LMFDB - Embedded newform 961.2.g.s.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.2
Root			$1.03739i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.s.448.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.391401 + 1.20461i) q^{2} +(0.993201 + 1.10306i) q^{3} +(0.320145 - 0.232599i) q^{4} +(1.90016 + 3.29117i) q^{5} +(-0.940018 + 1.62816i) q^{6} +(-0.228812 - 2.17700i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.0832892 - 0.792444i) q^{9} +O(q^{10})$	\(q+(0.391401 + 1.20461i) q^{2} +(0.993201 + 1.10306i) q^{3} +(0.320145 - 0.232599i) q^{4} +(1.90016 + 3.29117i) q^{5} +(-0.940018 + 1.62816i) q^{6} +(-0.228812 - 2.17700i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.0832892 - 0.792444i) q^{9} +(-3.22085 + 3.57712i) q^{10} +(-0.868412 - 0.386642i) q^{11} +(0.574538 + 0.122122i) q^{12} +(-0.164468 + 0.0349588i) q^{13} +(2.53288 - 1.12771i) q^{14} +(-1.74313 + 5.36479i) q^{15} +(-0.943109 + 2.90259i) q^{16} +(-6.00807 + 2.67497i) q^{17} +(0.987185 - 0.209833i) q^{18} +(1.12765 + 0.239689i) q^{19} +(1.37385 + 0.611677i) q^{20} +(2.17411 - 2.41459i) q^{21} +(0.125855 - 1.19743i) q^{22} +(3.74454 + 2.72056i) q^{23} +(0.470800 + 4.47937i) q^{24} +(-4.72122 + 8.17739i) q^{25} +(-0.106485 - 0.184437i) q^{26} +(4.55935 - 3.31256i) q^{27} +(-0.579620 - 0.643733i) q^{28} +(0.413068 + 1.27129i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(-0.436018 - 1.34192i) q^{33} +(-5.57386 - 6.19040i) q^{34} +(6.73010 - 4.88970i) q^{35} +(-0.157657 - 0.273070i) q^{36} +(1.93582 - 3.35295i) q^{37} +(0.152632 + 1.45219i) q^{38} +(-0.201911 - 0.146697i) q^{39} +(-1.20540 + 11.4686i) q^{40} +(0.219610 - 0.243902i) q^{41} +(3.75958 + 1.67388i) q^{42} +(-9.42012 - 2.00231i) q^{43} +(-0.367950 + 0.0782102i) q^{44} +(2.76634 - 1.23165i) q^{45} +(-1.81160 + 5.57554i) q^{46} +(1.74242 - 5.36260i) q^{47} +(-4.13843 + 1.84255i) q^{48} +(2.16007 - 0.459137i) q^{49} +(-11.6985 - 2.48658i) q^{50} +(-8.91787 - 3.97049i) q^{51} +(-0.0445222 + 0.0494469i) q^{52} +(0.766501 - 7.29277i) q^{53} +(5.77487 + 4.19569i) q^{54} +(-0.377616 - 3.59278i) q^{55} +(3.32116 - 5.75242i) q^{56} +(0.855590 + 1.48193i) q^{57} +(-1.36973 + 0.995171i) q^{58} +(-1.77528 - 1.97165i) q^{59} +(0.689791 + 2.12296i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(2.74856 + 8.45921i) q^{64} +(-0.427571 - 0.474866i) q^{65} +(1.44584 - 1.05046i) q^{66} +(-0.276003 - 0.478052i) q^{67} +(-1.30126 + 2.25385i) q^{68} +(0.718126 + 6.83252i) q^{69} +(8.52436 + 6.19331i) q^{70} +(-0.118848 + 1.13076i) q^{71} +(1.61786 - 1.79682i) q^{72} +(-7.23765 - 3.22241i) q^{73} +(4.79668 + 1.01956i) q^{74} +(-13.7093 + 2.91400i) q^{75} +(0.416762 - 0.185555i) q^{76} +(-0.643016 + 1.97900i) q^{77} +(0.0976845 - 0.300642i) q^{78} +(4.14958 - 1.84751i) q^{79} +(-11.3450 + 2.41145i) q^{80} +(5.84411 + 1.24220i) q^{81} +(0.379763 + 0.169081i) q^{82} +(0.218401 - 0.242559i) q^{83} +(0.134398 - 1.27871i) q^{84} +(-20.2201 - 14.6908i) q^{85} +(-1.27505 - 12.1313i) q^{86} +(-0.992053 + 1.71829i) q^{87} +(-1.44225 - 2.49806i) q^{88} +(11.9008 - 8.64641i) q^{89} +(2.56641 + 2.85028i) q^{90} +(0.113737 + 0.350048i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(1.35386 + 4.16674i) q^{95} +(2.18824 + 2.43029i) q^{96} +(-12.5553 + 9.12195i) q^{97} +(1.39853 + 2.42233i) q^{98} +(-0.378722 + 0.655965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9	\( 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} - 2 q^{11} - 20 q^{12} - 27 q^{13} - 6 q^{14} + 4 q^{15} - 2 q^{16} - 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20} + 29 q^{21} + 4 q^{22} + 21 q^{23} - 25 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 40 q^{28} + 26 q^{29} - 22 q^{30} - 42 q^{32} + 7 q^{33} + 28 q^{34} + 21 q^{35} + q^{36} - 8 q^{37} - 27 q^{38} + 2 q^{39} - 16 q^{40} - 3 q^{41} - 51 q^{42} + 8 q^{43} + 4 q^{44} + 25 q^{45} - 16 q^{46} + 4 q^{47} - 86 q^{48} + 27 q^{49} - 27 q^{50} + 13 q^{51} + 24 q^{52} + 66 q^{53} + 39 q^{54} - 52 q^{55} - 30 q^{56} - 17 q^{57} + 10 q^{58} - 51 q^{59} + 35 q^{60} - 60 q^{61} - 46 q^{63} - 32 q^{64} + 18 q^{65} + 20 q^{66} + 13 q^{67} + 30 q^{68} + 48 q^{69} + 27 q^{70} - 24 q^{71} + 2 q^{72} + 27 q^{73} + 28 q^{74} - 32 q^{75} + 18 q^{76} - 42 q^{77} + 15 q^{78} + 8 q^{79} - 39 q^{80} - 7 q^{81} + 29 q^{82} + 4 q^{83} - 27 q^{84} - 63 q^{85} + 34 q^{86} + 15 q^{87} - 17 q^{88} + 26 q^{89} + 57 q^{90} + 8 q^{91} - 64 q^{92} + 44 q^{94} + 28 q^{95} - 62 q^{96} - 37 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 - 2 * q^11 - 20 * q^12 - 27 * q^13 - 6 * q^14 + 4 * q^15 - 2 * q^16 - 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 + 29 * q^21 + 4 * q^22 + 21 * q^23 - 25 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 40 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 + 28 * q^34 + 21 * q^35 + q^36 - 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 - 51 * q^42 + 8 * q^43 + 4 * q^44 + 25 * q^45 - 16 * q^46 + 4 * q^47 - 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 + 24 * q^52 + 66 * q^53 + 39 * q^54 - 52 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 - 51 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 18 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 + 27 * q^73 + 28 * q^74 - 32 * q^75 + 18 * q^76 - 42 * q^77 + 15 * q^78 + 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 + 4 * q^83 - 27 * q^84 - 63 * q^85 + 34 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 + 57 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 - 62 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.391401	+	1.20461i	0.276763	+	0.851788i	0.988748	+	0.149593i	$0.0477964\pi$
$2$	0.391401	+	1.20461i	0.276763	+	0.851788i	−0.711985	+	0.702195i	$0.752204\pi$
$3$	0.993201	+	1.10306i	0.573425	+	0.636853i	0.958180	−	0.286166i	$-0.0923809\pi$
$3$	0.993201	+	1.10306i	0.573425	+	0.636853i	−0.384755	+	0.923019i	$0.625714\pi$
$4$	0.320145	−	0.232599i	0.160072	−	0.116299i
$5$	1.90016	+	3.29117i	0.849778	+	1.47186i	0.881407	+	0.472358i	$0.156597\pi$
$5$	1.90016	+	3.29117i	0.849778	+	1.47186i	−0.0316291	+	0.999500i	$0.510070\pi$
$6$	−0.940018	+	1.62816i	−0.383761	+	0.664693i
$7$	−0.228812	−	2.17700i	−0.0864827	−	0.822828i	−0.948676	−	0.316249i	$-0.897577\pi$
$7$	−0.228812	−	2.17700i	−0.0864827	−	0.822828i	0.862194	−	0.506579i	$-0.169090\pi$
$8$	2.45490	+	1.78359i	0.867938	+	0.630594i
$9$	0.0832892	−	0.792444i	0.0277631	−	0.264148i
$10$	−3.22085	+	3.57712i	−1.01852	+	1.13119i
$11$	−0.868412	−	0.386642i	−0.261836	−	0.116577i	0.271620	−	0.962404i	$-0.412441\pi$
$11$	−0.868412	−	0.386642i	−0.261836	−	0.116577i	−0.533456	+	0.845828i	$0.679107\pi$
$12$	0.574538	+	0.122122i	0.165855	+	0.0352536i
$13$	−0.164468	+	0.0349588i	−0.0456152	+	0.00969582i	−0.230663	−	0.973034i	$-0.574089\pi$
$13$	−0.164468	+	0.0349588i	−0.0456152	+	0.00969582i	0.185048	+	0.982730i	$0.440756\pi$
$14$	2.53288	−	1.12771i	0.676939	−	0.301393i
$15$	−1.74313	+	5.36479i	−0.450073	+	1.38518i
$16$	−0.943109	+	2.90259i	−0.235777	+	0.725648i
$17$	−6.00807	+	2.67497i	−1.45717	+	0.648775i	−0.973958	−	0.226728i	$-0.927197\pi$
$17$	−6.00807	+	2.67497i	−1.45717	+	0.648775i	−0.483214	+	0.875502i	$0.660531\pi$
$18$	0.987185	−	0.209833i	0.232682	−	0.0494581i
$19$	1.12765	+	0.239689i	0.258701	+	0.0549885i	0.335436	−	0.942063i	$-0.391116\pi$
$19$	1.12765	+	0.239689i	0.258701	+	0.0549885i	−0.0767355	+	0.997051i	$0.524450\pi$
$20$	1.37385	+	0.611677i	0.307202	+	0.136775i
$21$	2.17411	−	2.41459i	0.474429	−	0.526906i
$22$	0.125855	−	1.19743i	0.0268324	−	0.255293i
$23$	3.74454	+	2.72056i	0.780790	+	0.567277i	0.905216	−	0.424952i	$-0.139709\pi$
$23$	3.74454	+	2.72056i	0.780790	+	0.567277i	−0.124426	+	0.992229i	$0.539709\pi$
$24$	0.470800	+	4.47937i	0.0961017	+	0.914347i
$25$	−4.72122	+	8.17739i	−0.944244	+	1.63548i
$26$	−0.106485	−	0.184437i	−0.0208834	−	0.0361711i
$27$	4.55935	−	3.31256i	0.877446	−	0.637502i
$28$	−0.579620	−	0.643733i	−0.109538	−	0.121654i
$29$	0.413068	+	1.27129i	0.0767047	+	0.236073i	0.982056	−	0.188591i	$-0.0603921\pi$
$29$	0.413068	+	1.27129i	0.0767047	+	0.236073i	−0.905351	+	0.424664i	$0.860392\pi$
$30$	−7.14474			−1.30444
$31$		0			0
$31$		0			0
$32$	2.20322			0.389479
$33$	−0.436018	−	1.34192i	−0.0759010	−	0.233599i
$34$	−5.57386	−	6.19040i	−0.955909	−	1.06164i
$35$	6.73010	−	4.88970i	1.13759	−	0.826511i
$36$	−0.157657	−	0.273070i	−0.0262762	−	0.0455116i
$37$	1.93582	−	3.35295i	0.318248	−	0.551221i	−0.661875	−	0.749614i	$-0.730239\pi$
$37$	1.93582	−	3.35295i	0.318248	−	0.551221i	0.980122	+	0.198393i	$0.0635723\pi$
$38$	0.152632	+	1.45219i	0.0247601	+	0.235577i
$39$	−0.201911	−	0.146697i	−0.0323317	−	0.0234904i
$40$	−1.20540	+	11.4686i	−0.190590	+	1.81335i
$41$	0.219610	−	0.243902i	0.0342974	−	0.0380911i	−0.725752	−	0.687956i	$-0.758508\pi$
$41$	0.219610	−	0.243902i	0.0342974	−	0.0380911i	0.760049	+	0.649865i	$0.225175\pi$
$42$	3.75958	+	1.67388i	0.580117	+	0.258285i
$43$	−9.42012	−	2.00231i	−1.43656	−	0.305349i	−0.577147	−	0.816640i	$-0.695834\pi$
$43$	−9.42012	−	2.00231i	−1.43656	−	0.305349i	−0.859408	+	0.511291i	$0.829167\pi$
$44$	−0.367950	+	0.0782102i	−0.0554706	+	0.0117906i
$45$	2.76634	−	1.23165i	0.412381	−	0.183604i
$46$	−1.81160	+	5.57554i	−0.267106	+	0.822068i
$47$	1.74242	−	5.36260i	0.254157	−	0.782216i	−0.739837	−	0.672786i	$-0.765097\pi$
$47$	1.74242	−	5.36260i	0.254157	−	0.782216i	0.993994	−	0.109430i	$-0.0349026\pi$
$48$	−4.13843	+	1.84255i	−0.597331	+	0.265949i
$49$	2.16007	−	0.459137i	0.308581	−	0.0655909i
$50$	−11.6985	−	2.48658i	−1.65441	−	0.351656i
$51$	−8.91787	−	3.97049i	−1.24875	−	0.555980i
$52$	−0.0445222	+	0.0494469i	−0.00617412	+	0.00685706i
$53$	0.766501	−	7.29277i	0.105287	−	1.00174i	−0.806544	−	0.591174i	$-0.798665\pi$
$53$	0.766501	−	7.29277i	0.105287	−	1.00174i	0.911831	−	0.410566i	$-0.134669\pi$
$54$	5.77487	+	4.19569i	0.785861	+	0.570961i
$55$	−0.377616	−	3.59278i	−0.0509178	−	0.484450i
$56$	3.32116	−	5.75242i	0.443809	−	0.768699i
$57$	0.855590	+	1.48193i	0.113326	+	0.196286i
$58$	−1.36973	+	0.995171i	−0.179855	+	0.130672i
$59$	−1.77528	−	1.97165i	−0.231122	−	0.256687i	0.616417	−	0.787420i	$-0.288584\pi$
$59$	−1.77528	−	1.97165i	−0.231122	−	0.256687i	−0.847539	+	0.530733i	$0.821917\pi$
$60$	0.689791	+	2.12296i	0.0890516	+	0.274073i
$61$	−1.74967			−0.224023			−0.112011	−	0.993707i	$-0.535729\pi$
$61$	−1.74967			−0.224023			−0.112011	+	0.993707i	$0.535729\pi$
$62$		0			0
$63$	−1.74421			−0.219749
$64$	2.74856	+	8.45921i	0.343570	+	1.05740i
$65$	−0.427571	−	0.474866i	−0.0530337	−	0.0588999i
$66$	1.44584	−	1.05046i	0.177970	−	0.129303i
$67$	−0.276003	−	0.478052i	−0.0337192	−	0.0584033i	0.848673	−	0.528917i	$-0.177402\pi$
$67$	−0.276003	−	0.478052i	−0.0337192	−	0.0584033i	−0.882393	+	0.470514i	$0.844069\pi$
$68$	−1.30126	+	2.25385i	−0.157801	+	0.273319i
$69$	0.718126	+	6.83252i	0.0864523	+	0.822538i
$70$	8.52436	+	6.19331i	1.01886	+	0.740242i
$71$	−0.118848	+	1.13076i	−0.0141046	+	0.134197i	−0.999308	−	0.0371920i	$-0.988159\pi$
$71$	−0.118848	+	1.13076i	−0.0141046	+	0.134197i	0.985204	+	0.171389i	$0.0548254\pi$
$72$	1.61786	−	1.79682i	0.190667	−	0.211757i
$73$	−7.23765	−	3.22241i	−0.847103	−	0.377155i	−0.0631722	−	0.998003i	$-0.520122\pi$
$73$	−7.23765	−	3.22241i	−0.847103	−	0.377155i	−0.783931	+	0.620848i	$0.786788\pi$
$74$	4.79668	+	1.01956i	0.557602	+	0.118522i
$75$	−13.7093	+	2.91400i	−1.58301	+	0.336479i
$76$	0.416762	−	0.185555i	0.0478059	−	0.0212846i
$77$	−0.643016	+	1.97900i	−0.0732785	+	0.225528i
$78$	0.0976845	−	0.300642i	0.0110606	−	0.0340410i
$79$	4.14958	−	1.84751i	0.466864	−	0.207861i	−0.159802	−	0.987149i	$-0.551086\pi$
$79$	4.14958	−	1.84751i	0.466864	−	0.207861i	0.626666	+	0.779288i	$0.284419\pi$
$80$	−11.3450	+	2.41145i	−1.26841	+	0.269608i
$81$	5.84411	+	1.24220i	0.649345	+	0.138023i
$82$	0.379763	+	0.169081i	0.0419378	+	0.0186719i
$83$	0.218401	−	0.242559i	0.0239727	−	0.0266244i	−0.731039	−	0.682335i	$-0.760964\pi$
$83$	0.218401	−	0.242559i	0.0239727	−	0.0266244i	0.755012	+	0.655711i	$0.227631\pi$
$84$	0.134398	−	1.27871i	0.0146640	−	0.139519i
$85$	−20.2201	−	14.6908i	−2.19318	−	1.59344i
$86$	−1.27505	−	12.1313i	−0.137492	−	1.30815i
$87$	−0.992053	+	1.71829i	−0.106359	+	0.184220i
$88$	−1.44225	−	2.49806i	−0.153745	−	0.266294i
$89$	11.9008	−	8.64641i	1.26148	−	0.916518i	0.262649	−	0.964891i	$-0.415404\pi$
$89$	11.9008	−	8.64641i	1.26148	−	0.916518i	0.998829	+	0.0483734i	$0.0154037\pi$
$90$	2.56641	+	2.85028i	0.270523	+	0.300446i
$91$	0.113737	+	0.350048i	0.0119229	+	0.0366950i
$92$	1.83159			0.190957
$93$		0			0
$94$	7.14183			0.736623
$95$	1.35386	+	4.16674i	0.138903	+	0.427498i
$96$	2.18824	+	2.43029i	0.223337	+	0.248041i
$97$	−12.5553	+	9.12195i	−1.27480	+	0.926193i	−0.999383	−	0.0351325i	$-0.988815\pi$
$97$	−12.5553	+	9.12195i	−1.27480	+	0.926193i	−0.275413	+	0.961326i	$0.588815\pi$
$98$	1.39853	+	2.42233i	0.141273	+	0.244692i
$99$	−0.378722	+	0.655965i	−0.0380630	+	0.0659270i
$100$	0.390578	+	3.71610i	0.0390578	+	0.371610i
$101$	−3.94282	−	2.86463i	−0.392326	−	0.285041i	0.374082	−	0.927396i	$-0.377958\pi$
$101$	−3.94282	−	2.86463i	−0.392326	−	0.285041i	−0.766408	+	0.642354i	$0.777958\pi$
$102$	1.29243	−	12.2966i	0.127969	−	1.21755i
$103$	1.29184	−	1.43473i	0.127288	−	0.141368i	−0.676131	−	0.736781i	$-0.736345\pi$
$103$	1.29184	−	1.43473i	0.127288	−	0.141368i	0.803420	+	0.595413i	$0.203012\pi$
$104$	−0.466105	−	0.207523i	−0.0457053	−	0.0203493i
$105$	12.0780	+	2.56725i	1.17869	+	0.250538i
$106$	9.08496	−	1.93107i	0.882409	−	0.187562i
$107$	11.4445	−	5.09540i	1.10638	−	0.492591i	0.229501	−	0.973308i	$-0.426290\pi$
$107$	11.4445	−	5.09540i	1.10638	−	0.492591i	0.876876	+	0.480718i	$0.159624\pi$
$108$	0.689153	−	2.12100i	0.0663138	−	0.204093i
$109$	−3.17128	+	9.76021i	−0.303754	+	0.934858i	0.676385	+	0.736548i	$0.263545\pi$
$109$	−3.17128	+	9.76021i	−0.303754	+	0.934858i	−0.980139	+	0.198310i	$0.936455\pi$
$110$	4.18010	−	1.86110i	0.398557	−	0.177449i
$111$	5.62117	−	1.19482i	0.533537	−	0.113407i
$112$	6.53473	+	1.38900i	0.617474	+	0.131248i
$113$	−3.51070	−	1.56307i	−0.330259	−	0.147041i	0.234907	−	0.972018i	$-0.424521\pi$
$113$	−3.51070	−	1.56307i	−0.330259	−	0.147041i	−0.565166	+	0.824977i	$0.691188\pi$
$114$	−1.45026	+	1.61068i	−0.135830	+	0.150854i
$115$	−1.83863	+	17.4934i	−0.171453	+	1.63127i
$116$	0.427942	+	0.310918i	0.0397334	+	0.0288680i
$117$	0.0140045	+	0.133243i	0.00129471	+	0.0123184i
$118$	1.68022	−	2.91023i	0.154677	−	0.267908i
$119$	7.19811	+	12.4675i	0.659850	+	1.14289i
$120$	−13.8478	+	10.0610i	−1.26412	+	0.918439i
$121$	−6.75579	−	7.50306i	−0.614163	−	0.682097i
$122$	−0.684825	−	2.10767i	−0.0620011	−	0.190820i
$123$	0.487156			0.0439254
$124$		0			0
$125$	−16.8827			−1.51003
$126$	−0.682685	−	2.10109i	−0.0608184	−	0.187180i
$127$	4.91402	+	5.45757i	0.436049	+	0.484281i	0.920614	−	0.390474i	$-0.127689\pi$
$127$	4.91402	+	5.45757i	0.436049	+	0.484281i	−0.484565	+	0.874755i	$0.661022\pi$
$128$	−5.54936	+	4.03184i	−0.490499	+	0.356368i
$129$	−7.14740	−	12.3797i	−0.629294	−	1.08997i
$130$	0.404676	−	0.700920i	0.0354924	−	0.0614747i
$131$	−1.36239	−	12.9623i	−0.119033	−	1.13252i	−0.877088	−	0.480329i	$-0.840517\pi$
$131$	−1.36239	−	12.9623i	−0.119033	−	1.13252i	0.758056	−	0.652190i	$-0.226149\pi$
$132$	−0.451719	−	0.328193i	−0.0393171	−	0.0285655i
$133$	0.263784	−	2.50973i	0.0228729	−	0.217622i
$134$	0.467838	−	0.519586i	0.0404150	−	0.0448854i
$135$	19.5657	+	8.71121i	1.68395	+	0.749741i
$136$	−19.5203	−	4.14916i	−1.67385	−	0.355788i
$137$	0.131365	−	0.0279224i	0.0112232	−	0.00238557i	−0.202297	−	0.979324i	$-0.564841\pi$
$137$	0.131365	−	0.0279224i	0.0112232	−	0.00238557i	0.213520	+	0.976939i	$0.431507\pi$
$138$	−7.94944	+	3.53932i	−0.676701	+	0.301287i
$139$	3.56219	−	10.9633i	0.302141	−	0.929894i	−0.678588	−	0.734519i	$-0.737408\pi$
$139$	3.56219	−	10.9633i	0.302141	−	0.929894i	0.980729	−	0.195375i	$-0.0625924\pi$
$140$	1.01727	−	3.13083i	0.0859748	−	0.264603i
$141$	7.64585	−	3.40415i	0.643896	−	0.286681i
$142$	−1.40864	+	0.299416i	−0.118211	+	0.0251264i
$143$	0.156343	+	0.0332317i	0.0130740	+	0.00277897i
$144$	2.22159	+	0.989116i	0.185133	+	0.0824263i
$145$	−3.39915	+	3.77514i	−0.282284	+	0.313508i
$146$	1.04892	−	9.97980i	0.0868092	−	0.825934i
$147$	2.65184	+	1.92667i	0.218720	+	0.158909i
$148$	−0.160147	−	1.52370i	−0.0131640	−	0.125247i
$149$	2.72054	−	4.71211i	0.222875	−	0.386031i	−0.732805	−	0.680439i	$-0.761789\pi$
$149$	2.72054	−	4.71211i	0.222875	−	0.386031i	0.955680	+	0.294408i	$0.0951224\pi$
$150$	−8.87606	−	15.3738i	−0.724727	−	1.25526i
$151$	−11.0748	+	8.04630i	−0.901253	+	0.654799i	−0.938788	−	0.344497i	$-0.888050\pi$
$151$	−11.0748	+	8.04630i	−0.901253	+	0.654799i	0.0375344	+	0.999295i	$0.488050\pi$
$152$	2.34076	+	2.59968i	0.189861	+	0.210862i
$153$	1.61935	+	4.98386i	0.130917	+	0.402921i
$154$	−2.63560			−0.212383
$155$		0			0
$156$	−0.0987625			−0.00790733
$157$	−4.65236	−	14.3185i	−0.371299	−	1.14274i	−0.945942	−	0.324336i	$-0.894859\pi$
$157$	−4.65236	−	14.3185i	−0.371299	−	1.14274i	0.574644	−	0.818404i	$-0.305141\pi$
$158$	3.84968	+	4.27550i	0.306264	+	0.340141i
$159$	8.80566	−	6.39769i	0.698335	−	0.507370i
$160$	4.18648	+	7.25120i	0.330970	+	0.573257i
$161$	5.06587	−	8.77434i	0.399246	−	0.691515i
$162$	0.791022	+	7.52607i	0.0621485	+	0.591304i
$163$	−13.7841	−	10.0147i	−1.07965	−	0.784415i	−0.102032	−	0.994781i	$-0.532534\pi$
$163$	−13.7841	−	10.0147i	−1.07965	−	0.784415i	−0.977623	+	0.210366i	$0.932534\pi$
$164$	0.0135758	−	0.129165i	0.00106009	−	0.0100861i
$165$	3.58801	−	3.98488i	0.279326	−	0.310223i
$166$	0.377672	+	0.168150i	0.0293130	+	0.0130510i
$167$	15.8443	+	3.36780i	1.22607	+	0.260608i	0.775046	−	0.631905i	$-0.217727\pi$
$167$	15.8443	+	3.36780i	1.22607	+	0.260608i	0.451020	+	0.892514i	$0.351060\pi$
$168$	9.64385	−	2.04986i	0.744039	−	0.158150i
$169$	−11.8503	+	5.27608i	−0.911559	+	0.405852i
$170$	9.78245	−	30.1073i	0.750280	−	2.30912i
$171$	0.283861	−	0.873636i	0.0217074	−	0.0668086i
$172$	−3.48154	+	1.55008i	−0.265465	+	0.118192i
$173$	2.28027	−	0.484687i	0.173366	−	0.0368501i	−0.120411	−	0.992724i	$-0.538421\pi$
$173$	2.28027	−	0.484687i	0.173366	−	0.0368501i	0.293777	+	0.955874i	$0.405088\pi$
$174$	−2.45816	−	0.522497i	−0.186352	−	0.0396104i
$175$	18.8824	+	8.40700i	1.42738	+	0.635510i
$176$	1.94127	−	2.15600i	0.146329	−	0.162515i
$177$	0.411640	−	3.91649i	0.0309407	−	0.294382i
$178$	15.0735	+	10.9516i	1.12981	+	0.820854i
$179$	1.77391	+	16.8777i	0.132589	+	1.26150i	0.835210	+	0.549931i	$0.185346\pi$
$179$	1.77391	+	16.8777i	0.132589	+	1.26150i	−0.702621	+	0.711564i	$0.747987\pi$
$180$	0.599147	−	1.03775i	0.0446578	−	0.0773495i
$181$	3.66788	+	6.35296i	0.272631	+	0.472211i	0.969535	−	0.244954i	$-0.0787727\pi$
$181$	3.66788	+	6.35296i	0.272631	+	0.472211i	−0.696903	+	0.717165i	$0.745439\pi$
$182$	−0.377154	+	0.274018i	−0.0279565	+	0.0203116i
$183$	−1.73778	−	1.93000i	−0.128460	−	0.142669i
$184$	4.34009	+	13.3574i	0.319956	+	0.984723i
$185$	14.7135			1.08176
$186$		0			0
$187$	6.25174			0.457173
$188$	−0.689510	−	2.12209i	−0.0502877	−	0.154770i
$189$	−8.25466	−	9.16773i	−0.600438	−	0.666854i
$190$	−4.48939	+	3.26173i	−0.325695	+	0.236631i
$191$	−3.91138	−	6.77471i	−0.283018	−	0.490201i	0.689109	−	0.724658i	$-0.258002\pi$
$191$	−3.91138	−	6.77471i	−0.283018	−	0.490201i	−0.972127	+	0.234457i	$0.924669\pi$
$192$	−6.60115	+	11.4335i	−0.476397	+	0.825143i
$193$	0.484124	+	4.60613i	0.0348480	+	0.331557i	0.998032	+	0.0627124i	$0.0199751\pi$
$193$	0.484124	+	4.60613i	0.0348480	+	0.331557i	−0.963184	+	0.268844i	$0.913358\pi$
$194$	−15.9025	−	11.5539i	−1.14174	−	0.829520i
$195$	0.0991421	−	0.943274i	0.00709971	−	0.0675493i
$196$	0.584740	−	0.649419i	0.0417671	−	0.0463871i
$197$	−20.4491	−	9.10455i	−1.45694	−	0.648672i	−0.483031	−	0.875603i	$-0.660464\pi$
$197$	−20.4491	−	9.10455i	−1.45694	−	0.648672i	−0.973911	+	0.226931i	$0.927131\pi$
$198$	−0.938414	−	0.199466i	−0.0666902	−	0.0141754i
$199$	26.0224	−	5.53123i	1.84468	−	0.392099i	0.853116	−	0.521722i	$-0.174710\pi$
$199$	26.0224	−	5.53123i	1.84468	−	0.392099i	0.991563	+	0.129623i	$0.0413768\pi$
$200$	−26.1752	+	11.6540i	−1.85087	+	0.824060i
$201$	0.253194	−	0.779250i	0.0178589	−	0.0549640i
$202$	1.90753	−	5.87078i	0.134214	−	0.413067i
$203$	2.67308	−	1.19013i	0.187614	−	0.0835310i
$204$	−3.77854	+	0.803154i	−0.264551	+	0.0562320i
$205$	1.22002	+	0.259323i	0.0852098	+	0.0181119i
$206$	2.23392	+	0.994603i	0.155644	+	0.0692973i
$207$	2.46777	−	2.74074i	0.171522	−	0.190495i
$208$	0.0536403	−	0.510353i	0.00371929	−	0.0353866i
$209$	−0.886591	−	0.644146i	−0.0613268	−	0.0445565i
$210$	1.63480	+	15.5541i	0.112812	+	1.07333i
$211$	−0.663069	+	1.14847i	−0.0456476	+	0.0790639i	−0.887946	−	0.459947i	$-0.847868\pi$
$211$	−0.663069	+	1.14847i	−0.0456476	+	0.0790639i	0.842299	+	0.539011i	$0.181202\pi$
$212$	−1.45090	−	2.51303i	−0.0996481	−	0.172596i
$213$	−1.36534	+	0.991975i	−0.0935514	+	0.0679690i
$214$	10.6173	+	11.7918i	0.725786	+	0.806068i
$215$	−11.3098	−	34.8080i	−0.771322	−	2.37388i
$216$	17.1010			1.16357
$217$		0			0
$218$	−12.9985			−0.880368
$219$	−3.63393	−	11.1841i	−0.245558	−	0.755750i
$220$	−0.956568	−	1.06238i	−0.0644918	−	0.0716254i
$221$	0.894623	−	0.649982i	0.0601788	−	0.0437225i
$222$	3.63942	+	6.30366i	0.244262	+	0.423074i
$223$	6.05997	−	10.4962i	0.405806	−	0.702876i	−0.588609	−	0.808418i	$-0.700324\pi$
$223$	6.05997	−	10.4962i	0.405806	−	0.702876i	0.994415	+	0.105542i	$0.0336576\pi$
$224$	−0.504124	−	4.79642i	−0.0336832	−	0.320474i
$225$	6.08690	+	4.42239i	0.405793	+	0.294826i
$226$	0.508790	−	4.84081i	0.0338442	−	0.322006i
$227$	−10.6406	+	11.8176i	−0.706243	+	0.784362i	−0.984357	−	0.176186i	$-0.943624\pi$
$227$	−10.6406	+	11.8176i	−0.706243	+	0.784362i	0.278114	+	0.960548i	$0.410291\pi$
$228$	0.618607	+	0.275421i	0.0409682	+	0.0182402i
$229$	15.9424	+	3.38867i	1.05351	+	0.223930i	0.701942	−	0.712234i	$-0.252317\pi$
$229$	15.9424	+	3.38867i	1.05351	+	0.223930i	0.351564	+	0.936164i	$0.385650\pi$
$230$	−21.7924	+	4.63212i	−1.43695	+	0.305433i
$231$	−2.82160	+	1.25626i	−0.185648	+	0.0826557i
$232$	−1.25342	+	3.85764i	−0.0822912	+	0.253266i
$233$	−1.58308	+	4.87223i	−0.103711	+	0.319190i	−0.989426	−	0.145040i	$-0.953669\pi$
$233$	−1.58308	+	4.87223i	−0.103711	+	0.319190i	0.885715	+	0.464230i	$0.153669\pi$
$234$	−0.155025	+	0.0690216i	−0.0101343	+	0.00451208i
$235$	20.9601	−	4.45521i	1.36729	−	0.290626i
$236$	−1.02695	−	0.218285i	−0.0668488	−	0.0142092i
$237$	6.15928	+	2.74229i	0.400088	+	0.178131i
$238$	−12.2011	+	13.5507i	−0.790881	+	0.878362i
$239$	−0.895600	+	8.52106i	−0.0579315	+	0.551182i	0.926609	+	0.376026i	$0.122710\pi$
$239$	−0.895600	+	8.52106i	−0.0579315	+	0.551182i	−0.984541	+	0.175156i	$0.943957\pi$
$240$	−13.9278	−	10.1192i	−0.899037	−	0.653189i
$241$	0.715682	+	6.80926i	0.0461011	+	0.438623i	0.993090	+	0.117356i	$0.0374419\pi$
$241$	0.715682	+	6.80926i	0.0461011	+	0.438623i	−0.946989	+	0.321267i	$0.895891\pi$
$242$	6.39404	−	11.0748i	0.411024	−	0.711915i
$243$	−4.01935	−	6.96171i	−0.257841	−	0.446594i
$244$	−0.560149	+	0.406972i	−0.0358598	+	0.0260537i
$245$	5.61557	+	6.23673i	0.358766	+	0.398450i
$246$	0.190674	+	0.586833i	0.0121569	+	0.0374151i
$247$	−0.193842			−0.0123338
$248$		0			0
$249$	0.484474			0.0307023
$250$	−6.60791	−	20.3370i	−0.417921	−	1.28623i
$251$	15.1666	+	16.8442i	0.957306	+	1.06320i	0.997948	+	0.0640223i	$0.0203929\pi$
$251$	15.1666	+	16.8442i	0.957306	+	1.06320i	−0.0406424	+	0.999174i	$0.512940\pi$
$252$	−0.558399	+	0.405700i	−0.0351758	+	0.0255567i
$253$	−2.19992	−	3.81037i	−0.138308	−	0.239556i
$254$	−4.65089	+	8.05558i	−0.291823	+	0.505452i
$255$	−3.87780	−	36.8948i	−0.242838	−	2.31044i
$256$	7.36284	+	5.34941i	0.460177	+	0.334338i
$257$	1.74127	−	16.5671i	0.108618	−	1.03343i	−0.795444	−	0.606026i	$-0.792763\pi$
$257$	1.74127	−	16.5671i	0.108618	−	1.03343i	0.904062	−	0.427401i	$-0.140571\pi$
$258$	12.1152	−	13.4552i	0.754257	−	0.837687i
$259$	−7.74230	−	3.44709i	−0.481083	−	0.214192i
$260$	−0.247338	−	0.0525733i	−0.0153392	−	0.00326046i
$261$	1.04183	−	0.221448i	0.0644878	−	0.0137073i
$262$	15.0812	−	6.71460i	0.931722	−	0.414829i
$263$	−7.59760	+	23.3830i	−0.468488	+	1.44186i	0.386054	+	0.922476i	$0.373838\pi$
$263$	−7.59760	+	23.3830i	−0.468488	+	1.44186i	−0.854542	+	0.519382i	$0.826162\pi$
$264$	1.32306	−	4.07197i	0.0814289	−	0.250612i
$265$	25.4583	−	11.3348i	1.56389	−	0.696288i
$266$	3.12650	−	0.664557i	0.191698	−	0.0407466i
$267$	21.3574	+	4.53965i	1.30705	+	0.277822i
$268$	−0.199555	−	0.0888477i	−0.0121898	−	0.00542724i
$269$	8.37360	−	9.29982i	0.510547	−	0.567020i	−0.431666	−	0.902033i	$-0.642074\pi$
$269$	8.37360	−	9.29982i	0.510547	−	0.567020i	0.942213	+	0.335013i	$0.108741\pi$
$270$	−2.83557	+	26.9786i	−0.172567	+	1.64187i
$271$	21.9788	+	15.9685i	1.33512	+	0.970020i	0.999608	+	0.0279826i	$0.00890831\pi$
$271$	21.9788	+	15.9685i	1.33512	+	0.970020i	0.335509	+	0.942037i	$0.391092\pi$
$272$	−2.09807	−	19.9618i	−0.127214	−	1.21036i
$273$	−0.273160	+	0.473127i	−0.0165324	+	0.0286349i
$274$	0.0850519	+	0.147314i	0.00513817	+	0.00889957i
$275$	7.26169	−	5.27593i	0.437896	−	0.318150i
$276$	1.81914	+	2.02036i	0.109499	+	0.121611i
$277$	−4.68387	−	14.4155i	−0.281427	−	0.866142i	−0.987447	−	0.157951i	$-0.949511\pi$
$277$	−4.68387	−	14.4155i	−0.281427	−	0.866142i	0.706020	−	0.708192i	$-0.250489\pi$
$278$	14.6007			0.875694
$279$		0			0
$280$	25.2430			1.50855
$281$	9.34706	+	28.7673i	0.557599	+	1.71611i	0.688980	+	0.724780i	$0.258059\pi$
$281$	9.34706	+	28.7673i	0.557599	+	1.71611i	−0.131381	+	0.991332i	$0.541941\pi$
$282$	7.09327	+	7.87787i	0.422398	+	0.469120i
$283$	−2.54462	+	1.84877i	−0.151262	+	0.109898i	−0.660842	−	0.750525i	$-0.729801\pi$
$283$	−2.54462	+	1.84877i	−0.151262	+	0.109898i	0.509580	+	0.860423i	$0.329801\pi$
$284$	0.224965	+	0.389651i	0.0133492	+	0.0231215i
$285$	−3.25152	+	5.63179i	−0.192603	+	0.333599i
$286$	0.0211616	+	0.201339i	0.00125131	+	0.0119054i
$287$	−0.581224	−	0.422284i	−0.0343086	−	0.0249266i
$288$	0.183505	−	1.74593i	0.0108131	−	0.102880i
$289$	17.5663	−	19.5093i	1.03331	−	1.14761i
$290$	−5.87800	−	2.61705i	−0.345168	−	0.153679i
$291$	−22.5320	−	4.78932i	−1.32085	−	0.280755i
$292$	−3.06662	+	0.651831i	−0.179461	+	0.0381455i
$293$	1.73581	−	0.772833i	0.101407	−	0.0451494i	−0.355406	−	0.934712i	$-0.615657\pi$
$293$	1.73581	−	0.772833i	0.101407	−	0.0451494i	0.456813	+	0.889563i	$0.348991\pi$
$294$	−1.28295	+	3.94853i	−0.0748234	+	0.230283i
$295$	3.11573	−	9.58922i	0.181405	−	0.558306i
$296$	10.7325	−	4.77843i	0.623816	−	0.277741i
$297$	−5.24017	+	1.11383i	−0.304065	+	0.0646311i
$298$	6.74108	+	1.43286i	0.390500	+	0.0830034i
$299$	−0.710964	−	0.316542i	−0.0411161	−	0.0183061i
$300$	−3.71116	+	4.12166i	−0.214264	+	0.237964i
$301$	−2.20359	+	20.9657i	−0.127013	+	1.20845i
$302$	−14.0273	−	10.1915i	−0.807183	−	0.586453i
$303$	−0.756154	−	7.19433i	−0.0434399	−	0.413303i
$304$	−1.75922	+	3.04705i	−0.100898	+	0.174760i
$305$	−3.32466	−	5.75848i	−0.190370	−	0.329730i
$306$	−5.36979	+	3.90138i	−0.306970	+	0.223027i
$307$	15.2081	+	16.8903i	0.867970	+	0.963978i	0.999627	−	0.0273171i	$-0.00869640\pi$
$307$	15.2081	+	16.8903i	0.867970	+	0.963978i	−0.131657	+	0.991295i	$0.542030\pi$
$308$	0.254455	+	0.783131i	0.0144989	+	0.0446230i
$309$	2.86565			0.163021
$310$		0			0
$311$	15.8754			0.900213			0.450106	−	0.892975i	$-0.351386\pi$
$311$	15.8754			0.900213			0.450106	+	0.892975i	$0.351386\pi$
$312$	−0.234025	−	0.720254i	−0.0132490	−	0.0407764i
$313$	4.24854	+	4.71849i	0.240142	+	0.266705i	0.851153	−	0.524917i	$-0.175904\pi$
$313$	4.24854	+	4.71849i	0.240142	+	0.266705i	−0.611011	+	0.791622i	$0.709237\pi$
$314$	15.4272	−	11.2085i	0.870610	−	0.632535i
$315$	−3.31427	−	5.74049i	−0.186738	−	0.323440i
$316$	0.898737	−	1.55666i	0.0505579	−	0.0875689i
$317$	1.59939	+	15.2172i	0.0898307	+	0.854682i	0.942943	+	0.332955i	$0.108046\pi$
$317$	1.59939	+	15.2172i	0.0898307	+	0.854682i	−0.853112	+	0.521728i	$0.825288\pi$
$318$	11.1533	+	8.10332i	0.625444	+	0.454412i
$319$	0.132822	−	1.26371i	0.00743659	−	0.0707544i
$320$	−22.6180	+	25.1198i	−1.26439	+	1.40424i
$321$	16.9872	+	7.56318i	0.948131	+	0.422135i
$322$	12.5524	+	2.66810i	0.699520	+	0.148688i
$323$	−7.41616	+	1.57635i	−0.412646	+	0.0877107i
$324$	2.15989	−	0.961647i	0.119994	−	0.0534248i
$325$	0.490618	−	1.50997i	0.0272146	−	0.0837580i
$326$	6.66873	−	20.5243i	0.369347	−	1.13673i
$327$	−13.9158	+	6.19572i	−0.769547	+	0.342624i
$328$	0.974143	−	0.207060i	0.0537880	−	0.0114330i
$329$	−12.0731	−	2.56621i	−0.665609	−	0.141480i
$330$	6.20458	+	2.76246i	0.341551	+	0.152068i
$331$	−6.00073	+	6.66449i	−0.329830	+	0.366313i	−0.885136	−	0.465333i	$-0.845935\pi$
$331$	−6.00073	+	6.66449i	−0.329830	+	0.366313i	0.555306	+	0.831646i	$0.312601\pi$
$332$	0.0135011	−	0.128454i	0.000740967	−	0.00704983i
$333$	−2.49579	−	1.81330i	−0.136768	−	0.0993681i
$334$	2.14458	+	20.4043i	0.117346	+	1.11647i
$335$	1.04890	−	1.81675i	0.0573076	−	0.0992597i
$336$	4.95814	+	8.58776i	0.270489	+	0.468501i
$337$	3.53441	−	2.56790i	0.192532	−	0.139882i	−0.487343	−	0.873210i	$-0.662034\pi$
$337$	3.53441	−	2.56790i	0.192532	−	0.139882i	0.679875	+	0.733328i	$0.262034\pi$
$338$	−10.9938	−	12.2099i	−0.597985	−	0.664130i
$339$	−1.76268	−	5.42496i	−0.0957354	−	0.294643i
$340$	−9.89040			−0.536382
$341$		0			0
$342$	1.16349			0.0629145
$343$	−6.22883	−	19.1704i	−0.336325	−	1.03510i
$344$	−19.5542	−	21.7171i	−1.05429	−	1.17091i
$345$	−21.1224	+	15.3464i	−1.13719	+	0.826220i
$346$	1.47636	+	2.55713i	0.0793697	+	0.137472i
$347$	−12.2026	+	21.1356i	−0.655073	+	1.13462i	0.326803	+	0.945092i	$0.394029\pi$
$347$	−12.2026	+	21.1356i	−0.655073	+	1.13462i	−0.981876	+	0.189526i	$0.939305\pi$
$348$	0.0820707	+	0.780851i	0.00439945	+	0.0418580i
$349$	−10.5527	−	7.66702i	−0.564875	−	0.410406i	0.268365	−	0.963317i	$-0.413517\pi$
$349$	−10.5527	−	7.66702i	−0.564875	−	0.410406i	−0.833240	+	0.552911i	$0.813517\pi$
$350$	−2.73654	+	26.0365i	−0.146274	+	1.39171i
$351$	−0.634064	+	0.704199i	−0.0338438	+	0.0375874i
$352$	−1.91331	−	0.851859i	−0.101980	−	0.0454043i
$353$	−10.5883	−	2.25060i	−0.563556	−	0.119788i	−0.0826802	−	0.996576i	$-0.526348\pi$
$353$	−10.5883	−	2.25060i	−0.563556	−	0.119788i	−0.480876	+	0.876789i	$0.659681\pi$
$354$	4.87896	−	1.03705i	0.259314	−	0.0551188i
$355$	−3.94736	+	1.75748i	−0.209504	+	0.0932772i
$356$	1.79882	−	5.53621i	0.0953374	−	0.293418i
$357$	−6.60324	+	20.3227i	−0.349481	+	1.07559i
$358$	−19.6367	+	8.74281i	−1.03783	+	0.462072i
$359$	−33.0452	+	7.02397i	−1.74406	+	0.370711i	−0.966213	−	0.257747i	$-0.917020\pi$
$359$	−33.0452	+	7.02397i	−1.74406	+	0.370711i	−0.777844	+	0.628457i	$0.783687\pi$
$360$	8.98784	+	1.91042i	0.473701	+	0.100688i
$361$	−16.1432	−	7.18743i	−0.849643	−	0.378286i
$362$	−6.21722	+	6.90492i	−0.326770	+	0.362915i
$363$	1.56648	−	14.9041i	0.0822191	−	0.782262i
$364$	0.117833	+	0.0856108i	0.00617613	+	0.00448722i
$365$	−3.14719	−	29.9435i	−0.164731	−	1.56731i
$366$	1.64472	−	2.84875i	0.0859711	−	0.148906i
$367$	−11.3157	−	19.5993i	−0.590673	−	1.02308i	−0.994142	−	0.108082i	$-0.965529\pi$
$367$	−11.3157	−	19.5993i	−0.590673	−	1.02308i	0.403469	−	0.914993i	$-0.367804\pi$
$368$	−11.4282	+	8.30306i	−0.595735	+	0.432827i
$369$	−0.174988	−	0.194343i	−0.00910949	−	0.0101171i
$370$	5.75889	+	17.7240i	0.299390	+	0.921429i
$371$	−16.0517			−0.833365
$372$		0			0
$373$	−32.9720			−1.70723			−0.853613	−	0.520908i	$-0.825593\pi$
$373$	−32.9720			−1.70723			−0.853613	+	0.520908i	$0.825593\pi$
$374$	2.44694	+	7.53091i	0.126528	+	0.389414i
$375$	−16.7679	−	18.6226i	−0.865890	−	0.961669i
$376$	13.8421	−	10.0569i	0.713854	−	0.518645i
$377$	−0.112379	−	0.194647i	−0.00578783	−	0.0100248i
$378$	7.81265	−	13.5319i	0.401840	−	0.696006i
$379$	3.39633	+	32.3139i	0.174457	+	1.65985i	0.635222	+	0.772330i	$0.280909\pi$
$379$	3.39633	+	32.3139i	0.174457	+	1.65985i	−0.460764	+	0.887523i	$0.652425\pi$
$380$	1.40261	+	1.01905i	0.0719523	+	0.0522764i
$381$	−1.13943	+	10.8409i	−0.0583746	+	0.555397i
$382$	6.62996	−	7.36332i	0.339218	−	0.376740i
$383$	−24.4651	−	10.8926i	−1.25011	−	0.556585i	−0.328427	−	0.944529i	$-0.606519\pi$
$383$	−24.4651	−	10.8926i	−1.25011	−	0.556585i	−0.921683	+	0.387944i	$0.873185\pi$
$384$	−9.95899	−	2.11685i	−0.508218	−	0.108025i
$385$	−7.73507	+	1.64414i	−0.394216	+	0.0837931i
$386$	−5.35911	+	2.38603i	−0.272771	+	0.121446i
$387$	−2.37131	+	7.29815i	−0.120541	+	0.370986i
$388$	−1.89775	+	5.84069i	−0.0963439	+	0.296516i
$389$	−16.2040	+	7.21449i	−0.821576	+	0.365789i	−0.774084	−	0.633082i	$-0.781789\pi$
$389$	−16.2040	+	7.21449i	−0.821576	+	0.365789i	−0.0474917	+	0.998872i	$0.515123\pi$
$390$	1.17508	−	0.249771i	0.0595026	−	0.0126477i
$391$	−29.7749	−	6.32884i	−1.50578	−	0.320063i
$392$	6.12166	+	2.72554i	0.309191	+	0.137661i
$393$	12.9450	−	14.3769i	0.652991	−	0.725220i
$394$	2.96360	−	28.1968i	0.149304	−	1.42053i
$395$	13.9653	+	10.1464i	0.702673	+	0.510522i
$396$	0.0313309	+	0.298094i	0.00157444	+	0.0149798i
$397$	−4.97476	+	8.61654i	−0.249676	+	0.432452i	−0.963436	−	0.267939i	$-0.913658\pi$
$397$	−4.97476	+	8.61654i	−0.249676	+	0.432452i	0.713760	+	0.700391i	$0.246991\pi$
$398$	16.8482	+	29.1819i	0.844523	+	1.46276i
$399$	3.03038	−	2.20170i	0.151709	−	0.110223i
$400$	−19.2830	−	21.4159i	−0.964150	−	1.07080i
$401$	6.14807	+	18.9218i	0.307020	+	0.944911i	0.978916	+	0.204265i	$0.0654804\pi$
$401$	6.14807	+	18.9218i	0.307020	+	0.944911i	−0.671896	+	0.740646i	$0.734520\pi$
$402$	1.03779			0.0517604
$403$		0			0
$404$	−1.92858			−0.0959506
$405$	7.01643	+	21.5944i	0.348649	+	1.07303i
$406$	2.47990	+	2.75420i	0.123075	+	0.136689i
$407$	−2.97748	+	2.16327i	−0.147588	+	0.107229i
$408$	−14.8108	−	25.6530i	−0.733242	−	1.27001i
$409$	12.1628	−	21.0665i	0.601410	−	1.04167i	−0.391198	−	0.920306i	$-0.627939\pi$
$409$	12.1628	−	21.0665i	0.601410	−	1.04167i	0.992608	−	0.121365i	$-0.0387273\pi$
$410$	0.165134	+	1.57115i	0.00815539	+	0.0775934i
$411$	0.161271	+	0.117171i	0.00795493	+	0.00577960i
$412$	0.0798583	−	0.759801i	0.00393433	−	0.0374327i
$413$	−3.88608	+	4.31593i	−0.191221	+	0.212373i
$414$	4.26741	+	1.89998i	0.209732	+	0.0933787i
$415$	1.21330	+	0.257896i	0.0595587	+	0.0126596i
$416$	−0.362360	+	0.0770220i	−0.0177662	+	0.00377632i
$417$	15.6312	−	6.95944i	0.765461	−	0.340805i
$418$	0.428931	−	1.32012i	0.0209797	−	0.0645689i
$419$	−1.36176	+	4.19106i	−0.0665263	+	0.204747i	−0.978794	−	0.204848i	$-0.934330\pi$
$419$	−1.36176	+	4.19106i	−0.0665263	+	0.204747i	0.912267	+	0.409595i	$0.134330\pi$
$420$	4.46384	−	1.98743i	0.217813	−	0.0969767i
$421$	12.1522	−	2.58303i	0.592261	−	0.125889i	0.0979761	−	0.995189i	$-0.468763\pi$
$421$	12.1522	−	2.58303i	0.592261	−	0.125889i	0.494285	+	0.869300i	$0.335430\pi$
$422$	−1.64298	−	0.349227i	−0.0799792	−	0.0170001i
$423$	−4.10444	−	1.82741i	−0.199565	−	0.0888519i
$424$	14.8890	−	16.5359i	0.723074	−	0.803055i
$425$	6.49118	−	61.7595i	0.314869	−	2.99577i
$426$	−1.72934	−	1.25644i	−0.0837867	−	0.0608746i
$427$	0.400346	+	3.80904i	0.0193741	+	0.184332i
$428$	2.47870	−	4.29323i	0.119812	−	0.207521i
$429$	0.118623	+	0.205461i	0.00572718	+	0.00991976i
$430$	37.5033	−	27.2478i	1.80857	−	1.31400i
$431$	−12.4226	−	13.7967i	−0.598376	−	0.664564i	0.365532	−	0.930799i	$-0.380887\pi$
$431$	−12.4226	−	13.7967i	−0.598376	−	0.664564i	−0.963908	+	0.266235i	$0.914220\pi$
$432$	5.31504	+	16.3580i	0.255720	+	0.787025i
$433$	−36.1204			−1.73584			−0.867918	−	0.496708i	$-0.834542\pi$
$433$	−36.1204			−1.73584			−0.867918	+	0.496708i	$0.834542\pi$
$434$		0			0
$435$	−7.54024			−0.361527
$436$	1.25494	+	3.86231i	0.0601008	+	0.184971i
$437$	3.57043	+	3.96537i	0.170797	+	0.189689i
$438$	12.0501	−	8.75492i	0.575777	−	0.418326i
$439$	9.50469	+	16.4626i	0.453634	+	0.785718i	0.998609	−	0.0527352i	$-0.0167939\pi$
$439$	9.50469	+	16.4626i	0.453634	+	0.785718i	−0.544974	+	0.838453i	$0.683461\pi$
$440$	5.48103	−	9.49342i	0.261298	−	0.452581i
$441$	−0.183930	−	1.74997i	−0.00875856	−	0.0833321i
$442$	1.13313	+	0.823268i	0.0538975	+	0.0391588i
$443$	−1.30180	+	12.3858i	−0.0618504	+	0.588467i	0.919075	+	0.394083i	$0.128938\pi$
$443$	−1.30180	+	12.3858i	−0.0618504	+	0.588467i	−0.980925	+	0.194385i	$0.937729\pi$
$444$	1.52167	−	1.68999i	0.0722154	−	0.0802034i
$445$	51.0702	+	22.7379i	2.42096	+	1.07788i
$446$	15.0157	+	3.19168i	0.711013	+	0.151131i
$447$	7.89979	−	1.67915i	0.373647	−	0.0794212i
$448$	17.7868	−	7.91918i	0.840346	−	0.374146i
$449$	7.86034	−	24.1916i	0.370952	−	1.14167i	−0.575217	−	0.818001i	$-0.695082\pi$
$449$	7.86034	−	24.1916i	0.370952	−	1.14167i	0.946169	−	0.323673i	$-0.104918\pi$
$450$	−2.94483	+	9.06327i	−0.138821	+	0.427247i
$451$	−0.285015	+	0.126897i	−0.0134208	+	0.00597534i
$452$	−1.48750	+	0.316178i	−0.0699661	+	0.0148718i
$453$	−19.8750	−	4.22457i	−0.933811	−	0.198488i
$454$	−18.4004	−	8.19236i	−0.863571	−	0.384487i
$455$	−0.935949	+	1.03948i	−0.0438780	+	0.0487314i
$456$	−0.542758	+	5.16400i	−0.0254170	+	0.241826i
$457$	−25.8675	−	18.7938i	−1.21003	−	0.879138i	−0.214796	−	0.976659i	$-0.568909\pi$
$457$	−25.8675	−	18.7938i	−1.21003	−	0.879138i	−0.995233	+	0.0975213i	$0.968909\pi$
$458$	2.15787	+	20.5308i	0.100831	+	0.959339i
$459$	−18.5319	+	32.0982i	−0.864995	+	1.49822i
$460$	3.48032	+	6.02809i	0.162271	+	0.281061i
$461$	−15.6545	+	11.3737i	−0.729105	+	0.529726i	−0.889280	−	0.457363i	$-0.848794\pi$
$461$	−15.6545	+	11.3737i	−0.729105	+	0.529726i	0.160175	+	0.987089i	$0.448794\pi$
$462$	−2.61768	−	2.90723i	−0.121785	−	0.135256i
$463$	0.0128126	+	0.0394332i	0.000595453	+	0.00183262i	0.951354	−	0.308101i	$-0.0996933\pi$
$463$	0.0128126	+	0.0394332i	0.000595453	+	0.00183262i	−0.950758	+	0.309933i	$0.899693\pi$
$464$	−4.07961			−0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	7.82069	+	24.0696i	0.361898	+	1.11381i	0.951901	+	0.306407i	$0.0991269\pi$
$467$	7.82069	+	24.0696i	0.361898	+	1.11381i	−0.590002	+	0.807402i	$0.700873\pi$
$468$	0.0354757	+	0.0393998i	0.00163987	+	0.00182126i
$469$	−0.977565	+	0.710243i	−0.0451398	+	0.0327960i
$470$	13.5706	+	23.5050i	0.625966	+	1.08420i
$471$	11.1734	−	19.3530i	0.514845	−	0.891737i
$472$	−0.841526	−	8.00658i	−0.0387344	−	0.368533i
$473$	7.40637	+	5.38105i	0.340545	+	0.247421i
$474$	−0.892636	+	8.49287i	−0.0410001	+	0.390090i
$475$	−7.28391	+	8.08960i	−0.334209	+	0.371176i
$476$	5.20436	+	2.31713i	0.238542	+	0.106206i
$477$	−5.71528	−	1.21482i	−0.261684	−	0.0556228i
$478$	−10.6151	+	2.25631i	−0.485523	+	0.103201i
$479$	−19.4048	+	8.63955i	−0.886626	+	0.394751i	−0.798950	−	0.601398i	$-0.794611\pi$
$479$	−19.4048	+	8.63955i	−0.886626	+	0.394751i	−0.0876761	+	0.996149i	$0.527944\pi$
$480$	−3.84050	+	11.8198i	−0.175294	+	0.539499i
$481$	−0.201166	+	0.619127i	−0.00917240	+	0.0282298i
$482$	−7.92238	+	3.52727i	−0.360854	+	0.160663i
$483$	14.7101	−	3.12672i	0.669331	−	0.142271i
$484$	−3.90803	−	0.830678i	−0.177638	−	0.0377581i
$485$	−53.8790	−	23.9885i	−2.44652	−	1.08926i
$486$	6.81297	−	7.56657i	0.309043	−	0.343227i
$487$	−2.79739	+	26.6154i	−0.126762	+	1.20606i	0.727461	+	0.686149i	$0.240700\pi$
$487$	−2.79739	+	26.6154i	−0.126762	+	1.20606i	−0.854222	+	0.519908i	$0.825966\pi$
$488$	−4.29527	−	3.12070i	−0.194438	−	0.141267i
$489$	−2.64351	−	25.1514i	−0.119544	−	1.13738i
$490$	−5.31488	+	9.20564i	−0.240102	+	0.415868i
$491$	6.28320	+	10.8828i	0.283557	+	0.491135i	0.972258	−	0.233910i	$-0.0751522\pi$
$491$	6.28320	+	10.8828i	0.283557	+	0.491135i	−0.688701	+	0.725045i	$0.741819\pi$
$492$	0.155960	−	0.113312i	0.00703124	−	0.00510849i
$493$	−5.88240	−	6.53307i	−0.264930	−	0.294235i
$494$	−0.0758699	−	0.233503i	−0.00341355	−	0.0105058i
$495$	−2.87853			−0.129380
$496$		0			0
$497$	2.48886			0.111640
$498$	0.189624	+	0.583602i	0.00849725	+	0.0261518i
$499$	−15.4103	−	17.1149i	−0.689861	−	0.766168i	0.291867	−	0.956459i	$-0.405724\pi$
$499$	−15.4103	−	17.1149i	−0.689861	−	0.766168i	−0.981728	+	0.190291i	$0.939057\pi$
$500$	−5.40490	+	3.92689i	−0.241715	+	0.175616i
$501$	12.0216	+	20.8221i	0.537087	+	0.930263i
$502$	−14.3545	+	24.8626i	−0.640671	+	1.10967i
$503$	−0.0691538	−	0.657954i	−0.00308341	−	0.0293367i	0.992872	−	0.119185i	$-0.0380283\pi$
$503$	−0.0691538	−	0.657954i	−0.00308341	−	0.0293367i	−0.995955	+	0.0898487i	$0.971362\pi$
$504$	−4.28185	−	3.11095i	−0.190729	−	0.138573i
$505$	1.93600	−	18.4198i	0.0861507	−	0.819669i
$506$	3.72895	−	4.14142i	0.165772	−	0.184109i
$507$	−17.5895	−	7.83136i	−0.781178	−	0.347803i
$508$	2.84262	+	0.604218i	0.126121	+	0.0268078i
$509$	11.4124	−	2.42579i	0.505848	−	0.107521i	0.0520830	−	0.998643i	$-0.483414\pi$
$509$	11.4124	−	2.42579i	0.505848	−	0.107521i	0.453765	+	0.891121i	$0.350081\pi$
$510$	42.9261	−	19.1119i	1.90080	−	0.846291i
$511$	−5.35912	+	16.4937i	−0.237074	+	0.729638i
$512$	−7.80146	+	24.0104i	−0.344779	+	1.06112i
$513$	5.93533	−	2.64258i	0.262051	−	0.116673i
$514$	20.6384	−	4.38683i	0.910322	−	0.193495i
$515$	7.17664	+	1.52544i	0.316241	+	0.0672190i
$516$	−5.16770	−	2.30081i	−0.227495	−	0.101287i
$517$	−3.58654	+	3.98326i	−0.157736	+	0.175184i
$518$	1.12206	−	10.6756i	0.0493003	−	0.469061i
$519$	2.79941	+	2.03389i	0.122880	+	0.0892779i
$520$	−0.202679	−	1.92836i	−0.00888805	−	0.0845642i
$521$	15.9592	−	27.6422i	0.699186	−	1.21103i	−0.269563	−	0.962983i	$-0.586879\pi$
$521$	15.9592	−	27.6422i	0.699186	−	1.21103i	0.968749	−	0.248043i	$-0.0797874\pi$
$522$	0.674533	+	1.16833i	0.0295235	+	0.0511362i
$523$	0.00335774	−	0.00243954i	0.000146824	−	0.000106674i	−0.587712	−	0.809070i	$-0.699971\pi$
$523$	0.00335774	−	0.00243954i	0.000146824	−	0.000106674i	0.587859	+	0.808964i	$0.299971\pi$
$524$	−3.45117	−	3.83291i	−0.150765	−	0.167442i
$525$	9.48061	+	29.1783i	0.413768	+	1.27345i
$526$	−31.1411			−1.35782
$527$		0			0
$528$	4.30627			0.187406
$529$	−0.487316	−	1.49980i	−0.0211876	−	0.0652088i
$530$	23.6184	+	26.2308i	1.02592	+	1.13939i
$531$	−1.71029	+	1.24260i	−0.0742201	+	0.0539241i
$532$	−0.499312	−	0.864834i	−0.0216479	−	0.0374953i
$533$	−0.0275924	+	0.0477914i	−0.00119516	+	0.00207008i
$534$	2.89080	+	27.5041i	0.125097	+	1.19022i
$535$	38.5161	+	27.9836i	1.66520	+	1.20984i
$536$	0.175087	−	1.66585i	0.00756263	−	0.0719536i
$537$	−16.8552	+	18.7196i	−0.727357	+	0.807812i
$538$	14.4801	+	6.44695i	0.624281	+	0.277948i
$539$	−2.05335	−	0.436453i	−0.0884441	−	0.0187994i
$540$	8.29007	−	1.76211i	0.356748	−	0.0758291i
$541$	26.7441	−	11.9072i	1.14982	−	0.511932i	0.258814	−	0.965927i	$-0.416668\pi$
$541$	26.7441	−	11.9072i	1.14982	−	0.511932i	0.891004	+	0.453996i	$0.150002\pi$
$542$	−10.6333	+	32.7260i	−0.456740	+	1.40570i
$543$	−3.36476	+	10.3557i	−0.144395	+	0.444404i
$544$	−13.2371	+	5.89355i	−0.567537	+	0.252684i
$545$	−38.1485	+	8.10871i	−1.63410	+	0.347339i
$546$	−0.676848	−	0.143869i	−0.0289664	−	0.00615701i
$547$	37.6064	+	16.7434i	1.60793	+	0.715898i	0.997117	−	0.0758759i	$-0.0241753\pi$
$547$	37.6064	+	16.7434i	1.60793	+	0.715898i	0.610815	+	0.791773i	$0.290842\pi$
$548$	0.0355609	−	0.0394944i	0.00151909	−	0.00168712i
$549$	−0.145729	+	1.38652i	−0.00621956	+	0.0591752i
$550$	9.19767	+	6.68250i	0.392190	+	0.284943i
$551$	0.161081	+	1.53258i	0.00686226	+	0.0652901i
$552$	−10.4235	+	18.0540i	−0.443653	+	0.768429i
$553$	−4.97150	−	8.61089i	−0.211410	−	0.366172i
$554$	15.5318	−	11.2845i	0.659881	−	0.479432i
$555$	14.6135	+	16.2299i	0.620307	+	0.688921i
$556$	−1.40963	−	4.33840i	−0.0597817	−	0.183989i
$557$	−5.73810			−0.243131			−0.121566	−	0.992583i	$-0.538791\pi$
$557$	−5.73810			−0.243131			−0.121566	+	0.992583i	$0.538791\pi$
$558$		0			0
$559$	1.61931			0.0684894
$560$	7.84559	+	24.1462i	0.331537	+	1.02037i
$561$	6.20923	+	6.89605i	0.262154	+	0.291151i
$562$	−30.9949	+	22.5191i	−1.30744	+	0.949911i
$563$	7.14710	+	12.3791i	0.301214	+	0.521718i	0.976411	−	0.215919i	$-0.0692748\pi$
$563$	7.14710	+	12.3791i	0.301214	+	0.521718i	−0.675197	+	0.737637i	$0.735941\pi$
$564$	1.65598	−	2.86823i	0.0697292	−	0.120774i
$565$	−1.52658	−	14.5244i	−0.0642236	−	0.611046i
$566$	−3.22302	−	2.34166i	−0.135474	−	0.0984273i
$567$	1.36707	−	13.0068i	0.0574117	−	0.546236i
$568$	−2.30857	+	2.56393i	−0.0968655	+	0.107580i
$569$	13.1201	+	5.84147i	0.550025	+	0.244887i	0.662882	−	0.748724i	$-0.269333\pi$
$569$	13.1201	+	5.84147i	0.550025	+	0.244887i	−0.112856	+	0.993611i	$0.536000\pi$
$570$	−8.05676	−	1.71252i	−0.337461	−	0.0717294i
$571$	−32.6496	+	6.93989i	−1.36634	+	0.290425i	−0.831969	−	0.554823i	$-0.812786\pi$
$571$	−32.6496	+	6.93989i	−1.36634	+	0.290425i	−0.534374	+	0.845248i	$0.679453\pi$
$572$	0.0577819	−	0.0257262i	0.00241598	−	0.00107567i
$573$	3.58813	−	11.0431i	0.149896	−	0.461334i
$574$	0.281195	−	0.865430i	0.0117369	−	0.0361224i
$575$	−39.9259	+	17.7762i	−1.66502	+	0.741317i
$576$	6.93237	−	1.47352i	0.288849	−	0.0613967i
$577$	21.9884	+	4.67377i	0.915388	+	0.194572i	0.641440	−	0.767173i	$-0.278337\pi$
$577$	21.9884	+	4.67377i	0.915388	+	0.194572i	0.273948	+	0.961745i	$0.411670\pi$
$578$	30.3766	+	13.5245i	1.26350	+	0.562546i
$579$	−4.60001	+	5.10883i	−0.191170	+	0.212316i
$580$	−0.210127	+	1.99923i	−0.00872506	+	0.0830134i
$581$	−0.578024	−	0.419959i	−0.0239805	−	0.0174228i
$582$	−3.04979	−	29.0168i	−0.126418	−	1.20278i
$583$	−3.48533	+	6.03677i	−0.144348	+	0.250018i
$584$	−12.0203	−	20.8197i	−0.497402	−	0.861525i
$585$	−0.411917	+	0.299275i	−0.0170307	+	0.0123735i
$586$	1.61036	+	1.78849i	0.0665234	+	0.0738817i
$587$	−1.98271	−	6.10214i	−0.0818350	−	0.251862i	0.901765	−	0.432227i	$-0.142272\pi$
$587$	−1.98271	−	6.10214i	−0.0818350	−	0.251862i	−0.983600	+	0.180365i	$0.942272\pi$
$588$	1.29711			0.0534920
$589$		0			0
$590$	12.7708			0.525764
$591$	−10.2672	−	31.5993i	−0.422338	−	1.29982i
$592$	7.90654	+	8.78110i	0.324957	+	0.360901i
$593$	16.8762	−	12.2613i	0.693023	−	0.503510i	−0.184630	−	0.982808i	$-0.559109\pi$
$593$	16.8762	−	12.2613i	0.693023	−	0.503510i	0.877652	+	0.479298i	$0.159109\pi$
$594$	−3.39274	−	5.87640i	−0.139206	−	0.241112i
$595$	−27.3551	+	47.3805i	−1.12145	+	1.94241i
$596$	−0.225065	−	2.14135i	−0.00921903	−	0.0877132i
$597$	31.9467	+	23.2107i	1.30749	+	0.949950i
$598$	0.103037	−	0.980329i	0.00421349	−	0.0400886i
$599$	−7.73407	+	8.58955i	−0.316006	+	0.350960i	−0.880132	−	0.474728i	$-0.842546\pi$
$599$	−7.73407	+	8.58955i	−0.316006	+	0.350960i	0.564127	+	0.825688i	$0.309213\pi$
$600$	−38.8523	−	17.2981i	−1.58614	−	0.706194i
$601$	−4.22307	−	0.897641i	−0.172263	−	0.0366156i	0.120973	−	0.992656i	$-0.461399\pi$
$601$	−4.22307	−	0.897641i	−0.172263	−	0.0366156i	−0.293235	+	0.956040i	$0.594732\pi$
$602$	−26.1180	+	5.55156i	−1.06449	+	0.226265i
$603$	−0.401817	+	0.178901i	−0.0163633	+	0.00728540i
$604$	−1.67397	+	5.15196i	−0.0681130	+	0.209630i
$605$	11.8568	−	36.4915i	0.482048	−	1.48359i
$606$	8.37040	−	3.72674i	0.340024	−	0.151388i
$607$	−43.9279	+	9.33716i	−1.78298	+	0.378984i	−0.977046	−	0.213026i	$-0.931668\pi$
$607$	−43.9279	+	9.33716i	−1.78298	+	0.378984i	−0.805931	+	0.592010i	$0.798335\pi$
$608$	2.48446	+	0.528089i	0.100758	+	0.0214168i
$609$	3.96770	+	1.76653i	0.160779	+	0.0715836i
$610$	5.63544	−	6.25880i	0.228172	−	0.253411i
$611$	−0.0991017	+	0.942890i	−0.00400923	+	0.0381452i
$612$	1.67767	+	1.21890i	0.0678157	+	0.0492710i
$613$	0.272314	+	2.59089i	0.0109986	+	0.104645i	0.998644	−	0.0520611i	$-0.0165791\pi$
$613$	0.272314	+	2.59089i	0.0109986	+	0.104645i	−0.987645	+	0.156706i	$0.949912\pi$
$614$	−14.3937	+	24.9306i	−0.580883	+	1.00612i
$615$	0.925674	+	1.60332i	0.0373268	+	0.0646519i
$616$	−5.10826	+	3.71137i	−0.205818	+	0.149535i
$617$	−16.7194	−	18.5688i	−0.673099	−	0.747552i	0.305756	−	0.952110i	$-0.401091\pi$
$617$	−16.7194	−	18.5688i	−0.673099	−	0.747552i	−0.978854	+	0.204558i	$0.934424\pi$
$618$	1.12162	+	3.45199i	0.0451181	+	0.138859i
$619$	31.9083			1.28250			0.641252	−	0.767330i	$-0.278415\pi$
$619$	31.9083			1.28250			0.641252	+	0.767330i	$0.278415\pi$
$620$		0			0
$621$	26.0847			1.04674
$622$	6.21366	+	19.1237i	0.249145	+	0.766790i
$623$	−21.5463	−	23.9295i	−0.863233	−	0.958717i
$624$	0.616227	−	0.447715i	0.0246688	−	0.0179229i
$625$	−8.47372	−	14.6769i	−0.338949	−	0.587077i
$626$	−4.02105	+	6.96466i	−0.160713	+	0.278364i
$627$	−0.170030	−	1.61773i	−0.00679035	−	0.0646059i
$628$	−4.81989	−	3.50185i	−0.192335	−	0.139739i
$629$	−2.66156	+	25.3230i	−0.106123	+	1.00969i
$630$	5.61784	−	6.23924i	0.223820	−	0.248577i
$631$	−0.328649	−	0.146324i	−0.0130833	−	0.00582506i	0.400185	−	0.916435i	$-0.368946\pi$
$631$	−0.328649	−	0.146324i	−0.0130833	−	0.00582506i	−0.413268	+	0.910610i	$0.635613\pi$
$632$	13.4820	+	2.86569i	0.536285	+	0.113991i
$633$	−1.92539	+	0.409255i	−0.0765275	+	0.0162664i
$634$	−17.7048	+	7.88267i	−0.703146	+	0.313061i
$635$	−8.62439	+	26.5432i	−0.342249	+	1.05333i
$636$	1.33099	−	4.09637i	0.0527773	−	0.162432i
$637$	−0.339211	+	0.151027i	−0.0134400	+	0.00598389i
$638$	1.57427	−	0.334621i	0.0623259	−	0.0132478i
$639$	0.886166	+	0.188360i	0.0350562	+	0.00745142i
$640$	−23.8142	−	10.6028i	−0.941338	−	0.419111i
$641$	−20.6139	+	22.8940i	−0.814198	+	0.904259i	−0.996882	−	0.0789131i	$-0.974855\pi$
$641$	−20.6139	+	22.8940i	−0.814198	+	0.904259i	0.182683	+	0.983172i	$0.441522\pi$
$642$	−2.46187	+	23.4231i	−0.0971623	+	0.924438i
$643$	1.41726	+	1.02970i	0.0558915	+	0.0406075i	0.615380	−	0.788230i	$-0.289002\pi$
$643$	1.41726	+	1.02970i	0.0558915	+	0.0406075i	−0.559489	+	0.828838i	$0.689002\pi$
$644$	−0.419090	−	3.98737i	−0.0165145	−	0.157125i
$645$	27.1624	−	47.0467i	1.06952	−	1.85246i
$646$	−4.80159	−	8.31659i	−0.188916	−	0.327212i
$647$	19.9426	−	14.4891i	0.784024	−	0.569626i	−0.122160	−	0.992510i	$-0.538982\pi$
$647$	19.9426	−	14.4891i	0.784024	−	0.569626i	0.906184	+	0.422884i	$0.138982\pi$
$648$	12.1311	+	13.4730i	0.476555	+	0.529268i
$649$	0.779354	+	2.39861i	0.0305923	+	0.0941535i
$650$	2.01095			0.0788760
$651$		0			0
$652$	−6.74233			−0.264050
$653$	−0.0882751	−	0.271683i	−0.00345447	−	0.0106318i	0.949314	−	0.314328i	$-0.101779\pi$
$653$	−0.0882751	−	0.271683i	−0.00345447	−	0.0106318i	−0.952769	+	0.303696i	$0.901779\pi$
$654$	−12.9101	−	14.3381i	−0.504825	−	0.560665i
$655$	40.0723	−	29.1143i	1.56576	−	1.13759i
$656$	0.500831	+	0.867465i	0.0195542	+	0.0338688i
$657$	−3.15640	+	5.46704i	−0.123143	+	0.213290i
$658$	−1.63413	−	15.5477i	−0.0637052	−	0.606114i
$659$	−30.2772	−	21.9977i	−1.17943	−	0.856908i	−0.187325	−	0.982298i	$-0.559982\pi$
$659$	−30.2772	−	21.9977i	−1.17943	−	0.856908i	−0.992107	+	0.125391i	$0.959982\pi$
$660$	0.221802	−	2.11030i	0.00863363	−	0.0821435i
$661$	2.80471	−	3.11495i	0.109091	−	0.121157i	−0.686126	−	0.727482i	$-0.740690\pi$
$661$	2.80471	−	3.11495i	0.109091	−	0.121157i	0.795217	+	0.606325i	$0.207357\pi$
$662$	−10.3768	−	4.62005i	−0.403306	−	0.179563i
$663$	1.60551	+	0.341262i	0.0623528	+	0.0132535i
$664$	0.968780	−	0.205921i	0.0375960	−	0.00799127i
$665$	8.76120	−	3.90074i	0.339745	−	0.151264i
$666$	1.20746	−	3.71618i	0.0467881	−	0.143999i
$667$	−1.91188	+	5.88417i	−0.0740284	+	0.227836i
$668$	5.85580	−	2.60717i	0.226568	−	0.100875i
$669$	17.5967	−	3.74029i	0.680328	−	0.144608i
$670$	2.59902	+	0.552438i	0.100409	+	0.0213425i
$671$	1.51944	+	0.676498i	0.0586573	+	0.0261159i
$672$	4.79004	−	5.31988i	0.184780	−	0.205219i
$673$	−1.04243	+	9.91804i	−0.0401826	+	0.382312i	0.955887	+	0.293736i	$0.0948985\pi$
$673$	−1.04243	+	9.91804i	−0.0401826	+	0.382312i	−0.996069	+	0.0885767i	$0.971768\pi$
$674$	4.47669	+	3.25250i	0.172436	+	0.125282i
$675$	5.56242	+	52.9229i	0.214098	+	2.03700i
$676$	−2.56659	+	4.44546i	−0.0987150	+	0.170979i
$677$	23.8788	+	41.3594i	0.917738	+	1.58957i	0.802842	+	0.596192i	$0.203320\pi$
$677$	23.8788	+	41.3594i	0.917738	+	1.58957i	0.114896	+	0.993377i	$0.463346\pi$
$678$	5.84504	−	4.24667i	0.224477	−	0.163092i
$679$	22.7313	+	25.2456i	0.872346	+	0.968838i
$680$	−23.4360	−	72.1287i	−0.898730	−	2.76601i
$681$	−23.6038			−0.904500
$682$		0			0
$683$	27.7600			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$683$	27.7600			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$684$	−0.112330	−	0.345716i	−0.00429504	−	0.0132188i
$685$	0.341511	+	0.379287i	0.0130485	+	0.0144918i
$686$	20.6548	−	15.0066i	0.788606	−	0.572956i
$687$	12.0961	+	20.9511i	0.461496	+	0.799335i
$688$	14.6961	−	25.4544i	0.560283	−	0.970438i
$689$	0.128881	+	1.22622i	0.00490999	+	0.0467154i
$690$	−26.7537	−	19.4377i	−1.01850	−	0.739981i
$691$	−3.97532	+	37.8226i	−0.151228	+	1.43884i	0.611051	+	0.791592i	$0.290747\pi$
$691$	−3.97532	+	37.8226i	−0.151228	+	1.43884i	−0.762279	+	0.647249i	$0.775919\pi$
$692$	0.617280	−	0.685559i	0.0234655	−	0.0260610i
$693$	1.51469	+	0.674384i	0.0575384	+	0.0256177i
$694$	−30.2363	−	6.42692i	−1.14775	−	0.243963i
$695$	42.8508	−	9.10823i	1.62543	−	0.345495i
$696$	−5.50011	+	2.44881i	−0.208481	+	0.0928218i
$697$	−0.667006	+	2.05283i	−0.0252646	+	0.0777566i
$698$	5.10540	−	15.7128i	0.193242	−	0.594739i
$699$	−6.94668	+	3.09286i	−0.262748	+	0.116983i
$700$	8.00057	−	1.70057i	0.302393	−	0.0642756i
$701$	−40.1591	−	8.53607i	−1.51679	−	0.322403i	−0.627087	−	0.778949i	$-0.715753\pi$
$701$	−40.1591	−	8.53607i	−1.51679	−	0.322403i	−0.889700	+	0.456546i	$0.849086\pi$
$702$	−1.09646	−	0.488175i	−0.0413832	−	0.0184250i
$703$	2.98660	−	3.31695i	0.112642	−	0.125101i
$704$	0.883799	−	8.40879i	0.0333094	−	0.316918i
$705$	25.7320	+	18.6954i	0.969123	+	0.704109i
$706$	−1.43316	−	13.6356i	−0.0539377	−	0.513183i
$707$	−5.33413	+	9.23898i	−0.200611	+	0.347468i
$708$	−0.779187	−	1.34959i	−0.0292836	−	0.0507207i
$709$	−34.0319	+	24.7256i	−1.27809	+	0.928590i	−0.999494	−	0.0318175i	$-0.989870\pi$
$709$	−34.0319	+	24.7256i	−1.27809	+	0.928590i	−0.278600	+	0.960407i	$0.589870\pi$
$710$	−3.66208	−	4.06715i	−0.137435	−	0.152637i
$711$	−1.11843	−	3.44219i	−0.0419446	−	0.129092i
$712$	44.6368			1.67284
$713$		0			0
$714$	−27.0654			−1.01290
$715$	0.187705	+	0.577696i	0.00701977	+	0.0216046i
$716$	4.49363	+	4.99068i	0.167935	+	0.186511i
$717$	−10.2888	+	7.47522i	−0.384241	+	0.279167i
$718$	−21.3951	−	37.0573i	−0.798456	−	1.38297i
$719$	16.6345	−	28.8118i	0.620362	−	1.07450i	−0.369056	−	0.929407i	$-0.620319\pi$
$719$	16.6345	−	28.8118i	0.620362	−	1.07450i	0.989418	−	0.145092i	$-0.0463477\pi$
$720$	0.966025	+	9.19112i	0.0360016	+	0.342533i
$721$	−3.41899	−	2.48404i	−0.127330	−	0.0925106i
$722$	2.33956	−	22.2594i	0.0870695	−	0.828411i
$723$	−6.80021	+	7.55240i	−0.252902	+	0.280877i
$724$	2.65194	+	1.18072i	0.0985586	+	0.0438811i
$725$	−12.3460	−	2.62423i	−0.458520	−	0.0974615i
$726$	18.5667	−	3.94648i	0.689076	−	0.146468i
$727$	−29.8939	+	13.3096i	−1.10870	+	0.493626i	−0.877643	−	0.479314i	$-0.840885\pi$
$727$	−29.8939	+	13.3096i	−1.10870	+	0.493626i	−0.231058	+	0.972940i	$0.574219\pi$
$728$	−0.345127	+	1.06219i	−0.0127913	+	0.0393675i
$729$	9.22600	−	28.3947i	0.341704	−	1.05166i
$730$	34.8384	−	15.5110i	1.28943	−	0.574090i
$731$	61.9529	−	13.1685i	2.29141	−	0.487054i
$732$	−1.00525	−	0.213674i	−0.0371553	−	0.00789760i
$733$	−9.10248	−	4.05269i	−0.336208	−	0.149689i	0.231687	−	0.972790i	$-0.425575\pi$
$733$	−9.10248	−	4.05269i	−0.336208	−	0.149689i	−0.567895	+	0.823101i	$0.692242\pi$
$734$	19.1805	−	21.3021i	0.707967	−	0.786277i
$735$	−1.30210	+	12.3886i	−0.0480286	+	0.456962i
$736$	8.25005	+	5.99401i	0.304101	+	0.220942i
$737$	0.0548498	+	0.521861i	0.00202042	+	0.0192230i
$738$	0.165618	−	0.286858i	0.00609647	−	0.0105594i
$739$	−15.4792	−	26.8108i	−0.569412	−	0.986251i	−0.996624	−	0.0820995i	$-0.973837\pi$
$739$	−15.4792	−	26.8108i	−0.569412	−	0.986251i	0.427212	−	0.904152i	$-0.359496\pi$
$740$	4.71045	−	3.42234i	0.173160	−	0.125808i
$741$	−0.192524	−	0.213819i	−0.00707253	−	0.00785484i
$742$	−6.28267	−	19.3361i	−0.230644	−	0.709850i
$743$	1.11003			0.0407231			0.0203615	−	0.999793i	$-0.493518\pi$
$743$	1.11003			0.0407231			0.0203615	+	0.999793i	$0.493518\pi$
$744$		0			0
$745$	20.6778			0.757578
$746$	−12.9053	−	39.7184i	−0.472496	−	1.45419i
$747$	−0.174024	−	0.193274i	−0.00636722	−	0.00707151i
$748$	2.00146	−	1.45415i	0.0731807	−	0.0531689i
$749$	−13.7113	−	23.7487i	−0.501000	−	0.867757i
$750$	15.8700	−	27.4877i	0.579491	−	1.00371i
$751$	−2.94303	−	28.0011i	−0.107393	−	1.02177i	−0.906966	−	0.421205i	$-0.861607\pi$
$751$	−2.94303	−	28.0011i	−0.107393	−	1.02177i	0.799573	−	0.600569i	$-0.205059\pi$
$752$	13.9222	+	10.1150i	0.507689	+	0.368857i
$753$	−3.51672	+	33.4593i	−0.128156	+	1.21933i
$754$	0.190488	−	0.211558i	0.00693715	−	0.00770449i
$755$	−47.5256	−	21.1598i	−1.72964	−	0.770083i
$756$	−4.77509	−	1.01498i	−0.173668	−	0.0369143i
$757$	−37.8761	+	8.05082i	−1.37663	+	0.292612i	−0.836038	−	0.548672i	$-0.815134\pi$
$757$	−37.8761	+	8.05082i	−1.37663	+	0.292612i	−0.540594	+	0.841284i	$0.681800\pi$
$758$	−37.5963	+	16.7389i	−1.36556	+	0.607986i
$759$	2.01811	−	6.21110i	0.0732527	−	0.225449i
$760$	−4.10817	+	12.6436i	−0.149019	+	0.458633i
$761$	39.6816	−	17.6674i	1.43846	−	0.640441i	0.468442	−	0.883494i	$-0.344815\pi$
$761$	39.6816	−	17.6674i	1.43846	−	0.640441i	0.970013	+	0.243053i	$0.0781488\pi$
$762$	−13.5051	+	2.87059i	−0.489237	+	0.103990i
$763$	21.9736	+	4.67063i	0.795497	+	0.169088i
$764$	−2.82800	−	1.25911i	−0.102313	−	0.0455528i
$765$	−13.3257	+	14.7997i	−0.481792	+	0.535085i
$766$	3.54562	−	33.7343i	0.128108	−	1.21887i
$767$	0.360904	+	0.262212i	0.0130315	+	0.00946793i
$768$	1.41204	+	13.4347i	0.0509527	+	0.484783i
$769$	1.55509	−	2.69350i	0.0560781	−	0.0971302i	−0.836624	−	0.547778i	$-0.815474\pi$
$769$	1.55509	−	2.69350i	0.0560781	−	0.0971302i	0.892702	+	0.450648i	$0.148807\pi$
$770$	−5.00806	−	8.67422i	−0.180478	−	0.312597i
$771$	20.0040	−	14.5337i	0.720425	−	0.523419i
$772$	1.22637	+	1.36202i	0.0441380	+	0.0490203i
$773$	6.68718	+	20.5810i	0.240521	+	0.740248i	0.996341	+	0.0854684i	$0.0272387\pi$
$773$	6.68718	+	20.5810i	0.240521	+	0.740248i	−0.755820	+	0.654780i	$0.772761\pi$
$774$	−9.71956			−0.349362
$775$		0			0
$776$	−47.0918			−1.69050
$777$	−3.88730	−	11.9639i	−0.139456	−	0.429202i
$778$	−15.0329	−	16.6957i	−0.538956	−	0.598572i
$779$	0.306104	−	0.222398i	0.0109673	−	0.00796823i
$780$	−0.187665	−	0.325045i	−0.00671947	−	0.0116385i
$781$	0.540408	−	0.936015i	0.0193373	−	0.0334932i
$782$	−4.03014	−	38.3442i	−0.144117	−	1.37119i
$783$	6.09455	+	4.42795i	0.217801	+	0.158242i
$784$	−0.704493	+	6.70281i	−0.0251605	+	0.239386i
$785$	38.2844	−	42.5191i	1.36643	−	1.51757i
$786$	22.3853	+	9.96658i	0.798457	+	0.355496i
$787$	7.70441	+	1.63762i	0.274633	+	0.0583750i	0.343169	−	0.939274i	$-0.388500\pi$
$787$	7.70441	+	1.63762i	0.274633	+	0.0583750i	−0.0685364	+	0.997649i	$0.521833\pi$
$788$	−8.66439	+	1.84167i	−0.308656	+	0.0656069i
$789$	−33.3388	+	14.8434i	−1.18689	+	0.528439i
$790$	−6.75642	+	20.7941i	−0.240383	+	0.739822i
$791$	−2.59950	+	8.00044i	−0.0924276	+	0.284463i
$792$	−2.09970	+	0.934845i	−0.0746095	+	0.0332183i
$793$	0.287766	−	0.0611664i	0.0102189	−	0.00217208i
$794$	−12.3267	−	2.62012i	−0.437458	−	0.0929846i
$795$	37.7881	+	16.8243i	1.34021	+	0.596698i
$796$	7.04438	−	7.82357i	0.249681	−	0.277299i
$797$	−3.08549	+	29.3565i	−0.109294	+	1.03986i	0.793143	+	0.609036i	$0.208443\pi$
$797$	−3.08549	+	29.3565i	−0.109294	+	1.03986i	−0.902436	+	0.430823i	$0.858223\pi$
$798$	3.83828	+	2.78868i	0.135874	+	0.0987181i
$799$	3.87623	+	36.8798i	0.137131	+	1.30471i
$800$	−10.4019	+	18.0166i	−0.367763	+	0.636984i
$801$	−5.86059	−	10.1508i	−0.207074	−	0.358663i
$802$	−20.3870	+	14.8121i	−0.719892	+	0.523032i
$803$	5.03935	+	5.59676i	0.177835	+	0.197505i
$804$	−0.100194	−	0.308365i	−0.00353357	−	0.0108752i
$805$	38.5039			1.35708
$806$		0			0
$807$	18.5749			0.653869
$808$	−4.56992	−	14.0648i	−0.160769	−	0.494796i
$809$	−1.42359	−	1.58106i	−0.0500509	−	0.0555871i	0.717599	−	0.696456i	$-0.245241\pi$
$809$	−1.42359	−	1.58106i	−0.0500509	−	0.0555871i	−0.767650	+	0.640869i	$0.778574\pi$
$810$	−23.2665	+	16.9041i	−0.817503	+	0.593950i
$811$	−3.60252	−	6.23975i	−0.126502	−	0.219107i	0.795817	−	0.605537i	$-0.207042\pi$
$811$	−3.60252	−	6.23975i	−0.126502	−	0.219107i	−0.922319	+	0.386430i	$0.873708\pi$
$812$	0.578950	−	1.00277i	0.0203172	−	0.0351904i
$813$	4.21509	+	40.1039i	0.147830	+	1.40651i
$814$	−3.77129	−	2.74000i	−0.132183	−	0.0960369i
$815$	6.76824	−	64.3955i	0.237081	−	2.25568i
$816$	19.9352	−	22.1403i	0.697873	−	0.775066i
$817$	−10.1427	−	4.51580i	−0.354847	−	0.157988i
$818$	30.1374	+	6.40591i	1.05373	+	0.223977i
$819$	0.286866	−	0.0609753i	0.0100239	−	0.00213065i
$820$	0.450901	−	0.200754i	0.0157461	−	0.00701063i
$821$	12.9972	−	40.0012i	0.453604	−	1.39605i	−0.419161	−	0.907912i	$-0.637676\pi$
$821$	12.9972	−	40.0012i	0.453604	−	1.39605i	0.872766	−	0.488139i	$-0.162324\pi$
$822$	−0.0780229	+	0.240130i	−0.00272136	+	0.00837549i
$823$	−27.5644	+	12.2725i	−0.960834	+	0.427791i	−0.826370	−	0.563128i	$-0.809598\pi$
$823$	−27.5644	+	12.2725i	−0.960834	+	0.427791i	−0.134464	+	0.990918i	$0.542931\pi$
$824$	5.73030	−	1.21801i	0.199624	−	0.0424315i
$825$	13.0320	+	2.77003i	0.453715	+	0.0964402i
$826$	−6.72002	−	2.99195i	−0.233819	−	0.104103i
$827$	−2.58984	+	2.87631i	−0.0900576	+	0.100019i	−0.786489	−	0.617604i	$-0.788103\pi$
$827$	−2.58984	+	2.87631i	−0.0900576	+	0.100019i	0.696431	+	0.717623i	$0.254770\pi$
$828$	0.152552	−	1.45144i	0.00530155	−	0.0504409i
$829$	−10.6561	−	7.74208i	−0.370100	−	0.268894i	0.387152	−	0.922016i	$-0.373459\pi$
$829$	−10.6561	−	7.74208i	−0.370100	−	0.268894i	−0.757253	+	0.653122i	$0.773459\pi$
$830$	0.164225	+	1.56250i	0.00570034	+	0.0542351i
$831$	11.2491	−	19.4841i	0.390228	−	0.675895i
$832$	−0.747774	−	1.29518i	−0.0259244	−	0.0449024i
$833$	−11.7497	+	8.53663i	−0.407102	+	0.295777i
$834$	14.5015	+	16.1055i	0.502144	+	0.557688i
$835$	19.0226	+	58.5456i	0.658305	+	2.02605i
$836$	−0.433665			−0.0149986
$837$		0			0
$838$	−5.58159			−0.192813
$839$	−10.5835	−	32.5727i	−0.365384	−	1.12454i	−0.949740	−	0.313039i	$-0.898653\pi$
$839$	−10.5835	−	32.5727i	−0.365384	−	1.12454i	0.584356	−	0.811497i	$-0.301347\pi$
$840$	25.0713	+	27.8445i	0.865042	+	0.960727i
$841$	22.0159	−	15.9955i	0.759170	−	0.551569i
$842$	7.86792	+	13.6276i	0.271147	+	0.469640i
$843$	−22.4486	+	38.8821i	−0.773170	+	1.33917i
$844$	0.0548545	+	0.521906i	0.00188817	+	0.0179647i
$845$	−39.8819	−	28.9759i	−1.37198	−	0.996801i
$846$	0.594837	−	5.65950i	0.0204509	−	0.194578i
$847$	−14.7884	+	16.4241i	−0.508134	+	0.564340i
$848$	20.4450	+	9.10272i	0.702086	+	0.312589i
$849$	−4.56663	−	0.970667i	−0.156726	−	0.0333132i
$850$	76.9367	−	16.3534i	2.63891	−	0.560917i
$851$	16.3707	−	7.28869i	0.561179	−	0.249853i
$852$	−0.206373	+	0.635151i	−0.00707023	+	0.0217599i
$853$	−4.46464	+	13.7407i	−0.152866	+	0.470474i	−0.997938	−	0.0641782i	$-0.979557\pi$
$853$	−4.46464	+	13.7407i	−0.152866	+	0.470474i	0.845072	+	0.534652i	$0.179557\pi$
$854$	−4.43171	+	1.97312i	−0.151650	+	0.0675189i
$855$	3.41467	−	0.725810i	0.116779	−	0.0248222i
$856$	37.1831	+	7.90351i	1.27089	+	0.270136i
$857$	25.4268	+	11.3207i	0.868561	+	0.386708i	0.792120	−	0.610366i	$-0.208977\pi$
$857$	25.4268	+	11.3207i	0.868561	+	0.386708i	0.0764416	+	0.997074i	$0.475644\pi$
$858$	−0.201071	+	0.223312i	−0.00686446	+	0.00762376i
$859$	4.94630	−	47.0609i	0.168766	−	1.60570i	−0.502564	−	0.864540i	$-0.667610\pi$
$859$	4.94630	−	47.0609i	0.168766	−	1.60570i	0.671330	−	0.741159i	$-0.265723\pi$
$860$	−11.7171	−	8.51294i	−0.399548	−	0.290289i
$861$	−0.111467	−	1.06054i	−0.00379879	−	0.0361430i
$862$	11.7574	−	20.3644i	0.400459	−	0.693616i
$863$	−13.0267	−	22.5629i	−0.443434	−	0.768049i	0.554508	−	0.832178i	$-0.312906\pi$
$863$	−13.0267	−	22.5629i	−0.443434	−	0.768049i	−0.997942	+	0.0641289i	$0.979573\pi$
$864$	10.0453	−	7.29831i	0.341747	−	0.248294i
$865$	5.92808	+	6.58380i	0.201561	+	0.223856i
$866$	−14.1376	−	43.5110i	−0.480414	−	1.47856i
$867$	38.9668			1.32338
$868$		0			0
$869$	−4.31787			−0.146474
$870$	−2.95126	−	9.08305i	−0.100057	−	0.307944i
$871$	0.0621058	+	0.0689755i	0.00210438	+	0.00233715i
$872$	−25.1934	+	18.3041i	−0.853156	+	0.619854i
$873$	6.18291	+	10.7091i	0.209260	+	0.362449i
$874$	−3.37925	+	5.85303i	−0.114305	+	0.197982i
$875$	3.86296	+	36.7536i	0.130592	+	1.24250i
$876$	−3.76478	−	2.73527i	−0.127200	−	0.0924164i
$877$	3.58757	−	34.1335i	0.121144	−	1.15260i	−0.749952	−	0.661492i	$-0.769924\pi$
$877$	3.58757	−	34.1335i	0.121144	−	1.15260i	0.871096	−	0.491113i	$-0.163410\pi$
$878$	−16.1109	+	17.8929i	−0.543715	+	0.603857i
$879$	2.57649	+	1.14713i	0.0869029	+	0.0386916i
$880$	10.7845	+	2.29232i	0.363545	+	0.0772739i
$881$	3.55525	−	0.755691i	0.119779	−	0.0254599i	−0.147632	−	0.989042i	$-0.547165\pi$
$881$	3.55525	−	0.755691i	0.119779	−	0.0254599i	0.267411	+	0.963582i	$0.413832\pi$
$882$	2.03605	−	0.906506i	0.0685572	−	0.0305236i
$883$	12.1930	−	37.5262i	0.410327	−	1.26286i	−0.506037	−	0.862512i	$-0.668890\pi$
$883$	12.1930	−	37.5262i	0.410327	−	1.26286i	0.916364	−	0.400345i	$-0.131110\pi$
$884$	0.135224	−	0.416176i	0.00454807	−	0.0139975i
$885$	13.6720	−	6.08718i	0.459581	−	0.204618i
$886$	−15.4296	+	3.27966i	−0.518367	+	0.110182i
$887$	41.3783	+	8.79523i	1.38935	+	0.295315i	0.841045	−	0.540965i	$-0.181941\pi$
$887$	41.3783	+	8.79523i	1.38935	+	0.295315i	0.548303	+	0.836280i	$0.315274\pi$
$888$	15.9305	+	7.09270i	0.534591	+	0.238015i
$889$	10.7567	−	11.9466i	0.360769	−	0.400675i
$890$	−7.40137	+	70.4193i	−0.248094	+	2.36046i
$891$	−4.59481	−	3.33832i	−0.153932	−	0.111838i
$892$	−0.501330	−	4.76984i	−0.0167858	−	0.159706i
$893$	3.25019	−	5.62950i	0.108764	−	0.188384i
$894$	5.11471	+	8.85894i	0.171062	+	0.296287i
$895$	−52.1766	+	37.9085i	−1.74407	+	1.26714i
$896$	10.0471	+	11.1584i	0.335649	+	0.372776i
$897$	−0.356965	−	1.09863i	−0.0119187	−	0.0366821i
$898$	32.2180			1.07513
$899$		0			0
$900$	2.97733			0.0992444
$901$	14.9027	+	45.8659i	0.496482	+	1.52801i
$902$	−0.264417	−	0.293664i	−0.00880411	−	0.00977795i
$903$	−25.3151	+	18.3925i	−0.842433	+	0.612064i
$904$	−5.83056	−	10.0988i	−0.193921	−	0.335882i
$905$	−13.9391	+	24.1433i	−0.463352	+	0.802549i
$906$	−2.69016	−	25.5952i	−0.0893746	−	0.850343i
$907$	26.1863	+	19.0254i	0.869501	+	0.631730i	0.930453	−	0.366411i	$-0.119414\pi$
$907$	26.1863	+	19.0254i	0.869501	+	0.631730i	−0.0609518	+	0.998141i	$0.519414\pi$
$908$	−0.657778	+	6.25834i	−0.0218291	+	0.207690i
$909$	−2.59845	+	2.88588i	−0.0861853	+	0.0957184i
$910$	−1.61850	−	0.720600i	−0.0536526	−	0.0238877i
$911$	26.4694	+	5.62625i	0.876970	+	0.186406i	0.624336	−	0.781156i	$-0.285370\pi$
$911$	26.4694	+	5.62625i	0.876970	+	0.186406i	0.252635	+	0.967562i	$0.418703\pi$
$912$	−5.10834	+	1.08581i	−0.169154	+	0.0359548i
$913$	−0.283446	+	0.126198i	−0.00938070	+	0.00417656i
$914$	12.5146	−	38.5161i	0.413948	−	1.27400i
$915$	3.04990	−	9.38663i	0.100827	−	0.310312i
$916$	5.89209	−	2.62333i	0.194680	−	0.0866772i
$917$	−27.9071	+	5.93184i	−0.921574	+	0.195887i
$918$	−45.9192	−	9.76043i	−1.51556	−	0.322142i
$919$	18.9697	+	8.44586i	0.625753	+	0.278603i	0.695015	−	0.718995i	$-0.255398\pi$
$919$	18.9697	+	8.44586i	0.625753	+	0.278603i	−0.0692618	+	0.997599i	$0.522064\pi$
$920$	−35.7147	+	39.6652i	−1.17748	+	1.30772i
$921$	−3.52633	+	33.5508i	−0.116197	+	1.10554i
$922$	−19.8281	−	14.4059i	−0.653003	−	0.474434i
$923$	−0.0199833	−	0.190129i	−0.000657760	−	0.00625816i
$924$	−0.611117	+	1.05849i	−0.0201043	+	0.0348216i
$925$	18.2789	+	31.6600i	0.601007	+	1.04097i
$926$	−0.0424867	+	0.0308684i	−0.00139620	+	0.00101440i
$927$	−1.02935	−	1.14321i	−0.0338082	−	0.0375478i
$928$	0.910081	+	2.80094i	0.0298749	+	0.0919454i
$929$	−20.6589			−0.677798			−0.338899	−	0.940823i	$-0.610055\pi$
$929$	−20.6589			−0.677798			−0.338899	+	0.940823i	$0.610055\pi$
$930$		0			0
$931$	2.54585			0.0834368
$932$	0.626458	+	1.92804i	0.0205203	+	0.0631551i
$933$	15.7675	+	17.5116i	0.516204	+	0.573303i
$934$	−25.9335	+	18.8418i	−0.848569	+	0.616521i
$935$	11.8793	+	20.5756i	0.388495	+	0.672893i
$936$	−0.203272	+	0.352078i	−0.00664416	+	0.0115080i
$937$	−0.305286	−	2.90460i	−0.00997325	−	0.0948892i	0.988403	−	0.151854i	$-0.0485244\pi$
$937$	−0.305286	−	2.90460i	−0.00997325	−	0.0948892i	−0.998376	+	0.0569649i	$0.981858\pi$
$938$	−1.23819	−	0.899594i	−0.0404282	−	0.0293728i
$939$	−0.985121	+	9.37280i	−0.0321482	+	0.305870i
$940$	5.67400	−	6.30161i	0.185065	−	0.205536i
$941$	30.0101	+	13.3613i	0.978300	+	0.435567i	0.832668	−	0.553772i	$-0.186812\pi$
$941$	30.0101	+	13.3613i	0.978300	+	0.435567i	0.145631	+	0.989339i	$0.453479\pi$
$942$	27.6861	+	5.88485i	0.902061	+	0.191739i
$943$	1.48589	−	0.315836i	0.0483872	−	0.0102850i
$944$	7.39718	−	3.29344i	0.240758	−	0.107192i
$945$	14.4874	−	44.5877i	0.471276	−	1.45044i
$946$	−3.58319	+	11.0279i	−0.116500	+	0.358549i
$947$	35.7422	−	15.9135i	1.16147	−	0.517118i	0.266756	−	0.963764i	$-0.414048\pi$
$947$	35.7422	−	15.9135i	1.16147	−	0.517118i	0.894711	+	0.446646i	$0.147382\pi$
$948$	2.60971	−	0.554712i	0.0847596	−	0.0180162i
$949$	1.30301	+	0.276964i	0.0422976	+	0.00899064i
$950$	−12.5957	−	5.60799i	−0.408660	−	0.181947i
$951$	−15.1970	+	16.8779i	−0.492795	+	0.547305i
$952$	−4.56625	+	43.4449i	−0.147993	+	1.40806i
$953$	−4.87008	−	3.53832i	−0.157757	−	0.114617i	0.506106	−	0.862471i	$-0.331084\pi$
$953$	−4.87008	−	3.53832i	−0.157757	−	0.114617i	−0.663863	+	0.747854i	$0.731084\pi$
$954$	−0.773584	−	7.36016i	−0.0250457	−	0.238294i
$955$	14.8645	−	25.7461i	0.481004	−	0.833123i
$956$	1.69527	+	2.93629i	0.0548288	+	0.0949663i
$957$	1.52587	−	1.10861i	0.0493245	−	0.0358363i
$958$	−18.0023	−	19.9936i	−0.581629	−	0.645965i
$959$	−0.0908447	−	0.279591i	−0.00293353	−	0.00902848i
$960$	−50.1729			−1.61932
$961$		0			0
$962$	−0.824543			−0.0265843
$963$	−3.08462	−	9.49348i	−0.0994005	−	0.305923i
$964$	1.81295	+	2.01348i	0.0583911	+	0.0648498i
$965$	−14.2397	+	10.3457i	−0.458391	+	0.333041i
$966$	9.52401	+	16.4961i	0.306430	+	0.530753i
$967$	−13.1552	+	22.7854i	−0.423042	+	0.732730i	−0.996235	−	0.0866903i	$-0.972371\pi$
$967$	−13.1552	+	22.7854i	−0.423042	+	0.732730i	0.573194	+	0.819420i	$0.305704\pi$
$968$	−3.20240	−	30.4688i	−0.102929	−	0.979305i
$969$	−9.10455	−	6.61484i	−0.292480	−	0.212499i
$970$	7.80843	−	74.2922i	0.250714	−	2.38538i
$971$	−3.16892	+	3.51944i	−0.101695	+	0.112944i	−0.791844	−	0.610724i	$-0.790879\pi$
$971$	−3.16892	+	3.51944i	−0.101695	+	0.112944i	0.690148	+	0.723668i	$0.257545\pi$
$972$	−2.90606	−	1.29386i	−0.0932119	−	0.0415006i
$973$	−24.6821	−	5.24635i	−0.791273	−	0.168190i
$974$	−33.1560	+	7.04753i	−1.06239	+	0.225817i
$975$	2.15287	−	0.958519i	0.0689470	−	0.0306972i
$976$	1.65013	−	5.07859i	0.0528195	−	0.162562i
$977$	−5.33982	+	16.4343i	−0.170836	+	0.525780i	−0.999419	−	0.0340871i	$-0.989148\pi$
$977$	−5.33982	+	16.4343i	−0.170836	+	0.525780i	0.828583	+	0.559867i	$0.189148\pi$
$978$	29.2629	−	13.0287i	0.935724	−	0.416611i
$979$	−13.6778	+	2.90731i	−0.437146	+	0.0929182i
$980$	3.24845	+	0.690479i	0.103768	+	0.0220566i
$981$	7.47029	+	3.32599i	0.238508	+	0.106191i
$982$	−10.6503	+	11.8283i	−0.339865	+	0.377458i
$983$	4.28217	−	40.7421i	0.136580	−	1.29947i	−0.684649	−	0.728873i	$-0.740045\pi$
$983$	4.28217	−	40.7421i	0.136580	−	1.29947i	0.821229	−	0.570599i	$-0.193289\pi$
$984$	1.19592	+	0.868886i	0.0381245	+	0.0276991i
$985$	−8.89201	−	84.6018i	−0.283323	−	2.69564i
$986$	5.56742	−	9.64305i	0.177303	−	0.307097i
$987$	−9.16029	−	15.8661i	−0.291575	−	0.505023i
$988$	−0.0620574	+	0.0450873i	−0.00197431	+	0.00143442i
$989$	−29.8266	−	33.1258i	−0.948430	−	1.05334i
$990$	−1.12666	−	3.46750i	−0.0358076	−	0.110204i
$991$	14.1338			0.448975			0.224487	−	0.974477i	$-0.427929\pi$
$991$	14.1338			0.448975			0.224487	+	0.974477i	$0.427929\pi$
$992$		0			0
$993$	−13.3113			−0.422420
$994$	0.974142	+	2.99810i	0.0308979	+	0.0950940i
$995$	67.6510	+	75.1340i	2.14468	+	2.38191i
$996$	0.155102	−	0.112688i	0.00491459	−	0.00357066i
$997$	−7.72692	−	13.3834i	−0.244714	−	0.423857i	0.717337	−	0.696726i	$-0.245361\pi$
$997$	−7.72692	−	13.3834i	−0.244714	−	0.423857i	−0.962051	+	0.272869i	$0.912027\pi$
$998$	14.5852	−	25.2622i	0.461685	−	0.799662i
$999$	−2.28074	−	21.6998i	−0.0721593	−	0.686550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.s.547.2		16
31.2	even	5		961.2.g.k.235.1		16
31.3	odd	30		961.2.c.i.521.6		16
31.4	even	5		31.2.g.a.10.1	✓	16
31.5	even	3		961.2.d.p.531.3		16
31.6	odd	6		961.2.g.n.844.2		16
31.7	even	15		961.2.g.k.732.1		16
31.8	even	5		961.2.g.t.846.2		16
31.9	even	15		961.2.d.p.628.3		16
31.10	even	15		961.2.d.o.388.2		16
31.11	odd	30		961.2.d.n.374.2		16
31.12	odd	30		961.2.g.l.338.1		16
31.13	odd	30		961.2.a.j.1.6		8
31.14	even	15	inner	961.2.g.s.448.2		16
31.15	odd	10		961.2.c.i.439.6		16
31.16	even	5		961.2.c.j.439.6		16
31.17	odd	30		961.2.g.m.448.2		16
31.18	even	15		961.2.a.i.1.6		8
31.19	even	15		31.2.g.a.28.1	yes	16
31.20	even	15		961.2.d.o.374.2		16
31.21	odd	30		961.2.d.n.388.2		16
31.22	odd	30		961.2.d.q.628.3		16
31.23	odd	10		961.2.g.n.846.2		16
31.24	odd	30		961.2.g.j.732.1		16
31.25	even	3		961.2.g.t.844.2		16
31.26	odd	6		961.2.d.q.531.3		16
31.27	odd	10		961.2.g.l.816.1		16
31.28	even	15		961.2.c.j.521.6		16
31.29	odd	10		961.2.g.j.235.1		16
31.30	odd	2		961.2.g.m.547.2		16
93.35	odd	10		279.2.y.c.10.2		16
93.44	even	30		8649.2.a.be.1.3		8
93.50	odd	30		279.2.y.c.28.2		16
93.80	odd	30		8649.2.a.bf.1.3		8
124.19	odd	30		496.2.bg.c.369.2		16
124.35	odd	10		496.2.bg.c.289.2		16
155.4	even	10		775.2.bl.a.351.2		16
155.19	even	30		775.2.bl.a.276.2		16
155.97	odd	20		775.2.ck.a.599.4		32
155.112	odd	60		775.2.ck.a.524.1		32
155.128	odd	20		775.2.ck.a.599.1		32
155.143	odd	60		775.2.ck.a.524.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	31.4	even	5
31.2.g.a.28.1	yes	16	31.19	even	15
279.2.y.c.10.2		16	93.35	odd	10
279.2.y.c.28.2		16	93.50	odd	30
496.2.bg.c.289.2		16	124.35	odd	10
496.2.bg.c.369.2		16	124.19	odd	30
775.2.bl.a.276.2		16	155.19	even	30
775.2.bl.a.351.2		16	155.4	even	10
775.2.ck.a.524.1		32	155.112	odd	60
775.2.ck.a.524.4		32	155.143	odd	60
775.2.ck.a.599.1		32	155.128	odd	20
775.2.ck.a.599.4		32	155.97	odd	20
961.2.a.i.1.6		8	31.18	even	15
961.2.a.j.1.6		8	31.13	odd	30
961.2.c.i.439.6		16	31.15	odd	10
961.2.c.i.521.6		16	31.3	odd	30
961.2.c.j.439.6		16	31.16	even	5
961.2.c.j.521.6		16	31.28	even	15
961.2.d.n.374.2		16	31.11	odd	30
961.2.d.n.388.2		16	31.21	odd	30
961.2.d.o.374.2		16	31.20	even	15
961.2.d.o.388.2		16	31.10	even	15
961.2.d.p.531.3		16	31.5	even	3
961.2.d.p.628.3		16	31.9	even	15
961.2.d.q.531.3		16	31.26	odd	6
961.2.d.q.628.3		16	31.22	odd	30
961.2.g.j.235.1		16	31.29	odd	10
961.2.g.j.732.1		16	31.24	odd	30
961.2.g.k.235.1		16	31.2	even	5
961.2.g.k.732.1		16	31.7	even	15
961.2.g.l.338.1		16	31.12	odd	30
961.2.g.l.816.1		16	31.27	odd	10
961.2.g.m.448.2		16	31.17	odd	30
961.2.g.m.547.2		16	31.30	odd	2
961.2.g.n.844.2		16	31.6	odd	6
961.2.g.n.846.2		16	31.23	odd	10
961.2.g.s.448.2		16	31.14	even	15	inner
961.2.g.s.547.2		16	1.1	even	1	trivial
961.2.g.t.844.2		16	31.25	even	3
961.2.g.t.846.2		16	31.8	even	5
8649.2.a.be.1.3		8	93.44	even	30
8649.2.a.bf.1.3		8	93.80	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.391401 + 1.20461i) q^{2} +(0.993201 + 1.10306i) q^{3} +(0.320145 - 0.232599i) q^{4} +(1.90016 + 3.29117i) q^{5} +(-0.940018 + 1.62816i) q^{6} +(-0.228812 - 2.17700i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.0832892 - 0.792444i) q^{9} +O(q^{10})\)	\(q+(0.391401 + 1.20461i) q^{2} +(0.993201 + 1.10306i) q^{3} +(0.320145 - 0.232599i) q^{4} +(1.90016 + 3.29117i) q^{5} +(-0.940018 + 1.62816i) q^{6} +(-0.228812 - 2.17700i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.0832892 - 0.792444i) q^{9} +(-3.22085 + 3.57712i) q^{10} +(-0.868412 - 0.386642i) q^{11} +(0.574538 + 0.122122i) q^{12} +(-0.164468 + 0.0349588i) q^{13} +(2.53288 - 1.12771i) q^{14} +(-1.74313 + 5.36479i) q^{15} +(-0.943109 + 2.90259i) q^{16} +(-6.00807 + 2.67497i) q^{17} +(0.987185 - 0.209833i) q^{18} +(1.12765 + 0.239689i) q^{19} +(1.37385 + 0.611677i) q^{20} +(2.17411 - 2.41459i) q^{21} +(0.125855 - 1.19743i) q^{22} +(3.74454 + 2.72056i) q^{23} +(0.470800 + 4.47937i) q^{24} +(-4.72122 + 8.17739i) q^{25} +(-0.106485 - 0.184437i) q^{26} +(4.55935 - 3.31256i) q^{27} +(-0.579620 - 0.643733i) q^{28} +(0.413068 + 1.27129i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(-0.436018 - 1.34192i) q^{33} +(-5.57386 - 6.19040i) q^{34} +(6.73010 - 4.88970i) q^{35} +(-0.157657 - 0.273070i) q^{36} +(1.93582 - 3.35295i) q^{37} +(0.152632 + 1.45219i) q^{38} +(-0.201911 - 0.146697i) q^{39} +(-1.20540 + 11.4686i) q^{40} +(0.219610 - 0.243902i) q^{41} +(3.75958 + 1.67388i) q^{42} +(-9.42012 - 2.00231i) q^{43} +(-0.367950 + 0.0782102i) q^{44} +(2.76634 - 1.23165i) q^{45} +(-1.81160 + 5.57554i) q^{46} +(1.74242 - 5.36260i) q^{47} +(-4.13843 + 1.84255i) q^{48} +(2.16007 - 0.459137i) q^{49} +(-11.6985 - 2.48658i) q^{50} +(-8.91787 - 3.97049i) q^{51} +(-0.0445222 + 0.0494469i) q^{52} +(0.766501 - 7.29277i) q^{53} +(5.77487 + 4.19569i) q^{54} +(-0.377616 - 3.59278i) q^{55} +(3.32116 - 5.75242i) q^{56} +(0.855590 + 1.48193i) q^{57} +(-1.36973 + 0.995171i) q^{58} +(-1.77528 - 1.97165i) q^{59} +(0.689791 + 2.12296i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(2.74856 + 8.45921i) q^{64} +(-0.427571 - 0.474866i) q^{65} +(1.44584 - 1.05046i) q^{66} +(-0.276003 - 0.478052i) q^{67} +(-1.30126 + 2.25385i) q^{68} +(0.718126 + 6.83252i) q^{69} +(8.52436 + 6.19331i) q^{70} +(-0.118848 + 1.13076i) q^{71} +(1.61786 - 1.79682i) q^{72} +(-7.23765 - 3.22241i) q^{73} +(4.79668 + 1.01956i) q^{74} +(-13.7093 + 2.91400i) q^{75} +(0.416762 - 0.185555i) q^{76} +(-0.643016 + 1.97900i) q^{77} +(0.0976845 - 0.300642i) q^{78} +(4.14958 - 1.84751i) q^{79} +(-11.3450 + 2.41145i) q^{80} +(5.84411 + 1.24220i) q^{81} +(0.379763 + 0.169081i) q^{82} +(0.218401 - 0.242559i) q^{83} +(0.134398 - 1.27871i) q^{84} +(-20.2201 - 14.6908i) q^{85} +(-1.27505 - 12.1313i) q^{86} +(-0.992053 + 1.71829i) q^{87} +(-1.44225 - 2.49806i) q^{88} +(11.9008 - 8.64641i) q^{89} +(2.56641 + 2.85028i) q^{90} +(0.113737 + 0.350048i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(1.35386 + 4.16674i) q^{95} +(2.18824 + 2.43029i) q^{96} +(-12.5553 + 9.12195i) q^{97} +(1.39853 + 2.42233i) q^{98} +(-0.378722 + 0.655965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9	\( 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} - 2 q^{11} - 20 q^{12} - 27 q^{13} - 6 q^{14} + 4 q^{15} - 2 q^{16} - 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20} + 29 q^{21} + 4 q^{22} + 21 q^{23} - 25 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 40 q^{28} + 26 q^{29} - 22 q^{30} - 42 q^{32} + 7 q^{33} + 28 q^{34} + 21 q^{35} + q^{36} - 8 q^{37} - 27 q^{38} + 2 q^{39} - 16 q^{40} - 3 q^{41} - 51 q^{42} + 8 q^{43} + 4 q^{44} + 25 q^{45} - 16 q^{46} + 4 q^{47} - 86 q^{48} + 27 q^{49} - 27 q^{50} + 13 q^{51} + 24 q^{52} + 66 q^{53} + 39 q^{54} - 52 q^{55} - 30 q^{56} - 17 q^{57} + 10 q^{58} - 51 q^{59} + 35 q^{60} - 60 q^{61} - 46 q^{63} - 32 q^{64} + 18 q^{65} + 20 q^{66} + 13 q^{67} + 30 q^{68} + 48 q^{69} + 27 q^{70} - 24 q^{71} + 2 q^{72} + 27 q^{73} + 28 q^{74} - 32 q^{75} + 18 q^{76} - 42 q^{77} + 15 q^{78} + 8 q^{79} - 39 q^{80} - 7 q^{81} + 29 q^{82} + 4 q^{83} - 27 q^{84} - 63 q^{85} + 34 q^{86} + 15 q^{87} - 17 q^{88} + 26 q^{89} + 57 q^{90} + 8 q^{91} - 64 q^{92} + 44 q^{94} + 28 q^{95} - 62 q^{96} - 37 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 - 2 * q^11 - 20 * q^12 - 27 * q^13 - 6 * q^14 + 4 * q^15 - 2 * q^16 - 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 + 29 * q^21 + 4 * q^22 + 21 * q^23 - 25 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 40 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 + 28 * q^34 + 21 * q^35 + q^36 - 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 - 51 * q^42 + 8 * q^43 + 4 * q^44 + 25 * q^45 - 16 * q^46 + 4 * q^47 - 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 + 24 * q^52 + 66 * q^53 + 39 * q^54 - 52 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 - 51 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 18 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 + 27 * q^73 + 28 * q^74 - 32 * q^75 + 18 * q^76 - 42 * q^77 + 15 * q^78 + 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 + 4 * q^83 - 27 * q^84 - 63 * q^85 + 34 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 + 57 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 - 62 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more