LMFDB - Embedded newform 507.2.p.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52295 - 0.956827i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.95272 + 3.50180i) q^{4} +(4.16354 + 0.505545i) q^{5} +(0.645743 + 2.61988i) q^{6} +(0.140914 + 0.268489i) q^{7} +(-4.11396 - 7.83849i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-2.52295 - 0.956827i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.95272 + 3.50180i) q^{4} +(4.16354 + 0.505545i) q^{5} +(0.645743 + 2.61988i) q^{6} +(0.140914 + 0.268489i) q^{7} +(-4.11396 - 7.83849i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-10.0207 - 5.25925i) q^{10} +(4.36627 - 1.65591i) q^{11} +(0.636527 - 5.24227i) q^{12} +(-2.95668 - 2.06350i) q^{13} +(-0.0986205 - 0.812213i) q^{14} +(-1.94910 - 3.71371i) q^{15} +(1.60616 + 13.2279i) q^{16} +(3.30949 - 1.73696i) q^{17} +(1.78930 - 2.01970i) q^{18} +6.59384i q^{19} +(14.6870 + 16.5782i) q^{20} +(0.140914 - 0.268489i) q^{21} -12.6003 q^{22} -1.15577 q^{23} +(-4.11396 + 7.83849i) q^{24} +(12.2248 + 3.01313i) q^{25} +(5.48515 + 8.03513i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.383202 + 1.55471i) q^{28} +(-0.601786 + 1.58678i) q^{29} +(1.36411 + 11.2344i) q^{30} +(-0.757835 - 3.07466i) q^{31} +(4.36748 - 17.7196i) q^{32} +(-3.84311 - 2.65271i) q^{33} +(-10.0116 + 1.21563i) q^{34} +(0.450966 + 1.18910i) q^{35} +(-4.67589 + 2.45410i) q^{36} +(1.72030 + 6.97952i) q^{37} +(6.30917 - 16.6359i) q^{38} +(-0.0186350 + 3.60550i) q^{39} +(-13.1659 - 34.7156i) q^{40} +(1.53455 - 1.05923i) q^{41} +(-0.612415 + 0.542552i) q^{42} +(-5.38191 - 1.32652i) q^{43} +(23.0573 + 8.74449i) q^{44} +(-1.94910 + 3.71371i) q^{45} +(2.91596 + 1.10588i) q^{46} +(-0.433146 - 0.488920i) q^{47} +(9.97394 - 8.83614i) q^{48} +(3.92422 - 5.68522i) q^{49} +(-27.9594 - 19.2990i) q^{50} +(-3.30949 - 1.73696i) q^{51} +(-4.46099 - 18.5101i) q^{52} +(6.17479 - 3.24078i) q^{53} +(-2.67862 - 0.325243i) q^{54} +(19.0163 - 4.68709i) q^{55} +(1.52483 - 2.20910i) q^{56} +(5.42663 - 3.74573i) q^{57} +(3.03655 - 3.42756i) q^{58} +(-10.7213 - 1.30180i) q^{59} +(5.30041 - 21.5046i) q^{60} +(0.110262 + 0.0578700i) q^{61} +(-1.02994 + 8.48231i) q^{62} +(-0.301010 + 0.0365492i) q^{63} +(-12.8345 + 18.5940i) q^{64} +(-11.2671 - 10.0862i) q^{65} +(7.15778 + 10.3698i) q^{66} +(5.86163 + 6.61641i) q^{67} +(19.1640 + 4.72349i) q^{68} +(0.656555 + 0.951184i) q^{69} -3.43153i q^{70} +(-1.70176 + 1.17464i) q^{71} +(8.78794 - 1.06705i) q^{72} +(-4.86349 + 1.84448i) q^{73} +(2.33798 - 19.2550i) q^{74} +(-4.46470 - 11.7724i) q^{75} +(-23.0903 + 26.0636i) q^{76} +(1.05986 + 0.938955i) q^{77} +(3.49686 - 9.07866i) q^{78} +(4.66512 - 4.13293i) q^{79} +55.8868i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-4.88509 + 1.20407i) q^{82} +(-12.4115 - 8.56703i) q^{83} +(1.49719 - 0.567808i) q^{84} +(14.6573 - 5.55878i) q^{85} +(12.3090 + 8.49630i) q^{86} +(1.64775 - 0.406133i) q^{87} +(-30.9425 - 27.4127i) q^{88} +4.36851i q^{89} +(8.47086 - 7.50453i) q^{90} +(0.137388 - 1.08461i) q^{91} +(-4.56845 - 4.04729i) q^{92} +(-2.09989 + 2.37029i) q^{93} +(0.624991 + 1.64797i) q^{94} +(-3.33348 + 27.4537i) q^{95} +(-17.0639 + 6.47149i) q^{96} +(6.78285 - 0.823587i) q^{97} +(-15.3404 + 10.5887i) q^{98} +4.66973i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−2.52295	−	0.956827i	−1.78399	−	0.676579i	−0.998320	−	0.0579359i	$-0.981548\pi$
$2$	−2.52295	−	0.956827i	−1.78399	−	0.676579i	−0.785672	−	0.618643i	$-0.787683\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	3.95272	+	3.50180i	1.97636	+	1.75090i
$5$	4.16354	+	0.505545i	1.86199	+	0.226087i	0.972832	−	0.231512i	$-0.0743674\pi$
$5$	4.16354	+	0.505545i	1.86199	+	0.226087i	0.889159	+	0.457599i	$0.151290\pi$
$6$	0.645743	+	2.61988i	0.263624	+	1.06956i
$7$	0.140914	+	0.268489i	0.0532604	+	0.101479i	0.910631	−	0.413220i	$-0.135596\pi$
$7$	0.140914	+	0.268489i	0.0532604	+	0.101479i	−0.857371	+	0.514699i	$0.827904\pi$
$8$	−4.11396	−	7.83849i	−1.45450	−	2.77132i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−10.0207	−	5.25925i	−3.16881	−	1.66312i
$11$	4.36627	−	1.65591i	1.31648	−	0.499275i	0.406396	−	0.913697i	$-0.366785\pi$
$11$	4.36627	−	1.65591i	1.31648	−	0.499275i	0.910085	+	0.414422i	$0.136016\pi$
$12$	0.636527	−	5.24227i	0.183750	−	1.51331i
$13$	−2.95668	−	2.06350i	−0.820037	−	0.572311i
$13$	−2.95668	−	2.06350i	−0.820037	−	0.572311i
$14$	−0.0986205	−	0.812213i	−0.0263574	−	0.217073i
$15$	−1.94910	−	3.71371i	−0.503256	−	0.958875i
$16$	1.60616	+	13.2279i	0.401539	+	3.30697i
$17$	3.30949	−	1.73696i	0.802670	−	0.421274i	−0.0129109	−	0.999917i	$-0.504110\pi$
$17$	3.30949	−	1.73696i	0.802670	−	0.421274i	0.815581	+	0.578643i	$0.196417\pi$
$18$	1.78930	−	2.01970i	0.421742	−	0.476048i
$19$			6.59384i			1.51273i	0.654149	+	0.756366i	$0.273027\pi$
$19$			6.59384i			1.51273i	−0.654149	+	0.756366i	$0.726973\pi$
$20$	14.6870	+	16.5782i	3.28411	+	3.70699i
$21$	0.140914	−	0.268489i	0.0307499	−	0.0585890i
$22$	−12.6003			−2.68639
$23$	−1.15577			−0.240996			−0.120498	−	0.992714i	$-0.538449\pi$
$23$	−1.15577			−0.240996			−0.120498	+	0.992714i	$0.538449\pi$
$24$	−4.11396	+	7.83849i	−0.839758	+	1.60003i
$25$	12.2248	+	3.01313i	2.44495	+	0.602627i
$26$	5.48515	+	8.03513i	1.07573	+	1.57582i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−0.383202	+	1.55471i	−0.0724184	+	0.293813i
$29$	−0.601786	+	1.58678i	−0.111749	+	0.294658i	−0.979211	−	0.202846i	$-0.934981\pi$
$29$	−0.601786	+	1.58678i	−0.111749	+	0.294658i	0.867462	+	0.497504i	$0.165750\pi$
$30$	1.36411	+	11.2344i	0.249051	+	2.05112i
$31$	−0.757835	−	3.07466i	−0.136111	−	0.552224i	−0.998910	−	0.0466772i	$-0.985137\pi$
$31$	−0.757835	−	3.07466i	−0.136111	−	0.552224i	0.862799	−	0.505547i	$-0.168709\pi$
$32$	4.36748	−	17.7196i	0.772069	−	3.13241i
$33$	−3.84311	−	2.65271i	−0.669000	−	0.461777i
$34$	−10.0116	+	1.21563i	−1.71698	+	0.208479i
$35$	0.450966	+	1.18910i	0.0762272	+	0.200995i
$36$	−4.67589	+	2.45410i	−0.779316	+	0.409016i
$37$	1.72030	+	6.97952i	0.282815	+	1.14743i	0.924722	+	0.380644i	$0.124297\pi$
$37$	1.72030	+	6.97952i	0.282815	+	1.14743i	−0.641907	+	0.766783i	$0.721856\pi$
$38$	6.30917	−	16.6359i	1.02348	−	2.69870i
$39$	−0.0186350	+	3.60550i	−0.00298400	+	0.577343i
$40$	−13.1659	−	34.7156i	−2.08171	−	5.48902i
$41$	1.53455	−	1.05923i	0.239657	−	0.165423i	−0.442182	−	0.896925i	$-0.645796\pi$
$41$	1.53455	−	1.05923i	0.239657	−	0.165423i	0.681840	+	0.731502i	$0.261180\pi$
$42$	−0.612415	+	0.542552i	−0.0944977	+	0.0837176i
$43$	−5.38191	−	1.32652i	−0.820733	−	0.202293i	−0.193476	−	0.981105i	$-0.561976\pi$
$43$	−5.38191	−	1.32652i	−0.820733	−	0.202293i	−0.627257	+	0.778812i	$0.715822\pi$
$44$	23.0573	+	8.74449i	3.47602	+	1.31828i
$45$	−1.94910	+	3.71371i	−0.290555	+	0.553607i
$46$	2.91596	+	1.10588i	0.429934	+	0.163053i
$47$	−0.433146	−	0.488920i	−0.0631808	−	0.0713164i	0.716071	−	0.698028i	$-0.245939\pi$
$47$	−0.433146	−	0.488920i	−0.0631808	−	0.0713164i	−0.779251	+	0.626712i	$0.784400\pi$
$48$	9.97394	−	8.83614i	1.43961	−	1.27539i
$49$	3.92422	−	5.68522i	0.560603	−	0.812174i
$50$	−27.9594	−	19.2990i	−3.95405	−	2.72928i
$51$	−3.30949	−	1.73696i	−0.463422	−	0.243223i
$52$	−4.46099	−	18.5101i	−0.618628	−	2.56689i
$53$	6.17479	−	3.24078i	0.848173	−	0.445155i	0.0161318	−	0.999870i	$-0.494865\pi$
$53$	6.17479	−	3.24078i	0.848173	−	0.445155i	0.832041	+	0.554715i	$0.187173\pi$
$54$	−2.67862	−	0.325243i	−0.364514	−	0.0442600i
$55$	19.0163	−	4.68709i	2.56415	−	0.632007i
$56$	1.52483	−	2.20910i	0.203764	−	0.295204i
$57$	5.42663	−	3.74573i	0.718774	−	0.496134i
$58$	3.03655	−	3.42756i	0.398718	−	0.450060i
$59$	−10.7213	−	1.30180i	−1.39579	−	0.169479i	−0.612172	−	0.790724i	$-0.709704\pi$
$59$	−10.7213	−	1.30180i	−1.39579	−	0.169479i	−0.783617	+	0.621245i	$0.786627\pi$
$60$	5.30041	−	21.5046i	0.684280	−	2.77623i
$61$	0.110262	+	0.0578700i	0.0141176	+	0.00740950i	0.471767	−	0.881723i	$-0.343616\pi$
$61$	0.110262	+	0.0578700i	0.0141176	+	0.00740950i	−0.457650	+	0.889133i	$0.651309\pi$
$62$	−1.02994	+	8.48231i	−0.130802	+	1.07725i
$63$	−0.301010	+	0.0365492i	−0.0379237	+	0.00460477i
$64$	−12.8345	+	18.5940i	−1.60431	+	2.32425i
$65$	−11.2671	−	10.0862i	−1.39751	−	1.25104i
$66$	7.15778	+	10.3698i	0.881062	+	1.27644i
$67$	5.86163	+	6.61641i	0.716112	+	0.808323i	0.988073	−	0.153985i	$-0.0492107\pi$
$67$	5.86163	+	6.61641i	0.716112	+	0.808323i	−0.271961	+	0.962308i	$0.587672\pi$
$68$	19.1640	+	4.72349i	2.32397	+	0.572808i
$69$	0.656555	+	0.951184i	0.0790399	+	0.114509i
$70$		−	3.43153i		−	0.410147i
$71$	−1.70176	+	1.17464i	−0.201961	+	0.139404i	−0.664753	−	0.747063i	$-0.731463\pi$
$71$	−1.70176	+	1.17464i	−0.201961	+	0.139404i	0.462792	+	0.886467i	$0.346848\pi$
$72$	8.78794	−	1.06705i	1.03567	−	0.125753i
$73$	−4.86349	+	1.84448i	−0.569229	+	0.215880i	−0.622392	−	0.782706i	$-0.713839\pi$
$73$	−4.86349	+	1.84448i	−0.569229	+	0.215880i	0.0531630	+	0.998586i	$0.483070\pi$
$74$	2.33798	−	19.2550i	0.271784	−	2.23835i
$75$	−4.46470	−	11.7724i	−0.515539	−	1.35936i
$76$	−23.0903	+	26.0636i	−2.64864	+	2.98970i
$77$	1.05986	+	0.938955i	0.120782	+	0.107004i
$78$	3.49686	−	9.07866i	0.395941	−	1.02796i
$79$	4.66512	−	4.13293i	0.524867	−	0.464991i	−0.358596	−	0.933493i	$-0.616744\pi$
$79$	4.66512	−	4.13293i	0.524867	−	0.464991i	0.883463	+	0.468502i	$0.155206\pi$
$80$			55.8868i			6.24833i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−4.88509	+	1.20407i	−0.539468	+	0.132967i
$83$	−12.4115	−	8.56703i	−1.36234	−	0.940354i	−0.999965	−	0.00831993i	$-0.997352\pi$
$83$	−12.4115	−	8.56703i	−1.36234	−	0.940354i	−0.362372	−	0.932034i	$-0.618033\pi$
$84$	1.49719	−	0.567808i	0.163356	−	0.0619529i
$85$	14.6573	−	5.55878i	1.58981	−	0.602935i
$86$	12.3090	+	8.49630i	1.32731	+	0.916179i
$87$	1.64775	−	0.406133i	0.176657	−	0.0435421i
$88$	−30.9425	−	27.4127i	−3.29848	−	2.92220i
$89$			4.36851i			0.463061i	0.972828	+	0.231530i	$0.0743733\pi$
$89$			4.36851i			0.463061i	−0.972828	+	0.231530i	$0.925627\pi$
$90$	8.47086	−	7.50453i	0.892907	−	0.791047i
$91$	0.137388	−	1.08461i	0.0144021	−	0.113698i
$92$	−4.56845	−	4.04729i	−0.476294	−	0.421959i
$93$	−2.09989	+	2.37029i	−0.217749	+	0.245788i
$94$	0.624991	+	1.64797i	0.0644629	+	0.169975i
$95$	−3.33348	+	27.4537i	−0.342008	+	2.81669i
$96$	−17.0639	+	6.47149i	−1.74158	+	0.660494i
$97$	6.78285	−	0.823587i	0.688694	−	0.0836226i	0.231294	−	0.972884i	$-0.425704\pi$
$97$	6.78285	−	0.823587i	0.688694	−	0.0836226i	0.457400	+	0.889261i	$0.348781\pi$
$98$	−15.3404	+	10.5887i	−1.54961	+	1.06962i
$99$			4.66973i			0.469326i
$100$	37.7696	+	54.7188i	3.77696	+	5.47188i
$101$	18.1065	+	4.46286i	1.80167	+	0.444072i	0.990121	−	0.140215i	$-0.0447792\pi$
$101$	18.1065	+	4.46286i	1.80167	+	0.444072i	0.811548	+	0.584286i	$0.198625\pi$
$102$	6.68771	+	7.54886i	0.662182	+	0.747449i
$103$	−2.31418	−	3.35266i	−0.228023	−	0.330348i	0.692227	−	0.721680i	$-0.256630\pi$
$103$	−2.31418	−	3.35266i	−0.228023	−	0.330348i	−0.920250	+	0.391332i	$0.872014\pi$
$104$	−4.01101	+	31.6651i	−0.393312	+	3.10502i
$105$	0.722433	−	1.04662i	0.0705022	−	0.102140i
$106$	−18.6795	+	2.26811i	−1.81432	+	0.220298i
$107$	1.54238	−	12.7027i	0.149108	−	1.22801i	−0.705490	−	0.708720i	$-0.749273\pi$
$107$	1.54238	−	12.7027i	0.149108	−	1.22801i	0.854597	−	0.519291i	$-0.173804\pi$
$108$	4.67589	+	2.45410i	0.449938	+	0.236146i
$109$	0.139041	−	0.564113i	0.0133177	−	0.0540322i	−0.963907	−	0.266239i	$-0.914219\pi$
$109$	0.139041	−	0.564113i	0.0133177	−	0.0540322i	0.977225	+	0.212207i	$0.0680651\pi$
$110$	−52.4618	−	6.37002i	−5.00204	−	0.607357i
$111$	4.76679	−	5.38060i	0.452444	−	0.510704i
$112$	−3.32521	+	2.29523i	−0.314203	+	0.216878i
$113$	2.36427	−	3.42523i	0.222411	−	0.322219i	−0.695855	−	0.718183i	$-0.744974\pi$
$113$	2.36427	−	3.42523i	0.222411	−	0.322219i	0.918266	+	0.395964i	$0.129590\pi$
$114$	−17.2751	+	4.25793i	−1.61796	+	0.398792i
$115$	−4.81211	−	0.584296i	−0.448732	−	0.0544859i
$116$	−7.93528	+	4.16476i	−0.736773	+	0.386688i
$117$	2.97786	−	2.03282i	0.275303	−	0.187935i
$118$	25.8036	+	13.5428i	2.37541	+	1.24671i
$119$	0.932706	+	0.643801i	0.0855010	+	0.0590171i
$120$	−21.0913	+	30.5561i	−1.92537	+	2.78937i
$121$	8.08869	−	7.16596i	0.735336	−	0.651451i
$122$	−0.222814	−	0.251505i	−0.0201726	−	0.0227702i
$123$	−1.74345	−	0.661204i	−0.157202	−	0.0596188i
$124$	7.77133	−	14.8070i	0.697886	−	1.32971i
$125$	29.7671	+	11.2892i	2.66245	+	1.00974i
$126$	0.794403	+	0.195803i	0.0707711	+	0.0174435i
$127$	−7.26092	+	6.43262i	−0.644303	+	0.570802i	−0.920714	−	0.390237i	$-0.872393\pi$
$127$	−7.26092	+	6.43262i	−0.644303	+	0.570802i	0.276412	+	0.961039i	$0.410855\pi$
$128$	20.1333	−	13.8970i	1.77955	−	1.22833i
$129$	1.96557	+	5.18277i	0.173058	+	0.456318i
$130$	18.7755	+	36.2275i	1.64672	+	3.17737i
$131$	2.28491	−	6.02481i	0.199633	−	0.526390i	−0.797392	−	0.603461i	$-0.793788\pi$
$131$	2.28491	−	6.02481i	0.199633	−	0.526390i	0.997026	+	0.0770716i	$0.0245570\pi$
$132$	−5.90148	−	23.9432i	−0.513658	−	2.08399i
$133$	−1.77037	+	0.929163i	−0.153511	+	0.0805687i
$134$	−8.45781	−	22.3014i	−0.730644	−	1.92655i
$135$	4.16354	−	0.505545i	0.358340	−	0.0435104i
$136$	−27.2302	−	18.7957i	−2.33497	−	1.61172i
$137$	−0.535240	+	2.17155i	−0.0457286	+	0.185528i	−0.989365	−	0.145457i	$-0.953535\pi$
$137$	−0.535240	+	2.17155i	−0.0457286	+	0.185528i	0.943636	+	0.330985i	$0.107381\pi$
$138$	−0.746334	−	3.02799i	−0.0635321	−	0.257760i
$139$	−2.42006	−	19.9310i	−0.205266	−	1.69052i	−0.623215	−	0.782051i	$-0.714174\pi$
$139$	−2.42006	−	19.9310i	−0.205266	−	1.69052i	0.417948	−	0.908471i	$-0.362749\pi$
$140$	−2.38145	+	6.27938i	−0.201270	+	0.530704i
$141$	−0.156319	+	0.634210i	−0.0131644	+	0.0534101i
$142$	5.41737	−	1.33526i	0.454616	−	0.112053i
$143$	−16.3267	−	4.11378i	−1.36530	−	0.344012i
$144$	−12.9378	−	3.18889i	−1.07815	−	0.265741i
$145$	−3.30775	+	6.30239i	−0.274694	+	0.523385i
$146$	14.0352			1.16156
$147$	−6.90806			−0.569767
$148$	−17.6411	+	33.6122i	−1.45009	+	2.76291i
$149$	−12.0413	−	13.5918i	−0.986459	−	1.11348i	−0.993537	−	0.113507i	$-0.963791\pi$
$149$	−12.0413	−	13.5918i	−0.986459	−	1.11348i	0.00707777	−	0.999975i	$-0.497747\pi$
$150$			33.9732i			2.77390i
$151$	−12.3117	+	13.8970i	−1.00191	+	1.13093i	−0.0105273	+	0.999945i	$0.503351\pi$
$151$	−12.3117	+	13.8970i	−1.00191	+	1.13093i	−0.991385	+	0.130981i	$0.958187\pi$
$152$	51.6858	−	27.1268i	4.19227	−	2.20027i
$153$	0.450520	+	3.71036i	0.0364224	+	0.299965i
$154$	−1.77555	−	3.38304i	−0.143078	−	0.272613i
$155$	−1.60090	−	13.1846i	−0.128587	−	1.05901i
$156$	−12.6994	+	14.1863i	−1.01677	+	1.13581i
$157$	0.750621	−	6.18192i	0.0599061	−	0.493371i	−0.931617	−	0.363441i	$-0.881602\pi$
$157$	0.750621	−	6.18192i	0.0599061	−	0.493371i	0.991523	−	0.129930i	$-0.0414752\pi$
$158$	−15.7243	+	5.96346i	−1.25096	+	0.474427i
$159$	−6.17479	−	3.24078i	−0.489693	−	0.257011i
$160$	27.1422	−	71.5681i	2.14578	−	5.65796i
$161$	−0.162864	−	0.310312i	−0.0128355	−	0.0244560i
$162$	1.25396	+	2.38922i	0.0985203	+	0.187715i
$163$	5.42522	+	22.0110i	0.424936	+	1.72403i	0.659296	+	0.751884i	$0.270855\pi$
$163$	5.42522	+	22.0110i	0.424936	+	1.72403i	−0.234359	+	0.972150i	$0.575299\pi$
$164$	9.77486	+	1.18688i	0.763288	+	0.0926800i
$165$	−14.6599	−	12.9875i	−1.14127	−	1.01108i
$166$	23.1163	+	33.4898i	1.79418	+	2.59931i
$167$	−1.79915	−	0.682327i	−0.139222	−	0.0528000i	0.284010	−	0.958821i	$-0.408335\pi$
$167$	−1.79915	−	0.682327i	−0.139222	−	0.0528000i	−0.423232	+	0.906021i	$0.639104\pi$
$168$	−2.68426			−0.207095
$169$	4.48397	+	12.2022i	0.344921	+	0.938632i
$170$	−42.2984			−3.24414
$171$	−6.16535	−	2.33821i	−0.471476	−	0.178807i
$172$	−16.6279	−	24.0897i	−1.26787	−	1.83683i
$173$	4.88879	+	4.33109i	0.371688	+	0.329287i	0.828202	−	0.560429i	$-0.189364\pi$
$173$	4.88879	+	4.33109i	0.371688	+	0.329287i	−0.456514	+	0.889716i	$0.650902\pi$
$174$	−4.54578	−	0.551958i	−0.344615	−	0.0418438i
$175$	0.913645	+	3.70680i	0.0690650	+	0.280208i
$176$	28.9171	+	55.0969i	2.17971	+	4.15309i
$177$	5.01901	+	9.56293i	0.377252	+	0.718794i
$178$	4.17991	−	11.0215i	0.313297	−	0.826097i
$179$	−4.58821	−	2.40808i	−0.342939	−	0.179988i	0.284457	−	0.958689i	$-0.408187\pi$
$179$	−4.58821	−	2.40808i	−0.342939	−	0.179988i	−0.627396	+	0.778701i	$0.715879\pi$
$180$	−20.7089	+	7.85386i	−1.54355	+	0.585392i
$181$	−0.380426	+	3.13309i	−0.0282768	+	0.232881i	−0.999995	−	0.00326425i	$-0.998961\pi$
$181$	−0.380426	+	3.13309i	−0.0282768	+	0.232881i	0.971718	+	0.236145i	$0.0758840\pi$
$182$	−1.38441	+	2.60496i	−0.102619	+	0.193092i
$183$	−0.0150099	−	0.123618i	−0.00110957	−	0.00913809i
$184$	4.75481	+	9.05952i	0.350529	+	0.667877i
$185$	3.63406	+	29.9292i	0.267182	+	2.20044i
$186$	7.56587	−	3.97088i	0.554757	−	0.291159i
$187$	11.5739	−	13.0642i	0.846368	−	0.955352i
$188$		−	3.44935i		−	0.251570i
$189$	0.201073	+	0.226964i	0.0146259	+	0.0165092i
$190$	34.6787	−	66.0747i	2.51586	−	4.79356i
$191$	−7.56590			−0.547449			−0.273725	−	0.961808i	$-0.588256\pi$
$191$	−7.56590			−0.547449			−0.273725	+	0.961808i	$0.588256\pi$
$192$	22.5934			1.63054
$193$	6.57838	−	12.5340i	0.473522	−	0.902221i	−0.525165	−	0.851000i	$-0.675997\pi$
$193$	6.57838	−	12.5340i	0.473522	−	0.902221i	0.998687	−	0.0512205i	$-0.0163111\pi$
$194$	−17.9008	−	4.41215i	−1.28520	−	0.316774i
$195$	−1.90033	+	15.0022i	−0.136086	+	1.07433i
$196$	35.4199	−	8.73021i	2.52999	−	0.623587i
$197$	−1.67698	+	6.80377i	−0.119480	+	0.484748i	0.880464	+	0.474114i	$0.157231\pi$
$197$	−1.67698	+	6.80377i	−0.119480	+	0.484748i	−0.999943	+	0.0106348i	$0.996615\pi$
$198$	4.46813	−	11.7815i	0.317536	−	0.837273i
$199$	−0.514796	−	4.23973i	−0.0364929	−	0.300546i	−0.999515	−	0.0311256i	$-0.990091\pi$
$199$	−0.514796	−	4.23973i	−0.0364929	−	0.300546i	0.963023	−	0.269421i	$-0.0868323\pi$
$200$	−26.6737	−	108.220i	−1.88612	−	7.65228i
$201$	2.11542	−	8.58258i	0.149210	−	0.605368i
$202$	−41.4117	−	28.5844i	−2.91371	−	2.01119i
$203$	−0.510832	+	0.0620263i	−0.0358534	+	0.00435339i
$204$	−6.99902	−	18.4549i	−0.490029	−	1.29210i
$205$	6.92466	−	3.63434i	0.483639	−	0.253833i
$206$	2.63062	+	10.6729i	0.183284	+	0.743613i
$207$	0.409843	−	1.08067i	0.0284861	−	0.0751116i
$208$	22.5468	−	42.4250i	1.56334	−	2.94164i
$209$	10.9188	+	28.7905i	0.755270	+	1.99148i
$210$	−2.82410	+	1.94933i	−0.194881	+	0.134517i
$211$	−14.9037	+	13.2035i	−1.02601	+	0.908966i	−0.995889	−	0.0905801i	$-0.971128\pi$
$211$	−14.9037	+	13.2035i	−1.02601	+	0.908966i	−0.0301215	+	0.999546i	$0.509589\pi$
$212$	35.7558	+	8.81300i	2.45572	+	0.605280i
$213$	1.93342	+	0.733248i	0.132476	+	0.0502414i
$214$	−16.0456	+	30.5723i	−1.09685	+	2.08988i
$215$	−21.7372	−	8.24382i	−1.48246	−	0.562224i
$216$	−5.87029	−	6.62618i	−0.399422	−	0.450855i
$217$	0.718721	−	0.636731i	0.0487900	−	0.0432241i
$218$	−0.890552	+	1.29019i	−0.0603158	+	0.0873825i
$219$	4.28076	+	2.95479i	0.289267	+	0.199666i
$220$	91.5793	+	48.0645i	6.17427	+	3.24051i
$221$	−13.3693	−	1.69349i	−0.899319	−	0.113917i
$222$	−17.1747	+	9.01396i	−1.15269	+	0.604977i
$223$	−1.28502	−	0.156030i	−0.0860514	−	0.0104485i	0.0773977	−	0.997000i	$-0.475339\pi$
$223$	−1.28502	−	0.156030i	−0.0860514	−	0.0104485i	−0.163449	+	0.986552i	$0.552262\pi$
$224$	5.37294	−	1.32431i	0.358995	−	0.0884842i
$225$	−7.15229	+	10.3619i	−0.476819	+	0.690792i
$226$	−9.24227	+	6.37948i	−0.614787	+	0.424357i
$227$	5.68050	−	6.41196i	0.377028	−	0.425576i	−0.529114	−	0.848551i	$-0.677476\pi$
$227$	5.68050	−	6.41196i	0.377028	−	0.425576i	0.906142	+	0.422974i	$0.139014\pi$
$228$	34.5667	+	4.19716i	2.28924	+	0.277964i
$229$	−4.08577	+	16.5766i	−0.269995	+	1.09541i	0.666716	+	0.745312i	$0.267699\pi$
$229$	−4.08577	+	16.5766i	−0.269995	+	1.09541i	−0.936711	+	0.350102i	$0.886147\pi$
$230$	11.5816	+	6.07850i	0.763670	+	0.400805i
$231$	0.170675	−	1.40564i	0.0112296	−	0.0924840i
$232$	14.9137	−	1.81085i	0.979131	−	0.118888i
$233$	−15.1189	+	21.9035i	−0.990472	+	1.43495i	−0.0920803	+	0.995752i	$0.529352\pi$
$233$	−15.1189	+	21.9035i	−0.990472	+	1.43495i	−0.898392	+	0.439195i	$0.855264\pi$
$234$	−9.45803	+	2.27941i	−0.618291	+	0.149010i
$235$	−1.55625	−	2.25461i	−0.101518	−	0.147075i
$236$	−37.8195	−	42.6894i	−2.46184	−	2.77884i
$237$	−6.05143	−	1.49154i	−0.393082	−	0.0968861i
$238$	−1.73716	−	2.51671i	−0.112603	−	0.163134i
$239$		−	0.956191i		−	0.0618508i	−0.999522	−	0.0309254i	$-0.990155\pi$
$239$		−	0.956191i		−	0.0618508i	0.999522	−	0.0309254i	$-0.00984544\pi$
$240$	45.9939	−	31.7473i	2.96890	−	2.04928i
$241$	−23.1223	+	2.80755i	−1.48944	+	0.180850i	−0.824419	−	0.565979i	$-0.808498\pi$
$241$	−23.1223	+	2.80755i	−1.48944	+	0.180850i	−0.665016	+	0.746829i	$0.731575\pi$
$242$	−27.2639	+	10.3398i	−1.75259	+	0.664670i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	0.233186	+	0.614860i	0.0149282	+	0.0393624i
$245$	19.2128	−	21.6868i	1.22746	−	1.38552i
$246$	3.76598	+	3.33637i	0.240110	+	0.212719i
$247$	13.6064	−	19.4959i	0.865752	−	1.24050i
$248$	−20.9830	+	18.5893i	−1.33242	+	1.18042i
$249$			15.0811i			0.955724i
$250$	−64.2991	−	56.9640i	−4.06663	−	3.60272i
$251$	−11.6287	+	2.86622i	−0.733997	+	0.180914i	−0.588560	−	0.808453i	$-0.700305\pi$
$251$	−11.6287	+	2.86622i	−0.733997	+	0.180914i	−0.145437	+	0.989367i	$0.546459\pi$
$252$	−1.31780	−	0.909609i	−0.0830133	−	0.0573000i
$253$	−5.04643	+	1.91386i	−0.317266	+	0.120323i
$254$	24.4738	−	9.28169i	1.53562	−	0.582385i
$255$	−12.9011	−	8.90498i	−0.807898	−	0.557652i
$256$	−20.2185	+	4.98342i	−1.26366	+	0.311464i
$257$	−12.8085	−	11.3473i	−0.798971	−	0.707826i	0.161297	−	0.986906i	$-0.448432\pi$
$257$	−12.8085	−	11.3473i	−0.798971	−	0.707826i	−0.960268	+	0.279080i	$0.909971\pi$
$258$		−	14.9566i		−	0.931155i
$259$	−1.63151	+	1.44539i	−0.101377	+	0.0898122i
$260$	−9.21578	−	79.3229i	−0.571538	−	4.91940i
$261$	−1.27027	−	1.12536i	−0.0786277	−	0.0696580i
$262$	−11.5294	+	13.0140i	−0.712289	+	0.804008i
$263$	2.56686	+	6.76826i	0.158280	+	0.417349i	0.990573	−	0.136986i	$-0.0437417\pi$
$263$	2.56686	+	6.76826i	0.158280	+	0.417349i	−0.832293	+	0.554335i	$0.812972\pi$
$264$	−4.98283	+	41.0373i	−0.306672	+	2.52567i
$265$	27.3473	−	10.3715i	1.67993	−	0.637115i
$266$	5.35560	−	0.650288i	0.328373	−	0.0398717i
$267$	3.59521	−	2.48160i	0.220023	−	0.151871i
$268$			46.6791i			2.85138i
$269$	−5.31245	−	7.69641i	−0.323906	−	0.469258i	0.626876	−	0.779119i	$-0.284333\pi$
$269$	−5.31245	−	7.69641i	−0.323906	−	0.469258i	−0.950782	+	0.309860i	$0.899718\pi$
$270$	−10.9881	−	2.70832i	−0.668715	−	0.164823i
$271$	7.95236	+	8.97636i	0.483072	+	0.545275i	0.938628	−	0.344932i	$-0.112098\pi$
$271$	7.95236	+	8.97636i	0.483072	+	0.545275i	−0.455556	+	0.890207i	$0.650560\pi$
$272$	28.2918	+	40.9878i	1.71544	+	2.48525i
$273$	−0.970663	+	0.503062i	−0.0587472	+	0.0304467i
$274$	3.42818	−	4.96658i	0.207104	−	0.300042i
$275$	58.3661	−	7.08693i	3.51961	−	0.427358i
$276$	−0.735682	+	6.05888i	−0.0442828	+	0.364702i
$277$	0.668080	+	0.350635i	0.0401410	+	0.0210676i	0.484674	−	0.874695i	$-0.338938\pi$
$277$	0.668080	+	0.350635i	0.0401410	+	0.0210676i	−0.444533	+	0.895762i	$0.646630\pi$
$278$	−12.9648	+	52.6003i	−0.777578	+	3.15476i
$279$	3.14358	+	0.381700i	0.188201	+	0.0228518i
$280$	7.46550	−	8.42681i	0.446149	−	0.503598i
$281$	24.4292	−	16.8623i	1.45732	−	1.00592i	0.464599	−	0.885521i	$-0.346198\pi$
$281$	24.4292	−	16.8623i	1.45732	−	1.00592i	0.992726	−	0.120398i	$-0.0384169\pi$
$282$	1.00121	−	1.45051i	0.0596214	−	0.0863765i
$283$	−14.1600	+	3.49013i	−0.841726	+	0.207467i	−0.636528	−	0.771253i	$-0.719630\pi$
$283$	−14.1600	+	3.49013i	−0.841726	+	0.207467i	−0.205198	+	0.978720i	$0.565784\pi$
$284$	−10.8399	−	1.31620i	−0.643231	−	0.0781024i
$285$	24.4876	−	12.8521i	1.45052	−	0.761292i
$286$	37.2551	+	26.0006i	2.20294	+	1.53745i
$287$	0.500630	+	0.262751i	0.0295513	+	0.0155097i
$288$	15.0193	+	10.3671i	0.885024	+	0.610888i
$289$	−1.72137	+	2.49383i	−0.101257	+	0.146696i
$290$	14.3756	−	12.7356i	0.844163	−	0.747863i
$291$	−4.53090	−	5.11433i	−0.265606	−	0.299807i
$292$	−25.6830	−	9.74028i	−1.50298	−	0.570007i
$293$	−8.31569	+	15.8442i	−0.485808	+	0.925629i	0.511970	+	0.859003i	$0.328916\pi$
$293$	−8.31569	+	15.8442i	−0.485808	+	0.925629i	−0.997778	+	0.0666261i	$0.978777\pi$
$294$	17.4287	+	6.60982i	1.01646	+	0.385492i
$295$	−43.9802	−	10.8402i	−2.56063	−	0.631138i
$296$	47.6317	−	42.1980i	2.76854	−	2.45271i
$297$	3.84311	−	2.65271i	0.223000	−	0.153926i
$298$	17.3745	+	45.8128i	1.00648	+	2.65386i
$299$	3.41726	+	2.38493i	0.197625	+	0.137924i
$300$	23.5771	−	62.1676i	1.36122	−	3.58925i
$301$	−0.402229	−	1.63191i	−0.0231841	−	0.0940615i
$302$	44.3588	−	23.2813i	2.55256	−	1.33969i
$303$	−6.61283	−	17.4366i	−0.379897	−	1.00171i
$304$	−87.2226	+	10.5907i	−5.00256	+	0.607421i
$305$	0.429825	+	0.296686i	0.0246117	+	0.0169882i
$306$	2.41354	−	9.79212i	0.137973	−	0.559778i
$307$	4.98250	+	20.2148i	0.284366	+	1.15372i	0.923183	+	0.384361i	$0.125578\pi$
$307$	4.98250	+	20.2148i	0.284366	+	1.15372i	−0.638817	+	0.769359i	$0.720576\pi$
$308$	0.901297	+	7.42284i	0.0513561	+	0.422956i
$309$	−1.44459	+	3.80906i	−0.0821796	+	0.216690i
$310$	−8.57638	+	34.7957i	−0.487105	+	1.97626i
$311$	8.64661	−	2.13120i	0.490304	−	0.120849i	0.0135904	−	0.999908i	$-0.495674\pi$
$311$	8.64661	−	2.13120i	0.490304	−	0.120849i	0.476714	+	0.879058i	$0.341828\pi$
$312$	28.3384	−	14.6868i	1.60434	−	0.831477i
$313$	−9.93242	−	2.44812i	−0.561414	−	0.138376i	−0.0516107	−	0.998667i	$-0.516436\pi$
$313$	−9.93242	−	2.44812i	−0.561414	−	0.138376i	−0.509803	+	0.860291i	$0.670282\pi$
$314$	−7.80881	+	14.8784i	−0.440677	+	0.839639i
$315$	−1.27174			−0.0716546
$316$	32.9126			1.85148
$317$	−4.80482	+	9.15482i	−0.269866	+	0.514186i	−0.982244	−	0.187610i	$-0.939926\pi$
$317$	−4.80482	+	9.15482i	−0.269866	+	0.514186i	0.712378	+	0.701796i	$0.247618\pi$
$318$	12.4778	+	14.0845i	0.699720	+	0.789821i
$319$			7.92482i			0.443705i
$320$	−62.8370	+	70.9283i	−3.51270	+	3.96501i
$321$	−11.3303	+	5.94657i	−0.632393	+	0.331905i
$322$	0.113983	+	0.938734i	0.00635202	+	0.0523136i
$323$	11.4532	+	21.8223i	0.637274	+	1.21422i
$324$	−0.636527	−	5.24227i	−0.0353626	−	0.291237i
$325$	−29.9272	−	34.1346i	−1.66006	−	1.89345i
$326$	7.37317	−	60.7235i	0.408362	−	3.36317i
$327$	−0.543240	+	0.206024i	−0.0300412	+	0.0113931i
$328$	−14.6158	−	7.67098i	−0.807024	−	0.423559i
$329$	0.0702334	−	0.185190i	0.00387209	−	0.0102099i
$330$	24.5593	+	46.7938i	1.35194	+	2.57591i
$331$	6.37085	+	12.1386i	0.350173	+	0.667200i	0.995296	−	0.0968793i	$-0.0308861\pi$
$331$	6.37085	+	12.1386i	0.350173	+	0.667200i	−0.645123	+	0.764079i	$0.723194\pi$
$332$	−19.0590	−	77.3256i	−1.04600	−	4.24379i
$333$	−7.13599	−	0.866466i	−0.391050	−	0.0474821i
$334$	3.88628	+	3.44295i	0.212648	+	0.188390i
$335$	21.0602	+	30.5110i	1.15064	+	1.66699i
$336$	3.77787	+	1.43276i	0.206100	+	0.0781633i
$337$	3.32051			0.180880			0.0904399	−	0.995902i	$-0.471173\pi$
$337$	3.32051			0.180880			0.0904399	+	0.995902i	$0.471173\pi$
$338$	0.362589	−	35.0759i	0.0197223	−	1.90788i
$339$	−4.16197			−0.226047
$340$	77.4020	+	29.3547i	4.19771	+	1.59198i
$341$	−8.40026	−	12.1699i	−0.454900	−	0.659036i
$342$	13.3176	+	11.7984i	0.720133	+	0.637982i
$343$	4.18646	+	0.508329i	0.226048	+	0.0274472i
$344$	11.7430	+	47.6433i	0.633141	+	2.56875i
$345$	2.25272	+	4.29221i	0.121283	+	0.231085i
$346$	−8.19005	−	15.6048i	−0.440300	−	0.838921i
$347$	−3.89079	+	10.2592i	−0.208869	+	0.550741i	−0.997981	−	0.0635071i	$-0.979771\pi$
$347$	−3.89079	+	10.2592i	−0.208869	+	0.550741i	0.789113	+	0.614248i	$0.210541\pi$
$348$	7.93528	+	4.16476i	0.425376	+	0.223254i
$349$	−22.8890	+	8.68066i	−1.22522	+	0.464665i	−0.880503	−	0.474041i	$-0.842795\pi$
$349$	−22.8890	+	8.68066i	−1.22522	+	0.464665i	−0.344718	+	0.938706i	$0.612026\pi$
$350$	1.24169	−	10.2263i	0.0663713	−	0.546617i
$351$	−3.36460	−	1.29595i	−0.179589	−	0.0691729i
$352$	−10.2724	−	84.6006i	−0.547519	−	4.50923i
$353$	−4.95620	−	9.44325i	−0.263792	−	0.502614i	0.717149	−	0.696920i	$-0.245447\pi$
$353$	−4.95620	−	9.44325i	−0.263792	−	0.502614i	−0.980941	+	0.194306i	$0.937754\pi$
$354$	−3.51263	−	28.9291i	−0.186694	−	1.53756i
$355$	−7.67917	+	4.03034i	−0.407568	+	0.213908i
$356$	−15.2977	+	17.2675i	−0.810774	+	0.915174i
$357$		−	1.13332i		−	0.0599818i
$358$	9.27169	+	10.4656i	0.490024	+	0.553123i
$359$	−10.1145	+	19.2715i	−0.533821	+	1.01711i	0.457937	+	0.888984i	$0.348588\pi$
$359$	−10.1145	+	19.2715i	−0.533821	+	1.01711i	−0.991758	+	0.128126i	$0.959104\pi$
$360$	37.1284			1.95684
$361$	−24.4788			−1.28836
$362$	3.95762	−	7.54062i	0.208008	−	0.396326i
$363$	−10.4924	−	2.58614i	−0.550706	−	0.135737i
$364$	4.34115	−	3.80606i	0.227538	−	0.199492i
$365$	−21.1818	+	5.22085i	−1.10871	+	0.273272i
$366$	−0.0804117	+	0.326243i	−0.00420319	+	0.0170530i
$367$	3.54658	−	9.35157i	0.185130	−	0.488148i	−0.810033	−	0.586384i	$-0.800551\pi$
$367$	3.54658	−	9.35157i	0.185130	−	0.488148i	0.995163	+	0.0982364i	$0.0313201\pi$
$368$	−1.85635	−	15.2885i	−0.0967692	−	0.796966i
$369$	0.446233	+	1.81044i	0.0232300	+	0.0942477i
$370$	19.4685	−	78.9869i	1.01212	−	4.10633i
$371$	1.74022	+	1.20119i	0.0903480	+	0.0623627i
$372$	−16.6006	+	2.01567i	−0.860699	+	0.104508i
$373$	−6.93207	−	18.2784i	−0.358929	−	0.946418i	−0.985894	−	0.167371i	$-0.946472\pi$
$373$	−6.93207	−	18.2784i	−0.358929	−	0.946418i	0.626965	−	0.779048i	$-0.284297\pi$
$374$	−41.7006	+	21.8862i	−2.15629	+	1.13171i
$375$	−7.61884	−	30.9109i	−0.393435	−	1.59623i
$376$	−2.05045	+	5.40660i	−0.105744	+	0.278824i
$377$	5.05361	−	3.44983i	0.260274	−	0.177675i
$378$	−0.290130	−	0.765010i	−0.0149227	−	0.0393479i
$379$	28.0006	−	19.3274i	1.43829	−	0.992782i	0.442934	−	0.896554i	$-0.353937\pi$
$379$	28.0006	−	19.3274i	1.43829	−	0.992782i	0.995359	−	0.0962284i	$-0.0306779\pi$
$380$	−109.314	+	96.8436i	−5.60768	+	4.96797i
$381$	9.41861	+	2.32148i	0.482530	+	0.118933i
$382$	19.0884	+	7.23926i	0.976645	+	0.370393i
$383$	−11.6478	+	22.1931i	−0.595176	+	1.13401i	0.382512	+	0.923951i	$0.375059\pi$
$383$	−11.6478	+	22.1931i	−0.595176	+	1.13401i	−0.977688	+	0.210063i	$0.932633\pi$
$384$	−22.8740	−	8.67497i	−1.16729	−	0.442693i
$385$	3.93809	+	4.44518i	0.200703	+	0.226547i
$386$	−28.5898	+	25.3284i	−1.45518	+	1.28918i
$387$	3.14877	−	4.56178i	0.160061	−	0.231888i
$388$	29.6947	+	20.4968i	1.50752	+	1.04057i
$389$	−24.8895	−	13.0630i	−1.26195	−	0.662321i	−0.304937	−	0.952373i	$-0.598635\pi$
$389$	−24.8895	−	13.0630i	−1.26195	−	0.662321i	−0.957011	+	0.290051i	$0.906328\pi$
$390$	19.1490	−	36.0315i	0.969646	−	1.82453i
$391$	−3.82503	+	2.00753i	−0.193440	+	0.101525i
$392$	−60.7076	−	7.37124i	−3.06620	−	0.372304i
$393$	−6.25629	+	1.54204i	−0.315588	+	0.0777855i
$394$	10.7410	−	15.5610i	0.541121	−	0.783950i
$395$	21.5128	−	14.8492i	1.08243	−	0.747144i
$396$	−16.3525	+	18.4581i	−0.821743	+	0.927556i
$397$	−24.7576	−	3.00612i	−1.24255	−	0.150873i	−0.527262	−	0.849703i	$-0.676781\pi$
$397$	−24.7576	−	3.00612i	−1.24255	−	0.150873i	−0.715288	+	0.698830i	$0.753704\pi$
$398$	−2.75789	+	11.1892i	−0.138240	+	0.560863i
$399$	1.77037	+	0.929163i	0.0886295	+	0.0465163i
$400$	−20.2225	+	166.547i	−1.01113	+	8.32737i
$401$	−7.41533	+	0.900384i	−0.370304	+	0.0449630i	−0.303573	−	0.952808i	$-0.598180\pi$
$401$	−7.41533	+	0.900384i	−0.370304	+	0.0449630i	−0.0667302	+	0.997771i	$0.521257\pi$
$402$	−13.5491	+	19.6293i	−0.675769	+	0.979020i
$403$	−4.10386	+	10.6546i	−0.204428	+	0.530742i
$404$	55.9420	+	81.0460i	2.78322	+	4.03219i
$405$	−2.78121	−	3.13934i	−0.138200	−	0.155995i
$406$	1.34815	+	0.332289i	0.0669076	+	0.0164912i
$407$	19.0687	+	27.6258i	0.945203	+	1.36936i
$408$			33.0872i			1.63806i
$409$	18.6397	−	12.8661i	0.921676	−	0.636187i	−0.00981470	−	0.999952i	$-0.503124\pi$
$409$	18.6397	−	12.8661i	0.921676	−	0.636187i	0.931491	+	0.363765i	$0.118509\pi$
$410$	−20.9480	+	2.54355i	−1.03455	+	0.125617i
$411$	2.09120	−	0.793089i	0.103152	−	0.0391202i
$412$	2.59308	−	21.3559i	0.127752	−	1.05213i
$413$	−1.16125	−	3.06198i	−0.0571416	−	0.150670i
$414$	−2.06802	+	2.33432i	−0.101638	+	0.114725i
$415$	−47.3447	−	41.9437i	−2.32406	−	2.05894i
$416$	−49.4775	+	43.3789i	−2.42583	+	2.12682i
$417$	−15.0281	+	13.3137i	−0.735930	+	0.651977i
$418$		−	83.0844i		−	4.06379i
$419$	19.9006	+	17.6304i	0.972206	+	0.861299i	0.990357	−	0.138536i	$-0.0442397\pi$
$419$	19.9006	+	17.6304i	0.972206	+	0.861299i	−0.0181517	+	0.999835i	$0.505778\pi$
$420$	6.52064	−	1.60719i	0.318175	−	0.0784231i
$421$	3.14387	+	2.17005i	0.153223	+	0.105762i	0.642209	−	0.766529i	$-0.278018\pi$
$421$	3.14387	+	2.17005i	0.153223	+	0.105762i	−0.488987	+	0.872291i	$0.662633\pi$
$422$	50.2346	−	19.0515i	2.44538	−	0.927411i
$423$	0.610744	−	0.231625i	0.0296954	−	0.0112620i
$424$	−50.8056	−	35.0686i	−2.46734	−	1.70308i
$425$	45.6915	−	11.2619i	2.21636	−	0.546284i
$426$	−4.17632	−	3.69989i	−0.202343	−	0.179260i
$427$			0.0377588i			0.00182728i
$428$	50.5788	−	44.8089i	2.44482	−	2.16592i
$429$	5.88902	+	15.7735i	0.284325	+	0.761550i
$430$	46.9538	+	41.5974i	2.26431	+	2.00601i
$431$	7.21367	−	8.14255i	0.347470	−	0.392213i	−0.548630	−	0.836066i	$-0.684850\pi$
$431$	7.21367	−	8.14255i	0.347470	−	0.392213i	0.896100	+	0.443853i	$0.146389\pi$
$432$	4.72513	+	12.4591i	0.227338	+	0.599440i
$433$	−3.82633	+	31.5126i	−0.183882	+	1.51440i	0.550024	+	0.835149i	$0.314619\pi$
$433$	−3.82633	+	31.5126i	−0.183882	+	1.51440i	−0.733905	+	0.679252i	$0.762304\pi$
$434$	−2.42254	+	0.918747i	−0.116285	+	0.0441012i
$435$	7.06578	−	0.857941i	0.338778	−	0.0411351i
$436$	2.52500	−	1.74288i	0.120926	−	0.0834690i
$437$		−	7.62099i		−	0.364562i
$438$	−7.97289	−	11.5507i	−0.380959	−	0.551915i
$439$	−9.37268	−	2.31016i	−0.447333	−	0.110258i	0.00921263	−	0.999958i	$-0.497067\pi$
$439$	−9.37268	−	2.31016i	−0.447333	−	0.110258i	−0.456546	+	0.889700i	$0.650914\pi$
$440$	−114.972	−	129.776i	−5.48107	−	6.18685i
$441$	3.92422	+	5.68522i	0.186868	+	0.270725i
$442$	32.1097	+	17.0647i	1.52730	+	0.811687i
$443$	−11.5458	+	16.7270i	−0.548558	+	0.794724i	−0.994977	−	0.100100i	$-0.968084\pi$
$443$	−11.5458	+	16.7270i	−0.548558	+	0.794724i	0.446419	+	0.894824i	$0.352699\pi$
$444$	37.6836	−	4.57561i	1.78838	−	0.217149i
$445$	−2.20848	+	18.1884i	−0.104692	+	0.862215i
$446$	3.09275	+	1.62320i	0.146446	+	0.0768607i
$447$	−4.34560	+	17.6308i	−0.205540	+	0.833908i
$448$	−6.80083	−	0.825770i	−0.321309	−	0.0390140i
$449$	3.82028	−	4.31221i	0.180290	−	0.203506i	−0.651417	−	0.758720i	$-0.725825\pi$
$449$	3.82028	−	4.31221i	0.180290	−	0.203506i	0.831707	+	0.555214i	$0.187364\pi$
$450$	27.9594	−	19.2990i	1.31802	−	0.909762i
$451$	4.94630	−	7.16595i	0.232912	−	0.337432i
$452$	21.3398	−	5.25978i	1.00374	−	0.247399i
$453$	18.4309	+	2.23791i	0.865958	+	0.105146i
$454$	−20.4667	+	10.7418i	−0.960551	+	0.504136i
$455$	1.12034	−	4.44636i	0.0525223	−	0.208449i
$456$	−51.6858	−	27.1268i	−2.42041	−	1.27033i
$457$	−13.5780	−	9.37224i	−0.635154	−	0.438415i	0.206490	−	0.978449i	$-0.433796\pi$
$457$	−13.5780	−	9.37224i	−0.635154	−	0.438415i	−0.841643	+	0.540034i	$0.818411\pi$
$458$	26.1691	−	37.9125i	1.22280	−	1.77154i
$459$	2.79764	−	2.47850i	0.130583	−	0.115686i
$460$	−16.9748	−	19.1606i	−0.791455	−	0.893368i
$461$	−29.7566	−	11.2852i	−1.38590	−	0.525604i	−0.454876	−	0.890555i	$-0.650317\pi$
$461$	−29.7566	−	11.2852i	−1.38590	−	0.525604i	−0.931027	+	0.364951i	$0.881086\pi$
$462$	−1.77555	+	3.38304i	−0.0826063	+	0.157393i
$463$	−6.77863	−	2.57080i	−0.315030	−	0.119475i	0.192022	−	0.981391i	$-0.438495\pi$
$463$	−6.77863	−	2.57080i	−0.315030	−	0.119475i	−0.507052	+	0.861916i	$0.669265\pi$
$464$	−21.9563	−	5.41175i	−1.01930	−	0.251234i
$465$	−9.94127	+	8.80720i	−0.461015	+	0.408424i
$466$	59.1020	−	40.7952i	2.73785	−	1.88980i
$467$	−9.75623	−	25.7251i	−0.451465	−	1.19041i	−0.946831	−	0.321730i	$-0.895736\pi$
$467$	−9.75623	−	25.7251i	−0.451465	−	1.19041i	0.495367	−	0.868684i	$-0.335034\pi$
$468$	18.8892	+	2.39269i	0.873152	+	0.110602i
$469$	−0.950447	+	2.50612i	−0.0438876	+	0.115722i
$470$	1.76905	+	7.17733i	0.0816003	+	0.331065i
$471$	−5.51403	+	2.89398i	−0.254073	+	0.133348i
$472$	33.9027	+	89.3940i	1.56050	+	4.11469i
$473$	−25.6955	+	3.12000i	−1.18148	+	0.143458i
$474$	13.8403	+	9.55325i	0.635705	+	0.438795i
$475$	−19.8681	+	80.6082i	−0.911612	+	3.69856i
$476$	1.43226	+	5.81091i	0.0656476	+	0.266343i
$477$	0.840571	+	6.92272i	0.0384871	+	0.316970i
$478$	−0.914909	+	2.41242i	−0.0418470	+	0.110341i
$479$	−4.69680	+	19.0557i	−0.214602	+	0.870676i	0.760575	+	0.649250i	$0.224917\pi$
$479$	−4.69680	+	19.0557i	−0.214602	+	0.870676i	−0.975177	+	0.221426i	$0.928929\pi$
$480$	−74.3179	+	18.3177i	−3.39213	+	0.836086i
$481$	9.31583	−	24.1861i	0.424765	−	1.10279i
$482$	61.0225	+	15.0407i	2.77950	+	0.685085i
$483$	−0.162864	+	0.310312i	−0.00741059	+	0.0141197i
$484$	57.0661			2.59391
$485$	28.6570			1.30125
$486$	1.25396	−	2.38922i	0.0568807	−	0.108377i
$487$	−10.8379	−	12.2334i	−0.491111	−	0.554350i	0.449745	−	0.893157i	$-0.351515\pi$
$487$	−10.8379	−	12.2334i	−0.491111	−	0.554350i	−0.940856	+	0.338807i	$0.889976\pi$
$488$		−	1.10236i		−	0.0499016i
$489$	15.0328	−	16.9685i	0.679807	−	0.767344i
$490$	−69.2233	+	36.3312i	−3.12719	+	1.64128i
$491$	1.90358	+	15.6774i	0.0859076	+	0.707512i	0.970492	+	0.241133i	$0.0775189\pi$
$491$	1.90358	+	15.6774i	0.0859076	+	0.707512i	−0.884585	+	0.466380i	$0.845558\pi$
$492$	−4.57597	−	8.71878i	−0.206301	−	0.393073i
$493$	0.764560	+	6.29672i	0.0344340	+	0.283590i
$494$	−52.9824	+	36.1682i	−2.38379	+	1.62728i
$495$	−2.36076	+	19.4426i	−0.106108	+	0.873880i
$496$	39.4540	−	14.9629i	1.77154	−	0.671855i
$497$	−0.555178	−	0.291380i	−0.0249031	−	0.0130702i
$498$	14.4300	−	38.0487i	0.646623	−	1.70501i
$499$	−13.4676	−	25.6604i	−0.602894	−	1.14872i	−0.975349	−	0.220668i	$-0.929176\pi$
$499$	−13.4676	−	25.6604i	−0.602894	−	1.14872i	0.372456	−	0.928050i	$-0.378516\pi$
$500$	78.1286	+	148.862i	3.49402	+	6.65729i
$501$	0.460488	+	1.86828i	0.0205731	+	0.0834684i
$502$	32.0811	+	3.89535i	1.43185	+	0.173858i
$503$	10.7158	+	9.49335i	0.477793	+	0.423288i	0.867338	−	0.497720i	$-0.165829\pi$
$503$	10.7158	+	9.49335i	0.477793	+	0.423288i	−0.389545	+	0.921008i	$0.627368\pi$
$504$	1.52483	+	2.20910i	0.0679214	+	0.0984012i
$505$	73.1311	+	27.7350i	3.25429	+	1.23419i
$506$	14.5631			0.647408
$507$	7.49504	−	10.6219i	0.332866	−	0.471734i
$508$	−51.2261			−2.27279
$509$	34.9183	+	13.2428i	1.54773	+	0.586975i	0.972885	−	0.231290i	$-0.0742947\pi$
$509$	34.9183	+	13.2428i	1.54773	+	0.586975i	0.574841	+	0.818265i	$0.305064\pi$
$510$	24.0282	+	34.8109i	1.06399	+	1.54145i
$511$	−1.18055	−	1.04588i	−0.0522247	−	0.0462670i
$512$	7.20775	+	0.875180i	0.318541	+	0.0386778i
$513$	1.57801	+	6.40224i	0.0696708	+	0.282666i
$514$	21.4577	+	40.8842i	0.946457	+	1.80332i
$515$	−7.94024	−	15.1289i	−0.349889	−	0.666657i
$516$	−10.3797	+	27.3691i	−0.456942	+	1.20486i
$517$	−2.70084	−	1.41751i	−0.118783	−	0.0623420i
$518$	5.49920	−	2.08557i	0.241621	−	0.0916347i
$519$	0.787268	−	6.48373i	0.0345572	−	0.284604i
$520$	−32.7081	+	129.811i	−1.43435	+	5.69259i
$521$	−0.666852	−	5.49202i	−0.0292153	−	0.240610i	−1.00000		0.000656596i	$-0.999791\pi$
$521$	−0.666852	−	5.49202i	−0.0292153	−	0.240610i	0.970784	−	0.239953i	$-0.0771321\pi$
$522$	2.12805	+	4.05465i	0.0931420	+	0.177467i
$523$	1.40739	+	11.5909i	0.0615408	+	0.506834i	0.990588	+	0.136874i	$0.0437056\pi$
$523$	1.40739	+	11.5909i	0.0615408	+	0.506834i	−0.929048	+	0.369960i	$0.879371\pi$
$524$	30.1293	−	15.8131i	1.31620	−	0.690797i
$525$	2.53163	−	2.85762i	0.110489	−	0.124717i
$526$		−	19.5320i		−	0.851636i
$527$	−7.84859	−	8.85923i	−0.341890	−	0.385914i
$528$	28.9171	−	55.0969i	1.25846	−	2.39779i
$529$	−21.6642			−0.941921
$530$	−78.9195			−3.42805
$531$	5.01901	−	9.56293i	0.217807	−	0.414996i
$532$	−10.2515	−	2.52677i	−0.444460	−	0.109550i
$533$	−6.72290	−	0.0347473i	−0.291201	−	0.00150507i
$534$	−11.4450	+	2.82093i	−0.495273	+	0.122074i
$535$	12.8435	−	52.1082i	0.555274	−	2.25284i
$536$	27.7482	−	73.1660i	1.19854	−	3.16029i
$537$	0.624591	+	5.14397i	0.0269531	+	0.221979i
$538$	6.03889	+	24.5007i	0.260355	+	1.05630i
$539$	7.72003	−	31.3214i	0.332525	−	1.34911i
$540$	18.2276	+	12.5816i	0.784391	+	0.541426i
$541$	−25.9535	+	3.15132i	−1.11583	+	0.135486i	−0.657613	−	0.753356i	$-0.728434\pi$
$541$	−25.9535	+	3.15132i	−1.11583	+	0.135486i	−0.458214	+	0.888842i	$0.651511\pi$
$542$	−11.4746	−	30.2559i	−0.492874	−	1.29960i
$543$	2.79459	−	1.46671i	0.119927	−	0.0629427i
$544$	−16.3240	−	66.2289i	−0.699884	−	2.83954i
$545$	0.864088	−	2.27841i	0.0370135	−	0.0975965i
$546$	2.93027	−	0.340441i	0.125404	−	0.0145695i
$547$	1.83511	+	4.83879i	0.0784637	+	0.206892i	0.968508	−	0.248982i	$-0.0800960\pi$
$547$	1.83511	+	4.83879i	0.0784637	+	0.206892i	−0.890044	+	0.455874i	$0.849327\pi$
$548$	−9.72000	+	6.70923i	−0.415218	+	0.286604i
$549$	−0.0932089	+	0.0825759i	−0.00397806	+	0.00352425i
$550$	−154.036	−	37.9664i	−6.56810	−	1.61889i
$551$	−10.4630	−	3.96809i	−0.445738	−	0.169046i
$552$	4.75481	−	9.05952i	0.202378	−	0.385599i
$553$	1.76702	+	0.670144i	0.0751415	+	0.0284974i
$554$	−1.35003	−	1.52387i	−0.0573574	−	0.0647431i
$555$	22.5669	−	19.9925i	0.957910	−	0.848634i
$556$	60.2285	−	87.2560i	2.55426	−	3.70048i
$557$	17.8918	+	12.3499i	0.758102	+	0.523280i	0.883275	−	0.468855i	$-0.155333\pi$
$557$	17.8918	+	12.3499i	0.758102	+	0.523280i	−0.125173	+	0.992135i	$0.539949\pi$
$558$	−7.56587	−	3.97088i	−0.320289	−	0.168101i
$559$	13.1753	+	15.0276i	0.557257	+	0.635602i
$560$	−15.0050	+	7.87522i	−0.634076	+	0.332789i
$561$	−17.3264	−	2.10381i	−0.731521	−	0.0888227i
$562$	−77.7679	+	19.1681i	−3.28044	+	0.808556i
$563$	12.5958	−	18.2482i	0.530850	−	0.769069i	−0.462198	−	0.886777i	$-0.652939\pi$
$563$	12.5958	−	18.2482i	0.530850	−	0.769069i	0.993048	+	0.117708i	$0.0375546\pi$
$564$	−2.83876	+	1.95946i	−0.119533	+	0.0825080i
$565$	11.5753	−	13.0658i	0.486977	−	0.549684i
$566$	39.0644	+	4.74328i	1.64200	+	0.199375i
$567$	0.0725655	−	0.294410i	0.00304746	−	0.0123640i
$568$	16.2084	+	8.50680i	0.680087	+	0.356937i
$569$	4.70412	−	38.7419i	0.197207	−	1.62415i	−0.472368	−	0.881401i	$-0.656601\pi$
$569$	4.70412	−	38.7419i	0.197207	−	1.62415i	0.669575	−	0.742744i	$-0.266476\pi$
$570$	−74.0781	+	8.99471i	−3.10279	+	0.376747i
$571$	22.4742	−	32.5595i	0.940517	−	1.36257i	0.00857602	−	0.999963i	$-0.497270\pi$
$571$	22.4742	−	32.5595i	0.940517	−	1.36257i	0.931941	−	0.362611i	$-0.118114\pi$
$572$	−50.1290	−	73.4334i	−2.09600	−	3.07040i
$573$	4.29792	+	6.22661i	0.179548	+	0.260121i
$574$	−1.01166	−	1.14192i	−0.0422257	−	0.0476629i
$575$	−14.1291	−	3.48250i	−0.589223	−	0.145230i
$576$	−12.8345	−	18.5940i	−0.534771	−	0.774749i
$577$		−	10.5750i		−	0.440243i	−0.975472	−	0.220122i	$-0.929355\pi$
$577$		−	10.5750i		−	0.440243i	0.975472	−	0.220122i	$-0.0706455\pi$
$578$	6.72909	−	4.64476i	0.279893	−	0.193196i
$579$	−14.0523	+	1.70625i	−0.583992	+	0.0709095i
$580$	−35.1443	+	13.3285i	−1.45929	+	0.553435i
$581$	0.551202	−	4.53955i	0.0228677	−	0.188332i
$582$	6.53769	+	17.2385i	0.270996	+	0.714557i
$583$	21.5944	−	24.3750i	0.894348	−	1.00951i
$584$	34.4661	+	30.5343i	1.42622	+	1.26352i
$585$	13.4261	−	6.95829i	0.555101	−	0.287690i
$586$	36.1402	−	32.0174i	1.49294	−	1.32263i
$587$		−	22.4704i		−	0.927451i	−0.885979	−	0.463725i	$-0.846512\pi$
$587$		−	22.4704i		−	0.927451i	0.885979	−	0.463725i	$-0.153488\pi$
$588$	−27.3056	−	24.1906i	−1.12606	−	0.997606i
$589$	20.2738	−	4.99704i	0.835367	−	0.205900i
$590$	100.588	+	69.4306i	4.14113	+	2.85841i
$591$	6.55202	−	2.48485i	0.269514	−	0.102213i
$592$	−89.5613	+	33.9661i	−3.68095	+	1.39600i
$593$	−14.8097	−	10.2224i	−0.608163	−	0.419784i	0.223785	−	0.974639i	$-0.428159\pi$
$593$	−14.8097	−	10.2224i	−0.608163	−	0.419784i	−0.831948	+	0.554854i	$0.812774\pi$
$594$	−12.2342	+	3.01545i	−0.501973	+	0.123725i
$595$	3.55789	+	3.15201i	0.145859	+	0.129220i
$596$		−	95.8906i		−	3.92783i
$597$	−3.19679	+	2.83211i	−0.130836	+	0.115911i
$598$	−6.33959	−	9.28679i	−0.259245	−	0.379765i
$599$	−19.8737	−	17.6065i	−0.812016	−	0.719383i	0.151086	−	0.988521i	$-0.451723\pi$
$599$	−19.8737	−	17.6065i	−0.812016	−	0.719383i	−0.963102	+	0.269137i	$0.913261\pi$
$600$	−73.9106	+	83.4278i	−3.01739	+	3.40592i
$601$	−7.78584	−	20.5296i	−0.317591	−	0.837419i	−0.994821	−	0.101647i	$-0.967589\pi$
$601$	−7.78584	−	20.5296i	−0.317591	−	0.837419i	0.677230	−	0.735772i	$-0.263180\pi$
$602$	−0.546651	+	4.50208i	−0.0222798	+	0.183491i
$603$	−8.26501	+	3.13451i	−0.336577	+	0.127647i
$604$	−97.3294	+	11.8179i	−3.96028	+	0.480865i
$605$	37.3003	−	25.7465i	1.51647	−	1.04675i
$606$			50.3189i			2.04407i
$607$	24.3042	+	35.2107i	0.986477	+	1.42916i	0.901501	+	0.432776i	$0.142466\pi$
$607$	24.3042	+	35.2107i	0.986477	+	1.42916i	0.0849758	+	0.996383i	$0.472919\pi$
$608$	116.840	+	28.7985i	4.73849	+	1.16793i
$609$	0.341233	+	0.385172i	0.0138274	+	0.0156080i
$610$	−0.800546	−	1.15979i	−0.0324132	−	0.0469586i
$611$	0.271790	+	2.33938i	0.0109955	+	0.0946411i
$612$	−11.2122	+	16.2436i	−0.453226	+	0.656611i
$613$	44.7677	−	5.43579i	1.80815	−	0.219549i	0.854290	−	0.519796i	$-0.173992\pi$
$613$	44.7677	−	5.43579i	1.80815	−	0.219549i	0.953862	+	0.300247i	$0.0970690\pi$
$614$	6.77149	−	55.7682i	0.273275	−	2.25062i
$615$	−6.92466	−	3.63434i	−0.279229	−	0.146551i
$616$	2.99977	−	12.1705i	0.120864	−	0.490364i
$617$	−21.3526	−	2.59268i	−0.859624	−	0.104377i	−0.321159	−	0.947025i	$-0.604073\pi$
$617$	−21.3526	−	2.59268i	−0.859624	−	0.104377i	−0.538465	+	0.842648i	$0.680996\pi$
$618$	7.28923	−	8.22784i	0.293216	−	0.330972i
$619$	19.9658	−	13.7814i	0.802493	−	0.553921i	−0.0947280	−	0.995503i	$-0.530198\pi$
$619$	19.9658	−	13.7814i	0.802493	−	0.553921i	0.897221	+	0.441583i	$0.145583\pi$
$620$	39.8418	−	57.7209i	1.60009	−	2.31813i
$621$	−1.12219	+	0.276595i	−0.0450319	+	0.0110994i
$622$	−23.8541	−	2.89642i	−0.956463	−	0.116136i
$623$	−1.17289	+	0.615583i	−0.0469910	+	0.0246628i
$624$	−47.7231	+	5.54450i	−1.91045	+	0.221958i
$625$	62.4872	+	32.7958i	2.49949	+	1.31183i
$626$	22.7165	+	15.6801i	0.907935	+	0.626702i
$627$	17.4915	−	25.3409i	0.698545	−	1.01202i
$628$	24.6149	−	21.8069i	0.982240	−	0.870189i
$629$	17.8164	+	20.1106i	0.710388	+	0.801862i
$630$	3.20854	+	1.21684i	0.127831	+	0.0484800i
$631$	9.31317	−	17.7448i	0.370752	−	0.706408i	−0.626584	−	0.779354i	$-0.715548\pi$
$631$	9.31317	−	17.7448i	0.370752	−	0.706408i	0.997336	+	0.0729454i	$0.0232399\pi$
$632$	−51.5881	−	19.5648i	−2.05206	−	0.778245i
$633$	19.3325	+	4.76504i	0.768398	+	0.189393i
$634$	20.8819	−	18.4997i	0.829326	−	0.734719i
$635$	−33.4831	+	23.1117i	−1.32874	+	0.917160i
$636$	−13.0586	−	34.4328i	−0.517808	−	1.36535i
$637$	−23.3341	+	8.71179i	−0.924531	+	0.345173i
$638$	7.58269	−	19.9939i	0.300201	−	0.791566i
$639$	−0.494855	−	2.00770i	−0.0195761	−	0.0794235i
$640$	90.8513	−	47.6824i	3.59121	−	1.88481i
$641$	7.55216	+	19.9134i	0.298292	+	0.786532i	0.997437	+	0.0715518i	$0.0227951\pi$
$641$	7.55216	+	19.9134i	0.298292	+	0.786532i	−0.699145	+	0.714980i	$0.746436\pi$
$642$	34.2755	−	4.16179i	1.35274	−	0.164253i
$643$	−3.06190	−	2.11348i	−0.120750	−	0.0833474i	0.506159	−	0.862440i	$-0.331065\pi$
$643$	−3.06190	−	2.11348i	−0.120750	−	0.0833474i	−0.626909	+	0.779093i	$0.715680\pi$
$644$	0.442895	−	1.79690i	0.0174525	−	0.0708076i
$645$	5.56359	+	22.5724i	0.219066	+	0.888786i
$646$	−8.01570	−	66.0152i	−0.315373	−	2.59733i
$647$	−2.44761	+	6.45381i	−0.0962254	+	0.253725i	−0.974483	−	0.224463i	$-0.927937\pi$
$647$	−2.44761	+	6.45381i	−0.0962254	+	0.253725i	0.878257	+	0.478188i	$0.158706\pi$
$648$	−2.11854	+	8.59525i	−0.0832241	+	0.337653i
$649$	−48.9676	+	12.0694i	−1.92215	+	0.473767i
$650$	42.8437	+	114.755i	1.68047	+	4.50106i
$651$	−0.932299	−	0.229791i	−0.0365397	−	0.00900623i
$652$	−55.6338	+	106.001i	−2.17879	+	4.15133i
$653$	−31.8864			−1.24781			−0.623907	−	0.781499i	$-0.714455\pi$
$653$	−31.8864			−1.24781			−0.623907	+	0.781499i	$0.714455\pi$
$654$	1.56769			0.0613017
$655$	12.5591	−	23.9294i	0.490725	−	0.934998i
$656$	16.4761	+	18.5976i	0.643282	+	0.726115i
$657$		−	5.20151i		−	0.202930i
$658$	−0.354390	+	0.400024i	−0.0138156	+	0.0155946i
$659$	16.3089	−	8.55959i	0.635306	−	0.333434i	−0.116136	−	0.993233i	$-0.537051\pi$
$659$	16.3089	−	8.55959i	0.635306	−	0.333434i	0.751442	+	0.659799i	$0.229359\pi$
$660$	−12.4666	−	102.672i	−0.485263	−	3.99650i
$661$	17.0812	+	32.5454i	0.664380	+	1.26587i	0.951403	+	0.307947i	$0.0996421\pi$
$661$	17.0812	+	32.5454i	0.664380	+	1.26587i	−0.287023	+	0.957924i	$0.592666\pi$
$662$	−4.45873	−	36.7209i	−0.173293	−	1.42720i
$663$	6.20093	+	11.9648i	0.240824	+	0.464673i
$664$	−16.0923	+	132.532i	−0.624501	+	5.14323i
$665$	−7.84075	+	2.97360i	−0.304051	+	0.115311i
$666$	17.1747	+	9.01396i	0.665505	+	0.349284i
$667$	0.695529	−	1.83396i	0.0269310	−	0.0710112i
$668$	−4.72215	−	8.99730i	−0.182705	−	0.348116i
$669$	0.601565	+	1.14619i	0.0232579	+	0.0443141i
$670$	−23.9400	−	97.1286i	−0.924885	−	3.75240i
$671$	0.577262	+	0.0700923i	0.0222850	+	0.00270588i
$672$	−4.14206	−	3.66955i	−0.159784	−	0.141556i
$673$	13.6057	+	19.7112i	0.524460	+	0.759812i	0.992281	−	0.124012i	$-0.0395760\pi$
$673$	13.6057	+	19.7112i	0.524460	+	0.759812i	−0.467820	+	0.883824i	$0.654961\pi$
$674$	−8.37747	−	3.17716i	−0.322688	−	0.122380i
$675$	12.5906			0.484613
$676$	−25.0059	+	63.9339i	−0.961764	+	2.45900i
$677$	3.64567			0.140114			0.0700571	−	0.997543i	$-0.477682\pi$
$677$	3.64567			0.140114			0.0700571	+	0.997543i	$0.477682\pi$
$678$	10.5004	+	3.98228i	0.403266	+	0.152939i
$679$	1.17692	+	1.70506i	0.0451661	+	0.0654344i
$680$	−103.872	−	92.0226i	−3.98331	−	3.52891i
$681$	−8.50383	−	1.03255i	−0.325867	−	0.0395675i
$682$	9.54894	+	38.7416i	0.365648	+	1.48349i
$683$	2.37035	+	4.51633i	0.0906990	+	0.172813i	0.926580	−	0.376099i	$-0.122735\pi$
$683$	2.37035	+	4.51633i	0.0906990	+	0.172813i	−0.835880	+	0.548911i	$0.815042\pi$
$684$	−16.1819	−	30.8321i	−0.618732	−	1.17890i
$685$	−3.32631	+	8.77076i	−0.127092	+	0.335113i
$686$	−10.0758	−	5.28821i	−0.384697	−	0.201905i
$687$	15.9633	−	6.05407i	0.609037	−	0.230977i
$688$	8.90289	−	73.3219i	0.339419	−	2.79537i
$689$	−24.9442	−	3.15969i	−0.950300	−	0.120374i
$690$	−1.57660	−	12.9845i	−0.0600202	−	0.494310i
$691$	5.34274	+	10.1797i	0.203248	+	0.387256i	0.965650	−	0.259848i	$-0.0836724\pi$
$691$	5.34274	+	10.1797i	0.203248	+	0.387256i	−0.762402	+	0.647104i	$0.775980\pi$
$692$	4.15738	+	34.2391i	0.158040	+	1.30158i
$693$	−1.25377	+	0.658029i	−0.0476268	+	0.0249965i
$694$	19.6325	−	22.1605i	0.745240	−	0.841202i
$695$		−	84.2067i		−	3.19414i
$696$	−9.96224	−	11.2450i	−0.377618	−	0.426242i
$697$	3.23877	−	6.17096i	0.122677	−	0.233742i
$698$	66.0536			2.50017
$699$	26.6147			1.00666
$700$	−9.36911	+	17.8513i	−0.354119	+	0.674717i
$701$	38.0657	+	9.38235i	1.43772	+	0.354367i	0.879728	−	0.475478i	$-0.157725\pi$
$701$	38.0657	+	9.38235i	1.43772	+	0.354367i	0.557994	+	0.829845i	$0.311571\pi$
$702$	7.24869	+	6.48896i	0.273584	+	0.244910i
$703$	−46.0219	+	11.3434i	−1.73575	+	0.427823i
$704$	−25.2490	+	102.439i	−0.951607	+	3.86082i
$705$	−0.971461	+	2.56153i	−0.0365873	+	0.0964729i
$706$	3.46867	+	28.5670i	0.130545	+	1.07513i
$707$	1.35323	+	5.49028i	0.0508936	+	0.206483i
$708$	−13.6487	+	55.3751i	−0.512951	+	2.08113i
$709$	3.74626	+	2.58585i	0.140694	+	0.0971138i	0.636332	−	0.771415i	$-0.280451\pi$
$709$	3.74626	+	2.58585i	0.140694	+	0.0971138i	−0.495639	+	0.868529i	$0.665066\pi$
$710$	23.2305	−	2.82069i	0.871824	−	0.105859i
$711$	2.21009	+	5.82752i	0.0828847	+	0.218549i
$712$	34.2425	−	17.9719i	1.28329	−	0.673524i
$713$	0.875886	+	3.55361i	0.0328022	+	0.133084i
$714$	−1.08439	+	2.85931i	−0.0405824	+	0.107007i
$715$	−65.8969	−	25.3818i	−2.46441	−	0.949224i
$716$	−9.70328	−	25.5855i	−0.362629	−	0.956173i
$717$	−0.786930	+	0.543178i	−0.0293884	+	0.0202854i
$718$	43.9577	−	38.9431i	1.64049	−	1.45335i
$719$	−26.2086	−	6.45985i	−0.977418	−	0.240912i	−0.281918	−	0.959438i	$-0.590971\pi$
$719$	−26.2086	−	6.45985i	−0.977418	−	0.240912i	−0.695499	+	0.718527i	$0.744817\pi$
$720$	−52.2551	−	19.8177i	−1.94743	−	0.738563i
$721$	0.574053	−	1.09377i	0.0213789	−	0.0407340i
$722$	61.7586	+	23.4220i	2.29842	+	0.871675i
$723$	15.4455	+	17.4344i	0.574424	+	0.648391i
$724$	−12.4752	+	11.0520i	−0.463636	+	0.410746i
$725$	−12.1379	+	17.5847i	−0.450789	+	0.653081i
$726$	23.9972	+	16.5641i	0.890619	+	0.614750i
$727$	16.4481	+	8.63260i	0.610025	+	0.320166i	0.741293	−	0.671181i	$-0.234213\pi$
$727$	16.4481	+	8.63260i	0.610025	+	0.320166i	−0.131269	+	0.991347i	$0.541905\pi$
$728$	−9.06692	+	3.38513i	−0.336042	+	0.125461i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	58.4360	+	7.09541i	2.16281	+	0.262613i
$731$	−20.1155	+	4.95803i	−0.743999	+	0.183379i
$732$	0.373555	−	0.541188i	0.0138070	−	0.0200029i
$733$	5.38578	−	3.71754i	0.198928	−	0.137310i	−0.464437	−	0.885606i	$-0.653743\pi$
$733$	5.38578	−	3.71754i	0.198928	−	0.137310i	0.663365	+	0.748296i	$0.269128\pi$
$734$	−17.8957	+	20.2000i	−0.660541	+	0.745597i
$735$	−28.7620	−	3.49233i	−1.06090	−	0.128817i
$736$	−5.04782	+	20.4798i	−0.186065	+	0.754896i
$737$	36.5497	+	19.1827i	1.34632	+	0.706605i
$738$	0.606456	−	4.99461i	0.0223239	−	0.183854i
$739$	−49.7597	+	6.04192i	−1.83044	+	0.222256i	−0.961908	−	0.273375i	$-0.911860\pi$
$739$	−49.7597	+	6.04192i	−1.83044	+	0.222256i	−0.868533	+	0.495631i	$0.834937\pi$
$740$	−90.4417	+	131.027i	−3.32470	+	4.81666i
$741$	−23.7741	−	0.122877i	−0.873364	−	0.00451398i
$742$	−3.24116	−	4.69563i	−0.118987	−	0.172382i
$743$	−3.30102	−	3.72608i	−0.121103	−	0.136697i	0.684832	−	0.728701i	$-0.259875\pi$
$743$	−3.30102	−	3.72608i	−0.121103	−	0.136697i	−0.805935	+	0.592004i	$0.798337\pi$
$744$	27.2184	+	6.70872i	0.997873	+	0.245954i
$745$	−43.2630	−	62.6773i	−1.58503	−	2.29632i
$746$			52.7482i			1.93125i
$747$	12.4115	−	8.56703i	0.454112	−	0.313451i
$748$	91.4968	−	11.1097i	3.34546	−	0.406212i
$749$	3.62786	−	1.37587i	0.132559	−	0.0502731i
$750$	−10.3544	+	85.2764i	−0.378090	+	3.11385i
$751$	−4.73297	−	12.4798i	−0.172708	−	0.455395i	0.820514	−	0.571627i	$-0.193688\pi$
$751$	−4.73297	−	12.4798i	−0.172708	−	0.455395i	−0.993222	+	0.116232i	$0.962918\pi$
$752$	5.77168	−	6.51488i	0.210472	−	0.237573i
$753$	8.96471	+	7.94204i	0.326692	+	0.289424i
$754$	−16.0509	+	3.86830i	−0.584538	+	0.140875i
$755$	−58.2858	+	51.6367i	−2.12124	+	1.87925i
$756$			1.60124i			0.0582366i
$757$	−0.325828	−	0.288658i	−0.0118424	−	0.0104915i	0.657181	−	0.753733i	$-0.271749\pi$
$757$	−0.325828	−	0.288658i	−0.0118424	−	0.0104915i	−0.669023	+	0.743242i	$0.733287\pi$
$758$	−89.1370	+	21.9703i	−3.23760	+	0.797997i
$759$	4.44177	+	3.06593i	0.161226	+	0.111286i
$760$	228.910	−	86.8139i	8.30342	−	3.14907i
$761$	9.51794	−	3.60968i	0.345025	−	0.130851i	−0.176004	−	0.984389i	$-0.556317\pi$
$761$	9.51794	−	3.60968i	0.345025	−	0.130851i	0.521030	+	0.853539i	$0.325548\pi$
$762$	−21.5414	−	14.8690i	−0.780362	−	0.538645i
$763$	0.171051	−	0.0421602i	0.00619245	−	0.00152630i
$764$	−29.9059	−	26.4943i	−1.08196	−	0.958530i
$765$			15.6760i			0.566767i
$766$	50.6218	−	44.8470i	1.82904	−	1.62039i
$767$	29.0131	+	25.9723i	1.04760	+	0.937804i
$768$	15.5867	+	13.8086i	0.562437	+	0.498276i
$769$	−16.6898	+	18.8389i	−0.601851	+	0.679349i	−0.967926	−	0.251236i	$-0.919163\pi$
$769$	−16.6898	+	18.8389i	−0.601851	+	0.679349i	0.366075	+	0.930585i	$0.380701\pi$
$770$	−5.68231	−	14.9830i	−0.204776	−	0.539951i
$771$	−2.06262	+	16.9872i	−0.0742833	+	0.611778i
$772$	69.8942	−	26.5074i	2.51555	−	0.954022i
$773$	−31.2495	+	3.79438i	−1.12397	+	0.136474i	−0.661345	−	0.750081i	$-0.730014\pi$
$773$	−31.2495	+	3.79438i	−1.12397	+	0.136474i	−0.462622	+	0.886556i	$0.653091\pi$
$774$	−12.3090	+	8.49630i	−0.442438	+	0.305393i
$775$		−	39.8704i		−	1.43219i
$776$	−34.3600	−	49.7791i	−1.23345	−	1.78697i
$777$	2.11634	+	0.521630i	0.0759231	+	0.0187134i
$778$	50.2958	+	56.7723i	1.80319	+	2.03538i
$779$	6.98437	+	10.1186i	0.250241	+	0.362537i
$780$	−60.0463	+	52.6450i	−2.15000	+	1.88499i
$781$	−5.48525	+	7.94675i	−0.196278	+	0.284357i
$782$	11.5712	−	1.40500i	0.413785	−	0.0502426i
$783$	−0.204558	+	1.68469i	−0.00731031	+	0.0602058i
$784$	81.5064	+	42.7778i	2.91094	+	1.52778i
$785$	6.25048	−	25.3592i	0.223089	−	0.905109i
$786$	17.2598	+	2.09571i	0.615635	+	0.0747516i
$787$	−33.6393	+	37.9709i	−1.19911	+	1.35352i	−0.279762	+	0.960069i	$0.590256\pi$
$787$	−33.6393	+	37.9709i	−1.19911	+	1.35352i	−0.919348	+	0.393446i	$0.871283\pi$
$788$	−30.4541	+	21.0209i	−1.08488	+	0.748839i
$789$	4.11203	−	5.95730i	0.146392	−	0.212085i
$790$	−68.4837	+	16.8797i	−2.43654	+	0.600553i
$791$	1.25279	+	0.152117i	0.0445442	+	0.00540864i
$792$	36.6036	−	19.2111i	1.30065	−	0.682636i
$793$	−0.206596	−	0.398629i	−0.00733643	−	0.0141557i
$794$	59.5858	+	31.2731i	2.11462	+	1.10984i
$795$	−24.0706	−	16.6147i	−0.853696	−	0.589264i
$796$	12.8118	−	18.5612i	0.454104	−	0.657883i
$797$	−9.04710	+	8.01504i	−0.320465	+	0.283907i	−0.807983	−	0.589206i	$-0.799441\pi$
$797$	−9.04710	+	8.01504i	−0.320465	+	0.283907i	0.487518	+	0.873113i	$0.337902\pi$
$798$	−3.57751	−	4.03817i	−0.126642	−	0.142950i
$799$	−2.28273	−	0.865724i	−0.0807570	−	0.0306271i
$800$	106.783	−	203.458i	3.77534	−	7.19331i
$801$	−4.08463	−	1.54909i	−0.144323	−	0.0547346i
$802$	19.5700	+	4.82357i	0.691040	+	0.170326i
$803$	−18.1810	+	16.1070i	−0.641595	+	0.568404i
$804$	38.4161	−	26.5167i	1.35483	−	0.935173i
$805$	−0.521215	−	1.37433i	−0.0183704	−	0.0484388i
$806$	20.5484	−	22.9542i	0.723787	−	0.808529i
$807$	−3.31621	+	8.74412i	−0.116736	+	0.307808i
$808$	−39.5075	−	160.288i	−1.38987	−	5.63891i
$809$	−10.7462	+	5.64005i	−0.377817	+	0.198294i	−0.642932	−	0.765923i	$-0.722282\pi$
$809$	−10.7462	+	5.64005i	−0.377817	+	0.198294i	0.265115	+	0.964217i	$0.414590\pi$
$810$	4.01305	+	10.5815i	0.141004	+	0.371797i
$811$	10.3204	−	1.25313i	0.362400	−	0.0440033i	0.0626881	−	0.998033i	$-0.480033\pi$
$811$	10.3204	−	1.25313i	0.362400	−	0.0440033i	0.299711	+	0.954030i	$0.403110\pi$
$812$	−2.23638	−	1.54366i	−0.0784816	−	0.0541719i
$813$	2.86994	−	11.6438i	0.100653	−	0.408367i
$814$	−21.6763	−	87.9440i	−0.759752	−	3.08244i
$815$	11.4606	+	94.3863i	0.401446	+	3.30621i
$816$	17.6607	−	46.5674i	0.618248	−	1.63019i
$817$	8.74687	−	35.4875i	0.306014	−	1.24155i
$818$	−59.3377	+	14.6254i	−2.07469	+	0.511366i
$819$	0.965411	+	0.513068i	0.0337342	+	0.0179281i
$820$	40.0980	+	9.88326i	1.40028	+	0.345139i
$821$	−11.4106	+	21.7410i	−0.398232	+	0.758768i	−0.999179	−	0.0405214i	$-0.987098\pi$
$821$	−11.4106	+	21.7410i	−0.398232	+	0.758768i	0.600947	+	0.799289i	$0.294790\pi$
$822$	−6.03485			−0.210489
$823$	25.7888			0.898941			0.449470	−	0.893295i	$-0.351613\pi$
$823$	25.7888			0.898941			0.449470	+	0.893295i	$0.351613\pi$
$824$	−16.7594	+	31.9324i	−0.583841	+	1.11242i
$825$	−38.9882	−	44.0085i	−1.35739	−	1.53218i
$826$			8.83632i			0.307455i
$827$	−1.70181	+	1.92094i	−0.0591777	+	0.0667978i	−0.777354	−	0.629063i	$-0.783439\pi$
$827$	−1.70181	+	1.92094i	−0.0591777	+	0.0667978i	0.718176	+	0.695861i	$0.244977\pi$
$828$	5.40428	−	2.83638i	0.187812	−	0.0985712i
$829$	1.84408	+	15.1874i	0.0640476	+	0.527480i	0.989057	+	0.147535i	$0.0471339\pi$
$829$	1.84408	+	15.1874i	0.0640476	+	0.527480i	−0.925009	+	0.379945i	$0.875943\pi$
$830$	79.3151	+	151.122i	2.75307	+	5.24553i
$831$	−0.0909454	−	0.749003i	−0.00315486	−	0.0259826i
$832$	76.3162	−	28.4926i	2.64579	−	0.987804i
$833$	3.11222	−	25.6314i	0.107832	−	0.888075i
$834$	50.6541	−	19.2105i	1.75401	−	0.665207i
$835$	−7.14587	−	3.75044i	−0.247293	−	0.129789i
$836$	−57.6598	+	152.036i	−1.99420	+	5.25829i
$837$	−1.47163	−	2.80395i	−0.0508669	−	0.0969187i
$838$	−33.3388	−	63.5218i	−1.15167	−	2.19432i
$839$	−5.63771	−	22.8731i	−0.194635	−	0.789666i	−0.984355	−	0.176198i	$-0.943620\pi$
$839$	−5.63771	−	22.8731i	−0.194635	−	0.789666i	0.789719	−	0.613468i	$-0.210226\pi$
$840$	−11.1760	−	1.35701i	−0.385609	−	0.0468214i
$841$	19.5511	+	17.3208i	0.674175	+	0.597267i
$842$	−5.85544	−	8.48307i	−0.201792	−	0.292346i
$843$	−27.7548	−	10.5260i	−0.955924	−	0.362534i
$844$	−105.146			−3.61928
$845$	12.5004	+	53.0712i	0.430028	+	1.82571i
$846$	−1.76250			−0.0605960
$847$	3.06379	+	1.16194i	0.105273	+	0.0399248i
$848$	52.7863	+	76.4742i	1.81269	+	2.62614i
$849$	10.9161	+	9.67085i	0.374641	+	0.331903i
$850$	−126.053	−	15.3056i	−4.32358	−	0.524977i
$851$	−1.98828	−	8.06675i	−0.0681572	−	0.276525i
$852$	5.07456	+	9.66877i	0.173852	+	0.331247i
$853$	20.3524	+	38.7783i	0.696854	+	1.32774i	0.934350	+	0.356356i	$0.115981\pi$
$853$	20.3524	+	38.7783i	0.696854	+	1.32774i	−0.237496	+	0.971388i	$0.576327\pi$
$854$	0.0361287	−	0.0952634i	0.00123630	−	0.00325985i
$855$	−24.4876	−	12.8521i	−0.837458	−	0.439532i
$856$	−105.915	+	40.1682i	−3.62010	+	1.37292i
$857$	3.09669	−	25.5035i	0.105781	−	0.871183i	−0.839147	−	0.543905i	$-0.816945\pi$
$857$	3.09669	−	25.5035i	0.105781	−	0.871183i	0.944928	−	0.327279i	$-0.106132\pi$
$858$	0.234807	−	45.4304i	0.00801618	−	1.55097i
$859$	−0.652950	−	5.37753i	−0.0222784	−	0.183479i	0.977322	−	0.211760i	$-0.0679196\pi$
$859$	−0.652950	−	5.37753i	−0.0222784	−	0.183479i	−0.999600	+	0.0282814i	$0.990997\pi$
$860$	−57.0526	−	108.705i	−1.94548	−	3.70680i
$861$	−0.0681505	−	0.561270i	−0.00232256	−	0.0191280i
$862$	−25.9907	+	13.6410i	−0.885247	+	0.464613i
$863$	−20.7392	+	23.4098i	−0.705972	+	0.796878i	−0.986638	−	0.162928i	$-0.947906\pi$
$863$	−20.7392	+	23.4098i	−0.705972	+	0.796878i	0.280666	+	0.959805i	$0.409445\pi$
$864$		−	18.2499i		−	0.620873i
$865$	18.1651	+	20.5042i	0.617632	+	0.697162i
$866$	39.8058	−	75.8436i	1.35266	−	2.57727i
$867$	3.03024			0.102912
$868$	5.07061			0.172108
$869$	13.5254	−	25.7705i	0.458818	−	0.874205i
$870$	−18.6475	−	4.59619i	−0.632209	−	0.155826i
$871$	−3.67805	−	31.6581i	−0.124626	−	1.07269i
$872$	−4.99380	+	1.23086i	−0.169111	+	0.0416822i
$873$	−1.63516	+	6.63413i	−0.0553419	+	0.224531i
$874$	−7.29198	+	19.2274i	−0.246655	+	0.650375i
$875$	1.16358	+	9.58294i	0.0393362	+	0.323963i
$876$	6.57352	+	26.6698i	0.222099	+	0.901090i
$877$	−12.4479	+	50.5030i	−0.420335	+	1.70537i	0.254224	+	0.967145i	$0.418180\pi$
$877$	−12.4479	+	50.5030i	−0.420335	+	1.70537i	−0.674559	+	0.738221i	$0.735666\pi$
$878$	21.4363	+	14.7964i	0.723441	+	0.499355i
$879$	17.7634	−	2.15687i	0.599144	−	0.0727493i
$880$	92.5435	+	244.017i	3.11964	+	8.22581i
$881$	40.3612	−	21.1832i	1.35980	−	0.713680i	0.382190	−	0.924084i	$-0.375170\pi$
$881$	40.3612	−	21.1832i	1.35980	−	0.713680i	0.977615	+	0.210404i	$0.0674778\pi$
$882$	−4.46083	−	18.0983i	−0.150204	−	0.609402i
$883$	5.33599	−	14.0699i	0.179570	−	0.473488i	−0.814763	−	0.579794i	$-0.803133\pi$
$883$	5.33599	−	14.0699i	0.179570	−	0.473488i	0.994333	+	0.106306i	$0.0339022\pi$
$884$	−46.9149	−	53.5107i	−1.57792	−	1.79976i
$885$	16.0624	+	42.3529i	0.539930	+	1.42368i
$886$	45.1343	−	31.1540i	1.51632	−	1.04664i
$887$	−13.7213	+	12.1560i	−0.460715	+	0.408158i	−0.861296	−	0.508104i	$-0.830347\pi$
$887$	−13.7213	+	12.1560i	−0.460715	+	0.408158i	0.400581	+	0.916261i	$0.368808\pi$
$888$	−61.7861	−	15.2289i	−2.07341	−	0.511049i
$889$	−2.75025	−	1.04303i	−0.0922403	−	0.0349821i
$890$	22.9751	−	43.7753i	0.770126	−	1.46735i
$891$	−4.36627	−	1.65591i	−0.146276	−	0.0554750i
$892$	−4.53294	−	5.11663i	−0.151774	−	0.171318i
$893$	3.22386	−	2.85609i	0.107882	−	0.0955756i
$894$	27.8333	−	40.3235i	0.930886	−	1.34862i
$895$	−17.8858	−	12.3457i	−0.597856	−	0.412670i
$896$	6.56825	+	3.44728i	0.219430	+	0.115166i
$897$	0.0215379	−	4.16715i	0.000719130	−	0.139137i
$898$	−13.7644	+	7.22412i	−0.459324	+	0.241072i
$899$	5.33486	+	0.647769i	0.177927	+	0.0216043i
$900$	−64.5562	+	15.9117i	−2.15187	+	0.530389i
$901$	14.8063	−	21.4507i	0.493270	−	0.714626i
$902$	−19.3358	+	13.3466i	−0.643813	+	0.444392i
$903$	−1.11454	+	1.25806i	−0.0370896	+	0.0418655i
$904$	−36.5751	−	4.44102i	−1.21647	−	0.147706i
$905$	−3.16784	+	12.8524i	−0.105302	+	0.427229i
$906$	−44.3588	−	23.2813i	−1.47372	−	0.773470i
$907$	−2.84793	+	23.4548i	−0.0945641	+	0.778805i	0.865864	+	0.500279i	$0.166769\pi$
$907$	−2.84793	+	23.4548i	−0.0945641	+	0.778805i	−0.960429	+	0.278527i	$0.910154\pi$
$908$	44.9068	−	5.45267i	1.49028	−	0.180953i
$909$	−10.5935	+	15.3474i	−0.351365	+	0.509040i
$910$	−7.08096	+	10.1460i	−0.234731	+	0.336336i
$911$	−5.66434	−	8.20621i	−0.187668	−	0.271884i	0.717845	−	0.696203i	$-0.245129\pi$
$911$	−5.66434	−	8.20621i	−0.187668	−	0.271884i	−0.905513	+	0.424319i	$0.860513\pi$
$912$	58.2641	+	65.7666i	1.92932	+	2.17775i
$913$	−68.3782	−	16.8537i	−2.26299	−	0.557776i
$914$	25.2890	+	36.6375i	0.836487	+	1.21186i
$915$		−	0.522276i		−	0.0172659i
$916$	−74.1979	+	51.2151i	−2.45157	+	1.69220i
$917$	1.93957	−	0.235506i	0.0640501	−	0.00777710i
$918$	−9.42980	+	3.57625i	−0.311230	+	0.118034i
$919$	4.97692	−	40.9886i	0.164173	−	1.35209i	−0.644848	−	0.764311i	$-0.723079\pi$
$919$	4.97692	−	40.9886i	0.164173	−	1.35209i	0.809022	−	0.587779i	$-0.199998\pi$
$920$	15.2168	+	40.1234i	0.501683	+	1.32283i
$921$	13.8061	−	15.5838i	0.454926	−	0.513505i
$922$	64.2763	+	56.9439i	2.11683	+	1.87535i
$923$	7.45542	+	0.0385334i	0.245398	+	0.00126834i
$924$	5.59689	−	4.95841i	0.184124	−	0.163120i
$925$			90.5065i			2.97583i
$926$	14.6423	+	12.9720i	0.481176	+	0.426285i
$927$	3.95541	−	0.974922i	0.129913	−	0.0320206i
$928$	25.4888	+	17.5936i	0.836710	+	0.577539i
$929$	−25.6995	+	9.74652i	−0.843172	+	0.319773i	−0.738100	−	0.674692i	$-0.764277\pi$
$929$	−25.6995	+	9.74652i	−0.843172	+	0.319773i	−0.105072	+	0.994465i	$0.533507\pi$
$930$	33.5083	−	12.7080i	1.09878	−	0.416712i
$931$	37.4875	+	25.8757i	1.22860	+	0.848042i
$932$	−136.462	+	33.6350i	−4.46998	+	1.10175i
$933$	−6.66578	−	5.90536i	−0.218228	−	0.193333i
$934$			74.2380i			2.42914i
$935$	54.7930	−	48.5424i	1.79192	−	1.58750i
$936$	−28.1850	−	14.9790i	−0.921257	−	0.489602i
$937$	−10.8932	−	9.65057i	−0.355867	−	0.315270i	0.466181	−	0.884690i	$-0.345630\pi$
$937$	−10.8932	−	9.65057i	−0.355867	−	0.315270i	−0.822047	+	0.569419i	$0.807168\pi$
$938$	4.79586	−	5.41340i	0.156590	−	0.176754i
$939$	3.62749	+	9.56491i	0.118379	+	0.312139i
$940$	1.74380	−	14.3615i	0.0568766	−	0.468421i
$941$	36.0961	−	13.6895i	1.17670	−	0.446264i	0.312748	−	0.949836i	$-0.398751\pi$
$941$	36.0961	−	13.6895i	1.17670	−	0.446264i	0.863953	+	0.503573i	$0.167981\pi$
$942$	16.6806	−	2.02540i	0.543484	−	0.0659909i
$943$	−1.77360	+	1.22423i	−0.0577563	+	0.0398663i
$944$		−	143.911i		−	4.68389i
$945$	0.722433	+	1.04662i	0.0235007	+	0.0340467i
$946$	67.8136	+	16.7146i	2.20481	+	0.543437i
$947$	18.9937	+	21.4395i	0.617213	+	0.696690i	0.971120	−	0.238591i	$-0.0766854\pi$
$947$	18.9937	+	21.4395i	0.617213	+	0.696690i	−0.353907	+	0.935281i	$0.615147\pi$
$948$	−18.6965	−	27.0865i	−0.607234	−	0.879730i
$949$	18.1859	+	4.58225i	0.590339	+	0.148746i
$950$	127.254	−	184.360i	4.12868	−	5.98142i
$951$	10.2637	−	1.24624i	0.332824	−	0.0404121i
$952$	1.20931	−	9.95957i	0.0391940	−	0.322792i
$953$	−1.39614	−	0.732749i	−0.0452253	−	0.0237361i	0.441959	−	0.897035i	$-0.354284\pi$
$953$	−1.39614	−	0.732749i	−0.0452253	−	0.0237361i	−0.487184	+	0.873299i	$0.661976\pi$
$954$	4.50314	−	18.2699i	0.145794	−	0.591511i
$955$	−31.5009	−	3.82490i	−1.01935	−	0.123771i
$956$	3.34839	−	3.77955i	0.108295	−	0.122239i
$957$	6.52200	−	4.50181i	0.210826	−	0.145523i
$958$	30.0828	−	43.5824i	0.971930	−	1.40808i
$959$	−0.658460	+	0.162296i	−0.0212628	+	0.00524081i
$960$	94.0684	+	11.4220i	3.03604	+	0.368642i
$961$	18.5699	−	9.74626i	0.599030	−	0.314395i
$962$	−46.6452	+	52.1065i	−1.50390	+	1.67998i
$963$	11.3303	+	5.94657i	0.365112	+	0.191626i
$964$	−101.227	−	69.8721i	−3.26031	−	2.25043i
$965$	33.7258	−	48.8603i	1.08567	−	1.57287i
$966$	0.707813	−	0.627068i	0.0227735	−	0.0201756i
$967$	−12.9703	−	14.6405i	−0.417097	−	0.470806i	0.501982	−	0.864878i	$-0.332604\pi$
$967$	−12.9703	−	14.6405i	−0.417097	−	0.470806i	−0.919079	+	0.394072i	$0.871066\pi$
$968$	−89.4468	−	33.9227i	−2.87493	−	1.09032i
$969$	11.4532	−	21.8223i	0.367930	−	0.701033i
$970$	−72.3001	−	27.4198i	−2.32142	−	0.880397i
$971$	−14.9204	−	3.67756i	−0.478820	−	0.118018i	−0.00748340	−	0.999972i	$-0.502382\pi$
$971$	−14.9204	−	3.67756i	−0.478820	−	0.118018i	−0.471336	+	0.881954i	$0.656228\pi$
$972$	−3.95272	+	3.50180i	−0.126783	+	0.112320i
$973$	5.01022	−	3.45830i	0.160620	−	0.110868i
$974$	15.6381	+	41.2343i	0.501077	+	1.32123i
$975$	−11.0917	+	44.0203i	−0.355218	+	1.40978i
$976$	−0.588400	+	1.55148i	−0.0188342	+	0.0496618i
$977$	−5.61747	−	22.7910i	−0.179719	−	0.729148i	−0.989756	−	0.142770i	$-0.954399\pi$
$977$	−5.61747	−	22.7910i	−0.179719	−	0.729148i	0.810037	−	0.586379i	$-0.199447\pi$
$978$	−54.1629	+	28.4269i	−1.73194	+	0.908992i
$979$	7.23385	+	19.0741i	0.231195	+	0.609611i
$980$	151.885	−	18.4422i	4.85180	−	0.589116i
$981$	0.478150	+	0.330043i	0.0152661	+	0.0105375i
$982$	10.1979	−	41.3747i	0.325430	−	1.32032i
$983$	−14.1910	−	57.5751i	−0.452622	−	1.83636i	−0.542020	−	0.840365i	$-0.682340\pi$
$983$	−14.1910	−	57.5751i	−0.452622	−	1.83636i	0.0893977	−	0.995996i	$-0.471506\pi$
$984$	1.98964	+	16.3862i	0.0634276	+	0.522373i
$985$	−10.4218	+	27.4800i	−0.332065	+	0.875584i
$986$	4.09593	−	16.6178i	0.130441	−	0.529219i
$987$	−0.192306	+	0.0473991i	−0.00612116	+	0.00150873i
$988$	122.053	−	29.4151i	3.88302	−	0.935818i
$989$	6.22027	+	1.53316i	0.197793	+	0.0487516i
$990$	24.5593	−	46.7938i	0.780545	−	1.48720i
$991$	−4.06740			−0.129205			−0.0646026	−	0.997911i	$-0.520578\pi$
$991$	−4.06740			−0.129205			−0.0646026	+	0.997911i	$0.520578\pi$
$992$	−57.7914			−1.83488
$993$	6.37085	−	12.1386i	0.202173	−	0.385208i
$994$	1.12188	+	1.26635i	0.0355840	+	0.0401660i
$995$		−	17.9125i		−	0.567865i
$996$	−52.8109	+	59.6112i	−1.67338	+	1.88885i
$997$	26.5060	−	13.9114i	0.839454	−	0.440579i	0.0105326	−	0.999945i	$-0.496647\pi$
$997$	26.5060	−	13.9114i	0.839454	−	0.440579i	0.828921	+	0.559365i	$0.188955\pi$
$998$	9.42551	+	77.6260i	0.298359	+	2.45721i
$999$	3.34062	+	6.36502i	0.105692	+	0.201380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.1	✓	192
169.142	even	26	inner	507.2.p.b.142.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.1	✓	192	1.1	even	1	trivial
507.2.p.b.142.1	yes	192	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52295 - 0.956827i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.95272 + 3.50180i) q^{4} +(4.16354 + 0.505545i) q^{5} +(0.645743 + 2.61988i) q^{6} +(0.140914 + 0.268489i) q^{7} +(-4.11396 - 7.83849i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-2.52295 - 0.956827i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.95272 + 3.50180i) q^{4} +(4.16354 + 0.505545i) q^{5} +(0.645743 + 2.61988i) q^{6} +(0.140914 + 0.268489i) q^{7} +(-4.11396 - 7.83849i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-10.0207 - 5.25925i) q^{10} +(4.36627 - 1.65591i) q^{11} +(0.636527 - 5.24227i) q^{12} +(-2.95668 - 2.06350i) q^{13} +(-0.0986205 - 0.812213i) q^{14} +(-1.94910 - 3.71371i) q^{15} +(1.60616 + 13.2279i) q^{16} +(3.30949 - 1.73696i) q^{17} +(1.78930 - 2.01970i) q^{18} +6.59384i q^{19} +(14.6870 + 16.5782i) q^{20} +(0.140914 - 0.268489i) q^{21} -12.6003 q^{22} -1.15577 q^{23} +(-4.11396 + 7.83849i) q^{24} +(12.2248 + 3.01313i) q^{25} +(5.48515 + 8.03513i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.383202 + 1.55471i) q^{28} +(-0.601786 + 1.58678i) q^{29} +(1.36411 + 11.2344i) q^{30} +(-0.757835 - 3.07466i) q^{31} +(4.36748 - 17.7196i) q^{32} +(-3.84311 - 2.65271i) q^{33} +(-10.0116 + 1.21563i) q^{34} +(0.450966 + 1.18910i) q^{35} +(-4.67589 + 2.45410i) q^{36} +(1.72030 + 6.97952i) q^{37} +(6.30917 - 16.6359i) q^{38} +(-0.0186350 + 3.60550i) q^{39} +(-13.1659 - 34.7156i) q^{40} +(1.53455 - 1.05923i) q^{41} +(-0.612415 + 0.542552i) q^{42} +(-5.38191 - 1.32652i) q^{43} +(23.0573 + 8.74449i) q^{44} +(-1.94910 + 3.71371i) q^{45} +(2.91596 + 1.10588i) q^{46} +(-0.433146 - 0.488920i) q^{47} +(9.97394 - 8.83614i) q^{48} +(3.92422 - 5.68522i) q^{49} +(-27.9594 - 19.2990i) q^{50} +(-3.30949 - 1.73696i) q^{51} +(-4.46099 - 18.5101i) q^{52} +(6.17479 - 3.24078i) q^{53} +(-2.67862 - 0.325243i) q^{54} +(19.0163 - 4.68709i) q^{55} +(1.52483 - 2.20910i) q^{56} +(5.42663 - 3.74573i) q^{57} +(3.03655 - 3.42756i) q^{58} +(-10.7213 - 1.30180i) q^{59} +(5.30041 - 21.5046i) q^{60} +(0.110262 + 0.0578700i) q^{61} +(-1.02994 + 8.48231i) q^{62} +(-0.301010 + 0.0365492i) q^{63} +(-12.8345 + 18.5940i) q^{64} +(-11.2671 - 10.0862i) q^{65} +(7.15778 + 10.3698i) q^{66} +(5.86163 + 6.61641i) q^{67} +(19.1640 + 4.72349i) q^{68} +(0.656555 + 0.951184i) q^{69} -3.43153i q^{70} +(-1.70176 + 1.17464i) q^{71} +(8.78794 - 1.06705i) q^{72} +(-4.86349 + 1.84448i) q^{73} +(2.33798 - 19.2550i) q^{74} +(-4.46470 - 11.7724i) q^{75} +(-23.0903 + 26.0636i) q^{76} +(1.05986 + 0.938955i) q^{77} +(3.49686 - 9.07866i) q^{78} +(4.66512 - 4.13293i) q^{79} +55.8868i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-4.88509 + 1.20407i) q^{82} +(-12.4115 - 8.56703i) q^{83} +(1.49719 - 0.567808i) q^{84} +(14.6573 - 5.55878i) q^{85} +(12.3090 + 8.49630i) q^{86} +(1.64775 - 0.406133i) q^{87} +(-30.9425 - 27.4127i) q^{88} +4.36851i q^{89} +(8.47086 - 7.50453i) q^{90} +(0.137388 - 1.08461i) q^{91} +(-4.56845 - 4.04729i) q^{92} +(-2.09989 + 2.37029i) q^{93} +(0.624991 + 1.64797i) q^{94} +(-3.33348 + 27.4537i) q^{95} +(-17.0639 + 6.47149i) q^{96} +(6.78285 - 0.823587i) q^{97} +(-15.3404 + 10.5887i) q^{98} +4.66973i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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