LMFDB - Embedded newform 950.2.w.a.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

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

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-0.380740 + 0.747244i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.16957 + 0.541276i) q^{5} +(0.259158 - 0.797606i) q^{6} +(-1.83916 - 1.83916i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.34994 + 1.85804i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.380740 + 0.747244i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.16957 + 0.541276i) q^{5} +(0.259158 - 0.797606i) q^{6} +(-1.83916 - 1.83916i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.34994 + 1.85804i) q^{9} +(-2.22753 - 0.195217i) q^{10} +(-3.00261 - 2.18152i) q^{11} +(-0.131194 + 0.828327i) q^{12} +(0.658072 + 0.104228i) q^{13} +(2.10422 + 1.52881i) q^{14} +(-1.23051 + 1.41511i) q^{15} +(0.809017 - 0.587785i) q^{16} +(5.45407 - 2.77899i) q^{17} +(-1.62399 - 1.62399i) q^{18} +(1.86720 + 3.93873i) q^{19} +(2.23064 - 0.155649i) q^{20} +(2.07454 - 0.674059i) q^{21} +(3.30691 + 1.68495i) q^{22} +(1.70110 - 0.269427i) q^{23} -0.838652i q^{24} +(4.41404 + 2.34867i) q^{25} -0.666275 q^{26} +(-4.38737 + 0.694891i) q^{27} +(-2.31747 - 1.18081i) q^{28} +(1.92853 + 5.93541i) q^{29} +(0.993985 - 1.59018i) q^{30} +(3.39330 + 1.10255i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.77334 - 1.41309i) q^{33} +(-4.95220 + 3.59798i) q^{34} +(-2.99468 - 4.98567i) q^{35} +(1.85804 + 1.34994i) q^{36} +(1.85202 - 11.6932i) q^{37} +(-2.46036 - 3.59814i) q^{38} +(-0.328438 + 0.452057i) q^{39} +(-2.17883 + 0.502682i) q^{40} +(0.558272 + 0.768395i) q^{41} +(-1.94355 + 0.990290i) q^{42} +(1.20512 - 1.20512i) q^{43} +(-3.52978 - 1.14689i) q^{44} +(1.92308 + 4.76183i) q^{45} +(-1.63801 + 0.532220i) q^{46} +(-5.02558 + 9.86325i) q^{47} +(0.131194 + 0.828327i) q^{48} -0.235001i q^{49} +(-4.72711 - 1.62925i) q^{50} +5.13360i q^{51} +(0.658072 - 0.104228i) q^{52} +(3.97196 - 7.79542i) q^{53} +(4.22465 - 1.37267i) q^{54} +(-5.33355 - 6.35820i) q^{55} +(2.47366 + 0.803741i) q^{56} +(-3.65411 - 0.104378i) q^{57} +(-2.83329 - 5.56065i) q^{58} +(7.34987 - 5.33999i) q^{59} +(-0.732988 + 1.72610i) q^{60} +(10.1421 + 7.36864i) q^{61} +(-3.52400 - 0.558147i) q^{62} +(0.934466 - 5.89999i) q^{63} +(0.587785 - 0.809017i) q^{64} +(1.37131 + 0.582329i) q^{65} +(-2.51814 + 1.82954i) q^{66} +(5.06302 + 9.93673i) q^{67} +(4.32838 - 4.32838i) q^{68} +(-0.446348 + 1.37372i) q^{69} +(3.73774 + 4.45581i) q^{70} +(-8.53999 + 2.77481i) q^{71} +(-2.04634 - 1.04266i) q^{72} +(-4.68056 + 0.741328i) q^{73} +11.8390i q^{74} +(-3.43563 + 2.40413i) q^{75} +(2.99294 + 3.16896i) q^{76} +(1.51011 + 9.53443i) q^{77} +(0.253678 - 0.497870i) q^{78} +(3.77615 + 11.6218i) q^{79} +(2.07337 - 0.837338i) q^{80} +(-0.977930 + 3.00976i) q^{81} +(-0.671602 - 0.671602i) q^{82} +(4.13218 + 8.10985i) q^{83} +(1.76471 - 1.28214i) q^{84} +(13.3372 - 3.07704i) q^{85} +(-1.00176 + 1.37881i) q^{86} +(-5.16947 - 0.818764i) q^{87} +(3.66573 + 0.580595i) q^{88} +(8.57473 + 6.22991i) q^{89} +(-2.64432 - 4.40237i) q^{90} +(-1.01861 - 1.40199i) q^{91} +(1.53458 - 0.781908i) q^{92} +(-2.11584 + 2.11584i) q^{93} +(3.42075 - 10.5280i) q^{94} +(1.91907 + 9.55600i) q^{95} +(-0.259158 - 0.797606i) q^{96} +(-5.50698 - 2.80595i) q^{97} +(0.0367623 + 0.232108i) q^{98} -8.52390i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−0.380740	+	0.747244i	−0.219820	+	0.431422i	−0.974411	−	0.224774i	$-0.927836\pi$
$3$	−0.380740	+	0.747244i	−0.219820	+	0.431422i	0.754590	+	0.656196i	$0.227836\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	2.16957	+	0.541276i	0.970260	+	0.242066i
$5$	2.16957	+	0.541276i	0.970260	+	0.242066i
$6$	0.259158	−	0.797606i	0.105801	−	0.325621i
$7$	−1.83916	−	1.83916i	−0.695136	−	0.695136i	0.268221	−	0.963357i	$-0.413564\pi$
$7$	−1.83916	−	1.83916i	−0.695136	−	0.695136i	−0.963357	+	0.268221i	$0.913564\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	1.34994	+	1.85804i	0.449981	+	0.619346i
$10$	−2.22753	−	0.195217i	−0.704407	−	0.0617331i
$11$	−3.00261	−	2.18152i	−0.905320	−	0.657754i	0.0345068	−	0.999404i	$-0.489014\pi$
$11$	−3.00261	−	2.18152i	−0.905320	−	0.657754i	−0.939827	+	0.341651i	$0.889014\pi$
$12$	−0.131194	+	0.828327i	−0.0378725	+	0.239117i
$13$	0.658072	+	0.104228i	0.182516	+	0.0289077i	0.247023	−	0.969010i	$-0.420548\pi$
$13$	0.658072	+	0.104228i	0.182516	+	0.0289077i	−0.0645072	+	0.997917i	$0.520548\pi$
$14$	2.10422	+	1.52881i	0.562377	+	0.408591i
$15$	−1.23051	+	1.41511i	−0.317715	+	0.365380i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	5.45407	−	2.77899i	1.32281	−	0.674004i	0.357205	−	0.934026i	$-0.383730\pi$
$17$	5.45407	−	2.77899i	1.32281	−	0.674004i	0.965603	+	0.260022i	$0.0837298\pi$
$18$	−1.62399	−	1.62399i	−0.382777	−	0.382777i
$19$	1.86720	+	3.93873i	0.428365	+	0.903606i
$19$	1.86720	+	3.93873i	0.428365	+	0.903606i
$20$	2.23064	−	0.155649i	0.498787	−	0.0348041i
$21$	2.07454	−	0.674059i	0.452702	−	0.147092i
$22$	3.30691	+	1.68495i	0.705035	+	0.359233i
$23$	1.70110	−	0.269427i	0.354703	−	0.0561795i	0.0234597	−	0.999725i	$-0.492532\pi$
$23$	1.70110	−	0.269427i	0.354703	−	0.0561795i	0.331243	+	0.943545i	$0.392532\pi$
$24$		−	0.838652i		−	0.171189i
$25$	4.41404	+	2.34867i	0.882808	+	0.469734i
$26$	−0.666275			−0.130667
$27$	−4.38737	+	0.694891i	−0.844349	+	0.133732i
$28$	−2.31747	−	1.18081i	−0.437961	−	0.223152i
$29$	1.92853	+	5.93541i	0.358119	+	1.10218i	0.954179	+	0.299238i	$0.0967324\pi$
$29$	1.92853	+	5.93541i	0.358119	+	1.10218i	−0.596059	+	0.802941i	$0.703268\pi$
$30$	0.993985	−	1.59018i	0.181476	−	0.290326i
$31$	3.39330	+	1.10255i	0.609455	+	0.198024i	0.597453	−	0.801904i	$-0.296179\pi$
$31$	3.39330	+	1.10255i	0.609455	+	0.198024i	0.0120022	+	0.999928i	$0.496179\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.77334	−	1.41309i	0.482777	−	0.245987i
$34$	−4.95220	+	3.59798i	−0.849295	+	0.617049i
$35$	−2.99468	−	4.98567i	−0.506194	−	0.842732i
$36$	1.85804	+	1.34994i	0.309673	+	0.224991i
$37$	1.85202	−	11.6932i	0.304470	−	1.92235i	−0.0750791	−	0.997178i	$-0.523921\pi$
$37$	1.85202	−	11.6932i	0.304470	−	1.92235i	0.379549	−	0.925172i	$-0.376079\pi$
$38$	−2.46036	−	3.59814i	−0.399124	−	0.583695i
$39$	−0.328438	+	0.452057i	−0.0525922	+	0.0723870i
$40$	−2.17883	+	0.502682i	−0.344504	+	0.0794810i
$41$	0.558272	+	0.768395i	0.0871874	+	0.120003i	0.850383	−	0.526165i	$-0.176371\pi$
$41$	0.558272	+	0.768395i	0.0871874	+	0.120003i	−0.763195	+	0.646168i	$0.776371\pi$
$42$	−1.94355	+	0.990290i	−0.299897	+	0.152805i
$43$	1.20512	−	1.20512i	0.183779	−	0.183779i	−0.609221	−	0.793000i	$-0.708518\pi$
$43$	1.20512	−	1.20512i	0.183779	−	0.183779i	0.793000	+	0.609221i	$0.208518\pi$
$44$	−3.52978	−	1.14689i	−0.532134	−	0.172901i
$45$	1.92308	+	4.76183i	0.286676	+	0.709852i
$46$	−1.63801	+	0.532220i	−0.241511	+	0.0784716i
$47$	−5.02558	+	9.86325i	−0.733056	+	1.43870i	0.159235	+	0.987241i	$0.449097\pi$
$47$	−5.02558	+	9.86325i	−0.733056	+	1.43870i	−0.892290	+	0.451462i	$0.850903\pi$
$48$	0.131194	+	0.828327i	0.0189362	+	0.119559i
$49$		−	0.235001i		−	0.0335716i
$50$	−4.72711	−	1.62925i	−0.668514	−	0.230410i
$51$			5.13360i			0.718848i
$52$	0.658072	−	0.104228i	0.0912581	−	0.0144539i
$53$	3.97196	−	7.79542i	0.545591	−	1.07078i	−0.439419	−	0.898282i	$-0.644815\pi$
$53$	3.97196	−	7.79542i	0.545591	−	1.07078i	0.985009	−	0.172500i	$-0.0551845\pi$
$54$	4.22465	−	1.37267i	0.574902	−	0.186797i
$55$	−5.33355	−	6.35820i	−0.719176	−	0.857339i
$56$	2.47366	+	0.803741i	0.330557	+	0.107404i
$57$	−3.65411	−	0.104378i	−0.483999	−	0.0138251i
$58$	−2.83329	−	5.56065i	−0.372029	−	0.730149i
$59$	7.34987	−	5.33999i	0.956872	−	0.695208i	0.00444951	−	0.999990i	$-0.498584\pi$
$59$	7.34987	−	5.33999i	0.956872	−	0.695208i	0.952422	+	0.304782i	$0.0985837\pi$
$60$	−0.732988	+	1.72610i	−0.0946284	+	0.222838i
$61$	10.1421	+	7.36864i	1.29856	+	0.943457i	0.999940	−	0.0109158i	$-0.00347467\pi$
$61$	10.1421	+	7.36864i	1.29856	+	0.943457i	0.298617	+	0.954373i	$0.403475\pi$
$62$	−3.52400	−	0.558147i	−0.447549	−	0.0708848i
$63$	0.934466	−	5.89999i	0.117732	−	0.743328i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	1.37131	+	0.582329i	0.170091	+	0.0722290i
$66$	−2.51814	+	1.82954i	−0.309962	+	0.225201i
$67$	5.06302	+	9.93673i	0.618546	+	1.21396i	0.961550	+	0.274631i	$0.0885556\pi$
$67$	5.06302	+	9.93673i	0.618546	+	1.21396i	−0.343004	+	0.939334i	$0.611444\pi$
$68$	4.32838	−	4.32838i	0.524893	−	0.524893i
$69$	−0.446348	+	1.37372i	−0.0537339	+	0.165376i
$70$	3.73774	+	4.45581i	0.446746	+	0.532572i
$71$	−8.53999	+	2.77481i	−1.01351	+	0.329310i	−0.768252	−	0.640148i	$-0.778873\pi$
$71$	−8.53999	+	2.77481i	−1.01351	+	0.329310i	−0.245259	+	0.969458i	$0.578873\pi$
$72$	−2.04634	−	1.04266i	−0.241164	−	0.122879i
$73$	−4.68056	+	0.741328i	−0.547819	+	0.0867659i	−0.424208	−	0.905565i	$-0.639447\pi$
$73$	−4.68056	+	0.741328i	−0.547819	+	0.0867659i	−0.123611	+	0.992331i	$0.539447\pi$
$74$			11.8390i			1.37625i
$75$	−3.43563	+	2.40413i	−0.396713	+	0.277605i
$76$	2.99294	+	3.16896i	0.343314	+	0.363504i
$77$	1.51011	+	9.53443i	0.172092	+	1.08655i
$78$	0.253678	−	0.497870i	0.0287233	−	0.0563727i
$79$	3.77615	+	11.6218i	0.424850	+	1.30755i	0.903138	+	0.429351i	$0.141258\pi$
$79$	3.77615	+	11.6218i	0.424850	+	1.30755i	−0.478288	+	0.878203i	$0.658742\pi$
$80$	2.07337	−	0.837338i	0.231810	−	0.0936172i
$81$	−0.977930	+	3.00976i	−0.108659	+	0.334418i
$82$	−0.671602	−	0.671602i	−0.0741660	−	0.0741660i
$83$	4.13218	+	8.10985i	0.453565	+	0.890172i	0.998658	+	0.0517959i	$0.0164945\pi$
$83$	4.13218	+	8.10985i	0.453565	+	0.890172i	−0.545092	+	0.838376i	$0.683505\pi$
$84$	1.76471	−	1.28214i	0.192546	−	0.139893i
$85$	13.3372	−	3.07704i	1.44662	−	0.333752i
$86$	−1.00176	+	1.37881i	−0.108023	+	0.148681i
$87$	−5.16947	−	0.818764i	−0.554226	−	0.0877807i
$88$	3.66573	+	0.580595i	0.390768	+	0.0618916i
$89$	8.57473	+	6.22991i	0.908920	+	0.660369i	0.940741	−	0.339125i	$-0.110131\pi$
$89$	8.57473	+	6.22991i	0.908920	+	0.660369i	−0.0318218	+	0.999494i	$0.510131\pi$
$90$	−2.64432	−	4.40237i	−0.278736	−	0.464051i
$91$	−1.01861	−	1.40199i	−0.106779	−	0.146968i
$92$	1.53458	−	0.781908i	0.159991	−	0.0815196i
$93$	−2.11584	+	2.11584i	−0.219403	+	0.219403i
$94$	3.42075	−	10.5280i	0.352824	−	1.08588i
$95$	1.91907	+	9.55600i	0.196893	+	0.980425i
$96$	−0.259158	−	0.797606i	−0.0264502	−	0.0814053i
$97$	−5.50698	−	2.80595i	−0.559149	−	0.284901i	0.151489	−	0.988459i	$-0.451593\pi$
$97$	−5.50698	−	2.80595i	−0.559149	−	0.284901i	−0.710637	+	0.703558i	$0.751593\pi$
$98$	0.0367623	+	0.232108i	0.00371355	+	0.0234464i
$99$		−	8.52390i		−	0.856684i
$100$	4.92378	+	0.869705i	0.492378	+	0.0869705i
$101$	−1.75372			−0.174502			−0.0872509	−	0.996186i	$-0.527808\pi$
$101$	−1.75372			−0.174502			−0.0872509	+	0.996186i	$0.527808\pi$
$102$	−0.803072	−	5.07040i	−0.0795160	−	0.502044i
$103$	7.34573	−	14.4168i	0.723797	−	1.42053i	−0.176075	−	0.984377i	$-0.556340\pi$
$103$	7.34573	−	14.4168i	0.723797	−	1.42053i	0.899872	−	0.436154i	$-0.143660\pi$
$104$	−0.633665	+	0.205890i	−0.0621360	+	0.0201892i
$105$	4.86571	−	0.339517i	0.474844	−	0.0331334i
$106$	−2.70359	+	8.32079i	−0.262596	+	0.808187i
$107$	−0.126235	+	0.126235i	−0.0122036	+	0.0122036i	−0.713182	−	0.700979i	$-0.752747\pi$
$107$	−0.126235	+	0.126235i	−0.0122036	+	0.0122036i	0.700979	+	0.713182i	$0.252747\pi$
$108$	−3.95790	+	2.01665i	−0.380849	+	0.194052i
$109$	2.94457	−	2.13936i	0.282039	−	0.204913i	−0.437767	−	0.899088i	$-0.644231\pi$
$109$	2.94457	−	2.13936i	0.282039	−	0.204913i	0.719806	+	0.694175i	$0.244231\pi$
$110$	6.26253	+	5.44557i	0.597109	+	0.519214i
$111$	8.03254	+	5.83598i	0.762415	+	0.553927i
$112$	−2.56894	−	0.406880i	−0.242742	−	0.0384465i
$113$	−0.297314	−	0.0470899i	−0.0279689	−	0.00442984i	0.142434	−	0.989804i	$-0.454507\pi$
$113$	−0.297314	−	0.0470899i	−0.0279689	−	0.00442984i	−0.170403	+	0.985374i	$0.554507\pi$
$114$	3.62545	−	0.468536i	0.339554	−	0.0438824i
$115$	3.83648	+	0.336223i	0.357753	+	0.0313530i
$116$	3.66829	+	5.04896i	0.340592	+	0.468784i
$117$	0.694700	+	1.36343i	0.0642250	+	0.126049i
$118$	−6.42402	+	6.42402i	−0.591379	+	0.591379i
$119$	−15.1419	−	4.91990i	−1.38806	−	0.451007i
$120$	0.453943	−	1.81951i	0.0414391	−	0.166098i
$121$	0.857426	+	2.63889i	0.0779478	+	0.239899i
$122$	−11.1699	−	5.69135i	−1.01128	−	0.515271i
$123$	−0.786735	+	0.124607i	−0.0709375	+	0.0112354i
$124$	3.56793			0.320410
$125$	8.30527	+	7.48481i	0.742846	+	0.669462i
$126$			5.97353i			0.532164i
$127$	8.83539	−	1.39939i	0.784014	−	0.124176i	0.248421	−	0.968652i	$-0.420088\pi$
$127$	8.83539	−	1.39939i	0.784014	−	0.124176i	0.535593	+	0.844477i	$0.320088\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	0.441682	+	1.35936i	0.0388880	+	0.119685i
$130$	−1.44553	−	0.360639i	−0.126781	−	0.0316301i
$131$	−4.09192	+	12.5936i	−0.357513	+	1.10031i	0.597025	+	0.802222i	$0.296349\pi$
$131$	−4.09192	+	12.5936i	−0.357513	+	1.10031i	−0.954538	+	0.298089i	$0.903651\pi$
$132$	2.20094	−	2.20094i	0.191567	−	0.191567i
$133$	3.80987	−	10.6780i	0.330357	−	0.925901i
$134$	−6.55513	−	9.02236i	−0.566277	−	0.779413i
$135$	−9.89482	−	0.867167i	−0.851610	−	0.0746338i
$136$	−3.59798	+	4.95220i	−0.308524	+	0.424647i
$137$	−8.37094	−	1.32583i	−0.715177	−	0.113273i	−0.211767	−	0.977320i	$-0.567922\pi$
$137$	−8.37094	−	1.32583i	−0.715177	−	0.113273i	−0.503411	+	0.864047i	$0.667922\pi$
$138$	0.225956	−	1.42663i	0.0192346	−	0.121443i
$139$	2.83640	−	3.90397i	0.240581	−	0.331131i	−0.671604	−	0.740910i	$-0.734394\pi$
$139$	2.83640	−	3.90397i	0.240581	−	0.331131i	0.912185	+	0.409779i	$0.134394\pi$
$140$	−4.38877	−	3.81624i	−0.370919	−	0.322531i
$141$	−5.45682	−	7.51067i	−0.459547	−	0.632512i
$142$	8.00077	−	4.07660i	0.671410	−	0.342101i
$143$	−1.74855	−	1.74855i	−0.146222	−	0.146222i
$144$	2.18426	+	0.709708i	0.182021	+	0.0591423i
$145$	0.971381	+	13.9211i	0.0806688	+	1.15609i
$146$	4.50697	−	1.46440i	0.372999	−	0.121195i
$147$	0.175603	+	0.0894743i	0.0144835	+	0.00737972i
$148$	−1.85202	−	11.6932i	−0.152235	−	0.961175i
$149$			1.85207i			0.151728i	0.997118	+	0.0758639i	$0.0241714\pi$
$149$			1.85207i			0.151728i	−0.997118	+	0.0758639i	$0.975829\pi$
$150$	3.01725	−	2.91199i	0.246357	−	0.237763i
$151$		−	16.7818i		−	1.36568i	−0.730568	−	0.682840i	$-0.760745\pi$
$151$		−	16.7818i		−	1.36568i	0.730568	−	0.682840i	$-0.239255\pi$
$152$	−3.45183	−	2.66174i	−0.279980	−	0.215896i
$153$	12.5262	+	6.38240i	1.01268	+	0.515987i
$154$	−2.98303	−	9.18081i	−0.240379	−	0.739811i
$155$	6.76521	+	4.22877i	0.543395	+	0.339663i
$156$	−0.172670	+	0.531424i	−0.0138247	+	0.0425480i
$157$	−4.58683	−	4.58683i	−0.366069	−	0.366069i	0.499973	−	0.866041i	$-0.333343\pi$
$157$	−4.58683	−	4.58683i	−0.366069	−	0.366069i	−0.866041	+	0.499973i	$0.833343\pi$
$158$	−5.54771	−	10.8880i	−0.441352	−	0.866202i
$159$	4.31280	+	5.93605i	0.342027	+	0.470760i
$160$	−1.91686	+	1.15138i	−0.151541	+	0.0910242i
$161$	−3.62410	−	2.63307i	−0.285619	−	0.207515i
$162$	0.495060	−	3.12569i	0.0388956	−	0.245577i
$163$	0.928347	−	5.86135i	0.0727137	−	0.459096i	−0.924287	−	0.381699i	$-0.875339\pi$
$163$	0.928347	−	5.86135i	0.0727137	−	0.459096i	0.997000	−	0.0773972i	$-0.0246610\pi$
$164$	0.768395	+	0.558272i	0.0600016	+	0.0435937i
$165$	6.78182	−	1.56465i	0.527964	−	0.121807i
$166$	−5.34996	−	7.36359i	−0.415238	−	0.571526i
$167$	−1.76521	−	3.46441i	−0.136596	−	0.268084i	0.812568	−	0.582866i	$-0.198069\pi$
$167$	−1.76521	−	3.46441i	−0.136596	−	0.268084i	−0.949164	+	0.314782i	$0.898069\pi$
$168$	−1.54241	+	1.54241i	−0.119000	+	0.119000i
$169$	−11.9415	−	3.88004i	−0.918580	−	0.298465i
$170$	−12.6916	+	5.12555i	−0.973403	+	0.393112i
$171$	−4.79769	+	8.78639i	−0.366889	+	0.671912i
$172$	0.773736	−	1.51854i	0.0589968	−	0.115788i
$173$	2.50519	+	15.8171i	0.190466	+	1.20255i	0.878811	+	0.477171i	$0.158338\pi$
$173$	2.50519	+	15.8171i	0.190466	+	1.20255i	−0.688345	+	0.725384i	$0.741662\pi$
$174$	5.23391			0.396782
$175$	−3.79854	−	12.4377i	−0.287143	−	0.940201i
$176$	−3.71143			−0.279759
$177$	1.19189	+	7.52530i	0.0895880	+	0.565636i
$178$	−9.44373	−	4.81182i	−0.707838	−	0.360661i
$179$	−3.72780	−	11.4730i	−0.278629	−	0.857532i	−0.988236	−	0.152935i	$-0.951128\pi$
$179$	−3.72780	−	11.4730i	−0.278629	−	0.857532i	0.709607	−	0.704598i	$-0.248872\pi$
$180$	3.30045	+	3.93451i	0.246001	+	0.293261i
$181$	−24.5511	−	7.97714i	−1.82487	−	0.592937i	−0.999602	−	0.0281960i	$-0.991024\pi$
$181$	−24.5511	−	7.97714i	−1.82487	−	0.592937i	−0.825269	−	0.564741i	$-0.808976\pi$
$182$	1.22538	+	1.22538i	0.0908315	+	0.0908315i
$183$	−9.36766	+	4.77306i	−0.692477	+	0.352835i
$184$	−1.39337	+	1.01234i	−0.102721	+	0.0746309i
$185$	10.3473	−	24.3667i	0.760751	−	1.79148i
$186$	1.75880	−	2.42078i	0.128962	−	0.177500i
$187$	−22.4389	−	3.55397i	−1.64089	−	0.259892i
$188$	−1.73170	+	10.9335i	−0.126297	+	0.797407i
$189$	9.34707	+	6.79105i	0.679900	+	0.493976i
$190$	−3.39033	−	9.13814i	−0.245961	−	0.662951i
$191$	3.15917	−	2.29527i	0.228590	−	0.166080i	−0.467595	−	0.883943i	$-0.654879\pi$
$191$	3.15917	−	2.29527i	0.228590	−	0.166080i	0.696185	+	0.717863i	$0.254879\pi$
$192$	0.380740	+	0.747244i	0.0274775	+	0.0539277i
$193$	−7.09011	−	7.09011i	−0.510357	−	0.510357i	0.404279	−	0.914636i	$-0.367523\pi$
$193$	−7.09011	−	7.09011i	−0.510357	−	0.510357i	−0.914636	+	0.404279i	$0.867523\pi$
$194$	5.87812	+	1.90992i	0.422025	+	0.137124i
$195$	−0.957257	+	0.802991i	−0.0685506	+	0.0575034i
$196$	−0.0726193	−	0.223499i	−0.00518709	−	0.0159642i
$197$	−8.80553	+	17.2818i	−0.627368	+	1.23128i	0.330428	+	0.943831i	$0.392807\pi$
$197$	−8.80553	+	17.2818i	−0.627368	+	1.23128i	−0.957796	+	0.287448i	$0.907193\pi$
$198$	1.33343	+	8.41895i	0.0947628	+	0.598309i
$199$		−	3.09098i		−	0.219114i	−0.993981	−	0.109557i	$-0.965057\pi$
$199$		−	3.09098i		−	0.219114i	0.993981	−	0.109557i	$-0.0349432\pi$
$200$	−4.99921	−	0.0887485i	−0.353498	−	0.00627547i
$201$	−9.35286			−0.659700
$202$	1.73213	−	0.274342i	0.121872	−	0.0193027i
$203$	7.36928	−	14.4630i	0.517222	−	1.01511i
$204$	1.58637	+	4.88234i	0.111068	+	0.341832i
$205$	0.795294	+	1.96926i	0.0555457	+	0.137539i
$206$	−5.00001	+	15.3884i	−0.348367	+	1.07216i
$207$	2.79699	+	2.79699i	0.194404	+	0.194404i
$208$	0.593655	−	0.302482i	0.0411626	−	0.0209734i
$209$	2.98596	−	15.8998i	0.206543	−	1.09981i
$210$	−4.75269	+	1.09650i	−0.327967	+	0.0756657i
$211$	7.61170	−	10.4766i	0.524011	−	0.721239i	−0.462192	−	0.886780i	$-0.652937\pi$
$211$	7.61170	−	10.4766i	0.524011	−	0.721239i	0.986203	+	0.165541i	$0.0529369\pi$
$212$	1.36864	−	8.64128i	0.0939989	−	0.593486i
$213$	1.17805	−	7.43794i	0.0807190	−	0.509640i
$214$	0.104933	−	0.144428i	0.00717310	−	0.00987292i
$215$	3.26689	−	1.96229i	0.222800	−	0.133827i
$216$	3.59370	−	2.61098i	0.244520	−	0.177654i
$217$	−4.21305	−	8.26858i	−0.286001	−	0.561308i
$218$	−2.57365	+	2.57365i	−0.174310	+	0.174310i
$219$	1.22812	−	3.77978i	0.0829890	−	0.255414i
$220$	−7.03730	−	4.39885i	−0.474455	−	0.296570i
$221$	3.87882	−	1.26031i	0.260918	−	0.0847773i
$222$	−8.84659	−	4.50756i	−0.593744	−	0.302528i
$223$	−3.86366	−	24.3942i	−0.258730	−	1.63355i	−0.684706	−	0.728820i	$-0.740069\pi$
$223$	−3.86366	−	24.3942i	−0.258730	−	1.63355i	0.425976	−	0.904734i	$-0.359931\pi$
$224$	2.60096			0.173784
$225$	1.59479	+	11.3720i	0.106319	+	0.758136i
$226$	0.301020			0.0200235
$227$	−10.9769	+	1.73857i	−0.728562	+	0.115393i	−0.509687	−	0.860360i	$-0.670239\pi$
$227$	−10.9769	+	1.73857i	−0.728562	+	0.115393i	−0.218875	+	0.975753i	$0.570239\pi$
$228$	−3.50752	+	1.02991i	−0.232291	+	0.0682076i
$229$	−12.4305	+	4.03892i	−0.821432	+	0.266899i	−0.689432	−	0.724350i	$-0.742140\pi$
$229$	−12.4305	+	4.03892i	−0.821432	+	0.266899i	−0.132000	+	0.991250i	$0.542140\pi$
$230$	−3.84184	+	0.268074i	−0.253324	+	0.0176763i
$231$	−7.69951	−	2.50172i	−0.506590	−	0.164601i
$232$	−4.41295	−	4.41295i	−0.289725	−	0.289725i
$233$	8.73500	+	17.1434i	0.572249	+	1.12310i	0.977900	+	0.209074i	$0.0670449\pi$
$233$	8.73500	+	17.1434i	0.572249	+	1.12310i	−0.405651	+	0.914028i	$0.632955\pi$
$234$	−0.899434	−	1.23796i	−0.0587978	−	0.0809283i
$235$	−16.2421	+	18.6788i	−1.05952	+	1.21847i
$236$	5.33999	−	7.34987i	0.347604	−	0.478436i
$237$	−10.1221	−	1.60318i	−0.657498	−	0.104137i
$238$	15.7251	+	2.49061i	1.01931	+	0.161443i
$239$	10.6065	−	14.5986i	0.686079	−	0.944307i	−0.313908	−	0.949454i	$-0.601638\pi$
$239$	10.6065	−	14.5986i	0.686079	−	0.944307i	0.999987	+	0.00514670i	$0.00163825\pi$
$240$	−0.163719	+	1.86812i	−0.0105680	+	0.120587i
$241$	5.97330	+	8.22154i	0.384774	+	0.529596i	0.956841	−	0.290611i	$-0.0938585\pi$
$241$	5.97330	+	8.22154i	0.384774	+	0.529596i	−0.572068	+	0.820207i	$0.693858\pi$
$242$	−1.25968	−	2.47227i	−0.0809754	−	0.158923i
$243$	−11.2997	−	11.2997i	−0.724877	−	0.724877i
$244$	11.9227	+	3.87392i	0.763273	+	0.248002i
$245$	0.127200	−	0.509850i	0.00812654	−	0.0325731i
$246$	0.757556	−	0.246145i	0.0483000	−	0.0156936i
$247$	0.818224	+	2.78658i	0.0520623	+	0.177306i
$248$	−3.52400	+	0.558147i	−0.223774	+	0.0354424i
$249$	−7.63333			−0.483742
$250$	−9.37391	−	6.09343i	−0.592858	−	0.385382i
$251$	11.0423			0.696983			0.348491	−	0.937312i	$-0.386694\pi$
$251$	11.0423			0.696983			0.348491	+	0.937312i	$0.386694\pi$
$252$	−0.934466	−	5.89999i	−0.0588658	−	0.371664i
$253$	−5.69549	−	2.90200i	−0.358072	−	0.182447i
$254$	−8.50770	+	2.76432i	−0.533820	+	0.173449i
$255$	−2.77870	+	11.1377i	−0.174009	+	0.697469i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−20.7748	+	20.7748i	−1.29590	+	1.29590i	−0.364817	+	0.931079i	$0.618868\pi$
$257$	−20.7748	+	20.7748i	−1.29590	+	1.29590i	−0.931079	+	0.364817i	$0.881132\pi$
$258$	−0.648895	−	1.27353i	−0.0403984	−	0.0792864i
$259$	−24.9118	+	18.0995i	−1.54794	+	1.12465i
$260$	1.48415	+	0.130068i	0.0920429	+	0.00806650i
$261$	−8.42482	+	11.5958i	−0.521483	+	0.717760i
$262$	2.07146	−	13.0787i	0.127975	−	0.808005i
$263$	3.67728	−	23.2174i	0.226751	−	1.43165i	−0.567157	−	0.823610i	$-0.691957\pi$
$263$	3.67728	−	23.2174i	0.226751	−	1.43165i	0.793908	−	0.608038i	$-0.208043\pi$
$264$	−1.82954	+	2.51814i	−0.112600	+	0.154981i
$265$	12.8369	−	14.7627i	0.788565	−	0.906868i
$266$	−2.09255	+	11.1425i	−0.128303	+	0.683193i
$267$	−7.92001	+	4.03545i	−0.484697	+	0.246965i
$268$	7.88583	+	7.88583i	0.481704	+	0.481704i
$269$	−4.03971	+	12.4330i	−0.246306	+	0.758051i	0.749113	+	0.662442i	$0.230480\pi$
$269$	−4.03971	+	12.4330i	−0.246306	+	0.758051i	−0.995419	+	0.0956089i	$0.969520\pi$
$270$	9.90865	−	0.691400i	0.603021	−	0.0420773i
$271$	−1.26321	−	3.88776i	−0.0767346	−	0.236165i	0.905330	−	0.424708i	$-0.139623\pi$
$271$	−1.26321	−	3.88776i	−0.0767346	−	0.236165i	−0.982065	+	0.188544i	$0.939623\pi$
$272$	2.77899	−	5.45407i	0.168501	−	0.330702i
$273$	1.43545	−	0.227353i	0.0868776	−	0.0137601i
$274$	8.47528			0.512010
$275$	−8.12995	−	16.6815i	−0.490255	−	1.00593i
$276$			1.44441i			0.0869434i
$277$	−1.94607	−	12.2870i	−0.116928	−	0.738255i	−0.974583	−	0.224029i	$-0.928079\pi$
$277$	−1.94607	−	12.2870i	−0.116928	−	0.738255i	0.857654	−	0.514226i	$-0.171921\pi$
$278$	−2.19077	+	4.29962i	−0.131393	+	0.257874i
$279$	2.53219	+	7.79327i	0.151598	+	0.466571i
$280$	4.93173	+	3.08270i	0.294727	+	0.184227i
$281$	−7.17255	−	2.33050i	−0.427879	−	0.139026i	0.0871577	−	0.996195i	$-0.472222\pi$
$281$	−7.17255	−	2.33050i	−0.427879	−	0.139026i	−0.515036	+	0.857168i	$0.672222\pi$
$282$	6.56457	+	6.56457i	0.390914	+	0.390914i
$283$	−7.36738	−	14.4593i	−0.437945	−	0.859516i	−0.999486	−	0.0320667i	$-0.989791\pi$
$283$	−7.36738	−	14.4593i	−0.437945	−	0.859516i	0.561540	−	0.827449i	$-0.310209\pi$
$284$	−7.26455	+	5.27801i	−0.431072	+	0.313192i
$285$	−7.87134	−	2.20434i	−0.466258	−	0.130574i
$286$	2.00056	+	1.45349i	0.118296	+	0.0859468i
$287$	0.386450	−	2.43995i	0.0228114	−	0.144026i
$288$	−2.26839	−	0.359277i	−0.133666	−	0.0211706i
$289$	12.0318	−	16.5603i	0.707753	−	0.974138i
$290$	−3.13717	−	13.5978i	−0.184221	−	0.798490i
$291$	4.19345	−	3.04672i	0.245825	−	0.178602i
$292$	−4.22240	+	2.15142i	−0.247097	+	0.125902i
$293$	18.1992	+	18.1992i	1.06321	+	1.06321i	0.997863	+	0.0653473i	$0.0208155\pi$
$293$	18.1992	+	18.1992i	1.06321	+	1.06321i	0.0653473	+	0.997863i	$0.479184\pi$
$294$	−0.187438	−	0.0609023i	−0.0109316	−	0.00355190i
$295$	18.8364	−	7.60716i	1.09670	−	0.442906i
$296$	3.65844	+	11.2595i	0.212642	+	0.654446i
$297$	14.6895	+	7.48466i	0.852369	+	0.434304i
$298$	−0.289728	−	1.82927i	−0.0167835	−	0.105967i
$299$	1.14753			0.0663631
$300$	−2.52456	+	3.34814i	−0.145756	+	0.193305i
$301$	−4.43282			−0.255503
$302$	2.62525	+	16.5751i	0.151066	+	0.953793i
$303$	0.667712	−	1.31046i	0.0383591	−	0.0752839i
$304$	3.82572	+	2.08899i	0.219420	+	0.119812i
$305$	18.0154	+	21.4764i	1.03156	+	1.22974i
$306$	−13.3704	−	4.34430i	−0.764334	−	0.248347i
$307$	−6.67132	+	6.67132i	−0.380752	+	0.380752i	−0.871373	−	0.490621i	$-0.836770\pi$
$307$	−6.67132	+	6.67132i	−0.380752	+	0.380752i	0.490621	+	0.871373i	$0.336770\pi$
$308$	4.38250	+	8.60113i	0.249716	+	0.490095i
$309$	7.97607	+	10.9781i	0.453743	+	0.624523i
$310$	−7.34345	−	3.11840i	−0.417080	−	0.177113i
$311$	−9.92185	−	7.20865i	−0.562617	−	0.408765i	0.269799	−	0.962917i	$-0.413043\pi$
$311$	−9.92185	−	7.20865i	−0.562617	−	0.408765i	−0.832416	+	0.554152i	$0.813043\pi$
$312$	0.0874113	−	0.551893i	0.00494869	−	0.0312448i
$313$	0.118966	−	0.751119i	0.00672433	−	0.0424557i	−0.984098	−	0.177626i	$-0.943158\pi$
$313$	0.118966	−	0.751119i	0.00672433	−	0.0424557i	0.990822	+	0.135170i	$0.0431582\pi$
$314$	5.24789	+	3.81282i	0.296156	+	0.215170i
$315$	5.22091	−	12.2946i	0.294165	−	0.692723i
$316$	7.18266	+	9.88609i	0.404056	+	0.556136i
$317$	−12.6309	−	24.7894i	−0.709419	−	1.39231i	−0.910819	−	0.412805i	$-0.864549\pi$
$317$	−12.6309	−	24.7894i	−0.709419	−	1.39231i	0.201400	−	0.979509i	$-0.435451\pi$
$318$	−5.18830	−	5.18830i	−0.290945	−	0.290945i
$319$	7.15761	−	22.0288i	0.400749	−	1.23338i
$320$	1.71314	−	1.43706i	0.0957675	−	0.0803342i
$321$	−0.0462657	−	0.142391i	−0.00258230	−	0.00794750i
$322$	3.99139	+	2.03371i	0.222431	+	0.113334i
$323$	21.1295	+	16.2932i	1.17568	+	0.906577i
$324$			3.16465i			0.175814i
$325$	2.65996	+	2.00566i	0.147548	+	0.111254i
$326$			5.93441i			0.328677i
$327$	0.477506	+	3.01485i	0.0264061	+	0.166722i
$328$	−0.846268	−	0.431195i	−0.0467273	−	0.0238088i
$329$	27.3829	−	8.89724i	1.50967	−	0.490521i
$330$	−6.45356	+	2.60629i	−0.355257	+	0.143472i
$331$	27.0059	+	8.77474i	1.48438	+	0.482304i	0.935418	−	0.353545i	$-0.115024\pi$
$331$	27.0059	+	8.77474i	1.48438	+	0.482304i	0.548960	+	0.835848i	$0.315024\pi$
$332$	6.43601	+	6.43601i	0.353222	+	0.353222i
$333$	24.2265	−	12.3440i	1.32761	−	0.676449i
$334$	2.28543	+	3.14562i	0.125053	+	0.172121i
$335$	5.60603	+	24.2989i	0.306290	+	1.32759i
$336$	1.28214	−	1.76471i	0.0699463	−	0.0962728i
$337$	1.79005	−	11.3020i	0.0975104	−	0.615657i	−0.889738	−	0.456471i	$-0.849113\pi$
$337$	1.79005	−	11.3020i	0.0975104	−	0.615657i	0.987249	−	0.159186i	$-0.0508868\pi$
$338$	12.4015	+	1.96420i	0.674552	+	0.106839i
$339$	0.148387	−	0.204237i	0.00805927	−	0.0110926i
$340$	11.7336	−	7.04786i	0.636341	−	0.382224i
$341$	−7.78352	−	10.7131i	−0.421501	−	0.580146i
$342$	3.36413	−	9.42874i	0.181911	−	0.509848i
$343$	−13.3063	+	13.3063i	−0.718473	+	0.718473i
$344$	−0.526657	+	1.62088i	−0.0283955	+	0.0873922i
$345$	−1.71194	+	2.73877i	−0.0921678	+	0.147451i
$346$	−4.94869	−	15.2305i	−0.266043	−	0.818797i
$347$	−8.72189	+	17.1177i	−0.468215	+	0.918925i	0.529297	+	0.848436i	$0.322456\pi$
$347$	−8.72189	+	17.1177i	−0.468215	+	0.918925i	−0.997513	+	0.0704880i	$0.977544\pi$
$348$	−5.16947	+	0.818764i	−0.277113	+	0.0438904i
$349$		−	28.4350i		−	1.52209i	−0.648700	−	0.761044i	$-0.724687\pi$
$349$		−	28.4350i		−	1.52209i	0.648700	−	0.761044i	$-0.275313\pi$
$350$	5.69746	+	11.6903i	0.304542	+	0.624875i
$351$	−2.95963			−0.157973
$352$	3.66573	−	0.580595i	0.195384	−	0.0309458i
$353$	−32.4357	−	16.5268i	−1.72638	−	0.879635i	−0.975743	−	0.218920i	$-0.929747\pi$
$353$	−32.4357	−	16.5268i	−1.72638	−	0.879635i	−0.750637	−	0.660714i	$-0.770253\pi$
$354$	−2.35443	−	7.24620i	−0.125137	−	0.385131i
$355$	−20.0300	+	1.39764i	−1.06308	+	0.0741792i
$356$	10.0802	+	3.27526i	0.534250	+	0.173588i
$357$	9.44150	−	9.44150i	0.499697	−	0.499697i
$358$	5.47668	+	10.7486i	0.289452	+	0.568081i
$359$	−0.128391	−	0.176715i	−0.00677623	−	0.00932668i	0.805615	−	0.592439i	$-0.201835\pi$
$359$	−0.128391	−	0.176715i	−0.00677623	−	0.00932668i	−0.812392	+	0.583112i	$0.801835\pi$
$360$	−3.87531	−	3.36976i	−0.204247	−	0.177602i
$361$	−12.0271	+	14.7088i	−0.633007	+	0.774146i
$362$	25.4968	+	4.03829i	1.34008	+	0.212248i
$363$	−2.29835	−	0.364023i	−0.120632	−	0.0191062i
$364$	−1.40199	−	1.01861i	−0.0734842	−	0.0533894i
$365$	−10.5561	−	0.925117i	−0.552529	−	0.0484228i
$366$	8.50566	−	6.17972i	0.444598	−	0.323019i
$367$	−4.22294	+	2.15169i	−0.220436	+	0.112318i	−0.560721	−	0.828004i	$-0.689476\pi$
$367$	−4.22294	+	2.15169i	−0.220436	+	0.112318i	0.340286	+	0.940322i	$0.389476\pi$
$368$	1.21785	−	1.21785i	0.0634849	−	0.0634849i
$369$	−0.674072	+	2.07458i	−0.0350908	+	0.107998i
$370$	−6.40814	+	25.6854i	−0.333144	+	1.33532i
$371$	−21.6421	+	7.03193i	−1.12360	+	0.365080i
$372$	−1.35845	+	2.66612i	−0.0704326	+	0.138232i
$373$	−2.41827	−	15.2684i	−0.125213	−	0.790566i	−0.967747	−	0.251923i	$-0.918937\pi$
$373$	−2.41827	−	15.2684i	−0.125213	−	0.790566i	0.842534	−	0.538643i	$-0.181063\pi$
$374$	22.7186			1.17475
$375$	−8.75514	+	3.35630i	−0.452113	+	0.173319i
$376$		−	11.0698i		−	0.570881i
$377$	0.650475	+	4.10693i	0.0335011	+	0.211518i
$378$	−10.2943	−	5.24523i	−0.529484	−	0.269786i
$379$	1.01280	+	3.11708i	0.0520240	+	0.160114i	0.973693	−	0.227863i	$-0.0731740\pi$
$379$	1.01280	+	3.11708i	0.0520240	+	0.160114i	−0.921669	+	0.387977i	$0.873174\pi$
$380$	4.77811	+	8.49527i	0.245112	+	0.435798i
$381$	−2.31830	+	7.13500i	−0.118770	+	0.365537i
$382$	−2.76122	+	2.76122i	−0.141276	+	0.141276i
$383$	−8.37700	+	4.26830i	−0.428045	+	0.218100i	−0.654721	−	0.755870i	$-0.727214\pi$
$383$	−8.37700	+	4.26830i	−0.428045	+	0.218100i	0.226676	+	0.973970i	$0.427214\pi$
$384$	−0.492947	−	0.678484i	−0.0251556	−	0.0346237i
$385$	−1.88449	+	21.5030i	−0.0960423	+	1.09589i
$386$	8.11195	+	5.89368i	0.412888	+	0.299980i
$387$	3.86601	+	0.612316i	0.196520	+	0.0311258i
$388$	−6.10453	−	0.966863i	−0.309911	−	0.0490850i
$389$	20.2608	−	27.8866i	1.02726	−	1.41391i	0.120283	−	0.992740i	$-0.461620\pi$
$389$	20.2608	−	27.8866i	1.02726	−	1.41391i	0.906982	−	0.421169i	$-0.138380\pi$
$390$	0.819856	−	0.942853i	0.0415150	−	0.0477432i
$391$	8.52917	−	6.19681i	0.431339	−	0.313386i
$392$	0.106688	+	0.209387i	0.00538857	+	0.0105757i
$393$	−7.85257	−	7.85257i	−0.396110	−	0.396110i
$394$	5.99365	−	18.4466i	0.301956	−	0.929324i
$395$	1.90201	+	27.2582i	0.0957003	+	1.37151i
$396$	−2.63403	−	8.10671i	−0.132365	−	0.407377i
$397$	−9.59620	+	18.8336i	−0.481620	+	0.945232i	0.514522	+	0.857477i	$0.327969\pi$
$397$	−9.59620	+	18.8336i	−0.481620	+	0.945232i	−0.996142	+	0.0877550i	$0.972031\pi$
$398$	0.483536	+	3.05293i	0.0242375	+	0.153029i
$399$	6.52851	+	6.91245i	0.326835	+	0.346055i
$400$	4.95155	−	0.694393i	0.247577	−	0.0347197i
$401$		−	7.31545i		−	0.365316i	−0.983176	−	0.182658i	$-0.941530\pi$
$401$		−	7.31545i		−	0.365316i	0.983176	−	0.182658i	$-0.0584701\pi$
$402$	9.23771	−	1.46311i	0.460735	−	0.0729733i
$403$	2.11812	+	1.07924i	0.105511	+	0.0537606i
$404$	−1.66789	+	0.541930i	−0.0829805	+	0.0269620i
$405$	−3.75080	+	6.00054i	−0.186379	+	0.298169i
$406$	−5.01604	+	15.4378i	−0.248942	+	0.766164i
$407$	−31.0698	+	31.0698i	−1.54008	+	1.54008i
$408$	−2.33061	−	4.57407i	−0.115382	−	0.226450i
$409$	5.67272	−	4.12147i	0.280498	−	0.203794i	−0.438637	−	0.898664i	$-0.644539\pi$
$409$	5.67272	−	4.12147i	0.280498	−	0.203794i	0.719134	+	0.694871i	$0.244539\pi$
$410$	−1.09356	−	1.82061i	−0.0540072	−	0.0899134i
$411$	4.17787	−	5.75034i	0.206079	−	0.283643i
$412$	2.53117	−	15.9812i	0.124702	−	0.787335i
$413$	−23.3387	−	3.69648i	−1.14842	−	0.181892i
$414$	−3.20010	−	2.32501i	−0.157276	−	0.114268i
$415$	4.57536	+	19.8315i	0.224596	+	0.973491i
$416$	−0.539028	+	0.391626i	−0.0264280	+	0.0192011i
$417$	1.83729	+	3.60589i	0.0899725	+	0.176581i
$418$	−0.461919	+	16.1711i	−0.0225932	+	0.790956i
$419$	14.3544	+	4.66403i	0.701259	+	0.227853i	0.637879	−	0.770137i	$-0.279812\pi$
$419$	14.3544	+	4.66403i	0.701259	+	0.227853i	0.0633801	+	0.997989i	$0.479812\pi$
$420$	4.52265	−	1.82649i	0.220683	−	0.0891234i
$421$	−7.46729	+	2.42627i	−0.363933	+	0.118249i	−0.485275	−	0.874362i	$-0.661280\pi$
$421$	−7.46729	+	2.42627i	−0.363933	+	0.118249i	0.121341	+	0.992611i	$0.461280\pi$
$422$	−5.87908	+	11.5384i	−0.286189	+	0.561678i
$423$	−25.1106	+	3.97712i	−1.22092	+	0.193374i
$424$			8.74900i			0.424889i
$425$	30.6014	+	0.543252i	1.48439	+	0.0263516i
$426$			7.53066i			0.364862i
$427$	−5.10076	−	32.2049i	−0.246843	−	1.55851i
$428$	−0.0810479	+	0.159065i	−0.00391760	+	0.00768872i
$429$	1.97234	−	0.640853i	0.0952256	−	0.0309407i
$430$	−2.91970	+	2.44918i	−0.140801	+	0.118110i
$431$	−24.7487	−	8.04134i	−1.19210	−	0.387338i	−0.355253	−	0.934770i	$-0.615605\pi$
$431$	−24.7487	−	8.04134i	−1.19210	−	0.387338i	−0.836850	+	0.547433i	$0.815605\pi$
$432$	−3.14101	+	3.14101i	−0.151122	+	0.151122i
$433$	24.5180	−	12.4925i	1.17826	−	0.600353i	0.248540	−	0.968622i	$-0.420049\pi$
$433$	24.5180	−	12.4925i	1.17826	−	0.600353i	0.929720	+	0.368268i	$0.120049\pi$
$434$	5.45467	+	7.50772i	0.261833	+	0.360382i
$435$	−10.7723	−	4.57448i	−0.516494	−	0.219329i
$436$	2.13936	−	2.94457i	0.102457	−	0.141019i
$437$	4.23749	+	6.19708i	0.202706	+	0.296447i
$438$	−0.621717	+	3.92536i	−0.0297068	+	0.187561i
$439$	9.86767	+	7.16928i	0.470958	+	0.342171i	0.797815	−	0.602903i	$-0.205989\pi$
$439$	9.86767	+	7.16928i	0.470958	+	0.342171i	−0.326856	+	0.945074i	$0.605989\pi$
$440$	7.63879	+	3.24381i	0.364165	+	0.154643i
$441$	0.436641	−	0.317238i	0.0207924	−	0.0151066i
$442$	−3.63391	+	1.85157i	−0.172848	+	0.0880702i
$443$	−10.7469	+	10.7469i	−0.510600	+	0.510600i	−0.914710	−	0.404110i	$-0.867581\pi$
$443$	−10.7469	+	10.7469i	−0.510600	+	0.510600i	0.404110	+	0.914710i	$0.367581\pi$
$444$	9.44281	+	3.06816i	0.448136	+	0.145608i
$445$	15.2313	+	18.1575i	0.722035	+	0.860748i
$446$	7.63218	+	23.4894i	0.361394	+	1.11226i
$447$	−1.38395	−	0.705158i	−0.0654587	−	0.0333528i
$448$	−2.56894	+	0.406880i	−0.121371	+	0.0192233i
$449$	−19.5201			−0.921209			−0.460604	−	0.887606i	$-0.652367\pi$
$449$	−19.5201			−0.921209			−0.460604	+	0.887606i	$0.652367\pi$
$450$	−3.35413	−	10.9825i	−0.158115	−	0.517722i
$451$		−	3.52507i		−	0.165989i
$452$	−0.297314	+	0.0470899i	−0.0139845	+	0.00221492i
$453$	12.5401	+	6.38949i	0.589184	+	0.300204i
$454$	10.5698	−	3.43433i	0.496064	−	0.161181i
$455$	−1.45107	−	3.59306i	−0.0680271	−	0.168445i
$456$	3.30322	−	1.56593i	0.154688	−	0.0733314i
$457$	−16.8548	−	16.8548i	−0.788436	−	0.788436i	0.192802	−	0.981238i	$-0.438243\pi$
$457$	−16.8548	−	16.8548i	−0.788436	−	0.788436i	−0.981238	+	0.192802i	$0.938243\pi$
$458$	11.6456	−	5.93375i	0.544165	−	0.277266i
$459$	−21.9979	+	15.9824i	−1.02678	+	0.745996i
$460$	3.75261	−	0.865770i	0.174966	−	0.0403667i
$461$	5.34741	+	3.88512i	0.249054	+	0.180948i	0.705307	−	0.708902i	$-0.250809\pi$
$461$	5.34741	+	3.88512i	0.249054	+	0.180948i	−0.456253	+	0.889850i	$0.650809\pi$
$462$	7.99607	+	1.26645i	0.372011	+	0.0589207i
$463$	−0.142950	+	0.902551i	−0.00664345	+	0.0419451i	−0.990787	−	0.135427i	$-0.956759\pi$
$463$	−0.142950	+	0.902551i	−0.00664345	+	0.0419451i	0.984144	+	0.177372i	$0.0567595\pi$
$464$	5.04896	+	3.66829i	0.234392	+	0.170296i
$465$	−5.73571	+	3.44520i	−0.265987	+	0.159768i
$466$	−11.3093	−	15.5659i	−0.523892	−	0.721076i
$467$	15.0435	−	7.66506i	0.696131	−	0.354697i	−0.0698519	−	0.997557i	$-0.522253\pi$
$467$	15.0435	−	7.66506i	0.696131	−	0.354697i	0.765983	+	0.642861i	$0.222253\pi$
$468$	1.08202	+	1.08202i	0.0500164	+	0.0500164i
$469$	8.96352	−	27.5869i	0.413897	−	1.27384i
$470$	13.1201	−	20.9896i	0.605185	−	0.968178i
$471$	5.17387	−	1.68109i	0.238399	−	0.0774606i
$472$	−4.12448	+	8.09474i	−0.189844	+	0.372591i
$473$	−6.24750	+	0.989508i	−0.287261	+	0.0454976i
$474$	10.2482			0.470716
$475$	−1.00888	+	21.7711i	−0.0462907	+	0.998928i
$476$	−15.9211			−0.729744
$477$	19.8461	−	3.14332i	0.908691	−	0.143923i
$478$	−8.19221	+	16.0781i	−0.374703	+	0.735396i
$479$	−37.9708	+	12.3375i	−1.73493	+	0.563713i	−0.994148	−	0.108031i	$-0.965545\pi$
$479$	−37.9708	+	12.3375i	−1.73493	+	0.563713i	−0.740783	+	0.671744i	$0.765545\pi$
$480$	−0.130535	−	1.87073i	−0.00595808	−	0.0853870i
$481$	2.43752	−	7.50193i	0.111142	−	0.342058i
$482$	−7.18589	−	7.18589i	−0.327308	−	0.327308i
$483$	3.34739	−	1.70558i	0.152311	−	0.0776065i
$484$	1.63092	+	2.24477i	0.0741328	+	0.102035i
$485$	−10.4290	−	9.06848i	−0.473555	−	0.411779i
$486$	12.9283	+	9.39293i	0.586438	+	0.426072i
$487$	−2.88183	+	18.1952i	−0.130588	+	0.824501i	0.832246	+	0.554407i	$0.187055\pi$
$487$	−2.88183	+	18.1952i	−0.130588	+	0.824501i	−0.962834	+	0.270094i	$0.912945\pi$
$488$	−12.3819	−	1.96111i	−0.560504	−	0.0887751i
$489$	4.02640	+	2.92535i	0.182080	+	0.132289i
$490$	−0.0458763	+	0.523472i	−0.00207248	+	0.0236480i
$491$	23.6304	−	17.1685i	1.06643	−	0.774804i	0.0911598	−	0.995836i	$-0.470943\pi$
$491$	23.6304	−	17.1685i	1.06643	−	0.774804i	0.975266	+	0.221032i	$0.0709426\pi$
$492$	−0.709724	+	0.361623i	−0.0319968	+	0.0163032i
$493$	27.0128	+	27.0128i	1.21660	+	1.21660i
$494$	−1.24407	−	2.62427i	−0.0559732	−	0.118072i
$495$	4.61378	−	18.4932i	0.207374	−	0.831206i
$496$	3.39330	−	1.10255i	0.152364	−	0.0495060i
$497$	20.8097	+	10.6031i	0.933443	+	0.475613i
$498$	7.53935	−	1.19412i	0.337846	−	0.0535096i
$499$		−	42.8651i		−	1.91891i	−0.281870	−	0.959453i	$-0.590955\pi$
$499$		−	42.8651i		−	1.91891i	0.281870	−	0.959453i	$-0.409045\pi$
$500$	10.2117	+	4.55201i	0.456682	+	0.203572i
$501$	3.26085			0.145684
$502$	−10.9063	+	1.72739i	−0.486774	+	0.0770974i
$503$	33.4510	+	17.0441i	1.49151	+	0.759961i	0.994193	−	0.107610i	$-0.0343197\pi$
$503$	33.4510	+	17.0441i	1.49151	+	0.759961i	0.497314	+	0.867571i	$0.334320\pi$
$504$	1.84592	+	5.68116i	0.0822239	+	0.253059i
$505$	−3.80482	−	0.949248i	−0.169312	−	0.0422410i
$506$	6.07934	+	1.97530i	0.270260	+	0.0878127i
$507$	7.44596	−	7.44596i	0.330687	−	0.330687i
$508$	7.97052	−	4.06118i	0.353634	−	0.180186i
$509$	−29.1585	+	21.1849i	−1.29243	+	0.939003i	−0.999851	−	0.0172393i	$-0.994512\pi$
$509$	−29.1585	+	21.1849i	−1.29243	+	0.939003i	−0.292576	+	0.956242i	$0.594512\pi$
$510$	1.00217	−	11.4352i	0.0443767	−	0.506361i
$511$	9.97171	+	7.24487i	0.441123	+	0.320494i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	−10.9291	−	15.9831i	−0.482530	−	0.705673i
$514$	17.2691	−	23.7689i	0.761709	−	1.04840i
$515$	23.7405	−	27.3022i	1.04613	−	1.20308i
$516$	0.840130	+	1.15634i	0.0369846	+	0.0509050i
$517$	36.6067	−	18.6521i	1.60996	−	0.820317i
$518$	21.7737	−	21.7737i	0.956681	−	0.956681i
$519$	−12.7731	−	4.15023i	−0.560676	−	0.182175i
$520$	−1.48622	+	0.103705i	−0.0651751	+	0.00454775i
$521$	−19.5085	+	6.33869i	−0.854682	+	0.277703i	−0.703406	−	0.710789i	$-0.748338\pi$
$521$	−19.5085	+	6.33869i	−0.854682	+	0.277703i	−0.151276	+	0.988492i	$0.548338\pi$
$522$	6.50711	−	12.7709i	0.284809	−	0.558969i
$523$	6.69272	+	42.2562i	0.292652	+	1.84773i	0.495610	+	0.868545i	$0.334944\pi$
$523$	6.69272	+	42.2562i	0.292652	+	1.84773i	−0.202958	+	0.979187i	$0.565056\pi$
$524$			13.2417i			0.578468i
$525$	10.7402	+	1.89709i	0.468743	+	0.0827957i
$526$			23.5068i			1.02495i
$527$	21.5713	−	3.41656i	0.939661	−	0.148828i
$528$	1.41309	−	2.77334i	0.0614968	−	0.120694i
$529$	−19.0532	+	6.19075i	−0.828398	+	0.269163i
$530$	−10.3695	+	16.5891i	−0.450421	+	0.720586i
$531$	19.8438	+	6.44765i	0.861149	+	0.279804i
$532$	0.323712	−	11.3327i	0.0140347	−	0.491335i
$533$	0.287294	+	0.563847i	0.0124441	+	0.0244229i
$534$	7.19122	−	5.22472i	0.311194	−	0.226096i
$535$	−0.342203	+	0.205547i	−0.0147947	+	0.00888659i
$536$	−9.02236	−	6.55513i	−0.389707	−	0.283138i
$537$	9.99246	+	1.58265i	0.431207	+	0.0682964i
$538$	2.04503	−	12.9118i	0.0881677	−	0.556669i
$539$	−0.512660	+	0.705616i	−0.0220818	+	0.0303930i
$540$	−9.67850	+	2.23294i	−0.416496	+	0.0960905i
$541$	27.2166	−	19.7740i	1.17013	−	0.850151i	0.179108	−	0.983829i	$-0.442679\pi$
$541$	27.2166	−	19.7740i	1.17013	−	0.850151i	0.991025	+	0.133679i	$0.0426790\pi$
$542$	1.85584	+	3.64229i	0.0797151	+	0.156450i
$543$	15.3085	−	15.3085i	0.656950	−	0.656950i
$544$	−1.89157	+	5.82166i	−0.0811004	+	0.249601i
$545$	7.54643	−	3.04765i	0.323253	−	0.130547i
$546$	−1.38221	+	0.449109i	−0.0591533	+	0.0192201i
$547$	−11.8169	−	6.02099i	−0.505253	−	0.257439i	0.182734	−	0.983162i	$-0.441505\pi$
$547$	−11.8169	−	6.02099i	−0.505253	−	0.257439i	−0.687987	+	0.725723i	$0.741505\pi$
$548$	−8.37094	+	1.32583i	−0.357589	+	0.0566365i
$549$			28.7916i			1.22880i
$550$	10.6394	+	15.2043i	0.453666	+	0.648313i
$551$	−19.7770	+	18.6786i	−0.842529	+	0.795733i
$552$	−0.225956	−	1.42663i	−0.00961731	−	0.0607213i
$553$	14.4294	−	28.3192i	0.613599	−	1.20426i
$554$	3.84422	+	11.8313i	0.163325	+	0.502664i
$555$	14.2682	+	17.0094i	0.605653	+	0.722007i
$556$	1.49119	−	4.58940i	0.0632404	−	0.194634i
$557$	18.6626	+	18.6626i	0.790759	+	0.790759i	0.981618	−	0.190858i	$-0.0611271\pi$
$557$	18.6626	+	18.6626i	0.790759	+	0.790759i	−0.190858	+	0.981618i	$0.561127\pi$
$558$	−3.72015	−	7.30120i	−0.157486	−	0.309085i
$559$	0.918664	−	0.667449i	0.0388554	−	0.0282301i
$560$	−5.35325	−	2.27326i	−0.226216	−	0.0960627i
$561$	11.1991	−	15.4142i	0.472825	−	0.650787i
$562$	7.44882	+	1.17978i	0.314210	+	0.0497659i
$563$	24.8953	+	3.94303i	1.04921	+	0.166179i	0.657150	−	0.753759i	$-0.271762\pi$
$563$	24.8953	+	3.94303i	1.04921	+	0.166179i	0.392063	+	0.919938i	$0.371762\pi$
$564$	−7.51067	−	5.45682i	−0.316256	−	0.229774i
$565$	−0.619554	−	0.263094i	−0.0260648	−	0.0110684i
$566$	9.53861	+	13.1288i	0.400938	+	0.551843i
$567$	7.33399	−	3.73685i	0.307998	−	0.156933i
$568$	6.34945	−	6.34945i	0.266417	−	0.266417i
$569$	−7.34834	+	22.6159i	−0.308058	+	0.948106i	0.670460	+	0.741946i	$0.266097\pi$
$569$	−7.34834	+	22.6159i	−0.308058	+	0.948106i	−0.978518	+	0.206160i	$0.933903\pi$
$570$	8.11926	+	0.945850i	0.340078	+	0.0396173i
$571$	12.8692	+	39.6073i	0.538559	+	1.65751i	0.735830	+	0.677166i	$0.236792\pi$
$571$	12.8692	+	39.6073i	0.538559	+	1.65751i	−0.197271	+	0.980349i	$0.563208\pi$
$572$	−2.20331	−	1.12264i	−0.0921249	−	0.0469400i
$573$	0.512307	+	3.23458i	0.0214019	+	0.135126i
$574$			2.47036i			0.103111i
$575$	8.14150	+	2.80605i	0.339524	+	0.117020i
$576$	2.29666			0.0956943
$577$	0.548165	+	3.46098i	0.0228204	+	0.144082i	0.996468	−	0.0839766i	$-0.0267621\pi$
$577$	0.548165	+	3.46098i	0.0228204	+	0.144082i	−0.973647	+	0.228059i	$0.926762\pi$
$578$	−9.29306	+	18.2386i	−0.386540	+	0.758628i
$579$	7.99753	−	2.59856i	0.332366	−	0.107992i
$580$	5.22571	+	12.9396i	0.216986	+	0.537288i
$581$	7.31557	−	22.5150i	0.303501	−	0.934080i
$582$	−3.66521	+	3.66521i	−0.151928	+	0.151928i
$583$	−28.9321	+	14.7416i	−1.19825	+	0.610537i
$584$	3.83386	−	2.78546i	0.158646	−	0.115263i
$585$	0.769208	+	3.33407i	0.0318028	+	0.137847i
$586$	−20.8221	−	15.1282i	−0.860155	−	0.624939i
$587$	9.85329	+	1.56061i	0.406689	+	0.0644132i	0.356428	−	0.934323i	$-0.383995\pi$
$587$	9.85329	+	1.56061i	0.406689	+	0.0644132i	0.0502611	+	0.998736i	$0.483995\pi$
$588$	0.194658	+	0.0308307i	0.00802755	+	0.00127144i
$589$	1.99332	+	15.4240i	0.0821334	+	0.635534i
$590$	−17.4145	+	10.4602i	−0.716944	+	0.430639i
$591$	−9.56113	−	13.1598i	−0.393292	−	0.541321i
$592$	−5.37477	−	10.5486i	−0.220902	−	0.433544i
$593$	8.70315	−	8.70315i	0.357396	−	0.357396i	−0.505456	−	0.862852i	$-0.668676\pi$
$593$	8.70315	−	8.70315i	0.357396	−	0.357396i	0.862852	+	0.505456i	$0.168676\pi$
$594$	−15.6795	−	5.09457i	−0.643336	−	0.209033i
$595$	−30.1883	−	18.8700i	−1.23760	−	0.773595i
$596$	0.572322	+	1.76143i	0.0234432	+	0.0721508i
$597$	2.30972	+	1.17686i	0.0945305	+	0.0481657i
$598$	−1.13340	+	0.179513i	−0.0463481	+	0.00734082i
$599$	−9.36136			−0.382495			−0.191247	−	0.981542i	$-0.561253\pi$
$599$	−9.36136			−0.382495			−0.191247	+	0.981542i	$0.561253\pi$
$600$	1.96972	−	3.70184i	0.0804134	−	0.151127i
$601$			25.5344i			1.04157i	0.853688	+	0.520784i	$0.174360\pi$
$601$			25.5344i			1.04157i	−0.853688	+	0.520784i	$0.825640\pi$
$602$	4.37824	−	0.693445i	0.178444	−	0.0282627i
$603$	−11.6280	+	22.8213i	−0.473530	+	0.929356i
$604$	−5.18585	−	15.9604i	−0.211009	−	0.649420i
$605$	0.431876	+	6.18934i	0.0175583	+	0.251633i
$606$	−0.454490	+	1.39878i	−0.0184624	+	0.0568215i
$607$	10.8373	−	10.8373i	0.439874	−	0.439874i	−0.452096	−	0.891969i	$-0.649323\pi$
$607$	10.8373	−	10.8373i	0.439874	−	0.439874i	0.891969	+	0.452096i	$0.149323\pi$
$608$	−4.10541	−	1.46479i	−0.166496	−	0.0594052i
$609$	8.00164	+	11.0133i	0.324243	+	0.446282i
$610$	−21.1533	−	18.3938i	−0.856470	−	0.744742i
$611$	−4.33522	+	5.96692i	−0.175384	+	0.241396i
$612$	13.8854	+	2.19923i	0.561283	+	0.0888984i
$613$	−4.84266	+	30.5754i	−0.195593	+	1.23493i	0.673090	+	0.739560i	$0.264967\pi$
$613$	−4.84266	+	30.5754i	−0.195593	+	1.23493i	−0.868684	+	0.495367i	$0.835033\pi$
$614$	5.54556	−	7.63281i	0.223801	−	0.308035i
$615$	−1.77432	−	0.155499i	−0.0715475	−	0.00627032i
$616$	−5.67405	−	7.80966i	−0.228614	−	0.314660i
$617$	−17.0119	+	8.66801i	−0.684874	+	0.348961i	−0.761560	−	0.648095i	$-0.775566\pi$
$617$	−17.0119	+	8.66801i	−0.684874	+	0.348961i	0.0766858	+	0.997055i	$0.475566\pi$
$618$	−9.59523	−	9.59523i	−0.385977	−	0.385977i
$619$	−21.3899	−	6.94998i	−0.859731	−	0.279343i	−0.154215	−	0.988037i	$-0.549285\pi$
$619$	−21.3899	−	6.94998i	−0.859731	−	0.279343i	−0.705516	+	0.708694i	$0.749285\pi$
$620$	7.74086	+	1.93124i	0.310880	+	0.0775603i
$621$	−7.27612	+	2.36415i	−0.291980	+	0.0948702i
$622$	10.9274	+	5.56778i	0.438148	+	0.223248i
$623$	−4.31250	−	27.2281i	−0.172777	−	1.09087i
$624$			0.558773i			0.0223688i
$625$	13.9675	+	20.7342i	0.558700	+	0.829370i
$626$			0.760482i			0.0303950i
$627$	10.7442	+	8.28492i	0.429080	+	0.330868i
$628$	−5.77974	−	2.94492i	−0.230637	−	0.117515i
$629$	−22.3942	−	68.9223i	−0.892916	−	2.74811i
$630$	−3.23333	+	12.9600i	−0.128819	+	0.516338i
$631$	10.7965	−	33.2283i	0.429802	−	1.32280i	−0.468518	−	0.883454i	$-0.655212\pi$
$631$	10.7965	−	33.2283i	0.429802	−	1.32280i	0.898320	−	0.439342i	$-0.144788\pi$
$632$	−8.64076	−	8.64076i	−0.343711	−	0.343711i
$633$	4.93051	+	9.67666i	0.195970	+	0.384613i
$634$	16.3533	+	22.5083i	0.649471	+	0.893921i
$635$	19.9264	+	1.74632i	0.790756	+	0.0693006i
$636$	5.93605	+	4.31280i	0.235380	+	0.171013i
$637$	0.0244938	−	0.154648i	0.000970478	−	0.00612736i
$638$	−3.62341	+	22.8773i	−0.143452	+	0.905722i
$639$	−16.6842	−	12.1218i	−0.660018	−	0.479531i
$640$	−1.46724	+	1.68736i	−0.0579979	+	0.0666989i
$641$	0.443385	+	0.610267i	0.0175127	+	0.0241041i	0.817684	−	0.575668i	$-0.195258\pi$
$641$	0.443385	+	0.610267i	0.0175127	+	0.0241041i	−0.800171	+	0.599772i	$0.795258\pi$
$642$	0.0679710	+	0.133401i	0.00268260	+	0.00526490i
$643$	8.20117	−	8.20117i	0.323423	−	0.323423i	−0.526656	−	0.850079i	$-0.676554\pi$
$643$	8.20117	−	8.20117i	0.323423	−	0.323423i	0.850079	+	0.526656i	$0.176554\pi$
$644$	−4.26039	−	1.38428i	−0.167883	−	0.0545484i
$645$	0.222471	+	3.18829i	0.00875978	+	0.125539i
$646$	−23.4182	−	12.7872i	−0.921377	−	0.503106i
$647$	5.12574	−	10.0598i	0.201514	−	0.395493i	−0.768029	−	0.640415i	$-0.778762\pi$
$647$	5.12574	−	10.0598i	0.201514	−	0.395493i	0.969543	+	0.244922i	$0.0787624\pi$
$648$	−0.495060	−	3.12569i	−0.0194478	−	0.122789i
$649$	−33.7181			−1.32355
$650$	−2.94096	−	1.56486i	−0.115354	−	0.0613789i
$651$	7.78273			0.305029
$652$	−0.928347	−	5.86135i	−0.0363569	−	0.229548i
$653$	−11.5847	−	5.90269i	−0.453344	−	0.230990i	0.212382	−	0.977187i	$-0.431878\pi$
$653$	−11.5847	−	5.90269i	−0.453344	−	0.230990i	−0.665726	+	0.746197i	$0.731878\pi$
$654$	−0.943254	−	2.90304i	−0.0368842	−	0.113518i
$655$	−15.6943	+	25.1079i	−0.613228	+	0.981046i
$656$	0.903302	+	0.293501i	0.0352680	+	0.0114593i
$657$	−7.69592	−	7.69592i	−0.300246	−	0.300246i
$658$	−25.6539	+	13.0713i	−1.00009	+	0.509573i
$659$	−10.3505	+	7.52010i	−0.403199	+	0.292942i	−0.770843	−	0.637025i	$-0.780165\pi$
$659$	−10.3505	+	7.52010i	−0.403199	+	0.292942i	0.367643	+	0.929967i	$0.380165\pi$
$660$	5.96640	−	3.58377i	0.232242	−	0.139498i
$661$	21.7813	−	29.9794i	0.847194	−	1.16606i	−0.137280	−	0.990532i	$-0.543836\pi$
$661$	21.7813	−	29.9794i	0.847194	−	1.16606i	0.984474	−	0.175530i	$-0.0561638\pi$
$662$	−28.0461	−	4.44206i	−1.09004	−	0.172646i
$663$	−0.535067	+	3.37828i	−0.0207803	+	0.131201i
$664$	−7.36359	−	5.34996i	−0.285763	−	0.207619i
$665$	14.0455	−	21.1045i	0.544662	−	0.818396i
$666$	−21.9972	+	15.9819i	−0.852375	+	0.619287i
$667$	4.87978	+	9.57711i	0.188946	+	0.370827i
$668$	−2.74937	−	2.74937i	−0.106376	−	0.106376i
$669$	19.6995	+	6.40074i	0.761625	+	0.247467i
$670$	−9.33820	−	23.1227i	−0.360766	−	0.893310i
$671$	−14.3778	−	44.2502i	−0.555048	−	1.70826i
$672$	−0.990290	+	1.94355i	−0.0382013	+	0.0749742i
$673$	4.10746	+	25.9335i	0.158331	+	0.999662i	0.931044	+	0.364906i	$0.118899\pi$
$673$	4.10746	+	25.9335i	0.158331	+	0.999662i	−0.772713	+	0.634755i	$0.781101\pi$
$674$			11.4428i			0.440761i
$675$	−20.9981	−	7.23721i	−0.808217	−	0.278560i
$676$	−12.5561			−0.482926
$677$	16.1257	−	2.55407i	0.619763	−	0.0981608i	0.161346	−	0.986898i	$-0.448417\pi$
$677$	16.1257	−	2.55407i	0.619763	−	0.0981608i	0.458417	+	0.888737i	$0.348417\pi$
$678$	−0.114610	+	0.224935i	−0.00440158	+	0.00863859i
$679$	4.96762	+	15.2888i	0.190640	+	0.586729i
$680$	−10.4866	+	8.79662i	−0.402141	+	0.337335i
$681$	2.88021	−	8.86437i	0.110370	−	0.339683i
$682$	9.36359	+	9.36359i	0.358550	+	0.358550i
$683$	−24.0893	+	12.2741i	−0.921752	+	0.469656i	−0.849416	−	0.527724i	$-0.823045\pi$
$683$	−24.0893	+	12.2741i	−0.921752	+	0.469656i	−0.0723361	+	0.997380i	$0.523045\pi$
$684$	−1.84773	+	9.83892i	−0.0706499	+	0.376201i
$685$	−17.4437	−	7.40746i	−0.666488	−	0.283024i
$686$	11.0609	−	15.2240i	0.422308	−	0.581257i
$687$	1.71474	−	10.8264i	0.0654212	−	0.413053i
$688$	0.266611	−	1.68332i	0.0101645	−	0.0641758i
$689$	3.42634	−	4.71595i	0.130533	−	0.179663i
$690$	1.26243	−	2.97286i	0.0480597	−	0.113175i
$691$	−25.5943	+	18.5953i	−0.973653	+	0.707400i	−0.956281	−	0.292449i	$-0.905530\pi$
$691$	−25.5943	+	18.5953i	−0.973653	+	0.707400i	−0.0173716	+	0.999849i	$0.505530\pi$
$692$	7.27034	+	14.2688i	0.276377	+	0.542420i
$693$	−15.6768	+	15.6768i	−0.595512	+	0.595512i
$694$	5.93671	−	18.2713i	0.225355	−	0.693570i
$695$	8.26690	−	6.93466i	0.313581	−	0.263046i
$696$	4.97775	−	1.61737i	0.188681	−	0.0613062i
$697$	5.18022	+	2.63945i	0.196215	+	0.0999764i
$698$	4.44821	+	28.0849i	0.168367	+	1.06303i
$699$	−16.1361			−0.610323
$700$	−7.45608	−	10.6551i	−0.281813	−	0.402726i
$701$	−26.8124			−1.01269			−0.506345	−	0.862331i	$-0.669004\pi$
$701$	−26.8124			−1.01269			−0.506345	+	0.862331i	$0.669004\pi$
$702$	2.92319	−	0.462988i	0.110329	−	0.0174744i
$703$	49.5144	−	14.5389i	1.86747	−	0.548345i
$704$	−3.52978	+	1.14689i	−0.133033	+	0.0432252i
$705$	−7.77359	−	19.2485i	−0.292770	−	0.724942i
$706$	34.6218	+	11.2493i	1.30301	+	0.423373i
$707$	3.22537	+	3.22537i	0.121303	+	0.121303i
$708$	3.45900	+	6.78867i	0.129997	+	0.255134i
$709$	19.1381	+	26.3414i	0.718748	+	0.989271i	0.999564	+	0.0295101i	$0.00939471\pi$
$709$	19.1381	+	26.3414i	0.718748	+	0.989271i	−0.280817	+	0.959761i	$0.590605\pi$
$710$	19.5648	−	4.51382i	0.734253	−	0.169401i
$711$	−16.4962	+	22.7050i	−0.618654	+	0.851504i
$712$	−10.4685	−	1.65804i	−0.392322	−	0.0621377i
$713$	6.06939	+	0.961298i	0.227301	+	0.0360009i
$714$	−7.84828	+	10.8022i	−0.293715	+	0.404263i
$715$	−2.84716	−	4.74006i	−0.106478	−	0.177268i
$716$	−7.09070	−	9.75952i	−0.264992	−	0.364730i
$717$	6.87042	+	13.4840i	0.256580	+	0.503567i
$718$	0.154455	+	0.154455i	0.00576421	+	0.00576421i
$719$	−17.6905	−	5.74800i	−0.659745	−	0.214364i	−0.0400388	−	0.999198i	$-0.512748\pi$
$719$	−17.6905	−	5.74800i	−0.659745	−	0.214364i	−0.619706	+	0.784834i	$0.712748\pi$
$720$	4.35474	+	2.72204i	0.162292	+	0.101445i
$721$	−40.0247	+	13.0048i	−1.49060	+	0.484325i
$722$	9.57811	−	16.4091i	0.356460	−	0.610685i
$723$	−8.41777	+	1.33324i	−0.313060	+	0.0495839i
$724$	−25.8146			−0.959391
$725$	−5.42771	+	30.7286i	−0.201580	+	1.14123i
$726$	2.32700			0.0863630
$727$	−3.76461	−	23.7688i	−0.139622	−	0.881537i	−0.953695	−	0.300775i	$-0.902755\pi$
$727$	−3.76461	−	23.7688i	−0.139622	−	0.881537i	0.814073	−	0.580762i	$-0.197245\pi$
$728$	1.54407	+	0.786745i	0.0572272	+	0.0291587i
$729$	3.71663	−	1.20761i	0.137653	−	0.0447261i
$730$	10.5708	−	0.737604i	0.391243	−	0.0273000i
$731$	3.22380	−	9.92184i	0.119237	−	0.366973i
$732$	−7.43422	+	7.43422i	−0.274777	+	0.274777i
$733$	13.0482	+	25.6085i	0.481945	+	0.945870i	0.996105	+	0.0881758i	$0.0281037\pi$
$733$	13.0482	+	25.6085i	0.481945	+	0.945870i	−0.514160	+	0.857694i	$0.671896\pi$
$734$	3.83435	−	2.78582i	0.141528	−	0.102826i
$735$	0.332553	+	0.289170i	0.0122664	+	0.0106662i
$736$	−1.01234	+	1.39337i	−0.0373155	+	0.0513603i
$737$	6.47494	−	40.8812i	0.238508	−	1.50588i
$738$	0.341237	−	2.15449i	0.0125611	−	0.0793078i
$739$	−8.46803	+	11.6552i	−0.311502	+	0.428745i	−0.935849	−	0.352402i	$-0.885365\pi$
$739$	−8.46803	+	11.6552i	−0.311502	+	0.428745i	0.624347	+	0.781147i	$0.285365\pi$
$740$	2.31117	−	26.3716i	0.0849602	−	0.969440i
$741$	−2.39379	−	0.449550i	−0.0879380	−	0.0165146i
$742$	20.2756	−	10.3309i	0.744340	−	0.379260i
$743$	−22.8136	−	22.8136i	−0.836950	−	0.836950i	0.151506	−	0.988456i	$-0.451588\pi$
$743$	−22.8136	−	22.8136i	−0.836950	−	0.836950i	−0.988456	+	0.151506i	$0.951588\pi$
$744$	0.924657	−	2.84580i	0.0338996	−	0.104332i
$745$	−1.00248	+	4.01820i	−0.0367281	+	0.147215i
$746$	4.77700	+	14.7021i	0.174898	+	0.538281i
$747$	−9.49021	+	18.6256i	−0.347229	+	0.681475i
$748$	−22.4389	+	3.55397i	−0.820446	+	0.129946i
$749$	0.464332			0.0169663
$750$	8.12230	−	4.68459i	0.296585	−	0.171057i
$751$		−	7.20493i		−	0.262912i	−0.991322	−	0.131456i	$-0.958035\pi$
$751$		−	7.20493i		−	0.262912i	0.991322	−	0.131456i	$-0.0419652\pi$
$752$	1.73170	+	10.9335i	0.0631484	+	0.398704i
$753$	−4.20424	+	8.25129i	−0.153211	+	0.300694i
$754$	−1.28493	−	3.95461i	−0.0467945	−	0.144019i
$755$	9.08357	−	36.4092i	0.330585	−	1.32506i
$756$	10.9881	+	3.57026i	0.399635	+	0.129849i
$757$	8.96804	+	8.96804i	0.325949	+	0.325949i	0.851044	−	0.525095i	$-0.175970\pi$
$757$	8.96804	+	8.96804i	0.325949	+	0.325949i	−0.525095	+	0.851044i	$0.675970\pi$
$758$	−1.48795	−	2.92027i	−0.0540448	−	0.106069i
$759$	4.33700	−	3.15102i	0.157423	−	0.114375i
$760$	−6.04824	−	7.64322i	−0.219393	−	0.277249i
$761$	−38.0663	−	27.6568i	−1.37990	−	1.00256i	−0.996889	−	0.0788128i	$-0.974887\pi$
$761$	−38.0663	−	27.6568i	−1.37990	−	1.00256i	−0.383011	−	0.923744i	$-0.625113\pi$
$762$	1.17360	−	7.40981i	0.0425150	−	0.268429i
$763$	−9.35014	−	1.48092i	−0.338498	−	0.0536128i
$764$	2.29527	−	3.15917i	0.0830401	−	0.114295i
$765$	23.7217	+	20.6272i	0.857661	+	0.745777i
$766$	7.60616	−	5.52620i	0.274822	−	0.199670i
$767$	5.39332	−	2.74803i	0.194742	−	0.0992258i
$768$	0.593017	+	0.593017i	0.0213986	+	0.0213986i
$769$	−48.0322	−	15.6066i	−1.73209	−	0.562789i	−0.738338	−	0.674430i	$-0.764389\pi$
$769$	−48.0322	−	15.6066i	−1.73209	−	0.562789i	−0.993749	+	0.111641i	$0.964389\pi$
$770$	−1.50252	−	21.5330i	−0.0541470	−	0.775996i
$771$	−7.61405	−	23.4336i	−0.274213	−	0.843942i
$772$	−8.93406	−	4.55213i	−0.321544	−	0.163835i
$773$	−1.69440	−	10.6980i	−0.0609432	−	0.384780i	−0.999241	−	0.0389520i	$-0.987598\pi$
$773$	−1.69440	−	10.6980i	−0.0609432	−	0.384780i	0.938298	−	0.345828i	$-0.112402\pi$
$774$	−3.91420			−0.140693
$775$	12.3886	+	12.8365i	0.445013	+	0.461099i
$776$	6.18063			0.221872
$777$	−4.03981	−	25.5064i	−0.144928	−	0.915036i
$778$	−15.6490	+	30.7128i	−0.561042	+	1.10111i
$779$	−1.98409	+	3.63363i	−0.0710875	+	0.130188i
$780$	−0.662267	+	1.05950i	−0.0237130	+	0.0379361i
$781$	31.6956	+	10.2985i	1.13416	+	0.368510i
$782$	−7.45477	+	7.45477i	−0.266582	+	0.266582i
$783$	−12.5856	−	24.7007i	−0.449774	−	0.882732i
$784$	−0.138130	−	0.190120i	−0.00493322	−	0.00678999i
$785$	−7.46869	−	12.4342i	−0.266569	−	0.443794i
$786$	8.98430	+	6.52748i	0.320459	+	0.232827i
$787$	−5.81665	+	36.7249i	−0.207341	+	1.30910i	0.635986	+	0.771701i	$0.280594\pi$
$787$	−5.81665	+	36.7249i	−0.207341	+	1.30910i	−0.843327	+	0.537401i	$0.819406\pi$
$788$	−3.03418	+	19.1571i	−0.108088	+	0.682442i
$789$	15.9490	+	11.5876i	0.567800	+	0.412531i
$790$	−6.14271	−	26.6251i	−0.218548	−	0.947277i
$791$	0.460201	+	0.633413i	0.0163629	+	0.0225216i
$792$	3.86977	+	7.59485i	0.137506	+	0.269871i
$793$	5.90618	+	5.90618i	0.209735	+	0.209735i
$794$	6.53183	−	20.1029i	0.231806	−	0.713426i
$795$	6.14385	+	15.2131i	0.217900	+	0.539552i
$796$	−0.955165	−	2.93970i	−0.0338549	−	0.104195i
$797$	−11.8050	−	6.01494i	−0.418154	−	0.213060i	0.232238	−	0.972659i	$-0.425395\pi$
$797$	−11.8050	−	6.01494i	−0.418154	−	0.213060i	−0.650392	+	0.759599i	$0.725395\pi$
$798$	−7.52948	−	5.80606i	−0.266541	−	0.205532i
$799$			67.7609i			2.39721i
$800$	−4.78196	+	1.46044i	−0.169068	+	0.0516342i
$801$			24.3422i			0.860090i
$802$	1.14439	+	7.22538i	0.0404098	+	0.255137i
$803$	15.6711	+	7.98483i	0.553022	+	0.281779i
$804$	−8.89510	+	2.89019i	−0.313706	+	0.101929i
$805$	−6.43752	−	7.67425i	−0.226893	−	0.270482i
$806$	−2.26087	−	0.734602i	−0.0796358	−	0.0258752i
$807$	−7.75238	−	7.75238i	−0.272897	−	0.272897i
$808$	1.56258	−	0.796173i	0.0549713	−	0.0280093i
$809$	−6.42512	−	8.84342i	−0.225895	−	0.310918i	0.680993	−	0.732290i	$-0.261549\pi$
$809$	−6.42512	−	8.84342i	−0.225895	−	0.310918i	−0.906888	+	0.421372i	$0.861549\pi$
$810$	2.76593	−	6.51342i	0.0971847	−	0.228858i
$811$	13.1986	−	18.1663i	0.463464	−	0.637904i	−0.511758	−	0.859129i	$-0.671006\pi$
$811$	13.1986	−	18.1663i	0.463464	−	0.637904i	0.975223	+	0.221225i	$0.0710057\pi$
$812$	2.53928	−	16.0324i	0.0891113	−	0.562627i
$813$	3.38606	+	0.536300i	0.118754	+	0.0188089i
$814$	25.8269	−	35.5477i	0.905233	−	1.24595i
$815$	5.18672	−	12.2141i	0.181683	−	0.427841i
$816$	3.01745	+	4.15317i	0.105632	+	0.145390i
$817$	6.99684	+	2.49644i	0.244789	+	0.0873395i
$818$	−4.95813	+	4.95813i	−0.173357	+	0.173357i
$819$	1.22989	−	3.78522i	0.0429759	−	0.132266i
$820$	1.36490	+	1.62712i	0.0476645	+	0.0568215i
$821$	1.21573	+	3.74164i	0.0424294	+	0.130584i	0.970027	−	0.242996i	$-0.0781301\pi$
$821$	1.21573	+	3.74164i	0.0424294	+	0.130584i	−0.927598	+	0.373580i	$0.878130\pi$
$822$	−3.22688	+	6.33311i	−0.112550	+	0.220892i
$823$	−6.73133	+	1.06614i	−0.234639	+	0.0371632i	−0.272647	−	0.962114i	$-0.587899\pi$
$823$	−6.73133	+	1.06614i	−0.234639	+	0.0371632i	0.0380072	+	0.999277i	$0.487899\pi$
$824$			16.1804i			0.563670i
$825$	15.5605	+	0.276238i	0.541748	+	0.00961738i
$826$	23.6296			0.822178
$827$	−18.8364	+	2.98339i	−0.655005	+	0.103743i	−0.475087	−	0.879939i	$-0.657583\pi$
$827$	−18.8364	+	2.98339i	−0.655005	+	0.103743i	−0.179918	+	0.983682i	$0.557583\pi$
$828$	3.52442	+	1.79578i	0.122482	+	0.0624077i
$829$	5.84266	+	17.9818i	0.202924	+	0.624535i	0.999792	+	0.0203825i	$0.00648839\pi$
$829$	5.84266	+	17.9818i	0.202924	+	0.624535i	−0.796868	+	0.604153i	$0.793512\pi$
$830$	−7.62136	−	18.8716i	−0.264541	−	0.655043i
$831$	9.92235	+	3.22397i	0.344202	+	0.111838i
$832$	0.471127	−	0.471127i	0.0163334	−	0.0163334i
$833$	−0.653065	−	1.28171i	−0.0226274	−	0.0444087i
$834$	−2.37876	−	3.27408i	−0.0823696	−	0.113372i
$835$	−1.95453	−	8.47174i	−0.0676393	−	0.293177i
$836$	−2.07349	−	16.0443i	−0.0717132	−	0.554904i
$837$	−15.6538	−	2.47932i	−0.541075	−	0.0856979i
$838$	−14.9073	−	2.36109i	−0.514964	−	0.0815623i
$839$	39.1734	+	28.4611i	1.35242	+	0.982588i	0.998887	+	0.0471642i	$0.0150184\pi$
$839$	39.1734	+	28.4611i	1.35242	+	0.982588i	0.353529	+	0.935424i	$0.384982\pi$
$840$	−4.18124	+	2.51150i	−0.144266	+	0.0866549i
$841$	−8.04838	+	5.84749i	−0.277530	+	0.201638i
$842$	6.99580	−	3.56454i	0.241091	−	0.122842i
$843$	4.47234	−	4.47234i	0.154035	−	0.154035i
$844$	4.00171	−	12.3160i	0.137744	−	0.423934i
$845$	−23.8078	−	14.8817i	−0.819013	−	0.511945i
$846$	24.1792	−	7.85631i	0.831299	−	0.270106i
$847$	3.27638	−	6.43027i	0.112578	−	0.220947i
$848$	−1.36864	−	8.64128i	−0.0469995	−	0.296743i
$849$	13.6097			0.467083
$850$	−30.3097	+	4.25056i	−1.03961	+	0.145793i
$851$		−	20.3902i		−	0.698968i
$852$	−1.17805	−	7.43794i	−0.0403595	−	0.254820i
$853$	12.2740	+	6.25390i	0.420253	+	0.214129i	0.651312	−	0.758810i	$-0.274219\pi$
$853$	12.2740	+	6.25390i	0.420253	+	0.214129i	−0.231059	+	0.972940i	$0.574219\pi$
$854$	10.0759	+	31.0105i	0.344791	+	1.06116i
$855$	−15.1648	+	16.4658i	−0.518625	+	0.563118i
$856$	0.0551667	−	0.169786i	0.00188556	−	0.00580316i
$857$	10.7107	−	10.7107i	0.365872	−	0.365872i	−0.500097	−	0.865969i	$-0.666702\pi$
$857$	10.7107	−	10.7107i	0.365872	−	0.365872i	0.865969	+	0.500097i	$0.166702\pi$
$858$	−1.84781	+	0.941505i	−0.0630831	+	0.0321425i
$859$	−1.43854	−	1.97998i	−0.0490824	−	0.0675561i	0.783770	−	0.621051i	$-0.213294\pi$
$859$	−1.43854	−	1.97998i	−0.0490824	−	0.0675561i	−0.832853	+	0.553495i	$0.813294\pi$
$860$	2.50062	−	2.87577i	0.0852705	−	0.0980630i
$861$	1.67610	+	1.21776i	0.0571214	+	0.0415011i
$862$	25.7019	+	4.07079i	0.875411	+	0.138652i
$863$	−53.3393	−	8.44812i	−1.81569	−	0.287577i	−0.846230	−	0.532818i	$-0.821133\pi$
$863$	−53.3393	−	8.44812i	−1.81569	−	0.287577i	−0.969462	+	0.245241i	$0.921133\pi$
$864$	2.61098	−	3.59370i	0.0888272	−	0.122260i
$865$	−3.12627	+	35.6723i	−0.106296	+	1.21290i
$866$	−22.2619	+	16.1742i	−0.756489	+	0.549622i
$867$	7.79364	+	15.2959i	0.264686	+	0.519475i
$868$	−6.56198	−	6.56198i	−0.222728	−	0.222728i
$869$	14.0149	−	43.1334i	0.475423	−	1.46320i
$870$	11.3553	+	2.83299i	0.384981	+	0.0960474i
$871$	2.29614	+	7.06679i	0.0778017	+	0.239449i
$872$	−1.65239	+	3.24299i	−0.0559568	+	0.109821i
$873$	−2.22056	−	14.0201i	−0.0751545	−	0.474507i
$874$	−5.15475	−	5.45790i	−0.174362	−	0.184616i
$875$	−1.50896	−	29.0405i	−0.0510121	−	0.981747i
$876$		−	3.97429i		−	0.134279i
$877$	27.2678	−	4.31880i	0.920770	−	0.145836i	0.321984	−	0.946745i	$-0.395650\pi$
$877$	27.2678	−	4.31880i	0.920770	−	0.145836i	0.598786	+	0.800909i	$0.295650\pi$
$878$	−10.8677	−	5.53737i	−0.366767	−	0.186877i
$879$	−20.5284	+	6.67010i	−0.692407	+	0.224977i
$880$	−8.05219	−	2.00891i	−0.271439	−	0.0677203i
$881$	−1.62116	+	4.98942i	−0.0546183	+	0.168098i	−0.974644	−	0.223759i	$-0.928167\pi$
$881$	−1.62116	+	4.98942i	−0.0546183	+	0.168098i	0.920026	+	0.391857i	$0.128167\pi$
$882$	−0.381638	+	0.381638i	−0.0128504	+	0.0128504i
$883$	−3.59490	−	7.05539i	−0.120978	−	0.237433i	0.822573	−	0.568659i	$-0.192538\pi$
$883$	−3.59490	−	7.05539i	−0.120978	−	0.237433i	−0.943551	+	0.331226i	$0.892538\pi$
$884$	3.29952	−	2.39724i	0.110975	−	0.0806280i
$885$	−1.48738	+	16.9718i	−0.0499978	+	0.570500i
$886$	8.93339	−	12.2958i	0.300123	−	0.413084i
$887$	1.55228	−	9.80070i	0.0521204	−	0.329075i	−0.947827	−	0.318786i	$-0.896725\pi$
$887$	1.55228	−	9.80070i	0.0521204	−	0.329075i	0.999947	−	0.0102891i	$-0.00327518\pi$
$888$	−9.80652	−	1.55320i	−0.329085	−	0.0521220i
$889$	−18.8234	−	13.6760i	−0.631315	−	0.458677i
$890$	−17.8843	−	15.5512i	−0.599483	−	0.521279i
$891$	9.50219	−	6.90375i	0.318335	−	0.231284i
$892$	−11.2128	−	22.0063i	−0.375431	−	0.736825i
$893$	−48.2324	−	1.37773i	−1.61404	−	0.0461040i
$894$	1.47722	+	0.479979i	0.0494058	+	0.0160529i
$895$	−1.87766	−	26.9092i	−0.0627631	−	0.899476i
$896$	2.47366	−	0.803741i	0.0826392	−	0.0268511i
$897$	−0.436909	+	0.857482i	−0.0145880	+	0.0286305i
$898$	19.2797	−	3.05361i	0.643373	−	0.101900i
$899$			22.2670i			0.742644i
$900$	5.03088	+	10.3226i	0.167696	+	0.344088i
$901$		−	53.5548i		−	1.78417i
$902$	0.551442	+	3.48167i	0.0183610	+	0.115927i
$903$	1.68775	−	3.31240i	0.0561648	−	0.110230i
$904$	0.286287	−	0.0930203i	0.00952176	−	0.00309381i
$905$	−48.9475	−	30.5959i	−1.62707	−	1.01704i
$906$	−13.3852	−	4.34912i	−0.444694	−	0.144490i
$907$	−19.3777	+	19.3777i	−0.643427	+	0.643427i	−0.951396	−	0.307969i	$-0.900351\pi$
$907$	−19.3777	+	19.3777i	−0.643427	+	0.643427i	0.307969	+	0.951396i	$0.400351\pi$
$908$	−9.90240	+	5.04552i	−0.328623	+	0.167442i
$909$	−2.36743	−	3.25848i	−0.0785226	−	0.108077i
$910$	1.99528	+	3.32182i	0.0661429	+	0.110117i
$911$	7.97477	−	10.9763i	0.264216	−	0.363662i	−0.656211	−	0.754578i	$-0.727842\pi$
$911$	7.97477	−	10.9763i	0.264216	−	0.363662i	0.920426	+	0.390916i	$0.127842\pi$
$912$	−3.01759	+	2.06339i	−0.0999223	+	0.0683256i
$913$	5.28452	−	33.3651i	0.174892	−	1.10422i
$914$	19.2840	+	14.0106i	0.637858	+	0.463431i
$915$	−22.9073	+	5.28498i	−0.757292	+	0.174716i
$916$	−10.5740	+	7.68248i	−0.349376	+	0.253836i
$917$	30.6874	−	15.6360i	1.01339	−	0.516346i
$918$	19.2269	−	19.2269i	0.634582	−	0.634582i
$919$	−31.7140	−	10.3045i	−1.04615	−	0.339914i	−0.264992	−	0.964251i	$-0.585369\pi$
$919$	−31.7140	−	10.3045i	−1.04615	−	0.339914i	−0.781155	+	0.624337i	$0.785369\pi$
$920$	−3.57097	+	1.44215i	−0.117731	+	0.0475462i
$921$	−2.44507	−	7.52515i	−0.0805677	−	0.247962i
$922$	−5.88935	−	3.00077i	−0.193955	−	0.0988252i
$923$	−5.90914	+	0.935916i	−0.194502	+	0.0308061i
$924$	−8.09574			−0.266330
$925$	35.6383	−	47.2644i	1.17178	−	1.55405i
$926$		−	0.913801i		−	0.0300294i
$927$	36.7033	−	5.81324i	1.20550	−	0.190932i
$928$	−5.56065	−	2.83329i	−0.182537	−	0.0930074i
$929$	29.5163	−	9.59042i	0.968397	−	0.314651i	0.218228	−	0.975898i	$-0.429972\pi$
$929$	29.5163	−	9.59042i	0.968397	−	0.314651i	0.750169	+	0.661246i	$0.229972\pi$
$930$	5.12615	−	4.30005i	0.168093	−	0.141004i
$931$	0.925605	−	0.438794i	0.0303355	−	0.0143809i
$932$	13.6051	+	13.6051i	0.445649	+	0.445649i
$933$	9.16427	−	4.66943i	0.300025	−	0.152870i
$934$	−13.6592	+	9.92401i	−0.446944	+	0.324724i
$935$	−46.7590	−	19.8562i	−1.52918	−	0.649367i
$936$	−1.23796	−	0.899434i	−0.0404641	−	0.0293989i
$937$	−9.40017	−	1.48884i	−0.307090	−	0.0486383i	0.000987448	−	1.00000i	$-0.499686\pi$
$937$	−9.40017	−	1.48884i	−0.307090	−	0.0486383i	−0.308078	+	0.951361i	$0.599686\pi$
$938$	−4.53763	+	28.6495i	−0.148159	+	0.935438i
$939$	0.515974	+	0.374877i	0.0168382	+	0.0122337i
$940$	−9.67507	+	22.7836i	−0.315566	+	0.743120i
$941$	5.09782	+	7.01654i	0.166184	+	0.228733i	0.883985	−	0.467516i	$-0.154851\pi$
$941$	5.09782	+	7.01654i	0.166184	+	0.228733i	−0.717800	+	0.696249i	$0.754851\pi$
$942$	−4.84719	+	2.46977i	−0.157930	+	0.0804694i
$943$	1.15670	+	1.15670i	0.0376674	+	0.0376674i
$944$	2.80740	−	8.64029i	0.0913731	−	0.281218i
$945$	16.6033	+	19.7930i	0.540104	+	0.643866i
$946$	6.01579	−	1.95465i	0.195590	−	0.0635512i
$947$	−19.9268	+	39.1085i	−0.647533	+	1.27086i	0.300833	+	0.953677i	$0.402735\pi$
$947$	−19.9268	+	39.1085i	−0.647533	+	1.27086i	−0.948366	+	0.317178i	$0.897265\pi$
$948$	−10.1221	+	1.60318i	−0.328749	+	0.0520687i
$949$	−3.15741			−0.102494
$950$	−2.40929	−	21.6609i	−0.0781678	−	0.702773i
$951$	23.3328			0.756619
$952$	15.7251	−	2.49061i	0.509654	−	0.0807213i
$953$	−19.9389	+	39.1324i	−0.645885	+	1.26762i	0.303297	+	0.952896i	$0.401912\pi$
$953$	−19.9389	+	39.1324i	−0.645885	+	1.26762i	−0.949183	+	0.314726i	$0.898088\pi$
$954$	−19.1101	+	6.20923i	−0.618711	+	0.201031i
$955$	8.09641	−	3.26976i	0.261994	−	0.105807i
$956$	5.57618	−	17.1617i	0.180347	−	0.555050i
$957$	13.7357	+	13.7357i	0.444014	+	0.444014i
$958$	35.5733	−	18.1255i	1.14932	−	0.585609i
$959$	12.9571	+	17.8339i	0.418405	+	0.575886i
$960$	0.421575	+	1.82728i	0.0136063	+	0.0589753i
$961$	−14.7806	−	10.7388i	−0.476795	−	0.346412i
$962$	−1.23395	+	7.79088i	−0.0397843	+	0.251188i
$963$	−0.404960	−	0.0641394i	−0.0130497	−	0.00206686i
$964$	8.22154	+	5.97330i	0.264798	+	0.192387i
$965$	−11.5448	−	19.2202i	−0.371639	−	0.618719i
$966$	−3.03936	+	2.20823i	−0.0977899	+	0.0710485i
$967$	−2.96389	+	1.51018i	−0.0953122	+	0.0485640i	−0.500997	−	0.865449i	$-0.667033\pi$
$967$	−2.96389	+	1.51018i	−0.0953122	+	0.0485640i	0.405685	+	0.914013i	$0.367033\pi$
$968$	−1.96200	−	1.96200i	−0.0630611	−	0.0630611i
$969$	−20.2198	+	9.58545i	−0.649555	+	0.307929i
$970$	11.7192	+	7.32539i	0.376281	+	0.235204i
$971$	14.4423	−	4.69258i	0.463475	−	0.150592i	−0.0679657	−	0.997688i	$-0.521651\pi$
$971$	14.4423	−	4.69258i	0.463475	−	0.150592i	0.531441	+	0.847095i	$0.321651\pi$
$972$	−14.2385	−	7.25486i	−0.456699	−	0.232700i
$973$	−12.3966	+	1.96343i	−0.397417	+	0.0629447i
$974$		−	18.4220i		−	0.590278i
$975$	−2.51147	+	1.22400i	−0.0804315	+	0.0391995i
$976$	12.5363			0.401276
$977$	−11.8958	+	1.88411i	−0.380580	+	0.0602780i	−0.343794	−	0.939045i	$-0.611712\pi$
$977$	−11.8958	+	1.88411i	−0.380580	+	0.0602780i	−0.0367864	+	0.999323i	$0.511712\pi$
$978$	−4.43446	−	2.25947i	−0.141798	−	0.0722499i
$979$	−12.1559	−	37.4119i	−0.388503	−	1.19569i
$980$	−0.0365776	−	0.524204i	−0.00116843	−	0.0167451i
$981$	7.95002	+	2.58312i	0.253825	+	0.0824726i
$982$	−20.6538	+	20.6538i	−0.659088	+	0.659088i
$983$	13.0276	−	6.63788i	0.415515	−	0.211716i	−0.233719	−	0.972304i	$-0.575090\pi$
$983$	13.0276	−	6.63788i	0.415515	−	0.211716i	0.649234	+	0.760589i	$0.275090\pi$
$984$	0.644416	−	0.468196i	0.0205432	−	0.0149255i
$985$	−28.4584	+	32.7279i	−0.906761	+	1.04280i
$986$	−30.9060	−	22.4545i	−0.984247	−	0.715097i
$987$	−3.77735	+	23.8493i	−0.120234	+	0.759130i
$988$	1.63928	+	2.39735i	0.0521524	+	0.0762699i
$989$	1.72534	−	2.37472i	0.0548625	−	0.0755117i
$990$	−1.66401	+	18.9872i	−0.0528858	+	0.603454i
$991$	32.2734	+	44.4206i	1.02520	+	1.41107i	0.908493	+	0.417900i	$0.137234\pi$
$991$	32.2734	+	44.4206i	1.02520	+	1.41107i	0.116706	+	0.993166i	$0.462766\pi$
$992$	−3.17905	+	1.61981i	−0.100935	+	0.0514289i
$993$	−16.8391	+	16.8391i	−0.534373	+	0.534373i
$994$	−22.2122	−	7.21718i	−0.704528	−	0.228915i
$995$	1.67307	−	6.70609i	0.0530400	−	0.212597i
$996$	−7.25973	+	2.35883i	−0.230033	+	0.0747423i
$997$	−19.5900	+	38.4475i	−0.620422	+	1.21765i	0.340348	+	0.940299i	$0.389455\pi$
$997$	−19.5900	+	38.4475i	−0.620422	+	1.21765i	−0.960770	+	0.277346i	$0.910545\pi$
$998$	6.70558	+	42.3374i	0.212261	+	1.34017i
$999$			52.5893i			1.66385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.9	✓	400
19.18	odd	2	inner	950.2.w.a.37.42	yes	400
25.23	odd	20	inner	950.2.w.a.873.42	yes	400
475.398	even	20	inner	950.2.w.a.873.9	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.9	✓	400	1.1	even	1	trivial
950.2.w.a.37.42	yes	400	19.18	odd	2	inner
950.2.w.a.873.9	yes	400	475.398	even	20	inner
950.2.w.a.873.42	yes	400	25.23	odd	20	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.380740 + 0.747244i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.16957 + 0.541276i) q^{5} +(0.259158 - 0.797606i) q^{6} +(-1.83916 - 1.83916i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.34994 + 1.85804i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.380740 + 0.747244i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.16957 + 0.541276i) q^{5} +(0.259158 - 0.797606i) q^{6} +(-1.83916 - 1.83916i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.34994 + 1.85804i) q^{9} +(-2.22753 - 0.195217i) q^{10} +(-3.00261 - 2.18152i) q^{11} +(-0.131194 + 0.828327i) q^{12} +(0.658072 + 0.104228i) q^{13} +(2.10422 + 1.52881i) q^{14} +(-1.23051 + 1.41511i) q^{15} +(0.809017 - 0.587785i) q^{16} +(5.45407 - 2.77899i) q^{17} +(-1.62399 - 1.62399i) q^{18} +(1.86720 + 3.93873i) q^{19} +(2.23064 - 0.155649i) q^{20} +(2.07454 - 0.674059i) q^{21} +(3.30691 + 1.68495i) q^{22} +(1.70110 - 0.269427i) q^{23} -0.838652i q^{24} +(4.41404 + 2.34867i) q^{25} -0.666275 q^{26} +(-4.38737 + 0.694891i) q^{27} +(-2.31747 - 1.18081i) q^{28} +(1.92853 + 5.93541i) q^{29} +(0.993985 - 1.59018i) q^{30} +(3.39330 + 1.10255i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.77334 - 1.41309i) q^{33} +(-4.95220 + 3.59798i) q^{34} +(-2.99468 - 4.98567i) q^{35} +(1.85804 + 1.34994i) q^{36} +(1.85202 - 11.6932i) q^{37} +(-2.46036 - 3.59814i) q^{38} +(-0.328438 + 0.452057i) q^{39} +(-2.17883 + 0.502682i) q^{40} +(0.558272 + 0.768395i) q^{41} +(-1.94355 + 0.990290i) q^{42} +(1.20512 - 1.20512i) q^{43} +(-3.52978 - 1.14689i) q^{44} +(1.92308 + 4.76183i) q^{45} +(-1.63801 + 0.532220i) q^{46} +(-5.02558 + 9.86325i) q^{47} +(0.131194 + 0.828327i) q^{48} -0.235001i q^{49} +(-4.72711 - 1.62925i) q^{50} +5.13360i q^{51} +(0.658072 - 0.104228i) q^{52} +(3.97196 - 7.79542i) q^{53} +(4.22465 - 1.37267i) q^{54} +(-5.33355 - 6.35820i) q^{55} +(2.47366 + 0.803741i) q^{56} +(-3.65411 - 0.104378i) q^{57} +(-2.83329 - 5.56065i) q^{58} +(7.34987 - 5.33999i) q^{59} +(-0.732988 + 1.72610i) q^{60} +(10.1421 + 7.36864i) q^{61} +(-3.52400 - 0.558147i) q^{62} +(0.934466 - 5.89999i) q^{63} +(0.587785 - 0.809017i) q^{64} +(1.37131 + 0.582329i) q^{65} +(-2.51814 + 1.82954i) q^{66} +(5.06302 + 9.93673i) q^{67} +(4.32838 - 4.32838i) q^{68} +(-0.446348 + 1.37372i) q^{69} +(3.73774 + 4.45581i) q^{70} +(-8.53999 + 2.77481i) q^{71} +(-2.04634 - 1.04266i) q^{72} +(-4.68056 + 0.741328i) q^{73} +11.8390i q^{74} +(-3.43563 + 2.40413i) q^{75} +(2.99294 + 3.16896i) q^{76} +(1.51011 + 9.53443i) q^{77} +(0.253678 - 0.497870i) q^{78} +(3.77615 + 11.6218i) q^{79} +(2.07337 - 0.837338i) q^{80} +(-0.977930 + 3.00976i) q^{81} +(-0.671602 - 0.671602i) q^{82} +(4.13218 + 8.10985i) q^{83} +(1.76471 - 1.28214i) q^{84} +(13.3372 - 3.07704i) q^{85} +(-1.00176 + 1.37881i) q^{86} +(-5.16947 - 0.818764i) q^{87} +(3.66573 + 0.580595i) q^{88} +(8.57473 + 6.22991i) q^{89} +(-2.64432 - 4.40237i) q^{90} +(-1.01861 - 1.40199i) q^{91} +(1.53458 - 0.781908i) q^{92} +(-2.11584 + 2.11584i) q^{93} +(3.42075 - 10.5280i) q^{94} +(1.91907 + 9.55600i) q^{95} +(-0.259158 - 0.797606i) q^{96} +(-5.50698 - 2.80595i) q^{97} +(0.0367623 + 0.232108i) q^{98} -8.52390i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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