LMFDB - Embedded newform 483.2.v.a.41.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(41,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("483.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.v (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$600$
Relative dimension:	$60$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.15
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.468338 + 1.59501i) q^{2} +(-1.57515 - 0.720338i) q^{3} +(-0.642222 - 0.412731i) q^{4} +(0.0822804 - 0.572273i) q^{5} +(1.88665 - 2.17503i) q^{6} +(-1.81311 - 1.92682i) q^{7} +(-1.55355 + 1.34616i) q^{8} +(1.96223 + 2.26929i) q^{9} +(0.874248 + 0.399256i) q^{10} +(0.655249 + 2.23157i) q^{11} +(0.714293 + 1.11273i) q^{12} +(-3.01159 - 1.37535i) q^{13} +(3.92245 - 1.98954i) q^{14} +(-0.541834 + 0.842149i) q^{15} +(-2.05382 - 4.49724i) q^{16} +(6.14222 - 3.94737i) q^{17} +(-4.53853 + 2.06698i) q^{18} +(3.39161 - 5.27745i) q^{19} +(-0.289037 + 0.333567i) q^{20} +(1.46797 + 4.34109i) q^{21} -3.86627 q^{22} +(4.12483 - 2.44659i) q^{23} +(3.41678 - 1.00133i) q^{24} +(4.47674 + 1.31449i) q^{25} +(3.60414 - 4.15940i) q^{26} +(-1.45616 - 4.98795i) q^{27} +(0.369164 + 1.98577i) q^{28} +(-0.836844 - 1.30215i) q^{29} +(-1.08948 - 1.25864i) q^{30} +(-1.48228 + 1.28441i) q^{31} +(4.06561 - 0.584546i) q^{32} +(0.575369 - 3.98708i) q^{33} +(3.41947 + 11.6456i) q^{34} +(-1.25185 + 0.879056i) q^{35} +(-0.323579 - 2.26726i) q^{36} +(-0.267931 - 1.86350i) q^{37} +(6.82919 + 7.88130i) q^{38} +(3.75300 + 4.33574i) q^{39} +(0.642545 + 0.999819i) q^{40} +(-1.07315 + 7.46390i) q^{41} +(-7.61161 + 0.308340i) q^{42} +(7.59902 - 8.76973i) q^{43} +(0.500224 - 1.70361i) q^{44} +(1.46010 - 0.936211i) q^{45} +(1.97053 + 7.72499i) q^{46} -7.03096 q^{47} +(-0.00444747 + 8.56330i) q^{48} +(-0.425246 + 6.98707i) q^{49} +(-4.19326 + 6.52484i) q^{50} +(-12.5184 + 1.79324i) q^{51} +(1.36646 + 2.12625i) q^{52} +(5.49811 - 2.51090i) q^{53} +(8.63782 + 0.0134585i) q^{54} +(1.33098 - 0.191366i) q^{55} +(5.41057 + 0.552670i) q^{56} +(-9.14386 + 5.86970i) q^{57} +(2.46888 - 0.724929i) q^{58} +(-1.62803 + 3.56489i) q^{59} +(0.695559 - 0.317215i) q^{60} +(9.98580 - 8.65274i) q^{61} +(-1.35444 - 2.96580i) q^{62} +(0.814766 - 7.89532i) q^{63} +(0.435495 - 3.02894i) q^{64} +(-1.03487 + 1.61029i) q^{65} +(6.08997 + 2.78502i) q^{66} +(-10.8985 - 3.20008i) q^{67} -5.57387 q^{68} +(-8.25961 + 0.882485i) q^{69} +(-0.815818 - 2.40841i) q^{70} +(4.23097 - 14.4094i) q^{71} +(-6.10325 - 0.883987i) q^{72} +(-1.50295 + 2.33863i) q^{73} +(3.09779 + 0.445396i) q^{74} +(-6.10468 - 5.29529i) q^{75} +(-4.35634 + 1.98947i) q^{76} +(3.11179 - 5.30864i) q^{77} +(-8.67325 + 3.95550i) q^{78} +(-0.326638 + 0.715237i) q^{79} +(-2.74264 + 0.805312i) q^{80} +(-1.29934 + 8.90571i) q^{81} +(-11.4024 - 5.20732i) q^{82} +(0.0740193 + 0.514816i) q^{83} +(0.848937 - 3.39382i) q^{84} +(-1.75359 - 3.83982i) q^{85} +(10.4289 + 16.2277i) q^{86} +(0.380167 + 2.65391i) q^{87} +(-4.02202 - 2.58480i) q^{88} +(-6.53757 + 7.54476i) q^{89} +(0.809446 + 2.76735i) q^{90} +(2.81031 + 8.29643i) q^{91} +(-3.65884 - 0.131192i) q^{92} +(3.26003 - 0.955393i) q^{93} +(3.29287 - 11.2145i) q^{94} +(-2.74108 - 2.37516i) q^{95} +(-6.82503 - 2.00786i) q^{96} +(-3.87155 - 0.556645i) q^{97} +(-10.9453 - 3.95059i) q^{98} +(-3.77834 + 5.86580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) $ 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.468338	+	1.59501i	−0.331165	+	1.12785i	0.610702	+	0.791860i	$0.290887\pi$
$2$	−0.468338	+	1.59501i	−0.331165	+	1.12785i	−0.941867	+	0.335985i	$0.890931\pi$
$3$	−1.57515	−	0.720338i	−0.909416	−	0.415887i
$3$	−1.57515	−	0.720338i	−0.909416	−	0.415887i
$4$	−0.642222	−	0.412731i	−0.321111	−	0.206366i
$5$	0.0822804	−	0.572273i	0.0367969	−	0.255928i	−0.963117	−	0.269085i	$-0.913279\pi$
$5$	0.0822804	−	0.572273i	0.0367969	−	0.255928i	0.999913	+	0.0131565i	$0.00418795\pi$
$6$	1.88665	−	2.17503i	0.770224	−	0.887953i
$7$	−1.81311	−	1.92682i	−0.685292	−	0.728268i
$7$	−1.81311	−	1.92682i	−0.685292	−	0.728268i
$8$	−1.55355	+	1.34616i	−0.549264	+	0.475940i
$9$	1.96223	+	2.26929i	0.654075	+	0.756429i
$10$	0.874248	+	0.399256i	0.276462	+	0.126256i
$11$	0.655249	+	2.23157i	0.197565	+	0.672845i	0.997363	+	0.0725754i	$0.0231218\pi$
$11$	0.655249	+	2.23157i	0.197565	+	0.672845i	−0.799798	+	0.600269i	$0.795060\pi$
$12$	0.714293	+	1.11273i	0.206199	+	0.321218i
$13$	−3.01159	−	1.37535i	−0.835264	−	0.381452i	−0.0485883	−	0.998819i	$-0.515472\pi$
$13$	−3.01159	−	1.37535i	−0.835264	−	0.381452i	−0.786676	+	0.617367i	$0.788199\pi$
$14$	3.92245	−	1.98954i	1.04832	−	0.531726i
$15$	−0.541834	+	0.842149i	−0.139901	+	0.217442i
$16$	−2.05382	−	4.49724i	−0.513456	−	1.12431i
$17$	6.14222	−	3.94737i	1.48971	−	0.957377i	0.493557	−	0.869713i	$-0.335696\pi$
$17$	6.14222	−	3.94737i	1.48971	−	0.957377i	0.996150	−	0.0876636i	$-0.0279400\pi$
$18$	−4.53853	+	2.06698i	−1.06974	+	0.487193i
$19$	3.39161	−	5.27745i	0.778089	−	1.21073i	−0.195114	−	0.980781i	$-0.562508\pi$
$19$	3.39161	−	5.27745i	0.778089	−	1.21073i	0.973203	−	0.229950i	$-0.0738561\pi$
$20$	−0.289037	+	0.333567i	−0.0646307	+	0.0745878i
$21$	1.46797	+	4.34109i	0.320338	+	0.947303i
$22$	−3.86627			−0.824292
$23$	4.12483	−	2.44659i	0.860086	−	0.510149i
$23$	4.12483	−	2.44659i	0.860086	−	0.510149i
$24$	3.41678	−	1.00133i	0.697447	−	0.204395i
$25$	4.47674	+	1.31449i	0.895348	+	0.262898i
$26$	3.60414	−	4.15940i	0.706829	−	0.815725i
$27$	−1.45616	−	4.98795i	−0.280237	−	0.959931i
$28$	0.369164	+	1.98577i	0.0697654	+	0.375276i
$29$	−0.836844	−	1.30215i	−0.155398	−	0.241804i	0.754821	−	0.655930i	$-0.227724\pi$
$29$	−0.836844	−	1.30215i	−0.155398	−	0.241804i	−0.910219	+	0.414126i	$0.864087\pi$
$30$	−1.08948	−	1.25864i	−0.198910	−	0.229796i
$31$	−1.48228	+	1.28441i	−0.266226	+	0.230686i	−0.777736	−	0.628591i	$-0.783632\pi$
$31$	−1.48228	+	1.28441i	−0.266226	+	0.230686i	0.511510	+	0.859277i	$0.329086\pi$
$32$	4.06561	−	0.584546i	0.718705	−	0.103334i
$33$	0.575369	−	3.98708i	0.100159	−	0.694061i
$34$	3.41947	+	11.6456i	0.586434	+	1.99721i
$35$	−1.25185	+	0.879056i	−0.211601	+	0.148588i
$36$	−0.323579	−	2.26726i	−0.0539299	−	0.377876i
$37$	−0.267931	−	1.86350i	−0.0440476	−	0.306358i	−0.999921	−	0.0125785i	$-0.995996\pi$
$37$	−0.267931	−	1.86350i	−0.0440476	−	0.306358i	0.955873	−	0.293779i	$-0.0949131\pi$
$38$	6.82919	+	7.88130i	1.10784	+	1.27852i
$39$	3.75300	+	4.33574i	0.600961	+	0.694274i
$40$	0.642545	+	0.999819i	0.101595	+	0.158085i
$41$	−1.07315	+	7.46390i	−0.167597	+	1.16567i	0.716234	+	0.697860i	$0.245864\pi$
$41$	−1.07315	+	7.46390i	−0.167597	+	1.16567i	−0.883831	+	0.467805i	$0.845045\pi$
$42$	−7.61161	+	0.308340i	−1.17450	+	0.0475779i
$43$	7.59902	−	8.76973i	1.15884	−	1.33737i	0.227260	−	0.973834i	$-0.427023\pi$
$43$	7.59902	−	8.76973i	1.15884	−	1.33737i	0.931579	−	0.363538i	$-0.118431\pi$
$44$	0.500224	−	1.70361i	0.0754117	−	0.256829i
$45$	1.46010	−	0.936211i	0.217660	−	0.139562i
$46$	1.97053	+	7.72499i	0.290538	+	1.13899i
$47$	−7.03096			−1.02557			−0.512785	−	0.858517i	$-0.671386\pi$
$47$	−7.03096			−1.02557			−0.512785	+	0.858517i	$0.671386\pi$
$48$	−0.00444747	+	8.56330i	−0.000641937	+	1.23601i
$49$	−0.425246	+	6.98707i	−0.0607494	+	0.998153i
$50$	−4.19326	+	6.52484i	−0.593016	+	0.922751i
$51$	−12.5184	+	1.79324i	−1.75292	+	0.251103i
$52$	1.36646	+	2.12625i	0.189494	+	0.294858i
$53$	5.49811	−	2.51090i	0.755223	−	0.344899i	−0.000318123	−	1.00000i	$-0.500101\pi$
$53$	5.49811	−	2.51090i	0.755223	−	0.344899i	0.755541	+	0.655101i	$0.227374\pi$
$54$	8.63782	+	0.0134585i	1.17546	+	0.00183147i
$55$	1.33098	−	0.191366i	0.179470	−	0.0258039i
$56$	5.41057	+	0.552670i	0.723018	+	0.0738536i
$57$	−9.14386	+	5.86970i	−1.21113	+	0.777460i
$58$	2.46888	−	0.724929i	0.324180	−	0.0951878i
$59$	−1.62803	+	3.56489i	−0.211952	+	0.464109i	−0.985510	−	0.169615i	$-0.945748\pi$
$59$	−1.62803	+	3.56489i	−0.211952	+	0.464109i	0.773559	+	0.633725i	$0.218475\pi$
$60$	0.695559	−	0.317215i	0.0897963	−	0.0409522i
$61$	9.98580	−	8.65274i	1.27855	−	1.10787i	0.289992	−	0.957029i	$-0.406347\pi$
$61$	9.98580	−	8.65274i	1.27855	−	1.10787i	0.988558	−	0.150841i	$-0.0481982\pi$
$62$	−1.35444	−	2.96580i	−0.172013	−	0.376657i
$63$	0.814766	−	7.89532i	0.102651	−	0.994717i
$64$	0.435495	−	3.02894i	0.0544369	−	0.378617i
$65$	−1.03487	+	1.61029i	−0.128360	+	0.199731i
$66$	6.08997	+	2.78502i	0.749624	+	0.342812i
$67$	−10.8985	−	3.20008i	−1.33146	−	0.390952i	−0.462844	−	0.886440i	$-0.653171\pi$
$67$	−10.8985	−	3.20008i	−1.33146	−	0.390952i	−0.868615	+	0.495488i	$0.834989\pi$
$68$	−5.57387			−0.675931
$69$	−8.25961	+	0.882485i	−0.994341	+	0.106239i
$70$	−0.815818	−	2.40841i	−0.0975089	−	0.287860i
$71$	4.23097	−	14.4094i	0.502124	−	1.71008i	−0.184295	−	0.982871i	$-0.559000\pi$
$71$	4.23097	−	14.4094i	0.502124	−	1.71008i	0.686419	−	0.727206i	$-0.259182\pi$
$72$	−6.10325	−	0.883987i	−0.719275	−	0.104179i
$73$	−1.50295	+	2.33863i	−0.175907	+	0.273716i	−0.918000	−	0.396581i	$-0.870197\pi$
$73$	−1.50295	+	2.33863i	−0.175907	+	0.273716i	0.742093	+	0.670297i	$0.233833\pi$
$74$	3.09779	+	0.445396i	0.360111	+	0.0517762i
$75$	−6.10468	−	5.29529i	−0.704908	−	0.611447i
$76$	−4.35634	+	1.98947i	−0.499706	+	0.228208i
$77$	3.11179	−	5.30864i	0.354622	−	0.604976i
$78$	−8.67325	+	3.95550i	−0.982052	+	0.447872i
$79$	−0.326638	+	0.715237i	−0.0367496	+	0.0804705i	−0.927117	−	0.374773i	$-0.877721\pi$
$79$	−0.326638	+	0.715237i	−0.0367496	+	0.0804705i	0.890367	+	0.455244i	$0.150448\pi$
$80$	−2.74264	+	0.805312i	−0.306636	+	0.0900366i
$81$	−1.29934	+	8.90571i	−0.144371	+	0.989524i
$82$	−11.4024	−	5.20732i	−1.25919	−	0.575052i
$83$	0.0740193	+	0.514816i	0.00812468	+	0.0565084i	0.993480	−	0.114003i	$-0.0363672\pi$
$83$	0.0740193	+	0.514816i	0.00812468	+	0.0565084i	−0.985356	+	0.170511i	$0.945458\pi$
$84$	0.848937	−	3.39382i	0.0926266	−	0.370296i
$85$	−1.75359	−	3.83982i	−0.190203	−	0.416487i
$86$	10.4289	+	16.2277i	1.12458	+	1.74988i
$87$	0.380167	+	2.65391i	0.0407582	+	0.284529i
$88$	−4.02202	−	2.58480i	−0.428749	−	0.275540i
$89$	−6.53757	+	7.54476i	−0.692981	+	0.799742i	−0.987786	−	0.155815i	$-0.950200\pi$
$89$	−6.53757	+	7.54476i	−0.692981	+	0.799742i	0.294805	+	0.955557i	$0.404745\pi$
$90$	0.809446	+	2.76735i	0.0853231	+	0.291704i
$91$	2.81031	+	8.29643i	0.294600	+	0.869702i
$92$	−3.65884	−	0.131192i	−0.381460	−	0.0136777i
$93$	3.26003	−	0.955393i	0.338050	−	0.0990697i
$94$	3.29287	−	11.2145i	0.339633	−	1.15669i
$95$	−2.74108	−	2.37516i	−0.281229	−	0.243686i
$96$	−6.82503	−	2.00786i	−0.696577	−	0.204927i
$97$	−3.87155	−	0.556645i	−0.393096	−	0.0565187i	−0.0570672	−	0.998370i	$-0.518175\pi$
$97$	−3.87155	−	0.556645i	−0.393096	−	0.0565187i	−0.336029	+	0.941852i	$0.609084\pi$
$98$	−10.9453	−	3.95059i	−1.10564	−	0.399070i
$99$	−3.77834	+	5.86580i	−0.379737	+	0.589535i
$100$	−2.33253	−	2.69188i	−0.233253	−	0.269188i
$101$	1.16571	+	8.10768i	0.115992	+	0.806744i	0.961897	+	0.273411i	$0.0881518\pi$
$101$	1.16571	+	8.10768i	0.115992	+	0.806744i	−0.845905	+	0.533333i	$0.820939\pi$
$102$	3.00260	−	20.8068i	0.297302	−	2.06018i
$103$	−4.16436	−	14.1825i	−0.410327	−	1.39744i	−0.862745	−	0.505639i	$-0.831257\pi$
$103$	−4.16436	−	14.1825i	−0.410327	−	1.39744i	0.452418	−	0.891806i	$-0.350561\pi$
$104$	6.53010	−	1.91741i	0.640329	−	0.188017i
$105$	2.60507	−	0.482895i	0.254229	−	0.0471257i
$106$	1.42995	+	9.94551i	0.138889	+	0.965993i
$107$	−11.2021	+	9.70665i	−1.08294	+	0.938377i	−0.998315	−	0.0580355i	$-0.981516\pi$
$107$	−11.2021	+	9.70665i	−1.08294	+	0.938377i	−0.0846302	+	0.996412i	$0.526971\pi$
$108$	−1.12351	+	3.80437i	−0.108109	+	0.366076i
$109$	5.23973	−	3.36737i	0.501875	−	0.322535i	−0.265091	−	0.964223i	$-0.585402\pi$
$109$	5.23973	−	3.36737i	0.501875	−	0.322535i	0.766966	+	0.641688i	$0.221766\pi$
$110$	−0.318118	+	2.21256i	−0.0303314	+	0.210959i
$111$	−0.920318	+	3.12831i	−0.0873528	+	0.296926i
$112$	−4.94155	+	12.1113i	−0.466933	+	1.14441i
$113$	−2.34617	+	7.99034i	−0.220710	+	0.751668i	0.772468	+	0.635054i	$0.219022\pi$
$113$	−2.34617	+	7.99034i	−0.220710	+	0.751668i	−0.993177	+	0.116614i	$0.962796\pi$
$114$	−5.07982	−	17.3336i	−0.475769	−	1.62344i
$115$	−1.06072	−	2.56183i	−0.0989130	−	0.238892i
$116$			1.18166i			0.109715i
$117$	−2.78836	−	9.53290i	−0.257784	−	0.881317i
$118$	−4.92358	−	4.26631i	−0.453253	−	0.392746i
$119$	−18.7424	−	4.67792i	−1.71811	−	0.428824i
$120$	−0.291900	−	2.03772i	−0.0266467	−	0.186017i
$121$	4.70322	−	3.02258i	0.427565	−	0.274780i
$122$	9.12451	+	19.9799i	0.826095	+	1.80889i
$123$	7.06691	−	10.9838i	0.637201	−	0.990373i
$124$	1.48207	−	0.213089i	0.133094	−	0.0191360i
$125$	2.32147	−	5.08331i	0.207639	−	0.454665i
$126$	12.2116	+	4.99725i	1.08789	+	0.445190i
$127$	14.2370	−	4.18035i	1.26333	−	0.370946i	0.419594	−	0.907712i	$-0.362172\pi$
$127$	14.2370	−	4.18035i	1.26333	−	0.370946i	0.843731	+	0.536766i	$0.180354\pi$
$128$	12.0997	+	5.52575i	1.06947	+	0.488412i
$129$	−18.2868	+	8.33983i	−1.61006	+	0.734281i
$130$	−2.08376	−	2.40479i	−0.182758	−	0.210914i
$131$	−7.55221	−	16.5370i	−0.659840	−	1.44485i	−0.882672	−	0.469990i	$-0.844257\pi$
$131$	−7.55221	−	16.5370i	−0.659840	−	1.44485i	0.222832	−	0.974857i	$-0.428470\pi$
$132$	−2.01510	+	2.32312i	−0.175392	+	0.202201i
$133$	−16.3181	+	3.03360i	−1.41495	+	0.263046i
$134$	10.2083	−	15.8845i	0.881866	−	1.37221i
$135$	−2.97428	+	0.422908i	−0.255985	+	0.0363981i
$136$	−4.22847	+	14.4009i	−0.362589	+	1.23486i
$137$		−	3.21611i		−	0.274771i	−0.990518	−	0.137386i	$-0.956130\pi$
$137$		−	3.21611i		−	0.274771i	0.990518	−	0.137386i	$-0.0438700\pi$
$138$	2.46072	−	13.5875i	0.209470	−	1.15664i
$139$			8.79977i			0.746387i	0.927754	+	0.373193i	$0.121737\pi$
$139$			8.79977i			0.746387i	−0.927754	+	0.373193i	$0.878263\pi$
$140$	1.16678	−	0.0478722i	0.0986108	−	0.00404594i
$141$	11.0749	+	5.06467i	0.932671	+	0.426522i
$142$	21.0016	+	13.4969i	1.76242	+	1.13264i
$143$	1.09585	−	7.62177i	0.0916392	−	0.637365i
$144$	6.17548	−	13.4853i	0.514623	−	1.12378i
$145$	−0.814044	+	0.371761i	−0.0676027	+	0.0308731i
$146$	−3.02626	−	3.49249i	−0.250455	−	0.289041i
$147$	5.70288	−	10.6994i	0.470366	−	0.882472i
$148$	−0.597054	+	1.30737i	−0.0490775	+	0.107465i
$149$	−3.61434	−	12.3093i	−0.296099	−	1.00842i	−0.964382	−	0.264513i	$-0.914789\pi$
$149$	−3.61434	−	12.3093i	−0.296099	−	1.00842i	0.668284	−	0.743907i	$-0.267029\pi$
$150$	11.3051	−	7.25706i	0.923059	−	0.592537i
$151$	−4.98871	+	10.9237i	−0.405975	+	0.888962i	0.590654	+	0.806925i	$0.298870\pi$
$151$	−4.98871	+	10.9237i	−0.405975	+	0.888962i	−0.996629	+	0.0820367i	$0.973858\pi$
$152$	1.83525	+	12.7645i	0.148859	+	1.03533i
$153$	21.0101	+	6.19285i	1.69857	+	0.500662i
$154$	7.00998	+	7.44959i	0.564880	+	0.600305i
$155$	0.613068	+	0.953952i	0.0492428	+	0.0766233i
$156$	−0.620765	−	4.33349i	−0.0497010	−	0.346957i
$157$	3.38775	−	5.27144i	0.270372	−	0.420706i	−0.679344	−	0.733820i	$-0.737736\pi$
$157$	3.38775	−	5.27144i	0.270372	−	0.420706i	0.949716	+	0.313113i	$0.101372\pi$
$158$	−0.987837	−	0.855965i	−0.0785881	−	0.0680969i
$159$	−10.4691	−	0.00543725i	−0.830251	−	0.000431202i
$160$		−	2.37473i		−	0.187739i
$161$	−12.1929	−	3.51185i	−0.960935	−	0.276772i
$162$	−13.5962	−	6.24335i	−1.06822	−	0.490524i
$163$	−4.65697	−	1.36741i	−0.364762	−	0.107104i	0.0942153	−	0.995552i	$-0.469966\pi$
$163$	−4.65697	−	1.36741i	−0.364762	−	0.107104i	−0.458977	+	0.888448i	$0.651784\pi$
$164$	3.76978	−	4.35056i	0.294371	−	0.339722i
$165$	−2.23435	−	0.657326i	−0.173944	−	0.0511728i
$166$	−0.855804	−	0.123046i	−0.0664233	−	0.00955023i
$167$	−14.0143	+	9.00643i	−1.08446	+	0.696939i	−0.955583	−	0.294722i	$-0.904773\pi$
$167$	−14.0143	+	9.00643i	−1.08446	+	0.696939i	−0.128875	+	0.991661i	$0.541137\pi$
$168$	−8.12438	−	4.76798i	−0.626810	−	0.367858i
$169$	−1.33511	−	1.54080i	−0.102701	−	0.118523i
$170$	6.94583	−	0.998660i	0.532721	−	0.0765937i
$171$	18.6312	−	2.65901i	1.42476	−	0.203339i
$172$	−8.49980	+	2.49577i	−0.648104	+	0.190300i
$173$	19.5176	−	5.73088i	1.48390	−	0.435711i	0.563308	−	0.826247i	$-0.309528\pi$
$173$	19.5176	−	5.73088i	1.48390	−	0.435711i	0.920588	+	0.390536i	$0.127710\pi$
$174$	−4.41106	−	0.636554i	−0.334402	−	0.0482570i
$175$	−5.58405	−	11.0092i	−0.422115	−	0.832215i
$176$	8.69017	−	7.53007i	0.655046	−	0.567600i
$177$	5.13233	−	4.44252i	0.385770	−	0.333921i
$178$	−8.97220	−	13.9610i	−0.672495	−	1.04642i
$179$	−6.33517	−	0.910861i	−0.473513	−	0.0680809i	−0.0985728	−	0.995130i	$-0.531428\pi$
$179$	−6.33517	−	0.910861i	−0.473513	−	0.0680809i	−0.374940	+	0.927049i	$0.622337\pi$
$180$	−1.32411	−	0.00137539i	−0.0986937	−	0.000102516i
$181$	7.48822	+	6.48858i	0.556595	+	0.482292i	0.887142	−	0.461497i	$-0.152688\pi$
$181$	7.48822	+	6.48858i	0.556595	+	0.482292i	−0.330547	+	0.943790i	$0.607233\pi$
$182$	−14.5491	+	0.596941i	−1.07845	+	0.0442482i
$183$	−21.9621	+	6.43626i	−1.62348	+	0.475782i
$184$	−3.11464	+	9.35359i	−0.229614	+	0.689556i
$185$	−1.08848			−0.0800264
$186$	−0.00293298	+	5.64725i	−0.000215056	+	0.414076i
$187$	12.8335	+	11.1203i	0.938480	+	0.813198i
$188$	4.51544	+	2.90190i	0.329322	+	0.211642i
$189$	−6.97069	+	11.8495i	−0.507043	+	0.861921i
$190$	5.07216	−	3.25968i	0.367973	−	0.236482i
$191$	1.28291	−	0.585883i	0.0928278	−	0.0423930i	−0.368460	−	0.929644i	$-0.620115\pi$
$191$	1.28291	−	0.585883i	0.0928278	−	0.0423930i	0.461288	+	0.887251i	$0.347388\pi$
$192$	−2.86783	+	4.45734i	−0.206968	+	0.321681i
$193$	2.67960	+	18.6370i	0.192882	+	1.34152i	0.824333	+	0.566105i	$0.191550\pi$
$193$	2.67960	+	18.6370i	0.192882	+	1.34152i	−0.631451	+	0.775415i	$0.717541\pi$
$194$	2.70105	−	5.91448i	0.193924	−	0.424635i
$195$	2.79003	−	1.79099i	0.199798	−	0.128256i
$196$	3.15688	−	4.31174i	0.225492	−	0.307981i
$197$	−0.990784	−	0.452476i	−0.0705904	−	0.0322376i	0.379807	−	0.925066i	$-0.375990\pi$
$197$	−0.990784	−	0.452476i	−0.0705904	−	0.0322376i	−0.450397	+	0.892828i	$0.648718\pi$
$198$	−7.58650	−	8.77368i	−0.539149	−	0.623518i
$199$	−4.69501	+	4.06825i	−0.332820	+	0.288391i	−0.805198	−	0.593006i	$-0.797941\pi$
$199$	−4.69501	+	4.06825i	−0.332820	+	0.288391i	0.472378	+	0.881396i	$0.343396\pi$
$200$	−8.72437	+	3.98428i	−0.616906	+	0.281731i
$201$	14.8616	+	12.8912i	1.04826	+	0.909274i
$202$	−13.4778	−	1.93782i	−0.948295	−	0.136344i
$203$	−0.991721	+	3.97340i	−0.0696052	+	0.278878i
$204$	8.77971	+	4.01507i	0.614703	+	0.281111i
$205$	4.18309	+	1.22827i	0.292160	+	0.0857858i
$206$	24.5716			1.71199
$207$	13.6459	+	4.55966i	0.948453	+	0.316919i
$208$			16.3686i			1.13496i
$209$	13.9994	+	4.11059i	0.968357	+	0.284335i
$210$	−0.449832	+	4.38129i	−0.0310413	+	0.302337i
$211$	3.30104	+	2.12145i	0.227253	+	0.146047i	0.649313	−	0.760521i	$-0.275056\pi$
$211$	3.30104	+	2.12145i	0.227253	+	0.146047i	−0.422060	+	0.906568i	$0.638693\pi$
$212$	−4.56733	−	0.656683i	−0.313686	−	0.0451012i
$213$	−17.0441	+	19.6493i	−1.16784	+	1.34634i
$214$	−10.2359	−	22.4135i	−0.699710	−	1.53215i
$215$	−4.39343	−	5.07029i	−0.299629	−	0.345791i
$216$	8.97680	+	5.78882i	0.610794	+	0.393879i
$217$	5.16236	+	0.527316i	0.350444	+	0.0357966i
$218$	2.91703	+	9.93451i	0.197567	+	0.672850i
$219$	4.05198	−	2.60108i	0.273807	−	0.175764i
$220$	−0.933770	−	0.426438i	−0.0629547	−	0.0287505i
$221$	−23.9268	+	3.44016i	−1.60949	+	0.231410i
$222$	−4.55867	−	2.93303i	−0.305958	−	0.196852i
$223$	16.4479	−	7.51151i	1.10143	−	0.503008i	0.220088	−	0.975480i	$-0.429365\pi$
$223$	16.4479	−	7.51151i	1.10143	−	0.503008i	0.881346	+	0.472472i	$0.156638\pi$
$224$	−8.49772	−	6.77383i	−0.567778	−	0.452596i
$225$	5.80142	+	12.7383i	0.386761	+	0.849222i
$226$	−11.6459	−	7.48436i	−0.774673	−	0.497852i
$227$	1.51708	−	1.75080i	0.100692	−	0.116205i	−0.703167	−	0.711025i	$-0.748231\pi$
$227$	1.51708	−	1.75080i	0.100692	−	0.116205i	0.803859	+	0.594820i	$0.202777\pi$
$228$	8.29500	+	0.00430812i	0.549350	+	0.000285312i
$229$			9.55596i			0.631475i	0.948847	+	0.315738i	$0.102252\pi$
$229$			9.55596i			0.631475i	−0.948847	+	0.315738i	$0.897748\pi$
$230$	4.58294	−	0.492064i	0.302190	−	0.0324457i
$231$	−8.72557	+	6.12039i	−0.574100	+	0.402692i
$232$	3.05299	+	0.896439i	0.200439	+	0.0588541i
$233$	4.08738	+	3.54174i	0.267773	+	0.232027i	0.778389	−	0.627782i	$-0.216037\pi$
$233$	4.08738	+	3.54174i	0.267773	+	0.232027i	−0.510616	+	0.859809i	$0.670583\pi$
$234$	16.5110	+	0.0171504i	1.07936	+	0.00112116i
$235$	−0.578510	+	4.02363i	−0.0377378	+	0.262473i
$236$	2.51690	−	1.61751i	0.163836	−	0.105291i
$237$	1.02972	−	0.891320i	0.0668874	−	0.0578975i
$238$	16.2391	−	27.7035i	1.05263	−	1.79575i
$239$	−6.91542	+	0.994288i	−0.447322	+	0.0643151i	−0.362295	−	0.932064i	$-0.618007\pi$
$239$	−6.91542	+	0.994288i	−0.447322	+	0.0643151i	−0.0850267	+	0.996379i	$0.527098\pi$
$240$	4.90018	+	0.707137i	0.316305	+	0.0456455i
$241$	7.30514	+	24.8790i	0.470565	+	1.60260i	0.763058	+	0.646331i	$0.223697\pi$
$241$	7.30514	+	24.8790i	0.470565	+	1.60260i	−0.292492	+	0.956268i	$0.594485\pi$
$242$	2.61835	+	8.91729i	0.168314	+	0.573225i
$243$	8.46178	−	13.0919i	0.542824	−	0.839847i
$244$	−9.98435	+	1.43553i	−0.639183	+	0.0919006i
$245$	3.96352	+	0.818256i	0.253220	+	0.0522764i
$246$	14.2096	+	16.4159i	0.905969	+	1.04664i
$247$	−17.4724	+	11.2289i	−1.11175	+	0.714475i
$248$	0.573788	−	3.99079i	0.0364356	−	0.253415i
$249$	0.254249	−	0.864233i	0.0161124	−	0.0547686i
$250$	7.02072	+	6.08349i	0.444029	+	0.384754i
$251$	20.5563	+	6.03587i	1.29750	+	0.380981i	0.856324	−	0.516439i	$-0.172743\pi$
$251$	20.5563	+	6.03587i	1.29750	+	0.380981i	0.441178	+	0.897420i	$0.354561\pi$
$252$	−3.78191	+	4.73427i	−0.238238	+	0.298231i
$253$	8.16253	+	7.60173i	0.513174	+	0.477917i
$254$			24.6660i			1.54768i
$255$	−0.00379732	+	7.31148i	−0.000237797	+	0.457863i
$256$	−10.4726	+	12.0860i	−0.654535	+	0.755373i
$257$	−7.77683	−	4.99787i	−0.485106	−	0.311758i	0.275129	−	0.961407i	$-0.411280\pi$
$257$	−7.77683	−	4.99787i	−0.485106	−	0.311758i	−0.760234	+	0.649649i	$0.774916\pi$
$258$	−4.73773	−	33.0736i	−0.294958	−	2.05907i
$259$	−3.10484	+	3.89499i	−0.192925	+	0.242023i
$260$	1.32923	−	0.607039i	0.0824353	−	0.0376469i
$261$	1.31289	−	4.45416i	0.0812657	−	0.275706i
$262$	29.9138	−	4.30095i	1.84808	−	0.265714i
$263$	21.8709	+	9.98811i	1.34862	+	0.615893i	0.953125	−	0.302576i	$-0.0978467\pi$
$263$	21.8709	+	9.98811i	1.34862	+	0.615893i	0.395492	+	0.918469i	$0.370574\pi$
$264$	4.47338	+	6.96867i	0.275318	+	0.428892i
$265$	−0.984534	−	3.35302i	−0.0604795	−	0.205974i
$266$	2.80374	−	27.4483i	0.171908	−	1.68296i
$267$	15.7325	−	7.17490i	0.962811	−	0.439097i
$268$	5.67846	+	6.55329i	0.346867	+	0.400306i
$269$	−3.22682	−	7.06574i	−0.196742	−	0.430806i	0.785389	−	0.619003i	$-0.212463\pi$
$269$	−3.22682	−	7.06574i	−0.196742	−	0.430806i	−0.982131	+	0.188197i	$0.939736\pi$
$270$	0.718425	−	4.94208i	0.0437220	−	0.300766i
$271$	6.00825	+	0.863856i	0.364975	+	0.0524755i	0.322363	−	0.946616i	$-0.395523\pi$
$271$	6.00825	+	0.863856i	0.364975	+	0.0524755i	0.0426123	+	0.999092i	$0.486432\pi$
$272$	−30.3673	−	19.5159i	−1.84129	−	1.18332i
$273$	1.54957	−	15.0925i	0.0937841	−	0.913442i
$274$	5.12975	+	1.50623i	0.309899	+	0.0909947i
$275$			10.8515i			0.654369i
$276$	5.66874	+	2.84225i	0.341218	+	0.171083i
$277$	−12.4505			−0.748079			−0.374040	−	0.927413i	$-0.622028\pi$
$277$	−12.4505			−0.748079			−0.374040	+	0.927413i	$0.622028\pi$
$278$	−14.0358	−	4.12127i	−0.841809	−	0.247177i
$279$	−5.82326	−	0.843434i	−0.348630	−	0.0504951i
$280$	0.761462	−	3.05085i	0.0455061	−	0.182323i
$281$	−1.96681	−	0.282784i	−0.117330	−	0.0168695i	0.0833997	−	0.996516i	$-0.473422\pi$
$281$	−1.96681	−	0.282784i	−0.117330	−	0.0168695i	−0.200730	+	0.979647i	$0.564331\pi$
$282$	−13.2650	+	15.2926i	−0.789919	+	0.910659i
$283$	−8.48372	+	3.87438i	−0.504305	+	0.230308i	−0.651288	−	0.758831i	$-0.725771\pi$
$283$	−8.48372	+	3.87438i	−0.504305	+	0.230308i	0.146983	+	0.989139i	$0.453044\pi$
$284$	−8.66442	+	7.50776i	−0.514139	+	0.445504i
$285$	2.60671	+	5.71574i	0.154408	+	0.338572i
$286$	11.6436	+	5.31746i	0.688501	+	0.314428i
$287$	16.3273	−	11.4651i	0.963770	−	0.676766i
$288$	9.30415	+	8.07902i	0.548252	+	0.476061i
$289$	15.0831	−	33.0274i	0.887243	−	1.94279i
$290$	−0.211717	−	1.47252i	−0.0124324	−	0.0864694i
$291$	5.69732	+	3.66562i	0.333983	+	0.214883i
$292$	1.93045	−	0.881607i	0.112971	−	0.0515922i
$293$	17.1482	−	11.0204i	1.00181	−	0.643822i	0.0665460	−	0.997783i	$-0.478802\pi$
$293$	17.1482	−	11.0204i	1.00181	−	0.643822i	0.935260	+	0.353962i	$0.115166\pi$
$294$	14.3948	+	14.1071i	0.839523	+	0.822744i
$295$	1.90614	+	1.22500i	0.110980	+	0.0713222i
$296$	2.92482	+	2.53437i	0.170002	+	0.147307i
$297$	10.1768	−	6.51787i	0.590519	−	0.378205i
$298$	21.3263			1.23540
$299$	−15.7872	+	1.69505i	−0.912996	+	0.0980272i
$300$	1.73503	+	5.92034i	0.100172	+	0.341811i
$301$	−30.6755	+	1.25860i	−1.76811	+	0.0725445i
$302$	−15.0871	−	13.0731i	−0.868166	−	0.752270i
$303$	4.00410	−	13.6106i	0.230029	−	0.781906i
$304$	−30.6997	−	4.41396i	−1.76075	−	0.253158i
$305$	−4.13009	−	6.42655i	−0.236488	−	0.367983i
$306$	−19.7175	+	30.6111i	−1.12718	+	1.74992i
$307$	2.50245	−	2.16839i	0.142822	−	0.123756i	−0.580520	−	0.814246i	$-0.697151\pi$
$307$	2.50245	−	2.16839i	0.142822	−	0.123756i	0.723342	+	0.690490i	$0.242605\pi$
$308$	−4.18950	+	2.12499i	−0.238719	+	0.121083i
$309$	−3.65669	+	25.3394i	−0.208022	+	1.44151i
$310$	−1.80869	+	0.531079i	−0.102727	+	0.0301633i
$311$	10.0567	−	2.95290i	0.570261	−	0.167444i	0.0161251	−	0.999870i	$-0.494867\pi$
$311$	10.0567	−	2.95290i	0.570261	−	0.167444i	0.554136	+	0.832426i	$0.313049\pi$
$312$	−11.6671	−	1.68366i	−0.660519	−	0.0953185i
$313$	−29.2053	+	4.19909i	−1.65078	+	0.237346i	−0.903941	−	0.427657i	$-0.859339\pi$
$313$	−29.2053	+	4.19909i	−1.65078	+	0.237346i	−0.746840	+	0.665004i	$0.768430\pi$
$314$	6.82140	+	7.87232i	0.384954	+	0.444261i
$315$	−4.45124	−	1.11590i	−0.250799	−	0.0628738i
$316$	0.504975	−	0.324528i	0.0284071	−	0.0182561i
$317$	−30.8767	−	4.43940i	−1.73421	−	0.249341i	−0.798469	−	0.602036i	$-0.794356\pi$
$317$	−30.8767	−	4.43940i	−1.73421	−	0.249341i	−0.935739	+	0.352695i	$0.885265\pi$
$318$	4.91174	−	16.6958i	0.275437	−	0.936252i
$319$	2.35751	−	2.72072i	0.131995	−	0.152331i
$320$	−1.69755	−	0.498444i	−0.0948957	−	0.0278639i
$321$	24.6371	−	7.22020i	1.37511	−	0.402992i
$322$	11.3119	−	17.8031i	0.630385	−	0.992129i
$323$		−	45.8032i		−	2.54856i
$324$	4.51013	−	5.18317i	0.250563	−	0.287954i
$325$	−11.6742	−	10.1158i	−0.647569	−	0.561121i
$326$	4.36207	−	6.78752i	0.241593	−	0.375926i
$327$	−10.6790	+	1.52975i	−0.590552	+	0.0845955i
$328$	−8.38042	−	13.0402i	−0.462732	−	0.720024i
$329$	12.7479	+	13.5474i	0.702816	+	0.746891i
$330$	2.09488	−	3.25597i	0.115319	−	0.179235i
$331$	−0.762030	−	5.30003i	−0.0418849	−	0.291316i	−0.999988	−	0.00489258i	$-0.998443\pi$
$331$	−0.762030	−	5.30003i	−0.0418849	−	0.291316i	0.958103	−	0.286424i	$-0.0924665\pi$
$332$	0.164944	−	0.361176i	0.00905245	−	0.0198221i
$333$	3.70308	−	4.26462i	0.202928	−	0.233700i
$334$	−7.80196	−	26.5710i	−0.426904	−	1.45390i
$335$	−2.72805	+	5.97359i	−0.149049	+	0.326372i
$336$	16.5080	−	15.5177i	0.900584	−	0.846558i
$337$	−4.34316	−	5.01227i	−0.236587	−	0.273036i	0.625024	−	0.780606i	$-0.285089\pi$
$337$	−4.34316	−	5.01227i	−0.236587	−	0.273036i	−0.861611	+	0.507570i	$0.830544\pi$
$338$	3.08288	−	1.40791i	0.167687	−	0.0765800i
$339$	9.45133	−	10.8960i	0.513326	−	0.591788i
$340$	−0.458620	+	3.18977i	−0.0248722	+	0.172990i
$341$	−3.83751	−	2.46622i	−0.207813	−	0.133553i
$342$	−4.48454	+	30.9623i	−0.242496	+	1.67425i
$343$	14.2338	−	11.8490i	0.768554	−	0.639785i
$344$			23.8538i			1.28611i
$345$	−0.174582	+	4.79936i	−0.00939920	+	0.258389i
$346$			33.8148i			1.81790i
$347$	−2.47847	+	8.44089i	−0.133051	+	0.453131i	−0.998885	−	0.0472002i	$-0.984970\pi$
$347$	−2.47847	+	8.44089i	−0.133051	+	0.453131i	0.865834	+	0.500331i	$0.166788\pi$
$348$	0.851198	−	1.86130i	0.0456290	−	0.0997764i
$349$	3.92244	−	6.10344i	0.209964	−	0.326710i	−0.720259	−	0.693705i	$-0.755977\pi$
$349$	3.92244	−	6.10344i	0.209964	−	0.326710i	0.930223	+	0.366995i	$0.119614\pi$
$350$	20.1750	−	3.75062i	1.07840	−	0.200479i
$351$	−2.47481	+	17.0243i	−0.132096	+	0.908693i
$352$	3.96844	+	8.68968i	0.211519	+	0.463162i
$353$	9.85474	+	11.3730i	0.524515	+	0.605322i	0.954756	−	0.297392i	$-0.0961168\pi$
$353$	9.85474	+	11.3730i	0.524515	+	0.605322i	−0.430241	+	0.902714i	$0.641571\pi$
$354$	4.68222	+	10.2667i	0.248857	+	0.545671i
$355$	−7.89796	−	3.60688i	−0.419180	−	0.191433i
$356$	7.31253	−	2.14715i	0.387563	−	0.113799i
$357$	26.1525	+	20.8693i	1.38414	+	1.10452i
$358$	4.41984	−	9.67810i	0.233596	−	0.511504i
$359$	15.6105	−	2.24444i	0.823888	−	0.118457i	0.282540	−	0.959256i	$-0.408823\pi$
$359$	15.6105	−	2.24444i	0.823888	−	0.118457i	0.541348	+	0.840798i	$0.317914\pi$
$360$	−1.00806	+	3.41999i	−0.0531294	+	0.180249i
$361$	−8.45557	−	18.5151i	−0.445030	−	0.974480i
$362$	−13.8564	+	8.90496i	−0.728276	+	0.468035i
$363$	−9.58558	+	1.37312i	−0.503112	+	0.0720699i
$364$	1.61935	−	6.48805i	0.0848772	−	0.340066i
$365$	1.21467	+	1.05252i	0.0635788	+	0.0550914i
$366$	0.0197588	−	38.0442i	0.00103281	−	1.98860i
$367$			7.78696i			0.406476i	0.979129	+	0.203238i	$0.0651465\pi$
$367$			7.78696i			0.406476i	−0.979129	+	0.203238i	$0.934854\pi$
$368$	−19.4746	−	13.5255i	−1.01518	−	0.705065i
$369$	−19.0435	+	12.2106i	−0.991365	+	0.635658i
$370$	0.509776	−	1.73614i	0.0265020	−	0.0902574i
$371$	−14.8067	−	6.04130i	−0.768727	−	0.313649i
$372$	−2.48799	−	0.731942i	−0.128996	−	0.0379494i
$373$	−0.915912	+	6.37031i	−0.0474241	+	0.329842i	0.952273	+	0.305247i	$0.0987389\pi$
$373$	−0.915912	+	6.37031i	−0.0474241	+	0.329842i	−0.999697	+	0.0245956i	$0.992170\pi$
$374$	−23.7475	+	15.2616i	−1.22795	+	0.789158i
$375$	−7.31838	+	6.33476i	−0.377920	+	0.327126i
$376$	10.9230	−	9.46481i	0.563309	−	0.488110i
$377$	0.729316	+	5.07250i	0.0375617	+	0.261247i
$378$	−15.6354	−	16.6679i	−0.804198	−	0.857304i
$379$	26.6089	−	7.81308i	1.36681	−	0.401331i	0.485650	−	0.874154i	$-0.338583\pi$
$379$	26.6089	−	7.81308i	1.36681	−	0.401331i	0.881158	+	0.472823i	$0.156765\pi$
$380$	0.780080	+	2.65671i	0.0400172	+	0.136286i
$381$	−25.4367	−	3.67073i	−1.30316	−	0.188057i
$382$	0.333658	+	2.32064i	0.0170714	+	0.118734i
$383$	−4.03256	−	4.65382i	−0.206054	−	0.237799i	0.643311	−	0.765605i	$-0.277560\pi$
$383$	−4.03256	−	4.65382i	−0.206054	−	0.237799i	−0.849365	+	0.527806i	$0.823015\pi$
$384$	−15.0785	−	17.4198i	−0.769472	−	0.888950i
$385$	−2.78195	−	2.21759i	−0.141781	−	0.113019i
$386$	−30.9812	−	4.45443i	−1.57690	−	0.226724i
$387$	34.8120	+	0.0361602i	1.76960	+	0.00183813i
$388$	2.25665	+	1.95540i	0.114564	+	0.0992703i
$389$	−0.303021	+	1.03199i	−0.0153637	+	0.0523241i	−0.966818	−	0.255466i	$-0.917771\pi$
$389$	−0.303021	+	1.03199i	−0.0153637	+	0.0523241i	0.951454	+	0.307790i	$0.0995894\pi$
$390$	1.54998	+	5.28892i	0.0784865	+	0.267815i
$391$	15.6780	−	31.3097i	0.792872	−	1.58340i
$392$	−8.74508	−	11.4272i	−0.441693	−	0.577163i
$393$	−0.0163540	+	31.4885i	−0.000824950	+	1.58839i
$394$	1.18573	−	1.36840i	0.0597361	−	0.0689391i
$395$	0.382435	+	0.245776i	0.0192424	+	0.0123663i
$396$	4.84753	−	2.20771i	0.243598	−	0.110942i
$397$	12.4770	+	19.4146i	0.626202	+	0.974389i	0.998921	+	0.0464450i	$0.0147892\pi$
$397$	12.4770	+	19.4146i	0.626202	+	0.974389i	−0.372719	+	0.927944i	$0.621574\pi$
$398$	−4.29006	−	9.39392i	−0.215041	−	0.470875i
$399$	27.8887	+	6.97613i	1.39618	+	0.349243i
$400$	−3.28285	−	22.8327i	−0.164142	−	1.14164i
$401$	9.45685	+	4.31880i	0.472253	+	0.215671i	0.637301	−	0.770615i	$-0.280051\pi$
$401$	9.45685	+	4.31880i	0.472253	+	0.215671i	−0.165048	+	0.986285i	$0.552778\pi$
$402$	−27.5219	+	17.6671i	−1.37267	+	0.881153i
$403$	6.23053	−	1.82945i	0.310365	−	0.0911313i
$404$	2.59765	−	5.68805i	0.129238	−	0.282991i
$405$	4.98959	+	1.47634i	0.247935	+	0.0733600i
$406$	−5.87317	−	3.44270i	−0.291480	−	0.170859i
$407$	3.98298	−	1.81897i	0.197429	−	0.0901628i
$408$	17.0340	−	19.6377i	0.843308	−	0.972209i
$409$	24.2867	+	3.49190i	1.20090	+	0.172663i	0.713589	−	0.700565i	$-0.247068\pi$
$409$	24.2867	+	3.49190i	1.20090	+	0.172663i	0.487312	+	0.873228i	$0.337977\pi$
$410$	−3.91820	+	6.09684i	−0.193506	+	0.301102i
$411$	−2.31669	+	5.06588i	−0.114274	+	0.249881i
$412$	−3.17912	+	10.8271i	−0.156624	+	0.533412i
$413$	9.82070	−	3.32663i	0.483245	−	0.163693i
$414$	−13.6636	+	19.6299i	−0.671530	+	0.964756i
$415$	0.300705			0.0147610
$416$	−13.0479	−	3.83120i	−0.639725	−	0.187840i
$417$	6.33881	−	13.8610i	0.310413	−	0.678776i
$418$	−13.1129	+	20.4040i	−0.641372	+	0.997995i
$419$	−2.46958	+	17.1763i	−0.120647	+	0.839117i	0.836179	+	0.548456i	$0.184784\pi$
$419$	−2.46958	+	17.1763i	−0.120647	+	0.839117i	−0.956826	+	0.290661i	$0.906125\pi$
$420$	−1.87234	−	0.765069i	−0.0913609	−	0.0373315i
$421$	−6.65403	−	14.5703i	−0.324298	−	0.710113i	0.675327	−	0.737519i	$-0.264003\pi$
$421$	−6.65403	−	14.5703i	−0.324298	−	0.710113i	−0.999624	+	0.0274057i	$0.991275\pi$
$422$	−4.92975	+	4.27165i	−0.239977	+	0.207941i
$423$	−13.7963	−	15.9553i	−0.670801	−	0.775772i
$424$	−5.16152	+	11.3022i	−0.250666	+	0.548881i
$425$	32.6859	−	9.59744i	1.58550	−	0.465544i
$426$	−23.3585	−	36.3880i	−1.13172	−	1.76300i
$427$	−34.7776	−	3.55241i	−1.68301	−	0.171913i
$428$	11.2004	−	1.61038i	0.541394	−	0.0778407i
$429$	−7.21638	+	11.2161i	−0.348410	+	0.541518i
$430$	10.1448	−	4.63297i	0.489225	−	0.223422i
$431$	5.33003	+	8.29368i	0.256738	+	0.399493i	0.945565	−	0.325433i	$-0.105510\pi$
$431$	5.33003	+	8.29368i	0.256738	+	0.399493i	−0.688827	+	0.724926i	$0.741874\pi$
$432$	−19.4413	+	16.7930i	−0.935371	+	0.807956i
$433$	1.80069	−	2.80192i	0.0865354	−	0.134652i	−0.795287	−	0.606233i	$-0.792680\pi$
$433$	1.80069	−	2.80192i	0.0865354	−	0.134652i	0.881823	+	0.471581i	$0.156316\pi$
$434$	−3.25881	+	7.98708i	−0.156428	+	0.383392i
$435$	1.55004		0.000805034i	0.0743187		3.85984e-5i
$436$	−4.75489			−0.227718
$437$	1.07807	−	30.0665i	0.0515709	−	1.43827i
$438$	2.25106	+	7.68115i	0.107560	+	0.367019i
$439$	−1.30417	+	4.44158i	−0.0622445	+	0.211985i	−0.984743	−	0.174016i	$-0.944326\pi$
$439$	−1.30417	+	4.44158i	−0.0622445	+	0.211985i	0.922498	+	0.386001i	$0.126144\pi$
$440$	−1.81014	+	2.08902i	−0.0862952	+	0.0995899i
$441$	−16.6901	+	12.7452i	−0.794767	+	0.606915i
$442$	5.71875	−	39.7748i	0.272013	−	1.89189i
$443$	11.6329	+	18.1012i	0.552698	+	0.860014i	0.999399	−	0.0346689i	$-0.0110377\pi$
$443$	11.6329	+	18.1012i	0.552698	+	0.860014i	−0.446701	+	0.894683i	$0.647401\pi$
$444$	1.88220	−	1.62922i	0.0893251	−	0.0773195i
$445$	3.77974	+	4.36206i	0.179177	+	0.206781i
$446$	4.27778	+	29.7526i	0.202559	+	1.40883i
$447$	−3.17372	+	21.9926i	−0.150112	+	1.04022i
$448$	−6.62581	+	4.65268i	−0.313040	+	0.219819i
$449$	−6.75669	−	23.0112i	−0.318868	−	1.08597i	−0.950507	−	0.310702i	$-0.899436\pi$
$449$	−6.75669	−	23.0112i	−0.318868	−	1.08597i	0.631639	−	0.775263i	$-0.282382\pi$
$450$	−23.0349	+	3.28749i	−1.08587	+	0.154974i
$451$	−17.3594	+	2.49591i	−0.817423	+	0.117528i
$452$	4.80462	−	4.16323i	0.225991	−	0.195822i
$453$	15.7268	−	13.6130i	0.738908	−	0.639596i
$454$	2.08205	+	3.23973i	0.0977155	+	0.152048i
$455$	4.97906	−	0.925628i	0.233422	−	0.0433941i
$456$	6.30392	−	21.4280i	0.295208	−	1.00346i
$457$	−9.23367	+	10.6562i	−0.431933	+	0.498477i	−0.929435	−	0.368986i	$-0.879705\pi$
$457$	−9.23367	+	10.6562i	−0.431933	+	0.498477i	0.497502	+	0.867463i	$0.334251\pi$
$458$	−15.2419	−	4.47542i	−0.712206	−	0.209123i
$459$	−28.6333	−	24.8891i	−1.33649	−	1.16172i
$460$	−0.376128	+	2.08306i	−0.0175371	+	0.0971231i
$461$	0.132982			0.00619360			0.00309680	−	0.999995i	$-0.499014\pi$
$461$	0.132982			0.00619360			0.00309680	+	0.999995i	$0.499014\pi$
$462$	−5.67558	−	16.7838i	−0.264052	−	0.780854i
$463$	−11.6388	+	13.4319i	−0.540899	+	0.624231i	−0.958738	−	0.284290i	$-0.908242\pi$
$463$	−11.6388	+	13.4319i	−0.540899	+	0.624231i	0.417839	+	0.908521i	$0.362788\pi$
$464$	−4.13738	+	6.43789i	−0.192073	+	0.298871i
$465$	−0.278509	−	1.94424i	−0.0129155	−	0.0901619i
$466$	−7.56340	+	4.86070i	−0.350368	+	0.225168i
$467$	−10.2358	−	22.4133i	−0.473657	−	1.03716i	−0.984159	−	0.177287i	$-0.943268\pi$
$467$	−10.2358	−	22.4133i	−0.473657	−	1.03716i	0.510502	−	0.859876i	$-0.329459\pi$
$468$	−2.14378	+	7.27308i	−0.0990961	+	0.336198i
$469$	13.5942	+	26.8014i	0.627721	+	1.23758i
$470$	−6.14680	−	2.80715i	−0.283531	−	0.129484i
$471$	−9.13344	+	5.86301i	−0.420847	+	0.270153i
$472$	−2.26969	−	7.72984i	−0.104471	−	0.355795i
$473$	24.5496	+	11.2114i	1.12879	+	0.515501i
$474$	0.939411	+	2.05985i	0.0431486	+	0.0946122i
$475$	22.1205	−	19.1675i	1.01496	−	0.879467i
$476$	10.1061	+	10.7398i	0.463210	+	0.492259i
$477$	16.4865	+	7.54983i	0.754864	+	0.345683i
$478$	1.65286	−	11.4959i	0.0755999	−	0.525809i
$479$	−25.5629	−	16.4283i	−1.16800	−	0.750626i	−0.194855	−	0.980832i	$-0.562424\pi$
$479$	−25.5629	−	16.4283i	−1.16800	−	0.750626i	−0.973142	+	0.230206i	$0.926060\pi$
$480$	−1.71061	+	3.74057i	−0.0780784	+	0.170733i
$481$	−1.75606	+	5.98059i	−0.0800695	+	0.272692i
$482$	−43.1037			−1.96332
$483$	16.6760	+	14.3147i	0.758784	+	0.651342i
$484$	−4.26802			−0.194001
$485$	−0.637105	+	2.16978i	−0.0289295	+	0.0985247i
$486$	16.9188	+	19.6281i	0.767453	+	0.890349i
$487$	19.8586	+	12.7624i	0.899880	+	0.578318i	0.906755	−	0.421658i	$-0.138552\pi$
$487$	19.8586	+	12.7624i	0.899880	+	0.578318i	−0.00687449	+	0.999976i	$0.502188\pi$
$488$	−3.86548	+	26.8850i	−0.174982	+	1.21703i
$489$	6.35045	+	5.50847i	0.287177	+	0.249102i
$490$	−3.16140	+	5.93865i	−0.142817	+	0.268281i
$491$	−30.0809	+	26.0652i	−1.35753	+	1.17631i	−0.390809	+	0.920472i	$0.627805\pi$
$491$	−30.0809	+	26.0652i	−1.35753	+	1.17631i	−0.966721	+	0.255835i	$0.917650\pi$
$492$	−9.07187	+	4.13729i	−0.408991	+	0.186523i
$493$	−10.2802	−	4.69479i	−0.462995	−	0.211443i
$494$	−9.72717	−	33.1277i	−0.437646	−	1.49049i
$495$	3.04596	+	2.64488i	0.136906	+	0.118879i
$496$	8.82064	+	4.02825i	0.396058	+	0.180874i
$497$	−35.4354	+	17.9735i	−1.58950	+	0.806222i
$498$	1.25939	+	0.810285i	0.0564346	+	0.0363097i
$499$	−7.50313	−	16.4296i	−0.335886	−	0.735488i	0.664039	−	0.747698i	$-0.268841\pi$
$499$	−7.50313	−	16.4296i	−0.335886	−	0.735488i	−0.999925	+	0.0122097i	$0.996113\pi$
$500$	−3.58894	+	2.30647i	−0.160502	+	0.103149i
$501$	28.5623	−	4.09151i	1.27607	−	0.182795i
$502$	−19.2546	+	29.9607i	−0.859375	+	1.33721i
$503$	−7.13209	+	8.23088i	−0.318004	+	0.366997i	−0.892136	−	0.451766i	$-0.850794\pi$
$503$	−7.13209	+	8.23088i	−0.318004	+	0.366997i	0.574132	+	0.818763i	$0.305340\pi$
$504$	9.36260	+	13.3626i	0.417043	+	0.595218i
$505$	4.73572			0.210737
$506$	−15.9477	+	9.45917i	−0.708962	+	0.420511i
$507$	0.993110	+	3.38873i	0.0441056	+	0.150499i
$508$	−10.8686	−	3.19132i	−0.482218	−	0.141592i
$509$	16.0822	−	18.5598i	0.712830	−	0.822650i	−0.277595	−	0.960698i	$-0.589537\pi$
$509$	16.0822	−	18.5598i	0.712830	−	0.822650i	0.990426	+	0.138048i	$0.0440829\pi$
$510$	−11.6601	−	3.43030i	−0.516320	−	0.151896i
$511$	7.23112	−	1.34430i	0.319886	−	0.0594682i
$512$	0.0103572	+	0.0161161i	0.000457728	+	0.000712239i
$513$	−31.2624	−	9.23239i	−1.38027	−	0.407620i
$514$	11.6139	−	10.0635i	0.512265	−	0.443881i
$515$	−8.45891	+	1.21621i	−0.372744	+	0.0535925i
$516$	15.1863	+	2.19151i	0.668539	+	0.0964759i
$517$	−4.60703	−	15.6901i	−0.202617	−	0.690050i
$518$	−4.75845	−	6.77643i	−0.209074	−	0.297739i
$519$	−34.8714	−	5.03224i	−1.53069	−	0.220891i
$520$	−0.559982	−	3.89476i	−0.0245568	−	0.170797i
$521$	28.8196	+	33.2596i	1.26261	+	1.45713i	0.832179	+	0.554507i	$0.187093\pi$
$521$	28.8196	+	33.2596i	1.26261	+	1.45713i	0.430431	+	0.902624i	$0.358362\pi$
$522$	6.48958	+	4.18013i	0.284041	+	0.182959i
$523$	6.62375	+	10.3068i	0.289637	+	0.450683i	0.955330	−	0.295542i	$-0.0955004\pi$
$523$	6.62375	+	10.3068i	0.289637	+	0.450683i	−0.665693	+	0.746226i	$0.731864\pi$
$524$	−1.97515	+	13.7375i	−0.0862849	+	0.600124i
$525$	0.865420	+	21.3636i	0.0377700	+	0.932382i
$526$	−26.1742	+	30.2066i	−1.14125	+	1.31707i
$527$	−4.03449	+	13.7402i	−0.175745	+	0.598534i
$528$	−19.1126	+	5.60117i	−0.831767	+	0.243760i
$529$	11.0284	−	20.1835i	0.479496	−	0.877544i
$530$	5.80920			0.252336
$531$	−11.2843	+	3.30065i	−0.489698	+	0.143236i
$532$	11.7319	+	4.78672i	0.508641	+	0.207531i
$533$	13.4973	−	21.0022i	0.584634	−	0.909708i
$534$	4.07595	+	28.4538i	0.176384	+	1.23132i
$535$	4.63314	+	7.20931i	0.200308	+	0.311685i
$536$	21.2392	−	9.69960i	0.917392	−	0.418959i
$537$	9.32275	+	5.99821i	0.402307	+	0.258842i
$538$	12.7812	−	1.83766i	0.551037	−	0.0792271i
$539$	−15.8708	+	3.62931i	−0.683604	+	0.156325i
$540$	2.08470	+	0.955977i	0.0897110	+	0.0411387i
$541$	−14.4371	+	4.23912i	−0.620700	+	0.182254i	−0.576938	−	0.816788i	$-0.695753\pi$
$541$	−14.4371	+	4.23912i	−0.620700	+	0.182254i	−0.0437621	+	0.999042i	$0.513934\pi$
$542$	−4.19176	+	9.17867i	−0.180051	+	0.394258i
$543$	−7.12113	−	15.6146i	−0.305597	−	0.670085i
$544$	22.6644	−	19.6389i	0.971730	−	0.842009i
$545$	−1.49593	−	3.27562i	−0.0640785	−	0.140312i
$546$	23.3471	+	9.54000i	0.999163	+	0.408274i
$547$	0.816320	−	5.67763i	0.0349033	−	0.242758i	−0.964899	−	0.262620i	$-0.915414\pi$
$547$	0.816320	−	5.67763i	0.0349033	−	0.242758i	0.999803	+	0.0198617i	$0.00632260\pi$
$548$	−1.32739	+	2.06546i	−0.0567033	+	0.0882321i
$549$	39.2300	+	5.68201i	1.67429	+	0.242502i
$550$	−17.3083	−	5.08217i	−0.738028	−	0.216704i
$551$	−9.71031			−0.413673
$552$	11.6438	−	12.4898i	0.495592	−	0.531599i
$553$	1.97036	−	0.667434i	0.0837883	−	0.0283822i
$554$	5.83105	−	19.8587i	0.247738	−	0.843717i
$555$	1.71452	+	0.784071i	0.0727773	+	0.0332820i
$556$	3.63194	−	5.65141i	0.154029	−	0.239673i
$557$	6.61328	+	0.950846i	0.280214	+	0.0402886i	0.280989	−	0.959711i	$-0.409338\pi$
$557$	6.61328	+	0.950846i	0.280214	+	0.0402886i	−0.000775112		1.00000i	$0.500247\pi$
$558$	4.07255	−	8.89318i	0.172405	−	0.376478i
$559$	−34.9465	+	15.9595i	−1.47808	+	0.675017i
$560$	6.52440	+	3.82444i	0.275706	+	0.161612i
$561$	−12.2044	−	26.7607i	−0.515270	−	1.12984i
$562$	1.37218	−	3.00465i	0.0578818	−	0.126743i
$563$	−40.2483	+	11.8180i	−1.69627	+	0.498068i	−0.979872	−	0.199628i	$-0.936027\pi$
$563$	−40.2483	+	11.8180i	−1.69627	+	0.498068i	−0.716394	+	0.697696i	$0.754208\pi$
$564$	−5.02217	−	7.82358i	−0.211471	−	0.329432i
$565$	4.37961	+	2.00010i	0.184251	+	0.0841448i
$566$	−2.20645	−	15.3462i	−0.0927439	−	0.645048i
$567$	19.5155	−	13.6435i	0.819575	−	0.572972i
$568$	12.8243	+	28.0813i	0.538095	+	1.17826i
$569$	−8.21302	−	12.7797i	−0.344308	−	0.535753i	0.625311	−	0.780376i	$-0.284972\pi$
$569$	−8.21302	−	12.7797i	−0.344308	−	0.535753i	−0.969618	+	0.244623i	$0.921336\pi$
$570$	−10.3375	+	1.48083i	−0.432991	+	0.0620252i
$571$	−0.287555	−	0.184801i	−0.0120338	−	0.00773366i	0.534610	−	0.845099i	$-0.320458\pi$
$571$	−0.287555	−	0.184801i	−0.0120338	−	0.00773366i	−0.546644	+	0.837365i	$0.684095\pi$
$572$	−3.84952	+	4.44258i	−0.160956	+	0.185754i
$573$	−2.44281	−	0.00126871i	−0.102050	−	5.30010e-5i
$574$	10.6403	+	31.4118i	0.444120	+	1.31111i
$575$	21.6818	−	5.53069i	0.904193	−	0.230646i
$576$	7.72807	−	4.95520i	0.322003	−	0.206466i
$577$	6.30628	−	21.4772i	0.262534	−	0.894108i	−0.717715	−	0.696337i	$-0.754812\pi$
$577$	6.30628	−	21.4772i	0.262534	−	0.894108i	0.980248	−	0.197770i	$-0.0633700\pi$
$578$	45.6152	+	39.5258i	1.89734	+	1.64406i
$579$	9.20416	−	31.2864i	0.382512	−	1.30022i
$580$	0.676234	+	0.0972278i	0.0280791	+	0.00403717i
$581$	0.857750	−	1.07604i	0.0355855	−	0.0446417i
$582$	−8.51499	+	7.37055i	−0.352958	+	0.305519i
$583$	9.20589	+	10.6242i	0.381269	+	0.440008i
$584$	−0.813267	−	5.65639i	−0.0336532	−	0.234063i
$585$	−5.68484	+	0.811331i	−0.235039	+	0.0335444i
$586$	9.54663	+	32.5128i	0.394368	+	1.34309i
$587$	24.3253	−	7.14255i	1.00401	−	0.294805i	0.261911	−	0.965092i	$-0.415647\pi$
$587$	24.3253	−	7.14255i	1.00401	−	0.294805i	0.742102	+	0.670287i	$0.233829\pi$
$588$	−8.07849	+	4.51763i	−0.333151	+	0.186304i
$589$	1.75106	+	12.1789i	0.0721511	+	0.501822i
$590$	−2.84661	+	2.46660i	−0.117193	+	0.101548i
$591$	1.23470	+	1.42642i	0.0507889	+	0.0586750i
$592$	−7.83034	+	5.03225i	−0.321825	+	0.206824i
$593$	−2.90753	+	20.2223i	−0.119398	+	0.830431i	0.838824	+	0.544403i	$0.183244\pi$
$593$	−2.90753	+	20.2223i	−0.119398	+	0.830431i	−0.958221	+	0.286027i	$0.907665\pi$
$594$	5.62989	+	19.2847i	0.230997	+	0.791263i
$595$	−4.21918	+	10.3409i	−0.172969	+	0.423934i
$596$	−2.75923	+	9.39707i	−0.113022	+	0.384919i
$597$	10.3259	−	3.02613i	0.422610	−	0.123851i
$598$	4.69012	−	25.9746i	0.191793	−	1.06218i
$599$			28.2592i			1.15464i	0.816518	+	0.577320i	$0.195902\pi$
$599$			28.2592i			1.15464i	−0.816518	+	0.577320i	$0.804098\pi$
$600$	16.6123	+	0.00862781i	0.678193	+	0.000352229i
$601$	−16.0415	−	13.9001i	−0.654347	−	0.566995i	0.263141	−	0.964757i	$-0.415241\pi$
$601$	−16.0415	−	13.9001i	−0.654347	−	0.566995i	−0.917489	+	0.397762i	$0.869787\pi$
$602$	12.3591	−	49.5174i	0.503717	−	2.01818i
$603$	−14.1233	−	31.0110i	−0.575147	−	1.26287i
$604$	7.71242	−	4.95647i	0.313814	−	0.201676i
$605$	−1.34276	−	2.94022i	−0.0545908	−	0.119537i
$606$	19.8337	+	12.7609i	0.805691	+	0.518378i
$607$	−8.36553	+	1.20278i	−0.339546	+	0.0488194i	−0.309979	−	0.950743i	$-0.600322\pi$
$607$	−8.36553	+	1.20278i	−0.339546	+	0.0488194i	−0.0295674	+	0.999563i	$0.509413\pi$
$608$	10.7040	−	23.4386i	0.434107	−	0.950561i
$609$	4.42430	−	5.54434i	0.179282	−	0.224668i
$610$	12.1847	−	3.57776i	0.493345	−	0.144859i
$611$	21.1743	+	9.67000i	0.856622	+	0.391206i
$612$	−10.9372	−	12.6487i	−0.442110	−	0.511294i
$613$	1.17687	+	1.35818i	0.0475333	+	0.0548563i	0.779018	−	0.627001i	$-0.215718\pi$
$613$	1.17687	+	1.35818i	0.0475333	+	0.0548563i	−0.731485	+	0.681857i	$0.761172\pi$
$614$	2.28661	+	5.00698i	0.0922802	+	0.202065i
$615$	−5.70425	−	4.94795i	−0.230017	−	0.199520i
$616$	2.31195	+	12.4362i	0.0931511	+	0.501070i
$617$	−11.7928	+	18.3499i	−0.474759	+	0.738739i	−0.993206	−	0.116370i	$-0.962874\pi$
$617$	−11.7928	+	18.3499i	−0.474759	+	0.738739i	0.518447	+	0.855110i	$0.326510\pi$
$618$	−38.7041	−	17.6999i	−1.55691	−	0.711994i
$619$	−1.47090	+	5.00942i	−0.0591204	+	0.201345i	−0.983757	−	0.179505i	$-0.942550\pi$
$619$	−1.47090	+	5.00942i	−0.0591204	+	0.201345i	0.924637	+	0.380850i	$0.124369\pi$
$620$		−	0.865681i		−	0.0347666i
$621$	−18.2098	−	17.0118i	−0.730736	−	0.682660i
$622$			17.4235i			0.698618i
$623$	26.3907	−	1.08280i	1.05732	−	0.0433813i
$624$	11.7909	−	25.7830i	0.472013	−	1.03215i
$625$	16.9073	+	10.8657i	0.676292	+	0.434626i
$626$	6.98036	−	48.5494i	0.278991	−	1.94043i
$627$	−19.0902	−	16.5591i	−0.762388	−	0.661306i
$628$	−4.35137	+	1.98720i	−0.173639	+	0.0792981i
$629$	−9.00162	−	10.3884i	−0.358918	−	0.414213i
$630$	3.86456	−	6.57717i	0.153968	−	0.262041i
$631$	−6.30933	+	13.8155i	−0.251170	+	0.549987i	−0.992654	−	0.120984i	$-0.961395\pi$
$631$	−6.30933	+	13.8155i	−0.251170	+	0.549987i	0.741484	+	0.670971i	$0.234122\pi$
$632$	−0.455376	−	1.55087i	−0.0181139	−	0.0616902i
$633$	−3.67149	−	5.71948i	−0.145929	−	0.227329i
$634$	21.5416	−	47.1696i	0.855528	−	1.87334i
$635$	−1.22088	−	8.49138i	−0.0484490	−	0.336970i
$636$	6.72122	+	4.32440i	0.266514	+	0.171474i
$637$	10.8903	−	20.4573i	0.431489	−	0.810548i
$638$	3.23547	+	5.03448i	0.128093	+	0.199317i
$639$	41.0011	−	18.6731i	1.62198	−	0.738698i
$640$	4.15781	−	6.46968i	0.164352	−	0.255736i
$641$	−6.03117	−	5.22604i	−0.238217	−	0.206416i	0.527568	−	0.849513i	$-0.323104\pi$
$641$	−6.03117	−	5.22604i	−0.238217	−	0.206416i	−0.765785	+	0.643097i	$0.777649\pi$
$642$	−0.0221654	+	42.6780i	−0.000874798	+	1.68436i
$643$			21.0208i			0.828980i	0.910054	+	0.414490i	$0.136040\pi$
$643$			21.0208i			0.828980i	−0.910054	+	0.414490i	$0.863960\pi$
$644$	6.38110	+	7.28778i	0.251451	+	0.287179i
$645$	3.26801	+	11.1512i	0.128678	+	0.439080i
$646$	73.0567	+	21.4514i	2.87438	+	0.843994i
$647$	−21.4903	+	24.8012i	−0.844872	+	0.975034i	−0.999917	−	0.0128735i	$-0.995902\pi$
$647$	−21.4903	+	24.8012i	−0.844872	+	0.975034i	0.155045	+	0.987907i	$0.450448\pi$
$648$	−9.96994	−	15.5846i	−0.391656	−	0.612221i
$649$	−9.02209	−	1.29718i	−0.354148	−	0.0509188i
$650$	21.6023	−	13.8829i	0.847310	−	0.544533i
$651$	−7.75168	−	4.54925i	−0.303812	−	0.178299i
$652$	2.42643	+	2.80025i	0.0950265	+	0.109666i
$653$	−14.5432	+	2.09100i	−0.569119	+	0.0818270i	−0.420867	−	0.907123i	$-0.638274\pi$
$653$	−14.5432	+	2.09100i	−0.569119	+	0.0818270i	−0.148253	+	0.988950i	$0.547365\pi$
$654$	2.56142	−	17.7496i	0.100160	−	0.694066i
$655$	−10.0851	+	2.96125i	−0.394057	+	0.115706i
$656$	35.7710	−	10.5033i	1.39662	−	0.410086i
$657$	−8.25615	+	1.17830i	−0.322103	+	0.0459700i
$658$	−27.5786	+	13.9884i	−1.07513	+	0.545323i
$659$	−10.2897	+	8.91606i	−0.400829	+	0.347320i	−0.831829	−	0.555031i	$-0.812706\pi$
$659$	−10.2897	+	8.91606i	−0.400829	+	0.347320i	0.431000	+	0.902352i	$0.358161\pi$
$660$	1.16365	+	1.34434i	0.0452951	+	0.0523282i
$661$	−13.5541	−	21.0906i	−0.527193	−	0.820328i	0.470892	−	0.882191i	$-0.343932\pi$
$661$	−13.5541	−	21.0906i	−0.527193	−	0.820328i	−0.998085	+	0.0618631i	$0.980296\pi$
$662$	8.81051	+	1.26676i	0.342430	+	0.0492341i
$663$	40.1665	+	11.8166i	1.55994	+	0.458919i
$664$	−0.808018	−	0.700151i	−0.0313572	−	0.0271711i
$665$	0.393389	+	9.58798i	0.0152550	+	0.371806i
$666$	5.06784	+	7.90375i	0.196375	+	0.306264i
$667$	−6.63767	−	3.32375i	−0.257012	−	0.128696i
$668$	12.7175			0.492055
$669$	−31.3189	−	0.0162659i	−1.21086	−	0.000628875i
$670$	−8.25031	−	7.14893i	−0.318737	−	0.276187i
$671$	25.8524	+	16.6143i	0.998021	+	0.641389i
$672$	8.50577	+	16.7911i	0.328117	+	0.647729i
$673$	−28.6369	+	18.4038i	−1.10387	+	0.709415i	−0.959949	−	0.280174i	$-0.909608\pi$
$673$	−28.6369	+	18.4038i	−1.10387	+	0.709415i	−0.143922	+	0.989589i	$0.545971\pi$
$674$	10.0287	−	4.57996i	0.386292	−	0.176413i
$675$	0.0377741	−	24.2438i	0.00145393	−	0.933146i
$676$	0.221502	+	1.54058i	0.00851930	+	0.0592530i
$677$	−9.69897	+	21.2378i	−0.372762	+	0.816235i	0.626559	+	0.779374i	$0.284463\pi$
$677$	−9.69897	+	21.2378i	−0.372762	+	0.816235i	−0.999320	+	0.0368603i	$0.988264\pi$
$678$	12.9528	+	20.1780i	0.497450	+	0.774932i
$679$	5.94700	+	8.46902i	0.228225	+	0.325011i
$680$	7.89330	+	3.60475i	0.302694	+	0.138236i
$681$	−3.65081	+	1.66498i	−0.139899	+	0.0638021i
$682$	5.73091	−	4.96586i	0.219448	−	0.190153i
$683$	21.1932	−	9.67863i	0.810937	−	0.370342i	0.0336066	−	0.999435i	$-0.489301\pi$
$683$	21.1932	−	9.67863i	0.810937	−	0.370342i	0.777330	+	0.629093i	$0.216573\pi$
$684$	−13.0628	−	5.98199i	−0.499469	−	0.228727i
$685$	−1.84050	−	0.264623i	−0.0703217	−	0.0101107i
$686$	12.2330	+	28.2525i	0.467060	+	1.07868i
$687$	6.88352	−	15.0521i	0.262623	−	0.574274i
$688$	−55.0467	−	16.1632i	−2.09863	−	0.616215i
$689$	−20.0114			−0.762373
$690$	−7.57329	−	2.52619i	−0.288310	−	0.0961703i
$691$		−	35.2821i		−	1.34219i	−0.741369	−	0.671097i	$-0.765823\pi$
$691$		−	35.2821i		−	1.34219i	0.741369	−	0.671097i	$-0.234177\pi$
$692$	−14.8999	−	4.37502i	−0.566411	−	0.166313i
$693$	18.1529	−	3.35520i	0.689571	−	0.127453i
$694$	−12.3026	−	7.90639i	−0.466999	−	0.300122i
$695$	5.03587	+	0.724049i	0.191021	+	0.0274647i
$696$	−4.16320	−	3.61122i	−0.157806	−	0.136883i
$697$	22.8712	+	50.0810i	0.866310	+	1.89695i
$698$	7.89804	+	9.11483i	0.298945	+	0.345001i
$699$	−3.88701	−	8.52308i	−0.147020	−	0.322373i
$700$	−0.957626	+	9.37505i	−0.0361949	+	0.354343i
$701$	−1.30722	−	4.45197i	−0.0493729	−	0.168149i	0.931116	−	0.364723i	$-0.118836\pi$
$701$	−1.30722	−	4.45197i	−0.0493729	−	0.168149i	−0.980489	+	0.196575i	$0.937018\pi$
$702$	−25.9950	−	11.9205i	−0.981119	−	0.449911i
$703$	−10.7433	−	4.90628i	−0.405190	−	0.185044i
$704$	7.04466	−	1.01287i	0.265505	−	0.0381739i
$705$	3.80962	−	5.92111i	0.143478	−	0.223002i
$706$	−22.7554	+	10.3920i	−0.856411	+	0.391110i
$707$	13.5084	−	16.9462i	0.508038	−	0.637329i
$708$	−5.12966	+	0.734815i	−0.192785	+	0.0276160i
$709$	−19.1999	−	12.3390i	−0.721066	−	0.463401i	0.127942	−	0.991782i	$-0.459163\pi$
$709$	−19.1999	−	12.3390i	−0.721066	−	0.463401i	−0.849007	+	0.528381i	$0.822799\pi$
$710$	9.45194	−	10.9081i	0.354725	−	0.409375i
$711$	−2.26402	+	0.662222i	−0.0849073	+	0.0248353i
$712$		−	20.5218i		−	0.769087i
$713$	−2.97175	+	8.92449i	−0.111293	+	0.334225i
$714$	−45.5350	+	31.9397i	−1.70411	+	1.19531i
$715$	−4.27157	−	1.25424i	−0.159748	−	0.0469061i
$716$	3.69265	+	3.19970i	0.138001	+	0.119578i
$717$	11.6091	+	3.41529i	0.433549	+	0.127546i
$718$	−3.73105	+	25.9500i	−0.139242	+	0.968447i
$719$	17.6742	−	11.3585i	0.659138	−	0.423602i	−0.167857	−	0.985811i	$-0.553685\pi$
$719$	17.6742	−	11.3585i	0.659138	−	0.423602i	0.826995	+	0.562209i	$0.190048\pi$
$720$	−7.20916	−	4.64364i	−0.268670	−	0.173058i
$721$	−19.7767	+	33.7385i	−0.736521	+	1.25649i
$722$	33.4919	−	4.81541i	1.24644	−	0.179211i
$723$	6.41458	−	44.4505i	0.238561	−	1.65313i
$724$	−2.13106	−	7.25773i	−0.0792003	−	0.269731i
$725$	−2.03466	−	6.92943i	−0.0755655	−	0.257353i
$726$	2.29915	−	15.9322i	0.0853295	−	0.591300i
$727$	−11.0538	+	1.58930i	−0.409964	+	0.0589440i	−0.344212	−	0.938892i	$-0.611854\pi$
$727$	−11.0538	+	1.58930i	−0.409964	+	0.0589440i	−0.0657524	+	0.997836i	$0.520945\pi$
$728$	−15.5343	−	9.10582i	−0.575739	−	0.337484i
$729$	−22.7592	+	14.5265i	−0.842934	+	0.538017i
$730$	−2.24766	+	1.44448i	−0.0831896	+	0.0534627i
$731$	12.0575	−	83.8618i	0.445963	−	3.10174i
$732$	16.7610	+	4.93092i	0.619503	+	0.182252i
$733$	24.2764	+	21.0356i	0.896669	+	0.776968i	0.975518	−	0.219918i	$-0.0705791\pi$
$733$	24.2764	+	21.0356i	0.896669	+	0.776968i	−0.0788492	+	0.996887i	$0.525125\pi$
$734$	−12.4203	−	3.64693i	−0.458442	−	0.134611i
$735$	−5.65374	−	4.14396i	−0.208541	−	0.152852i
$736$	15.3398	−	12.3580i	0.565432	−	0.455523i
$737$		−	26.4176i		−	0.973103i
$738$	−10.5572	−	36.0933i	−0.388618	−	1.32861i
$739$	10.2365	−	11.8136i	0.376557	−	0.434570i	−0.535562	−	0.844496i	$-0.679900\pi$
$739$	10.2365	−	11.8136i	0.376557	−	0.434570i	0.912119	+	0.409926i	$0.134446\pi$
$740$	0.699044	+	0.449248i	0.0256974	+	0.0165147i
$741$	35.6104	−	5.10113i	1.30818	−	0.187395i
$742$	16.5705	−	20.7876i	0.608323	−	0.763136i
$743$	1.68817	−	0.770964i	0.0619331	−	0.0282839i	−0.384208	−	0.923247i	$-0.625525\pi$
$743$	1.68817	−	0.770964i	0.0619331	−	0.0282839i	0.446141	+	0.894963i	$0.352798\pi$
$744$	−3.77852	+	5.87278i	−0.138527	+	0.215307i
$745$	−7.34168	+	1.05557i	−0.268978	+	0.0386733i
$746$	−9.73178	−	4.44435i	−0.356306	−	0.162719i
$747$	−1.02302	+	1.17816i	−0.0374304	+	0.0431065i
$748$	−3.65227	−	12.4385i	−0.133540	−	0.454797i
$749$	39.0135	+	3.98509i	1.42552	+	0.145612i
$750$	−6.67655	−	14.6397i	−0.243793	−	0.534567i
$751$	15.1076	+	17.4351i	0.551285	+	0.636217i	0.961182	−	0.275915i	$-0.0889808\pi$
$751$	15.1076	+	17.4351i	0.551285	+	0.636217i	−0.409897	+	0.912132i	$0.634435\pi$
$752$	14.4403	+	31.6199i	0.526585	+	1.15306i
$753$	−28.0315	−	24.3149i	−1.02152	−	0.886085i
$754$	−8.43228	−	1.21238i	−0.307085	−	0.0441522i
$755$	5.84089	+	3.75371i	0.212572	+	0.136612i
$756$	9.36737	−	4.73296i	0.340688	−	0.172136i
$757$	−2.92714	−	0.859486i	−0.106389	−	0.0312385i	0.228105	−	0.973637i	$-0.426747\pi$
$757$	−2.92714	−	0.859486i	−0.106389	−	0.0312385i	−0.334494	+	0.942398i	$0.608565\pi$
$758$			46.1007i			1.67445i
$759$	−7.38143	−	17.8537i	−0.267929	−	0.648048i
$760$	7.45576			0.270449
$761$	41.1584	+	12.0852i	1.49199	+	0.438089i	0.923176	−	0.384376i	$-0.125583\pi$
$761$	41.1584	+	12.0852i	1.49199	+	0.438089i	0.568816	+	0.822465i	$0.307402\pi$
$762$	17.7678	−	38.8527i	0.643661	−	1.40749i
$763$	−15.9885	−	3.99058i	−0.578823	−	0.144469i
$764$	−1.06572	−	0.153228i	−0.0385565	−	0.00554359i
$765$	5.27272	−	11.5140i	0.190636	−	0.416289i
$766$	9.31151	−	4.25242i	0.336439	−	0.153646i
$767$	9.80592	−	8.49687i	0.354071	−	0.306804i
$768$	25.2019	−	11.4935i	0.909395	−	0.414736i
$769$	26.0872	+	11.9136i	0.940727	+	0.429616i	0.825930	−	0.563773i	$-0.190651\pi$
$769$	26.0872	+	11.9136i	0.940727	+	0.429616i	0.114798	+	0.993389i	$0.463378\pi$
$770$	4.83998	−	3.39867i	0.174421	−	0.122479i
$771$	8.64957	+	13.4744i	0.311506	+	0.485267i
$772$	5.97117	−	13.0750i	0.214907	−	0.470581i
$773$	−2.85683	−	19.8697i	−0.102753	−	0.714663i	−0.974448	−	0.224614i	$-0.927888\pi$
$773$	−2.85683	−	19.8697i	−0.102753	−	0.714663i	0.871695	−	0.490049i	$-0.163021\pi$
$774$	−16.3615	+	55.5088i	−0.588102	+	1.99522i
$775$	−8.32414	+	3.80151i	−0.299012	+	0.136554i
$776$	6.76399	−	4.34695i	0.242813	−	0.156046i
$777$	7.69631	−	3.89868i	0.276104	−	0.139865i
$778$	−1.50413	−	0.966644i	−0.0539256	−	0.0346559i
$779$	35.7507	+	30.9781i	1.28090	+	1.10991i
$780$	−2.53102	−	0.00131452i	−0.0906249	−	4.70673e-5i
$781$	34.9279			1.24982
$782$	42.5968	+	39.6702i	1.52326	+	1.41860i
$783$	−5.27650	+	6.07027i	−0.188567	+	0.216934i
$784$	32.2959	−	12.4378i	1.15343	−	0.444206i
$785$	−2.73795	−	2.37245i	−0.0977218	−	0.0846764i
$786$	−50.2170	−	14.7734i	−1.79118	−	0.526949i
$787$	22.3652	+	3.21564i	0.797235	+	0.114625i	0.528882	−	0.848696i	$-0.322611\pi$
$787$	22.3652	+	3.21564i	0.797235	+	0.114625i	0.268353	+	0.963321i	$0.413521\pi$
$788$	0.449552	+	0.699517i	0.0160146	+	0.0249193i
$789$	−27.2552	−	31.4873i	−0.970312	−	1.12098i
$790$	−0.571125	+	0.494883i	−0.0203197	+	0.0176071i
$791$	19.6498	−	9.96673i	0.698666	−	0.354376i
$792$	−2.02647	−	14.1991i	−0.0720074	−	0.504542i
$793$	−41.9736	+	12.3246i	−1.49053	+	0.437658i
$794$	−36.8100	+	10.8084i	−1.30634	+	0.383575i
$795$	−0.864511	+	5.99072i	−0.0306610	+	0.212469i
$796$	4.69433	−	0.674943i	0.166386	−	0.0239227i
$797$	−9.74523	−	11.2466i	−0.345194	−	0.398375i	0.556431	−	0.830894i	$-0.312170\pi$
$797$	−9.74523	−	11.2466i	−0.345194	−	0.398375i	−0.901625	+	0.432519i	$0.857625\pi$
$798$	−24.1884	+	41.2156i	−0.856259	+	1.45902i
$799$	−43.1857	+	27.7538i	−1.52780	+	0.981858i
$800$	18.9690	+	2.72734i	0.670657	+	0.0964259i
$801$	−29.9494	−	0.0311093i	−1.05821	−	0.00109919i
$802$	−11.3176	+	13.0612i	−0.399637	+	0.461205i
$803$	−6.20363	−	1.82155i	−0.218921	−	0.0642811i
$804$	−4.22387	−	14.4129i	−0.148964	−	0.508302i
$805$	−3.01297	+	6.68871i	−0.106193	+	0.235746i
$806$			10.7946i			0.380223i
$807$	−0.00698754	+	13.4540i	−0.000245973	+	0.473604i
$808$	−12.7252	−	11.0265i	−0.447672	−	0.387910i
$809$	−18.7334	+	29.1498i	−0.658632	+	1.02485i	0.337863	+	0.941195i	$0.390296\pi$
$809$	−18.7334	+	29.1498i	−0.658632	+	1.02485i	−0.996495	+	0.0836562i	$0.973340\pi$
$810$	−4.69160	+	7.26704i	−0.164846	+	0.255338i
$811$	4.12953	+	6.42568i	0.145008	+	0.225636i	0.906158	−	0.422939i	$-0.139002\pi$
$811$	4.12953	+	6.42568i	0.145008	+	0.225636i	−0.761151	+	0.648575i	$0.775365\pi$
$812$	2.27685	−	2.14249i	0.0799018	−	0.0751867i
$813$	−8.84166	−	5.68868i	−0.310090	−	0.199511i
$814$	1.03589	+	7.20480i	0.0363081	+	0.252528i
$815$	−1.16571	+	2.55254i	−0.0408330	+	0.0894117i
$816$	33.7752	+	52.6153i	1.18237	+	1.84190i
$817$	−20.5089	−	69.8470i	−0.717516	−	2.44364i
$818$	−16.9440	+	37.1023i	−0.592434	+	1.29725i
$819$	−13.3125	+	22.6569i	−0.465178	+	0.791695i
$820$	−2.17953	−	2.51531i	−0.0761124	−	0.0878384i
$821$	17.1196	−	7.81826i	0.597478	−	0.272859i	−0.0936338	−	0.995607i	$-0.529848\pi$
$821$	17.1196	−	7.81826i	0.597478	−	0.272859i	0.691112	+	0.722747i	$0.257121\pi$
$822$	−6.99515	−	6.06770i	−0.243984	−	0.211635i
$823$	2.36016	−	16.4153i	0.0822701	−	0.572201i	−0.906437	−	0.422341i	$-0.861209\pi$
$823$	2.36016	−	16.4153i	0.0822701	−	0.572201i	0.988707	−	0.149860i	$-0.0478823\pi$
$824$	25.5615	+	16.4274i	0.890478	+	0.572275i
$825$	7.81674	−	17.0928i	0.272144	−	0.595094i
$826$	0.706614	+	17.2221i	0.0245863	+	0.599235i
$827$		−	19.7824i		−	0.687903i	−0.938987	−	0.343951i	$-0.888234\pi$
$827$		−	19.7824i		−	0.687903i	0.938987	−	0.343951i	$-0.111766\pi$
$828$	−6.88176	−	8.56039i	−0.239158	−	0.297494i
$829$			12.6371i			0.438906i	0.975623	+	0.219453i	$0.0704273\pi$
$829$			12.6371i			0.438906i	−0.975623	+	0.219453i	$0.929573\pi$
$830$	−0.140832	+	0.479629i	−0.00488835	+	0.0166482i
$831$	19.6115	+	8.96858i	0.680315	+	0.311117i
$832$	−5.47737	+	8.52295i	−0.189894	+	0.295480i
$833$	24.9686	+	44.5947i	0.865110	+	1.54512i
$834$	19.1398	+	16.6021i	0.662757	+	0.574885i
$835$	4.00104	+	8.76105i	0.138462	+	0.303189i
$836$	−7.29414	−	8.41788i	−0.252273	−	0.291139i
$837$	8.56499	+	5.52326i	0.296049	+	0.190912i
$838$	−26.2398	−	11.9833i	−0.906440	−	0.413957i
$839$	−42.8089	+	12.5698i	−1.47793	+	0.433959i	−0.918667	−	0.395032i	$-0.870733\pi$
$839$	−42.8089	+	12.5698i	−1.47793	+	0.433959i	−0.559262	+	0.828991i	$0.688915\pi$
$840$	−3.39706	+	4.25705i	−0.117210	+	0.146882i
$841$	11.0517	−	24.1999i	0.381094	−	0.834480i
$842$	26.3562	−	3.78945i	0.908294	−	0.130593i
$843$	2.89433	+	1.86220i	0.0996859	+	0.0641374i
$844$	−1.24441	−	2.72489i	−0.0428345	−	0.0937945i
$845$	−0.991612	+	0.637270i	−0.0341125	+	0.0219228i
$846$	31.9102	−	14.5329i	1.09710	−	0.499651i
$847$	−14.3514	−	3.58197i	−0.493120	−	0.123078i
$848$	−22.5843	−	19.5694i	−0.775547	−	0.672015i
$849$	16.1540	+	0.00838982i	0.554405	+	0.000287938i
$850$			56.6293i			1.94237i
$851$	−5.66439	−	7.03111i	−0.194173	−	0.241023i
$852$	19.0559	−	5.58458i	0.652845	−	0.191324i
$853$	−15.5623	+	53.0004i	−0.532844	+	1.81470i	0.0455770	+	0.998961i	$0.485487\pi$
$853$	−15.5623	+	53.0004i	−0.532844	+	1.81470i	−0.578421	+	0.815739i	$0.696331\pi$
$854$	21.9538	−	53.8071i	0.751245	−	1.84124i
$855$	0.0113023	−	10.8809i	0.000386530	−	0.372119i
$856$	4.33629	−	30.1596i	0.148211	−	1.03083i
$857$	−25.8711	+	16.6263i	−0.883739	+	0.567944i	−0.901926	−	0.431890i	$-0.857847\pi$
$857$	−25.8711	+	16.6263i	−0.883739	+	0.567944i	0.0181874	+	0.999835i	$0.494210\pi$
$858$	−14.5101	−	16.7632i	−0.495367	−	0.572285i
$859$	26.3889	−	22.8661i	0.900378	−	0.780182i	−0.0758068	−	0.997123i	$-0.524153\pi$
$859$	26.3889	−	22.8661i	0.900378	−	0.780182i	0.976185	+	0.216941i	$0.0696078\pi$
$860$	0.728892	+	5.06956i	0.0248550	+	0.172870i
$861$	−33.9768	+	6.29818i	−1.15793	+	0.214642i
$862$	−15.7248	+	4.61722i	−0.535589	+	0.157263i
$863$	−5.52963	−	18.8322i	−0.188231	−	0.641055i	−0.998487	−	0.0549799i	$-0.982491\pi$
$863$	−5.52963	−	18.8322i	−0.188231	−	0.641055i	0.810257	−	0.586075i	$-0.199328\pi$
$864$	−8.83584	−	19.4278i	−0.300601	−	0.660949i
$865$	−1.67371	−	11.6409i	−0.0569080	−	0.395804i
$866$	3.62577	+	4.18436i	0.123209	+	0.142191i
$867$	−47.5492	+	41.1584i	−1.61486	+	1.39781i
$868$	−3.09774	−	2.46932i	−0.105144	−	0.0838142i
$869$	−1.81013	−	0.260258i	−0.0614046	−	0.00882865i
$870$	−0.727227	+	2.47196i	−0.0246553	+	0.0838072i
$871$	28.4204	+	24.6265i	0.962990	+	0.834435i
$872$	−3.60717	+	12.2849i	−0.122154	+	0.416019i
$873$	−6.33367	−	9.87792i	−0.214362	−	0.334317i
$874$	47.4515	+	15.8008i	1.60507	+	0.534470i
$875$	−14.0037	+	4.74357i	−0.473411	+	0.160362i
$876$	−3.67581	−	0.00190908i	−0.124194	−	6.45020e-5i
$877$	11.6204	−	13.4107i	0.392394	−	0.452847i	−0.524837	−	0.851203i	$-0.675874\pi$
$877$	11.6204	−	13.4107i	0.392394	−	0.452847i	0.917231	+	0.398356i	$0.130419\pi$
$878$	−6.47360	−	4.16033i	−0.218473	−	0.140404i
$879$	−34.9494	+	5.00645i	−1.17882	+	0.168863i
$880$	−3.59422	−	5.59272i	−0.121161	−	0.188531i
$881$	−11.7665	−	25.7650i	−0.396423	−	0.868045i	−0.997620	−	0.0689445i	$-0.978037\pi$
$881$	−11.7665	−	25.7650i	−0.396423	−	0.868045i	0.601198	−	0.799100i	$-0.294690\pi$
$882$	−12.5122	−	32.5900i	−0.421307	−	1.09736i
$883$	7.34265	+	51.0692i	0.247100	+	1.71862i	0.614809	+	0.788676i	$0.289233\pi$
$883$	7.34265	+	51.0692i	0.247100	+	1.71862i	−0.367709	+	0.929941i	$0.619858\pi$
$884$	16.7862	+	7.66600i	0.564581	+	0.257835i
$885$	−2.12005	−	3.30263i	−0.0712646	−	0.111017i
$886$	−34.3198	+	10.0772i	−1.15300	+	0.338551i
$887$	2.55901	−	5.60345i	0.0859232	−	0.188145i	−0.861793	−	0.507260i	$-0.830658\pi$
$887$	2.55901	−	5.60345i	0.0859232	−	0.188145i	0.947716	+	0.319115i	$0.103386\pi$
$888$	−2.78144	−	6.09888i	−0.0933390	−	0.204665i
$889$	−33.8680	−	19.8526i	−1.13590	−	0.665834i
$890$	−8.72774	+	3.98583i	−0.292555	+	0.133605i
$891$	−20.7251	+	2.93589i	−0.694318	+	0.0983561i
$892$	−13.6635	−	1.96451i	−0.457486	−	0.0657766i
$893$	−23.8463	+	37.1055i	−0.797985	+	1.24169i
$894$	−33.5922	−	15.3621i	−1.12349	−	0.513787i
$895$	−1.04252	+	3.55050i	−0.0348477	+	0.118680i
$896$	−11.2910	−	33.3327i	−0.377207	−	1.11357i
$897$	26.0883	+	8.70214i	0.871062	+	0.290556i
$898$	39.8676			1.33040
$899$	2.91294	+	0.855315i	0.0971519	+	0.0285264i
$900$	1.53171	−	10.5753i	0.0510569	−	0.352509i
$901$	23.8591	−	37.1256i	0.794863	−	1.23683i
$902$	4.14908	−	28.8575i	0.138149	−	0.960848i
$903$	49.2254	+	20.1143i	1.63812	+	0.669361i
$904$	−7.11138	−	15.5717i	−0.236521	−	0.517908i
$905$	4.32937	−	3.75142i	0.143913	−	0.124701i
$906$	14.3475	+	31.4599i	0.476665	+	1.04519i
$907$	−3.64522	+	7.98193i	−0.121038	+	0.265036i	−0.960446	−	0.278465i	$-0.910174\pi$
$907$	−3.64522	+	7.98193i	−0.121038	+	0.265036i	0.839409	+	0.543501i	$0.182902\pi$
$908$	−1.69691	+	0.498259i	−0.0563141	+	0.0165353i
$909$	−16.1113	+	18.5544i	−0.534377	+	0.615411i
$910$	−0.855493	+	8.37517i	−0.0283593	+	0.277634i
$911$	40.3759	−	5.80517i	1.33771	−	0.192334i	0.563949	−	0.825810i	$-0.309281\pi$
$911$	40.3759	−	5.80517i	1.33771	−	0.192334i	0.773763	+	0.633476i	$0.218372\pi$
$912$	45.1773	+	29.0669i	1.49597	+	0.962500i
$913$	−1.10035	+	0.502512i	−0.0364162	+	0.0166307i
$914$	−12.6723	−	19.7185i	−0.419164	−	0.652232i
$915$	1.87625	+	13.0979i	0.0620268	+	0.433002i
$916$	3.94404	−	6.13705i	0.130315	−	0.202774i
$917$	−18.1708	+	44.5352i	−0.600053	+	1.47068i
$918$	53.1085	−	34.0140i	1.75284	−	1.12263i
$919$	−24.2485			−0.799886			−0.399943	−	0.916540i	$-0.630970\pi$
$919$	−24.2485			−0.799886			−0.399943	+	0.916540i	$0.630970\pi$
$920$	5.09653	+	2.55204i	0.168028	+	0.0841382i
$921$	−5.50372	+	1.61293i	−0.181354	+	0.0531480i
$922$	−0.0622807	+	0.212109i	−0.00205111	+	0.00698543i
$923$	−32.5598	+	37.5760i	−1.07172	+	1.23683i
$924$	8.12983	−	0.329333i	0.267452	−	0.0108343i
$925$	1.25010	−	8.69460i	0.0411029	−	0.285877i
$926$	−15.9731	−	24.8547i	−0.524909	−	0.816775i
$927$	24.0128	−	37.2794i	0.788684	−	1.22442i
$928$	−4.16345	−	4.80488i	−0.136672	−	0.157728i
$929$	−4.90765	−	34.1334i	−0.161015	−	1.11988i	−0.896726	−	0.442586i	$-0.854061\pi$
$929$	−4.90765	−	34.1334i	−0.161015	−	1.11988i	0.735711	−	0.677295i	$-0.236848\pi$
$930$	3.23152	+	0.466336i	0.105966	+	0.0152918i
$931$	35.4317	+	25.9416i	1.16123	+	0.850203i
$932$	−1.16322	−	3.96157i	−0.0381026	−	0.129766i
$933$	−17.9679	−	2.59292i	−0.588242	−	0.0848883i
$934$	40.5433	−	5.82925i	1.32662	−	0.190739i
$935$	7.41980	−	6.42929i	0.242653	−	0.210260i
$936$	17.1647	+	11.0563i	0.561045	+	0.361386i
$937$	7.65650	+	11.9138i	0.250127	+	0.389205i	0.943499	−	0.331374i	$-0.107512\pi$
$937$	7.65650	+	11.9138i	0.250127	+	0.389205i	−0.693372	+	0.720579i	$0.743876\pi$
$938$	−49.1153	+	9.13076i	−1.60367	+	0.298130i
$939$	49.0276	+	14.4235i	1.59996	+	0.470692i
$940$	2.03221	−	2.34529i	0.0662833	−	0.0764950i
$941$	4.67867	+	1.37378i	0.152520	+	0.0447840i	0.357101	−	0.934066i	$-0.383765\pi$
$941$	4.67867	+	1.37378i	0.152520	+	0.0447840i	−0.204581	+	0.978850i	$0.565583\pi$
$942$	−5.07404	−	17.3138i	−0.165321	−	0.564115i
$943$	13.8345	+	33.4129i	0.450515	+	1.08807i
$944$	19.3759			0.630631
$945$	6.20757	+	4.96411i	0.201932	+	0.161483i
$946$	−29.3799	+	33.9062i	−0.955221	+	1.10238i
$947$	−19.3067	+	30.0419i	−0.627385	+	0.976230i	0.371473	+	0.928444i	$0.378853\pi$
$947$	−19.3067	+	30.0419i	−0.627385	+	0.976230i	−0.998858	+	0.0477858i	$0.984784\pi$
$948$	−1.02918	+	0.147429i	−0.0334263	+	0.00478826i
$949$	7.74268	−	4.97592i	0.251338	−	0.161525i
$950$	20.2126	+	44.2594i	0.655783	+	1.43597i
$951$	45.4377	+	29.2344i	1.47342	+	0.947990i
$952$	35.4145	−	17.9629i	1.14779	−	0.582181i
$953$	3.34201	+	1.52625i	0.108258	+	0.0494399i	0.468808	−	0.883300i	$-0.344684\pi$
$953$	3.34201	+	1.52625i	0.108258	+	0.0494399i	−0.360550	+	0.932740i	$0.617411\pi$
$954$	−19.7633	+	22.7603i	−0.639862	+	0.736892i
$955$	−0.229727	−	0.782379i	−0.00743380	−	0.0253172i
$956$	4.85161	+	2.21566i	0.156912	+	0.0716595i
$957$	−5.67328	+	2.58734i	−0.183391	+	0.0836369i
$958$	38.1754	−	33.0792i	1.23339	−	1.06874i
$959$	−6.19686	+	5.83118i	−0.200107	+	0.188299i
$960$	2.31485	+	2.00793i	0.0747114	+	0.0648058i
$961$	−3.86429	+	26.8768i	−0.124655	+	0.866992i
$962$	−8.71670	−	5.60188i	−0.281038	−	0.180612i
$963$	−44.0082	−	6.37408i	−1.41814	−	0.205402i
$964$	5.57682	−	18.9929i	0.179617	−	0.611721i
$965$	10.8859			0.350430
$966$	−30.6422	+	19.8943i	−0.985896	+	0.640089i
$967$	11.3632			0.365415			0.182708	−	0.983167i	$-0.441514\pi$
$967$	11.3632			0.365415			0.182708	+	0.983167i	$0.441514\pi$
$968$	−3.23783	+	11.0270i	−0.104068	+	0.354422i
$969$	−32.9938	+	72.1471i	−1.05991	+	2.31770i
$970$	−3.16245	−	2.03238i	−0.101540	−	0.0652559i
$971$	−1.76499	+	12.2758i	−0.0566414	+	0.393949i	0.941704	+	0.336443i	$0.109224\pi$
$971$	−1.76499	+	12.2758i	−0.0566414	+	0.393949i	−0.998345	+	0.0575062i	$0.981685\pi$
$972$	−10.8378	+	4.91548i	−0.347622	+	0.157664i
$973$	16.9555	−	15.9550i	0.543570	−	0.511493i
$974$	−29.6567	+	25.6977i	−0.950262	+	0.823407i
$975$	11.1019	+	24.3433i	0.355546	+	0.779608i
$976$	−59.4225	−	27.1374i	−1.90207	−	0.868646i
$977$	−10.0203	−	34.1261i	−0.320579	−	1.09179i	−0.949355	−	0.314205i	$-0.898262\pi$
$977$	−10.0203	−	34.1261i	−0.320579	−	1.09179i	0.628776	−	0.777586i	$-0.283556\pi$
$978$	−11.7602	+	7.54922i	−0.376051	+	0.241398i
$979$	−21.1204	−	9.64537i	−0.675011	−	0.308267i
$980$	−2.20774	−	2.16137i	−0.0705237	−	0.0690424i
$981$	17.9231	+	5.28291i	0.572239	+	0.168670i
$982$	−27.4864	−	60.1867i	−0.877125	−	1.92064i
$983$	−12.3544	+	7.93968i	−0.394044	+	0.253237i	−0.722627	−	0.691239i	$-0.757065\pi$
$983$	−12.3544	+	7.93968i	−0.394044	+	0.253237i	0.328583	+	0.944475i	$0.393429\pi$
$984$	3.80712	+	26.5771i	0.121366	+	0.847246i
$985$	−0.340462	+	0.529769i	−0.0108480	+	0.0168798i
$986$	12.3029	−	14.1983i	0.391803	−	0.452164i
$987$	−10.3213	−	30.5220i	−0.328529	−	0.971527i
$988$	15.8557			0.504437
$989$	9.88871	−	54.7653i	0.314443	−	1.74144i
$990$	−5.64516	+	3.61964i	−0.179415	+	0.115040i
$991$	16.6319	+	4.88355i	0.528328	+	0.155131i	0.535009	−	0.844847i	$-0.320308\pi$
$991$	16.6319	+	4.88355i	0.528328	+	0.155131i	−0.00668049	+	0.999978i	$0.502126\pi$
$992$	−5.27559	+	6.08836i	−0.167500	+	0.193305i
$993$	−2.61750	+	8.89729i	−0.0830639	+	0.282347i
$994$	−12.0722	−	64.9377i	−0.382907	−	2.05970i
$995$	1.94184	+	3.02156i	0.0615605	+	0.0957900i
$996$	−0.519981	+	0.450093i	−0.0164762	+	0.0142617i
$997$	6.15149	−	5.33030i	0.194820	−	0.168812i	−0.551989	−	0.833852i	$-0.686131\pi$
$997$	6.15149	−	5.33030i	0.194820	−	0.168812i	0.746808	+	0.665040i	$0.231585\pi$
$998$	29.7194	−	4.27300i	0.940750	−	0.135259i
$999$	−8.90490	+	4.04997i	−0.281739	+	0.128136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.15	✓	600
3.2	odd	2	inner	483.2.v.a.41.45	yes	600
7.6	odd	2	inner	483.2.v.a.41.16	yes	600
21.20	even	2	inner	483.2.v.a.41.46	yes	600
23.9	even	11	inner	483.2.v.a.377.46	yes	600
69.32	odd	22	inner	483.2.v.a.377.16	yes	600
161.55	odd	22	inner	483.2.v.a.377.45	yes	600
483.377	even	22	inner	483.2.v.a.377.15	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.15	✓	600	1.1	even	1	trivial
483.2.v.a.41.16	yes	600	7.6	odd	2	inner
483.2.v.a.41.45	yes	600	3.2	odd	2	inner
483.2.v.a.41.46	yes	600	21.20	even	2	inner
483.2.v.a.377.15	yes	600	483.377	even	22	inner
483.2.v.a.377.16	yes	600	69.32	odd	22	inner
483.2.v.a.377.45	yes	600	161.55	odd	22	inner
483.2.v.a.377.46	yes	600	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.468338 + 1.59501i) q^{2} +(-1.57515 - 0.720338i) q^{3} +(-0.642222 - 0.412731i) q^{4} +(0.0822804 - 0.572273i) q^{5} +(1.88665 - 2.17503i) q^{6} +(-1.81311 - 1.92682i) q^{7} +(-1.55355 + 1.34616i) q^{8} +(1.96223 + 2.26929i) q^{9} +(0.874248 + 0.399256i) q^{10} +(0.655249 + 2.23157i) q^{11} +(0.714293 + 1.11273i) q^{12} +(-3.01159 - 1.37535i) q^{13} +(3.92245 - 1.98954i) q^{14} +(-0.541834 + 0.842149i) q^{15} +(-2.05382 - 4.49724i) q^{16} +(6.14222 - 3.94737i) q^{17} +(-4.53853 + 2.06698i) q^{18} +(3.39161 - 5.27745i) q^{19} +(-0.289037 + 0.333567i) q^{20} +(1.46797 + 4.34109i) q^{21} -3.86627 q^{22} +(4.12483 - 2.44659i) q^{23} +(3.41678 - 1.00133i) q^{24} +(4.47674 + 1.31449i) q^{25} +(3.60414 - 4.15940i) q^{26} +(-1.45616 - 4.98795i) q^{27} +(0.369164 + 1.98577i) q^{28} +(-0.836844 - 1.30215i) q^{29} +(-1.08948 - 1.25864i) q^{30} +(-1.48228 + 1.28441i) q^{31} +(4.06561 - 0.584546i) q^{32} +(0.575369 - 3.98708i) q^{33} +(3.41947 + 11.6456i) q^{34} +(-1.25185 + 0.879056i) q^{35} +(-0.323579 - 2.26726i) q^{36} +(-0.267931 - 1.86350i) q^{37} +(6.82919 + 7.88130i) q^{38} +(3.75300 + 4.33574i) q^{39} +(0.642545 + 0.999819i) q^{40} +(-1.07315 + 7.46390i) q^{41} +(-7.61161 + 0.308340i) q^{42} +(7.59902 - 8.76973i) q^{43} +(0.500224 - 1.70361i) q^{44} +(1.46010 - 0.936211i) q^{45} +(1.97053 + 7.72499i) q^{46} -7.03096 q^{47} +(-0.00444747 + 8.56330i) q^{48} +(-0.425246 + 6.98707i) q^{49} +(-4.19326 + 6.52484i) q^{50} +(-12.5184 + 1.79324i) q^{51} +(1.36646 + 2.12625i) q^{52} +(5.49811 - 2.51090i) q^{53} +(8.63782 + 0.0134585i) q^{54} +(1.33098 - 0.191366i) q^{55} +(5.41057 + 0.552670i) q^{56} +(-9.14386 + 5.86970i) q^{57} +(2.46888 - 0.724929i) q^{58} +(-1.62803 + 3.56489i) q^{59} +(0.695559 - 0.317215i) q^{60} +(9.98580 - 8.65274i) q^{61} +(-1.35444 - 2.96580i) q^{62} +(0.814766 - 7.89532i) q^{63} +(0.435495 - 3.02894i) q^{64} +(-1.03487 + 1.61029i) q^{65} +(6.08997 + 2.78502i) q^{66} +(-10.8985 - 3.20008i) q^{67} -5.57387 q^{68} +(-8.25961 + 0.882485i) q^{69} +(-0.815818 - 2.40841i) q^{70} +(4.23097 - 14.4094i) q^{71} +(-6.10325 - 0.883987i) q^{72} +(-1.50295 + 2.33863i) q^{73} +(3.09779 + 0.445396i) q^{74} +(-6.10468 - 5.29529i) q^{75} +(-4.35634 + 1.98947i) q^{76} +(3.11179 - 5.30864i) q^{77} +(-8.67325 + 3.95550i) q^{78} +(-0.326638 + 0.715237i) q^{79} +(-2.74264 + 0.805312i) q^{80} +(-1.29934 + 8.90571i) q^{81} +(-11.4024 - 5.20732i) q^{82} +(0.0740193 + 0.514816i) q^{83} +(0.848937 - 3.39382i) q^{84} +(-1.75359 - 3.83982i) q^{85} +(10.4289 + 16.2277i) q^{86} +(0.380167 + 2.65391i) q^{87} +(-4.02202 - 2.58480i) q^{88} +(-6.53757 + 7.54476i) q^{89} +(0.809446 + 2.76735i) q^{90} +(2.81031 + 8.29643i) q^{91} +(-3.65884 - 0.131192i) q^{92} +(3.26003 - 0.955393i) q^{93} +(3.29287 - 11.2145i) q^{94} +(-2.74108 - 2.37516i) q^{95} +(-6.82503 - 2.00786i) q^{96} +(-3.87155 - 0.556645i) q^{97} +(-10.9453 - 3.95059i) q^{98} +(-3.77834 + 5.86580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) \) 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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