LMFDB - Embedded newform 135.2.q.a.32.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

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

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			32.3
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.174019 + 1.98905i) q^{2} +(-1.19471 + 1.25406i) q^{3} +(-1.95641 - 0.344968i) q^{4} +(-1.97598 - 1.04667i) q^{5} +(-2.28648 - 2.59457i) q^{6} +(-0.808730 + 1.15499i) q^{7} +(-0.00692938 + 0.0258608i) q^{8} +(-0.145327 - 2.99648i) q^{9} +O(q^{10})$	\(q+(-0.174019 + 1.98905i) q^{2} +(-1.19471 + 1.25406i) q^{3} +(-1.95641 - 0.344968i) q^{4} +(-1.97598 - 1.04667i) q^{5} +(-2.28648 - 2.59457i) q^{6} +(-0.808730 + 1.15499i) q^{7} +(-0.00692938 + 0.0258608i) q^{8} +(-0.145327 - 2.99648i) q^{9} +(2.42573 - 3.74817i) q^{10} +(-1.21986 + 3.35154i) q^{11} +(2.76996 - 2.04132i) q^{12} +(3.03799 - 0.265789i) q^{13} +(-2.15659 - 1.80959i) q^{14} +(3.67331 - 1.22753i) q^{15} +(-3.78380 - 1.37719i) q^{16} +(1.05009 + 3.91899i) q^{17} +(5.98543 + 0.232383i) q^{18} +(1.42357 - 0.821896i) q^{19} +(3.50476 + 2.72936i) q^{20} +(-0.482221 - 2.39407i) q^{21} +(-6.45408 - 3.00959i) q^{22} +(-5.24614 + 3.67339i) q^{23} +(-0.0241523 - 0.0395861i) q^{24} +(2.80898 + 4.13638i) q^{25} +6.08895i q^{26} +(3.93138 + 3.39768i) q^{27} +(1.98064 - 1.98064i) q^{28} +(2.12205 - 1.78061i) q^{29} +(1.80238 + 7.51999i) q^{30} +(-1.13538 + 6.43905i) q^{31} +(3.37512 - 7.23797i) q^{32} +(-2.74564 - 5.53389i) q^{33} +(-7.97779 + 1.40670i) q^{34} +(2.80692 - 1.43576i) q^{35} +(-0.749370 + 5.91247i) q^{36} +(-2.80529 + 0.751675i) q^{37} +(1.38706 + 2.97456i) q^{38} +(-3.29620 + 4.12736i) q^{39} +(0.0407599 - 0.0438476i) q^{40} +(5.92728 - 7.06386i) q^{41} +(4.84583 - 0.542546i) q^{42} +(5.17078 - 2.41117i) q^{43} +(3.54272 - 6.13617i) q^{44} +(-2.84915 + 6.07308i) q^{45} +(-6.39361 - 11.0741i) q^{46} +(6.52449 + 4.56850i) q^{47} +(6.24763 - 3.09976i) q^{48} +(1.71419 + 4.70971i) q^{49} +(-8.71627 + 4.86738i) q^{50} +(-6.16920 - 3.36519i) q^{51} +(-6.03524 - 0.528015i) q^{52} +(-8.37726 - 8.37726i) q^{53} +(-7.44228 + 7.22844i) q^{54} +(5.91836 - 5.34577i) q^{55} +(-0.0242649 - 0.0289177i) q^{56} +(-0.670045 + 2.76716i) q^{57} +(3.17244 + 4.53071i) q^{58} +(13.4607 - 4.89929i) q^{59} +(-7.60995 + 1.13437i) q^{60} +(1.11559 + 6.32681i) q^{61} +(-12.6100 - 3.37884i) q^{62} +(3.57842 + 2.25549i) q^{63} +(6.83499 + 3.94619i) q^{64} +(-6.28119 - 2.65457i) q^{65} +(11.4850 - 4.49821i) q^{66} +(-1.01692 - 11.6234i) q^{67} +(-0.702481 - 8.02940i) q^{68} +(1.66098 - 10.9676i) q^{69} +(2.36733 + 5.83294i) q^{70} +(0.966172 + 0.557819i) q^{71} +(0.0784983 + 0.0170055i) q^{72} +(-8.19480 - 2.19579i) q^{73} +(-1.00694 - 5.71065i) q^{74} +(-8.54318 - 1.41916i) q^{75} +(-3.06861 + 1.11688i) q^{76} +(-2.88444 - 4.11941i) q^{77} +(-7.63590 - 7.27454i) q^{78} +(3.51532 + 4.18939i) q^{79} +(6.03525 + 6.68168i) q^{80} +(-8.95776 + 0.870937i) q^{81} +(13.0189 + 13.0189i) q^{82} +(-6.05220 - 0.529499i) q^{83} +(0.117545 + 4.85013i) q^{84} +(2.02692 - 8.84293i) q^{85} +(3.89612 + 10.7045i) q^{86} +(-0.302247 + 4.78848i) q^{87} +(-0.0782205 - 0.0547706i) q^{88} +(0.0742532 + 0.128610i) q^{89} +(-11.5838 - 6.72393i) q^{90} +(-2.14993 + 3.72378i) q^{91} +(11.5308 - 5.37690i) q^{92} +(-6.71849 - 9.11664i) q^{93} +(-10.2223 + 12.1825i) q^{94} +(-3.67319 + 0.134049i) q^{95} +(5.04455 + 12.8799i) q^{96} +(5.45218 + 11.6922i) q^{97} +(-9.66613 + 2.59003i) q^{98} +(10.2201 + 3.16821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.174019	+	1.98905i	−0.123050	+	1.40647i	0.644071	+	0.764966i	$0.277244\pi$
$2$	−0.174019	+	1.98905i	−0.123050	+	1.40647i	−0.767121	+	0.641503i	$0.778311\pi$
$3$	−1.19471	+	1.25406i	−0.689767	+	0.724031i
$3$	−1.19471	+	1.25406i	−0.689767	+	0.724031i
$4$	−1.95641	−	0.344968i	−0.978205	−	0.172484i
$5$	−1.97598	−	1.04667i	−0.883684	−	0.468084i
$5$	−1.97598	−	1.04667i	−0.883684	−	0.468084i
$6$	−2.28648	−	2.59457i	−0.933451	−	1.05923i
$7$	−0.808730	+	1.15499i	−0.305671	+	0.436543i	−0.942372	−	0.334567i	$-0.891410\pi$
$7$	−0.808730	+	1.15499i	−0.305671	+	0.436543i	0.636701	+	0.771111i	$0.280299\pi$
$8$	−0.00692938	+	0.0258608i	−0.00244991	+	0.00914317i
$9$	−0.145327	−	2.99648i	−0.0484422	−	0.998826i
$10$	2.42573	−	3.74817i	0.767082	−	1.18528i
$11$	−1.21986	+	3.35154i	−0.367801	+	1.01053i	0.608394	+	0.793635i	$0.291814\pi$
$11$	−1.21986	+	3.35154i	−0.367801	+	1.01053i	−0.976196	+	0.216891i	$0.930408\pi$
$12$	2.76996	−	2.04132i	0.799618	−	0.589277i
$13$	3.03799	−	0.265789i	0.842586	−	0.0737167i	0.342315	−	0.939585i	$-0.388789\pi$
$13$	3.03799	−	0.265789i	0.842586	−	0.0737167i	0.500271	+	0.865869i	$0.333234\pi$
$14$	−2.15659	−	1.80959i	−0.576372	−	0.483633i
$15$	3.67331	−	1.22753i	0.948444	−	0.316946i
$16$	−3.78380	−	1.37719i	−0.945951	−	0.344298i
$17$	1.05009	+	3.91899i	0.254684	+	0.950495i	0.968266	+	0.249922i	$0.0804051\pi$
$17$	1.05009	+	3.91899i	0.254684	+	0.950495i	−0.713582	+	0.700572i	$0.752928\pi$
$18$	5.98543	+	0.232383i	1.41078	+	0.0547731i
$19$	1.42357	−	0.821896i	0.326588	−	0.188556i	−0.327737	−	0.944769i	$-0.606286\pi$
$19$	1.42357	−	0.821896i	0.326588	−	0.188556i	0.654325	+	0.756213i	$0.272953\pi$
$20$	3.50476	+	2.72936i	0.783687	+	0.610303i
$21$	−0.482221	−	2.39407i	−0.105229	−	0.522429i
$22$	−6.45408	−	3.00959i	−1.37602	−	0.641646i
$23$	−5.24614	+	3.67339i	−1.09390	+	0.765954i	−0.973936	−	0.226824i	$-0.927166\pi$
$23$	−5.24614	+	3.67339i	−1.09390	+	0.765954i	−0.119960	+	0.992779i	$0.538277\pi$
$24$	−0.0241523	−	0.0395861i	−0.00493008	−	0.00808047i
$25$	2.80898	+	4.13638i	0.561795	+	0.827276i
$26$			6.08895i			1.19414i
$27$	3.93138	+	3.39768i	0.756595	+	0.653884i
$28$	1.98064	−	1.98064i	0.374306	−	0.374306i
$29$	2.12205	−	1.78061i	0.394054	−	0.330651i	−0.424136	−	0.905599i	$-0.639422\pi$
$29$	2.12205	−	1.78061i	0.394054	−	0.330651i	0.818190	+	0.574948i	$0.194978\pi$
$30$	1.80238	+	7.51999i	0.329069	+	1.37296i
$31$	−1.13538	+	6.43905i	−0.203920	+	1.15649i	0.695211	+	0.718806i	$0.255311\pi$
$31$	−1.13538	+	6.43905i	−0.203920	+	1.15649i	−0.899130	+	0.437681i	$0.855800\pi$
$32$	3.37512	−	7.23797i	0.596643	−	1.27951i
$33$	−2.74564	−	5.53389i	−0.477955	−	0.963327i
$34$	−7.97779	+	1.40670i	−1.36818	+	0.241247i
$35$	2.80692	−	1.43576i	0.474456	−	0.242687i
$36$	−0.749370	+	5.91247i	−0.124895	+	0.985412i
$37$	−2.80529	+	0.751675i	−0.461186	+	0.123575i	−0.481929	−	0.876210i	$-0.660064\pi$
$37$	−2.80529	+	0.751675i	−0.461186	+	0.123575i	0.0207425	+	0.999785i	$0.493397\pi$
$38$	1.38706	+	2.97456i	0.225011	+	0.482538i
$39$	−3.29620	+	4.12736i	−0.527815	+	0.660906i
$40$	0.0407599	−	0.0438476i	0.00644471	−	0.00693292i
$41$	5.92728	−	7.06386i	0.925686	−	1.10319i	−0.0687280	−	0.997635i	$-0.521894\pi$
$41$	5.92728	−	7.06386i	0.925686	−	1.10319i	0.994414	−	0.105554i	$-0.0336615\pi$
$42$	4.84583	−	0.542546i	0.747728	−	0.0837167i
$43$	5.17078	−	2.41117i	0.788536	−	0.367701i	0.0137353	−	0.999906i	$-0.495628\pi$
$43$	5.17078	−	2.41117i	0.788536	−	0.367701i	0.774801	+	0.632205i	$0.217850\pi$
$44$	3.54272	−	6.13617i	0.534085	−	0.925062i
$45$	−2.84915	+	6.07308i	−0.424726	+	0.905322i
$46$	−6.39361	−	11.0741i	−0.942687	−	1.63278i
$47$	6.52449	+	4.56850i	0.951695	+	0.666384i	0.942723	−	0.333576i	$-0.108255\pi$
$47$	6.52449	+	4.56850i	0.951695	+	0.666384i	0.00897134	+	0.999960i	$0.497144\pi$
$48$	6.24763	−	3.09976i	0.901768	−	0.447412i
$49$	1.71419	+	4.70971i	0.244885	+	0.672815i
$50$	−8.71627	+	4.86738i	−1.23267	+	0.688351i
$51$	−6.16920	−	3.36519i	−0.863861	−	0.471221i
$52$	−6.03524	−	0.528015i	−0.836937	−	0.0732225i
$53$	−8.37726	−	8.37726i	−1.15070	−	1.15070i	−0.986412	−	0.164293i	$-0.947466\pi$
$53$	−8.37726	−	8.37726i	−1.15070	−	1.15070i	−0.164293	−	0.986412i	$-0.552534\pi$
$54$	−7.44228	+	7.22844i	−1.01277	+	0.983667i
$55$	5.91836	−	5.34577i	0.798031	−	0.720824i
$56$	−0.0242649	−	0.0289177i	−0.00324253	−	0.00386429i
$57$	−0.670045	+	2.76716i	−0.0887496	+	0.366520i
$58$	3.17244	+	4.53071i	0.416561	+	0.594911i
$59$	13.4607	−	4.89929i	1.75243	−	0.637833i	0.752643	−	0.658429i	$-0.228779\pi$
$59$	13.4607	−	4.89929i	1.75243	−	0.637833i	0.999788	+	0.0205964i	$0.00655651\pi$
$60$	−7.60995	+	1.13437i	−0.982440	+	0.146447i
$61$	1.11559	+	6.32681i	0.142836	+	0.810066i	0.969079	+	0.246751i	$0.0793630\pi$
$61$	1.11559	+	6.32681i	0.142836	+	0.810066i	−0.826242	+	0.563315i	$0.809526\pi$
$62$	−12.6100	−	3.37884i	−1.60147	−	0.429113i
$63$	3.57842	+	2.25549i	0.450838	+	0.284165i
$64$	6.83499	+	3.94619i	0.854374	+	0.493273i
$65$	−6.28119	−	2.65457i	−0.779085	−	0.329258i
$66$	11.4850	−	4.49821i	1.41370	−	0.553691i
$67$	−1.01692	−	11.6234i	−0.124236	−	1.42002i	−0.760893	−	0.648877i	$-0.775239\pi$
$67$	−1.01692	−	11.6234i	−0.124236	−	1.42002i	0.636658	−	0.771147i	$-0.280317\pi$
$68$	−0.702481	−	8.02940i	−0.0851884	−	0.973708i
$69$	1.66098	−	10.9676i	0.199959	−	1.32034i
$70$	2.36733	+	5.83294i	0.282950	+	0.697169i
$71$	0.966172	+	0.557819i	0.114663	+	0.0662010i	0.556235	−	0.831025i	$-0.312245\pi$
$71$	0.966172	+	0.557819i	0.114663	+	0.0662010i	−0.441571	+	0.897226i	$0.645579\pi$
$72$	0.0784983	+	0.0170055i	0.00925112	+	0.00200411i
$73$	−8.19480	−	2.19579i	−0.959129	−	0.256998i	−0.254898	−	0.966968i	$-0.582042\pi$
$73$	−8.19480	−	2.19579i	−0.959129	−	0.256998i	−0.704232	+	0.709970i	$0.748708\pi$
$74$	−1.00694	−	5.71065i	−0.117055	−	0.663850i
$75$	−8.54318	−	1.41916i	−0.986482	−	0.163871i
$76$	−3.06861	+	1.11688i	−0.351993	+	0.128115i
$77$	−2.88444	−	4.11941i	−0.328712	−	0.469450i
$78$	−7.63590	−	7.27454i	−0.864596	−	0.823680i
$79$	3.51532	+	4.18939i	0.395504	+	0.471344i	0.926644	−	0.375941i	$-0.122680\pi$
$79$	3.51532	+	4.18939i	0.395504	+	0.471344i	−0.531139	+	0.847284i	$0.678236\pi$
$80$	6.03525	+	6.68168i	0.674761	+	0.747035i
$81$	−8.95776	+	0.870937i	−0.995307	+	0.0967707i
$82$	13.0189	+	13.0189i	1.43770	+	1.43770i
$83$	−6.05220	−	0.529499i	−0.664315	−	0.0581201i	−0.249989	−	0.968249i	$-0.580427\pi$
$83$	−6.05220	−	0.529499i	−0.664315	−	0.0581201i	−0.414326	+	0.910129i	$0.635983\pi$
$84$	0.117545	+	4.85013i	0.0128252	+	0.529193i
$85$	2.02692	−	8.84293i	0.219850	−	0.959151i
$86$	3.89612	+	10.7045i	0.420130	+	1.15430i
$87$	−0.302247	+	4.78848i	−0.0324042	+	0.513379i
$88$	−0.0782205	−	0.0547706i	−0.00833833	−	0.00583856i
$89$	0.0742532	+	0.128610i	0.00787082	+	0.0136327i	0.869934	−	0.493168i	$-0.164161\pi$
$89$	0.0742532	+	0.128610i	0.00787082	+	0.0136327i	−0.862063	+	0.506801i	$0.830828\pi$
$90$	−11.5838	−	6.72393i	−1.22104	−	0.708764i
$91$	−2.14993	+	3.72378i	−0.225374	+	0.390358i
$92$	11.5308	−	5.37690i	1.20217	−	0.560581i
$93$	−6.71849	−	9.11664i	−0.696675	−	0.945351i
$94$	−10.2223	+	12.1825i	−1.05435	+	1.25653i
$95$	−3.67319	+	0.134049i	−0.376861	+	0.0137532i
$96$	5.04455	+	12.8799i	0.514857	+	1.31455i
$97$	5.45218	+	11.6922i	0.553585	+	1.18717i	0.961667	+	0.274222i	$0.0884202\pi$
$97$	5.45218	+	11.6922i	0.553585	+	1.18717i	−0.408081	+	0.912946i	$0.633802\pi$
$98$	−9.66613	+	2.59003i	−0.976427	+	0.261633i
$99$	10.2201	+	3.16821i	1.02716	+	0.318417i
$100$	−4.06859	−	9.06146i	−0.406859	−	0.906146i
$101$	−5.20108	+	0.917090i	−0.517526	+	0.0912539i	−0.426310	−	0.904577i	$-0.640187\pi$
$101$	−5.20108	+	0.917090i	−0.517526	+	0.0912539i	−0.0912166	+	0.995831i	$0.529076\pi$
$102$	7.76708	−	11.6852i	0.769055	−	1.15701i
$103$	−1.36382	+	2.92471i	−0.134381	+	0.288181i	−0.961971	−	0.273153i	$-0.911934\pi$
$103$	−1.36382	+	2.92471i	−0.134381	+	0.288181i	0.827590	+	0.561333i	$0.189711\pi$
$104$	−0.0141778	+	0.0804065i	−0.00139025	+	0.00788451i
$105$	−1.55294	+	5.23535i	−0.151551	+	0.510918i
$106$	18.1206	−	15.2050i	1.76002	−	1.47684i
$107$	−9.12902	+	9.12902i	−0.882536	+	0.882536i	−0.993792	−	0.111256i	$-0.964513\pi$
$107$	−9.12902	+	9.12902i	−0.882536	+	0.882536i	0.111256	+	0.993792i	$0.464513\pi$
$108$	−6.51931	−	8.00346i	−0.627321	−	0.770133i
$109$		−	7.32304i		−	0.701420i	−0.936484	−	0.350710i	$-0.885940\pi$
$109$		−	7.32304i		−	0.701420i	0.936484	−	0.350710i	$-0.114060\pi$
$110$	9.60309	+	12.7022i	0.915619	+	1.21110i
$111$	2.40887	−	4.41603i	0.228639	−	0.419151i
$112$	4.65071	−	3.25646i	0.439451	−	0.307707i
$113$	13.7937	+	6.43209i	1.29760	+	0.605081i	0.943885	−	0.330273i	$-0.107141\pi$
$113$	13.7937	+	6.43209i	1.29760	+	0.605081i	0.353714	+	0.935354i	$0.384919\pi$
$114$	−5.38742	−	1.81429i	−0.504578	−	0.169924i
$115$	14.2111	−	1.76757i	1.32519	−	0.164827i
$116$	−4.76585	+	2.75156i	−0.442498	+	0.255476i
$117$	−1.23793	−	9.06463i	−0.114447	−	0.838026i
$118$	7.40249	+	27.6265i	0.681455	+	2.54322i
$119$	−5.37561	−	1.95656i	−0.492782	−	0.179358i
$120$	0.00629109	+	0.103501i	0.000574296	+	0.00944827i
$121$	−1.31824	−	1.10614i	−0.119840	−	0.100558i
$122$	−12.7785	+	1.11797i	−1.15691	+	0.101216i
$123$	1.77710	+	15.8724i	0.160236	+	1.43117i
$124$	4.44253	−	12.2057i	0.398951	−	1.09611i
$125$	−1.22106	−	11.1135i	−0.109215	−	0.994018i
$126$	−5.10899	+	6.72514i	−0.455145	+	0.599124i
$127$	−1.72091	+	6.42251i	−0.152706	+	0.569905i	0.846585	+	0.532253i	$0.178655\pi$
$127$	−1.72091	+	6.42251i	−0.152706	+	0.569905i	−0.999291	+	0.0376522i	$0.988012\pi$
$128$	0.122848	−	0.175446i	0.0108584	−	0.0155074i
$129$	−3.15384	+	9.36512i	−0.277680	+	0.824553i
$130$	6.37310	−	12.0316i	0.558958	−	1.05524i
$131$	11.6386	+	2.05219i	1.01687	+	0.179301i	0.657149	−	0.753761i	$-0.271762\pi$
$131$	11.6386	+	2.05219i	1.01687	+	0.179301i	0.359717	+	0.933062i	$0.382873\pi$
$132$	3.46259	+	11.7737i	0.301379	+	1.02477i
$133$	−0.202002	+	2.30889i	−0.0175158	+	0.200206i
$134$	23.2964			2.01251
$135$	−4.21209	−	10.8286i	−0.362519	−	0.931976i
$136$	−0.108625			−0.00931449
$137$	1.05604	−	12.0706i	0.0902237	−	1.03126i	−0.807255	−	0.590203i	$-0.799048\pi$
$137$	1.05604	−	12.0706i	0.0902237	−	1.03126i	0.897478	−	0.441059i	$-0.145397\pi$
$138$	21.5260	+	5.21235i	1.83242	+	0.443704i
$139$	−12.8272	−	2.26177i	−1.08799	−	0.191841i	−0.399242	−	0.916846i	$-0.630727\pi$
$139$	−12.8272	−	2.26177i	−1.08799	−	0.191841i	−0.688744	+	0.725005i	$0.741838\pi$
$140$	−5.98677	+	1.84063i	−0.505974	+	0.155562i
$141$	−13.5240	+	2.72406i	−1.13893	+	0.229407i
$142$	−1.27766	+	1.82469i	−0.107219	+	0.153125i
$143$	−2.81511	+	10.5061i	−0.235412	+	0.878568i
$144$	−3.57684	+	11.5382i	−0.298070	+	0.961519i
$145$	−6.05682	+	1.29737i	−0.502992	+	0.107740i
$146$	5.79358	−	15.9177i	0.479480	−	1.31736i
$147$	−7.95422	−	3.47704i	−0.656053	−	0.286782i
$148$	5.74760	−	0.502850i	0.472450	−	0.0413340i
$149$	−2.75179	−	2.30902i	−0.225435	−	0.189162i	0.523074	−	0.852288i	$-0.324785\pi$
$149$	−2.75179	−	2.30902i	−0.225435	−	0.189162i	−0.748509	+	0.663125i	$0.769230\pi$
$150$	4.30946	−	16.7458i	0.351866	−	1.36729i
$151$	0.415850	+	0.151357i	0.0338414	+	0.0123173i	0.358885	−	0.933382i	$-0.383157\pi$
$151$	0.415850	+	0.151357i	0.0338414	+	0.0123173i	−0.325044	+	0.945699i	$0.605379\pi$
$152$	0.0113905	+	0.0425098i	0.000923888	+	0.00344800i
$153$	11.5906	−	3.71611i	0.937041	−	0.300429i
$154$	8.69564	−	5.02043i	0.700715	−	0.404558i
$155$	8.98302	−	11.5351i	0.721533	−	0.926518i
$156$	7.87253	−	6.93772i	0.630307	−	0.555462i
$157$	−1.15550	−	0.538818i	−0.0922189	−	0.0430024i	0.375961	−	0.926635i	$-0.377312\pi$
$157$	−1.15550	−	0.538818i	−0.0922189	−	0.0430024i	−0.468180	+	0.883633i	$0.655090\pi$
$158$	−8.94463	+	6.26310i	−0.711597	+	0.498265i
$159$	20.5140	−	0.497163i	1.62686	−	0.0394276i
$160$	−14.2449	+	10.7694i	−1.12616	+	0.851400i
$161$		−	9.02999i		−	0.711663i
$162$	−0.173513	−	17.9690i	−0.0136325	−	1.41178i
$163$	−2.53097	+	2.53097i	−0.198241	+	0.198241i	−0.799245	−	0.601005i	$-0.794767\pi$
$163$	−2.53097	+	2.53097i	−0.198241	+	0.198241i	0.601005	+	0.799245i	$0.294767\pi$
$164$	−14.0330	+	11.7751i	−1.09579	+	0.919479i
$165$	−0.366816	+	13.8086i	−0.0285566	+	1.07500i
$166$	2.10640	−	11.9460i	0.163488	−	0.927187i
$167$	5.09841	−	10.9336i	0.394527	−	0.846066i	−0.604258	−	0.796789i	$-0.706530\pi$
$167$	5.09841	−	10.9336i	0.394527	−	0.846066i	0.998785	−	0.0492772i	$-0.0156918\pi$
$168$	0.0652540	+	0.00411880i	0.00503446	+	0.000317772i
$169$	−3.64378	+	0.642497i	−0.280291	+	0.0494228i
$170$	17.2363	+	5.57048i	1.32196	+	0.427236i
$171$	−2.66968	−	4.14624i	−0.204155	−	0.317071i
$172$	−10.9479	+	2.93349i	−0.834773	+	0.223677i
$173$	2.45576	+	5.26639i	0.186708	+	0.400397i	0.977274	−	0.211980i	$-0.0679913\pi$
$173$	2.45576	+	5.26639i	0.186708	+	0.400397i	−0.790566	+	0.612377i	$0.790214\pi$
$174$	−9.47192	−	1.43447i	−0.718065	−	0.108747i
$175$	−7.04916	−	0.100886i	−0.532867	−	0.00762623i
$176$	9.23141	−	11.0016i	0.695844	−	0.829274i
$177$	−9.93764	+	22.7337i	−0.746959	+	1.70877i
$178$	−0.268733	+	0.125312i	−0.0201424	+	0.00939256i
$179$	−9.76891	+	16.9203i	−0.730163	+	1.26468i	0.226651	+	0.973976i	$0.427222\pi$
$179$	−9.76891	+	16.9203i	−0.730163	+	1.26468i	−0.956813	+	0.290703i	$0.906111\pi$
$180$	7.66913	−	10.8986i	0.571623	−	0.812332i
$181$	5.30360	+	9.18610i	0.394213	+	0.682797i	0.993000	−	0.118111i	$-0.0376838\pi$
$181$	5.30360	+	9.18610i	0.394213	+	0.682797i	−0.598787	+	0.800908i	$0.704350\pi$
$182$	−7.03265	−	4.92432i	−0.521295	−	0.365015i
$183$	−9.26700	−	6.15971i	−0.685037	−	0.455339i
$184$	−0.0586442	−	0.161124i	−0.00432331	−	0.0118782i
$185$	6.32994	+	1.45091i	0.465386	+	0.106673i
$186$	19.3026	−	11.7769i	1.41533	−	0.863527i
$187$	−14.4156	−	1.26120i	−1.05417	−	0.0922282i
$188$	−11.1886	−	11.1886i	−0.816012	−	0.816012i
$189$	−7.10370	+	1.79289i	−0.516718	+	0.130413i
$190$	0.372574	−	7.32947i	0.0270293	−	0.531735i
$191$	−3.07377	−	3.66318i	−0.222410	−	0.265058i	0.643288	−	0.765624i	$-0.277570\pi$
$191$	−3.07377	−	3.66318i	−0.222410	−	0.265058i	−0.865698	+	0.500566i	$0.833125\pi$
$192$	−13.1146	+	3.85693i	−0.946464	+	0.278350i
$193$	3.12066	+	4.45676i	0.224630	+	0.320804i	0.915609	−	0.402070i	$-0.131709\pi$
$193$	3.12066	+	4.45676i	0.224630	+	0.320804i	−0.690979	+	0.722875i	$0.742820\pi$
$194$	−24.2052	+	8.80997i	−1.73783	+	0.632519i
$195$	10.8332	−	4.70554i	0.775781	−	0.336970i
$196$	−1.72897	−	9.80546i	−0.123498	−	0.700390i
$197$	−7.75934	−	2.07911i	−0.552830	−	0.148130i	−0.0284197	−	0.999596i	$-0.509048\pi$
$197$	−7.75934	−	2.07911i	−0.552830	−	0.148130i	−0.524410	+	0.851466i	$0.675714\pi$
$198$	−8.08021	+	19.7769i	−0.574236	+	1.40548i
$199$	−10.5312	−	6.08020i	−0.746539	−	0.431014i	0.0779033	−	0.996961i	$-0.475177\pi$
$199$	−10.5312	−	6.08020i	−0.746539	−	0.431014i	−0.824442	+	0.565947i	$0.808511\pi$
$200$	−0.126435	+	0.0439798i	−0.00894027	+	0.00310984i
$201$	15.7913	+	12.6113i	1.11384	+	0.889535i
$202$	−0.919049	−	10.5048i	−0.0646641	−	0.739114i
$203$	0.340415	+	3.89096i	0.0238925	+	0.273092i
$204$	10.9086	+	8.71187i	0.763755	+	0.609953i
$205$	−19.1057	+	7.75414i	−1.33440	+	0.541573i
$206$	−5.58006	−	3.22165i	−0.388781	−	0.224463i
$207$	11.7696	+	15.1861i	0.818046	+	1.05551i
$208$	−11.8612	−	3.17819i	−0.822425	−	0.220368i
$209$	1.01806	+	5.77373i	0.0704210	+	0.399377i
$210$	−10.1431	−	3.99991i	−0.699942	−	0.276020i
$211$	2.80282	−	1.02014i	0.192954	−	0.0702295i	−0.243736	−	0.969842i	$-0.578373\pi$
$211$	2.80282	−	1.02014i	0.192954	−	0.0702295i	0.436690	+	0.899612i	$0.356151\pi$
$212$	13.4995	+	19.2792i	0.927147	+	1.32410i
$213$	−1.85384	+	0.545202i	−0.127023	+	0.0373567i
$214$	−16.5694	−	19.7467i	−1.13266	−	1.34985i
$215$	−12.7410	−	0.647657i	−0.868932	−	0.0441698i
$216$	−0.115109	+	0.0781249i	−0.00783216	+	0.00531573i
$217$	−6.51879	−	6.51879i	−0.442524	−	0.442524i
$218$	14.5659	+	1.27435i	0.986525	+	0.0863097i
$219$	12.5441	−	7.65343i	0.847650	−	0.517171i
$220$	−13.4229	+	8.41688i	−0.904968	+	0.567466i
$221$	4.23179	+	11.6267i	0.284661	+	0.782099i
$222$	8.36450	+	5.55982i	0.561389	+	0.373151i
$223$	−6.63181	−	4.64364i	−0.444099	−	0.310961i	0.330052	−	0.943963i	$-0.392934\pi$
$223$	−6.63181	−	4.64364i	−0.444099	−	0.310961i	−0.774151	+	0.633002i	$0.781823\pi$
$224$	5.63019	+	9.75178i	0.376183	+	0.651568i
$225$	11.9864	−	9.01816i	0.799090	−	0.601211i
$226$	−15.1941	+	26.3170i	−1.01070	+	1.75058i
$227$	6.98639	−	3.25781i	0.463703	−	0.216228i	−0.176704	−	0.984264i	$-0.556544\pi$
$227$	6.98639	−	3.25781i	0.463703	−	0.216228i	0.640407	+	0.768036i	$0.278766\pi$
$228$	2.26547	−	5.18256i	0.150034	−	0.343224i
$229$	−2.93595	+	3.49893i	−0.194013	+	0.231216i	−0.854277	−	0.519818i	$-0.826000\pi$
$229$	−2.93595	+	3.49893i	−0.194013	+	0.231216i	0.660264	+	0.751033i	$0.270444\pi$
$230$	1.04278	+	28.5741i	0.0687591	+	1.88412i
$231$	8.61205	+	1.30425i	0.566631	+	0.0858132i
$232$	0.0313435	+	0.0672163i	0.00205780	+	0.00441297i
$233$	19.3377	−	5.18153i	1.26686	−	0.339454i	0.438032	−	0.898960i	$-0.355676\pi$
$233$	19.3377	−	5.18153i	1.26686	−	0.339454i	0.828826	+	0.559506i	$0.189009\pi$
$234$	18.2454	−	0.884887i	1.19274	−	0.0578469i
$235$	−8.11055	−	15.8562i	−0.529074	−	1.03435i
$236$	−28.0247	+	4.94151i	−1.82425	+	0.321665i
$237$	−9.45354	−	0.596702i	−0.614073	−	0.0387600i
$238$	4.82716	−	10.3519i	0.312898	−	0.671012i
$239$	2.31345	−	13.1202i	0.149645	−	0.848678i	−0.813875	−	0.581040i	$-0.802646\pi$
$239$	2.31345	−	13.1202i	0.149645	−	0.848678i	0.963520	−	0.267638i	$-0.0862431\pi$
$240$	−15.5896	−	0.414126i	−1.00630	−	0.0267317i
$241$	19.5457	−	16.4008i	1.25905	−	1.05647i	0.263267	−	0.964723i	$-0.415200\pi$
$241$	19.5457	−	16.4008i	1.25905	−	1.05647i	0.995783	−	0.0917454i	$-0.0292446\pi$
$242$	2.42956	−	2.42956i	0.156178	−	0.156178i
$243$	9.60974	−	12.2741i	0.616465	−	0.787382i
$244$		−	12.7627i		−	0.817047i
$245$	1.54229	−	11.1005i	0.0985330	−	0.709183i
$246$	−31.8803	+	0.772629i	−2.03261	+	0.0492610i
$247$	4.10632	−	2.87528i	0.261279	−	0.182950i
$248$	−0.158651	−	0.0739804i	−0.0100744	−	0.00469776i
$249$	7.89466	−	6.95722i	0.500304	−	0.440896i
$250$	22.3177	−	0.494800i	1.41149	−	0.0312939i
$251$	17.4693	−	10.0859i	1.10265	−	0.636617i	0.165736	−	0.986170i	$-0.447000\pi$
$251$	17.4693	−	10.0859i	1.10265	−	0.636617i	0.936917	+	0.349553i	$0.113667\pi$
$252$	−6.22278	−	5.64710i	−0.391998	−	0.355734i
$253$	−5.91193	−	22.0636i	−0.371680	−	1.38713i
$254$	−12.4752	−	4.54060i	−0.782764	−	0.284903i
$255$	8.66797	+	13.1066i	0.542809	+	0.820769i
$256$	12.4194	+	10.4211i	0.776213	+	0.651320i
$257$	8.53743	−	0.746929i	0.532550	−	0.0465921i	0.182291	−	0.983245i	$-0.441649\pi$
$257$	8.53743	−	0.746929i	0.532550	−	0.0465921i	0.350260	+	0.936653i	$0.386093\pi$
$258$	−18.0788	−	7.90284i	−1.12554	−	0.492009i
$259$	1.40055	−	3.84797i	0.0870257	−	0.239101i
$260$	11.3728	+	7.36023i	0.705314	+	0.456462i
$261$	−5.64394	−	6.09989i	−0.349351	−	0.377574i
$262$	−6.10724	+	22.7925i	−0.377307	+	1.40813i
$263$	−11.5873	+	16.5483i	−0.714501	+	1.02041i	0.283607	+	0.958941i	$0.408469\pi$
$263$	−11.5873	+	16.5483i	−0.714501	+	1.02041i	−0.998109	+	0.0614734i	$0.980420\pi$
$264$	0.162137	−	0.0326580i	0.00997881	−	0.00200996i
$265$	7.78508	+	25.3215i	0.478233	+	1.55549i
$266$	−4.55734	−	0.803581i	−0.279428	−	0.0492707i
$267$	−0.249996	−	0.0605344i	−0.0152995	−	0.00370464i
$268$	−2.02019	+	23.0909i	−0.123403	+	1.41050i
$269$	11.8522			0.722639			0.361320	−	0.932442i	$-0.382326\pi$
$269$	11.8522			0.722639			0.361320	+	0.932442i	$0.382326\pi$
$270$	22.2716	−	6.49366i	1.35540	−	0.395191i
$271$	24.7671			1.50450			0.752249	−	0.658879i	$-0.228969\pi$
$271$	24.7671			1.50450			0.752249	+	0.658879i	$0.228969\pi$
$272$	1.42387	−	16.2749i	0.0863345	−	0.986808i
$273$	−2.10130	−	7.14498i	−0.127176	−	0.432434i
$274$	23.8252	+	4.20103i	1.43934	+	0.253794i
$275$	−17.2898	+	4.36858i	−1.04261	+	0.263436i
$276$	−7.03304	+	20.8842i	−0.423339	+	1.25708i
$277$	16.7314	−	23.8949i	1.00529	−	1.43571i	0.108064	−	0.994144i	$-0.465535\pi$
$277$	16.7314	−	23.8949i	1.00529	−	1.43571i	0.897230	−	0.441564i	$-0.145576\pi$
$278$	6.73095	−	25.1202i	0.403695	−	1.50661i
$279$	19.4595	+	2.46637i	1.16501	+	0.147658i
$280$	0.0176796	+	0.0825380i	0.00105656	+	0.00493259i
$281$	−10.0345	+	27.5694i	−0.598605	+	1.64465i	0.155450	+	0.987844i	$0.450317\pi$
$281$	−10.0345	+	27.5694i	−0.598605	+	1.64465i	−0.754055	+	0.656811i	$0.771905\pi$
$282$	−3.06483	−	27.3740i	−0.182508	−	1.63010i
$283$	13.5237	−	1.18317i	0.803902	−	0.0703324i	0.322205	−	0.946670i	$-0.395576\pi$
$283$	13.5237	−	1.18317i	0.803902	−	0.0703324i	0.481697	+	0.876338i	$0.340020\pi$
$284$	−1.69780	−	1.42462i	−0.100746	−	0.0845357i
$285$	4.22029	−	4.76654i	0.249989	−	0.282345i
$286$	−20.4073	−	7.42766i	−1.20671	−	0.439207i
$287$	3.36509	+	12.5587i	0.198635	+	0.741315i
$288$	−22.1789	−	9.06161i	−1.30691	−	0.533960i
$289$	0.466643	−	0.269416i	0.0274496	−	0.0158480i
$290$	−1.52652	−	12.2731i	−0.0896405	−	0.720699i
$291$	−21.1765	−	7.13150i	−1.24139	−	0.418056i
$292$	15.2749	+	7.12281i	0.893897	+	0.416831i
$293$	6.76405	−	4.73624i	0.395160	−	0.276694i	−0.359062	−	0.933314i	$-0.616903\pi$
$293$	6.76405	−	4.73624i	0.395160	−	0.276694i	0.754222	+	0.656620i	$0.228014\pi$
$294$	8.30019	−	15.2162i	0.484077	−	0.887429i
$295$	−31.7259	−	4.40796i	−1.84715	−	0.256642i
$296$		−	0.0777556i		−	0.00451945i
$297$	−16.1832	+	9.03148i	−0.939043	+	0.524060i
$298$	5.07162	−	5.07162i	0.293791	−	0.293791i
$299$	−14.9614	+	12.5541i	−0.865238	+	0.726021i
$300$	16.2244	+	5.72359i	0.936717	+	0.330451i
$301$	−1.39689	+	7.92216i	−0.0805155	+	0.456626i
$302$	−0.373422	+	0.800806i	−0.0214880	+	0.0460812i
$303$	5.06370	−	7.61811i	0.290902	−	0.437649i
$304$	−6.51840	+	1.14937i	−0.373856	+	0.0659209i
$305$	4.41769	−	13.6693i	0.252956	−	0.782702i
$306$	5.37453	+	23.7008i	0.307241	+	1.35489i
$307$	10.0251	−	2.68621i	0.572161	−	0.153310i	0.0388737	−	0.999244i	$-0.487623\pi$
$307$	10.0251	−	2.68621i	0.572161	−	0.153310i	0.533288	+	0.845934i	$0.320956\pi$
$308$	4.22208	+	9.05429i	0.240575	+	0.515916i
$309$	−2.03840	−	5.20450i	−0.115960	−	0.296073i
$310$	21.3805	+	19.8750i	1.21433	+	1.12882i
$311$	−12.2675	+	14.6199i	−0.695627	+	0.829016i	−0.992024	−	0.126049i	$-0.959770\pi$
$311$	−12.2675	+	14.6199i	−0.695627	+	0.829016i	0.296397	+	0.955065i	$0.404215\pi$
$312$	−0.0838961	−	0.113842i	−0.00474968	−	0.00644506i
$313$	14.9199	−	6.95728i	0.843325	−	0.393249i	0.0475700	−	0.998868i	$-0.484852\pi$
$313$	14.9199	−	6.95728i	0.843325	−	0.393249i	0.795755	+	0.605619i	$0.207075\pi$
$314$	1.27281	−	2.20458i	0.0718291	−	0.124412i
$315$	−4.71013	−	8.20221i	−0.265386	−	0.462142i
$316$	−5.43220	−	9.40884i	−0.305585	−	0.529289i
$317$	6.12095	+	4.28594i	0.343787	+	0.240722i	0.732699	−	0.680553i	$-0.238260\pi$
$317$	6.12095	+	4.28594i	0.343787	+	0.240722i	−0.388912	+	0.921275i	$0.627149\pi$
$318$	−2.58094	+	40.8898i	−0.144732	+	2.29299i
$319$	3.37917	+	9.28420i	0.189197	+	0.519816i
$320$	−9.37545	−	14.9515i	−0.524104	−	0.835816i
$321$	−0.541778	−	22.3549i	−0.0302391	−	1.24773i
$322$	17.9611	+	1.57139i	1.00093	+	0.0875702i
$323$	4.71587	+	4.71587i	0.262398	+	0.262398i
$324$	17.8255	+	1.38623i	0.990305	+	0.0770128i
$325$	9.63304	+	11.8197i	0.534345	+	0.655638i
$326$	−4.59378	−	5.47465i	−0.254426	−	0.303213i
$327$	9.18352	+	8.74892i	0.507850	+	0.483816i
$328$	0.141605	+	0.202232i	0.00781881	+	0.0111664i
$329$	−10.5531	+	3.84101i	−0.581811	+	0.211762i
$330$	−27.4022	−	3.13258i	−1.50844	−	0.172443i
$331$	1.44127	+	8.17383i	0.0792192	+	0.449274i	0.998455	+	0.0555668i	$0.0176966\pi$
$331$	1.44127	+	8.17383i	0.0792192	+	0.449274i	−0.919236	+	0.393707i	$0.871192\pi$
$332$	11.6579	+	3.12373i	0.639812	+	0.171437i
$333$	2.66006	+	8.29674i	0.145770	+	0.454659i
$334$	20.8602	+	12.0436i	1.14142	+	0.658998i
$335$	−10.1564	+	24.0319i	−0.554904	+	1.31301i
$336$	−1.47246	+	9.72280i	−0.0803295	+	0.530422i
$337$	1.36820	+	15.6386i	0.0745305	+	0.851888i	0.937807	+	0.347157i	$0.112853\pi$
$337$	1.36820	+	15.6386i	0.0745305	+	0.851888i	−0.863277	+	0.504731i	$0.831592\pi$
$338$	−0.643869	−	7.35946i	−0.0350219	−	0.400302i
$339$	−24.5457	+	9.61357i	−1.33314	+	0.522138i
$340$	−7.01602	+	16.6012i	−0.380497	+	0.900325i
$341$	−20.1957	−	11.6600i	−1.09366	−	0.631424i
$342$	8.71164	−	4.58858i	0.471072	−	0.248122i
$343$	−16.3595	−	4.38351i	−0.883330	−	0.236687i
$344$	0.0265246	+	0.150428i	0.00143011	+	0.00811056i
$345$	−14.7615	+	19.9333i	−0.794732	+	1.07317i
$346$	−10.9025	+	3.96817i	−0.586120	+	0.213330i
$347$	0.526226	+	0.751529i	0.0282493	+	0.0403442i	0.833028	−	0.553230i	$-0.186605\pi$
$347$	0.526226	+	0.751529i	0.0282493	+	0.0403442i	−0.804779	+	0.593575i	$0.797716\pi$
$348$	2.24319	−	9.26397i	0.120248	−	0.496601i
$349$	23.1000	+	27.5295i	1.23652	+	1.47362i	0.827861	+	0.560934i	$0.189558\pi$
$349$	23.1000	+	27.5295i	1.23652	+	1.47362i	0.408655	+	0.912689i	$0.365998\pi$
$350$	1.42736	−	14.0036i	0.0762953	−	0.748522i
$351$	12.8466	+	9.27719i	0.685698	+	0.495180i
$352$	20.1412	+	20.1412i	1.07353	+	1.07353i
$353$	4.80917	+	0.420748i	0.255966	+	0.0223942i	0.214417	−	0.976742i	$-0.431215\pi$
$353$	4.80917	+	0.420748i	0.255966	+	0.0223942i	0.0415497	+	0.999136i	$0.486771\pi$
$354$	−43.4891	−	23.7225i	−2.31142	−	1.26084i
$355$	−1.32528	−	2.11350i	−0.0703387	−	0.112173i
$356$	−0.100903	−	0.277229i	−0.00534786	−	0.0146931i
$357$	8.87596	−	4.40381i	0.469765	−	0.233074i
$358$	−31.9552	−	22.3753i	−1.68889	−	1.18257i
$359$	−1.88801	−	3.27013i	−0.0996454	−	0.172591i	0.811892	−	0.583807i	$-0.198438\pi$
$359$	−1.88801	−	3.27013i	−0.0996454	−	0.172591i	−0.911538	+	0.411216i	$0.865104\pi$
$360$	−0.137312	−	0.115764i	−0.00723697	−	0.00610130i
$361$	−8.14897	+	14.1144i	−0.428893	+	0.742865i
$362$	−19.1945	+	8.95055i	−1.00884	+	0.470430i
$363$	2.96208	−	0.331639i	0.155469	−	0.0174065i
$364$	5.49072	−	6.54359i	0.287792	−	0.342977i
$365$	13.8945	+	12.9161i	0.727271	+	0.676058i
$366$	13.8646	−	17.3606i	0.724713	−	0.907453i
$367$	−10.6549	−	22.8495i	−0.556181	−	1.19273i	−0.960542	−	0.278135i	$-0.910284\pi$
$367$	−10.6549	−	22.8495i	−0.556181	−	1.19273i	0.404361	−	0.914600i	$-0.367494\pi$
$368$	24.9093	−	6.67443i	1.29849	−	0.347929i
$369$	−22.0281	−	16.7344i	−1.14674	−	0.871158i
$370$	−3.98746	+	12.3381i	−0.207298	+	0.641425i
$371$	16.4505	−	2.90067i	0.854070	−	0.150596i
$372$	9.99918	+	20.1535i	0.518433	+	1.04491i
$373$	4.65880	−	9.99084i	0.241224	−	0.517306i	−0.748003	−	0.663695i	$-0.768987\pi$
$373$	4.65880	−	9.99084i	0.241224	−	0.517306i	0.989227	+	0.146389i	$0.0467651\pi$
$374$	5.01718	−	28.4538i	0.259432	−	1.47131i
$375$	15.3958	+	11.7461i	0.795033	+	0.606566i
$376$	−0.163356	+	0.137072i	−0.00842442	+	0.00706893i
$377$	5.97348	−	5.97348i	0.307650	−	0.307650i
$378$	−2.32996	−	14.4416i	−0.119840	−	0.742795i
$379$		−	6.15292i		−	0.316054i	−0.987435	−	0.158027i	$-0.949487\pi$
$379$		−	6.15292i		−	0.316054i	0.987435	−	0.158027i	$-0.0505134\pi$
$380$	7.23250	+	1.00488i	0.371019	+	0.0515490i
$381$	−5.99822	−	9.83116i	−0.307298	−	0.503666i
$382$	7.82113	−	5.47641i	0.400164	−	0.280198i
$383$	−15.9793	−	7.45128i	−0.816506	−	0.380743i	−0.0309400	−	0.999521i	$-0.509850\pi$
$383$	−15.9793	−	7.45128i	−0.816506	−	0.380743i	−0.785566	+	0.618778i	$0.787628\pi$
$384$	0.0732508	+	0.363666i	0.00373806	+	0.0185583i
$385$	1.38794	+	11.1589i	0.0707361	+	0.568710i
$386$	−9.40775	+	5.43157i	−0.478842	+	0.276460i
$387$	−7.97648	−	15.1437i	−0.405467	−	0.769798i
$388$	−6.63326	−	24.7556i	−0.336753	−	1.25678i
$389$	13.1982	+	4.80373i	0.669173	+	0.243559i	0.654192	−	0.756329i	$-0.273009\pi$
$389$	13.1982	+	4.80373i	0.669173	+	0.243559i	0.0149811	+	0.999888i	$0.495231\pi$
$390$	7.47435	+	22.3666i	0.378479	+	1.13258i
$391$	−19.9049	−	16.7022i	−1.00663	−	0.844666i
$392$	−0.133675	+	0.0116951i	−0.00675161	+	0.000590689i
$393$	−16.4783	+	12.1437i	−0.831220	+	0.612567i
$394$	5.48572	−	15.0719i	0.276366	−	0.759311i
$395$	−2.56129	−	11.9575i	−0.128873	−	0.601648i
$396$	−18.9017	−	9.72392i	−0.949848	−	0.488646i
$397$	7.83331	−	29.2343i	0.393143	−	1.46723i	−0.431778	−	0.901980i	$-0.642114\pi$
$397$	7.83331	−	29.2343i	0.393143	−	1.46723i	0.824921	−	0.565248i	$-0.191220\pi$
$398$	13.9264	−	19.8890i	0.698070	−	0.996947i
$399$	−2.65415	−	3.01178i	−0.132874	−	0.150778i
$400$	−4.93203	−	19.5197i	−0.246601	−	0.975987i
$401$	−16.0405	−	2.82837i	−0.801024	−	0.141242i	−0.241873	−	0.970308i	$-0.577762\pi$
$401$	−16.0405	−	2.82837i	−0.801024	−	0.141242i	−0.559151	+	0.829066i	$0.688873\pi$
$402$	−27.8325	+	29.2151i	−1.38816	+	1.45712i
$403$	−1.73783	+	19.8635i	−0.0865676	+	0.989472i
$404$	10.4918			0.521987
$405$	18.6119	+	7.65484i	0.924834	+	0.380372i
$406$	−7.79855			−0.387035
$407$	0.902792	−	10.3190i	0.0447497	−	0.511492i
$408$	0.129775	−	0.136222i	0.00642483	−	0.00674398i
$409$	−19.2731	−	3.39837i	−0.952995	−	0.168039i	−0.324529	−	0.945876i	$-0.605206\pi$
$409$	−19.2731	−	3.39837i	−0.952995	−	0.168039i	−0.628466	+	0.777837i	$0.716317\pi$
$410$	−12.0986	−	39.3515i	−0.597507	−	1.94343i
$411$	13.8756	+	15.7452i	0.684432	+	0.776656i
$412$	3.67712	−	5.25147i	0.181159	−	0.258721i
$413$	−5.22744	+	19.5091i	−0.257226	+	0.959979i
$414$	−32.2540	+	20.7677i	−1.58520	+	1.02068i
$415$	11.4048	+	7.38092i	0.559840	+	0.362315i
$416$	8.32980	−	22.8859i	0.408402	−	1.12208i
$417$	18.1612	−	13.3838i	0.889356	−	0.655410i
$418$	−11.6614	+	1.02024i	−0.570377	+	0.0499015i
$419$	0.141106	+	0.118402i	0.00689349	+	0.00578432i	0.646228	−	0.763145i	$-0.276346\pi$
$419$	0.141106	+	0.118402i	0.00689349	+	0.00578432i	−0.639334	+	0.768929i	$0.720790\pi$
$420$	4.84421	−	9.70678i	0.236373	−	0.473643i
$421$	−17.1952	−	6.25854i	−0.838043	−	0.305023i	−0.112887	−	0.993608i	$-0.536010\pi$
$421$	−17.1952	−	6.25854i	−0.838043	−	0.305023i	−0.725155	+	0.688585i	$0.758232\pi$
$422$	1.54137	+	5.75246i	0.0750325	+	0.280025i
$423$	12.7412	−	20.2144i	0.619499	−	0.982858i
$424$	0.274692	−	0.158593i	0.0133402	−	0.00770197i
$425$	−13.2608	+	15.3519i	−0.643241	+	0.744678i
$426$	−0.761831	−	3.78224i	−0.0369108	−	0.183250i
$427$	−8.20959	−	3.82819i	−0.397290	−	0.185259i
$428$	21.0093	−	14.7109i	1.01552	−	0.711078i
$429$	−9.81207	−	16.0821i	−0.473731	−	0.776453i
$430$	3.50540	−	25.2298i	0.169046	−	1.21669i
$431$			20.4312i			0.984138i	0.870556	+	0.492069i	$0.163759\pi$
$431$			20.4312i			0.984138i	−0.870556	+	0.492069i	$0.836241\pi$
$432$	−10.1963	−	18.2704i	−0.490571	−	0.879036i
$433$	−1.40075	+	1.40075i	−0.0673156	+	0.0673156i	−0.739963	−	0.672647i	$-0.765157\pi$
$433$	−1.40075	+	1.40075i	−0.0673156	+	0.0673156i	0.672647	+	0.739963i	$0.265157\pi$
$434$	14.1006	−	11.8318i	0.676849	−	0.567944i
$435$	5.60918	−	9.14559i	0.268940	−	0.438497i
$436$	−2.52621	+	14.3269i	−0.120984	+	0.686132i
$437$	−4.44908	+	9.54109i	−0.212829	+	0.456412i
$438$	13.0401	+	26.2826i	0.623081	+	1.25583i
$439$	−13.9335	+	2.45686i	−0.665012	+	0.117259i	−0.495957	−	0.868347i	$-0.665183\pi$
$439$	−13.9335	+	2.45686i	−0.665012	+	0.117259i	−0.169055	+	0.985607i	$0.554071\pi$
$440$	0.0972354	+	0.190096i	0.00463552	+	0.00906248i
$441$	13.8634	−	5.82099i	0.660163	−	0.277190i
$442$	−23.8625	+	6.39395i	−1.13503	+	0.304129i
$443$	−6.78197	−	14.5440i	−0.322221	−	0.691005i	0.676757	−	0.736207i	$-0.263385\pi$
$443$	−6.78197	−	14.5440i	−0.322221	−	0.691005i	−0.998978	+	0.0452014i	$0.985607\pi$
$444$	−6.23612	+	7.80858i	−0.295953	+	0.370579i
$445$	−0.0121105	−	0.331849i	−0.000574094	−	0.0157312i
$446$	10.3905	−	12.3829i	0.492004	−	0.586347i
$447$	6.18324	−	0.692284i	0.292457	−	0.0327439i
$448$	−10.0854	+	4.70292i	−0.476493	+	0.222192i
$449$	2.86184	−	4.95685i	0.135059	−	0.233928i	−0.790561	−	0.612383i	$-0.790211\pi$
$449$	2.86184	−	4.95685i	0.135059	−	0.233928i	0.925620	+	0.378455i	$0.123544\pi$
$450$	15.8517	+	25.4108i	0.747256	+	1.19787i
$451$	16.4443	+	28.4824i	0.774333	+	1.34118i
$452$	−24.7672	−	17.3422i	−1.16495	−	0.815708i
$453$	−0.686631	+	0.340672i	−0.0322608	+	0.0160062i
$454$	5.26417	+	14.4632i	0.247060	+	0.678791i
$455$	8.14577	−	5.10785i	0.381879	−	0.239460i
$456$	−0.0669181	−	0.0365026i	−0.00313373	−	0.00170939i
$457$	19.6843	+	1.72215i	0.920793	+	0.0805589i	0.537686	−	0.843145i	$-0.319299\pi$
$457$	19.6843	+	1.72215i	0.920793	+	0.0805589i	0.383107	+	0.923704i	$0.374854\pi$
$458$	−6.44862	−	6.44862i	−0.301324	−	0.301324i
$459$	−9.18716	+	18.9749i	−0.428820	+	0.885673i
$460$	−28.4124	−	1.44427i	−1.32474	−	0.0673394i
$461$	−11.6371	−	13.8685i	−0.541993	−	0.645922i	0.423640	−	0.905830i	$-0.360752\pi$
$461$	−11.6371	−	13.8685i	−0.541993	−	0.645922i	−0.965633	+	0.259909i	$0.916308\pi$
$462$	−4.09287	+	16.9028i	−0.190418	+	0.786390i
$463$	−7.50444	−	10.7175i	−0.348761	−	0.498082i	0.605997	−	0.795467i	$-0.292774\pi$
$463$	−7.50444	−	10.7175i	−0.348761	−	0.498082i	−0.954758	+	0.297385i	$0.903886\pi$
$464$	−10.4816	+	3.81501i	−0.486598	+	0.177107i
$465$	3.73351	+	25.0463i	0.173138	+	1.16149i
$466$	6.94118	+	39.3654i	0.321544	+	1.82357i
$467$	−7.87106	−	2.10904i	−0.364229	−	0.0975949i	0.0720628	−	0.997400i	$-0.477042\pi$
$467$	−7.87106	−	2.10904i	−0.364229	−	0.0975949i	−0.436292	+	0.899805i	$0.643708\pi$
$468$	−0.705104	+	18.1612i	−0.0325934	+	0.839501i
$469$	14.2473	+	8.22566i	0.657877	+	0.379826i
$470$	32.9501	−	13.3730i	1.51988	−	0.616850i
$471$	2.05620	−	0.805332i	0.0947447	−	0.0371077i
$472$	0.0334253	+	0.382053i	0.00153852	+	0.0175854i
$473$	1.77351	+	20.2713i	0.0815462	+	0.932077i
$474$	2.83197	−	18.6997i	0.130076	−	0.858905i
$475$	7.39844	+	3.57972i	0.339464	+	0.164249i
$476$	9.84196	+	5.68226i	0.451105	+	0.260446i
$477$	−23.8848	+	26.3197i	−1.09361	+	1.20510i
$478$	25.6942	+	6.88474i	1.17523	+	0.314901i
$479$	4.41454	+	25.0361i	0.201706	+	1.14393i	0.902540	+	0.430606i	$0.141700\pi$
$479$	4.41454	+	25.0361i	0.201706	+	1.14393i	−0.700835	+	0.713324i	$0.747189\pi$
$480$	3.51305	−	30.7303i	0.160348	−	1.40264i
$481$	−8.32264	+	3.02919i	−0.379480	+	0.138119i
$482$	29.2206	+	41.7314i	1.33096	+	1.90081i
$483$	11.3241	+	10.7882i	0.515266	+	0.490882i
$484$	2.19744	+	2.61881i	0.0998838	+	0.119037i
$485$	1.46449	−	28.8102i	0.0664991	−	1.30821i
$486$	22.7414	+	21.2501i	1.03157	+	0.963926i
$487$	−20.8770	−	20.8770i	−0.946027	−	0.946027i	0.0525891	−	0.998616i	$-0.483253\pi$
$487$	−20.8770	−	20.8770i	−0.946027	−	0.946027i	−0.998616	+	0.0525891i	$0.983253\pi$
$488$	−0.171347	−	0.0149909i	−0.00775651	−	0.000678606i
$489$	−0.150205	−	6.19776i	−0.00679250	−	0.280273i
$490$	21.8110	+	4.99937i	0.985319	+	0.225849i
$491$	−4.08765	−	11.2307i	−0.184473	−	0.506835i	0.812640	−	0.582766i	$-0.198029\pi$
$491$	−4.08765	−	11.2307i	−0.184473	−	0.506835i	−0.997113	+	0.0759306i	$0.975807\pi$
$492$	1.99874	−	31.6660i	0.0901103	−	1.42761i
$493$	9.20652	+	6.44648i	0.414641	+	0.290335i
$494$	5.00448	+	8.66802i	0.225162	+	0.389993i
$495$	−16.8786	−	16.9573i	−0.758636	−	0.762176i
$496$	13.1638	−	22.8004i	0.591074	−	1.02377i
$497$	−1.42564	+	0.664789i	−0.0639489	+	0.0298199i
$498$	12.4644	+	16.9135i	0.558544	+	0.757914i
$499$	−3.31792	+	3.95415i	−0.148531	+	0.177012i	−0.835180	−	0.549977i	$-0.814636\pi$
$499$	−3.31792	+	3.95415i	−0.148531	+	0.177012i	0.686649	+	0.726989i	$0.259081\pi$
$500$	−1.44488	+	22.1637i	−0.0646172	+	0.991191i
$501$	7.62022	+	19.4562i	0.340446	+	0.869238i
$502$	17.0214	+	36.5024i	0.759700	+	1.62918i
$503$	−9.73055	+	2.60729i	−0.433864	+	0.116253i	−0.469139	−	0.883124i	$-0.655436\pi$
$503$	−9.73055	+	2.60729i	−0.433864	+	0.116253i	0.0352755	+	0.999378i	$0.488769\pi$
$504$	−0.0831250	+	0.0769116i	−0.00370268	+	0.00342592i
$505$	11.2371	+	3.63164i	0.500044	+	0.161606i
$506$	44.9144	−	7.91962i	1.99669	−	0.352070i
$507$	3.54754	−	5.33711i	0.157552	−	0.237030i
$508$	5.58236	−	11.9714i	0.247677	−	0.531145i
$509$	5.57060	−	31.5924i	0.246912	−	1.40031i	−0.569097	−	0.822270i	$-0.692707\pi$
$509$	5.57060	−	31.5924i	0.246912	−	1.40031i	0.816009	−	0.578039i	$-0.196182\pi$
$510$	−27.5781	+	14.9602i	−1.22118	+	0.662448i
$511$	9.16349	−	7.68908i	0.405369	−	0.340145i
$512$	−22.5864	+	22.5864i	−0.998188	+	0.998188i
$513$	8.38912	+	1.60563i	0.370389	+	0.0708904i
$514$			17.1113i			0.754749i
$515$	5.75607	−	4.35171i	0.253643	−	0.191759i
$516$	9.40087	−	17.2340i	0.413850	−	0.758686i
$517$	−23.2704	+	16.2941i	−1.02343	+	0.716615i
$518$	7.41007	+	3.45537i	0.325580	+	0.151820i
$519$	−9.53829	−	3.21216i	−0.418685	−	0.140998i
$520$	0.112174	−	0.144042i	0.00491915	−	0.00631666i
$521$	−5.58144	+	3.22245i	−0.244528	+	0.141178i	−0.617256	−	0.786762i	$-0.711756\pi$
$521$	−5.58144	+	3.22245i	−0.244528	+	0.141178i	0.372728	+	0.927941i	$0.378422\pi$
$522$	13.1151	−	10.1646i	0.574034	−	0.444891i
$523$	1.81234	+	6.76374i	0.0792481	+	0.295758i	0.994163	−	0.107889i	$-0.0344091\pi$
$523$	1.81234	+	6.76374i	0.0792481	+	0.295758i	−0.914915	+	0.403647i	$0.867742\pi$
$524$	−22.0619	−	8.02986i	−0.963777	−	0.350786i
$525$	8.54824	−	8.71954i	0.373076	−	0.380552i
$526$	−30.8990	−	25.9273i	−1.34726	−	1.13049i
$527$	−26.4268	+	2.31205i	−1.15117	+	0.100714i
$528$	2.76773	+	24.7204i	0.120450	+	1.07582i
$529$	6.16176	−	16.9293i	0.267902	−	0.736056i
$530$	−51.7203	+	11.0785i	−2.24659	+	0.481218i
$531$	−16.6368	−	39.6226i	−0.721975	−	1.71948i
$532$	1.19169	−	4.44745i	0.0516663	−	0.192821i
$533$	16.1295	−	23.0353i	0.698646	−	0.997770i
$534$	0.163910	−	0.486720i	0.00709307	−	0.0210624i
$535$	27.5938	−	8.48370i	1.19298	−	0.366782i
$536$	0.307637	+	0.0542447i	0.0132879	+	0.00234301i
$537$	−9.54796	−	32.4656i	−0.412025	−	1.40099i
$538$	−2.06250	+	23.5745i	−0.0889208	+	1.01637i
$539$	−17.8758			−0.769966
$540$	4.50505	+	22.6382i	0.193867	+	0.974193i
$541$	−34.0530			−1.46405			−0.732026	−	0.681276i	$-0.761425\pi$
$541$	−34.0530			−1.46405			−0.732026	+	0.681276i	$0.761425\pi$
$542$	−4.30996	+	49.2630i	−0.185128	+	2.11603i
$543$	−17.8562	−	4.32372i	−0.766282	−	0.185549i
$544$	31.9097	+	5.62655i	1.36812	+	0.241236i
$545$	−7.66478	+	14.4702i	−0.328323	+	0.619833i
$546$	14.5774	−	2.93622i	0.623854	−	0.125659i
$547$	−14.1563	+	20.2173i	−0.605281	+	0.864431i	−0.998485	−	0.0550200i	$-0.982478\pi$
$547$	−14.1563	+	20.2173i	−0.605281	+	0.864431i	0.393204	+	0.919451i	$0.371367\pi$
$548$	−6.23002	+	23.2508i	−0.266133	+	0.993224i
$549$	18.7960	−	4.26229i	0.802195	−	0.181910i
$550$	−5.68057	−	35.1504i	−0.242220	−	1.49882i
$551$	1.55740	−	4.27891i	0.0663474	−	0.182288i
$552$	0.272122	+	0.118953i	0.0115823	+	0.00506298i
$553$	−7.68163	+	0.672056i	−0.326656	+	0.0285787i
$554$	44.6166	+	37.4378i	1.89558	+	1.59058i
$555$	−9.38198	+	6.20470i	−0.398243	+	0.263375i
$556$	24.3149	+	8.84992i	1.03118	+	0.375320i
$557$	−2.28192	−	8.51625i	−0.0966881	−	0.360845i	0.900582	−	0.434686i	$-0.143141\pi$
$557$	−2.28192	−	8.51625i	−0.0966881	−	0.360845i	−0.997270	+	0.0738415i	$0.976474\pi$
$558$	−8.29204	+	38.2766i	−0.351030	+	1.62038i
$559$	15.0679	−	8.69945i	0.637304	−	0.367948i
$560$	−12.5981	+	1.56695i	−0.532368	+	0.0662159i
$561$	18.8041	−	16.5712i	0.793910	−	0.699638i
$562$	−53.0907	−	24.7566i	−2.23950	−	1.04429i
$563$	−19.1342	+	13.3979i	−0.806411	+	0.564655i	−0.902486	−	0.430719i	$-0.858260\pi$
$563$	−19.1342	+	13.3979i	−0.806411	+	0.564655i	0.0960749	+	0.995374i	$0.469371\pi$
$564$	27.3983	−	0.664007i	1.15368	−	0.0279597i
$565$	−20.5237	−	27.1471i	−0.863440	−	1.14209i
$566$			27.1052i			1.13932i
$567$	6.23849	−	11.0504i	0.261992	−	0.464075i
$568$	−0.0211206	+	0.0211206i	−0.000886202	+	0.000886202i
$569$	−1.82798	+	1.53386i	−0.0766330	+	0.0643027i	−0.680300	−	0.732934i	$-0.738150\pi$
$569$	−1.82798	+	1.53386i	−0.0766330	+	0.0643027i	0.603667	+	0.797237i	$0.293706\pi$
$570$	8.74646	+	9.22383i	0.366349	+	0.386344i
$571$	6.32573	−	35.8750i	0.264724	−	1.50132i	−0.505097	−	0.863063i	$-0.668543\pi$
$571$	6.32573	−	35.8750i	0.264724	−	1.50132i	0.769821	−	0.638260i	$-0.220346\pi$
$572$	9.13180	−	19.5832i	0.381820	−	0.818815i
$573$	8.26611	+	0.521753i	0.345322	+	0.0217965i
$574$	−25.5654	+	4.50787i	−1.06708	+	0.188155i
$575$	−29.9308	−	11.3816i	−1.24820	−	0.474645i
$576$	10.8314	−	21.0544i	0.451306	−	0.877266i
$577$	24.2875	−	6.50782i	1.01110	−	0.270924i	0.285012	−	0.958524i	$-0.408002\pi$
$577$	24.2875	−	6.50782i	1.01110	−	0.270924i	0.726090	+	0.687600i	$0.241336\pi$
$578$	0.454677	+	0.975058i	0.0189121	+	0.0405571i
$579$	−9.31732	−	1.41106i	−0.387215	−	0.0586415i
$580$	12.2972	−	0.448774i	0.510612	−	0.0186343i
$581$	5.50616	−	6.56198i	0.228434	−	0.272237i
$582$	17.8700	−	40.8801i	0.740736	−	1.69454i
$583$	38.2957	−	17.8576i	1.58605	−	0.739586i
$584$	0.113570	−	0.196709i	0.00469955	−	0.00813986i
$585$	−7.04152	+	19.2072i	−0.291131	+	0.794121i
$586$	8.24353	+	14.2782i	0.340537	+	0.589828i
$587$	24.9444	+	17.4662i	1.02956	+	0.720909i	0.960947	−	0.276734i	$-0.0892521\pi$
$587$	24.9444	+	17.4662i	1.02956	+	0.720909i	0.0686181	+	0.997643i	$0.478141\pi$
$588$	14.3622	+	9.54647i	0.592289	+	0.393690i
$589$	3.67594	+	10.0996i	0.151465	+	0.416145i
$590$	14.2886	−	62.3373i	0.588251	−	2.56638i
$591$	11.8775	−	7.24673i	0.488575	−	0.298091i
$592$	11.6499	+	1.01923i	0.478806	+	0.0418901i
$593$	26.7405	+	26.7405i	1.09810	+	1.09810i	0.994633	+	0.103470i	$0.0329946\pi$
$593$	26.7405	+	26.7405i	1.09810	+	1.09810i	0.103470	+	0.994633i	$0.467005\pi$
$594$	−15.1479	−	33.7608i	−0.621524	−	1.38522i
$595$	8.57423	+	9.49260i	0.351509	+	0.389159i
$596$	4.58708	+	5.46667i	0.187894	+	0.223924i
$597$	20.2067	−	5.94268i	0.827006	−	0.243218i
$598$	−22.3671	−	31.9435i	−0.914658	−	1.30627i
$599$	1.09294	−	0.397799i	0.0446564	−	0.0162536i	−0.319595	−	0.947554i	$-0.603547\pi$
$599$	1.09294	−	0.397799i	0.0446564	−	0.0162536i	0.364252	+	0.931301i	$0.381325\pi$
$600$	0.0958996	−	0.211100i	0.00391509	−	0.00861811i
$601$	2.53128	+	14.3556i	0.103253	+	0.585578i	0.991904	+	0.126993i	$0.0405325\pi$
$601$	2.53128	+	14.3556i	0.103253	+	0.585578i	−0.888650	+	0.458585i	$0.848356\pi$
$602$	−15.5145	−	4.15709i	−0.632323	−	0.169430i
$603$	−34.6815	+	4.73635i	−1.41234	+	0.192879i
$604$	−0.761360	−	0.439571i	−0.0309793	−	0.0178859i
$605$	1.44706	+	3.56547i	0.0588315	+	0.144957i
$606$	14.2716	+	11.3976i	0.579744	+	0.462998i
$607$	−2.89333	−	33.0709i	−0.117437	−	1.34231i	−0.794896	−	0.606746i	$-0.792475\pi$
$607$	−2.89333	−	33.0709i	−0.117437	−	1.34231i	0.677459	−	0.735560i	$-0.263081\pi$
$608$	−1.14415	−	13.0777i	−0.0464015	−	0.530372i
$609$	−5.28619	−	4.22168i	−0.214207	−	0.171071i
$610$	26.4201	+	11.1657i	1.06972	+	0.452086i
$611$	21.0356	+	12.1449i	0.851008	+	0.491330i
$612$	−23.9578	+	3.27186i	−0.968438	+	0.132257i
$613$	−11.4101	−	3.05733i	−0.460849	−	0.123484i	0.0209221	−	0.999781i	$-0.493340\pi$
$613$	−11.4101	−	3.05733i	−0.460849	−	0.123484i	−0.481772	+	0.876297i	$0.660006\pi$
$614$	3.59845	+	20.4078i	0.145221	+	0.823592i
$615$	13.1016	−	33.2236i	0.528309	−	1.33971i
$616$	0.126518	−	0.0460490i	0.00509757	−	0.00185537i
$617$	26.4363	+	37.7549i	1.06428	+	1.51996i	0.837827	+	0.545935i	$0.183826\pi$
$617$	26.4363	+	37.7549i	1.06428	+	1.51996i	0.226458	+	0.974021i	$0.427285\pi$
$618$	10.7067	−	3.14878i	0.430687	−	0.126663i
$619$	−8.15117	−	9.71419i	−0.327623	−	0.390446i	0.576939	−	0.816787i	$-0.304247\pi$
$619$	−8.15117	−	9.71419i	−0.327623	−	0.390446i	−0.904563	+	0.426341i	$0.859802\pi$
$620$	−21.5537	+	19.4684i	−0.865617	+	0.781871i
$621$	−33.1056	−	3.38321i	−1.32848	−	0.135764i
$622$	−26.9448	−	26.9448i	−1.08039	−	1.08039i
$623$	−0.208594	−	0.0182496i	−0.00835713	−	0.000731154i
$624$	18.1563	−	11.0776i	0.726835	−	0.443459i
$625$	−9.21929	+	23.2380i	−0.368772	+	0.929520i
$626$	11.2420	+	30.8872i	0.449321	+	1.23450i
$627$	−8.45689	−	5.62123i	−0.337736	−	0.224490i
$628$	2.07476	+	1.45276i	0.0827918	+	0.0579714i
$629$	−5.89161	−	10.2046i	−0.234914	−	0.406883i
$630$	17.1342	−	7.94133i	0.682644	−	0.316390i
$631$	16.7330	−	28.9824i	0.666131	−	1.15377i	−0.312847	−	0.949804i	$-0.601283\pi$
$631$	16.7330	−	28.9824i	0.666131	−	1.15377i	0.978977	−	0.203969i	$-0.0653841\pi$
$632$	−0.132700	+	0.0618790i	−0.00527852	+	0.00246142i
$633$	−2.06924	+	4.73367i	−0.0822449	+	0.188147i
$634$	−9.59010	+	11.4290i	−0.380871	+	0.453905i
$635$	10.1227	−	10.8895i	0.401707	−	0.432137i
$636$	−40.3053	−	6.10401i	−1.59821	−	0.242040i
$637$	6.45949	+	13.8524i	0.255934	+	0.548853i
$638$	−19.0548	+	5.10571i	−0.754385	+	0.202137i
$639$	1.53108	−	2.97618i	0.0605687	−	0.117736i
$640$	−0.426379	+	0.218096i	−0.0168541	+	0.00862098i
$641$	−2.02936	+	0.357831i	−0.0801548	+	0.0141335i	−0.213582	−	0.976925i	$-0.568513\pi$
$641$	−2.02936	+	0.357831i	−0.0801548	+	0.0141335i	0.133427	+	0.991059i	$0.457402\pi$
$642$	44.5592	+	2.81255i	1.75861	+	0.111003i
$643$	−13.7938	+	29.5810i	−0.543976	+	1.16656i	0.421682	+	0.906744i	$0.361440\pi$
$643$	−13.7938	+	29.5810i	−0.543976	+	1.16656i	−0.965658	+	0.259816i	$0.916338\pi$
$644$	−3.11506	+	17.6664i	−0.122750	+	0.696153i
$645$	16.0341	−	15.2043i	0.631341	−	0.598667i
$646$	−10.2007	+	8.55944i	−0.401343	+	0.336767i
$647$	10.7867	−	10.7867i	0.424069	−	0.424069i	−0.462533	−	0.886602i	$-0.653059\pi$
$647$	10.7867	−	10.7867i	0.424069	−	0.424069i	0.886602	+	0.462533i	$0.153059\pi$
$648$	0.0395486	−	0.237690i	0.00155362	−	0.00933734i
$649$			51.0904i			2.00547i
$650$	−25.1862	+	17.1037i	−0.987885	+	0.670863i
$651$	15.9630	−	0.386870i	0.625640	−	0.0151626i
$652$	5.82472	−	4.07851i	0.228114	−	0.159727i
$653$	16.4977	+	7.69299i	0.645604	+	0.301050i	0.717705	−	0.696347i	$-0.245193\pi$
$653$	16.4977	+	7.69299i	0.645604	+	0.301050i	−0.0721010	+	0.997397i	$0.522970\pi$
$654$	−19.0001	+	16.7440i	−0.742963	+	0.654741i
$655$	−20.8496	−	16.2368i	−0.814661	−	0.634424i
$656$	−32.1559	+	18.5652i	−1.25548	+	0.724851i
$657$	−5.38872	+	24.8747i	−0.210234	+	0.970453i
$658$	−5.80351	−	21.6590i	−0.226245	−	0.844356i
$659$	1.94388	+	0.707516i	0.0757229	+	0.0275609i	0.379604	−	0.925149i	$-0.376060\pi$
$659$	1.94388	+	0.707516i	0.0757229	+	0.0275609i	−0.303881	+	0.952710i	$0.598283\pi$
$660$	5.48117	−	26.8888i	0.213354	−	1.04664i
$661$	10.2051	+	8.56308i	0.396932	+	0.333065i	0.819306	−	0.573356i	$-0.194359\pi$
$661$	10.2051	+	8.56308i	0.396932	+	0.333065i	−0.422374	+	0.906421i	$0.638803\pi$
$662$	−16.5089	+	1.44434i	−0.641638	+	0.0561360i
$663$	−19.6364	−	8.58369i	−0.762614	−	0.333363i
$664$	0.0556313	−	0.152846i	0.00215891	−	0.00593156i
$665$	2.81579	−	4.35089i	0.109192	−	0.168720i
$666$	−16.9655	+	3.84719i	−0.657400	+	0.149076i
$667$	−4.59169	+	17.1364i	−0.177791	+	0.663525i
$668$	−13.7463	+	19.6318i	−0.531861	+	0.759576i
$669$	13.7465	−	2.76886i	0.531470	−	0.107050i
$670$	−46.0332	−	24.3836i	−1.77842	−	0.942021i
$671$	−22.5654	−	3.97889i	−0.871128	−	0.153603i
$672$	−18.9558	−	4.58998i	−0.731235	−	0.177062i
$673$	3.35297	−	38.3246i	0.129247	−	1.47730i	−0.603805	−	0.797132i	$-0.706349\pi$
$673$	3.35297	−	38.3246i	0.129247	−	1.47730i	0.733052	−	0.680172i	$-0.238095\pi$
$674$	−31.3440			−1.20732
$675$	−3.01093	+	25.8057i	−0.115891	+	0.993262i
$676$	7.35037			0.282707
$677$	−1.13659	+	12.9913i	−0.0436829	+	0.499297i	0.942565	+	0.334023i	$0.108406\pi$
$677$	−1.13659	+	12.9913i	−0.0436829	+	0.499297i	−0.986248	+	0.165274i	$0.947149\pi$
$678$	−14.8504	−	50.4955i	−0.570327	−	1.93927i
$679$	−17.9137	−	3.15867i	−0.687465	−	0.121219i
$680$	0.214640	+	0.113694i	0.00823107	+	0.00435996i
$681$	−4.26124	+	12.6535i	−0.163291	+	0.484883i
$682$	26.7067	−	38.1411i	1.02265	−	1.46050i
$683$	5.95787	−	22.2351i	0.227972	−	0.850801i	−0.753221	−	0.657768i	$-0.771501\pi$
$683$	5.95787	−	22.2351i	0.227972	−	0.850801i	0.981192	−	0.193033i	$-0.0618326\pi$
$684$	3.79266	+	9.03270i	0.145016	+	0.345374i
$685$	−14.7206	+	22.7459i	−0.562446	+	0.869078i
$686$	11.5659	−	31.7770i	0.441587	−	1.21325i
$687$	−0.880248	−	7.86207i	−0.0335836	−	0.299957i
$688$	−22.8859	+	2.00225i	−0.872515	+	0.0763352i
$689$	−27.6766	−	23.2234i	−1.05439	−	0.884741i
$690$	−37.0794	−	32.8301i	−1.41159	−	1.24982i
$691$	−20.2420	−	7.36747i	−0.770040	−	0.280272i	−0.0730269	−	0.997330i	$-0.523266\pi$
$691$	−20.2420	−	7.36747i	−0.770040	−	0.280272i	−0.697013	+	0.717058i	$0.745488\pi$
$692$	−2.98774	−	11.1504i	−0.113577	−	0.423874i
$693$	−11.9245	+	9.24182i	−0.452975	+	0.351068i
$694$	−1.58640	+	0.915908i	−0.0602189	+	0.0347674i
$695$	22.9789	+	17.8950i	0.871638	+	0.678795i
$696$	−0.121740	−	0.0409976i	−0.00461453	−	0.00155401i
$697$	33.9074	+	15.8113i	1.28433	+	0.598894i
$698$	−58.7774	+	41.1564i	−2.22476	+	1.55779i
$699$	−16.6051	+	30.4411i	−0.628062	+	1.15139i
$700$	13.7563	+	2.62911i	0.519937	+	0.0993710i
$701$		−	10.6311i		−	0.401531i	−0.979639	−	0.200766i	$-0.935657\pi$
$701$		−	10.6311i		−	0.401531i	0.979639	−	0.200766i	$-0.0643430\pi$
$702$	−20.6883	+	23.9380i	−0.780830	+	0.903482i
$703$	−3.37571	+	3.37571i	−0.127317	+	0.127317i
$704$	−21.5635	+	18.0939i	−0.812705	+	0.681941i
$705$	29.5744	+	8.77250i	1.11384	+	0.330391i
$706$	−1.67378	+	9.49245i	−0.0629934	+	0.357253i
$707$	3.14704	−	6.74885i	0.118357	−	0.253816i
$708$	27.2845	−	41.0483i	1.02541	−	1.54269i
$709$	6.87515	−	1.21227i	0.258202	−	0.0455279i	−0.0430488	−	0.999073i	$-0.513707\pi$
$709$	6.87515	−	1.21227i	0.258202	−	0.0455279i	0.301250	+	0.953545i	$0.402596\pi$
$710$	4.43447	−	2.26826i	0.166423	−	0.0851263i
$711$	12.0426	−	11.1424i	0.451631	−	0.417873i
$712$	−0.00384049	+	0.00102906i	−0.000143929	+	3.85655e-5i
$713$	−17.6968	−	37.9508i	−0.662749	−	1.42127i
$714$	7.21479	+	18.4210i	0.270007	+	0.689390i
$715$	16.5590	−	17.8134i	0.619273	−	0.666184i
$716$	24.9489	−	29.7330i	0.932386	−	1.11117i
$717$	13.6897	+	18.5761i	0.511249	+	0.693738i
$718$	6.83299	−	3.18628i	0.255005	−	0.118911i
$719$	−2.82089	+	4.88592i	−0.105201	+	0.182214i	−0.913820	−	0.406118i	$-0.866882\pi$
$719$	−2.82089	+	4.88592i	−0.105201	+	0.182214i	0.808619	+	0.588333i	$0.200215\pi$
$720$	19.1444	−	19.0555i	0.713471	−	0.710157i
$721$	−2.27504	−	3.94049i	−0.0847271	−	0.146752i
$722$	−26.6562	−	18.6649i	−0.992041	−	0.694635i
$723$	−2.78393	+	44.1057i	−0.103535	+	1.64031i
$724$	−7.20710	−	19.8013i	−0.267850	−	0.735911i
$725$	13.3261	+	3.77590i	0.494917	+	0.140234i
$726$	0.144187	+	5.94944i	0.00535127	+	0.220804i
$727$	−12.0758	−	1.05650i	−0.447867	−	0.0391832i	−0.139008	−	0.990291i	$-0.544391\pi$
$727$	−12.0758	−	1.05650i	−0.447867	−	0.0391832i	−0.308858	+	0.951108i	$0.599947\pi$
$728$	−0.0814023	−	0.0814023i	−0.00301697	−	0.00301697i
$729$	3.91154	+	26.7152i	0.144872	+	0.989450i
$730$	−28.1086	+	25.3892i	−1.04034	+	0.939695i
$731$	14.8791	+	17.7323i	0.550325	+	0.655852i
$732$	16.0052	+	15.2477i	0.591568	+	0.563572i
$733$	0.808383	+	1.15449i	0.0298583	+	0.0426421i	0.833804	−	0.552061i	$-0.186158\pi$
$733$	0.808383	+	1.15449i	0.0298583	+	0.0426421i	−0.803945	+	0.594703i	$0.797270\pi$
$734$	47.3029	−	17.2169i	1.74598	−	0.635486i
$735$	12.0780	+	15.1960i	0.445505	+	0.560512i
$736$	8.88151	+	50.3696i	0.327377	+	1.85665i
$737$	40.1967	+	10.7707i	1.48066	+	0.396743i
$738$	37.1188	−	40.9028i	1.36636	−	1.50565i
$739$	−7.65920	−	4.42204i	−0.281748	−	0.162667i	0.352466	−	0.935824i	$-0.385343\pi$
$739$	−7.65920	−	4.42204i	−0.281748	−	0.162667i	−0.634215	+	0.773157i	$0.718676\pi$
$740$	−11.8834	−	5.02220i	−0.436844	−	0.184620i
$741$	−1.30010	+	8.58470i	−0.0477605	+	0.315367i
$742$	2.90687	+	33.2257i	0.106715	+	1.21975i
$743$	−1.77243	−	20.2590i	−0.0650242	−	0.743230i	−0.956799	−	0.290751i	$-0.906095\pi$
$743$	−1.77243	−	20.2590i	−0.0650242	−	0.743230i	0.891775	−	0.452480i	$-0.149461\pi$
$744$	0.282318	−	0.110573i	0.0103503	−	0.00405380i
$745$	3.02069	+	7.44278i	0.110670	+	0.272682i
$746$	19.0615	+	11.0052i	0.697892	+	0.402928i
$747$	−0.707086	+	18.2122i	−0.0258709	+	0.666351i
$748$	27.7677	+	7.44034i	1.01529	+	0.272046i
$749$	−3.16098	−	17.9268i	−0.115500	−	0.655031i
$750$	−26.0427	+	28.5788i	−0.950945	+	1.04355i
$751$	−8.99657	+	3.27448i	−0.328290	+	0.119488i	−0.500906	−	0.865501i	$-0.667000\pi$
$751$	−8.99657	+	3.27448i	−0.328290	+	0.119488i	0.172617	+	0.984989i	$0.444778\pi$
$752$	−18.3957	−	26.2718i	−0.670822	−	0.958032i
$753$	−8.22247	+	33.9573i	−0.299643	+	1.23747i
$754$	10.8420	+	12.9210i	0.394844	+	0.470556i
$755$	−0.663290	−	0.734334i	−0.0241396	−	0.0267252i
$756$	14.5162	−	1.05707i	0.527950	−	0.0384454i
$757$	−20.8479	−	20.8479i	−0.757730	−	0.757730i	0.218179	−	0.975909i	$-0.429988\pi$
$757$	−20.8479	−	20.8479i	−0.757730	−	0.757730i	−0.975909	+	0.218179i	$0.929988\pi$
$758$	12.2385	+	1.07073i	0.444521	+	0.0388905i
$759$	34.7322	+	18.9458i	1.26070	+	0.687688i
$760$	0.0219863	−	0.0959204i	0.000797526	−	0.00347940i
$761$	−9.01441	−	24.7669i	−0.326772	−	0.897799i	−0.988923	−	0.148428i	$-0.952579\pi$
$761$	−9.01441	−	24.7669i	−0.326772	−	0.897799i	0.662151	−	0.749370i	$-0.269644\pi$
$762$	20.5985	−	10.2199i	0.746203	−	0.370229i
$763$	8.45800	+	5.92236i	0.306200	+	0.214404i
$764$	4.74988	+	8.22703i	0.171845	+	0.297644i
$765$	−26.7922	−	4.78851i	−0.968675	−	0.173129i
$766$	17.6017	−	30.4870i	0.635974	−	1.10154i
$767$	39.5912	−	18.4617i	1.42955	−	0.666612i
$768$	−27.9063	+	3.12443i	−1.00698	+	0.112743i
$769$	28.0565	−	33.4364i	1.01174	−	1.20575i	0.0332544	−	0.999447i	$-0.489413\pi$
$769$	28.0565	−	33.4364i	1.01174	−	1.20575i	0.978489	−	0.206301i	$-0.0661427\pi$
$770$	−22.4371	+	0.818821i	−0.808577	+	0.0295083i
$771$	−9.26308	+	11.5988i	−0.333602	+	0.417721i
$772$	−4.56784	−	9.79577i	−0.164400	−	0.352558i
$773$	−11.4730	+	3.07418i	−0.412655	+	0.110571i	−0.459173	−	0.888347i	$-0.651854\pi$
$773$	−11.4730	+	3.07418i	−0.412655	+	0.110571i	0.0465178	+	0.998917i	$0.485188\pi$
$774$	31.5096	−	13.2303i	1.13259	−	0.475553i
$775$	−29.8236	+	13.3908i	−1.07130	+	0.481011i
$776$	−0.340151	+	0.0599778i	−0.0122107	+	0.00215308i
$777$	3.15233	+	6.35358i	0.113089	+	0.227933i
$778$	−11.8516	+	25.4158i	−0.424900	+	0.911201i
$779$	2.63212	−	14.9275i	0.0943053	−	0.534832i
$780$	−22.8174	+	5.46886i	−0.816995	+	0.195816i
$781$	−3.04814	+	2.55770i	−0.109071	+	0.0915216i
$782$	36.6853	−	36.6853i	1.31186	−	1.31186i
$783$	14.3925	+	0.209781i	0.514346	+	0.00749695i
$784$		−	20.1814i		−	0.720763i
$785$	1.71928	+	2.27412i	0.0613637	+	0.0811667i
$786$	−21.2868	−	34.8893i	−0.759274	−	1.24446i
$787$	−44.2832	+	31.0074i	−1.57852	+	1.10529i	−0.635733	+	0.771909i	$0.719302\pi$
$787$	−44.2832	+	31.0074i	−1.57852	+	1.10529i	−0.942791	+	0.333385i	$0.891809\pi$
$788$	14.4632	+	6.74431i	0.515231	+	0.240256i
$789$	−6.90913	−	34.3016i	−0.245972	−	1.22117i
$790$	24.2298	−	3.01370i	0.862057	−	0.107222i
$791$	−18.5843	+	10.7297i	−0.660783	+	0.381503i
$792$	−0.152751	+	0.242346i	−0.00542778	+	0.00861138i
$793$	5.07074	+	18.9243i	0.180067	+	0.672020i
$794$	56.7853	+	20.6681i	2.01523	+	0.733485i
$795$	−41.0555	−	20.4889i	−1.45609	−	0.726667i
$796$	18.5059	+	15.5283i	0.655925	+	0.550386i
$797$	11.2740	−	0.986343i	0.399344	−	0.0349381i	0.114285	−	0.993448i	$-0.463542\pi$
$797$	11.2740	−	0.986343i	0.399344	−	0.0349381i	0.285059	+	0.958510i	$0.407987\pi$
$798$	6.45244	−	4.75512i	0.228414	−	0.168329i
$799$	−11.0526	+	30.3667i	−0.391012	+	1.07430i
$800$	39.4197	−	6.37051i	1.39370	−	0.225232i
$801$	0.374587	−	0.241188i	0.0132354	−	0.00852198i
$802$	8.41712	−	31.4131i	0.297219	−	1.10924i
$803$	17.3558	−	24.7866i	0.612472	−	0.874701i
$804$	−26.5438	−	30.1204i	−0.936129	−	1.06227i
$805$	−9.45139	+	17.8431i	−0.333118	+	0.628886i
$806$	−39.2070	−	6.91326i	−1.38101	−	0.243509i
$807$	−14.1599	+	14.8633i	−0.498453	+	0.523213i
$808$	0.0123236	−	0.140859i	0.000433541	−	0.00495540i
$809$	−3.55739			−0.125071			−0.0625355	−	0.998043i	$-0.519919\pi$
$809$	−3.55739			−0.125071			−0.0625355	+	0.998043i	$0.519919\pi$
$810$	−18.4647	+	35.6879i	−0.648782	+	1.25394i
$811$	46.5652			1.63512			0.817562	−	0.575840i	$-0.195325\pi$
$811$	46.5652			1.63512			0.817562	+	0.575840i	$0.195325\pi$
$812$	0.676266	−	7.72975i	0.0237323	−	0.271261i
$813$	−29.5896	+	31.0595i	−1.03775	+	1.08930i
$814$	20.3678	+	3.59139i	0.713891	+	0.125878i
$815$	7.65022	−	2.35206i	0.267976	−	0.0823890i
$816$	18.7085	+	21.2294i	0.654929	+	0.743177i
$817$	5.37921	−	7.68231i	0.188195	−	0.268770i
$818$	10.1134	−	37.7438i	0.353607	−	1.31968i
$819$	11.4707	+	5.90104i	0.400818	+	0.206199i
$820$	40.0535	−	8.57943i	1.39873	−	0.299607i
$821$	−14.8508	+	40.8021i	−0.518295	+	1.42400i	0.354102	+	0.935207i	$0.384787\pi$
$821$	−14.8508	+	40.8021i	−0.518295	+	1.42400i	−0.872397	+	0.488798i	$0.837436\pi$
$822$	−33.7326	+	24.8592i	−1.17656	+	0.867065i
$823$	18.2148	−	1.59358i	0.634926	−	0.0555489i	0.234851	−	0.972031i	$-0.424540\pi$
$823$	18.2148	−	1.59358i	0.634926	−	0.0555489i	0.400075	+	0.916482i	$0.368984\pi$
$824$	−0.0661850	−	0.0555358i	−0.00230567	−	0.00193468i
$825$	15.1778	−	26.9016i	0.528425	−	0.936594i
$826$	−37.8948	−	13.7926i	−1.31853	−	0.479905i
$827$	−10.3795	−	38.7367i	−0.360929	−	1.34701i	−0.872856	−	0.487978i	$-0.837735\pi$
$827$	−10.3795	−	38.7367i	−0.360929	−	1.34701i	0.511927	−	0.859029i	$-0.328932\pi$
$828$	−17.7875	−	33.7704i	−0.618158	−	1.17360i
$829$	23.7438	−	13.7085i	0.824656	−	0.476115i	−0.0273634	−	0.999626i	$-0.508711\pi$
$829$	23.7438	−	13.7085i	0.824656	−	0.476115i	0.852019	+	0.523510i	$0.175378\pi$
$830$	−16.6656	+	21.4003i	−0.578473	+	0.742814i
$831$	9.97644	+	49.5298i	0.346079	+	1.71817i
$832$	21.8135	+	10.1718i	0.756246	+	0.352643i
$833$	−16.6572	+	11.6635i	−0.577139	+	0.404117i
$834$	23.4607	+	38.4524i	0.812378	+	1.33150i
$835$	−21.5182	+	16.2682i	−0.744667	+	0.562983i
$836$		−	11.6470i		−	0.402819i
$837$	−26.3414	+	21.4567i	−0.910493	+	0.741652i
$838$	−0.260063	+	0.260063i	−0.00898371	+	0.00898371i
$839$	29.8408	−	25.0394i	1.03022	−	0.864456i	0.0393413	−	0.999226i	$-0.487474\pi$
$839$	29.8408	−	25.0394i	1.03022	−	0.864456i	0.990877	+	0.134770i	$0.0430296\pi$
$840$	−0.124630	−	0.0764379i	−0.00430013	−	0.00263736i
$841$	−3.70328	+	21.0024i	−0.127699	+	0.724219i
$842$	15.4408	−	33.1130i	0.532126	−	1.14115i
$843$	−22.5854	−	45.5213i	−0.777883	−	1.56784i
$844$	−5.83537	+	1.02893i	−0.200862	+	0.0354174i
$845$	7.87251	+	2.54426i	0.270823	+	0.0875254i
$846$	37.9902	+	28.8606i	1.30613	+	0.992247i
$847$	2.34368	−	0.627986i	0.0805297	−	0.0215779i
$848$	20.1608	+	43.2350i	0.692324	+	1.48469i
$849$	−14.6732	+	18.3731i	−0.503583	+	0.630563i
$850$	−28.2281	−	29.0478i	−0.968215	−	0.996331i
$851$	11.9557	−	14.2483i	0.409838	−	0.488425i
$852$	3.81494	−	0.427126i	0.130698	−	0.0146331i
$853$	−37.3837	+	17.4323i	−1.27999	+	0.596871i	−0.939234	−	0.343279i	$-0.888462\pi$
$853$	−37.3837	+	17.4323i	−1.27999	+	0.596871i	−0.340761	+	0.940150i	$0.610685\pi$
$854$	9.04308	−	15.6631i	0.309448	−	0.535980i
$855$	0.935488	+	10.9871i	0.0319930	+	0.375752i
$856$	−0.172825	−	0.299342i	−0.00590705	−	0.0102313i
$857$	−27.6158	−	19.3368i	−0.943338	−	0.660532i	−0.00271892	−	0.999996i	$-0.500865\pi$
$857$	−27.6158	−	19.3368i	−0.943338	−	0.660532i	−0.940619	+	0.339464i	$0.889754\pi$
$858$	33.6956	−	16.7181i	1.15035	−	0.570746i
$859$	−10.4264	−	28.6463i	−0.355745	−	0.977401i	−0.980489	−	0.196572i	$-0.937019\pi$
$859$	−10.4264	−	28.6463i	−0.355745	−	0.977401i	0.624745	−	0.780829i	$-0.285203\pi$
$860$	24.7033	+	5.66233i	0.842375	+	0.193084i
$861$	−19.7696	−	10.7840i	−0.673747	−	0.367517i
$862$	−40.6387	−	3.55542i	−1.38416	−	0.121098i
$863$	32.8323	+	32.8323i	1.11763	+	1.11763i	0.992089	+	0.125536i	$0.0400652\pi$
$863$	32.8323	+	32.8323i	1.11763	+	1.11763i	0.125536	+	0.992089i	$0.459935\pi$
$864$	37.8612	−	16.9877i	1.28806	−	0.577932i
$865$	0.659633	−	12.9766i	0.0224282	−	0.441219i
$866$	−2.54240	−	3.02991i	−0.0863941	−	0.102960i
$867$	−0.219640	+	0.907073i	−0.00745936	+	0.0308058i
$868$	10.5047	+	15.0022i	0.356551	+	0.509208i
$869$	−18.3291	+	6.67124i	−0.621772	+	0.226306i
$870$	17.2149	+	12.7484i	0.583640	+	0.432212i
$871$	−6.17875	−	35.0414i	−0.209359	−	1.18733i
$872$	0.189380	+	0.0507441i	0.00641320	+	0.00171841i
$873$	34.2432	−	18.0365i	1.15896	−	0.610444i
$874$	−18.2035	−	10.5098i	−0.615741	−	0.355498i
$875$	13.8234	+	7.57747i	0.467316	+	0.256165i
$876$	−27.1816	+	10.6459i	−0.918380	+	0.359693i
$877$	2.57111	+	29.3879i	0.0868201	+	0.992358i	0.907245	+	0.420603i	$0.138182\pi$
$877$	2.57111	+	29.3879i	0.0868201	+	0.992358i	−0.820425	+	0.571755i	$0.806263\pi$
$878$	−2.46211	−	28.1420i	−0.0830921	−	0.949747i
$879$	−2.14157	+	14.1410i	−0.0722334	+	0.476963i
$880$	−29.7560	+	12.0766i	−1.00308	+	0.407104i
$881$	12.5327	+	7.23578i	0.422239	+	0.243780i	0.696035	−	0.718008i	$-0.254946\pi$
$881$	12.5327	+	7.23578i	0.422239	+	0.243780i	−0.273796	+	0.961788i	$0.588279\pi$
$882$	9.16572	+	28.5879i	0.308626	+	0.962606i
$883$	30.5819	+	8.19438i	1.02916	+	0.275763i	0.733615	−	0.679565i	$-0.237832\pi$
$883$	30.5819	+	8.19438i	1.02916	+	0.275763i	0.295547	+	0.955328i	$0.404498\pi$
$884$	−4.26826	−	24.2065i	−0.143557	−	0.814153i
$885$	43.4312	−	34.5199i	1.45992	−	1.16037i
$886$	30.1088	−	10.9587i	1.01153	−	0.368166i
$887$	7.29567	+	10.4193i	0.244965	+	0.349846i	0.922740	−	0.385423i	$-0.125945\pi$
$887$	7.29567	+	10.4193i	0.244965	+	0.349846i	−0.677775	+	0.735269i	$0.737056\pi$
$888$	0.0975101	+	0.0928956i	0.00327222	+	0.00311737i
$889$	−6.02616	−	7.18169i	−0.202111	−	0.240866i
$890$	0.662171	+	0.0336597i	0.0221960	+	0.00112828i
$891$	8.00823	−	31.0847i	0.268286	−	1.04138i
$892$	11.3726	+	11.3726i	0.380784	+	0.380784i
$893$	13.0429	+	1.14110i	0.436463	+	0.0381856i
$894$	0.300984	+	12.4192i	0.0100664	+	0.415361i
$895$	37.0130	−	23.2093i	1.23721	−	0.775800i
$896$	0.103286	+	0.283776i	0.00345055	+	0.00948030i
$897$	2.13097	−	33.7609i	0.0711511	−	1.12724i
$898$	9.36140	+	6.55492i	0.312394	+	0.218741i
$899$	9.05610	+	15.6856i	0.302038	+	0.523145i
$900$	−26.5612	+	13.5083i	−0.885373	+	0.450277i
$901$	24.0335	−	41.6272i	0.800672	−	1.38680i
$902$	−59.5145	+	27.7520i	−1.98161	+	0.924042i
$903$	−8.26597	−	11.2165i	−0.275074	−	0.373261i
$904$	−0.261921	+	0.312145i	−0.00871135	+	0.0103818i
$905$	−0.865005	−	23.7026i	−0.0287537	−	0.787902i
$906$	−0.558126	−	1.42503i	−0.0185425	−	0.0473433i
$907$	22.8941	+	49.0966i	0.760188	+	1.63023i	0.776305	+	0.630357i	$0.217092\pi$
$907$	22.8941	+	49.0966i	0.760188	+	1.63023i	−0.0161177	+	0.999870i	$0.505131\pi$
$908$	−14.7921	+	3.96353i	−0.490892	+	0.131534i
$909$	3.50390	+	15.4516i	0.116217	+	0.512498i
$910$	8.74225	+	17.0912i	0.289803	+	0.566567i
$911$	−11.6520	+	2.05456i	−0.386047	+	0.0680705i	−0.363303	−	0.931671i	$-0.618351\pi$
$911$	−11.6520	+	2.05456i	−0.386047	+	0.0680705i	−0.0227434	+	0.999741i	$0.507240\pi$
$912$	6.34623	−	9.54762i	0.210145	−	0.316153i
$913$	9.15747	−	19.6383i	0.303068	−	0.649931i
$914$	−6.85089	+	38.8533i	−0.226607	+	1.28515i
$915$	11.8642	+	21.8709i	0.392219	+	0.723030i
$916$	6.95094	−	5.83253i	0.229666	−	0.192712i
$917$	−11.7827	+	11.7827i	−0.389099	+	0.389099i
$918$	−36.1433	−	21.5757i	−1.19291	−	0.712104i
$919$			33.2177i			1.09575i	0.836560	+	0.547875i	$0.184563\pi$
$919$			33.2177i			1.09575i	−0.836560	+	0.547875i	$0.815437\pi$
$920$	−0.0527631	+	0.379758i	−0.00173955	+	0.0125202i
$921$	−8.60841	+	15.7813i	−0.283657	+	0.520011i
$922$	29.6102	−	20.7333i	0.975161	−	0.682815i
$923$	3.08348	+	1.43785i	0.101494	+	0.0473274i
$924$	−16.3988	−	5.52252i	−0.539480	−	0.181678i
$925$	−10.9892	−	9.49230i	−0.361323	−	0.312105i
$926$	22.6234	−	13.0616i	0.743452	−	0.429232i
$927$	8.96204	+	3.66161i	0.294352	+	0.120263i
$928$	−5.72583	−	21.3691i	−0.187960	−	0.701475i
$929$	−29.9496	−	10.9008i	−0.982616	−	0.357643i	−0.199759	−	0.979845i	$-0.564016\pi$
$929$	−29.9496	−	10.9008i	−0.982616	−	0.357643i	−0.782857	+	0.622202i	$0.786238\pi$
$930$	−50.4680	+	3.06760i	−1.65491	+	0.100591i
$931$	6.31115	+	5.29569i	0.206840	+	0.173559i
$932$	−39.6200	+	3.46630i	−1.29780	+	0.113543i
$933$	−3.67801	−	32.8507i	−0.120413	−	1.07548i
$934$	5.56470	−	15.2889i	0.182083	−	0.500268i
$935$	27.1648	+	17.5804i	0.888385	+	0.574941i
$936$	0.242997	+	0.0307984i	0.00794260	+	0.00100668i
$937$	−2.56266	+	9.56398i	−0.0837184	+	0.312441i	−0.995068	−	0.0991909i	$-0.968375\pi$
$937$	−2.56266	+	9.56398i	−0.0837184	+	0.312441i	0.911350	+	0.411632i	$0.135041\pi$
$938$	−18.8405	+	26.9070i	−0.615165	+	0.878546i
$939$	−9.10019	+	27.0224i	−0.296973	+	0.881843i
$940$	10.3977	+	33.8191i	0.339135	+	1.10306i
$941$	−31.4053	−	5.53759i	−1.02378	−	0.180520i	−0.363544	−	0.931577i	$-0.618433\pi$
$941$	−31.4053	−	5.53759i	−1.02378	−	0.180520i	−0.660238	+	0.751057i	$0.729545\pi$
$942$	1.24403	+	4.23002i	0.0405325	+	0.137822i
$943$	−5.14706	+	58.8312i	−0.167611	+	1.91581i
$944$	−57.6798			−1.87732
$945$	15.9133	+	3.89250i	0.517660	+	0.126623i
$946$	−40.6293			−1.32097
$947$	1.23567	−	14.1237i	0.0401537	−	0.458959i	−0.949327	−	0.314291i	$-0.898233\pi$
$947$	1.23567	−	14.1237i	0.0401537	−	0.458959i	0.989480	−	0.144668i	$-0.0462114\pi$
$948$	18.2892	+	4.42856i	0.594004	+	0.143833i
$949$	−25.4793	−	4.49269i	−0.827094	−	0.145839i
$950$	−8.40771	+	14.0929i	−0.272782	+	0.457234i
$951$	−12.6876	+	2.55557i	−0.411423	+	0.0828702i
$952$	0.0878480	−	0.125460i	0.00284717	−	0.00406618i
$953$	5.23169	−	19.5249i	0.169471	−	0.632475i	−0.827956	−	0.560792i	$-0.810497\pi$
$953$	5.23169	−	19.5249i	0.169471	−	0.632475i	0.997428	−	0.0716822i	$-0.0228367\pi$
$954$	−48.1947	−	52.0882i	−1.56036	−	1.68642i
$955$	2.23958	+	10.4556i	0.0724710	+	0.338334i
$956$	−9.05213	+	24.8705i	−0.292767	+	0.804370i
$957$	−15.6801	−	6.85427i	−0.506865	−	0.221567i
$958$	−50.5662	+	4.42397i	−1.63372	+	0.142932i
$959$	13.0873	+	10.9816i	0.422612	+	0.354613i
$960$	29.9511	+	6.10541i	0.966667	+	0.197051i
$961$	−11.0418	−	4.01888i	−0.356186	−	0.129641i
$962$	−4.57691	−	17.0813i	−0.147565	−	0.550722i
$963$	28.6816	+	26.0282i	0.924252	+	0.838748i
$964$	−43.8972	+	25.3440i	−1.41383	+	0.816277i
$965$	−1.50161	−	12.0727i	−0.0483384	−	0.388635i
$966$	−23.4289	+	20.6469i	−0.753814	+	0.664303i
$967$	15.6175	+	7.28255i	0.502224	+	0.234191i	0.657185	−	0.753730i	$-0.271747\pi$
$967$	15.6175	+	7.28255i	0.502224	+	0.234191i	−0.154960	+	0.987921i	$0.549525\pi$
$968$	0.0377402	−	0.0264260i	0.00121302	−	0.000849363i
$969$	−11.5481	+	0.279872i	−0.370978	+	0.00899078i
$970$	57.0500	+	7.92647i	1.83177	+	0.254504i
$971$		−	4.56855i		−	0.146612i	−0.997310	−	0.0733058i	$-0.976645\pi$
$971$		−	4.56855i		−	0.146612i	0.997310	−	0.0733058i	$-0.0233549\pi$
$972$	−23.0348	+	20.6981i	−0.738840	+	0.663891i
$973$	12.9860	−	12.9860i	0.416313	−	0.416313i
$974$	45.1583	−	37.8923i	1.44697	−	1.21415i
$975$	−26.3313	−	2.04071i	−0.843276	−	0.0653549i
$976$	4.49207	−	25.4758i	0.143788	−	0.815460i
$977$	7.48700	−	16.0559i	0.239530	−	0.513675i	−0.749389	−	0.662130i	$-0.769652\pi$
$977$	7.48700	−	16.0559i	0.239530	−	0.513675i	0.988919	+	0.148456i	$0.0474302\pi$
$978$	12.3538	+	0.779764i	0.395030	+	0.0249341i
$979$	−0.521620	+	0.0919757i	−0.0166711	+	0.00293956i
$980$	−6.84665	+	21.1850i	−0.218708	+	0.676731i
$981$	−21.9433	+	1.06423i	−0.700596	+	0.0339783i
$982$	23.0498	−	6.17616i	0.735547	−	0.197089i
$983$	−18.5557	−	39.7929i	−0.591836	−	1.26920i	−0.942972	−	0.332872i	$-0.891982\pi$
$983$	−18.5557	−	39.7929i	−0.591836	−	1.26920i	0.351136	−	0.936324i	$-0.385795\pi$
$984$	−0.422788	−	0.0640289i	−0.0134780	−	0.00204117i
$985$	13.1561	+	12.2297i	0.419190	+	0.389671i
$986$	−14.4245	+	17.1904i	−0.459368	+	0.547454i
$987$	7.79105	−	17.8231i	0.247992	−	0.567316i
$988$	−9.02553	+	4.20867i	−0.287140	+	0.133896i
$989$	−18.2695	+	31.6436i	−0.580935	+	1.00621i
$990$	36.6661	−	30.6214i	1.16533	−	0.973212i
$991$	13.5103	+	23.4004i	0.429167	+	0.743340i	0.996799	−	0.0799428i	$-0.0254738\pi$
$991$	13.5103	+	23.4004i	0.429167	+	0.743340i	−0.567632	+	0.823282i	$0.692140\pi$
$992$	42.7736	+	29.9504i	1.35806	+	0.950926i
$993$	−11.9724	−	7.95794i	−0.379931	−	0.252537i
$994$	−1.07421	−	2.95136i	−0.0340718	−	0.0936115i
$995$	14.4455	+	23.0370i	0.457954	+	0.730323i
$996$	−17.8452	+	10.8878i	−0.565447	+	0.344992i
$997$	18.7346	+	1.63906i	0.593329	+	0.0519096i	0.379866	−	0.925041i	$-0.375970\pi$
$997$	18.7346	+	1.63906i	0.593329	+	0.0519096i	0.213463	+	0.976951i	$0.431526\pi$
$998$	−7.28760	−	7.28760i	−0.230685	−	0.230685i
$999$	−13.5826	−	6.57635i	−0.429735	−	0.208066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.32.3	✓	192
3.2	odd	2		405.2.r.a.287.14		192
5.2	odd	4		675.2.ba.b.518.3		192
5.3	odd	4	inner	135.2.q.a.113.14	yes	192
5.4	even	2		675.2.ba.b.32.14		192
15.8	even	4		405.2.r.a.368.3		192
27.11	odd	18	inner	135.2.q.a.92.14	yes	192
27.16	even	9		405.2.r.a.197.3		192
135.38	even	36	inner	135.2.q.a.38.3	yes	192
135.43	odd	36		405.2.r.a.278.14		192
135.92	even	36		675.2.ba.b.443.14		192
135.119	odd	18		675.2.ba.b.632.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.3	✓	192	1.1	even	1	trivial
135.2.q.a.38.3	yes	192	135.38	even	36	inner
135.2.q.a.92.14	yes	192	27.11	odd	18	inner
135.2.q.a.113.14	yes	192	5.3	odd	4	inner
405.2.r.a.197.3		192	27.16	even	9
405.2.r.a.278.14		192	135.43	odd	36
405.2.r.a.287.14		192	3.2	odd	2
405.2.r.a.368.3		192	15.8	even	4
675.2.ba.b.32.14		192	5.4	even	2
675.2.ba.b.443.14		192	135.92	even	36
675.2.ba.b.518.3		192	5.2	odd	4
675.2.ba.b.632.3		192	135.119	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.174019 + 1.98905i) q^{2} +(-1.19471 + 1.25406i) q^{3} +(-1.95641 - 0.344968i) q^{4} +(-1.97598 - 1.04667i) q^{5} +(-2.28648 - 2.59457i) q^{6} +(-0.808730 + 1.15499i) q^{7} +(-0.00692938 + 0.0258608i) q^{8} +(-0.145327 - 2.99648i) q^{9} +O(q^{10})\)	\(q+(-0.174019 + 1.98905i) q^{2} +(-1.19471 + 1.25406i) q^{3} +(-1.95641 - 0.344968i) q^{4} +(-1.97598 - 1.04667i) q^{5} +(-2.28648 - 2.59457i) q^{6} +(-0.808730 + 1.15499i) q^{7} +(-0.00692938 + 0.0258608i) q^{8} +(-0.145327 - 2.99648i) q^{9} +(2.42573 - 3.74817i) q^{10} +(-1.21986 + 3.35154i) q^{11} +(2.76996 - 2.04132i) q^{12} +(3.03799 - 0.265789i) q^{13} +(-2.15659 - 1.80959i) q^{14} +(3.67331 - 1.22753i) q^{15} +(-3.78380 - 1.37719i) q^{16} +(1.05009 + 3.91899i) q^{17} +(5.98543 + 0.232383i) q^{18} +(1.42357 - 0.821896i) q^{19} +(3.50476 + 2.72936i) q^{20} +(-0.482221 - 2.39407i) q^{21} +(-6.45408 - 3.00959i) q^{22} +(-5.24614 + 3.67339i) q^{23} +(-0.0241523 - 0.0395861i) q^{24} +(2.80898 + 4.13638i) q^{25} +6.08895i q^{26} +(3.93138 + 3.39768i) q^{27} +(1.98064 - 1.98064i) q^{28} +(2.12205 - 1.78061i) q^{29} +(1.80238 + 7.51999i) q^{30} +(-1.13538 + 6.43905i) q^{31} +(3.37512 - 7.23797i) q^{32} +(-2.74564 - 5.53389i) q^{33} +(-7.97779 + 1.40670i) q^{34} +(2.80692 - 1.43576i) q^{35} +(-0.749370 + 5.91247i) q^{36} +(-2.80529 + 0.751675i) q^{37} +(1.38706 + 2.97456i) q^{38} +(-3.29620 + 4.12736i) q^{39} +(0.0407599 - 0.0438476i) q^{40} +(5.92728 - 7.06386i) q^{41} +(4.84583 - 0.542546i) q^{42} +(5.17078 - 2.41117i) q^{43} +(3.54272 - 6.13617i) q^{44} +(-2.84915 + 6.07308i) q^{45} +(-6.39361 - 11.0741i) q^{46} +(6.52449 + 4.56850i) q^{47} +(6.24763 - 3.09976i) q^{48} +(1.71419 + 4.70971i) q^{49} +(-8.71627 + 4.86738i) q^{50} +(-6.16920 - 3.36519i) q^{51} +(-6.03524 - 0.528015i) q^{52} +(-8.37726 - 8.37726i) q^{53} +(-7.44228 + 7.22844i) q^{54} +(5.91836 - 5.34577i) q^{55} +(-0.0242649 - 0.0289177i) q^{56} +(-0.670045 + 2.76716i) q^{57} +(3.17244 + 4.53071i) q^{58} +(13.4607 - 4.89929i) q^{59} +(-7.60995 + 1.13437i) q^{60} +(1.11559 + 6.32681i) q^{61} +(-12.6100 - 3.37884i) q^{62} +(3.57842 + 2.25549i) q^{63} +(6.83499 + 3.94619i) q^{64} +(-6.28119 - 2.65457i) q^{65} +(11.4850 - 4.49821i) q^{66} +(-1.01692 - 11.6234i) q^{67} +(-0.702481 - 8.02940i) q^{68} +(1.66098 - 10.9676i) q^{69} +(2.36733 + 5.83294i) q^{70} +(0.966172 + 0.557819i) q^{71} +(0.0784983 + 0.0170055i) q^{72} +(-8.19480 - 2.19579i) q^{73} +(-1.00694 - 5.71065i) q^{74} +(-8.54318 - 1.41916i) q^{75} +(-3.06861 + 1.11688i) q^{76} +(-2.88444 - 4.11941i) q^{77} +(-7.63590 - 7.27454i) q^{78} +(3.51532 + 4.18939i) q^{79} +(6.03525 + 6.68168i) q^{80} +(-8.95776 + 0.870937i) q^{81} +(13.0189 + 13.0189i) q^{82} +(-6.05220 - 0.529499i) q^{83} +(0.117545 + 4.85013i) q^{84} +(2.02692 - 8.84293i) q^{85} +(3.89612 + 10.7045i) q^{86} +(-0.302247 + 4.78848i) q^{87} +(-0.0782205 - 0.0547706i) q^{88} +(0.0742532 + 0.128610i) q^{89} +(-11.5838 - 6.72393i) q^{90} +(-2.14993 + 3.72378i) q^{91} +(11.5308 - 5.37690i) q^{92} +(-6.71849 - 9.11664i) q^{93} +(-10.2223 + 12.1825i) q^{94} +(-3.67319 + 0.134049i) q^{95} +(5.04455 + 12.8799i) q^{96} +(5.45218 + 11.6922i) q^{97} +(-9.66613 + 2.59003i) q^{98} +(10.2201 + 3.16821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more