LMFDB - Embedded newform 574.2.r.c.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(9,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("574.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.r (of order $12$, degree $4$, 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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	574.9
Dual form			574.2.r.c.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.855646 + 3.19332i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.112148 + 0.0647489i) q^{5} +(-2.33767 + 2.33767i) q^{6} +(1.76095 + 1.97460i) q^{7} +1.00000i q^{8} +(-6.86706 - 3.96470i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.855646 + 3.19332i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.112148 + 0.0647489i) q^{5} +(-2.33767 + 2.33767i) q^{6} +(1.76095 + 1.97460i) q^{7} +1.00000i q^{8} +(-6.86706 - 3.96470i) q^{9} +(0.0647489 + 0.112148i) q^{10} +(-0.341672 + 1.27514i) q^{11} +(-3.19332 + 0.855646i) q^{12} +(-1.29095 - 1.29095i) q^{13} +(0.537724 + 2.59053i) q^{14} +(-0.302723 + 0.302723i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.64173 + 0.439899i) q^{17} +(-3.96470 - 6.86706i) q^{18} +(2.18739 + 8.16346i) q^{19} +0.129498i q^{20} +(-7.81228 + 3.93370i) q^{21} +(-0.933465 + 0.933465i) q^{22} +(3.04631 - 5.27637i) q^{23} +(-3.19332 - 0.855646i) q^{24} +(-2.49162 - 4.31560i) q^{25} +(-0.472520 - 1.76347i) q^{26} +(11.5233 - 11.5233i) q^{27} +(-0.829584 + 2.51233i) q^{28} +(0.557230 + 0.557230i) q^{29} +(-0.413527 + 0.110804i) q^{30} +(-3.61838 - 6.26721i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.77956 - 2.18213i) q^{33} +(1.20183 + 1.20183i) q^{34} +(0.0696340 + 0.335468i) q^{35} -7.92939i q^{36} +(-1.18770 + 2.05716i) q^{37} +(-2.18739 + 8.16346i) q^{38} +(5.22700 - 3.01781i) q^{39} +(-0.0647489 + 0.112148i) q^{40} +(5.82841 - 2.65136i) q^{41} +(-8.73248 - 0.499458i) q^{42} -4.87615i q^{43} +(-1.27514 + 0.341672i) q^{44} +(-0.513419 - 0.889269i) q^{45} +(5.27637 - 3.04631i) q^{46} +(2.50337 + 9.34271i) q^{47} +(-2.33767 - 2.33767i) q^{48} +(-0.798124 + 6.95435i) q^{49} -4.98323i q^{50} +(-2.80947 + 4.86615i) q^{51} +(0.472520 - 1.76347i) q^{52} +(-1.66723 + 6.22220i) q^{53} +(15.7411 - 4.21782i) q^{54} +(-0.120882 + 0.120882i) q^{55} +(-1.97460 + 1.76095i) q^{56} -27.9401 q^{57} +(0.203960 + 0.761190i) q^{58} +(5.61681 + 9.72859i) q^{59} +(-0.413527 - 0.110804i) q^{60} +(1.11014 + 0.640940i) q^{61} -7.23675i q^{62} +(-4.26382 - 20.5413i) q^{63} -1.00000 q^{64} +(-0.0611903 - 0.228365i) q^{65} +(-2.18213 - 3.77956i) q^{66} +(-5.66932 - 1.51909i) q^{67} +(0.439899 + 1.64173i) q^{68} +(14.2425 + 14.2425i) q^{69} +(-0.107429 + 0.325341i) q^{70} +(3.42428 + 3.42428i) q^{71} +(3.96470 - 6.86706i) q^{72} +(10.0742 - 5.81633i) q^{73} +(-2.05716 + 1.18770i) q^{74} +(15.9130 - 4.26388i) q^{75} +(-5.97607 + 5.97607i) q^{76} +(-3.11956 + 1.57078i) q^{77} +6.03562 q^{78} +(-9.94342 + 2.66433i) q^{79} +(-0.112148 + 0.0647489i) q^{80} +(15.0435 + 26.0562i) q^{81} +(6.37323 + 0.618062i) q^{82} -2.75983 q^{83} +(-7.31282 - 4.79879i) q^{84} +(0.155634 + 0.155634i) q^{85} +(2.43808 - 4.22287i) q^{86} +(-2.25620 + 1.30262i) q^{87} +(-1.27514 - 0.341672i) q^{88} +(10.7257 - 2.87393i) q^{89} -1.02684i q^{90} +(0.275819 - 4.82241i) q^{91} +6.09263 q^{92} +(23.1092 - 6.19210i) q^{93} +(-2.50337 + 9.34271i) q^{94} +(-0.283263 + 1.05715i) q^{95} +(-0.855646 - 3.19332i) q^{96} +(-5.82863 + 5.82863i) q^{97} +(-4.16837 + 5.62358i) q^{98} +(7.40181 - 7.40181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7	$ 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7} + 12 q^{10} - 4 q^{12} - 28 q^{13} + 12 q^{14} + 20 q^{15} - 20 q^{16} + 14 q^{17} - 16 q^{18} + 24 q^{23} - 4 q^{24} - 20 q^{25} + 14 q^{26} + 4 q^{27} + 44 q^{29} + 10 q^{30} - 8 q^{31} + 28 q^{34} - 2 q^{35} - 16 q^{37} - 12 q^{40} + 4 q^{41} - 64 q^{42} - 36 q^{45} + 2 q^{47} - 8 q^{48} + 28 q^{51} - 14 q^{52} + 20 q^{53} + 2 q^{54} - 44 q^{55} + 12 q^{56} - 40 q^{57} - 22 q^{58} - 8 q^{59} + 10 q^{60} + 24 q^{63} - 40 q^{64} + 36 q^{65} - 48 q^{66} + 6 q^{67} - 14 q^{68} - 36 q^{69} + 8 q^{70} + 40 q^{71} + 16 q^{72} + 36 q^{75} - 26 q^{79} + 84 q^{81} - 22 q^{82} - 24 q^{83} + 164 q^{85} - 28 q^{86} + 16 q^{89} + 48 q^{92} + 46 q^{93} - 2 q^{94} - 18 q^{95} + 4 q^{96} + 8 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7 + 12 * q^10 - 4 * q^12 - 28 * q^13 + 12 * q^14 + 20 * q^15 - 20 * q^16 + 14 * q^17 - 16 * q^18 + 24 * q^23 - 4 * q^24 - 20 * q^25 + 14 * q^26 + 4 * q^27 + 44 * q^29 + 10 * q^30 - 8 * q^31 + 28 * q^34 - 2 * q^35 - 16 * q^37 - 12 * q^40 + 4 * q^41 - 64 * q^42 - 36 * q^45 + 2 * q^47 - 8 * q^48 + 28 * q^51 - 14 * q^52 + 20 * q^53 + 2 * q^54 - 44 * q^55 + 12 * q^56 - 40 * q^57 - 22 * q^58 - 8 * q^59 + 10 * q^60 + 24 * q^63 - 40 * q^64 + 36 * q^65 - 48 * q^66 + 6 * q^67 - 14 * q^68 - 36 * q^69 + 8 * q^70 + 40 * q^71 + 16 * q^72 + 36 * q^75 - 26 * q^79 + 84 * q^81 - 22 * q^82 - 24 * q^83 + 164 * q^85 - 28 * q^86 + 16 * q^89 + 48 * q^92 + 46 * q^93 - 2 * q^94 - 18 * q^95 + 4 * q^96 + 8 * q^97 + 24 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.855646	+	3.19332i	−0.494008	+	1.84366i	0.0415111	+	0.999138i	$0.486783\pi$
$3$	−0.855646	+	3.19332i	−0.494008	+	1.84366i	−0.535519	+	0.844523i	$0.679884\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.112148	+	0.0647489i	0.0501543	+	0.0289566i	0.524867	−	0.851184i	$-0.324115\pi$
$5$	0.112148	+	0.0647489i	0.0501543	+	0.0289566i	−0.474713	+	0.880141i	$0.657448\pi$
$6$	−2.33767	+	2.33767i	−0.954349	+	0.954349i
$7$	1.76095	+	1.97460i	0.665576	+	0.746330i
$7$	1.76095	+	1.97460i	0.665576	+	0.746330i
$8$			1.00000i			0.353553i
$9$	−6.86706	−	3.96470i	−2.28902	−	1.32157i
$10$	0.0647489	+	0.112148i	0.0204754	+	0.0354644i
$11$	−0.341672	+	1.27514i	−0.103018	+	0.384468i	−0.998113	−	0.0614076i	$-0.980441\pi$
$11$	−0.341672	+	1.27514i	−0.103018	+	0.384468i	0.895095	+	0.445876i	$0.147108\pi$
$12$	−3.19332	+	0.855646i	−0.921831	+	0.247004i
$13$	−1.29095	−	1.29095i	−0.358045	−	0.358045i	0.505047	−	0.863092i	$-0.331475\pi$
$13$	−1.29095	−	1.29095i	−0.358045	−	0.358045i	−0.863092	+	0.505047i	$0.831475\pi$
$14$	0.537724	+	2.59053i	0.143713	+	0.692349i
$15$	−0.302723	+	0.302723i	−0.0781627	+	0.0781627i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.64173	+	0.439899i	0.398177	+	0.106691i	0.452350	−	0.891840i	$-0.350586\pi$
$17$	1.64173	+	0.439899i	0.398177	+	0.106691i	−0.0541733	+	0.998532i	$0.517252\pi$
$18$	−3.96470	−	6.86706i	−0.934488	−	1.61858i
$19$	2.18739	+	8.16346i	0.501822	+	1.87283i	0.487857	+	0.872924i	$0.337779\pi$
$19$	2.18739	+	8.16346i	0.501822	+	1.87283i	0.0139658	+	0.999902i	$0.495554\pi$
$20$			0.129498i			0.0289566i
$21$	−7.81228	+	3.93370i	−1.70478	+	0.858404i
$22$	−0.933465	+	0.933465i	−0.199015	+	0.199015i
$23$	3.04631	−	5.27637i	0.635200	−	1.10020i	−0.351272	−	0.936273i	$-0.614251\pi$
$23$	3.04631	−	5.27637i	0.635200	−	1.10020i	0.986473	−	0.163926i	$-0.0524158\pi$
$24$	−3.19332	−	0.855646i	−0.651833	−	0.174658i
$25$	−2.49162	−	4.31560i	−0.498323	−	0.863121i
$26$	−0.472520	−	1.76347i	−0.0926688	−	0.345845i
$27$	11.5233	−	11.5233i	2.21766	−	2.21766i
$28$	−0.829584	+	2.51233i	−0.156777	+	0.474785i
$29$	0.557230	+	0.557230i	0.103475	+	0.103475i	0.756949	−	0.653474i	$-0.226689\pi$
$29$	0.557230	+	0.557230i	0.103475	+	0.103475i	−0.653474	+	0.756949i	$0.726689\pi$
$30$	−0.413527	+	0.110804i	−0.0754994	+	0.0202300i
$31$	−3.61838	−	6.26721i	−0.649880	−	1.12562i	−0.983151	−	0.182794i	$-0.941486\pi$
$31$	−3.61838	−	6.26721i	−0.649880	−	1.12562i	0.333272	−	0.942831i	$-0.391847\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.77956	−	2.18213i	−0.657938	−	0.379860i
$34$	1.20183	+	1.20183i	0.206112	+	0.206112i
$35$	0.0696340	+	0.335468i	0.0117703	+	0.0567045i
$36$		−	7.92939i		−	1.32157i
$37$	−1.18770	+	2.05716i	−0.195257	+	0.338195i	−0.946985	−	0.321279i	$-0.895887\pi$
$37$	−1.18770	+	2.05716i	−0.195257	+	0.338195i	0.751728	+	0.659474i	$0.229221\pi$
$38$	−2.18739	+	8.16346i	−0.354842	+	1.32429i
$39$	5.22700	−	3.01781i	0.836990	−	0.483237i
$40$	−0.0647489	+	0.112148i	−0.0102377	+	0.0177322i
$41$	5.82841	−	2.65136i	0.910244	−	0.414072i
$41$	5.82841	−	2.65136i	0.910244	−	0.414072i
$42$	−8.73248	−	0.499458i	−1.34745	−	0.0770680i
$43$		−	4.87615i		−	0.743606i	−0.928312	−	0.371803i	$-0.878740\pi$
$43$		−	4.87615i		−	0.743606i	0.928312	−	0.371803i	$-0.121260\pi$
$44$	−1.27514	+	0.341672i	−0.192234	+	0.0515090i
$45$	−0.513419	−	0.889269i	−0.0765361	−	0.132564i
$46$	5.27637	−	3.04631i	0.777958	−	0.449154i
$47$	2.50337	+	9.34271i	0.365154	+	1.36277i	0.867212	+	0.497940i	$0.165910\pi$
$47$	2.50337	+	9.34271i	0.365154	+	1.36277i	−0.502057	+	0.864834i	$0.667423\pi$
$48$	−2.33767	−	2.33767i	−0.337413	−	0.337413i
$49$	−0.798124	+	6.95435i	−0.114018	+	0.993479i
$50$		−	4.98323i		−	0.704735i
$51$	−2.80947	+	4.86615i	−0.393405	+	0.681397i
$52$	0.472520	−	1.76347i	0.0655268	−	0.244549i
$53$	−1.66723	+	6.22220i	−0.229012	+	0.854685i	0.751745	+	0.659454i	$0.229212\pi$
$53$	−1.66723	+	6.22220i	−0.229012	+	0.854685i	−0.980757	+	0.195231i	$0.937454\pi$
$54$	15.7411	−	4.21782i	2.14209	−	0.573972i
$55$	−0.120882	+	0.120882i	−0.0162997	+	0.0162997i
$56$	−1.97460	+	1.76095i	−0.263868	+	0.235317i
$57$	−27.9401			−3.70076
$58$	0.203960	+	0.761190i	0.0267813	+	0.0999492i
$59$	5.61681	+	9.72859i	0.731246	+	1.26656i	0.956351	+	0.292221i	$0.0943941\pi$
$59$	5.61681	+	9.72859i	0.731246	+	1.26656i	−0.225105	+	0.974334i	$0.572273\pi$
$60$	−0.413527	−	0.110804i	−0.0533861	−	0.0143048i
$61$	1.11014	+	0.640940i	0.142139	+	0.0820640i	0.569383	−	0.822072i	$-0.307182\pi$
$61$	1.11014	+	0.640940i	0.142139	+	0.0820640i	−0.427244	+	0.904136i	$0.640515\pi$
$62$		−	7.23675i		−	0.919069i
$63$	−4.26382	−	20.5413i	−0.537191	−	2.58797i
$64$	−1.00000			−0.125000
$65$	−0.0611903	−	0.228365i	−0.00758973	−	0.0283252i
$66$	−2.18213	−	3.77956i	−0.268602	−	0.465232i
$67$	−5.66932	−	1.51909i	−0.692618	−	0.185586i	−0.104696	−	0.994504i	$-0.533387\pi$
$67$	−5.66932	−	1.51909i	−0.692618	−	0.185586i	−0.587922	+	0.808918i	$0.700054\pi$
$68$	0.439899	+	1.64173i	0.0533456	+	0.199089i
$69$	14.2425	+	14.2425i	1.71460	+	1.71460i
$70$	−0.107429	+	0.325341i	−0.0128402	+	0.0388857i
$71$	3.42428	+	3.42428i	0.406388	+	0.406388i	0.880477	−	0.474089i	$-0.157223\pi$
$71$	3.42428	+	3.42428i	0.406388	+	0.406388i	−0.474089	+	0.880477i	$0.657223\pi$
$72$	3.96470	−	6.86706i	0.467244	−	0.809290i
$73$	10.0742	−	5.81633i	1.17909	−	0.680750i	0.223289	−	0.974752i	$-0.428321\pi$
$73$	10.0742	−	5.81633i	1.17909	−	0.680750i	0.955805	+	0.294003i	$0.0949875\pi$
$74$	−2.05716	+	1.18770i	−0.239140	+	0.138068i
$75$	15.9130	−	4.26388i	1.83748	−	0.492351i
$76$	−5.97607	+	5.97607i	−0.685502	+	0.685502i
$77$	−3.11956	+	1.57078i	−0.355507	+	0.179007i
$78$	6.03562			0.683400
$79$	−9.94342	+	2.66433i	−1.11872	+	0.299761i	−0.770366	−	0.637602i	$-0.779926\pi$
$79$	−9.94342	+	2.66433i	−1.11872	+	0.299761i	−0.348356	+	0.937362i	$0.613260\pi$
$80$	−0.112148	+	0.0647489i	−0.0125386	+	0.00723915i
$81$	15.0435	+	26.0562i	1.67151	+	2.89513i
$82$	6.37323	+	0.618062i	0.703805	+	0.0682535i
$83$	−2.75983			−0.302930			−0.151465	−	0.988463i	$-0.548399\pi$
$83$	−2.75983			−0.302930			−0.151465	+	0.988463i	$0.548399\pi$
$84$	−7.31282	−	4.79879i	−0.797895	−	0.523590i
$85$	0.155634	+	0.155634i	0.0168809	+	0.0168809i
$86$	2.43808	−	4.22287i	0.262905	−	0.455364i
$87$	−2.25620	+	1.30262i	−0.241890	+	0.139655i
$88$	−1.27514	−	0.341672i	−0.135930	−	0.0364223i
$89$	10.7257	−	2.87393i	1.13692	−	0.304636i	0.359207	−	0.933258i	$-0.383047\pi$
$89$	10.7257	−	2.87393i	1.13692	−	0.304636i	0.777712	+	0.628621i	$0.216380\pi$
$90$		−	1.02684i		−	0.108238i
$91$	0.275819	−	4.82241i	0.0289137	−	0.505526i
$92$	6.09263			0.635200
$93$	23.1092	−	6.19210i	2.39632	−	0.642091i
$94$	−2.50337	+	9.34271i	−0.258203	+	0.963627i
$95$	−0.283263	+	1.05715i	−0.0290621	+	0.108461i
$96$	−0.855646	−	3.19332i	−0.0873290	−	0.325916i
$97$	−5.82863	+	5.82863i	−0.591808	+	0.591808i	−0.938119	−	0.346312i	$-0.887434\pi$
$97$	−5.82863	+	5.82863i	−0.591808	+	0.591808i	0.346312	+	0.938119i	$0.387434\pi$
$98$	−4.16837	+	5.62358i	−0.421069	+	0.568068i
$99$	7.40181	−	7.40181i	0.743910	−	0.743910i
$100$	2.49162	−	4.31560i	0.249162	−	0.431560i
$101$	−16.8765	−	4.52204i	−1.67927	−	0.449959i	−0.711685	−	0.702499i	$-0.752067\pi$
$101$	−16.8765	−	4.52204i	−1.67927	−	0.449959i	−0.967586	+	0.252540i	$0.918734\pi$
$102$	−4.86615	+	2.80947i	−0.481821	+	0.278179i
$103$	5.26534	+	3.03994i	0.518809	+	0.299534i	0.736447	−	0.676495i	$-0.236502\pi$
$103$	5.26534	+	3.03994i	0.518809	+	0.299534i	−0.217638	+	0.976029i	$0.569835\pi$
$104$	1.29095	−	1.29095i	0.126588	−	0.126588i
$105$	−1.13084	−	0.0646787i	−0.110358	−	0.00631199i
$106$	−4.55497	+	4.55497i	−0.442418	+	0.442418i
$107$	0.468888	−	0.812137i	0.0453291	−	0.0785122i	−0.842471	−	0.538742i	$-0.818900\pi$
$107$	0.468888	−	0.812137i	0.0453291	−	0.0785122i	0.887800	+	0.460230i	$0.152233\pi$
$108$	15.7411	+	4.21782i	1.51469	+	0.405860i
$109$	5.20129	+	1.39368i	0.498194	+	0.133491i	0.499162	−	0.866509i	$-0.333641\pi$
$109$	5.20129	+	1.39368i	0.498194	+	0.133491i	−0.000967909		1.00000i	$0.500308\pi$
$110$	−0.165127	+	0.0442458i	−0.0157443	+	0.00421867i
$111$	−5.55291	−	5.55291i	−0.527059	−	0.527059i
$112$	−2.59053	+	0.537724i	−0.244782	+	0.0508101i
$113$	−4.48404			−0.421823			−0.210912	−	0.977505i	$-0.567643\pi$
$113$	−4.48404			−0.421823			−0.210912	+	0.977505i	$0.567643\pi$
$114$	−24.1969	−	13.9701i	−2.26624	−	1.30842i
$115$	0.683278	−	0.394491i	0.0637160	−	0.0367865i
$116$	−0.203960	+	0.761190i	−0.0189372	+	0.0706748i
$117$	3.74680	+	13.9832i	0.346392	+	1.29275i
$118$			11.2336i			1.03414i
$119$	2.02237	+	4.01640i	0.185390	+	0.368183i
$120$	−0.302723	−	0.302723i	−0.0276347	−	0.0276347i
$121$	8.01705	+	4.62864i	0.728822	+	0.420786i
$122$	0.640940	+	1.11014i	0.0580280	+	0.100507i
$123$	3.47956	+	20.8806i	0.313741	+	1.88274i
$124$	3.61838	−	6.26721i	0.324940	−	0.562812i
$125$		−	1.29281i		−	0.115632i
$126$	6.57809	−	19.9212i	0.586023	−	1.77472i
$127$	−0.613722			−0.0544590			−0.0272295	−	0.999629i	$-0.508668\pi$
$127$	−0.613722			−0.0544590			−0.0272295	+	0.999629i	$0.508668\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	15.5711	+	4.17226i	1.37096	+	0.367347i
$130$	0.0611903	−	0.228365i	0.00536675	−	0.0200290i
$131$	19.0588	+	11.0036i	1.66517	+	0.961389i	0.970184	+	0.242369i	$0.0779244\pi$
$131$	19.0588	+	11.0036i	1.66517	+	0.961389i	0.694990	+	0.719020i	$0.255409\pi$
$132$		−	4.36426i		−	0.379860i
$133$	−12.2677	+	18.6947i	−1.06375	+	1.62103i
$134$	−4.15023	−	4.15023i	−0.358525	−	0.358525i
$135$	2.03844	−	0.546198i	0.175441	−	0.0470092i
$136$	−0.439899	+	1.64173i	−0.0377210	+	0.140777i
$137$	11.4289	+	3.06237i	0.976440	+	0.261636i	0.711545	−	0.702641i	$-0.247996\pi$
$137$	11.4289	+	3.06237i	0.976440	+	0.261636i	0.264895	+	0.964277i	$0.414663\pi$
$138$	5.21313	+	19.4557i	0.443771	+	1.65618i
$139$	1.98701			0.168536			0.0842680	−	0.996443i	$-0.473145\pi$
$139$	1.98701			0.168536			0.0842680	+	0.996443i	$0.473145\pi$
$140$	−0.255707	+	0.228039i	−0.0216112	+	0.0192728i
$141$	−31.9762			−2.69288
$142$	1.25338	+	4.67766i	0.105181	+	0.392540i
$143$	2.08722	−	1.20506i	0.174542	−	0.100772i
$144$	6.86706	−	3.96470i	0.572255	−	0.330391i
$145$	0.0264124	+	0.0985725i	0.00219343	+	0.00818600i
$146$	11.6327			0.962726
$147$	−21.5245	−	8.49913i	−1.77531	−	0.700996i
$148$	−2.37540			−0.195257
$149$	1.22526	+	4.57272i	0.100377	+	0.374612i	0.997780	−	0.0666005i	$-0.0212153\pi$
$149$	1.22526	+	4.57272i	0.100377	+	0.374612i	−0.897403	+	0.441212i	$0.854549\pi$
$150$	15.9130	+	4.26388i	1.29929	+	0.348145i
$151$	5.81478	−	21.7010i	0.473200	−	1.76601i	−0.154959	−	0.987921i	$-0.549525\pi$
$151$	5.81478	−	21.7010i	0.473200	−	1.76601i	0.628159	−	0.778085i	$-0.283809\pi$
$152$	−8.16346	+	2.18739i	−0.662144	+	0.177421i
$153$	−9.52976	−	9.52976i	−0.770435	−	0.770435i
$154$	−3.48701	−	0.199441i	−0.280991	−	0.0160714i
$155$		−	0.937144i		−	0.0752732i
$156$	5.22700	+	3.01781i	0.418495	+	0.241618i
$157$	−2.59261	+	9.67576i	−0.206913	+	0.772210i	0.781945	+	0.623347i	$0.214228\pi$
$157$	−2.59261	+	9.67576i	−0.206913	+	0.772210i	−0.988858	+	0.148862i	$0.952439\pi$
$158$	−9.94342	−	2.66433i	−0.791056	−	0.211963i
$159$	−18.4429	−	10.6480i	−1.46262	−	0.844442i
$160$	−0.129498			−0.0102377
$161$	15.7831	−	3.27615i	1.24389	−	0.258197i
$162$			30.0871i			2.36387i
$163$	7.77322	−	13.4636i	0.608846	−	1.05455i	−0.382585	−	0.923920i	$-0.624966\pi$
$163$	7.77322	−	13.4636i	0.608846	−	1.05455i	0.991431	−	0.130632i	$-0.0417005\pi$
$164$	5.21034	+	3.72187i	0.406860	+	0.290629i
$165$	−0.282581	−	0.489445i	−0.0219989	−	0.0381033i
$166$	−2.39008	−	1.37991i	−0.185506	−	0.107102i
$167$	−0.579491	−	0.579491i	−0.0448423	−	0.0448423i	0.684330	−	0.729172i	$-0.260095\pi$
$167$	−0.579491	−	0.579491i	−0.0448423	−	0.0448423i	−0.729172	+	0.684330i	$0.760095\pi$
$168$	−3.93370	−	7.81228i	−0.303491	−	0.602731i
$169$		−	9.66690i		−	0.743608i
$170$	0.0569660	+	0.212600i	0.00436909	+	0.0163057i
$171$	17.3447	−	64.7313i	1.32638	−	4.95013i
$172$	4.22287	−	2.43808i	0.321991	−	0.185902i
$173$	−14.5070	−	8.37560i	−1.10294	−	0.636785i	−0.165951	−	0.986134i	$-0.553069\pi$
$173$	−14.5070	−	8.37560i	−1.10294	−	0.636785i	−0.936993	+	0.349349i	$0.886403\pi$
$174$	−2.60524			−0.197503
$175$	4.13401	−	12.5195i	0.312501	−	0.946386i
$176$	−0.933465	−	0.933465i	−0.0703626	−	0.0703626i
$177$	−35.8725	+	9.61200i	−2.69634	+	0.722482i
$178$	10.7257	+	2.87393i	0.803923	+	0.215411i
$179$	−1.66361	−	0.445762i	−0.124344	−	0.0333178i	0.196111	−	0.980582i	$-0.437169\pi$
$179$	−1.66361	−	0.445762i	−0.124344	−	0.0333178i	−0.320454	+	0.947264i	$0.603836\pi$
$180$	0.513419	−	0.889269i	0.0382680	−	0.0662822i
$181$	4.96414	−	4.96414i	0.368982	−	0.368982i	−0.498124	−	0.867106i	$-0.665978\pi$
$181$	4.96414	−	4.96414i	0.368982	−	0.368982i	0.867106	+	0.498124i	$0.165978\pi$
$182$	2.65007	−	4.03842i	0.196436	−	0.299347i
$183$	−2.99661	+	2.99661i	−0.221516	+	0.221516i
$184$	5.27637	+	3.04631i	0.388979	+	0.224577i
$185$	−0.266398	+	0.153805i	−0.0195860	+	0.0113080i
$186$	23.1092	+	6.19210i	1.69445	+	0.454027i
$187$	−1.12186	+	1.94312i	−0.0820388	+	0.142095i
$188$	−6.83934	+	6.83934i	−0.498810	+	0.498810i
$189$	43.0458	+	2.46202i	3.13112	+	0.179086i
$190$	−0.773888	+	0.773888i	−0.0561437	+	0.0561437i
$191$	−4.13564	−	15.4344i	−0.299244	−	1.11679i	−0.937788	−	0.347209i	$-0.887130\pi$
$191$	−4.13564	−	15.4344i	−0.299244	−	1.11679i	0.638544	−	0.769585i	$-0.279537\pi$
$192$	0.855646	−	3.19332i	0.0617509	−	0.230458i
$193$	0.895147	−	3.34074i	0.0644341	−	0.240471i	−0.926196	−	0.377042i	$-0.876941\pi$
$193$	0.895147	−	3.34074i	0.0644341	−	0.240471i	0.990630	+	0.136570i	$0.0436080\pi$
$194$	−7.96206	+	2.13343i	−0.571642	+	0.153171i
$195$	0.781600			0.0559715
$196$	−6.42171	+	2.78598i	−0.458693	+	0.198999i
$197$			4.86405i			0.346549i	0.984874	+	0.173275i	$0.0554348\pi$
$197$			4.86405i			0.346549i	−0.984874	+	0.173275i	$0.944565\pi$
$198$	10.1111	−	2.70925i	0.718562	−	0.192538i
$199$	−19.1524	−	5.13186i	−1.35768	−	0.363788i	−0.494714	−	0.869056i	$-0.664727\pi$
$199$	−19.1524	−	5.13186i	−1.35768	−	0.363788i	−0.862963	+	0.505268i	$0.831394\pi$
$200$	4.31560	−	2.49162i	0.305159	−	0.176184i
$201$	9.70187	−	16.8041i	0.684317	−	1.18527i
$202$	−12.3544	−	12.3544i	−0.869255	−	0.869255i
$203$	−0.119056	+	2.08156i	−0.00835607	+	0.146097i
$204$	−5.61895			−0.393405
$205$	0.825319	+	0.0800376i	0.0576428	+	0.00559007i
$206$	3.03994	+	5.26534i	0.211803	+	0.366853i
$207$	−41.8384	+	24.1554i	−2.90797	+	1.67892i
$208$	1.76347	−	0.472520i	0.122275	−	0.0327634i
$209$	−11.1569			−0.771739
$210$	−0.946995	−	0.621432i	−0.0653488	−	0.0428829i
$211$	11.4786	−	11.4786i	0.790220	−	0.790220i	−0.191309	−	0.981530i	$-0.561273\pi$
$211$	11.4786	−	11.4786i	0.790220	−	0.790220i	0.981530	+	0.191309i	$0.0612734\pi$
$212$	−6.22220	+	1.66723i	−0.427343	+	0.114506i
$213$	−13.8648	+	8.00484i	−0.950000	+	0.548483i
$214$	0.812137	−	0.468888i	0.0555165	−	0.0320525i
$215$	0.315726	−	0.546853i	0.0215323	−	0.0372950i
$216$	11.5233	+	11.5233i	0.784060	+	0.784060i
$217$	6.00349	−	18.1811i	0.407544	−	1.23421i
$218$	3.80761	+	3.80761i	0.257884	+	0.257884i
$219$	9.95344	+	37.1467i	0.672591	+	2.51014i
$220$	−0.165127	−	0.0442458i	−0.0111329	−	0.00298305i
$221$	−1.55150	−	2.68727i	−0.104365	−	0.180766i
$222$	−2.03251	−	7.58541i	−0.136413	−	0.509100i
$223$	−12.7715			−0.855245			−0.427622	−	0.903958i	$-0.640649\pi$
$223$	−12.7715			−0.855245			−0.427622	+	0.903958i	$0.640649\pi$
$224$	−2.51233	−	0.829584i	−0.167862	−	0.0554289i
$225$			39.5140i			2.63427i
$226$	−3.88329	−	2.24202i	−0.258313	−	0.149137i
$227$	15.8083	+	4.23582i	1.04923	+	0.281141i	0.741935	−	0.670472i	$-0.233908\pi$
$227$	15.8083	+	4.23582i	1.04923	+	0.281141i	0.307299	+	0.951613i	$0.400575\pi$
$228$	−13.9701	−	24.1969i	−0.925190	−	1.60248i
$229$	−5.76006	−	21.4968i	−0.380635	−	1.42055i	−0.844934	−	0.534871i	$-0.820360\pi$
$229$	−5.76006	−	21.4968i	−0.380635	−	1.42055i	0.464299	−	0.885679i	$-0.346306\pi$
$230$	0.788982			0.0520239
$231$	−2.34677	−	11.3058i	−0.154406	−	0.743865i
$232$	−0.557230	+	0.557230i	−0.0365839	+	0.0365839i
$233$	−10.0469	+	2.69207i	−0.658197	+	0.176363i	−0.572432	−	0.819952i	$-0.694000\pi$
$233$	−10.0469	+	2.69207i	−0.658197	+	0.176363i	−0.0857647	+	0.996315i	$0.527333\pi$
$234$	−3.74680	+	13.9832i	−0.244936	+	0.914113i
$235$	−0.324181	+	1.20986i	−0.0211472	+	0.0789226i
$236$	−5.61681	+	9.72859i	−0.365623	+	0.633278i
$237$		−	34.0322i		−	2.21063i
$238$	−0.256778	+	4.48949i	−0.0166444	+	0.291010i
$239$	11.7094	+	11.7094i	0.757420	+	0.757420i	0.975852	−	0.218432i	$-0.0700941\pi$
$239$	11.7094	+	11.7094i	0.757420	+	0.757420i	−0.218432	+	0.975852i	$0.570094\pi$
$240$	−0.110804	−	0.413527i	−0.00715239	−	0.0266931i
$241$	11.5569	−	6.67236i	0.744443	−	0.429804i	−0.0792396	−	0.996856i	$-0.525249\pi$
$241$	11.5569	−	6.67236i	0.744443	−	0.429804i	0.823682	+	0.567051i	$0.191916\pi$
$242$	4.62864	+	8.01705i	0.297540	+	0.515355i
$243$	−48.8542	+	13.0905i	−3.13400	+	0.839753i
$244$			1.28188i			0.0820640i
$245$	−0.539795	+	0.728242i	−0.0344862	+	0.0465256i
$246$	−7.42689	+	19.8229i	−0.473521	+	1.26386i
$247$	7.71480	−	13.3624i	0.490881	−	0.850231i
$248$	6.26721	−	3.61838i	0.397968	−	0.229767i
$249$	2.36143	−	8.81299i	0.149650	−	0.558501i
$250$	0.646403	−	1.11960i	0.0408821	−	0.0708099i
$251$		−	15.3084i		−	0.966257i	−0.875550	−	0.483128i	$-0.839500\pi$
$251$		−	15.3084i		−	0.966257i	0.875550	−	0.483128i	$-0.160500\pi$
$252$	15.6574	−	13.9632i	0.986324	−	0.879602i
$253$	5.68725	+	5.68725i	0.357555	+	0.357555i
$254$	−0.531498	−	0.306861i	−0.0333492	−	0.0192542i
$255$	−0.630156	+	0.363821i	−0.0394619	+	0.0227833i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.2172	+	5.41718i	−1.26111	+	0.337914i	−0.826620	−	0.562761i	$-0.809739\pi$
$257$	−20.2172	+	5.41718i	−1.26111	+	0.337914i	−0.434493	+	0.900675i	$0.643073\pi$
$258$	11.3988	+	11.3988i	0.709660	+	0.709660i
$259$	−6.15356	+	1.27731i	−0.382364	+	0.0793682i
$260$	0.167175	−	0.167175i	0.0103678	−	0.0103678i
$261$	−1.61728	−	6.03578i	−0.100107	−	0.373605i
$262$	11.0036	+	19.0588i	0.679804	+	1.17746i
$263$	3.47742	+	0.931773i	0.214427	+	0.0574556i	0.364433	−	0.931229i	$-0.381263\pi$
$263$	3.47742	+	0.931773i	0.214427	+	0.0574556i	−0.150006	+	0.988685i	$0.547929\pi$
$264$	2.18213	−	3.77956i	0.134301	−	0.232616i
$265$	−0.589858	+	0.589858i	−0.0362347	+	0.0362347i
$266$	−19.9715	+	10.0562i	−1.22453	+	0.616585i
$267$			36.7095i			2.24659i
$268$	−1.51909	−	5.66932i	−0.0927932	−	0.346309i
$269$	8.47628	+	14.6814i	0.516808	+	0.895138i	0.999809	+	0.0195184i	$0.00621330\pi$
$269$	8.47628	+	14.6814i	0.516808	+	0.895138i	−0.483001	+	0.875620i	$0.660453\pi$
$270$	2.03844	+	0.546198i	0.124055	+	0.0332405i
$271$	−7.88455	+	13.6564i	−0.478952	+	0.829570i	−0.999709	−	0.0241355i	$-0.992317\pi$
$271$	−7.88455	+	13.6564i	−0.478952	+	0.829570i	0.520756	+	0.853705i	$0.325650\pi$
$272$	−1.20183	+	1.20183i	−0.0728715	+	0.0728715i
$273$	15.1635	+	5.00705i	0.917735	+	0.303041i
$274$	8.36656	+	8.36656i	0.505442	+	0.505442i
$275$	6.35430	−	1.70263i	0.383179	−	0.102672i
$276$	−5.21313	+	19.4557i	−0.313794	+	1.17109i
$277$	−2.27150	−	3.93435i	−0.136481	−	0.236392i	0.789681	−	0.613517i	$-0.210246\pi$
$277$	−2.27150	−	3.93435i	−0.136481	−	0.236392i	−0.926162	+	0.377125i	$0.876913\pi$
$278$	1.72080	+	0.993505i	0.103207	+	0.0595865i
$279$			57.3831i			3.43543i
$280$	−0.335468	+	0.0696340i	−0.0200481	+	0.00416143i
$281$	8.29476	−	8.29476i	0.494824	−	0.494824i	−0.414998	−	0.909822i	$-0.636218\pi$
$281$	8.29476	−	8.29476i	0.494824	−	0.494824i	0.909822	+	0.414998i	$0.136218\pi$
$282$	−27.6922	−	15.9881i	−1.64905	−	0.952078i
$283$	−4.98510	−	8.63445i	−0.296334	−	0.513265i	0.678961	−	0.734175i	$-0.262431\pi$
$283$	−4.98510	−	8.63445i	−0.296334	−	0.513265i	−0.975294	+	0.220910i	$0.929097\pi$
$284$	−1.25338	+	4.67766i	−0.0743741	+	0.277568i
$285$	−3.13344	−	1.80909i	−0.185609	−	0.107161i
$286$	2.41011			0.142513
$287$	15.4989	+	6.83990i	0.914871	+	0.403746i
$288$	7.92939			0.467244
$289$	−12.2207	−	7.05561i	−0.718863	−	0.415036i
$290$	−0.0264124	+	0.0985725i	−0.00155099	+	0.00578838i
$291$	−13.6254	−	23.5999i	−0.798736	−	1.38345i
$292$	10.0742	+	5.81633i	0.589547	+	0.340375i
$293$	13.0382	−	13.0382i	0.761697	−	0.761697i	−0.214932	−	0.976629i	$-0.568953\pi$
$293$	13.0382	−	13.0382i	0.761697	−	0.761697i	0.976629	+	0.214932i	$0.0689529\pi$
$294$	−14.3912	−	18.1227i	−0.839313	−	1.05694i
$295$			1.45473i			0.0846975i
$296$	−2.05716	−	1.18770i	−0.119570	−	0.0690338i
$297$	10.7566	+	18.6310i	0.624160	+	1.08108i
$298$	−1.22526	+	4.57272i	−0.0709772	+	0.264890i
$299$	−10.7442	+	2.87889i	−0.621351	+	0.166490i
$300$	11.6491	+	11.6491i	0.672564	+	0.672564i
$301$	9.62847	−	8.58665i	0.554976	−	0.494926i
$302$	15.8863	−	15.8863i	0.914152	−	0.914152i
$303$	28.8806	−	50.0226i	1.65915	−	2.87372i
$304$	−8.16346	−	2.18739i	−0.468207	−	0.125456i
$305$	0.0830004	+	0.143761i	0.00475259	+	0.00823172i
$306$	−3.48813	−	13.0179i	−0.199403	−	0.744183i
$307$			11.1560i			0.636705i	0.947972	+	0.318353i	$0.103130\pi$
$307$			11.1560i			0.636705i	−0.947972	+	0.318353i	$0.896870\pi$
$308$	−2.92012	−	1.91622i	−0.166389	−	0.109187i
$309$	−14.2128	+	14.2128i	−0.808536	+	0.808536i
$310$	0.468572	−	0.811590i	0.0266131	−	0.0460952i
$311$	6.79862	+	1.82168i	0.385514	+	0.103298i	0.446370	−	0.894848i	$-0.352716\pi$
$311$	6.79862	+	1.82168i	0.385514	+	0.103298i	−0.0608562	+	0.998147i	$0.519383\pi$
$312$	3.01781	+	5.22700i	0.170850	+	0.295921i
$313$	−0.258460	−	0.964584i	−0.0146090	−	0.0545215i	0.958237	−	0.285977i	$-0.0923180\pi$
$313$	−0.258460	−	0.964584i	−0.0146090	−	0.0545215i	−0.972846	+	0.231455i	$0.925651\pi$
$314$	−7.08315	+	7.08315i	−0.399725	+	0.399725i
$315$	0.851849	−	2.57976i	0.0479962	−	0.145353i
$316$	−7.27909	−	7.27909i	−0.409481	−	0.409481i
$317$	28.2278	−	7.56362i	1.58543	−	0.424815i	0.644830	−	0.764326i	$-0.276928\pi$
$317$	28.2278	−	7.56362i	1.58543	−	0.424815i	0.940602	+	0.339511i	$0.110262\pi$
$318$	−10.6480	−	18.4429i	−0.597111	−	1.03423i
$319$	−0.900934	+	0.520155i	−0.0504426	+	0.0291231i
$320$	−0.112148	−	0.0647489i	−0.00626929	−	0.00361957i
$321$	2.19221	+	2.19221i	0.122357	+	0.122357i
$322$	15.3067	+	5.05434i	0.853008	+	0.281668i
$323$			14.3644i			0.799257i
$324$	−15.0435	+	26.0562i	−0.835753	+	1.44757i
$325$	−2.35468	+	8.78777i	−0.130614	+	0.487458i
$326$	13.4636	−	7.77322i	0.745681	−	0.430519i
$327$	−8.90094	+	15.4169i	−0.492223	+	0.852555i
$328$	2.65136	+	5.82841i	0.146397	+	0.321820i
$329$	−14.0398	+	21.3952i	−0.774042	+	1.17956i
$330$		−	0.565163i		−	0.0311112i
$331$	7.69025	−	2.06060i	0.422695	−	0.113261i	−0.0412003	−	0.999151i	$-0.513118\pi$
$331$	7.69025	−	2.06060i	0.422695	−	0.113261i	0.463895	+	0.885890i	$0.346452\pi$
$332$	−1.37991	−	2.39008i	−0.0757326	−	0.131173i
$333$	16.3120	−	9.41776i	0.893894	−	0.516090i
$334$	−0.212108	−	0.791599i	−0.0116060	−	0.0433144i
$335$	−0.537446	−	0.537446i	−0.0293638	−	0.0293638i
$336$	0.499458	−	8.73248i	0.0272477	−	0.476396i
$337$		−	19.6719i		−	1.07159i	−0.844347	−	0.535797i	$-0.820011\pi$
$337$		−	19.6719i		−	1.07159i	0.844347	−	0.535797i	$-0.179989\pi$
$338$	4.83345	−	8.37178i	0.262905	−	0.455365i
$339$	3.83675	−	14.3190i	0.208384	−	0.777699i
$340$	−0.0569660	+	0.212600i	−0.00308941	+	0.0115298i
$341$	9.22785	−	2.47260i	0.499716	−	0.133899i
$342$	47.3866	−	47.3866i	2.56237	−	2.56237i
$343$	−15.1375	+	10.6703i	−0.817351	+	0.576140i
$344$	4.87615			0.262905
$345$	0.675089	+	2.51947i	0.0363456	+	0.135644i
$346$	−8.37560	−	14.5070i	−0.450275	−	0.779899i
$347$	−0.315825	−	0.0846251i	−0.0169544	−	0.00454291i	0.250332	−	0.968160i	$-0.419460\pi$
$347$	−0.315825	−	0.0846251i	−0.0169544	−	0.00454291i	−0.267286	+	0.963617i	$0.586127\pi$
$348$	−2.25620	−	1.30262i	−0.120945	−	0.0698277i
$349$		−	26.7716i		−	1.43305i	−0.697560	−	0.716527i	$-0.745731\pi$
$349$		−	26.7716i		−	1.43305i	0.697560	−	0.716527i	$-0.254269\pi$
$350$	9.83991	−	8.77521i	0.525965	−	0.469055i
$351$	−29.7520			−1.58804
$352$	−0.341672	−	1.27514i	−0.0182112	−	0.0679650i
$353$	−5.04880	−	8.74477i	−0.268720	−	0.465437i	0.699811	−	0.714328i	$-0.253267\pi$
$353$	−5.04880	−	8.74477i	−0.268720	−	0.465437i	−0.968532	+	0.248890i	$0.919934\pi$
$354$	−35.8725	−	9.61200i	−1.90660	−	0.510872i
$355$	0.162309	+	0.605747i	0.00861448	+	0.0321497i
$356$	7.85174	+	7.85174i	0.416141	+	0.416141i
$357$	−14.5561	+	3.02144i	−0.770388	+	0.159912i
$358$	−1.21784	−	1.21784i	−0.0643650	−	0.0643650i
$359$	11.1978	−	19.3951i	0.590996	−	1.02364i	−0.403103	−	0.915155i	$-0.632068\pi$
$359$	11.1978	−	19.3951i	0.590996	−	1.02364i	0.994099	−	0.108480i	$-0.0345984\pi$
$360$	0.889269	−	0.513419i	0.0468686	−	0.0270596i
$361$	−45.4029	+	26.2134i	−2.38963	+	1.37965i
$362$	6.78114	−	1.81700i	0.356409	−	0.0954995i
$363$	−21.6405	+	21.6405i	−1.13583	+	1.13583i
$364$	4.31424	−	2.17234i	0.226128	−	0.113861i
$365$	1.50640			0.0788488
$366$	−4.09345	+	1.09684i	−0.213968	+	0.0573326i
$367$	−28.2164	+	16.2907i	−1.47288	+	0.850369i	−0.999535	−	0.0305063i	$-0.990288\pi$
$367$	−28.2164	+	16.2907i	−1.47288	+	0.850369i	−0.473348	+	0.880875i	$0.656955\pi$
$368$	3.04631	+	5.27637i	0.158800	+	0.275050i
$369$	−50.5358	−	4.90085i	−2.63079	−	0.255128i
$370$	−0.307610			−0.0159919
$371$	−15.2223	+	7.66485i	−0.790302	+	0.397939i
$372$	16.9171	+	16.9171i	0.877113	+	0.877113i
$373$	−1.45935	+	2.52767i	−0.0755624	+	0.130878i	−0.901331	−	0.433132i	$-0.857409\pi$
$373$	−1.45935	+	2.52767i	−0.0755624	+	0.130878i	0.825768	+	0.564009i	$0.190742\pi$
$374$	−1.94312	+	1.12186i	−0.100477	+	0.0580102i
$375$	4.12834	+	1.10618i	0.213186	+	0.0571231i
$376$	−9.34271	+	2.50337i	−0.481813	+	0.129102i
$377$		−	1.43871i		−	0.0740974i
$378$	36.0478	+	23.6551i	1.85410	+	1.21669i
$379$	16.5820			0.851761			0.425880	−	0.904779i	$-0.359964\pi$
$379$	16.5820			0.851761			0.425880	+	0.904779i	$0.359964\pi$
$380$	−1.05715	+	0.283263i	−0.0542307	+	0.0145311i
$381$	0.525129	−	1.95981i	0.0269031	−	0.100404i
$382$	4.13564	−	15.4344i	0.211598	−	0.789693i
$383$	−6.26359	−	23.3760i	−0.320054	−	1.19446i	−0.919191	−	0.393812i	$-0.871156\pi$
$383$	−6.26359	−	23.3760i	−0.320054	−	1.19446i	0.599137	−	0.800647i	$-0.295511\pi$
$384$	2.33767	−	2.33767i	0.119294	−	0.119294i
$385$	−0.451560	−	0.0258271i	−0.0230136	−	0.00131627i
$386$	2.44559	−	2.44559i	0.124477	−	0.124477i
$387$	−19.3325	+	33.4848i	−0.982724	+	1.70213i
$388$	−7.96206	−	2.13343i	−0.404212	−	0.108308i
$389$	25.2141	−	14.5574i	1.27841	−	0.738088i	0.301850	−	0.953355i	$-0.402396\pi$
$389$	25.2141	−	14.5574i	1.27841	−	0.738088i	0.976555	+	0.215268i	$0.0690624\pi$
$390$	0.676885	+	0.390800i	0.0342754	+	0.0197889i
$391$	7.32228	−	7.32228i	0.370304	−	0.370304i
$392$	−6.95435	−	0.798124i	−0.351248	−	0.0403114i
$393$	−51.4455	+	51.4455i	−2.59508	+	2.59508i
$394$	−2.43203	+	4.21239i	−0.122524	+	0.212217i
$395$	−1.28765	−	0.345025i	−0.0647887	−	0.0173601i
$396$	10.1111	+	2.70925i	0.508100	+	0.136145i
$397$	6.46971	−	1.73355i	0.324706	−	0.0870046i	−0.0927841	−	0.995686i	$-0.529577\pi$
$397$	6.46971	−	1.73355i	0.324706	−	0.0870046i	0.417490	+	0.908682i	$0.362910\pi$
$398$	−14.0205	−	14.0205i	−0.702785	−	0.702785i
$399$	−49.2011	−	55.1707i	−2.46314	−	2.76199i
$400$	4.98323			0.249162
$401$	14.9557	+	8.63465i	0.746850	+	0.431194i	0.824555	−	0.565782i	$-0.191426\pi$
$401$	14.9557	+	8.63465i	0.746850	+	0.431194i	−0.0777048	+	0.996976i	$0.524759\pi$
$402$	16.8041	−	9.70187i	0.838114	−	0.483885i
$403$	−3.41951	+	12.7618i	−0.170338	+	0.635710i
$404$	−4.52204	−	16.8765i	−0.224980	−	0.839636i
$405$			3.89621i			0.193604i
$406$	−1.14389	+	1.74316i	−0.0567701	+	0.0865115i
$407$	−2.21736	−	2.21736i	−0.109910	−	0.109910i
$408$	−4.86615	−	2.80947i	−0.240910	−	0.139090i
$409$	14.4700	+	25.0627i	0.715494	+	1.23927i	0.962769	+	0.270326i	$0.0871316\pi$
$409$	14.4700	+	25.0627i	0.715494	+	1.23927i	−0.247275	+	0.968945i	$0.579535\pi$
$410$	0.674728	+	0.481974i	0.0333224	+	0.0238030i
$411$	−19.5583	+	33.8759i	−0.964737	+	1.67097i
$412$			6.07989i			0.299534i
$413$	−9.31922	+	28.2225i	−0.458569	+	1.38874i
$414$	−48.3108			−2.37435
$415$	−0.309510	−	0.178696i	−0.0151932	−	0.00877183i
$416$	1.76347	+	0.472520i	0.0864612	+	0.0231672i
$417$	−1.70018	+	6.34515i	−0.0832581	+	0.310723i
$418$	−9.66216	−	5.57845i	−0.472592	−	0.272851i
$419$			4.84321i			0.236606i	0.992978	+	0.118303i	$0.0377455\pi$
$419$			4.84321i			0.236606i	−0.992978	+	0.118303i	$0.962255\pi$
$420$	−0.509405	−	1.01167i	−0.0248564	−	0.0493646i
$421$	−22.2043	−	22.2043i	−1.08217	−	1.08217i	−0.996307	−	0.0858623i	$-0.972635\pi$
$421$	−22.2043	−	22.2043i	−1.08217	−	1.08217i	−0.0858623	−	0.996307i	$-0.527365\pi$
$422$	15.6801	−	4.20146i	0.763294	−	0.204524i
$423$	19.8502	−	74.0820i	0.965150	−	3.60199i
$424$	−6.22220	−	1.66723i	−0.302177	−	0.0809680i
$425$	−2.19212	−	8.18110i	−0.106333	−	0.396842i
$426$	−16.0097			−0.775672
$427$	0.689297	+	3.32075i	0.0333574	+	0.160702i
$428$	0.937775			0.0453291
$429$	2.06220	+	7.69625i	0.0995641	+	0.371578i
$430$	0.546853	−	0.315726i	0.0263716	−	0.0152256i
$431$	−8.66505	+	5.00277i	−0.417381	+	0.240975i	−0.693956	−	0.720017i	$-0.744134\pi$
$431$	−8.66505	+	5.00277i	−0.417381	+	0.240975i	0.276575	+	0.960992i	$0.410800\pi$
$432$	4.21782	+	15.7411i	0.202930	+	0.757344i
$433$	−24.7629			−1.19003			−0.595013	−	0.803716i	$-0.702853\pi$
$433$	−24.7629			−1.19003			−0.595013	+	0.803716i	$0.702853\pi$
$434$	14.2897	−	12.7435i	0.685929	−	0.611710i
$435$	−0.337373			−0.0161758
$436$	1.39368	+	5.20129i	0.0667453	+	0.249097i
$437$	49.7369	+	13.3270i	2.37924	+	0.637515i
$438$	−9.95344	+	37.1467i	−0.475594	+	1.77494i
$439$	39.6477	−	10.6236i	1.89228	−	0.507036i	0.894027	−	0.448013i	$-0.147868\pi$
$439$	39.6477	−	10.6236i	1.89228	−	0.507036i	0.998257	−	0.0590227i	$-0.0187984\pi$
$440$	−0.120882	−	0.120882i	−0.00576281	−	0.00576281i
$441$	33.0527	−	44.5916i	1.57394	−	2.12341i
$442$		−	3.10300i		−	0.147594i
$443$	9.14284	+	5.27862i	0.434389	+	0.250795i	0.701215	−	0.712950i	$-0.252641\pi$
$443$	9.14284	+	5.27862i	0.434389	+	0.250795i	−0.266825	+	0.963745i	$0.585975\pi$
$444$	2.03251	−	7.58541i	0.0964585	−	0.359988i
$445$	1.38895	+	0.372168i	0.0658426	+	0.0176425i
$446$	−11.0605	−	6.38576i	−0.523728	−	0.302375i
$447$	−15.6505			−0.740244
$448$	−1.76095	−	1.97460i	−0.0831970	−	0.0932913i
$449$		−	11.8645i		−	0.559921i	−0.960012	−	0.279960i	$-0.909679\pi$
$449$		−	11.8645i		−	0.559921i	0.960012	−	0.279960i	$-0.0903213\pi$
$450$	−19.7570	+	34.2201i	−0.931354	+	1.61315i
$451$	1.38944	+	8.33791i	0.0654261	+	0.392617i
$452$	−2.24202	−	3.88329i	−0.105456	−	0.182655i
$453$	64.3229	+	37.1368i	3.02215	+	1.74484i
$454$	11.5725	+	11.5725i	0.543123	+	0.543123i
$455$	0.343178	−	0.522966i	0.0160884	−	0.0245170i
$456$		−	27.9401i		−	1.30842i
$457$	−8.52509	−	31.8161i	−0.398787	−	1.48829i	−0.815234	−	0.579132i	$-0.803392\pi$
$457$	−8.52509	−	31.8161i	−0.398787	−	1.48829i	0.416447	−	0.909160i	$-0.363275\pi$
$458$	5.76006	−	21.4968i	0.269150	−	1.00448i
$459$	23.9872	−	13.8490i	1.11963	−	0.646416i
$460$	0.683278	+	0.394491i	0.0318580	+	0.0183932i
$461$	−14.6149			−0.680682			−0.340341	−	0.940302i	$-0.610542\pi$
$461$	−14.6149			−0.680682			−0.340341	+	0.940302i	$0.610542\pi$
$462$	3.62052	−	10.9645i	0.168442	−	0.510113i
$463$	3.23309	+	3.23309i	0.150255	+	0.150255i	0.778232	−	0.627977i	$-0.216117\pi$
$463$	3.23309	+	3.23309i	0.150255	+	0.150255i	−0.627977	+	0.778232i	$0.716117\pi$
$464$	−0.761190	+	0.203960i	−0.0353374	+	0.00946862i
$465$	2.99260	+	0.801863i	0.138778	+	0.0371855i
$466$	−10.0469	−	2.69207i	−0.465415	−	0.124708i
$467$	8.20925	−	14.2188i	0.379879	−	0.657969i	−0.611166	−	0.791503i	$-0.709299\pi$
$467$	8.20925	−	14.2188i	0.379879	−	0.657969i	0.991044	+	0.133533i	$0.0426324\pi$
$468$	−10.2364	+	10.2364i	−0.473180	+	0.473180i
$469$	−6.98378	−	13.8697i	−0.322481	−	0.640443i
$470$	−0.885679	+	0.885679i	−0.0408533	+	0.0408533i
$471$	−28.6794	−	16.5581i	−1.32148	−	0.762955i
$472$	−9.72859	+	5.61681i	−0.447795	+	0.258534i
$473$	6.21776	+	1.66604i	0.285893	+	0.0766048i
$474$	17.0161	−	29.4727i	0.781575	−	1.35373i
$475$	29.7801	−	29.7801i	1.36641	−	1.36641i
$476$	−2.46712	+	3.75962i	−0.113080	+	0.172322i
$477$	36.1181	−	36.1181i	1.65374	−	1.65374i
$478$	4.28595	+	15.9954i	0.196035	+	0.731612i
$479$	−3.22322	+	12.0292i	−0.147273	+	0.549629i	0.852371	+	0.522937i	$0.175164\pi$
$479$	−3.22322	+	12.0292i	−0.147273	+	0.549629i	−0.999644	+	0.0266916i	$0.991503\pi$
$480$	0.110804	−	0.413527i	0.00505750	−	0.0188749i
$481$	4.18895	−	1.12243i	0.191000	−	0.0511782i
$482$	13.3447			0.607835
$483$	−3.04301	+	53.2038i	−0.138462	+	2.42086i
$484$			9.25729i			0.420786i
$485$	−1.03107	+	0.276274i	−0.0468184	+	0.0125450i
$486$	−48.8542	−	13.0905i	−2.21607	−	0.593795i
$487$	0.444420	−	0.256586i	0.0201386	−	0.0116270i	−0.489897	−	0.871780i	$-0.662966\pi$
$487$	0.444420	−	0.256586i	0.0201386	−	0.0116270i	0.510035	+	0.860153i	$0.329632\pi$
$488$	−0.640940	+	1.11014i	−0.0290140	+	0.0502537i
$489$	36.3424	+	36.3424i	1.64346	+	1.64346i
$490$	−0.831597	+	0.360778i	−0.0375677	+	0.0162983i
$491$	40.7458			1.83883			0.919416	−	0.393287i	$-0.128662\pi$
$491$	40.7458			1.83883			0.919416	+	0.393287i	$0.128662\pi$
$492$	−16.3433	+	13.4537i	−0.736814	+	0.606538i
$493$	0.669694	+	1.15994i	0.0301615	+	0.0522413i
$494$	13.3624	−	7.71480i	0.601204	−	0.347105i
$495$	1.30936	−	0.350842i	0.0588514	−	0.0157692i
$496$	7.23675			0.324940
$497$	−0.731620	+	12.7916i	−0.0328176	+	0.573781i
$498$	6.45156	−	6.45156i	0.289101	−	0.289101i
$499$	−25.0606	+	6.71498i	−1.12187	+	0.300604i	−0.771639	−	0.636061i	$-0.780563\pi$
$499$	−25.0606	+	6.71498i	−1.12187	+	0.300604i	−0.350229	+	0.936664i	$0.613896\pi$
$500$	1.11960	−	0.646403i	0.0500702	−	0.0289080i
$501$	2.34634	−	1.35466i	0.104827	−	0.0605216i
$502$	7.65419	−	13.2575i	0.341623	−	0.591709i
$503$	−18.4755	−	18.4755i	−0.823780	−	0.823780i	0.162868	−	0.986648i	$-0.447926\pi$
$503$	−18.4755	−	18.4755i	−0.823780	−	0.823780i	−0.986648	+	0.162868i	$0.947926\pi$
$504$	20.5413	−	4.26382i	0.914984	−	0.189926i
$505$	−1.59987	−	1.59987i	−0.0711933	−	0.0711933i
$506$	2.08168	+	7.76893i	0.0925419	+	0.345371i
$507$	30.8695	+	8.27145i	1.37096	+	0.367348i
$508$	−0.306861	−	0.531498i	−0.0136147	−	0.0235814i
$509$	5.31476	+	19.8350i	0.235573	+	0.879169i	0.977890	+	0.209121i	$0.0670602\pi$
$509$	5.31476	+	19.8350i	0.235573	+	0.879169i	−0.742317	+	0.670049i	$0.766273\pi$
$510$	−0.727641			−0.0322205
$511$	29.2250	+	9.65026i	1.29284	+	0.426902i
$512$		−	1.00000i		−	0.0441942i
$513$	119.276	+	68.8640i	5.26616	+	3.04042i
$514$	−20.2172	−	5.41718i	−0.891742	−	0.238941i
$515$	0.393666	+	0.681849i	0.0173470	+	0.0300459i
$516$	4.17226	+	15.5711i	0.183674	+	0.685479i
$517$	−12.7686			−0.561561
$518$	−5.96779	−	1.97060i	−0.262210	−	0.0865830i
$519$	39.1588	−	39.1588i	1.71888	−	1.71888i
$520$	0.228365	−	0.0611903i	0.0100145	−	0.00268337i
$521$	−10.3876	+	38.7671i	−0.455089	+	1.69842i	0.232737	+	0.972540i	$0.425232\pi$
$521$	−10.3876	+	38.7671i	−0.455089	+	1.69842i	−0.687826	+	0.725876i	$0.741435\pi$
$522$	1.61728	−	6.03578i	0.0707865	−	0.264179i
$523$	1.15562	−	2.00159i	0.0505317	−	0.0875236i	−0.839653	−	0.543123i	$-0.817242\pi$
$523$	1.15562	−	2.00159i	0.0505317	−	0.0875236i	0.890185	+	0.455599i	$0.150575\pi$
$524$			22.0072i			0.961389i
$525$	36.4415	+	23.9135i	1.59044	+	1.04367i
$526$	2.54565	+	2.54565i	0.110996	+	0.110996i
$527$	−3.18344	−	11.8808i	−0.138673	−	0.517534i
$528$	3.77956	−	2.18213i	0.164484	−	0.0949651i
$529$	−7.06005	−	12.2284i	−0.306959	−	0.531668i
$530$	−0.805761	+	0.215903i	−0.0350000	+	0.00937823i
$531$		−	89.0757i		−	3.86556i
$532$	−22.3239	−	1.27682i	−0.967864	−	0.0553574i
$533$	−10.9469	−	4.10141i	−0.474165	−	0.177652i
$534$	−18.3548	+	31.7914i	−0.794288	+	1.37575i
$535$	0.105170	−	0.0607199i	0.00454689	−	0.00262515i
$536$	1.51909	−	5.66932i	0.0656147	−	0.244877i
$537$	2.84691	−	4.93100i	0.122853	−	0.212788i
$538$			16.9526i			0.730877i
$539$	−8.59505	−	3.39382i	−0.370215	−	0.146182i
$540$	1.49224	+	1.49224i	0.0642158	+	0.0642158i
$541$	−7.67115	−	4.42894i	−0.329809	−	0.190415i	0.325947	−	0.945388i	$-0.394317\pi$
$541$	−7.67115	−	4.42894i	−0.329809	−	0.190415i	−0.655756	+	0.754973i	$0.727650\pi$
$542$	−13.6564	+	7.88455i	−0.586594	+	0.338670i
$543$	11.6045	+	20.0996i	0.497998	+	0.862557i
$544$	−1.64173	+	0.439899i	−0.0703884	+	0.0188605i
$545$	0.493077	+	0.493077i	0.0211211	+	0.0211211i
$546$	10.6284	+	11.9180i	0.454854	+	0.510042i
$547$	−17.6277	+	17.6277i	−0.753707	+	0.753707i	−0.975169	−	0.221462i	$-0.928917\pi$
$547$	−17.6277	+	17.6277i	−0.753707	+	0.753707i	0.221462	+	0.975169i	$0.428917\pi$
$548$	3.06237	+	11.4289i	0.130818	+	0.488220i
$549$	−5.08227	−	8.80275i	−0.216906	−	0.375692i
$550$	6.35430	+	1.70263i	0.270948	+	0.0726004i
$551$	−3.33004	+	5.76781i	−0.141865	+	0.245717i
$552$	−14.2425	+	14.2425i	−0.606203	+	0.606203i
$553$	−22.7708	−	14.9426i	−0.968314	−	0.635422i
$554$		−	4.54300i		−	0.193013i
$555$	−0.263205	−	0.982294i	−0.0111724	−	0.0416961i
$556$	0.993505	+	1.72080i	0.0421340	+	0.0729783i
$557$	−33.8728	−	9.07619i	−1.43524	−	0.384571i	−0.544374	−	0.838843i	$-0.683233\pi$
$557$	−33.8728	−	9.07619i	−1.43524	−	0.384571i	−0.890863	+	0.454272i	$0.849899\pi$
$558$	−28.6915	+	49.6952i	−1.21461	+	2.10377i
$559$	−6.29487	+	6.29487i	−0.266244	+	0.266244i
$560$	−0.325341	−	0.107429i	−0.0137482	−	0.00453971i
$561$	−5.24509	−	5.24509i	−0.221448	−	0.221448i
$562$	11.3309	−	3.03609i	0.477963	−	0.128070i
$563$	−4.81409	+	17.9664i	−0.202890	+	0.757194i	0.787193	+	0.616707i	$0.211534\pi$
$563$	−4.81409	+	17.9664i	−0.202890	+	0.757194i	−0.990082	+	0.140487i	$0.955133\pi$
$564$	−15.9881	−	27.6922i	−0.673221	−	1.16605i
$565$	−0.502878	−	0.290337i	−0.0211562	−	0.0122146i
$566$		−	9.97020i		−	0.419079i
$567$	−24.9598	+	75.5886i	−1.04821	+	3.17442i
$568$	−3.42428	+	3.42428i	−0.143680	+	0.143680i
$569$	−31.9167	−	18.4271i	−1.33802	−	0.772504i	−0.351503	−	0.936187i	$-0.614329\pi$
$569$	−31.9167	−	18.4271i	−1.33802	−	0.772504i	−0.986513	+	0.163683i	$0.947663\pi$
$570$	−1.80909	−	3.13344i	−0.0757746	−	0.131245i
$571$	0.657694	−	2.45455i	0.0275236	−	0.102720i	−0.950798	−	0.309813i	$-0.899734\pi$
$571$	0.657694	−	2.45455i	0.0275236	−	0.102720i	0.978321	+	0.207093i	$0.0664003\pi$
$572$	2.08722	+	1.20506i	0.0872710	+	0.0503859i
$573$	52.8255			2.20682
$574$	10.0025	+	13.6730i	0.417496	+	0.570699i
$575$	−30.3610			−1.26614
$576$	6.86706	+	3.96470i	0.286127	+	0.165196i
$577$	−1.43115	+	5.34114i	−0.0595797	+	0.222355i	−0.989296	−	0.145922i	$-0.953385\pi$
$577$	−1.43115	+	5.34114i	−0.0595797	+	0.222355i	0.929716	+	0.368276i	$0.120052\pi$
$578$	−7.05561	−	12.2207i	−0.293475	−	0.508313i
$579$	9.90209	+	5.71698i	0.411517	+	0.237589i
$580$	−0.0721601	+	0.0721601i	−0.00299628	+	0.00299628i
$581$	−4.85991	−	5.44956i	−0.201623	−	0.226086i
$582$		−	27.2508i		−	1.12958i
$583$	−7.36451	−	4.25190i	−0.305007	−	0.176096i
$584$	5.81633	+	10.0742i	0.240681	+	0.416872i
$585$	−0.485202	+	1.81080i	−0.0200606	+	0.0748673i
$586$	17.8105	−	4.77230i	0.735743	−	0.197142i
$587$	−4.50062	−	4.50062i	−0.185761	−	0.185761i	0.608100	−	0.793860i	$-0.291932\pi$
$587$	−4.50062	−	4.50062i	−0.185761	−	0.185761i	−0.793860	+	0.608100i	$0.791932\pi$
$588$	−3.40180	−	22.8903i	−0.140288	−	0.943982i
$589$	43.2473	−	43.2473i	1.78198	−	1.78198i
$590$	−0.727364	+	1.25983i	−0.0299451	+	0.0518664i
$591$	−15.5324	−	4.16191i	−0.638919	−	0.171198i
$592$	−1.18770	−	2.05716i	−0.0488143	−	0.0845488i
$593$	0.352489	+	1.31551i	0.0144750	+	0.0540214i	0.972786	−	0.231707i	$-0.0744311\pi$
$593$	0.352489	+	1.31551i	0.0144750	+	0.0540214i	−0.958311	+	0.285729i	$0.907764\pi$
$594$			21.5132i			0.882696i
$595$	−0.0332522	+	0.581379i	−0.00136321	+	0.0238342i
$596$	−3.34746	+	3.34746i	−0.137117	+	0.137117i
$597$	32.7753	−	56.7685i	1.34140	−	2.32338i
$598$	−10.7442	−	2.87889i	−0.439361	−	0.117727i
$599$	14.8664	+	25.7493i	0.607423	+	1.05209i	0.991663	+	0.128855i	$0.0411302\pi$
$599$	14.8664	+	25.7493i	0.607423	+	1.05209i	−0.384240	+	0.923233i	$0.625537\pi$
$600$	4.26388	+	15.9130i	0.174072	+	0.649647i
$601$	−24.4918	+	24.4918i	−0.999040	+	0.999040i	−1.00000		0.000959616i	$-0.999695\pi$
$601$	−24.4918	+	24.4918i	−0.999040	+	0.999040i	0.000959616		1.00000i	$0.499695\pi$
$602$	12.6318	−	2.62202i	0.514835	−	0.106866i
$603$	32.9088	+	32.9088i	1.34015	+	1.34015i
$604$	21.7010	−	5.81478i	0.883003	−	0.236600i
$605$	0.599399	+	1.03819i	0.0243690	+	0.0422084i
$606$	50.0226	−	28.8806i	2.03203	−	1.17319i
$607$	−4.93321	−	2.84819i	−0.200233	−	0.115604i	0.396531	−	0.918021i	$-0.370214\pi$
$607$	−4.93321	−	2.84819i	−0.200233	−	0.115604i	−0.596764	+	0.802417i	$0.703547\pi$
$608$	−5.97607	−	5.97607i	−0.242362	−	0.242362i
$609$	−6.54521	−	2.16126i	−0.265225	−	0.0875788i
$610$			0.166001i			0.00672117i
$611$	8.82924	−	15.2927i	0.357193	−	0.618676i
$612$	3.48813	−	13.0179i	0.140999	−	0.526217i
$613$	2.01728	−	1.16468i	0.0814771	−	0.0470408i	−0.458708	−	0.888587i	$-0.651688\pi$
$613$	2.01728	−	1.16468i	0.0814771	−	0.0470408i	0.540185	+	0.841546i	$0.318354\pi$
$614$	−5.57799	+	9.66136i	−0.225109	+	0.389901i
$615$	−0.961766	+	2.56702i	−0.0387822	+	0.103512i
$616$	−1.57078	−	3.11956i	−0.0632886	−	0.125691i
$617$			14.5158i			0.584385i	0.956359	+	0.292193i	$0.0943848\pi$
$617$			14.5158i			0.584385i	−0.956359	+	0.292193i	$0.905615\pi$
$618$	−19.4150	+	5.20223i	−0.780985	+	0.209264i
$619$	20.1627	+	34.9227i	0.810405	+	1.40366i	0.912581	+	0.408897i	$0.134086\pi$
$619$	20.1627	+	34.9227i	0.810405	+	1.40366i	−0.102175	+	0.994766i	$0.532580\pi$
$620$	0.811590	−	0.468572i	0.0325942	−	0.0188183i
$621$	−25.6976	−	95.9047i	−1.03121	−	3.84852i
$622$	4.97693	+	4.97693i	0.199557	+	0.199557i
$623$	24.5622	+	16.1181i	0.984065	+	0.645758i
$624$			6.03562i			0.241618i
$625$	−12.3744	+	21.4330i	−0.494975	+	0.857321i
$626$	0.258460	−	0.964584i	0.0103301	−	0.0385525i
$627$	9.54636	−	35.6275i	0.381245	−	1.42283i
$628$	−9.67576	+	2.59261i	−0.386105	+	0.103456i
$629$	−2.85482	+	2.85482i	−0.113829	+	0.113829i
$630$	2.02760	−	1.80821i	0.0807815	−	0.0720408i
$631$	26.2092			1.04337			0.521687	−	0.853137i	$-0.325303\pi$
$631$	26.2092			1.04337			0.521687	+	0.853137i	$0.325303\pi$
$632$	−2.66433	−	9.94342i	−0.105981	−	0.395528i
$633$	26.8332	+	46.4765i	1.06652	+	1.84727i
$634$	28.2278	+	7.56362i	1.12107	+	0.300390i
$635$	−0.0688279	−	0.0397378i	−0.00273135	−	0.00157695i
$636$		−	21.2960i		−	0.844442i
$637$	10.0081	−	7.94738i	0.396533	−	0.314887i
$638$	−1.04031			−0.0411862
$639$	−9.93850	−	37.0910i	−0.393161	−	1.46730i
$640$	−0.0647489	−	0.112148i	−0.00255942	−	0.00443305i
$641$	−28.2843	−	7.57875i	−1.11716	−	0.299343i	−0.347427	−	0.937707i	$-0.612945\pi$
$641$	−28.2843	−	7.57875i	−1.11716	−	0.299343i	−0.769734	+	0.638364i	$0.779611\pi$
$642$	0.802404	+	2.99461i	0.0316683	+	0.118188i
$643$	13.2260	+	13.2260i	0.521581	+	0.521581i	0.918049	−	0.396467i	$-0.129764\pi$
$643$	13.2260	+	13.2260i	0.521581	+	0.521581i	−0.396467	+	0.918049i	$0.629764\pi$
$644$	10.7288	+	12.0305i	0.422774	+	0.474069i
$645$	1.47612	+	1.47612i	0.0581223	+	0.0581223i
$646$	−7.18220	+	12.4399i	−0.282580	+	0.489443i
$647$	18.7183	−	10.8070i	0.735894	−	0.424869i	−0.0846806	−	0.996408i	$-0.526987\pi$
$647$	18.7183	−	10.8070i	0.735894	−	0.424869i	0.820574	+	0.571540i	$0.193654\pi$
$648$	−26.0562	+	15.0435i	−1.02358	+	0.590966i
$649$	−14.3244	+	3.83821i	−0.562282	+	0.150663i
$650$	−6.43310	+	6.43310i	−0.252327	+	0.252327i
$651$	52.9211	+	34.7276i	2.07414	+	1.36108i
$652$	15.5464			0.608846
$653$	12.4278	−	3.33003i	0.486339	−	0.130314i	−0.00731371	−	0.999973i	$-0.502328\pi$
$653$	12.4278	−	3.33003i	0.486339	−	0.130314i	0.493653	+	0.869659i	$0.335661\pi$
$654$	−15.4169	+	8.90094i	−0.602847	+	0.348054i
$655$	1.42494	+	2.46807i	0.0556771	+	0.0964355i
$656$	−0.618062	+	6.37323i	−0.0241313	+	0.248833i
$657$	−92.2399			−3.59862
$658$	−22.8565	+	11.5089i	−0.891038	+	0.448662i
$659$	17.6194	+	17.6194i	0.686355	+	0.686355i	0.961424	−	0.275069i	$-0.0887008\pi$
$659$	17.6194	+	17.6194i	0.686355	+	0.686355i	−0.275069	+	0.961424i	$0.588701\pi$
$660$	0.282581	−	0.489445i	0.0109995	−	0.0190516i
$661$	−8.92205	+	5.15115i	−0.347027	+	0.200356i	−0.663375	−	0.748287i	$-0.730877\pi$
$661$	−8.92205	+	5.15115i	−0.347027	+	0.200356i	0.316348	+	0.948643i	$0.397543\pi$
$662$	7.69025	+	2.06060i	0.298890	+	0.0800874i
$663$	9.90884	−	2.65507i	0.384828	−	0.103114i
$664$		−	2.75983i		−	0.107102i
$665$	−2.58626	+	1.30226i	−0.100291	+	0.0504993i
$666$	18.8355			0.729861
$667$	4.63765	−	1.24265i	0.179570	−	0.0481158i
$668$	0.212108	−	0.791599i	0.00820672	−	0.0306279i
$669$	10.9279	−	40.7835i	0.422497	−	1.57678i
$670$	−0.196719	−	0.734165i	−0.00759991	−	0.0283633i
$671$	−1.19659	+	1.19659i	−0.0461939	+	0.0461939i
$672$	4.79879	−	7.31282i	0.185117	−	0.282098i
$673$	15.8555	−	15.8555i	0.611185	−	0.611185i	−0.332070	−	0.943255i	$-0.607747\pi$
$673$	15.8555	−	15.8555i	0.611185	−	0.611185i	0.943255	+	0.332070i	$0.107747\pi$
$674$	9.83593	−	17.0363i	0.378866	−	0.656215i
$675$	−78.4416	−	21.0184i	−3.01922	−	0.808997i
$676$	8.37178	−	4.83345i	0.321992	−	0.185902i
$677$	31.4576	+	18.1621i	1.20901	+	0.698025i	0.962544	−	0.271126i	$-0.0873959\pi$
$677$	31.4576	+	18.1621i	1.20901	+	0.698025i	0.246470	+	0.969150i	$0.420729\pi$
$678$	10.4822	−	10.4822i	0.402567	−	0.402567i
$679$	−21.7732	−	1.24532i	−0.835577	−	0.0477911i
$680$	−0.155634	+	0.155634i	−0.00596829	+	0.00596829i
$681$	−27.0526	+	46.8565i	−1.03666	+	1.79555i
$682$	9.22785	+	2.47260i	0.353353	+	0.0946806i
$683$	6.13320	+	1.64339i	0.234680	+	0.0628824i	0.374242	−	0.927331i	$-0.377903\pi$
$683$	6.13320	+	1.64339i	0.234680	+	0.0628824i	−0.139562	+	0.990213i	$0.544569\pi$
$684$	64.7313	−	17.3447i	2.47506	−	0.663191i
$685$	1.08345	+	1.08345i	0.0413965	+	0.0413965i
$686$	−18.4446	+	1.67195i	−0.704219	+	0.0638354i
$687$	73.5747			2.80705
$688$	4.22287	+	2.43808i	0.160995	+	0.0929508i
$689$	10.1849	−	5.88023i	0.388012	−	0.224019i
$690$	−0.675089	+	2.51947i	−0.0257002	+	0.0959145i
$691$	−4.14817	−	15.4812i	−0.157804	−	0.588931i	−0.998849	−	0.0479665i	$-0.984726\pi$
$691$	−4.14817	−	15.4812i	−0.157804	−	0.588931i	0.841045	−	0.540965i	$-0.181941\pi$
$692$		−	16.7512i		−	0.636785i
$693$	27.6498	+	1.58144i	1.05033	+	0.0600741i
$694$	−0.231200	−	0.231200i	−0.00877623	−	0.00877623i
$695$	0.222840	+	0.128657i	0.00845280	+	0.00488023i
$696$	−1.30262	−	2.25620i	−0.0493757	−	0.0855212i
$697$	10.7350	−	1.78889i	0.406616	−	0.0677590i
$698$	13.3858	−	23.1849i	0.506661	−	0.877562i
$699$		−	34.3865i		−	1.30062i
$700$	12.9092	−	2.67960i	0.487922	−	0.101279i
$701$	9.15908			0.345934			0.172967	−	0.984928i	$-0.444665\pi$
$701$	9.15908			0.345934			0.172967	+	0.984928i	$0.444665\pi$
$702$	−25.7660	−	14.8760i	−0.972473	−	0.561458i
$703$	−19.3915	−	5.19594i	−0.731365	−	0.195969i
$704$	0.341672	−	1.27514i	0.0128772	−	0.0480585i
$705$	−3.58608	−	2.07042i	−0.135060	−	0.0779767i
$706$		−	10.0976i		−	0.380028i
$707$	−20.7893	−	41.2874i	−0.781864	−	1.55277i
$708$	−26.2605	−	26.2605i	−0.986929	−	0.986929i
$709$	−36.5858	+	9.80313i	−1.37401	+	0.368164i	−0.868941	−	0.494916i	$-0.835199\pi$
$709$	−36.5858	+	9.80313i	−1.37401	+	0.368164i	−0.505067	+	0.863080i	$0.668532\pi$
$710$	−0.162309	+	0.605747i	−0.00609136	+	0.0227333i
$711$	78.8452	+	21.1265i	2.95693	+	0.792306i
$712$	2.87393	+	10.7257i	0.107705	+	0.401962i
$713$	−44.0908			−1.65121
$714$	−14.1166	−	4.66139i	−0.528302	−	0.174448i
$715$	0.312104			0.0116720
$716$	−0.445762	−	1.66361i	−0.0166589	−	0.0621718i
$717$	−47.4110	+	27.3728i	−1.77060	+	1.02226i
$718$	19.3951	−	11.1978i	0.723819	−	0.417897i
$719$	7.61829	+	28.4318i	0.284114	+	1.06033i	0.949484	+	0.313815i	$0.101607\pi$
$719$	7.61829	+	28.4318i	0.284114	+	1.06033i	−0.665370	+	0.746514i	$0.731726\pi$
$720$	1.02684			0.0382680
$721$	3.26930	+	15.7501i	0.121755	+	0.586566i
$722$	−52.4268			−1.95112
$723$	11.4184	+	42.6139i	0.424653	+	1.58483i
$724$	6.78114	+	1.81700i	0.252019	+	0.0675283i
$725$	1.01638	−	3.79319i	0.0377475	−	0.140875i
$726$	−29.5614	+	7.92096i	−1.09713	+	0.293974i
$727$	−19.8112	−	19.8112i	−0.734756	−	0.734756i	0.236802	−	0.971558i	$-0.423901\pi$
$727$	−19.8112	−	19.8112i	−0.734756	−	0.734756i	−0.971558	+	0.236802i	$0.923901\pi$
$728$	4.82241	+	0.275819i	0.178730	+	0.0102225i
$729$		−	76.9465i		−	2.84987i
$730$	1.30458	+	0.753202i	0.0482848	+	0.0278772i
$731$	2.14502	−	8.00531i	0.0793363	−	0.296087i
$732$	−4.09345	−	1.09684i	−0.151298	−	0.0405402i
$733$	−15.2326	−	8.79455i	−0.562629	−	0.324834i	0.191571	−	0.981479i	$-0.438642\pi$
$733$	−15.2326	−	8.79455i	−0.562629	−	0.324834i	−0.754200	+	0.656645i	$0.771975\pi$
$734$	−32.5815			−1.20260
$735$	−1.86363	−	2.34685i	−0.0687411	−	0.0865650i
$736$			6.09263i			0.224577i
$737$	3.87410	−	6.71013i	0.142704	−	0.247171i
$738$	−41.3149	−	29.5122i	−1.52082	−	1.08636i
$739$	−6.96634	−	12.0661i	−0.256261	−	0.443857i	0.708976	−	0.705232i	$-0.249157\pi$
$739$	−6.96634	−	12.0661i	−0.256261	−	0.443857i	−0.965237	+	0.261375i	$0.915824\pi$
$740$	−0.266398	−	0.153805i	−0.00979298	−	0.00565398i
$741$	36.0693	+	36.0693i	1.32504	+	1.32504i
$742$	−17.0153	−	0.973198i	−0.624652	−	0.0357272i
$743$			4.25773i			0.156201i	0.996945	+	0.0781004i	$0.0248855\pi$
$743$			4.25773i			0.156201i	−0.996945	+	0.0781004i	$0.975115\pi$
$744$	6.19210	+	23.1092i	0.227013	+	0.847226i
$745$	−0.158668	+	0.592157i	−0.00581315	+	0.0216950i
$746$	−2.52767	+	1.45935i	−0.0925446	+	0.0534307i
$747$	18.9519	+	10.9419i	0.693413	+	0.400342i
$748$	−2.24373			−0.0820388
$749$	2.42934	−	0.504264i	0.0887660	−	0.0184254i
$750$	3.02215	+	3.02215i	0.110353	+	0.110353i
$751$	−0.214559	+	0.0574910i	−0.00782938	+	0.00209788i	−0.262732	−	0.964869i	$-0.584623\pi$
$751$	−0.214559	+	0.0574910i	−0.00782938	+	0.00209788i	0.254902	+	0.966967i	$0.417957\pi$
$752$	−9.34271	−	2.50337i	−0.340694	−	0.0912886i
$753$	48.8845	+	13.0986i	1.78145	+	0.477338i
$754$	0.719356	−	1.24596i	0.0261974	−	0.0453752i
$755$	2.05724	−	2.05724i	0.0748705	−	0.0748705i
$756$	19.3907	+	38.5098i	0.705235	+	1.40059i
$757$	−24.8227	+	24.8227i	−0.902195	+	0.902195i	−0.995626	−	0.0934304i	$-0.970217\pi$
$757$	−24.8227	+	24.8227i	−0.902195	+	0.902195i	0.0934304	+	0.995626i	$0.470217\pi$
$758$	14.3604	+	8.29101i	0.521595	+	0.301143i
$759$	−23.0275	+	13.2949i	−0.835844	+	0.482575i
$760$	−1.05715	−	0.283263i	−0.0383469	−	0.0102750i
$761$	−0.439345	+	0.760967i	−0.0159262	+	0.0275850i	−0.873879	−	0.486144i	$-0.838403\pi$
$761$	−0.439345	+	0.760967i	−0.0159262	+	0.0275850i	0.857952	+	0.513729i	$0.171736\pi$
$762$	1.43468	−	1.43468i	0.0519729	−	0.0519729i
$763$	6.40724	+	12.7247i	0.231958	+	0.460665i
$764$	11.2988	−	11.2988i	0.408775	−	0.408775i
$765$	−0.451706	−	1.68579i	−0.0163315	−	0.0609498i
$766$	6.26359	−	23.3760i	0.226313	−	0.844610i
$767$	5.30811	−	19.8101i	0.191665	−	0.715302i
$768$	3.19332	−	0.855646i	0.115229	−	0.0308755i
$769$	−51.7216			−1.86513			−0.932564	−	0.361004i	$-0.882434\pi$
$769$	−51.7216			−1.86513			−0.932564	+	0.361004i	$0.882434\pi$
$770$	−0.378149	−	0.248147i	−0.0136275	−	0.00894259i
$771$		−	69.1950i		−	2.49200i
$772$	3.34074	−	0.895147i	0.120236	−	0.0322171i
$773$	−7.35664	−	1.97121i	−0.264600	−	0.0708993i	0.124080	−	0.992272i	$-0.460402\pi$
$773$	−7.35664	−	1.97121i	−0.264600	−	0.0708993i	−0.388680	+	0.921373i	$0.627069\pi$
$774$	−33.4848	+	19.3325i	−1.20359	+	0.694891i
$775$	−18.0312	+	31.2310i	−0.647700	+	1.12185i
$776$	−5.82863	−	5.82863i	−0.209236	−	0.209236i
$777$	1.18641	−	20.7432i	0.0425624	−	0.744158i
$778$	29.1147			1.04381
$779$	34.3932	+	41.7804i	1.23227	+	1.49694i
$780$	0.390800	+	0.676885i	0.0139929	+	0.0242364i
$781$	−5.53641	+	3.19645i	−0.198108	+	0.114378i
$782$	10.0024	−	2.68014i	0.357686	−	0.0958417i
$783$	12.8422			0.458944
$784$	−5.62358	−	4.16837i	−0.200842	−	0.148870i
$785$	−0.917252	+	0.917252i	−0.0327381	+	0.0327381i
$786$	−70.2759	+	18.8304i	−2.50666	+	0.671657i
$787$	−39.1309	+	22.5922i	−1.39486	+	0.805326i	−0.993849	−	0.110746i	$-0.964676\pi$
$787$	−39.1309	+	22.5922i	−1.39486	+	0.805326i	−0.401016	+	0.916071i	$0.631343\pi$
$788$	−4.21239	+	2.43203i	−0.150060	+	0.0866373i
$789$	−5.95089	+	10.3072i	−0.211857	+	0.366947i
$790$	−0.942625	−	0.942625i	−0.0335371	−	0.0335371i
$791$	−7.89617	−	8.85421i	−0.280755	−	0.314819i
$792$	7.40181	+	7.40181i	0.263012	+	0.263012i
$793$	−0.605715	−	2.26056i	−0.0215096	−	0.0802747i
$794$	6.46971	+	1.73355i	0.229602	+	0.0615215i
$795$	−1.37889	−	2.38831i	−0.0489043	−	0.0847048i
$796$	−5.13186	−	19.1524i	−0.181894	−	0.678838i
$797$	−52.0711			−1.84445			−0.922227	−	0.386650i	$-0.873632\pi$
$797$	−52.0711			−1.84445			−0.922227	+	0.386650i	$0.873632\pi$
$798$	−15.0241	−	72.3798i	−0.531846	−	2.56222i
$799$			16.4394i			0.581584i
$800$	4.31560	+	2.49162i	0.152580	+	0.0880919i
$801$	−85.0481	−	22.7886i	−3.00503	−	0.805194i
$802$	8.63465	+	14.9557i	0.304900	+	0.528103i
$803$	3.97455	+	14.8332i	0.140259	+	0.523453i
$804$	19.4037			0.684317
$805$	1.98218	+	0.654526i	0.0698627	+	0.0230690i
$806$	−9.34228	+	9.34228i	−0.329068	+	0.329068i
$807$	−54.1349	+	14.5054i	−1.90564	+	0.510614i
$808$	4.52204	−	16.8765i	0.159085	−	0.593712i
$809$	−2.26526	+	8.45406i	−0.0796423	+	0.297229i	−0.994246	−	0.107123i	$-0.965836\pi$
$809$	−2.26526	+	8.45406i	−0.0796423	+	0.297229i	0.914604	+	0.404352i	$0.132503\pi$
$810$	−1.94811	+	3.37422i	−0.0684495	+	0.118558i
$811$			44.7465i			1.57126i	0.618695	+	0.785631i	$0.287662\pi$
$811$			44.7465i			1.57126i	−0.618695	+	0.785631i	$0.712338\pi$
$812$	−1.86221	+	0.937676i	−0.0653509	+	0.0329060i
$813$	−36.8629	−	36.8629i	−1.29284	−	1.29284i
$814$	−0.811609	−	3.02897i	−0.0284469	−	0.106165i
$815$	1.74351	−	1.00662i	0.0610724	−	0.0352602i
$816$	−2.80947	−	4.86615i	−0.0983512	−	0.170349i
$817$	39.8063	−	10.6661i	1.39265	−	0.373158i
$818$			28.9399i			1.01186i
$819$	−21.0135	+	32.0222i	−0.734269	+	1.11895i
$820$	0.343345	+	0.754766i	0.0119901	+	0.0263576i
$821$	23.2000	−	40.1835i	0.809685	−	1.40242i	−0.103398	−	0.994640i	$-0.532971\pi$
$821$	23.2000	−	40.1835i	0.809685	−	1.40242i	0.913082	−	0.407775i	$-0.133695\pi$
$822$	−33.8759	+	19.5583i	−1.18156	+	0.682172i
$823$	3.18883	−	11.9009i	0.111156	−	0.414838i	−0.887815	−	0.460200i	$-0.847778\pi$
$823$	3.18883	−	11.9009i	0.111156	−	0.414838i	0.998971	+	0.0453623i	$0.0144442\pi$
$824$	−3.03994	+	5.26534i	−0.105901	+	0.183427i
$825$			21.7481i			0.757173i
$826$	−22.1819	+	19.7818i	−0.771808	+	0.688297i
$827$	−21.7933	−	21.7933i	−0.757826	−	0.757826i	0.218101	−	0.975926i	$-0.430014\pi$
$827$	−21.7933	−	21.7933i	−0.757826	−	0.757826i	−0.975926	+	0.218101i	$0.930014\pi$
$828$	−41.8384	−	24.1554i	−1.45399	−	0.839459i
$829$	43.9416	−	25.3697i	1.52615	−	0.881125i	0.526635	−	0.850092i	$-0.323454\pi$
$829$	43.9416	−	25.3697i	1.52615	−	0.881125i	0.999518	−	0.0310333i	$-0.00987981\pi$
$830$	−0.178696	−	0.309510i	−0.00620262	−	0.0107433i
$831$	14.5072	−	3.88720i	0.503250	−	0.134845i
$832$	1.29095	+	1.29095i	0.0447556	+	0.0447556i
$833$	−4.36952	+	11.0660i	−0.151395	+	0.383416i
$834$	−4.64497	+	4.64497i	−0.160842	+	0.160842i
$835$	−0.0274676	−	0.102510i	−0.000950554	−	0.00354752i
$836$	−5.57845	−	9.66216i	−0.192935	−	0.334173i
$837$	−113.914	−	30.5233i	−3.93746	−	1.05504i
$838$	−2.42160	+	4.19434i	−0.0836530	+	0.144891i
$839$	20.2654	−	20.2654i	0.699640	−	0.699640i	−0.264692	−	0.964333i	$-0.585270\pi$
$839$	20.2654	−	20.2654i	0.699640	−	0.699640i	0.964333	+	0.264692i	$0.0852705\pi$
$840$	0.0646787	−	1.13084i	0.00223163	−	0.0390176i
$841$		−	28.3790i		−	0.978586i
$842$	−8.12732	−	30.3316i	−0.280086	−	1.04530i
$843$	19.3904	+	33.5852i	0.667841	+	1.15673i
$844$	15.6801	+	4.20146i	0.539731	+	0.144620i
$845$	0.625921	−	1.08413i	0.0215323	−	0.0372951i
$846$	54.2318	−	54.2318i	1.86453	−	1.86453i
$847$	4.97786	+	23.9813i	0.171041	+	0.824007i
$848$	−4.55497	−	4.55497i	−0.156418	−	0.156418i
$849$	31.8380	−	8.53097i	1.09268	−	0.292782i
$850$	2.19212	−	8.18110i	0.0751891	−	0.280609i
$851$	7.23623	+	12.5335i	0.248055	+	0.429643i
$852$	−13.8648	−	8.00484i	−0.475000	−	0.274241i
$853$		−	1.44682i		−	0.0495380i	−0.999693	−	0.0247690i	$-0.992115\pi$
$853$		−	1.44682i		−	0.0495380i	0.999693	−	0.0247690i	$-0.00788503\pi$
$854$	−1.06343	+	3.22050i	−0.0363897	+	0.110203i
$855$	6.13646	−	6.13646i	0.209862	−	0.209862i
$856$	0.812137	+	0.468888i	0.0277583	+	0.0160262i
$857$	−22.9531	−	39.7559i	−0.784063	−	1.35804i	−0.929557	−	0.368678i	$-0.879811\pi$
$857$	−22.9531	−	39.7559i	−0.784063	−	1.35804i	0.145494	−	0.989359i	$-0.453523\pi$
$858$	−2.06220	+	7.69625i	−0.0704024	+	0.262746i
$859$	−23.3503	−	13.4813i	−0.796701	−	0.459975i	0.0456156	−	0.998959i	$-0.485475\pi$
$859$	−23.3503	−	13.4813i	−0.796701	−	0.459975i	−0.842316	+	0.538984i	$0.818808\pi$
$860$	0.631451			0.0215323
$861$	−35.1035	+	43.6403i	−1.19632	+	1.48726i
$862$	−10.0055			−0.340790
$863$	24.6630	+	14.2392i	0.839537	+	0.484707i	0.857107	−	0.515138i	$-0.172259\pi$
$863$	24.6630	+	14.2392i	0.839537	+	0.484707i	−0.0175695	+	0.999846i	$0.505593\pi$
$864$	−4.21782	+	15.7411i	−0.143493	+	0.535523i
$865$	−1.08462	−	1.87862i	−0.0368782	−	0.0638750i
$866$	−21.4453	−	12.3814i	−0.728740	−	0.420738i
$867$	32.9874	−	32.9874i	1.12031	−	1.12031i
$868$	18.7470	−	3.89137i	0.636316	−	0.132082i
$869$		−	13.5895i		−	0.460994i
$870$	−0.292173	−	0.168686i	−0.00990560	−	0.00571900i
$871$	5.35774	+	9.27987i	0.181540	+	0.314437i
$872$	−1.39368	+	5.20129i	−0.0471960	+	0.176138i
$873$	63.1343	−	16.9168i	2.13677	−	0.572546i
$874$	36.4100	+	36.4100i	1.23158	+	1.23158i
$875$	2.55278	−	2.27656i	0.0862997	−	0.0769619i
$876$	−27.1933	+	27.1933i	−0.918776	+	0.918776i
$877$	−8.92696	+	15.4619i	−0.301442	+	0.522113i	−0.976463	−	0.215686i	$-0.930801\pi$
$877$	−8.92696	+	15.4619i	−0.301442	+	0.522113i	0.675021	+	0.737799i	$0.264135\pi$
$878$	39.6477	+	10.6236i	1.33805	+	0.358528i
$879$	30.4789	+	52.7910i	1.02803	+	1.78060i
$880$	−0.0442458	−	0.165127i	−0.00149152	−	0.00556644i
$881$		−	33.7904i		−	1.13843i	−0.822190	−	0.569214i	$-0.807248\pi$
$881$		−	33.7904i		−	1.13843i	0.822190	−	0.569214i	$-0.192752\pi$
$882$	50.9202	−	22.0911i	1.71457	−	0.743847i
$883$	4.80123	−	4.80123i	0.161574	−	0.161574i	−0.621690	−	0.783264i	$-0.713553\pi$
$883$	4.80123	−	4.80123i	0.161574	−	0.161574i	0.783264	+	0.621690i	$0.213553\pi$
$884$	1.55150	−	2.68727i	0.0521825	−	0.0903828i
$885$	−4.64541	−	1.24473i	−0.156154	−	0.0418412i
$886$	5.27862	+	9.14284i	0.177339	+	0.307160i
$887$	−4.67109	−	17.4327i	−0.156840	−	0.585334i	−0.998941	−	0.0460144i	$-0.985348\pi$
$887$	−4.67109	−	17.4327i	−0.156840	−	0.585334i	0.842101	−	0.539320i	$-0.181319\pi$
$888$	5.55291	−	5.55291i	0.186343	−	0.186343i
$889$	−1.08073	−	1.21186i	−0.0362466	−	0.0406444i
$890$	1.01678	+	1.01678i	0.0340826	+	0.0340826i
$891$	−38.3652	+	10.2799i	−1.28528	+	0.344390i
$892$	−6.38576	−	11.0605i	−0.213811	−	0.370332i
$893$	−70.7930	+	40.8723i	−2.36900	+	1.36774i
$894$	−13.5537	−	7.82526i	−0.453305	−	0.261716i
$895$	−0.157708	−	0.157708i	−0.00527160	−	0.00527160i
$896$	−0.537724	−	2.59053i	−0.0179641	−	0.0865436i
$897$		−	36.7728i		−	1.22781i
$898$	5.93225	−	10.2750i	0.197962	−	0.342880i
$899$	1.47601	−	5.50855i	0.0492277	−	0.183720i
$900$	−34.2201	+	19.7570i	−1.14067	+	0.658567i
$901$	−5.47428	+	9.48174i	−0.182375	+	0.315882i
$902$	−2.96567	+	7.91556i	−0.0987458	+	0.263559i
$903$	19.1813	+	38.0939i	0.638314	+	1.26769i
$904$		−	4.48404i		−	0.149137i
$905$	0.878143	−	0.235298i	0.0291905	−	0.00782156i
$906$	37.1368	+	64.3229i	1.23379	+	2.13698i
$907$	−48.8436	+	28.1999i	−1.62183	+	0.936362i	−0.635395	+	0.772187i	$0.719163\pi$
$907$	−48.8436	+	28.1999i	−1.62183	+	0.936362i	−0.986431	+	0.164175i	$0.947504\pi$
$908$	4.23582	+	15.8083i	0.140571	+	0.524617i
$909$	97.9631	+	97.9631i	3.24923	+	3.24923i
$910$	0.558684	−	0.281313i	0.0185202	−	0.00932543i
$911$			20.7687i			0.688098i	0.938952	+	0.344049i	$0.111799\pi$
$911$			20.7687i			0.688098i	−0.938952	+	0.344049i	$0.888201\pi$
$912$	13.9701	−	24.1969i	0.462595	−	0.801238i
$913$	0.942955	−	3.51916i	0.0312073	−	0.116467i
$914$	8.52509	−	31.8161i	0.281985	−	1.05238i
$915$	−0.530093	+	0.142038i	−0.0175243	+	0.00469563i
$916$	15.7368	−	15.7368i	0.519957	−	0.519957i
$917$	11.8338	+	57.0103i	0.390786	+	1.88265i
$918$	27.6980			0.914170
$919$	1.98811	+	7.41974i	0.0655818	+	0.244755i	0.990933	−	0.134356i	$-0.0428966\pi$
$919$	1.98811	+	7.41974i	0.0655818	+	0.244755i	−0.925351	+	0.379111i	$0.876230\pi$
$920$	0.394491	+	0.683278i	0.0130060	+	0.0225270i
$921$	−35.6246	−	9.54557i	−1.17387	−	0.314537i
$922$	−12.6568	−	7.30743i	−0.416831	−	0.240657i
$923$		−	8.84115i		−	0.291010i
$924$	8.61769	−	7.68524i	0.283501	−	0.252826i
$925$	11.8372			0.389204
$926$	1.18339	+	4.41649i	0.0388888	+	0.145135i
$927$	−24.1049	−	41.7509i	−0.791709	−	1.37128i
$928$	−0.761190	−	0.203960i	−0.0249873	−	0.00669533i
$929$	2.26587	+	8.45633i	0.0743407	+	0.277443i	0.993083	−	0.117414i	$-0.0374606\pi$
$929$	2.26587	+	8.45633i	0.0743407	+	0.277443i	−0.918742	+	0.394858i	$0.870794\pi$
$930$	2.19073	+	2.19073i	0.0718369	+	0.0718369i
$931$	−58.5174	+	8.69644i	−1.91783	+	0.285014i
$932$	−7.35487	−	7.35487i	−0.240917	−	0.240917i
$933$	−11.6344	+	20.1514i	−0.380894	+	0.659727i
$934$	14.2188	−	8.20925i	0.465255	−	0.268615i
$935$	−0.251630	+	0.145279i	−0.00822919	+	0.00475113i
$936$	−13.9832	+	3.74680i	−0.457057	+	0.122468i
$937$	22.4543	−	22.4543i	0.733549	−	0.733549i	−0.237772	−	0.971321i	$-0.576417\pi$
$937$	22.4543	−	22.4543i	0.733549	−	0.733549i	0.971321	+	0.237772i	$0.0764170\pi$
$938$	0.886723	−	15.5034i	0.0289525	−	0.506204i
$939$	3.30137			0.107736
$940$	−1.20986	+	0.324181i	−0.0394613	+	0.0105736i
$941$	−38.1423	+	22.0215i	−1.24341	+	0.717880i	−0.969786	−	0.243958i	$-0.921554\pi$
$941$	−38.1423	+	22.0215i	−1.24341	+	0.717880i	−0.273619	+	0.961838i	$0.588221\pi$
$942$	−16.5581	−	28.6794i	−0.539490	−	0.934425i
$943$	3.76562	−	38.8297i	0.122625	−	1.26447i
$944$	−11.2336			−0.365623
$945$	4.66811	+	3.06328i	0.151854	+	0.0996486i
$946$	4.55172	+	4.55172i	0.147989	+	0.147989i
$947$	8.58047	−	14.8618i	0.278828	−	0.482944i	−0.692266	−	0.721643i	$-0.743387\pi$
$947$	8.58047	−	14.8618i	0.278828	−	0.482944i	0.971094	+	0.238699i	$0.0767208\pi$
$948$	29.4727	−	17.0161i	0.957230	−	0.552657i
$949$	−20.5138	−	5.49667i	−0.665907	−	0.178429i
$950$	40.6804	−	10.9003i	1.31985	−	0.353652i
$951$			96.6121i			3.13286i
$952$	−4.01640	+	2.02237i	−0.130172	+	0.0655453i
$953$	−20.3450			−0.659038			−0.329519	−	0.944149i	$-0.606887\pi$
$953$	−20.3450			−0.659038			−0.329519	+	0.944149i	$0.606887\pi$
$954$	49.3383	−	13.2202i	1.59739	−	0.428018i
$955$	0.535556	−	1.99872i	0.0173302	−	0.0646771i
$956$	−4.28595	+	15.9954i	−0.138618	+	0.517328i
$957$	−0.890137	−	3.32204i	−0.0287740	−	0.107386i
$958$	−8.80600	+	8.80600i	−0.284509	+	0.284509i
$959$	14.0788	+	27.9603i	0.454628	+	0.902885i
$960$	0.302723	−	0.302723i	0.00977034	−	0.00977034i
$961$	−10.6853	+	18.5075i	−0.344687	+	0.597016i
$962$	4.18895	+	1.12243i	0.135057	+	0.0361885i
$963$	−6.43975	+	3.71799i	−0.207518	+	0.119811i
$964$	11.5569	+	6.67236i	0.372221	+	0.214902i
$965$	0.316698	−	0.316698i	0.0101949	−	0.0101949i
$966$	−29.2372	+	44.5543i	−0.940692	+	1.43351i
$967$	21.6636	−	21.6636i	0.696653	−	0.696653i	−0.267034	−	0.963687i	$-0.586044\pi$
$967$	21.6636	−	21.6636i	0.696653	−	0.696653i	0.963687	+	0.267034i	$0.0860436\pi$
$968$	−4.62864	+	8.01705i	−0.148770	+	0.257678i
$969$	−45.8701	−	12.2908i	−1.47356	−	0.394839i
$970$	−1.03107	−	0.276274i	−0.0331056	−	0.00887062i
$971$	−31.1715	+	8.35239i	−1.00034	+	0.268041i	−0.721589	−	0.692322i	$-0.756588\pi$
$971$	−31.1715	+	8.35239i	−1.00034	+	0.268041i	−0.278753	+	0.960363i	$0.589921\pi$
$972$	−35.7638	−	35.7638i	−1.14712	−	1.14712i
$973$	3.49902	+	3.92356i	0.112174	+	0.125784i
$974$	0.513172			0.0164431
$975$	−26.0474	−	15.0385i	−0.834183	−	0.481616i
$976$	−1.11014	+	0.640940i	−0.0355348	+	0.0205160i
$977$	−12.0191	+	44.8560i	−0.384526	+	1.43507i	0.454386	+	0.890805i	$0.349859\pi$
$977$	−12.0191	+	44.8560i	−0.384526	+	1.43507i	−0.838912	+	0.544267i	$0.816808\pi$
$978$	13.3023	+	49.6447i	0.425359	+	1.58746i
$979$			14.6586i			0.468492i
$980$	−0.900573	−	0.103355i	−0.0287678	−	0.00330157i
$981$	−30.1920	−	30.1920i	−0.963958	−	0.963958i
$982$	35.2869	+	20.3729i	1.12605	+	0.650125i
$983$	−25.9546	−	44.9546i	−0.827822	−	1.43383i	−0.899743	−	0.436419i	$-0.856246\pi$
$983$	−25.9546	−	44.9546i	−0.827822	−	1.43383i	0.0719213	−	0.997410i	$-0.477087\pi$
$984$	−20.8806	+	3.47956i	−0.665648	+	0.110924i
$985$	−0.314942	+	0.545495i	−0.0100349	+	0.0173809i
$986$			1.33939i			0.0426548i
$987$	−56.3085	−	63.1404i	−1.79232	−	2.00978i
$988$	15.4296			0.490881
$989$	−25.7284	−	14.8543i	−0.818115	−	0.472339i
$990$	1.30936	+	0.350842i	0.0416142	+	0.0111505i
$991$	1.07994	−	4.03041i	0.0343056	−	0.128030i	−0.946649	−	0.322265i	$-0.895556\pi$
$991$	1.07994	−	4.03041i	0.0343056	−	0.128030i	0.980955	+	0.194235i	$0.0622224\pi$
$992$	6.26721	+	3.61838i	0.198984	+	0.114884i
$993$			26.3205i			0.835257i
$994$	−7.02940	+	10.7120i	−0.222959	+	0.339765i
$995$	−1.81563	−	1.81563i	−0.0575592	−	0.0575592i
$996$	8.81299	−	2.36143i	0.279250	−	0.0748249i
$997$	−1.39743	+	5.21527i	−0.0442570	+	0.165169i	−0.984517	−	0.175287i	$-0.943915\pi$
$997$	−1.39743	+	5.21527i	−0.0442570	+	0.165169i	0.940260	+	0.340456i	$0.110581\pi$
$998$	−25.0606	−	6.71498i	−0.793280	−	0.212559i
$999$	10.0190	+	37.3915i	0.316988	+	1.18301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.r.c.9.1	✓	40
7.4	even	3	inner	574.2.r.c.501.10	yes	40
41.32	even	4	inner	574.2.r.c.401.10	yes	40
287.32	even	12	inner	574.2.r.c.319.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.r.c.9.1	✓	40	1.1	even	1	trivial
574.2.r.c.319.1	yes	40	287.32	even	12	inner
574.2.r.c.401.10	yes	40	41.32	even	4	inner
574.2.r.c.501.10	yes	40	7.4	even	3	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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.855646 + 3.19332i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.112148 + 0.0647489i) q^{5} +(-2.33767 + 2.33767i) q^{6} +(1.76095 + 1.97460i) q^{7} +1.00000i q^{8} +(-6.86706 - 3.96470i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.855646 + 3.19332i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.112148 + 0.0647489i) q^{5} +(-2.33767 + 2.33767i) q^{6} +(1.76095 + 1.97460i) q^{7} +1.00000i q^{8} +(-6.86706 - 3.96470i) q^{9} +(0.0647489 + 0.112148i) q^{10} +(-0.341672 + 1.27514i) q^{11} +(-3.19332 + 0.855646i) q^{12} +(-1.29095 - 1.29095i) q^{13} +(0.537724 + 2.59053i) q^{14} +(-0.302723 + 0.302723i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.64173 + 0.439899i) q^{17} +(-3.96470 - 6.86706i) q^{18} +(2.18739 + 8.16346i) q^{19} +0.129498i q^{20} +(-7.81228 + 3.93370i) q^{21} +(-0.933465 + 0.933465i) q^{22} +(3.04631 - 5.27637i) q^{23} +(-3.19332 - 0.855646i) q^{24} +(-2.49162 - 4.31560i) q^{25} +(-0.472520 - 1.76347i) q^{26} +(11.5233 - 11.5233i) q^{27} +(-0.829584 + 2.51233i) q^{28} +(0.557230 + 0.557230i) q^{29} +(-0.413527 + 0.110804i) q^{30} +(-3.61838 - 6.26721i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.77956 - 2.18213i) q^{33} +(1.20183 + 1.20183i) q^{34} +(0.0696340 + 0.335468i) q^{35} -7.92939i q^{36} +(-1.18770 + 2.05716i) q^{37} +(-2.18739 + 8.16346i) q^{38} +(5.22700 - 3.01781i) q^{39} +(-0.0647489 + 0.112148i) q^{40} +(5.82841 - 2.65136i) q^{41} +(-8.73248 - 0.499458i) q^{42} -4.87615i q^{43} +(-1.27514 + 0.341672i) q^{44} +(-0.513419 - 0.889269i) q^{45} +(5.27637 - 3.04631i) q^{46} +(2.50337 + 9.34271i) q^{47} +(-2.33767 - 2.33767i) q^{48} +(-0.798124 + 6.95435i) q^{49} -4.98323i q^{50} +(-2.80947 + 4.86615i) q^{51} +(0.472520 - 1.76347i) q^{52} +(-1.66723 + 6.22220i) q^{53} +(15.7411 - 4.21782i) q^{54} +(-0.120882 + 0.120882i) q^{55} +(-1.97460 + 1.76095i) q^{56} -27.9401 q^{57} +(0.203960 + 0.761190i) q^{58} +(5.61681 + 9.72859i) q^{59} +(-0.413527 - 0.110804i) q^{60} +(1.11014 + 0.640940i) q^{61} -7.23675i q^{62} +(-4.26382 - 20.5413i) q^{63} -1.00000 q^{64} +(-0.0611903 - 0.228365i) q^{65} +(-2.18213 - 3.77956i) q^{66} +(-5.66932 - 1.51909i) q^{67} +(0.439899 + 1.64173i) q^{68} +(14.2425 + 14.2425i) q^{69} +(-0.107429 + 0.325341i) q^{70} +(3.42428 + 3.42428i) q^{71} +(3.96470 - 6.86706i) q^{72} +(10.0742 - 5.81633i) q^{73} +(-2.05716 + 1.18770i) q^{74} +(15.9130 - 4.26388i) q^{75} +(-5.97607 + 5.97607i) q^{76} +(-3.11956 + 1.57078i) q^{77} +6.03562 q^{78} +(-9.94342 + 2.66433i) q^{79} +(-0.112148 + 0.0647489i) q^{80} +(15.0435 + 26.0562i) q^{81} +(6.37323 + 0.618062i) q^{82} -2.75983 q^{83} +(-7.31282 - 4.79879i) q^{84} +(0.155634 + 0.155634i) q^{85} +(2.43808 - 4.22287i) q^{86} +(-2.25620 + 1.30262i) q^{87} +(-1.27514 - 0.341672i) q^{88} +(10.7257 - 2.87393i) q^{89} -1.02684i q^{90} +(0.275819 - 4.82241i) q^{91} +6.09263 q^{92} +(23.1092 - 6.19210i) q^{93} +(-2.50337 + 9.34271i) q^{94} +(-0.283263 + 1.05715i) q^{95} +(-0.855646 - 3.19332i) q^{96} +(-5.82863 + 5.82863i) q^{97} +(-4.16837 + 5.62358i) q^{98} +(7.40181 - 7.40181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7	\( 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7} + 12 q^{10} - 4 q^{12} - 28 q^{13} + 12 q^{14} + 20 q^{15} - 20 q^{16} + 14 q^{17} - 16 q^{18} + 24 q^{23} - 4 q^{24} - 20 q^{25} + 14 q^{26} + 4 q^{27} + 44 q^{29} + 10 q^{30} - 8 q^{31} + 28 q^{34} - 2 q^{35} - 16 q^{37} - 12 q^{40} + 4 q^{41} - 64 q^{42} - 36 q^{45} + 2 q^{47} - 8 q^{48} + 28 q^{51} - 14 q^{52} + 20 q^{53} + 2 q^{54} - 44 q^{55} + 12 q^{56} - 40 q^{57} - 22 q^{58} - 8 q^{59} + 10 q^{60} + 24 q^{63} - 40 q^{64} + 36 q^{65} - 48 q^{66} + 6 q^{67} - 14 q^{68} - 36 q^{69} + 8 q^{70} + 40 q^{71} + 16 q^{72} + 36 q^{75} - 26 q^{79} + 84 q^{81} - 22 q^{82} - 24 q^{83} + 164 q^{85} - 28 q^{86} + 16 q^{89} + 48 q^{92} + 46 q^{93} - 2 q^{94} - 18 q^{95} + 4 q^{96} + 8 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7 + 12 * q^10 - 4 * q^12 - 28 * q^13 + 12 * q^14 + 20 * q^15 - 20 * q^16 + 14 * q^17 - 16 * q^18 + 24 * q^23 - 4 * q^24 - 20 * q^25 + 14 * q^26 + 4 * q^27 + 44 * q^29 + 10 * q^30 - 8 * q^31 + 28 * q^34 - 2 * q^35 - 16 * q^37 - 12 * q^40 + 4 * q^41 - 64 * q^42 - 36 * q^45 + 2 * q^47 - 8 * q^48 + 28 * q^51 - 14 * q^52 + 20 * q^53 + 2 * q^54 - 44 * q^55 + 12 * q^56 - 40 * q^57 - 22 * q^58 - 8 * q^59 + 10 * q^60 + 24 * q^63 - 40 * q^64 + 36 * q^65 - 48 * q^66 + 6 * q^67 - 14 * q^68 - 36 * q^69 + 8 * q^70 + 40 * q^71 + 16 * q^72 + 36 * q^75 - 26 * q^79 + 84 * q^81 - 22 * q^82 - 24 * q^83 + 164 * q^85 - 28 * q^86 + 16 * q^89 + 48 * q^92 + 46 * q^93 - 2 * q^94 - 18 * q^95 + 4 * q^96 + 8 * q^97 + 24 * q^98 - 12 * q^99

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