LMFDB - Embedded newform 675.2.ba.b.257.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.16
Character	$\chi$	$=$	675.257
Dual form			675.2.ba.b.218.16

$q$-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} +(0.674088 + 4.56031i) q^{6} +(-1.30062 - 2.78918i) q^{7} +(-2.12414 + 7.92739i) q^{8} +(-0.166591 + 2.99537i) q^{9} +(-0.426793 - 0.508631i) q^{11} +(-3.94140 + 7.87366i) q^{12} +(0.269123 + 0.384347i) q^{13} +(1.42232 - 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-1.20591 - 4.50051i) q^{17} +(-4.93586 + 6.27613i) q^{18} +(4.80938 - 2.77670i) q^{19} +(1.96154 - 4.95639i) q^{21} +(-0.154018 - 1.76044i) q^{22} +(0.0602123 + 0.0280775i) q^{23} +(-12.5032 + 6.76283i) q^{24} +1.24878i q^{26} +(-3.96733 + 3.35563i) q^{27} +(11.0626 - 11.0626i) q^{28} +(0.434735 + 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(-14.6055 + 1.27781i) q^{32} +(0.132015 - 1.14243i) q^{33} +(4.24128 - 11.6528i) q^{34} +(-14.5986 + 4.41223i) q^{36} +(2.44933 - 0.656295i) q^{37} +(14.7241 + 1.28820i) q^{38} +(-0.163296 + 0.796105i) q^{39} +(1.62695 + 0.286875i) q^{41} +(11.8428 - 7.81137i) q^{42} +(-0.732214 + 8.36925i) q^{43} +(1.68769 - 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(3.71355 - 1.73166i) q^{47} +(-20.0895 - 2.32146i) q^{48} +(-1.58841 + 1.89299i) q^{49} +(4.22761 - 6.87413i) q^{51} +(-1.36812 + 1.95387i) q^{52} +(-7.52870 - 7.52870i) q^{53} +(-13.7721 + 1.25944i) q^{54} +(24.8736 - 4.38589i) q^{56} +(9.21828 + 2.74662i) q^{57} +(-2.81598 + 6.03890i) q^{58} +(-3.49452 - 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(4.83286 + 1.29496i) q^{62} +(8.57130 - 3.43118i) q^{63} +(-13.5701 - 7.83468i) q^{64} +(2.03182 - 2.28917i) q^{66} +(4.48268 - 3.13881i) q^{67} +(19.4024 - 13.5857i) q^{68} +(0.0363384 + 0.109184i) q^{69} +(-5.33043 - 3.07752i) q^{71} +(-23.3916 - 7.68321i) q^{72} +(-13.6146 - 3.64803i) q^{73} +(6.34185 + 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(-0.863572 + 1.85194i) q^{77} +(-1.57133 + 1.48637i) q^{78} +(-5.34198 + 0.941936i) q^{79} +(-8.94450 - 0.998001i) q^{81} +(3.10910 + 3.10910i) q^{82} +(-3.25316 + 4.64599i) q^{83} +(27.0873 + 0.752663i) q^{84} +(-14.3727 + 17.1287i) q^{86} +(-2.58488 + 3.48160i) q^{87} +(4.93869 - 2.30295i) q^{88} +(-3.08131 - 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(-0.0294359 + 0.336454i) q^{92} +(2.91164 + 1.45751i) q^{93} +(10.7397 + 1.89370i) q^{94} +(-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} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.18018	+	1.52658i	1.54162	+	1.07945i	0.964936	+	0.262484i	$0.0845416\pi$
$2$	2.18018	+	1.52658i	1.54162	+	1.07945i	0.576682	+	0.816969i	$0.304347\pi$
$3$	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
$5$		0			0
$5$		0			0
$6$	0.674088	+	4.56031i	0.275195	+	1.86174i
$7$	−1.30062	−	2.78918i	−0.491587	−	1.05421i	−0.983054	−	0.183315i	$-0.941317\pi$
$7$	−1.30062	−	2.78918i	−0.491587	−	1.05421i	0.491468	−	0.870896i	$-0.336461\pi$
$8$	−2.12414	+	7.92739i	−0.750996	+	2.80276i
$9$	−0.166591	+	2.99537i	−0.0555302	+	0.998457i
$10$		0			0
$11$	−0.426793	−	0.508631i	−0.128683	−	0.153358i	0.697856	−	0.716238i	$-0.254138\pi$
$11$	−0.426793	−	0.508631i	−0.128683	−	0.153358i	−0.826538	+	0.562880i	$0.809693\pi$
$12$	−3.94140	+	7.87366i	−1.13778	+	2.27293i
$13$	0.269123	+	0.384347i	0.0746412	+	0.106599i	0.854737	−	0.519062i	$-0.173718\pi$
$13$	0.269123	+	0.384347i	0.0746412	+	0.106599i	−0.780096	+	0.625660i	$0.784830\pi$
$14$	1.42232	−	8.06640i	0.380132	−	2.15584i
$15$		0			0
$16$	−8.94423	+	7.50510i	−2.23606	+	1.87627i
$17$	−1.20591	−	4.50051i	−0.292476	−	1.09153i	−0.943201	−	0.332221i	$-0.892202\pi$
$17$	−1.20591	−	4.50051i	−0.292476	−	1.09153i	0.650726	−	0.759313i	$-0.274465\pi$
$18$	−4.93586	+	6.27613i	−1.16339	+	1.47930i
$19$	4.80938	−	2.77670i	1.10335	−	0.637018i	0.166249	−	0.986084i	$-0.446834\pi$
$19$	4.80938	−	2.77670i	1.10335	−	0.637018i	0.937098	+	0.349066i	$0.113501\pi$
$20$		0			0
$21$	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	$-0.358906\pi$
$23$	0.0602123	+	0.0280775i	0.0125551	+	0.00585456i	−0.416331	+	0.909213i	$0.636684\pi$
$24$	−12.5032	+	6.76283i	−2.55221	+	1.38046i
$25$		0			0
$26$			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	0.998197	+	0.0600247i	$0.0191180\pi$
$29$	0.434735	+	2.46551i	0.0807283	+	0.457833i	−0.917469	+	0.397808i	$0.869771\pi$
$30$		0			0
$31$	1.76652	−	0.642961i	0.317276	−	0.115479i	−0.178473	−	0.983945i	$-0.557116\pi$
$31$	1.76652	−	0.642961i	0.317276	−	0.115479i	0.495749	+	0.868466i	$0.334893\pi$
$32$	−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
$35$		0			0
$36$	−14.5986	+	4.41223i	−2.43310	+	0.735372i
$37$	2.44933	−	0.656295i	0.402667	−	0.107894i	−0.0518010	−	0.998657i	$-0.516496\pi$
$37$	2.44933	−	0.656295i	0.402667	−	0.107894i	0.454468	+	0.890763i	$0.349830\pi$
$38$	14.7241	+	1.28820i	2.38857	+	0.208973i
$39$	−0.163296	+	0.796105i	−0.0261483	+	0.127479i
$40$		0			0
$41$	1.62695	+	0.286875i	0.254087	+	0.0448023i	0.299241	−	0.954178i	$-0.403267\pi$
$41$	1.62695	+	0.286875i	0.254087	+	0.0448023i	−0.0451539	+	0.998980i	$0.514378\pi$
$42$	11.8428	−	7.81137i	1.82738	−	1.20532i
$43$	−0.732214	+	8.36925i	−0.111662	+	1.27630i	0.709133	+	0.705075i	$0.249087\pi$
$43$	−0.732214	+	8.36925i	−0.111662	+	1.27630i	−0.820794	+	0.571224i	$0.806469\pi$
$44$	1.68769	−	2.92316i	0.254428	−	0.440682i
$45$		0			0
$46$	0.0884111	+	0.153133i	0.0130355	+	0.0225782i
$47$	3.71355	−	1.73166i	0.541677	−	0.252588i	−0.132468	−	0.991187i	$-0.542290\pi$
$47$	3.71355	−	1.73166i	0.541677	−	0.252588i	0.674145	+	0.738599i	$0.264512\pi$
$48$	−20.0895	−	2.32146i	−2.89967	−	0.335075i
$49$	−1.58841	+	1.89299i	−0.226916	+	0.270428i
$50$		0			0
$51$	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	−0.999396	−	0.0347509i	$-0.988936\pi$
$53$	−7.52870	−	7.52870i	−1.03415	−	1.03415i	−0.0347509	−	0.999396i	$-0.511064\pi$
$54$	−13.7721	+	1.25944i	−1.87415	+	0.171388i
$55$		0			0
$56$	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	0.386320	−	0.922365i	$-0.373746\pi$
$59$	−3.49452	−	2.93225i	−0.454948	−	0.381747i	−0.841268	+	0.540618i	$0.818190\pi$
$60$		0			0
$61$	−5.84534	−	2.12753i	−0.748419	−	0.272402i	−0.0604785	−	0.998169i	$-0.519263\pi$
$61$	−5.84534	−	2.12753i	−0.748419	−	0.272402i	−0.687940	+	0.725767i	$0.741485\pi$
$62$	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			0
$66$	2.03182	−	2.28917i	0.250100	−	0.281777i
$67$	4.48268	−	3.13881i	0.547646	−	0.383466i	−0.266758	−	0.963763i	$-0.585953\pi$
$67$	4.48268	−	3.13881i	0.547646	−	0.383466i	0.814405	+	0.580297i	$0.197064\pi$
$68$	19.4024	−	13.5857i	2.35288	−	1.64751i
$69$	0.0363384	+	0.109184i	0.00437462	+	0.0131442i
$70$		0			0
$71$	−5.33043	−	3.07752i	−0.632605	−	0.365235i	0.149155	−	0.988814i	$-0.452345\pi$
$71$	−5.33043	−	3.07752i	−0.632605	−	0.365235i	−0.781760	+	0.623579i	$0.785678\pi$
$72$	−23.3916	−	7.68321i	−2.75673	−	0.905475i
$73$	−13.6146	−	3.64803i	−1.59347	−	0.426970i	−0.650410	−	0.759583i	$-0.725403\pi$
$73$	−13.6146	−	3.64803i	−1.59347	−	0.426970i	−0.943063	+	0.332613i	$0.892070\pi$
$74$	6.34185	+	2.30824i	0.737225	+	0.268328i
$75$		0			0
$76$	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	−0.465876	−	0.884850i	$-0.654261\pi$
$79$	−5.34198	+	0.941936i	−0.601020	+	0.105976i	−0.135144	+	0.990826i	$0.543150\pi$
$80$		0			0
$81$	−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	$-0.906312\pi$
$83$	−3.25316	+	4.64599i	−0.357081	+	0.509964i	0.599916	+	0.800063i	$0.295201\pi$
$84$	27.0873	+	0.752663i	2.95547	+	0.0821222i
$85$		0			0
$86$	−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	0.655220	−	0.755438i	$-0.272576\pi$
$89$	−3.08131	−	5.33699i	−0.326619	−	0.565720i	−0.981839	+	0.189718i	$0.939243\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	−18.9921	−	16.8570i	−1.93837	−	1.72046i
$97$	13.5821	+	1.18828i	1.37906	+	0.120652i	0.752433	−	0.658669i	$-0.228880\pi$
$97$	13.5821	+	1.18828i	1.37906	+	0.120652i	0.626625	+	0.779321i	$0.284436\pi$
$98$	−6.35281	+	1.70223i	−0.641731	+	0.171951i
$99$	1.59464	−	1.19367i	0.160267	−	0.119968i
$100$		0			0
$101$	−0.629841	+	1.73048i	−0.0626716	+	0.172189i	−0.967076	−	0.254487i	$-0.918093\pi$
$101$	−0.629841	+	1.73048i	−0.0626716	+	0.172189i	0.904405	+	0.426676i	$0.140316\pi$
$102$	19.7108	−	8.53305i	1.95166	−	0.844898i
$103$	16.2704	−	1.42347i	1.60317	−	0.140259i	0.749833	−	0.661627i	$-0.230134\pi$
$103$	16.2704	−	1.42347i	1.60317	−	0.140259i	0.853332	+	0.521368i	$0.174578\pi$
$104$	−3.61852	+	1.31704i	−0.354826	+	0.129146i
$105$		0			0
$106$	−4.92077	−	27.9071i	−0.477947	−	2.71057i
$107$	−10.4880	+	10.4880i	−1.01391	+	1.01391i	−0.0140087	+	0.999902i	$0.504459\pi$
$107$	−10.4880	+	10.4880i	−1.01391	+	1.01391i	−0.999902	+	0.0140087i	$0.995541\pi$
$108$	−22.9279	−	13.1176i	−2.20624	−	1.26225i
$109$			9.34913i			0.895484i	0.894163	+	0.447742i	$0.147772\pi$
$109$			9.34913i			0.895484i	−0.894163	+	0.447742i	$0.852228\pi$
$110$		0			0
$111$	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	0.296094	+	0.955159i	$0.404316\pi$
$113$	1.81095	+	20.6993i	0.170360	+	1.94722i	−0.125734	+	0.992064i	$0.540129\pi$
$114$	15.9045	+	20.0605i	1.48960	+	1.87884i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	23.9249	+	5.60417i	2.13140	+	0.499259i
$127$	1.97054	−	7.35416i	0.174857	−	0.652576i	−0.821719	−	0.569893i	$-0.806984\pi$
$127$	1.97054	−	7.35416i	0.174857	−	0.652576i	0.996576	−	0.0826829i	$-0.0263489\pi$
$128$	−5.23265	−	11.2214i	−0.462505	−	0.991845i
$129$	−11.4025	+	9.04019i	−1.00393	+	0.795945i
$130$		0			0
$131$	4.01388	+	11.0280i	0.350694	+	0.963524i	0.982148	+	0.188111i	$0.0602363\pi$
$131$	4.01388	+	11.0280i	0.350694	+	0.963524i	−0.631454	+	0.775414i	$0.717541\pi$
$132$	5.68695	−	1.35570i	0.494986	−	0.117999i
$133$	−13.9999	−	9.80281i	−1.21394	−	0.850012i
$134$	14.5647			1.25820
$135$		0			0
$136$	38.2388			3.27895
$137$	−5.50755	−	3.85643i	−0.470542	−	0.329477i	0.314139	−	0.949377i	$-0.398284\pi$
$137$	−5.50755	−	3.85643i	−0.470542	−	0.329477i	−0.784681	+	0.619900i	$0.787173\pi$
$138$	−0.0874536	+	0.293514i	−0.00744454	+	0.0249855i
$139$	−0.519349	−	1.42690i	−0.0440506	−	0.121028i	0.915717	−	0.401824i	$-0.131624\pi$
$139$	−0.519349	−	1.42690i	−0.0440506	−	0.121028i	−0.959767	+	0.280796i	$0.909402\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	−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	−0.330355	−	0.943857i	$-0.607168\pi$
$149$	3.69731	−	20.9685i	0.302895	−	1.71780i	0.633250	−	0.773947i	$-0.281720\pi$
$150$		0			0
$151$	6.08208	−	5.10347i	0.494952	−	0.415314i	−0.360845	−	0.932626i	$-0.617512\pi$
$151$	6.08208	−	5.10347i	0.494952	−	0.415314i	0.855797	+	0.517312i	$0.173067\pi$
$152$	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
$155$		0			0
$156$	−4.08694	+	0.604116i	−0.327217	+	0.0483680i
$157$	1.19160	+	13.6200i	0.0950997	+	1.08699i	0.882424	+	0.470455i	$0.155910\pi$
$157$	1.19160	+	13.6200i	0.0950997	+	1.08699i	−0.787324	+	0.616539i	$0.788534\pi$
$158$	−13.0844	−	6.10136i	−1.04094	−	0.485398i
$159$	0.512227	−	18.4344i	0.0406223	−	1.46194i
$160$		0			0
$161$		−	0.204461i		−	0.0161138i
$162$	−17.9771	−	15.8303i	−1.41241	−	1.24374i
$163$	−13.8462	+	13.8462i	−1.08452	+	1.08452i	−0.0884330	+	0.996082i	$0.528186\pi$
$163$	−13.8462	+	13.8462i	−1.08452	+	1.08452i	−0.996082	+	0.0884330i	$0.971814\pi$
$164$	1.45836	+	8.27077i	0.113879	+	0.645839i
$165$		0			0
$166$	−14.1849	+	5.16289i	−1.10096	+	0.400718i
$167$	−21.8892	+	1.91506i	−1.69384	+	0.148192i	−0.892809	−	0.450435i	$-0.851269\pi$
$167$	−21.8892	+	1.91506i	−1.69384	+	0.148192i	−0.801028	+	0.598627i	$0.795713\pi$
$168$	35.1246	+	26.0779i	2.70992	+	2.01195i
$169$	4.37097	−	12.0091i	0.336228	−	0.923779i
$170$		0			0
$171$	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	$-0.517785\pi$
$173$	−3.73833	−	0.327061i	−0.284220	−	0.0248660i	−0.228374	+	0.973573i	$0.573341\pi$
$174$	−10.9504	+	3.64450i	−0.830149	+	0.276288i
$175$		0			0
$176$	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	0.459791	+	0.888027i	$0.347924\pi$
$179$	−7.21345	+	12.4941i	−0.539158	+	0.933850i	−0.998950	+	0.0458226i	$0.985409\pi$
$180$		0			0
$181$	−7.06370	−	12.2347i	−0.525041	−	0.909397i	−0.999575	−	0.0291599i	$-0.990717\pi$
$181$	−7.06370	−	12.2347i	−0.525041	−	0.909397i	0.474534	−	0.880237i	$-0.342617\pi$
$182$	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
$185$		0			0
$186$	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
$190$		0			0
$191$	−2.54718	+	0.449136i	−0.184307	+	0.0324983i	−0.265040	−	0.964237i	$-0.585385\pi$
$191$	−2.54718	+	0.449136i	−0.184307	+	0.0324983i	0.0807326	+	0.996736i	$0.474274\pi$
$192$	−6.29352	−	26.4003i	−0.454195	−	1.90528i
$193$	6.02445	−	12.9195i	0.433649	−	0.929963i	−0.561112	−	0.827740i	$-0.689626\pi$
$193$	6.02445	−	12.9195i	0.433649	−	0.929963i	0.994761	−	0.102224i	$-0.0325958\pi$
$194$	27.7975	+	23.3248i	1.99574	+	1.67463i
$195$		0			0
$196$	−11.8046	−	4.29654i	−0.843189	−	0.306896i
$197$	8.06170	+	2.16013i	0.574372	+	0.153903i	0.534301	−	0.845294i	$-0.320575\pi$
$197$	8.06170	+	2.16013i	0.574372	+	0.153903i	0.0400711	+	0.999197i	$0.487242\pi$
$198$	5.29882	−	0.168070i	0.376571	−	0.0119442i
$199$	3.27312	+	1.88973i	0.232025	+	0.133960i	0.611506	−	0.791240i	$-0.290564\pi$
$199$	3.27312	+	1.88973i	0.232025	+	0.133960i	−0.379481	+	0.925200i	$0.623897\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	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
$210$		0			0
$211$	−13.6392	−	11.4447i	−0.938964	−	0.787885i	0.0384403	−	0.999261i	$-0.487761\pi$
$211$	−13.6392	−	11.4447i	−0.938964	−	0.787885i	−0.977405	+	0.211376i	$0.932205\pi$
$212$	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
$215$		0			0
$216$	−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
$220$		0			0
$221$	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	$-0.417396\pi$
$223$	17.3515	−	8.09113i	1.16194	−	0.541822i	0.905337	+	0.424694i	$0.139618\pi$
$224$	22.5602	+	39.0754i	1.50737	+	2.61083i
$225$		0			0
$226$	−27.6508	+	47.8926i	−1.83930	+	3.18577i
$227$	0.0420779	−	0.480953i	0.00279281	−	0.0319220i	−0.994670	−	0.103106i	$-0.967122\pi$
$227$	0.0420779	−	0.480953i	0.00279281	−	0.0319220i	0.997463	+	0.0711836i	$0.0226776\pi$
$228$	2.90709	+	48.8115i	0.192526	+	3.23262i
$229$	14.7979	+	2.60927i	0.977875	+	0.172426i	0.639672	−	0.768648i	$-0.279070\pi$
$229$	14.7979	+	2.60927i	0.977875	+	0.172426i	0.338203	+	0.941073i	$0.390181\pi$
$230$		0			0
$231$	−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	$-0.577562\pi$
$233$	0.534587	−	0.143242i	0.0350220	−	0.00938411i	0.276287	+	0.961075i	$0.410896\pi$
$234$	−3.74056	−	0.208035i	−0.244528	−	0.0135997i
$235$		0			0
$236$	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	−0.508406	−	0.861118i	$-0.669765\pi$
$239$	−5.32354	+	1.93761i	−0.344351	+	0.125334i	0.164054	+	0.986451i	$0.447543\pi$
$240$		0			0
$241$	0.317967	+	1.80328i	0.0204821	+	0.116160i	0.993335	−	0.115266i	$-0.0367721\pi$
$241$	0.317967	+	1.80328i	0.0204821	+	0.116160i	−0.972853	+	0.231426i	$0.925661\pi$
$242$	19.8720	−	19.8720i	1.27742	−	1.27742i
$243$	−9.39045	−	12.4426i	−0.602397	−	0.798196i
$244$		−	31.6225i		−	2.02442i
$245$		0			0
$246$	−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
$250$		0			0
$251$	−16.8470	+	9.72663i	−1.06337	+	0.613939i	−0.926364	−	0.376630i	$-0.877083\pi$
$251$	−16.8470	+	9.72663i	−1.06337	+	0.613939i	−0.137011	+	0.990570i	$0.543749\pi$
$252$	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
$255$		0			0
$256$	0.280392	−	1.59018i	0.0175245	−	0.0993864i
$257$	17.1627	+	24.5109i	1.07058	+	1.52895i	0.829553	+	0.558428i	$0.188595\pi$
$257$	17.1627	+	24.5109i	1.07058	+	1.52895i	0.241027	+	0.970518i	$0.422516\pi$
$258$	−38.6600	+	2.30248i	−2.40686	+	0.143346i
$259$	−5.01616	−	5.97802i	−0.311689	−	0.371456i
$260$		0			0
$261$	−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	$-0.0555577\pi$
$263$	3.54766	+	7.60797i	0.218758	+	0.469128i	−0.766049	+	0.642782i	$0.777780\pi$
$264$	8.77607	+	3.47321i	0.540130	+	0.213761i
$265$		0			0
$266$	−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	$0.521515\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	−0.458394	+	0.363427i	−0.0275920	+	0.0218757i
$277$	−4.78156	−	10.2541i	−0.287296	−	0.616108i	0.708700	−	0.705510i	$-0.249282\pi$
$277$	−4.78156	−	10.2541i	−0.287296	−	0.616108i	−0.995996	+	0.0894020i	$0.971504\pi$
$278$	1.04600	−	3.90372i	0.0627348	−	0.234130i
$279$	1.63162	+	5.39850i	0.0976826	+	0.323199i
$280$		0			0
$281$	13.9719	+	16.6511i	0.833496	+	0.993322i	0.999974	+	0.00727642i	$0.00231618\pi$
$281$	13.9719	+	16.6511i	0.833496	+	0.993322i	−0.166478	+	0.986045i	$0.553239\pi$
$282$	10.4001	+	15.7676i	0.619320	+	0.938950i
$283$	7.52820	+	10.7514i	0.447505	+	0.639103i	0.978005	−	0.208582i	$-0.0668848\pi$
$283$	7.52820	+	10.7514i	0.447505	+	0.639103i	−0.530500	+	0.847685i	$0.677996\pi$
$284$	5.43342	−	30.8145i	0.322414	−	1.82850i
$285$		0			0
$286$	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
$290$		0			0
$291$	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	$-0.321367\pi$
$293$	3.86399	+	1.80181i	0.225736	+	0.105263i	−0.306460	+	0.951884i	$0.599145\pi$
$294$	−9.70336	−	5.96760i	−0.565912	−	0.348037i
$295$		0			0
$296$			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
$300$		0			0
$301$	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
$305$		0			0
$306$	34.1980	+	14.6455i	1.95497	+	0.837225i
$307$	−17.9955	+	4.82189i	−1.02706	+	0.275200i	−0.732741	−	0.680508i	$-0.761759\pi$
$307$	−17.9955	+	4.82189i	−1.02706	+	0.275200i	−0.294318	+	0.955707i	$0.595093\pi$
$308$	−10.3482	−	0.905354i	−0.589646	−	0.0515873i
$309$	21.1570	+	18.7785i	1.20358	+	1.06827i
$310$		0			0
$311$	−8.07539	−	1.42391i	−0.457913	−	0.0807425i	−0.0600667	−	0.998194i	$-0.519131\pi$
$311$	−8.07539	−	1.42391i	−0.457913	−	0.0807425i	−0.397847	+	0.917452i	$0.630242\pi$
$312$	−5.96418	−	2.98555i	−0.337655	−	0.169023i
$313$	1.66176	−	18.9940i	0.0939283	−	1.07360i	−0.792230	−	0.610222i	$-0.791080\pi$
$313$	1.66176	−	18.9940i	0.0939283	−	1.07360i	0.886158	−	0.463382i	$-0.153364\pi$
$314$	−18.1941	+	31.5131i	−1.02675	+	1.77839i
$315$		0			0
$316$	−13.7877	−	23.8811i	−0.775621	−	1.34342i
$317$	−15.3899	+	7.17642i	−0.864382	+	0.403068i	−0.803661	−	0.595087i	$-0.797118\pi$
$317$	−15.3899	+	7.17642i	−0.864382	+	0.403068i	−0.0607206	+	0.998155i	$0.519340\pi$
$318$	29.2582	−	39.4082i	1.64072	−	2.20990i
$319$	1.06849	−	1.27338i	0.0598241	−	0.0712956i
$320$		0			0
$321$	−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
$325$		0			0
$326$	−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
$330$		0			0
$331$	13.3657	+	4.86470i	0.734643	+	0.267388i	0.682129	−	0.731232i	$-0.261054\pi$
$331$	13.3657	+	4.86470i	0.734643	+	0.267388i	0.0525142	+	0.998620i	$0.483277\pi$
$332$	−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
$335$		0			0
$336$	19.6537	+	59.0526i	1.07220	+	3.22158i
$337$	−5.58245	+	3.90887i	−0.304095	+	0.212930i	−0.715657	−	0.698452i	$-0.753872\pi$
$337$	−5.58245	+	3.90887i	−0.304095	+	0.212930i	0.411561	+	0.911382i	$0.364984\pi$
$338$	27.8623	−	19.5094i	1.51551	−	1.06117i
$339$	−23.8902	+	26.9161i	−1.29754	+	1.46188i
$340$		0			0
$341$	−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			0
$346$	−7.65094	−	6.41990i	−0.411317	−	0.345136i
$347$	−5.81216	+	12.4642i	−0.312013	+	0.669114i	−0.998304	−	0.0582130i	$-0.981460\pi$
$347$	−5.81216	+	12.4642i	−0.312013	+	0.669114i	0.686291	+	0.727327i	$0.259238\pi$
$348$	−21.1260	−	6.29459i	−1.13247	−	0.337425i
$349$	26.3484	−	4.64594i	1.41040	−	0.248691i	0.583990	−	0.811761i	$-0.301491\pi$
$349$	26.3484	−	4.64594i	1.41040	−	0.248691i	0.826409	+	0.563070i	$0.190380\pi$
$350$		0			0
$351$	−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	$-0.805155\pi$
$353$	0.0271374	−	0.0387563i	0.00144438	−	0.00206279i	0.819874	+	0.572545i	$0.194044\pi$
$354$	11.0164	−	17.9127i	0.585513	−	0.952049i
$355$		0			0
$356$	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	0.502512	−	0.864570i	$-0.332409\pi$
$359$	−9.42597	−	16.3263i	−0.497484	−	0.861667i	−0.999996	+	0.00290290i	$0.999076\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	5.76192	−	28.0907i	0.301180	−	1.46832i
$367$	19.7504	+	1.72794i	1.03096	+	0.0901977i	0.590063	−	0.807357i	$-0.299103\pi$
$367$	19.7504	+	1.72794i	1.03096	+	0.0901977i	0.440902	+	0.897555i	$0.354659\pi$
$368$	−0.749277	+	0.200768i	−0.0390588	+	0.0104658i
$369$	−1.13033	+	4.82552i	−0.0588427	+	0.251207i
$370$		0			0
$371$	−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	$-0.712789\pi$
$373$	−21.1273	+	1.84840i	−1.09393	+	0.0957063i	−0.474120	+	0.880460i	$0.657234\pi$
$374$	−7.73714	+	2.81609i	−0.400078	+	0.145616i
$375$		0			0
$376$	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	$0.0405955\pi$
$379$			4.95221i			0.254378i	−0.991878	+	0.127189i	$0.959405\pi$
$380$		0			0
$381$	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	−0.751620	−	0.659596i	$-0.770727\pi$
$383$	−2.46502	−	28.1753i	−0.125957	−	1.43969i	0.625663	−	0.780093i	$-0.284828\pi$
$384$	7.89166	−	19.9406i	0.402720	−	1.01759i
$385$		0			0
$386$	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	0.143463	−	0.989656i	$-0.454176\pi$
$389$	22.5434	−	18.9162i	1.14300	−	0.959088i	0.999533	+	0.0305681i	$0.00973165\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	8.47479	+	5.54221i	0.425874	+	0.278507i
$397$	5.07320	−	18.9334i	0.254616	−	0.950242i	−0.713687	−	0.700465i	$-0.752976\pi$
$397$	5.07320	−	18.9334i	0.254616	−	0.950242i	0.968303	−	0.249777i	$-0.0803573\pi$
$398$	4.25115	+	9.11662i	0.213091	+	0.456975i
$399$	−4.32861	−	29.2837i	−0.216702	−	1.46602i
$400$		0			0
$401$	−0.0115561	−	0.0317502i	−0.000577086	−	0.00158553i	0.939404	−	0.342813i	$-0.111380\pi$
$401$	−0.0115561	−	0.0317502i	−0.000577086	−	0.00158553i	−0.939981	+	0.341227i	$0.889157\pi$
$402$	17.3356	+	18.3266i	0.864624	+	0.914047i
$403$	0.722531	+	0.505922i	0.0359918	+	0.0252018i
$404$	−9.36163			−0.465759
$405$		0			0
$406$	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	0.991643	−	0.129010i	$-0.0411799\pi$
$409$	3.01485	+	8.28322i	0.149075	+	0.409579i	−0.842569	+	0.538589i	$0.818958\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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	0.438384	+	0.898788i	$0.355551\pi$
$419$	−5.75122	+	32.6168i	−0.280966	+	1.59344i	−0.719350	+	0.694648i	$0.755560\pi$
$420$		0			0
$421$	12.7180	−	10.6716i	0.619835	−	0.520104i	−0.277916	−	0.960605i	$-0.589644\pi$
$421$	12.7180	−	10.6716i	0.619835	−	0.520104i	0.897752	+	0.440502i	$0.145199\pi$
$422$	−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
$425$		0			0
$426$	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
$430$		0			0
$431$		−	14.4385i		−	0.695480i	−0.937591	−	0.347740i	$-0.886949\pi$
$431$		−	14.4385i		−	0.695480i	0.937591	−	0.347740i	$-0.113051\pi$
$432$	10.3004	−	59.7888i	0.495577	−	2.87659i
$433$	−16.4822	+	16.4822i	−0.792085	+	0.792085i	−0.981833	−	0.189748i	$-0.939233\pi$
$433$	−16.4822	+	16.4822i	−0.792085	+	0.792085i	0.189748	+	0.981833i	$0.439233\pi$
$434$	−2.67381	−	15.1640i	−0.128347	−	0.727893i
$435$		0			0
$436$	−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	0.346121	+	0.938190i	$0.387499\pi$
$439$	−10.9388	+	30.0541i	−0.522080	+	1.43440i	−0.868201	+	0.496213i	$0.834723\pi$
$440$		0			0
$441$	−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	$-0.612524\pi$
$443$	−17.8910	−	1.56526i	−0.850027	−	0.0743677i	−0.503839	+	0.863798i	$0.668080\pi$
$444$	−4.48633	+	21.8719i	−0.212912	+	1.03799i
$445$		0			0
$446$	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	−0.979035	−	0.203694i	$-0.934705\pi$
$449$	−6.63475	+	11.4917i	−0.313113	+	0.542328i	0.665921	+	0.746022i	$0.268039\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	−41.3545	+	67.2427i	−1.93660	+	3.14893i
$457$	4.61784	−	6.59496i	0.216013	−	0.308499i	−0.696491	−	0.717565i	$-0.745257\pi$
$457$	4.61784	−	6.59496i	0.216013	−	0.308499i	0.912505	+	0.409066i	$0.134145\pi$
$458$	28.2789	+	28.2789i	1.32138	+	1.32138i
$459$	19.8863	+	13.8084i	0.928213	+	0.644522i
$460$		0			0
$461$	−14.1578	+	2.49640i	−0.659393	+	0.116269i	−0.493324	−	0.869846i	$-0.664218\pi$
$461$	−14.1578	+	2.49640i	−0.659393	+	0.116269i	−0.166068	+	0.986114i	$0.553107\pi$
$462$	−9.02752	−	2.68979i	−0.419998	−	0.125140i
$463$	−8.79261	+	18.8558i	−0.408627	+	0.876304i	0.589044	+	0.808101i	$0.299504\pi$
$463$	−8.79261	+	18.8558i	−0.408627	+	0.876304i	−0.997671	+	0.0682032i	$0.978273\pi$
$464$	−22.3922	−	18.7893i	−1.03953	−	0.872272i
$465$		0			0
$466$	1.38417	+	0.503795i	0.0641202	+	0.0233378i
$467$	23.8222	+	6.38314i	1.10236	+	0.295376i	0.763725	−	0.645542i	$-0.223368\pi$
$467$	23.8222	+	6.38314i	1.10236	+	0.295376i	0.338635	+	0.940918i	$0.390035\pi$
$468$	−5.62465	−	4.42351i	−0.260000	−	0.204477i
$469$	−14.5849	−	8.42062i	−0.673470	−	0.388828i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	0.846995	−	0.531601i	$-0.178409\pi$
$479$	25.2593	+	9.19362i	1.15412	+	0.420067i	0.307130	+	0.951668i	$0.400632\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−1.47818	−	41.4624i	−0.0670516	−	1.88077i
$487$	−1.39406	−	1.39406i	−0.0631711	−	0.0631711i	0.674815	−	0.737987i	$-0.264223\pi$
$487$	−1.39406	−	1.39406i	−0.0631711	−	0.0631711i	−0.737987	+	0.674815i	$0.764223\pi$
$488$	29.2821	−	41.8191i	1.32554	−	1.89306i
$489$	−33.9029	−	0.942045i	−1.53314	−	0.0426008i
$490$		0			0
$491$	−15.2423	+	18.1651i	−0.687875	+	0.819777i	−0.991097	−	0.133143i	$-0.957493\pi$
$491$	−15.2423	+	18.1651i	−0.687875	+	0.819777i	0.303222	+	0.952920i	$0.401938\pi$
$492$	−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
$495$		0			0
$496$	−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	0.815067	−	0.579366i	$-0.196700\pi$
$499$	30.8900	+	5.44673i	1.38282	+	0.243829i	0.567758	+	0.823196i	$0.307811\pi$
$500$		0			0
$501$	−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	$-0.539449\pi$
$503$	5.95437	−	1.59547i	0.265492	−	0.0711385i	0.389109	+	0.921192i	$0.372783\pi$
$504$	8.99365	+	75.2363i	0.400609	+	3.35129i
$505$		0			0
$506$	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	0.0992061	−	0.995067i	$-0.468370\pi$
$509$	18.3832	−	6.69092i	0.814819	−	0.296570i	0.715613	+	0.698497i	$0.246147\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	−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
$520$		0			0
$521$	1.02507	−	0.591824i	0.0449091	−	0.0259283i	−0.477377	−	0.878698i	$-0.658413\pi$
$521$	1.02507	−	0.591824i	0.0449091	−	0.0259283i	0.522286	+	0.852770i	$0.325079\pi$
$522$	−17.6196	−	9.44094i	−0.771190	−	0.413219i
$523$	11.5734	+	43.1925i	0.506069	+	1.88868i	0.456106	+	0.889926i	$0.349244\pi$
$523$	11.5734	+	43.1925i	0.506069	+	1.88868i	0.0499636	+	0.998751i	$0.484089\pi$
$524$	−45.7023	+	38.3488i	−1.99652	+	1.67528i
$525$		0			0
$526$	−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
$530$		0			0
$531$	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
$535$		0			0
$536$	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
$540$		0			0
$541$	−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
$545$		0			0
$546$	6.18944	+	2.44953i	0.264884	+	0.104830i
$547$	4.68743	+	10.0522i	0.200420	+	0.429802i	0.980671	−	0.195665i	$-0.0626864\pi$
$547$	4.68743	+	10.0522i	0.200420	+	0.429802i	−0.780251	+	0.625467i	$0.784909\pi$
$548$	8.84632	−	33.0149i	0.377896	−	1.41033i
$549$	7.34652	−	17.1545i	0.313542	−	0.732137i
$550$		0			0
$551$	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
$555$		0			0
$556$	5.91335	−	4.96189i	0.250782	−	0.210431i
$557$	−3.48849	−	13.0192i	−0.147812	−	0.551642i	−0.999614	−	0.0277782i	$-0.991157\pi$
$557$	−3.48849	−	13.0192i	−0.147812	−	0.551642i	0.851802	−	0.523864i	$-0.175510\pi$
$558$	−4.68399	+	14.2605i	−0.198289	+	0.603694i
$559$	−3.41375	+	1.97093i	−0.144386	+	0.0833615i
$560$		0			0
$561$	−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	$-0.0700436\pi$
$563$	34.0720	+	15.8881i	1.43596	+	0.669601i	0.460078	+	0.887878i	$0.347821\pi$
$564$	−1.00210	+	36.0644i	−0.0421962	+	1.51858i
$565$		0			0
$566$			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	0.996679	+	0.0814360i	$0.0259506\pi$
$569$	2.09817	+	11.8993i	0.0879598	+	0.498845i	−0.908719	+	0.417409i	$0.862938\pi$
$570$		0			0
$571$	0.672547	−	0.244787i	0.0281452	−	0.0102440i	−0.327909	−	0.944709i	$-0.606344\pi$
$571$	0.672547	−	0.244787i	0.0281452	−	0.0102440i	0.356054	+	0.934465i	$0.384122\pi$
$572$	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			0
$576$	25.7284	−	39.3422i	1.07202	−	1.63926i
$577$	36.1045	−	9.67417i	1.50305	−	0.402741i	0.588930	−	0.808184i	$-0.299549\pi$
$577$	36.1045	−	9.67417i	1.50305	−	0.402741i	0.914120	+	0.405443i	$0.132883\pi$
$578$	−12.4848	−	1.09228i	−0.519300	−	0.0454328i
$579$	23.4271	−	7.79694i	0.973596	−	0.324030i
$580$		0			0
$581$	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
$585$		0			0
$586$	5.67358	+	9.82693i	0.234373	+	0.405947i
$587$	8.34577	−	3.89170i	0.344467	−	0.160628i	−0.242683	−	0.970106i	$-0.578028\pi$
$587$	8.34577	−	3.89170i	0.344467	−	0.160628i	0.587150	+	0.809478i	$0.300250\pi$
$588$	−8.64423	−	19.9677i	−0.356482	−	0.823452i
$589$	6.71056	−	7.99734i	0.276504	−	0.329525i
$590$		0			0
$591$	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	$-0.343440\pi$
$593$	−9.96484	−	9.96484i	−0.409207	−	0.409207i	−0.881462	+	0.472255i	$0.843440\pi$
$594$	6.51843	+	6.46741i	0.267454	+	0.265361i
$595$		0			0
$596$	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	0.518037	−	0.855358i	$-0.326663\pi$
$599$	−5.73610	−	4.81316i	−0.234371	−	0.196660i	−0.752407	+	0.658698i	$0.771107\pi$
$600$		0			0
$601$	−20.4882	−	7.45708i	−0.835730	−	0.304181i	−0.111522	−	0.993762i	$-0.535572\pi$
$601$	−20.4882	−	7.45708i	−0.835730	−	0.304181i	−0.724208	+	0.689581i	$0.757795\pi$
$602$	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
$605$		0			0
$606$	−8.31607	−	1.70578i	−0.337817	−	0.0692926i
$607$	18.7469	−	13.1267i	0.760912	−	0.532796i	−0.127503	−	0.991838i	$-0.540696\pi$
$607$	18.7469	−	13.1267i	0.760912	−	0.532796i	0.888415	+	0.459042i	$0.151807\pi$
$608$	−66.6953	+	46.7005i	−2.70485	+	1.89396i
$609$	13.0727	+	2.68146i	0.529734	+	0.108658i
$610$		0			0
$611$	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	$-0.318860\pi$
$613$	14.4667	+	3.87633i	0.584303	+	0.156564i	0.0454549	+	0.998966i	$0.485526\pi$
$614$	−46.5944	−	16.9590i	−1.88040	−	0.684409i
$615$		0			0
$616$	−12.8467	−	10.7796i	−0.517607	−	0.434324i
$617$	−0.200538	+	0.430054i	−0.00807334	+	0.0173133i	−0.910303	−	0.413942i	$-0.864152\pi$
$617$	−0.200538	+	0.430054i	−0.00807334	+	0.0173133i	0.902230	+	0.431256i	$0.141929\pi$
$618$	17.4591	+	73.2383i	0.702309	+	2.94608i
$619$	−10.1152	+	1.78359i	−0.406565	+	0.0716885i	−0.373191	−	0.927754i	$-0.621736\pi$
$619$	−10.1152	+	1.78359i	−0.406565	+	0.0716885i	−0.0333743	+	0.999443i	$0.510625\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		0			0
$631$	−6.48152	+	11.2263i	−0.258025	+	0.446913i	−0.965713	−	0.259613i	$-0.916405\pi$
$631$	−6.48152	+	11.2263i	−0.258025	+	0.446913i	0.707688	+	0.706526i	$0.249738\pi$
$632$	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
$635$		0			0
$636$	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
$640$		0			0
$641$	16.0051	−	43.9737i	0.632164	−	1.73686i	−0.0428806	−	0.999080i	$-0.513653\pi$
$641$	16.0051	−	43.9737i	0.632164	−	1.73686i	0.675045	−	0.737777i	$-0.264124\pi$
$642$	−54.8982	−	40.7586i	−2.16666	−	1.60861i
$643$	22.0886	−	1.93250i	0.871088	−	0.0762103i	0.357160	−	0.934043i	$-0.383745\pi$
$643$	22.0886	−	1.93250i	0.871088	−	0.0762103i	0.513928	+	0.857833i	$0.328190\pi$
$644$	0.976716	−	0.355496i	0.0384880	−	0.0140085i
$645$		0			0
$646$	−11.9584	−	67.8196i	−0.470498	−	2.66833i
$647$	23.9696	−	23.9696i	0.942341	−	0.942341i	−0.0560849	−	0.998426i	$-0.517862\pi$
$647$	23.9696	−	23.9696i	0.942341	−	0.942341i	0.998426	+	0.0560849i	$0.0178617\pi$
$648$	26.9109	−	68.7866i	1.05716	−	2.70219i
$649$			3.02889i			0.118894i
$650$		0			0
$651$	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	0.994614	+	0.103652i	$0.0330530\pi$
$653$	0.846075	+	9.67068i	0.0331095	+	0.378443i	−0.961504	+	0.274791i	$0.911391\pi$
$654$	−42.6349	+	6.30213i	−1.66716	+	0.246433i
$655$		0			0
$656$	−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	−0.898502	−	0.438970i	$-0.855343\pi$
$659$	−15.9731	+	13.4030i	−0.622224	+	0.522108i	0.276278	+	0.961078i	$0.410899\pi$
$660$		0			0
$661$	−6.68365	+	37.9049i	−0.259964	+	1.47433i	0.523038	+	0.852310i	$0.324799\pi$
$661$	−6.68365	+	37.9049i	−0.259964	+	1.47433i	−0.783002	+	0.622020i	$0.786312\pi$
$662$	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
$665$		0			0
$666$	−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
$670$		0			0
$671$	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	$-0.435424\pi$
$673$	−16.8631	−	11.8077i	−0.650026	−	0.455153i	−0.851510	+	0.524339i	$0.824313\pi$
$674$	−18.1379			−0.698646
$675$		0			0
$676$	64.9678			2.49876
$677$	−18.5670	−	13.0007i	−0.713588	−	0.499659i	0.159515	−	0.987195i	$-0.449007\pi$
$677$	−18.5670	−	13.0007i	−0.713588	−	0.499659i	−0.873103	+	0.487536i	$0.837896\pi$
$678$	−93.1743	+	22.2116i	−3.57834	+	0.853032i
$679$	−14.3508	−	39.4285i	−0.550734	−	1.51313i
$680$		0			0
$681$	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	$-0.966797\pi$
$683$	−2.12172	+	7.91835i	−0.0811852	+	0.302987i	0.913379	+	0.407110i	$0.133463\pi$
$684$	−57.9589	+	61.7561i	−2.21611	+	2.36130i
$685$		0			0
$686$	−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			0
$691$	2.09562	−	1.75844i	0.0797212	−	0.0668941i	−0.602056	−	0.798454i	$-0.705652\pi$
$691$	2.09562	−	1.75844i	0.0797212	−	0.0668941i	0.681777	+	0.731560i	$0.261207\pi$
$692$	−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
$695$		0			0
$696$	−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
$700$		0			0
$701$		−	45.2015i		−	1.70724i	−0.520899	−	0.853618i	$-0.674403\pi$
$701$		−	45.2015i		−	1.70724i	0.520899	−	0.853618i	$-0.325597\pi$
$702$	−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
$705$		0			0
$706$	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	0.740018	+	0.672587i	$0.234817\pi$
$709$	−6.90171	+	18.9623i	−0.259199	+	0.712144i	−0.999217	+	0.0395569i	$0.987405\pi$
$710$		0			0
$711$	−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			0
$716$	−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	−0.295852	−	0.955234i	$-0.595604\pi$
$719$	18.2157	−	31.5505i	0.679331	−	1.17664i	0.975183	−	0.221402i	$-0.0710631\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	48.6574	+	1.35202i	1.80585	+	0.0501782i
$727$	7.67153	−	10.9561i	0.284521	−	0.406338i	−0.651296	−	0.758824i	$-0.725774\pi$
$727$	7.67153	−	10.9561i	0.284521	−	0.406338i	0.935817	+	0.352485i	$0.114663\pi$
$728$	8.37976	+	8.37976i	0.310575	+	0.310575i
$729$	4.47945	−	26.6258i	0.165906	−	0.986142i
$730$		0			0
$731$	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	−0.244474	−	0.969656i	$-0.578615\pi$
$733$	17.7462	−	38.0568i	0.655470	−	1.40566i	0.899944	−	0.436005i	$-0.143607\pi$
$734$	40.4216	+	33.9178i	1.49199	+	1.25193i
$735$		0			0
$736$	−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	0.971768	−	0.235938i	$-0.0758162\pi$
$739$	34.0711	+	19.6709i	1.25332	+	0.723607i	0.281556	+	0.959545i	$0.409150\pi$
$740$		0			0
$741$	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	$-0.770828\pi$
$743$	−10.6136	+	7.43173i	−0.389376	+	0.272644i	0.362453	+	0.932002i	$0.381939\pi$
$744$	−17.7390	+	19.9858i	−0.650342	+	0.732714i
$745$		0			0
$746$	−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
$750$		0			0
$751$	30.6700	+	25.7352i	1.11916	+	0.939089i	0.998562	−	0.0536119i	$-0.0170734\pi$
$751$	30.6700	+	25.7352i	1.11916	+	0.939089i	0.120601	+	0.992701i	$0.461518\pi$
$752$	−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
$755$		0			0
$756$	−6.76700	+	81.0112i	−0.246113	+	2.94635i
$757$	−0.846964	−	0.846964i	−0.0307834	−	0.0307834i	0.691548	−	0.722331i	$-0.256929\pi$
$757$	−0.846964	−	0.846964i	−0.0307834	−	0.0307834i	−0.722331	+	0.691548i	$0.756929\pi$
$758$	−7.55993	+	10.7967i	−0.274589	+	0.392154i
$759$	0.0400255	−	0.0650817i	0.00145283	−	0.00236232i
$760$		0			0
$761$	−3.25980	+	3.88488i	−0.118168	+	0.140827i	−0.821885	−	0.569653i	$-0.807078\pi$
$761$	−3.25980	+	3.88488i	−0.118168	+	0.140827i	0.703718	+	0.710480i	$0.251522\pi$
$762$	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
$765$		0			0
$766$	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	0.622800	−	0.782381i	$-0.285995\pi$
$769$	26.0795	+	4.59852i	0.940451	+	0.165827i	0.317651	+	0.948208i	$0.397106\pi$
$770$		0			0
$771$	−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	$-0.520739\pi$
$773$	10.4941	−	2.81189i	0.377447	−	0.101137i	0.442555	+	0.896742i	$0.354072\pi$
$774$	−48.9124	−	45.9049i	−1.75812	−	1.65002i
$775$		0			0
$776$	−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
$780$		0			0
$781$	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
$785$		0			0
$786$	−47.5856	+	25.7384i	−1.69732	+	0.918058i
$787$	−7.22332	−	3.36829i	−0.257484	−	0.120067i	0.289591	−	0.957151i	$-0.406481\pi$
$787$	−7.22332	−	3.36829i	−0.257484	−	0.120067i	−0.547074	+	0.837084i	$0.684259\pi$
$788$	3.69786	+	42.2668i	0.131731	+	1.50569i
$789$	−5.35043	+	13.5194i	−0.190480	+	0.481303i
$790$		0			0
$791$	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
$795$		0			0
$796$	−3.33636	+	18.9215i	−0.118254	+	0.670653i
$797$	0.435383	+	0.621792i	0.0154221	+	0.0220250i	0.826789	−	0.562512i	$-0.190165\pi$
$797$	0.435383	+	0.621792i	0.0154221	+	0.0220250i	−0.811367	+	0.584537i	$0.801276\pi$
$798$	35.2667	−	70.4517i	1.24843	−	2.49396i
$799$	−12.2715	−	14.6246i	−0.434136	−	0.517383i
$800$		0			0
$801$	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			0
$806$	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	$0.521746\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	−1.59034	−	1.89529i	−0.0555031	−	0.0661461i	0.737579	−	0.675261i	$-0.235969\pi$
$821$	−1.59034	−	1.89529i	−0.0555031	−	0.0661461i	−0.793082	+	0.609115i	$0.791525\pi$
$822$	13.8739	−	27.7157i	0.483909	−	0.966697i
$823$	18.8527	+	26.9245i	0.657164	+	0.938528i	1.00000		0.000867529i	$-0.000276143\pi$
$823$	18.8527	+	26.9245i	0.657164	+	0.938528i	−0.342835	+	0.939396i	$0.611387\pi$
$824$	−23.2761	+	132.005i	−0.810860	+	4.59862i
$825$		0			0
$826$	−28.6230	+	24.0176i	−0.995923	+	0.835678i
$827$	−2.22968	−	8.32126i	−0.0775334	−	0.289359i	0.916262	−	0.400579i	$-0.131191\pi$
$827$	−2.22968	−	8.32126i	−0.0775334	−	0.289359i	−0.993796	+	0.111220i	$0.964524\pi$
$828$	−1.00290	−	0.144222i	−0.0348532	−	0.00501205i
$829$	−7.38409	+	4.26321i	−0.256460	+	0.148067i	−0.622719	−	0.782446i	$-0.713972\pi$
$829$	−7.38409	+	4.26321i	−0.256460	+	0.148067i	0.366259	+	0.930513i	$0.380639\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$		−	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	0.727789	+	0.685802i	$0.240548\pi$
$839$	8.06541	+	45.7412i	0.278449	+	1.57916i	−0.449340	+	0.893361i	$0.648341\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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
$850$		0			0
$851$	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	0.900430	+	0.435001i	$0.143252\pi$
$853$	−1.80662	+	20.6498i	−0.0618575	+	0.707035i	−0.962288	+	0.272034i	$0.912304\pi$
$854$	−25.4755	+	44.1248i	−0.871752	+	1.50992i
$855$		0			0
$856$	−60.8644	−	105.420i	−2.08030	−	3.60319i
$857$	−3.98725	+	1.85929i	−0.136202	+	0.0635120i	−0.489524	−	0.871990i	$-0.662830\pi$
$857$	−3.98725	+	1.85929i	−0.136202	+	0.0635120i	0.353322	+	0.935502i	$0.385052\pi$
$858$	1.42665	+	0.164858i	0.0487049	+	0.00562814i
$859$	−27.5782	+	32.8664i	−0.940956	+	1.12139i	0.0514862	+	0.998674i	$0.483604\pi$
$859$	−27.5782	+	32.8664i	−0.940956	+	1.12139i	−0.992442	+	0.122714i	$0.960840\pi$
$860$		0			0
$861$	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	−0.999934	−	0.0114553i	$-0.996354\pi$
$863$	−29.7115	−	29.7115i	−1.01139	−	1.01139i	−0.0114553	−	0.999934i	$-0.503646\pi$
$864$	53.6570	−	54.0802i	1.82545	−	1.83985i
$865$		0			0
$866$	−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
$870$		0			0
$871$	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
$875$		0			0
$876$	82.3842	−	92.8188i	2.78350	−	3.13606i
$877$	9.47306	−	6.63310i	0.319882	−	0.223984i	−0.402596	−	0.915378i	$-0.631892\pi$
$877$	9.47306	−	6.63310i	0.319882	−	0.223984i	0.722478	+	0.691394i	$0.243003\pi$
$878$	−69.7284	+	48.8243i	−2.35322	+	1.64774i
$879$	2.33193	+	7.00662i	0.0786540	+	0.236328i
$880$		0			0
$881$	12.7653	+	7.37007i	0.430075	+	0.248304i	0.699379	−	0.714751i	$-0.253460\pi$
$881$	12.7653	+	7.37007i	0.430075	+	0.248304i	−0.269304	+	0.963055i	$0.586794\pi$
$882$	−4.04050	−	19.3126i	−0.136051	−	0.650289i
$883$	15.3517	+	4.11349i	0.516627	+	0.138430i	0.507706	−	0.861530i	$-0.330494\pi$
$883$	15.3517	+	4.11349i	0.516627	+	0.138430i	0.00892106	+	0.999960i	$0.497160\pi$
$884$	10.4432	+	3.80103i	0.351244	+	0.127842i
$885$		0			0
$886$	−36.6160	−	30.7245i	−1.23014	−	1.03221i
$887$	−3.15396	+	6.76369i	−0.105900	+	0.227102i	−0.952116	−	0.305737i	$-0.901097\pi$
$887$	−3.15396	+	6.76369i	−0.105900	+	0.227102i	0.846216	+	0.532839i	$0.178875\pi$
$888$	−26.1861	+	24.7702i	−0.878747	+	0.831232i
$889$	−23.0750	+	4.06875i	−0.773911	+	0.136461i
$890$		0			0
$891$	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
$895$		0			0
$896$	−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
$900$		0			0
$901$	−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
$905$		0			0
$906$	27.3733	+	24.2960i	0.909415	+	0.807180i
$907$	−16.3212	−	1.42792i	−0.541937	−	0.0474134i	−0.187099	−	0.982341i	$-0.559908\pi$
$907$	−16.3212	−	1.42792i	−0.541937	−	0.0474134i	−0.354838	+	0.934928i	$0.615464\pi$
$908$	2.37069	−	0.635223i	0.0786740	−	0.0210806i
$909$	−5.07849	−	2.17489i	−0.168443	−	0.0721365i
$910$		0			0
$911$	−0.825532	+	2.26813i	−0.0273511	+	0.0751465i	−0.952617	−	0.304173i	$-0.901620\pi$
$911$	−0.825532	+	2.26813i	−0.0273511	+	0.0751465i	0.925266	+	0.379320i	$0.123842\pi$
$912$	−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
$915$		0			0
$916$	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	$-0.970123\pi$
$919$		−	5.68243i		−	0.187446i	0.995598	−	0.0937230i	$-0.0298768\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	−0.991522	−	0.129941i	$-0.958521\pi$
$929$	−31.5686	+	26.4892i	−1.03573	+	0.869082i	−0.0442093	+	0.999022i	$0.514077\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−3.34220	−	11.0582i	−0.109243	−	0.361450i
$937$	2.09031	−	7.80116i	0.0682876	−	0.254853i	−0.923340	−	0.383983i	$-0.874552\pi$
$937$	2.09031	−	7.80116i	0.0682876	−	0.254853i	0.991628	+	0.129131i	$0.0412186\pi$
$938$	−18.9430	−	40.6235i	−0.618512	−	1.32640i
$939$	25.8779	−	20.5167i	0.844493	−	0.669538i
$940$		0			0
$941$	17.0461	+	46.8337i	0.555686	+	1.52673i	0.825833	+	0.563915i	$0.190706\pi$
$941$	17.0461	+	46.8337i	0.555686	+	1.52673i	−0.270147	+	0.962819i	$0.587072\pi$
$942$	−61.3082	+	14.6151i	−1.99753	+	0.476186i
$943$	0.0899076	+	0.0629540i	0.00292780	+	0.00205006i
$944$	53.2626			1.73355
$945$		0			0
$946$	14.8463			0.482696
$947$	39.8496	+	27.9030i	1.29494	+	0.906726i	0.998827	−	0.0484276i	$-0.0154210\pi$
$947$	39.8496	+	27.9030i	1.29494	+	0.906726i	0.296112	+	0.955153i	$0.404310\pi$
$948$	13.6384	−	45.7735i	0.442955	−	1.48666i
$949$	−2.26190	−	6.21452i	−0.0734244	−	0.201732i
$950$		0			0
$951$	−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	−0.350148	−	0.936694i	$-0.613869\pi$
$953$	13.0100	−	48.5541i	0.421436	−	1.57282i	0.771584	−	0.636127i	$-0.219465\pi$
$954$	84.4117	−	10.0905i	2.73293	−	0.326691i
$955$		0			0
$956$	−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
$960$		0			0
$961$	−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
$965$		0			0
$966$	0.932406	−	0.137825i	0.0299997	−	0.00443444i
$967$	4.33600	+	49.5607i	0.139436	+	1.59377i	0.667533	+	0.744581i	$0.267350\pi$
$967$	4.33600	+	49.5607i	0.139436	+	1.59377i	−0.528096	+	0.849185i	$0.677094\pi$
$968$	78.5400	+	36.6238i	2.52437	+	1.17713i
$969$	1.24481	−	44.7991i	0.0399891	−	1.43916i
$970$		0			0
$971$		−	40.2818i		−	1.29270i	−0.763039	−	0.646352i	$-0.776294\pi$
$971$		−	40.2818i		−	1.29270i	0.763039	−	0.646352i	$-0.223706\pi$
$972$	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
$975$		0			0
$976$	68.2493	−	24.8407i	2.18461	−	0.795132i
$977$	37.7958	−	3.30670i	1.20919	−	0.105791i	0.535328	−	0.844644i	$-0.320188\pi$
$977$	37.7958	−	3.30670i	1.20919	−	0.105791i	0.673866	+	0.738854i	$0.264633\pi$
$978$	−72.4763	−	53.8093i	−2.31754	−	1.72063i
$979$	−1.39948	+	3.84504i	−0.0447276	+	0.122888i
$980$		0			0
$981$	−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	$-0.278654\pi$
$983$	35.6886	+	3.12235i	1.13829	+	0.0995874i	0.497614	+	0.867399i	$0.334210\pi$
$984$	−22.2822	+	7.41591i	−0.710330	+	0.236411i
$985$		0			0
$986$	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
$990$		0			0
$991$	21.8850	+	37.9060i	0.695201	+	1.20412i	0.970113	+	0.242654i	$0.0780179\pi$
$991$	21.8850	+	37.9060i	0.695201	+	1.20412i	−0.274912	+	0.961469i	$0.588649\pi$
$992$	−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
$995$		0			0
$996$	−23.7590	−	43.9260i	−0.752833	−	1.39185i
$997$	−13.9764	+	19.9603i	−0.442636	+	0.632150i	−0.977034	−	0.213083i	$-0.931649\pi$
$997$	−13.9764	+	19.9603i	−0.442636	+	0.632150i	0.534398	+	0.845233i	$0.320538\pi$
$998$	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	675.2.ba.b.257.16		192
5.2	odd	4		135.2.q.a.68.1	yes	192
5.3	odd	4	inner	675.2.ba.b.68.16		192
5.4	even	2		135.2.q.a.122.1	yes	192
15.2	even	4		405.2.r.a.233.16		192
15.14	odd	2		405.2.r.a.152.16		192
27.2	odd	18	inner	675.2.ba.b.407.16		192
135.2	even	36		135.2.q.a.83.1	yes	192
135.29	odd	18		135.2.q.a.2.1	✓	192
135.52	odd	36		405.2.r.a.8.16		192
135.79	even	18		405.2.r.a.332.16		192
135.83	even	36	inner	675.2.ba.b.218.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.1	✓	192	135.29	odd	18
135.2.q.a.68.1	yes	192	5.2	odd	4
135.2.q.a.83.1	yes	192	135.2	even	36
135.2.q.a.122.1	yes	192	5.4	even	2
405.2.r.a.8.16		192	135.52	odd	36
405.2.r.a.152.16		192	15.14	odd	2
405.2.r.a.233.16		192	15.2	even	4
405.2.r.a.332.16		192	135.79	even	18
675.2.ba.b.68.16		192	5.3	odd	4	inner
675.2.ba.b.218.16		192	135.83	even	36	inner
675.2.ba.b.257.16		192	1.1	even	1	trivial
675.2.ba.b.407.16		192	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (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} +(0.674088 + 4.56031i) q^{6} +(-1.30062 - 2.78918i) q^{7} +(-2.12414 + 7.92739i) q^{8} +(-0.166591 + 2.99537i) q^{9} +(-0.426793 - 0.508631i) q^{11} +(-3.94140 + 7.87366i) q^{12} +(0.269123 + 0.384347i) q^{13} +(1.42232 - 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-1.20591 - 4.50051i) q^{17} +(-4.93586 + 6.27613i) q^{18} +(4.80938 - 2.77670i) q^{19} +(1.96154 - 4.95639i) q^{21} +(-0.154018 - 1.76044i) q^{22} +(0.0602123 + 0.0280775i) q^{23} +(-12.5032 + 6.76283i) q^{24} +1.24878i q^{26} +(-3.96733 + 3.35563i) q^{27} +(11.0626 - 11.0626i) q^{28} +(0.434735 + 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(-14.6055 + 1.27781i) q^{32} +(0.132015 - 1.14243i) q^{33} +(4.24128 - 11.6528i) q^{34} +(-14.5986 + 4.41223i) q^{36} +(2.44933 - 0.656295i) q^{37} +(14.7241 + 1.28820i) q^{38} +(-0.163296 + 0.796105i) q^{39} +(1.62695 + 0.286875i) q^{41} +(11.8428 - 7.81137i) q^{42} +(-0.732214 + 8.36925i) q^{43} +(1.68769 - 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(3.71355 - 1.73166i) q^{47} +(-20.0895 - 2.32146i) q^{48} +(-1.58841 + 1.89299i) q^{49} +(4.22761 - 6.87413i) q^{51} +(-1.36812 + 1.95387i) q^{52} +(-7.52870 - 7.52870i) q^{53} +(-13.7721 + 1.25944i) q^{54} +(24.8736 - 4.38589i) q^{56} +(9.21828 + 2.74662i) q^{57} +(-2.81598 + 6.03890i) q^{58} +(-3.49452 - 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(4.83286 + 1.29496i) q^{62} +(8.57130 - 3.43118i) q^{63} +(-13.5701 - 7.83468i) q^{64} +(2.03182 - 2.28917i) q^{66} +(4.48268 - 3.13881i) q^{67} +(19.4024 - 13.5857i) q^{68} +(0.0363384 + 0.109184i) q^{69} +(-5.33043 - 3.07752i) q^{71} +(-23.3916 - 7.68321i) q^{72} +(-13.6146 - 3.64803i) q^{73} +(6.34185 + 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(-0.863572 + 1.85194i) q^{77} +(-1.57133 + 1.48637i) q^{78} +(-5.34198 + 0.941936i) q^{79} +(-8.94450 - 0.998001i) q^{81} +(3.10910 + 3.10910i) q^{82} +(-3.25316 + 4.64599i) q^{83} +(27.0873 + 0.752663i) q^{84} +(-14.3727 + 17.1287i) q^{86} +(-2.58488 + 3.48160i) q^{87} +(4.93869 - 2.30295i) q^{88} +(-3.08131 - 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(-0.0294359 + 0.336454i) q^{92} +(2.91164 + 1.45751i) q^{93} +(10.7397 + 1.89370i) q^{94} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

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