LMFDB - Embedded newform 103.2.e.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,2,Mod(8,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("103.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	103.e (of order $17$, degree $16$, 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:	$0.822459140819$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	103.14
Dual form			103.2.e.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26998 + 1.68173i) q^{2} +(-0.772826 - 1.55204i) q^{3} +(-0.668028 - 2.34787i) q^{4} +(-0.164776 - 1.77821i) q^{5} +(3.59159 + 0.671384i) q^{6} +(2.76848 - 1.07252i) q^{7} +(0.866715 + 0.335767i) q^{8} +(-0.00367427 + 0.00486551i) q^{9} +O(q^{10})$	\(q+(-1.26998 + 1.68173i) q^{2} +(-0.772826 - 1.55204i) q^{3} +(-0.668028 - 2.34787i) q^{4} +(-0.164776 - 1.77821i) q^{5} +(3.59159 + 0.671384i) q^{6} +(2.76848 - 1.07252i) q^{7} +(0.866715 + 0.335767i) q^{8} +(-0.00367427 + 0.00486551i) q^{9} +(3.19973 + 1.98119i) q^{10} +(0.555351 - 0.735403i) q^{11} +(-3.12773 + 2.85130i) q^{12} +(-0.679861 + 0.263379i) q^{13} +(-1.71224 + 6.01791i) q^{14} +(-2.63252 + 1.62999i) q^{15} +(2.48548 - 1.53894i) q^{16} +(-0.493160 + 0.0921875i) q^{17} +(-0.00351622 - 0.0123582i) q^{18} +(-0.0131985 + 0.0265061i) q^{19} +(-4.06494 + 1.57477i) q^{20} +(-3.80414 - 3.46794i) q^{21} +(0.531463 + 1.86790i) q^{22} +(-4.34474 - 5.75337i) q^{23} +(-0.148694 - 1.60467i) q^{24} +(1.77998 - 0.332735i) q^{25} +(0.420478 - 1.47783i) q^{26} +(-5.10247 - 0.953818i) q^{27} +(-4.36755 - 5.78358i) q^{28} +(0.927930 + 10.0140i) q^{29} +(0.602057 - 6.49723i) q^{30} +(5.99551 - 3.71226i) q^{31} +(-0.739953 + 7.98536i) q^{32} +(-1.57057 - 0.293590i) q^{33} +(0.471269 - 0.946437i) q^{34} +(-2.36334 - 4.74623i) q^{35} +(0.0138781 + 0.00537641i) q^{36} +(-7.82439 + 7.13287i) q^{37} +(-0.0278142 - 0.0558584i) q^{38} +(0.934190 + 0.851627i) q^{39} +(0.454252 - 1.59653i) q^{40} +(-0.476361 + 5.14076i) q^{41} +(10.6633 - 1.99332i) q^{42} +(5.55316 + 5.06238i) q^{43} +(-2.09762 - 0.812624i) q^{44} +(0.00925735 + 0.00573191i) q^{45} +15.1933 q^{46} +11.1556 q^{47} +(-4.30935 - 2.66824i) q^{48} +(1.34114 - 1.22261i) q^{49} +(-1.70097 + 3.41600i) q^{50} +(0.524205 + 0.694160i) q^{51} +(1.07255 + 1.42028i) q^{52} +(0.301714 - 0.605923i) q^{53} +(8.08411 - 7.36964i) q^{54} +(-1.39921 - 0.866355i) q^{55} +2.75960 q^{56} +0.0513387 q^{57} +(-18.0192 - 11.1570i) q^{58} +(9.20578 + 3.56634i) q^{59} +(5.58560 + 5.09195i) q^{60} +(3.42843 - 0.640885i) q^{61} +(-1.37117 + 14.7973i) q^{62} +(-0.00495380 + 0.0174108i) q^{63} +(-8.16871 - 7.44677i) q^{64} +(0.580369 + 1.16554i) q^{65} +(2.48833 - 2.26841i) q^{66} +(-14.8159 - 5.73972i) q^{67} +(0.545889 + 1.09629i) q^{68} +(-5.57175 + 11.1896i) q^{69} +(10.9833 + 2.05313i) q^{70} +(0.322095 - 3.47595i) q^{71} +(-0.00481822 + 0.00298331i) q^{72} +(-0.137321 + 1.48193i) q^{73} +(-2.05872 - 22.2171i) q^{74} +(-1.89203 - 2.50545i) q^{75} +(0.0710498 + 0.0132815i) q^{76} +(0.748747 - 2.63157i) q^{77} +(-2.61861 + 0.489503i) q^{78} +(-0.00741842 - 0.0800575i) q^{79} +(-3.14612 - 4.16613i) q^{80} +(2.46796 + 8.67399i) q^{81} +(-8.04038 - 7.32978i) q^{82} +(-0.288703 + 0.111844i) q^{83} +(-5.60100 + 11.2483i) q^{84} +(0.245190 + 0.861753i) q^{85} +(-15.5660 + 2.90978i) q^{86} +(14.8250 - 9.17924i) q^{87} +(0.728255 - 0.450916i) q^{88} +(2.76025 - 9.70126i) q^{89} +(-0.0213962 + 0.00828892i) q^{90} +(-1.59970 + 1.45832i) q^{91} +(-10.6058 + 14.0443i) q^{92} +(-10.3951 - 6.43635i) q^{93} +(-14.1674 + 18.7607i) q^{94} +(0.0493082 + 0.0191021i) q^{95} +(12.9655 - 5.02285i) q^{96} +(8.89122 + 1.66206i) q^{97} +(0.352875 + 3.80813i) q^{98} +(0.00153761 + 0.00540413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 15 q^{2} - 11 q^{3} - 19 q^{4} - 11 q^{5} - 5 q^{6} - 5 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) $ 112 * q - 15 * q^2 - 11 * q^3 - 19 * q^4 - 11 * q^5 - 5 * q^6 - 5 * q^7 - 5 * q^8 - 8 * q^9	\( 112 q - 15 q^{2} - 11 q^{3} - 19 q^{4} - 11 q^{5} - 5 q^{6} - 5 q^{7} - 5 q^{8} - 8 q^{9} - 59 q^{10} - q^{11} - 41 q^{12} + q^{13} - 21 q^{14} + 13 q^{15} - q^{16} - 11 q^{17} + 19 q^{18} - 12 q^{19} + 31 q^{20} - 7 q^{21} + 23 q^{22} - 22 q^{23} + 73 q^{24} - 52 q^{25} + 18 q^{26} + 13 q^{27} - 50 q^{28} + 7 q^{29} - 13 q^{30} + 31 q^{31} + 34 q^{32} + 13 q^{33} - 91 q^{34} + 23 q^{35} - 53 q^{36} - 30 q^{37} + 15 q^{38} - 105 q^{39} + 75 q^{40} + 11 q^{41} + 57 q^{42} + 37 q^{43} + 83 q^{44} - 4 q^{45} - 56 q^{46} - 154 q^{47} - 9 q^{48} + 20 q^{49} + 12 q^{50} + 51 q^{51} + 113 q^{52} + 27 q^{53} + 95 q^{54} + 12 q^{55} + 8 q^{56} - 40 q^{57} - 13 q^{58} - 9 q^{59} - 84 q^{60} + 29 q^{61} + 41 q^{62} + 103 q^{63} - 57 q^{64} + 47 q^{65} - 3 q^{66} + 10 q^{67} - 105 q^{68} - 35 q^{69} + 143 q^{70} + 11 q^{71} + 135 q^{72} - 40 q^{73} + 97 q^{74} - 117 q^{75} + 131 q^{76} - 19 q^{77} + 81 q^{78} + 77 q^{79} - 29 q^{80} + 104 q^{81} - 162 q^{82} + 73 q^{83} - 163 q^{84} + 55 q^{85} - 99 q^{86} + 75 q^{87} - 63 q^{88} + 54 q^{89} + 107 q^{90} - 113 q^{91} - 11 q^{92} - 197 q^{93} + 33 q^{94} - 146 q^{95} + 49 q^{96} - 142 q^{97} - 2 q^{98} + 102 q^{99}+O(q^{100}) \) 112 * q - 15 * q^2 - 11 * q^3 - 19 * q^4 - 11 * q^5 - 5 * q^6 - 5 * q^7 - 5 * q^8 - 8 * q^9 - 59 * q^10 - q^11 - 41 * q^12 + q^13 - 21 * q^14 + 13 * q^15 - q^16 - 11 * q^17 + 19 * q^18 - 12 * q^19 + 31 * q^20 - 7 * q^21 + 23 * q^22 - 22 * q^23 + 73 * q^24 - 52 * q^25 + 18 * q^26 + 13 * q^27 - 50 * q^28 + 7 * q^29 - 13 * q^30 + 31 * q^31 + 34 * q^32 + 13 * q^33 - 91 * q^34 + 23 * q^35 - 53 * q^36 - 30 * q^37 + 15 * q^38 - 105 * q^39 + 75 * q^40 + 11 * q^41 + 57 * q^42 + 37 * q^43 + 83 * q^44 - 4 * q^45 - 56 * q^46 - 154 * q^47 - 9 * q^48 + 20 * q^49 + 12 * q^50 + 51 * q^51 + 113 * q^52 + 27 * q^53 + 95 * q^54 + 12 * q^55 + 8 * q^56 - 40 * q^57 - 13 * q^58 - 9 * q^59 - 84 * q^60 + 29 * q^61 + 41 * q^62 + 103 * q^63 - 57 * q^64 + 47 * q^65 - 3 * q^66 + 10 * q^67 - 105 * q^68 - 35 * q^69 + 143 * q^70 + 11 * q^71 + 135 * q^72 - 40 * q^73 + 97 * q^74 - 117 * q^75 + 131 * q^76 - 19 * q^77 + 81 * q^78 + 77 * q^79 - 29 * q^80 + 104 * q^81 - 162 * q^82 + 73 * q^83 - 163 * q^84 + 55 * q^85 - 99 * q^86 + 75 * q^87 - 63 * q^88 + 54 * q^89 + 107 * q^90 - 113 * q^91 - 11 * q^92 - 197 * q^93 + 33 * q^94 - 146 * q^95 + 49 * q^96 - 142 * q^97 - 2 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/103\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{8}{17}\right)$

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 $

$2$	−1.26998	+	1.68173i	−0.898012	+	1.18916i	0.0832584	+	0.996528i	$0.473467\pi$
$2$	−1.26998	+	1.68173i	−0.898012	+	1.18916i	−0.981271	+	0.192633i	$0.938297\pi$
$3$	−0.772826	−	1.55204i	−0.446191	−	0.896072i	−0.998067	−	0.0621463i	$-0.980205\pi$
$3$	−0.772826	−	1.55204i	−0.446191	−	0.896072i	0.551876	−	0.833926i	$-0.313912\pi$
$4$	−0.668028	−	2.34787i	−0.334014	−	1.17394i
$5$	−0.164776	−	1.77821i	−0.0736899	−	0.795241i	−0.949744	−	0.313028i	$-0.898657\pi$
$5$	−0.164776	−	1.77821i	−0.0736899	−	0.795241i	0.876054	−	0.482213i	$-0.160167\pi$
$6$	3.59159	+	0.671384i	1.46626	+	0.274091i
$7$	2.76848	−	1.07252i	1.04639	−	0.405373i	0.224173	−	0.974549i	$-0.428032\pi$
$7$	2.76848	−	1.07252i	1.04639	−	0.405373i	0.822215	+	0.569177i	$0.192738\pi$
$8$	0.866715	+	0.335767i	0.306430	+	0.118712i
$9$	−0.00367427	+	0.00486551i	−0.00122476	+	0.00162184i
$10$	3.19973	+	1.98119i	1.01184	+	0.626507i
$11$	0.555351	−	0.735403i	0.167445	−	0.221732i	−0.706556	−	0.707657i	$-0.749752\pi$
$11$	0.555351	−	0.735403i	0.167445	−	0.221732i	0.874001	+	0.485924i	$0.161517\pi$
$12$	−3.12773	+	2.85130i	−0.902898	+	0.823101i
$13$	−0.679861	+	0.263379i	−0.188559	+	0.0730483i	−0.453670	−	0.891170i	$-0.649886\pi$
$13$	−0.679861	+	0.263379i	−0.188559	+	0.0730483i	0.265111	+	0.964218i	$0.414591\pi$
$14$	−1.71224	+	6.01791i	−0.457616	+	1.60835i
$15$	−2.63252	+	1.62999i	−0.679714	+	0.420861i
$16$	2.48548	−	1.53894i	0.621370	−	0.384736i
$17$	−0.493160	+	0.0921875i	−0.119609	+	0.0223588i	−0.243214	−	0.969973i	$-0.578202\pi$
$17$	−0.493160	+	0.0921875i	−0.119609	+	0.0223588i	0.123605	+	0.992332i	$0.460555\pi$
$18$	−0.00351622	−	0.0123582i	−0.000828781	−	0.00291286i
$19$	−0.0131985	+	0.0265061i	−0.00302793	+	0.00608091i	−0.896672	−	0.442695i	$-0.854022\pi$
$19$	−0.0131985	+	0.0265061i	−0.00302793	+	0.00608091i	0.893644	+	0.448776i	$0.148140\pi$
$20$	−4.06494	+	1.57477i	−0.908949	+	0.352129i
$21$	−3.80414	−	3.46794i	−0.830132	−	0.756766i
$22$	0.531463	+	1.86790i	0.113308	+	0.398237i
$23$	−4.34474	−	5.75337i	−0.905941	−	1.19966i	−0.979312	−	0.202356i	$-0.935140\pi$
$23$	−4.34474	−	5.75337i	−0.905941	−	1.19966i	0.0733706	−	0.997305i	$-0.476624\pi$
$24$	−0.148694	−	1.60467i	−0.0303521	−	0.327551i
$25$	1.77998	−	0.332735i	0.355995	−	0.0665470i
$26$	0.420478	−	1.47783i	0.0824626	−	0.289826i
$27$	−5.10247	−	0.953818i	−0.981972	−	0.183562i
$28$	−4.36755	−	5.78358i	−0.825390	−	1.09299i
$29$	0.927930	+	10.0140i	0.172312	+	1.85955i	0.442538	+	0.896750i	$0.354078\pi$
$29$	0.927930	+	10.0140i	0.172312	+	1.85955i	−0.270226	+	0.962797i	$0.587098\pi$
$30$	0.602057	−	6.49723i	0.109920	−	1.18623i
$31$	5.99551	−	3.71226i	1.07682	−	0.666742i	0.130988	−	0.991384i	$-0.458185\pi$
$31$	5.99551	−	3.71226i	1.07682	−	0.666742i	0.945837	+	0.324642i	$0.105244\pi$
$32$	−0.739953	+	7.98536i	−0.130806	+	1.41163i
$33$	−1.57057	−	0.293590i	−0.273401	−	0.0511074i
$34$	0.471269	−	0.946437i	0.0808220	−	0.162313i
$35$	−2.36334	−	4.74623i	−0.399477	−	0.802259i
$36$	0.0138781	+	0.00537641i	0.00231302	+	0.000896069i
$37$	−7.82439	+	7.13287i	−1.28632	+	1.17264i	−0.311353	+	0.950294i	$0.600782\pi$
$37$	−7.82439	+	7.13287i	−1.28632	+	1.17264i	−0.974969	+	0.222342i	$0.928630\pi$
$38$	−0.0278142	−	0.0558584i	−0.00451206	−	0.00906143i
$39$	0.934190	+	0.851627i	0.149590	+	0.136369i
$40$	0.454252	−	1.59653i	0.0718235	−	0.252433i
$41$	−0.476361	+	5.14076i	−0.0743952	+	0.802852i	0.874034	+	0.485864i	$0.161495\pi$
$41$	−0.476361	+	5.14076i	−0.0743952	+	0.802852i	−0.948430	+	0.316988i	$0.897329\pi$
$42$	10.6633	−	1.99332i	1.64539	−	0.307576i
$43$	5.55316	+	5.06238i	0.846849	+	0.772005i	0.975573	−	0.219675i	$-0.0704998\pi$
$43$	5.55316	+	5.06238i	0.846849	+	0.772005i	−0.128724	+	0.991681i	$0.541088\pi$
$44$	−2.09762	−	0.812624i	−0.316229	−	0.122508i
$45$	0.00925735	+	0.00573191i	0.00138000	+	0.000854462i
$46$	15.1933			2.24014
$47$	11.1556			1.62721			0.813606	−	0.581417i	$-0.197501\pi$
$47$	11.1556			1.62721			0.813606	+	0.581417i	$0.197501\pi$
$48$	−4.30935	−	2.66824i	−0.622001	−	0.385127i
$49$	1.34114	−	1.22261i	0.191592	−	0.174659i
$50$	−1.70097	+	3.41600i	−0.240553	+	0.483095i
$51$	0.524205	+	0.694160i	0.0734034	+	0.0972019i
$52$	1.07255	+	1.42028i	0.148736	+	0.196958i
$53$	0.301714	−	0.605923i	0.0414436	−	0.0832300i	−0.873474	−	0.486871i	$-0.838138\pi$
$53$	0.301714	−	0.605923i	0.0414436	−	0.0832300i	0.914917	+	0.403641i	$0.132256\pi$
$54$	8.08411	−	7.36964i	1.10011	−	1.00288i
$55$	−1.39921	−	0.866355i	−0.188670	−	0.116819i
$56$	2.75960			0.368767
$57$	0.0513387			0.00679997
$58$	−18.0192	−	11.1570i	−2.36604	−	1.46499i
$59$	9.20578	+	3.56634i	1.19849	+	0.464298i	0.876017	−	0.482280i	$-0.160191\pi$
$59$	9.20578	+	3.56634i	1.19849	+	0.464298i	0.322474	+	0.946578i	$0.395485\pi$
$60$	5.58560	+	5.09195i	0.721098	+	0.657368i
$61$	3.42843	−	0.640885i	0.438966	−	0.0820569i	0.0403725	−	0.999185i	$-0.487146\pi$
$61$	3.42843	−	0.640885i	0.438966	−	0.0820569i	0.398593	+	0.917128i	$0.369498\pi$
$62$	−1.37117	+	14.7973i	−0.174139	+	1.87926i
$63$	−0.00495380	+	0.0174108i	−0.000624120	+	0.00219355i
$64$	−8.16871	−	7.44677i	−1.02109	−	0.930846i
$65$	0.580369	+	1.16554i	0.0719860	+	0.144567i
$66$	2.48833	−	2.26841i	0.306292	−	0.279222i
$67$	−14.8159	−	5.73972i	−1.81005	−	0.701218i	−0.992025	−	0.126039i	$-0.959774\pi$
$67$	−14.8159	−	5.73972i	−1.81005	−	0.701218i	−0.818027	−	0.575179i	$-0.804932\pi$
$68$	0.545889	+	1.09629i	0.0661988	+	0.132945i
$69$	−5.57175	+	11.1896i	−0.670760	+	1.34707i
$70$	10.9833	+	2.05313i	1.31275	+	0.245396i
$71$	0.322095	−	3.47595i	0.0382256	−	0.412520i	−0.955024	−	0.296527i	$-0.904172\pi$
$71$	0.322095	−	3.47595i	0.0382256	−	0.412520i	0.993250	−	0.115993i	$-0.0370050\pi$
$72$	−0.00481822	+	0.00298331i	−0.000567833	+	0.000351587i
$73$	−0.137321	+	1.48193i	−0.0160722	+	0.173446i	−0.999987	−	0.00519452i	$-0.998347\pi$
$73$	−0.137321	+	1.48193i	−0.0160722	+	0.173446i	0.983914	+	0.178641i	$0.0571701\pi$
$74$	−2.05872	−	22.2171i	−0.239321	−	2.58269i
$75$	−1.89203	−	2.50545i	−0.218473	−	0.289305i
$76$	0.0710498	+	0.0132815i	0.00814997	+	0.00152349i
$77$	0.748747	−	2.63157i	0.0853277	−	0.299896i
$78$	−2.61861	+	0.489503i	−0.296499	+	0.0554253i
$79$	−0.00741842	−	0.0800575i	−0.000834638	−	0.00900718i	0.995307	−	0.0967710i	$-0.0308514\pi$
$79$	−0.00741842	−	0.0800575i	−0.000834638	−	0.00900718i	−0.996141	+	0.0877638i	$0.972028\pi$
$80$	−3.14612	−	4.16613i	−0.351747	−	0.465788i
$81$	2.46796	+	8.67399i	0.274218	+	0.963776i
$82$	−8.04038	−	7.32978i	−0.887912	−	0.809439i
$83$	−0.288703	+	0.111844i	−0.0316893	+	0.0122765i	−0.377034	−	0.926199i	$-0.623056\pi$
$83$	−0.288703	+	0.111844i	−0.0316893	+	0.0122765i	0.345345	+	0.938476i	$0.387762\pi$
$84$	−5.60100	+	11.2483i	−0.611119	+	1.22729i
$85$	0.245190	+	0.861753i	0.0265946	+	0.0934702i
$86$	−15.5660	+	2.90978i	−1.67852	+	0.313770i
$87$	14.8250	−	9.17924i	1.58940	−	0.984117i
$88$	0.728255	−	0.450916i	0.0776322	−	0.0480678i
$89$	2.76025	−	9.70126i	0.292585	−	1.02833i	−0.666568	−	0.745444i	$-0.732237\pi$
$89$	2.76025	−	9.70126i	0.292585	−	1.02833i	0.959153	−	0.282887i	$-0.0912921\pi$
$90$	−0.0213962	+	0.00828892i	−0.00225535	+	0.000873729i
$91$	−1.59970	+	1.45832i	−0.167695	+	0.152874i
$92$	−10.6058	+	14.0443i	−1.10573	+	1.46422i
$93$	−10.3951	−	6.43635i	−1.07792	−	0.667419i
$94$	−14.1674	+	18.7607i	−1.46126	+	1.93502i
$95$	0.0493082	+	0.0191021i	0.00505892	+	0.00195983i
$96$	12.9655	−	5.02285i	1.32328	−	0.512643i
$97$	8.89122	+	1.66206i	0.902766	+	0.168756i	0.614614	−	0.788828i	$-0.289312\pi$
$97$	8.89122	+	1.66206i	0.902766	+	0.168756i	0.288153	+	0.957584i	$0.406959\pi$
$98$	0.352875	+	3.80813i	0.0356458	+	0.384679i
$99$	0.00153761	+	0.00540413i	0.000154535	+	0.000543136i
$100$	−1.97029	−	3.95688i	−0.197029	−	0.395688i
$101$	1.81329	−	2.40118i	0.180429	−	0.238927i	−0.698810	−	0.715307i	$-0.746287\pi$
$101$	1.81329	−	2.40118i	0.180429	−	0.238927i	0.879239	+	0.476381i	$0.158052\pi$
$102$	−1.83312			−0.181506
$103$	−2.62365	+	9.80390i	−0.258516	+	0.966007i
$103$	−2.62365	+	9.80390i	−0.258516	+	0.966007i
$104$	−0.677679			−0.0664519
$105$	−5.53990	+	7.33601i	−0.540639	+	0.715921i
$106$	0.635827	+	1.27691i	0.0617569	+	0.124025i
$107$	−1.91028	−	6.71394i	−0.184674	−	0.649061i	−0.997759	−	0.0669156i	$-0.978684\pi$
$107$	−1.91028	−	6.71394i	−0.184674	−	0.649061i	0.813085	−	0.582145i	$-0.197786\pi$
$108$	1.16915	+	12.6171i	0.112502	+	1.21408i
$109$	5.11940	+	0.956982i	0.490350	+	0.0916623i	0.423117	−	0.906075i	$-0.360936\pi$
$109$	5.11940	+	0.956982i	0.490350	+	0.0916623i	0.0672329	+	0.997737i	$0.478583\pi$
$110$	3.23395	−	1.25284i	0.308345	−	0.119453i
$111$	17.1174	+	6.63132i	1.62471	+	0.629417i
$112$	5.23047	−	6.92626i	0.494233	−	0.654470i
$113$	−0.181516	−	0.112390i	−0.0170756	−	0.0105728i	0.517868	−	0.855461i	$-0.326726\pi$
$113$	−0.181516	−	0.112390i	−0.0170756	−	0.0105728i	−0.534943	+	0.844888i	$0.679667\pi$
$114$	−0.0651992	+	0.0863376i	−0.00610646	+	0.00808626i
$115$	−9.51481	+	8.67389i	−0.887260	+	0.808845i
$116$	22.8916	−	8.86827i	2.12544	−	0.823398i
$117$	0.00121651	−	0.00427560i	0.000112467	−	0.000395279i
$118$	−17.6888	+	10.9524i	−1.62838	+	1.00825i
$119$	−1.26643	+	0.784141i	−0.116094	+	0.0718821i
$120$	−2.82894	+	0.528820i	−0.258246	+	0.0482745i
$121$	2.77789	+	9.76327i	0.252535	+	0.887570i
$122$	−3.27625	+	6.57960i	−0.296618	+	0.595689i
$123$	8.34682	−	3.23358i	0.752608	−	0.291562i
$124$	−12.7211	−	11.5968i	−1.14239	−	1.04142i
$125$	−3.32855	−	11.6986i	−0.297715	−	1.04636i
$126$	−0.0229890	−	0.0304423i	−0.00204802	−	0.00271202i
$127$	−0.655899	−	7.07828i	−0.0582016	−	0.628096i	−0.974014	−	0.226489i	$-0.927275\pi$
$127$	−0.655899	−	7.07828i	−0.0582016	−	0.628096i	0.915812	−	0.401607i	$-0.131548\pi$
$128$	7.13150	−	1.33311i	0.630341	−	0.117831i
$129$	3.56540	−	12.5311i	0.313916	−	1.10330i
$130$	−2.69718	−	0.504190i	−0.236558	−	0.0442204i
$131$	10.5900	+	14.0234i	0.925251	+	1.22523i	0.974029	+	0.226421i	$0.0727026\pi$
$131$	10.5900	+	14.0234i	0.925251	+	1.22523i	−0.0487780	+	0.998810i	$0.515533\pi$
$132$	0.359870	+	3.88362i	0.0313227	+	0.338026i
$133$	−0.00811151	+	0.0875371i	−0.000703357	+	0.00759043i
$134$	28.4686	−	17.6270i	2.45931	−	1.52274i
$135$	−0.855327	+	9.23045i	−0.0736149	+	0.794431i
$136$	−0.458382	−	0.0856865i	−0.0393060	−	0.00734756i
$137$	−2.27328	+	4.56536i	−0.194219	+	0.390045i	−0.970771	−	0.240009i	$-0.922850\pi$
$137$	−2.27328	+	4.56536i	−0.194219	+	0.390045i	0.776551	+	0.630054i	$0.216967\pi$
$138$	−11.7418	−	23.5807i	−0.999529	−	2.00732i
$139$	−5.54399	−	2.14775i	−0.470235	−	0.182170i	0.114452	−	0.993429i	$-0.463489\pi$
$139$	−5.54399	−	2.14775i	−0.470235	−	0.182170i	−0.584687	+	0.811259i	$0.698783\pi$
$140$	−9.56476	+	8.71943i	−0.808370	+	0.736927i
$141$	−8.62134	−	17.3140i	−0.726047	−	1.45810i
$142$	5.43655	+	4.95607i	0.456225	+	0.415904i
$143$	−0.183871	+	0.646240i	−0.0153761	+	0.0540413i
$144$	−0.00164456	+	0.0177476i	−0.000137047	+	0.00147897i
$145$	17.6541	−	3.30012i	1.46609	−	0.274060i
$146$	−2.31780	−	2.11296i	−0.191823	−	0.174869i
$147$	−2.93402	−	1.13664i	−0.241994	−	0.0937488i
$148$	21.9740	+	13.6057i	1.80625	+	1.11838i
$149$	−18.0009			−1.47469			−0.737344	−	0.675518i	$-0.763920\pi$
$149$	−18.0009			−1.47469			−0.737344	+	0.675518i	$0.763920\pi$
$150$	6.61633			0.540221
$151$	−13.1637	−	8.15062i	−1.07125	−	0.663288i	−0.126792	−	0.991929i	$-0.540468\pi$
$151$	−13.1637	−	8.15062i	−1.07125	−	0.663288i	−0.944455	+	0.328641i	$0.893409\pi$
$152$	−0.0203392	+	0.0185416i	−0.00164972	+	0.00150392i
$153$	0.00136346	−	0.00273820i	0.000110229	−	0.000221370i
$154$	3.47469	+	4.60124i	0.279999	+	0.370778i
$155$	−7.58910	−	10.0496i	−0.609572	−	0.807203i
$156$	1.37545	−	2.76227i	0.110124	−	0.221159i
$157$	−6.41416	+	5.84728i	−0.511906	+	0.466664i	−0.887951	−	0.459937i	$-0.847872\pi$
$157$	−6.41416	+	5.84728i	−0.511906	+	0.466664i	0.376045	+	0.926601i	$0.377284\pi$
$158$	0.144056	+	0.0891958i	0.0114605	+	0.00709604i
$159$	−1.17359			−0.0930718
$160$	14.3216			1.13222
$161$	−18.1989	−	11.2683i	−1.43428	−	0.888066i
$162$	−17.7215	−	6.86536i	−1.39234	−	0.539394i
$163$	11.0162	+	10.0426i	0.862854	+	0.786595i	0.978403	−	0.206707i	$-0.0662746\pi$
$163$	11.0162	+	10.0426i	0.862854	+	0.786595i	−0.115549	+	0.993302i	$0.536863\pi$
$164$	12.3881	−	2.31573i	0.967346	−	0.180828i
$165$	−0.263274	+	2.84118i	−0.0204959	+	0.221185i
$166$	0.178556	−	0.627560i	0.0138586	−	0.0487081i
$167$	−4.91535	−	4.48093i	−0.380361	−	0.346745i	0.460825	−	0.887491i	$-0.347554\pi$
$167$	−4.91535	−	4.48093i	−0.380361	−	0.346745i	−0.841186	+	0.540746i	$0.818142\pi$
$168$	−2.13269	−	4.28302i	−0.164541	−	0.330442i
$169$	−9.21427	+	8.39992i	−0.708790	+	0.646148i
$170$	−1.76062	−	0.682068i	−0.135033	−	0.0523122i
$171$	−8.04710e−5	0	0.000161608i	−6.15377e−6	0	1.23584e-5i
$172$	8.17615	−	16.4199i	0.623426	−	1.25201i
$173$	22.9724	+	4.29429i	1.74656	+	0.326489i	0.957632	−	0.287994i	$-0.0929883\pi$
$173$	22.9724	+	4.29429i	1.74656	+	0.326489i	0.788930	+	0.614483i	$0.210635\pi$
$174$	−3.39047	+	36.5890i	−0.257031	+	2.77381i
$175$	4.57097	−	2.83022i	0.345533	−	0.213945i
$176$	0.248569	−	2.68248i	0.0187366	−	0.202200i
$177$	−1.57935	−	17.0439i	−0.118711	−	1.28110i
$178$	12.8094	+	16.9624i	0.960106	+	1.27139i
$179$	15.4145	+	2.88147i	1.15213	+	0.215371i	0.724955	−	0.688796i	$-0.241860\pi$
$179$	15.4145	+	2.88147i	1.15213	+	0.215371i	0.427179	+	0.904167i	$0.359507\pi$
$180$	0.00727363	−	0.0255642i	0.000542144	−	0.00190544i
$181$	−13.2843	+	2.48326i	−0.987412	+	0.184579i	−0.652597	−	0.757705i	$-0.726321\pi$
$181$	−13.2843	+	2.48326i	−0.987412	+	0.184579i	−0.334814	+	0.942284i	$0.608674\pi$
$182$	−0.420907	−	4.54231i	−0.0311997	−	0.336698i
$183$	−3.64426	−	4.82578i	−0.269392	−	0.356732i
$184$	−1.83386	−	6.44535i	−0.135194	−	0.475158i
$185$	13.9730	+	12.7381i	1.02732	+	0.936524i
$186$	24.0257	−	9.30762i	1.76165	−	0.682468i
$187$	−0.206082	+	0.413868i	−0.0150702	+	0.0302650i
$188$	−7.45225	−	26.1919i	−0.543511	−	1.91024i
$189$	−15.1491	+	2.83186i	−1.10193	+	0.205987i
$190$	−0.0947451	+	0.0586637i	−0.00687353	+	0.00425591i
$191$	−9.58894	+	5.93722i	−0.693832	+	0.429602i	−0.827531	−	0.561420i	$-0.810255\pi$
$191$	−9.58894	+	5.93722i	−0.693832	+	0.429602i	0.133700	+	0.991022i	$0.457314\pi$
$192$	−5.24471	+	18.4332i	−0.378504	+	1.33031i
$193$	6.07365	−	2.35294i	0.437191	−	0.169369i	−0.132580	−	0.991172i	$-0.542326\pi$
$193$	6.07365	−	2.35294i	0.437191	−	0.169369i	0.569771	+	0.821804i	$0.307032\pi$
$194$	−14.0868	+	12.8418i	−1.01137	+	0.921989i
$195$	1.36044	−	1.80152i	0.0974233	−	0.129009i
$196$	−3.76646	−	2.33209i	−0.269033	−	0.166578i
$197$	−3.11759	+	4.12836i	−0.222119	+	0.294133i	−0.895408	−	0.445246i	$-0.853116\pi$
$197$	−3.11759	+	4.12836i	−0.222119	+	0.294133i	0.673289	+	0.739379i	$0.264881\pi$
$198$	−0.0110410	−	0.00427731i	−0.000784651	−	0.000303975i
$199$	3.14369	−	1.21787i	0.222850	−	0.0863326i	−0.247228	−	0.968957i	$-0.579520\pi$
$199$	3.14369	−	1.21787i	0.222850	−	0.0863326i	0.470078	+	0.882625i	$0.344226\pi$
$200$	1.65445	+	0.309271i	0.116987	+	0.0218687i
$201$	2.54183	+	27.4307i	0.179287	+	1.93482i
$202$	1.73529	+	6.09891i	0.122095	+	0.429118i
$203$	13.3091	+	26.7283i	0.934115	+	1.87596i
$204$	1.27962	−	1.69449i	0.0895911	−	0.118638i
$205$	9.21986			0.643943
$206$	−13.1555	−	16.8630i	−0.916587	−	1.17490i
$207$	0.0439568			0.00305521
$208$	−1.28445	+	1.70089i	−0.0890609	+	0.117936i
$209$	0.0121629	+	0.0244264i	0.000841324	+	0.00168961i
$210$	−5.30160	−	18.6332i	−0.365845	−	1.28581i
$211$	0.356636	+	3.84872i	0.0245519	+	0.264957i	0.999158	+	0.0410303i	$0.0130640\pi$
$211$	0.356636	+	3.84872i	0.0245519	+	0.264957i	−0.974606	+	0.223926i	$0.928112\pi$
$212$	−1.62418	−	0.303613i	−0.111549	−	0.0208522i
$213$	−5.64375	+	2.18640i	−0.386704	+	0.149810i
$214$	13.7170	+	5.31400i	0.937677	+	0.363258i
$215$	8.08696	−	10.7089i	0.551526	−	0.730338i
$216$	−4.10213	−	2.53993i	−0.279114	−	0.172820i
$217$	12.6170	−	16.7076i	0.856498	−	1.13419i
$218$	−8.11093	+	7.39409i	−0.549342	+	0.500791i
$219$	2.40614	−	0.932143i	0.162592	−	0.0629884i
$220$	−1.09938	+	3.86392i	−0.0741202	+	0.260506i
$221$	0.311000	−	0.192563i	0.0209201	−	0.0129532i
$222$	−32.8909	+	20.3652i	−2.20749	+	1.36682i
$223$	−2.95746	+	0.552845i	−0.198046	+	0.0370212i	−0.281838	−	0.959462i	$-0.590944\pi$
$223$	−2.95746	+	0.552845i	−0.198046	+	0.0370212i	0.0837917	+	0.996483i	$0.473297\pi$
$224$	6.51588	+	22.9009i	0.435361	+	1.53013i
$225$	−0.00492117	+	0.00988305i	−0.000328078	+	0.000658870i
$226$	0.419531	−	0.162527i	0.0279068	−	0.0108112i
$227$	−7.71644	−	7.03447i	−0.512158	−	0.466894i	0.375877	−	0.926670i	$-0.377342\pi$
$227$	−7.71644	−	7.03447i	−0.512158	−	0.466894i	−0.888035	+	0.459776i	$0.847930\pi$
$228$	−0.0342956	−	0.120537i	−0.00227128	−	0.00798274i
$229$	−13.6434	−	18.0668i	−0.901583	−	1.19389i	−0.980404	−	0.197000i	$-0.936880\pi$
$229$	−13.6434	−	18.0668i	−0.901583	−	1.19389i	0.0788208	−	0.996889i	$-0.474885\pi$
$230$	−2.50349	−	27.0170i	−0.165075	−	1.78145i
$231$	−4.66297	+	0.871660i	−0.306801	+	0.0573510i
$232$	−2.55811	+	8.99082i	−0.167948	+	0.590276i
$233$	14.0376	+	2.62407i	0.919631	+	0.171909i	0.622221	−	0.782841i	$-0.286230\pi$
$233$	14.0376	+	2.62407i	0.919631	+	0.171909i	0.297409	+	0.954750i	$0.403877\pi$
$234$	0.00564544	+	0.00747577i	0.000369054	+	0.000488707i
$235$	−1.83817	−	19.8370i	−0.119909	−	1.29403i
$236$	2.22360	−	23.9964i	0.144744	−	1.56203i
$237$	−0.118520	+	0.0733842i	−0.00769868	+	0.00476682i
$238$	0.289633	−	3.12564i	0.0187741	−	0.202605i
$239$	−26.2995	−	4.91623i	−1.70117	−	0.318005i	−0.758489	−	0.651686i	$-0.774062\pi$
$239$	−26.2995	−	4.91623i	−1.70117	−	0.318005i	−0.942686	+	0.333681i	$0.891709\pi$
$240$	−4.03462	+	8.10261i	−0.260433	+	0.523021i
$241$	−3.65360	−	7.33742i	−0.235349	−	0.472645i	0.745731	−	0.666247i	$-0.232100\pi$
$241$	−3.65360	−	7.33742i	−0.235349	−	0.472645i	−0.981080	+	0.193602i	$0.937983\pi$
$242$	−19.9470	−	7.72752i	−1.28224	−	0.496744i
$243$	0.0468250	−	0.0426866i	0.00300382	−	0.00273835i
$244$	−3.79501	−	7.62140i	−0.242950	−	0.487910i
$245$	−2.39505	−	2.18338i	−0.153014	−	0.139491i
$246$	−5.16232	+	18.1437i	−0.329137	+	1.15680i
$247$	0.00199196	−	0.0214966i	0.000126745	−	0.00136780i
$248$	6.44285	−	1.20438i	0.409121	−	0.0764780i
$249$	0.396704	+	0.361644i	0.0251401	+	0.0229182i
$250$	23.9011	+	9.25934i	1.51164	+	0.585612i
$251$	0.349495	+	0.216398i	0.0220599	+	0.0136589i	0.537418	−	0.843316i	$-0.319400\pi$
$251$	0.349495	+	0.216398i	0.0220599	+	0.0136589i	−0.515358	+	0.856975i	$0.672341\pi$
$252$	0.0441876			0.00278356
$253$	−6.64390			−0.417699
$254$	12.7367	+	7.88624i	0.799172	+	0.494827i
$255$	1.14799	−	1.04653i	0.0718898	−	0.0655362i
$256$	3.03909	−	6.10331i	0.189943	−	0.381457i
$257$	9.17959	+	12.1557i	0.572607	+	0.758254i	0.988510	−	0.151155i	$-0.0482991\pi$
$257$	9.17959	+	12.1557i	0.572607	+	0.758254i	−0.415903	+	0.909409i	$0.636534\pi$
$258$	16.5459	+	21.9103i	1.03010	+	1.36407i
$259$	−14.0116	+	28.1390i	−0.870636	+	1.74847i
$260$	2.34883	−	2.14125i	0.145669	−	0.132794i
$261$	−0.0521325	−	0.0322791i	−0.00322692	−	0.00199803i
$262$	−37.0326			−2.28788
$263$	−2.09769			−0.129349			−0.0646747	−	0.997906i	$-0.520601\pi$
$263$	−2.09769			−0.129349			−0.0646747	+	0.997906i	$0.520601\pi$
$264$	−1.26266	−	0.781803i	−0.0777111	−	0.0481167i
$265$	−1.12718	−	0.436670i	−0.0692419	−	0.0268244i
$266$	−0.136912	−	0.124812i	−0.00839462	−	0.00765271i
$267$	−17.1900	+	3.21336i	−1.05201	+	0.196654i
$268$	−3.57869	+	38.6202i	−0.218603	+	2.35910i
$269$	2.07844	−	7.30497i	0.126725	−	0.445392i	−0.872327	−	0.488923i	$-0.837390\pi$
$269$	2.07844	−	7.30497i	0.126725	−	0.445392i	0.999052	+	0.0435306i	$0.0138606\pi$
$270$	−14.4369	−	13.1609i	−0.878599	−	0.800949i
$271$	−8.04381	−	16.1542i	−0.488627	−	0.981295i	−0.993034	−	0.117829i	$-0.962407\pi$
$271$	−8.04381	−	16.1542i	−0.488627	−	0.981295i	0.504407	−	0.863466i	$-0.331711\pi$
$272$	−1.08387	+	0.988076i	−0.0657191	+	0.0599109i
$273$	3.49967	+	1.35578i	0.211810	+	0.0820556i
$274$	−4.79066	−	9.62095i	−0.289415	−	0.581223i
$275$	0.743816	−	1.49378i	0.0448538	−	0.0900786i
$276$	29.9938	+	5.60681i	1.80541	+	0.337490i
$277$	2.22255	−	23.9851i	0.133540	−	1.44113i	−0.620452	−	0.784244i	$-0.713051\pi$
$277$	2.22255	−	23.9851i	0.133540	−	1.44113i	0.753992	−	0.656883i	$-0.228126\pi$
$278$	10.6527	−	6.59587i	0.638907	−	0.395594i
$279$	−0.00396703	+	0.0428111i	−0.000237500	+	0.00256303i
$280$	−0.454715	−	4.90716i	−0.0271744	−	0.293259i
$281$	1.11590	+	1.47770i	0.0665693	+	0.0881520i	0.830084	−	0.557639i	$-0.188293\pi$
$281$	1.11590	+	1.47770i	0.0665693	+	0.0881520i	−0.763514	+	0.645791i	$0.776528\pi$
$282$	40.0663	+	7.48969i	2.38591	+	0.446005i
$283$	4.19069	−	14.7288i	0.249111	−	0.875534i	−0.731872	−	0.681442i	$-0.761353\pi$
$283$	4.19069	−	14.7288i	0.249111	−	0.875534i	0.980983	−	0.194092i	$-0.0621761\pi$
$284$	−8.37627	+	1.56580i	−0.497040	+	0.0929129i
$285$	−0.00845936	−	0.0912911i	−0.000501090	−	0.00540762i
$286$	−0.853286	−	1.12993i	−0.0504559	−	0.0668144i
$287$	4.19475	+	14.7430i	0.247608	+	0.870252i
$288$	−0.0361341	−	0.0329406i	−0.00212922	−	0.00194104i
$289$	−15.6173	+	6.05018i	−0.918666	+	0.355893i
$290$	−16.8704	+	33.8804i	−0.990666	+	1.98953i
$291$	−4.29178	−	15.0840i	−0.251588	−	0.884242i
$292$	3.57111	−	0.667556i	0.208983	−	0.0390658i
$293$	22.4736	−	13.9151i	1.31292	−	0.812927i	0.321919	−	0.946767i	$-0.395672\pi$
$293$	22.4736	−	13.9151i	1.31292	−	0.812927i	0.991003	+	0.133840i	$0.0427309\pi$
$294$	5.63767	−	3.49070i	0.328796	−	0.203582i
$295$	4.82482	−	16.9575i	0.280912	−	0.987303i
$296$	−9.17649	+	3.55499i	−0.533373	+	0.206630i
$297$	−3.53510	+	3.22267i	−0.205128	+	0.186998i
$298$	22.8608	−	30.2725i	1.32429	−	1.75364i
$299$	4.46914	+	2.76717i	0.258457	+	0.160030i
$300$	−4.61856	+	6.11596i	−0.266652	+	0.353105i
$301$	20.8033	+	8.05925i	1.19908	+	0.464527i
$302$	30.4248	−	11.7866i	1.75075	−	0.678244i
$303$	−5.12809	−	0.958607i	−0.294601	−	0.0550705i
$304$	0.00798687	+	0.0861920i	0.000458078	+	0.00494345i
$305$	−1.70455	−	5.99088i	−0.0976024	−	0.343037i
$306$	0.00287333	+	0.00577043i	0.000164257	+	0.000329873i
$307$	−9.23709	+	12.2319i	−0.527189	+	0.698111i	−0.981224	−	0.192873i	$-0.938219\pi$
$307$	−9.23709	+	12.2319i	−0.527189	+	0.698111i	0.454035	+	0.890984i	$0.349984\pi$
$308$	−6.67879			−0.380559
$309$	17.2437	−	3.50468i	0.980960	−	0.199374i
$310$	26.5387			1.50730
$311$	17.7455	−	23.4988i	1.00625	−	1.33250i	0.0638725	−	0.997958i	$-0.479655\pi$
$311$	17.7455	−	23.4988i	1.00625	−	1.33250i	0.942382	−	0.334538i	$-0.108580\pi$
$312$	0.523728	+	1.05179i	0.0296503	+	0.0595458i
$313$	7.07436	+	24.8638i	0.399866	+	1.40538i	0.856692	+	0.515828i	$0.172516\pi$
$313$	7.07436	+	24.8638i	0.399866	+	1.40538i	−0.456826	+	0.889556i	$0.651014\pi$
$314$	−1.68767	−	18.2128i	−0.0952405	−	1.02781i
$315$	0.0317764	+	0.00594003i	0.00179040	+	0.000334683i
$316$	−0.183009	+	0.0708982i	−0.0102951	+	0.00398833i
$317$	−21.1053	−	8.17623i	−1.18539	−	0.459223i	−0.313815	−	0.949484i	$-0.601607\pi$
$317$	−21.1053	−	8.17623i	−1.18539	−	0.459223i	−0.871576	+	0.490261i	$0.836901\pi$
$318$	1.49044	−	1.97366i	0.0835797	−	0.110677i
$319$	7.87963	+	4.87886i	0.441175	+	0.273164i
$320$	−11.8959	+	15.7528i	−0.665003	+	0.880606i
$321$	−8.94400	+	8.15354i	−0.499206	+	0.455086i
$322$	42.0625	−	16.2951i	2.34405	−	0.908090i
$323$	0.00406542	−	0.0142885i	0.000226206	−	0.000795031i
$324$	18.7168	−	11.5889i	1.03982	−	0.643829i
$325$	−1.12250	+	0.695022i	−0.0622651	+	0.0385529i
$326$	−30.8792	+	5.77233i	−1.71024	+	0.319700i
$327$	−2.47113	−	8.68512i	−0.136654	−	0.480288i
$328$	−2.13897	+	4.29562i	−0.118105	+	0.237186i
$329$	30.8841	−	11.9646i	1.70270	−	0.659628i
$330$	−4.44373	−	4.05100i	−0.244620	−	0.223000i
$331$	−3.27628	−	11.5149i	−0.180081	−	0.632917i	−0.998315	−	0.0580323i	$-0.981517\pi$
$331$	−3.27628	−	11.5149i	−0.180081	−	0.632917i	0.818234	−	0.574885i	$-0.194953\pi$
$332$	0.455458	+	0.603123i	0.0249965	+	0.0331007i
$333$	−0.00595621	−	0.0642777i	−0.000326398	−	0.00352240i
$334$	13.7781	−	2.57557i	0.753904	−	0.140929i
$335$	−7.76514	+	27.2916i	−0.424255	+	1.49110i
$336$	−14.7921	−	2.76512i	−0.806975	−	0.150850i
$337$	13.3635	+	17.6961i	0.727955	+	0.963968i	0.999999	+	0.00168331i	$0.000535815\pi$
$337$	13.3635	+	17.6961i	0.727955	+	0.963968i	−0.272044	+	0.962285i	$0.587699\pi$
$338$	−2.42442	−	26.1636i	−0.131871	−	1.42311i
$339$	−0.0341538	+	0.368579i	−0.00185498	+	0.0200184i
$340$	1.85949	−	1.15135i	0.100845	−	0.0624407i
$341$	0.599601	−	6.47072i	0.0324702	−	0.350409i
$342$	0.000373977	0	6.99083e-5i	2.02223e−5	0	3.78021e-6i
$343$	−6.86203	+	13.7808i	−0.370515	+	0.744094i
$344$	3.11323	+	6.25220i	0.167854	+	0.337096i
$345$	20.8155	+	8.06398i	1.12067	+	0.434150i
$346$	−36.3964	+	33.1797i	−1.95668	+	1.78375i
$347$	4.98306	+	10.0073i	0.267505	+	0.537222i	0.987664	−	0.156587i	$-0.0500491\pi$
$347$	4.98306	+	10.0073i	0.267505	+	0.537222i	−0.720160	+	0.693808i	$0.755931\pi$
$348$	−31.4552	−	28.6752i	−1.68617	−	1.53715i
$349$	−2.40891	+	8.46644i	−0.128946	+	0.453198i	−0.999225	−	0.0393607i	$-0.987468\pi$
$349$	−2.40891	+	8.46644i	−0.128946	+	0.453198i	0.870279	+	0.492559i	$0.163938\pi$
$350$	−1.04538	+	11.2814i	−0.0558779	+	0.603019i
$351$	3.72019	−	0.695424i	0.198569	−	0.0371190i
$352$	5.46153	+	4.97884i	0.291100	+	0.265373i
$353$	−13.3063	−	5.15488i	−0.708222	−	0.274366i	−0.0199307	−	0.999801i	$-0.506345\pi$
$353$	−13.3063	−	5.15488i	−0.708222	−	0.274366i	−0.688291	+	0.725435i	$0.741639\pi$
$354$	30.6690	+	18.9894i	1.63004	+	1.00928i
$355$	−6.23406			−0.330870
$356$	−24.6212			−1.30492
$357$	2.19575	+	1.35955i	0.116211	+	0.0719551i
$358$	−24.4220	+	22.2636i	−1.29074	+	1.17667i
$359$	−16.0255	+	32.1835i	−0.845793	+	1.69858i	−0.140015	+	0.990149i	$0.544715\pi$
$359$	−16.0255	+	32.1835i	−0.845793	+	1.69858i	−0.705779	+	0.708433i	$0.749403\pi$
$360$	0.00609889	+	0.00807624i	0.000321440	+	0.000425655i
$361$	11.4495	+	15.1616i	0.602607	+	0.797980i
$362$	12.6946	−	25.4942i	0.667214	−	1.33995i
$363$	13.0062	−	11.8567i	0.682648	−	0.622316i
$364$	4.49260	+	2.78170i	0.235476	+	0.145801i
$365$	2.65781			0.139116
$366$	12.7438			0.666129
$367$	−9.05754	−	5.60819i	−0.472800	−	0.292745i	0.269274	−	0.963064i	$-0.413216\pi$
$367$	−9.05754	−	5.60819i	−0.472800	−	0.292745i	−0.742074	+	0.670318i	$0.766158\pi$
$368$	−19.6529	−	7.61357i	−1.02448	−	0.396885i
$369$	−0.0232622	−	0.0212063i	−0.00121098	−	0.00110395i
$370$	−39.1675	+	7.32168i	−2.03622	+	0.380636i
$371$	0.185427	−	2.00108i	0.00962691	−	0.103891i
$372$	−8.16755	+	28.7060i	−0.423468	+	1.48834i
$373$	−12.8297	−	11.6958i	−0.664295	−	0.605585i	0.269668	−	0.962953i	$-0.413086\pi$
$373$	−12.8297	−	11.6958i	−0.664295	−	0.605585i	−0.933964	+	0.357368i	$0.883674\pi$
$374$	−0.434293	−	0.872177i	−0.0224567	−	0.0450992i
$375$	−15.5844	+	14.2071i	−0.804775	+	0.733649i
$376$	9.66872	+	3.74568i	0.498626	+	0.193169i
$377$	−3.26834	−	6.56370i	−0.168328	−	0.338048i
$378$	14.4767	−	29.0731i	0.744599	−	1.49536i
$379$	−7.97170	−	1.49017i	−0.409478	−	0.0765448i	−0.0250197	−	0.999687i	$-0.507965\pi$
$379$	−7.97170	−	1.49017i	−0.409478	−	0.0765448i	−0.384459	+	0.923142i	$0.625612\pi$
$380$	0.0119101	−	0.128530i	0.000610974	−	0.00659346i
$381$	−10.4789	+	6.48826i	−0.536850	+	0.332404i
$382$	2.19299	−	23.6662i	0.112203	−	1.21087i
$383$	2.84670	+	30.7208i	0.145460	+	1.56976i	0.685469	+	0.728102i	$0.259597\pi$
$383$	2.84670	+	30.7208i	0.145460	+	1.56976i	−0.540009	+	0.841659i	$0.681579\pi$
$384$	−7.58044	−	10.0381i	−0.386838	−	0.512256i
$385$	−4.80287	−	0.897813i	−0.244777	−	0.0457568i
$386$	−3.75641	+	13.2024i	−0.191196	+	0.671985i
$387$	−0.0450349	+	0.00841847i	−0.00228925	+	0.000427935i
$388$	−2.03728	−	21.9858i	−0.103427	−	1.11616i
$389$	−13.8593	−	18.3527i	−0.702695	−	0.930518i	0.297009	−	0.954875i	$-0.404011\pi$
$389$	−13.8593	−	18.3527i	−0.702695	−	0.930518i	−0.999703	+	0.0243566i	$0.992246\pi$
$390$	1.30192	+	4.57579i	0.0659254	+	0.231704i
$391$	2.67304	+	2.43680i	0.135181	+	0.123234i
$392$	1.57290	−	0.609345i	0.0794435	−	0.0307766i
$393$	13.5807	−	27.2738i	0.685057	−	1.37578i
$394$	−2.98349	−	10.4859i	−0.150306	−	0.528270i
$395$	−0.141137	+	0.0263831i	−0.00710137	+	0.00132748i
$396$	0.0116611	−	0.00722022i	0.000585990	−	0.000362830i
$397$	28.7215	−	17.7836i	1.44149	−	0.892533i	0.441501	−	0.897261i	$-0.354446\pi$
$397$	28.7215	−	17.7836i	1.44149	−	0.892533i	0.999989	+	0.00472751i	$0.00150482\pi$
$398$	−1.94430	+	6.83350i	−0.0974589	+	0.342532i
$399$	0.142130	−	0.0550615i	0.00711541	−	0.00275652i
$400$	3.91203	−	3.56629i	0.195602	−	0.178314i
$401$	9.10334	−	12.0548i	0.454599	−	0.601986i	−0.511777	−	0.859118i	$-0.671013\pi$
$401$	9.10334	−	12.0548i	0.454599	−	0.601986i	0.966376	+	0.257132i	$0.0827775\pi$
$402$	−49.3591	−	30.5619i	−2.46181	−	1.52429i
$403$	−3.09838	+	4.10291i	−0.154341	+	0.204381i
$404$	−6.84900	−	2.65332i	−0.340750	−	0.132007i
$405$	15.0175	−	5.81783i	0.746227	−	0.289090i
$406$	−61.8520	−	11.5621i	−3.06966	−	0.573819i
$407$	0.900258	+	9.71533i	0.0446241	+	0.481571i
$408$	0.221260	+	0.777650i	0.0109540	+	0.0384994i
$409$	−10.1321	−	20.3480i	−0.501000	−	1.00614i	−0.990930	−	0.134381i	$-0.957095\pi$
$409$	−10.1321	−	20.3480i	−0.501000	−	1.00614i	0.489930	−	0.871762i	$-0.337022\pi$
$410$	−11.7090	+	15.5053i	−0.578269	+	0.765751i
$411$	8.84248			0.436167
$412$	24.7710	−	0.389272i	1.22038	−	0.0191781i
$413$	29.3110			1.44230
$414$	−0.0558244	+	0.0739234i	−0.00274362	+	0.00363314i
$415$	0.246454	+	0.494946i	0.0120980	+	0.0242960i
$416$	−1.60012	−	5.62382i	−0.0784521	−	0.275731i
$417$	0.951132	+	10.2644i	0.0465771	+	0.502647i
$418$	−0.0565251	−	0.0105664i	−0.00276473	−	0.000516818i
$419$	−2.64949	+	1.02642i	−0.129436	+	0.0501437i	−0.425089	−	0.905152i	$-0.639757\pi$
$419$	−2.64949	+	1.02642i	−0.129436	+	0.0501437i	0.295653	+	0.955296i	$0.404463\pi$
$420$	20.9248	+	8.10632i	1.02103	+	0.395548i
$421$	−20.0929	+	26.6073i	−0.979267	+	1.29676i	−0.0244074	+	0.999702i	$0.507770\pi$
$421$	−20.0929	+	26.6073i	−0.979267	+	1.29676i	−0.954860	+	0.297057i	$0.903995\pi$
$422$	−6.92542	−	4.28804i	−0.337124	−	0.208738i
$423$	−0.0409887	+	0.0542777i	−0.00199294	+	0.00263907i
$424$	0.464949	−	0.423857i	0.0225799	−	0.0205843i
$425$	−0.847138	+	0.328183i	−0.0410922	+	0.0159192i
$426$	3.49053	−	12.2679i	0.169117	−	0.594384i
$427$	8.80420	−	5.45133i	0.426065	−	0.263808i
$428$	−14.4874	+	8.97019i	−0.700273	+	0.433590i
$429$	1.14509	−	0.214055i	0.0552856	−	0.0103347i
$430$	7.73910	+	27.2001i	0.373213	+	1.31171i
$431$	−6.45815	+	12.9697i	−0.311078	+	0.624729i	−0.994435	−	0.105356i	$-0.966402\pi$
$431$	−6.45815	+	12.9697i	−0.311078	+	0.624729i	0.683357	+	0.730085i	$0.260519\pi$
$432$	−14.1500	+	5.48173i	−0.680791	+	0.263740i
$433$	7.06247	+	6.43829i	0.339401	+	0.309405i	0.825393	−	0.564558i	$-0.190954\pi$
$433$	7.06247	+	6.43829i	0.339401	+	0.309405i	−0.485992	+	0.873963i	$0.661542\pi$
$434$	12.0743	+	42.4367i	0.579584	+	2.03703i
$435$	−18.7654	−	24.8494i	−0.899734	−	1.19144i
$436$	−1.17303	−	12.6590i	−0.0561779	−	0.606256i
$437$	0.209843	−	0.0392265i	0.0100382	−	0.00187646i
$438$	−1.48814	+	5.23028i	−0.0711062	+	0.249912i
$439$	−7.06141	−	1.32001i	−0.337023	−	0.0630004i	0.0125180	−	0.999922i	$-0.496015\pi$
$439$	−7.06141	−	1.32001i	−0.337023	−	0.0630004i	−0.349541	+	0.936921i	$0.613662\pi$
$440$	−0.921824	−	1.22069i	−0.0439462	−	0.0581942i
$441$	0.00102093	+	0.0110176i	4.86155e−5	+	0.000524645i
$442$	−0.0711256	+	0.767568i	−0.00338310	+	0.0365095i
$443$	0.100869	−	0.0624557i	0.00479245	−	0.00296736i	−0.524034	−	0.851697i	$-0.675573\pi$
$443$	0.100869	−	0.0624557i	0.00479245	−	0.00296736i	0.528826	+	0.848730i	$0.322632\pi$
$444$	4.13460	−	44.6194i	0.196219	−	2.11754i
$445$	−17.7057	−	3.30977i	−0.839332	−	0.156898i
$446$	2.82618	−	5.67574i	0.133824	−	0.268754i
$447$	13.9115	+	27.9381i	0.657993	+	1.32143i
$448$	−30.6017	−	11.8552i	−1.44580	−	0.560104i
$449$	10.0122	−	9.12728i	0.472503	−	0.430743i	−0.402091	−	0.915600i	$-0.631716\pi$
$449$	10.0122	−	9.12728i	0.472503	−	0.430743i	0.874594	+	0.484857i	$0.161128\pi$
$450$	−0.0103708	−	0.0208274i	−0.000488884	−	0.000981811i
$451$	3.51598	+	3.20524i	0.165561	+	0.150929i
$452$	−0.142620	+	0.501256i	−0.00670827	+	0.0235771i
$453$	−2.47687	+	26.7296i	−0.116373	+	1.25587i
$454$	21.6298	−	4.04331i	1.01514	−	0.189762i
$455$	2.85680	+	2.60432i	0.133929	+	0.122092i
$456$	0.0444960	+	0.0172378i	0.00208371	+	0.000807235i
$457$	24.8974	+	15.4158i	1.16465	+	0.721121i	0.965897	−	0.258928i	$-0.0833693\pi$
$457$	24.8974	+	15.4158i	1.16465	+	0.721121i	0.198754	+	0.980049i	$0.436310\pi$
$458$	47.7103			2.22936
$459$	2.60427			0.121557
$460$	26.7214	+	16.5452i	1.24589	+	0.771422i
$461$	−13.5107	+	12.3167i	−0.629258	+	0.573645i	−0.924218	−	0.381865i	$-0.875282\pi$
$461$	−13.5107	+	12.3167i	−0.629258	+	0.573645i	0.294960	+	0.955510i	$0.404694\pi$
$462$	4.45599	−	8.94883i	0.207311	−	0.416337i
$463$	12.0019	+	15.8930i	0.557773	+	0.738611i	0.986308	−	0.164914i	$-0.0527347\pi$
$463$	12.0019	+	15.8930i	0.557773	+	0.738611i	−0.428535	+	0.903525i	$0.640970\pi$
$464$	17.7173	+	23.4615i	0.822505	+	1.08917i
$465$	−9.73235	+	19.5452i	−0.451327	+	0.906387i
$466$	−22.2404	+	20.2748i	−1.03027	+	0.939212i
$467$	16.1954	+	10.0278i	0.749434	+	0.464030i	0.847263	−	0.531173i	$-0.178249\pi$
$467$	16.1954	+	10.0278i	0.749434	+	0.464030i	−0.0978291	+	0.995203i	$0.531190\pi$
$468$	−0.0108512			−0.000501598
$469$	−47.1736			−2.17827
$470$	35.6949	+	22.1014i	1.64648	+	1.01946i
$471$	14.0323	+	5.43613i	0.646573	+	0.250484i
$472$	6.78133	+	6.18200i	0.312136	+	0.284549i
$473$	6.80684	−	1.27242i	0.312979	−	0.0585059i
$474$	0.0271054	−	0.292514i	0.00124499	−	0.0134356i
$475$	−0.0146734	+	0.0515717i	−0.000673263	+	0.00236627i
$476$	2.68708	+	2.44959i	0.123162	+	0.112277i
$477$	0.00183955	+	0.00369432i	8.42273e−5	+	0.000169151i
$478$	41.6677	−	37.9851i	1.90583	−	1.73740i
$479$	11.6464	+	4.51185i	0.532139	+	0.206152i	0.612293	−	0.790631i	$-0.290247\pi$
$479$	11.6464	+	4.51185i	0.532139	+	0.206152i	−0.0801541	+	0.996782i	$0.525541\pi$
$480$	−11.0681	−	22.2277i	−0.505187	−	1.01455i
$481$	3.44084	−	6.91014i	0.156889	−	0.315075i
$482$	16.9795	+	3.17403i	0.773397	+	0.144573i
$483$	−3.42429	+	36.9539i	−0.155810	+	1.68146i
$484$	21.0672	−	13.0443i	0.957601	−	0.592921i
$485$	1.49043	−	16.0843i	0.0676771	−	0.730353i
$486$	0.0123204	+	0.132958i	0.000558863	+	0.00603110i
$487$	−14.3272	−	18.9723i	−0.649229	−	0.859718i	0.347734	−	0.937593i	$-0.386951\pi$
$487$	−14.3272	−	18.9723i	−0.649229	−	0.859718i	−0.996963	+	0.0778753i	$0.975186\pi$
$488$	3.18666	+	0.595690i	0.144253	+	0.0269656i
$489$	7.07292	−	24.8587i	0.319849	−	1.12415i
$490$	6.71352	−	1.25497i	0.303286	−	0.0566940i
$491$	0.503906	+	5.43801i	0.0227410	+	0.245414i	0.999515	+	0.0311420i	$0.00991439\pi$
$491$	0.503906	+	5.43801i	0.0227410	+	0.245414i	−0.976774	+	0.214272i	$0.931262\pi$
$492$	−13.1679	−	17.4372i	−0.593656	−	0.786128i
$493$	−1.38078	−	4.85294i	−0.0621872	−	0.218565i
$494$	0.0336217	+	0.0306503i	0.00151271	+	0.00137902i
$495$	0.00935634	−	0.00362467i	0.000420536	−	0.000162917i
$496$	9.18875	−	18.4535i	0.412587	−	0.828587i
$497$	−2.83630	−	9.96857i	−0.127226	−	0.447152i
$498$	−1.11199	+	0.207867i	−0.0498296	+	0.00931476i
$499$	18.3801	−	11.3805i	0.822807	−	0.509461i	−0.0492951	−	0.998784i	$-0.515697\pi$
$499$	18.3801	−	11.3805i	0.822807	−	0.509461i	0.872102	+	0.489324i	$0.162756\pi$
$500$	−25.2434	+	15.6300i	−1.12892	+	0.698996i
$501$	−3.15589	+	11.0918i	−0.140995	+	0.495545i
$502$	−0.807774	+	0.312933i	−0.0360527	+	0.0139669i
$503$	−16.6911	+	15.2159i	−0.744218	+	0.678445i	−0.954169	−	0.299267i	$-0.903258\pi$
$503$	−16.6911	+	15.2159i	−0.744218	+	0.678445i	0.209951	+	0.977712i	$0.432670\pi$
$504$	−0.0101395	+	0.0134269i	−0.000451649	+	0.000598080i
$505$	−4.56860	−	2.82876i	−0.203300	−	0.125878i
$506$	8.43763	−	11.1732i	0.375099	−	0.496711i
$507$	20.1581	+	7.80928i	0.895251	+	0.346822i
$508$	−16.1807	+	6.26845i	−0.717904	+	0.278118i
$509$	−28.1850	−	5.26869i	−1.24928	−	0.233530i	−0.482759	−	0.875753i	$-0.660365\pi$
$509$	−28.1850	−	5.26869i	−1.24928	−	0.233530i	−0.766518	+	0.642223i	$0.778012\pi$
$510$	0.302054	+	3.25968i	0.0133752	+	0.144341i
$511$	1.20922	+	4.24997i	0.0534927	+	0.188008i
$512$	12.8722	+	25.8509i	0.568877	+	1.14246i
$513$	0.0926267	−	0.122658i	0.00408957	−	0.00541547i
$514$	−32.1006			−1.41589
$515$	17.8657	+	3.04997i	0.787258	+	0.134398i
$516$	−31.8032			−1.40006
$517$	6.19527	−	8.20387i	0.272468	−	0.360806i
$518$	−29.5277	−	59.2996i	−1.29737	−	2.60548i
$519$	−11.0888	−	38.9730i	−0.486743	−	1.71072i
$520$	0.111665	+	1.20506i	0.00489684	+	0.0528453i
$521$	−12.7633	−	2.38587i	−0.559169	−	0.104527i	−0.103424	−	0.994637i	$-0.532980\pi$
$521$	−12.7633	−	2.38587i	−0.559169	−	0.104527i	−0.455745	+	0.890110i	$0.650627\pi$
$522$	0.120492	−	0.0466789i	0.00527379	−	0.00204308i
$523$	−27.9725	−	10.8366i	−1.22315	−	0.473852i	−0.338883	−	0.940829i	$-0.610049\pi$
$523$	−27.9725	−	10.8366i	−1.22315	−	0.473852i	−0.884269	+	0.466977i	$0.845343\pi$
$524$	25.8508	−	34.2320i	1.12930	−	1.49543i
$525$	−7.92519	−	4.90707i	−0.345884	−	0.214162i
$526$	2.66403	−	3.52775i	0.116157	−	0.153817i
$527$	−2.61452	+	2.38345i	−0.113890	+	0.103825i
$528$	−4.35543	+	1.68730i	−0.189546	+	0.0734305i
$529$	−7.93022	+	27.8718i	−0.344792	+	1.21182i
$530$	2.16585	−	1.34104i	0.0940786	−	0.0582510i
$531$	−0.0511766	+	0.0316872i	−0.00222087	+	0.00137511i
$532$	0.210945	−	0.0394324i	0.00914562	−	0.00170961i
$533$	−1.03011	−	3.62046i	−0.0446191	−	0.156820i
$534$	16.4269	−	32.9897i	0.710863	−	1.42761i
$535$	−11.6240	+	4.50318i	−0.502551	+	0.194689i
$536$	−10.9140	−	9.94939i	−0.471412	−	0.429748i
$537$	−7.44056	−	26.1508i	−0.321084	−	1.12849i
$538$	9.64539	+	12.7726i	0.415842	+	0.550664i
$539$	−0.154309	−	1.66526i	−0.00664656	−	0.0717278i
$540$	22.2433	−	4.15800i	0.957200	−	0.178932i
$541$	2.26266	−	7.95241i	0.0972792	−	0.341901i	−0.897872	−	0.440256i	$-0.854888\pi$
$541$	2.26266	−	7.95241i	0.0972792	−	0.341901i	0.995151	+	0.0983553i	$0.0313582\pi$
$542$	37.3824	+	6.98798i	1.60571	+	0.300159i
$543$	14.1206	+	18.6986i	0.605971	+	0.802435i
$544$	−0.371236	−	4.00627i	−0.0159166	−	0.171768i
$545$	0.858165	−	9.26108i	0.0367598	−	0.396701i
$546$	−6.72457	+	4.16368i	−0.287785	+	0.178189i
$547$	2.75730	−	29.7560i	0.117894	−	1.27228i	−0.707091	−	0.707122i	$-0.749993\pi$
$547$	2.75730	−	29.7560i	0.117894	−	1.27228i	0.824985	−	0.565154i	$-0.191183\pi$
$548$	12.2375	+	2.28758i	0.522760	+	0.0977207i
$549$	−0.00947874	+	0.0190359i	−0.000404543	+	0.000812431i
$550$	1.56750	+	3.14797i	0.0668386	+	0.134230i
$551$	−0.277678	−	0.107573i	−0.0118295	−	0.00458277i
$552$	−8.58621	+	7.82736i	−0.365453	+	0.333155i
$553$	−0.106401	−	0.213682i	−0.00452462	−	0.00908666i
$554$	37.5139	+	34.1984i	1.59381	+	1.45295i
$555$	8.97137	−	31.5311i	0.380813	−	1.33842i
$556$	−1.33911	+	14.4513i	−0.0567911	+	0.612874i
$557$	−18.6814	+	3.49215i	−0.791554	+	0.147967i	−0.563974	−	0.825792i	$-0.690728\pi$
$557$	−18.6814	+	3.49215i	−0.791554	+	0.147967i	−0.227580	+	0.973759i	$0.573081\pi$
$558$	−0.0669585	−	0.0610407i	−0.00283458	−	0.00258406i
$559$	−5.10870	−	1.97912i	−0.216075	−	0.0837080i
$560$	−13.1782	−	8.15961i	−0.556881	−	0.344806i
$561$	0.801606			0.0338438
$562$	−3.90226			−0.164607
$563$	1.08624	+	0.672569i	0.0457794	+	0.0283454i	0.549131	−	0.835736i	$-0.314959\pi$
$563$	1.08624	+	0.672569i	0.0457794	+	0.0283454i	−0.503352	+	0.864082i	$0.667900\pi$
$564$	−34.8917	+	31.8080i	−1.46921	+	1.33936i
$565$	−0.169944	+	0.341293i	−0.00714959	+	0.0143583i
$566$	19.4477	+	25.7529i	0.817446	+	1.08247i
$567$	16.1355	+	21.3669i	0.677627	+	0.897324i
$568$	1.44627	−	2.90451i	0.0606843	−	0.121871i
$569$	−13.8678	+	12.6422i	−0.581368	+	0.529987i	−0.910074	−	0.414445i	$-0.863976\pi$
$569$	−13.8678	+	12.6422i	−0.581368	+	0.529987i	0.328706	+	0.944432i	$0.393387\pi$
$570$	0.164270	+	0.101712i	0.00688051	+	0.00426023i
$571$	29.9118			1.25177			0.625885	−	0.779915i	$-0.284738\pi$
$571$	29.9118			1.25177			0.625885	+	0.779915i	$0.284738\pi$
$572$	1.64012			0.0685769
$573$	16.6254	+	10.2940i	0.694536	+	0.430039i
$574$	−30.1210	−	11.6689i	−1.25722	−	0.487051i
$575$	−9.64788	−	8.79521i	−0.402344	−	0.366785i
$576$	0.0662464	−	0.0123836i	0.00276027	−	0.000515983i
$577$	1.74909	−	18.8757i	0.0728156	−	0.785806i	−0.878531	−	0.477685i	$-0.841476\pi$
$577$	1.74909	−	18.8757i	0.0728156	−	0.785806i	0.951347	−	0.308121i	$-0.0997003\pi$
$578$	9.65895	−	33.9477i	0.401759	−	1.41204i
$579$	−8.34574	−	7.60815i	−0.346837	−	0.316184i
$580$	−19.5417	−	39.2449i	−0.811423	−	1.62956i
$581$	−0.679315	+	0.619277i	−0.0281827	+	0.0256920i
$582$	30.8177	+	11.9388i	1.27744	+	0.494881i
$583$	−0.278041	−	0.558381i	−0.0115153	−	0.0231258i
$584$	−0.616600	+	1.23830i	−0.0255151	+	0.0512412i
$585$	−0.00780338	−	0.00145870i	−0.000322630	−	6.03100e-5i
$586$	−5.13971	+	55.4663i	−0.212320	+	2.29129i
$587$	−25.0377	+	15.5027i	−1.03342	+	0.639864i	−0.934768	−	0.355259i	$-0.884393\pi$
$587$	−25.0377	+	15.5027i	−1.03342	+	0.639864i	−0.0986474	+	0.995122i	$0.531452\pi$
$588$	−0.708692	+	7.64801i	−0.0292260	+	0.315399i
$589$	0.0192660	+	0.207913i	0.000793842	+	0.00856692i
$590$	22.3904	+	29.6497i	0.921800	+	1.22066i
$591$	8.81674	+	1.64813i	0.362672	+	0.0677952i
$592$	−8.47027	+	29.7699i	−0.348126	+	1.22354i
$593$	−30.3281	+	5.66930i	−1.24542	+	0.232810i	−0.764887	−	0.644164i	$-0.777205\pi$
$593$	−30.3281	+	5.66930i	−1.24542	+	0.232810i	−0.480537	+	0.876975i	$0.659558\pi$
$594$	−0.930141	−	10.0378i	−0.0381641	−	0.411857i
$595$	1.60305	+	2.12278i	0.0657185	+	0.0870254i
$596$	12.0251	+	42.2637i	0.492566	+	1.73119i
$597$	−4.31971	−	3.93794i	−0.176794	−	0.161169i
$598$	−10.3294	+	4.00161i	−0.422399	+	0.163638i
$599$	3.02913	−	6.08330i	0.123767	−	0.248557i	−0.824611	−	0.565700i	$-0.808606\pi$
$599$	3.02913	−	6.08330i	0.123767	−	0.248557i	0.948378	+	0.317143i	$0.102724\pi$
$600$	−0.798601	−	2.80679i	−0.0326028	−	0.114587i
$601$	17.3100	−	3.23579i	0.706088	−	0.131991i	0.181555	−	0.983381i	$-0.441887\pi$
$601$	17.3100	−	3.23579i	0.706088	−	0.131991i	0.524533	+	0.851390i	$0.324240\pi$
$602$	−39.9733	+	24.7504i	−1.62919	+	1.00875i
$603$	0.0823643	−	0.0509978i	0.00335413	−	0.00207679i
$604$	−10.3429	+	36.3515i	−0.420847	+	1.47912i
$605$	16.9034	−	6.54843i	0.687223	−	0.266231i
$606$	8.12470	−	7.40664i	0.330043	−	0.300874i
$607$	−12.1341	+	16.0681i	−0.492507	+	0.652185i	−0.974605	−	0.223933i	$-0.928110\pi$
$607$	−12.1341	+	16.0681i	−0.492507	+	0.652185i	0.482097	+	0.876118i	$0.339875\pi$
$608$	−0.201894	−	0.125008i	−0.00818790	−	0.00506973i
$609$	31.1978	−	41.3126i	1.26420	−	1.67407i
$610$	12.2398	+	4.74172i	0.495574	+	0.191986i
$611$	−7.58426	+	2.93816i	−0.306826	+	0.118865i
$612$	−0.00733977	−	0.00137204i	−0.000296693	−	5.54615e-5i
$613$	−4.55585	−	49.1655i	−0.184009	−	1.98578i	−0.167243	−	0.985916i	$-0.553487\pi$
$613$	−4.55585	−	49.1655i	−0.184009	−	1.98578i	−0.0167657	−	0.999859i	$-0.505337\pi$
$614$	−8.83976	−	31.0685i	−0.356744	−	1.25382i
$615$	−7.12534	−	14.3096i	−0.287322	−	0.577019i
$616$	1.53255	−	2.02942i	0.0617480	−	0.0817676i
$617$	−18.6453			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$617$	−18.6453			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$618$	−16.0053	+	33.4501i	−0.643826	+	1.34556i
$619$	−2.50213			−0.100569			−0.0502846	−	0.998735i	$-0.516013\pi$
$619$	−2.50213			−0.100569			−0.0502846	+	0.998735i	$0.516013\pi$
$620$	−18.5255	+	24.5317i	−0.744000	+	0.985215i
$621$	16.6813	+	33.5005i	0.669396	+	1.34433i
$622$	16.9822	+	59.6862i	0.680923	+	2.39320i
$623$	−2.76306	−	29.8182i	−0.110700	−	1.19464i
$624$	3.63252	+	0.679035i	0.145417	+	0.0271832i
$625$	−11.8116	+	4.57583i	−0.472463	+	0.183033i
$626$	−50.7984	−	19.6794i	−2.03031	−	0.786548i
$627$	0.0285110	−	0.0377546i	0.00113862	−	0.00150777i
$628$	18.0135	+	11.1535i	0.718817	+	0.445073i
$629$	3.20111	−	4.23896i	0.127637	−	0.169018i
$630$	−0.0503449	+	0.0458955i	−0.00200579	+	0.00182852i
$631$	28.9401	−	11.2115i	1.15209	−	0.446321i	0.291975	−	0.956426i	$-0.405688\pi$
$631$	28.9401	−	11.2115i	1.15209	−	0.446321i	0.860112	+	0.510105i	$0.170394\pi$
$632$	0.0204510	−	0.0718779i	0.000813498	−	0.00285915i
$633$	5.69776	−	3.52790i	0.226466	−	0.140222i
$634$	40.5535	−	25.1097i	1.61059	−	0.997232i
$635$	−12.4786	+	2.33266i	−0.495199	+	0.0925686i
$636$	0.783991	+	2.75544i	0.0310873	+	0.109260i
$637$	−0.589779	+	1.18444i	−0.0233679	+	0.0469291i
$638$	−18.2119	+	7.05533i	−0.721016	+	0.279323i
$639$	0.0157288	+	0.0143387i	0.000622223	+	0.000567232i
$640$	−3.54565	−	12.4617i	−0.140154	−	0.492590i
$641$	3.87600	+	5.13265i	0.153093	+	0.202728i	0.868100	−	0.496390i	$-0.165341\pi$
$641$	3.87600	+	5.13265i	0.153093	+	0.202728i	−0.715007	+	0.699117i	$0.753577\pi$
$642$	−2.35331	−	25.3962i	−0.0928776	−	1.00231i
$643$	−28.6559	+	5.35672i	−1.13008	+	0.211248i	−0.715397	−	0.698718i	$-0.753754\pi$
$643$	−28.6559	+	5.35672i	−1.13008	+	0.211248i	−0.414682	+	0.909966i	$0.636107\pi$
$644$	−14.2991	+	50.2563i	−0.563465	+	1.98038i
$645$	−22.8704	−	4.27522i	−0.900522	−	0.168337i
$646$	0.0188663	+	0.0249830i	0.000742284	+	0.000982943i
$647$	−2.82924	−	30.5324i	−0.111229	−	1.20035i	−0.850143	−	0.526552i	$-0.823484\pi$
$647$	−2.82924	−	30.5324i	−0.111229	−	1.20035i	0.738914	−	0.673800i	$-0.235339\pi$
$648$	−0.773420	+	8.34653i	−0.0303828	+	0.327883i
$649$	7.73514	−	4.78939i	0.303631	−	0.188000i
$650$	0.256716	−	2.77040i	0.0100692	−	0.108664i
$651$	−35.6817	−	6.67006i	−1.39847	−	0.261420i
$652$	16.2196	−	32.5733i	0.635208	−	1.27567i
$653$	−0.132825	−	0.266749i	−0.00519785	−	0.0104387i	0.892549	−	0.450950i	$-0.148915\pi$
$653$	−0.132825	−	0.266749i	−0.00519785	−	0.0104387i	−0.897747	+	0.440511i	$0.854797\pi$
$654$	17.7443	+	6.87417i	0.693856	+	0.268801i
$655$	23.1916	−	21.1420i	0.906172	−	0.826085i
$656$	6.72736	+	13.5104i	0.262659	+	0.527491i
$657$	−0.00670578	−	0.00611313i	−0.000261618	−	0.000238496i
$658$	−19.1011	+	67.1334i	−0.744638	+	2.61713i
$659$	−1.47519	+	15.9199i	−0.0574654	+	0.620151i	0.917491	+	0.397756i	$0.130211\pi$
$659$	−1.47519	+	15.9199i	−0.0574654	+	0.620151i	−0.974957	+	0.222395i	$0.928613\pi$
$660$	6.84660	−	1.27985i	0.266504	−	0.0498182i
$661$	−2.15823	−	1.96748i	−0.0839453	−	0.0765262i	0.630636	−	0.776079i	$-0.282794\pi$
$661$	−2.15823	−	1.96748i	−0.0839453	−	0.0765262i	−0.714581	+	0.699553i	$0.753383\pi$
$662$	23.5258	+	9.11393i	0.914355	+	0.354223i
$663$	−0.539214	−	0.333867i	−0.0209413	−	0.0129663i
$664$	−0.287777			−0.0111679
$665$	0.156996			0.00608805
$666$	0.115662	+	0.0716148i	0.00448181	+	0.00277502i
$667$	53.5824	−	48.8468i	2.07472	−	1.89136i
$668$	−7.23707	+	14.5340i	−0.280011	+	0.562337i
$669$	3.14364	+	4.16285i	0.121540	+	0.160945i
$670$	−36.0355	−	47.7187i	−1.39217	−	1.84353i
$671$	1.43267	−	2.87720i	0.0553078	−	0.111073i
$672$	30.5076	−	27.8114i	1.17686	−	1.07285i
$673$	9.20032	+	5.69660i	0.354646	+	0.219588i	0.692179	−	0.721726i	$-0.256651\pi$
$673$	9.20032	+	5.69660i	0.354646	+	0.219588i	−0.337532	+	0.941314i	$0.609592\pi$
$674$	−46.7314			−1.80003
$675$	−9.39965			−0.361793
$676$	25.8773	+	16.0226i	0.995282	+	0.616253i
$677$	20.1550	+	7.80811i	0.774621	+	0.300090i	0.715917	−	0.698185i	$-0.246009\pi$
$677$	20.1550	+	7.80811i	0.774621	+	0.300090i	0.0587045	+	0.998275i	$0.481303\pi$
$678$	−0.576474	−	0.525525i	−0.0221393	−	0.0201827i
$679$	26.3978	−	4.93460i	1.01305	−	0.189372i
$680$	−0.0768386	+	0.829220i	−0.00294662	+	0.0317991i
$681$	−4.95433	+	17.4127i	−0.189850	+	0.667255i
$682$	10.1205	+	9.22606i	0.387534	+	0.353284i
$683$	10.1259	+	20.3356i	0.387457	+	0.778119i	0.999923	−	0.0123775i	$-0.00393999\pi$
$683$	10.1259	+	20.3356i	0.387457	+	0.778119i	−0.612466	+	0.790497i	$0.709822\pi$
$684$	−0.000325677	0	0.000296894i	−1.24526e−5	0	1.13520e-5i
$685$	8.49276	+	3.29011i	0.324492	+	0.125709i
$686$	−14.4609	−	29.0414i	−0.552120	−	1.10881i
$687$	−17.4965	+	35.1377i	−0.667532	+	1.34059i
$688$	21.5930	+	4.03643i	0.823225	+	0.153887i
$689$	−0.0455357	+	0.491409i	−0.00173477	+	0.0187212i
$690$	−39.9968	+	24.7650i	−1.52265	+	0.942786i
$691$	1.36030	−	14.6800i	0.0517482	−	0.558452i	−0.929908	−	0.367792i	$-0.880114\pi$
$691$	1.36030	−	14.6800i	0.0517482	−	0.558452i	0.981656	−	0.190660i	$-0.0610627\pi$
$692$	−5.26377	−	56.8051i	−0.200098	−	2.15941i
$693$	0.0100529	+	0.0133121i	0.000381877	+	0.000505686i
$694$	−23.1580	−	4.32898i	−0.879065	−	0.164326i
$695$	−2.90565	+	10.2123i	−0.110218	+	0.387374i
$696$	15.9311	−	2.97804i	0.603867	−	0.112882i
$697$	−0.238992	−	2.57913i	−0.00905245	−	0.0976915i
$698$	−11.1790	−	14.8034i	−0.423131	−	0.560315i
$699$	−6.77590	−	23.8148i	−0.256288	−	0.900760i
$700$	−9.69854	−	8.84138i	−0.366570	−	0.334173i
$701$	22.4320	−	8.69022i	0.847246	−	0.328225i	0.101812	−	0.994804i	$-0.467536\pi$
$701$	22.4320	−	8.69022i	0.847246	−	0.328225i	0.745435	+	0.666579i	$0.232242\pi$
$702$	−3.55506	+	7.13952i	−0.134177	+	0.269464i
$703$	−0.0857946	−	0.301537i	−0.00323580	−	0.0113727i
$704$	−10.0129	+	1.87173i	−0.377375	+	0.0705435i
$705$	−29.3674	+	18.1835i	−1.10604	+	0.684830i
$706$	25.5678	−	15.8309i	0.962258	−	0.595805i
$707$	2.44475	−	8.59241i	0.0919444	−	0.323151i
$708$	−38.9619	+	15.0939i	−1.46428	+	0.567265i
$709$	20.0099	−	18.2414i	0.751487	−	0.685071i	−0.204373	−	0.978893i	$-0.565516\pi$
$709$	20.0099	−	18.2414i	0.751487	−	0.685071i	0.955860	+	0.293822i	$0.0949274\pi$
$710$	7.91714	−	10.4840i	0.297125	−	0.393457i
$711$	0.000416778	0	0.000258058i	1.56304e−5	0	9.67794e-6i
$712$	5.64971	−	7.48142i	0.211732	−	0.280378i
$713$	−47.4069	−	18.3655i	−1.77540	−	0.687795i
$714$	−5.07496	+	1.96605i	−0.189926	+	0.0735776i
$715$	1.17945	+	0.220477i	0.0441089	+	0.00824539i
$716$	−3.53199	−	38.1162i	−0.131997	−	1.42447i
$717$	12.6947	+	44.6174i	0.474094	+	1.66627i
$718$	−33.7718	−	67.8230i	−1.26035	−	2.53113i
$719$	−11.2145	+	14.8504i	−0.418232	+	0.553828i	−0.957548	−	0.288275i	$-0.906918\pi$
$719$	−11.2145	+	14.8504i	−0.418232	+	0.553828i	0.539316	+	0.842104i	$0.318683\pi$
$720$	0.0318301			0.00118624
$721$	3.25130	+	29.9558i	0.121085	+	1.11561i
$722$	−40.0384			−1.49008
$723$	−8.56440	+	11.3411i	−0.318513	+	0.421780i
$724$	14.7046	+	29.5309i	0.546494	+	1.09751i
$725$	4.98369	+	17.5159i	0.185090	+	0.650522i
$726$	3.42213	+	36.9307i	0.127007	+	1.37063i
$727$	−36.6655	−	6.85396i	−1.35985	−	0.254199i	−0.547222	−	0.836987i	$-0.684315\pi$
$727$	−36.6655	−	6.85396i	−1.35985	−	0.254199i	−0.812624	+	0.582788i	$0.801962\pi$
$728$	−1.87614	+	0.726822i	−0.0695345	+	0.0269378i
$729$	25.1254	+	9.73362i	0.930569	+	0.360505i
$730$	−3.37537	+	4.46971i	−0.124928	+	0.165431i
$731$	−3.20528	−	1.98463i	−0.118552	−	0.0734041i
$732$	−8.89586	+	11.7800i	−0.328800	+	0.435402i
$733$	−36.4386	+	33.2182i	−1.34589	+	1.22694i	−0.394524	+	0.918886i	$0.629090\pi$
$733$	−36.4386	+	33.2182i	−1.34589	+	1.22694i	−0.951368	+	0.308057i	$0.900321\pi$
$734$	20.9344	−	8.11001i	0.772701	−	0.299346i
$735$	−1.53774	+	5.40460i	−0.0567204	+	0.199352i
$736$	49.1576	−	30.4371i	1.81197	−	1.12193i
$737$	−12.4490	+	7.70812i	−0.458566	+	0.283932i
$738$	0.0652056	−	0.0121890i	0.00240025	−	0.000448685i
$739$	2.84701	+	10.0062i	0.104729	+	0.368084i	0.996418	−	0.0845646i	$-0.0269499\pi$
$739$	2.84701	+	10.0062i	0.104729	+	0.368084i	−0.891689	+	0.452648i	$0.850479\pi$
$740$	20.5731	−	41.3163i	0.756281	−	1.51882i
$741$	−0.0349031	+	0.0135216i	−0.00128220	+	0.000496727i
$742$	3.12978	+	2.85317i	0.114898	+	0.104743i
$743$	−10.0665	−	35.3799i	−0.369302	−	1.29796i	−0.894533	−	0.447003i	$-0.852491\pi$
$743$	−10.0665	−	35.3799i	−0.369302	−	1.29796i	0.525230	−	0.850960i	$-0.323979\pi$
$744$	−6.84844	−	9.06880i	−0.251076	−	0.332478i
$745$	2.96610	+	32.0094i	0.108670	+	1.17273i
$746$	35.9626	−	6.72257i	1.31668	−	0.246131i
$747$	0.000516593	−	0.00181563i	1.89011e−5	−	6.64306e-5i
$748$	1.10938	+	0.207379i	0.0405628	+	0.00758251i
$749$	−12.4894	−	16.5386i	−0.456352	−	0.604308i
$750$	−4.10050	−	44.2514i	−0.149729	−	1.61583i
$751$	−1.32216	+	14.2684i	−0.0482464	+	0.520661i	0.936977	+	0.349390i	$0.113611\pi$
$751$	−1.32216	+	14.2684i	−0.0482464	+	0.520661i	−0.985224	+	0.171272i	$0.945212\pi$
$752$	27.7270	−	17.1679i	1.01110	−	0.626047i
$753$	0.0657605	−	0.709669i	0.00239645	−	0.0258618i
$754$	15.1891	+	2.83933i	0.553154	+	0.103402i
$755$	−12.3245	+	24.7509i	−0.448534	+	0.900777i
$756$	16.7689	+	33.6764i	0.609877	+	1.22480i
$757$	26.2998	+	10.1886i	0.955883	+	0.370311i	0.788124	−	0.615517i	$-0.211053\pi$
$757$	26.2998	+	10.1886i	0.955883	+	0.370311i	0.167759	+	0.985828i	$0.446347\pi$
$758$	12.6300	−	11.5137i	0.458741	−	0.418198i
$759$	5.13458	+	10.3116i	0.186373	+	0.374288i
$760$	0.0363223	+	0.0331121i	0.00131755	+	0.00120110i
$761$	12.4167	−	43.6402i	0.450105	−	1.58196i	−0.322178	−	0.946679i	$-0.604415\pi$
$761$	12.4167	−	43.6402i	0.450105	−	1.58196i	0.772284	−	0.635278i	$-0.219114\pi$
$762$	2.39652	−	25.8626i	0.0868169	−	0.936904i
$763$	15.1994	−	2.84125i	0.550254	−	0.102860i
$764$	20.3455	+	18.5474i	0.736075	+	0.671021i
$765$	−0.00509376	−	0.00197333i	−0.000184165	−	7.13460e-5i
$766$	−55.2793	−	34.2275i	−1.99732	−	1.23669i
$767$	−7.19795			−0.259903
$768$	−11.8213			−0.426564
$769$	42.6945	+	26.4353i	1.53960	+	0.953282i	0.993284	+	0.115705i	$0.0369127\pi$
$769$	42.6945	+	26.4353i	1.53960	+	0.953282i	0.546319	+	0.837577i	$0.316029\pi$
$770$	7.60944	−	6.93692i	0.274225	−	0.249989i
$771$	11.7720	−	23.6414i	0.423959	−	0.851424i
$772$	−9.58178	−	12.6883i	−0.344856	−	0.456663i
$773$	−8.87174	−	11.7481i	−0.319094	−	0.422549i	0.609995	−	0.792406i	$-0.291172\pi$
$773$	−8.87174	−	11.7481i	−0.319094	−	0.422549i	−0.929089	+	0.369856i	$0.879407\pi$
$774$	0.0430359	−	0.0864277i	0.00154689	−	0.00310658i
$775$	9.43665	−	8.60265i	0.338975	−	0.309016i
$776$	7.14808	+	4.42591i	0.256601	+	0.158881i
$777$	54.5014			1.95523
$778$	48.4653			1.73756
$779$	−0.129974	−	0.0804765i	−0.00465680	−	0.00288337i
$780$	−5.13855	−	1.99068i	−0.183989	−	0.0712779i
$781$	−2.37735	−	2.16724i	−0.0850684	−	0.0775501i
$782$	−7.49274	+	1.40064i	−0.267940	+	0.0500867i
$783$	4.81676	−	51.9811i	0.172137	−	1.85765i
$784$	1.45185	−	5.10272i	0.0518518	−	0.182240i
$785$	11.4546	+	10.4423i	0.408833	+	0.372700i
$786$	28.6198	+	57.4762i	1.02083	+	2.05011i
$787$	−5.80494	+	5.29190i	−0.206924	+	0.188636i	−0.770523	−	0.637413i	$-0.780005\pi$
$787$	−5.80494	+	5.29190i	−0.206924	+	0.188636i	0.563599	+	0.826049i	$0.309416\pi$
$788$	11.7755	+	4.56185i	0.419485	+	0.162509i
$789$	1.62115	+	3.25571i	0.0577145	+	0.115906i
$790$	0.134872	−	0.270860i	0.00479854	−	0.00963676i
$791$	−0.623064	−	0.116471i	−0.0221536	−	0.00414123i
$792$	−0.000481862		0.00520012i	−1.71222e−5		0.000184778i
$793$	−2.16206	+	1.33869i	−0.0767771	+	0.0475383i
$794$	−6.56861	+	70.8865i	−0.233111	+	2.51567i
$795$	0.193379	+	2.08690i	0.00685846	+	0.0740145i
$796$	−4.95948	−	6.56741i	−0.175784	−	0.232776i
$797$	−6.81015	−	1.27304i	−0.241228	−	0.0450933i	0.0617470	−	0.998092i	$-0.480333\pi$
$797$	−6.81015	−	1.27304i	−0.241228	−	0.0450933i	−0.302975	+	0.952998i	$0.597980\pi$
$798$	−0.0879042	+	0.308951i	−0.00311178	+	0.0109368i
$799$	−5.50149	+	1.02841i	−0.194629	+	0.0363824i
$800$	1.33991	+	14.4600i	0.0473730	+	0.511237i
$801$	0.0370597	+	0.0490750i	0.00130944	+	0.00173398i
$802$	8.71176	+	30.6187i	0.307623	+	1.08118i
$803$	1.01355	+	0.923976i	0.0357675	+	0.0326064i
$804$	62.7059	−	24.2924i	2.21147	−	0.856727i
$805$	−17.0387	+	34.2183i	−0.600535	+	1.20604i
$806$	−2.96510	−	10.4213i	−0.104441	−	0.367073i
$807$	−12.9439	+	2.41964i	−0.455647	+	0.0851752i
$808$	2.37784	−	1.47230i	0.0836522	−	0.0517952i
$809$	−20.3936	+	12.6272i	−0.717000	+	0.443948i	−0.835845	−	0.548965i	$-0.815022\pi$
$809$	−20.3936	+	12.6272i	−0.717000	+	0.443948i	0.118845	+	0.992913i	$0.462081\pi$
$810$	−9.28800	+	32.6439i	−0.326347	+	1.14699i
$811$	23.4193	−	9.07270i	0.822364	−	0.318586i	0.0869579	−	0.996212i	$-0.472285\pi$
$811$	23.4193	−	9.07270i	0.822364	−	0.318586i	0.735406	+	0.677626i	$0.236991\pi$
$812$	53.8637	−	49.1033i	1.89025	−	1.72319i
$813$	−18.8555	+	24.9687i	−0.661290	+	0.875690i
$814$	−17.4818	−	10.8243i	−0.612738	−	0.379391i
$815$	16.0426	−	21.2439i	0.561949	−	0.744141i
$816$	2.37118	+	0.918599i	0.0830078	+	0.0321574i
$817$	−0.207477	+	0.0803770i	−0.00725870	+	0.00281203i
$818$	47.0873	+	8.80215i	1.64637	+	0.307760i
$819$	−0.00121775	−	0.0131416i	−4.25517e−5	−	0.000459206i
$820$	−6.15912	−	21.6471i	−0.215086	−	0.755948i
$821$	2.02021	+	4.05712i	0.0705057	+	0.141594i	0.927612	−	0.373545i	$-0.121858\pi$
$821$	2.02021	+	4.05712i	0.0705057	+	0.141594i	−0.857106	+	0.515139i	$0.827740\pi$
$822$	−11.2298	+	14.8706i	−0.391684	+	0.518673i
$823$	−3.96267			−0.138130			−0.0690650	−	0.997612i	$-0.522002\pi$
$823$	−3.96267			−0.138130			−0.0690650	+	0.997612i	$0.522002\pi$
$824$	−5.56578	+	7.61625i	−0.193893	+	0.265325i
$825$	−2.89326			−0.100730
$826$	−37.2244	+	49.2931i	−1.29520	+	1.71513i
$827$	−16.8961	−	33.9319i	−0.587533	−	1.17993i	−0.967013	−	0.254726i	$-0.918015\pi$
$827$	−16.8961	−	33.9319i	−0.587533	−	1.17993i	0.379480	−	0.925200i	$-0.376103\pi$
$828$	−0.0293644	−	0.103205i	−0.00102048	−	0.00358662i
$829$	1.38064	+	14.8995i	0.0479516	+	0.517481i	0.985506	+	0.169641i	$0.0542610\pi$
$829$	1.38064	+	14.8995i	0.0479516	+	0.517481i	−0.937554	+	0.347839i	$0.886916\pi$
$830$	−1.14536	−	0.214104i	−0.0397559	−	0.00743167i
$831$	−38.9436	+	15.0868i	−1.35094	+	0.523357i
$832$	7.51491	+	2.91129i	0.260533	+	0.100931i
$833$	−0.548688	+	0.726580i	−0.0190109	+	0.0251745i
$834$	−18.4698	−	11.4360i	−0.639555	−	0.395996i
$835$	−7.15812	+	9.47888i	−0.247717	+	0.328030i
$836$	0.0492248	−	0.0448744i	0.00170248	−	0.00155201i
$837$	−34.1327	+	13.2231i	−1.17980	+	0.457057i
$838$	1.63865	−	5.75924i	0.0566061	−	0.198950i
$839$	11.8697	−	7.34944i	0.409789	−	0.253731i	−0.306022	−	0.952024i	$-0.598998\pi$
$839$	11.8697	−	7.34944i	0.409789	−	0.253731i	0.715811	+	0.698294i	$0.246057\pi$
$840$	−7.26470	+	4.49811i	−0.250656	+	0.155200i
$841$	−70.9122	+	13.2558i	−2.44525	+	0.457096i
$842$	−19.2286	−	67.5815i	−0.662661	−	2.32901i
$843$	1.43105	−	2.87393i	0.0492879	−	0.0989835i
$844$	8.79806	−	3.40839i	0.302842	−	0.117322i
$845$	16.4551	+	15.0008i	0.566074	+	0.516045i
$846$	−0.0392255	−	0.137863i	−0.00134860	−	0.00473984i
$847$	18.1618	+	24.0501i	0.624047	+	0.826371i
$848$	−0.182578	−	1.97033i	−0.00626976	−	0.0676615i
$849$	−26.0983	+	4.87863i	−0.895693	+	0.167434i
$850$	0.523935	−	1.84144i	0.0179708	−	0.0631609i
$851$	75.0330	+	14.0261i	2.57210	+	0.480808i
$852$	8.90358	+	11.7902i	0.305032	+	0.403927i
$853$	3.34329	+	36.0798i	0.114472	+	1.23535i	0.838238	+	0.545304i	$0.183586\pi$
$853$	3.34329	+	36.0798i	0.114472	+	1.23535i	−0.723766	+	0.690045i	$0.757591\pi$
$854$	−2.01352	+	21.7293i	−0.0689012	+	0.743563i
$855$	−0.000274113	0	0.000169724i	−9.37447e−6	0	5.80443e-6i
$856$	0.598651	−	6.46047i	0.0204615	−	0.220814i
$857$	−1.41922	−	0.265299i	−0.0484798	−	0.00906244i	0.159454	−	0.987205i	$-0.449027\pi$
$857$	−1.41922	−	0.265299i	−0.0484798	−	0.00906244i	−0.207934	+	0.978143i	$0.566674\pi$
$858$	−1.09426	+	2.19758i	−0.0373576	+	0.0750241i
$859$	12.1785	+	24.4578i	0.415526	+	0.834489i	0.999738	+	0.0228881i	$0.00728614\pi$
$859$	12.1785	+	24.4578i	0.415526	+	0.834489i	−0.584212	+	0.811601i	$0.698596\pi$
$860$	−30.5454	−	11.8333i	−1.04159	−	0.403513i
$861$	19.6400	−	17.9042i	0.669328	−	0.610174i
$862$	−13.6098	−	27.3321i	−0.463551	−	0.930936i
$863$	16.9033	+	15.4094i	0.575395	+	0.524542i	0.908245	−	0.418438i	$-0.137422\pi$
$863$	16.9033	+	15.4094i	0.575395	+	0.524542i	−0.332850	+	0.942980i	$0.608010\pi$
$864$	11.3922	−	40.0393i	0.387570	−	1.36217i
$865$	3.85087	−	41.5575i	0.130933	−	1.41300i
$866$	−19.7967	+	3.70064i	−0.672718	+	0.125753i
$867$	21.4596	+	19.5630i	0.728806	+	0.664395i
$868$	−47.6558	−	18.4620i	−1.61754	−	0.626640i
$869$	−0.0629944	−	0.0390045i	−0.00213694	−	0.00132314i
$870$	65.6217			2.22479
$871$	11.5845			0.392525
$872$	4.11574	+	2.54836i	0.139377	+	0.0862983i
$873$	−0.0407555	+	0.0371535i	−0.00137936	+	0.00125746i
$874$	−0.200529	+	0.402716i	−0.00678298	+	0.0136221i
$875$	−21.7620	−	28.8176i	−0.735690	−	0.974211i
$876$	−3.79592	−	5.02661i	−0.128252	−	0.169834i
$877$	−4.36118	+	8.75844i	−0.147267	+	0.295751i	−0.956498	−	0.291739i	$-0.905766\pi$
$877$	−4.36118	+	8.75844i	−0.147267	+	0.295751i	0.809231	+	0.587490i	$0.199884\pi$
$878$	11.1877	−	10.1990i	0.377568	−	0.344199i
$879$	−38.9650	−	24.1261i	−1.31426	−	0.813752i
$880$	−4.81099			−0.162178
$881$	−32.8998			−1.10842			−0.554212	−	0.832376i	$-0.686980\pi$
$881$	−32.8998			−1.10842			−0.554212	+	0.832376i	$0.686980\pi$
$882$	−0.0198251	−	0.0122752i	−0.000667545	−	0.000413326i
$883$	29.6731	+	11.4954i	0.998580	+	0.386852i	0.804383	−	0.594110i	$-0.202496\pi$
$883$	29.6731	+	11.4954i	0.998580	+	0.386852i	0.194197	+	0.980963i	$0.437790\pi$
$884$	−0.659870	−	0.601551i	−0.0221938	−	0.0202323i
$885$	−30.0475	+	5.61685i	−1.01004	+	0.188808i
$886$	−0.0230689	+	0.248953i	−0.000775013	+	0.00836372i
$887$	13.4165	−	47.1543i	0.450484	−	1.58329i	−0.321028	−	0.947070i	$-0.604028\pi$
$887$	13.4165	−	47.1543i	0.450484	−	1.58329i	0.771511	−	0.636216i	$-0.219501\pi$
$888$	12.6093	+	11.4949i	0.423141	+	0.385744i
$889$	−9.40741	−	18.8926i	−0.315514	−	0.633638i
$890$	28.0521	−	25.5728i	0.940308	−	0.857204i
$891$	7.74946	+	3.00216i	0.259617	+	0.100576i
$892$	3.27368	+	6.57443i	0.109611	+	0.220128i
$893$	−0.147237	+	0.295691i	−0.00492709	+	0.00989493i
$894$	−64.6517	−	12.0855i	−2.16227	−	0.404199i
$895$	2.58393	−	27.8851i	0.0863713	−	0.932095i
$896$	18.3136	−	11.3393i	0.611816	−	0.378820i
$897$	0.840908	−	9.07484i	0.0280771	−	0.303000i
$898$	2.63435	+	28.4292i	0.0879095	+	0.948694i
$899$	42.7379	+	56.5941i	1.42539	+	1.88752i
$900$	0.0264916	+	0.00495214i	0.000883054	+	0.000165071i
$901$	−0.0929346	+	0.326631i	−0.00309610	+	0.0108817i
$902$	−9.85558	+	1.84233i	−0.328155	+	0.0613428i
$903$	−3.56904	−	38.5160i	−0.118770	−	1.28173i
$904$	−0.119586	−	0.158357i	−0.00397736	−	0.00526688i
$905$	6.60469	+	23.2131i	0.219547	+	0.771629i
$906$	−41.8064	−	38.1116i	−1.38892	−	1.26617i
$907$	−27.1437	+	10.5155i	−0.901291	+	0.349162i	−0.766900	−	0.641766i	$-0.778202\pi$
$907$	−27.1437	+	10.5155i	−0.901291	+	0.349162i	−0.134391	+	0.990928i	$0.542908\pi$
$908$	−11.3612	+	22.8165i	−0.377036	+	0.757191i
$909$	0.00502048	+	0.0176452i	0.000166519	+	0.000585253i
$910$	−8.00784	+	1.49692i	−0.265457	+	0.0496226i
$911$	−23.3680	+	14.4689i	−0.774217	+	0.479375i	−0.855810	−	0.517291i	$-0.826940\pi$
$911$	−23.3680	+	14.4689i	−0.774217	+	0.479375i	0.0815928	+	0.996666i	$0.473999\pi$
$912$	0.127601	−	0.0790074i	0.00422530	−	0.00261620i
$913$	−0.0780809	+	0.274426i	−0.00258410	+	0.00908217i
$914$	−57.5444	+	22.2928i	−1.90340	+	0.737381i
$915$	−7.98078	+	7.27545i	−0.263837	+	0.240519i
$916$	−33.3044	+	44.1022i	−1.10041	+	1.45718i
$917$	44.3585	+	27.4656i	1.46485	+	0.906995i
$918$	−3.30737	+	4.37966i	−0.109159	+	0.144550i
$919$	−11.2380	−	4.35364i	−0.370709	−	0.143613i	0.168679	−	0.985671i	$-0.446050\pi$
$919$	−11.2380	−	4.35364i	−0.370709	−	0.143613i	−0.539387	+	0.842058i	$0.681344\pi$
$920$	−11.1590	+	4.32303i	−0.367902	+	0.142526i
$921$	26.1231	+	4.88325i	0.860785	+	0.160909i
$922$	−3.55489	−	38.3633i	−0.117074	−	1.26343i
$923$	0.696516	+	2.44800i	0.0229261	+	0.0805769i
$924$	5.16154	+	10.3658i	0.169802	+	0.341009i
$925$	−11.5539	+	15.2998i	−0.379889	+	0.503054i
$926$	−41.9698			−1.37921
$927$	−0.0380610	−	0.0487875i	−0.00125009	−	0.00160239i
$928$	−80.6518			−2.64752
$929$	1.85720	−	2.45933i	0.0609328	−	0.0806881i	−0.766530	−	0.642208i	$-0.778019\pi$
$929$	1.85720	−	2.45933i	0.0609328	−	0.0806881i	0.827463	+	0.561520i	$0.189783\pi$
$930$	−20.5098	−	41.1892i	−0.672542	−	1.35065i
$931$	0.0147057	+	0.0516850i	0.000481958	+	0.00169391i
$932$	−3.21648	−	34.7113i	−0.105359	−	1.13701i
$933$	−50.1854	−	9.38127i	−1.64300	−	0.307129i
$934$	−37.4318	+	14.5012i	−1.22481	+	0.474493i
$935$	0.769902	+	0.298262i	0.0251785	+	0.00975420i
$936$	0.00248997	−	0.00329726i	8.13874e−5	−	0.000107774i
$937$	18.7479	+	11.6082i	0.612466	+	0.379223i	0.797332	−	0.603541i	$-0.206244\pi$
$937$	18.7479	+	11.6082i	0.612466	+	0.379223i	−0.184866	+	0.982764i	$0.559185\pi$
$938$	59.9095	−	79.3330i	1.95612	−	2.59032i
$939$	33.1224	−	30.1951i	1.08091	−	0.985379i
$940$	−45.3469	+	17.5675i	−1.47905	+	0.572988i
$941$	−2.25492	+	7.92523i	−0.0735084	+	0.258355i	−0.989866	−	0.142006i	$-0.954645\pi$
$941$	−2.25492	+	7.92523i	−0.0735084	+	0.258355i	0.916357	+	0.400361i	$0.131115\pi$
$942$	−26.9628	+	16.6947i	−0.878495	+	0.543941i
$943$	31.6464	−	19.5946i	1.03055	−	0.638088i
$944$	28.3692	−	5.30312i	0.923339	−	0.172602i
$945$	7.53185	+	26.4717i	0.245011	+	0.861124i
$946$	−6.50470	+	13.0632i	−0.211486	+	0.424721i
$947$	−27.2480	+	10.5559i	−0.885440	+	0.343021i	−0.760650	−	0.649162i	$-0.775120\pi$
$947$	−27.2480	+	10.5559i	−0.885440	+	0.343021i	−0.124790	+	0.992183i	$0.539826\pi$
$948$	0.251471	+	0.229246i	0.00816741	+	0.00744557i
$949$	−0.296950	−	1.04367i	−0.00963941	−	0.0338790i
$950$	−0.0680946	−	0.0901718i	−0.00220928	−	0.00292556i
$951$	3.62084	+	39.0751i	0.117414	+	1.26710i
$952$	−1.36092	+	0.254401i	−0.0441078	+	0.00824517i
$953$	−4.07753	+	14.3310i	−0.132084	+	0.464228i	−0.999440	−	0.0334608i	$-0.989347\pi$
$953$	−4.07753	+	14.3310i	−0.132084	+	0.464228i	0.867356	+	0.497688i	$0.165818\pi$
$954$	−0.00854903	−	0.00159809i	−0.000276785	−	5.17401e-5i
$955$	12.1377	+	16.0729i	0.392766	+	0.520106i
$956$	6.02611	+	65.0321i	0.194898	+	2.10329i
$957$	1.48262	−	16.0000i	0.0479263	−	0.517208i
$958$	−22.3785	+	13.8562i	−0.723015	+	0.447672i
$959$	−1.39711	+	15.0772i	−0.0451151	+	0.486869i
$960$	33.6424	+	6.28886i	1.08581	+	0.202972i
$961$	8.34733	−	16.7637i	0.269269	−	0.540765i
$962$	7.25117	+	14.5623i	0.233787	+	0.469508i
$963$	0.0396856	+	0.0153743i	0.00127885	+	0.000495430i
$964$	−14.7866	+	13.4798i	−0.476245	+	0.434155i
$965$	−5.18482	−	10.4125i	−0.166905	−	0.335191i
$966$	−57.7977	−	52.6895i	−1.85961	−	1.69526i
$967$	−3.17631	+	11.1636i	−0.102143	+	0.358996i	−0.996000	−	0.0893570i	$-0.971519\pi$
$967$	−3.17631	+	11.1636i	−0.102143	+	0.358996i	0.893856	+	0.448353i	$0.147989\pi$
$968$	−0.870546	+	9.39469i	−0.0279804	+	0.301957i
$969$	−0.0253182	+	0.00473278i	−0.000813337	+	0.000152039i
$970$	25.1567	+	22.9333i	0.807732	+	0.736345i
$971$	−18.2983	−	7.08880i	−0.587221	−	0.227490i	0.0492564	−	0.998786i	$-0.484315\pi$
$971$	−18.2983	−	7.08880i	−0.587221	−	0.227490i	−0.636477	+	0.771296i	$0.719609\pi$
$972$	−0.131503	−	0.0814232i	−0.00421796	−	0.00261165i
$973$	−17.6519			−0.565895
$974$	50.1016			1.60536
$975$	1.94620	+	1.20504i	0.0623283	+	0.0385921i
$976$	7.53502	−	6.86908i	0.241190	−	0.219874i
$977$	0.300528	−	0.603541i	0.00961474	−	0.0193090i	−0.890304	−	0.455367i	$-0.849508\pi$
$977$	0.300528	−	0.603541i	0.00961474	−	0.0193090i	0.899919	+	0.436058i	$0.143626\pi$
$978$	32.8231	+	43.4649i	1.04957	+	1.38985i
$979$	−5.60143	−	7.41750i	−0.179023	−	0.237064i
$980$	−3.52634	+	7.08184i	−0.112645	+	0.226221i
$981$	−0.0234663	+	0.0213923i	−0.000749220	+	0.000683004i
$982$	−9.78520	−	6.05874i	−0.312258	−	0.193342i
$983$	45.3946			1.44786			0.723932	−	0.689871i	$-0.242333\pi$
$983$	45.3946			1.44786			0.723932	+	0.689871i	$0.242333\pi$
$984$	8.32004			0.265233
$985$	7.85480	+	4.86349i	0.250275	+	0.154964i
$986$	9.91489	+	3.84105i	0.315754	+	0.122324i
$987$	−42.4375	−	38.6869i	−1.35080	−	1.23142i
$988$	−0.0518021	+	0.00968349i	−0.00164804	+	0.000308073i
$989$	4.99866	−	53.9441i	0.158948	−	1.71532i
$990$	−0.00578668	+	0.0203381i	−0.000183913	+	0.000646386i
$991$	−3.15223	−	2.87364i	−0.100134	−	0.0912842i	0.622081	−	0.782953i	$-0.286288\pi$
$991$	−3.15223	−	2.87364i	−0.100134	−	0.0912842i	−0.722215	+	0.691669i	$0.756876\pi$
$992$	25.2074	+	50.6232i	0.800334	+	1.60729i
$993$	−15.3397	+	13.9840i	−0.486790	+	0.443767i
$994$	20.3665	+	7.89001i	0.645985	+	0.250256i
$995$	−2.68364	−	5.38947i	−0.0850771	−	0.170858i
$996$	0.584084	−	1.17300i	0.0185074	−	0.0371679i
$997$	21.5555	+	4.02942i	0.682669	+	0.127613i	0.513650	−	0.858000i	$-0.328293\pi$
$997$	21.5555	+	4.02942i	0.682669	+	0.127613i	0.169019	+	0.985613i	$0.445940\pi$
$998$	−4.20353	+	45.3634i	−0.133061	+	1.43595i
$999$	46.7272	−	28.9323i	1.47838	−	0.915376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.2.e.a.14.2	✓	112
3.2	odd	2		927.2.u.a.838.6		112
103.81	even	17	inner	103.2.e.a.81.2	yes	112
309.287	odd	34		927.2.u.a.802.6		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.2.e.a.14.2	✓	112	1.1	even	1	trivial
103.2.e.a.81.2	yes	112	103.81	even	17	inner
927.2.u.a.802.6		112	309.287	odd	34
927.2.u.a.838.6		112	3.2	odd	2

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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	103.e (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26998 + 1.68173i) q^{2} +(-0.772826 - 1.55204i) q^{3} +(-0.668028 - 2.34787i) q^{4} +(-0.164776 - 1.77821i) q^{5} +(3.59159 + 0.671384i) q^{6} +(2.76848 - 1.07252i) q^{7} +(0.866715 + 0.335767i) q^{8} +(-0.00367427 + 0.00486551i) q^{9} +O(q^{10})\)	\(q+(-1.26998 + 1.68173i) q^{2} +(-0.772826 - 1.55204i) q^{3} +(-0.668028 - 2.34787i) q^{4} +(-0.164776 - 1.77821i) q^{5} +(3.59159 + 0.671384i) q^{6} +(2.76848 - 1.07252i) q^{7} +(0.866715 + 0.335767i) q^{8} +(-0.00367427 + 0.00486551i) q^{9} +(3.19973 + 1.98119i) q^{10} +(0.555351 - 0.735403i) q^{11} +(-3.12773 + 2.85130i) q^{12} +(-0.679861 + 0.263379i) q^{13} +(-1.71224 + 6.01791i) q^{14} +(-2.63252 + 1.62999i) q^{15} +(2.48548 - 1.53894i) q^{16} +(-0.493160 + 0.0921875i) q^{17} +(-0.00351622 - 0.0123582i) q^{18} +(-0.0131985 + 0.0265061i) q^{19} +(-4.06494 + 1.57477i) q^{20} +(-3.80414 - 3.46794i) q^{21} +(0.531463 + 1.86790i) q^{22} +(-4.34474 - 5.75337i) q^{23} +(-0.148694 - 1.60467i) q^{24} +(1.77998 - 0.332735i) q^{25} +(0.420478 - 1.47783i) q^{26} +(-5.10247 - 0.953818i) q^{27} +(-4.36755 - 5.78358i) q^{28} +(0.927930 + 10.0140i) q^{29} +(0.602057 - 6.49723i) q^{30} +(5.99551 - 3.71226i) q^{31} +(-0.739953 + 7.98536i) q^{32} +(-1.57057 - 0.293590i) q^{33} +(0.471269 - 0.946437i) q^{34} +(-2.36334 - 4.74623i) q^{35} +(0.0138781 + 0.00537641i) q^{36} +(-7.82439 + 7.13287i) q^{37} +(-0.0278142 - 0.0558584i) q^{38} +(0.934190 + 0.851627i) q^{39} +(0.454252 - 1.59653i) q^{40} +(-0.476361 + 5.14076i) q^{41} +(10.6633 - 1.99332i) q^{42} +(5.55316 + 5.06238i) q^{43} +(-2.09762 - 0.812624i) q^{44} +(0.00925735 + 0.00573191i) q^{45} +15.1933 q^{46} +11.1556 q^{47} +(-4.30935 - 2.66824i) q^{48} +(1.34114 - 1.22261i) q^{49} +(-1.70097 + 3.41600i) q^{50} +(0.524205 + 0.694160i) q^{51} +(1.07255 + 1.42028i) q^{52} +(0.301714 - 0.605923i) q^{53} +(8.08411 - 7.36964i) q^{54} +(-1.39921 - 0.866355i) q^{55} +2.75960 q^{56} +0.0513387 q^{57} +(-18.0192 - 11.1570i) q^{58} +(9.20578 + 3.56634i) q^{59} +(5.58560 + 5.09195i) q^{60} +(3.42843 - 0.640885i) q^{61} +(-1.37117 + 14.7973i) q^{62} +(-0.00495380 + 0.0174108i) q^{63} +(-8.16871 - 7.44677i) q^{64} +(0.580369 + 1.16554i) q^{65} +(2.48833 - 2.26841i) q^{66} +(-14.8159 - 5.73972i) q^{67} +(0.545889 + 1.09629i) q^{68} +(-5.57175 + 11.1896i) q^{69} +(10.9833 + 2.05313i) q^{70} +(0.322095 - 3.47595i) q^{71} +(-0.00481822 + 0.00298331i) q^{72} +(-0.137321 + 1.48193i) q^{73} +(-2.05872 - 22.2171i) q^{74} +(-1.89203 - 2.50545i) q^{75} +(0.0710498 + 0.0132815i) q^{76} +(0.748747 - 2.63157i) q^{77} +(-2.61861 + 0.489503i) q^{78} +(-0.00741842 - 0.0800575i) q^{79} +(-3.14612 - 4.16613i) q^{80} +(2.46796 + 8.67399i) q^{81} +(-8.04038 - 7.32978i) q^{82} +(-0.288703 + 0.111844i) q^{83} +(-5.60100 + 11.2483i) q^{84} +(0.245190 + 0.861753i) q^{85} +(-15.5660 + 2.90978i) q^{86} +(14.8250 - 9.17924i) q^{87} +(0.728255 - 0.450916i) q^{88} +(2.76025 - 9.70126i) q^{89} +(-0.0213962 + 0.00828892i) q^{90} +(-1.59970 + 1.45832i) q^{91} +(-10.6058 + 14.0443i) q^{92} +(-10.3951 - 6.43635i) q^{93} +(-14.1674 + 18.7607i) q^{94} +(0.0493082 + 0.0191021i) q^{95} +(12.9655 - 5.02285i) q^{96} +(8.89122 + 1.66206i) q^{97} +(0.352875 + 3.80813i) q^{98} +(0.00153761 + 0.00540413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 15 q^{2} - 11 q^{3} - 19 q^{4} - 11 q^{5} - 5 q^{6} - 5 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) 112 * q - 15 * q^2 - 11 * q^3 - 19 * q^4 - 11 * q^5 - 5 * q^6 - 5 * q^7 - 5 * q^8 - 8 * q^9	\( 112 q - 15 q^{2} - 11 q^{3} - 19 q^{4} - 11 q^{5} - 5 q^{6} - 5 q^{7} - 5 q^{8} - 8 q^{9} - 59 q^{10} - q^{11} - 41 q^{12} + q^{13} - 21 q^{14} + 13 q^{15} - q^{16} - 11 q^{17} + 19 q^{18} - 12 q^{19} + 31 q^{20} - 7 q^{21} + 23 q^{22} - 22 q^{23} + 73 q^{24} - 52 q^{25} + 18 q^{26} + 13 q^{27} - 50 q^{28} + 7 q^{29} - 13 q^{30} + 31 q^{31} + 34 q^{32} + 13 q^{33} - 91 q^{34} + 23 q^{35} - 53 q^{36} - 30 q^{37} + 15 q^{38} - 105 q^{39} + 75 q^{40} + 11 q^{41} + 57 q^{42} + 37 q^{43} + 83 q^{44} - 4 q^{45} - 56 q^{46} - 154 q^{47} - 9 q^{48} + 20 q^{49} + 12 q^{50} + 51 q^{51} + 113 q^{52} + 27 q^{53} + 95 q^{54} + 12 q^{55} + 8 q^{56} - 40 q^{57} - 13 q^{58} - 9 q^{59} - 84 q^{60} + 29 q^{61} + 41 q^{62} + 103 q^{63} - 57 q^{64} + 47 q^{65} - 3 q^{66} + 10 q^{67} - 105 q^{68} - 35 q^{69} + 143 q^{70} + 11 q^{71} + 135 q^{72} - 40 q^{73} + 97 q^{74} - 117 q^{75} + 131 q^{76} - 19 q^{77} + 81 q^{78} + 77 q^{79} - 29 q^{80} + 104 q^{81} - 162 q^{82} + 73 q^{83} - 163 q^{84} + 55 q^{85} - 99 q^{86} + 75 q^{87} - 63 q^{88} + 54 q^{89} + 107 q^{90} - 113 q^{91} - 11 q^{92} - 197 q^{93} + 33 q^{94} - 146 q^{95} + 49 q^{96} - 142 q^{97} - 2 q^{98} + 102 q^{99}+O(q^{100}) \) 112 * q - 15 * q^2 - 11 * q^3 - 19 * q^4 - 11 * q^5 - 5 * q^6 - 5 * q^7 - 5 * q^8 - 8 * q^9 - 59 * q^10 - q^11 - 41 * q^12 + q^13 - 21 * q^14 + 13 * q^15 - q^16 - 11 * q^17 + 19 * q^18 - 12 * q^19 + 31 * q^20 - 7 * q^21 + 23 * q^22 - 22 * q^23 + 73 * q^24 - 52 * q^25 + 18 * q^26 + 13 * q^27 - 50 * q^28 + 7 * q^29 - 13 * q^30 + 31 * q^31 + 34 * q^32 + 13 * q^33 - 91 * q^34 + 23 * q^35 - 53 * q^36 - 30 * q^37 + 15 * q^38 - 105 * q^39 + 75 * q^40 + 11 * q^41 + 57 * q^42 + 37 * q^43 + 83 * q^44 - 4 * q^45 - 56 * q^46 - 154 * q^47 - 9 * q^48 + 20 * q^49 + 12 * q^50 + 51 * q^51 + 113 * q^52 + 27 * q^53 + 95 * q^54 + 12 * q^55 + 8 * q^56 - 40 * q^57 - 13 * q^58 - 9 * q^59 - 84 * q^60 + 29 * q^61 + 41 * q^62 + 103 * q^63 - 57 * q^64 + 47 * q^65 - 3 * q^66 + 10 * q^67 - 105 * q^68 - 35 * q^69 + 143 * q^70 + 11 * q^71 + 135 * q^72 - 40 * q^73 + 97 * q^74 - 117 * q^75 + 131 * q^76 - 19 * q^77 + 81 * q^78 + 77 * q^79 - 29 * q^80 + 104 * q^81 - 162 * q^82 + 73 * q^83 - 163 * q^84 + 55 * q^85 - 99 * q^86 + 75 * q^87 - 63 * q^88 + 54 * q^89 + 107 * q^90 - 113 * q^91 - 11 * q^92 - 197 * q^93 + 33 * q^94 - 146 * q^95 + 49 * q^96 - 142 * q^97 - 2 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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