LMFDB - Embedded newform 67.2.e.c.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, 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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			14.1
Root			$-0.625078 + 0.721379i$ of defining polynomial
Character	$\chi$	$=$	67.14
Dual form			67.2.e.c.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.797176 - 1.74557i) q^{2} +(-2.14425 - 1.37802i) q^{3} +(-1.10181 + 1.27155i) q^{4} +(0.201991 + 1.40488i) q^{5} +(-0.696097 + 4.84146i) q^{6} +(-0.918948 - 2.01222i) q^{7} +(-0.584585 - 0.171650i) q^{8} +(1.45260 + 3.18076i) q^{9} +O(q^{10})$	\(q+(-0.797176 - 1.74557i) q^{2} +(-2.14425 - 1.37802i) q^{3} +(-1.10181 + 1.27155i) q^{4} +(0.201991 + 1.40488i) q^{5} +(-0.696097 + 4.84146i) q^{6} +(-0.918948 - 2.01222i) q^{7} +(-0.584585 - 0.171650i) q^{8} +(1.45260 + 3.18076i) q^{9} +(2.29130 - 1.47253i) q^{10} +(-0.553204 - 3.84762i) q^{11} +(4.11478 - 1.20821i) q^{12} +(6.05411 - 1.77765i) q^{13} +(-2.77990 + 3.20818i) q^{14} +(1.50284 - 3.29076i) q^{15} +(0.645282 + 4.48803i) q^{16} +(-2.92877 - 3.37998i) q^{17} +(4.39426 - 5.07124i) q^{18} +(-0.654654 + 1.43349i) q^{19} +(-2.00894 - 1.29107i) q^{20} +(-0.802430 + 5.58102i) q^{21} +(-6.27529 + 4.03289i) q^{22} +(4.14315 + 2.66264i) q^{23} +(1.01696 + 1.17363i) q^{24} +(2.86458 - 0.841116i) q^{25} +(-7.92919 - 9.15078i) q^{26} +(0.180192 - 1.25327i) q^{27} +(3.57114 + 1.04858i) q^{28} -4.86467 q^{29} -6.94228 q^{30} +(7.43776 + 2.18392i) q^{31} +(6.29469 - 4.04535i) q^{32} +(-4.11591 + 9.01258i) q^{33} +(-3.56525 + 7.80681i) q^{34} +(2.64130 - 1.69746i) q^{35} +(-5.64499 - 1.65752i) q^{36} -3.80153 q^{37} +3.02414 q^{38} +(-15.4311 - 4.53099i) q^{39} +(0.123066 - 0.855944i) q^{40} +(4.04946 + 4.67333i) q^{41} +(10.3817 - 3.04836i) q^{42} +(-7.42037 - 8.56356i) q^{43} +(5.50198 + 3.53591i) q^{44} +(-4.17517 + 2.68322i) q^{45} +(1.34501 - 9.35475i) q^{46} +(4.42323 + 2.84264i) q^{47} +(4.80097 - 10.5127i) q^{48} +(1.37948 - 1.59200i) q^{49} +(-3.75180 - 4.32981i) q^{50} +(1.62231 + 11.2834i) q^{51} +(-4.41009 + 9.65675i) q^{52} +(-0.289752 + 0.334391i) q^{53} +(-2.33131 + 0.684534i) q^{54} +(5.29370 - 1.55437i) q^{55} +(0.191807 + 1.33405i) q^{56} +(3.37913 - 2.17163i) q^{57} +(3.87800 + 8.49163i) q^{58} +(2.98896 + 0.877638i) q^{59} +(2.52854 + 5.53673i) q^{60} +(0.240303 - 1.67134i) q^{61} +(-2.11701 - 14.7241i) q^{62} +(5.06550 - 5.84590i) q^{63} +(-4.45062 - 2.86024i) q^{64} +(3.72026 + 8.14623i) q^{65} +19.0132 q^{66} +(-7.70184 + 2.77157i) q^{67} +7.52477 q^{68} +(-5.21475 - 11.4187i) q^{69} +(-5.06862 - 3.25741i) q^{70} +(2.25142 - 2.59828i) q^{71} +(-0.303194 - 2.10876i) q^{72} +(-1.34946 + 9.38572i) q^{73} +(3.03049 + 6.63584i) q^{74} +(-7.30144 - 2.14390i) q^{75} +(-1.10146 - 2.41186i) q^{76} +(-7.23387 + 4.64893i) q^{77} +(4.39216 + 30.5482i) q^{78} +(-6.91577 + 2.03065i) q^{79} +(-6.17481 + 1.81309i) q^{80} +(4.75625 - 5.48900i) q^{81} +(4.92950 - 10.7941i) q^{82} +(-0.0107435 - 0.0747227i) q^{83} +(-6.21245 - 7.16955i) q^{84} +(4.15688 - 4.79730i) q^{85} +(-9.03296 + 19.7794i) q^{86} +(10.4311 + 6.70364i) q^{87} +(-0.337048 + 2.34422i) q^{88} +(4.17767 - 2.68483i) q^{89} +(8.01209 + 5.14906i) q^{90} +(-9.14042 - 10.5486i) q^{91} +(-7.95064 + 2.33452i) q^{92} +(-12.9389 - 14.9323i) q^{93} +(1.43593 - 9.98714i) q^{94} +(-2.14612 - 0.630157i) q^{95} -19.0720 q^{96} -7.27011 q^{97} +(-3.87864 - 1.13887i) q^{98} +(11.4348 - 7.34867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.797176	−	1.74557i	−0.563688	−	1.23431i	−0.950090	−	0.311975i	$-0.899010\pi$
$2$	−0.797176	−	1.74557i	−0.563688	−	1.23431i	0.386402	−	0.922330i	$-0.373718\pi$
$3$	−2.14425	−	1.37802i	−1.23798	−	0.795603i	−0.252867	−	0.967501i	$-0.581374\pi$
$3$	−2.14425	−	1.37802i	−1.23798	−	0.795603i	−0.985115	+	0.171898i	$0.945010\pi$
$4$	−1.10181	+	1.27155i	−0.550904	+	0.635777i
$5$	0.201991	+	1.40488i	0.0903332	+	0.628282i	0.983816	+	0.179183i	$0.0573455\pi$
$5$	0.201991	+	1.40488i	0.0903332	+	0.628282i	−0.893482	+	0.449098i	$0.851745\pi$
$6$	−0.696097	+	4.84146i	−0.284181	+	1.97652i
$7$	−0.918948	−	2.01222i	−0.347330	−	0.760546i	−0.999996	−	0.00290030i	$-0.999077\pi$
$7$	−0.918948	−	2.01222i	−0.347330	−	0.760546i	0.652666	−	0.757646i	$-0.273650\pi$
$8$	−0.584585	−	0.171650i	−0.206682	−	0.0606873i
$9$	1.45260	+	3.18076i	0.484201	+	1.06025i
$10$	2.29130	−	1.47253i	0.724571	−	0.465654i
$11$	−0.553204	−	3.84762i	−0.166797	−	1.16010i	−0.885451	−	0.464733i	$-0.846150\pi$
$11$	−0.553204	−	3.84762i	−0.166797	−	1.16010i	0.718654	−	0.695368i	$-0.244759\pi$
$12$	4.11478	−	1.20821i	1.18784	−	0.348780i
$13$	6.05411	−	1.77765i	1.67911	−	0.493030i	0.703159	−	0.711033i	$-0.251772\pi$
$13$	6.05411	−	1.77765i	1.67911	−	0.493030i	0.975948	+	0.218002i	$0.0699540\pi$
$14$	−2.77990	+	3.20818i	−0.742960	+	0.857422i
$15$	1.50284	−	3.29076i	0.388032	−	0.849671i
$16$	0.645282	+	4.48803i	0.161320	+	1.12201i
$17$	−2.92877	−	3.37998i	−0.710331	−	0.819765i	0.279778	−	0.960065i	$-0.409739\pi$
$17$	−2.92877	−	3.37998i	−0.710331	−	0.819765i	−0.990109	+	0.140299i	$0.955194\pi$
$18$	4.39426	−	5.07124i	1.03574	−	1.19530i
$19$	−0.654654	+	1.43349i	−0.150188	+	0.328866i	−0.969740	−	0.244139i	$-0.921495\pi$
$19$	−0.654654	+	1.43349i	−0.150188	+	0.328866i	0.819553	+	0.573004i	$0.194222\pi$
$20$	−2.00894	−	1.29107i	−0.449212	−	0.288691i
$21$	−0.802430	+	5.58102i	−0.175105	+	1.21788i
$22$	−6.27529	+	4.03289i	−1.33790	+	0.859814i
$23$	4.14315	+	2.66264i	0.863906	+	0.555199i	0.895883	−	0.444290i	$-0.146544\pi$
$23$	4.14315	+	2.66264i	0.863906	+	0.555199i	−0.0319769	+	0.999489i	$0.510180\pi$
$24$	1.01696	+	1.17363i	0.207586	+	0.239567i
$25$	2.86458	−	0.841116i	0.572915	−	0.168223i
$26$	−7.92919	−	9.15078i	−1.55504	−	1.79462i
$27$	0.180192	−	1.25327i	0.0346780	−	0.241191i
$28$	3.57114	+	1.04858i	0.674883	+	0.198164i
$29$	−4.86467			−0.903347			−0.451674	−	0.892183i	$-0.649173\pi$
$29$	−4.86467			−0.903347			−0.451674	+	0.892183i	$0.649173\pi$
$30$	−6.94228			−1.26748
$31$	7.43776	+	2.18392i	1.33586	+	0.392244i	0.870191	−	0.492714i	$-0.163995\pi$
$31$	7.43776	+	2.18392i	1.33586	+	0.392244i	0.465670	+	0.884958i	$0.345813\pi$
$32$	6.29469	−	4.04535i	1.11275	−	0.715123i
$33$	−4.11591	+	9.01258i	−0.716487	+	1.56889i
$34$	−3.56525	+	7.80681i	−0.611436	+	1.33886i
$35$	2.64130	−	1.69746i	0.446462	−	0.286923i
$36$	−5.64499	−	1.65752i	−0.940832	−	0.276253i
$37$	−3.80153			−0.624968			−0.312484	−	0.949923i	$-0.601161\pi$
$37$	−3.80153			−0.624968			−0.312484	+	0.949923i	$0.601161\pi$
$38$	3.02414			0.490580
$39$	−15.4311	−	4.53099i	−2.47096	−	0.725540i
$40$	0.123066	−	0.855944i	0.0194585	−	0.135337i
$41$	4.04946	+	4.67333i	0.632420	+	0.729852i	0.978016	−	0.208532i	$-0.0668685\pi$
$41$	4.04946	+	4.67333i	0.632420	+	0.729852i	−0.345596	+	0.938384i	$0.612323\pi$
$42$	10.3817	−	3.04836i	1.60194	−	0.470372i
$43$	−7.42037	−	8.56356i	−1.13160	−	1.30593i	−0.946315	−	0.323244i	$-0.895226\pi$
$43$	−7.42037	−	8.56356i	−1.13160	−	1.30593i	−0.185280	−	0.982686i	$-0.559319\pi$
$44$	5.50198	+	3.53591i	0.829455	+	0.533058i
$45$	−4.17517	+	2.68322i	−0.622397	+	0.399990i
$46$	1.34501	−	9.35475i	0.198311	−	1.37928i
$47$	4.42323	+	2.84264i	0.645194	+	0.414641i	0.821907	−	0.569621i	$-0.192910\pi$
$47$	4.42323	+	2.84264i	0.645194	+	0.414641i	−0.176713	+	0.984262i	$0.556546\pi$
$48$	4.80097	−	10.5127i	0.692961	−	1.51737i
$49$	1.37948	−	1.59200i	0.197068	−	0.227429i
$50$	−3.75180	−	4.32981i	−0.530584	−	0.612327i
$51$	1.62231	+	11.2834i	0.227169	+	1.58000i
$52$	−4.41009	+	9.65675i	−0.611569	+	1.33915i
$53$	−0.289752	+	0.334391i	−0.0398005	+	0.0459322i	−0.775301	−	0.631592i	$-0.782402\pi$
$53$	−0.289752	+	0.334391i	−0.0398005	+	0.0459322i	0.735500	+	0.677524i	$0.236947\pi$
$54$	−2.33131	+	0.684534i	−0.317251	+	0.0931533i
$55$	5.29370	−	1.55437i	0.713803	−	0.209591i
$56$	0.191807	+	1.33405i	0.0256313	+	0.178270i
$57$	3.37913	−	2.17163i	0.447576	−	0.287640i
$58$	3.87800	+	8.49163i	0.509206	+	1.11501i
$59$	2.98896	+	0.877638i	0.389129	+	0.114259i	0.470444	−	0.882430i	$-0.344094\pi$
$59$	2.98896	+	0.877638i	0.389129	+	0.114259i	−0.0813148	+	0.996688i	$0.525912\pi$
$60$	2.52854	+	5.53673i	0.326433	+	0.714788i
$61$	0.240303	−	1.67134i	0.0307676	−	0.213993i	−0.968638	−	0.248478i	$-0.920070\pi$
$61$	0.240303	−	1.67134i	0.0307676	−	0.213993i	0.999405	+	0.0344843i	$0.0109789\pi$
$62$	−2.11701	−	14.7241i	−0.268860	−	1.86996i
$63$	5.06550	−	5.84590i	0.638193	−	0.736514i
$64$	−4.45062	−	2.86024i	−0.556327	−	0.357530i
$65$	3.72026	+	8.14623i	0.461441	+	1.01042i
$66$	19.0132			2.34036
$67$	−7.70184	+	2.77157i	−0.940930	+	0.338602i
$67$	−7.70184	+	2.77157i	−0.940930	+	0.338602i
$68$	7.52477			0.912512
$69$	−5.21475	−	11.4187i	−0.627783	−	1.37465i
$70$	−5.06862	−	3.25741i	−0.605816	−	0.389334i
$71$	2.25142	−	2.59828i	0.267195	−	0.308359i	−0.606258	−	0.795268i	$-0.707330\pi$
$71$	2.25142	−	2.59828i	0.267195	−	0.308359i	0.873453	+	0.486909i	$0.161876\pi$
$72$	−0.303194	−	2.10876i	−0.0357318	−	0.248520i
$73$	−1.34946	+	9.38572i	−0.157943	+	1.09852i	0.744474	+	0.667651i	$0.232700\pi$
$73$	−1.34946	+	9.38572i	−0.157943	+	1.09852i	−0.902417	+	0.430864i	$0.858209\pi$
$74$	3.03049	+	6.63584i	0.352287	+	0.771401i
$75$	−7.30144	−	2.14390i	−0.843098	−	0.247556i
$76$	−1.10146	−	2.41186i	−0.126346	−	0.276659i
$77$	−7.23387	+	4.64893i	−0.824376	+	0.529795i
$78$	4.39216	+	30.5482i	0.497314	+	3.45890i
$79$	−6.91577	+	2.03065i	−0.778085	+	0.228467i	−0.646577	−	0.762849i	$-0.723800\pi$
$79$	−6.91577	+	2.03065i	−0.778085	+	0.228467i	−0.131508	+	0.991315i	$0.541982\pi$
$80$	−6.17481	+	1.81309i	−0.690364	+	0.202709i
$81$	4.75625	−	5.48900i	0.528472	−	0.609889i
$82$	4.92950	−	10.7941i	0.544372	−	1.19201i
$83$	−0.0107435	−	0.0747227i	−0.00117925	−	0.00820188i	0.989223	−	0.146415i	$-0.0467733\pi$
$83$	−0.0107435	−	0.0747227i	−0.00117925	−	0.00820188i	−0.990403	+	0.138213i	$0.955864\pi$
$84$	−6.21245	−	7.16955i	−0.677834	−	0.782262i
$85$	4.15688	−	4.79730i	0.450877	−	0.520340i
$86$	−9.03296	+	19.7794i	−0.974050	+	2.13287i
$87$	10.4311	+	6.70364i	1.11833	+	0.718705i
$88$	−0.337048	+	2.34422i	−0.0359294	+	0.249894i
$89$	4.17767	−	2.68483i	0.442832	−	0.284591i	−0.300163	−	0.953888i	$-0.597041\pi$
$89$	4.17767	−	2.68483i	0.442832	−	0.284591i	0.742995	+	0.669297i	$0.233405\pi$
$90$	8.01209	+	5.14906i	0.844548	+	0.542758i
$91$	−9.14042	−	10.5486i	−0.958176	−	1.10579i
$92$	−7.95064	+	2.33452i	−0.828912	+	0.243391i
$93$	−12.9389	−	14.9323i	−1.34170	−	1.54841i
$94$	1.43593	−	9.98714i	0.148105	−	1.03009i
$95$	−2.14612	−	0.630157i	−0.220187	−	0.0646528i
$96$	−19.0720			−1.94652
$97$	−7.27011			−0.738168			−0.369084	−	0.929396i	$-0.620328\pi$
$97$	−7.27011			−0.738168			−0.369084	+	0.929396i	$0.620328\pi$
$98$	−3.87864	−	1.13887i	−0.391802	−	0.115043i
$99$	11.4348	−	7.34867i	1.14924	−	0.738569i
$100$	−2.08669	+	4.56921i	−0.208669	+	0.456921i
$101$	8.27537	−	18.1205i	0.823430	−	1.80306i	0.290578	−	0.956851i	$-0.406152\pi$
$101$	8.27537	−	18.1205i	0.823430	−	1.80306i	0.532852	−	0.846208i	$-0.321120\pi$
$102$	18.4028	−	11.8267i	1.82214	−	1.17102i
$103$	9.12973	+	2.68073i	0.899579	+	0.264140i	0.698648	−	0.715465i	$-0.253785\pi$
$103$	9.12973	+	2.68073i	0.899579	+	0.264140i	0.200931	+	0.979605i	$0.435603\pi$
$104$	−3.84427			−0.376962
$105$	−8.00275			−0.780988
$106$	0.814687	+	0.239214i	0.0791294	+	0.0232345i
$107$	−1.61618	+	11.2408i	−0.156242	+	1.08669i	0.749238	+	0.662301i	$0.230420\pi$
$107$	−1.61618	+	11.2408i	−0.156242	+	1.08669i	−0.905480	+	0.424389i	$0.860489\pi$
$108$	1.39506	+	1.60998i	0.134239	+	0.154921i
$109$	−2.35779	+	0.692309i	−0.225835	+	0.0663112i	−0.392692	−	0.919670i	$-0.628456\pi$
$109$	−2.35779	+	0.692309i	−0.225835	+	0.0663112i	0.166857	+	0.985981i	$0.446638\pi$
$110$	−6.93327	−	8.00143i	−0.661062	−	0.762906i
$111$	8.15142	+	5.23860i	0.773699	+	0.497226i
$112$	8.43791	−	5.42271i	0.797307	−	0.512398i
$113$	−0.875744	+	6.09093i	−0.0823831	+	0.572987i	0.906262	+	0.422717i	$0.138923\pi$
$113$	−0.875744	+	6.09093i	−0.0823831	+	0.572987i	−0.988645	+	0.150270i	$0.951986\pi$
$114$	−6.48450	−	4.16733i	−0.607329	−	0.390306i
$115$	−2.90381	+	6.35846i	−0.270782	+	0.592929i
$116$	5.35993	−	6.18569i	0.497657	−	0.574327i
$117$	14.4485	+	16.6744i	1.33576	+	1.54155i
$118$	−0.850747	−	5.91707i	−0.0783176	−	0.544711i
$119$	−4.10986	+	8.99934i	−0.376750	+	0.824968i
$120$	−1.44340	+	1.66577i	−0.131763	+	0.152063i
$121$	−3.94372	+	1.15798i	−0.358520	+	0.105271i
$122$	−3.10901	+	0.912887i	−0.281476	+	0.0826489i
$123$	−2.24309	−	15.6010i	−0.202253	−	1.40670i
$124$	−10.9720	+	7.05125i	−0.985311	+	0.633221i
$125$	4.70833	+	10.3098i	0.421126	+	0.922138i
$126$	−14.2425	−	4.18198i	−1.26882	−	0.372561i
$127$	2.39991	+	5.25506i	0.212957	+	0.466312i	0.985722	−	0.168381i	$-0.0538540\pi$
$127$	2.39991	+	5.25506i	0.212957	+	0.466312i	−0.772765	+	0.634693i	$0.781127\pi$
$128$	0.684919	−	4.76371i	0.0605388	−	0.421057i
$129$	4.11031	+	28.5878i	0.361893	+	2.51702i
$130$	11.2541	−	12.9879i	0.987051	−	1.13912i
$131$	6.10487	+	3.92336i	0.533385	+	0.342786i	0.779447	−	0.626468i	$-0.215500\pi$
$131$	6.10487	+	3.92336i	0.533385	+	0.342786i	−0.246062	+	0.969254i	$0.579137\pi$
$132$	−6.92504	−	15.1637i	−0.602748	−	1.31983i
$133$	3.48609			0.302282
$134$	10.9777	+	11.2347i	0.948329	+	0.970529i
$135$	1.79708			0.154668
$136$	1.13194	+	2.47861i	0.0970632	+	0.212539i
$137$	7.24755	+	4.65772i	0.619200	+	0.397936i	0.812297	−	0.583244i	$-0.198217\pi$
$137$	7.24755	+	4.65772i	0.619200	+	0.397936i	−0.193097	+	0.981180i	$0.561853\pi$
$138$	−15.7751	+	18.2054i	−1.34287	+	1.54975i
$139$	0.0862444	+	0.599843i	0.00731515	+	0.0508780i	0.993152	−	0.116829i	$-0.0372729\pi$
$139$	0.0862444	+	0.599843i	0.00731515	+	0.0508780i	−0.985837	+	0.167707i	$0.946364\pi$
$140$	−0.751793	+	5.22884i	−0.0635381	+	0.441917i
$141$	−5.56728	−	12.1906i	−0.468849	−	1.02664i
$142$	−6.33026	−	1.85873i	−0.531224	−	0.155981i
$143$	−10.1889	−	22.3105i	−0.852036	−	1.86570i
$144$	−13.3380	+	8.57181i	−1.11150	+	0.714318i
$145$	−0.982622	−	6.83428i	−0.0816023	−	0.567556i
$146$	17.4592	−	5.12648i	1.44493	−	0.424271i
$147$	−5.15177	+	1.51269i	−0.424910	+	0.124765i
$148$	4.18856	−	4.83385i	0.344297	−	0.397340i
$149$	1.31795	−	2.88590i	0.107971	−	0.236422i	−0.847933	−	0.530103i	$-0.822153\pi$
$149$	1.31795	−	2.88590i	0.107971	−	0.236422i	0.955903	+	0.293681i	$0.0948804\pi$
$150$	2.07821	+	14.4542i	0.169685	+	1.18018i
$151$	2.36476	+	2.72908i	0.192441	+	0.222089i	0.843768	−	0.536709i	$-0.180333\pi$
$151$	2.36476	+	2.72908i	0.192441	+	0.222089i	−0.651326	+	0.758798i	$0.725787\pi$
$152$	0.628759	−	0.725627i	0.0509991	−	0.0588561i
$153$	6.49655	−	14.2255i	0.525215	−	1.15006i
$154$	13.8817	+	8.92123i	1.11862	+	0.718893i
$155$	−1.56579	+	10.8903i	−0.125767	+	0.874730i
$156$	22.7636	−	14.6293i	1.82254	−	1.17128i
$157$	5.76957	+	3.70788i	0.460462	+	0.295921i	0.750231	−	0.661176i	$-0.229942\pi$
$157$	5.76957	+	3.70788i	0.460462	+	0.295921i	−0.289769	+	0.957097i	$0.593579\pi$
$158$	9.05774	+	10.4532i	0.720595	+	0.831611i
$159$	1.08210	−	0.317733i	0.0858160	−	0.0251979i
$160$	6.95470	+	8.02615i	0.549817	+	0.634523i
$161$	1.55047	−	10.7837i	0.122194	−	0.849877i
$162$	−13.3730	−	3.92667i	−1.05068	−	0.308508i
$163$	12.7790			1.00092			0.500462	−	0.865758i	$-0.333163\pi$
$163$	12.7790			1.00092			0.500462	+	0.865758i	$0.333163\pi$
$164$	−10.4041			−0.812426
$165$	−13.4930	−	3.96189i	−1.05043	−	0.308433i
$166$	−0.121869	+	0.0783206i	−0.00945889	+	0.00607886i
$167$	2.71118	−	5.93665i	0.209797	−	0.459392i	−0.775255	−	0.631649i	$-0.782379\pi$
$167$	2.71118	−	5.93665i	0.209797	−	0.459392i	0.985052	+	0.172257i	$0.0551058\pi$
$168$	1.42707	−	3.12484i	0.110101	−	0.241087i
$169$	22.5559	−	14.4958i	1.73507	−	1.11506i
$170$	−11.6878	−	3.43184i	−0.896412	−	0.263210i
$171$	−5.51054			−0.421401
$172$	19.0648			1.45368
$173$	−2.34216	−	0.687720i	−0.178071	−	0.0522864i	0.191481	−	0.981496i	$-0.438671\pi$
$173$	−2.34216	−	0.687720i	−0.178071	−	0.0522864i	−0.369552	+	0.929210i	$0.620489\pi$
$174$	3.38629	−	23.5521i	0.256714	−	1.78548i
$175$	−4.32490	−	4.99120i	−0.326932	−	0.377300i
$176$	16.9113	−	4.96560i	1.27473	−	0.374296i
$177$	−5.19966	−	6.00073i	−0.390831	−	0.451043i
$178$	−8.01689	−	5.15214i	−0.600891	−	0.386170i
$179$	0.889847	−	0.571870i	0.0665103	−	0.0427436i	−0.506963	−	0.861968i	$-0.669232\pi$
$179$	0.889847	−	0.571870i	0.0665103	−	0.0427436i	0.573473	+	0.819224i	$0.305596\pi$
$180$	1.18838	−	8.26534i	0.0885764	−	0.616062i
$181$	3.54707	+	2.27956i	0.263652	+	0.169439i	0.665788	−	0.746141i	$-0.268096\pi$
$181$	3.54707	+	2.27956i	0.263652	+	0.169439i	−0.402136	+	0.915580i	$0.631732\pi$
$182$	−11.1268	+	24.3643i	−0.824775	+	1.80600i
$183$	−2.81842	+	3.25263i	−0.208343	+	0.240441i
$184$	−1.96498	−	2.26771i	−0.144860	−	0.167178i
$185$	−0.767876	−	5.34069i	−0.0564554	−	0.392656i
$186$	−15.7508	+	34.4894i	−1.15490	+	2.52889i
$187$	−11.3847	+	13.1386i	−0.832529	+	0.960790i
$188$	−8.48811	+	2.49234i	−0.619059	+	0.181772i
$189$	−2.68743	+	0.789100i	−0.195482	+	0.0573986i
$190$	0.610849	+	4.24855i	0.0443156	+	0.308222i
$191$	−10.0172	+	6.43764i	−0.724816	+	0.465811i	−0.850309	−	0.526283i	$-0.823585\pi$
$191$	−10.0172	+	6.43764i	−0.724816	+	0.465811i	0.125493	+	0.992094i	$0.459949\pi$
$192$	5.60175	+	12.2661i	0.404271	+	0.885231i
$193$	−9.43198	−	2.76948i	−0.678929	−	0.199351i	−0.0759534	−	0.997111i	$-0.524200\pi$
$193$	−9.43198	−	2.76948i	−0.678929	−	0.199351i	−0.602975	+	0.797760i	$0.706018\pi$
$194$	5.79555	+	12.6905i	0.416096	+	0.911124i
$195$	3.24855	−	22.5941i	0.232633	−	1.61800i
$196$	0.504398	+	3.50816i	0.0360284	+	0.250583i
$197$	−15.2961	+	17.6526i	−1.08980	+	1.25770i	−0.125725	+	0.992065i	$0.540126\pi$
$197$	−15.2961	+	17.6526i	−1.08980	+	1.25770i	−0.964075	+	0.265631i	$0.914420\pi$
$198$	−21.9431	−	14.1020i	−1.55943	−	1.00218i
$199$	−8.57490	−	18.7764i	−0.607859	−	1.33102i	−0.924029	−	0.382322i	$-0.875124\pi$
$199$	−8.57490	−	18.7764i	−0.607859	−	1.33102i	0.316170	−	0.948702i	$-0.397603\pi$
$200$	−1.81897			−0.128620
$201$	20.3340	+	4.67038i	1.43425	+	0.329423i
$202$	−38.2276			−2.68968
$203$	4.47038	+	9.78877i	0.313759	+	0.687037i
$204$	−16.1350	−	10.3693i	−1.12967	−	0.725997i
$205$	−5.74751	+	6.63298i	−0.401424	+	0.463268i
$206$	−2.59859	−	18.0736i	−0.181053	−	1.25925i
$207$	−2.45086	+	17.0461i	−0.170347	+	1.18479i
$208$	11.8847	+	26.0239i	0.824058	+	1.80444i
$209$	5.87769	+	1.72584i	0.406568	+	0.119379i
$210$	6.37960	+	13.9694i	0.440234	+	0.963978i
$211$	−8.80461	+	5.65838i	−0.606134	+	0.389539i	−0.807406	−	0.589997i	$-0.799129\pi$
$211$	−8.80461	+	5.65838i	−0.606134	+	0.389539i	0.201271	+	0.979536i	$0.435493\pi$
$212$	−0.105946	−	0.736870i	−0.00727639	−	0.0506084i
$213$	−8.40810	+	2.46884i	−0.576114	+	0.169162i
$214$	20.9100	−	6.13973i	1.42938	−	0.419704i
$215$	10.5319	−	12.1545i	0.718271	−	0.828929i
$216$	−0.320460	+	0.701710i	−0.0218046	+	0.0477453i
$217$	−2.44039	−	16.9733i	−0.165665	−	1.15222i
$218$	3.08805	+	3.56379i	0.209149	+	0.241371i
$219$	15.8273	−	18.2657i	1.06951	−	1.23428i
$220$	−3.85617	+	8.44385i	−0.259983	+	0.569284i
$221$	−23.7395	−	15.2564i	−1.59689	−	1.02626i
$222$	2.64624	−	18.4050i	0.177604	−	1.23526i
$223$	−13.4087	+	8.61724i	−0.897912	+	0.577053i	−0.906170	−	0.422913i	$-0.861008\pi$
$223$	−13.4087	+	8.61724i	−0.897912	+	0.577053i	0.00825805	+	0.999966i	$0.497371\pi$
$224$	−13.9246	−	8.94880i	−0.930377	−	0.597917i
$225$	6.83648	+	7.88971i	0.455765	+	0.525981i
$226$	11.3303	−	3.32687i	0.753679	−	0.221300i
$227$	6.63998	+	7.66294i	0.440711	+	0.508607i	0.932034	−	0.362370i	$-0.118032\pi$
$227$	6.63998	+	7.66294i	0.440711	+	0.508607i	−0.491324	+	0.870977i	$0.663487\pi$
$228$	−0.961800	+	6.68946i	−0.0636967	+	0.443020i
$229$	−10.9291	−	3.20906i	−0.722213	−	0.212061i	−0.100087	−	0.994979i	$-0.531912\pi$
$229$	−10.9291	−	3.20906i	−0.722213	−	0.212061i	−0.622125	+	0.782918i	$0.713730\pi$
$230$	13.4140			0.884492
$231$	21.9176			1.44207
$232$	2.84381	+	0.835019i	0.186706	+	0.0548217i
$233$	19.2338	−	12.3608i	1.26005	−	0.809783i	0.271757	−	0.962366i	$-0.412395\pi$
$233$	19.2338	−	12.3608i	1.26005	−	0.809783i	0.988291	+	0.152583i	$0.0487590\pi$
$234$	17.5884	−	38.5133i	1.14979	−	2.51769i
$235$	−3.10011	+	6.78829i	−0.202229	+	0.442819i
$236$	−4.40922	+	2.83364i	−0.287016	+	0.184454i
$237$	17.6274	+	5.17588i	1.14502	+	0.336210i
$238$	18.9853			1.23063
$239$	−5.60924			−0.362832			−0.181416	−	0.983406i	$-0.558068\pi$
$239$	−5.60924			−0.362832			−0.181416	+	0.983406i	$0.558068\pi$
$240$	15.7388	+	4.62133i	1.01593	+	0.298305i
$241$	−2.38743	+	16.6049i	−0.153788	+	1.06962i	0.756008	+	0.654562i	$0.227147\pi$
$241$	−2.38743	+	16.6049i	−0.153788	+	1.06962i	−0.909796	+	0.415056i	$0.863762\pi$
$242$	5.16517	+	5.96092i	0.332030	+	0.383183i
$243$	−21.4071	+	6.28570i	−1.37327	+	0.403228i
$244$	1.86043	+	2.14705i	0.119102	+	0.137451i
$245$	2.51522	+	1.61643i	0.160691	+	0.103270i
$246$	−25.4446	+	16.3522i	−1.62229	+	1.04258i
$247$	−1.41510	+	9.84225i	−0.0900408	+	0.626248i
$248$	−3.97313	−	2.55338i	−0.252294	−	0.162140i
$249$	−0.0799330	+	0.175029i	−0.00506555	+	0.0110920i
$250$	14.2431	−	16.4375i	0.900816	−	1.03960i
$251$	17.1233	+	19.7613i	1.08081	+	1.24733i	0.967258	+	0.253793i	$0.0816783\pi$
$251$	17.1233	+	19.7613i	1.08081	+	1.24733i	0.113555	+	0.993532i	$0.463776\pi$
$252$	1.85217	+	12.8821i	0.116676	+	0.811497i
$253$	7.95282	−	17.4142i	0.499989	−	1.09482i
$254$	7.25994	−	8.37842i	0.455529	−	0.525709i
$255$	−15.5242	+	4.55831i	−0.972161	+	0.285452i
$256$	−19.0137	+	5.58293i	−1.18836	+	0.348933i
$257$	2.33365	+	16.2309i	0.145569	+	1.01245i	0.923361	+	0.383933i	$0.125431\pi$
$257$	2.33365	+	16.2309i	0.145569	+	1.01245i	−0.777792	+	0.628522i	$0.783660\pi$
$258$	46.6255	−	29.9644i	2.90277	−	1.86550i
$259$	3.49341	+	7.64950i	0.217070	+	0.475317i
$260$	−14.4574	−	4.24507i	−0.896608	−	0.263268i
$261$	−7.06644	−	15.4733i	−0.437401	−	0.957776i
$262$	1.98185	−	13.7841i	0.122439	−	0.851584i
$263$	−2.30166	−	16.0084i	−0.141926	−	0.987119i	−0.928952	−	0.370199i	$-0.879289\pi$
$263$	−2.30166	−	16.0084i	−0.141926	−	0.987119i	0.787026	−	0.616920i	$-0.211620\pi$
$264$	3.95310	−	4.56212i	0.243297	−	0.280779i
$265$	−0.528307	−	0.339522i	−0.0324536	−	0.0208567i
$266$	−2.77902	−	6.08521i	−0.170393	−	0.373108i
$267$	−12.6577			−0.774640
$268$	4.96174	−	12.8471i	0.303087	−	0.784759i
$269$	−20.2633			−1.23548			−0.617738	−	0.786384i	$-0.711951\pi$
$269$	−20.2633			−1.23548			−0.617738	+	0.786384i	$0.711951\pi$
$270$	−1.43259	−	3.13694i	−0.0871848	−	0.190908i
$271$	2.71908	+	1.74745i	0.165172	+	0.106150i	0.620615	−	0.784115i	$-0.286883\pi$
$271$	2.71908	+	1.74745i	0.165172	+	0.106150i	−0.455443	+	0.890265i	$0.650519\pi$
$272$	13.2796	−	15.3254i	0.805193	−	0.929242i
$273$	5.06309	+	35.2145i	0.306432	+	2.13128i
$274$	2.35281	−	16.3641i	0.142138	−	0.988594i
$275$	−4.82099	−	10.5565i	−0.290717	−	0.636580i
$276$	20.2652	+	5.95039i	1.21982	+	0.358172i
$277$	−10.6982	−	23.4259i	−0.642795	−	1.40752i	−0.897721	−	0.440564i	$-0.854778\pi$
$277$	−10.6982	−	23.4259i	−0.642795	−	1.40752i	0.254926	−	0.966960i	$-0.417949\pi$
$278$	0.978316	−	0.628726i	0.0586755	−	0.0377085i
$279$	3.85758	+	26.8301i	0.230947	+	1.60627i
$280$	−1.83543	+	0.538932i	−0.109688	+	0.0322074i
$281$	−10.5849	+	3.10802i	−0.631445	+	0.185409i	−0.581766	−	0.813356i	$-0.697638\pi$
$281$	−10.5849	+	3.10802i	−0.631445	+	0.185409i	−0.0496788	+	0.998765i	$0.515820\pi$
$282$	−16.8415	+	19.4362i	−1.00290	+	1.15741i
$283$	−0.843653	+	1.84734i	−0.0501500	+	0.109813i	−0.933048	−	0.359751i	$-0.882862\pi$
$283$	−0.843653	+	1.84734i	−0.0501500	+	0.109813i	0.882898	+	0.469564i	$0.155589\pi$
$284$	0.823219	+	5.72561i	0.0488490	+	0.339753i
$285$	3.73344	+	4.30862i	0.221150	+	0.255220i
$286$	−30.8222	+	35.5708i	−1.82256	+	2.10334i
$287$	5.68250	−	12.4429i	0.335427	−	0.734484i
$288$	22.0109	+	14.1456i	1.29701	+	0.833536i
$289$	−0.427222	+	2.97139i	−0.0251307	+	0.174788i
$290$	−11.1464	+	7.16336i	−0.654539	+	0.420647i
$291$	15.5889	+	10.0184i	0.913838	+	0.587288i
$292$	−10.4476	−	12.0572i	−0.611400	−	0.705593i
$293$	3.89561	−	1.14385i	0.227584	−	0.0668247i	−0.165952	−	0.986134i	$-0.553070\pi$
$293$	3.89561	−	1.14385i	0.227584	−	0.0668247i	0.393536	+	0.919309i	$0.371252\pi$
$294$	6.74738	+	7.78689i	0.393515	+	0.454141i
$295$	−0.629232	+	4.37640i	−0.0366353	+	0.254804i
$296$	2.22232	+	0.652531i	0.129170	+	0.0379276i
$297$	−4.92177			−0.285590
$298$	−6.08819			−0.352679
$299$	29.8163	+	8.75486i	1.72432	+	0.506306i
$300$	10.7709	−	6.92201i	0.621856	−	0.399643i
$301$	−10.4128	+	22.8008i	−0.600183	+	1.31422i
$302$	2.87867	−	6.30341i	0.165649	−	0.362720i
$303$	−42.7150	+	27.4512i	−2.45391	+	1.57703i
$304$	−6.85599	−	2.01310i	−0.393218	−	0.115459i
$305$	2.39657			0.137227
$306$	−30.0105			−1.71558
$307$	15.2482	+	4.47727i	0.870259	+	0.255531i	0.686225	−	0.727389i	$-0.259266\pi$
$307$	15.2482	+	4.47727i	0.870259	+	0.255531i	0.184033	+	0.982920i	$0.441085\pi$
$308$	2.05898	−	14.3205i	0.117321	−	0.815985i
$309$	−15.8823	−	18.3291i	−0.903512	−	1.04271i
$310$	20.2580	−	5.94828i	1.15058	−	0.337840i
$311$	−6.64598	−	7.66987i	−0.376859	−	0.434918i	0.535359	−	0.844625i	$-0.320176\pi$
$311$	−6.64598	−	7.66987i	−0.376859	−	0.434918i	−0.912217	+	0.409707i	$0.865631\pi$
$312$	8.24307	+	5.29750i	0.466672	+	0.299912i
$313$	4.40924	−	2.83364i	0.249225	−	0.160167i	−0.410064	−	0.912057i	$-0.634494\pi$
$313$	4.40924	−	2.83364i	0.249225	−	0.160167i	0.659289	+	0.751890i	$0.270857\pi$
$314$	1.87300	−	13.0270i	0.105700	−	0.735157i
$315$	9.23597	+	5.93560i	0.520388	+	0.334433i
$316$	5.03777	−	11.0312i	0.283397	−	0.620552i
$317$	1.58665	−	1.83109i	0.0891149	−	0.102844i	−0.709441	−	0.704765i	$-0.751052\pi$
$317$	1.58665	−	1.83109i	0.0891149	−	0.102844i	0.798556	+	0.601921i	$0.205598\pi$
$318$	−1.41725	−	1.63559i	−0.0794753	−	0.0917194i
$319$	2.69116	+	18.7174i	0.150676	+	1.04797i
$320$	3.11930	−	6.83032i	0.174374	−	0.381827i
$321$	18.9556	−	21.8759i	1.05800	−	1.22100i
$322$	−20.0598	+	5.89008i	−1.11789	+	0.328241i
$323$	6.76250	−	1.98565i	0.376276	−	0.110484i
$324$	1.73909	+	12.0956i	0.0966162	+	0.671980i
$325$	15.8473	−	10.1844i	0.879047	−	0.564929i
$326$	−10.1871	−	22.3066i	−0.564210	−	1.23545i
$327$	6.00970	+	1.76461i	0.332337	+	0.0975830i
$328$	−1.56508	−	3.42705i	−0.0864171	−	0.189227i
$329$	1.65528	−	11.5127i	0.0912585	−	0.634717i
$330$	3.84050	+	26.7113i	0.211413	+	1.47041i
$331$	−15.3092	+	17.6678i	−0.841472	+	0.971110i	−0.999868	−	0.0162657i	$-0.994822\pi$
$331$	−15.3092	+	17.6678i	−0.841472	+	0.971110i	0.158396	+	0.987376i	$0.449368\pi$
$332$	0.106851	+	0.0686691i	0.00586422	+	0.00376871i
$333$	−5.52211	−	12.0917i	−0.302610	−	0.662623i
$334$	−12.5241			−0.685290
$335$	−5.44944	−	10.2603i	−0.297734	−	0.560582i
$336$	−25.5656			−1.39472
$337$	−8.10344	−	17.7441i	−0.441423	−	0.966581i	−0.991335	−	0.131358i	$-0.958066\pi$
$337$	−8.10344	−	17.7441i	−0.441423	−	0.966581i	0.549912	−	0.835222i	$-0.314661\pi$
$338$	−43.2844	−	27.8172i	−2.35436	−	1.51306i
$339$	10.2713	−	11.8537i	0.557859	−	0.643803i
$340$	1.51994	+	10.5714i	0.0824302	+	0.573314i
$341$	4.28831	−	29.8258i	0.232225	−	1.61516i
$342$	4.39287	+	9.61904i	0.237539	+	0.520138i
$343$	−19.3287	−	5.67543i	−1.04365	−	0.306444i
$344$	2.86790	+	6.27983i	0.154627	+	0.338586i
$345$	14.9886	−	9.63259i	0.806959	−	0.518601i
$346$	0.666648	+	4.63664i	0.0358392	+	0.249267i
$347$	24.5197	−	7.19963i	1.31629	−	0.386497i	0.453135	−	0.891442i	$-0.350305\pi$
$347$	24.5197	−	7.19963i	1.31629	−	0.386497i	0.863151	+	0.504945i	$0.168487\pi$
$348$	−20.0171	+	5.87754i	−1.07303	+	0.315069i
$349$	−19.8911	+	22.9556i	−1.06475	+	1.22878i	−0.0922829	+	0.995733i	$0.529416\pi$
$349$	−19.8911	+	22.9556i	−1.06475	+	1.22878i	−0.972464	+	0.233051i	$0.925129\pi$
$350$	−5.26480	+	11.5283i	−0.281415	+	0.616213i
$351$	−1.13696	−	7.90772i	−0.0606864	−	0.422083i
$352$	−19.0472	−	21.9816i	−1.01522	−	1.17163i
$353$	−3.33146	+	3.84472i	−0.177316	+	0.204634i	−0.837449	−	0.546515i	$-0.815954\pi$
$353$	−3.33146	+	3.84472i	−0.177316	+	0.204634i	0.660134	+	0.751148i	$0.270500\pi$
$354$	−6.32966	+	13.8600i	−0.336418	+	0.736652i
$355$	4.10504	+	2.63815i	0.217873	+	0.140018i
$356$	−1.18909	+	8.27030i	−0.0630216	+	0.438325i
$357$	21.2139	−	13.6333i	1.12276	−	0.721552i
$358$	−1.70760	−	1.09741i	−0.0902497	−	0.0580000i
$359$	7.23468	+	8.34927i	0.381832	+	0.440657i	0.913835	−	0.406085i	$-0.133106\pi$
$359$	7.23468	+	8.34927i	0.381832	+	0.440657i	−0.532004	+	0.846742i	$0.678561\pi$
$360$	2.90131	−	0.851903i	0.152913	−	0.0448992i
$361$	10.8160	+	12.4824i	0.569265	+	0.656966i
$362$	1.15150	−	8.00888i	0.0605216	−	0.420937i
$363$	10.0520	+	2.95154i	0.527595	+	0.154916i
$364$	23.4841			1.23090
$365$	−13.4584			−0.704444
$366$	7.92446	+	2.32683i	0.414218	+	0.121625i
$367$	−23.5592	+	15.1406i	−1.22978	+	0.790332i	−0.983857	−	0.178957i	$-0.942728\pi$
$367$	−23.5592	+	15.1406i	−1.22978	+	0.790332i	−0.245923	+	0.969289i	$0.579091\pi$
$368$	−9.27652	+	20.3127i	−0.483572	+	1.05887i
$369$	−8.98246	+	19.6688i	−0.467608	+	1.02392i
$370$	−8.71043	+	5.59785i	−0.452834	+	0.291019i
$371$	0.939134	+	0.275755i	0.0487574	+	0.0143165i
$372$	33.2434			1.72359
$373$	38.0586			1.97060			0.985299	−	0.170841i	$-0.0546484\pi$
$373$	38.0586			1.97060			0.985299	+	0.170841i	$0.0546484\pi$
$374$	32.0099	+	9.39897i	1.65520	+	0.486009i
$375$	4.11134	−	28.5950i	0.212309	−	1.47664i
$376$	−2.09782	−	2.42101i	−0.108187	−	0.124854i
$377$	−29.4513	+	8.64767i	−1.51682	+	0.445378i
$378$	3.51978	+	4.06204i	0.181038	+	0.208929i
$379$	−13.5596	−	8.71423i	−0.696510	−	0.447620i	0.143885	−	0.989594i	$-0.454040\pi$
$379$	−13.5596	−	8.71423i	−0.696510	−	0.447620i	−0.840395	+	0.541975i	$0.817677\pi$
$380$	3.16589	−	2.03459i	0.162407	−	0.104372i
$381$	2.09561	−	14.5753i	0.107361	−	0.746715i
$382$	19.2228	+	12.3537i	0.983523	+	0.632072i
$383$	−7.54063	+	16.5117i	−0.385308	+	0.843707i	0.613243	+	0.789894i	$0.289865\pi$
$383$	−7.54063	+	16.5117i	−0.385308	+	0.843707i	−0.998551	+	0.0538129i	$0.982863\pi$
$384$	−8.03315	+	9.27075i	−0.409940	+	0.473096i
$385$	−7.99237	−	9.22368i	−0.407329	−	0.470082i
$386$	2.68462	+	18.6719i	0.136644	+	0.950377i
$387$	16.4597	−	36.0418i	0.836696	−	1.83211i
$388$	8.01026	−	9.24433i	0.406659	−	0.469310i
$389$	17.7121	−	5.20076i	0.898041	−	0.263689i	0.200042	−	0.979787i	$-0.435892\pi$
$389$	17.7121	−	5.20076i	0.898041	−	0.263689i	0.697999	+	0.716099i	$0.254074\pi$
$390$	−42.0293	+	12.3409i	−2.12824	+	0.624907i
$391$	−3.13466	−	21.8020i	−0.158526	−	1.10258i
$392$	−1.07969	+	0.693874i	−0.0545326	+	0.0350460i
$393$	−7.68386	−	16.8253i	−0.387600	−	0.848725i
$394$	43.0075	+	12.6281i	2.16669	+	0.636197i
$395$	−4.24975	−	9.30566i	−0.213828	−	0.468219i
$396$	−3.25467	+	22.6367i	−0.163553	+	1.13754i
$397$	−0.271165	−	1.88599i	−0.0136094	−	0.0946554i	0.981885	−	0.189480i	$-0.0606801\pi$
$397$	−0.271165	−	1.88599i	−0.0136094	−	0.0946554i	−0.995494	+	0.0948244i	$0.969771\pi$
$398$	−25.9399	+	29.9362i	−1.30025	+	1.50057i
$399$	−7.47503	−	4.80391i	−0.374220	−	0.240496i
$400$	5.62341	+	12.3136i	0.281171	+	0.615678i
$401$	−37.6170			−1.87850			−0.939251	−	0.343230i	$-0.888479\pi$
$401$	−37.6170			−1.87850			−0.939251	+	0.343230i	$0.888479\pi$
$402$	−8.05725	−	39.2175i	−0.401859	−	1.95599i
$403$	48.9112			2.43644
$404$	13.9234	+	30.4879i	0.692713	+	1.51683i
$405$	8.67211	+	5.57323i	0.430921	+	0.276936i
$406$	13.5233	−	15.6067i	0.671151	−	0.774549i
$407$	2.10302	+	14.6268i	0.104243	+	0.725026i
$408$	0.988417	−	6.87459i	0.0489339	−	0.340343i
$409$	9.94666	+	21.7801i	0.491830	+	1.07696i	0.979039	+	0.203673i	$0.0652879\pi$
$409$	9.94666	+	21.7801i	0.491830	+	1.07696i	−0.487209	+	0.873286i	$0.661985\pi$
$410$	16.1601	+	4.74504i	0.798092	+	0.234341i
$411$	−9.12210	−	19.9746i	−0.449960	−	0.985275i
$412$	−13.4679	+	8.65530i	−0.663516	+	0.426416i
$413$	−0.980702	−	6.82093i	−0.0482572	−	0.335636i
$414$	31.7089	−	9.31059i	1.55841	−	0.457590i
$415$	0.102806	−	0.0301867i	0.00504656	−	0.00148180i
$416$	30.9175	−	35.6807i	1.51586	−	1.74939i
$417$	0.641669	−	1.40506i	0.0314227	−	0.0688060i
$418$	−1.67296	−	11.6357i	−0.0818273	−	0.569122i
$419$	−17.0855	−	19.7177i	−0.834681	−	0.963274i	0.165054	−	0.986285i	$-0.447220\pi$
$419$	−17.0855	−	19.7177i	−0.834681	−	0.963274i	−0.999735	+	0.0230108i	$0.992675\pi$
$420$	8.81749	−	10.1759i	0.430250	−	0.496535i
$421$	−0.992681	+	2.17367i	−0.0483803	+	0.105938i	−0.932279	−	0.361741i	$-0.882182\pi$
$421$	−0.992681	+	2.17367i	−0.0483803	+	0.105938i	0.883898	+	0.467679i	$0.154910\pi$
$422$	16.8959	+	10.8584i	0.822481	+	0.528576i
$423$	−2.61654	+	18.1984i	−0.127220	+	0.884838i
$424$	0.226783	−	0.145744i	0.0110135	−	0.00707797i
$425$	−11.2326	−	7.21878i	−0.544863	−	0.350162i
$426$	11.0123	+	12.7088i	0.533546	+	0.615745i
$427$	−3.58392	+	1.05234i	−0.173438	+	0.0509261i
$428$	−12.5126	−	14.4403i	−0.604818	−	0.697997i
$429$	−8.89696	+	61.8797i	−0.429549	+	2.98758i
$430$	−29.6123	−	8.69496i	−1.42803	−	0.419308i
$431$	11.4043			0.549325			0.274662	−	0.961541i	$-0.411434\pi$
$431$	11.4043			0.549325			0.274662	+	0.961541i	$0.411434\pi$
$432$	5.74097			0.276213
$433$	−5.76570	−	1.69296i	−0.277082	−	0.0813586i	0.140239	−	0.990118i	$-0.455213\pi$
$433$	−5.76570	−	1.69296i	−0.277082	−	0.0813586i	−0.417321	+	0.908759i	$0.637031\pi$
$434$	−27.6827	+	17.7906i	−1.32881	+	0.853975i
$435$	−7.31082	+	16.0085i	−0.350527	+	0.767548i
$436$	1.71752	−	3.76085i	0.0822543	−	0.180112i
$437$	−6.52920	+	4.19606i	−0.312334	+	0.200725i
$438$	−44.5013	−	13.0668i	−2.12635	−	0.624354i
$439$	24.0640			1.14851			0.574257	−	0.818675i	$-0.305291\pi$
$439$	24.0640			1.14851			0.574257	+	0.818675i	$0.305291\pi$
$440$	−3.36143			−0.160250
$441$	7.06761	+	2.07524i	0.336553	+	0.0988208i
$442$	−7.70666	+	53.6010i	−0.366569	+	2.54954i
$443$	−4.43512	−	5.11840i	−0.210719	−	0.243183i	0.640545	−	0.767921i	$-0.278709\pi$
$443$	−4.43512	−	5.11840i	−0.210719	−	0.243183i	−0.851264	+	0.524738i	$0.824163\pi$
$444$	−15.6425	+	4.59304i	−0.742359	+	0.217976i
$445$	4.61571	+	5.32682i	0.218806	+	0.252515i
$446$	25.7311	+	16.5364i	1.21840	+	0.783020i
$447$	−6.80285	+	4.37193i	−0.321764	+	0.206785i
$448$	−1.66553	+	11.5840i	−0.0786888	+	0.547293i
$449$	27.0142	+	17.3610i	1.27488	+	0.819315i	0.990247	−	0.139322i	$-0.0444923\pi$
$449$	27.0142	+	17.3610i	1.27488	+	0.819315i	0.284632	+	0.958637i	$0.408129\pi$
$450$	8.32218	−	18.2230i	0.392312	−	0.859042i
$451$	15.7410	−	18.1661i	0.741216	−	0.855408i
$452$	−6.78005	−	7.82459i	−0.318907	−	0.368038i
$453$	−1.30989	−	9.11052i	−0.0615442	−	0.428049i
$454$	8.08298	−	17.6993i	0.379353	−	0.830668i
$455$	12.9732	−	14.9719i	0.608195	−	0.701894i
$456$	−2.34815	+	0.689478i	−0.109962	+	0.0322878i
$457$	26.9953	−	7.92654i	1.26279	−	0.370788i	0.419256	−	0.907868i	$-0.362291\pi$
$457$	26.9953	−	7.92654i	1.26279	−	0.370788i	0.843531	+	0.537080i	$0.180473\pi$
$458$	3.11073	+	21.6356i	0.145355	+	1.01097i
$459$	−4.76375	+	3.06148i	−0.222353	+	0.142898i
$460$	−4.88568	−	10.6981i	−0.227796	−	0.498804i
$461$	4.68753	+	1.37638i	0.218320	+	0.0641045i	0.389063	−	0.921211i	$-0.372799\pi$
$461$	4.68753	+	1.37638i	0.218320	+	0.0641045i	−0.170743	+	0.985316i	$0.554617\pi$
$462$	−17.4721	−	38.2586i	−0.812877	−	1.77995i
$463$	1.07384	−	7.46871i	0.0499055	−	0.347100i	−0.949535	−	0.313660i	$-0.898445\pi$
$463$	1.07384	−	7.46871i	0.0499055	−	0.347100i	0.999441	−	0.0334400i	$-0.0106463\pi$
$464$	−3.13908	−	21.8328i	−0.145728	−	1.01356i
$465$	18.3645	−	21.1938i	0.851635	−	0.982839i
$466$	−36.9094	−	23.7202i	−1.70979	−	1.09882i
$467$	0.514234	+	1.12601i	0.0237959	+	0.0521057i	0.921157	−	0.389192i	$-0.127246\pi$
$467$	0.514234	+	1.12601i	0.0237959	+	0.0521057i	−0.897361	+	0.441297i	$0.854518\pi$
$468$	−37.1219			−1.71596
$469$	12.6546	+	12.9508i	0.584335	+	0.598014i
$470$	14.3208			0.660568
$471$	−7.26184	−	15.9012i	−0.334608	−	0.732689i
$472$	−1.59665	−	1.02611i	−0.0734920	−	0.0472304i
$473$	−28.8443	+	33.2881i	−1.32626	+	1.53059i
$474$	−5.01729	−	34.8960i	−0.230452	−	1.60283i
$475$	−0.669574	+	4.65699i	−0.0307221	+	0.213677i
$476$	−6.91487	−	15.1415i	−0.316943	−	0.694007i
$477$	−1.48451	−	0.435892i	−0.0679711	−	0.0199581i
$478$	4.47155	+	9.79133i	0.204524	+	0.447845i
$479$	2.64133	−	1.69748i	0.120685	−	0.0775599i	−0.478905	−	0.877866i	$-0.658966\pi$
$479$	2.64133	−	1.69748i	0.120685	−	0.0775599i	0.599591	+	0.800307i	$0.295330\pi$
$480$	−3.85237	−	26.7938i	−0.175836	−	1.22296i
$481$	−23.0149	+	6.75778i	−1.04939	+	0.308128i
$482$	30.8883	−	9.06962i	1.40692	−	0.413110i
$483$	−18.1848	+	20.9864i	−0.827439	+	0.954915i
$484$	2.87278	−	6.29052i	0.130581	−	0.285933i
$485$	−1.46850	−	10.2136i	−0.0666811	−	0.463777i
$486$	28.0374	+	32.3569i	1.27180	+	1.46774i
$487$	26.9956	−	31.1546i	1.22329	−	1.41175i	0.341644	−	0.939830i	$-0.389016\pi$
$487$	26.9956	−	31.1546i	1.22329	−	1.41175i	0.881643	−	0.471918i	$-0.156438\pi$
$488$	−0.427362	+	0.935793i	−0.0193458	+	0.0423614i
$489$	−27.4012	−	17.6097i	−1.23913	−	0.796339i
$490$	0.816527	−	5.67907i	0.0368869	−	0.256554i
$491$	−1.61178	+	1.03583i	−0.0727384	+	0.0467461i	−0.576505	−	0.817094i	$-0.695584\pi$
$491$	−1.61178	+	1.03583i	−0.0727384	+	0.0467461i	0.503766	+	0.863840i	$0.331947\pi$
$492$	22.3090	+	14.3371i	1.00577	+	0.646368i
$493$	14.2475	+	16.4425i	0.641675	+	0.740533i
$494$	18.3084	−	5.37584i	0.823736	−	0.241871i
$495$	12.6337	+	14.5801i	0.567843	+	0.655326i
$496$	−5.00207	+	34.7902i	−0.224600	+	1.56212i
$497$	−7.29724	−	2.14266i	−0.327326	−	0.0961116i
$498$	0.369246			0.0165463
$499$	−10.0911			−0.451738			−0.225869	−	0.974158i	$-0.572522\pi$
$499$	−10.0911			−0.451738			−0.225869	+	0.974158i	$0.572522\pi$
$500$	−18.2972	−	5.37253i	−0.818274	−	0.240267i
$501$	−13.9943	+	8.99359i	−0.625219	+	0.401804i
$502$	20.8446	−	45.6432i	0.930338	−	2.03716i
$503$	−15.0351	+	32.9223i	−0.670382	+	1.46793i	0.202140	+	0.979357i	$0.435211\pi$
$503$	−15.0351	+	32.9223i	−0.670382	+	1.46793i	−0.872522	+	0.488575i	$0.837517\pi$
$504$	−3.96466	+	2.54793i	−0.176600	+	0.113494i
$505$	27.1287	+	7.96571i	1.20721	+	0.354469i
$506$	−36.7376			−1.63318
$507$	−68.3410			−3.03513
$508$	−9.32633	−	2.73846i	−0.413789	−	0.121499i
$509$	1.97026	−	13.7035i	0.0873303	−	0.607396i	−0.898415	−	0.439148i	$-0.855280\pi$
$509$	1.97026	−	13.7035i	0.0873303	−	0.607396i	0.985745	−	0.168247i	$-0.0538107\pi$
$510$	20.3323	+	23.4648i	0.900331	+	1.03904i
$511$	20.1262	−	5.90958i	0.890330	−	0.261424i
$512$	18.5994	+	21.4648i	0.821984	+	0.948620i
$513$	1.67858	+	1.07876i	0.0741112	+	0.0476284i
$514$	26.4718	−	17.0124i	1.16762	−	0.750385i
$515$	−1.92198	+	13.3677i	−0.0846925	+	0.589050i
$516$	−40.8797	−	26.2718i	−1.79963	−	1.15655i
$517$	8.49043	−	18.5915i	0.373409	−	0.817651i
$518$	10.5679	−	12.1960i	0.464326	−	0.535861i
$519$	4.07447	+	4.70219i	0.178850	+	0.206403i
$520$	−0.776510	−	5.40074i	−0.0340522	−	0.236838i
$521$	−16.5510	+	36.2416i	−0.725112	+	1.58777i	0.0814863	+	0.996674i	$0.474033\pi$
$521$	−16.5510	+	36.2416i	−0.725112	+	1.58777i	−0.806598	+	0.591100i	$0.798694\pi$
$522$	−21.3766	+	24.6699i	−0.935629	+	1.07977i
$523$	16.6382	−	4.88541i	0.727537	−	0.213624i	0.103069	−	0.994674i	$-0.467134\pi$
$523$	16.6382	−	4.88541i	0.727537	−	0.213624i	0.624468	+	0.781050i	$0.285316\pi$
$524$	−11.7152	+	3.43988i	−0.511779	+	0.150272i
$525$	2.39566	+	16.6622i	0.104555	+	0.727198i
$526$	−26.1089	+	16.7792i	−1.13840	+	0.731608i
$527$	−14.4019	−	31.5357i	−0.627355	−	1.37372i
$528$	−43.1047	−	12.6567i	−1.87589	−	0.550811i
$529$	0.521484	+	1.14189i	0.0226732	+	0.0496474i
$530$	−0.171507	+	1.19286i	−0.00744978	+	0.0518144i
$531$	1.55022	+	10.7820i	0.0672738	+	0.467899i
$532$	−3.84100	+	4.43275i	−0.166528	+	0.192184i
$533$	32.8234	+	21.0943i	1.42174	+	0.913697i
$534$	10.0904	+	22.0949i	0.436655	+	0.956142i
$535$	−16.1184			−0.696861
$536$	4.97812	−	0.298203i	0.215022	−	0.0128804i
$537$	−2.69610			−0.116345
$538$	16.1534	+	35.3710i	0.696423	+	1.52495i
$539$	−6.88856	−	4.42701i	−0.296711	−	0.190685i
$540$	−1.98004	+	2.28509i	−0.0852074	+	0.0983346i
$541$	−1.15295	−	8.01892i	−0.0495691	−	0.344760i	−0.999480	−	0.0322401i	$-0.989736\pi$
$541$	−1.15295	−	8.01892i	−0.0495691	−	0.344760i	0.949911	−	0.312520i	$-0.101173\pi$
$542$	0.882708	−	6.13937i	0.0379155	−	0.263708i
$543$	−4.46450	−	9.77590i	−0.191590	−	0.419524i
$544$	−32.1089	−	9.42802i	−1.37666	−	0.404223i
$545$	−1.44886	−	3.17257i	−0.0620625	−	0.135898i
$546$	57.4333	−	36.9101i	2.45792	−	1.57961i
$547$	−1.25951	−	8.76006i	−0.0538526	−	0.374553i	−0.998870	−	0.0475323i	$-0.984864\pi$
$547$	−1.25951	−	8.76006i	−0.0538526	−	0.374553i	0.945017	−	0.327021i	$-0.106045\pi$
$548$	−13.9079	+	4.08374i	−0.594118	+	0.174449i
$549$	5.66519	−	1.66345i	0.241785	−	0.0709943i
$550$	−14.5839	+	16.8308i	−0.621861	+	0.717666i
$551$	3.18468	−	6.97347i	0.135672	−	0.297080i
$552$	1.08845	+	7.57032i	0.0463274	+	0.322214i
$553$	10.4414	+	12.0500i	0.444011	+	0.512417i
$554$	−32.3632	+	37.3491i	−1.37498	+	1.58681i
$555$	−5.71309	+	12.5099i	−0.242507	+	0.531017i
$556$	−0.857757	−	0.551247i	−0.0363770	−	0.0233781i
$557$	−3.60220	+	25.0538i	−0.152630	+	1.06156i	0.759159	+	0.650905i	$0.225610\pi$
$557$	−3.60220	+	25.0538i	−0.152630	+	1.06156i	−0.911789	+	0.410659i	$0.865299\pi$
$558$	43.7586	−	28.1220i	1.85245	−	1.19050i
$559$	−60.1467	−	38.6539i	−2.54393	−	1.63489i
$560$	9.32265	+	10.7589i	0.393954	+	0.454647i
$561$	42.5169	−	12.4841i	1.79506	−	0.527078i
$562$	13.8633	+	15.9991i	0.584789	+	0.674882i
$563$	3.05299	−	21.2340i	0.128668	−	0.894906i	−0.818577	−	0.574396i	$-0.805237\pi$
$563$	3.05299	−	21.2340i	0.128668	−	0.894906i	0.947245	−	0.320509i	$-0.103854\pi$
$564$	21.6351	+	6.35264i	0.911003	+	0.267495i
$565$	−8.73392			−0.367439
$566$	3.89721			0.163812
$567$	−15.4158	−	4.52649i	−0.647403	−	0.190095i
$568$	−1.76214	+	1.13246i	−0.0739378	+	0.0475170i
$569$	−8.83639	+	19.3490i	−0.370441	+	0.811152i	0.628990	+	0.777413i	$0.283469\pi$
$569$	−8.83639	+	19.3490i	−0.370441	+	0.811152i	−0.999431	+	0.0337385i	$0.989259\pi$
$570$	4.54479	−	9.95170i	0.190360	−	0.416831i
$571$	−13.5548	+	8.71115i	−0.567251	+	0.364550i	−0.792613	−	0.609725i	$-0.791280\pi$
$571$	−13.5548	+	8.71115i	−0.567251	+	0.364550i	0.225362	+	0.974275i	$0.427644\pi$
$572$	39.5952	+	11.6262i	1.65556	+	0.486115i
$573$	30.3505			1.26791
$574$	−26.2500			−1.09565
$575$	14.1080	+	4.14247i	0.588342	+	0.172753i
$576$	2.63274	−	18.3111i	0.109697	−	0.762963i
$577$	−3.67554	−	4.24180i	−0.153015	−	0.176589i	0.674067	−	0.738670i	$-0.264546\pi$
$577$	−3.67554	−	4.24180i	−0.153015	−	0.176589i	−0.827082	+	0.562082i	$0.810001\pi$
$578$	5.52735	−	1.62298i	0.229907	−	0.0675069i
$579$	16.4081	+	18.9359i	0.681897	+	0.786951i
$580$	9.77282	+	6.28061i	0.405794	+	0.260788i
$581$	−0.140485	+	0.0902845i	−0.00582832	+	0.00374563i
$582$	5.06070	−	35.1980i	0.209773	−	1.45900i
$583$	1.44690	+	0.929868i	0.0599246	+	0.0385112i
$584$	2.39993	−	5.25512i	0.0993099	−	0.217458i
$585$	−20.5071	+	23.6665i	−0.847864	+	0.978488i
$586$	−5.10216	−	5.88821i	−0.210768	−	0.243240i
$587$	−5.03757	−	35.0371i	−0.207923	−	1.44614i	−0.779919	−	0.625880i	$-0.784740\pi$
$587$	−5.03757	−	35.0371i	−0.207923	−	1.44614i	0.571997	−	0.820256i	$-0.306169\pi$
$588$	3.75278	−	8.21745i	0.154762	−	0.338882i
$589$	−7.99979	+	9.23225i	−0.329626	+	0.380408i
$590$	8.14093	−	2.39039i	0.335157	−	0.0984110i
$591$	57.1243	−	16.7732i	2.34978	−	0.689957i
$592$	−2.45306	−	17.0614i	−0.100820	−	0.701219i
$593$	−21.2111	+	13.6315i	−0.871034	+	0.559780i	−0.898069	−	0.439855i	$-0.855030\pi$
$593$	−21.2111	+	13.6315i	−0.871034	+	0.559780i	0.0270347	+	0.999634i	$0.491394\pi$
$594$	3.92351	+	8.59130i	0.160984	+	0.352505i
$595$	−13.4732	−	3.95607i	−0.552345	−	0.162183i
$596$	2.21746	+	4.85555i	0.0908306	+	0.198891i
$597$	−7.48764	+	52.0777i	−0.306449	+	2.13140i
$598$	−8.48660	−	59.0256i	−0.347043	−	2.41374i
$599$	25.1394	−	29.0124i	1.02717	−	1.18541i	0.0446960	−	0.999001i	$-0.485768\pi$
$599$	25.1394	−	29.0124i	1.02717	−	1.18541i	0.982471	−	0.186414i	$-0.0596865\pi$
$600$	3.90031	+	2.50658i	0.159230	+	0.102331i
$601$	−7.46957	−	16.3561i	−0.304690	−	0.667178i	0.693911	−	0.720061i	$-0.255886\pi$
$601$	−7.46957	−	16.3561i	−0.304690	−	0.667178i	−0.998601	+	0.0528829i	$0.983159\pi$
$602$	48.1013			1.96046
$603$	−20.0034	−	20.4717i	−0.814602	−	0.833671i
$604$	−6.07568			−0.247216
$605$	−2.42342	−	5.30655i	−0.0985260	−	0.215742i
$606$	81.9694	+	52.6785i	3.32978	+	2.13992i
$607$	8.41136	−	9.70723i	0.341407	−	0.394004i	−0.558918	−	0.829223i	$-0.688783\pi$
$607$	8.41136	−	9.70723i	0.341407	−	0.394004i	0.900325	+	0.435219i	$0.143329\pi$
$608$	1.67813	+	11.6717i	0.0680573	+	0.473349i
$609$	3.90356	−	27.1498i	0.158180	−	1.10017i
$610$	−1.91049	−	4.18339i	−0.0773535	−	0.169380i
$611$	31.8319	+	9.34669i	1.28778	+	0.378127i
$612$	10.9305	+	23.9344i	0.441839	+	0.967493i
$613$	−22.2554	+	14.3027i	−0.898888	+	0.577680i	−0.906460	−	0.422291i	$-0.861226\pi$
$613$	−22.2554	+	14.3027i	−0.898888	+	0.577680i	0.00757210	+	0.999971i	$0.497590\pi$
$614$	−4.34008	−	30.1859i	−0.175151	−	1.21820i
$615$	21.4645	−	6.30255i	0.865532	−	0.254143i
$616$	5.02680	−	1.47600i	0.202536	−	0.0594698i
$617$	−6.20482	+	7.16074i	−0.249797	+	0.288281i	−0.866775	−	0.498699i	$-0.833811\pi$
$617$	−6.20482	+	7.16074i	−0.249797	+	0.288281i	0.616978	+	0.786980i	$0.288357\pi$
$618$	−19.3338	+	42.3352i	−0.777721	+	1.70297i
$619$	0.636409	+	4.42632i	0.0255794	+	0.177909i	0.998606	−	0.0527845i	$-0.0168097\pi$
$619$	0.636409	+	4.42632i	0.0255794	+	0.177909i	−0.973026	+	0.230693i	$0.925901\pi$
$620$	−12.1224	−	13.9900i	−0.486847	−	0.561852i
$621$	4.08356	−	4.71268i	0.163868	−	0.189113i
$622$	−8.09028	+	17.7153i	−0.324391	+	0.710317i
$623$	−9.24151	−	5.93916i	−0.370253	−	0.237947i
$624$	10.3778	−	72.1793i	0.415445	−	2.88948i
$625$	−0.975153	+	0.626693i	−0.0390061	+	0.0250677i
$626$	−8.46126	−	5.43772i	−0.338180	−	0.217335i
$627$	−10.2250	−	11.8002i	−0.408346	−	0.471256i
$628$	−11.0717	+	3.25095i	−0.441810	+	0.129727i
$629$	11.1338	+	12.8491i	0.443934	+	0.512327i
$630$	2.99832	−	20.8538i	0.119456	−	0.830834i
$631$	10.2034	+	2.99599i	0.406191	+	0.119268i	0.478444	−	0.878118i	$-0.341201\pi$
$631$	10.2034	+	2.99599i	0.406191	+	0.119268i	−0.0722536	+	0.997386i	$0.523019\pi$
$632$	4.39142			0.174681
$633$	26.6767			1.06030
$634$	−4.46113	−	1.30991i	−0.177174	−	0.0520230i
$635$	−6.89797	+	4.43306i	−0.273738	+	0.175921i
$636$	−0.788251	+	1.72603i	−0.0312562	+	0.0684415i
$637$	5.52150	−	12.0904i	0.218770	−	0.479039i
$638$	30.5272	−	19.6187i	1.20859	−	0.776711i
$639$	11.5349	+	3.38696i	0.456314	+	0.133986i
$640$	6.83080			0.270011
$641$	−2.21249			−0.0873882			−0.0436941	−	0.999045i	$-0.513913\pi$
$641$	−2.21249			−0.0873882			−0.0436941	+	0.999045i	$0.513913\pi$
$642$	−53.2970	−	15.6494i	−2.10346	−	0.617632i
$643$	−5.67300	+	39.4566i	−0.223721	+	1.55602i	0.500062	+	0.865990i	$0.333311\pi$
$643$	−5.67300	+	39.4566i	−0.223721	+	1.55602i	−0.723784	+	0.690027i	$0.757599\pi$
$644$	12.0038	+	13.8531i	0.473015	+	0.545889i
$645$	−39.3322	+	11.5490i	−1.54871	+	0.454741i
$646$	−8.85699	−	10.2215i	−0.348474	−	0.402160i
$647$	4.78324	+	3.07400i	0.188049	+	0.120851i	0.631278	−	0.775557i	$-0.282531\pi$
$647$	4.78324	+	3.07400i	0.188049	+	0.120851i	−0.443229	+	0.896408i	$0.646167\pi$
$648$	−3.72262	+	2.39238i	−0.146238	+	0.0939815i
$649$	1.72331	−	11.9859i	0.0676459	−	0.470487i
$650$	−30.4107	−	19.5437i	−1.19280	−	0.766569i
$651$	−18.1568	+	39.7579i	−0.711621	+	1.55823i
$652$	−14.0800	+	16.2491i	−0.551413	+	0.636365i
$653$	−3.74699	−	4.32426i	−0.146631	−	0.169221i	0.677683	−	0.735354i	$-0.262984\pi$
$653$	−3.74699	−	4.32426i	−0.146631	−	0.169221i	−0.824314	+	0.566133i	$0.808439\pi$
$654$	−1.71054	−	11.8971i	−0.0668874	−	0.465212i
$655$	−4.27872	+	9.36909i	−0.167183	+	0.366081i
$656$	−18.3610	+	21.1897i	−0.716877	+	0.827320i
$657$	−31.8139	+	9.34141i	−1.24118	+	0.364443i
$658$	−21.4158	+	6.28825i	−0.834876	+	0.245142i
$659$	−5.85038	−	40.6903i	−0.227898	−	1.58507i	−0.706939	−	0.707275i	$-0.749924\pi$
$659$	−5.85038	−	40.6903i	−0.227898	−	1.58507i	0.479040	−	0.877793i	$-0.340985\pi$
$660$	19.9044	−	12.7918i	0.774778	−	0.497920i
$661$	8.49335	+	18.5978i	0.330353	+	0.723372i	0.999810	−	0.0194786i	$-0.00620062\pi$
$661$	8.49335	+	18.5978i	0.330353	+	0.723372i	−0.669457	+	0.742850i	$0.733473\pi$
$662$	43.0445	+	12.6390i	1.67297	+	0.491229i
$663$	29.8796	+	65.4272i	1.16043	+	2.54098i
$664$	−0.00654563	+	0.0455259i	−0.000254020	+	0.00176675i
$665$	0.704159	+	4.89753i	0.0273061	+	0.189918i
$666$	−16.7049	+	19.2785i	−0.647302	+	0.747026i
$667$	−20.1551	−	12.9529i	−0.780407	−	0.501537i
$668$	4.56158	+	9.98846i	0.176493	+	0.386465i
$669$	40.6263			1.57070
$670$	−13.5660	+	17.6917i	−0.524100	+	0.683489i
$671$	−6.56362			−0.253386
$672$	17.5261	+	38.3769i	0.676085	+	1.48042i
$673$	−13.5297	−	8.69498i	−0.521530	−	0.335167i	0.253247	−	0.967402i	$-0.418501\pi$
$673$	−13.5297	−	8.69498i	−0.521530	−	0.335167i	−0.774777	+	0.632235i	$0.782138\pi$
$674$	−24.5137	+	28.2903i	−0.944231	+	1.08970i
$675$	−0.537966	−	3.74164i	−0.0207063	−	0.144016i
$676$	−6.42008	+	44.6526i	−0.246926	+	1.71741i
$677$	−11.9241	−	26.1102i	−0.458281	−	1.00350i	−0.987876	−	0.155245i	$-0.950383\pi$
$677$	−11.9241	−	26.1102i	−0.458281	−	1.00350i	0.529595	−	0.848251i	$-0.322344\pi$
$678$	−28.8794	−	8.47977i	−1.10911	−	0.325663i
$679$	6.68085	+	14.6290i	0.256388	+	0.561410i
$680$	−3.25350	+	2.09090i	−0.124766	+	0.0801824i
$681$	−3.67804	−	25.5813i	−0.140943	−	0.980278i
$682$	−55.4816	+	16.2909i	−2.12450	+	0.623810i
$683$	−34.9813	+	10.2714i	−1.33852	+	0.393025i	−0.871142	−	0.491032i	$-0.836620\pi$
$683$	−34.9813	+	10.2714i	−1.33852	+	0.393025i	−0.467379	+	0.884057i	$0.654802\pi$
$684$	6.07155	−	7.00695i	0.232152	−	0.267917i
$685$	−5.07959	+	11.1228i	−0.194081	+	0.424979i
$686$	5.50153	+	38.2640i	0.210049	+	1.46093i
$687$	19.0124	+	21.9415i	0.725370	+	0.837122i
$688$	33.6453	−	38.8287i	1.28272	−	1.48033i
$689$	−1.15976	+	2.53952i	−0.0441833	+	0.0967479i
$690$	−28.7629	−	18.4848i	−1.09499	−	0.703704i
$691$	4.76525	−	33.1431i	0.181279	−	1.26082i	−0.672465	−	0.740129i	$-0.734765\pi$
$691$	4.76525	−	33.1431i	0.181279	−	1.26082i	0.853744	−	0.520693i	$-0.174326\pi$
$692$	3.45508	−	2.22045i	0.131342	−	0.0844087i
$693$	−25.2950	−	16.2561i	−0.960879	−	0.617520i
$694$	−32.1140	−	37.0615i	−1.21903	−	1.40684i
$695$	−0.825287	+	0.242326i	−0.0313049	+	0.00919195i
$696$	−4.94717	−	5.70933i	−0.187522	−	0.216412i
$697$	3.93582	−	27.3742i	0.149080	−	1.03687i
$698$	55.9273	+	16.4217i	2.11688	+	0.621572i
$699$	−58.2755			−2.20418
$700$	11.1118			0.419987
$701$	−22.3215	−	6.55419i	−0.843072	−	0.247548i	−0.168449	−	0.985710i	$-0.553876\pi$
$701$	−22.3215	−	6.55419i	−0.843072	−	0.247548i	−0.674623	+	0.738162i	$0.735694\pi$
$702$	−12.8971	+	8.28848i	−0.486771	+	0.312829i
$703$	2.48869	−	5.44946i	0.0938626	−	0.205530i
$704$	−8.54300	+	18.7066i	−0.321977	+	0.705030i
$705$	16.0018	−	10.2838i	0.602664	−	0.387309i
$706$	9.36699	+	2.75040i	0.352531	+	0.103512i
$707$	−44.0670			−1.65731
$708$	13.3593			0.502073
$709$	−19.8397	−	5.82545i	−0.745095	−	0.218779i	−0.112918	−	0.993604i	$-0.536020\pi$
$709$	−19.8397	−	5.82545i	−0.745095	−	0.218779i	−0.632176	+	0.774825i	$0.717838\pi$
$710$	1.33264	−	9.26871i	0.0500130	−	0.347848i
$711$	−16.5049	−	19.0477i	−0.618982	−	0.714343i
$712$	−2.90305	+	0.852413i	−0.108797	+	0.0319455i
$713$	25.0007	+	28.8524i	0.936285	+	1.08053i
$714$	−40.7091	−	26.1622i	−1.52350	−	0.979094i
$715$	29.2855	−	18.8207i	1.09522	−	0.703853i
$716$	−0.253277	+	1.76158i	−0.00946540	+	0.0658333i
$717$	12.0276	+	7.72968i	0.449179	+	0.288670i
$718$	8.80693	−	19.2845i	0.328672	−	0.719690i
$719$	15.0115	−	17.3242i	0.559836	−	0.646085i	−0.403310	−	0.915063i	$-0.632140\pi$
$719$	15.0115	−	17.3242i	0.559836	−	0.646085i	0.963146	+	0.268978i	$0.0866859\pi$
$720$	−14.7365	−	17.0069i	−0.549198	−	0.633808i
$721$	−2.99554	−	20.8344i	−0.111560	−	0.775915i
$722$	13.1666	−	28.8308i	0.490009	−	1.07297i
$723$	28.0013	−	32.3152i	1.04138	−	1.20181i
$724$	−6.80678	+	1.99865i	−0.252972	+	0.0742793i
$725$	−13.9352	+	4.09175i	−0.517542	+	0.151964i
$726$	−2.86111	−	19.8994i	−0.106186	−	0.738537i
$727$	−1.80712	+	1.16136i	−0.0670222	+	0.0430725i	−0.573723	−	0.819050i	$-0.694501\pi$
$727$	−1.80712	+	1.16136i	−0.0670222	+	0.0430725i	0.506701	+	0.862122i	$0.330865\pi$
$728$	3.53269	+	7.73551i	0.130930	+	0.286697i
$729$	33.6577	+	9.88280i	1.24658	+	0.366029i
$730$	10.7287	+	23.4926i	0.397087	+	0.869499i
$731$	−7.21212	+	50.1614i	−0.266750	+	1.85529i
$732$	−1.03054	−	7.16754i	−0.0380897	−	0.264920i
$733$	25.8217	−	29.7998i	0.953745	−	1.10068i	−0.0410883	−	0.999156i	$-0.513083\pi$
$733$	25.8217	−	29.7998i	0.953745	−	1.10068i	0.994833	−	0.101525i	$-0.0323720\pi$
$734$	45.2098	+	29.0546i	1.66872	+	1.07242i
$735$	−3.16577	−	6.93206i	−0.116771	−	0.255693i
$736$	36.8511			1.35835
$737$	14.9247	+	28.1005i	0.549757	+	1.03510i
$738$	41.4940			1.52741
$739$	12.3231	+	26.9837i	0.453311	+	0.992612i	0.988962	+	0.148173i	$0.0473391\pi$
$739$	12.3231	+	26.9837i	0.453311	+	0.992612i	−0.535651	+	0.844440i	$0.679934\pi$
$740$	7.63703	+	4.90802i	0.280743	+	0.180423i
$741$	16.5972	−	19.1542i	0.609713	−	0.703647i
$742$	−0.267305	−	1.85915i	−0.00981309	−	0.0682516i
$743$	2.68991	−	18.7087i	0.0986831	−	0.686356i	−0.879085	−	0.476666i	$-0.841845\pi$
$743$	2.68991	−	18.7087i	0.0986831	−	0.686356i	0.977768	−	0.209691i	$-0.0672457\pi$
$744$	5.00077	+	10.9501i	0.183337	+	0.401452i
$745$	4.32056	+	1.26863i	0.158293	+	0.0464791i
$746$	−30.3393	−	66.4339i	−1.11080	−	2.43232i
$747$	0.222069	−	0.142715i	0.00812506	−	0.00522166i
$748$	−4.16273	−	28.9524i	−0.152205	−	1.05861i
$749$	24.1041	−	7.07761i	0.880745	−	0.258610i
$750$	−53.1921	+	15.6186i	−1.94230	+	0.570311i
$751$	−2.12860	+	2.45653i	−0.0776736	+	0.0896402i	−0.793256	−	0.608888i	$-0.791616\pi$
$751$	−2.12860	+	2.45653i	−0.0776736	+	0.0896402i	0.715583	+	0.698528i	$0.246161\pi$
$752$	−9.90362	+	21.6859i	−0.361148	+	0.790803i
$753$	−9.48499	−	65.9695i	−0.345652	−	2.40406i
$754$	38.5729	+	44.5155i	1.40474	+	1.62116i
$755$	−3.35637	+	3.87345i	−0.122151	+	0.140969i
$756$	1.95765	−	4.28664i	0.0711989	−	0.155904i
$757$	20.3645	+	13.0875i	0.740160	+	0.475672i	0.855597	−	0.517643i	$-0.173190\pi$
$757$	20.3645	+	13.0875i	0.740160	+	0.475672i	−0.115437	+	0.993315i	$0.536827\pi$
$758$	−4.40192	+	30.6160i	−0.159885	+	1.11202i
$759$	−41.0501	+	26.3813i	−1.49002	+	0.957580i
$760$	1.14642	+	0.736761i	0.0415851	+	0.0267251i
$761$	−27.3324	−	31.5433i	−0.990799	−	1.14344i	−0.989658	−	0.143444i	$-0.954182\pi$
$761$	−27.3324	−	31.5433i	−0.990799	−	1.14344i	−0.00114096	−	0.999999i	$-0.500363\pi$
$762$	−27.1128	+	7.96103i	−0.982192	+	0.288398i
$763$	3.55976	+	4.10818i	0.128872	+	0.148726i
$764$	2.85118	−	19.8304i	0.103152	−	0.717439i
$765$	21.2973	+	6.25346i	0.770006	+	0.226094i
$766$	34.8335			1.25859
$767$	19.6556			0.709723
$768$	48.4635	+	14.2302i	1.74878	+	0.513487i
$769$	−27.3944	+	17.6053i	−0.987867	+	0.634864i	−0.931574	−	0.363551i	$-0.881564\pi$
$769$	−27.3944	+	17.6053i	−0.987867	+	0.634864i	−0.0562926	+	0.998414i	$0.517928\pi$
$770$	−9.72927	+	21.3041i	−0.350619	+	0.767748i
$771$	17.3626	−	38.0189i	0.625300	−	1.36922i
$772$	13.9138	−	8.94184i	0.500768	−	0.321824i
$773$	−1.36700	−	0.401387i	−0.0491676	−	0.0144369i	0.257056	−	0.966396i	$-0.417247\pi$
$773$	−1.36700	−	0.401387i	−0.0491676	−	0.0144369i	−0.306224	+	0.951960i	$0.599066\pi$
$774$	−76.0349			−2.73302
$775$	23.1430			0.831320
$776$	4.25000	+	1.24791i	0.152566	+	0.0447974i
$777$	3.05046	−	21.2164i	0.109435	−	0.761135i
$778$	−23.1980	−	26.7719i	−0.831688	−	0.959819i
$779$	−9.35018	+	2.74546i	−0.335005	+	0.0983663i
$780$	25.1504	+	29.0251i	0.900528	+	1.03927i
$781$	−11.2427	−	7.22524i	−0.402295	−	0.258539i
$782$	−35.5581	+	22.8518i	−1.27155	+	0.817179i
$783$	−0.876577	+	6.09673i	−0.0313263	+	0.217879i
$784$	8.03512	+	5.16386i	0.286968	+	0.184423i
$785$	−4.04372	+	8.85451i	−0.144327	+	0.316031i
$786$	−23.2444	+	26.8255i	−0.829100	+	0.956833i
$787$	33.4017	+	38.5476i	1.19064	+	1.37407i	0.910183	+	0.414206i	$0.135941\pi$
$787$	33.4017	+	38.5476i	1.19064	+	1.37407i	0.280457	+	0.959866i	$0.409514\pi$
$788$	−5.59291	−	38.8996i	−0.199239	−	1.38574i
$789$	−17.1246	+	37.4977i	−0.609652	+	1.33495i
$790$	−12.8559	+	14.8365i	−0.457392	+	0.527859i
$791$	13.0610	−	3.83507i	0.464397	−	0.136359i
$792$	−7.94598	+	2.33315i	−0.282348	+	0.0829049i
$793$	−1.51624	−	10.5457i	−0.0538431	−	0.374487i
$794$	−3.07597	+	1.97681i	−0.109162	+	0.0701542i
$795$	0.664951	+	1.45604i	0.0235834	+	0.0516404i
$796$	33.3231	+	9.78455i	1.18111	+	0.346804i
$797$	−13.5570	−	29.6856i	−0.480213	−	1.05152i	−0.982405	−	0.186763i	$-0.940200\pi$
$797$	−13.5570	−	29.6856i	−0.480213	−	1.05152i	0.502192	−	0.864756i	$-0.332527\pi$
$798$	−2.42666	+	16.8778i	−0.0859027	+	0.597466i
$799$	−3.34656	−	23.2758i	−0.118393	−	0.823440i
$800$	14.6290	−	16.8828i	0.517213	−	0.596896i
$801$	14.6083	+	9.38817i	0.516158	+	0.331715i
$802$	29.9873	+	65.6631i	1.05889	+	2.31865i
$803$	36.8592			1.30073
$804$	−28.3428	+	20.7099i	−0.999572	+	0.730380i
$805$	15.4630			0.545000
$806$	−38.9908	−	85.3780i	−1.37339	−	3.00731i
$807$	43.4496	+	27.9233i	1.52950	+	0.982948i
$808$	−7.94804	+	9.17252i	−0.279611	+	0.322688i
$809$	−3.15179	−	21.9212i	−0.110811	−	0.770709i	−0.967134	−	0.254268i	$-0.918166\pi$
$809$	−3.15179	−	21.9212i	−0.110811	−	0.770709i	0.856323	−	0.516441i	$-0.172743\pi$
$810$	2.81527	−	19.5806i	0.0989184	−	0.687993i
$811$	9.00785	+	19.7244i	0.316308	+	0.692618i	0.999284	−	0.0378221i	$-0.0120420\pi$
$811$	9.00785	+	19.7244i	0.316308	+	0.692618i	−0.682976	+	0.730441i	$0.739315\pi$
$812$	−17.3725	−	5.10101i	−0.609654	−	0.179010i
$813$	−3.42236	−	7.49391i	−0.120027	−	0.262823i
$814$	23.8557	−	15.3311i	0.836142	−	0.537356i
$815$	2.58124	+	17.9529i	0.0904168	+	0.628863i
$816$	−49.5935	+	14.5620i	−1.73612	+	0.509771i
$817$	17.1336	−	5.03087i	0.599427	−	0.176008i
$818$	30.0895	−	34.7252i	1.05206	−	1.21414i
$819$	20.2751	−	44.3964i	0.708471	−	1.55133i
$820$	−2.10154	−	14.6165i	−0.0733890	−	0.510432i
$821$	−18.3812	−	21.2131i	−0.641509	−	0.740341i	0.338132	−	0.941099i	$-0.390205\pi$
$821$	−18.3812	−	21.2131i	−0.641509	−	0.740341i	−0.979641	+	0.200758i	$0.935660\pi$
$822$	−27.5952	+	31.8465i	−0.962492	+	1.11078i
$823$	8.98177	−	19.6673i	0.313085	−	0.685560i	−0.686032	−	0.727571i	$-0.740649\pi$
$823$	8.98177	−	19.6673i	0.313085	−	0.685560i	0.999117	+	0.0420110i	$0.0133764\pi$
$824$	−4.87696	−	3.13423i	−0.169897	−	0.109186i
$825$	−4.20971	+	29.2792i	−0.146563	+	1.01937i
$826$	−11.1246	+	7.14937i	−0.387075	+	0.248758i
$827$	36.4091	+	23.3987i	1.26607	+	0.813652i	0.989103	−	0.147227i	$-0.0470349\pi$
$827$	36.4091	+	23.3987i	1.26607	+	0.813652i	0.276965	+	0.960880i	$0.410671\pi$
$828$	−18.9747	−	21.8979i	−0.659415	−	0.761006i
$829$	−32.8733	+	9.65248i	−1.14174	+	0.335245i	−0.797311	−	0.603569i	$-0.793745\pi$
$829$	−32.8733	+	9.65248i	−1.14174	+	0.335245i	−0.344427	+	0.938813i	$0.611927\pi$
$830$	−0.134648	−	0.155392i	−0.00467369	−	0.00539372i
$831$	−9.34175	+	64.9733i	−0.324062	+	2.25390i
$832$	−32.0290	−	9.40456i	−1.11041	−	0.326044i
$833$	−9.42112			−0.326422
$834$	−2.96415			−0.102640
$835$	8.88792	+	2.60973i	0.307579	+	0.0903134i
$836$	−8.67059	+	5.57225i	−0.299878	+	0.192720i
$837$	4.07726	−	8.92796i	0.140931	−	0.308595i
$838$	−20.7985	+	45.5424i	−0.718474	+	1.57324i
$839$	−10.4962	+	6.74551i	−0.362369	+	0.232881i	−0.709138	−	0.705070i	$-0.750915\pi$
$839$	−10.4962	+	6.74551i	−0.362369	+	0.232881i	0.346768	+	0.937951i	$0.387279\pi$
$840$	4.67829	+	1.37367i	0.161416	+	0.0473961i
$841$	−5.33495			−0.183964
$842$	4.58563			0.158031
$843$	26.9797	+	7.92194i	0.929229	+	0.272846i
$844$	2.50605	−	17.4300i	0.0862619	−	0.599965i
$845$	24.9209	+	28.7603i	0.857307	+	0.989385i
$846$	33.8525	−	9.93999i	1.16387	−	0.341744i
$847$	5.95417	+	6.87148i	0.204588	+	0.236107i
$848$	−1.68773	−	1.08464i	−0.0579569	−	0.0372466i
$849$	4.35468	−	2.79859i	0.149452	−	0.0960472i
$850$	−3.64651	+	25.3620i	−0.125074	+	0.869909i
$851$	−15.7503	−	10.1221i	−0.539914	−	0.346981i
$852$	6.12485	−	13.4115i	0.209834	−	0.459472i
$853$	−2.25447	+	2.60180i	−0.0771917	+	0.0890839i	−0.793032	−	0.609180i	$-0.791499\pi$
$853$	−2.25447	+	2.60180i	−0.0771917	+	0.0890839i	0.715840	+	0.698264i	$0.246044\pi$
$854$	4.69394	+	5.41710i	0.160623	+	0.185369i
$855$	−1.11308	−	7.74165i	−0.0380666	−	0.264759i
$856$	2.87428	−	6.29379i	0.0982408	−	0.215117i
$857$	−14.5465	+	16.7876i	−0.496899	+	0.573452i	−0.947696	−	0.319175i	$-0.896594\pi$
$857$	−14.5465	+	16.7876i	−0.496899	+	0.573452i	0.450797	+	0.892626i	$0.351140\pi$
$858$	115.108	−	33.7987i	3.92972	−	1.15387i
$859$	0.231912	−	0.0680956i	0.00791275	−	0.00232339i	−0.277774	−	0.960647i	$-0.589597\pi$
$859$	0.231912	−	0.0680956i	0.00791275	−	0.00232339i	0.285687	+	0.958323i	$0.407778\pi$
$860$	3.85093	+	26.7838i	0.131316	+	0.913321i
$861$	−29.3314	+	18.8501i	−0.999610	+	0.642411i
$862$	−9.09121	−	19.9070i	−0.309648	−	0.678034i
$863$	−40.6806	−	11.9449i	−1.38478	−	0.406609i	−0.497351	−	0.867549i	$-0.665694\pi$
$863$	−40.6806	−	11.9449i	−1.38478	−	0.406609i	−0.887431	+	0.460940i	$0.847512\pi$
$864$	−3.93564	−	8.61785i	−0.133893	−	0.293185i
$865$	0.493068	−	3.42937i	0.0167648	−	0.116602i
$866$	1.64109	+	11.4140i	0.0557665	+	0.387864i
$867$	5.01072	−	5.78268i	0.170173	−	0.196390i
$868$	24.2713	+	15.5982i	0.823821	+	0.529438i
$869$	11.6390	+	25.4859i	0.394827	+	0.864550i
$870$	33.7719			1.14498
$871$	−41.7009	+	30.4706i	−1.41298	+	1.03246i
$872$	1.49716			0.0507003
$873$	−10.5606	−	23.1244i	−0.357421	−	0.782644i
$874$	12.5294	+	8.05218i	0.423815	+	0.272369i
$875$	16.4189	−	18.9484i	0.555059	−	0.640572i
$876$	5.78717	+	40.2506i	0.195530	+	1.35994i
$877$	−2.72635	+	18.9622i	−0.0920622	+	0.640307i	0.890584	+	0.454818i	$0.150296\pi$
$877$	−2.72635	+	18.9622i	−0.0920622	+	0.640307i	−0.982646	+	0.185488i	$0.940613\pi$
$878$	−19.1833	−	42.0055i	−0.647404	−	1.41762i
$879$	−9.92941	−	2.91554i	−0.334911	−	0.0983386i
$880$	10.3920	+	22.7553i	0.350314	+	0.767081i
$881$	29.4114	−	18.9016i	0.990896	−	0.636810i	0.0585148	−	0.998287i	$-0.481364\pi$
$881$	29.4114	−	18.9016i	0.990896	−	0.636810i	0.932381	+	0.361476i	$0.117727\pi$
$882$	−2.01165	−	13.9913i	−0.0677358	−	0.471113i
$883$	−2.32753	+	0.683425i	−0.0783276	+	0.0229991i	−0.320662	−	0.947194i	$-0.603905\pi$
$883$	−2.32753	+	0.683425i	−0.0783276	+	0.0229991i	0.242334	+	0.970193i	$0.422087\pi$
$884$	45.5557	−	13.3764i	1.53221	−	0.449896i
$885$	7.38002	−	8.51700i	0.248077	−	0.286296i
$886$	−5.39896	+	11.8221i	−0.181382	+	0.397171i
$887$	5.11156	+	35.5517i	0.171629	+	1.19371i	0.875442	+	0.483323i	$0.160570\pi$
$887$	5.11156	+	35.5517i	0.171629	+	1.19371i	−0.703812	+	0.710386i	$0.748520\pi$
$888$	−3.86600	−	4.46160i	−0.129734	−	0.149721i
$889$	8.36893	−	9.65826i	0.280685	−	0.323928i
$890$	5.61880	−	12.3035i	0.188343	−	0.412413i
$891$	−23.7508	−	15.2637i	−0.795680	−	0.511353i
$892$	3.81651	−	26.5444i	0.127786	−	0.888773i
$893$	−6.97058	+	4.47972i	−0.233262	+	0.149908i
$894$	13.0546	+	8.38967i	0.436610	+	0.280592i
$895$	0.983150	+	1.13462i	0.0328631	+	0.0379260i
$896$	−10.2150	+	2.99940i	−0.341260	+	0.100203i
$897$	−51.8691	−	59.8602i	−1.73186	−	1.99867i
$898$	8.76975	−	60.9949i	0.292650	−	2.03543i
$899$	−36.1823	−	10.6241i	−1.20675	−	0.354333i
$900$	−17.5647			−0.585489
$901$	1.97885			0.0659251
$902$	−44.2586	−	12.9955i	−1.47365	−	0.432702i
$903$	53.7477	−	34.5416i	1.78861	−	1.14947i
$904$	1.55745	−	3.41035i	0.0518001	−	0.113426i
$905$	−2.48604	+	5.44366i	−0.0826387	+	0.180953i
$906$	−14.8588	+	9.54919i	−0.493652	+	0.317251i
$907$	−1.39686	−	0.410155i	−0.0463820	−	0.0136190i	0.258459	−	0.966022i	$-0.416785\pi$
$907$	−1.39686	−	0.410155i	−0.0463820	−	0.0136190i	−0.304841	+	0.952403i	$0.598603\pi$
$908$	−17.0598			−0.566150
$909$	69.6578			2.31040
$910$	−36.4765	−	10.7105i	−1.20918	−	0.355048i
$911$	0.328387	−	2.28398i	0.0108799	−	0.0756716i	−0.983658	−	0.180047i	$-0.942375\pi$
$911$	0.328387	−	2.28398i	0.0108799	−	0.0756716i	0.994538	+	0.104375i	$0.0332842\pi$
$912$	11.9268	+	13.7643i	0.394937	+	0.455782i
$913$	−0.281561	+	0.0826738i	−0.00931831	+	0.00273610i
$914$	−35.3563	−	40.8034i	−1.16948	−	1.34966i
$915$	−5.13885	−	3.30254i	−0.169885	−	0.109178i
$916$	16.1222	−	10.3611i	0.532693	−	0.342341i
$917$	2.28459	−	15.8897i	0.0754438	−	0.524723i
$918$	9.14157	+	5.87493i	0.301717	+	0.193902i
$919$	−4.62666	+	10.1310i	−0.152619	+	0.334190i	−0.970463	−	0.241251i	$-0.922442\pi$
$919$	−4.62666	+	10.1310i	−0.152619	+	0.334190i	0.817843	+	0.575441i	$0.195170\pi$
$920$	2.78895	−	3.21862i	0.0919490	−	0.106115i
$921$	−26.5261	−	30.6127i	−0.874064	−	1.00872i
$922$	−1.33421	−	9.27963i	−0.0439399	−	0.305608i
$923$	9.01153	−	19.7325i	0.296618	−	0.649503i
$924$	−24.1489	+	27.8694i	−0.794442	+	0.916834i
$925$	−10.8898	+	3.19753i	−0.358054	+	0.105134i
$926$	−13.8932	+	4.07941i	−0.456559	+	0.134058i
$927$	4.73512	+	32.9335i	0.155522	+	1.08168i
$928$	−30.6216	+	19.6793i	−1.00520	+	0.646005i
$929$	−7.19807	−	15.7616i	−0.236161	−	0.517121i	0.754030	−	0.656840i	$-0.228107\pi$
$929$	−7.19807	−	15.7616i	−0.236161	−	0.517121i	−0.990191	+	0.139719i	$0.955380\pi$
$930$	−51.6350	−	15.1614i	−1.69318	−	0.497162i
$931$	1.37904	+	3.01968i	0.0451963	+	0.0989661i
$932$	−5.47451	+	38.0760i	−0.179323	+	1.24722i
$933$	3.68136	+	25.6044i	0.120522	+	0.838251i
$934$	1.55560	−	1.79526i	0.0509009	−	0.0587428i
$935$	−20.7578	−	13.3402i	−0.678852	−	0.436271i
$936$	−5.58420	−	12.2277i	−0.182525	−	0.399675i
$937$	−47.2579			−1.54385			−0.771924	−	0.635715i	$-0.780705\pi$
$937$	−47.2579			−1.54385			−0.771924	+	0.635715i	$0.780705\pi$
$938$	12.5187	−	32.4136i	0.408749	−	1.05834i
$939$	−13.3593			−0.435965
$940$	−5.21596	−	11.4214i	−0.170126	−	0.372523i
$941$	5.21041	+	3.34853i	0.169854	+	0.109159i	0.622806	−	0.782376i	$-0.285993\pi$
$941$	5.21041	+	3.34853i	0.169854	+	0.109159i	−0.452952	+	0.891535i	$0.649629\pi$
$942$	−21.9677	+	25.3521i	−0.715748	+	0.826017i
$943$	4.33413	+	30.1446i	0.141139	+	0.981642i
$944$	−2.01015	+	13.9809i	−0.0654247	+	0.455039i
$945$	−1.65143	−	3.61612i	−0.0537209	−	0.117632i
$946$	81.1008	+	23.8133i	2.63681	+	0.774239i
$947$	21.8090	+	47.7550i	0.708697	+	1.55183i	0.829097	+	0.559104i	$0.188855\pi$
$947$	21.8090	+	47.7550i	0.708697	+	1.55183i	−0.120400	+	0.992725i	$0.538418\pi$
$948$	−26.0034	+	16.7114i	−0.844553	+	0.542761i
$949$	8.51470	+	59.2210i	0.276399	+	1.92240i
$950$	8.66287	−	2.54365i	0.281061	−	0.0825268i
$951$	−5.92544	+	1.73987i	−0.192146	+	0.0564191i
$952$	3.94730	−	4.55542i	0.127933	−	0.147642i
$953$	−7.47164	+	16.3606i	−0.242030	+	0.529972i	−0.991195	−	0.132412i	$-0.957728\pi$
$953$	−7.47164	+	16.3606i	−0.242030	+	0.529972i	0.749165	+	0.662384i	$0.230455\pi$
$954$	0.422536	+	2.93880i	0.0136801	+	0.0951472i
$955$	−11.0675	−	12.7726i	−0.358135	−	0.413310i
$956$	6.18031	−	7.13246i	0.199885	−	0.230680i
$957$	20.0225	−	43.8432i	0.647237	−	1.41725i
$958$	−5.06868	−	3.25744i	−0.163762	−	0.105243i
$959$	2.71221	−	18.8638i	0.0875818	−	0.609145i
$960$	−16.1009	+	10.3474i	−0.519655	+	0.333962i
$961$	24.4719	+	15.7271i	0.789416	+	0.507327i
$962$	30.1431	+	34.7870i	0.971852	+	1.12158i
$963$	−38.1019	+	11.1877i	−1.22782	+	0.360520i
$964$	−18.4836	−	21.3312i	−0.595316	−	0.687032i
$965$	1.98561	−	13.8102i	0.0639190	−	0.444566i
$966$	51.1298	+	15.0131i	1.64507	+	0.483037i
$967$	−2.78178			−0.0894560			−0.0447280	−	0.998999i	$-0.514242\pi$
$967$	−2.78178			−0.0894560			−0.0447280	+	0.998999i	$0.514242\pi$
$968$	2.50420			0.0804882
$969$	−17.2368	−	5.06117i	−0.553724	−	0.162588i
$970$	−16.6580	+	10.7054i	−0.534855	+	0.343730i
$971$	−6.67739	+	14.6215i	−0.214288	+	0.469225i	−0.986000	−	0.166748i	$-0.946674\pi$
$971$	−6.67739	+	14.6215i	−0.214288	+	0.469225i	0.771712	+	0.635972i	$0.219401\pi$
$972$	15.5939	−	34.1460i	0.500176	−	1.09523i
$973$	1.12776	−	0.724767i	0.0361543	−	0.0232350i
$974$	−75.9027	−	22.2870i	−2.43208	−	0.714123i
$975$	−48.0148			−1.53770
$976$	7.65610			0.245066
$977$	−21.8824	−	6.42526i	−0.700081	−	0.205562i	−0.0877251	−	0.996145i	$-0.527960\pi$
$977$	−21.8824	−	6.42526i	−0.700081	−	0.205562i	−0.612356	+	0.790582i	$0.709778\pi$
$978$	−8.89540	+	61.8689i	−0.284443	+	1.97835i
$979$	−12.6413	−	14.5888i	−0.404018	−	0.466261i
$980$	−4.82667	+	1.41724i	−0.154182	+	0.0452720i
$981$	−5.62699	−	6.49390i	−0.179656	−	0.207334i
$982$	3.09297	+	1.98773i	0.0987008	+	0.0634311i
$983$	27.2861	−	17.5357i	0.870292	−	0.559303i	−0.0275499	−	0.999620i	$-0.508771\pi$
$983$	27.2861	−	17.5357i	0.870292	−	0.559303i	0.897842	+	0.440318i	$0.145134\pi$
$984$	−1.36664	+	9.50516i	−0.0435668	+	0.303013i
$985$	−27.8895	−	17.9235i	−0.888632	−	0.571089i
$986$	17.3438	−	37.9776i	0.552339	−	1.20945i
$987$	−19.4141	+	22.4051i	−0.617959	+	0.713163i
$988$	−10.9558	−	12.6437i	−0.348550	−	0.402248i
$989$	−7.94200	−	55.2379i	−0.252541	−	1.75646i
$990$	15.3793	−	33.6759i	0.488786	−	1.07029i
$991$	21.3358	−	24.6228i	0.677754	−	0.782170i	−0.307814	−	0.951446i	$-0.599598\pi$
$991$	21.3358	−	24.6228i	0.677754	−	0.782170i	0.985569	+	0.169276i	$0.0541431\pi$
$992$	55.6531	−	16.3412i	1.76699	−	0.518834i
$993$	57.1734	−	16.7876i	1.81434	−	0.532740i
$994$	2.07701	+	14.4459i	0.0658788	+	0.458197i
$995$	24.6466	−	15.8394i	0.781348	−	0.502142i
$996$	−0.134488	−	0.294487i	−0.00426141	−	0.00933118i
$997$	46.5776	+	13.6764i	1.47513	+	0.433137i	0.917762	−	0.397131i	$-0.129994\pi$
$997$	46.5776	+	13.6764i	1.47513	+	0.433137i	0.557366	+	0.830267i	$0.311812\pi$
$998$	8.04434	+	17.6147i	0.254639	+	0.557582i
$999$	−0.685007	+	4.76433i	−0.0216726	+	0.150737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.14.1	✓	20
3.2	odd	2		603.2.u.c.550.1		20
67.15	even	11		4489.2.a.l.1.1		10
67.24	even	11	inner	67.2.e.c.24.1	yes	20
67.52	odd	22		4489.2.a.m.1.10		10
201.158	odd	22		603.2.u.c.91.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.14.1	✓	20	1.1	even	1	trivial
67.2.e.c.24.1	yes	20	67.24	even	11	inner
603.2.u.c.91.1		20	201.158	odd	22
603.2.u.c.550.1		20	3.2	odd	2
4489.2.a.l.1.1		10	67.15	even	11
4489.2.a.m.1.10		10	67.52	odd	22

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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.797176 - 1.74557i) q^{2} +(-2.14425 - 1.37802i) q^{3} +(-1.10181 + 1.27155i) q^{4} +(0.201991 + 1.40488i) q^{5} +(-0.696097 + 4.84146i) q^{6} +(-0.918948 - 2.01222i) q^{7} +(-0.584585 - 0.171650i) q^{8} +(1.45260 + 3.18076i) q^{9} +O(q^{10})\)	\(q+(-0.797176 - 1.74557i) q^{2} +(-2.14425 - 1.37802i) q^{3} +(-1.10181 + 1.27155i) q^{4} +(0.201991 + 1.40488i) q^{5} +(-0.696097 + 4.84146i) q^{6} +(-0.918948 - 2.01222i) q^{7} +(-0.584585 - 0.171650i) q^{8} +(1.45260 + 3.18076i) q^{9} +(2.29130 - 1.47253i) q^{10} +(-0.553204 - 3.84762i) q^{11} +(4.11478 - 1.20821i) q^{12} +(6.05411 - 1.77765i) q^{13} +(-2.77990 + 3.20818i) q^{14} +(1.50284 - 3.29076i) q^{15} +(0.645282 + 4.48803i) q^{16} +(-2.92877 - 3.37998i) q^{17} +(4.39426 - 5.07124i) q^{18} +(-0.654654 + 1.43349i) q^{19} +(-2.00894 - 1.29107i) q^{20} +(-0.802430 + 5.58102i) q^{21} +(-6.27529 + 4.03289i) q^{22} +(4.14315 + 2.66264i) q^{23} +(1.01696 + 1.17363i) q^{24} +(2.86458 - 0.841116i) q^{25} +(-7.92919 - 9.15078i) q^{26} +(0.180192 - 1.25327i) q^{27} +(3.57114 + 1.04858i) q^{28} -4.86467 q^{29} -6.94228 q^{30} +(7.43776 + 2.18392i) q^{31} +(6.29469 - 4.04535i) q^{32} +(-4.11591 + 9.01258i) q^{33} +(-3.56525 + 7.80681i) q^{34} +(2.64130 - 1.69746i) q^{35} +(-5.64499 - 1.65752i) q^{36} -3.80153 q^{37} +3.02414 q^{38} +(-15.4311 - 4.53099i) q^{39} +(0.123066 - 0.855944i) q^{40} +(4.04946 + 4.67333i) q^{41} +(10.3817 - 3.04836i) q^{42} +(-7.42037 - 8.56356i) q^{43} +(5.50198 + 3.53591i) q^{44} +(-4.17517 + 2.68322i) q^{45} +(1.34501 - 9.35475i) q^{46} +(4.42323 + 2.84264i) q^{47} +(4.80097 - 10.5127i) q^{48} +(1.37948 - 1.59200i) q^{49} +(-3.75180 - 4.32981i) q^{50} +(1.62231 + 11.2834i) q^{51} +(-4.41009 + 9.65675i) q^{52} +(-0.289752 + 0.334391i) q^{53} +(-2.33131 + 0.684534i) q^{54} +(5.29370 - 1.55437i) q^{55} +(0.191807 + 1.33405i) q^{56} +(3.37913 - 2.17163i) q^{57} +(3.87800 + 8.49163i) q^{58} +(2.98896 + 0.877638i) q^{59} +(2.52854 + 5.53673i) q^{60} +(0.240303 - 1.67134i) q^{61} +(-2.11701 - 14.7241i) q^{62} +(5.06550 - 5.84590i) q^{63} +(-4.45062 - 2.86024i) q^{64} +(3.72026 + 8.14623i) q^{65} +19.0132 q^{66} +(-7.70184 + 2.77157i) q^{67} +7.52477 q^{68} +(-5.21475 - 11.4187i) q^{69} +(-5.06862 - 3.25741i) q^{70} +(2.25142 - 2.59828i) q^{71} +(-0.303194 - 2.10876i) q^{72} +(-1.34946 + 9.38572i) q^{73} +(3.03049 + 6.63584i) q^{74} +(-7.30144 - 2.14390i) q^{75} +(-1.10146 - 2.41186i) q^{76} +(-7.23387 + 4.64893i) q^{77} +(4.39216 + 30.5482i) q^{78} +(-6.91577 + 2.03065i) q^{79} +(-6.17481 + 1.81309i) q^{80} +(4.75625 - 5.48900i) q^{81} +(4.92950 - 10.7941i) q^{82} +(-0.0107435 - 0.0747227i) q^{83} +(-6.21245 - 7.16955i) q^{84} +(4.15688 - 4.79730i) q^{85} +(-9.03296 + 19.7794i) q^{86} +(10.4311 + 6.70364i) q^{87} +(-0.337048 + 2.34422i) q^{88} +(4.17767 - 2.68483i) q^{89} +(8.01209 + 5.14906i) q^{90} +(-9.14042 - 10.5486i) q^{91} +(-7.95064 + 2.33452i) q^{92} +(-12.9389 - 14.9323i) q^{93} +(1.43593 - 9.98714i) q^{94} +(-2.14612 - 0.630157i) q^{95} -19.0720 q^{96} -7.27011 q^{97} +(-3.87864 - 1.13887i) q^{98} +(11.4348 - 7.34867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more