LMFDB - Embedded newform 756.2.cf.a.659.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.39
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.598460 + 1.28135i) q^{2} +(1.71844 + 0.216716i) q^{3} +(-1.28369 - 1.53367i) q^{4} +(0.0372347 - 0.102301i) q^{5} +(-1.30611 + 2.07222i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.73340 - 0.727012i) q^{8} +(2.90607 + 0.744826i) q^{9} +(0.108800 + 0.108934i) q^{10} +(-1.44739 + 0.526808i) q^{11} +(-1.87358 - 2.91371i) q^{12} +(-3.59352 + 3.01532i) q^{13} +(-0.811871 + 1.15796i) q^{14} +(0.0861559 - 0.167730i) q^{15} +(-0.704275 + 3.93751i) q^{16} +(1.89301 - 1.09293i) q^{17} +(-2.69355 + 3.27793i) q^{18} +(5.71979 + 3.30232i) q^{19} +(-0.204694 + 0.0742178i) q^{20} +(1.65470 + 0.511827i) q^{21} +(0.191184 - 2.16988i) q^{22} +(-0.158950 - 0.901452i) q^{23} +(4.85473 - 0.656956i) q^{24} +(3.82114 + 3.20632i) q^{25} +(-1.71309 - 6.40909i) q^{26} +(4.83249 + 1.90973i) q^{27} +(-0.997870 - 1.73328i) q^{28} +(5.10650 - 6.08569i) q^{29} +(0.163359 + 0.210775i) q^{30} +(-1.99748 + 0.352209i) q^{31} +(-4.62383 - 3.25886i) q^{32} +(-2.60142 + 0.591614i) q^{33} +(0.267530 + 3.07968i) q^{34} +(0.0544335 - 0.0942816i) q^{35} +(-2.58818 - 5.41307i) q^{36} +(2.92633 + 5.06854i) q^{37} +(-7.65448 + 5.35272i) q^{38} +(-6.82871 + 4.40287i) q^{39} +(0.0274028 - 0.306701i) q^{40} +(6.36935 + 7.59070i) q^{41} +(-1.64610 + 1.81393i) q^{42} +(0.354332 + 0.973518i) q^{43} +(2.66595 + 1.54356i) q^{44} +(0.184403 - 0.269562i) q^{45} +(1.25020 + 0.335813i) q^{46} +(-0.676829 + 3.83849i) q^{47} +(-2.06357 + 6.61375i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.39520 + 2.97735i) q^{50} +(3.48988 - 1.46789i) q^{51} +(9.23747 + 1.64052i) q^{52} -5.33962i q^{53} +(-5.33907 + 5.04919i) q^{54} +0.167686i q^{55} +(2.81811 - 0.241318i) q^{56} +(9.11345 + 6.91441i) q^{57} +(4.74183 + 10.1852i) q^{58} +(-13.1469 - 4.78506i) q^{59} +(-0.367839 + 0.0831784i) q^{60} +(1.31772 - 7.47315i) q^{61} +(0.744108 - 2.77024i) q^{62} +(2.73258 + 1.23814i) q^{63} +(6.94291 - 3.97442i) q^{64} +(0.174668 + 0.479897i) q^{65} +(0.798786 - 3.68738i) q^{66} +(-4.10480 - 4.89191i) q^{67} +(-4.10624 - 1.50027i) q^{68} +(-0.0777876 - 1.58354i) q^{69} +(0.0882309 + 0.126172i) q^{70} +(-4.10149 - 7.10399i) q^{71} +(8.48493 - 0.0768433i) q^{72} +(-2.00789 + 3.47777i) q^{73} +(-8.24584 + 0.716311i) q^{74} +(5.87154 + 6.33797i) q^{75} +(-2.27778 - 13.0114i) q^{76} +(-1.51688 + 0.267467i) q^{77} +(-1.55489 - 11.3849i) q^{78} +(-8.81797 + 10.5088i) q^{79} +(0.376590 + 0.218660i) q^{80} +(7.89047 + 4.32903i) q^{81} +(-13.5381 + 3.61861i) q^{82} +(-9.78967 - 8.21451i) q^{83} +(-1.33915 - 3.19479i) q^{84} +(-0.0413228 - 0.234353i) q^{85} +(-1.45947 - 0.128591i) q^{86} +(10.0941 - 9.35122i) q^{87} +(-3.57330 + 2.49224i) q^{88} +(-2.13011 - 1.22982i) q^{89} +(0.235044 + 0.397606i) q^{90} +(-4.06253 + 2.34550i) q^{91} +(-1.17848 + 1.40096i) q^{92} +(-3.50887 + 0.172365i) q^{93} +(-4.51337 - 3.16443i) q^{94} +(0.550807 - 0.462182i) q^{95} +(-7.23953 - 6.60222i) q^{96} +(13.3215 - 4.84861i) q^{97} +(-1.00061 + 0.999385i) q^{98} +(-4.59860 + 0.452884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.598460	+	1.28135i	−0.423175	+	0.906048i
$2$	−0.598460	+	1.28135i	−0.423175	+	0.906048i
$3$	1.71844	+	0.216716i	0.992142	+	0.125121i
$3$	1.71844	+	0.216716i	0.992142	+	0.125121i
$4$	−1.28369	−	1.53367i	−0.641845	−	0.766834i
$5$	0.0372347	−	0.102301i	0.0166519	−	0.0457506i	−0.931088	−	0.364794i	$-0.881139\pi$
$5$	0.0372347	−	0.102301i	0.0166519	−	0.0457506i	0.947740	+	0.319043i	$0.103362\pi$
$6$	−1.30611	+	2.07222i	−0.533215	+	0.845980i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	2.73340	−	0.727012i	0.966401	−	0.257038i
$9$	2.90607	+	0.744826i	0.968690	+	0.248275i
$10$	0.108800	+	0.108934i	0.0344056	+	0.0344479i
$11$	−1.44739	+	0.526808i	−0.436405	+	0.158838i	−0.550874	−	0.834588i	$-0.685706\pi$
$11$	−1.44739	+	0.526808i	−0.436405	+	0.158838i	0.114469	+	0.993427i	$0.463483\pi$
$12$	−1.87358	−	2.91371i	−0.540855	−	0.841116i
$13$	−3.59352	+	3.01532i	−0.996663	+	0.836299i	−0.986519	−	0.163649i	$-0.947673\pi$
$13$	−3.59352	+	3.01532i	−0.996663	+	0.836299i	−0.0101440	+	0.999949i	$0.503229\pi$
$14$	−0.811871	+	1.15796i	−0.216982	+	0.309477i
$15$	0.0861559	−	0.167730i	0.0222454	−	0.0433076i
$16$	−0.704275	+	3.93751i	−0.176069	+	0.984378i
$17$	1.89301	−	1.09293i	0.459123	−	0.265075i	−0.252552	−	0.967583i	$-0.581270\pi$
$17$	1.89301	−	1.09293i	0.459123	−	0.265075i	0.711675	+	0.702508i	$0.247937\pi$
$18$	−2.69355	+	3.27793i	−0.634875	+	0.772615i
$19$	5.71979	+	3.30232i	1.31221	+	0.757605i	0.982462	−	0.186464i	$-0.0597027\pi$
$19$	5.71979	+	3.30232i	1.31221	+	0.757605i	0.329749	+	0.944069i	$0.393036\pi$
$20$	−0.204694	+	0.0742178i	−0.0457710	+	0.0165956i
$21$	1.65470	+	0.511827i	0.361085	+	0.111690i
$22$	0.191184	−	2.16988i	0.0407606	−	0.462620i
$23$	−0.158950	−	0.901452i	−0.0331434	−	0.187966i	0.963741	−	0.266838i	$-0.0859790\pi$
$23$	−0.158950	−	0.901452i	−0.0331434	−	0.187966i	−0.996885	+	0.0788728i	$0.974868\pi$
$24$	4.85473	−	0.656956i	0.990968	−	0.134101i
$25$	3.82114	+	3.20632i	0.764229	+	0.641264i
$26$	−1.71309	−	6.40909i	−0.335964	−	1.25693i
$27$	4.83249	+	1.90973i	0.930013	+	0.367527i
$28$	−0.997870	−	1.73328i	−0.188580	−	0.327559i
$29$	5.10650	−	6.08569i	0.948253	−	1.13008i	−0.0431280	−	0.999070i	$-0.513732\pi$
$29$	5.10650	−	6.08569i	0.948253	−	1.13008i	0.991381	−	0.131014i	$-0.0418232\pi$
$30$	0.163359	+	0.210775i	0.0298251	+	0.0384821i
$31$	−1.99748	+	0.352209i	−0.358757	+	0.0632586i	−0.350122	−	0.936704i	$-0.613860\pi$
$31$	−1.99748	+	0.352209i	−0.358757	+	0.0632586i	−0.00863527	+	0.999963i	$0.502749\pi$
$32$	−4.62383	−	3.25886i	−0.817386	−	0.576091i
$33$	−2.60142	+	0.591614i	−0.452850	+	0.102987i
$34$	0.267530	+	3.07968i	0.0458810	+	0.528161i
$35$	0.0544335	−	0.0942816i	0.00920094	−	0.0159365i
$36$	−2.58818	−	5.41307i	−0.431363	−	0.902178i
$37$	2.92633	+	5.06854i	0.481085	+	0.833264i	0.999764	−	0.0217052i	$-0.00690952\pi$
$37$	2.92633	+	5.06854i	0.481085	+	0.833264i	−0.518679	+	0.854969i	$0.673576\pi$
$38$	−7.65448	+	5.35272i	−1.24172	+	0.868326i
$39$	−6.82871	+	4.40287i	−1.09347	+	0.705024i
$40$	0.0274028	−	0.306701i	0.00433276	−	0.0484936i
$41$	6.36935	+	7.59070i	0.994726	+	1.18547i	0.982636	+	0.185541i	$0.0594039\pi$
$41$	6.36935	+	7.59070i	0.994726	+	1.18547i	0.0120896	+	0.999927i	$0.496152\pi$
$42$	−1.64610	+	1.81393i	−0.253999	+	0.279896i
$43$	0.354332	+	0.973518i	0.0540351	+	0.148460i	0.963774	−	0.266721i	$-0.0859403\pi$
$43$	0.354332	+	0.973518i	0.0540351	+	0.148460i	−0.909739	+	0.415181i	$0.863718\pi$
$44$	2.66595	+	1.54356i	0.401907	+	0.232700i
$45$	0.184403	−	0.269562i	0.0274892	−	0.0401839i
$46$	1.25020	+	0.335813i	0.184331	+	0.0495129i
$47$	−0.676829	+	3.83849i	−0.0987256	+	0.559901i	0.894816	+	0.446435i	$0.147306\pi$
$47$	−0.676829	+	3.83849i	−0.0987256	+	0.559901i	−0.993542	+	0.113466i	$0.963805\pi$
$48$	−2.06357	+	6.61375i	−0.297851	+	0.954612i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−6.39520	+	2.97735i	−0.904418	+	0.421061i
$51$	3.48988	−	1.46789i	0.488681	−	0.205546i
$52$	9.23747	+	1.64052i	1.28101	+	0.227500i
$53$		−	5.33962i		−	0.733453i	−0.930329	−	0.366726i	$-0.880479\pi$
$53$		−	5.33962i		−	0.733453i	0.930329	−	0.366726i	$-0.119521\pi$
$54$	−5.33907	+	5.04919i	−0.726556	+	0.687107i
$55$			0.167686i			0.0226108i
$56$	2.81811	−	0.241318i	0.376586	−	0.0322475i
$57$	9.11345	+	6.91441i	1.20711	+	0.915836i
$58$	4.74183	+	10.1852i	0.622633	+	1.33739i
$59$	−13.1469	−	4.78506i	−1.71157	−	0.622962i	−0.714517	−	0.699618i	$-0.753353\pi$
$59$	−13.1469	−	4.78506i	−1.71157	−	0.622962i	−0.997058	+	0.0766560i	$0.975576\pi$
$60$	−0.367839	+	0.0831784i	−0.0474878	+	0.0107383i
$61$	1.31772	−	7.47315i	0.168717	−	0.956839i	−0.776433	−	0.630200i	$-0.782973\pi$
$61$	1.31772	−	7.47315i	0.168717	−	0.956839i	0.945149	−	0.326639i	$-0.105916\pi$
$62$	0.744108	−	2.77024i	0.0945018	−	0.351821i
$63$	2.73258	+	1.23814i	0.344273	+	0.155991i
$64$	6.94291	−	3.97442i	0.867863	−	0.496803i
$65$	0.174668	+	0.479897i	0.0216649	+	0.0595239i
$66$	0.798786	−	3.68738i	0.0983237	−	0.453885i
$67$	−4.10480	−	4.89191i	−0.501481	−	0.597642i	0.454618	−	0.890687i	$-0.349776\pi$
$67$	−4.10480	−	4.89191i	−0.501481	−	0.597642i	−0.956099	+	0.293045i	$0.905331\pi$
$68$	−4.10624	−	1.50027i	−0.497954	−	0.181934i
$69$	−0.0777876	−	1.58354i	−0.00936453	−	0.190636i
$70$	0.0882309	+	0.126172i	0.0105456	+	0.0150804i
$71$	−4.10149	−	7.10399i	−0.486757	−	0.843088i	0.513127	−	0.858313i	$-0.328487\pi$
$71$	−4.10149	−	7.10399i	−0.486757	−	0.843088i	−0.999884	+	0.0152246i	$0.995154\pi$
$72$	8.48493	−	0.0768433i	0.999959	−	0.00905607i
$73$	−2.00789	+	3.47777i	−0.235006	+	0.407042i	−0.959274	−	0.282476i	$-0.908844\pi$
$73$	−2.00789	+	3.47777i	−0.235006	+	0.407042i	0.724269	+	0.689518i	$0.242178\pi$
$74$	−8.24584	+	0.716311i	−0.958560	+	0.0832695i
$75$	5.87154	+	6.33797i	0.677987	+	0.731846i
$76$	−2.27778	−	13.0114i	−0.261279	−	1.49251i
$77$	−1.51688	+	0.267467i	−0.172865	+	0.0304807i
$78$	−1.55489	−	11.3849i	−0.176056	−	1.28908i
$79$	−8.81797	+	10.5088i	−0.992099	+	1.18234i	−0.00887060	+	0.999961i	$0.502824\pi$
$79$	−8.81797	+	10.5088i	−0.992099	+	1.18234i	−0.983229	+	0.182377i	$0.941621\pi$
$80$	0.376590	+	0.218660i	0.0421040	+	0.0244470i
$81$	7.89047	+	4.32903i	0.876719	+	0.481003i
$82$	−13.5381	+	3.61861i	−1.49503	+	0.399609i
$83$	−9.78967	−	8.21451i	−1.07456	−	0.901659i	−0.0790984	−	0.996867i	$-0.525204\pi$
$83$	−9.78967	−	8.21451i	−1.07456	−	0.901659i	−0.995457	+	0.0952074i	$0.969649\pi$
$84$	−1.33915	−	3.19479i	−0.146113	−	0.348580i
$85$	−0.0413228	−	0.234353i	−0.00448208	−	0.0254191i
$86$	−1.45947	−	0.128591i	−0.157378	−	0.0138663i
$87$	10.0941	−	9.35122i	1.08220	−	1.00256i
$88$	−3.57330	+	2.49224i	−0.380915	+	0.265674i
$89$	−2.13011	−	1.22982i	−0.225791	−	0.130361i	0.382838	−	0.923816i	$-0.374947\pi$
$89$	−2.13011	−	1.22982i	−0.225791	−	0.130361i	−0.608629	+	0.793455i	$0.708280\pi$
$90$	0.235044	+	0.397606i	0.0247758	+	0.0419114i
$91$	−4.06253	+	2.34550i	−0.425869	+	0.245875i
$92$	−1.17848	+	1.40096i	−0.122866	+	0.146060i
$93$	−3.50887	+	0.172365i	−0.363853	+	0.0178734i
$94$	−4.51337	−	3.16443i	−0.465519	−	0.326386i
$95$	0.550807	−	0.462182i	0.0565116	−	0.0474189i
$96$	−7.23953	−	6.60222i	−0.738881	−	0.673836i
$97$	13.3215	−	4.84861i	1.35259	−	0.492302i	0.438834	−	0.898568i	$-0.355391\pi$
$97$	13.3215	−	4.84861i	1.35259	−	0.492302i	0.913755	+	0.406266i	$0.133169\pi$
$98$	−1.00061	+	0.999385i	−0.101077	+	0.100953i
$99$	−4.59860	+	0.452884i	−0.462177	+	0.0455166i
$100$	0.0122632	−	9.97629i	0.00122632	−	0.997629i
$101$	1.35706	+	0.239286i	0.135032	+	0.0238098i	0.240756	−	0.970586i	$-0.422605\pi$
$101$	1.35706	+	0.239286i	0.135032	+	0.0238098i	−0.105724	+	0.994396i	$0.533716\pi$
$102$	−0.207681	+	5.35022i	−0.0205635	+	0.529751i
$103$	1.61952	−	4.44959i	0.159576	−	0.438431i	−0.833977	−	0.551799i	$-0.813942\pi$
$103$	1.61952	−	4.44959i	0.159576	−	0.438431i	0.993553	+	0.113368i	$0.0361638\pi$
$104$	−7.63033	+	10.8546i	−0.748216	+	1.06438i
$105$	0.113973	−	0.150221i	0.0111226	−	0.0146600i
$106$	6.84189	+	3.19555i	0.664543	+	0.310379i
$107$	−5.60395			−0.541755			−0.270877	−	0.962614i	$-0.587314\pi$
$107$	−5.60395			−0.541755			−0.270877	+	0.962614i	$0.587314\pi$
$108$	−3.27453	−	9.86293i	−0.315092	−	0.949061i
$109$	2.24633			0.215159			0.107580	−	0.994196i	$-0.465690\pi$
$109$	2.24633			0.215159			0.107580	+	0.994196i	$0.465690\pi$
$110$	−0.214863	−	0.100353i	−0.0204864	−	0.00956831i
$111$	3.93028	+	9.34417i	0.373046	+	0.886909i
$112$	−1.37732	+	3.75540i	−0.130144	+	0.354852i
$113$	3.95728	−	10.8725i	0.372269	−	1.02280i	−0.602213	−	0.798336i	$-0.705714\pi$
$113$	3.95728	−	10.8725i	0.372269	−	1.02280i	0.974482	−	0.224466i	$-0.0720637\pi$
$114$	−14.3138	+	7.53948i	−1.34061	+	0.706137i
$115$	−0.0981383	−	0.0173044i	−0.00915145	−	0.00161365i
$116$	−15.8886	−	0.0195308i	−1.47522	−	0.00181339i
$117$	−12.6889	+	6.08618i	−1.17309	+	0.562668i
$118$	13.9992	−	13.9820i	1.28873	−	1.28715i
$119$	2.05404	−	0.747609i	0.188293	−	0.0685332i
$120$	0.113557	−	0.521108i	0.0103663	−	0.0475704i
$121$	−6.60907	+	5.54567i	−0.600825	+	0.504152i
$122$	8.78709	+	6.16084i	0.795546	+	0.557776i
$123$	9.30033	+	14.4245i	0.838582	+	1.30061i
$124$	3.10431	+	2.61134i	0.278775	+	0.234505i
$125$	0.941698	−	0.543690i	0.0842280	−	0.0486291i
$126$	−3.22183	+	2.76040i	−0.287023	+	0.245916i
$127$	−12.3893	−	7.15298i	−1.09938	−	0.634725i	−0.163319	−	0.986573i	$-0.552220\pi$
$127$	−12.3893	−	7.15298i	−1.09938	−	0.634725i	−0.936057	+	0.351849i	$0.885553\pi$
$128$	0.937556	+	11.2748i	0.0828690	+	0.996560i
$129$	0.397921	+	1.74972i	0.0350350	+	0.154054i
$130$	−0.719445	−	0.0633889i	−0.0630995	−	0.00555957i
$131$	1.25104	+	7.09497i	0.109303	+	0.619891i	0.989414	+	0.145122i	$0.0463573\pi$
$131$	1.25104	+	7.09497i	0.109303	+	0.619891i	−0.880110	+	0.474769i	$0.842532\pi$
$132$	4.24676	+	3.23027i	0.369633	+	0.281159i
$133$	5.05945	+	4.24539i	0.438710	+	0.368122i
$134$	8.72478	−	2.33205i	0.753706	−	0.201459i
$135$	0.375304	−	0.423262i	0.0323010	−	0.0364286i
$136$	4.37978	−	4.36366i	0.375563	−	0.374181i
$137$	−4.96639	+	5.91871i	−0.424307	+	0.505669i	−0.935271	−	0.353933i	$-0.884844\pi$
$137$	−4.96639	+	5.91871i	−0.424307	+	0.505669i	0.510964	+	0.859602i	$0.329289\pi$
$138$	2.07561	+	0.848011i	0.176688	+	0.0721875i
$139$	8.91865	−	1.57260i	0.756470	−	0.133386i	0.217905	−	0.975970i	$-0.430078\pi$
$139$	8.91865	−	1.57260i	0.756470	−	0.133386i	0.538565	+	0.842584i	$0.318967\pi$
$140$	−0.214472	+	0.0375455i	−0.0181262	+	0.00317317i
$141$	−1.99495	+	6.44953i	−0.168005	+	0.543148i
$142$	11.5572	−	1.00397i	0.969862	−	0.0842513i
$143$	3.61274	−	6.25744i	0.302112	−	0.523273i
$144$	−4.97943	+	10.9181i	−0.414953	+	0.909843i
$145$	−0.432436	−	0.749001i	−0.0359118	−	0.0622011i
$146$	−3.25458	−	4.65411i	−0.269351	−	0.385177i
$147$	1.54068	+	0.791387i	0.127073	+	0.0652725i
$148$	4.01697	−	10.9945i	0.330193	−	0.903739i
$149$	−5.74436	−	6.84586i	−0.470596	−	0.560835i	0.477576	−	0.878590i	$-0.341515\pi$
$149$	−5.74436	−	6.84586i	−0.470596	−	0.560835i	−0.948173	+	0.317755i	$0.897071\pi$
$150$	−11.6350	+	3.73045i	−0.949995	+	0.304590i
$151$	5.85864	+	16.0965i	0.476769	+	1.30991i	0.912220	+	0.409701i	$0.134367\pi$
$151$	5.85864	+	16.0965i	0.476769	+	1.30991i	−0.435451	+	0.900213i	$0.643411\pi$
$152$	18.0353	+	4.86820i	1.46285	+	0.394863i
$153$	6.31527	−	1.76617i	0.510559	−	0.142786i
$154$	0.565075	−	2.10372i	0.0455351	−	0.169522i
$155$	−0.0383439	+	0.217459i	−0.00307986	+	0.0174667i
$156$	15.5185	+	4.82105i	1.24247	+	0.385993i
$157$	−15.9097	−	5.79064i	−1.26973	−	0.462143i	−0.382706	−	0.923870i	$-0.625008\pi$
$157$	−15.9097	−	5.79064i	−1.26973	−	0.462143i	−0.887022	+	0.461727i	$0.847230\pi$
$158$	−8.18826	−	17.5880i	−0.651423	−	1.39923i
$159$	1.15718	−	9.17581i	0.0917703	−	0.727689i
$160$	−0.505553	+	0.351682i	−0.0399675	+	0.0278029i
$161$		−	0.915358i		−	0.0721403i
$162$	−10.2691	+	7.51966i	−0.806818	+	0.590801i
$163$		−	7.08873i		−	0.555232i	−0.960692	−	0.277616i	$-0.910456\pi$
$163$		−	7.08873i		−	0.555232i	0.960692	−	0.277616i	$-0.0895443\pi$
$164$	3.46533	−	19.5126i	0.270597	−	1.52368i
$165$	−0.0363402	+	0.288158i	−0.00282908	+	0.0224331i
$166$	16.3843	−	7.62789i	1.27167	−	0.592039i
$167$	−7.99833	−	2.91115i	−0.618929	−	0.225272i	0.0134764	−	0.999909i	$-0.495710\pi$
$167$	−7.99833	−	2.91115i	−0.618929	−	0.225272i	−0.632406	+	0.774637i	$0.717932\pi$
$168$	4.89506	+	0.196039i	0.377662	+	0.0151248i
$169$	1.56379	−	8.86871i	0.120292	−	0.682208i
$170$	0.325017	+	0.0873022i	0.0249277	+	0.00669577i
$171$	14.1625	+	13.8570i	1.08303	+	1.05967i
$172$	1.03820	−	1.79312i	0.0791621	−	0.136724i
$173$	−5.08942	−	13.9831i	−0.386941	−	1.06311i	−0.968371	−	0.249516i	$-0.919729\pi$
$173$	−5.08942	−	13.9831i	−0.386941	−	1.06311i	0.581429	−	0.813597i	$-0.302494\pi$
$174$	5.94125	+	18.5303i	0.450405	+	1.40478i
$175$	3.20632	+	3.82114i	0.242375	+	0.288851i
$176$	−1.05495	−	6.07014i	−0.0795197	−	0.457554i
$177$	−21.5551	−	11.0720i	−1.62018	−	0.832220i
$178$	2.85061	−	1.99341i	0.213662	−	0.149412i
$179$	0.531463	+	0.920522i	0.0397234	+	0.0688030i	0.885204	−	0.465204i	$-0.154019\pi$
$179$	0.531463	+	0.920522i	0.0397234	+	0.0688030i	−0.845480	+	0.534007i	$0.820686\pi$
$180$	−0.650135	+	0.0632205i	−0.0484582	+	0.00471218i
$181$	11.3274	−	19.6196i	0.841956	−	1.45831i	−0.0462833	−	0.998928i	$-0.514738\pi$
$181$	11.3274	−	19.6196i	0.841956	−	1.45831i	0.888239	−	0.459382i	$-0.151929\pi$
$182$	−0.574136	−	6.60919i	−0.0425578	−	0.489906i
$183$	3.88397	−	12.5566i	0.287111	−	0.928210i
$184$	−1.08984	−	2.34847i	−0.0803441	−	0.173131i
$185$	0.627480	−	0.110642i	0.0461333	−	0.00813454i
$186$	1.87906	−	4.59923i	0.137779	−	0.337232i
$187$	−2.16417	+	2.57915i	−0.158260	+	0.188606i
$188$	6.75580	−	3.88940i	0.492718	−	0.283664i
$189$	4.42745	+	2.71987i	0.322050	+	0.197841i
$190$	0.262579	+	0.982372i	0.0190495	+	0.0712687i
$191$	−5.67685	−	4.76345i	−0.410763	−	0.344671i	0.413873	−	0.910334i	$-0.364176\pi$
$191$	−5.67685	−	4.76345i	−0.410763	−	0.344671i	−0.824636	+	0.565664i	$0.808620\pi$
$192$	12.7923	−	5.32517i	0.923204	−	0.384311i
$193$	−3.37566	−	19.1443i	−0.242985	−	1.37804i	−0.825125	−	0.564950i	$-0.808896\pi$
$193$	−3.37566	−	19.1443i	−0.242985	−	1.37804i	0.582140	−	0.813089i	$-0.302216\pi$
$194$	−1.75961	+	19.9711i	−0.126333	+	1.43384i
$195$	0.196155	+	0.862527i	0.0140470	+	0.0617668i
$196$	−0.681730	−	1.88022i	−0.0486950	−	0.134302i
$197$	16.9085	+	9.76211i	1.20468	+	0.695521i	0.961592	−	0.274483i	$-0.0885067\pi$
$197$	16.9085	+	9.76211i	1.20468	+	0.695521i	0.243087	+	0.970005i	$0.421840\pi$
$198$	2.17178	−	6.16343i	0.154342	−	0.438016i
$199$	2.26353	−	1.30685i	0.160457	−	0.0926401i	−0.417621	−	0.908621i	$-0.637136\pi$
$199$	2.26353	−	1.30685i	0.160457	−	0.0926401i	0.578079	+	0.815981i	$0.303803\pi$
$200$	12.7757	+	5.98612i	0.903381	+	0.423283i
$201$	−5.99370	−	9.29602i	−0.422763	−	0.655691i
$202$	−1.11875	+	1.59566i	−0.0787151	+	0.112270i
$203$	6.08569	−	5.10650i	0.427131	−	0.358406i
$204$	−6.73119	−	3.46800i	−0.471277	−	0.242809i
$205$	1.01370	−	0.368957i	0.0707999	−	0.0257691i
$206$	4.73224	+	4.73806i	0.329711	+	0.330117i
$207$	0.209504	−	2.73807i	0.0145615	−	0.190309i
$208$	−9.34203	−	16.2731i	−0.647753	−	1.12834i
$209$	−10.0185	−	1.76653i	−0.692992	−	0.122193i
$210$	0.124276	+	0.235940i	0.00857587	+	0.0162814i
$211$	6.96369	−	19.1326i	0.479400	−	1.31714i	−0.430603	−	0.902541i	$-0.641699\pi$
$211$	6.96369	−	19.1326i	0.479400	−	1.31714i	0.910004	−	0.414600i	$-0.136079\pi$
$212$	−8.18920	+	6.85442i	−0.562437	+	0.470763i
$213$	−5.50861	−	13.0966i	−0.377444	−	0.897366i
$214$	3.35374	−	7.18060i	0.229257	−	0.490856i
$215$	0.112786			0.00769192
$216$	14.5975	+	1.70677i	0.993234	+	0.116131i
$217$	−2.02829			−0.137689
$218$	−1.34434	+	2.87832i	−0.0910500	+	0.194944i
$219$	−4.20413	+	5.54119i	−0.284088	+	0.374439i
$220$	0.257174	−	0.215257i	0.0173387	−	0.0145126i
$221$	−3.50704	+	9.63551i	−0.235909	+	0.648154i
$222$	−14.3252	−	0.556066i	−0.961446	−	0.0373207i
$223$	2.87022	+	0.506098i	0.192204	+	0.0338908i	0.268922	−	0.963162i	$-0.413333\pi$
$223$	2.87022	+	0.506098i	0.192204	+	0.0338908i	−0.0767172	+	0.997053i	$0.524444\pi$
$224$	−3.98769	−	4.01227i	−0.266439	−	0.268081i
$225$	8.71635	+	12.1639i	0.581090	+	0.810925i
$226$	11.5632	+	11.5774i	0.769172	+	0.770118i
$227$	24.3825	−	8.87450i	1.61832	−	0.589021i	0.635262	−	0.772297i	$-0.280892\pi$
$227$	24.3825	−	8.87450i	1.61832	−	0.589021i	0.983062	+	0.183276i	$0.0586700\pi$
$228$	−1.09444	−	22.8530i	−0.0724812	−	1.51348i
$229$	−17.1266	+	14.3709i	−1.13176	+	0.949657i	−0.999138	−	0.0415096i	$-0.986783\pi$
$229$	−17.1266	+	14.3709i	−1.13176	+	0.949657i	−0.132620	+	0.991167i	$0.542339\pi$
$230$	0.0809048	−	0.115393i	0.00533471	−	0.00760879i
$231$	−2.66463	+	0.130894i	−0.175320	+	0.00861220i
$232$	9.53371	−	20.3471i	0.625919	−	1.33585i
$233$	13.8380	−	7.98939i	0.906560	−	0.523403i	0.0272371	−	0.999629i	$-0.491329\pi$
$233$	13.8380	−	7.98939i	0.906560	−	0.523403i	0.879323	+	0.476226i	$0.157996\pi$
$234$	−0.204700	−	19.9012i	−0.0133816	−	1.30098i
$235$	0.367481	+	0.212165i	0.0239718	+	0.0138401i
$236$	9.53780	+	26.3055i	0.620858	+	1.71234i
$237$	−17.4306	+	16.1478i	−1.13224	+	1.04891i
$238$	−0.271315	+	3.07935i	−0.0175868	+	0.199604i
$239$	−1.90343	−	10.7949i	−0.123122	−	0.698262i	−0.982405	−	0.186761i	$-0.940201\pi$
$239$	−1.90343	−	10.7949i	−0.123122	−	0.698262i	0.859283	−	0.511500i	$-0.170910\pi$
$240$	0.599760	+	0.457368i	0.0387143	+	0.0295230i
$241$	18.5003	+	15.5236i	1.19171	+	0.999962i	0.999828	+	0.0185436i	$0.00590294\pi$
$241$	18.5003	+	15.5236i	1.19171	+	0.999962i	0.191880	+	0.981418i	$0.438542\pi$
$242$	−3.15065	−	11.7874i	−0.202532	−	0.757721i
$243$	12.6211	+	9.14916i	0.809646	+	0.586919i
$244$	−13.1529	+	7.57228i	−0.842027	+	0.484765i
$245$	0.0699783	−	0.0833969i	0.00447075	−	0.00532803i
$246$	−24.0486	+	3.28444i	−1.53329	+	0.209408i
$247$	−30.5117	+	5.38004i	−1.94142	+	0.342324i
$248$	−5.20383	+	2.41491i	−0.330444	+	0.153347i
$249$	−15.0427	−	16.2377i	−0.953295	−	1.02902i
$250$	0.133085	+	1.53202i	0.00841706	+	0.0968933i
$251$	−2.29868	+	3.98142i	−0.145091	+	0.251305i	−0.929407	−	0.369056i	$-0.879681\pi$
$251$	−2.29868	+	3.98142i	−0.145091	+	0.251305i	0.784316	+	0.620362i	$0.213014\pi$
$252$	−1.60889	−	5.78027i	−0.101350	−	0.364123i
$253$	0.704955	+	1.22102i	0.0443201	+	0.0767647i
$254$	16.5800	−	11.5942i	1.04032	−	0.727487i
$255$	−0.0202227	−	0.411677i	−0.00126639	−	0.0257802i
$256$	−15.0080	−	5.54618i	−0.938000	−	0.346636i
$257$	19.9096	+	23.7274i	1.24193	+	1.48007i	0.818880	+	0.573964i	$0.194595\pi$
$257$	19.9096	+	23.7274i	1.24193	+	1.48007i	0.423047	+	0.906108i	$0.360960\pi$
$258$	−2.48014	−	0.537264i	−0.154407	−	0.0334486i
$259$	2.00172	+	5.49969i	0.124381	+	0.341734i
$260$	0.511782	−	0.883922i	0.0317394	−	0.0548185i
$261$	19.3726	−	13.8820i	1.19913	−	0.859272i
$262$	−9.83981	−	2.64305i	−0.607905	−	0.163288i
$263$	3.76224	−	21.3367i	0.231990	−	1.31568i	−0.616872	−	0.787064i	$-0.711600\pi$
$263$	3.76224	−	21.3367i	0.231990	−	1.31568i	0.848862	−	0.528615i	$-0.177289\pi$
$264$	−6.68061	+	3.50838i	−0.411163	+	0.215926i
$265$	−0.546251	−	0.198819i	−0.0335559	−	0.0122134i
$266$	−8.46769	+	3.94221i	−0.519187	+	0.241713i
$267$	−3.39395	−	2.57500i	−0.207706	−	0.157587i
$268$	−2.23327	+	12.5751i	−0.136419	+	0.768146i
$269$			15.9892i			0.974879i	0.873157	+	0.487440i	$0.162069\pi$
$269$			15.9892i			0.974879i	−0.873157	+	0.487440i	$0.837931\pi$
$270$	0.317741	+	0.734200i	0.0193371	+	0.0446820i
$271$			6.14842i			0.373490i	0.982408	+	0.186745i	$0.0597938\pi$
$271$			6.14842i			0.373490i	−0.982408	+	0.186745i	$0.940206\pi$
$272$	2.97023	+	8.22348i	0.180097	+	0.498622i
$273$	−7.48952	+	3.15019i	−0.453286	+	0.190658i
$274$	−4.61173	−	9.90577i	−0.278605	−	0.598429i
$275$	−7.21980	−	2.62779i	−0.435371	−	0.158462i
$276$	−2.32877	+	2.15207i	−0.140175	+	0.129540i
$277$	0.976978	−	5.54072i	0.0587009	−	0.332909i	−0.941288	−	0.337604i	$-0.890383\pi$
$277$	0.976978	−	5.54072i	0.0587009	−	0.332909i	0.999989	+	0.00469505i	$0.00149449\pi$
$278$	−3.32241	+	12.3690i	−0.199265	+	0.741844i
$279$	−6.06713	−	0.464228i	−0.363230	−	0.0277926i
$280$	0.0802444	−	0.297283i	0.00479552	−	0.0177660i
$281$	−7.49845	−	20.6018i	−0.447320	−	1.22900i	−0.934583	−	0.355746i	$-0.884227\pi$
$281$	−7.49845	−	20.6018i	−0.447320	−	1.22900i	0.487263	−	0.873256i	$-0.337995\pi$
$282$	−7.07017	−	6.41600i	−0.421023	−	0.382067i
$283$	6.34531	+	7.56204i	0.377189	+	0.449517i	0.920925	−	0.389740i	$-0.127435\pi$
$283$	6.34531	+	7.56204i	0.377189	+	0.449517i	−0.543736	+	0.839257i	$0.682991\pi$
$284$	−5.63011	+	15.4096i	−0.334086	+	0.914394i
$285$	1.04669	−	0.674864i	0.0620006	−	0.0399755i
$286$	5.85586	+	8.37399i	0.346264	+	0.495164i
$287$	4.95448	+	8.58141i	0.292454	+	0.506544i
$288$	−11.0099	−	12.9144i	−0.648764	−	0.760990i
$289$	−6.11100	+	10.5846i	−0.359471	+	0.622622i
$290$	1.21852	−	0.105852i	0.0715542	−	0.00621587i
$291$	23.9429	−	5.44508i	1.40356	−	0.319196i
$292$	7.91125	−	1.38494i	0.462971	−	0.0810476i
$293$	−13.6181	+	2.40125i	−0.795581	+	0.140282i	−0.556642	−	0.830752i	$-0.687911\pi$
$293$	−13.6181	+	2.40125i	−0.795581	+	0.140282i	−0.238938	+	0.971035i	$0.576799\pi$
$294$	−1.93608	+	1.50053i	−0.112914	+	0.0875129i
$295$	−0.979038	+	1.16677i	−0.0570018	+	0.0679321i
$296$	11.6837	+	11.7269i	0.679101	+	0.681610i
$297$	−8.00056	−	0.218335i	−0.464240	−	0.0126691i
$298$	12.2097	−	3.26353i	0.707288	−	0.189051i
$299$	3.28936	+	2.76010i	0.190228	+	0.159621i
$300$	2.18309	−	17.1410i	0.126041	−	0.989636i
$301$	0.179899	+	1.02026i	0.0103692	+	0.0588066i
$302$	−24.1313	−	2.12616i	−1.38860	−	0.122347i
$303$	2.28016	+	0.705294i	0.130992	+	0.0405181i
$304$	−17.0312	+	20.1960i	−0.976809	+	1.15832i
$305$	−0.715450	−	0.413065i	−0.0409665	−	0.0236520i
$306$	−1.51636	+	9.14902i	−0.0866848	+	0.523015i
$307$	−13.8127	+	7.97477i	−0.788333	+	0.455144i	−0.839375	−	0.543552i	$-0.817079\pi$
$307$	−13.8127	+	7.97477i	−0.788333	+	0.455144i	0.0510424	+	0.998696i	$0.483746\pi$
$308$	2.35741	+	1.98305i	0.134326	+	0.112995i
$309$	3.74734	−	7.29538i	0.213179	−	0.415019i
$310$	−0.255693	−	0.179272i	−0.0145224	−	0.0101820i
$311$	−0.448015	+	0.375929i	−0.0254046	+	0.0213170i	−0.655402	−	0.755281i	$-0.727501\pi$
$311$	−0.448015	+	0.375929i	−0.0254046	+	0.0213170i	0.629997	+	0.776598i	$0.283056\pi$
$312$	−15.4646	+	16.9993i	−0.875512	+	0.962399i
$313$	−15.5841	+	5.67214i	−0.880863	+	0.320608i	−0.742558	−	0.669782i	$-0.766388\pi$
$313$	−15.5841	+	5.67214i	−0.880863	+	0.320608i	−0.138305	+	0.990390i	$0.544165\pi$
$314$	16.9411	−	16.9203i	0.956042	−	0.954867i
$315$	0.228411	−	0.233445i	0.0128695	−	0.0131531i
$316$	27.4366	+	0.0337261i	1.54343	+	0.00189724i
$317$	−30.0089	−	5.29137i	−1.68547	−	0.297193i	−0.752884	−	0.658153i	$-0.771338\pi$
$317$	−30.0089	−	5.29137i	−1.68547	−	0.297193i	−0.932581	+	0.360960i	$0.882449\pi$
$318$	11.0649	+	6.97410i	0.620486	+	0.391088i
$319$	−4.18512	+	11.4985i	−0.234322	+	0.643793i
$320$	−0.148072	−	0.858256i	−0.00827750	−	0.0479780i
$321$	−9.63006	−	1.21447i	−0.537497	−	0.0677848i
$322$	1.17289	+	0.547805i	0.0653626	+	0.0305280i
$323$	14.4369			0.803288
$324$	−3.48963	−	17.6585i	−0.193868	−	0.981028i
$325$	−23.3994			−1.29797
$326$	9.08311	+	4.24232i	0.503067	+	0.234960i
$327$	3.86018	+	0.486814i	0.213468	+	0.0269209i
$328$	22.9285	+	16.1178i	1.26601	+	0.889956i
$329$	−1.33309	+	3.66264i	−0.0734958	+	0.201928i
$330$	−0.347482	−	0.219015i	−0.0191282	−	0.0120564i
$331$	−21.6284	−	3.81368i	−1.18881	−	0.209619i	−0.455952	−	0.890004i	$-0.650701\pi$
$331$	−21.6284	−	3.81368i	−1.18881	−	0.209619i	−0.732854	+	0.680385i	$0.761812\pi$
$332$	−0.0314181	+	25.5590i	−0.00172429	+	1.40273i
$333$	4.72892	+	16.9091i	0.259143	+	0.926615i
$334$	8.51687	−	8.50641i	0.466023	−	0.465450i
$335$	−0.653290	+	0.237778i	−0.0356931	+	0.0129912i
$336$	−3.18069	+	6.15493i	−0.173521	+	0.335779i
$337$	−1.68977	+	1.41788i	−0.0920474	+	0.0772369i	−0.687650	−	0.726042i	$-0.741358\pi$
$337$	−1.68977	+	1.41788i	−0.0920474	+	0.0772369i	0.595603	+	0.803279i	$0.296913\pi$
$338$	10.4280	+	7.31133i	0.567209	+	0.397684i
$339$	9.15659	−	17.8262i	0.497318	−	0.968185i
$340$	−0.306374	+	0.364212i	−0.0166155	+	0.0197522i
$341$	2.70558	−	1.56207i	0.146516	−	0.0845908i
$342$	−26.2313	+	9.85411i	−1.41843	+	0.532849i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	1.67629	+	2.40341i	0.0903794	+	0.129583i
$345$	−0.164895	−	0.0510047i	−0.00887763	−	0.00274600i
$346$	20.9629	+	1.84700i	1.12697	+	0.0992955i
$347$	−4.97090	−	28.1914i	−0.266852	−	1.51339i	−0.763709	−	0.645561i	$-0.776624\pi$
$347$	−4.97090	−	28.1914i	−0.266852	−	1.51339i	0.496857	−	0.867833i	$-0.334487\pi$
$348$	−27.2993	−	3.47687i	−1.46340	−	0.186380i
$349$	−13.0018	−	10.9098i	−0.695972	−	0.583990i	0.224652	−	0.974439i	$-0.427875\pi$
$349$	−13.0018	−	10.9098i	−0.695972	−	0.583990i	−0.920625	+	0.390449i	$0.872320\pi$
$350$	−6.81506	+	1.82160i	−0.364280	+	0.0973686i
$351$	−23.1241	+	7.70885i	−1.23427	+	0.411468i
$352$	8.40929	+	2.28098i	0.448217	+	0.121577i
$353$	2.11244	−	2.51750i	0.112434	−	0.133993i	−0.706892	−	0.707321i	$-0.749903\pi$
$353$	2.11244	−	2.51750i	0.112434	−	0.133993i	0.819326	+	0.573328i	$0.194348\pi$
$354$	27.0869	−	20.9934i	1.43965	−	1.11578i
$355$	−0.879466	+	0.155074i	−0.0466772	+	0.00823045i
$356$	0.848269	+	4.84559i	0.0449581	+	0.256816i
$357$	3.69176	−	0.839578i	0.195389	−	0.0444352i
$358$	−1.49757	+	0.130093i	−0.0791488	+	0.00687561i
$359$	8.01609	−	13.8843i	0.423073	−	0.732784i	−0.573165	−	0.819440i	$-0.694285\pi$
$359$	8.01609	−	13.8843i	0.423073	−	0.732784i	0.996238	+	0.0866559i	$0.0276181\pi$
$360$	0.308073	−	0.870882i	0.0162369	−	0.0458995i
$361$	12.3107	+	21.3227i	0.647931	+	1.12225i
$362$	18.3605	+	26.2558i	0.965004	+	1.37997i
$363$	−12.5591	+	8.09761i	−0.659183	+	0.425014i
$364$	8.81225	+	3.21967i	0.461888	+	0.168757i
$365$	0.281018	+	0.334904i	0.0147091	+	0.0175297i
$366$	13.7649	+	12.4913i	0.719504	+	0.652932i
$367$	−8.83472	−	24.2732i	−0.461168	−	1.26705i	−0.924608	−	0.380921i	$-0.875607\pi$
$367$	−8.83472	−	24.2732i	−0.461168	−	1.26705i	0.463439	−	0.886129i	$-0.346615\pi$
$368$	3.66142	+	0.00900153i	0.190865	+	0.000469237i
$369$	12.8560	+	26.8032i	0.669258	+	1.39532i
$370$	−0.233752	+	0.870234i	−0.0121522	+	0.0452413i
$371$	0.927215	−	5.25850i	0.0481386	−	0.273008i
$372$	4.76866	+	5.16018i	0.247243	+	0.267543i
$373$	−25.3110	−	9.21246i	−1.31056	−	0.477003i	−0.410135	−	0.912025i	$-0.634519\pi$
$373$	−25.3110	−	9.21246i	−1.31056	−	0.477003i	−0.900420	+	0.435021i	$0.856741\pi$
$374$	−2.00962	−	4.31656i	−0.103915	−	0.223204i
$375$	1.73608	−	0.730217i	0.0896506	−	0.0377082i
$376$	0.940585	+	10.9842i	0.0485070	+	0.566465i
$377$			37.2667i			1.91933i
$378$	−6.13474	+	4.04536i	−0.315537	+	0.208071i
$379$			36.1545i			1.85713i	0.371165	+	0.928567i	$0.378958\pi$
$379$			36.1545i			1.85713i	−0.371165	+	0.928567i	$0.621042\pi$
$380$	−1.41590	−	0.251456i	−0.0726342	−	0.0128994i
$381$	−19.7402	−	14.9769i	−1.01132	−	0.767292i
$382$	9.50099	−	4.42328i	0.486113	−	0.226315i
$383$	19.3687	+	7.04961i	0.989692	+	0.360218i	0.785601	−	0.618734i	$-0.212354\pi$
$383$	19.3687	+	7.04961i	0.989692	+	0.360218i	0.204091	+	0.978952i	$0.434576\pi$
$384$	−0.832293	+	19.5782i	−0.0424728	+	0.999098i
$385$	−0.0291183	+	0.165138i	−0.00148401	+	0.00841623i
$386$	26.5507	+	7.13173i	1.35139	+	0.362995i
$387$	0.304611	+	3.09303i	0.0154842	+	0.157227i
$388$	−24.5368	−	14.2066i	−1.24567	−	0.721230i
$389$	2.32971	+	6.40083i	0.118121	+	0.324535i	0.984637	−	0.174615i	$-0.0558680\pi$
$389$	2.32971	+	6.40083i	0.118121	+	0.324535i	−0.866516	+	0.499150i	$0.833646\pi$
$390$	−1.22259	−	0.264845i	−0.0619080	−	0.0134110i
$391$	−1.28612	−	1.53274i	−0.0650419	−	0.0775139i
$392$	2.81720	+	0.251709i	0.142290	+	0.0127132i
$393$	0.612236	+	12.4634i	0.0308832	+	0.628696i
$394$	−22.6277	+	15.8234i	−1.13997	+	0.797169i
$395$	0.746736	+	1.29339i	0.0375724	+	0.0650773i
$396$	6.59775	+	6.47136i	0.331550	+	0.325198i
$397$	−0.298016	+	0.516178i	−0.0149570	+	0.0259062i	−0.873407	−	0.486991i	$-0.838094\pi$
$397$	−0.298016	+	0.516178i	−0.0149570	+	0.0259062i	0.858450	+	0.512897i	$0.171428\pi$
$398$	0.319893	+	3.68246i	0.0160348	+	0.184585i
$399$	7.77432	+	8.39190i	0.389203	+	0.420121i
$400$	−15.3161	+	12.7877i	−0.765803	+	0.639383i
$401$	14.9651	−	2.63876i	0.747323	−	0.131773i	0.212998	−	0.977053i	$-0.431677\pi$
$401$	14.9651	−	2.63876i	0.747323	−	0.131773i	0.534325	+	0.845279i	$0.320566\pi$
$402$	15.4984	−	2.11669i	0.772990	−	0.105571i
$403$	6.11594	−	7.28869i	0.304657	−	0.363076i
$404$	−1.37506	−	2.38844i	−0.0684116	−	0.118830i
$405$	0.736665	−	0.646017i	0.0366052	−	0.0321008i
$406$	2.90114	+	10.8539i	0.143981	+	0.538670i
$407$	−6.90569	−	5.79456i	−0.342302	−	0.287226i
$408$	8.47206	−	6.54951i	0.419429	−	0.324249i
$409$	3.10531	+	17.6111i	0.153548	+	0.870811i	0.960102	+	0.279651i	$0.0902188\pi$
$409$	3.10531	+	17.6111i	0.153548	+	0.870811i	−0.806554	+	0.591160i	$0.798670\pi$
$410$	−0.133898	+	1.51971i	−0.00661277	+	0.0750530i
$411$	−9.81711	+	9.09465i	−0.484242	+	0.448606i
$412$	−8.90315	+	3.22809i	−0.438627	+	0.159037i
$413$	−12.1162	−	6.99529i	−0.596199	−	0.344216i
$414$	3.38303	+	1.90707i	0.166267	+	0.0937275i
$415$	−1.20487	+	0.695633i	−0.0591448	+	0.0341473i
$416$	26.4423	−	2.23154i	1.29644	−	0.109410i
$417$	15.6670	−	0.769604i	0.767215	−	0.0376877i
$418$	8.25918	−	11.7799i	0.403970	−	0.576175i
$419$	−6.76864	+	5.67956i	−0.330670	+	0.277465i	−0.792973	−	0.609257i	$-0.791468\pi$
$419$	−6.76864	+	5.67956i	−0.330670	+	0.277465i	0.462303	+	0.886722i	$0.347023\pi$
$420$	−0.376694	+	0.0180401i	−0.0183808	+	0.000880268i
$421$	27.6731	−	10.0722i	1.34870	−	0.490888i	0.436160	−	0.899869i	$-0.356338\pi$
$421$	27.6731	−	10.0722i	1.34870	−	0.490888i	0.912543	+	0.408982i	$0.134116\pi$
$422$	20.3480	+	20.3730i	0.990523	+	0.991741i
$423$	−4.82591	+	10.6508i	−0.234644	+	0.517859i
$424$	−3.88197	−	14.5953i	−0.188525	−	0.708810i
$425$	10.7378	+	1.89336i	0.520858	+	0.0918413i
$426$	20.0780	+	0.779373i	0.972782	+	0.0377608i
$427$	2.59540	−	7.13080i	0.125600	−	0.345084i
$428$	7.19375	+	8.59461i	0.347723	+	0.415436i
$429$	7.56435	−	9.97010i	0.365210	−	0.481361i
$430$	−0.0674978	+	0.144517i	−0.00325503	+	0.00696925i
$431$	−16.7569			−0.807151			−0.403576	−	0.914946i	$-0.632233\pi$
$431$	−16.7569			−0.807151			−0.403576	+	0.914946i	$0.632233\pi$
$432$	−10.9230	+	17.6830i	−0.525532	+	0.850774i
$433$	9.71729			0.466983			0.233492	−	0.972359i	$-0.424985\pi$
$433$	9.71729			0.466983			0.233492	+	0.972359i	$0.424985\pi$
$434$	1.21385	−	2.59894i	0.0582667	−	0.124753i
$435$	−0.580794	−	1.38083i	−0.0278470	−	0.0662056i
$436$	−2.88359	−	3.44512i	−0.138099	−	0.164991i
$437$	2.06772	−	5.68102i	0.0989126	−	0.271760i
$438$	−4.58418	−	8.70312i	−0.219041	−	0.415851i
$439$	14.8748	+	2.62282i	0.709934	+	0.125181i	0.516943	−	0.856020i	$-0.327070\pi$
$439$	14.8748	+	2.62282i	0.709934	+	0.125181i	0.192991	+	0.981200i	$0.438181\pi$
$440$	0.121910	+	0.458352i	0.00581181	+	0.0218511i
$441$	2.47607	+	1.69384i	0.117908	+	0.0806591i
$442$	−10.2476	−	10.2602i	−0.487428	−	0.488028i
$443$	−3.44677	+	1.25452i	−0.163761	+	0.0596042i	−0.422600	−	0.906316i	$-0.638882\pi$
$443$	−3.44677	+	1.25452i	−0.163761	+	0.0596042i	0.258839	+	0.965921i	$0.416660\pi$
$444$	9.28559	−	18.0228i	0.440674	−	0.855323i
$445$	−0.205126	+	0.172122i	−0.00972393	+	0.00815934i
$446$	−2.36620	+	3.37487i	−0.112043	+	0.159805i
$447$	−8.38773	−	13.0091i	−0.396726	−	0.615309i
$448$	7.52758	−	2.70842i	0.355645	−	0.127961i
$449$	−20.1880	+	11.6555i	−0.952729	+	0.550058i	−0.893928	−	0.448211i	$-0.852061\pi$
$449$	−20.1880	+	11.6555i	−0.952729	+	0.550058i	−0.0588013	+	0.998270i	$0.518728\pi$
$450$	−20.8025	+	3.88907i	−0.980640	+	0.183332i
$451$	−13.2178	−	7.63129i	−0.622401	−	0.359344i
$452$	−21.7548	+	7.88782i	−1.02326	+	0.371012i
$453$	6.57936	+	28.9305i	0.309125	+	1.35927i
$454$	−3.22065	+	36.5534i	−0.151153	+	1.71554i
$455$	0.0886813	+	0.502937i	0.00415744	+	0.0235780i
$456$	29.9375	+	12.2742i	1.40195	+	0.574794i
$457$	−16.5150	−	13.8577i	−0.772539	−	0.648237i	0.168819	−	0.985647i	$-0.446005\pi$
$457$	−16.5150	−	13.8577i	−0.772539	−	0.648237i	−0.941358	+	0.337410i	$0.890449\pi$
$458$	−8.16453	−	30.5455i	−0.381503	−	1.42730i
$459$	11.2352	−	1.66644i	0.524413	−	0.0777826i
$460$	0.0994400	+	0.172725i	0.00463641	+	0.00805335i
$461$	7.55961	−	9.00920i	0.352086	−	0.419600i	−0.560712	−	0.828011i	$-0.689472\pi$
$461$	7.55961	−	9.00920i	0.352086	−	0.419600i	0.912798	+	0.408411i	$0.133917\pi$
$462$	1.42696	−	3.49265i	0.0663880	−	0.162493i
$463$	−27.5568	+	4.85901i	−1.28067	+	0.225817i	−0.772266	−	0.635300i	$-0.780877\pi$
$463$	−27.5568	+	4.85901i	−1.28067	+	0.225817i	−0.508407	+	0.861117i	$0.669765\pi$
$464$	20.3661	+	24.3929i	0.945471	+	1.13241i
$465$	−0.113018	+	0.365381i	−0.00524111	+	0.0169441i
$466$	1.95566	+	22.5126i	0.0905941	+	1.04288i
$467$	−18.3116	+	31.7166i	−0.847358	+	1.46767i	0.0361989	+	0.999345i	$0.488475\pi$
$467$	−18.3116	+	31.7166i	−0.847358	+	1.46767i	−0.883557	+	0.468323i	$0.844858\pi$
$468$	25.6228	+	11.6478i	1.18441	+	0.538419i
$469$	−3.19297	−	5.53038i	−0.147438	−	0.255369i
$470$	−0.491780	+	0.343898i	−0.0226841	+	0.0158628i
$471$	−26.0849	−	13.3987i	−1.20193	−	0.617381i
$472$	−39.4144	−	3.52155i	−1.81419	−	0.162093i
$473$	−1.02571	−	1.22240i	−0.0471623	−	0.0562059i
$474$	−10.2594	−	31.9984i	−0.471231	−	1.46974i
$475$	11.2678	+	30.9581i	0.517004	+	1.42046i
$476$	−3.78334	−	2.19052i	−0.173409	−	0.100402i
$477$	3.97708	−	15.5173i	0.182098	−	0.710488i
$478$	14.9711	+	4.02135i	0.684761	+	0.183932i
$479$	−6.87445	+	38.9869i	−0.314101	+	1.78136i	0.263112	+	0.964765i	$0.415251\pi$
$479$	−6.87445	+	38.9869i	−0.314101	+	1.78136i	−0.577214	+	0.816593i	$0.695860\pi$
$480$	−0.944978	+	0.494783i	−0.0431321	+	0.0225836i
$481$	−25.7991	−	9.39010i	−1.17634	−	0.428152i
$482$	−30.9628	+	14.4150i	−1.41031	+	0.656586i
$483$	0.198373	−	1.57299i	0.00902626	−	0.0715734i
$484$	16.9892	+	3.01720i	0.772237	+	0.137145i
$485$		−	1.54334i		−	0.0700795i
$486$	−19.2765	+	10.6966i	−0.874399	+	0.485208i
$487$			20.6005i			0.933500i	0.884389	+	0.466750i	$0.154575\pi$
$487$			20.6005i			0.933500i	−0.884389	+	0.466750i	$0.845425\pi$
$488$	−1.83123	−	21.3851i	−0.0828957	−	0.968057i
$489$	1.53624	−	12.1815i	0.0694711	−	0.550869i
$490$	0.0649810	+	0.139576i	0.00293554	+	0.00630541i
$491$	−13.3265	−	4.85044i	−0.601416	−	0.218897i	0.0233272	−	0.999728i	$-0.492574\pi$
$491$	−13.3265	−	4.85044i	−0.601416	−	0.218897i	−0.624743	+	0.780830i	$0.714796\pi$
$492$	10.1836	−	32.7802i	0.459114	−	1.47785i
$493$	3.01543	−	17.1013i	0.135808	−	0.770205i
$494$	11.3664	−	42.3158i	0.511397	−	1.90388i
$495$	−0.124897	+	0.487307i	−0.00561369	+	0.0219028i
$496$	0.0199460	−	8.11313i	0.000895600	−	0.364290i
$497$	−2.80558	−	7.70828i	−0.125848	−	0.345763i
$498$	29.8086	−	9.55732i	1.33576	−	0.428274i
$499$	−8.30376	−	9.89603i	−0.371727	−	0.443007i	0.547458	−	0.836833i	$-0.315596\pi$
$499$	−8.30376	−	9.89603i	−0.371727	−	0.443007i	−0.919185	+	0.393826i	$0.871151\pi$
$500$	−2.04269	−	0.746323i	−0.0913518	−	0.0333766i
$501$	−13.1138	−	6.73600i	−0.585879	−	0.300942i
$502$	−3.72591	−	5.32812i	−0.166296	−	0.237806i
$503$	−0.237733	−	0.411766i	−0.0106000	−	0.0183598i	0.860677	−	0.509152i	$-0.170041\pi$
$503$	−0.237733	−	0.411766i	−0.0106000	−	0.0183598i	−0.871277	+	0.490792i	$0.836707\pi$
$504$	8.36937	+	1.39772i	0.372801	+	0.0622593i
$505$	0.0750089	−	0.129919i	0.00333785	−	0.00578133i
$506$	−1.98643	+	0.172560i	−0.0883077	+	0.00767123i
$507$	4.60927	−	14.9014i	0.204705	−	0.661796i
$508$	4.93377	+	28.1833i	0.218901	+	1.25043i
$509$	15.3208	−	2.70147i	0.679081	−	0.119740i	0.176540	−	0.984293i	$-0.443510\pi$
$509$	15.3208	−	2.70147i	0.679081	−	0.119740i	0.502541	+	0.864553i	$0.332398\pi$
$510$	0.539602	+	0.220460i	0.0238940	+	0.00976213i
$511$	−2.58129	+	3.07627i	−0.114190	+	0.136086i
$512$	16.0883	−	15.9113i	0.711007	−	0.703185i
$513$	21.3343	+	26.8817i	0.941932	+	1.18686i
$514$	−42.3180	+	11.3112i	−1.86657	+	0.498916i
$515$	−0.394897	−	0.331358i	−0.0174013	−	0.0146014i
$516$	2.17268	−	2.85638i	0.0956471	−	0.125745i
$517$	−1.04251	−	5.91235i	−0.0458494	−	0.260025i
$518$	−8.24496	−	0.726447i	−0.362263	−	0.0319182i
$519$	−5.71551	−	25.1320i	−0.250883	−	1.10317i
$520$	0.826328	+	1.18476i	0.0362369	+	0.0519552i
$521$	30.6943	+	17.7214i	1.34474	+	0.776387i	0.987499	−	0.157625i	$-0.0503836\pi$
$521$	30.6943	+	17.7214i	1.34474	+	0.776387i	0.357242	+	0.934012i	$0.383717\pi$
$522$	6.19386	+	33.1308i	0.271098	+	1.45010i
$523$	12.6938	−	7.32879i	0.555063	−	0.320466i	−0.196099	−	0.980584i	$-0.562827\pi$
$523$	12.6938	−	7.32879i	0.555063	−	0.320466i	0.751162	+	0.660118i	$0.229494\pi$
$524$	9.27539	−	11.0264i	0.405197	−	0.481692i
$525$	4.68176	+	7.26126i	0.204329	+	0.316907i
$526$	25.0882	+	17.5899i	1.09390	+	0.766956i
$527$	−3.39631	+	2.84984i	−0.147945	+	0.124141i
$528$	−0.497371	−	10.6598i	−0.0216453	−	0.463908i
$529$	20.8256	−	7.57989i	0.905460	−	0.329560i
$530$	0.581665	−	0.580950i	0.0252659	−	0.0252349i
$531$	−34.6416	−	23.6978i	−1.50332	−	1.02840i
$532$	0.0162373	−	13.2093i	0.000703978	−	0.572695i
$533$	−45.7768	−	8.07168i	−1.98281	−	0.349623i
$534$	5.33061	−	2.80778i	0.230678	−	0.121505i
$535$	−0.208662	+	0.573293i	−0.00902122	+	0.0247856i
$536$	−14.7765	−	10.3873i	−0.638248	−	0.448662i
$537$	0.713796	+	1.69704i	0.0308026	+	0.0732326i
$538$	−20.4877	−	9.56890i	−0.883287	−	0.412545i
$539$	−1.54028			−0.0663446
$540$	−1.13092	−	0.0322539i	−0.0486670	−	0.00138799i
$541$	10.9794			0.472041			0.236020	−	0.971748i	$-0.424157\pi$
$541$	10.9794			0.472041			0.236020	+	0.971748i	$0.424157\pi$
$542$	−7.87825	−	3.67958i	−0.338400	−	0.158052i
$543$	23.7172	−	31.2602i	1.01780	−	1.34150i
$544$	−12.3147	−	1.11554i	−0.527988	−	0.0478284i
$545$	0.0836413	−	0.229803i	0.00358280	−	0.00984366i
$546$	0.445697	−	11.4819i	0.0190741	−	0.491381i
$547$	7.85474	+	1.38500i	0.335845	+	0.0592185i	0.339027	−	0.940776i	$-0.389902\pi$
$547$	7.85474	+	1.38500i	0.335845	+	0.0592185i	−0.00318290	+	0.999995i	$0.501013\pi$
$548$	15.4526	+	0.0189950i	0.660104	+	0.000811425i
$549$	9.39558	−	20.7360i	0.400994	−	0.884992i
$550$	7.68788	−	7.67843i	0.327812	−	0.327409i
$551$	49.3050	−	17.9456i	2.10046	−	0.764506i
$552$	−1.36388	−	4.27188i	−0.0580504	−	0.181823i
$553$	−10.5088	+	8.81797i	−0.446882	+	0.374978i
$554$	6.51489	+	4.56774i	0.276791	+	0.194065i
$555$	1.10226	−	0.0541462i	0.0467885	−	0.00229838i
$556$	−13.8606	−	11.6595i	−0.587822	−	0.494474i
$557$	−23.0301	+	13.2965i	−0.975819	+	0.563389i	−0.901005	−	0.433808i	$-0.857169\pi$
$557$	−23.0301	+	13.2965i	−0.975819	+	0.563389i	−0.0748135	+	0.997198i	$0.523836\pi$
$558$	4.22577	−	7.49627i	0.178891	−	0.317342i
$559$	−4.20876	−	2.42993i	−0.178012	−	0.102775i
$560$	0.332899	+	0.280733i	0.0140675	+	0.0118631i
$561$	−4.27793	+	3.96311i	−0.180614	+	0.167323i
$562$	30.8856	+	2.72127i	1.30283	+	0.114790i
$563$	2.98341	+	16.9197i	0.125736	+	0.713082i	0.980868	+	0.194673i	$0.0623645\pi$
$563$	2.98341	+	16.9197i	0.125736	+	0.713082i	−0.855133	+	0.518409i	$0.826524\pi$
$564$	12.4523	−	5.21961i	0.524338	−	0.219785i
$565$	−0.964928	−	0.809671i	−0.0405948	−	0.0340631i
$566$	−13.4870	+	3.60495i	−0.566901	+	0.151527i
$567$	7.01887	+	5.63343i	0.294765	+	0.236582i
$568$	−16.3757	−	16.4362i	−0.687108	−	0.689647i
$569$	21.8177	−	26.0013i	0.914646	−	1.09003i	−0.0809901	−	0.996715i	$-0.525808\pi$
$569$	21.8177	−	26.0013i	0.914646	−	1.09003i	0.995636	−	0.0933180i	$-0.0297473\pi$
$570$	0.238330	+	1.74505i	0.00998255	+	0.0730922i
$571$	−7.52233	+	1.32639i	−0.314800	+	0.0555077i	−0.328816	−	0.944394i	$-0.606649\pi$
$571$	−7.52233	+	1.32639i	−0.314800	+	0.0555077i	0.0140161	+	0.999902i	$0.495538\pi$
$572$	−14.2345	+	2.49188i	−0.595173	+	0.104191i
$573$	−8.72302	−	9.41596i	−0.364409	−	0.393357i
$574$	−13.9608	+	1.21277i	−0.582713	+	0.0506199i
$575$	2.28297	−	3.95422i	0.0952065	−	0.164902i
$576$	23.1368	−	6.37869i	0.964034	−	0.265779i
$577$	11.1833	+	19.3700i	0.465566	+	0.806383i	0.999227	−	0.0393151i	$-0.0125176\pi$
$577$	11.1833	+	19.3700i	0.465566	+	0.806383i	−0.533661	+	0.845698i	$0.679184\pi$
$578$	−9.90529	−	14.1647i	−0.412006	−	0.589176i
$579$	−1.65199	−	33.6299i	−0.0686545	−	1.39761i
$580$	−0.593605	+	1.62470i	−0.0246481	+	0.0674619i
$581$	−8.21451	−	9.78967i	−0.340795	−	0.406144i
$582$	−7.35184	+	33.9378i	−0.304744	+	1.40677i
$583$	2.81295	+	7.72852i	0.116500	+	0.320082i
$584$	−2.95998	+	10.9659i	−0.122485	+	0.453771i
$585$	0.150158	+	1.52471i	0.00620827	+	0.0630390i
$586$	5.07309	−	18.8866i	0.209567	−	0.780198i
$587$	−0.309297	+	1.75411i	−0.0127660	+	0.0723998i	−0.990525	−	0.137331i	$-0.956148\pi$
$587$	−0.309297	+	1.75411i	−0.0127660	+	0.0723998i	0.977759	+	0.209731i	$0.0672587\pi$
$588$	−0.764037	−	3.37879i	−0.0315083	−	0.139339i
$589$	−12.5883	−	4.58175i	−0.518690	−	0.188788i
$590$	−0.909123	−	1.95275i	−0.0374280	−	0.0803935i
$591$	26.9406	+	20.4399i	1.10819	+	0.840786i
$592$	−22.0184	+	7.95279i	−0.904950	+	0.326858i
$593$		−	18.6090i		−	0.764179i	−0.924125	−	0.382089i	$-0.875205\pi$
$593$		−	18.6090i		−	0.764179i	0.924125	−	0.382089i	$-0.124795\pi$
$594$	5.06778	−	10.1208i	0.207934	−	0.415262i
$595$		−	0.237968i		−	0.00975575i
$596$	−3.12530	+	17.5979i	−0.128017	+	0.720838i
$597$	4.17295	−	1.75520i	0.170788	−	0.0718355i
$598$	−5.50519	+	2.56299i	−0.225124	+	0.104809i
$599$	25.0862	+	9.13064i	1.02500	+	0.373068i	0.799173	−	0.601100i	$-0.205271\pi$
$599$	25.0862	+	9.13064i	1.02500	+	0.373068i	0.225823	+	0.974168i	$0.427493\pi$
$600$	20.6570	+	13.0555i	0.843320	+	0.532988i
$601$	4.10854	−	23.3007i	0.167591	−	0.950455i	−0.778762	−	0.627320i	$-0.784152\pi$
$601$	4.10854	−	23.3007i	0.167591	−	0.950455i	0.946353	−	0.323135i	$-0.104737\pi$
$602$	−1.41496	−	0.380071i	−0.0576696	−	0.0154905i
$603$	−8.28521	−	17.2736i	−0.337400	−	0.703435i
$604$	17.1660	−	29.6481i	0.698474	−	1.20637i
$605$	0.321243	+	0.882609i	0.0130604	+	0.0358832i
$606$	−2.26831	+	2.49959i	−0.0921438	+	0.101539i
$607$	22.3365	+	26.6196i	0.906611	+	1.08046i	0.996424	+	0.0844978i	$0.0269286\pi$
$607$	22.3365	+	26.6196i	0.906611	+	1.08046i	−0.0898131	+	0.995959i	$0.528627\pi$
$608$	−15.6855	−	33.9094i	−0.636132	−	1.37521i
$609$	11.5645	−	7.45634i	0.468619	−	0.302146i
$610$	0.957447	−	0.669535i	0.0387659	−	0.0271087i
$611$	−9.14207	−	15.8345i	−0.369848	−	0.640596i
$612$	−10.8156	−	7.41831i	−0.437193	−	0.299867i
$613$	10.0774	−	17.4545i	0.407021	−	0.704981i	−0.587533	−	0.809200i	$-0.699901\pi$
$613$	10.0774	−	17.4545i	0.407021	−	0.704981i	0.994554	+	0.104219i	$0.0332343\pi$
$614$	−1.95208	−	22.4714i	−0.0787795	−	0.906873i
$615$	1.82194	−	0.414345i	0.0734678	−	0.0167080i
$616$	−3.95179	+	1.83389i	−0.159222	+	0.0738893i
$617$	5.32587	−	0.939095i	0.214412	−	0.0378065i	−0.0654105	−	0.997858i	$-0.520836\pi$
$617$	5.32587	−	0.939095i	0.214412	−	0.0378065i	0.279822	+	0.960052i	$0.409725\pi$
$618$	7.10526	+	9.16763i	0.285815	+	0.368776i
$619$	0.992098	−	1.18234i	0.0398758	−	0.0475221i	−0.745738	−	0.666239i	$-0.767903\pi$
$619$	0.992098	−	1.18234i	0.0398758	−	0.0475221i	0.785614	+	0.618717i	$0.212347\pi$
$620$	0.382732	−	0.220343i	0.0153709	−	0.00884920i
$621$	0.953403	−	4.65981i	0.0382588	−	0.186992i
$622$	−0.213576	−	0.799041i	−0.00856362	−	0.0320386i
$623$	−1.88419	−	1.58103i	−0.0754886	−	0.0633425i
$624$	−12.5271	−	29.9890i	−0.501484	−	1.20052i
$625$	4.31036	+	24.4453i	0.172414	+	0.977810i
$626$	2.05848	−	23.3631i	0.0822733	−	0.933778i
$627$	−16.8333	−	5.20683i	−0.672257	−	0.207941i
$628$	11.5422	+	31.8335i	0.460582	+	1.27030i
$629$	11.0791	+	6.39655i	0.441754	+	0.255047i
$630$	0.162429	+	0.432381i	0.00647133	+	0.0172265i
$631$	35.9719	−	20.7684i	1.43202	−	0.826777i	0.434745	−	0.900554i	$-0.356838\pi$
$631$	35.9719	−	20.7684i	1.43202	−	0.826777i	0.997275	+	0.0737765i	$0.0235051\pi$
$632$	−16.4629	+	35.1356i	−0.654861	+	1.39762i
$633$	16.1130	−	31.3690i	0.640435	−	1.24681i
$634$	24.7392	−	35.2850i	0.982518	−	1.40135i
$635$	−1.19307	+	1.00111i	−0.0473457	+	0.0397278i
$636$	−15.5581	+	10.0042i	−0.616919	+	0.396691i
$637$	−4.40810	+	1.60442i	−0.174655	+	0.0635694i
$638$	−12.2289	−	12.2440i	−0.484148	−	0.484744i
$639$	−6.62798	−	23.6996i	−0.262199	−	0.937540i
$640$	1.18834	+	0.323900i	0.0469732	+	0.0128033i
$641$	−42.7284	−	7.53418i	−1.68767	−	0.297582i	−0.754310	−	0.656518i	$-0.772028\pi$
$641$	−42.7284	−	7.53418i	−1.68767	−	0.297582i	−0.933362	+	0.358936i	$0.883140\pi$
$642$	7.31935	−	11.6126i	0.288872	−	0.458313i
$643$	6.03680	−	16.5860i	0.238068	−	0.654087i	−0.761911	−	0.647682i	$-0.775739\pi$
$643$	6.03680	−	16.5860i	0.238068	−	0.654087i	0.999979	−	0.00640580i	$-0.00203904\pi$
$644$	−1.40386	+	1.17504i	−0.0553197	+	0.0463029i
$645$	0.193815	+	0.0244424i	0.00763148	+	0.000962420i
$646$	−8.63988	+	18.4986i	−0.339932	+	0.727817i
$647$	16.0164			0.629670			0.314835	−	0.949146i	$-0.398051\pi$
$647$	16.0164			0.629670			0.314835	+	0.949146i	$0.398051\pi$
$648$	24.7150	+	6.09648i	0.970898	+	0.239493i
$649$	21.5495			0.845890
$650$	14.0036	−	29.9827i	0.549267	−	1.17602i
$651$	−3.48549	−	0.439562i	−0.136607	−	0.0172278i
$652$	−10.8718	+	9.09973i	−0.425771	+	0.356373i
$653$	−1.43506	+	3.94279i	−0.0561581	+	0.154293i	−0.964600	−	0.263719i	$-0.915051\pi$
$653$	−1.43506	+	3.94279i	−0.0561581	+	0.154293i	0.908441	+	0.418012i	$0.137273\pi$
$654$	−2.93394	+	4.65488i	−0.114726	+	0.182020i
$655$	0.772408	+	0.136196i	0.0301805	+	0.00532163i
$656$	−34.3742	+	19.7335i	−1.34209	+	0.770462i
$657$	−8.42540	+	8.61110i	−0.328706	+	0.335951i
$658$	−3.89530	−	3.90010i	−0.151855	−	0.152042i
$659$	−10.3124	+	3.75339i	−0.401713	+	0.146211i	−0.534972	−	0.844870i	$-0.679678\pi$
$659$	−10.3124	+	3.75339i	−0.401713	+	0.146211i	0.133259	+	0.991081i	$0.457456\pi$
$660$	0.488588	−	0.314172i	0.0190183	−	0.0122291i
$661$	−25.0995	+	21.0610i	−0.976258	+	0.819178i	−0.983521	−	0.180796i	$-0.942133\pi$
$661$	−25.0995	+	21.0610i	−0.976258	+	0.819178i	0.00726275	+	0.999974i	$0.497688\pi$
$662$	17.8304	−	25.4312i	0.692998	−	0.988410i
$663$	−8.11480	+	15.7980i	−0.315153	+	0.613544i
$664$	−32.7311	−	15.3363i	−1.27021	−	0.595164i
$665$	0.622696	−	0.359514i	0.0241471	−	0.0139414i
$666$	−24.4965	−	4.06007i	−0.949221	−	0.157324i
$667$	−6.29763	−	3.63594i	−0.243845	−	0.140784i
$668$	5.80264	+	16.0038i	0.224511	+	0.619206i
$669$	4.82263	+	1.49172i	0.186453	+	0.0576733i
$670$	0.0862922	−	0.979391i	0.00333376	−	0.0378372i
$671$	2.02966	+	11.5108i	0.0783541	+	0.444368i
$672$	−5.98308	−	7.75904i	−0.230802	−	0.299312i
$673$	−9.59434	−	8.05061i	−0.369835	−	0.310328i	0.438862	−	0.898555i	$-0.355382\pi$
$673$	−9.59434	−	8.05061i	−0.369835	−	0.310328i	−0.808696	+	0.588227i	$0.799826\pi$
$674$	−0.805539	−	3.01372i	−0.0310282	−	0.116084i
$675$	12.3424	+	22.7918i	0.475060	+	0.877259i
$676$	−15.6091	+	8.98634i	−0.600349	+	0.345629i
$677$	0.402170	−	0.479287i	0.0154566	−	0.0184205i	−0.758261	−	0.651951i	$-0.773951\pi$
$677$	0.402170	−	0.479287i	0.0154566	−	0.0184205i	0.773717	+	0.633531i	$0.218395\pi$
$678$	17.3616	+	22.4010i	0.666770	+	0.860306i
$679$	13.9610	−	2.46171i	0.535775	−	0.0944716i
$680$	−0.283329	−	0.610537i	−0.0108652	−	0.0234130i
$681$	43.8231	−	9.96623i	1.67930	−	0.381907i
$682$	0.382366	+	4.40162i	0.0146416	+	0.168547i
$683$	−13.3675	+	23.1531i	−0.511492	+	0.885929i	0.488420	+	0.872609i	$0.337574\pi$
$683$	−13.3675	+	23.1531i	−0.511492	+	0.885929i	−0.999911	+	0.0133206i	$0.995760\pi$
$684$	3.07187	−	39.5086i	0.117456	−	1.51065i
$685$	0.420571	+	0.728450i	0.0160692	+	0.0278326i
$686$	−1.15895	+	0.810447i	−0.0442491	+	0.0309430i
$687$	−32.5454	+	20.9840i	−1.24169	+	0.800588i
$688$	−4.08278	+	0.709560i	−0.155655	+	0.0270517i
$689$	16.1007	+	19.1880i	0.613386	+	0.731005i
$690$	0.164038	−	0.180763i	0.00624480	−	0.00688152i
$691$	−7.78679	−	21.3940i	−0.296223	−	0.813867i	−0.995123	−	0.0986468i	$-0.968549\pi$
$691$	−7.78679	−	21.3940i	−0.296223	−	0.813867i	0.698899	−	0.715220i	$-0.253674\pi$
$692$	−14.9121	+	25.7554i	−0.566874	+	0.979074i
$693$	−4.60738	−	0.352535i	−0.175020	−	0.0133917i
$694$	39.0978	+	10.5020i	1.48413	+	0.398650i
$695$	0.171204	−	0.970946i	0.00649414	−	0.0368301i
$696$	20.7926	−	32.8991i	0.788143	−	1.24704i
$697$	20.3534	+	7.40803i	0.770939	+	0.280599i
$698$	21.7603	−	10.1307i	0.823641	−	0.383454i
$699$	25.5113	−	10.7304i	0.964924	−	0.405860i
$700$	1.74444	−	9.82260i	0.0659337	−	0.371259i
$701$			9.69791i			0.366285i	0.983086	+	0.183142i	$0.0586270\pi$
$701$			9.69791i			0.366285i	−0.983086	+	0.183142i	$0.941373\pi$
$702$	3.96114	−	34.2434i	0.149504	−	1.29243i
$703$			38.6547i			1.45789i
$704$	−7.95535	+	9.41012i	−0.299829	+	0.354657i
$705$	0.585515	+	0.444232i	0.0220518	+	0.0167308i
$706$	1.96158	+	4.21339i	0.0738251	+	0.158573i
$707$	1.29489	+	0.471301i	0.0486993	+	0.0177251i
$708$	10.6893	+	47.2713i	0.401729	+	1.77656i
$709$	−5.11585	+	29.0134i	−0.192130	+	1.08962i	0.724318	+	0.689466i	$0.242155\pi$
$709$	−5.11585	+	29.0134i	−0.192130	+	1.08962i	−0.916447	+	0.400155i	$0.868956\pi$
$710$	0.327623	−	1.21970i	0.0122955	−	0.0457747i
$711$	−33.4529	+	23.9716i	−1.25458	+	0.899005i
$712$	−6.71653	−	1.81297i	−0.251713	−	0.0679439i
$713$	0.634999	+	1.74464i	0.0237809	+	0.0653374i
$714$	−1.13358	+	5.23287i	−0.0424232	+	0.195835i
$715$	−0.505626	−	0.602582i	−0.0189094	−	0.0225353i
$716$	0.729540	−	1.99675i	0.0272642	−	0.0746222i
$717$	−0.931505	−	18.9628i	−0.0347877	−	0.708179i
$718$	12.9932	+	18.5806i	0.484903	+	0.693420i
$719$	4.18118	+	7.24202i	0.155932	+	0.270082i	0.933398	−	0.358843i	$-0.116829\pi$
$719$	4.18118	+	7.24202i	0.155932	+	0.270082i	−0.777466	+	0.628925i	$0.783495\pi$
$720$	0.931532	+	0.915936i	0.0347161	+	0.0341349i
$721$	2.36758	−	4.10076i	0.0881732	−	0.152720i
$722$	−34.6892	+	3.01343i	−1.29100	+	0.112148i
$723$	28.4274	+	30.6856i	1.05723	+	1.14121i
$724$	−44.6307	+	7.81304i	−1.65869	+	0.290369i
$725$	39.0253	−	6.88121i	1.44936	−	0.255562i
$726$	−2.85970	−	20.9387i	−0.106133	−	0.777107i
$727$	−20.0332	+	23.8746i	−0.742990	+	0.885461i	−0.996646	−	0.0818338i	$-0.973922\pi$
$727$	−20.0332	+	23.8746i	−0.742990	+	0.885461i	0.253656	+	0.967294i	$0.418367\pi$
$728$	−9.39929	+	9.36469i	−0.348361	+	0.347079i
$729$	19.7059	+	18.4575i	0.729847	+	0.683610i
$730$	−0.597305	+	0.159654i	−0.0221073	+	0.00590906i
$731$	1.73474	+	1.45562i	0.0641618	+	0.0538381i
$732$	−24.2435	+	10.1621i	−0.896064	+	0.375601i
$733$	0.508394	+	2.88325i	0.0187780	+	0.106495i	0.992756	−	0.120147i	$-0.0383365\pi$
$733$	0.508394	+	2.88325i	0.0187780	+	0.106495i	−0.973978	+	0.226642i	$0.927225\pi$
$734$	36.3895	+	3.20621i	1.34316	+	0.118343i
$735$	0.138327	−	0.128147i	0.00510227	−	0.00472678i
$736$	−2.20275	+	4.68616i	−0.0811944	+	0.172734i
$737$	8.51835	+	4.91807i	0.313777	+	0.181159i
$738$	−42.0379	+	0.432393i	−1.54744	+	0.0159166i
$739$	29.2977	−	16.9151i	1.07774	−	0.622231i	0.147451	−	0.989069i	$-0.452893\pi$
$739$	29.2977	−	16.9151i	1.07774	−	0.622231i	0.930285	+	0.366839i	$0.119560\pi$
$740$	−0.975179	−	0.820317i	−0.0358483	−	0.0301554i
$741$	−53.5985	+	2.63290i	−1.96899	+	0.0967222i
$742$	6.18305	+	4.33508i	0.226987	+	0.159146i
$743$	1.22486	−	1.02778i	0.0449357	−	0.0377055i	−0.620043	−	0.784568i	$-0.712885\pi$
$743$	1.22486	−	1.02778i	0.0449357	−	0.0377055i	0.664979	+	0.746862i	$0.268441\pi$
$744$	−9.46582	+	3.02213i	−0.347034	+	0.110797i
$745$	−0.914231	+	0.332753i	−0.0334948	+	0.0121911i
$746$	26.9520	−	26.9189i	0.986782	−	0.985570i
$747$	−22.3311	−	31.1635i	−0.817051	−	1.14021i
$748$	6.73369	+	0.00827730i	0.246208	+	0.000302648i
$749$	−5.51882	−	0.973116i	−0.201653	−	0.0355569i
$750$	−0.103313	+	2.66152i	−0.00377246	+	0.0971850i
$751$	18.0388	−	49.5612i	0.658245	−	1.80851i	0.0735007	−	0.997295i	$-0.476583\pi$
$751$	18.0388	−	49.5612i	0.658245	−	1.80851i	0.584744	−	0.811218i	$-0.301195\pi$
$752$	−14.6374	−	5.36837i	−0.533771	−	0.195764i
$753$	−4.81297	+	6.34368i	−0.175395	+	0.231176i
$754$	−47.7516	−	22.3027i	−1.73901	−	0.812215i
$755$	1.86484			0.0678684
$756$	−1.51210	−	10.2817i	−0.0549947	−	0.373942i
$757$	−33.7023			−1.22493			−0.612466	−	0.790497i	$-0.709822\pi$
$757$	−33.7023			−1.22493			−0.612466	+	0.790497i	$0.709822\pi$
$758$	−46.3264	−	21.6371i	−1.68265	−	0.785893i
$759$	0.946809	+	2.25102i	0.0343670	+	0.0817068i
$760$	1.16956	−	1.66377i	0.0424245	−	0.0603513i
$761$	11.4170	−	31.3680i	0.413866	−	1.13709i	−0.541251	−	0.840861i	$-0.682049\pi$
$761$	11.4170	−	31.3680i	0.413866	−	1.13709i	0.955117	−	0.296227i	$-0.0957286\pi$
$762$	31.0043	−	16.3309i	1.12317	−	0.591604i
$763$	2.21220	+	0.390071i	0.0800870	+	0.0141215i
$764$	−0.0182188	+	14.8212i	−0.000659132	+	0.536212i
$765$	0.0544654	−	0.711824i	0.00196920	−	0.0257361i
$766$	−20.6244	+	20.5990i	−0.745188	+	0.744273i
$767$	61.6719	−	22.4468i	2.22684	−	0.810505i
$768$	−24.5884	−	12.7832i	−0.887257	−	0.461276i
$769$	9.27191	−	7.78006i	0.334354	−	0.280556i	−0.460117	−	0.887858i	$-0.652193\pi$
$769$	9.27191	−	7.78006i	0.334354	−	0.280556i	0.794471	+	0.607302i	$0.207748\pi$
$770$	−0.194173	−	0.136139i	−0.00699751	−	0.00490612i
$771$	29.0714	+	45.0888i	1.04698	+	1.62383i
$772$	−25.0277	+	29.7525i	−0.900768	+	1.07082i
$773$	−1.08695	+	0.627551i	−0.0390949	+	0.0225714i	−0.519420	−	0.854519i	$-0.673852\pi$
$773$	−1.08695	+	0.627551i	−0.0390949	+	0.0225714i	0.480325	+	0.877090i	$0.340519\pi$
$774$	−4.14553	−	1.46074i	−0.149008	−	0.0525052i
$775$	−8.76193	−	5.05870i	−0.314738	−	0.181714i
$776$	32.8878	−	22.9380i	1.18060	−	0.823428i
$777$	2.24797	+	9.88469i	0.0806456	+	0.354611i
$778$	−9.59592	−	0.845477i	−0.344030	−	0.0303118i
$779$	11.3644	+	64.4509i	0.407173	+	2.30919i
$780$	1.07103	−	1.40806i	0.0383489	−	0.0504165i
$781$	9.67889	+	8.12156i	0.346338	+	0.290612i
$782$	2.73366	−	0.730681i	0.0977554	−	0.0261291i
$783$	36.2991	−	19.6570i	1.29722	−	0.702483i
$784$	−2.00851	+	3.45917i	−0.0717325	+	0.123542i
$785$	−1.18478	+	1.41197i	−0.0422867	+	0.0503953i
$786$	−16.3363	−	6.67436i	−0.582697	−	0.238067i
$787$	−13.4432	+	2.37039i	−0.479197	+	0.0844954i	−0.408029	−	0.912969i	$-0.633784\pi$
$787$	−13.4432	+	2.37039i	−0.479197	+	0.0844954i	−0.0711681	+	0.997464i	$0.522673\pi$
$788$	−6.73341	−	38.4635i	−0.239868	−	1.37021i
$789$	11.0892	−	35.8505i	0.394785	−	1.27631i
$790$	−2.10416	+	0.182787i	−0.0748628	+	0.00650329i
$791$	5.78515	−	10.0202i	0.205696	−	0.356277i
$792$	−12.2405	+	4.58115i	−0.434949	+	0.162784i
$793$	17.7987	+	30.8283i	0.632050	+	1.09474i
$794$	−0.483052	−	0.690773i	−0.0171429	−	0.0245146i
$795$	−0.895612	−	0.460040i	−0.0317641	−	0.0163159i
$796$	−4.90995	−	1.79391i	−0.174028	−	0.0635835i
$797$	15.3386	+	18.2799i	0.543322	+	0.647506i	0.965929	−	0.258807i	$-0.0833294\pi$
$797$	15.3386	+	18.2799i	0.543322	+	0.647506i	−0.422607	+	0.906313i	$0.638885\pi$
$798$	−15.4055	+	4.93937i	−0.545350	+	0.174852i
$799$	2.91396	+	8.00603i	0.103088	+	0.283233i
$800$	−7.21936	−	27.2781i	−0.255243	−	0.964425i
$801$	−5.27425	−	5.16050i	−0.186356	−	0.182337i
$802$	−5.57488	+	20.7547i	−0.196856	+	0.732874i
$803$	1.07409	−	6.09146i	0.0379038	−	0.214963i
$804$	−6.56296	+	21.1256i	−0.231458	+	0.745041i
$805$	−0.0936425	−	0.0340831i	−0.00330046	−	0.00120127i
$806$	5.67919	+	12.1986i	0.200041	+	0.429678i
$807$	−3.46511	+	27.4765i	−0.121978	+	0.967218i
$808$	3.88334	−	0.332534i	0.136615	−	0.0116985i
$809$			17.0535i			0.599569i	0.954007	+	0.299784i	$0.0969147\pi$
$809$			17.0535i			0.599569i	−0.954007	+	0.299784i	$0.903085\pi$
$810$	0.386905	+	1.33054i	0.0135945	+	0.0467503i
$811$		−	15.5476i		−	0.545951i	−0.962021	−	0.272976i	$-0.911992\pi$
$811$		−	15.5476i		−	0.545951i	0.962021	−	0.272976i	$-0.0880079\pi$
$812$	−15.6438	−	2.77826i	−0.548990	−	0.0974977i
$813$	−1.33246	+	10.5657i	−0.0467314	+	0.370555i
$814$	11.5576	−	5.38076i	0.405094	−	0.188595i
$815$	−0.725187	−	0.263947i	−0.0254022	−	0.00924565i
$816$	3.32200	+	14.7753i	0.116293	+	0.517237i
$817$	−1.18817	+	6.73844i	−0.0415687	+	0.235748i
$818$	−24.4243	−	6.56055i	−0.853974	−	0.229384i
$819$	−13.5530	+	3.79031i	−0.473579	+	0.132444i
$820$	−1.86714	−	1.08105i	−0.0652032	−	0.0377520i
$821$	−7.42180	−	20.3912i	−0.259022	−	0.711658i	−0.999228	−	0.0392781i	$-0.987494\pi$
$821$	−7.42180	−	20.3912i	−0.259022	−	0.711658i	0.740206	−	0.672380i	$-0.234728\pi$
$822$	−5.77824	−	18.0219i	−0.201539	−	0.628586i
$823$	19.8954	+	23.7105i	0.693511	+	0.826495i	0.991776	−	0.127989i	$-0.0408521\pi$
$823$	19.8954	+	23.7105i	0.693511	+	0.826495i	−0.298264	+	0.954483i	$0.596408\pi$
$824$	1.19188	−	13.3399i	0.0415211	−	0.464717i
$825$	−11.8373	−	6.08035i	−0.412122	−	0.211691i
$826$	16.2145	−	11.3386i	0.564173	−	0.394522i
$827$	1.40574	+	2.43481i	0.0488824	+	0.0846668i	0.889431	−	0.457069i	$-0.151101\pi$
$827$	1.40574	+	2.43481i	0.0488824	+	0.0846668i	−0.840549	+	0.541736i	$0.817767\pi$
$828$	−4.46823	+	3.19353i	−0.155282	+	0.110983i
$829$	2.40826	−	4.17123i	0.0836424	−	0.144873i	−0.821170	−	0.570684i	$-0.806678\pi$
$829$	2.40826	−	4.17123i	0.0836424	−	0.144873i	0.904812	+	0.425812i	$0.140011\pi$
$830$	−0.170278	−	1.96017i	−0.00591045	−	0.0680383i
$831$	2.87964	−	9.30966i	0.0998935	−	0.322949i
$832$	−12.9653	+	35.2172i	−0.449491	+	1.22094i
$833$	2.15265	−	0.379571i	0.0745851	−	0.0131514i
$834$	−8.38993	+	20.5354i	−0.290519	+	0.711082i
$835$	−0.595631	+	0.709845i	−0.0206126	+	0.0245652i
$836$	10.1514	+	17.6327i	0.351092	+	0.609839i
$837$	−10.3254	−	2.11259i	−0.356898	−	0.0730218i
$838$	−3.22672	−	12.0720i	−0.111465	−	0.417019i
$839$	−17.6527	−	14.8124i	−0.609438	−	0.511379i	0.285026	−	0.958520i	$-0.407998\pi$
$839$	−17.6527	−	14.8124i	−0.609438	−	0.511379i	−0.894464	+	0.447141i	$0.852442\pi$
$840$	0.202321	−	0.493472i	0.00698074	−	0.0170264i
$841$	−5.92346	−	33.5936i	−0.204257	−	1.15840i
$842$	−3.65530	+	41.4865i	−0.125970	+	1.42972i
$843$	−8.42089	−	37.0280i	−0.290031	−	1.27531i
$844$	−38.2823	+	13.8803i	−1.31773	+	0.477781i
$845$	−0.849055	−	0.490202i	−0.0292084	−	0.0168635i
$846$	−10.7592	−	12.5577i	−0.369909	−	0.431744i
$847$	−7.47166	+	4.31377i	−0.256729	+	0.148223i
$848$	21.0248	+	3.76056i	0.721995	+	0.129138i
$849$	9.26522	+	14.3700i	0.317981	+	0.493179i
$850$	−8.85216	+	12.6257i	−0.303627	+	0.433057i
$851$	4.10391	−	3.44359i	0.140680	−	0.118045i
$852$	−13.0145	+	25.2604i	−0.445870	+	0.865407i
$853$	40.5794	−	14.7697i	1.38941	−	0.505705i	0.464395	−	0.885628i	$-0.346272\pi$
$853$	40.5794	−	14.7697i	1.38941	−	0.505705i	0.925018	+	0.379924i	$0.124050\pi$
$854$	7.58377	+	7.59310i	0.259511	+	0.259831i
$855$	1.94493	−	0.932878i	0.0665152	−	0.0319037i
$856$	−15.3178	+	4.07414i	−0.523553	+	0.139251i
$857$	−6.07011	−	1.07032i	−0.207351	−	0.0365616i	0.0690077	−	0.997616i	$-0.478017\pi$
$857$	−6.07011	−	1.07032i	−0.207351	−	0.0365616i	−0.276359	+	0.961055i	$0.589128\pi$
$858$	8.24817	+	15.6593i	0.281588	+	0.534598i
$859$	8.48355	−	23.3084i	0.289455	−	0.795271i	−0.706688	−	0.707525i	$-0.749812\pi$
$859$	8.48355	−	23.3084i	0.289455	−	0.795271i	0.996143	−	0.0877455i	$-0.0279662\pi$
$860$	−0.144782	−	0.172976i	−0.00493703	−	0.00589843i
$861$	6.65424	+	15.8203i	0.226776	+	0.539156i
$862$	10.0283	−	21.4714i	0.341567	−	0.731318i
$863$	−39.7716			−1.35384			−0.676921	−	0.736055i	$-0.736686\pi$
$863$	−39.7716			−1.35384			−0.676921	+	0.736055i	$0.736686\pi$
$864$	−16.1211	−	24.5787i	−0.548450	−	0.836184i
$865$	−1.61999			−0.0550813
$866$	−5.81541	+	12.4512i	−0.197616	+	0.423109i
$867$	−12.7952	+	16.8646i	−0.434549	+	0.572751i
$868$	2.60370	+	3.11072i	0.0883752	+	0.105585i
$869$	7.22692	−	19.8558i	0.245156	−	0.673562i
$870$	2.11690	+	0.0821723i	0.0717696	+	0.00278590i
$871$	29.5013	+	5.20188i	0.999615	+	0.176259i
$872$	6.14010	−	1.63311i	0.207930	−	0.0553040i
$873$	42.3244	−	4.16824i	1.43247	−	0.141074i
$874$	6.04190	+	6.04933i	0.204370	+	0.204622i
$875$	1.02180	−	0.371906i	0.0345432	−	0.0125727i
$876$	13.8951	−	0.665447i	0.469474	−	0.0224834i
$877$	1.37224	−	1.15145i	0.0463373	−	0.0388816i	−0.619325	−	0.785135i	$-0.712594\pi$
$877$	1.37224	−	1.15145i	0.0463373	−	0.0388816i	0.665662	+	0.746253i	$0.268149\pi$
$878$	−12.2627	+	17.4901i	−0.413846	+	0.590261i
$879$	−23.9223	+	1.17513i	−0.806881	+	0.0396362i
$880$	−0.660265	−	0.118097i	−0.0222575	−	0.00398105i
$881$	−10.0204	+	5.78529i	−0.337596	+	0.194911i	−0.659209	−	0.751960i	$-0.729109\pi$
$881$	−10.0204	+	5.78529i	−0.337596	+	0.194911i	0.321612	+	0.946871i	$0.395775\pi$
$882$	−3.65222	+	2.15900i	−0.122977	+	0.0726973i
$883$	2.53017	+	1.46079i	0.0851470	+	0.0491596i	0.541969	−	0.840399i	$-0.317679\pi$
$883$	2.53017	+	1.46079i	0.0851470	+	0.0491596i	−0.456822	+	0.889558i	$0.651012\pi$
$884$	19.2796	−	6.99038i	0.648444	−	0.235112i
$885$	−1.93528	+	1.79285i	−0.0650536	+	0.0602661i
$886$	0.455280	−	5.16729i	0.0152954	−	0.173599i
$887$	−0.347362	−	1.96999i	−0.0116633	−	0.0661457i	0.978421	−	0.206623i	$-0.0662474\pi$
$887$	−0.347362	−	1.96999i	−0.0116633	−	0.0661457i	−0.990084	+	0.140477i	$0.955136\pi$
$888$	17.5363	+	22.6839i	0.588481	+	0.761224i
$889$	−10.9590	−	9.19570i	−0.367553	−	0.308414i
$890$	−0.0977871	−	0.365846i	−0.00327783	−	0.0122632i
$891$	−13.7012	−	2.10904i	−0.459006	−	0.0706556i
$892$	−2.90829	−	5.05164i	−0.0973769	−	0.169141i
$893$	−16.5472	+	19.7202i	−0.553732	+	0.659913i
$894$	21.6889	−	2.96215i	0.725384	−	0.0990692i
$895$	0.113960	−	0.0200942i	0.00380925	−	0.000671673i
$896$	−1.03454	+	11.2663i	−0.0345614	+	0.376381i
$897$	5.05440	+	5.45592i	0.168762	+	0.182168i
$898$	−2.85306	−	32.8431i	−0.0952079	−	1.09599i
$899$	−8.05667	+	13.9546i	−0.268705	+	0.465411i
$900$	7.46623	−	28.9826i	0.248874	−	0.966088i
$901$	−5.83583	−	10.1080i	−0.194420	−	0.336745i
$902$	17.6886	−	12.3695i	0.588967	−	0.411860i
$903$	0.0880395	+	1.79224i	0.00292977	+	0.0596419i
$904$	2.91235	−	32.5959i	0.0968632	−	1.08412i
$905$	−1.58534	−	1.88933i	−0.0526984	−	0.0628036i
$906$	−41.0074	−	8.88332i	−1.36238	−	0.295128i
$907$	−19.2121	−	52.7849i	−0.637928	−	1.75269i	−0.658138	−	0.752897i	$-0.728656\pi$
$907$	−19.2121	−	52.7849i	−0.637928	−	1.75269i	0.0202105	−	0.999796i	$-0.493566\pi$
$908$	−44.9101	−	26.0025i	−1.49040	−	0.862925i
$909$	3.76547	+	1.70615i	0.124893	+	0.0565895i
$910$	−0.697508	−	0.187356i	−0.0231222	−	0.00621080i
$911$	−5.48420	+	31.1025i	−0.181700	+	1.03047i	0.748423	+	0.663222i	$0.230811\pi$
$911$	−5.48420	+	31.1025i	−0.181700	+	1.03047i	−0.930123	+	0.367249i	$0.880300\pi$
$912$	−33.6440	+	31.0147i	−1.11406	+	1.02700i
$913$	18.4970	+	6.73234i	0.612160	+	0.222808i
$914$	27.6401	−	12.8681i	0.914253	−	0.425639i
$915$	−1.13994	−	0.864877i	−0.0376852	−	0.0285919i
$916$	44.0255	+	7.81869i	1.45464	+	0.258337i
$917$			7.20443i			0.237911i
$918$	−4.58852	+	15.3934i	−0.151444	+	0.508058i
$919$		−	21.6347i		−	0.713662i	−0.934169	−	0.356831i	$-0.883857\pi$
$919$		−	21.6347i		−	0.713662i	0.934169	−	0.356831i	$-0.116143\pi$
$920$	−0.280831	+	0.0240479i	−0.00925874	+	0.000792835i
$921$	−25.4646	+	10.7107i	−0.839086	+	0.352931i
$922$	7.01976	+	15.0781i	0.231184	+	0.496571i
$923$	36.1596	+	13.1610i	1.19021	+	0.433200i
$924$	3.62131	+	3.91864i	0.119132	+	0.128914i
$925$	−5.06947	+	28.7504i	−0.166683	+	0.945306i
$926$	10.2656	−	38.2177i	0.337348	−	1.25591i
$927$	8.02060	−	11.7246i	0.263431	−	0.385085i
$928$	−43.4440	+	11.4978i	−1.42612	+	0.377434i
$929$	19.2174	+	52.7993i	0.630501	+	1.73229i	0.679691	+	0.733499i	$0.262114\pi$
$929$	19.2174	+	52.7993i	0.630501	+	1.73229i	−0.0491894	+	0.998789i	$0.515664\pi$
$930$	−0.400542	−	0.363481i	−0.0131343	−	0.0119190i
$931$	4.24539	+	5.05945i	0.139137	+	0.165817i
$932$	−30.0168	−	10.9670i	−0.983234	−	0.359237i
$933$	−0.851357	+	0.548920i	−0.0278722	+	0.0179708i
$934$	−29.6811	−	42.4445i	−0.971196	−	1.38883i
$935$	0.183269	+	0.317431i	0.00599354	+	0.0103811i
$936$	−30.2591	+	25.8609i	−0.989048	+	0.845291i
$937$	12.9985	−	22.5140i	0.424641	−	0.735500i	−0.571746	−	0.820431i	$-0.693734\pi$
$937$	12.9985	−	22.5140i	0.424641	−	0.735500i	0.996387	+	0.0849307i	$0.0270669\pi$
$938$	8.99719	−	0.781580i	0.293769	−	0.0255195i
$939$	−28.0095	+	6.36991i	−0.914056	+	0.207874i
$940$	−0.146341	−	0.835949i	−0.00477312	−	0.0272657i
$941$	56.3869	−	9.94252i	1.83816	−	0.324117i	0.856704	−	0.515809i	$-0.172509\pi$
$941$	56.3869	−	9.94252i	1.83816	−	0.324117i	0.981455	+	0.191692i	$0.0613974\pi$
$942$	32.7792	−	25.4051i	1.06800	−	0.827743i
$943$	5.83024	−	6.94821i	0.189859	−	0.226265i
$944$	28.1002	−	48.3959i	0.914585	−	1.57515i
$945$	0.443101	−	0.351661i	0.0144141	−	0.0114395i
$946$	2.18016	−	0.582737i	0.0708832	−	0.0189464i
$947$	−39.4893	−	33.1355i	−1.28323	−	1.07676i	−0.992790	−	0.119866i	$-0.961754\pi$
$947$	−39.4893	−	33.1355i	−1.28323	−	1.07676i	−0.290441	−	0.956893i	$-0.593802\pi$
$948$	47.1409	+	6.00391i	1.53106	+	0.194998i
$949$	−3.27119	−	18.5519i	−0.106187	−	0.602219i
$950$	−46.4114	−	4.08922i	−1.50578	−	0.132672i
$951$	−50.4217	−	15.5963i	−1.63504	−	0.505744i
$952$	5.07098	−	3.53682i	0.164351	−	0.114629i
$953$	0.136594	+	0.0788626i	0.00442472	+	0.00255461i	0.502211	−	0.864745i	$-0.332520\pi$
$953$	0.136594	+	0.0788626i	0.00442472	+	0.00255461i	−0.497786	+	0.867300i	$0.665854\pi$
$954$	17.5029	+	14.3825i	0.566677	+	0.465651i
$955$	−0.698684	+	0.403385i	−0.0226089	+	0.0130532i
$956$	−14.1123	+	16.7765i	−0.456425	+	0.542590i
$957$	−9.68378	+	18.8525i	−0.313032	+	0.609415i
$958$	−45.8416	−	32.1407i	−1.48108	−	1.03842i
$959$	−5.91871	+	4.96639i	−0.191125	+	0.160373i
$960$	−0.0684559	−	1.50695i	−0.00220940	−	0.0486366i
$961$	−25.2646	+	9.19557i	−0.814988	+	0.296631i
$962$	27.4717	−	27.4379i	0.885723	−	0.884634i
$963$	−16.2855	−	4.17397i	−0.524792	−	0.134504i
$964$	0.0593731	−	48.3008i	0.00191228	−	1.55566i
$965$	−2.08418	−	0.367498i	−0.0670922	−	0.0118302i
$966$	1.89682	+	1.19555i	0.0610292	+	0.0384663i
$967$	−3.28077	+	9.01383i	−0.105502	+	0.289865i	−0.981200	−	0.192995i	$-0.938180\pi$
$967$	−3.28077	+	9.01383i	−0.105502	+	0.289865i	0.875697	+	0.482860i	$0.160402\pi$
$968$	−14.0334	+	19.9634i	−0.451052	+	0.641648i
$969$	24.8089	+	3.12869i	0.796975	+	0.100508i
$970$	1.97755	+	0.923628i	0.0634954	+	0.0296559i
$971$	−24.3849			−0.782548			−0.391274	−	0.920274i	$-0.627965\pi$
$971$	−24.3849			−0.782548			−0.391274	+	0.920274i	$0.627965\pi$
$972$	−2.16984	−	31.1013i	−0.0695978	−	0.997575i
$973$	9.05623			0.290330
$974$	−26.3964	−	12.3286i	−0.845796	−	0.395034i
$975$	−40.2105	−	5.07102i	−1.28777	−	0.162403i
$976$	28.4976	+	10.4517i	0.912186	+	0.334550i
$977$	0.437696	−	1.20256i	0.0140031	−	0.0384733i	−0.932494	−	0.361185i	$-0.882372\pi$
$977$	0.437696	−	1.20256i	0.0140031	−	0.0384733i	0.946497	+	0.322712i	$0.104594\pi$
$978$	14.6894	+	9.25862i	0.469715	+	0.296058i
$979$	3.73098	+	0.657873i	0.119243	+	0.0210257i
$980$	−0.217734		0.000267646i	−0.00695525		8.54965e-6i
$981$	6.52798	+	1.67312i	0.208422	+	0.0534187i
$982$	14.1905	−	14.1730i	0.452836	−	0.452279i
$983$	−18.9617	+	6.90149i	−0.604784	+	0.220123i	−0.626219	−	0.779647i	$-0.715399\pi$
$983$	−18.9617	+	6.90149i	−0.604784	+	0.220123i	0.0214357	+	0.999770i	$0.493176\pi$
$984$	35.9083	+	32.6664i	1.14471	+	1.04137i
$985$	1.62826	−	1.36627i	0.0518807	−	0.0435331i
$986$	20.1081	+	14.0983i	0.640372	+	0.448980i
$987$	−3.08459	+	6.00512i	−0.0981836	+	0.191145i
$988$	47.4188	+	39.8886i	1.50859	+	1.26902i
$989$	0.821258	−	0.474154i	0.0261145	−	0.0150772i
$990$	−0.549662	−	0.451669i	−0.0174694	−	0.0143550i
$991$	31.2682	+	18.0527i	0.993266	+	0.573463i	0.906249	−	0.422744i	$-0.138933\pi$
$991$	31.2682	+	18.0527i	0.993266	+	0.573463i	0.0870174	+	0.996207i	$0.472266\pi$
$992$	10.3838	+	4.88094i	0.329686	+	0.154970i
$993$	−36.3407	−	11.2408i	−1.15324	−	0.356716i
$994$	11.5560	+	1.01818i	0.366534	+	0.0322946i
$995$	−0.0494108	−	0.280223i	−0.00156643	−	0.00888365i
$996$	−5.59303	+	43.9148i	−0.177222	+	1.39149i
$997$	31.2649	+	26.2344i	0.990170	+	0.830851i	0.985592	−	0.169139i	$-0.0540985\pi$
$997$	31.2649	+	26.2344i	0.990170	+	0.830851i	0.00457737	+	0.999990i	$0.498543\pi$
$998$	17.6497	−	4.71760i	0.558692	−	0.149333i
$999$	4.46189	+	30.0822i	0.141168	+	0.951758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.39	yes	648
4.3	odd	2	inner	756.2.cf.a.659.23	yes	648
27.5	odd	18	inner	756.2.cf.a.491.23	✓	648
108.59	even	18	inner	756.2.cf.a.491.39	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.23	✓	648	27.5	odd	18	inner
756.2.cf.a.491.39	yes	648	108.59	even	18	inner
756.2.cf.a.659.23	yes	648	4.3	odd	2	inner
756.2.cf.a.659.39	yes	648	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.598460 + 1.28135i) q^{2} +(1.71844 + 0.216716i) q^{3} +(-1.28369 - 1.53367i) q^{4} +(0.0372347 - 0.102301i) q^{5} +(-1.30611 + 2.07222i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.73340 - 0.727012i) q^{8} +(2.90607 + 0.744826i) q^{9} +(0.108800 + 0.108934i) q^{10} +(-1.44739 + 0.526808i) q^{11} +(-1.87358 - 2.91371i) q^{12} +(-3.59352 + 3.01532i) q^{13} +(-0.811871 + 1.15796i) q^{14} +(0.0861559 - 0.167730i) q^{15} +(-0.704275 + 3.93751i) q^{16} +(1.89301 - 1.09293i) q^{17} +(-2.69355 + 3.27793i) q^{18} +(5.71979 + 3.30232i) q^{19} +(-0.204694 + 0.0742178i) q^{20} +(1.65470 + 0.511827i) q^{21} +(0.191184 - 2.16988i) q^{22} +(-0.158950 - 0.901452i) q^{23} +(4.85473 - 0.656956i) q^{24} +(3.82114 + 3.20632i) q^{25} +(-1.71309 - 6.40909i) q^{26} +(4.83249 + 1.90973i) q^{27} +(-0.997870 - 1.73328i) q^{28} +(5.10650 - 6.08569i) q^{29} +(0.163359 + 0.210775i) q^{30} +(-1.99748 + 0.352209i) q^{31} +(-4.62383 - 3.25886i) q^{32} +(-2.60142 + 0.591614i) q^{33} +(0.267530 + 3.07968i) q^{34} +(0.0544335 - 0.0942816i) q^{35} +(-2.58818 - 5.41307i) q^{36} +(2.92633 + 5.06854i) q^{37} +(-7.65448 + 5.35272i) q^{38} +(-6.82871 + 4.40287i) q^{39} +(0.0274028 - 0.306701i) q^{40} +(6.36935 + 7.59070i) q^{41} +(-1.64610 + 1.81393i) q^{42} +(0.354332 + 0.973518i) q^{43} +(2.66595 + 1.54356i) q^{44} +(0.184403 - 0.269562i) q^{45} +(1.25020 + 0.335813i) q^{46} +(-0.676829 + 3.83849i) q^{47} +(-2.06357 + 6.61375i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.39520 + 2.97735i) q^{50} +(3.48988 - 1.46789i) q^{51} +(9.23747 + 1.64052i) q^{52} -5.33962i q^{53} +(-5.33907 + 5.04919i) q^{54} +0.167686i q^{55} +(2.81811 - 0.241318i) q^{56} +(9.11345 + 6.91441i) q^{57} +(4.74183 + 10.1852i) q^{58} +(-13.1469 - 4.78506i) q^{59} +(-0.367839 + 0.0831784i) q^{60} +(1.31772 - 7.47315i) q^{61} +(0.744108 - 2.77024i) q^{62} +(2.73258 + 1.23814i) q^{63} +(6.94291 - 3.97442i) q^{64} +(0.174668 + 0.479897i) q^{65} +(0.798786 - 3.68738i) q^{66} +(-4.10480 - 4.89191i) q^{67} +(-4.10624 - 1.50027i) q^{68} +(-0.0777876 - 1.58354i) q^{69} +(0.0882309 + 0.126172i) q^{70} +(-4.10149 - 7.10399i) q^{71} +(8.48493 - 0.0768433i) q^{72} +(-2.00789 + 3.47777i) q^{73} +(-8.24584 + 0.716311i) q^{74} +(5.87154 + 6.33797i) q^{75} +(-2.27778 - 13.0114i) q^{76} +(-1.51688 + 0.267467i) q^{77} +(-1.55489 - 11.3849i) q^{78} +(-8.81797 + 10.5088i) q^{79} +(0.376590 + 0.218660i) q^{80} +(7.89047 + 4.32903i) q^{81} +(-13.5381 + 3.61861i) q^{82} +(-9.78967 - 8.21451i) q^{83} +(-1.33915 - 3.19479i) q^{84} +(-0.0413228 - 0.234353i) q^{85} +(-1.45947 - 0.128591i) q^{86} +(10.0941 - 9.35122i) q^{87} +(-3.57330 + 2.49224i) q^{88} +(-2.13011 - 1.22982i) q^{89} +(0.235044 + 0.397606i) q^{90} +(-4.06253 + 2.34550i) q^{91} +(-1.17848 + 1.40096i) q^{92} +(-3.50887 + 0.172365i) q^{93} +(-4.51337 - 3.16443i) q^{94} +(0.550807 - 0.462182i) q^{95} +(-7.23953 - 6.60222i) q^{96} +(13.3215 - 4.84861i) q^{97} +(-1.00061 + 0.999385i) q^{98} +(-4.59860 + 0.452884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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