LMFDB - Embedded newform 630.2.bt.a.317.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("630.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bt (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.47
Character	$\chi$	$=$	630.317
Dual form			630.2.bt.a.473.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.73115 - 0.0558589i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.02346 + 0.951627i) q^{5} +(1.68662 + 0.394099i) q^{6} +(0.554174 - 2.58706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99376 - 0.193400i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.73115 - 0.0558589i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.02346 + 0.951627i) q^{5} +(1.68662 + 0.394099i) q^{6} +(0.554174 - 2.58706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99376 - 0.193400i) q^{9} +(-2.20082 + 0.395490i) q^{10} +4.54436i q^{11} +(1.52715 + 0.817200i) q^{12} +(4.22459 + 1.13198i) q^{13} +(1.20487 - 2.35548i) q^{14} +(-3.44976 + 1.76044i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.13496 - 0.304112i) q^{17} +(2.94181 + 0.588032i) q^{18} +(5.35282 + 3.09045i) q^{19} +(-2.22818 - 0.187599i) q^{20} +(0.814849 - 4.50955i) q^{21} +(-1.17617 + 4.38951i) q^{22} +(-5.32448 - 5.32448i) q^{23} +(1.26361 + 1.18461i) q^{24} +(3.18881 - 3.85116i) q^{25} +(3.78767 + 2.18681i) q^{26} +(5.17184 - 0.502033i) q^{27} +(1.77346 - 1.96337i) q^{28} +(3.13342 - 5.42724i) q^{29} +(-3.78785 + 0.807587i) q^{30} +(0.179481 - 0.310870i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.253843 + 7.86697i) q^{33} +(-1.01758 - 0.587499i) q^{34} +(1.34057 + 5.76219i) q^{35} +(2.68937 + 1.32939i) q^{36} +(-9.20775 + 2.46721i) q^{37} +(4.37056 + 4.37056i) q^{38} +(7.37664 + 1.72364i) q^{39} +(-2.10371 - 0.757903i) q^{40} +(-8.04851 + 4.64681i) q^{41} +(1.95424 - 4.14499i) q^{42} +(-2.19596 - 8.19545i) q^{43} +(-2.27218 + 3.93553i) q^{44} +(-5.87372 + 3.24028i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(-2.94175 - 0.788240i) q^{47} +(0.913950 + 1.47129i) q^{48} +(-6.38578 - 2.86737i) q^{49} +(4.07691 - 2.89461i) q^{50} +(-1.98178 - 0.463066i) q^{51} +(3.09262 + 3.09262i) q^{52} +(-0.0189078 + 0.0705647i) q^{53} +(5.12555 + 0.853645i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(2.22119 - 1.43747i) q^{56} +(9.43915 + 5.05103i) q^{57} +(4.43132 - 4.43132i) q^{58} +(-4.25394 + 7.36804i) q^{59} +(-3.86780 - 0.200298i) q^{60} +(2.94582 + 5.10230i) q^{61} +(0.253824 - 0.253824i) q^{62} +(1.15873 - 7.85222i) q^{63} +1.00000i q^{64} +(-9.62553 + 1.72972i) q^{65} +(-1.79093 + 7.66461i) q^{66} +(-9.24538 + 2.47729i) q^{67} +(-0.830850 - 0.830850i) q^{68} +(-9.51489 - 8.92005i) q^{69} +(-0.196479 + 5.91282i) q^{70} -13.2021i q^{71} +(2.25366 + 1.98015i) q^{72} +(-9.16835 - 2.45665i) q^{73} -9.53256 q^{74} +(5.30519 - 6.84507i) q^{75} +(3.09045 + 5.35282i) q^{76} +(11.7565 + 2.51837i) q^{77} +(6.67917 + 3.57412i) q^{78} +(4.56295 - 2.63442i) q^{79} +(-1.83586 - 1.27656i) q^{80} +(8.92519 - 1.15799i) q^{81} +(-8.97694 + 2.40536i) q^{82} +(3.57191 - 0.957089i) q^{83} +(2.96045 - 3.49796i) q^{84} +(2.58596 - 0.464700i) q^{85} -8.48456i q^{86} +(5.12126 - 9.57039i) q^{87} +(-3.21335 + 3.21335i) q^{88} +(-2.74487 + 4.75426i) q^{89} +(-6.51222 + 1.60964i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-1.94889 - 7.27337i) q^{92} +(0.293343 - 0.548188i) q^{93} +(-2.63750 - 1.52276i) q^{94} +(-13.7722 - 1.15953i) q^{95} +(0.502010 + 1.65770i) q^{96} +(-3.37208 + 0.903546i) q^{97} +(-5.42606 - 4.42243i) q^{98} +(0.878880 + 13.6047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	1.73115	−	0.0558589i	0.999480	−	0.0322501i
$3$	1.73115	−	0.0558589i	0.999480	−	0.0322501i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.02346	+	0.951627i	−0.904921	+	0.425580i
$5$	−2.02346	+	0.951627i	−0.904921	+	0.425580i
$6$	1.68662	+	0.394099i	0.688560	+	0.160890i
$7$	0.554174	−	2.58706i	0.209458	−	0.977818i
$7$	0.554174	−	2.58706i	0.209458	−	0.977818i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.99376	−	0.193400i	0.997920	−	0.0644667i
$10$	−2.20082	+	0.395490i	−0.695959	+	0.125065i
$11$			4.54436i			1.37018i	0.728460	+	0.685088i	$0.240236\pi$
$11$			4.54436i			1.37018i	−0.728460	+	0.685088i	$0.759764\pi$
$12$	1.52715	+	0.817200i	0.440850	+	0.235905i
$13$	4.22459	+	1.13198i	1.17169	+	0.313954i	0.791626	−	0.611006i	$-0.209235\pi$
$13$	4.22459	+	1.13198i	1.17169	+	0.313954i	0.380065	+	0.924960i	$0.375901\pi$
$14$	1.20487	−	2.35548i	0.322016	−	0.629528i
$15$	−3.44976	+	1.76044i	−0.890725	+	0.454543i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.13496	−	0.304112i	−0.275269	−	0.0737580i	0.118544	−	0.992949i	$-0.462177\pi$
$17$	−1.13496	−	0.304112i	−0.275269	−	0.0737580i	−0.393812	+	0.919191i	$0.628844\pi$
$18$	2.94181	+	0.588032i	0.693390	+	0.138600i
$19$	5.35282	+	3.09045i	1.22802	+	0.708998i	0.966615	−	0.256232i	$-0.0824810\pi$
$19$	5.35282	+	3.09045i	1.22802	+	0.708998i	0.261405	+	0.965229i	$0.415814\pi$
$20$	−2.22818	−	0.187599i	−0.498237	−	0.0419484i
$21$	0.814849	−	4.50955i	0.177815	−	0.984064i
$22$	−1.17617	+	4.38951i	−0.250760	+	0.935848i
$23$	−5.32448	−	5.32448i	−1.11023	−	1.11023i	−0.993119	−	0.117112i	$-0.962636\pi$
$23$	−5.32448	−	5.32448i	−1.11023	−	1.11023i	−0.117112	−	0.993119i	$-0.537364\pi$
$24$	1.26361	+	1.18461i	0.257932	+	0.241807i
$25$	3.18881	−	3.85116i	0.637763	−	0.770233i
$26$	3.78767	+	2.18681i	0.742823	+	0.428869i
$27$	5.17184	−	0.502033i	0.995322	−	0.0966163i
$28$	1.77346	−	1.96337i	0.335152	−	0.371043i
$29$	3.13342	−	5.42724i	0.581861	−	1.00781i	−0.413398	−	0.910551i	$-0.635658\pi$
$29$	3.13342	−	5.42724i	0.581861	−	1.00781i	0.995259	−	0.0972625i	$-0.0310086\pi$
$30$	−3.78785	+	0.807587i	−0.691564	+	0.147445i
$31$	0.179481	−	0.310870i	0.0322357	−	0.0558338i	−0.849457	−	0.527657i	$-0.823071\pi$
$31$	0.179481	−	0.310870i	0.0322357	−	0.0558338i	0.881693	+	0.471823i	$0.156404\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.253843	+	7.86697i	0.0441884	+	1.36946i
$34$	−1.01758	−	0.587499i	−0.174513	−	0.100755i
$35$	1.34057	+	5.76219i	0.226597	+	0.973989i
$36$	2.68937	+	1.32939i	0.448229	+	0.221565i
$37$	−9.20775	+	2.46721i	−1.51374	+	0.405607i	−0.917677	−	0.397328i	$-0.869938\pi$
$37$	−9.20775	+	2.46721i	−1.51374	+	0.405607i	−0.596068	+	0.802934i	$0.703271\pi$
$38$	4.37056	+	4.37056i	0.708998	+	0.708998i
$39$	7.37664	+	1.72364i	1.18121	+	0.276003i
$40$	−2.10371	−	0.757903i	−0.332625	−	0.119835i
$41$	−8.04851	+	4.64681i	−1.25697	+	0.725709i	−0.972483	−	0.232972i	$-0.925155\pi$
$41$	−8.04851	+	4.64681i	−1.25697	+	0.725709i	−0.284482	+	0.958681i	$0.591822\pi$
$42$	1.95424	−	4.14499i	0.301546	−	0.639586i
$43$	−2.19596	−	8.19545i	−0.334881	−	1.24979i	−0.903998	−	0.427537i	$-0.859381\pi$
$43$	−2.19596	−	8.19545i	−0.334881	−	1.24979i	0.569116	−	0.822257i	$-0.307285\pi$
$44$	−2.27218	+	3.93553i	−0.342544	+	0.593304i
$45$	−5.87372	+	3.24028i	−0.875602	+	0.483032i
$46$	−3.76497	−	6.52113i	−0.555115	−	0.961488i
$47$	−2.94175	−	0.788240i	−0.429099	−	0.114977i	0.0378043	−	0.999285i	$-0.487964\pi$
$47$	−2.94175	−	0.788240i	−0.429099	−	0.114977i	−0.466903	+	0.884308i	$0.654630\pi$
$48$	0.913950	+	1.47129i	0.131917	+	0.212362i
$49$	−6.38578	−	2.86737i	−0.912254	−	0.409624i
$50$	4.07691	−	2.89461i	0.576562	−	0.409360i
$51$	−1.98178	−	0.463066i	−0.277504	−	0.0648422i
$52$	3.09262	+	3.09262i	0.428869	+	0.428869i
$53$	−0.0189078	+	0.0705647i	−0.00259718	+	0.00969281i	−0.967212	−	0.253969i	$-0.918264\pi$
$53$	−0.0189078	+	0.0705647i	−0.00259718	+	0.00969281i	0.964615	+	0.263662i	$0.0849304\pi$
$54$	5.12555	+	0.853645i	0.697499	+	0.116166i
$55$	−4.32453	−	9.19535i	−0.583120	−	1.23990i
$56$	2.22119	−	1.43747i	0.296819	−	0.192090i
$57$	9.43915	+	5.05103i	1.25025	+	0.669025i
$58$	4.43132	−	4.43132i	0.581861	−	0.581861i
$59$	−4.25394	+	7.36804i	−0.553816	+	0.959237i	0.444179	+	0.895938i	$0.353495\pi$
$59$	−4.25394	+	7.36804i	−0.553816	+	0.959237i	−0.997995	+	0.0632989i	$0.979838\pi$
$60$	−3.86780	−	0.200298i	−0.499331	−	0.0258584i
$61$	2.94582	+	5.10230i	0.377173	+	0.653283i	0.990650	−	0.136430i	$-0.0435628\pi$
$61$	2.94582	+	5.10230i	0.377173	+	0.653283i	−0.613477	+	0.789713i	$0.710230\pi$
$62$	0.253824	−	0.253824i	0.0322357	−	0.0322357i
$63$	1.15873	−	7.85222i	0.145986	−	0.989287i
$64$			1.00000i			0.125000i
$65$	−9.62553	+	1.72972i	−1.19390	+	0.214546i
$66$	−1.79093	+	7.66461i	−0.220448	+	0.943448i
$67$	−9.24538	+	2.47729i	−1.12950	+	0.302649i	−0.774723	−	0.632301i	$-0.782111\pi$
$67$	−9.24538	+	2.47729i	−1.12950	+	0.302649i	−0.354779	+	0.934950i	$0.615444\pi$
$68$	−0.830850	−	0.830850i	−0.100755	−	0.100755i
$69$	−9.51489	−	8.92005i	−1.14546	−	1.07385i
$70$	−0.196479	+	5.91282i	−0.0234837	+	0.706717i
$71$		−	13.2021i		−	1.56680i	−0.621520	−	0.783398i	$-0.713485\pi$
$71$		−	13.2021i		−	1.56680i	0.621520	−	0.783398i	$-0.286515\pi$
$72$	2.25366	+	1.98015i	0.265597	+	0.233363i
$73$	−9.16835	−	2.45665i	−1.07307	−	0.287529i	−0.321319	−	0.946971i	$-0.604126\pi$
$73$	−9.16835	−	2.45665i	−1.07307	−	0.287529i	−0.751756	+	0.659442i	$0.770793\pi$
$74$	−9.53256			−1.10814
$75$	5.30519	−	6.84507i	0.612591	−	0.790400i
$76$	3.09045	+	5.35282i	0.354499	+	0.614010i
$77$	11.7565	+	2.51837i	1.33978	+	0.286995i
$78$	6.67917	+	3.57412i	0.756267	+	0.404690i
$79$	4.56295	−	2.63442i	0.513372	−	0.296395i	−0.220847	−	0.975309i	$-0.570882\pi$
$79$	4.56295	−	2.63442i	0.513372	−	0.296395i	0.734219	+	0.678913i	$0.237549\pi$
$80$	−1.83586	−	1.27656i	−0.205256	−	0.142724i
$81$	8.92519	−	1.15799i	0.991688	−	0.128665i
$82$	−8.97694	+	2.40536i	−0.991338	+	0.265628i
$83$	3.57191	−	0.957089i	0.392068	−	0.105054i	−0.0573990	−	0.998351i	$-0.518281\pi$
$83$	3.57191	−	0.957089i	0.392068	−	0.105054i	0.449467	+	0.893297i	$0.351614\pi$
$84$	2.96045	−	3.49796i	0.323012	−	0.381659i
$85$	2.58596	−	0.464700i	0.280486	−	0.0504038i
$86$		−	8.48456i		−	0.914913i
$87$	5.12126	−	9.57039i	0.549056	−	1.02605i
$88$	−3.21335	+	3.21335i	−0.342544	+	0.342544i
$89$	−2.74487	+	4.75426i	−0.290956	+	0.503951i	−0.974036	−	0.226393i	$-0.927307\pi$
$89$	−2.74487	+	4.75426i	−0.290956	+	0.503951i	0.683080	+	0.730344i	$0.260640\pi$
$90$	−6.51222	+	1.60964i	−0.686449	+	0.169671i
$91$	5.26966	−	10.3020i	0.552410	−	1.07994i
$92$	−1.94889	−	7.27337i	−0.203186	−	0.758301i
$93$	0.293343	−	0.548188i	0.0304183	−	0.0568444i
$94$	−2.63750	−	1.52276i	−0.272038	−	0.157061i
$95$	−13.7722	−	1.15953i	−1.41300	−	0.118965i
$96$	0.502010	+	1.65770i	0.0512362	+	0.169189i
$97$	−3.37208	+	0.903546i	−0.342383	+	0.0917412i	−0.425913	−	0.904764i	$-0.640047\pi$
$97$	−3.37208	+	0.903546i	−0.342383	+	0.0917412i	0.0835303	+	0.996505i	$0.473380\pi$
$98$	−5.42606	−	4.42243i	−0.548115	−	0.446733i
$99$	0.878880	+	13.6047i	0.0883308	+	1.36733i
$100$	4.68718	−	1.74080i	0.468718	−	0.174080i
$101$		−	9.50946i		−	0.946227i	−0.881001	−	0.473114i	$-0.843130\pi$
$101$		−	9.50946i		−	0.946227i	0.881001	−	0.473114i	$-0.156870\pi$
$102$	−1.79440	−	0.960209i	−0.177672	−	0.0950748i
$103$	2.17566	−	2.17566i	0.214375	−	0.214375i	−0.591748	−	0.806123i	$-0.701562\pi$
$103$	2.17566	−	2.17566i	0.214375	−	0.214375i	0.806123	+	0.591748i	$0.201562\pi$
$104$	2.18681	+	3.78767i	0.214434	+	0.371411i
$105$	2.64259	+	9.90034i	0.257890	+	0.966174i
$106$	−0.0365270	+	0.0632666i	−0.00354782	+	0.00614500i
$107$	3.52788	+	13.1662i	0.341053	+	1.27283i	0.897156	+	0.441713i	$0.145629\pi$
$107$	3.52788	+	13.1662i	0.341053	+	1.27283i	−0.556104	+	0.831113i	$0.687704\pi$
$108$	4.72996	+	2.15115i	0.455141	+	0.206994i
$109$	−0.421534	+	0.243373i	−0.0403756	+	0.0233109i	−0.520052	−	0.854135i	$-0.674087\pi$
$109$	−0.421534	+	0.243373i	−0.0403756	+	0.0233109i	0.479676	+	0.877446i	$0.340754\pi$
$110$	−1.79725	−	10.0013i	−0.171361	−	0.953586i
$111$	−15.8022	+	4.78544i	−1.49988	+	0.454214i
$112$	2.51755	−	0.813602i	0.237886	−	0.0768782i
$113$	0.762725	−	2.84653i	0.0717511	−	0.267779i	−0.920726	−	0.390210i	$-0.872402\pi$
$113$	0.762725	−	2.84653i	0.0717511	−	0.267779i	0.992477	+	0.122431i	$0.0390691\pi$
$114$	7.81022	+	7.32195i	0.731494	+	0.685764i
$115$	15.8408	+	5.70697i	1.47716	+	0.532178i
$116$	5.42724	−	3.13342i	0.503907	−	0.290931i
$117$	12.8663	+	2.57183i	1.18949	+	0.237766i
$118$	−6.01598	+	6.01598i	−0.553816	+	0.553816i
$119$	−1.41572	+	2.76769i	−0.129779	+	0.253713i
$120$	−3.68417	−	1.19453i	−0.336317	−	0.109046i
$121$	−9.65121			−0.877382
$122$	1.52487	+	5.69088i	0.138055	+	0.515228i
$123$	−13.6736	+	8.49390i	−1.23291	+	0.765869i
$124$	0.310870	−	0.179481i	0.0279169	−	0.0161178i
$125$	−2.78758	+	10.8273i	−0.249329	+	0.968419i
$126$	3.15155	−	7.28476i	0.280762	−	0.648978i
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	0.968999	−	0.247064i	$-0.0794659\pi$
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	−0.247064	+	0.968999i	$0.579466\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−4.25933	−	14.0649i	−0.375013	−	1.23834i
$130$	−9.74524	−	0.820487i	−0.854714	−	0.0719615i
$131$			9.30859i			0.813295i	0.913585	+	0.406648i	$0.133302\pi$
$131$			9.30859i			0.813295i	−0.913585	+	0.406648i	$0.866698\pi$
$132$	−3.71365	+	6.93992i	−0.323232	+	0.604042i
$133$	10.9616	−	12.1354i	0.950489	−	1.05227i
$134$	−9.57152			−0.826853
$135$	−9.98729	+	5.93751i	−0.859569	+	0.511019i
$136$	−0.587499	−	1.01758i	−0.0503777	−	0.0872567i
$137$	13.1600	−	13.1600i	1.12433	−	1.12433i	0.133253	−	0.991082i	$-0.457458\pi$
$137$	13.1600	−	13.1600i	1.12433	−	1.12433i	0.991082	−	0.133253i	$-0.0425422\pi$
$138$	−6.88200	−	11.0787i	−0.585835	−	0.943085i
$139$	14.1952	−	8.19559i	1.20402	−	0.695141i	0.242573	−	0.970133i	$-0.422009\pi$
$139$	14.1952	−	8.19559i	1.20402	−	0.695141i	0.961446	+	0.274992i	$0.0886754\pi$
$140$	−1.72013	+	5.66049i	−0.145378	+	0.478399i
$141$	−5.13665	−	1.20024i	−0.432584	−	0.101078i
$142$	3.41694	−	12.7522i	0.286744	−	1.07014i
$143$	−5.14411	+	19.1981i	−0.430172	+	1.60542i
$144$	1.66437	+	2.49597i	0.138697	+	0.207998i
$145$	−1.17565	+	13.9637i	−0.0976327	+	1.15962i
$146$	−8.22012	−	4.74589i	−0.680302	−	0.392772i
$147$	−11.2149	−	4.60714i	−0.924990	−	0.379991i
$148$	−9.20775	−	2.46721i	−0.756872	−	0.202803i
$149$	4.48602			0.367509			0.183754	−	0.982972i	$-0.441175\pi$
$149$	4.48602			0.367509			0.183754	+	0.982972i	$0.441175\pi$
$150$	6.89606	−	5.23874i	0.563061	−	0.427742i
$151$	−1.18802			−0.0966800			−0.0483400	−	0.998831i	$-0.515393\pi$
$151$	−1.18802			−0.0966800			−0.0483400	+	0.998831i	$0.515393\pi$
$152$	1.59973	+	5.97029i	0.129756	+	0.484254i
$153$	−3.45662	−	0.690937i	−0.279451	−	0.0558589i
$154$	10.7041	+	5.47537i	0.862565	+	0.441218i
$155$	−0.0673408	+	0.799832i	−0.00540895	+	0.0642441i
$156$	5.52653	+	5.18103i	0.442477	+	0.414815i
$157$	−4.23335	+	1.13432i	−0.337858	+	0.0905287i	−0.423759	−	0.905775i	$-0.639290\pi$
$157$	−4.23335	+	1.13432i	−0.337858	+	0.0905287i	0.0859013	+	0.996304i	$0.472623\pi$
$158$	5.08931	−	1.36368i	0.404884	−	0.108488i
$159$	−0.0287905	+	0.123214i	−0.00228324	+	0.00977153i
$160$	−1.44291	−	1.70822i	−0.114072	−	0.135046i
$161$	−16.7254	+	10.8241i	−1.31815	+	0.853056i
$162$	8.92078	+	1.19148i	0.700883	+	0.0936115i
$163$	−4.60602	−	17.1899i	−0.360771	−	1.34642i	−0.873064	−	0.487606i	$-0.837870\pi$
$163$	−4.60602	−	17.1899i	−0.360771	−	1.34642i	0.512293	−	0.858811i	$-0.328796\pi$
$164$	−9.29362			−0.725709
$165$	−8.00006	−	15.6770i	−0.622804	−	1.22045i
$166$	3.69791			0.287013
$167$	12.4613	+	3.33901i	0.964287	+	0.258380i	0.706414	−	0.707799i	$-0.250312\pi$
$167$	12.4613	+	3.33901i	0.964287	+	0.258380i	0.257873	+	0.966179i	$0.416978\pi$
$168$	3.76492	−	2.61255i	0.290470	−	0.201562i
$169$	5.30750	+	3.06428i	0.408269	+	0.235714i
$170$	2.61811	+	0.220429i	0.200800	+	0.0169061i
$171$	16.6227	+	8.21683i	1.27117	+	0.628356i
$172$	2.19596	−	8.19545i	0.167441	−	0.624897i
$173$	3.95942	−	14.7767i	0.301029	−	1.12346i	−0.635281	−	0.772281i	$-0.719116\pi$
$173$	3.95942	−	14.7767i	0.301029	−	1.12346i	0.936310	−	0.351174i	$-0.114218\pi$
$174$	7.42375	−	7.91881i	0.562793	−	0.600324i
$175$	−8.19604	−	10.3839i	−0.619563	−	0.784947i
$176$	−3.93553	+	2.27218i	−0.296652	+	0.171272i
$177$	−6.95264	+	12.9928i	−0.522592	+	0.976599i
$178$	−3.88184	+	3.88184i	−0.290956	+	0.290956i
$179$	−5.38279	−	9.32327i	−0.402329	−	0.696854i	0.591678	−	0.806175i	$-0.298466\pi$
$179$	−5.38279	−	9.32327i	−0.402329	−	0.696854i	−0.994007	+	0.109321i	$0.965132\pi$
$180$	−6.70693	−	0.130695i	−0.499905	−	0.00974144i
$181$	0.210492			0.0156458			0.00782288	−	0.999969i	$-0.497510\pi$
$181$	0.210492			0.0156458			0.00782288	+	0.999969i	$0.497510\pi$
$182$	7.75644	−	8.58706i	0.574946	−	0.636515i
$183$	5.38466	+	8.66830i	0.398045	+	0.640779i
$184$		−	7.52995i		−	0.555115i
$185$	16.2837	−	13.7546i	1.19720	−	1.01126i
$186$	0.425229	−	0.453586i	0.0311793	−	0.0332585i
$187$	1.38199	−	5.15767i	0.101061	−	0.377167i
$188$	−2.15351	−	2.15351i	−0.157061	−	0.157061i
$189$	1.56731	−	13.6581i	0.114005	−	0.993480i
$190$	−13.0028	−	4.68452i	−0.943322	−	0.339851i
$191$	−18.7304	+	10.8140i	−1.35528	+	0.782473i	−0.988984	−	0.148025i	$-0.952709\pi$
$191$	−18.7304	+	10.8140i	−1.35528	+	0.782473i	−0.366299	+	0.930497i	$0.619375\pi$
$192$	0.0558589	+	1.73115i	0.00403127	+	0.124935i
$193$	−5.58407	−	20.8400i	−0.401950	−	1.50010i	−0.809613	−	0.586965i	$-0.800323\pi$
$193$	−5.58407	−	20.8400i	−0.401950	−	1.50010i	0.407663	−	0.913133i	$-0.366344\pi$
$194$	−3.49103			−0.250642
$195$	−16.5666	+	3.53208i	−1.18636	+	0.252938i
$196$	−4.09656	−	5.67610i	−0.292612	−	0.405436i
$197$	−3.69607	+	3.69607i	−0.263334	+	0.263334i	−0.826407	−	0.563073i	$-0.809619\pi$
$197$	−3.69607	+	3.69607i	−0.263334	+	0.263334i	0.563073	+	0.826407i	$0.309619\pi$
$198$	−2.67223	+	13.3686i	−0.189907	+	0.950067i
$199$	−3.82151	+	2.20635i	−0.270900	+	0.156404i	−0.629296	−	0.777165i	$-0.716657\pi$
$199$	−3.82151	+	2.20635i	−0.270900	+	0.156404i	0.358397	+	0.933569i	$0.383323\pi$
$200$	4.97802	−	0.468353i	0.351999	−	0.0331176i
$201$	−15.8668	+	4.80500i	−1.11915	+	0.338918i
$202$	2.46123	−	9.18544i	0.173172	−	0.646285i
$203$	−12.3041	−	11.1140i	−0.863582	−	0.780049i
$204$	−1.48474	−	1.39191i	−0.103952	−	0.0974535i
$205$	11.8638	−	17.0618i	0.828606	−	1.19165i
$206$	2.66463	−	1.53843i	0.185654	−	0.107187i
$207$	−16.9700	−	14.9105i	−1.17949	−	1.03635i
$208$	1.13198	+	4.22459i	0.0784885	+	0.292923i
$209$	−14.0441	+	24.3251i	−0.971452	+	1.68260i
$210$	−0.00985118	+	10.2469i	−0.000679796	+	0.707106i
$211$	7.09284	+	12.2852i	0.488291	+	0.845745i	0.999909	−	0.0134680i	$-0.00428714\pi$
$211$	7.09284	+	12.2852i	0.488291	+	0.845745i	−0.511618	+	0.859213i	$0.670954\pi$
$212$	−0.0516570	+	0.0516570i	−0.00354782	+	0.00354782i
$213$	−0.737452	−	22.8547i	−0.0505294	−	1.56598i
$214$			13.6307i			0.931774i
$215$	12.2425	+	14.4935i	0.834929	+	0.988446i
$216$	4.01204	+	3.30205i	0.272984	+	0.224676i
$217$	−0.704776	−	0.636604i	−0.0478433	−	0.0432155i
$218$	−0.470160	+	0.125979i	−0.0318433	+	0.00853238i
$219$	−16.0090	−	3.74070i	−1.08179	−	0.252773i
$220$	0.852518	−	10.1257i	0.0574767	−	0.682673i
$221$	−4.45050	−	2.56950i	−0.299373	−	0.172843i
$222$	−16.5023	+	0.532478i	−1.10756	+	0.0357376i
$223$	0.613728	+	2.29046i	0.0410982	+	0.153381i	0.983426	−	0.181312i	$-0.0580343\pi$
$223$	0.613728	+	2.29046i	0.0410982	+	0.153381i	−0.942327	+	0.334692i	$0.891368\pi$
$224$	2.64234	−	0.134290i	0.176549	−	0.00897260i
$225$	8.80172	−	12.1462i	0.586782	−	0.809745i
$226$	1.47347	−	2.55213i	0.0980139	−	0.169765i
$227$	0.388994	−	0.388994i	0.0258184	−	0.0258184i	−0.694080	−	0.719898i	$-0.744188\pi$
$227$	0.388994	−	0.388994i	0.0258184	−	0.0258184i	0.719898	+	0.694080i	$0.244188\pi$
$228$	5.64903	+	9.09390i	0.374116	+	0.602258i
$229$			19.6829i			1.30068i	0.759643	+	0.650340i	$0.225374\pi$
$229$			19.6829i			1.30068i	−0.759643	+	0.650340i	$0.774626\pi$
$230$	13.8240	+	9.61242i	0.911526	+	0.633824i
$231$	20.4930	+	3.70297i	1.34834	+	0.243637i
$232$	6.05330	−	1.62198i	0.397419	−	0.106488i
$233$	−5.84244	+	1.56548i	−0.382751	+	0.102558i	−0.445064	−	0.895499i	$-0.646819\pi$
$233$	−5.84244	+	1.56548i	−0.382751	+	0.102558i	0.0623128	+	0.998057i	$0.480152\pi$
$234$	11.7623	+	5.81425i	0.768925	+	0.380089i
$235$	6.70264	−	1.20447i	0.437232	−	0.0785713i
$236$	−7.36804	+	4.25394i	−0.479619	+	0.276908i
$237$	7.75199	−	4.81546i	0.503546	−	0.312798i
$238$	−2.08381	+	2.30696i	−0.135074	+	0.149538i
$239$	10.1819	+	17.6355i	0.658610	+	1.14075i	0.980976	+	0.194131i	$0.0621888\pi$
$239$	10.1819	+	17.6355i	0.658610	+	1.14075i	−0.322365	+	0.946615i	$0.604478\pi$
$240$	−3.24946	−	2.10736i	−0.209752	−	0.136030i
$241$	−9.48551			−0.611016			−0.305508	−	0.952190i	$-0.598826\pi$
$241$	−9.48551			−0.611016			−0.305508	+	0.952190i	$0.598826\pi$
$242$	−9.32235	−	2.49792i	−0.599263	−	0.160572i
$243$	15.3862	−	2.50320i	0.987023	−	0.160580i
$244$			5.89163i			0.377173i
$245$	15.6501	−	0.274865i	0.999846	−	0.0175605i
$246$	−15.4061	+	4.66549i	−0.982255	+	0.297461i
$247$	19.1152	+	19.1152i	1.21627	+	1.21627i
$248$	0.346730	−	0.0929061i	0.0220174	−	0.00589954i
$249$	6.13004	−	1.85639i	0.388476	−	0.117644i
$250$	−5.49489	+	9.73685i	−0.347528	+	0.615812i
$251$			12.4751i			0.787419i	0.919235	+	0.393710i	$0.128808\pi$
$251$			12.4751i			0.787419i	−0.919235	+	0.393710i	$0.871192\pi$
$252$	4.92960	−	6.22086i	0.310535	−	0.391877i
$253$	24.1963	−	24.1963i	1.52121	−	1.52121i
$254$	5.75287	+	9.96427i	0.360967	+	0.625214i
$255$	4.45072	−	0.948914i	0.278715	−	0.0594233i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.74272	−	7.74272i	0.482978	−	0.482978i	−0.423104	−	0.906081i	$-0.639059\pi$
$257$	7.74272	−	7.74272i	0.482978	−	0.482978i	0.906081	+	0.423104i	$0.139059\pi$
$258$	−0.473938	−	14.6880i	−0.0295061	−	0.914437i
$259$	1.28012	+	25.1883i	0.0795430	+	1.56512i
$260$	−9.20082	−	3.31478i	−0.570611	−	0.205574i
$261$	8.33107	−	16.8539i	0.515680	−	1.04323i
$262$	−2.40924	+	8.99141i	−0.148843	+	0.555491i
$263$	6.04074	+	6.04074i	0.372488	+	0.372488i	0.868383	−	0.495895i	$-0.165160\pi$
$263$	6.04074	+	6.04074i	0.372488	+	0.372488i	−0.495895	+	0.868383i	$0.665160\pi$
$264$	−5.38329	+	5.74228i	−0.331319	+	0.353413i
$265$	−0.0288921	−	0.160778i	−0.00177483	−	0.00987653i
$266$	13.7289	−	8.88485i	0.841776	−	0.544765i
$267$	−4.48622	+	8.38366i	−0.274552	+	0.513072i
$268$	−9.24538	−	2.47729i	−0.564751	−	0.151325i
$269$	−1.89941	−	3.28987i	−0.115809	−	0.200587i	0.802294	−	0.596929i	$-0.203613\pi$
$269$	−1.89941	−	3.28987i	−0.115809	−	0.200587i	−0.918103	+	0.396342i	$0.870279\pi$
$270$	−11.1837	+	3.15029i	−0.680620	+	0.191721i
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	0.434452	+	0.900695i	$0.356942\pi$
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	−0.997251	+	0.0741005i	$0.976391\pi$
$272$	−0.304112	−	1.13496i	−0.0184395	−	0.0688172i
$273$	8.54711	−	18.1286i	0.517294	−	1.09719i
$274$	16.1176	−	9.30553i	0.973702	−	0.562167i
$275$	17.5011	+	14.4911i	1.05535	+	0.873847i
$276$	−3.78011	−	12.4824i	−0.227536	−	0.751354i
$277$	−14.0238	−	14.0238i	−0.842611	−	0.842611i	0.146587	−	0.989198i	$-0.453171\pi$
$277$	−14.0238	−	14.0238i	−0.842611	−	0.842611i	−0.989198	+	0.146587i	$0.953171\pi$
$278$	15.8327	−	4.24235i	0.949580	−	0.254439i
$279$	0.477200	−	0.965381i	0.0285692	−	0.0577958i
$280$	−3.12656	+	5.02241i	−0.186848	+	0.300146i
$281$	10.0568	+	5.80629i	0.599938	+	0.346374i	0.769017	−	0.639228i	$-0.220746\pi$
$281$	10.0568	+	5.80629i	0.599938	+	0.346374i	−0.169079	+	0.985602i	$0.554079\pi$
$282$	−4.65097	−	2.48880i	−0.276961	−	0.148206i
$283$	6.71429	+	25.0581i	0.399123	+	1.48955i	0.814643	+	0.579963i	$0.196933\pi$
$283$	6.71429	+	25.0581i	0.399123	+	1.48955i	−0.415520	+	0.909584i	$0.636400\pi$
$284$	6.60103	−	11.4333i	0.391699	−	0.678443i
$285$	−23.9065	−	1.23802i	−1.41610	−	0.0733342i
$286$	−9.93766	+	17.2125i	−0.587626	+	1.01780i
$287$	7.56130	+	23.3971i	0.446330	+	1.38109i
$288$	0.961652	+	2.84169i	0.0566659	+	0.167448i
$289$	−13.5268	−	7.80969i	−0.795693	−	0.459393i
$290$	−4.74966	+	13.1836i	−0.278909	+	0.774167i
$291$	−5.78711	+	1.75253i	−0.339246	+	0.102735i
$292$	−6.71170	−	6.71170i	−0.392772	−	0.392772i
$293$	1.79568	−	6.70156i	0.104905	−	0.391510i	−0.893430	−	0.449203i	$-0.851708\pi$
$293$	1.79568	−	6.70156i	0.104905	−	0.391510i	0.998334	+	0.0576935i	$0.0183746\pi$
$294$	−9.64036	−	7.35279i	−0.562237	−	0.428823i
$295$	1.59607	−	18.9571i	0.0929268	−	1.10373i
$296$	−8.25544	−	4.76628i	−0.479838	−	0.277034i
$297$	2.28142	+	23.5027i	0.132381	+	1.36377i
$298$	4.33316	+	1.16107i	0.251013	+	0.0672588i
$299$	−16.4666	−	28.5209i	−0.952287	−	1.64941i
$300$	8.01696	−	3.27541i	0.462860	−	0.189106i
$301$	−22.4191	+	1.13939i	−1.29221	+	0.0656732i
$302$	−1.14754	−	0.307483i	−0.0660337	−	0.0176937i
$303$	−0.531188	−	16.4623i	−0.0305160	−	0.945735i
$304$			6.18090i			0.354499i
$305$	−10.8162	−	7.52101i	−0.619336	−	0.430652i
$306$	−3.16001	−	1.56203i	−0.180646	−	0.0892954i
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	0.875333	−	0.483520i	$-0.160642\pi$
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	−0.483520	+	0.875333i	$0.660642\pi$
$308$	8.92228	+	8.05924i	0.508394	+	0.459218i
$309$	3.64487	−	3.88793i	0.207349	−	0.221177i
$310$	−0.272058	+	0.755150i	−0.0154519	+	0.0428896i
$311$	−0.815666	−	0.470925i	−0.0462522	−	0.0267037i	0.476696	−	0.879068i	$-0.341834\pi$
$311$	−0.815666	−	0.470925i	−0.0462522	−	0.0267037i	−0.522948	+	0.852365i	$0.675168\pi$
$312$	3.99727	+	6.43487i	0.226301	+	0.364303i
$313$	16.1654	+	4.33150i	0.913720	+	0.244831i	0.684899	−	0.728638i	$-0.259846\pi$
$313$	16.1654	+	4.33150i	0.913720	+	0.244831i	0.228821	+	0.973468i	$0.426513\pi$
$314$	−4.38268			−0.247329
$315$	5.12774	+	16.9914i	0.288915	+	0.957355i
$316$	5.26884			0.296395
$317$	11.6829	+	3.13043i	0.656179	+	0.175823i	0.571521	−	0.820588i	$-0.306354\pi$
$317$	11.6829	+	3.13043i	0.656179	+	0.175823i	0.0846578	+	0.996410i	$0.473020\pi$
$318$	−0.0596997	+	0.111564i	−0.00334779	+	0.00625622i
$319$	24.6633	+	14.2394i	1.38088	+	0.797252i
$320$	−0.951627	−	2.02346i	−0.0531976	−	0.113115i
$321$	6.84273	+	22.5956i	0.381924	+	1.26117i
$322$	−18.9570	+	6.12638i	−1.05643	+	0.341410i
$323$	−5.13540	−	5.13540i	−0.285741	−	0.285741i
$324$	8.30844	+	3.45975i	0.461580	+	0.192208i
$325$	17.8309	−	12.6599i	0.989079	−	0.702247i
$326$		−	17.7963i		−	0.985645i
$327$	−0.716144	+	0.444861i	−0.0396029	+	0.0246009i
$328$	−8.97694	−	2.40536i	−0.495669	−	0.132814i
$329$	−3.66947	+	7.17368i	−0.202305	+	0.395498i
$330$	−3.66997	−	17.2134i	−0.202025	−	0.947564i
$331$	9.07201	+	15.7132i	0.498643	+	0.863674i	0.999999	−	0.00156673i	$-0.000498705\pi$
$331$	9.07201	+	15.7132i	0.498643	+	0.863674i	−0.501356	+	0.865241i	$0.667165\pi$
$332$	3.57191	+	0.957089i	0.196034	+	0.0525271i
$333$	−27.0886	+	9.16701i	−1.48445	+	0.502349i
$334$	11.1725	+	6.45046i	0.611334	+	0.352954i
$335$	16.3502	−	13.8109i	0.893308	−	0.754568i
$336$	4.31281	−	1.54909i	0.235283	−	0.0845100i
$337$	−3.01532	+	11.2533i	−0.164255	+	0.613007i	0.833879	+	0.551947i	$0.186115\pi$
$337$	−3.01532	+	11.2533i	−0.164255	+	0.613007i	−0.998134	+	0.0610603i	$0.980552\pi$
$338$	4.33355	+	4.33355i	0.235714	+	0.235714i
$339$	1.16139	−	4.97037i	0.0630779	−	0.269954i
$340$	2.47185	+	0.890536i	0.134055	+	0.0482961i
$341$	1.41270	+	0.815625i	0.0765022	+	0.0441686i
$342$	13.9297	+	12.2391i	0.753230	+	0.661816i
$343$	−10.9569	+	14.9314i	−0.591617	+	0.806219i
$344$	4.24228	−	7.34784i	0.228728	−	0.396169i
$345$	27.7416	+	8.99478i	1.49356	+	0.484263i
$346$	7.64901	−	13.2485i	0.411213	−	0.712242i
$347$	−2.16636	−	8.08498i	−0.116296	−	0.434024i	0.883084	−	0.469215i	$-0.155463\pi$
$347$	−2.16636	−	8.08498i	−0.116296	−	0.434024i	−0.999381	+	0.0351902i	$0.988796\pi$
$348$	9.22034	−	5.72758i	0.494262	−	0.307030i
$349$	−13.2937	−	7.67509i	−0.711593	−	0.410838i	0.100058	−	0.994982i	$-0.468097\pi$
$349$	−13.2937	−	7.67509i	−0.711593	−	0.410838i	−0.811651	+	0.584143i	$0.801431\pi$
$350$	−5.22923	−	12.1513i	−0.279514	−	0.649517i
$351$	22.4172	+	3.73352i	1.19654	+	0.199281i
$352$	−4.38951	+	1.17617i	−0.233962	+	0.0626899i
$353$	11.9208	+	11.9208i	0.634481	+	0.634481i	0.949189	−	0.314708i	$-0.101907\pi$
$353$	11.9208	+	11.9208i	0.634481	+	0.634481i	−0.314708	+	0.949189i	$0.601907\pi$
$354$	−10.0785	+	10.7506i	−0.535667	+	0.571388i
$355$	12.5634	+	26.7139i	0.666798	+	1.41783i
$356$	−4.75426	+	2.74487i	−0.251975	+	0.145478i
$357$	−2.29623	+	4.87036i	−0.121529	+	0.257767i
$358$	−2.78634	−	10.3988i	−0.147263	−	0.549591i
$359$	14.1397	−	24.4907i	0.746264	−	1.29257i	−0.203337	−	0.979109i	$-0.565179\pi$
$359$	14.1397	−	24.4907i	0.746264	−	1.29257i	0.949602	−	0.313459i	$-0.101488\pi$
$360$	−6.44457	−	1.86212i	−0.339659	−	0.0981425i
$361$	9.60175	+	16.6307i	0.505355	+	0.875301i
$362$	0.203320	+	0.0544794i	0.0106863	+	0.00286337i
$363$	−16.7077	+	0.539106i	−0.876926	+	0.0282957i
$364$	9.71464	−	6.28694i	0.509186	−	0.329525i
$365$	20.8896	−	3.75390i	1.09341	−	0.196488i
$366$	2.95766	+	9.76659i	0.154599	+	0.510508i
$367$	−13.9010	−	13.9010i	−0.725627	−	0.725627i	0.244118	−	0.969745i	$-0.421502\pi$
$367$	−13.9010	−	13.9010i	−0.725627	−	0.725627i	−0.969745	+	0.244118i	$0.921502\pi$
$368$	1.94889	−	7.27337i	0.101593	−	0.379151i
$369$	−23.1966	+	15.4680i	−1.20757	+	0.805232i
$370$	19.2888	−	9.07144i	1.00278	−	0.471602i
$371$	0.172077	+	0.0880207i	0.00893380	+	0.00456981i
$372$	0.528136	−	0.328073i	0.0273826	−	0.0170098i
$373$	3.80852	−	3.80852i	0.197198	−	0.197198i	−0.601600	−	0.798798i	$-0.705470\pi$
$373$	3.80852	−	3.80852i	0.197198	−	0.197198i	0.798798	+	0.601600i	$0.205470\pi$
$374$	2.66981	−	4.62424i	0.138053	−	0.239114i
$375$	−4.22092	+	18.8993i	−0.217967	+	0.975956i
$376$	−1.52276	−	2.63750i	−0.0785305	−	0.136019i
$377$	19.3809	−	19.3809i	0.998169	−	0.998169i
$378$	5.04888	−	12.7871i	0.259687	−	0.657695i
$379$			19.4353i			0.998326i	0.866508	+	0.499163i	$0.166359\pi$
$379$			19.4353i			0.998326i	−0.866508	+	0.499163i	$0.833641\pi$
$380$	−11.3473	−	7.89027i	−0.582104	−	0.404763i
$381$	14.5387	+	13.6298i	0.744842	+	0.698277i
$382$	−20.8910	+	5.59773i	−1.06888	+	0.286405i
$383$	10.1754	+	10.1754i	0.519938	+	0.519938i	0.917553	−	0.397615i	$-0.130162\pi$
$383$	10.1754	+	10.1754i	0.519938	+	0.519938i	−0.397615	+	0.917553i	$0.630162\pi$
$384$	−0.394099	+	1.68662i	−0.0201113	+	0.0860700i
$385$	−26.1855	+	6.09201i	−1.33454	+	0.310478i
$386$		−	21.5752i		−	1.09815i
$387$	−8.15919	−	24.1105i	−0.414755	−	1.22561i
$388$	−3.37208	−	0.903546i	−0.171191	−	0.0458706i
$389$	−6.29071			−0.318952			−0.159476	−	0.987202i	$-0.550980\pi$
$389$	−6.29071			−0.318952			−0.159476	+	0.987202i	$0.550980\pi$
$390$	−16.9163	−	0.876029i	−0.856590	−	0.0443594i
$391$	4.42384	+	7.66232i	0.223723	+	0.387500i
$392$	−2.48789	−	6.54296i	−0.125658	−	0.330470i
$393$	0.519968	+	16.1146i	0.0262289	+	0.812872i
$394$	−4.52674	+	2.61352i	−0.228054	+	0.131667i
$395$	−6.72598	+	9.67288i	−0.338421	+	0.486695i
$396$	−6.04123	+	12.2215i	−0.303583	+	0.614152i
$397$	−14.9394	+	4.00301i	−0.749788	+	0.200905i	−0.613424	−	0.789754i	$-0.710208\pi$
$397$	−14.9394	+	4.00301i	−0.749788	+	0.200905i	−0.136364	+	0.990659i	$0.543542\pi$
$398$	−4.26234	+	1.14209i	−0.213652	+	0.0572478i
$399$	18.2983	−	21.6205i	0.916059	−	1.08238i
$400$	4.92961	+	0.836011i	0.246481	+	0.0418005i
$401$			6.08822i			0.304031i	0.988378	+	0.152015i	$0.0485764\pi$
$401$			6.08822i			0.304031i	−0.988378	+	0.152015i	$0.951424\pi$
$402$	−16.5697	+	0.534654i	−0.826423	+	0.0266661i
$403$	1.11013	−	1.11013i	0.0552995	−	0.0552995i
$404$	4.75473	−	8.23544i	0.236557	−	0.409728i
$405$	−16.9578	+	10.8366i	−0.842642	+	0.538475i
$406$	−9.00838	−	13.9198i	−0.447078	−	0.690830i
$407$	−11.2119	−	41.8433i	−0.555752	−	2.07410i
$408$	−1.07389	−	1.72876i	−0.0531655	−	0.0855866i
$409$	−1.46766	−	0.847356i	−0.0725713	−	0.0418991i	0.463275	−	0.886214i	$-0.346674\pi$
$409$	−1.46766	−	0.847356i	−0.0725713	−	0.0418991i	−0.535847	+	0.844315i	$0.680007\pi$
$410$	15.8755	−	13.4099i	0.784036	−	0.662266i
$411$	22.0468	−	23.5170i	1.08749	−	1.16001i
$412$	2.97201	−	0.796349i	0.146421	−	0.0392333i
$413$	16.7042	+	15.0884i	0.821958	+	0.742451i
$414$	−12.5326	−	18.7945i	−0.615944	−	0.923701i
$415$	−6.31683	+	5.33576i	−0.310081	+	0.261922i
$416$			4.37362i			0.214434i
$417$	24.1162	−	14.9807i	1.18097	−	0.733609i
$418$	−19.8614	+	19.8614i	−0.971452	+	0.971452i
$419$	2.28863	+	3.96402i	0.111807	+	0.193655i	0.916499	−	0.400037i	$-0.131003\pi$
$419$	2.28863	+	3.96402i	0.111807	+	0.193655i	−0.804692	+	0.593693i	$0.797670\pi$
$420$	−2.66162	+	9.89524i	−0.129874	+	0.482838i
$421$	5.63946	−	9.76784i	0.274851	−	0.476055i	−0.695247	−	0.718771i	$-0.744705\pi$
$421$	5.63946	−	9.76784i	0.274851	−	0.476055i	0.970097	+	0.242716i	$0.0780383\pi$
$422$	3.67152	+	13.7023i	0.178727	+	0.667018i
$423$	−8.95935	−	1.79087i	−0.435618	−	0.0870749i
$424$	−0.0632666	+	0.0365270i	−0.00307250	+	0.00177391i
$425$	−4.79037	+	3.40117i	−0.232367	+	0.164981i
$426$	5.20292	−	22.2669i	0.252082	−	1.07883i
$427$	14.8325	−	4.79344i	0.717794	−	0.231971i
$428$	−3.52788	+	13.1662i	−0.170526	+	0.636413i
$429$	−7.83284	+	33.5221i	−0.378173	+	1.61846i
$430$	8.07413	+	17.1682i	0.389369	+	0.827924i
$431$	1.92684	−	1.11246i	0.0928126	−	0.0535854i	−0.452875	−	0.891574i	$-0.649602\pi$
$431$	1.92684	−	1.11246i	0.0928126	−	0.0535854i	0.545688	+	0.837988i	$0.316268\pi$
$432$	3.02069	+	4.22793i	0.145333	+	0.203416i
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.0446415	−	0.999003i	$-0.485785\pi$
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.999003	−	0.0446415i	$-0.0142146\pi$
$434$	−0.515996	−	0.797321i	−0.0247686	−	0.0382727i
$435$	−1.25524	+	24.2389i	−0.0601840	+	1.16217i
$436$	−0.486746			−0.0233109
$437$	−12.0459	−	44.9560i	−0.576234	−	2.15054i
$438$	−14.4954	−	7.75668i	−0.692615	−	0.370628i
$439$	12.4395	−	7.18196i	0.593706	−	0.342776i	−0.172856	−	0.984947i	$-0.555299\pi$
$439$	12.4395	−	7.18196i	0.593706	−	0.342776i	0.766562	+	0.642171i	$0.221966\pi$
$440$	3.44419	−	9.56000i	0.164195	−	0.455755i
$441$	−19.6720	−	7.34920i	−0.936764	−	0.349962i
$442$	−3.63382	−	3.63382i	−0.172843	−	0.172843i
$443$	−2.46956	+	9.21653i	−0.117332	+	0.437891i	−0.999451	−	0.0331371i	$-0.989450\pi$
$443$	−2.46956	+	9.21653i	−0.117332	+	0.437891i	0.882118	+	0.471028i	$0.156117\pi$
$444$	−16.0778	−	3.75677i	−0.763019	−	0.178289i
$445$	1.02987	−	12.2322i	0.0488206	−	0.579861i
$446$			2.37126i			0.112282i
$447$	7.76597	−	0.250584i	0.367318	−	0.0118522i
$448$	2.58706	+	0.554174i	0.122227	+	0.0261823i
$449$	−40.8669			−1.92863			−0.964313	−	0.264764i	$-0.914706\pi$
$449$	−40.8669			−1.92863			−0.964313	+	0.264764i	$0.914706\pi$
$450$	11.6455	−	9.45425i	0.548973	−	0.445678i
$451$	−21.1168	−	36.5753i	−0.994350	−	1.72226i
$452$	2.08380	−	2.08380i	0.0980139	−	0.0980139i
$453$	−2.05665	+	0.0663617i	−0.0966297	+	0.00311794i
$454$	0.476418	−	0.275060i	0.0223594	−	0.0129092i
$455$	−0.859325	+	25.8604i	−0.0402858	+	1.21236i
$456$	3.10287	+	10.2461i	0.145305	+	0.479818i
$457$	−6.01924	+	22.4641i	−0.281568	+	1.05083i	0.669742	+	0.742594i	$0.266405\pi$
$457$	−6.01924	+	22.4641i	−0.281568	+	1.05083i	−0.951311	+	0.308234i	$0.900262\pi$
$458$	−5.09430	+	19.0122i	−0.238041	+	0.888381i
$459$	−6.02252	−	1.00303i	−0.281107	−	0.0468175i
$460$	10.8651	+	12.8628i	0.506586	+	0.599731i
$461$	−15.9837	−	9.22818i	−0.744434	−	0.429799i	0.0792453	−	0.996855i	$-0.474749\pi$
$461$	−15.9837	−	9.22818i	−0.744434	−	0.429799i	−0.823679	+	0.567056i	$0.808082\pi$
$462$	18.8363	+	8.88077i	0.876345	+	0.413171i
$463$	17.9673	+	4.81433i	0.835012	+	0.223741i	0.650899	−	0.759164i	$-0.274392\pi$
$463$	17.9673	+	4.81433i	0.835012	+	0.223741i	0.184113	+	0.982905i	$0.441059\pi$
$464$	6.26684			0.290931
$465$	−0.0718993	+	1.38839i	−0.00333425	+	0.0643851i
$466$	−6.04854			−0.280193
$467$	0.760775	+	2.83925i	0.0352045	+	0.131385i	0.981292	−	0.192527i	$-0.0616684\pi$
$467$	0.760775	+	2.83925i	0.0352045	+	0.131385i	−0.946087	+	0.323912i	$0.895002\pi$
$468$	9.85667	+	8.66044i	0.455625	+	0.400329i
$469$	1.28535	+	25.2912i	0.0593521	+	1.16784i
$470$	6.78600	+	0.571338i	0.313015	+	0.0263539i
$471$	−7.26520	+	2.20015i	−0.334763	+	0.101378i
$472$	−8.21798	+	2.20200i	−0.378263	+	0.101355i
$473$	37.2431	−	9.97925i	1.71244	−	0.458847i
$474$	8.73418	−	2.64501i	0.401174	−	0.121489i
$475$	28.9710	−	10.7597i	1.32928	−	0.493689i
$476$	−2.60990	+	1.68902i	−0.119624	+	0.0774163i
$477$	−0.0429581	+	0.214911i	−0.00196691	+	0.00984008i
$478$	5.27052	+	19.6699i	0.241068	+	0.899679i
$479$	−0.235352			−0.0107535			−0.00537676	−	0.999986i	$-0.501711\pi$
$479$	−0.235352			−0.0107535			−0.00537676	+	0.999986i	$0.501711\pi$
$480$	−2.59332	−	2.87658i	−0.118368	−	0.131297i
$481$	−41.6918			−1.90098
$482$	−9.16230	−	2.45503i	−0.417331	−	0.111824i
$483$	−28.3496	+	19.6723i	−1.28995	+	0.895123i
$484$	−8.35819	−	4.82560i	−0.379918	−	0.219346i
$485$	5.96344	−	5.03726i	0.270786	−	0.228730i
$486$	15.5098	+	1.56433i	0.703537	+	0.0709592i
$487$	3.92751	−	14.6577i	0.177973	−	0.664202i	−0.818054	−	0.575142i	$-0.804947\pi$
$487$	3.92751	−	14.6577i	0.177973	−	0.664202i	0.996026	−	0.0890606i	$-0.0283865\pi$
$488$	−1.52487	+	5.69088i	−0.0690275	+	0.257614i
$489$	−8.93392	−	29.5010i	−0.404006	−	1.33408i
$490$	15.1879	+	3.78504i	0.686121	+	0.170990i
$491$	−2.37876	+	1.37337i	−0.107352	+	0.0619795i	−0.552715	−	0.833371i	$-0.686408\pi$
$491$	−2.37876	+	1.37337i	−0.107352	+	0.0619795i	0.445363	+	0.895350i	$0.353075\pi$
$492$	−16.0886	+	0.519131i	−0.725332	+	0.0234042i
$493$	−5.20680	+	5.20680i	−0.234502	+	0.234502i
$494$	13.5165	+	23.4112i	0.608134	+	1.05332i
$495$	−14.7250	−	26.6923i	−0.661839	−	1.19973i
$496$	0.358961			0.0161178
$497$	−34.1545	−	7.31624i	−1.53204	−	0.328178i
$498$	6.40163	−	0.206561i	0.286864	−	0.00925622i
$499$			34.6887i			1.55288i	0.630192	+	0.776439i	$0.282976\pi$
$499$			34.6887i			1.55288i	−0.630192	+	0.776439i	$0.717024\pi$
$500$	−7.82774	+	7.98289i	−0.350067	+	0.357006i
$501$	21.7590	+	5.08424i	0.972119	+	0.227147i
$502$	−3.22879	+	12.0500i	−0.144108	+	0.537817i
$503$	−23.1452	−	23.1452i	−1.03199	−	1.03199i	−0.999471	−	0.0325210i	$-0.989646\pi$
$503$	−23.1452	−	23.1452i	−1.03199	−	1.03199i	−0.0325210	−	0.999471i	$-0.510354\pi$
$504$	6.37170	−	4.73301i	0.283818	−	0.210825i
$505$	9.04946	+	19.2421i	0.402696	+	0.856260i
$506$	29.6343	−	17.1094i	1.31741	−	0.760606i
$507$	9.35924	+	5.00826i	0.415658	+	0.222425i
$508$	2.97791	+	11.1137i	0.132123	+	0.493091i
$509$	37.4631			1.66052			0.830262	−	0.557373i	$-0.188191\pi$
$509$	37.4631			1.66052			0.830262	+	0.557373i	$0.188191\pi$
$510$	4.54466	+	0.235350i	0.201241	+	0.0104215i
$511$	−11.4364	+	22.3577i	−0.505916	+	0.989046i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	29.2354	+	13.2960i	1.29078	+	0.587034i
$514$	9.48286	−	5.47493i	0.418271	−	0.241489i
$515$	−2.33196	+	6.47280i	−0.102758	+	0.285226i
$516$	3.34375	−	14.3102i	0.147201	−	0.629972i
$517$	3.58205	−	13.3684i	0.157538	−	0.587941i
$518$	−5.28270	+	24.6613i	−0.232109	+	1.08356i
$519$	6.02893	−	25.8019i	0.264641	−	1.13258i
$520$	−8.02938	−	5.58318i	−0.352112	−	0.244839i
$521$	28.8826	−	16.6754i	1.26537	−	0.730562i	0.291263	−	0.956643i	$-0.405925\pi$
$521$	28.8826	−	16.6754i	1.26537	−	0.730562i	0.974109	+	0.226081i	$0.0725913\pi$
$522$	12.4093	−	14.1233i	0.543140	−	0.618162i
$523$	10.4614	+	39.0426i	0.457447	+	1.70722i	0.680793	+	0.732476i	$0.261635\pi$
$523$	10.4614	+	39.0426i	0.457447	+	1.70722i	−0.223346	+	0.974739i	$0.571698\pi$
$524$	−4.65430	+	8.06148i	−0.203324	+	0.352167i
$525$	−14.7686	−	17.5182i	−0.644555	−	0.764558i
$526$	4.27144	+	7.39836i	0.186244	+	0.322584i
$527$	−0.298243	+	0.298243i	−0.0129917	+	0.0129917i
$528$	−6.68607	+	4.15332i	−0.290974	+	0.180750i
$529$			33.7001i			1.46522i
$530$	0.0137049	−	0.162778i	0.000595301	−	0.00707061i
$531$	−11.3103	+	22.8809i	−0.490825	+	0.992944i
$532$	15.5607	−	5.02879i	0.674642	−	0.218026i
$533$	−39.2618	+	10.5202i	−1.70062	+	0.455679i
$534$	−6.50321	+	6.93688i	−0.281421	+	0.300188i
$535$	−19.6679	−	23.2841i	−0.850316	−	1.00666i
$536$	−8.28918	−	4.78576i	−0.358038	−	0.206713i
$537$	−9.83921	−	15.8393i	−0.424593	−	0.683516i
$538$	−0.983206	−	3.66937i	−0.0423890	−	0.158198i
$539$	13.0304	−	29.0193i	0.561257	−	1.24995i
$540$	−11.6180	+	0.148389i	−0.499959	+	0.00638563i
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	−0.295010	−	0.955494i	$-0.595323\pi$
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	0.974987	−	0.222261i	$-0.0713438\pi$
$542$	−13.1024	+	13.1024i	−0.562798	+	0.562798i
$543$	0.364393	−	0.0117579i	0.0156376	−	0.000504578i
$544$		−	1.17500i		−	0.0503777i
$545$	0.621359	−	0.893599i	0.0266161	−	0.0382776i
$546$	12.9479	−	15.2987i	0.554119	−	0.654726i
$547$	−20.4222	+	5.47211i	−0.873190	+	0.233971i	−0.667467	−	0.744640i	$-0.732621\pi$
$547$	−20.4222	+	5.47211i	−0.873190	+	0.233971i	−0.205723	+	0.978610i	$0.565955\pi$
$548$	17.9769	−	4.81689i	0.767935	−	0.205768i
$549$	9.80585	+	14.7053i	0.418504	+	0.627609i
$550$	13.1542	+	18.5270i	0.560896	+	0.789992i
$551$	33.5452	−	19.3673i	1.42907	−	0.825076i
$552$	−0.420615	−	13.0355i	−0.0179025	−	0.554826i
$553$	−4.28674	−	13.2646i	−0.182291	−	0.564067i
$554$	−9.91635	−	17.1756i	−0.421305	−	0.729722i
$555$	27.4212	−	24.7209i	1.16396	−	1.04935i
$556$	16.3912			0.695141
$557$	−1.68142	−	0.450534i	−0.0712439	−	0.0190898i	0.223021	−	0.974814i	$-0.428408\pi$
$557$	−1.68142	−	0.450534i	−0.0712439	−	0.0190898i	−0.294265	+	0.955724i	$0.595075\pi$
$558$	0.710799	−	0.808978i	0.0300905	−	0.0342468i
$559$		−	37.1082i		−	1.56951i
$560$	−4.31992	+	4.04206i	−0.182550	+	0.170808i
$561$	2.10434	−	9.00590i	0.0888452	−	0.380230i
$562$	8.21134	+	8.21134i	0.346374	+	0.346374i
$563$	13.3204	−	3.56920i	0.561390	−	0.150424i	0.0330450	−	0.999454i	$-0.489480\pi$
$563$	13.3204	−	3.56920i	0.561390	−	0.150424i	0.528345	+	0.849030i	$0.322813\pi$
$564$	−3.84835	−	3.60776i	−0.162045	−	0.151914i
$565$	1.16549	+	6.48568i	0.0490324	+	0.272855i
$566$			25.9420i			1.09042i
$567$	1.95033	−	23.7318i	0.0819061	−	0.996640i
$568$	9.33527	−	9.33527i	0.391699	−	0.391699i
$569$	−8.34560	−	14.4550i	−0.349866	−	0.605985i	0.636360	−	0.771393i	$-0.280439\pi$
$569$	−8.34560	−	14.4550i	−0.349866	−	0.605985i	−0.986225	+	0.165407i	$0.947106\pi$
$570$	−22.7715	−	7.38329i	−0.953792	−	0.309252i
$571$	−10.1607	+	17.5989i	−0.425214	+	0.736492i	−0.996440	−	0.0843004i	$-0.973134\pi$
$571$	−10.1607	+	17.5989i	−0.425214	+	0.736492i	0.571226	+	0.820793i	$0.306468\pi$
$572$	−14.0540	+	14.0540i	−0.587626	+	0.587626i
$573$	−31.8210	+	19.7669i	−1.32934	+	0.825774i
$574$	1.24804	+	24.5569i	0.0520920	+	1.02499i
$575$	−37.4842	+	3.52668i	−1.56320	+	0.147073i
$576$	0.193400	+	2.99376i	0.00805834	+	0.124740i
$577$	−5.50888	+	20.5594i	−0.229338	+	0.855900i	0.751282	+	0.659981i	$0.229436\pi$
$577$	−5.50888	+	20.5594i	−0.229338	+	0.855900i	−0.980620	+	0.195919i	$0.937231\pi$
$578$	−11.0446	−	11.0446i	−0.459393	−	0.459393i
$579$	−10.8310	−	35.7653i	−0.450119	−	1.48635i
$580$	−7.99998	+	11.5051i	−0.332181	+	0.477722i
$581$	−0.496590	−	9.77114i	−0.0206020	−	0.405375i
$582$	−6.04350	+	0.195005i	−0.250511	+	0.00808323i
$583$	−0.320672	−	0.0859237i	−0.0132809	−	0.00355860i
$584$	−4.74589	−	8.22012i	−0.196386	−	0.340151i
$585$	−28.4820	+	7.03995i	−1.17759	+	0.291066i
$586$	3.46898	−	6.00846i	0.143302	−	0.248207i
$587$	−0.793359	−	2.96086i	−0.0327455	−	0.122208i	0.947618	−	0.319405i	$-0.103483\pi$
$587$	−0.793359	−	2.96086i	−0.0327455	−	0.122208i	−0.980364	+	0.197197i	$0.936816\pi$
$588$	−7.40883	−	9.59736i	−0.305535	−	0.395788i
$589$	1.92145	−	1.10935i	0.0791721	−	0.0457101i
$590$	6.44815	−	17.8981i	0.265466	−	0.736852i
$591$	−6.19199	+	6.60491i	−0.254704	+	0.271690i
$592$	−6.74054	−	6.74054i	−0.277034	−	0.277034i
$593$	23.6708	−	6.34257i	0.972042	−	0.260458i	0.262352	−	0.964972i	$-0.415502\pi$
$593$	23.6708	−	6.34257i	0.972042	−	0.260458i	0.709690	+	0.704514i	$0.248835\pi$
$594$	−3.87927	+	23.2924i	−0.159168	+	0.955697i
$595$	0.230863	−	6.94755i	0.00946444	−	0.284822i
$596$	3.88501	+	2.24301i	0.159136	+	0.0918772i
$597$	−6.49236	+	4.03299i	−0.265715	+	0.165059i
$598$	−8.52373	−	31.8110i	−0.348561	−	1.30085i
$599$	−14.9433	+	25.8825i	−0.610565	+	1.05753i	0.380580	+	0.924748i	$0.375724\pi$
$599$	−14.9433	+	25.8825i	−0.610565	+	1.05753i	−0.991145	+	0.132782i	$0.957609\pi$
$600$	8.59153	−	1.08886i	0.350748	−	0.0444524i
$601$	0.0345488	−	0.0598402i	0.00140927	−	0.00244093i	−0.865320	−	0.501220i	$-0.832885\pi$
$601$	0.0345488	−	0.0598402i	0.00140927	−	0.00244093i	0.866729	+	0.498779i	$0.166218\pi$
$602$	−21.9501	−	4.70192i	−0.894618	−	0.191636i
$603$	−27.1993	+	9.20447i	−1.10764	+	0.374835i
$604$	−1.02886	−	0.594012i	−0.0418637	−	0.0241700i
$605$	19.5289	−	9.18435i	0.793961	−	0.373397i
$606$	3.74767	−	16.0388i	0.152239	−	0.651534i
$607$	26.6712	+	26.6712i	1.08255	+	1.08255i	0.996271	+	0.0862787i	$0.0274976\pi$
$607$	26.6712	+	26.6712i	1.08255	+	1.08255i	0.0862787	+	0.996271i	$0.472502\pi$
$608$	−1.59973	+	5.97029i	−0.0648778	+	0.242127i
$609$	−21.9211	−	18.5527i	−0.888289	−	0.751793i
$610$	−8.50111	−	10.0642i	−0.344200	−	0.407487i
$611$	−11.5354	−	6.65999i	−0.466674	−	0.269434i
$612$	−2.64805	−	2.32668i	−0.107041	−	0.0940504i
$613$	−36.4169	−	9.75789i	−1.47087	−	0.394117i	−0.567638	−	0.823278i	$-0.692143\pi$
$613$	−36.4169	−	9.75789i	−1.47087	−	0.394117i	−0.903228	+	0.429161i	$0.858809\pi$
$614$	4.85438	+	8.40804i	0.195907	+	0.339321i
$615$	19.5850	−	30.1993i	0.789745	−	1.21775i
$616$	6.53237	+	10.0939i	0.263197	+	0.406694i
$617$	20.1462	+	5.39816i	0.811056	+	0.217322i	0.640433	−	0.768014i	$-0.278755\pi$
$617$	20.1462	+	5.39816i	0.811056	+	0.217322i	0.170624	+	0.985336i	$0.445422\pi$
$618$	4.52695	−	2.81209i	0.182100	−	0.113119i
$619$		−	31.3473i		−	1.25995i	−0.776614	−	0.629977i	$-0.783064\pi$
$619$		−	31.3473i		−	1.25995i	0.776614	−	0.629977i	$-0.216936\pi$
$620$	−0.458235	+	0.659005i	−0.0184032	+	0.0264663i
$621$	−30.2104	−	24.8643i	−1.21230	−	0.997770i
$622$	−0.665989	−	0.665989i	−0.0267037	−	0.0267037i
$623$	10.7784	+	9.73585i	0.431829	+	0.390059i
$624$	2.19560	+	7.25017i	0.0878944	+	0.290239i
$625$	−4.66294	−	24.5613i	−0.186518	−	0.982452i
$626$	14.4935	+	8.36781i	0.579276	+	0.334445i
$627$	−22.9537	+	42.8949i	−0.916682	+	1.71306i
$628$	−4.23335	−	1.13432i	−0.168929	−	0.0452644i
$629$	11.2007			0.446603
$630$	0.555329	+	17.7395i	0.0221248	+	0.706761i
$631$	1.35271			0.0538504			0.0269252	−	0.999637i	$-0.491428\pi$
$631$	1.35271			0.0538504			0.0269252	+	0.999637i	$0.491428\pi$
$632$	5.08931	+	1.36368i	0.202442	+	0.0542441i
$633$	12.9650	+	20.8712i	0.515312	+	0.829557i
$634$	10.4746	+	6.04753i	0.416001	+	0.240178i
$635$	−24.2047	−	8.72024i	−0.960535	−	0.346052i
$636$	−0.0865405	+	0.0923115i	−0.00343155	+	0.00366039i
$637$	−23.7315	−	19.3420i	−0.940278	−	0.766359i
$638$	20.1375	+	20.1375i	0.797252	+	0.797252i
$639$	−2.55328	−	39.5238i	−0.101006	−	1.56354i
$640$	−0.395490	−	2.20082i	−0.0156331	−	0.0869949i
$641$		−	30.0591i		−	1.18726i	−0.804737	−	0.593632i	$-0.797694\pi$
$641$		−	30.0591i		−	1.18726i	0.804737	−	0.593632i	$-0.202306\pi$
$642$	0.761394	+	23.5967i	0.0300498	+	0.931289i
$643$	−36.7798	−	9.85511i	−1.45045	−	0.388648i	−0.554272	−	0.832336i	$-0.687003\pi$
$643$	−36.7798	−	9.85511i	−1.45045	−	0.388648i	−0.896181	+	0.443688i	$0.853670\pi$
$644$	−19.8967	+	1.01119i	−0.784040	+	0.0398466i
$645$	22.0031	+	24.4065i	0.866372	+	0.961005i
$646$	−3.63127	−	6.28955i	−0.142871	−	0.247459i
$647$	28.5483	+	7.64948i	1.12235	+	0.300732i	0.771833	−	0.635825i	$-0.219340\pi$
$647$	28.5483	+	7.64948i	1.12235	+	0.300732i	0.350515	+	0.936557i	$0.386007\pi$
$648$	7.12989	+	5.49224i	0.280088	+	0.215756i
$649$	−33.4830	−	19.3314i	−1.31432	−	0.758825i
$650$	20.4999	−	7.61360i	0.804074	−	0.298630i
$651$	−1.25563	−	1.06269i	−0.0492121	−	0.0416500i
$652$	4.60602	−	17.1899i	0.180386	−	0.673208i
$653$	−19.4926	−	19.4926i	−0.762806	−	0.762806i	0.214023	−	0.976829i	$-0.431343\pi$
$653$	−19.4926	−	19.4926i	−0.762806	−	0.762806i	−0.976829	+	0.214023i	$0.931343\pi$
$654$	−0.806881	+	0.244351i	−0.0315515	+	0.00955489i
$655$	−8.85830	−	18.8356i	−0.346123	−	0.735968i
$656$	−8.04851	−	4.64681i	−0.314241	−	0.181427i
$657$	−27.9230	−	5.58147i	−1.08938	−	0.217754i
$658$	−5.40112	+	5.97951i	−0.210558	+	0.233106i
$659$	−16.0689	+	27.8321i	−0.625954	+	1.08418i	0.362402	+	0.932022i	$0.381957\pi$
$659$	−16.0689	+	27.8321i	−0.625954	+	1.08418i	−0.988356	+	0.152162i	$0.951377\pi$
$660$	0.910227	−	17.5767i	0.0354305	−	0.684171i
$661$	−3.58598	+	6.21110i	−0.139479	+	0.241584i	−0.927299	−	0.374321i	$-0.877876\pi$
$661$	−3.58598	+	6.21110i	−0.139479	+	0.241584i	0.787821	+	0.615904i	$0.211209\pi$
$662$	4.69602	+	17.5258i	0.182516	+	0.681158i
$663$	−7.84802	−	4.19959i	−0.304792	−	0.163099i
$664$	3.20248	+	1.84895i	0.124280	+	0.0717534i
$665$	−10.6320	+	34.9869i	−0.412290	+	1.35673i
$666$	−28.5382	+	1.84360i	−1.10583	+	0.0714380i
$667$	−45.5810	+	12.2134i	−1.76490	+	0.472905i
$668$	9.12233	+	9.12233i	0.352954	+	0.352954i
$669$	1.19040	+	3.93085i	0.0460234	+	0.151976i
$670$	19.3676	−	9.10851i	0.748236	−	0.351892i
$671$	−23.1867	+	13.3868i	−0.895113	+	0.516794i
$672$	4.56679	−	0.380074i	0.176168	−	0.0146617i
$673$	11.7689	+	43.9221i	0.453658	+	1.69307i	0.692004	+	0.721894i	$0.256728\pi$
$673$	11.7689	+	43.9221i	0.453658	+	1.69307i	−0.238346	+	0.971180i	$0.576605\pi$
$674$	−5.82514	+	10.0894i	−0.224376	+	0.388631i
$675$	14.5586	−	21.5185i	0.560362	−	0.828248i
$676$	3.06428	+	5.30750i	0.117857	+	0.204134i
$677$	9.97669	+	2.67325i	0.383435	+	0.102741i	0.445387	−	0.895338i	$-0.353066\pi$
$677$	9.97669	+	2.67325i	0.383435	+	0.102741i	−0.0619522	+	0.998079i	$0.519733\pi$
$678$	2.40824	−	4.50042i	0.0924879	−	0.172838i
$679$	0.468809	+	9.22450i	0.0179913	+	0.354004i
$680$	2.15714	+	1.49995i	0.0827225	+	0.0575206i
$681$	0.651677	−	0.695135i	0.0249723	−	0.0266376i
$682$	1.15347	+	1.15347i	0.0441686	+	0.0441686i
$683$	0.809428	−	3.02083i	0.0309719	−	0.115589i	−0.948709	−	0.316150i	$-0.897610\pi$
$683$	0.809428	−	3.02083i	0.0309719	−	0.115589i	0.979681	+	0.200561i	$0.0642765\pi$
$684$	10.2873	+	15.4273i	0.393345	+	0.589879i
$685$	−14.1054	+	39.1522i	−0.538939	+	1.49593i
$686$	−14.4481	+	11.5868i	−0.551630	+	0.442385i
$687$	1.09946	+	34.0740i	0.0419471	+	1.30000i
$688$	5.99949	−	5.99949i	0.228728	−	0.228728i
$689$	−0.159755	+	0.276704i	−0.00608619	+	0.0105416i
$690$	24.4683	+	15.8683i	0.931492	+	0.604097i
$691$	−15.4143	−	26.6983i	−0.586386	−	1.01565i	−0.994701	−	0.102809i	$-0.967217\pi$
$691$	−15.4143	−	26.6983i	−0.586386	−	1.01565i	0.408315	−	0.912841i	$-0.366117\pi$
$692$	10.8173	−	10.8173i	0.411213	−	0.411213i
$693$	35.6833	+	5.26567i	1.35550	+	0.200026i
$694$		−	8.37019i		−	0.317728i
$695$	−20.9243	+	30.0920i	−0.793703	+	1.14145i
$696$	10.3886	−	3.14602i	0.393778	−	0.119249i
$697$	10.5479	−	2.82630i	0.399530	−	0.107054i
$698$	−10.8542	−	10.8542i	−0.410838	−	0.410838i
$699$	−10.0267	+	3.03643i	−0.379244	+	0.114848i
$700$	−1.90604	−	13.0907i	−0.0720417	−	0.494783i
$701$		−	40.5025i		−	1.52976i	−0.644174	−	0.764879i	$-0.722799\pi$
$701$		−	40.5025i		−	1.52976i	0.644174	−	0.764879i	$-0.277201\pi$
$702$	20.6871	+	9.40831i	0.780783	+	0.355094i
$703$	−56.9122	−	15.2496i	−2.14648	−	0.575148i
$704$	−4.54436			−0.171272
$705$	11.5360	−	2.45953i	0.434471	−	0.0926312i
$706$	8.42929	+	14.6000i	0.317240	+	0.549477i
$707$	−24.6016	−	5.26990i	−0.925237	−	0.198195i
$708$	−12.5176	+	7.77578i	−0.470439	+	0.292232i
$709$	−11.6317	+	6.71555i	−0.436837	+	0.252208i	−0.702255	−	0.711926i	$-0.747823\pi$
$709$	−11.6317	+	6.71555i	−0.436837	+	0.252208i	0.265418	+	0.964133i	$0.414490\pi$
$710$	5.22128	+	29.0553i	0.195951	+	1.09043i
$711$	13.1509	−	8.76930i	0.493196	−	0.328874i
$712$	−5.30269	+	1.42085i	−0.198727	+	0.0532487i
$713$	−2.61086	+	0.699578i	−0.0977775	+	0.0261994i
$714$	−3.47853	+	4.11010i	−0.130181	+	0.153817i
$715$	−7.86048	−	43.7419i	−0.293965	−	1.63585i
$716$		−	10.7656i		−	0.402329i
$717$	18.6114	+	29.9610i	0.695057	+	1.11891i
$718$	19.9965	−	19.9965i	0.746264	−	0.746264i
$719$	−2.12346	+	3.67795i	−0.0791919	+	0.137164i	−0.902901	−	0.429848i	$-0.858567\pi$
$719$	−2.12346	+	3.67795i	−0.0791919	+	0.137164i	0.823710	+	0.567012i	$0.191901\pi$
$720$	−5.74302	−	3.46665i	−0.214030	−	0.129194i
$721$	−4.42288	−	6.83428i	−0.164717	−	0.254522i
$722$	4.97023	+	18.5492i	0.184973	+	0.690328i
$723$	−16.4208	+	0.529850i	−0.610698	+	0.0197053i
$724$	0.182292	+	0.105246i	0.00677481	+	0.00391144i
$725$	−10.9093	−	29.3738i	−0.405162	−	1.09091i
$726$	−16.2779	−	3.80353i	−0.604130	−	0.141162i
$727$	13.0179	−	3.48815i	0.482809	−	0.129368i	−0.00920135	−	0.999958i	$-0.502929\pi$
$727$	13.0179	−	3.48815i	0.482809	−	0.129368i	0.492010	+	0.870589i	$0.336262\pi$
$728$	11.0108	−	3.55839i	0.408088	−	0.131883i
$729$	26.4959	−	5.19287i	0.981331	−	0.192329i
$730$	21.1494	+	1.78065i	0.782775	+	0.0659048i
$731$			9.96934i			0.368729i
$732$	0.329100	+	10.1993i	0.0121639	+	0.376977i
$733$	−17.4201	+	17.4201i	−0.643427	+	0.643427i	−0.951396	−	0.307970i	$-0.900350\pi$
$733$	−17.4201	+	17.4201i	−0.643427	+	0.643427i	0.307970	+	0.951396i	$0.400350\pi$
$734$	−9.82951	−	17.0252i	−0.362814	−	0.628412i
$735$	27.0772	−	1.35003i	0.998759	−	0.0497965i
$736$	3.76497	−	6.52113i	0.138779	−	0.240372i
$737$	−11.2577	−	42.0143i	−0.414683	−	1.54762i
$738$	−26.4096	+	8.93723i	−0.972151	+	0.328984i
$739$	21.0639	−	12.1612i	0.774847	−	0.447358i	−0.0597540	−	0.998213i	$-0.519032\pi$
$739$	21.0639	−	12.1612i	0.774847	−	0.447358i	0.834601	+	0.550855i	$0.185698\pi$
$740$	20.9794	−	3.77003i	0.771218	−	0.138589i
$741$	34.1589	+	32.0234i	1.25486	+	1.17641i
$742$	0.143432	+	0.129558i	0.00526557	+	0.00475624i
$743$	−5.25592	+	19.6154i	−0.192821	+	0.719618i	0.799999	+	0.600001i	$0.204833\pi$
$743$	−5.25592	+	19.6154i	−0.192821	+	0.719618i	−0.992820	+	0.119617i	$0.961833\pi$
$744$	0.595052	−	0.180202i	0.0218157	−	0.00660654i
$745$	−9.07730	+	4.26901i	−0.332566	+	0.156405i
$746$	4.66447	−	2.69303i	0.170778	−	0.0985990i
$747$	10.5083	−	3.55610i	0.384480	−	0.130111i
$748$	3.77568	−	3.77568i	0.138053	−	0.138053i
$749$	36.0169	−	1.83046i	1.31603	−	0.0668834i
$750$	−8.96859	+	17.1629i	−0.327487	+	0.626700i
$751$	31.6555			1.15512			0.577562	−	0.816347i	$-0.304004\pi$
$751$	31.6555			1.15512			0.577562	+	0.816347i	$0.304004\pi$
$752$	−0.788240	−	2.94175i	−0.0287442	−	0.107275i
$753$	0.696844	+	21.5962i	0.0253944	+	0.787010i
$754$	23.7367	−	13.7044i	0.864439	−	0.499084i
$755$	2.40392	−	1.13055i	0.0874877	−	0.0411451i
$756$	8.18638	−	11.0446i	0.297736	−	0.401688i
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	0.614619	−	0.788824i	$-0.289310\pi$
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	−0.788824	+	0.614619i	$0.789310\pi$
$758$	−5.03024	+	18.7731i	−0.182706	+	0.681870i
$759$	40.5359	−	43.2391i	1.47136	−	1.56948i
$760$	−8.91849	−	10.5583i	−0.323508	−	0.382990i
$761$		−	10.5394i		−	0.382054i	−0.981585	−	0.191027i	$-0.938818\pi$
$761$		−	10.5394i		−	0.382054i	0.981585	−	0.191027i	$-0.0611817\pi$
$762$	10.5157	+	16.9283i	0.380943	+	0.613247i
$763$	0.396017	+	1.22541i	0.0143368	+	0.0443627i
$764$	−21.6280			−0.782473
$765$	7.65186	−	1.89132i	0.276653	−	0.0683810i
$766$	7.19509	+	12.4623i	0.259969	+	0.450280i
$767$	−26.3116	+	26.3116i	−0.950057	+	0.950057i
$768$	−0.817200	+	1.52715i	−0.0294882	+	0.0551062i
$769$	15.0585	−	8.69401i	0.543022	−	0.313514i	−0.203281	−	0.979121i	$-0.565160\pi$
$769$	15.0585	−	8.69401i	0.543022	−	0.313514i	0.746303	+	0.665607i	$0.231827\pi$
$770$	−26.8700	−	0.892871i	−0.968326	−	0.0321768i
$771$	12.9713	−	13.8363i	0.467150	−	0.498303i
$772$	5.58407	−	20.8400i	0.200975	−	0.750049i
$773$	−8.00635	+	29.8801i	−0.287968	+	1.07471i	0.658674	+	0.752428i	$0.271118\pi$
$773$	−8.00635	+	29.8801i	−0.287968	+	1.07471i	−0.946643	+	0.322285i	$0.895549\pi$
$774$	−1.64091	−	25.4007i	−0.0589815	−	0.913010i
$775$	−0.624880	−	1.68252i	−0.0224464	−	0.0604377i
$776$	−3.02332	−	1.74552i	−0.108531	−	0.0626604i
$777$	3.62307	+	43.5332i	0.129977	+	1.56174i
$778$	−6.07636	−	1.62816i	−0.217848	−	0.0583722i
$779$	−57.4429			−2.05811
$780$	−16.1132	−	5.22444i	−0.576943	−	0.187065i
$781$	59.9949			2.14679
$782$	2.28995	+	8.54620i	0.0818884	+	0.305612i
$783$	13.4809	−	29.6419i	0.481768	−	1.05932i
$784$	−0.709677	−	6.96393i	−0.0253456	−	0.248712i
$785$	7.48657	−	6.32383i	0.267207	−	0.225707i
$786$	−3.66851	+	15.7001i	−0.130851	+	0.560002i
$787$	6.54148	−	1.75278i	0.233179	−	0.0624800i	−0.140337	−	0.990104i	$-0.544819\pi$
$787$	6.54148	−	1.75278i	0.233179	−	0.0624800i	0.373516	+	0.927624i	$0.378152\pi$
$788$	−5.04892	+	1.35285i	−0.179860	+	0.0481935i
$789$	10.7948	+	10.1200i	0.384307	+	0.360281i
$790$	−9.00032	+	7.60247i	−0.320217	+	0.270484i
$791$	−6.94146	−	3.55069i	−0.246810	−	0.126248i
$792$	−8.99853	+	10.2415i	−0.319749	+	0.363914i
$793$	6.66919	+	24.8898i	0.236830	+	0.883861i
$794$	−15.4664			−0.548883
$795$	−0.0589975	−	0.276718i	−0.00209242	−	0.00981416i
$796$	−4.41270			−0.156404
$797$	−9.79545	−	2.62468i	−0.346973	−	0.0929710i	0.0811240	−	0.996704i	$-0.474149\pi$
$797$	−9.79545	−	2.62468i	−0.346973	−	0.0929710i	−0.428097	+	0.903733i	$0.640816\pi$
$798$	23.2706	−	16.1479i	0.823769	−	0.571629i
$799$	3.09906	+	1.78925i	0.109637	+	0.0632989i
$800$	4.54527	+	2.08340i	0.160699	+	0.0736594i
$801$	−7.29802	+	14.7640i	−0.257863	+	0.521659i
$802$	−1.57575	+	5.88077i	−0.0556415	+	0.207657i
$803$	11.1639	−	41.6643i	0.393966	−	1.47030i
$804$	−16.1435	−	3.77213i	−0.569338	−	0.133033i
$805$	23.5429	−	37.8185i	0.829777	−	1.33293i
$806$	1.35963	−	0.784981i	0.0478908	−	0.0276498i
$807$	−3.47193	−	5.58916i	−0.122218	−	0.196748i
$808$	6.72421	−	6.72421i	0.236557	−	0.236557i
$809$	−1.25982	−	2.18207i	−0.0442929	−	0.0767175i	0.843029	−	0.537868i	$-0.180770\pi$
$809$	−1.25982	−	2.18207i	−0.0442929	−	0.0767175i	−0.887322	+	0.461151i	$0.847437\pi$
$810$	−19.1847	+	6.07834i	−0.674083	+	0.213571i
$811$	−6.87827			−0.241529			−0.120764	−	0.992681i	$-0.538535\pi$
$811$	−6.87827			−0.241529			−0.120764	+	0.992681i	$0.538535\pi$
$812$	−5.09871	−	15.7771i	−0.178930	−	0.553667i
$813$	−15.1424	+	28.2976i	−0.531068	+	0.992439i
$814$		−	43.3194i		−	1.51834i
$815$	25.6785	+	30.3999i	0.899478	+	1.06486i
$816$	−0.589861	−	1.94780i	−0.0206493	−	0.0681867i
$817$	13.5730	−	50.6552i	0.474860	−	1.77220i
$818$	−1.19834	−	1.19834i	−0.0418991	−	0.0418991i
$819$	13.7837	−	31.8608i	0.481641	−	1.11331i
$820$	18.8053	−	8.84405i	0.656709	−	0.308848i
$821$	−12.9311	+	7.46579i	−0.451300	+	0.260558i	−0.708379	−	0.705832i	$-0.750573\pi$
$821$	−12.9311	+	7.46579i	−0.451300	+	0.260558i	0.257079	+	0.966390i	$0.417240\pi$
$822$	27.3823	−	17.0096i	0.955066	−	0.593277i
$823$	6.95712	+	25.9643i	0.242510	+	0.905060i	0.974619	+	0.223872i	$0.0718697\pi$
$823$	6.95712	+	25.9643i	0.242510	+	0.905060i	−0.732108	+	0.681188i	$0.761464\pi$
$824$	3.07685			0.107187
$825$	31.1064	+	24.1087i	1.08299	+	0.839357i
$826$	12.2298	+	18.8976i	0.425529	+	0.657532i
$827$	5.42032	−	5.42032i	0.188483	−	0.188483i	−0.606557	−	0.795040i	$-0.707450\pi$
$827$	5.42032	−	5.42032i	0.188483	−	0.188483i	0.795040	+	0.606557i	$0.207450\pi$
$828$	−7.24119	−	21.3978i	−0.251649	−	0.743625i
$829$	−12.1226	+	6.99901i	−0.421037	+	0.243086i	−0.695521	−	0.718506i	$-0.744826\pi$
$829$	−12.1226	+	6.99901i	−0.421037	+	0.243086i	0.274484	+	0.961592i	$0.411493\pi$
$830$	−7.48259	+	3.51903i	−0.259724	+	0.122147i
$831$	−25.0607	−	23.4940i	−0.869347	−	0.814998i
$832$	−1.13198	+	4.22459i	−0.0392442	+	0.146461i
$833$	6.37562	+	5.19635i	0.220902	+	0.180043i
$834$	27.1717	−	8.22854i	0.940880	−	0.284931i
$835$	−28.3926	+	5.10219i	−0.982565	+	0.176568i
$836$	−24.3251	+	14.0441i	−0.841302	+	0.485726i
$837$	0.772179	−	1.69787i	0.0266904	−	0.0586871i
$838$	1.18468	+	4.42129i	0.0409241	+	0.152731i
$839$	−16.7773	+	29.0592i	−0.579217	+	1.00323i	0.416352	+	0.909203i	$0.363308\pi$
$839$	−16.7773	+	29.0592i	−0.579217	+	1.00323i	−0.995569	+	0.0940302i	$0.970025\pi$
$840$	−5.13200	+	8.86919i	−0.177071	+	0.306016i
$841$	−5.13662	−	8.89689i	−0.177125	−	0.306789i
$842$	7.97541	−	7.97541i	0.274851	−	0.274851i
$843$	17.7341	+	9.48980i	0.610796	+	0.326846i
$844$			14.1857i			0.488291i
$845$	−13.6556	−	1.14971i	−0.469766	−	0.0395514i
$846$	−8.19055	−	4.04869i	−0.281597	−	0.139197i
$847$	−5.34845	+	24.9683i	−0.183775	+	0.857920i
$848$	−0.0705647	+	0.0189078i	−0.00242320	+	0.000649295i
$849$	13.0232	+	43.0042i	0.446953	+	1.47590i
$850$	−5.50743	+	2.04544i	−0.188903	+	0.0701579i
$851$	62.1630	+	35.8899i	2.13092	+	1.23029i
$852$	10.7887	−	20.1615i	0.369615	−	0.690722i
$853$	1.52862	+	5.70488i	0.0523389	+	0.195331i	0.987145	−	0.159827i	$-0.0510936\pi$
$853$	1.52862	+	5.70488i	0.0523389	+	0.195331i	−0.934806	+	0.355158i	$0.884427\pi$
$854$	15.5677	−	0.791184i	0.532716	−	0.0270738i
$855$	−41.4549	−	0.807814i	−1.41773	−	0.0276266i
$856$	−6.81534	+	11.8045i	−0.232943	+	0.403470i
$857$	−0.500131	+	0.500131i	−0.0170842	+	0.0170842i	−0.715597	−	0.698513i	$-0.753845\pi$
$857$	−0.500131	+	0.500131i	−0.0170842	+	0.0170842i	0.698513	+	0.715597i	$0.253845\pi$
$858$	−16.2421	+	30.3526i	−0.554496	+	1.03622i
$859$		−	38.7200i		−	1.32111i	−0.750778	−	0.660555i	$-0.770321\pi$
$859$		−	38.7200i		−	1.32111i	0.750778	−	0.660555i	$-0.229679\pi$
$860$	3.35555	+	18.6729i	0.114423	+	0.636742i
$861$	14.3967	+	40.0816i	0.490638	+	1.36598i
$862$	2.14911	−	0.575852i	0.0731990	−	0.0196136i
$863$	4.74346	−	1.27101i	0.161469	−	0.0432655i	−0.177179	−	0.984179i	$-0.556697\pi$
$863$	4.74346	−	1.27101i	0.161469	−	0.0432655i	0.338648	+	0.940913i	$0.390030\pi$
$864$	1.82350	+	4.86568i	0.0620367	+	0.165534i
$865$	6.05021	+	33.6681i	0.205713	+	1.14475i
$866$	26.5976	−	15.3561i	0.903823	−	0.521822i
$867$	−23.8531	−	12.7642i	−0.810094	−	0.433493i
$868$	−0.292052	−	0.903703i	−0.00991288	−	0.0306737i
$869$	11.9718	+	20.7357i	0.406114	+	0.703410i
$870$	−7.48595	+	23.0881i	−0.253797	+	0.782759i
$871$	−41.8622			−1.41845
$872$	−0.470160	−	0.125979i	−0.0159216	−	0.00426619i
$873$	−9.92045	+	3.35716i	−0.335756	+	0.113623i
$874$		−	46.5419i		−	1.57430i
$875$	26.4660	+	13.2118i	0.894713	+	0.446641i
$876$	−11.9939	−	11.2440i	−0.405235	−	0.379901i
$877$	−1.29700	−	1.29700i	−0.0437966	−	0.0437966i	0.684869	−	0.728666i	$-0.259859\pi$
$877$	−1.29700	−	1.29700i	−0.0437966	−	0.0437966i	−0.728666	+	0.684869i	$0.759859\pi$
$878$	13.8745	−	3.71766i	0.468241	−	0.125465i
$879$	2.73425	−	11.7017i	0.0922239	−	0.394689i
$880$	5.80114	−	8.34283i	0.195556	−	0.281237i
$881$		−	9.87338i		−	0.332643i	−0.986072	−	0.166321i	$-0.946811\pi$
$881$		−	9.87338i		−	0.332643i	0.986072	−	0.166321i	$-0.0531889\pi$
$882$	−17.0996	−	12.1903i	−0.575774	−	0.410468i
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	−0.280884	−	0.959742i	$-0.590628\pi$
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	0.959742	+	0.280884i	$0.0906277\pi$
$884$	−2.56950	−	4.45050i	−0.0864216	−	0.149687i
$885$	1.70411	−	32.9068i	0.0572831	−	1.10615i
$886$	−4.77083	+	8.26332i	−0.160279	+	0.277612i
$887$	8.78931	−	8.78931i	0.295116	−	0.295116i	−0.543981	−	0.839097i	$-0.683084\pi$
$887$	8.78931	−	8.78931i	0.295116	−	0.295116i	0.839097	+	0.543981i	$0.183084\pi$
$888$	−14.5576	−	7.79001i	−0.488523	−	0.261415i
$889$	25.5564	−	16.5392i	0.857136	−	0.554705i
$890$	4.16070	−	11.5488i	0.139467	−	0.387117i
$891$	5.26231	+	40.5593i	0.176294	+	1.35879i
$892$	−0.613728	+	2.29046i	−0.0205491	+	0.0766904i
$893$	−13.3106	−	13.3106i	−0.445424	−	0.445424i
$894$	7.56621	+	1.76794i	0.253052	+	0.0591286i
$895$	19.7642	+	13.7429i	0.660643	+	0.459374i
$896$	2.35548	+	1.20487i	0.0786910	+	0.0402520i
$897$	−30.0993	−	48.4542i	−1.00498	−	1.61784i
$898$	−39.4744	−	10.5771i	−1.31728	−	0.352963i
$899$	−1.12478	−	1.94817i	−0.0375134	−	0.0649751i
$900$	13.6956	−	6.11804i	0.456520	−	0.203935i
$901$	0.0429192	−	0.0743382i	0.00142985	−	0.00247656i
$902$	−10.9308	−	40.7945i	−0.363957	−	1.35831i
$903$	−38.7472	+	3.22475i	−1.28942	+	0.107313i
$904$	2.55213	−	1.47347i	0.0848825	−	0.0490069i
$905$	−0.425923	+	0.200310i	−0.0141582	+	0.00665853i
$906$	−2.00374	−	0.468199i	−0.0665699	−	0.0155549i
$907$	23.5846	+	23.5846i	0.783113	+	0.783113i	0.980355	−	0.197242i	$-0.0631983\pi$
$907$	23.5846	+	23.5846i	0.783113	+	0.783113i	−0.197242	+	0.980355i	$0.563198\pi$
$908$	0.531375	−	0.142382i	0.0176343	−	0.00472510i
$909$	−1.83913	−	28.4690i	−0.0610002	−	0.944259i
$910$	−7.52321	+	24.7568i	−0.249392	+	0.820681i
$911$	−18.7417	−	10.8205i	−0.620941	−	0.358501i	0.156294	−	0.987711i	$-0.450045\pi$
$911$	−18.7417	−	10.8205i	−0.620941	−	0.358501i	−0.777235	+	0.629210i	$0.783379\pi$
$912$	0.345258	+	10.7001i	0.0114326	+	0.354314i
$913$	4.34936	+	16.2320i	0.143943	+	0.537202i
$914$	−11.6283	+	20.1408i	−0.384630	+	0.666198i
$915$	−19.1446	−	12.4158i	−0.632903	−	0.410454i
$916$	−9.84143	+	17.0459i	−0.325170	+	0.563211i
$917$	24.0819	+	5.15858i	0.795255	+	0.170351i
$918$	−5.55770	−	2.52760i	−0.183432	−	0.0834231i
$919$	21.8011	+	12.5868i	0.719150	+	0.415202i	0.814440	−	0.580248i	$-0.197044\pi$
$919$	21.8011	+	12.5868i	0.719150	+	0.415202i	−0.0952895	+	0.995450i	$0.530378\pi$
$920$	7.16570	+	15.2366i	0.236246	+	0.502335i
$921$	12.2681	+	11.5011i	0.404246	+	0.378974i
$922$	−13.0506	−	13.0506i	−0.429799	−	0.429799i
$923$	14.9444	−	55.7733i	0.491902	−	1.83580i
$924$	15.8960	+	13.4534i	0.522939	+	0.442583i
$925$	−19.8602	+	43.3280i	−0.652998	+	1.42462i
$926$	16.1091	+	9.30057i	0.529377	+	0.305636i
$927$	6.09264	−	6.93419i	0.200109	−	0.227749i
$928$	6.05330	+	1.62198i	0.198709	+	0.0532440i
$929$	16.6278	+	28.8002i	0.545541	+	0.944905i	0.998573	+	0.0534108i	$0.0170093\pi$
$929$	16.6278	+	28.8002i	0.545541	+	0.944905i	−0.453031	+	0.891495i	$0.649657\pi$
$930$	−0.428791	+	1.32247i	−0.0140606	+	0.0433656i
$931$	−25.3205	−	35.0834i	−0.829844	−	1.14981i
$932$	−5.84244	−	1.56548i	−0.191376	−	0.0512789i
$933$	−1.43835	−	0.769680i	−0.0470893	−	0.0251982i
$934$			2.93941i			0.0961804i
$935$	2.11176	+	11.7515i	0.0690621	+	0.384316i
$936$	7.27932	+	10.9164i	0.237932	+	0.356815i
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	0.804469	−	0.593994i	$-0.202450\pi$
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	−0.593994	+	0.804469i	$0.702450\pi$
$938$	−5.30429	+	24.7621i	−0.173191	+	0.808512i
$939$	28.2266	+	6.59549i	0.921141	+	0.215236i
$940$	6.40690	+	2.30822i	0.208970	+	0.0752857i
$941$	−40.4672	−	23.3637i	−1.31919	−	0.761636i	−0.335594	−	0.942007i	$-0.608937\pi$
$941$	−40.4672	−	23.3637i	−1.31919	−	0.761636i	−0.983599	+	0.180370i	$0.942270\pi$
$942$	−7.58708	+	0.244812i	−0.247200	+	0.00797640i
$943$	67.5959	+	18.1123i	2.20123	+	0.589817i
$944$	−8.50788			−0.276908
$945$	9.82600	+	29.1282i	0.319640	+	0.947539i
$946$	38.5569			1.25359
$947$	27.5187	+	7.37361i	0.894237	+	0.239610i	0.676540	−	0.736406i	$-0.263479\pi$
$947$	27.5187	+	7.37361i	0.894237	+	0.239610i	0.217698	+	0.976016i	$0.430145\pi$
$948$	9.12115	−	0.294312i	0.296241	−	0.00955879i
$949$	−35.9517	−	20.7567i	−1.16704	−	0.673792i
$950$	30.7686	−	2.89484i	0.998266	−	0.0939212i
$951$	20.3998	+	4.76665i	0.661508	+	0.154569i
$952$	−2.95812	+	0.955981i	−0.0958731	+	0.0309835i
$953$	−10.3138	−	10.3138i	−0.334098	−	0.334098i	0.520042	−	0.854140i	$-0.325916\pi$
$953$	−10.3138	−	10.3138i	−0.334098	−	0.334098i	−0.854140	+	0.520042i	$0.825916\pi$
$954$	−0.0971173	+	0.196469i	−0.00314429	+	0.00636093i
$955$	27.6094	−	39.7060i	0.893418	−	1.28486i
$956$			20.3637i			0.658610i
$957$	43.4913	+	23.2728i	1.40587	+	0.752304i
$958$	−0.227333	−	0.0609136i	−0.00734479	−	0.00196803i
$959$	−26.7528	−	41.3387i	−0.863893	−	1.33490i
$960$	−1.76044	−	3.44976i	−0.0568179	−	0.111341i
$961$	15.4356	+	26.7352i	0.497922	+	0.862426i
$962$	−40.2712	−	10.7906i	−1.29840	−	0.347904i
$963$	13.1080	+	38.7342i	0.422398	+	1.24819i
$964$	−8.21469	−	4.74276i	−0.264577	−	0.152754i
$965$	31.1311	+	36.8551i	1.00214	+	1.18641i
$966$	−32.4752	+	11.6646i	−1.04487	+	0.375302i
$967$	−12.2705	+	45.7943i	−0.394594	+	1.47265i	0.427876	+	0.903837i	$0.359262\pi$
$967$	−12.2705	+	45.7943i	−0.394594	+	1.47265i	−0.822470	+	0.568808i	$0.807405\pi$
$968$	−6.82443	−	6.82443i	−0.219346	−	0.219346i
$969$	−9.17700	−	8.60328i	−0.294808	−	0.276377i
$970$	7.06398	−	3.32216i	0.226811	−	0.106668i
$971$	29.2801	+	16.9049i	0.939642	+	0.542503i	0.889848	−	0.456257i	$-0.150810\pi$
$971$	29.2801	+	16.9049i	0.939642	+	0.542503i	0.0497939	+	0.998760i	$0.484144\pi$
$972$	14.5764	+	5.52525i	0.467538	+	0.177222i
$973$	−13.3359	−	41.2656i	−0.427529	−	1.32291i
$974$	7.58737	−	13.1417i	0.243115	−	0.421087i
$975$	30.1607	−	22.9123i	0.965917	−	0.733780i
$976$	−2.94582	+	5.10230i	−0.0942933	+	0.163321i
$977$	13.7677	+	51.3818i	0.440468	+	1.64385i	0.727632	+	0.685968i	$0.240621\pi$
$977$	13.7677	+	51.3818i	0.440468	+	1.64385i	−0.287163	+	0.957882i	$0.592712\pi$
$978$	−0.994081	−	30.8080i	−0.0317872	−	0.985133i
$979$	−21.6051	−	12.4737i	−0.690501	−	0.398661i
$980$	13.6908	+	7.58699i	0.437336	+	0.242358i
$981$	−1.21490	+	0.810124i	−0.0387889	+	0.0258653i
$982$	−2.65316	+	0.710911i	−0.0846656	+	0.0226861i
$983$	−38.2310	−	38.2310i	−1.21938	−	1.21938i	−0.967849	−	0.251532i	$-0.919066\pi$
$983$	−38.2310	−	38.2310i	−1.21938	−	1.21938i	−0.251532	−	0.967849i	$-0.580934\pi$
$984$	−15.6748	−	3.66260i	−0.499694	−	0.116760i
$985$	3.96158	−	10.9961i	0.126227	−	0.350366i
$986$	−6.37700	+	3.68176i	−0.203085	+	0.117251i
$987$	−5.95169	+	12.6237i	−0.189444	+	0.401816i
$988$	6.99663	+	26.1118i	0.222593	+	0.830727i
$989$	−31.9441	+	55.3289i	−1.01576	+	1.75936i
$990$	−7.31478	−	29.5939i	−0.232479	−	0.940556i
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	0.963880	−	0.266337i	$-0.0858134\pi$
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	−0.712595	+	0.701576i	$0.752480\pi$
$992$	0.346730	+	0.0929061i	0.0110087	+	0.00294977i
$993$	16.5827	+	26.6951i	0.526237	+	0.847144i
$994$	−31.0972	−	15.9068i	−0.986343	−	0.504533i
$995$	5.63306	−	8.10112i	0.178580	−	0.256823i
$996$	6.23697	+	1.45734i	0.197626	+	0.0461777i
$997$	−34.8123	−	34.8123i	−1.10252	−	1.10252i	−0.994106	−	0.108412i	$-0.965424\pi$
$997$	−34.8123	−	34.8123i	−1.10252	−	1.10252i	−0.108412	−	0.994106i	$-0.534576\pi$
$998$	−8.97809	+	33.5067i	−0.284196	+	1.06064i
$999$	−46.3824	+	17.3826i	−1.46747	+	0.549961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.317.47	✓	192
5.3	odd	4	inner	630.2.bt.a.443.38	yes	192
7.4	even	3		630.2.cd.a.137.7	yes	192
9.5	odd	6		630.2.cd.a.527.43	yes	192
35.18	odd	12		630.2.cd.a.263.43	yes	192
45.23	even	12		630.2.cd.a.23.7	yes	192
63.32	odd	6	inner	630.2.bt.a.347.38	yes	192
315.158	even	12	inner	630.2.bt.a.473.47	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.47	✓	192	1.1	even	1	trivial
630.2.bt.a.347.38	yes	192	63.32	odd	6	inner
630.2.bt.a.443.38	yes	192	5.3	odd	4	inner
630.2.bt.a.473.47	yes	192	315.158	even	12	inner
630.2.cd.a.23.7	yes	192	45.23	even	12
630.2.cd.a.137.7	yes	192	7.4	even	3
630.2.cd.a.263.43	yes	192	35.18	odd	12
630.2.cd.a.527.43	yes	192	9.5	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.73115 - 0.0558589i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.02346 + 0.951627i) q^{5} +(1.68662 + 0.394099i) q^{6} +(0.554174 - 2.58706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99376 - 0.193400i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.73115 - 0.0558589i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.02346 + 0.951627i) q^{5} +(1.68662 + 0.394099i) q^{6} +(0.554174 - 2.58706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99376 - 0.193400i) q^{9} +(-2.20082 + 0.395490i) q^{10} +4.54436i q^{11} +(1.52715 + 0.817200i) q^{12} +(4.22459 + 1.13198i) q^{13} +(1.20487 - 2.35548i) q^{14} +(-3.44976 + 1.76044i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.13496 - 0.304112i) q^{17} +(2.94181 + 0.588032i) q^{18} +(5.35282 + 3.09045i) q^{19} +(-2.22818 - 0.187599i) q^{20} +(0.814849 - 4.50955i) q^{21} +(-1.17617 + 4.38951i) q^{22} +(-5.32448 - 5.32448i) q^{23} +(1.26361 + 1.18461i) q^{24} +(3.18881 - 3.85116i) q^{25} +(3.78767 + 2.18681i) q^{26} +(5.17184 - 0.502033i) q^{27} +(1.77346 - 1.96337i) q^{28} +(3.13342 - 5.42724i) q^{29} +(-3.78785 + 0.807587i) q^{30} +(0.179481 - 0.310870i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.253843 + 7.86697i) q^{33} +(-1.01758 - 0.587499i) q^{34} +(1.34057 + 5.76219i) q^{35} +(2.68937 + 1.32939i) q^{36} +(-9.20775 + 2.46721i) q^{37} +(4.37056 + 4.37056i) q^{38} +(7.37664 + 1.72364i) q^{39} +(-2.10371 - 0.757903i) q^{40} +(-8.04851 + 4.64681i) q^{41} +(1.95424 - 4.14499i) q^{42} +(-2.19596 - 8.19545i) q^{43} +(-2.27218 + 3.93553i) q^{44} +(-5.87372 + 3.24028i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(-2.94175 - 0.788240i) q^{47} +(0.913950 + 1.47129i) q^{48} +(-6.38578 - 2.86737i) q^{49} +(4.07691 - 2.89461i) q^{50} +(-1.98178 - 0.463066i) q^{51} +(3.09262 + 3.09262i) q^{52} +(-0.0189078 + 0.0705647i) q^{53} +(5.12555 + 0.853645i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(2.22119 - 1.43747i) q^{56} +(9.43915 + 5.05103i) q^{57} +(4.43132 - 4.43132i) q^{58} +(-4.25394 + 7.36804i) q^{59} +(-3.86780 - 0.200298i) q^{60} +(2.94582 + 5.10230i) q^{61} +(0.253824 - 0.253824i) q^{62} +(1.15873 - 7.85222i) q^{63} +1.00000i q^{64} +(-9.62553 + 1.72972i) q^{65} +(-1.79093 + 7.66461i) q^{66} +(-9.24538 + 2.47729i) q^{67} +(-0.830850 - 0.830850i) q^{68} +(-9.51489 - 8.92005i) q^{69} +(-0.196479 + 5.91282i) q^{70} -13.2021i q^{71} +(2.25366 + 1.98015i) q^{72} +(-9.16835 - 2.45665i) q^{73} -9.53256 q^{74} +(5.30519 - 6.84507i) q^{75} +(3.09045 + 5.35282i) q^{76} +(11.7565 + 2.51837i) q^{77} +(6.67917 + 3.57412i) q^{78} +(4.56295 - 2.63442i) q^{79} +(-1.83586 - 1.27656i) q^{80} +(8.92519 - 1.15799i) q^{81} +(-8.97694 + 2.40536i) q^{82} +(3.57191 - 0.957089i) q^{83} +(2.96045 - 3.49796i) q^{84} +(2.58596 - 0.464700i) q^{85} -8.48456i q^{86} +(5.12126 - 9.57039i) q^{87} +(-3.21335 + 3.21335i) q^{88} +(-2.74487 + 4.75426i) q^{89} +(-6.51222 + 1.60964i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-1.94889 - 7.27337i) q^{92} +(0.293343 - 0.548188i) q^{93} +(-2.63750 - 1.52276i) q^{94} +(-13.7722 - 1.15953i) q^{95} +(0.502010 + 1.65770i) q^{96} +(-3.37208 + 0.903546i) q^{97} +(-5.42606 - 4.42243i) q^{98} +(0.878880 + 13.6047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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