LMFDB - Embedded newform 230.2.l.a.113.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.977147 - 0.212565i) q^{2} +(0.755212 - 1.00884i) q^{3} +(0.909632 - 0.415415i) q^{4} +(1.82179 + 1.29657i) q^{5} +(0.523507 - 1.14632i) q^{6} +(-1.79627 + 0.128472i) q^{7} +(0.800541 - 0.599278i) q^{8} +(0.397775 + 1.35470i) q^{9} +(2.05576 + 0.879687i) q^{10} +(-0.836716 - 1.30196i) q^{11} +(0.267875 - 1.23140i) q^{12} +(0.141245 - 1.97487i) q^{13} +(-1.72791 + 0.507360i) q^{14} +(2.68387 - 0.858720i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-6.65602 + 2.48257i) q^{17} +(0.676646 + 1.23918i) q^{18} +(-1.28595 - 2.81584i) q^{19} +(2.19577 + 0.422600i) q^{20} +(-1.22696 + 1.90918i) q^{21} +(-1.09434 - 1.09434i) q^{22} +(-1.99348 - 4.36188i) q^{23} -1.26020i q^{24} +(1.63783 + 4.72414i) q^{25} +(-0.281771 - 1.95976i) q^{26} +(5.20932 + 1.94298i) q^{27} +(-1.58057 + 0.863059i) q^{28} +(1.50176 + 0.685829i) q^{29} +(2.44000 - 1.40959i) q^{30} +(-0.456293 + 3.17359i) q^{31} +(0.479249 - 0.877679i) q^{32} +(-1.94537 - 0.139135i) q^{33} +(-5.97620 + 3.84067i) q^{34} +(-3.43900 - 2.09493i) q^{35} +(0.924590 + 1.06703i) q^{36} +(-1.23799 - 0.675994i) q^{37} +(-1.85511 - 2.47814i) q^{38} +(-1.88567 - 1.63394i) q^{39} +(2.23542 - 0.0538024i) q^{40} +(6.67297 + 1.95936i) q^{41} +(-0.793090 + 2.12636i) q^{42} +(0.877639 + 0.656992i) q^{43} +(-1.30196 - 0.836716i) q^{44} +(-1.03179 + 2.98371i) q^{45} +(-2.87511 - 3.83845i) q^{46} +(-8.44176 + 8.44176i) q^{47} +(-0.267875 - 1.23140i) q^{48} +(-3.71867 + 0.534664i) q^{49} +(2.60459 + 4.26803i) q^{50} +(-2.52218 + 8.58976i) q^{51} +(-0.691909 - 1.85508i) q^{52} +(0.186324 + 2.60514i) q^{53} +(5.50328 + 0.791253i) q^{54} +(0.163752 - 3.45675i) q^{55} +(-1.36100 + 1.17931i) q^{56} +(-3.81191 - 0.829230i) q^{57} +(1.61322 + 0.350935i) q^{58} +(4.49488 - 3.89484i) q^{59} +(2.08461 - 1.89604i) q^{60} +(-2.10332 - 0.302411i) q^{61} +(0.228729 + 3.19805i) q^{62} +(-0.888551 - 2.38230i) q^{63} +(0.281733 - 0.959493i) q^{64} +(2.81787 - 3.41466i) q^{65} +(-1.93049 + 0.277562i) q^{66} +(-2.01591 - 9.26697i) q^{67} +(-5.02323 + 5.02323i) q^{68} +(-5.90596 - 1.28303i) q^{69} +(-3.80571 - 1.31605i) q^{70} +(5.43514 + 3.49295i) q^{71} +(1.13027 + 0.846113i) q^{72} +(5.12732 - 13.7469i) q^{73} +(-1.35339 - 0.397392i) q^{74} +(6.00283 + 1.91541i) q^{75} +(-2.33948 - 2.02717i) q^{76} +(1.67023 + 2.23117i) q^{77} +(-2.18989 - 1.19577i) q^{78} +(2.07903 + 2.39933i) q^{79} +(2.17290 - 0.527746i) q^{80} +(2.33104 - 1.49807i) q^{81} +(6.93697 + 0.496142i) q^{82} +(5.73166 - 10.4967i) q^{83} +(-0.322976 + 2.24635i) q^{84} +(-15.3447 - 4.10726i) q^{85} +(0.997236 + 0.455422i) q^{86} +(1.82604 - 0.997093i) q^{87} +(-1.45006 - 0.540844i) q^{88} +(2.68362 + 18.6650i) q^{89} +(-0.373979 + 3.13485i) q^{90} +3.56554i q^{91} +(-3.62533 - 3.13959i) q^{92} +(2.85706 + 2.85706i) q^{93} +(-6.45441 + 10.0433i) q^{94} +(1.30819 - 6.79719i) q^{95} +(-0.523507 - 1.14632i) q^{96} +(-5.36961 - 9.83370i) q^{97} +(-3.52004 + 1.31291i) q^{98} +(1.43093 - 1.65138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.977147	−	0.212565i	0.690947	−	0.150306i
$2$	0.977147	−	0.212565i	0.690947	−	0.150306i
$3$	0.755212	−	1.00884i	0.436022	−	0.582457i	−0.527678	−	0.849444i	$-0.676937\pi$
$3$	0.755212	−	1.00884i	0.436022	−	0.582457i	0.963700	+	0.266988i	$0.0860282\pi$
$4$	0.909632	−	0.415415i	0.454816	−	0.207708i
$5$	1.82179	+	1.29657i	0.814729	+	0.579842i
$5$	1.82179	+	1.29657i	0.814729	+	0.579842i
$6$	0.523507	−	1.14632i	0.213721	−	0.467984i
$7$	−1.79627	+	0.128472i	−0.678926	+	0.0485577i	−0.406544	−	0.913631i	$-0.633266\pi$
$7$	−1.79627	+	0.128472i	−0.678926	+	0.0485577i	−0.272382	+	0.962189i	$0.587812\pi$
$8$	0.800541	−	0.599278i	0.283034	−	0.211877i
$9$	0.397775	+	1.35470i	0.132592	+	0.451565i
$10$	2.05576	+	0.879687i	0.650089	+	0.278181i
$11$	−0.836716	−	1.30196i	−0.252279	−	0.392554i	0.691896	−	0.721997i	$-0.256776\pi$
$11$	−0.836716	−	1.30196i	−0.252279	−	0.392554i	−0.944176	+	0.329443i	$0.893139\pi$
$12$	0.267875	−	1.23140i	0.0773290	−	0.355476i
$13$	0.141245	−	1.97487i	0.0391744	−	0.547730i	−0.939532	−	0.342462i	$-0.888739\pi$
$13$	0.141245	−	1.97487i	0.0391744	−	0.547730i	0.978706	−	0.205267i	$-0.0658064\pi$
$14$	−1.72791	+	0.507360i	−0.461803	+	0.135598i
$15$	2.68387	−	0.858720i	0.692972	−	0.221721i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	−6.65602	+	2.48257i	−1.61432	+	0.602111i	−0.984618	−	0.174723i	$-0.944097\pi$
$17$	−6.65602	+	2.48257i	−1.61432	+	0.602111i	−0.629705	+	0.776834i	$0.716824\pi$
$18$	0.676646	+	1.23918i	0.159487	+	0.292078i
$19$	−1.28595	−	2.81584i	−0.295017	−	0.645998i	0.702845	−	0.711343i	$-0.251913\pi$
$19$	−1.28595	−	2.81584i	−0.295017	−	0.645998i	−0.997863	+	0.0653448i	$0.979185\pi$
$20$	2.19577	+	0.422600i	0.490989	+	0.0944962i
$21$	−1.22696	+	1.90918i	−0.267744	+	0.416617i
$22$	−1.09434	−	1.09434i	−0.233315	−	0.233315i
$23$	−1.99348	−	4.36188i	−0.415670	−	0.909515i
$23$	−1.99348	−	4.36188i	−0.415670	−	0.909515i
$24$		−	1.26020i		−	0.257238i
$25$	1.63783	+	4.72414i	0.327566	+	0.944828i
$26$	−0.281771	−	1.95976i	−0.0552598	−	0.384341i
$27$	5.20932	+	1.94298i	1.00253	+	0.373926i
$28$	−1.58057	+	0.863059i	−0.298701	+	0.163103i
$29$	1.50176	+	0.685829i	0.278869	+	0.127355i	0.549940	−	0.835204i	$-0.314651\pi$
$29$	1.50176	+	0.685829i	0.278869	+	0.127355i	−0.271071	+	0.962559i	$0.587378\pi$
$30$	2.44000	−	1.40959i	0.445481	−	0.257355i
$31$	−0.456293	+	3.17359i	−0.0819527	+	0.569993i	0.906928	+	0.421285i	$0.138421\pi$
$31$	−0.456293	+	3.17359i	−0.0819527	+	0.569993i	−0.988881	+	0.148708i	$0.952488\pi$
$32$	0.479249	−	0.877679i	0.0847201	−	0.155153i
$33$	−1.94537	−	0.139135i	−0.338645	−	0.0242204i
$34$	−5.97620	+	3.84067i	−1.02491	+	0.658670i
$35$	−3.43900	−	2.09493i	−0.581296	−	0.354109i
$36$	0.924590	+	1.06703i	0.154098	+	0.177839i
$37$	−1.23799	−	0.675994i	−0.203524	−	0.111133i	0.374255	−	0.927326i	$-0.377899\pi$
$37$	−1.23799	−	0.675994i	−0.203524	−	0.111133i	−0.577779	+	0.816193i	$0.696080\pi$
$38$	−1.85511	−	2.47814i	−0.300939	−	0.402007i
$39$	−1.88567	−	1.63394i	−0.301948	−	0.261640i
$40$	2.23542	−	0.0538024i	0.353451	−	0.00850691i
$41$	6.67297	+	1.95936i	1.04214	+	0.306001i	0.757639	−	0.652674i	$-0.226353\pi$
$41$	6.67297	+	1.95936i	1.04214	+	0.306001i	0.284505	+	0.958675i	$0.408171\pi$
$42$	−0.793090	+	2.12636i	−0.122377	+	0.328104i
$43$	0.877639	+	0.656992i	0.133839	+	0.100190i	0.664100	−	0.747644i	$-0.268815\pi$
$43$	0.877639	+	0.656992i	0.133839	+	0.100190i	−0.530261	+	0.847835i	$0.677906\pi$
$44$	−1.30196	−	0.836716i	−0.196277	−	0.126140i
$45$	−1.03179	+	2.98371i	−0.153811	+	0.444785i
$46$	−2.87511	−	3.83845i	−0.423912	−	0.565949i
$47$	−8.44176	+	8.44176i	−1.23136	+	1.23136i	−0.267915	+	0.963443i	$0.586334\pi$
$47$	−8.44176	+	8.44176i	−1.23136	+	1.23136i	−0.963443	+	0.267915i	$0.913666\pi$
$48$	−0.267875	−	1.23140i	−0.0386645	−	0.177738i
$49$	−3.71867	+	0.534664i	−0.531239	+	0.0763806i
$50$	2.60459	+	4.26803i	0.368345	+	0.603591i
$51$	−2.52218	+	8.58976i	−0.353176	+	1.20281i
$52$	−0.691909	−	1.85508i	−0.0959505	−	0.257253i
$53$	0.186324	+	2.60514i	0.0255935	+	0.357844i	0.994070	+	0.108740i	$0.0346816\pi$
$53$	0.186324	+	2.60514i	0.0255935	+	0.357844i	−0.968477	+	0.249104i	$0.919864\pi$
$54$	5.50328	+	0.791253i	0.748902	+	0.107676i
$55$	0.163752	−	3.45675i	0.0220803	−	0.466107i
$56$	−1.36100	+	1.17931i	−0.181871	+	0.157592i
$57$	−3.81191	−	0.829230i	−0.504900	−	0.109834i
$58$	1.61322	+	0.350935i	0.211826	+	0.0460800i
$59$	4.49488	−	3.89484i	0.585184	−	0.507065i	−0.311199	−	0.950345i	$-0.600731\pi$
$59$	4.49488	−	3.89484i	0.585184	−	0.507065i	0.896383	+	0.443280i	$0.146185\pi$
$60$	2.08461	−	1.89604i	0.269122	−	0.244778i
$61$	−2.10332	−	0.302411i	−0.269302	−	0.0387198i	0.00634081	−	0.999980i	$-0.497982\pi$
$61$	−2.10332	−	0.302411i	−0.269302	−	0.0387198i	−0.275643	+	0.961260i	$0.588891\pi$
$62$	0.228729	+	3.19805i	0.0290487	+	0.406153i
$63$	−0.888551	−	2.38230i	−0.111947	−	0.300141i
$64$	0.281733	−	0.959493i	0.0352166	−	0.119937i
$65$	2.81787	−	3.41466i	0.349513	−	0.423536i
$66$	−1.93049	+	0.277562i	−0.237626	+	0.0341655i
$67$	−2.01591	−	9.26697i	−0.246282	−	1.13214i	−0.919621	−	0.392806i	$-0.871504\pi$
$67$	−2.01591	−	9.26697i	−0.246282	−	1.13214i	0.673339	−	0.739334i	$-0.264859\pi$
$68$	−5.02323	+	5.02323i	−0.609157	+	0.609157i
$69$	−5.90596	−	1.28303i	−0.710995	−	0.154459i
$70$	−3.80571	−	1.31605i	−0.454870	−	0.157298i
$71$	5.43514	+	3.49295i	0.645032	+	0.414537i	0.821848	−	0.569707i	$-0.192943\pi$
$71$	5.43514	+	3.49295i	0.645032	+	0.414537i	−0.176816	+	0.984244i	$0.556580\pi$
$72$	1.13027	+	0.846113i	0.133204	+	0.0997153i
$73$	5.12732	−	13.7469i	0.600107	−	1.60895i	−0.180253	−	0.983620i	$-0.557692\pi$
$73$	5.12732	−	13.7469i	0.600107	−	1.60895i	0.780361	−	0.625330i	$-0.215036\pi$
$74$	−1.35339	−	0.397392i	−0.157329	−	0.0461958i
$75$	6.00283	+	1.91541i	0.693148	+	0.221173i
$76$	−2.33948	−	2.02717i	−0.268357	−	0.232533i
$77$	1.67023	+	2.23117i	0.190341	+	0.254265i
$78$	−2.18989	−	1.19577i	−0.247956	−	0.135394i
$79$	2.07903	+	2.39933i	0.233909	+	0.269945i	0.860554	−	0.509360i	$-0.170118\pi$
$79$	2.07903	+	2.39933i	0.233909	+	0.269945i	−0.626645	+	0.779305i	$0.715572\pi$
$80$	2.17290	−	0.527746i	0.242937	−	0.0590038i
$81$	2.33104	−	1.49807i	0.259004	−	0.166452i
$82$	6.93697	+	0.496142i	0.766060	+	0.0547897i
$83$	5.73166	−	10.4967i	0.629131	−	1.15217i	−0.347588	−	0.937647i	$-0.612999\pi$
$83$	5.73166	−	10.4967i	0.629131	−	1.15217i	0.976719	−	0.214520i	$-0.0688189\pi$
$84$	−0.322976	+	2.24635i	−0.0352396	+	0.245097i
$85$	−15.3447	−	4.10726i	−1.66436	−	0.445495i
$86$	0.997236	+	0.455422i	0.107535	+	0.0491095i
$87$	1.82604	−	0.997093i	0.195772	−	0.106900i
$88$	−1.45006	−	0.540844i	−0.154577	−	0.0576541i
$89$	2.68362	+	18.6650i	0.284463	+	1.97848i	0.176112	+	0.984370i	$0.443648\pi$
$89$	2.68362	+	18.6650i	0.284463	+	1.97848i	0.108351	+	0.994113i	$0.465443\pi$
$90$	−0.373979	+	3.13485i	−0.0394208	+	0.330442i
$91$			3.56554i			0.373770i
$92$	−3.62533	−	3.13959i	−0.377967	−	0.327324i
$93$	2.85706	+	2.85706i	0.296263	+	0.296263i
$94$	−6.45441	+	10.0433i	−0.665722	+	1.03588i
$95$	1.30819	−	6.79719i	0.134218	−	0.697377i
$96$	−0.523507	−	1.14632i	−0.0534302	−	0.116996i
$97$	−5.36961	−	9.83370i	−0.545201	−	0.998461i	−0.994466	−	0.105062i	$-0.966496\pi$
$97$	−5.36961	−	9.83370i	−0.545201	−	0.998461i	0.449265	−	0.893399i	$-0.351686\pi$
$98$	−3.52004	+	1.31291i	−0.355577	+	0.132624i
$99$	1.43093	−	1.65138i	0.143814	−	0.165970i
$100$	3.45230	+	3.61685i	0.345230	+	0.361685i
$101$	9.27112	−	2.72225i	0.922511	−	0.270874i	0.214213	−	0.976787i	$-0.431281\pi$
$101$	9.27112	−	2.72225i	0.922511	−	0.270874i	0.708298	+	0.705913i	$0.249463\pi$
$102$	−0.638656	+	8.92958i	−0.0632364	+	0.884160i
$103$	−1.56384	+	7.18885i	−0.154090	+	0.708339i	0.833658	+	0.552281i	$0.186242\pi$
$103$	−1.56384	+	7.18885i	−0.154090	+	0.708339i	−0.987748	+	0.156058i	$0.950121\pi$
$104$	−1.07042	−	1.66561i	−0.104963	−	0.163326i
$105$	−4.71063	+	1.88729i	−0.459711	+	0.184181i
$106$	0.735829	+	2.50600i	0.0714700	+	0.243404i
$107$	9.57092	−	7.16470i	0.925256	−	0.692638i	−0.0264497	−	0.999650i	$-0.508420\pi$
$107$	9.57092	−	7.16470i	0.925256	−	0.692638i	0.951706	+	0.307012i	$0.0993293\pi$
$108$	5.54571	−	0.396637i	0.533636	−	0.0381664i
$109$	−6.38050	+	13.9713i	−0.611141	+	1.33821i	0.310649	+	0.950525i	$0.399453\pi$
$109$	−6.38050	+	13.9713i	−0.611141	+	1.33821i	−0.921791	+	0.387688i	$0.873274\pi$
$110$	−0.574774	−	3.41256i	−0.0548026	−	0.325374i
$111$	−1.61692	+	0.738422i	−0.153471	+	0.0700879i
$112$	−1.07921	+	1.44166i	−0.101976	+	0.136224i
$113$	7.01696	−	1.52645i	0.660100	−	0.143596i	0.129978	−	0.991517i	$-0.458509\pi$
$113$	7.01696	−	1.52645i	0.660100	−	0.143596i	0.530123	+	0.847921i	$0.322146\pi$
$114$	−3.90106			−0.365368
$115$	2.02377	−	10.5311i	0.188717	−	0.982031i
$116$	1.65095			0.153287
$117$	2.73153	−	0.594208i	0.252530	−	0.0549346i
$118$	3.56425	−	4.76128i	0.328116	−	0.438312i
$119$	11.6371	−	5.31447i	1.06677	−	0.487177i
$120$	1.63394	−	2.29582i	0.149157	−	0.209579i
$121$	3.57457	−	7.82722i	0.324961	−	0.711565i
$122$	−2.11953	+	0.151592i	−0.191893	+	0.0137245i
$123$	7.01620	−	5.25226i	0.632630	−	0.473581i
$124$	0.903297	+	3.07635i	0.0811185	+	0.276264i
$125$	−3.14138	+	10.7299i	−0.280974	+	0.959715i
$126$	−1.37464	−	2.13898i	−0.122462	−	0.190555i
$127$	2.44622	−	11.2451i	0.217067	−	0.997839i	−0.731643	−	0.681688i	$-0.761246\pi$
$127$	2.44622	−	11.2451i	0.217067	−	0.997839i	0.948709	−	0.316150i	$-0.102390\pi$
$128$	0.0713392	−	0.997452i	0.00630555	−	0.0881631i
$129$	1.32561	−	0.389233i	0.116713	−	0.0342701i
$130$	2.02763	−	3.93560i	0.177835	−	0.345175i
$131$	0.766219	−	0.884264i	0.0669449	−	0.0772585i	−0.721289	−	0.692634i	$-0.756450\pi$
$131$	0.766219	−	0.884264i	0.0669449	−	0.0772585i	0.788234	+	0.615375i	$0.210996\pi$
$132$	−1.82737	+	0.681573i	−0.159052	+	0.0593233i
$133$	2.67167	+	4.89280i	0.231663	+	0.424259i
$134$	−3.93967	−	8.62668i	−0.340336	−	0.745231i
$135$	6.97109	+	10.2939i	0.599976	+	0.885960i
$136$	−3.84067	+	5.97620i	−0.329335	+	0.512455i
$137$	−1.05080	−	1.05080i	−0.0897757	−	0.0897757i	0.660793	−	0.750568i	$-0.270220\pi$
$137$	−1.05080	−	1.05080i	−0.0897757	−	0.0897757i	−0.750568	+	0.660793i	$0.770220\pi$
$138$	−6.04372	+	0.00169451i	−0.514476	+	0.000144246i
$139$		−	11.2451i		−	0.953794i	−0.878959	−	0.476897i	$-0.841761\pi$
$139$		−	11.2451i		−	0.953794i	0.878959	−	0.476897i	$-0.158239\pi$
$140$	−3.99849	−	0.477009i	−0.337934	−	0.0403146i
$141$	2.14111	+	14.8917i	0.180314	+	1.25411i
$142$	6.05341	+	2.25780i	0.507991	+	0.189471i
$143$	−2.68937	+	1.46851i	−0.224897	+	0.122803i
$144$	1.28430	+	0.586519i	0.107025	+	0.0488766i
$145$	1.84666	+	3.19656i	0.153357	+	0.265460i
$146$	2.08804	−	14.5226i	0.172807	−	1.20190i
$147$	−2.26899	+	4.15535i	−0.187143	+	0.342727i
$148$	−1.40693	−	0.100626i	−0.115649	−	0.00827140i
$149$	11.3764	−	7.31118i	0.931992	−	0.598955i	0.0158788	−	0.999874i	$-0.494945\pi$
$149$	11.3764	−	7.31118i	0.931992	−	0.598955i	0.916114	+	0.400919i	$0.131309\pi$
$150$	6.27280	+	0.595643i	0.512172	+	0.0486341i
$151$	−11.1971	−	12.9221i	−0.911207	−	1.05159i	−0.998464	−	0.0554030i	$-0.982356\pi$
$151$	−11.1971	−	12.9221i	−0.911207	−	1.05159i	0.0872572	−	0.996186i	$-0.472190\pi$
$152$	−2.71693	−	1.48355i	−0.220372	−	0.120332i
$153$	−6.01072	−	8.02938i	−0.485938	−	0.649137i
$154$	2.10633	+	1.82515i	0.169733	+	0.147074i
$155$	−4.94604	+	5.18999i	−0.397275	+	0.416870i
$156$	−2.39402	−	0.702949i	−0.191675	−	0.0562810i
$157$	−0.262770	+	0.704513i	−0.0209713	+	0.0562262i	−0.947014	−	0.321194i	$-0.895916\pi$
$157$	−0.262770	+	0.704513i	−0.0209713	+	0.0562262i	0.926042	+	0.377420i	$0.123189\pi$
$158$	2.54153	+	1.90256i	0.202193	+	0.151360i
$159$	2.76890	+	1.77946i	0.219588	+	0.141121i
$160$	2.01106	−	0.977568i	0.158988	−	0.0772835i
$161$	4.14121	+	7.57901i	0.326373	+	0.597310i
$162$	1.95933	−	1.95933i	0.153940	−	0.153940i
$163$	1.63610	+	7.52102i	0.128149	+	0.589092i	0.995771	+	0.0918678i	$0.0292837\pi$
$163$	1.63610	+	7.52102i	0.128149	+	0.589092i	−0.867622	+	0.497224i	$0.834353\pi$
$164$	6.88390	−	0.989755i	0.537542	−	0.0772869i
$165$	−3.36365	−	2.77578i	−0.261860	−	0.216094i
$166$	3.36943	−	11.4752i	0.261518	−	0.890649i
$167$	4.62485	+	12.3997i	0.357882	+	0.959518i	0.983743	+	0.179583i	$0.0574749\pi$
$167$	4.62485	+	12.3997i	0.357882	+	0.959518i	−0.625861	+	0.779934i	$0.715252\pi$
$168$	0.161900	+	2.26366i	0.0124909	+	0.174646i
$169$	8.98752	+	1.29221i	0.691348	+	0.0994008i
$170$	−15.8671	−	0.751650i	−1.21695	−	0.0576490i
$171$	3.30309	−	2.86214i	0.252593	−	0.218873i
$172$	1.07125	+	0.233037i	0.0816823	+	0.0177689i
$173$	−18.7490	−	4.07860i	−1.42546	−	0.310090i	−0.567318	−	0.823499i	$-0.692019\pi$
$173$	−18.7490	−	4.07860i	−1.42546	−	0.310090i	−0.858144	+	0.513408i	$0.828383\pi$
$174$	1.57236	−	1.36246i	0.119200	−	0.103288i
$175$	−3.54890	−	8.27542i	−0.268272	−	0.625563i
$176$	−1.53188	−	0.220252i	−0.115470	−	0.0166021i
$177$	−0.534699	−	7.47606i	−0.0401904	−	0.561935i
$178$	6.58981	+	17.6680i	0.493927	+	1.32427i
$179$	−2.41685	+	8.23104i	−0.180644	+	0.615217i	0.818525	+	0.574470i	$0.194792\pi$
$179$	−2.41685	+	8.23104i	−0.180644	+	0.615217i	−0.999170	+	0.0407469i	$0.987026\pi$
$180$	0.300927	+	3.14270i	0.0224298	+	0.234243i
$181$	−15.0926	+	2.16999i	−1.12183	+	0.161294i	−0.678172	−	0.734903i	$-0.737227\pi$
$181$	−15.0926	+	2.16999i	−1.12183	+	0.161294i	−0.443655	+	0.896198i	$0.646318\pi$
$182$	0.757910	+	3.48406i	0.0561800	+	0.258256i
$183$	−1.89354	+	1.89354i	−0.139974	+	0.139974i
$184$	−4.20984	−	2.29722i	−0.310354	−	0.169353i
$185$	−1.37889	−	2.83666i	−0.101378	−	0.208555i
$186$	3.39908	+	2.18446i	0.249233	+	0.160172i
$187$	8.80139	+	6.58864i	0.643622	+	0.481809i
$188$	−4.17206	+	11.1857i	−0.304279	+	0.815803i
$189$	−9.60697	−	2.82086i	−0.698804	−	0.205187i
$190$	−0.166550	−	6.91993i	−0.0120828	−	0.502024i
$191$	6.07092	+	5.26049i	0.439277	+	0.380635i	0.846234	−	0.532812i	$-0.178865\pi$
$191$	6.07092	+	5.26049i	0.439277	+	0.380635i	−0.406957	+	0.913447i	$0.633410\pi$
$192$	−0.755212	−	1.00884i	−0.0545027	−	0.0728071i
$193$	−2.95318	−	1.61256i	−0.212575	−	0.116074i	0.369435	−	0.929257i	$-0.379551\pi$
$193$	−2.95318	−	1.61256i	−0.212575	−	0.116074i	−0.582009	+	0.813182i	$0.697733\pi$
$194$	−7.33720	−	8.46758i	−0.526780	−	0.607937i
$195$	−1.31677	−	5.42158i	−0.0942962	−	0.388248i
$196$	−3.16052	+	2.03114i	−0.225751	+	0.145081i
$197$	7.42545	+	0.531079i	0.529041	+	0.0378378i	0.333306	−	0.942819i	$-0.391836\pi$
$197$	7.42545	+	0.531079i	0.529041	+	0.0378378i	0.195736	+	0.980657i	$0.437290\pi$
$198$	1.04720	−	1.91781i	0.0744214	−	0.136293i
$199$	−0.419665	+	2.91884i	−0.0297493	+	0.206911i	−0.999275	−	0.0380799i	$-0.987876\pi$
$199$	−0.419665	+	2.91884i	−0.0297493	+	0.206911i	0.969525	+	0.244991i	$0.0787850\pi$
$200$	4.14222	+	2.80036i	0.292899	+	0.198015i
$201$	−10.8714	−	4.96479i	−0.766807	−	0.350189i
$202$	8.48059	−	4.63075i	0.596692	−	0.325819i
$203$	−2.78567	−	1.03900i	−0.195516	−	0.0729236i
$204$	1.27406	+	8.86127i	0.0892019	+	0.620413i
$205$	9.61631	+	12.2215i	0.671632	+	0.853587i
$206$			7.35698i			0.512585i
$207$	5.11607	−	4.43561i	0.355591	−	0.308296i
$208$	−1.40001	−	1.40001i	−0.0970732	−	0.0970732i
$209$	−2.59012	+	4.03031i	−0.179162	+	0.278782i
$210$	−4.20181	+	2.84548i	−0.289952	+	0.196357i
$211$	−1.05048	−	2.30023i	−0.0723179	−	0.158354i	0.870021	−	0.493015i	$-0.164105\pi$
$211$	−1.05048	−	2.30023i	−0.0723179	−	0.158354i	−0.942339	+	0.334661i	$0.891378\pi$
$212$	1.25170	+	2.29232i	0.0859672	+	0.157437i
$213$	7.62852	−	2.84529i	0.522698	−	0.194956i
$214$	7.82923	−	9.03541i	0.535195	−	0.617648i
$215$	0.747039	+	2.33482i	0.0509476	+	0.159233i
$216$	5.33466	−	1.56640i	0.362978	−	0.106580i
$217$	0.411909	−	5.75924i	0.0279622	−	0.390963i
$218$	−3.26486	+	15.0083i	−0.221124	+	1.01649i
$219$	−9.99625	−	15.5545i	−0.675484	−	1.05107i
$220$	−1.28703	−	3.21239i	−0.0867715	−	0.216579i
$221$	3.96261	+	13.4954i	0.266554	+	0.907800i
$222$	−1.42300	+	1.06525i	−0.0955058	+	0.0714947i
$223$	−22.2870	+	1.59399i	−1.49244	+	0.106742i	−0.793560	−	0.608492i	$-0.791775\pi$
$223$	−22.2870	+	1.59399i	−1.49244	+	0.106742i	−0.698885	+	0.715234i	$0.746320\pi$
$224$	−0.748103	+	1.63812i	−0.0499848	+	0.109451i
$225$	−5.74829	+	4.09791i	−0.383219	+	0.273194i
$226$	6.53213	−	2.98313i	0.434511	−	0.198435i
$227$	−14.6619	+	19.5859i	−0.973141	+	1.29996i	−0.0192491	+	0.999815i	$0.506128\pi$
$227$	−14.6619	+	19.5859i	−0.973141	+	1.29996i	−0.953892	+	0.300150i	$0.902963\pi$
$228$	−3.81191	+	0.829230i	−0.252450	+	0.0549171i
$229$	−2.45057			−0.161938			−0.0809690	−	0.996717i	$-0.525801\pi$
$229$	−2.45057			−0.161938			−0.0809690	+	0.996717i	$0.525801\pi$
$230$	−0.261033	−	10.7206i	−0.0172120	−	0.706897i
$231$	3.51228			0.231091
$232$	1.61322	−	0.350935i	0.105913	−	0.0230400i
$233$	−15.2882	+	20.4226i	−1.00156	+	1.33793i	−0.0610643	+	0.998134i	$0.519449\pi$
$233$	−15.2882	+	20.4226i	−1.00156	+	1.33793i	−0.940499	+	0.339798i	$0.889641\pi$
$234$	2.54280	−	1.16126i	0.166228	−	0.0759137i
$235$	−26.3244	+	4.43380i	−1.71722	+	0.289229i
$236$	2.47071	−	5.41011i	0.160830	−	0.352168i
$237$	3.99065	−	0.285417i	0.259221	−	0.0185398i
$238$	10.2415	−	7.66666i	0.663855	−	0.496955i
$239$	−6.33520	−	21.5757i	−0.409790	−	1.39562i	−0.863447	−	0.504440i	$-0.831699\pi$
$239$	−6.33520	−	21.5757i	−0.409790	−	1.39562i	0.453657	−	0.891176i	$-0.350119\pi$
$240$	1.10858	−	2.59068i	0.0715588	−	0.167227i
$241$	−0.448728	−	0.698234i	−0.0289051	−	0.0449772i	0.826500	−	0.562936i	$-0.190328\pi$
$241$	−0.448728	−	0.698234i	−0.0289051	−	0.0449772i	−0.855405	+	0.517959i	$0.826692\pi$
$242$	1.82909	−	8.40817i	0.117578	−	0.540498i
$243$	−0.940801	+	13.1541i	−0.0603524	+	0.843837i
$244$	−2.03887	+	0.598666i	−0.130525	+	0.0383257i
$245$	−7.46786	−	3.84746i	−0.477104	−	0.245805i
$246$	5.73941	−	6.62363i	0.365931	−	0.422307i
$247$	−5.74255	+	2.14186i	−0.365389	+	0.136283i
$248$	1.53658	+	2.81403i	0.0975729	+	0.178691i
$249$	−6.26097	−	13.7096i	−0.396773	−	0.868812i
$250$	−0.788779	+	11.1525i	−0.0498867	+	0.705345i
$251$	−0.611467	+	0.951461i	−0.0385955	+	0.0600557i	−0.860015	−	0.510268i	$-0.829546\pi$
$251$	−0.611467	+	0.951461i	−0.0385955	+	0.0600557i	0.821420	+	0.570324i	$0.193182\pi$
$252$	−1.79790	−	1.79790i	−0.113257	−	0.113257i
$253$	−4.01100	+	6.24508i	−0.252169	+	0.392625i
$254$		−	11.5081i		−	0.722080i
$255$	−15.7321	+	12.3786i	−0.985181	+	0.775175i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−7.95409	−	2.96672i	−0.496163	−	0.185059i	0.0889105	−	0.996040i	$-0.471661\pi$
$257$	−7.95409	−	2.96672i	−0.496163	−	0.185059i	−0.585073	+	0.810981i	$0.698934\pi$
$258$	1.21257	−	0.662116i	0.0754916	−	0.0412215i
$259$	2.31061	+	1.05522i	0.143574	+	0.0655682i
$260$	1.14472	−	4.27667i	0.0709926	−	0.265228i
$261$	−0.331730	+	2.30723i	−0.0205335	+	0.142814i
$262$	0.560745	−	1.02693i	0.0346429	−	0.0634438i
$263$	20.2317	+	1.44700i	1.24754	+	0.0892259i	0.679439	−	0.733732i	$-0.262223\pi$
$263$	20.2317	+	1.44700i	1.24754	+	0.0892259i	0.568102	+	0.822958i	$0.307678\pi$
$264$	−1.64073	+	1.05443i	−0.100980	+	0.0648958i
$265$	−3.03830	+	4.98760i	−0.186641	+	0.306386i
$266$	3.65065	+	4.21308i	0.223836	+	0.258320i
$267$	20.8568	+	11.3887i	1.27641	+	0.696974i
$268$	−5.68337	−	7.59209i	−0.347167	−	0.463761i
$269$	17.9196	+	15.5274i	1.09258	+	0.946723i	0.998805	−	0.0488711i	$-0.0155623\pi$
$269$	17.9196	+	15.5274i	1.09258	+	0.946723i	0.0937711	+	0.995594i	$0.470108\pi$
$270$	8.99991	+	8.57687i	0.547717	+	0.521972i
$271$	−18.4876	−	5.42846i	−1.12304	−	0.329755i	−0.333073	−	0.942901i	$-0.608086\pi$
$271$	−18.4876	−	5.42846i	−1.12304	−	0.329755i	−0.789970	+	0.613146i	$0.789904\pi$
$272$	−2.48257	+	6.65602i	−0.150528	+	0.403581i
$273$	3.59708	+	2.69274i	0.217705	+	0.162972i
$274$	−1.25015	−	0.803421i	−0.0755241	−	0.0485364i
$275$	4.78022	−	6.08515i	0.288258	−	0.366948i
$276$	−5.90524	+	1.28634i	−0.355454	+	0.0774287i
$277$	−7.26337	+	7.26337i	−0.436413	+	0.436413i	−0.890803	−	0.454390i	$-0.849857\pi$
$277$	−7.26337	+	7.26337i	−0.436413	+	0.436413i	0.454390	+	0.890803i	$0.349857\pi$
$278$	−2.39031	−	10.9881i	−0.143361	−	0.659021i
$279$	−4.48075	+	0.644234i	−0.268255	+	0.0385693i
$280$	−4.00851	+	0.383832i	−0.239554	+	0.0229383i
$281$	6.53768	−	22.2653i	0.390005	−	1.32824i	−0.497510	−	0.867458i	$-0.665752\pi$
$281$	6.53768	−	22.2653i	0.390005	−	1.32824i	0.887515	−	0.460778i	$-0.152430\pi$
$282$	5.25765	+	14.0963i	0.313088	+	0.839422i
$283$	1.92013	+	26.8469i	0.114140	+	1.59588i	0.655567	+	0.755137i	$0.272430\pi$
$283$	1.92013	+	26.8469i	0.114140	+	1.59588i	−0.541427	+	0.840747i	$0.682116\pi$
$284$	6.39500	+	0.919462i	0.379473	+	0.0545600i
$285$	−5.86934	−	6.45308i	−0.347670	−	0.382247i
$286$	−2.31576	+	2.00662i	−0.136934	+	0.118654i
$287$	−12.2382	−	2.66225i	−0.722397	−	0.157148i
$288$	1.37962	+	0.300118i	0.0812950	+	0.0176846i
$289$	25.2917	−	21.9154i	1.48775	−	1.28914i
$290$	2.48394	+	2.73098i	0.145862	+	0.160368i
$291$	−13.9759	−	2.00943i	−0.819280	−	0.117795i
$292$	−1.04668	−	14.6346i	−0.0612526	−	0.856423i
$293$	7.86438	+	21.0852i	0.459442	+	1.23181i	0.935791	+	0.352556i	$0.114687\pi$
$293$	7.86438	+	21.0852i	0.459442	+	1.23181i	−0.476349	+	0.879257i	$0.658040\pi$
$294$	−1.33386	+	4.54269i	−0.0777920	+	0.264935i
$295$	13.2386	−	1.26766i	0.770783	−	0.0738059i
$296$	−1.39617	+	0.200739i	−0.0811508	+	0.0116677i
$297$	−1.82905	−	8.40803i	−0.106132	−	0.487883i
$298$	9.56233	−	9.56233i	0.553931	−	0.553931i
$299$	−8.89571	+	3.32077i	−0.514452	+	0.192045i
$300$	6.25606	−	0.751349i	0.361194	−	0.0433791i
$301$	−1.66088	−	1.06738i	−0.0957316	−	0.0615230i
$302$	−13.6880	−	10.2467i	−0.787656	−	0.589632i
$303$	4.25533	−	11.4090i	0.244463	−	0.655429i
$304$	−2.97019	−	0.872126i	−0.170352	−	0.0500199i
$305$	−3.43970	−	3.27802i	−0.196957	−	0.187699i
$306$	−7.58013	−	6.56822i	−0.433327	−	0.375480i
$307$	7.49905	+	10.0176i	0.427994	+	0.571732i	0.961758	−	0.273901i	$-0.0883140\pi$
$307$	7.49905	+	10.0176i	0.427994	+	0.571732i	−0.533764	+	0.845633i	$0.679223\pi$
$308$	2.44616	+	1.33570i	0.139383	+	0.0761087i
$309$	6.07141	+	7.00678i	0.345390	+	0.398602i
$310$	−3.72979	+	6.12274i	−0.211838	+	0.347748i
$311$	−26.3295	+	16.9209i	−1.49301	+	0.959497i	−0.497237	+	0.867615i	$0.665652\pi$
$311$	−26.3295	+	16.9209i	−1.49301	+	0.959497i	−0.995770	+	0.0918829i	$0.970711\pi$
$312$	−2.48874	−	0.177998i	−0.140897	−	0.0100771i
$313$	11.7784	−	21.5705i	0.665755	−	1.21924i	−0.298537	−	0.954398i	$-0.596499\pi$
$313$	11.7784	−	21.5705i	0.665755	−	1.21924i	0.964292	−	0.264841i	$-0.0853196\pi$
$314$	−0.107010	+	0.744268i	−0.00603890	+	0.0420015i
$315$	1.47005	−	5.49211i	0.0828282	−	0.309445i
$316$	2.88787	+	1.31884i	0.162455	+	0.0741908i
$317$	24.8988	−	13.5958i	1.39846	−	0.763615i	0.409568	−	0.912279i	$-0.365679\pi$
$317$	24.8988	−	13.5958i	1.39846	−	0.763615i	0.988888	+	0.148665i	$0.0474975\pi$
$318$	3.08387	+	1.15023i	0.172935	+	0.0645014i
$319$	−0.363625	−	2.52906i	−0.0203591	−	0.141600i
$320$	1.75730	−	1.38271i	0.0982363	−	0.0772958i
$321$		−	15.0664i		−	0.840927i
$322$	5.65761	+	6.52553i	0.315286	+	0.363653i
$323$	15.5498	+	15.5498i	0.865216	+	0.865216i
$324$	1.49807	−	2.33104i	0.0832260	−	0.129502i
$325$	9.56089	−	2.56724i	0.530343	−	0.142405i
$326$	3.19742	+	7.00137i	0.177089	+	0.387770i
$327$	9.27629	+	16.9883i	0.512980	+	0.939453i
$328$	6.51619	−	2.43041i	0.359797	−	0.134197i
$329$	14.0791	−	16.2482i	0.776208	−	0.895792i
$330$	−3.87682	−	1.99734i	−0.213412	−	0.109950i
$331$	6.34437	−	1.86288i	0.348718	−	0.102393i	−0.102683	−	0.994714i	$-0.532743\pi$
$331$	6.34437	−	1.86288i	0.348718	−	0.102393i	0.451401	+	0.892321i	$0.350924\pi$
$332$	0.853193	−	11.9292i	0.0468250	−	0.654700i
$333$	0.423325	−	1.94599i	0.0231981	−	0.106640i
$334$	7.15490	+	11.1332i	0.391499	+	0.609184i
$335$	8.34269	−	19.4962i	0.455810	−	1.06519i
$336$	0.639377	+	2.17752i	0.0348809	+	0.118793i
$337$	4.65617	−	3.48557i	0.253638	−	0.189871i	−0.464891	−	0.885368i	$-0.653907\pi$
$337$	4.65617	−	3.48557i	0.253638	−	0.189871i	0.718529	+	0.695497i	$0.244816\pi$
$338$	9.05681	−	0.647756i	0.492626	−	0.0352333i
$339$	3.75935	−	8.23182i	0.204180	−	0.447091i
$340$	−15.6642	+	2.63832i	−0.849512	+	0.143083i
$341$	4.51366	−	2.06132i	0.244428	−	0.111627i
$342$	2.61921	−	3.49886i	0.141631	−	0.189196i
$343$	18.9290	−	4.11774i	1.02207	−	0.222337i
$344$	1.09631			0.0591089
$345$	−9.09589	−	9.99489i	−0.489706	−	0.538107i
$346$	−19.1875			−1.03153
$347$	−19.8861	+	4.32596i	−1.06754	+	0.232230i	−0.711820	−	0.702362i	$-0.752129\pi$
$347$	−19.8861	+	4.32596i	−1.06754	+	0.232230i	−0.355722	+	0.934592i	$0.615765\pi$
$348$	1.24682	−	1.66555i	0.0668364	−	0.0892830i
$349$	3.23673	−	1.47816i	0.173258	−	0.0791244i	−0.326898	−	0.945060i	$-0.606003\pi$
$349$	3.23673	−	1.47816i	0.173258	−	0.0791244i	0.500156	+	0.865935i	$0.333276\pi$
$350$	−5.22687	−	7.33192i	−0.279388	−	0.391908i
$351$	4.57292	−	10.0133i	0.244084	−	0.534470i
$352$	−1.54369	+	0.110407i	−0.0822792	+	0.00588472i
$353$	7.53867	−	5.64338i	0.401243	−	0.300367i	−0.379532	−	0.925178i	$-0.623915\pi$
$353$	7.53867	−	5.64338i	0.401243	−	0.300367i	0.780776	+	0.624812i	$0.214824\pi$
$354$	−2.11163	−	7.19155i	−0.112232	−	0.382227i
$355$	5.37283	+	13.4104i	0.285160	+	0.711752i
$356$	10.1948	+	15.8634i	0.540324	+	0.840761i
$357$	3.42697	−	15.7535i	0.181375	−	0.833766i
$358$	−0.611986	+	8.55668i	−0.0323444	+	0.452234i
$359$	−21.8010	+	6.40135i	−1.15061	+	0.337850i	−0.800778	−	0.598962i	$-0.795580\pi$
$359$	−21.8010	+	6.40135i	−1.15061	+	0.337850i	−0.349834	+	0.936812i	$0.613762\pi$
$360$	0.962080	+	3.00691i	0.0507060	+	0.158478i
$361$	6.16707	−	7.11718i	0.324583	−	0.374588i
$362$	−14.2865	+	5.32857i	−0.750879	+	0.280063i
$363$	−5.19689	−	9.51739i	−0.272766	−	0.499534i
$364$	1.48118	+	3.24333i	0.0776349	+	0.169997i
$365$	27.1646	−	18.3960i	1.42186	−	0.962890i
$366$	−1.44776	+	2.25276i	−0.0756758	+	0.117754i
$367$	−6.38920	−	6.38920i	−0.333514	−	0.333514i	0.520405	−	0.853919i	$-0.325781\pi$
$367$	−6.38920	−	6.38920i	−0.333514	−	0.333514i	−0.853919	+	0.520405i	$0.825781\pi$
$368$	−4.60195	−	1.34985i	−0.239893	−	0.0703659i
$369$			9.81924i			0.511169i
$370$	−1.95035	−	2.47873i	−0.101394	−	0.128863i
$371$	−0.669375	−	4.65560i	−0.0347522	−	0.241707i
$372$	3.78574	+	1.41201i	0.196281	+	0.0732092i
$373$	−10.0472	+	5.48617i	−0.520223	+	0.284063i	−0.717830	−	0.696218i	$-0.754865\pi$
$373$	−10.0472	+	5.48617i	−0.520223	+	0.284063i	0.197607	+	0.980281i	$0.436683\pi$
$374$	10.0008	+	4.56720i	0.517127	+	0.236164i
$375$	8.45244	+	11.2725i	0.436482	+	0.582112i
$376$	−1.69902	+	11.8169i	−0.0876202	+	0.609412i
$377$	1.56654	−	2.86890i	0.0806809	−	0.147756i
$378$	−9.98703	−	0.714287i	−0.513678	−	0.0367389i
$379$	12.4319	−	7.98949i	0.638583	−	0.410392i	−0.180896	−	0.983502i	$-0.557900\pi$
$379$	12.4319	−	7.98949i	0.638583	−	0.410392i	0.819478	+	0.573110i	$0.194263\pi$
$380$	−1.63368	−	6.72638i	−0.0838060	−	0.345056i
$381$	−9.49712	−	10.9603i	−0.486552	−	0.561511i
$382$	7.05038	+	3.84980i	0.360729	+	0.196973i
$383$	12.9799	+	17.3391i	0.663241	+	0.885986i	0.998421	−	0.0561677i	$-0.0178882\pi$
$383$	12.9799	+	17.3391i	0.663241	+	0.885986i	−0.335180	+	0.942154i	$0.608797\pi$
$384$	−0.952398	−	0.825258i	−0.0486019	−	0.0421138i
$385$	0.149951	+	6.23028i	0.00764223	+	0.317525i
$386$	−3.22846	−	0.947963i	−0.164325	−	0.0482500i
$387$	−0.540922	+	1.45027i	−0.0274966	+	0.0737213i
$388$	−8.96943	−	6.71443i	−0.455354	−	0.340874i
$389$	28.2443	+	18.1515i	1.43204	+	0.920319i	0.999828	+	0.0185491i	$0.00590469\pi$
$389$	28.2443	+	18.1515i	1.43204	+	0.920319i	0.432216	+	0.901770i	$0.357732\pi$
$390$	−2.43912	−	5.01778i	−0.123510	−	0.254085i
$391$	24.0973	+	24.0838i	1.21865	+	1.21797i
$392$	−2.65654	+	2.65654i	−0.134175	+	0.134175i
$393$	−0.313428	−	1.44080i	−0.0158103	−	0.0726789i
$394$	7.36865	−	1.05945i	0.371227	−	0.0533744i
$395$	0.676664	+	7.06666i	0.0340467	+	0.355562i
$396$	0.615611	−	2.09658i	0.0309356	−	0.105357i
$397$	6.47580	+	17.3623i	0.325011	+	0.871389i	0.991991	+	0.126312i	$0.0403142\pi$
$397$	6.47580	+	17.3623i	0.325011	+	0.871389i	−0.666979	+	0.745076i	$0.732413\pi$
$398$	0.210369	+	2.94134i	0.0105448	+	0.147436i
$399$	6.95375	+	0.999798i	0.348123	+	0.0500525i
$400$	4.64282	+	1.85587i	0.232141	+	0.0927933i
$401$	8.28826	−	7.18182i	0.413896	−	0.358643i	−0.422882	−	0.906185i	$-0.638982\pi$
$401$	8.28826	−	7.18182i	0.413896	−	0.358643i	0.836778	+	0.547542i	$0.184436\pi$
$402$	−11.6783	−	2.54045i	−0.582459	−	0.126706i
$403$	6.20297	+	1.34937i	0.308992	+	0.0672171i
$404$	7.30244	−	6.32760i	0.363310	−	0.314810i
$405$	6.18901	+	0.293184i	0.307534	+	0.0145684i
$406$	−2.94286	−	0.423120i	−0.146052	−	0.0209991i
$407$	0.155732	+	2.17742i	0.00771937	+	0.107931i
$408$	3.12854	+	8.38794i	0.154886	+	0.415265i
$409$	−3.09786	+	10.5503i	−0.153179	+	0.521681i	−0.999947	−	0.0102819i	$-0.996727\pi$
$409$	−3.09786	+	10.5503i	−0.153179	+	0.521681i	0.846768	+	0.531963i	$0.178545\pi$
$410$	11.9944	+	9.89811i	0.592362	+	0.488833i
$411$	−1.85367	+	0.266517i	−0.0914346	+	0.0131463i
$412$	1.56384	+	7.18885i	0.0770448	+	0.354169i
$413$	−7.57364	+	7.57364i	−0.372674	+	0.372674i
$414$	4.05629	−	5.42174i	0.199356	−	0.266464i
$415$	24.0516	−	11.6914i	1.18065	−	0.573907i
$416$	−1.66561	−	1.07042i	−0.0816632	−	0.0524817i
$417$	−11.3445	−	8.49241i	−0.555544	−	0.415875i
$418$	−1.67423	+	4.48877i	−0.0818891	+	0.219553i
$419$	−34.8148	−	10.2225i	−1.70081	−	0.499404i	−0.719938	−	0.694039i	$-0.755830\pi$
$419$	−34.8148	−	10.2225i	−1.70081	−	0.499404i	−0.980876	+	0.194635i	$0.937648\pi$
$420$	−3.50093	+	3.67361i	−0.170828	+	0.179254i
$421$	−9.11140	−	7.89507i	−0.444062	−	0.384782i	0.403931	−	0.914790i	$-0.367644\pi$
$421$	−9.11140	−	7.89507i	−0.444062	−	0.384782i	−0.847993	+	0.530007i	$0.822189\pi$
$422$	−1.51542	−	2.02437i	−0.0737695	−	0.0985446i
$423$	−14.7939	−	8.07810i	−0.719306	−	0.392771i
$424$	1.71036	+	1.97387i	0.0830626	+	0.0958594i
$425$	−22.6294	−	27.3780i	−1.09769	−	1.32803i
$426$	6.84938	−	4.40183i	0.331853	−	0.213269i
$427$	3.81697	+	0.272995i	0.184716	+	0.0132112i
$428$	5.72969	−	10.4931i	0.276955	−	0.507205i
$429$	−0.549549	+	3.82219i	−0.0265325	+	0.184537i
$430$	1.22627	+	2.12267i	0.0591359	+	0.102364i
$431$	5.55718	+	2.53788i	0.267680	+	0.122245i	0.544734	−	0.838609i	$-0.316631\pi$
$431$	5.55718	+	2.53788i	0.267680	+	0.122245i	−0.277054	+	0.960854i	$0.589358\pi$
$432$	4.87979	−	2.66456i	0.234779	−	0.128199i
$433$	−13.9021	−	5.18521i	−0.668092	−	0.249185i	−0.00754669	−	0.999972i	$-0.502402\pi$
$433$	−13.9021	−	5.18521i	−0.668092	−	0.249185i	−0.660545	+	0.750786i	$0.729675\pi$
$434$	−0.821719	−	5.71518i	−0.0394438	−	0.274337i
$435$	4.61946	+	0.551089i	0.221486	+	0.0264227i
$436$			15.3593i			0.735579i
$437$	−9.71884	+	11.2225i	−0.464915	+	0.536845i
$438$	−13.0741	−	13.0741i	−0.624707	−	0.624707i
$439$	−13.8612	+	21.5685i	−0.661561	+	1.02941i	0.334641	+	0.942346i	$0.391385\pi$
$439$	−13.8612	+	21.5685i	−0.661561	+	1.02941i	−0.996203	+	0.0870640i	$0.972252\pi$
$440$	−1.94046	−	2.86540i	−0.0925078	−	0.136603i
$441$	−2.20350	−	4.82499i	−0.104929	−	0.229762i
$442$	6.74071	+	12.3447i	0.320623	+	0.587177i
$443$	10.6143	−	3.95893i	0.504301	−	0.188094i	−0.0844211	−	0.996430i	$-0.526904\pi$
$443$	10.6143	−	3.95893i	0.504301	−	0.188094i	0.588722	+	0.808336i	$0.299631\pi$
$444$	−1.16405	+	1.34338i	−0.0552433	+	0.0637542i
$445$	−19.3114	+	37.4831i	−0.915448	+	1.77687i
$446$	−21.4388	+	6.29500i	−1.01516	+	0.298077i
$447$	1.21576	−	16.9985i	0.0575034	−	0.804003i
$448$	−0.382800	+	1.75970i	−0.0180856	+	0.0831381i
$449$	−17.6416	−	27.4509i	−0.832560	−	1.29549i	−0.953062	−	0.302775i	$-0.902087\pi$
$449$	−17.6416	−	27.4509i	−0.832560	−	1.29549i	0.120503	−	0.992713i	$-0.461549\pi$
$450$	−4.74585	+	5.22614i	−0.223722	+	0.246363i
$451$	−3.03238	−	10.3273i	−0.142789	−	0.486296i
$452$	5.74875	−	4.30346i	0.270398	−	0.202418i
$453$	−21.4926	+	1.53718i	−1.00981	+	0.0722231i
$454$	−10.1635	+	22.2549i	−0.476996	+	1.04448i
$455$	−4.62296	+	6.49566i	−0.216728	+	0.304521i
$456$	−3.54853	+	1.62056i	−0.166175	+	0.0758897i
$457$	16.5967	−	22.1705i	0.776359	−	1.03709i	−0.221718	−	0.975111i	$-0.571166\pi$
$457$	16.5967	−	22.1705i	0.776359	−	1.03709i	0.998077	−	0.0619835i	$-0.0197426\pi$
$458$	−2.39456	+	0.520906i	−0.111891	+	0.0243403i
$459$	−39.4969			−1.84356
$460$	−2.53390	−	10.4201i	−0.118144	−	0.485842i
$461$	7.60961			0.354415			0.177207	−	0.984174i	$-0.443294\pi$
$461$	7.60961			0.354415			0.177207	+	0.984174i	$0.443294\pi$
$462$	3.43201	−	0.746589i	0.159672	−	0.0347345i
$463$	−11.6338	+	15.5410i	−0.540669	+	0.722249i	−0.984796	−	0.173715i	$-0.944423\pi$
$463$	−11.6338	+	15.5410i	−0.540669	+	0.722249i	0.444127	+	0.895964i	$0.353514\pi$
$464$	1.50176	−	0.685829i	0.0697173	−	0.0318388i
$465$	1.50059	+	8.90933i	0.0695883	+	0.413160i
$466$	−10.5977	+	23.2057i	−0.490927	+	1.07498i
$467$	−38.9638	+	2.78674i	−1.80303	+	0.128955i	−0.932041	−	0.362352i	$-0.881974\pi$
$467$	−38.9638	+	2.78674i	−1.80303	+	0.128955i	−0.870986	+	0.491307i	$0.836519\pi$
$468$	2.23784	−	1.67523i	0.103444	−	0.0774375i
$469$	4.81165	+	16.3870i	0.222181	+	0.756680i
$470$	−24.7803	+	9.92813i	−1.14303	+	0.457951i
$471$	0.512297	+	0.797150i	0.0236054	+	0.0367307i
$472$	1.26425	−	5.81166i	0.0581918	−	0.267503i
$473$	0.121040	−	1.69236i	0.00556543	−	0.0778149i
$474$	3.83878	−	1.12717i	0.176321	−	0.0517726i
$475$	11.1963	−	10.6869i	0.513719	−	0.490348i
$476$	8.37774	−	9.66843i	0.383993	−	0.443152i
$477$	−3.45506	+	1.28867i	−0.158196	+	0.0590042i
$478$	−10.7767	−	19.7360i	−0.492913	−	0.902703i
$479$	−0.0613405	−	0.134317i	−0.00280272	−	0.00613710i	0.908225	−	0.418481i	$-0.137437\pi$
$479$	−0.0613405	−	0.134317i	−0.00280272	−	0.00613710i	−0.911028	+	0.412344i	$0.864710\pi$
$480$	0.532562	−	2.76712i	0.0243080	−	0.126301i
$481$	−1.50986	+	2.34939i	−0.0688437	+	0.107123i
$482$	−0.586893	−	0.586893i	−0.0267323	−	0.0267323i
$483$	10.7735	+	1.54592i	0.490213	+	0.0703417i
$484$		−	8.60482i		−	0.391128i
$485$	2.96776	−	24.8770i	0.134759	−	1.12961i
$486$	1.87681	+	13.0535i	0.0851337	+	0.592118i
$487$	21.6396	+	8.07115i	0.980584	+	0.365739i	0.788091	−	0.615559i	$-0.211070\pi$
$487$	21.6396	+	8.07115i	0.980584	+	0.365739i	0.192493	+	0.981298i	$0.438343\pi$
$488$	−1.86502	+	1.01838i	−0.0844255	+	0.0460998i
$489$	8.82315	+	4.02940i	0.398996	+	0.182216i
$490$	−8.11504	−	2.17213i	−0.366600	−	0.0981266i
$491$	4.14203	−	28.8085i	0.186927	−	1.30011i	−0.652979	−	0.757376i	$-0.726481\pi$
$491$	4.14203	−	28.8085i	0.186927	−	1.30011i	0.839906	−	0.542732i	$-0.182610\pi$
$492$	4.20029	−	7.69226i	0.189364	−	0.346794i
$493$	−11.6983	−	0.836682i	−0.526867	−	0.0376823i
$494$	−5.15603	+	3.31358i	−0.231981	+	0.149085i
$495$	4.74798	−	1.15317i	0.213406	−	0.0518312i
$496$	2.09963	+	2.42310i	0.0942761	+	0.108800i
$497$	−10.2117	−	5.57602i	−0.458058	−	0.250119i
$498$	−9.03208	−	12.0654i	−0.404737	−	0.540666i
$499$	28.7063	+	24.8742i	1.28507	+	1.11352i	0.987297	+	0.158885i	$0.0507899\pi$
$499$	28.7063	+	24.8742i	1.28507	+	1.11352i	0.297775	+	0.954636i	$0.403756\pi$
$500$	1.59988	+	11.0653i	0.0715487	+	0.494854i
$501$	16.0021	+	4.69864i	0.714922	+	0.209920i
$502$	−0.395245	+	1.05969i	−0.0176407	+	0.0472965i
$503$	−25.5131	−	19.0988i	−1.13757	−	0.851575i	−0.147076	−	0.989125i	$-0.546986\pi$
$503$	−25.5131	−	19.0988i	−1.13757	−	0.851575i	−0.990495	+	0.137550i	$0.956077\pi$
$504$	−2.13898	−	1.37464i	−0.0952777	−	0.0612312i
$505$	20.4196	+	7.06126i	0.908660	+	0.314222i
$506$	−2.59185	+	6.95496i	−0.115222	+	0.309186i
$507$	8.09112	−	8.09112i	0.359339	−	0.359339i
$508$	−2.44622	−	11.2451i	−0.108533	−	0.498919i
$509$	−41.3586	+	5.94647i	−1.83319	+	0.263573i	−0.970315	−	0.241846i	$-0.922247\pi$
$509$	−41.3586	+	5.94647i	−1.83319	+	0.263573i	−0.862874	+	0.505419i	$0.831338\pi$
$510$	−12.7413	+	15.4398i	−0.564194	+	0.683684i
$511$	−7.44396	+	25.3518i	−0.329301	+	1.12150i
$512$	−0.349464	−	0.936950i	−0.0154443	−	0.0414077i
$513$	−1.22782	−	17.1672i	−0.0542097	−	0.757950i
$514$	−8.40294	−	1.20816i	−0.370638	−	0.0532897i
$515$	−12.1698	+	11.0690i	−0.536266	+	0.487756i
$516$	1.04412	−	0.904736i	0.0459649	−	0.0398288i
$517$	18.0541	+	3.92744i	0.794021	+	0.172729i
$518$	2.48211	+	0.539950i	0.109058	+	0.0237240i
$519$	−18.2742	+	15.8347i	−0.802147	+	0.695064i
$520$	0.209490	−	4.42226i	0.00918675	−	0.193929i
$521$	37.5169	+	5.39412i	1.64365	+	0.236321i	0.901143	−	0.433522i	$-0.142729\pi$
$521$	37.5169	+	5.39412i	1.64365	+	0.236321i	0.742503	+	0.669843i	$0.233638\pi$
$522$	0.166288	+	2.32502i	0.00727825	+	0.101763i
$523$	−5.99365	−	16.0696i	−0.262084	−	0.702674i	−0.999625	−	0.0273723i	$-0.991286\pi$
$523$	−5.99365	−	16.0696i	−0.262084	−	0.702674i	0.737541	−	0.675302i	$-0.235987\pi$
$524$	0.329641	−	1.12265i	0.0144004	−	0.0490434i
$525$	−11.0288	−	2.66940i	−0.481336	−	0.116502i
$526$	20.0769	−	2.88663i	0.875397	−	0.125863i
$527$	−4.84155	−	22.2562i	−0.210901	−	0.969497i
$528$	−1.37910	+	1.37910i	−0.0600175	+	0.0600175i
$529$	−15.0520	+	17.3907i	−0.654437	+	0.756117i
$530$	−1.90867	+	5.51946i	−0.0829075	+	0.239750i
$531$	7.06427	+	4.53993i	0.306563	+	0.197016i
$532$	4.46278	+	3.34079i	0.193486	+	0.144842i
$533$	4.81201	−	12.9015i	0.208431	−	0.558826i
$534$	22.8009	+	6.69496i	0.986693	+	0.289719i
$535$	26.7257	−	0.643238i	1.15545	−	0.0278096i
$536$	−7.16730	−	6.21050i	−0.309580	−	0.268253i
$537$	6.47861	+	8.65441i	0.279573	+	0.373465i
$538$	20.8107	+	11.3635i	0.897211	+	0.489914i
$539$	3.80758	+	4.39418i	0.164004	+	0.189271i
$540$	10.6174	+	6.46779i	0.456899	+	0.278329i
$541$	−6.27842	+	4.03489i	−0.269930	+	0.173474i	−0.668603	−	0.743620i	$-0.733107\pi$
$541$	−6.27842	+	4.03489i	−0.269930	+	0.173474i	0.398673	+	0.917093i	$0.369471\pi$
$542$	−19.2190	−	1.37457i	−0.825528	−	0.0590429i
$543$	−9.20895	+	16.8649i	−0.395194	+	0.723743i
$544$	−1.01099	+	7.03162i	−0.0433460	+	0.301478i
$545$	−29.7387	+	17.1801i	−1.27387	+	0.735915i
$546$	4.08726	+	1.86659i	0.174918	+	0.0798826i
$547$	−18.8244	+	10.2789i	−0.804874	+	0.439494i	−0.828337	−	0.560230i	$-0.810713\pi$
$547$	−18.8244	+	10.2789i	−0.804874	+	0.439494i	0.0234631	+	0.999725i	$0.492531\pi$
$548$	−1.39236	−	0.519322i	−0.0594785	−	0.0221843i
$549$	−0.426971	−	2.96965i	−0.0182227	−	0.126741i
$550$	3.37749	−	6.96219i	0.144017	−	0.296869i
$551$		−	5.11065i		−	0.217721i
$552$	−5.49686	+	2.51219i	−0.233962	+	0.106926i
$553$	−4.04274	−	4.04274i	−0.171915	−	0.171915i
$554$	−5.55344	+	8.64132i	−0.235943	+	0.367134i
$555$	−3.90310	−	0.751194i	−0.165677	−	0.0318864i
$556$	−4.67137	−	10.2289i	−0.198110	−	0.433801i
$557$	7.10247	+	13.0072i	0.300941	+	0.551133i	0.983767	−	0.179448i	$-0.0574312\pi$
$557$	7.10247	+	13.0072i	0.300941	+	0.551133i	−0.682826	+	0.730581i	$0.739249\pi$
$558$	−4.24141	+	1.58196i	−0.179553	+	0.0669699i
$559$	1.42144	−	1.64042i	0.0601203	−	0.0693826i
$560$	−3.83531	+	1.22713i	−0.162071	+	0.0518557i
$561$	13.2938	−	3.90342i	0.561266	−	0.164803i
$562$	1.65545	−	23.1461i	0.0698307	−	0.976361i
$563$	0.287612	−	1.32213i	0.0121214	−	0.0557213i	−0.970689	−	0.240339i	$-0.922741\pi$
$563$	0.287612	−	1.32213i	0.0121214	−	0.0557213i	0.982810	+	0.184618i	$0.0591049\pi$
$564$	8.13387	+	12.6566i	0.342498	+	0.532937i
$565$	14.7626	+	6.31710i	0.621066	+	0.265762i
$566$	7.58297	+	25.8252i	0.318736	+	1.08552i
$567$	−3.99471	+	2.99041i	−0.167762	+	0.125585i
$568$	6.44430	−	0.460905i	0.270397	−	0.0193392i
$569$	12.1243	−	26.5484i	0.508275	−	1.11297i	−0.465415	−	0.885093i	$-0.654095\pi$
$569$	12.1243	−	26.5484i	0.508275	−	1.11297i	0.973690	−	0.227875i	$-0.0731778\pi$
$570$	−7.10691	−	5.05799i	−0.297676	−	0.211856i
$571$	−27.0759	+	12.3652i	−1.13309	+	0.517466i	−0.891549	−	0.452924i	$-0.850381\pi$
$571$	−27.0759	+	12.3652i	−1.13309	+	0.517466i	−0.241543	+	0.970390i	$0.577653\pi$
$572$	−1.83630	+	2.45301i	−0.0767795	+	0.102565i
$573$	9.89185	−	2.15184i	0.413238	−	0.0898944i
$574$	−12.5244			−0.522759
$575$	17.3412	−	16.5615i	0.723177	−	0.690663i
$576$	1.41189			0.0588286
$577$	21.1854	−	4.60860i	0.881959	−	0.191858i	0.251291	−	0.967912i	$-0.419145\pi$
$577$	21.1854	−	4.60860i	0.881959	−	0.191858i	0.630667	+	0.776053i	$0.282781\pi$
$578$	20.0553	−	26.7907i	0.834190	−	1.11435i
$579$	−3.85710	+	1.76148i	−0.160295	+	0.0732045i
$580$	3.00768	+	2.14057i	0.124887	+	0.0888822i
$581$	−8.94707	+	19.5913i	−0.371187	+	0.812786i
$582$	−14.0836	+	1.00728i	−0.583784	+	0.0417531i
$583$	3.23588	−	2.42235i	0.134016	−	0.100323i
$584$	−4.13356	−	14.0776i	−0.171048	−	0.582536i
$585$	5.74670	+	2.45909i	0.237597	+	0.101671i
$586$	12.1666	+	18.9317i	0.502600	+	0.782060i
$587$	−4.64510	+	21.3532i	−0.191724	+	0.881339i	0.776277	+	0.630392i	$0.217106\pi$
$587$	−4.64510	+	21.3532i	−0.191724	+	0.881339i	−0.968001	+	0.250947i	$0.919258\pi$
$588$	−0.337753	+	4.72241i	−0.0139287	+	0.194749i
$589$	9.52308	−	2.79623i	0.392392	−	0.115217i
$590$	12.6666	−	4.05276i	0.521477	−	0.166850i
$591$	6.14356	−	7.09005i	0.252712	−	0.291646i
$592$	−1.32159	+	0.492929i	−0.0543172	+	0.0202593i
$593$	11.6744	+	21.3800i	0.479410	+	0.877973i	0.999712	+	0.0239911i	$0.00763735\pi$
$593$	11.6744	+	21.3800i	0.479410	+	0.877973i	−0.520303	+	0.853982i	$0.674181\pi$
$594$	−3.57451	−	7.82708i	−0.146664	−	0.321149i
$595$	28.0908	+	5.40639i	1.15161	+	0.221640i
$596$	7.31118	−	11.3764i	0.299478	−	0.465996i
$597$	2.62772	+	2.62772i	0.107545	+	0.107545i
$598$	−7.98654	+	5.13580i	−0.326594	+	0.210019i
$599$		−	7.05450i		−	0.288239i	−0.989560	−	0.144120i	$-0.953965\pi$
$599$		−	7.05450i		−	0.288239i	0.989560	−	0.144120i	$-0.0460350\pi$
$600$	5.95338	−	2.06400i	0.243046	−	0.0842624i
$601$	−3.05396	−	21.2408i	−0.124574	−	0.866429i	−0.952271	−	0.305254i	$-0.901259\pi$
$601$	−3.05396	−	21.2408i	−0.124574	−	0.866429i	0.827697	−	0.561175i	$-0.189651\pi$
$602$	−1.84981	−	0.689945i	−0.0753928	−	0.0281200i
$603$	11.7520	−	6.41710i	0.478580	−	0.261325i
$604$	−15.5533	−	7.10295i	−0.632854	−	0.289015i
$605$	16.6606	−	9.62487i	0.677351	−	0.391307i
$606$	1.73293	−	12.0528i	0.0703955	−	0.489611i
$607$	−1.70979	+	3.13124i	−0.0693982	+	0.127093i	−0.910075	−	0.414445i	$-0.863976\pi$
$607$	−1.70979	+	3.13124i	−0.0693982	+	0.127093i	0.840676	+	0.541538i	$0.182158\pi$
$608$	−3.08769	−	0.220836i	−0.125223	−	0.00895609i
$609$	−3.15196	+	2.02564i	−0.127724	+	0.0820832i
$610$	−4.05789	−	2.47195i	−0.164299	−	0.100086i
$611$	15.4790	+	17.8637i	0.626213	+	0.722689i
$612$	−8.80307	−	4.80684i	−0.355843	−	0.194305i
$613$	−11.0584	−	14.7723i	−0.446646	−	0.596649i	0.519556	−	0.854437i	$-0.326097\pi$
$613$	−11.0584	−	14.7723i	−0.446646	−	0.596649i	−0.966202	+	0.257787i	$0.917007\pi$
$614$	9.45706	+	8.19459i	0.381656	+	0.330707i
$615$	19.5919	−	0.471542i	0.790024	−	0.0190144i
$616$	2.67418	+	0.785210i	0.107746	+	0.0316370i
$617$	−12.3966	+	33.2367i	−0.499070	+	1.33806i	0.406418	+	0.913687i	$0.366778\pi$
$617$	−12.3966	+	33.2367i	−0.499070	+	1.33806i	−0.905488	+	0.424371i	$0.860495\pi$
$618$	7.42205	+	5.55608i	0.298559	+	0.223498i
$619$	−29.5824	−	19.0115i	−1.18902	−	0.764135i	−0.211995	−	0.977271i	$-0.567996\pi$
$619$	−29.5824	−	19.0115i	−1.18902	−	0.764135i	−0.977023	+	0.213136i	$0.931632\pi$
$620$	−2.34307	+	6.77564i	−0.0941001	+	0.272116i
$621$	−1.90966	−	26.5958i	−0.0766321	−	1.06725i
$622$	−22.1310	+	22.1310i	−0.887371	+	0.887371i
$623$	−7.21842	−	33.1825i	−0.289200	−	1.32943i
$624$	−2.46970	+	0.355089i	−0.0988670	+	0.0142149i
$625$	−19.6350	+	15.4747i	−0.785401	+	0.618987i
$626$	6.92409	−	23.5813i	0.276742	−	0.942497i
$627$	2.10986	+	5.65677i	0.0842599	+	0.225910i
$628$	0.0536415	+	0.750006i	0.00214053	+	0.0299285i
$629$	9.91830	+	1.42604i	0.395468	+	0.0568598i
$630$	0.269028	−	5.67908i	0.0107183	−	0.226260i
$631$	13.1181	−	11.3669i	0.522223	−	0.452509i	−0.353422	−	0.935464i	$-0.614982\pi$
$631$	13.1181	−	11.3669i	0.522223	−	0.452509i	0.875645	+	0.482955i	$0.160437\pi$
$632$	3.10221	+	0.674844i	0.123399	+	0.0268439i
$633$	−3.11391	−	0.677389i	−0.123767	−	0.0269238i
$634$	21.4398	−	18.5777i	0.851483	−	0.737814i
$635$	19.0365	−	17.3145i	0.755439	−	0.687104i
$636$	3.25790	+	0.468415i	0.129184	+	0.0185738i
$637$	0.530646	+	7.41941i	0.0210250	+	0.293968i
$638$	−0.892906	−	2.39397i	−0.0353505	−	0.0947783i
$639$	−2.56993	+	8.75237i	−0.101665	+	0.346238i
$640$	1.42323	−	1.72465i	0.0562580	−	0.0681728i
$641$	−1.40406	+	0.201873i	−0.0554570	+	0.00797351i	−0.169987	−	0.985446i	$-0.554373\pi$
$641$	−1.40406	+	0.201873i	−0.0554570	+	0.00797351i	0.114530	+	0.993420i	$0.463464\pi$
$642$	−3.20260	−	14.7221i	−0.126397	−	0.581036i
$643$	26.7122	−	26.7122i	1.05343	−	1.05343i	0.0549368	−	0.998490i	$-0.482504\pi$
$643$	26.7122	−	26.7122i	1.05343	−	1.05343i	0.998490	−	0.0549368i	$-0.0174957\pi$
$644$	6.91541	+	5.17379i	0.272505	+	0.203876i
$645$	2.91964	+	1.00964i	0.114961	+	0.0397544i
$646$	18.4998	+	11.8891i	0.727866	+	0.467771i
$647$	−12.4323	−	9.30671i	−0.488765	−	0.365885i	0.326289	−	0.945270i	$-0.394202\pi$
$647$	−12.4323	−	9.30671i	−0.488765	−	0.365885i	−0.815054	+	0.579385i	$0.803293\pi$
$648$	0.968334	−	2.59620i	0.0380398	−	0.101989i
$649$	−8.83184	−	2.59326i	−0.346680	−	0.101794i
$650$	8.79669	−	4.54088i	0.345035	−	0.178108i
$651$	−5.49910	−	4.76500i	−0.215527	−	0.186755i
$652$	4.61259	+	6.16170i	0.180643	+	0.241311i
$653$	−12.5316	−	6.84276i	−0.490398	−	0.267778i	0.214967	−	0.976621i	$-0.431035\pi$
$653$	−12.5316	−	6.84276i	−0.490398	−	0.267778i	−0.705366	+	0.708843i	$0.749217\pi$
$654$	12.6754	+	14.6282i	0.495648	+	0.572008i
$655$	2.54240	−	0.617489i	0.0993397	−	0.0241273i
$656$	5.85066	−	3.75999i	0.228430	−	0.146803i
$657$	20.6624	+	1.47780i	0.806115	+	0.0576545i
$658$	10.3036	−	18.8696i	0.401676	−	0.735614i
$659$	−2.27007	+	15.7887i	−0.0884292	+	0.615039i	0.896625	+	0.442792i	$0.146012\pi$
$659$	−2.27007	+	15.7887i	−0.0884292	+	0.615039i	−0.985054	+	0.172247i	$0.944897\pi$
$660$	−4.21278	−	1.12762i	−0.163982	−	0.0438926i
$661$	−24.3237	−	11.1083i	−0.946083	−	0.432062i	−0.118217	−	0.992988i	$-0.537718\pi$
$661$	−24.3237	−	11.1083i	−0.946083	−	0.432062i	−0.827866	+	0.560926i	$0.810445\pi$
$662$	5.80340	−	3.16890i	0.225556	−	0.123163i
$663$	16.6074	+	6.19424i	0.644978	+	0.240564i
$664$	−1.70204	−	11.8379i	−0.0660519	−	0.459401i
$665$	−1.47662	+	12.3776i	−0.0572609	+	0.479984i
$666$		−	1.99151i		−	0.0771693i
$667$	−0.00221992	−	7.91768i	−8.59557e−5	−	0.306574i
$668$	9.35793	+	9.35793i	0.362069	+	0.362069i
$669$	−15.2233	+	23.6879i	−0.588566	+	0.915826i
$670$	4.00781	−	20.8240i	0.154835	−	0.804502i
$671$	1.36615	+	2.99146i	0.0527397	+	0.115484i
$672$	1.08763	+	1.99185i	0.0419562	+	0.0768371i
$673$	−9.12761	+	3.40442i	−0.351843	+	0.131231i	−0.519171	−	0.854671i	$-0.673759\pi$
$673$	−9.12761	+	3.40442i	−0.351843	+	0.131231i	0.167327	+	0.985901i	$0.446486\pi$
$674$	3.80885	−	4.39565i	0.146712	−	0.169314i
$675$	−0.646912	+	27.7918i	−0.0248997	+	1.06971i
$676$	8.71214	−	2.55812i	0.335082	−	0.0983891i
$677$	2.81124	−	39.3063i	0.108045	−	1.51066i	−0.597426	−	0.801924i	$-0.703810\pi$
$677$	2.81124	−	39.3063i	0.108045	−	1.51066i	0.705471	−	0.708739i	$-0.250736\pi$
$678$	1.92363	−	8.84280i	0.0738767	−	0.339606i
$679$	10.9086	+	16.9741i	0.418634	+	0.651408i
$680$	−14.7454	+	5.90769i	−0.565462	+	0.226550i
$681$	8.68637	+	29.5831i	0.332862	+	1.13363i
$682$	3.97234	−	2.97366i	0.152109	−	0.113867i
$683$	−30.7863	+	2.20188i	−1.17801	+	0.0842527i	−0.646576	−	0.762849i	$-0.723800\pi$
$683$	−30.7863	+	2.20188i	−1.17801	+	0.0842527i	−0.531430	+	0.847102i	$0.678345\pi$
$684$	1.81562	−	3.97565i	0.0694219	−	0.152013i
$685$	−0.551903	−	3.27676i	−0.0210871	−	0.125199i
$686$	17.6211	−	8.04728i	0.672776	−	0.307247i
$687$	−1.85070	+	2.47224i	−0.0706085	+	0.0943219i
$688$	1.07125	−	0.233037i	0.0408411	−	0.00888445i
$689$	5.17113			0.197004
$690$	−11.0126	−	7.83300i	−0.419242	−	0.298197i
$691$	13.7887			0.524548			0.262274	−	0.964993i	$-0.415528\pi$
$691$	13.7887			0.524548			0.262274	+	0.964993i	$0.415528\pi$
$692$	−18.7490	+	4.07860i	−0.712731	+	0.155045i
$693$	−2.35818	+	3.15016i	−0.0895798	+	0.119665i
$694$	−18.5121	+	8.45419i	−0.702710	+	0.320917i
$695$	14.5800	−	20.4861i	0.553050	−	0.777084i
$696$	0.864285	−	1.89252i	0.0327606	−	0.0717358i
$697$	−49.2797	+	3.52456i	−1.86660	+	0.133502i
$698$	2.84855	−	2.13240i	0.107819	−	0.0807126i
$699$	9.05745	+	30.8468i	0.342584	+	1.16673i
$700$	−6.66593	−	6.05332i	−0.251948	−	0.228794i
$701$	−19.6326	−	30.5490i	−0.741514	−	1.15382i	−0.983034	−	0.183423i	$-0.941282\pi$
$701$	−19.6326	−	30.5490i	−0.741514	−	1.15382i	0.241520	−	0.970396i	$-0.422354\pi$
$702$	2.33993	−	10.7565i	0.0883151	−	0.405978i
$703$	−0.311496	+	4.35528i	−0.0117483	+	0.164262i
$704$	−1.48495	+	0.436020i	−0.0559660	+	0.0164331i
$705$	−15.4075	+	29.9057i	−0.580279	+	1.12631i
$706$	6.16680	−	7.11687i	0.232091	−	0.267847i
$707$	−16.3037	+	6.08096i	−0.613164	+	0.228698i
$708$	−3.59205	−	6.57834i	−0.134997	−	0.247229i
$709$	−0.0431597	−	0.0945066i	−0.00162090	−	0.00354927i	0.908820	−	0.417189i	$-0.136985\pi$
$709$	−0.0431597	−	0.0945066i	−0.00162090	−	0.00354927i	−0.910441	+	0.413640i	$0.864257\pi$
$710$	8.10064	+	11.9619i	0.304011	+	0.448922i
$711$	−2.42337	+	3.77084i	−0.0908836	+	0.141418i
$712$	13.3338	+	13.3338i	0.499707	+	0.499707i
$713$	14.7524	−	4.33620i	0.552483	−	0.162392i
$714$		−	16.1220i		−	0.603350i
$715$	−6.80349	−	0.811638i	−0.254436	−	0.0303535i
$716$	1.22085	+	8.49122i	0.0456254	+	0.317332i
$717$	−26.5509	−	9.90299i	−0.991563	−	0.369834i
$718$	−19.9421	+	10.8892i	−0.744231	+	0.406381i
$719$	−25.5689	−	11.6769i	−0.953560	−	0.435476i	−0.123001	−	0.992407i	$-0.539252\pi$
$719$	−25.5689	−	11.6769i	−0.953560	−	0.435476i	−0.830559	+	0.556930i	$0.811979\pi$
$720$	1.57926	+	2.73369i	0.0588555	+	0.101879i
$721$	1.88551	−	13.1140i	0.0702202	−	0.488392i
$722$	4.51327	−	8.26544i	0.167966	−	0.307608i
$723$	−1.04329	−	0.0746179i	−0.0388005	−	0.00277507i
$724$	−12.8273	+	8.24360i	−0.476723	+	0.306371i
$725$	−0.780332	+	8.21778i	−0.0289808	+	0.305201i
$726$	−7.10119	−	8.19521i	−0.263550	−	0.304153i
$727$	11.3695	+	6.20823i	0.421672	+	0.230251i	0.676052	−	0.736854i	$-0.263689\pi$
$727$	11.3695	+	6.20823i	0.421672	+	0.230251i	−0.254380	+	0.967104i	$0.581871\pi$
$728$	2.13675	+	2.85436i	0.0791932	+	0.105790i
$729$	18.8423	+	16.3269i	0.697863	+	0.604702i
$730$	22.6335	−	23.7498i	0.837703	−	0.879021i
$731$	−7.47261	−	2.19416i	−0.276385	−	0.0811538i
$732$	−0.935817	+	2.50902i	−0.0345888	+	0.0927362i
$733$	−3.74191	−	2.80116i	−0.138210	−	0.103463i	0.527935	−	0.849285i	$-0.322966\pi$
$733$	−3.74191	−	2.80116i	−0.138210	−	0.103463i	−0.666146	+	0.745821i	$0.732057\pi$
$734$	−7.60131	−	4.88507i	−0.280570	−	0.180311i
$735$	−9.52131	+	4.62827i	−0.351199	+	0.170716i
$736$	−4.78371	−	0.340789i	−0.176330	−	0.0125617i
$737$	−10.3784	+	10.3784i	−0.382295	+	0.382295i
$738$	2.08723	+	9.59484i	0.0768320	+	0.353191i
$739$	30.5018	−	4.38550i	1.12203	−	0.161323i	0.443766	−	0.896143i	$-0.353642\pi$
$739$	30.5018	−	4.38550i	1.12203	−	0.161323i	0.678263	+	0.734820i	$0.262733\pi$
$740$	−2.43267	−	2.00750i	−0.0894267	−	0.0737973i
$741$	−2.17604	+	7.41090i	−0.0799386	+	0.272246i
$742$	−1.64370	−	4.40692i	−0.0603420	−	0.161783i
$743$	1.49118	+	20.8494i	0.0547060	+	0.764889i	0.948573	+	0.316558i	$0.102527\pi$
$743$	1.49118	+	20.8494i	0.0547060	+	0.764889i	−0.893867	+	0.448332i	$0.852018\pi$
$744$	3.99937	+	0.575022i	0.146624	+	0.0210813i
$745$	30.2049	+	1.43086i	1.10662	+	0.0524225i
$746$	−8.65140	+	7.49648i	−0.316750	+	0.274466i
$747$	16.4998	+	3.58931i	0.603697	+	0.131326i
$748$	10.7430	+	2.33701i	0.392805	+	0.0854494i
$749$	−16.2715	+	14.0993i	−0.594547	+	0.515178i
$750$	10.6554	+	9.21824i	0.389081	+	0.336603i
$751$	−29.4548	−	4.23497i	−1.07482	−	0.154536i	−0.417899	−	0.908494i	$-0.637233\pi$
$751$	−29.4548	−	4.23497i	−1.07482	−	0.154536i	−0.656923	+	0.753957i	$0.728142\pi$
$752$	0.851679	+	11.9080i	0.0310576	+	0.434241i
$753$	0.498090	+	1.33543i	0.0181514	+	0.0486658i
$754$	0.920910	−	3.13633i	0.0335376	−	0.114218i
$755$	−3.64433	−	38.0592i	−0.132631	−	1.38512i
$756$	−9.91063	+	1.42493i	−0.360446	+	0.0518243i
$757$	−0.446616	−	2.05306i	−0.0162325	−	0.0746198i	0.968318	−	0.249720i	$-0.0803386\pi$
$757$	−0.446616	−	2.05306i	−0.0162325	−	0.0746198i	−0.984551	+	0.175100i	$0.943975\pi$
$758$	10.4495	−	10.4495i	0.379543	−	0.379543i
$759$	3.27117	+	8.76283i	0.118736	+	0.318071i
$760$	−3.02614	−	6.22540i	−0.109770	−	0.225819i
$761$	27.9691	+	17.9746i	1.01388	+	0.651580i	0.938394	−	0.345567i	$-0.112313\pi$
$761$	27.9691	+	17.9746i	1.01388	+	0.651580i	0.0754846	+	0.997147i	$0.475950\pi$
$762$	−11.6099	−	8.69103i	−0.420581	−	0.314843i
$763$	9.66618	−	25.9160i	0.349939	−	0.938223i
$764$	7.70759	+	2.26315i	0.278851	+	0.0818780i
$765$	−0.539635	−	22.4211i	−0.0195106	−	0.810638i
$766$	16.3689	+	14.1838i	0.591434	+	0.512480i
$767$	−7.05691	−	9.42693i	−0.254810	−	0.340387i
$768$	−1.10605	−	0.603951i	−0.0399113	−	0.0217932i
$769$	6.65520	+	7.68051i	0.239993	+	0.276966i	0.862950	−	0.505290i	$-0.168614\pi$
$769$	6.65520	+	7.68051i	0.239993	+	0.276966i	−0.622957	+	0.782256i	$0.714069\pi$
$770$	1.47087	+	6.05603i	0.0530064	+	0.218244i
$771$	−8.99999	+	5.78394i	−0.324127	+	0.208304i
$772$	−3.35619	−	0.240039i	−0.120792	−	0.00863920i
$773$	−7.57154	+	13.8662i	−0.272329	+	0.498734i	−0.977673	−	0.210132i	$-0.932611\pi$
$773$	−7.57154	+	13.8662i	−0.272329	+	0.498734i	0.705344	+	0.708865i	$0.250793\pi$
$774$	−0.220284	+	1.53211i	−0.00791794	+	0.0550705i
$775$	−15.7398	+	3.04221i	−0.565391	+	0.109279i
$776$	−10.1917	−	4.65440i	−0.365861	−	0.167083i
$777$	2.80955	−	1.53413i	0.100792	−	0.0550367i
$778$	31.4572	+	11.7329i	1.12780	+	0.420646i
$779$	−3.06387	−	21.3097i	−0.109774	−	0.763498i
$780$	−3.44999	−	4.38464i	−0.123529	−	0.156995i
$781$		−	9.99891i		−	0.357789i
$782$	28.6660	+	18.4112i	1.02510	+	0.658383i
$783$	6.49059	+	6.49059i	0.231955	+	0.231955i
$784$	−2.03114	+	3.16052i	−0.0725407	+	0.112876i
$785$	−1.39216	+	0.942775i	−0.0496883	+	0.0336491i
$786$	−0.612529	−	1.34125i	−0.0218482	−	0.0478409i
$787$	−0.470582	−	0.861807i	−0.0167745	−	0.0307201i	0.869157	−	0.494536i	$-0.164662\pi$
$787$	−0.470582	−	0.861807i	−0.0167745	−	0.0307201i	−0.885932	+	0.463816i	$0.846480\pi$
$788$	6.97505	−	2.60156i	0.248476	−	0.0926767i
$789$	16.7390	−	19.3179i	0.595925	−	0.687735i
$790$	2.16333	+	6.76133i	0.0769677	+	0.240557i
$791$	−12.4083	+	3.64339i	−0.441187	+	0.129544i
$792$	0.155883	−	2.17952i	0.00553904	−	0.0774460i
$793$	−0.894306	+	4.11106i	−0.0317577	+	0.145988i
$794$	10.0184	+	15.5890i	0.355541	+	0.553232i
$795$	2.73716	+	6.83187i	0.0970770	+	0.242301i
$796$	0.830788	+	2.82940i	0.0294465	+	0.100286i
$797$	40.4317	−	30.2668i	1.43216	−	1.07211i	0.448162	−	0.893952i	$-0.352079\pi$
$797$	40.4317	−	30.2668i	1.43216	−	1.07211i	0.984003	−	0.178153i	$-0.0570120\pi$
$798$	7.00736	−	0.501176i	0.248058	−	0.0177414i
$799$	35.2313	−	77.1458i	1.24639	−	2.72922i
$800$	4.93121	+	0.826551i	0.174345	+	0.0292230i
$801$	−24.2179	+	11.0599i	−0.855697	+	0.390784i
$802$	6.57224	−	8.77949i	0.232074	−	0.310014i
$803$	−22.1879	+	4.82669i	−0.782995	+	0.170330i
$804$	−11.9514			−0.421493
$805$	−2.28228	+	19.1767i	−0.0804397	+	0.675890i
$806$	6.34804			0.223600
$807$	29.1978	−	6.35160i	1.02781	−	0.223587i
$808$	5.79053	−	7.73524i	0.203710	−	0.272125i
$809$	−32.1604	+	14.6872i	−1.13070	+	0.516373i	−0.890787	−	0.454422i	$-0.849846\pi$
$809$	−32.1604	+	14.6872i	−1.13070	+	0.516373i	−0.239912	+	0.970795i	$0.577119\pi$
$810$	6.10989	−	1.02908i	0.214680	−	0.0361583i
$811$	−2.76469	+	6.05382i	−0.0970813	+	0.212578i	−0.951941	−	0.306280i	$-0.900916\pi$
$811$	−2.76469	+	6.05382i	−0.0970813	+	0.212578i	0.854860	+	0.518859i	$0.173643\pi$
$812$	−2.96555	+	0.212100i	−0.104070	+	0.00744326i
$813$	−19.4385	+	14.5515i	−0.681739	+	0.510344i
$814$	0.615018	+	2.09456i	0.0215564	+	0.0734143i
$815$	−6.77088	+	15.8230i	−0.237174	+	0.554257i
$816$	4.84003	+	7.53123i	0.169435	+	0.263646i
$817$	0.721384	−	3.31615i	0.0252380	−	0.116017i
$818$	−0.784427	+	10.9677i	−0.0274269	+	0.383478i
$819$	−4.83022	+	1.41828i	−0.168782	+	0.0495588i
$820$	13.8243	+	7.12231i	0.482765	+	0.248722i
$821$	−4.70385	+	5.42853i	−0.164166	+	0.189457i	−0.831872	−	0.554968i	$-0.812731\pi$
$821$	−4.70385	+	5.42853i	−0.164166	+	0.189457i	0.667706	+	0.744425i	$0.267276\pi$
$822$	−1.75465	+	0.654452i	−0.0612005	+	0.0228266i
$823$	7.90673	+	14.4801i	0.275611	+	0.504744i	0.978418	−	0.206637i	$-0.0662518\pi$
$823$	7.90673	+	14.4801i	0.275611	+	0.504744i	−0.702806	+	0.711381i	$0.748070\pi$
$824$	3.05620	+	6.69215i	0.106468	+	0.233132i
$825$	−2.52889	−	9.41808i	−0.0880446	−	0.327895i
$826$	−5.79067	+	9.01045i	−0.201483	+	0.313514i
$827$	38.1482	+	38.1482i	1.32654	+	1.32654i	0.908365	+	0.418178i	$0.137331\pi$
$827$	38.1482	+	38.1482i	1.32654	+	1.32654i	0.418178	+	0.908365i	$0.362669\pi$
$828$	2.81112	−	6.16007i	0.0976932	−	0.214077i
$829$		−	13.6934i		−	0.475593i	−0.971315	−	0.237797i	$-0.923575\pi$
$829$		−	13.6934i		−	0.475593i	0.971315	−	0.237797i	$-0.0764252\pi$
$830$	21.0168	−	16.5367i	0.729503	−	0.573998i
$831$	1.84223	+	12.8130i	0.0639063	+	0.444478i
$832$	−1.85508	−	0.691909i	−0.0643133	−	0.0239876i
$833$	23.4242	−	12.7906i	0.811601	−	0.443168i
$834$	−12.8905	−	5.88688i	−0.446360	−	0.203846i
$835$	−7.65154	+	28.5861i	−0.264792	+	0.989262i
$836$	−0.681807	+	4.74207i	−0.0235808	+	0.164008i
$837$	−8.54319	+	15.6457i	−0.295296	+	0.540794i
$838$	−36.1921	−	2.58851i	−1.25024	−	0.0894186i
$839$	33.1961	−	21.3338i	1.14606	−	0.736525i	0.177206	−	0.984174i	$-0.443294\pi$
$839$	33.1961	−	21.3338i	1.14606	−	0.736525i	0.968850	+	0.247648i	$0.0796578\pi$
$840$	−2.64004	+	4.33383i	−0.0910902	+	0.149531i
$841$	−17.2060	−	19.8568i	−0.593312	−	0.684719i
$842$	−10.5814	−	5.77788i	−0.364659	−	0.199119i
$843$	−17.5249	−	23.4105i	−0.603589	−	0.806301i
$844$	−1.91110	−	1.65598i	−0.0657827	−	0.0570011i
$845$	14.6979	+	14.0071i	0.505624	+	0.481857i
$846$	−16.1730	−	4.74881i	−0.556038	−	0.163268i
$847$	−5.41532	+	14.5190i	−0.186072	+	0.498880i
$848$	2.09085	+	1.56519i	0.0718002	+	0.0537489i
$849$	28.5345	+	18.3380i	0.979301	+	0.629359i
$850$	−27.9319	−	21.9421i	−0.958056	−	0.752606i
$851$	−0.480693	+	6.74755i	−0.0164779	+	0.231303i
$852$	5.75717	−	5.75717i	0.197237	−	0.197237i
$853$	4.81737	+	22.1451i	0.164944	+	0.758234i	0.983075	+	0.183203i	$0.0586465\pi$
$853$	4.81737	+	22.1451i	0.164944	+	0.758234i	−0.818131	+	0.575031i	$0.804990\pi$
$854$	3.78777	−	0.544600i	0.129615	−	0.0186358i
$855$	9.72849	−	0.931545i	0.332707	−	0.0318582i
$856$	3.36827	−	11.4713i	0.115125	−	0.392080i
$857$	−11.9991	−	32.1708i	−0.409881	−	1.09893i	−0.963862	−	0.266404i	$-0.914165\pi$
$857$	−11.9991	−	32.1708i	−0.409881	−	1.09893i	0.553981	−	0.832530i	$-0.313108\pi$
$858$	0.275476	+	3.85166i	0.00940460	+	0.131494i
$859$	−38.6395	−	5.55552i	−1.31836	−	0.189552i	−0.553016	−	0.833171i	$-0.686523\pi$
$859$	−38.6395	−	5.55552i	−1.31836	−	0.189552i	−0.765346	+	0.643619i	$0.777432\pi$
$860$	1.64945	+	1.81349i	0.0562457	+	0.0618397i
$861$	−11.9282	+	10.3359i	−0.406513	+	0.352245i
$862$	5.96965	+	1.29862i	0.203327	+	0.0442311i
$863$	2.05863	+	0.447827i	0.0700765	+	0.0152442i	0.247467	−	0.968896i	$-0.420402\pi$
$863$	2.05863	+	0.447827i	0.0700765	+	0.0152442i	−0.177390	+	0.984141i	$0.556766\pi$
$864$	4.20187	−	3.64094i	0.142951	−	0.123867i
$865$	−28.8686	−	31.7397i	−0.981562	−	1.07918i
$866$	−14.6866	−	2.11161i	−0.499071	−	0.0717555i
$867$	−3.00864	−	42.0662i	−0.102179	−	1.42864i
$868$	−2.01779	−	5.40990i	−0.0684882	−	0.183624i
$869$	1.38426	−	4.71436i	0.0469578	−	0.159924i
$870$	4.63103	−	0.443441i	0.157007	−	0.0150341i
$871$	−18.5858	+	2.67223i	−0.629755	+	0.0905451i
$872$	3.26486	+	15.0083i	0.110562	+	0.508246i
$873$	11.1858	−	11.1858i	0.378581	−	0.378581i
$874$	−7.11122	+	13.0319i	−0.240541	+	0.440811i
$875$	4.26428	−	19.6774i	0.144159	−	0.665219i
$876$	−15.5545	−	9.99625i	−0.525537	−	0.337742i
$877$	23.1822	+	17.3540i	0.782808	+	0.586003i	0.914170	−	0.405332i	$-0.132844\pi$
$877$	23.1822	+	17.3540i	0.782808	+	0.586003i	−0.131361	+	0.991335i	$0.541935\pi$
$878$	−8.95976	+	24.0220i	−0.302377	+	0.810704i
$879$	27.2110	+	7.98987i	0.917804	+	0.269492i
$880$	−2.50520	−	2.38744i	−0.0844503	−	0.0804807i
$881$	26.7636	+	23.1908i	0.901689	+	0.781318i	0.976419	−	0.215885i	$-0.0692638\pi$
$881$	26.7636	+	23.1908i	0.901689	+	0.781318i	−0.0747292	+	0.997204i	$0.523809\pi$
$882$	−3.17877	−	4.24634i	−0.107035	−	0.142982i
$883$	4.55404	+	2.48669i	0.153256	+	0.0836839i	0.554047	−	0.832486i	$-0.313083\pi$
$883$	4.55404	+	2.48669i	0.153256	+	0.0836839i	−0.400791	+	0.916169i	$0.631265\pi$
$884$	9.21072	+	10.6297i	0.309790	+	0.357517i
$885$	8.71911	−	14.3131i	0.293090	−	0.481129i
$886$	9.53020	−	6.12469i	0.320173	−	0.205763i
$887$	−33.4738	−	2.39409i	−1.12394	−	0.0803857i	−0.503030	−	0.864269i	$-0.667782\pi$
$887$	−33.4738	−	2.39409i	−1.12394	−	0.0803857i	−0.620908	+	0.783883i	$0.713236\pi$
$888$	−0.851890	+	1.56012i	−0.0285876	+	0.0523542i
$889$	−2.94939	+	20.5134i	−0.0989193	+	0.687999i
$890$	−10.9025	+	40.7315i	−0.365451	+	1.36532i
$891$	−3.90083	−	1.78145i	−0.130683	−	0.0596809i
$892$	−19.6108	+	10.7083i	−0.656617	+	0.358540i
$893$	34.6263	+	12.9150i	1.15873	+	0.432182i
$894$	−2.42532	−	16.8685i	−0.0811149	−	0.564167i
$895$	−15.0751	+	11.8616i	−0.503905	+	0.396490i
$896$			1.80086i			0.0601624i
$897$	−3.36801	+	11.4823i	−0.112454	+	0.383382i
$898$	−23.0736	−	23.0736i	−0.769975	−	0.769975i
$899$	−2.86178	+	4.45302i	−0.0954457	+	0.148516i
$900$	−3.52650	+	6.11551i	−0.117550	+	0.203850i
$901$	−7.70762	−	16.8773i	−0.256778	−	0.562266i
$902$	−5.15832	−	9.44675i	−0.171753	−	0.314542i
$903$	−2.33114	+	0.869471i	−0.0775755	+	0.0289342i
$904$	4.70260	−	5.42709i	0.156406	−	0.180502i
$905$	−30.3091	−	15.6153i	−1.00751	−	0.519071i
$906$	−20.6747	+	6.07064i	−0.686870	+	0.201683i
$907$	0.450987	−	6.30563i	0.0149748	−	0.209375i	−0.984456	−	0.175633i	$-0.943803\pi$
$907$	0.450987	−	6.30563i	0.0149748	−	0.209375i	0.999431	−	0.0337423i	$-0.0107425\pi$
$908$	−5.20060	+	23.9068i	−0.172588	+	0.793373i
$909$	7.37563	+	11.4767i	0.244634	+	0.380658i
$910$	−3.13656	+	7.32990i	−0.103976	+	0.242984i
$911$	6.80444	+	23.1738i	0.225441	+	0.767782i	0.992069	+	0.125691i	$0.0401148\pi$
$911$	6.80444	+	23.1738i	0.225441	+	0.767782i	−0.766628	+	0.642091i	$0.778067\pi$
$912$	−3.12296	+	2.33782i	−0.103412	+	0.0774129i
$913$	−18.4621	+	1.32043i	−0.611005	+	0.0437000i
$914$	11.5047	−	25.1918i	0.380541	−	0.833269i
$915$	−5.90472	+	0.994527i	−0.195204	+	0.0328781i
$916$	−2.22911	+	1.01800i	−0.0736520	+	0.0336358i
$917$	−1.26273	+	1.68681i	−0.0416991	+	0.0557035i
$918$	−38.5943	+	8.39568i	−1.27380	+	0.277099i
$919$	−34.9536			−1.15301			−0.576507	−	0.817092i	$-0.695585\pi$
$919$	−34.9536			−1.15301			−0.576507	+	0.817092i	$0.695585\pi$
$920$	−4.69095	−	9.64339i	−0.154656	−	0.317933i
$921$	15.7695			0.519624
$922$	7.43570	−	1.61754i	0.244882	−	0.0532708i
$923$	7.66580	−	10.2403i	0.252323	−	0.337064i
$924$	3.19488	−	1.45905i	0.105104	−	0.0479994i
$925$	1.16587	−	6.95561i	0.0383337	−	0.228699i
$926$	−8.06448	+	17.6587i	−0.265015	+	0.580302i
$927$	−10.3608	+	0.741017i	−0.340292	+	0.0243382i
$928$	1.32165	−	0.989377i	0.0433854	−	0.0324779i
$929$	0.620212	+	2.11225i	0.0203485	+	0.0693006i	0.969041	−	0.246898i	$-0.0794114\pi$
$929$	0.620212	+	2.11225i	0.0203485	+	0.0693006i	−0.948693	+	0.316199i	$0.897593\pi$
$930$	3.36011	+	8.38675i	0.110182	+	0.275012i
$931$	6.28756	+	9.78363i	0.206066	+	0.320646i
$932$	−5.42276	+	24.9280i	−0.177628	+	0.816545i
$933$	−2.81374	+	39.3412i	−0.0921177	+	1.28797i
$934$	−37.4809	+	11.0054i	−1.22641	+	0.360108i
$935$	7.49167	+	23.4147i	0.245004	+	0.765743i
$936$	1.83061	−	2.11263i	0.0598353	−	0.0690536i
$937$	−31.9759	+	11.9264i	−1.04461	+	0.389618i	−0.812432	−	0.583056i	$-0.801857\pi$
$937$	−31.9759	+	11.9264i	−1.04461	+	0.389618i	−0.232175	+	0.972674i	$0.574584\pi$
$938$	8.18499	+	14.9897i	0.267250	+	0.489431i
$939$	−12.8661	−	28.1729i	−0.419871	−	0.919388i
$940$	−22.1037	+	14.9687i	−0.720942	+	0.488225i
$941$	−27.9247	+	43.4517i	−0.910319	+	1.41648i	−0.00117561	+	0.999999i	$0.500374\pi$
$941$	−27.9247	+	43.4517i	−0.910319	+	1.41648i	−0.909143	+	0.416484i	$0.863262\pi$
$942$	0.670036	+	0.670036i	0.0218310	+	0.0218310i
$943$	−4.75596	−	33.0127i	−0.154875	−	1.07504i
$944$		−	5.94758i		−	0.193577i
$945$	−13.8444	−	17.5951i	−0.450359	−	0.572368i
$946$	−0.241464	−	1.67942i	−0.00785066	−	0.0546025i
$947$	9.96084	+	3.71520i	0.323684	+	0.120728i	0.506053	−	0.862502i	$-0.331104\pi$
$947$	9.96084	+	3.71520i	0.323684	+	0.120728i	−0.182369	+	0.983230i	$0.558377\pi$
$948$	3.51146	−	1.91740i	0.114047	−	0.0622743i
$949$	−26.4241	−	12.0675i	−0.857761	−	0.391726i
$950$	8.66873	−	12.8226i	0.281251	−	0.416020i
$951$	5.08784	−	35.3867i	0.164985	−	1.14749i
$952$	6.13111	−	11.2283i	0.198710	−	0.363911i
$953$	−13.6497	−	0.976247i	−0.442157	−	0.0316237i	−0.151514	−	0.988455i	$-0.548415\pi$
$953$	−13.6497	−	0.976247i	−0.442157	−	0.0316237i	−0.290644	+	0.956831i	$0.593869\pi$
$954$	−3.10218	+	1.99365i	−0.100437	+	0.0645468i
$955$	4.23937	+	17.4549i	0.137183	+	0.564826i
$956$	−14.7256	−	16.9942i	−0.476259	−	0.549632i
$957$	−2.82605	−	1.54314i	−0.0913531	−	0.0498826i
$958$	−0.0884898	−	0.118209i	−0.00285898	−	0.00381915i
$959$	2.02251	+	1.75252i	0.0653104	+	0.0565918i
$960$	−0.0678020	−	2.81708i	−0.00218830	−	0.0909210i
$961$	19.8808	+	5.83754i	0.641317	+	0.188308i
$962$	−0.975957	+	2.61664i	−0.0314661	+	0.0843639i
$963$	13.5131	+	10.1158i	0.435452	+	0.325976i
$964$	−0.698234	−	0.448728i	−0.0224886	−	0.0144525i
$965$	−3.28928	−	6.76674i	−0.105886	−	0.217829i
$966$	10.8559	−	0.779491i	0.349284	−	0.0250797i
$967$	−5.10685	+	5.10685i	−0.164225	+	0.164225i	−0.784436	−	0.620210i	$-0.787047\pi$
$967$	−5.10685	+	5.10685i	−0.164225	+	0.164225i	0.620210	+	0.784436i	$0.287047\pi$
$968$	−1.82909	−	8.40817i	−0.0587890	−	0.270249i
$969$	27.4308	−	3.94395i	0.881204	−	0.126698i
$970$	−2.38805	−	24.9393i	−0.0766756	−	0.800753i
$971$	−7.27820	+	24.7873i	−0.233568	+	0.795461i	0.756392	+	0.654118i	$0.226960\pi$
$971$	−7.27820	+	24.7873i	−0.233568	+	0.795461i	−0.989961	+	0.141343i	$0.954858\pi$
$972$	4.60863	+	12.3562i	0.147822	+	0.396326i
$973$	1.44467	+	20.1992i	0.0463141	+	0.647556i
$974$	22.8607	+	3.28688i	0.732505	+	0.105318i
$975$	4.63056	−	11.5843i	0.148296	−	0.370993i
$976$	−1.60593	+	1.39154i	−0.0514045	+	0.0445422i
$977$	39.1170	+	8.50939i	1.25147	+	0.272240i	0.788997	−	0.614396i	$-0.210600\pi$
$977$	39.1170	+	8.50939i	1.25147	+	0.272240i	0.462468	+	0.886636i	$0.346964\pi$
$978$	9.47802	+	2.06182i	0.303074	+	0.0659296i
$979$	22.0555	−	19.1112i	0.704898	−	0.610797i
$980$	−8.39130	−	0.397510i	−0.268050	−	0.0126980i
$981$	−21.4649	−	3.08619i	−0.685323	−	0.0985345i
$982$	−2.07631	−	29.0305i	−0.0662576	−	0.926402i
$983$	−4.35112	−	11.6658i	−0.138779	−	0.372082i	0.848904	−	0.528547i	$-0.177263\pi$
$983$	−4.35112	−	11.6658i	−0.138779	−	0.372082i	−0.987684	+	0.156465i	$0.949990\pi$
$984$	2.46919	−	8.40931i	0.0787151	−	0.268079i
$985$	12.8390	+	10.5951i	0.409085	+	0.337588i
$986$	−11.6089	+	1.66910i	−0.369701	+	0.0531550i
$987$	−5.75918	−	26.4745i	−0.183317	−	0.842693i
$988$	−4.33384	+	4.33384i	−0.137878	+	0.137878i
$989$	1.11616	−	5.13786i	0.0354920	−	0.163375i
$990$	4.39435	−	2.13607i	0.139661	−	0.0678889i
$991$	1.61540	+	1.03816i	0.0513150	+	0.0329782i	0.566047	−	0.824373i	$-0.308472\pi$
$991$	1.61540	+	1.03816i	0.0513150	+	0.0329782i	−0.514732	+	0.857351i	$0.672108\pi$
$992$	2.56671	+	1.92142i	0.0814932	+	0.0610051i
$993$	2.91199	−	7.80735i	0.0924093	−	0.247759i
$994$	−11.1636	−	3.27793i	−0.354088	−	0.103970i
$995$	−4.54901	+	4.77338i	−0.144213	+	0.151326i
$996$	−11.3904	−	9.86981i	−0.360917	−	0.312737i
$997$	−37.3000	−	49.8269i	−1.18130	−	1.57804i	−0.725993	−	0.687702i	$-0.758620\pi$
$997$	−37.3000	−	49.8269i	−1.18130	−	1.57804i	−0.455309	−	0.890334i	$-0.650471\pi$
$998$	33.3377	+	18.2038i	1.05529	+	0.576230i
$999$	−5.13565	−	5.92686i	−0.162485	−	0.187518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.113.11	yes	240
5.2	odd	4	inner	230.2.l.a.67.8	yes	240
23.11	odd	22	inner	230.2.l.a.103.8	yes	240
115.57	even	44	inner	230.2.l.a.57.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.11	✓	240	115.57	even	44	inner
230.2.l.a.67.8	yes	240	5.2	odd	4	inner
230.2.l.a.103.8	yes	240	23.11	odd	22	inner
230.2.l.a.113.11	yes	240	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.977147 - 0.212565i) q^{2} +(0.755212 - 1.00884i) q^{3} +(0.909632 - 0.415415i) q^{4} +(1.82179 + 1.29657i) q^{5} +(0.523507 - 1.14632i) q^{6} +(-1.79627 + 0.128472i) q^{7} +(0.800541 - 0.599278i) q^{8} +(0.397775 + 1.35470i) q^{9} +(2.05576 + 0.879687i) q^{10} +(-0.836716 - 1.30196i) q^{11} +(0.267875 - 1.23140i) q^{12} +(0.141245 - 1.97487i) q^{13} +(-1.72791 + 0.507360i) q^{14} +(2.68387 - 0.858720i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-6.65602 + 2.48257i) q^{17} +(0.676646 + 1.23918i) q^{18} +(-1.28595 - 2.81584i) q^{19} +(2.19577 + 0.422600i) q^{20} +(-1.22696 + 1.90918i) q^{21} +(-1.09434 - 1.09434i) q^{22} +(-1.99348 - 4.36188i) q^{23} -1.26020i q^{24} +(1.63783 + 4.72414i) q^{25} +(-0.281771 - 1.95976i) q^{26} +(5.20932 + 1.94298i) q^{27} +(-1.58057 + 0.863059i) q^{28} +(1.50176 + 0.685829i) q^{29} +(2.44000 - 1.40959i) q^{30} +(-0.456293 + 3.17359i) q^{31} +(0.479249 - 0.877679i) q^{32} +(-1.94537 - 0.139135i) q^{33} +(-5.97620 + 3.84067i) q^{34} +(-3.43900 - 2.09493i) q^{35} +(0.924590 + 1.06703i) q^{36} +(-1.23799 - 0.675994i) q^{37} +(-1.85511 - 2.47814i) q^{38} +(-1.88567 - 1.63394i) q^{39} +(2.23542 - 0.0538024i) q^{40} +(6.67297 + 1.95936i) q^{41} +(-0.793090 + 2.12636i) q^{42} +(0.877639 + 0.656992i) q^{43} +(-1.30196 - 0.836716i) q^{44} +(-1.03179 + 2.98371i) q^{45} +(-2.87511 - 3.83845i) q^{46} +(-8.44176 + 8.44176i) q^{47} +(-0.267875 - 1.23140i) q^{48} +(-3.71867 + 0.534664i) q^{49} +(2.60459 + 4.26803i) q^{50} +(-2.52218 + 8.58976i) q^{51} +(-0.691909 - 1.85508i) q^{52} +(0.186324 + 2.60514i) q^{53} +(5.50328 + 0.791253i) q^{54} +(0.163752 - 3.45675i) q^{55} +(-1.36100 + 1.17931i) q^{56} +(-3.81191 - 0.829230i) q^{57} +(1.61322 + 0.350935i) q^{58} +(4.49488 - 3.89484i) q^{59} +(2.08461 - 1.89604i) q^{60} +(-2.10332 - 0.302411i) q^{61} +(0.228729 + 3.19805i) q^{62} +(-0.888551 - 2.38230i) q^{63} +(0.281733 - 0.959493i) q^{64} +(2.81787 - 3.41466i) q^{65} +(-1.93049 + 0.277562i) q^{66} +(-2.01591 - 9.26697i) q^{67} +(-5.02323 + 5.02323i) q^{68} +(-5.90596 - 1.28303i) q^{69} +(-3.80571 - 1.31605i) q^{70} +(5.43514 + 3.49295i) q^{71} +(1.13027 + 0.846113i) q^{72} +(5.12732 - 13.7469i) q^{73} +(-1.35339 - 0.397392i) q^{74} +(6.00283 + 1.91541i) q^{75} +(-2.33948 - 2.02717i) q^{76} +(1.67023 + 2.23117i) q^{77} +(-2.18989 - 1.19577i) q^{78} +(2.07903 + 2.39933i) q^{79} +(2.17290 - 0.527746i) q^{80} +(2.33104 - 1.49807i) q^{81} +(6.93697 + 0.496142i) q^{82} +(5.73166 - 10.4967i) q^{83} +(-0.322976 + 2.24635i) q^{84} +(-15.3447 - 4.10726i) q^{85} +(0.997236 + 0.455422i) q^{86} +(1.82604 - 0.997093i) q^{87} +(-1.45006 - 0.540844i) q^{88} +(2.68362 + 18.6650i) q^{89} +(-0.373979 + 3.13485i) q^{90} +3.56554i q^{91} +(-3.62533 - 3.13959i) q^{92} +(2.85706 + 2.85706i) q^{93} +(-6.45441 + 10.0433i) q^{94} +(1.30819 - 6.79719i) q^{95} +(-0.523507 - 1.14632i) q^{96} +(-5.36961 - 9.83370i) q^{97} +(-3.52004 + 1.31291i) q^{98} +(1.43093 - 1.65138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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