LMFDB - Embedded newform 896.2.bn.b.533.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$784$
Relative dimension:	$49$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			533.36
Character	$\chi$	$=$	896.533
Dual form			896.2.bn.b.701.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929496 + 1.06585i) q^{2} +(0.253065 + 0.207685i) q^{3} +(-0.272074 + 1.98141i) q^{4} +(1.24953 + 4.11915i) q^{5} +(0.0138617 + 0.462773i) q^{6} +(0.980785 + 0.195090i) q^{7} +(-2.36478 + 1.55172i) q^{8} +(-0.564362 - 2.83724i) q^{9} +O(q^{10})$	\(q+(0.929496 + 1.06585i) q^{2} +(0.253065 + 0.207685i) q^{3} +(-0.272074 + 1.98141i) q^{4} +(1.24953 + 4.11915i) q^{5} +(0.0138617 + 0.462773i) q^{6} +(0.980785 + 0.195090i) q^{7} +(-2.36478 + 1.55172i) q^{8} +(-0.564362 - 2.83724i) q^{9} +(-3.22896 + 5.16055i) q^{10} +(0.0251124 - 0.254971i) q^{11} +(-0.480362 + 0.444920i) q^{12} +(5.01358 + 1.52085i) q^{13} +(0.703699 + 1.22671i) q^{14} +(-0.539274 + 1.30192i) q^{15} +(-3.85195 - 1.07818i) q^{16} +(0.132192 + 0.319140i) q^{17} +(2.49950 - 3.23873i) q^{18} +(2.68250 + 5.01860i) q^{19} +(-8.50168 + 1.35512i) q^{20} +(0.207685 + 0.253065i) q^{21} +(0.295103 - 0.210228i) q^{22} +(4.53668 - 6.78962i) q^{23} +(-0.920712 - 0.0984426i) q^{24} +(-11.2487 + 7.51615i) q^{25} +(3.03910 + 6.75735i) q^{26} +(0.909405 - 1.70138i) q^{27} +(-0.653400 + 1.89026i) q^{28} +(-5.78100 + 0.569379i) q^{29} +(-1.88891 + 0.635347i) q^{30} +(-7.30033 - 7.30033i) q^{31} +(-2.43120 - 5.10777i) q^{32} +(0.0593088 - 0.0593088i) q^{33} +(-0.217283 + 0.437536i) q^{34} +(0.421915 + 4.28377i) q^{35} +(5.77528 - 0.346292i) q^{36} +(-2.20497 - 1.17858i) q^{37} +(-2.85571 + 7.52391i) q^{38} +(0.952904 + 1.42612i) q^{39} +(-9.34663 - 7.80194i) q^{40} +(-3.03746 - 2.02957i) q^{41} +(-0.0766871 + 0.456585i) q^{42} +(3.43185 - 2.81645i) q^{43} +(0.498369 + 0.119129i) q^{44} +(10.9818 - 5.86991i) q^{45} +(11.4535 - 1.47550i) q^{46} +(3.70578 - 1.53498i) q^{47} +(-0.750874 - 1.07284i) q^{48} +(0.923880 + 0.382683i) q^{49} +(-18.4667 - 5.00322i) q^{50} +(-0.0328275 + 0.108218i) q^{51} +(-4.37749 + 9.52016i) q^{52} +(5.24740 + 0.516824i) q^{53} +(2.65870 - 0.612134i) q^{54} +(1.08164 - 0.215152i) q^{55} +(-2.62206 + 1.06056i) q^{56} +(-0.363443 + 1.82715i) q^{57} +(-5.98029 - 5.63245i) q^{58} +(-2.16521 + 0.656808i) q^{59} +(-2.43292 - 1.42274i) q^{60} +(1.46000 - 1.77902i) q^{61} +(0.995431 - 14.5667i) q^{62} -2.89282i q^{63} +(3.18433 - 7.33894i) q^{64} +22.5520i q^{65} +(0.118342 + 0.00808701i) q^{66} +(-2.04894 + 2.49664i) q^{67} +(-0.668313 + 0.175097i) q^{68} +(2.55818 - 0.776015i) q^{69} +(-4.17369 + 4.43145i) q^{70} +(0.933779 - 4.69443i) q^{71} +(5.73719 + 5.83370i) q^{72} +(9.53654 - 1.89693i) q^{73} +(-0.793319 - 3.44565i) q^{74} +(-4.40766 - 0.434116i) q^{75} +(-10.6737 + 3.94969i) q^{76} +(0.0743722 - 0.245172i) q^{77} +(-0.634312 + 2.34123i) q^{78} +(-1.93848 - 0.802944i) q^{79} +(-0.371950 - 17.2140i) q^{80} +(-7.43437 + 3.07942i) q^{81} +(-0.660094 - 5.12395i) q^{82} +(1.81848 - 0.971996i) q^{83} +(-0.557931 + 0.342657i) q^{84} +(-1.14941 + 0.943294i) q^{85} +(6.19181 + 1.03996i) q^{86} +(-1.58122 - 1.05654i) q^{87} +(0.336258 + 0.641916i) q^{88} +(5.76047 + 8.62115i) q^{89} +(16.4640 + 6.24893i) q^{90} +(4.62054 + 2.46973i) q^{91} +(12.2187 + 10.8363i) q^{92} +(-0.331289 - 3.36363i) q^{93} +(5.08057 + 2.52304i) q^{94} +(-17.3205 + 17.3205i) q^{95} +(0.445557 - 1.79752i) q^{96} +(-11.7188 - 11.7188i) q^{97} +(0.450859 + 1.34042i) q^{98} +(-0.737586 + 0.0726459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q+O(q^{10}) $ 784 * q	$ 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) $ 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{32}\right)$

Coefficient data

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

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

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

$2$	0.929496	+	1.06585i	0.657253	+	0.753670i
$2$	0.929496	+	1.06585i	0.657253	+	0.753670i
$3$	0.253065	+	0.207685i	0.146107	+	0.119907i	0.704608	−	0.709597i	$-0.251123\pi$
$3$	0.253065	+	0.207685i	0.146107	+	0.119907i	−0.558500	+	0.829504i	$0.688623\pi$
$4$	−0.272074	+	1.98141i	−0.136037	+	0.990704i
$5$	1.24953	+	4.11915i	0.558807	+	1.84214i	0.538951	+	0.842337i	$0.318821\pi$
$5$	1.24953	+	4.11915i	0.558807	+	1.84214i	0.0198555	+	0.999803i	$0.493679\pi$
$6$	0.0138617	+	0.462773i	0.00565903	+	0.188926i
$7$	0.980785	+	0.195090i	0.370702	+	0.0737372i
$7$	0.980785	+	0.195090i	0.370702	+	0.0737372i
$8$	−2.36478	+	1.55172i	−0.836074	+	0.548616i
$9$	−0.564362	−	2.83724i	−0.188121	−	0.945747i
$10$	−3.22896	+	5.16055i	−1.02109	+	1.63191i
$11$	0.0251124	−	0.254971i	0.00757168	−	0.0768766i	−0.990656	−	0.136382i	$-0.956452\pi$
$11$	0.0251124	−	0.254971i	0.00757168	−	0.0768766i	0.998228	+	0.0595057i	$0.0189525\pi$
$12$	−0.480362	+	0.444920i	−0.138669	+	0.128437i
$13$	5.01358	+	1.52085i	1.39052	+	0.421808i	0.894719	−	0.446630i	$-0.147376\pi$
$13$	5.01358	+	1.52085i	1.39052	+	0.421808i	0.495797	+	0.868438i	$0.334876\pi$
$14$	0.703699	+	1.22671i	0.188071	+	0.327851i
$15$	−0.539274	+	1.30192i	−0.139240	+	0.336155i
$16$	−3.85195	−	1.07818i	−0.962988	−	0.269545i
$17$	0.132192	+	0.319140i	0.0320613	+	0.0774028i	0.939099	−	0.343646i	$-0.111662\pi$
$17$	0.132192	+	0.319140i	0.0320613	+	0.0774028i	−0.907038	+	0.421049i	$0.861662\pi$
$18$	2.49950	−	3.23873i	0.589138	−	0.763376i
$19$	2.68250	+	5.01860i	0.615407	+	1.15135i	0.975825	+	0.218555i	$0.0701342\pi$
$19$	2.68250	+	5.01860i	0.615407	+	1.15135i	−0.360418	+	0.932791i	$0.617366\pi$
$20$	−8.50168	+	1.35512i	−1.90103	+	0.303013i
$21$	0.207685	+	0.253065i	0.0453207	+	0.0552234i
$22$	0.295103	−	0.210228i	0.0629161	−	0.0448208i
$23$	4.53668	−	6.78962i	0.945963	−	1.41573i	0.0367855	−	0.999323i	$-0.488288\pi$
$23$	4.53668	−	6.78962i	0.945963	−	1.41573i	0.909177	−	0.416410i	$-0.136712\pi$
$24$	−0.920712	−	0.0984426i	−0.187940	−	0.0200945i
$25$	−11.2487	+	7.51615i	−2.24974	+	1.50323i
$26$	3.03910	+	6.75735i	0.596017	+	1.32523i
$27$	0.909405	−	1.70138i	0.175015	−	0.327430i
$28$	−0.653400	+	1.89026i	−0.123481	+	0.357225i
$29$	−5.78100	+	0.569379i	−1.07350	+	0.105731i	−0.619291	−	0.785162i	$-0.712580\pi$
$29$	−5.78100	+	0.569379i	−1.07350	+	0.105731i	−0.454214	+	0.890893i	$0.650080\pi$
$30$	−1.88891	+	0.635347i	−0.344866	+	0.115998i
$31$	−7.30033	−	7.30033i	−1.31118	−	1.31118i	−0.920547	−	0.390631i	$-0.872257\pi$
$31$	−7.30033	−	7.30033i	−1.31118	−	1.31118i	−0.390631	−	0.920547i	$-0.627743\pi$
$32$	−2.43120	−	5.10777i	−0.429779	−	0.902934i
$33$	0.0593088	−	0.0593088i	0.0103243	−	0.0103243i
$34$	−0.217283	+	0.437536i	−0.0372638	+	0.0750369i
$35$	0.421915	+	4.28377i	0.0713166	+	0.724090i
$36$	5.77528	−	0.346292i	0.962546	−	0.0577154i
$37$	−2.20497	−	1.17858i	−0.362494	−	0.193757i	0.280087	−	0.959975i	$-0.409637\pi$
$37$	−2.20497	−	1.17858i	−0.362494	−	0.193757i	−0.642582	+	0.766217i	$0.722137\pi$
$38$	−2.85571	+	7.52391i	−0.463257	+	1.22054i
$39$	0.952904	+	1.42612i	0.152587	+	0.228362i
$40$	−9.34663	−	7.80194i	−1.47783	−	1.23360i
$41$	−3.03746	−	2.02957i	−0.474372	−	0.316965i	0.295300	−	0.955404i	$-0.404580\pi$
$41$	−3.03746	−	2.02957i	−0.474372	−	0.316965i	−0.769672	+	0.638439i	$0.779580\pi$
$42$	−0.0766871	+	0.456585i	−0.0118331	+	0.0704526i
$43$	3.43185	−	2.81645i	0.523353	−	0.429504i	−0.335263	−	0.942125i	$-0.608825\pi$
$43$	3.43185	−	2.81645i	0.523353	−	0.429504i	0.858615	+	0.512620i	$0.171325\pi$
$44$	0.498369	+	0.119129i	0.0751319	+	0.0179594i
$45$	10.9818	−	5.86991i	1.63707	−	0.875034i
$46$	11.4535	−	1.47550i	1.68873	−	0.217551i
$47$	3.70578	−	1.53498i	0.540543	−	0.223900i	−0.0956706	−	0.995413i	$-0.530500\pi$
$47$	3.70578	−	1.53498i	0.540543	−	0.223900i	0.636214	+	0.771513i	$0.280500\pi$
$48$	−0.750874	−	1.07284i	−0.108379	−	0.154852i
$49$	0.923880	+	0.382683i	0.131983	+	0.0546691i
$50$	−18.4667	−	5.00322i	−2.61159	−	0.707562i
$51$	−0.0328275	+	0.108218i	−0.00459677	+	0.0151535i
$52$	−4.37749	+	9.52016i	−0.607049	+	1.32021i
$53$	5.24740	+	0.516824i	0.720787	+	0.0709913i	0.451757	−	0.892141i	$-0.350797\pi$
$53$	5.24740	+	0.516824i	0.720787	+	0.0709913i	0.269029	+	0.963132i	$0.413297\pi$
$54$	2.65870	−	0.612134i	0.361804	−	0.0833009i
$55$	1.08164	−	0.215152i	0.145849	−	0.0290111i
$56$	−2.62206	+	1.06056i	−0.350388	+	0.141723i
$57$	−0.363443	+	1.82715i	−0.0481391	+	0.242012i
$58$	−5.98029	−	5.63245i	−0.785251	−	0.739576i
$59$	−2.16521	+	0.656808i	−0.281886	+	0.0855092i	−0.428062	−	0.903749i	$-0.640803\pi$
$59$	−2.16521	+	0.656808i	−0.281886	+	0.0855092i	0.146176	+	0.989259i	$0.453303\pi$
$60$	−2.43292	−	1.42274i	−0.314088	−	0.183675i
$61$	1.46000	−	1.77902i	0.186934	−	0.227780i	−0.671108	−	0.741360i	$-0.734181\pi$
$61$	1.46000	−	1.77902i	0.186934	−	0.227780i	0.858041	+	0.513580i	$0.171681\pi$
$62$	0.995431	−	14.5667i	0.126420	−	1.84997i
$63$		−	2.89282i		−	0.364462i
$64$	3.18433	−	7.33894i	0.398041	−	0.917368i
$65$			22.5520i			2.79723i
$66$	0.118342	+	0.00808701i	0.0145668	+	0.000995442i
$67$	−2.04894	+	2.49664i	−0.250318	+	0.305013i	−0.882976	−	0.469418i	$-0.844464\pi$
$67$	−2.04894	+	2.49664i	−0.250318	+	0.305013i	0.632658	+	0.774431i	$0.281964\pi$
$68$	−0.668313	+	0.175097i	−0.0810448	+	0.0212336i
$69$	2.55818	−	0.776015i	0.307969	−	0.0934213i
$70$	−4.17369	+	4.43145i	−0.498852	+	0.529659i
$71$	0.933779	−	4.69443i	0.110819	−	0.557126i	−0.884985	−	0.465619i	$-0.845832\pi$
$71$	0.933779	−	4.69443i	0.110819	−	0.557126i	0.995804	−	0.0915068i	$-0.0291683\pi$
$72$	5.73719	+	5.83370i	0.676135	+	0.687509i
$73$	9.53654	−	1.89693i	1.11617	−	0.222019i	0.397656	−	0.917535i	$-0.369824\pi$
$73$	9.53654	−	1.89693i	1.11617	−	0.222019i	0.718511	+	0.695515i	$0.244824\pi$
$74$	−0.793319	−	3.44565i	−0.0922215	−	0.400549i
$75$	−4.40766	−	0.434116i	−0.508952	−	0.0501274i
$76$	−10.6737	+	3.94969i	−1.22436	+	0.453061i
$77$	0.0743722	−	0.245172i	0.00847550	−	0.0279400i
$78$	−0.634312	+	2.34123i	−0.0718217	+	0.265092i
$79$	−1.93848	−	0.802944i	−0.218096	−	0.0903383i	0.270960	−	0.962590i	$-0.412659\pi$
$79$	−1.93848	−	0.802944i	−0.218096	−	0.0903383i	−0.489056	+	0.872252i	$0.662659\pi$
$80$	−0.371950	−	17.2140i	−0.0415853	−	1.92458i
$81$	−7.43437	+	3.07942i	−0.826042	+	0.342158i
$82$	−0.660094	−	5.12395i	−0.0728952	−	0.565846i
$83$	1.81848	−	0.971996i	0.199604	−	0.106690i	−0.368567	−	0.929601i	$-0.620151\pi$
$83$	1.81848	−	0.971996i	0.199604	−	0.106690i	0.568171	+	0.822911i	$0.307651\pi$
$84$	−0.557931	+	0.342657i	−0.0608753	+	0.0373869i
$85$	−1.14941	+	0.943294i	−0.124671	+	0.102315i
$86$	6.19181	+	1.03996i	0.667680	+	0.112142i
$87$	−1.58122	−	1.05654i	−0.169525	−	0.113273i
$88$	0.336258	+	0.641916i	0.0358452	+	0.0684285i
$89$	5.76047	+	8.62115i	0.610608	+	0.913840i	0.999974	−	0.00724338i	$-0.00230566\pi$
$89$	5.76047	+	8.62115i	0.610608	+	0.913840i	−0.389365	+	0.921083i	$0.627306\pi$
$90$	16.4640	+	6.24893i	1.73546	+	0.658695i
$91$	4.62054	+	2.46973i	0.484364	+	0.258898i
$92$	12.2187	+	10.8363i	1.27389	+	1.12976i
$93$	−0.331289	−	3.36363i	−0.0343531	−	0.348793i
$94$	5.08057	+	2.52304i	0.524021	+	0.260232i
$95$	−17.3205	+	17.3205i	−1.77705	+	1.77705i
$96$	0.445557	−	1.79752i	0.0454745	−	0.183459i
$97$	−11.7188	−	11.7188i	−1.18986	−	1.18986i	−0.977105	−	0.212757i	$-0.931756\pi$
$97$	−11.7188	−	11.7188i	−1.18986	−	1.18986i	−0.212757	−	0.977105i	$-0.568244\pi$
$98$	0.450859	+	1.34042i	0.0455437	+	0.135403i
$99$	−0.737586	+	0.0726459i	−0.0741302	+	0.00730118i
$100$	−11.8321	−	24.3332i	−1.18321	−	2.43332i
$101$	−8.55421	+	16.0038i	−0.851176	+	1.59244i	−0.0463514	+	0.998925i	$0.514759\pi$
$101$	−8.55421	+	16.0038i	−0.851176	+	1.59244i	−0.804824	+	0.593513i	$0.797741\pi$
$102$	−0.145857	+	0.0655987i	−0.0144420	+	0.00649524i
$103$	6.96459	−	4.65359i	0.686241	−	0.458532i	−0.162938	−	0.986636i	$-0.552097\pi$
$103$	6.96459	−	4.65359i	0.686241	−	0.458532i	0.849179	+	0.528104i	$0.177097\pi$
$104$	−14.2159	+	4.18320i	−1.39399	+	0.410196i
$105$	−0.782905	+	1.17170i	−0.0764037	+	0.114346i
$106$	4.32659	+	6.07333i	0.420235	+	0.589894i
$107$	8.48135	+	10.3346i	0.819923	+	0.999080i	0.999881	+	0.0154052i	$0.00490383\pi$
$107$	8.48135	+	10.3346i	0.819923	+	0.999080i	−0.179958	+	0.983674i	$0.557596\pi$
$108$	3.12370	+	2.26480i	0.300578	+	0.217931i
$109$	5.22897	+	9.78272i	0.500845	+	0.937015i	0.997608	+	0.0691283i	$0.0220218\pi$
$109$	5.22897	+	9.78272i	0.500845	+	0.937015i	−0.496763	+	0.867886i	$0.665478\pi$
$110$	1.23470	+	0.952885i	0.117724	+	0.0908540i
$111$	−0.313227	−	0.756197i	−0.0297302	−	0.0717751i
$112$	−3.56760	−	1.80894i	−0.337106	−	0.170929i
$113$	−4.29865	+	10.3779i	−0.404383	+	0.976267i	0.582206	+	0.813041i	$0.302190\pi$
$113$	−4.29865	+	10.3779i	−0.404383	+	0.976267i	−0.986589	+	0.163225i	$0.947810\pi$
$114$	−2.28529	+	1.31095i	−0.214037	+	0.122782i
$115$	33.6362	+	10.2034i	3.13659	+	0.951474i
$116$	0.444688	−	11.6094i	0.0412883	−	1.07791i
$117$	1.48555	−	15.0830i	0.137339	−	1.39443i
$118$	−2.71261	−	1.69729i	−0.249716	−	0.156248i
$119$	0.0673910	+	0.338797i	0.00617772	+	0.0310575i
$120$	−0.744958	−	3.91556i	−0.0680051	−	0.357440i
$121$	10.7243	+	2.13319i	0.974933	+	0.193926i
$122$	3.25323	−	0.0974461i	0.294533	−	0.00882236i
$123$	−0.347165	−	1.14445i	−0.0313028	−	0.103191i
$124$	16.4512	−	12.4787i	1.47736	−	1.12062i
$125$	−28.3787	−	23.2898i	−2.53826	−	2.08310i
$126$	3.08332	−	2.68887i	0.274684	−	0.239544i
$127$	18.6397			1.65401			0.827003	−	0.562198i	$-0.190044\pi$
$127$	18.6397			1.65401			0.827003	+	0.562198i	$0.190044\pi$
$128$	10.7820	−	3.42750i	0.953006	−	0.302951i
$129$	1.45342			0.127966
$130$	−24.0371	+	20.9620i	−2.10819	+	1.83849i
$131$	6.47844	+	5.31672i	0.566024	+	0.464524i	0.873359	−	0.487078i	$-0.161937\pi$
$131$	6.47844	+	5.31672i	0.566024	+	0.464524i	−0.307335	+	0.951601i	$0.599437\pi$
$132$	0.101379	+	0.133651i	0.00882387	+	0.0116328i
$133$	1.65187	+	5.44550i	0.143236	+	0.472185i
$134$	−4.56553	+	0.136754i	−0.394402	+	0.0118138i
$135$	8.14456	+	1.62005i	0.700972	+	0.139432i
$136$	−0.807821	−	0.549569i	−0.0692701	−	0.0471252i
$137$	−0.622920	−	3.13163i	−0.0532197	−	0.267553i	0.945009	−	0.327044i	$-0.106052\pi$
$137$	−0.622920	−	3.13163i	−0.0532197	−	0.267553i	−0.998229	+	0.0594904i	$0.981052\pi$
$138$	3.20493	+	2.00533i	0.272822	+	0.170705i
$139$	1.44815	−	14.7033i	0.122830	−	1.24712i	−0.714192	−	0.699950i	$-0.753206\pi$
$139$	1.44815	−	14.7033i	0.122830	−	1.24712i	0.837022	−	0.547169i	$-0.184294\pi$
$140$	−8.60269	−	0.329518i	−0.727060	−	0.0278493i
$141$	1.25660	+	0.381185i	0.105825	+	0.0321016i
$142$	5.87150	−	3.36818i	0.492725	−	0.282652i
$143$	0.513676	−	1.24012i	0.0429557	−	0.103704i
$144$	−0.885157	+	11.5374i	−0.0737630	+	0.961449i
$145$	−9.56889	−	23.1014i	−0.794653	−	1.91846i
$146$	10.8860	+	8.40133i	0.900934	+	0.695299i
$147$	0.154324	+	0.288720i	0.0127284	+	0.0238132i
$148$	2.93516	−	4.04828i	0.241269	−	0.332766i
$149$	−6.48951	−	7.90749i	−0.531641	−	0.647807i	0.436057	−	0.899919i	$-0.356375\pi$
$149$	−6.48951	−	7.90749i	−0.531641	−	0.647807i	−0.967698	+	0.252112i	$0.918875\pi$
$150$	−3.63420	−	5.10141i	−0.296731	−	0.416529i
$151$	−5.57717	+	8.34682i	−0.453863	+	0.679255i	−0.985875	−	0.167482i	$-0.946436\pi$
$151$	−5.57717	+	8.34682i	−0.453863	+	0.679255i	0.532012	+	0.846737i	$0.321436\pi$
$152$	−14.1310	−	7.70538i	−1.14617	−	0.624989i
$153$	0.830873	−	0.555171i	0.0671721	−	0.0448829i
$154$	0.330446	−	0.148617i	0.0266281	−	0.0119759i
$155$	20.9492	−	39.1931i	1.68268	−	3.14807i
$156$	−3.08499	+	1.50008i	−0.246997	+	0.120103i
$157$	8.05343	−	0.793194i	0.642734	−	0.0633038i	0.228601	−	0.973520i	$-0.426585\pi$
$157$	8.05343	−	0.793194i	0.642734	−	0.0633038i	0.414133	+	0.910216i	$0.364085\pi$
$158$	−0.945990	−	2.81246i	−0.0752589	−	0.223747i
$159$	1.22060	+	1.22060i	0.0967998	+	0.0967998i
$160$	18.0018	−	16.3968i	1.42317	−	1.29628i
$161$	5.77409	−	5.77409i	0.455062	−	0.455062i
$162$	−10.1924	−	5.06162i	−0.800792	−	0.397679i
$163$	−0.777254	−	7.89160i	−0.0608793	−	0.618118i	−0.976418	−	0.215888i	$-0.930735\pi$
$163$	−0.777254	−	7.89160i	−0.0608793	−	0.618118i	0.915539	−	0.402230i	$-0.131765\pi$
$164$	4.84781	−	5.46625i	0.378550	−	0.426843i
$165$	0.318410	+	0.170194i	0.0247882	+	0.0132496i
$166$	2.72627	+	1.03476i	0.211600	+	0.0803128i
$167$	6.67821	+	9.99465i	0.516776	+	0.773409i	0.994459	−	0.105122i	$-0.0335235\pi$
$167$	6.67821	+	9.99465i	0.516776	+	0.773409i	−0.477684	+	0.878532i	$0.658523\pi$
$168$	−0.883816	−	0.276173i	−0.0681879	−	0.0213072i
$169$	12.0139	+	8.02740i	0.924143	+	0.617493i
$170$	−2.07378	−	0.348308i	−0.159052	−	0.0267140i
$171$	12.7251	−	10.4432i	0.973111	−	0.798611i
$172$	4.64681	+	7.56618i	0.354316	+	0.576916i
$173$	−19.4246	+	10.3827i	−1.47683	+	0.789380i	−0.996162	−	0.0875247i	$-0.972104\pi$
$173$	−19.4246	+	10.3827i	−1.47683	+	0.789380i	−0.480664	+	0.876905i	$0.659604\pi$
$174$	−0.343628	−	2.66740i	−0.0260503	−	0.202215i
$175$	−12.4989	+	5.17722i	−0.944829	+	0.391361i
$176$	−0.371636	+	0.955059i	−0.0280131	+	0.0719903i
$177$	−0.684348	−	0.283466i	−0.0514388	−	0.0213066i
$178$	−3.83452	+	14.1531i	−0.287410	+	1.06082i
$179$	2.58416	−	8.51882i	0.193149	−	0.636726i	−0.805855	−	0.592112i	$-0.798294\pi$
$179$	2.58416	−	8.51882i	0.193149	−	0.636726i	0.999004	−	0.0446141i	$-0.0142058\pi$
$180$	8.64281	+	23.3565i	0.644197	+	1.74089i
$181$	6.99446	+	0.688894i	0.519894	+	0.0512051i	0.354561	−	0.935033i	$-0.384630\pi$
$181$	6.99446	+	0.688894i	0.519894	+	0.0512051i	0.165333	+	0.986238i	$0.447130\pi$
$182$	1.66241	+	7.22041i	0.123226	+	0.535212i
$183$	0.738951	−	0.146986i	0.0546248	−	0.0108656i
$184$	−0.192636	+	23.0956i	−0.0142013	+	1.70263i
$185$	2.09957	−	10.5553i	0.154364	−	0.776038i
$186$	3.27720	−	3.47959i	0.240296	−	0.255136i
$187$	0.0846911	−	0.0256908i	0.00619322	−	0.00187869i
$188$	2.03318	+	7.76029i	0.148285	+	0.565977i
$189$	1.22385	−	1.49127i	0.0890222	−	0.108474i
$190$	−34.5604	−	2.36172i	−2.50727	−	0.171337i
$191$			9.68843i			0.701030i	0.936557	+	0.350515i	$0.113993\pi$
$191$			9.68843i			0.701030i	−0.936557	+	0.350515i	$0.886007\pi$
$192$	2.33003	−	1.19589i	0.168156	−	0.0863062i
$193$		−	8.47204i		−	0.609831i	−0.952379	−	0.304916i	$-0.901372\pi$
$193$		−	8.47204i		−	0.609831i	0.952379	−	0.304916i	$-0.0986282\pi$
$194$	1.59791	−	23.3830i	0.114723	−	1.67880i
$195$	−4.68373	+	5.70714i	−0.335409	+	0.408697i
$196$	−1.00962	+	1.72646i	−0.0721154	+	0.123319i
$197$	−16.4225	+	4.98170i	−1.17005	+	0.354932i	−0.814746	−	0.579818i	$-0.803124\pi$
$197$	−16.4225	+	4.98170i	−1.17005	+	0.354932i	−0.355307	+	0.934750i	$0.615624\pi$
$198$	−0.763013	−	0.718632i	−0.0542250	−	0.0510710i
$199$	4.39957	−	22.1181i	0.311877	−	1.56791i	−0.433426	−	0.901189i	$-0.642696\pi$
$199$	4.39957	−	22.1181i	0.311877	−	1.56791i	0.745304	−	0.666725i	$-0.232304\pi$
$200$	14.9377	−	35.2289i	1.05626	−	2.49106i
$201$	−1.03703	+	0.206279i	−0.0731466	+	0.0145498i
$202$	−25.0088	+	5.75796i	−1.75961	+	0.405129i
$203$	−5.78100	−	0.569379i	−0.405747	−	0.0399626i
$204$	−0.205492	−	0.0944878i	−0.0143873	−	0.00661547i
$205$	4.56469	−	15.0478i	0.318812	−	1.05098i
$206$	11.4336	+	3.09772i	0.796616	+	0.215828i
$207$	−21.8241	−	9.03984i	−1.51688	−	0.628312i
$208$	−17.6723	−	11.2638i	−1.22535	−	0.781003i
$209$	1.34696	−	0.557929i	0.0931712	−	0.0385928i
$210$	−1.97656	+	0.254631i	−0.136396	+	0.0175712i
$211$	−20.6896	+	11.0588i	−1.42433	+	0.761322i	−0.990217	−	0.139535i	$-0.955439\pi$
$211$	−20.6896	+	11.0588i	−1.42433	+	0.761322i	−0.434117	+	0.900857i	$0.642939\pi$
$212$	−2.45172	+	10.2566i	−0.168385	+	0.704428i
$213$	1.21127	−	0.994064i	0.0829949	−	0.0681122i
$214$	−3.13171	+	18.6458i	−0.214079	+	1.27460i
$215$	15.8896	+	10.6171i	1.08366	+	0.724078i
$216$	0.489523	+	5.43452i	0.0333078	+	0.369772i
$217$	−5.73583	−	8.58428i	−0.389374	−	0.582739i
$218$	−5.56661	+	14.6663i	−0.377018	+	0.993327i
$219$	2.80733	+	1.50055i	0.189702	+	0.101398i
$220$	0.132017	+	2.20171i	0.00890059	+	0.148439i
$221$	0.177391	+	1.80108i	0.0119326	+	0.121154i
$222$	0.514850	−	1.03674i	0.0345545	−	0.0695811i
$223$	5.13206	−	5.13206i	0.343668	−	0.343668i	−0.514076	−	0.857744i	$-0.671865\pi$
$223$	5.13206	−	5.13206i	0.343668	−	0.343668i	0.857744	+	0.514076i	$0.171865\pi$
$224$	−1.38801	−	5.48393i	−0.0927400	−	0.366410i
$225$	27.6735	+	27.6735i	1.84490	+	1.84490i
$226$	−15.0568	+	5.06446i	−1.00156	+	0.336883i
$227$	−3.35967	+	0.330899i	−0.222989	+	0.0219625i	−0.208895	−	0.977938i	$-0.566987\pi$
$227$	−3.35967	+	0.330899i	−0.222989	+	0.0219625i	−0.0140946	+	0.999901i	$0.504487\pi$
$228$	−3.52144	−	1.21725i	−0.233213	−	0.0806142i
$229$	9.14168	−	17.1029i	0.604099	−	1.13019i	−0.375042	−	0.927008i	$-0.622372\pi$
$229$	9.14168	−	17.1029i	0.604099	−	1.13019i	0.979141	−	0.203182i	$-0.0651284\pi$
$230$	20.3894	+	45.3352i	1.34443	+	2.98931i
$231$	0.0697398	−	0.0465986i	0.00458854	−	0.00306596i
$232$	12.7873	−	10.3170i	0.839524	−	0.677341i
$233$	−3.91030	+	5.85218i	−0.256173	+	0.383389i	−0.937157	−	0.348909i	$-0.886552\pi$
$233$	−3.91030	+	5.85218i	−0.256173	+	0.383389i	0.680984	+	0.732298i	$0.261552\pi$
$234$	17.4571	−	12.4362i	1.14120	−	0.812983i
$235$	10.9533	+	13.3466i	0.714515	+	0.870639i
$236$	−0.712309	−	4.46886i	−0.0463673	−	0.290898i
$237$	−0.323802	−	0.605791i	−0.0210332	−	0.0393504i
$238$	−0.298468	+	0.386739i	−0.0193468	+	0.0250686i
$239$	−8.46104	−	20.4267i	−0.547299	−	1.32130i	−0.919480	−	0.393136i	$-0.871390\pi$
$239$	−8.46104	−	20.4267i	−0.547299	−	1.32130i	0.372181	−	0.928160i	$-0.378610\pi$
$240$	3.48096	−	4.43351i	0.224695	−	0.286182i
$241$	2.80611	−	6.77455i	0.180757	−	0.436387i	−0.807366	−	0.590051i	$-0.799107\pi$
$241$	2.80611	−	6.77455i	0.180757	−	0.436387i	0.988123	+	0.153664i	$0.0491074\pi$
$242$	7.69450	+	13.4132i	0.494621	+	0.862236i
$243$	−8.05924	−	2.44474i	−0.517000	−	0.156830i
$244$	3.12773	+	3.37688i	0.200232	+	0.216183i
$245$	−0.421915	+	4.28377i	−0.0269551	+	0.273680i
$246$	0.897123	−	1.43379i	0.0571985	−	0.0914149i
$247$	5.81636	+	29.2408i	0.370086	+	1.86055i
$248$	28.5917	+	5.93557i	1.81558	+	0.376909i
$249$	0.662063	+	0.131693i	0.0419565	+	0.00834568i
$250$	−1.55445	−	51.8952i	−0.0983121	−	3.28214i
$251$	1.32264	+	4.36015i	0.0834841	+	0.275210i	0.988737	−	0.149663i	$-0.0478188\pi$
$251$	1.32264	+	4.36015i	0.0834841	+	0.275210i	−0.905253	+	0.424873i	$0.860319\pi$
$252$	5.73186	+	0.787062i	0.361074	+	0.0495803i
$253$	−1.61723	−	1.32722i	−0.101674	−	0.0834419i
$254$	17.3255	+	19.8671i	1.08710	+	1.24657i
$255$	−0.486784			−0.0304836
$256$	13.6751	+	8.30619i	0.854691	+	0.519137i
$257$	2.81094			0.175341			0.0876707	−	0.996150i	$-0.472058\pi$
$257$	2.81094			0.175341			0.0876707	+	0.996150i	$0.472058\pi$
$258$	1.35095	+	1.54913i	0.0841062	+	0.0964444i
$259$	−1.93267	−	1.58610i	−0.120090	−	0.0985556i
$260$	−44.6848	−	6.13582i	−2.77123	−	0.380527i
$261$	4.87804	+	16.0808i	0.301943	+	0.995373i
$262$	0.354859	+	11.8469i	0.0219232	+	0.731905i
$263$	10.7311	+	2.13454i	0.661705	+	0.131621i	0.514508	−	0.857486i	$-0.327975\pi$
$263$	10.7311	+	2.13454i	0.661705	+	0.131621i	0.147197	+	0.989107i	$0.452975\pi$
$264$	−0.0482213	+	0.232283i	−0.00296782	+	0.0142960i
$265$	4.42792	+	22.2606i	0.272005	+	1.36746i
$266$	−4.26868	+	6.82222i	−0.261729	+	0.418297i
$267$	−0.332712	+	3.37808i	−0.0203616	+	0.206735i
$268$	−4.38940	−	4.73906i	−0.268125	−	0.289484i
$269$	−5.86152	−	1.77807i	−0.357383	−	0.108411i	0.106487	−	0.994314i	$-0.466040\pi$
$269$	−5.86152	−	1.77807i	−0.357383	−	0.108411i	−0.463870	+	0.885903i	$0.653540\pi$
$270$	5.84360	+	10.1867i	0.355630	+	0.619944i
$271$	−4.40125	+	10.6255i	−0.267357	+	0.645456i	−0.999357	−	0.0358480i	$-0.988587\pi$
$271$	−4.40125	+	10.6255i	−0.267357	+	0.645456i	0.732001	+	0.681304i	$0.238587\pi$
$272$	−0.165108	−	1.37184i	−0.0100111	−	0.0831799i
$273$	0.656372	+	1.58462i	0.0397254	+	0.0959057i
$274$	2.75885	−	3.57478i	0.166668	−	0.215960i
$275$	1.63392	+	3.05684i	0.0985289	+	0.184335i
$276$	0.841589	+	5.27993i	0.0506577	+	0.317814i
$277$	−14.7568	−	17.9813i	−0.886652	−	1.08039i	−0.996259	−	0.0864137i	$-0.972459\pi$
$277$	−14.7568	−	17.9813i	−0.886652	−	1.08039i	0.109607	−	0.993975i	$-0.465041\pi$
$278$	17.0176	−	12.1232i	1.02065	−	0.727099i
$279$	−16.5928	+	24.8328i	−0.993383	+	1.48670i
$280$	−7.64495	−	9.47547i	−0.456873	−	0.566267i
$281$	−14.2057	+	9.49192i	−0.847439	+	0.566241i	−0.901738	−	0.432284i	$-0.857708\pi$
$281$	−14.2057	+	9.49192i	−0.847439	+	0.566241i	0.0542983	+	0.998525i	$0.482708\pi$
$282$	0.761717	+	1.69366i	0.0453596	+	0.100856i
$283$	5.64788	−	10.5664i	0.335732	−	0.628110i	−0.656242	−	0.754550i	$-0.727855\pi$
$283$	5.64788	−	10.5664i	0.335732	−	0.628110i	0.991974	+	0.126440i	$0.0403551\pi$
$284$	9.04751	+	3.12743i	0.536871	+	0.185579i
$285$	−7.98043	+	0.786004i	−0.472720	+	0.0465589i
$286$	1.79925	−	0.605188i	0.106392	−	0.0357855i
$287$	−2.58315	−	2.58315i	−0.152478	−	0.152478i
$288$	−13.1199	+	9.78052i	−0.773097	+	0.576323i
$289$	11.9364	−	11.9364i	0.702144	−	0.702144i
$290$	15.7283	−	31.6716i	0.923600	−	1.85982i
$291$	−0.531798	−	5.39944i	−0.0311746	−	0.316521i
$292$	1.16396	+	19.4119i	0.0681155	+	1.13599i
$293$	−17.4152	−	9.30861i	−1.01741	−	0.543815i	−0.123630	−	0.992328i	$-0.539454\pi$
$293$	−17.4152	−	9.30861i	−1.01741	−	0.543815i	−0.893776	+	0.448514i	$0.851954\pi$
$294$	−0.164289	+	0.432851i	−0.00958152	+	0.0252444i
$295$	−5.41098	−	8.09811i	−0.315040	−	0.471490i
$296$	7.04308	−	0.634417i	0.409371	−	0.0368747i
$297$	−0.410964	−	0.274597i	−0.0238466	−	0.0159338i
$298$	2.39623	−	14.2668i	0.138810	−	0.826455i
$299$	33.0710	−	27.1407i	1.91254	−	1.56958i
$300$	2.05937	−	8.61525i	0.118898	−	0.497402i
$301$	3.91537	−	2.09281i	0.225678	−	0.120628i
$302$	−14.0804	+	1.81391i	−0.810237	+	0.104379i
$303$	−5.48853	+	2.27342i	−0.315308	+	0.130605i
$304$	−4.92190	−	22.2236i	−0.282290	−	1.27461i
$305$	9.15234	+	3.79102i	0.524062	+	0.217073i
$306$	1.36402	+	0.369556i	0.0779760	+	0.0211261i
$307$	−6.28061	+	20.7044i	−0.358454	+	1.18166i	0.573537	+	0.819180i	$0.305571\pi$
$307$	−6.28061	+	20.7044i	−0.358454	+	1.18166i	−0.931990	+	0.362483i	$0.881929\pi$
$308$	0.465552	+	0.214067i	0.0265273	+	0.0121976i
$309$	2.72898	+	0.268781i	0.155246	+	0.0152904i
$310$	61.2462	−	14.1012i	3.47855	−	0.800894i
$311$	−9.78954	+	1.94726i	−0.555114	+	0.110419i	−0.464672	−	0.885483i	$-0.653828\pi$
$311$	−9.78954	+	1.94726i	−0.555114	+	0.110419i	−0.0904416	+	0.995902i	$0.528828\pi$
$312$	−4.46635	−	1.89382i	−0.252857	−	0.107216i
$313$	−2.58324	+	12.9868i	−0.146013	+	0.734058i	0.836515	+	0.547944i	$0.184589\pi$
$313$	−2.58324	+	12.9868i	−0.146013	+	0.734058i	−0.982528	+	0.186114i	$0.940411\pi$
$314$	8.33106	+	7.84648i	0.470149	+	0.442803i
$315$	11.9160	−	3.61467i	0.671389	−	0.203664i
$316$	2.11837	−	3.62246i	0.119168	−	0.203779i
$317$	1.74607	−	2.12759i	0.0980690	−	0.119497i	−0.721663	−	0.692244i	$-0.756622\pi$
$317$	1.74607	−	2.12759i	0.0980690	−	0.119497i	0.819732	+	0.572747i	$0.194122\pi$
$318$	−0.166434	+	2.43552i	−0.00933315	+	0.136577i
$319$			1.48828i			0.0833280i
$320$	34.2091	+	3.94649i	1.91235	+	0.220616i
$321$			4.37677i			0.244288i
$322$	11.5213	+	0.787322i	0.642058	+	0.0438758i
$323$	−1.24703	+	1.51951i	−0.0693867	+	0.0845479i
$324$	−4.07888	−	15.5684i	−0.226605	−	0.864909i
$325$	−67.8273	+	20.5752i	−3.76238	+	1.14131i
$326$	7.68881	−	8.16365i	0.425844	−	0.452143i
$327$	−0.708456	+	3.56165i	−0.0391777	+	0.196960i
$328$	10.3322	+	0.0861792i	0.570502	+	0.00475845i
$329$	3.93403	−	0.782528i	0.216890	−	0.0431422i
$330$	0.114560	+	0.497572i	0.00630631	+	0.0273904i
$331$	−27.3058	−	2.68939i	−1.50086	−	0.147822i	−0.686054	−	0.727551i	$-0.740659\pi$
$331$	−27.3058	−	2.68939i	−1.50086	−	0.147822i	−0.814810	+	0.579728i	$0.803159\pi$
$332$	1.43116	+	3.86760i	0.0785451	+	0.212262i
$333$	−2.09951	+	6.92117i	−0.115053	+	0.379278i
$334$	−4.44543	+	16.4080i	−0.243243	+	0.897804i
$335$	−12.8443	−	5.32027i	−0.701757	−	0.290677i
$336$	−0.527144	−	1.19872i	−0.0287581	−	0.0653954i
$337$	−23.9544	+	9.92225i	−1.30488	+	0.540499i	−0.923386	−	0.383872i	$-0.874590\pi$
$337$	−23.9544	+	9.92225i	−1.30488	+	0.540499i	−0.381495	+	0.924371i	$0.624590\pi$
$338$	2.61082	+	20.2664i	0.142010	+	1.10235i
$339$	−3.24317	+	1.73351i	−0.176145	+	0.0941513i
$340$	−1.55633	−	2.53409i	−0.0844037	−	0.137430i
$341$	−2.04470	+	1.67804i	−0.110727	+	0.0908711i
$342$	22.9588	+	3.85611i	1.24147	+	0.208515i
$343$	0.831470	+	0.555570i	0.0448951	+	0.0299980i
$344$	−3.74522	+	11.9855i	−0.201929	+	0.646217i
$345$	6.39305	+	9.56787i	0.344190	+	0.515117i
$346$	−29.1215	−	11.0531i	−1.56558	−	0.594217i
$347$	−12.9959	−	6.94646i	−0.697658	−	0.372906i	0.0841264	−	0.996455i	$-0.473190\pi$
$347$	−12.9959	−	6.94646i	−0.697658	−	0.372906i	−0.781784	+	0.623549i	$0.785690\pi$
$348$	2.52364	−	2.84559i	0.135282	−	0.152540i
$349$	−0.874861	−	8.88261i	−0.0468302	−	0.475475i	−0.989786	−	0.142558i	$-0.954467\pi$
$349$	−0.874861	−	8.88261i	−0.0468302	−	0.475475i	0.942956	−	0.332917i	$-0.108033\pi$
$350$	−17.1358	−	8.50976i	−0.915948	−	0.454866i
$351$	7.14692	−	7.14692i	0.381474	−	0.381474i
$352$	−1.36338	+	0.491616i	−0.0726686	+	0.0262032i
$353$	9.24711	+	9.24711i	0.492174	+	0.492174i	0.908991	−	0.416817i	$-0.136854\pi$
$353$	9.24711	+	9.24711i	0.492174	+	0.492174i	−0.416817	+	0.908991i	$0.636854\pi$
$354$	−0.333966	−	0.992894i	−0.0177501	−	0.0527717i
$355$	20.5038	−	2.01945i	1.08823	−	0.107181i
$356$	−18.6493	+	9.06824i	−0.988410	+	0.480616i
$357$	−0.0533089	+	0.0997340i	−0.00282141	+	0.00527848i
$358$	11.4817	−	5.16389i	0.606829	−	0.272920i
$359$	7.47786	−	4.99655i	0.394666	−	0.263708i	−0.342364	−	0.939567i	$-0.611228\pi$
$359$	7.47786	−	4.99655i	0.394666	−	0.263708i	0.737030	+	0.675860i	$0.236228\pi$
$360$	−16.8611	+	30.9217i	−0.888658	+	1.62972i
$361$	−7.43472	+	11.1268i	−0.391301	+	0.585623i
$362$	5.76707	+	8.09537i	0.303110	+	0.425483i
$363$	2.27091	+	2.76711i	0.119192	+	0.145235i
$364$	−6.15067	+	8.48322i	−0.322383	+	0.444642i
$365$	19.7300	+	36.9121i	1.03271	+	1.93207i
$366$	0.843517	+	0.650988i	0.0440914	+	0.0340277i
$367$	−9.32173	−	22.5046i	−0.486590	−	1.17473i	−0.956425	−	0.291978i	$-0.905686\pi$
$367$	−9.32173	−	22.5046i	−0.486590	−	1.17473i	0.469835	−	0.882754i	$-0.344314\pi$
$368$	−24.7955	+	21.2619i	−1.29255	+	1.10835i
$369$	−4.04414	+	9.76341i	−0.210529	+	0.508263i
$370$	13.2019	−	7.57325i	0.686333	−	0.393714i
$371$	5.04575	+	1.53061i	0.261962	+	0.0794654i
$372$	6.75486	+	0.258739i	0.350223	+	0.0134150i
$373$	1.48699	−	15.0977i	0.0769934	−	0.781727i	−0.876718	−	0.481004i	$-0.840272\pi$
$373$	1.48699	−	15.0977i	0.0769934	−	0.781727i	0.953712	−	0.300723i	$-0.0972278\pi$
$374$	0.106103	+	0.0663885i	0.00548643	+	0.00343287i
$375$	−2.34471	−	11.7877i	−0.121080	−	0.608712i
$376$	−6.38147	+	9.38023i	−0.329099	+	0.483748i
$377$	−29.8494	−	5.93742i	−1.53732	−	0.305793i
$378$	2.72704	−	0.0816848i	0.140264	−	0.00420141i
$379$	−5.71282	−	18.8326i	−0.293448	−	0.967368i	−0.972426	−	0.233210i	$-0.925077\pi$
$379$	−5.71282	−	18.8326i	−0.293448	−	0.967368i	0.678979	−	0.734158i	$-0.262423\pi$
$380$	−29.6065	−	39.0314i	−1.51878	−	2.00227i
$381$	4.71706	+	3.87119i	0.241662	+	0.198327i
$382$	−10.3264	+	9.00536i	−0.528345	+	0.460754i
$383$	−11.4374			−0.584425			−0.292212	−	0.956353i	$-0.594391\pi$
$383$	−11.4374			−0.584425			−0.292212	+	0.956353i	$0.594391\pi$
$384$	3.44040	+	1.37189i	0.175567	+	0.0700089i
$385$	1.10283			0.0562055
$386$	9.02993	−	7.87473i	0.459611	−	0.400813i
$387$	−9.92775	−	8.14749i	−0.504656	−	0.414160i
$388$	26.4081	−	20.0313i	1.34067	−	1.01694i
$389$	−1.80083	−	5.93655i	−0.0913058	−	0.300995i	0.899379	−	0.437170i	$-0.144019\pi$
$389$	−1.80083	−	5.93655i	−0.0913058	−	0.300995i	−0.990685	+	0.136175i	$0.956519\pi$
$390$	−10.4365	+	0.312610i	−0.528471	+	0.0158296i
$391$	2.76655	+	0.550301i	0.139911	+	0.0278299i
$392$	−2.77859	+	0.528642i	−0.140340	+	0.0267005i
$393$	0.535264	+	2.69095i	0.0270005	+	0.135741i
$394$	−20.5744	−	12.8734i	−1.03652	−	0.648554i
$395$	0.885259	−	8.98819i	0.0445422	−	0.452245i
$396$	0.0567369	−	1.48122i	0.00285113	−	0.0744343i
$397$	14.0967	+	4.27618i	0.707492	+	0.214615i	0.623469	−	0.781848i	$-0.285723\pi$
$397$	14.0967	+	4.27618i	0.707492	+	0.214615i	0.0840235	+	0.996464i	$0.473223\pi$
$398$	27.6640	−	15.8694i	1.38667	−	0.795463i
$399$	−0.712918	+	1.72114i	−0.0356906	+	0.0861646i
$400$	51.4333	−	16.8237i	2.57166	−	0.841186i
$401$	8.93380	+	21.5681i	0.446133	+	1.07706i	0.973759	+	0.227583i	$0.0730822\pi$
$401$	8.93380	+	21.5681i	0.446133	+	1.07706i	−0.527626	+	0.849477i	$0.676918\pi$
$402$	−1.18378	−	0.913586i	−0.0590416	−	0.0455655i
$403$	−25.4981	−	47.7035i	−1.27015	−	2.37628i
$404$	−29.3827	−	21.3036i	−1.46184	−	1.05989i
$405$	−21.9741	−	26.7755i	−1.09190	−	1.33048i
$406$	−4.76655	−	6.69092i	−0.236560	−	0.332065i
$407$	−0.355876	+	0.532605i	−0.0176401	+	0.0264003i
$408$	−0.0902940	−	0.306850i	−0.00447022	−	0.0151913i
$409$	8.08221	−	5.40036i	0.399640	−	0.267031i	−0.339469	−	0.940617i	$-0.610247\pi$
$409$	8.08221	−	5.40036i	0.399640	−	0.267031i	0.739108	+	0.673587i	$0.235247\pi$
$410$	20.2815	−	9.12156i	1.00163	−	0.450482i
$411$	0.492754	−	0.921879i	0.0243058	−	0.0454729i
$412$	7.32577	+	15.0658i	0.360915	+	0.742239i
$413$	−2.25174	+	0.221777i	−0.110801	+	0.0109129i
$414$	−10.6503	−	31.6637i	−0.523434	−	1.55619i
$415$	6.27604	+	6.27604i	0.308079	+	0.308079i
$416$	−4.42083	−	29.3057i	−0.216749	−	1.43683i
$417$	3.42014	−	3.42014i	0.167485	−	0.167485i
$418$	1.84666	+	0.917065i	0.0903233	+	0.0448551i
$419$	1.18859	+	12.0680i	0.0580666	+	0.589560i	0.979558	+	0.201161i	$0.0644715\pi$
$419$	1.18859	+	12.0680i	0.0580666	+	0.589560i	−0.921492	+	0.388398i	$0.873028\pi$
$420$	−2.10861	−	1.87004i	−0.102889	−	0.0912487i
$421$	1.16843	+	0.624538i	0.0569457	+	0.0304381i	0.499624	−	0.866242i	$-0.333472\pi$
$421$	1.16843	+	0.624538i	0.0569457	+	0.0304381i	−0.442678	+	0.896681i	$0.645972\pi$
$422$	−31.0180	−	11.7729i	−1.50993	−	0.573096i
$423$	−6.44652	−	9.64790i	−0.313440	−	0.469097i
$424$	−13.2109	+	6.92033i	−0.641578	+	0.336081i
$425$	−3.88570	−	2.59634i	−0.188484	−	0.125941i
$426$	2.18540	+	0.367055i	0.105883	+	0.0177839i
$427$	1.77902	−	1.46000i	0.0860926	−	0.0706544i
$428$	−22.7845	+	13.9933i	−1.10133	+	0.676389i
$429$	0.387549	−	0.207149i	0.0187110	−	0.0100013i
$430$	3.45309	+	26.8044i	0.166523	+	1.29262i
$431$	−10.2929	+	4.26347i	−0.495793	+	0.205364i	−0.616547	−	0.787318i	$-0.711469\pi$
$431$	−10.2929	+	4.26347i	−0.495793	+	0.205364i	0.120754	+	0.992682i	$0.461469\pi$
$432$	−5.33737	+	5.57312i	−0.256795	+	0.268137i
$433$	36.5276	+	15.1302i	1.75541	+	0.727113i	0.997174	+	0.0751276i	$0.0239364\pi$
$433$	36.5276	+	15.1302i	1.75541	+	0.727113i	0.758232	+	0.651985i	$0.226064\pi$
$434$	3.81813	−	14.0926i	0.183276	−	0.676466i
$435$	2.37626	−	7.83347i	0.113933	−	0.375586i
$436$	−20.8062	+	7.69910i	−0.996437	+	0.368720i
$437$	46.2440	+	4.55464i	2.21215	+	0.217878i
$438$	1.01004	+	4.38695i	0.0482617	+	0.209617i
$439$	−13.4121	+	2.66783i	−0.640125	+	0.127329i	−0.504473	−	0.863428i	$-0.668313\pi$
$439$	−13.4121	+	2.66783i	−0.640125	+	0.127329i	−0.135652	+	0.990756i	$0.543313\pi$
$440$	−2.22398	+	2.18719i	−0.106024	+	0.104270i
$441$	0.564362	−	2.83724i	0.0268744	−	0.135107i
$442$	−1.75480	+	1.86317i	−0.0834671	+	0.0886218i
$443$	−18.8999	+	5.73322i	−0.897961	+	0.272394i	−0.705331	−	0.708878i	$-0.749202\pi$
$443$	−18.8999	+	5.73322i	−0.897961	+	0.272394i	−0.192630	+	0.981271i	$0.561702\pi$
$444$	1.58356	−	0.414889i	0.0751522	−	0.0196898i
$445$	−28.3139	+	34.5006i	−1.34221	+	1.63549i
$446$	10.2402	+	0.699778i	0.484889	+	0.0331355i
$447$		−	3.34889i		−	0.158397i
$448$	4.55490	−	6.57669i	0.215199	−	0.310720i
$449$		−	2.73838i		−	0.129232i	−0.997910	−	0.0646161i	$-0.979418\pi$
$449$		−	2.73838i		−	0.129232i	0.997910	−	0.0646161i	$-0.0205823\pi$
$450$	−3.77340	+	55.2182i	−0.177880	+	2.60301i
$451$	−0.593758	+	0.723496i	−0.0279590	+	0.0340681i
$452$	−19.3932	−	11.3409i	−0.912180	−	0.533432i
$453$	−3.14490	+	0.953995i	−0.147760	+	0.0448226i
$454$	−3.47549	−	3.27334i	−0.163113	−	0.153625i
$455$	−4.39968	+	22.1187i	−0.206260	+	1.03694i
$456$	−1.97576	−	4.88476i	−0.0925237	−	0.228750i
$457$	−5.18639	+	1.03164i	−0.242609	+	0.0482579i	−0.314897	−	0.949126i	$-0.601970\pi$
$457$	−5.18639	+	1.03164i	−0.242609	+	0.0482579i	0.0722880	+	0.997384i	$0.476970\pi$
$458$	26.7263	−	6.15340i	1.24884	−	0.287529i
$459$	0.663194	+	0.0653189i	0.0309552	+	0.00304882i
$460$	−29.3687	+	63.8709i	−1.36932	+	2.97799i
$461$	−3.61936	+	11.9314i	−0.168571	+	0.555703i	0.831429	+	0.555630i	$0.187523\pi$
$461$	−3.61936	+	11.9314i	−0.168571	+	0.555703i	−1.00000		7.22299e-5i	$0.999977\pi$
$462$	0.114490	+	0.0310189i	0.00532656	+	0.00144313i
$463$	3.16742	+	1.31199i	0.147202	+	0.0609732i	0.455068	−	0.890457i	$-0.349615\pi$
$463$	3.16742	+	1.31199i	0.147202	+	0.0609732i	−0.307866	+	0.951430i	$0.599615\pi$
$464$	22.8820	+	4.03973i	1.06227	+	0.187540i
$465$	13.4414	−	5.56759i	0.623328	−	0.258191i
$466$	−9.87216	+	1.27178i	−0.457319	+	0.0589142i
$467$	31.3350	−	16.7489i	1.45001	−	0.775048i	0.456604	−	0.889670i	$-0.349066\pi$
$467$	31.3350	−	16.7489i	1.45001	−	0.775048i	0.993409	+	0.114622i	$0.0365658\pi$
$468$	29.4815	+	7.04718i	1.36278	+	0.325756i
$469$	−2.49664	+	2.04894i	−0.115284	+	0.0946113i
$470$	−4.04447	+	24.0802i	−0.186557	+	1.11074i
$471$	2.20278	+	1.47185i	0.101499	+	0.0678193i
$472$	4.10105	−	4.91300i	0.188766	−	0.226139i
$473$	−0.631930	−	0.945750i	−0.0290562	−	0.0434856i
$474$	0.344710	−	0.908205i	0.0158330	−	0.0417152i
$475$	−67.8952	−	36.2908i	−3.11525	−	1.66513i
$476$	−0.689631	+	0.0413510i	−0.0316092	+	0.00189532i
$477$	−1.49508	−	15.1798i	−0.0684551	−	0.695036i
$478$	13.9074	−	28.0048i	0.636108	−	1.28091i
$479$	−13.8423	+	13.8423i	−0.632472	+	0.632472i	−0.948688	−	0.316215i	$-0.897588\pi$
$479$	−13.8423	+	13.8423i	−0.632472	+	0.632472i	0.316215	+	0.948688i	$0.397588\pi$
$480$	7.96100	−	0.410744i	0.363368	−	0.0187478i
$481$	−9.26233	−	9.26233i	−0.422326	−	0.422326i
$482$	9.82893	−	3.30602i	0.447695	−	0.150585i
$483$	2.66042	−	0.262028i	0.121053	−	0.0119227i
$484$	−7.14451	+	20.6687i	−0.324750	+	0.939488i
$485$	33.6285	−	62.9144i	1.52699	−	2.85680i
$486$	−4.88530	−	10.8623i	−0.221602	−	0.492725i
$487$	10.5737	−	7.06513i	0.479141	−	0.320152i	−0.292439	−	0.956284i	$-0.594467\pi$
$487$	10.5737	−	7.06513i	0.479141	−	0.320152i	0.771580	+	0.636133i	$0.219467\pi$
$488$	−0.692038	+	6.47248i	−0.0313271	+	0.292996i
$489$	1.44227	−	2.15851i	0.0652218	−	0.0976114i
$490$	−4.95803	+	3.53205i	−0.223981	+	0.159562i
$491$	7.88982	+	9.61378i	0.356063	+	0.433864i	0.919979	−	0.391969i	$-0.128206\pi$
$491$	7.88982	+	9.61378i	0.356063	+	0.433864i	−0.563916	+	0.825832i	$0.690706\pi$
$492$	2.36207	−	0.376500i	0.106491	−	0.0169739i
$493$	−0.945914	−	1.76968i	−0.0426018	−	0.0797024i
$494$	−25.7601	+	33.3786i	−1.15900	+	1.50177i
$495$	−1.22088	−	2.94745i	−0.0548743	−	0.132478i
$496$	20.2495	+	35.9916i	0.909228	+	1.61607i
$497$	1.83167	−	4.42205i	0.0821618	−	0.198356i
$498$	0.475021	+	0.828068i	0.0212862	+	0.0371066i
$499$	−1.72690	−	0.523850i	−0.0773067	−	0.0234507i	0.251394	−	0.967885i	$-0.419111\pi$
$499$	−1.72690	−	0.523850i	−0.0773067	−	0.0234507i	−0.328701	+	0.944434i	$0.606611\pi$
$500$	53.8676	−	49.8932i	2.40903	−	2.23129i
$501$	−0.385719	+	3.91627i	−0.0172326	+	0.174966i
$502$	−3.41788	+	5.46248i	−0.152548	+	0.243802i
$503$	−5.71479	−	28.7302i	−0.254810	−	1.28102i	−0.870163	−	0.492765i	$-0.835986\pi$
$503$	−5.71479	−	28.7302i	−0.254810	−	1.28102i	0.615353	−	0.788252i	$-0.289014\pi$
$504$	4.48886	+	6.84088i	0.199950	+	0.304717i
$505$	−76.6108	−	15.2388i	−3.40914	−	0.678119i
$506$	−0.0885841	−	2.95737i	−0.00393804	−	0.131471i
$507$	1.37312	+	4.52656i	0.0609823	+	0.201032i
$508$	−5.07138	+	36.9328i	−0.225006	+	1.63863i
$509$	6.88355	+	5.64918i	0.305108	+	0.250395i	0.774471	−	0.632610i	$-0.218016\pi$
$509$	6.88355	+	5.64918i	0.305108	+	0.250395i	−0.469363	+	0.883005i	$0.655516\pi$
$510$	−0.452464	−	0.518839i	−0.0200354	−	0.0229746i
$511$	9.72337			0.430136
$512$	3.85777	+	22.2961i	0.170491	+	0.985359i
$513$	10.9780			0.484691
$514$	2.61276	+	2.99604i	0.115244	+	0.132150i
$515$	27.8713	+	22.8734i	1.22816	+	1.00792i
$516$	−0.395437	+	2.87981i	−0.0174082	+	0.126777i
$517$	−0.298315	−	0.983413i	−0.0131199	−	0.0432504i
$518$	−0.105863	−	3.53421i	−0.00465134	−	0.155284i
$519$	−7.07203	−	1.40671i	−0.310428	−	0.0617479i
$520$	−34.9944	−	53.3305i	−1.53461	−	2.33870i
$521$	−0.816331	−	4.10397i	−0.0357641	−	0.179798i	0.958774	−	0.284168i	$-0.0917174\pi$
$521$	−0.816331	−	4.10397i	−0.0357641	−	0.179798i	−0.994539	+	0.104370i	$0.966717\pi$
$522$	−12.6056	+	20.1463i	−0.551730	+	0.881778i
$523$	−2.96032	+	30.0567i	−0.129446	+	1.31429i	0.682643	+	0.730752i	$0.260830\pi$
$523$	−2.96032	+	30.0567i	−0.129446	+	1.31429i	−0.812089	+	0.583534i	$0.801670\pi$
$524$	−12.2972	+	11.3899i	−0.537206	+	0.497570i
$525$	−4.23827	−	1.28567i	−0.184973	−	0.0561111i
$526$	7.69937	+	13.4217i	0.335709	+	0.585216i
$527$	1.36478	−	3.29487i	0.0594508	−	0.143527i
$528$	−0.292400	+	0.164509i	−0.0127251	+	0.00715934i
$529$	−16.7157	−	40.3554i	−0.726771	−	1.75458i
$530$	−19.6108	+	25.4107i	−0.851838	+	1.10377i
$531$	3.08548	+	5.77253i	0.133899	+	0.250507i
$532$	−11.2392	+	1.79146i	−0.487280	+	0.0776695i
$533$	−12.1419	−	14.7949i	−0.525923	−	0.640839i
$534$	−3.90978	+	2.78529i	−0.169193	+	0.120531i
$535$	−31.9719	+	47.8493i	−1.38227	+	2.06871i
$536$	0.971196	−	9.08339i	0.0419493	−	0.392342i
$537$	2.42319	−	1.61913i	0.104569	−	0.0698705i
$538$	−3.55310	−	7.90022i	−0.153185	−	0.340603i
$539$	0.120774	−	0.225952i	0.00520210	−	0.00973245i
$540$	−5.42591	+	15.6969i	−0.233494	+	0.675488i
$541$	5.26698	−	0.518752i	0.226445	−	0.0223029i	0.0158418	−	0.999875i	$-0.494957\pi$
$541$	5.26698	−	0.518752i	0.226445	−	0.0223029i	0.210603	+	0.977572i	$0.432457\pi$
$542$	−15.4162	+	5.18533i	−0.662182	+	0.222729i
$543$	1.62698	+	1.62698i	0.0698205	+	0.0698205i
$544$	1.30871	−	1.45110i	0.0561104	−	0.0622153i
$545$	−33.7627	+	33.7627i	−1.44624	+	1.44624i
$546$	−1.07887	+	2.17249i	−0.0461716	+	0.0929741i
$547$	−0.192379	−	1.95325i	−0.00822552	−	0.0835151i	0.990196	−	0.139688i	$-0.0446101\pi$
$547$	−0.192379	−	1.95325i	−0.00822552	−	0.0835151i	−0.998421	+	0.0561732i	$0.982110\pi$
$548$	6.37452	−	0.382223i	0.272306	−	0.0163278i
$549$	−5.87146	−	3.13836i	−0.250588	−	0.133942i
$550$	−1.73942	+	4.58284i	−0.0741691	+	0.195413i
$551$	−18.3650	−	27.4852i	−0.782376	−	1.17091i
$552$	−4.84536	+	5.80468i	−0.206232	+	0.247064i
$553$	−1.74458	−	1.16569i	−0.0741873	−	0.0495704i
$554$	5.44891	−	32.4421i	0.231502	−	1.37833i
$555$	2.72350	−	2.23512i	0.115606	−	0.0948756i
$556$	28.7393	+	6.86977i	1.21882	+	0.291343i
$557$	8.65926	−	4.62847i	0.366905	−	0.196115i	−0.277633	−	0.960687i	$-0.589550\pi$
$557$	8.65926	−	4.62847i	0.366905	−	0.196115i	0.644538	+	0.764573i	$0.277050\pi$
$558$	−41.8910	+	5.39661i	−1.77339	+	0.228457i
$559$	21.4893	−	8.90114i	0.908899	−	0.376478i
$560$	2.99348	−	16.9558i	0.126498	−	0.716513i
$561$	0.0267680	+	0.0110877i	0.00113014	+	0.000468121i
$562$	−23.3211	−	6.31841i	−0.983741	−	0.266526i
$563$	−3.64453	+	12.0144i	−0.153598	+	0.506346i	−0.999642	−	0.0267681i	$-0.991478\pi$
$563$	−3.64453	+	12.0144i	−0.153598	+	0.506346i	0.846043	+	0.533114i	$0.178978\pi$
$564$	−1.09717	+	2.38612i	−0.0461992	+	0.100474i
$565$	−48.1192	−	4.73933i	−2.02439	−	0.199385i
$566$	16.5119	−	3.80167i	0.694048	−	0.159796i
$567$	−7.89229	+	1.56987i	−0.331445	+	0.0659285i
$568$	5.07626	+	12.5502i	0.212995	+	0.526596i
$569$	−5.39373	+	27.1161i	−0.226117	+	1.13677i	0.686241	+	0.727374i	$0.259259\pi$
$569$	−5.39373	+	27.1161i	−0.226117	+	1.13677i	−0.912358	+	0.409393i	$0.865741\pi$
$570$	−8.25554	−	7.77536i	−0.345787	−	0.325674i
$571$	18.9199	−	5.73928i	0.791772	−	0.240181i	0.131607	−	0.991302i	$-0.457986\pi$
$571$	18.9199	−	5.73928i	0.791772	−	0.240181i	0.660165	+	0.751120i	$0.270486\pi$
$572$	2.31743	+	1.35521i	0.0968967	+	0.0566640i
$573$	−2.01215	+	2.45181i	−0.0840586	+	0.102426i
$574$	0.352223	−	5.15427i	0.0147015	−	0.215135i
$575$			110.473i			4.60704i
$576$	−22.6195	−	4.89288i	−0.942477	−	0.203870i
$577$			19.7402i			0.821796i	0.911681	+	0.410898i	$0.134785\pi$
$577$			19.7402i			0.821796i	−0.911681	+	0.410898i	$0.865215\pi$
$578$	23.8173	+	1.62758i	0.990670	+	0.0676986i
$579$	1.75952	−	2.14398i	0.0731231	−	0.0891008i
$580$	48.3766	−	12.6746i	2.00873	−	0.526284i
$581$	1.97316	−	0.598552i	0.0818606	−	0.0248321i
$582$	5.26069	−	5.58557i	0.218063	−	0.231530i
$583$	0.263550	−	1.32496i	0.0109151	−	0.0548741i
$584$	−19.6083	+	19.2839i	−0.811395	+	0.797972i
$585$	63.9855	−	12.7275i	2.64548	−	0.526218i
$586$	−6.26576	−	27.2143i	−0.258836	−	1.12421i
$587$	−14.6105	−	1.43901i	−0.603040	−	0.0593943i	−0.208110	−	0.978105i	$-0.566731\pi$
$587$	−14.6105	−	1.43901i	−0.603040	−	0.0593943i	−0.394930	+	0.918711i	$0.629231\pi$
$588$	−0.614060	+	0.227226i	−0.0253234	+	0.00937063i
$589$	17.0543	−	56.2206i	0.702711	−	2.31653i
$590$	3.60188	−	13.2945i	0.148287	−	0.547324i
$591$	−5.19058	−	2.15001i	−0.213512	−	0.0884396i
$592$	7.22271	+	6.91718i	0.296852	+	0.284294i
$593$	9.40528	−	3.89579i	0.386228	−	0.159981i	−0.181116	−	0.983462i	$-0.557971\pi$
$593$	9.40528	−	3.89579i	0.386228	−	0.159981i	0.567344	+	0.823481i	$0.307971\pi$
$594$	−0.0893098	−	0.693264i	−0.00366442	−	0.0284450i
$595$	−1.31135	+	0.700931i	−0.0537601	+	0.0287354i
$596$	17.4336	−	10.7069i	0.714107	−	0.438573i
$597$	5.70700	−	4.68361i	0.233572	−	0.191687i
$598$	59.6672	+	10.0216i	2.43997	+	0.409813i
$599$	−36.9787	−	24.7084i	−1.51091	−	1.00956i	−0.987525	−	0.157460i	$-0.949669\pi$
$599$	−36.9787	−	24.7084i	−1.51091	−	1.00956i	−0.523384	−	0.852097i	$-0.675331\pi$
$600$	11.0967	−	5.81286i	0.453023	−	0.237309i
$601$	22.7621	+	34.0660i	0.928487	+	1.38958i	0.920981	+	0.389607i	$0.127389\pi$
$601$	22.7621	+	34.0660i	0.928487	+	1.38958i	0.00750602	+	0.999972i	$0.497611\pi$
$602$	5.86994	+	2.22794i	0.239241	+	0.0908041i
$603$	8.23992	+	4.40433i	0.335555	+	0.179358i
$604$	−15.0210	−	13.3216i	−0.611198	−	0.542048i
$605$	4.61337	+	46.8403i	0.187560	+	1.90433i
$606$	−7.52470	−	3.73681i	−0.305670	−	0.151798i
$607$	6.13911	−	6.13911i	0.249179	−	0.249179i	−0.571455	−	0.820634i	$-0.693621\pi$
$607$	6.13911	−	6.13911i	0.249179	−	0.249179i	0.820634	+	0.571455i	$0.193621\pi$
$608$	19.1122	−	25.9028i	0.775100	−	1.05050i
$609$	−1.34472	−	1.34472i	−0.0544908	−	0.0544908i
$610$	4.46640	+	13.2788i	0.180839	+	0.537642i
$611$	20.9137	−	2.05982i	0.846077	−	0.0833314i
$612$	0.873962	+	1.79734i	0.0353278	+	0.0726534i
$613$	19.2496	−	36.0135i	0.777485	−	1.45457i	−0.110096	−	0.993921i	$-0.535116\pi$
$613$	19.2496	−	36.0135i	0.777485	−	1.45457i	0.887581	−	0.460652i	$-0.152384\pi$
$614$	−27.9056	+	12.5505i	−1.12618	+	0.506496i
$615$	4.28036	−	2.86005i	0.172601	−	0.115328i
$616$	0.204565	+	0.695183i	0.00824217	+	0.0280097i
$617$	−21.0679	+	31.5303i	−0.848161	+	1.26936i	0.113061	+	0.993588i	$0.463935\pi$
$617$	−21.0679	+	31.5303i	−0.848161	+	1.26936i	−0.961222	+	0.275775i	$0.911065\pi$
$618$	2.25009	+	3.15851i	0.0905121	+	0.127054i
$619$	−4.90966	−	5.98244i	−0.197336	−	0.240455i	0.664936	−	0.746901i	$-0.268459\pi$
$619$	−4.90966	−	5.98244i	−0.197336	−	0.240455i	−0.862272	+	0.506446i	$0.830959\pi$
$620$	71.9579	+	52.1723i	2.88990	+	2.09529i
$621$	−7.42602	−	13.8931i	−0.297996	−	0.557511i
$622$	−11.1748	−	8.62421i	−0.448070	−	0.345799i
$623$	3.96788	+	9.57931i	0.158970	+	0.383787i
$624$	−2.13293	−	6.52075i	−0.0853854	−	0.261039i
$625$	34.5879	−	83.5027i	1.38352	−	3.34011i
$626$	−16.2431	+	9.31785i	−0.649205	+	0.372416i
$627$	0.456743	+	0.138551i	0.0182405	+	0.00553321i
$628$	−0.619489	+	16.1729i	−0.0247203	+	0.645370i
$629$	0.0846526	−	0.859493i	0.00337532	−	0.0342702i
$630$	14.9286	+	9.34083i	0.594768	+	0.372147i
$631$	2.45232	+	12.3286i	0.0976253	+	0.490795i	0.998402	+	0.0565127i	$0.0179981\pi$
$631$	2.45232	+	12.3286i	0.0976253	+	0.490795i	−0.900777	+	0.434283i	$0.857002\pi$
$632$	5.83001	−	1.10919i	0.231905	−	0.0441214i
$633$	−7.53259	−	1.49833i	−0.299394	−	0.0595531i
$634$	3.89066	−	0.116540i	0.154518	−	0.00462837i
$635$	23.2909	+	76.7797i	0.924270	+	3.04691i
$636$	−2.75060	+	2.08641i	−0.109068	+	0.0827316i
$637$	4.04994	+	3.32370i	0.160464	+	0.131690i
$638$	−1.58629	+	1.38336i	−0.0628018	+	0.0547676i
$639$	−13.8462			−0.547747
$640$	27.5909	+	40.1300i	1.09062	+	1.58628i
$641$	10.5602			0.417102			0.208551	−	0.978011i	$-0.433125\pi$
$641$	10.5602			0.417102			0.208551	+	0.978011i	$0.433125\pi$
$642$	−4.66498	+	4.06819i	−0.184112	+	0.160559i
$643$	11.6823	+	9.58741i	0.460705	+	0.378091i	0.835924	−	0.548846i	$-0.184932\pi$
$643$	11.6823	+	9.58741i	0.460705	+	0.378091i	−0.375219	+	0.926936i	$0.622432\pi$
$644$	9.86985	+	13.0118i	0.388927	+	0.512737i
$645$	1.81609	+	5.98685i	0.0715085	+	0.235732i
$646$	−2.77868	+	0.0832317i	−0.109326	+	0.00327471i
$647$	−20.8973	−	4.15673i	−0.821558	−	0.163418i	−0.233624	−	0.972327i	$-0.575058\pi$
$647$	−20.8973	−	4.15673i	−0.821558	−	0.163418i	−0.587934	+	0.808909i	$0.700058\pi$
$648$	12.8022	−	18.8182i	0.502919	−	0.739249i
$649$	0.113093	+	0.568559i	0.00443930	+	0.0223179i
$650$	−84.9753	−	53.1692i	−3.33300	−	2.08547i
$651$	0.331289	−	3.36363i	0.0129842	−	0.131831i
$652$	15.8479	+	0.607040i	0.620653	+	0.0237735i
$653$	33.7497	+	10.2378i	1.32073	+	0.400638i	0.870452	−	0.492253i	$-0.163826\pi$
$653$	33.7497	+	10.2378i	1.32073	+	0.400638i	0.450274	+	0.892891i	$0.351326\pi$
$654$	−4.45469	+	2.55543i	−0.174192	+	0.0999252i
$655$	−13.8054	+	33.3291i	−0.539420	+	1.30227i
$656$	9.51191	+	11.0927i	0.371378	+	0.433098i
$657$	−10.7641	−	25.9869i	−0.419948	−	1.01384i
$658$	4.49073	+	3.46573i	0.175067	+	0.135108i
$659$	19.8388	+	37.1158i	0.772810	+	1.44583i	0.891560	+	0.452902i	$0.149611\pi$
$659$	19.8388	+	37.1158i	0.772810	+	1.44583i	−0.118750	+	0.992924i	$0.537889\pi$
$660$	−0.423854	+	0.584595i	−0.0164985	+	0.0227553i
$661$	−27.8202	−	33.8990i	−1.08208	−	1.31852i	−0.944677	−	0.328002i	$-0.893625\pi$
$661$	−27.8202	−	33.8990i	−1.08208	−	1.31852i	−0.137402	−	0.990515i	$-0.543875\pi$
$662$	−22.5142	−	31.6037i	−0.875038	−	1.22831i
$663$	−0.329166	+	0.492632i	−0.0127838	+	0.0191322i
$664$	−2.79202	+	5.12032i	−0.108352	+	0.198707i
$665$	−20.3668	+	13.6086i	−0.789789	+	0.527720i
$666$	−9.32842	+	4.19543i	−0.361469	+	0.162570i
$667$	−22.3607	+	41.8339i	−0.865809	+	1.61981i
$668$	−21.6204	+	10.5130i	−0.836520	+	0.406759i
$669$	2.36460	−	0.232893i	0.0914207	−	0.00900416i
$670$	−6.26808	−	18.6352i	−0.242157	−	0.719942i
$671$	−0.416933	−	0.416933i	−0.0160955	−	0.0160955i
$672$	0.787675	−	1.67606i	0.0303852	−	0.0646554i
$673$	33.0025	−	33.0025i	1.27215	−	1.27215i	0.327200	−	0.944955i	$-0.393895\pi$
$673$	33.0025	−	33.0025i	1.27215	−	1.27215i	0.944955	−	0.327200i	$-0.106105\pi$
$674$	−32.8412	−	16.3091i	−1.26500	−	0.628205i
$675$	2.55817	+	25.9735i	0.0984640	+	0.999722i
$676$	−19.1742	+	21.6203i	−0.737470	+	0.831550i
$677$	19.1259	+	10.2230i	0.735068	+	0.392902i	0.796045	−	0.605237i	$-0.206922\pi$
$677$	19.1259	+	10.2230i	0.735068	+	0.392902i	−0.0609773	+	0.998139i	$0.519422\pi$
$678$	−4.86217	−	1.84544i	−0.186731	−	0.0708737i
$679$	−9.20739	−	13.7798i	−0.353347	−	0.528821i
$680$	1.25436	−	4.01424i	0.0481026	−	0.153939i
$681$	−0.918939	−	0.614016i	−0.0352138	−	0.0235291i
$682$	−3.68908	−	0.619611i	−0.141262	−	0.0237261i
$683$	−1.65823	+	1.36087i	−0.0634504	+	0.0520724i	−0.665584	−	0.746323i	$-0.731817\pi$
$683$	−1.65823	+	1.36087i	−0.0634504	+	0.0520724i	0.602134	+	0.798395i	$0.294317\pi$
$684$	17.2301	+	28.0549i	0.658808	+	1.07270i
$685$	12.1213	−	6.47897i	0.463131	−	0.247549i
$686$	0.180693	+	1.40262i	0.00689889	+	0.0535524i
$687$	5.86546	−	2.42955i	0.223781	−	0.0926933i
$688$	−16.2560	+	7.14867i	−0.619753	+	0.272541i
$689$	25.5223	+	10.5717i	0.972321	+	0.402748i
$690$	−4.25561	+	15.7073i	−0.162008	+	0.597968i
$691$	8.27089	−	27.2655i	0.314640	−	1.03723i	−0.646903	−	0.762572i	$-0.723936\pi$
$691$	8.27089	−	27.2655i	0.314640	−	1.03723i	0.961543	−	0.274656i	$-0.0885639\pi$
$692$	−15.2874	−	41.3129i	−0.581139	−	1.57048i
$693$	−0.737586	−	0.0726459i	−0.0280186	−	0.00275959i
$694$	−4.67577	−	20.3084i	−0.177490	−	0.770897i
$695$	62.3747	−	12.4071i	2.36601	−	0.470628i
$696$	5.37869	+	0.0448627i	0.203879	+	0.00170051i
$697$	0.246187	−	1.23767i	0.00932501	−	0.0468800i
$698$	8.65436	−	9.18883i	0.327572	−	0.347802i
$699$	−2.20498	+	0.668872i	−0.0833998	+	0.0252991i
$700$	−6.85755	−	26.1740i	−0.259191	−	0.989285i
$701$	15.5186	−	18.9094i	0.586129	−	0.714200i	−0.392519	−	0.919744i	$-0.628396\pi$
$701$	15.5186	−	18.9094i	0.586129	−	0.714200i	0.978648	+	0.205544i	$0.0658964\pi$
$702$	14.2606	+	0.974512i	0.538231	+	0.0367806i
$703$		−	14.2274i		−	0.536596i
$704$	−1.79125	−	0.996209i	−0.0675103	−	0.0375460i
$705$			5.65242i			0.212882i
$706$	−1.26088	+	18.4512i	−0.0474539	+	0.694420i
$707$	−11.5120	+	14.0275i	−0.432955	+	0.527557i
$708$	0.747856	−	1.27885i	0.0281061	−	0.0480621i
$709$	10.5747	−	3.20781i	0.397142	−	0.120472i	−0.0853953	−	0.996347i	$-0.527215\pi$
$709$	10.5747	−	3.20781i	0.397142	−	0.120472i	0.482537	+	0.875875i	$0.339715\pi$
$710$	21.2107	+	19.9769i	0.796022	+	0.749721i
$711$	−1.18414	+	5.95308i	−0.0444088	+	0.223258i
$712$	−26.9998	−	11.4484i	−1.01186	−	0.429049i
$713$	−82.6857	+	16.4472i	−3.09660	+	0.615953i
$714$	−0.155852	+	0.0358830i	−0.00583261	+	0.00134289i
$715$	5.75011	+	0.566336i	0.215042	+	0.0211798i
$716$	16.1762	+	7.43801i	0.604532	+	0.277972i
$717$	2.10114	−	6.92654i	0.0784686	−	0.258676i
$718$	12.2762	+	3.32601i	0.458144	+	0.124126i
$719$	−28.7180	−	11.8954i	−1.07100	−	0.443623i	−0.223657	−	0.974668i	$-0.571800\pi$
$719$	−28.7180	−	11.8954i	−1.07100	−	0.443623i	−0.847344	+	0.531045i	$0.821800\pi$
$720$	−48.6303	+	10.7702i	−1.81234	+	0.401383i
$721$	7.73864	−	3.20545i	0.288202	−	0.119377i
$722$	−18.7701	+	2.41806i	−0.698550	+	0.0899908i
$723$	2.11710	−	1.13162i	0.0787360	−	0.0420852i
$724$	−3.26799	+	13.6714i	−0.121454	+	0.508095i
$725$	60.7493	−	49.8557i	2.25617	−	1.85159i
$726$	−0.838524	+	4.99246i	−0.0311205	+	0.185288i
$727$	−43.8889	−	29.3256i	−1.62775	−	1.08763i	−0.927563	−	0.373666i	$-0.878100\pi$
$727$	−43.8889	−	29.3256i	−1.62775	−	1.08763i	−0.700186	−	0.713961i	$-0.746900\pi$
$728$	−14.7589	+	1.32943i	−0.547000	+	0.0492719i
$729$	11.8801	+	17.7798i	0.440003	+	0.658512i
$730$	−21.0039	+	55.3389i	−0.777389	+	2.04818i
$731$	1.35251	+	0.722929i	0.0500242	+	0.0267385i
$732$	0.0901908	+	1.50415i	0.00333355	+	0.0555951i
$733$	2.82389	+	28.6714i	0.104303	+	1.05900i	0.894779	+	0.446510i	$0.147333\pi$
$733$	2.82389	+	28.6714i	0.104303	+	1.05900i	−0.790476	+	0.612493i	$0.790167\pi$
$734$	15.3221	−	30.8535i	0.565548	−	1.13883i
$735$	−0.996449	+	0.996449i	−0.0367546	+	0.0367546i
$736$	−45.7093	−	6.66540i	−1.68487	−	0.245690i
$737$	0.585117	+	0.585117i	0.0215531	+	0.0215531i
$738$	−14.1653	+	4.76461i	−0.521434	+	0.175388i
$739$	−46.8216	+	4.61153i	−1.72236	+	0.169638i	−0.910304	−	0.413940i	$-0.864152\pi$
$739$	−46.8216	+	4.61153i	−1.72236	+	0.169638i	−0.812057	+	0.583578i	$0.801652\pi$
$740$	20.3430	+	7.03192i	0.747825	+	0.258499i
$741$	−4.60097	+	8.60781i	−0.169021	+	0.316216i
$742$	3.05860	+	6.80071i	0.112285	+	0.249662i
$743$	−11.4563	+	7.65489i	−0.420293	+	0.280831i	−0.747679	−	0.664060i	$-0.768832\pi$
$743$	−11.4563	+	7.65489i	−0.420293	+	0.280831i	0.327387	+	0.944890i	$0.393832\pi$
$744$	6.00284	+	7.44017i	0.220075	+	0.272770i
$745$	24.4633	−	36.6119i	0.896266	−	1.34136i
$746$	17.4740	−	12.4483i	0.639768	−	0.455765i
$747$	−3.78407	−	4.61090i	−0.138452	−	0.168704i
$748$	0.0278616	+	0.174797i	0.00101872	+	0.00639122i
$749$	6.30221	+	11.7906i	0.230278	+	0.430820i
$750$	10.3845	−	13.4557i	0.379188	−	0.491333i
$751$	−17.0952	−	41.2714i	−0.623811	−	1.50601i	−0.847194	−	0.531283i	$-0.821710\pi$
$751$	−17.0952	−	41.2714i	−0.623811	−	1.50601i	0.223383	−	0.974731i	$-0.428290\pi$
$752$	−15.9295	+	1.91719i	−0.580888	+	0.0699128i
$753$	−0.570826	+	1.37810i	−0.0208021	+	0.0502206i
$754$	−21.4165	−	37.3338i	−0.779944	−	1.35962i
$755$	−41.3506	−	12.5436i	−1.50490	−	0.456508i
$756$	2.62183	+	2.83069i	0.0953552	+	0.102951i
$757$	−2.41617	+	24.5318i	−0.0878172	+	0.891623i	0.845836	+	0.533444i	$0.179102\pi$
$757$	−2.41617	+	24.5318i	−0.0878172	+	0.891623i	−0.933653	+	0.358179i	$0.883398\pi$
$758$	14.7627	−	23.5939i	0.536207	−	0.856968i
$759$	−0.133619	−	0.671749i	−0.00485007	−	0.0243829i
$760$	14.0825	−	67.8357i	0.510827	−	2.46066i
$761$	7.99543	+	1.59039i	0.289834	+	0.0576516i	0.337866	−	0.941194i	$-0.390295\pi$
$761$	7.99543	+	1.59039i	0.289834	+	0.0576516i	−0.0480319	+	0.998846i	$0.515295\pi$
$762$	0.258379	+	8.62594i	0.00936007	+	0.312485i
$763$	3.21999	+	10.6149i	0.116571	+	0.384284i
$764$	−19.1967	−	2.63597i	−0.694513	−	0.0953660i
$765$	3.32503	+	2.72879i	0.120217	+	0.0986594i
$766$	−10.6310	−	12.1906i	−0.384115	−	0.440464i
$767$	−11.8543			−0.428035
$768$	1.73561	+	4.94212i	0.0626285	+	0.178333i
$769$	−19.1872			−0.691908			−0.345954	−	0.938251i	$-0.612445\pi$
$769$	−19.1872			−0.691908			−0.345954	+	0.938251i	$0.612445\pi$
$770$	1.02508	+	1.17545i	0.0369413	+	0.0423604i
$771$	0.711351	+	0.583791i	0.0256187	+	0.0210247i
$772$	16.7866	+	2.30502i	0.604162	+	0.0829596i
$773$	−7.95408	−	26.2211i	−0.286088	−	0.943107i	−0.975734	−	0.218960i	$-0.929734\pi$
$773$	−7.95408	−	26.2211i	−0.286088	−	0.943107i	0.689645	−	0.724147i	$-0.257766\pi$
$774$	−0.543795	−	18.1546i	−0.0195463	−	0.652552i
$775$	136.990	+	27.2490i	4.92082	+	0.978812i
$776$	45.8966	+	9.52802i	1.64759	+	0.342036i
$777$	−0.159682	−	0.802775i	−0.00572855	−	0.0287994i
$778$	4.65360	−	7.43741i	0.166840	−	0.266644i
$779$	2.03760	−	20.6881i	0.0730046	−	0.741228i
$780$	−10.0338	−	10.8331i	−0.359269	−	0.387888i
$781$	−1.17349	−	0.355975i	−0.0419908	−	0.0127378i
$782$	1.98496	+	3.46023i	0.0709820	+	0.123738i
$783$	−4.28854	+	10.3535i	−0.153260	+	0.370003i
$784$	−3.14614	−	2.47019i	−0.112362	−	0.0882209i
$785$	13.3303	+	32.1822i	0.475778	+	1.14863i
$786$	−2.37063	+	3.07174i	−0.0845575	+	0.109565i
$787$	−0.290489	−	0.543466i	−0.0103548	−	0.0193725i	0.876691	−	0.481055i	$-0.159746\pi$
$787$	−0.290489	−	0.543466i	−0.0103548	−	0.0193725i	−0.887045	+	0.461682i	$0.847246\pi$
$788$	−5.40265	−	33.8950i	−0.192462	−	1.20746i
$789$	2.27234	+	2.76886i	0.0808976	+	0.0985740i
$790$	10.4029	−	7.41093i	0.370119	−	0.263669i
$791$	−6.24067	+	9.33982i	−0.221893	+	0.332086i
$792$	1.63150	−	1.31632i	0.0579728	−	0.0467733i
$793$	10.0254	−	6.69879i	0.356014	−	0.237881i
$794$	8.54504	+	18.9996i	0.303252	+	0.674272i
$795$	−3.50266	+	6.55301i	−0.124226	+	0.232411i
$796$	42.6281	+	14.7351i	1.51091	+	0.522272i
$797$	24.8270	−	2.44524i	0.879416	−	0.0866149i	0.351777	−	0.936084i	$-0.385577\pi$
$797$	24.8270	−	2.44524i	0.879416	−	0.0866149i	0.527639	+	0.849469i	$0.323077\pi$
$798$	−2.49713	+	0.839926i	−0.0883974	+	0.0297331i
$799$	0.979750	+	0.979750i	0.0346611	+	0.0346611i
$800$	65.7386	+	39.1826i	2.32421	+	1.38531i
$801$	21.2093	−	21.2093i	0.749393	−	0.749393i
$802$	−14.6844	+	29.5696i	−0.518525	+	1.04414i
$803$	−0.244177	−	2.47917i	−0.00861683	−	0.0874882i
$804$	−0.126572	−	2.11091i	−0.00446386	−	0.0744459i
$805$	30.9993	+	16.5695i	1.09258	+	0.583996i
$806$	27.1445	−	71.5173i	0.956123	−	2.51909i
$807$	−1.11407	−	1.66732i	−0.0392171	−	0.0586925i
$808$	−4.60464	−	51.1192i	−0.161991	−	1.79837i
$809$	26.6774	+	17.8253i	0.937928	+	0.626703i	0.927733	−	0.373245i	$-0.121755\pi$
$809$	26.6774	+	17.8253i	0.937928	+	0.626703i	0.0101950	+	0.999948i	$0.496755\pi$
$810$	8.11384	−	48.3088i	0.285091	−	1.69740i
$811$	11.0136	−	9.03866i	0.386741	−	0.317390i	−0.420853	−	0.907129i	$-0.638269\pi$
$811$	11.0136	−	9.03866i	0.386741	−	0.317390i	0.807594	+	0.589739i	$0.200769\pi$
$812$	2.70103	−	11.2996i	0.0947876	−	0.396538i
$813$	−3.32057	+	1.77488i	−0.116458	+	0.0622479i
$814$	−0.898463	+	0.115745i	−0.0314911	+	0.00405684i
$815$	31.5355	−	13.0624i	1.10464	−	0.457557i
$816$	0.243128	−	0.381455i	0.00851118	−	0.0133536i
$817$	23.3406	+	9.66798i	0.816583	+	0.338240i
$818$	13.2684	+	3.59481i	0.463917	+	0.125690i
$819$	4.39956	−	14.5034i	0.153733	−	0.506790i
$820$	28.5738	+	13.1386i	0.997841	+	0.458820i
$821$	−51.7396	−	5.09590i	−1.80572	−	0.177848i	−0.861632	−	0.507533i	$-0.830558\pi$
$821$	−51.7396	−	5.09590i	−1.80572	−	0.177848i	−0.944091	+	0.329685i	$0.893058\pi$
$822$	1.44060	−	0.331680i	0.0502466	−	0.0115687i
$823$	6.47249	−	1.28746i	0.225617	−	0.0448780i	−0.0809871	−	0.996715i	$-0.525807\pi$
$823$	6.47249	−	1.28746i	0.225617	−	0.0448780i	0.306604	+	0.951837i	$0.400807\pi$
$824$	−9.24862	+	21.8118i	−0.322191	+	0.759850i
$825$	−0.221374	+	1.11292i	−0.00770725	+	0.0387470i
$826$	−2.32936	−	2.19388i	−0.0810490	−	0.0763347i
$827$	−14.0651	+	4.26661i	−0.489093	+	0.148365i	−0.525192	−	0.850984i	$-0.676007\pi$
$827$	−14.0651	+	4.26661i	−0.489093	+	0.148365i	0.0360997	+	0.999348i	$0.488507\pi$
$828$	23.8494	−	40.7829i	0.828823	−	1.41730i
$829$	−2.28293	+	2.78175i	−0.0792893	+	0.0966143i	−0.811144	−	0.584846i	$-0.801155\pi$
$829$	−2.28293	+	2.78175i	−0.0792893	+	0.0966143i	0.731855	+	0.681460i	$0.238655\pi$
$830$	−0.855765	+	12.5229i	−0.0297040	+	0.434675i
$831$		−	7.61521i		−	0.264169i
$832$	27.1263	−	31.9515i	0.940436	−	1.10772i
$833$			0.345435i			0.0119686i
$834$	6.82436	+	0.466351i	0.236308	+	0.0161484i
$835$	−32.8248	+	39.9972i	−1.13595	+	1.38416i
$836$	0.739012	+	2.82068i	0.0255593	+	0.0975551i
$837$	−19.0596	+	5.78166i	−0.658795	+	0.199843i
$838$	−11.7579	+	12.4840i	−0.406169	+	0.431253i
$839$	0.768467	−	3.86335i	0.0265304	−	0.133377i	−0.965250	−	0.261328i	$-0.915840\pi$
$839$	0.768467	−	3.86335i	0.0265304	−	0.133377i	0.991781	+	0.127950i	$0.0408397\pi$
$840$	0.0332436	−	3.98566i	0.00114701	−	0.137518i
$841$	4.65301	−	0.925541i	0.160449	−	0.0319152i
$842$	0.420385	+	1.82587i	0.0144874	+	0.0629238i
$843$	−5.56630	−	0.548232i	−0.191713	−	0.0188821i
$844$	−16.2830	−	44.0034i	−0.560483	−	1.51466i
$845$	−18.0544	+	59.5174i	−0.621090	+	2.04746i
$846$	4.29120	−	15.8387i	0.147535	−	0.544546i
$847$	10.1020	+	4.18440i	0.347110	+	0.143778i
$848$	−19.6555	−	7.64842i	−0.674973	−	0.262648i
$849$	3.62378	−	1.50102i	0.124368	−	0.0515148i
$850$	−0.844431	−	6.55486i	−0.0289637	−	0.224830i
$851$	−18.0053	+	9.62405i	−0.617215	+	0.329908i
$852$	1.64009	+	2.67048i	0.0561886	+	0.0914891i
$853$	−25.6196	+	21.0254i	−0.877198	+	0.719898i	−0.960989	−	0.276586i	$-0.910797\pi$
$853$	−25.6196	+	21.0254i	−0.877198	+	0.719898i	0.0837915	+	0.996483i	$0.473297\pi$
$854$	3.20973	+	0.539100i	0.109835	+	0.0184476i
$855$	58.9174	+	39.3674i	2.01493	+	1.34634i
$856$	−36.0928	−	11.2782i	−1.23363	−	0.385482i
$857$	−13.7373	−	20.5593i	−0.469257	−	0.702293i	0.519054	−	0.854741i	$-0.326284\pi$
$857$	−13.7373	−	20.5593i	−0.469257	−	0.702293i	−0.988311	+	0.152449i	$0.951284\pi$
$858$	0.581016	+	0.220525i	0.0198355	+	0.00752859i
$859$	42.2191	+	22.5666i	1.44050	+	0.769962i	0.992287	−	0.123965i	$-0.0395611\pi$
$859$	42.2191	+	22.5666i	1.44050	+	0.769962i	0.448212	+	0.893927i	$0.352061\pi$
$860$	−25.3599	+	28.5951i	−0.864765	+	0.975085i
$861$	−0.117223	−	1.19019i	−0.00399496	−	0.0405615i
$862$	−14.1115	−	7.00784i	−0.480638	−	0.238688i
$863$	19.4449	−	19.4449i	0.661913	−	0.661913i	−0.293918	−	0.955831i	$-0.594959\pi$
$863$	19.4449	−	19.4449i	0.661913	−	0.661913i	0.955831	+	0.293918i	$0.0949592\pi$
$864$	−10.9012	−	0.508647i	−0.370866	−	0.0173045i
$865$	−67.0394	−	67.0394i	−2.27941	−	2.27941i
$866$	17.8257	+	52.9965i	0.605742	+	1.80089i
$867$	5.49972	−	0.541675i	0.186780	−	0.0183963i
$868$	18.5695	−	9.02947i	0.630291	−	0.306480i
$869$	−0.253407	+	0.474092i	−0.00859625	+	0.0160825i
$870$	10.5580	−	4.74845i	0.357951	−	0.160987i
$871$	−14.0696	+	9.40097i	−0.476729	+	0.318540i
$872$	−27.5454	−	15.0200i	−0.932805	−	0.508642i
$873$	−26.6354	+	39.8626i	−0.901471	+	1.34915i
$874$	38.1291	+	53.5227i	1.28973	+	1.81043i
$875$	−23.2898	−	28.3787i	−0.787338	−	0.959374i
$876$	−3.73700	+	5.15421i	−0.126262	+	0.174145i
$877$	15.7268	+	29.4227i	0.531056	+	0.993535i	0.994230	+	0.107268i	$0.0342104\pi$
$877$	15.7268	+	29.4227i	0.531056	+	0.993535i	−0.463174	+	0.886267i	$0.653290\pi$
$878$	−15.3100	−	11.8156i	−0.516688	−	0.398756i
$879$	−2.47392	−	5.97257i	−0.0834432	−	0.201450i
$880$	−4.39840	−	0.337448i	−0.148270	−	0.0113754i
$881$	14.5940	−	35.2331i	0.491685	−	1.18703i	−0.462177	−	0.886787i	$-0.652932\pi$
$881$	14.5940	−	35.2331i	0.491685	−	1.18703i	0.953862	−	0.300245i	$-0.0970683\pi$
$882$	3.54865	−	2.03568i	0.119489	−	0.0685448i
$883$	−55.6784	−	16.8899i	−1.87373	−	0.568389i	−0.996013	−	0.0892044i	$-0.971568\pi$
$883$	−55.6784	−	16.8899i	−1.87373	−	0.568389i	−0.877714	−	0.479185i	$-0.840932\pi$
$884$	−3.61693	−	0.138543i	−0.121651	−	0.00465971i
$885$	0.312526	−	3.17313i	0.0105055	−	0.106664i
$886$	−23.6781	−	14.8155i	−0.795483	−	0.497735i
$887$	−3.81172	−	19.1628i	−0.127985	−	0.643425i	−0.990513	−	0.137416i	$-0.956120\pi$
$887$	−3.81172	−	19.1628i	−0.127985	−	0.643425i	0.862528	−	0.506009i	$-0.168880\pi$
$888$	1.91412	+	1.30220i	0.0642336	+	0.0436988i
$889$	18.2815	+	3.63642i	0.613143	+	0.121962i
$890$	−63.0902	+	1.88978i	−2.11479	+	0.0633456i
$891$	0.598467	+	1.97288i	0.0200494	+	0.0660940i
$892$	8.77240	+	11.5650i	0.293722	+	0.387225i
$893$	17.6442	+	14.4802i	0.590441	+	0.484562i
$894$	3.56941	−	3.11278i	0.119379	−	0.104107i
$895$	38.3193			1.28087
$896$	11.2435	−	1.25817i	0.375620	−	0.0420326i
$897$	14.0058			0.467641
$898$	2.91870	−	2.54531i	0.0973984	−	0.0849382i
$899$	46.3599	+	38.0466i	1.54619	+	1.26892i
$900$	−62.3617	+	47.3032i	−2.07872	+	1.57677i
$901$	0.528726	+	1.74298i	0.0176144	+	0.0580670i
$902$	−1.32303	+	0.0396297i	−0.0440522	+	0.00131953i
$903$	1.42549	+	0.283548i	0.0474374	+	0.00943588i
$904$	−5.93819	−	31.2116i	−0.197501	−	1.03808i
$905$	5.90213	+	29.6720i	0.196194	+	0.986332i
$906$	−3.93999	−	2.46526i	−0.130897	−	0.0819027i
$907$	1.86809	−	18.9670i	0.0620288	−	0.629789i	−0.913037	−	0.407876i	$-0.866270\pi$
$907$	1.86809	−	18.9670i	0.0620288	−	0.629789i	0.975066	−	0.221914i	$-0.0712303\pi$
$908$	0.258434	−	6.74691i	0.00857643	−	0.223904i
$909$	50.2343	+	15.2384i	1.66617	+	0.505426i
$910$	−27.6647	+	15.8698i	−0.917076	+	0.526080i
$911$	5.24032	−	12.6513i	0.173620	−	0.419155i	−0.812985	−	0.582285i	$-0.802159\pi$
$911$	5.24032	−	12.6513i	0.173620	−	0.419155i	0.986605	+	0.163130i	$0.0521589\pi$
$912$	3.36996	−	6.64623i	0.111590	−	0.220079i
$913$	−0.202164	−	0.488068i	−0.00669066	−	0.0161527i
$914$	−5.92030	−	4.56901i	−0.195826	−	0.151129i
$915$	1.52880	+	2.86018i	0.0505406	+	0.0945548i
$916$	31.4006	+	22.7666i	1.03750	+	0.752231i
$917$	5.31672	+	6.47844i	0.175574	+	0.213937i
$918$	0.546816	+	0.767579i	0.0180476	+	0.0253339i
$919$	15.3683	−	23.0003i	0.506954	−	0.758710i	−0.486409	−	0.873731i	$-0.661694\pi$
$919$	15.3683	−	23.0003i	0.506954	−	0.758710i	0.993363	+	0.115021i	$0.0366937\pi$
$920$	−95.3748	+	28.0651i	−3.14442	+	0.925280i
$921$	−5.88941	+	3.93518i	−0.194063	+	0.129668i
$922$	−16.0813	+	7.23253i	−0.529610	+	0.238191i
$923$	11.8211	−	22.1157i	0.389096	−	0.727948i
$924$	0.0733565	+	0.150861i	0.00241325	+	0.00496297i
$925$	33.6615	−	3.31536i	1.10678	−	0.109008i
$926$	1.54572	+	4.59548i	0.0507955	+	0.151017i
$927$	−17.1339	−	17.1339i	−0.562751	−	0.562751i
$928$	16.9630	+	28.1437i	0.556838	+	0.923863i
$929$	6.26843	−	6.26843i	0.205661	−	0.205661i	−0.596760	−	0.802420i	$-0.703545\pi$
$929$	6.26843	−	6.26843i	0.205661	−	0.205661i	0.802420	+	0.596760i	$0.203545\pi$
$930$	18.4279	+	9.15142i	0.604275	+	0.300087i
$931$	0.557770	+	5.66313i	0.0182802	+	0.185602i
$932$	−10.5317	−	9.34013i	−0.344976	−	0.305946i
$933$	−2.88181	−	1.54036i	−0.0943462	−	0.0504291i
$934$	46.9776	+	17.8304i	1.53716	+	0.583429i
$935$	0.211648	+	0.316754i	0.00692163	+	0.0103590i
$936$	19.8917	+	37.9731i	0.650179	+	1.24119i
$937$	−30.7051	−	20.5165i	−1.00309	−	0.670245i	−0.0584311	−	0.998291i	$-0.518610\pi$
$937$	−30.7051	−	20.5165i	−1.00309	−	0.670245i	−0.944662	+	0.328046i	$0.893610\pi$
$938$	−4.50449	−	0.756564i	−0.147077	−	0.0247027i
$939$	−3.35090	+	2.75001i	−0.109352	+	0.0897433i
$940$	−29.4253	+	18.0717i	−0.959746	+	0.589434i
$941$	37.1098	−	19.8356i	1.20974	−	0.646622i	0.261820	−	0.965117i	$-0.415677\pi$
$941$	37.1098	−	19.8356i	1.20974	−	0.646622i	0.947925	+	0.318495i	$0.103177\pi$
$942$	0.478703	+	3.71591i	0.0155970	+	0.121071i
$943$	−27.5600	+	11.4157i	−0.897475	+	0.371747i
$944$	9.04843	−	0.195514i	0.294501	−	0.00636342i
$945$	7.67201	+	3.17785i	0.249570	+	0.103375i
$946$	0.420652	−	1.55261i	0.0136766	−	0.0504798i
$947$	−5.28224	+	17.4132i	−0.171650	+	0.565853i	0.828335	+	0.560234i	$0.189289\pi$
$947$	−5.28224	+	17.4132i	−0.171650	+	0.565853i	−0.999984	+	0.00561931i	$0.998211\pi$
$948$	1.28842	−	0.476764i	0.0418458	−	0.0154846i
$949$	50.6971	+	4.99323i	1.64570	+	0.162087i
$950$	−24.4278	−	106.098i	−0.792544	−	3.44228i
$951$	0.883739	−	0.175787i	0.0286572	−	0.00570027i
$952$	−0.685083	−	0.696608i	−0.0222037	−	0.0225772i
$953$	8.66535	−	43.5636i	0.280698	−	1.41116i	−0.540895	−	0.841090i	$-0.681914\pi$
$953$	8.66535	−	43.5636i	0.280698	−	1.41116i	0.821593	−	0.570075i	$-0.193086\pi$
$954$	14.7897	−	15.7031i	0.478836	−	0.508407i
$955$	−39.9081	+	12.1060i	−1.29140	+	0.391741i
$956$	42.7757	−	11.2072i	1.38347	−	0.362466i
$957$	−0.309095	+	0.376633i	−0.00999162	+	0.0121748i
$958$	−27.6203	−	1.88746i	−0.892370	−	0.0609811i
$959$		−	3.19298i		−	0.103107i
$960$	7.83751	+	8.10345i	0.252955	+	0.261538i
$961$			75.5897i			2.43838i
$962$	1.26296	−	18.4816i	0.0407194	−	0.595869i
$963$	24.5351	−	29.8961i	0.790632	−	0.963387i
$964$	12.6597	+	7.40323i	0.407741	+	0.238442i
$965$	34.8976	−	10.5861i	1.12339	−	0.340778i
$966$	2.75213	+	2.59205i	0.0885484	+	0.0833980i
$967$	5.41044	−	27.2001i	0.173988	−	0.874697i	−0.790882	−	0.611969i	$-0.790378\pi$
$967$	5.41044	−	27.2001i	0.173988	−	0.874697i	0.964870	−	0.262728i	$-0.0846223\pi$
$968$	−28.6706	+	11.5965i	−0.921507	+	0.372727i
$969$	−0.631161	+	0.125546i	−0.0202758	+	0.00403311i
$970$	98.3149	−	22.6358i	3.15670	−	0.726792i
$971$	−31.2786	−	3.08068i	−1.00378	−	0.0988636i	−0.417250	−	0.908792i	$-0.637006\pi$
$971$	−31.2786	−	3.08068i	−1.00378	−	0.0988636i	−0.586529	+	0.809928i	$0.699506\pi$
$972$	7.03674	−	15.3035i	0.225704	−	0.490860i
$973$	4.28880	−	14.1383i	0.137493	−	0.453252i
$974$	17.3586	+	4.70299i	0.556205	+	0.150693i
$975$	−21.4379	−	8.87987i	−0.686562	−	0.284383i
$976$	−7.54195	+	5.27854i	−0.241412	+	0.168962i
$977$	−11.7212	+	4.85508i	−0.374995	+	0.155328i	−0.562217	−	0.826990i	$-0.690051\pi$
$977$	−11.7212	+	4.85508i	−0.374995	+	0.155328i	0.187222	+	0.982318i	$0.440051\pi$
$978$	3.64124	−	0.469083i	0.116434	−	0.0149996i
$979$	2.34280	−	1.25225i	0.0748762	−	0.0400222i
$980$	−8.37311	−	2.00149i	−0.267469	−	0.0639352i
$981$	24.8049	−	20.3568i	0.791959	−	0.649944i
$982$	−2.91329	+	17.3453i	−0.0929667	+	0.553512i
$983$	−6.92118	−	4.62459i	−0.220751	−	0.147501i	0.440278	−	0.897862i	$-0.354880\pi$
$983$	−6.92118	−	4.62459i	−0.220751	−	0.147501i	−0.661029	+	0.750360i	$0.729880\pi$
$984$	2.59683	+	2.16766i	0.0827840	+	0.0691025i
$985$	−41.0407	−	61.4218i	−1.30767	−	1.95706i
$986$	1.00699	−	2.65312i	0.0320692	−	0.0844924i
$987$	1.15809	+	0.619011i	0.0368623	+	0.0197033i
$988$	−59.5205	+	3.56891i	−1.89360	+	0.113542i
$989$	−3.55340	−	36.0783i	−0.112992	−	1.14722i
$990$	2.00675	−	4.04092i	0.0637786	−	0.128429i
$991$	−32.1148	+	32.1148i	−1.02016	+	1.02016i	−0.0203661	+	0.999793i	$0.506483\pi$
$991$	−32.1148	+	32.1148i	−1.02016	+	1.02016i	−0.999793	+	0.0203661i	$0.993517\pi$
$992$	−19.5399	+	55.0369i	−0.620391	+	1.74742i
$993$	−6.35161	−	6.35161i	−0.201562	−	0.201562i
$994$	6.41578	−	2.15799i	0.203496	−	0.0684473i
$995$	96.6054	−	9.51480i	3.06260	−	0.301639i
$996$	−0.441067	+	1.27599i	−0.0139757	+	0.0404312i
$997$	−0.0341379	+	0.0638675i	−0.00108116	+	0.00202270i	−0.882461	−	0.470385i	$-0.844115\pi$
$997$	−0.0341379	+	0.0638675i	−0.00108116	+	0.00202270i	0.881380	+	0.472408i	$0.156615\pi$
$998$	−1.04680	−	2.32753i	−0.0331359	−	0.0736768i
$999$	−4.01042	+	2.67968i	−0.126884	+	0.0847812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.b.533.36	✓	784
128.61	even	32	inner	896.2.bn.b.701.36	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.b.533.36	✓	784	1.1	even	1	trivial
896.2.bn.b.701.36	yes	784	128.61	even	32	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929496 + 1.06585i) q^{2} +(0.253065 + 0.207685i) q^{3} +(-0.272074 + 1.98141i) q^{4} +(1.24953 + 4.11915i) q^{5} +(0.0138617 + 0.462773i) q^{6} +(0.980785 + 0.195090i) q^{7} +(-2.36478 + 1.55172i) q^{8} +(-0.564362 - 2.83724i) q^{9} +O(q^{10})\)	\(q+(0.929496 + 1.06585i) q^{2} +(0.253065 + 0.207685i) q^{3} +(-0.272074 + 1.98141i) q^{4} +(1.24953 + 4.11915i) q^{5} +(0.0138617 + 0.462773i) q^{6} +(0.980785 + 0.195090i) q^{7} +(-2.36478 + 1.55172i) q^{8} +(-0.564362 - 2.83724i) q^{9} +(-3.22896 + 5.16055i) q^{10} +(0.0251124 - 0.254971i) q^{11} +(-0.480362 + 0.444920i) q^{12} +(5.01358 + 1.52085i) q^{13} +(0.703699 + 1.22671i) q^{14} +(-0.539274 + 1.30192i) q^{15} +(-3.85195 - 1.07818i) q^{16} +(0.132192 + 0.319140i) q^{17} +(2.49950 - 3.23873i) q^{18} +(2.68250 + 5.01860i) q^{19} +(-8.50168 + 1.35512i) q^{20} +(0.207685 + 0.253065i) q^{21} +(0.295103 - 0.210228i) q^{22} +(4.53668 - 6.78962i) q^{23} +(-0.920712 - 0.0984426i) q^{24} +(-11.2487 + 7.51615i) q^{25} +(3.03910 + 6.75735i) q^{26} +(0.909405 - 1.70138i) q^{27} +(-0.653400 + 1.89026i) q^{28} +(-5.78100 + 0.569379i) q^{29} +(-1.88891 + 0.635347i) q^{30} +(-7.30033 - 7.30033i) q^{31} +(-2.43120 - 5.10777i) q^{32} +(0.0593088 - 0.0593088i) q^{33} +(-0.217283 + 0.437536i) q^{34} +(0.421915 + 4.28377i) q^{35} +(5.77528 - 0.346292i) q^{36} +(-2.20497 - 1.17858i) q^{37} +(-2.85571 + 7.52391i) q^{38} +(0.952904 + 1.42612i) q^{39} +(-9.34663 - 7.80194i) q^{40} +(-3.03746 - 2.02957i) q^{41} +(-0.0766871 + 0.456585i) q^{42} +(3.43185 - 2.81645i) q^{43} +(0.498369 + 0.119129i) q^{44} +(10.9818 - 5.86991i) q^{45} +(11.4535 - 1.47550i) q^{46} +(3.70578 - 1.53498i) q^{47} +(-0.750874 - 1.07284i) q^{48} +(0.923880 + 0.382683i) q^{49} +(-18.4667 - 5.00322i) q^{50} +(-0.0328275 + 0.108218i) q^{51} +(-4.37749 + 9.52016i) q^{52} +(5.24740 + 0.516824i) q^{53} +(2.65870 - 0.612134i) q^{54} +(1.08164 - 0.215152i) q^{55} +(-2.62206 + 1.06056i) q^{56} +(-0.363443 + 1.82715i) q^{57} +(-5.98029 - 5.63245i) q^{58} +(-2.16521 + 0.656808i) q^{59} +(-2.43292 - 1.42274i) q^{60} +(1.46000 - 1.77902i) q^{61} +(0.995431 - 14.5667i) q^{62} -2.89282i q^{63} +(3.18433 - 7.33894i) q^{64} +22.5520i q^{65} +(0.118342 + 0.00808701i) q^{66} +(-2.04894 + 2.49664i) q^{67} +(-0.668313 + 0.175097i) q^{68} +(2.55818 - 0.776015i) q^{69} +(-4.17369 + 4.43145i) q^{70} +(0.933779 - 4.69443i) q^{71} +(5.73719 + 5.83370i) q^{72} +(9.53654 - 1.89693i) q^{73} +(-0.793319 - 3.44565i) q^{74} +(-4.40766 - 0.434116i) q^{75} +(-10.6737 + 3.94969i) q^{76} +(0.0743722 - 0.245172i) q^{77} +(-0.634312 + 2.34123i) q^{78} +(-1.93848 - 0.802944i) q^{79} +(-0.371950 - 17.2140i) q^{80} +(-7.43437 + 3.07942i) q^{81} +(-0.660094 - 5.12395i) q^{82} +(1.81848 - 0.971996i) q^{83} +(-0.557931 + 0.342657i) q^{84} +(-1.14941 + 0.943294i) q^{85} +(6.19181 + 1.03996i) q^{86} +(-1.58122 - 1.05654i) q^{87} +(0.336258 + 0.641916i) q^{88} +(5.76047 + 8.62115i) q^{89} +(16.4640 + 6.24893i) q^{90} +(4.62054 + 2.46973i) q^{91} +(12.2187 + 10.8363i) q^{92} +(-0.331289 - 3.36363i) q^{93} +(5.08057 + 2.52304i) q^{94} +(-17.3205 + 17.3205i) q^{95} +(0.445557 - 1.79752i) q^{96} +(-11.7188 - 11.7188i) q^{97} +(0.450859 + 1.34042i) q^{98} +(-0.737586 + 0.0726459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q+O(q^{10}) \) 784 * q	\( 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) \) 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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