LMFDB - Embedded newform 627.2.be.a.439.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(10,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

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

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

chi := DirichletCharacter("627.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.be (of order $18$, degree $6$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			439.31
Character	$\chi$	$=$	627.439
Dual form			627.2.be.a.10.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.296656 - 1.68242i) q^{2} +(0.642788 - 0.766044i) q^{3} +(-0.863144 - 0.314159i) q^{4} +(-2.17291 + 0.790873i) q^{5} +(-1.09812 - 1.30869i) q^{6} +(-3.30762 + 1.90965i) q^{7} +(0.923770 - 1.60002i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.685974 + 3.89035i) q^{10} +(-3.12308 - 1.11640i) q^{11} +(-0.795477 + 0.459269i) q^{12} +(-2.99816 + 2.51575i) q^{13} +(2.23161 + 6.13130i) q^{14} +(-0.790873 + 2.17291i) q^{15} +(-3.82514 - 3.20967i) q^{16} +(-0.113235 - 0.0199663i) q^{17} -1.70837 q^{18} +(-2.69644 - 3.42479i) q^{19} +2.12399 q^{20} +(-0.663215 + 3.76128i) q^{21} +(-2.80473 + 4.92315i) q^{22} +(3.70986 + 1.35028i) q^{23} +(-0.631896 - 1.73612i) q^{24} +(0.265815 - 0.223045i) q^{25} +(3.34313 + 5.79047i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(3.45488 - 0.609189i) q^{28} +(0.0543456 + 0.308209i) q^{29} +(3.42112 + 1.97518i) q^{30} +(-2.34116 + 1.35167i) q^{31} +(-3.70417 + 3.10817i) q^{32} +(-2.86269 + 1.67482i) q^{33} +(-0.0671835 + 0.184585i) q^{34} +(5.67684 - 6.76540i) q^{35} +(-0.159502 + 0.904583i) q^{36} +6.00912i q^{37} +(-6.56185 + 3.52056i) q^{38} +3.91382i q^{39} +(-0.741855 + 4.20727i) q^{40} +(-0.828613 - 0.695288i) q^{41} +(6.13130 + 2.23161i) q^{42} +(-3.59749 - 9.88402i) q^{43} +(2.34494 + 1.94475i) q^{44} +(1.15618 + 2.00256i) q^{45} +(3.37229 - 5.84097i) q^{46} +(-0.195328 - 1.10776i) q^{47} +(-4.91750 + 0.867089i) q^{48} +(3.79355 - 6.57061i) q^{49} +(-0.296399 - 0.513379i) q^{50} +(-0.0880810 + 0.0739087i) q^{51} +(3.37819 - 1.22956i) q^{52} +(4.33203 - 11.9021i) q^{53} +(-1.09812 + 1.30869i) q^{54} +(7.66909 - 0.0441393i) q^{55} +7.05632i q^{56} +(-4.35678 - 0.135821i) q^{57} +0.534659 q^{58} +(-3.47260 - 0.612314i) q^{59} +(1.36527 - 1.62707i) q^{60} +(1.61428 - 4.43520i) q^{61} +(1.57955 + 4.33979i) q^{62} +(2.45500 + 2.92576i) q^{63} +(-0.862990 - 1.49474i) q^{64} +(4.52507 - 7.83765i) q^{65} +(1.96851 + 5.31309i) q^{66} +(8.54881 - 1.50739i) q^{67} +(0.0914652 + 0.0528075i) q^{68} +(3.41903 - 1.97398i) q^{69} +(-9.69816 - 11.5578i) q^{70} +(0.977423 + 2.68545i) q^{71} +(-1.73612 - 0.631896i) q^{72} +(-7.00027 + 8.34260i) q^{73} +(10.1099 + 1.78264i) q^{74} -0.346996i q^{75} +(1.25149 + 3.80320i) q^{76} +(12.4619 - 2.27140i) q^{77} +(6.58468 + 1.16106i) q^{78} +(4.90702 + 4.11748i) q^{79} +(10.8501 + 3.94912i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-1.41558 + 1.18781i) q^{82} +(6.81158 - 3.93267i) q^{83} +(1.75409 - 3.03817i) q^{84} +(0.261839 - 0.0461693i) q^{85} +(-17.6963 + 3.12033i) q^{86} +(0.271035 + 0.156482i) q^{87} +(-4.67127 + 3.96569i) q^{88} +(-5.79174 - 6.90232i) q^{89} +(3.71213 - 1.35111i) q^{90} +(5.11254 - 14.0466i) q^{91} +(-2.77794 - 2.33097i) q^{92} +(-0.469429 + 2.66226i) q^{93} -1.92166 q^{94} +(8.56769 + 5.30921i) q^{95} +4.83545i q^{96} +(-16.6934 - 2.94349i) q^{97} +(-9.92915 - 8.33154i) q^{98} +(-0.557118 + 3.26950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) $ 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.296656	−	1.68242i	0.209767	−	1.18965i	−0.679992	−	0.733220i	$-0.738017\pi$
$2$	0.296656	−	1.68242i	0.209767	−	1.18965i	0.889759	−	0.456430i	$-0.150872\pi$
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	−0.863144	−	0.314159i	−0.431572	−	0.157079i
$5$	−2.17291	+	0.790873i	−0.971753	+	0.353689i	−0.778628	−	0.627485i	$-0.784084\pi$
$5$	−2.17291	+	0.790873i	−0.971753	+	0.353689i	−0.193124	+	0.981174i	$0.561862\pi$
$6$	−1.09812	−	1.30869i	−0.448306	−	0.534270i
$7$	−3.30762	+	1.90965i	−1.25016	+	0.721781i	−0.971141	−	0.238505i	$-0.923343\pi$
$7$	−3.30762	+	1.90965i	−1.25016	+	0.721781i	−0.279020	+	0.960285i	$0.590009\pi$
$8$	0.923770	−	1.60002i	0.326602	−	0.565691i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	0.685974	+	3.89035i	0.216924	+	1.23024i
$11$	−3.12308	−	1.11640i	−0.941646	−	0.336606i
$11$	−3.12308	−	1.11640i	−0.941646	−	0.336606i
$12$	−0.795477	+	0.459269i	−0.229635	+	0.132580i
$13$	−2.99816	+	2.51575i	−0.831539	+	0.697744i	−0.955644	−	0.294525i	$-0.904839\pi$
$13$	−2.99816	+	2.51575i	−0.831539	+	0.697744i	0.124105	+	0.992269i	$0.460394\pi$
$14$	2.23161	+	6.13130i	0.596423	+	1.63866i
$15$	−0.790873	+	2.17291i	−0.204202	+	0.561042i
$16$	−3.82514	−	3.20967i	−0.956285	−	0.802418i
$17$	−0.113235	−	0.0199663i	−0.0274635	−	0.00484255i	0.159900	−	0.987133i	$-0.448883\pi$
$17$	−0.113235	−	0.0199663i	−0.0274635	−	0.00484255i	−0.187363	+	0.982291i	$0.559994\pi$
$18$	−1.70837			−0.402667
$19$	−2.69644	−	3.42479i	−0.618606	−	0.785701i
$19$	−2.69644	−	3.42479i	−0.618606	−	0.785701i
$20$	2.12399			0.474938
$21$	−0.663215	+	3.76128i	−0.144725	+	0.820779i
$22$	−2.80473	+	4.92315i	−0.597970	+	1.04962i
$23$	3.70986	+	1.35028i	0.773559	+	0.281553i	0.698484	−	0.715625i	$-0.253858\pi$
$23$	3.70986	+	1.35028i	0.773559	+	0.281553i	0.0750750	+	0.997178i	$0.476080\pi$
$24$	−0.631896	−	1.73612i	−0.128985	−	0.354384i
$25$	0.265815	−	0.223045i	0.0531629	−	0.0446090i
$26$	3.34313	+	5.79047i	0.655642	+	1.13560i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	3.45488	−	0.609189i	0.652911	−	0.115126i
$29$	0.0543456	+	0.308209i	0.0100917	+	0.0572330i	0.989438	−	0.144958i	$-0.0463048\pi$
$29$	0.0543456	+	0.308209i	0.0100917	+	0.0572330i	−0.979346	+	0.202191i	$0.935194\pi$
$30$	3.42112	+	1.97518i	0.624608	+	0.360618i
$31$	−2.34116	+	1.35167i	−0.420484	+	0.242767i	−0.695284	−	0.718735i	$-0.744722\pi$
$31$	−2.34116	+	1.35167i	−0.420484	+	0.242767i	0.274800	+	0.961501i	$0.411388\pi$
$32$	−3.70417	+	3.10817i	−0.654811	+	0.549451i
$33$	−2.86269	+	1.67482i	−0.498330	+	0.291548i
$34$	−0.0671835	+	0.184585i	−0.0115219	+	0.0316561i
$35$	5.67684	−	6.76540i	0.959561	−	1.14356i
$36$	−0.159502	+	0.904583i	−0.0265837	+	0.150764i
$37$			6.00912i			0.987893i	0.869492	+	0.493947i	$0.164446\pi$
$37$			6.00912i			0.987893i	−0.869492	+	0.493947i	$0.835554\pi$
$38$	−6.56185	+	3.52056i	−1.06447	+	0.571110i
$39$			3.91382i			0.626712i
$40$	−0.741855	+	4.20727i	−0.117298	+	0.665228i
$41$	−0.828613	−	0.695288i	−0.129408	−	0.108586i	0.575787	−	0.817600i	$-0.304696\pi$
$41$	−0.828613	−	0.695288i	−0.129408	−	0.108586i	−0.705194	+	0.709014i	$0.749140\pi$
$42$	6.13130	+	2.23161i	0.946081	+	0.344345i
$43$	−3.59749	−	9.88402i	−0.548612	−	1.50730i	−0.835585	−	0.549361i	$-0.814871\pi$
$43$	−3.59749	−	9.88402i	−0.548612	−	1.50730i	0.286973	−	0.957939i	$-0.407351\pi$
$44$	2.34494	+	1.94475i	0.353514	+	0.293183i
$45$	1.15618	+	2.00256i	0.172353	+	0.298524i
$46$	3.37229	−	5.84097i	0.497217	−	0.861204i
$47$	−0.195328	−	1.10776i	−0.0284915	−	0.161583i	0.967242	−	0.253854i	$-0.0816984\pi$
$47$	−0.195328	−	1.10776i	−0.0284915	−	0.161583i	−0.995734	+	0.0922713i	$0.970587\pi$
$48$	−4.91750	+	0.867089i	−0.709780	+	0.125153i
$49$	3.79355	−	6.57061i	0.541935	−	0.938659i
$50$	−0.296399	−	0.513379i	−0.0419172	−	0.0726028i
$51$	−0.0880810	+	0.0739087i	−0.0123338	+	0.0103493i
$52$	3.37819	−	1.22956i	0.468470	−	0.170509i
$53$	4.33203	−	11.9021i	0.595050	−	1.63489i	−0.165951	−	0.986134i	$-0.553069\pi$
$53$	4.33203	−	11.9021i	0.595050	−	1.63489i	0.761000	−	0.648752i	$-0.224709\pi$
$54$	−1.09812	+	1.30869i	−0.149435	+	0.178090i
$55$	7.66909	−	0.0441393i	1.03410	−	0.00595174i
$56$			7.05632i			0.942940i
$57$	−4.35678	−	0.135821i	−0.577070	−	0.0179900i
$58$	0.534659			0.0702042
$59$	−3.47260	−	0.612314i	−0.452094	−	0.0797164i	−0.0570353	−	0.998372i	$-0.518165\pi$
$59$	−3.47260	−	0.612314i	−0.452094	−	0.0797164i	−0.395059	+	0.918656i	$0.629276\pi$
$60$	1.36527	−	1.62707i	0.176256	−	0.210054i
$61$	1.61428	−	4.43520i	0.206688	−	0.567870i	−0.792426	−	0.609968i	$-0.791182\pi$
$61$	1.61428	−	4.43520i	0.206688	−	0.567870i	0.999113	+	0.0420987i	$0.0134044\pi$
$62$	1.57955	+	4.33979i	0.200603	+	0.551153i
$63$	2.45500	+	2.92576i	0.309301	+	0.368611i
$64$	−0.862990	−	1.49474i	−0.107874	−	0.186843i
$65$	4.52507	−	7.83765i	0.561266	−	0.972141i
$66$	1.96851	+	5.31309i	0.242307	+	0.653996i
$67$	8.54881	−	1.50739i	1.04440	−	0.184157i	0.374977	−	0.927034i	$-0.377651\pi$
$67$	8.54881	−	1.50739i	1.04440	−	0.184157i	0.669427	+	0.742878i	$0.266540\pi$
$68$	0.0914652	+	0.0528075i	0.0110918	+	0.00640385i
$69$	3.41903	−	1.97398i	0.411602	−	0.237639i
$70$	−9.69816	−	11.5578i	−1.15915	−	1.38142i
$71$	0.977423	+	2.68545i	0.115999	+	0.318704i	0.984082	−	0.177714i	$-0.0568703\pi$
$71$	0.977423	+	2.68545i	0.115999	+	0.318704i	−0.868083	+	0.496419i	$0.834648\pi$
$72$	−1.73612	−	0.631896i	−0.204604	−	0.0744697i
$73$	−7.00027	+	8.34260i	−0.819320	+	0.976428i	−0.999975	−	0.00711894i	$-0.997734\pi$
$73$	−7.00027	+	8.34260i	−0.819320	+	0.976428i	0.180655	+	0.983547i	$0.442178\pi$
$74$	10.1099	+	1.78264i	1.17525	+	0.207228i
$75$		−	0.346996i		−	0.0400677i
$76$	1.25149	+	3.80320i	0.143555	+	0.436257i
$77$	12.4619	−	2.27140i	1.42016	−	0.258850i
$78$	6.58468	+	1.16106i	0.745568	+	0.131464i
$79$	4.90702	+	4.11748i	0.552083	+	0.463253i	0.875646	−	0.482954i	$-0.160436\pi$
$79$	4.90702	+	4.11748i	0.552083	+	0.463253i	−0.323563	+	0.946207i	$0.604881\pi$
$80$	10.8501	+	3.94912i	1.21308	+	0.441525i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−1.41558	+	1.18781i	−0.156325	+	0.131172i
$83$	6.81158	−	3.93267i	0.747668	−	0.431666i	−0.0771825	−	0.997017i	$-0.524592\pi$
$83$	6.81158	−	3.93267i	0.747668	−	0.431666i	0.824851	+	0.565350i	$0.191259\pi$
$84$	1.75409	−	3.03817i	0.191387	−	0.331492i
$85$	0.261839	−	0.0461693i	0.0284005	−	0.00500777i
$86$	−17.6963	+	3.12033i	−1.90824	+	0.336474i
$87$	0.271035	+	0.156482i	0.0290580	+	0.0167766i
$88$	−4.67127	+	3.96569i	−0.497959	+	0.422744i
$89$	−5.79174	−	6.90232i	−0.613923	−	0.731645i	0.366090	−	0.930579i	$-0.380696\pi$
$89$	−5.79174	−	6.90232i	−0.613923	−	0.731645i	−0.980013	+	0.198935i	$0.936252\pi$
$90$	3.71213	−	1.35111i	0.391293	−	0.142419i
$91$	5.11254	−	14.0466i	0.535940	−	1.47248i
$92$	−2.77794	−	2.33097i	−0.289620	−	0.243020i
$93$	−0.469429	+	2.66226i	−0.0486775	+	0.276064i
$94$	−1.92166			−0.198204
$95$	8.56769	+	5.30921i	0.879026	+	0.544713i
$96$			4.83545i			0.493516i
$97$	−16.6934	−	2.94349i	−1.69496	−	0.298866i	−0.759028	−	0.651058i	$-0.774325\pi$
$97$	−16.6934	−	2.94349i	−1.69496	−	0.298866i	−0.935928	+	0.352192i	$0.885437\pi$
$98$	−9.92915	−	8.33154i	−1.00300	−	0.841613i
$99$	−0.557118	+	3.26950i	−0.0559925	+	0.328597i
$100$	−0.299508	+	0.109012i	−0.0299508	+	0.0109012i
$101$	8.61757	+	10.2700i	0.857480	+	1.02191i	0.999487	+	0.0320394i	$0.0102002\pi$
$101$	8.61757	+	10.2700i	0.857480	+	1.02191i	−0.142006	+	0.989866i	$0.545355\pi$
$102$	0.0982157	+	0.170115i	0.00972480	+	0.0168439i
$103$	−14.1025	−	8.14207i	−1.38956	−	0.802262i	−0.396293	−	0.918124i	$-0.629704\pi$
$103$	−14.1025	−	8.14207i	−1.38956	−	0.802262i	−0.993265	+	0.115862i	$0.963037\pi$
$104$	1.25564	+	7.12108i	0.123125	+	0.698279i
$105$	−1.53359	−	8.69743i	−0.149663	−	0.848782i
$106$	−18.7393	−	10.8191i	−1.82012	−	1.05085i
$107$	2.86881	+	4.96892i	0.277338	+	0.480364i	0.970722	−	0.240204i	$-0.0772145\pi$
$107$	2.86881	+	4.96892i	0.277338	+	0.480364i	−0.693384	+	0.720568i	$0.743881\pi$
$108$	0.590425	+	0.703641i	0.0568137	+	0.0677079i
$109$	−12.2231	+	4.44883i	−1.17076	+	0.426121i	−0.852929	−	0.522027i	$-0.825176\pi$
$109$	−12.2231	+	4.44883i	−1.17076	+	0.426121i	−0.317829	+	0.948148i	$0.602954\pi$
$110$	2.20082	−	12.9157i	0.209840	−	1.23147i
$111$	4.60325	+	3.86259i	0.436921	+	0.366621i
$112$	18.7814	+	3.31168i	1.77468	+	0.312924i
$113$			1.45137i			0.136534i	0.997667	+	0.0682668i	$0.0217469\pi$
$113$			1.45137i			0.136534i	−0.997667	+	0.0682668i	$0.978253\pi$
$114$	−1.52097	+	7.28964i	−0.142452	+	0.682737i
$115$	−9.12907			−0.851290
$116$	0.0499185	−	0.283102i	0.00463482	−	0.0262854i
$117$	2.99816	+	2.51575i	0.277180	+	0.232581i
$118$	−2.06034	+	5.66073i	−0.189669	+	0.521112i
$119$	0.412666	−	0.150198i	0.0378290	−	0.0137686i
$120$	2.74610	+	3.27267i	0.250683	+	0.298753i
$121$	8.50732	+	6.97320i	0.773393	+	0.633927i
$122$	−6.98298	−	4.03163i	−0.632210	−	0.365006i
$123$	−1.06524	+	0.187831i	−0.0960498	+	0.0169362i
$124$	2.44539	−	0.431188i	0.219603	−	0.0387219i
$125$	5.37970	−	9.31792i	0.481175	−	0.833420i
$126$	5.65064	−	3.26240i	0.503399	−	0.290638i
$127$	3.93155	−	3.29896i	0.348869	−	0.292736i	−0.451467	−	0.892288i	$-0.649099\pi$
$127$	3.93155	−	3.29896i	0.348869	−	0.292736i	0.800336	+	0.599552i	$0.204655\pi$
$128$	−11.8585	+	4.31613i	−1.04815	+	0.381495i
$129$	−9.88402	−	3.59749i	−0.870240	−	0.316741i
$130$	−11.8438	−	9.93815i	−1.03877	−	0.871634i
$131$	−16.6756	−	2.94035i	−1.45695	−	0.256900i	−0.611624	−	0.791149i	$-0.709483\pi$
$131$	−16.6756	−	2.94035i	−1.45695	−	0.256900i	−0.845327	+	0.534249i	$0.820594\pi$
$132$	2.99707	−	0.546268i	0.260861	−	0.0475465i
$133$	15.4590	+	6.17863i	1.34046	+	0.535755i
$134$		−	14.8299i		−	1.28110i
$135$	2.27723	+	0.401537i	0.195993	+	0.0345588i
$136$	−0.136549	+	0.162733i	−0.0117090	+	0.0139543i
$137$	6.95601	+	2.53178i	0.594292	+	0.216305i	0.621616	−	0.783322i	$-0.286476\pi$
$137$	6.95601	+	2.53178i	0.594292	+	0.216305i	−0.0273242	+	0.999627i	$0.508699\pi$
$138$	−2.30678	−	6.33783i	−0.196366	−	0.539512i
$139$	8.75943	+	10.4391i	0.742965	+	0.885431i	0.996644	−	0.0818573i	$-0.0260852\pi$
$139$	8.75943	+	10.4391i	0.742965	+	0.885431i	−0.253679	+	0.967288i	$0.581641\pi$
$140$	−7.02534	+	4.05608i	−0.593749	+	0.342801i
$141$	−0.974146	−	0.562424i	−0.0820379	−	0.0473646i
$142$	4.80801	−	0.847782i	0.403479	−	0.0711442i
$143$	12.1721	−	4.50978i	1.01788	−	0.377127i
$144$	−2.49668	+	4.32438i	−0.208057	+	0.360365i
$145$	−0.361842	−	0.626729i	−0.0300494	−	0.0520470i
$146$	11.9591	+	14.2523i	0.989740	+	1.17953i
$147$	−2.59494	−	7.12953i	−0.214027	−	0.588034i
$148$	1.88782	−	5.18673i	0.155178	−	0.426347i
$149$	1.85271	−	2.20797i	0.151780	−	0.180884i	−0.684797	−	0.728734i	$-0.740109\pi$
$149$	1.85271	−	2.20797i	0.151780	−	0.180884i	0.836577	+	0.547850i	$0.184554\pi$
$150$	−0.583793	−	0.102938i	−0.0476665	−	0.00840489i
$151$	−7.56454			−0.615594			−0.307797	−	0.951452i	$-0.599592\pi$
$151$	−7.56454			−0.615594			−0.307797	+	0.951452i	$0.599592\pi$
$152$	−7.97062	+	1.15063i	−0.646502	+	0.0933283i
$153$			0.114982i			0.00929571i
$154$	−0.124548	−	21.6399i	−0.0100364	−	1.74380i
$155$	4.01811	−	4.78860i	0.322743	−	0.384630i
$156$	1.22956	−	3.37819i	0.0984435	−	0.270471i
$157$	−8.20184	+	2.98523i	−0.654578	+	0.238247i	−0.647894	−	0.761731i	$-0.724350\pi$
$157$	−8.20184	+	2.98523i	−0.654578	+	0.238247i	−0.00668432	+	0.999978i	$0.502128\pi$
$158$	8.38302	−	7.03419i	0.666917	−	0.559610i
$159$	−6.33300	−	10.9691i	−0.502240	−	0.869904i
$160$	5.59064	−	9.68327i	0.441979	−	0.765530i
$161$	−14.8494	+	2.61834i	−1.17029	+	0.206354i
$162$	0.296656	+	1.68242i	0.0233075	+	0.132183i
$163$	3.46802	−	6.00679i	0.271636	−	0.470488i	−0.697645	−	0.716444i	$-0.745769\pi$
$163$	3.46802	−	6.00679i	0.271636	−	0.470488i	0.969281	+	0.245956i	$0.0791019\pi$
$164$	0.496781	+	0.860449i	0.0387921	+	0.0671898i
$165$	4.89579	−	5.90324i	0.381136	−	0.459567i
$166$	−4.59570	−	12.6266i	−0.356696	−	0.980013i
$167$	−8.08130	−	2.94135i	−0.625349	−	0.227609i	0.00985646	−	0.999951i	$-0.496863\pi$
$167$	−8.08130	−	2.94135i	−0.625349	−	0.227609i	−0.635206	+	0.772343i	$0.719085\pi$
$168$	5.40545	+	4.53571i	0.417040	+	0.349938i
$169$	0.402510	−	2.28275i	0.0309623	−	0.175596i
$170$		−	0.454220i		−	0.0348371i
$171$	−2.90453	+	3.25018i	−0.222115	+	0.248548i
$172$			9.66151i			0.736683i
$173$	−1.93909	+	10.9972i	−0.147427	+	0.836098i	0.817960	+	0.575275i	$0.195105\pi$
$173$	−1.93909	+	10.9972i	−0.147427	+	0.836098i	−0.965387	+	0.260823i	$0.916006\pi$
$174$	0.343672	−	0.409573i	0.0260537	−	0.0310496i
$175$	−0.453274	+	1.24536i	−0.0342643	+	0.0941404i
$176$	8.36297	+	14.2945i	0.630382	+	1.07748i
$177$	−2.70121	+	2.26658i	−0.203035	+	0.170367i
$178$	−13.3307	+	7.69651i	−0.999182	+	0.576878i
$179$	−17.7440	−	10.2445i	−1.32625	−	0.765711i	−0.341533	−	0.939870i	$-0.610946\pi$
$179$	−17.7440	−	10.2445i	−1.32625	−	0.765711i	−0.984718	+	0.174158i	$0.944280\pi$
$180$	−0.368827	−	2.09172i	−0.0274907	−	0.155908i
$181$	20.5230	−	3.61875i	1.52546	−	0.268980i	0.652884	−	0.757458i	$-0.273559\pi$
$181$	20.5230	−	3.61875i	1.52546	−	0.268980i	0.872576	+	0.488478i	$0.162448\pi$
$182$	−22.1156	−	12.7684i	−1.63932	−	0.946459i
$183$	−2.35992	−	4.08751i	−0.174450	−	0.302157i
$184$	5.58753	−	4.68849i	0.411918	−	0.345640i
$185$	−4.75245	−	13.0572i	−0.349407	−	0.959988i
$186$	4.33979	+	1.57955i	0.318208	+	0.115818i
$187$	0.331351	+	0.188771i	0.0242308	+	0.0138043i
$188$	−0.179416	+	1.01752i	−0.0130853	+	0.0742102i
$189$	3.81931			0.277814
$190$	11.4740	−	12.8394i	0.832409	−	0.931470i
$191$	−13.4325			−0.971945			−0.485973	−	0.873974i	$-0.661534\pi$
$191$	−13.4325			−0.971945			−0.485973	+	0.873974i	$0.661534\pi$
$192$	−1.69976	−	0.299713i	−0.122670	−	0.0216299i
$193$	1.20570	+	1.01170i	0.0867883	+	0.0728240i	0.685150	−	0.728402i	$-0.259737\pi$
$193$	1.20570	+	1.01170i	0.0867883	+	0.0728240i	−0.598361	+	0.801226i	$0.704181\pi$
$194$	−9.90438	+	27.2121i	−0.711093	+	1.95371i
$195$	−3.09533	−	8.50435i	−0.221661	−	0.609009i
$196$	−5.33859	+	4.47961i	−0.381328	+	0.319972i
$197$	8.64955	−	4.99382i	0.616255	−	0.355795i	−0.159154	−	0.987254i	$-0.550877\pi$
$197$	8.64955	−	4.99382i	0.616255	−	0.355795i	0.775410	+	0.631459i	$0.217543\pi$
$198$	5.33539	+	1.90722i	0.379170	+	0.135540i
$199$	−1.70788	−	9.68585i	−0.121068	−	0.686612i	−0.983566	−	0.180550i	$-0.942212\pi$
$199$	−1.70788	−	9.68585i	−0.121068	−	0.686612i	0.862498	−	0.506061i	$-0.168899\pi$
$200$	−0.111324	−	0.631350i	−0.00787180	−	0.0446432i
$201$	4.34035	−	7.51770i	0.306144	−	0.530258i
$202$	19.8349	−	11.4517i	1.39558	−	0.805739i
$203$	−0.768327	−	0.915656i	−0.0539260	−	0.0642665i
$204$	0.0992456	−	0.0361224i	0.00694858	−	0.00252908i
$205$	2.35038	+	0.855469i	0.164158	+	0.0597485i
$206$	−17.8820	+	21.3109i	−1.24589	+	1.48480i
$207$	0.685555	−	3.88797i	0.0476493	−	0.270233i
$208$	19.5431			1.35507
$209$	4.59779	+	13.7062i	0.318036	+	0.948079i
$210$	−15.0877			−1.04115
$211$	−0.951963	+	5.39885i	−0.0655358	+	0.371672i	0.934347	+	0.356364i	$0.115984\pi$
$211$	−0.951963	+	5.39885i	−0.0655358	+	0.371672i	−0.999883	+	0.0153076i	$0.995127\pi$
$212$	−7.47832	+	8.91232i	−0.513613	+	0.612100i
$213$	2.68545	+	0.977423i	0.184004	+	0.0669719i
$214$	9.21085	−	3.35248i	0.629641	−	0.229171i
$215$	15.6340	+	18.6319i	1.06623	+	1.27068i
$216$	−1.60002	+	0.923770i	−0.108867	+	0.0628546i
$217$	5.16243	−	8.94159i	0.350449	−	0.606995i
$218$	3.85876	+	21.8841i	0.261348	+	1.48218i
$219$	1.89111	+	10.7250i	0.127790	+	0.724731i
$220$	−6.63340	−	2.37121i	−0.447223	−	0.159867i
$221$	0.389726	−	0.225008i	0.0262158	−	0.0151357i
$222$	7.86407	−	6.59874i	0.527802	−	0.442879i
$223$	7.51859	+	20.6572i	0.503482	+	1.38331i	0.887853	+	0.460127i	$0.152196\pi$
$223$	7.51859	+	20.6572i	0.503482	+	1.38331i	−0.384371	+	0.923179i	$0.625582\pi$
$224$	6.31645	−	17.3543i	0.422035	−	1.15953i
$225$	−0.265815	−	0.223045i	−0.0177210	−	0.0148697i
$226$	2.44182	+	0.430558i	0.162427	+	0.0286403i
$227$	9.70287			0.644002			0.322001	−	0.946739i	$-0.395645\pi$
$227$	9.70287			0.644002			0.322001	+	0.946739i	$0.395645\pi$
$228$	3.71786	+	1.48595i	0.246221	+	0.0984097i
$229$	−28.2410			−1.86622			−0.933108	−	0.359595i	$-0.882915\pi$
$229$	−28.2410			−1.86622			−0.933108	+	0.359595i	$0.882915\pi$
$230$	−2.70819	+	15.3589i	−0.178573	+	1.01274i
$231$	6.27036	−	11.0064i	0.412559	−	0.724167i
$232$	0.543343	+	0.197761i	0.0356722	+	0.0129836i
$233$	−4.90375	−	13.4729i	−0.321255	−	0.882641i	−0.990241	−	0.139366i	$-0.955494\pi$
$233$	−4.90375	−	13.4729i	−0.321255	−	0.882641i	0.668986	−	0.743275i	$-0.266729\pi$
$234$	5.12197	−	4.29784i	0.334834	−	0.280959i
$235$	1.30052	+	2.25257i	0.0848369	+	0.146942i
$236$	2.80499	+	1.61946i	0.182589	+	0.105418i
$237$	6.30834	−	1.11233i	0.409771	−	0.0722537i
$238$	−0.130276	−	0.738834i	−0.00844456	−	0.0478915i
$239$	−10.6131	−	6.12749i	−0.686506	−	0.396354i	0.115796	−	0.993273i	$-0.463058\pi$
$239$	−10.6131	−	6.12749i	−0.686506	−	0.396354i	−0.802302	+	0.596919i	$0.796392\pi$
$240$	9.99951	−	5.77322i	0.645466	−	0.372660i
$241$	−10.9479	+	9.18638i	−0.705216	+	0.591747i	−0.923252	−	0.384194i	$-0.874479\pi$
$241$	−10.9479	+	9.18638i	−0.705216	+	0.591747i	0.218036	+	0.975941i	$0.430035\pi$
$242$	14.2556	−	12.2442i	0.916384	−	0.787089i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	−2.78671	+	3.32108i	−0.178401	+	0.212610i
$245$	−3.04650	+	17.2775i	−0.194633	+	1.10382i
$246$			1.84791i			0.117818i
$247$	16.7003	+	3.48449i	1.06261	+	0.221713i
$248$			4.99452i			0.317152i
$249$	1.36580	−	7.74585i	0.0865542	−	0.490873i
$250$	−14.0807	−	11.8151i	−0.890543	−	0.747254i
$251$	8.11675	+	2.95425i	0.512325	+	0.186471i	0.585229	−	0.810868i	$-0.301005\pi$
$251$	8.11675	+	2.95425i	0.512325	+	0.186471i	−0.0729045	+	0.997339i	$0.523227\pi$
$252$	−1.19987	−	3.29661i	−0.0755845	−	0.207667i
$253$	−10.0788	−	8.35871i	−0.633646	−	0.525508i
$254$	−4.38392	−	7.59317i	−0.275072	−	0.476438i
$255$	0.132939	−	0.230258i	0.00832498	−	0.0144193i
$256$	3.14423	+	17.8318i	0.196514	+	1.11449i
$257$	−30.0779	+	5.30355i	−1.87621	+	0.330826i	−0.990946	−	0.134262i	$-0.957133\pi$
$257$	−30.0779	+	5.30355i	−1.87621	+	0.330826i	−0.885264	+	0.465089i	$0.846022\pi$
$258$	−8.98464	+	15.5619i	−0.559359	+	0.968839i
$259$	−11.4753	−	19.8759i	−0.713042	−	1.23503i
$260$	−6.36805	+	5.34343i	−0.394930	+	0.331385i
$261$	0.294090	−	0.107040i	0.0182037	−	0.00662561i
$262$	−9.89381	+	27.1830i	−0.611241	+	1.67937i
$263$	7.58171	−	9.03553i	0.467508	−	0.557154i	−0.479842	−	0.877355i	$-0.659306\pi$
$263$	7.58171	−	9.03553i	0.467508	−	0.557154i	0.947350	+	0.320201i	$0.103750\pi$
$264$	0.0352667	+	6.12750i	0.00217051	+	0.377121i
$265$			29.2883i			1.79917i
$266$	14.9810	−	24.1755i	0.918546	−	1.48230i
$267$	−9.01034			−0.551424
$268$	−7.85241	−	1.38459i	−0.479662	−	0.0845774i
$269$	1.04095	−	1.24055i	0.0634676	−	0.0756378i	−0.733377	−	0.679823i	$-0.762057\pi$
$269$	1.04095	−	1.24055i	0.0634676	−	0.0756378i	0.796844	+	0.604185i	$0.206501\pi$
$270$	1.35111	−	3.71213i	0.0822257	−	0.225913i
$271$	1.29245	+	3.55098i	0.0785109	+	0.215707i	0.972738	−	0.231906i	$-0.0744963\pi$
$271$	1.29245	+	3.55098i	0.0785109	+	0.215707i	−0.894227	+	0.447613i	$0.852274\pi$
$272$	0.369053	+	0.439821i	0.0223771	+	0.0266680i
$273$	−7.47403	−	12.9454i	−0.452349	−	0.783491i
$274$	6.32305	−	10.9519i	0.381990	−	0.661626i
$275$	−1.07917	+	0.399834i	−0.0650763	+	0.0241109i
$276$	−3.57125	+	0.629708i	−0.214964	+	0.0379040i
$277$	8.79143	+	5.07574i	0.528226	+	0.304971i	0.740294	−	0.672284i	$-0.234686\pi$
$277$	8.79143	+	5.07574i	0.528226	+	0.304971i	−0.212068	+	0.977255i	$0.568020\pi$
$278$	20.1614	−	11.6402i	1.20920	−	0.698134i
$279$	1.73767	+	2.07087i	0.104032	+	0.123980i
$280$	−5.58065	−	15.3327i	−0.333508	−	0.916305i
$281$	30.1729	+	10.9820i	1.79997	+	0.655134i	0.998358	+	0.0572845i	$0.0182442\pi$
$281$	30.1729	+	10.9820i	1.79997	+	0.655134i	0.801608	+	0.597850i	$0.203978\pi$
$282$	−1.23522	+	1.47208i	−0.0735562	+	0.0876609i
$283$	16.4999	+	2.90937i	0.980815	+	0.172944i	0.640994	−	0.767546i	$-0.278522\pi$
$283$	16.4999	+	2.90937i	0.980815	+	0.172944i	0.339821	+	0.940490i	$0.389633\pi$
$284$		−	2.62499i		−	0.155765i
$285$	9.57429	−	3.15053i	0.567132	−	0.186622i
$286$	−3.97642	−	21.8164i	−0.235130	−	1.29003i
$287$	4.06849	+	0.717385i	0.240155	+	0.0423459i
$288$	3.70417	+	3.10817i	0.218270	+	0.183150i
$289$	−15.9624	−	5.80982i	−0.938962	−	0.341754i
$290$	−1.16176	+	0.422847i	−0.0682211	+	0.0248304i
$291$	−12.9851	+	10.8958i	−0.761203	+	0.638725i
$292$	8.66314	−	5.00167i	0.506972	−	0.292700i
$293$	4.77523	−	8.27095i	0.278972	−	0.483194i	−0.692157	−	0.721747i	$-0.743340\pi$
$293$	4.77523	−	8.27095i	0.278972	−	0.483194i	0.971130	+	0.238553i	$0.0766730\pi$
$294$	−12.7647	+	2.25076i	−0.744450	+	0.131267i
$295$	8.02990	−	1.41589i	0.467519	−	0.0824362i
$296$	9.61469	+	5.55105i	0.558843	+	0.322648i
$297$	2.14647	+	2.52837i	0.124551	+	0.146711i
$298$	−3.16512	−	3.77204i	−0.183350	−	0.218508i
$299$	−14.5197	+	5.28474i	−0.839697	+	0.305625i
$300$	−0.109012	+	0.299508i	−0.00629380	+	0.0172921i
$301$	30.7742	+	25.8226i	1.77379	+	1.48839i
$302$	−2.24407	+	12.7267i	−0.129131	+	0.732341i
$303$	13.4066			0.770187
$304$	−0.678205	+	21.7550i	−0.0388977	+	1.24773i
$305$			10.9140i			0.624932i
$306$	0.193447	+	0.0341100i	0.0110586	+	0.00194994i
$307$	9.75728	+	8.18733i	0.556877	+	0.467275i	0.877262	−	0.480012i	$-0.159368\pi$
$307$	9.75728	+	8.18733i	0.556877	+	0.467275i	−0.320385	+	0.947288i	$0.603812\pi$
$308$	−11.4700	−	1.95447i	−0.653563	−	0.111366i
$309$	−15.3021	+	5.56950i	−0.870505	+	0.316838i
$310$	−6.86444	−	8.18072i	−0.389874	−	0.464633i
$311$	8.65806	+	14.9962i	0.490954	+	0.850357i	0.999946	−	0.0104145i	$-0.00331509\pi$
$311$	8.65806	+	14.9962i	0.490954	+	0.850357i	−0.508992	+	0.860771i	$0.669982\pi$
$312$	6.26217	+	3.61547i	0.354526	+	0.204685i
$313$	4.14654	+	23.5162i	0.234377	+	1.32922i	0.843923	+	0.536465i	$0.180241\pi$
$313$	4.14654	+	23.5162i	0.234377	+	1.32922i	−0.609546	+	0.792751i	$0.708648\pi$
$314$	2.58928	+	14.6845i	0.146121	+	0.828695i
$315$	−7.64839	−	4.41580i	−0.430938	−	0.248802i
$316$	−2.94192	−	5.09556i	−0.165496	−	0.286647i
$317$	−5.57799	−	6.64759i	−0.313291	−	0.373366i	0.586304	−	0.810091i	$-0.300583\pi$
$317$	−5.57799	−	6.64759i	−0.313291	−	0.373366i	−0.899595	+	0.436726i	$0.856138\pi$
$318$	−20.3333	+	7.40072i	−1.14024	+	0.415012i
$319$	0.174358	−	1.02323i	0.00976216	−	0.0572902i
$320$	3.05735	+	2.56542i	0.170911	+	0.143411i
$321$	5.65045	+	0.996326i	0.315377	+	0.0556095i
$322$			25.7596i			1.43553i
$323$	0.236950	+	0.441644i	0.0131843	+	0.0245737i
$324$	0.918538			0.0510299
$325$	−0.235828	+	1.33745i	−0.0130814	+	0.0741882i
$326$	−9.07712	−	7.61661i	−0.502735	−	0.421845i
$327$	−4.44883	+	12.2231i	−0.246021	+	0.675937i
$328$	−1.87792	+	0.683507i	−0.103691	+	0.0377404i
$329$	2.76150	+	3.29103i	0.152247	+	0.181440i
$330$	−8.47936	−	9.98799i	−0.466773	−	0.549821i
$331$	18.4067	+	10.6271i	1.01173	+	0.584120i	0.911697	−	0.410864i	$-0.134773\pi$
$331$	18.4067	+	10.6271i	1.01173	+	0.584120i	0.100029	+	0.994984i	$0.468106\pi$
$332$	−7.11485	+	1.25454i	−0.390478	+	0.0688519i
$333$	5.91783	−	1.04347i	0.324295	−	0.0571820i
$334$	−7.34595	+	12.7236i	−0.401952	+	0.696202i
$335$	−17.3836	+	10.0364i	−0.949768	+	0.548349i
$336$	14.6094	−	12.2587i	0.797007	−	0.668768i
$337$	31.0543	−	11.3028i	1.69164	−	0.615705i	0.696806	−	0.717260i	$-0.254604\pi$
$337$	31.0543	−	11.3028i	1.69164	−	0.615705i	0.994830	+	0.101555i	$0.0323817\pi$
$338$	−3.72113	−	1.35438i	−0.202403	−	0.0736685i
$339$	1.11182	+	0.932924i	0.0603855	+	0.0506695i
$340$	−0.240509	−	0.0424083i	−0.0130434	−	0.00229991i
$341$	8.82063	−	1.60771i	0.477664	−	0.0870625i
$342$	4.60653	+	5.85082i	0.249092	+	0.316376i
$343$			2.24228i			0.121072i
$344$	−19.1379	−	3.37452i	−1.03184	−	0.181942i
$345$	−5.86806	+	6.99328i	−0.315925	+	0.376505i
$346$	17.9266	+	6.52474i	0.963739	+	0.350772i
$347$	−12.1309	−	33.3293i	−0.651220	−	1.78921i	−0.613191	−	0.789934i	$-0.710115\pi$
$347$	−12.1309	−	33.3293i	−0.651220	−	1.78921i	−0.0380282	−	0.999277i	$-0.512108\pi$
$348$	−0.184782	−	0.220214i	−0.00990534	−	0.0118047i
$349$	−26.1475	+	15.0963i	−1.39964	+	0.808084i	−0.994355	−	0.106105i	$-0.966162\pi$
$349$	−26.1475	+	15.0963i	−1.39964	+	0.808084i	−0.405287	+	0.914189i	$0.632829\pi$
$350$	1.96075	+	1.13204i	0.104807	+	0.0605101i
$351$	3.85436	−	0.679627i	0.205730	−	0.0362758i
$352$	15.0384	−	5.57175i	0.801548	−	0.296975i
$353$	−4.98582	+	8.63570i	−0.265369	+	0.459632i	−0.967660	−	0.252258i	$-0.918827\pi$
$353$	−4.98582	+	8.63570i	−0.265369	+	0.459632i	0.702291	+	0.711889i	$0.252160\pi$
$354$	3.01201	+	5.21695i	0.160086	+	0.277278i
$355$	−4.24770	−	5.06221i	−0.225444	−	0.268674i
$356$	2.83068	+	7.77722i	0.150026	+	0.412192i
$357$	0.150198	−	0.412666i	0.00794932	−	0.0218406i
$358$	−22.4994	+	26.8138i	−1.18913	+	1.41715i
$359$	5.85516	+	1.03242i	0.309023	+	0.0544892i	0.326009	−	0.945367i	$-0.394296\pi$
$359$	5.85516	+	1.03242i	0.309023	+	0.0544892i	−0.0169858	+	0.999856i	$0.505407\pi$
$360$	4.27217			0.225163
$361$	−4.45842	+	18.4695i	−0.234653	+	0.972079i
$362$		−	35.6018i		−	1.87119i
$363$	10.8102	−	2.03470i	0.567387	−	0.106794i
$364$	−8.82571	+	10.5181i	−0.462593	+	0.551297i
$365$	8.61299	−	23.6640i	0.450825	−	1.23863i
$366$	−7.57698	+	2.75780i	−0.396055	+	0.144152i
$367$	25.2676	−	21.2020i	1.31896	−	1.10674i	0.332431	−	0.943128i	$-0.392131\pi$
$367$	25.2676	−	21.2020i	1.31896	−	1.10674i	0.986525	−	0.163608i	$-0.0523132\pi$
$368$	−9.85678	−	17.0724i	−0.513820	−	0.889962i
$369$	−0.540838	+	0.936760i	−0.0281549	+	0.0487658i
$370$	−23.3776	+	4.12210i	−1.21534	+	0.214298i
$371$	8.40029	+	47.6404i	0.436121	+	2.47337i
$372$	1.24156	−	2.15044i	0.0643718	−	0.111495i
$373$	15.4084	+	26.6882i	0.797818	+	1.38186i	0.921034	+	0.389481i	$0.127346\pi$
$373$	15.4084	+	26.6882i	0.797818	+	1.38186i	−0.123217	+	0.992380i	$0.539321\pi$
$374$	0.415890	−	0.501472i	0.0215052	−	0.0259305i
$375$	−3.67993	−	10.1105i	−0.190031	−	0.522106i
$376$	−1.95287	−	0.710787i	−0.100712	−	0.0366560i
$377$	−0.938315	−	0.787340i	−0.0483257	−	0.0405501i
$378$	1.13302	−	6.42567i	0.0582762	−	0.330501i
$379$		−	26.5195i		−	1.36221i	−0.732184	−	0.681107i	$-0.761499\pi$
$379$		−	26.5195i		−	1.36221i	0.732184	−	0.681107i	$-0.238501\pi$
$380$	−5.72721	−	7.27422i	−0.293800	−	0.373160i
$381$		−	5.13228i		−	0.262934i
$382$	−3.98484	+	22.5992i	−0.203882	+	1.15627i
$383$	14.3342	−	17.0828i	0.732441	−	0.872890i	−0.263335	−	0.964705i	$-0.584822\pi$
$383$	14.3342	−	17.0828i	0.732441	−	0.872890i	0.995776	+	0.0918148i	$0.0292668\pi$
$384$	−4.31613	+	11.8585i	−0.220256	+	0.605150i
$385$	−25.2821	+	14.7913i	−1.28850	+	0.753835i
$386$	2.05979	−	1.72837i	0.104840	−	0.0879716i
$387$	−9.10916	+	5.25918i	−0.463045	+	0.267339i
$388$	13.4841	+	7.78503i	0.684549	+	0.395225i
$389$	0.365563	+	2.07321i	0.0185348	+	0.105116i	0.992672	−	0.120843i	$-0.0385597\pi$
$389$	0.365563	+	2.07321i	0.0185348	+	0.105116i	−0.974137	+	0.225959i	$0.927449\pi$
$390$	−15.2261	+	2.68478i	−0.771005	+	0.135949i
$391$	−0.393125	−	0.226971i	−0.0198812	−	0.0114784i
$392$	−7.00873	−	12.1395i	−0.353994	−	0.613136i
$393$	−12.9713	+	10.8842i	−0.654315	+	0.549035i
$394$	−5.83576	−	16.0336i	−0.294001	−	0.807762i
$395$	−13.9189	−	5.06606i	−0.700335	−	0.254901i
$396$	1.50801	−	2.64702i	0.0757805	−	0.133018i
$397$	0.183099	−	1.03841i	0.00918950	−	0.0521162i	−0.979868	−	0.199645i	$-0.936021\pi$
$397$	0.183099	−	1.03841i	0.00918950	−	0.0521162i	0.989058	+	0.147529i	$0.0471321\pi$
$398$	−16.8023			−0.842223
$399$	14.6699	−	7.87070i	0.734415	−	0.394028i
$400$	−1.73268			−0.0866339
$401$	−31.2791	−	5.51535i	−1.56200	−	0.275424i	−0.675224	−	0.737613i	$-0.735953\pi$
$401$	−31.2791	−	5.51535i	−1.56200	−	0.275424i	−0.886781	+	0.462190i	$0.847064\pi$
$402$	−11.3603	−	9.53245i	−0.566602	−	0.475435i
$403$	3.61869	−	9.94228i	0.180260	−	0.495260i
$404$	−4.21179	−	11.5718i	−0.209544	−	0.575718i
$405$	1.77137	−	1.48635i	0.0880200	−	0.0738576i
$406$	−1.76845	+	1.02101i	−0.0877665	+	0.0506720i
$407$	6.70856	−	18.7670i	0.332531	−	0.930245i
$408$	0.0368886	+	0.209206i	0.00182626	+	0.0103572i
$409$	3.48212	+	19.7481i	0.172180	+	0.976479i	0.941349	+	0.337434i	$0.109559\pi$
$409$	3.48212	+	19.7481i	0.172180	+	0.976479i	−0.769170	+	0.639045i	$0.779330\pi$
$410$	2.13651	−	3.70055i	0.105515	−	0.182757i
$411$	6.41069	−	3.70121i	0.316216	−	0.182567i
$412$	9.61456	+	11.4582i	0.473675	+	0.564504i
$413$	12.6553	−	4.60617i	0.622729	−	0.226655i
$414$	−6.33783	−	2.30678i	−0.311487	−	0.113372i
$415$	−11.6907	+	13.9324i	−0.573873	+	0.683915i
$416$	3.28630	−	18.6375i	0.161124	−	0.913781i
$417$	13.6273			0.667329
$418$	24.4236	−	3.66937i	1.19460	−	0.179475i
$419$	−7.77246			−0.379710			−0.189855	−	0.981812i	$-0.560802\pi$
$419$	−7.77246			−0.379710			−0.189855	+	0.981812i	$0.560802\pi$
$420$	−1.40866	+	7.98892i	−0.0687357	+	0.389819i
$421$	−18.0744	+	21.5402i	−0.880893	+	1.04981i	0.117496	+	0.993073i	$0.462513\pi$
$421$	−18.0744	+	21.5402i	−0.880893	+	1.04981i	−0.998389	+	0.0567341i	$0.981931\pi$
$422$	8.80072	+	3.20320i	0.428412	+	0.155929i
$423$	−1.05701	+	0.384720i	−0.0513936	+	0.0187057i
$424$	−15.0418	−	17.9262i	−0.730496	−	0.870571i
$425$	−0.0345528	+	0.0199491i	−0.00167606	+	0.000967673i
$426$	2.44109	−	4.22809i	0.118271	−	0.204852i
$427$	3.13027	+	17.7527i	0.151485	+	0.859112i
$428$	−0.915164	−	5.19015i	−0.0442361	−	0.250875i
$429$	4.36937	−	12.2232i	0.210955	−	0.590141i
$430$	35.9846	−	20.7757i	1.73533	−	1.00189i
$431$	−5.19043	+	4.35529i	−0.250014	+	0.209787i	−0.759178	−	0.650883i	$-0.774399\pi$
$431$	−5.19043	+	4.35529i	−0.250014	+	0.209787i	0.509164	+	0.860669i	$0.329955\pi$
$432$	1.70783	+	4.69223i	0.0821681	+	0.225755i
$433$	−7.78378	+	21.3858i	−0.374065	+	1.02773i	0.599710	+	0.800218i	$0.295283\pi$
$433$	−7.78378	+	21.3858i	−0.374065	+	1.02773i	−0.973774	+	0.227516i	$0.926940\pi$
$434$	−13.5120	−	11.3379i	−0.648598	−	0.544239i
$435$	−0.712690	−	0.125666i	−0.0341709	−	0.00602525i
$436$	11.9479			0.572201
$437$	−5.37899	−	16.3465i	−0.257312	−	0.781957i
$438$	18.6050			0.888982
$439$	−0.714059	+	4.04963i	−0.0340802	+	0.193278i	−0.997095	−	0.0761709i	$-0.975731\pi$
$439$	−0.714059	+	4.04963i	−0.0340802	+	0.193278i	0.963015	+	0.269449i	$0.0868417\pi$
$440$	7.01386	−	12.3115i	0.334372	−	0.586926i
$441$	−7.12953	−	2.59494i	−0.339502	−	0.123568i
$442$	−0.262944	−	0.722432i	−0.0125070	−	0.0343626i
$443$	22.4300	−	18.8210i	1.06568	−	0.894212i	0.0710258	−	0.997474i	$-0.477373\pi$
$443$	22.4300	−	18.8210i	1.06568	−	0.894212i	0.994654	+	0.103263i	$0.0329283\pi$
$444$	−2.75980	−	4.78012i	−0.130974	−	0.226854i
$445$	18.0437	+	10.4176i	0.855356	+	0.493840i
$446$	36.9844	−	6.52135i	1.75126	−	0.308795i
$447$	−0.500506	−	2.83851i	−0.0236731	−	0.134257i
$448$	5.70888	+	3.29602i	0.269719	+	0.155722i
$449$	7.93087	−	4.57889i	0.374281	−	0.216091i	−0.301046	−	0.953610i	$-0.597336\pi$
$449$	7.93087	−	4.57889i	0.374281	−	0.216091i	0.675327	+	0.737518i	$0.264002\pi$
$450$	−0.454110	+	0.381044i	−0.0214070	+	0.0179626i
$451$	1.81161	+	3.09650i	0.0853054	+	0.145809i
$452$	0.455961	−	1.25274i	0.0214466	−	0.0589240i
$453$	−4.86239	+	5.79478i	−0.228455	+	0.272262i
$454$	2.87841	−	16.3243i	0.135091	−	0.766137i
$455$			34.5653i			1.62044i
$456$	−4.24198	+	6.84546i	−0.198649	+	0.320568i
$457$		−	25.9353i		−	1.21320i	−0.795007	−	0.606600i	$-0.792533\pi$
$457$		−	25.9353i		−	1.21320i	0.795007	−	0.606600i	$-0.207467\pi$
$458$	−8.37785	+	47.5132i	−0.391471	+	2.22014i
$459$	0.0880810	+	0.0739087i	0.00411127	+	0.00344976i
$460$	7.87970	+	2.86798i	0.367393	+	0.133720i
$461$	−11.4111	−	31.3517i	−0.531467	−	1.46019i	−0.857326	−	0.514774i	$-0.827876\pi$
$461$	−11.4111	−	31.3517i	−0.531467	−	1.46019i	0.325859	−	0.945418i	$-0.394346\pi$
$462$	−16.6572	−	13.8145i	−0.774964	−	0.642708i
$463$	−6.86639	−	11.8929i	−0.319108	−	0.552711i	0.661194	−	0.750215i	$-0.270050\pi$
$463$	−6.86639	−	11.8929i	−0.319108	−	0.552711i	−0.980302	+	0.197504i	$0.936717\pi$
$464$	0.781371	−	1.35337i	0.0362743	−	0.0628288i
$465$	−1.08549	−	6.15611i	−0.0503383	−	0.285483i
$466$	−24.1218	+	4.25333i	−1.11742	+	0.197032i
$467$	11.4957	−	19.9112i	0.531960	−	0.921381i	−0.467344	−	0.884075i	$-0.654789\pi$
$467$	11.4957	−	19.9112i	0.531960	−	0.921381i	0.999304	−	0.0373058i	$-0.0118776\pi$
$468$	−1.79749	−	3.11335i	−0.0830892	−	0.143915i
$469$	−25.3976	+	21.3111i	−1.17275	+	0.984056i
$470$	4.17558	−	1.51979i	0.192605	−	0.0701026i
$471$	−2.98523	+	8.20184i	−0.137552	+	0.377921i
$472$	−4.18760	+	4.99059i	−0.192750	+	0.229710i
$473$	0.200779	+	34.8849i	0.00923183	+	1.60401i
$474$		−	10.9433i		−	0.502640i
$475$	−1.48064	−	0.308933i	−0.0679362	−	0.0141748i
$476$	−0.403376			−0.0184887
$477$	−12.4736	−	2.19943i	−0.571126	−	0.100705i
$478$	−13.4575	+	16.0380i	−0.615530	+	0.733560i
$479$	−3.29250	+	9.04608i	−0.150438	+	0.413326i	−0.991905	−	0.126983i	$-0.959471\pi$
$479$	−3.29250	+	9.04608i	−0.150438	+	0.413326i	0.841467	+	0.540309i	$0.181693\pi$
$480$	−3.82422	−	10.5070i	−0.174551	−	0.479575i
$481$	−15.1175	−	18.0163i	−0.689297	−	0.821472i
$482$	12.2076	+	21.1441i	0.556040	+	0.963090i
$483$	−7.53921	+	13.0583i	−0.343046	+	0.594173i
$484$	−5.15235	−	8.69152i	−0.234198	−	0.395069i
$485$	38.6011	−	6.80641i	1.75278	−	0.309063i
$486$	1.47949	+	0.854186i	0.0671112	+	0.0387467i
$487$	2.62087	−	1.51316i	0.118763	−	0.0685679i	−0.439442	−	0.898271i	$-0.644824\pi$
$487$	2.62087	−	1.51316i	0.118763	−	0.0685679i	0.558205	+	0.829703i	$0.311490\pi$
$488$	−5.60517	−	6.67999i	−0.253734	−	0.302389i
$489$	−2.37226	−	6.51774i	−0.107278	−	0.294743i
$490$	28.1643	+	10.2510i	1.27233	+	0.463091i
$491$	−20.9996	+	25.0263i	−0.947697	+	1.12942i	0.0437676	+	0.999042i	$0.486064\pi$
$491$	−20.9996	+	25.0263i	−0.947697	+	1.12942i	−0.991464	+	0.130379i	$0.958381\pi$
$492$	0.978467	+	0.172530i	0.0441127	+	0.00777826i
$493$		−	0.0359851i		−	0.00162069i
$494$	10.8166	−	27.0632i	0.486662	−	1.21763i
$495$	−1.37519	−	7.54492i	−0.0618103	−	0.339119i
$496$	13.2937	+	2.34403i	0.596903	+	0.105250i
$497$	−8.36121	−	7.01589i	−0.375052	−	0.314706i
$498$	−12.6266	−	4.59570i	−0.565811	−	0.205938i
$499$	−10.2591	+	3.73400i	−0.459260	+	0.167157i	−0.561281	−	0.827625i	$-0.689691\pi$
$499$	−10.2591	+	3.73400i	−0.459260	+	0.167157i	0.102021	+	0.994782i	$0.467469\pi$
$500$	−7.57076	+	6.35262i	−0.338575	+	0.284098i
$501$	−7.44776	+	4.29997i	−0.332741	+	0.192108i
$502$	7.37817	−	12.7794i	0.329304	−	0.570371i
$503$	19.1098	−	3.36957i	0.852064	−	0.150242i	0.269474	−	0.963008i	$-0.413150\pi$
$503$	19.1098	−	3.36957i	0.852064	−	0.150242i	0.582590	+	0.812766i	$0.302039\pi$
$504$	6.94912	−	1.22532i	0.309538	−	0.0545800i
$505$	−26.8474	−	15.5004i	−1.19470	−	0.689758i
$506$	−17.0528	+	14.4770i	−0.758088	+	0.643583i
$507$	−1.48996	−	1.77566i	−0.0661713	−	0.0788599i
$508$	−4.42989	+	1.61235i	−0.196545	+	0.0715364i
$509$	13.4461	−	36.9428i	0.595987	−	1.63746i	−0.163203	−	0.986592i	$-0.552183\pi$
$509$	13.4461	−	36.9428i	0.595987	−	1.63746i	0.759190	−	0.650869i	$-0.225595\pi$
$510$	−0.347952	−	0.291967i	−0.0154076	−	0.0129285i
$511$	7.22274	−	40.9622i	0.319515	−	1.81206i
$512$	5.69427			0.251654
$513$	0.622789	+	4.31418i	0.0274968	+	0.190476i
$514$			52.1770i			2.30143i
$515$	37.0827	+	6.53868i	1.63406	+	0.288129i
$516$	7.40115	+	6.21030i	0.325817	+	0.273393i
$517$	−0.626673	+	3.67769i	−0.0275610	+	0.161744i
$518$	−36.8437	+	13.4100i	−1.61882	+	0.589203i
$519$	7.17788	+	8.55427i	0.315074	+	0.375491i
$520$	−8.36025	−	14.4804i	−0.366621	−	0.635007i
$521$	−28.5571	−	16.4875i	−1.25111	−	0.722328i	−0.279780	−	0.960064i	$-0.590261\pi$
$521$	−28.5571	−	16.4875i	−1.25111	−	0.722328i	−0.971330	+	0.237736i	$0.923595\pi$
$522$	−0.0928426	−	0.526536i	−0.00406361	−	0.0230459i
$523$	−7.10050	−	40.2689i	−0.310483	−	1.76084i	−0.596500	−	0.802613i	$-0.703442\pi$
$523$	−7.10050	−	40.2689i	−0.310483	−	1.76084i	0.286016	−	0.958225i	$-0.407669\pi$
$524$	13.4697	+	7.77672i	0.588425	+	0.339727i
$525$	0.662642	+	1.14773i	0.0289201	+	0.0500910i
$526$	−12.9524	−	15.4360i	−0.564751	−	0.673044i
$527$	0.292088	−	0.106311i	0.0127236	−	0.00463100i
$528$	16.3258	+	2.78189i	0.710489	+	0.121066i
$529$	−5.67921	−	4.76542i	−0.246922	−	0.207192i
$530$	49.2752	+	8.68855i	2.14038	+	0.377407i
$531$			3.52617i			0.153023i
$532$	−11.4022	−	10.1896i	−0.494349	−	0.441776i
$533$	4.23348			0.183373
$534$	−2.67297	+	15.1592i	−0.115671	+	0.656001i
$535$	−10.1634	−	8.52813i	−0.439403	−	0.368703i
$536$	5.48529	−	15.0707i	0.236929	−	0.650956i
$537$	−19.2534	+	7.00767i	−0.830846	+	0.302403i
$538$	−1.77832	−	2.11932i	−0.0766690	−	0.0913706i
$539$	−19.1830	+	16.2855i	−0.826269	+	0.701465i
$540$	−1.83943	−	1.06199i	−0.0791564	−	0.0457010i
$541$	−41.9833	+	7.40278i	−1.80500	+	0.318270i	−0.971996	−	0.234996i	$-0.924492\pi$
$541$	−41.9833	+	7.40278i	−1.80500	+	0.318270i	−0.833005	+	0.553266i	$0.813381\pi$
$542$	6.35766	−	1.12103i	0.273085	−	0.0481522i
$543$	10.4198	−	18.0476i	0.447156	−	0.774496i
$544$	0.481499	−	0.277994i	0.0206441	−	0.0119189i
$545$	23.0411	−	19.3338i	0.986973	−	0.828169i
$546$	−23.9968	+	8.73412i	−1.02697	+	0.373786i
$547$	−2.55536	−	0.930074i	−0.109259	−	0.0397671i	0.286812	−	0.957987i	$-0.407404\pi$
$547$	−2.55536	−	0.930074i	−0.109259	−	0.0397671i	−0.396071	+	0.918220i	$0.629627\pi$
$548$	−5.20865	−	4.37058i	−0.222503	−	0.186702i
$549$	−4.64814	−	0.819592i	−0.198378	−	0.0349794i
$550$	0.352546	+	1.93423i	0.0150326	+	0.0824757i
$551$	0.909013	−	1.01719i	0.0387253	−	0.0433338i
$552$		−	7.29400i		−	0.310453i
$553$	−24.0935	−	4.24833i	−1.02456	−	0.180657i
$554$	11.1475	−	13.2851i	0.473614	−	0.564431i
$555$	−13.0572	−	4.75245i	−0.554249	−	0.201730i
$556$	−4.28112	−	11.7623i	−0.181560	−	0.498831i
$557$	0.655006	+	0.780606i	0.0277535	+	0.0330753i	0.779743	−	0.626100i	$-0.215350\pi$
$557$	0.655006	+	0.780606i	0.0277535	+	0.0330753i	−0.751989	+	0.659175i	$0.770905\pi$
$558$	3.99957	−	2.30915i	0.169315	−	0.0977542i
$559$	35.6516	+	20.5835i	1.50790	+	0.870588i
$560$	−43.4294	+	7.65778i	−1.83523	+	0.323600i
$561$	0.357596	−	0.132490i	0.0150977	−	0.00559373i
$562$	27.4274	−	47.5056i	1.15695	−	2.00390i
$563$	−3.88641	−	6.73146i	−0.163793	−	0.283697i	0.772433	−	0.635096i	$-0.219039\pi$
$563$	−3.88641	−	6.73146i	−0.163793	−	0.283697i	−0.936226	+	0.351399i	$0.885706\pi$
$564$	0.664138	+	0.791489i	0.0279653	+	0.0333277i
$565$	−1.14785	−	3.15369i	−0.0482904	−	0.132677i
$566$	9.78956	−	26.8966i	0.411486	−	1.13055i
$567$	2.45500	−	2.92576i	0.103100	−	0.122870i
$568$	5.19968	+	0.916843i	0.218174	+	0.0384699i
$569$	−44.8416			−1.87986			−0.939930	−	0.341368i	$-0.889110\pi$
$569$	−44.8416			−1.87986			−0.939930	+	0.341368i	$0.889110\pi$
$570$	−2.46025	−	17.0426i	−0.103048	−	0.713836i
$571$			2.36458i			0.0989544i	0.998775	+	0.0494772i	$0.0157555\pi$
$571$			2.36458i			0.0989544i	−0.998775	+	0.0494772i	$0.984244\pi$
$572$	−11.9230	+	0.0686228i	−0.498527	+	0.00286926i
$573$	−8.63428	+	10.2899i	−0.360702	+	0.429868i
$574$	2.41388	−	6.63209i	0.100754	−	0.276818i
$575$	1.28731	−	0.468542i	0.0536844	−	0.0195395i
$576$	−1.32218	+	1.10944i	−0.0550907	+	0.0462266i
$577$	2.81754	+	4.88012i	0.117296	+	0.203162i	0.918695	−	0.394967i	$-0.129244\pi$
$577$	2.81754	+	4.88012i	0.117296	+	0.203162i	−0.801399	+	0.598130i	$0.795911\pi$
$578$	−14.5099	+	25.1318i	−0.603531	+	1.04535i
$579$	1.55002	−	0.273310i	0.0644166	−	0.0113584i
$580$	0.115429	+	0.654633i	0.00479295	+	0.0271822i
$581$	−15.0201	+	26.0155i	−0.623137	+	1.07931i
$582$	14.4792	+	25.0788i	0.600183	+	1.03955i
$583$	−26.8168	+	32.3352i	−1.11064	+	1.33919i
$584$	6.88166	+	18.9072i	0.284765	+	0.782386i
$585$	−8.50435	−	3.09533i	−0.351612	−	0.127976i
$586$	−12.4986	−	10.4876i	−0.516312	−	0.433237i
$587$	−1.46695	+	8.31951i	−0.0605477	+	0.343383i	0.939452	+	0.342680i	$0.111335\pi$
$587$	−1.46695	+	8.31951i	−0.0605477	+	0.343383i	−1.00000		0.000702596i	$0.999776\pi$
$588$			6.96903i			0.287398i
$589$	10.9420	+	4.37329i	0.450856	+	0.180198i
$590$		−	13.9297i		−	0.573476i
$591$	1.73434	−	9.83591i	0.0713411	−	0.404595i
$592$	19.2873	−	22.9857i	0.792704	−	0.944707i
$593$	−12.3350	+	33.8902i	−0.506539	+	1.39170i	0.378247	+	0.925705i	$0.376527\pi$
$593$	−12.3350	+	33.8902i	−0.506539	+	1.39170i	−0.884785	+	0.465999i	$0.845695\pi$
$594$	4.89054	−	2.86121i	0.200661	−	0.117397i
$595$	−0.777896	+	0.652732i	−0.0318906	+	0.0267594i
$596$	−2.29281	+	1.32375i	−0.0939170	+	0.0542230i
$597$	−8.51759	−	4.91763i	−0.348602	−	0.201265i
$598$	4.58379	+	25.9960i	0.187445	+	1.06306i
$599$	−13.6743	+	2.41114i	−0.558715	+	0.0985165i	−0.445873	−	0.895096i	$-0.647107\pi$
$599$	−13.6743	+	2.41114i	−0.558715	+	0.0985165i	−0.112842	+	0.993613i	$0.535995\pi$
$600$	−0.555200	−	0.320545i	−0.0226659	−	0.0130862i
$601$	−11.5012	−	19.9207i	−0.469144	−	0.812581i	0.530234	−	0.847852i	$-0.322104\pi$
$601$	−11.5012	−	19.9207i	−0.469144	−	0.812581i	−0.999378	+	0.0352701i	$0.988771\pi$
$602$	52.5737	−	44.1146i	2.14275	−	1.79798i
$603$	−2.96897	−	8.15718i	−0.120906	−	0.332186i
$604$	6.52929	+	2.37647i	0.265673	+	0.0966970i
$605$	−24.0005	−	8.42390i	−0.975759	−	0.342480i
$606$	3.97713	−	22.5554i	0.161560	−	0.916252i
$607$	−6.54682			−0.265727			−0.132864	−	0.991134i	$-0.542417\pi$
$607$	−6.54682			−0.265727			−0.132864	+	0.991134i	$0.542417\pi$
$608$	20.6329	+	4.30502i	0.836774	+	0.174592i
$609$	−1.19530			−0.0484362
$610$	18.3619	+	3.23769i	0.743450	+	0.131090i
$611$	3.37247	+	2.82984i	0.136436	+	0.114483i
$612$	0.0361224	−	0.0992456i	0.00146016	−	0.00401177i
$613$	−5.41659	−	14.8820i	−0.218774	−	0.601077i	0.780949	−	0.624595i	$-0.214736\pi$
$613$	−5.41659	−	14.8820i	−0.218774	−	0.601077i	−0.999723	+	0.0235173i	$0.992514\pi$
$614$	16.6691	−	13.9870i	0.672709	−	0.564470i
$615$	2.16612	−	1.25061i	0.0873465	−	0.0504295i
$616$	7.87765	−	22.0375i	0.317400	−	0.887916i
$617$	−1.43999	−	8.16657i	−0.0579717	−	0.328774i	0.942005	−	0.335599i	$-0.108939\pi$
$617$	−1.43999	−	8.16657i	−0.0579717	−	0.328774i	−0.999977	+	0.00682503i	$0.997828\pi$
$618$	4.83078	+	27.3967i	0.194323	+	1.10206i
$619$	2.33473	−	4.04387i	0.0938407	−	0.162537i	−0.815283	−	0.579062i	$-0.803419\pi$
$619$	2.33473	−	4.04387i	0.0938407	−	0.162537i	0.909124	+	0.416525i	$0.136752\pi$
$620$	−4.97259	+	2.87093i	−0.199704	+	0.115299i
$621$	−2.53769	−	3.02431i	−0.101834	−	0.121361i
$622$	27.7984	−	10.1178i	1.11461	−	0.405686i
$623$	32.3379	+	11.7700i	1.29559	+	0.471556i
$624$	12.5621	−	14.9709i	0.502885	−	0.599315i
$625$	−4.62157	+	26.2102i	−0.184863	+	1.04841i
$626$	40.7942			1.63047
$627$	13.4550	+	5.28808i	0.537340	+	0.211185i
$628$	8.01720			0.319921
$629$	0.119980	−	0.680441i	0.00478392	−	0.0271310i
$630$	−9.69816	+	11.5578i	−0.386384	+	0.460475i
$631$	43.3830	+	15.7901i	1.72705	+	0.628595i	0.998414	−	0.0563046i	$-0.0179318\pi$
$631$	43.3830	+	15.7901i	1.72705	+	0.628595i	0.728637	+	0.684900i	$0.240154\pi$
$632$	11.1210	−	4.04771i	0.442369	−	0.161009i
$633$	3.52385	+	4.19956i	0.140060	+	0.166917i
$634$	−12.8388	+	7.41247i	−0.509893	+	0.294387i
$635$	−5.93383	+	10.2777i	−0.235477	+	0.407858i
$636$	2.02026	+	11.4575i	0.0801085	+	0.454318i
$637$	5.15639	+	29.2434i	0.204304	+	1.15866i
$638$	−1.66979	−	0.596891i	−0.0661074	−	0.0236312i
$639$	2.47492	−	1.42890i	0.0979064	−	0.0565263i
$640$	22.3538	−	18.7571i	0.883612	−	0.741438i
$641$	−13.2884	−	36.5095i	−0.524859	−	1.44204i	−0.865052	−	0.501682i	$-0.832715\pi$
$641$	−13.2884	−	36.5095i	−0.524859	−	1.44204i	0.340193	−	0.940355i	$-0.389507\pi$
$642$	3.35248	−	9.21085i	0.132312	−	0.363523i
$643$	−8.20234	−	6.88258i	−0.323469	−	0.271423i	0.466564	−	0.884488i	$-0.345492\pi$
$643$	−8.20234	−	6.88258i	−0.323469	−	0.271423i	−0.790032	+	0.613065i	$0.789936\pi$
$644$	13.6397	+	2.40505i	0.537479	+	0.0947721i
$645$	24.3222			0.957686
$646$	0.813322	−	0.267633i	0.0319997	−	0.0105299i
$647$	23.2871			0.915511			0.457755	−	0.889078i	$-0.348654\pi$
$647$	23.2871			0.915511			0.457755	+	0.889078i	$0.348654\pi$
$648$	−0.320822	+	1.81947i	−0.0126031	+	0.0714756i
$649$	10.1616	+	5.78911i	0.398880	+	0.227242i
$650$	2.18019	+	0.793523i	0.0855140	+	0.0311245i
$651$	−3.53131	−	9.70219i	−0.138403	−	0.380259i
$652$	−4.88048	+	4.09521i	−0.191134	+	0.160381i
$653$	23.1567	+	40.1086i	0.906192	+	1.56957i	0.819310	+	0.573351i	$0.194357\pi$
$653$	23.1567	+	40.1086i	0.906192	+	1.56957i	0.0868819	+	0.996219i	$0.472310\pi$
$654$	19.2446	+	11.1109i	0.752522	+	0.434469i
$655$	38.5599	−	6.79914i	1.50666	−	0.265665i
$656$	0.937910	+	5.31915i	0.0366192	+	0.207678i
$657$	9.43144	+	5.44525i	0.367956	+	0.212439i
$658$	6.35611	−	3.66970i	0.247787	−	0.143060i
$659$	36.4432	−	30.5795i	1.41963	−	1.19121i	0.468085	−	0.883683i	$-0.344944\pi$
$659$	36.4432	−	30.5795i	1.41963	−	1.19121i	0.951540	−	0.307524i	$-0.0995003\pi$
$660$	−6.08032	+	3.55729i	−0.236676	+	0.138467i
$661$	−4.17822	+	11.4796i	−0.162514	+	0.446503i	−0.994044	−	0.108976i	$-0.965243\pi$
$661$	−4.17822	+	11.4796i	−0.162514	+	0.446503i	0.831531	+	0.555479i	$0.187465\pi$
$662$	23.3398	−	27.8152i	0.907126	−	1.08107i
$663$	0.0781446	−	0.443180i	0.00303488	−	0.0172117i
$664$		−	14.5315i		−	0.563933i
$665$	−38.4774	−	1.19952i	−1.49209	−	0.0465154i
$666$		−	10.2658i		−	0.397792i
$667$	−0.214554	+	1.21680i	−0.00830756	+	0.0471145i
$668$	6.05127	+	5.07762i	0.234131	+	0.196459i
$669$	20.6572	+	7.51859i	0.798652	+	0.290686i
$670$	11.7285	+	32.2239i	0.453113	+	1.24492i
$671$	−9.99299	+	12.0493i	−0.385775	+	0.465160i
$672$	−9.23402	−	15.9938i	−0.356210	−	0.616974i
$673$	18.2821	−	31.6656i	0.704725	−	1.22062i	−0.262066	−	0.965050i	$-0.584404\pi$
$673$	18.2821	−	31.6656i	0.704725	−	1.22062i	0.966791	−	0.255569i	$-0.0822628\pi$
$674$	−9.80368	−	55.5994i	−0.377623	−	2.14161i
$675$	−0.341725	+	0.0602553i	−0.0131530	+	0.00231923i
$676$	−1.06457	+	1.84388i	−0.0409449	+	0.0709187i
$677$	−5.39494	−	9.34431i	−0.207344	−	0.359131i	0.743533	−	0.668699i	$-0.233149\pi$
$677$	−5.39494	−	9.34431i	−0.207344	−	0.359131i	−0.950877	+	0.309569i	$0.899815\pi$
$678$	1.89940	−	1.59378i	0.0729458	−	0.0612088i
$679$	60.8363	−	22.1426i	2.33468	−	0.849755i
$680$	0.168008	−	0.461597i	0.00644280	−	0.0177014i
$681$	6.23689	−	7.43283i	0.238998	−	0.284827i
$682$	−0.0881562	−	15.3169i	−0.00337568	−	0.586515i
$683$			14.8505i			0.568239i	0.958789	+	0.284120i	$0.0917013\pi$
$683$			14.8505i			0.568239i	−0.958789	+	0.284120i	$0.908299\pi$
$684$	3.52810	−	1.89289i	0.134900	−	0.0723766i
$685$	−17.1171			−0.654009
$686$	3.77246	+	0.665186i	0.144033	+	0.0253969i
$687$	−18.1530	+	21.6338i	−0.692578	+	0.825383i
$688$	−17.9636	+	49.3545i	−0.684855	+	1.88162i
$689$	16.9548	+	46.5828i	0.645925	+	1.77466i
$690$	10.0248	+	11.9471i	0.381639	+	0.454819i
$691$	−16.3034	−	28.2383i	−0.620209	−	1.07423i	−0.989446	−	0.144899i	$-0.953714\pi$
$691$	−16.3034	−	28.2383i	−0.620209	−	1.07423i	0.369237	−	0.929335i	$-0.379619\pi$
$692$	5.12857	−	8.88294i	0.194959	−	0.337679i
$693$	−4.40087	−	11.8781i	−0.167175	−	0.451213i
$694$	−59.6726	+	10.5219i	−2.26514	+	0.399405i
$695$	−27.2894	−	15.7555i	−1.03515	−	0.597642i
$696$	0.500747	−	0.289107i	0.0189808	−	0.0109586i
$697$	0.0799454	+	0.0952752i	0.00302815	+	0.00360880i
$698$	17.6414	+	48.4694i	0.667738	+	1.83459i
$699$	−13.4729	−	4.90375i	−0.509593	−	0.185477i
$700$	0.782481	−	0.932525i	0.0295750	−	0.0352461i
$701$	−44.0780	−	7.77215i	−1.66480	−	0.293550i	−0.739608	−	0.673038i	$-0.764989\pi$
$701$	−44.0780	−	7.77215i	−1.66480	−	0.293550i	−0.925197	+	0.379488i	$0.876100\pi$
$702$		−	6.68626i		−	0.252357i
$703$	20.5800	−	16.2032i	0.776189	−	0.611117i
$704$	1.02647	+	5.63165i	0.0386864	+	0.212251i
$705$	2.56153	+	0.451667i	0.0964729	+	0.0170108i
$706$	13.0498	+	10.9501i	0.491135	+	0.412112i
$707$	−48.1158	−	17.5127i	−1.80958	−	0.658633i
$708$	3.04359	−	1.10778i	0.114385	−	0.0416328i
$709$	−4.52696	+	3.79857i	−0.170014	+	0.142658i	−0.723825	−	0.689984i	$-0.757618\pi$
$709$	−4.52696	+	3.79857i	−0.170014	+	0.142658i	0.553811	+	0.832643i	$0.313173\pi$
$710$	−9.77686	+	5.64467i	−0.366919	+	0.211841i
$711$	3.20283	−	5.54746i	0.120115	−	0.208046i
$712$	−16.3941	+	2.89072i	−0.614393	+	0.108334i
$713$	−10.5105	+	1.85328i	−0.393621	+	0.0694060i
$714$	−0.649720	−	0.375116i	−0.0243151	−	0.0140384i
$715$	−22.8821	+	19.4259i	−0.855742	+	0.726487i
$716$	12.0972	+	14.4169i	0.452095	+	0.538786i
$717$	−11.5159	+	4.19145i	−0.430070	+	0.156533i
$718$	3.47393	−	9.54456i	0.129646	−	0.356200i
$719$	−14.8912	−	12.4952i	−0.555348	−	0.465993i	0.321399	−	0.946944i	$-0.395847\pi$
$719$	−14.8912	−	12.4952i	−0.555348	−	0.465993i	−0.876747	+	0.480951i	$0.840291\pi$
$720$	2.00502	−	11.3710i	0.0747226	−	0.423773i
$721$	62.1941			2.31623
$722$	29.7508	+	12.9800i	1.10721	+	0.483066i
$723$			14.2915i			0.531505i
$724$	−18.8511	−	3.32396i	−0.700597	−	0.123534i
$725$	0.0831904	+	0.0698050i	0.00308961	+	0.00259249i
$726$	−0.216308	−	18.7909i	−0.00802794	−	0.697394i
$727$	16.1220	−	5.86792i	0.597931	−	0.217629i	−0.0252830	−	0.999680i	$-0.508049\pi$
$727$	16.1220	−	5.86792i	0.597931	−	0.217629i	0.623214	+	0.782051i	$0.285826\pi$
$728$	−17.7520	−	21.1560i	−0.657931	−	0.784092i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−37.2577	−	21.5107i	−1.37897	−	0.796148i
$731$	0.210013	+	1.19104i	0.00776762	+	0.0440523i
$732$	0.752827	+	4.26949i	0.0278253	+	0.157805i
$733$	−39.2885	−	22.6832i	−1.45115	−	0.837824i	−0.452606	−	0.891710i	$-0.649506\pi$
$733$	−39.2885	−	22.6832i	−1.45115	−	0.837824i	−0.998547	+	0.0538866i	$0.982839\pi$
$734$	−28.1749	−	48.8003i	−1.03995	−	1.80125i
$735$	11.2771	+	13.4395i	0.415962	+	0.495725i
$736$	−17.9388	+	6.52920i	−0.661234	+	0.240670i
$737$	−28.3815	−	4.83617i	−1.04545	−	0.178143i
$738$	1.41558	+	1.18781i	0.0521082	+	0.0437240i
$739$	25.0212	+	4.41192i	0.920421	+	0.162295i	0.613732	−	0.789515i	$-0.289668\pi$
$739$	25.0212	+	4.41192i	0.920421	+	0.162295i	0.306689	+	0.951810i	$0.400779\pi$
$740$			12.7633i			0.469188i
$741$	13.4040	−	10.5534i	0.492409	−	0.387688i
$742$	82.6431			3.03392
$743$	2.47326	−	14.0266i	0.0907352	−	0.514585i	−0.905236	−	0.424910i	$-0.860306\pi$
$743$	2.47326	−	14.0266i	0.0907352	−	0.514585i	0.995971	−	0.0896755i	$-0.0285830\pi$
$744$	3.82602	+	3.21041i	0.140269	+	0.117700i
$745$	−2.27953	+	6.26297i	−0.0835156	+	0.229457i
$746$	49.4717	−	18.0062i	1.81129	−	0.659255i
$747$	−5.05574	−	6.02520i	−0.184980	−	0.220450i
$748$	−0.226700	−	0.267034i	−0.00828896	−	0.00976372i
$749$	−18.9778	−	10.9569i	−0.693434	−	0.400355i
$750$	−18.1018	+	3.19184i	−0.660985	+	0.116550i
$751$	−43.0555	+	7.59185i	−1.57112	+	0.277031i	−0.890284	−	0.455406i	$-0.849494\pi$
$751$	−43.0555	+	7.59185i	−1.57112	+	0.277031i	−0.680835	+	0.732437i	$0.738383\pi$
$752$	−2.80839	+	4.86427i	−0.102411	+	0.177382i
$753$	7.48043	−	4.31883i	0.272602	−	0.157387i
$754$	−1.60299	+	1.34507i	−0.0583775	+	0.0489846i
$755$	16.4370	−	5.98259i	0.598205	−	0.217729i
$756$	−3.29661	−	1.19987i	−0.119896	−	0.0436388i
$757$	35.3026	+	29.6224i	1.28309	+	1.07664i	0.992810	+	0.119703i	$0.0381941\pi$
$757$	35.3026	+	29.6224i	1.28309	+	1.07664i	0.290284	+	0.956941i	$0.406250\pi$
$758$	−44.6169	−	7.86715i	−1.62056	−	0.285748i
$759$	−12.8816	+	2.34790i	−0.467574	+	0.0852235i
$760$	16.4094	−	8.80395i	0.595231	−	0.319353i
$761$			39.7870i			1.44228i	0.692791	+	0.721139i	$0.256381\pi$
$761$			39.7870i			1.44228i	−0.692791	+	0.721139i	$0.743619\pi$
$762$	−8.63464	−	1.52252i	−0.312800	−	0.0551551i
$763$	31.9335	−	38.0569i	1.15607	−	1.37775i
$764$	11.5942	+	4.21995i	0.419464	+	0.152672i
$765$	−0.0909358	−	0.249844i	−0.00328779	−	0.00903313i
$766$	−24.4881	−	29.1838i	−0.884791	−	1.05445i
$767$	11.9518	−	6.90040i	0.431556	−	0.249159i
$768$	15.6810	+	9.05344i	0.565840	+	0.326688i
$769$	−2.21015	+	0.389709i	−0.0797000	+	0.0140533i	−0.213356	−	0.976975i	$-0.568439\pi$
$769$	−2.21015	+	0.389709i	−0.0797000	+	0.0140533i	0.133656	+	0.991028i	$0.457328\pi$
$770$	17.3851	+	46.9230i	0.626515	+	1.69099i
$771$	−15.2710	+	26.4501i	−0.549970	+	0.952577i
$772$	−0.722858	−	1.25203i	−0.0260162	−	0.0450614i
$773$	−15.7636	−	18.7863i	−0.566977	−	0.675696i	0.404031	−	0.914745i	$-0.367609\pi$
$773$	−15.7636	−	18.7863i	−0.566977	−	0.675696i	−0.971008	+	0.239049i	$0.923164\pi$
$774$	6.14585	+	16.8856i	0.220908	+	0.606940i
$775$	−0.320831	+	0.881476i	−0.0115246	+	0.0316635i
$776$	−20.1305	+	23.9906i	−0.722642	+	0.861211i
$777$	−22.6020	−	3.98534i	−0.810842	−	0.142973i
$778$	3.59646			0.128939
$779$	−0.146915	+	4.71263i	−0.00526377	+	0.168848i
$780$			8.31290i			0.297650i
$781$	−0.0545509	−	9.47808i	−0.00195198	−	0.339152i
$782$	−0.498483	+	0.594069i	−0.0178257	+	0.0212439i
$783$	0.107040	−	0.294090i	0.00382530	−	0.0105099i
$784$	−35.6004	+	12.9575i	−1.27144	+	0.462767i
$785$	15.4609	−	12.9732i	0.551823	−	0.463034i
$786$	14.4638	+	25.0520i	0.515906	+	0.893575i
$787$	−15.0545	+	26.0751i	−0.536634	+	0.929477i	0.462448	+	0.886646i	$0.346971\pi$
$787$	−15.0545	+	26.0751i	−0.536634	+	0.929477i	−0.999082	+	0.0428311i	$0.986362\pi$
$788$	−9.03466	+	1.59305i	−0.321846	+	0.0567502i
$789$	−2.04819	−	11.6158i	−0.0729174	−	0.413535i
$790$	−12.6524	+	21.9145i	−0.450151	+	0.779684i
$791$	−2.77162	−	4.80058i	−0.0985473	−	0.170689i
$792$	4.71660	+	3.91166i	0.167597	+	0.138995i
$793$	6.31800	+	17.3586i	0.224359	+	0.616421i
$794$	−1.69272	−	0.616100i	−0.0600724	−	0.0218646i
$795$	22.4362	+	18.8262i	0.795728	+	0.667695i
$796$	−1.56875	+	8.89682i	−0.0556029	+	0.315339i
$797$		−	12.1850i		−	0.431616i	−0.976436	−	0.215808i	$-0.930761\pi$
$797$		−	12.1850i		−	0.431616i	0.976436	−	0.215808i	$-0.0692385\pi$
$798$	−8.88989	−	27.0159i	−0.314699	−	0.956351i
$799$			0.129337i			0.00457560i
$800$	−0.291361	+	1.65239i	−0.0103012	+	0.0584209i
$801$	−5.79174	+	6.90232i	−0.204641	+	0.243882i
$802$	−18.5583	+	50.9884i	−0.655315	+	1.80046i
$803$	31.1761	−	18.2396i	1.10018	−	0.643661i
$804$	−6.10809	+	5.12530i	−0.215416	+	0.180755i
$805$	30.1955	−	17.4334i	1.06425	−	0.614445i
$806$	−15.6536	−	9.03760i	−0.551374	−	0.318336i
$807$	−0.281210	−	1.59482i	−0.00989907	−	0.0561404i
$808$	24.3929	−	4.30112i	0.858138	−	0.151313i
$809$	−31.7958	−	18.3573i	−1.11788	−	0.645408i	−0.177021	−	0.984207i	$-0.556646\pi$
$809$	−31.7958	−	18.3573i	−1.11788	−	0.645408i	−0.940859	+	0.338799i	$0.889979\pi$
$810$	−1.97518	−	3.42112i	−0.0694009	−	0.120206i
$811$	−7.24559	+	6.07978i	−0.254427	+	0.213490i	−0.761076	−	0.648663i	$-0.775329\pi$
$811$	−7.24559	+	6.07978i	−0.254427	+	0.213490i	0.506649	+	0.862153i	$0.330884\pi$
$812$	0.375515	+	1.03172i	0.0131780	+	0.0362063i
$813$	3.55098	+	1.29245i	0.124538	+	0.0453283i
$814$	−29.5838	−	16.8539i	−1.03691	−	0.590731i
$815$	−2.78507	+	15.7949i	−0.0975569	+	0.553272i
$816$	0.574145			0.0200991
$817$	−24.1503	+	38.9723i	−0.844913	+	1.36347i
$818$	34.2575			1.19779
$819$	−14.7210	−	2.59570i	−0.514392	−	0.0907012i
$820$	−1.75996	−	1.47678i	−0.0614606	−	0.0515716i
$821$	−16.7363	+	45.9827i	−0.584102	+	1.60481i	0.197001	+	0.980403i	$0.436880\pi$
$821$	−16.7363	+	45.9827i	−0.584102	+	1.60481i	−0.781102	+	0.624403i	$0.785342\pi$
$822$	−4.32522	−	11.8835i	−0.150860	−	0.414483i
$823$	−18.2056	+	15.2763i	−0.634608	+	0.532500i	−0.902357	−	0.430989i	$-0.858165\pi$
$823$	−18.2056	+	15.2763i	−0.634608	+	0.532500i	0.267749	+	0.963489i	$0.413720\pi$
$824$	−26.0549	+	15.0428i	−0.907665	+	0.524041i
$825$	−0.387385	+	1.08370i	−0.0134870	+	0.0377295i
$826$	−3.99522	−	22.6580i	−0.139012	−	0.788374i
$827$	3.19619	+	18.1265i	0.111142	+	0.630319i	0.988588	+	0.150644i	$0.0481346\pi$
$827$	3.19619	+	18.1265i	0.111142	+	0.630319i	−0.877446	+	0.479676i	$0.840754\pi$
$828$	−1.81317	+	3.14051i	−0.0630121	+	0.109140i
$829$	17.7994	−	10.2765i	0.618199	−	0.356917i	−0.157968	−	0.987444i	$-0.550494\pi$
$829$	17.7994	−	10.2765i	0.618199	−	0.356917i	0.776167	+	0.630527i	$0.217161\pi$
$830$	19.9720	+	23.8018i	0.693240	+	0.826171i
$831$	9.53926	−	3.47201i	0.330913	−	0.120443i
$832$	6.34778	+	2.31040i	0.220070	+	0.0800988i
$833$	−0.560752	+	0.668279i	−0.0194289	+	0.0231545i
$834$	4.04260	−	22.9267i	0.139984	−	0.793888i
$835$	19.8861			0.688188
$836$	0.337376	−	13.2749i	0.0116684	−	0.459121i
$837$	2.70333			0.0934409
$838$	−2.30575	+	13.0765i	−0.0796507	+	0.451721i
$839$	11.1661	−	13.3072i	0.385496	−	0.459416i	−0.538045	−	0.842916i	$-0.680837\pi$
$839$	11.1661	−	13.3072i	0.385496	−	0.459416i	0.923541	+	0.383500i	$0.125281\pi$
$840$	−15.3327	−	5.58065i	−0.529029	−	0.192551i
$841$	27.1590	−	9.88508i	0.936519	−	0.340865i
$842$	30.8778	+	36.7988i	1.06412	+	1.26817i
$843$	27.8075	−	16.0547i	0.957742	−	0.552953i
$844$	2.51777	−	4.36091i	0.0866654	−	0.150109i
$845$	0.930746	+	5.27852i	0.0320186	+	0.181587i
$846$	0.333693	+	1.89246i	0.0114726	+	0.0650643i
$847$	−41.4553	−	6.81865i	−1.42442	−	0.234291i
$848$	−54.7726	+	31.6230i	−1.88090	+	1.08594i
$849$	12.8346	−	10.7695i	0.440483	−	0.369609i
$850$	0.0233124	+	0.0640504i	0.000799610	+	0.00219691i
$851$	−8.11399	+	22.2930i	−0.278144	+	0.764194i
$852$	−2.01086	−	1.68731i	−0.0688910	−	0.0578064i
$853$	4.94060	+	0.871162i	0.169163	+	0.0298280i	0.257588	−	0.966255i	$-0.417072\pi$
$853$	4.94060	+	0.871162i	0.169163	+	0.0298280i	−0.0884250	+	0.996083i	$0.528183\pi$
$854$	30.7960			1.05382
$855$	3.74079	−	9.35946i	0.127932	−	0.320087i
$856$	10.6005			0.362317
$857$	4.41129	−	25.0177i	0.150687	−	0.854587i	−0.811937	−	0.583745i	$-0.801587\pi$
$857$	4.41129	−	25.0177i	0.150687	−	0.854587i	0.962624	−	0.270842i	$-0.0873021\pi$
$858$	−19.2683	−	10.9772i	−0.657809	−	0.374755i
$859$	−34.2346	−	12.4604i	−1.16807	−	0.425142i	−0.316095	−	0.948728i	$-0.602372\pi$
$859$	−34.2346	−	12.4604i	−1.16807	−	0.425142i	−0.851973	+	0.523586i	$0.824594\pi$
$860$	−7.64103	−	20.9936i	−0.260557	−	0.715874i
$861$	3.16472	−	2.65552i	0.107854	−	0.0904998i
$862$	5.78764	+	10.0245i	0.197128	+	0.341436i
$863$	−15.4389	−	8.91367i	−0.525547	−	0.303425i	0.213654	−	0.976909i	$-0.431463\pi$
$863$	−15.4389	−	8.91367i	−0.525547	−	0.303425i	−0.739201	+	0.673485i	$0.764797\pi$
$864$	4.76199	−	0.839667i	0.162006	−	0.0285660i
$865$	−4.48388	−	25.4293i	−0.152457	−	0.864624i
$866$	33.6707	+	19.4398i	1.14418	+	0.660591i
$867$	−14.7110	+	8.49339i	−0.499611	+	0.288451i
$868$	−7.26499	+	6.09605i	−0.246590	+	0.206914i
$869$	−10.7283	−	18.3374i	−0.363933	−	0.622054i
$870$	−0.422847	+	1.16176i	−0.0143359	+	0.0393875i
$871$	−21.8385	+	26.0261i	−0.739969	+	0.881860i
$872$	−4.17310	+	23.6668i	−0.141319	+	0.801460i
$873$			16.9509i			0.573701i
$874$	−29.0973	+	4.20045i	−0.984230	+	0.142082i
$875$			41.0935i			1.38921i
$876$	1.73706	−	9.85136i	0.0586898	−	0.332847i
$877$	−2.65339	−	2.22646i	−0.0895987	−	0.0751823i	0.596888	−	0.802324i	$-0.296404\pi$
$877$	−2.65339	−	2.22646i	−0.0895987	−	0.0751823i	−0.686487	+	0.727142i	$0.740848\pi$
$878$	6.60135	+	2.40269i	0.222785	+	0.0810870i
$879$	−3.26645	−	8.97450i	−0.110175	−	0.302703i
$880$	−29.4770	−	24.4464i	−0.993670	−	0.824089i
$881$	14.1119	+	24.4426i	0.475443	+	0.823491i	0.999604	−	0.0281279i	$-0.00895457\pi$
$881$	14.1119	+	24.4426i	0.475443	+	0.823491i	−0.524162	+	0.851619i	$0.675621\pi$
$882$	−6.48079	+	11.2251i	−0.218220	+	0.377967i
$883$	−6.52726	−	37.0179i	−0.219660	−	1.24575i	−0.872635	−	0.488373i	$-0.837590\pi$
$883$	−6.52726	−	37.0179i	−0.219660	−	1.24575i	0.652975	−	0.757379i	$-0.273521\pi$
$884$	−0.407078	+	0.0717788i	−0.0136915	+	0.00241418i
$885$	4.07689	−	7.06137i	0.137043	−	0.237365i
$886$	−25.0108	−	43.3200i	−0.840254	−	1.45536i
$887$	−37.1902	+	31.2063i	−1.24872	+	1.04780i	−0.251933	+	0.967745i	$0.581066\pi$
$887$	−37.1902	+	31.2063i	−1.24872	+	1.04780i	−0.996790	+	0.0800588i	$0.974489\pi$
$888$	10.4326	−	3.79714i	0.350094	−	0.127424i
$889$	−6.70419	+	18.4196i	−0.224851	+	0.617773i
$890$	22.8795	−	27.2667i	0.766922	−	0.913982i
$891$	3.31657	−	0.0190884i	0.111109	−	0.000639487i
$892$		−	20.1921i		−	0.676082i
$893$	−3.26715	+	3.65596i	−0.109331	+	0.122342i
$894$	−4.92405			−0.164685
$895$	46.6582	+	8.22710i	1.55961	+	0.275002i
$896$	30.9809	−	36.9216i	1.03500	−	1.23347i
$897$	−5.28474	+	14.5197i	−0.176452	+	0.484799i
$898$	−5.35087	−	14.7014i	−0.178561	−	0.490592i
$899$	−0.543828	−	0.648109i	−0.0181377	−	0.0216156i
$900$	0.159365	+	0.276028i	0.00531215	+	0.00920092i
$901$	−0.728178	+	1.26124i	−0.0242591	+	0.0420181i
$902$	5.74704	−	2.12929i	0.191356	−	0.0708976i
$903$	39.5625	−	6.97594i	1.31656	−	0.232145i
$904$	2.32222	+	1.34073i	0.0772359	+	0.0445921i
$905$	−41.7325	+	24.0943i	−1.38723	+	0.800920i
$906$	8.30678	+	9.89964i	0.275974	+	0.328893i
$907$	1.27049	+	3.49063i	0.0421858	+	0.115905i	0.958997	−	0.283417i	$-0.0914680\pi$
$907$	1.27049	+	3.49063i	0.0421858	+	0.115905i	−0.916811	+	0.399321i	$0.869246\pi$
$908$	−8.37497	−	3.04824i	−0.277933	−	0.101159i
$909$	8.61757	−	10.2700i	0.285827	−	0.340635i
$910$	58.1532	+	10.2540i	1.92776	+	0.339916i
$911$		−	18.6454i		−	0.617749i	−0.951103	−	0.308875i	$-0.900048\pi$
$911$		−	18.6454i		−	0.617749i	0.951103	−	0.308875i	$-0.0999524\pi$
$912$	16.2294	+	14.5034i	0.537408	+	0.480255i
$913$	−25.6636	+	4.67763i	−0.849340	+	0.154807i
$914$	−43.6340	−	7.69385i	−1.44328	−	0.254490i
$915$	8.36058	+	7.01536i	0.276392	+	0.231921i
$916$	24.3760	+	8.87215i	0.805406	+	0.293144i
$917$	60.7714	−	22.1190i	2.00685	−	0.730433i
$918$	0.150475	−	0.126264i	0.00496642	−	0.00416732i
$919$	−3.22865	+	1.86406i	−0.106503	+	0.0614897i	−0.552305	−	0.833642i	$-0.686252\pi$
$919$	−3.22865	+	1.86406i	−0.106503	+	0.0614897i	0.445802	+	0.895131i	$0.352918\pi$
$920$	−8.43316	+	14.6067i	−0.278033	+	0.481568i
$921$	12.5437	−	2.21179i	0.413329	−	0.0728811i
$922$	−56.1318	+	9.89755i	−1.84860	+	0.325958i
$923$	−9.68639	−	5.59244i	−0.318832	−	0.184077i
$924$	−8.86997	+	7.53021i	−0.291801	+	0.247726i
$925$	1.34030	+	1.59731i	0.0440689	+	0.0525193i
$926$	−22.0458	+	8.02403i	−0.724471	+	0.263686i
$927$	−5.56950	+	15.3021i	−0.182926	+	0.502586i
$928$	−1.15927	−	0.972744i	−0.0380549	−	0.0319319i
$929$	−4.15772	+	23.5796i	−0.136410	+	0.773621i	0.837457	+	0.546503i	$0.184041\pi$
$929$	−4.15772	+	23.5796i	−0.136410	+	0.773621i	−0.973867	+	0.227118i	$0.927070\pi$
$930$	−10.6792			−0.350184
$931$	−32.7321	+	4.72516i	−1.07275	+	0.154861i
$932$			13.1696i			0.431385i
$933$	17.0531	+	3.00691i	0.558292	+	0.0984419i
$934$	−30.0887	−	25.2474i	−0.984533	−	0.826122i
$935$	−0.869289	−	0.148126i	−0.0284288	−	0.00484423i
$936$	6.79485	−	2.47312i	0.222097	−	0.0808366i
$937$	−7.96987	−	9.49812i	−0.260364	−	0.310290i	0.619987	−	0.784612i	$-0.287138\pi$
$937$	−7.96987	−	9.49812i	−0.260364	−	0.310290i	−0.880352	+	0.474322i	$0.842693\pi$
$938$	28.3199	+	49.0515i	0.924677	+	1.60159i
$939$	20.6798	+	11.9395i	0.674860	+	0.389631i
$940$	−0.414874	−	2.35287i	−0.0135317	−	0.0767420i
$941$	1.09209	+	6.19357i	0.0356012	+	0.201905i	0.997420	−	0.0717811i	$-0.0228683\pi$
$941$	1.09209	+	6.19357i	0.0356012	+	0.201905i	−0.961819	+	0.273686i	$0.911757\pi$
$942$	12.9133	+	7.45552i	0.420740	+	0.242914i
$943$	−2.13520	−	3.69828i	−0.0695318	−	0.120433i
$944$	11.3179	+	13.4881i	0.368365	+	0.439000i
$945$	−8.29899	+	3.02058i	−0.269966	+	0.0982596i
$946$	58.7505	+	10.0110i	1.91014	+	0.325486i
$947$	−16.2857	−	13.6653i	−0.529214	−	0.444063i	0.338616	−	0.940925i	$-0.390041\pi$
$947$	−16.2857	−	13.6653i	−0.529214	−	0.444063i	−0.867830	+	0.496862i	$0.834486\pi$
$948$	−5.79445	−	1.02172i	−0.188195	−	0.0331839i
$949$		−	42.6234i		−	1.38361i
$950$	−0.958993	+	2.39940i	−0.0311138	+	0.0778469i
$951$	−8.67781			−0.281397
$952$	0.140889	−	0.799021i	0.00456624	−	0.0258964i
$953$	−12.6830	−	10.6423i	−0.410844	−	0.344739i	0.413823	−	0.910357i	$-0.364193\pi$
$953$	−12.6830	−	10.6423i	−0.410844	−	0.344739i	−0.824667	+	0.565618i	$0.808638\pi$
$954$	−7.40072	+	20.3333i	−0.239607	+	0.658315i
$955$	29.1877	−	10.6234i	0.944490	−	0.343766i
$956$	7.23565	+	8.62311i	0.234018	+	0.278891i
$957$	−0.671768	−	0.791289i	−0.0217152	−	0.0255787i
$958$	14.2426	+	8.22294i	0.460156	+	0.265671i
$959$	−27.8426	+	4.90940i	−0.899085	+	0.158533i
$960$	3.93045	−	0.693044i	0.126855	−	0.0223679i
$961$	−11.8460	+	20.5179i	−0.382129	+	0.661866i
$962$	−34.7956	+	20.0893i	−1.12186	+	0.647704i
$963$	4.39527	−	3.68807i	0.141636	−	0.118846i
$964$	12.3356	−	4.48979i	0.397303	−	0.144606i
$965$	−3.42000	−	1.24478i	−0.110094	−	0.0400709i
$966$	19.7330	+	16.5579i	0.634898	+	0.532743i
$967$	−20.7399	−	3.65700i	−0.666950	−	0.117601i	−0.170085	−	0.985429i	$-0.554404\pi$
$967$	−20.7399	−	3.65700i	−0.666950	−	0.117601i	−0.496864	+	0.867828i	$0.665515\pi$
$968$	19.0160	−	7.17022i	0.611199	−	0.230459i
$969$	0.490627	+	0.102369i	0.0157612	+	0.00328856i
$970$		−	66.9623i		−	2.15003i
$971$	51.5953	+	9.09765i	1.65577	+	0.291957i	0.921929	−	0.387360i	$-0.126613\pi$
$971$	51.5953	+	9.09765i	1.65577	+	0.291957i	0.733844	+	0.679318i	$0.237724\pi$
$972$	0.590425	−	0.703641i	0.0189379	−	0.0225693i
$973$	−48.9078	−	17.8010i	−1.56791	−	0.570674i
$974$	−1.76827	−	4.85829i	−0.0566592	−	0.155670i
$975$	0.872957	+	1.04035i	0.0279570	+	0.0333178i
$976$	−20.4104	+	11.7840i	−0.653321	+	0.377195i
$977$	−27.3269	−	15.7772i	−0.874264	−	0.504757i	−0.00550130	−	0.999985i	$-0.501751\pi$
$977$	−27.3269	−	15.7772i	−0.874264	−	0.504757i	−0.868763	+	0.495228i	$0.835084\pi$
$978$	−11.6693	+	2.05762i	−0.373144	+	0.0657953i
$979$	10.3824	+	28.0224i	0.331821	+	0.895600i
$980$	8.05745	−	13.9559i	0.257386	−	0.445805i
$981$	6.50376	+	11.2648i	0.207649	+	0.359659i
$982$	35.8751	+	42.7542i	1.14482	+	1.36434i
$983$	12.4931	+	34.3246i	0.398469	+	1.09479i	0.963030	+	0.269394i	$0.0868233\pi$
$983$	12.4931	+	34.3246i	0.398469	+	1.09479i	−0.564561	+	0.825391i	$0.690954\pi$
$984$	−0.683507	+	1.87792i	−0.0217894	+	0.0598659i
$985$	−14.8452	+	17.6918i	−0.473007	+	0.563708i
$986$	−0.0605420	−	0.0106752i	−0.00192805	−	0.000339967i
$987$	4.29614			0.136747
$988$	−13.3201	−	8.25415i	−0.423768	−	0.262600i
$989$		−	41.5260i		−	1.32045i
$990$	−13.1017	+	0.0754064i	−0.416399	+	0.00239657i
$991$	−4.54771	+	5.41975i	−0.144463	+	0.172164i	−0.833424	−	0.552634i	$-0.813623\pi$
$991$	−4.54771	+	5.41975i	−0.144463	+	0.172164i	0.688961	+	0.724798i	$0.258067\pi$
$992$	4.47083	−	12.2835i	0.141949	−	0.390002i
$993$	19.9725	−	7.26939i	0.633808	−	0.230687i
$994$	−14.2841	+	11.9858i	−0.453063	+	0.380165i
$995$	11.3713	+	19.6957i	0.360495	+	0.624396i
$996$	−3.61231	+	6.25670i	−0.114460	+	0.198251i
$997$	38.7529	−	6.83319i	1.22732	−	0.216409i	0.477845	−	0.878444i	$-0.341418\pi$
$997$	38.7529	−	6.83319i	1.22732	−	0.216409i	0.749473	+	0.662035i	$0.230307\pi$
$998$	3.23874	+	18.3678i	0.102520	+	0.581422i
$999$	3.00456	−	5.20405i	0.0950601	−	0.164649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.be.a.439.31	yes	240
11.10	odd	2	inner	627.2.be.a.439.10	yes	240
19.10	odd	18	inner	627.2.be.a.10.10	✓	240
209.10	even	18	inner	627.2.be.a.10.31	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.be.a.10.10	✓	240	19.10	odd	18	inner
627.2.be.a.10.31	yes	240	209.10	even	18	inner
627.2.be.a.439.10	yes	240	11.10	odd	2	inner
627.2.be.a.439.31	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.296656 - 1.68242i) q^{2} +(0.642788 - 0.766044i) q^{3} +(-0.863144 - 0.314159i) q^{4} +(-2.17291 + 0.790873i) q^{5} +(-1.09812 - 1.30869i) q^{6} +(-3.30762 + 1.90965i) q^{7} +(0.923770 - 1.60002i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.685974 + 3.89035i) q^{10} +(-3.12308 - 1.11640i) q^{11} +(-0.795477 + 0.459269i) q^{12} +(-2.99816 + 2.51575i) q^{13} +(2.23161 + 6.13130i) q^{14} +(-0.790873 + 2.17291i) q^{15} +(-3.82514 - 3.20967i) q^{16} +(-0.113235 - 0.0199663i) q^{17} -1.70837 q^{18} +(-2.69644 - 3.42479i) q^{19} +2.12399 q^{20} +(-0.663215 + 3.76128i) q^{21} +(-2.80473 + 4.92315i) q^{22} +(3.70986 + 1.35028i) q^{23} +(-0.631896 - 1.73612i) q^{24} +(0.265815 - 0.223045i) q^{25} +(3.34313 + 5.79047i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(3.45488 - 0.609189i) q^{28} +(0.0543456 + 0.308209i) q^{29} +(3.42112 + 1.97518i) q^{30} +(-2.34116 + 1.35167i) q^{31} +(-3.70417 + 3.10817i) q^{32} +(-2.86269 + 1.67482i) q^{33} +(-0.0671835 + 0.184585i) q^{34} +(5.67684 - 6.76540i) q^{35} +(-0.159502 + 0.904583i) q^{36} +6.00912i q^{37} +(-6.56185 + 3.52056i) q^{38} +3.91382i q^{39} +(-0.741855 + 4.20727i) q^{40} +(-0.828613 - 0.695288i) q^{41} +(6.13130 + 2.23161i) q^{42} +(-3.59749 - 9.88402i) q^{43} +(2.34494 + 1.94475i) q^{44} +(1.15618 + 2.00256i) q^{45} +(3.37229 - 5.84097i) q^{46} +(-0.195328 - 1.10776i) q^{47} +(-4.91750 + 0.867089i) q^{48} +(3.79355 - 6.57061i) q^{49} +(-0.296399 - 0.513379i) q^{50} +(-0.0880810 + 0.0739087i) q^{51} +(3.37819 - 1.22956i) q^{52} +(4.33203 - 11.9021i) q^{53} +(-1.09812 + 1.30869i) q^{54} +(7.66909 - 0.0441393i) q^{55} +7.05632i q^{56} +(-4.35678 - 0.135821i) q^{57} +0.534659 q^{58} +(-3.47260 - 0.612314i) q^{59} +(1.36527 - 1.62707i) q^{60} +(1.61428 - 4.43520i) q^{61} +(1.57955 + 4.33979i) q^{62} +(2.45500 + 2.92576i) q^{63} +(-0.862990 - 1.49474i) q^{64} +(4.52507 - 7.83765i) q^{65} +(1.96851 + 5.31309i) q^{66} +(8.54881 - 1.50739i) q^{67} +(0.0914652 + 0.0528075i) q^{68} +(3.41903 - 1.97398i) q^{69} +(-9.69816 - 11.5578i) q^{70} +(0.977423 + 2.68545i) q^{71} +(-1.73612 - 0.631896i) q^{72} +(-7.00027 + 8.34260i) q^{73} +(10.1099 + 1.78264i) q^{74} -0.346996i q^{75} +(1.25149 + 3.80320i) q^{76} +(12.4619 - 2.27140i) q^{77} +(6.58468 + 1.16106i) q^{78} +(4.90702 + 4.11748i) q^{79} +(10.8501 + 3.94912i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-1.41558 + 1.18781i) q^{82} +(6.81158 - 3.93267i) q^{83} +(1.75409 - 3.03817i) q^{84} +(0.261839 - 0.0461693i) q^{85} +(-17.6963 + 3.12033i) q^{86} +(0.271035 + 0.156482i) q^{87} +(-4.67127 + 3.96569i) q^{88} +(-5.79174 - 6.90232i) q^{89} +(3.71213 - 1.35111i) q^{90} +(5.11254 - 14.0466i) q^{91} +(-2.77794 - 2.33097i) q^{92} +(-0.469429 + 2.66226i) q^{93} -1.92166 q^{94} +(8.56769 + 5.30921i) q^{95} +4.83545i q^{96} +(-16.6934 - 2.94349i) q^{97} +(-9.92915 - 8.33154i) q^{98} +(-0.557118 + 3.26950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) \) 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Introduction

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