LMFDB - Embedded newform 690.2.m.g.121.2

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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	690.121
Dual form			690.2.m.g.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.188781 + 1.31300i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.188781 + 1.31300i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-1.37573 - 3.01243i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.119230 - 0.829266i) q^{13} +(1.11592 + 0.717161i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.35615 - 5.02726i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-4.28346 - 4.94338i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.551049 - 1.20663i) q^{21} -3.31170 q^{22} +(-3.75276 - 2.98611i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.803857 - 0.236034i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.11592 - 0.717161i) q^{28} +(-3.58395 + 4.13609i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-2.09882 + 0.616268i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.471304 + 3.27799i) q^{33} +(-2.76335 - 6.05089i) q^{34} +(0.551049 + 1.20663i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.797314 - 0.512403i) q^{37} +(-6.27607 + 1.84282i) q^{38} +(-0.119230 + 0.829266i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-0.106571 + 0.0684892i) q^{41} +(-0.868674 - 1.00250i) q^{42} +(-1.86611 - 0.547940i) q^{43} +(-1.37573 + 3.01243i) q^{44} +1.00000 q^{45} +(-4.27521 + 2.17315i) q^{46} +7.35491 q^{47} +(0.415415 - 0.909632i) q^{48} +(5.02812 + 1.47639i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(-5.59604 + 3.59635i) q^{51} +(-0.548638 + 0.633162i) q^{52} +(1.08325 - 7.53417i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-2.78598 - 1.79044i) q^{55} +(-0.188781 - 1.31300i) q^{56} +(2.71724 + 5.94992i) q^{57} +(2.27350 + 4.97827i) q^{58} +(-1.02489 - 7.12828i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-13.6565 + 4.00990i) q^{61} +(-0.311303 + 2.16516i) q^{62} +(-0.868674 + 1.00250i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.548638 - 0.633162i) q^{65} +(3.17756 + 0.933014i) q^{66} +(2.30217 - 5.04105i) q^{67} -6.65202 q^{68} +(2.75946 + 3.92242i) q^{69} +1.32650 q^{70} +(-3.19536 + 6.99686i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-6.56875 - 7.58074i) q^{73} +(-0.797314 + 0.512403i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(-0.930885 + 6.47445i) q^{76} +(4.21503 - 1.23765i) q^{77} +(0.704797 + 0.452945i) q^{78} +(0.0967853 + 0.673156i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.0180287 + 0.125392i) q^{82} +(5.66470 + 3.64048i) q^{83} +(-1.27277 + 0.373719i) q^{84} +(0.946681 - 6.58431i) q^{85} +(-1.27363 + 1.46985i) q^{86} +(4.60404 - 2.95884i) q^{87} +(2.16870 + 2.50282i) q^{88} +(17.0069 + 4.99368i) q^{89} +(0.415415 - 0.909632i) q^{90} +1.11133 q^{91} +(0.200784 + 4.79163i) q^{92} +2.18742 q^{93} +(3.05534 - 6.69026i) q^{94} +(-6.27607 - 1.84282i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(10.1243 - 6.50651i) q^{97} +(3.43173 - 3.96042i) q^{98} +(0.471304 - 3.27799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	−0.188781	+	1.31300i	−0.0713525	+	0.496267i	0.922539	+	0.385904i	$0.126110\pi$
$7$	−0.188781	+	1.31300i	−0.0713525	+	0.496267i	−0.993891	+	0.110363i	$0.964799\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	−1.37573	−	3.01243i	−0.414799	−	0.908282i	−0.995553	−	0.0942033i	$-0.969970\pi$
$11$	−1.37573	−	3.01243i	−0.414799	−	0.908282i	0.580754	−	0.814079i	$-0.302758\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.119230	−	0.829266i	−0.0330686	−	0.229997i	0.966584	−	0.256350i	$-0.0825198\pi$
$13$	−0.119230	−	0.829266i	−0.0330686	−	0.229997i	−0.999653	+	0.0263526i	$0.991611\pi$
$14$	1.11592	+	0.717161i	0.298243	+	0.191669i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	4.35615	−	5.02726i	1.05652	−	1.21929i	0.0816169	−	0.996664i	$-0.473992\pi$
$17$	4.35615	−	5.02726i	1.05652	−	1.21929i	0.974904	−	0.222626i	$-0.0714630\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	−4.28346	−	4.94338i	−0.982693	−	1.13409i	−0.990965	−	0.134122i	$-0.957178\pi$
$19$	−4.28346	−	4.94338i	−0.982693	−	1.13409i	0.00827174	−	0.999966i	$-0.497367\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	0.551049	−	1.20663i	0.120249	−	0.263308i
$22$	−3.31170			−0.706057
$23$	−3.75276	−	2.98611i	−0.782504	−	0.622646i
$23$	−3.75276	−	2.98611i	−0.782504	−	0.622646i
$24$	1.00000			0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−0.803857	−	0.236034i	−0.157649	−	0.0462900i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	1.11592	−	0.717161i	0.210890	−	0.135531i
$29$	−3.58395	+	4.13609i	−0.665522	+	0.768054i	−0.983669	−	0.179988i	$-0.942394\pi$
$29$	−3.58395	+	4.13609i	−0.665522	+	0.768054i	0.318147	+	0.948042i	$0.396940\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	−2.09882	+	0.616268i	−0.376959	+	0.110685i	−0.464723	−	0.885456i	$-0.653846\pi$
$31$	−2.09882	+	0.616268i	−0.376959	+	0.110685i	0.0877641	+	0.996141i	$0.472028\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	0.471304	+	3.27799i	0.0820436	+	0.570626i
$34$	−2.76335	−	6.05089i	−0.473910	−	1.03772i
$35$	0.551049	+	1.20663i	0.0931442	+	0.203957i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.797314	−	0.512403i	−0.131078	−	0.0842385i	0.473459	−	0.880816i	$-0.343005\pi$
$37$	−0.797314	−	0.512403i	−0.131078	−	0.0842385i	−0.604536	+	0.796577i	$0.706642\pi$
$38$	−6.27607	+	1.84282i	−1.01811	+	0.298945i
$39$	−0.119230	+	0.829266i	−0.0190921	+	0.132789i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	−0.106571	+	0.0684892i	−0.0166436	+	0.0106962i	−0.548936	−	0.835864i	$-0.684967\pi$
$41$	−0.106571	+	0.0684892i	−0.0166436	+	0.0106962i	0.532293	+	0.846560i	$0.321331\pi$
$42$	−0.868674	−	1.00250i	−0.134039	−	0.154690i
$43$	−1.86611	−	0.547940i	−0.284579	−	0.0835600i	0.136328	−	0.990664i	$-0.456470\pi$
$43$	−1.86611	−	0.547940i	−0.284579	−	0.0835600i	−0.420907	+	0.907104i	$0.638288\pi$
$44$	−1.37573	+	3.01243i	−0.207399	+	0.454141i
$45$	1.00000			0.149071
$46$	−4.27521	+	2.17315i	−0.630345	+	0.320414i
$47$	7.35491			1.07282			0.536412	−	0.843956i	$-0.319779\pi$
$47$	7.35491			1.07282			0.536412	+	0.843956i	$0.319779\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	5.02812	+	1.47639i	0.718303	+	0.210913i
$50$	−0.654861	−	0.755750i	−0.0926113	−	0.106879i
$51$	−5.59604	+	3.59635i	−0.783602	+	0.503590i
$52$	−0.548638	+	0.633162i	−0.0760824	+	0.0878038i
$53$	1.08325	−	7.53417i	0.148796	−	1.03490i	−0.769399	−	0.638769i	$-0.779444\pi$
$53$	1.08325	−	7.53417i	0.148796	−	1.03490i	0.918195	−	0.396129i	$-0.129647\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−2.78598	−	1.79044i	−0.375662	−	0.241423i
$56$	−0.188781	−	1.31300i	−0.0252269	−	0.175457i
$57$	2.71724	+	5.94992i	0.359907	+	0.788087i
$58$	2.27350	+	4.97827i	0.298525	+	0.653679i
$59$	−1.02489	−	7.12828i	−0.133430	−	0.928023i	−0.941037	−	0.338303i	$-0.890147\pi$
$59$	−1.02489	−	7.12828i	−0.133430	−	0.928023i	0.807608	−	0.589720i	$-0.200762\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	−13.6565	+	4.00990i	−1.74853	+	0.513415i	−0.990345	−	0.138622i	$-0.955733\pi$
$61$	−13.6565	+	4.00990i	−1.74853	+	0.513415i	−0.758187	+	0.652038i	$0.773914\pi$
$62$	−0.311303	+	2.16516i	−0.0395355	+	0.274975i
$63$	−0.868674	+	1.00250i	−0.109443	+	0.126304i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.548638	−	0.633162i	−0.0680502	−	0.0785341i
$66$	3.17756	+	0.933014i	0.391130	+	0.114846i
$67$	2.30217	−	5.04105i	0.281255	−	0.615863i	−0.715298	−	0.698819i	$-0.753709\pi$
$67$	2.30217	−	5.04105i	0.281255	−	0.615863i	0.996553	+	0.0829568i	$0.0264364\pi$
$68$	−6.65202			−0.806676
$69$	2.75946	+	3.92242i	0.332200	+	0.472204i
$70$	1.32650			0.158547
$71$	−3.19536	+	6.99686i	−0.379219	+	0.830375i	0.619742	+	0.784806i	$0.287237\pi$
$71$	−3.19536	+	6.99686i	−0.379219	+	0.830375i	−0.998961	+	0.0455690i	$0.985490\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	−6.56875	−	7.58074i	−0.768814	−	0.887259i	0.227435	−	0.973793i	$-0.426966\pi$
$73$	−6.56875	−	7.58074i	−0.768814	−	0.887259i	−0.996249	+	0.0865344i	$0.972421\pi$
$74$	−0.797314	+	0.512403i	−0.0926859	+	0.0595656i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	−0.930885	+	6.47445i	−0.106780	+	0.742670i
$77$	4.21503	−	1.23765i	0.480348	−	0.141043i
$78$	0.704797	+	0.452945i	0.0798025	+	0.0512859i
$79$	0.0967853	+	0.673156i	0.0108892	+	0.0757360i	0.994541	−	0.104343i	$-0.0332739\pi$
$79$	0.0967853	+	0.673156i	0.0108892	+	0.0757360i	−0.983652	+	0.180079i	$0.942365\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	0.0180287	+	0.125392i	0.00199093	+	0.0138472i
$83$	5.66470	+	3.64048i	0.621782	+	0.399595i	0.813259	−	0.581902i	$-0.197691\pi$
$83$	5.66470	+	3.64048i	0.621782	+	0.399595i	−0.191477	+	0.981497i	$0.561328\pi$
$84$	−1.27277	+	0.373719i	−0.138871	+	0.0407761i
$85$	0.946681	−	6.58431i	0.102682	−	0.714169i
$86$	−1.27363	+	1.46985i	−0.137340	+	0.158498i
$87$	4.60404	−	2.95884i	0.493605	−	0.317221i
$88$	2.16870	+	2.50282i	0.231185	+	0.266801i
$89$	17.0069	+	4.99368i	1.80273	+	0.529329i	0.997935	−	0.0642276i	$-0.0204584\pi$
$89$	17.0069	+	4.99368i	1.80273	+	0.529329i	0.804793	+	0.593556i	$0.202277\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	1.11133			0.116499
$92$	0.200784	+	4.79163i	0.0209332	+	0.499562i
$93$	2.18742			0.226825
$94$	3.05534	−	6.69026i	0.315134	−	0.690048i
$95$	−6.27607	−	1.84282i	−0.643911	−	0.189069i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	10.1243	−	6.50651i	1.02797	−	0.660636i	0.0859866	−	0.996296i	$-0.472596\pi$
$97$	10.1243	−	6.50651i	1.02797	−	0.660636i	0.941983	+	0.335660i	$0.108959\pi$
$98$	3.43173	−	3.96042i	0.346657	−	0.400063i
$99$	0.471304	−	3.27799i	0.0473679	−	0.329451i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	11.7751	+	7.56737i	1.17166	+	0.752981i	0.973835	−	0.227256i	$-0.0729753\pi$
$101$	11.7751	+	7.56737i	1.17166	+	0.752981i	0.197827	+	0.980237i	$0.436612\pi$
$102$	0.946681	+	6.58431i	0.0937354	+	0.651944i
$103$	−1.92169	−	4.20791i	−0.189350	−	0.414618i	0.791019	−	0.611792i	$-0.209551\pi$
$103$	−1.92169	−	4.20791i	−0.189350	−	0.414618i	−0.980369	+	0.197174i	$0.936824\pi$
$104$	0.348032	+	0.762084i	0.0341273	+	0.0747284i
$105$	−0.188781	−	1.31300i	−0.0184231	−	0.128136i
$106$	−6.40332	−	4.11517i	−0.621946	−	0.399700i
$107$	12.7263	−	3.73679i	1.23030	−	0.361249i	0.398939	−	0.916978i	$-0.369379\pi$
$107$	12.7263	−	3.73679i	1.23030	−	0.361249i	0.831364	+	0.555728i	$0.187560\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−4.51839	+	5.21450i	−0.432783	+	0.499458i	−0.929689	−	0.368346i	$-0.879924\pi$
$109$	−4.51839	+	5.21450i	−0.432783	+	0.499458i	0.496906	+	0.867805i	$0.334470\pi$
$110$	−2.78598	+	1.79044i	−0.265633	+	0.170712i
$111$	0.620657	+	0.716276i	0.0589101	+	0.0679859i
$112$	−1.27277	−	0.373719i	−0.120265	−	0.0353131i
$113$	1.67759	−	3.67341i	0.157814	−	0.345565i	−0.814164	−	0.580635i	$-0.802805\pi$
$113$	1.67759	−	3.67341i	0.157814	−	0.345565i	0.971979	+	0.235070i	$0.0755318\pi$
$114$	6.54102			0.612623
$115$	−4.77143	−	0.483179i	−0.444938	−	0.0450567i
$116$	5.47284			0.508140
$117$	0.348032	−	0.762084i	0.0321756	−	0.0704546i
$118$	−6.90987	−	2.02892i	−0.636105	−	0.186777i
$119$	5.77844	+	6.66867i	0.529708	+	0.611316i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	0.0213649	−	0.0246564i	0.00194226	−	0.00224149i
$122$	−2.02557	+	14.0881i	−0.183386	+	1.27548i
$123$	0.121550	−	0.0356903i	0.0109598	−	0.00321809i
$124$	1.84018	+	1.18261i	0.165253	+	0.106202i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	0.551049	+	1.20663i	0.0490913	+	0.107495i
$127$	1.72031	+	3.76695i	0.152653	+	0.334263i	0.970473	−	0.241211i	$-0.0775447\pi$
$127$	1.72031	+	3.76695i	0.152653	+	0.334263i	−0.817820	+	0.575474i	$0.804817\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	1.63615	+	1.05149i	0.144055	+	0.0925784i
$130$	−0.803857	+	0.236034i	−0.0705029	+	0.0207015i
$131$	−1.04865	+	7.29355i	−0.0916213	+	0.637240i	0.891327	+	0.453360i	$0.149775\pi$
$131$	−1.04865	+	7.29355i	−0.0916213	+	0.637240i	−0.982949	+	0.183880i	$0.941134\pi$
$132$	2.16870	−	2.50282i	0.188761	−	0.217842i
$133$	7.29929	−	4.69097i	0.632929	−	0.406758i
$134$	−3.62915	−	4.18826i	−0.313510	−	0.361810i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	−2.76335	+	6.05089i	−0.236955	+	0.518860i
$137$	12.0309			1.02787			0.513933	−	0.857831i	$-0.328188\pi$
$137$	12.0309			1.02787			0.513933	+	0.857831i	$0.328188\pi$
$138$	4.71428	−	0.880660i	0.401306	−	0.0749668i
$139$	−4.24808			−0.360318			−0.180159	−	0.983638i	$-0.557661\pi$
$139$	−4.24808			−0.360318			−0.180159	+	0.983638i	$0.557661\pi$
$140$	0.551049	−	1.20663i	0.0465721	−	0.101979i
$141$	−7.05698	−	2.07212i	−0.594305	−	0.174504i
$142$	5.03717	+	5.81320i	0.422710	+	0.487833i
$143$	−2.33408	+	1.50002i	−0.195185	+	0.125438i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.778866	+	5.41713i	−0.0646813	+	0.449868i
$146$	−9.62445	+	2.82599i	−0.796525	+	0.233881i
$147$	−4.40850	−	2.83317i	−0.363607	−	0.233676i
$148$	0.134882	+	0.938122i	0.0110872	+	0.0771132i
$149$	7.06463	+	15.4694i	0.578757	+	1.26730i	0.942002	+	0.335608i	$0.108942\pi$
$149$	7.06463	+	15.4694i	0.578757	+	1.26730i	−0.363244	+	0.931694i	$0.618331\pi$
$150$	0.415415	+	0.909632i	0.0339185	+	0.0742711i
$151$	−1.66829	−	11.6032i	−0.135764	−	0.944257i	−0.937848	−	0.347046i	$-0.887185\pi$
$151$	−1.66829	−	11.6032i	−0.135764	−	0.944257i	0.802084	−	0.597211i	$-0.203724\pi$
$152$	5.50266	+	3.53634i	0.446325	+	0.286835i
$153$	6.38257	−	1.87409i	0.516000	−	0.151511i
$154$	0.625186	−	4.34827i	0.0503789	−	0.350393i
$155$	−1.43246	+	1.65314i	−0.115058	+	0.132784i
$156$	0.704797	−	0.452945i	0.0564289	−	0.0362646i
$157$	6.57902	+	7.59260i	0.525063	+	0.605955i	0.954891	−	0.296955i	$-0.0959713\pi$
$157$	6.57902	+	7.59260i	0.525063	+	0.605955i	−0.429828	+	0.902911i	$0.641426\pi$
$158$	0.652531	+	0.191600i	0.0519126	+	0.0152429i
$159$	−3.16199	+	6.92380i	−0.250762	+	0.549093i
$160$	1.00000			0.0790569
$161$	4.62920	−	4.36365i	0.364832	−	0.343904i
$162$	1.00000			0.0785674
$163$	−6.81631	+	14.9256i	−0.533895	+	1.16907i	0.430011	+	0.902823i	$0.358510\pi$
$163$	−6.81631	+	14.9256i	−0.533895	+	1.16907i	−0.963906	+	0.266243i	$0.914218\pi$
$164$	0.121550	+	0.0356903i	0.00949146	+	0.00278695i
$165$	2.16870	+	2.50282i	0.168833	+	0.194844i
$166$	5.66470	−	3.64048i	0.439666	−	0.282556i
$167$	−0.920903	+	1.06278i	−0.0712616	+	0.0822403i	−0.790261	−	0.612771i	$-0.790055\pi$
$167$	−0.920903	+	1.06278i	−0.0712616	+	0.0822403i	0.718999	+	0.695011i	$0.244600\pi$
$168$	−0.188781	+	1.31300i	−0.0145648	+	0.101300i
$169$	11.7999	−	3.46478i	0.907688	−	0.266521i
$170$	−5.59604	−	3.59635i	−0.429196	−	0.275828i
$171$	−0.930885	−	6.47445i	−0.0711865	−	0.495113i
$172$	0.807938	+	1.76914i	0.0616047	+	0.134895i
$173$	−0.218237	−	0.477873i	−0.0165923	−	0.0363320i	0.901154	−	0.433498i	$-0.142721\pi$
$173$	−0.218237	−	0.477873i	−0.0165923	−	0.0363320i	−0.917747	+	0.397166i	$0.869994\pi$
$174$	−0.778866	−	5.41713i	−0.0590457	−	0.410672i
$175$	1.11592	+	0.717161i	0.0843560	+	0.0542123i
$176$	3.17756	−	0.933014i	0.239517	−	0.0703286i
$177$	−1.02489	+	7.12828i	−0.0770356	+	0.535794i
$178$	11.6073	−	13.3956i	0.870006	−	1.00404i
$179$	−4.72325	+	3.03545i	−0.353032	+	0.226880i	−0.705122	−	0.709086i	$-0.749108\pi$
$179$	−4.72325	+	3.03545i	−0.353032	+	0.226880i	0.352089	+	0.935966i	$0.385471\pi$
$180$	−0.654861	−	0.755750i	−0.0488104	−	0.0563302i
$181$	−4.75457	−	1.39607i	−0.353404	−	0.103769i	0.100212	−	0.994966i	$-0.468048\pi$
$181$	−4.75457	−	1.39607i	−0.353404	−	0.103769i	−0.453616	+	0.891197i	$0.649866\pi$
$182$	0.461665	−	1.01091i	0.0342209	−	0.0749333i
$183$	14.2330			1.05213
$184$	4.44203	+	1.80787i	0.327470	+	0.133278i
$185$	−0.947769			−0.0696814
$186$	0.908688	−	1.98975i	0.0666283	−	0.145896i
$187$	−21.1372	−	6.20643i	−1.54570	−	0.453859i
$188$	−4.81644	−	5.55847i	−0.351275	−	0.405393i
$189$	1.11592	−	0.717161i	0.0811716	−	0.0521658i
$190$	−4.28346	+	4.94338i	−0.310755	+	0.358630i
$191$	2.26811	−	15.7751i	0.164115	−	1.14144i	−0.726660	−	0.686997i	$-0.758928\pi$
$191$	2.26811	−	15.7751i	0.164115	−	1.14144i	0.890775	−	0.454445i	$-0.150163\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	19.7321	+	12.6811i	1.42035	+	0.912803i	0.999985	+	0.00544806i	$0.00173418\pi$
$193$	19.7321	+	12.6811i	1.42035	+	0.912803i	0.420365	+	0.907355i	$0.361902\pi$
$194$	−1.71273	−	11.9123i	−0.122967	−	0.855254i
$195$	0.348032	+	0.762084i	0.0249231	+	0.0545739i
$196$	−2.17694	−	4.76683i	−0.155496	−	0.340488i
$197$	−3.30089	−	22.9582i	−0.235179	−	1.63570i	−0.675143	−	0.737687i	$-0.735918\pi$
$197$	−3.30089	−	22.9582i	−0.235179	−	1.63570i	0.439964	−	0.898015i	$-0.354991\pi$
$198$	−2.78598	−	1.79044i	−0.197991	−	0.127241i
$199$	−3.10057	+	0.910409i	−0.219793	+	0.0645372i	−0.389775	−	0.920910i	$-0.627447\pi$
$199$	−3.10057	+	0.910409i	−0.219793	+	0.0645372i	0.169982	+	0.985447i	$0.445629\pi$
$200$	−0.142315	+	0.989821i	−0.0100632	+	0.0699909i
$201$	−3.62915	+	4.18826i	−0.255980	+	0.295417i
$202$	11.7751	−	7.56737i	0.828490	−	0.532438i
$203$	−4.75411	−	5.48654i	−0.333673	−	0.385079i
$204$	6.38257	+	1.87409i	0.446869	+	0.131213i
$205$	−0.0526254	+	0.115234i	−0.00367552	+	0.00804826i
$206$	−4.62595			−0.322305
$207$	−1.54261	−	4.54096i	−0.107219	−	0.315619i
$208$	0.837793			0.0580905
$209$	−8.99869	+	19.7044i	−0.622452	+	1.36298i
$210$	−1.27277	−	0.373719i	−0.0878294	−	0.0257890i
$211$	−14.5487	−	16.7901i	−1.00157	−	1.15588i	−0.987762	−	0.155971i	$-0.950149\pi$
$211$	−14.5487	−	16.7901i	−1.00157	−	1.15588i	−0.0138104	−	0.999905i	$-0.504396\pi$
$212$	−6.40332	+	4.11517i	−0.439782	+	0.282631i
$213$	5.03717	−	5.81320i	0.345141	−	0.398314i
$214$	1.88761	−	13.1286i	0.129034	−	0.897454i
$215$	−1.86611	+	0.547940i	−0.127268	+	0.0373692i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−0.412944	−	2.87209i	−0.0280324	−	0.194970i
$218$	2.86627	+	6.27625i	0.194128	+	0.425081i
$219$	4.16693	+	9.12430i	0.281575	+	0.616563i
$220$	0.471304	+	3.27799i	0.0317753	+	0.221002i
$221$	−4.68832	−	3.01300i	−0.315371	−	0.202676i
$222$	0.909378	−	0.267017i	0.0610334	−	0.0179210i
$223$	−0.607602	+	4.22597i	−0.0406881	+	0.282992i	0.959312	+	0.282349i	$0.0911136\pi$
$223$	−0.607602	+	4.22597i	−0.0406881	+	0.282992i	−1.00000		0.000642567i	$0.999795\pi$
$224$	−0.868674	+	1.00250i	−0.0580407	+	0.0669826i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	−2.64455	−	3.05198i	−0.175913	−	0.203014i
$227$	24.4519	+	7.17972i	1.62293	+	0.476535i	0.961803	−	0.273741i	$-0.0882611\pi$
$227$	24.4519	+	7.17972i	1.62293	+	0.476535i	0.661125	+	0.750276i	$0.270079\pi$
$228$	2.71724	−	5.94992i	0.179954	−	0.394043i
$229$	−24.4996			−1.61898			−0.809490	−	0.587133i	$-0.800257\pi$
$229$	−24.4996			−1.61898			−0.809490	+	0.587133i	$0.800257\pi$
$230$	−2.42164	+	4.13953i	−0.159678	+	0.272952i
$231$	−4.39298			−0.289037
$232$	2.27350	−	4.97827i	0.149263	−	0.326839i
$233$	−18.6139	−	5.46554i	−1.21944	−	0.358059i	−0.392183	−	0.919887i	$-0.628280\pi$
$233$	−18.6139	−	5.46554i	−1.21944	−	0.358059i	−0.827254	+	0.561828i	$0.810098\pi$
$234$	−0.548638	−	0.633162i	−0.0358656	−	0.0413911i
$235$	6.18734	−	3.97636i	0.403618	−	0.259389i
$236$	−4.71603	+	5.44259i	−0.306988	+	0.354283i
$237$	0.0967853	−	0.673156i	0.00628688	−	0.0437262i
$238$	8.46649	−	2.48598i	0.548801	−	0.161142i
$239$	5.99817	+	3.85479i	0.387990	+	0.249346i	0.720064	−	0.693907i	$-0.244112\pi$
$239$	5.99817	+	3.85479i	0.387990	+	0.249346i	−0.332075	+	0.943253i	$0.607749\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	5.44242	+	11.9172i	0.350577	+	0.767657i	0.999974	+	0.00720702i	$0.00229409\pi$
$241$	5.44242	+	11.9172i	0.350577	+	0.767657i	−0.649397	+	0.760450i	$0.724979\pi$
$242$	−0.0135530	−	0.0296769i	−0.000871218	−	0.00190770i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	11.9736	+	7.69494i	0.766529	+	0.492618i
$245$	5.02812	−	1.47639i	0.321235	−	0.0943231i
$246$	0.0180287	−	0.125392i	0.00114947	−	0.00799471i
$247$	−3.58865	+	4.14153i	−0.228341	+	0.263519i
$248$	1.84018	−	1.18261i	0.116851	−	0.0750958i
$249$	−4.40960	−	5.08895i	−0.279447	−	0.322499i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	−12.1715	+	26.6520i	−0.768261	+	1.68226i	−0.0378176	+	0.999285i	$0.512041\pi$
$251$	−12.1715	+	26.6520i	−0.768261	+	1.68226i	−0.730444	+	0.682973i	$0.760687\pi$
$252$	1.32650			0.0835618
$253$	−3.83265	+	15.4130i	−0.240957	+	0.969007i
$254$	4.14118			0.259841
$255$	−2.76335	+	6.05089i	−0.173048	+	0.378921i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−3.59520	−	4.14908i	−0.224262	−	0.258812i	0.632457	−	0.774595i	$-0.282047\pi$
$257$	−3.59520	−	4.14908i	−0.224262	−	0.258812i	−0.856719	+	0.515783i	$0.827501\pi$
$258$	1.63615	−	1.05149i	0.101862	−	0.0654628i
$259$	0.823302	−	0.950141i	0.0511575	−	0.0590389i
$260$	−0.119230	+	0.829266i	−0.00739436	+	0.0514289i
$261$	−5.25115	+	1.54188i	−0.325038	+	0.0954398i
$262$	6.19882	+	3.98374i	0.382964	+	0.246116i
$263$	1.67399	+	11.6429i	0.103223	+	0.717929i	0.974049	+	0.226338i	$0.0726754\pi$
$263$	1.67399	+	11.6429i	0.103223	+	0.717929i	−0.870826	+	0.491591i	$0.836415\pi$
$264$	−1.37573	−	3.01243i	−0.0846704	−	0.185402i
$265$	−3.16199	−	6.92380i	−0.194240	−	0.425325i
$266$	−1.23482	−	8.58836i	−0.0757117	−	0.526586i
$267$	−14.9111	−	9.58279i	−0.912546	−	0.586458i
$268$	−5.31738	+	1.56132i	−0.324810	+	0.0953729i
$269$	4.34255	−	30.2031i	0.264770	−	1.84151i	−0.230869	−	0.972985i	$-0.574157\pi$
$269$	4.34255	−	30.2031i	0.264770	−	1.84151i	0.495639	−	0.868529i	$-0.334934\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	−1.91901	+	1.23327i	−0.116571	+	0.0749158i	−0.597627	−	0.801774i	$-0.703890\pi$
$271$	−1.91901	+	1.23327i	−0.116571	+	0.0749158i	0.481056	+	0.876690i	$0.340253\pi$
$272$	4.35615	+	5.02726i	0.264130	+	0.304823i
$273$	−1.06632	−	0.313099i	−0.0645365	−	0.0189496i
$274$	4.99780	−	10.9437i	0.301928	−	0.661130i
$275$	−3.31170			−0.199703
$276$	1.15731	−	4.65410i	0.0696616	−	0.280144i
$277$	12.9595			0.778659			0.389329	−	0.921099i	$-0.372707\pi$
$277$	12.9595			0.778659			0.389329	+	0.921099i	$0.372707\pi$
$278$	−1.76472	+	3.86419i	−0.105841	+	0.231759i
$279$	−2.09882	−	0.616268i	−0.125653	−	0.0368950i
$280$	−0.868674	−	1.00250i	−0.0519132	−	0.0599110i
$281$	4.29140	−	2.75792i	0.256004	−	0.164523i	−0.406344	−	0.913720i	$-0.633197\pi$
$281$	4.29140	−	2.75792i	0.256004	−	0.164523i	0.662348	+	0.749197i	$0.269560\pi$
$282$	−4.81644	+	5.55847i	−0.286815	+	0.331002i
$283$	−1.69832	+	11.8120i	−0.100954	+	0.702153i	0.874991	+	0.484139i	$0.160867\pi$
$283$	−1.69832	+	11.8120i	−0.100954	+	0.702153i	−0.975946	+	0.218014i	$0.930042\pi$
$284$	7.38039	−	2.16708i	0.437946	−	0.128592i
$285$	5.50266	+	3.53634i	0.325949	+	0.209475i
$286$	0.394856	+	2.74628i	0.0233483	+	0.162391i
$287$	−0.0698077	−	0.152858i	−0.00412062	−	0.00902290i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−3.87799	−	26.9720i	−0.228117	−	1.58659i
$290$	4.60404	+	2.95884i	0.270359	+	0.173749i
$291$	−11.5473	+	3.39060i	−0.676916	+	0.198760i
$292$	−1.42753	+	9.92866i	−0.0835397	+	0.581031i
$293$	0.756833	−	0.873431i	0.0442146	−	0.0510264i	−0.733211	−	0.680001i	$-0.761979\pi$
$293$	0.756833	−	0.873431i	0.0442146	−	0.0510264i	0.777426	+	0.628974i	$0.216525\pi$
$294$	−4.40850	+	2.83317i	−0.257109	+	0.165234i
$295$	−4.71603	−	5.44259i	−0.274578	−	0.316880i
$296$	0.909378	+	0.267017i	0.0528565	+	0.0155201i
$297$	−1.37573	+	3.01243i	−0.0798280	+	0.174799i
$298$	17.0062			0.985143
$299$	−2.02883	+	3.46807i	−0.117330	+	0.200563i
$300$	1.00000			0.0577350
$301$	1.07173	−	2.34676i	0.0617735	−	0.135265i
$302$	−11.2477	−	3.30262i	−0.647232	−	0.190045i
$303$	−9.16611	−	10.5783i	−0.526579	−	0.607705i
$304$	5.50266	−	3.53634i	0.315599	−	0.202823i
$305$	−9.32064	+	10.7566i	−0.533698	+	0.615921i
$306$	0.946681	−	6.58431i	0.0541182	−	0.376400i
$307$	−1.85037	+	0.543319i	−0.105606	+	0.0310089i	−0.334109	−	0.942534i	$-0.608435\pi$
$307$	−1.85037	+	0.543319i	−0.105606	+	0.0310089i	0.228502	+	0.973543i	$0.426617\pi$
$308$	−3.69561	−	2.37502i	−0.210577	−	0.135330i
$309$	0.658342	+	4.57887i	0.0374517	+	0.260483i
$310$	0.908688	+	1.98975i	0.0516100	+	0.113010i
$311$	4.73426	+	10.3666i	0.268455	+	0.587835i	0.995066	−	0.0992140i	$-0.0316328\pi$
$311$	4.73426	+	10.3666i	0.268455	+	0.587835i	−0.726611	+	0.687049i	$0.758906\pi$
$312$	−0.119230	−	0.829266i	−0.00675009	−	0.0469479i
$313$	20.9187	+	13.4437i	1.18240	+	0.759881i	0.975826	−	0.218551i	$-0.0701329\pi$
$313$	20.9187	+	13.4437i	1.18240	+	0.759881i	0.206572	+	0.978431i	$0.433769\pi$
$314$	9.63950	−	2.83041i	0.543988	−	0.159729i
$315$	−0.188781	+	1.31300i	−0.0106366	+	0.0739792i
$316$	0.445357	−	0.513969i	0.0250533	−	0.0289130i
$317$	−17.5754	+	11.2950i	−0.987134	+	0.634393i	−0.931379	−	0.364052i	$-0.881393\pi$
$317$	−17.5754	+	11.2950i	−0.987134	+	0.634393i	−0.0557557	+	0.998444i	$0.517757\pi$
$318$	4.98457	+	5.75250i	0.279521	+	0.322584i
$319$	17.3902	+	5.10624i	0.973667	+	0.285894i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	−13.2636			−0.740303
$322$	−2.04627	−	6.02360i	−0.114034	−	0.335682i
$323$	−43.5110			−2.42102
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−0.803857	−	0.236034i	−0.0445899	−	0.0130928i
$326$	10.7452	+	12.4007i	0.595124	+	0.686809i
$327$	5.80446	−	3.73030i	0.320987	−	0.206286i
$328$	0.0829588	−	0.0957395i	0.00458063	−	0.00528633i
$329$	−1.38847	+	9.65700i	−0.0765486	+	0.532407i
$330$	3.17756	−	0.933014i	0.174919	−	0.0513608i
$331$	9.01534	+	5.79381i	0.495528	+	0.318457i	0.764425	−	0.644712i	$-0.223023\pi$
$331$	9.01534	+	5.79381i	0.495528	+	0.318457i	−0.268897	+	0.963169i	$0.586659\pi$
$332$	−0.958298	−	6.66511i	−0.0525934	−	0.365795i
$333$	−0.393717	−	0.862121i	−0.0215756	−	0.0472439i
$334$	0.584181	+	1.27918i	0.0319649	+	0.0699935i
$335$	−0.788689	−	5.48545i	−0.0430907	−	0.299702i
$336$	1.11592	+	0.717161i	0.0608787	+	0.0391243i
$337$	−24.3675	+	7.15493i	−1.32738	+	0.389754i	−0.867151	−	0.498046i	$-0.834051\pi$
$337$	−24.3675	+	7.15493i	−1.32738	+	0.389754i	−0.460230	+	0.887800i	$0.652233\pi$
$338$	1.75020	−	12.1729i	0.0951985	−	0.662120i
$339$	−2.64455	+	3.05198i	−0.143632	+	0.165761i
$340$	−5.59604	+	3.59635i	−0.303488	+	0.195040i
$341$	4.74387	+	5.47472i	0.256895	+	0.296473i
$342$	−6.27607	−	1.84282i	−0.339371	−	0.0996483i
$343$	−6.74505	+	14.7696i	−0.364199	+	0.797484i
$344$	1.94489			0.104862
$345$	4.44203	+	1.80787i	0.239151	+	0.0973327i
$346$	−0.525348			−0.0282429
$347$	13.1718	−	28.8423i	0.707102	−	1.54834i	−0.124041	−	0.992277i	$-0.539585\pi$
$347$	13.1718	−	28.8423i	0.707102	−	1.54834i	0.831142	−	0.556060i	$-0.187687\pi$
$348$	−5.25115	−	1.54188i	−0.281491	−	0.0826533i
$349$	8.58368	+	9.90610i	0.459474	+	0.530261i	0.937454	−	0.348110i	$-0.113176\pi$
$349$	8.58368	+	9.90610i	0.459474	+	0.530261i	−0.477980	+	0.878371i	$0.658631\pi$
$350$	1.11592	−	0.717161i	0.0596487	−	0.0383339i
$351$	−0.548638	+	0.633162i	−0.0292841	+	0.0337957i
$352$	0.471304	−	3.27799i	0.0251206	−	0.174718i
$353$	−12.2250	+	3.58960i	−0.650674	+	0.191055i	−0.590380	−	0.807126i	$-0.701022\pi$
$353$	−12.2250	+	3.58960i	−0.650674	+	0.191055i	−0.0602940	+	0.998181i	$0.519204\pi$
$354$	6.05836	+	3.89347i	0.321998	+	0.206936i
$355$	1.09468	+	7.61368i	0.0580997	+	0.404092i
$356$	−7.36318	−	16.1231i	−0.390248	−	0.854524i
$357$	−3.66559	−	8.02652i	−0.194003	−	0.424808i
$358$	0.799032	+	5.55739i	0.0422302	+	0.293717i
$359$	−9.51841	−	6.11711i	−0.502362	−	0.322849i	0.264798	−	0.964304i	$-0.414695\pi$
$359$	−9.51841	−	6.11711i	−0.502362	−	0.322849i	−0.767161	+	0.641455i	$0.778331\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	−3.38496	+	23.5429i	−0.178156	+	1.23910i
$362$	−3.24503	+	3.74496i	−0.170555	+	0.196831i
$363$	−0.0274460	+	0.0176385i	−0.00144054	+	0.000925780i
$364$	−0.727769	−	0.839890i	−0.0381455	−	0.0440222i
$365$	−9.62445	−	2.82599i	−0.503767	−	0.147919i
$366$	5.91260	−	12.9468i	0.309057	−	0.676740i
$367$	5.41379			0.282598			0.141299	−	0.989967i	$-0.454872\pi$
$367$	5.41379			0.282598			0.141299	+	0.989967i	$0.454872\pi$
$368$	3.48978	−	3.28959i	0.181918	−	0.171482i
$369$	−0.126682			−0.00659478
$370$	−0.393717	+	0.862121i	−0.0204684	+	0.0448195i
$371$	9.68787	+	2.84462i	0.502969	+	0.147685i
$372$	−1.43246	−	1.65314i	−0.0742694	−	0.0857115i
$373$	29.1821	−	18.7542i	1.51099	−	0.971057i	0.517684	−	0.855572i	$-0.326794\pi$
$373$	29.1821	−	18.7542i	1.51099	−	0.971057i	0.993309	−	0.115485i	$-0.0368421\pi$
$374$	−14.4263	+	16.6488i	−0.745964	+	0.860889i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	−7.05698	+	2.07212i	−0.363936	+	0.106861i
$377$	3.85724	+	2.47890i	0.198658	+	0.127670i
$378$	−0.188781	−	1.31300i	−0.00970984	−	0.0675334i
$379$	−5.15144	−	11.2801i	−0.264612	−	0.579419i	0.729958	−	0.683492i	$-0.239540\pi$
$379$	−5.15144	−	11.2801i	−0.264612	−	0.579419i	−0.994570	+	0.104073i	$0.966812\pi$
$380$	2.71724	+	5.94992i	0.139391	+	0.305225i
$381$	−0.589352	−	4.09903i	−0.0301934	−	0.210000i
$382$	−13.4073	−	8.61634i	−0.685976	−	0.440850i
$383$	−13.0658	+	3.83647i	−0.667632	+	0.196035i	−0.597948	−	0.801535i	$-0.704017\pi$
$383$	−13.0658	+	3.83647i	−0.667632	+	0.196035i	−0.0696839	+	0.997569i	$0.522199\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	2.87679	−	3.31999i	0.146615	−	0.169202i
$386$	19.7321	−	12.6811i	1.00434	−	0.645449i
$387$	−1.27363	−	1.46985i	−0.0647425	−	0.0747168i
$388$	−11.5473	−	3.39060i	−0.586226	−	0.172132i
$389$	−10.6043	+	23.2202i	−0.537660	+	1.17731i	0.424650	+	0.905358i	$0.360397\pi$
$389$	−10.6043	+	23.2202i	−0.537660	+	1.17731i	−0.962310	+	0.271954i	$0.912330\pi$
$390$	0.837793			0.0424233
$391$	−31.3595	+	5.85817i	−1.58592	+	0.296260i
$392$	−5.24039			−0.264680
$393$	3.06101	−	6.70267i	0.154407	−	0.338105i
$394$	−22.2547	−	6.53458i	−1.12118	−	0.329207i
$395$	0.445357	+	0.513969i	0.0224083	+	0.0258606i
$396$	−2.78598	+	1.79044i	−0.140001	+	0.0899731i
$397$	−0.224868	+	0.259512i	−0.0112858	+	0.0130245i	−0.761364	−	0.648324i	$-0.775470\pi$
$397$	−0.224868	+	0.259512i	−0.0112858	+	0.0130245i	0.750079	+	0.661349i	$0.230016\pi$
$398$	−0.459885	+	3.19857i	−0.0230520	+	0.160330i
$399$	−8.32521	+	2.44450i	−0.416782	+	0.122378i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−5.01036	−	34.8478i	−0.250205	−	1.74022i	−0.596970	−	0.802264i	$-0.703629\pi$
$401$	−5.01036	−	34.8478i	−0.250205	−	1.74022i	0.346764	−	0.937952i	$-0.387280\pi$
$402$	2.30217	+	5.04105i	0.114822	+	0.251425i
$403$	0.761293	+	1.66700i	0.0379227	+	0.0830391i
$404$	−1.99199	−	13.8546i	−0.0991050	−	0.689290i
$405$	0.841254	+	0.540641i	0.0418022	+	0.0268647i
$406$	−6.96566	+	2.04530i	−0.345700	+	0.101507i
$407$	−0.446688	+	3.10678i	−0.0221415	+	0.153997i
$408$	4.35615	−	5.02726i	0.215661	−	0.248887i
$409$	−15.6714	+	10.0714i	−0.774900	+	0.497998i	−0.867338	−	0.497720i	$-0.834171\pi$
$409$	−15.6714	+	10.0714i	−0.774900	+	0.497998i	0.0924374	+	0.995719i	$0.470534\pi$
$410$	0.0829588	+	0.0957395i	0.00409704	+	0.00472824i
$411$	−11.5435	−	3.38948i	−0.569400	−	0.167191i
$412$	−1.92169	+	4.20791i	−0.0946749	+	0.207309i
$413$	9.55291			0.470068
$414$	−4.77143	−	0.483179i	−0.234503	−	0.0237469i
$415$	6.73365			0.330542
$416$	0.348032	−	0.762084i	0.0170637	−	0.0373642i
$417$	4.07600	+	1.19682i	0.199603	+	0.0586087i
$418$	14.1855	+	16.3710i	0.693838	+	0.800731i
$419$	23.3553	−	15.0096i	1.14098	−	0.733265i	0.173159	−	0.984894i	$-0.444603\pi$
$419$	23.3553	−	15.0096i	1.14098	−	0.733265i	0.967824	+	0.251629i	$0.0809663\pi$
$420$	−0.868674	+	1.00250i	−0.0423869	+	0.0489171i
$421$	3.62561	−	25.2167i	0.176702	−	1.22899i	−0.687629	−	0.726062i	$-0.741348\pi$
$421$	3.62561	−	25.2167i	0.176702	−	1.22899i	0.864331	−	0.502924i	$-0.167742\pi$
$422$	−21.3165	+	6.25909i	−1.03767	+	0.304688i
$423$	6.18734	+	3.97636i	0.300839	+	0.193337i
$424$	1.08325	+	7.53417i	0.0526073	+	0.365892i
$425$	−2.76335	−	6.05089i	−0.134042	−	0.293511i
$426$	−3.19536	−	6.99686i	−0.154816	−	0.338999i
$427$	−2.68692	−	18.6879i	−0.130029	−	0.904373i
$428$	−11.1581	−	7.17085i	−0.539345	−	0.346616i
$429$	2.66213	−	0.781673i	0.128529	−	0.0377395i
$430$	−0.276787	+	1.92510i	−0.0133479	+	0.0928364i
$431$	14.4668	−	16.6956i	0.696842	−	0.804198i	−0.291481	−	0.956577i	$-0.594148\pi$
$431$	14.4668	−	16.6956i	0.696842	−	0.804198i	0.988322	+	0.152379i	$0.0486933\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	5.94939	+	6.86596i	0.285909	+	0.329957i	0.880477	−	0.474089i	$-0.157222\pi$
$433$	5.94939	+	6.86596i	0.285909	+	0.329957i	−0.594568	+	0.804045i	$0.702677\pi$
$434$	−2.78408	−	0.817481i	−0.133640	−	0.0392403i
$435$	2.27350	−	4.97827i	0.109006	−	0.238690i
$436$	6.89977			0.330439
$437$	1.31334	+	31.3421i	0.0628253	+	1.49930i
$438$	10.0308			0.479288
$439$	−7.93377	+	17.3725i	−0.378658	+	0.829145i	0.620337	+	0.784335i	$0.286996\pi$
$439$	−7.93377	+	17.3725i	−0.378658	+	0.829145i	−0.998996	+	0.0448104i	$0.985732\pi$
$440$	3.17756	+	0.933014i	0.151484	+	0.0444797i
$441$	3.43173	+	3.96042i	0.163416	+	0.188592i
$442$	−4.68832	+	3.01300i	−0.223001	+	0.143314i
$443$	−1.23947	+	1.43042i	−0.0588890	+	0.0679615i	−0.784430	−	0.620218i	$-0.787044\pi$
$443$	−1.23947	+	1.43042i	−0.0588890	+	0.0679615i	0.725541	+	0.688179i	$0.241590\pi$
$444$	0.134882	−	0.938122i	0.00640120	−	0.0445213i
$445$	17.0069	−	4.99368i	0.806204	−	0.236723i
$446$	3.59167	+	2.30822i	0.170070	+	0.109298i
$447$	−2.42024	−	16.8331i	−0.114473	−	0.796179i
$448$	0.551049	+	1.20663i	0.0260346	+	0.0570078i
$449$	−9.96793	−	21.8267i	−0.470416	−	1.03007i	−0.984989	−	0.172620i	$-0.944777\pi$
$449$	−9.96793	−	21.8267i	−0.470416	−	1.03007i	0.514573	−	0.857447i	$-0.327950\pi$
$450$	−0.142315	−	0.989821i	−0.00670879	−	0.0466606i
$451$	0.352932	+	0.226816i	0.0166189	+	0.0106803i
$452$	−3.87476	+	1.13773i	−0.182253	+	0.0535144i
$453$	−1.66829	+	11.6032i	−0.0783832	+	0.545167i
$454$	16.6886	−	19.2597i	0.783234	−	0.903900i
$455$	0.934914	−	0.600833i	0.0438294	−	0.0281675i
$456$	−4.28346	−	4.94338i	−0.200591	−	0.231495i
$457$	−0.785138	−	0.230537i	−0.0367272	−	0.0107841i	0.263317	−	0.964709i	$-0.415183\pi$
$457$	−0.785138	−	0.230537i	−0.0367272	−	0.0107841i	−0.300045	+	0.953925i	$0.597002\pi$
$458$	−10.1775	+	22.2856i	−0.475564	+	1.04134i
$459$	−6.65202			−0.310490
$460$	2.75946	+	3.92242i	0.128660	+	0.182884i
$461$	−23.9880			−1.11723			−0.558617	−	0.829426i	$-0.688668\pi$
$461$	−23.9880			−1.11723			−0.558617	+	0.829426i	$0.688668\pi$
$462$	−1.82491	+	3.99599i	−0.0849025	+	0.185911i
$463$	−22.1134	−	6.49309i	−1.02770	−	0.301759i	−0.275923	−	0.961180i	$-0.588984\pi$
$463$	−22.1134	−	6.49309i	−1.02770	−	0.301759i	−0.751775	+	0.659420i	$0.770802\pi$
$464$	−3.58395	−	4.13609i	−0.166381	−	0.192013i
$465$	1.84018	−	1.18261i	0.0853362	−	0.0548422i
$466$	−12.7041	+	14.6613i	−0.588507	+	0.679173i
$467$	5.27018	−	36.6549i	0.243875	−	1.69619i	−0.388440	−	0.921474i	$-0.626986\pi$
$467$	5.27018	−	36.6549i	0.243875	−	1.69619i	0.632314	−	0.774712i	$-0.282105\pi$
$468$	−0.803857	+	0.236034i	−0.0371583	+	0.0109107i
$469$	6.18430	+	3.97441i	0.285564	+	0.183521i
$470$	−1.04671	−	7.28005i	−0.0482813	−	0.335804i
$471$	−4.17345	−	9.13857i	−0.192302	−	0.421083i
$472$	2.99165	+	6.55079i	0.137702	+	0.301525i
$473$	0.916637	+	6.37535i	0.0421470	+	0.293139i
$474$	−0.572119	−	0.367678i	−0.0262783	−	0.0168880i
$475$	−6.27607	+	1.84282i	−0.287966	+	0.0845544i
$476$	1.25577	−	8.73410i	0.0575583	−	0.400327i
$477$	4.98457	−	5.75250i	0.228228	−	0.263389i
$478$	5.99817	−	3.85479i	0.274350	−	0.176314i
$479$	−7.65346	−	8.83257i	−0.349696	−	0.403570i	0.553465	−	0.832872i	$-0.313305\pi$
$479$	−7.65346	−	8.83257i	−0.349696	−	0.403570i	−0.903161	+	0.429302i	$0.858760\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−0.329854	+	0.722279i	−0.0150400	+	0.0329331i
$482$	13.1012			0.596742
$483$	−5.67107	+	2.88269i	−0.258043	+	0.131167i
$484$	−0.0326251			−0.00148296
$485$	4.99944	−	10.9472i	0.227013	−	0.497089i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	15.3412	+	17.7047i	0.695176	+	0.802276i	0.988092	−	0.153862i	$-0.0491711\pi$
$487$	15.3412	+	17.7047i	0.695176	+	0.802276i	−0.292916	+	0.956138i	$0.594626\pi$
$488$	11.9736	−	7.69494i	0.542018	−	0.348334i
$489$	10.7452	−	12.4007i	0.485917	−	0.560778i
$490$	0.745786	−	5.18705i	0.0336912	−	0.234327i
$491$	17.6563	−	5.18435i	0.796816	−	0.233966i	0.142111	−	0.989851i	$-0.454611\pi$
$491$	17.6563	−	5.18435i	0.796816	−	0.233966i	0.654705	+	0.755884i	$0.272793\pi$
$492$	−0.106571	−	0.0684892i	−0.00480461	−	0.00308773i
$493$	5.18103	+	36.0349i	0.233342	+	1.62293i
$494$	2.27648	+	4.98481i	0.102424	+	0.224277i
$495$	−1.37573	−	3.01243i	−0.0618345	−	0.135399i
$496$	−0.311303	−	2.16516i	−0.0139779	−	0.0972185i
$497$	−8.58366	−	5.51638i	−0.385030	−	0.247444i
$498$	−6.46089	+	1.89709i	−0.289519	+	0.0850105i
$499$	−1.16786	+	8.12261i	−0.0522804	+	0.363618i	0.946841	+	0.321703i	$0.104255\pi$
$499$	−1.16786	+	8.12261i	−0.0522804	+	0.363618i	−0.999121	+	0.0419155i	$0.986654\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	1.18302	−	0.760281i	0.0528534	−	0.0339668i
$502$	19.1872	+	22.1433i	0.856369	+	0.988302i
$503$	17.2071	+	5.05246i	0.767226	+	0.225278i	0.641849	−	0.766831i	$-0.278168\pi$
$503$	17.2071	+	5.05246i	0.767226	+	0.225278i	0.125377	+	0.992109i	$0.459986\pi$
$504$	0.551049	−	1.20663i	0.0245457	−	0.0537475i
$505$	13.9970			0.622860
$506$	12.4280	+	9.88909i	0.552492	+	0.439624i
$507$	−12.2981			−0.546178
$508$	1.72031	−	3.76695i	0.0763264	−	0.167131i
$509$	−4.43398	−	1.30194i	−0.196533	−	0.0577073i	0.181985	−	0.983301i	$-0.441748\pi$
$509$	−4.43398	−	1.30194i	−0.196533	−	0.0577073i	−0.378518	+	0.925594i	$0.623566\pi$
$510$	4.35615	+	5.02726i	0.192893	+	0.222611i
$511$	11.1936	−	7.19367i	0.495174	−	0.318229i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−0.930885	+	6.47445i	−0.0410996	+	0.285854i
$514$	−5.26763	+	1.54672i	−0.232345	+	0.0682228i
$515$	−3.89160	−	2.50098i	−0.171484	−	0.110206i
$516$	−0.276787	−	1.92510i	−0.0121849	−	0.0847477i
$517$	−10.1184	−	22.1562i	−0.445006	−	0.974427i
$518$	−0.522267	−	1.14361i	−0.0229471	−	0.0502471i
$519$	0.0747648	+	0.520001i	0.00328181	+	0.0228255i
$520$	0.704797	+	0.452945i	0.0309074	+	0.0198630i
$521$	−4.99662	+	1.46714i	−0.218906	+	0.0642766i	−0.389347	−	0.921091i	$-0.627299\pi$
$521$	−4.99662	+	1.46714i	−0.218906	+	0.0642766i	0.170440	+	0.985368i	$0.445481\pi$
$522$	−0.778866	+	5.41713i	−0.0340900	+	0.237101i
$523$	15.1080	−	17.4355i	0.660626	−	0.762403i	−0.322254	−	0.946653i	$-0.604440\pi$
$523$	15.1080	−	17.4355i	0.660626	−	0.762403i	0.982879	+	0.184251i	$0.0589858\pi$
$524$	6.19882	−	3.98374i	0.270797	−	0.174030i
$525$	−0.868674	−	1.00250i	−0.0379120	−	0.0437528i
$526$	11.2861	+	3.31390i	0.492098	+	0.144493i
$527$	−6.04461	+	13.2359i	−0.263307	+	0.576563i
$528$	−3.31170			−0.144123
$529$	5.16635	+	22.4122i	0.224624	+	0.974446i
$530$	−7.61165			−0.330629
$531$	2.99165	−	6.55079i	0.129826	−	0.284280i
$532$	−8.32521	−	2.44450i	−0.360944	−	0.105983i
$533$	0.0695023	+	0.0802099i	0.00301048	+	0.00347428i
$534$	−14.9111	+	9.58279i	−0.645267	+	0.414688i
$535$	8.68582	−	10.0240i	0.375521	−	0.433374i
$536$	−0.788689	+	5.48545i	−0.0340662	+	0.236935i
$537$	5.38711	−	1.58180i	0.232471	−	0.0682596i
$538$	−25.6697	−	16.4969i	−1.10670	−	0.711233i
$539$	−2.46982	−	17.1780i	−0.106383	−	0.739908i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	−5.35319	−	11.7219i	−0.230152	−	0.503962i	0.758958	−	0.651139i	$-0.225709\pi$
$541$	−5.35319	−	11.7219i	−0.230152	−	0.503962i	−0.989110	+	0.147177i	$0.952981\pi$
$542$	0.324638	+	2.25791i	0.0139444	+	0.0969854i
$543$	4.16866	+	2.67903i	0.178894	+	0.114968i
$544$	6.38257	−	1.87409i	0.273650	−	0.0803510i
$545$	−0.981940	+	6.82954i	−0.0420617	+	0.292545i
$546$	−0.727769	+	0.839890i	−0.0311456	+	0.0359440i
$547$	−1.94908	+	1.25259i	−0.0833365	+	0.0535571i	−0.581645	−	0.813442i	$-0.697591\pi$
$547$	−1.94908	+	1.25259i	−0.0833365	+	0.0535571i	0.498309	+	0.867000i	$0.333955\pi$
$548$	−7.87853	−	9.09231i	−0.336554	−	0.388404i
$549$	−13.6565	−	4.00990i	−0.582844	−	0.171138i
$550$	−1.37573	+	3.01243i	−0.0586614	+	0.128450i
$551$	35.7980			1.52504
$552$	−3.75276	−	2.98611i	−0.159728	−	0.127097i
$553$	−0.902126			−0.0383623
$554$	5.38356	−	11.7883i	0.228725	−	0.500839i
$555$	0.909378	+	0.267017i	0.0386009	+	0.0113343i
$556$	2.78190	+	3.21049i	0.117979	+	0.136155i
$557$	0.726261	−	0.466739i	0.0307727	−	0.0197764i	−0.525164	−	0.851001i	$-0.675996\pi$
$557$	0.726261	−	0.466739i	0.0307727	−	0.0197764i	0.555937	+	0.831225i	$0.312360\pi$
$558$	−1.43246	+	1.65314i	−0.0606408	+	0.0699832i
$559$	−0.231890	+	1.61283i	−0.00980792	+	0.0682156i
$560$	−1.27277	+	0.373719i	−0.0537843	+	0.0157925i
$561$	18.5324	+	11.9101i	0.782439	+	0.502843i
$562$	−0.725976	−	5.04928i	−0.0306235	−	0.212991i
$563$	−14.1812	−	31.0525i	−0.597667	−	1.30871i	−0.930697	−	0.365791i	$-0.880798\pi$
$563$	−14.1812	−	31.0525i	−0.597667	−	1.30871i	0.333030	−	0.942916i	$-0.391929\pi$
$564$	3.05534	+	6.69026i	0.128653	+	0.281711i
$565$	−0.574716	−	3.99724i	−0.0241785	−	0.168165i
$566$	10.0391	+	6.45174i	0.421975	+	0.271187i
$567$	−1.27277	+	0.373719i	−0.0534513	+	0.0156947i
$568$	1.09468	−	7.61368i	0.0459318	−	0.319463i
$569$	16.4640	−	19.0004i	0.690205	−	0.796540i	−0.297189	−	0.954819i	$-0.596049\pi$
$569$	16.4640	−	19.0004i	0.690205	−	0.796540i	0.987394	+	0.158279i	$0.0505946\pi$
$570$	5.50266	−	3.53634i	0.230481	−	0.148121i
$571$	6.02376	+	6.95179i	0.252087	+	0.290924i	0.867662	−	0.497154i	$-0.165622\pi$
$571$	6.02376	+	6.95179i	0.252087	+	0.290924i	−0.615575	+	0.788078i	$0.711076\pi$
$572$	2.66213	+	0.781673i	0.111309	+	0.0326834i
$573$	−6.62058	+	14.4971i	−0.276579	+	0.605623i
$574$	−0.168043			−0.00701399
$575$	−4.27521	+	2.17315i	−0.178289	+	0.0906268i
$576$	1.00000			0.0416667
$577$	−17.1398	+	37.5309i	−0.713538	+	1.56243i	0.109207	+	0.994019i	$0.465169\pi$
$577$	−17.1398	+	37.5309i	−0.713538	+	1.56243i	−0.822745	+	0.568411i	$0.807558\pi$
$578$	−26.1456	−	7.67704i	−1.08751	−	0.319323i
$579$	−15.3602	−	17.7266i	−0.638347	−	0.736692i
$580$	4.60404	−	2.95884i	0.191173	−	0.122859i
$581$	−5.84934	+	6.75050i	−0.242672	+	0.280058i
$582$	−1.71273	+	11.9123i	−0.0709950	+	0.493781i
$583$	−24.1864	+	7.10178i	−1.00170	+	0.294126i
$584$	8.43841	+	5.42304i	0.349184	+	0.224407i
$585$	−0.119230	−	0.829266i	−0.00492957	−	0.0342859i
$586$	−0.480102	−	1.05128i	−0.0198328	−	0.0434278i
$587$	8.90200	+	19.4927i	0.367425	+	0.804549i	0.999559	+	0.0296896i	$0.00945189\pi$
$587$	8.90200	+	19.4927i	0.367425	+	0.804549i	−0.632134	+	0.774859i	$0.717821\pi$
$588$	0.745786	+	5.18705i	0.0307557	+	0.213910i
$589$	12.0366	+	7.73548i	0.495961	+	0.318735i
$590$	−6.90987	+	2.02892i	−0.284475	+	0.0835293i
$591$	−3.30089	+	22.9582i	−0.135780	+	0.944373i
$592$	0.620657	−	0.716276i	0.0255088	−	0.0294388i
$593$	0.576131	−	0.370257i	0.0236588	−	0.0152046i	−0.528758	−	0.848773i	$-0.677342\pi$
$593$	0.576131	−	0.370257i	0.0236588	−	0.0152046i	0.552417	+	0.833568i	$0.313706\pi$
$594$	2.16870	+	2.50282i	0.0889830	+	0.102692i
$595$	8.46649	+	2.48598i	0.347092	+	0.101915i
$596$	7.06463	−	15.4694i	0.289379	−	0.633651i
$597$	3.23146			0.132255
$598$	2.31186	+	3.28618i	0.0945388	+	0.134382i
$599$	44.7482			1.82836			0.914180	−	0.405307i	$-0.132835\pi$
$599$	44.7482			1.82836			0.914180	+	0.405307i	$0.132835\pi$
$600$	0.415415	−	0.909632i	0.0169592	−	0.0371356i
$601$	30.7334	+	9.02413i	1.25364	+	0.368102i	0.840124	−	0.542395i	$-0.182482\pi$
$601$	30.7334	+	9.02413i	1.25364	+	0.368102i	0.413516	+	0.910497i	$0.364301\pi$
$602$	−1.68948	−	1.94976i	−0.0688580	−	0.0794664i
$603$	4.66211	−	2.99616i	0.189856	−	0.122013i
$604$	−7.67663	+	8.85930i	−0.312358	+	0.360480i
$605$	0.00464304	−	0.0322930i	0.000188766	−	0.00131290i
$606$	−13.4301	+	3.94342i	−0.545559	+	0.160191i
$607$	5.12186	+	3.29162i	0.207890	+	0.133603i	0.640443	−	0.768006i	$-0.278751\pi$
$607$	5.12186	+	3.29162i	0.207890	+	0.133603i	−0.432553	+	0.901609i	$0.642387\pi$
$608$	−0.930885	−	6.47445i	−0.0377524	−	0.262573i
$609$	3.01580	+	6.60368i	0.122206	+	0.267595i
$610$	5.91260	+	12.9468i	0.239394	+	0.524201i
$611$	−0.876929	−	6.09917i	−0.0354767	−	0.246746i
$612$	−5.59604	−	3.59635i	−0.226206	−	0.145374i
$613$	18.6274	−	5.46950i	0.752353	−	0.220911i	0.116999	−	0.993132i	$-0.462672\pi$
$613$	18.6274	−	5.46950i	0.752353	−	0.220911i	0.635354	+	0.772221i	$0.280854\pi$
$614$	−0.274453	+	1.90886i	−0.0110760	+	0.0770354i
$615$	0.0829588	−	0.0957395i	0.00334522	−	0.00386059i
$616$	−3.69561	+	2.37502i	−0.148900	+	0.0956925i
$617$	−23.2722	−	26.8576i	−0.936904	−	1.08124i	−0.996547	−	0.0830252i	$-0.973542\pi$
$617$	−23.2722	−	26.8576i	−0.936904	−	1.08124i	0.0596433	−	0.998220i	$-0.481004\pi$
$618$	4.43857	+	1.30328i	0.178545	+	0.0524257i
$619$	−5.51382	+	12.0736i	−0.221619	+	0.485278i	−0.987483	−	0.157724i	$-0.949584\pi$
$619$	−5.51382	+	12.0736i	−0.221619	+	0.485278i	0.765864	+	0.643003i	$0.222312\pi$
$620$	2.18742			0.0878490
$621$	0.200784	+	4.79163i	0.00805720	+	0.192281i
$622$	11.3965			0.456957
$623$	−9.76727	+	21.3873i	−0.391318	+	0.856866i
$624$	−0.803857	−	0.236034i	−0.0321800	−	0.00944891i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	20.9187	−	13.4437i	0.836081	−	0.537317i
$627$	14.1855	−	16.3710i	0.566516	−	0.653794i
$628$	1.42976	−	9.94419i	0.0570536	−	0.396816i
$629$	−6.04920	+	1.77621i	−0.241197	+	0.0708219i
$630$	1.11592	+	0.717161i	0.0444595	+	0.0285724i
$631$	0.598173	+	4.16038i	0.0238129	+	0.165622i	0.998258	−	0.0590048i	$-0.0187927\pi$
$631$	0.598173	+	4.16038i	0.0238129	+	0.165622i	−0.974445	+	0.224627i	$0.927884\pi$
$632$	−0.282515	−	0.618621i	−0.0112378	−	0.0246074i
$633$	9.22904	+	20.2088i	0.366822	+	0.803227i
$634$	2.97323	+	20.6793i	0.118082	+	0.821280i
$635$	3.48378	+	2.23889i	0.138250	+	0.0888477i
$636$	7.30332	−	2.14445i	0.289596	−	0.0850329i
$637$	0.624814	−	4.34568i	0.0247560	−	0.172182i
$638$	11.8690	−	13.6975i	0.469897	−	0.542290i
$639$	−6.47090	+	4.15859i	−0.255985	+	0.164511i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	24.4631	+	7.18301i	0.966234	+	0.283712i	0.726531	−	0.687134i	$-0.241131\pi$
$641$	24.4631	+	7.18301i	0.966234	+	0.283712i	0.239704	+	0.970846i	$0.422950\pi$
$642$	−5.50991	+	12.0650i	−0.217459	+	0.476168i
$643$	28.7862			1.13522			0.567608	−	0.823299i	$-0.307869\pi$
$643$	28.7862			1.13522			0.567608	+	0.823299i	$0.307869\pi$
$644$	−6.32931	−	0.640938i	−0.249410	−	0.0252565i
$645$	1.94489			0.0765801
$646$	−18.0751	+	39.5790i	−0.711157	+	1.55722i
$647$	18.5223	+	5.43864i	0.728187	+	0.213815i	0.624754	−	0.780821i	$-0.285199\pi$
$647$	18.5223	+	5.43864i	0.728187	+	0.213815i	0.103433	+	0.994636i	$0.467017\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	−20.0635	+	12.8940i	−0.787560	+	0.506134i
$650$	−0.548638	+	0.633162i	−0.0215193	+	0.0248347i
$651$	−0.412944	+	2.87209i	−0.0161845	+	0.112566i
$652$	15.7438	−	4.62279i	0.616574	−	0.181042i
$653$	−24.6848	−	15.8639i	−0.965989	−	0.620803i	−0.0403398	−	0.999186i	$-0.512844\pi$
$653$	−24.6848	−	15.8639i	−0.965989	−	0.620803i	−0.925649	+	0.378383i	$0.876480\pi$
$654$	−0.981940	−	6.82954i	−0.0383969	−	0.267056i
$655$	3.06101	+	6.70267i	0.119603	+	0.261895i
$656$	−0.0526254	−	0.115234i	−0.00205468	−	0.00449912i
$657$	−1.42753	−	9.92866i	−0.0556931	−	0.387354i
$658$	8.20752	+	5.27465i	0.319963	+	0.205627i
$659$	−23.0140	+	6.75753i	−0.896499	+	0.263236i	−0.697348	−	0.716733i	$-0.745637\pi$
$659$	−23.0140	+	6.75753i	−0.896499	+	0.263236i	−0.199151	+	0.979969i	$0.563819\pi$
$660$	0.471304	−	3.27799i	0.0183455	−	0.127596i
$661$	29.2218	−	33.7237i	1.13659	−	1.31170i	0.192773	−	0.981243i	$-0.438252\pi$
$661$	29.2218	−	33.7237i	1.13659	−	1.31170i	0.943821	−	0.330457i	$-0.107203\pi$
$662$	9.01534	−	5.79381i	0.350391	−	0.225183i
$663$	3.64955	+	4.21181i	0.141737	+	0.163573i
$664$	−6.46089	−	1.89709i	−0.250731	−	0.0736213i
$665$	3.60442	−	7.89259i	0.139774	−	0.306061i
$666$	−0.947769			−0.0367253
$667$	25.8005	−	4.81971i	0.998999	−	0.186620i
$668$	1.40626			0.0544098
$669$	1.77358	−	3.88360i	0.0685706	−	0.150149i
$670$	−5.31738	−	1.56132i	−0.205428	−	0.0603191i
$671$	30.8672	+	35.6226i	1.19161	+	1.37520i
$672$	1.11592	−	0.717161i	0.0430477	−	0.0276651i
$673$	7.67888	−	8.86191i	0.295999	−	0.341601i	−0.588196	−	0.808718i	$-0.700162\pi$
$673$	7.67888	−	8.86191i	0.295999	−	0.341601i	0.884196	+	0.467117i	$0.154707\pi$
$674$	−3.61426	+	25.1377i	−0.139216	+	0.968268i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−10.3458	−	6.64886i	−0.397916	−	0.255725i
$677$	−0.339063	−	2.35823i	−0.0130312	−	0.0906343i	0.982268	−	0.187483i	$-0.0600329\pi$
$677$	−0.339063	−	2.35823i	−0.0130312	−	0.0906343i	−0.995299	+	0.0968485i	$0.969124\pi$
$678$	1.67759	+	3.67341i	0.0644274	+	0.141076i
$679$	6.63177	+	14.5215i	0.254504	+	0.557286i
$680$	0.946681	+	6.58431i	0.0363036	+	0.252497i
$681$	−21.4386	−	13.7778i	−0.821531	−	0.527966i
$682$	6.95066	−	2.04090i	0.266154	−	0.0781500i
$683$	4.61383	−	32.0899i	0.176543	−	1.22789i	−0.688144	−	0.725574i	$-0.741574\pi$
$683$	4.61383	−	32.0899i	0.176543	−	1.22789i	0.864687	−	0.502311i	$-0.167517\pi$
$684$	−4.28346	+	4.94338i	−0.163782	+	0.189015i
$685$	10.1210	−	6.50437i	0.386703	−	0.248519i
$686$	10.6329	+	12.2710i	0.405966	+	0.468510i
$687$	23.5072	+	6.90234i	0.896856	+	0.263341i
$688$	0.807938	−	1.76914i	0.0308023	−	0.0674477i
$689$	−6.37699			−0.242944
$690$	3.48978	−	3.28959i	0.132854	−	0.125233i
$691$	24.4378			0.929657			0.464828	−	0.885401i	$-0.346116\pi$
$691$	24.4378			0.929657			0.464828	+	0.885401i	$0.346116\pi$
$692$	−0.218237	+	0.477873i	−0.00829614	+	0.0181660i
$693$	4.21503	+	1.23765i	0.160116	+	0.0470143i
$694$	−20.7641	−	23.9631i	−0.788195	−	0.909625i
$695$	−3.57371	+	2.29669i	−0.135559	+	0.0871183i
$696$	−3.58395	+	4.13609i	−0.135849	+	0.156778i
$697$	−0.119927	+	0.834111i	−0.00454256	+	0.0315942i
$698$	12.5767	−	3.69285i	0.476035	−	0.139776i
$699$	16.3201	+	10.4883i	0.617283	+	0.396703i
$700$	−0.188781	−	1.31300i	−0.00713525	−	0.0496267i
$701$	2.76501	+	6.05453i	0.104433	+	0.228676i	0.954634	−	0.297782i	$-0.0962468\pi$
$701$	2.76501	+	6.05453i	0.104433	+	0.228676i	−0.850201	+	0.526458i	$0.823520\pi$
$702$	0.348032	+	0.762084i	0.0131356	+	0.0287630i
$703$	0.882264	+	6.13628i	0.0332752	+	0.231434i
$704$	−2.78598	−	1.79044i	−0.105001	−	0.0674798i
$705$	−7.05698	+	2.07212i	−0.265781	+	0.0780405i
$706$	−1.81326	+	12.6115i	−0.0682428	+	0.474639i
$707$	−12.1589	+	14.0321i	−0.457281	+	0.527730i
$708$	6.05836	−	3.89347i	0.227687	−	0.146326i
$709$	−6.66346	−	7.69004i	−0.250251	−	0.288806i	0.616700	−	0.787198i	$-0.288469\pi$
$709$	−6.66346	−	7.69004i	−0.250251	−	0.288806i	−0.866951	+	0.498393i	$0.833924\pi$
$710$	7.38039	+	2.16708i	0.276981	+	0.0813290i
$711$	−0.282515	+	0.618621i	−0.0105951	+	0.0232001i
$712$	−17.7249			−0.664268
$713$	9.71659	+	3.95458i	0.363889	+	0.148100i
$714$	−8.82392			−0.330227
$715$	−1.15258	+	2.52379i	−0.0431040	+	0.0943846i
$716$	5.38711	+	1.58180i	0.201326	+	0.0591146i
$717$	−4.66918	−	5.38853i	−0.174374	−	0.201238i
$718$	−9.51841	+	6.11711i	−0.355224	+	0.228288i
$719$	−22.3379	+	25.7793i	−0.833063	+	0.961406i	−0.999697	−	0.0246129i	$-0.992165\pi$
$719$	−22.3379	+	25.7793i	−0.833063	+	0.961406i	0.166634	+	0.986019i	$0.446710\pi$
$720$	−0.142315	+	0.989821i	−0.00530376	+	0.0368885i
$721$	5.88777	−	1.72881i	0.219272	−	0.0643841i
$722$	20.0092	+	12.8591i	0.744666	+	0.478568i
$723$	−1.86449	−	12.9678i	−0.0693411	−	0.482278i
$724$	2.05850	+	4.50749i	0.0765036	+	0.167520i
$725$	2.27350	+	4.97827i	0.0844356	+	0.184888i
$726$	0.00464304	+	0.0322930i	0.000172319	+	0.00119851i
$727$	−31.4906	−	20.2378i	−1.16792	−	0.750578i	−0.194794	−	0.980844i	$-0.562404\pi$
$727$	−31.4906	−	20.2378i	−1.16792	−	0.750578i	−0.973128	+	0.230266i	$0.926040\pi$
$728$	−1.06632	+	0.313099i	−0.0395204	+	0.0116042i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−6.56875	+	7.58074i	−0.243120	+	0.280576i
$731$	−10.8837	+	6.99452i	−0.402548	+	0.258702i
$732$	−9.32064	−	10.7566i	−0.344501	−	0.397575i
$733$	−8.78058	−	2.57821i	−0.324318	−	0.0952284i	0.115521	−	0.993305i	$-0.463146\pi$
$733$	−8.78058	−	2.57821i	−0.324318	−	0.0952284i	−0.439839	+	0.898077i	$0.644964\pi$
$734$	2.24897	−	4.92456i	0.0830110	−	0.181769i
$735$	−5.24039			−0.193295
$736$	−1.54261	−	4.54096i	−0.0568613	−	0.167382i
$737$	−18.3530			−0.676041
$738$	−0.0526254	+	0.115234i	−0.00193717	+	0.00424181i
$739$	−47.2710	−	13.8800i	−1.73889	−	0.510584i	−0.750285	−	0.661114i	$-0.770084\pi$
$739$	−47.2710	−	13.8800i	−1.73889	−	0.510584i	−0.988605	+	0.150530i	$0.951902\pi$
$740$	0.620657	+	0.716276i	0.0228158	+	0.0263308i
$741$	4.61009	−	2.96273i	0.169356	−	0.108838i
$742$	6.61204	−	7.63070i	0.242736	−	0.280132i
$743$	−4.88079	+	33.9466i	−0.179059	+	1.24538i	0.679888	+	0.733316i	$0.262028\pi$
$743$	−4.88079	+	33.9466i	−0.179059	+	1.24538i	−0.858947	+	0.512065i	$0.828881\pi$
$744$	−2.09882	+	0.616268i	−0.0769464	+	0.0225935i
$745$	14.3065	+	9.19425i	0.524151	+	0.336851i
$746$	−4.93674	−	34.3358i	−0.180747	−	1.25712i
$747$	2.79726	+	6.12514i	0.102346	+	0.224107i
$748$	9.15139	+	20.0388i	0.334608	+	0.732689i
$749$	2.50392	+	17.4151i	0.0914912	+	0.636335i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	42.6065	−	12.5104i	1.55473	−	0.456511i	0.612222	−	0.790686i	$-0.290276\pi$
$751$	42.6065	−	12.5104i	1.55473	−	0.456511i	0.942511	+	0.334175i	$0.108458\pi$
$752$	−1.04671	+	7.28005i	−0.0381697	+	0.265476i
$753$	19.1872	−	22.1433i	0.699222	−	0.806945i
$754$	3.85724	−	2.47890i	0.140472	−	0.0902761i
$755$	−7.67663	−	8.85930i	−0.279381	−	0.322423i
$756$	−1.27277	−	0.373719i	−0.0462902	−	0.0135920i
$757$	−1.20108	+	2.62999i	−0.0436538	+	0.0955885i	−0.930202	−	0.367047i	$-0.880369\pi$
$757$	−1.20108	+	2.62999i	−0.0436538	+	0.0955885i	0.886549	+	0.462635i	$0.153096\pi$
$758$	−12.4007			−0.450414
$759$	8.01975	−	13.7089i	0.291098	−	0.497601i
$760$	6.54102			0.237268
$761$	−9.17197	+	20.0838i	−0.332484	+	0.728038i	−0.999861	−	0.0166820i	$-0.994690\pi$
$761$	−9.17197	+	20.0838i	−0.332484	+	0.728038i	0.667377	+	0.744720i	$0.267417\pi$
$762$	−3.97343	−	1.16671i	−0.143942	−	0.0422653i
$763$	−5.99365	−	6.91704i	−0.216985	−	0.250414i
$764$	−13.4073	+	8.61634i	−0.485059	+	0.311728i
$765$	4.35615	−	5.02726i	0.157497	−	0.181761i
$766$	−1.93796	+	13.4788i	−0.0700214	+	0.487009i
$767$	−5.78904	+	1.69982i	−0.209030	+	0.0613768i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	3.84871	+	26.7684i	0.138788	+	0.965293i	0.933569	+	0.358397i	$0.116677\pi$
$769$	3.84871	+	26.7684i	0.138788	+	0.965293i	−0.794781	+	0.606896i	$0.792414\pi$
$770$	−1.82491	−	3.99599i	−0.0657652	−	0.144006i
$771$	2.28064	+	4.99390i	0.0821351	+	0.179851i
$772$	−3.33808	−	23.2169i	−0.120140	−	0.835594i
$773$	−9.72527	−	6.25005i	−0.349794	−	0.224799i	0.353931	−	0.935272i	$-0.384845\pi$
$773$	−9.72527	−	6.25005i	−0.349794	−	0.224799i	−0.703725	+	0.710473i	$0.748481\pi$
$774$	−1.86611	+	0.547940i	−0.0670760	+	0.0196953i
$775$	−0.311303	+	2.16516i	−0.0111823	+	0.0777748i
$776$	−7.88113	+	9.09530i	−0.282916	+	0.326502i
$777$	−1.05764	+	0.679703i	−0.0379426	+	0.0243842i
$778$	16.7167	+	19.2921i	0.599321	+	0.691654i
$779$	0.795062	+	0.233451i	0.0284860	+	0.00836426i
$780$	0.348032	−	0.762084i	0.0124615	−	0.0272870i
$781$	25.4735			0.911514
$782$	−7.69842	+	30.9592i	−0.275295	+	1.10710i
$783$	5.47284			0.195583
$784$	−2.17694	+	4.76683i	−0.0777478	+	0.170244i
$785$	9.63950	+	2.83041i	0.344048	+	0.101022i
$786$	−4.82537	−	5.56878i	−0.172115	−	0.198632i
$787$	−14.6707	+	9.42830i	−0.522955	+	0.336082i	−0.775340	−	0.631544i	$-0.782421\pi$
$787$	−14.6707	+	9.42830i	−0.522955	+	0.336082i	0.252385	+	0.967627i	$0.418785\pi$
$788$	−15.1890	+	17.5291i	−0.541086	+	0.624447i
$789$	1.67399	−	11.6429i	0.0595956	−	0.414497i
$790$	0.652531	−	0.191600i	0.0232160	−	0.00681683i
$791$	4.50649	+	2.89614i	0.160232	+	0.102975i
$792$	0.471304	+	3.27799i	0.0167471	+	0.116478i
$793$	4.95354	+	10.8467i	0.175905	+	0.385179i
$794$	0.142647	+	0.312353i	0.00506234	+	0.0110850i
$795$	1.08325	+	7.53417i	0.0384189	+	0.267210i
$796$	2.71848	+	1.74706i	0.0963540	+	0.0619230i
$797$	37.4048	−	10.9830i	1.32494	−	0.389039i	0.458670	−	0.888607i	$-0.348326\pi$
$797$	37.4048	−	10.9830i	1.32494	−	0.389039i	0.866275	+	0.499568i	$0.166508\pi$
$798$	−1.23482	+	8.58836i	−0.0437122	+	0.304025i
$799$	32.0391	−	36.9750i	1.13346	−	1.30808i
$800$	0.841254	−	0.540641i	0.0297428	−	0.0191145i
$801$	11.6073	+	13.3956i	0.410125	+	0.473309i
$802$	−33.7800	−	9.91872i	−1.19281	−	0.350242i
$803$	−13.7996	+	30.2170i	−0.486978	+	1.06633i
$804$	5.54186			0.195446
$805$	1.53517	−	6.17367i	0.0541076	−	0.217593i
$806$	1.83261			0.0645509
$807$	−12.6758	+	27.7562i	−0.446210	+	0.977064i
$808$	−13.4301	−	3.94342i	−0.472468	−	0.138729i
$809$	−20.8335	−	24.0432i	−0.732468	−	0.845313i	0.260279	−	0.965533i	$-0.416185\pi$
$809$	−20.8335	−	24.0432i	−0.732468	−	0.845313i	−0.992747	+	0.120220i	$0.961640\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	21.0481	−	24.2908i	0.739097	−	0.852964i	−0.254367	−	0.967108i	$-0.581867\pi$
$811$	21.0481	−	24.2908i	0.739097	−	0.852964i	0.993464	+	0.114144i	$0.0364125\pi$
$812$	−1.03317	+	7.18584i	−0.0362571	+	0.252173i
$813$	2.18872	−	0.642667i	0.0767619	−	0.0225393i
$814$	2.64047	+	1.69693i	0.0925483	+	0.0594772i
$815$	2.33516	+	16.2414i	0.0817972	+	0.568912i
$816$	−2.76335	−	6.05089i	−0.0967366	−	0.211824i
$817$	5.28474	+	11.5720i	0.184890	+	0.404852i
$818$	2.65113	+	18.4390i	0.0926945	+	0.644705i
$819$	0.934914	+	0.600833i	0.0326685	+	0.0209948i
$820$	0.121550	−	0.0356903i	0.00424471	−	0.00124636i
$821$	−4.06775	+	28.2919i	−0.141966	+	0.987393i	0.786928	+	0.617045i	$0.211670\pi$
$821$	−4.06775	+	28.2919i	−0.141966	+	0.987393i	−0.928893	+	0.370347i	$0.879239\pi$
$822$	−7.87853	+	9.09231i	−0.274795	+	0.317131i
$823$	5.71617	−	3.67356i	0.199253	−	0.128052i	−0.437210	−	0.899360i	$-0.644033\pi$
$823$	5.71617	−	3.67356i	0.199253	−	0.128052i	0.636463	+	0.771307i	$0.280397\pi$
$824$	3.02935	+	3.49606i	0.105533	+	0.121791i
$825$	3.17756	+	0.933014i	0.110628	+	0.0324834i
$826$	3.96842	−	8.68964i	0.138079	−	0.302351i
$827$	−0.686821			−0.0238831			−0.0119415	−	0.999929i	$-0.503801\pi$
$827$	−0.686821			−0.0238831			−0.0119415	+	0.999929i	$0.503801\pi$
$828$	−2.42164	+	4.13953i	−0.0841578	+	0.143858i
$829$	−4.91917			−0.170850			−0.0854250	−	0.996345i	$-0.527225\pi$
$829$	−4.91917			−0.170850			−0.0854250	+	0.996345i	$0.527225\pi$
$830$	2.79726	−	6.12514i	0.0970943	−	0.212607i
$831$	−12.4345	−	3.65110i	−0.431349	−	0.126655i
$832$	−0.548638	−	0.633162i	−0.0190206	−	0.0219509i
$833$	29.3254	−	18.8463i	1.01607	−	0.652986i
$834$	2.78190	−	3.21049i	0.0963294	−	0.111170i
$835$	−0.200131	+	1.39194i	−0.00692583	+	0.0481702i
$836$	20.7845	−	6.10287i	0.718846	−	0.211072i
$837$	1.84018	+	1.18261i	0.0636058	+	0.0408770i
$838$	−3.95102	−	27.4799i	−0.136486	−	0.949279i
$839$	22.7249	+	49.7606i	0.784550	+	1.71793i	0.691630	+	0.722252i	$0.256893\pi$
$839$	22.7249	+	49.7606i	0.784550	+	1.71793i	0.0929201	+	0.995674i	$0.470380\pi$
$840$	0.551049	+	1.20663i	0.0190130	+	0.0416326i
$841$	−0.135477	−	0.942265i	−0.00467163	−	0.0324919i
$842$	−21.4318	−	13.7734i	−0.738588	−	0.474662i
$843$	−4.89456	+	1.43717i	−0.168578	+	0.0494989i
$844$	−3.16173	+	21.9903i	−0.108831	+	0.756938i
$845$	8.05354	−	9.29429i	0.277050	−	0.319733i
$846$	6.18734	−	3.97636i	0.212725	−	0.136710i
$847$	0.0283406	+	0.0327068i	0.000973794	+	0.00112382i
$848$	7.30332	+	2.14445i	0.250797	+	0.0736407i
$849$	4.95736	−	10.8551i	0.170136	−	0.372546i
$850$	−6.65202			−0.228162
$851$	1.46204	+	4.30379i	0.0501180	+	0.147532i
$852$	−7.69197			−0.263523
$853$	−1.22034	+	2.67216i	−0.0417835	+	0.0914932i	−0.929373	−	0.369143i	$-0.879651\pi$
$853$	−1.22034	+	2.67216i	−0.0417835	+	0.0914932i	0.887589	+	0.460636i	$0.152379\pi$
$854$	−18.1153	−	5.31914i	−0.619894	−	0.182017i
$855$	−4.28346	−	4.94338i	−0.146491	−	0.169060i
$856$	−11.1581	+	7.17085i	−0.381375	+	0.245095i
$857$	−2.33824	+	2.69847i	−0.0798726	+	0.0921779i	−0.794279	−	0.607553i	$-0.792151\pi$
$857$	−2.33824	+	2.69847i	−0.0798726	+	0.0921779i	0.714407	+	0.699731i	$0.246697\pi$
$858$	0.394856	−	2.74628i	0.0134802	−	0.0937565i
$859$	21.9882	−	6.45632i	0.750228	−	0.220287i	0.115804	−	0.993272i	$-0.463056\pi$
$859$	21.9882	−	6.45632i	0.750228	−	0.220287i	0.634424	+	0.772985i	$0.281237\pi$
$860$	1.63615	+	1.05149i	0.0557922	+	0.0358555i
$861$	0.0239151	+	0.166333i	0.000815023	+	0.00566861i
$862$	−9.17711	−	20.0951i	−0.312574	−	0.684441i
$863$	−5.48922	−	12.0197i	−0.186855	−	0.409156i	0.792901	−	0.609351i	$-0.208570\pi$
$863$	−5.48922	−	12.0197i	−0.186855	−	0.409156i	−0.979756	+	0.200195i	$0.935842\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	−0.441951	−	0.284025i	−0.0150268	−	0.00965713i
$866$	8.71696	−	2.55953i	0.296214	−	0.0869764i
$867$	−3.87799	+	26.9720i	−0.131703	+	0.916018i
$868$	−1.90016	+	2.19290i	−0.0644955	+	0.0744318i
$869$	1.89469	−	1.21764i	0.0642728	−	0.0413057i
$870$	−3.58395	−	4.13609i	−0.121507	−	0.140227i
$871$	−4.45486	−	1.30807i	−0.150947	−	0.0443221i
$872$	2.86627	−	6.27625i	0.0970641	−	0.212541i
$873$	12.0348			0.407317
$874$	29.0554	+	11.8253i	0.982813	+	0.399998i
$875$	1.32650			0.0448439
$876$	4.16693	−	9.12430i	0.140787	−	0.308282i
$877$	−45.4875	−	13.3563i	−1.53600	−	0.451011i	−0.599121	−	0.800658i	$-0.704483\pi$
$877$	−45.4875	−	13.3563i	−1.53600	−	0.451011i	−0.936881	+	0.349647i	$0.886301\pi$
$878$	12.5068	+	14.4336i	0.422084	+	0.487111i
$879$	−0.972250	+	0.624827i	−0.0327932	+	0.0210749i
$880$	2.16870	−	2.50282i	0.0731070	−	0.0843700i
$881$	5.03837	−	35.0427i	0.169747	−	1.18062i	−0.709659	−	0.704545i	$-0.751151\pi$
$881$	5.03837	−	35.0427i	0.169747	−	1.18062i	0.879406	−	0.476072i	$-0.157940\pi$
$882$	5.02812	−	1.47639i	0.169306	−	0.0497126i
$883$	−38.8307	−	24.9550i	−1.30676	−	0.839801i	−0.312825	−	0.949811i	$-0.601275\pi$
$883$	−38.8307	−	24.9550i	−1.30676	−	0.839801i	−0.993931	+	0.110010i	$0.964912\pi$
$884$	0.793123	+	5.51629i	0.0266756	+	0.185533i
$885$	2.99165	+	6.55079i	0.100563	+	0.220202i
$886$	0.786265	+	1.72168i	0.0264151	+	0.0578410i
$887$	−7.31344	−	50.8661i	−0.245561	−	1.70792i	−0.623282	−	0.781997i	$-0.714201\pi$
$887$	−7.31344	−	50.8661i	−0.245561	−	1.70792i	0.377720	−	0.925920i	$-0.376708\pi$
$888$	−0.797314	−	0.512403i	−0.0267561	−	0.0171951i
$889$	−5.27077	+	1.54764i	−0.176776	+	0.0519061i
$890$	2.52251	−	17.5445i	0.0845549	−	0.588092i
$891$	2.16870	−	2.50282i	0.0726543	−	0.0838476i
$892$	3.59167	−	2.30822i	0.120258	−	0.0772851i
$893$	−31.5045	−	36.3581i	−1.05426	−	1.21668i
$894$	−16.3173	−	4.79120i	−0.545733	−	0.160242i
$895$	−2.33236	+	5.10716i	−0.0779623	+	0.170714i
$896$	1.32650			0.0443153
$897$	2.92372	−	2.75600i	0.0976201	−	0.0920201i
$898$	−23.9951			−0.800727
$899$	4.97310	−	10.8896i	0.165862	−	0.363188i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−33.1575	−	38.2657i	−1.10463	−	1.27482i
$902$	0.352932	−	0.226816i	0.0117514	−	0.00755214i
$903$	−1.68948	+	1.94976i	−0.0562223	+	0.0648840i
$904$	−0.574716	+	3.99724i	−0.0191148	+	0.132946i
$905$	−4.75457	+	1.39607i	−0.158047	+	0.0464068i
$906$	9.86163	+	6.33768i	0.327631	+	0.210555i
$907$	3.86075	+	26.8521i	0.128194	+	0.891609i	0.947842	+	0.318741i	$0.103260\pi$
$907$	3.86075	+	26.8521i	0.128194	+	0.891609i	−0.819648	+	0.572868i	$0.805831\pi$
$908$	−10.5865	−	23.1812i	−0.351326	−	0.769296i
$909$	5.81458	+	12.7322i	0.192857	+	0.422299i
$910$	−0.158159	−	1.10002i	−0.00524293	−	0.0364654i
$911$	27.4840	+	17.6629i	0.910586	+	0.585198i	0.909912	−	0.414802i	$-0.136149\pi$
$911$	27.4840	+	17.6629i	0.910586	+	0.585198i	0.000674336		1.00000i	$0.499785\pi$
$912$	−6.27607	+	1.84282i	−0.207821	+	0.0610218i
$913$	3.17360	−	22.0729i	0.105031	−	0.730505i
$914$	−0.535862	+	0.618418i	−0.0177248	+	0.0204555i
$915$	11.9736	−	7.69494i	0.395834	−	0.254387i
$916$	16.0438	+	18.5156i	0.530103	+	0.611772i
$917$	−9.37846	−	2.75377i	−0.309704	−	0.0909373i
$918$	−2.76335	+	6.05089i	−0.0912041	+	0.199709i
$919$	16.0053			0.527967			0.263984	−	0.964527i	$-0.414963\pi$
$919$	16.0053			0.527967			0.263984	+	0.964527i	$0.414963\pi$
$920$	4.71428	−	0.880660i	0.155425	−	0.0290345i
$921$	1.92849			0.0635460
$922$	−9.96498	+	21.8203i	−0.328179	+	0.718612i
$923$	6.18324	+	1.81556i	0.203524	+	0.0597600i
$924$	2.87679	+	3.31999i	0.0946394	+	0.109220i
$925$	−0.797314	+	0.512403i	−0.0262155	+	0.0168477i
$926$	−15.0926	+	17.4178i	−0.495973	+	0.572383i
$927$	0.658342	−	4.57887i	0.0216228	−	0.150390i
$928$	−5.25115	+	1.54188i	−0.172377	+	0.0506146i
$929$	−15.4390	−	9.92202i	−0.506536	−	0.325531i	0.262290	−	0.964989i	$-0.415522\pi$
$929$	−15.4390	−	9.92202i	−0.506536	−	0.325531i	−0.768826	+	0.639458i	$0.779159\pi$
$930$	−0.311303	−	2.16516i	−0.0102080	−	0.0709983i
$931$	−14.2394	−	31.1799i	−0.466678	−	1.02188i
$932$	8.05894	+	17.6466i	0.263979	+	0.578034i
$933$	−1.62189	−	11.2805i	−0.0530982	−	0.369306i
$934$	−31.1531	−	20.0209i	−1.01936	−	0.655104i
$935$	−21.1372	+	6.20643i	−0.691259	+	0.202972i
$936$	−0.119230	+	0.829266i	−0.00389717	+	0.0271054i
$937$	−15.3184	+	17.6784i	−0.500431	+	0.577528i	−0.948623	−	0.316410i	$-0.897523\pi$
$937$	−15.3184	+	17.6784i	−0.500431	+	0.577528i	0.448192	+	0.893937i	$0.352068\pi$
$938$	6.18430	−	3.97441i	0.201924	−	0.129769i
$939$	−16.2839	−	18.7926i	−0.531404	−	0.613273i
$940$	−7.05698	−	2.07212i	−0.230173	−	0.0675850i
$941$	−13.5818	+	29.7400i	−0.442754	+	0.969495i	0.548331	+	0.836261i	$0.315263\pi$
$941$	−13.5818	+	29.7400i	−0.442754	+	0.969495i	−0.991085	+	0.133234i	$0.957464\pi$
$942$	−10.0464			−0.327331
$943$	0.604452	+	0.0612099i	0.0196837	+	0.00199327i
$944$	7.20158			0.234392
$945$	0.551049	−	1.20663i	0.0179256	−	0.0392516i
$946$	6.18001	+	1.81461i	0.200929	+	0.0589982i
$947$	30.0022	+	34.6244i	0.974940	+	1.12514i	0.992120	+	0.125289i	$0.0399857\pi$
$947$	30.0022	+	34.6244i	0.974940	+	1.12514i	−0.0171801	+	0.999852i	$0.505469\pi$
$948$	−0.572119	+	0.367678i	−0.0185815	+	0.0119416i
$949$	−5.50326	+	6.35110i	−0.178643	+	0.206165i
$950$	−0.930885	+	6.47445i	−0.0302019	+	0.210059i
$951$	20.0457	−	5.88594i	0.650026	−	0.190865i
$952$	−7.42315	−	4.77057i	−0.240586	−	0.154615i
$953$	−5.45611	−	37.9481i	−0.176741	−	1.22926i	−0.864242	−	0.503076i	$-0.832202\pi$
$953$	−5.45611	−	37.9481i	−0.176741	−	1.22926i	0.687501	−	0.726183i	$-0.258708\pi$
$954$	−3.16199	−	6.92380i	−0.102373	−	0.224166i
$955$	−6.62058	−	14.4971i	−0.214237	−	0.469114i
$956$	−1.01471	−	7.05747i	−0.0328181	−	0.228255i
$957$	−15.2472	−	9.79880i	−0.492873	−	0.316750i
$958$	−11.2138	+	3.29265i	−0.362300	+	0.106381i
$959$	−2.27120	+	15.7965i	−0.0733407	+	0.510096i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	−22.0536	+	14.1730i	−0.711407	+	0.457193i
$962$	0.519982	+	0.600091i	0.0167649	+	0.0193477i
$963$	12.7263	+	3.73679i	0.410101	+	0.120416i
$964$	5.44242	−	11.9172i	0.175289	−	0.383828i
$965$	23.4556			0.755063
$966$	0.266341	+	6.35610i	0.00856937	+	0.204504i
$967$	−36.6913			−1.17991			−0.589957	−	0.807435i	$-0.700855\pi$
$967$	−36.6913			−1.17991			−0.589957	+	0.807435i	$0.700855\pi$
$968$	−0.0135530	+	0.0296769i	−0.000435609	+	0.000953850i
$969$	41.7485	+	12.2585i	1.34116	+	0.393799i
$970$	−7.88113	−	9.09530i	−0.253048	−	0.292033i
$971$	40.0002	−	25.7066i	1.28367	−	0.824964i	0.292333	−	0.956317i	$-0.405568\pi$
$971$	40.0002	−	25.7066i	1.28367	−	0.824964i	0.991336	+	0.131353i	$0.0419321\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	0.801957	−	5.57773i	0.0257095	−	0.178814i
$974$	22.4777	−	6.60006i	0.720233	−	0.211479i
$975$	0.704797	+	0.452945i	0.0225716	+	0.0145059i
$976$	−2.02557	−	14.0881i	−0.0648369	−	0.450950i
$977$	−13.2558	−	29.0261i	−0.424090	−	0.928627i	−0.994249	−	0.107093i	$-0.965846\pi$
$977$	−13.2558	−	29.0261i	−0.424090	−	0.928627i	0.570159	−	0.821534i	$-0.306881\pi$
$978$	−6.81631	−	14.9256i	−0.217962	−	0.477269i
$979$	−8.35382	−	58.1021i	−0.266989	−	1.85695i
$980$	−4.40850	−	2.83317i	−0.140824	−	0.0905023i
$981$	−6.62028	+	1.94389i	−0.211369	+	0.0620636i
$982$	2.61883	−	18.2144i	0.0835702	−	0.581243i
$983$	−12.9245	+	14.9156i	−0.412226	+	0.475734i	−0.923453	−	0.383711i	$-0.874646\pi$
$983$	−12.9245	+	14.9156i	−0.412226	+	0.475734i	0.511227	+	0.859446i	$0.329191\pi$
$984$	−0.106571	+	0.0684892i	−0.00339737	+	0.00218336i
$985$	−15.1890	−	17.5291i	−0.483962	−	0.558522i
$986$	34.9308	+	10.2566i	1.11242	+	0.326637i
$987$	4.05291	−	8.87464i	0.129006	−	0.282483i
$988$	5.48003			0.174343
$989$	5.36685	+	7.62869i	0.170656	+	0.242578i
$990$	−3.31170			−0.105253
$991$	−16.6117	+	36.3746i	−0.527689	+	1.15548i	0.438756	+	0.898606i	$0.355419\pi$
$991$	−16.6117	+	36.3746i	−0.527689	+	1.15548i	−0.966445	+	0.256872i	$0.917308\pi$
$992$	−2.09882	−	0.616268i	−0.0666375	−	0.0195665i
$993$	−7.01785	−	8.09904i	−0.222705	−	0.257015i
$994$	−8.58366	+	5.51638i	−0.272257	+	0.174969i
$995$	−2.11616	+	2.44218i	−0.0670868	+	0.0774223i
$996$	−0.958298	+	6.66511i	−0.0303648	+	0.211192i
$997$	−4.15438	+	1.21984i	−0.131571	+	0.0386326i	−0.346855	−	0.937919i	$-0.612750\pi$
$997$	−4.15438	+	1.21984i	−0.131571	+	0.0386326i	0.215284	+	0.976551i	$0.430932\pi$
$998$	6.90344	+	4.43657i	0.218525	+	0.140437i
$999$	0.134882	+	0.938122i	0.00426746	+	0.0296809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.121.2	✓	30
23.4	even	11	inner	690.2.m.g.211.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.121.2	✓	30	1.1	even	1	trivial
690.2.m.g.211.2	yes	30	23.4	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)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.188781 + 1.31300i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.188781 + 1.31300i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-1.37573 - 3.01243i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.119230 - 0.829266i) q^{13} +(1.11592 + 0.717161i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.35615 - 5.02726i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-4.28346 - 4.94338i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.551049 - 1.20663i) q^{21} -3.31170 q^{22} +(-3.75276 - 2.98611i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.803857 - 0.236034i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.11592 - 0.717161i) q^{28} +(-3.58395 + 4.13609i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-2.09882 + 0.616268i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.471304 + 3.27799i) q^{33} +(-2.76335 - 6.05089i) q^{34} +(0.551049 + 1.20663i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.797314 - 0.512403i) q^{37} +(-6.27607 + 1.84282i) q^{38} +(-0.119230 + 0.829266i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-0.106571 + 0.0684892i) q^{41} +(-0.868674 - 1.00250i) q^{42} +(-1.86611 - 0.547940i) q^{43} +(-1.37573 + 3.01243i) q^{44} +1.00000 q^{45} +(-4.27521 + 2.17315i) q^{46} +7.35491 q^{47} +(0.415415 - 0.909632i) q^{48} +(5.02812 + 1.47639i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(-5.59604 + 3.59635i) q^{51} +(-0.548638 + 0.633162i) q^{52} +(1.08325 - 7.53417i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-2.78598 - 1.79044i) q^{55} +(-0.188781 - 1.31300i) q^{56} +(2.71724 + 5.94992i) q^{57} +(2.27350 + 4.97827i) q^{58} +(-1.02489 - 7.12828i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-13.6565 + 4.00990i) q^{61} +(-0.311303 + 2.16516i) q^{62} +(-0.868674 + 1.00250i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.548638 - 0.633162i) q^{65} +(3.17756 + 0.933014i) q^{66} +(2.30217 - 5.04105i) q^{67} -6.65202 q^{68} +(2.75946 + 3.92242i) q^{69} +1.32650 q^{70} +(-3.19536 + 6.99686i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-6.56875 - 7.58074i) q^{73} +(-0.797314 + 0.512403i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(-0.930885 + 6.47445i) q^{76} +(4.21503 - 1.23765i) q^{77} +(0.704797 + 0.452945i) q^{78} +(0.0967853 + 0.673156i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.0180287 + 0.125392i) q^{82} +(5.66470 + 3.64048i) q^{83} +(-1.27277 + 0.373719i) q^{84} +(0.946681 - 6.58431i) q^{85} +(-1.27363 + 1.46985i) q^{86} +(4.60404 - 2.95884i) q^{87} +(2.16870 + 2.50282i) q^{88} +(17.0069 + 4.99368i) q^{89} +(0.415415 - 0.909632i) q^{90} +1.11133 q^{91} +(0.200784 + 4.79163i) q^{92} +2.18742 q^{93} +(3.05534 - 6.69026i) q^{94} +(-6.27607 - 1.84282i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(10.1243 - 6.50651i) q^{97} +(3.43173 - 3.96042i) q^{98} +(0.471304 - 3.27799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

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