LMFDB - Embedded newform 230.2.l.a.103.8

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			103.8
Character	$\chi$	$=$	230.103
Dual form			230.2.l.a.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212565 - 0.977147i) q^{2} +(-1.00884 + 0.755212i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.23356 - 0.105808i) q^{5} +(0.523507 + 1.14632i) q^{6} +(-0.128472 + 1.79627i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(-0.397775 + 1.35470i) q^{9} +(-0.578168 + 2.16003i) q^{10} +(-0.836716 + 1.30196i) q^{11} +(1.23140 - 0.267875i) q^{12} +(-1.97487 + 0.141245i) q^{13} +(1.72791 + 0.507360i) q^{14} +(2.33323 - 1.58007i) q^{15} +(0.654861 + 0.755750i) q^{16} +(-2.48257 + 6.65602i) q^{17} +(1.23918 + 0.676646i) q^{18} +(1.28595 - 2.81584i) q^{19} +(1.98777 + 1.02410i) q^{20} +(-1.22696 - 1.90918i) q^{21} +(1.09434 + 1.09434i) q^{22} +(-4.36188 - 1.99348i) q^{23} -1.26020i q^{24} +(4.97761 + 0.472657i) q^{25} +(-0.281771 + 1.95976i) q^{26} +(-1.94298 - 5.20932i) q^{27} +(0.863059 - 1.58057i) q^{28} +(-1.50176 + 0.685829i) q^{29} +(-1.04800 - 2.61577i) q^{30} +(-0.456293 - 3.17359i) q^{31} +(0.877679 - 0.479249i) q^{32} +(-0.139135 - 1.94537i) q^{33} +(5.97620 + 3.84067i) q^{34} +(0.477009 - 3.99849i) q^{35} +(0.924590 - 1.06703i) q^{36} +(0.675994 + 1.23799i) q^{37} +(-2.47814 - 1.85511i) q^{38} +(1.88567 - 1.63394i) q^{39} +(1.42323 - 1.72465i) q^{40} +(6.67297 - 1.95936i) q^{41} +(-2.12636 + 0.793090i) q^{42} +(0.656992 + 0.877639i) 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} +(-1.23140 - 0.267875i) q^{48} +(3.71867 + 0.534664i) q^{49} +(1.51992 - 4.76339i) q^{50} +(-2.52218 - 8.58976i) q^{51} +(1.85508 + 0.691909i) q^{52} +(2.60514 + 0.186324i) q^{53} +(-5.50328 + 0.791253i) q^{54} +(2.00661 - 2.81947i) q^{55} +(-1.36100 - 1.17931i) q^{56} +(0.829230 + 3.81191i) q^{57} +(0.350935 + 1.61322i) q^{58} +(-4.49488 - 3.89484i) q^{59} +(-2.77876 + 0.468025i) q^{60} +(-2.10332 + 0.302411i) q^{61} +(-3.19805 - 0.228729i) q^{62} +(-2.38230 - 0.888551i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(4.42594 - 0.106524i) q^{65} +(-1.93049 - 0.277562i) q^{66} +(9.26697 + 2.01591i) 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} +(-0.846113 - 1.13027i) q^{72} +(-13.7469 + 5.12732i) q^{73} +(1.35339 - 0.397392i) q^{74} +(-5.37859 + 3.28231i) q^{75} +(-2.33948 + 2.02717i) q^{76} +(-2.23117 - 1.67023i) q^{77} +(-1.19577 - 2.18989i) q^{78} +(-2.07903 + 2.39933i) q^{79} +(-1.38271 - 1.75730i) q^{80} +(2.33104 + 1.49807i) q^{81} +(-0.496142 - 6.93697i) q^{82} +(-10.4967 + 5.73166i) q^{83} +(0.322976 + 2.24635i) q^{84} +(6.24923 - 14.6040i) q^{85} +(0.997236 - 0.455422i) q^{86} +(0.997093 - 1.82604i) q^{87} +(-0.540844 - 1.45006i) q^{88} +(-2.68362 + 18.6650i) q^{89} +(-2.69620 - 1.64245i) q^{90} -3.56554i q^{91} +(3.13959 + 3.62533i) q^{92} +(2.85706 + 2.85706i) q^{93} +(6.45441 + 10.0433i) q^{94} +(-3.17019 + 6.15329i) q^{95} +(-0.523507 + 1.14632i) q^{96} +(9.83370 + 5.36961i) q^{97} +(1.31291 - 3.52004i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$3$	−1.00884	+	0.755212i	−0.582457	+	0.436022i	−0.849444	−	0.527678i	$-0.823063\pi$
$3$	−1.00884	+	0.755212i	−0.582457	+	0.436022i	0.266988	+	0.963700i	$0.413972\pi$
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−2.23356	−	0.105808i	−0.998880	−	0.0473187i
$5$	−2.23356	−	0.105808i	−0.998880	−	0.0473187i
$6$	0.523507	+	1.14632i	0.213721	+	0.467984i
$7$	−0.128472	+	1.79627i	−0.0485577	+	0.678926i	0.913631	+	0.406544i	$0.133266\pi$
$7$	−0.128472	+	1.79627i	−0.0485577	+	0.678926i	−0.962189	+	0.272382i	$0.912188\pi$
$8$	−0.599278	+	0.800541i	−0.211877	+	0.283034i
$9$	−0.397775	+	1.35470i	−0.132592	+	0.451565i
$10$	−0.578168	+	2.16003i	−0.182833	+	0.683061i
$11$	−0.836716	+	1.30196i	−0.252279	+	0.392554i	−0.944176	−	0.329443i	$-0.893139\pi$
$11$	−0.836716	+	1.30196i	−0.252279	+	0.392554i	0.691896	+	0.721997i	$0.256776\pi$
$12$	1.23140	−	0.267875i	0.355476	−	0.0773290i
$13$	−1.97487	+	0.141245i	−0.547730	+	0.0391744i	−0.342462	−	0.939532i	$-0.611261\pi$
$13$	−1.97487	+	0.141245i	−0.547730	+	0.0391744i	−0.205267	+	0.978706i	$0.565806\pi$
$14$	1.72791	+	0.507360i	0.461803	+	0.135598i
$15$	2.33323	−	1.58007i	0.602436	−	0.407972i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	−2.48257	+	6.65602i	−0.602111	+	1.61432i	0.174723	+	0.984618i	$0.444097\pi$
$17$	−2.48257	+	6.65602i	−0.602111	+	1.61432i	−0.776834	+	0.629705i	$0.783176\pi$
$18$	1.23918	+	0.676646i	0.292078	+	0.159487i
$19$	1.28595	−	2.81584i	0.295017	−	0.645998i	−0.702845	−	0.711343i	$-0.748087\pi$
$19$	1.28595	−	2.81584i	0.295017	−	0.645998i	0.997863	+	0.0653448i	$0.0208147\pi$
$20$	1.98777	+	1.02410i	0.444478	+	0.228996i
$21$	−1.22696	−	1.90918i	−0.267744	−	0.416617i
$22$	1.09434	+	1.09434i	0.233315	+	0.233315i
$23$	−4.36188	−	1.99348i	−0.909515	−	0.415670i
$23$	−4.36188	−	1.99348i	−0.909515	−	0.415670i
$24$		−	1.26020i		−	0.257238i
$25$	4.97761	+	0.472657i	0.995522	+	0.0945313i
$26$	−0.281771	+	1.95976i	−0.0552598	+	0.384341i
$27$	−1.94298	−	5.20932i	−0.373926	−	1.00253i
$28$	0.863059	−	1.58057i	0.163103	−	0.298701i
$29$	−1.50176	+	0.685829i	−0.278869	+	0.127355i	−0.549940	−	0.835204i	$-0.685349\pi$
$29$	−1.50176	+	0.685829i	−0.278869	+	0.127355i	0.271071	+	0.962559i	$0.412622\pi$
$30$	−1.04800	−	2.61577i	−0.191337	−	0.477572i
$31$	−0.456293	−	3.17359i	−0.0819527	−	0.569993i	−0.988881	−	0.148708i	$-0.952488\pi$
$31$	−0.456293	−	3.17359i	−0.0819527	−	0.569993i	0.906928	−	0.421285i	$-0.138421\pi$
$32$	0.877679	−	0.479249i	0.155153	−	0.0847201i
$33$	−0.139135	−	1.94537i	−0.0242204	−	0.338645i
$34$	5.97620	+	3.84067i	1.02491	+	0.658670i
$35$	0.477009	−	3.99849i	0.0806292	−	0.675868i
$36$	0.924590	−	1.06703i	0.154098	−	0.177839i
$37$	0.675994	+	1.23799i	0.111133	+	0.203524i	0.927326	−	0.374255i	$-0.122101\pi$
$37$	0.675994	+	1.23799i	0.111133	+	0.203524i	−0.816193	+	0.577779i	$0.803920\pi$
$38$	−2.47814	−	1.85511i	−0.402007	−	0.300939i
$39$	1.88567	−	1.63394i	0.301948	−	0.261640i
$40$	1.42323	−	1.72465i	0.225032	−	0.272691i
$41$	6.67297	−	1.95936i	1.04214	−	0.306001i	0.284505	−	0.958675i	$-0.408171\pi$
$41$	6.67297	−	1.95936i	1.04214	−	0.306001i	0.757639	+	0.652674i	$0.226353\pi$
$42$	−2.12636	+	0.793090i	−0.328104	+	0.122377i
$43$	0.656992	+	0.877639i	0.100190	+	0.133839i	0.847835	−	0.530261i	$-0.177906\pi$
$43$	0.656992	+	0.877639i	0.100190	+	0.133839i	−0.747644	+	0.664100i	$0.768815\pi$
$44$	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	$0.913666\pi$
$48$	−1.23140	−	0.267875i	−0.177738	−	0.0386645i
$49$	3.71867	+	0.534664i	0.531239	+	0.0763806i
$50$	1.51992	−	4.76339i	0.214949	−	0.673644i
$51$	−2.52218	−	8.58976i	−0.353176	−	1.20281i
$52$	1.85508	+	0.691909i	0.257253	+	0.0959505i
$53$	2.60514	+	0.186324i	0.357844	+	0.0255935i	0.249104	−	0.968477i	$-0.419864\pi$
$53$	2.60514	+	0.186324i	0.357844	+	0.0255935i	0.108740	+	0.994070i	$0.465318\pi$
$54$	−5.50328	+	0.791253i	−0.748902	+	0.107676i
$55$	2.00661	−	2.81947i	0.270572	−	0.380177i
$56$	−1.36100	−	1.17931i	−0.181871	−	0.157592i
$57$	0.829230	+	3.81191i	0.109834	+	0.504900i
$58$	0.350935	+	1.61322i	0.0460800	+	0.211826i
$59$	−4.49488	−	3.89484i	−0.585184	−	0.507065i	0.311199	−	0.950345i	$-0.399269\pi$
$59$	−4.49488	−	3.89484i	−0.585184	−	0.507065i	−0.896383	+	0.443280i	$0.853815\pi$
$60$	−2.77876	+	0.468025i	−0.358737	+	0.0604217i
$61$	−2.10332	+	0.302411i	−0.269302	+	0.0387198i	−0.275643	−	0.961260i	$-0.588891\pi$
$61$	−2.10332	+	0.302411i	−0.269302	+	0.0387198i	0.00634081	+	0.999980i	$0.497982\pi$
$62$	−3.19805	−	0.228729i	−0.406153	−	0.0290487i
$63$	−2.38230	−	0.888551i	−0.300141	−	0.111947i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	4.42594	−	0.106524i	0.548970	−	0.0132127i
$66$	−1.93049	−	0.277562i	−0.237626	−	0.0341655i
$67$	9.26697	+	2.01591i	1.13214	+	0.246282i	0.739334	−	0.673339i	$-0.235141\pi$
$67$	9.26697	+	2.01591i	1.13214	+	0.246282i	0.392806	+	0.919621i	$0.371504\pi$
$68$	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	−0.176816	−	0.984244i	$-0.556580\pi$
$71$	5.43514	−	3.49295i	0.645032	−	0.414537i	0.821848	+	0.569707i	$0.192943\pi$
$72$	−0.846113	−	1.13027i	−0.0997153	−	0.133204i
$73$	−13.7469	+	5.12732i	−1.60895	+	0.600107i	−0.983620	−	0.180253i	$-0.942308\pi$
$73$	−13.7469	+	5.12732i	−1.60895	+	0.600107i	−0.625330	+	0.780361i	$0.715036\pi$
$74$	1.35339	−	0.397392i	0.157329	−	0.0461958i
$75$	−5.37859	+	3.28231i	−0.621066	+	0.379009i
$76$	−2.33948	+	2.02717i	−0.268357	+	0.232533i
$77$	−2.23117	−	1.67023i	−0.254265	−	0.190341i
$78$	−1.19577	−	2.18989i	−0.135394	−	0.247956i
$79$	−2.07903	+	2.39933i	−0.233909	+	0.269945i	−0.860554	−	0.509360i	$-0.829882\pi$
$79$	−2.07903	+	2.39933i	−0.233909	+	0.269945i	0.626645	+	0.779305i	$0.284428\pi$
$80$	−1.38271	−	1.75730i	−0.154592	−	0.196473i
$81$	2.33104	+	1.49807i	0.259004	+	0.166452i
$82$	−0.496142	−	6.93697i	−0.0547897	−	0.766060i
$83$	−10.4967	+	5.73166i	−1.15217	+	0.629131i	−0.937647	−	0.347588i	$-0.887001\pi$
$83$	−10.4967	+	5.73166i	−1.15217	+	0.629131i	−0.214520	+	0.976719i	$0.568819\pi$
$84$	0.322976	+	2.24635i	0.0352396	+	0.245097i
$85$	6.24923	−	14.6040i	0.677824	−	1.58402i
$86$	0.997236	−	0.455422i	0.107535	−	0.0491095i
$87$	0.997093	−	1.82604i	0.106900	−	0.195772i
$88$	−0.540844	−	1.45006i	−0.0576541	−	0.154577i
$89$	−2.68362	+	18.6650i	−0.284463	+	1.97848i	−0.108351	+	0.994113i	$0.534557\pi$
$89$	−2.68362	+	18.6650i	−0.284463	+	1.97848i	−0.176112	+	0.984370i	$0.556352\pi$
$90$	−2.69620	−	1.64245i	−0.284205	−	0.173129i
$91$		−	3.56554i		−	0.373770i
$92$	3.13959	+	3.62533i	0.327324	+	0.377967i
$93$	2.85706	+	2.85706i	0.296263	+	0.296263i
$94$	6.45441	+	10.0433i	0.665722	+	1.03588i
$95$	−3.17019	+	6.15329i	−0.325255	+	0.631314i
$96$	−0.523507	+	1.14632i	−0.0534302	+	0.116996i
$97$	9.83370	+	5.36961i	0.998461	+	0.545201i	0.893399	−	0.449265i	$-0.148314\pi$
$97$	9.83370	+	5.36961i	0.998461	+	0.545201i	0.105062	+	0.994466i	$0.466496\pi$
$98$	1.31291	−	3.52004i	0.132624	−	0.355577i
$99$	−1.43093	−	1.65138i	−0.143814	−	0.165970i
$100$	−4.33144	−	2.49772i	−0.433144	−	0.249772i
$101$	9.27112	+	2.72225i	0.922511	+	0.270874i	0.708298	−	0.705913i	$-0.249463\pi$
$101$	9.27112	+	2.72225i	0.922511	+	0.270874i	0.214213	+	0.976787i	$0.431281\pi$
$102$	−8.92958	+	0.638656i	−0.884160	+	0.0632364i
$103$	7.18885	−	1.56384i	0.708339	−	0.154090i	0.156058	−	0.987748i	$-0.450121\pi$
$103$	7.18885	−	1.56384i	0.708339	−	0.154090i	0.552281	+	0.833658i	$0.313758\pi$
$104$	1.07042	−	1.66561i	0.104963	−	0.163326i
$105$	2.53848	+	4.39410i	0.247730	+	0.428820i
$106$	0.735829	−	2.50600i	0.0714700	−	0.243404i
$107$	7.16470	−	9.57092i	0.692638	−	0.925256i	−0.307012	−	0.951706i	$-0.599329\pi$
$107$	7.16470	−	9.57092i	0.692638	−	0.925256i	0.999650	+	0.0264497i	$0.00842018\pi$
$108$	−0.396637	+	5.54571i	−0.0381664	+	0.533636i
$109$	6.38050	+	13.9713i	0.611141	+	1.33821i	0.921791	+	0.387688i	$0.126726\pi$
$109$	6.38050	+	13.9713i	0.611141	+	1.33821i	−0.310649	+	0.950525i	$0.600547\pi$
$110$	−2.32850	−	2.56008i	−0.222014	−	0.244094i
$111$	−1.61692	−	0.738422i	−0.153471	−	0.0700879i
$112$	−1.44166	+	1.07921i	−0.136224	+	0.101976i
$113$	−1.52645	+	7.01696i	−0.143596	+	0.660100i	0.847921	+	0.530123i	$0.177854\pi$
$113$	−1.52645	+	7.01696i	−0.143596	+	0.660100i	−0.991517	+	0.129978i	$0.958509\pi$
$114$	3.90106			0.365368
$115$	9.53162	+	4.91409i	0.888828	+	0.458241i
$116$	1.65095			0.153287
$117$	0.594208	−	2.73153i	0.0549346	−	0.252530i
$118$	−4.76128	+	3.56425i	−0.438312	+	0.328116i
$119$	−11.6371	−	5.31447i	−1.06677	−	0.487177i
$120$	−0.133339	+	2.81474i	−0.0121722	+	0.256950i
$121$	3.57457	+	7.82722i	0.324961	+	0.711565i
$122$	−0.151592	+	2.11953i	−0.0137245	+	0.191893i
$123$	−5.25226	+	7.01620i	−0.473581	+	0.632630i
$124$	−0.903297	+	3.07635i	−0.0811185	+	0.276264i
$125$	−11.0678	−	1.58238i	−0.989934	−	0.141532i
$126$	−1.37464	+	2.13898i	−0.122462	+	0.190555i
$127$	11.2451	−	2.44622i	0.997839	−	0.217067i	0.316150	−	0.948709i	$-0.397610\pi$
$127$	11.2451	−	2.44622i	0.997839	−	0.217067i	0.681688	+	0.731643i	$0.261246\pi$
$128$	−0.997452	+	0.0713392i	−0.0881631	+	0.00630555i
$129$	−1.32561	−	0.389233i	−0.116713	−	0.0342701i
$130$	0.836711	−	4.34743i	0.0733844	−	0.381295i
$131$	0.766219	+	0.884264i	0.0669449	+	0.0772585i	0.788234	−	0.615375i	$-0.210996\pi$
$131$	0.766219	+	0.884264i	0.0669449	+	0.0772585i	−0.721289	+	0.692634i	$0.756450\pi$
$132$	−0.681573	+	1.82737i	−0.0593233	+	0.159052i
$133$	4.89280	+	2.67167i	0.424259	+	0.231663i
$134$	3.93967	−	8.62668i	0.340336	−	0.745231i
$135$	3.78858	+	11.8409i	0.326069	+	1.01911i
$136$	−3.84067	−	5.97620i	−0.329335	−	0.512455i
$137$	1.05080	+	1.05080i	0.0897757	+	0.0897757i	0.750568	−	0.660793i	$-0.229780\pi$
$137$	1.05080	+	1.05080i	0.0897757	+	0.0897757i	−0.660793	+	0.750568i	$0.729780\pi$
$138$	0.00169451	−	6.04372i	0.000144246	−	0.514476i
$139$		−	11.2451i		−	0.953794i	−0.878959	−	0.476897i	$-0.841761\pi$
$139$		−	11.2451i		−	0.953794i	0.878959	−	0.476897i	$-0.158239\pi$
$140$	−2.09493	+	3.43900i	−0.177054	+	0.290648i
$141$	2.14111	−	14.8917i	0.180314	−	1.25411i
$142$	−2.25780	−	6.05341i	−0.189471	−	0.507991i
$143$	1.46851	−	2.68937i	0.122803	−	0.224897i
$144$	−1.28430	+	0.586519i	−0.107025	+	0.0488766i
$145$	3.42684	−	1.37295i	0.284583	−	0.114017i
$146$	2.08804	+	14.5226i	0.172807	+	1.20190i
$147$	−4.15535	+	2.26899i	−0.342727	+	0.187143i
$148$	−0.100626	−	1.40693i	−0.00827140	−	0.115649i
$149$	−11.3764	−	7.31118i	−0.931992	−	0.598955i	−0.0158788	−	0.999874i	$-0.505055\pi$
$149$	−11.3764	−	7.31118i	−0.931992	−	0.598955i	−0.916114	+	0.400919i	$0.868691\pi$
$150$	2.06400	+	5.95338i	0.168525	+	0.486091i
$151$	−11.1971	+	12.9221i	−0.911207	+	1.05159i	0.0872572	+	0.996186i	$0.472190\pi$
$151$	−11.1971	+	12.9221i	−0.911207	+	1.05159i	−0.998464	+	0.0554030i	$0.982356\pi$
$152$	1.48355	+	2.71693i	0.120332	+	0.220372i
$153$	−8.02938	−	6.01072i	−0.649137	−	0.485938i
$154$	−2.10633	+	1.82515i	−0.169733	+	0.147074i
$155$	0.683369	+	7.13669i	0.0548895	+	0.573233i
$156$	−2.39402	+	0.702949i	−0.191675	+	0.0562810i
$157$	−0.704513	+	0.262770i	−0.0562262	+	0.0209713i	−0.377420	−	0.926042i	$-0.623189\pi$
$157$	−0.704513	+	0.262770i	−0.0562262	+	0.0209713i	0.321194	+	0.947014i	$0.395916\pi$
$158$	1.90256	+	2.54153i	0.151360	+	0.202193i
$159$	−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
$163$	7.52102	+	1.63610i	0.589092	+	0.128149i	0.497224	−	0.867622i	$-0.334353\pi$
$163$	7.52102	+	1.63610i	0.589092	+	0.128149i	0.0918678	+	0.995771i	$0.470716\pi$
$164$	−6.88390	−	0.989755i	−0.537542	−	0.0772869i
$165$	0.104933	+	4.35983i	0.00816901	+	0.339412i
$166$	3.36943	+	11.4752i	0.261518	+	0.890649i
$167$	−12.3997	−	4.62485i	−0.959518	−	0.357882i	−0.179583	−	0.983743i	$-0.557475\pi$
$167$	−12.3997	−	4.62485i	−0.959518	−	0.357882i	−0.779934	+	0.625861i	$0.784748\pi$
$168$	2.26366	+	0.161900i	0.174646	+	0.0124909i
$169$	−8.98752	+	1.29221i	−0.691348	+	0.0994008i
$170$	−12.9419	−	9.21071i	−0.992595	−	0.706430i
$171$	3.30309	+	2.86214i	0.252593	+	0.218873i
$172$	−0.233037	−	1.07125i	−0.0177689	−	0.0816823i
$173$	−4.07860	−	18.7490i	−0.310090	−	1.42546i	−0.823499	−	0.567318i	$-0.807981\pi$
$173$	−4.07860	−	18.7490i	−0.310090	−	1.42546i	0.513408	−	0.858144i	$-0.328383\pi$
$174$	−1.57236	−	1.36246i	−0.119200	−	0.103288i
$175$	−1.48850	+	8.88040i	−0.112520	+	0.671295i
$176$	−1.53188	+	0.220252i	−0.115470	+	0.0166021i
$177$	7.47606	+	0.534699i	0.561935	+	0.0401904i
$178$	17.6680	+	6.58981i	1.32427	+	0.493927i
$179$	2.41685	+	8.23104i	0.180644	+	0.615217i	0.999170	+	0.0407469i	$0.0129737\pi$
$179$	2.41685	+	8.23104i	0.180644	+	0.615217i	−0.818525	+	0.574470i	$0.805208\pi$
$180$	−2.17803	+	2.28546i	−0.162341	+	0.170348i
$181$	−15.0926	−	2.16999i	−1.12183	−	0.161294i	−0.443655	−	0.896198i	$-0.646318\pi$
$181$	−15.0926	−	2.16999i	−1.12183	−	0.161294i	−0.678172	+	0.734903i	$0.737227\pi$
$182$	−3.48406	−	0.757910i	−0.258256	−	0.0561800i
$183$	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
$187$	−6.58864	−	8.80139i	−0.481809	−	0.643622i
$188$	11.1857	−	4.17206i	0.815803	−	0.304279i
$189$	9.60697	−	2.82086i	0.698804	−	0.205187i
$190$	5.33880	+	4.40572i	0.387317	+	0.319624i
$191$	6.07092	−	5.26049i	0.439277	−	0.380635i	−0.406957	−	0.913447i	$-0.633410\pi$
$191$	6.07092	−	5.26049i	0.439277	−	0.380635i	0.846234	+	0.532812i	$0.178865\pi$
$192$	1.00884	+	0.755212i	0.0728071	+	0.0545027i
$193$	−1.61256	−	2.95318i	−0.116074	−	0.212575i	0.813182	−	0.582009i	$-0.197733\pi$
$193$	−1.61256	−	2.95318i	−0.116074	−	0.212575i	−0.929257	+	0.369435i	$0.879551\pi$
$194$	7.33720	−	8.46758i	0.526780	−	0.607937i
$195$	−4.38464	+	3.44999i	−0.313990	+	0.247059i
$196$	−3.16052	−	2.03114i	−0.225751	−	0.145081i
$197$	−0.531079	−	7.42545i	−0.0378378	−	0.529041i	−0.980657	−	0.195736i	$-0.937290\pi$
$197$	−0.531079	−	7.42545i	−0.0378378	−	0.529041i	0.942819	−	0.333306i	$-0.108164\pi$
$198$	−1.91781	+	1.04720i	−0.136293	+	0.0744214i
$199$	0.419665	+	2.91884i	0.0297493	+	0.206911i	0.999275	−	0.0380799i	$-0.0121241\pi$
$199$	0.419665	+	2.91884i	0.0297493	+	0.206911i	−0.969525	+	0.244991i	$0.921215\pi$
$200$	−3.36135	+	3.70153i	−0.237683	+	0.261738i
$201$	−10.8714	+	4.96479i	−0.766807	+	0.350189i
$202$	4.63075	−	8.48059i	0.325819	−	0.596692i
$203$	−1.03900	−	2.78567i	−0.0729236	−	0.195516i
$204$	−1.27406	+	8.86127i	−0.0892019	+	0.620413i
$205$	−15.1118	+	3.67031i	−1.05546	+	0.256345i
$206$		−	7.35698i		−	0.512585i
$207$	4.43561	−	5.11607i	0.308296	−	0.355591i
$208$	−1.40001	−	1.40001i	−0.0970732	−	0.0970732i
$209$	2.59012	+	4.03031i	0.179162	+	0.278782i
$210$	4.83327	−	1.54643i	0.333527	−	0.106714i
$211$	−1.05048	+	2.30023i	−0.0723179	+	0.158354i	−0.942339	−	0.334661i	$-0.891378\pi$
$211$	−1.05048	+	2.30023i	−0.0723179	+	0.158354i	0.870021	+	0.493015i	$0.164105\pi$
$212$	−2.29232	−	1.25170i	−0.157437	−	0.0859672i
$213$	−2.84529	+	7.62852i	−0.194956	+	0.522698i
$214$	−7.82923	−	9.03541i	−0.535195	−	0.617648i
$215$	−1.37457	−	2.02978i	−0.0937451	−	0.138430i
$216$	5.33466	+	1.56640i	0.362978	+	0.106580i
$217$	5.75924	−	0.411909i	0.390963	−	0.0279622i
$218$	15.0083	−	3.26486i	1.01649	−	0.221124i
$219$	9.99625	−	15.5545i	0.675484	−	1.05107i
$220$	−2.99653	+	1.73110i	−0.202026	+	0.116711i
$221$	3.96261	−	13.4954i	0.266554	−	0.907800i
$222$	−1.06525	+	1.42300i	−0.0714947	+	0.0955058i
$223$	1.59399	−	22.2870i	0.106742	−	1.49244i	−0.608492	−	0.793560i	$-0.708225\pi$
$223$	1.59399	−	22.2870i	0.106742	−	1.49244i	0.715234	−	0.698885i	$-0.246320\pi$
$224$	0.748103	+	1.63812i	0.0499848	+	0.109451i
$225$	−2.62027	+	6.55514i	−0.174685	+	0.437009i
$226$	6.53213	+	2.98313i	0.434511	+	0.198435i
$227$	−19.5859	+	14.6619i	−1.29996	+	0.973141i	−0.300150	+	0.953892i	$0.597037\pi$
$227$	−19.5859	+	14.6619i	−1.29996	+	0.973141i	−0.999815	+	0.0192491i	$0.993872\pi$
$228$	0.829230	−	3.81191i	0.0549171	−	0.252450i
$229$	2.45057			0.161938			0.0809690	−	0.996717i	$-0.474199\pi$
$229$	2.45057			0.161938			0.0809690	+	0.996717i	$0.474199\pi$
$230$	6.82788	−	8.26922i	0.450217	−	0.545256i
$231$	3.51228			0.231091
$232$	0.350935	−	1.61322i	0.0230400	−	0.105913i
$233$	20.4226	−	15.2882i	1.33793	−	1.00156i	0.339798	−	0.940499i	$-0.389641\pi$
$233$	20.4226	−	15.2882i	1.33793	−	1.00156i	0.998134	−	0.0610643i	$-0.0194495\pi$
$234$	−2.54280	−	1.16126i	−0.166228	−	0.0759137i
$235$	19.7484	−	17.9620i	1.28824	−	1.17171i
$236$	2.47071	+	5.41011i	0.160830	+	0.352168i
$237$	0.285417	−	3.99065i	0.0185398	−	0.259221i
$238$	−7.66666	+	10.2415i	−0.496955	+	0.663855i
$239$	6.33520	−	21.5757i	0.409790	−	1.39562i	−0.453657	−	0.891176i	$-0.649881\pi$
$239$	6.33520	−	21.5757i	0.409790	−	1.39562i	0.863447	−	0.504440i	$-0.168301\pi$
$240$	2.72207	+	0.728609i	0.175709	+	0.0470315i
$241$	−0.448728	+	0.698234i	−0.0289051	+	0.0449772i	−0.855405	−	0.517959i	$-0.826692\pi$
$241$	−0.448728	+	0.698234i	−0.0289051	+	0.0449772i	0.826500	+	0.562936i	$0.190328\pi$
$242$	8.40817	−	1.82909i	0.540498	−	0.117578i
$243$	13.1541	−	0.940801i	0.843837	−	0.0603524i
$244$	2.03887	+	0.598666i	0.130525	+	0.0383257i
$245$	−8.24932	−	1.58767i	−0.527030	−	0.101433i
$246$	5.73941	+	6.62363i	0.365931	+	0.422307i
$247$	−2.14186	+	5.74255i	−0.136283	+	0.365389i
$248$	2.81403	+	1.53658i	0.178691	+	0.0975729i
$249$	6.26097	−	13.7096i	0.396773	−	0.868812i
$250$	−3.89884	+	10.4785i	−0.246585	+	0.662719i
$251$	−0.611467	−	0.951461i	−0.0385955	−	0.0600557i	0.821420	−	0.570324i	$-0.193182\pi$
$251$	−0.611467	−	0.951461i	−0.0385955	−	0.0600557i	−0.860015	+	0.510268i	$0.829546\pi$
$252$	1.79790	+	1.79790i	0.113257	+	0.113257i
$253$	6.24508	−	4.01100i	0.392625	−	0.252169i
$254$		−	11.5081i		−	0.722080i
$255$	4.72459	+	19.4526i	0.295865	+	1.21817i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	2.96672	+	7.95409i	0.185059	+	0.496163i	0.996040	−	0.0889105i	$-0.0283385\pi$
$257$	2.96672	+	7.95409i	0.185059	+	0.496163i	−0.810981	+	0.585073i	$0.801066\pi$
$258$	−0.662116	+	1.21257i	−0.0412215	+	0.0754916i
$259$	−2.31061	+	1.05522i	−0.143574	+	0.0655682i
$260$	−4.07023	−	1.74170i	−0.252425	−	0.108016i
$261$	−0.331730	−	2.30723i	−0.0205335	−	0.142814i
$262$	1.02693	−	0.560745i	0.0634438	−	0.0346429i
$263$	1.44700	+	20.2317i	0.0892259	+	1.24754i	0.822958	+	0.568102i	$0.192322\pi$
$263$	1.44700	+	20.2317i	0.0892259	+	1.24754i	−0.733732	+	0.679439i	$0.762223\pi$
$264$	1.64073	+	1.05443i	0.100980	+	0.0648958i
$265$	−5.79904	−	0.691810i	−0.356232	−	0.0424975i
$266$	3.65065	−	4.21308i	0.223836	−	0.258320i
$267$	−11.3887	−	20.8568i	−0.696974	−	1.27641i
$268$	−7.59209	−	5.68337i	−0.463761	−	0.347167i
$269$	−17.9196	+	15.5274i	−1.09258	+	0.946723i	−0.998805	−	0.0488711i	$-0.984438\pi$
$269$	−17.9196	+	15.5274i	−1.09258	+	0.946723i	−0.0937711	+	0.995594i	$0.529892\pi$
$270$	12.3757	−	1.18502i	0.753158	−	0.0721182i
$271$	−18.4876	+	5.42846i	−1.12304	+	0.329755i	−0.789970	−	0.613146i	$-0.789904\pi$
$271$	−18.4876	+	5.42846i	−1.12304	+	0.329755i	−0.333073	+	0.942901i	$0.608086\pi$
$272$	−6.65602	+	2.48257i	−0.403581	+	0.150528i
$273$	2.69274	+	3.59708i	0.162972	+	0.217705i
$274$	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	$0.349857\pi$
$278$	−10.9881	−	2.39031i	−0.659021	−	0.143361i
$279$	4.48075	+	0.644234i	0.268255	+	0.0385693i
$280$	2.91509	+	2.77807i	0.174210	+	0.166021i
$281$	6.53768	+	22.2653i	0.390005	+	1.32824i	0.887515	+	0.460778i	$0.152430\pi$
$281$	6.53768	+	22.2653i	0.390005	+	1.32824i	−0.497510	+	0.867458i	$0.665752\pi$
$282$	−14.0963	−	5.25765i	−0.839422	−	0.313088i
$283$	26.8469	+	1.92013i	1.59588	+	0.114140i	0.840747	−	0.541427i	$-0.182116\pi$
$283$	26.8469	+	1.92013i	1.59588	+	0.114140i	0.755137	+	0.655567i	$0.227570\pi$
$284$	−6.39500	+	0.919462i	−0.379473	+	0.0545600i
$285$	−1.44881	−	8.60188i	−0.0858200	−	0.509531i
$286$	−2.31576	−	2.00662i	−0.136934	−	0.118654i
$287$	2.66225	+	12.2382i	0.157148	+	0.722397i
$288$	0.300118	+	1.37962i	0.0176846	+	0.0812950i
$289$	−25.2917	−	21.9154i	−1.48775	−	1.28914i
$290$	−0.613144	−	3.64036i	−0.0360050	−	0.213769i
$291$	−13.9759	+	2.00943i	−0.819280	+	0.117795i
$292$	14.6346	+	1.04668i	0.856423	+	0.0612526i
$293$	21.0852	+	7.86438i	1.23181	+	0.459442i	0.879257	−	0.476349i	$-0.158040\pi$
$293$	21.0852	+	7.86438i	1.23181	+	0.459442i	0.352556	+	0.935791i	$0.385313\pi$
$294$	1.33386	+	4.54269i	0.0777920	+	0.264935i
$295$	9.62750	+	9.17496i	0.560535	+	0.534187i
$296$	−1.39617	−	0.200739i	−0.0811508	−	0.0116677i
$297$	8.40803	+	1.82905i	0.487883	+	0.106132i
$298$	−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
$302$	10.2467	+	13.6880i	0.589632	+	0.787656i
$303$	−11.4090	+	4.25533i	−0.655429	+	0.244463i
$304$	2.97019	−	0.872126i	0.170352	−	0.0500199i
$305$	4.72989	−	0.452908i	0.270833	−	0.0259334i
$306$	−7.58013	+	6.56822i	−0.433327	+	0.375480i
$307$	−10.0176	−	7.49905i	−0.571732	−	0.427994i	0.273901	−	0.961758i	$-0.411686\pi$
$307$	−10.0176	−	7.49905i	−0.571732	−	0.427994i	−0.845633	+	0.533764i	$0.820777\pi$
$308$	1.33570	+	2.44616i	0.0761087	+	0.139383i
$309$	−6.07141	+	7.00678i	−0.345390	+	0.398602i
$310$	7.11885	+	0.849260i	0.404324	+	0.0482347i
$311$	−26.3295	−	16.9209i	−1.49301	−	0.959497i	−0.995770	−	0.0918829i	$-0.970711\pi$
$311$	−26.3295	−	16.9209i	−1.49301	−	0.959497i	−0.497237	−	0.867615i	$-0.665652\pi$
$312$	0.177998	+	2.48874i	0.0100771	+	0.140897i
$313$	−21.5705	+	11.7784i	−1.21924	+	0.665755i	−0.954398	−	0.298537i	$-0.903501\pi$
$313$	−21.5705	+	11.7784i	−1.21924	+	0.665755i	−0.264841	+	0.964292i	$0.585320\pi$
$314$	0.107010	+	0.744268i	0.00603890	+	0.0420015i
$315$	5.22699	+	2.23670i	0.294508	+	0.126024i
$316$	2.88787	−	1.31884i	0.162455	−	0.0741908i
$317$	13.5958	−	24.8988i	0.763615	−	1.39846i	−0.148665	−	0.988888i	$-0.547498\pi$
$317$	13.5958	−	24.8988i	0.763615	−	1.39846i	0.912279	−	0.409568i	$-0.134321\pi$
$318$	1.15023	+	3.08387i	0.0645014	+	0.172935i
$319$	0.363625	−	2.52906i	0.0203591	−	0.141600i
$320$	0.527746	+	2.17290i	0.0295019	+	0.121469i
$321$			15.0664i			0.840927i
$322$	−6.52553	−	5.65761i	−0.363653	−	0.315286i
$323$	15.5498	+	15.5498i	0.865216	+	0.865216i
$324$	−1.49807	−	2.33104i	−0.0832260	−	0.129502i
$325$	−9.89688	−	0.230370i	−0.548980	−	0.0127786i
$326$	3.19742	−	7.00137i	0.177089	−	0.387770i
$327$	−16.9883	−	9.27629i	−0.939453	−	0.512980i
$328$	−2.43041	+	6.51619i	−0.134197	+	0.359797i
$329$	−14.0791	−	16.2482i	−0.776208	−	0.895792i
$330$	4.28249	+	0.824213i	0.235744	+	0.0453714i
$331$	6.34437	+	1.86288i	0.348718	+	0.102393i	0.451401	−	0.892321i	$-0.350924\pi$
$331$	6.34437	+	1.86288i	0.348718	+	0.102393i	−0.102683	+	0.994714i	$0.532743\pi$
$332$	11.9292	−	0.853193i	0.654700	−	0.0468250i
$333$	−1.94599	+	0.423325i	−0.106640	+	0.0231981i
$334$	−7.15490	+	11.1332i	−0.391499	+	0.609184i
$335$	−20.4851	−	5.48317i	−1.11922	−	0.299577i
$336$	0.639377	−	2.17752i	0.0348809	−	0.118793i
$337$	3.48557	−	4.65617i	0.189871	−	0.253638i	−0.695497	−	0.718529i	$-0.744816\pi$
$337$	3.48557	−	4.65617i	0.189871	−	0.253638i	0.885368	+	0.464891i	$0.153907\pi$
$338$	−0.647756	+	9.05681i	−0.0352333	+	0.492626i
$339$	−3.75935	−	8.23182i	−0.204180	−	0.447091i
$340$	−11.7512	+	10.6882i	−0.637299	+	0.579650i
$341$	4.51366	+	2.06132i	0.244428	+	0.111627i
$342$	3.49886	−	2.61921i	0.189196	−	0.141631i
$343$	−4.11774	+	18.9290i	−0.222337	+	1.02207i
$344$	−1.09631			−0.0591089
$345$	−13.3271	+	2.24083i	−0.717507	+	0.120642i
$346$	−19.1875			−1.03153
$347$	−4.32596	+	19.8861i	−0.232230	+	1.06754i	0.702362	+	0.711820i	$0.252129\pi$
$347$	−4.32596	+	19.8861i	−0.232230	+	1.06754i	−0.934592	+	0.355722i	$0.884235\pi$
$348$	−1.66555	+	1.24682i	−0.0892830	+	0.0668364i
$349$	−3.23673	−	1.47816i	−0.173258	−	0.0791244i	0.326898	−	0.945060i	$-0.393997\pi$
$349$	−3.23673	−	1.47816i	−0.173258	−	0.0791244i	−0.500156	+	0.865935i	$0.666724\pi$
$350$	8.36106	+	3.34215i	0.446917	+	0.178645i
$351$	4.57292	+	10.0133i	0.244084	+	0.534470i
$352$	−0.110407	+	1.54369i	−0.00588472	+	0.0822792i
$353$	−5.64338	+	7.53867i	−0.300367	+	0.401243i	−0.925178	−	0.379532i	$-0.876085\pi$
$353$	−5.64338	+	7.53867i	−0.300367	+	0.401243i	0.624812	+	0.780776i	$0.285176\pi$
$354$	2.11163	−	7.19155i	0.112232	−	0.382227i
$355$	−12.5093	+	7.22665i	−0.663925	+	0.383551i
$356$	10.1948	−	15.8634i	0.540324	−	0.840761i
$357$	15.7535	−	3.42697i	0.833766	−	0.181375i
$358$	8.55668	−	0.611986i	0.452234	−	0.0323444i
$359$	21.8010	+	6.40135i	1.15061	+	0.337850i	0.800778	−	0.598962i	$-0.204420\pi$
$359$	21.8010	+	6.40135i	1.15061	+	0.337850i	0.349834	+	0.936812i	$0.386238\pi$
$360$	1.77025	+	2.61406i	0.0933006	+	0.137773i
$361$	6.16707	+	7.11718i	0.324583	+	0.374588i
$362$	−5.32857	+	14.2865i	−0.280063	+	0.750879i
$363$	−9.51739	−	5.19689i	−0.499534	−	0.272766i
$364$	−1.48118	+	3.24333i	−0.0776349	+	0.169997i
$365$	31.2470	−	9.99767i	1.63554	−	0.523302i
$366$	−1.44776	−	2.25276i	−0.0756758	−	0.117754i
$367$	6.38920	+	6.38920i	0.333514	+	0.333514i	0.853919	−	0.520405i	$-0.174219\pi$
$367$	6.38920	+	6.38920i	0.333514	+	0.333514i	−0.520405	+	0.853919i	$0.674219\pi$
$368$	−1.34985	−	4.60195i	−0.0703659	−	0.239893i
$369$			9.81924i			0.511169i
$370$	−3.06493	+	0.744400i	−0.159338	+	0.0386995i
$371$	−0.669375	+	4.65560i	−0.0347522	+	0.241707i
$372$	−1.41201	−	3.78574i	−0.0732092	−	0.196281i
$373$	5.48617	−	10.0472i	0.284063	−	0.520223i	−0.696218	−	0.717830i	$-0.745135\pi$
$373$	5.48617	−	10.0472i	0.284063	−	0.520223i	0.980281	+	0.197607i	$0.0633171\pi$
$374$	−10.0008	+	4.56720i	−0.517127	+	0.236164i
$375$	12.3607	−	6.76215i	0.638305	−	0.349196i
$376$	−1.69902	−	11.8169i	−0.0876202	−	0.609412i
$377$	2.86890	−	1.56654i	0.147756	−	0.0806809i
$378$	−0.714287	−	9.98703i	−0.0367389	−	0.513678i
$379$	−12.4319	−	7.98949i	−0.638583	−	0.410392i	0.180896	−	0.983502i	$-0.442100\pi$
$379$	−12.4319	−	7.98949i	−0.638583	−	0.410392i	−0.819478	+	0.573110i	$0.805737\pi$
$380$	5.43988	−	4.28029i	0.279060	−	0.219574i
$381$	−9.49712	+	10.9603i	−0.486552	+	0.561511i
$382$	−3.84980	−	7.05038i	−0.196973	−	0.360729i
$383$	17.3391	+	12.9799i	0.885986	+	0.663241i	0.942154	−	0.335180i	$-0.108797\pi$
$383$	17.3391	+	12.9799i	0.885986	+	0.663241i	−0.0561677	+	0.998421i	$0.517888\pi$
$384$	0.952398	−	0.825258i	0.0486019	−	0.0421138i
$385$	4.80673	+	3.96664i	0.244974	+	0.202159i
$386$	−3.22846	+	0.947963i	−0.164325	+	0.0482500i
$387$	−1.45027	+	0.540922i	−0.0737213	+	0.0274966i
$388$	−6.71443	−	8.96943i	−0.340874	−	0.455354i
$389$	−28.2443	+	18.1515i	−1.43204	+	0.920319i	−0.432216	+	0.901770i	$0.642268\pi$
$389$	−28.2443	+	18.1515i	−1.43204	+	0.920319i	−0.999828	+	0.0185491i	$0.994095\pi$
$390$	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
$393$	−1.44080	−	0.313428i	−0.0726789	−	0.0158103i
$394$	−7.36865	−	1.05945i	−0.371227	−	0.0533744i
$395$	4.89751	−	5.13907i	0.246420	−	0.258575i
$396$	0.615611	+	2.09658i	0.0309356	+	0.105357i
$397$	−17.3623	−	6.47580i	−0.871389	−	0.325011i	−0.126312	−	0.991991i	$-0.540314\pi$
$397$	−17.3623	−	6.47580i	−0.871389	−	0.325011i	−0.745076	+	0.666979i	$0.767587\pi$
$398$	2.94134	+	0.210369i	0.147436	+	0.0105448i
$399$	−6.95375	+	0.999798i	−0.348123	+	0.0500525i
$400$	2.90243	+	4.07135i	0.145122	+	0.203568i
$401$	8.28826	+	7.18182i	0.413896	+	0.358643i	0.836778	−	0.547542i	$-0.184436\pi$
$401$	8.28826	+	7.18182i	0.413896	+	0.358643i	−0.422882	+	0.906185i	$0.638982\pi$
$402$	2.54045	+	11.6783i	0.126706	+	0.582459i
$403$	1.34937	+	6.20297i	0.0672171	+	0.308992i
$404$	−7.30244	−	6.32760i	−0.363310	−	0.314810i
$405$	−5.04802	−	3.59267i	−0.250838	−	0.178521i
$406$	−2.94286	+	0.423120i	−0.146052	+	0.0209991i
$407$	−2.17742	−	0.155732i	−0.107931	−	0.00771937i
$408$	8.38794	+	3.12854i	0.415265	+	0.154886i
$409$	3.09786	+	10.5503i	0.153179	+	0.521681i	0.999947	−	0.0102819i	$-0.00327287\pi$
$409$	3.09786	+	10.5503i	0.153179	+	0.521681i	−0.846768	+	0.531963i	$0.821455\pi$
$410$	0.374179	+	15.5467i	0.0184794	+	0.767795i
$411$	−1.85367	−	0.266517i	−0.0914346	−	0.0131463i
$412$	−7.18885	−	1.56384i	−0.354169	−	0.0770448i
$413$	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
$417$	8.49241	+	11.3445i	0.415875	+	0.555544i
$418$	4.48877	−	1.67423i	0.219553	−	0.0818891i
$419$	34.8148	−	10.2225i	1.70081	−	0.499404i	0.719938	−	0.694039i	$-0.244170\pi$
$419$	34.8148	−	10.2225i	1.70081	−	0.499404i	0.980876	+	0.194635i	$0.0623522\pi$
$420$	−0.483706	−	5.05153i	−0.0236025	−	0.246490i
$421$	−9.11140	+	7.89507i	−0.444062	+	0.384782i	−0.847993	−	0.530007i	$-0.822189\pi$
$421$	−9.11140	+	7.89507i	−0.444062	+	0.384782i	0.403931	+	0.914790i	$0.367644\pi$
$422$	2.02437	+	1.51542i	0.0985446	+	0.0737695i
$423$	−8.07810	−	14.7939i	−0.392771	−	0.719306i
$424$	−1.71036	+	1.97387i	−0.0830626	+	0.0958594i
$425$	−15.5033	+	31.9577i	−0.752019	+	1.55017i
$426$	6.84938	+	4.40183i	0.331853	+	0.213269i
$427$	−0.272995	−	3.81697i	−0.0132112	−	0.184716i
$428$	−10.4931	+	5.72969i	−0.507205	+	0.276955i
$429$	0.549549	+	3.82219i	0.0265325	+	0.184537i
$430$	−2.27558	+	0.911699i	−0.109738	+	0.0439661i
$431$	5.55718	−	2.53788i	0.267680	−	0.122245i	−0.277054	−	0.960854i	$-0.589358\pi$
$431$	5.55718	−	2.53788i	0.267680	−	0.122245i	0.544734	+	0.838609i	$0.316631\pi$
$432$	2.66456	−	4.87979i	0.128199	−	0.234779i
$433$	−5.18521	−	13.9021i	−0.249185	−	0.668092i	−0.999972	−	0.00754669i	$-0.997598\pi$
$433$	−5.18521	−	13.9021i	−0.249185	−	0.668092i	0.750786	−	0.660545i	$-0.229675\pi$
$434$	0.821719	−	5.71518i	0.0394438	−	0.274337i
$435$	−2.42028	+	3.97308i	−0.116044	+	0.190494i
$436$		−	15.3593i		−	0.735579i
$437$	−11.2225	+	9.71884i	−0.536845	+	0.464915i
$438$	−13.0741	−	13.0741i	−0.624707	−	0.624707i
$439$	13.8612	+	21.5685i	0.661561	+	1.02941i	0.996203	+	0.0870640i	$0.0277484\pi$
$439$	13.8612	+	21.5685i	0.661561	+	1.02941i	−0.334641	+	0.942346i	$0.608615\pi$
$440$	1.05458	+	3.29602i	0.0502752	+	0.157132i
$441$	−2.20350	+	4.82499i	−0.104929	+	0.229762i
$442$	−12.3447	−	6.74071i	−0.587177	−	0.320623i
$443$	−3.95893	+	10.6143i	−0.188094	+	0.504301i	−0.996430	−	0.0844211i	$-0.973096\pi$
$443$	−3.95893	+	10.6143i	−0.188094	+	0.504301i	0.808336	+	0.588722i	$0.200369\pi$
$444$	1.16405	+	1.34338i	0.0552433	+	0.0637542i
$445$	7.96893	−	41.4054i	0.377763	−	1.96281i
$446$	−21.4388	−	6.29500i	−1.01516	−	0.298077i
$447$	16.9985	−	1.21576i	0.804003	−	0.0575034i
$448$	1.75970	−	0.382800i	0.0831381	−	0.0180856i
$449$	17.6416	−	27.4509i	0.832560	−	1.29549i	−0.120503	−	0.992713i	$-0.538451\pi$
$449$	17.6416	−	27.4509i	0.832560	−	1.29549i	0.953062	−	0.302775i	$-0.0979130\pi$
$450$	5.84835	+	3.95379i	0.275694	+	0.186383i
$451$	−3.03238	+	10.3273i	−0.142789	+	0.486296i
$452$	4.30346	−	5.74875i	0.202418	−	0.270398i
$453$	1.53718	−	21.4926i	0.0722231	−	1.00981i
$454$	10.1635	+	22.2549i	0.476996	+	1.04448i
$455$	−0.377262	+	7.96386i	−0.0176863	+	0.373352i
$456$	−3.54853	−	1.62056i	−0.166175	−	0.0758897i
$457$	22.1705	−	16.5967i	1.03709	−	0.776359i	0.0619835	−	0.998077i	$-0.480257\pi$
$457$	22.1705	−	16.5967i	1.03709	−	0.776359i	0.975111	+	0.221718i	$0.0711665\pi$
$458$	0.520906	−	2.39456i	0.0243403	−	0.111891i
$459$	39.4969			1.84356
$460$	−6.62887	−	8.42959i	−0.309073	−	0.393032i
$461$	7.60961			0.354415			0.177207	−	0.984174i	$-0.443294\pi$
$461$	7.60961			0.354415			0.177207	+	0.984174i	$0.443294\pi$
$462$	0.746589	−	3.43201i	0.0347345	−	0.159672i
$463$	15.5410	−	11.6338i	0.722249	−	0.540669i	−0.173715	−	0.984796i	$-0.555577\pi$
$463$	15.5410	−	11.6338i	0.722249	−	0.540669i	0.895964	+	0.444127i	$0.146486\pi$
$464$	−1.50176	−	0.685829i	−0.0697173	−	0.0318388i
$465$	−6.07912	−	6.68372i	−0.281913	−	0.309950i
$466$	−10.5977	−	23.2057i	−0.490927	−	1.07498i
$467$	−2.78674	+	38.9638i	−0.128955	+	1.80303i	0.362352	+	0.932041i	$0.381974\pi$
$467$	−2.78674	+	38.9638i	−0.128955	+	1.80303i	−0.491307	+	0.870986i	$0.663481\pi$
$468$	−1.67523	+	2.23784i	−0.0774375	+	0.103444i
$469$	−4.81165	+	16.3870i	−0.222181	+	0.756680i
$470$	−13.3537	−	23.1152i	−0.615960	−	1.06622i
$471$	0.512297	−	0.797150i	0.0236054	−	0.0367307i
$472$	5.81166	−	1.26425i	0.267503	−	0.0581918i
$473$	−1.69236	+	0.121040i	−0.0778149	+	0.00556543i
$474$	−3.83878	−	1.12717i	−0.176321	−	0.0517726i
$475$	7.73189	−	13.4083i	0.354763	−	0.615217i
$476$	8.37774	+	9.66843i	0.383993	+	0.443152i
$477$	−1.28867	+	3.45506i	−0.0590042	+	0.158196i
$478$	−19.7360	−	10.7767i	−0.902703	−	0.492913i
$479$	0.0613405	−	0.134317i	0.00280272	−	0.00613710i	−0.908225	−	0.418481i	$-0.862563\pi$
$479$	0.0613405	−	0.134317i	0.00280272	−	0.00613710i	0.911028	+	0.412344i	$0.135290\pi$
$480$	1.29058	−	2.50499i	0.0589065	−	0.114337i
$481$	−1.50986	−	2.34939i	−0.0688437	−	0.107123i
$482$	0.586893	+	0.586893i	0.0267323	+	0.0267323i
$483$	1.54592	+	10.7735i	0.0703417	+	0.490213i
$484$		−	8.60482i		−	0.391128i
$485$	−21.3961	−	13.0338i	−0.971545	−	0.591836i
$486$	1.87681	−	13.0535i	0.0851337	−	0.592118i
$487$	−8.07115	−	21.6396i	−0.365739	−	0.980584i	−0.981298	−	0.192493i	$-0.938343\pi$
$487$	−8.07115	−	21.6396i	−0.365739	−	0.980584i	0.615559	−	0.788091i	$-0.288930\pi$
$488$	1.01838	−	1.86502i	0.0460998	−	0.0844255i
$489$	−8.82315	+	4.02940i	−0.398996	+	0.182216i
$490$	−3.30491	+	7.72331i	−0.149300	+	0.348904i
$491$	4.14203	+	28.8085i	0.186927	+	1.30011i	0.839906	+	0.542732i	$0.182610\pi$
$491$	4.14203	+	28.8085i	0.186927	+	1.30011i	−0.652979	+	0.757376i	$0.726481\pi$
$492$	7.69226	−	4.20029i	0.346794	−	0.189364i
$493$	−0.836682	−	11.6983i	−0.0376823	−	0.526867i
$494$	5.15603	+	3.31358i	0.231981	+	0.149085i
$495$	3.02134	+	3.83987i	0.135799	+	0.172589i
$496$	2.09963	−	2.42310i	0.0942761	−	0.108800i
$497$	5.57602	+	10.2117i	0.250119	+	0.458058i
$498$	−12.0654	−	9.03208i	−0.540666	−	0.404737i
$499$	−28.7063	+	24.8742i	−1.28507	+	1.11352i	−0.297775	+	0.954636i	$0.596244\pi$
$499$	−28.7063	+	24.8742i	−1.28507	+	1.11352i	−0.987297	+	0.158885i	$0.949210\pi$
$500$	9.41028	+	6.03711i	0.420840	+	0.269988i
$501$	16.0021	−	4.69864i	0.714922	−	0.209920i
$502$	−1.05969	+	0.395245i	−0.0472965	+	0.0176407i
$503$	−19.0988	−	25.5131i	−0.851575	−	1.13757i	−0.989125	−	0.147076i	$-0.953014\pi$
$503$	−19.0988	−	25.5131i	−0.851575	−	1.13757i	0.137550	−	0.990495i	$-0.456077\pi$
$504$	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
$508$	−11.2451	−	2.44622i	−0.498919	−	0.108533i
$509$	41.3586	+	5.94647i	1.83319	+	0.263573i	0.970315	−	0.241846i	$-0.0777528\pi$
$509$	41.3586	+	5.94647i	1.83319	+	0.263573i	0.862874	+	0.505419i	$0.168662\pi$
$510$	20.0124	−	0.481660i	0.886162	−	0.0213283i
$511$	−7.44396	−	25.3518i	−0.329301	−	1.12150i
$512$	0.936950	+	0.349464i	0.0414077	+	0.0154443i
$513$	−17.1672	−	1.22782i	−0.757950	−	0.0542097i
$514$	8.40294	−	1.20816i	0.370638	−	0.0532897i
$515$	−16.2222	+	2.73230i	−0.714837	+	0.120399i
$516$	1.04412	+	0.904736i	0.0459649	+	0.0398288i
$517$	−3.92744	−	18.0541i	−0.172729	−	0.794021i
$518$	0.539950	+	2.48211i	0.0237240	+	0.109058i
$519$	18.2742	+	15.8347i	0.802147	+	0.695064i
$520$	−2.56709	+	3.60698i	−0.112574	+	0.158177i
$521$	37.5169	−	5.39412i	1.64365	−	0.236321i	0.742503	−	0.669843i	$-0.233638\pi$
$521$	37.5169	−	5.39412i	1.64365	−	0.236321i	0.901143	+	0.433522i	$0.142729\pi$
$522$	−2.32502	−	0.166288i	−0.101763	−	0.00727825i
$523$	−16.0696	−	5.99365i	−0.702674	−	0.262084i	−0.0273723	−	0.999625i	$-0.508714\pi$
$523$	−16.0696	−	5.99365i	−0.702674	−	0.262084i	−0.675302	+	0.737541i	$0.735987\pi$
$524$	−0.329641	−	1.12265i	−0.0144004	−	0.0490434i
$525$	−5.20492	−	10.0831i	−0.227161	−	0.440062i
$526$	20.0769	+	2.88663i	0.875397	+	0.125863i
$527$	22.2562	+	4.84155i	0.969497	+	0.210901i
$528$	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
$532$	−3.34079	−	4.46278i	−0.144842	−	0.193486i
$533$	−12.9015	+	4.81201i	−0.558826	+	0.208431i
$534$	−22.8009	+	6.69496i	−0.986693	+	0.289719i
$535$	−17.0155	+	20.6192i	−0.735644	+	0.891445i
$536$	−7.16730	+	6.21050i	−0.309580	+	0.268253i
$537$	−8.65441	−	6.47861i	−0.373465	−	0.279573i
$538$	11.3635	+	20.8107i	0.489914	+	0.897211i
$539$	−3.80758	+	4.39418i	−0.164004	+	0.189271i
$540$	1.47269	−	12.3447i	0.0633746	−	0.531232i
$541$	−6.27842	−	4.03489i	−0.269930	−	0.173474i	0.398673	−	0.917093i	$-0.369471\pi$
$541$	−6.27842	−	4.03489i	−0.269930	−	0.173474i	−0.668603	+	0.743620i	$0.733107\pi$
$542$	1.37457	+	19.2190i	0.0590429	+	0.825528i
$543$	16.8649	−	9.20895i	0.723743	−	0.395194i
$544$	1.01099	+	7.03162i	0.0433460	+	0.301478i
$545$	−12.7730	−	31.8810i	−0.547134	−	1.36563i
$546$	4.08726	−	1.86659i	0.174918	−	0.0798826i
$547$	−10.2789	+	18.8244i	−0.439494	+	0.804874i	−0.999725	−	0.0234631i	$-0.992531\pi$
$547$	−10.2789	+	18.8244i	−0.439494	+	0.804874i	0.560230	+	0.828337i	$0.310713\pi$
$548$	−0.519322	−	1.39236i	−0.0221843	−	0.0594785i
$549$	0.426971	−	2.96965i	0.0182227	−	0.126741i
$550$	4.92997	+	5.96447i	0.210215	+	0.254326i
$551$			5.11065i			0.217721i
$552$	−2.51219	+	5.49686i	−0.106926	+	0.233962i
$553$	−4.04274	−	4.04274i	−0.171915	−	0.171915i
$554$	5.55344	+	8.64132i	0.235943	+	0.367134i
$555$	3.53336	+	1.82039i	0.149983	+	0.0772714i
$556$	−4.67137	+	10.2289i	−0.198110	+	0.433801i
$557$	−13.0072	−	7.10247i	−0.551133	−	0.300941i	0.179448	−	0.983767i	$-0.442569\pi$
$557$	−13.0072	−	7.10247i	−0.551133	−	0.300941i	−0.730581	+	0.682826i	$0.760751\pi$
$558$	1.58196	−	4.24141i	0.0669699	−	0.179553i
$559$	−1.42144	−	1.64042i	−0.0601203	−	0.0693826i
$560$	3.33423	−	2.25795i	0.140897	−	0.0954159i
$561$	13.2938	+	3.90342i	0.561266	+	0.164803i
$562$	23.1461	−	1.65545i	0.976361	−	0.0698307i
$563$	−1.32213	+	0.287612i	−0.0557213	+	0.0121214i	−0.240339	−	0.970689i	$-0.577259\pi$
$563$	−1.32213	+	0.287612i	−0.0557213	+	0.0121214i	0.184618	+	0.982810i	$0.440895\pi$
$564$	−8.13387	+	12.6566i	−0.342498	+	0.532937i
$565$	4.15187	−	15.5113i	0.174670	−	0.652566i
$566$	7.58297	−	25.8252i	0.318736	−	1.08552i
$567$	−2.99041	+	3.99471i	−0.125585	+	0.167762i
$568$	−0.460905	+	6.44430i	−0.0193392	+	0.270397i
$569$	−12.1243	−	26.5484i	−0.508275	−	1.11297i	−0.973690	−	0.227875i	$-0.926822\pi$
$569$	−12.1243	−	26.5484i	−0.508275	−	1.11297i	0.465415	−	0.885093i	$-0.345905\pi$
$570$	−8.71327	−	0.412762i	−0.364959	−	0.0172887i
$571$	−27.0759	−	12.3652i	−1.13309	−	0.517466i	−0.241543	−	0.970390i	$-0.577653\pi$
$571$	−27.0759	−	12.3652i	−1.13309	−	0.517466i	−0.891549	+	0.452924i	$0.850381\pi$
$572$	−2.45301	+	1.83630i	−0.102565	+	0.0767795i
$573$	−2.15184	+	9.89185i	−0.0898944	+	0.413238i
$574$	12.5244			0.522759
$575$	−20.7695	−	11.9845i	−0.866149	−	0.499786i
$576$	1.41189			0.0588286
$577$	4.60860	−	21.1854i	0.191858	−	0.881959i	−0.776053	−	0.630667i	$-0.782781\pi$
$577$	4.60860	−	21.1854i	0.191858	−	0.881959i	0.967912	−	0.251291i	$-0.0808552\pi$
$578$	−26.7907	+	20.0553i	−1.11435	+	0.834190i
$579$	3.85710	+	1.76148i	0.160295	+	0.0732045i
$580$	−3.68750	−	0.174683i	−0.153115	−	0.00725333i
$581$	−8.94707	−	19.5913i	−0.371187	−	0.812786i
$582$	−1.00728	+	14.0836i	−0.0417531	+	0.583784i
$583$	−2.42235	+	3.23588i	−0.100323	+	0.134016i
$584$	4.13356	−	14.0776i	0.171048	−	0.582536i
$585$	−1.61622	+	6.03817i	−0.0668224	+	0.249648i
$586$	12.1666	−	18.9317i	0.502600	−	0.782060i
$587$	−21.3532	+	4.64510i	−0.881339	+	0.191724i	−0.630392	−	0.776277i	$-0.717106\pi$
$587$	−21.3532	+	4.64510i	−0.881339	+	0.191724i	−0.250947	+	0.968001i	$0.580742\pi$
$588$	4.72241	−	0.337753i	0.194749	−	0.0139287i
$589$	−9.52308	−	2.79623i	−0.392392	−	0.115217i
$590$	11.0118	−	7.45720i	0.453347	−	0.307008i
$591$	6.14356	+	7.09005i	0.252712	+	0.291646i
$592$	−0.492929	+	1.32159i	−0.0202593	+	0.0543172i
$593$	21.3800	+	11.6744i	0.877973	+	0.479410i	0.853982	−	0.520303i	$-0.174181\pi$
$593$	21.3800	+	11.6744i	0.877973	+	0.479410i	0.0239911	+	0.999712i	$0.492363\pi$
$594$	3.57451	−	7.82708i	0.146664	−	0.321149i
$595$	25.4298	+	13.1015i	1.04252	+	0.537109i
$596$	7.31118	+	11.3764i	0.299478	+	0.465996i
$597$	−2.62772	−	2.62772i	−0.107545	−	0.107545i
$598$	5.13580	−	7.98654i	0.210019	−	0.326594i
$599$		−	7.05450i		−	0.288239i	−0.989560	−	0.144120i	$-0.953965\pi$
$599$		−	7.05450i		−	0.288239i	0.989560	−	0.144120i	$-0.0460350\pi$
$600$	0.595643	−	6.27280i	0.0243170	−	0.256086i
$601$	−3.05396	+	21.2408i	−0.124574	+	0.866429i	0.827697	+	0.561175i	$0.189651\pi$
$601$	−3.05396	+	21.2408i	−0.124574	+	0.866429i	−0.952271	+	0.305254i	$0.901259\pi$
$602$	0.689945	+	1.84981i	0.0281200	+	0.0753928i
$603$	−6.41710	+	11.7520i	−0.261325	+	0.478580i
$604$	15.5533	−	7.10295i	0.632854	−	0.289015i
$605$	−7.15585	−	17.8608i	−0.290927	−	0.726145i
$606$	1.73293	+	12.0528i	0.0703955	+	0.489611i
$607$	−3.13124	+	1.70979i	−0.127093	+	0.0693982i	−0.541538	−	0.840676i	$-0.682158\pi$
$607$	−3.13124	+	1.70979i	−0.127093	+	0.0693982i	0.414445	+	0.910075i	$0.363976\pi$
$608$	−0.220836	−	3.08769i	−0.00895609	−	0.125223i
$609$	3.15196	+	2.02564i	0.127724	+	0.0820832i
$610$	0.562853	−	4.71807i	0.0227892	−	0.191029i
$611$	15.4790	−	17.8637i	0.626213	−	0.722689i
$612$	4.80684	+	8.80307i	0.194305	+	0.355843i
$613$	−14.7723	−	11.0584i	−0.596649	−	0.446646i	0.257787	−	0.966202i	$-0.417007\pi$
$613$	−14.7723	−	11.0584i	−0.596649	−	0.446646i	−0.854437	+	0.519556i	$0.826097\pi$
$614$	−9.45706	+	8.19459i	−0.381656	+	0.330707i
$615$	12.4736	−	15.1154i	0.502985	−	0.609512i
$616$	2.67418	−	0.785210i	0.107746	−	0.0316370i
$617$	−33.2367	+	12.3966i	−1.33806	+	0.499070i	−0.913687	−	0.406418i	$-0.866778\pi$
$617$	−33.2367	+	12.3966i	−1.33806	+	0.499070i	−0.424371	+	0.905488i	$0.639505\pi$
$618$	5.55608	+	7.42205i	0.223498	+	0.298559i
$619$	29.5824	−	19.0115i	1.18902	−	0.764135i	0.211995	−	0.977271i	$-0.432004\pi$
$619$	29.5824	−	19.0115i	1.18902	−	0.764135i	0.977023	+	0.213136i	$0.0683677\pi$
$620$	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
$623$	−33.1825	−	7.21842i	−1.32943	−	0.289200i
$624$	2.46970	+	0.355089i	0.0988670	+	0.0142149i
$625$	24.5532	+	4.70540i	0.982128	+	0.188216i
$626$	6.92409	+	23.5813i	0.276742	+	0.942497i
$627$	−5.65677	−	2.10986i	−0.225910	−	0.0842599i
$628$	0.750006	+	0.0536415i	0.0299285	+	0.00214053i
$629$	−9.91830	+	1.42604i	−0.395468	+	0.0568598i
$630$	3.29666	−	4.63210i	0.131342	−	0.184547i
$631$	13.1181	+	11.3669i	0.522223	+	0.452509i	0.875645	−	0.482955i	$-0.160437\pi$
$631$	13.1181	+	11.3669i	0.522223	+	0.452509i	−0.353422	+	0.935464i	$0.614982\pi$
$632$	−0.674844	−	3.10221i	−0.0268439	−	0.123399i
$633$	−0.677389	−	3.11391i	−0.0269238	−	0.123767i
$634$	−21.4398	−	18.5777i	−0.851483	−	0.737814i
$635$	−25.3754	+	4.27396i	−1.00699	+	0.169607i
$636$	3.25790	−	0.468415i	0.129184	−	0.0185738i
$637$	−7.41941	−	0.530646i	−0.293968	−	0.0210250i
$638$	−2.39397	−	0.892906i	−0.0947783	−	0.0353505i
$639$	2.56993	+	8.75237i	0.101665	+	0.346238i
$640$	2.23542	−	0.0538024i	0.0883628	−	0.00212673i
$641$	−1.40406	−	0.201873i	−0.0554570	−	0.00797351i	0.114530	−	0.993420i	$-0.463464\pi$
$641$	−1.40406	−	0.201873i	−0.0554570	−	0.00797351i	−0.169987	+	0.985446i	$0.554373\pi$
$642$	14.7221	+	3.20260i	0.581036	+	0.126397i
$643$	−26.7122	+	26.7122i	−1.05343	+	1.05343i	−0.0549368	+	0.998490i	$0.517496\pi$
$643$	−26.7122	+	26.7122i	−1.05343	+	1.05343i	−0.998490	+	0.0549368i	$0.982504\pi$
$644$	−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
$647$	9.30671	+	12.4323i	0.365885	+	0.488765i	0.945270	−	0.326289i	$-0.105798\pi$
$647$	9.30671	+	12.4323i	0.365885	+	0.488765i	−0.579385	+	0.815054i	$0.696707\pi$
$648$	−2.59620	+	0.968334i	−0.101989	+	0.0380398i
$649$	8.83184	−	2.59326i	0.346680	−	0.101794i
$650$	−2.32884	+	9.62174i	−0.0913446	+	0.377396i
$651$	−5.49910	+	4.76500i	−0.215527	+	0.186755i
$652$	−6.16170	−	4.61259i	−0.241311	−	0.180643i
$653$	−6.84276	−	12.5316i	−0.267778	−	0.490398i	0.708843	−	0.705366i	$-0.249217\pi$
$653$	−6.84276	−	12.5316i	−0.267778	−	0.490398i	−0.976621	+	0.214967i	$0.931035\pi$
$654$	−12.6754	+	14.6282i	−0.495648	+	0.572008i
$655$	−1.61784	−	2.05613i	−0.0632141	−	0.0803397i
$656$	5.85066	+	3.75999i	0.228430	+	0.146803i
$657$	−1.47780	−	20.6624i	−0.0576545	−	0.806115i
$658$	−18.8696	+	10.3036i	−0.735614	+	0.401676i
$659$	2.27007	+	15.7887i	0.0884292	+	0.615039i	0.985054	+	0.172247i	$0.0551027\pi$
$659$	2.27007	+	15.7887i	0.0884292	+	0.615039i	−0.896625	+	0.442792i	$0.853988\pi$
$660$	1.71569	−	4.00943i	0.0667830	−	0.156067i
$661$	−24.3237	+	11.1083i	−0.946083	+	0.432062i	−0.827866	−	0.560926i	$-0.810445\pi$
$661$	−24.3237	+	11.1083i	−0.946083	+	0.432062i	−0.118217	+	0.992988i	$0.537718\pi$
$662$	3.16890	−	5.80340i	0.123163	−	0.225556i
$663$	6.19424	+	16.6074i	0.240564	+	0.644978i
$664$	1.70204	−	11.8379i	0.0660519	−	0.459401i
$665$	−10.6457	−	6.48504i	−0.412822	−	0.251479i
$666$			1.99151i			0.0771693i
$667$	7.91768	+	0.00221992i	0.306574	+	8.59557e-5i
$668$	9.35793	+	9.35793i	0.362069	+	0.362069i
$669$	15.2233	+	23.6879i	0.588566	+	0.915826i
$670$	−9.71227	+	18.8514i	−0.375218	+	0.728292i
$671$	1.36615	−	2.99146i	0.0527397	−	0.115484i
$672$	−1.99185	−	1.08763i	−0.0768371	−	0.0419562i
$673$	3.40442	−	9.12761i	0.131231	−	0.351843i	−0.854671	−	0.519171i	$-0.826241\pi$
$673$	3.40442	−	9.12761i	0.131231	−	0.351843i	0.985901	+	0.167327i	$0.0535136\pi$
$674$	−3.80885	−	4.39565i	−0.146712	−	0.169314i
$675$	−7.20916	−	26.8483i	−0.277481	−	1.03339i
$676$	8.71214	+	2.55812i	0.335082	+	0.0983891i
$677$	39.3063	−	2.81124i	1.51066	−	0.108045i	0.708739	−	0.705471i	$-0.249264\pi$
$677$	39.3063	−	2.81124i	1.51066	−	0.108045i	0.801924	+	0.597426i	$0.203810\pi$
$678$	−8.84280	+	1.92363i	−0.339606	+	0.0738767i
$679$	−10.9086	+	16.9741i	−0.418634	+	0.651408i
$680$	7.94606	+	13.7546i	0.304717	+	0.527465i
$681$	8.68637	−	29.5831i	0.332862	−	1.13363i
$682$	2.97366	−	3.97234i	0.113867	−	0.152109i
$683$	2.20188	−	30.7863i	0.0842527	−	1.17801i	−0.762849	−	0.646576i	$-0.776200\pi$
$683$	2.20188	−	30.7863i	0.0842527	−	1.17801i	0.847102	−	0.531430i	$-0.178345\pi$
$684$	−1.81562	−	3.97565i	−0.0694219	−	0.152013i
$685$	−2.23584	−	2.45821i	−0.0854271	−	0.0939232i
$686$	17.6211	+	8.04728i	0.672776	+	0.307247i
$687$	−2.47224	+	1.85070i	−0.0943219	+	0.0706085i
$688$	−0.233037	+	1.07125i	−0.00888445	+	0.0408411i
$689$	−5.17113			−0.197004
$690$	−0.643257	+	13.4989i	−0.0244884	+	0.513893i
$691$	13.7887			0.524548			0.262274	−	0.964993i	$-0.415528\pi$
$691$	13.7887			0.524548			0.262274	+	0.964993i	$0.415528\pi$
$692$	−4.07860	+	18.7490i	−0.155045	+	0.712731i
$693$	3.15016	−	2.35818i	0.119665	−	0.0895798i
$694$	18.5121	+	8.45419i	0.702710	+	0.320917i
$695$	−1.18982	+	25.1166i	−0.0451323	+	0.952726i
$696$	0.864285	+	1.89252i	0.0327606	+	0.0717358i
$697$	−3.52456	+	49.2797i	−0.133502	+	1.86660i
$698$	−2.13240	+	2.84855i	−0.0807126	+	0.107819i
$699$	−9.05745	+	30.8468i	−0.342584	+	1.16673i
$700$	5.04304	−	7.45955i	0.190609	−	0.281945i
$701$	−19.6326	+	30.5490i	−0.741514	+	1.15382i	0.241520	+	0.970396i	$0.422354\pi$
$701$	−19.6326	+	30.5490i	−0.741514	+	1.15382i	−0.983034	+	0.183423i	$0.941282\pi$
$702$	10.7565	−	2.33993i	0.405978	−	0.0883151i
$703$	4.35528	−	0.311496i	0.164262	−	0.0117483i
$704$	1.48495	+	0.436020i	0.0559660	+	0.0164331i
$705$	−6.35796	+	33.0351i	−0.239455	+	1.24417i
$706$	6.16680	+	7.11687i	0.232091	+	0.267847i
$707$	−6.08096	+	16.3037i	−0.228698	+	0.613164i
$708$	−6.57834	−	3.59205i	−0.247229	−	0.134997i
$709$	0.0431597	−	0.0945066i	0.00162090	−	0.00354927i	−0.908820	−	0.417189i	$-0.863015\pi$
$709$	0.0431597	−	0.0945066i	0.00162090	−	0.00354927i	0.910441	+	0.413640i	$0.135743\pi$
$710$	4.40245	+	13.7596i	0.165221	+	0.516387i
$711$	−2.42337	−	3.77084i	−0.0908836	−	0.141418i
$712$	−13.3338	−	13.3338i	−0.499707	−	0.499707i
$713$	−4.33620	+	14.7524i	−0.162392	+	0.552483i
$714$		−	16.1220i		−	0.603350i
$715$	−3.56456	+	5.85150i	−0.133307	+	0.218834i
$716$	1.22085	−	8.49122i	0.0456254	−	0.317332i
$717$	9.90299	+	26.5509i	0.369834	+	0.991563i
$718$	10.8892	−	19.9421i	0.406381	−	0.744231i
$719$	25.5689	−	11.6769i	0.953560	−	0.435476i	0.123001	−	0.992407i	$-0.460748\pi$
$719$	25.5689	−	11.6769i	0.953560	−	0.435476i	0.830559	+	0.556930i	$0.188021\pi$
$720$	2.93062	−	1.17414i	0.109218	−	0.0437576i
$721$	1.88551	+	13.1140i	0.0702202	+	0.488392i
$722$	8.26544	−	4.51327i	0.307608	−	0.167966i
$723$	−0.0746179	−	1.04329i	−0.00277507	−	0.0388005i
$724$	12.8273	+	8.24360i	0.476723	+	0.306371i
$725$	−7.79932	+	2.70398i	−0.289660	+	0.100423i
$726$	−7.10119	+	8.19521i	−0.263550	+	0.304153i
$727$	−6.20823	−	11.3695i	−0.230251	−	0.421672i	0.736854	−	0.676052i	$-0.236311\pi$
$727$	−6.20823	−	11.3695i	−0.230251	−	0.421672i	−0.967104	+	0.254380i	$0.918129\pi$
$728$	2.85436	+	2.13675i	0.105790	+	0.0791932i
$729$	−18.8423	+	16.3269i	−0.697863	+	0.604702i
$730$	−3.12716	−	32.6581i	−0.115741	−	1.20873i
$731$	−7.47261	+	2.19416i	−0.276385	+	0.0811538i
$732$	−2.50902	+	0.935817i	−0.0927362	+	0.0345888i
$733$	−2.80116	−	3.74191i	−0.103463	−	0.138210i	0.745821	−	0.666146i	$-0.232057\pi$
$733$	−2.80116	−	3.74191i	−0.103463	−	0.138210i	−0.849285	+	0.527935i	$0.822966\pi$
$734$	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
$738$	9.59484	+	2.08723i	0.353191	+	0.0768320i
$739$	−30.5018	−	4.38550i	−1.12203	−	0.161323i	−0.443766	−	0.896143i	$-0.646358\pi$
$739$	−30.5018	−	4.38550i	−1.12203	−	0.161323i	−0.678263	+	0.734820i	$0.737267\pi$
$740$	0.0758898	+	3.15312i	0.00278977	+	0.115911i
$741$	−2.17604	−	7.41090i	−0.0799386	−	0.272246i
$742$	4.40692	+	1.64370i	0.161783	+	0.0603420i
$743$	20.8494	+	1.49118i	0.764889	+	0.0547060i	0.448332	−	0.893867i	$-0.352018\pi$
$743$	20.8494	+	1.49118i	0.764889	+	0.0547060i	0.316558	+	0.948573i	$0.397473\pi$
$744$	−3.99937	+	0.575022i	−0.146624	+	0.0210813i
$745$	24.6364	+	17.5337i	0.902607	+	0.642385i
$746$	−8.65140	−	7.49648i	−0.316750	−	0.274466i
$747$	−3.58931	−	16.4998i	−0.131326	−	0.603697i
$748$	2.33701	+	10.7430i	0.0854494	+	0.392805i
$749$	16.2715	+	14.0993i	0.594547	+	0.515178i
$750$	−3.98016	−	13.5156i	−0.145335	−	0.493521i
$751$	−29.4548	+	4.23497i	−1.07482	+	0.154536i	−0.656923	−	0.753957i	$-0.728142\pi$
$751$	−29.4548	+	4.23497i	−1.07482	+	0.154536i	−0.417899	+	0.908494i	$0.637233\pi$
$752$	−11.9080	−	0.851679i	−0.434241	−	0.0310576i
$753$	1.33543	+	0.498090i	0.0486658	+	0.0181514i
$754$	−0.920910	−	3.13633i	−0.0335376	−	0.114218i
$755$	26.3767	−	27.6777i	0.959946	−	1.00729i
$756$	−9.91063	−	1.42493i	−0.360446	−	0.0518243i
$757$	2.05306	+	0.446616i	0.0746198	+	0.0162325i	0.249720	−	0.968318i	$-0.419661\pi$
$757$	2.05306	+	0.446616i	0.0746198	+	0.0162325i	−0.175100	+	0.984551i	$0.556025\pi$
$758$	−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	0.0754846	−	0.997147i	$-0.475950\pi$
$761$	27.9691	−	17.9746i	1.01388	−	0.651580i	0.938394	+	0.345567i	$0.112313\pi$
$762$	8.69103	+	11.6099i	0.314843	+	0.420581i
$763$	−25.9160	+	9.66618i	−0.938223	+	0.349939i
$764$	−7.70759	+	2.26315i	−0.278851	+	0.0818780i
$765$	17.2982	+	14.2749i	0.625416	+	0.516110i
$766$	16.3689	−	14.1838i	0.591434	−	0.512480i
$767$	9.42693	+	7.05691i	0.340387	+	0.254810i
$768$	−0.603951	−	1.10605i	−0.0217932	−	0.0399113i
$769$	−6.65520	+	7.68051i	−0.239993	+	0.276966i	−0.862950	−	0.505290i	$-0.831386\pi$
$769$	−6.65520	+	7.68051i	−0.239993	+	0.276966i	0.622957	+	0.782256i	$0.285931\pi$
$770$	4.89774	−	3.85371i	0.176502	−	0.138878i
$771$	−8.99999	−	5.78394i	−0.324127	−	0.208304i
$772$	0.240039	+	3.35619i	0.00863920	+	0.120792i
$773$	13.8662	−	7.57154i	0.498734	−	0.272329i	−0.210132	−	0.977673i	$-0.567389\pi$
$773$	13.8662	−	7.57154i	0.498734	−	0.272329i	0.708865	+	0.705344i	$0.249207\pi$
$774$	0.220284	+	1.53211i	0.00791794	+	0.0550705i
$775$	−0.771232	−	16.0126i	−0.0277035	−	0.575188i
$776$	−10.1917	+	4.65440i	−0.365861	+	0.167083i
$777$	1.53413	−	2.80955i	0.0550367	−	0.100792i
$778$	11.7329	+	31.4572i	0.420646	+	1.12780i
$779$	3.06387	−	21.3097i	0.109774	−	0.763498i
$780$	5.42158	−	1.31677i	0.194124	−	0.0471481i
$781$			9.99891i			0.357789i
$782$	−18.4112	−	28.6660i	−0.658383	−	1.02510i
$783$	6.49059	+	6.49059i	0.231955	+	0.231955i
$784$	2.03114	+	3.16052i	0.0725407	+	0.112876i
$785$	1.60138	−	0.512370i	0.0571556	−	0.0182873i
$786$	−0.612529	+	1.34125i	−0.0218482	+	0.0478409i
$787$	0.861807	+	0.470582i	0.0307201	+	0.0167745i	0.494536	−	0.869157i	$-0.335338\pi$
$787$	0.861807	+	0.470582i	0.0307201	+	0.0167745i	−0.463816	+	0.885932i	$0.653520\pi$
$788$	−2.60156	+	6.97505i	−0.0926767	+	0.248476i
$789$	−16.7390	−	19.3179i	−0.595925	−	0.687735i
$790$	−3.98059	−	5.87797i	−0.141623	−	0.209129i
$791$	−12.4083	−	3.64339i	−0.441187	−	0.129544i
$792$	2.17952	−	0.155883i	0.0774460	−	0.00553904i
$793$	4.11106	−	0.894306i	0.145988	−	0.0317577i
$794$	−10.0184	+	15.5890i	−0.355541	+	0.553232i
$795$	6.37279	−	3.68157i	0.226020	−	0.130572i
$796$	0.830788	−	2.82940i	0.0294465	−	0.100286i
$797$	30.2668	−	40.4317i	1.07211	−	1.43216i	0.178153	−	0.984003i	$-0.442988\pi$
$797$	30.2668	−	40.4317i	1.07211	−	1.43216i	0.893952	−	0.448162i	$-0.147921\pi$
$798$	−0.501176	+	7.00736i	−0.0177414	+	0.248058i
$799$	−35.2313	−	77.1458i	−1.24639	−	2.72922i
$800$	4.59526	−	1.97067i	0.162467	−	0.0696738i
$801$	−24.2179	−	11.0599i	−0.855697	−	0.390784i
$802$	8.77949	−	6.57224i	0.310014	−	0.232074i
$803$	4.82669	−	22.1879i	0.170330	−	0.782995i
$804$	11.9514			0.421493
$805$	−10.0516	+	16.4900i	−0.354272	+	0.581197i
$806$	6.34804			0.223600
$807$	6.35160	−	29.1978i	0.223587	−	1.02781i
$808$	−7.73524	+	5.79053i	−0.272125	+	0.203710i
$809$	32.1604	+	14.6872i	1.13070	+	0.516373i	0.890787	−	0.454422i	$-0.150154\pi$
$809$	32.1604	+	14.6872i	1.13070	+	0.516373i	0.239912	+	0.970795i	$0.422881\pi$
$810$	−4.58360	+	4.16898i	−0.161051	+	0.146483i
$811$	−2.76469	−	6.05382i	−0.0970813	−	0.212578i	0.854860	−	0.518859i	$-0.173643\pi$
$811$	−2.76469	−	6.05382i	−0.0970813	−	0.212578i	−0.951941	+	0.306280i	$0.900916\pi$
$812$	−0.212100	+	2.96555i	−0.00744326	+	0.104070i
$813$	14.5515	−	19.4385i	0.510344	−	0.681739i
$814$	−0.615018	+	2.09456i	−0.0215564	+	0.0734143i
$815$	−16.6256	−	4.45011i	−0.582368	−	0.155881i
$816$	4.84003	−	7.53123i	0.169435	−	0.263646i
$817$	3.31615	−	0.721384i	0.116017	−	0.0252380i
$818$	10.9677	−	0.784427i	0.383478	−	0.0274269i
$819$	4.83022	+	1.41828i	0.168782	+	0.0495588i
$820$	15.2709	+	2.93905i	0.533283	+	0.102636i
$821$	−4.70385	−	5.42853i	−0.164166	−	0.189457i	0.667706	−	0.744425i	$-0.267276\pi$
$821$	−4.70385	−	5.42853i	−0.164166	−	0.189457i	−0.831872	+	0.554968i	$0.812731\pi$
$822$	−0.654452	+	1.75465i	−0.0228266	+	0.0612005i
$823$	14.4801	+	7.90673i	0.504744	+	0.275611i	0.711381	−	0.702806i	$-0.248070\pi$
$823$	14.4801	+	7.90673i	0.504744	+	0.275611i	−0.206637	+	0.978418i	$0.566252\pi$
$824$	−3.05620	+	6.69215i	−0.106468	+	0.233132i
$825$	0.226929	−	9.74905i	0.00790065	−	0.339418i
$826$	−5.79067	−	9.01045i	−0.201483	−	0.313514i
$827$	−38.1482	−	38.1482i	−1.32654	−	1.32654i	−0.908365	−	0.418178i	$-0.862669\pi$
$827$	−38.1482	−	38.1482i	−1.32654	−	1.32654i	−0.418178	−	0.908365i	$-0.637331\pi$
$828$	−6.16007	+	2.81112i	−0.214077	+	0.0976932i
$829$		−	13.6934i		−	0.475593i	−0.971315	−	0.237797i	$-0.923575\pi$
$829$		−	13.6934i		−	0.475593i	0.971315	−	0.237797i	$-0.0764252\pi$
$830$	−6.31166	−	25.9871i	−0.219081	−	0.902026i
$831$	1.84223	−	12.8130i	0.0639063	−	0.444478i
$832$	0.691909	+	1.85508i	0.0239876	+	0.0643133i
$833$	−12.7906	+	23.4242i	−0.443168	+	0.811601i
$834$	12.8905	−	5.88688i	0.446360	−	0.203846i
$835$	27.2062	+	11.6419i	0.941508	+	0.402884i
$836$	−0.681807	−	4.74207i	−0.0235808	−	0.164008i
$837$	−15.6457	+	8.54319i	−0.540794	+	0.295296i
$838$	−2.58851	−	36.1921i	−0.0894186	−	1.25024i
$839$	−33.1961	−	21.3338i	−1.14606	−	0.736525i	−0.177206	−	0.984174i	$-0.556706\pi$
$839$	−33.1961	−	21.3338i	−1.14606	−	0.736525i	−0.968850	+	0.247648i	$0.920342\pi$
$840$	−5.03891	−	0.601128i	−0.173859	−	0.0207409i
$841$	−17.2060	+	19.8568i	−0.593312	+	0.684719i
$842$	5.77788	+	10.5814i	0.199119	+	0.364659i
$843$	−23.4105	−	17.5249i	−0.806301	−	0.603589i
$844$	1.91110	−	1.65598i	0.0657827	−	0.0570011i
$845$	20.2109	−	1.93529i	0.695277	−	0.0665758i
$846$	−16.1730	+	4.74881i	−0.556038	+	0.163268i
$847$	−14.5190	+	5.41532i	−0.498880	+	0.186072i
$848$	1.56519	+	2.09085i	0.0537489	+	0.0718002i
$849$	−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
$853$	22.1451	+	4.81737i	0.758234	+	0.164944i	0.575031	−	0.818131i	$-0.304990\pi$
$853$	22.1451	+	4.81737i	0.758234	+	0.164944i	0.183203	+	0.983075i	$0.441354\pi$
$854$	−3.78777	−	0.544600i	−0.129615	−	0.0186358i
$855$	−7.07482	−	6.74227i	−0.241954	−	0.230581i
$856$	3.36827	+	11.4713i	0.115125	+	0.392080i
$857$	32.1708	+	11.9991i	1.09893	+	0.409881i	0.832530	−	0.553981i	$-0.186892\pi$
$857$	32.1708	+	11.9991i	1.09893	+	0.409881i	0.266404	+	0.963862i	$0.414165\pi$
$858$	3.85166	+	0.275476i	0.131494	+	0.00940460i
$859$	38.6395	−	5.55552i	1.31836	−	0.189552i	0.553016	−	0.833171i	$-0.313477\pi$
$859$	38.6395	−	5.55552i	1.31836	−	0.189552i	0.765346	+	0.643619i	$0.222568\pi$
$860$	0.407156	+	2.41737i	0.0138839	+	0.0824316i
$861$	−11.9282	−	10.3359i	−0.406513	−	0.352245i
$862$	−1.29862	−	5.96965i	−0.0442311	−	0.203327i
$863$	0.447827	+	2.05863i	0.0152442	+	0.0700765i	0.984141	−	0.177390i	$-0.0567655\pi$
$863$	0.447827	+	2.05863i	0.0152442	+	0.0700765i	−0.968896	+	0.247467i	$0.920402\pi$
$864$	−4.20187	−	3.64094i	−0.142951	−	0.123867i
$865$	7.12602	+	42.3087i	0.242292	+	1.43854i
$866$	−14.6866	+	2.11161i	−0.499071	+	0.0717555i
$867$	42.0662	+	3.00864i	1.42864	+	0.102179i
$868$	−5.40990	−	2.01779i	−0.183624	−	0.0684882i
$869$	−1.38426	−	4.71436i	−0.0469578	−	0.159924i
$870$	3.36781	+	3.20951i	0.114179	+	0.108812i
$871$	−18.5858	−	2.67223i	−0.629755	−	0.0905451i
$872$	−15.0083	−	3.26486i	−0.508246	−	0.110562i
$873$	−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
$877$	−17.3540	−	23.1822i	−0.586003	−	0.782808i	0.405332	−	0.914170i	$-0.367156\pi$
$877$	−17.3540	−	23.1822i	−0.586003	−	0.782808i	−0.991335	+	0.131361i	$0.958065\pi$
$878$	24.0220	−	8.95976i	0.810704	−	0.302377i
$879$	−27.2110	+	7.98987i	−0.917804	+	0.269492i
$880$	3.44487	−	0.329861i	0.116126	−	0.0111196i
$881$	26.7636	−	23.1908i	0.901689	−	0.781318i	−0.0747292	−	0.997204i	$-0.523809\pi$
$881$	26.7636	−	23.1908i	0.901689	−	0.781318i	0.976419	+	0.215885i	$0.0692638\pi$
$882$	4.24634	+	3.17877i	0.142982	+	0.107035i
$883$	2.48669	+	4.55404i	0.0836839	+	0.153256i	0.916169	−	0.400791i	$-0.131265\pi$
$883$	2.48669	+	4.55404i	0.0836839	+	0.153256i	−0.832486	+	0.554047i	$0.813083\pi$
$884$	−9.21072	+	10.6297i	−0.309790	+	0.357517i
$885$	−16.6417	−	1.98531i	−0.559404	−	0.0667354i
$886$	9.53020	+	6.12469i	0.320173	+	0.205763i
$887$	2.39409	+	33.4738i	0.0803857	+	1.12394i	0.864269	+	0.503030i	$0.167782\pi$
$887$	2.39409	+	33.4738i	0.0803857	+	1.12394i	−0.783883	+	0.620908i	$0.786764\pi$
$888$	1.56012	−	0.851890i	0.0523542	−	0.0285876i
$889$	2.94939	+	20.5134i	0.0989193	+	0.687999i
$890$	−38.7653	−	16.5882i	−1.29942	−	0.556037i
$891$	−3.90083	+	1.78145i	−0.130683	+	0.0596809i
$892$	−10.7083	+	19.6108i	−0.358540	+	0.656617i
$893$	12.9150	+	34.6263i	0.432182	+	1.15873i
$894$	2.42532	−	16.8685i	0.0811149	−	0.564167i
$895$	−4.52729	−	18.6403i	−0.151330	−	0.623076i
$896$		−	1.80086i		−	0.0601624i
$897$	−11.4823	+	3.36801i	−0.383382	+	0.112454i
$898$	−23.0736	−	23.0736i	−0.769975	−	0.769975i
$899$	2.86178	+	4.45302i	0.0954457	+	0.148516i
$900$	5.10659	−	4.87426i	0.170220	−	0.162475i
$901$	−7.70762	+	16.8773i	−0.256778	+	0.562266i
$902$	9.44675	+	5.15832i	0.314542	+	0.171753i
$903$	0.869471	−	2.33114i	0.0289342	−	0.0775755i
$904$	−4.70260	−	5.42709i	−0.156406	−	0.180502i
$905$	33.4807	+	6.44373i	1.11294	+	0.214197i
$906$	−20.6747	−	6.07064i	−0.686870	−	0.201683i
$907$	6.30563	−	0.450987i	0.209375	−	0.0149748i	0.0337423	−	0.999431i	$-0.489257\pi$
$907$	6.30563	−	0.450987i	0.209375	−	0.0149748i	0.175633	+	0.984456i	$0.443803\pi$
$908$	23.9068	−	5.20060i	0.793373	−	0.172588i
$909$	−7.37563	+	11.4767i	−0.244634	+	0.380658i
$910$	7.70167	+	2.06148i	0.255308	+	0.0683374i
$911$	6.80444	−	23.1738i	0.225441	−	0.767782i	−0.766628	−	0.642091i	$-0.778067\pi$
$911$	6.80444	−	23.1738i	0.225441	−	0.767782i	0.992069	−	0.125691i	$-0.0401148\pi$
$912$	−2.33782	+	3.12296i	−0.0774129	+	0.103412i
$913$	1.32043	−	18.4621i	0.0437000	−	0.611005i
$914$	−11.5047	−	25.1918i	−0.380541	−	0.833269i
$915$	−4.42968	+	4.02898i	−0.146441	+	0.133194i
$916$	−2.22911	−	1.01800i	−0.0736520	−	0.0336358i
$917$	−1.68681	+	1.26273i	−0.0557035	+	0.0416991i
$918$	8.39568	−	38.5943i	0.277099	−	1.27380i
$919$	34.9536			1.15301			0.576507	−	0.817092i	$-0.304415\pi$
$919$	34.9536			1.15301			0.576507	+	0.817092i	$0.304415\pi$
$920$	−9.64602	+	4.68555i	−0.318020	+	0.154478i
$921$	15.7695			0.519624
$922$	1.61754	−	7.43570i	0.0532708	−	0.244882i
$923$	−10.2403	+	7.66580i	−0.337064	+	0.252323i
$924$	−3.19488	−	1.45905i	−0.105104	−	0.0479994i
$925$	2.77969	+	6.48175i	0.0913957	+	0.213119i
$926$	−8.06448	−	17.6587i	−0.265015	−	0.580302i
$927$	−0.741017	+	10.3608i	−0.0243382	+	0.340292i
$928$	−0.989377	+	1.32165i	−0.0324779	+	0.0433854i
$929$	−0.620212	+	2.11225i	−0.0203485	+	0.0693006i	−0.969041	−	0.246898i	$-0.920589\pi$
$929$	−0.620212	+	2.11225i	−0.0203485	+	0.0693006i	0.948693	+	0.316199i	$0.102407\pi$
$930$	−7.82319	+	4.51947i	−0.256532	+	0.148199i
$931$	6.28756	−	9.78363i	0.206066	−	0.320646i
$932$	−24.9280	+	5.42276i	−0.816545	+	0.177628i
$933$	39.3412	−	2.81374i	1.28797	−	0.0921177i
$934$	37.4809	+	11.0054i	1.22641	+	0.360108i
$935$	13.7849	+	20.3556i	0.450814	+	0.665699i
$936$	1.83061	+	2.11263i	0.0598353	+	0.0690536i
$937$	−11.9264	+	31.9759i	−0.389618	+	1.04461i	0.583056	+	0.812432i	$0.301857\pi$
$937$	−11.9264	+	31.9759i	−0.389618	+	1.04461i	−0.972674	+	0.232175i	$0.925416\pi$
$938$	14.9897	+	8.18499i	0.489431	+	0.267250i
$939$	12.8661	−	28.1729i	0.419871	−	0.919388i
$940$	−25.4255	+	8.13503i	−0.829287	+	0.265335i
$941$	−27.9247	−	43.4517i	−0.910319	−	1.41648i	−0.909143	−	0.416484i	$-0.863262\pi$
$941$	−27.9247	−	43.4517i	−0.910319	−	1.41648i	−0.00117561	−	0.999999i	$-0.500374\pi$
$942$	−0.670036	−	0.670036i	−0.0218310	−	0.0218310i
$943$	−33.0127	−	4.75596i	−1.07504	−	0.154875i
$944$		−	5.94758i		−	0.193577i
$945$	−21.7562	+	5.28408i	−0.707730	+	0.171891i
$946$	−0.241464	+	1.67942i	−0.00785066	+	0.0546025i
$947$	−3.71520	−	9.96084i	−0.120728	−	0.323684i	0.862502	−	0.506053i	$-0.168896\pi$
$947$	−3.71520	−	9.96084i	−0.120728	−	0.323684i	−0.983230	+	0.182369i	$0.941623\pi$
$948$	−1.91740	+	3.51146i	−0.0622743	+	0.114047i
$949$	26.4241	−	12.0675i	0.857761	−	0.391726i
$950$	−11.4584	−	10.4053i	−0.371759	−	0.337594i
$951$	5.08784	+	35.3867i	0.164985	+	1.14749i
$952$	11.2283	−	6.13111i	0.363911	−	0.198710i
$953$	−0.976247	−	13.6497i	−0.0316237	−	0.442157i	−0.988455	−	0.151514i	$-0.951585\pi$
$953$	−0.976247	−	13.6497i	−0.0316237	−	0.442157i	0.956831	−	0.290644i	$-0.0938694\pi$
$954$	3.10218	+	1.99365i	0.100437	+	0.0645468i
$955$	−14.1164	+	11.1073i	−0.456796	+	0.359423i
$956$	−14.7256	+	16.9942i	−0.476259	+	0.549632i
$957$	1.54314	+	2.82605i	0.0498826	+	0.0913531i
$958$	−0.118209	−	0.0884898i	−0.00381915	−	0.00285898i
$959$	−2.02251	+	1.75252i	−0.0653104	+	0.0565918i
$960$	−2.17341	−	1.79356i	−0.0701465	−	0.0578868i
$961$	19.8808	−	5.83754i	0.641317	−	0.188308i
$962$	−2.61664	+	0.975957i	−0.0843639	+	0.0314661i
$963$	10.1158	+	13.5131i	0.325976	+	0.435452i
$964$	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	$0.287047\pi$
$968$	−8.40817	−	1.82909i	−0.270249	−	0.0587890i
$969$	−27.4308	−	3.94395i	−0.881204	−	0.126698i
$970$	−17.2840	+	18.1365i	−0.554957	+	0.582329i
$971$	−7.27820	−	24.7873i	−0.233568	−	0.795461i	−0.989961	−	0.141343i	$-0.954858\pi$
$971$	−7.27820	−	24.7873i	−0.233568	−	0.795461i	0.756392	−	0.654118i	$-0.226960\pi$
$972$	−12.3562	−	4.60863i	−0.396326	−	0.147822i
$973$	20.1992	+	1.44467i	0.647556	+	0.0463141i
$974$	−22.8607	+	3.28688i	−0.732505	+	0.105318i
$975$	10.1584	−	7.24183i	0.325329	−	0.231924i
$976$	−1.60593	−	1.39154i	−0.0514045	−	0.0445422i
$977$	−8.50939	−	39.1170i	−0.272240	−	1.25147i	−0.886636	−	0.462468i	$-0.846964\pi$
$977$	−8.50939	−	39.1170i	−0.272240	−	1.25147i	0.614396	−	0.788997i	$-0.289400\pi$
$978$	2.06182	+	9.47802i	0.0659296	+	0.303074i
$979$	−22.0555	−	19.1112i	−0.704898	−	0.610797i
$980$	6.84430	+	4.87109i	0.218633	+	0.155601i
$981$	−21.4649	+	3.08619i	−0.685323	+	0.0985345i
$982$	29.0305	+	2.07631i	0.926402	+	0.0662576i
$983$	−11.6658	−	4.35112i	−0.372082	−	0.138779i	0.156465	−	0.987684i	$-0.449990\pi$
$983$	−11.6658	−	4.35112i	−0.372082	−	0.138779i	−0.528547	+	0.848904i	$0.677263\pi$
$984$	−2.46919	−	8.40931i	−0.0787151	−	0.268079i
$985$	0.400528	+	16.6414i	0.0127619	+	0.530239i
$986$	−11.6089	−	1.66910i	−0.369701	−	0.0531550i
$987$	26.4745	+	5.75918i	0.842693	+	0.183317i
$988$	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	−0.514732	−	0.857351i	$-0.672108\pi$
$991$	1.61540	−	1.03816i	0.0513150	−	0.0329782i	0.566047	+	0.824373i	$0.308472\pi$
$992$	−1.92142	−	2.56671i	−0.0610051	−	0.0814932i
$993$	−7.80735	+	2.91199i	−0.247759	+	0.0924093i
$994$	11.1636	−	3.27793i	0.354088	−	0.103970i
$995$	−0.628514	−	6.56381i	−0.0199252	−	0.208087i
$996$	−11.3904	+	9.86981i	−0.360917	+	0.312737i
$997$	49.8269	+	37.3000i	1.57804	+	1.18130i	0.890334	+	0.455309i	$0.150471\pi$
$997$	49.8269	+	37.3000i	1.57804	+	1.18130i	0.687702	+	0.725993i	$0.258620\pi$
$998$	18.2038	+	33.3377i	0.576230	+	1.05529i
$999$	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.103.8	yes	240
5.2	odd	4	inner	230.2.l.a.57.11	✓	240
23.21	odd	22	inner	230.2.l.a.113.11	yes	240
115.67	even	44	inner	230.2.l.a.67.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.11	✓	240	5.2	odd	4	inner
230.2.l.a.67.8	yes	240	115.67	even	44	inner
230.2.l.a.103.8	yes	240	1.1	even	1	trivial
230.2.l.a.113.11	yes	240	23.21	odd	22	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 $\F_{q}$
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+(0.212565 - 0.977147i) q^{2} +(-1.00884 + 0.755212i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.23356 - 0.105808i) q^{5} +(0.523507 + 1.14632i) q^{6} +(-0.128472 + 1.79627i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(-0.397775 + 1.35470i) q^{9} +(-0.578168 + 2.16003i) q^{10} +(-0.836716 + 1.30196i) q^{11} +(1.23140 - 0.267875i) q^{12} +(-1.97487 + 0.141245i) q^{13} +(1.72791 + 0.507360i) q^{14} +(2.33323 - 1.58007i) q^{15} +(0.654861 + 0.755750i) q^{16} +(-2.48257 + 6.65602i) q^{17} +(1.23918 + 0.676646i) q^{18} +(1.28595 - 2.81584i) q^{19} +(1.98777 + 1.02410i) q^{20} +(-1.22696 - 1.90918i) q^{21} +(1.09434 + 1.09434i) q^{22} +(-4.36188 - 1.99348i) q^{23} -1.26020i q^{24} +(4.97761 + 0.472657i) q^{25} +(-0.281771 + 1.95976i) q^{26} +(-1.94298 - 5.20932i) q^{27} +(0.863059 - 1.58057i) q^{28} +(-1.50176 + 0.685829i) q^{29} +(-1.04800 - 2.61577i) q^{30} +(-0.456293 - 3.17359i) q^{31} +(0.877679 - 0.479249i) q^{32} +(-0.139135 - 1.94537i) q^{33} +(5.97620 + 3.84067i) q^{34} +(0.477009 - 3.99849i) q^{35} +(0.924590 - 1.06703i) q^{36} +(0.675994 + 1.23799i) q^{37} +(-2.47814 - 1.85511i) q^{38} +(1.88567 - 1.63394i) q^{39} +(1.42323 - 1.72465i) q^{40} +(6.67297 - 1.95936i) q^{41} +(-2.12636 + 0.793090i) q^{42} +(0.656992 + 0.877639i) 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} +(-1.23140 - 0.267875i) q^{48} +(3.71867 + 0.534664i) q^{49} +(1.51992 - 4.76339i) q^{50} +(-2.52218 - 8.58976i) q^{51} +(1.85508 + 0.691909i) q^{52} +(2.60514 + 0.186324i) q^{53} +(-5.50328 + 0.791253i) q^{54} +(2.00661 - 2.81947i) q^{55} +(-1.36100 - 1.17931i) q^{56} +(0.829230 + 3.81191i) q^{57} +(0.350935 + 1.61322i) q^{58} +(-4.49488 - 3.89484i) q^{59} +(-2.77876 + 0.468025i) q^{60} +(-2.10332 + 0.302411i) q^{61} +(-3.19805 - 0.228729i) q^{62} +(-2.38230 - 0.888551i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(4.42594 - 0.106524i) q^{65} +(-1.93049 - 0.277562i) q^{66} +(9.26697 + 2.01591i) 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} +(-0.846113 - 1.13027i) q^{72} +(-13.7469 + 5.12732i) q^{73} +(1.35339 - 0.397392i) q^{74} +(-5.37859 + 3.28231i) q^{75} +(-2.33948 + 2.02717i) q^{76} +(-2.23117 - 1.67023i) q^{77} +(-1.19577 - 2.18989i) q^{78} +(-2.07903 + 2.39933i) q^{79} +(-1.38271 - 1.75730i) q^{80} +(2.33104 + 1.49807i) q^{81} +(-0.496142 - 6.93697i) q^{82} +(-10.4967 + 5.73166i) q^{83} +(0.322976 + 2.24635i) q^{84} +(6.24923 - 14.6040i) q^{85} +(0.997236 - 0.455422i) q^{86} +(0.997093 - 1.82604i) q^{87} +(-0.540844 - 1.45006i) q^{88} +(-2.68362 + 18.6650i) q^{89} +(-2.69620 - 1.64245i) q^{90} -3.56554i q^{91} +(3.13959 + 3.62533i) q^{92} +(2.85706 + 2.85706i) q^{93} +(6.45441 + 10.0433i) q^{94} +(-3.17019 + 6.15329i) q^{95} +(-0.523507 + 1.14632i) q^{96} +(9.83370 + 5.36961i) q^{97} +(1.31291 - 3.52004i) 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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