\pi$
$907$	3.39562e9	−	5.88139e9i	0.151110	−	0.261730i	0.931636	+	0.363393i	$0.118382\pi$
$908$	7.10569e9	−	3.47457e10i	0.314996	−	1.54028i
$909$	1.43237e8	−	4.30419e9i	0.00632529	−	0.190072i
$910$	−5.51938e9	−	5.58591e8i	−0.242798	−	0.0245725i
$911$	7.18939e9	−	1.24524e10i	0.315049	−	0.545680i	−0.664399	−	0.747378i	$-0.731312\pi$
$911$	7.18939e9	−	1.24524e10i	0.315049	−	0.545680i	0.979448	+	0.201698i	$0.0646458\pi$
$912$	1.98259e10	+	1.60942e10i	0.865468	+	0.702566i
$913$	−2.57043e9	−	4.45211e9i	−0.111778	−	0.193606i
$914$	4.20955e9	+	9.35749e9i	0.182358	+	0.405366i
$915$	−5.66908e10	+	1.41840e10i	−2.44646	+	0.612103i
$916$	1.06137e10	+	9.40937e9i	0.456282	+	0.404507i
$917$	1.24165e10			0.531748
$918$	3.98521e9	+	3.57428e10i	0.170021	+	1.52489i
$919$		−	2.30956e10i		−	0.981577i	−0.871279	−	0.490788i	$-0.836709\pi$
$919$		−	2.30956e10i		−	0.981577i	0.871279	−	0.490788i	$-0.163291\pi$
$920$	3.41647e9	−	3.14855e9i	0.144650	−	0.133307i
$921$	1.36408e9	+	5.45198e9i	0.0575350	+	0.229957i
$922$	−2.65372e9	−	5.89901e9i	−0.111506	−	0.247868i
$923$	−3.06897e9	+	1.77187e9i	−0.128465	+	0.0741696i
$924$	−3.62257e9	−	1.88667e9i	−0.151065	−	0.0786762i
$925$	4.75651e10	+	2.74617e10i	1.97603	+	1.14086i
$926$	−1.60699e9	+	1.58785e10i	−0.0665082	+	0.657160i
$927$	1.18983e10	−	1.91109e10i	0.490575	−	0.787958i
$928$	−7.71350e9	−	4.25718e9i	−0.316835	−	0.174865i
$929$	−5.38648e9	−	3.10988e9i	−0.220419	−	0.127259i	0.385725	−	0.922614i	$-0.373951\pi$
$929$	−5.38648e9	−	3.10988e9i	−0.220419	−	0.127259i	−0.606144	+	0.795355i	$0.707285\pi$
$930$	−4.09956e10	−	5.19691e10i	−1.67127	−	2.11863i
$931$	9.89991e9	+	1.71471e10i	0.402075	+	0.696415i
$932$	1.68034e10	−	5.60345e9i	0.679894	−	0.226725i
$933$	−2.47592e10	+	2.39490e10i	−0.998047	+	0.965386i
$934$	−1.92692e10	−	1.38867e10i	−0.773838	−	0.557678i
$935$	−2.06570e10			−0.826467
$936$	5.26337e9	−	4.53634e9i	0.209797	−	0.180818i
$937$	−9.98609e9			−0.396558			−0.198279	−	0.980146i	$-0.563535\pi$
$937$	−9.98609e9			−0.396558			−0.198279	+	0.980146i	$0.563535\pi$
$938$	1.31644e10	+	9.48712e9i	0.520824	+	0.375340i
$939$	1.31286e10	+	3.75290e9i	0.517473	+	0.147924i
$940$	1.32808e10	+	3.98259e10i	0.521526	+	1.56393i
$941$	2.01713e10	+	3.49377e10i	0.789169	+	1.36688i	0.926477	+	0.376352i	$0.122822\pi$
$941$	2.01713e10	+	3.49377e10i	0.789169	+	1.36688i	−0.137308	+	0.990528i	$0.543845\pi$
$942$	3.61173e10	−	5.24836e9i	1.40779	−	0.204572i
$943$	3.24150e7	+	1.87148e7i	0.00125879	+	0.000726766i
$944$	−6.12298e9	+	1.43441e10i	−0.236898	+	0.554972i
$945$	−1.69494e10	+	1.53370e10i	−0.653345	+	0.591192i
$946$	−2.23061e8	+	2.20404e9i	−0.00856653	+	0.0846450i
$947$	−4.93748e9	−	2.85066e9i	−0.188921	−	0.109074i	0.402556	−	0.915395i	$-0.368122\pi$
$947$	−4.93748e9	−	2.85066e9i	−0.188921	−	0.109074i	−0.591477	+	0.806322i	$0.701455\pi$
$948$	2.74282e10	−	1.19229e9i	1.04560	−	0.0454520i
$949$	1.25872e10	−	7.26725e9i	0.478078	−	0.276018i
$950$	2.15905e10	+	4.79940e10i	0.817016	+	1.81616i
$951$	2.03314e10	+	5.81189e9i	0.766541	+	0.219122i
$952$	1.58544e10	−	1.46111e10i	0.595554	−	0.548851i
$953$			2.86656e10i			1.07284i	0.843951	+	0.536421i	$0.180224\pi$
$953$			2.86656e10i			1.07284i	−0.843951	+	0.536421i	$0.819776\pi$
$954$	−4.08474e9	+	3.02712e10i	−0.152316	+	1.12878i
$955$	5.63723e10			2.09437
$956$	3.33892e9	−	3.76629e9i	0.123596	−	0.139415i
$957$	2.20130e9	+	2.27578e9i	0.0811873	+	0.0839340i
$958$	−2.02929e10	−	4.51095e10i	−0.745702	−	1.65764i
$959$	−1.15537e10	−	2.00115e10i	−0.423014	−	0.732682i
$960$	−4.51483e10	+	7.45254e9i	−1.64699	+	0.271866i
$961$	2.21920e10	−	3.84376e10i	0.806611	−	1.39709i
$962$	−9.71818e9	−	9.83533e8i	−0.351943	−	0.0356185i
$963$	1.63075e10	+	3.05489e10i	0.588429	+	1.10231i
$964$	3.24877e10	+	6.64390e9i	1.16802	+	0.238866i
$965$	−4.17155e10	+	7.22533e10i	−1.49435	+	2.58829i
$966$	6.45257e8	−	1.61883e9i	0.0230310	−	0.0577805i
$967$	1.97110e10	−	1.13802e10i	0.700997	−	0.404721i	−0.106722	−	0.994289i	$-0.534035\pi$
$967$	1.97110e10	−	1.13802e10i	0.700997	−	0.404721i	0.807719	+	0.589568i	$0.200702\pi$
$968$	−5.54227e9	−	2.46671e10i	−0.196392	−	0.874085i
$969$	4.69940e10	−	1.17579e10i	1.65924	−	0.415140i
$970$	9.23883e7	−	1.28199e8i	0.00325024	−	0.00451006i
$971$		−	4.79801e10i		−	1.68188i	−0.541132	−	0.840938i	$-0.682004\pi$
$971$		−	4.79801e10i		−	1.68188i	0.541132	−	0.840938i	$-0.317996\pi$
$972$	6.61024e8	−	2.86231e10i	0.0230880	−	0.999733i
$973$		−	1.02499e10i		−	0.356719i
$974$	3.89055e10	+	2.80378e10i	1.34913	+	0.972272i
$975$	1.38918e10	−	3.47572e9i	0.480001	−	0.120096i
$976$	−4.35638e10	+	5.25956e9i	−1.49986	+	0.181082i
$977$	1.56449e10	−	9.03258e9i	0.536712	−	0.309871i	−0.207033	−	0.978334i	$-0.566381\pi$
$977$	1.56449e10	−	9.03258e9i	0.536712	−	0.309871i	0.743745	+	0.668463i	$0.233047\pi$
$978$	3.74170e10	+	1.49142e10i	1.27904	+	0.509818i
$979$	−7.60073e9	+	1.31648e10i	−0.258890	+	0.448411i
$980$	−3.47607e10	−	7.10877e9i	−1.17977	−	0.241270i
$981$	−1.38080e10	−	2.58667e10i	−0.466971	−	0.874780i
$982$	−1.91461e9	+	1.89180e10i	−0.0645193	+	0.637508i
$983$	1.05604e10	−	1.82911e10i	0.354603	−	0.614191i	−0.632447	−	0.774604i	$-0.717949\pi$
$983$	1.05604e10	−	1.82911e10i	0.354603	−	0.614191i	0.987050	+	0.160413i	$0.0512826\pi$
$984$	−1.65698e8	−	3.29310e8i	−0.00554416	−	0.0110185i
$985$	2.80788e9	+	4.86339e9i	0.0936164	+	0.162148i
$986$	−1.52421e10	+	6.85680e9i	−0.506379	+	0.227799i
$987$	1.09481e10	+	1.13185e10i	0.362434	+	0.374696i
$988$	−7.00347e9	−	6.20878e9i	−0.231028	−	0.204813i
$989$	−9.45197e8			−0.0310696
$990$	1.62970e10	+	2.19909e9i	0.533808	+	0.0720312i
$991$		−	1.34218e10i		−	0.438079i	−0.975716	−	0.219040i	$-0.929708\pi$
$991$		−	1.34218e10i		−	0.438079i	0.975716	−	0.219040i	$-0.0702924\pi$
$992$	−2.56769e10	−	4.25564e10i	−0.835125	−	1.38412i
$993$	1.51596e10	+	4.33349e9i	0.491321	+	0.140448i
$994$	7.98303e9	−	3.59124e9i	0.257819	−	0.115982i
$995$	4.55832e9	−	2.63175e9i	0.146698	−	0.0846961i
$996$	−2.15829e10	+	9.38202e8i	−0.692154	+	0.0300877i
$997$	1.47069e9	+	8.49102e8i	0.0469989	+	0.0271348i	0.523315	−	0.852139i	$-0.324695\pi$
$997$	1.47069e9	+	8.49102e8i	0.0469989	+	0.0271348i	−0.476316	+	0.879274i	$0.658028\pi$
$998$	4.78312e10	+	4.84078e9i	1.52319	+	0.154155i
$999$	−2.98434e10	+	2.70044e10i	−0.947042	+	0.856949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.l.b.11.24	✓	160
8.3	odd	2	inner	72.8.l.b.11.52	yes	160
9.5	odd	6	inner	72.8.l.b.59.52	yes	160
72.59	even	6	inner	72.8.l.b.59.24	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.8.l.b.11.24	✓	160	1.1	even	1	trivial
72.8.l.b.11.52	yes	160	8.3	odd	2	inner
72.8.l.b.59.24	yes	160	72.59	even	6	inner
72.8.l.b.59.52	yes	160	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.61467 + 9.17857i) q^{2} +(11.3508 + 45.3669i) q^{3} +(-40.4922 - 121.426i) q^{4} +(233.289 + 404.068i) q^{5} +(-491.485 - 195.904i) q^{6} +(-414.838 - 239.507i) q^{7} +(1382.36 + 431.535i) q^{8} +(-1929.32 + 1029.90i) q^{9} +O(q^{10})\)	\(q+(-6.61467 + 9.17857i) q^{2} +(11.3508 + 45.3669i) q^{3} +(-40.4922 - 121.426i) q^{4} +(233.289 + 404.068i) q^{5} +(-491.485 - 195.904i) q^{6} +(-414.838 - 239.507i) q^{7} +(1382.36 + 431.535i) q^{8} +(-1929.32 + 1029.90i) q^{9} +(-5251.90 - 531.521i) q^{10} +(1233.61 + 712.228i) q^{11} +(5049.13 - 3215.29i) q^{12} +(-1900.02 + 1096.97i) q^{13} +(4942.34 - 2223.36i) q^{14} +(-15683.3 + 15170.1i) q^{15} +(-13104.8 + 9833.66i) q^{16} +31080.9i q^{17} +(3308.80 - 24520.8i) q^{18} -33328.0 q^{19} +(39618.2 - 44689.1i) q^{20} +(6156.95 - 21538.5i) q^{21} +(-14697.2 + 6611.66i) q^{22} +(-3438.06 - 5954.89i) q^{23} +(-3886.53 + 67611.9i) q^{24} +(-69785.0 + 120871. i) q^{25} +(2499.32 - 24695.5i) q^{26} +(-68622.7 - 75837.2i) q^{27} +(-12284.7 + 60070.4i) q^{28} +(23764.9 - 41162.1i) q^{29} +(-35499.7 - 244296. i) q^{30} +(232212. - 134068. i) q^{31} +(-3575.20 - 185329. i) q^{32} +(-18309.1 + 64049.7i) q^{33} +(-285278. - 205590. i) q^{34} -223497. i q^{35} +(203180. + 192567. i) q^{36} -393519. i q^{37} +(220454. - 305903. i) q^{38} +(-71333.0 - 73746.4i) q^{39} +(148120. + 659242. i) q^{40} +(-4714.14 + 2721.71i) q^{41} +(156966. + 198982. i) q^{42} +(68730.4 - 119045. i) q^{43} +(36531.5 - 178633. i) q^{44} +(-866239. - 539312. i) q^{45} +(77399.0 + 7833.20i) q^{46} +(-351478. + 608777. i) q^{47} +(-594872. - 482903. i) q^{48} +(-297045. - 514497. i) q^{49} +(-647819. - 1.44005e6i) q^{50} +(-1.41004e6 + 352792. i) q^{51} +(210138. + 186293. i) q^{52} -1.23451e6 q^{53} +(1.14999e6 - 128221. i) q^{54} +664619. i q^{55} +(-470101. - 510102. i) q^{56} +(-378299. - 1.51199e6i) q^{57} +(220612. + 490402. i) q^{58} +(824388. - 475961. i) q^{59} +(2.47710e6 + 1.29010e6i) q^{60} +(2.31942e6 + 1.33912e6i) q^{61} +(-305457. + 3.01819e6i) q^{62} +(1.04702e6 + 34843.2i) q^{63} +(1.72471e6 + 1.19308e6i) q^{64} +(-886505. - 511824. i) q^{65} +(-466776. - 591719. i) q^{66} +(1.49709e6 + 2.59304e6i) q^{67} +(3.77404e6 - 1.25853e6i) q^{68} +(231131. - 223567. i) q^{69} +(2.05138e6 + 1.47836e6i) q^{70} +1.61523e6 q^{71} +(-3.11146e6 + 591128. i) q^{72} -6.62481e6 q^{73} +(3.61195e6 + 2.60300e6i) q^{74} +(-6.27567e6 - 1.79395e6i) q^{75} +(1.34953e6 + 4.04690e6i) q^{76} +(-341166. - 590918. i) q^{77} +(1.14873e6 - 166927. i) q^{78} +(3.97194e6 + 2.29320e6i) q^{79} +(-7.03066e6 - 3.00113e6i) q^{80} +(2.66158e6 - 3.97401e6i) q^{81} +(6201.09 - 61272.3i) q^{82} +(-3.12548e6 - 1.80450e6i) q^{83} +(-2.86465e6 + 124525. i) q^{84} +(-1.25588e7 + 7.25082e6i) q^{85} +(638030. + 1.41829e6i) q^{86} +(2.13715e6 + 610921. i) q^{87} +(1.39795e6 + 1.51691e6i) q^{88} +1.06718e7i q^{89} +(1.06800e7 - 4.38346e6i) q^{90} +1.05093e6 q^{91} +(-583867. + 658598. i) q^{92} +(8.71803e6 + 9.01298e6i) q^{93} +(-3.26279e6 - 7.25293e6i) q^{94} +(-7.77506e6 - 1.34668e7i) q^{95} +(8.36724e6 - 2.26583e6i) q^{96} +(-14967.7 + 25924.8i) q^{97} +(6.68720e6 + 676781. i) q^{98} +(-3.11356e6 - 103614. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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