LMFDB - Embedded newform 425.2.r.a.69.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.8
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80321 + 0.585900i) q^{2} +(0.0268065 + 0.0368959i) q^{3} +(1.29027 - 0.937434i) q^{4} +(0.943879 + 2.02709i) q^{5} +(-0.0699551 - 0.0508253i) q^{6} -0.426178i q^{7} +(0.451510 - 0.621450i) q^{8} +(0.926408 - 2.85119i) q^{9} +(-2.88969 - 3.10226i) q^{10} +(-1.70752 - 5.25519i) q^{11} +(0.0691750 + 0.0224763i) q^{12} +(1.38488 + 0.449976i) q^{13} +(0.249697 + 0.768489i) q^{14} +(-0.0494893 + 0.0891644i) q^{15} +(-1.43574 + 4.41875i) q^{16} +(-0.587785 + 0.809017i) q^{17} +5.68409i q^{18} +(-4.16200 - 3.02387i) q^{19} +(3.11812 + 1.73066i) q^{20} +(0.0157242 - 0.0114243i) q^{21} +(6.15803 + 8.47580i) q^{22} +(5.87772 - 1.90979i) q^{23} +0.0350323 q^{24} +(-3.21819 + 3.82665i) q^{25} -2.76088 q^{26} +(0.260152 - 0.0845286i) q^{27} +(-0.399513 - 0.549883i) q^{28} +(8.45213 - 6.14083i) q^{29} +(0.0369984 - 0.189778i) q^{30} +(-1.97401 - 1.43420i) q^{31} -7.27283i q^{32} +(0.148123 - 0.203873i) q^{33} +(0.585900 - 1.80321i) q^{34} +(0.863900 - 0.402260i) q^{35} +(-1.47749 - 4.54724i) q^{36} +(0.364580 + 0.118459i) q^{37} +(9.27666 + 3.01417i) q^{38} +(0.0205215 + 0.0631588i) q^{39} +(1.68591 + 0.328677i) q^{40} +(1.69822 - 5.22657i) q^{41} +(-0.0216606 + 0.0298133i) q^{42} -0.400907i q^{43} +(-7.12955 - 5.17992i) q^{44} +(6.65404 - 0.813266i) q^{45} +(-9.47985 + 6.88751i) q^{46} +(1.46661 + 2.01862i) q^{47} +(-0.201521 + 0.0654781i) q^{48} +6.81837 q^{49} +(3.56104 - 8.78581i) q^{50} -0.0456059 q^{51} +(2.20869 - 0.717647i) q^{52} +(4.61335 + 6.34974i) q^{53} +(-0.419585 + 0.304846i) q^{54} +(9.04106 - 8.42155i) q^{55} +(-0.264848 - 0.192423i) q^{56} -0.234620i q^{57} +(-11.6431 + 16.0253i) q^{58} +(0.908087 - 2.79480i) q^{59} +(0.0197313 + 0.161439i) q^{60} +(2.78832 + 8.58157i) q^{61} +(4.39985 + 1.42960i) q^{62} +(-1.21511 - 0.394814i) q^{63} +(1.38967 + 4.27698i) q^{64} +(0.395020 + 3.23200i) q^{65} +(-0.147648 + 0.454412i) q^{66} +(-0.917637 + 1.26302i) q^{67} +1.59486i q^{68} +(0.228024 + 0.165669i) q^{69} +(-1.32211 + 1.23152i) q^{70} +(-10.8497 + 7.88275i) q^{71} +(-1.35359 - 1.86306i) q^{72} +(-9.32082 + 3.02852i) q^{73} -0.726820 q^{74} +(-0.227456 - 0.0161589i) q^{75} -8.20477 q^{76} +(-2.23965 + 0.727705i) q^{77} +(-0.0740094 - 0.101865i) q^{78} +(8.75922 - 6.36395i) q^{79} +(-10.3124 + 1.26039i) q^{80} +(-7.26601 - 5.27907i) q^{81} +10.4196i q^{82} +(9.10493 - 12.5319i) q^{83} +(0.00957890 - 0.0294808i) q^{84} +(-2.19475 - 0.427880i) q^{85} +(0.234891 + 0.722920i) q^{86} +(0.453143 + 0.147235i) q^{87} +(-4.03680 - 1.31164i) q^{88} +(-2.54723 - 7.83958i) q^{89} +(-11.5222 + 5.36509i) q^{90} +(0.191770 - 0.590206i) q^{91} +(5.79353 - 7.97411i) q^{92} -0.111279i q^{93} +(-3.82732 - 2.78071i) q^{94} +(2.20123 - 11.2909i) q^{95} +(0.268338 - 0.194959i) q^{96} +(6.99297 + 9.62500i) q^{97} +(-12.2950 + 3.99488i) q^{98} -16.5654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.80321	+	0.585900i	−1.27506	+	0.414294i	−0.866839	−	0.498588i	$-0.833852\pi$
$2$	−1.80321	+	0.585900i	−1.27506	+	0.414294i	−0.408225	+	0.912881i	$0.633852\pi$
$3$	0.0268065	+	0.0368959i	0.0154767	+	0.0213019i	0.816685	−	0.577083i	$-0.195809\pi$
$3$	0.0268065	+	0.0368959i	0.0154767	+	0.0213019i	−0.801209	+	0.598385i	$0.795809\pi$
$4$	1.29027	−	0.937434i	0.645133	−	0.468717i
$5$	0.943879	+	2.02709i	0.422115	+	0.906542i
$5$	0.943879	+	2.02709i	0.422115	+	0.906542i
$6$	−0.0699551	−	0.0508253i	−0.0285590	−	0.0207494i
$7$		−	0.426178i		−	0.161080i	−0.996751	−	0.0805400i	$-0.974336\pi$
$7$		−	0.426178i		−	0.161080i	0.996751	−	0.0805400i	$-0.0256645\pi$
$8$	0.451510	−	0.621450i	0.159633	−	0.219716i
$9$	0.926408	−	2.85119i	0.308803	−	0.950397i
$10$	−2.88969	−	3.10226i	−0.913799	−	0.981020i
$11$	−1.70752	−	5.25519i	−0.514835	−	1.58450i	−0.783582	−	0.621289i	$-0.786609\pi$
$11$	−1.70752	−	5.25519i	−0.514835	−	1.58450i	0.268746	−	0.963211i	$-0.413391\pi$
$12$	0.0691750	+	0.0224763i	0.0199691	+	0.00648835i
$13$	1.38488	+	0.449976i	0.384097	+	0.124801i	0.494700	−	0.869064i	$-0.335278\pi$
$13$	1.38488	+	0.449976i	0.384097	+	0.124801i	−0.110602	+	0.993865i	$0.535278\pi$
$14$	0.249697	+	0.768489i	0.0667344	+	0.205387i
$15$	−0.0494893	+	0.0891644i	−0.0127781	+	0.0230221i
$16$	−1.43574	+	4.41875i	−0.358934	+	1.10469i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			5.68409i			1.33975i
$19$	−4.16200	−	3.02387i	−0.954828	−	0.693723i	−0.00288426	−	0.999996i	$-0.500918\pi$
$19$	−4.16200	−	3.02387i	−0.954828	−	0.693723i	−0.951944	+	0.306273i	$0.900918\pi$
$20$	3.11812	+	1.73066i	0.697232	+	0.386988i
$21$	0.0157242	−	0.0114243i	0.00343131	−	0.00249299i
$22$	6.15803	+	8.47580i	1.31290	+	1.80705i
$23$	5.87772	−	1.90979i	1.22559	−	0.398218i	0.376475	−	0.926427i	$-0.377136\pi$
$23$	5.87772	−	1.90979i	1.22559	−	0.398218i	0.849115	+	0.528208i	$0.177136\pi$
$24$	0.0350323			0.00715095
$25$	−3.21819	+	3.82665i	−0.643637	+	0.765331i
$26$	−2.76088			−0.541453
$27$	0.260152	−	0.0845286i	0.0500663	−	0.0162675i
$28$	−0.399513	−	0.549883i	−0.0755009	−	0.103918i
$29$	8.45213	−	6.14083i	1.56952	−	1.14032i	0.641907	−	0.766783i	$-0.278144\pi$
$29$	8.45213	−	6.14083i	1.56952	−	1.14032i	0.927614	−	0.373540i	$-0.121856\pi$
$30$	0.0369984	−	0.189778i	0.00675496	−	0.0346486i
$31$	−1.97401	−	1.43420i	−0.354542	−	0.257590i	0.396230	−	0.918151i	$-0.370318\pi$
$31$	−1.97401	−	1.43420i	−0.354542	−	0.257590i	−0.750772	+	0.660561i	$0.770318\pi$
$32$		−	7.27283i		−	1.28567i
$33$	0.148123	−	0.203873i	0.0257849	−	0.0354898i
$34$	0.585900	−	1.80321i	0.100481	−	0.309249i
$35$	0.863900	−	0.402260i	0.146026	−	0.0679944i
$36$	−1.47749	−	4.54724i	−0.246248	−	0.757874i
$37$	0.364580	+	0.118459i	0.0599365	+	0.0194746i	0.338832	−	0.940847i	$-0.389968\pi$
$37$	0.364580	+	0.118459i	0.0599365	+	0.0194746i	−0.278895	+	0.960322i	$0.589968\pi$
$38$	9.27666	+	3.01417i	1.50487	+	0.488963i
$39$	0.0205215	+	0.0631588i	0.00328608	+	0.0101135i
$40$	1.68591	+	0.328677i	0.266565	+	0.0519685i
$41$	1.69822	−	5.22657i	0.265217	−	0.816253i	−0.726427	−	0.687244i	$-0.758820\pi$
$41$	1.69822	−	5.22657i	0.265217	−	0.816253i	0.991643	−	0.129009i	$-0.0411797\pi$
$42$	−0.0216606	+	0.0298133i	−0.00334231	+	0.00460029i
$43$		−	0.400907i		−	0.0611377i	−0.999533	−	0.0305688i	$-0.990268\pi$
$43$		−	0.400907i		−	0.0611377i	0.999533	−	0.0305688i	$-0.00973188\pi$
$44$	−7.12955	−	5.17992i	−1.07482	−	0.780902i
$45$	6.65404	−	0.813266i	0.991925	−	0.121235i
$46$	−9.47985	+	6.88751i	−1.39773	+	1.01551i
$47$	1.46661	+	2.01862i	0.213927	+	0.294445i	0.902472	−	0.430748i	$-0.141750\pi$
$47$	1.46661	+	2.01862i	0.213927	+	0.294445i	−0.688545	+	0.725194i	$0.741750\pi$
$48$	−0.201521	+	0.0654781i	−0.0290870	+	0.00945094i
$49$	6.81837			0.974053
$50$	3.56104	−	8.78581i	0.503607	−	1.24250i
$51$	−0.0456059			−0.00638610
$52$	2.20869	−	0.717647i	0.306290	−	0.0995198i
$53$	4.61335	+	6.34974i	0.633693	+	0.872203i	0.998260	−	0.0589739i	$-0.0187829\pi$
$53$	4.61335	+	6.34974i	0.633693	+	0.872203i	−0.364567	+	0.931177i	$0.618783\pi$
$54$	−0.419585	+	0.304846i	−0.0570983	+	0.0414843i
$55$	9.04106	−	8.42155i	1.21910	−	1.13556i
$56$	−0.264848	−	0.192423i	−0.0353918	−	0.0257137i
$57$		−	0.234620i		−	0.0310762i
$58$	−11.6431	+	16.0253i	−1.52881	+	2.10423i
$59$	0.908087	−	2.79480i	0.118223	−	0.363852i	−0.874383	−	0.485237i	$-0.838733\pi$
$59$	0.908087	−	2.79480i	0.118223	−	0.363852i	0.992606	+	0.121384i	$0.0387334\pi$
$60$	0.0197313	+	0.161439i	0.00254730	+	0.0208417i
$61$	2.78832	+	8.58157i	0.357008	+	1.09876i	0.954836	+	0.297133i	$0.0960304\pi$
$61$	2.78832	+	8.58157i	0.357008	+	1.09876i	−0.597828	+	0.801624i	$0.703970\pi$
$62$	4.39985	+	1.42960i	0.558782	+	0.181559i
$63$	−1.21511	−	0.394814i	−0.153090	−	0.0497419i
$64$	1.38967	+	4.27698i	0.173709	+	0.534622i
$65$	0.395020	+	3.23200i	0.0489962	+	0.400881i
$66$	−0.147648	+	0.454412i	−0.0181742	+	0.0559343i
$67$	−0.917637	+	1.26302i	−0.112107	+	0.154302i	−0.861383	−	0.507955i	$-0.830402\pi$
$67$	−0.917637	+	1.26302i	−0.112107	+	0.154302i	0.749276	+	0.662258i	$0.230402\pi$
$68$			1.59486i			0.193405i
$69$	0.228024	+	0.165669i	0.0274509	+	0.0199443i
$70$	−1.32211	+	1.23152i	−0.158023	+	0.147195i
$71$	−10.8497	+	7.88275i	−1.28762	+	0.935511i	−0.999754	−	0.0221599i	$-0.992946\pi$
$71$	−10.8497	+	7.88275i	−1.28762	+	0.935511i	−0.287866	+	0.957671i	$0.592946\pi$
$72$	−1.35359	−	1.86306i	−0.159522	−	0.219563i
$73$	−9.32082	+	3.02852i	−1.09092	+	0.354461i	−0.798602	−	0.601860i	$-0.794427\pi$
$73$	−9.32082	+	3.02852i	−1.09092	+	0.354461i	−0.292318	+	0.956321i	$0.594427\pi$
$74$	−0.726820			−0.0844912
$75$	−0.227456	−	0.0161589i	−0.0262644	−	0.00186587i
$76$	−8.20477			−0.941151
$77$	−2.23965	+	0.727705i	−0.255231	+	0.0829297i
$78$	−0.0740094	−	0.101865i	−0.00837992	−	0.0115340i
$79$	8.75922	−	6.36395i	0.985489	−	0.716000i	0.0265607	−	0.999647i	$-0.491544\pi$
$79$	8.75922	−	6.36395i	0.985489	−	0.716000i	0.958929	+	0.283647i	$0.0915445\pi$
$80$	−10.3124	+	1.26039i	−1.15296	+	0.140916i
$81$	−7.26601	−	5.27907i	−0.807335	−	0.586563i
$82$			10.4196i			1.15065i
$83$	9.10493	−	12.5319i	0.999396	−	1.37555i	0.0737010	−	0.997280i	$-0.476519\pi$
$83$	9.10493	−	12.5319i	0.999396	−	1.37555i	0.925695	−	0.378270i	$-0.123481\pi$
$84$	0.00957890	−	0.0294808i	0.00104514	−	0.00321662i
$85$	−2.19475	−	0.427880i	−0.238054	−	0.0464101i
$86$	0.234891	+	0.722920i	0.0253290	+	0.0779545i
$87$	0.453143	+	0.147235i	0.0485820	+	0.0157853i
$88$	−4.03680	−	1.31164i	−0.430324	−	0.139821i
$89$	−2.54723	−	7.83958i	−0.270006	−	0.830994i	−0.990498	−	0.137530i	$-0.956084\pi$
$89$	−2.54723	−	7.83958i	−0.270006	−	0.830994i	0.720491	−	0.693464i	$-0.243916\pi$
$90$	−11.5222	+	5.36509i	−1.21454	+	0.565530i
$91$	0.191770	−	0.590206i	0.0201029	−	0.0618704i
$92$	5.79353	−	7.97411i	0.604018	−	0.831359i
$93$		−	0.111279i		−	0.0115391i
$94$	−3.82732	−	2.78071i	−0.394758	−	0.286808i
$95$	2.20123	−	11.2909i	0.225842	−	1.15842i
$96$	0.268338	−	0.194959i	0.0273871	−	0.0198979i
$97$	6.99297	+	9.62500i	0.710028	+	0.977270i	0.999796	+	0.0201734i	$0.00642181\pi$
$97$	6.99297	+	9.62500i	0.710028	+	0.977270i	−0.289768	+	0.957097i	$0.593578\pi$
$98$	−12.2950	+	3.99488i	−1.24198	+	0.403544i
$99$	−16.5654			−1.66489
$100$	−0.565084	+	7.95424i	−0.0565084	+	0.795424i
$101$	−0.108179			−0.0107642			−0.00538209	−	0.999986i	$-0.501713\pi$
$101$	−0.108179			−0.0107642			−0.00538209	+	0.999986i	$0.501713\pi$
$102$	0.0822371	−	0.0267205i	0.00814269	−	0.00264572i
$103$	0.924328	+	1.27223i	0.0910767	+	0.125356i	0.852124	−	0.523340i	$-0.175314\pi$
$103$	0.924328	+	1.27223i	0.0910767	+	0.125356i	−0.761047	+	0.648697i	$0.775314\pi$
$104$	0.904925	−	0.657467i	0.0887352	−	0.0644699i
$105$	0.0379999	+	0.0210912i	0.00370841	+	0.00205829i
$106$	−12.0392	−	8.74697i	−1.16935	−	0.849581i
$107$			3.39280i			0.327994i	0.986461	+	0.163997i	$0.0524388\pi$
$107$			3.39280i			0.327994i	−0.986461	+	0.163997i	$0.947561\pi$
$108$	0.256426	−	0.352940i	0.0246746	−	0.0339617i
$109$	0.143667	−	0.442161i	0.0137608	−	0.0423513i	−0.943940	−	0.330116i	$-0.892912\pi$
$109$	0.143667	−	0.442161i	0.0137608	−	0.0423513i	0.957701	+	0.287765i	$0.0929121\pi$
$110$	−11.3688	+	20.4830i	−1.08397	+	1.95298i
$111$	0.00540243	+	0.0166270i	0.000512776	+	0.00157816i
$112$	1.88317	+	0.611879i	0.177943	+	0.0578172i
$113$	−13.0697	−	4.24659i	−1.22949	−	0.399486i	−0.378961	−	0.925413i	$-0.623719\pi$
$113$	−13.0697	−	4.24659i	−1.22949	−	0.399486i	−0.850530	+	0.525927i	$0.823719\pi$
$114$	0.137464	+	0.423070i	0.0128747	+	0.0396241i
$115$	9.41917	+	10.1121i	0.878342	+	0.942955i
$116$	5.14888	−	15.8466i	0.478061	−	1.47132i
$117$	2.56593	−	3.53170i	0.237221	−	0.326506i
$118$			5.57168i			0.512914i
$119$	0.344785	+	0.250501i	0.0316064	+	0.0229634i
$120$	0.0330663	+	0.0710137i	0.00301853	+	0.00648264i
$121$	−15.8022	+	11.4810i	−1.43657	+	1.04373i
$122$	−10.0559	−	13.8407i	−0.910416	−	1.25308i
$123$	0.238362	−	0.0774486i	0.0214924	−	0.00698331i
$124$	−3.89146			−0.349464
$125$	−10.7945	−	2.91165i	−0.965494	−	0.260426i
$126$	2.42243			0.215807
$127$	−18.8641	+	6.12932i	−1.67392	+	0.543889i	−0.983716	−	0.179728i	$-0.942478\pi$
$127$	−18.8641	+	6.12932i	−1.67392	+	0.543889i	−0.690202	+	0.723617i	$0.742478\pi$
$128$	3.53797	+	4.86959i	0.312715	+	0.430415i
$129$	0.0147918	−	0.0107469i	0.00130235	−	0.000946211i
$130$	−2.60594	−	5.59655i	−0.228556	−	0.490850i
$131$	−2.03184	−	1.47622i	−0.177523	−	0.128978i	0.495476	−	0.868622i	$-0.334994\pi$
$131$	−2.03184	−	1.47622i	−0.177523	−	0.128978i	−0.672998	+	0.739644i	$0.734994\pi$
$132$		−	0.401906i		−	0.0349815i
$133$	−1.28871	+	1.77375i	−0.111745	+	0.153804i
$134$	0.914693	−	2.81514i	0.0790175	−	0.243191i
$135$	0.416899	+	0.447567i	0.0358810	+	0.0385205i
$136$	0.237373	+	0.730558i	0.0203545	+	0.0626448i
$137$	2.24660	+	0.729965i	0.191940	+	0.0623651i	0.403410	−	0.915019i	$-0.367825\pi$
$137$	2.24660	+	0.729965i	0.191940	+	0.0623651i	−0.211470	+	0.977385i	$0.567825\pi$
$138$	−0.508242	−	0.165138i	−0.0432645	−	0.0140575i
$139$	3.62486	+	11.1562i	0.307456	+	0.946253i	0.978749	+	0.205061i	$0.0657393\pi$
$139$	3.62486	+	11.1562i	0.307456	+	0.946253i	−0.671293	+	0.741192i	$0.734261\pi$
$140$	0.737570	−	1.32887i	0.0623360	−	0.112310i
$141$	−0.0351641	+	0.108224i	−0.00296135	+	0.00911409i
$142$	14.9458	−	20.5711i	1.25422	−	1.72629i
$143$		−	8.04616i		−	0.672854i
$144$	11.2686	+	8.18713i	0.939051	+	0.682260i
$145$	20.4258	+	11.3370i	1.69627	+	0.941488i
$146$	15.0330	−	10.9221i	1.24414	−	0.903922i
$147$	0.182776	+	0.251570i	0.0150751	+	0.0207492i
$148$	0.581453	−	0.188925i	0.0477951	−	0.0155296i
$149$	12.4178			1.01730			0.508651	−	0.860973i	$-0.330144\pi$
$149$	12.4178			1.01730			0.508651	+	0.860973i	$0.330144\pi$
$150$	0.419619	−	0.104128i	0.0342618	−	0.00850206i
$151$	5.42198			0.441235			0.220617	−	0.975360i	$-0.429193\pi$
$151$	5.42198			0.441235			0.220617	+	0.975360i	$0.429193\pi$
$152$	−3.75837	+	1.22117i	−0.304844	+	0.0990497i
$153$	1.76213	+	2.42537i	0.142460	+	0.196079i
$154$	3.61220	−	2.62441i	0.291079	−	0.211481i
$155$	1.04403	−	5.35520i	0.0838584	−	0.430140i
$156$	0.0856854	+	0.0622541i	0.00686033	+	0.00498432i
$157$		−	18.8030i		−	1.50065i	−0.661072	−	0.750323i	$-0.729898\pi$
$157$		−	18.8030i		−	1.50065i	0.661072	−	0.750323i	$-0.270102\pi$
$158$	−12.0661	+	16.6076i	−0.959928	+	1.32123i
$159$	−0.110612	+	0.340428i	−0.00877208	+	0.0269977i
$160$	14.7427	−	6.86467i	1.16551	−	0.542700i
$161$	−0.813909	−	2.50495i	−0.0641450	−	0.197418i
$162$	16.1952	+	5.26213i	1.27241	+	0.413432i
$163$	−10.2261	−	3.32266i	−0.800970	−	0.260251i	−0.120202	−	0.992749i	$-0.538354\pi$
$163$	−10.2261	−	3.32266i	−0.800970	−	0.260251i	−0.680769	+	0.732498i	$0.738354\pi$
$164$	−2.70841	−	8.33564i	−0.211492	−	0.650904i
$165$	0.553080	+	0.107826i	0.0430572	+	0.00839426i
$166$	−9.07572	+	27.9322i	−0.704413	+	2.16796i
$167$	10.1318	−	13.9452i	0.784019	−	1.07911i	−0.210808	−	0.977528i	$-0.567609\pi$
$167$	10.1318	−	13.9452i	0.784019	−	1.07911i	0.994827	−	0.101582i	$-0.0323905\pi$
$168$		−	0.0149300i		−	0.00115187i
$169$	−8.80180	−	6.39488i	−0.677061	−	0.491914i
$170$	4.20829	−	0.514344i	0.322761	−	0.0394484i
$171$	−12.4773	+	9.06532i	−0.954166	+	0.693242i
$172$	−0.375823	−	0.517277i	−0.0286563	−	0.0394420i
$173$	−11.4807	+	3.73031i	−0.872863	+	0.283610i	−0.710991	−	0.703201i	$-0.751753\pi$
$173$	−11.4807	+	3.73031i	−0.872863	+	0.283610i	−0.161872	+	0.986812i	$0.551753\pi$
$174$	−0.903379			−0.0684850
$175$	1.63083	+	1.37152i	0.123279	+	0.103677i
$176$	25.6729			1.93517
$177$	0.127459	−	0.0414141i	0.00958044	−	0.00311287i
$178$	9.18641	+	12.6440i	0.688551	+	0.947709i
$179$	−9.71924	+	7.06144i	−0.726450	+	0.527797i	−0.888439	−	0.458996i	$-0.848209\pi$
$179$	−9.71924	+	7.06144i	−0.726450	+	0.527797i	0.161988	+	0.986793i	$0.448209\pi$
$180$	7.82310	−	7.28705i	0.583100	−	0.543145i
$181$	10.8532	+	7.88528i	0.806709	+	0.586108i	0.912875	−	0.408240i	$-0.133857\pi$
$181$	10.8532	+	7.88528i	0.806709	+	0.586108i	−0.106166	+	0.994348i	$0.533857\pi$
$182$			1.17663i			0.0872173i
$183$	−0.241880	+	0.332919i	−0.0178803	+	0.0246101i
$184$	1.46701	−	4.51500i	0.108150	−	0.332850i
$185$	0.103992	+	0.850847i	0.00764563	+	0.0625555i
$186$	0.0651981	+	0.200659i	0.00478056	+	0.0147130i
$187$	5.25519	+	1.70752i	0.384298	+	0.124866i
$188$	3.78464	+	1.22970i	0.276023	+	0.0896853i
$189$	−0.0360242	−	0.110871i	−0.00262038	−	0.00806469i
$190$	2.64605	+	21.6496i	0.191965	+	1.57063i
$191$	4.22551	−	13.0048i	0.305747	−	0.940993i	−0.673650	−	0.739050i	$-0.735275\pi$
$191$	4.22551	−	13.0048i	0.305747	−	0.940993i	0.979397	−	0.201943i	$-0.0647254\pi$
$192$	−0.120551	+	0.165924i	−0.00870001	+	0.0119745i
$193$		−	19.2613i		−	1.38646i	−0.720716	−	0.693231i	$-0.756187\pi$
$193$		−	19.2613i		−	1.38646i	0.720716	−	0.693231i	$-0.243813\pi$
$194$	−18.2491	−	13.2587i	−1.31021	−	0.951922i
$195$	−0.108659	+	0.101213i	−0.00778121	+	0.00724803i
$196$	8.79752	−	6.39177i	0.628394	−	0.456555i
$197$	12.5753	+	17.3085i	0.895956	+	1.23318i	0.971740	+	0.236053i	$0.0758538\pi$
$197$	12.5753	+	17.3085i	0.895956	+	1.23318i	−0.0757847	+	0.997124i	$0.524146\pi$
$198$	29.8710	−	9.70567i	2.12284	−	0.689752i
$199$	1.60323			0.113650			0.0568249	−	0.998384i	$-0.481902\pi$
$199$	1.60323			0.113650			0.0568249	+	0.998384i	$0.481902\pi$
$200$	0.925031	+	3.72771i	0.0654096	+	0.263589i
$201$	−0.0711989			−0.00502198
$202$	0.195069	−	0.0633819i	0.0137250	−	0.00445953i
$203$	−2.61708	−	3.60211i	−0.183683	−	0.252818i
$204$	−0.0588438	+	0.0427525i	−0.00411989	+	0.00299327i
$205$	12.1976	−	1.49081i	0.851920	−	0.104123i
$206$	−2.41216	−	1.75254i	−0.168063	−	0.122105i
$207$		−	18.5278i		−	1.28777i
$208$	−3.97666	+	5.47340i	−0.275731	+	0.379512i
$209$	−8.78434	+	27.0354i	−0.607625	+	1.87008i
$210$	−0.0808792	−	0.0157679i	−0.00558120	−	0.00108809i
$211$	4.24094	+	13.0523i	0.291959	+	0.898556i	0.984226	+	0.176915i	$0.0566119\pi$
$211$	4.24094	+	13.0523i	0.291959	+	0.898556i	−0.692267	+	0.721641i	$0.743388\pi$
$212$	11.9049	+	3.86814i	0.817633	+	0.265665i
$213$	−0.581683	−	0.189000i	−0.0398563	−	0.0129501i
$214$	−1.98784	−	6.11794i	−0.135886	−	0.418214i
$215$	0.812674	−	0.378407i	0.0554239	−	0.0258072i
$216$	0.0649310	−	0.199837i	0.00441800	−	0.0135972i
$217$	−0.611224	+	0.841278i	−0.0414926	+	0.0571097i
$218$			0.881485i			0.0597017i
$219$	−0.361598	−	0.262716i	−0.0244345	−	0.0177527i
$220$	3.77073	−	19.3414i	0.254223	−	1.30400i
$221$	−1.17805	+	0.855905i	−0.0792443	+	0.0575744i
$222$	−0.0194835	−	0.0268167i	−0.00130765	−	0.00179982i
$223$	20.4635	−	6.64900i	1.37034	−	0.445250i	0.470857	−	0.882210i	$-0.343945\pi$
$223$	20.4635	−	6.64900i	1.37034	−	0.445250i	0.899481	+	0.436960i	$0.143945\pi$
$224$	−3.09952			−0.207095
$225$	7.92917	+	12.7207i	0.528611	+	0.848047i
$226$	26.0555			1.73319
$227$	−23.1381	+	7.51802i	−1.53573	+	0.498989i	−0.950194	−	0.311658i	$-0.899116\pi$
$227$	−23.1381	+	7.51802i	−1.53573	+	0.498989i	−0.585535	+	0.810647i	$0.699116\pi$
$228$	−0.219941	−	0.302723i	−0.0145659	−	0.0200483i
$229$	−19.9733	+	14.5115i	−1.31987	+	0.958945i	−0.319941	+	0.947438i	$0.603663\pi$
$229$	−19.9733	+	14.5115i	−1.31987	+	0.958945i	−0.999934	+	0.0115074i	$0.996337\pi$
$230$	−22.9094	−	12.7155i	−1.51060	−	0.838437i
$231$	−0.0868863	−	0.0631266i	−0.00571670	−	0.00415343i
$232$		−	8.02522i		−	0.526881i
$233$	5.79677	−	7.97857i	0.379759	−	0.522694i	−0.575761	−	0.817618i	$-0.695294\pi$
$233$	5.79677	−	7.97857i	0.379759	−	0.522694i	0.955521	+	0.294924i	$0.0952943\pi$
$234$	−2.55770	+	7.87180i	−0.167202	+	0.514595i
$235$	−2.70761	+	4.87828i	−0.176625	+	0.318224i
$236$	−1.44827	−	4.45731i	−0.0942743	−	0.290146i
$237$	0.469607	+	0.152585i	0.0305043	+	0.00991144i
$238$	−0.768489	−	0.249697i	−0.0498138	−	0.0161855i
$239$	−1.72644	−	5.31344i	−0.111674	−	0.343698i	0.879565	−	0.475779i	$-0.157834\pi$
$239$	−1.72644	−	5.31344i	−0.111674	−	0.343698i	−0.991239	+	0.132082i	$0.957834\pi$
$240$	−0.322941	−	0.346697i	−0.0208458	−	0.0223792i
$241$	1.74534	−	5.37161i	0.112427	−	0.346016i	−0.878974	−	0.476869i	$-0.841772\pi$
$241$	1.74534	−	5.37161i	0.112427	−	0.346016i	0.991402	+	0.130853i	$0.0417716\pi$
$242$	21.7681	−	29.9612i	1.39931	−	1.92598i
$243$		−	1.23022i		−	0.0789187i
$244$	11.6423	+	8.45865i	0.745324	+	0.541509i
$245$	6.43572	+	13.8215i	0.411163	+	0.883020i
$246$	−0.384441	+	0.279313i	−0.0245111	+	0.0178083i
$247$	−4.40321	−	6.06050i	−0.280170	−	0.385621i
$248$	−1.78257	+	0.579191i	−0.113193	+	0.0367787i
$249$	0.706446			0.0447692
$250$	21.1708	−	1.07419i	1.33896	−	0.0679376i
$251$	1.47791			0.0932847			0.0466424	−	0.998912i	$-0.485148\pi$
$251$	1.47791			0.0932847			0.0466424	+	0.998912i	$0.485148\pi$
$252$	−1.93793	+	0.629673i	−0.122078	+	0.0396657i
$253$	−20.0726	−	27.6276i	−1.26195	−	1.73693i
$254$	30.4248	−	22.1049i	1.90902	−	1.38699i
$255$	−0.0430464	−	0.0924472i	−0.00269567	−	0.00578927i
$256$	−16.5092	−	11.9947i	−1.03183	−	0.749666i
$257$			12.5478i			0.782712i	0.920239	+	0.391356i	$0.127994\pi$
$257$			12.5478i			0.782712i	−0.920239	+	0.391356i	$0.872006\pi$
$258$	−0.0203762	+	0.0280455i	−0.00126857	+	0.00174603i
$259$	0.0504846	−	0.155376i	0.00313696	−	0.00965458i
$260$	3.53947	+	3.79984i	0.219509	+	0.235656i
$261$	−9.67856	−	29.7875i	−0.599088	−	1.84380i
$262$	4.52876	+	1.47148i	0.279787	+	0.0909084i
$263$	−3.83811	−	1.24708i	−0.236668	−	0.0768982i	0.188282	−	0.982115i	$-0.439708\pi$
$263$	−3.83811	−	1.24708i	−0.236668	−	0.0768982i	−0.424950	+	0.905217i	$0.639708\pi$
$264$	−0.0598183	−	0.184102i	−0.00368156	−	0.0113307i
$265$	−8.51704	+	15.3451i	−0.523198	+	0.942640i
$266$	1.28457	−	3.95350i	0.0787621	−	0.242405i
$267$	0.220966	−	0.304134i	0.0135229	−	0.0186127i
$268$			2.48986i			0.152092i
$269$	20.3275	+	14.7688i	1.23939	+	0.900468i	0.997557	−	0.0698502i	$-0.0222521\pi$
$269$	20.3275	+	14.7688i	1.23939	+	0.900468i	0.241831	+	0.970318i	$0.422252\pi$
$270$	−1.01399	−	0.562798i	−0.0617094	−	0.0342508i
$271$	25.5033	−	18.5292i	1.54921	−	1.12557i	0.605005	−	0.796222i	$-0.293171\pi$
$271$	25.5033	−	18.5292i	1.54921	−	1.12557i	0.944209	−	0.329348i	$-0.106829\pi$
$272$	−2.73094	−	3.75881i	−0.165587	−	0.227911i
$273$	0.0269169	−	0.00874582i	0.00162908	−	0.000529321i
$274$	−4.47879			−0.270573
$275$	25.6049	+	10.3781i	1.54403	+	0.625824i
$276$	0.449516			0.0270577
$277$	−26.0856	+	8.47573i	−1.56733	+	0.509257i	−0.958754	−	0.284237i	$-0.908260\pi$
$277$	−26.0856	+	8.47573i	−1.56733	+	0.509257i	−0.608578	+	0.793494i	$0.708260\pi$
$278$	−13.0728	−	17.9931i	−0.784053	−	1.07916i
$279$	−5.91792	+	4.29962i	−0.354296	+	0.257411i
$280$	0.140075	−	0.718495i	0.00837108	−	0.0429383i
$281$	5.99562	+	4.35607i	0.357669	+	0.259862i	0.752079	−	0.659073i	$-0.229051\pi$
$281$	5.99562	+	4.35607i	0.357669	+	0.259862i	−0.394410	+	0.918934i	$0.629051\pi$
$282$		−	0.215753i		−	0.0128479i
$283$	−2.07005	+	2.84917i	−0.123051	+	0.169366i	−0.866098	−	0.499873i	$-0.833380\pi$
$283$	−2.07005	+	2.84917i	−0.123051	+	0.169366i	0.743047	+	0.669239i	$0.233380\pi$
$284$	−6.60942	+	20.3417i	−0.392197	+	1.20706i
$285$	0.475596	−	0.221453i	0.0281719	−	0.0131177i
$286$	4.71424	+	14.5090i	0.278759	+	0.857932i
$287$	−2.22745	−	0.723742i	−0.131482	−	0.0427211i
$288$	−20.7362	−	6.73761i	−1.22189	−	0.397018i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−43.4744	−	8.47560i	−2.55291	−	0.497705i
$291$	−0.167666	+	0.516024i	−0.00982878	+	0.0302499i
$292$	−9.18731	+	12.6452i	−0.537647	+	0.740007i
$293$			8.90518i			0.520246i	0.965575	+	0.260123i	$0.0837632\pi$
$293$			8.90518i			0.520246i	−0.965575	+	0.260123i	$0.916237\pi$
$294$	−0.476980	−	0.346546i	−0.0278180	−	0.0202110i
$295$	6.52244	−	0.797182i	0.379751	−	0.0464138i
$296$	0.238228	−	0.173083i	0.0138467	−	0.0100602i
$297$	−0.888428	−	1.22282i	−0.0515518	−	0.0709550i
$298$	−22.3919	+	7.27556i	−1.29713	+	0.421462i
$299$	8.99932			0.520444
$300$	−0.308627	+	0.192376i	−0.0178186	+	0.0111068i
$301$	−0.170857			−0.00984806
$302$	−9.77700	+	3.17674i	−0.562603	+	0.182801i
$303$	−0.00289989	−	0.00399135i	−0.000166594	−	0.000229297i
$304$	19.3372	−	14.0493i	1.10907	−	0.805785i
$305$	−14.7638	+	13.7521i	−0.845371	+	0.787445i
$306$	−4.59852	−	3.34102i	−0.262880	−	0.190994i
$307$			7.52817i			0.429655i	0.976652	+	0.214828i	$0.0689190\pi$
$307$			7.52817i			0.429655i	−0.976652	+	0.214828i	$0.931081\pi$
$308$	−2.20757	+	3.03845i	−0.125788	+	0.173132i
$309$	−0.0221621	+	0.0682079i	−0.00126076	+	0.00388021i
$310$	1.25500	+	10.2683i	0.0712794	+	0.583198i
$311$	7.08252	+	21.7977i	0.401613	+	1.23604i	0.923691	+	0.383139i	$0.125157\pi$
$311$	7.08252	+	21.7977i	0.401613	+	1.23604i	−0.522078	+	0.852898i	$0.674843\pi$
$312$	0.0485157	+	0.0157637i	0.00274666	+	0.000892444i
$313$	12.7194	+	4.13280i	0.718945	+	0.233599i	0.645566	−	0.763705i	$-0.276622\pi$
$313$	12.7194	+	4.13280i	0.718945	+	0.233599i	0.0733793	+	0.997304i	$0.476622\pi$
$314$	11.0167	+	33.9059i	0.621708	+	1.91342i
$315$	−0.346596	−	2.83580i	−0.0195285	−	0.159779i
$316$	5.33596	−	16.4224i	0.300171	−	0.923831i
$317$	−16.2575	+	22.3766i	−0.913114	+	1.25679i	0.0529780	+	0.998596i	$0.483129\pi$
$317$	−16.2575	+	22.3766i	−0.913114	+	1.25679i	−0.966092	+	0.258198i	$0.916871\pi$
$318$		−	0.678672i		−	0.0380580i
$319$	−46.7034	−	33.9320i	−2.61489	−	1.89983i
$320$	−7.35814	+	6.85394i	−0.411332	+	0.383147i
$321$	−0.125180	+	0.0909489i	−0.00698689	+	0.00507627i
$322$	2.93530	+	4.04010i	0.163578	+	0.225146i
$323$	4.89272	−	1.58974i	0.272238	−	0.0884556i
$324$	−14.3239			−0.795771
$325$	−6.17871	+	3.85136i	−0.342733	+	0.213635i
$326$	20.3866			1.12911
$327$	0.0201651	−	0.00655205i	0.00111513	−	0.000362329i
$328$	−2.48129	−	3.41520i	−0.137006	−	0.188573i
$329$	0.860289	−	0.625036i	0.0474292	−	0.0344594i
$330$	−1.06050	+	0.129615i	−0.0583784	+	0.00713509i
$331$	2.98522	+	2.16889i	0.164083	+	0.119213i	0.666796	−	0.745240i	$-0.267665\pi$
$331$	2.98522	+	2.16889i	0.164083	+	0.119213i	−0.502714	+	0.864453i	$0.667665\pi$
$332$		−	24.7047i		−	1.35585i
$333$	0.675499	−	0.929745i	0.0370171	−	0.0509497i
$334$	−10.0993	+	31.0823i	−0.552607	+	1.70075i
$335$	−3.42639	−	0.667996i	−0.187204	−	0.0364965i
$336$	0.0279053	+	0.0858836i	0.00152236	+	0.00468534i
$337$	12.2629	+	3.98447i	0.668005	+	0.217048i	0.623336	−	0.781954i	$-0.285777\pi$
$337$	12.2629	+	3.98447i	0.668005	+	0.217048i	0.0446686	+	0.999002i	$0.485777\pi$
$338$	19.6183	+	6.37437i	1.06709	+	0.346720i
$339$	−0.193670	−	0.596054i	−0.0105187	−	0.0323732i
$340$	−3.23292	+	1.50535i	−0.175330	+	0.0816392i
$341$	−4.16635	+	12.8227i	−0.225620	+	0.694388i
$342$	17.1879	−	23.6572i	0.929418	−	1.27923i
$343$		−	5.88908i		−	0.317981i
$344$	−0.249143	−	0.181013i	−0.0134329	−	0.00975958i
$345$	−0.120599	+	0.618598i	−0.00649285	+	0.0333042i
$346$	18.5166	−	13.4531i	0.995459	−	0.723243i
$347$	−5.04817	−	6.94822i	−0.271000	−	0.373000i	0.651727	−	0.758454i	$-0.274045\pi$
$347$	−5.04817	−	6.94822i	−0.271000	−	0.373000i	−0.922727	+	0.385454i	$0.874045\pi$
$348$	0.722699	−	0.234819i	0.0387407	−	0.0125876i
$349$	1.11826			0.0598593			0.0299296	−	0.999552i	$-0.490472\pi$
$349$	1.11826			0.0598593			0.0299296	+	0.999552i	$0.490472\pi$
$350$	−3.74431	−	1.51764i	−0.200142	−	0.0811211i
$351$	0.398316			0.0212606
$352$	−38.2201	+	12.4185i	−2.03714	+	0.661907i
$353$	12.5435	+	17.2646i	0.667623	+	0.918904i	0.999704	−	0.0243468i	$-0.00775059\pi$
$353$	12.5435	+	17.2646i	0.667623	+	0.918904i	−0.332081	+	0.943251i	$0.607751\pi$
$354$	−0.205572	+	0.149357i	−0.0109260	+	0.00793823i
$355$	−26.2198	−	14.5529i	−1.39160	−	0.772388i
$356$	−10.6357	−	7.72729i	−0.563691	−	0.409545i
$357$			0.0194362i			0.00102867i
$358$	13.3886	−	18.4278i	0.707608	−	0.973939i
$359$	9.01754	−	27.7531i	0.475927	−	1.46475i	−0.368776	−	0.929518i	$-0.620223\pi$
$359$	9.01754	−	27.7531i	0.475927	−	1.46475i	0.844703	−	0.535235i	$-0.179777\pi$
$360$	2.49896	−	4.50235i	0.131707	−	0.237295i
$361$	2.30713	+	7.10061i	0.121428	+	0.373716i
$362$	−24.1906	−	7.85999i	−1.27143	−	0.413112i
$363$	−0.847205	−	0.275273i	−0.0444667	−	0.0144481i
$364$	−0.305845	−	0.941295i	−0.0160306	−	0.0493372i
$365$	−14.9368	−	16.0356i	−0.781828	−	0.839341i
$366$	0.241104	−	0.742041i	0.0126027	−	0.0387871i
$367$	−20.2421	+	27.8609i	−1.05663	+	1.45433i	−0.173713	+	0.984796i	$0.555576\pi$
$367$	−20.2421	+	27.8609i	−1.05663	+	1.45433i	−0.882917	+	0.469529i	$0.844424\pi$
$368$			28.7141i			1.49683i
$369$	−13.3287	−	9.68388i	−0.693865	−	0.504123i
$370$	−0.686030	−	1.47333i	−0.0356650	−	0.0765948i
$371$	2.70612	−	1.96611i	0.140495	−	0.102075i
$372$	−0.104316	−	0.143579i	−0.00540855	−	0.00744423i
$373$	−7.53294	+	2.44760i	−0.390041	+	0.126732i	−0.497471	−	0.867481i	$-0.665738\pi$
$373$	−7.53294	+	2.44760i	−0.390041	+	0.126732i	0.107430	+	0.994213i	$0.465738\pi$
$374$	−10.4767			−0.541736
$375$	−0.181935	−	0.476326i	−0.00939511	−	0.0245974i
$376$	1.91666			0.0988440
$377$	14.4684	−	4.70108i	0.745162	−	0.242118i
$378$	0.129919	+	0.178818i	0.00668230	+	0.00919739i
$379$	−7.10386	+	5.16125i	−0.364901	+	0.265116i	−0.755093	−	0.655617i	$-0.772408\pi$
$379$	−7.10386	+	5.16125i	−0.364901	+	0.265116i	0.390193	+	0.920733i	$0.372408\pi$
$380$	−7.74431	−	16.6318i	−0.397275	−	0.853193i
$381$	−0.731827	−	0.531703i	−0.0374926	−	0.0272400i
$382$			25.9261i			1.32650i
$383$	0.142031	−	0.195488i	0.00725743	−	0.00998899i	−0.805373	−	0.592769i	$-0.798035\pi$
$383$	0.142031	−	0.195488i	0.00725743	−	0.00998899i	0.812630	+	0.582780i	$0.198035\pi$
$384$	−0.0848278	+	0.261073i	−0.00432885	+	0.0133228i
$385$	−3.58908	−	3.85310i	−0.182916	−	0.196372i
$386$	11.2852	+	34.7323i	0.574402	+	1.76783i
$387$	−1.14306	−	0.371403i	−0.0581051	−	0.0188795i
$388$	18.0456	+	5.86337i	0.916126	+	0.297667i
$389$	5.84234	+	17.9809i	0.296218	+	0.911666i	0.982810	+	0.184622i	$0.0591062\pi$
$389$	5.84234	+	17.9809i	0.296218	+	0.911666i	−0.686591	+	0.727044i	$0.740894\pi$
$390$	0.136634	−	0.246172i	0.00691873	−	0.0124654i
$391$	−1.90979	+	5.87772i	−0.0965821	+	0.297249i
$392$	3.07856	−	4.23728i	0.155491	−	0.214015i
$393$		−	0.114539i		−	0.00577772i
$394$	−32.8170	−	23.8430i	−1.65330	−	1.20119i
$395$	21.1679	+	11.7489i	1.06507	+	0.591153i
$396$	−21.3738	+	15.5290i	−1.07407	+	0.780361i
$397$	6.92263	+	9.52818i	0.347437	+	0.478206i	0.946595	−	0.322425i	$-0.104498\pi$
$397$	6.92263	+	9.52818i	0.347437	+	0.478206i	−0.599158	+	0.800631i	$0.704498\pi$
$398$	−2.89096	+	0.939331i	−0.144911	+	0.0470844i
$399$	−0.0999898			−0.00500575
$400$	−12.2885	−	19.7144i	−0.614427	−	0.985721i
$401$	−0.740335			−0.0369706			−0.0184853	−	0.999829i	$-0.505884\pi$
$401$	−0.740335			−0.0369706			−0.0184853	+	0.999829i	$0.505884\pi$
$402$	0.128387	−	0.0417154i	0.00640335	−	0.00208057i
$403$	−2.08841	−	2.87445i	−0.104031	−	0.143187i
$404$	−0.139579	+	0.101410i	−0.00694433	+	0.00504535i
$405$	3.84291	−	19.7117i	0.190956	−	0.979480i
$406$	6.82963	+	4.96202i	0.338949	+	0.246261i
$407$		−	2.11821i		−	0.104996i
$408$	−0.0205915	+	0.0283418i	−0.00101943	+	0.00140313i
$409$	3.52775	−	10.8573i	0.174436	−	0.536859i	−0.825171	−	0.564883i	$-0.808921\pi$
$409$	3.52775	−	10.8573i	0.174436	−	0.536859i	0.999607	+	0.0280239i	$0.00892145\pi$
$410$	−21.1215	+	9.83485i	−1.04312	+	0.485709i
$411$	0.0332907	+	0.102458i	0.00164211	+	0.00505389i
$412$	2.38526	+	0.775018i	0.117513	+	0.0381824i
$413$	−1.19108	−	0.387006i	−0.0586094	−	0.0190433i
$414$	10.8554	+	33.4095i	0.533514	+	1.64199i
$415$	33.9972	+	6.62795i	1.66886	+	0.325353i
$416$	3.27260	−	10.0720i	0.160452	−	0.493821i
$417$	−0.314447	+	0.432800i	−0.0153986	+	0.0211943i
$418$		−	53.8974i		−	2.63621i
$419$	8.59824	+	6.24699i	0.420052	+	0.305185i	0.777659	−	0.628687i	$-0.216407\pi$
$419$	8.59824	+	6.24699i	0.420052	+	0.305185i	−0.357607	+	0.933872i	$0.616407\pi$
$420$	0.0688016	−	0.00840903i	0.00335717	−	0.000410319i
$421$	−17.5683	+	12.7641i	−0.856228	+	0.622086i	−0.926856	−	0.375417i	$-0.877500\pi$
$421$	−17.5683	+	12.7641i	−0.856228	+	0.622086i	0.0706283	+	0.997503i	$0.477500\pi$
$422$	−15.2947	−	21.0513i	−0.744532	−	1.02476i
$423$	7.11414	−	2.31152i	0.345901	−	0.112390i
$424$	6.02902			0.292795
$425$	−1.20423	−	4.85282i	−0.0584135	−	0.235396i
$426$	1.15963			0.0561845
$427$	3.65727	−	1.18832i	0.176988	−	0.0575068i
$428$	3.18052	+	4.37761i	0.153736	+	0.211600i
$429$	0.296871	−	0.215689i	0.0143331	−	0.0104136i
$430$	−1.24372	+	1.15849i	−0.0599773	+	0.0558676i
$431$	−12.8359	−	9.32586i	−0.618286	−	0.449211i	0.234037	−	0.972228i	$-0.424806\pi$
$431$	−12.8359	−	9.32586i	−0.618286	−	0.449211i	−0.852322	+	0.523017i	$0.824806\pi$
$432$			1.27091i			0.0611466i
$433$	10.8579	−	14.9447i	0.521800	−	0.718196i	−0.464054	−	0.885807i	$-0.653605\pi$
$433$	10.8579	−	14.9447i	0.521800	−	0.718196i	0.985853	+	0.167612i	$0.0536055\pi$
$434$	0.609263	−	1.87512i	0.0292456	−	0.0900086i
$435$	0.129253	+	1.05753i	0.00619722	+	0.0507049i
$436$	−0.229128	−	0.705183i	−0.0109732	−	0.0337722i
$437$	−30.2380	−	9.82493i	−1.44648	−	0.469990i
$438$	0.805964	+	0.261874i	0.0385105	+	0.0125128i
$439$	11.4082	+	35.1108i	0.544483	+	1.67575i	0.722216	+	0.691668i	$0.243124\pi$
$439$	11.4082	+	35.1108i	0.544483	+	1.67575i	−0.177733	+	0.984079i	$0.556876\pi$
$440$	−1.15145	−	9.42098i	−0.0548930	−	0.449127i
$441$	6.31660	−	19.4405i	0.300790	−	0.925737i
$442$	1.62280	−	2.23360i	0.0771889	−	0.106241i
$443$			20.7162i			0.984257i	0.870523	+	0.492128i	$0.163781\pi$
$443$			20.7162i			0.984257i	−0.870523	+	0.492128i	$0.836219\pi$
$444$	0.0225573	+	0.0163888i	0.00107052	+	0.000777779i
$445$	13.4872	−	12.5631i	0.639357	−	0.595547i
$446$	−33.0044	+	23.9791i	−1.56280	+	1.13544i
$447$	0.332876	+	0.458165i	0.0157445	+	0.0216705i
$448$	1.82275	−	0.592248i	0.0861170	−	0.0279811i
$449$	−8.90683			−0.420339			−0.210170	−	0.977665i	$-0.567402\pi$
$449$	−8.90683			−0.420339			−0.210170	+	0.977665i	$0.567402\pi$
$450$	−21.7510	−	18.2925i	−1.02535	−	0.862315i
$451$	−30.3664			−1.42990
$452$	−20.8443	+	6.77271i	−0.980432	+	0.318562i
$453$	0.145344	+	0.200049i	0.00682887	+	0.00939913i
$454$	37.3181	−	27.1132i	1.75143	−	1.27249i
$455$	1.37741	−	0.168349i	0.0645739	−	0.00789231i
$456$	−0.145805	−	0.105933i	−0.00682793	−	0.00496078i
$457$			32.2881i			1.51037i	0.655510	+	0.755186i	$0.272454\pi$
$457$			32.2881i			1.51037i	−0.655510	+	0.755186i	$0.727546\pi$
$458$	27.5139	−	37.8696i	1.28564	−	1.76953i
$459$	−0.0845286	+	0.260152i	−0.00394546	+	0.0121429i
$460$	21.6326	+	4.21741i	1.00863	+	0.196638i
$461$	2.15546	+	6.63383i	0.100390	+	0.308968i	0.988621	−	0.150429i	$-0.0480655\pi$
$461$	2.15546	+	6.63383i	0.100390	+	0.308968i	−0.888231	+	0.459397i	$0.848065\pi$
$462$	0.193660	+	0.0629241i	0.00900990	+	0.00292749i
$463$	−9.52608	−	3.09521i	−0.442714	−	0.143847i	0.0791733	−	0.996861i	$-0.474772\pi$
$463$	−9.52608	−	3.09521i	−0.442714	−	0.143847i	−0.521888	+	0.853014i	$0.674772\pi$
$464$	14.9997	+	46.1644i	0.696345	+	2.14313i
$465$	0.225572	−	0.105034i	0.0104606	−	0.00487081i
$466$	−5.77818	+	17.7834i	−0.267669	+	0.823800i
$467$	17.3073	−	23.8215i	0.800887	−	1.10233i	−0.191779	−	0.981438i	$-0.561426\pi$
$467$	17.3073	−	23.8215i	0.800887	−	1.10233i	0.992666	−	0.120889i	$-0.0385744\pi$
$468$		−	6.96223i		−	0.321829i
$469$	0.538271	+	0.391076i	0.0248550	+	0.0180582i
$470$	2.02422	−	10.3830i	0.0933704	−	0.478931i
$471$	0.693755	−	0.504043i	0.0319666	−	0.0232251i
$472$	−1.32682	−	1.82621i	−0.0610719	−	0.0840582i
$473$	−2.10684	+	0.684554i	−0.0968727	+	0.0314758i
$474$	−0.936202			−0.0430012
$475$	24.9654	−	6.19516i	1.14549	−	0.284253i
$476$	0.679693			0.0311537
$477$	22.3782	−	7.27111i	1.02463	−	0.332921i
$478$	6.22628	+	8.56975i	0.284784	+	0.391971i
$479$	7.26714	−	5.27988i	0.332044	−	0.241244i	−0.409253	−	0.912421i	$-0.634211\pi$
$479$	7.26714	−	5.27988i	0.332044	−	0.241244i	0.741297	+	0.671177i	$0.234211\pi$
$480$	0.648478	+	0.359927i	0.0295988	+	0.0164284i
$481$	0.451596	+	0.328104i	0.0205910	+	0.0149603i
$482$			10.7088i			0.487771i
$483$	0.0706046	−	0.0971789i	0.00321262	−	0.00442179i
$484$	−9.62644	+	29.6271i	−0.437565	+	1.34669i
$485$	−12.9102	+	23.2602i	−0.586223	+	1.05619i
$486$	0.720786	+	2.21835i	0.0326955	+	0.100626i
$487$	−10.4419	−	3.39277i	−0.473167	−	0.153741i	0.0627198	−	0.998031i	$-0.480023\pi$
$487$	−10.4419	−	3.39277i	−0.473167	−	0.153741i	−0.535887	+	0.844290i	$0.680023\pi$
$488$	6.59197	+	2.14186i	0.298404	+	0.0969574i
$489$	−0.151533	−	0.466370i	−0.00685256	−	0.0210900i
$490$	−19.7030	−	21.1523i	−0.890089	−	0.955566i
$491$	10.1893	−	31.3594i	0.459836	−	1.41523i	−0.405525	−	0.914084i	$-0.632911\pi$
$491$	10.1893	−	31.3594i	0.459836	−	1.41523i	0.865362	−	0.501147i	$-0.167089\pi$
$492$	0.234948	−	0.323378i	0.0105923	−	0.0145790i
$493$			10.4474i			0.470527i
$494$	11.4908	+	8.34854i	0.516995	+	0.375619i
$495$	−15.6357	−	33.5796i	−0.702774	−	1.50929i
$496$	9.17152	−	6.66350i	0.411814	−	0.299200i
$497$	3.35945	+	4.62389i	0.150692	+	0.207410i
$498$	−1.27387	+	0.413906i	−0.0570836	+	0.0185476i
$499$	35.2034			1.57592			0.787961	−	0.615725i	$-0.211137\pi$
$499$	35.2034			1.57592			0.787961	+	0.615725i	$0.211137\pi$
$500$	−16.6573	+	6.36236i	−0.744939	+	0.284534i
$501$	0.786117			0.0351211
$502$	−2.66498	+	0.865906i	−0.118944	+	0.0386473i
$503$	8.69872	+	11.9728i	0.387857	+	0.533839i	0.957645	−	0.287953i	$-0.0929747\pi$
$503$	8.69872	+	11.9728i	0.387857	+	0.533839i	−0.569788	+	0.821792i	$0.692975\pi$
$504$	−0.793993	+	0.576870i	−0.0353673	+	0.0256958i
$505$	−0.102108	−	0.219288i	−0.00454373	−	0.00975818i
$506$	52.3822	+	38.0579i	2.32867	+	1.69188i
$507$		−	0.496175i		−	0.0220359i
$508$	−18.5939	+	25.5923i	−0.824971	+	1.13547i
$509$	−7.39683	+	22.7651i	−0.327859	+	1.00905i	0.642275	+	0.766475i	$0.277991\pi$
$509$	−7.39683	+	22.7651i	−0.327859	+	1.00905i	−0.970134	+	0.242571i	$0.922009\pi$
$510$	0.131787	+	0.141481i	0.00583561	+	0.00626489i
$511$	1.29069	+	3.97233i	0.0570966	+	0.175725i
$512$	25.3482	+	8.23614i	1.12024	+	0.363990i
$513$	−1.33836	−	0.434859i	−0.0590899	−	0.0191995i
$514$	−7.35177	−	22.6264i	−0.324273	−	0.998009i
$515$	−1.70647	+	3.07452i	−0.0751959	+	0.135480i
$516$	0.00901090	−	0.0277327i	0.000396683	−	0.00122086i
$517$	8.10395	−	11.1541i	0.356411	−	0.490558i
$518$			0.309755i			0.0136098i
$519$	−0.445391	−	0.323595i	−0.0195505	−	0.0142043i
$520$	2.18688	+	1.21380i	0.0959012	+	0.0532285i
$521$	7.56225	−	5.49430i	0.331308	−	0.240710i	−0.409677	−	0.912231i	$-0.634359\pi$
$521$	7.56225	−	5.49430i	0.331308	−	0.240710i	0.740986	+	0.671521i	$0.234359\pi$
$522$	34.9050	+	48.0426i	1.52775	+	2.10277i
$523$	15.3996	−	5.00363i	0.673378	−	0.218794i	0.0476839	−	0.998862i	$-0.484816\pi$
$523$	15.3996	−	5.00363i	0.673378	−	0.218794i	0.625694	+	0.780069i	$0.284816\pi$
$524$	−4.00547			−0.174980
$525$	−0.00688656	+	0.0969367i	−0.000300554	+	0.00423066i
$526$	7.65160			0.333626
$527$	2.32058	−	0.754004i	0.101086	−	0.0328449i
$528$	0.688200	+	0.947226i	0.0299500	+	0.0412227i
$529$	12.2929	−	8.93135i	0.534476	−	0.388320i
$530$	6.36737	−	32.6606i	0.276581	−	1.41868i
$531$	−7.12726	−	5.17826i	−0.309297	−	0.224717i
$532$			3.49669i			0.151601i
$533$	4.70366	−	6.47403i	0.203738	−	0.280422i
$534$	−0.220257	+	0.677882i	−0.00953147	+	0.0293348i
$535$	−6.87751	+	3.20239i	−0.297340	+	0.138451i
$536$	0.370581	+	1.14053i	0.0160067	+	0.0492634i
$537$	−0.521077	−	0.169308i	−0.0224861	−	0.00730619i
$538$	−45.3078	−	14.7214i	−1.95336	−	0.634685i
$539$	−11.6425	−	35.8319i	−0.501477	−	1.54339i
$540$	0.957476	+	0.186666i	0.0412032	+	0.00803282i
$541$	2.06383	−	6.35182i	0.0887310	−	0.273086i	−0.896838	−	0.442359i	$-0.854142\pi$
$541$	2.06383	−	6.35182i	0.0887310	−	0.273086i	0.985569	+	0.169273i	$0.0541418\pi$
$542$	−35.1316	+	48.3545i	−1.50903	+	2.07700i
$543$			0.611814i			0.0262555i
$544$	5.88384	+	4.27486i	0.252268	+	0.183283i
$545$	1.03190	−	0.126121i	0.0442019	−	0.00540242i
$546$	−0.0434127	+	0.0315412i	−0.00185789	+	0.00134984i
$547$	11.7148	+	16.1240i	0.500888	+	0.689413i	0.982350	−	0.187054i	$-0.0598939\pi$
$547$	11.7148	+	16.1240i	0.500888	+	0.689413i	−0.481462	+	0.876467i	$0.659894\pi$
$548$	3.58301	−	1.16419i	0.153059	−	0.0497317i
$549$	27.0508			1.15450
$550$	−52.2516	−	3.71205i	−2.22802	−	0.158283i
$551$	−53.7468			−2.28969
$552$	0.205910	−	0.0669044i	0.00876413	−	0.00284764i
$553$	−2.71217	−	3.73298i	−0.115333	−	0.158743i
$554$	42.0720	−	30.5671i	1.78747	−	1.29867i
$555$	−0.0286051	+	0.0266451i	−0.00121422	+	0.00113102i
$556$	15.1352	+	10.9964i	0.641875	+	0.466350i
$557$			6.89094i			0.291978i	0.989286	+	0.145989i	$0.0466365\pi$
$557$			6.89094i			0.291978i	−0.989286	+	0.145989i	$0.953364\pi$
$558$	8.15212	−	11.2204i	0.345107	−	0.474999i
$559$	0.180398	−	0.555209i	0.00763003	−	0.0234828i
$560$	0.537151	+	4.39490i	0.0226988	+	0.185718i
$561$	0.0778727	+	0.239668i	0.00328779	+	0.0101188i
$562$	−13.3636	−	4.34210i	−0.563710	−	0.183160i
$563$	15.7070	+	5.10353i	0.661973	+	0.215088i	0.620686	−	0.784059i	$-0.286854\pi$
$563$	15.7070	+	5.10353i	0.661973	+	0.215088i	0.0412871	+	0.999147i	$0.486854\pi$
$564$	0.0560817	+	0.172602i	0.00236146	+	0.00726784i
$565$	−3.72796	−	30.5017i	−0.156836	−	1.28321i
$566$	2.06340	−	6.35051i	0.0867314	−	0.266932i
$567$	−2.24982	+	3.09661i	−0.0944836	+	0.130045i
$568$			10.3017i			0.432249i
$569$	21.3121	+	15.4841i	0.893448	+	0.649128i	0.936775	−	0.349933i	$-0.113796\pi$
$569$	21.3121	+	15.4841i	0.893448	+	0.649128i	−0.0433269	+	0.999061i	$0.513796\pi$
$570$	−0.727852	+	0.677978i	−0.0304864	+	0.0283974i
$571$	−19.0782	+	13.8612i	−0.798400	+	0.580071i	−0.910444	−	0.413632i	$-0.864260\pi$
$571$	−19.0782	+	13.8612i	−0.798400	+	0.580071i	0.112045	+	0.993703i	$0.464260\pi$
$572$	−7.54275	−	10.3817i	−0.315378	−	0.434081i
$573$	0.593094	−	0.192708i	0.0247769	−	0.00805049i
$574$	4.44060			0.185347
$575$	−11.6075	+	28.6381i	−0.484067	+	1.19429i
$576$	13.4819			0.561745
$577$	−26.4263	+	8.58643i	−1.10014	+	0.357458i	−0.802157	−	0.597113i	$-0.796314\pi$
$577$	−26.4263	+	8.58643i	−1.10014	+	0.357458i	−0.297985	+	0.954571i	$0.596314\pi$
$578$	1.11445	+	1.53391i	0.0463549	+	0.0638020i
$579$	0.710665	−	0.516328i	0.0295342	−	0.0214579i
$580$	36.9824	−	4.52005i	1.53561	−	0.187685i
$581$	−5.34080	−	3.88032i	−0.221574	−	0.160983i
$582$		−	1.02874i		−	0.0426425i
$583$	25.4917	−	35.0863i	1.05576	−	1.45313i
$584$	−2.32637	+	7.15983i	−0.0962658	+	0.296276i
$585$	9.58101	+	1.86788i	0.396126	+	0.0772272i
$586$	−5.21754	−	16.0579i	−0.215535	−	0.663348i
$587$	40.5073	+	13.1616i	1.67192	+	0.543238i	0.983316	−	0.181904i	$-0.0582261\pi$
$587$	40.5073	+	13.1616i	1.67192	+	0.543238i	0.688599	+	0.725142i	$0.258226\pi$
$588$	0.471661	+	0.153252i	0.0194510	+	0.00632000i
$589$	3.87898	+	11.9383i	0.159831	+	0.491908i
$590$	−11.2943	+	5.25899i	−0.464978	+	0.216509i
$591$	−0.301512	+	0.927957i	−0.0124025	+	0.0381711i
$592$	−1.04688	+	1.44091i	−0.0430266	+	0.0592210i
$593$		−	26.3286i		−	1.08119i	−0.841284	−	0.540593i	$-0.818200\pi$
$593$		−	26.3286i		−	1.08119i	0.841284	−	0.540593i	$-0.181800\pi$
$594$	2.31847	+	1.68447i	0.0951281	+	0.0691146i
$595$	−0.182353	+	0.935353i	−0.00747573	+	0.0383457i
$596$	16.0222	−	11.6408i	0.656296	−	0.476827i
$597$	0.0429769	+	0.0591526i	0.00175893	+	0.00242095i
$598$	−16.2277	+	5.27270i	−0.663600	+	0.215617i
$599$	−46.7588			−1.91051			−0.955256	−	0.295779i	$-0.904421\pi$
$599$	−46.7588			−1.91051			−0.955256	+	0.295779i	$0.904421\pi$
$600$	−0.112741	+	0.134057i	−0.00460262	+	0.00547284i
$601$	25.1034			1.02399			0.511995	−	0.858989i	$-0.328907\pi$
$601$	25.1034			1.02399			0.511995	+	0.858989i	$0.328907\pi$
$602$	0.308092	−	0.100105i	0.0125569	−	0.00407999i
$603$	2.75100	+	3.78643i	0.112030	+	0.154195i
$604$	6.99581	−	5.08275i	0.284655	−	0.206814i
$605$	−38.1884	−	21.1959i	−1.55258	−	0.861736i
$606$	0.00756765	+	0.00549822i	0.000307415	+	0.000223350i
$607$			25.3934i			1.03068i	0.856984	+	0.515342i	$0.172335\pi$
$607$			25.3934i			1.03068i	−0.856984	+	0.515342i	$0.827665\pi$
$608$	−21.9921	+	30.2695i	−0.891897	+	1.22759i
$609$	0.0627483	−	0.193119i	0.00254269	−	0.00782560i
$610$	18.5649	−	33.4481i	0.751669	−	1.35427i
$611$	1.12275	+	3.45548i	0.0454218	+	0.139794i
$612$	4.54724	+	1.47749i	0.183811	+	0.0597240i
$613$	−8.38685	−	2.72505i	−0.338742	−	0.110064i	0.134707	−	0.990886i	$-0.456991\pi$
$613$	−8.38685	−	2.72505i	−0.338742	−	0.110064i	−0.473448	+	0.880822i	$0.656991\pi$
$614$	−4.41075	−	13.5749i	−0.178003	−	0.547838i
$615$	0.381981	+	0.410080i	0.0154029	+	0.0165360i
$616$	−0.558990	+	1.72039i	−0.0225223	+	0.0693166i
$617$	−17.7967	+	24.4950i	−0.716467	+	0.986132i	0.283167	+	0.959071i	$0.408615\pi$
$617$	−17.7967	+	24.4950i	−0.716467	+	0.986132i	−0.999634	+	0.0270616i	$0.991385\pi$
$618$		−	0.135978i		−	0.00546984i
$619$	−17.5631	−	12.7604i	−0.705923	−	0.512883i	0.175933	−	0.984402i	$-0.443706\pi$
$619$	−17.5631	−	12.7604i	−0.705923	−	0.512883i	−0.881856	+	0.471519i	$0.843706\pi$
$620$	−3.67307	−	7.88835i	−0.147514	−	0.316804i
$621$	1.36767	−	0.993672i	0.0548828	−	0.0398747i
$622$	−25.5426	−	35.1563i	−1.02416	−	1.40964i
$623$	−3.34105	+	1.08557i	−0.133856	+	0.0434926i
$624$	−0.308546			−0.0123517
$625$	−4.28656	−	24.6298i	−0.171462	−	0.985191i
$626$	−25.3573			−1.01348
$627$	−1.23297	+	0.400617i	−0.0492402	+	0.0159991i
$628$	−17.6266	−	24.2609i	−0.703378	−	0.968117i
$629$	−0.310130	+	0.225323i	−0.0123657	+	0.00898420i
$630$	2.28648	+	4.91049i	0.0910956	+	0.195638i
$631$	−15.6672	−	11.3829i	−0.623703	−	0.453147i	0.230510	−	0.973070i	$-0.425961\pi$
$631$	−15.6672	−	11.3829i	−0.623703	−	0.453147i	−0.854213	+	0.519923i	$0.825961\pi$
$632$		−	8.31680i		−	0.330825i
$633$	−0.367891	+	0.506359i	−0.0146224	+	0.0201260i
$634$	16.2054	−	49.8750i	0.643598	−	1.98079i
$635$	−30.2301	−	32.4539i	−1.19964	−	1.28789i
$636$	0.176410	+	0.542934i	0.00699511	+	0.0215287i
$637$	9.44265	+	3.06810i	0.374131	+	0.121563i
$638$	104.097	+	33.8231i	4.12124	+	1.33907i
$639$	12.4240	+	38.2372i	0.491486	+	1.51264i
$640$	−6.53169	+	11.7681i	−0.258188	+	0.465174i
$641$	5.19865	−	15.9998i	0.205334	−	0.631954i	−0.794365	−	0.607441i	$-0.792196\pi$
$641$	5.19865	−	15.9998i	0.205334	−	0.631954i	0.999699	−	0.0245136i	$-0.00780370\pi$
$642$	0.172440	−	0.237343i	0.00680567	−	0.00936720i
$643$			6.52107i			0.257166i	0.991699	+	0.128583i	$0.0410429\pi$
$643$			6.52107i			0.257166i	−0.991699	+	0.128583i	$0.958957\pi$
$644$	−3.39839	−	2.46907i	−0.133915	−	0.0972951i
$645$	0.0357466	+	0.0198406i	0.00140752	+	0.000781222i
$646$	−7.89120	+	5.73329i	−0.310475	+	0.225573i
$647$	−16.4701	−	22.6691i	−0.647505	−	0.891214i	0.351483	−	0.936194i	$-0.385677\pi$
$647$	−16.4701	−	22.6691i	−0.647505	−	0.891214i	−0.998988	+	0.0449806i	$0.985677\pi$
$648$	−6.56135	+	2.13191i	−0.257754	+	0.0837494i
$649$	−16.2378			−0.637390
$650$	8.88502	−	10.5649i	0.348499	−	0.414391i
$651$	−0.0474245			−0.00185871
$652$	−16.3092	+	5.29917i	−0.638717	+	0.207532i
$653$	−1.80990	−	2.49111i	−0.0708269	−	0.0974848i	0.772134	−	0.635460i	$-0.219189\pi$
$653$	−1.80990	−	2.49111i	−0.0708269	−	0.0974848i	−0.842961	+	0.537975i	$0.819189\pi$
$654$	−0.0325232	+	0.0236295i	−0.00127176	+	0.000923986i
$655$	1.07462	−	5.51209i	0.0419887	−	0.215375i
$656$	20.6567	+	15.0080i	0.806509	+	0.585963i
$657$			29.3811i			1.14627i
$658$	−1.18508	+	1.63112i	−0.0461991	+	0.0635876i
$659$	−3.26168	+	10.0384i	−0.127057	+	0.391041i	−0.994270	−	0.106896i	$-0.965909\pi$
$659$	−3.26168	+	10.0384i	−0.127057	+	0.391041i	0.867213	+	0.497937i	$0.165909\pi$
$660$	0.814700	−	0.379351i	0.0317122	−	0.0147662i
$661$	12.1553	+	37.4100i	0.472784	+	1.45508i	0.848922	+	0.528517i	$0.177252\pi$
$661$	12.1553	+	37.4100i	0.472784	+	1.45508i	−0.376138	+	0.926564i	$0.622748\pi$
$662$	−6.65375	−	2.16193i	−0.258605	−	0.0840259i
$663$	−0.0631588	−	0.0205215i	−0.00245288	−	0.000796990i
$664$	−3.67696	−	11.3165i	−0.142694	−	0.439166i
$665$	−4.81193	−	0.938116i	−0.186599	−	0.0363786i
$666$	−0.673332	+	2.07230i	−0.0260911	+	0.0803001i
$667$	37.9516	−	52.2359i	1.46949	−	2.02258i
$668$		−	27.4909i		−	1.06365i
$669$	0.793875	+	0.576784i	0.0306930	+	0.0222998i
$670$	6.56990	−	0.802982i	0.253817	−	0.0310219i
$671$	40.3367	−	29.3063i	1.55718	−	1.13136i
$672$	−0.0830871	−	0.114360i	−0.00320516	−	0.00441152i
$673$	38.5391	−	12.5221i	1.48558	−	0.482693i	0.549802	−	0.835295i	$-0.314703\pi$
$673$	38.5391	−	12.5221i	1.48558	−	0.482693i	0.935773	+	0.352603i	$0.114703\pi$
$674$	−24.4472			−0.941671
$675$	−0.513757	+	1.26754i	−0.0197745	+	0.0487877i
$676$	−17.3514			−0.667363
$677$	−11.2100	+	3.64234i	−0.430834	+	0.139986i	−0.516403	−	0.856346i	$-0.672729\pi$
$677$	−11.2100	+	3.64234i	−0.430834	+	0.139986i	0.0855690	+	0.996332i	$0.472729\pi$
$678$	0.698455	+	0.961341i	0.0268240	+	0.0369201i
$679$	4.10196	−	2.98025i	0.157419	−	0.114371i
$680$	−1.25686	+	1.17073i	−0.0481982	+	0.0448956i
$681$	−0.897635	−	0.652170i	−0.0343974	−	0.0249912i
$682$		−	25.5631i		−	0.978863i
$683$	−18.0811	+	24.8866i	−0.691856	+	0.952258i	0.308144	+	0.951340i	$0.400292\pi$
$683$	−18.0811	+	24.8866i	−0.691856	+	0.952258i	−1.00000		0.000917923i	$0.999708\pi$
$684$	−7.60096	+	23.3934i	−0.290630	+	0.894468i
$685$	0.640814	+	5.24306i	0.0244843	+	0.200327i
$686$	3.45041	+	10.6193i	0.131737	+	0.405446i
$687$	−1.07083	−	0.347933i	−0.0408546	−	0.0132745i
$688$	1.77150	+	0.575597i	0.0675380	+	0.0219444i
$689$	3.53173	+	10.8695i	0.134548	+	0.414096i
$690$	−0.144970	−	1.18612i	−0.00551890	−	0.0451549i
$691$	−7.06214	+	21.7350i	−0.268656	+	0.826839i	0.722172	+	0.691714i	$0.243144\pi$
$691$	−7.06214	+	21.7350i	−0.268656	+	0.826839i	−0.990828	+	0.135126i	$0.956856\pi$
$692$	−11.3163	+	15.5755i	−0.430180	+	0.592092i
$693$			7.05981i			0.268180i
$694$	13.1739	+	9.57139i	0.500074	+	0.363325i
$695$	−19.1931	+	17.8780i	−0.728036	+	0.678150i
$696$	0.296098	−	0.215128i	0.0112236	−	0.00815439i
$697$	3.23020	+	4.44599i	0.122353	+	0.168404i
$698$	−2.01647	+	0.655190i	−0.0763245	+	0.0247993i
$699$	0.449768			0.0170118
$700$	3.38992	+	0.240826i	0.128127	+	0.00910237i
$701$	−19.7061			−0.744288			−0.372144	−	0.928175i	$-0.621377\pi$
$701$	−19.7061			−0.744288			−0.372144	+	0.928175i	$0.621377\pi$
$702$	−0.718249	+	0.233373i	−0.0271086	+	0.00880811i
$703$	−1.15918	−	1.59547i	−0.0437191	−	0.0601742i
$704$	20.1035	−	14.6060i	0.757677	−	0.550485i
$705$	−0.252570	+	0.0308695i	−0.00951234	+	0.00116261i
$706$	−32.7340	−	23.7826i	−1.23196	−	0.895070i
$707$			0.0461033i			0.00173389i
$708$	0.125634	−	0.172920i	0.00472161	−	0.00649873i
$709$	−2.85263	+	8.77949i	−0.107133	+	0.329721i	−0.990225	−	0.139478i	$-0.955457\pi$
$709$	−2.85263	+	8.77949i	−0.107133	+	0.329721i	0.883092	+	0.469199i	$0.155457\pi$
$710$	55.8065	+	10.8798i	2.09438	+	0.408312i
$711$	−10.0302	−	30.8698i	−0.376162	−	1.15771i
$712$	−6.02201	−	1.95667i	−0.225684	−	0.0733292i
$713$	−14.3417	−	4.65990i	−0.537100	−	0.174514i
$714$	−0.0113877	−	0.0350476i	−0.000426173	−	0.00131162i
$715$	16.3103	−	7.59460i	0.609971	−	0.284022i
$716$	−5.92078	+	18.2223i	−0.221270	+	0.680999i
$717$	0.149765	−	0.206133i	0.00559306	−	0.00769818i
$718$			55.3282i			2.06483i
$719$	1.67590	+	1.21761i	0.0625004	+	0.0454092i	0.618597	−	0.785709i	$-0.287701\pi$
$719$	1.67590	+	1.21761i	0.0625004	+	0.0454092i	−0.556096	+	0.831118i	$0.687701\pi$
$720$	−5.95984	+	30.5701i	−0.222110	+	1.13928i
$721$	0.542195	−	0.393928i	0.0201924	−	0.0146706i
$722$	−8.32049	−	11.4522i	−0.309657	−	0.426206i
$723$	0.244977	−	0.0795979i	0.00911080	−	0.00296028i
$724$	21.3954			0.795154
$725$	−3.70168	+	52.1057i	−0.137477	+	1.93516i
$726$	1.68897			0.0626837
$727$	−0.447090	+	0.145268i	−0.0165816	+	0.00538770i	−0.317296	−	0.948327i	$-0.602775\pi$
$727$	−0.447090	+	0.145268i	−0.0165816	+	0.00538770i	0.300714	+	0.953714i	$0.402775\pi$
$728$	−0.280198	−	0.385659i	−0.0103848	−	0.0142935i
$729$	−21.7526	+	15.8042i	−0.805654	+	0.585342i
$730$	36.3295	+	20.1641i	1.34461	+	0.746308i
$731$	0.324340	+	0.235647i	0.0119962	+	0.00871572i
$732$			0.656301i			0.0242576i
$733$	18.5643	−	25.5515i	0.685686	−	0.943766i	−0.314298	−	0.949324i	$-0.601769\pi$
$733$	18.5643	−	25.5515i	0.685686	−	0.943766i	0.999985	+	0.00555791i	$0.00176915\pi$
$734$	20.1772	−	62.0990i	0.744753	−	2.29211i
$735$	−0.337437	+	0.607956i	−0.0124465	+	0.0224248i
$736$	−13.8896	−	42.7477i	−0.511976	−	1.57570i
$737$	8.20429	+	2.66574i	0.302209	+	0.0981936i
$738$	29.7083	+	9.65281i	1.09358	+	0.355325i
$739$	−1.12536	−	3.46351i	−0.0413971	−	0.127407i	0.928222	−	0.372027i	$-0.121337\pi$
$739$	−1.12536	−	3.46351i	−0.0413971	−	0.127407i	−0.969619	+	0.244619i	$0.921337\pi$
$740$	0.931790	+	1.00033i	0.0342533	+	0.0367730i
$741$	0.105573	−	0.324921i	0.00387833	−	0.0119363i
$742$	−3.72776	+	5.13082i	−0.136850	+	0.188359i
$743$			11.3829i			0.417599i	0.977958	+	0.208800i	$0.0669557\pi$
$743$			11.3829i			0.417599i	−0.977958	+	0.208800i	$0.933044\pi$
$744$	−0.0691541	−	0.0502434i	−0.00253531	−	0.00184201i
$745$	11.7209	+	25.1719i	0.429419	+	0.922228i
$746$	12.1495	−	8.82709i	0.444823	−	0.323183i
$747$	−27.2959	−	37.5695i	−0.998703	−	1.37460i
$748$	8.38128	−	2.72324i	0.306450	−	0.0995717i
$749$	1.44593			0.0528333
$750$	0.607148	+	0.752322i	0.0221699	+	0.0274709i
$751$	−8.13759			−0.296945			−0.148472	−	0.988917i	$-0.547436\pi$
$751$	−8.13759			−0.296945			−0.148472	+	0.988917i	$0.547436\pi$
$752$	−11.0254	+	3.58237i	−0.402055	+	0.130636i
$753$	0.0396175	+	0.0545288i	0.00144374	+	0.00198714i
$754$	−23.3353	+	16.9541i	−0.849822	+	0.617432i
$755$	5.11770	+	10.9908i	0.186252	+	0.399998i
$756$	−0.150415	−	0.109283i	−0.00547055	−	0.00397459i
$757$			7.32686i			0.266299i	0.991096	+	0.133150i	$0.0425091\pi$
$757$			7.32686i			0.266299i	−0.991096	+	0.133150i	$0.957491\pi$
$758$	9.78579	−	13.4690i	0.355436	−	0.489216i
$759$	0.481269	−	1.48119i	0.0174690	−	0.0537640i
$760$	−6.02286	−	6.46591i	−0.218472	−	0.234543i
$761$	−12.6527	−	38.9411i	−0.458661	−	1.41161i	−0.866782	−	0.498687i	$-0.833816\pi$
$761$	−12.6527	−	38.9411i	−0.458661	−	1.41161i	0.408121	−	0.912928i	$-0.366184\pi$
$762$	1.63116	+	0.529997i	0.0590909	+	0.0191998i
$763$	−0.188439	−	0.0612275i	−0.00682195	−	0.00221659i
$764$	−6.73909	−	20.7408i	−0.243812	−	0.750375i
$765$	−3.25320	+	5.86126i	−0.117620	+	0.211914i
$766$	−0.141575	+	0.435723i	−0.00511531	+	0.0157433i
$767$	2.51519	−	3.46186i	0.0908182	−	0.125000i
$768$		−	0.930658i		−	0.0335822i
$769$	−24.3436	−	17.6866i	−0.877851	−	0.637796i	0.0548310	−	0.998496i	$-0.482538\pi$
$769$	−24.3436	−	17.6866i	−0.877851	−	0.637796i	−0.932682	+	0.360699i	$0.882538\pi$
$770$	8.72940	+	4.84512i	0.314586	+	0.174606i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80321 + 0.585900i) q^{2} +(0.0268065 + 0.0368959i) q^{3} +(1.29027 - 0.937434i) q^{4} +(0.943879 + 2.02709i) q^{5} +(-0.0699551 - 0.0508253i) q^{6} -0.426178i q^{7} +(0.451510 - 0.621450i) q^{8} +(0.926408 - 2.85119i) q^{9} +(-2.88969 - 3.10226i) q^{10} +(-1.70752 - 5.25519i) q^{11} +(0.0691750 + 0.0224763i) q^{12} +(1.38488 + 0.449976i) q^{13} +(0.249697 + 0.768489i) q^{14} +(-0.0494893 + 0.0891644i) q^{15} +(-1.43574 + 4.41875i) q^{16} +(-0.587785 + 0.809017i) q^{17} +5.68409i q^{18} +(-4.16200 - 3.02387i) q^{19} +(3.11812 + 1.73066i) q^{20} +(0.0157242 - 0.0114243i) q^{21} +(6.15803 + 8.47580i) q^{22} +(5.87772 - 1.90979i) q^{23} +0.0350323 q^{24} +(-3.21819 + 3.82665i) q^{25} -2.76088 q^{26} +(0.260152 - 0.0845286i) q^{27} +(-0.399513 - 0.549883i) q^{28} +(8.45213 - 6.14083i) q^{29} +(0.0369984 - 0.189778i) q^{30} +(-1.97401 - 1.43420i) q^{31} -7.27283i q^{32} +(0.148123 - 0.203873i) q^{33} +(0.585900 - 1.80321i) q^{34} +(0.863900 - 0.402260i) q^{35} +(-1.47749 - 4.54724i) q^{36} +(0.364580 + 0.118459i) q^{37} +(9.27666 + 3.01417i) q^{38} +(0.0205215 + 0.0631588i) q^{39} +(1.68591 + 0.328677i) q^{40} +(1.69822 - 5.22657i) q^{41} +(-0.0216606 + 0.0298133i) q^{42} -0.400907i q^{43} +(-7.12955 - 5.17992i) q^{44} +(6.65404 - 0.813266i) q^{45} +(-9.47985 + 6.88751i) q^{46} +(1.46661 + 2.01862i) q^{47} +(-0.201521 + 0.0654781i) q^{48} +6.81837 q^{49} +(3.56104 - 8.78581i) q^{50} -0.0456059 q^{51} +(2.20869 - 0.717647i) q^{52} +(4.61335 + 6.34974i) q^{53} +(-0.419585 + 0.304846i) q^{54} +(9.04106 - 8.42155i) q^{55} +(-0.264848 - 0.192423i) q^{56} -0.234620i q^{57} +(-11.6431 + 16.0253i) q^{58} +(0.908087 - 2.79480i) q^{59} +(0.0197313 + 0.161439i) q^{60} +(2.78832 + 8.58157i) q^{61} +(4.39985 + 1.42960i) q^{62} +(-1.21511 - 0.394814i) q^{63} +(1.38967 + 4.27698i) q^{64} +(0.395020 + 3.23200i) q^{65} +(-0.147648 + 0.454412i) q^{66} +(-0.917637 + 1.26302i) q^{67} +1.59486i q^{68} +(0.228024 + 0.165669i) q^{69} +(-1.32211 + 1.23152i) q^{70} +(-10.8497 + 7.88275i) q^{71} +(-1.35359 - 1.86306i) q^{72} +(-9.32082 + 3.02852i) q^{73} -0.726820 q^{74} +(-0.227456 - 0.0161589i) q^{75} -8.20477 q^{76} +(-2.23965 + 0.727705i) q^{77} +(-0.0740094 - 0.101865i) q^{78} +(8.75922 - 6.36395i) q^{79} +(-10.3124 + 1.26039i) q^{80} +(-7.26601 - 5.27907i) q^{81} +10.4196i q^{82} +(9.10493 - 12.5319i) q^{83} +(0.00957890 - 0.0294808i) q^{84} +(-2.19475 - 0.427880i) q^{85} +(0.234891 + 0.722920i) q^{86} +(0.453143 + 0.147235i) q^{87} +(-4.03680 - 1.31164i) q^{88} +(-2.54723 - 7.83958i) q^{89} +(-11.5222 + 5.36509i) q^{90} +(0.191770 - 0.590206i) q^{91} +(5.79353 - 7.97411i) q^{92} -0.111279i q^{93} +(-3.82732 - 2.78071i) q^{94} +(2.20123 - 11.2909i) q^{95} +(0.268338 - 0.194959i) q^{96} +(6.99297 + 9.62500i) q^{97} +(-12.2950 + 3.99488i) q^{98} -16.5654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

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