LMFDB - Embedded newform 690.2.m.d.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$1.63205 - 1.88348i$ of defining polynomial
Character	$\chi$	$=$	690.31
Dual form			690.2.m.d.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-2.73875 - 1.76009i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-2.73875 - 1.76009i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.635822 + 4.42224i) q^{11} +(0.142315 + 0.989821i) q^{12} +(2.77441 - 1.78300i) q^{13} +(2.13194 - 2.46039i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.84008 - 0.540297i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(3.60473 + 1.05844i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.463314 + 3.22242i) q^{21} -4.46771 q^{22} +(2.83694 + 3.86675i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.37002 + 2.99992i) q^{26} +(0.959493 + 0.281733i) q^{27} +(2.13194 + 2.46039i) q^{28} +(7.45937 - 2.19027i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-1.72695 + 3.78149i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(3.75848 - 2.41543i) q^{33} +(0.272927 + 1.89825i) q^{34} +(-0.463314 - 3.22242i) q^{35} +(0.841254 - 0.540641i) q^{36} +(6.24956 - 7.21237i) q^{37} +(-1.56068 + 3.41741i) q^{38} +(-2.77441 - 1.78300i) q^{39} +(0.959493 - 0.281733i) q^{40} +(0.324003 + 0.373920i) q^{41} +(-3.12368 - 0.917196i) q^{42} +(1.18820 + 2.60180i) q^{43} +(0.635822 - 4.42224i) q^{44} -1.00000 q^{45} +(-4.23113 + 2.25777i) q^{46} +8.80706 q^{47} +(0.142315 - 0.989821i) q^{48} +(1.49493 + 3.27345i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-1.25587 - 1.44935i) q^{51} +(-3.16436 + 0.929139i) q^{52} +(-3.03605 - 1.95115i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-2.92573 + 3.37647i) q^{55} +(-2.73875 + 1.76009i) q^{56} +(-0.534664 - 3.71867i) q^{57} +(1.10640 + 7.69515i) q^{58} +(-1.37257 + 0.882100i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(-3.11945 + 6.83065i) q^{61} +(-3.49722 - 2.24753i) q^{62} +(3.12368 - 0.917196i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(3.16436 + 0.929139i) q^{65} +(1.85596 + 4.06397i) q^{66} +(-2.11146 + 14.6855i) q^{67} -1.91777 q^{68} +(2.33881 - 4.18688i) q^{69} +3.25556 q^{70} +(-0.834410 + 5.80345i) q^{71} +(0.415415 + 0.909632i) q^{72} +(3.37885 + 0.992119i) q^{73} +(6.24956 + 7.21237i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-3.16052 - 2.03114i) q^{76} +(6.04217 - 13.2305i) q^{77} +(2.15970 - 2.49242i) q^{78} +(-11.1689 + 7.17784i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-0.416224 + 0.267491i) q^{82} +(5.57333 - 6.43196i) q^{83} +(1.35241 - 2.96136i) q^{84} +(1.61333 + 1.03682i) q^{85} +(-2.74442 + 0.805834i) q^{86} +(-5.09107 - 5.87541i) q^{87} +(4.28674 + 1.25870i) q^{88} +(-4.54010 - 9.94144i) q^{89} +(0.142315 - 0.989821i) q^{90} -10.7366 q^{91} +(-1.63264 - 4.50938i) q^{92} +4.15716 q^{93} +(-1.25337 + 8.71741i) q^{94} +(1.56068 + 3.41741i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-3.42665 - 3.95456i) q^{97} +(-3.45288 + 1.01386i) q^{98} +(-3.75848 - 2.41543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−2.73875	−	1.76009i	−1.03515	−	0.665250i	−0.0913671	−	0.995817i	$-0.529124\pi$
$7$	−2.73875	−	1.76009i	−1.03515	−	0.665250i	−0.943783	+	0.330567i	$0.892760\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	0.635822	+	4.42224i	0.191708	+	1.33336i	0.827487	+	0.561484i	$0.189770\pi$
$11$	0.635822	+	4.42224i	0.191708	+	1.33336i	−0.635780	+	0.771871i	$0.719321\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	2.77441	−	1.78300i	0.769482	−	0.494516i	−0.0960455	−	0.995377i	$-0.530619\pi$
$13$	2.77441	−	1.78300i	0.769482	−	0.494516i	0.865528	+	0.500861i	$0.166983\pi$
$14$	2.13194	−	2.46039i	0.569784	−	0.657566i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	1.84008	−	0.540297i	0.446286	−	0.131041i	−0.0508649	−	0.998706i	$-0.516198\pi$
$17$	1.84008	−	0.540297i	0.446286	−	0.131041i	0.497151	+	0.867664i	$0.334380\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	3.60473	+	1.05844i	0.826982	+	0.242824i	0.667720	−	0.744413i	$-0.267270\pi$
$19$	3.60473	+	1.05844i	0.826982	+	0.242824i	0.159262	+	0.987236i	$0.449089\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	−0.463314	+	3.22242i	−0.101103	+	0.703190i
$22$	−4.46771			−0.952520
$23$	2.83694	+	3.86675i	0.591543	+	0.806273i
$23$	2.83694	+	3.86675i	0.591543	+	0.806273i
$24$	−1.00000			−0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	1.37002	+	2.99992i	0.268682	+	0.588332i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	2.13194	+	2.46039i	0.402898	+	0.464969i
$29$	7.45937	−	2.19027i	1.38517	−	0.406723i	0.497605	−	0.867404i	$-0.334213\pi$
$29$	7.45937	−	2.19027i	1.38517	−	0.406723i	0.887566	+	0.460681i	$0.152395\pi$
$30$	0.841254	+	0.540641i	0.153591	+	0.0987071i
$31$	−1.72695	+	3.78149i	−0.310169	+	0.679175i	−0.998951	−	0.0457936i	$-0.985418\pi$
$31$	−1.72695	+	3.78149i	−0.310169	+	0.679175i	0.688782	+	0.724968i	$0.258146\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	3.75848	−	2.41543i	0.654267	−	0.420472i
$34$	0.272927	+	1.89825i	0.0468065	+	0.325547i
$35$	−0.463314	−	3.22242i	−0.0783144	−	0.544688i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	6.24956	−	7.21237i	1.02742	−	1.18571i	0.0450078	−	0.998987i	$-0.485669\pi$
$37$	6.24956	−	7.21237i	1.02742	−	1.18571i	0.982413	−	0.186720i	$-0.0597858\pi$
$38$	−1.56068	+	3.41741i	−0.253175	+	0.554377i
$39$	−2.77441	−	1.78300i	−0.444261	−	0.285509i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	0.324003	+	0.373920i	0.0506008	+	0.0583964i	0.780486	−	0.625174i	$-0.214972\pi$
$41$	0.324003	+	0.373920i	0.0506008	+	0.0583964i	−0.729885	+	0.683570i	$0.760426\pi$
$42$	−3.12368	−	0.917196i	−0.481995	−	0.141526i
$43$	1.18820	+	2.60180i	0.181199	+	0.396771i	0.978335	−	0.207030i	$-0.0663796\pi$
$43$	1.18820	+	2.60180i	0.181199	+	0.396771i	−0.797135	+	0.603801i	$0.793652\pi$
$44$	0.635822	−	4.42224i	0.0958538	−	0.666678i
$45$	−1.00000			−0.149071
$46$	−4.23113	+	2.25777i	−0.623846	+	0.332890i
$47$	8.80706			1.28464			0.642321	−	0.766436i	$-0.277972\pi$
$47$	8.80706			1.28464			0.642321	+	0.766436i	$0.277972\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	1.49493	+	3.27345i	0.213562	+	0.467635i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	−1.25587	−	1.44935i	−0.175857	−	0.202950i
$52$	−3.16436	+	0.929139i	−0.438817	+	0.128848i
$53$	−3.03605	−	1.95115i	−0.417034	−	0.268011i	0.315253	−	0.949008i	$-0.397911\pi$
$53$	−3.03605	−	1.95115i	−0.417034	−	0.268011i	−0.732287	+	0.680996i	$0.761547\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	−2.92573	+	3.37647i	−0.394505	+	0.455283i
$56$	−2.73875	+	1.76009i	−0.365981	+	0.235201i
$57$	−0.534664	−	3.71867i	−0.0708180	−	0.492550i
$58$	1.10640	+	7.69515i	0.145277	+	1.01042i
$59$	−1.37257	+	0.882100i	−0.178694	+	0.114840i	−0.626930	−	0.779076i	$-0.715689\pi$
$59$	−1.37257	+	0.882100i	−0.178694	+	0.114840i	0.448236	+	0.893915i	$0.352052\pi$
$60$	−0.654861	+	0.755750i	−0.0845422	+	0.0975669i
$61$	−3.11945	+	6.83065i	−0.399405	+	0.874575i	0.597925	+	0.801552i	$0.295992\pi$
$61$	−3.11945	+	6.83065i	−0.399405	+	0.874575i	−0.997330	+	0.0730228i	$0.976735\pi$
$62$	−3.49722	−	2.24753i	−0.444148	−	0.285437i
$63$	3.12368	−	0.917196i	0.393547	−	0.115556i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	3.16436	+	0.929139i	0.392490	+	0.115245i
$66$	1.85596	+	4.06397i	0.228452	+	0.500241i
$67$	−2.11146	+	14.6855i	−0.257955	+	1.79412i	0.289389	+	0.957212i	$0.406548\pi$
$67$	−2.11146	+	14.6855i	−0.257955	+	1.79412i	−0.547344	+	0.836908i	$0.684361\pi$
$68$	−1.91777			−0.232563
$69$	2.33881	−	4.18688i	0.281560	−	0.504041i
$70$	3.25556			0.389113
$71$	−0.834410	+	5.80345i	−0.0990263	+	0.688743i	0.878471	+	0.477795i	$0.158564\pi$
$71$	−0.834410	+	5.80345i	−0.0990263	+	0.688743i	−0.977497	+	0.210947i	$0.932345\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	3.37885	+	0.992119i	0.395464	+	0.116119i	0.473417	−	0.880838i	$-0.343020\pi$
$73$	3.37885	+	0.992119i	0.395464	+	0.116119i	−0.0779532	+	0.996957i	$0.524838\pi$
$74$	6.24956	+	7.21237i	0.726496	+	0.838421i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	−3.16052	−	2.03114i	−0.362536	−	0.232988i
$77$	6.04217	−	13.2305i	0.688569	−	1.50776i
$78$	2.15970	−	2.49242i	0.244537	−	0.282211i
$79$	−11.1689	+	7.17784i	−1.25660	+	0.807570i	−0.987816	−	0.155629i	$-0.950260\pi$
$79$	−11.1689	+	7.17784i	−1.25660	+	0.807570i	−0.268789	+	0.963199i	$0.586623\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−0.416224	+	0.267491i	−0.0459643	+	0.0295394i
$83$	5.57333	−	6.43196i	0.611752	−	0.705999i	−0.362367	−	0.932036i	$-0.618031\pi$
$83$	5.57333	−	6.43196i	0.611752	−	0.705999i	0.974119	+	0.226036i	$0.0725767\pi$
$84$	1.35241	−	2.96136i	0.147560	−	0.323111i
$85$	1.61333	+	1.03682i	0.174990	+	0.112459i
$86$	−2.74442	+	0.805834i	−0.295938	+	0.0868953i
$87$	−5.09107	−	5.87541i	−0.545820	−	0.629910i
$88$	4.28674	+	1.25870i	0.456968	+	0.134178i
$89$	−4.54010	−	9.94144i	−0.481250	−	1.05379i	−0.982118	−	0.188266i	$-0.939713\pi$
$89$	−4.54010	−	9.94144i	−0.481250	−	1.05379i	0.500868	−	0.865524i	$-0.333014\pi$
$90$	0.142315	−	0.989821i	0.0150013	−	0.104336i
$91$	−10.7366			−1.12551
$92$	−1.63264	−	4.50938i	−0.170214	−	0.470135i
$93$	4.15716			0.431077
$94$	−1.25337	+	8.71741i	−0.129276	+	0.899132i
$95$	1.56068	+	3.41741i	0.160122	+	0.350619i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−3.42665	−	3.95456i	−0.347923	−	0.401525i	0.554634	−	0.832094i	$-0.312858\pi$
$97$	−3.42665	−	3.95456i	−0.347923	−	0.401525i	−0.902557	+	0.430570i	$0.858313\pi$
$98$	−3.45288	+	1.01386i	−0.348793	+	0.102415i
$99$	−3.75848	−	2.41543i	−0.377741	−	0.242760i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	7.06972	−	8.15890i	0.703464	−	0.811841i	−0.285752	−	0.958304i	$-0.592243\pi$
$101$	7.06972	−	8.15890i	0.703464	−	0.811841i	0.989216	+	0.146463i	$0.0467889\pi$
$102$	1.61333	−	1.03682i	0.159743	−	0.102661i
$103$	−1.05240	−	7.31960i	−0.103696	−	0.721222i	−0.973643	−	0.228077i	$-0.926756\pi$
$103$	−1.05240	−	7.31960i	−0.103696	−	0.721222i	0.869947	−	0.493145i	$-0.164153\pi$
$104$	−0.469347	−	3.26438i	−0.0460232	−	0.320099i
$105$	−2.73875	+	1.76009i	−0.267274	+	0.171767i
$106$	2.36337	−	2.72747i	0.229551	−	0.264916i
$107$	2.96302	−	6.48810i	0.286446	−	0.627229i	−0.710637	−	0.703559i	$-0.751593\pi$
$107$	2.96302	−	6.48810i	0.286446	−	0.627229i	0.997083	+	0.0763304i	$0.0243204\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	6.49966	−	1.90847i	0.622555	−	0.182799i	0.0447828	−	0.998997i	$-0.485740\pi$
$109$	6.49966	−	1.90847i	0.622555	−	0.182799i	0.577772	+	0.816198i	$0.303922\pi$
$110$	−2.92573	−	3.37647i	−0.278957	−	0.321934i
$111$	−9.15677	−	2.68867i	−0.869122	−	0.255197i
$112$	−1.35241	−	2.96136i	−0.127790	−	0.279822i
$113$	−2.51884	+	17.5189i	−0.236953	+	1.64804i	0.429917	+	0.902868i	$0.358543\pi$
$113$	−2.51884	+	17.5189i	−0.236953	+	1.64804i	−0.666870	+	0.745174i	$0.732366\pi$
$114$	3.75691			0.351867
$115$	−1.06449	+	4.67620i	−0.0992646	+	0.436058i
$116$	−7.77428			−0.721824
$117$	−0.469347	+	3.26438i	−0.0433911	+	0.301792i
$118$	−0.677783	−	1.48414i	−0.0623950	−	0.136626i
$119$	−5.99050	−	1.75897i	−0.549148	−	0.161244i
$120$	−0.654861	−	0.755750i	−0.0597803	−	0.0689902i
$121$	−8.59750	+	2.52445i	−0.781591	+	0.229496i
$122$	−6.31718	−	4.05980i	−0.571930	−	0.367557i
$123$	0.205533	−	0.450055i	0.0185323	−	0.0405801i
$124$	2.72236	−	3.14177i	0.244475	−	0.282139i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.463314	+	3.22242i	0.0412753	+	0.287076i
$127$	−0.847354	−	5.89348i	−0.0751906	−	0.522962i	−0.992254	−	0.124222i	$-0.960357\pi$
$127$	−0.847354	−	5.89348i	−0.0751906	−	0.522962i	0.917064	−	0.398740i	$-0.130552\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	1.87308	−	2.16165i	0.164916	−	0.190323i
$130$	−1.37002	+	2.99992i	−0.120158	+	0.263110i
$131$	11.0769	+	7.11869i	0.967793	+	0.621963i	0.926144	−	0.377169i	$-0.123102\pi$
$131$	11.0769	+	7.11869i	0.967793	+	0.621963i	0.0416491	+	0.999132i	$0.486739\pi$
$132$	−4.28674	+	1.25870i	−0.373113	+	0.109556i
$133$	−8.00950	−	9.24345i	−0.694511	−	0.801509i
$134$	−14.2355	−	4.17993i	−1.22976	−	0.361091i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	0.272927	−	1.89825i	0.0234033	−	0.162773i
$137$	−14.9511			−1.27736			−0.638679	−	0.769474i	$-0.720519\pi$
$137$	−14.9511			−1.27736			−0.638679	+	0.769474i	$0.720519\pi$
$138$	3.81142	+	2.91086i	0.324449	+	0.247789i
$139$	−12.2999			−1.04327			−0.521633	−	0.853170i	$-0.674677\pi$
$139$	−12.2999			−1.04327			−0.521633	+	0.853170i	$0.674677\pi$
$140$	−0.463314	+	3.22242i	−0.0391572	+	0.272344i
$141$	−3.65858	−	8.01118i	−0.308108	−	0.674663i
$142$	−5.62563	−	1.65183i	−0.472093	−	0.138619i
$143$	9.64890	+	11.1354i	0.806881	+	0.931191i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	6.54014	+	4.20310i	0.543129	+	0.349048i
$146$	−1.46288	+	3.20326i	−0.121069	+	0.265104i
$147$	2.35661	−	2.71968i	0.194370	−	0.224315i
$148$	−8.02837	+	5.15952i	−0.659928	+	0.424110i
$149$	−1.11990	−	7.78907i	−0.0917457	−	0.638105i	−0.982864	−	0.184334i	$-0.940987\pi$
$149$	−1.11990	−	7.78907i	−0.0917457	−	0.638105i	0.891118	−	0.453771i	$-0.149922\pi$
$150$	0.142315	+	0.989821i	0.0116200	+	0.0808186i
$151$	−2.74293	+	1.76277i	−0.223216	+	0.143452i	−0.647470	−	0.762091i	$-0.724173\pi$
$151$	−2.74293	+	1.76277i	−0.223216	+	0.143452i	0.424254	+	0.905543i	$0.360537\pi$
$152$	2.46025	−	2.83928i	0.199553	−	0.230296i
$153$	−0.796669	+	1.74446i	−0.0644069	+	0.141031i
$154$	12.2359	+	7.86356i	0.986000	+	0.633664i
$155$	−3.98877	+	1.17121i	−0.320385	+	0.0940736i
$156$	2.15970	+	2.49242i	0.172914	+	0.199553i
$157$	−11.2825	−	3.31284i	−0.900440	−	0.264393i	−0.201429	−	0.979503i	$-0.564558\pi$
$157$	−11.2825	−	3.31284i	−0.900440	−	0.264393i	−0.699012	+	0.715110i	$0.746377\pi$
$158$	−5.51528	−	12.0768i	−0.438772	−	0.960776i
$159$	−0.513609	+	3.57223i	−0.0407318	+	0.283296i
$160$	−1.00000			−0.0790569
$161$	−0.963852	−	15.5833i	−0.0759622	−	1.22814i
$162$	1.00000			0.0785674
$163$	2.99917	−	20.8597i	0.234913	−	1.63386i	−0.441448	−	0.897287i	$-0.645535\pi$
$163$	2.99917	−	20.8597i	0.234913	−	1.63386i	0.676361	−	0.736570i	$-0.263556\pi$
$164$	−0.205533	−	0.450055i	−0.0160495	−	0.0351434i
$165$	4.28674	+	1.25870i	0.333722	+	0.0979897i
$166$	5.57333	+	6.43196i	0.432574	+	0.499217i
$167$	13.2159	−	3.88054i	1.02268	−	0.300285i	0.272947	−	0.962029i	$-0.412002\pi$
$167$	13.2159	−	3.88054i	1.02268	−	0.300285i	0.749730	+	0.661744i	$0.230183\pi$
$168$	2.73875	+	1.76009i	0.211299	+	0.135794i
$169$	−0.882156	+	1.93165i	−0.0678582	+	0.148589i
$170$	−1.25587	+	1.44935i	−0.0963208	+	0.111160i
$171$	−3.16052	+	2.03114i	−0.241691	+	0.155325i
$172$	−0.407060	−	2.83117i	−0.0310380	−	0.215874i
$173$	−0.486807	−	3.38582i	−0.0370113	−	0.257419i	0.962912	−	0.269816i	$-0.0869629\pi$
$173$	−0.486807	−	3.38582i	−0.0370113	−	0.257419i	−0.999923	+	0.0123970i	$0.996054\pi$
$174$	6.54014	−	4.20310i	0.495807	−	0.318636i
$175$	2.13194	−	2.46039i	0.161159	−	0.185988i
$176$	−1.85596	+	4.06397i	−0.139898	+	0.306334i
$177$	1.37257	+	0.882100i	0.103169	+	0.0663027i
$178$	10.4864	−	3.07908i	0.785987	−	0.230786i
$179$	−12.1722	−	14.0474i	−0.909790	−	1.04995i	−0.998546	−	0.0539002i	$-0.982835\pi$
$179$	−12.1722	−	14.0474i	−0.909790	−	1.04995i	0.0887564	−	0.996053i	$-0.471711\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	6.93379	+	15.1829i	0.515384	+	1.12853i	0.971158	+	0.238439i	$0.0766356\pi$
$181$	6.93379	+	15.1829i	0.515384	+	1.12853i	−0.455773	+	0.890096i	$0.650637\pi$
$182$	1.52798	−	10.6274i	0.113262	−	0.787753i
$183$	7.50924			0.555099
$184$	4.69583	−	0.974266i	0.346181	−	0.0718239i
$185$	9.54334			0.701640
$186$	−0.591625	+	4.11485i	−0.0433801	+	0.301715i
$187$	3.55929	+	7.79375i	0.260281	+	0.569936i
$188$	−8.45031	−	2.48123i	−0.616302	−	0.180963i
$189$	−2.13194	−	2.46039i	−0.155076	−	0.178967i
$190$	−3.60473	+	1.05844i	−0.261515	+	0.0767876i
$191$	11.3500	+	7.29419i	0.821256	+	0.527789i	0.882488	−	0.470334i	$-0.155867\pi$
$191$	11.3500	+	7.29419i	0.821256	+	0.527789i	−0.0612322	+	0.998124i	$0.519503\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	6.90747	−	7.97165i	0.497211	−	0.573812i	−0.450567	−	0.892742i	$-0.648778\pi$
$193$	6.90747	−	7.97165i	0.497211	−	0.573812i	0.947778	+	0.318931i	$0.103324\pi$
$194$	4.40197	−	2.82897i	0.316043	−	0.203109i
$195$	−0.469347	−	3.26438i	−0.0336106	−	0.233767i
$196$	−0.512141	−	3.56202i	−0.0365815	−	0.254430i
$197$	−0.941353	+	0.604971i	−0.0670686	+	0.0431024i	−0.573745	−	0.819034i	$-0.694510\pi$
$197$	−0.941353	+	0.604971i	−0.0670686	+	0.0431024i	0.506677	+	0.862136i	$0.330874\pi$
$198$	2.92573	−	3.37647i	0.207923	−	0.239955i
$199$	11.4345	−	25.0380i	0.810568	−	1.77490i	0.205621	−	0.978632i	$-0.434078\pi$
$199$	11.4345	−	25.0380i	0.810568	−	1.77490i	0.604947	−	0.796266i	$-0.293194\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	14.2355	−	4.17993i	1.00410	−	0.294829i
$202$	7.06972	+	8.15890i	0.497424	+	0.574058i
$203$	−24.2844	−	7.13055i	−1.70443	−	0.500466i
$204$	0.796669	+	1.74446i	0.0557780	+	0.122137i
$205$	−0.0704126	+	0.489731i	−0.00491783	+	0.0342043i
$206$	7.39487			0.515225
$207$	−4.78010	−	0.388166i	−0.332240	−	0.0269794i
$208$	3.29795			0.228671
$209$	−2.38873	+	16.6140i	−0.165232	+	1.14921i
$210$	−1.35241	−	2.96136i	−0.0933250	−	0.204353i
$211$	−3.48588	−	1.02355i	−0.239978	−	0.0704638i	0.159532	−	0.987193i	$-0.449001\pi$
$211$	−3.48588	−	1.02355i	−0.239978	−	0.0704638i	−0.399510	+	0.916729i	$0.630820\pi$
$212$	2.36337	+	2.72747i	0.162317	+	0.187324i
$213$	5.62563	−	1.65183i	0.385462	−	0.113182i
$214$	6.00038	+	3.85621i	0.410178	+	0.263605i
$215$	−1.18820	+	2.60180i	−0.0810348	+	0.177441i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	11.3854	−	7.31696i	0.772892	−	0.496708i
$218$	0.964049	+	6.70511i	0.0652937	+	0.454127i
$219$	−0.501161	−	3.48565i	−0.0338653	−	0.235538i
$220$	3.75848	−	2.41543i	0.253397	−	0.162848i
$221$	4.14179	−	4.77988i	0.278607	−	0.321530i
$222$	3.96445	−	8.68093i	0.266076	−	0.582626i
$223$	−18.6561	−	11.9896i	−1.24931	−	0.802881i	−0.262524	−	0.964925i	$-0.584555\pi$
$223$	−18.6561	−	11.9896i	−1.24931	−	0.802881i	−0.986783	+	0.162044i	$0.948191\pi$
$224$	3.12368	−	0.917196i	0.208710	−	0.0612828i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−16.9821	−	4.98641i	−1.12964	−	0.331691i
$227$	−0.938365	−	2.05473i	−0.0622815	−	0.136377i	0.875932	−	0.482435i	$-0.160247\pi$
$227$	−0.938365	−	2.05473i	−0.0622815	−	0.136377i	−0.938213	+	0.346057i	$0.887520\pi$
$228$	−0.534664	+	3.71867i	−0.0354090	+	0.246275i
$229$	3.92388			0.259297			0.129649	−	0.991560i	$-0.458615\pi$
$229$	3.92388			0.259297			0.129649	+	0.991560i	$0.458615\pi$
$230$	−4.47711	−	1.71915i	−0.295212	−	0.113358i
$231$	−14.5449			−0.956984
$232$	1.10640	−	7.69515i	0.0726385	−	0.505212i
$233$	−5.13215	−	11.2378i	−0.336218	−	0.736215i	0.663713	−	0.747988i	$-0.268980\pi$
$233$	−5.13215	−	11.2378i	−0.336218	−	0.736215i	−0.999931	+	0.0117728i	$0.996253\pi$
$234$	−3.16436	−	0.929139i	−0.206860	−	0.0607397i
$235$	5.76739	+	6.65593i	0.376223	+	0.434185i
$236$	1.56549	−	0.459670i	0.101905	−	0.0299219i
$237$	11.1689	+	7.17784i	0.725501	+	0.466251i
$238$	2.59360	−	5.67919i	0.168118	−	0.368127i
$239$	−7.27248	+	8.39289i	−0.470417	+	0.542891i	−0.940528	−	0.339717i	$-0.889669\pi$
$239$	−7.27248	+	8.39289i	−0.470417	+	0.542891i	0.470110	+	0.882608i	$0.344214\pi$
$240$	0.841254	−	0.540641i	0.0543027	−	0.0348982i
$241$	4.20857	+	29.2712i	0.271098	+	1.88553i	0.437119	+	0.899403i	$0.355999\pi$
$241$	4.20857	+	29.2712i	0.271098	+	1.88553i	−0.166022	+	0.986122i	$0.553092\pi$
$242$	−1.27521	−	8.86926i	−0.0819734	−	0.570137i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	4.91751	−	5.67511i	0.314811	−	0.363311i
$245$	−1.49493	+	3.27345i	−0.0955077	+	0.209133i
$246$	0.416224	+	0.267491i	0.0265375	+	0.0170546i
$247$	11.8882	−	3.49069i	0.756428	−	0.222107i
$248$	2.72236	+	3.14177i	0.172870	+	0.199503i
$249$	−8.16596	−	2.39774i	−0.517497	−	0.151951i
$250$	−0.415415	−	0.909632i	−0.0262732	−	0.0575302i
$251$	−3.55470	+	24.7235i	−0.224371	+	1.56053i	0.496856	+	0.867833i	$0.334488\pi$
$251$	−3.55470	+	24.7235i	−0.224371	+	1.56053i	−0.721227	+	0.692699i	$0.756421\pi$
$252$	−3.25556			−0.205081
$253$	−15.2959	+	15.0042i	−0.961645	+	0.943306i
$254$	5.95408			0.373592
$255$	0.272927	−	1.89825i	0.0170913	−	0.118873i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	15.9099	+	4.67157i	0.992434	+	0.291405i	0.737348	−	0.675514i	$-0.236078\pi$
$257$	15.9099	+	4.67157i	0.992434	+	0.291405i	0.255086	+	0.966918i	$0.417896\pi$
$258$	1.87308	+	2.16165i	0.116613	+	0.134579i
$259$	−29.8104	+	8.75311i	−1.85233	+	0.543892i
$260$	−2.77441	−	1.78300i	−0.172062	−	0.110577i
$261$	−3.22955	+	7.07174i	−0.199904	+	0.437730i
$262$	−8.62264	+	9.95106i	−0.532709	+	0.614779i
$263$	−17.3078	+	11.1230i	−1.06724	+	0.685875i	−0.951576	−	0.307413i	$-0.900537\pi$
$263$	−17.3078	+	11.1230i	−1.06724	+	0.685875i	−0.115666	+	0.993288i	$0.536900\pi$
$264$	−0.635822	−	4.42224i	−0.0391321	−	0.272170i
$265$	−0.513609	−	3.57223i	−0.0315507	−	0.219440i
$266$	10.2892	−	6.61249i	0.630874	−	0.405438i
$267$	−7.15702	+	8.25964i	−0.438003	+	0.505482i
$268$	6.16331	−	13.4958i	0.376484	−	0.824385i
$269$	21.7097	+	13.9520i	1.32366	+	0.850667i	0.995574	−	0.0939799i	$-0.0299589\pi$
$269$	21.7097	+	13.9520i	1.32366	+	0.850667i	0.328089	+	0.944647i	$0.393595\pi$
$270$	−0.959493	+	0.281733i	−0.0583929	+	0.0171457i
$271$	9.41568	+	10.8663i	0.571962	+	0.660079i	0.965857	−	0.259076i	$-0.0834182\pi$
$271$	9.41568	+	10.8663i	0.571962	+	0.660079i	−0.393895	+	0.919155i	$0.628873\pi$
$272$	1.84008	+	0.540297i	0.111571	+	0.0327603i
$273$	4.46016	+	9.76640i	0.269941	+	0.591089i
$274$	2.12776	−	14.7989i	0.128543	−	0.894034i
$275$	−4.46771			−0.269413
$276$	−3.42365	+	3.35836i	−0.206080	+	0.202150i
$277$	4.02957			0.242114			0.121057	−	0.992646i	$-0.461372\pi$
$277$	4.02957			0.242114			0.121057	+	0.992646i	$0.461372\pi$
$278$	1.75046	−	12.1747i	0.104986	−	0.730192i
$279$	−1.72695	−	3.78149i	−0.103390	−	0.226392i
$280$	−3.12368	−	0.917196i	−0.186676	−	0.0548130i
$281$	6.19836	+	7.15329i	0.369763	+	0.426730i	0.909887	−	0.414856i	$-0.136168\pi$
$281$	6.19836	+	7.15329i	0.369763	+	0.426730i	−0.540124	+	0.841586i	$0.681623\pi$
$282$	8.45031	−	2.48123i	0.503209	−	0.147755i
$283$	−12.9707	−	8.33574i	−0.771026	−	0.495508i	0.0950185	−	0.995476i	$-0.469709\pi$
$283$	−12.9707	−	8.33574i	−0.771026	−	0.495508i	−0.866044	+	0.499967i	$0.833345\pi$
$284$	2.43563	−	5.33329i	0.144528	−	0.316473i
$285$	2.46025	−	2.83928i	0.145733	−	0.168185i
$286$	−12.3953	+	7.96595i	−0.732947	+	0.471037i
$287$	−0.229232	−	1.59435i	−0.0135312	−	0.0941112i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−11.2073	+	7.20251i	−0.659254	+	0.423677i
$290$	−5.09107	+	5.87541i	−0.298958	+	0.345016i
$291$	−2.17371	+	4.75977i	−0.127425	+	0.279023i
$292$	−2.96247	−	1.90386i	−0.173365	−	0.111415i
$293$	−24.2528	+	7.12127i	−1.41686	+	0.416029i	−0.898440	−	0.439095i	$-0.855299\pi$
$293$	−24.2528	+	7.12127i	−1.41686	+	0.416029i	−0.518423	+	0.855124i	$0.673481\pi$
$294$	2.35661	+	2.71968i	0.137440	+	0.158615i
$295$	−1.56549	−	0.459670i	−0.0911464	−	0.0267630i
$296$	−3.96445	−	8.68093i	−0.230429	−	0.504569i
$297$	−0.635822	+	4.42224i	−0.0368941	+	0.256604i
$298$	7.86916			0.455848
$299$	14.7653	+	5.66967i	0.853897	+	0.327885i
$300$	−1.00000			−0.0577350
$301$	1.32521	−	9.21702i	0.0763837	−	0.531260i
$302$	−1.35447	−	2.96588i	−0.0779411	−	0.170667i
$303$	−10.3585	−	3.04152i	−0.595078	−	0.174731i
$304$	2.46025	+	2.83928i	0.141105	+	0.162844i
$305$	−7.20506	+	2.11560i	−0.412561	+	0.121139i
$306$	−1.61333	−	1.03682i	−0.0922278	−	0.0592712i
$307$	6.27632	−	13.7432i	0.358209	−	0.784367i	−0.641641	−	0.767005i	$-0.721746\pi$
$307$	6.27632	−	13.7432i	0.358209	−	0.784367i	0.999849	−	0.0173619i	$-0.00552675\pi$
$308$	−9.52488	+	10.9923i	−0.542730	+	0.626344i
$309$	−6.22096	+	3.99797i	−0.353898	+	0.227437i
$310$	−0.591625	−	4.11485i	−0.0336021	−	0.233708i
$311$	−2.64495	−	18.3960i	−0.149981	−	1.04314i	−0.916246	−	0.400617i	$-0.868796\pi$
$311$	−2.64495	−	18.3960i	−0.149981	−	1.04314i	0.766265	−	0.642525i	$-0.222113\pi$
$312$	−2.77441	+	1.78300i	−0.157070	+	0.100943i
$313$	8.42064	−	9.71794i	0.475963	−	0.549290i	−0.466098	−	0.884733i	$-0.654341\pi$
$313$	8.42064	−	9.71794i	0.475963	−	0.549290i	0.942061	+	0.335443i	$0.108886\pi$
$314$	4.88478	−	10.6962i	0.275664	−	0.603620i
$315$	2.73875	+	1.76009i	0.154311	+	0.0991697i
$316$	12.7388	−	3.74044i	0.716611	−	0.210416i
$317$	17.4083	+	20.0902i	0.977745	+	1.12838i	0.991713	+	0.128475i	$0.0410084\pi$
$317$	17.4083	+	20.0902i	0.977745	+	1.12838i	−0.0139676	+	0.999902i	$0.504446\pi$
$318$	−3.46277	−	1.01676i	−0.194183	−	0.0570172i
$319$	14.4287	+	31.5945i	0.807853	+	1.76895i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	−7.13267			−0.398107
$322$	15.5619	+	1.26370i	0.867229	+	0.0704231i
$323$	7.20488			0.400890
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	1.37002	+	2.99992i	0.0759948	+	0.166405i
$326$	20.2205	+	5.93729i	1.11991	+	0.328836i
$327$	−4.43607	−	5.11949i	−0.245315	−	0.283109i
$328$	0.474725	−	0.139392i	0.0262123	−	0.00769663i
$329$	−24.1203	−	15.5012i	−1.32980	−	0.854608i
$330$	−1.85596	+	4.06397i	−0.102167	+	0.223714i
$331$	−1.49789	+	1.72865i	−0.0823314	+	0.0950155i	−0.795421	−	0.606058i	$-0.792750\pi$
$331$	−1.49789	+	1.72865i	−0.0823314	+	0.0950155i	0.713089	+	0.701073i	$0.247295\pi$
$332$	−7.15966	+	4.60123i	−0.392937	+	0.252526i
$333$	1.35816	+	9.44620i	0.0744266	+	0.517649i
$334$	1.96022	+	13.6336i	0.107259	+	0.746000i
$335$	−12.4813	+	8.02123i	−0.681925	+	0.438246i
$336$	−2.13194	+	2.46039i	−0.116307	+	0.134225i
$337$	6.58975	−	14.4295i	0.358967	−	0.786027i	−0.640864	−	0.767654i	$-0.721424\pi$
$337$	6.58975	−	14.4295i	0.358967	−	0.786027i	0.999831	−	0.0183734i	$-0.00584877\pi$
$338$	−1.78645	−	1.14808i	−0.0971700	−	0.0624473i
$339$	16.9821	−	4.98641i	0.922344	−	0.270825i
$340$	−1.25587	−	1.44935i	−0.0681091	−	0.0786021i
$341$	−17.8207	−	5.23262i	−0.965043	−	0.283362i
$342$	−1.56068	−	3.41741i	−0.0843918	−	0.184792i
$343$	−1.57589	+	10.9606i	−0.0850903	+	0.591816i
$344$	2.86028			0.154216
$345$	4.69583	−	0.974266i	0.252815	−	0.0524527i
$346$	3.42064			0.183894
$347$	−3.15265	+	21.9272i	−0.169243	+	1.17711i	0.711210	+	0.702979i	$0.248147\pi$
$347$	−3.15265	+	21.9272i	−0.169243	+	1.17711i	−0.880453	+	0.474133i	$0.842762\pi$
$348$	3.22955	+	7.07174i	0.173122	+	0.379085i
$349$	4.13814	+	1.21507i	0.221510	+	0.0650411i	0.390604	−	0.920559i	$-0.372266\pi$
$349$	4.13814	+	1.21507i	0.221510	+	0.0650411i	−0.169095	+	0.985600i	$0.554084\pi$
$350$	2.13194	+	2.46039i	0.113957	+	0.131513i
$351$	3.16436	−	0.929139i	0.168901	−	0.0495938i
$352$	−3.75848	−	2.41543i	−0.200328	−	0.128743i
$353$	−5.09611	+	11.1589i	−0.271238	+	0.593929i	−0.995411	−	0.0956893i	$-0.969494\pi$
$353$	−5.09611	+	11.1589i	−0.271238	+	0.593929i	0.724173	+	0.689618i	$0.242222\pi$
$354$	−1.06846	+	1.23307i	−0.0567879	+	0.0655368i
$355$	−4.93238	+	3.16985i	−0.261783	+	0.168238i
$356$	1.55537	+	10.8178i	0.0824344	+	0.573344i
$357$	0.888528	+	6.17985i	0.0470259	+	0.327072i
$358$	15.6367	−	10.0491i	0.826426	−	0.531112i
$359$	−12.5346	+	14.4657i	−0.661549	+	0.763468i	−0.983029	−	0.183448i	$-0.941274\pi$
$359$	−12.5346	+	14.4657i	−0.661549	+	0.763468i	0.321481	+	0.946916i	$0.395820\pi$
$360$	−0.415415	+	0.909632i	−0.0218943	+	0.0479418i
$361$	−4.11004	−	2.64136i	−0.216318	−	0.139019i
$362$	−16.0151	+	4.70246i	−0.841736	+	0.247156i
$363$	5.86785	+	6.77186i	0.307982	+	0.355431i
$364$	10.3017	+	3.02486i	0.539958	+	0.158546i
$365$	1.46288	+	3.20326i	0.0765707	+	0.167666i
$366$	−1.06868	+	7.43281i	−0.0558606	+	0.388519i
$367$	13.7250			0.716437			0.358219	−	0.933638i	$-0.383384\pi$
$367$	13.7250			0.716437			0.358219	+	0.933638i	$0.383384\pi$
$368$	0.296064	+	4.78668i	0.0154334	+	0.249523i
$369$	−0.494767			−0.0257565
$370$	−1.35816	+	9.44620i	−0.0706073	+	0.491085i
$371$	4.88079	+	10.6874i	0.253398	+	0.554864i
$372$	−3.98877	−	1.17121i	−0.206808	−	0.0607243i
$373$	19.6433	+	22.6696i	1.01709	+	1.17379i	0.984691	+	0.174311i	$0.0557699\pi$
$373$	19.6433	+	22.6696i	1.01709	+	1.17379i	0.0324008	+	0.999475i	$0.489685\pi$
$374$	−8.22096	+	2.41389i	−0.425096	+	0.124819i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	3.65858	−	8.01118i	0.188677	−	0.413145i
$377$	16.7901	−	19.3768i	0.864733	−	0.997956i
$378$	2.73875	−	1.76009i	0.140866	−	0.0905291i
$379$	−3.00299	−	20.8863i	−0.154253	−	1.07286i	−0.908987	−	0.416825i	$-0.863143\pi$
$379$	−3.00299	−	20.8863i	−0.154253	−	1.07286i	0.754734	−	0.656031i	$-0.227766\pi$
$380$	−0.534664	−	3.71867i	−0.0274277	−	0.190764i
$381$	−5.00889	+	3.21902i	−0.256613	+	0.164915i
$382$	−8.83522	+	10.1964i	−0.452049	+	0.521693i
$383$	8.71954	−	19.0931i	0.445548	−	0.975614i	−0.544999	−	0.838437i	$-0.683470\pi$
$383$	8.71954	−	19.0931i	0.445548	−	0.975614i	0.990547	−	0.137177i	$-0.0438028\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	13.9557	−	4.09777i	0.711249	−	0.208842i
$386$	6.90747	+	7.97165i	0.351581	+	0.405746i
$387$	−2.74442	−	0.805834i	−0.139507	−	0.0409628i
$388$	2.17371	+	4.75977i	0.110354	+	0.241641i
$389$	−3.54654	+	24.6668i	−0.179817	+	1.25065i	0.677368	+	0.735645i	$0.263121\pi$
$389$	−3.54654	+	24.6668i	−0.179817	+	1.25065i	−0.857185	+	0.515009i	$0.827788\pi$
$390$	3.29795			0.166998
$391$	7.30940	+	5.58235i	0.369652	+	0.282312i
$392$	3.59865			0.181759
$393$	1.87388	−	13.0331i	0.0945247	−	0.657434i
$394$	−0.464845	−	1.01787i	−0.0234185	−	0.0512794i
$395$	−12.7388	−	3.74044i	−0.640956	−	0.188202i
$396$	2.92573	+	3.37647i	0.147023	+	0.169674i
$397$	−36.5968	+	10.7458i	−1.83674	+	0.539316i	−0.999966	−	0.00823065i	$-0.997380\pi$
$397$	−36.5968	+	10.7458i	−1.83674	+	0.539316i	−0.836775	+	0.547547i	$0.815562\pi$
$398$	23.1559	+	14.8814i	1.16070	+	0.745936i
$399$	−5.08087	+	11.1256i	−0.254362	+	0.556975i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	25.2467	−	16.2251i	1.26076	−	0.810242i	0.272372	−	0.962192i	$-0.412192\pi$
$401$	25.2467	−	16.2251i	1.26076	−	0.810242i	0.988388	+	0.151950i	$0.0485554\pi$
$402$	2.11146	+	14.6855i	0.105310	+	0.732446i
$403$	1.95115	+	13.5705i	0.0971936	+	0.675997i
$404$	−9.08198	+	5.83663i	−0.451845	+	0.290383i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	10.5140	−	23.0224i	0.521801	−	1.14258i
$407$	35.8684	+	23.0512i	1.77793	+	1.14261i
$408$	−1.84008	+	0.540297i	−0.0910977	+	0.0267487i
$409$	−12.6878	−	14.6425i	−0.627370	−	0.724023i	0.349719	−	0.936855i	$-0.386277\pi$
$409$	−12.6878	−	14.6425i	−0.627370	−	0.724023i	−0.977089	+	0.212831i	$0.931732\pi$
$410$	−0.474725	−	0.139392i	−0.0234450	−	0.00688407i
$411$	6.21090	+	13.6000i	0.306361	+	0.670838i
$412$	−1.05240	+	7.31960i	−0.0518480	+	0.360611i
$413$	5.31171			0.261372
$414$	1.06449	−	4.67620i	0.0523170	−	0.229823i
$415$	8.51070			0.417774
$416$	−0.469347	+	3.26438i	−0.0230116	+	0.160049i
$417$	5.10958	+	11.1884i	0.250217	+	0.547899i
$418$	−16.1049	−	4.72883i	−0.787717	−	0.231294i
$419$	−22.4412	−	25.8985i	−1.09632	−	1.26523i	−0.961633	−	0.274337i	$-0.911541\pi$
$419$	−22.4412	−	25.8985i	−1.09632	−	1.26523i	−0.134690	−	0.990888i	$-0.543004\pi$
$420$	3.12368	−	0.917196i	0.152420	−	0.0447546i
$421$	−0.0698465	−	0.0448876i	−0.00340411	−	0.00218769i	0.538938	−	0.842346i	$-0.318826\pi$
$421$	−0.0698465	−	0.0448876i	−0.00340411	−	0.00218769i	−0.542342	+	0.840158i	$0.682462\pi$
$422$	1.50922	−	3.30473i	0.0734676	−	0.160872i
$423$	−5.76739	+	6.65593i	−0.280420	+	0.323622i
$424$	−3.03605	+	1.95115i	−0.147444	+	0.0947564i
$425$	0.272927	+	1.89825i	0.0132389	+	0.0920785i
$426$	0.834410	+	5.80345i	0.0404273	+	0.281178i
$427$	20.5659	−	13.2169i	0.995255	−	0.639611i
$428$	−4.67090	+	5.39051i	−0.225777	+	0.260560i
$429$	6.12084	−	13.4028i	0.295517	−	0.647092i
$430$	−2.40622	−	1.54638i	−0.116038	−	0.0745732i
$431$	10.0305	−	2.94522i	0.483152	−	0.141866i	−0.0310806	−	0.999517i	$-0.509895\pi$
$431$	10.0305	−	2.94522i	0.483152	−	0.141866i	0.514233	+	0.857651i	$0.328077\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	7.77335	+	2.28246i	0.373563	+	0.109688i	0.463124	−	0.886293i	$-0.346728\pi$
$433$	7.77335	+	2.28246i	0.373563	+	0.109688i	−0.0895612	+	0.995981i	$0.528546\pi$
$434$	5.62217	+	12.3108i	0.269873	+	0.590939i
$435$	1.10640	−	7.69515i	0.0530476	−	0.368954i
$436$	−6.77406			−0.324419
$437$	6.13367	+	16.9413i	0.293413	+	0.810414i
$438$	3.52149			0.168263
$439$	2.90499	−	20.2046i	0.138648	−	0.964315i	−0.795124	−	0.606446i	$-0.792594\pi$
$439$	2.90499	−	20.2046i	0.138648	−	0.964315i	0.933772	−	0.357869i	$-0.116496\pi$
$440$	1.85596	+	4.06397i	0.0884792	+	0.193742i
$441$	−3.45288	−	1.01386i	−0.164423	−	0.0482789i
$442$	4.14179	+	4.77988i	0.197005	+	0.227356i
$443$	−35.2806	+	10.3593i	−1.67623	+	0.492187i	−0.975271	−	0.221011i	$-0.929064\pi$
$443$	−35.2806	+	10.3593i	−1.67623	+	0.492187i	−0.700963	+	0.713198i	$0.747246\pi$
$444$	8.02837	+	5.15952i	0.381009	+	0.244860i
$445$	4.54010	−	9.94144i	0.215221	−	0.471269i
$446$	14.5226	−	16.7600i	0.687664	−	0.793607i
$447$	−6.61996	+	4.25439i	−0.313113	+	0.201226i
$448$	0.463314	+	3.22242i	0.0218895	+	0.152245i
$449$	−4.08066	−	28.3816i	−0.192578	−	1.33941i	−0.825152	−	0.564910i	$-0.808911\pi$
$449$	−4.08066	−	28.3816i	−0.192578	−	1.33941i	0.632574	−	0.774500i	$-0.281998\pi$
$450$	0.841254	−	0.540641i	0.0396571	−	0.0254861i
$451$	−1.44755	+	1.67057i	−0.0681626	+	0.0786639i
$452$	7.35247	−	16.0997i	0.345831	−	0.757264i
$453$	2.74293	+	1.76277i	0.128874	+	0.0828223i
$454$	2.16736	−	0.636395i	0.101719	−	0.0298675i
$455$	−7.03101	−	8.11422i	−0.329619	−	0.380400i
$456$	−3.60473	−	1.05844i	−0.168807	−	0.0495662i
$457$	−11.6194	−	25.4429i	−0.543531	−	1.19017i	−0.959738	−	0.280897i	$-0.909368\pi$
$457$	−11.6194	−	25.4429i	−0.543531	−	1.19017i	0.416207	−	0.909270i	$-0.363359\pi$
$458$	−0.558427	+	3.88394i	−0.0260936	+	0.181485i
$459$	1.91777			0.0895137
$460$	2.33881	−	4.18688i	0.109048	−	0.195214i
$461$	−3.31577			−0.154431			−0.0772154	−	0.997014i	$-0.524603\pi$
$461$	−3.31577			−0.154431			−0.0772154	+	0.997014i	$0.524603\pi$
$462$	2.06995	−	14.3968i	0.0963030	−	0.669802i
$463$	−4.83260	−	10.5819i	−0.224590	−	0.491783i	0.763472	−	0.645841i	$-0.223493\pi$
$463$	−4.83260	−	10.5819i	−0.224590	−	0.491783i	−0.988062	+	0.154058i	$0.950766\pi$
$464$	7.45937	+	2.19027i	0.346293	+	0.101681i
$465$	2.72236	+	3.14177i	0.126246	+	0.145696i
$466$	11.8538	−	3.48060i	0.549118	−	0.161236i
$467$	−6.23324	−	4.00586i	−0.288440	−	0.185369i	0.388417	−	0.921484i	$-0.373022\pi$
$467$	−6.23324	−	4.00586i	−0.288440	−	0.185369i	−0.676857	+	0.736115i	$0.736658\pi$
$468$	1.37002	−	2.99992i	0.0633290	−	0.138671i
$469$	31.6305	−	36.5035i	1.46056	−	1.68558i
$470$	−7.40897	+	4.76145i	−0.341750	+	0.219629i
$471$	1.67345	+	11.6391i	0.0771086	+	0.536302i
$472$	0.232198	+	1.61497i	0.0106878	+	0.0743352i
$473$	−10.7503	+	6.90880i	−0.494299	+	0.317667i
$474$	−8.69429	+	10.0337i	−0.399342	+	0.460865i
$475$	−1.56068	+	3.41741i	−0.0716088	+	0.156801i
$476$	5.25228	+	3.37544i	0.240738	+	0.154713i
$477$	3.46277	−	1.01676i	0.158550	−	0.0465544i
$478$	−7.27248	−	8.39289i	−0.332635	−	0.383882i
$479$	34.3147	+	10.0757i	1.56788	+	0.460371i	0.946383	−	0.323046i	$-0.104707\pi$
$479$	34.3147	+	10.0757i	1.56788	+	0.460371i	0.621497	+	0.783417i	$0.286525\pi$
$480$	0.415415	+	0.909632i	0.0189610	+	0.0415188i
$481$	4.47913	−	31.1531i	0.204231	−	1.42046i
$482$	−29.5722			−1.34698
$483$	−13.7747	+	7.35030i	−0.626770	+	0.334450i
$484$	8.96046			0.407294
$485$	0.744681	−	5.17937i	0.0338142	−	0.235183i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	−28.5660	−	8.38774i	−1.29445	−	0.380085i	−0.439242	−	0.898369i	$-0.644753\pi$
$487$	−28.5660	−	8.38774i	−1.29445	−	0.380085i	−0.855209	+	0.518284i	$0.826571\pi$
$488$	4.91751	+	5.67511i	0.222605	+	0.256900i
$489$	−20.2205	+	5.93729i	−0.914404	+	0.268493i
$490$	−3.02738	−	1.94558i	−0.136763	−	0.0878922i
$491$	2.01475	−	4.41169i	0.0909245	−	0.199097i	−0.858706	−	0.512468i	$-0.828731\pi$
$491$	2.01475	−	4.41169i	0.0909245	−	0.199097i	0.949631	+	0.313371i	$0.101458\pi$
$492$	−0.324003	+	0.373920i	−0.0146072	+	0.0168576i
$493$	12.5425	−	8.06056i	0.564884	−	0.363029i
$494$	1.76329	+	12.2640i	0.0793343	+	0.551782i
$495$	−0.635822	−	4.42224i	−0.0285781	−	0.198765i
$496$	−3.49722	+	2.24753i	−0.157030	+	0.100917i
$497$	12.4998	−	14.4256i	0.560693	−	0.647075i
$498$	3.53547	−	7.74161i	0.158428	−	0.346910i
$499$	9.24112	+	5.93891i	0.413689	+	0.265862i	0.730888	−	0.682497i	$-0.239106\pi$
$499$	9.24112	+	5.93891i	0.413689	+	0.265862i	−0.317199	+	0.948359i	$0.602742\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	−9.01994	−	10.4096i	−0.402981	−	0.465065i
$502$	−23.9659	−	7.03703i	−1.06965	−	0.314078i
$503$	8.49158	+	18.5940i	0.378621	+	0.829064i	0.998998	+	0.0447605i	$0.0142525\pi$
$503$	8.49158	+	18.5940i	0.378621	+	0.829064i	−0.620377	+	0.784304i	$0.713020\pi$
$504$	0.463314	−	3.22242i	0.0206376	−	0.143538i
$505$	10.7958			0.480405
$506$	−12.6746	−	17.2755i	−0.563456	−	0.767991i
$507$	2.12355			0.0943104
$508$	−0.847354	+	5.89348i	−0.0375953	+	0.261481i
$509$	3.22049	+	7.05189i	0.142746	+	0.312570i	0.967479	−	0.252953i	$-0.0814018\pi$
$509$	3.22049	+	7.05189i	0.142746	+	0.312570i	−0.824733	+	0.565523i	$0.808675\pi$
$510$	1.84008	+	0.540297i	0.0814803	+	0.0239248i
$511$	−7.50760	−	8.66423i	−0.332116	−	0.383283i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	3.16052	+	2.03114i	0.139540	+	0.0896770i
$514$	−6.88824	+	15.0831i	−0.303827	+	0.665289i
$515$	4.84261	−	5.58867i	0.213391	−	0.246266i
$516$	−2.40622	+	1.54638i	−0.105928	+	0.0680757i
$517$	5.59972	+	38.9469i	0.246275	+	1.71288i
$518$	−4.42156	−	30.7526i	−0.194272	−	1.35119i
$519$	−2.87762	+	1.84933i	−0.126314	+	0.0811768i
$520$	2.15970	−	2.49242i	0.0947089	−	0.109300i
$521$	6.05666	−	13.2622i	0.265347	−	0.581029i	−0.729319	−	0.684174i	$-0.760163\pi$
$521$	6.05666	−	13.2622i	0.265347	−	0.581029i	0.994666	+	0.103144i	$0.0328903\pi$
$522$	−6.54014	−	4.20310i	−0.286254	−	0.183965i
$523$	−31.8515	+	9.35246i	−1.39277	+	0.408954i	−0.890195	−	0.455579i	$-0.849432\pi$
$523$	−31.8515	+	9.35246i	−1.39277	+	0.408954i	−0.502575	+	0.864533i	$0.667614\pi$
$524$	−8.62264	−	9.95106i	−0.376682	−	0.434714i
$525$	−3.12368	−	0.917196i	−0.136329	−	0.0400297i
$526$	−8.54666	−	18.7146i	−0.372652	−	0.815994i
$527$	−1.13460	+	7.89131i	−0.0494239	+	0.343751i
$528$	4.46771			0.194432
$529$	−6.90353	+	21.9395i	−0.300153	+	0.953891i
$530$	3.60896			0.156763
$531$	0.232198	−	1.61497i	0.0100765	−	0.0700839i
$532$	5.08087	+	11.1256i	0.220284	+	0.482354i
$533$	1.56562	+	0.459707i	0.0678144	+	0.0199121i
$534$	−7.15702	−	8.25964i	−0.309715	−	0.357430i
$535$	6.84374	−	2.00950i	0.295881	−	0.0868785i
$536$	12.4813	+	8.02123i	0.539109	+	0.346464i
$537$	−7.72149	+	16.9077i	−0.333207	+	0.729621i
$538$	−16.8996	+	19.5031i	−0.728592	+	0.840840i
$539$	−13.5254	+	8.69228i	−0.582582	+	0.374403i
$540$	−0.142315	−	0.989821i	−0.00612426	−	0.0425951i
$541$	−4.49001	−	31.2287i	−0.193041	−	1.34263i	−0.823902	−	0.566732i	$-0.808208\pi$
$541$	−4.49001	−	31.2287i	−0.193041	−	1.34263i	0.630862	−	0.775895i	$-0.282702\pi$
$542$	−12.0957	+	7.77341i	−0.519553	+	0.333896i
$543$	10.9304	−	12.6144i	0.469070	−	0.541335i
$544$	−0.796669	+	1.74446i	−0.0341569	+	0.0747932i
$545$	5.69870	+	3.66233i	0.244106	+	0.156877i
$546$	−10.3017	+	3.02486i	−0.440874	+	0.129452i
$547$	−24.3963	−	28.1549i	−1.04311	−	1.20382i	−0.978573	−	0.205900i	$-0.933988\pi$
$547$	−24.3963	−	28.1549i	−1.04311	−	1.20382i	−0.0645388	−	0.997915i	$-0.520558\pi$
$548$	14.3455	+	4.21221i	0.612808	+	0.179937i
$549$	−3.11945	−	6.83065i	−0.133135	−	0.291525i
$550$	0.635822	−	4.42224i	0.0271115	−	0.188565i
$551$	29.2073			1.24427
$552$	−2.83694	−	3.86675i	−0.120748	−	0.164580i
$553$	43.2225			1.83801
$554$	−0.573468	+	3.98856i	−0.0243643	+	0.169458i
$555$	−3.96445	−	8.68093i	−0.168281	−	0.368485i
$556$	11.8017	+	3.46529i	0.500503	+	0.146961i
$557$	8.37966	+	9.67064i	0.355058	+	0.409758i	0.904978	−	0.425459i	$-0.139887\pi$
$557$	8.37966	+	9.67064i	0.355058	+	0.409758i	−0.549920	+	0.835217i	$0.685342\pi$
$558$	3.98877	−	1.17121i	0.168858	−	0.0495812i
$559$	7.93558	+	5.09989i	0.335639	+	0.215702i
$560$	1.35241	−	2.96136i	0.0571496	−	0.125140i
$561$	5.61087	−	6.47528i	0.236891	−	0.273387i
$562$	−7.96260	+	5.11725i	−0.335882	+	0.215858i
$563$	3.55111	+	24.6985i	0.149661	+	1.04092i	0.916774	+	0.399405i	$0.130783\pi$
$563$	3.55111	+	24.6985i	0.149661	+	1.04092i	−0.767113	+	0.641512i	$0.778308\pi$
$564$	1.25337	+	8.71741i	0.0527766	+	0.367069i
$565$	−14.8894	+	9.56885i	−0.626403	+	0.402564i
$566$	10.0968	−	11.6523i	0.424401	−	0.489784i
$567$	−1.35241	+	2.96136i	−0.0567958	+	0.124365i
$568$	4.93238	+	3.16985i	0.206958	+	0.133004i
$569$	35.9547	−	10.5572i	1.50730	−	0.442583i	0.579283	−	0.815126i	$-0.303333\pi$
$569$	35.9547	−	10.5572i	1.50730	−	0.442583i	0.928015	+	0.372544i	$0.121514\pi$
$570$	2.46025	+	2.83928i	0.103049	+	0.118925i
$571$	−40.0445	−	11.7581i	−1.67581	−	0.492062i	−0.700639	−	0.713516i	$-0.747101\pi$
$571$	−40.0445	−	11.7581i	−1.67581	−	0.492062i	−0.975171	+	0.221454i	$0.928920\pi$
$572$	−6.12084	−	13.4028i	−0.255925	−	0.560398i
$573$	1.92008	−	13.3544i	0.0802124	−	0.557889i
$574$	1.61074			0.0672310
$575$	−4.23113	+	2.25777i	−0.176450	+	0.0941555i
$576$	1.00000			0.0416667
$577$	1.23040	−	8.55765i	0.0512224	−	0.356260i	−0.948050	−	0.318121i	$-0.896948\pi$
$577$	1.23040	−	8.55765i	0.0512224	−	0.356260i	0.999272	−	0.0381385i	$-0.0121428\pi$
$578$	−5.53423	−	12.1183i	−0.230194	−	0.504054i
$579$	−10.1207	−	2.97171i	−0.420603	−	0.123500i
$580$	−5.09107	−	5.87541i	−0.211395	−	0.243963i
$581$	−26.5847	+	7.80599i	−1.10292	+	0.323847i
$582$	−4.40197	−	2.82897i	−0.182468	−	0.117265i
$583$	6.69807	−	14.6667i	0.277406	−	0.607434i
$584$	2.30609	−	2.66137i	0.0954265	−	0.110128i
$585$	−2.77441	+	1.78300i	−0.114708	+	0.0737181i
$586$	−3.59725	−	25.0194i	−0.148601	−	1.03354i
$587$	−1.29880	−	9.03337i	−0.0536073	−	0.372847i	−0.998911	−	0.0466555i	$-0.985144\pi$
$587$	−1.29880	−	9.03337i	−0.0536073	−	0.372847i	0.945304	−	0.326191i	$-0.105765\pi$
$588$	−3.02738	+	1.94558i	−0.124847	+	0.0802342i
$589$	−10.2277	+	11.8034i	−0.421424	+	0.486349i
$590$	0.677783	−	1.48414i	0.0279039	−	0.0611010i
$591$	0.941353	+	0.604971i	0.0387221	+	0.0248852i
$592$	9.15677	−	2.68867i	0.376341	−	0.110504i
$593$	−19.9815	−	23.0599i	−0.820541	−	0.946955i	0.178777	−	0.983890i	$-0.442786\pi$
$593$	−19.9815	−	23.0599i	−0.820541	−	0.946955i	−0.999318	+	0.0369347i	$0.988241\pi$
$594$	−4.28674	−	1.25870i	−0.175887	−	0.0516451i
$595$	−2.59360	−	5.67919i	−0.106327	−	0.232824i
$596$	−1.11990	+	7.78907i	−0.0458728	+	0.319053i
$597$	−27.5254			−1.12654
$598$	−7.71328	+	13.8081i	−0.315419	+	0.564655i
$599$	13.1299			0.536474			0.268237	−	0.963353i	$-0.413559\pi$
$599$	13.1299			0.536474			0.268237	+	0.963353i	$0.413559\pi$
$600$	0.142315	−	0.989821i	0.00580998	−	0.0404093i
$601$	7.82893	+	17.1430i	0.319349	+	0.699276i	0.999426	−	0.0338641i	$-0.0107813\pi$
$601$	7.82893	+	17.1430i	0.319349	+	0.699276i	−0.680078	+	0.733140i	$0.738054\pi$
$602$	8.93461	+	2.62344i	0.364147	+	0.106923i
$603$	−9.71585	−	11.2127i	−0.395660	−	0.456616i
$604$	3.12845	−	0.918596i	0.127295	−	0.0373772i
$605$	−7.53802	−	4.84439i	−0.306464	−	0.196952i
$606$	4.48472	−	9.82018i	0.182179	−	0.398917i
$607$	11.9399	−	13.7794i	0.484627	−	0.559290i	−0.459795	−	0.888025i	$-0.652077\pi$
$607$	11.9399	−	13.7794i	0.484627	−	0.559290i	0.944422	+	0.328735i	$0.106622\pi$
$608$	−3.16052	+	2.03114i	−0.128176	+	0.0823736i
$609$	3.60194	+	25.0520i	0.145958	+	1.01516i
$610$	−1.06868	−	7.43281i	−0.0432694	−	0.300946i
$611$	24.4344	−	15.7030i	0.988509	−	0.635276i
$612$	1.25587	−	1.44935i	0.0507655	−	0.0585865i
$613$	−1.20758	+	2.64422i	−0.0487735	+	0.106799i	−0.932450	−	0.361299i	$-0.882333\pi$
$613$	−1.20758	+	2.64422i	−0.0487735	+	0.106799i	0.883676	+	0.468098i	$0.155061\pi$
$614$	12.7101	+	8.16830i	0.512939	+	0.329646i
$615$	0.474725	−	0.139392i	0.0191428	−	0.00562082i
$616$	−9.52488	−	10.9923i	−0.383768	−	0.442892i
$617$	0.274975	+	0.0807399i	0.0110701	+	0.00325047i	0.287263	−	0.957852i	$-0.407255\pi$
$617$	0.274975	+	0.0807399i	0.0110701	+	0.00325047i	−0.276193	+	0.961102i	$0.589073\pi$
$618$	−3.07194	−	6.72661i	−0.123572	−	0.270584i
$619$	1.78422	−	12.4095i	0.0717138	−	0.498780i	−0.922032	−	0.387114i	$-0.873472\pi$
$619$	1.78422	−	12.4095i	0.0717138	−	0.498780i	0.993746	−	0.111667i	$-0.0356189\pi$
$620$	4.15716			0.166956
$621$	1.63264	+	4.50938i	0.0655154	+	0.180955i
$622$	18.5852			0.745198
$623$	−5.06359	+	35.2181i	−0.202869	+	1.41098i
$624$	−1.37002	−	2.99992i	−0.0548445	−	0.120093i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	8.42064	+	9.71794i	0.336556	+	0.388407i
$627$	16.1049	−	4.72883i	0.643168	−	0.188851i
$628$	9.89213	+	6.35729i	0.394739	+	0.253683i
$629$	7.60288	−	16.6480i	0.303147	−	0.663799i
$630$	−2.13194	+	2.46039i	−0.0849384	+	0.0980241i
$631$	31.0104	−	19.9292i	1.23450	−	0.793368i	0.249918	−	0.968267i	$-0.419596\pi$
$631$	31.0104	−	19.9292i	1.23450	−	0.793368i	0.984586	+	0.174899i	$0.0559598\pi$
$632$	1.88945	+	13.1414i	0.0751583	+	0.522737i
$633$	0.517035	+	3.59606i	0.0205503	+	0.142931i
$634$	−22.3632	+	14.3719i	−0.888155	+	0.570782i
$635$	3.89910	−	4.49980i	0.154731	−	0.178569i
$636$	1.49922	−	3.28283i	0.0594478	−	0.130173i
$637$	9.98412	+	6.41640i	0.395585	+	0.254227i
$638$	−33.3263	+	9.78549i	−1.31940	+	0.387411i
$639$	−3.83953	−	4.43106i	−0.151890	−	0.175290i
$640$	0.959493	+	0.281733i	0.0379273	+	0.0111365i
$641$	−2.43352	−	5.32867i	−0.0961183	−	0.210470i	0.855465	−	0.517861i	$-0.173271\pi$
$641$	−2.43352	−	5.32867i	−0.0961183	−	0.210470i	−0.951583	+	0.307391i	$0.900544\pi$
$642$	1.01508	−	7.06007i	0.0400622	−	0.278639i
$643$	−19.4532			−0.767159			−0.383580	−	0.923508i	$-0.625309\pi$
$643$	−19.4532			−0.767159			−0.383580	+	0.923508i	$0.625309\pi$
$644$	−3.46552	+	15.2236i	−0.136561	+	0.599895i
$645$	2.86028			0.112623
$646$	−1.02536	+	7.13154i	−0.0403423	+	0.280587i
$647$	7.96056	+	17.4312i	0.312962	+	0.685291i	0.999110	−	0.0421704i	$-0.0134272\pi$
$647$	7.96056	+	17.4312i	0.312962	+	0.685291i	−0.686148	+	0.727462i	$0.740700\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−4.77357	−	5.50899i	−0.187379	−	0.216247i
$650$	−3.16436	+	0.929139i	−0.124116	+	0.0364438i
$651$	−11.3854	−	7.31696i	−0.446230	−	0.286774i
$652$	−8.75454	+	19.1698i	−0.342854	+	0.750746i
$653$	11.4435	−	13.2065i	0.447820	−	0.516812i	−0.486290	−	0.873798i	$-0.661650\pi$
$653$	11.4435	−	13.2065i	0.447820	−	0.516812i	0.934110	+	0.356986i	$0.116196\pi$
$654$	5.69870	−	3.66233i	0.222837	−	0.143209i
$655$	1.87388	+	13.0331i	0.0732185	+	0.509246i
$656$	0.0704126	+	0.489731i	0.00274915	+	0.0191208i
$657$	−2.96247	+	1.90386i	−0.115577	+	0.0742767i
$658$	18.7761	−	21.6688i	0.731968	−	0.844736i
$659$	2.76160	−	6.04706i	0.107577	−	0.235560i	−0.848186	−	0.529698i	$-0.822305\pi$
$659$	2.76160	−	6.04706i	0.107577	−	0.235560i	0.955763	+	0.294138i	$0.0950326\pi$
$660$	−3.75848	−	2.41543i	−0.146299	−	0.0940204i
$661$	−35.3633	+	10.3836i	−1.37547	+	0.403875i	−0.884191	−	0.467126i	$-0.845289\pi$
$661$	−35.3633	+	10.3836i	−1.37547	+	0.403875i	−0.491281	+	0.871001i	$0.663471\pi$
$662$	−1.49789	−	1.72865i	−0.0582171	−	0.0671861i
$663$	−6.06849	−	1.78187i	−0.235681	−	0.0692021i
$664$	−3.53547	−	7.74161i	−0.137203	−	0.300433i
$665$	1.74063	−	12.1063i	0.0674987	−	0.469464i
$666$	−9.54334			−0.369797
$667$	29.6310	+	22.6299i	1.14732	+	0.876232i
$668$	−13.7738			−0.532926
$669$	−3.15606	+	21.9509i	−0.122020	+	0.848670i
$670$	−6.16331	−	13.4958i	−0.238109	−	0.521387i
$671$	−32.1902	−	9.45188i	−1.24269	−	0.364886i
$672$	−2.13194	−	2.46039i	−0.0822412	−	0.0949114i
$673$	32.5511	−	9.55786i	1.25475	−	0.368429i	0.414213	−	0.910180i	$-0.364057\pi$
$673$	32.5511	−	9.55786i	1.25475	−	0.368429i	0.840539	+	0.541751i	$0.182239\pi$
$674$	13.3449	+	8.57622i	0.514025	+	0.330344i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	1.39063	−	1.60488i	0.0534859	−	0.0617260i
$677$	−10.7369	+	6.90022i	−0.412654	+	0.265197i	−0.730455	−	0.682961i	$-0.760692\pi$
$677$	−10.7369	+	6.90022i	−0.412654	+	0.265197i	0.317801	+	0.948157i	$0.397056\pi$
$678$	2.51884	+	17.5189i	0.0967356	+	0.672811i
$679$	2.42435	+	16.8617i	0.0930381	+	0.647094i
$680$	1.61333	−	1.03682i	0.0618683	−	0.0397603i
$681$	−1.47924	+	1.70713i	−0.0566846	+	0.0654175i
$682$	7.71550	−	16.8946i	0.295442	−	0.646927i
$683$	−23.6167	−	15.1775i	−0.903666	−	0.580751i	0.00420904	−	0.999991i	$-0.498660\pi$
$683$	−23.6167	−	15.1775i	−0.903666	−	0.580751i	−0.907875	+	0.419240i	$0.862297\pi$
$684$	3.60473	−	1.05844i	0.137830	−	0.0404706i
$685$	−9.79088	−	11.2993i	−0.374090	−	0.431723i
$686$	−10.6247	−	3.11971i	−0.405655	−	0.119111i
$687$	−1.63004	−	3.56929i	−0.0621899	−	0.136177i
$688$	−0.407060	+	2.83117i	−0.0155190	+	0.107937i
$689$	−11.9022			−0.453436
$690$	0.296064	+	4.78668i	0.0112709	+	0.182226i
$691$	4.45155			0.169345			0.0846725	−	0.996409i	$-0.473016\pi$
$691$	4.45155			0.169345			0.0846725	+	0.996409i	$0.473016\pi$
$692$	−0.486807	+	3.38582i	−0.0185056	+	0.128709i
$693$	6.04217	+	13.2305i	0.229523	+	0.502585i
$694$	−21.2553	−	6.24112i	−0.806841	−	0.236910i
$695$	−8.05474	−	9.29567i	−0.305534	−	0.352605i
$696$	−7.45937	+	2.19027i	−0.282747	+	0.0830219i
$697$	0.798221	+	0.512985i	0.0302348	+	0.0194307i
$698$	−1.79162	+	3.92310i	−0.0678138	+	0.148491i
$699$	−8.09032	+	9.33673i	−0.306004	+	0.353148i
$700$	−2.73875	+	1.76009i	−0.103515	+	0.0665250i
$701$	−2.60094	−	18.0899i	−0.0982361	−	0.683247i	−0.978117	−	0.208054i	$-0.933287\pi$
$701$	−2.60094	−	18.0899i	−0.0982361	−	0.683247i	0.879881	−	0.475194i	$-0.157622\pi$
$702$	0.469347	+	3.26438i	0.0177143	+	0.123206i
$703$	30.1619	−	19.3839i	1.13758	−	0.731076i
$704$	2.92573	−	3.37647i	0.110268	−	0.127256i
$705$	3.65858	−	8.01118i	0.137790	−	0.301718i
$706$	−10.3201	−	6.63231i	−0.388401	−	0.249610i
$707$	−33.7226	+	9.90184i	−1.26827	+	0.372397i
$708$	−1.06846	−	1.23307i	−0.0401551	−	0.0463415i
$709$	−20.1722	−	5.92309i	−0.757583	−	0.222446i	−0.119943	−	0.992781i	$-0.538271\pi$
$709$	−20.1722	−	5.92309i	−0.757583	−	0.222446i	−0.637640	+	0.770334i	$0.720089\pi$
$710$	−2.43563	−	5.33329i	−0.0914076	−	0.200155i
$711$	1.88945	−	13.1414i	0.0708599	−	0.492841i
$712$	−10.9291			−0.409584
$713$	−19.5213	+	4.05018i	−0.731079	+	0.151680i
$714$	−6.24340			−0.233653
$715$	−2.09691	+	14.5843i	−0.0784198	+	0.545422i
$716$	7.72149	+	16.9077i	0.288565	+	0.631870i
$717$	10.6555	+	3.12875i	0.397938	+	0.116845i
$718$	−12.5346	−	14.4657i	−0.467786	−	0.539853i
$719$	41.7536	−	12.2600i	1.55715	−	0.457219i	0.613920	−	0.789369i	$-0.289592\pi$
$719$	41.7536	−	12.2600i	1.55715	−	0.457219i	0.943227	+	0.332149i	$0.107774\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	−10.0009	+	21.8989i	−0.372452	+	0.815556i
$722$	3.19940	−	3.69230i	0.119069	−	0.137413i
$723$	24.8777	−	15.9880i	0.925213	−	0.594598i
$724$	−2.37541	−	16.5213i	−0.0882814	−	0.614011i
$725$	1.10640	+	7.69515i	0.0410905	+	0.285791i
$726$	−7.53802	+	4.84439i	−0.279762	+	0.179792i
$727$	−8.27371	+	9.54837i	−0.306855	+	0.354129i	−0.888142	−	0.459569i	$-0.848004\pi$
$727$	−8.27371	+	9.54837i	−0.306855	+	0.354129i	0.581287	+	0.813698i	$0.302549\pi$
$728$	−4.46016	+	9.76640i	−0.165305	+	0.361967i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−3.37885	+	0.992119i	−0.125057	+	0.0367200i
$731$	3.59214	+	4.14555i	0.132860	+	0.153329i
$732$	−7.20506	−	2.11560i	−0.266307	−	0.0781947i
$733$	10.1354	+	22.1934i	0.374360	+	0.819733i	0.999239	+	0.0390117i	$0.0124210\pi$
$733$	10.1354	+	22.1934i	0.374360	+	0.819733i	−0.624879	+	0.780721i	$0.714852\pi$
$734$	−1.95327	+	13.5853i	−0.0720964	+	0.501441i
$735$	3.59865			0.132738
$736$	−4.78010	−	0.388166i	−0.176197	−	0.0143080i
$737$	−66.2853			−2.44165
$738$	0.0704126	−	0.489731i	0.00259192	−	0.0180272i
$739$	−12.5247	−	27.4254i	−0.460730	−	1.00886i	−0.987321	−	0.158739i	$-0.949257\pi$
$739$	−12.5247	−	27.4254i	−0.460730	−	1.00886i	0.526591	−	0.850119i	$-0.323470\pi$
$740$	−9.15677	−	2.68867i	−0.336609	−	0.0988374i
$741$	−8.11378	−	9.36381i	−0.298067	−	0.343988i
$742$	−11.2733	+	3.31013i	−0.413854	+	0.121519i
$743$	−33.5329	−	21.5503i	−1.23020	−	0.790604i	−0.246281	−	0.969198i	$-0.579209\pi$
$743$	−33.5329	−	21.5503i	−1.23020	−	0.790604i	−0.983923	+	0.178594i	$0.942845\pi$
$744$	1.72695	−	3.78149i	0.0633129	−	0.138636i
$745$	5.15321	−	5.94712i	0.188799	−	0.217885i
$746$	−25.2344	+	16.2171i	−0.923896	+	0.593752i
$747$	1.21120	+	8.42408i	0.0443155	+	0.308221i
$748$	−1.21936	−	8.48082i	−0.0445841	−	0.310089i
$749$	−19.5346	+	12.5541i	−0.713778	+	0.458717i
$750$	−0.654861	+	0.755750i	−0.0239121	+	0.0275961i
$751$	−0.145843	+	0.319352i	−0.00532189	+	0.0116533i	−0.912274	−	0.409580i	$-0.865675\pi$
$751$	−0.145843	+	0.319352i	−0.00532189	+	0.0116533i	0.906952	+	0.421233i	$0.138403\pi$
$752$	7.40897	+	4.76145i	0.270177	+	0.173632i
$753$	23.9659	−	7.03703i	0.873367	−	0.256444i
$754$	16.7901	+	19.3768i	0.611459	+	0.705661i
$755$	−3.12845	−	0.918596i	−0.113856	−	0.0334311i
$756$	1.35241	+	2.96136i	0.0491866	+	0.107704i
$757$	−1.71659	+	11.9391i	−0.0623905	+	0.433936i	0.934554	+	0.355822i	$0.115799\pi$
$757$	−1.71659	+	11.9391i	−0.0623905	+	0.433936i	−0.996944	+	0.0781140i	$0.975110\pi$
$758$	21.1011			0.766425
$759$	20.0024	+	7.68068i	0.726043	+	0.278791i
$760$	3.75691			0.136278
$761$	4.09398	−	28.4743i	0.148407	−	1.03219i	−0.770422	−	0.637535i	$-0.779954\pi$
$761$	4.09398	−	28.4743i	0.148407	−	1.03219i	0.918828	−	0.394657i	$-0.129137\pi$
$762$	−2.47342	−	5.41603i	−0.0896024	−	0.196202i
$763$	−21.1600	−	6.21314i	−0.766044	−	0.224931i
$764$	−8.83522	−	10.1964i	−0.319647	−	0.368892i
$765$	−1.84008	+	0.540297i	−0.0665284	+	0.0195345i
$766$	17.6579	+	11.3480i	0.638005	+	0.410021i
$767$	−2.23529	+	4.89461i	−0.0807118	+	0.176734i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	−27.4759	+	17.6577i	−0.990805	+	0.636752i	−0.932357	−	0.361539i	$-0.882252\pi$
$769$	−27.4759	+	17.6577i	−0.990805	+	0.636752i	−0.0584481	+	0.998290i	$0.518615\pi$
$770$	2.06995	+	14.3968i	0.0745960	+	0.518826i
$771$	−2.35981	−	16.4128i	−0.0849864	−	0.591093i
$772$	−8.87354	+	5.70268i	−0.319366	+	0.205244i
$773$	18.1377	−	20.9321i	0.652369	−	0.752874i	−0.329142	−	0.944280i	$-0.606760\pi$
$773$	18.1377	−	20.9321i	0.652369	−	0.752874i	0.981511	+	0.191407i	$0.0613050\pi$
$774$	1.18820	−	2.60180i	0.0427091	−	0.0935198i
$775$	−3.49722	−	2.24753i	−0.125624	−	0.0807337i
$776$	−5.02067	+	1.47420i	−0.180232	+	0.0529208i
$777$	20.3458	+	23.4803i	0.729901	+	0.842351i
$778$	−23.9110	−	7.02089i	−0.857249	−	0.251711i
$779$	0.772171	+	1.69082i	0.0276659	+	0.0605799i
$780$	−0.469347	+	3.26438i	−0.0168053	+	0.116883i
$781$	−26.1948			−0.937323
$782$	−6.56577	+	6.44055i	−0.234791	+	0.230314i
$783$	7.77428			0.277830
$784$	−0.512141	+	3.56202i	−0.0182908	+	0.127215i
$785$	−4.88478	−	10.6962i	−0.174345	−	0.381763i
$786$	12.6338	+	3.70961i	0.450632	+	0.132317i
$787$	13.9619	+	16.1129i	0.497689	+	0.574363i	0.947904	−	0.318557i	$-0.103198\pi$
$787$	13.9619	+	16.1129i	0.497689	+	0.574363i	−0.450215	+	0.892920i	$0.648653\pi$
$788$	1.07366	−	0.315255i	0.0382476	−	0.0112305i
$789$	17.3078	+	11.1230i	0.616173	+	0.395990i
$790$	5.51528	−	12.0768i	0.196225	−	0.429672i
$791$	37.7333	−	43.5466i	1.34164	−	1.54834i
$792$	−3.75848	+	2.41543i	−0.133552	+	0.0858285i
$793$	3.52444	+	24.5130i	0.125156	+	0.870482i
$794$	−5.42815	−	37.7536i	−0.192638	−	1.33982i
$795$	−3.03605	+	1.95115i	−0.107678	+	0.0692003i
$796$	−18.0253	+	20.8023i	−0.638891	+	0.737319i
$797$	−12.4542	+	27.2709i	−0.441150	+	0.965983i	0.550236	+	0.835009i	$0.314538\pi$
$797$	−12.4542	+	27.2709i	−0.441150	+	0.965983i	−0.991386	+	0.130974i	$0.958190\pi$
$798$	−10.2892	−	6.61249i	−0.364235	−	0.234080i
$799$	16.2057	−	4.75843i	0.573317	−	0.168341i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	10.4864	+	3.07908i	0.370518	+	0.108794i
$802$	12.4669	+	27.2988i	0.440223	+	0.963954i
$803$	−2.23904	+	15.5729i	−0.0790141	+	0.549555i
$804$	−14.8365			−0.523244
$805$	11.1459	−	10.9333i	0.392841	−	0.385349i
$806$	−13.7101			−0.482917
$807$	3.67263	−	25.5437i	0.129283	−	0.899181i
$808$	−4.48472	−	9.82018i	−0.157772	−	0.345473i
$809$	10.6568	+	3.12911i	0.374672	+	0.110014i	0.463647	−	0.886020i	$-0.346541\pi$
$809$	10.6568	+	3.12911i	0.374672	+	0.110014i	−0.0889742	+	0.996034i	$0.528359\pi$
$810$	0.654861	+	0.755750i	0.0230095	+	0.0265543i
$811$	−9.20539	+	2.70295i	−0.323245	+	0.0949133i	−0.439329	−	0.898326i	$-0.644784\pi$
$811$	−9.20539	+	2.70295i	−0.323245	+	0.0949133i	0.116084	+	0.993239i	$0.462966\pi$
$812$	21.2918	+	13.6834i	0.747196	+	0.480194i
$813$	5.97289	−	13.0788i	0.209479	−	0.458694i
$814$	−27.9212	+	32.2228i	−0.978639	+	1.12941i
$815$	17.7287	−	11.3936i	0.621011	−	0.399099i
$816$	−0.272927	−	1.89825i	−0.00955434	−	0.0664519i
$817$	1.52929	+	10.6364i	0.0535031	+	0.372122i
$818$	16.2991	−	10.4748i	0.569884	−	0.366242i
$819$	7.03101	−	8.11422i	0.245683	−	0.283534i
$820$	0.205533	−	0.450055i	0.00717754	−	0.0157166i
$821$	−10.1775	−	6.54067i	−0.355197	−	0.228271i	0.350858	−	0.936429i	$-0.385890\pi$
$821$	−10.1775	−	6.54067i	−0.355197	−	0.228271i	−0.706054	+	0.708158i	$0.749526\pi$
$822$	−14.3455	+	4.21221i	−0.500355	+	0.146918i
$823$	−28.4659	−	32.8514i	−0.992260	−	1.14513i	−0.989412	−	0.145133i	$-0.953639\pi$
$823$	−28.4659	−	32.8514i	−0.992260	−	1.14513i	−0.00284735	−	0.999996i	$-0.500906\pi$
$824$	−7.09533	−	2.08338i	−0.247177	−	0.0725779i
$825$	1.85596	+	4.06397i	0.0646161	+	0.141489i
$826$	−0.755935	+	5.25764i	−0.0263023	+	0.182937i
$827$	−12.9536			−0.450440			−0.225220	−	0.974308i	$-0.572310\pi$
$827$	−12.9536			−0.450440			−0.225220	+	0.974308i	$0.572310\pi$
$828$	4.47711	+	1.71915i	0.155590	+	0.0597446i
$829$	24.6815			0.857225			0.428612	−	0.903488i	$-0.359003\pi$
$829$	24.6815			0.857225			0.428612	+	0.903488i	$0.359003\pi$
$830$	−1.21120	+	8.42408i	−0.0420414	+	0.292404i
$831$	−1.67395	−	3.66543i	−0.0580685	−	0.127152i
$832$	−3.16436	−	0.929139i	−0.109704	−	0.0322121i
$833$	4.51943	+	5.21570i	0.156589	+	0.180713i
$834$	−11.8017	+	3.46529i	−0.408659	+	0.119993i
$835$	11.5873	+	7.44670i	0.400995	+	0.257704i
$836$	6.97266	−	15.2680i	0.241154	−	0.528055i
$837$	−2.72236	+	3.14177i	−0.0940985	+	0.108596i
$838$	28.8286	−	18.5270i	0.995868	−	0.640006i
$839$	2.95143	+	20.5276i	0.101895	+	0.708692i	0.975169	+	0.221463i	$0.0710832\pi$
$839$	2.95143	+	20.5276i	0.101895	+	0.708692i	−0.873274	+	0.487229i	$0.838008\pi$
$840$	0.463314	+	3.22242i	0.0159859	+	0.111184i
$841$	26.4486	−	16.9975i	0.912021	−	0.586120i
$842$	0.0543710	−	0.0627474i	0.00187375	−	0.00216242i
$843$	3.93197	−	8.60982i	0.135424	−	0.296538i
$844$	3.05631	+	1.96417i	0.105202	+	0.0676095i
$845$	−2.03754	+	0.598274i	−0.0700934	+	0.0205813i
$846$	−5.76739	−	6.65593i	−0.198287	−	0.228836i
$847$	27.9896	+	8.21850i	0.961736	+	0.282391i
$848$	−1.49922	−	3.28283i	−0.0514833	−	0.112733i
$849$	−2.19425	+	15.2613i	−0.0753063	+	0.523767i
$850$	−1.91777			−0.0657788
$851$	45.6181	+	3.70440i	1.56377	+	0.126985i
$852$	−5.86313			−0.200868
$853$	3.30599	−	22.9937i	0.113195	−	0.787288i	−0.851582	−	0.524221i	$-0.824357\pi$
$853$	3.30599	−	22.9937i	0.113195	−	0.787288i	0.964777	−	0.263068i	$-0.0847342\pi$
$854$	10.1556	+	22.2376i	0.347516	+	0.760953i
$855$	−3.60473	−	1.05844i	−0.123279	−	0.0361980i
$856$	−4.67090	−	5.39051i	−0.159648	−	0.184244i
$857$	−42.6891	+	12.5346i	−1.45823	+	0.428175i	−0.912254	−	0.409625i	$-0.865659\pi$
$857$	−42.6891	+	12.5346i	−1.45823	+	0.428175i	−0.545977	+	0.837800i	$0.683841\pi$
$858$	12.3953	+	7.96595i	0.423167	+	0.271953i
$859$	−13.8425	+	30.3108i	−0.472300	+	1.03419i	0.512210	+	0.858861i	$0.328827\pi$
$859$	−13.8425	+	30.3108i	−0.472300	+	1.03419i	−0.984509	+	0.175332i	$0.943900\pi$
$860$	1.87308	−	2.16165i	0.0638716	−	0.0737118i
$861$	−1.35504	+	0.870832i	−0.0461797	+	0.0296779i
$862$	1.48775	+	10.3476i	0.0506731	+	0.352439i
$863$	−3.22560	−	22.4346i	−0.109801	−	0.763681i	−0.968106	−	0.250542i	$-0.919391\pi$
$863$	−3.22560	−	22.4346i	−0.109801	−	0.763681i	0.858305	−	0.513140i	$-0.171518\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	2.24004	−	2.58514i	0.0761636	−	0.0878975i
$866$	−3.36549	+	7.36940i	−0.114364	+	0.250422i
$867$	11.2073	+	7.20251i	0.380621	+	0.244610i
$868$	−12.9857	+	3.81293i	−0.440762	+	0.129419i
$869$	−38.8436	−	44.8279i	−1.31768	−	1.52068i
$870$	7.45937	+	2.19027i	0.252896	+	0.0742571i
$871$	20.3263	+	44.5083i	0.688729	+	1.50811i
$872$	0.964049	−	6.70511i	0.0326468	−	0.227064i
$873$	5.23263			0.177098
$874$	−17.6418	+	3.66023i	−0.596743	+	0.123809i
$875$	3.25556			0.110058
$876$	−0.501161	+	3.48565i	−0.0169326	+	0.117769i
$877$	−13.8147	−	30.2500i	−0.466490	−	1.02147i	−0.985960	−	0.166982i	$-0.946598\pi$
$877$	−13.8147	−	30.2500i	−0.466490	−	1.02147i	0.519470	−	0.854489i	$-0.326130\pi$
$878$	19.5856	+	5.75084i	0.660981	+	0.194081i
$879$	16.5527	+	19.1028i	0.558309	+	0.644323i
$880$	−4.28674	+	1.25870i	−0.144506	+	0.0424308i
$881$	−10.8188	−	6.95282i	−0.364495	−	0.234247i	0.345554	−	0.938399i	$-0.387691\pi$
$881$	−10.8188	−	6.95282i	−0.364495	−	0.234247i	−0.710049	+	0.704152i	$0.751327\pi$
$882$	1.49493	−	3.27345i	0.0503370	−	0.110223i
$883$	26.0623	−	30.0775i	0.877067	−	1.01219i	−0.122738	−	0.992439i	$-0.539167\pi$
$883$	26.0623	−	30.0775i	0.877067	−	1.01219i	0.999805	−	0.0197502i	$-0.00628708\pi$
$884$	−5.32067	+	3.41939i	−0.178953	+	0.115006i
$885$	0.232198	+	1.61497i	0.00780526	+	0.0542868i
$886$	−5.23293	−	36.3958i	−0.175804	−	1.22274i
$887$	49.3074	−	31.6879i	1.65558	−	1.06398i	0.731452	−	0.681893i	$-0.238843\pi$
$887$	49.3074	−	31.6879i	1.65558	−	1.06398i	0.924128	−	0.382083i	$-0.124793\pi$
$888$	−6.24956	+	7.21237i	−0.209721	+	0.242031i
$889$	−8.05234	+	17.6322i	−0.270067	+	0.591364i
$890$	9.19412	+	5.90870i	0.308188	+	0.198060i
$891$	4.28674	−	1.25870i	0.143611	−	0.0421680i
$892$	14.5226	+	16.7600i	0.486252	+	0.561165i
$893$	31.7471	+	9.32178i	1.06237	+	0.311941i
$894$	−3.26897	−	7.15804i	−0.109331	−	0.239401i
$895$	2.64526	−	18.3982i	0.0884214	−	0.614984i
$896$	−3.25556			−0.108761
$897$	−0.976402	−	15.7862i	−0.0326011	−	0.527087i
$898$	28.6734			0.956845
$899$	−4.59946	+	31.9900i	−0.153401	+	1.06693i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	−6.64079	−	1.94991i	−0.221237	−	0.0649610i
$902$	−1.44755	−	1.67057i	−0.0481983	−	0.0556237i
$903$	−8.93461	+	2.62344i	−0.297325	+	0.0873025i
$904$	14.8894	+	9.56885i	0.495215	+	0.318255i
$905$	−6.93379	+	15.1829i	−0.230487	+	0.504696i
$906$	−2.13519	+	2.46414i	−0.0709370	+	0.0818656i
$907$	−22.0816	+	14.1910i	−0.733209	+	0.471205i	−0.853209	−	0.521569i	$-0.825347\pi$
$907$	−22.0816	+	14.1910i	−0.733209	+	0.471205i	0.120000	+	0.992774i	$0.461711\pi$
$908$	0.321470	+	2.23587i	0.0106683	+	0.0742000i
$909$	1.53640	+	10.6859i	0.0509591	+	0.354428i
$910$	9.03224	−	5.80467i	0.299416	−	0.192423i
$911$	3.53130	−	4.07534i	0.116997	−	0.135022i	−0.694230	−	0.719754i	$-0.744255\pi$
$911$	3.53130	−	4.07534i	0.116997	−	0.135022i	0.811227	+	0.584732i	$0.198800\pi$
$912$	1.56068	−	3.41741i	0.0516792	−	0.113162i
$913$	31.9873	+	20.5570i	1.05863	+	0.680337i
$914$	26.8375	−	7.88020i	0.887705	−	0.260654i
$915$	4.91751	+	5.67511i	0.162568	+	0.187613i
$916$	−3.76494	−	1.10549i	−0.124397	−	0.0365263i
$917$	−17.8073	−	38.9926i	−0.588050	−	1.28765i
$918$	−0.272927	+	1.89825i	−0.00900792	+	0.0626515i
$919$	−33.7827			−1.11439			−0.557194	−	0.830383i	$-0.688122\pi$
$919$	−33.7827			−1.11439			−0.557194	+	0.830383i	$0.688122\pi$
$920$	3.81142	+	2.91086i	0.125659	+	0.0959683i
$921$	−15.1086			−0.497844
$922$	0.471883	−	3.28202i	0.0155406	−	0.108088i
$923$	8.03258	+	17.5889i	0.264396	+	0.578946i
$924$	13.9557	+	4.09777i	0.459110	+	0.134807i
$925$	6.24956	+	7.21237i	0.205484	+	0.237141i
$926$	11.1620	−	3.27744i	0.366804	−	0.107704i
$927$	6.22096	+	3.99797i	0.204323	+	0.131311i
$928$	−3.22955	+	7.07174i	−0.106015	+	0.232141i
$929$	−5.83024	+	6.72846i	−0.191284	+	0.220754i	−0.843288	−	0.537462i	$-0.819383\pi$
$929$	−5.83024	+	6.72846i	−0.191284	+	0.220754i	0.652004	+	0.758216i	$0.273929\pi$
$930$	−3.49722	+	2.24753i	−0.114679	+	0.0736994i
$931$	1.92407	+	13.3822i	0.0630588	+	0.438584i
$932$	1.75820	+	12.2285i	0.0575916	+	0.400558i
$933$	−15.6348	+	10.0479i	−0.511862	+	0.328954i
$934$	4.85217	−	5.59970i	0.158768	−	0.183228i
$935$	−3.55929	+	7.79375i	−0.116401	+	0.254883i
$936$	2.77441	+	1.78300i	0.0906844	+	0.0582793i
$937$	−24.6883	+	7.24913i	−0.806531	+	0.236819i	−0.658907	−	0.752225i	$-0.728981\pi$
$937$	−24.6883	+	7.24913i	−0.806531	+	0.236819i	−0.147624	+	0.989044i	$0.547163\pi$
$938$	31.6305	+	36.5035i	1.03277	+	1.19188i
$939$	−12.3378	−	3.62271i	−0.402629	−	0.118223i
$940$	−3.65858	−	8.01118i	−0.119330	−	0.261296i
$941$	−5.71349	+	39.7382i	−0.186254	+	1.29543i	0.655347	+	0.755328i	$0.272522\pi$
$941$	−5.71349	+	39.7382i	−0.186254	+	1.29543i	−0.841601	+	0.540099i	$0.818387\pi$
$942$	−11.7588			−0.383122
$943$	−0.526676	+	2.31363i	−0.0171509	+	0.0753421i
$944$	−1.63158			−0.0531035
$945$	0.463314	−	3.22242i	0.0150716	−	0.104825i
$946$	−5.30855	−	11.6241i	−0.172596	−	0.377932i
$947$	37.5646	+	11.0300i	1.22068	+	0.358425i	0.827727	−	0.561131i	$-0.189634\pi$
$947$	37.5646	+	11.0300i	1.22068	+	0.358425i	0.392958	+	0.919556i	$0.371452\pi$
$948$	−8.69429	−	10.0337i	−0.282377	−	0.325881i
$949$	11.1433	−	3.27195i	0.361725	−	0.106212i
$950$	−3.16052	−	2.03114i	−0.102541	−	0.0658989i
$951$	11.0430	−	24.1809i	0.358095	−	0.784119i
$952$	−4.08856	+	4.71844i	−0.132511	+	0.152926i
$953$	−35.6067	+	22.8830i	−1.15341	+	0.741254i	−0.970316	−	0.241841i	$-0.922249\pi$
$953$	−35.6067	+	22.8830i	−1.15341	+	0.741254i	−0.183098	+	0.983095i	$0.558612\pi$
$954$	0.513609	+	3.57223i	0.0166287	+	0.115655i
$955$	1.92008	+	13.3544i	0.0621322	+	0.432139i
$956$	9.34244	−	6.00402i	0.302156	−	0.194184i
$957$	22.7455	−	26.2497i	0.735256	−	0.848531i
$958$	−14.8567	+	32.5315i	−0.479997	+	1.05105i
$959$	40.9473	+	26.3152i	1.32226	+	0.849762i
$960$	−0.959493	+	0.281733i	−0.0309675	+	0.00909288i
$961$	8.98340	+	10.3674i	0.289787	+	0.334432i
$962$	30.1985	+	8.86708i	0.973639	+	0.285886i
$963$	2.96302	+	6.48810i	0.0954819	+	0.209076i
$964$	4.20857	−	29.2712i	0.135549	−	0.942763i
$965$	10.5480			0.339552
$966$	−5.31514	−	14.6805i	−0.171012	−	0.472339i
$967$	−11.6829			−0.375696			−0.187848	−	0.982198i	$-0.560151\pi$
$967$	−11.6829			−0.375696			−0.187848	+	0.982198i	$0.560151\pi$
$968$	−1.27521	+	8.86926i	−0.0409867	+	0.285069i
$969$	−2.99302	−	6.55379i	−0.0961495	−	0.210538i
$970$	5.02067	+	1.47420i	0.161204	+	0.0473338i
$971$	−19.3960	−	22.3842i	−0.622448	−	0.718343i	0.353722	−	0.935351i	$-0.384916\pi$
$971$	−19.3960	−	22.3842i	−0.622448	−	0.718343i	−0.976170	+	0.217007i	$0.930370\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	33.6864	+	21.6489i	1.07994	+	0.694033i
$974$	12.3677	−	27.0816i	0.396288	−	0.867749i
$975$	2.15970	−	2.49242i	0.0691656	−	0.0798214i
$976$	−6.31718	+	4.05980i	−0.202208	+	0.129951i
$977$	−3.26152	−	22.6844i	−0.104345	−	0.725737i	−0.973081	−	0.230462i	$-0.925976\pi$
$977$	−3.26152	−	22.6844i	−0.104345	−	0.725737i	0.868736	−	0.495275i	$-0.164933\pi$
$978$	−2.99917	−	20.8597i	−0.0959029	−	0.667019i
$979$	41.0767	−	26.3984i	1.31282	−	0.843696i
$980$	2.35661	−	2.71968i	0.0752793	−	0.0868769i
$981$	−2.81405	+	6.16190i	−0.0898456	+	0.196734i
$982$	4.08006	+	2.62209i	0.130200	+	0.0836744i
$983$	−16.1784	+	4.75042i	−0.516012	+	0.151515i	−0.529362	−	0.848396i	$-0.677569\pi$
$983$	−16.1784	+	4.75042i	−0.516012	+	0.151515i	0.0133501	+	0.999911i	$0.495750\pi$
$984$	−0.324003	−	0.373920i	−0.0103288	−	0.0119201i
$985$	−1.07366	−	0.315255i	−0.0342097	−	0.0100449i
$986$	6.19353	+	13.5619i	0.197242	+	0.431900i
$987$	−4.08043	+	28.3800i	−0.129882	+	0.903346i
$988$	−12.3901			−0.394181
$989$	−6.68966	+	11.9756i	−0.212719	+	0.380803i
$990$	4.46771			0.141993
$991$	−1.03401	+	7.19172i	−0.0328465	+	0.228453i	−0.999632	−	0.0271378i	$-0.991361\pi$
$991$	−1.03401	+	7.19172i	−0.0328465	+	0.228453i	0.966785	+	0.255590i	$0.0822698\pi$
$992$	−1.72695	−	3.78149i	−0.0548306	−	0.120062i
$993$	2.19468	+	0.644418i	0.0696462	+	0.0204500i
$994$	12.4998	+	14.4256i	0.396470	+	0.457551i
$995$	26.4105	−	7.75481i	0.837268	−	0.245844i
$996$	7.15966	+	4.60123i	0.226863	+	0.145796i
$997$	16.2390	−	35.5584i	0.514294	−	1.12615i	−0.457261	−	0.889333i	$-0.651169\pi$
$997$	16.2390	−	35.5584i	0.514294	−	1.12615i	0.971555	−	0.236814i	$-0.0761033\pi$
$998$	−7.19361	+	8.30187i	−0.227710	+	0.262791i
$999$	8.02837	−	5.15952i	0.254006	−	0.163240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.31.1	✓	20
23.3	even	11	inner	690.2.m.d.601.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.31.1	✓	20	1.1	even	1	trivial
690.2.m.d.601.1	yes	20	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-2.73875 - 1.76009i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-2.73875 - 1.76009i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.635822 + 4.42224i) q^{11} +(0.142315 + 0.989821i) q^{12} +(2.77441 - 1.78300i) q^{13} +(2.13194 - 2.46039i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.84008 - 0.540297i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(3.60473 + 1.05844i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.463314 + 3.22242i) q^{21} -4.46771 q^{22} +(2.83694 + 3.86675i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.37002 + 2.99992i) q^{26} +(0.959493 + 0.281733i) q^{27} +(2.13194 + 2.46039i) q^{28} +(7.45937 - 2.19027i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-1.72695 + 3.78149i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(3.75848 - 2.41543i) q^{33} +(0.272927 + 1.89825i) q^{34} +(-0.463314 - 3.22242i) q^{35} +(0.841254 - 0.540641i) q^{36} +(6.24956 - 7.21237i) q^{37} +(-1.56068 + 3.41741i) q^{38} +(-2.77441 - 1.78300i) q^{39} +(0.959493 - 0.281733i) q^{40} +(0.324003 + 0.373920i) q^{41} +(-3.12368 - 0.917196i) q^{42} +(1.18820 + 2.60180i) q^{43} +(0.635822 - 4.42224i) q^{44} -1.00000 q^{45} +(-4.23113 + 2.25777i) q^{46} +8.80706 q^{47} +(0.142315 - 0.989821i) q^{48} +(1.49493 + 3.27345i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-1.25587 - 1.44935i) q^{51} +(-3.16436 + 0.929139i) q^{52} +(-3.03605 - 1.95115i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-2.92573 + 3.37647i) q^{55} +(-2.73875 + 1.76009i) q^{56} +(-0.534664 - 3.71867i) q^{57} +(1.10640 + 7.69515i) q^{58} +(-1.37257 + 0.882100i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(-3.11945 + 6.83065i) q^{61} +(-3.49722 - 2.24753i) q^{62} +(3.12368 - 0.917196i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(3.16436 + 0.929139i) q^{65} +(1.85596 + 4.06397i) q^{66} +(-2.11146 + 14.6855i) q^{67} -1.91777 q^{68} +(2.33881 - 4.18688i) q^{69} +3.25556 q^{70} +(-0.834410 + 5.80345i) q^{71} +(0.415415 + 0.909632i) q^{72} +(3.37885 + 0.992119i) q^{73} +(6.24956 + 7.21237i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-3.16052 - 2.03114i) q^{76} +(6.04217 - 13.2305i) q^{77} +(2.15970 - 2.49242i) q^{78} +(-11.1689 + 7.17784i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-0.416224 + 0.267491i) q^{82} +(5.57333 - 6.43196i) q^{83} +(1.35241 - 2.96136i) q^{84} +(1.61333 + 1.03682i) q^{85} +(-2.74442 + 0.805834i) q^{86} +(-5.09107 - 5.87541i) q^{87} +(4.28674 + 1.25870i) q^{88} +(-4.54010 - 9.94144i) q^{89} +(0.142315 - 0.989821i) q^{90} -10.7366 q^{91} +(-1.63264 - 4.50938i) q^{92} +4.15716 q^{93} +(-1.25337 + 8.71741i) q^{94} +(1.56068 + 3.41741i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-3.42665 - 3.95456i) q^{97} +(-3.45288 + 1.01386i) q^{98} +(-3.75848 - 2.41543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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