LMFDB - Embedded newform 72.8.l.b.11.48

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			11.48
Character	$\chi$	$=$	72.11
Dual form			72.8.l.b.59.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.47193 + 10.7678i) q^{2} +(-25.6457 - 39.1063i) q^{3} +(-103.891 + 74.7702i) q^{4} +(-98.8581 - 171.227i) q^{5} +(332.048 - 411.922i) q^{6} +(-950.958 - 549.036i) q^{7} +(-1165.82 - 859.085i) q^{8} +(-871.598 + 2005.81i) q^{9} +O(q^{10})$	\(q+(3.47193 + 10.7678i) q^{2} +(-25.6457 - 39.1063i) q^{3} +(-103.891 + 74.7702i) q^{4} +(-98.8581 - 171.227i) q^{5} +(332.048 - 411.922i) q^{6} +(-950.958 - 549.036i) q^{7} +(-1165.82 - 859.085i) q^{8} +(-871.598 + 2005.81i) q^{9} +(1500.51 - 1658.97i) q^{10} +(3226.13 + 1862.60i) q^{11} +(5588.35 + 2145.27i) q^{12} +(730.005 - 421.469i) q^{13} +(2610.25 - 12145.9i) q^{14} +(-4160.77 + 8257.21i) q^{15} +(5202.82 - 15536.0i) q^{16} +13521.6i q^{17} +(-24624.3 - 2421.15i) q^{18} +21892.6 q^{19} +(23073.2 + 10397.4i) q^{20} +(2917.23 + 51268.8i) q^{21} +(-8855.27 + 41205.1i) q^{22} +(30461.1 + 52760.2i) q^{23} +(-3697.45 + 67622.5i) q^{24} +(19516.6 - 33803.8i) q^{25} +(7072.82 + 6397.24i) q^{26} +(100793. - 17355.5i) q^{27} +(139848. - 14063.3i) q^{28} +(-47452.0 + 82189.2i) q^{29} +(-103358. - 16133.9i) q^{30} +(-41282.9 + 23834.7i) q^{31} +(185352. + 2083.15i) q^{32} +(-9896.70 - 173929. i) q^{33} +(-145598. + 46946.2i) q^{34} +217106. i q^{35} +(-59423.6 - 273556. i) q^{36} +168256. i q^{37} +(76009.8 + 235736. i) q^{38} +(-35203.5 - 17738.9i) q^{39} +(-31848.4 + 284547. i) q^{40} +(-118889. + 68640.3i) q^{41} +(-541924. + 209414. i) q^{42} +(-389691. + 674965. i) q^{43} +(-474434. + 47709.7i) q^{44} +(429614. - 49049.5i) q^{45} +(-462353. + 511179. i) q^{46} +(527377. - 913444. i) q^{47} +(-740983. + 194967. i) q^{48} +(191109. + 331010. i) q^{49} +(431754. + 92786.8i) q^{50} +(528781. - 346772. i) q^{51} +(-44327.9 + 98369.6i) q^{52} -777411. q^{53} +(536826. + 1.02506e6i) q^{54} -736534. i q^{55} +(636973. + 1.45703e6i) q^{56} +(-561452. - 856139. i) q^{57} +(-1.04975e6 - 225598. i) q^{58} +(2.18187e6 - 1.25970e6i) q^{59} +(-185125. - 1.16895e6i) q^{60} +(849675. + 490560. i) q^{61} +(-399979. - 361774. i) q^{62} +(1.93012e6 - 1.42890e6i) q^{63} +(621099. + 2.00307e6i) q^{64} +(-144334. - 83331.2i) q^{65} +(1.83848e6 - 710437. i) q^{66} +(1.88942e6 + 3.27257e6i) q^{67} +(-1.01102e6 - 1.40478e6i) q^{68} +(1.28206e6 - 2.54429e6i) q^{69} +(-2.33776e6 + 753779. i) q^{70} +5.08282e6 q^{71} +(2.73929e6 - 1.58963e6i) q^{72} -906322. q^{73} +(-1.81175e6 + 584175. i) q^{74} +(-1.82246e6 + 103699. i) q^{75} +(-2.27446e6 + 1.63692e6i) q^{76} +(-2.04527e6 - 3.54252e6i) q^{77} +(68784.8 - 440653. i) q^{78} +(1.71450e6 + 989868. i) q^{79} +(-3.17452e6 + 644991. i) q^{80} +(-3.26360e6 - 3.49653e6i) q^{81} +(-1.15188e6 - 1.04185e6i) q^{82} +(-5.96595e6 - 3.44444e6i) q^{83} +(-4.13645e6 - 5.10826e6i) q^{84} +(2.31527e6 - 1.33672e6i) q^{85} +(-8.62088e6 - 1.85269e6i) q^{86} +(4.43105e6 - 252130. i) q^{87} +(-2.16093e6 - 4.94297e6i) q^{88} +5.79858e6i q^{89} +(2.01975e6 + 4.45571e6i) q^{90} -925605. q^{91} +(-7.10954e6 - 3.20374e6i) q^{92} +(1.99082e6 + 1.00316e6i) q^{93} +(1.16668e7 + 2.50728e6i) q^{94} +(-2.16427e6 - 3.74862e6i) q^{95} +(-4.67202e6 - 7.30185e6i) q^{96} +(5.60226e6 - 9.70339e6i) q^{97} +(-2.90073e6 + 3.20707e6i) q^{98} +(-6.54792e6 + 4.84756e6i) 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 $

$2$	3.47193	+	10.7678i	0.306879	+	0.951749i
$2$	3.47193	+	10.7678i	0.306879	+	0.951749i
$3$	−25.6457	−	39.1063i	−0.548390	−	0.836222i
$3$	−25.6457	−	39.1063i	−0.548390	−	0.836222i
$4$	−103.891	+	74.7702i	−0.811651	+	0.584142i
$5$	−98.8581	−	171.227i	−0.353686	−	0.612601i	0.633207	−	0.773983i	$-0.281738\pi$
$5$	−98.8581	−	171.227i	−0.353686	−	0.612601i	−0.986892	+	0.161382i	$0.948405\pi$
$6$	332.048	−	411.922i	0.627584	−	0.778549i
$7$	−950.958	−	549.036i	−1.04790	−	0.605003i	−0.125836	−	0.992051i	$-0.540161\pi$
$7$	−950.958	−	549.036i	−1.04790	−	0.605003i	−0.922059	+	0.387048i	$0.873495\pi$
$8$	−1165.82	−	859.085i	−0.805035	−	0.593227i
$9$	−871.598	+	2005.81i	−0.398536	+	0.917153i
$10$	1500.51	−	1658.97i	0.474504	−	0.524614i
$11$	3226.13	+	1862.60i	0.730814	+	0.421936i	0.818720	−	0.574193i	$-0.194684\pi$
$11$	3226.13	+	1862.60i	0.730814	+	0.421936i	−0.0879059	+	0.996129i	$0.528017\pi$
$12$	5588.35	+	2145.27i	0.933575	+	0.358383i
$13$	730.005	−	421.469i	0.0921561	−	0.0532064i	−0.453214	−	0.891402i	$-0.649723\pi$
$13$	730.005	−	421.469i	0.0921561	−	0.0532064i	0.545370	+	0.838196i	$0.316389\pi$
$14$	2610.25	−	12145.9i	0.254234	−	1.18300i
$15$	−4160.77	+	8257.21i	−0.318313	+	0.631704i
$16$	5202.82	−	15536.0i	0.317555	−	0.948240i
$17$			13521.6i			0.667510i	0.942660	+	0.333755i	$0.108316\pi$
$17$			13521.6i			0.667510i	−0.942660	+	0.333755i	$0.891684\pi$
$18$	−24624.3	−	2421.15i	−0.995201	−	0.0978516i
$19$	21892.6			0.732252			0.366126	−	0.930565i	$-0.380684\pi$
$19$	21892.6			0.732252			0.366126	+	0.930565i	$0.380684\pi$
$20$	23073.2	+	10397.4i	0.644916	+	0.290616i
$21$	2917.23	+	51268.8i	0.0687389	+	1.20805i
$22$	−8855.27	+	41205.1i	−0.177306	+	0.825034i
$23$	30461.1	+	52760.2i	0.522033	+	0.904189i	0.999671	+	0.0256318i	$0.00815974\pi$
$23$	30461.1	+	52760.2i	0.522033	+	0.904189i	−0.477638	+	0.878557i	$0.658507\pi$
$24$	−3697.45	+	67622.5i	−0.0545963	+	0.998509i
$25$	19516.6	−	33803.8i	0.249813	−	0.432689i
$26$	7072.82	+	6397.24i	0.0789198	+	0.0713816i
$27$	100793.	−	17355.5i	0.985497	−	0.169693i
$28$	139848.	−	14063.3i	1.20393	−	0.121069i
$29$	−47452.0	+	82189.2i	−0.361295	+	0.625780i	−0.988174	−	0.153336i	$-0.950998\pi$
$29$	−47452.0	+	82189.2i	−0.361295	+	0.625780i	0.626880	+	0.779116i	$0.284332\pi$
$30$	−103358.	−	16133.9i	−0.698907	−	0.109098i
$31$	−41282.9	+	23834.7i	−0.248888	+	0.143696i	−0.619255	−	0.785190i	$-0.712565\pi$
$31$	−41282.9	+	23834.7i	−0.248888	+	0.143696i	0.370367	+	0.928886i	$0.379232\pi$
$32$	185352.	+	2083.15i	0.999937	+	0.0112382i
$33$	−9896.70	−	173929.i	−0.0479393	−	0.842508i
$34$	−145598.	+	46946.2i	−0.635302	+	0.204845i
$35$			217106.i			0.855923i
$36$	−59423.6	−	273556.i	−0.212276	−	0.977210i
$37$			168256.i			0.546091i	0.962001	+	0.273046i	$0.0880310\pi$
$37$			168256.i			0.546091i	−0.962001	+	0.273046i	$0.911969\pi$
$38$	76009.8	+	235736.i	0.224712	+	0.696920i
$39$	−35203.5	−	17738.9i	−0.0950299	−	0.0478852i
$40$	−31848.4	+	284547.i	−0.0786824	+	0.702981i
$41$	−118889.	+	68640.3i	−0.269399	+	0.155538i	−0.628615	−	0.777717i	$-0.716378\pi$
$41$	−118889.	+	68640.3i	−0.269399	+	0.155538i	0.359215	+	0.933255i	$0.383044\pi$
$42$	−541924.	+	209414.i	−1.12867	+	0.436147i
$43$	−389691.	+	674965.i	−0.747448	+	1.29462i	0.201594	+	0.979469i	$0.435388\pi$
$43$	−389691.	+	674965.i	−0.747448	+	1.29462i	−0.949042	+	0.315149i	$0.897946\pi$
$44$	−474434.	+	47709.7i	−0.839636	+	0.0844350i
$45$	429614.	−	49049.5i	0.702805	−	0.0802400i
$46$	−462353.	+	511179.i	−0.700359	+	0.774321i
$47$	527377.	−	913444.i	0.740933	−	1.28333i	−0.211138	−	0.977456i	$-0.567717\pi$
$47$	527377.	−	913444.i	0.740933	−	1.28333i	0.952071	−	0.305877i	$-0.0989498\pi$
$48$	−740983.	+	194967.i	−0.967084	+	0.254459i
$49$	191109.	+	331010.i	0.232057	+	0.401934i
$50$	431754.	+	92786.8i	0.488473	+	0.104976i
$51$	528781.	−	346772.i	0.558187	−	0.366056i
$52$	−44327.9	+	98369.6i	−0.0437185	+	0.0970173i
$53$	−777411.			−0.717274			−0.358637	−	0.933477i	$-0.616758\pi$
$53$	−777411.			−0.717274			−0.358637	+	0.933477i	$0.616758\pi$
$54$	536826.	+	1.02506e6i	0.463933	+	0.885870i
$55$		−	736534.i		−	0.596930i
$56$	636973.	+	1.45703e6i	0.484689	+	1.10869i
$57$	−561452.	−	856139.i	−0.401560	−	0.612326i
$58$	−1.04975e6	−	225598.i	−0.706459	−	0.151823i
$59$	2.18187e6	−	1.25970e6i	1.38308	−	0.798520i	0.390554	−	0.920580i	$-0.372284\pi$
$59$	2.18187e6	−	1.25970e6i	1.38308	−	0.798520i	0.992523	+	0.122061i	$0.0389502\pi$
$60$	−185125.	−	1.16895e6i	−0.110646	−	0.698664i
$61$	849675.	+	490560.i	0.479290	+	0.276718i	0.720121	−	0.693849i	$-0.244086\pi$
$61$	849675.	+	490560.i	0.479290	+	0.276718i	−0.240830	+	0.970567i	$0.577420\pi$
$62$	−399979.	−	361774.i	−0.213141	−	0.192782i
$63$	1.93012e6	−	1.42890e6i	0.972504	−	0.719965i
$64$	621099.	+	2.00307e6i	0.296163	+	0.955137i
$65$	−144334.	−	83331.2i	−0.0651886	−	0.0376366i
$66$	1.83848e6	−	710437.i	0.787145	−	0.304174i
$67$	1.88942e6	+	3.27257e6i	0.767479	+	1.32931i	0.938926	+	0.344119i	$0.111822\pi$
$67$	1.88942e6	+	3.27257e6i	0.767479	+	1.32931i	−0.171447	+	0.985193i	$0.554844\pi$
$68$	−1.01102e6	−	1.40478e6i	−0.389921	−	0.541786i
$69$	1.28206e6	−	2.54429e6i	0.469825	−	0.932384i
$70$	−2.33776e6	+	753779.i	−0.814623	+	0.262664i
$71$	5.08282e6			1.68539			0.842695	−	0.538391i	$-0.180968\pi$
$71$	5.08282e6			1.68539			0.842695	+	0.538391i	$0.180968\pi$
$72$	2.73929e6	−	1.58963e6i	0.864915	−	0.501918i
$73$	−906322.			−0.272679			−0.136340	−	0.990662i	$-0.543534\pi$
$73$	−906322.			−0.272679			−0.136340	+	0.990662i	$0.543534\pi$
$74$	−1.81175e6	+	584175.i	−0.519742	+	0.167584i
$75$	−1.82246e6	+	103699.i	−0.498819	+	0.0283831i
$76$	−2.27446e6	+	1.63692e6i	−0.594333	+	0.427740i
$77$	−2.04527e6	−	3.54252e6i	−0.510544	−	0.884289i
$78$	68784.8	−	440653.i	0.0164120	−	0.105139i
$79$	1.71450e6	+	989868.i	0.391240	+	0.225882i	0.682697	−	0.730701i	$-0.260807\pi$
$79$	1.71450e6	+	989868.i	0.391240	+	0.225882i	−0.291457	+	0.956584i	$0.594140\pi$
$80$	−3.17452e6	+	644991.i	−0.693208	+	0.140844i
$81$	−3.26360e6	−	3.49653e6i	−0.682338	−	0.731037i
$82$	−1.15188e6	−	1.04185e6i	−0.230706	−	0.208669i
$83$	−5.96595e6	−	3.44444e6i	−1.14527	−	0.661220i	−0.197537	−	0.980295i	$-0.563294\pi$
$83$	−5.96595e6	−	3.44444e6i	−1.14527	−	0.661220i	−0.947729	+	0.319076i	$0.896627\pi$
$84$	−4.13645e6	−	5.10826e6i	−0.761466	−	0.940363i
$85$	2.31527e6	−	1.33672e6i	0.408918	−	0.236089i
$86$	−8.62088e6	−	1.85269e6i	−1.46153	−	0.314092i
$87$	4.43105e6	−	252130.i	0.721422	−	0.0410494i
$88$	−2.16093e6	−	4.94297e6i	−0.338027	−	0.773212i
$89$			5.79858e6i			0.871881i	0.899976	+	0.435940i	$0.143584\pi$
$89$			5.79858e6i			0.871881i	−0.899976	+	0.435940i	$0.856416\pi$
$90$	2.01975e6	+	4.45571e6i	0.292044	+	0.644270i
$91$	−925605.			−0.128760
$92$	−7.10954e6	−	3.20374e6i	−0.951884	−	0.428944i
$93$	1.99082e6	+	1.00316e6i	0.256650	+	0.129325i
$94$	1.16668e7	+	2.50728e6i	1.44879	+	0.311354i
$95$	−2.16427e6	−	3.74862e6i	−0.258987	−	0.448579i
$96$	−4.67202e6	−	7.30185e6i	−0.538958	−	0.842333i
$97$	5.60226e6	−	9.70339e6i	0.623249	−	1.07950i	−0.365627	−	0.930761i	$-0.619145\pi$
$97$	5.60226e6	−	9.70339e6i	0.623249	−	1.07950i	0.988877	−	0.148738i	$-0.0475212\pi$
$98$	−2.90073e6	+	3.20707e6i	−0.311327	+	0.344205i
$99$	−6.54792e6	+	4.84756e6i	−0.678235	+	0.502111i
$100$	499909.	+	4.97119e6i	0.0499909	+	0.497119i
$101$	6.08433e6	−	1.05384e7i	0.587608	−	1.01777i	−0.406937	−	0.913456i	$-0.633403\pi$
$101$	6.08433e6	−	1.05384e7i	0.587608	−	1.01777i	0.994545	−	0.104311i	$-0.0332637\pi$
$102$	5.56986e6	+	4.48984e6i	0.519689	+	0.418919i
$103$	−3.66737e6	+	2.11736e6i	−0.330693	+	0.190926i	−0.656149	−	0.754632i	$-0.727816\pi$
$103$	−3.66737e6	+	2.11736e6i	−0.330693	+	0.190926i	0.325456	+	0.945557i	$0.394482\pi$
$104$	−1.21313e6	−	135781.i	−0.105752	−	0.0118365i
$105$	8.49022e6	−	5.56784e6i	0.715742	−	0.469380i
$106$	−2.69912e6	−	8.37102e6i	−0.220116	−	0.682665i
$107$			2.39408e7i			1.88927i	0.328119	+	0.944637i	$0.393585\pi$
$107$			2.39408e7i			1.88927i	−0.328119	+	0.944637i	$0.606415\pi$
$108$	−9.17380e6	+	9.33937e6i	−0.700755	+	0.713402i
$109$			1.62490e7i			1.20180i	0.799322	+	0.600902i	$0.205192\pi$
$109$			1.62490e7i			1.20180i	−0.799322	+	0.600902i	$0.794808\pi$
$110$	7.93086e6	−	2.55720e6i	0.568127	−	0.183185i
$111$	6.57987e6	−	4.31505e6i	0.456654	−	0.299471i
$112$	−1.34775e7	+	1.19175e7i	−0.906452	+	0.801535i
$113$	−1.18730e6	+	685490.i	−0.0774082	+	0.0446917i	−0.538205	−	0.842814i	$-0.680897\pi$
$113$	−1.18730e6	+	685490.i	−0.0774082	+	0.0446917i	0.460796	+	0.887506i	$0.347564\pi$
$114$	7.26942e6	−	9.01807e6i	0.459550	−	0.570094i
$115$	6.02266e6	−	1.04315e7i	0.369271	−	0.639597i
$116$	−1.21546e6	−	1.20867e7i	−0.0722999	−	0.718963i
$117$	209116.	+	1.83160e6i	0.0120708	+	0.105726i
$118$	2.11395e7	+	1.91203e7i	1.18443	+	1.07129i
$119$	7.42386e6	−	1.28585e7i	0.403846	−	0.699481i
$120$	1.19443e7	−	6.05193e6i	0.630998	−	0.319712i
$121$	−2.80500e6	−	4.85840e6i	−0.143941	−	0.249313i
$122$	−2.33224e6	+	1.08523e7i	−0.116282	+	0.541083i
$123$	5.73324e6	+	2.88896e6i	0.277800	+	0.139982i
$124$	2.50681e6	−	5.56296e6i	0.118072	−	0.262017i
$125$	−2.31641e7			−1.06079
$126$	2.20874e7	+	1.58221e7i	0.983666	+	0.704638i
$127$			4.43984e7i			1.92333i	0.274220	+	0.961667i	$0.411580\pi$
$127$			4.43984e7i			1.92333i	−0.274220	+	0.961667i	$0.588420\pi$
$128$	−1.94122e7	+	1.36424e7i	−0.818165	+	0.574984i
$129$	3.63893e7	−	2.07057e6i	1.49248	−	0.0849232i
$130$	396176.	−	1.84348e6i	0.0158156	−	0.0735930i
$131$	−5.81110e6	+	3.35504e6i	−0.225844	+	0.130391i	−0.608653	−	0.793436i	$-0.708290\pi$
$131$	−5.81110e6	+	3.35504e6i	−0.225844	+	0.130391i	0.382809	+	0.923827i	$0.374957\pi$
$132$	1.40329e7	+	1.73298e7i	0.531055	+	0.655820i
$133$	−2.08190e7	−	1.20198e7i	−0.767324	−	0.443015i
$134$	−2.86785e7	+	3.17070e7i	−1.02965	+	1.13838i
$135$	−1.29359e7	−	1.55427e7i	−0.452510	−	0.543699i
$136$	1.16162e7	−	1.57637e7i	0.395985	−	0.537369i
$137$	−3.63317e7	−	2.09761e7i	−1.20716	−	0.696953i	−0.245020	−	0.969518i	$-0.578795\pi$
$137$	−3.63317e7	−	2.09761e7i	−1.20716	−	0.696953i	−0.962137	+	0.272565i	$0.912128\pi$
$138$	3.18477e7	+	4.97134e6i	1.03157	+	0.161026i
$139$	2.13569e7	+	3.69912e7i	0.674507	+	1.16828i	0.976613	+	0.215005i	$0.0689769\pi$
$139$	2.13569e7	+	3.69912e7i	0.674507	+	1.16828i	−0.302106	+	0.953274i	$0.597690\pi$
$140$	−1.62331e7	−	2.25555e7i	−0.499981	−	0.694711i
$141$	−4.92463e7	+	2.80215e6i	−1.47947	+	0.0841830i
$142$	1.76472e7	+	5.47308e7i	0.517210	+	1.60407i
$143$	3.14012e6			0.0897986
$144$	2.66275e7	+	2.39770e7i	0.743124	+	0.669154i
$145$	1.87641e7			0.511139
$146$	−3.14669e6	−	9.75910e6i	−0.0836795	−	0.259522i
$147$	8.04345e6	−	1.59625e7i	0.208849	−	0.414468i
$148$	−1.25806e7	−	1.74804e7i	−0.318995	−	0.443236i
$149$	−3.11480e6	−	5.39499e6i	−0.0771398	−	0.133610i	0.824875	−	0.565315i	$-0.191245\pi$
$149$	−3.11480e6	−	5.39499e6i	−0.0771398	−	0.133610i	−0.902015	+	0.431705i	$0.857912\pi$
$150$	−7.44407e6	−	1.92638e7i	−0.180091	−	0.466040i
$151$	4.68514e7	+	2.70496e7i	1.10740	+	0.639355i	0.938154	−	0.346219i	$-0.112535\pi$
$151$	4.68514e7	+	2.70496e7i	1.10740	+	0.639355i	0.169242	+	0.985575i	$0.445868\pi$
$152$	−2.55228e7	−	1.88076e7i	−0.589489	−	0.434392i
$153$	−2.71219e7	−	1.17854e7i	−0.612209	−	0.266027i
$154$	3.10441e7	−	3.43225e7i	0.684946	−	0.757279i
$155$	8.16231e6	+	4.71251e6i	0.176056	+	0.101646i
$156$	4.98369e6	−	789257.i	0.105103	−	0.0166449i
$157$	−6.15194e7	+	3.55183e7i	−1.26871	+	0.732492i	−0.974745	−	0.223323i	$-0.928310\pi$
$157$	−6.15194e7	+	3.55183e7i	−1.26871	+	0.732492i	−0.293969	+	0.955815i	$0.594976\pi$
$158$	−4.70607e6	+	2.18982e7i	−0.0949202	+	0.441680i
$159$	1.99372e7	+	3.04016e7i	0.393346	+	0.599801i
$160$	−1.79669e7	−	3.19433e7i	−0.346779	−	0.616537i
$161$		−	6.68969e7i		−	1.26333i
$162$	2.63189e7	−	4.72815e7i	0.486368	−	0.873754i
$163$	−5.40664e6			−0.0977847			−0.0488924	−	0.998804i	$-0.515569\pi$
$163$	−5.40664e6			−0.0977847			−0.0488924	+	0.998804i	$0.515569\pi$
$164$	7.21923e6	−	1.60205e7i	0.127802	−	0.283610i
$165$	−2.88031e7	+	1.88889e7i	−0.499166	+	0.327351i
$166$	1.63757e7	−	7.61991e7i	0.277857	−	1.29292i
$167$	2.34103e6	+	4.05478e6i	0.0388955	+	0.0673689i	0.884818	−	0.465937i	$-0.154283\pi$
$167$	2.34103e6	+	4.05478e6i	0.0388955	+	0.0673689i	−0.845922	+	0.533306i	$0.820949\pi$
$168$	4.06433e7	−	6.22761e7i	0.661312	−	1.01330i
$169$	−3.10190e7	+	5.37265e7i	−0.494338	+	0.856219i
$170$	2.24321e7	+	2.02894e7i	0.350185	+	0.316736i
$171$	−1.90816e7	+	4.39126e7i	−0.291829	+	0.671587i
$172$	−9.98175e6	−	9.92603e7i	−0.149574	−	1.48739i
$173$	−1.00379e7	+	1.73861e7i	−0.147394	+	0.255294i	−0.930264	−	0.366892i	$-0.880422\pi$
$173$	−1.00379e7	+	1.73861e7i	−0.147394	+	0.255294i	0.782870	+	0.622186i	$0.213755\pi$
$174$	1.80992e7	+	4.68373e7i	0.260458	+	0.674015i
$175$	−3.71190e7	+	2.14307e7i	−0.523556	+	0.302275i
$176$	4.57223e7	−	4.04302e7i	0.632170	−	0.558999i
$177$	−1.05218e8	−	5.30187e7i	−1.42621	−	0.718659i
$178$	−6.24380e7	+	2.01323e7i	−0.829811	+	0.267561i
$179$			9.95579e7i			1.29745i	0.761023	+	0.648724i	$0.224697\pi$
$179$			9.95579e7i			1.29745i	−0.761023	+	0.648724i	$0.775303\pi$
$180$	−4.09658e7	+	3.72182e7i	−0.523561	+	0.475665i
$181$			1.37091e8i			1.71844i	0.511605	+	0.859221i	$0.329051\pi$
$181$			1.37091e8i			1.71844i	−0.511605	+	0.859221i	$0.670949\pi$
$182$	−3.21364e6	−	9.96674e6i	−0.0395137	−	0.122547i
$183$	−2.60653e6	−	4.58084e7i	−0.0314400	−	0.552543i
$184$	9.81343e6	−	8.76773e7i	0.116134	−	1.03759i
$185$	2.88101e7	−	1.66335e7i	0.334536	−	0.193145i
$186$	−3.88989e6	+	2.49196e7i	−0.0443243	+	0.283953i
$187$	−2.51855e7	+	4.36225e7i	−0.281646	+	0.487826i
$188$	1.35085e7	+	1.34331e8i	0.148271	+	1.47443i
$189$	−1.05378e8	−	3.88344e7i	−1.13536	−	0.418408i
$190$	3.28502e7	−	3.63194e7i	0.347457	−	0.384150i
$191$	8.29893e7	−	1.43742e8i	0.861798	−	1.49268i	−0.00839431	−	0.999965i	$-0.502672\pi$
$191$	8.29893e7	−	1.43742e8i	0.861798	−	1.49268i	0.870192	−	0.492713i	$-0.163995\pi$
$192$	6.24040e7	−	7.56589e7i	0.636294	−	0.771446i
$193$	−5.10742e7	−	8.84632e7i	−0.511389	−	0.885752i	−0.999913	−	0.0132012i	$-0.995798\pi$
$193$	−5.10742e7	−	8.84632e7i	−0.511389	−	0.885752i	0.488524	−	0.872551i	$-0.337536\pi$
$194$	1.23935e8	+	2.66345e7i	1.21867	+	0.261902i
$195$	442769.	+	7.78144e6i	0.00427618	+	0.0751517i
$196$	−4.46042e7	−	2.00998e7i	−0.423136	−	0.190676i
$197$	1.20214e8			1.12027			0.560135	−	0.828401i	$-0.310749\pi$
$197$	1.20214e8			1.12027			0.560135	+	0.828401i	$0.310749\pi$
$198$	−7.49316e7	−	5.36763e7i	−0.686020	−	0.491422i
$199$		−	8.05849e7i		−	0.724883i	−0.932006	−	0.362442i	$-0.881943\pi$
$199$		−	8.05849e7i		−	0.724883i	0.932006	−	0.362442i	$-0.118057\pi$
$200$	−5.17932e7	+	2.26426e7i	−0.457791	+	0.200134i
$201$	7.95225e7	−	1.57815e8i	0.690723	−	1.37077i
$202$	1.34599e8	+	2.89264e7i	1.14898	+	0.246924i
$203$	9.02496e7	−	5.21057e7i	0.757198	−	0.437168i
$204$	−2.90075e7	+	7.55636e7i	−0.239224	+	0.623171i
$205$	2.35062e7	+	1.35713e7i	0.190565	+	0.110023i
$206$	−3.55322e7	−	3.21382e7i	−0.283196	−	0.256146i
$207$	−1.32377e8	+	1.51136e7i	−1.03733	+	0.118433i
$208$	−2.74983e6	−	1.35342e7i	−0.0211877	−	0.104282i
$209$	7.06284e7	+	4.07773e7i	0.535140	+	0.308963i
$210$	8.94310e7	+	7.20899e7i	0.666378	+	0.537164i
$211$	−5.78301e7	−	1.00165e8i	−0.423804	−	0.734050i	0.572504	−	0.819902i	$-0.305972\pi$
$211$	−5.78301e7	−	1.00165e8i	−0.423804	−	0.734050i	−0.996308	+	0.0858517i	$0.972639\pi$
$212$	8.07663e7	−	5.81272e7i	0.582177	−	0.418990i
$213$	−1.30352e8	−	1.98770e8i	−0.924252	−	1.40936i
$214$	−2.57790e8	+	8.31208e7i	−1.79811	+	0.579777i
$215$	1.54097e8			1.05745
$216$	−1.32415e8	−	6.63560e7i	−0.894026	−	0.448015i
$217$	5.23444e7			0.347745
$218$	−1.74966e8	+	5.64155e7i	−1.14382	+	0.368808i
$219$	2.32432e7	+	3.54428e7i	0.149535	+	0.228021i
$220$	5.50708e7	+	7.65195e7i	0.348692	+	0.484499i
$221$	5.69895e6	+	9.87086e6i	0.0355158	+	0.0615152i
$222$	6.93085e7	+	5.58693e7i	0.425159	+	0.342718i
$223$	4.89158e7	+	2.82415e7i	0.295381	+	0.170538i	0.640366	−	0.768070i	$-0.278783\pi$
$223$	4.89158e7	+	2.82415e7i	0.295381	+	0.170538i	−0.344985	+	0.938608i	$0.612116\pi$
$224$	−1.75118e8	−	1.03746e8i	−1.04103	−	0.616741i
$225$	5.07935e7	+	6.86101e7i	0.297282	+	0.401559i
$226$	−1.15035e7	−	1.04047e7i	−0.0662902	−	0.0599583i
$227$	7.23972e7	+	4.17985e7i	0.410801	+	0.237176i	0.691134	−	0.722727i	$-0.257112\pi$
$227$	7.23972e7	+	4.17985e7i	0.410801	+	0.237176i	−0.280333	+	0.959903i	$0.590445\pi$
$228$	1.22344e8	+	4.69656e7i	0.683612	+	0.262427i
$229$	2.46192e8	−	1.42139e8i	1.35472	−	0.782148i	0.365814	−	0.930688i	$-0.380791\pi$
$229$	2.46192e8	−	1.42139e8i	1.35472	−	0.782148i	0.988906	+	0.148540i	$0.0474574\pi$
$230$	1.33235e8	+	2.86332e7i	0.722057	+	0.155175i
$231$	−8.60821e7	+	1.70833e8i	−0.459485	+	0.911864i
$232$	1.25928e8	−	5.50522e7i	0.662085	−	0.289446i
$233$			6.39135e7i			0.331015i	0.986209	+	0.165507i	$0.0529261\pi$
$233$			6.39135e7i			0.331015i	−0.986209	+	0.165507i	$0.947074\pi$
$234$	−1.89963e7	+	8.61093e6i	−0.0969202	+	0.0439334i
$235$	−2.08542e8			−1.04823
$236$	−1.32489e8	+	2.94011e8i	−0.656126	+	1.45603i
$237$	−5.25953e6	−	9.24336e7i	−0.0256642	−	0.451035i
$238$	1.64233e8	+	3.52948e7i	0.789662	+	0.169704i
$239$	8.72535e7	+	1.51128e8i	0.413419	+	0.716063i	0.995261	−	0.0972391i	$-0.0310011\pi$
$239$	8.72535e7	+	1.51128e8i	0.413419	+	0.716063i	−0.581842	+	0.813302i	$0.697668\pi$
$240$	1.06636e8	+	1.07602e8i	0.497925	+	0.502438i
$241$	−4.92887e7	+	8.53705e7i	−0.226823	+	0.392870i	−0.956865	−	0.290533i	$-0.906167\pi$
$241$	−4.92887e7	+	8.53705e7i	−0.226823	+	0.392870i	0.730042	+	0.683403i	$0.239501\pi$
$242$	4.25755e7	−	4.70717e7i	0.193111	−	0.213504i
$243$	−5.30387e7	+	2.17298e8i	−0.237122	+	0.971480i
$244$	−1.24953e8	+	1.25655e7i	−0.550659	+	0.0553750i
$245$	3.77853e7	−	6.54460e7i	0.164150	−	0.284316i
$246$	−1.12023e7	+	7.17647e7i	−0.0479771	+	0.307353i
$247$	1.59817e7	−	9.22706e6i	0.0674815	−	0.0389605i
$248$	6.86043e7	+	7.67866e6i	0.285608	+	0.0319672i
$249$	1.83016e7	+	3.21641e8i	0.0751261	+	1.32030i
$250$	−8.04242e7	−	2.49427e8i	−0.325534	−	1.00961i
$251$		−	1.78570e8i		−	0.712772i	−0.934339	−	0.356386i	$-0.884009\pi$
$251$		−	1.78570e8i		−	0.712772i	0.934339	−	0.356386i	$-0.115991\pi$
$252$	−9.36828e7	+	2.92766e8i	−0.368772	+	1.15244i
$253$			2.26948e8i			0.881058i
$254$	−4.78074e8	+	1.54148e8i	−1.83053	+	0.590230i
$255$	−1.11651e8	−	5.62605e7i	−0.421669	−	0.212477i
$256$	−2.14297e8	−	1.61662e8i	−0.798318	−	0.602237i
$257$	−2.85453e7	+	1.64806e7i	−0.104898	+	0.0605631i	−0.551531	−	0.834154i	$-0.685956\pi$
$257$	−2.85453e7	+	1.64806e7i	−0.104898	+	0.0605631i	0.446633	+	0.894717i	$0.352623\pi$
$258$	1.48637e8	+	3.84644e8i	0.538836	+	1.39441i
$259$	9.23787e7	−	1.60005e8i	0.330387	−	0.572247i
$260$	2.12257e7	−	2.13449e6i	0.0748955	−	0.00753159i
$261$	−1.23497e8	−	1.66816e8i	−0.429947	−	0.580758i
$262$	−5.63022e7	−	5.09243e7i	−0.193406	−	0.174933i
$263$	1.99764e8	−	3.46002e8i	0.677131	−	1.17283i	−0.298710	−	0.954344i	$-0.596556\pi$
$263$	1.99764e8	−	3.46002e8i	0.677131	−	1.17283i	0.975841	−	0.218481i	$-0.0701103\pi$
$264$	−1.37882e8	+	2.11272e8i	−0.461206	+	0.706688i
$265$	7.68534e7	+	1.33114e8i	0.253690	+	0.439403i
$266$	5.71452e7	−	2.65907e8i	0.186163	−	0.866251i
$267$	2.26761e8	−	1.48709e8i	0.729086	−	0.478131i
$268$	−4.40985e8	−	1.98719e8i	−1.39943	−	0.630621i
$269$	3.57895e8			1.12104			0.560522	−	0.828140i	$-0.310601\pi$
$269$	3.57895e8			1.12104			0.560522	+	0.828140i	$0.310601\pi$
$270$	1.22448e8	−	1.93254e8i	0.378599	−	0.597525i
$271$			5.53439e8i			1.68918i	0.535410	+	0.844592i	$0.320157\pi$
$271$			5.53439e8i			1.68918i	−0.535410	+	0.844592i	$0.679843\pi$
$272$	2.10072e8	+	7.03507e7i	0.632960	+	0.211971i
$273$	2.37378e7	+	3.61969e7i	0.0706107	+	0.107672i
$274$	9.97255e7	−	4.64041e8i	0.292873	−	1.36279i
$275$	1.25926e8	−	7.27036e7i	0.365134	−	0.210810i
$276$	5.70426e7	+	3.60190e8i	0.163312	+	1.03122i
$277$	1.72613e8	+	9.96579e7i	0.487970	+	0.281730i	0.723732	−	0.690081i	$-0.242425\pi$
$277$	1.72613e8	+	9.96579e7i	0.487970	+	0.281730i	−0.235762	+	0.971811i	$0.575759\pi$
$278$	−3.24165e8	+	3.58398e8i	−0.904917	+	1.00048i
$279$	−1.18258e7	−	1.03580e8i	−0.0326000	−	0.285537i
$280$	1.86513e8	−	2.53106e8i	0.507757	−	0.689048i
$281$	−1.78541e8	−	1.03081e8i	−0.480027	−	0.277143i	0.240401	−	0.970674i	$-0.422721\pi$
$281$	−1.78541e8	−	1.03081e8i	−0.480027	−	0.277143i	−0.720428	+	0.693530i	$0.756054\pi$
$282$	−2.01153e8	−	5.20546e8i	−0.534140	−	1.38225i
$283$	−2.06789e8	−	3.58169e8i	−0.542344	−	0.939368i	−0.998769	−	0.0496059i	$-0.984203\pi$
$283$	−2.06789e8	−	3.58169e8i	−0.542344	−	0.939368i	0.456424	−	0.889762i	$-0.349130\pi$
$284$	−5.28061e8	+	3.80044e8i	−1.36795	+	0.984508i
$285$	−9.10904e7	+	1.80772e8i	−0.233086	+	0.462567i
$286$	1.09023e7	+	3.38122e7i	0.0275573	+	0.0854657i
$287$	1.50744e8			0.376403
$288$	−1.65731e8	+	3.69966e8i	−0.408818	+	0.912616i
$289$	2.27504e8			0.554430
$290$	6.51476e7	+	2.02048e8i	0.156857	+	0.486475i
$291$	−5.23137e8	+	2.97668e7i	−1.24449	+	0.0708121i
$292$	9.41590e7	−	6.77659e7i	0.221321	−	0.159284i
$293$	1.20727e8	+	2.09106e8i	0.280395	+	0.485658i	0.971482	−	0.237114i	$-0.0762014\pi$
$293$	1.20727e8	+	2.09106e8i	0.280395	+	0.485658i	−0.691087	+	0.722771i	$0.742868\pi$
$294$	1.99808e8	+	3.11895e7i	0.458560	+	0.0715801i
$295$	−4.31390e8	−	2.49063e8i	−0.978348	−	0.564850i
$296$	1.44546e8	−	1.96156e8i	0.323956	−	0.439623i
$297$	3.57496e8	+	1.31746e8i	0.791814	+	0.291802i
$298$	4.72779e7	−	5.22706e7i	0.103491	−	0.114420i
$299$	4.44735e7	+	2.56768e7i	0.0962171	+	0.0555510i
$300$	1.81584e8	−	1.47039e8i	0.388287	−	0.314419i
$301$	7.41160e8	−	4.27909e8i	1.56650	−	0.904416i
$302$	−1.28600e8	+	5.98401e8i	−0.268669	+	1.25017i
$303$	−5.68153e8	+	3.23283e7i	−1.17332	+	0.0667626i
$304$	1.13904e8	−	3.40123e8i	0.232530	−	0.694351i
$305$		−	1.93983e8i		−	0.391485i
$306$	3.27379e7	−	3.32961e8i	0.0653170	−	0.664307i
$307$	6.01082e8			1.18563			0.592815	−	0.805339i	$-0.298017\pi$
$307$	6.01082e8			1.18563			0.592815	+	0.805339i	$0.298017\pi$
$308$	4.77361e8	+	2.15111e8i	0.930935	+	0.419503i
$309$	1.76854e8	+	8.91161e7i	0.341005	+	0.171831i
$310$	−2.24044e7	+	1.04252e8i	−0.0427137	+	0.198755i
$311$	−1.13509e8	−	1.96604e8i	−0.213978	−	0.370621i	0.738978	−	0.673730i	$-0.235309\pi$
$311$	−1.13509e8	−	1.96604e8i	−0.213978	−	0.370621i	−0.952956	+	0.303109i	$0.901976\pi$
$312$	2.58016e7	+	5.09231e7i	0.0480956	+	0.0949235i
$313$	−4.60355e8	+	7.97358e8i	−0.848570	+	1.46977i	0.0339140	+	0.999425i	$0.489203\pi$
$313$	−4.60355e8	+	7.97358e8i	−0.848570	+	1.46977i	−0.882484	+	0.470342i	$0.844131\pi$
$314$	−5.96045e8	−	5.39112e8i	−1.08649	−	0.982710i
$315$	−4.35475e8	−	1.89230e8i	−0.785012	−	0.341116i
$316$	−2.52135e8	+	2.53550e7i	−0.449498	+	0.0452021i
$317$	9.73903e7	−	1.68685e8i	0.171715	−	0.297419i	−0.767305	−	0.641283i	$-0.778402\pi$
$317$	9.73903e7	−	1.68685e8i	0.171715	−	0.297419i	0.939020	+	0.343864i	$0.111736\pi$
$318$	−2.58138e8	+	3.20233e8i	−0.450150	+	0.558433i
$319$	−3.06172e8	+	1.76769e8i	−0.528078	+	0.304886i
$320$	2.81579e8	−	3.04369e8i	0.480370	−	0.519248i
$321$	9.36234e8	−	6.13977e8i	1.57985	−	1.03606i
$322$	7.20333e8	−	2.32262e8i	1.20237	−	0.387688i
$323$			2.96024e8i			0.488786i
$324$	6.00496e8	+	1.19238e8i	0.980850	+	0.194764i
$325$		−	3.29026e7i		−	0.0531666i
$326$	−1.87715e7	−	5.82177e7i	−0.0300080	−	0.0930665i
$327$	6.35438e8	−	4.16717e8i	1.00498	−	0.659058i
$328$	1.97570e8	+	2.21133e7i	0.309145	+	0.0346016i
$329$	−1.00303e9	+	5.79098e8i	−1.55284	+	0.896533i
$330$	−3.03395e8	−	2.44565e8i	−0.464739	−	0.374624i
$331$	1.59451e8	−	2.76176e8i	0.241673	−	0.418590i	−0.719518	−	0.694474i	$-0.755637\pi$
$331$	1.59451e8	−	2.76176e8i	0.241673	−	0.418590i	0.961191	+	0.275884i	$0.0889706\pi$
$332$	8.77352e8	−	8.82277e7i	1.31580	−	0.132319i
$333$	−3.37491e8	−	1.46652e8i	−0.500849	−	0.217637i
$334$	−3.55332e7	+	3.92857e7i	−0.0521821	+	0.0576928i
$335$	3.73569e8	−	6.47040e8i	0.542892	−	0.940317i
$336$	8.11688e8	+	2.21420e8i	1.16735	+	0.318442i
$337$	9.12807e6	+	1.58103e7i	0.0129920	+	0.0225027i	0.872448	−	0.488706i	$-0.162531\pi$
$337$	9.12807e6	+	1.58103e7i	0.0129920	+	0.0225027i	−0.859456	+	0.511209i	$0.829198\pi$
$338$	−6.86212e8	−	1.47472e8i	−0.966607	−	0.207731i
$339$	5.72561e7	+	2.88511e7i	0.0798221	+	0.0402220i
$340$	−1.40590e8	+	3.11988e8i	−0.193989	+	0.430488i
$341$	−1.77579e8			−0.242522
$342$	−5.39092e8	−	5.30054e7i	−0.728738	−	0.0716521i
$343$			4.84607e8i			0.648426i
$344$	1.03416e9	−	4.52107e8i	1.36972	−	0.598807i
$345$	−5.62394e8	+	3.20006e7i	−0.737350	+	0.0419557i
$346$	−2.22061e8	−	4.77224e7i	−0.288208	−	0.0619378i
$347$	4.29631e8	−	2.48048e8i	0.552004	−	0.318700i	−0.197926	−	0.980217i	$-0.563420\pi$
$347$	4.29631e8	−	2.48048e8i	0.552004	−	0.318700i	0.749930	+	0.661517i	$0.230087\pi$
$348$	−4.41496e8	+	3.57505e8i	−0.561564	+	0.454731i
$349$	2.16759e8	+	1.25146e8i	0.272953	+	0.157590i	0.630229	−	0.776409i	$-0.282961\pi$
$349$	2.16759e8	+	1.25146e8i	0.272953	+	0.157590i	−0.357276	+	0.933999i	$0.616294\pi$
$350$	−3.59636e8	−	3.25284e8i	−0.448358	−	0.405532i
$351$	6.62643e7	−	5.51505e7i	0.0817908	−	0.0680729i
$352$	5.94089e8	+	3.51958e8i	0.726026	+	0.430122i
$353$	−2.99424e8	−	1.72873e8i	−0.362306	−	0.209177i	0.307786	−	0.951456i	$-0.400412\pi$
$353$	−2.99424e8	−	1.72873e8i	−0.362306	−	0.209177i	−0.670092	+	0.742278i	$0.733745\pi$
$354$	2.05587e8	−	1.31704e9i	0.246311	−	1.57793i
$355$	−5.02478e8	−	8.70317e8i	−0.596098	−	1.03247i
$356$	−4.33562e8	−	6.02423e8i	−0.509302	−	0.707663i
$357$	−6.93238e8	+	3.94457e7i	−0.806387	+	0.0458839i
$358$	−1.07202e9	+	3.45659e8i	−1.23485	+	0.398159i
$359$	−1.54596e9			−1.76347			−0.881733	−	0.471749i	$-0.843623\pi$
$359$	−1.54596e9			−1.76347			−0.881733	+	0.471749i	$0.843623\pi$
$360$	−5.42989e8	−	3.11892e8i	−0.613384	−	0.352327i
$361$	−4.14584e8			−0.463807
$362$	−1.47617e9	+	4.75972e8i	−1.63552	+	0.527353i
$363$	−1.18058e8	+	2.34290e8i	−0.129545	+	0.257087i
$364$	9.61624e7	−	6.92077e7i	0.104508	−	0.0752142i
$365$	8.95972e7	+	1.55187e8i	0.0964428	+	0.167044i
$366$	4.84206e8	−	1.87110e8i	0.516234	−	0.199487i
$367$	−1.24820e9	−	7.20650e8i	−1.31812	−	0.761015i	−0.334691	−	0.942328i	$-0.608632\pi$
$367$	−1.24820e9	−	7.20650e8i	−1.31812	−	0.761015i	−0.983425	+	0.181314i	$0.941965\pi$
$368$	9.78164e8	−	1.98741e8i	1.02316	−	0.207883i
$369$	−3.40566e7	−	2.98295e8i	−0.0352865	−	0.309068i
$370$	2.79133e8	+	2.52471e8i	0.286487	+	0.259123i
$371$	7.39285e8	+	4.26827e8i	0.751629	+	0.433953i
$372$	−2.81835e8	+	4.46337e7i	−0.283854	+	0.0449535i
$373$	−5.53082e8	+	3.19322e8i	−0.551834	+	0.318602i	−0.749861	−	0.661595i	$-0.769880\pi$
$373$	−5.53082e8	+	3.19322e8i	−0.551834	+	0.318602i	0.198027	+	0.980197i	$0.436547\pi$
$374$	−5.57161e8	−	1.19738e8i	−0.550719	−	0.118353i
$375$	5.94059e8	+	9.05861e8i	0.581728	+	0.887058i
$376$	−1.39955e9	+	6.11846e8i	−1.35779	+	0.593587i
$377$			7.99981e7i			0.0768927i
$378$	5.22947e7	−	1.26952e9i	0.0498008	−	1.20898i
$379$	4.11329e8			0.388107			0.194054	−	0.980991i	$-0.437836\pi$
$379$	4.11329e8			0.388107			0.194054	+	0.980991i	$0.437836\pi$
$380$	5.05134e8	+	2.27626e8i	0.472241	+	0.212804i
$381$	1.73626e9	−	1.13863e9i	1.60833	−	1.05474i
$382$	1.83592e9	+	3.94551e8i	1.68512	+	0.362144i
$383$	−2.34111e8	−	4.05492e8i	−0.212924	−	0.368796i	0.739704	−	0.672932i	$-0.234965\pi$
$383$	−2.34111e8	−	4.05492e8i	−0.212924	−	0.368796i	−0.952629	+	0.304136i	$0.901632\pi$
$384$	1.03134e9	+	4.09271e8i	0.929488	+	0.368852i
$385$	−4.04383e8	+	7.00413e8i	−0.361144	+	0.625520i
$386$	7.75228e8	−	8.57096e8i	0.686079	−	0.758532i
$387$	−1.01420e9	−	1.36995e9i	−0.889478	−	1.20148i
$388$	1.43499e8	+	1.42698e9i	0.124721	+	1.24024i
$389$	−9.28669e8	+	1.60850e9i	−0.799903	+	1.38547i	0.119776	+	0.992801i	$0.461782\pi$
$389$	−9.28669e8	+	1.60850e9i	−0.799903	+	1.38547i	−0.919679	+	0.392671i	$0.871551\pi$
$390$	−8.22518e7	+	3.17843e7i	−0.0702133	+	0.0271323i
$391$	−7.13404e8	+	4.11884e8i	−0.603555	+	0.348463i
$392$	6.15681e7	−	5.50075e8i	0.0516243	−	0.461233i
$393$	2.80233e8	+	1.41208e8i	0.232887	+	0.117351i
$394$	4.17375e8	+	1.29444e9i	0.343787	+	1.06622i
$395$		−	3.91426e8i		−	0.319565i
$396$	3.17819e8	−	9.93209e8i	0.257186	−	0.803725i
$397$			6.90086e8i			0.553524i	0.960939	+	0.276762i	$0.0892613\pi$
$397$			6.90086e8i			0.553524i	−0.960939	+	0.276762i	$0.910739\pi$
$398$	8.67723e8	−	2.79786e8i	0.689907	−	0.222451i
$399$	6.38658e7	+	1.12241e9i	0.0503342	+	0.884598i
$400$	−4.23633e8	−	4.79085e8i	−0.330963	−	0.374285i
$401$	1.18120e7	−	6.81968e6i	0.00914785	−	0.00528151i	−0.495419	−	0.868654i	$-0.664986\pi$
$401$	1.18120e7	−	6.81968e6i	0.00914785	−	0.00528151i	0.504567	+	0.863373i	$0.331652\pi$
$402$	1.97542e9	+	3.08358e8i	1.51659	+	0.236736i
$403$	−2.00912e7	+	3.47989e7i	−0.0152911	+	0.0264849i
$404$	1.55847e8	+	1.54977e9i	0.117588	+	1.16932i
$405$	−2.76067e8	+	9.04478e8i	−0.206501	+	0.676558i
$406$	8.74404e8	+	7.90883e8i	0.648442	+	0.586504i
$407$	−3.13395e8	+	5.42816e8i	−0.230415	+	0.399091i
$408$	−9.14367e8	−	4.99956e7i	−0.666515	−	0.0364436i
$409$	1.32831e9	+	2.30070e9i	0.959992	+	1.66276i	0.722506	+	0.691365i	$0.242990\pi$
$409$	1.32831e9	+	2.30070e9i	0.959992	+	1.66276i	0.237487	+	0.971391i	$0.423676\pi$
$410$	−6.45212e7	+	3.00229e8i	−0.0462338	+	0.215134i
$411$	1.11454e8	+	1.95874e9i	0.0791860	+	1.39165i
$412$	2.22693e8	−	4.94186e8i	0.156880	−	0.348137i
$413$	−2.76648e9			−1.93243
$414$	−6.22344e8	−	1.37294e9i	−0.431052	−	0.950931i
$415$			1.36204e9i			0.935455i
$416$	1.36186e8	−	7.65994e7i	0.0927482	−	0.0521673i
$417$	8.98876e8	−	1.78385e9i	0.607049	−	1.20471i
$418$	−1.93865e8	+	9.02089e8i	−0.129832	+	0.604133i
$419$	1.46771e8	−	8.47383e7i	0.0974746	−	0.0562770i	−0.450470	−	0.892791i	$-0.648744\pi$
$419$	1.46771e8	−	8.47383e7i	0.0974746	−	0.0562770i	0.547945	+	0.836514i	$0.315410\pi$
$420$	−4.65752e8	+	1.21327e9i	−0.306748	+	0.799068i
$421$	1.07488e9	+	6.20585e8i	0.702061	+	0.405335i	0.808114	−	0.589026i	$-0.200488\pi$
$421$	1.07488e9	+	6.20585e8i	0.702061	+	0.405335i	−0.106054	+	0.994360i	$0.533822\pi$
$422$	8.77771e8	−	9.70468e8i	0.568575	−	0.628619i
$423$	1.37254e9	+	1.85398e9i	0.881724	+	1.19100i
$424$	9.06318e8	+	6.67862e8i	0.577431	+	0.425507i
$425$	4.57083e8	+	2.63897e8i	0.288824	+	0.166753i
$426$	1.68774e9	−	2.09373e9i	1.05772	−	1.31216i
$427$	−5.38670e8	−	9.33004e8i	−0.334831	−	0.579944i
$428$	−1.79006e9	−	2.48724e9i	−1.10360	−	1.53343i
$429$	−8.05304e7	−	1.22798e8i	−0.0492447	−	0.0750916i
$430$	5.35013e8	+	1.65928e9i	0.324508	+	1.00642i
$431$	3.76130e8			0.226291			0.113146	−	0.993578i	$-0.463907\pi$
$431$	3.76130e8			0.226291			0.113146	+	0.993578i	$0.463907\pi$
$432$	2.54772e8	−	1.65621e9i	0.152040	−	0.988374i
$433$	2.75525e9			1.63100			0.815500	−	0.578757i	$-0.196462\pi$
$433$	2.75525e9			1.63100			0.815500	+	0.578757i	$0.196462\pi$
$434$	1.81736e8	+	5.63635e8i	0.106716	+	0.330966i
$435$	−4.81217e8	−	7.33792e8i	−0.280303	−	0.427426i
$436$	−1.21494e9	−	1.68813e9i	−0.702025	−	0.975446i
$437$	6.66874e8	+	1.15506e9i	0.382260	+	0.662094i
$438$	−3.00943e8	+	3.73334e8i	−0.171129	+	0.212294i
$439$	−2.36521e9	−	1.36555e9i	−1.33427	−	0.770341i	−0.348318	−	0.937376i	$-0.613247\pi$
$439$	−2.36521e9	−	1.36555e9i	−1.33427	−	0.770341i	−0.985951	+	0.167036i	$0.946580\pi$
$440$	−6.32745e8	+	8.58663e8i	−0.354115	+	0.480550i
$441$	−8.30514e8	+	9.48206e7i	−0.461118	+	0.0526463i
$442$	−8.65012e7	+	9.56361e7i	−0.0476479	+	0.0526798i
$443$	1.36001e9	+	7.85205e8i	0.743243	+	0.429111i	0.823247	−	0.567683i	$-0.192160\pi$
$443$	1.36001e9	+	7.85205e8i	0.743243	+	0.429111i	−0.0800045	+	0.996795i	$0.525493\pi$
$444$	−3.60955e8	+	9.40275e8i	−0.195710	+	0.509817i
$445$	9.92876e8	−	5.73237e8i	0.534115	−	0.308372i
$446$	−1.34267e8	+	6.24768e8i	−0.0716634	+	0.333462i
$447$	−1.31097e8	+	2.60166e8i	−0.0694250	+	0.137776i
$448$	5.09117e8	−	2.24584e9i	0.267513	−	1.18006i
$449$		−	2.03032e9i		−	1.05853i	−0.848457	−	0.529265i	$-0.822468\pi$
$449$		−	2.03032e9i		−	1.05853i	0.848457	−	0.529265i	$-0.177532\pi$
$450$	−5.62429e8	+	7.85144e8i	−0.290954	+	0.406168i
$451$	−5.11399e8			−0.262508
$452$	7.20963e7	−	1.59991e8i	0.0367222	−	0.0814915i
$453$	−1.43725e8	−	2.52589e9i	−0.0726420	−	1.27665i
$454$	−1.98720e8	+	9.24681e8i	−0.0996659	+	0.463763i
$455$	9.15036e7	+	1.58489e8i	0.0455405	+	0.0788785i
$456$	−8.09470e7	+	1.48044e9i	−0.0399782	+	0.731160i
$457$	3.25149e8	−	5.63174e8i	0.159358	−	0.276017i	−0.775279	−	0.631619i	$-0.782391\pi$
$457$	3.25149e8	−	5.63174e8i	0.159358	−	0.276017i	0.934638	+	0.355602i	$0.115724\pi$
$458$	2.38529e9	+	2.15745e9i	1.16014	+	1.04933i
$459$	2.34675e8	+	1.36288e9i	0.113272	+	0.657830i
$460$	1.54267e8	+	1.53406e9i	0.0738961	+	0.734837i
$461$	−2.86088e8	+	4.95519e8i	−0.136002	+	0.235563i	−0.925980	−	0.377573i	$-0.876759\pi$
$461$	−2.86088e8	+	4.95519e8i	−0.136002	+	0.235563i	0.789978	+	0.613136i	$0.210092\pi$
$462$	−2.13837e9	−	3.33794e8i	−1.00887	−	0.157482i
$463$	1.01815e9	−	5.87828e8i	0.476736	−	0.275243i	−0.242320	−	0.970197i	$-0.577908\pi$
$463$	1.01815e9	−	5.87828e8i	0.476736	−	0.275243i	0.719055	+	0.694953i	$0.244575\pi$
$464$	1.03000e9	+	1.16483e9i	0.478659	+	0.541314i
$465$	−2.50393e7	−	4.40053e8i	−0.0115488	−	0.202964i
$466$	−6.88209e8	+	2.21904e8i	−0.315043	+	0.101581i
$467$			1.60587e9i			0.729627i	0.931081	+	0.364813i	$0.118867\pi$
$467$			1.60587e9i			0.729627i	−0.931081	+	0.364813i	$0.881133\pi$
$468$	−1.58675e8	−	1.74652e8i	−0.0715563	−	0.0787614i
$469$		−	4.14943e9i		−	1.85731i
$470$	−7.24045e8	−	2.24554e9i	−0.321679	−	0.997651i
$471$	2.96669e9	+	1.49490e9i	1.30828	+	0.659235i
$472$	−3.62584e9	−	4.05829e8i	−1.58713	−	0.177642i
$473$	−2.51439e9	+	1.45168e9i	−1.09249	+	0.630750i
$474$	9.77046e8	−	3.77557e8i	0.421396	−	0.162839i
$475$	4.27271e8	−	7.40055e8i	0.182926	−	0.316837i
$476$	1.90159e8	+	1.89097e9i	0.0808149	+	0.803638i
$477$	6.77590e8	−	1.55934e9i	0.285860	−	0.657850i
$478$	−1.32437e9	+	1.46423e9i	−0.554642	+	0.613215i
$479$	2.12568e9	−	3.68178e9i	0.883738	−	1.53068i	0.0365840	−	0.999331i	$-0.488352\pi$
$479$	2.12568e9	−	3.68178e9i	0.883738	−	1.53068i	0.847154	−	0.531348i	$-0.178314\pi$
$480$	−7.88409e8	+	1.52182e9i	−0.325392	+	0.628087i
$481$	7.09148e7	+	1.22828e8i	0.0290555	+	0.0503257i
$482$	−1.09038e9	−	2.34330e8i	−0.443520	−	0.0953156i
$483$	−2.61609e9	+	1.71562e9i	−1.05642	+	0.692796i
$484$	6.54678e8	+	2.95015e8i	0.262464	+	0.118273i
$485$	−2.21531e9			−0.881737
$486$	−2.52397e9	+	1.83334e8i	−0.997372	+	0.0724461i
$487$		−	4.88156e9i		−	1.91517i	−0.288152	−	0.957585i	$-0.593041\pi$
$487$		−	4.88156e9i		−	1.91517i	0.288152	−	0.957585i	$-0.406959\pi$
$488$	−5.69132e8	−	1.30185e9i	−0.221689	−	0.507096i
$489$	1.38657e8	+	2.11434e8i	0.0536242	+	0.0817698i
$490$	8.35898e8	+	1.79640e8i	0.320972	+	0.0689791i
$491$	−1.27837e9	+	7.38068e8i	−0.487385	+	0.281392i	−0.723489	−	0.690336i	$-0.757463\pi$
$491$	−1.27837e9	+	7.38068e8i	−0.487385	+	0.281392i	0.236104	+	0.971728i	$0.424129\pi$
$492$	−8.11642e8	+	1.28538e8i	−0.307246	+	0.0486580i
$493$	−1.11133e9	−	6.41629e8i	−0.417715	−	0.241168i
$494$	1.54843e8	+	1.40053e8i	0.0577892	+	0.0522693i
$495$	1.47735e9	+	6.41962e8i	0.547476	+	0.237898i
$496$	1.55507e8	+	7.65378e8i	0.0572223	+	0.281637i
$497$	−4.83355e9	−	2.79065e9i	−1.76611	−	1.01967i
$498$	−3.39983e9	+	1.31378e9i	−1.23354	+	0.476674i
$499$	−1.06739e9	−	1.84877e9i	−0.384566	−	0.666087i	0.607143	−	0.794592i	$-0.292315\pi$
$499$	−1.06739e9	−	1.84877e9i	−0.384566	−	0.666087i	−0.991709	+	0.128505i	$0.958982\pi$
$500$	2.40655e9	−	1.73198e9i	0.860993	−	0.619654i
$501$	9.85300e7	−	1.95536e8i	0.0350055	−	0.0694697i
$502$	1.92281e9	−	6.19983e8i	0.678380	−	0.218734i
$503$	−4.53304e8			−0.158819			−0.0794094	−	0.996842i	$-0.525303\pi$
$503$	−4.53304e8			−0.158819			−0.0794094	+	0.996842i	$0.525303\pi$
$504$	−3.47771e9	+	7.70635e6i	−1.21000	+	0.00268128i
$505$	−2.40594e9			−0.831314
$506$	−2.44373e9	+	7.87949e8i	−0.838546	+	0.270378i
$507$	2.89654e9	−	1.64815e8i	0.987080	−	0.0561655i
$508$	−3.31968e9	−	4.61261e9i	−1.12350	−	1.56108i
$509$	1.76822e9	+	3.06264e9i	0.594325	+	1.02940i	0.993642	+	0.112588i	$0.0359139\pi$
$509$	1.76822e9	+	3.06264e9i	0.594325	+	1.02940i	−0.399317	+	0.916813i	$0.630753\pi$
$510$	2.18157e8	−	1.39757e9i	0.0728238	−	0.466528i
$511$	8.61873e8	+	4.97603e8i	0.285740	+	0.164972i
$512$	9.96718e8	−	2.86878e9i	0.328192	−	0.944611i
$513$	2.20662e9	−	3.79958e8i	0.721632	−	0.124258i
$514$	−2.76568e8	−	2.50151e8i	−0.0898319	−	0.0812513i
$515$	7.25099e8	+	4.18636e8i	0.233923	+	0.135055i
$516$	−3.62571e9	+	2.93595e9i	−1.16177	+	0.940750i
$517$	3.40277e9	−	1.96459e9i	1.08297	−	0.625252i
$518$	2.04363e9	+	4.39191e8i	0.646024	+	0.138835i
$519$	9.37333e8	−	5.33348e7i	0.294312	−	0.0167465i
$520$	9.66781e7	+	2.21144e8i	0.0301520	+	0.0689704i
$521$		−	2.74895e9i		−	0.851597i	−0.904818	−	0.425799i	$-0.859993\pi$
$521$		−	2.74895e9i		−	0.851597i	0.904818	−	0.425799i	$-0.140007\pi$
$522$	1.36747e9	−	1.90897e9i	0.420794	−	0.587424i
$523$	−5.09410e7			−0.0155708			−0.00778541	−	0.999970i	$-0.502478\pi$
$523$	−5.09410e7			−0.0155708			−0.00778541	+	0.999970i	$0.502478\pi$
$524$	3.52866e8	−	7.83057e8i	0.107140	−	0.237757i
$525$	1.79002e9	+	9.01981e8i	0.539882	+	0.272045i
$526$	4.41925e9	+	9.49727e8i	1.32403	+	0.284544i
$527$	−3.22284e8	−	5.58213e8i	−0.0959185	−	0.166136i
$528$	−2.75365e9	−	7.51169e8i	−0.814123	−	0.222085i
$529$	−1.53346e8	+	2.65604e8i	−0.0450379	+	0.0780080i
$530$	−1.16652e9	+	1.28971e9i	−0.340350	+	0.376292i
$531$	6.25014e8	+	5.47437e9i	0.181159	+	1.58673i
$532$	3.06164e9	−	3.07882e8i	0.881583	−	0.0886531i
$533$	−5.78595e7	+	1.00216e8i	−0.0165512	+	0.0286675i
$534$	2.38857e9	+	1.92541e9i	0.678801	+	0.547179i
$535$	4.09931e9	−	2.36674e9i	1.15737	−	0.668209i
$536$	6.08700e8	−	5.43838e9i	0.170737	−	1.52543i
$537$	3.89334e9	−	2.55323e9i	1.08496	−	0.711508i
$538$	1.24259e9	+	3.85374e9i	0.344024	+	1.06695i
$539$			1.42384e9i			0.391652i
$540$	2.50606e9	+	6.47532e8i	0.684878	+	0.176963i
$541$		−	4.57272e8i		−	0.124161i	−0.998071	−	0.0620803i	$-0.980226\pi$
$541$		−	4.57272e8i		−	0.124161i	0.998071	−	0.0620803i	$-0.0197735\pi$
$542$	−5.95932e9	+	1.92150e9i	−1.60768	+	0.518375i
$543$	5.36113e9	−	3.51580e9i	1.43700	−	0.942377i
$544$	−2.81676e7	+	2.50626e9i	−0.00750160	+	0.667468i
$545$	2.78227e9	−	1.60635e9i	0.736227	−	0.425061i
$546$	−3.07346e8	+	3.81277e8i	−0.0808077	+	0.100246i
$547$	1.04211e9	−	1.80498e9i	0.272243	−	0.471539i	−0.697193	−	0.716884i	$-0.745568\pi$
$547$	1.04211e9	−	1.80498e9i	0.272243	−	0.471539i	0.969436	+	0.245345i	$0.0789012\pi$
$548$	5.34294e9	−	5.37293e8i	1.38691	−	0.139470i
$549$	−1.72455e9	+	1.27672e9i	−0.444807	+	0.329300i
$550$	1.22007e9	+	1.10353e9i	0.312690	+	0.282823i
$551$	−1.03885e9	+	1.79934e9i	−0.264559	+	0.458229i
$552$	−3.68040e9	+	1.86478e9i	−0.931341	+	0.471890i
$553$	−1.08695e9	−	1.88264e9i	−0.273319	−	0.473402i
$554$	−4.73798e8	+	2.20466e9i	−0.118388	+	0.550882i
$555$	−1.38933e9	−	7.00077e8i	−0.344968	−	0.173828i
$556$	−4.98464e9	−	2.24621e9i	−1.22991	−	0.554228i
$557$	−5.69566e9			−1.39653			−0.698266	−	0.715838i	$-0.746045\pi$
$557$	−5.69566e9			−1.39653			−0.698266	+	0.715838i	$0.746045\pi$
$558$	1.07427e9	−	4.86962e8i	0.261755	−	0.118652i
$559$			6.56970e8i			0.159076i
$560$	3.37296e9	+	1.12957e9i	0.811620	+	0.271803i
$561$	2.35181e9	−	1.33820e8i	0.562383	−	0.0320000i
$562$	4.90070e8	−	2.28038e9i	0.116461	−	0.541914i
$563$	2.35534e9	−	1.35986e9i	0.556255	−	0.321154i	−0.195386	−	0.980726i	$-0.562596\pi$
$563$	2.35534e9	−	1.35986e9i	0.556255	−	0.321154i	0.751641	+	0.659572i	$0.229263\pi$
$564$	4.90675e9	−	3.97328e9i	1.15164	−	0.932550i
$565$	2.34749e8	+	1.35532e8i	0.0547563	+	0.0316136i
$566$	3.13874e9	−	3.47021e9i	0.727609	−	0.804448i
$567$	1.18383e9	+	5.11688e9i	0.272740	+	1.17887i
$568$	−5.92563e9	−	4.36657e9i	−1.35680	−	0.999819i
$569$	−2.06204e9	−	1.19052e9i	−0.469250	−	0.270921i	0.246676	−	0.969098i	$-0.420662\pi$
$569$	−2.06204e9	−	1.19052e9i	−0.469250	−	0.270921i	−0.715926	+	0.698177i	$0.753995\pi$
$570$	−2.26278e9	−	3.53214e8i	−0.511776	−	0.0798870i
$571$	2.27326e9	+	3.93740e9i	0.511003	+	0.885082i	0.999919	+	0.0127516i	$0.00405907\pi$
$571$	2.27326e9	+	3.93740e9i	0.511003	+	0.885082i	−0.488916	+	0.872331i	$0.662608\pi$
$572$	−3.26231e8	+	2.34787e8i	−0.0728852	+	0.0524552i
$573$	−7.74952e9	+	4.40953e8i	−1.72081	+	0.0979153i
$574$	5.23373e8	+	1.62318e9i	0.115510	+	0.358241i
$575$	2.37800e9			0.521643
$576$	−4.55913e9	−	5.00062e8i	−0.994038	−	0.109030i
$577$	−3.90230e9			−0.845679			−0.422840	−	0.906205i	$-0.638967\pi$
$577$	−3.90230e9			−0.845679			−0.422840	+	0.906205i	$0.638967\pi$
$578$	7.89879e8	+	2.44972e9i	0.170143	+	0.527678i
$579$	−2.14963e9	+	4.26602e9i	−0.460245	+	0.913373i
$580$	−1.94942e9	+	1.40299e9i	−0.414866	+	0.298578i
$581$	3.78224e9	+	6.55104e9i	0.800079	+	1.38578i
$582$	−2.13682e9	−	5.52969e9i	−0.449301	−	1.16271i
$583$	−2.50803e9	−	1.44801e9i	−0.524194	−	0.302644i
$584$	1.05660e9	+	7.78607e8i	0.219517	+	0.161761i
$585$	2.92948e8	−	2.16875e8i	0.0604985	−	0.0447883i
$586$	−1.83246e9	+	2.02597e9i	−0.376177	+	0.415903i
$587$	7.84644e9	+	4.53014e9i	1.60118	+	0.924440i	0.991252	+	0.131979i	$0.0421333\pi$
$587$	7.84644e9	+	4.53014e9i	1.60118	+	0.924440i	0.609924	+	0.792460i	$0.291200\pi$
$588$	3.57877e8	+	2.25978e9i	0.0725960	+	0.458401i
$589$	−9.03793e8	+	5.21805e8i	−0.182249	+	0.105222i
$590$	1.18411e9	−	5.50986e9i	0.237361	−	1.10448i
$591$	−3.08297e9	−	4.70112e9i	−0.614346	−	0.936796i
$592$	2.61402e9	+	8.75408e8i	0.517826	+	0.173414i
$593$			2.59242e9i			0.510522i	0.966872	+	0.255261i	$0.0821614\pi$
$593$			2.59242e9i			0.510522i	−0.966872	+	0.255261i	$0.917839\pi$
$594$	−1.77410e8	+	4.30686e9i	−0.0347316	+	0.843156i
$595$	−2.93564e9			−0.571337
$596$	7.26986e8	+	3.27599e8i	0.140658	+	0.0633841i
$597$	−3.15138e9	+	2.06666e9i	−0.606164	+	0.397519i
$598$	−1.22074e8	+	5.68031e8i	−0.0233436	+	0.108622i
$599$	4.08477e9	+	7.07503e9i	0.776558	+	1.34504i	0.933915	+	0.357495i	$0.116369\pi$
$599$	4.08477e9	+	7.07503e9i	0.776558	+	1.34504i	−0.157357	+	0.987542i	$0.550297\pi$
$600$	2.21374e9	+	1.44475e9i	0.418405	+	0.273064i
$601$	−2.89479e9	+	5.01393e9i	−0.543948	+	0.942145i	0.454725	+	0.890632i	$0.349738\pi$
$601$	−2.89479e9	+	5.01393e9i	−0.543948	+	0.942145i	−0.998672	+	0.0515130i	$0.983596\pi$
$602$	7.18090e9	+	6.49499e9i	1.34150	+	1.21336i
$603$	−8.21098e9	+	9.37455e8i	−1.52505	+	0.174116i
$604$	−6.88996e9	+	6.92863e8i	−1.27229	+	0.127944i
$605$	−5.54593e8	+	9.60584e8i	−0.101819	+	0.176356i
$606$	−2.32069e9	−	6.00552e9i	−0.423607	−	1.09622i
$607$	−5.82825e9	+	3.36494e9i	−1.05774	+	0.610685i	−0.924805	−	0.380441i	$-0.875772\pi$
$607$	−5.82825e9	+	3.36494e9i	−1.05774	+	0.610685i	−0.132932	+	0.991125i	$0.542439\pi$
$608$	4.05785e9	+	4.56057e7i	0.732206	+	0.00822918i
$609$	−4.35217e9	−	2.19304e9i	−0.780810	−	0.393447i
$610$	2.08878e9	−	6.73498e8i	0.372595	−	0.120138i
$611$		−	8.89092e8i		−	0.157689i
$612$	3.69893e9	−	8.03504e8i	0.652298	−	0.141696i
$613$		−	5.83962e9i		−	1.02394i	−0.859005	−	0.511968i	$-0.828917\pi$
$613$		−	5.83962e9i		−	1.02394i	0.859005	−	0.511968i	$-0.171083\pi$
$614$	2.08692e9	+	6.47233e9i	0.363844	+	1.12842i
$615$	−7.21093e7	−	1.26728e9i	−0.0125005	−	0.219690i
$616$	−6.58910e8	+	5.88698e9i	−0.113578	+	1.01475i
$617$	4.42163e9	−	2.55283e9i	0.757851	−	0.437546i	−0.0706725	−	0.997500i	$-0.522515\pi$
$617$	4.42163e9	−	2.55283e9i	0.757851	−	0.437546i	0.828524	+	0.559954i	$0.189181\pi$
$618$	−3.45559e8	+	2.21374e9i	−0.0588928	+	0.377282i
$619$	3.77141e9	−	6.53228e9i	0.639127	−	1.10700i	−0.346498	−	0.938051i	$-0.612629\pi$
$619$	3.77141e9	−	6.53228e9i	0.639127	−	1.10700i	0.985625	−	0.168949i	$-0.0540374\pi$
$620$	−1.20035e9	+	1.20709e8i	−0.202272	+	0.0203408i
$621$	3.98593e9	+	4.78917e9i	0.667897	+	0.802490i
$622$	1.72289e9	−	1.90484e9i	0.287073	−	0.317389i
$623$	3.18363e9	−	5.51421e9i	0.527490	−	0.913640i
$624$	−4.58749e8	+	4.54628e8i	−0.0755838	+	0.0749049i
$625$	7.65221e8	+	1.32540e9i	0.125374	+	0.217154i
$626$	−1.01841e10	−	2.18864e9i	−1.65926	−	0.356586i
$627$	−2.16665e8	−	3.80778e9i	−0.0351036	−	0.616929i
$628$	3.73563e9	−	8.28986e9i	0.601873	−	1.33564i
$629$	−2.27510e9			−0.364522
$630$	5.25648e8	−	5.34610e9i	0.0837535	−	0.851815i
$631$			4.09363e8i			0.0648642i	0.999474	+	0.0324321i	$0.0103253\pi$
$631$			4.09363e8i			0.0648642i	−0.999474	+	0.0324321i	$0.989675\pi$
$632$	−1.14841e9	−	2.62691e9i	−0.180962	−	0.413937i
$633$	−2.43397e9	+	4.83031e9i	−0.381419	+	0.756941i
$634$	2.15450e9	+	4.63017e8i	0.335764	+	0.0721580i
$635$	7.60222e9	−	4.38915e9i	1.17824	−	0.680255i
$636$	−4.34445e9	−	1.66776e9i	−0.669629	−	0.257059i
$637$	2.79021e8	+	1.61093e8i	0.0427709	+	0.0246938i
$638$	−2.96642e9	−	2.68307e9i	−0.452231	−	0.409035i
$639$	−4.43018e9	+	1.01952e10i	−0.671689	+	1.54576i
$640$	4.25501e9	+	1.97524e9i	0.641609	+	0.297845i
$641$	−4.04041e8	−	2.33273e8i	−0.0605930	−	0.0349834i	0.469397	−	0.882987i	$-0.344471\pi$
$641$	−4.04041e8	−	2.33273e8i	−0.0605930	−	0.0349834i	−0.529990	+	0.848004i	$0.677804\pi$
$642$	9.86173e9	+	7.94949e9i	1.47089	+	1.18568i
$643$	6.13571e8	+	1.06274e9i	0.0910179	+	0.157648i	0.907940	−	0.419101i	$-0.137655\pi$
$643$	6.13571e8	+	1.06274e9i	0.0910179	+	0.157648i	−0.816922	+	0.576748i	$0.804321\pi$
$644$	5.00190e9	+	6.95001e9i	0.737963	+	1.02538i
$645$	−3.95191e9	−	6.02614e9i	−0.579893	−	0.884260i
$646$	−3.18753e9	+	1.02778e9i	−0.465201	+	0.149998i
$647$	−1.12006e10			−1.62584			−0.812918	−	0.582379i	$-0.802122\pi$
$647$	−1.12006e10			−1.62584			−0.812918	+	0.582379i	$0.802122\pi$
$648$	8.00946e8	+	6.88001e9i	0.115635	+	0.993292i
$649$	9.38530e9			1.34770
$650$	3.54289e8	−	1.14236e8i	0.0506012	−	0.0163157i
$651$	−1.34241e9	−	2.04700e9i	−0.190700	−	0.290793i
$652$	5.61703e8	−	4.04256e8i	0.0793671	−	0.0571202i
$653$	−9.62222e8	−	1.66662e9i	−0.135232	−	0.234229i	0.790454	−	0.612521i	$-0.209845\pi$
$653$	−9.62222e8	−	1.66662e9i	−0.135232	−	0.234229i	−0.925686	+	0.378293i	$0.876511\pi$
$654$	6.69332e9	+	5.39546e9i	0.935663	+	0.754234i
$655$	1.14895e9	+	6.63346e8i	0.159756	+	0.0922349i
$656$	4.47837e8	+	2.20417e9i	0.0619380	+	0.304847i
$657$	7.89948e8	−	1.81791e9i	0.108673	−	0.250089i
$658$	−9.71806e9	−	8.78981e9i	−1.32981	−	1.20279i
$659$	−5.36861e9	−	3.09957e9i	−0.730741	−	0.421893i	0.0879524	−	0.996125i	$-0.471968\pi$
$659$	−5.36861e9	−	3.09957e9i	−0.730741	−	0.421893i	−0.818693	+	0.574231i	$0.805301\pi$
$660$	1.58006e9	−	4.11601e9i	0.213929	−	0.557279i
$661$	1.11878e9	−	6.45928e8i	0.150674	−	0.0869920i	−0.422767	−	0.906238i	$-0.638941\pi$
$661$	1.11878e9	−	6.45928e8i	0.150674	−	0.0869920i	0.573442	+	0.819246i	$0.305608\pi$
$662$	3.52742e9	+	7.58066e8i	0.472556	+	0.101556i
$663$	2.39859e8	−	4.76009e8i	0.0319638	−	0.0634334i
$664$	3.99613e9	+	9.14084e9i	0.529726	+	1.21171i
$665$			4.75304e9i			0.626751i
$666$	4.07374e8	−	4.14320e9i	0.0534359	−	0.543471i
$667$	−5.78176e9			−0.754431
$668$	−5.46389e8	−	2.46217e8i	−0.0709226	−	0.0319596i
$669$	−1.50058e8	−	2.63719e9i	−0.0193761	−	0.340525i
$670$	8.26421e9	+	1.77604e9i	1.06155	+	0.228134i
$671$	1.82744e9	+	3.16522e9i	0.233515	+	0.404459i
$672$	4.33914e8	+	9.50885e9i	0.0551583	+	1.20875i
$673$	−1.90773e8	+	3.30429e8i	−0.0241248	+	0.0417854i	−0.877836	−	0.478962i	$-0.841013\pi$
$673$	−1.90773e8	+	3.30429e8i	−0.0241248	+	0.0417854i	0.853711	+	0.520747i	$0.174347\pi$
$674$	−1.38550e8	+	1.53182e8i	−0.0174300	+	0.0192707i
$675$	1.38045e9	−	3.74590e9i	0.172766	−	0.468805i
$676$	−7.94536e8	−	7.90101e9i	−0.0989237	−	0.983715i
$677$	2.01904e9	−	3.49708e9i	0.250083	−	0.433157i	−0.713465	−	0.700690i	$-0.752875\pi$
$677$	2.01904e9	−	3.49708e9i	0.250083	−	0.433157i	0.963548	+	0.267534i	$0.0862087\pi$
$678$	−1.11874e8	+	7.16692e8i	−0.0137856	+	0.0883139i
$679$	−1.06550e10	+	6.15168e9i	−1.30620	+	0.754135i
$680$	−3.84754e9	−	4.30642e8i	−0.469247	−	0.0525213i
$681$	−2.22091e8	−	3.90313e9i	−0.0269473	−	0.473586i
$682$	−6.16541e8	−	1.91213e9i	−0.0744247	−	0.230820i
$683$		−	1.21115e9i		−	0.145454i	−0.997352	−	0.0727270i	$-0.976830\pi$
$683$		−	1.21115e9i		−	0.145454i	0.997352	−	0.0727270i	$-0.0231702\pi$
$684$	−1.30094e9	−	5.98887e9i	−0.155439	−	0.715564i
$685$			8.29464e9i			0.986008i
$686$	−5.21815e9	+	1.68252e9i	−0.617138	+	0.198988i
$687$	−1.18723e10	−	5.98239e9i	−1.39697	−	0.703925i
$688$	8.45874e9	+	9.56595e9i	0.990253	+	1.11987i
$689$	−5.67514e8	+	3.27654e8i	−0.0661012	+	0.0381636i
$690$	−2.29717e9	−	5.94464e9i	−0.266208	−	0.688897i
$691$	−3.61367e9	+	6.25906e9i	−0.416654	+	0.721665i	−0.995600	−	0.0937001i	$-0.970131\pi$
$691$	−3.61367e9	+	6.25906e9i	−0.416654	+	0.721665i	0.578947	+	0.815365i	$0.303464\pi$
$692$	−2.57115e8	−	2.55680e9i	−0.0294955	−	0.293309i
$693$	8.88828e9	−	1.01478e9i	1.01450	−	0.115826i
$694$	4.16258e9	+	3.76498e9i	0.472720	+	0.427567i
$695$	4.22260e9	−	7.31376e9i	0.477126	−	0.826407i
$696$	−5.38239e9	−	3.51271e9i	−0.605122	−	0.394921i
$697$	−9.28129e8	−	1.60757e9i	−0.103823	−	0.179827i
$698$	−5.94974e8	+	2.76852e9i	−0.0662222	+	0.308144i
$699$	2.49942e9	−	1.63911e9i	0.276802	−	0.181525i
$700$	2.25397e9	−	5.00186e9i	0.248373	−	0.551173i
$701$	−4.59622e9			−0.503950			−0.251975	−	0.967734i	$-0.581080\pi$
$701$	−4.59622e9			−0.503950			−0.251975	+	0.967734i	$0.581080\pi$
$702$	8.23915e8	+	5.22042e8i	0.0898882	+	0.0569542i
$703$			3.68358e9i			0.399877i
$704$	−1.72718e9	+	7.61901e9i	−0.186566	+	0.822989i
$705$	5.34820e9	+	8.15530e9i	0.574839	+	0.876553i
$706$	8.21878e8	−	3.82434e9i	0.0879004	−	0.409016i
$707$	−1.15719e10	+	6.68103e9i	−1.23150	+	0.711009i
$708$	1.48954e10	−	2.35896e9i	1.57738	−	0.249807i
$709$	1.13410e10	+	6.54770e9i	1.19505	+	0.689965i	0.959449	−	0.281883i	$-0.0909591\pi$
$709$	1.13410e10	+	6.54770e9i	1.19505	+	0.689965i	0.235606	+	0.971849i	$0.424292\pi$
$710$	7.62684e9	−	8.43227e9i	0.799724	−	0.884179i
$711$	−3.47985e9	+	2.57620e9i	−0.363092	+	0.268804i
$712$	4.98147e9	−	6.76008e9i	0.517223	−	0.701895i
$713$	−2.51505e9	−	1.45206e9i	−0.259856	−	0.150028i
$714$	−2.83162e9	−	7.32770e9i	−0.291133	−	0.753397i
$715$	−3.10426e8	−	5.37674e8i	−0.0317605	−	0.0550108i
$716$	−7.44397e9	−	1.03432e10i	−0.757895	−	1.05308i
$717$	3.67236e9	−	7.28793e9i	0.372073	−	0.738392i
$718$	−5.36746e9	−	1.66466e10i	−0.541170	−	1.67838i
$719$	9.61770e7			0.00964984			0.00482492	−	0.999988i	$-0.498464\pi$
$719$	9.61770e7			0.00964984			0.00482492	+	0.999988i	$0.498464\pi$
$720$	1.47318e9	−	6.92967e9i	0.147093	−	0.691909i
$721$	4.65002e9			0.462042
$722$	−1.43941e9	−	4.46416e9i	−0.142332	−	0.441427i
$723$	4.60256e9	−	2.61889e8i	0.452914	−	0.0257711i
$724$	−1.02503e10	−	1.42426e10i	−1.00381	−	1.39477i
$725$	1.85221e9	+	3.20812e9i	0.180512	+	0.312656i
$726$	−2.93268e9	−	4.57783e8i	−0.284437	−	0.0443999i
$727$	3.62628e9	+	2.09363e9i	0.350018	+	0.202083i	0.664693	−	0.747116i	$-0.268562\pi$
$727$	3.62628e9	+	2.09363e9i	0.350018	+	0.202083i	−0.314675	+	0.949199i	$0.601896\pi$
$728$	1.07908e9	+	7.95173e8i	0.103656	+	0.0763839i
$729$	9.85793e9	−	3.49861e9i	0.942409	−	0.334464i
$730$	−1.35995e9	+	1.50356e9i	−0.129387	+	0.143051i
$731$	−9.12663e9	−	5.26926e9i	−0.864171	−	0.498929i
$732$	3.69590e9	+	4.56420e9i	0.348282	+	0.430107i
$733$	−1.19405e10	+	6.89388e9i	−1.11985	+	0.646546i	−0.941363	−	0.337396i	$-0.890454\pi$
$733$	−1.19405e10	+	6.89388e9i	−1.11985	+	0.646546i	−0.178488	+	0.983942i	$0.557121\pi$
$734$	3.42614e9	−	1.59424e10i	0.319793	−	1.48805i
$735$	−3.52838e9	+	2.00767e8i	−0.327770	+	0.0186503i
$736$	5.53612e9	+	9.84267e9i	0.511839	+	0.909998i
$737$			1.40770e10i			1.29531i
$738$	3.09374e9	−	1.40238e9i	0.283326	−	0.128430i
$739$	−9.78953e9			−0.892291			−0.446145	−	0.894961i	$-0.647204\pi$
$739$	−9.78953e9			−0.892291			−0.446145	+	0.894961i	$0.647204\pi$
$740$	−1.74943e9	+	3.88221e9i	−0.158703	+	0.352183i
$741$	−7.70699e8	−	3.88352e8i	−0.0695858	−	0.0350640i
$742$	−2.02924e9	+	9.44239e9i	−0.182355	+	0.848532i
$743$	−4.30346e9	−	7.45380e9i	−0.384908	−	0.666680i	0.606849	−	0.794817i	$-0.292433\pi$
$743$	−4.30346e9	−	7.45380e9i	−0.384908	−	0.666680i	−0.991756	+	0.128138i	$0.959100\pi$
$744$	−1.45912e9	−	2.87978e9i	−0.129893	−	0.256363i
$745$	−6.15847e8	+	1.06668e9i	−0.0545664	+	0.0945119i
$746$	−5.35866e9	−	4.84682e9i	−0.472575	−	0.427435i
$747$	1.21088e10	−	8.96441e9i	1.06287	−	0.786864i
$748$	−6.45113e8	−	6.41512e9i	−0.0563612	−	0.560466i
$749$	1.31443e10	−	2.27666e10i	1.14302	−	1.97976i
$750$	−7.69160e9	+	9.54180e9i	−0.665737	+	0.825878i
$751$	−4.07823e9	+	2.35457e9i	−0.351344	+	0.202848i	−0.665277	−	0.746597i	$-0.731687\pi$
$751$	−4.07823e9	+	2.35457e9i	−0.351344	+	0.202848i	0.313933	+	0.949445i	$0.398353\pi$
$752$	−1.14474e10	−	1.29458e10i	−0.981621	−	1.11011i
$753$	−6.98320e9	+	4.57955e9i	−0.596036	+	0.390877i
$754$	−8.61404e8	+	2.77748e8i	−0.0731825	+	0.0235967i
$755$		−	1.06963e10i		−	0.904523i
$756$	1.38515e10	−	3.84460e9i	1.16593	−	0.323612i
$757$			5.92377e9i			0.496321i	0.968719	+	0.248161i	$0.0798261\pi$
$757$			5.92377e9i			0.496321i	−0.968719	+	0.248161i	$0.920174\pi$
$758$	1.42811e9	+	4.42911e9i	0.119102	+	0.369381i
$759$	8.87509e9	−	5.82024e9i	0.736761	−	0.483164i
$760$	−6.97246e8	+	6.22948e9i	−0.0576154	+	0.514760i
$761$	−1.40891e10	+	8.13432e9i	−1.15887	+	0.669075i	−0.951033	−	0.309088i	$-0.899976\pi$
$761$	−1.40891e10	+	8.13432e9i	−1.15887	+	0.669075i	−0.207839	+	0.978163i	$0.566643\pi$
$762$	1.82887e10	+	1.47424e10i	1.49741	+	1.20705i
$763$	8.92128e9	−	1.54521e10i	0.727095	−	1.25937i
$764$	2.12573e9	+	2.11386e10i	0.172457	+	1.71495i
$765$	6.63229e8	+	5.80909e9i	0.0535610	+	0.469130i
$766$	3.55344e9	−	3.92870e9i	0.285659	−	0.315826i
$767$	1.06185e9	−	1.83918e9i	0.0849726	−	0.147177i
$768$	−8.26198e8	+	1.25263e10i	−0.0658142	+	0.997832i
$769$	−1.90474e9	−	3.29910e9i	−0.151040	−	0.261610i	0.780570	−	0.625069i	$-0.214929\pi$
$769$	−1.90474e9	−	3.29910e9i	−0.151040	−	0.261610i	−0.931610	+	0.363459i	$0.881596\pi$
$770$	−8.94590e9	−	1.92254e9i	−0.706166	−	0.151760i
$771$	1.37656e9	+	6.93643e8i	0.108169	+	0.0545061i
$772$	1.19206e10	+	5.37173e9i	0.932475	+	0.420197i
$773$	1.25296e10			0.975683			0.487842	−	0.872932i	$-0.337784\pi$
$773$	1.25296e10			0.975683			0.487842	+	0.872932i	$0.337784\pi$
$774$	1.12301e10	−	1.56771e10i	0.870542	−	1.21527i
$775$			1.86070e9i			0.143588i
$776$	−1.48672e10	+	6.49955e9i	−1.14213	+	0.499307i
$777$	−8.62630e9	+	4.90842e8i	−0.659707	+	0.0375377i
$778$	−2.05443e10	−	4.41511e9i	−1.56409	−	0.336135i
$779$	−2.60278e9	+	1.50272e9i	−0.197268	+	0.113893i
$780$	−6.27820e8	−	7.75318e8i	−0.0473701	−	0.0584991i
$781$	1.63978e10	+	9.46728e9i	1.23171	+	0.711126i
$782$	−6.91198e9	−	6.25177e9i	−0.516867	−	0.467497i
$783$	−3.35637e9	+	9.10762e9i	−0.249864	+	0.678014i
$784$	6.13686e9	−	1.24687e9i	0.454821	−	0.0924092i
$785$	1.21634e10	+	7.02254e9i	0.897451	+	0.518144i
$786$	−5.47552e8	+	3.50776e9i	−0.0402204	+	0.257662i
$787$	1.55146e8	+	2.68721e8i	0.0113456	+	0.0196512i	0.871642	−	0.490142i	$-0.163055\pi$
$787$	1.55146e8	+	2.68721e8i	0.0113456	+	0.0196512i	−0.860297	+	0.509793i	$0.829722\pi$
$788$	−1.24892e10	+	8.98843e9i	−0.909269	+	0.654398i
$789$	−1.86539e10	+	1.06142e9i	−1.35208	+	0.0769340i
$790$	4.21480e9	−	1.35901e9i	0.304146	−	0.0980678i
$791$	1.50543e9			0.108154
$792$	1.17981e10	−	2.61438e7i	0.843869	−	0.00186995i
$793$	8.27023e8			0.0588927
$794$	−7.43071e9	+	2.39593e9i	−0.526816	+	0.169865i
$795$	3.23463e9	−	6.41925e9i	0.228318	−	0.453105i
$796$	6.02536e9	+	8.37208e9i	0.423435	+	0.588352i
$797$	−1.40585e9	−	2.43500e9i	−0.0983635	−	0.170371i	0.812644	−	0.582761i	$-0.198027\pi$
$797$	−1.40585e9	−	2.43500e9i	−0.0983635	−	0.170371i	−0.911007	+	0.412390i	$0.864694\pi$
$798$	−1.18641e10	+	4.58463e9i	−0.826469	+	0.319370i
$799$	1.23513e10	+	7.13101e9i	0.856639	+	0.494581i
$800$	3.68787e9	−	6.22495e9i	0.254660	−	0.429854i
$801$	−1.16309e10	−	5.05404e9i	−0.799648	−	0.347476i
$802$	1.14444e8	+	1.03512e8i	0.00783395	+	0.00708567i
$803$	−2.92391e9	−	1.68812e9i	−0.199278	−	0.115053i
$804$	3.53819e9	+	2.23416e10i	0.240096	+	1.51606i
$805$	−1.14546e10	+	6.61331e9i	−0.773916	+	0.446820i
$806$	−4.44463e8	−	9.55183e7i	−0.0298995	−	0.00642560i
$807$	−9.17846e9	−	1.39959e10i	−0.614770	−	0.937442i
$808$	−1.61466e10	+	7.05884e9i	−1.07681	+	0.470753i
$809$		−	1.79807e10i		−	1.19395i	−0.802260	−	0.596975i	$-0.796369\pi$
$809$		−	1.79807e10i		−	1.19395i	0.802260	−	0.596975i	$-0.203631\pi$
$810$	−1.06977e10	+	1.67650e8i	−0.707284	+	0.0110842i
$811$	2.52692e10			1.66348			0.831741	−	0.555164i	$-0.187344\pi$
$811$	2.52692e10			1.66348			0.831741	+	0.555164i	$0.187344\pi$
$812$	−5.48020e9	+	1.21613e10i	−0.359212	+	0.797140i
$813$	2.16429e10	−	1.41933e10i	1.41253	−	0.926333i
$814$	−6.93302e9	−	1.48995e9i	−0.450544	−	0.0968251i
$815$	5.34490e8	+	9.25765e8i	0.0345850	+	0.0599031i
$816$	−2.63628e9	−	1.00193e10i	−0.169854	−	0.645538i
$817$	−8.53137e9	+	1.47768e10i	−0.547321	+	0.947987i
$818$	−2.01617e10	+	2.22909e10i	−1.28792	+	1.42394i
$819$	8.06756e8	−	1.85659e9i	0.0513155	−	0.118093i
$820$	−3.45682e9	+	3.47622e8i	−0.218942	+	0.0220171i
$821$	8.13977e9	−	1.40985e10i	0.513347	−	0.889144i	−0.486533	−	0.873662i	$-0.661739\pi$
$821$	8.13977e9	−	1.40985e10i	0.513347	−	0.889144i	0.999880	−	0.0154813i	$-0.00492804\pi$
$822$	−2.07044e10	+	8.00074e9i	−1.30020	+	0.502434i
$823$	1.42976e10	−	8.25474e9i	0.894056	−	0.516184i	0.0187892	−	0.999823i	$-0.494019\pi$
$823$	1.42976e10	−	8.25474e9i	0.894056	−	0.516184i	0.875267	+	0.483640i	$0.160686\pi$
$824$	6.09447e9	+	6.82134e8i	0.379482	+	0.0424741i
$825$	−6.07263e9	−	3.05997e9i	−0.376520	−	0.189727i
$826$	−9.60505e9	−	2.97890e10i	−0.593020	−	1.83918i
$827$			7.47272e9i			0.459419i	0.973259	+	0.229710i	$0.0737777\pi$
$827$			7.47272e9i			0.459419i	−0.973259	+	0.229710i	$0.926222\pi$
$828$	1.26228e10	−	1.14680e10i	0.772767	−	0.702073i
$829$			2.17454e9i			0.132565i	0.997801	+	0.0662823i	$0.0211138\pi$
$829$			2.17454e9i			0.132565i	−0.997801	+	0.0662823i	$0.978886\pi$
$830$	−1.46662e10	+	4.72893e9i	−0.890318	+	0.287071i
$831$	−5.29519e8	−	9.30603e9i	−0.0320094	−	0.562549i
$832$	1.29764e9	+	1.20048e9i	0.0781126	+	0.0722640i
$833$	−4.47580e9	+	2.58410e9i	−0.268295	+	0.154900i
$834$	2.23290e10	+	3.48550e9i	1.33287	+	0.208058i
$835$	4.62859e8	−	8.01696e8i	0.0275135	−	0.0476548i
$836$	−1.03866e10	+	1.04449e9i	−0.614826	+	0.0618277i
$837$	−3.74735e9	+	3.11885e9i	−0.220895	+	0.183846i
$838$	1.42203e9	+	1.28620e9i	0.0834744	+	0.0755011i
$839$	6.84256e9	−	1.18517e10i	0.399992	−	0.692807i	−0.593732	−	0.804663i	$-0.702346\pi$
$839$	6.84256e9	−	1.18517e10i	0.399992	−	0.692807i	0.993724	+	0.111856i	$0.0356794\pi$
$840$	−1.46813e10	−	8.02741e8i	−0.854646	−	0.0467302i
$841$	4.12156e9	+	7.13875e9i	0.238933	+	0.413843i
$842$	−2.95041e9	+	1.37288e10i	−0.170330	+	0.792574i
$843$	5.47705e8	+	9.62563e9i	0.0314884	+	0.553392i
$844$	1.34974e10	+	6.08227e9i	0.772771	+	0.348231i
$845$	1.22659e10			0.699361
$846$	−1.51979e10	+	2.12161e10i	−0.862954	+	1.20467i
$847$			6.16017e9i			0.348338i
$848$	−4.04473e9	+	1.20778e10i	−0.227774	+	0.680148i
$849$	−8.70341e9	+	1.72722e10i	−0.488104	+	0.968661i
$850$	−1.25463e9	+	5.83802e9i	−0.0700728	+	0.326061i
$851$	−8.87724e9	+	5.12528e9i	−0.493770	+	0.285078i
$852$	2.84046e10	+	1.09040e10i	1.57344	+	0.604015i
$853$	−1.65436e10	−	9.55146e9i	−0.912659	−	0.526924i	−0.0313734	−	0.999508i	$-0.509988\pi$
$853$	−1.65436e10	−	9.55146e9i	−0.912659	−	0.526924i	−0.881286	+	0.472584i	$0.843321\pi$
$854$	8.17618e9	−	9.03962e9i	0.449208	−	0.496647i
$855$	9.40540e9	−	1.07382e9i	0.514631	−	0.0587559i
$856$	2.05671e10	−	2.79105e10i	1.12077	−	1.52093i
$857$	2.47159e10	+	1.42697e10i	1.34135	+	0.774431i	0.987006	−	0.160683i	$-0.0513698\pi$
$857$	2.47159e10	+	1.42697e10i	1.34135	+	0.774431i	0.354347	+	0.935114i	$0.384703\pi$
$858$	1.04267e9	−	1.29348e9i	0.0563562	−	0.0699126i
$859$	1.66266e10	+	2.87981e10i	0.895008	+	1.55020i	0.833794	+	0.552075i	$0.186164\pi$
$859$	1.66266e10	+	2.87981e10i	0.895008	+	1.55020i	0.0612139	+	0.998125i	$0.480503\pi$
$860$	−1.60093e10	+	1.15218e10i	−0.858278	+	0.617699i
$861$	−3.86593e9	−	5.89503e9i	−0.206416	−	0.314757i
$862$	1.30590e9	+	4.05009e9i	0.0694439	+	0.215372i
$863$	−1.74869e10			−0.926135			−0.463068	−	0.886323i	$-0.653251\pi$
$863$	−1.74869e10			−0.926135			−0.463068	+	0.886323i	$0.653251\pi$
$864$	1.87183e10	−	3.00691e9i	0.987342	−	0.158607i
$865$	3.96930e9			0.208525
$866$	9.56606e9	+	2.96680e10i	0.500519	+	1.55230i
$867$	−5.83449e9	−	8.89683e9i	−0.304044	−	0.463627i
$868$	−5.43813e9	+	3.91381e9i	−0.282248	+	0.203133i
$869$	3.68746e9	+	6.38688e9i	0.190616	+	0.330156i
$870$	6.23058e9	−	7.72933e9i	0.320783	−	0.397946i
$871$	2.75857e9	+	1.59266e9i	0.141456	+	0.0816695i
$872$	1.39593e10	−	1.89433e10i	0.712943	−	0.967495i
$873$	1.45803e10	+	1.96945e10i	0.741679	+	1.00183i
$874$	−1.01221e10	+	1.11911e10i	−0.512840	+	0.566998i
$875$	2.20281e10	+	1.27179e10i	1.11160	+	0.641782i
$876$	−5.06484e9	−	1.94430e9i	−0.254567	−	0.0977236i
$877$	−1.39487e10	+	8.05331e9i	−0.698291	+	0.403158i	−0.806710	−	0.590947i	$-0.798754\pi$
$877$	−1.39487e10	+	8.05331e9i	−0.698291	+	0.403158i	0.108420	+	0.994105i	$0.465421\pi$
$878$	6.49217e9	−	3.02092e10i	0.323712	−	1.50629i
$879$	5.08122e9	−	1.00839e10i	0.252352	−	0.500802i
$880$	−1.14428e10	−	3.83206e9i	−0.566033	−	0.189558i
$881$		−	1.64306e10i		−	0.809541i	−0.914418	−	0.404771i	$-0.867351\pi$
$881$		−	1.64306e10i		−	0.809541i	0.914418	−	0.404771i	$-0.132649\pi$
$882$	−3.90450e9	−	8.61360e9i	−0.191613	−	0.422712i
$883$	−2.82754e10			−1.38212			−0.691061	−	0.722796i	$-0.742856\pi$
$883$	−2.82754e10			−1.38212			−0.691061	+	0.722796i	$0.742856\pi$
$884$	−1.33012e9	−	5.99386e8i	−0.0647601	−	0.0291826i
$885$	1.32336e9	+	2.32575e10i	0.0641768	+	1.12787i
$886$	−3.73305e9	+	1.73706e10i	−0.180321	+	0.839065i
$887$	4.58328e9	+	7.93847e9i	0.220518	+	0.381948i	0.954965	−	0.296718i	$-0.0958920\pi$
$887$	4.58328e9	+	7.93847e9i	0.220518	+	0.381948i	−0.734448	+	0.678665i	$0.762559\pi$
$888$	−1.13779e10	−	6.22119e8i	−0.545277	−	0.0298146i
$889$	2.43763e10	−	4.22210e10i	1.16362	−	2.01545i
$890$	9.61971e9	+	8.70085e9i	0.457401	+	0.413711i
$891$	−4.01614e9	−	1.73590e10i	−0.190212	−	0.822155i
$892$	−7.19355e9	+	7.23393e8i	−0.339364	+	0.0341269i
$893$	1.15457e10	−	1.99977e10i	0.542550	−	0.939724i
$894$	−3.25658e9	−	5.08344e8i	−0.152434	−	0.0237945i
$895$	1.70470e10	−	9.84211e9i	0.794819	−	0.458889i
$896$	2.59504e10	−	2.31533e9i	1.20522	−	0.107531i
$897$	−1.36430e8	−	2.39769e9i	−0.00631157	−	0.110923i
$898$	2.18621e10	−	7.04915e9i	1.00745	−	0.324840i
$899$		−	4.52402e9i		−	0.207666i
$900$	−1.04070e10	−	3.33016e9i	−0.475857	−	0.152270i
$901$		−	1.05119e10i		−	0.478788i
$902$	−1.77554e9	−	5.50665e9i	−0.0805580	−	0.249841i
$903$	−3.57415e10	−	1.80100e10i	−1.61534	−	0.813965i
$904$	1.97307e9	+	2.20839e8i	0.0888287	+	0.00994230i
$905$	2.34738e10	−	1.35526e10i	1.05272	−	0.607788i
$906$	2.66993e10	−	1.03173e10i	1.19275	−	0.460912i
$907$	−4.94281e9	+	8.56121e9i	−0.219963	+	0.380986i	−0.954796	−	0.297261i	$-0.903927\pi$
$907$	−4.94281e9	+	8.56121e9i	−0.219963	+	0.380986i	0.734834	+	0.678247i	$0.237260\pi$
$908$	−1.06467e10	+	1.07065e9i	−0.471971	+	0.0474621i
$909$	1.58349e10	+	2.13892e10i	0.699265	+	0.944543i
$910$	−1.38888e9	+	1.53556e9i	−0.0610971	+	0.0675493i
$911$	−9.30309e9	+	1.61134e10i	−0.407674	+	0.706112i	−0.994629	−	0.103508i	$-0.966993\pi$
$911$	−9.30309e9	+	1.61134e10i	−0.407674	+	0.706112i	0.586955	+	0.809620i	$0.300327\pi$
$912$	−1.62221e10	+	4.26835e9i	−0.708149	+	0.186328i
$913$	−1.28313e10	−	2.22244e10i	−0.557984	−	0.966457i
$914$	7.19304e9	+	1.54583e9i	0.311602	+	0.0669655i
$915$	−7.58596e9	+	4.97484e9i	−0.327369	+	0.214687i
$916$	−1.49494e10	+	3.31748e10i	−0.642674	+	1.42618i
$917$	7.36814e9			0.315548
$918$	−1.38605e10	+	7.25876e9i	−0.591328	+	0.309680i
$919$			3.91114e10i			1.66226i	0.556078	+	0.831130i	$0.312305\pi$
$919$			3.91114e10i			1.66226i	−0.556078	+	0.831130i	$0.687695\pi$
$920$	−1.59829e10	+	6.98729e9i	−0.676703	+	0.295836i
$921$	−1.54151e10	−	2.35061e10i	−0.650188	−	0.991450i
$922$	−6.32893e9	−	1.36013e9i	−0.265933	−	0.0571508i
$923$	3.71048e9	−	2.14225e9i	0.155319	−	0.0896735i
$924$	−3.83005e9	−	2.41845e10i	−0.159717	−	1.00852i
$925$	5.68771e9	+	3.28380e9i	0.236288	+	0.136421i
$926$	9.86456e9	+	8.92232e9i	0.408262	+	0.369266i
$927$	−1.05055e9	−	9.20155e9i	−0.0433149	−	0.379387i
$928$	−8.96654e9	+	1.51351e10i	−0.368304	+	0.621681i
$929$	2.26377e10	+	1.30699e10i	0.926354	+	0.534831i	0.885657	−	0.464341i	$-0.153709\pi$
$929$	2.26377e10	+	1.30699e10i	0.926354	+	0.534831i	0.0406973	+	0.999172i	$0.487042\pi$
$930$	4.65147e9	−	1.79745e9i	0.189627	−	0.0732769i
$931$	4.18387e9	+	7.24668e9i	0.169924	+	0.294317i
$932$	−4.77883e9	−	6.64006e9i	−0.193360	−	0.268668i
$933$	−4.77741e9	+	9.48095e9i	−0.192578	+	0.382179i
$934$	−1.72917e10	+	5.57547e9i	−0.694421	+	0.223907i
$935$	9.95915e9			0.398457
$936$	1.32971e9	−	2.31496e9i	0.0530020	−	0.0922738i
$937$	−4.38689e10			−1.74208			−0.871040	−	0.491212i	$-0.836554\pi$
$937$	−4.38689e10			−1.74208			−0.871040	+	0.491212i	$0.836554\pi$
$938$	4.46803e10	−	1.44066e10i	1.76769	−	0.569968i
$939$	4.29878e10	−	2.44604e9i	1.69440	−	0.0964125i
$940$	2.16657e10	−	1.55927e10i	0.850796	−	0.612315i
$941$	1.89658e9	+	3.28497e9i	0.0742005	+	0.128519i	0.900738	−	0.434362i	$-0.143026\pi$
$941$	1.89658e9	+	3.28497e9i	0.0742005	+	0.128519i	−0.826538	+	0.562881i	$0.809693\pi$
$942$	−5.79668e9	+	3.71350e10i	−0.225944	+	1.44746i
$943$	−7.24295e9	−	4.18172e9i	−0.281271	−	0.162392i
$944$	−8.21881e9	−	4.04514e10i	−0.317985	−	1.56506i
$945$	3.76799e9	+	2.18827e10i	0.145244	+	0.843509i
$946$	−2.43612e10	−	2.20343e10i	−0.935578	−	0.846213i
$947$	−2.94770e10	−	1.70185e10i	−1.12787	−	0.651174i	−0.184469	−	0.982838i	$-0.559057\pi$
$947$	−2.94770e10	−	1.70185e10i	−1.12787	−	0.651174i	−0.943398	+	0.331664i	$0.892390\pi$
$948$	7.45770e9	+	9.20979e9i	0.284299	+	0.351092i
$949$	−6.61619e8	+	3.81986e8i	−0.0251291	+	0.0145083i
$950$	9.45223e9	+	2.03135e9i	0.357686	+	0.0768691i
$951$	−9.09428e9	+	5.17470e8i	−0.342876	+	0.0195098i
$952$	−1.97014e10	+	8.61292e9i	−0.740061	+	0.323535i
$953$		−	3.48030e9i		−	0.130254i	−0.997877	−	0.0651270i	$-0.979255\pi$
$953$		−	3.48030e9i		−	0.130254i	0.997877	−	0.0651270i	$-0.0207453\pi$
$954$	1.91432e10	+	1.88223e9i	0.713832	+	0.0701865i
$955$	−3.28167e10			−1.21922
$956$	−2.03647e10	−	9.17688e9i	−0.753835	−	0.339698i
$957$	1.47647e10	+	7.43989e9i	0.544546	+	0.274394i
$958$	4.70250e10	+	1.01060e10i	1.72802	+	0.371364i
$959$	2.30333e10	+	3.98948e10i	0.843316	+	1.46067i
$960$	−1.91240e10	−	3.20577e9i	−0.697637	−	0.116945i
$961$	−1.26201e10	+	2.18587e10i	−0.458703	+	0.794497i
$962$	−1.07638e9	+	1.19005e9i	−0.0389809	+	0.0430974i
$963$	−4.80207e10	−	2.08667e10i	−1.73275	−	0.752943i
$964$	−1.26251e9	−	1.25546e10i	−0.0453904	−	0.451370i
$965$	−1.00982e10	+	1.74906e10i	−0.361742	+	0.626555i
$966$	−2.75563e10	−	2.22130e10i	−0.983561	−	0.792844i
$967$	3.42477e10	−	1.97729e10i	1.21798	−	0.703200i	0.253493	−	0.967337i	$-0.418421\pi$
$967$	3.42477e10	−	1.97729e10i	1.21798	−	0.703200i	0.964485	+	0.264137i	$0.0850873\pi$
$968$	−9.03665e8	+	8.07372e9i	−0.0320217	+	0.286095i
$969$	1.15764e10	−	7.59175e9i	0.408734	−	0.268046i
$970$	−7.69142e9	−	2.38541e10i	−0.270586	−	0.839192i
$971$		−	1.15968e10i		−	0.406510i	−0.979126	−	0.203255i	$-0.934848\pi$
$971$		−	1.15968e10i		−	0.406510i	0.979126	−	0.203255i	$-0.0651520\pi$
$972$	−1.07372e10	−	2.65411e10i	−0.375023	−	0.927016i
$973$		−	4.69028e10i		−	1.63231i
$974$	5.25637e10	−	1.69485e10i	1.82276	−	0.587724i
$975$	−1.28670e9	+	8.43810e8i	−0.0444591	+	0.0291560i
$976$	1.20420e10	−	1.06482e10i	0.414596	−	0.366609i
$977$	−2.47147e10	+	1.42691e10i	−0.847862	+	0.489513i	−0.859929	−	0.510414i	$-0.829492\pi$
$977$	−2.47147e10	+	1.42691e10i	−0.847862	+	0.489513i	0.0120672	+	0.999927i	$0.496159\pi$
$978$	−1.79527e9	+	2.22712e9i	−0.0613682	+	0.0761302i
$979$	−1.08005e10	+	1.87070e10i	−0.367877	+	0.637182i
$980$	9.67852e8	+	9.62449e9i	0.0328486	+	0.326653i
$981$	−3.25925e10	−	1.41626e10i	−1.10224	−	0.478962i
$982$	−1.23858e10	−	1.12027e10i	−0.417382	−	0.377515i
$983$	−3.48985e9	+	6.04459e9i	−0.117184	+	0.202969i	−0.918651	−	0.395071i	$-0.870720\pi$
$983$	−3.48985e9	+	6.04459e9i	−0.117184	+	0.202969i	0.801467	+	0.598040i	$0.204053\pi$
$984$	−4.20204e9	−	8.29333e9i	−0.140598	−	0.277489i
$985$	−1.18841e10	−	2.05839e10i	−0.396224	−	0.686279i
$986$	3.05046e9	−	1.41943e10i	0.101343	−	0.471569i
$987$	4.83697e10	+	2.43733e10i	1.60126	+	0.806870i
$988$	−9.70455e8	+	2.15357e9i	−0.0320130	+	0.0710411i
$989$	−4.74817e10			−1.56077
$990$	−1.78326e9	+	1.81367e10i	−0.0584106	+	0.594065i
$991$		−	2.32498e10i		−	0.758860i	−0.925220	−	0.379430i	$-0.876120\pi$
$991$		−	2.32498e10i		−	0.758860i	0.925220	−	0.379430i	$-0.123880\pi$
$992$	−7.70153e9	+	4.33182e9i	−0.250488	+	0.140890i
$993$	−1.48894e10	+	8.47219e8i	−0.482565	+	0.0274583i
$994$	1.32674e10	−	6.17356e10i	0.428483	−	1.99381i
$995$	−1.37983e10	+	7.96647e9i	−0.444064	+	0.256381i
$996$	−2.59506e10	−	3.20473e10i	−0.832222	−	1.02774i
$997$	−1.11867e10	−	6.45863e9i	−0.357494	−	0.206399i	0.310487	−	0.950578i	$-0.399508\pi$
$997$	−1.11867e10	−	6.45863e9i	−0.357494	−	0.206399i	−0.667981	+	0.744179i	$0.732841\pi$
$998$	1.62013e10	−	1.79122e10i	0.515933	−	0.570418i
$999$	2.92017e9	+	1.69590e10i	0.0926679	+	0.538171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.l.b.11.48	✓	160
8.3	odd	2	inner	72.8.l.b.11.74	yes	160
9.5	odd	6	inner	72.8.l.b.59.74	yes	160
72.59	even	6	inner	72.8.l.b.59.48	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.8.l.b.11.48	✓	160	1.1	even	1	trivial
72.8.l.b.11.74	yes	160	8.3	odd	2	inner
72.8.l.b.59.48	yes	160	72.59	even	6	inner
72.8.l.b.59.74	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)

\(f(q)\)	\(=\)	\(q+(3.47193 + 10.7678i) q^{2} +(-25.6457 - 39.1063i) q^{3} +(-103.891 + 74.7702i) q^{4} +(-98.8581 - 171.227i) q^{5} +(332.048 - 411.922i) q^{6} +(-950.958 - 549.036i) q^{7} +(-1165.82 - 859.085i) q^{8} +(-871.598 + 2005.81i) q^{9} +O(q^{10})\)	\(q+(3.47193 + 10.7678i) q^{2} +(-25.6457 - 39.1063i) q^{3} +(-103.891 + 74.7702i) q^{4} +(-98.8581 - 171.227i) q^{5} +(332.048 - 411.922i) q^{6} +(-950.958 - 549.036i) q^{7} +(-1165.82 - 859.085i) q^{8} +(-871.598 + 2005.81i) q^{9} +(1500.51 - 1658.97i) q^{10} +(3226.13 + 1862.60i) q^{11} +(5588.35 + 2145.27i) q^{12} +(730.005 - 421.469i) q^{13} +(2610.25 - 12145.9i) q^{14} +(-4160.77 + 8257.21i) q^{15} +(5202.82 - 15536.0i) q^{16} +13521.6i q^{17} +(-24624.3 - 2421.15i) q^{18} +21892.6 q^{19} +(23073.2 + 10397.4i) q^{20} +(2917.23 + 51268.8i) q^{21} +(-8855.27 + 41205.1i) q^{22} +(30461.1 + 52760.2i) q^{23} +(-3697.45 + 67622.5i) q^{24} +(19516.6 - 33803.8i) q^{25} +(7072.82 + 6397.24i) q^{26} +(100793. - 17355.5i) q^{27} +(139848. - 14063.3i) q^{28} +(-47452.0 + 82189.2i) q^{29} +(-103358. - 16133.9i) q^{30} +(-41282.9 + 23834.7i) q^{31} +(185352. + 2083.15i) q^{32} +(-9896.70 - 173929. i) q^{33} +(-145598. + 46946.2i) q^{34} +217106. i q^{35} +(-59423.6 - 273556. i) q^{36} +168256. i q^{37} +(76009.8 + 235736. i) q^{38} +(-35203.5 - 17738.9i) q^{39} +(-31848.4 + 284547. i) q^{40} +(-118889. + 68640.3i) q^{41} +(-541924. + 209414. i) q^{42} +(-389691. + 674965. i) q^{43} +(-474434. + 47709.7i) q^{44} +(429614. - 49049.5i) q^{45} +(-462353. + 511179. i) q^{46} +(527377. - 913444. i) q^{47} +(-740983. + 194967. i) q^{48} +(191109. + 331010. i) q^{49} +(431754. + 92786.8i) q^{50} +(528781. - 346772. i) q^{51} +(-44327.9 + 98369.6i) q^{52} -777411. q^{53} +(536826. + 1.02506e6i) q^{54} -736534. i q^{55} +(636973. + 1.45703e6i) q^{56} +(-561452. - 856139. i) q^{57} +(-1.04975e6 - 225598. i) q^{58} +(2.18187e6 - 1.25970e6i) q^{59} +(-185125. - 1.16895e6i) q^{60} +(849675. + 490560. i) q^{61} +(-399979. - 361774. i) q^{62} +(1.93012e6 - 1.42890e6i) q^{63} +(621099. + 2.00307e6i) q^{64} +(-144334. - 83331.2i) q^{65} +(1.83848e6 - 710437. i) q^{66} +(1.88942e6 + 3.27257e6i) q^{67} +(-1.01102e6 - 1.40478e6i) q^{68} +(1.28206e6 - 2.54429e6i) q^{69} +(-2.33776e6 + 753779. i) q^{70} +5.08282e6 q^{71} +(2.73929e6 - 1.58963e6i) q^{72} -906322. q^{73} +(-1.81175e6 + 584175. i) q^{74} +(-1.82246e6 + 103699. i) q^{75} +(-2.27446e6 + 1.63692e6i) q^{76} +(-2.04527e6 - 3.54252e6i) q^{77} +(68784.8 - 440653. i) q^{78} +(1.71450e6 + 989868. i) q^{79} +(-3.17452e6 + 644991. i) q^{80} +(-3.26360e6 - 3.49653e6i) q^{81} +(-1.15188e6 - 1.04185e6i) q^{82} +(-5.96595e6 - 3.44444e6i) q^{83} +(-4.13645e6 - 5.10826e6i) q^{84} +(2.31527e6 - 1.33672e6i) q^{85} +(-8.62088e6 - 1.85269e6i) q^{86} +(4.43105e6 - 252130. i) q^{87} +(-2.16093e6 - 4.94297e6i) q^{88} +5.79858e6i q^{89} +(2.01975e6 + 4.45571e6i) q^{90} -925605. q^{91} +(-7.10954e6 - 3.20374e6i) q^{92} +(1.99082e6 + 1.00316e6i) q^{93} +(1.16668e7 + 2.50728e6i) q^{94} +(-2.16427e6 - 3.74862e6i) q^{95} +(-4.67202e6 - 7.30185e6i) q^{96} +(5.60226e6 - 9.70339e6i) q^{97} +(-2.90073e6 + 3.20707e6i) q^{98} +(-6.54792e6 + 4.84756e6i) 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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