LMFDB - Embedded newform 350.2.o.d.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.478584585616890104119296.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 $ x^16 - 31x^12 + 336x^8 - 19375*x^4 + 390625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$0.0811201 - 2.23460i$ of defining polynomial
Character	$\chi$	$=$	350.143
Dual form			350.2.o.d.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.788227 - 2.94170i) q^{3} +(0.866025 + 0.500000i) q^{4} +3.04547i q^{6} +(-2.01297 + 1.71696i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.43424 + 3.13746i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.788227 - 2.94170i) q^{3} +(0.866025 + 0.500000i) q^{4} +3.04547i q^{6} +(-2.01297 + 1.71696i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.43424 + 3.13746i) q^{9} +(-1.13746 + 1.97014i) q^{11} +(0.788227 - 2.94170i) q^{12} +(-3.37822 + 3.37822i) q^{13} +(2.38876 - 1.13746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.34607 - 0.896575i) q^{17} +(6.06110 - 1.62407i) q^{18} +(-3.70219 - 6.41238i) q^{19} +(6.63746 + 4.56821i) q^{21} +(1.60861 - 1.60861i) q^{22} +(-0.776457 + 2.89778i) q^{23} +(-1.52274 + 2.63746i) q^{24} +(4.13746 - 2.38876i) q^{26} +(7.05246 + 7.05246i) q^{27} +(-2.60176 + 0.480443i) q^{28} +5.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(6.69213 + 1.79315i) q^{33} -3.46410 q^{34} -6.27492 q^{36} +(-2.19740 - 0.588792i) q^{37} +(1.91639 + 7.15208i) q^{38} +(12.6005 + 7.27492i) q^{39} +5.19615i q^{41} +(-5.22895 - 6.13045i) q^{42} +(-0.512711 - 0.512711i) q^{43} +(-1.97014 + 1.13746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-0.123242 + 0.459945i) q^{47} +(2.15348 - 2.15348i) q^{48} +(1.10411 - 6.91238i) q^{49} +(-5.27492 - 9.13642i) q^{51} +(-4.61474 + 1.23651i) q^{52} +(-12.3878 + 3.31929i) q^{53} +(-4.98684 - 8.63746i) q^{54} +(2.63746 + 0.209313i) q^{56} +(-15.9451 + 15.9451i) q^{57} +(1.36525 - 5.09518i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-1.08762 + 0.627940i) q^{61} +(2.44949 + 2.44949i) q^{62} +(5.55208 - 15.6460i) q^{63} +1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(-2.91816 - 10.8907i) q^{67} +(3.34607 + 0.896575i) q^{68} +9.13642 q^{69} -6.00000 q^{71} +(6.06110 + 1.62407i) q^{72} +(0.216697 + 0.808725i) q^{73} +(1.97014 + 1.13746i) q^{74} -7.40437i q^{76} +(-1.09297 - 5.91880i) q^{77} +(-10.2883 - 10.2883i) q^{78} +(-8.66025 + 5.00000i) q^{79} +(5.77492 - 10.0025i) q^{81} +(1.34486 - 5.01910i) q^{82} +(-0.888041 + 0.888041i) q^{83} +(3.46410 + 7.27492i) q^{84} +(0.362541 + 0.627940i) q^{86} +(15.5172 - 4.15783i) q^{87} +(2.19740 - 0.588792i) q^{88} +(4.56821 + 7.91238i) q^{89} +(1.00000 - 12.6005i) q^{91} +(-2.12132 + 2.12132i) q^{92} +(-2.73050 + 10.1904i) q^{93} +(0.238085 - 0.412376i) q^{94} +(-2.63746 + 1.52274i) q^{96} +(1.18406 + 1.18406i) q^{97} +(-2.85554 + 6.39108i) q^{98} -14.2749i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 12 q^{11} + 8 q^{16} + 76 q^{21} + 36 q^{26} - 48 q^{31} - 40 q^{36} + 24 q^{46} - 24 q^{51} + 12 q^{56} - 108 q^{61} - 96 q^{66} - 96 q^{71} + 32 q^{81} + 36 q^{86} + 16 q^{91} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^11 + 8 * q^16 + 76 * q^21 + 36 * q^26 - 48 * q^31 - 40 * q^36 + 24 * q^46 - 24 * q^51 + 12 * q^56 - 108 * q^61 - 96 * q^66 - 96 * q^71 + 32 * q^81 + 36 * q^86 + 16 * q^91 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.788227	−	2.94170i	−0.455083	−	1.69839i	−0.687844	−	0.725859i	$-0.741443\pi$
$3$	−0.788227	−	2.94170i	−0.455083	−	1.69839i	0.232761	−	0.972534i	$-0.425224\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			3.04547i			1.24331i
$7$	−2.01297	+	1.71696i	−0.760832	+	0.648949i
$7$	−2.01297	+	1.71696i	−0.760832	+	0.648949i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−5.43424	+	3.13746i	−1.81141	+	1.04582i
$10$		0			0
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	−0.984980	−	0.172666i	$-0.944762\pi$
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	0.642024	+	0.766685i	$0.278095\pi$
$12$	0.788227	−	2.94170i	0.227542	−	0.849196i
$13$	−3.37822	+	3.37822i	−0.936950	+	0.936950i	−0.998127	−	0.0611771i	$-0.980515\pi$
$13$	−3.37822	+	3.37822i	−0.936950	+	0.936950i	0.0611771	+	0.998127i	$0.480515\pi$
$14$	2.38876	−	1.13746i	0.638424	−	0.303999i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.34607	−	0.896575i	0.811540	−	0.217451i	0.170896	−	0.985289i	$-0.445334\pi$
$17$	3.34607	−	0.896575i	0.811540	−	0.217451i	0.640644	+	0.767838i	$0.278667\pi$
$18$	6.06110	−	1.62407i	1.42862	−	0.382797i
$19$	−3.70219	−	6.41238i	−0.849340	−	1.47110i	−0.881798	−	0.471627i	$-0.843667\pi$
$19$	−3.70219	−	6.41238i	−0.849340	−	1.47110i	0.0324583	−	0.999473i	$-0.489666\pi$
$20$		0			0
$21$	6.63746	+	4.56821i	1.44841	+	0.996866i
$22$	1.60861	−	1.60861i	0.342957	−	0.342957i
$23$	−0.776457	+	2.89778i	−0.161903	+	0.604228i	0.836512	+	0.547948i	$0.184591\pi$
$23$	−0.776457	+	2.89778i	−0.161903	+	0.604228i	−0.998415	+	0.0562805i	$0.982076\pi$
$24$	−1.52274	+	2.63746i	−0.310827	+	0.538369i
$25$		0			0
$26$	4.13746	−	2.38876i	0.811422	−	0.468475i
$27$	7.05246	+	7.05246i	1.35725	+	1.35725i
$28$	−2.60176	+	0.480443i	−0.491687	+	0.0907953i
$29$			5.27492i			0.979528i	0.871855	+	0.489764i	$0.162917\pi$
$29$			5.27492i			0.979528i	−0.871855	+	0.489764i	$0.837083\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	6.69213	+	1.79315i	1.16495	+	0.312148i
$34$	−3.46410			−0.594089
$35$		0			0
$36$	−6.27492			−1.04582
$37$	−2.19740	−	0.588792i	−0.361251	−	0.0967968i	0.0736283	−	0.997286i	$-0.476542\pi$
$37$	−2.19740	−	0.588792i	−0.361251	−	0.0967968i	−0.434879	+	0.900489i	$0.643209\pi$
$38$	1.91639	+	7.15208i	0.310880	+	1.16022i
$39$	12.6005	+	7.27492i	2.01770	+	1.16492i
$40$		0			0
$41$			5.19615i			0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$			5.19615i			0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$	−5.22895	−	6.13045i	−0.806845	−	0.945950i
$43$	−0.512711	−	0.512711i	−0.0781877	−	0.0781877i	0.666931	−	0.745119i	$-0.267607\pi$
$43$	−0.512711	−	0.512711i	−0.0781877	−	0.0781877i	−0.745119	+	0.666931i	$0.767607\pi$
$44$	−1.97014	+	1.13746i	−0.297009	+	0.171478i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−0.123242	+	0.459945i	−0.0179767	+	0.0670899i	−0.974332	−	0.225118i	$-0.927723\pi$
$47$	−0.123242	+	0.459945i	−0.0179767	+	0.0670899i	0.956355	+	0.292208i	$0.0943899\pi$
$48$	2.15348	−	2.15348i	0.310827	−	0.310827i
$49$	1.10411	−	6.91238i	0.157730	−	0.987482i
$50$		0			0
$51$	−5.27492	−	9.13642i	−0.738636	−	1.27936i
$52$	−4.61474	+	1.23651i	−0.639949	+	0.171474i
$53$	−12.3878	+	3.31929i	−1.70159	+	0.455940i	−0.973339	−	0.229371i	$-0.926333\pi$
$53$	−12.3878	+	3.31929i	−1.70159	+	0.455940i	−0.728251	+	0.685311i	$0.759666\pi$
$54$	−4.98684	−	8.63746i	−0.678623	−	1.17541i
$55$		0			0
$56$	2.63746	+	0.209313i	0.352445	+	0.0279707i
$57$	−15.9451	+	15.9451i	−2.11199	+	2.11199i
$58$	1.36525	−	5.09518i	0.179266	−	0.669030i
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	−0.299552	−	0.954080i	$-0.596837\pi$
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	0.976034	−	0.217620i	$-0.0698294\pi$
$60$		0			0
$61$	−1.08762	+	0.627940i	−0.139256	+	0.0803995i	−0.568009	−	0.823022i	$-0.692286\pi$
$61$	−1.08762	+	0.627940i	−0.139256	+	0.0803995i	0.428753	+	0.903422i	$0.358953\pi$
$62$	2.44949	+	2.44949i	0.311086	+	0.311086i
$63$	5.55208	−	15.6460i	0.699497	−	1.97121i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−6.00000	−	3.46410i	−0.738549	−	0.426401i
$67$	−2.91816	−	10.8907i	−0.356510	−	1.33051i	−0.878573	−	0.477608i	$-0.841504\pi$
$67$	−2.91816	−	10.8907i	−0.356510	−	1.33051i	0.522063	−	0.852907i	$-0.325163\pi$
$68$	3.34607	+	0.896575i	0.405770	+	0.108726i
$69$	9.13642			1.09990
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	6.06110	+	1.62407i	0.714308	+	0.191398i
$73$	0.216697	+	0.808725i	0.0253625	+	0.0946541i	0.977447	−	0.211181i	$-0.0677310\pi$
$73$	0.216697	+	0.808725i	0.0253625	+	0.0946541i	−0.952084	+	0.305835i	$0.901064\pi$
$74$	1.97014	+	1.13746i	0.229024	+	0.132227i
$75$		0			0
$76$		−	7.40437i		−	0.849340i
$77$	−1.09297	−	5.91880i	−0.124555	−	0.674510i
$78$	−10.2883	−	10.2883i	−1.16492	−	1.16492i
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.0737937	+	0.997274i	$0.523511\pi$
$80$		0			0
$81$	5.77492	−	10.0025i	0.641657	−	1.11138i
$82$	1.34486	−	5.01910i	0.148515	−	0.554267i
$83$	−0.888041	+	0.888041i	−0.0974752	+	0.0974752i	−0.754163	−	0.656688i	$-0.771957\pi$
$83$	−0.888041	+	0.888041i	−0.0974752	+	0.0974752i	0.656688	+	0.754163i	$0.271957\pi$
$84$	3.46410	+	7.27492i	0.377964	+	0.793759i
$85$		0			0
$86$	0.362541	+	0.627940i	0.0390938	+	0.0677125i
$87$	15.5172	−	4.15783i	1.66362	−	0.445766i
$88$	2.19740	−	0.588792i	0.234244	−	0.0627654i
$89$	4.56821	+	7.91238i	0.484230	+	0.838710i	0.999836	−	0.0181154i	$-0.00576663\pi$
$89$	4.56821	+	7.91238i	0.484230	+	0.838710i	−0.515606	+	0.856826i	$0.672433\pi$
$90$		0			0
$91$	1.00000	−	12.6005i	0.104828	−	1.32089i
$92$	−2.12132	+	2.12132i	−0.221163	+	0.221163i
$93$	−2.73050	+	10.1904i	−0.283139	+	1.05669i
$94$	0.238085	−	0.412376i	0.0245566	−	0.0425333i
$95$		0			0
$96$	−2.63746	+	1.52274i	−0.269184	+	0.155414i
$97$	1.18406	+	1.18406i	0.120223	+	0.120223i	0.764658	−	0.644436i	$-0.222908\pi$
$97$	1.18406	+	1.18406i	0.120223	+	0.120223i	−0.644436	+	0.764658i	$0.722908\pi$
$98$	−2.85554	+	6.39108i	−0.288453	+	0.645596i
$99$		−	14.2749i		−	1.43468i
$100$		0			0
$101$	−7.91238	−	4.56821i	−0.787311	−	0.454554i	0.0517042	−	0.998662i	$-0.483535\pi$
$101$	−7.91238	−	4.56821i	−0.787311	−	0.454554i	−0.839015	+	0.544108i	$0.816868\pi$
$102$	2.73050	+	10.1904i	0.270360	+	1.00900i
$103$	−0.404362	−	0.108349i	−0.0398430	−	0.0106759i	0.238842	−	0.971058i	$-0.423232\pi$
$103$	−0.404362	−	0.108349i	−0.0398430	−	0.0106759i	−0.278685	+	0.960382i	$0.589899\pi$
$104$	4.77753			0.468475
$105$		0			0
$106$	12.8248			1.24565
$107$	15.2855	+	4.09575i	1.47771	+	0.395951i	0.905567	−	0.424204i	$-0.139446\pi$
$107$	15.2855	+	4.09575i	1.47771	+	0.395951i	0.572142	+	0.820155i	$0.306113\pi$
$108$	2.58138	+	9.63383i	0.248393	+	0.927016i
$109$	−11.9726	−	6.91238i	−1.14677	−	0.662086i	−0.198669	−	0.980067i	$-0.563662\pi$
$109$	−11.9726	−	6.91238i	−1.14677	−	0.662086i	−0.948097	+	0.317981i	$0.896995\pi$
$110$		0			0
$111$			6.92820i			0.657596i
$112$	−2.49342	−	0.884806i	−0.235606	−	0.0836063i
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$	19.5287	−	11.2749i	1.82903	−	1.05599i
$115$		0			0
$116$	−2.63746	+	4.56821i	−0.244882	+	0.424148i
$117$	7.75903	−	28.9571i	0.717322	−	2.67708i
$118$	−7.34847	+	7.34847i	−0.676481	+	0.676481i
$119$	−5.19615	+	7.54983i	−0.476331	+	0.692092i
$120$		0			0
$121$	2.91238	+	5.04438i	0.264761	+	0.458580i
$122$	1.21309	−	0.325046i	0.109828	−	0.0294283i
$123$	15.2855	−	4.09575i	1.37825	−	0.369301i
$124$	−1.73205	−	3.00000i	−0.155543	−	0.269408i
$125$		0			0
$126$	−9.41238	+	13.6759i	−0.838521	+	1.21834i
$127$	−6.87667	+	6.87667i	−0.610206	+	0.610206i	−0.943000	−	0.332794i	$-0.892009\pi$
$127$	−6.87667	+	6.87667i	−0.610206	+	0.610206i	0.332794	+	0.943000i	$0.392009\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−1.10411	+	1.91238i	−0.0972115	+	0.168375i
$130$		0			0
$131$	−3.41238	+	1.97014i	−0.298141	+	0.172132i	−0.641607	−	0.767033i	$-0.721732\pi$
$131$	−3.41238	+	1.97014i	−0.298141	+	0.172132i	0.343467	+	0.939165i	$0.388399\pi$
$132$	4.89898	+	4.89898i	0.426401	+	0.426401i
$133$	18.4622	+	6.55143i	1.60087	+	0.568081i
$134$			11.2749i			0.974004i
$135$		0			0
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$	−8.82511	−	2.36468i	−0.751243	−	0.201295i
$139$	−21.7370			−1.84370			−0.921852	−	0.387542i	$-0.873324\pi$
$139$	−21.7370			−1.84370			−0.921852	+	0.387542i	$0.873324\pi$
$140$		0			0
$141$	1.45017			0.122126
$142$	5.79555	+	1.55291i	0.486352	+	0.130318i
$143$	−2.81297	−	10.4981i	−0.235232	−	0.877899i
$144$	−5.43424	−	3.13746i	−0.452853	−	0.261455i
$145$		0			0
$146$		−	0.837253i		−	0.0692916i
$147$	−21.2044	+	2.20055i	−1.74891	+	0.181499i
$148$	−1.60861	−	1.60861i	−0.132227	−	0.132227i
$149$	8.50848	−	4.91238i	0.697042	−	0.402438i	−0.109203	−	0.994020i	$-0.534830\pi$
$149$	8.50848	−	4.91238i	0.697042	−	0.402438i	0.806245	+	0.591582i	$0.201496\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−1.91639	+	7.15208i	−0.155440	+	0.580110i
$153$	−15.3703	+	15.3703i	−1.24262	+	1.24262i
$154$	−0.476171	+	6.00000i	−0.0383709	+	0.483494i
$155$		0			0
$156$	7.27492	+	12.6005i	0.582460	+	1.00885i
$157$	−5.42346	+	1.45321i	−0.432839	+	0.115979i	−0.468659	−	0.883379i	$-0.655263\pi$
$157$	−5.42346	+	1.45321i	−0.432839	+	0.115979i	0.0358194	+	0.999358i	$0.488596\pi$
$158$	9.65926	−	2.58819i	0.768449	−	0.205905i
$159$	19.5287	+	33.8248i	1.54873	+	2.68248i
$160$		0			0
$161$	−3.41238	−	7.16629i	−0.268933	−	0.564783i
$162$	−8.16697	+	8.16697i	−0.641657	+	0.641657i
$163$	3.10583	−	11.5911i	0.243267	−	0.907886i	−0.730979	−	0.682400i	$-0.760936\pi$
$163$	3.10583	−	11.5911i	0.243267	−	0.907886i	0.974246	−	0.225486i	$-0.0723970\pi$
$164$	−2.59808	+	4.50000i	−0.202876	+	0.351391i
$165$		0			0
$166$	1.08762	−	0.627940i	0.0844160	−	0.0487376i
$167$	1.22474	+	1.22474i	0.0947736	+	0.0947736i	0.752904	−	0.658130i	$-0.228652\pi$
$167$	1.22474	+	1.22474i	0.0947736	+	0.0947736i	−0.658130	+	0.752904i	$0.728652\pi$
$168$	−1.46318	−	7.92361i	−0.112887	−	0.611319i
$169$		−	9.82475i		−	0.755750i
$170$		0			0
$171$	40.2371	+	23.2309i	3.07701	+	1.77651i
$172$	−0.187665	−	0.700376i	−0.0143093	−	0.0534032i
$173$	17.1903	+	4.60612i	1.30695	+	0.350197i	0.844075	−	0.536226i	$-0.180150\pi$
$173$	17.1903	+	4.60612i	1.30695	+	0.350197i	0.462877	+	0.886422i	$0.346817\pi$
$174$	−16.0646			−1.21786
$175$		0			0
$176$	−2.27492			−0.171478
$177$	−30.5711	−	8.19149i	−2.29786	−	0.615710i
$178$	−2.36468	−	8.82511i	−0.177240	−	0.661470i
$179$	−11.1066	−	6.41238i	−0.830143	−	0.479283i	0.0237584	−	0.999718i	$-0.492437\pi$
$179$	−11.1066	−	6.41238i	−0.830143	−	0.479283i	−0.853902	+	0.520434i	$0.825770\pi$
$180$		0			0
$181$		−	8.18408i		−	0.608318i	−0.952621	−	0.304159i	$-0.901625\pi$
$181$		−	8.18408i		−	0.608318i	0.952621	−	0.304159i	$-0.0983754\pi$
$182$	−4.22718	+	11.9124i	−0.313340	+	0.883002i
$183$	2.70451	+	2.70451i	0.199923	+	0.199923i
$184$	2.59808	−	1.50000i	0.191533	−	0.110581i
$185$		0			0
$186$	5.27492	−	9.13642i	0.386776	−	0.669915i
$187$	−2.03963	+	7.61202i	−0.149153	+	0.556646i
$188$	−0.336703	+	0.336703i	−0.0245566	+	0.0245566i
$189$	−26.3052	−	2.08762i	−1.91342	−	0.151852i
$190$		0			0
$191$	10.5498	+	18.2728i	0.763359	+	1.32218i	0.941110	+	0.338101i	$0.109785\pi$
$191$	10.5498	+	18.2728i	0.763359	+	1.32218i	−0.177750	+	0.984076i	$0.556882\pi$
$192$	2.94170	−	0.788227i	0.212299	−	0.0568854i
$193$	−4.39480	+	1.17758i	−0.316345	+	0.0847643i	−0.413498	−	0.910505i	$-0.635693\pi$
$193$	−4.39480	+	1.17758i	−0.316345	+	0.0847643i	0.0971530	+	0.995269i	$0.469026\pi$
$194$	−0.837253	−	1.45017i	−0.0601113	−	0.104116i
$195$		0			0
$196$	4.41238	−	5.43424i	0.315170	−	0.388160i
$197$	4.82583	−	4.82583i	0.343826	−	0.343826i	−0.513978	−	0.857804i	$-0.671829\pi$
$197$	4.82583	−	4.82583i	0.343826	−	0.343826i	0.857804	+	0.513978i	$0.171829\pi$
$198$	−3.69462	+	13.7885i	−0.262565	+	0.979907i
$199$	3.94027	−	6.82475i	0.279318	−	0.483794i	−0.691897	−	0.721996i	$-0.743225\pi$
$199$	3.94027	−	6.82475i	0.279318	−	0.483794i	0.971216	+	0.238202i	$0.0765581\pi$
$200$		0			0
$201$	−29.7371	+	17.1687i	−2.09750	+	1.21099i
$202$	6.46043	+	6.46043i	0.454554	+	0.454554i
$203$	−9.05681	−	10.6183i	−0.635664	−	0.745256i
$204$		−	10.5498i		−	0.738636i
$205$		0			0
$206$	0.362541	+	0.209313i	0.0252595	+	0.0145836i
$207$	−4.87220	−	18.1833i	−0.338642	−	1.26383i
$208$	−4.61474	−	1.23651i	−0.319974	−	0.0857369i
$209$	16.8443			1.16515
$210$		0			0
$211$	16.8248			1.15826			0.579132	−	0.815234i	$-0.303392\pi$
$211$	16.8248			1.15826			0.579132	+	0.815234i	$0.303392\pi$
$212$	−12.3878	−	3.31929i	−0.850795	−	0.227970i
$213$	4.72936	+	17.6502i	0.324051	+	1.20937i
$214$	−13.7046	−	7.91238i	−0.936830	−	0.540879i
$215$		0			0
$216$		−	9.97368i		−	0.678623i
$217$	9.01277	−	1.66430i	0.611827	−	0.112980i
$218$	9.77558	+	9.77558i	0.662086	+	0.662086i
$219$	2.20822	−	1.27492i	0.149218	−	0.0861509i
$220$		0			0
$221$	−8.27492	+	14.3326i	−0.556631	+	0.964113i
$222$	1.79315	−	6.69213i	0.120348	−	0.449146i
$223$	6.16441	−	6.16441i	0.412800	−	0.412800i	−0.469913	−	0.882713i	$-0.655715\pi$
$223$	6.16441	−	6.16441i	0.412800	−	0.412800i	0.882713	+	0.469913i	$0.155715\pi$
$224$	2.17945	+	1.50000i	0.145621	+	0.100223i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	3.34607	−	0.896575i	0.222086	−	0.0595078i	−0.146060	−	0.989276i	$-0.546659\pi$
$227$	3.34607	−	0.896575i	0.222086	−	0.0595078i	0.368146	+	0.929768i	$0.379993\pi$
$228$	−21.7815	+	5.83633i	−1.44251	+	0.386520i
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	0.998846	−	0.0480291i	$-0.0152940\pi$
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	−0.541017	+	0.841011i	$0.681961\pi$
$230$		0			0
$231$	−16.5498	+	7.88054i	−1.08890	+	0.518502i
$232$	3.72993	−	3.72993i	0.244882	−	0.244882i
$233$	5.08567	−	18.9800i	0.333173	−	1.24342i	−0.572663	−	0.819791i	$-0.694090\pi$
$233$	5.08567	−	18.9800i	0.333173	−	1.24342i	0.905836	−	0.423628i	$-0.139244\pi$
$234$	−14.9893	+	25.9622i	−0.979880	+	1.69720i
$235$		0			0
$236$	9.00000	−	5.19615i	0.585850	−	0.338241i
$237$	21.5348	+	21.5348i	1.39883	+	1.39883i
$238$	6.97314	−	5.94772i	0.452001	−	0.385533i
$239$			10.5498i			0.682412i	0.939989	+	0.341206i	$0.110835\pi$
$239$			10.5498i			0.682412i	−0.939989	+	0.341206i	$0.889165\pi$
$240$		0			0
$241$	−3.41238	−	1.97014i	−0.219810	−	0.126908i	0.386052	−	0.922477i	$-0.373839\pi$
$241$	−3.41238	−	1.97014i	−0.219810	−	0.126908i	−0.605862	+	0.795569i	$0.707172\pi$
$242$	−1.50756	−	5.62628i	−0.0969094	−	0.361671i
$243$	−5.07468	−	1.35976i	−0.325541	−	0.0872284i
$244$	−1.25588			−0.0803995
$245$		0			0
$246$	−15.8248			−1.00895
$247$	34.1692	+	9.15562i	2.17414	+	0.582558i
$248$	0.896575	+	3.34607i	0.0569326	+	0.212475i
$249$	3.31233	+	1.91238i	0.209911	+	0.121192i
$250$		0			0
$251$			6.45203i			0.407249i	0.979049	+	0.203624i	$0.0652721\pi$
$251$			6.45203i			0.407249i	−0.979049	+	0.203624i	$0.934728\pi$
$252$	12.6312	−	10.7738i	0.795693	−	0.678684i
$253$	−4.82583	−	4.82583i	−0.303397	−	0.303397i
$254$	8.42217	−	4.86254i	0.528454	−	0.305103i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.03963	−	7.61202i	0.127229	−	0.474825i	−0.872680	−	0.488292i	$-0.837620\pi$
$257$	2.03963	−	7.61202i	0.127229	−	0.474825i	0.999909	+	0.0134670i	$0.00428682\pi$
$258$	1.56145	−	1.56145i	0.0972115	−	0.0972115i
$259$	5.43424	−	2.58762i	0.337667	−	0.160787i
$260$		0			0
$261$	−16.5498	−	28.6652i	−1.02441	−	1.77433i
$262$	3.80601	−	1.01982i	0.235136	−	0.0630045i
$263$	3.69443	−	0.989919i	0.227808	−	0.0610410i	−0.143109	−	0.989707i	$-0.545710\pi$
$263$	3.69443	−	0.989919i	0.227808	−	0.0610410i	0.370917	+	0.928666i	$0.379043\pi$
$264$	−3.46410	−	6.00000i	−0.213201	−	0.369274i
$265$		0			0
$266$	−16.1375	−	11.1066i	−0.989451	−	0.680987i
$267$	19.6751	−	19.6751i	1.20409	−	1.20409i
$268$	2.91816	−	10.8907i	0.178255	−	0.665257i
$269$	9.76436	−	16.9124i	0.595344	−	1.03117i	−0.398154	−	0.917318i	$-0.630349\pi$
$269$	9.76436	−	16.9124i	0.595344	−	1.03117i	0.993498	−	0.113847i	$-0.0363175\pi$
$270$		0			0
$271$	15.8248	−	9.13642i	0.961285	−	0.554998i	0.0647169	−	0.997904i	$-0.479386\pi$
$271$	15.8248	−	9.13642i	0.961285	−	0.554998i	0.896568	+	0.442905i	$0.146052\pi$
$272$	2.44949	+	2.44949i	0.148522	+	0.148522i
$273$	−37.8552	+	6.99037i	−2.29110	+	0.423076i
$274$		0			0
$275$		0			0
$276$	7.91238	+	4.56821i	0.476269	+	0.274974i
$277$	3.90808	+	14.5852i	0.234814	+	0.876337i	0.978233	+	0.207511i	$0.0665363\pi$
$277$	3.90808	+	14.5852i	0.234814	+	0.876337i	−0.743419	+	0.668826i	$0.766797\pi$
$278$	20.9963	+	5.62594i	1.25927	+	0.337421i
$279$	21.7370			1.30136
$280$		0			0
$281$	29.3746			1.75234			0.876170	−	0.482001i	$-0.160090\pi$
$281$	29.3746			1.75234			0.876170	+	0.482001i	$0.160090\pi$
$282$	−1.40075	−	0.375330i	−0.0834136	−	0.0223506i
$283$	7.20239	+	26.8797i	0.428138	+	1.59783i	0.756974	+	0.653445i	$0.226677\pi$
$283$	7.20239	+	26.8797i	0.428138	+	1.59783i	−0.328837	+	0.944387i	$0.606657\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$			10.8685i			0.642666i
$287$	−8.92158	−	10.4597i	−0.526624	−	0.617417i
$288$	4.43704	+	4.43704i	0.261455	+	0.261455i
$289$	−4.33013	+	2.50000i	−0.254713	+	0.147059i
$290$		0			0
$291$	2.54983	−	4.41644i	0.149474	−	0.258896i
$292$	−0.216697	+	0.808725i	−0.0126812	+	0.0473270i
$293$	12.5842	−	12.5842i	0.735174	−	0.735174i	−0.236466	−	0.971640i	$-0.575989\pi$
$293$	12.5842	−	12.5842i	0.735174	−	0.735174i	0.971640	+	0.236466i	$0.0759891\pi$
$294$	21.0515	+	3.36254i	1.22775	+	0.196107i
$295$		0			0
$296$	1.13746	+	1.97014i	0.0661134	+	0.114512i
$297$	−21.9162	+	5.87242i	−1.27171	+	0.340752i
$298$	−9.48998	+	2.54283i	−0.549740	+	0.147302i
$299$	−7.16629	−	12.4124i	−0.414437	−	0.717826i
$300$		0			0
$301$	1.91238	+	0.151770i	0.110228	+	0.00874785i
$302$	1.41421	−	1.41421i	0.0813788	−	0.0813788i
$303$	−7.20158	+	26.8766i	−0.413720	+	1.54402i
$304$	3.70219	−	6.41238i	0.212335	−	0.367775i
$305$		0			0
$306$	18.8248	−	10.8685i	1.07614	−	0.621309i
$307$	−13.2169	−	13.2169i	−0.754327	−	0.754327i	0.220957	−	0.975284i	$-0.429082\pi$
$307$	−13.2169	−	13.2169i	−0.754327	−	0.754327i	−0.975284	+	0.220957i	$0.929082\pi$
$308$	2.01286	−	5.67231i	0.114693	−	0.323210i
$309$			1.27492i			0.0725275i
$310$		0			0
$311$	−22.6495	−	13.0767i	−1.28434	−	0.741511i	−0.306698	−	0.951807i	$-0.599224\pi$
$311$	−22.6495	−	13.0767i	−1.28434	−	0.741511i	−0.977638	+	0.210296i	$0.932557\pi$
$312$	−3.76577	−	14.0541i	−0.213195	−	0.795655i
$313$	−10.8469	−	2.90642i	−0.613104	−	0.164281i	−0.0611132	−	0.998131i	$-0.519465\pi$
$313$	−10.8469	−	2.90642i	−0.613104	−	0.164281i	−0.551991	+	0.833850i	$0.686132\pi$
$314$	5.61478			0.316860
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−17.3867	−	4.65874i	−0.976532	−	0.261661i	−0.264949	−	0.964262i	$-0.585355\pi$
$317$	−17.3867	−	4.65874i	−0.976532	−	0.261661i	−0.711584	+	0.702601i	$0.752022\pi$
$318$	−10.1088	−	37.7266i	−0.566874	−	2.11560i
$319$	−10.3923	−	6.00000i	−0.581857	−	0.335936i
$320$		0			0
$321$		−	48.1939i		−	2.68992i
$322$	1.44133	+	7.80529i	0.0803222	+	0.434972i
$323$	−18.1369	−	18.1369i	−1.00917	−	1.00917i
$324$	10.0025	−	5.77492i	0.555692	−	0.320829i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−10.8970	+	40.6683i	−0.602608	+	2.24896i
$328$	3.67423	−	3.67423i	0.202876	−	0.202876i
$329$	−0.541624	−	1.13746i	−0.0298607	−	0.0627101i
$330$		0			0
$331$	−14.4124	−	24.9630i	−0.792176	−	1.37209i	−0.924617	−	0.380898i	$-0.875615\pi$
$331$	−14.4124	−	24.9630i	−0.792176	−	1.37209i	0.132441	−	0.991191i	$-0.457718\pi$
$332$	−1.21309	+	0.325046i	−0.0665768	+	0.0178392i
$333$	13.7885	−	3.69462i	0.755606	−	0.202464i
$334$	−0.866025	−	1.50000i	−0.0473868	−	0.0820763i
$335$		0			0
$336$	−0.637459	+	8.03231i	−0.0347762	+	0.438199i
$337$	−17.1115	+	17.1115i	−0.932124	+	0.932124i	−0.997838	−	0.0657148i	$-0.979067\pi$
$337$	−17.1115	+	17.1115i	−0.932124	+	0.932124i	0.0657148	+	0.997838i	$0.479067\pi$
$338$	−2.54283	+	9.48998i	−0.138312	+	0.516187i
$339$	−9.13642	+	15.8248i	−0.496222	+	0.859483i
$340$		0			0
$341$	6.82475	−	3.94027i	0.369581	−	0.213378i
$342$	−32.8535	−	32.8535i	−1.77651	−	1.77651i
$343$	9.64572	+	15.8101i	0.520820	+	0.853667i
$344$			0.725083i			0.0390938i
$345$		0			0
$346$	−15.4124	−	8.89834i	−0.828574	−	0.478378i
$347$	7.20158	+	26.8766i	0.386601	+	1.44281i	0.835628	+	0.549296i	$0.185104\pi$
$347$	7.20158	+	26.8766i	0.386601	+	1.44281i	−0.449027	+	0.893518i	$0.648229\pi$
$348$	15.5172	+	4.15783i	0.831811	+	0.222883i
$349$	9.13642			0.489062			0.244531	−	0.969642i	$-0.421366\pi$
$349$	9.13642			0.489062			0.244531	+	0.969642i	$0.421366\pi$
$350$		0			0
$351$	−47.6495			−2.54334
$352$	2.19740	+	0.588792i	0.117122	+	0.0313827i
$353$	−6.52251	−	24.3423i	−0.347158	−	1.29561i	−0.890070	−	0.455823i	$-0.849345\pi$
$353$	−6.52251	−	24.3423i	−0.347158	−	1.29561i	0.542912	−	0.839789i	$-0.317322\pi$
$354$	27.4093	+	15.8248i	1.45679	+	0.841076i
$355$		0			0
$356$			9.13642i			0.484230i
$357$	26.3051	+	9.33455i	1.39221	+	0.494037i
$358$	9.06847	+	9.06847i	0.479283	+	0.479283i
$359$	−27.4093	+	15.8248i	−1.44661	+	0.835198i	−0.998277	−	0.0586703i	$-0.981314\pi$
$359$	−27.4093	+	15.8248i	−1.44661	+	0.835198i	−0.448329	+	0.893869i	$0.647981\pi$
$360$		0			0
$361$	−17.9124	+	31.0251i	−0.942757	+	1.63290i
$362$	−2.11820	+	7.90522i	−0.111330	+	0.415489i
$363$	12.5435	−	12.5435i	0.658361	−	0.658361i
$364$	7.16629	−	10.4124i	0.375616	−	0.545757i
$365$		0			0
$366$	−1.91238	−	3.31233i	−0.0999615	−	0.173138i
$367$	−14.2486	+	3.81789i	−0.743769	+	0.199292i	−0.610753	−	0.791821i	$-0.709133\pi$
$367$	−14.2486	+	3.81789i	−0.743769	+	0.199292i	−0.133017	+	0.991114i	$0.542466\pi$
$368$	−2.89778	+	0.776457i	−0.151057	+	0.0404756i
$369$	−16.3027	−	28.2371i	−0.848685	−	1.46997i
$370$		0			0
$371$	19.2371	−	27.9509i	0.998742	−	1.45114i
$372$	−7.45986	+	7.45986i	−0.386776	+	0.386776i
$373$	1.92824	−	7.19631i	0.0998407	−	0.372611i	−0.897868	−	0.440264i	$-0.854885\pi$
$373$	1.92824	−	7.19631i	0.0998407	−	0.372611i	0.997709	+	0.0676538i	$0.0215513\pi$
$374$	3.94027	−	6.82475i	0.203747	−	0.352900i
$375$		0			0
$376$	0.412376	−	0.238085i	0.0212667	−	0.0122783i
$377$	−17.8198	−	17.8198i	−0.917768	−	0.917768i
$378$	24.8685	+	8.82477i	1.27910	+	0.453897i
$379$		−	3.17525i		−	0.163102i	−0.996669	−	0.0815508i	$-0.974013\pi$
$379$		−	3.17525i		−	0.163102i	0.996669	−	0.0815508i	$-0.0259873\pi$
$380$		0			0
$381$	25.6495	+	14.8087i	1.31406	+	0.758675i
$382$	−5.46100	−	20.3807i	−0.279409	−	1.04277i
$383$	−30.2813	−	8.11386i	−1.54730	−	0.414599i	−0.618687	−	0.785638i	$-0.712335\pi$
$383$	−30.2813	−	8.11386i	−1.54730	−	0.414599i	−0.928617	+	0.371039i	$0.879002\pi$
$384$	−3.04547			−0.155414
$385$		0			0
$386$	4.54983			0.231580
$387$	4.39480	+	1.17758i	0.223400	+	0.0598599i
$388$	0.433394	+	1.61745i	0.0220023	+	0.0821136i
$389$	23.4690	+	13.5498i	1.18993	+	0.687004i	0.958290	−	0.285799i	$-0.0922589\pi$
$389$	23.4690	+	13.5498i	1.18993	+	0.687004i	0.231636	+	0.972803i	$0.425592\pi$
$390$		0			0
$391$			10.3923i			0.525561i
$392$	−5.66851	+	4.10706i	−0.286303	+	0.207438i
$393$	8.48528	+	8.48528i	0.428026	+	0.428026i
$394$	−5.91041	+	3.41238i	−0.297762	+	0.171913i
$395$		0			0
$396$	7.13746	−	12.3624i	0.358671	−	0.621236i
$397$	4.94606	−	18.4589i	0.248236	−	0.926428i	−0.723494	−	0.690331i	$-0.757465\pi$
$397$	4.94606	−	18.4589i	0.248236	−	0.926428i	0.971729	−	0.236097i	$-0.0758683\pi$
$398$	−5.57239	+	5.57239i	−0.279318	+	0.279318i
$399$	4.71998	−	59.4743i	0.236295	−	2.97744i
$400$		0			0
$401$	−6.04983	−	10.4786i	−0.302114	−	0.523277i	0.674500	−	0.738275i	$-0.264359\pi$
$401$	−6.04983	−	10.4786i	−0.302114	−	0.523277i	−0.976615	+	0.214997i	$0.931026\pi$
$402$	33.1675	−	8.88719i	1.65424	−	0.443253i
$403$	15.9859	−	4.28341i	0.796315	−	0.213372i
$404$	−4.56821	−	7.91238i	−0.227277	−	0.393655i
$405$		0			0
$406$	6.00000	+	12.6005i	0.297775	+	0.625354i
$407$	3.65945	−	3.65945i	0.181392	−	0.181392i
$408$	−2.73050	+	10.1904i	−0.135180	+	0.504498i
$409$	2.35999	−	4.08762i	0.116694	−	0.202120i	−0.801762	−	0.597644i	$-0.796104\pi$
$409$	2.35999	−	4.08762i	0.116694	−	0.202120i	0.918456	+	0.395524i	$0.129437\pi$
$410$		0			0
$411$		0			0
$412$	−0.296014	−	0.296014i	−0.0145836	−	0.0145836i
$413$	4.99291	+	27.0383i	0.245685	+	1.33047i
$414$			18.8248i			0.925186i
$415$		0			0
$416$	4.13746	+	2.38876i	0.202856	+	0.117119i
$417$	17.1336	+	63.9437i	0.839038	+	3.13133i
$418$	−16.2704	−	4.35964i	−0.795810	−	0.213237i
$419$	11.8208			0.577485			0.288742	−	0.957407i	$-0.406763\pi$
$419$	11.8208			0.577485			0.288742	+	0.957407i	$0.406763\pi$
$420$		0			0
$421$	12.1752			0.593385			0.296693	−	0.954973i	$-0.404116\pi$
$421$	12.1752			0.593385			0.296693	+	0.954973i	$0.404116\pi$
$422$	−16.2515	−	4.35457i	−0.791109	−	0.211977i
$423$	−0.773333	−	2.88612i	−0.0376008	−	0.140328i
$424$	11.1066	+	6.41238i	0.539382	+	0.311412i
$425$		0			0
$426$		−	18.2728i		−	0.885322i
$427$	1.11121	−	3.13143i	0.0537752	−	0.151541i
$428$	11.1898	+	11.1898i	0.540879	+	0.540879i
$429$	−28.6652	+	16.5498i	−1.38397	+	0.799034i
$430$		0			0
$431$	9.72508	−	16.8443i	0.468441	−	0.811363i	−0.530909	−	0.847429i	$-0.678149\pi$
$431$	9.72508	−	16.8443i	0.468441	−	0.811363i	0.999349	+	0.0360659i	$0.0114826\pi$
$432$	−2.58138	+	9.63383i	−0.124197	+	0.463508i
$433$	−14.1049	+	14.1049i	−0.677839	+	0.677839i	−0.959511	−	0.281672i	$-0.909111\pi$
$433$	−14.1049	+	14.1049i	−0.677839	+	0.677839i	0.281672	+	0.959511i	$0.409111\pi$
$434$	−9.13642	−	0.725083i	−0.438562	−	0.0348051i
$435$		0			0
$436$	−6.91238	−	11.9726i	−0.331043	−	0.573383i
$437$	21.4562	−	5.74918i	1.02639	−	0.275021i
$438$	−2.46295	+	0.659946i	−0.117684	+	0.0315334i
$439$	10.3923	+	18.0000i	0.495998	+	0.859093i	0.999989	−	0.00461537i	$-0.00146912\pi$
$439$	10.3923	+	18.0000i	0.495998	+	0.859093i	−0.503992	+	0.863708i	$0.668136\pi$
$440$		0			0
$441$	15.6873	+	41.0276i	0.747014	+	1.95370i
$442$	11.7025	−	11.7025i	0.556631	−	0.556631i
$443$	−8.75449	+	32.6722i	−0.415938	+	1.55230i	0.367010	+	0.930217i	$0.380381\pi$
$443$	−8.75449	+	32.6722i	−0.415938	+	1.55230i	−0.782949	+	0.622086i	$0.786285\pi$
$444$	−3.46410	+	6.00000i	−0.164399	+	0.284747i
$445$		0			0
$446$	−7.54983	+	4.35890i	−0.357495	+	0.206400i
$447$	−21.1574	−	21.1574i	−1.00071	−	1.00071i
$448$	−1.71696	−	2.01297i	−0.0811186	−	0.0951040i
$449$			37.5498i			1.77209i	0.463603	+	0.886043i	$0.346556\pi$
$449$			37.5498i			1.77209i	−0.463603	+	0.886043i	$0.653444\pi$
$450$		0			0
$451$	−10.2371	−	5.91041i	−0.482048	−	0.278310i
$452$	−1.55291	−	5.79555i	−0.0730429	−	0.272600i
$453$	5.88341	+	1.57645i	0.276427	+	0.0740683i
$454$	−3.46410			−0.162578
$455$		0			0
$456$	22.5498			1.05599
$457$	18.7874	+	5.03407i	0.878838	+	0.235484i	0.669906	−	0.742446i	$-0.266334\pi$
$457$	18.7874	+	5.03407i	0.878838	+	0.235484i	0.208932	+	0.977930i	$0.433001\pi$
$458$	−3.58630	−	13.3843i	−0.167577	−	0.625405i
$459$	29.9210	+	17.2749i	1.39659	+	0.806324i
$460$		0			0
$461$			36.5457i			1.70210i	0.525082	+	0.851051i	$0.324035\pi$
$461$			36.5457i			1.70210i	−0.525082	+	0.851051i	$0.675965\pi$
$462$	18.0255	−	3.32861i	0.838624	−	0.154861i
$463$	11.6320	+	11.6320i	0.540586	+	0.540586i	0.923701	−	0.383115i	$-0.125149\pi$
$463$	11.6320	+	11.6320i	0.540586	+	0.540586i	−0.383115	+	0.923701i	$0.625149\pi$
$464$	−4.56821	+	2.63746i	−0.212074	+	0.122441i
$465$		0			0
$466$	−9.82475	+	17.0170i	−0.455123	+	0.788296i
$467$	−6.84756	+	25.5554i	−0.316867	+	1.18256i	0.605371	+	0.795943i	$0.293025\pi$
$467$	−6.84756	+	25.5554i	−0.316867	+	1.18256i	−0.922239	+	0.386621i	$0.873642\pi$
$468$	21.1981	−	21.1981i	0.979880	−	0.979880i
$469$	24.5731	+	16.9124i	1.13468	+	0.780941i
$470$		0			0
$471$	8.54983	+	14.8087i	0.393956	+	0.682351i
$472$	−10.0382	+	2.68973i	−0.462045	+	0.123805i
$473$	1.59330	−	0.426923i	0.0732599	−	0.0196299i
$474$	−15.2274	−	26.3746i	−0.699416	−	1.21142i
$475$		0			0
$476$	−8.27492	+	3.94027i	−0.379280	+	0.180602i
$477$	56.9039	−	56.9039i	2.60545	−	2.60545i
$478$	2.73050	−	10.1904i	0.124890	−	0.466096i
$479$	−9.13642	+	15.8248i	−0.417454	+	0.723051i	−0.995683	−	0.0928234i	$-0.970411\pi$
$479$	−9.13642	+	15.8248i	−0.417454	+	0.723051i	0.578229	+	0.815875i	$0.303744\pi$
$480$		0			0
$481$	9.41238	−	5.43424i	0.429167	−	0.247780i
$482$	2.78619	+	2.78619i	0.126908	+	0.126908i
$483$	−18.3914	+	15.6869i	−0.836836	+	0.713777i
$484$			5.82475i			0.264761i
$485$		0			0
$486$	4.54983	+	2.62685i	0.206385	+	0.119156i
$487$	−5.46100	−	20.3807i	−0.247461	−	0.923538i	−0.972130	−	0.234441i	$-0.924674\pi$
$487$	−5.46100	−	20.3807i	−0.247461	−	0.923538i	0.724669	−	0.689097i	$-0.241993\pi$
$488$	1.21309	+	0.325046i	0.0549139	+	0.0147141i
$489$	−36.5457			−1.65265
$490$		0			0
$491$	−34.5498			−1.55921			−0.779606	−	0.626270i	$-0.784581\pi$
$491$	−34.5498			−1.55921			−0.779606	+	0.626270i	$0.784581\pi$
$492$	15.2855	+	4.09575i	0.689125	+	0.184651i
$493$	4.72936	+	17.6502i	0.213000	+	0.794926i
$494$	−30.6353	−	17.6873i	−1.37835	−	0.795789i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	12.0778	−	10.3017i	0.541765	−	0.462097i
$498$	−2.70451	−	2.70451i	−0.121192	−	0.121192i
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	−0.420455	−	0.907314i	$-0.638129\pi$
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	0.575529	+	0.817781i	$0.304796\pi$
$500$		0			0
$501$	2.63746	−	4.56821i	0.117833	−	0.204093i
$502$	1.66991	−	6.23218i	0.0745317	−	0.278156i
$503$	5.78702	−	5.78702i	0.258031	−	0.258031i	−0.566222	−	0.824253i	$-0.691596\pi$
$503$	5.78702	−	5.78702i	0.258031	−	0.258031i	0.824253	+	0.566222i	$0.191596\pi$
$504$	−14.9893	+	7.13746i	−0.667676	+	0.317928i
$505$		0			0
$506$	3.41238	+	5.91041i	0.151699	+	0.262750i
$507$	−28.9015	+	7.74413i	−1.28356	+	0.343929i
$508$	−9.39371	+	2.51704i	−0.416778	+	0.111675i
$509$	−18.9008	−	32.7371i	−0.837763	−	1.45105i	−0.891761	−	0.452507i	$-0.850530\pi$
$509$	−18.9008	−	32.7371i	−0.837763	−	1.45105i	0.0539983	−	0.998541i	$-0.482803\pi$
$510$		0			0
$511$	−1.82475	−	1.25588i	−0.0807223	−	0.0555569i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	19.1135	−	71.3325i	0.843881	−	3.14941i
$514$	−3.94027	+	6.82475i	−0.173798	+	0.301027i
$515$		0			0
$516$	−1.91238	+	1.10411i	−0.0841877	+	0.0486058i
$517$	−0.765972	−	0.765972i	−0.0336874	−	0.0336874i
$518$	−5.91880	+	1.09297i	−0.260057	+	0.0480223i
$519$		−	54.1993i		−	2.37909i
$520$		0			0
$521$	10.2371	+	5.91041i	0.448497	+	0.258940i	0.707195	−	0.707018i	$-0.249960\pi$
$521$	10.2371	+	5.91041i	0.448497	+	0.258940i	−0.258698	+	0.965958i	$0.583294\pi$
$522$	8.56682	+	31.9718i	0.374960	+	1.39937i
$523$	−39.3441	−	10.5422i	−1.72040	−	0.460979i	−0.742461	−	0.669889i	$-0.766341\pi$
$523$	−39.3441	−	10.5422i	−1.72040	−	0.460979i	−0.977935	+	0.208911i	$0.933008\pi$
$524$	−3.94027			−0.172132
$525$		0			0
$526$	−3.82475			−0.166767
$527$	−11.5911	−	3.10583i	−0.504917	−	0.135292i
$528$	1.79315	+	6.69213i	0.0780369	+	0.291238i
$529$	12.1244	+	7.00000i	0.527146	+	0.304348i
$530$		0			0
$531$			65.2109i			2.82991i
$532$	12.7130	+	14.9048i	0.551178	+	0.646205i
$533$	−17.5538	−	17.5538i	−0.760337	−	0.760337i
$534$	−24.0969	+	13.9124i	−1.04278	+	0.602047i
$535$		0			0
$536$	−5.63746	+	9.76436i	−0.243501	+	0.421756i
$537$	−10.1088	+	37.7266i	−0.436228	+	1.62802i
$538$	−13.8089	+	13.8089i	−0.595344	+	0.595344i
$539$	12.3624	+	10.0378i	0.532488	+	0.432358i
$540$		0			0
$541$	15.9124	+	27.5610i	0.684126	+	1.18494i	0.973710	+	0.227789i	$0.0731497\pi$
$541$	15.9124	+	27.5610i	0.684126	+	1.18494i	−0.289584	+	0.957153i	$0.593517\pi$
$542$	−17.6502	+	4.72936i	−0.758142	+	0.203143i
$543$	−24.0751	+	6.45091i	−1.03316	+	0.276835i
$544$	−1.73205	−	3.00000i	−0.0742611	−	0.128624i
$545$		0			0
$546$	38.3746	+	3.04547i	1.64228	+	0.130334i
$547$	6.94715	−	6.94715i	0.297039	−	0.297039i	−0.542814	−	0.839853i	$-0.682641\pi$
$547$	6.94715	−	6.94715i	0.297039	−	0.297039i	0.839853	+	0.542814i	$0.182641\pi$
$548$		0			0
$549$	3.94027	−	6.82475i	0.168167	−	0.291273i
$550$		0			0
$551$	33.8248	−	19.5287i	1.44098	−	0.831952i
$552$	−6.46043	−	6.46043i	−0.274974	−	0.274974i
$553$	8.84806	−	24.9342i	0.376258	−	1.06031i
$554$		−	15.0997i		−	0.641523i
$555$		0			0
$556$	−18.8248	−	10.8685i	−0.798347	−	0.460926i
$557$	−11.0839	−	41.3655i	−0.469638	−	1.75271i	−0.641035	−	0.767512i	$-0.721495\pi$
$557$	−11.0839	−	41.3655i	−0.469638	−	1.75271i	0.171397	−	0.985202i	$-0.445172\pi$
$558$	−20.9963	−	5.62594i	−0.888844	−	0.238165i
$559$	3.46410			0.146516
$560$		0			0
$561$	24.0000			1.01328
$562$	−28.3737	−	7.60270i	−1.19687	−	0.320701i
$563$	5.05441	+	18.8633i	0.213018	+	0.794993i	0.986855	+	0.161609i	$0.0516683\pi$
$563$	5.05441	+	18.8633i	0.213018	+	0.794993i	−0.773837	+	0.633385i	$0.781665\pi$
$564$	1.25588	+	0.725083i	0.0528821	+	0.0305315i
$565$		0			0
$566$		−	27.8279i		−	1.16969i
$567$	5.54904	+	30.0499i	0.233038	+	1.26198i
$568$	4.24264	+	4.24264i	0.178017	+	0.178017i
$569$	−11.1066	+	6.41238i	−0.465611	+	0.268821i	−0.714401	−	0.699737i	$-0.753301\pi$
$569$	−11.1066	+	6.41238i	−0.465611	+	0.268821i	0.248789	+	0.968558i	$0.419967\pi$
$570$		0			0
$571$	−7.82475	+	13.5529i	−0.327456	+	0.567170i	−0.982006	−	0.188848i	$-0.939525\pi$
$571$	−7.82475	+	13.5529i	−0.327456	+	0.567170i	0.654551	+	0.756018i	$0.272858\pi$
$572$	2.81297	−	10.4981i	0.117616	−	0.438949i
$573$	45.4376	−	45.4376i	1.89818	−	1.89818i
$574$	5.91041	+	12.4124i	0.246696	+	0.518083i
$575$		0			0
$576$	−3.13746	−	5.43424i	−0.130727	−	0.226427i
$577$	−38.5353	+	10.3255i	−1.60425	+	0.429857i	−0.946322	−	0.323227i	$-0.895232\pi$
$577$	−38.5353	+	10.3255i	−1.60425	+	0.429857i	−0.657925	+	0.753083i	$0.728566\pi$
$578$	4.82963	−	1.29410i	0.200886	−	0.0538273i
$579$	6.92820	+	12.0000i	0.287926	+	0.498703i
$580$		0			0
$581$	0.262873	−	3.31233i	0.0109058	−	0.137419i
$582$	−3.60601	+	3.60601i	−0.149474	+	0.149474i
$583$	7.55111	−	28.1811i	0.312735	−	1.16714i
$584$	0.418627	−	0.725083i	0.0173229	−	0.0300041i
$585$		0			0
$586$	−15.4124	+	8.89834i	−0.636679	+	0.367587i
$587$	−7.34847	−	7.34847i	−0.303304	−	0.303304i	0.539001	−	0.842305i	$-0.318802\pi$
$587$	−7.34847	−	7.34847i	−0.303304	−	0.303304i	−0.842305	+	0.539001i	$0.818802\pi$
$588$	−19.4639	−	8.69649i	−0.802676	−	0.358637i
$589$			25.6495i			1.05687i
$590$		0			0
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	−0.588792	−	2.19740i	−0.0241992	−	0.0903126i
$593$	18.5701	+	4.97585i	0.762583	+	0.204333i	0.619092	−	0.785318i	$-0.287501\pi$
$593$	18.5701	+	4.97585i	0.762583	+	0.204333i	0.143491	+	0.989652i	$0.454167\pi$
$594$	22.6893			0.930953
$595$		0			0
$596$	9.82475			0.402438
$597$	−23.1822	−	6.21166i	−0.948785	−	0.254226i
$598$	3.70954	+	13.8442i	0.151695	+	0.566132i
$599$	−28.6652	−	16.5498i	−1.17123	−	0.676208i	−0.217258	−	0.976114i	$-0.569711\pi$
$599$	−28.6652	−	16.5498i	−1.17123	−	0.676208i	−0.953969	+	0.299906i	$0.903045\pi$
$600$		0			0
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$	−1.80793	−	0.641557i	−0.0736858	−	0.0261479i
$603$	50.0272	+	50.0272i	2.03727	+	2.03727i
$604$	−1.73205	+	1.00000i	−0.0704761	+	0.0406894i
$605$		0			0
$606$	13.9124	−	24.0969i	0.565152	−	0.978871i
$607$	5.64083	−	21.0519i	0.228954	−	0.854469i	−0.751827	−	0.659360i	$-0.770827\pi$
$607$	5.64083	−	21.0519i	0.228954	−	0.854469i	0.980782	−	0.195109i	$-0.0625060\pi$
$608$	−5.23568	+	5.23568i	−0.212335	+	0.212335i
$609$	−24.0969	+	35.0120i	−0.976457	+	1.41876i
$610$		0			0
$611$	−1.13746	−	1.97014i	−0.0460166	−	0.0797032i
$612$	−20.9963	+	5.62594i	−0.848724	+	0.227415i
$613$	−35.5700	+	9.53095i	−1.43666	+	0.384951i	−0.891362	−	0.453292i	$-0.850249\pi$
$613$	−35.5700	+	9.53095i	−1.43666	+	0.384951i	−0.545296	+	0.838244i	$0.683583\pi$
$614$	9.34574	+	16.1873i	0.377163	+	0.653266i
$615$		0			0
$616$	−3.41238	+	4.95807i	−0.137489	+	0.199766i
$617$	−9.65166	+	9.65166i	−0.388561	+	0.388561i	−0.874174	−	0.485613i	$-0.838596\pi$
$617$	−9.65166	+	9.65166i	−0.388561	+	0.388561i	0.485613	+	0.874174i	$0.338596\pi$
$618$	0.329973	−	1.23148i	0.0132735	−	0.0495372i
$619$	−5.43424	+	9.41238i	−0.218420	+	0.378315i	−0.954325	−	0.298770i	$-0.903424\pi$
$619$	−5.43424	+	9.41238i	−0.218420	+	0.378315i	0.735905	+	0.677085i	$0.236757\pi$
$620$		0			0
$621$	−25.9124	+	14.9605i	−1.03983	+	0.600345i
$622$	18.4932	+	18.4932i	0.741511	+	0.741511i
$623$	−22.7809	−	8.08396i	−0.912697	−	0.323877i
$624$			14.5498i			0.582460i
$625$		0			0
$626$	9.72508	+	5.61478i	0.388692	+	0.224412i
$627$	−13.2772	−	49.5510i	−0.530239	−	1.97888i
$628$	−5.42346	−	1.45321i	−0.216420	−	0.0579895i
$629$	−7.88054			−0.314218
$630$		0			0
$631$	9.64950			0.384141			0.192070	−	0.981381i	$-0.438480\pi$
$631$	9.64950			0.384141			0.192070	+	0.981381i	$0.438480\pi$
$632$	9.65926	+	2.58819i	0.384225	+	0.102953i
$633$	−13.2617	−	49.4934i	−0.527106	−	1.96719i
$634$	15.5885	+	9.00000i	0.619097	+	0.357436i
$635$		0			0
$636$			39.0575i			1.54873i
$637$	19.6216	+	27.0815i	0.777436	+	1.07301i
$638$	8.48528	+	8.48528i	0.335936	+	0.335936i
$639$	32.6054	−	18.8248i	1.28985	−	0.744696i
$640$		0			0
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$	−12.4735	+	46.5517i	−0.492290	+	1.83725i
$643$	−19.6773	+	19.6773i	−0.775997	+	0.775997i	−0.979147	−	0.203151i	$-0.934882\pi$
$643$	−19.6773	+	19.6773i	−0.775997	+	0.775997i	0.203151	+	0.979147i	$0.434882\pi$
$644$	0.627940	−	7.91238i	0.0247443	−	0.311791i
$645$		0			0
$646$	12.8248	+	22.2131i	0.504583	+	0.873964i
$647$	5.01910	−	1.34486i	0.197321	−	0.0528720i	−0.158805	−	0.987310i	$-0.550764\pi$
$647$	5.01910	−	1.34486i	0.197321	−	0.0528720i	0.356126	+	0.934438i	$0.384097\pi$
$648$	−11.1563	+	2.98932i	−0.438260	+	0.117431i
$649$	11.8208	+	20.4743i	0.464008	+	0.803685i
$650$		0			0
$651$	−12.0000	−	25.2011i	−0.470317	−	0.987707i
$652$	8.48528	−	8.48528i	0.332309	−	0.332309i
$653$	−9.95787	+	37.1633i	−0.389682	+	1.45431i	0.440972	+	0.897521i	$0.354634\pi$
$653$	−9.95787	+	37.1633i	−0.389682	+	1.45431i	−0.830653	+	0.556790i	$0.812033\pi$
$654$	21.0515	−	36.4622i	0.823177	−	1.42579i
$655$		0			0
$656$	−4.50000	+	2.59808i	−0.175695	+	0.101438i
$657$	−3.71492	−	3.71492i	−0.144933	−	0.144933i
$658$	0.228773	+	1.23888i	0.00891850	+	0.0482967i
$659$			1.45017i			0.0564904i	0.999601	+	0.0282452i	$0.00899193\pi$
$659$			1.45017i			0.0564904i	−0.999601	+	0.0282452i	$0.991008\pi$
$660$		0			0
$661$	−19.9124	−	11.4964i	−0.774502	−	0.447159i	0.0599765	−	0.998200i	$-0.480897\pi$
$661$	−19.9124	−	11.4964i	−0.774502	−	0.447159i	−0.834478	+	0.551041i	$0.814231\pi$
$662$	7.46039	+	27.8426i	0.289956	+	1.08213i
$663$	48.6847	+	13.0450i	1.89076	+	0.506627i
$664$	1.25588			0.0487376
$665$		0			0
$666$	−14.2749			−0.553142
$667$	−15.2855	−	4.09575i	−0.591858	−	0.158588i
$668$	0.448288	+	1.67303i	0.0173448	+	0.0647316i
$669$	−22.9928	−	13.2749i	−0.888954	−	0.513238i
$670$		0			0
$671$		−	2.85702i		−	0.110294i
$672$	2.69465	−	7.59363i	0.103949	−	0.292931i
$673$	29.8394	+	29.8394i	1.15023	+	1.15023i	0.986507	+	0.163719i	$0.0523490\pi$
$673$	29.8394	+	29.8394i	1.15023	+	1.15023i	0.163719	+	0.986507i	$0.447651\pi$
$674$	20.9572	−	12.0997i	0.807243	−	0.466062i
$675$		0			0
$676$	4.91238	−	8.50848i	0.188938	−	0.327249i
$677$	2.16288	−	8.07197i	0.0831261	−	0.310231i	−0.911827	−	0.410575i	$-0.865328\pi$
$677$	2.16288	−	8.07197i	0.0831261	−	0.310231i	0.994953	+	0.100345i	$0.0319945\pi$
$678$	12.9209	−	12.9209i	0.496222	−	0.496222i
$679$	−4.41644	−	0.350497i	−0.169488	−	0.0134508i
$680$		0			0
$681$	−5.27492	−	9.13642i	−0.202135	−	0.350109i
$682$	−7.61202	+	2.03963i	−0.291479	+	0.0781017i
$683$	7.89668	−	2.11591i	0.302158	−	0.0809630i	−0.104555	−	0.994519i	$-0.533342\pi$
$683$	7.89668	−	2.11591i	0.302158	−	0.0809630i	0.406713	+	0.913556i	$0.366675\pi$
$684$	23.2309	+	40.2371i	0.888256	+	1.53851i
$685$		0			0
$686$	−5.22508	−	17.7679i	−0.199495	−	0.678382i
$687$	29.8394	−	29.8394i	1.13845	−	1.13845i
$688$	0.187665	−	0.700376i	0.00715467	−	0.0267016i
$689$	30.6353	−	53.0619i	1.16711	−	2.02150i
$690$		0			0
$691$	−32.4743	+	18.7490i	−1.23538	+	0.713246i	−0.968146	−	0.250386i	$-0.919443\pi$
$691$	−32.4743	+	18.7490i	−1.23538	+	0.713246i	−0.267233	+	0.963632i	$0.586109\pi$
$692$	12.5842	+	12.5842i	0.478378	+	0.478378i
$693$	24.5094	+	28.7350i	0.931036	+	1.09155i
$694$		−	27.8248i		−	1.05621i
$695$		0			0
$696$	−13.9124	−	8.03231i	−0.527347	−	0.304464i
$697$	4.65874	+	17.3867i	0.176462	+	0.658567i
$698$	−8.82511	−	2.36468i	−0.334035	−	0.0895045i
$699$	−59.8421			−2.26343
$700$		0			0
$701$	−0.725083			−0.0273860			−0.0136930	−	0.999906i	$-0.504359\pi$
$701$	−0.725083			−0.0273860			−0.0136930	+	0.999906i	$0.504359\pi$
$702$	46.0259	+	12.3326i	1.73714	+	0.465464i
$703$	4.35964	+	16.2704i	0.164427	+	0.613649i
$704$	−1.97014	−	1.13746i	−0.0742523	−	0.0428696i
$705$		0			0
$706$			25.2011i			0.948454i
$707$	23.7708	−	4.38953i	0.893994	−	0.165085i
$708$	−22.3796	−	22.3796i	−0.841076	−	0.841076i
$709$	31.0251	−	17.9124i	1.16517	−	0.672713i	0.212635	−	0.977132i	$-0.431795\pi$
$709$	31.0251	−	17.9124i	1.16517	−	0.672713i	0.952538	+	0.304418i	$0.0984620\pi$
$710$		0			0
$711$	31.3746	−	54.3424i	1.17664	−	2.03800i
$712$	2.36468	−	8.82511i	0.0886202	−	0.330735i
$713$	7.34847	−	7.34847i	0.275202	−	0.275202i
$714$	−22.9928	−	15.8248i	−0.860485	−	0.592226i
$715$		0			0
$716$	−6.41238	−	11.1066i	−0.239642	−	0.415072i
$717$	31.0345	−	8.31566i	1.15900	−	0.310554i
$718$	30.5711	−	8.19149i	1.14090	−	0.305704i
$719$	−6.45203	−	11.1752i	−0.240620	−	0.416766i	0.720271	−	0.693693i	$-0.244017\pi$
$719$	−6.45203	−	11.1752i	−0.240620	−	0.416766i	−0.960891	+	0.276926i	$0.910684\pi$
$720$		0			0
$721$	1.00000	−	0.476171i	0.0372419	−	0.0177335i
$722$	25.3319	−	25.3319i	0.942757	−	0.942757i
$723$	−3.10583	+	11.5911i	−0.115507	+	0.431078i
$724$	4.09204	−	7.08762i	0.152080	−	0.263409i
$725$		0			0
$726$	−15.3625	+	8.86957i	−0.570157	+	0.329181i
$727$	−23.3515	−	23.3515i	−0.866060	−	0.866060i	0.125973	−	0.992034i	$-0.459795\pi$
$727$	−23.3515	−	23.3515i	−0.866060	−	0.866060i	−0.992034	+	0.125973i	$0.959795\pi$
$728$	−9.61702	+	8.20281i	−0.356431	+	0.304016i
$729$		−	18.6495i		−	0.690722i
$730$		0			0
$731$	−2.17525	−	1.25588i	−0.0804545	−	0.0464504i
$732$	0.989919	+	3.69443i	0.0365884	+	0.136550i
$733$	−34.7293	−	9.30569i	−1.28276	−	0.343714i	−0.447852	−	0.894108i	$-0.647811\pi$
$733$	−34.7293	−	9.30569i	−1.28276	−	0.343714i	−0.834905	+	0.550394i	$0.814477\pi$
$734$	14.7512			0.544477
$735$		0			0
$736$	3.00000			0.110581
$737$	24.7755	+	6.63858i	0.912618	+	0.244535i
$738$	8.43891	+	31.4944i	0.310640	+	1.15933i
$739$	23.2309	+	13.4124i	0.854563	+	0.493382i	0.862188	−	0.506589i	$-0.169094\pi$
$739$	23.2309	+	13.4124i	0.854563	+	0.493382i	−0.00762477	+	0.999971i	$0.502427\pi$
$740$		0			0
$741$		−	107.732i		−	3.95765i
$742$	−25.8159	+	22.0196i	−0.947730	+	0.808363i
$743$	10.6066	+	10.6066i	0.389118	+	0.389118i	0.874373	−	0.485254i	$-0.161273\pi$
$743$	10.6066	+	10.6066i	0.389118	+	0.389118i	−0.485254	+	0.874373i	$0.661273\pi$
$744$	9.13642	−	5.27492i	0.334958	−	0.193388i
$745$		0			0
$746$	−3.72508	+	6.45203i	−0.136385	+	0.236226i
$747$	2.03963	−	7.61202i	0.0746263	−	0.278509i
$748$	−5.57239	+	5.57239i	−0.203747	+	0.203747i
$749$	−37.8016	+	18.0000i	−1.38124	+	0.657706i
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−0.459945	+	0.123242i	−0.0167725	+	0.00449417i
$753$	18.9800	−	5.08567i	0.691668	−	0.185332i
$754$	12.6005	+	21.8248i	0.458884	+	0.794811i
$755$		0			0
$756$	−21.7371	−	14.9605i	−0.790572	−	0.544109i
$757$	−4.24264	+	4.24264i	−0.154201	+	0.154201i	−0.779992	−	0.625790i	$-0.784777\pi$
$757$	−4.24264	+	4.24264i	−0.154201	+	0.154201i	0.625790	+	0.779992i	$0.284777\pi$
$758$	−0.821815	+	3.06705i	−0.0298497	+	0.111400i
$759$	−10.3923	+	18.0000i	−0.377217	+	0.653359i
$760$		0			0
$761$	−32.5876	+	18.8145i	−1.18130	+	0.682024i	−0.956315	−	0.292338i	$-0.905567\pi$
$761$	−32.5876	+	18.8145i	−1.18130	+	0.682024i	−0.224985	+	0.974362i	$0.572233\pi$
$762$	−20.9427	−	20.9427i	−0.758675	−	0.758675i
$763$	35.9687	−	6.64201i	1.30216	−	0.240457i
$764$			21.0997i			0.763359i
$765$		0			0
$766$	27.1495	+	15.6748i	0.980951	+	0.566353i
$767$	12.8502	+	47.9577i	0.463995	+	1.73165i
$768$	2.94170	+	0.788227i	0.106150	+	0.0284427i
$769$	47.4142			1.70980			0.854899	−	0.518794i	$-0.173619\pi$
$769$	47.4142			1.70980			0.854899	+	0.518794i	$0.173619\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	−4.39480	−	1.17758i	−0.158172	−	0.0423822i
$773$	−5.25621	−	19.6164i	−0.189053	−	0.705555i	−0.993727	−	0.111837i	$-0.964326\pi$
$773$	−5.25621	−	19.6164i	−0.189053	−	0.705555i	0.804674	−	0.593717i	$-0.202340\pi$
$774$	−3.94027	−	2.27492i	−0.141630	−	0.0817702i
$775$		0			0
$776$		−	1.67451i		−	0.0601113i
$777$	−11.8954	−	13.9463i	−0.426746	−	0.500320i
$778$	−19.1624	−	19.1624i	−0.687004	−	0.687004i
$779$	33.3197	−	19.2371i	1.19380	−	0.689242i
$780$		0			0
$781$	6.82475	−	11.8208i	0.244209	−	0.422982i
$782$	2.68973	−	10.0382i	0.0961844	−	0.358965i
$783$	−37.2011	+	37.2011i	−1.32946	+	1.32946i
$784$	6.53835	−	2.50000i	0.233512	−	0.0892857i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	15.6284	−	4.18762i	0.557092	−	0.149272i	0.0307222	−	0.999528i	$-0.490219\pi$
$787$	15.6284	−	4.18762i	0.557092	−	0.149272i	0.526370	+	0.850255i	$0.323553\pi$
$788$	6.59220	−	1.76638i	0.234838	−	0.0629245i
$789$	−5.82409	−	10.0876i	−0.207343	−	0.359129i
$790$		0			0
$791$	15.8248	+	1.25588i	0.562663	+	0.0446540i
$792$	−10.0939	+	10.0939i	−0.358671	+	0.358671i
$793$	1.55291	−	5.79555i	0.0551456	−	0.205806i
$794$	−9.55505	+	16.5498i	−0.339096	+	0.587332i
$795$		0			0
$796$	6.82475	−	3.94027i	0.241897	−	0.139659i
$797$	−9.79796	−	9.79796i	−0.347062	−	0.347062i	0.511952	−	0.859014i	$-0.328922\pi$
$797$	−9.79796	−	9.79796i	−0.347062	−	0.347062i	−0.859014	+	0.511952i	$0.828922\pi$
$798$	−19.9522	+	56.2261i	−0.706301	+	1.99038i
$799$			1.64950i			0.0583552i
$800$		0			0
$801$	−49.6495	−	28.6652i	−1.75428	−	1.01283i
$802$	3.13162	+	11.6874i	0.110582	+	0.412696i
$803$	−1.83978	−	0.492968i	−0.0649245	−	0.0173965i
$804$	−34.3375			−1.21099
$805$		0			0
$806$	−16.5498			−0.582943
$807$	−57.4477	−	15.3931i	−2.02226	−	0.541862i
$808$	2.36468	+	8.82511i	0.0831892	+	0.310466i
$809$	−20.8709	−	12.0498i	−0.733783	−	0.423650i	0.0860217	−	0.996293i	$-0.472585\pi$
$809$	−20.8709	−	12.0498i	−0.733783	−	0.423650i	−0.819804	+	0.572644i	$0.805918\pi$
$810$		0			0
$811$		−	22.2131i		−	0.780008i	−0.920813	−	0.390004i	$-0.872474\pi$
$811$		−	22.2131i		−	0.780008i	0.920813	−	0.390004i	$-0.127526\pi$
$812$	−2.53430	−	13.7241i	−0.0889365	−	0.481621i
$813$	−39.3501	−	39.3501i	−1.38007	−	1.38007i
$814$	−4.48190	+	2.58762i	−0.157090	+	0.0906962i
$815$		0			0
$816$	5.27492	−	9.13642i	0.184659	−	0.319839i
$817$	−1.38954	+	5.18585i	−0.0486140	+	0.181430i
$818$	−3.33753	+	3.33753i	−0.116694	+	0.116694i
$819$	34.0994	+	71.6117i	1.19153	+	2.50232i
$820$		0			0
$821$	6.09967	+	10.5649i	0.212880	+	0.368719i	0.952615	−	0.304180i	$-0.0983824\pi$
$821$	6.09967	+	10.5649i	0.212880	+	0.368719i	−0.739735	+	0.672899i	$0.765049\pi$
$822$		0			0
$823$	3.69443	−	0.989919i	0.128780	−	0.0345064i	−0.193854	−	0.981030i	$-0.562099\pi$
$823$	3.69443	−	0.989919i	0.128780	−	0.0345064i	0.322633	+	0.946524i	$0.395432\pi$
$824$	0.209313	+	0.362541i	0.00729178	+	0.0126297i
$825$		0			0
$826$	2.17525	−	27.4093i	0.0756866	−	0.953691i
$827$	−29.3267	+	29.3267i	−1.01979	+	1.01979i	−0.0199900	+	0.999800i	$0.506363\pi$
$827$	−29.3267	+	29.3267i	−1.01979	+	1.01979i	−0.999800	+	0.0199900i	$0.993637\pi$
$828$	4.87220	−	18.1833i	0.169321	−	0.631914i
$829$	−7.40437	+	12.8248i	−0.257165	+	0.445422i	−0.965481	−	0.260473i	$-0.916122\pi$
$829$	−7.40437	+	12.8248i	−0.257165	+	0.445422i	0.708317	+	0.705895i	$0.249455\pi$
$830$		0			0
$831$	39.8248	−	22.9928i	1.38151	−	0.797612i
$832$	−3.37822	−	3.37822i	−0.117119	−	0.117119i
$833$	−2.50304	−	24.1192i	−0.0867252	−	0.835680i
$834$		−	66.1993i		−	2.29230i
$835$		0			0
$836$	14.5876	+	8.42217i	0.504524	+	0.291287i
$837$	−8.94216	−	33.3726i	−0.309086	−	1.15353i
$838$	−11.4180	−	3.05945i	−0.394429	−	0.105687i
$839$	−28.6652			−0.989631			−0.494816	−	0.868998i	$-0.664764\pi$
$839$	−28.6652			−0.989631			−0.494816	+	0.868998i	$0.664764\pi$
$840$		0			0
$841$	1.17525			0.0405258
$842$	−11.7604	−	3.15119i	−0.405290	−	0.108597i
$843$	−23.1538	−	86.4113i	−0.797461	−	2.97616i
$844$	14.5707	+	8.41238i	0.501543	+	0.289566i
$845$		0			0
$846$			2.98793i			0.102727i
$847$	−14.5235	−	5.15377i	−0.499034	−	0.177086i
$848$	−9.06847	−	9.06847i	−0.311412	−	0.311412i
$849$	73.3949	−	42.3746i	2.51891	−	1.45429i
$850$		0			0
$851$	3.41238	−	5.91041i	0.116975	−	0.202606i
$852$	−4.72936	+	17.6502i	−0.162025	+	0.604686i
$853$	28.0359	−	28.0359i	0.959930	−	0.959930i	−0.0392974	−	0.999228i	$-0.512512\pi$
$853$	28.0359	−	28.0359i	0.959930	−	0.959930i	0.999228	+	0.0392974i	$0.0125120\pi$
$854$	−1.88382	+	2.73713i	−0.0644630	+	0.0936626i
$855$		0			0
$856$	−7.91238	−	13.7046i	−0.270439	−	0.468415i
$857$	35.3004	−	9.45872i	1.20584	−	0.323104i	0.400711	−	0.916204i	$-0.368763\pi$
$857$	35.3004	−	9.45872i	1.20584	−	0.323104i	0.805128	+	0.593101i	$0.202096\pi$
$858$	31.9718	−	8.56682i	1.09150	−	0.292467i
$859$	14.3326	+	24.8248i	0.489021	+	0.847010i	0.999920	−	0.0126311i	$-0.00402073\pi$
$859$	14.3326	+	24.8248i	0.489021	+	0.847010i	−0.510899	+	0.859641i	$0.670687\pi$
$860$		0			0
$861$	−23.7371	+	34.4892i	−0.808959	+	1.17539i
$862$	−13.7533	+	13.7533i	−0.468441	+	0.468441i
$863$	−10.0939	+	37.6711i	−0.343602	+	1.28234i	0.550635	+	0.834746i	$0.314385\pi$
$863$	−10.0939	+	37.6711i	−0.343602	+	1.28234i	−0.894237	+	0.447593i	$0.852281\pi$
$864$	4.98684	−	8.63746i	0.169656	−	0.293852i
$865$		0			0
$866$	17.2749	−	9.97368i	0.587026	−	0.338919i
$867$	10.7674	+	10.7674i	0.365679	+	0.365679i
$868$	8.63744	+	3.06506i	0.293174	+	0.104035i
$869$		−	22.7492i		−	0.771713i
$870$		0			0
$871$	46.6495	+	26.9331i	1.58066	+	0.912593i
$872$	3.57811	+	13.3537i	0.121170	+	0.452213i
$873$	−10.1494	−	2.71951i	−0.343504	−	0.0920416i
$874$	−22.2131			−0.751370
$875$		0			0
$876$	2.54983			0.0861509
$877$	35.5700	+	9.53095i	1.20111	+	0.321837i	0.803269	−	0.595616i	$-0.203092\pi$
$877$	35.5700	+	9.53095i	1.20111	+	0.321837i	0.397844	+	0.917453i	$0.369759\pi$
$878$	−5.37945	−	20.0764i	−0.181548	−	0.677545i
$879$	−46.9380	−	27.0997i	−1.58318	−	0.914049i
$880$		0			0
$881$			20.9572i			0.706067i	0.935611	+	0.353034i	$0.114850\pi$
$881$			20.9572i			0.706067i	−0.935611	+	0.353034i	$0.885150\pi$
$882$	−4.53404	−	43.6898i	−0.152669	−	1.47111i
$883$	−14.9197	−	14.9197i	−0.502089	−	0.502089i	0.409998	−	0.912086i	$-0.365529\pi$
$883$	−14.9197	−	14.9197i	−0.502089	−	0.502089i	−0.912086	+	0.409998i	$0.865529\pi$
$884$	−14.3326	+	8.27492i	−0.482057	+	0.278316i
$885$		0			0
$886$	16.9124	−	29.2931i	0.568182	−	0.984121i
$887$	−4.40432	+	16.4371i	−0.147882	+	0.551905i	0.851728	+	0.523985i	$0.175555\pi$
$887$	−4.40432	+	16.4371i	−0.147882	+	0.551905i	−0.999610	+	0.0279202i	$0.991112\pi$
$888$	4.89898	−	4.89898i	0.164399	−	0.164399i
$889$	2.03559	−	25.6495i	0.0682715	−	0.860257i
$890$		0			0
$891$	13.1375	+	22.7547i	0.440121	+	0.762313i
$892$	8.42075	−	2.25633i	0.281947	−	0.0755476i
$893$	3.40561	−	0.912530i	0.113964	−	0.0305367i
$894$	14.9605	+	25.9124i	0.500355	+	0.866639i
$895$		0			0
$896$	1.13746	+	2.38876i	0.0379998	+	0.0798030i
$897$	−30.8649	+	30.8649i	−1.03055	+	1.03055i
$898$	9.71861	−	36.2704i	0.324314	−	1.21036i
$899$	9.13642	−	15.8248i	0.304717	−	0.527785i
$900$		0			0
$901$	−38.4743	+	22.2131i	−1.28176	+	0.740026i
$902$	8.35858	+	8.35858i	0.278310	+	0.278310i
$903$	−1.06093	−	5.74527i	−0.0353054	−	0.191191i
$904$			6.00000i			0.199557i
$905$		0			0
$906$	−5.27492	−	3.04547i	−0.175247	−	0.101179i
$907$	6.45091	+	24.0751i	0.214199	+	0.799402i	0.986447	+	0.164081i	$0.0524657\pi$
$907$	6.45091	+	24.0751i	0.214199	+	0.799402i	−0.772248	+	0.635321i	$0.780868\pi$
$908$	3.34607	+	0.896575i	0.111043	+	0.0297539i
$909$	57.3303			1.90153
$910$		0			0
$911$	25.6495			0.849806			0.424903	−	0.905239i	$-0.360308\pi$
$911$	25.6495			0.849806			0.424903	+	0.905239i	$0.360308\pi$
$912$	−21.7815	−	5.83633i	−0.721256	−	0.193260i
$913$	−0.739452	−	2.75967i	−0.0244723	−	0.0913318i
$914$	−16.8443	−	9.72508i	−0.557161	−	0.321677i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	3.48638	−	9.82473i	0.115130	−	0.324441i
$918$	−24.4304	−	24.4304i	−0.806324	−	0.806324i
$919$	−10.0888	+	5.82475i	−0.332798	+	0.192141i	−0.657083	−	0.753819i	$-0.728210\pi$
$919$	−10.0888	+	5.82475i	−0.332798	+	0.192141i	0.324285	+	0.945959i	$0.394876\pi$
$920$		0			0
$921$	−28.4622	+	49.2980i	−0.937862	+	1.62442i
$922$	9.45872	−	35.3004i	0.311506	−	1.16256i
$923$	20.2693	−	20.2693i	0.667173	−	0.667173i
$924$	−18.2728	−	1.45017i	−0.601133	−	0.0477069i
$925$		0			0
$926$	−8.22508	−	14.2463i	−0.270293	−	0.468161i
$927$	2.53734	−	0.679878i	0.0833372	−	0.0223301i
$928$	5.09518	−	1.36525i	0.167257	−	0.0448165i
$929$	6.53835	+	11.3248i	0.214516	+	0.371553i	0.953123	−	0.302584i	$-0.0978492\pi$
$929$	6.53835	+	11.3248i	0.214516	+	0.371553i	−0.738607	+	0.674137i	$0.764516\pi$
$930$		0			0
$931$	−48.4124	+	18.5109i	−1.58665	+	0.606671i
$932$	13.8943	−	13.8943i	0.455123	−	0.455123i
$933$	−20.6148	+	76.9355i	−0.674899	+	2.51876i
$934$	13.2285	−	22.9124i	0.432849	−	0.749716i
$935$		0			0
$936$	−25.9622	+	14.9893i	−0.848601	+	0.489940i
$937$	−30.2300	−	30.2300i	−0.987572	−	0.987572i	0.0123513	−	0.999924i	$-0.496068\pi$
$937$	−30.2300	−	30.2300i	−0.987572	−	0.987572i	−0.999924	+	0.0123513i	$0.996068\pi$
$938$	−19.3586	−	22.6961i	−0.632079	−	0.741054i
$939$			34.1993i			1.11605i
$940$		0			0
$941$	−49.6495	−	28.6652i	−1.61853	−	0.934457i	−0.987301	−	0.158859i	$-0.949219\pi$
$941$	−49.6495	−	28.6652i	−1.61853	−	0.934457i	−0.631226	−	0.775599i	$-0.717448\pi$
$942$	−4.42572	−	16.5170i	−0.144198	−	0.538153i
$943$	−15.0573	−	4.03459i	−0.490333	−	0.131384i
$944$	10.3923			0.338241
$945$		0			0
$946$	−1.64950			−0.0536300
$947$	−3.69443	−	0.989919i	−0.120053	−	0.0321680i	0.198292	−	0.980143i	$-0.436460\pi$
$947$	−3.69443	−	0.989919i	−0.120053	−	0.0321680i	−0.318345	+	0.947975i	$0.603127\pi$
$948$	7.88227	+	29.4170i	0.256004	+	0.955421i
$949$	−3.46410	−	2.00000i	−0.112449	−	0.0649227i
$950$		0			0
$951$			54.8185i			1.77761i
$952$	9.01277	−	1.66430i	0.292106	−	0.0539404i
$953$	36.2739	+	36.2739i	1.17503	+	1.17503i	0.980995	+	0.194031i	$0.0621561\pi$
$953$	36.2739	+	36.2739i	1.17503	+	1.17503i	0.194031	+	0.980995i	$0.437844\pi$
$954$	−69.6927	+	40.2371i	−2.25639	+	1.30273i
$955$		0			0
$956$	−5.27492	+	9.13642i	−0.170603	+	0.295493i
$957$	−9.45872	+	35.3004i	−0.305757	+	1.14110i
$958$	12.9209	−	12.9209i	0.417454	−	0.417454i
$959$		0			0
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	−10.4981	+	2.81297i	−0.338474	+	0.0906937i
$963$	−95.9155	+	25.7005i	−3.09083	+	0.828186i
$964$	−1.97014	−	3.41238i	−0.0634538	−	0.109905i
$965$		0			0
$966$	21.8248	−	10.3923i	0.702200	−	0.334367i
$967$	−17.6242	+	17.6242i	−0.566757	+	0.566757i	−0.931218	−	0.364462i	$-0.881253\pi$
$967$	−17.6242	+	17.6242i	−0.566757	+	0.566757i	0.364462	+	0.931218i	$0.381253\pi$
$968$	1.50756	−	5.62628i	0.0484547	−	0.180835i
$969$	−39.0575	+	67.6495i	−1.25471	+	2.17322i
$970$		0			0
$971$	7.76287	−	4.48190i	0.249122	−	0.143831i	−0.370240	−	0.928936i	$-0.620725\pi$
$971$	7.76287	−	4.48190i	0.249122	−	0.143831i	0.619362	+	0.785105i	$0.287391\pi$
$972$	−3.71492	−	3.71492i	−0.119156	−	0.119156i
$973$	43.7559	−	37.3214i	1.40275	−	1.19647i
$974$			21.0997i			0.676077i
$975$		0			0
$976$	−1.08762	−	0.627940i	−0.0348140	−	0.0200999i
$977$	−6.63858	−	24.7755i	−0.212387	−	0.792639i	−0.987070	−	0.160289i	$-0.948757\pi$
$977$	−6.63858	−	24.7755i	−0.212387	−	0.792639i	0.774683	−	0.632350i	$-0.217909\pi$
$978$	35.3004	+	9.45872i	1.12878	+	0.302457i
$979$	−20.7846			−0.664279
$980$		0			0
$981$	86.7492			2.76969
$982$	33.3726	+	8.94216i	1.06496	+	0.285356i
$983$	4.52756	+	16.8971i	0.144407	+	0.538933i	0.999781	+	0.0209228i	$0.00666042\pi$
$983$	4.52756	+	16.8971i	0.144407	+	0.538933i	−0.855374	+	0.518010i	$0.826673\pi$
$984$	−13.7046	−	7.91238i	−0.436888	−	0.252237i
$985$		0			0
$986$		−	18.2728i		−	0.581926i
$987$	−2.91914	+	2.48987i	−0.0929173	+	0.0792535i
$988$	25.0136	+	25.0136i	0.795789	+	0.795789i
$989$	1.88382	−	1.08762i	0.0599020	−	0.0345844i
$990$		0			0
$991$	−11.8248	+	20.4811i	−0.375626	+	0.650603i	−0.990420	−	0.138084i	$-0.955905\pi$
$991$	−11.8248	+	20.4811i	−0.375626	+	0.650603i	0.614795	+	0.788687i	$0.289239\pi$
$992$	−0.896575	+	3.34607i	−0.0284663	+	0.106238i
$993$	−62.0734	+	62.0734i	−1.96984	+	1.96984i
$994$	−14.3326	+	6.82475i	−0.454602	+	0.216468i
$995$		0			0
$996$	1.91238	+	3.31233i	0.0605959	+	0.104955i
$997$	20.8851	−	5.59615i	0.661438	−	0.177232i	0.0875432	−	0.996161i	$-0.472098\pi$
$997$	20.8851	−	5.59615i	0.661438	−	0.177232i	0.573895	+	0.818929i	$0.305432\pi$
$998$	−3.86370	+	1.03528i	−0.122303	+	0.0327711i
$999$	−11.3446	−	19.6495i	−0.358929	−	0.621683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.d.143.1	✓	16
5.2	odd	4	inner	350.2.o.d.157.3	yes	16
5.3	odd	4	inner	350.2.o.d.157.2	yes	16
5.4	even	2	inner	350.2.o.d.143.4	yes	16
7.5	odd	6	inner	350.2.o.d.243.3	yes	16
35.12	even	12	inner	350.2.o.d.257.1	yes	16
35.19	odd	6	inner	350.2.o.d.243.2	yes	16
35.33	even	12	inner	350.2.o.d.257.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.d.143.1	✓	16	1.1	even	1	trivial
350.2.o.d.143.4	yes	16	5.4	even	2	inner
350.2.o.d.157.2	yes	16	5.3	odd	4	inner
350.2.o.d.157.3	yes	16	5.2	odd	4	inner
350.2.o.d.243.2	yes	16	35.19	odd	6	inner
350.2.o.d.243.3	yes	16	7.5	odd	6	inner
350.2.o.d.257.1	yes	16	35.12	even	12	inner
350.2.o.d.257.4	yes	16	35.33	even	12	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.788227 - 2.94170i) q^{3} +(0.866025 + 0.500000i) q^{4} +3.04547i q^{6} +(-2.01297 + 1.71696i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.43424 + 3.13746i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.788227 - 2.94170i) q^{3} +(0.866025 + 0.500000i) q^{4} +3.04547i q^{6} +(-2.01297 + 1.71696i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.43424 + 3.13746i) q^{9} +(-1.13746 + 1.97014i) q^{11} +(0.788227 - 2.94170i) q^{12} +(-3.37822 + 3.37822i) q^{13} +(2.38876 - 1.13746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.34607 - 0.896575i) q^{17} +(6.06110 - 1.62407i) q^{18} +(-3.70219 - 6.41238i) q^{19} +(6.63746 + 4.56821i) q^{21} +(1.60861 - 1.60861i) q^{22} +(-0.776457 + 2.89778i) q^{23} +(-1.52274 + 2.63746i) q^{24} +(4.13746 - 2.38876i) q^{26} +(7.05246 + 7.05246i) q^{27} +(-2.60176 + 0.480443i) q^{28} +5.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(6.69213 + 1.79315i) q^{33} -3.46410 q^{34} -6.27492 q^{36} +(-2.19740 - 0.588792i) q^{37} +(1.91639 + 7.15208i) q^{38} +(12.6005 + 7.27492i) q^{39} +5.19615i q^{41} +(-5.22895 - 6.13045i) q^{42} +(-0.512711 - 0.512711i) q^{43} +(-1.97014 + 1.13746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-0.123242 + 0.459945i) q^{47} +(2.15348 - 2.15348i) q^{48} +(1.10411 - 6.91238i) q^{49} +(-5.27492 - 9.13642i) q^{51} +(-4.61474 + 1.23651i) q^{52} +(-12.3878 + 3.31929i) q^{53} +(-4.98684 - 8.63746i) q^{54} +(2.63746 + 0.209313i) q^{56} +(-15.9451 + 15.9451i) q^{57} +(1.36525 - 5.09518i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-1.08762 + 0.627940i) q^{61} +(2.44949 + 2.44949i) q^{62} +(5.55208 - 15.6460i) q^{63} +1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(-2.91816 - 10.8907i) q^{67} +(3.34607 + 0.896575i) q^{68} +9.13642 q^{69} -6.00000 q^{71} +(6.06110 + 1.62407i) q^{72} +(0.216697 + 0.808725i) q^{73} +(1.97014 + 1.13746i) q^{74} -7.40437i q^{76} +(-1.09297 - 5.91880i) q^{77} +(-10.2883 - 10.2883i) q^{78} +(-8.66025 + 5.00000i) q^{79} +(5.77492 - 10.0025i) q^{81} +(1.34486 - 5.01910i) q^{82} +(-0.888041 + 0.888041i) q^{83} +(3.46410 + 7.27492i) q^{84} +(0.362541 + 0.627940i) q^{86} +(15.5172 - 4.15783i) q^{87} +(2.19740 - 0.588792i) q^{88} +(4.56821 + 7.91238i) q^{89} +(1.00000 - 12.6005i) q^{91} +(-2.12132 + 2.12132i) q^{92} +(-2.73050 + 10.1904i) q^{93} +(0.238085 - 0.412376i) q^{94} +(-2.63746 + 1.52274i) q^{96} +(1.18406 + 1.18406i) q^{97} +(-2.85554 + 6.39108i) q^{98} -14.2749i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 12 q^{11} + 8 q^{16} + 76 q^{21} + 36 q^{26} - 48 q^{31} - 40 q^{36} + 24 q^{46} - 24 q^{51} + 12 q^{56} - 108 q^{61} - 96 q^{66} - 96 q^{71} + 32 q^{81} + 36 q^{86} + 16 q^{91} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^11 + 8 * q^16 + 76 * q^21 + 36 * q^26 - 48 * q^31 - 40 * q^36 + 24 * q^46 - 24 * q^51 + 12 * q^56 - 108 * q^61 - 96 * q^66 - 96 * q^71 + 32 * q^81 + 36 * q^86 + 16 * q^91 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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