LMFDB - Embedded newform 135.2.q.a.83.1

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			83.1
Character	$\chi$	$=$	135.83
Dual form			135.2.q.a.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18018 + 1.52658i) q^{2} +(-1.19025 + 1.25829i) q^{3} +(1.73870 - 4.77703i) q^{4} +(1.64880 - 1.51045i) q^{5} +(0.674088 - 4.56031i) q^{6} +(1.30062 - 2.78918i) q^{7} +(2.12414 + 7.92739i) q^{8} +(-0.166591 - 2.99537i) q^{9} +(-1.28885 + 5.81007i) q^{10} +(-0.426793 + 0.508631i) q^{11} +(3.94140 + 7.87366i) q^{12} +(-0.269123 + 0.384347i) q^{13} +(1.42232 + 8.06640i) q^{14} +(-0.0619022 + 3.87249i) q^{15} +(-8.94423 - 7.50510i) q^{16} +(1.20591 - 4.50051i) q^{17} +(4.93586 + 6.27613i) q^{18} +(4.80938 + 2.77670i) q^{19} +(-4.34871 - 10.5026i) q^{20} +(1.96154 + 4.95639i) q^{21} +(0.154018 - 1.76044i) q^{22} +(-0.0602123 + 0.0280775i) q^{23} +(-12.5032 - 6.76283i) q^{24} +(0.437073 - 4.98086i) q^{25} -1.24878i q^{26} +(3.96733 + 3.35563i) q^{27} +(-11.0626 - 11.0626i) q^{28} +(0.434735 - 2.46551i) q^{29} +(-5.77669 - 8.53721i) q^{30} +(1.76652 + 0.642961i) q^{31} +(14.6055 + 1.27781i) q^{32} +(-0.132015 - 1.14243i) q^{33} +(4.24128 + 11.6528i) q^{34} +(-2.06847 - 6.56331i) q^{35} +(-14.5986 - 4.41223i) q^{36} +(-2.44933 - 0.656295i) q^{37} +(-14.7241 + 1.28820i) q^{38} +(-0.163296 - 0.796105i) q^{39} +(15.4762 + 9.86226i) q^{40} +(1.62695 - 0.286875i) q^{41} +(-11.8428 - 7.81137i) q^{42} +(0.732214 + 8.36925i) q^{43} +(1.68769 + 2.92316i) q^{44} +(-4.79904 - 4.68714i) q^{45} +(0.0884111 - 0.153133i) q^{46} +(-3.71355 - 1.73166i) q^{47} +(20.0895 - 2.32146i) q^{48} +(-1.58841 - 1.89299i) q^{49} +(6.65077 + 11.5264i) q^{50} +(4.22761 + 6.87413i) q^{51} +(1.36812 + 1.95387i) q^{52} +(7.52870 - 7.52870i) q^{53} +(-13.7721 - 1.25944i) q^{54} +(0.0645683 + 1.48328i) q^{55} +(24.8736 + 4.38589i) q^{56} +(-9.21828 + 2.74662i) q^{57} +(2.81598 + 6.03890i) q^{58} +(-3.49452 + 2.93225i) q^{59} +(18.3914 + 7.02879i) q^{60} +(-5.84534 + 2.12753i) q^{61} +(-4.83286 + 1.29496i) q^{62} +(-8.57130 - 3.43118i) q^{63} +(-13.5701 + 7.83468i) q^{64} +(0.136808 + 1.04021i) q^{65} +(2.03182 + 2.28917i) q^{66} +(-4.48268 - 3.13881i) q^{67} +(-19.4024 - 13.5857i) q^{68} +(0.0363384 - 0.109184i) q^{69} +(14.5290 + 11.1515i) q^{70} +(-5.33043 + 3.07752i) q^{71} +(23.3916 - 7.68321i) q^{72} +(13.6146 - 3.64803i) q^{73} +(6.34185 - 2.30824i) q^{74} +(5.74714 + 6.47845i) q^{75} +(21.6264 - 18.1467i) q^{76} +(0.863572 + 1.85194i) q^{77} +(1.57133 + 1.48637i) q^{78} +(-5.34198 - 0.941936i) q^{79} +(-26.0833 + 1.13543i) q^{80} +(-8.94450 + 0.998001i) q^{81} +(-3.10910 + 3.10910i) q^{82} +(3.25316 + 4.64599i) q^{83} +(27.0873 - 0.752663i) q^{84} +(-4.80950 - 9.24190i) q^{85} +(-14.3727 - 17.1287i) q^{86} +(2.58488 + 3.48160i) q^{87} +(-4.93869 - 2.30295i) q^{88} +(-3.08131 + 5.33699i) q^{89} +(17.6180 + 2.89269i) q^{90} +(0.721988 + 1.25052i) q^{91} +(0.0294359 + 0.336454i) q^{92} +(-2.91164 + 1.45751i) q^{93} +(10.7397 - 1.89370i) q^{94} +(12.1238 - 2.68612i) q^{95} +(-18.9921 + 16.8570i) q^{96} +(-13.5821 + 1.18828i) q^{97} +(6.35281 + 1.70223i) q^{98} +(1.59464 + 1.19367i) 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} - 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}+ \cdots + 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

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.18018	+	1.52658i	−1.54162	+	1.07945i	−0.576682	+	0.816969i	$0.695653\pi$
$2$	−2.18018	+	1.52658i	−1.54162	+	1.07945i	−0.964936	+	0.262484i	$0.915458\pi$
$3$	−1.19025	+	1.25829i	−0.687193	+	0.726474i
$3$	−1.19025	+	1.25829i	−0.687193	+	0.726474i
$4$	1.73870	−	4.77703i	0.869348	−	2.38851i
$5$	1.64880	−	1.51045i	0.737365	−	0.675494i
$5$	1.64880	−	1.51045i	0.737365	−	0.675494i
$6$	0.674088	−	4.56031i	0.275195	−	1.86174i
$7$	1.30062	−	2.78918i	0.491587	−	1.05421i	−0.491468	−	0.870896i	$-0.663539\pi$
$7$	1.30062	−	2.78918i	0.491587	−	1.05421i	0.983054	−	0.183315i	$-0.0586829\pi$
$8$	2.12414	+	7.92739i	0.750996	+	2.80276i
$9$	−0.166591	−	2.99537i	−0.0555302	−	0.998457i
$10$	−1.28885	+	5.81007i	−0.407571	+	1.83731i
$11$	−0.426793	+	0.508631i	−0.128683	+	0.153358i	−0.826538	−	0.562880i	$-0.809693\pi$
$11$	−0.426793	+	0.508631i	−0.128683	+	0.153358i	0.697856	+	0.716238i	$0.254138\pi$
$12$	3.94140	+	7.87366i	1.13778	+	2.27293i
$13$	−0.269123	+	0.384347i	−0.0746412	+	0.106599i	−0.854737	−	0.519062i	$-0.826282\pi$
$13$	−0.269123	+	0.384347i	−0.0746412	+	0.106599i	0.780096	+	0.625660i	$0.215170\pi$
$14$	1.42232	+	8.06640i	0.380132	+	2.15584i
$15$	−0.0619022	+	3.87249i	−0.0159831	+	0.999872i
$16$	−8.94423	−	7.50510i	−2.23606	−	1.87627i
$17$	1.20591	−	4.50051i	0.292476	−	1.09153i	−0.650726	−	0.759313i	$-0.725535\pi$
$17$	1.20591	−	4.50051i	0.292476	−	1.09153i	0.943201	−	0.332221i	$-0.107798\pi$
$18$	4.93586	+	6.27613i	1.16339	+	1.47930i
$19$	4.80938	+	2.77670i	1.10335	+	0.637018i	0.937098	−	0.349066i	$-0.113501\pi$
$19$	4.80938	+	2.77670i	1.10335	+	0.637018i	0.166249	+	0.986084i	$0.446834\pi$
$20$	−4.34871	−	10.5026i	−0.972401	−	2.34845i
$21$	1.96154	+	4.95639i	0.428042	+	1.08157i
$22$	0.154018	−	1.76044i	0.0328368	−	0.375327i
$23$	−0.0602123	+	0.0280775i	−0.0125551	+	0.00585456i	−0.428886	−	0.903359i	$-0.641094\pi$
$23$	−0.0602123	+	0.0280775i	−0.0125551	+	0.00585456i	0.416331	+	0.909213i	$0.363316\pi$
$24$	−12.5032	−	6.76283i	−2.55221	−	1.38046i
$25$	0.437073	−	4.98086i	0.0874146	−	0.996172i
$26$		−	1.24878i		−	0.244906i
$27$	3.96733	+	3.35563i	0.763513	+	0.645792i
$28$	−11.0626	−	11.0626i	−2.09064	−	2.09064i
$29$	0.434735	−	2.46551i	0.0807283	−	0.457833i	−0.917469	−	0.397808i	$-0.869771\pi$
$29$	0.434735	−	2.46551i	0.0807283	−	0.457833i	0.998197	−	0.0600247i	$-0.0191180\pi$
$30$	−5.77669	−	8.53721i	−1.05467	−	1.55867i
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	0.495749	−	0.868466i	$-0.334893\pi$
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	−0.178473	+	0.983945i	$0.557116\pi$
$32$	14.6055	+	1.27781i	2.58191	+	0.225888i
$33$	−0.132015	−	1.14243i	−0.0229808	−	0.198871i
$34$	4.24128	+	11.6528i	0.727373	+	1.99844i
$35$	−2.06847	−	6.56331i	−0.349635	−	1.10940i
$36$	−14.5986	−	4.41223i	−2.43310	−	0.735372i
$37$	−2.44933	−	0.656295i	−0.402667	−	0.107894i	0.0518010	−	0.998657i	$-0.483504\pi$
$37$	−2.44933	−	0.656295i	−0.402667	−	0.107894i	−0.454468	+	0.890763i	$0.650170\pi$
$38$	−14.7241	+	1.28820i	−2.38857	+	0.208973i
$39$	−0.163296	−	0.796105i	−0.0261483	−	0.127479i
$40$	15.4762	+	9.86226i	2.44700	+	1.55936i
$41$	1.62695	−	0.286875i	0.254087	−	0.0448023i	−0.0451539	−	0.998980i	$-0.514378\pi$
$41$	1.62695	−	0.286875i	0.254087	−	0.0448023i	0.299241	+	0.954178i	$0.403267\pi$
$42$	−11.8428	−	7.81137i	−1.82738	−	1.20532i
$43$	0.732214	+	8.36925i	0.111662	+	1.27630i	0.820794	+	0.571224i	$0.193531\pi$
$43$	0.732214	+	8.36925i	0.111662	+	1.27630i	−0.709133	+	0.705075i	$0.750913\pi$
$44$	1.68769	+	2.92316i	0.254428	+	0.440682i
$45$	−4.79904	−	4.68714i	−0.715398	−	0.698717i
$46$	0.0884111	−	0.153133i	0.0130355	−	0.0225782i
$47$	−3.71355	−	1.73166i	−0.541677	−	0.252588i	0.132468	−	0.991187i	$-0.457710\pi$
$47$	−3.71355	−	1.73166i	−0.541677	−	0.252588i	−0.674145	+	0.738599i	$0.735488\pi$
$48$	20.0895	−	2.32146i	2.89967	−	0.335075i
$49$	−1.58841	−	1.89299i	−0.226916	−	0.270428i
$50$	6.65077	+	11.5264i	0.940561	+	1.63008i
$51$	4.22761	+	6.87413i	0.591984	+	0.962571i
$52$	1.36812	+	1.95387i	0.189723	+	0.270953i
$53$	7.52870	−	7.52870i	1.03415	−	1.03415i	0.0347509	−	0.999396i	$-0.488936\pi$
$53$	7.52870	−	7.52870i	1.03415	−	1.03415i	0.999396	−	0.0347509i	$-0.0110638\pi$
$54$	−13.7721	−	1.25944i	−1.87415	−	0.171388i
$55$	0.0645683	+	1.48328i	0.00870639	+	0.200005i
$56$	24.8736	+	4.38589i	3.32388	+	0.586089i
$57$	−9.21828	+	2.74662i	−1.22099	+	0.363799i
$58$	2.81598	+	6.03890i	0.369757	+	0.792946i
$59$	−3.49452	+	2.93225i	−0.454948	+	0.381747i	−0.841268	−	0.540618i	$-0.818190\pi$
$59$	−3.49452	+	2.93225i	−0.454948	+	0.381747i	0.386320	+	0.922365i	$0.373746\pi$
$60$	18.3914	+	7.02879i	2.37431	+	0.907413i
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.687940	−	0.725767i	$-0.741485\pi$
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.0604785	+	0.998169i	$0.519263\pi$
$62$	−4.83286	+	1.29496i	−0.613773	+	0.164460i
$63$	−8.57130	−	3.43118i	−1.07988	−	0.432288i
$64$	−13.5701	+	7.83468i	−1.69626	+	0.979335i
$65$	0.136808	+	1.04021i	0.0169690	+	0.129022i
$66$	2.03182	+	2.28917i	0.250100	+	0.281777i
$67$	−4.48268	−	3.13881i	−0.547646	−	0.383466i	0.266758	−	0.963763i	$-0.414047\pi$
$67$	−4.48268	−	3.13881i	−0.547646	−	0.383466i	−0.814405	+	0.580297i	$0.802936\pi$
$68$	−19.4024	−	13.5857i	−2.35288	−	1.64751i
$69$	0.0363384	−	0.109184i	0.00437462	−	0.0131442i
$70$	14.5290	+	11.1515i	1.73655	+	1.33286i
$71$	−5.33043	+	3.07752i	−0.632605	+	0.365235i	−0.781760	−	0.623579i	$-0.785678\pi$
$71$	−5.33043	+	3.07752i	−0.632605	+	0.365235i	0.149155	+	0.988814i	$0.452345\pi$
$72$	23.3916	−	7.68321i	2.75673	−	0.905475i
$73$	13.6146	−	3.64803i	1.59347	−	0.426970i	0.650410	−	0.759583i	$-0.274597\pi$
$73$	13.6146	−	3.64803i	1.59347	−	0.426970i	0.943063	+	0.332613i	$0.107930\pi$
$74$	6.34185	−	2.30824i	0.737225	−	0.268328i
$75$	5.74714	+	6.47845i	0.663623	+	0.748067i
$76$	21.6264	−	18.1467i	2.48072	−	2.08157i
$77$	0.863572	+	1.85194i	0.0984131	+	0.211048i
$78$	1.57133	+	1.48637i	0.177918	+	0.168298i
$79$	−5.34198	−	0.941936i	−0.601020	−	0.105976i	−0.135144	−	0.990826i	$-0.543150\pi$
$79$	−5.34198	−	0.941936i	−0.601020	−	0.105976i	−0.465876	+	0.884850i	$0.654261\pi$
$80$	−26.0833	+	1.13543i	−2.91620	+	0.126945i
$81$	−8.94450	+	0.998001i	−0.993833	+	0.110889i
$82$	−3.10910	+	3.10910i	−0.343343	+	0.343343i
$83$	3.25316	+	4.64599i	0.357081	+	0.509964i	0.956997	−	0.290099i	$-0.0936882\pi$
$83$	3.25316	+	4.64599i	0.357081	+	0.509964i	−0.599916	+	0.800063i	$0.704799\pi$
$84$	27.0873	−	0.752663i	2.95547	−	0.0821222i
$85$	−4.80950	−	9.24190i	−0.521664	−	1.00242i
$86$	−14.3727	−	17.1287i	−1.54984	−	1.84703i
$87$	2.58488	+	3.48160i	0.277128	+	0.373267i
$88$	−4.93869	−	2.30295i	−0.526466	−	0.245495i
$89$	−3.08131	+	5.33699i	−0.326619	+	0.565720i	−0.981839	−	0.189718i	$-0.939243\pi$
$89$	−3.08131	+	5.33699i	−0.326619	+	0.565720i	0.655220	+	0.755438i	$0.272576\pi$
$90$	17.6180	+	2.89269i	1.85710	+	0.304916i
$91$	0.721988	+	1.25052i	0.0756849	+	0.131090i
$92$	0.0294359	+	0.336454i	0.00306891	+	0.0350778i
$93$	−2.91164	+	1.45751i	−0.301923	+	0.151137i
$94$	10.7397	−	1.89370i	1.10772	−	0.195320i
$95$	12.1238	−	2.68612i	1.24387	−	0.275590i
$96$	−18.9921	+	16.8570i	−1.93837	+	1.72046i
$97$	−13.5821	+	1.18828i	−1.37906	+	0.120652i	−0.752433	−	0.658669i	$-0.771120\pi$
$97$	−13.5821	+	1.18828i	−1.37906	+	0.120652i	−0.626625	+	0.779321i	$0.715564\pi$
$98$	6.35281	+	1.70223i	0.641731	+	0.171951i
$99$	1.59464	+	1.19367i	0.160267	+	0.119968i
$100$	−23.0338	−	10.7481i	−2.30338	−	1.07481i
$101$	−0.629841	−	1.73048i	−0.0626716	−	0.172189i	0.904405	−	0.426676i	$-0.140316\pi$
$101$	−0.629841	−	1.73048i	−0.0626716	−	0.172189i	−0.967076	+	0.254487i	$0.918093\pi$
$102$	−19.7108	−	8.53305i	−1.95166	−	0.844898i
$103$	−16.2704	−	1.42347i	−1.60317	−	0.140259i	−0.749833	−	0.661627i	$-0.769866\pi$
$103$	−16.2704	−	1.42347i	−1.60317	−	0.140259i	−0.853332	+	0.521368i	$0.825422\pi$
$104$	−3.61852	−	1.31704i	−0.354826	−	0.129146i
$105$	10.7206	+	5.20928i	1.04622	+	0.508373i
$106$	−4.92077	+	27.9071i	−0.477947	+	2.71057i
$107$	10.4880	+	10.4880i	1.01391	+	1.01391i	0.999902	+	0.0140087i	$0.00445924\pi$
$107$	10.4880	+	10.4880i	1.01391	+	1.01391i	0.0140087	+	0.999902i	$0.495541\pi$
$108$	22.9279	−	13.1176i	2.20624	−	1.26225i
$109$		−	9.34913i		−	0.895484i	−0.894163	−	0.447742i	$-0.852228\pi$
$109$		−	9.34913i		−	0.895484i	0.894163	−	0.447742i	$-0.147772\pi$
$110$	−2.40511	−	3.13525i	−0.229318	−	0.298934i
$111$	3.74113	−	2.30081i	0.355092	−	0.218383i
$112$	−32.5661	+	15.1858i	−3.07721	+	1.43492i
$113$	−1.81095	+	20.6993i	−0.170360	+	1.94722i	0.125734	+	0.992064i	$0.459871\pi$
$113$	−1.81095	+	20.6993i	−0.170360	+	1.94722i	−0.296094	+	0.955159i	$0.595684\pi$
$114$	15.9045	−	20.0605i	1.48960	−	1.87884i
$115$	−0.0568683	+	0.137242i	−0.00530300	+	0.0127979i
$116$	−11.0219	−	6.36351i	−1.02336	−	0.590837i
$117$	1.19610	+	0.742094i	0.110579	+	0.0686066i
$118$	3.14237	−	11.7275i	0.289278	−	1.07960i
$119$	−10.9843	−	9.21693i	−1.00693	−	0.844915i
$120$	−30.8302	+	7.73498i	−2.81440	+	0.706104i
$121$	1.83358	+	10.3987i	0.166689	+	0.945339i
$122$	9.49604	−	13.5617i	0.859731	−	1.22782i
$123$	−1.57551	+	2.38863i	−0.142059	+	0.215375i
$124$	6.14289	−	7.32081i	0.551648	−	0.657428i
$125$	−6.80270	−	8.87261i	−0.608452	−	0.793591i
$126$	23.9249	−	5.60417i	2.13140	−	0.499259i
$127$	−1.97054	−	7.35416i	−0.174857	−	0.652576i	−0.996576	−	0.0826829i	$-0.973651\pi$
$127$	−1.97054	−	7.35416i	−0.174857	−	0.652576i	0.821719	−	0.569893i	$-0.193016\pi$
$128$	5.23265	−	11.2214i	0.462505	−	0.991845i
$129$	−11.4025	−	9.04019i	−1.00393	−	0.795945i
$130$	−1.88622	−	2.05899i	−0.165433	−	0.180585i
$131$	4.01388	−	11.0280i	0.350694	−	0.963524i	−0.631454	−	0.775414i	$-0.717541\pi$
$131$	4.01388	−	11.0280i	0.350694	−	0.963524i	0.982148	−	0.188111i	$-0.0602363\pi$
$132$	−5.68695	−	1.35570i	−0.494986	−	0.117999i
$133$	13.9999	−	9.80281i	1.21394	−	0.850012i
$134$	14.5647			1.25820
$135$	11.6099	−	0.459700i	0.999217	−	0.0395647i
$136$	38.2388			3.27895
$137$	5.50755	−	3.85643i	0.470542	−	0.329477i	−0.314139	−	0.949377i	$-0.601716\pi$
$137$	5.50755	−	3.85643i	0.470542	−	0.329477i	0.784681	+	0.619900i	$0.212827\pi$
$138$	0.0874536	+	0.293514i	0.00744454	+	0.0249855i
$139$	−0.519349	+	1.42690i	−0.0440506	+	0.121028i	−0.959767	−	0.280796i	$-0.909402\pi$
$139$	−0.519349	+	1.42690i	−0.0440506	+	0.121028i	0.915717	+	0.401824i	$0.131624\pi$
$140$	−34.9496	−	1.53048i	−2.95378	−	0.129349i
$141$	6.59899	−	2.61161i	0.555735	−	0.219937i
$142$	6.92320	−	14.8468i	0.580982	−	1.24592i
$143$	−0.0806315	−	0.300921i	−0.00674274	−	0.0251643i
$144$	−20.9905	+	28.0416i	−1.74921	+	2.33680i
$145$	−3.00724	−	4.72177i	−0.249737	−	0.392122i
$146$	−24.1133	+	28.7372i	−1.99563	+	2.37830i
$147$	4.27255	+	0.254462i	0.352394	+	0.0209876i
$148$	−7.39377	+	10.5594i	−0.607764	+	0.867978i
$149$	3.69731	+	20.9685i	0.302895	+	1.71780i	0.633250	+	0.773947i	$0.281720\pi$
$149$	3.69731	+	20.9685i	0.302895	+	1.71780i	−0.330355	+	0.943857i	$0.607168\pi$
$150$	−22.4196	−	5.35073i	−1.83056	−	0.436885i
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	0.855797	−	0.517312i	$-0.173067\pi$
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	−0.360845	+	0.932626i	$0.617512\pi$
$152$	−11.7962	+	44.0239i	−0.956797	+	3.57081i
$153$	−13.6816	−	2.86240i	−1.10609	−	0.231411i
$154$	−4.70986	−	2.71924i	−0.379531	−	0.219123i
$155$	3.88380	−	1.60813i	0.311954	−	0.129168i
$156$	−4.08694	−	0.604116i	−0.327217	−	0.0483680i
$157$	−1.19160	+	13.6200i	−0.0950997	+	1.08699i	0.787324	+	0.616539i	$0.211466\pi$
$157$	−1.19160	+	13.6200i	−0.0950997	+	1.08699i	−0.882424	+	0.470455i	$0.844090\pi$
$158$	13.0844	−	6.10136i	1.04094	−	0.485398i
$159$	0.512227	+	18.4344i	0.0406223	+	1.46194i
$160$	26.0116	−	19.9540i	2.05640	−	1.57750i
$161$			0.204461i			0.0161138i
$162$	17.9771	−	15.8303i	1.41241	−	1.24374i
$163$	13.8462	+	13.8462i	1.08452	+	1.08452i	0.996082	+	0.0884330i	$0.0281859\pi$
$163$	13.8462	+	13.8462i	1.08452	+	1.08452i	0.0884330	+	0.996082i	$0.471814\pi$
$164$	1.45836	−	8.27077i	0.113879	−	0.645839i
$165$	−1.94325	−	1.68423i	−0.151282	−	0.131117i
$166$	−14.1849	−	5.16289i	−1.10096	−	0.400718i
$167$	21.8892	+	1.91506i	1.69384	+	0.148192i	0.892809	−	0.450435i	$-0.148731\pi$
$167$	21.8892	+	1.91506i	1.69384	+	0.148192i	0.801028	+	0.598627i	$0.204287\pi$
$168$	−35.1246	+	26.0779i	−2.70992	+	2.01195i
$169$	4.37097	+	12.0091i	0.336228	+	0.923779i
$170$	24.5940	+	12.8069i	1.88628	+	0.982245i
$171$	7.51604	−	14.8685i	0.574766	−	1.13702i
$172$	41.2533	+	11.0538i	3.14553	+	0.842842i
$173$	3.73833	−	0.327061i	0.284220	−	0.0248660i	0.0558456	−	0.998439i	$-0.482215\pi$
$173$	3.73833	−	0.327061i	0.284220	−	0.0248660i	0.228374	+	0.973573i	$0.426659\pi$
$174$	−10.9504	−	3.64450i	−0.830149	−	0.276288i
$175$	−13.3241	−	7.69726i	−1.00720	−	0.581858i
$176$	7.63466	−	1.34620i	0.575484	−	0.101473i
$177$	0.469743	−	7.88725i	0.0353081	−	0.592842i
$178$	−1.42952	−	16.3394i	−0.107147	−	1.22469i
$179$	−7.21345	−	12.4941i	−0.539158	−	0.933850i	−0.998950	−	0.0458226i	$-0.985409\pi$
$179$	−7.21345	−	12.4941i	−0.539158	−	0.933850i	0.459791	−	0.888027i	$-0.347924\pi$
$180$	−30.7347	+	14.7756i	−2.29083	+	1.10131i
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	0.474534	+	0.880237i	$0.342617\pi$
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	−0.999575	+	0.0291599i	$0.990717\pi$
$182$	−3.48308	−	1.62419i	−0.258183	−	0.120393i
$183$	4.28039	−	9.88743i	0.316415	−	0.730900i
$184$	−0.350480	−	0.417686i	−0.0258378	−	0.0307922i
$185$	−5.02975	+	2.61749i	−0.369794	+	0.192442i
$186$	4.12289	−	7.62247i	0.302305	−	0.558907i
$187$	1.77443	+	2.53415i	0.129759	+	0.185315i
$188$	−14.7289	+	14.7289i	−1.07422	+	1.07422i
$189$	14.5194	−	6.70121i	1.05613	−	0.487442i
$190$	−22.3314	+	24.3641i	−1.62009	+	1.76756i
$191$	−2.54718	−	0.449136i	−0.184307	−	0.0324983i	0.0807326	−	0.996736i	$-0.474274\pi$
$191$	−2.54718	−	0.449136i	−0.184307	−	0.0324983i	−0.265040	+	0.964237i	$0.585385\pi$
$192$	6.29352	−	26.4003i	0.454195	−	1.90528i
$193$	−6.02445	−	12.9195i	−0.433649	−	0.929963i	−0.994761	−	0.102224i	$-0.967404\pi$
$193$	−6.02445	−	12.9195i	−0.433649	−	0.929963i	0.561112	−	0.827740i	$-0.310374\pi$
$194$	27.7975	−	23.3248i	1.99574	−	1.67463i
$195$	−1.47172	−	1.06597i	−0.105392	−	0.0763355i
$196$	−11.8046	+	4.29654i	−0.843189	+	0.306896i
$197$	−8.06170	+	2.16013i	−0.574372	+	0.153903i	−0.534301	−	0.845294i	$-0.679425\pi$
$197$	−8.06170	+	2.16013i	−0.574372	+	0.153903i	−0.0400711	+	0.999197i	$0.512758\pi$
$198$	−5.29882	−	0.168070i	−0.376571	−	0.0119442i
$199$	3.27312	−	1.88973i	0.232025	−	0.133960i	−0.379481	−	0.925200i	$-0.623897\pi$
$199$	3.27312	−	1.88973i	0.232025	−	0.133960i	0.611506	+	0.791240i	$0.290564\pi$
$200$	40.4136	−	7.11519i	2.85768	−	0.503120i
$201$	9.28506	−	1.90454i	0.654917	−	0.134336i
$202$	4.01487	+	2.81124i	0.282485	+	0.197798i
$203$	−6.31132	−	4.41923i	−0.442968	−	0.310169i
$204$	40.1885	−	8.24340i	2.81376	−	0.577153i
$205$	2.24920	−	2.93043i	0.157091	−	0.204670i
$206$	37.6453	−	21.7345i	2.62287	−	1.51432i
$207$	0.0941332	+	0.175681i	0.00654271	+	0.0122107i
$208$	5.29166	−	1.41790i	0.366911	−	0.0983134i
$209$	−3.46492	+	1.26113i	−0.239674	+	0.0872341i
$210$	−31.3251	+	5.00860i	−2.16164	+	0.345626i
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	−0.977405	−	0.211376i	$-0.932205\pi$
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	0.0384403	+	0.999261i	$0.487761\pi$
$212$	−22.8747	−	49.0550i	−1.57104	−	3.36911i
$213$	2.47214	−	10.3703i	0.169388	−	0.710558i
$214$	−38.8763	−	6.85495i	−2.65753	−	0.468594i
$215$	13.8486	+	12.6932i	0.944468	+	0.865671i
$216$	−18.1743	+	38.5784i	−1.23660	+	2.62493i
$217$	4.09090	−	4.09090i	0.277708	−	0.277708i
$218$	14.2722	+	20.3828i	0.966633	+	1.38049i
$219$	−11.6146	+	21.4733i	−0.784842	+	1.45103i
$220$	7.19794	+	2.27053i	0.485285	+	0.153079i
$221$	1.40522	+	1.67468i	0.0945254	+	0.112651i
$222$	−4.64397	+	10.7273i	−0.311683	+	0.719968i
$223$	−17.3515	−	8.09113i	−1.16194	−	0.541822i	−0.256605	−	0.966516i	$-0.582604\pi$
$223$	−17.3515	−	8.09113i	−1.16194	−	0.541822i	−0.905337	+	0.424694i	$0.860382\pi$
$224$	22.5602	−	39.0754i	1.50737	−	2.61083i
$225$	−14.9923	−	0.479431i	−0.999489	−	0.0319621i
$226$	−27.6508	−	47.8926i	−1.83930	−	3.18577i
$227$	−0.0420779	−	0.480953i	−0.00279281	−	0.0319220i	0.994670	−	0.103106i	$-0.0328779\pi$
$227$	−0.0420779	−	0.480953i	−0.00279281	−	0.0319220i	−0.997463	+	0.0711836i	$0.977322\pi$
$228$	−2.90709	+	48.8115i	−0.192526	+	3.23262i
$229$	14.7979	−	2.60927i	0.977875	−	0.172426i	0.338203	−	0.941073i	$-0.390181\pi$
$229$	14.7979	−	2.60927i	0.977875	−	0.172426i	0.639672	+	0.768648i	$0.279070\pi$
$230$	−0.0855272	−	0.386026i	−0.00563950	−	0.0254538i
$231$	−3.35814	−	1.11765i	−0.220950	−	0.0735359i
$232$	20.4685	−	1.79076i	1.34382	−	0.117569i
$233$	−0.534587	−	0.143242i	−0.0350220	−	0.00938411i	0.241266	−	0.970459i	$-0.422438\pi$
$233$	−0.534587	−	0.143242i	−0.0350220	−	0.00938411i	−0.276287	+	0.961075i	$0.589104\pi$
$234$	−3.74056	+	0.208035i	−0.244528	+	0.0135997i
$235$	−8.73847	+	2.75398i	−0.570035	+	0.179650i
$236$	7.93154	+	21.7917i	0.516299	+	1.41852i
$237$	7.54355	−	5.60062i	0.490006	−	0.363800i
$238$	38.0181	+	3.32615i	2.46435	+	0.215602i
$239$	−5.32354	−	1.93761i	−0.344351	−	0.125334i	0.164054	−	0.986451i	$-0.447543\pi$
$239$	−5.32354	−	1.93761i	−0.344351	−	0.125334i	−0.508406	+	0.861118i	$0.669765\pi$
$240$	29.6171	−	34.1718i	1.91177	−	2.20578i
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	−0.972853	−	0.231426i	$-0.925661\pi$
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	0.993335	+	0.115266i	$0.0367721\pi$
$242$	−19.8720	−	19.8720i	−1.27742	−	1.27742i
$243$	9.39045	−	12.4426i	0.602397	−	0.798196i
$244$			31.6225i			2.02442i
$245$	−5.47824	−	0.721948i	−0.349992	−	0.0461236i
$246$	−0.211532	−	7.61277i	−0.0134868	−	0.485372i
$247$	−2.36153	+	1.10120i	−0.150261	+	0.0700677i
$248$	−1.34467	+	15.3696i	−0.0853866	+	0.975973i
$249$	−9.71810	−	1.43649i	−0.615859	−	0.0910340i
$250$	28.3758	+	8.95902i	1.79464	+	0.566618i
$251$	−16.8470	−	9.72663i	−1.06337	−	0.613939i	−0.137011	−	0.990570i	$-0.543749\pi$
$251$	−16.8470	−	9.72663i	−1.06337	−	0.613939i	−0.926364	+	0.376630i	$0.877083\pi$
$252$	−31.2937	+	34.9796i	−1.97132	+	2.20351i
$253$	0.0114171	−	0.0426091i	0.000717786	−	0.00267881i
$254$	15.5228	+	13.0252i	0.973988	+	0.817273i
$255$	17.3535	+	4.94846i	1.08672	+	0.309884i
$256$	0.280392	+	1.59018i	0.0175245	+	0.0993864i
$257$	−17.1627	+	24.5109i	−1.07058	+	1.52895i	−0.241027	+	0.970518i	$0.577484\pi$
$257$	−17.1627	+	24.5109i	−1.07058	+	1.52895i	−0.829553	+	0.558428i	$0.811405\pi$
$258$	38.6600	+	2.30248i	2.40686	+	0.143346i
$259$	−5.01616	+	5.97802i	−0.311689	+	0.371456i
$260$	5.20697	+	1.15507i	0.322923	+	0.0716343i
$261$	−7.45753	−	0.891463i	−0.461609	−	0.0551802i
$262$	8.08418	+	30.1706i	0.499442	+	1.86394i
$263$	−3.54766	+	7.60797i	−0.218758	+	0.469128i	−0.984807	−	0.173655i	$-0.944442\pi$
$263$	−3.54766	+	7.60797i	−0.218758	+	0.469128i	0.766049	+	0.642782i	$0.222220\pi$
$264$	8.77607	−	3.47321i	0.540130	−	0.213761i
$265$	1.04157	−	23.7851i	0.0639834	−	1.46110i
$266$	−15.5574	+	42.7437i	−0.953888	+	2.62079i
$267$	−3.04794	−	10.2296i	−0.186531	−	0.626039i
$268$	−22.7882	+	15.9565i	−1.39201	+	0.974696i
$269$	−2.21545			−0.135079			−0.0675393	−	0.997717i	$-0.521515\pi$
$269$	−2.21545			−0.135079			−0.0675393	+	0.997717i	$0.521515\pi$
$270$	−24.6098	+	18.7256i	−1.49770	+	1.13960i
$271$	−5.87725			−0.357017			−0.178509	−	0.983938i	$-0.557127\pi$
$271$	−5.87725			−0.357017			−0.178509	+	0.983938i	$0.557127\pi$
$272$	−44.5627	+	31.2031i	−2.70201	+	1.89197i
$273$	−2.43287	−	0.579966i	−0.147244	−	0.0351011i
$274$	−6.12031	+	16.8154i	−0.369741	+	1.01586i
$275$	2.34688	+	2.34810i	0.141522	+	0.141596i
$276$	−0.458394	−	0.363427i	−0.0275920	−	0.0218757i
$277$	4.78156	−	10.2541i	0.287296	−	0.616108i	−0.708700	−	0.705510i	$-0.750718\pi$
$277$	4.78156	−	10.2541i	0.287296	−	0.616108i	0.995996	+	0.0894020i	$0.0284956\pi$
$278$	−1.04600	−	3.90372i	−0.0627348	−	0.234130i
$279$	1.63162	−	5.39850i	0.0976826	−	0.323199i
$280$	47.6362	−	30.3389i	2.84681	−	1.81310i
$281$	13.9719	−	16.6511i	0.833496	−	0.993322i	−0.166478	−	0.986045i	$-0.553239\pi$
$281$	13.9719	−	16.6511i	0.833496	−	0.993322i	0.999974	−	0.00727642i	$-0.00231618\pi$
$282$	−10.4001	+	15.7676i	−0.619320	+	0.938950i
$283$	−7.52820	+	10.7514i	−0.447505	+	0.639103i	−0.978005	−	0.208582i	$-0.933115\pi$
$283$	−7.52820	+	10.7514i	−0.447505	+	0.639103i	0.530500	+	0.847685i	$0.322004\pi$
$284$	5.43342	+	30.8145i	0.322414	+	1.82850i
$285$	−11.0504	+	18.4524i	−0.654572	+	1.09303i
$286$	0.635170	+	0.532971i	0.0375584	+	0.0315152i
$287$	1.31589	−	4.91097i	0.0776745	−	0.289885i
$288$	1.39439	−	43.9617i	0.0821654	−	2.59047i
$289$	−4.07794	−	2.35440i	−0.239879	−	0.138494i
$290$	13.7645	+	5.70352i	0.808276	+	0.334922i
$291$	14.6710	−	18.5046i	0.860029	−	1.08476i
$292$	6.24497	−	71.3804i	0.365460	−	4.17722i
$293$	−3.86399	+	1.80181i	−0.225736	+	0.105263i	−0.532196	−	0.846621i	$-0.678633\pi$
$293$	−3.86399	+	1.80181i	−0.225736	+	0.105263i	0.306460	+	0.951884i	$0.400855\pi$
$294$	−9.70336	+	5.96760i	−0.565912	+	0.348037i
$295$	−1.33274	+	10.1130i	−0.0775950	+	0.588801i
$296$		−	20.8108i		−	1.20960i
$297$	−3.40001	+	0.585751i	−0.197288	+	0.0339887i
$298$	−40.0708	−	40.0708i	−2.32124	−	2.32124i
$299$	0.00541301	−	0.0306987i	0.000313043	−	0.00177535i
$300$	40.9403	−	16.1902i	2.36369	−	0.934742i
$301$	24.2957	+	8.84290i	1.40038	+	0.509696i
$302$	−21.0508	−	1.84171i	−1.21134	−	0.105978i
$303$	2.92711	+	1.26718i	0.168158	+	0.0727977i
$304$	−22.1768	−	60.9303i	−1.27193	−	3.49459i
$305$	−6.42425	+	12.3370i	−0.367852	+	0.706413i
$306$	34.1980	−	14.6455i	1.95497	−	0.837225i
$307$	17.9955	+	4.82189i	1.02706	+	0.275200i	0.732741	−	0.680508i	$-0.238241\pi$
$307$	17.9955	+	4.82189i	1.02706	+	0.275200i	0.294318	+	0.955707i	$0.404907\pi$
$308$	10.3482	−	0.905354i	0.589646	−	0.0515873i
$309$	21.1570	−	18.7785i	1.20358	−	1.06827i
$310$	−6.01243	+	9.43492i	−0.341483	+	0.535868i
$311$	−8.07539	+	1.42391i	−0.457913	+	0.0807425i	−0.397847	−	0.917452i	$-0.630242\pi$
$311$	−8.07539	+	1.42391i	−0.457913	+	0.0807425i	−0.0600667	+	0.998194i	$0.519131\pi$
$312$	5.96418	−	2.98555i	0.337655	−	0.169023i
$313$	−1.66176	−	18.9940i	−0.0939283	−	1.07360i	−0.886158	−	0.463382i	$-0.846636\pi$
$313$	−1.66176	−	18.9940i	−0.0939283	−	1.07360i	0.792230	−	0.610222i	$-0.208920\pi$
$314$	−18.1941	−	31.5131i	−1.02675	−	1.77839i
$315$	−19.3150	+	7.28921i	−1.08828	+	0.410701i
$316$	−13.7877	+	23.8811i	−0.775621	+	1.34342i
$317$	15.3899	+	7.17642i	0.864382	+	0.403068i	0.803661	−	0.595087i	$-0.202882\pi$
$317$	15.3899	+	7.17642i	0.864382	+	0.403068i	0.0607206	+	0.998155i	$0.480660\pi$
$318$	−29.2582	−	39.4082i	−1.64072	−	2.20990i
$319$	1.06849	+	1.27338i	0.0598241	+	0.0712956i
$320$	−10.5404	+	33.4147i	−0.589226	+	1.86794i
$321$	−25.6803	+	0.713566i	−1.43333	+	0.0398274i
$322$	−0.312125	−	0.445761i	−0.0173941	−	0.0248413i
$323$	18.2962	−	18.2962i	1.01803	−	1.01803i
$324$	−10.7843	+	44.4633i	−0.599127	+	2.47019i
$325$	1.79675	+	1.50845i	0.0996659	+	0.0836738i
$326$	−51.3243	−	9.04986i	−2.84259	−	0.501225i
$327$	11.7639	+	11.1278i	0.650546	+	0.615371i
$328$	5.73003	+	12.2881i	0.316388	+	0.678497i
$329$	−9.65980	+	8.10554i	−0.532562	+	0.446873i
$330$	6.80774	+	0.705409i	0.374754	+	0.0388315i
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.0525142	−	0.998620i	$-0.483277\pi$
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.682129	+	0.731232i	$0.261054\pi$
$332$	27.8503	−	7.46247i	1.52848	−	0.409556i
$333$	−1.55781	+	7.44597i	−0.0853676	+	0.408037i
$334$	−50.6458	+	29.2404i	−2.77122	+	1.59996i
$335$	−12.1320	+	1.59561i	−0.662845	+	0.0871775i
$336$	19.6537	−	59.0526i	1.07220	−	3.22158i
$337$	5.58245	+	3.90887i	0.304095	+	0.212930i	0.715657	−	0.698452i	$-0.246128\pi$
$337$	5.58245	+	3.90887i	0.304095	+	0.212930i	−0.411561	+	0.911382i	$0.635016\pi$
$338$	−27.8623	−	19.5094i	−1.51551	−	1.06117i
$339$	−23.8902	−	26.9161i	−1.29754	−	1.46188i
$340$	−52.5111	+	6.90628i	−2.84781	+	0.374545i
$341$	−1.08097	+	0.624097i	−0.0585377	+	0.0337968i
$342$	6.31153	+	43.8897i	0.341288	+	2.37328i
$343$	13.4628	−	3.60734i	0.726922	−	0.194778i
$344$	−64.7910	+	23.5820i	−3.49330	+	1.27146i
$345$	−0.105002	−	0.234910i	−0.00565314	−	0.0126471i
$346$	−7.65094	+	6.41990i	−0.411317	+	0.345136i
$347$	5.81216	+	12.4642i	0.312013	+	0.669114i	0.998304	−	0.0582130i	$-0.0185402\pi$
$347$	5.81216	+	12.4642i	0.312013	+	0.669114i	−0.686291	+	0.727327i	$0.740762\pi$
$348$	21.1260	−	6.29459i	1.13247	−	0.337425i
$349$	26.3484	+	4.64594i	1.41040	+	0.248691i	0.826409	−	0.563070i	$-0.190380\pi$
$349$	26.3484	+	4.64594i	1.41040	+	0.248691i	0.583990	+	0.811761i	$0.301491\pi$
$350$	40.7993	−	3.55879i	2.18081	−	0.190225i
$351$	−2.35743	+	0.621756i	−0.125830	+	0.0331869i
$352$	−6.88345	+	6.88345i	−0.366889	+	0.366889i
$353$	−0.0271374	−	0.0387563i	−0.00144438	−	0.00206279i	0.818429	−	0.574607i	$-0.194845\pi$
$353$	−0.0271374	−	0.0387563i	−0.00144438	−	0.00206279i	−0.819874	+	0.572545i	$0.805956\pi$
$354$	11.0164	+	17.9127i	0.585513	+	0.952049i
$355$	−4.14035	+	13.1256i	−0.219747	+	0.696633i
$356$	20.1375	+	23.9989i	1.06729	+	1.27194i
$357$	24.6717	−	2.85097i	1.30576	−	0.150889i
$358$	34.7997	+	16.2274i	1.83922	+	0.857644i
$359$	−9.42597	+	16.3263i	−0.497484	+	0.861667i	−0.999996	−	0.00290290i	$-0.999076\pi$
$359$	−9.42597	+	16.3263i	−0.497484	+	0.861667i	0.502512	+	0.864570i	$0.332409\pi$
$360$	26.9629	−	48.0000i	1.42107	−	2.52982i
$361$	5.92010	+	10.2539i	0.311584	+	0.539680i
$362$	−3.27707	−	37.4571i	−0.172239	−	1.96870i
$363$	−15.2670	−	10.0700i	−0.801312	−	0.528535i
$364$	7.22909	−	1.27468i	0.378907	−	0.0668116i
$365$	16.9376	−	26.5791i	0.886556	−	1.39122i
$366$	5.76192	+	28.0907i	0.301180	+	1.46832i
$367$	−19.7504	+	1.72794i	−1.03096	+	0.0901977i	−0.590063	−	0.807357i	$-0.700897\pi$
$367$	−19.7504	+	1.72794i	−1.03096	+	0.0901977i	−0.440902	+	0.897555i	$0.645341\pi$
$368$	0.749277	+	0.200768i	0.0390588	+	0.0104658i
$369$	−1.13033	−	4.82552i	−0.0588427	−	0.251207i
$370$	6.96994	−	13.3849i	0.362350	−	0.695847i
$371$	−11.2070	−	30.7909i	−0.581836	−	1.59858i
$372$	1.90011	+	16.4432i	0.0985160	+	0.852538i
$373$	21.1273	+	1.84840i	1.09393	+	0.0957063i	0.619808	−	0.784754i	$-0.287211\pi$
$373$	21.1273	+	1.84840i	1.09393	+	0.0957063i	0.474120	+	0.880460i	$0.342766\pi$
$374$	−7.73714	−	2.81609i	−0.400078	−	0.145616i
$375$	19.2613	+	2.00089i	0.994648	+	0.103325i
$376$	5.83943	−	33.1170i	0.301145	−	1.70788i
$377$	0.830613	+	0.830613i	0.0427788	+	0.0427788i
$378$	−21.4250	+	36.7749i	−1.10199	+	1.89150i
$379$		−	4.95221i		−	0.254378i	−0.991878	−	0.127189i	$-0.959405\pi$
$379$		−	4.95221i		−	0.254378i	0.991878	−	0.127189i	$-0.0405955\pi$
$380$	8.24787	−	62.5860i	0.423107	−	3.21059i
$381$	11.5991	+	6.27381i	0.594241	+	0.321417i
$382$	6.23894	−	2.90926i	0.319212	−	0.148851i
$383$	2.46502	−	28.1753i	0.125957	−	1.43969i	−0.625663	−	0.780093i	$-0.715172\pi$
$383$	2.46502	−	28.1753i	0.125957	−	1.43969i	0.751620	−	0.659596i	$-0.229273\pi$
$384$	7.89166	+	19.9406i	0.402720	+	1.01759i
$385$	4.22111	+	1.74909i	0.215128	+	0.0891416i
$386$	32.8569	+	18.9699i	1.67237	+	0.965545i
$387$	24.9470	−	3.58749i	1.26813	−	0.182362i
$388$	−17.9388	+	66.9484i	−0.910703	+	3.39879i
$389$	22.5434	+	18.9162i	1.14300	+	0.959088i	0.999533	−	0.0305681i	$-0.00973165\pi$
$389$	22.5434	+	18.9162i	1.14300	+	0.959088i	0.143463	+	0.989656i	$0.454176\pi$
$390$	4.83589	+	0.0773023i	0.244875	+	0.00391436i
$391$	0.0537524	+	0.304845i	0.00271838	+	0.0154167i
$392$	11.6325	−	16.6129i	0.587530	−	0.839080i
$393$	9.09894	+	18.1768i	0.458981	+	0.916898i
$394$	14.2783	−	17.0163i	0.719332	−	0.857267i
$395$	−10.2306	+	6.51574i	−0.514757	+	0.327843i
$396$	8.47479	−	5.54221i	0.425874	−	0.278507i
$397$	−5.07320	−	18.9334i	−0.254616	−	0.950242i	−0.968303	−	0.249777i	$-0.919643\pi$
$397$	−5.07320	−	18.9334i	−0.254616	−	0.950242i	0.713687	−	0.700465i	$-0.247024\pi$
$398$	−4.25115	+	9.11662i	−0.213091	+	0.456975i
$399$	−4.32861	+	29.2837i	−0.216702	+	1.46602i
$400$	−41.2911	+	41.2697i	−2.06456	+	2.06348i
$401$	−0.0115561	+	0.0317502i	−0.000577086	+	0.00158553i	−0.939981	−	0.341227i	$-0.889157\pi$
$401$	−0.0115561	+	0.0317502i	−0.000577086	+	0.00158553i	0.939404	+	0.342813i	$0.111380\pi$
$402$	−17.3356	+	18.3266i	−0.864624	+	0.914047i
$403$	−0.722531	+	0.505922i	−0.0359918	+	0.0252018i
$404$	−9.36163			−0.465759
$405$	−13.2402	+	15.1557i	−0.657913	+	0.753094i
$406$	20.5061			1.01770
$407$	1.37917	−	0.965702i	0.0683627	−	0.0478681i
$408$	−45.5139	+	48.1156i	−2.25327	+	2.38207i
$409$	3.01485	−	8.28322i	0.149075	−	0.409579i	−0.842569	−	0.538589i	$-0.818958\pi$
$409$	3.01485	−	8.28322i	0.149075	−	0.409579i	0.991643	+	0.129010i	$0.0411799\pi$
$410$	−0.430135	+	9.82242i	−0.0212428	+	0.485095i
$411$	−1.70288	+	11.5202i	−0.0839967	+	0.568251i
$412$	−35.0892	+	75.2490i	−1.72872	+	3.70725i
$413$	3.63355	+	13.5606i	0.178795	+	0.667272i
$414$	−0.473417	−	0.239314i	−0.0232672	−	0.0117616i
$415$	12.3814	+	2.74657i	0.607777	+	0.134824i
$416$	−4.42180	+	5.26969i	−0.216796	+	0.258368i
$417$	−1.17730	−	2.35187i	−0.0576525	−	0.115171i
$418$	5.62894	−	8.03896i	0.275320	−	0.393198i
$419$	−5.75122	−	32.6168i	−0.280966	−	1.59344i	−0.719350	−	0.694648i	$-0.755560\pi$
$419$	−5.75122	−	32.6168i	−0.280966	−	1.59344i	0.438384	−	0.898788i	$-0.355551\pi$
$420$	43.5247	−	42.1551i	2.12379	−	2.05696i
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	0.897752	−	0.440502i	$-0.145199\pi$
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	−0.277916	+	0.960605i	$0.589644\pi$
$422$	12.2648	−	45.7728i	0.597040	−	2.22819i
$423$	−4.56831	+	11.4119i	−0.222119	+	0.554867i
$424$	75.6750	+	43.6910i	3.67510	+	2.12182i
$425$	−21.8893	−	7.97351i	−1.06179	−	0.386772i
$426$	10.4413	+	26.3829i	0.505882	+	1.27826i
$427$	−1.66848	+	19.0708i	−0.0807433	+	0.922901i
$428$	68.3368	−	31.8660i	3.30318	−	1.54030i
$429$	0.474618	+	0.256714i	0.0229148	+	0.0123943i
$430$	−49.5696	−	6.53252i	−2.39046	−	0.315026i
$431$			14.4385i			0.695480i	0.937591	+	0.347740i	$0.113051\pi$
$431$			14.4385i			0.695480i	−0.937591	+	0.347740i	$0.886949\pi$
$432$	−10.3004	−	59.7888i	−0.495577	−	2.87659i
$433$	16.4822	+	16.4822i	0.792085	+	0.792085i	0.981833	−	0.189748i	$-0.0607670\pi$
$433$	16.4822	+	16.4822i	0.792085	+	0.792085i	−0.189748	+	0.981833i	$0.560767\pi$
$434$	−2.67381	+	15.1640i	−0.128347	+	0.727893i
$435$	9.52073	+	1.83613i	0.456484	+	0.0880356i
$436$	−44.6611	−	16.2553i	−2.13888	−	0.778488i
$437$	−0.367547	−	0.0321562i	−0.0175821	−	0.00153824i
$438$	−7.45870	−	64.5461i	−0.356390	−	3.08413i
$439$	−10.9388	−	30.0541i	−0.522080	−	1.43440i	−0.868201	−	0.496213i	$-0.834723\pi$
$439$	−10.9388	−	30.0541i	−0.522080	−	1.43440i	0.346121	−	0.938190i	$-0.387499\pi$
$440$	−11.6214	+	3.66255i	−0.554028	+	0.174605i
$441$	−5.40560	+	5.07323i	−0.257410	+	0.241582i
$442$	−5.62015	−	1.50592i	−0.267323	−	0.0716291i
$443$	17.8910	−	1.56526i	0.850027	−	0.0743677i	0.346188	−	0.938165i	$-0.387476\pi$
$443$	17.8910	−	1.56526i	0.850027	−	0.0743677i	0.503839	+	0.863798i	$0.331920\pi$
$444$	−4.48633	−	21.8719i	−0.212912	−	1.03799i
$445$	2.98080	+	13.4538i	0.141304	+	0.637771i
$446$	50.1811	−	8.84827i	2.37614	−	0.418978i
$447$	−30.7852	−	20.3055i	−1.45609	−	0.960418i
$448$	4.20289	+	48.0392i	0.198568	+	2.26964i
$449$	−6.63475	−	11.4917i	−0.313113	−	0.542328i	0.665921	−	0.746022i	$-0.268039\pi$
$449$	−6.63475	−	11.4917i	−0.313113	−	0.542328i	−0.979035	+	0.203694i	$0.934705\pi$
$450$	33.4178	−	21.8417i	1.57533	−	1.02963i
$451$	−0.548456	+	0.949953i	−0.0258258	+	0.0447316i
$452$	95.7323	+	44.6407i	4.50287	+	2.09972i
$453$	−13.6609	+	1.57860i	−0.641843	+	0.0741689i
$454$	0.825948	+	0.984327i	0.0387637	+	0.0461968i
$455$	3.07926	+	0.971328i	0.144358	+	0.0455365i
$456$	−41.3545	−	67.2427i	−1.93660	−	3.14893i
$457$	−4.61784	−	6.59496i	−0.216013	−	0.308499i	0.696491	−	0.717565i	$-0.254743\pi$
$457$	−4.61784	−	6.59496i	−0.216013	−	0.308499i	−0.912505	+	0.409066i	$0.865855\pi$
$458$	−28.2789	+	28.2789i	−1.32138	+	1.32138i
$459$	19.8863	−	13.8084i	0.928213	−	0.644522i
$460$	0.556732	+	0.510284i	0.0259578	+	0.0237921i
$461$	−14.1578	−	2.49640i	−0.659393	−	0.116269i	−0.166068	−	0.986114i	$-0.553107\pi$
$461$	−14.1578	−	2.49640i	−0.659393	−	0.116269i	−0.493324	+	0.869846i	$0.664218\pi$
$462$	9.02752	−	2.68979i	0.419998	−	0.125140i
$463$	8.79261	+	18.8558i	0.408627	+	0.876304i	0.997671	+	0.0682032i	$0.0217266\pi$
$463$	8.79261	+	18.8558i	0.408627	+	0.876304i	−0.589044	+	0.808101i	$0.700496\pi$
$464$	−22.3922	+	18.7893i	−1.03953	+	0.872272i
$465$	−2.59921	+	6.80103i	−0.120535	+	0.315390i
$466$	1.38417	−	0.503795i	0.0641202	−	0.0233378i
$467$	−23.8222	+	6.38314i	−1.10236	+	0.295376i	−0.763725	−	0.645542i	$-0.776632\pi$
$467$	−23.8222	+	6.38314i	−1.10236	+	0.295376i	−0.338635	+	0.940918i	$0.609965\pi$
$468$	5.62465	−	4.42351i	0.260000	−	0.204477i
$469$	−14.5849	+	8.42062i	−0.673470	+	0.388828i
$470$	14.8473	−	19.3441i	0.684853	−	0.892278i
$471$	−15.7196	−	17.7106i	−0.724322	−	0.816063i
$472$	−30.6679	−	21.4739i	−1.41161	−	0.988418i
$473$	−4.56937	−	3.19951i	−0.210100	−	0.147113i
$474$	−7.89648	+	23.7262i	−0.362698	+	1.08978i
$475$	15.9324	−	22.7412i	0.731028	−	1.04344i
$476$	−63.1279	+	36.4469i	−2.89346	+	1.67054i
$477$	−23.8055	−	21.2970i	−1.08998	−	0.975125i
$478$	14.5642	−	3.90246i	0.666150	−	0.178494i
$479$	25.2593	−	9.19362i	1.15412	−	0.420067i	0.307130	−	0.951668i	$-0.400632\pi$
$479$	25.2593	−	9.19362i	1.15412	−	0.420067i	0.846995	+	0.531601i	$0.178409\pi$
$480$	−5.85244	+	56.4805i	−0.267126	+	2.57797i
$481$	0.911414	−	0.764768i	0.0415569	−	0.0348704i
$482$	2.05962	+	4.41687i	0.0938132	+	0.201183i
$483$	−0.257271	−	0.243361i	−0.0117063	−	0.0110733i
$484$	52.8631	+	9.32118i	2.40287	+	0.423690i
$485$	−20.5994	+	22.4744i	−0.935369	+	1.02051i
$486$	−1.47818	+	41.4624i	−0.0670516	+	1.88077i
$487$	1.39406	−	1.39406i	0.0631711	−	0.0631711i	−0.674815	−	0.737987i	$-0.735777\pi$
$487$	1.39406	−	1.39406i	0.0631711	−	0.0631711i	0.737987	+	0.674815i	$0.235777\pi$
$488$	−29.2821	−	41.8191i	−1.32554	−	1.89306i
$489$	−33.9029	+	0.942045i	−1.53314	+	0.0426008i
$490$	13.0456	−	6.78898i	0.589342	−	0.306695i
$491$	−15.2423	−	18.1651i	−0.687875	−	0.819777i	0.303222	−	0.952920i	$-0.401938\pi$
$491$	−15.2423	−	18.1651i	−0.687875	−	0.819777i	−0.991097	+	0.133143i	$0.957493\pi$
$492$	8.67121	+	11.6794i	0.390928	+	0.526546i
$493$	−10.5718	−	4.92970i	−0.476129	−	0.222023i
$494$	3.46749	−	6.00587i	0.156010	−	0.270217i
$495$	4.43222	−	0.440507i	0.199213	−	0.0197993i
$496$	−10.9747	−	19.0087i	−0.492778	−	0.853516i
$497$	1.65093	+	18.8702i	0.0740542	+	0.846444i
$498$	23.3801	−	11.7036i	1.04769	−	0.524451i
$499$	30.8900	−	5.44673i	1.38282	−	0.243829i	0.567758	−	0.823196i	$-0.307811\pi$
$499$	30.8900	−	5.44673i	1.38282	−	0.243829i	0.815067	+	0.579366i	$0.196700\pi$
$500$	−54.2126	+	17.0699i	−2.42446	+	0.763390i
$501$	−28.4634	+	25.2636i	−1.27165	+	1.12869i
$502$	51.5779	−	4.51248i	2.30204	−	0.201402i
$503$	−5.95437	−	1.59547i	−0.265492	−	0.0711385i	0.123617	−	0.992330i	$-0.460551\pi$
$503$	−5.95437	−	1.59547i	−0.265492	−	0.0711385i	−0.389109	+	0.921192i	$0.627217\pi$
$504$	8.99365	−	75.2363i	0.400609	−	3.35129i
$505$	−3.65228	−	1.90186i	−0.162524	−	0.0846317i
$506$	0.0401548	+	0.110325i	0.00178510	+	0.00490452i
$507$	−20.3135	−	8.79397i	−0.902156	−	0.390554i
$508$	−38.5572	−	3.37332i	−1.71070	−	0.149667i
$509$	18.3832	+	6.69092i	0.814819	+	0.296570i	0.715613	−	0.698497i	$-0.246147\pi$
$509$	18.3832	+	6.69092i	0.814819	+	0.296570i	0.0992061	+	0.995067i	$0.468370\pi$
$510$	−45.3880	+	15.7030i	−2.00981	+	0.695339i
$511$	7.53240	−	42.7184i	0.333214	−	1.88975i
$512$	14.4712	+	14.4712i	0.639545	+	0.639545i
$513$	9.76284	+	27.1546i	0.431040	+	1.19890i
$514$		−	79.6382i		−	3.51269i
$515$	−28.9766	+	22.2286i	−1.27686	+	0.979507i
$516$	−63.0107	+	38.7518i	−2.77389	+	1.70595i
$517$	2.46569	−	1.14977i	0.108441	−	0.0505668i
$518$	1.81020	−	20.6907i	0.0795357	−	0.909097i
$519$	−4.03802	+	5.09319i	−0.177250	+	0.223566i
$520$	−7.95554	+	3.29408i	−0.348873	+	0.144455i
$521$	1.02507	+	0.591824i	0.0449091	+	0.0259283i	0.522286	−	0.852770i	$-0.325079\pi$
$521$	1.02507	+	0.591824i	0.0449091	+	0.0259283i	−0.477377	+	0.878698i	$0.658413\pi$
$522$	17.6196	−	9.44094i	0.771190	−	0.413219i
$523$	−11.5734	+	43.1925i	−0.506069	+	1.88868i	−0.0499636	+	0.998751i	$0.515911\pi$
$523$	−11.5734	+	43.1925i	−0.506069	+	1.88868i	−0.456106	+	0.889926i	$0.650756\pi$
$524$	−45.7023	−	38.3488i	−1.99652	−	1.67528i
$525$	25.5444	−	7.60383i	1.11485	−	0.331858i
$526$	−3.87963	−	22.0025i	−0.169160	−	0.959354i
$527$	5.02391	−	7.17489i	0.218845	−	0.312543i
$528$	−7.39328	+	11.2089i	−0.321751	+	0.487806i
$529$	−14.7813	+	17.6156i	−0.642664	+	0.765897i
$530$	34.0389	+	53.4457i	1.47856	+	2.32153i
$531$	9.36533	+	9.97890i	0.406421	+	0.433047i
$532$	−22.4868	−	83.9219i	−0.974927	−	3.63848i
$533$	−0.327589	+	0.702518i	−0.0141895	+	0.0304294i
$534$	22.2613	+	17.6493i	0.963339	+	0.763762i
$535$	33.1341	+	1.45098i	1.43251	+	0.0627313i
$536$	15.3607	−	42.2032i	0.663482	−	1.82290i
$537$	24.3070	+	5.79449i	1.04892	+	0.250051i
$538$	4.83008	−	3.38206i	0.208240	−	0.145811i
$539$	1.64076			0.0706724
$540$	17.9900	−	56.2599i	0.774167	−	2.42104i
$541$	−0.781277			−0.0335897			−0.0167949	−	0.999859i	$-0.505346\pi$
$541$	−0.781277			−0.0335897			−0.0167949	+	0.999859i	$0.505346\pi$
$542$	12.8134	−	8.97207i	0.550384	−	0.385383i
$543$	−6.98719	−	23.4506i	−0.299849	−	1.00636i
$544$	23.3637	−	64.1912i	1.00171	−	2.75218i
$545$	−14.1214	−	15.4148i	−0.604895	−	0.660299i
$546$	6.18944	−	2.44953i	0.264884	−	0.104830i
$547$	−4.68743	+	10.0522i	−0.200420	+	0.429802i	−0.980671	−	0.195665i	$-0.937314\pi$
$547$	−4.68743	+	10.0522i	−0.200420	+	0.429802i	0.780251	+	0.625467i	$0.215091\pi$
$548$	−8.84632	−	33.0149i	−0.377896	−	1.41033i
$549$	7.34652	+	17.1545i	0.313542	+	0.732137i
$550$	−8.70118	−	1.53658i	−0.371020	−	0.0655202i
$551$	8.93677	−	10.6504i	0.380719	−	0.453724i
$552$	0.942732	+	0.0561466i	0.0401253	+	0.00238976i
$553$	−9.57510	+	13.6747i	−0.407175	+	0.581505i
$554$	5.22900	+	29.6551i	0.222159	+	1.25993i
$555$	2.69311	−	9.44436i	0.114316	−	0.400891i
$556$	5.91335	+	4.96189i	0.250782	+	0.210431i
$557$	3.48849	−	13.0192i	0.147812	−	0.551642i	−0.851802	−	0.523864i	$-0.824490\pi$
$557$	3.48849	−	13.0192i	0.147812	−	0.551642i	0.999614	−	0.0277782i	$-0.00884322\pi$
$558$	4.68399	+	14.2605i	0.198289	+	0.603694i
$559$	−3.41375	−	1.97093i	−0.144386	−	0.0833615i
$560$	−30.7575	+	74.2278i	−1.29974	+	3.13670i
$561$	−5.30071	−	0.783531i	−0.223796	−	0.0330807i
$562$	−5.04211	+	57.6316i	−0.212689	+	2.43104i
$563$	−34.0720	+	15.8881i	−1.43596	+	0.669601i	−0.975887	−	0.218277i	$-0.929956\pi$
$563$	−34.0720	+	15.8881i	−1.43596	+	0.669601i	−0.460078	+	0.887878i	$0.652179\pi$
$564$	−1.00210	−	36.0644i	−0.0421962	−	1.51858i
$565$	28.2793	+	36.8643i	1.18972	+	1.55089i
$566$		−	34.9323i		−	1.46831i
$567$	−8.84975	+	26.2458i	−0.371654	+	1.10222i
$568$	−35.7193	−	35.7193i	−1.49875	−	1.49875i
$569$	2.09817	−	11.8993i	0.0879598	−	0.498845i	−0.908719	−	0.417409i	$-0.862938\pi$
$569$	2.09817	−	11.8993i	0.0879598	−	0.498845i	0.996679	−	0.0814360i	$-0.0259506\pi$
$570$	−4.07707	−	57.0988i	−0.170770	−	2.39161i
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	0.356054	−	0.934465i	$-0.384122\pi$
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	−0.327909	+	0.944709i	$0.606344\pi$
$572$	−1.57770	−	0.138031i	−0.0659670	−	0.00577137i
$573$	3.59693	−	2.67050i	0.150264	−	0.111562i
$574$	4.62809	+	12.7156i	0.193173	+	0.530738i
$575$	0.113533	+	0.312181i	0.00473464	+	0.0130189i
$576$	25.7284	+	39.3422i	1.07202	+	1.63926i
$577$	−36.1045	−	9.67417i	−1.50305	−	0.402741i	−0.588930	−	0.808184i	$-0.700451\pi$
$577$	−36.1045	−	9.67417i	−1.50305	−	0.402741i	−0.914120	+	0.405443i	$0.867117\pi$
$578$	12.4848	−	1.09228i	0.519300	−	0.0454328i
$579$	23.4271	+	7.79694i	0.973596	+	0.324030i
$580$	−27.7847	+	6.15593i	−1.15370	+	0.255611i
$581$	17.1896	−	3.03100i	0.713146	−	0.125747i
$582$	−3.73662	+	62.7398i	−0.154888	+	2.60065i
$583$	0.616142	+	7.04253i	0.0255180	+	0.291672i
$584$	57.8388	+	100.180i	2.39339	+	4.14547i
$585$	3.09302	−	0.583081i	0.127881	−	0.0241074i
$586$	5.67358	−	9.82693i	0.234373	−	0.405947i
$587$	−8.34577	−	3.89170i	−0.344467	−	0.160628i	0.242683	−	0.970106i	$-0.421972\pi$
$587$	−8.34577	−	3.89170i	−0.344467	−	0.160628i	−0.587150	+	0.809478i	$0.699750\pi$
$588$	8.64423	−	19.9677i	0.356482	−	0.823452i
$589$	6.71056	+	7.99734i	0.276504	+	0.329525i
$590$	−12.5327	−	24.0826i	−0.515961	−	0.991467i
$591$	6.87740	−	12.7151i	0.282899	−	0.523028i
$592$	16.9818	+	24.2525i	0.697946	+	0.996771i
$593$	9.96484	−	9.96484i	0.409207	−	0.409207i	−0.472255	−	0.881462i	$-0.656560\pi$
$593$	9.96484	−	9.96484i	0.409207	−	0.409207i	0.881462	+	0.472255i	$0.156560\pi$
$594$	6.51843	−	6.46741i	0.267454	−	0.265361i
$595$	−32.0326	+	1.39441i	−1.31321	+	0.0571651i
$596$	106.595	+	18.7957i	4.36632	+	0.769900i
$597$	−1.51800	+	6.36780i	−0.0621278	+	0.260617i
$598$	0.0350626	+	0.0751920i	0.00143382	+	0.00307483i
$599$	−5.73610	+	4.81316i	−0.234371	+	0.196660i	−0.752407	−	0.658698i	$-0.771107\pi$
$599$	−5.73610	+	4.81316i	−0.234371	+	0.196660i	0.518037	+	0.855358i	$0.326663\pi$
$600$	−39.1495	+	59.3210i	−1.59827	+	2.42177i
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.724208	−	0.689581i	$-0.757795\pi$
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.111522	+	0.993762i	$0.535572\pi$
$602$	−66.4682	+	17.8101i	−2.70904	+	0.725886i
$603$	−8.65512	+	13.9502i	−0.352464	+	0.568095i
$604$	34.9543	−	20.1809i	1.42227	−	0.821148i
$605$	18.7300	+	14.3759i	0.761481	+	0.584462i
$606$	−8.31607	+	1.70578i	−0.337817	+	0.0692926i
$607$	−18.7469	−	13.1267i	−0.760912	−	0.532796i	0.127503	−	0.991838i	$-0.459304\pi$
$607$	−18.7469	−	13.1267i	−0.760912	−	0.532796i	−0.888415	+	0.459042i	$0.848193\pi$
$608$	66.6953	+	46.7005i	2.70485	+	1.89396i
$609$	13.0727	−	2.68146i	0.529734	−	0.108658i
$610$	−4.82731	−	36.7039i	−0.195452	−	1.48610i
$611$	1.66496	−	0.961264i	0.0673570	−	0.0388886i
$612$	−37.4619	+	60.3805i	−1.51431	+	2.44074i
$613$	−14.4667	+	3.87633i	−0.584303	+	0.156564i	−0.538848	−	0.842403i	$-0.681140\pi$
$613$	−14.4667	+	3.87633i	−0.584303	+	0.156564i	−0.0454549	+	0.998966i	$0.514474\pi$
$614$	−46.5944	+	16.9590i	−1.88040	+	0.684409i
$615$	1.01021	+	6.31810i	0.0407355	+	0.254770i
$616$	−12.8467	+	10.7796i	−0.517607	+	0.434324i
$617$	0.200538	+	0.430054i	0.00807334	+	0.0173133i	0.910303	−	0.413942i	$-0.135848\pi$
$617$	0.200538	+	0.430054i	0.00807334	+	0.0173133i	−0.902230	+	0.431256i	$0.858071\pi$
$618$	−17.4591	+	73.2383i	−0.702309	+	2.94608i
$619$	−10.1152	−	1.78359i	−0.406565	−	0.0716885i	−0.0333743	−	0.999443i	$-0.510625\pi$
$619$	−10.1152	−	1.78359i	−0.406565	−	0.0716885i	−0.373191	+	0.927754i	$0.621736\pi$
$620$	−0.929342	−	21.3491i	−0.0373233	−	0.857399i
$621$	−0.333100	−	0.0906578i	−0.0133668	−	0.00363797i
$622$	15.4321	−	15.4321i	0.618770	−	0.618770i
$623$	10.8782	+	15.5357i	0.435827	+	0.622425i
$624$	−4.51429	+	8.34610i	−0.180716	+	0.334111i
$625$	−24.6179	−	4.35400i	−0.984717	−	0.174160i
$626$	32.6187	+	38.8735i	1.30371	+	1.55370i
$627$	2.53727	−	5.86095i	0.101329	−	0.234064i
$628$	62.9913	+	29.3733i	2.51363	+	1.17212i
$629$	−5.90732	+	10.2318i	−0.235540	+	0.407968i
$630$	30.9825	−	45.3776i	1.23437	−	1.80789i
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	0.707688	−	0.706526i	$-0.249738\pi$
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	−0.965713	+	0.259613i	$0.916405\pi$
$632$	−3.88002	−	44.3488i	−0.154339	−	1.76410i
$633$	1.83343	−	30.7842i	0.0728722	−	1.22356i
$634$	−44.5080	+	7.84797i	−1.76764	+	0.311683i
$635$	−14.3571	−	9.14912i	−0.569745	−	0.363072i
$636$	88.9521	+	29.6048i	3.52718	+	1.17391i
$637$	1.15504	−	0.101053i	0.0457645	−	0.00400388i
$638$	−4.27341	−	1.14506i	−0.169186	−	0.0453333i
$639$	10.1063	+	15.4539i	0.399800	+	0.611347i
$640$	−8.32187	−	26.4056i	−0.328951	−	1.04377i
$641$	16.0051	+	43.9737i	0.632164	+	1.73686i	0.675045	+	0.737777i	$0.264124\pi$
$641$	16.0051	+	43.9737i	0.632164	+	1.73686i	−0.0428806	+	0.999080i	$0.513653\pi$
$642$	54.8982	−	40.7586i	2.16666	−	1.60861i
$643$	−22.0886	−	1.93250i	−0.871088	−	0.0762103i	−0.357160	−	0.934043i	$-0.616255\pi$
$643$	−22.0886	−	1.93250i	−0.871088	−	0.0762103i	−0.513928	+	0.857833i	$0.671810\pi$
$644$	0.976716	+	0.355496i	0.0384880	+	0.0140085i
$645$	−32.4551	+	2.31742i	−1.27792	+	0.0912482i
$646$	−11.9584	+	67.8196i	−0.470498	+	2.66833i
$647$	−23.9696	−	23.9696i	−0.942341	−	0.942341i	0.0560849	−	0.998426i	$-0.482138\pi$
$647$	−23.9696	−	23.9696i	−0.942341	−	0.942341i	−0.998426	+	0.0560849i	$0.982138\pi$
$648$	−26.9109	−	68.7866i	−1.05716	−	2.70219i
$649$		−	3.02889i		−	0.118894i
$650$	−6.22001	−	0.545809i	−0.243969	−	0.0214084i
$651$	0.278331	+	10.0167i	0.0109086	+	0.392587i
$652$	90.2178	−	42.0693i	3.53320	−	1.64756i
$653$	−0.846075	+	9.67068i	−0.0331095	+	0.378443i	0.961504	+	0.274791i	$0.0886085\pi$
$653$	−0.846075	+	9.67068i	−0.0331095	+	0.378443i	−0.994614	+	0.103652i	$0.966947\pi$
$654$	−42.6349	−	6.30213i	−1.66716	−	0.246433i
$655$	−10.0392	−	24.2458i	−0.392266	−	0.947361i
$656$	−16.7048	−	9.64453i	−0.652214	−	0.376556i
$657$	−13.1953	−	40.1732i	−0.514797	−	1.56731i
$658$	8.68636	−	32.4179i	0.338629	−	1.26378i
$659$	−15.9731	−	13.4030i	−0.622224	−	0.522108i	0.276278	−	0.961078i	$-0.410899\pi$
$659$	−15.9731	−	13.4030i	−0.622224	−	0.522108i	−0.898502	+	0.438970i	$0.855343\pi$
$660$	−11.4244	+	6.35459i	−0.444693	+	0.247352i
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	−0.783002	−	0.622020i	$-0.786312\pi$
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	0.523038	−	0.852310i	$-0.324799\pi$
$662$	−21.7132	+	31.0096i	−0.843906	+	1.20522i
$663$	−3.77980	−	0.225115i	−0.146795	−	0.00874274i
$664$	−29.9205	+	35.6578i	−1.16114	+	1.38379i
$665$	8.27629	−	37.3090i	0.320941	−	1.44678i
$666$	−7.97054	−	18.6117i	−0.308852	−	0.721187i
$667$	0.0430488	+	0.160660i	0.00166685	+	0.00622079i
$668$	47.2070	−	101.236i	1.82649	−	3.91693i
$669$	30.8337	−	12.2027i	1.19210	−	0.471784i
$670$	24.0142	−	21.9992i	0.927749	−	0.849904i
$671$	1.41262	−	3.88114i	0.0545335	−	0.149830i
$672$	22.3158	+	74.8969i	0.860853	+	2.88921i
$673$	16.8631	−	11.8077i	0.650026	−	0.455153i	−0.201484	−	0.979492i	$-0.564576\pi$
$673$	16.8631	−	11.8077i	0.650026	−	0.455153i	0.851510	+	0.524339i	$0.175687\pi$
$674$	−18.1379			−0.698646
$675$	18.4480	−	18.2941i	0.710062	−	0.704139i
$676$	64.9678			2.49876
$677$	18.5670	−	13.0007i	0.713588	−	0.499659i	−0.159515	−	0.987195i	$-0.550993\pi$
$677$	18.5670	−	13.0007i	0.713588	−	0.499659i	0.873103	+	0.487536i	$0.162104\pi$
$678$	93.1743	+	22.2116i	3.57834	+	0.853032i
$679$	−14.3508	+	39.4285i	−0.550734	+	1.51313i
$680$	63.0481	−	57.7579i	2.41778	−	2.21491i
$681$	0.655262	+	0.519510i	0.0251097	+	0.0199077i
$682$	1.40397	−	3.01082i	0.0537608	−	0.115290i
$683$	2.12172	+	7.91835i	0.0811852	+	0.302987i	0.994564	−	0.104122i	$-0.0332033\pi$
$683$	2.12172	+	7.91835i	0.0811852	+	0.302987i	−0.913379	+	0.407110i	$0.866537\pi$
$684$	−57.9589	−	61.7561i	−2.21611	−	2.36130i
$685$	3.25589	−	14.6774i	0.124401	−	0.560793i
$686$	−23.8444	+	28.4166i	−0.910382	+	1.08495i
$687$	−14.3301	+	21.7258i	−0.546726	+	0.828891i
$688$	56.2630	−	80.3518i	2.14500	−	3.06338i
$689$	0.867490	+	4.91978i	0.0330487	+	0.187429i
$690$	0.587531	+	0.351850i	0.0223669	+	0.0133947i
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	0.681777	−	0.731560i	$-0.261207\pi$
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	−0.602056	+	0.798454i	$0.705652\pi$
$692$	4.93744	−	18.4268i	0.187693	−	0.700481i
$693$	5.40337	−	2.89523i	0.205257	−	0.109981i
$694$	−31.6991	−	18.3015i	−1.20328	−	0.694715i
$695$	1.29896	+	3.13712i	0.0492724	+	0.118998i
$696$	−22.1094	+	27.8867i	−0.838054	+	1.05704i
$697$	0.670867	−	7.66804i	0.0254109	−	0.290448i
$698$	−64.5366	+	30.0939i	−2.44275	+	1.13907i
$699$	0.816535	−	0.502171i	0.0308842	−	0.0189939i
$700$	−59.9365	+	50.2662i	−2.26539	+	1.89988i
$701$			45.2015i			1.70724i	0.520899	+	0.853618i	$0.325597\pi$
$701$			45.2015i			1.70724i	−0.520899	+	0.853618i	$0.674403\pi$
$702$	4.19045	−	4.95433i	0.158158	−	0.186989i
$703$	−9.95741	−	9.95741i	−0.375551	−	0.375551i
$704$	1.80664	−	10.2459i	0.0680901	−	0.386158i
$705$	6.93569	−	14.2735i	0.261213	−	0.537570i
$706$	0.118329	+	0.0430682i	0.00445337	+	0.00162089i
$707$	−5.64579	−	0.493942i	−0.212332	−	0.0185766i
$708$	−36.8609	−	15.9575i	−1.38532	−	0.599720i
$709$	−6.90171	−	18.9623i	−0.259199	−	0.712144i	−0.999217	−	0.0395569i	$-0.987405\pi$
$709$	−6.90171	−	18.9623i	−0.259199	−	0.712144i	0.740018	−	0.672587i	$-0.234817\pi$
$710$	−11.0105	−	34.9366i	−0.413216	−	1.31115i
$711$	−1.93152	+	16.1581i	−0.0724378	+	0.605978i
$712$	−48.8536	−	13.0903i	−1.83086	−	0.490579i
$713$	−0.124419	+	0.0108853i	−0.00465953	+	0.000407656i
$714$	−49.4365	+	43.8788i	−1.85011	+	1.64212i
$715$	−0.587471	−	0.374368i	−0.0219702	−	0.0140006i
$716$	−72.2265	+	12.7355i	−2.69923	+	0.475947i
$717$	8.77444	−	4.39231i	0.327688	−	0.164034i
$718$	−4.37300	−	49.9836i	−0.163199	−	1.86537i
$719$	18.2157	+	31.5505i	0.679331	+	1.17664i	0.975183	+	0.221402i	$0.0710631\pi$
$719$	18.2157	+	31.5505i	0.679331	+	1.17664i	−0.295852	+	0.955234i	$0.595604\pi$
$720$	7.74626	+	77.9401i	0.288686	+	2.90465i
$721$	−25.1318	+	43.5295i	−0.935957	+	1.62113i
$722$	−28.5603	−	13.3179i	−1.06290	−	0.495640i
$723$	1.89059	+	2.54646i	0.0703118	+	0.0947037i
$724$	46.1638	+	55.0159i	1.71566	+	2.04465i
$725$	−12.0903	−	3.24296i	−0.449024	−	0.120441i
$726$	48.6574	−	1.35202i	1.80585	−	0.0501782i
$727$	−7.67153	−	10.9561i	−0.284521	−	0.406338i	0.651296	−	0.758824i	$-0.274226\pi$
$727$	−7.67153	−	10.9561i	−0.284521	−	0.406338i	−0.935817	+	0.352485i	$0.885337\pi$
$728$	−8.37976	+	8.37976i	−0.310575	+	0.310575i
$729$	4.47945	+	26.6258i	0.165906	+	0.986142i
$730$	3.64805	+	83.8038i	0.135020	+	3.10172i
$731$	38.5489	+	6.79721i	1.42578	+	0.251404i
$732$	−39.7903	−	37.6388i	−1.47069	−	1.39117i
$733$	−17.7462	−	38.0568i	−0.655470	−	1.40566i	−0.899944	−	0.436005i	$-0.856393\pi$
$733$	−17.7462	−	38.0568i	−0.655470	−	1.40566i	0.244474	−	0.969656i	$-0.421385\pi$
$734$	40.4216	−	33.9178i	1.49199	−	1.25193i
$735$	7.42892	−	6.03392i	0.274020	−	0.222564i
$736$	−0.915308	+	0.333145i	−0.0337387	+	0.0122799i
$737$	3.50967	−	0.940413i	0.129280	−	0.0346406i
$738$	9.83085	+	8.79496i	0.361879	+	0.323747i
$739$	34.0711	−	19.6709i	1.25332	−	0.723607i	0.281556	−	0.959545i	$-0.409150\pi$
$739$	34.0711	−	19.6709i	1.25332	−	0.723607i	0.971768	+	0.235938i	$0.0758162\pi$
$740$	3.75862	+	28.5783i	0.138170	+	1.05056i
$741$	1.42519	−	4.28220i	0.0523557	−	0.157310i
$742$	71.4378	+	50.0213i	2.62256	+	1.83634i
$743$	10.6136	+	7.43173i	0.389376	+	0.272644i	0.751829	−	0.659358i	$-0.229172\pi$
$743$	10.6136	+	7.43173i	0.389376	+	0.272644i	−0.362453	+	0.932002i	$0.618061\pi$
$744$	−17.7390	−	19.9858i	−0.650342	−	0.732714i
$745$	37.7680	+	28.9882i	1.38371	+	1.06204i
$746$	−48.8829	+	28.2225i	−1.78973	+	1.03330i
$747$	13.3745	−	10.5184i	0.489349	−	0.384848i
$748$	15.1909	−	4.07039i	0.555434	−	0.148828i
$749$	42.8937	−	15.6120i	1.56730	−	0.570451i
$750$	−45.0475	+	25.0415i	−1.64490	+	0.914387i
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.120601	−	0.992701i	$-0.461518\pi$
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.998562	+	0.0536119i	$0.0170734\pi$
$752$	20.2186	+	43.3589i	0.737296	+	1.58114i
$753$	32.2912	−	9.62128i	1.17676	−	0.350619i
$754$	−3.07888	−	0.542889i	−0.112126	−	0.0197709i
$755$	17.7367	−	0.772091i	0.645503	−	0.0280993i
$756$	−6.76700	−	81.0112i	−0.246113	−	2.94635i
$757$	0.846964	−	0.846964i	0.0307834	−	0.0307834i	−0.691548	−	0.722331i	$-0.743071\pi$
$757$	0.846964	−	0.846964i	0.0307834	−	0.0307834i	0.722331	+	0.691548i	$0.243071\pi$
$758$	7.55993	+	10.7967i	0.274589	+	0.392154i
$759$	0.0400255	+	0.0650817i	0.00145283	+	0.00236232i
$760$	47.0465	+	90.4042i	1.70656	+	3.27930i
$761$	−3.25980	−	3.88488i	−0.118168	−	0.140827i	0.703718	−	0.710480i	$-0.251522\pi$
$761$	−3.25980	−	3.88488i	−0.118168	−	0.140827i	−0.821885	+	0.569653i	$0.807078\pi$
$762$	−34.8656	+	4.02893i	−1.26305	+	0.145953i
$763$	−26.0764	−	12.1596i	−0.944029	−	0.440208i
$764$	−6.57430	+	11.3870i	−0.237850	+	0.411968i
$765$	−26.8817	+	15.9459i	−0.971910	+	0.576524i
$766$	37.6375	+	65.1901i	1.35990	+	2.35542i
$767$	−0.186547	−	2.13224i	−0.00673583	−	0.0769909i
$768$	−2.33465	−	1.53991i	−0.0842444	−	0.0555666i
$769$	26.0795	−	4.59852i	0.940451	−	0.165827i	0.317651	−	0.948208i	$-0.397106\pi$
$769$	26.0795	−	4.59852i	0.940451	−	0.165827i	0.622800	+	0.782381i	$0.285995\pi$
$770$	−11.8729	+	2.63054i	−0.427869	+	0.0947980i
$771$	−10.4138	−	50.7698i	−0.375045	−	1.82843i
$772$	−72.1914	+	6.31593i	−2.59822	+	0.227315i
$773$	−10.4941	−	2.81189i	−0.377447	−	0.101137i	0.0651074	−	0.997878i	$-0.479261\pi$
$773$	−10.4941	−	2.81189i	−0.377447	−	0.101137i	−0.442555	+	0.896742i	$0.645928\pi$
$774$	−48.9124	+	45.9049i	−1.75812	+	1.65002i
$775$	3.97460	−	8.51777i	0.142772	−	0.305967i
$776$	−38.2703	−	105.147i	−1.37383	−	3.77455i
$777$	−1.55159	−	13.4271i	−0.0556629	−	0.481696i
$778$	−78.0256	−	6.82635i	−2.79735	−	0.244737i
$779$	8.62118	+	3.13785i	0.308886	+	0.112425i
$780$	−7.65103	+	5.17706i	−0.273951	+	0.185369i
$781$	0.709661	−	4.02469i	0.0253937	−	0.144015i
$782$	−0.582559	−	0.582559i	−0.0208323	−	0.0208323i
$783$	9.99807	−	8.32267i	0.357302	−	0.297428i
$784$			28.8525i			1.03045i
$785$	18.6076	+	24.2565i	0.664135	+	0.865751i
$786$	−47.5856	−	25.7384i	−1.69732	−	0.918058i
$787$	7.22332	−	3.36829i	0.257484	−	0.120067i	−0.289591	−	0.957151i	$-0.593519\pi$
$787$	7.22332	−	3.36829i	0.257484	−	0.120067i	0.547074	+	0.837084i	$0.315741\pi$
$788$	−3.69786	+	42.2668i	−0.131731	+	1.50569i
$789$	−5.35043	−	13.5194i	−0.190480	−	0.481303i
$790$	12.3577	−	29.8233i	0.439669	−	1.06106i
$791$	55.3786	+	31.9729i	1.96904	+	1.13682i
$792$	−6.07544	+	15.1769i	−0.215882	+	0.539286i
$793$	0.755404	−	2.81921i	0.0268252	−	0.100113i
$794$	39.9638	+	33.5336i	1.41826	+	1.19006i
$795$	28.6888	+	29.6209i	1.01749	+	1.05054i
$796$	−3.33636	−	18.9215i	−0.118254	−	0.670653i
$797$	−0.435383	+	0.621792i	−0.0154221	+	0.0220250i	−0.826789	−	0.562512i	$-0.809835\pi$
$797$	−0.435383	+	0.621792i	−0.0154221	+	0.0220250i	0.811367	+	0.584537i	$0.198724\pi$
$798$	−35.2667	−	70.4517i	−1.24843	−	2.49396i
$799$	−12.2715	+	14.6246i	−0.434136	+	0.517383i
$800$	12.7483	−	72.1894i	0.450720	−	2.55228i
$801$	16.4996	+	8.34059i	0.582984	+	0.294700i
$802$	−0.0232747	−	0.0868625i	−0.000821859	−	0.00306722i
$803$	−3.95512	+	8.48179i	−0.139573	+	0.299316i
$804$	7.04587	−	47.6664i	0.248489	−	1.68106i
$805$	0.308828	+	0.337115i	0.0108848	+	0.0118817i
$806$	0.802918	−	2.20600i	0.0282816	−	0.0777030i
$807$	2.63695	−	2.78768i	0.0928251	−	0.0981311i
$808$	12.3803	−	8.66877i	0.435537	−	0.304966i
$809$	−3.88327			−0.136528			−0.0682642	−	0.997667i	$-0.521746\pi$
$809$	−3.88327			−0.136528			−0.0682642	+	0.997667i	$0.521746\pi$
$810$	5.72969	−	53.2544i	0.201321	−	1.87117i
$811$	−22.9810			−0.806974			−0.403487	−	0.914985i	$-0.632202\pi$
$811$	−22.9810			−0.806974			−0.403487	+	0.914985i	$0.632202\pi$
$812$	−32.0843	+	22.4656i	−1.12594	+	0.788390i
$813$	6.99542	−	7.39528i	0.245340	−	0.259364i
$814$	−1.53261	+	4.21081i	−0.0537179	+	0.147589i
$815$	43.7435	+	1.91558i	1.53227	+	0.0670997i
$816$	13.7783	−	93.2125i	0.482337	−	3.26309i
$817$	−19.7174	+	42.2840i	−0.689824	+	1.47933i
$818$	6.07207	+	22.6613i	0.212305	+	0.792333i
$819$	3.62550	−	2.37095i	0.126685	−	0.0828476i
$820$	−10.0881	−	15.8396i	−0.352290	−	0.553143i
$821$	−1.59034	+	1.89529i	−0.0555031	+	0.0661461i	−0.793082	−	0.609115i	$-0.791525\pi$
$821$	−1.59034	+	1.89529i	−0.0555031	+	0.0661461i	0.737579	+	0.675261i	$0.235969\pi$
$822$	−13.8739	−	27.7157i	−0.483909	−	0.966697i
$823$	−18.8527	+	26.9245i	−0.657164	+	0.938528i	−1.00000		0.000867529i	$-0.999724\pi$
$823$	−18.8527	+	26.9245i	−0.657164	+	0.938528i	0.342835	+	0.939396i	$0.388613\pi$
$824$	−23.2761	−	132.005i	−0.810860	−	4.59862i
$825$	−5.74798	+	0.158222i	−0.200119	+	0.00550858i
$826$	−28.6230	−	24.0176i	−0.995923	−	0.835678i
$827$	2.22968	−	8.32126i	0.0775334	−	0.289359i	−0.916262	−	0.400579i	$-0.868809\pi$
$827$	2.22968	−	8.32126i	0.0775334	−	0.289359i	0.993796	+	0.111220i	$0.0354758\pi$
$828$	1.00290	−	0.144222i	0.0348532	−	0.00501205i
$829$	−7.38409	−	4.26321i	−0.256460	−	0.148067i	0.366259	−	0.930513i	$-0.380639\pi$
$829$	−7.38409	−	4.26321i	−0.256460	−	0.148067i	−0.622719	+	0.782446i	$0.713972\pi$
$830$	−31.1864	+	12.9131i	−1.08250	+	0.448220i
$831$	7.21135	+	18.2216i	0.250159	+	0.632099i
$832$	0.640776	−	7.32410i	0.0222149	−	0.253918i
$833$	−10.4349	+	4.86588i	−0.361548	+	0.168593i
$834$	6.15702	+	3.33025i	0.213200	+	0.115317i
$835$	38.9835	−	29.9050i	1.34908	−	1.03491i
$836$			18.7448i			0.648301i
$837$	4.85083	+	8.47863i	0.167669	+	0.293064i
$838$	62.3307	+	62.3307i	2.15318	+	2.15318i
$839$	8.06541	−	45.7412i	0.278449	−	1.57916i	−0.449340	−	0.893361i	$-0.648341\pi$
$839$	8.06541	−	45.7412i	0.278449	−	1.57916i	0.727789	−	0.685802i	$-0.240548\pi$
$840$	−18.5240	+	96.0513i	−0.639140	+	3.31408i
$841$	21.3614	+	7.77490i	0.736599	+	0.268100i
$842$	−44.0185	−	3.85112i	−1.51698	−	0.132718i
$843$	4.32178	+	37.3998i	0.148850	+	1.28812i
$844$	30.9571	+	85.0539i	1.06559	+	2.92768i
$845$	25.3461	+	13.1985i	0.871931	+	0.454042i
$846$	−7.46146	−	31.8539i	−0.256530	−	1.09516i
$847$	31.3887	+	8.41058i	1.07853	+	0.288991i
$848$	−123.842	+	10.8348i	−4.25276	+	0.372068i
$849$	−4.56789	−	22.2695i	−0.156770	−	0.764288i
$850$	59.8948	−	16.0321i	2.05438	−	0.549896i
$851$	0.165907	−	0.0292538i	0.00568721	−	0.00100281i
$852$	−45.2407	−	29.8402i	−1.54992	−	1.02231i
$853$	1.80662	+	20.6498i	0.0618575	+	0.707035i	0.962288	+	0.272034i	$0.0876964\pi$
$853$	1.80662	+	20.6498i	0.0618575	+	0.707035i	−0.900430	+	0.435001i	$0.856748\pi$
$854$	−25.4755	−	44.1248i	−0.871752	−	1.50992i
$855$	−10.0656	−	35.8677i	−0.344238	−	1.22665i
$856$	−60.8644	+	105.420i	−2.08030	+	3.60319i
$857$	3.98725	+	1.85929i	0.136202	+	0.0635120i	0.489524	−	0.871990i	$-0.337170\pi$
$857$	3.98725	+	1.85929i	0.136202	+	0.0635120i	−0.353322	+	0.935502i	$0.614948\pi$
$858$	−1.42665	+	0.164858i	−0.0487049	+	0.00562814i
$859$	−27.5782	−	32.8664i	−0.940956	−	1.12139i	−0.992442	−	0.122714i	$-0.960840\pi$
$859$	−27.5782	−	32.8664i	−0.940956	−	1.12139i	0.0514862	−	0.998674i	$-0.483604\pi$
$860$	84.7145	−	44.0856i	2.88874	−	1.50331i
$861$	4.61318	+	7.50107i	0.157217	+	0.255636i
$862$	−22.0415	−	31.4786i	−0.750738	−	1.07217i
$863$	29.7115	−	29.7115i	1.01139	−	1.01139i	0.0114553	−	0.999934i	$-0.496354\pi$
$863$	29.7115	−	29.7115i	1.01139	−	1.01139i	0.999934	−	0.0114553i	$-0.00364642\pi$
$864$	53.6570	+	54.0802i	1.82545	+	1.83985i
$865$	5.66974	−	6.18582i	0.192777	−	0.210324i
$866$	−61.0955	−	10.7728i	−2.07611	−	0.366074i
$867$	7.81631	−	2.32890i	0.265456	−	0.0790936i
$868$	−12.4295	−	26.6552i	−0.421885	−	0.904736i
$869$	2.75902	−	2.31509i	0.0935932	−	0.0785340i
$870$	−23.5599	+	10.5310i	−0.798755	+	0.357036i
$871$	2.41278	−	0.878181i	0.0817540	−	0.0297560i
$872$	74.1142	−	19.8588i	2.50982	−	0.672505i
$873$	5.82201	+	40.4856i	0.197045	+	1.37023i
$874$	0.850406	−	0.490982i	0.0287654	−	0.0166077i
$875$	−33.5950	+	7.43410i	−1.13572	+	0.251318i
$876$	82.3842	+	92.8188i	2.78350	+	3.13606i
$877$	−9.47306	−	6.63310i	−0.319882	−	0.223984i	0.402596	−	0.915378i	$-0.368108\pi$
$877$	−9.47306	−	6.63310i	−0.319882	−	0.223984i	−0.722478	+	0.691394i	$0.756997\pi$
$878$	69.7284	+	48.8243i	2.35322	+	1.64774i
$879$	2.33193	−	7.00662i	0.0786540	−	0.236328i
$880$	10.5547	−	13.7514i	0.355797	−	0.463559i
$881$	12.7653	−	7.37007i	0.430075	−	0.248304i	−0.269304	−	0.963055i	$-0.586794\pi$
$881$	12.7653	−	7.37007i	0.430075	−	0.248304i	0.699379	+	0.714751i	$0.253460\pi$
$882$	4.04050	−	19.3126i	0.136051	−	0.650289i
$883$	−15.3517	+	4.11349i	−0.516627	+	0.138430i	−0.507706	−	0.861530i	$-0.669506\pi$
$883$	−15.3517	+	4.11349i	−0.516627	+	0.138430i	−0.00892106	+	0.999960i	$0.502840\pi$
$884$	10.4432	−	3.80103i	0.351244	−	0.127842i
$885$	−11.1388	−	13.7140i	−0.374426	−	0.460991i
$886$	−36.6160	+	30.7245i	−1.23014	+	1.03221i
$887$	3.15396	+	6.76369i	0.105900	+	0.227102i	0.952116	−	0.305737i	$-0.0989028\pi$
$887$	3.15396	+	6.76369i	0.105900	+	0.227102i	−0.846216	+	0.532839i	$0.821125\pi$
$888$	26.1861	+	24.7702i	0.878747	+	0.831232i
$889$	−23.0750	−	4.06875i	−0.773911	−	0.136461i
$890$	−27.0369	−	24.7812i	−0.906280	−	0.830669i
$891$	3.30983	−	4.97539i	0.110883	−	0.166682i
$892$	−68.8206	+	68.8206i	−2.30428	+	2.30428i
$893$	−13.0516	−	18.6396i	−0.436755	−	0.623750i
$894$	98.1150	−	2.72628i	3.28146	−	0.0911803i
$895$	−30.7652	−	9.70462i	−1.02837	−	0.324390i
$896$	−24.4930	−	29.1896i	−0.818253	−	0.975156i
$897$	0.0321851	+	0.0433504i	0.00107463	+	0.00144743i
$898$	32.0079	+	14.9255i	1.06812	+	0.498072i
$899$	2.35319	−	4.07585i	0.0784834	−	0.135937i
$900$	−28.3574	+	70.7853i	−0.945246	+	2.35951i
$901$	−24.8041	−	42.9619i	−0.826344	−	1.43127i
$902$	−0.254446	−	2.90833i	−0.00847211	−	0.0968367i
$903$	−40.0450	+	20.0457i	−1.33261	+	0.667080i
$904$	−167.938	+	29.6120i	−5.58553	+	0.984880i
$905$	6.83328	+	30.8419i	0.227146	+	1.02522i
$906$	27.3733	−	24.2960i	0.909415	−	0.807180i
$907$	16.3212	−	1.42792i	0.541937	−	0.0474134i	0.187099	−	0.982341i	$-0.440092\pi$
$907$	16.3212	−	1.42792i	0.541937	−	0.0474134i	0.354838	+	0.934928i	$0.384536\pi$
$908$	−2.37069	−	0.635223i	−0.0786740	−	0.0210806i
$909$	−5.07849	+	2.17489i	−0.168443	+	0.0721365i
$910$	−8.19614	+	2.58306i	−0.271700	+	0.0856277i
$911$	−0.825532	−	2.26813i	−0.0273511	−	0.0751465i	0.925266	−	0.379320i	$-0.123842\pi$
$911$	−0.825532	−	2.26813i	−0.0273511	−	0.0751465i	−0.952617	+	0.304173i	$0.901620\pi$
$912$	103.064	+	44.6177i	3.41279	+	1.47744i
$913$	−3.75152	−	0.328216i	−0.124157	−	0.0108624i
$914$	20.1354	+	7.32869i	0.666020	+	0.242412i
$915$	−7.87699	−	22.7677i	−0.260405	−	0.752677i
$916$	13.2645	−	75.2269i	0.438273	−	2.48557i
$917$	−25.5387	−	25.5387i	−0.843361	−	0.843361i
$918$	−22.2760	+	60.4628i	−0.735218	+	1.99557i
$919$			5.68243i			0.187446i	0.995598	+	0.0937230i	$0.0298768\pi$
$919$			5.68243i			0.187446i	−0.995598	+	0.0937230i	$0.970123\pi$
$920$	−1.20877	−	0.159297i	−0.0398519	−	0.00525186i
$921$	−27.4866	+	16.9043i	−0.905714	+	0.557017i
$922$	34.6774	−	16.1703i	1.14204	−	0.532541i
$923$	0.251702	−	2.87697i	0.00828487	−	0.0946965i
$924$	−11.1778	+	14.0987i	−0.367724	+	0.463813i
$925$	−4.33945	+	11.9129i	−0.142680	+	0.391694i
$926$	−47.9543	−	27.6864i	−1.57588	−	0.909832i
$927$	−1.55334	+	48.9729i	−0.0510183	+	1.60848i
$928$	9.49998	−	35.4544i	0.311852	−	1.16385i
$929$	−31.5686	−	26.4892i	−1.03573	−	0.869082i	−0.0442093	−	0.999022i	$-0.514077\pi$
$929$	−31.5686	−	26.4892i	−1.03573	−	0.869082i	−0.991522	+	0.129941i	$0.958521\pi$
$930$	−4.71555	−	18.7953i	−0.154629	−	0.616324i
$931$	−2.38300	−	13.5147i	−0.0780996	−	0.442925i
$932$	−1.61376	+	2.30468i	−0.0528604	+	0.0754924i
$933$	7.82008	−	11.8560i	0.256018	−	0.388148i
$934$	42.1923	−	50.2828i	1.38057	−	1.64530i
$935$	6.75338	+	1.49811i	0.220859	+	0.0489934i
$936$	−3.34220	+	11.0582i	−0.109243	+	0.361450i
$937$	−2.09031	−	7.80116i	−0.0682876	−	0.254853i	0.923340	−	0.383983i	$-0.125448\pi$
$937$	−2.09031	−	7.80116i	−0.0682876	−	0.254853i	−0.991628	+	0.129131i	$0.958781\pi$
$938$	18.9430	−	40.6235i	0.618512	−	1.32640i
$939$	25.8779	+	20.5167i	0.844493	+	0.669538i
$940$	−2.03770	+	46.5323i	−0.0664625	+	1.51772i
$941$	17.0461	−	46.8337i	0.555686	−	1.52673i	−0.270147	−	0.962819i	$-0.587072\pi$
$941$	17.0461	−	46.8337i	0.555686	−	1.52673i	0.825833	−	0.563915i	$-0.190706\pi$
$942$	61.3082	+	14.6151i	1.99753	+	0.476186i
$943$	−0.0899076	+	0.0629540i	−0.00292780	+	0.00205006i
$944$	53.2626			1.73355
$945$	13.8178	−	32.9799i	0.449492	−	1.07283i
$946$	14.8463			0.482696
$947$	−39.8496	+	27.9030i	−1.29494	+	0.906726i	−0.998827	−	0.0484276i	$-0.984579\pi$
$947$	−39.8496	+	27.9030i	−1.29494	+	0.906726i	−0.296112	+	0.955153i	$0.595690\pi$
$948$	−13.6384	−	45.7735i	−0.442955	−	1.48666i
$949$	−2.26190	+	6.21452i	−0.0734244	+	0.201732i
$950$	−0.0192021	+	73.9019i	−0.000622999	+	2.39770i
$951$	−27.3479	+	10.8232i	−0.886816	+	0.350966i
$952$	49.7340	−	106.655i	1.61189	−	3.45671i
$953$	−13.0100	−	48.5541i	−0.421436	−	1.57282i	−0.771584	−	0.636127i	$-0.780535\pi$
$953$	−13.0100	−	48.5541i	−0.421436	−	1.57282i	0.350148	−	0.936694i	$-0.386131\pi$
$954$	84.4117	+	10.0905i	2.73293	+	0.326691i
$955$	−4.87818	+	3.10685i	−0.157854	+	0.100535i
$956$	−18.5120	+	22.0618i	−0.598722	+	0.713529i
$957$	−2.87406	−	0.171171i	−0.0929051	−	0.00553318i
$958$	−41.0349	+	58.6039i	−1.32578	+	1.89341i
$959$	−3.59307	−	20.3773i	−0.116026	−	0.658017i
$960$	−29.4997	−	53.0349i	−0.952098	−	1.71169i
$961$	−21.0402	−	17.6548i	−0.678716	−	0.569510i
$962$	−0.819569	+	3.05867i	−0.0264240	+	0.0986156i
$963$	29.6682	−	33.1626i	0.956043	−	1.06865i
$964$	−8.06148	−	4.65430i	−0.259643	−	0.149905i
$965$	−29.4473	−	12.2020i	−0.947943	−	0.392795i
$966$	0.932406	+	0.137825i	0.0299997	+	0.00443444i
$967$	−4.33600	+	49.5607i	−0.139436	+	1.59377i	0.528096	+	0.849185i	$0.322906\pi$
$967$	−4.33600	+	49.5607i	−0.139436	+	1.59377i	−0.667533	+	0.744581i	$0.732650\pi$
$968$	−78.5400	+	36.6238i	−2.52437	+	1.17713i
$969$	1.24481	+	44.7991i	0.0399891	+	1.43916i
$970$	10.6014	−	80.4447i	0.340390	−	2.58292i
$971$			40.2818i			1.29270i	0.763039	+	0.646352i	$0.223706\pi$
$971$			40.2818i			1.29270i	−0.763039	+	0.646352i	$0.776294\pi$
$972$	−43.1118	−	66.4924i	−1.38281	−	2.13275i
$973$	3.30441	+	3.30441i	0.105934	+	0.105934i
$974$	−0.911162	+	5.16745i	−0.0291955	+	0.165576i
$975$	−4.03666	+	0.465398i	−0.129277	+	0.0149047i
$976$	68.2493	+	24.8407i	2.18461	+	0.795132i
$977$	−37.7958	−	3.30670i	−1.20919	−	0.105791i	−0.535328	−	0.844644i	$-0.679812\pi$
$977$	−37.7958	−	3.30670i	−1.20919	−	0.105791i	−0.673866	+	0.738854i	$0.735367\pi$
$978$	72.4763	−	53.8093i	2.31754	−	1.72063i
$979$	−1.39948	−	3.84504i	−0.0447276	−	0.122888i
$980$	−12.9738	+	24.9145i	−0.414432	+	0.795864i
$981$	−28.0041	+	1.55748i	−0.894102	+	0.0497264i
$982$	60.9612	+	16.3345i	1.94535	+	0.521255i
$983$	−35.6886	+	3.12235i	−1.13829	+	0.0995874i	−0.640676	−	0.767811i	$-0.721346\pi$
$983$	−35.6886	+	3.12235i	−1.13829	+	0.0995874i	−0.497614	+	0.867399i	$0.665790\pi$
$984$	−22.2822	−	7.41591i	−0.710330	−	0.236411i
$985$	−10.0294	+	15.7384i	−0.319562	+	0.501468i
$986$	30.5739	−	5.39101i	0.973672	−	0.171685i
$987$	1.29850	−	21.8025i	0.0413316	−	0.693981i
$988$	1.15448	+	13.1958i	0.0367289	+	0.419813i
$989$	−0.279076	−	0.483373i	−0.00887409	−	0.0153704i
$990$	−8.99055	+	7.72650i	−0.285739	+	0.245564i
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	−0.274912	−	0.961469i	$-0.588649\pi$
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	0.970113	−	0.242654i	$-0.0780179\pi$
$992$	24.9793	+	11.6480i	0.793094	+	0.369826i
$993$	−9.78732	+	22.6081i	−0.310591	+	0.717447i
$994$	−32.4061	−	38.6201i	−1.02786	−	1.22495i
$995$	2.54236	−	8.05968i	0.0805981	−	0.255509i
$996$	−23.7590	+	43.9260i	−0.752833	+	1.39185i
$997$	13.9764	+	19.9603i	0.442636	+	0.632150i	0.977034	−	0.213083i	$-0.0683505\pi$
$997$	13.9764	+	19.9603i	0.442636	+	0.632150i	−0.534398	+	0.845233i	$0.679462\pi$
$998$	−59.0307	+	59.0307i	−1.86859	+	1.86859i
$999$	−7.51500	−	10.8228i	−0.237764	−	0.342418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.83.1	yes	192
3.2	odd	2		405.2.r.a.8.16		192
5.2	odd	4	inner	135.2.q.a.2.1	✓	192
5.3	odd	4		675.2.ba.b.407.16		192
5.4	even	2		675.2.ba.b.218.16		192
15.2	even	4		405.2.r.a.332.16		192
27.13	even	9		405.2.r.a.233.16		192
27.14	odd	18	inner	135.2.q.a.68.1	yes	192
135.14	odd	18		675.2.ba.b.68.16		192
135.67	odd	36		405.2.r.a.152.16		192
135.68	even	36		675.2.ba.b.257.16		192
135.122	even	36	inner	135.2.q.a.122.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.1	✓	192	5.2	odd	4	inner
135.2.q.a.68.1	yes	192	27.14	odd	18	inner
135.2.q.a.83.1	yes	192	1.1	even	1	trivial
135.2.q.a.122.1	yes	192	135.122	even	36	inner
405.2.r.a.8.16		192	3.2	odd	2
405.2.r.a.152.16		192	135.67	odd	36
405.2.r.a.233.16		192	27.13	even	9
405.2.r.a.332.16		192	15.2	even	4
675.2.ba.b.68.16		192	135.14	odd	18
675.2.ba.b.218.16		192	5.4	even	2
675.2.ba.b.257.16		192	135.68	even	36
675.2.ba.b.407.16		192	5.3	odd	4

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+(-2.18018 + 1.52658i) q^{2} +(-1.19025 + 1.25829i) q^{3} +(1.73870 - 4.77703i) q^{4} +(1.64880 - 1.51045i) q^{5} +(0.674088 - 4.56031i) q^{6} +(1.30062 - 2.78918i) q^{7} +(2.12414 + 7.92739i) q^{8} +(-0.166591 - 2.99537i) q^{9} +(-1.28885 + 5.81007i) q^{10} +(-0.426793 + 0.508631i) q^{11} +(3.94140 + 7.87366i) q^{12} +(-0.269123 + 0.384347i) q^{13} +(1.42232 + 8.06640i) q^{14} +(-0.0619022 + 3.87249i) q^{15} +(-8.94423 - 7.50510i) q^{16} +(1.20591 - 4.50051i) q^{17} +(4.93586 + 6.27613i) q^{18} +(4.80938 + 2.77670i) q^{19} +(-4.34871 - 10.5026i) q^{20} +(1.96154 + 4.95639i) q^{21} +(0.154018 - 1.76044i) q^{22} +(-0.0602123 + 0.0280775i) q^{23} +(-12.5032 - 6.76283i) q^{24} +(0.437073 - 4.98086i) q^{25} -1.24878i q^{26} +(3.96733 + 3.35563i) q^{27} +(-11.0626 - 11.0626i) q^{28} +(0.434735 - 2.46551i) q^{29} +(-5.77669 - 8.53721i) q^{30} +(1.76652 + 0.642961i) q^{31} +(14.6055 + 1.27781i) q^{32} +(-0.132015 - 1.14243i) q^{33} +(4.24128 + 11.6528i) q^{34} +(-2.06847 - 6.56331i) q^{35} +(-14.5986 - 4.41223i) q^{36} +(-2.44933 - 0.656295i) q^{37} +(-14.7241 + 1.28820i) q^{38} +(-0.163296 - 0.796105i) q^{39} +(15.4762 + 9.86226i) q^{40} +(1.62695 - 0.286875i) q^{41} +(-11.8428 - 7.81137i) q^{42} +(0.732214 + 8.36925i) q^{43} +(1.68769 + 2.92316i) q^{44} +(-4.79904 - 4.68714i) q^{45} +(0.0884111 - 0.153133i) q^{46} +(-3.71355 - 1.73166i) q^{47} +(20.0895 - 2.32146i) q^{48} +(-1.58841 - 1.89299i) q^{49} +(6.65077 + 11.5264i) q^{50} +(4.22761 + 6.87413i) q^{51} +(1.36812 + 1.95387i) q^{52} +(7.52870 - 7.52870i) q^{53} +(-13.7721 - 1.25944i) q^{54} +(0.0645683 + 1.48328i) q^{55} +(24.8736 + 4.38589i) q^{56} +(-9.21828 + 2.74662i) q^{57} +(2.81598 + 6.03890i) q^{58} +(-3.49452 + 2.93225i) q^{59} +(18.3914 + 7.02879i) q^{60} +(-5.84534 + 2.12753i) q^{61} +(-4.83286 + 1.29496i) q^{62} +(-8.57130 - 3.43118i) q^{63} +(-13.5701 + 7.83468i) q^{64} +(0.136808 + 1.04021i) q^{65} +(2.03182 + 2.28917i) q^{66} +(-4.48268 - 3.13881i) q^{67} +(-19.4024 - 13.5857i) q^{68} +(0.0363384 - 0.109184i) q^{69} +(14.5290 + 11.1515i) q^{70} +(-5.33043 + 3.07752i) q^{71} +(23.3916 - 7.68321i) q^{72} +(13.6146 - 3.64803i) q^{73} +(6.34185 - 2.30824i) q^{74} +(5.74714 + 6.47845i) q^{75} +(21.6264 - 18.1467i) q^{76} +(0.863572 + 1.85194i) q^{77} +(1.57133 + 1.48637i) q^{78} +(-5.34198 - 0.941936i) q^{79} +(-26.0833 + 1.13543i) q^{80} +(-8.94450 + 0.998001i) q^{81} +(-3.10910 + 3.10910i) q^{82} +(3.25316 + 4.64599i) q^{83} +(27.0873 - 0.752663i) q^{84} +(-4.80950 - 9.24190i) q^{85} +(-14.3727 - 17.1287i) q^{86} +(2.58488 + 3.48160i) q^{87} +(-4.93869 - 2.30295i) q^{88} +(-3.08131 + 5.33699i) q^{89} +(17.6180 + 2.89269i) q^{90} +(0.721988 + 1.25052i) q^{91} +(0.0294359 + 0.336454i) q^{92} +(-2.91164 + 1.45751i) q^{93} +(10.7397 - 1.89370i) q^{94} +(12.1238 - 2.68612i) q^{95} +(-18.9921 + 16.8570i) q^{96} +(-13.5821 + 1.18828i) q^{97} +(6.35281 + 1.70223i) q^{98} +(1.59464 + 1.19367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 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

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Representations

Groups

Database

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