LMFDB - Embedded newform 95.2.r.a.72.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(2,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("95.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.r (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			72.1
Character	$\chi$	$=$	95.72
Dual form			95.2.r.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46137 + 1.14775i) q^{2} +(-0.378859 + 0.541067i) q^{3} +(3.45542 - 4.11800i) q^{4} +(1.16036 - 1.91143i) q^{5} +(0.311499 - 1.76660i) q^{6} +(1.06230 - 0.284643i) q^{7} +(-2.37278 + 8.85533i) q^{8} +(0.876841 + 2.40910i) q^{9} +O(q^{10})$	\(q+(-2.46137 + 1.14775i) q^{2} +(-0.378859 + 0.541067i) q^{3} +(3.45542 - 4.11800i) q^{4} +(1.16036 - 1.91143i) q^{5} +(0.311499 - 1.76660i) q^{6} +(1.06230 - 0.284643i) q^{7} +(-2.37278 + 8.85533i) q^{8} +(0.876841 + 2.40910i) q^{9} +(-0.662211 + 6.03654i) q^{10} +(-0.0283658 - 0.0491311i) q^{11} +(0.918999 + 3.42975i) q^{12} +(4.35721 - 3.05095i) q^{13} +(-2.28801 + 1.91987i) q^{14} +(0.594600 + 1.35199i) q^{15} +(-2.45651 - 13.9316i) q^{16} +(0.142917 + 0.306486i) q^{17} +(-4.92329 - 4.92329i) q^{18} +(1.60878 + 4.05115i) q^{19} +(-3.86177 - 11.3831i) q^{20} +(-0.248452 + 0.682615i) q^{21} +(0.126209 + 0.0883726i) q^{22} +(1.50764 - 0.131902i) q^{23} +(-3.89238 - 4.63875i) q^{24} +(-2.30714 - 4.43589i) q^{25} +(-7.22295 + 12.5105i) q^{26} +(-3.54972 - 0.951146i) q^{27} +(2.49853 - 5.35812i) q^{28} +(4.78022 - 1.73986i) q^{29} +(-3.01529 - 2.64530i) q^{30} +(-5.87120 - 3.38974i) q^{31} +(11.5197 + 16.4518i) q^{32} +(0.0373298 + 0.00326594i) q^{33} +(-0.703540 - 0.590341i) q^{34} +(0.688574 - 2.36080i) q^{35} +(12.9505 + 4.71361i) q^{36} +(-1.21298 + 1.21298i) q^{37} +(-8.60952 - 8.12489i) q^{38} +3.51342i q^{39} +(14.1731 + 14.8108i) q^{40} +(-2.68375 + 0.473218i) q^{41} +(-0.171944 - 1.96533i) q^{42} +(-0.775106 + 8.85950i) q^{43} +(-0.300338 - 0.0529576i) q^{44} +(5.62228 + 1.11940i) q^{45} +(-3.55948 + 2.05506i) q^{46} +(-6.92356 - 3.22851i) q^{47} +(8.46859 + 3.94897i) q^{48} +(-5.01471 + 2.89525i) q^{49} +(10.7700 + 8.27032i) q^{50} +(-0.219974 - 0.0387874i) q^{51} +(2.49214 - 28.4853i) q^{52} +(-0.623266 - 7.12396i) q^{53} +(9.82886 - 1.73309i) q^{54} +(-0.126825 - 0.00279023i) q^{55} +10.0824i q^{56} +(-2.80144 - 0.664359i) q^{57} +(-9.76896 + 9.76896i) q^{58} +(-5.81577 - 2.11677i) q^{59} +(7.62210 + 2.22313i) q^{60} +(-0.917954 - 0.770255i) q^{61} +(18.3418 + 1.60470i) q^{62} +(1.61720 + 2.30961i) q^{63} +(-22.7343 - 13.1256i) q^{64} +(-0.775764 - 11.8687i) q^{65} +(-0.0956310 + 0.0348068i) q^{66} +(-3.34587 + 7.17523i) q^{67} +(1.75594 + 0.470504i) q^{68} +(-0.499817 + 0.865708i) q^{69} +(1.01479 + 6.60112i) q^{70} +(4.15020 + 4.94602i) q^{71} +(-23.4139 + 2.04845i) q^{72} +(-1.52994 - 1.07128i) q^{73} +(1.59339 - 4.37781i) q^{74} +(3.27419 + 0.432258i) q^{75} +(22.2417 + 7.37346i) q^{76} +(-0.0441179 - 0.0441179i) q^{77} +(-4.03254 - 8.64781i) q^{78} +(0.552952 + 3.13594i) q^{79} +(-29.4797 - 11.4702i) q^{80} +(-4.03228 + 3.38348i) q^{81} +(6.06257 - 4.24506i) q^{82} +(0.558456 + 2.08419i) q^{83} +(1.95251 + 3.38184i) q^{84} +(0.751660 + 0.0824575i) q^{85} +(-8.26071 - 22.6961i) q^{86} +(-0.869651 + 3.24558i) q^{87} +(0.502378 - 0.134612i) q^{88} +(2.29549 - 13.0183i) q^{89} +(-15.1233 + 3.69776i) q^{90} +(3.76024 - 4.48128i) q^{91} +(4.66637 - 6.66426i) q^{92} +(4.05843 - 1.89248i) q^{93} +20.7470 q^{94} +(9.61026 + 1.62571i) q^{95} -13.2658 q^{96} +(-1.52540 + 0.711305i) q^{97} +(9.02002 - 12.8819i) q^{98} +(0.0934894 - 0.111416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.46137	+	1.14775i	−1.74045	+	0.811585i	−0.752163	+	0.658977i	$0.770989\pi$
$2$	−2.46137	+	1.14775i	−1.74045	+	0.811585i	−0.988287	+	0.152608i	$0.951233\pi$
$3$	−0.378859	+	0.541067i	−0.218734	+	0.312385i	−0.913490	−	0.406861i	$-0.866623\pi$
$3$	−0.378859	+	0.541067i	−0.218734	+	0.312385i	0.694756	+	0.719246i	$0.255512\pi$
$4$	3.45542	−	4.11800i	1.72771	−	2.05900i
$5$	1.16036	−	1.91143i	0.518928	−	0.854818i
$5$	1.16036	−	1.91143i	0.518928	−	0.854818i
$6$	0.311499	−	1.76660i	0.127169	−	0.721212i
$7$	1.06230	−	0.284643i	0.401512	−	0.107585i	−0.0524111	−	0.998626i	$-0.516691\pi$
$7$	1.06230	−	0.284643i	0.401512	−	0.107585i	0.453923	+	0.891041i	$0.350024\pi$
$8$	−2.37278	+	8.85533i	−0.838904	+	3.13083i
$9$	0.876841	+	2.40910i	0.292280	+	0.803034i
$10$	−0.662211	+	6.03654i	−0.209410	+	1.90892i
$11$	−0.0283658	−	0.0491311i	−0.00855262	−	0.0148136i	0.861717	−	0.507389i	$-0.169389\pi$
$11$	−0.0283658	−	0.0491311i	−0.00855262	−	0.0148136i	−0.870270	+	0.492575i	$0.836056\pi$
$12$	0.918999	+	3.42975i	0.265292	+	0.990084i
$13$	4.35721	−	3.05095i	1.20847	−	0.846181i	0.216958	−	0.976181i	$-0.430387\pi$
$13$	4.35721	−	3.05095i	1.20847	−	0.846181i	0.991514	+	0.130000i	$0.0414977\pi$
$14$	−2.28801	+	1.91987i	−0.611498	+	0.513108i
$15$	0.594600	+	1.35199i	0.153525	+	0.349083i
$16$	−2.45651	−	13.9316i	−0.614129	−	3.48290i
$17$	0.142917	+	0.306486i	0.0346624	+	0.0743337i	0.922877	−	0.385096i	$-0.125832\pi$
$17$	0.142917	+	0.306486i	0.0346624	+	0.0743337i	−0.888214	+	0.459430i	$0.848054\pi$
$18$	−4.92329	−	4.92329i	−1.16043	−	1.16043i
$19$	1.60878	+	4.05115i	0.369079	+	0.929398i
$19$	1.60878	+	4.05115i	0.369079	+	0.929398i
$20$	−3.86177	−	11.3831i	−0.863517	−	2.54535i
$21$	−0.248452	+	0.682615i	−0.0542166	+	0.148959i
$22$	0.126209	+	0.0883726i	0.0269079	+	0.0188411i
$23$	1.50764	−	0.131902i	0.314366	−	0.0275034i	0.0711188	−	0.997468i	$-0.477343\pi$
$23$	1.50764	−	0.131902i	0.314366	−	0.0275034i	0.243247	+	0.969964i	$0.421788\pi$
$24$	−3.89238	−	4.63875i	−0.794528	−	0.946881i
$25$	−2.30714	−	4.43589i	−0.461428	−	0.887177i
$26$	−7.22295	+	12.5105i	−1.41654	+	2.45351i
$27$	−3.54972	−	0.951146i	−0.683145	−	0.183048i
$28$	2.49853	−	5.35812i	0.472178	−	1.01259i
$29$	4.78022	−	1.73986i	0.887665	−	0.323084i	0.142366	−	0.989814i	$-0.454529\pi$
$29$	4.78022	−	1.73986i	0.887665	−	0.323084i	0.745299	+	0.666730i	$0.232307\pi$
$30$	−3.01529	−	2.64530i	−0.550513	−	0.482963i
$31$	−5.87120	−	3.38974i	−1.05450	−	0.608816i	−0.130594	−	0.991436i	$-0.541688\pi$
$31$	−5.87120	−	3.38974i	−1.05450	−	0.608816i	−0.923906	+	0.382620i	$0.875022\pi$
$32$	11.5197	+	16.4518i	2.03641	+	2.90829i
$33$	0.0373298	+	0.00326594i	0.00649829	+	0.000568527i
$34$	−0.703540	−	0.590341i	−0.120656	−	0.101243i
$35$	0.688574	−	2.36080i	0.116390	−	0.399049i
$36$	12.9505	+	4.71361i	2.15842	+	0.785602i
$37$	−1.21298	+	1.21298i	−0.199413	+	0.199413i	−0.799748	−	0.600335i	$-0.795034\pi$
$37$	−1.21298	+	1.21298i	−0.199413	+	0.199413i	0.600335	+	0.799748i	$0.295034\pi$
$38$	−8.60952	−	8.12489i	−1.39665	−	1.31803i
$39$			3.51342i			0.562597i
$40$	14.1731	+	14.8108i	2.24096	+	2.34179i
$41$	−2.68375	+	0.473218i	−0.419132	+	0.0739043i	−0.379237	−	0.925300i	$-0.623813\pi$
$41$	−2.68375	+	0.473218i	−0.419132	+	0.0739043i	−0.0398951	+	0.999204i	$0.512702\pi$
$42$	−0.171944	−	1.96533i	−0.0265315	−	0.303257i
$43$	−0.775106	+	8.85950i	−0.118203	+	1.35106i	0.673061	+	0.739587i	$0.264979\pi$
$43$	−0.775106	+	8.85950i	−0.118203	+	1.35106i	−0.791264	+	0.611475i	$0.790577\pi$
$44$	−0.300338	−	0.0529576i	−0.0452776	−	0.00798367i
$45$	5.62228	+	1.11940i	0.838120	+	0.166870i
$46$	−3.55948	+	2.05506i	−0.524816	+	0.303003i
$47$	−6.92356	−	3.22851i	−1.00990	−	0.470926i	−0.154006	−	0.988070i	$-0.549218\pi$
$47$	−6.92356	−	3.22851i	−1.00990	−	0.470926i	−0.855899	+	0.517144i	$0.826995\pi$
$48$	8.46859	+	3.94897i	1.22234	+	0.569984i
$49$	−5.01471	+	2.89525i	−0.716388	+	0.413607i
$50$	10.7700	+	8.27032i	1.52311	+	1.16960i
$51$	−0.219974	−	0.0387874i	−0.0308026	−	0.00543132i
$52$	2.49214	−	28.4853i	0.345598	−	3.95020i
$53$	−0.623266	−	7.12396i	−0.0856121	−	0.978551i	−0.910569	−	0.413356i	$-0.864356\pi$
$53$	−0.623266	−	7.12396i	−0.0856121	−	0.978551i	0.824957	−	0.565195i	$-0.191199\pi$
$54$	9.82886	−	1.73309i	1.33754	−	0.235844i
$55$	−0.126825	−	0.00279023i	−0.0171011	−	0.000376235i
$56$			10.0824i			1.34732i
$57$	−2.80144	−	0.664359i	−0.371060	−	0.0879965i
$58$	−9.76896	+	9.76896i	−1.28273	+	1.28273i
$59$	−5.81577	−	2.11677i	−0.757149	−	0.275580i	−0.0655384	−	0.997850i	$-0.520876\pi$
$59$	−5.81577	−	2.11677i	−0.757149	−	0.275580i	−0.691611	+	0.722270i	$0.743099\pi$
$60$	7.62210	+	2.22313i	0.984009	+	0.287005i
$61$	−0.917954	−	0.770255i	−0.117532	−	0.0986211i	0.582127	−	0.813098i	$-0.302220\pi$
$61$	−0.917954	−	0.770255i	−0.117532	−	0.0986211i	−0.699659	+	0.714477i	$0.746665\pi$
$62$	18.3418	+	1.60470i	2.32941	+	0.203797i
$63$	1.61720	+	2.30961i	0.203749	+	0.290983i
$64$	−22.7343	−	13.1256i	−2.84178	−	1.64070i
$65$	−0.775764	−	11.8687i	−0.0962217	−	1.47213i
$66$	−0.0956310	+	0.0348068i	−0.0117714	+	0.00428442i
$67$	−3.34587	+	7.17523i	−0.408763	+	0.876594i	0.588896	+	0.808209i	$0.299563\pi$
$67$	−3.34587	+	7.17523i	−0.408763	+	0.876594i	−0.997659	+	0.0683857i	$0.978215\pi$
$68$	1.75594	+	0.470504i	0.212940	+	0.0570570i
$69$	−0.499817	+	0.865708i	−0.0601709	+	0.104219i
$70$	1.01479	+	6.60112i	0.121291	+	0.788985i
$71$	4.15020	+	4.94602i	0.492538	+	0.586984i	0.953861	−	0.300248i	$-0.0970695\pi$
$71$	4.15020	+	4.94602i	0.492538	+	0.586984i	−0.461323	+	0.887232i	$0.652625\pi$
$72$	−23.4139	+	2.04845i	−2.75936	+	0.241413i
$73$	−1.52994	−	1.07128i	−0.179066	−	0.125383i	0.480607	−	0.876936i	$-0.340416\pi$
$73$	−1.52994	−	1.07128i	−0.179066	−	0.125383i	−0.659673	+	0.751553i	$0.729305\pi$
$74$	1.59339	−	4.37781i	0.185228	−	0.508910i
$75$	3.27419	+	0.432258i	0.378071	+	0.0499128i
$76$	22.2417	+	7.37346i	2.55129	+	0.845793i
$77$	−0.0441179	−	0.0441179i	−0.00502770	−	0.00502770i
$78$	−4.03254	−	8.64781i	−0.456595	−	0.979172i
$79$	0.552952	+	3.13594i	0.0622119	+	0.352821i	0.999984	+	0.00557123i	$0.00177339\pi$
$79$	0.552952	+	3.13594i	0.0622119	+	0.352821i	−0.937773	+	0.347250i	$0.887116\pi$
$80$	−29.4797	−	11.4702i	−3.29593	−	1.28240i
$81$	−4.03228	+	3.38348i	−0.448031	+	0.375942i
$82$	6.06257	−	4.24506i	0.669499	−	0.468788i
$83$	0.558456	+	2.08419i	0.0612986	+	0.228769i	0.989778	−	0.142613i	$-0.0455505\pi$
$83$	0.558456	+	2.08419i	0.0612986	+	0.228769i	−0.928480	+	0.371383i	$0.878884\pi$
$84$	1.95251	+	3.38184i	0.213036	+	0.368990i
$85$	0.751660	+	0.0824575i	0.0815290	+	0.00894377i
$86$	−8.26071	−	22.6961i	−0.890776	−	2.44739i
$87$	−0.869651	+	3.24558i	−0.0932364	+	0.347963i
$88$	0.502378	−	0.134612i	0.0535537	−	0.0143497i
$89$	2.29549	−	13.0183i	0.243321	−	1.37994i	−0.581039	−	0.813876i	$-0.697354\pi$
$89$	2.29549	−	13.0183i	0.243321	−	1.37994i	0.824360	−	0.566066i	$-0.191535\pi$
$90$	−15.1233	+	3.69776i	−1.59414	+	0.389778i
$91$	3.76024	−	4.48128i	0.394180	−	0.469765i
$92$	4.66637	−	6.66426i	0.486502	−	0.694797i
$93$	4.05843	−	1.89248i	0.420840	−	0.196241i
$94$	20.7470			2.13989
$95$	9.61026	+	1.62571i	0.985992	+	0.166795i
$96$	−13.2658			−1.35394
$97$	−1.52540	+	0.711305i	−0.154881	+	0.0722221i	−0.498513	−	0.866882i	$-0.666120\pi$
$97$	−1.52540	+	0.711305i	−0.154881	+	0.0722221i	0.343632	+	0.939104i	$0.388343\pi$
$98$	9.02002	−	12.8819i	0.911160	−	1.30127i
$99$	0.0934894	−	0.111416i	0.00939604	−	0.0111978i
$100$	−26.2391	−	5.82701i	−2.62391	−	0.582701i
$101$	−1.29107	+	7.32203i	−0.128466	+	0.728569i	0.850722	+	0.525616i	$0.176165\pi$
$101$	−1.29107	+	7.32203i	−0.128466	+	0.728569i	−0.979188	+	0.202953i	$0.934946\pi$
$102$	0.585956	−	0.157006i	0.0580183	−	0.0155460i
$103$	1.52483	−	5.69076i	0.150246	−	0.560727i	−0.849219	−	0.528040i	$-0.822927\pi$
$103$	1.52483	−	5.69076i	0.150246	−	0.560727i	0.999466	−	0.0326867i	$-0.0104064\pi$
$104$	16.6785	+	45.8237i	1.63546	+	4.49339i
$105$	1.01648	+	1.26698i	0.0991983	+	0.123644i
$106$	9.71065	+	16.8193i	0.943181	+	1.63364i
$107$	2.83390	+	10.5763i	0.273963	+	1.02245i	0.956533	+	0.291624i	$0.0941957\pi$
$107$	2.83390	+	10.5763i	0.273963	+	1.02245i	−0.682570	+	0.730821i	$0.739138\pi$
$108$	−16.1826	+	11.3312i	−1.55717	+	1.09034i
$109$	−13.6104	+	11.4204i	−1.30364	+	1.09388i	−0.314131	+	0.949380i	$0.601713\pi$
$109$	−13.6104	+	11.4204i	−1.30364	+	1.09388i	−0.989505	+	0.144500i	$0.953843\pi$
$110$	0.315366	−	0.138696i	0.0300690	−	0.0132242i
$111$	−0.196755	−	1.11585i	−0.0186752	−	0.105912i
$112$	−6.57509	−	14.1003i	−0.621287	−	1.33235i
$113$	10.5263	+	10.5263i	0.990227	+	0.990227i	0.999953	−	0.00972576i	$-0.00309585\pi$
$113$	10.5263	+	10.5263i	0.990227	+	0.990227i	−0.00972576	+	0.999953i	$0.503096\pi$
$114$	7.65790	−	1.58014i	0.717228	−	0.147994i
$115$	1.49728	−	3.03481i	0.139623	−	0.282998i
$116$	9.35291	−	25.6969i	0.868396	−	2.38590i
$117$	11.1706	+	7.82176i	1.03272	+	0.723122i
$118$	16.7443	−	1.46494i	1.54144	−	0.134858i
$119$	0.239059	+	0.284900i	0.0219145	+	0.0261167i
$120$	−13.3832	+	2.05740i	−1.22171	+	0.187814i
$121$	5.49839	−	9.52349i	0.499854	−	0.865772i
$122$	3.14349	+	0.842295i	0.284598	+	0.0762578i
$123$	0.760722	−	1.63137i	0.0685920	−	0.147096i
$124$	−34.2464	+	12.4647i	−3.07542	+	1.11936i
$125$	−11.1560	−	0.737269i	−0.997823	−	0.0659433i
$126$	−6.63139	−	3.82864i	−0.590772	−	0.341082i
$127$	−3.13191	−	4.47283i	−0.277912	−	0.396899i	0.655794	−	0.754940i	$-0.272334\pi$
$127$	−3.13191	−	4.47283i	−0.277912	−	0.396899i	−0.933706	+	0.358040i	$0.883445\pi$
$128$	31.0074	+	2.71280i	2.74069	+	0.239780i
$129$	−4.49992	−	3.77589i	−0.396196	−	0.332448i
$130$	15.5318	+	28.3228i	1.36223	+	2.48408i
$131$	−4.92980	−	1.79430i	−0.430719	−	0.156769i	0.117558	−	0.993066i	$-0.462494\pi$
$131$	−4.92980	−	1.79430i	−0.430719	−	0.156769i	−0.548276	+	0.836297i	$0.684716\pi$
$132$	0.142439	−	0.142439i	0.0123977	−	0.0123977i
$133$	2.86214	+	3.84562i	0.248179	+	0.333457i
$134$		−	21.5011i		−	1.85741i
$135$	−5.93700	+	5.68139i	−0.510976	+	0.488976i
$136$	−3.05314	+	0.538351i	−0.261805	+	0.0461632i
$137$	−0.763133	−	8.72265i	−0.0651989	−	0.745226i	−0.956484	−	0.291784i	$-0.905751\pi$
$137$	−0.763133	−	8.72265i	−0.0651989	−	0.745226i	0.891285	−	0.453443i	$-0.149804\pi$
$138$	0.236613	−	2.70449i	0.0201418	−	0.230222i
$139$	11.1570	+	1.96728i	0.946323	+	0.166862i	0.625454	−	0.780261i	$-0.284914\pi$
$139$	11.1570	+	1.96728i	0.946323	+	0.166862i	0.320869	+	0.947123i	$0.396025\pi$
$140$	−7.34249	−	10.9931i	−0.620554	−	0.929087i
$141$	4.36989	−	2.52296i	0.368011	−	0.212471i
$142$	−15.8920	−	7.41055i	−1.33363	−	0.621880i
$143$	−0.273492	−	0.127532i	−0.0228706	−	0.0106647i
$144$	31.4086	−	18.1338i	2.61739	−	1.51115i
$145$	2.22115	−	11.1559i	0.184456	−	0.926450i
$146$	4.99531	+	0.880808i	0.413415	+	0.0728962i
$147$	0.333348	−	3.81018i	0.0274941	−	0.314259i
$148$	0.803709	+	9.18643i	0.0660644	+	0.755120i
$149$	−7.05432	+	1.24387i	−0.577913	+	0.101902i	−0.454961	−	0.890511i	$-0.650347\pi$
$149$	−7.05432	+	1.24387i	−0.577913	+	0.101902i	−0.122951	+	0.992413i	$0.539236\pi$
$150$	−8.55512	+	2.69402i	−0.698522	+	0.219966i
$151$		−	7.53494i		−	0.613185i	−0.951841	−	0.306592i	$-0.900811\pi$
$151$		−	7.53494i		−	0.613185i	0.951841	−	0.306592i	$-0.0991888\pi$
$152$	−39.6916	+	4.63378i	−3.21941	+	0.375849i
$153$	−0.613040	+	0.613040i	−0.0495613	+	0.0495613i
$154$	0.159227	+	0.0579538i	0.0128309	+	0.00467005i
$155$	−13.2920	+	7.28910i	−1.06764	+	0.585474i
$156$	14.4683	+	12.1403i	1.15839	+	0.972003i
$157$	10.4062	+	0.910428i	0.830508	+	0.0726601i	0.494477	−	0.869191i	$-0.335360\pi$
$157$	10.4062	+	0.910428i	0.830508	+	0.0726601i	0.336031	+	0.941851i	$0.390915\pi$
$158$	−4.96031	−	7.08406i	−0.394621	−	0.563578i
$159$	4.09067	+	2.36175i	0.324411	+	0.187299i
$160$	44.8134	−	2.92910i	3.54281	−	0.231566i
$161$	1.56403	−	0.569260i	0.123263	−	0.0448640i
$162$	6.04151	−	12.9561i	0.474666	−	1.01792i
$163$	−18.5404	−	4.96787i	−1.45219	−	0.389114i	−0.555407	−	0.831579i	$-0.687437\pi$
$163$	−18.5404	−	4.96787i	−1.45219	−	0.389114i	−0.896786	+	0.442465i	$0.854104\pi$
$164$	−7.32477	+	12.6869i	−0.571969	+	0.990679i
$165$	0.0495586	−	0.0675638i	0.00385813	−	0.00525983i
$166$	−3.76670	−	4.48898i	−0.292353	−	0.348413i
$167$	−8.38975	+	0.734008i	−0.649218	+	0.0567992i	−0.407008	−	0.913425i	$-0.633428\pi$
$167$	−8.38975	+	0.734008i	−0.649218	+	0.0567992i	−0.242210	+	0.970224i	$0.577872\pi$
$168$	−5.45526	−	3.81982i	−0.420883	−	0.294705i
$169$	5.23070	−	14.3712i	0.402361	−	1.10548i
$170$	−1.94475	+	0.659764i	−0.149156	+	0.0506016i
$171$	−8.34899	+	7.42793i	−0.638464	+	0.568028i
$172$	33.8051	+	33.8051i	2.57762	+	2.57762i
$173$	2.34141	+	5.02117i	0.178014	+	0.381753i	0.974987	−	0.222263i	$-0.0713443\pi$
$173$	2.34141	+	5.02117i	0.178014	+	0.381753i	−0.796973	+	0.604015i	$0.793567\pi$
$174$	−1.58460	−	8.98671i	−0.120128	−	0.681281i
$175$	−3.71352	−	4.05554i	−0.280716	−	0.306570i
$176$	−0.614793	+	0.515872i	−0.0463417	+	0.0388853i
$177$	3.34867	−	2.34476i	0.251702	−	0.176243i
$178$	9.29183	+	34.6776i	0.696452	+	2.59920i
$179$	−2.17359	−	3.76476i	−0.162461	−	0.281391i	0.773289	−	0.634053i	$-0.218610\pi$
$179$	−2.17359	−	3.76476i	−0.162461	−	0.281391i	−0.935751	+	0.352662i	$0.885277\pi$
$180$	24.0370	−	19.2846i	1.79161	−	1.43739i
$181$	2.79502	+	7.67925i	0.207752	+	0.570794i	0.999181	−	0.0404674i	$-0.0128847\pi$
$181$	2.79502	+	7.67925i	0.207752	+	0.570794i	−0.791429	+	0.611261i	$0.790662\pi$
$182$	−4.11192	+	15.3459i	−0.304796	+	1.13751i
$183$	0.764535	−	0.204856i	0.0565160	−	0.0151434i
$184$	−2.40927	+	13.6637i	−0.177614	+	1.00730i
$185$	0.911041	+	3.72603i	0.0669811	+	0.273943i
$186$	−7.81720	+	9.31617i	−0.573185	+	0.683095i
$187$	0.0110040	−	0.0157154i	0.000804693	−	0.00114922i
$188$	−37.2188	+	17.3554i	−2.71446	+	1.26577i
$189$	−4.04162			−0.293984
$190$	−25.5203	+	7.02874i	−1.85144	+	0.509918i
$191$	0.00222991			0.000161351			8.06753e−5	−	1.00000i	$-0.499974\pi$
$191$	0.00222991			0.000161351			8.06753e−5		1.00000i	$0.499974\pi$
$192$	15.7149	−	7.32799i	1.13413	−	0.528852i
$193$	−9.80519	+	14.0033i	−0.705793	+	1.00798i	0.292864	+	0.956154i	$0.405392\pi$
$193$	−9.80519	+	14.0033i	−0.705793	+	1.00798i	−0.998656	+	0.0518222i	$0.983497\pi$
$194$	2.93816	−	3.50157i	0.210948	−	0.251398i
$195$	6.71566	+	4.07682i	0.480918	+	0.291947i
$196$	−5.40528	+	30.6549i	−0.386092	+	2.18964i
$197$	12.3964	−	3.32160i	0.883206	−	0.236654i	0.211416	−	0.977396i	$-0.432192\pi$
$197$	12.3964	−	3.32160i	0.883206	−	0.236654i	0.671790	+	0.740742i	$0.265526\pi$
$198$	−0.102233	+	0.381540i	−0.00726540	+	0.0271148i
$199$	−4.52720	−	12.4384i	−0.320925	−	0.881733i	−0.990317	−	0.138824i	$-0.955668\pi$
$199$	−4.52720	−	12.4384i	−0.320925	−	0.881733i	0.669392	−	0.742909i	$-0.266555\pi$
$200$	44.7556	−	9.90513i	3.16470	−	0.700398i
$201$	−2.61467	−	4.52874i	−0.184424	−	0.319433i
$202$	−5.22609	−	19.5040i	−0.367707	−	1.37230i
$203$	4.58280	−	3.20891i	0.321650	−	0.225221i
$204$	−0.919829	+	0.771828i	−0.0644009	+	0.0540388i
$205$	−2.20959	+	5.67892i	−0.154324	+	0.396633i
$206$	2.77842	+	15.7572i	0.193581	+	1.09786i
$207$	1.63973	+	3.51641i	0.113969	+	0.244408i
$208$	−53.2081	−	53.2081i	−3.68932	−	3.68932i
$209$	0.153403	−	0.193955i	0.0106111	−	0.0134162i
$210$	−3.95611	−	1.95182i	−0.272997	−	0.134689i
$211$	9.32616	−	25.6234i	0.642039	−	1.76399i	−0.00318404	−	0.999995i	$-0.501014\pi$
$211$	9.32616	−	25.6234i	0.642039	−	1.76399i	0.645223	−	0.763994i	$-0.276764\pi$
$212$	−31.4901	−	22.0496i	−2.16275	−	1.51437i
$213$	−4.24847	+	0.371693i	−0.291100	+	0.0254680i
$214$	−19.1142	−	22.7794i	−1.30662	−	1.55717i
$215$	16.0349	+	11.7617i	1.09357	+	0.802145i
$216$	16.8454	−	29.1771i	1.14619	−	1.98525i
$217$	−7.20186	−	1.92973i	−0.488894	−	0.130999i
$218$	20.3922	−	43.7313i	1.38114	−	2.96185i
$219$	1.15926	−	0.421938i	0.0783358	−	0.0285119i
$220$	−0.449724	+	0.512625i	−0.0303204	+	0.0345612i
$221$	1.55779	+	0.899390i	0.104788	+	0.0604995i
$222$	1.76501	+	2.52070i	0.118460	+	0.169178i
$223$	11.7255	+	1.02585i	0.785199	+	0.0686960i	0.472701	−	0.881223i	$-0.343279\pi$
$223$	11.7255	+	1.02585i	0.785199	+	0.0686960i	0.312497	+	0.949919i	$0.398834\pi$
$224$	16.9202	+	14.1978i	1.13053	+	0.948628i
$225$	8.66351	−	9.44771i	0.577567	−	0.629847i
$226$	−37.9905	−	13.8274i	−2.52709	−	0.919787i
$227$	9.52453	−	9.52453i	0.632165	−	0.632165i	−0.316445	−	0.948611i	$-0.602489\pi$
$227$	9.52453	−	9.52453i	0.632165	−	0.632165i	0.948611	+	0.316445i	$0.102489\pi$
$228$	−12.4160	+	9.24072i	−0.822268	+	0.611981i
$229$		−	1.76078i		−	0.116356i	−0.998306	−	0.0581779i	$-0.981471\pi$
$229$		−	1.76078i		−	0.116356i	0.998306	−	0.0581779i	$-0.0185291\pi$
$230$	−0.202148	+	9.18831i	−0.0133293	+	0.605859i
$231$	0.0405852	−	0.00715626i	0.00267031	−	0.000470847i
$232$	4.06462	+	46.4588i	0.266855	+	3.05017i
$233$	−0.796864	+	9.10820i	−0.0522043	+	0.596698i	0.924367	+	0.381504i	$0.124594\pi$
$233$	−0.796864	+	9.10820i	−0.0522043	+	0.596698i	−0.976571	+	0.215194i	$0.930962\pi$
$234$	−36.4725	−	6.43108i	−2.38428	−	0.420413i
$235$	−14.2049	+	9.48769i	−0.926624	+	0.618908i
$236$	−28.8128	+	16.6351i	−1.87555	+	1.08285i
$237$	−1.90625	−	0.888897i	−0.123824	−	0.0577401i
$238$	−0.915408	−	0.426862i	−0.0593371	−	0.0276694i
$239$	−15.0401	+	8.68339i	−0.972861	+	0.561682i	−0.900107	−	0.435668i	$-0.856512\pi$
$239$	−15.0401	+	8.68339i	−0.972861	+	0.561682i	−0.0727537	+	0.997350i	$0.523179\pi$
$240$	17.3748	−	11.6049i	1.12154	−	0.749094i
$241$	−6.90516	−	1.21757i	−0.444800	−	0.0784303i	−0.0532380	−	0.998582i	$-0.516954\pi$
$241$	−6.90516	−	1.21757i	−0.444800	−	0.0784303i	−0.391562	+	0.920152i	$0.628065\pi$
$242$	−2.60293	+	29.7516i	−0.167323	+	1.91251i
$243$	−1.26390	−	14.4465i	−0.0810794	−	0.926742i
$244$	−6.34383	+	1.11859i	−0.406122	+	0.0716103i
$245$	−0.284794	+	12.9448i	−0.0181948	+	0.827013i
$246$			4.88853i			0.311681i
$247$	19.3696	+	12.7434i	1.23246	+	0.810843i
$248$	43.9484	−	43.9484i	2.79072	−	2.79072i
$249$	−1.33926	−	0.487451i	−0.0848722	−	0.0308910i
$250$	28.3052	−	10.9897i	1.79018	−	0.695047i
$251$	20.1710	+	16.9254i	1.27318	+	1.06832i	0.994146	+	0.108043i	$0.0344585\pi$
$251$	20.1710	+	16.9254i	1.27318	+	1.06832i	0.279034	+	0.960281i	$0.409986\pi$
$252$	15.0991	+	1.32100i	0.951153	+	0.0832151i
$253$	−0.0492461	−	0.0703307i	−0.00309607	−	0.00442165i
$254$	12.8425	+	7.41462i	0.805810	+	0.465234i
$255$	−0.329388	+	0.375459i	−0.0206271	+	0.0235121i
$256$	−30.0980	+	10.9548i	−1.88113	+	0.684674i
$257$	7.01710	−	15.0482i	0.437714	−	0.938682i	−0.556458	−	0.830876i	$-0.687840\pi$
$257$	7.01710	−	15.0482i	0.437714	−	0.938682i	0.994172	−	0.107806i	$-0.0343824\pi$
$258$	15.4098	+	4.12903i	0.959370	+	0.257062i
$259$	−0.943287	+	1.63382i	−0.0586130	+	0.101521i
$260$	−51.5559	−	37.8167i	−3.19736	−	2.34529i
$261$	8.38300	+	9.99047i	0.518895	+	0.618394i
$262$	14.1935	−	1.24177i	0.876875	−	0.0767166i
$263$	−11.6641	−	8.16726i	−0.719237	−	0.503615i	0.155729	−	0.987800i	$-0.450227\pi$
$263$	−11.6641	−	8.16726i	−0.719237	−	0.503615i	−0.874966	+	0.484185i	$0.839116\pi$
$264$	−0.117496	+	0.322819i	−0.00723140	+	0.0198681i
$265$	−14.3402	−	7.07501i	−0.880910	−	0.434614i
$266$	−11.4586	−	6.18045i	−0.702572	−	0.378947i
$267$	6.17413	+	6.17413i	0.377850	+	0.377850i
$268$	17.9863	+	38.5717i	1.09869	+	2.35614i
$269$	3.01835	+	17.1179i	0.184032	+	1.04370i	0.927192	+	0.374585i	$0.122215\pi$
$269$	3.01835	+	17.1179i	0.184032	+	1.04370i	−0.743160	+	0.669114i	$0.766674\pi$
$270$	8.09230	−	20.7982i	0.492482	−	1.26574i
$271$	12.7715	−	10.7165i	0.775812	−	0.650984i	−0.166378	−	0.986062i	$-0.553207\pi$
$271$	12.7715	−	10.7165i	0.775812	−	0.650984i	0.942190	+	0.335078i	$0.108763\pi$
$272$	3.91875	−	2.74394i	0.237609	−	0.166376i
$273$	1.00007	+	3.73231i	0.0605270	+	0.225890i
$274$	11.8898	+	20.5938i	0.718290	+	1.24411i
$275$	−0.152496	+	0.239180i	−0.00919585	+	0.0144231i
$276$	1.83791	+	5.04963i	0.110629	+	0.303952i
$277$	−1.81234	+	6.76374i	−0.108893	+	0.406394i	−0.998758	−	0.0498306i	$-0.984132\pi$
$277$	−1.81234	+	6.76374i	−0.108893	+	0.406394i	0.889865	+	0.456224i	$0.150799\pi$
$278$	−29.7194	+	7.96329i	−1.78245	+	0.477606i
$279$	3.01812	−	17.1166i	0.180690	−	1.02474i
$280$	19.2719	+	11.6992i	1.15171	+	0.699162i
$281$	−8.31169	+	9.90549i	−0.495834	+	0.590912i	−0.954691	−	0.297598i	$-0.903814\pi$
$281$	−8.31169	+	9.90549i	−0.495834	+	0.590912i	0.458857	+	0.888510i	$0.348259\pi$
$282$	−7.86017	+	11.2255i	−0.468066	+	0.668468i
$283$	27.1358	−	12.6536i	1.61306	−	0.752181i	0.613753	−	0.789498i	$-0.289659\pi$
$283$	27.1358	−	12.6536i	1.61306	−	0.752181i	0.999303	+	0.0373174i	$0.0118813\pi$
$284$	34.7084			2.05956
$285$	−4.52055	+	4.58387i	−0.267774	+	0.271525i
$286$	0.819540			0.0484604
$287$	−2.71626	+	1.26661i	−0.160336	+	0.0747658i
$288$	−29.5331	+	42.1776i	−1.74025	+	2.48534i
$289$	10.8539	−	12.9352i	0.638464	−	0.760891i
$290$	7.33722	+	30.0082i	0.430856	+	1.76214i
$291$	0.193047	−	1.09483i	0.0113166	−	0.0641799i
$292$	−9.69810	+	2.59860i	−0.567538	+	0.152071i
$293$	0.260812	−	0.973364i	0.0152368	−	0.0568646i	−0.957889	−	0.287139i	$-0.907296\pi$
$293$	0.260812	−	0.973364i	0.0152368	−	0.0568646i	0.973126	+	0.230275i	$0.0739624\pi$
$294$	3.55267	+	9.76087i	0.207196	+	0.569265i
$295$	−10.7944	+	8.66025i	−0.628476	+	0.504219i
$296$	−7.86323	−	13.6195i	−0.457041	−	0.791618i
$297$	0.0539601	+	0.201382i	0.00313108	+	0.0116854i
$298$	15.9356	−	11.1582i	0.923126	−	0.646380i
$299$	6.16669	−	5.17447i	0.356629	−	0.299247i
$300$	13.0937	−	11.9895i	0.755967	−	0.692214i
$301$	1.69840	+	9.63209i	0.0978940	+	0.555185i
$302$	8.64826	+	18.5463i	0.497651	+	1.06722i
$303$	−3.47257	−	3.47257i	−0.199494	−	0.199494i
$304$	52.4870	−	32.3645i	3.01033	−	1.85623i
$305$	−2.53745	+	0.860836i	−0.145294	+	0.0492913i
$306$	0.805297	−	2.21254i	0.0460358	−	0.126482i
$307$	−15.7815	−	11.0503i	−0.900696	−	0.630674i	0.0287684	−	0.999586i	$-0.490841\pi$
$307$	−15.7815	−	11.0503i	−0.900696	−	0.630674i	−0.929464	+	0.368912i	$0.879730\pi$
$308$	−0.334123	+	0.0292320i	−0.0190384	+	0.00166565i
$309$	2.50138	+	2.98103i	0.142299	+	0.169585i
$310$	24.3503	−	33.1970i	1.38300	−	1.88547i
$311$	7.85674	−	13.6083i	0.445515	−	0.771655i	−0.552573	−	0.833465i	$-0.686354\pi$
$311$	7.85674	−	13.6083i	0.445515	−	0.771655i	0.998088	+	0.0618098i	$0.0196872\pi$
$312$	−31.1125	−	8.33656i	−1.76140	−	0.471965i
$313$	−9.85042	+	21.1243i	−0.556779	+	1.19402i	0.403501	+	0.914979i	$0.367793\pi$
$313$	−9.85042	+	21.1243i	−0.556779	+	1.19402i	−0.960280	+	0.279037i	$0.909985\pi$
$314$	−26.6585	+	9.70291i	−1.50443	+	0.547567i
$315$	6.29119	−	0.411206i	0.354468	−	0.0231688i
$316$	14.8245	+	8.55893i	0.833944	+	0.481478i
$317$	10.4773	+	14.9632i	0.588465	+	0.840415i	0.997394	−	0.0721514i	$-0.0229865\pi$
$317$	10.4773	+	14.9632i	0.588465	+	0.840415i	−0.408929	+	0.912566i	$0.634098\pi$
$318$	−12.7793	−	1.11805i	−0.716630	−	0.0626970i
$319$	−0.221076	−	0.185505i	−0.0123779	−	0.0103863i
$320$	−51.4686	+	28.2246i	−2.87718	+	1.57780i
$321$	−6.79611	−	2.47358i	−0.379322	−	0.138062i
$322$	−3.19628	+	3.19628i	−0.178122	+	0.178122i
$323$	−1.01170	+	1.07204i	−0.0562924	+	0.0596501i
$324$			28.2963i			1.57201i
$325$	−23.5864	−	12.2891i	−1.30834	−	0.681677i
$326$	51.3365	−	9.05201i	2.84327	−	0.501345i
$327$	−1.02282	−	11.6908i	−0.0565619	−	0.646505i
$328$	2.17745	−	24.8884i	0.120230	−	1.37423i
$329$	−8.27388	−	1.45891i	−0.456154	−	0.0804322i
$330$	−0.0444352	+	0.223180i	−0.00244608	+	0.0122857i
$331$	14.4168	−	8.32352i	0.792417	−	0.457502i	−0.0483958	−	0.998828i	$-0.515411\pi$
$331$	14.4168	−	8.32352i	0.792417	−	0.457502i	0.840813	+	0.541326i	$0.182078\pi$
$332$	10.5124	+	4.90201i	0.576942	+	0.269033i
$333$	−3.98579	−	1.85861i	−0.218420	−	0.101851i
$334$	19.8078	−	11.4360i	1.08383	−	0.625752i
$335$	9.83257	+	14.7212i	0.537211	+	0.804307i
$336$	10.1202	+	1.78447i	0.552104	+	0.0973509i
$337$	0.672016	−	7.68118i	0.0366071	−	0.418421i	−0.955675	−	0.294422i	$-0.904873\pi$
$337$	0.672016	−	7.68118i	0.0366071	−	0.418421i	0.992282	−	0.123998i	$-0.0395717\pi$
$338$	3.61997	+	41.3764i	0.196900	+	2.25058i
$339$	−9.68337	+	1.70744i	−0.525929	+	0.0927354i
$340$	2.93686	−	2.81042i	0.159274	−	0.152416i
$341$			0.384612i			0.0208279i
$342$	12.0245	−	27.8655i	0.650211	−	1.50679i
$343$	−9.94664	+	9.94664i	−0.537068	+	0.537068i
$344$	−76.6147	−	27.8855i	−4.13079	−	1.50348i
$345$	1.07478	+	1.95990i	0.0578640	+	0.105517i
$346$	−11.5261	−	9.67159i	−0.619650	−	0.519948i
$347$	−27.9964	−	2.44937i	−1.50292	−	0.131489i	−0.694245	−	0.719739i	$-0.744262\pi$
$347$	−27.9964	−	2.44937i	−1.50292	−	0.131489i	−0.808679	+	0.588250i	$0.799817\pi$
$348$	10.3603	+	14.7961i	0.555371	+	0.793152i
$349$	4.32023	+	2.49429i	0.231257	+	0.133516i	0.611152	−	0.791514i	$-0.290707\pi$
$349$	4.32023	+	2.49429i	0.231257	+	0.133516i	−0.379895	+	0.925030i	$0.624040\pi$
$350$	13.7951	+	5.71996i	0.737380	+	0.305745i
$351$	−18.3688	+	6.68569i	−0.980453	+	0.356856i
$352$	0.481529	−	1.03264i	0.0256656	−	0.0550400i
$353$	−4.61752	−	1.23726i	−0.245766	−	0.0658528i	0.133833	−	0.991004i	$-0.457271\pi$
$353$	−4.61752	−	1.23726i	−0.245766	−	0.0658528i	−0.379599	+	0.925151i	$0.623938\pi$
$354$	−5.55110	+	9.61478i	−0.295037	+	0.511020i
$355$	14.2697	−	2.19368i	0.757356	−	0.116428i
$356$	−45.6777	−	54.4366i	−2.42092	−	2.88513i
$357$	−0.244720	+	0.0214102i	−0.0129519	+	0.00113315i
$358$	9.67101	+	6.77172i	0.511129	+	0.357896i
$359$	6.95669	−	19.1134i	0.367160	−	1.00876i	−0.609276	−	0.792958i	$-0.708540\pi$
$359$	6.95669	−	19.1134i	0.367160	−	1.00876i	0.976436	−	0.215806i	$-0.0692379\pi$
$360$	−23.2531	+	47.1311i	−1.22554	+	2.48403i
$361$	−13.8237	+	13.0348i	−0.727561	+	0.686043i
$362$	−15.6935	−	15.6935i	−0.824830	−	0.824830i
$363$	3.06973	+	6.58306i	0.161119	+	0.345521i
$364$	−5.46073	−	30.9693i	−0.286220	−	1.62323i
$365$	−3.82295	+	1.68131i	−0.200102	+	0.0880040i
$366$	−1.64668	+	1.38173i	−0.0860731	+	0.0722239i
$367$	−19.0491	+	13.3384i	−0.994357	+	0.696256i	−0.953026	−	0.302889i	$-0.902049\pi$
$367$	−19.0491	+	13.3384i	−0.994357	+	0.696256i	−0.0413313	+	0.999145i	$0.513160\pi$
$368$	−5.54115	−	20.6799i	−0.288852	−	1.07801i
$369$	−3.49326	−	6.05050i	−0.181852	−	0.314976i
$370$	−6.51897	−	8.12548i	−0.338905	−	0.422423i
$371$	−2.68988	−	7.39039i	−0.139652	−	0.383690i
$372$	6.23034	−	23.2519i	0.323028	−	1.20556i
$373$	3.99297	−	1.06991i	0.206748	−	0.0553980i	−0.153959	−	0.988077i	$-0.549202\pi$
$373$	3.99297	−	1.06991i	0.206748	−	0.0553980i	0.360707	+	0.932679i	$0.382536\pi$
$374$	−0.00904755	+	0.0513112i	−0.000467838	+	0.00265324i
$375$	4.62546	−	5.75682i	0.238858	−	0.297281i
$376$	45.0176	−	53.6499i	2.32160	−	2.76678i
$377$	15.5202	−	22.1651i	0.799331	−	1.14156i
$378$	9.94790	−	4.63878i	0.511665	−	0.238593i
$379$	10.0723			0.517382			0.258691	−	0.965960i	$-0.416709\pi$
$379$	10.0723			0.517382			0.258691	+	0.965960i	$0.416709\pi$
$380$	39.9021	−	33.9576i	2.04694	−	1.74199i
$381$	3.60665			0.184774
$382$	−0.00548862	+	0.00255939i	−0.000280822	+	0.000130950i
$383$	5.48402	−	7.83199i	0.280220	−	0.400196i	−0.654227	−	0.756299i	$-0.727006\pi$
$383$	5.48402	−	7.83199i	0.280220	−	0.400196i	0.934447	+	0.356103i	$0.115895\pi$
$384$	−13.2152	+	15.7493i	−0.674387	+	0.803703i
$385$	−0.135521	+	0.0331358i	−0.00690678	+	0.00168876i
$386$	8.06187	−	45.7211i	0.410338	−	2.32714i
$387$	−22.0231	+	5.90107i	−1.11950	+	0.299968i
$388$	−2.34173	+	8.73945i	−0.118883	+	0.443678i
$389$	12.1465	+	33.3722i	0.615852	+	1.69204i	0.716916	+	0.697160i	$0.245553\pi$
$389$	12.1465	+	33.3722i	0.615852	+	1.69204i	−0.101064	+	0.994880i	$0.532225\pi$
$390$	−21.2089	−	2.32663i	−1.07395	−	0.117813i
$391$	0.255893	+	0.443220i	0.0129411	+	0.0224146i
$392$	−13.7396	−	51.2767i	−0.693953	−	2.58987i
$393$	2.83853	−	1.98756i	0.143185	−	0.100259i
$394$	−26.6997	+	22.4037i	−1.34511	+	1.12868i
$395$	6.63576	+	2.58189i	0.333882	+	0.129909i
$396$	−0.135768	−	0.769980i	−0.00682261	−	0.0386929i
$397$	5.24990	+	11.2585i	0.263485	+	0.565046i	0.992890	−	0.119037i	$-0.0379806\pi$
$397$	5.24990	+	11.2585i	0.263485	+	0.565046i	−0.729405	+	0.684082i	$0.760203\pi$
$398$	25.4193	+	25.4193i	1.27415	+	1.27415i
$399$	−3.16508	+	0.0916615i	−0.158452	+	0.00458881i
$400$	−56.1314	+	43.0390i	−2.80657	+	2.15195i
$401$	−8.13235	+	22.3435i	−0.406110	+	1.11578i	0.553107	+	0.833110i	$0.313442\pi$
$401$	−8.13235	+	22.3435i	−0.406110	+	1.11578i	−0.959218	+	0.282669i	$0.908780\pi$
$402$	11.6335	+	8.14589i	0.580228	+	0.406280i
$403$	−35.9240	+	3.14294i	−1.78950	+	0.156561i
$404$	25.6910	+	30.6173i	1.27817	+	1.52327i
$405$	1.78841	+	11.6335i	0.0888669	+	0.578072i
$406$	−7.59692	+	13.1582i	−0.377029	+	0.653033i
$407$	0.0940025	+	0.0251879i	0.00465953	+	0.00124852i
$408$	0.865426	−	1.85591i	0.0428450	−	0.0918813i
$409$	−0.681493	+	0.248043i	−0.0336976	+	0.0122649i	−0.358814	−	0.933409i	$-0.616819\pi$
$409$	−0.681493	+	0.248043i	−0.0336976	+	0.0122649i	0.325116	+	0.945674i	$0.394597\pi$
$410$	−1.07939	−	16.5140i	−0.0533073	−	0.815567i
$411$	5.00866	+	2.89175i	0.247059	+	0.142639i
$412$	−18.1656	−	25.9432i	−0.894956	−	1.27813i
$413$	−6.78063	−	0.593228i	−0.333653	−	0.0291909i
$414$	−8.07196	−	6.77318i	−0.396715	−	0.332883i
$415$	4.63179	+	1.35095i	0.227366	+	0.0663156i
$416$	100.387	+	36.5379i	4.92188	+	1.79142i
$417$	−5.29135	+	5.29135i	−0.259119	+	0.259119i
$418$	−0.154968	+	0.653465i	−0.00757975	+	0.0319620i
$419$			7.41128i			0.362065i	0.983477	+	0.181032i	$0.0579439\pi$
$419$			7.41128i			0.362065i	−0.983477	+	0.181032i	$0.942056\pi$
$420$	8.72977	+	0.192060i	0.425969	+	0.00937159i
$421$	−18.9012	+	3.33280i	−0.921190	+	0.162431i	−0.614081	−	0.789243i	$-0.710473\pi$
$421$	−18.9012	+	3.33280i	−0.921190	+	0.162431i	−0.307110	+	0.951674i	$0.599362\pi$
$422$	6.45428	+	73.7728i	0.314190	+	3.59120i
$423$	1.70694	−	19.5104i	0.0829944	−	0.948630i
$424$	64.5639	+	11.3844i	3.13550	+	0.552873i
$425$	1.02981	−	1.34107i	0.0499530	−	0.0650513i
$426$	10.0304	−	5.79107i	0.485976	−	0.280578i
$427$	−1.19439	−	0.556954i	−0.0578007	−	0.0269529i
$428$	53.3453	+	24.8753i	2.57854	+	1.20240i
$429$	0.172618	−	0.0996611i	0.00833408	−	0.00481168i
$430$	−52.9675	−	10.5458i	−2.55432	−	0.508565i
$431$	−18.9647	−	3.34399i	−0.913498	−	0.161074i	−0.302907	−	0.953020i	$-0.597957\pi$
$431$	−18.9647	−	3.34399i	−0.913498	−	0.161074i	−0.610591	+	0.791946i	$0.709068\pi$
$432$	−4.53102	+	51.7898i	−0.217999	+	2.49174i
$433$	−1.24176	−	14.1934i	−0.0596751	−	0.682089i	−0.965836	−	0.259155i	$-0.916556\pi$
$433$	−1.24176	−	14.1934i	−0.0596751	−	0.682089i	0.906161	−	0.422934i	$-0.139000\pi$
$434$	19.9413	−	3.51618i	0.957212	−	0.168782i
$435$	5.19460	+	5.42831i	0.249062	+	0.260268i
$436$			95.5099i			4.57409i
$437$	2.95982	+	5.89550i	0.141587	+	0.282020i
$438$	−2.36909	+	2.36909i	−0.113200	+	0.113200i
$439$	32.9575	+	11.9955i	1.57297	+	0.572516i	0.973661	−	0.228000i	$-0.0732186\pi$
$439$	32.9575	+	11.9955i	1.57297	+	0.572516i	0.599312	+	0.800515i	$0.295441\pi$
$440$	0.325637	−	1.11646i	0.0155241	−	0.0532251i
$441$	−11.3721	−	9.54229i	−0.541526	−	0.454395i
$442$	−4.86657	−	0.425770i	−0.231479	−	0.0202518i
$443$	−15.6814	−	22.3954i	−0.745046	−	1.06404i	−0.995393	−	0.0958795i	$-0.969434\pi$
$443$	−15.6814	−	22.3954i	−0.745046	−	1.06404i	0.250347	−	0.968156i	$-0.419455\pi$
$444$	−5.27496	−	3.04550i	−0.250339	−	0.144533i
$445$	−22.2201	−	19.4936i	−1.05333	−	0.924085i
$446$	−30.0382	+	10.9330i	−1.42235	+	0.517694i
$447$	1.99958	−	4.28811i	0.0945768	−	0.202821i
$448$	−27.8868	−	7.47224i	−1.31753	−	0.353030i
$449$	8.59814	−	14.8924i	0.405771	−	0.702816i	−0.588640	−	0.808395i	$-0.700336\pi$
$449$	8.59814	−	14.8924i	0.405771	−	0.702816i	0.994411	+	0.105579i	$0.0336697\pi$
$450$	−10.4804	+	33.1979i	−0.494052	+	1.56496i
$451$	0.0993767	+	0.118433i	0.00467947	+	0.00557677i
$452$	79.7197	−	6.97457i	3.74970	−	0.328056i
$453$	4.07690	+	2.85468i	0.191550	+	0.134125i
$454$	−12.5116	+	34.3752i	−0.587196	+	1.61331i
$455$	−4.20243	−	12.3873i	−0.197013	−	0.580726i
$456$	12.5303	−	23.2313i	0.586786	−	1.08791i
$457$	−25.3702	−	25.3702i	−1.18677	−	1.18677i	−0.977956	−	0.208810i	$-0.933041\pi$
$457$	−25.3702	−	25.3702i	−1.18677	−	1.18677i	−0.208810	−	0.977956i	$-0.566959\pi$
$458$	2.02095	+	4.33393i	0.0944326	+	0.202511i
$459$	−0.215802	−	1.22387i	−0.0100728	−	0.0571255i
$460$	−7.32363	−	16.6524i	−0.341466	−	0.776420i
$461$	−17.5641	+	14.7380i	−0.818040	+	0.686417i	−0.952512	−	0.304500i	$-0.901511\pi$
$461$	−17.5641	+	14.7380i	−0.818040	+	0.686417i	0.134472	+	0.990917i	$0.457066\pi$
$462$	−0.0916814	+	0.0641960i	−0.00426541	+	0.00298667i
$463$	−6.85057	−	25.5667i	−0.318373	−	1.18819i	−0.920808	−	0.390017i	$-0.872469\pi$
$463$	−6.85057	−	25.5667i	−0.318373	−	1.18819i	0.602435	−	0.798168i	$-0.294197\pi$
$464$	−35.9817	−	62.3221i	−1.67041	−	2.89323i
$465$	1.09189	−	9.95337i	0.0506352	−	0.461577i
$466$	−8.49260	−	23.3332i	−0.393412	−	1.08089i
$467$	2.83331	−	10.5741i	0.131110	−	0.489310i	−0.868874	−	0.495034i	$-0.835156\pi$
$467$	2.83331	−	10.5741i	0.131110	−	0.489310i	0.999984	+	0.00572460i	$0.00182221\pi$
$468$	70.8092	−	18.9733i	3.27316	−	0.877039i
$469$	−1.51194	+	8.57464i	−0.0698149	+	0.395940i
$470$	24.0739	−	39.6564i	1.11045	−	1.82921i
$471$	−4.43510	+	5.28555i	−0.204359	+	0.243545i
$472$	32.5442	−	46.4780i	1.49797	−	2.13932i
$473$	0.457263	−	0.213225i	0.0210250	−	0.00980412i
$474$	5.71221			0.262370
$475$	14.2588	−	16.4829i	0.654237	−	0.756289i
$476$	1.99927			0.0916363
$477$	16.6158	−	7.74809i	0.760787	−	0.354761i
$478$	27.0527	−	38.6353i	1.23736	−	1.76714i
$479$	−10.2823	+	12.2540i	−0.469812	+	0.559901i	−0.947964	−	0.318377i	$-0.896862\pi$
$479$	−10.2823	+	12.2540i	−0.469812	+	0.559901i	0.478152	+	0.878277i	$0.341307\pi$
$480$	−15.3931	+	25.3567i	−0.702596	+	1.15737i
$481$	−1.58447	+	8.98597i	−0.0722456	+	0.409725i
$482$	18.3936	−	4.92855i	0.837806	−	0.224489i
$483$	−0.284539	+	1.06191i	−0.0129470	+	0.0483187i
$484$	−20.2186	−	55.5500i	−0.919025	−	2.52500i
$485$	−0.410396	+	3.74106i	−0.0186351	+	0.169873i
$486$	19.6919	+	34.1074i	0.893245	+	1.54714i
$487$	3.46496	+	12.9314i	0.157012	+	0.585978i	0.998925	+	0.0463639i	$0.0147634\pi$
$487$	3.46496	+	12.9314i	0.157012	+	0.585978i	−0.841912	+	0.539615i	$0.818570\pi$
$488$	8.99897	−	6.30115i	0.407364	−	0.285239i
$489$	9.71213	−	8.14944i	0.439198	−	0.368531i
$490$	−14.1565	−	32.1888i	−0.639524	−	1.45414i
$491$	2.17040	+	12.3090i	0.0979489	+	0.555496i	0.993804	+	0.111149i	$0.0354531\pi$
$491$	2.17040	+	12.3090i	0.0979489	+	0.555496i	−0.895855	+	0.444347i	$0.853436\pi$
$492$	−4.08939	−	8.76973i	−0.184364	−	0.395370i
$493$	1.21641	+	1.21641i	0.0547846	+	0.0547846i
$494$	−62.3021	−	9.13461i	−2.80310	−	0.410986i
$495$	−0.104484	−	0.307981i	−0.00469619	−	0.0138427i
$496$	−32.8018	+	90.1221i	−1.47284	+	4.04660i
$497$	5.81661	+	4.07284i	0.260911	+	0.182692i
$498$	3.85589	−	0.337346i	0.172786	−	0.0151169i
$499$	16.4159	+	19.5637i	0.734878	+	0.875794i	0.995985	−	0.0895162i	$-0.0285321\pi$
$499$	16.4159	+	19.5637i	0.734878	+	0.875794i	−0.261107	+	0.965310i	$0.584088\pi$
$500$	−41.5847	+	43.3929i	−1.85972	+	1.94059i
$501$	2.78138	−	4.81750i	0.124263	−	0.215230i
$502$	−69.0744	−	18.5084i	−3.08294	−	0.826072i
$503$	−3.45788	+	7.41545i	−0.154179	+	0.330638i	−0.968192	−	0.250209i	$-0.919501\pi$
$503$	−3.45788	+	7.41545i	−0.154179	+	0.330638i	0.814013	+	0.580847i	$0.197279\pi$
$504$	−24.2896	+	8.84069i	−1.08194	+	0.393796i
$505$	12.4975	+	10.9640i	0.556130	+	0.487890i
$506$	0.201935	+	0.116587i	0.00897711	+	0.00518294i
$507$	5.79409	+	8.27482i	0.257325	+	0.367498i
$508$	−29.2412	−	2.55827i	−1.29737	−	0.113505i
$509$	16.8963	+	14.1777i	0.748914	+	0.628414i	0.935216	−	0.354079i	$-0.115206\pi$
$509$	16.8963	+	14.1777i	0.748914	+	0.628414i	−0.186301	+	0.982493i	$0.559650\pi$
$510$	0.379811	−	1.30220i	0.0168183	−	0.0576623i
$511$	−1.93019	−	0.702532i	−0.0853866	−	0.0310782i
$512$	17.4903	−	17.4903i	0.772969	−	0.772969i
$513$	−1.85748	−	15.9107i	−0.0820099	−	0.702473i
$514$			45.0931i			1.98897i
$515$	−9.10814	−	9.51793i	−0.401353	−	0.419410i
$516$	−31.0982	+	5.48345i	−1.36902	+	0.241396i
$517$	0.0377725	+	0.431741i	0.00166123	+	0.0189880i
$518$	0.446551	−	5.10410i	0.0196203	−	0.224261i
$519$	−3.60385	−	0.635457i	−0.158192	−	0.0278934i
$520$	106.942	+	21.2921i	4.68971	+	0.933722i
$521$	21.4600	−	12.3900i	0.940182	−	0.542814i	0.0501643	−	0.998741i	$-0.484025\pi$
$521$	21.4600	−	12.3900i	0.940182	−	0.542814i	0.890017	+	0.455927i	$0.150692\pi$
$522$	−32.1002	−	14.9686i	−1.40499	−	0.655157i
$523$	38.5530	+	17.9776i	1.68581	+	0.786104i	0.998197	+	0.0600235i	$0.0191176\pi$
$523$	38.5530	+	17.9776i	1.68581	+	0.786104i	0.687609	+	0.726081i	$0.258660\pi$
$524$	−24.4234	+	14.1009i	−1.06694	+	0.616000i
$525$	3.60122	−	0.472787i	0.157170	−	0.0206341i
$526$	38.0836	+	6.71516i	1.66052	+	0.292795i
$527$	0.199814	−	2.28389i	0.00870405	−	0.0994878i
$528$	−0.0462016	−	0.528087i	−0.00201067	−	0.0229820i
$529$	−20.3950	+	3.59619i	−0.886738	+	0.156356i
$530$	43.4168	+	0.955197i	1.88591	+	0.0414911i
$531$		−	15.8669i		−	0.688563i
$532$	25.7262	+	1.50191i	1.11537	+	0.0651159i
$533$	−10.2499	+	10.2499i	−0.443973	+	0.443973i
$534$	−22.2832	−	8.11041i	−0.964288	−	0.350972i
$535$	23.5041	+	6.85543i	1.01617	+	0.296386i
$536$	−55.6001	−	46.6540i	−2.40156	−	2.01515i
$537$	2.86047	+	0.250259i	0.123438	+	0.0107995i
$538$	−27.0765	−	38.6692i	−1.16735	−	1.66715i
$539$	0.284493	+	0.164252i	0.0122540	+	0.00707484i
$540$	2.88118	+	44.0801i	0.123986	+	1.89691i
$541$	28.1749	−	10.2548i	1.21133	−	0.440889i	0.344167	−	0.938908i	$-0.388161\pi$
$541$	28.1749	−	10.2548i	1.21133	−	0.440889i	0.867166	+	0.498019i	$0.165939\pi$
$542$	−19.1353	+	41.0359i	−0.821933	+	1.76264i
$543$	−5.21390	−	1.39706i	−0.223750	−	0.0599536i
$544$	−3.39588	+	5.88184i	−0.145597	+	0.252182i
$545$	6.03652	+	39.2671i	0.258576	+	1.68202i
$546$	−6.74532	−	8.03875i	−0.288673	−	0.344027i
$547$	−16.4117	+	1.43584i	−0.701714	+	0.0613920i	−0.432428	−	0.901668i	$-0.642343\pi$
$547$	−16.4117	+	1.43584i	−0.701714	+	0.0613920i	−0.269285	+	0.963060i	$0.586788\pi$
$548$	−38.5569	−	26.9978i	−1.64707	−	1.15329i
$549$	1.05072	−	2.88684i	0.0448438	−	0.123207i
$550$	0.100828	−	0.763738i	0.00429934	−	0.0325659i
$551$	14.7388	+	16.5664i	0.627892	+	0.705751i
$552$	−6.48018	−	6.48018i	−0.275815	−	0.275815i
$553$	1.48003	+	3.17393i	0.0629371	+	0.134969i
$554$	−3.30228	−	18.7282i	−0.140300	−	0.795684i
$555$	−2.36119	−	0.918706i	−0.100227	−	0.0389969i
$556$	46.6533	−	39.1467i	1.97854	−	1.66019i
$557$	35.5264	−	24.8758i	1.50530	−	1.05402i	0.526268	−	0.850319i	$-0.323591\pi$
$557$	35.5264	−	24.8758i	1.50530	−	1.05402i	0.979033	−	0.203704i	$-0.0652980\pi$
$558$	12.2170	+	45.5943i	0.517185	+	1.93016i
$559$	23.6526	+	40.9675i	1.00040	+	1.73274i
$560$	−34.5812	−	3.79358i	−1.46132	−	0.160308i
$561$	0.00433409	+	0.0119078i	0.000182985	+	0.000502748i
$562$	9.08906	−	33.9208i	0.383399	−	1.43086i
$563$	2.87367	−	0.769996i	0.121111	−	0.0324515i	−0.197755	−	0.980252i	$-0.563365\pi$
$563$	2.87367	−	0.769996i	0.121111	−	0.0324515i	0.318865	+	0.947800i	$0.396698\pi$
$564$	4.71024	−	26.7131i	0.198337	−	1.12482i
$565$	32.3344	−	7.90600i	1.36032	−	0.332608i
$566$	−52.2679	+	62.2905i	−2.19699	+	2.61827i
$567$	−3.32041	+	4.74204i	−0.139444	+	0.199147i
$568$	−53.6461	+	25.0156i	−2.25094	+	1.04963i
$569$	−23.8332			−0.999138			−0.499569	−	0.866274i	$-0.666508\pi$
$569$	−23.8332			−0.999138			−0.499569	+	0.866274i	$0.666508\pi$
$570$	5.86558	−	16.4711i	0.245682	−	0.689898i
$571$	35.7609			1.49655			0.748273	−	0.663391i	$-0.230883\pi$
$571$	35.7609			1.49655			0.748273	+	0.663391i	$0.230883\pi$
$572$	−1.47020	+	0.685568i	−0.0614723	+	0.0286650i
$573$	−0.000844821		0.00120653i	−3.52929e−5		5.04035e-5i
$574$	5.23195	−	6.23520i	0.218377	−	0.260252i
$575$	−4.06345	−	6.38342i	−0.169458	−	0.266207i
$576$	11.6866	−	66.2783i	0.486944	−	2.76159i
$577$	−17.3980	+	4.66177i	−0.724286	+	0.194072i	−0.602083	−	0.798433i	$-0.705663\pi$
$577$	−17.3980	+	4.66177i	−0.724286	+	0.194072i	−0.122203	+	0.992505i	$0.538996\pi$
$578$	−11.8690	+	44.2958i	−0.493686	+	1.84246i
$579$	−3.86191	−	10.6105i	−0.160496	−	0.440958i
$580$	−38.2652	−	47.6951i	−1.58888	−	1.98043i
$581$	1.18650	+	2.05508i	0.0492243	+	0.0852589i
$582$	0.781431	+	2.91634i	0.0323914	+	0.120886i
$583$	−0.332328	+	0.232699i	−0.0137636	+	0.00963740i
$584$	13.1167	−	11.0062i	0.542774	−	0.455441i
$585$	27.9127	−	12.2759i	1.15405	−	0.507544i
$586$	0.475229	+	2.69516i	0.0196315	+	0.111336i
$587$	2.68895	+	5.76648i	0.110985	+	0.238008i	0.953953	−	0.299955i	$-0.0969717\pi$
$587$	2.68895	+	5.76648i	0.110985	+	0.238008i	−0.842968	+	0.537963i	$0.819194\pi$
$588$	−14.5385	−	14.5385i	−0.599558	−	0.599558i
$589$	4.28689	−	29.2385i	0.176638	−	1.20475i
$590$	16.6292	−	33.7054i	0.684615	−	1.38763i
$591$	−2.89927	+	7.96569i	−0.119260	+	0.327665i
$592$	19.8785	+	13.9191i	0.817001	+	0.572070i
$593$	22.3952	−	1.95932i	0.919659	−	0.0804597i	0.382514	−	0.923950i	$-0.375058\pi$
$593$	22.3952	−	1.95932i	0.919659	−	0.0804597i	0.537145	+	0.843490i	$0.319503\pi$
$594$	−0.363953	−	0.433742i	−0.0149332	−	0.0177966i
$595$	0.821961	−	0.126360i	0.0336971	−	0.00518026i
$596$	−19.2534	+	33.3478i	−0.788648	+	1.36598i
$597$	8.44516	+	2.26287i	0.345637	+	0.0926133i
$598$	−9.23948	+	19.8141i	−0.377830	+	0.810260i
$599$	20.6125	−	7.50233i	0.842203	−	0.306537i	0.115346	−	0.993325i	$-0.463202\pi$
$599$	20.6125	−	7.50233i	0.842203	−	0.306537i	0.726857	+	0.686789i	$0.240980\pi$
$600$	−11.5967	+	27.9684i	−0.473434	+	1.14181i
$601$	−21.7022	−	12.5298i	−0.885253	−	0.511101i	−0.0128660	−	0.999917i	$-0.504095\pi$
$601$	−21.7022	−	12.5298i	−0.885253	−	0.511101i	−0.872387	+	0.488816i	$0.837429\pi$
$602$	−15.2357	−	21.7588i	−0.620959	−	0.886822i
$603$	−20.2197	−	1.76899i	−0.823408	−	0.0720389i
$604$	−31.0289	−	26.0363i	−1.26255	−	1.05940i
$605$	−11.8234	−	21.5605i	−0.480690	−	0.876557i
$606$	12.5329	+	4.56162i	0.509116	+	0.185303i
$607$	6.57784	−	6.57784i	0.266986	−	0.266986i	−0.560898	−	0.827885i	$-0.689544\pi$
$607$	6.57784	−	6.57784i	0.266986	−	0.266986i	0.827885	+	0.560898i	$0.189544\pi$
$608$	−48.1161	+	73.1352i	−1.95136	+	2.96602i
$609$			3.69533i			0.149742i
$610$	5.25756	−	5.03120i	0.212872	−	0.203707i
$611$	−40.0174	+	7.05614i	−1.61893	+	0.285461i
$612$	0.406193	+	4.64281i	0.0164194	+	0.187674i
$613$	1.12709	−	12.8827i	0.0455227	−	0.520327i	−0.938862	−	0.344295i	$-0.888118\pi$
$613$	1.12709	−	12.8827i	0.0455227	−	0.520327i	0.984384	−	0.176032i	$-0.0563263\pi$
$614$	51.5270	+	9.08561i	2.07946	+	0.366665i
$615$	−2.23555	−	3.34704i	−0.0901460	−	0.134966i
$616$	0.495361	−	0.285997i	0.0199586	−	0.0115231i
$617$	24.5841	+	11.4638i	0.989719	+	0.461513i	0.848918	−	0.528524i	$-0.177255\pi$
$617$	24.5841	+	11.4638i	0.989719	+	0.461513i	0.140801	+	0.990038i	$0.455032\pi$
$618$	−9.57832	−	4.46644i	−0.385296	−	0.179667i
$619$	34.6066	−	19.9802i	1.39096	−	0.803070i	0.397537	−	0.917586i	$-0.369865\pi$
$619$	34.6066	−	19.9802i	1.39096	−	0.803070i	0.993421	+	0.114516i	$0.0365317\pi$
$620$	−15.9127	+	79.9232i	−0.639069	+	3.20979i
$621$	−5.47718	−	0.965775i	−0.219792	−	0.0387552i
$622$	−3.71937	+	42.5126i	−0.149133	+	1.70460i
$623$	−1.26708	−	14.4828i	−0.0507645	−	0.580241i
$624$	48.9475	−	8.63076i	1.95947	−	0.345507i
$625$	−14.3542	+	20.4684i	−0.574168	+	0.818738i
$626$		−	63.3005i		−	2.53000i
$627$	0.0468246	+	0.156483i	0.00187000	+	0.00624933i
$628$	39.7070	−	39.7070i	1.58448	−	1.58448i
$629$	−0.545117	−	0.198406i	−0.0217353	−	0.00791098i
$630$	−15.0130	+	8.23287i	−0.598131	+	0.328005i
$631$	4.78002	+	4.01092i	0.190290	+	0.159672i	0.732955	−	0.680277i	$-0.238140\pi$
$631$	4.78002	+	4.01092i	0.190290	+	0.159672i	−0.542666	+	0.839949i	$0.682585\pi$
$632$	−29.0819	−	2.54433i	−1.15681	−	0.101208i
$633$	10.3307	+	14.7537i	0.410608	+	0.586408i
$634$	−42.9626	−	24.8045i	−1.70626	−	0.985111i
$635$	−12.1836	+	0.796350i	−0.483493	+	0.0316022i
$636$	23.8606	−	8.68456i	0.946136	−	0.344365i
$637$	−13.0169	+	27.9148i	−0.515748	+	1.10603i
$638$	0.757064	+	0.202855i	0.0299725	+	0.00803110i
$639$	−8.27639	+	14.3351i	−0.327409	+	0.567089i
$640$	41.1650	−	56.1207i	1.62719	−	2.21837i
$641$	21.0702	+	25.1105i	0.832223	+	0.991805i	0.999982	+	0.00597660i	$0.00190242\pi$
$641$	21.0702	+	25.1105i	0.832223	+	0.991805i	−0.167759	+	0.985828i	$0.553653\pi$
$642$	19.5668	−	1.71187i	0.772239	−	0.0675622i
$643$	−10.2509	−	7.17778i	−0.404257	−	0.283064i	0.353712	−	0.935354i	$-0.384919\pi$
$643$	−10.2509	−	7.17778i	−0.404257	−	0.283064i	−0.757969	+	0.652290i	$0.773808\pi$
$644$	3.06015	−	8.40770i	0.120587	−	0.331310i
$645$	−12.4389	+	4.21992i	−0.489780	+	0.166159i
$646$	1.25972	−	3.79988i	0.0495630	−	0.149504i
$647$	−26.3408	−	26.3408i	−1.03556	−	1.03556i	−0.999344	−	0.0362200i	$-0.988468\pi$
$647$	−26.3408	−	26.3408i	−1.03556	−	1.03556i	−0.0362200	−	0.999344i	$-0.511532\pi$
$648$	−20.3941	−	43.7354i	−0.801158	−	1.71809i
$649$	0.0609702	+	0.345779i	0.00239329	+	0.0135730i
$650$	72.1596	+	3.17665i	2.83033	+	0.124598i
$651$	3.77260	−	3.16559i	0.147860	−	0.124069i
$652$	−84.5223	+	59.1832i	−3.31015	+	2.31779i
$653$	−8.49167	−	31.6914i	−0.332305	−	1.24018i	−0.906762	−	0.421644i	$-0.861453\pi$
$653$	−8.49167	−	31.6914i	−0.332305	−	1.24018i	0.574457	−	0.818535i	$-0.305213\pi$
$654$	15.9357	+	27.6015i	0.623137	+	1.07931i
$655$	−9.15001	+	7.34094i	−0.357520	+	0.286834i
$656$	13.1854	+	36.2265i	0.514802	+	1.41441i
$657$	1.23930	−	4.62512i	0.0483496	−	0.180443i
$658$	22.0395	−	5.90547i	0.859190	−	0.230219i
$659$	−0.758457	+	4.30142i	−0.0295453	+	0.167560i	−0.996010	−	0.0892388i	$-0.971557\pi$
$659$	−0.758457	+	4.30142i	−0.0295453	+	0.167560i	0.966465	+	0.256799i	$0.0826677\pi$
$660$	−0.106982	−	0.437543i	−0.00416429	−	0.0170313i
$661$	13.8200	−	16.4701i	0.537536	−	0.640611i	−0.427097	−	0.904206i	$-0.640464\pi$
$661$	13.8200	−	16.4701i	0.537536	−	0.640611i	0.964633	+	0.263595i	$0.0849082\pi$
$662$	−25.9316	+	37.0342i	−1.00786	+	1.43937i
$663$	−1.07681	+	0.502126i	−0.0418199	+	0.0195009i
$664$	−19.7813			−0.767662
$665$	10.6717	−	1.00849i	0.413832	−	0.0391077i
$666$	11.9437			0.462810
$667$	6.97739	−	3.25361i	0.270166	−	0.125980i
$668$	−25.9674	+	37.0853i	−1.00471	+	1.43487i
$669$	−4.99737	+	5.95563i	−0.193209	+	0.230258i
$670$	−41.0979	−	24.9490i	−1.58775	−	0.963863i
$671$	−0.0118049	+	0.0669490i	−0.000455724	+	0.00258454i
$672$	−14.0923	+	3.77603i	−0.543623	+	0.145663i
$673$	−10.4445	+	38.9795i	−0.402607	+	1.50255i	0.405821	+	0.913952i	$0.366986\pi$
$673$	−10.4445	+	38.9795i	−0.402607	+	1.50255i	−0.808428	+	0.588595i	$0.799681\pi$
$674$	7.16203	+	19.6775i	0.275871	+	0.757950i
$675$	3.97054	+	17.9406i	0.152826	+	0.690534i
$676$	−41.1065	−	71.1986i	−1.58102	−	2.73841i
$677$	−7.17569	−	26.7801i	−0.275784	−	1.02924i	−0.955314	−	0.295593i	$-0.904483\pi$
$677$	−7.17569	−	26.7801i	−0.275784	−	1.02924i	0.679530	−	0.733648i	$-0.262184\pi$
$678$	21.8746	−	15.3168i	0.840090	−	0.588237i
$679$	−1.41797	+	1.18981i	−0.0544165	+	0.0456609i
$680$	−2.51371	+	6.46055i	−0.0963965	+	0.247751i
$681$	1.54495	+	8.76186i	0.0592027	+	0.335755i
$682$	−0.441440	−	0.946670i	−0.0169036	−	0.0362499i
$683$	16.4100	+	16.4100i	0.627913	+	0.627913i	0.947543	−	0.319630i	$-0.103558\pi$
$683$	16.4100	+	16.4100i	0.627913	+	0.627913i	−0.319630	+	0.947543i	$0.603558\pi$
$684$	1.73900	+	60.0478i	0.0664922	+	2.29598i
$685$	−17.5583	−	8.66272i	−0.670867	−	0.330985i
$686$	13.0660	−	35.8986i	0.498864	−	1.37062i
$687$	0.952701	+	0.667088i	0.0363478	+	0.0254510i
$688$	125.331	−	10.9650i	4.77820	−	0.418038i
$689$	−24.4505	−	29.1390i	−0.931491	−	1.11011i
$690$	−4.89490	−	3.59045i	−0.186346	−	0.136686i
$691$	−2.59960	+	4.50263i	−0.0988933	+	0.171288i	−0.911227	−	0.411905i	$-0.864864\pi$
$691$	−2.59960	+	4.50263i	−0.0988933	+	0.171288i	0.812334	+	0.583193i	$0.198197\pi$
$692$	28.7678	+	7.70830i	1.09359	+	0.293025i
$693$	0.0676001	−	0.144969i	0.00256792	−	0.00550691i
$694$	71.7206	−	26.1042i	2.72248	−	0.990901i
$695$	16.7064	−	19.0431i	0.633710	−	0.722345i
$696$	−26.6772	−	15.4021i	−1.01120	−	0.583815i
$697$	−0.528588	−	0.754901i	−0.0200217	−	0.0285939i
$698$	−13.4965	−	1.18079i	−0.510850	−	0.0446936i
$699$	−4.62624	−	3.88188i	−0.174981	−	0.146826i
$700$	−29.5325	+	1.27874i	−1.11622	+	0.0483317i
$701$	−42.3332	−	15.4080i	−1.59890	−	0.581954i	−0.619702	−	0.784838i	$-0.712746\pi$
$701$	−42.3332	−	15.4080i	−1.59890	−	0.581954i	−0.979203	+	0.202884i	$0.934969\pi$
$702$	37.5388	−	37.5388i	1.41681	−	1.41681i
$703$	−6.86540	−	2.96256i	−0.258934	−	0.111735i
$704$			1.48928i			0.0561293i
$705$	0.248173	−	11.2803i	0.00934674	−	0.424840i
$706$	12.7855	−	2.25443i	0.481188	−	0.0848465i
$707$	0.712656	+	8.14570i	0.0268022	+	0.306351i
$708$	1.91530	−	21.8920i	0.0719814	−	0.822751i
$709$	−26.1551	−	4.61185i	−0.982276	−	0.173202i	−0.340626	−	0.940199i	$-0.610639\pi$
$709$	−26.1551	−	4.61185i	−0.982276	−	0.173202i	−0.641650	+	0.766997i	$0.721750\pi$
$710$	−32.6051	+	21.7776i	−1.22365	+	0.817297i
$711$	−7.06996	+	4.08184i	−0.265144	+	0.153081i
$712$	109.835	+	51.2169i	4.11624	+	1.91944i
$713$	−9.29880	−	4.33610i	−0.348243	−	0.162388i
$714$	0.577771	−	0.333576i	0.0216226	−	0.0124838i
$715$	−0.561117	+	0.374780i	−0.0209846	+	0.0140160i
$716$	−23.0139	−	4.05798i	−0.860071	−	0.151654i
$717$	0.999773	−	11.4275i	0.0373372	−	0.426766i
$718$	4.81446	+	55.0296i	0.179674	+	2.05369i
$719$	−34.9293	+	6.15897i	−1.30264	+	0.229691i	−0.781568	−	0.623820i	$-0.785580\pi$
$719$	−34.9293	+	6.15897i	−1.30264	+	0.229691i	−0.521074	+	0.853511i	$0.674469\pi$
$720$	1.78375	−	81.0771i	0.0664763	−	3.02157i
$721$		−	6.47934i		−	0.241303i
$722$	19.0644	−	47.9496i	0.709502	−	1.78450i
$723$	3.27487	−	3.27487i	0.121794	−	0.121794i
$724$	41.2811	+	15.0251i	1.53420	+	0.558403i
$725$	−18.7465	−	17.1904i	−0.696227	−	0.638437i
$726$	−15.1115	−	12.6800i	−0.560839	−	0.470600i
$727$	6.96216	+	0.609110i	0.258212	+	0.0225906i	0.215527	−	0.976498i	$-0.430853\pi$
$727$	6.96216	+	0.609110i	0.258212	+	0.0225906i	0.0426854	+	0.999089i	$0.486409\pi$
$728$	30.7610	+	43.9312i	1.14008	+	1.62820i
$729$	−5.38031	−	3.10632i	−0.199271	−	0.115049i
$730$	7.47995	−	8.52614i	0.276845	−	0.315567i
$731$	−2.82608	+	1.02861i	−0.104527	+	0.0380445i
$732$	1.79819	−	3.85622i	0.0664628	−	0.142530i
$733$	27.8780	+	7.46989i	1.02970	+	0.275907i	0.733838	−	0.679324i	$-0.237727\pi$
$733$	27.8780	+	7.46989i	1.02970	+	0.275907i	0.295860	+	0.955231i	$0.404394\pi$
$734$	31.5778	−	54.6943i	1.16556	−	2.01880i
$735$	−6.89611	−	5.05835i	−0.254367	−	0.186580i
$736$	19.5376	+	23.2840i	0.720164	+	0.858258i
$737$	0.447435	−	0.0391455i	0.0164815	−	0.00144194i
$738$	15.5427	+	10.8831i	0.572134	+	0.400613i
$739$	−9.45805	+	25.9858i	−0.347920	+	0.955902i	0.635104	+	0.772426i	$0.280957\pi$
$739$	−9.45805	+	25.9858i	−0.347920	+	0.955902i	−0.983024	+	0.183476i	$0.941265\pi$
$740$	18.4918	+	9.12331i	0.679773	+	0.335379i
$741$	−14.2334	+	5.65231i	−0.522877	+	0.207643i
$742$	15.1031	+	15.1031i	0.554454	+	0.554454i
$743$	18.1744	+	38.9751i	0.666754	+	1.42986i	0.890396	+	0.455187i	$0.150428\pi$
$743$	18.1744	+	38.9751i	0.666754	+	1.42986i	−0.223641	+	0.974671i	$0.571794\pi$
$744$	7.12876	+	40.4292i	0.261353	+	1.48221i
$745$	−5.80797	+	14.9272i	−0.212787	+	0.546890i
$746$	−8.60017	+	7.21640i	−0.314874	+	0.264211i
$747$	−4.53134	+	3.17288i	−0.165793	+	0.116090i
$748$	−0.0266925	−	0.0996177i	−0.000975974	−	0.00364238i
$749$	6.02091	+	10.4285i	0.219999	+	0.381050i
$750$	−4.77755	+	19.4785i	−0.174451	+	0.711256i
$751$	−13.6486	−	37.4992i	−0.498044	−	1.36836i	−0.893162	−	0.449735i	$-0.851519\pi$
$751$	−13.6486	−	37.4992i	−0.498044	−	1.36836i	0.395118	−	0.918630i	$-0.370704\pi$
$752$	−27.9704	+	104.387i	−1.01998	+	3.80660i
$753$	−16.7997	+	4.50148i	−0.612217	+	0.164043i
$754$	−12.7608	+	72.3700i	−0.464720	+	2.63556i
$755$	−14.4025	−	8.74322i	−0.524161	−	0.318198i
$756$	−13.9655	+	16.6434i	−0.507919	+	0.605314i
$757$	14.5923	−	20.8400i	0.530368	−	0.757443i	−0.461163	−	0.887315i	$-0.652568\pi$
$757$	14.5923	−	20.8400i	0.530368	−	0.757443i	0.991531	+	0.129872i	$0.0414566\pi$
$758$	−24.7917	+	11.5606i	−0.900477	+	0.419899i
$759$	0.0567109			0.00205848
$760$	−37.1992	+	81.2446i	−1.34936	+	2.94705i
$761$	46.3395			1.67981			0.839903	−	0.542737i	$-0.182612\pi$
$761$	46.3395			1.67981			0.839903	+	0.542737i	$0.182612\pi$
$762$	−8.87729	+	4.13955i	−0.321590	+	0.149960i
$763$	−11.2076	+	16.0060i	−0.405741	+	0.579458i
$764$	0.00770526	−	0.00918277i	0.000278767	−	0.000332221i
$765$	0.460439	+	1.88313i	0.0166472	+	0.0680847i
$766$	−4.50898	+	25.5717i	−0.162916	+	0.923944i
$767$	−31.7987	+	8.52043i	−1.14818	+	0.307655i
$768$	5.47563	−	20.4353i	0.197585	−	0.737397i
$769$	−0.957858	−	2.63169i	−0.0345412	−	0.0949013i	0.921223	−	0.389034i	$-0.127191\pi$
$769$	−0.957858	−	2.63169i	−0.0345412	−	0.0949013i	−0.955764	+	0.294133i	$0.904969\pi$
$770$	0.295535	−	0.237104i	0.0106503	−	0.00854464i
$771$	5.48360	+	9.49787i	0.197487	+	0.342057i
$772$	23.7845	+	88.7649i	0.856022	+	3.19472i
$773$	15.0743	−	10.5551i	0.542184	−	0.379642i	−0.270164	−	0.962814i	$-0.587078\pi$
$773$	15.0743	−	10.5551i	0.542184	−	0.379642i	0.812348	+	0.583173i	$0.198189\pi$
$774$	47.4339	−	39.8018i	1.70498	−	1.43065i
$775$	−1.49081	+	33.8646i	−0.0535514	+	1.21645i
$776$	−2.67941	−	15.1957i	−0.0961851	−	0.545493i
$777$	−0.526633	−	1.12937i	−0.0188929	−	0.0405159i
$778$	−68.2001	−	68.2001i	−2.44509	−	2.44509i
$779$	−6.23465	−	10.1110i	−0.223379	−	0.362264i
$780$	39.9938	−	13.5680i	1.43201	−	0.485812i
$781$	0.125279	−	0.344202i	0.00448284	−	0.0123165i
$782$	−1.13856	−	0.797225i	−0.0407147	−	0.0285087i
$783$	−18.6233	+	1.62933i	−0.665544	+	0.0582276i
$784$	52.6541	+	62.7507i	1.88050	+	2.24110i
$785$	13.8152	−	18.8344i	0.493085	−	0.672228i
$786$	−4.70544	+	8.15006i	−0.167838	+	0.290703i
$787$	24.4616	+	6.55446i	0.871962	+	0.233641i	0.666936	−	0.745115i	$-0.267605\pi$
$787$	24.4616	+	6.55446i	0.871962	+	0.233641i	0.205026	+	0.978757i	$0.434272\pi$
$788$	29.1563	−	62.5259i	1.03865	−	2.22739i
$789$	8.83807	−	3.21679i	0.314644	−	0.114521i
$790$	−19.2964	+	1.26126i	−0.686536	+	0.0448735i
$791$	14.1783	+	8.18584i	0.504122	+	0.291055i
$792$	0.764799	+	1.09225i	0.0271760	+	0.0388113i
$793$	−6.34973	−	0.555529i	−0.225485	−	0.0197274i
$794$	−25.8439	−	21.6856i	−0.917165	−	0.769593i
$795$	9.26095	−	5.07856i	0.328452	−	0.180118i
$796$	−66.8646	−	24.3367i	−2.36995	−	0.862593i
$797$	−29.4472	+	29.4472i	−1.04307	+	1.04307i	−0.0440431	+	0.999030i	$0.514024\pi$
$797$	−29.4472	+	29.4472i	−1.04307	+	1.04307i	−0.999030	+	0.0440431i	$0.985976\pi$
$798$	7.68523	−	3.85835i	0.272054	−	0.136584i
$799$		−	2.58338i		−	0.0913933i
$800$	46.4007	−	89.0565i	1.64051	−	3.14862i
$801$	33.3753	−	5.88497i	1.17926	−	0.207935i
$802$	−5.62809	−	64.3294i	−0.198735	−	2.27155i
$803$	−0.00923489	+	0.105555i	−0.000325892	+	0.00372497i
$804$	−27.6841	−	4.88146i	−0.976344	−	0.172156i
$805$	0.726730	−	3.65008i	0.0256139	−	0.128648i
$806$	84.8148	−	48.9678i	2.98747	−	1.72482i
$807$	−10.4055	−	4.85215i	−0.366290	−	0.170804i
$808$	−61.7756	−	28.8064i	−2.17326	−	1.01341i
$809$	−5.30197	+	3.06110i	−0.186407	+	0.107622i	−0.590300	−	0.807184i	$-0.700990\pi$
$809$	−5.30197	+	3.06110i	−0.186407	+	0.107622i	0.403892	+	0.914807i	$0.367657\pi$
$810$	−17.7543	−	26.5816i	−0.623823	−	0.933981i
$811$	−46.3500	−	8.17276i	−1.62757	−	0.286984i	−0.715991	−	0.698110i	$-0.754025\pi$
$811$	−46.3500	−	8.17276i	−1.62757	−	0.286984i	−0.911579	+	0.411126i	$0.865136\pi$
$812$	2.62117	−	29.9601i	0.0919851	−	1.05139i
$813$	0.959775	+	10.9703i	0.0336608	+	0.384744i
$814$	−0.260284	+	0.0458951i	−0.00912296	+	0.00160862i
$815$	−31.0092	+	29.6741i	−1.08620	+	1.03944i
$816$			3.15987i			0.110618i
$817$	−37.1382	+	11.1129i	−1.29930	+	0.388791i
$818$	1.39271	−	1.39271i	0.0486950	−	0.0486950i
$819$	14.0930	+	5.12943i	0.492449	+	0.179237i
$820$	15.7507	+	28.7221i	0.550040	+	1.00302i
$821$	13.1817	+	11.0608i	0.460045	+	0.386024i	0.843148	−	0.537682i	$-0.180700\pi$
$821$	13.1817	+	11.0608i	0.460045	+	0.386024i	−0.383103	+	0.923706i	$0.625144\pi$
$822$	−15.6472	−	1.36895i	−0.545757	−	0.0477476i
$823$	13.6562	+	19.5030i	0.476024	+	0.679833i	0.983309	−	0.181946i	$-0.0582395\pi$
$823$	13.6562	+	19.5030i	0.476024	+	0.679833i	−0.507284	+	0.861779i	$0.669351\pi$
$824$	46.7755	+	27.0058i	1.62950	+	0.940792i
$825$	−0.0716379	−	0.173126i	−0.00249411	−	0.00602747i
$826$	17.3705	−	6.32235i	0.604397	−	0.219983i
$827$	5.93147	−	12.7201i	0.206257	−	0.442320i	−0.775781	−	0.631002i	$-0.782644\pi$
$827$	5.93147	−	12.7201i	0.206257	−	0.442320i	0.982038	+	0.188682i	$0.0604216\pi$
$828$	20.1465	+	5.39825i	0.700141	+	0.187602i
$829$	21.5549	−	37.3342i	0.748634	−	1.29667i	−0.199844	−	0.979828i	$-0.564044\pi$
$829$	21.5549	−	37.3342i	0.748634	−	1.29667i	0.948478	−	0.316844i	$-0.102623\pi$
$830$	−12.9511	+	1.99097i	−0.449539	+	0.0691077i
$831$	−2.97301	−	3.54310i	−0.103133	−	0.122909i
$832$	−139.104	+	12.1700i	−4.82255	+	0.421918i
$833$	−1.60404	−	1.12316i	−0.0555766	−	0.0389151i
$834$	6.95079	−	19.0971i	0.240686	−	0.661280i
$835$	−8.33210	+	16.8881i	−0.288344	+	0.584438i
$836$	−0.268637	−	1.30191i	−0.00929102	−	0.0450275i
$837$	17.6170	+	17.6170i	0.608933	+	0.608933i
$838$	−8.50633	−	18.2419i	−0.293846	−	0.630155i
$839$	−9.84832	−	55.8526i	−0.340002	−	1.92825i	−0.370782	−	0.928720i	$-0.620910\pi$
$839$	−9.84832	−	55.8526i	−0.340002	−	1.92825i	0.0307802	−	0.999526i	$-0.490201\pi$
$840$	−13.6314	+	5.99501i	−0.470327	+	0.206848i
$841$	−2.39185	+	2.00700i	−0.0824778	+	0.0692071i
$842$	42.6977	−	29.8972i	1.47146	−	1.03033i
$843$	−2.21057	−	8.24996i	−0.0761361	−	0.284144i
$844$	−73.2916	−	126.945i	−2.52280	−	4.36962i
$845$	−21.4001	−	26.6739i	−0.736187	−	0.917609i
$846$	18.1918	+	49.9815i	0.625447	+	1.71840i
$847$	3.13016	−	11.6819i	0.107553	−	0.401395i
$848$	−97.7170	+	26.1832i	−3.35562	+	0.899135i
$849$	−3.43418	+	19.4762i	−0.117861	+	0.668422i
$850$	−0.995516	+	4.48283i	−0.0341459	+	0.153760i
$851$	−1.66875	+	1.98874i	−0.0572041	+	0.0681732i
$852$	−13.1496	+	18.7795i	−0.450497	+	0.643377i
$853$	41.3939	−	19.3023i	1.41730	−	0.660897i	0.445192	−	0.895435i	$-0.353136\pi$
$853$	41.3939	−	19.3023i	1.41730	−	0.660897i	0.972107	+	0.234538i	$0.0753578\pi$
$854$	3.57909			0.122474
$855$	4.51016	+	24.5776i	0.154244	+	0.840536i
$856$	−100.380			−3.43093
$857$	−17.7948	+	8.29783i	−0.607857	+	0.283449i	−0.702075	−	0.712103i	$-0.747743\pi$
$857$	−17.7948	+	8.29783i	−0.607857	+	0.283449i	0.0942175	+	0.995552i	$0.469965\pi$
$858$	−0.310490	+	0.443426i	−0.0106000	+	0.0151383i
$859$	−22.4224	+	26.7220i	−0.765042	+	0.911742i	−0.998156	−	0.0607079i	$-0.980664\pi$
$859$	−22.4224	+	26.7220i	−0.765042	+	0.911742i	0.233114	+	0.972450i	$0.425109\pi$
$860$	103.842	−	25.3902i	3.54099	−	0.865798i
$861$	0.343757	−	1.94954i	0.0117152	−	0.0664403i
$862$	50.5172	−	13.5360i	1.72062	−	0.461040i
$863$	0.165571	−	0.617921i	0.00563612	−	0.0210343i	−0.963051	−	0.269321i	$-0.913201\pi$
$863$	0.165571	−	0.617921i	0.00563612	−	0.0210343i	0.968687	+	0.248287i	$0.0798675\pi$
$864$	−25.2436	−	69.3562i	−0.858804	−	2.35954i
$865$	12.3145	+	1.35091i	0.418706	+	0.0459322i
$866$	19.3469	+	33.5098i	0.657435	+	1.13871i
$867$	2.88669	+	10.7733i	0.0980371	+	0.365879i
$868$	−32.8320	+	22.9892i	−1.11439	+	0.780306i
$869$	0.138387	−	0.116121i	0.00469447	−	0.00393913i
$870$	−19.0162	−	7.39894i	−0.644709	−	0.250848i
$871$	7.31264	+	41.4720i	0.247779	+	1.40523i
$872$	−68.8374	−	147.622i	−2.33113	−	4.99912i
$873$	−3.05114	−	3.05114i	−0.103265	−	0.103265i
$874$	−14.0518	−	11.1138i	−0.475309	−	0.375931i
$875$	−12.0609	+	2.39228i	−0.407733	+	0.0808737i
$876$	2.26820	−	6.23182i	0.0766353	−	0.210554i
$877$	18.6179	+	13.0364i	0.628683	+	0.440208i	0.844006	−	0.536335i	$-0.180191\pi$
$877$	18.6179	+	13.0364i	0.628683	+	0.440208i	−0.215323	+	0.976543i	$0.569080\pi$
$878$	−94.8883	+	8.30165i	−3.20233	+	0.280167i
$879$	0.427844	+	0.509885i	0.0144308	+	0.0171980i
$880$	0.272676	+	1.77373i	0.00919189	+	0.0597924i
$881$	26.0649	−	45.1458i	0.878150	−	1.52100i	0.0247803	−	0.999693i	$-0.492111\pi$
$881$	26.0649	−	45.1458i	0.878150	−	1.52100i	0.853369	−	0.521307i	$-0.174555\pi$
$882$	38.9430	+	10.4347i	1.31128	+	0.351356i
$883$	−13.4512	+	28.8463i	−0.452670	+	0.970755i	0.539042	+	0.842279i	$0.318786\pi$
$883$	−13.4512	+	28.8463i	−0.452670	+	0.970755i	−0.991713	+	0.128476i	$0.958991\pi$
$884$	9.08650	−	3.30721i	0.305612	−	0.111234i
$885$	−0.596203	−	9.12152i	−0.0200411	−	0.306617i
$886$	64.3021	+	37.1248i	2.16027	+	1.24723i
$887$	19.9904	+	28.5492i	0.671210	+	0.958588i	0.999900	+	0.0141497i	$0.00450415\pi$
$887$	19.9904	+	28.5492i	0.671210	+	0.958588i	−0.328690	+	0.944438i	$0.606607\pi$
$888$	10.3481	+	0.905343i	0.347260	+	0.0303813i
$889$	−4.60019	−	3.86002i	−0.154285	−	0.129461i
$890$	77.0657	+	22.4777i	2.58325	+	0.753454i
$891$	0.280613	+	0.102135i	0.00940089	+	0.00342164i
$892$	44.7410	−	44.7410i	1.49804	−	1.49804i
$893$	1.94071	−	33.2423i	0.0649432	−	1.11241i
$894$			12.8496i			0.429756i
$895$	−9.71822	−	0.213807i	−0.324844	−	0.00714677i
$896$	33.7114	−	5.94423i	1.12622	−	0.198583i
$897$	0.463426	+	5.29699i	0.0154733	+	0.176861i
$898$	−4.07034	+	46.5242i	−0.135829	+	1.55253i
$899$	−33.9633	−	5.98865i	−1.13274	−	0.199733i
$900$	−8.96969	−	68.3221i	−0.298990	−	2.27740i
$901$	2.09432	−	1.20915i	0.0697718	−	0.0402828i
$902$	−0.380534	−	0.177446i	−0.0126704	−	0.00590830i
$903$	−5.85506	−	2.73026i	−0.194844	−	0.0908573i
$904$	−118.190	+	68.2370i	−3.93094	+	2.26953i
$905$	17.9216	+	3.56819i	0.595733	+	0.118610i
$906$	−13.3112	−	2.34713i	−0.442236	−	0.0779781i
$907$	1.41661	−	16.1919i	0.0470376	−	0.537643i	−0.935720	−	0.352744i	$-0.885249\pi$
$907$	1.41661	−	16.1919i	0.0470376	−	0.537643i	0.982758	−	0.184899i	$-0.0591957\pi$
$908$	−6.31084	−	72.1333i	−0.209433	−	2.39383i
$909$	−18.7716	+	3.30994i	−0.622614	+	0.109784i
$910$	24.5613	+	25.6664i	0.814200	+	0.850832i
$911$		−	9.96658i		−	0.330207i	−0.986276	−	0.165104i	$-0.947204\pi$
$911$		−	9.96658i		−	0.330207i	0.986276	−	0.165104i	$-0.0527959\pi$
$912$	−2.37378	+	40.6606i	−0.0786039	+	1.34641i
$913$	0.0865573	−	0.0865573i	0.00286463	−	0.00286463i
$914$	91.5640	+	33.3266i	3.02867	+	1.10235i
$915$	0.495564	−	1.69906i	0.0163828	−	0.0561693i
$916$	−7.25091	−	6.08424i	−0.239577	−	0.201029i
$917$	−5.74767	−	0.502856i	−0.189805	−	0.0166058i
$918$	1.93588	+	2.76472i	0.0638934	+	0.0912492i
$919$	−6.75011	−	3.89718i	−0.222666	−	0.128556i	0.384518	−	0.923117i	$-0.374368\pi$
$919$	−6.75011	−	3.89718i	−0.222666	−	0.128556i	−0.607184	+	0.794561i	$0.707701\pi$
$920$	23.3215	+	20.4599i	0.768888	+	0.674543i
$921$	11.9579	−	4.35232i	0.394026	−	0.143414i
$922$	26.3160	−	56.4349i	0.866672	−	1.85858i
$923$	33.1733	+	8.88877i	1.09191	+	0.292577i
$924$	0.110769	−	0.191858i	0.00364404	−	0.00631166i
$925$	8.17918	+	2.58213i	0.268930	+	0.0849000i
$926$	46.2061	+	55.0663i	1.51843	+	1.80959i
$927$	15.0467	−	1.31641i	0.494197	−	0.0432366i
$928$	83.6903	+	58.6006i	2.74727	+	1.92366i
$929$	14.1921	−	38.9925i	0.465628	−	1.27930i	−0.455567	−	0.890202i	$-0.650563\pi$
$929$	14.1921	−	38.9925i	0.465628	−	1.27930i	0.921195	−	0.389102i	$-0.127214\pi$
$930$	8.73649	+	25.7521i	0.286481	+	0.844446i
$931$	−19.7966	−	15.6576i	−0.648809	−	0.513156i
$932$	34.7541	+	34.7541i	1.13841	+	1.13841i
$933$	4.38639	+	9.40664i	0.143604	+	0.307960i
$934$	5.16261	+	29.2786i	0.168926	+	0.958026i
$935$	−0.0172703	−	0.0392689i	−0.000564798	−	0.00128423i
$936$	−95.7697	+	80.3603i	−3.13033	+	2.62666i
$937$	−7.17499	+	5.02398i	−0.234397	+	0.164126i	−0.684874	−	0.728662i	$-0.740143\pi$
$937$	−7.17499	+	5.02398i	−0.234397	+	0.164126i	0.450477	+	0.892788i	$0.351254\pi$
$938$	−6.12014	−	22.8407i	−0.199830	−	0.745775i
$939$	−7.69773	−	13.3329i	−0.251206	−	0.435102i
$940$	−10.0134	+	91.2796i	−0.326602	+	2.97721i
$941$	−0.873533	−	2.40001i	−0.0284764	−	0.0782382i	0.924640	−	0.380843i	$-0.124366\pi$
$941$	−0.873533	−	2.40001i	−0.0284764	−	0.0782382i	−0.953116	+	0.302605i	$0.902144\pi$
$942$	4.84990	−	18.1001i	0.158018	−	0.589732i
$943$	−3.98373	+	1.06744i	−0.129728	+	0.0347605i
$944$	−15.2034	+	86.2228i	−0.494829	+	2.80631i
$945$	−4.68972	+	7.72527i	−0.152557	+	0.251303i
$946$	−0.880763	+	1.04965i	−0.0286361	+	0.0341271i
$947$	3.47463	−	4.96228i	0.112910	−	0.161253i	−0.758719	−	0.651418i	$-0.774175\pi$
$947$	3.47463	−	4.96228i	0.112910	−	0.161253i	0.871630	+	0.490165i	$0.163064\pi$
$948$	−10.2474	+	4.77842i	−0.332818	+	0.155196i
$949$	−9.93468			−0.322493
$950$	−16.1777	+	56.9362i	−0.524874	+	1.84725i
$951$	−12.0655			−0.391250
$952$	−3.09012	+	1.44095i	−0.100151	+	0.0467013i
$953$	14.6549	−	20.9293i	0.474718	−	0.677967i	−0.508362	−	0.861143i	$-0.669749\pi$
$953$	14.6549	−	20.9293i	0.474718	−	0.677967i	0.983080	+	0.183176i	$0.0586379\pi$
$954$	−32.0048	+	38.1418i	−1.03619	+	1.23489i
$955$	0.00258749	−	0.00426232i	8.37292e−5	−	0.000137925i
$956$	−16.2115	+	91.9397i	−0.524316	+	2.97354i
$957$	0.184127	−	0.0493368i	0.00595199	−	0.00159483i
$958$	11.2440	−	41.9633i	0.363278	−	1.35577i
$959$	−3.29352	−	9.04887i	−0.106353	−	0.292203i
$960$	4.22797	−	38.5411i	0.136457	−	1.24391i
$961$	7.48070	+	12.9569i	0.241313	+	0.417966i
$962$	−6.41373	−	23.9364i	−0.206787	−	0.771739i
$963$	−22.9944	+	16.1008i	−0.740984	+	0.518843i
$964$	−28.8741	+	24.2283i	−0.929973	+	0.780340i
$965$	15.3888	+	34.9907i	0.495381	+	1.12639i
$966$	−0.518461	−	2.94034i	−0.0166812	−	0.0946038i
$967$	23.9316	+	51.3215i	0.769588	+	1.65039i	0.759560	+	0.650438i	$0.225415\pi$
$967$	23.9316	+	51.3215i	0.769588	+	1.65039i	0.0100288	+	0.999950i	$0.496808\pi$
$968$	71.2872	+	71.2872i	2.29126	+	2.29126i
$969$	−0.196756	−	0.953550i	−0.00632072	−	0.0306324i
$970$	−3.28369	−	9.67916i	−0.105433	−	0.310779i
$971$	17.6741	−	48.5591i	0.567188	−	1.55834i	−0.241687	−	0.970354i	$-0.577701\pi$
$971$	17.6741	−	48.5591i	0.567188	−	1.55834i	0.808875	−	0.587981i	$-0.200077\pi$
$972$	−63.8579	−	44.7138i	−2.04824	−	1.43420i
$973$	12.4121	−	1.08591i	0.397912	−	0.0348128i
$974$	−23.3706	−	27.8520i	−0.748844	−	0.892437i
$975$	15.5851	−	8.10596i	0.499124	−	0.259598i
$976$	−8.47591	+	14.6807i	−0.271307	+	0.469918i
$977$	5.27403	+	1.41317i	0.168731	+	0.0452114i	0.342196	−	0.939629i	$-0.388829\pi$
$977$	5.27403	+	1.41317i	0.168731	+	0.0452114i	−0.173464	+	0.984840i	$0.555496\pi$
$978$	−14.5516	+	31.2059i	−0.465308	+	0.997855i
$979$	−0.704719	+	0.256497i	−0.0225229	+	0.00819767i
$980$	52.3227	+	45.9025i	1.67139	+	1.46630i
$981$	−39.4471	−	22.7748i	−1.25945	−	0.727144i
$982$	−19.4698	−	27.8058i	−0.621307	−	0.887318i
$983$	61.5326	+	5.38341i	1.96259	+	0.171704i	0.996311	−	0.0858119i	$-0.0273484\pi$
$983$	61.5326	+	5.38341i	1.96259	+	0.171704i	0.966274	+	0.257516i	$0.0829040\pi$
$984$	12.6413	+	10.6073i	0.402991	+	0.338149i
$985$	8.03522	−	27.5491i	0.256023	−	0.877787i
$986$	−4.39019	−	1.59790i	−0.139812	−	0.0508875i
$987$	3.92400	−	3.92400i	0.124902	−	0.124902i
$988$	119.408	−	35.7305i	3.79886	−	1.13674i
$989$			13.4592i			0.427978i
$990$	0.610660	+	0.638134i	0.0194080	+	0.0202812i
$991$	35.6180	−	6.28041i	1.13144	−	0.199504i	0.423583	−	0.905857i	$-0.360772\pi$
$991$	35.6180	−	6.28041i	1.13144	−	0.199504i	0.707859	+	0.706354i	$0.249661\pi$
$992$	−11.8670	−	135.640i	−0.376778	−	4.30659i
$993$	−0.958339	+	10.9539i	−0.0304120	+	0.347611i
$994$	−18.9914	−	3.34870i	−0.602372	−	0.106214i
$995$	−29.0283	−	5.77953i	−0.920258	−	0.183223i
$996$	−6.63503	+	3.83073i	−0.210239	+	0.121381i
$997$	30.5123	+	14.2281i	0.966335	+	0.450609i	0.840720	−	0.541470i	$-0.182132\pi$
$997$	30.5123	+	14.2281i	0.966335	+	0.450609i	0.125615	+	0.992079i	$0.459910\pi$
$998$	−62.8600	−	29.3121i	−1.98980	−	0.927859i
$999$	5.45948	−	3.15203i	0.172730	−	0.0997259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.r.a.72.1	yes	96
3.2	odd	2		855.2.dl.a.262.8		96
5.2	odd	4		475.2.bb.b.243.1		96
5.3	odd	4	inner	95.2.r.a.53.8	yes	96
5.4	even	2		475.2.bb.b.357.8		96
15.8	even	4		855.2.dl.a.433.1		96
19.14	odd	18	inner	95.2.r.a.52.8	yes	96
57.14	even	18		855.2.dl.a.622.1		96
95.14	odd	18		475.2.bb.b.432.1		96
95.33	even	36	inner	95.2.r.a.33.1	✓	96
95.52	even	36		475.2.bb.b.318.8		96
285.128	odd	36		855.2.dl.a.793.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.33.1	✓	96	95.33	even	36	inner
95.2.r.a.52.8	yes	96	19.14	odd	18	inner
95.2.r.a.53.8	yes	96	5.3	odd	4	inner
95.2.r.a.72.1	yes	96	1.1	even	1	trivial
475.2.bb.b.243.1		96	5.2	odd	4
475.2.bb.b.318.8		96	95.52	even	36
475.2.bb.b.357.8		96	5.4	even	2
475.2.bb.b.432.1		96	95.14	odd	18
855.2.dl.a.262.8		96	3.2	odd	2
855.2.dl.a.433.1		96	15.8	even	4
855.2.dl.a.622.1		96	57.14	even	18
855.2.dl.a.793.8		96	285.128	odd	36

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46137 + 1.14775i) q^{2} +(-0.378859 + 0.541067i) q^{3} +(3.45542 - 4.11800i) q^{4} +(1.16036 - 1.91143i) q^{5} +(0.311499 - 1.76660i) q^{6} +(1.06230 - 0.284643i) q^{7} +(-2.37278 + 8.85533i) q^{8} +(0.876841 + 2.40910i) q^{9} +O(q^{10})\)	\(q+(-2.46137 + 1.14775i) q^{2} +(-0.378859 + 0.541067i) q^{3} +(3.45542 - 4.11800i) q^{4} +(1.16036 - 1.91143i) q^{5} +(0.311499 - 1.76660i) q^{6} +(1.06230 - 0.284643i) q^{7} +(-2.37278 + 8.85533i) q^{8} +(0.876841 + 2.40910i) q^{9} +(-0.662211 + 6.03654i) q^{10} +(-0.0283658 - 0.0491311i) q^{11} +(0.918999 + 3.42975i) q^{12} +(4.35721 - 3.05095i) q^{13} +(-2.28801 + 1.91987i) q^{14} +(0.594600 + 1.35199i) q^{15} +(-2.45651 - 13.9316i) q^{16} +(0.142917 + 0.306486i) q^{17} +(-4.92329 - 4.92329i) q^{18} +(1.60878 + 4.05115i) q^{19} +(-3.86177 - 11.3831i) q^{20} +(-0.248452 + 0.682615i) q^{21} +(0.126209 + 0.0883726i) q^{22} +(1.50764 - 0.131902i) q^{23} +(-3.89238 - 4.63875i) q^{24} +(-2.30714 - 4.43589i) q^{25} +(-7.22295 + 12.5105i) q^{26} +(-3.54972 - 0.951146i) q^{27} +(2.49853 - 5.35812i) q^{28} +(4.78022 - 1.73986i) q^{29} +(-3.01529 - 2.64530i) q^{30} +(-5.87120 - 3.38974i) q^{31} +(11.5197 + 16.4518i) q^{32} +(0.0373298 + 0.00326594i) q^{33} +(-0.703540 - 0.590341i) q^{34} +(0.688574 - 2.36080i) q^{35} +(12.9505 + 4.71361i) q^{36} +(-1.21298 + 1.21298i) q^{37} +(-8.60952 - 8.12489i) q^{38} +3.51342i q^{39} +(14.1731 + 14.8108i) q^{40} +(-2.68375 + 0.473218i) q^{41} +(-0.171944 - 1.96533i) q^{42} +(-0.775106 + 8.85950i) q^{43} +(-0.300338 - 0.0529576i) q^{44} +(5.62228 + 1.11940i) q^{45} +(-3.55948 + 2.05506i) q^{46} +(-6.92356 - 3.22851i) q^{47} +(8.46859 + 3.94897i) q^{48} +(-5.01471 + 2.89525i) q^{49} +(10.7700 + 8.27032i) q^{50} +(-0.219974 - 0.0387874i) q^{51} +(2.49214 - 28.4853i) q^{52} +(-0.623266 - 7.12396i) q^{53} +(9.82886 - 1.73309i) q^{54} +(-0.126825 - 0.00279023i) q^{55} +10.0824i q^{56} +(-2.80144 - 0.664359i) q^{57} +(-9.76896 + 9.76896i) q^{58} +(-5.81577 - 2.11677i) q^{59} +(7.62210 + 2.22313i) q^{60} +(-0.917954 - 0.770255i) q^{61} +(18.3418 + 1.60470i) q^{62} +(1.61720 + 2.30961i) q^{63} +(-22.7343 - 13.1256i) q^{64} +(-0.775764 - 11.8687i) q^{65} +(-0.0956310 + 0.0348068i) q^{66} +(-3.34587 + 7.17523i) q^{67} +(1.75594 + 0.470504i) q^{68} +(-0.499817 + 0.865708i) q^{69} +(1.01479 + 6.60112i) q^{70} +(4.15020 + 4.94602i) q^{71} +(-23.4139 + 2.04845i) q^{72} +(-1.52994 - 1.07128i) q^{73} +(1.59339 - 4.37781i) q^{74} +(3.27419 + 0.432258i) q^{75} +(22.2417 + 7.37346i) q^{76} +(-0.0441179 - 0.0441179i) q^{77} +(-4.03254 - 8.64781i) q^{78} +(0.552952 + 3.13594i) q^{79} +(-29.4797 - 11.4702i) q^{80} +(-4.03228 + 3.38348i) q^{81} +(6.06257 - 4.24506i) q^{82} +(0.558456 + 2.08419i) q^{83} +(1.95251 + 3.38184i) q^{84} +(0.751660 + 0.0824575i) q^{85} +(-8.26071 - 22.6961i) q^{86} +(-0.869651 + 3.24558i) q^{87} +(0.502378 - 0.134612i) q^{88} +(2.29549 - 13.0183i) q^{89} +(-15.1233 + 3.69776i) q^{90} +(3.76024 - 4.48128i) q^{91} +(4.66637 - 6.66426i) q^{92} +(4.05843 - 1.89248i) q^{93} +20.7470 q^{94} +(9.61026 + 1.62571i) q^{95} -13.2658 q^{96} +(-1.52540 + 0.711305i) q^{97} +(9.02002 - 12.8819i) q^{98} +(0.0934894 - 0.111416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more