LMFDB - Embedded newform 950.2.bb.e.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.1
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.e.857.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.243772 + 2.78632i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.14260 - 1.79785i) q^{6} +(0.966713 + 3.60782i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-4.74974 - 0.837508i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.243772 + 2.78632i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.14260 - 1.79785i) q^{6} +(0.966713 + 3.60782i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-4.74974 - 0.837508i) q^{9} +(2.60674 + 4.51500i) q^{11} +(2.70166 - 0.723908i) q^{12} +(-3.16293 + 0.276720i) q^{13} +(-3.50984 - 1.27748i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(3.38023 + 2.36686i) q^{17} +(3.41039 - 3.41039i) q^{18} +(4.33423 - 0.463042i) q^{19} +(-10.2882 + 1.81409i) q^{21} +(-5.19364 - 0.454385i) q^{22} +(-1.35927 - 0.633838i) q^{23} +(-0.956619 + 2.62829i) q^{24} +(1.58751 - 2.74964i) q^{26} +(1.31970 - 4.92518i) q^{27} +(3.05961 - 2.14236i) q^{28} +(0.0615751 - 0.349210i) q^{29} +(1.91258 + 1.10423i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-13.2157 + 6.16259i) q^{33} +(-3.87764 + 1.41135i) q^{34} +(0.837508 + 4.74974i) q^{36} +(-5.12376 - 5.12376i) q^{37} +(-2.10671 + 3.81599i) q^{38} -8.88040i q^{39} +(1.86254 + 2.21969i) q^{41} +(4.41506 - 9.46813i) q^{42} +(3.58104 + 7.67957i) q^{43} +(3.35116 - 3.99376i) q^{44} +(1.29886 - 0.749894i) q^{46} +(-6.31034 - 9.01210i) q^{47} +(-1.60427 - 2.29114i) q^{48} +(-6.01967 + 3.47546i) q^{49} +(-7.41885 + 8.84144i) q^{51} +(1.34182 + 2.87754i) q^{52} +(3.88318 - 8.32751i) q^{53} +(3.27752 + 3.90600i) q^{54} +3.73509i q^{56} +(0.233620 + 12.1895i) q^{57} +(0.250738 + 0.250738i) q^{58} +(-0.395008 - 2.24020i) q^{59} +(-3.76709 + 1.37111i) q^{61} +(-2.00154 + 0.933333i) q^{62} +(-1.57006 - 17.9459i) q^{63} +(0.866025 + 0.500000i) q^{64} +(2.53212 - 14.3604i) q^{66} +(10.6670 - 7.46911i) q^{67} +(1.06802 - 3.98589i) q^{68} +(2.09743 - 3.63285i) q^{69} +(2.49378 - 6.85160i) q^{71} +(-4.37114 - 2.03830i) q^{72} +(3.50795 + 0.306906i) q^{73} +(7.13601 - 1.25827i) q^{74} +(-1.91751 - 3.91448i) q^{76} +(-13.7694 + 13.7694i) q^{77} +(7.27439 + 5.09359i) q^{78} +(-0.936891 + 0.786145i) q^{79} +(-0.195039 - 0.0709885i) q^{81} +(-2.88657 + 0.252542i) q^{82} +(0.954892 - 0.255862i) q^{83} +(5.22346 + 9.04730i) q^{84} +(-8.34474 - 1.47140i) q^{86} +(0.958000 + 0.256695i) q^{87} +(1.34935 + 5.03583i) q^{88} +(-2.19759 - 1.84399i) q^{89} +(-4.05600 - 11.1438i) q^{91} +(-0.130715 + 1.49408i) q^{92} +(-3.54296 + 5.05988i) q^{93} +11.0017 q^{94} +2.79697 q^{96} +(9.93194 - 14.1843i) q^{97} +(0.605812 - 6.92446i) q^{98} +(-8.59999 - 23.6283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$	−0.243772	+	2.78632i	−0.140742	+	1.60868i	0.517369	+	0.855763i	$0.326912\pi$
$3$	−0.243772	+	2.78632i	−0.140742	+	1.60868i	−0.658110	+	0.752921i	$0.728644\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	−2.14260	−	1.79785i	−0.874713	−	0.733971i
$7$	0.966713	+	3.60782i	0.365383	+	1.36363i	0.866901	+	0.498481i	$0.166109\pi$
$7$	0.966713	+	3.60782i	0.365383	+	1.36363i	−0.501518	+	0.865147i	$0.667225\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−4.74974	−	0.837508i	−1.58325	−	0.279169i
$10$		0			0
$11$	2.60674	+	4.51500i	0.785961	+	1.36133i	0.928423	+	0.371525i	$0.121165\pi$
$11$	2.60674	+	4.51500i	0.785961	+	1.36133i	−0.142462	+	0.989800i	$0.545502\pi$
$12$	2.70166	−	0.723908i	0.779902	−	0.208974i
$13$	−3.16293	+	0.276720i	−0.877239	+	0.0767484i	−0.516872	−	0.856062i	$-0.672904\pi$
$13$	−3.16293	+	0.276720i	−0.877239	+	0.0767484i	−0.360366	+	0.932811i	$0.617348\pi$
$14$	−3.50984	−	1.27748i	−0.938044	−	0.341420i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	3.38023	+	2.36686i	0.819826	+	0.574049i	0.906509	−	0.422187i	$-0.138738\pi$
$17$	3.38023	+	2.36686i	0.819826	+	0.574049i	−0.0866822	+	0.996236i	$0.527626\pi$
$18$	3.41039	−	3.41039i	0.803836	−	0.803836i
$19$	4.33423	−	0.463042i	0.994342	−	0.106229i
$19$	4.33423	−	0.463042i	0.994342	−	0.106229i
$20$		0			0
$21$	−10.2882	+	1.81409i	−2.24507	+	0.395867i
$22$	−5.19364	−	0.454385i	−1.10729	−	0.0968751i
$23$	−1.35927	−	0.633838i	−0.283427	−	0.132164i	0.275706	−	0.961242i	$-0.411088\pi$
$23$	−1.35927	−	0.633838i	−0.283427	−	0.132164i	−0.559134	+	0.829078i	$0.688866\pi$
$24$	−0.956619	+	2.62829i	−0.195269	+	0.536497i
$25$		0			0
$26$	1.58751	−	2.74964i	0.311335	−	0.539249i
$27$	1.31970	−	4.92518i	0.253976	−	0.947850i
$28$	3.05961	−	2.14236i	0.578212	−	0.404868i
$29$	0.0615751	−	0.349210i	0.0114342	−	0.0648466i	−0.978557	−	0.205977i	$-0.933963\pi$
$29$	0.0615751	−	0.349210i	0.0114342	−	0.0648466i	0.989991	+	0.141131i	$0.0450738\pi$
$30$		0			0
$31$	1.91258	+	1.10423i	0.343509	+	0.198325i	0.661823	−	0.749660i	$-0.269783\pi$
$31$	1.91258	+	1.10423i	0.343509	+	0.198325i	−0.318314	+	0.947985i	$0.603117\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$	−13.2157	+	6.16259i	−2.30056	+	1.07277i
$34$	−3.87764	+	1.41135i	−0.665010	+	0.242044i
$35$		0			0
$36$	0.837508	+	4.74974i	0.139585	+	0.791624i
$37$	−5.12376	−	5.12376i	−0.842342	−	0.842342i	0.146821	−	0.989163i	$-0.453096\pi$
$37$	−5.12376	−	5.12376i	−0.842342	−	0.842342i	−0.989163	+	0.146821i	$0.953096\pi$
$38$	−2.10671	+	3.81599i	−0.341754	+	0.619035i
$39$		−	8.88040i		−	1.42200i
$40$		0			0
$41$	1.86254	+	2.21969i	0.290880	+	0.346657i	0.891618	−	0.452789i	$-0.149571\pi$
$41$	1.86254	+	2.21969i	0.290880	+	0.346657i	−0.600738	+	0.799446i	$0.705127\pi$
$42$	4.41506	−	9.46813i	0.681259	−	1.46096i
$43$	3.58104	+	7.67957i	0.546104	+	1.17112i	0.964797	+	0.262996i	$0.0847107\pi$
$43$	3.58104	+	7.67957i	0.546104	+	1.17112i	−0.418693	+	0.908128i	$0.637512\pi$
$44$	3.35116	−	3.99376i	0.505206	−	0.602081i
$45$		0			0
$46$	1.29886	−	0.749894i	0.191506	−	0.110566i
$47$	−6.31034	−	9.01210i	−0.920458	−	1.31455i	−0.949105	−	0.314961i	$-0.898009\pi$
$47$	−6.31034	−	9.01210i	−0.920458	−	1.31455i	0.0286468	−	0.999590i	$-0.490880\pi$
$48$	−1.60427	−	2.29114i	−0.231557	−	0.330698i
$49$	−6.01967	+	3.47546i	−0.859952	+	0.496494i
$50$		0			0
$51$	−7.41885	+	8.84144i	−1.03885	+	1.23805i
$52$	1.34182	+	2.87754i	0.186077	+	0.399043i
$53$	3.88318	−	8.32751i	0.533396	−	1.14387i	−0.436355	−	0.899775i	$-0.643731\pi$
$53$	3.88318	−	8.32751i	0.533396	−	1.14387i	0.969751	−	0.244097i	$-0.0784914\pi$
$54$	3.27752	+	3.90600i	0.446014	+	0.531539i
$55$		0			0
$56$			3.73509i			0.499123i
$57$	0.233620	+	12.1895i	0.0309438	+	1.61453i
$58$	0.250738	+	0.250738i	0.0329235	+	0.0329235i
$59$	−0.395008	−	2.24020i	−0.0514257	−	0.291650i	0.948239	−	0.317559i	$-0.102863\pi$
$59$	−0.395008	−	2.24020i	−0.0514257	−	0.291650i	−0.999664	+	0.0259091i	$0.991752\pi$
$60$		0			0
$61$	−3.76709	+	1.37111i	−0.482326	+	0.175552i	−0.571728	−	0.820443i	$-0.693727\pi$
$61$	−3.76709	+	1.37111i	−0.482326	+	0.175552i	0.0894019	+	0.995996i	$0.471504\pi$
$62$	−2.00154	+	0.933333i	−0.254196	+	0.118533i
$63$	−1.57006	−	17.9459i	−0.197809	−	2.26097i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	2.53212	−	14.3604i	0.311683	−	1.76764i
$67$	10.6670	−	7.46911i	1.30318	−	0.912498i	0.303989	−	0.952676i	$-0.401681\pi$
$67$	10.6670	−	7.46911i	1.30318	−	0.912498i	0.999193	+	0.0401779i	$0.0127925\pi$
$68$	1.06802	−	3.98589i	0.129516	−	0.483360i
$69$	2.09743	−	3.63285i	0.252501	−	0.437344i
$70$		0			0
$71$	2.49378	−	6.85160i	0.295957	−	0.813135i	−0.699208	−	0.714918i	$-0.746464\pi$
$71$	2.49378	−	6.85160i	0.295957	−	0.813135i	0.995165	−	0.0982170i	$-0.0313139\pi$
$72$	−4.37114	−	2.03830i	−0.515144	−	0.240215i
$73$	3.50795	+	0.306906i	0.410574	+	0.0359206i	0.290572	−	0.956853i	$-0.406154\pi$
$73$	3.50795	+	0.306906i	0.410574	+	0.0359206i	0.120002	+	0.992774i	$0.461710\pi$
$74$	7.13601	−	1.25827i	0.829545	−	0.146271i
$75$		0			0
$76$	−1.91751	−	3.91448i	−0.219954	−	0.449022i
$77$	−13.7694	+	13.7694i	−1.56916	+	1.56916i
$78$	7.27439	+	5.09359i	0.823663	+	0.576735i
$79$	−0.936891	+	0.786145i	−0.105409	+	0.0884482i	−0.693969	−	0.720005i	$-0.744139\pi$
$79$	−0.936891	+	0.786145i	−0.105409	+	0.0884482i	0.588560	+	0.808453i	$0.299695\pi$
$80$		0			0
$81$	−0.195039	−	0.0709885i	−0.0216710	−	0.00788761i
$82$	−2.88657	+	0.252542i	−0.318768	+	0.0278886i
$83$	0.954892	−	0.255862i	0.104813	−	0.0280846i	−0.206031	−	0.978545i	$-0.566055\pi$
$83$	0.954892	−	0.255862i	0.104813	−	0.0280846i	0.310844	+	0.950461i	$0.399388\pi$
$84$	5.22346	+	9.04730i	0.569926	+	0.987141i
$85$		0			0
$86$	−8.34474	−	1.47140i	−0.899837	−	0.158665i
$87$	0.958000	+	0.256695i	0.102708	+	0.0275206i
$88$	1.34935	+	5.03583i	0.143841	+	0.536822i
$89$	−2.19759	−	1.84399i	−0.232944	−	0.195463i	0.518843	−	0.854870i	$-0.326363\pi$
$89$	−2.19759	−	1.84399i	−0.232944	−	0.195463i	−0.751786	+	0.659407i	$0.770808\pi$
$90$		0			0
$91$	−4.05600	−	11.1438i	−0.425185	−	1.16818i
$92$	−0.130715	+	1.49408i	−0.0136280	+	0.155769i
$93$	−3.54296	+	5.05988i	−0.367388	+	0.524685i
$94$	11.0017			1.13474
$95$		0			0
$96$	2.79697			0.285464
$97$	9.93194	−	14.1843i	1.00844	−	1.44019i	0.113744	−	0.993510i	$-0.463716\pi$
$97$	9.93194	−	14.1843i	1.00844	−	1.44019i	0.894691	−	0.446685i	$-0.147395\pi$
$98$	0.605812	−	6.92446i	0.0611962	−	0.699476i
$99$	−8.59999	−	23.6283i	−0.864332	−	2.37473i
$100$		0			0
$101$	2.27553	+	1.90939i	0.226424	+	0.189992i	0.748941	−	0.662637i	$-0.230563\pi$
$101$	2.27553	+	1.90939i	0.226424	+	0.189992i	−0.522517	+	0.852629i	$0.675007\pi$
$102$	−2.98721	−	11.1484i	−0.295777	−	1.10386i
$103$	−1.72839	−	0.463120i	−0.170303	−	0.0456326i	0.172660	−	0.984982i	$-0.444764\pi$
$103$	−1.72839	−	0.463120i	−0.170303	−	0.0456326i	−0.342963	+	0.939349i	$0.611431\pi$
$104$	−3.12678	−	0.551335i	−0.306606	−	0.0540628i
$105$		0			0
$106$	4.59419	+	7.95738i	0.446228	+	0.772889i
$107$	3.48647	−	0.934197i	0.337050	−	0.0903122i	−0.0863245	−	0.996267i	$-0.527512\pi$
$107$	3.48647	−	0.934197i	0.337050	−	0.0903122i	0.423374	+	0.905955i	$0.360846\pi$
$108$	−5.07951	+	0.444400i	−0.488776	+	0.0427624i
$109$	1.27157	+	0.462814i	0.121794	+	0.0443295i	0.402198	−	0.915553i	$-0.368246\pi$
$109$	1.27157	+	0.462814i	0.121794	+	0.0443295i	−0.280404	+	0.959882i	$0.590468\pi$
$110$		0			0
$111$	15.5255	−	13.0274i	1.47361	−	1.23651i
$112$	−3.05961	−	2.14236i	−0.289106	−	0.202434i
$113$	7.99572	−	7.99572i	0.752174	−	0.752174i	−0.222710	−	0.974885i	$-0.571490\pi$
$113$	7.99572	−	7.99572i	0.752174	−	0.752174i	0.974885	+	0.222710i	$0.0714904\pi$
$114$	−10.1190	−	6.80021i	−0.947732	−	0.636898i
$115$		0			0
$116$	−0.349210	+	0.0615751i	−0.0324233	+	0.00571710i
$117$	15.2549	+	1.33463i	1.41031	+	0.123386i
$118$	2.06163	+	0.961356i	0.189789	+	0.0885000i
$119$	−5.27151	+	14.4833i	−0.483238	+	1.32769i
$120$		0			0
$121$	−8.09018	+	14.0126i	−0.735471	+	1.27387i
$122$	1.03757	−	3.87225i	0.0939369	−	0.350577i
$123$	−6.63879	+	4.64853i	−0.598600	+	0.419144i
$124$	0.383494	−	2.17490i	0.0344388	−	0.195312i
$125$		0			0
$126$	15.6009	+	9.00721i	1.38984	+	0.802426i
$127$	1.44842	+	16.5555i	0.128527	+	1.46907i	0.737215	+	0.675658i	$0.236140\pi$
$127$	1.44842	+	16.5555i	0.128527	+	1.46907i	−0.608688	+	0.793409i	$0.708304\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	−22.2707	+	8.10588i	−1.96083	+	0.713683i
$130$		0			0
$131$	−1.10162	−	6.24758i	−0.0962487	−	0.545854i	−0.994358	−	0.106080i	$-0.966170\pi$
$131$	−1.10162	−	6.24758i	−0.0962487	−	0.545854i	0.898109	−	0.439773i	$-0.144941\pi$
$132$	10.3110	+	10.3110i	0.897455	+	0.897455i
$133$	5.86053	+	15.1895i	0.508173	+	1.31710i
$134$			13.0220i			1.12493i
$135$		0			0
$136$	2.65246	+	3.16108i	0.227447	+	0.271061i
$137$	−2.79288	+	5.98935i	−0.238612	+	0.511704i	−0.988750	−	0.149576i	$-0.952209\pi$
$137$	−2.79288	+	5.98935i	−0.238612	+	0.511704i	0.750138	+	0.661281i	$0.229987\pi$
$138$	1.77282	+	3.80183i	0.150913	+	0.323633i
$139$	−2.34938	+	2.79989i	−0.199272	+	0.237483i	−0.856422	−	0.516277i	$-0.827318\pi$
$139$	−2.34938	+	2.79989i	−0.199272	+	0.237483i	0.657150	+	0.753760i	$0.271762\pi$
$140$		0			0
$141$	26.6489	−	15.3858i	2.24424	−	1.29571i
$142$	4.18213	+	5.97270i	0.350957	+	0.501218i
$143$	−9.49432	−	13.5593i	−0.793955	−	1.13389i
$144$	4.17686	−	2.41151i	0.348071	−	0.200959i
$145$		0			0
$146$	−2.26348	+	2.69751i	−0.187327	+	0.223248i
$147$	−8.21632	−	17.6199i	−0.677670	−	1.45327i
$148$	−3.06233	+	6.56719i	−0.251722	+	0.539820i
$149$	0.816989	+	0.973650i	0.0669303	+	0.0797645i	0.798471	−	0.602034i	$-0.205643\pi$
$149$	0.816989	+	0.973650i	0.0669303	+	0.0797645i	−0.731540	+	0.681798i	$0.761198\pi$
$150$		0			0
$151$			16.9234i			1.37721i	0.725137	+	0.688604i	$0.241776\pi$
$151$			16.9234i			1.37721i	−0.725137	+	0.688604i	$0.758224\pi$
$152$	4.30639	+	0.674519i	0.349295	+	0.0547107i
$153$	−14.0730	−	14.0730i	−1.13773	−	1.13773i
$154$	−3.38142	−	19.1770i	−0.272483	−	1.54533i
$155$		0			0
$156$	−8.34484	+	3.03727i	−0.668122	+	0.243177i
$157$	−12.0779	+	5.63201i	−0.963920	+	0.449483i	−0.839867	−	0.542792i	$-0.817367\pi$
$157$	−12.0779	+	5.63201i	−0.963920	+	0.449483i	−0.124053	+	0.992276i	$0.539589\pi$
$158$	−0.106594	−	1.21837i	−0.00848013	−	0.0969284i
$159$	22.2565	+	12.8498i	1.76506	+	1.01906i
$160$		0			0
$161$	0.972751	−	5.51674i	0.0766635	−	0.434780i
$162$	0.170020	−	0.119049i	0.0133581	−	0.00935341i
$163$	−6.37574	+	23.7946i	−0.499387	+	1.86374i	0.00454038	+	0.999990i	$0.498555\pi$
$163$	−6.37574	+	23.7946i	−0.499387	+	1.86374i	−0.503927	+	0.863746i	$0.668112\pi$
$164$	1.44880	−	2.50939i	0.113132	−	0.195950i
$165$		0			0
$166$	−0.338113	+	0.928958i	−0.0262427	+	0.0721011i
$167$	−19.2868	−	8.99359i	−1.49246	−	0.695945i	−0.506394	−	0.862303i	$-0.669022\pi$
$167$	−19.2868	−	8.99359i	−1.49246	−	0.695945i	−0.986066	+	0.166357i	$0.946799\pi$
$168$	−10.4072	−	0.910509i	−0.802931	−	0.0702473i
$169$	−2.87496	+	0.506933i	−0.221151	+	0.0389948i
$170$		0			0
$171$	−20.9743	−	1.43063i	−1.60395	−	0.109403i
$172$	5.99165	−	5.99165i	0.456859	−	0.456859i
$173$	12.1396	+	8.50027i	0.922960	+	0.646264i	0.935374	−	0.353659i	$-0.115063\pi$
$173$	12.1396	+	8.50027i	0.922960	+	0.646264i	−0.0124142	+	0.999923i	$0.503952\pi$
$174$	−0.759759	+	0.637513i	−0.0575972	+	0.0483298i
$175$		0			0
$176$	−4.89907	−	1.78311i	−0.369281	−	0.134407i
$177$	6.33822	−	0.554523i	0.476410	−	0.0416805i
$178$	2.77100	−	0.742486i	0.207695	−	0.0556517i
$179$	−3.06536	−	5.30935i	−0.229116	−	0.396840i	0.728431	−	0.685120i	$-0.240250\pi$
$179$	−3.06536	−	5.30935i	−0.229116	−	0.396840i	−0.957546	+	0.288280i	$0.906917\pi$
$180$		0			0
$181$	4.61343	+	0.813472i	0.342914	+	0.0604649i	0.342453	−	0.939535i	$-0.388742\pi$
$181$	4.61343	+	0.813472i	0.342914	+	0.0604649i	0.000460610		1.00000i	$0.499853\pi$
$182$	11.4549	+	3.06932i	0.849092	+	0.227513i
$183$	−2.90204	−	10.8306i	−0.214525	−	0.800617i
$184$	−1.14890	−	0.964046i	−0.0846984	−	0.0710704i
$185$		0			0
$186$	−2.11265	−	5.80445i	−0.154907	−	0.425603i
$187$	−1.87502	+	21.4316i	−0.137115	+	1.56723i
$188$	−6.31034	+	9.01210i	−0.460229	+	0.657275i
$189$	19.0449			1.38531
$190$		0			0
$191$	−21.1712			−1.53190			−0.765948	−	0.642902i	$-0.777730\pi$
$191$	−21.1712			−1.53190			−0.765948	+	0.642902i	$0.777730\pi$
$192$	−1.60427	+	2.29114i	−0.115778	+	0.165349i
$193$	−1.46645	+	16.7615i	−0.105557	+	1.20652i	0.739989	+	0.672619i	$0.234831\pi$
$193$	−1.46645	+	16.7615i	−0.105557	+	1.20652i	−0.845546	+	0.533903i	$0.820725\pi$
$194$	5.92235	+	16.2715i	0.425200	+	1.16823i
$195$		0			0
$196$	5.32471	+	4.46796i	0.380336	+	0.319140i
$197$	0.837682	+	3.12627i	0.0596824	+	0.222738i	0.989325	−	0.145724i	$-0.0465512\pi$
$197$	0.837682	+	3.12627i	0.0596824	+	0.222738i	−0.929643	+	0.368462i	$0.879885\pi$
$198$	24.2879	+	6.50793i	1.72607	+	0.462498i
$199$	12.5136	+	2.20649i	0.887068	+	0.156414i	0.598574	−	0.801068i	$-0.295734\pi$
$199$	12.5136	+	2.20649i	0.887068	+	0.156414i	0.288494	+	0.957482i	$0.406846\pi$
$200$		0			0
$201$	18.2110	+	31.5425i	1.28451	+	2.22483i
$202$	−2.86927	+	0.768820i	−0.201881	+	0.0540940i
$203$	1.31941	−	0.115434i	0.0926045	−	0.00810185i
$204$	10.8456	+	3.94749i	0.759346	+	0.276379i
$205$		0			0
$206$	1.37073	−	1.15018i	0.0955032	−	0.0801367i
$207$	5.92534	+	4.14897i	0.411840	+	0.288373i
$208$	2.24507	−	2.24507i	0.155668	−	0.155668i
$209$	13.3889	+	18.3621i	0.926126	+	1.27013i
$210$		0			0
$211$	13.0691	−	2.30443i	0.899711	−	0.158643i	0.295383	−	0.955379i	$-0.404553\pi$
$211$	13.0691	−	2.30443i	0.899711	−	0.158643i	0.604328	+	0.796736i	$0.293442\pi$
$212$	−9.15342	−	0.800821i	−0.628660	−	0.0550006i
$213$	18.4829	+	8.61870i	1.26642	+	0.590543i
$214$	−1.23451	+	3.39178i	−0.0843892	+	0.231857i
$215$		0			0
$216$	2.54946	−	4.41579i	0.173469	−	0.300457i
$217$	−2.13494	+	7.96771i	−0.144929	+	0.540883i
$218$	−1.10846	+	0.776150i	−0.0750742	+	0.0525675i
$219$	−1.71028	+	9.69946i	−0.115570	+	0.655429i
$220$		0			0
$221$	−11.3464	−	6.55084i	−0.763241	−	0.440657i
$222$	1.76639	+	20.1900i	0.118553	+	1.35506i
$223$	−8.96847	+	4.18207i	−0.600573	+	0.280052i	−0.699033	−	0.715089i	$-0.746386\pi$
$223$	−8.96847	+	4.18207i	−0.600573	+	0.280052i	0.0984601	+	0.995141i	$0.468608\pi$
$224$	3.50984	−	1.27748i	0.234511	−	0.0853550i
$225$		0			0
$226$	1.96355	+	11.1359i	0.130614	+	0.740747i
$227$	8.27055	+	8.27055i	0.548936	+	0.548936i	0.926133	−	0.377197i	$-0.123112\pi$
$227$	8.27055	+	8.27055i	0.548936	+	0.548936i	−0.377197	+	0.926133i	$0.623112\pi$
$228$	11.3744	−	4.38857i	0.753290	−	0.290640i
$229$			21.2193i			1.40221i	0.713057	+	0.701106i	$0.247310\pi$
$229$			21.2193i			1.40221i	−0.713057	+	0.701106i	$0.752690\pi$
$230$		0			0
$231$	−35.0093	−	41.7225i	−2.30344	−	2.74514i
$232$	0.149859	−	0.321374i	0.00983873	−	0.0210992i
$233$	−6.26198	−	13.4289i	−0.410236	−	0.879754i	−0.997521	−	0.0703733i	$-0.977581\pi$
$233$	−6.26198	−	13.4289i	−0.410236	−	0.879754i	0.587285	−	0.809380i	$-0.300197\pi$
$234$	−9.84309	+	11.7305i	−0.643463	+	0.766849i
$235$		0			0
$236$	−1.97000	+	1.13738i	−0.128236	+	0.0740372i
$237$	−1.96207	−	2.80212i	−0.127450	−	0.182017i
$238$	−8.84045	−	12.6255i	−0.573041	−	0.818388i
$239$	−7.76469	+	4.48295i	−0.502256	+	0.289978i	−0.729645	−	0.683826i	$-0.760315\pi$
$239$	−7.76469	+	4.48295i	−0.502256	+	0.289978i	0.227389	+	0.973804i	$0.426981\pi$
$240$		0			0
$241$	6.17537	−	7.35952i	0.397791	−	0.474069i	−0.529554	−	0.848276i	$-0.677641\pi$
$241$	6.17537	−	7.35952i	0.397791	−	0.474069i	0.927345	+	0.374208i	$0.122085\pi$
$242$	−6.83811	−	14.6644i	−0.439570	−	0.942662i
$243$	6.71003	−	14.3897i	0.430448	−	0.923100i
$244$	2.57684	+	3.07096i	0.164965	+	0.196598i
$245$		0			0
$246$		−	8.10447i		−	0.516722i
$247$	−13.5807	+	2.66394i	−0.864122	+	0.169502i
$248$	1.56161	+	1.56161i	0.0991625	+	0.0991625i
$249$	0.480140	+	2.72301i	0.0304276	+	0.172564i
$250$		0			0
$251$	20.0814	−	7.30903i	1.26753	−	0.461342i	0.381239	−	0.924477i	$-0.375498\pi$
$251$	20.0814	−	7.30903i	1.26753	−	0.461342i	0.886288	+	0.463135i	$0.153275\pi$
$252$	−16.3266	+	7.61322i	−1.02848	+	0.479588i
$253$	−0.681481	−	7.78936i	−0.0428443	−	0.489713i
$254$	−14.3923	−	8.30939i	−0.903053	−	0.521378i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.12503	+	2.18817i	−0.194934	+	0.136494i	−0.666969	−	0.745086i	$-0.732409\pi$
$257$	−3.12503	+	2.18817i	−0.194934	+	0.136494i	0.472035	+	0.881580i	$0.343520\pi$
$258$	6.13401	−	22.8925i	0.381887	−	1.42522i
$259$	13.5324	−	23.4388i	0.840864	−	1.45642i
$260$		0			0
$261$	−0.584932	+	1.60709i	−0.0362064	+	0.0994762i
$262$	5.74958	+	2.68107i	0.355210	+	0.165637i
$263$	20.0637	+	1.75535i	1.23718	+	0.108240i	0.686908	−	0.726744i	$-0.258967\pi$
$263$	20.0637	+	1.75535i	1.23718	+	0.108240i	0.550275	+	0.834983i	$0.314523\pi$
$264$	−14.3604	+	2.53212i	−0.883821	+	0.155841i
$265$		0			0
$266$	−15.8040	−	3.91168i	−0.969005	−	0.239841i
$267$	5.67367	−	5.67367i	0.347223	−	0.347223i
$268$	−10.6670	−	7.46911i	−0.651591	−	0.456249i
$269$	11.8051	−	9.90566i	0.719770	−	0.603959i	−0.207552	−	0.978224i	$-0.566549\pi$
$269$	11.8051	−	9.90566i	0.719770	−	0.603959i	0.927322	+	0.374265i	$0.122105\pi$
$270$		0			0
$271$	−4.66625	−	1.69838i	−0.283455	−	0.103169i	0.196380	−	0.980528i	$-0.437081\pi$
$271$	−4.66625	−	1.69838i	−0.283455	−	0.103169i	−0.479835	+	0.877359i	$0.659303\pi$
$272$	−4.11080	+	0.359648i	−0.249254	+	0.0218069i
$273$	32.0389	−	8.58479i	1.93908	−	0.519575i
$274$	−3.30426	−	5.72314i	−0.199617	−	0.345748i
$275$		0			0
$276$	−4.13113	−	0.728429i	−0.248665	−	0.0438463i
$277$	18.0335	+	4.83206i	1.08353	+	0.290331i	0.756041	−	0.654525i	$-0.227131\pi$
$277$	18.0335	+	4.83206i	1.08353	+	0.290331i	0.327488	+	0.944855i	$0.393798\pi$
$278$	−0.945982	−	3.53045i	−0.0567362	−	0.211743i
$279$	−8.15945	−	6.84659i	−0.488494	−	0.409895i
$280$		0			0
$281$	−0.854833	−	2.34863i	−0.0509951	−	0.140108i	0.911580	−	0.411122i	$-0.134863\pi$
$281$	−0.854833	−	2.34863i	−0.0509951	−	0.140108i	−0.962575	+	0.271014i	$0.912641\pi$
$282$	−2.68191	+	30.6544i	−0.159706	+	1.82544i
$283$	−7.34241	+	10.4861i	−0.436461	+	0.623331i	−0.975776	−	0.218773i	$-0.929795\pi$
$283$	−7.34241	+	10.4861i	−0.436461	+	0.623331i	0.539315	+	0.842104i	$0.318683\pi$
$284$	−7.29132			−0.432660
$285$		0			0
$286$	16.5528			0.978790
$287$	−6.20769	+	8.86550i	−0.366428	+	0.523314i
$288$	−0.420354	+	4.80466i	−0.0247696	+	0.283118i
$289$	0.00957679	+	0.0263120i	0.000563341	+	0.00154777i
$290$		0			0
$291$	37.1008	+	31.1313i	2.17489	+	1.82495i
$292$	−0.911392	−	3.40136i	−0.0533352	−	0.199050i
$293$	−11.9320	−	3.19717i	−0.697076	−	0.186781i	−0.107155	−	0.994242i	$-0.534174\pi$
$293$	−11.9320	−	3.19717i	−0.697076	−	0.186781i	−0.589920	+	0.807461i	$0.700841\pi$
$294$	19.1461	+	3.37597i	1.11662	+	0.196891i
$295$		0			0
$296$	−3.62305	−	6.27530i	−0.210585	−	0.364745i
$297$	25.6773	−	6.88021i	1.48995	−	0.399230i
$298$	−1.26617	+	0.110776i	−0.0733474	+	0.00641707i
$299$	4.47467	+	1.62865i	0.258777	+	0.0941871i
$300$		0			0
$301$	−24.2447	+	20.3437i	−1.39744	+	1.17259i
$302$	−13.8629	−	9.70687i	−0.797718	−	0.558568i
$303$	−5.87490	+	5.87490i	−0.337504	+	0.337504i
$304$	−3.02258	+	3.14070i	−0.173357	+	0.180132i
$305$		0			0
$306$	19.5998	−	3.45598i	1.12045	−	0.197565i
$307$	3.62720	+	0.317339i	0.207015	+	0.0181115i	0.190192	−	0.981747i	$-0.439089\pi$
$307$	3.62720	+	0.317339i	0.207015	+	0.0181115i	0.0168235	+	0.999858i	$0.494645\pi$
$308$	17.6484	+	8.22957i	1.00561	+	0.468923i
$309$	1.71173	−	4.70295i	0.0973771	−	0.267541i
$310$		0			0
$311$	14.7301	−	25.5133i	0.835268	−	1.44673i	−0.0585438	−	0.998285i	$-0.518646\pi$
$311$	14.7301	−	25.5133i	0.835268	−	1.44673i	0.893812	−	0.448442i	$-0.148021\pi$
$312$	2.29842	−	8.57780i	0.130122	−	0.485622i
$313$	10.6385	−	7.44913i	0.601321	−	0.421050i	−0.232883	−	0.972505i	$-0.574816\pi$
$313$	10.6385	−	7.44913i	0.601321	−	0.421050i	0.834205	+	0.551455i	$0.185927\pi$
$314$	2.31412	−	13.1240i	0.130593	−	0.740631i
$315$		0			0
$316$	1.05917	+	0.611512i	0.0595830	+	0.0344003i
$317$	−0.0390303	−	0.446118i	−0.00219216	−	0.0250565i	0.995020	−	0.0996771i	$-0.0317810\pi$
$317$	−0.0390303	−	0.446118i	−0.00219216	−	0.0250565i	−0.997212	+	0.0746206i	$0.976225\pi$
$318$	−23.2918	+	10.8611i	−1.30614	+	0.609062i
$319$	1.73719	−	0.632287i	0.0972641	−	0.0354012i
$320$		0			0
$321$	1.75307	+	9.94216i	0.0978469	+	0.554917i
$322$	3.96111	+	3.96111i	0.220744	+	0.220744i
$323$	15.7467	+	8.69335i	0.876168	+	0.483711i
$324$			0.207556i			0.0115309i
$325$		0			0
$326$	−15.8344	−	18.8707i	−0.876987	−	1.04515i
$327$	−1.59952	+	3.43018i	−0.0884537	+	0.189690i
$328$	1.22458	+	2.62611i	0.0676159	+	0.145003i
$329$	26.4138	−	31.4787i	1.45624	−	1.73548i
$330$		0			0
$331$	7.66033	−	4.42269i	0.421050	−	0.243093i	−0.274477	−	0.961594i	$-0.588505\pi$
$331$	7.66033	−	4.42269i	0.421050	−	0.243093i	0.695526	+	0.718501i	$0.255171\pi$
$332$	−0.567024	−	0.809795i	−0.0311195	−	0.0444432i
$333$	20.0454	+	28.6278i	1.09848	+	1.56879i
$334$	18.4296	−	10.6403i	1.00842	−	0.582213i
$335$		0			0
$336$	6.71515	−	8.00281i	0.366342	−	0.436589i
$337$	0.993468	+	2.13050i	0.0541176	+	0.116056i	0.931507	−	0.363723i	$-0.118495\pi$
$337$	0.993468	+	2.13050i	0.0541176	+	0.116056i	−0.877389	+	0.479779i	$0.840717\pi$
$338$	1.23375	−	2.64579i	0.0671073	−	0.143912i
$339$	20.3295	+	24.2278i	1.10415	+	1.31587i
$340$		0			0
$341$			11.5137i			0.623503i
$342$	13.2023	−	16.3606i	0.713897	−	0.884679i
$343$	0.129651	+	0.129651i	0.00700048	+	0.00700048i
$344$	1.47140	+	8.34474i	0.0793327	+	0.449918i
$345$		0			0
$346$	−13.9260	+	5.06866i	−0.748668	+	0.272493i
$347$	15.9651	−	7.44467i	0.857054	−	0.399651i	0.0561348	−	0.998423i	$-0.482122\pi$
$347$	15.9651	−	7.44467i	0.857054	−	0.399651i	0.800919	+	0.598772i	$0.204345\pi$
$348$	−0.0864406	−	0.988021i	−0.00463370	−	0.0529635i
$349$	−5.48199	−	3.16503i	−0.293444	−	0.169420i	0.346050	−	0.938216i	$-0.387523\pi$
$349$	−5.48199	−	3.16503i	−0.293444	−	0.169420i	−0.639494	+	0.768796i	$0.720856\pi$
$350$		0			0
$351$	−2.81121	+	15.9432i	−0.150051	+	0.850983i
$352$	4.27063	−	2.99033i	0.227625	−	0.159385i
$353$	7.80961	−	29.1459i	0.415664	−	1.55128i	−0.367839	−	0.929890i	$-0.619902\pi$
$353$	7.80961	−	29.1459i	0.415664	−	1.55128i	0.783502	−	0.621389i	$-0.213431\pi$
$354$	−3.18122	+	5.51003i	−0.169080	+	0.292855i
$355$		0			0
$356$	−0.981169	+	2.69574i	−0.0520019	+	0.142874i
$357$	−39.0702	−	18.2187i	−2.06782	−	0.964238i
$358$	6.10739	+	0.534327i	0.322785	+	0.0282401i
$359$	−8.31595	+	1.46633i	−0.438899	+	0.0773897i	−0.388731	−	0.921351i	$-0.627087\pi$
$359$	−8.31595	+	1.46633i	−0.438899	+	0.0773897i	−0.0501675	+	0.998741i	$0.515976\pi$
$360$		0			0
$361$	18.5712	−	4.01386i	0.977431	−	0.211256i
$362$	−3.31251	+	3.31251i	−0.174102	+	0.174102i
$363$	−37.0715	−	25.9577i	−1.94575	−	1.36243i
$364$	−9.08449	+	7.62279i	−0.476157	+	0.399543i
$365$		0			0
$366$	10.5364	+	3.83494i	0.550747	+	0.200455i
$367$	−11.6154	+	1.01622i	−0.606319	+	0.0530461i	−0.386182	−	0.922423i	$-0.626206\pi$
$367$	−11.6154	+	1.01622i	−0.606319	+	0.0530461i	−0.220138	+	0.975469i	$0.570651\pi$
$368$	1.44868	−	0.388174i	0.0755179	−	0.0202350i
$369$	−6.98757	−	12.1028i	−0.363759	−	0.630048i
$370$		0			0
$371$	33.7981	+	5.95951i	1.75471	+	0.309403i
$372$	5.96649	+	1.59872i	0.309348	+	0.0828896i
$373$	−4.66442	−	17.4079i	−0.241515	−	0.901345i	−0.975103	−	0.221751i	$-0.928823\pi$
$373$	−4.66442	−	17.4079i	−0.241515	−	0.901345i	0.733589	−	0.679594i	$-0.237844\pi$
$374$	−16.4802	−	13.8286i	−0.852173	−	0.715058i
$375$		0			0
$376$	−3.76282	−	10.3383i	−0.194053	−	0.533155i
$377$	−0.0981241	+	1.12156i	−0.00505365	+	0.0577635i
$378$	−10.9237	+	15.6007i	−0.561855	+	0.802413i
$379$	−30.6184			−1.57276			−0.786380	−	0.617743i	$-0.788047\pi$
$379$	−30.6184			−1.57276			−0.786380	+	0.617743i	$0.788047\pi$
$380$		0			0
$381$	−46.4822			−2.38135
$382$	12.1433	−	17.3425i	0.621306	−	0.887317i
$383$	0.520365	−	5.94780i	0.0265894	−	0.303919i	−0.971242	−	0.238095i	$-0.923477\pi$
$383$	0.520365	−	5.94780i	0.0265894	−	0.303919i	0.997831	−	0.0658235i	$-0.0209674\pi$
$384$	−0.956619	−	2.62829i	−0.0488172	−	0.134124i
$385$		0			0
$386$	−12.8891	−	10.8153i	−0.656040	−	0.550483i
$387$	−10.5773	−	39.4752i	−0.537676	−	2.00664i
$388$	−16.7258	−	4.48166i	−0.849123	−	0.227522i
$389$	−10.4827	−	1.84838i	−0.531493	−	0.0937166i	−0.0985402	−	0.995133i	$-0.531417\pi$
$389$	−10.4827	−	1.84838i	−0.531493	−	0.0937166i	−0.432953	+	0.901416i	$0.642528\pi$
$390$		0			0
$391$	−3.09444	−	5.35973i	−0.156493	−	0.271053i
$392$	−6.71406	+	1.79903i	−0.339111	+	0.0908646i
$393$	17.6763	−	1.54648i	0.891652	−	0.0780095i
$394$	−3.04137	−	1.10697i	−0.153222	−	0.0557682i
$395$		0			0
$396$	−19.2620	+	16.1627i	−0.967950	+	0.812206i
$397$	9.84469	+	6.89333i	0.494091	+	0.345966i	0.793915	−	0.608028i	$-0.208039\pi$
$397$	9.84469	+	6.89333i	0.494091	+	0.345966i	−0.299824	+	0.953994i	$0.596928\pi$
$398$	−8.98497	+	8.98497i	−0.450376	+	0.450376i
$399$	−43.7515	+	12.6266i	−2.19032	+	0.632119i
$400$		0			0
$401$	−33.8771	+	5.97344i	−1.69174	+	0.298300i	−0.934798	−	0.355181i	$-0.884419\pi$
$401$	−33.8771	+	5.97344i	−1.69174	+	0.298300i	−0.756943	+	0.653480i	$0.773308\pi$
$402$	−36.2835	−	3.17440i	−1.80966	−	0.158324i
$403$	−6.35491	−	2.96334i	−0.316560	−	0.147615i
$404$	1.01597	−	2.79135i	0.0505463	−	0.138875i
$405$		0			0
$406$	−0.662226	+	1.14701i	−0.0328657	+	0.0569251i
$407$	9.77750	−	36.4901i	0.484653	−	1.80875i
$408$	−9.45439	+	6.62003i	−0.468062	+	0.327741i
$409$	−5.39560	+	30.6000i	−0.266795	+	1.51307i	0.497079	+	0.867705i	$0.334406\pi$
$409$	−5.39560	+	30.6000i	−0.266795	+	1.51307i	−0.763874	+	0.645365i	$0.776705\pi$
$410$		0			0
$411$	−16.0074	−	9.24189i	−0.789588	−	0.455869i
$412$	0.155953	+	1.78255i	0.00768325	+	0.0878199i
$413$	7.70040	−	3.59075i	0.378912	−	0.176689i
$414$	−6.79727	+	2.47401i	−0.334068	+	0.121591i
$415$		0			0
$416$	0.551335	+	3.12678i	0.0270314	+	0.153303i
$417$	−7.22868	−	7.22868i	−0.353990	−	0.353990i
$418$	−22.7209	+	0.435463i	−1.11131	+	0.0212992i
$419$			22.0520i			1.07731i	0.842527	+	0.538654i	$0.181067\pi$
$419$			22.0520i			1.07731i	−0.842527	+	0.538654i	$0.818933\pi$
$420$		0			0
$421$	17.4535	+	20.8002i	0.850629	+	1.01374i	0.999690	+	0.0249123i	$0.00793066\pi$
$421$	17.4535	+	20.8002i	0.850629	+	1.01374i	−0.149060	+	0.988828i	$0.547625\pi$
$422$	−5.60843	+	12.0273i	−0.273014	+	0.585480i
$423$	22.4248	+	48.0901i	1.09033	+	2.33822i
$424$	5.90618	−	7.03871i	0.286830	−	0.341830i
$425$		0			0
$426$	−17.6614	+	10.1968i	−0.855695	+	0.494036i
$427$	−8.58840	−	12.2655i	−0.415622	−	0.593569i
$428$	−2.07030	−	2.95670i	−0.100072	−	0.142917i
$429$	40.0950	−	23.1489i	1.93581	−	1.11764i
$430$		0			0
$431$	−3.98773	+	4.75240i	−0.192082	+	0.228915i	−0.853487	−	0.521115i	$-0.825516\pi$
$431$	−3.98773	+	4.75240i	−0.192082	+	0.228915i	0.661404	+	0.750030i	$0.269961\pi$
$432$	2.15490	+	4.62119i	0.103677	+	0.222337i
$433$	−2.15570	+	4.62291i	−0.103596	+	0.222163i	−0.951273	−	0.308351i	$-0.900223\pi$
$433$	−2.15570	+	4.62291i	−0.103596	+	0.222163i	0.847677	+	0.530513i	$0.178001\pi$
$434$	−5.30221	−	6.31893i	−0.254514	−	0.303318i
$435$		0			0
$436$		−	1.35318i		−	0.0648054i
$437$	−6.18489	−	2.11780i	−0.295863	−	0.101308i
$438$	−6.96436	−	6.96436i	−0.332770	−	0.332770i
$439$	−1.27281	−	7.21846i	−0.0607478	−	0.344518i	−0.999999	−	0.00128797i	$-0.999590\pi$
$439$	−1.27281	−	7.21846i	−0.0607478	−	0.344518i	0.939251	−	0.343230i	$-0.111521\pi$
$440$		0			0
$441$	31.5026	−	11.4660i	1.50012	−	0.546000i
$442$	11.8742	−	5.53701i	0.564796	−	0.263369i
$443$	1.92376	+	21.9887i	0.0914007	+	1.04471i	0.893961	+	0.448144i	$0.147915\pi$
$443$	1.92376	+	21.9887i	0.0914007	+	1.04471i	−0.802561	+	0.596571i	$0.796530\pi$
$444$	−17.5518	−	10.1335i	−0.832972	−	0.480917i
$445$		0			0
$446$	1.71836	−	9.74528i	0.0813665	−	0.461452i
$447$	−2.91206	+	2.03905i	−0.137736	+	0.0964436i
$448$	−0.966713	+	3.60782i	−0.0456729	+	0.170454i
$449$	0.503020	−	0.871256i	0.0237390	−	0.0411171i	−0.853912	−	0.520418i	$-0.825776\pi$
$449$	0.503020	−	0.871256i	0.0237390	−	0.0411171i	0.877651	+	0.479301i	$0.159110\pi$
$450$		0			0
$451$	−5.16674	+	14.1955i	−0.243292	+	0.668440i
$452$	−10.2482	−	4.77882i	−0.482036	−	0.224777i
$453$	−47.1541	−	4.12545i	−2.21549	−	0.193831i
$454$	−11.5186	+	2.03104i	−0.540596	+	0.0953217i
$455$		0			0
$456$	−2.92920	+	11.8346i	−0.137172	+	0.554205i
$457$	−22.2043	+	22.2043i	−1.03867	+	1.03867i	−0.0394508	+	0.999222i	$0.512561\pi$
$457$	−22.2043	+	22.2043i	−1.03867	+	1.03867i	−0.999222	+	0.0394508i	$0.987439\pi$
$458$	−17.3819	−	12.1709i	−0.812201	−	0.568709i
$459$	16.1181	−	13.5247i	0.752328	−	0.631278i
$460$		0			0
$461$	−7.48738	−	2.72518i	−0.348722	−	0.126924i	0.161720	−	0.986837i	$-0.448296\pi$
$461$	−7.48738	−	2.72518i	−0.348722	−	0.126924i	−0.510442	+	0.859912i	$0.670518\pi$
$462$	54.2575	−	4.74692i	2.52429	−	0.220847i
$463$	1.67321	−	0.448336i	0.0777609	−	0.0208360i	−0.219729	−	0.975561i	$-0.570517\pi$
$463$	1.67321	−	0.448336i	0.0777609	−	0.0208360i	0.297490	+	0.954725i	$0.403851\pi$
$464$	0.177298	+	0.307090i	0.00823087	+	0.0142563i
$465$		0			0
$466$	14.5920	+	2.57296i	0.675961	+	0.119190i
$467$	25.3592	+	6.79497i	1.17348	+	0.314434i	0.792339	−	0.610081i	$-0.208863\pi$
$467$	25.3592	+	6.79497i	1.17348	+	0.314434i	0.381145	+	0.924515i	$0.375530\pi$
$468$	−3.96333	−	14.7913i	−0.183205	−	0.683730i
$469$	37.2592	+	31.2641i	1.72047	+	1.44364i
$470$		0			0
$471$	−12.7483	−	35.0258i	−0.587413	−	1.61390i
$472$	0.198259	−	2.26611i	0.00912559	−	0.104306i
$473$	−25.3385	+	36.1871i	−1.16506	+	1.66388i
$474$	3.42076			0.157121
$475$		0			0
$476$	15.4129			0.706447
$477$	−25.4185	+	36.3013i	−1.16383	+	1.66212i
$478$	0.781429	−	8.93178i	0.0357417	−	0.408530i
$479$	−1.76042	−	4.83671i	−0.0804356	−	0.220995i	0.892956	−	0.450145i	$-0.148628\pi$
$479$	−1.76042	−	4.83671i	−0.0804356	−	0.220995i	−0.973391	+	0.229150i	$0.926405\pi$
$480$		0			0
$481$	17.6240	+	14.7883i	0.803583	+	0.674286i
$482$	2.48652	+	9.27982i	0.113258	+	0.422684i
$483$	15.1343	+	4.05522i	0.688634	+	0.184519i
$484$	15.9345	+	2.80969i	0.724297	+	0.127713i
$485$		0			0
$486$	7.93864	+	13.7501i	0.360104	+	0.623718i
$487$	33.5176	−	8.98101i	1.51883	−	0.406968i	0.599471	−	0.800397i	$-0.295378\pi$
$487$	33.5176	−	8.98101i	1.51883	−	0.406968i	0.919355	+	0.393428i	$0.128711\pi$
$488$	−3.99359	+	0.349394i	−0.180782	+	0.0158163i
$489$	−64.7452	−	23.5653i	−2.92788	−	1.06566i
$490$		0			0
$491$	−1.28719	+	1.08008i	−0.0580903	+	0.0487435i	−0.671371	−	0.741122i	$-0.734294\pi$
$491$	−1.28719	+	1.08008i	−0.0580903	+	0.0487435i	0.613280	+	0.789865i	$0.289850\pi$
$492$	6.63879	+	4.64853i	0.299300	+	0.209572i
$493$	1.03467	−	1.03467i	0.0465992	−	0.0465992i
$494$	5.60742	−	12.6527i	0.252290	−	0.569270i
$495$		0			0
$496$	−2.17490	+	0.383494i	−0.0976560	+	0.0172194i
$497$	27.1301	+	2.37358i	1.21695	+	0.106470i
$498$	−2.50595	−	1.16855i	−0.112295	−	0.0523638i
$499$	12.8055	−	35.1829i	0.573254	−	1.57500i	−0.226076	−	0.974110i	$-0.572590\pi$
$499$	12.8055	−	35.1829i	0.573254	−	1.57500i	0.799330	−	0.600892i	$-0.205188\pi$
$500$		0			0
$501$	29.7606	−	51.5469i	1.32961	−	2.30295i
$502$	−5.53101	+	20.6420i	−0.246861	+	0.921298i
$503$	−32.7522	+	22.9334i	−1.46035	+	1.02255i	−0.470197	+	0.882562i	$0.655817\pi$
$503$	−32.7522	+	22.9334i	−1.46035	+	1.02255i	−0.990153	+	0.139987i	$0.955294\pi$
$504$	3.12817	−	17.7407i	0.139340	−	0.790235i
$505$		0			0
$506$	6.77155	+	3.90956i	0.301032	+	0.173801i
$507$	−0.711644	−	8.13413i	−0.0316052	−	0.361250i
$508$	15.0617	−	7.02340i	0.668257	−	0.311613i
$509$	9.44634	−	3.43819i	0.418702	−	0.152395i	−0.124073	−	0.992273i	$-0.539596\pi$
$509$	9.44634	−	3.43819i	0.418702	−	0.152395i	0.542775	+	0.839878i	$0.317374\pi$
$510$		0			0
$511$	2.28392	+	12.9527i	0.101035	+	0.572996i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.43931	−	21.9579i	0.151849	−	0.969467i
$514$		−	3.81496i		−	0.168271i
$515$		0			0
$516$	15.2341	+	18.1553i	0.670643	+	0.799241i
$517$	24.2403	−	51.9834i	1.06609	−	2.28623i
$518$	11.4381	+	24.5291i	0.502561	+	1.07775i
$519$	−26.6438	+	31.7528i	−1.16953	+	1.39379i
$520$		0			0
$521$	−28.3947	+	16.3937i	−1.24399	+	0.718220i	−0.969905	−	0.243484i	$-0.921710\pi$
$521$	−28.3947	+	16.3937i	−1.24399	+	0.718220i	−0.274089	+	0.961704i	$0.588376\pi$
$522$	−0.980945	−	1.40094i	−0.0429348	−	0.0613173i
$523$	0.830687	+	1.18634i	0.0363234	+	0.0518752i	0.836903	−	0.547351i	$-0.184364\pi$
$523$	0.830687	+	1.18634i	0.0363234	+	0.0518752i	−0.800580	+	0.599226i	$0.795475\pi$
$524$	−5.49403	+	3.17198i	−0.240008	+	0.138569i
$525$		0			0
$526$	−12.9460	+	15.4284i	−0.564472	+	0.672711i
$527$	3.85140	+	8.25935i	0.167770	+	0.359783i
$528$	6.16259	−	13.2157i	0.268192	−	0.575140i
$529$	−13.3383	−	15.8959i	−0.579924	−	0.691126i
$530$		0			0
$531$			10.9712i			0.476110i
$532$	12.2691	−	10.7022i	0.531931	−	0.464000i
$533$	−6.50531	−	6.50531i	−0.281776	−	0.281776i
$534$	1.39332	+	7.90189i	0.0602947	+	0.341948i
$535$		0			0
$536$	12.2367	−	4.45379i	0.528544	−	0.192374i
$537$	15.5408	−	7.24680i	0.670636	−	0.312723i
$538$	1.34311	+	15.3518i	0.0579056	+	0.661864i
$539$	−31.3834	−	18.1192i	−1.35178	−	0.780450i
$540$		0			0
$541$	−0.346454	+	1.96484i	−0.0148952	+	0.0844751i	−0.991349	−	0.131251i	$-0.958101\pi$
$541$	−0.346454	+	1.96484i	−0.0148952	+	0.0844751i	0.976454	+	0.215726i	$0.0692118\pi$
$542$	4.06768	−	2.84822i	0.174722	−	0.122342i
$543$	−3.39122	+	12.6562i	−0.145531	+	0.543130i
$544$	2.06325	−	3.57365i	0.0884611	−	0.153219i
$545$		0			0
$546$	−11.3445	+	31.1688i	−0.485500	+	1.33390i
$547$	−7.25681	−	3.38391i	−0.310279	−	0.144685i	0.261241	−	0.965274i	$-0.415868\pi$
$547$	−7.25681	−	3.38391i	−0.310279	−	0.144685i	−0.571520	+	0.820588i	$0.693646\pi$
$548$	6.58337	+	0.575970i	0.281227	+	0.0246042i
$549$	19.0410	−	3.35744i	0.812650	−	0.143292i
$550$		0			0
$551$	0.105182	−	1.54207i	0.00448091	−	0.0656943i
$552$	2.96621	−	2.96621i	0.126250	−	0.126250i
$553$	−3.74198	−	2.62016i	−0.159125	−	0.111421i
$554$	−14.3018	+	12.0006i	−0.607625	+	0.509858i
$555$		0			0
$556$	3.43457	+	1.25008i	0.145658	+	0.0530153i
$557$	29.4631	−	2.57769i	1.24839	−	0.109220i	0.556271	−	0.831001i	$-0.312232\pi$
$557$	29.4631	−	2.57769i	1.24839	−	0.109220i	0.692122	+	0.721781i	$0.256676\pi$
$558$	10.2885	−	2.75679i	0.435546	−	0.116704i
$559$	−13.4517	−	23.2990i	−0.568946	−	0.985443i
$560$		0			0
$561$	−59.2581	−	10.4488i	−2.50188	−	0.441149i
$562$	2.41420	+	0.646883i	0.101837	+	0.0272871i
$563$	−9.89901	−	36.9436i	−0.417193	−	1.55699i	−0.780402	−	0.625279i	$-0.784985\pi$
$563$	−9.89901	−	36.9436i	−0.417193	−	1.55699i	0.363208	−	0.931708i	$-0.381681\pi$
$564$	−23.5723	−	19.7795i	−0.992575	−	0.832869i
$565$		0			0
$566$	−4.37824	−	12.0291i	−0.184031	−	0.505621i
$567$	0.0675668	−	0.772292i	0.00283754	−	0.0324332i
$568$	4.18213	−	5.97270i	0.175478	−	0.250609i
$569$	33.3384			1.39762			0.698810	−	0.715308i	$-0.253713\pi$
$569$	33.3384			1.39762			0.698810	+	0.715308i	$0.253713\pi$
$570$		0			0
$571$	23.2049			0.971093			0.485547	−	0.874211i	$-0.338621\pi$
$571$	23.2049			0.971093			0.485547	+	0.874211i	$0.338621\pi$
$572$	−9.49432	+	13.5593i	−0.396978	+	0.566943i
$573$	5.16094	−	58.9899i	0.215602	−	2.46434i
$574$	−3.70161	−	10.1701i	−0.154502	−	0.424491i
$575$		0			0
$576$	−3.69465	−	3.10018i	−0.153944	−	0.129174i
$577$	1.71810	+	6.41205i	0.0715256	+	0.266937i	0.992423	−	0.122868i	$-0.0392091\pi$
$577$	1.71810	+	6.41205i	0.0715256	+	0.266937i	−0.920897	+	0.389805i	$0.872542\pi$
$578$	−0.0270466	−	0.00724711i	−0.00112499	−	0.000301440i
$579$	−46.3456	−	8.17198i	−1.92606	−	0.339616i
$580$		0			0
$581$	1.84621	+	3.19773i	0.0765938	+	0.132664i
$582$	−46.7814	+	12.5350i	−1.93915	+	0.519594i
$583$	47.7212	−	4.17506i	1.97641	−	0.172913i
$584$	3.30899	+	1.20437i	0.136927	+	0.0498373i
$585$		0			0
$586$	9.46289	−	7.94031i	0.390908	−	0.328011i
$587$	−28.8390	−	20.1933i	−1.19031	−	0.833466i	−0.201046	−	0.979582i	$-0.564434\pi$
$587$	−28.8390	−	20.1933i	−1.19031	−	0.833466i	−0.989268	+	0.146116i	$0.953323\pi$
$588$	−13.7472	+	13.7472i	−0.566924	+	0.566924i
$589$	8.80086	+	3.90038i	0.362633	+	0.160712i
$590$		0			0
$591$	−8.91501	+	1.57196i	−0.366714	+	0.0646616i
$592$	7.21852	+	0.631539i	0.296679	+	0.0259561i
$593$	6.16362	+	2.87415i	0.253110	+	0.118027i	0.545033	−	0.838415i	$-0.316517\pi$
$593$	6.16362	+	2.87415i	0.253110	+	0.118027i	−0.291923	+	0.956442i	$0.594295\pi$
$594$	−9.09195	+	24.9799i	−0.373047	+	1.02494i
$595$		0			0
$596$	0.635505	−	1.10073i	0.0260313	−	0.0450875i
$597$	−9.19846	+	34.3291i	−0.376468	+	1.40500i
$598$	−3.90068	+	2.73128i	−0.159510	+	0.111690i
$599$	−6.45318	+	36.5978i	−0.263670	+	1.49534i	0.509127	+	0.860691i	$0.329968\pi$
$599$	−6.45318	+	36.5978i	−0.263670	+	1.49534i	−0.772797	+	0.634654i	$0.781143\pi$
$600$		0			0
$601$	−10.7935	−	6.23163i	−0.440276	−	0.254193i	0.263439	−	0.964676i	$-0.415143\pi$
$601$	−10.7935	−	6.23163i	−0.440276	−	0.254193i	−0.703715	+	0.710483i	$0.748477\pi$
$602$	−2.75841	−	31.5288i	−0.112424	−	1.28502i
$603$	−56.9210	+	26.5427i	−2.31800	+	1.08090i
$604$	15.9028	−	5.78815i	0.647076	−	0.235516i
$605$		0			0
$606$	−1.44273	−	8.18214i	−0.0586070	−	0.332377i
$607$	−32.0938	−	32.0938i	−1.30265	−	1.30265i	−0.926600	−	0.376047i	$-0.877283\pi$
$607$	−32.0938	−	32.0938i	−1.30265	−	1.30265i	−0.376047	−	0.926600i	$-0.622717\pi$
$608$	−0.839033	−	4.27739i	−0.0340273	−	0.173471i
$609$			3.70444i			0.150112i
$610$		0			0
$611$	22.4530	+	26.7584i	0.908351	+	1.08253i
$612$	−8.41102	+	18.0375i	−0.339996	+	0.729123i
$613$	−7.90736	−	16.9574i	−0.319375	−	0.684902i	0.679432	−	0.733739i	$-0.262226\pi$
$613$	−7.90736	−	16.9574i	−0.319375	−	0.684902i	−0.998807	+	0.0488366i	$0.984449\pi$
$614$	−2.34042	+	2.78921i	−0.0944518	+	0.112563i
$615$		0			0
$616$	−16.8640	+	9.73641i	−0.679468	+	0.392291i
$617$	−0.180545	−	0.257845i	−0.00726847	−	0.0103805i	0.815501	−	0.578755i	$-0.196461\pi$
$617$	−0.180545	−	0.257845i	−0.00726847	−	0.0103805i	−0.822770	+	0.568375i	$0.807572\pi$
$618$	2.87062	+	4.09967i	0.115473	+	0.164913i
$619$	1.87464	−	1.08233i	0.0753482	−	0.0435023i	−0.461853	−	0.886957i	$-0.652815\pi$
$619$	1.87464	−	1.08233i	0.0753482	−	0.0435023i	0.537201	+	0.843454i	$0.319482\pi$
$620$		0			0
$621$	−4.91559	+	5.85817i	−0.197256	+	0.235080i
$622$	12.4504	+	26.7000i	0.499217	+	1.07057i
$623$	4.52837	−	9.71112i	0.181425	−	0.389068i
$624$	5.70821	+	6.80278i	0.228511	+	0.272329i
$625$		0			0
$626$			12.9872i			0.519071i
$627$	−54.4264	+	32.8295i	−2.17358	+	1.31108i
$628$	9.42323	+	9.42323i	0.376028	+	0.376028i
$629$	−5.19226	−	29.4468i	−0.207029	−	1.17412i
$630$		0			0
$631$	20.4517	−	7.44380i	0.814169	−	0.296333i	0.0988239	−	0.995105i	$-0.468492\pi$
$631$	20.4517	−	7.44380i	0.814169	−	0.296333i	0.715345	+	0.698772i	$0.246270\pi$
$632$	−1.10844	+	0.516873i	−0.0440912	+	0.0205601i
$633$	3.23501	+	36.9764i	0.128580	+	1.46968i
$634$	0.387826	+	0.223911i	0.0154025	+	0.00889265i
$635$		0			0
$636$	4.46269	−	25.3092i	0.176957	−	1.00357i
$637$	18.0780	−	12.6584i	0.716278	−	0.501543i
$638$	−0.478474	+	1.78569i	−0.0189430	+	0.0706961i
$639$	−17.5831	+	30.4548i	−0.695576	+	1.20477i
$640$		0			0
$641$	14.2858	−	39.2500i	0.564256	−	1.55028i	−0.249078	−	0.968483i	$-0.580127\pi$
$641$	14.2858	−	39.2500i	0.564256	−	1.55028i	0.813334	−	0.581797i	$-0.197650\pi$
$642$	−9.14966	−	4.26656i	−0.361108	−	0.168388i
$643$	35.3695	+	3.09443i	1.39484	+	0.122032i	0.759653	−	0.650329i	$-0.225369\pi$
$643$	35.3695	+	3.09443i	1.39484	+	0.122032i	0.635184	+	0.772361i	$0.280924\pi$
$644$	−5.51674	+	0.972751i	−0.217390	+	0.0383318i
$645$		0			0
$646$	−16.1531	+	7.91262i	−0.635535	+	0.311318i
$647$	31.3231	−	31.3231i	1.23144	−	1.23144i	0.268027	−	0.963411i	$-0.413628\pi$
$647$	31.3231	−	31.3231i	1.23144	−	1.23144i	0.963411	−	0.268027i	$-0.0863718\pi$
$648$	−0.170020	−	0.119049i	−0.00667903	−	0.00467671i
$649$	9.08485	−	7.62309i	0.356611	−	0.299232i
$650$		0			0
$651$	−21.6802	−	7.89093i	−0.849712	−	0.309270i
$652$	24.5402	−	2.14699i	0.961070	−	0.0840827i
$653$	12.8934	−	3.45477i	0.504558	−	0.135196i	0.00244319	−	0.999997i	$-0.499222\pi$
$653$	12.8934	−	3.45477i	0.504558	−	0.135196i	0.502114	+	0.864801i	$0.332556\pi$
$654$	−1.89239	−	3.27772i	−0.0739985	−	0.128169i
$655$		0			0
$656$	−2.85357	−	0.503162i	−0.111413	−	0.0196452i
$657$	−16.4048	−	4.39566i	−0.640013	−	0.171491i
$658$	10.6355	+	39.6923i	0.414616	+	1.54737i
$659$	10.2540	+	8.60409i	0.399437	+	0.335168i	0.820276	−	0.571968i	$-0.193820\pi$
$659$	10.2540	+	8.60409i	0.399437	+	0.335168i	−0.420839	+	0.907135i	$0.638264\pi$
$660$		0			0
$661$	−4.26927	−	11.7297i	−0.166056	−	0.456234i	0.828556	−	0.559906i	$-0.189163\pi$
$661$	−4.26927	−	11.7297i	−0.166056	−	0.456234i	−0.994611	+	0.103672i	$0.966941\pi$
$662$	−0.770926	+	8.81173i	−0.0299629	+	0.342477i
$663$	21.0187	−	30.0178i	0.816298	−	1.16579i
$664$	0.988577			0.0383642
$665$		0			0
$666$	−34.9481			−1.35421
$667$	−0.305040	+	0.435642i	−0.0118112	+	0.0168681i
$668$	−1.85473	+	21.1997i	−0.0717617	+	0.820240i
$669$	−9.46633	−	26.0085i	−0.365989	−	1.00555i
$670$		0			0
$671$	−16.0104	−	13.4343i	−0.618073	−	0.518625i
$672$	2.70386	+	10.0910i	0.104304	+	0.389267i
$673$	−25.4400	−	6.81662i	−0.980639	−	0.262761i	−0.267325	−	0.963606i	$-0.586140\pi$
$673$	−25.4400	−	6.81662i	−0.980639	−	0.262761i	−0.713314	+	0.700845i	$0.752806\pi$
$674$	−2.31503	−	0.408203i	−0.0891717	−	0.0157234i
$675$		0			0
$676$	1.45965	+	2.52819i	0.0561405	+	0.0972383i
$677$	−14.7436	+	3.95054i	−0.566642	+	0.151831i	−0.530756	−	0.847524i	$-0.678092\pi$
$677$	−14.7436	+	3.95054i	−0.566642	+	0.151831i	−0.0358862	+	0.999356i	$0.511425\pi$
$678$	−31.5068	+	2.75649i	−1.21001	+	0.105862i
$679$	60.7757	+	22.1205i	2.33236	+	0.848908i
$680$		0			0
$681$	−25.0605	+	21.0283i	−0.960322	+	0.805806i
$682$	−9.43149	−	6.60400i	−0.361150	−	0.252880i
$683$	15.9399	−	15.9399i	0.609922	−	0.609922i	−0.333004	−	0.942925i	$-0.608062\pi$
$683$	15.9399	−	15.9399i	0.609922	−	0.609922i	0.942925	+	0.333004i	$0.108062\pi$
$684$	5.82929	+	20.1987i	0.222888	+	0.772317i
$685$		0			0
$686$	−0.180568	+	0.0318391i	−0.00689413	+	0.00121562i
$687$	−59.1239	−	5.17267i	−2.25572	−	0.197350i
$688$	−7.67957	−	3.58104i	−0.292781	−	0.136526i
$689$	−9.97783	+	27.4139i	−0.380125	+	1.04439i
$690$		0			0
$691$	20.2834	−	35.1318i	0.771615	−	1.33648i	−0.165062	−	0.986283i	$-0.552782\pi$
$691$	20.2834	−	35.1318i	0.771615	−	1.33648i	0.936677	−	0.350194i	$-0.113884\pi$
$692$	3.83564	−	14.3148i	0.145809	−	0.544167i
$693$	76.9329	−	53.8690i	2.92244	−	2.04631i
$694$	−3.05892	+	17.3480i	−0.116115	+	0.658520i
$695$		0			0
$696$	0.858920	+	0.495897i	0.0325573	+	0.0187969i
$697$	1.04211	+	11.9114i	0.0394729	+	0.451177i
$698$	5.73698	−	2.67520i	0.217148	−	0.101258i
$699$	38.9436	−	14.1743i	1.47298	−	0.536122i
$700$		0			0
$701$	4.75251	+	26.9528i	0.179500	+	1.01799i	0.932820	+	0.360341i	$0.117340\pi$
$701$	4.75251	+	26.9528i	0.179500	+	1.01799i	−0.753321	+	0.657654i	$0.771549\pi$
$702$	−11.4474	−	11.4474i	−0.432056	−	0.432056i
$703$	−24.5801	−	19.8351i	−0.927057	−	0.748094i
$704$			5.21348i			0.196490i
$705$		0			0
$706$	19.3955	+	23.1146i	0.729959	+	0.869931i
$707$	−4.68897	+	10.0555i	−0.176347	+	0.378177i
$708$	−2.68888	−	5.76632i	−0.101054	−	0.216712i
$709$	7.19780	−	8.57800i	0.270319	−	0.322154i	−0.613759	−	0.789494i	$-0.710343\pi$
$709$	7.19780	−	8.57800i	0.270319	−	0.322154i	0.884078	+	0.467340i	$0.154788\pi$
$710$		0			0
$711$	5.10840	−	2.94933i	0.191580	−	0.110609i
$712$	−1.64545	−	2.34994i	−0.0616657	−	0.0880677i
$713$	−1.89981	−	2.71321i	−0.0711484	−	0.101610i
$714$	37.3337	−	21.5546i	1.39718	−	0.806661i
$715$		0			0
$716$	−3.94075	+	4.69640i	−0.147273	+	0.175513i
$717$	−10.5981	−	22.7278i	−0.395794	−	0.848784i
$718$	3.56869	−	7.65308i	0.133182	−	0.285610i
$719$	−27.4944	−	32.7665i	−1.02537	−	1.22198i	−0.974758	−	0.223265i	$-0.928328\pi$
$719$	−27.4944	−	32.7665i	−1.02537	−	1.22198i	−0.0506086	−	0.998719i	$-0.516116\pi$
$720$		0			0
$721$		−	6.68342i		−	0.248904i
$722$	−7.36403	+	17.5149i	−0.274061	+	0.651836i
$723$	19.0006	+	19.0006i	0.706641	+	0.706641i
$724$	−0.813472	−	4.61343i	−0.0302325	−	0.171457i
$725$		0			0
$726$	42.5266	−	15.4784i	1.57831	−	0.574458i
$727$	−13.4096	+	6.25300i	−0.497335	+	0.231911i	−0.655067	−	0.755571i	$-0.727360\pi$
$727$	−13.4096	+	6.25300i	−0.497335	+	0.231911i	0.157732	+	0.987482i	$0.449582\pi$
$728$	−1.03358	−	11.8138i	−0.0383069	−	0.437850i
$729$	37.9194	+	21.8928i	1.40442	+	0.810843i
$730$		0			0
$731$	−6.07174	+	34.4346i	−0.224572	+	1.27361i
$732$	−9.18483	+	6.43129i	−0.339481	+	0.237707i
$733$	−9.53138	+	35.5716i	−0.352050	+	1.31387i	0.532107	+	0.846677i	$0.321400\pi$
$733$	−9.53138	+	35.5716i	−0.352050	+	1.31387i	−0.884157	+	0.467190i	$0.845266\pi$
$734$	5.82989	−	10.0977i	0.215185	−	0.372711i
$735$		0			0
$736$	−0.512958	+	1.40934i	−0.0189079	+	0.0519490i
$737$	61.5292	+	28.6915i	2.26646	+	1.05687i
$738$	13.9220	+	1.21801i	0.512475	+	0.0448357i
$739$	−3.16407	+	0.557912i	−0.116392	+	0.0205231i	−0.231541	−	0.972825i	$-0.574377\pi$
$739$	−3.16407	+	0.557912i	−0.116392	+	0.0205231i	0.115149	+	0.993348i	$0.463266\pi$
$740$		0			0
$741$	−4.11199	−	38.4897i	−0.151058	−	1.41396i
$742$	−24.2675	+	24.2675i	−0.890889	+	0.890889i
$743$	−17.9344	−	12.5578i	−0.657950	−	0.460702i	0.196314	−	0.980541i	$-0.437103\pi$
$743$	−17.9344	−	12.5578i	−0.657950	−	0.460702i	−0.854264	+	0.519839i	$0.825992\pi$
$744$	−4.73183	+	3.97048i	−0.173477	+	0.145565i
$745$		0			0
$746$	16.9351	+	6.16387i	0.620038	+	0.225675i
$747$	−4.74978	+	0.415552i	−0.173785	+	0.0152042i
$748$	20.7804	−	5.56808i	0.759805	−	0.203589i
$749$	6.74083	+	11.6755i	0.246305	+	0.426612i
$750$		0			0
$751$	−30.5802	−	5.39212i	−1.11589	−	0.196761i	−0.414853	−	0.909888i	$-0.636167\pi$
$751$	−30.5802	−	5.39212i	−1.11589	−	0.196761i	−0.701035	+	0.713127i	$0.747278\pi$
$752$	10.6269	+	2.84746i	0.387522	+	0.103836i
$753$	15.4700	+	57.7350i	0.563760	+	2.10398i
$754$	−0.862450	−	0.723681i	−0.0314086	−	0.0263549i
$755$		0			0
$756$	−6.51375	−	17.8964i	−0.236903	−	0.650885i
$757$	1.03954	−	11.8819i	0.0377825	−	0.431856i	−0.953620	−	0.301012i	$-0.902676\pi$
$757$	1.03954	−	11.8819i	0.0377825	−	0.431856i	0.991403	−	0.130844i	$-0.0417689\pi$
$758$	17.5620	−	25.0811i	0.637880	−	0.910987i
$759$	21.8698			0.793823
$760$		0			0
$761$	−10.1631			−0.368411			−0.184205	−	0.982888i	$-0.558971\pi$
$761$	−10.1631			−0.368411			−0.184205	+	0.982888i	$0.558971\pi$
$762$	26.6611	−	38.0760i	0.965829	−	1.37935i
$763$	−0.440506	+	5.03501i	−0.0159474	+	0.182279i
$764$	7.24099	+	19.8944i	0.261970	+	0.719756i
$765$		0			0
$766$	4.57369	+	3.83778i	0.165254	+	0.138665i
$767$	1.86929	+	6.97630i	0.0674963	+	0.251899i
$768$	2.70166	+	0.723908i	0.0974878	+	0.0261218i
$769$	33.4491	+	5.89798i	1.20621	+	0.212687i	0.740379	−	0.672190i	$-0.234646\pi$
$769$	33.4491	+	5.89798i	1.20621	+	0.212687i	0.465826	+	0.884876i	$0.345757\pi$
$770$		0			0
$771$	−5.33515	−	9.24075i	−0.192141	−	0.332798i
$772$	16.2523	−	4.35478i	0.584931	−	0.156732i
$773$	13.9757	−	1.22271i	0.502671	−	0.0439780i	0.166999	−	0.985957i	$-0.446592\pi$
$773$	13.9757	−	1.22271i	0.502671	−	0.0439780i	0.335672	+	0.941979i	$0.391037\pi$
$774$	38.4031	+	13.9776i	1.38037	+	0.502414i
$775$		0			0
$776$	13.2647	−	11.1304i	0.476174	−	0.399557i
$777$	62.0093	+	43.4194i	2.22457	+	1.55766i
$778$	7.52673	−	7.52673i	0.269846	−	0.269846i
$779$	9.10048	+	8.75821i	0.326059	+	0.313795i
$780$		0			0
$781$	37.4356	−	6.60091i	1.33955	−	0.236199i
$782$	6.16533	+	0.539396i	0.220472	+	0.0192888i
$783$	−1.63866	−	0.764119i	−0.0585609	−	0.0273074i
$784$	2.37735	−	6.53172i	0.0849054	−	0.233276i
$785$		0			0
$786$	−8.87192	+	15.3666i	−0.316451	+	0.548109i
$787$	2.96874	−	11.0795i	0.105824	−	0.394941i	−0.892613	−	0.450823i	$-0.851130\pi$
$787$	2.96874	−	11.0795i	0.105824	−	0.394941i	0.998437	+	0.0558821i	$0.0177971\pi$
$788$	2.65123	−	1.85641i	0.0944462	−	0.0661319i
$789$	−9.78194	+	55.4762i	−0.348246	+	1.97500i
$790$		0			0
$791$	36.5767	+	21.1176i	1.30052	+	0.750855i
$792$	−2.19150	−	25.0490i	−0.0778717	−	0.890078i
$793$	11.5356	−	5.37914i	0.409642	−	0.191019i
$794$	−11.2934	+	4.11045i	−0.400787	+	0.145874i
$795$		0			0
$796$	−2.20649	−	12.5136i	−0.0782070	−	0.443534i
$797$	−4.02945	−	4.02945i	−0.142731	−	0.142731i	0.632131	−	0.774862i	$-0.282180\pi$
$797$	−4.02945	−	4.02945i	−0.142731	−	0.142731i	−0.774862	+	0.632131i	$0.782180\pi$
$798$	14.7518	−	43.0814i	0.522207	−	1.52507i
$799$		−	45.3987i		−	1.60609i
$800$		0			0
$801$	8.89362	+	10.5990i	0.314241	+	0.374497i
$802$	14.5379	−	31.1767i	0.513353	−	1.10089i
$803$	7.75863	+	16.6384i	0.273796	+	0.587157i
$804$	23.4117	−	27.9009i	0.825666	−	0.983991i
$805$		0			0
$806$	6.07245	−	3.50593i	0.213893	−	0.123491i
$807$	24.7226	+	35.3076i	0.870277	+	1.24288i
$808$	1.70380	+	2.43328i	0.0599396	+	0.0856026i
$809$	−40.2605	+	23.2444i	−1.41548	+	0.817229i	−0.995898	−	0.0904866i	$-0.971158\pi$
$809$	−40.2605	+	23.2444i	−1.41548	+	0.817229i	−0.419585	+	0.907716i	$0.637824\pi$
$810$		0			0
$811$	15.9337	−	18.9890i	0.559508	−	0.666795i	−0.409935	−	0.912115i	$-0.634448\pi$
$811$	15.9337	−	18.9890i	0.559508	−	0.666795i	0.969442	+	0.245320i	$0.0788929\pi$
$812$	−0.559737	−	1.20036i	−0.0196429	−	0.0421244i
$813$	5.86972	−	12.5877i	0.205860	−	0.441469i
$814$	24.2828	+	28.9391i	0.851113	+	1.01432i
$815$		0			0
$816$		−	11.5417i		−	0.404040i
$817$	19.0771	+	31.6269i	0.667422	+	1.10649i
$818$	−21.9712	−	21.9712i	−0.768206	−	0.768206i
$819$	9.93197	+	56.3270i	0.347051	+	1.96823i
$820$		0			0
$821$	29.8183	−	10.8530i	1.04067	−	0.378772i	0.235534	−	0.971866i	$-0.424316\pi$
$821$	29.8183	−	10.8530i	1.04067	−	0.378772i	0.805133	+	0.593095i	$0.202094\pi$
$822$	16.7520	−	7.81158i	0.584293	−	0.272460i
$823$	4.53640	+	51.8513i	0.158129	+	1.80742i	0.498241	+	0.867039i	$0.333980\pi$
$823$	4.53640	+	51.8513i	0.158129	+	1.80742i	−0.340112	+	0.940385i	$0.610465\pi$
$824$	−1.54963	−	0.894679i	−0.0539839	−	0.0311676i
$825$		0			0
$826$	−1.47539	+	8.36737i	−0.0513355	+	0.291138i
$827$	−39.1319	+	27.4005i	−1.36075	+	0.952808i	−0.360956	+	0.932583i	$0.617549\pi$
$827$	−39.1319	+	27.4005i	−1.36075	+	0.952808i	−0.999795	+	0.0202253i	$0.993562\pi$
$828$	1.87217	−	6.98703i	0.0650624	−	0.242816i
$829$	−0.789427	+	1.36733i	−0.0274179	+	0.0474892i	−0.879409	−	0.476067i	$-0.842062\pi$
$829$	−0.789427	+	1.36733i	−0.0274179	+	0.0474892i	0.851991	+	0.523557i	$0.175395\pi$
$830$		0			0
$831$	−17.8597	+	49.0693i	−0.619548	+	1.70219i
$832$	−2.87754	−	1.34182i	−0.0997606	−	0.0465191i
$833$	−28.5738	−	2.49988i	−0.990023	−	0.0866158i
$834$	10.0676	−	1.77519i	0.348612	−	0.0614697i
$835$		0			0
$836$	12.6754	−	18.8616i	0.438389	−	0.652342i
$837$	7.96253	−	7.96253i	0.275225	−	0.275225i
$838$	−18.0639	−	12.6485i	−0.624007	−	0.436934i
$839$	4.61880	−	3.87563i	0.159459	−	0.133802i	−0.559567	−	0.828785i	$-0.689033\pi$
$839$	4.61880	−	3.87563i	0.159459	−	0.133802i	0.719026	+	0.694983i	$0.244588\pi$
$840$		0			0
$841$	27.1329	+	9.87558i	0.935618	+	0.340537i
$842$	−27.0494	+	2.36652i	−0.932185	+	0.0815556i
$843$	6.75244	−	1.80931i	0.232566	−	0.0623160i
$844$	−6.63533	−	11.4927i	−0.228398	−	0.395596i
$845$		0			0
$846$	−52.2555	−	9.21405i	−1.79658	−	0.316786i
$847$	−58.3758	−	15.6418i	−2.00582	−	0.537457i
$848$	2.37813	+	8.87530i	0.0816653	+	0.304779i
$849$	−27.4277	−	23.0145i	−0.941315	−	0.789857i
$850$		0			0
$851$	3.71694	+	10.2122i	0.127415	+	0.350070i
$852$	1.77742	−	20.3160i	0.0608933	−	0.696014i
$853$	−10.0603	+	14.3676i	−0.344458	+	0.491938i	−0.953580	−	0.301139i	$-0.902633\pi$
$853$	−10.0603	+	14.3676i	−0.344458	+	0.491938i	0.609122	+	0.793077i	$0.291522\pi$
$854$	14.9734			0.512380
$855$		0			0
$856$	3.60946			0.123369
$857$	−19.8447	+	28.3411i	−0.677882	+	0.968115i	0.321891	+	0.946777i	$0.395682\pi$
$857$	−19.8447	+	28.3411i	−0.677882	+	0.968115i	−0.999772	+	0.0213384i	$0.993207\pi$
$858$	−4.03511	+	46.1216i	−0.137757	+	1.57456i
$859$	−5.78845	−	15.9036i	−0.197499	−	0.542625i	0.800924	−	0.598767i	$-0.204342\pi$
$859$	−5.78845	−	15.9036i	−0.197499	−	0.542625i	−0.998423	+	0.0561419i	$0.982120\pi$
$860$		0			0
$861$	−23.1889	−	19.4578i	−0.790275	−	0.663120i
$862$	−1.60567	−	5.99242i	−0.0546892	−	0.204103i
$863$	−20.7811	−	5.56828i	−0.707397	−	0.189547i	−0.112856	−	0.993611i	$-0.536000\pi$
$863$	−20.7811	−	5.56828i	−0.707397	−	0.189547i	−0.594542	+	0.804065i	$0.702666\pi$
$864$	−5.02145	−	0.885418i	−0.170833	−	0.0301225i
$865$		0			0
$866$	−2.55041	−	4.41743i	−0.0866663	−	0.150111i
$867$	−0.0756483	+	0.0202699i	−0.00256915	+	0.000688402i
$868$	8.21739	−	0.718928i	0.278916	−	0.0244020i
$869$	−5.99168	−	2.18079i	−0.203254	−	0.0739783i
$870$		0			0
$871$	−31.6721	+	26.5761i	−1.07317	+	0.900495i
$872$	1.10846	+	0.776150i	0.0375371	+	0.0262838i
$873$	−59.0536	+	59.0536i	−1.99866	+	1.99866i
$874$	5.28231	−	3.85164i	0.178677	−	0.130284i
$875$		0			0
$876$	9.69946	−	1.71028i	0.327714	−	0.0577849i
$877$	41.2273	+	3.60693i	1.39215	+	0.121797i	0.758424	−	0.651761i	$-0.225970\pi$
$877$	41.2273	+	3.60693i	1.39215	+	0.121797i	0.633725	+	0.773559i	$0.281525\pi$
$878$	6.64307	+	3.09771i	0.224193	+	0.104543i
$879$	11.8170	−	32.4670i	0.398579	−	1.09509i
$880$		0			0
$881$	−21.7611	+	37.6914i	−0.733152	+	1.26986i	0.222378	+	0.974961i	$0.428618\pi$
$881$	−21.7611	+	37.6914i	−0.733152	+	1.26986i	−0.955530	+	0.294895i	$0.904715\pi$
$882$	−8.67674	+	32.3820i	−0.292161	+	1.09036i
$883$	17.8820	−	12.5211i	0.601777	−	0.421369i	−0.232593	−	0.972574i	$-0.574721\pi$
$883$	17.8820	−	12.5211i	0.601777	−	0.421369i	0.834370	+	0.551205i	$0.185832\pi$
$884$	−2.27508	+	12.9026i	−0.0765193	+	0.433963i
$885$		0			0
$886$	−19.1155	−	11.0363i	−0.642198	−	0.370773i
$887$	1.31558	+	15.0371i	0.0441728	+	0.504898i	0.985763	+	0.168138i	$0.0537754\pi$
$887$	1.31558	+	15.0371i	0.0441728	+	0.504898i	−0.941591	+	0.336760i	$0.890669\pi$
$888$	18.3682	−	8.56524i	0.616397	−	0.287431i
$889$	−58.3293	+	21.2301i	−1.95630	+	0.712035i
$890$		0			0
$891$	−0.187903	−	1.06565i	−0.00629499	−	0.0357007i
$892$	6.99726	+	6.99726i	0.234285	+	0.234285i
$893$	−31.5235	−	36.1386i	−1.05489	−	1.20933i
$894$		−	3.55497i		−	0.118896i
$895$		0			0
$896$	−2.40087	−	2.86125i	−0.0802075	−	0.0955875i
$897$	−5.62873	+	12.0709i	−0.187938	+	0.403034i
$898$	0.425171	+	0.911782i	0.0141881	+	0.0304266i
$899$	0.503374	−	0.599897i	0.0167885	−	0.0200077i
$900$		0			0
$901$	32.8361	−	18.9579i	1.09393	−	0.631581i
$902$	−8.66476	−	12.3746i	−0.288505	−	0.412028i
$903$	−50.7740	−	72.5128i	−1.68965	−	2.41307i
$904$	9.79272	−	5.65383i	0.325701	−	0.188044i
$905$		0			0
$906$	30.4258	−	36.2601i	1.01083	−	1.20466i
$907$	7.64216	+	16.3887i	0.253754	+	0.544177i	0.991378	−	0.131035i	$-0.0418301\pi$
$907$	7.64216	+	16.3887i	0.253754	+	0.544177i	−0.737624	+	0.675212i	$0.764052\pi$
$908$	4.94308	−	10.6005i	0.164042	−	0.351789i
$909$	−9.20904	−	10.9749i	−0.305445	−	0.364015i
$910$		0			0
$911$			18.7758i			0.622069i	0.950399	+	0.311035i	$0.100676\pi$
$911$			18.7758i			0.622069i	−0.950399	+	0.311035i	$0.899324\pi$
$912$	−8.01419	−	9.18749i	−0.265376	−	0.304228i
$913$	3.64437	+	3.64437i	0.120611	+	0.120611i
$914$	−5.45283	−	30.9245i	−0.180364	−	1.02289i
$915$		0			0
$916$	19.9396	−	7.25744i	0.658824	−	0.239792i
$917$	21.4752	−	10.0141i	0.709174	−	0.330693i
$918$	1.83382	+	20.9606i	0.0605249	+	0.691803i
$919$	−12.6932	−	7.32842i	−0.418710	−	0.241742i	0.275815	−	0.961211i	$-0.411052\pi$
$919$	−12.6932	−	7.32842i	−0.418710	−	0.241742i	−0.694525	+	0.719468i	$0.744385\pi$
$920$		0			0
$921$	−1.76842	+	10.0292i	−0.0582713	+	0.330473i
$922$	6.52692	−	4.57020i	0.214953	−	0.150512i
$923$	−5.99167	+	22.3612i	−0.197218	+	0.736028i
$924$	−27.2324	+	47.1679i	−0.895880	+	1.55171i
$925$		0			0
$926$	−0.592461	+	1.62777i	−0.0194695	+	0.0534919i
$927$	7.82153	+	3.64724i	0.256893	+	0.119791i
$928$	−0.353247	−	0.0309051i	−0.0115959	−	0.00101451i
$929$	11.5080	−	2.02917i	0.377565	−	0.0665748i	0.0183545	−	0.999832i	$-0.494157\pi$
$929$	11.5080	−	2.02917i	0.377565	−	0.0665748i	0.359210	+	0.933257i	$0.383046\pi$
$930$		0			0
$931$	−24.4814	+	17.8508i	−0.802344	+	0.585036i
$932$	−10.4773	+	10.4773i	−0.343195	+	0.343195i
$933$	67.4975	+	47.2623i	2.20977	+	1.54730i
$934$	−20.1116	+	16.8756i	−0.658070	+	0.552186i
$935$		0			0
$936$	14.3896	+	5.23740i	0.470340	+	0.171190i
$937$	−46.7237	+	4.08779i	−1.52640	+	0.133542i	−0.819213	−	0.573489i	$-0.805589\pi$
$937$	−46.7237	+	4.08779i	−1.52640	+	0.133542i	−0.707182	+	0.707032i	$0.750034\pi$
$938$	−46.9811	+	12.5885i	−1.53399	+	0.411030i
$939$	18.1623	+	31.4581i	0.592705	+	1.02659i
$940$		0			0
$941$	9.67514	+	1.70599i	0.315401	+	0.0556137i	0.329108	−	0.944292i	$-0.393252\pi$
$941$	9.67514	+	1.70599i	0.315401	+	0.0556137i	−0.0137070	+	0.999906i	$0.504363\pi$
$942$	36.0036	+	9.64714i	1.17306	+	0.314321i
$943$	−1.12477	−	4.19770i	−0.0366276	−	0.136696i
$944$	1.74257	+	1.46219i	0.0567158	+	0.0475902i
$945$		0			0
$946$	−15.1092	−	41.5121i	−0.491242	−	1.34968i
$947$	−0.633145	+	7.23687i	−0.0205744	+	0.235167i	0.978944	+	0.204130i	$0.0654365\pi$
$947$	−0.633145	+	7.23687i	−0.0205744	+	0.235167i	−0.999518	+	0.0310369i	$0.990119\pi$
$948$	−1.96207	+	2.80212i	−0.0637249	+	0.0910087i
$949$	−11.1803			−0.362929
$950$		0			0
$951$	1.25254			0.0406165
$952$	−8.84045	+	12.6255i	−0.286521	+	0.409194i
$953$	1.31757	−	15.0599i	0.0426802	−	0.487837i	−0.944531	−	0.328421i	$-0.893483\pi$
$953$	1.31757	−	15.0599i	0.0426802	−	0.487837i	0.987212	−	0.159416i	$-0.0509610\pi$
$954$	−15.1569	−	41.6432i	−0.490722	−	1.34825i
$955$		0			0
$956$	6.86828	+	5.76317i	0.222136	+	0.186394i
$957$	1.33828	+	4.99451i	0.0432603	+	0.161450i
$958$	4.97174	+	1.33217i	0.160630	+	0.0430405i
$959$	−24.3084	−	4.28623i	−0.784959	−	0.138410i
$960$		0			0
$961$	−13.0614	−	22.6230i	−0.421334	−	0.729773i
$962$	−22.2225	+	5.95450i	−0.716482	+	0.191981i
$963$	−17.3422	+	1.51725i	−0.558846	+	0.0488927i
$964$	−9.02779	−	3.28585i	−0.290766	−	0.105830i
$965$		0			0
$966$	−12.0025	+	10.0713i	−0.386175	+	0.324039i
$967$	42.8550	+	30.0074i	1.37812	+	0.964972i	0.999218	+	0.0395366i	$0.0125882\pi$
$967$	42.8550	+	30.0074i	1.37812	+	0.964972i	0.378905	+	0.925436i	$0.376301\pi$
$968$	−11.4412	+	11.4412i	−0.367735	+	0.367735i
$969$	−28.0611	+	41.7561i	−0.901452	+	1.34140i
$970$		0			0
$971$	−11.8050	+	2.08154i	−0.378840	+	0.0667997i	−0.359826	−	0.933020i	$-0.617164\pi$
$971$	−11.8050	+	2.08154i	−0.378840	+	0.0667997i	−0.0190140	+	0.999819i	$0.506053\pi$
$972$	−15.8169	−	1.38380i	−0.507326	−	0.0443853i
$973$	−12.3727	−	5.76947i	−0.396650	−	0.184961i
$974$	−11.8681	+	32.6073i	−0.380278	+	1.04480i
$975$		0			0
$976$	2.00442	−	3.47177i	0.0641601	−	0.111128i
$977$	5.71733	−	21.3374i	0.182914	−	0.682643i	−0.812154	−	0.583443i	$-0.801705\pi$
$977$	5.71733	−	21.3374i	0.182914	−	0.682643i	0.995068	−	0.0991998i	$-0.0316283\pi$
$978$	56.4399	−	39.5196i	1.80475	−	1.26370i
$979$	2.59711	−	14.7289i	0.0830039	−	0.470739i
$980$		0			0
$981$	−5.65202	−	3.26320i	−0.180455	−	0.104186i
$982$	−0.146449	−	1.67392i	−0.00467337	−	0.0534169i
$983$	−1.55811	+	0.726558i	−0.0496960	+	0.0231736i	−0.447307	−	0.894380i	$-0.647617\pi$
$983$	−1.55811	+	0.726558i	−0.0496960	+	0.0231736i	0.397611	+	0.917554i	$0.369839\pi$
$984$	−7.61571	+	2.77189i	−0.242780	+	0.0883647i
$985$		0			0
$986$	0.254090	+	1.44101i	0.00809186	+	0.0458912i
$987$	81.2709	+	81.2709i	2.58688	+	2.58688i
$988$	7.14817	+	11.8506i	0.227414	+	0.377018i
$989$		−	12.7084i		−	0.404104i
$990$		0			0
$991$	27.6507	+	32.9528i	0.878353	+	1.04678i	0.998539	+	0.0540291i	$0.0172064\pi$
$991$	27.6507	+	32.9528i	0.878353	+	1.04678i	−0.120186	+	0.992751i	$0.538349\pi$
$992$	0.933333	−	2.00154i	0.0296333	−	0.0635489i
$993$	10.4557	+	22.4223i	0.331801	+	0.711549i
$994$	−17.5055	+	20.8623i	−0.555241	+	0.661711i
$995$		0			0
$996$	2.39457	−	1.38251i	0.0758750	−	0.0438064i
$997$	−13.9141	−	19.8713i	−0.440663	−	0.629332i	0.535972	−	0.844235i	$-0.319945\pi$
$997$	−13.9141	−	19.8713i	−0.440663	−	0.629332i	−0.976635	+	0.214904i	$0.931056\pi$
$998$	21.4752	+	30.6697i	0.679785	+	0.970834i
$999$	−31.9973	+	18.4736i	−1.01235	+	0.584480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.143.1		120
5.2	odd	4	inner	950.2.bb.e.257.5		120
5.3	odd	4		190.2.r.a.67.6	✓	120
5.4	even	2		190.2.r.a.143.10	yes	120
19.2	odd	18	inner	950.2.bb.e.743.5		120
95.2	even	36	inner	950.2.bb.e.857.1		120
95.59	odd	18		190.2.r.a.173.6	yes	120
95.78	even	36		190.2.r.a.97.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.6	✓	120	5.3	odd	4
190.2.r.a.97.10	yes	120	95.78	even	36
190.2.r.a.143.10	yes	120	5.4	even	2
190.2.r.a.173.6	yes	120	95.59	odd	18
950.2.bb.e.143.1		120	1.1	even	1	trivial
950.2.bb.e.257.5		120	5.2	odd	4	inner
950.2.bb.e.743.5		120	19.2	odd	18	inner
950.2.bb.e.857.1		120	95.2	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.243772 + 2.78632i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.14260 - 1.79785i) q^{6} +(0.966713 + 3.60782i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-4.74974 - 0.837508i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.243772 + 2.78632i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.14260 - 1.79785i) q^{6} +(0.966713 + 3.60782i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-4.74974 - 0.837508i) q^{9} +(2.60674 + 4.51500i) q^{11} +(2.70166 - 0.723908i) q^{12} +(-3.16293 + 0.276720i) q^{13} +(-3.50984 - 1.27748i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(3.38023 + 2.36686i) q^{17} +(3.41039 - 3.41039i) q^{18} +(4.33423 - 0.463042i) q^{19} +(-10.2882 + 1.81409i) q^{21} +(-5.19364 - 0.454385i) q^{22} +(-1.35927 - 0.633838i) q^{23} +(-0.956619 + 2.62829i) q^{24} +(1.58751 - 2.74964i) q^{26} +(1.31970 - 4.92518i) q^{27} +(3.05961 - 2.14236i) q^{28} +(0.0615751 - 0.349210i) q^{29} +(1.91258 + 1.10423i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-13.2157 + 6.16259i) q^{33} +(-3.87764 + 1.41135i) q^{34} +(0.837508 + 4.74974i) q^{36} +(-5.12376 - 5.12376i) q^{37} +(-2.10671 + 3.81599i) q^{38} -8.88040i q^{39} +(1.86254 + 2.21969i) q^{41} +(4.41506 - 9.46813i) q^{42} +(3.58104 + 7.67957i) q^{43} +(3.35116 - 3.99376i) q^{44} +(1.29886 - 0.749894i) q^{46} +(-6.31034 - 9.01210i) q^{47} +(-1.60427 - 2.29114i) q^{48} +(-6.01967 + 3.47546i) q^{49} +(-7.41885 + 8.84144i) q^{51} +(1.34182 + 2.87754i) q^{52} +(3.88318 - 8.32751i) q^{53} +(3.27752 + 3.90600i) q^{54} +3.73509i q^{56} +(0.233620 + 12.1895i) q^{57} +(0.250738 + 0.250738i) q^{58} +(-0.395008 - 2.24020i) q^{59} +(-3.76709 + 1.37111i) q^{61} +(-2.00154 + 0.933333i) q^{62} +(-1.57006 - 17.9459i) q^{63} +(0.866025 + 0.500000i) q^{64} +(2.53212 - 14.3604i) q^{66} +(10.6670 - 7.46911i) q^{67} +(1.06802 - 3.98589i) q^{68} +(2.09743 - 3.63285i) q^{69} +(2.49378 - 6.85160i) q^{71} +(-4.37114 - 2.03830i) q^{72} +(3.50795 + 0.306906i) q^{73} +(7.13601 - 1.25827i) q^{74} +(-1.91751 - 3.91448i) q^{76} +(-13.7694 + 13.7694i) q^{77} +(7.27439 + 5.09359i) q^{78} +(-0.936891 + 0.786145i) q^{79} +(-0.195039 - 0.0709885i) q^{81} +(-2.88657 + 0.252542i) q^{82} +(0.954892 - 0.255862i) q^{83} +(5.22346 + 9.04730i) q^{84} +(-8.34474 - 1.47140i) q^{86} +(0.958000 + 0.256695i) q^{87} +(1.34935 + 5.03583i) q^{88} +(-2.19759 - 1.84399i) q^{89} +(-4.05600 - 11.1438i) q^{91} +(-0.130715 + 1.49408i) q^{92} +(-3.54296 + 5.05988i) q^{93} +11.0017 q^{94} +2.79697 q^{96} +(9.93194 - 14.1843i) q^{97} +(0.605812 - 6.92446i) q^{98} +(-8.59999 - 23.6283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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