LMFDB - Embedded newform 627.2.be.a.439.10

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			439.10
Character	$\chi$	$=$	627.439
Dual form			627.2.be.a.10.10

$q$-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} +(2.52837 + 2.14647i) 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} +(-4.36132 + 3.61701i) 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} +(3.26950 - 0.557118i) 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} +(-1.50801 - 2.64702i) 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} +(-7.19149 - 2.66446i) 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} +(-0.0326102 + 5.66594i) 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} +(-5.77002 + 2.06259i) 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} +(1.67482 - 2.86269i) 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	$0.261983\pi$
$2$	−0.296656	+	1.68242i	−0.209767	+	1.18965i	−0.889759	+	0.456430i	$0.849128\pi$
$3$	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	0.279020	−	0.960285i	$-0.409991\pi$
$7$	3.30762	−	1.90965i	1.25016	−	0.721781i	0.971141	+	0.238505i	$0.0766572\pi$
$8$	−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
$11$	2.52837	+	2.14647i	0.762332	+	0.647186i
$11$	2.52837	+	2.14647i	0.762332	+	0.647186i
$12$	−0.795477	+	0.459269i	−0.229635	+	0.132580i
$13$	2.99816	−	2.51575i	0.831539	−	0.697744i	−0.124105	−	0.992269i	$-0.539606\pi$
$13$	2.99816	−	2.51575i	0.831539	−	0.697744i	0.955644	+	0.294525i	$0.0951614\pi$
$14$	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	0.187363	−	0.982291i	$-0.440006\pi$
$17$	0.113235	+	0.0199663i	0.0274635	+	0.00484255i	−0.159900	+	0.987133i	$0.551117\pi$
$18$	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
$22$	−4.36132	+	3.61701i	−0.929837	+	0.771150i
$23$	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	0.979346	−	0.202191i	$-0.0648063\pi$
$29$	−0.0543456	−	0.308209i	−0.0100917	−	0.0572330i	−0.989438	+	0.144958i	$0.953695\pi$
$30$	−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
$33$	3.26950	−	0.557118i	0.569147	−	0.0969818i
$34$	−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	0.705194	−	0.709014i	$-0.250860\pi$
$41$	0.828613	+	0.695288i	0.129408	+	0.108586i	−0.575787	+	0.817600i	$0.695304\pi$
$42$	6.13130	+	2.23161i	0.946081	+	0.344345i
$43$	3.59749	+	9.88402i	0.548612	+	1.50730i	0.835585	+	0.549361i	$0.185129\pi$
$43$	3.59749	+	9.88402i	0.548612	+	1.50730i	−0.286973	+	0.957939i	$0.592649\pi$
$44$	−1.50801	−	2.64702i	−0.227342	−	0.399054i
$45$	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
$55$	−7.19149	−	2.66446i	−0.969701	−	0.359276i
$56$			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	−0.999113	−	0.0420987i	$-0.986596\pi$
$61$	−1.61428	+	4.43520i	−0.206688	+	0.567870i	0.792426	+	0.609968i	$0.208818\pi$
$62$	−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
$66$	−0.0326102	+	5.66594i	−0.00401404	+	0.697429i
$67$	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	−0.180655	−	0.983547i	$-0.557822\pi$
$73$	7.00027	−	8.34260i	0.819320	−	0.976428i	0.999975	+	0.00711894i	$0.00226605\pi$
$74$	−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	0.323563	−	0.946207i	$-0.395119\pi$
$79$	−4.90702	−	4.11748i	−0.552083	−	0.463253i	−0.875646	+	0.482954i	$0.839564\pi$
$80$	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	−0.824851	−	0.565350i	$-0.808741\pi$
$83$	−6.81158	+	3.93267i	−0.747668	+	0.431666i	0.0771825	+	0.997017i	$0.475408\pi$
$84$	−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
$88$	−5.77002	+	2.06259i	−0.615087	+	0.219873i
$89$	−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
$99$	1.67482	−	2.86269i	0.168325	−	0.287711i
$100$	−0.299508	+	0.109012i	−0.0299508	+	0.0109012i
$101$	−8.61757	−	10.2700i	−0.857480	−	1.02191i	−0.999487	−	0.0320394i	$-0.989800\pi$
$101$	−8.61757	−	10.2700i	−0.857480	−	1.02191i	0.142006	−	0.989866i	$-0.454645\pi$
$102$	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	0.693384	−	0.720568i	$-0.256119\pi$
$107$	−2.86881	−	4.96892i	−0.277338	−	0.480364i	−0.970722	+	0.240204i	$0.922786\pi$
$108$	0.590425	+	0.703641i	0.0568137	+	0.0677079i
$109$	12.2231	−	4.44883i	1.17076	−	0.426121i	0.317829	−	0.948148i	$-0.397046\pi$
$109$	12.2231	−	4.44883i	1.17076	−	0.426121i	0.852929	+	0.522027i	$0.174824\pi$
$110$	6.61614	−	11.3087i	0.630824	−	1.07824i
$111$	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
$121$	1.78531	+	10.8542i	0.162301	+	0.986741i
$122$	−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	−0.800336	−	0.599552i	$-0.795345\pi$
$127$	−3.93155	+	3.29896i	−0.348869	+	0.292736i	0.451467	+	0.892288i	$0.350901\pi$
$128$	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	0.845327	−	0.534249i	$-0.179406\pi$
$131$	16.6756	+	2.94035i	1.45695	+	0.256900i	0.611624	+	0.791149i	$0.290517\pi$
$132$	−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	0.253679	−	0.967288i	$-0.418359\pi$
$139$	−8.75943	−	10.4391i	−0.742965	−	0.885431i	−0.996644	+	0.0818573i	$0.973915\pi$
$140$	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
$143$	12.9804	+	0.0747087i	1.08548	+	0.00624745i
$144$	−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	−0.836577	−	0.547850i	$-0.815446\pi$
$149$	−1.85271	+	2.20797i	−0.151780	+	0.180884i	0.684797	+	0.728734i	$0.259891\pi$
$150$	0.583793	+	0.102938i	0.0476665	+	0.00840489i
$151$	7.56454			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$151$	7.56454			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$152$	−7.97062	+	1.15063i	−0.646502	+	0.0933283i
$153$		−	0.114982i		−	0.00929571i
$154$	−7.51833	+	20.2923i	−0.605845	+	1.63520i
$155$	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
$165$	−6.66370	+	3.79632i	−0.518768	+	0.295543i
$166$	−4.59570	−	12.6266i	−0.356696	−	0.980013i
$167$	8.08130	+	2.94135i	0.625349	+	0.227609i	0.635206	−	0.772343i	$-0.280915\pi$
$167$	8.08130	+	2.94135i	0.625349	+	0.227609i	−0.00985646	+	0.999951i	$0.503137\pi$
$168$	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	$-0.804895\pi$
$173$	1.93909	−	10.9972i	0.147427	−	0.836098i	0.965387	−	0.260823i	$-0.0839939\pi$
$174$	0.343672	−	0.409573i	0.0260537	−	0.0310496i
$175$	0.453274	−	1.24536i	0.0342643	−	0.0941404i
$176$	−2.78189	−	16.3258i	−0.209693	−	1.23060i
$177$	−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
$187$	0.243442	+	0.293538i	0.0178023	+	0.0214656i
$188$	−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	0.598361	−	0.801226i	$-0.295819\pi$
$193$	−1.20570	−	1.01170i	−0.0867883	−	0.0728240i	−0.685150	+	0.728402i	$0.740263\pi$
$194$	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	−0.775410	−	0.631459i	$-0.782457\pi$
$197$	−8.64955	+	4.99382i	−0.616255	+	0.355795i	0.159154	+	0.987254i	$0.449123\pi$
$198$	4.31940	+	3.66698i	0.306966	+	0.260601i
$199$	−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
$209$	−0.533625	+	14.4470i	−0.0369116	+	0.999319i
$210$	−15.0877			−1.04115
$211$	0.951963	−	5.39885i	0.0655358	−	0.371672i	−0.934347	−	0.356364i	$-0.884016\pi$
$211$	0.951963	−	5.39885i	0.0655358	−	0.371672i	0.999883	−	0.0153076i	$-0.00487275\pi$
$212$	−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
$220$	5.37023	+	4.55908i	0.362061	+	0.307373i
$221$	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	$-0.604355\pi$
$227$	−9.70287			−0.644002			−0.322001	+	0.946739i	$0.604355\pi$
$228$	−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
$231$	9.75034	−	8.08634i	0.641525	−	0.532042i
$232$	0.543343	+	0.197761i	0.0356722	+	0.0129836i
$233$	4.90375	+	13.4729i	0.321255	+	0.882641i	0.990241	+	0.139366i	$0.0445064\pi$
$233$	4.90375	+	13.4729i	0.321255	+	0.882641i	−0.668986	+	0.743275i	$0.733271\pi$
$234$	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	0.802302	−	0.596919i	$-0.203608\pi$
$239$	10.6131	+	6.12749i	0.686506	+	0.396354i	−0.115796	+	0.993273i	$0.536942\pi$
$240$	9.99951	−	5.77322i	0.645466	−	0.372660i
$241$	10.9479	−	9.18638i	0.705216	−	0.591747i	−0.218036	−	0.975941i	$-0.569965\pi$
$241$	10.9479	−	9.18638i	0.705216	−	0.591747i	0.923252	+	0.384194i	$0.125521\pi$
$242$	−18.7909	−	0.216308i	−1.20792	−	0.0139048i
$243$	−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
$253$	6.48156	+	11.3771i	0.407492	+	0.715273i
$254$	−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	−0.947350	−	0.320201i	$-0.896250\pi$
$263$	−7.58171	+	9.03553i	−0.467508	+	0.557154i	0.479842	+	0.877355i	$0.340694\pi$
$264$	−2.12887	+	5.74590i	−0.131023	+	0.353636i
$265$			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	0.894227	−	0.447613i	$-0.147726\pi$
$271$	−1.29245	−	3.55098i	−0.0785109	−	0.215707i	−0.972738	+	0.231906i	$0.925504\pi$
$272$	−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
$275$	1.15084	+	0.00662362i	0.0693981	+	0.000399419i
$276$	−3.57125	+	0.629708i	−0.214964	+	0.0379040i
$277$	−8.79143	−	5.07574i	−0.528226	−	0.304971i	0.212068	−	0.977255i	$-0.431980\pi$
$277$	−8.79143	−	5.07574i	−0.528226	−	0.304971i	−0.740294	+	0.672284i	$0.765314\pi$
$278$	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	$-0.981756\pi$
$281$	−30.1729	−	10.9820i	−1.79997	−	0.655134i	−0.801608	−	0.597850i	$-0.796022\pi$
$282$	1.23522	−	1.47208i	0.0735562	−	0.0876609i
$283$	−16.4999	−	2.90937i	−0.980815	−	0.172944i	−0.339821	−	0.940490i	$-0.610367\pi$
$283$	−16.4999	−	2.90937i	−0.980815	−	0.172944i	−0.640994	+	0.767546i	$0.721478\pi$
$284$		−	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	−0.971130	−	0.238553i	$-0.923327\pi$
$293$	−4.77523	+	8.27095i	−0.278972	+	0.483194i	0.692157	+	0.721747i	$0.256660\pi$
$294$	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
$297$	−1.11640	−	3.12308i	−0.0647799	−	0.181220i
$298$	−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	0.320385	−	0.947288i	$-0.396188\pi$
$307$	−9.75728	−	8.18733i	−0.556877	−	0.467275i	−0.877262	+	0.480012i	$0.840632\pi$
$308$	−10.0428	−	5.87555i	−0.572243	−	0.334791i
$309$	−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
$319$	0.524157	−	0.895918i	0.0293472	−	0.0501618i
$320$	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
$330$	−4.41018	−	12.3373i	−0.242772	−	0.679148i
$331$	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	−0.994830	−	0.101555i	$-0.967618\pi$
$337$	−31.0543	+	11.3028i	−1.69164	+	0.615705i	−0.696806	+	0.717260i	$0.745396\pi$
$338$	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	$0.289885\pi$
$347$	12.1309	+	33.3293i	0.651220	+	1.78921i	0.0380282	+	0.999277i	$0.487892\pi$
$348$	0.184782	+	0.220214i	0.00990534	+	0.0118047i
$349$	26.1475	−	15.0963i	1.39964	−	0.808084i	0.405287	−	0.914189i	$-0.367171\pi$
$349$	26.1475	−	15.0963i	1.39964	−	0.808084i	0.994355	+	0.106105i	$0.0338381\pi$
$350$	1.96075	+	1.13204i	0.104807	+	0.0605101i
$351$	−3.85436	+	0.679627i	−0.205730	+	0.0362758i
$352$	16.0371	+	0.0923012i	0.854780	+	0.00491967i
$353$	−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	0.0169858	−	0.999856i	$-0.494593\pi$
$359$	−5.85516	−	1.03242i	−0.309023	−	0.0544892i	−0.326009	+	0.945367i	$0.605704\pi$
$360$	−4.27217			−0.225163
$361$	−4.45842	+	18.4695i	−0.234653	+	0.972079i
$362$			35.6018i			1.87119i
$363$	9.46234	+	5.60929i	0.496644	+	0.294411i
$364$	−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	$-0.872654\pi$
$373$	−15.4084	−	26.6882i	−0.797818	−	1.38186i	0.123217	−	0.992380i	$-0.460679\pi$
$374$	−0.566072	+	0.322492i	−0.0292709	+	0.0166757i
$375$	−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
$385$	−28.8749	+	4.92024i	−1.47160	+	0.250759i
$386$	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
$396$	−2.34494	+	1.94475i	−0.117838	+	0.0977276i
$397$	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
$407$	−12.8984	+	15.1933i	−0.639351	+	0.753103i
$408$	0.0368886	+	0.209206i	0.00182626	+	0.0103572i
$409$	−3.48212	−	19.7481i	−0.172180	−	0.976479i	−0.941349	−	0.337434i	$-0.890441\pi$
$409$	−3.48212	−	19.7481i	−0.172180	−	0.976479i	0.769170	−	0.639045i	$-0.220670\pi$
$410$	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
$418$	−24.1476	−	5.18356i	−1.18110	−	0.253536i
$419$	−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
$429$	8.40090	−	9.89558i	0.405599	−	0.477763i
$430$	35.9846	−	20.7757i	1.73533	−	1.00189i
$431$	5.19043	−	4.35529i	0.250014	−	0.209787i	−0.509164	−	0.860669i	$-0.670045\pi$
$431$	5.19043	−	4.35529i	0.250014	−	0.209787i	0.759178	+	0.650883i	$0.225601\pi$
$432$	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	−0.963015	−	0.269449i	$-0.913158\pi$
$439$	0.714059	−	4.04963i	0.0340802	−	0.193278i	0.997095	+	0.0761709i	$0.0242695\pi$
$440$	10.9065	−	9.04516i	0.519946	−	0.431211i
$441$	−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
$451$	0.602621	+	3.53654i	0.0283763	+	0.166529i
$452$	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	$0.207467\pi$
$457$			25.9353i			1.21320i	−0.795007	+	0.606600i	$0.792533\pi$
$458$	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	$0.172124\pi$
$461$	11.4111	+	31.3517i	0.531467	+	1.46019i	−0.325859	+	0.945418i	$0.605654\pi$
$462$	10.7121	+	18.8030i	0.498373	+	0.874796i
$463$	−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
$473$	−12.1200	+	32.7124i	−0.557278	+	1.50412i
$474$		−	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	−0.841467	−	0.540309i	$-0.818307\pi$
$479$	3.29250	−	9.04608i	0.150438	−	0.413326i	0.991905	+	0.126983i	$0.0405295\pi$
$480$	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
$484$	1.86895	−	9.92956i	0.0849521	−	0.451344i
$485$	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	$-0.513936\pi$
$491$	20.9996	−	25.0263i	0.947697	−	1.12942i	0.991464	−	0.130379i	$-0.0416194\pi$
$492$	−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	−0.582590	−	0.812766i	$-0.697961\pi$
$503$	−19.1098	+	3.36957i	−0.852064	+	0.150242i	−0.269474	+	0.963008i	$0.586850\pi$
$504$	6.94912	−	1.22532i	0.309538	−	0.0545800i
$505$	26.8474	+	15.5004i	1.19470	+	0.689758i
$506$	−21.0639	+	7.52962i	−0.936403	+	0.334732i
$507$	−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
$517$	1.88391	−	3.22009i	0.0828544	−	0.141619i
$518$	−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	$0.296558\pi$
$523$	7.10050	+	40.2689i	0.310483	+	1.76084i	−0.286016	+	0.958225i	$0.592331\pi$
$524$	−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
$528$	−14.2945	−	8.36297i	−0.622086	−	0.363951i
$529$	−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
$539$	23.6951	−	8.47020i	1.02062	−	0.364837i
$540$	−1.83943	−	1.06199i	−0.0791564	−	0.0457010i
$541$	41.9833	−	7.40278i	1.80500	−	0.318270i	0.833005	−	0.553266i	$-0.186619\pi$
$541$	41.9833	−	7.40278i	1.80500	−	0.318270i	0.971996	+	0.234996i	$0.0755076\pi$
$542$	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	0.396071	−	0.918220i	$-0.370373\pi$
$547$	2.55536	+	0.930074i	0.109259	+	0.0397671i	−0.286812	+	0.957987i	$0.592596\pi$
$548$	−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	0.751989	−	0.659175i	$-0.229095\pi$
$557$	−0.655006	−	0.780606i	−0.0277535	−	0.0330753i	−0.779743	+	0.626100i	$0.784650\pi$
$558$	−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
$561$	0.381344	+	0.00219482i	0.0161004	+	9.26654e-5i
$562$	27.4274	−	47.5056i	1.15695	−	2.00390i
$563$	3.88641	+	6.73146i	0.163793	+	0.283697i	0.936226	−	0.351399i	$-0.114294\pi$
$563$	3.88641	+	6.73146i	0.163793	+	0.283697i	−0.772433	+	0.635096i	$0.780961\pi$
$564$	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	$-0.110890\pi$
$569$	44.8416			1.87986			0.939930	+	0.341368i	$0.110890\pi$
$570$	−2.46025	−	17.0426i	−0.103048	−	0.713836i
$571$		−	2.36458i		−	0.0989544i	−0.998775	−	0.0494772i	$-0.984244\pi$
$571$		−	2.36458i		−	0.0989544i	0.998775	−	0.0494772i	$-0.0157555\pi$
$572$	−11.1805	−	4.14240i	−0.467481	−	0.173203i
$573$	−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
$583$	36.5006	−	20.7945i	1.51170	−	0.861218i
$584$	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	$-0.623473\pi$
$593$	12.3350	−	33.8902i	0.506539	−	1.39170i	0.884785	−	0.465999i	$-0.154305\pi$
$594$	5.58552	−	0.951765i	0.229177	−	0.0390514i
$595$	−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	0.999378	−	0.0352701i	$-0.0112291\pi$
$601$	11.5012	+	19.9207i	0.469144	+	0.812581i	−0.530234	+	0.847852i	$0.677896\pi$
$602$	−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
$605$	−12.4636	−	22.1731i	−0.506716	−	0.901464i
$606$	3.97713	−	22.5554i	0.161560	−	0.916252i
$607$	6.54682			0.265727			0.132864	−	0.991134i	$-0.457583\pi$
$607$	6.54682			0.265727			0.132864	+	0.991134i	$0.457583\pi$
$608$	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	0.999723	−	0.0235173i	$-0.00748649\pi$
$613$	5.41659	+	14.8820i	0.218774	+	0.601077i	−0.780949	+	0.624595i	$0.785264\pi$
$614$	16.6691	−	13.9870i	0.672709	−	0.564470i
$615$	−2.16612	+	1.25061i	−0.0873465	+	0.0504295i
$616$	−15.1462	+	17.8410i	−0.610258	+	0.718834i
$617$	−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
$627$	10.7240	+	9.69512i	0.428276	+	0.387186i
$628$	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
$638$	1.35182	+	1.14763i	0.0535189	+	0.0454351i
$639$	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
$649$	−7.46571	−	9.00200i	−0.293055	−	0.353359i
$650$	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	$0.655056\pi$
$659$	−36.4432	+	30.5795i	−1.41963	+	1.19121i	−0.951540	+	0.307524i	$0.900500\pi$
$660$	6.94438	−	1.18331i	0.270309	−	0.0460604i
$661$	−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
$671$	−13.6015	+	7.74882i	−0.525082	+	0.299140i
$672$	−9.23402	−	15.9938i	−0.356210	−	0.616974i
$673$	−18.2821	+	31.6656i	−0.704725	+	1.22062i	0.262066	+	0.965050i	$0.415596\pi$
$673$	−18.2821	+	31.6656i	−0.704725	+	1.22062i	−0.966791	+	0.255569i	$0.917737\pi$
$674$	−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	0.950877	−	0.309569i	$-0.100185\pi$
$677$	5.39494	+	9.34431i	0.207344	+	0.359131i	−0.743533	+	0.668699i	$0.766851\pi$
$678$	−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
$682$	5.32154	−	14.3630i	0.203772	−	0.549990i
$683$			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
$693$	0.0729046	−	12.6670i	0.00276942	−	0.481179i
$694$	−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	0.925197	−	0.379488i	$-0.123900\pi$
$701$	44.0780	+	7.77215i	1.66480	+	0.293550i	0.739608	+	0.673038i	$0.235011\pi$
$702$		−	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
$715$	−28.2644	+	10.1035i	−1.05703	+	0.377851i
$716$	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
$726$	−12.2442	+	14.2556i	−0.454426	+	0.529075i
$727$	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	0.998547	−	0.0538866i	$-0.0171610\pi$
$733$	39.2885	+	22.6832i	1.45115	+	0.837824i	0.452606	+	0.891710i	$0.350494\pi$
$734$	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
$737$	24.8501	+	14.5386i	0.915366	+	0.535535i
$738$	1.41558	+	1.18781i	0.0521082	+	0.0437240i
$739$	−25.0212	−	4.41192i	−0.920421	−	0.162295i	−0.306689	−	0.951810i	$-0.599221\pi$
$739$	−25.0212	−	4.41192i	−0.920421	−	0.162295i	−0.613732	+	0.789515i	$0.710332\pi$
$740$			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	$0.139694\pi$
$743$	−2.47326	+	14.0266i	−0.0907352	+	0.514585i	−0.995971	+	0.0896755i	$0.971417\pi$
$744$	−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
$748$	−0.117908	−	0.329845i	−0.00431115	−	0.0120603i
$749$	−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	$-0.743619\pi$
$761$		−	39.7870i		−	1.44228i	0.692791	−	0.721139i	$-0.256381\pi$
$762$	−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	−0.133656	−	0.991028i	$-0.542672\pi$
$769$	2.21015	−	0.389709i	0.0797000	−	0.0140533i	0.213356	+	0.976975i	$0.431561\pi$
$770$	0.288000	−	50.0393i	0.0103788	−	1.80329i
$771$	−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
$781$	−3.29295	+	8.88782i	−0.117831	+	0.318031i
$782$	−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	$-0.653029\pi$
$787$	15.0545	−	26.0751i	0.536634	−	0.929477i	0.999082	−	0.0428311i	$-0.0136377\pi$
$788$	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
$792$	3.03321	+	5.32420i	0.107780	+	0.189187i
$793$	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
$803$	35.6064	−	6.06729i	1.25652	−	0.214110i
$804$	−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	0.940859	−	0.338799i	$-0.110021\pi$
$809$	31.7958	+	18.3573i	1.11788	+	0.645408i	0.177021	+	0.984207i	$0.443354\pi$
$810$	1.97518	+	3.42112i	0.0694009	+	0.120206i
$811$	7.24559	−	6.07978i	0.254427	−	0.213490i	−0.506649	−	0.862153i	$-0.669116\pi$
$811$	7.24559	−	6.07978i	0.254427	−	0.213490i	0.761076	+	0.648663i	$0.224671\pi$
$812$	0.375515	+	1.03172i	0.0131780	+	0.0362063i
$813$	−3.55098	−	1.29245i	−0.124538	−	0.0453283i
$814$	−21.7351	−	26.2077i	−0.761814	−	0.918580i
$815$	−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	$-0.563120\pi$
$821$	16.7363	−	45.9827i	0.584102	−	1.60481i	0.781102	−	0.624403i	$-0.214658\pi$
$822$	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
$825$	0.744818	−	0.877335i	0.0259312	−	0.0305449i
$826$	−3.99522	−	22.6580i	−0.139012	−	0.788374i
$827$	−3.19619	−	18.1265i	−0.111142	−	0.630319i	−0.988588	−	0.150644i	$-0.951865\pi$
$827$	−3.19619	−	18.1265i	−0.111142	−	0.630319i	0.877446	−	0.479676i	$-0.159246\pi$
$828$	−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
$836$	4.99924	−	12.3022i	0.172902	−	0.425480i
$837$	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
$847$	26.6328	+	32.4920i	0.915113	+	1.11644i
$848$	−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	0.0884250	−	0.996083i	$-0.471817\pi$
$853$	−4.94060	−	0.871162i	−0.169163	−	0.0298280i	−0.257588	+	0.966255i	$0.582928\pi$
$854$	−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	$0.198413\pi$
$857$	−4.41129	+	25.0177i	−0.150687	+	0.854587i	−0.962624	+	0.270842i	$0.912698\pi$
$858$	14.1563	+	17.0694i	0.483289	+	0.582740i
$859$	−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
$869$	−3.56871	−	20.9433i	−0.121060	−	0.710453i
$870$	−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	0.686487	−	0.727142i	$-0.259152\pi$
$877$	2.65339	+	2.22646i	0.0895987	+	0.0751823i	−0.596888	+	0.802324i	$0.703596\pi$
$878$	6.60135	+	2.40269i	0.222785	+	0.0810870i
$879$	3.26645	+	8.97450i	0.110175	+	0.302703i
$880$	18.9564	+	33.2743i	0.639021	+	1.12168i
$881$	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	$-0.418934\pi$
$887$	37.1902	−	31.2063i	1.24872	−	1.04780i	0.996790	−	0.0800588i	$-0.0255108\pi$
$888$	−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
$891$	−3.11003	−	1.15227i	−0.104190	−	0.0386025i
$892$		−	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
$902$	−6.12871	−	0.0352737i	−0.204064	−	0.00117449i
$903$	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	−0.445802	−	0.895131i	$-0.647082\pi$
$919$	3.22865	−	1.86406i	0.106503	−	0.0614897i	0.552305	+	0.833642i	$0.313748\pi$
$920$	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
$924$	−10.9563	+	3.91652i	−0.360437	+	0.128844i
$925$	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
$935$	−0.761128	−	0.445298i	−0.0248915	−	0.0145628i
$936$	6.79485	−	2.47312i	0.222097	−	0.0808366i
$937$	7.96987	+	9.49812i	0.260364	+	0.310290i	0.880352	−	0.474322i	$-0.157307\pi$
$937$	7.96987	+	9.49812i	0.260364	+	0.310290i	−0.619987	+	0.784612i	$0.712862\pi$
$938$	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	0.961819	−	0.273686i	$-0.0882428\pi$
$941$	−1.09209	−	6.19357i	−0.0356012	−	0.201905i	−0.997420	+	0.0717811i	$0.977132\pi$
$942$	−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
$946$	−51.4405	−	30.0952i	−1.67247	−	0.978480i
$947$	−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	0.824667	−	0.565618i	$-0.191362\pi$
$953$	12.6830	+	10.6423i	0.410844	+	0.344739i	−0.413823	+	0.910357i	$0.635807\pi$
$954$	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
$957$	−0.349392	−	0.977413i	−0.0112942	−	0.0315953i
$958$	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	0.496864	−	0.867828i	$-0.334485\pi$
$967$	20.7399	+	3.65700i	0.666950	+	0.117601i	0.170085	+	0.985429i	$0.445596\pi$
$968$	−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
$979$	0.171993	−	29.8834i	0.00549693	−	0.955078i
$980$	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
$990$	−12.2858	−	4.55190i	−0.390467	−	0.144669i
$991$	−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	−0.749473	−	0.662035i	$-0.769693\pi$
$997$	−38.7529	+	6.83319i	−1.22732	+	0.216409i	−0.477845	+	0.878444i	$0.658582\pi$
$998$	−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.439.10	yes	240
11.10	odd	2	inner	627.2.be.a.439.31	yes	240
19.10	odd	18	inner	627.2.be.a.10.31	yes	240
209.10	even	18	inner	627.2.be.a.10.10	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.be.a.10.10	✓	240	209.10	even	18	inner
627.2.be.a.10.31	yes	240	19.10	odd	18	inner
627.2.be.a.439.10	yes	240	1.1	even	1	trivial
627.2.be.a.439.31	yes	240	11.10	odd	2	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
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} +(2.52837 + 2.14647i) 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} +(-4.36132 + 3.61701i) 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} +(3.26950 - 0.557118i) 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} +(-1.50801 - 2.64702i) 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} +(-7.19149 - 2.66446i) 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} +(-0.0326102 + 5.66594i) 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} +(-5.77002 + 2.06259i) 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} +(1.67482 - 2.86269i) 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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