LMFDB - Embedded newform 675.2.ba.b.68.16

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			68.16
Character	$\chi$	$=$	675.68
Dual form			675.2.ba.b.407.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52658 - 2.18018i) q^{2} +(-1.25829 + 1.19025i) q^{3} +(-1.73870 - 4.77703i) q^{4} +(0.674088 + 4.56031i) q^{6} +(-2.78918 + 1.30062i) q^{7} +(-7.92739 - 2.12414i) q^{8} +(0.166591 - 2.99537i) q^{9} +(-0.426793 - 0.508631i) q^{11} +(7.87366 + 3.94140i) q^{12} +(-0.384347 + 0.269123i) q^{13} +(-1.42232 + 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-4.50051 + 1.20591i) q^{17} +(-6.27613 - 4.93586i) q^{18} +(-4.80938 + 2.77670i) q^{19} +(1.96154 - 4.95639i) q^{21} +(-1.76044 + 0.154018i) q^{22} +(-0.0280775 + 0.0602123i) q^{23} +(12.5032 - 6.76283i) q^{24} +1.24878i q^{26} +(3.35563 + 3.96733i) q^{27} +(11.0626 + 11.0626i) q^{28} +(-0.434735 - 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(1.27781 + 14.6055i) q^{32} +(1.14243 + 0.132015i) q^{33} +(-4.24128 + 11.6528i) q^{34} +(-14.5986 + 4.41223i) q^{36} +(-0.656295 - 2.44933i) q^{37} +(-1.28820 + 14.7241i) q^{38} +(0.163296 - 0.796105i) q^{39} +(1.62695 + 0.286875i) q^{41} +(-7.81137 - 11.8428i) q^{42} +(-8.36925 - 0.732214i) q^{43} +(-1.68769 + 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(-1.73166 - 3.71355i) q^{47} +(2.32146 - 20.0895i) q^{48} +(1.58841 - 1.89299i) q^{49} +(4.22761 - 6.87413i) q^{51} +(1.95387 + 1.36812i) q^{52} +(7.52870 - 7.52870i) q^{53} +(13.7721 - 1.25944i) q^{54} +(24.8736 - 4.38589i) q^{56} +(2.74662 - 9.21828i) q^{57} +(-6.03890 - 2.81598i) q^{58} +(3.49452 + 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(1.29496 - 4.83286i) q^{62} +(3.43118 + 8.57130i) q^{63} +(13.5701 + 7.83468i) q^{64} +(2.03182 - 2.28917i) q^{66} +(-3.13881 - 4.48268i) q^{67} +(13.5857 + 19.4024i) q^{68} +(-0.0363384 - 0.109184i) q^{69} +(-5.33043 - 3.07752i) q^{71} +(-7.68321 + 23.3916i) q^{72} +(3.64803 - 13.6146i) q^{73} +(-6.34185 - 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(1.85194 + 0.863572i) q^{77} +(-1.48637 - 1.57133i) q^{78} +(5.34198 - 0.941936i) q^{79} +(-8.94450 - 0.998001i) q^{81} +(3.10910 - 3.10910i) q^{82} +(-4.64599 - 3.25316i) q^{83} +(-27.0873 - 0.752663i) q^{84} +(-14.3727 + 17.1287i) q^{86} +(3.48160 + 2.58488i) q^{87} +(2.30295 + 4.93869i) q^{88} +(3.08131 + 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(0.336454 + 0.0294359i) q^{92} +(-1.45751 + 2.91164i) q^{93} +(-10.7397 - 1.89370i) q^{94} +(-18.9921 - 16.8570i) q^{96} +(1.18828 - 13.5821i) q^{97} +(-1.70223 - 6.35281i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.52658	−	2.18018i	1.07945	−	1.54162i	0.262484	−	0.964936i	$-0.415458\pi$
$2$	1.52658	−	2.18018i	1.07945	−	1.54162i	0.816969	−	0.576682i	$-0.195653\pi$
$3$	−1.25829	+	1.19025i	−0.726474	+	0.687193i
$3$	−1.25829	+	1.19025i	−0.726474	+	0.687193i
$4$	−1.73870	−	4.77703i	−0.869348	−	2.38851i
$5$		0			0
$5$		0			0
$6$	0.674088	+	4.56031i	0.275195	+	1.86174i
$7$	−2.78918	+	1.30062i	−1.05421	+	0.491587i	−0.870896	−	0.491468i	$-0.836461\pi$
$7$	−2.78918	+	1.30062i	−1.05421	+	0.491587i	−0.183315	+	0.983054i	$0.558683\pi$
$8$	−7.92739	−	2.12414i	−2.80276	−	0.750996i
$9$	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	$0.809693\pi$
$12$	7.87366	+	3.94140i	2.27293	+	1.13778i
$13$	−0.384347	+	0.269123i	−0.106599	+	0.0746412i	−0.625660	−	0.780096i	$-0.715170\pi$
$13$	−0.384347	+	0.269123i	−0.106599	+	0.0746412i	0.519062	+	0.854737i	$0.326282\pi$
$14$	−1.42232	+	8.06640i	−0.380132	+	2.15584i
$15$		0			0
$16$	−8.94423	+	7.50510i	−2.23606	+	1.87627i
$17$	−4.50051	+	1.20591i	−1.09153	+	0.292476i	−0.759313	−	0.650726i	$-0.774465\pi$
$17$	−4.50051	+	1.20591i	−1.09153	+	0.292476i	−0.332221	+	0.943201i	$0.607798\pi$
$18$	−6.27613	−	4.93586i	−1.47930	−	1.16339i
$19$	−4.80938	+	2.77670i	−1.10335	+	0.637018i	−0.937098	−	0.349066i	$-0.886499\pi$
$19$	−4.80938	+	2.77670i	−1.10335	+	0.637018i	−0.166249	+	0.986084i	$0.553166\pi$
$20$		0			0
$21$	1.96154	−	4.95639i	0.428042	−	1.08157i
$22$	−1.76044	+	0.154018i	−0.375327	+	0.0328368i
$23$	−0.0280775	+	0.0602123i	−0.00585456	+	0.0125551i	−0.909213	−	0.416331i	$-0.863316\pi$
$23$	−0.0280775	+	0.0602123i	−0.00585456	+	0.0125551i	0.903359	+	0.428886i	$0.141094\pi$
$24$	12.5032	−	6.76283i	2.55221	−	1.38046i
$25$		0			0
$26$			1.24878i			0.244906i
$27$	3.35563	+	3.96733i	0.645792	+	0.763513i
$28$	11.0626	+	11.0626i	2.09064	+	2.09064i
$29$	−0.434735	−	2.46551i	−0.0807283	−	0.457833i	−0.998197	−	0.0600247i	$-0.980882\pi$
$29$	−0.434735	−	2.46551i	−0.0807283	−	0.457833i	0.917469	−	0.397808i	$-0.130229\pi$
$30$		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	$0.334893\pi$
$32$	1.27781	+	14.6055i	0.225888	+	2.58191i
$33$	1.14243	+	0.132015i	0.198871	+	0.0229808i
$34$	−4.24128	+	11.6528i	−0.727373	+	1.99844i
$35$		0			0
$36$	−14.5986	+	4.41223i	−2.43310	+	0.735372i
$37$	−0.656295	−	2.44933i	−0.107894	−	0.402667i	0.890763	−	0.454468i	$-0.150170\pi$
$37$	−0.656295	−	2.44933i	−0.107894	−	0.402667i	−0.998657	+	0.0518010i	$0.983504\pi$
$38$	−1.28820	+	14.7241i	−0.208973	+	2.38857i
$39$	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	$0.514378\pi$
$42$	−7.81137	−	11.8428i	−1.20532	−	1.82738i
$43$	−8.36925	−	0.732214i	−1.27630	−	0.111662i	−0.571224	−	0.820794i	$-0.693531\pi$
$43$	−8.36925	−	0.732214i	−1.27630	−	0.111662i	−0.705075	+	0.709133i	$0.749087\pi$
$44$	−1.68769	+	2.92316i	−0.254428	+	0.440682i
$45$		0			0
$46$	0.0884111	+	0.153133i	0.0130355	+	0.0225782i
$47$	−1.73166	−	3.71355i	−0.252588	−	0.541677i	0.738599	−	0.674145i	$-0.235488\pi$
$47$	−1.73166	−	3.71355i	−0.252588	−	0.541677i	−0.991187	+	0.132468i	$0.957710\pi$
$48$	2.32146	−	20.0895i	0.335075	−	2.89967i
$49$	1.58841	−	1.89299i	0.226916	−	0.270428i
$50$		0			0
$51$	4.22761	−	6.87413i	0.591984	−	0.962571i
$52$	1.95387	+	1.36812i	0.270953	+	0.189723i
$53$	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			0
$56$	24.8736	−	4.38589i	3.32388	−	0.586089i
$57$	2.74662	−	9.21828i	0.363799	−	1.22099i
$58$	−6.03890	−	2.81598i	−0.792946	−	0.369757i
$59$	3.49452	+	2.93225i	0.454948	+	0.381747i	0.841268	−	0.540618i	$-0.181810\pi$
$59$	3.49452	+	2.93225i	0.454948	+	0.381747i	−0.386320	+	0.922365i	$0.626254\pi$
$60$		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	$0.741485\pi$
$62$	1.29496	−	4.83286i	0.164460	−	0.613773i
$63$	3.43118	+	8.57130i	0.432288	+	1.07988i
$64$	13.5701	+	7.83468i	1.69626	+	0.979335i
$65$		0			0
$66$	2.03182	−	2.28917i	0.250100	−	0.281777i
$67$	−3.13881	−	4.48268i	−0.383466	−	0.547646i	0.580297	−	0.814405i	$-0.302936\pi$
$67$	−3.13881	−	4.48268i	−0.383466	−	0.547646i	−0.963763	+	0.266758i	$0.914047\pi$
$68$	13.5857	+	19.4024i	1.64751	+	2.35288i
$69$	−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	$0.785678\pi$
$72$	−7.68321	+	23.3916i	−0.905475	+	2.75673i
$73$	3.64803	−	13.6146i	0.426970	−	1.59347i	−0.332613	−	0.943063i	$-0.607930\pi$
$73$	3.64803	−	13.6146i	0.426970	−	1.59347i	0.759583	−	0.650410i	$-0.225403\pi$
$74$	−6.34185	−	2.30824i	−0.737225	−	0.268328i
$75$		0			0
$76$	21.6264	+	18.1467i	2.48072	+	2.08157i
$77$	1.85194	+	0.863572i	0.211048	+	0.0984131i
$78$	−1.48637	−	1.57133i	−0.168298	−	0.177918i
$79$	5.34198	−	0.941936i	0.601020	−	0.105976i	0.135144	−	0.990826i	$-0.456850\pi$
$79$	5.34198	−	0.941936i	0.601020	−	0.105976i	0.465876	+	0.884850i	$0.345739\pi$
$80$		0			0
$81$	−8.94450	−	0.998001i	−0.993833	−	0.110889i
$82$	3.10910	−	3.10910i	0.343343	−	0.343343i
$83$	−4.64599	−	3.25316i	−0.509964	−	0.357081i	0.290099	−	0.956997i	$-0.406312\pi$
$83$	−4.64599	−	3.25316i	−0.509964	−	0.357081i	−0.800063	+	0.599916i	$0.795201\pi$
$84$	−27.0873	−	0.752663i	−2.95547	−	0.0821222i
$85$		0			0
$86$	−14.3727	+	17.1287i	−1.54984	+	1.84703i
$87$	3.48160	+	2.58488i	0.373267	+	0.277128i
$88$	2.30295	+	4.93869i	0.245495	+	0.526466i
$89$	3.08131	+	5.33699i	0.326619	+	0.565720i	0.981839	−	0.189718i	$-0.0607574\pi$
$89$	3.08131	+	5.33699i	0.326619	+	0.565720i	−0.655220	+	0.755438i	$0.727424\pi$
$90$		0			0
$91$	0.721988	−	1.25052i	0.0756849	−	0.131090i
$92$	0.336454	+	0.0294359i	0.0350778	+	0.00306891i
$93$	−1.45751	+	2.91164i	−0.151137	+	0.301923i
$94$	−10.7397	−	1.89370i	−1.10772	−	0.195320i
$95$		0			0
$96$	−18.9921	−	16.8570i	−1.93837	−	1.72046i
$97$	1.18828	−	13.5821i	0.120652	−	1.37906i	−0.658669	−	0.752433i	$-0.728880\pi$
$97$	1.18828	−	13.5821i	0.120652	−	1.37906i	0.779321	−	0.626625i	$-0.215564\pi$
$98$	−1.70223	−	6.35281i	−0.171951	−	0.641731i
$99$	−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	$0.140316\pi$
$102$	−8.53305	−	19.7108i	−0.844898	−	1.95166i
$103$	1.42347	+	16.2704i	0.140259	+	1.60317i	0.661627	+	0.749833i	$0.269866\pi$
$103$	1.42347	+	16.2704i	0.140259	+	1.60317i	−0.521368	+	0.853332i	$0.674578\pi$
$104$	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	0.999902	+	0.0140087i	$0.00445924\pi$
$107$	10.4880	+	10.4880i	1.01391	+	1.01391i	0.0140087	+	0.999902i	$0.495541\pi$
$108$	13.1176	−	22.9279i	1.26225	−	2.20624i
$109$		−	9.34913i		−	0.895484i	−0.894163	−	0.447742i	$-0.852228\pi$
$109$		−	9.34913i		−	0.895484i	0.894163	−	0.447742i	$-0.147772\pi$
$110$		0			0
$111$	3.74113	+	2.30081i	0.355092	+	0.218383i
$112$	15.1858	−	32.5661i	1.43492	−	3.07721i
$113$	−20.6993	+	1.81095i	−1.94722	+	0.170360i	−0.992064	−	0.125734i	$-0.959871\pi$
$113$	−20.6993	+	1.81095i	−1.94722	+	0.170360i	−0.955159	+	0.296094i	$0.904316\pi$
$114$	−15.9045	−	20.0605i	−1.48960	−	1.87884i
$115$		0			0
$116$	−11.0219	+	6.36351i	−1.02336	+	0.590837i
$117$	0.742094	+	1.19610i	0.0686066	+	0.110579i
$118$	11.7275	−	3.14237i	1.07960	−	0.289278i
$119$	10.9843	−	9.21693i	1.00693	−	0.844915i
$120$		0			0
$121$	1.83358	−	10.3987i	0.166689	−	0.945339i
$122$	−13.5617	+	9.49604i	−1.22782	+	0.859731i
$123$	−2.38863	+	1.57551i	−0.215375	+	0.142059i
$124$	−6.14289	−	7.32081i	−0.551648	−	0.657428i
$125$		0			0
$126$	23.9249	+	5.60417i	2.13140	+	0.499259i
$127$	−7.35416	−	1.97054i	−0.652576	−	0.174857i	−0.0826829	−	0.996576i	$-0.526349\pi$
$127$	−7.35416	−	1.97054i	−0.652576	−	0.174857i	−0.569893	+	0.821719i	$0.693016\pi$
$128$	11.2214	−	5.23265i	0.991845	−	0.462505i
$129$	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	$0.717541\pi$
$132$	−1.35570	−	5.68695i	−0.117999	−	0.494986i
$133$	9.80281	−	13.9999i	0.850012	−	1.21394i
$134$	−14.5647			−1.25820
$135$		0			0
$136$	38.2388			3.27895
$137$	−3.85643	+	5.50755i	−0.329477	+	0.470542i	−0.949377	−	0.314139i	$-0.898284\pi$
$137$	−3.85643	+	5.50755i	−0.329477	+	0.470542i	0.619900	+	0.784681i	$0.287173\pi$
$138$	−0.293514	−	0.0874536i	−0.0249855	−	0.00744454i
$139$	0.519349	+	1.42690i	0.0440506	+	0.121028i	0.959767	−	0.280796i	$-0.0905985\pi$
$139$	0.519349	+	1.42690i	0.0440506	+	0.121028i	−0.915717	+	0.401824i	$0.868376\pi$
$140$		0			0
$141$	6.59899	+	2.61161i	0.555735	+	0.219937i
$142$	−14.8468	+	6.92320i	−1.24592	+	0.580982i
$143$	0.300921	+	0.0806315i	0.0251643	+	0.00674274i
$144$	20.9905	+	28.0416i	1.74921	+	2.33680i
$145$		0			0
$146$	−24.1133	−	28.7372i	−1.99563	−	2.37830i
$147$	0.254462	+	4.27255i	0.0209876	+	0.352394i
$148$	−10.5594	+	7.39377i	−0.867978	+	0.607764i
$149$	−3.69731	+	20.9685i	−0.302895	+	1.71780i	0.330355	+	0.943857i	$0.392832\pi$
$149$	−3.69731	+	20.9685i	−0.302895	+	1.71780i	−0.633250	+	0.773947i	$0.718280\pi$
$150$		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	$0.173067\pi$
$152$	44.0239	−	11.7962i	3.57081	−	0.956797i
$153$	2.86240	+	13.6816i	0.231411	+	1.10609i
$154$	4.70986	−	2.71924i	0.379531	−	0.219123i
$155$		0			0
$156$	−4.08694	+	0.604116i	−0.327217	+	0.0483680i
$157$	13.6200	−	1.19160i	1.08699	−	0.0950997i	0.470455	−	0.882424i	$-0.344090\pi$
$157$	13.6200	−	1.19160i	1.08699	−	0.0950997i	0.616539	+	0.787324i	$0.288534\pi$
$158$	6.10136	−	13.0844i	0.485398	−	1.04094i
$159$	−0.512227	+	18.4344i	−0.0406223	+	1.46194i
$160$		0			0
$161$		−	0.204461i		−	0.0161138i
$162$	−15.8303	+	17.9771i	−1.24374	+	1.41241i
$163$	−13.8462	−	13.8462i	−1.08452	−	1.08452i	−0.996082	−	0.0884330i	$-0.971814\pi$
$163$	−13.8462	−	13.8462i	−1.08452	−	1.08452i	−0.0884330	−	0.996082i	$-0.528186\pi$
$164$	−1.45836	−	8.27077i	−0.113879	−	0.645839i
$165$		0			0
$166$	−14.1849	+	5.16289i	−1.10096	+	0.400718i
$167$	1.91506	+	21.8892i	0.148192	+	1.69384i	0.598627	+	0.801028i	$0.295713\pi$
$167$	1.91506	+	21.8892i	0.148192	+	1.69384i	−0.450435	+	0.892809i	$0.648731\pi$
$168$	−26.0779	+	35.1246i	−2.01195	+	2.70992i
$169$	−4.37097	+	12.0091i	−0.336228	+	0.923779i
$170$		0			0
$171$	7.51604	+	14.8685i	0.574766	+	1.13702i
$172$	11.0538	+	41.2533i	0.842842	+	3.14553i
$173$	0.327061	−	3.73833i	0.0248660	−	0.284220i	−0.973573	−	0.228374i	$-0.926659\pi$
$173$	0.327061	−	3.73833i	0.0248660	−	0.284220i	0.998439	−	0.0558456i	$-0.0177854\pi$
$174$	10.9504	−	3.64450i	0.830149	−	0.276288i
$175$		0			0
$176$	7.63466	+	1.34620i	0.575484	+	0.101473i
$177$	−7.88725	+	0.469743i	−0.592842	+	0.0353081i
$178$	16.3394	+	1.42952i	1.22469	+	0.107147i
$179$	7.21345	−	12.4941i	0.539158	−	0.933850i	−0.459791	−	0.888027i	$-0.652076\pi$
$179$	7.21345	−	12.4941i	0.539158	−	0.933850i	0.998950	−	0.0458226i	$-0.0145909\pi$
$180$		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	$-0.342617\pi$
$182$	−1.62419	−	3.48308i	−0.120393	−	0.258183i
$183$	9.88743	−	4.28039i	0.730900	−	0.316415i
$184$	0.350480	−	0.417686i	0.0258378	−	0.0307922i
$185$		0			0
$186$	4.12289	+	7.62247i	0.302305	+	0.558907i
$187$	2.53415	+	1.77443i	0.185315	+	0.129759i
$188$	−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	$0.474274\pi$
$192$	−26.4003	+	6.29352i	−1.90528	+	0.454195i
$193$	12.9195	+	6.02445i	0.929963	+	0.433649i	0.827740	−	0.561112i	$-0.189626\pi$
$193$	12.9195	+	6.02445i	0.929963	+	0.433649i	0.102224	+	0.994761i	$0.467404\pi$
$194$	−27.7975	−	23.3248i	−1.99574	−	1.67463i
$195$		0			0
$196$	−11.8046	−	4.29654i	−0.843189	−	0.306896i
$197$	2.16013	−	8.06170i	0.153903	−	0.574372i	−0.845294	−	0.534301i	$-0.820575\pi$
$197$	2.16013	−	8.06170i	0.153903	−	0.574372i	0.999197	−	0.0400711i	$-0.0127585\pi$
$198$	0.168070	+	5.29882i	0.0119442	+	0.376571i
$199$	−3.27312	−	1.88973i	−0.232025	−	0.133960i	0.379481	−	0.925200i	$-0.376103\pi$
$199$	−3.27312	−	1.88973i	−0.232025	−	0.133960i	−0.611506	+	0.791240i	$0.709436\pi$
$200$		0			0
$201$	9.28506	+	1.90454i	0.654917	+	0.134336i
$202$	2.81124	+	4.01487i	0.197798	+	0.282485i
$203$	4.41923	+	6.31132i	0.310169	+	0.442968i
$204$	−40.1885	−	8.24340i	−2.81376	−	0.577153i
$205$		0			0
$206$	37.6453	+	21.7345i	2.62287	+	1.51432i
$207$	0.175681	+	0.0941332i	0.0122107	+	0.00654271i
$208$	1.41790	−	5.29166i	0.0983134	−	0.366911i
$209$	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	$0.932205\pi$
$212$	−49.0550	−	22.8747i	−3.36911	−	1.57104i
$213$	10.3703	−	2.47214i	0.710558	−	0.169388i
$214$	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
$218$	−20.3828	−	14.2722i	−1.38049	−	0.966633i
$219$	11.6146	+	21.4733i	0.784842	+	1.45103i
$220$		0			0
$221$	1.40522	−	1.67468i	0.0945254	−	0.112651i
$222$	10.7273	−	4.64397i	0.719968	−	0.311683i
$223$	8.09113	+	17.3515i	0.541822	+	1.16194i	0.966516	+	0.256605i	$0.0826039\pi$
$223$	8.09113	+	17.3515i	0.541822	+	1.16194i	−0.424694	+	0.905337i	$0.639618\pi$
$224$	−22.5602	−	39.0754i	−1.50737	−	2.61083i
$225$		0			0
$226$	−27.6508	+	47.8926i	−1.83930	+	3.18577i
$227$	−0.480953	−	0.0420779i	−0.0319220	−	0.00279281i	0.0711836	−	0.997463i	$-0.477322\pi$
$227$	−0.480953	−	0.0420779i	−0.0319220	−	0.00279281i	−0.103106	+	0.994670i	$0.532878\pi$
$228$	−48.8115	+	2.90709i	−3.23262	+	0.192526i
$229$	−14.7979	−	2.60927i	−0.977875	−	0.172426i	−0.338203	−	0.941073i	$-0.609819\pi$
$229$	−14.7979	−	2.60927i	−0.977875	−	0.172426i	−0.639672	+	0.768648i	$0.720930\pi$
$230$		0			0
$231$	−3.35814	+	1.11765i	−0.220950	+	0.0735359i
$232$	−1.79076	+	20.4685i	−0.117569	+	1.34382i
$233$	0.143242	+	0.534587i	0.00938411	+	0.0350220i	0.970459	−	0.241266i	$-0.0775625\pi$
$233$	0.143242	+	0.534587i	0.00938411	+	0.0350220i	−0.961075	+	0.276287i	$0.910896\pi$
$234$	3.74056	+	0.208035i	0.244528	+	0.0135997i
$235$		0			0
$236$	7.93154	−	21.7917i	0.516299	−	1.41852i
$237$	−5.60062	+	7.54355i	−0.363800	+	0.490006i
$238$	−3.32615	−	38.0181i	−0.215602	−	2.46435i
$239$	5.32354	−	1.93761i	0.344351	−	0.125334i	−0.164054	−	0.986451i	$-0.552457\pi$
$239$	5.32354	−	1.93761i	0.344351	−	0.125334i	0.508406	+	0.861118i	$0.330235\pi$
$240$		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
$243$	12.4426	−	9.39045i	0.798196	−	0.602397i
$244$			31.6225i			2.02442i
$245$		0			0
$246$	−0.211532	+	7.61277i	−0.0134868	+	0.485372i
$247$	1.10120	−	2.36153i	0.0700677	−	0.150261i
$248$	−15.3696	+	1.34467i	−0.975973	+	0.0853866i
$249$	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	$0.543749\pi$
$252$	34.9796	−	31.2937i	2.20351	−	1.97132i
$253$	0.0426091	−	0.0114171i	0.00267881	−	0.000717786i
$254$	−15.5228	+	13.0252i	−0.973988	+	0.817273i
$255$		0			0
$256$	0.280392	−	1.59018i	0.0175245	−	0.0993864i
$257$	24.5109	−	17.1627i	1.52895	−	1.07058i	0.558428	−	0.829553i	$-0.311405\pi$
$257$	24.5109	−	17.1627i	1.52895	−	1.07058i	0.970518	−	0.241027i	$-0.0774842\pi$
$258$	−2.30248	−	38.6600i	−0.143346	−	2.40686i
$259$	5.01616	+	5.97802i	0.311689	+	0.371456i
$260$		0			0
$261$	−7.45753	+	0.891463i	−0.461609	+	0.0551802i
$262$	30.1706	+	8.08418i	1.86394	+	0.499442i
$263$	−7.60797	+	3.54766i	−0.469128	+	0.218758i	−0.642782	−	0.766049i	$-0.722220\pi$
$263$	−7.60797	+	3.54766i	−0.469128	+	0.218758i	0.173655	+	0.984807i	$0.444442\pi$
$264$	−8.77607	−	3.47321i	−0.540130	−	0.213761i
$265$		0			0
$266$	−15.5574	−	42.7437i	−0.953888	−	2.62079i
$267$	−10.2296	−	3.04794i	−0.626039	−	0.186531i
$268$	−15.9565	+	22.7882i	−0.974696	+	1.39201i
$269$	2.21545			0.135079			0.0675393	−	0.997717i	$-0.478485\pi$
$269$	2.21545			0.135079			0.0675393	+	0.997717i	$0.478485\pi$
$270$		0			0
$271$	−5.87725			−0.357017			−0.178509	−	0.983938i	$-0.557127\pi$
$271$	−5.87725			−0.357017			−0.178509	+	0.983938i	$0.557127\pi$
$272$	31.2031	−	44.5627i	1.89197	−	2.70201i
$273$	0.579966	+	2.43287i	0.0351011	+	0.147244i
$274$	6.12031	+	16.8154i	0.369741	+	1.01586i
$275$		0			0
$276$	−0.458394	+	0.363427i	−0.0275920	+	0.0218757i
$277$	−10.2541	+	4.78156i	−0.616108	+	0.287296i	−0.705510	−	0.708700i	$-0.749282\pi$
$277$	−10.2541	+	4.78156i	−0.616108	+	0.287296i	0.0894020	+	0.995996i	$0.471504\pi$
$278$	3.90372	+	1.04600i	0.234130	+	0.0627348i
$279$	−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	$0.553239\pi$
$282$	15.7676	−	10.4001i	0.938950	−	0.619320i
$283$	−10.7514	+	7.52820i	−0.639103	+	0.447505i	−0.847685	−	0.530500i	$-0.822004\pi$
$283$	−10.7514	+	7.52820i	−0.639103	+	0.447505i	0.208582	+	0.978005i	$0.433115\pi$
$284$	−5.43342	+	30.8145i	−0.322414	+	1.82850i
$285$		0			0
$286$	0.635170	−	0.532971i	0.0375584	−	0.0315152i
$287$	−4.91097	+	1.31589i	−0.289885	+	0.0776745i
$288$	43.9617	−	1.39439i	2.59047	−	0.0821654i
$289$	4.07794	−	2.35440i	0.239879	−	0.138494i
$290$		0			0
$291$	14.6710	+	18.5046i	0.860029	+	1.08476i
$292$	−71.3804	+	6.24497i	−4.17722	+	0.365460i
$293$	−1.80181	+	3.86399i	−0.105263	+	0.225736i	−0.951884	−	0.306460i	$-0.900855\pi$
$293$	−1.80181	+	3.86399i	−0.105263	+	0.225736i	0.846621	+	0.532196i	$0.178633\pi$
$294$	9.70336	+	5.96760i	0.565912	+	0.348037i
$295$		0			0
$296$			20.8108i			1.20960i
$297$	0.585751	−	3.40001i	0.0339887	−	0.197288i
$298$	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
$302$	−1.84171	−	21.0508i	−0.105978	−	1.21134i
$303$	−1.26718	−	2.92711i	−0.0727977	−	0.168158i
$304$	22.1768	−	60.9303i	1.27193	−	3.49459i
$305$		0			0
$306$	34.1980	+	14.6455i	1.95497	+	0.837225i
$307$	4.82189	+	17.9955i	0.275200	+	1.02706i	0.955707	+	0.294318i	$0.0950926\pi$
$307$	4.82189	+	17.9955i	0.275200	+	1.02706i	−0.680508	+	0.732741i	$0.738241\pi$
$308$	0.905354	−	10.3482i	0.0515873	−	0.589646i
$309$	−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	$0.630242\pi$
$312$	−2.98555	+	5.96418i	−0.169023	+	0.337655i
$313$	18.9940	+	1.66176i	1.07360	+	0.0939283i	0.610222	−	0.792230i	$-0.291080\pi$
$313$	18.9940	+	1.66176i	1.07360	+	0.0939283i	0.463382	+	0.886158i	$0.346636\pi$
$314$	18.1941	−	31.5131i	1.02675	−	1.77839i
$315$		0			0
$316$	−13.7877	−	23.8811i	−0.775621	−	1.34342i
$317$	7.17642	+	15.3899i	0.403068	+	0.864382i	0.998155	+	0.0607206i	$0.0193399\pi$
$317$	7.17642	+	15.3899i	0.403068	+	0.864382i	−0.595087	+	0.803661i	$0.702882\pi$
$318$	39.4082	+	29.2582i	2.20990	+	1.64072i
$319$	−1.06849	+	1.27338i	−0.0598241	+	0.0712956i
$320$		0			0
$321$	−25.6803	−	0.713566i	−1.43333	−	0.0398274i
$322$	−0.445761	−	0.312125i	−0.0248413	−	0.0173941i
$323$	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
$327$	11.1278	+	11.7639i	0.615371	+	0.650546i
$328$	−12.2881	−	5.73003i	−0.678497	−	0.316388i
$329$	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	$0.483277\pi$
$332$	−7.46247	+	27.8503i	−0.409556	+	1.52848i
$333$	−7.44597	+	1.55781i	−0.408037	+	0.0853676i
$334$	50.6458	+	29.2404i	2.77122	+	1.59996i
$335$		0			0
$336$	19.6537	+	59.0526i	1.07220	+	3.22158i
$337$	3.90887	+	5.58245i	0.212930	+	0.304095i	0.911382	−	0.411561i	$-0.135016\pi$
$337$	3.90887	+	5.58245i	0.212930	+	0.304095i	−0.698452	+	0.715657i	$0.746128\pi$
$338$	19.5094	+	27.8623i	1.06117	+	1.51551i
$339$	23.8902	−	26.9161i	1.29754	−	1.46188i
$340$		0			0
$341$	−1.08097	−	0.624097i	−0.0585377	−	0.0337968i
$342$	43.8897	+	6.31153i	2.37328	+	0.341288i
$343$	3.60734	−	13.4628i	0.194778	−	0.726922i
$344$	64.7910	+	23.5820i	3.49330	+	1.27146i
$345$		0			0
$346$	−7.65094	−	6.41990i	−0.411317	−	0.345136i
$347$	12.4642	+	5.81216i	0.669114	+	0.312013i	0.727327	−	0.686291i	$-0.240762\pi$
$347$	12.4642	+	5.81216i	0.669114	+	0.312013i	−0.0582130	+	0.998304i	$0.518540\pi$
$348$	6.29459	−	21.1260i	0.337425	−	1.13247i
$349$	−26.3484	+	4.64594i	−1.41040	+	0.248691i	−0.826409	−	0.563070i	$-0.809620\pi$
$349$	−26.3484	+	4.64594i	−1.41040	+	0.248691i	−0.583990	+	0.811761i	$0.698509\pi$
$350$		0			0
$351$	−2.35743	−	0.621756i	−0.125830	−	0.0331869i
$352$	6.88345	−	6.88345i	0.366889	−	0.366889i
$353$	0.0387563	+	0.0271374i	0.00206279	+	0.00144438i	0.574607	−	0.818429i	$-0.305155\pi$
$353$	0.0387563	+	0.0271374i	0.00206279	+	0.00144438i	−0.572545	+	0.819874i	$0.694044\pi$
$354$	−11.0164	+	17.9127i	−0.585513	+	0.952049i
$355$		0			0
$356$	20.1375	−	23.9989i	1.06729	−	1.27194i
$357$	−2.85097	+	24.6717i	−0.150889	+	1.30576i
$358$	−16.2274	−	34.7997i	−0.857644	−	1.83922i
$359$	9.42597	+	16.3263i	0.497484	+	0.861667i	0.999996	−	0.00290290i	$-0.000924023\pi$
$359$	9.42597	+	16.3263i	0.497484	+	0.861667i	−0.502512	+	0.864570i	$0.667591\pi$
$360$		0			0
$361$	5.92010	−	10.2539i	0.311584	−	0.539680i
$362$	−37.4571	−	3.27707i	−1.96870	−	0.172239i
$363$	10.0700	+	15.2670i	0.528535	+	0.801312i
$364$	−7.22909	−	1.27468i	−0.378907	−	0.0668116i
$365$		0			0
$366$	5.76192	−	28.0907i	0.301180	−	1.46832i
$367$	1.72794	−	19.7504i	0.0901977	−	1.03096i	−0.807357	−	0.590063i	$-0.799103\pi$
$367$	1.72794	−	19.7504i	0.0901977	−	1.03096i	0.897555	−	0.440902i	$-0.145341\pi$
$368$	−0.200768	−	0.749277i	−0.0104658	−	0.0390588i
$369$	1.13033	−	4.82552i	0.0588427	−	0.251207i
$370$		0			0
$371$	−11.2070	+	30.7909i	−0.581836	+	1.59858i
$372$	16.4432	+	1.90011i	0.852538	+	0.0985160i
$373$	−1.84840	−	21.1273i	−0.0957063	−	1.09393i	−0.880460	−	0.474120i	$-0.842766\pi$
$373$	−1.84840	−	21.1273i	−0.0957063	−	1.09393i	0.784754	−	0.619808i	$-0.212789\pi$
$374$	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
$378$	−36.7749	+	21.4250i	−1.89150	+	1.10199i
$379$		−	4.95221i		−	0.254378i	−0.991878	−	0.127189i	$-0.959405\pi$
$379$		−	4.95221i		−	0.254378i	0.991878	−	0.127189i	$-0.0405955\pi$
$380$		0			0
$381$	11.5991	−	6.27381i	0.594241	−	0.321417i
$382$	−2.90926	+	6.23894i	−0.148851	+	0.319212i
$383$	28.1753	−	2.46502i	1.43969	−	0.125957i	0.659596	−	0.751620i	$-0.270727\pi$
$383$	28.1753	−	2.46502i	1.43969	−	0.125957i	0.780093	+	0.625663i	$0.215172\pi$
$384$	−7.89166	+	19.9406i	−0.402720	+	1.01759i
$385$		0			0
$386$	32.8569	−	18.9699i	1.67237	−	0.965545i
$387$	−3.58749	+	24.9470i	−0.182362	+	1.26813i
$388$	−66.9484	+	17.9388i	−3.39879	+	0.910703i
$389$	−22.5434	+	18.9162i	−1.14300	+	0.959088i	−0.999533	−	0.0305681i	$-0.990268\pi$
$389$	−22.5434	+	18.9162i	−1.14300	+	0.959088i	−0.143463	+	0.989656i	$0.545824\pi$
$390$		0			0
$391$	0.0537524	−	0.304845i	0.00271838	−	0.0154167i
$392$	−16.6129	+	11.6325i	−0.839080	+	0.587530i
$393$	−18.1768	−	9.09894i	−0.916898	−	0.458981i
$394$	−14.2783	−	17.0163i	−0.719332	−	0.857267i
$395$		0			0
$396$	8.47479	+	5.54221i	0.425874	+	0.278507i
$397$	−18.9334	−	5.07320i	−0.950242	−	0.254616i	−0.249777	−	0.968303i	$-0.580357\pi$
$397$	−18.9334	−	5.07320i	−0.950242	−	0.254616i	−0.700465	+	0.713687i	$0.747024\pi$
$398$	−9.11662	+	4.25115i	−0.456975	+	0.213091i
$399$	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	$0.889157\pi$
$402$	18.3266	−	17.3356i	0.914047	−	0.864624i
$403$	−0.505922	+	0.722531i	−0.0252018	+	0.0359918i
$404$	9.36163			0.465759
$405$		0			0
$406$	20.5061			1.01770
$407$	−0.965702	+	1.37917i	−0.0478681	+	0.0683627i
$408$	−48.1156	+	45.5139i	−2.38207	+	2.25327i
$409$	−3.01485	−	8.28322i	−0.149075	−	0.409579i	0.842569	−	0.538589i	$-0.181042\pi$
$409$	−3.01485	−	8.28322i	−0.149075	−	0.409579i	−0.991643	+	0.129010i	$0.958820\pi$
$410$		0			0
$411$	−1.70288	−	11.5202i	−0.0839967	−	0.568251i
$412$	75.2490	−	35.0892i	3.70725	−	1.72872i
$413$	−13.5606	−	3.63355i	−0.667272	−	0.178795i
$414$	0.473417	−	0.239314i	0.0232672	−	0.0117616i
$415$		0			0
$416$	−4.42180	−	5.26969i	−0.216796	−	0.258368i
$417$	−2.35187	−	1.17730i	−0.115171	−	0.0576525i
$418$	8.03896	−	5.62894i	0.393198	−	0.275320i
$419$	5.75122	−	32.6168i	0.280966	−	1.59344i	−0.438384	−	0.898788i	$-0.644449\pi$
$419$	5.75122	−	32.6168i	0.280966	−	1.59344i	0.719350	−	0.694648i	$-0.244440\pi$
$420$		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	$0.145199\pi$
$422$	−45.7728	+	12.2648i	−2.22819	+	0.597040i
$423$	−11.4119	+	4.56831i	−0.554867	+	0.222119i
$424$	−75.6750	+	43.6910i	−3.67510	+	2.12182i
$425$		0			0
$426$	10.4413	−	26.3829i	0.505882	−	1.27826i
$427$	19.0708	−	1.66848i	0.922901	−	0.0807433i
$428$	31.8660	−	68.3368i	1.54030	−	3.30318i
$429$	−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	$-0.113051\pi$
$432$	−59.7888	−	10.3004i	−2.87659	−	0.495577i
$433$	−16.4822	−	16.4822i	−0.792085	−	0.792085i	0.189748	−	0.981833i	$-0.439233\pi$
$433$	−16.4822	−	16.4822i	−0.792085	−	0.792085i	−0.981833	+	0.189748i	$0.939233\pi$
$434$	2.67381	+	15.1640i	0.128347	+	0.727893i
$435$		0			0
$436$	−44.6611	+	16.2553i	−2.13888	+	0.778488i
$437$	−0.0321562	−	0.367547i	−0.00153824	−	0.0175821i
$438$	64.5461	+	7.45870i	3.08413	+	0.356390i
$439$	10.9388	−	30.0541i	0.522080	−	1.43440i	−0.346121	−	0.938190i	$-0.612501\pi$
$439$	10.9388	−	30.0541i	0.522080	−	1.43440i	0.868201	−	0.496213i	$-0.165277\pi$
$440$		0			0
$441$	−5.40560	−	5.07323i	−0.257410	−	0.241582i
$442$	−1.50592	−	5.62015i	−0.0716291	−	0.267323i
$443$	1.56526	−	17.8910i	0.0743677	−	0.850027i	−0.863798	−	0.503839i	$-0.831920\pi$
$443$	1.56526	−	17.8910i	0.0743677	−	0.850027i	0.938165	−	0.346188i	$-0.112524\pi$
$444$	4.48633	−	21.8719i	0.212912	−	1.03799i
$445$		0			0
$446$	50.1811	+	8.84827i	2.37614	+	0.418978i
$447$	−20.3055	−	30.7852i	−0.960418	−	1.45609i
$448$	−48.0392	−	4.20289i	−2.26964	−	0.198568i
$449$	6.63475	−	11.4917i	0.313113	−	0.542328i	−0.665921	−	0.746022i	$-0.731961\pi$
$449$	6.63475	−	11.4917i	0.313113	−	0.542328i	0.979035	+	0.203694i	$0.0652947\pi$
$450$		0			0
$451$	−0.548456	−	0.949953i	−0.0258258	−	0.0447316i
$452$	44.6407	+	95.7323i	2.09972	+	4.50287i
$453$	−1.57860	+	13.6609i	−0.0741689	+	0.641843i
$454$	−0.825948	+	0.984327i	−0.0387637	+	0.0461968i
$455$		0			0
$456$	−41.3545	+	67.2427i	−1.93660	+	3.14893i
$457$	−6.59496	−	4.61784i	−0.308499	−	0.216013i	0.409066	−	0.912505i	$-0.365855\pi$
$457$	−6.59496	−	4.61784i	−0.308499	−	0.216013i	−0.717565	+	0.696491i	$0.754743\pi$
$458$	−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	$0.553107\pi$
$462$	−2.68979	+	9.02752i	−0.125140	+	0.419998i
$463$	−18.8558	−	8.79261i	−0.876304	−	0.408627i	−0.0682032	−	0.997671i	$-0.521727\pi$
$463$	−18.8558	−	8.79261i	−0.876304	−	0.408627i	−0.808101	+	0.589044i	$0.799504\pi$
$464$	22.3922	+	18.7893i	1.03953	+	0.872272i
$465$		0			0
$466$	1.38417	+	0.503795i	0.0641202	+	0.0233378i
$467$	6.38314	−	23.8222i	0.295376	−	1.10236i	−0.645542	−	0.763725i	$-0.723368\pi$
$467$	6.38314	−	23.8222i	0.295376	−	1.10236i	0.940918	−	0.338635i	$-0.109965\pi$
$468$	4.42351	−	5.62465i	0.204477	−	0.260000i
$469$	14.5849	+	8.42062i	0.673470	+	0.388828i
$470$		0			0
$471$	−15.7196	+	17.7106i	−0.724322	+	0.816063i
$472$	−21.4739	−	30.6679i	−0.988418	−	1.41161i
$473$	3.19951	+	4.56937i	0.147113	+	0.210100i
$474$	7.89648	+	23.7262i	0.362698	+	1.08978i
$475$		0			0
$476$	−63.1279	−	36.4469i	−2.89346	−	1.67054i
$477$	−21.2970	−	23.8055i	−0.975125	−	1.08998i
$478$	3.90246	−	14.5642i	0.178494	−	0.666150i
$479$	−25.2593	−	9.19362i	−1.15412	−	0.420067i	−0.307130	−	0.951668i	$-0.599368\pi$
$479$	−25.2593	−	9.19362i	−1.15412	−	0.420067i	−0.846995	+	0.531601i	$0.821591\pi$
$480$		0			0
$481$	0.911414	+	0.764768i	0.0415569	+	0.0348704i
$482$	4.41687	+	2.05962i	0.201183	+	0.0938132i
$483$	0.243361	+	0.257271i	0.0110733	+	0.0117063i
$484$	−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	−0.737987	−	0.674815i	$-0.764223\pi$
$487$	−1.39406	+	1.39406i	−0.0631711	+	0.0631711i	0.674815	+	0.737987i	$0.264223\pi$
$488$	41.8191	+	29.2821i	1.89306	+	1.32554i
$489$	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	$0.401938\pi$
$492$	11.6794	+	8.67121i	0.526546	+	0.390928i
$493$	4.92970	+	10.5718i	0.222023	+	0.476129i
$494$	−3.46749	−	6.00587i	−0.156010	−	0.270217i
$495$		0			0
$496$	−10.9747	+	19.0087i	−0.492778	+	0.853516i
$497$	18.8702	+	1.65093i	0.846444	+	0.0740542i
$498$	11.7036	−	23.3801i	0.524451	−	1.04769i
$499$	−30.8900	−	5.44673i	−1.38282	−	0.243829i	−0.567758	−	0.823196i	$-0.692189\pi$
$499$	−30.8900	−	5.44673i	−1.38282	−	0.243829i	−0.815067	+	0.579366i	$0.803300\pi$
$500$		0			0
$501$	−28.4634	−	25.2636i	−1.27165	−	1.12869i
$502$	−4.51248	+	51.5779i	−0.201402	+	2.30204i
$503$	1.59547	+	5.95437i	0.0711385	+	0.265492i	0.992330	−	0.123617i	$-0.0394495\pi$
$503$	1.59547	+	5.95437i	0.0711385	+	0.265492i	−0.921192	+	0.389109i	$0.872783\pi$
$504$	−8.99365	−	75.2363i	−0.400609	−	3.35129i
$505$		0			0
$506$	0.0401548	−	0.110325i	0.00178510	−	0.00490452i
$507$	−8.79397	−	20.3135i	−0.390554	−	0.902156i
$508$	3.37332	+	38.5572i	0.149667	+	1.71070i
$509$	−18.3832	+	6.69092i	−0.814819	+	0.296570i	−0.715613	−	0.698497i	$-0.753853\pi$
$509$	−18.3832	+	6.69092i	−0.814819	+	0.296570i	−0.0992061	+	0.995067i	$0.531630\pi$
$510$		0			0
$511$	7.53240	+	42.7184i	0.333214	+	1.88975i
$512$	14.4712	+	14.4712i	0.639545	+	0.639545i
$513$	−27.1546	−	9.76284i	−1.19890	−	0.431040i
$514$		−	79.6382i		−	3.51269i
$515$		0			0
$516$	−63.0107	−	38.7518i	−2.77389	−	1.70595i
$517$	−1.14977	+	2.46569i	−0.0505668	+	0.108441i
$518$	20.6907	−	1.81020i	0.909097	−	0.0795357i
$519$	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	$0.325079\pi$
$522$	−9.44094	+	17.6196i	−0.413219	+	0.771190i
$523$	−43.1925	+	11.5734i	−1.88868	+	0.506069i	−0.889926	+	0.456106i	$0.849244\pi$
$523$	−43.1925	+	11.5734i	−1.88868	+	0.506069i	−0.998751	+	0.0499636i	$0.984089\pi$
$524$	45.7023	−	38.3488i	1.99652	−	1.67528i
$525$		0			0
$526$	−3.87963	+	22.0025i	−0.169160	+	0.959354i
$527$	−7.17489	+	5.02391i	−0.312543	+	0.218845i
$528$	−11.2089	+	7.39328i	−0.487806	+	0.321751i
$529$	14.7813	+	17.6156i	0.642664	+	0.765897i
$530$		0			0
$531$	9.36533	−	9.97890i	0.406421	−	0.433047i
$532$	−83.9219	−	22.4868i	−3.63848	−	0.974927i
$533$	−0.702518	+	0.327589i	−0.0304294	+	0.0141895i
$534$	−22.2613	+	17.6493i	−0.963339	+	0.763762i
$535$		0			0
$536$	15.3607	+	42.2032i	0.663482	+	1.82290i
$537$	5.79449	+	24.3070i	0.250051	+	1.04892i
$538$	3.38206	−	4.83008i	0.145811	−	0.208240i
$539$	−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	$0.505346\pi$
$542$	−8.97207	+	12.8134i	−0.385383	+	0.550384i
$543$	23.4506	+	6.98719i	1.00636	+	0.299849i
$544$	−23.3637	−	64.1912i	−1.00171	−	2.75218i
$545$		0			0
$546$	6.18944	+	2.44953i	0.264884	+	0.104830i
$547$	10.0522	−	4.68743i	0.429802	−	0.200420i	−0.195665	−	0.980671i	$-0.562686\pi$
$547$	10.0522	−	4.68743i	0.429802	−	0.200420i	0.625467	+	0.780251i	$0.284909\pi$
$548$	33.0149	+	8.84632i	1.41033	+	0.377896i
$549$	−7.34652	+	17.1545i	−0.313542	+	0.732137i
$550$		0			0
$551$	8.93677	+	10.6504i	0.380719	+	0.453724i
$552$	0.0561466	+	0.942732i	0.00238976	+	0.0401253i
$553$	−13.6747	+	9.57510i	−0.581505	+	0.407175i
$554$	−5.22900	+	29.6551i	−0.222159	+	1.25993i
$555$		0			0
$556$	5.91335	−	4.96189i	0.250782	−	0.210431i
$557$	−13.0192	+	3.48849i	−0.551642	+	0.147812i	−0.523864	−	0.851802i	$-0.675510\pi$
$557$	−13.0192	+	3.48849i	−0.551642	+	0.147812i	−0.0277782	+	0.999614i	$0.508843\pi$
$558$	−14.2605	−	4.68399i	−0.603694	−	0.198289i
$559$	3.41375	−	1.97093i	0.144386	−	0.0833615i
$560$		0			0
$561$	−5.30071	+	0.783531i	−0.223796	+	0.0330807i
$562$	57.6316	−	5.04211i	2.43104	−	0.212689i
$563$	−15.8881	+	34.0720i	−0.669601	+	1.43596i	0.218277	+	0.975887i	$0.429956\pi$
$563$	−15.8881	+	34.0720i	−0.669601	+	1.43596i	−0.887878	+	0.460078i	$0.847821\pi$
$564$	1.00210	−	36.0644i	0.0421962	−	1.51858i
$565$		0			0
$566$			34.9323i			1.46831i
$567$	26.2458	−	8.84975i	1.10222	−	0.371654i
$568$	35.7193	+	35.7193i	1.49875	+	1.49875i
$569$	−2.09817	−	11.8993i	−0.0879598	−	0.498845i	−0.996679	−	0.0814360i	$-0.974049\pi$
$569$	−2.09817	−	11.8993i	−0.0879598	−	0.498845i	0.908719	−	0.417409i	$-0.137062\pi$
$570$		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	$0.384122\pi$
$572$	−0.138031	−	1.57770i	−0.00577137	−	0.0659670i
$573$	2.67050	−	3.59693i	0.111562	−	0.150264i
$574$	−4.62809	+	12.7156i	−0.193173	+	0.530738i
$575$		0			0
$576$	25.7284	−	39.3422i	1.07202	−	1.63926i
$577$	−9.67417	−	36.1045i	−0.402741	−	1.50305i	−0.808184	−	0.588930i	$-0.799549\pi$
$577$	−9.67417	−	36.1045i	−0.402741	−	1.50305i	0.405443	−	0.914120i	$-0.367117\pi$
$578$	1.09228	−	12.4848i	0.0454328	−	0.519300i
$579$	−23.4271	+	7.79694i	−0.973596	+	0.324030i
$580$		0			0
$581$	17.1896	+	3.03100i	0.713146	+	0.125747i
$582$	62.7398	−	3.73662i	2.60065	−	0.154888i
$583$	−7.04253	−	0.616142i	−0.291672	−	0.0255180i
$584$	−57.8388	+	100.180i	−2.39339	+	4.14547i
$585$		0			0
$586$	5.67358	+	9.82693i	0.234373	+	0.405947i
$587$	−3.89170	−	8.34577i	−0.160628	−	0.344467i	0.809478	−	0.587150i	$-0.199750\pi$
$587$	−3.89170	−	8.34577i	−0.160628	−	0.344467i	−0.970106	+	0.242683i	$0.921972\pi$
$588$	19.9677	−	8.64423i	0.823452	−	0.356482i
$589$	−6.71056	+	7.99734i	−0.276504	+	0.329525i
$590$		0			0
$591$	6.87740	+	12.7151i	0.282899	+	0.523028i
$592$	24.2525	+	16.9818i	0.996771	+	0.697946i
$593$	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
$595$		0			0
$596$	106.595	−	18.7957i	4.36632	−	0.769900i
$597$	6.36780	−	1.51800i	0.260617	−	0.0621278i
$598$	−0.0751920	−	0.0350626i	−0.00307483	−	0.00143382i
$599$	5.73610	+	4.81316i	0.234371	+	0.196660i	0.752407	−	0.658698i	$-0.228893\pi$
$599$	5.73610	+	4.81316i	0.234371	+	0.196660i	−0.518037	+	0.855358i	$0.673337\pi$
$600$		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	$0.757795\pi$
$602$	17.8101	−	66.4682i	0.725886	−	2.70904i
$603$	−13.9502	+	8.65512i	−0.568095	+	0.352464i
$604$	−34.9543	−	20.1809i	−1.42227	−	0.821148i
$605$		0			0
$606$	−8.31607	−	1.70578i	−0.337817	−	0.0692926i
$607$	−13.1267	−	18.7469i	−0.532796	−	0.760912i	0.459042	−	0.888415i	$-0.348193\pi$
$607$	−13.1267	−	18.7469i	−0.532796	−	0.760912i	−0.991838	+	0.127503i	$0.959304\pi$
$608$	−46.7005	−	66.6953i	−1.89396	−	2.70485i
$609$	−13.0727	−	2.68146i	−0.529734	−	0.108658i
$610$		0			0
$611$	1.66496	+	0.961264i	0.0673570	+	0.0388886i
$612$	60.3805	−	37.4619i	2.44074	−	1.51431i
$613$	−3.87633	+	14.4667i	−0.156564	+	0.584303i	0.842403	+	0.538848i	$0.181140\pi$
$613$	−3.87633	+	14.4667i	−0.156564	+	0.584303i	−0.998966	+	0.0454549i	$0.985526\pi$
$614$	46.5944	+	16.9590i	1.88040	+	0.684409i
$615$		0			0
$616$	−12.8467	−	10.7796i	−0.517607	−	0.434324i
$617$	0.430054	+	0.200538i	0.0173133	+	0.00807334i	0.431256	−	0.902230i	$-0.358071\pi$
$617$	0.430054	+	0.200538i	0.0173133	+	0.00807334i	−0.413942	+	0.910303i	$0.635848\pi$
$618$	−73.2383	+	17.4591i	−2.94608	+	0.702309i
$619$	10.1152	−	1.78359i	0.406565	−	0.0716885i	0.0333743	−	0.999443i	$-0.489375\pi$
$619$	10.1152	−	1.78359i	0.406565	−	0.0716885i	0.373191	+	0.927754i	$0.378264\pi$
$620$		0			0
$621$	−0.333100	+	0.0906578i	−0.0133668	+	0.00363797i
$622$	−15.4321	+	15.4321i	−0.618770	+	0.618770i
$623$	−15.5357	−	10.8782i	−0.622425	−	0.435827i
$624$	4.51429	+	8.34610i	0.180716	+	0.334111i
$625$		0			0
$626$	32.6187	−	38.8735i	1.30371	−	1.55370i
$627$	−5.86095	+	2.53727i	−0.234064	+	0.101329i
$628$	−29.3733	−	62.9913i	−1.17212	−	2.51363i
$629$	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	$0.249738\pi$
$632$	−44.3488	−	3.88002i	−1.76410	−	0.154339i
$633$	30.7842	−	1.83343i	1.22356	−	0.0728722i
$634$	44.5080	+	7.84797i	1.76764	+	0.311683i
$635$		0			0
$636$	88.9521	−	29.6048i	3.52718	−	1.17391i
$637$	−0.101053	+	1.15504i	−0.00400388	+	0.0457645i
$638$	1.14506	+	4.27341i	0.0453333	+	0.169186i
$639$	−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	$-0.264124\pi$
$642$	−40.7586	+	54.8982i	−1.60861	+	2.16666i
$643$	1.93250	+	22.0886i	0.0762103	+	0.871088i	0.934043	+	0.357160i	$0.116255\pi$
$643$	1.93250	+	22.0886i	0.0762103	+	0.871088i	−0.857833	+	0.513928i	$0.828190\pi$
$644$	−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	$-0.482138\pi$
$647$	−23.9696	−	23.9696i	−0.942341	−	0.942341i	−0.998426	+	0.0560849i	$0.982138\pi$
$648$	68.7866	+	26.9109i	2.70219	+	1.05716i
$649$		−	3.02889i		−	0.118894i
$650$		0			0
$651$	0.278331	−	10.0167i	0.0109086	−	0.392587i
$652$	−42.0693	+	90.2178i	−1.64756	+	3.53320i
$653$	−9.67068	+	0.846075i	−0.378443	+	0.0331095i	−0.274791	−	0.961504i	$-0.588609\pi$
$653$	−9.67068	+	0.846075i	−0.378443	+	0.0331095i	−0.103652	+	0.994614i	$0.533053\pi$
$654$	42.6349	−	6.30213i	1.66716	−	0.246433i
$655$		0			0
$656$	−16.7048	+	9.64453i	−0.652214	+	0.376556i
$657$	−40.1732	−	13.1953i	−1.56731	−	0.514797i
$658$	32.4179	−	8.68636i	1.26378	−	0.338629i
$659$	15.9731	−	13.4030i	0.622224	−	0.522108i	−0.276278	−	0.961078i	$-0.589101\pi$
$659$	15.9731	−	13.4030i	0.622224	−	0.522108i	0.898502	+	0.438970i	$0.144657\pi$
$660$		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	$0.786312\pi$
$662$	31.0096	−	21.7132i	1.20522	−	0.843906i
$663$	0.225115	+	3.77980i	0.00874274	+	0.146795i
$664$	29.9205	+	35.6578i	1.16114	+	1.38379i
$665$		0			0
$666$	−7.97054	+	18.6117i	−0.308852	+	0.721187i
$667$	0.160660	+	0.0430488i	0.00622079	+	0.00166685i
$668$	101.236	−	47.2070i	3.91693	−	1.82649i
$669$	−30.8337	−	12.2027i	−1.19210	−	0.471784i
$670$		0			0
$671$	1.41262	+	3.88114i	0.0545335	+	0.149830i
$672$	74.8969	+	22.3158i	2.88921	+	0.860853i
$673$	11.8077	−	16.8631i	0.455153	−	0.650026i	−0.524339	−	0.851510i	$-0.675687\pi$
$673$	11.8077	−	16.8631i	0.455153	−	0.650026i	0.979492	+	0.201484i	$0.0645763\pi$
$674$	18.1379			0.698646
$675$		0			0
$676$	64.9678			2.49876
$677$	−13.0007	+	18.5670i	−0.499659	+	0.713588i	−0.987195	−	0.159515i	$-0.949007\pi$
$677$	−13.0007	+	18.5670i	−0.499659	+	0.713588i	0.487536	+	0.873103i	$0.337896\pi$
$678$	−22.2116	−	93.1743i	−0.853032	−	3.57834i
$679$	14.3508	+	39.4285i	0.550734	+	1.51313i
$680$		0			0
$681$	0.655262	−	0.519510i	0.0251097	−	0.0199077i
$682$	−3.01082	+	1.40397i	−0.115290	+	0.0537608i
$683$	−7.91835	−	2.12172i	−0.302987	−	0.0811852i	0.104122	−	0.994564i	$-0.466797\pi$
$683$	−7.91835	−	2.12172i	−0.302987	−	0.0811852i	−0.407110	+	0.913379i	$0.633463\pi$
$684$	57.9589	−	61.7561i	2.21611	−	2.36130i
$685$		0			0
$686$	−23.8444	−	28.4166i	−0.910382	−	1.08495i
$687$	21.7258	−	14.3301i	0.828891	−	0.546726i
$688$	80.3518	−	56.2630i	3.06338	−	2.14500i
$689$	−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	$0.261207\pi$
$692$	−18.4268	+	4.93744i	−0.700481	+	0.187693i
$693$	2.89523	−	5.40337i	0.109981	−	0.205257i
$694$	31.6991	−	18.3015i	1.20328	−	0.694715i
$695$		0			0
$696$	−22.1094	−	27.8867i	−0.838054	−	1.05704i
$697$	−7.66804	+	0.670867i	−0.290448	+	0.0254109i
$698$	−30.0939	+	64.5366i	−1.13907	+	2.44275i
$699$	−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	$-0.325597\pi$
$702$	−4.95433	+	4.19045i	−0.186989	+	0.158158i
$703$	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
$707$	−0.493942	−	5.64579i	−0.0185766	−	0.212332i
$708$	15.9575	+	36.8609i	0.599720	+	1.38532i
$709$	6.90171	−	18.9623i	0.259199	−	0.712144i	−0.740018	−	0.672587i	$-0.765183\pi$
$709$	6.90171	−	18.9623i	0.259199	−	0.712144i	0.999217	−	0.0395569i	$-0.0125946\pi$
$710$		0			0
$711$	−1.93152	−	16.1581i	−0.0724378	−	0.605978i
$712$	−13.0903	−	48.8536i	−0.490579	−	1.83086i
$713$	−0.0108853	+	0.124419i	−0.000407656	+	0.00465953i
$714$	49.4365	+	43.8788i	1.85011	+	1.64212i
$715$		0			0
$716$	−72.2265	−	12.7355i	−2.69923	−	0.475947i
$717$	−4.39231	+	8.77444i	−0.164034	+	0.327688i
$718$	49.9836	+	4.37300i	1.86537	+	0.163199i
$719$	−18.2157	+	31.5505i	−0.679331	+	1.17664i	0.295852	+	0.955234i	$0.404396\pi$
$719$	−18.2157	+	31.5505i	−0.679331	+	1.17664i	−0.975183	+	0.221402i	$0.928937\pi$
$720$		0			0
$721$	−25.1318	−	43.5295i	−0.935957	−	1.62113i
$722$	−13.3179	−	28.5603i	−0.495640	−	1.06290i
$723$	−2.54646	−	1.89059i	−0.0947037	−	0.0703118i
$724$	−46.1638	+	55.0159i	−1.71566	+	2.04465i
$725$		0			0
$726$	48.6574	+	1.35202i	1.80585	+	0.0501782i
$727$	−10.9561	−	7.67153i	−0.406338	−	0.284521i	0.352485	−	0.935817i	$-0.385337\pi$
$727$	−10.9561	−	7.67153i	−0.406338	−	0.284521i	−0.758824	+	0.651296i	$0.774226\pi$
$728$	−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
$732$	−37.6388	−	39.7903i	−1.39117	−	1.47069i
$733$	38.0568	+	17.7462i	1.40566	+	0.655470i	0.969656	−	0.244474i	$-0.0786152\pi$
$733$	38.0568	+	17.7462i	1.40566	+	0.655470i	0.436005	+	0.899944i	$0.356393\pi$
$734$	−40.4216	−	33.9178i	−1.49199	−	1.25193i
$735$		0			0
$736$	−0.915308	−	0.333145i	−0.0337387	−	0.0122799i
$737$	−0.940413	+	3.50967i	−0.0346406	+	0.129280i
$738$	−8.79496	−	9.83085i	−0.323747	−	0.361879i
$739$	−34.0711	−	19.6709i	−1.25332	−	0.723607i	−0.281556	−	0.959545i	$-0.590850\pi$
$739$	−34.0711	−	19.6709i	−1.25332	−	0.723607i	−0.971768	+	0.235938i	$0.924184\pi$
$740$		0			0
$741$	1.42519	+	4.28220i	0.0523557	+	0.157310i
$742$	50.0213	+	71.4378i	1.83634	+	2.62256i
$743$	−7.43173	−	10.6136i	−0.272644	−	0.389376i	0.659358	−	0.751829i	$-0.270828\pi$
$743$	−7.43173	−	10.6136i	−0.272644	−	0.389376i	−0.932002	+	0.362453i	$0.881939\pi$
$744$	17.7390	−	19.9858i	0.650342	−	0.732714i
$745$		0			0
$746$	−48.8829	−	28.2225i	−1.78973	−	1.03330i
$747$	−10.5184	+	13.3745i	−0.384848	+	0.489349i
$748$	4.07039	−	15.1909i	0.148828	−	0.555434i
$749$	−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	$0.461518\pi$
$752$	43.3589	+	20.2186i	1.58114	+	0.737296i
$753$	9.62128	−	32.2912i	0.350619	−	1.17676i
$754$	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	−0.722331	−	0.691548i	$-0.756929\pi$
$757$	−0.846964	+	0.846964i	−0.0307834	+	0.0307834i	0.691548	+	0.722331i	$0.256929\pi$
$758$	−10.7967	−	7.55993i	−0.392154	−	0.274589i
$759$	−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	$0.251522\pi$
$762$	4.02893	−	34.8656i	0.145953	−	1.26305i
$763$	12.1596	+	26.0764i	0.440208	+	0.944029i
$764$	6.57430	+	11.3870i	0.237850	+	0.411968i
$765$		0			0
$766$	37.6375	−	65.1901i	1.35990	−	2.35542i
$767$	−2.13224	−	0.186547i	−0.0769909	−	0.00673583i
$768$	1.53991	+	2.33465i	0.0555666	+	0.0842444i
$769$	−26.0795	−	4.59852i	−0.940451	−	0.165827i	−0.317651	−	0.948208i	$-0.602894\pi$
$769$	−26.0795	−	4.59852i	−0.940451	−	0.165827i	−0.622800	+	0.782381i	$0.714005\pi$
$770$		0			0
$771$	−10.4138	+	50.7698i	−0.375045	+	1.82843i
$772$	6.31593	−	72.1914i	0.227315	−	2.59822i
$773$	2.81189	+	10.4941i	0.101137	+	0.377447i	0.997878	−	0.0651074i	$-0.0207390\pi$
$773$	2.81189	+	10.4941i	0.101137	+	0.377447i	−0.896742	+	0.442555i	$0.854072\pi$
$774$	48.9124	+	45.9049i	1.75812	+	1.65002i
$775$		0			0
$776$	−38.2703	+	105.147i	−1.37383	+	3.77455i
$777$	−13.4271	−	1.55159i	−0.481696	−	0.0556629i
$778$	6.82635	+	78.0256i	0.244737	+	2.79735i
$779$	−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
$783$	8.32267	−	9.99807i	0.297428	−	0.357302i
$784$			28.8525i			1.03045i
$785$		0			0
$786$	−47.5856	+	25.7384i	−1.69732	+	0.918058i
$787$	−3.36829	+	7.22332i	−0.120067	+	0.257484i	−0.957151	−	0.289591i	$-0.906481\pi$
$787$	−3.36829	+	7.22332i	−0.120067	+	0.257484i	0.837084	+	0.547074i	$0.184259\pi$
$788$	−42.2668	+	3.69786i	−1.50569	+	0.131731i
$789$	5.35043	−	13.5194i	0.190480	−	0.481303i
$790$		0			0
$791$	55.3786	−	31.9729i	1.96904	−	1.13682i
$792$	15.1769	−	6.07544i	0.539286	−	0.215882i
$793$	2.81921	−	0.755404i	0.100113	−	0.0268252i
$794$	−39.9638	+	33.5336i	−1.41826	+	1.19006i
$795$		0			0
$796$	−3.33636	+	18.9215i	−0.118254	+	0.670653i
$797$	0.621792	−	0.435383i	0.0220250	−	0.0154221i	−0.562512	−	0.826789i	$-0.690165\pi$
$797$	0.621792	−	0.435383i	0.0220250	−	0.0154221i	0.584537	+	0.811367i	$0.301276\pi$
$798$	70.4517	+	35.2667i	2.49396	+	1.24843i
$799$	12.2715	+	14.6246i	0.434136	+	0.517383i
$800$		0			0
$801$	16.4996	−	8.34059i	0.582984	−	0.294700i
$802$	−0.0868625	−	0.0232747i	−0.00306722	−	0.000821859i
$803$	−8.48179	+	3.95512i	−0.299316	+	0.139573i
$804$	−7.04587	−	47.6664i	−0.248489	−	1.68106i
$805$		0			0
$806$	0.802918	+	2.20600i	0.0282816	+	0.0777030i
$807$	−2.78768	+	2.63695i	−0.0981311	+	0.0928251i
$808$	8.66877	−	12.3803i	0.304966	−	0.435537i
$809$	3.88327			0.136528			0.0682642	−	0.997667i	$-0.478254\pi$
$809$	3.88327			0.136528			0.0682642	+	0.997667i	$0.478254\pi$
$810$		0			0
$811$	−22.9810			−0.806974			−0.403487	−	0.914985i	$-0.632202\pi$
$811$	−22.9810			−0.806974			−0.403487	+	0.914985i	$0.632202\pi$
$812$	22.4656	−	32.0843i	0.788390	−	1.12594i
$813$	7.39528	−	6.99542i	0.259364	−	0.245340i
$814$	1.53261	+	4.21081i	0.0537179	+	0.147589i
$815$		0			0
$816$	13.7783	+	93.2125i	0.482337	+	3.26309i
$817$	42.2840	−	19.7174i	1.47933	−	0.689824i
$818$	−22.6613	−	6.07207i	−0.792333	−	0.212305i
$819$	−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	$0.791525\pi$
$822$	−27.7157	−	13.8739i	−0.966697	−	0.483909i
$823$	−26.9245	+	18.8527i	−0.938528	+	0.657164i	−0.939396	−	0.342835i	$-0.888613\pi$
$823$	−26.9245	+	18.8527i	−0.938528	+	0.657164i	0.000867529		1.00000i	$0.499724\pi$
$824$	23.2761	−	132.005i	0.810860	−	4.59862i
$825$		0			0
$826$	−28.6230	+	24.0176i	−0.995923	+	0.835678i
$827$	−8.32126	+	2.22968i	−0.289359	+	0.0775334i	−0.400579	−	0.916262i	$-0.631191\pi$
$827$	−8.32126	+	2.22968i	−0.289359	+	0.0775334i	0.111220	+	0.993796i	$0.464524\pi$
$828$	0.144222	−	1.00290i	0.00501205	−	0.0348532i
$829$	7.38409	−	4.26321i	0.256460	−	0.148067i	−0.366259	−	0.930513i	$-0.619361\pi$
$829$	7.38409	−	4.26321i	0.256460	−	0.148067i	0.622719	+	0.782446i	$0.286028\pi$
$830$		0			0
$831$	7.21135	−	18.2216i	0.250159	−	0.632099i
$832$	−7.32410	+	0.640776i	−0.253918	+	0.0222149i
$833$	−4.86588	+	10.4349i	−0.168593	+	0.361548i
$834$	−6.15702	+	3.33025i	−0.213200	+	0.115317i
$835$		0			0
$836$		−	18.7448i		−	0.648301i
$837$	8.47863	+	4.85083i	0.293064	+	0.167669i
$838$	−62.3307	−	62.3307i	−2.15318	−	2.15318i
$839$	−8.06541	−	45.7412i	−0.278449	−	1.57916i	−0.727789	−	0.685802i	$-0.759452\pi$
$839$	−8.06541	−	45.7412i	−0.278449	−	1.57916i	0.449340	−	0.893361i	$-0.351659\pi$
$840$		0			0
$841$	21.3614	−	7.77490i	0.736599	−	0.268100i
$842$	−3.85112	−	44.0185i	−0.132718	−	1.51698i
$843$	−37.3998	−	4.32178i	−1.28812	−	0.148850i
$844$	−30.9571	+	85.0539i	−1.06559	+	2.92768i
$845$		0			0
$846$	−7.46146	+	31.8539i	−0.256530	+	1.09516i
$847$	8.41058	+	31.3887i	0.288991	+	1.07853i
$848$	−10.8348	+	123.842i	−0.372068	+	4.25276i
$849$	4.56789	−	22.2695i	0.156770	−	0.764288i
$850$		0			0
$851$	0.165907	+	0.0292538i	0.00568721	+	0.00100281i
$852$	−29.8402	−	45.2407i	−1.02231	−	1.54992i
$853$	−20.6498	−	1.80662i	−0.707035	−	0.0618575i	−0.272034	−	0.962288i	$-0.587696\pi$
$853$	−20.6498	−	1.80662i	−0.707035	−	0.0618575i	−0.435001	+	0.900430i	$0.643252\pi$
$854$	25.4755	−	44.1248i	0.871752	−	1.50992i
$855$		0			0
$856$	−60.8644	−	105.420i	−2.08030	−	3.60319i
$857$	1.85929	+	3.98725i	0.0635120	+	0.136202i	0.935502	−	0.353322i	$-0.114948\pi$
$857$	1.85929	+	3.98725i	0.0635120	+	0.136202i	−0.871990	+	0.489524i	$0.837170\pi$
$858$	−0.164858	+	1.42665i	−0.00562814	+	0.0487049i
$859$	27.5782	−	32.8664i	0.940956	−	1.12139i	−0.0514862	−	0.998674i	$-0.516396\pi$
$859$	27.5782	−	32.8664i	0.940956	−	1.12139i	0.992442	−	0.122714i	$-0.0391598\pi$
$860$		0			0
$861$	4.61318	−	7.50107i	0.157217	−	0.255636i
$862$	−31.4786	−	22.0415i	−1.07217	−	0.750738i
$863$	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
$865$		0			0
$866$	−61.0955	+	10.7728i	−2.07611	+	0.366074i
$867$	−2.32890	+	7.81631i	−0.0790936	+	0.265456i
$868$	26.6552	+	12.4295i	0.904736	+	0.421885i
$869$	−2.75902	−	2.31509i	−0.0935932	−	0.0785340i
$870$		0			0
$871$	2.41278	+	0.878181i	0.0817540	+	0.0297560i
$872$	−19.8588	+	74.1142i	−0.672505	+	2.50982i
$873$	−40.4856	−	5.82201i	−1.37023	−	0.197045i
$874$	−0.850406	−	0.490982i	−0.0287654	−	0.0166077i
$875$		0			0
$876$	82.3842	−	92.8188i	2.78350	−	3.13606i
$877$	−6.63310	−	9.47306i	−0.223984	−	0.319882i	0.691394	−	0.722478i	$-0.256997\pi$
$877$	−6.63310	−	9.47306i	−0.223984	−	0.319882i	−0.915378	+	0.402596i	$0.868108\pi$
$878$	−48.8243	−	69.7284i	−1.64774	−	2.35322i
$879$	−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	$0.586794\pi$
$882$	−19.3126	+	4.04050i	−0.650289	+	0.136051i
$883$	−4.11349	+	15.3517i	−0.138430	+	0.516627i	0.861530	+	0.507706i	$0.169506\pi$
$883$	−4.11349	+	15.3517i	−0.138430	+	0.516627i	−0.999960	+	0.00892106i	$0.997160\pi$
$884$	−10.4432	−	3.80103i	−0.351244	−	0.127842i
$885$		0			0
$886$	−36.6160	−	30.7245i	−1.23014	−	1.03221i
$887$	6.76369	+	3.15396i	0.227102	+	0.105900i	0.532839	−	0.846216i	$-0.321125\pi$
$887$	6.76369	+	3.15396i	0.227102	+	0.105900i	−0.305737	+	0.952116i	$0.598903\pi$
$888$	−24.7702	−	26.1861i	−0.831232	−	0.878747i
$889$	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
$893$	18.6396	+	13.0516i	0.623750	+	0.436755i
$894$	−98.1150	−	2.72628i	−3.28146	−	0.0911803i
$895$		0			0
$896$	−24.4930	+	29.1896i	−0.818253	+	0.975156i
$897$	0.0433504	+	0.0321851i	0.00144743	+	0.00107463i
$898$	−14.9255	−	32.0079i	−0.498072	−	1.06812i
$899$	−2.35319	−	4.07585i	−0.0784834	−	0.135937i
$900$		0			0
$901$	−24.8041	+	42.9619i	−0.826344	+	1.43127i
$902$	−2.90833	−	0.254446i	−0.0968367	−	0.00847211i
$903$	−20.0457	+	40.0450i	−0.667080	+	1.33261i
$904$	167.938	+	29.6120i	5.58553	+	0.984880i
$905$		0			0
$906$	27.3733	+	24.2960i	0.909415	+	0.807180i
$907$	−1.42792	+	16.3212i	−0.0474134	+	0.541937i	0.934928	+	0.354838i	$0.115464\pi$
$907$	−1.42792	+	16.3212i	−0.0474134	+	0.541937i	−0.982341	+	0.187099i	$0.940092\pi$
$908$	0.635223	+	2.37069i	0.0210806	+	0.0786740i
$909$	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	$0.123842\pi$
$912$	44.6177	+	103.064i	1.47744	+	3.41279i
$913$	0.328216	+	3.75152i	0.0108624	+	0.124157i
$914$	−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
$918$	−60.4628	+	22.2760i	−1.99557	+	0.735218i
$919$			5.68243i			0.187446i	0.995598	+	0.0937230i	$0.0298768\pi$
$919$			5.68243i			0.187446i	−0.995598	+	0.0937230i	$0.970123\pi$
$920$		0			0
$921$	−27.4866	−	16.9043i	−0.905714	−	0.557017i
$922$	−16.1703	+	34.6774i	−0.532541	+	1.14204i
$923$	2.87697	−	0.251702i	0.0946965	−	0.00828487i
$924$	11.1778	+	14.0987i	0.367724	+	0.463813i
$925$		0			0
$926$	−47.9543	+	27.6864i	−1.57588	+	0.909832i
$927$	48.9729	−	1.55334i	1.60848	−	0.0510183i
$928$	35.4544	−	9.49998i	1.16385	−	0.311852i
$929$	31.5686	−	26.4892i	1.03573	−	0.869082i	0.0442093	−	0.999022i	$-0.485923\pi$
$929$	31.5686	−	26.4892i	1.03573	−	0.869082i	0.991522	+	0.129941i	$0.0414787\pi$
$930$		0			0
$931$	−2.38300	+	13.5147i	−0.0780996	+	0.442925i
$932$	2.30468	−	1.61376i	0.0754924	−	0.0528604i
$933$	11.8560	−	7.82008i	0.388148	−	0.256018i
$934$	−42.1923	−	50.2828i	−1.38057	−	1.64530i
$935$		0			0
$936$	−3.34220	−	11.0582i	−0.109243	−	0.361450i
$937$	−7.80116	−	2.09031i	−0.254853	−	0.0682876i	0.129131	−	0.991628i	$-0.458781\pi$
$937$	−7.80116	−	2.09031i	−0.254853	−	0.0682876i	−0.383983	+	0.923340i	$0.625448\pi$
$938$	40.6235	−	18.9430i	1.32640	−	0.618512i
$939$	−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	$0.587072\pi$
$942$	14.6151	+	61.3082i	0.476186	+	1.99753i
$943$	−0.0629540	+	0.0899076i	−0.00205006	+	0.00292780i
$944$	−53.2626			−1.73355
$945$		0			0
$946$	14.8463			0.482696
$947$	27.9030	−	39.8496i	0.906726	−	1.29494i	−0.0484276	−	0.998827i	$-0.515421\pi$
$947$	27.9030	−	39.8496i	0.906726	−	1.29494i	0.955153	−	0.296112i	$-0.0956901\pi$
$948$	45.7735	+	13.6384i	1.48666	+	0.442955i
$949$	2.26190	+	6.21452i	0.0734244	+	0.201732i
$950$		0			0
$951$	−27.3479	−	10.8232i	−0.886816	−	0.350966i
$952$	−106.655	+	49.7340i	−3.45671	+	1.61189i
$953$	48.5541	+	13.0100i	1.57282	+	0.421436i	0.936694	−	0.350148i	$-0.113869\pi$
$953$	48.5541	+	13.0100i	1.57282	+	0.421436i	0.636127	+	0.771584i	$0.280535\pi$
$954$	−84.4117	+	10.0905i	−2.73293	+	0.326691i
$955$		0			0
$956$	−18.5120	−	22.0618i	−0.598722	−	0.713529i
$957$	−0.171171	−	2.87406i	−0.00553318	−	0.0929051i
$958$	−58.6039	+	41.0349i	−1.89341	+	1.32578i
$959$	3.59307	−	20.3773i	0.116026	−	0.658017i
$960$		0			0
$961$	−21.0402	+	17.6548i	−0.678716	+	0.569510i
$962$	3.05867	−	0.819569i	0.0986156	−	0.0264240i
$963$	33.1626	−	29.6682i	1.06865	−	0.956043i
$964$	8.06148	−	4.65430i	0.259643	−	0.149905i
$965$		0			0
$966$	0.932406	−	0.137825i	0.0299997	−	0.00443444i
$967$	49.5607	−	4.33600i	1.59377	−	0.139436i	0.744581	−	0.667533i	$-0.232650\pi$
$967$	49.5607	−	4.33600i	1.59377	−	0.139436i	0.849185	+	0.528096i	$0.177094\pi$
$968$	−36.6238	+	78.5400i	−1.17713	+	2.52437i
$969$	−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	$-0.223706\pi$
$972$	−66.4924	−	43.1118i	−2.13275	−	1.38281i
$973$	−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
$977$	−3.30670	−	37.7958i	−0.105791	−	1.20919i	−0.844644	−	0.535328i	$-0.820188\pi$
$977$	−3.30670	−	37.7958i	−0.105791	−	1.20919i	0.738854	−	0.673866i	$-0.235367\pi$
$978$	53.8093	−	72.4763i	1.72063	−	2.31754i
$979$	1.39948	−	3.84504i	0.0447276	−	0.122888i
$980$		0			0
$981$	−28.0041	−	1.55748i	−0.894102	−	0.0497264i
$982$	16.3345	+	60.9612i	0.521255	+	1.94535i
$983$	−3.12235	+	35.6886i	−0.0995874	+	1.13829i	0.767811	+	0.640676i	$0.221346\pi$
$983$	−3.12235	+	35.6886i	−0.0995874	+	1.13829i	−0.867399	+	0.497614i	$0.834210\pi$
$984$	22.2822	−	7.41591i	0.710330	−	0.236411i
$985$		0			0
$986$	30.5739	+	5.39101i	0.973672	+	0.171685i
$987$	−21.8025	+	1.29850i	−0.693981	+	0.0413316i
$988$	−13.1958	−	1.15448i	−0.419813	−	0.0367289i
$989$	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	$0.588649\pi$
$992$	11.6480	+	24.9793i	0.369826	+	0.793094i
$993$	−22.6081	+	9.78732i	−0.717447	+	0.310591i
$994$	32.4061	−	38.6201i	1.02786	−	1.22495i
$995$		0			0
$996$	−23.7590	−	43.9260i	−0.752833	−	1.39185i
$997$	19.9603	+	13.9764i	0.632150	+	0.442636i	0.845233	−	0.534398i	$-0.179462\pi$
$997$	19.9603	+	13.9764i	0.632150	+	0.442636i	−0.213083	+	0.977034i	$0.568351\pi$
$998$	−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.68.16		192
5.2	odd	4	inner	675.2.ba.b.257.16		192
5.3	odd	4		135.2.q.a.122.1	yes	192
5.4	even	2		135.2.q.a.68.1	yes	192
15.8	even	4		405.2.r.a.152.16		192
15.14	odd	2		405.2.r.a.233.16		192
27.2	odd	18	inner	675.2.ba.b.218.16		192
135.2	even	36	inner	675.2.ba.b.407.16		192
135.29	odd	18		135.2.q.a.83.1	yes	192
135.79	even	18		405.2.r.a.8.16		192
135.83	even	36		135.2.q.a.2.1	✓	192
135.133	odd	36		405.2.r.a.332.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.1	✓	192	135.83	even	36
135.2.q.a.68.1	yes	192	5.4	even	2
135.2.q.a.83.1	yes	192	135.29	odd	18
135.2.q.a.122.1	yes	192	5.3	odd	4
405.2.r.a.8.16		192	135.79	even	18
405.2.r.a.152.16		192	15.8	even	4
405.2.r.a.233.16		192	15.14	odd	2
405.2.r.a.332.16		192	135.133	odd	36
675.2.ba.b.68.16		192	1.1	even	1	trivial
675.2.ba.b.218.16		192	27.2	odd	18	inner
675.2.ba.b.257.16		192	5.2	odd	4	inner
675.2.ba.b.407.16		192	135.2	even	36	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+(1.52658 - 2.18018i) q^{2} +(-1.25829 + 1.19025i) q^{3} +(-1.73870 - 4.77703i) q^{4} +(0.674088 + 4.56031i) q^{6} +(-2.78918 + 1.30062i) q^{7} +(-7.92739 - 2.12414i) q^{8} +(0.166591 - 2.99537i) q^{9} +(-0.426793 - 0.508631i) q^{11} +(7.87366 + 3.94140i) q^{12} +(-0.384347 + 0.269123i) q^{13} +(-1.42232 + 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-4.50051 + 1.20591i) q^{17} +(-6.27613 - 4.93586i) q^{18} +(-4.80938 + 2.77670i) q^{19} +(1.96154 - 4.95639i) q^{21} +(-1.76044 + 0.154018i) q^{22} +(-0.0280775 + 0.0602123i) q^{23} +(12.5032 - 6.76283i) q^{24} +1.24878i q^{26} +(3.35563 + 3.96733i) q^{27} +(11.0626 + 11.0626i) q^{28} +(-0.434735 - 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(1.27781 + 14.6055i) q^{32} +(1.14243 + 0.132015i) q^{33} +(-4.24128 + 11.6528i) q^{34} +(-14.5986 + 4.41223i) q^{36} +(-0.656295 - 2.44933i) q^{37} +(-1.28820 + 14.7241i) q^{38} +(0.163296 - 0.796105i) q^{39} +(1.62695 + 0.286875i) q^{41} +(-7.81137 - 11.8428i) q^{42} +(-8.36925 - 0.732214i) q^{43} +(-1.68769 + 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(-1.73166 - 3.71355i) q^{47} +(2.32146 - 20.0895i) q^{48} +(1.58841 - 1.89299i) q^{49} +(4.22761 - 6.87413i) q^{51} +(1.95387 + 1.36812i) q^{52} +(7.52870 - 7.52870i) q^{53} +(13.7721 - 1.25944i) q^{54} +(24.8736 - 4.38589i) q^{56} +(2.74662 - 9.21828i) q^{57} +(-6.03890 - 2.81598i) q^{58} +(3.49452 + 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(1.29496 - 4.83286i) q^{62} +(3.43118 + 8.57130i) q^{63} +(13.5701 + 7.83468i) q^{64} +(2.03182 - 2.28917i) q^{66} +(-3.13881 - 4.48268i) q^{67} +(13.5857 + 19.4024i) q^{68} +(-0.0363384 - 0.109184i) q^{69} +(-5.33043 - 3.07752i) q^{71} +(-7.68321 + 23.3916i) q^{72} +(3.64803 - 13.6146i) q^{73} +(-6.34185 - 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(1.85194 + 0.863572i) q^{77} +(-1.48637 - 1.57133i) q^{78} +(5.34198 - 0.941936i) q^{79} +(-8.94450 - 0.998001i) q^{81} +(3.10910 - 3.10910i) q^{82} +(-4.64599 - 3.25316i) q^{83} +(-27.0873 - 0.752663i) q^{84} +(-14.3727 + 17.1287i) q^{86} +(3.48160 + 2.58488i) q^{87} +(2.30295 + 4.93869i) q^{88} +(3.08131 + 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(0.336454 + 0.0294359i) q^{92} +(-1.45751 + 2.91164i) q^{93} +(-10.7397 - 1.89370i) q^{94} +(-18.9921 - 16.8570i) q^{96} +(1.18828 - 13.5821i) q^{97} +(-1.70223 - 6.35281i) 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

L-functions

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