LMFDB - Embedded newform 630.2.i.g.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (of order $3$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$1.22323 - 1.22626i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.g.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.67359 + 0.446216i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67359 + 0.446216i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.60178 - 1.49356i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.67359 + 0.446216i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67359 + 0.446216i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.60178 - 1.49356i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.13657 + 3.70065i) q^{11} +(-1.67359 + 0.446216i) q^{12} +(2.57903 - 4.46702i) q^{13} +(1.40545 + 2.24159i) q^{14} +(1.22323 + 1.22626i) q^{15} +1.00000 q^{16} +(0.765442 + 1.32578i) q^{17} +(2.60178 - 1.49356i) q^{18} +(-0.678316 + 1.17488i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.35237 - 3.12436i) q^{21} +(-2.13657 + 3.70065i) q^{22} +(4.34447 + 7.52485i) q^{23} +(-1.67359 + 0.446216i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.57903 - 4.46702i) q^{26} +(-3.68785 + 3.66056i) q^{27} +(1.40545 + 2.24159i) q^{28} +(4.80226 + 8.31776i) q^{29} +(1.22323 + 1.22626i) q^{30} +5.16605 q^{31} +1.00000 q^{32} +(1.92444 - 7.14672i) q^{33} +(0.765442 + 1.32578i) q^{34} +(1.23855 - 2.33795i) q^{35} +(2.60178 - 1.49356i) q^{36} +(1.07286 - 1.85825i) q^{37} +(-0.678316 + 1.17488i) q^{38} +(-2.32298 + 8.62674i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.69364 - 2.93347i) q^{41} +(-3.35237 - 3.12436i) q^{42} +(-4.60472 - 7.97561i) q^{43} +(-2.13657 + 3.70065i) q^{44} +(-2.59435 - 1.50643i) q^{45} +(4.34447 + 7.52485i) q^{46} +10.1180 q^{47} +(-1.67359 + 0.446216i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.87262 - 1.87726i) q^{51} +(2.57903 - 4.46702i) q^{52} +(-1.17832 - 2.04090i) q^{53} +(-3.68785 + 3.66056i) q^{54} +4.27314 q^{55} +(1.40545 + 2.24159i) q^{56} +(0.610970 - 2.26893i) q^{57} +(4.80226 + 8.31776i) q^{58} -11.5227 q^{59} +(1.22323 + 1.22626i) q^{60} -4.13399 q^{61} +5.16605 q^{62} +(7.00462 + 3.73300i) q^{63} +1.00000 q^{64} -5.15806 q^{65} +(1.92444 - 7.14672i) q^{66} +9.57147 q^{67} +(0.765442 + 1.32578i) q^{68} +(-10.6286 - 10.6549i) q^{69} +(1.23855 - 2.33795i) q^{70} -7.27314 q^{71} +(2.60178 - 1.49356i) q^{72} +(-1.83021 - 3.17001i) q^{73} +(1.07286 - 1.85825i) q^{74} +(0.450358 - 1.67248i) q^{75} +(-0.678316 + 1.17488i) q^{76} +(-11.2982 + 0.411749i) q^{77} +(-2.32298 + 8.62674i) q^{78} -6.44646 q^{79} +(-0.500000 - 0.866025i) q^{80} +(4.53854 - 7.77185i) q^{81} +(1.69364 - 2.93347i) q^{82} +(-4.21040 - 7.29263i) q^{83} +(-3.35237 - 3.12436i) q^{84} +(0.765442 - 1.32578i) q^{85} +(-4.60472 - 7.97561i) q^{86} +(-11.7485 - 11.7776i) q^{87} +(-2.13657 + 3.70065i) q^{88} +(-6.50852 + 11.2731i) q^{89} +(-2.59435 - 1.50643i) q^{90} +(13.6379 - 0.497019i) q^{91} +(4.34447 + 7.52485i) q^{92} +(-8.64583 + 2.30518i) q^{93} +10.1180 q^{94} +1.35663 q^{95} +(-1.67359 + 0.446216i) q^{96} +(-4.67765 - 8.10193i) q^{97} +(-3.04944 + 6.30087i) q^{98} +(-0.0317385 + 12.8194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.67359	+	0.446216i	−0.966245	+	0.257623i
$3$	−1.67359	+	0.446216i	−0.966245	+	0.257623i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.67359	+	0.446216i	−0.683239	+	0.182167i
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$8$	1.00000			0.353553
$9$	2.60178	−	1.49356i	0.867261	−	0.497854i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.13657	+	3.70065i	−0.644200	+	1.11579i	0.340286	+	0.940322i	$0.389476\pi$
$11$	−2.13657	+	3.70065i	−0.644200	+	1.11579i	−0.984486	+	0.175465i	$0.943857\pi$
$12$	−1.67359	+	0.446216i	−0.483123	+	0.128812i
$13$	2.57903	−	4.46702i	0.715295	−	1.23893i	−0.247551	−	0.968875i	$-0.579626\pi$
$13$	2.57903	−	4.46702i	0.715295	−	1.23893i	0.962846	−	0.270052i	$-0.0870410\pi$
$14$	1.40545	+	2.24159i	0.375621	+	0.599090i
$15$	1.22323	+	1.22626i	0.315836	+	0.316619i
$16$	1.00000			0.250000
$17$	0.765442	+	1.32578i	0.185647	+	0.321550i	0.943794	−	0.330533i	$-0.107229\pi$
$17$	0.765442	+	1.32578i	0.185647	+	0.321550i	−0.758147	+	0.652083i	$0.773895\pi$
$18$	2.60178	−	1.49356i	0.613246	−	0.352036i
$19$	−0.678316	+	1.17488i	−0.155616	+	0.269535i	−0.933283	−	0.359141i	$-0.883070\pi$
$19$	−0.678316	+	1.17488i	−0.155616	+	0.269535i	0.777667	+	0.628676i	$0.216403\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−3.35237	−	3.12436i	−0.731547	−	0.681791i
$22$	−2.13657	+	3.70065i	−0.455518	+	0.788980i
$23$	4.34447	+	7.52485i	0.905886	+	1.56904i	0.819724	+	0.572759i	$0.194127\pi$
$23$	4.34447	+	7.52485i	0.905886	+	1.56904i	0.0861614	+	0.996281i	$0.472540\pi$
$24$	−1.67359	+	0.446216i	−0.341619	+	0.0910835i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.57903	−	4.46702i	0.505790	−	0.876054i
$27$	−3.68785	+	3.66056i	−0.709728	+	0.704476i
$28$	1.40545	+	2.24159i	0.265604	+	0.423620i
$29$	4.80226	+	8.31776i	0.891757	+	1.54457i	0.837767	+	0.546028i	$0.183861\pi$
$29$	4.80226	+	8.31776i	0.891757	+	1.54457i	0.0539901	+	0.998541i	$0.482806\pi$
$30$	1.22323	+	1.22626i	0.223330	+	0.223883i
$31$	5.16605			0.927850			0.463925	−	0.885875i	$-0.346441\pi$
$31$	5.16605			0.927850			0.463925	+	0.885875i	$0.346441\pi$
$32$	1.00000			0.176777
$33$	1.92444	−	7.14672i	0.335003	−	1.24408i
$34$	0.765442	+	1.32578i	0.131272	+	0.227370i
$35$	1.23855	−	2.33795i	0.209353	−	0.395185i
$36$	2.60178	−	1.49356i	0.433630	−	0.248927i
$37$	1.07286	−	1.85825i	0.176377	−	0.305494i	−0.764260	−	0.644908i	$-0.776896\pi$
$37$	1.07286	−	1.85825i	0.176377	−	0.305494i	0.940637	+	0.339415i	$0.110229\pi$
$38$	−0.678316	+	1.17488i	−0.110037	+	0.190590i
$39$	−2.32298	+	8.62674i	−0.371974	+	1.38138i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.69364	−	2.93347i	0.264502	−	0.458130i	−0.702931	−	0.711258i	$-0.748126\pi$
$41$	1.69364	−	2.93347i	0.264502	−	0.458130i	0.967433	+	0.253127i	$0.0814592\pi$
$42$	−3.35237	−	3.12436i	−0.517282	−	0.482099i
$43$	−4.60472	−	7.97561i	−0.702213	−	1.21627i	−0.967688	−	0.252151i	$-0.918862\pi$
$43$	−4.60472	−	7.97561i	−0.702213	−	1.21627i	0.265475	−	0.964118i	$-0.414471\pi$
$44$	−2.13657	+	3.70065i	−0.322100	+	0.557893i
$45$	−2.59435	−	1.50643i	−0.386744	−	0.224565i
$46$	4.34447	+	7.52485i	0.640558	+	1.10948i
$47$	10.1180			1.47586			0.737928	−	0.674879i	$-0.235804\pi$
$47$	10.1180			1.47586			0.737928	+	0.674879i	$0.235804\pi$
$48$	−1.67359	+	0.446216i	−0.241561	+	0.0644058i
$49$	−3.04944	+	6.30087i	−0.435635	+	0.900124i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−1.87262	−	1.87726i	−0.262219	−	0.262869i
$52$	2.57903	−	4.46702i	0.357647	−	0.619464i
$53$	−1.17832	−	2.04090i	−0.161854	−	0.280339i	0.773680	−	0.633577i	$-0.218414\pi$
$53$	−1.17832	−	2.04090i	−0.161854	−	0.280339i	−0.935534	+	0.353238i	$0.885081\pi$
$54$	−3.68785	+	3.66056i	−0.501853	+	0.498140i
$55$	4.27314			0.576190
$56$	1.40545	+	2.24159i	0.187811	+	0.299545i
$57$	0.610970	−	2.26893i	0.0809250	−	0.300528i
$58$	4.80226	+	8.31776i	0.630568	+	1.09218i
$59$	−11.5227			−1.50013			−0.750063	−	0.661367i	$-0.769977\pi$
$59$	−11.5227			−1.50013			−0.750063	+	0.661367i	$0.769977\pi$
$60$	1.22323	+	1.22626i	0.157918	+	0.158309i
$61$	−4.13399			−0.529303			−0.264652	−	0.964344i	$-0.585257\pi$
$61$	−4.13399			−0.529303			−0.264652	+	0.964344i	$0.585257\pi$
$62$	5.16605			0.656089
$63$	7.00462	+	3.73300i	0.882499	+	0.470314i
$64$	1.00000			0.125000
$65$	−5.15806			−0.639779
$66$	1.92444	−	7.14672i	0.236883	−	0.879701i
$67$	9.57147			1.16934			0.584670	−	0.811271i	$-0.301224\pi$
$67$	9.57147			1.16934			0.584670	+	0.811271i	$0.301224\pi$
$68$	0.765442	+	1.32578i	0.0928235	+	0.160775i
$69$	−10.6286	−	10.6549i	−1.27953	−	1.28270i
$70$	1.23855	−	2.33795i	0.148035	−	0.279438i
$71$	−7.27314			−0.863163			−0.431581	−	0.902074i	$-0.642044\pi$
$71$	−7.27314			−0.863163			−0.431581	+	0.902074i	$0.642044\pi$
$72$	2.60178	−	1.49356i	0.306623	−	0.176018i
$73$	−1.83021	−	3.17001i	−0.214209	−	0.371022i	0.738818	−	0.673905i	$-0.235384\pi$
$73$	−1.83021	−	3.17001i	−0.214209	−	0.371022i	−0.953028	+	0.302883i	$0.902051\pi$
$74$	1.07286	−	1.85825i	0.124717	−	0.216017i
$75$	0.450358	−	1.67248i	0.0520029	−	0.193121i
$76$	−0.678316	+	1.17488i	−0.0778081	+	0.134768i
$77$	−11.2982	+	0.411749i	−1.28754	+	0.0469232i
$78$	−2.32298	+	8.62674i	−0.263025	+	0.976786i
$79$	−6.44646			−0.725283			−0.362641	−	0.931929i	$-0.618125\pi$
$79$	−6.44646			−0.725283			−0.362641	+	0.931929i	$0.618125\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	4.53854	−	7.77185i	0.504282	−	0.863539i
$82$	1.69364	−	2.93347i	0.187031	−	0.323947i
$83$	−4.21040	−	7.29263i	−0.462152	−	0.800471i	0.536916	−	0.843636i	$-0.319589\pi$
$83$	−4.21040	−	7.29263i	−0.462152	−	0.800471i	−0.999068	+	0.0431651i	$0.986256\pi$
$84$	−3.35237	−	3.12436i	−0.365773	−	0.340896i
$85$	0.765442	−	1.32578i	0.0830238	−	0.143801i
$86$	−4.60472	−	7.97561i	−0.496540	−	0.860032i
$87$	−11.7485	−	11.7776i	−1.25957	−	1.26270i
$88$	−2.13657	+	3.70065i	−0.227759	+	0.394490i
$89$	−6.50852	+	11.2731i	−0.689902	+	1.19495i	0.281967	+	0.959424i	$0.409013\pi$
$89$	−6.50852	+	11.2731i	−0.689902	+	1.19495i	−0.971869	+	0.235521i	$0.924320\pi$
$90$	−2.59435	−	1.50643i	−0.273469	−	0.158791i
$91$	13.6379	−	0.497019i	1.42964	−	0.0521017i
$92$	4.34447	+	7.52485i	0.452943	+	0.784520i
$93$	−8.64583	+	2.30518i	−0.896531	+	0.239036i
$94$	10.1180			1.04359
$95$	1.35663			0.139187
$96$	−1.67359	+	0.446216i	−0.170810	+	0.0455418i
$97$	−4.67765	−	8.10193i	−0.474943	−	0.822626i	0.524645	−	0.851321i	$-0.324198\pi$
$97$	−4.67765	−	8.10193i	−0.474943	−	0.822626i	−0.999588	+	0.0286952i	$0.990865\pi$
$98$	−3.04944	+	6.30087i	−0.308040	+	0.636484i
$99$	−0.0317385	+	12.8194i	−0.00318984	+	1.28840i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−0.00554702	+	0.00960773i	−0.000551949	+	0.000956004i	−0.866301	−	0.499522i	$-0.833509\pi$
$101$	−0.00554702	+	0.00960773i	−0.000551949	+	0.000956004i	0.865749	+	0.500478i	$0.166842\pi$
$102$	−1.87262	−	1.87726i	−0.185417	−	0.185877i
$103$	−4.33975	−	7.51666i	−0.427608	−	0.740638i	0.569052	−	0.822301i	$-0.307310\pi$
$103$	−4.33975	−	7.51666i	−0.427608	−	0.740638i	−0.996660	+	0.0816630i	$0.973977\pi$
$104$	2.57903	−	4.46702i	0.252895	−	0.438027i
$105$	−1.02959	+	4.46542i	−0.100478	+	0.435780i
$106$	−1.17832	−	2.04090i	−0.114448	−	0.198230i
$107$	5.98800	−	10.3715i	0.578882	−	1.00265i	−0.416726	−	0.909032i	$-0.636822\pi$
$107$	5.98800	−	10.3715i	0.578882	−	1.00265i	0.995608	−	0.0936210i	$-0.0298442\pi$
$108$	−3.68785	+	3.66056i	−0.354864	+	0.352238i
$109$	4.23436	+	7.33412i	0.405578	+	0.702482i	0.994389	−	0.105789i	$-0.0337369\pi$
$109$	4.23436	+	7.33412i	0.405578	+	0.702482i	−0.588811	+	0.808271i	$0.700404\pi$
$110$	4.27314			0.407428
$111$	−0.966342	+	3.58866i	−0.0917211	+	0.340621i
$112$	1.40545	+	2.24159i	0.132802	+	0.211810i
$113$	7.72987	−	13.3885i	0.727165	−	1.25949i	−0.230912	−	0.972975i	$-0.574171\pi$
$113$	7.72987	−	13.3885i	0.727165	−	1.25949i	0.958077	−	0.286512i	$-0.0924958\pi$
$114$	0.610970	−	2.26893i	0.0572226	−	0.212505i
$115$	4.34447	−	7.52485i	0.405124	−	0.701696i
$116$	4.80226	+	8.31776i	0.445879	+	0.772285i
$117$	0.0383113	−	15.4741i	0.00354188	−	1.43059i
$118$	−11.5227			−1.06075
$119$	−1.89608	+	3.57912i	−0.173813	+	0.328098i
$120$	1.22323	+	1.22626i	0.111665	+	0.111942i
$121$	−3.62985	−	6.28709i	−0.329986	−	0.571553i
$122$	−4.13399			−0.374274
$123$	−1.52549	+	5.66514i	−0.137549	+	0.510808i
$124$	5.16605			0.463925
$125$	1.00000			0.0894427
$126$	7.00462	+	3.73300i	0.624021	+	0.332562i
$127$	−9.87266			−0.876057			−0.438029	−	0.898961i	$-0.644323\pi$
$127$	−9.87266			−0.876057			−0.438029	+	0.898961i	$0.644323\pi$
$128$	1.00000			0.0883883
$129$	11.2652	+	11.2932i	0.991849	+	0.994308i
$130$	−5.15806			−0.452392
$131$	−3.16775	−	5.48671i	−0.276768	−	0.479376i	0.693812	−	0.720156i	$-0.255930\pi$
$131$	−3.16775	−	5.48671i	−0.276768	−	0.479376i	−0.970580	+	0.240781i	$0.922597\pi$
$132$	1.92444	−	7.14672i	0.167501	−	0.622042i
$133$	−3.58693	+	0.130722i	−0.311026	+	0.0113350i
$134$	9.57147			0.826849
$135$	5.01407	+	1.36349i	0.431542	+	0.117351i
$136$	0.765442	+	1.32578i	0.0656361	+	0.113685i
$137$	−0.820898	+	1.42184i	−0.0701341	+	0.121476i	−0.898960	−	0.438031i	$-0.855676\pi$
$137$	−0.820898	+	1.42184i	−0.0701341	+	0.121476i	0.828826	+	0.559507i	$0.189009\pi$
$138$	−10.6286	−	10.6549i	−0.904763	−	0.907006i
$139$	1.54119	−	2.66942i	0.130722	−	0.226417i	−0.793233	−	0.608918i	$-0.791604\pi$
$139$	1.54119	−	2.66942i	0.130722	−	0.226417i	0.923955	+	0.382501i	$0.124937\pi$
$140$	1.23855	−	2.33795i	0.104677	−	0.197593i
$141$	−16.9333	+	4.51480i	−1.42604	+	0.380215i
$142$	−7.27314			−0.610348
$143$	11.0206	+	19.0882i	0.921585	+	1.59623i
$144$	2.60178	−	1.49356i	0.216815	−	0.124464i
$145$	4.80226	−	8.31776i	0.398806	−	0.690752i
$146$	−1.83021	−	3.17001i	−0.151469	−	0.262352i
$147$	2.29196	−	11.9058i	0.189037	−	0.981970i
$148$	1.07286	−	1.85825i	0.0881884	−	0.152747i
$149$	−6.99840	−	12.1216i	−0.573331	−	0.993038i	−0.996221	−	0.0868573i	$-0.972318\pi$
$149$	−6.99840	−	12.1216i	−0.573331	−	0.993038i	0.422890	−	0.906181i	$-0.361016\pi$
$150$	0.450358	−	1.67248i	0.0367716	−	0.136557i
$151$	10.9011	−	18.8812i	0.887117	−	1.53653i	0.0438487	−	0.999038i	$-0.486038\pi$
$151$	10.9011	−	18.8812i	0.887117	−	1.53653i	0.843268	−	0.537493i	$-0.180629\pi$
$152$	−0.678316	+	1.17488i	−0.0550187	+	0.0952951i
$153$	3.97166	+	2.30617i	0.321089	+	0.186442i
$154$	−11.2982	+	0.411749i	−0.910432	+	0.0331797i
$155$	−2.58302	−	4.47393i	−0.207473	−	0.359355i
$156$	−2.32298	+	8.62674i	−0.185987	+	0.690692i
$157$	−6.19018			−0.494030			−0.247015	−	0.969012i	$-0.579450\pi$
$157$	−6.19018			−0.494030			−0.247015	+	0.969012i	$0.579450\pi$
$158$	−6.44646			−0.512852
$159$	2.88270	+	2.88984i	0.228613	+	0.229179i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−10.7617	+	20.3143i	−0.848141	+	1.60099i
$162$	4.53854	−	7.77185i	0.356581	−	0.610614i
$163$	2.42476	−	4.19981i	0.189922	−	0.328954i	−0.755302	−	0.655377i	$-0.772510\pi$
$163$	2.42476	−	4.19981i	0.189922	−	0.328954i	0.945224	+	0.326422i	$0.105843\pi$
$164$	1.69364	−	2.93347i	0.132251	−	0.229065i
$165$	−7.15146	+	1.90674i	−0.556741	+	0.148440i
$166$	−4.21040	−	7.29263i	−0.326791	−	0.566018i
$167$	−4.20095	+	7.27625i	−0.325079	+	0.563053i	−0.981528	−	0.191317i	$-0.938724\pi$
$167$	−4.20095	+	7.27625i	−0.325079	+	0.563053i	0.656449	+	0.754370i	$0.272058\pi$
$168$	−3.35237	−	3.12436i	−0.258641	−	0.241050i
$169$	−6.80282	−	11.7828i	−0.523294	−	0.906371i
$170$	0.765442	−	1.32578i	0.0587067	−	0.101683i
$171$	−0.0100763	+	4.06988i	−0.000770554	+	0.311232i
$172$	−4.60472	−	7.97561i	−0.351107	−	0.608134i
$173$	−1.66675			−0.126721			−0.0633603	−	0.997991i	$-0.520182\pi$
$173$	−1.66675			−0.126721			−0.0633603	+	0.997991i	$0.520182\pi$
$174$	−11.7485	−	11.7776i	−0.890653	−	0.892861i
$175$	−2.64400	+	0.0963576i	−0.199867	+	0.00728395i
$176$	−2.13657	+	3.70065i	−0.161050	+	0.278947i
$177$	19.2842	−	5.14161i	1.44949	−	0.386467i
$178$	−6.50852	+	11.2731i	−0.487834	+	0.844954i
$179$	10.7128	+	18.5550i	0.800709	+	1.38687i	0.919150	+	0.393907i	$0.128877\pi$
$179$	10.7128	+	18.5550i	0.800709	+	1.38687i	−0.118442	+	0.992961i	$0.537790\pi$
$180$	−2.59435	−	1.50643i	−0.193372	−	0.112282i
$181$	19.7789			1.47015			0.735075	−	0.677985i	$-0.237147\pi$
$181$	19.7789			1.47015			0.735075	+	0.677985i	$0.237147\pi$
$182$	13.6379	−	0.497019i	1.01091	−	0.0368415i
$183$	6.91859	−	1.84465i	0.511437	−	0.136361i
$184$	4.34447	+	7.52485i	0.320279	+	0.554739i
$185$	−2.14572			−0.157756
$186$	−8.64583	+	2.30518i	−0.633943	+	0.169024i
$187$	−6.54168			−0.478375
$188$	10.1180			0.737928
$189$	−13.3886	−	3.12193i	−0.973875	−	0.227087i
$190$	1.35663			0.0984204
$191$	0.0842687			0.00609747			0.00304874	−	0.999995i	$-0.499030\pi$
$191$	0.0842687			0.00609747			0.00304874	+	0.999995i	$0.499030\pi$
$192$	−1.67359	+	0.446216i	−0.120781	+	0.0322029i
$193$	10.5925			0.762468			0.381234	−	0.924479i	$-0.375499\pi$
$193$	10.5925			0.762468			0.381234	+	0.924479i	$0.375499\pi$
$194$	−4.67765	−	8.10193i	−0.335836	−	0.581684i
$195$	8.63247	−	2.30161i	0.618184	−	0.164822i
$196$	−3.04944	+	6.30087i	−0.217817	+	0.450062i
$197$	−17.9858			−1.28144			−0.640718	−	0.767776i	$-0.721363\pi$
$197$	−17.9858			−1.28144			−0.640718	+	0.767776i	$0.721363\pi$
$198$	−0.0317385	+	12.8194i	−0.00225556	+	0.911033i
$199$	11.6593	+	20.1945i	0.826504	+	1.43155i	0.900764	+	0.434309i	$0.143007\pi$
$199$	11.6593	+	20.1945i	0.826504	+	1.43155i	−0.0742598	+	0.997239i	$0.523659\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−16.0187	+	4.27094i	−1.12987	+	0.301249i
$202$	−0.00554702	+	0.00960773i	−0.000390287	+	0.000675997i
$203$	−11.8957	+	22.4549i	−0.834913	+	1.57602i
$204$	−1.87262	−	1.87726i	−0.131110	−	0.131435i
$205$	−3.38728			−0.236578
$206$	−4.33975	−	7.51666i	−0.302364	−	0.523710i
$207$	22.5422	+	13.0893i	1.56679	+	0.909767i
$208$	2.57903	−	4.46702i	0.178824	−	0.309732i
$209$	−2.89854	−	5.02041i	−0.200496	−	0.347269i
$210$	−1.02959	+	4.46542i	−0.0710485	+	0.308143i
$211$	−2.29045	+	3.96718i	−0.157681	+	0.273112i	−0.934032	−	0.357189i	$-0.883735\pi$
$211$	−2.29045	+	3.96718i	−0.157681	+	0.273112i	0.776351	+	0.630301i	$0.217068\pi$
$212$	−1.17832	−	2.04090i	−0.0809270	−	0.140170i
$213$	12.1722	−	3.24539i	0.834027	−	0.222371i
$214$	5.98800	−	10.3715i	0.409331	−	0.708983i
$215$	−4.60472	+	7.97561i	−0.314039	+	0.543932i
$216$	−3.68785	+	3.66056i	−0.250927	+	0.249070i
$217$	7.26060	+	11.5802i	0.492882	+	0.786112i
$218$	4.23436	+	7.33412i	0.286787	+	0.496730i
$219$	4.47752	+	4.48862i	0.302563	+	0.303313i
$220$	4.27314			0.288095
$221$	7.89640			0.531169
$222$	−0.966342	+	3.58866i	−0.0648566	+	0.240855i
$223$	12.1076	+	20.9711i	0.810788	+	1.40433i	0.912313	+	0.409493i	$0.134294\pi$
$223$	12.1076	+	20.9711i	0.810788	+	1.40433i	−0.101525	+	0.994833i	$0.532372\pi$
$224$	1.40545	+	2.24159i	0.0939053	+	0.149772i
$225$	−0.00742745	+	2.99999i	−0.000495163	+	0.199999i
$226$	7.72987	−	13.3885i	0.514183	−	0.890592i
$227$	−4.71096	+	8.15962i	−0.312677	+	0.541573i	−0.978941	−	0.204143i	$-0.934559\pi$
$227$	−4.71096	+	8.15962i	−0.312677	+	0.541573i	0.666264	+	0.745716i	$0.267893\pi$
$228$	0.610970	−	2.26893i	0.0404625	−	0.150264i
$229$	−4.13516	−	7.16232i	−0.273259	−	0.473299i	0.696435	−	0.717620i	$-0.254768\pi$
$229$	−4.13516	−	7.16232i	−0.273259	−	0.473299i	−0.969695	+	0.244321i	$0.921435\pi$
$230$	4.34447	−	7.52485i	0.286466	−	0.496174i
$231$	18.7247	−	5.73052i	1.23200	−	0.377041i
$232$	4.80226	+	8.31776i	0.315284	+	0.546088i
$233$	6.18028	−	10.7046i	0.404883	−	0.701279i	−0.589425	−	0.807823i	$-0.700645\pi$
$233$	6.18028	−	10.7046i	0.404883	−	0.701279i	0.994308	+	0.106545i	$0.0339788\pi$
$234$	0.0383113	−	15.4741i	0.00250449	−	1.01158i
$235$	−5.05898	−	8.76241i	−0.330012	−	0.571597i
$236$	−11.5227			−0.750063
$237$	10.7887	−	2.87651i	0.700801	−	0.186850i
$238$	−1.89608	+	3.57912i	−0.122904	+	0.232000i
$239$	−6.74114	+	11.6760i	−0.436048	+	0.755257i	−0.997381	−	0.0723331i	$-0.976956\pi$
$239$	−6.74114	+	11.6760i	−0.436048	+	0.755257i	0.561333	+	0.827590i	$0.310289\pi$
$240$	1.22323	+	1.22626i	0.0789590	+	0.0791547i
$241$	−7.50216	+	12.9941i	−0.483257	+	0.837025i	−0.999815	−	0.0192268i	$-0.993880\pi$
$241$	−7.50216	+	12.9941i	−0.483257	+	0.837025i	0.516558	+	0.856252i	$0.327213\pi$
$242$	−3.62985	−	6.28709i	−0.233336	−	0.404149i
$243$	−4.12771	+	15.0320i	−0.264793	+	0.964305i
$244$	−4.13399			−0.264652
$245$	6.98143	−	0.509538i	0.446027	−	0.0325532i
$246$	−1.52549	+	5.66514i	−0.0972616	+	0.361196i
$247$	3.49880	+	6.06009i	0.222623	+	0.385594i
$248$	5.16605			0.328044
$249$	10.3006	+	10.3261i	0.652772	+	0.654390i
$250$	1.00000			0.0632456
$251$	−24.3891			−1.53943			−0.769714	−	0.638389i	$-0.779601\pi$
$251$	−24.3891			−1.53943			−0.769714	+	0.638389i	$0.779601\pi$
$252$	7.00462	+	3.73300i	0.441250	+	0.235157i
$253$	−37.1291			−2.33428
$254$	−9.87266			−0.619466
$255$	−0.689446	+	2.56037i	−0.0431748	+	0.160336i
$256$	1.00000			0.0625000
$257$	4.70491	+	8.14914i	0.293484	+	0.508330i	0.974631	−	0.223817i	$-0.0718519\pi$
$257$	4.70491	+	8.14914i	0.293484	+	0.508330i	−0.681147	+	0.732147i	$0.738519\pi$
$258$	11.2652	+	11.2932i	0.701343	+	0.703082i
$259$	5.67327	−	0.206756i	0.352520	−	0.0128472i
$260$	−5.15806			−0.319890
$261$	24.9175	+	14.4685i	1.54236	+	0.895579i
$262$	−3.16775	−	5.48671i	−0.195704	−	0.338970i
$263$	7.09001	−	12.2803i	0.437189	−	0.757233i	−0.560283	−	0.828302i	$-0.689307\pi$
$263$	7.09001	−	12.2803i	0.437189	−	0.757233i	0.997471	+	0.0710681i	$0.0226408\pi$
$264$	1.92444	−	7.14672i	0.118441	−	0.439850i
$265$	−1.17832	+	2.04090i	−0.0723833	+	0.125372i
$266$	−3.58693	+	0.130722i	−0.219929	+	0.00801506i
$267$	5.86234	−	21.7707i	0.358769	−	1.33235i
$268$	9.57147			0.584670
$269$	−4.33682	−	7.51159i	−0.264421	−	0.457990i	0.702991	−	0.711199i	$-0.251847\pi$
$269$	−4.33682	−	7.51159i	−0.264421	−	0.457990i	−0.967412	+	0.253209i	$0.918514\pi$
$270$	5.01407	+	1.36349i	0.305147	+	0.0829796i
$271$	12.9744	−	22.4723i	0.788137	−	1.36509i	−0.138970	−	0.990297i	$-0.544379\pi$
$271$	12.9744	−	22.4723i	0.788137	−	1.36509i	0.927107	−	0.374797i	$-0.122287\pi$
$272$	0.765442	+	1.32578i	0.0464117	+	0.0803875i
$273$	−22.6024	+	6.91726i	−1.36796	+	0.418652i
$274$	−0.820898	+	1.42184i	−0.0495923	+	0.0858964i
$275$	−2.13657	−	3.70065i	−0.128840	−	0.223157i
$276$	−10.6286	−	10.6549i	−0.639764	−	0.641350i
$277$	7.53988	−	13.0594i	0.453027	−	0.784666i	−0.545545	−	0.838081i	$-0.683677\pi$
$277$	7.53988	−	13.0594i	0.453027	−	0.784666i	0.998572	+	0.0534153i	$0.0170107\pi$
$278$	1.54119	−	2.66942i	0.0924343	−	0.160101i
$279$	13.4409	−	7.71582i	0.804688	−	0.461934i
$280$	1.23855	−	2.33795i	0.0740175	−	0.139719i
$281$	−7.33403	−	12.7029i	−0.437512	−	0.757792i	0.559985	−	0.828503i	$-0.310807\pi$
$281$	−7.33403	−	12.7029i	−0.437512	−	0.757792i	−0.997497	+	0.0707103i	$0.977473\pi$
$282$	−16.9333	+	4.51480i	−1.00836	+	0.268852i
$283$	−11.8762			−0.705966			−0.352983	−	0.935630i	$-0.614833\pi$
$283$	−11.8762			−0.705966			−0.352983	+	0.935630i	$0.614833\pi$
$284$	−7.27314			−0.431581
$285$	−2.27044	+	0.605351i	−0.134489	+	0.0358579i
$286$	11.0206	+	19.0882i	0.651659	+	1.12871i
$287$	8.95594	−	0.326390i	0.528653	−	0.0192662i
$288$	2.60178	−	1.49356i	0.153311	−	0.0880090i
$289$	7.32820	−	12.6928i	0.431070	−	0.746636i
$290$	4.80226	−	8.31776i	0.281998	−	0.488436i
$291$	11.4437	+	11.4720i	0.670839	+	0.672502i
$292$	−1.83021	−	3.17001i	−0.107105	−	0.185511i
$293$	12.7190	−	22.0299i	0.743051	−	1.28700i	−0.208049	−	0.978118i	$-0.566711\pi$
$293$	12.7190	−	22.0299i	0.743051	−	1.28700i	0.951100	−	0.308883i	$-0.0999552\pi$
$294$	2.29196	−	11.9058i	0.133670	−	0.694358i
$295$	5.76134	+	9.97893i	0.335438	+	0.580996i
$296$	1.07286	−	1.85825i	0.0623586	−	0.108008i
$297$	−5.66710	−	21.4685i	−0.328838	−	1.24573i
$298$	−6.99840	−	12.1216i	−0.405406	−	0.702184i
$299$	44.8182			2.59190
$300$	0.450358	−	1.67248i	0.0260015	−	0.0965605i
$301$	11.4064	−	21.5312i	0.657451	−	1.24104i
$302$	10.9011	−	18.8812i	0.627286	−	1.08649i
$303$	0.00499630	−	0.0185545i	0.000287030	−	0.00106593i
$304$	−0.678316	+	1.17488i	−0.0389041	+	0.0673838i
$305$	2.06700	+	3.58014i	0.118356	+	0.204998i
$306$	3.97166	+	2.30617i	0.227044	+	0.131835i
$307$	7.51672			0.429002			0.214501	−	0.976724i	$-0.431187\pi$
$307$	7.51672			0.429002			0.214501	+	0.976724i	$0.431187\pi$
$308$	−11.2982	+	0.411749i	−0.643772	+	0.0234616i
$309$	10.6170	+	10.6433i	0.603980	+	0.605477i
$310$	−2.58302	−	4.47393i	−0.146706	−	0.254102i
$311$	−24.5570			−1.39250			−0.696250	−	0.717799i	$-0.745150\pi$
$311$	−24.5570			−1.39250			−0.696250	+	0.717799i	$0.745150\pi$
$312$	−2.32298	+	8.62674i	−0.131513	+	0.488393i
$313$	−19.1101			−1.08017			−0.540084	−	0.841611i	$-0.681607\pi$
$313$	−19.1101			−1.08017			−0.540084	+	0.841611i	$0.681607\pi$
$314$	−6.19018			−0.349332
$315$	−0.269434	−	7.93268i	−0.0151809	−	0.446956i
$316$	−6.44646			−0.362641
$317$	1.00054			0.0561957			0.0280978	−	0.999605i	$-0.491055\pi$
$317$	1.00054			0.0561957			0.0280978	+	0.999605i	$0.491055\pi$
$318$	2.88270	+	2.88984i	0.161654	+	0.162054i
$319$	−41.0414			−2.29788
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−5.39350	+	20.0296i	−0.301036	+	1.11794i
$322$	−10.7617	+	20.3143i	−0.599726	+	1.13207i
$323$	−2.07684			−0.115559
$324$	4.53854	−	7.77185i	0.252141	−	0.431769i
$325$	2.57903	+	4.46702i	0.143059	+	0.247785i
$326$	2.42476	−	4.19981i	0.134295	−	0.232606i
$327$	−10.3592	−	10.3849i	−0.572863	−	0.574284i
$328$	1.69364	−	2.93347i	0.0935155	−	0.161974i
$329$	14.2203	+	22.6803i	0.783988	+	1.25041i
$330$	−7.15146	+	1.90674i	−0.393675	+	0.104963i
$331$	−4.00106			−0.219918			−0.109959	−	0.993936i	$-0.535072\pi$
$331$	−4.00106			−0.219918			−0.109959	+	0.993936i	$0.535072\pi$
$332$	−4.21040	−	7.29263i	−0.231076	−	0.400235i
$333$	0.0159372	−	6.43713i	0.000873353	−	0.352753i
$334$	−4.20095	+	7.27625i	−0.229866	+	0.398139i
$335$	−4.78573	−	8.28913i	−0.261473	−	0.452884i
$336$	−3.35237	−	3.12436i	−0.182887	−	0.170448i
$337$	−15.9279	+	27.5879i	−0.867646	+	1.50281i	−0.00324955	+	0.999995i	$0.501034\pi$
$337$	−15.9279	+	27.5879i	−0.867646	+	1.50281i	−0.864396	+	0.502812i	$0.832299\pi$
$338$	−6.80282	−	11.7828i	−0.370024	−	0.640901i
$339$	−6.96242	+	25.8560i	−0.378147	+	1.40431i
$340$	0.765442	−	1.32578i	0.0415119	−	0.0719007i
$341$	−11.0376	+	19.1177i	−0.597720	+	1.03528i
$342$	−0.0100763	+	4.06988i	−0.000544864	+	0.220074i
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$	−4.60472	−	7.97561i	−0.248270	−	0.430016i
$345$	−3.91314	+	14.5321i	−0.210676	+	0.782380i
$346$	−1.66675			−0.0896049
$347$	−8.25454			−0.443127			−0.221563	−	0.975146i	$-0.571116\pi$
$347$	−8.25454			−0.443127			−0.221563	+	0.975146i	$0.571116\pi$
$348$	−11.7485	−	11.7776i	−0.629787	−	0.631348i
$349$	0.793152	+	1.37378i	0.0424564	+	0.0735367i	0.886473	−	0.462781i	$-0.153148\pi$
$349$	0.793152	+	1.37378i	0.0424564	+	0.0735367i	−0.844016	+	0.536318i	$0.819815\pi$
$350$	−2.64400	+	0.0963576i	−0.141328	+	0.00515053i
$351$	6.84070	+	25.9144i	0.365130	+	1.38321i
$352$	−2.13657	+	3.70065i	−0.113879	+	0.197245i
$353$	6.36496	−	11.0244i	0.338773	−	0.586772i	−0.645429	−	0.763820i	$-0.723322\pi$
$353$	6.36496	−	11.0244i	0.338773	−	0.586772i	0.984202	+	0.177048i	$0.0566548\pi$
$354$	19.2842	−	5.14161i	1.02494	−	0.273273i
$355$	3.63657	+	6.29872i	0.193009	+	0.334301i
$356$	−6.50852	+	11.2731i	−0.344951	+	0.597473i
$357$	1.57618	−	6.83603i	0.0834204	−	0.361801i
$358$	10.7128	+	18.5550i	0.566187	+	0.980664i
$359$	−0.786031	+	1.36145i	−0.0414851	+	0.0718544i	−0.886022	−	0.463642i	$-0.846542\pi$
$359$	−0.786031	+	1.36145i	−0.0414851	+	0.0718544i	0.844537	+	0.535497i	$0.179876\pi$
$360$	−2.59435	−	1.50643i	−0.136734	−	0.0793957i
$361$	8.57978	+	14.8606i	0.451567	+	0.782137i
$362$	19.7789			1.03955
$363$	8.88027	+	8.90228i	0.466093	+	0.467249i
$364$	13.6379	−	0.497019i	0.714820	−	0.0260509i
$365$	−1.83021	+	3.17001i	−0.0957974	+	0.165926i
$366$	6.91859	−	1.84465i	0.361640	−	0.0964216i
$367$	14.5348	−	25.1750i	0.758710	−	1.31412i	−0.184799	−	0.982776i	$-0.559163\pi$
$367$	14.5348	−	25.1750i	0.758710	−	1.31412i	0.943509	−	0.331348i	$-0.107503\pi$
$368$	4.34447	+	7.52485i	0.226471	+	0.392260i
$369$	0.0251588	−	10.1618i	0.00130972	−	0.529002i
$370$	−2.14572			−0.111550
$371$	2.91881	−	5.50968i	0.151537	−	0.286048i
$372$	−8.64583	+	2.30518i	−0.448265	+	0.119518i
$373$	14.4271	+	24.9884i	0.747005	+	1.29385i	0.949252	+	0.314516i	$0.101842\pi$
$373$	14.4271	+	24.9884i	0.747005	+	1.29385i	−0.202247	+	0.979335i	$0.564824\pi$
$374$	−6.54168			−0.338262
$375$	−1.67359	+	0.446216i	−0.0864236	+	0.0230425i
$376$	10.1180			0.521794
$377$	49.5407			2.55148
$378$	−13.3886	−	3.12193i	−0.688633	−	0.160575i
$379$	−28.2079			−1.44894			−0.724472	−	0.689304i	$-0.757917\pi$
$379$	−28.2079			−1.44894			−0.724472	+	0.689304i	$0.757917\pi$
$380$	1.35663			0.0695937
$381$	16.5228	−	4.40534i	0.846486	−	0.225693i
$382$	0.0842687			0.00431156
$383$	3.59518	+	6.22704i	0.183705	+	0.318187i	0.943139	−	0.332397i	$-0.107857\pi$
$383$	3.59518	+	6.22704i	0.183705	+	0.318187i	−0.759434	+	0.650584i	$0.774524\pi$
$384$	−1.67359	+	0.446216i	−0.0854048	+	0.0227709i
$385$	6.00566	+	9.57862i	0.306077	+	0.488172i
$386$	10.5925			0.539147
$387$	−23.8926	−	13.8734i	−1.21453	−	0.705222i
$388$	−4.67765	−	8.10193i	−0.237472	−	0.411313i
$389$	18.6082	−	32.2303i	0.943471	−	1.63414i	0.184688	−	0.982797i	$-0.440872\pi$
$389$	18.6082	−	32.2303i	0.943471	−	1.63414i	0.758783	−	0.651343i	$-0.225794\pi$
$390$	8.63247	−	2.30161i	0.437122	−	0.116547i
$391$	−6.65089	+	11.5197i	−0.336350	+	0.582575i
$392$	−3.04944	+	6.30087i	−0.154020	+	0.318242i
$393$	7.74976	+	7.76897i	0.390924	+	0.391893i
$394$	−17.9858			−0.906113
$395$	3.22323	+	5.58279i	0.162178	+	0.280901i
$396$	−0.0317385	+	12.8194i	−0.00159492	+	0.644198i
$397$	−4.61549	+	7.99427i	−0.231645	+	0.401221i	−0.958292	−	0.285790i	$-0.907744\pi$
$397$	−4.61549	+	7.99427i	−0.231645	+	0.401221i	0.726647	+	0.687011i	$0.241077\pi$
$398$	11.6593	+	20.1945i	0.584427	+	1.01226i
$399$	5.94470	−	1.81932i	0.297607	−	0.0910799i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−6.38363	−	11.0568i	−0.318783	−	0.552149i	0.661451	−	0.749988i	$-0.269941\pi$
$401$	−6.38363	−	11.0568i	−0.318783	−	0.552149i	−0.980234	+	0.197839i	$0.936608\pi$
$402$	−16.0187	+	4.27094i	−0.798939	+	0.213015i
$403$	13.3234	−	23.0768i	0.663686	−	1.14954i
$404$	−0.00554702	+	0.00960773i	−0.000275975	+	0.000478002i
$405$	−8.99989	−	0.0445646i	−0.447208	−	0.00221443i
$406$	−11.8957	+	22.4549i	−0.590373	+	1.11442i
$407$	4.58447	+	7.94054i	0.227244	+	0.393598i
$408$	−1.87262	−	1.87726i	−0.0927085	−	0.0929383i
$409$	−13.6602			−0.675452			−0.337726	−	0.941244i	$-0.609658\pi$
$409$	−13.6602			−0.675452			−0.337726	+	0.941244i	$0.609658\pi$
$410$	−3.38728			−0.167286
$411$	0.739397	−	2.74587i	0.0364718	−	0.135444i
$412$	−4.33975	−	7.51666i	−0.213804	−	0.370319i
$413$	−16.1945	−	25.8291i	−0.796880	−	1.27097i
$414$	22.5422	+	13.0893i	1.10789	+	0.643303i
$415$	−4.21040	+	7.29263i	−0.206681	+	0.357981i
$416$	2.57903	−	4.46702i	0.126447	−	0.219013i
$417$	−1.38817	+	5.15520i	−0.0679792	+	0.252451i
$418$	−2.89854	−	5.02041i	−0.141772	−	0.245556i
$419$	14.0027	−	24.2535i	0.684078	−	1.18486i	−0.289647	−	0.957134i	$-0.593538\pi$
$419$	14.0027	−	24.2535i	0.684078	−	1.18486i	0.973725	−	0.227725i	$-0.0731287\pi$
$420$	−1.02959	+	4.46542i	−0.0502389	+	0.217890i
$421$	7.73475	+	13.3970i	0.376969	+	0.652929i	0.990620	−	0.136649i	$-0.0436331\pi$
$421$	7.73475	+	13.3970i	0.376969	+	0.652929i	−0.613651	+	0.789577i	$0.710300\pi$
$422$	−2.29045	+	3.96718i	−0.111497	+	0.193119i
$423$	26.3247	−	15.1118i	1.27995	−	0.734762i
$424$	−1.17832	−	2.04090i	−0.0572241	−	0.0991150i
$425$	−1.53088			−0.0742588
$426$	12.1722	−	3.24539i	0.589746	−	0.157240i
$427$	−5.81010	−	9.26671i	−0.281171	−	0.448447i
$428$	5.98800	−	10.3715i	0.289441	−	0.501327i
$429$	−26.9613	−	27.0281i	−1.30170	−	1.30493i
$430$	−4.60472	+	7.97561i	−0.222059	+	0.384618i
$431$	−14.0831	−	24.3926i	−0.678359	−	1.17495i	−0.975475	−	0.220110i	$-0.929358\pi$
$431$	−14.0831	−	24.3926i	−0.678359	−	1.17495i	0.297116	−	0.954841i	$-0.403975\pi$
$432$	−3.68785	+	3.66056i	−0.177432	+	0.176119i
$433$	21.0723			1.01267			0.506335	−	0.862337i	$-0.331000\pi$
$433$	21.0723			1.01267			0.506335	+	0.862337i	$0.331000\pi$
$434$	7.26060	+	11.5802i	0.348520	+	0.555865i
$435$	−4.32548	+	16.0633i	−0.207391	+	0.770178i
$436$	4.23436	+	7.33412i	0.202789	+	0.351241i
$437$	−11.7877			−0.563882
$438$	4.47752	+	4.48862i	0.213944	+	0.214474i
$439$	12.5687			0.599872			0.299936	−	0.953959i	$-0.403035\pi$
$439$	12.5687			0.599872			0.299936	+	0.953959i	$0.403035\pi$
$440$	4.27314			0.203714
$441$	1.47676	+	20.9480i	0.0703217	+	0.997524i
$442$	7.89640			0.375593
$443$	14.3908			0.683729			0.341864	−	0.939749i	$-0.388942\pi$
$443$	14.3908			0.683729			0.341864	+	0.939749i	$0.388942\pi$
$444$	−0.966342	+	3.58866i	−0.0458605	+	0.170310i
$445$	13.0170			0.617067
$446$	12.1076	+	20.9711i	0.573314	+	0.993008i
$447$	17.1213	+	17.1637i	0.809808	+	0.811816i
$448$	1.40545	+	2.24159i	0.0664011	+	0.105905i
$449$	11.2511			0.530973			0.265486	−	0.964115i	$-0.414467\pi$
$449$	11.2511			0.530973			0.265486	+	0.964115i	$0.414467\pi$
$450$	−0.00742745	+	2.99999i	−0.000350133	+	0.141421i
$451$	7.23715	+	12.5351i	0.340784	+	0.590255i
$452$	7.72987	−	13.3885i	0.363582	−	0.629743i
$453$	−9.81878	+	36.4636i	−0.461327	+	1.71321i
$454$	−4.71096	+	8.15962i	−0.221096	+	0.382950i
$455$	−7.24938	−	11.5623i	−0.339856	−	0.542047i
$456$	0.610970	−	2.26893i	0.0286113	−	0.106253i
$457$	−4.96710			−0.232351			−0.116176	−	0.993229i	$-0.537064\pi$
$457$	−4.96710			−0.232351			−0.116176	+	0.993229i	$0.537064\pi$
$458$	−4.13516	−	7.16232i	−0.193224	−	0.334673i
$459$	−7.67596	−	2.08735i	−0.358283	−	0.0974292i
$460$	4.34447	−	7.52485i	0.202562	−	0.350848i
$461$	−10.1629	−	17.6027i	−0.473335	−	0.819840i	0.526199	−	0.850361i	$-0.323617\pi$
$461$	−10.1629	−	17.6027i	−0.473335	−	0.819840i	−0.999534	+	0.0305210i	$0.990283\pi$
$462$	18.7247	−	5.73052i	0.871152	−	0.266608i
$463$	8.34268	−	14.4499i	0.387717	−	0.671546i	−0.604425	−	0.796662i	$-0.706597\pi$
$463$	8.34268	−	14.4499i	0.387717	−	0.671546i	0.992142	+	0.125116i	$0.0399304\pi$
$464$	4.80226	+	8.31776i	0.222939	+	0.386142i
$465$	6.31925	+	6.33492i	0.293048	+	0.293775i
$466$	6.18028	−	10.7046i	0.286296	−	0.495879i
$467$	−17.1435	+	29.6935i	−0.793308	+	1.37405i	0.130600	+	0.991435i	$0.458310\pi$
$467$	−17.1435	+	29.6935i	−0.793308	+	1.37405i	−0.923908	+	0.382615i	$0.875024\pi$
$468$	0.0383113	−	15.4741i	0.00177094	−	0.715293i
$469$	13.4522	+	21.4553i	0.621164	+	0.990713i
$470$	−5.05898	−	8.76241i	−0.233353	−	0.404180i
$471$	10.3598	−	2.76216i	0.477355	−	0.127274i
$472$	−11.5227			−0.530374
$473$	39.3532			1.80946
$474$	10.7887	−	2.87651i	0.495541	−	0.132123i
$475$	−0.678316	−	1.17488i	−0.0311233	−	0.0539071i
$476$	−1.89608	+	3.57912i	−0.0869065	+	0.164049i
$477$	−6.11394	−	3.55009i	−0.279938	−	0.162548i
$478$	−6.74114	+	11.6760i	−0.308332	+	0.534047i
$479$	−10.0398	+	17.3895i	−0.458731	+	0.794546i	−0.998894	−	0.0470146i	$-0.985029\pi$
$479$	−10.0398	+	17.3895i	−0.458731	+	0.794546i	0.540163	+	0.841560i	$0.318363\pi$
$480$	1.22323	+	1.22626i	0.0558325	+	0.0559709i
$481$	−5.53387	−	9.58495i	−0.252323	−	0.437036i
$482$	−7.50216	+	12.9941i	−0.341714	+	0.591866i
$483$	8.94606	−	38.7998i	0.407060	−	1.76545i
$484$	−3.62985	−	6.28709i	−0.164993	−	0.285777i
$485$	−4.67765	+	8.10193i	−0.212401	+	0.367889i
$486$	−4.12771	+	15.0320i	−0.187237	+	0.681867i
$487$	7.56980	+	13.1113i	0.343021	+	0.594129i	0.984992	−	0.172599i	$-0.0552166\pi$
$487$	7.56980	+	13.1113i	0.343021	+	0.594129i	−0.641972	+	0.766728i	$0.721883\pi$
$488$	−4.13399			−0.187137
$489$	−2.18402	+	8.11071i	−0.0987649	+	0.366779i
$490$	6.98143	−	0.509538i	0.315389	−	0.0230186i
$491$	12.5900	−	21.8064i	0.568177	−	0.984111i	−0.428570	−	0.903509i	$-0.640982\pi$
$491$	12.5900	−	21.8064i	0.568177	−	0.984111i	0.996746	−	0.0806021i	$-0.0256843\pi$
$492$	−1.52549	+	5.66514i	−0.0687743	+	0.255404i
$493$	−7.35170	+	12.7335i	−0.331104	+	0.573489i
$494$	3.49880	+	6.06009i	0.157418	+	0.272656i
$495$	11.1178	−	6.38220i	0.499707	−	0.286859i
$496$	5.16605			0.231962
$497$	−10.2220	−	16.3034i	−0.458519	−	0.731307i
$498$	10.3006	+	10.3261i	0.461579	+	0.462724i
$499$	−1.23811	−	2.14447i	−0.0554254	−	0.0959997i	0.836981	−	0.547231i	$-0.184318\pi$
$499$	−1.23811	−	2.14447i	−0.0554254	−	0.0959997i	−0.892407	+	0.451232i	$0.850985\pi$
$500$	1.00000			0.0447214
$501$	3.78386	−	14.0520i	0.169051	−	0.627795i
$502$	−24.3891			−1.08854
$503$	−6.23467			−0.277990			−0.138995	−	0.990293i	$-0.544387\pi$
$503$	−6.23467			−0.277990			−0.138995	+	0.990293i	$0.544387\pi$
$504$	7.00462	+	3.73300i	0.312011	+	0.166281i
$505$	0.0110940			0.000493679
$506$	−37.1291			−1.65059
$507$	16.6428	+	16.6840i	0.739132	+	0.740964i
$508$	−9.87266			−0.438029
$509$	2.93954	+	5.09143i	0.130293	+	0.225673i	0.923789	−	0.382901i	$-0.125075\pi$
$509$	2.93954	+	5.09143i	0.130293	+	0.225673i	−0.793497	+	0.608575i	$0.791742\pi$
$510$	−0.689446	+	2.56037i	−0.0305292	+	0.113375i
$511$	4.53360	−	8.55785i	0.200555	−	0.378577i
$512$	1.00000			0.0441942
$513$	−1.79918	−	6.81579i	−0.0794359	−	0.300925i
$514$	4.70491	+	8.14914i	0.207525	+	0.359443i
$515$	−4.33975	+	7.51666i	−0.191232	+	0.331224i
$516$	11.2652	+	11.2932i	0.495925	+	0.497154i
$517$	−21.6177	+	37.4430i	−0.950746	+	1.64674i
$518$	5.67327	−	0.206756i	0.249269	−	0.00908434i
$519$	2.78945	−	0.743730i	0.122443	−	0.0326461i
$520$	−5.15806			−0.226196
$521$	4.48094	+	7.76122i	0.196314	+	0.340025i	0.947330	−	0.320258i	$-0.103770\pi$
$521$	4.48094	+	7.76122i	0.196314	+	0.340025i	−0.751017	+	0.660283i	$0.770436\pi$
$522$	24.9175	+	14.4685i	1.09061	+	0.633270i
$523$	11.1315	−	19.2802i	0.486744	−	0.843066i	−0.513139	−	0.858305i	$-0.671518\pi$
$523$	11.1315	−	19.2802i	0.486744	−	0.843066i	0.999884	+	0.0152392i	$0.00485096\pi$
$524$	−3.16775	−	5.48671i	−0.138384	−	0.239688i
$525$	4.38196	−	1.34106i	0.191244	−	0.0585285i
$526$	7.09001	−	12.2803i	0.309139	−	0.535445i
$527$	3.95431	+	6.84907i	0.172252	+	0.298350i
$528$	1.92444	−	7.14672i	0.0837507	−	0.311021i
$529$	−26.2489	+	45.4645i	−1.14126	+	1.97672i
$530$	−1.17832	+	2.04090i	−0.0511828	+	0.0886511i
$531$	−29.9795	+	17.2098i	−1.30100	+	0.746844i
$532$	−3.58693	+	0.130722i	−0.155513	+	0.00566750i
$533$	−8.73589	−	15.1310i	−0.378394	−	0.655397i
$534$	5.86234	−	21.7707i	0.253688	−	0.942110i
$535$	−11.9760			−0.517768
$536$	9.57147			0.413424
$537$	−26.2083	−	26.2732i	−1.13097	−	1.13377i
$538$	−4.33682	−	7.51159i	−0.186974	−	0.323848i
$539$	−16.8019	−	24.7471i	−0.723710	−	1.06593i
$540$	5.01407	+	1.36349i	0.215771	+	0.0586754i
$541$	−1.64785	+	2.85416i	−0.0708466	+	0.122710i	−0.899273	−	0.437389i	$-0.855903\pi$
$541$	−1.64785	+	2.85416i	−0.0708466	+	0.122710i	0.828426	+	0.560099i	$0.189237\pi$
$542$	12.9744	−	22.4723i	0.557297	−	0.965267i
$543$	−33.1016	+	8.82565i	−1.42053	+	0.378745i
$544$	0.765442	+	1.32578i	0.0328181	+	0.0568425i
$545$	4.23436	−	7.33412i	0.181380	−	0.314159i
$546$	−22.6024	+	6.91726i	−0.967295	+	0.296031i
$547$	−17.2194	−	29.8249i	−0.736248	−	1.27522i	−0.954173	−	0.299254i	$-0.903262\pi$
$547$	−17.2194	−	29.8249i	−0.736248	−	1.27522i	0.217925	−	0.975966i	$-0.430071\pi$
$548$	−0.820898	+	1.42184i	−0.0350670	+	0.0607379i
$549$	−10.7557	+	6.17438i	−0.459044	+	0.263516i
$550$	−2.13657	−	3.70065i	−0.0911036	−	0.157796i
$551$	−13.0298			−0.555088
$552$	−10.6286	−	10.6549i	−0.452382	−	0.453503i
$553$	−9.06015	−	14.4503i	−0.385277	−	0.614489i
$554$	7.53988	−	13.0594i	0.320339	−	0.554843i
$555$	3.59104	−	0.957454i	0.152431	−	0.0406417i
$556$	1.54119	−	2.66942i	0.0653609	−	0.113208i
$557$	4.33676	+	7.51149i	0.183754	+	0.318272i	0.943156	−	0.332350i	$-0.107842\pi$
$557$	4.33676	+	7.51149i	0.183754	+	0.318272i	−0.759402	+	0.650622i	$0.774508\pi$
$558$	13.4409	−	7.71582i	0.569000	−	0.326637i
$559$	−47.5029			−2.00916
$560$	1.23855	−	2.33795i	0.0523383	−	0.0987963i
$561$	10.9481	−	2.91900i	0.462227	−	0.123240i
$562$	−7.33403	−	12.7029i	−0.309367	−	0.535840i
$563$	−29.8588			−1.25840			−0.629199	−	0.777244i	$-0.716617\pi$
$563$	−29.8588			−1.25840			−0.629199	+	0.777244i	$0.716617\pi$
$564$	−16.9333	+	4.51480i	−0.713020	+	0.190107i
$565$	−15.4597			−0.650396
$566$	−11.8762			−0.499193
$567$	23.8000	−	0.749379i	0.999505	−	0.0314710i
$568$	−7.27314			−0.305174
$569$	11.3329			0.475101			0.237551	−	0.971375i	$-0.423655\pi$
$569$	11.3329			0.475101			0.237551	+	0.971375i	$0.423655\pi$
$570$	−2.27044	+	0.605351i	−0.0950982	+	0.0253554i
$571$	−18.3370			−0.767379			−0.383689	−	0.923462i	$-0.625347\pi$
$571$	−18.3370			−0.767379			−0.383689	+	0.923462i	$0.625347\pi$
$572$	11.0206	+	19.0882i	0.460793	+	0.798116i
$573$	−0.141031	+	0.0376021i	−0.00589166	+	0.00157085i
$574$	8.95594	−	0.326390i	0.373814	−	0.0136232i
$575$	−8.68895			−0.362354
$576$	2.60178	−	1.49356i	0.108408	−	0.0622318i
$577$	3.61299	+	6.25789i	0.150411	+	0.260519i	0.931379	−	0.364052i	$-0.118607\pi$
$577$	3.61299	+	6.25789i	0.150411	+	0.260519i	−0.780968	+	0.624571i	$0.785274\pi$
$578$	7.32820	−	12.6928i	0.304813	−	0.527951i
$579$	−17.7275	+	4.72657i	−0.736732	+	0.196429i
$580$	4.80226	−	8.31776i	0.199403	−	0.345376i
$581$	10.4296	−	19.6874i	0.432692	−	0.816771i
$582$	11.4437	+	11.4720i	0.474355	+	0.475531i
$583$	10.0702			0.417065
$584$	−1.83021	−	3.17001i	−0.0757345	−	0.131176i
$585$	−13.4202	+	7.70390i	−0.554855	+	0.318517i
$586$	12.7190	−	22.0299i	0.525416	−	0.910047i
$587$	4.29046	+	7.43130i	0.177086	+	0.306723i	0.940881	−	0.338736i	$-0.109999\pi$
$587$	4.29046	+	7.43130i	0.177086	+	0.306723i	−0.763795	+	0.645459i	$0.776666\pi$
$588$	2.29196	−	11.9058i	0.0945187	−	0.490985i
$589$	−3.50421	+	6.06947i	−0.144388	+	0.250088i
$590$	5.76134	+	9.97893i	0.237191	+	0.410826i
$591$	30.1008	−	8.02557i	1.23818	−	0.330128i
$592$	1.07286	−	1.85825i	0.0440942	−	0.0763734i
$593$	4.27179	−	7.39897i	0.175422	−	0.303839i	−0.764886	−	0.644166i	$-0.777204\pi$
$593$	4.27179	−	7.39897i	0.175422	−	0.303839i	0.940307	+	0.340327i	$0.110538\pi$
$594$	−5.66710	−	21.4685i	−0.232524	−	0.880863i
$595$	4.04765	−	0.147512i	0.165938	−	0.00604741i
$596$	−6.99840	−	12.1216i	−0.286665	−	0.496519i
$597$	−28.5239	−	28.5946i	−1.16741	−	1.17030i
$598$	44.8182			1.83275
$599$	−37.1586			−1.51826			−0.759129	−	0.650940i	$-0.774375\pi$
$599$	−37.1586			−1.51826			−0.759129	+	0.650940i	$0.774375\pi$
$600$	0.450358	−	1.67248i	0.0183858	−	0.0682786i
$601$	2.50271	+	4.33482i	0.102088	+	0.176821i	0.912545	−	0.408977i	$-0.134114\pi$
$601$	2.50271	+	4.33482i	0.102088	+	0.176821i	−0.810457	+	0.585798i	$0.800781\pi$
$602$	11.4064	−	21.5312i	0.464888	−	0.877545i
$603$	24.9029	−	14.2956i	1.01412	−	0.582161i
$604$	10.9011	−	18.8812i	0.443558	−	0.768266i
$605$	−3.62985	+	6.28709i	−0.147574	+	0.255606i
$606$	0.00499630	−	0.0185545i	0.000202961	−	0.000753726i
$607$	11.3049	+	19.5807i	0.458853	+	0.794756i	0.998901	−	0.0468783i	$-0.0149273\pi$
$607$	11.3049	+	19.5807i	0.458853	+	0.794756i	−0.540048	+	0.841634i	$0.681594\pi$
$608$	−0.678316	+	1.17488i	−0.0275093	+	0.0476476i
$609$	9.88872	−	42.8882i	0.400711	−	1.73792i
$610$	2.06700	+	3.58014i	0.0836902	+	0.144956i
$611$	26.0946	−	45.1971i	1.05567	−	1.82848i
$612$	3.97166	+	2.30617i	0.160545	+	0.0932212i
$613$	−18.4103	−	31.8875i	−0.743583	−	1.28792i	−0.950854	−	0.309640i	$-0.899791\pi$
$613$	−18.4103	−	31.8875i	−0.743583	−	1.28792i	0.207271	−	0.978284i	$-0.433542\pi$
$614$	7.51672			0.303350
$615$	5.66890	−	1.51146i	0.228592	−	0.0609478i
$616$	−11.2982	+	0.411749i	−0.455216	+	0.0165898i
$617$	12.9942	−	22.5066i	0.523126	−	0.906081i	−0.476512	−	0.879168i	$-0.658099\pi$
$617$	12.9942	−	22.5066i	0.523126	−	0.906081i	0.999638	−	0.0269130i	$-0.00856772\pi$
$618$	10.6170	+	10.6433i	0.427078	+	0.428137i
$619$	1.91129	−	3.31045i	0.0768212	−	0.133058i	−0.825056	−	0.565052i	$-0.808856\pi$
$619$	1.91129	−	3.31045i	0.0768212	−	0.133058i	0.901877	+	0.431993i	$0.142190\pi$
$620$	−2.58302	−	4.47393i	−0.103737	−	0.179677i
$621$	−43.5670	−	11.8473i	−1.74828	−	0.475417i
$622$	−24.5570			−0.984646
$623$	−34.4170	+	1.25429i	−1.37889	+	0.0502521i
$624$	−2.32298	+	8.62674i	−0.0929935	+	0.345346i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−19.1101			−0.763794
$627$	7.09114	+	7.10872i	0.283193	+	0.283895i
$628$	−6.19018			−0.247015
$629$	3.28484			0.130975
$630$	−0.269434	−	7.93268i	−0.0107345	−	0.316046i
$631$	3.91330			0.155786			0.0778930	−	0.996962i	$-0.475181\pi$
$631$	3.91330			0.155786			0.0778930	+	0.996962i	$0.475181\pi$
$632$	−6.44646			−0.256426
$633$	2.06305	−	7.66145i	0.0819988	−	0.304515i
$634$	1.00054			0.0397364
$635$	4.93633	+	8.54998i	0.195892	+	0.339295i
$636$	2.88270	+	2.88984i	0.114306	+	0.114590i
$637$	20.2815	+	29.8720i	0.803580	+	1.18357i
$638$	−41.0414			−1.62485
$639$	−18.9231	+	10.8629i	−0.748587	+	0.429729i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	7.92237	−	13.7219i	0.312915	−	0.541984i	−0.666077	−	0.745883i	$-0.732028\pi$
$641$	7.92237	−	13.7219i	0.312915	−	0.541984i	0.978992	+	0.203898i	$0.0653612\pi$
$642$	−5.39350	+	20.0296i	−0.212864	+	0.790505i
$643$	−3.56273	+	6.17084i	−0.140500	+	0.243354i	−0.927685	−	0.373363i	$-0.878204\pi$
$643$	−3.56273	+	6.17084i	−0.140500	+	0.243354i	0.787185	+	0.616717i	$0.211538\pi$
$644$	−10.7617	+	20.3143i	−0.424070	+	0.800495i
$645$	4.14755	−	15.4026i	0.163310	−	0.606476i
$646$	−2.07684			−0.0817124
$647$	−0.670586	−	1.16149i	−0.0263635	−	0.0456629i	0.852543	−	0.522658i	$-0.175059\pi$
$647$	−0.670586	−	1.16149i	−0.0263635	−	0.0456629i	−0.878906	+	0.476995i	$0.841726\pi$
$648$	4.53854	−	7.77185i	0.178291	−	0.305307i
$649$	24.6190	−	42.6414i	0.966380	−	1.67382i
$650$	2.57903	+	4.46702i	0.101158	+	0.175211i
$651$	−17.3185	−	16.1406i	−0.678766	−	0.632600i
$652$	2.42476	−	4.19981i	0.0949609	−	0.164477i
$653$	3.02357	+	5.23697i	0.118321	+	0.204939i	0.919103	−	0.394018i	$-0.128915\pi$
$653$	3.02357	+	5.23697i	0.118321	+	0.204939i	−0.800781	+	0.598957i	$0.795582\pi$
$654$	−10.3592	−	10.3849i	−0.405076	−	0.406080i
$655$	−3.16775	+	5.48671i	−0.123774	+	0.214383i
$656$	1.69364	−	2.93347i	0.0661254	−	0.114533i
$657$	−9.49641	−	5.51415i	−0.370490	−	0.215127i
$658$	14.2203	+	22.6803i	0.554363	+	0.884171i
$659$	13.6456	+	23.6349i	0.531557	+	0.920684i	0.999322	+	0.0368307i	$0.0117262\pi$
$659$	13.6456	+	23.6349i	0.531557	+	0.920684i	−0.467764	+	0.883853i	$0.654940\pi$
$660$	−7.15146	+	1.90674i	−0.278370	+	0.0742199i
$661$	−5.68967			−0.221302			−0.110651	−	0.993859i	$-0.535294\pi$
$661$	−5.68967			−0.221302			−0.110651	+	0.993859i	$0.535294\pi$
$662$	−4.00106			−0.155506
$663$	−13.2153	+	3.52350i	−0.513240	+	0.136841i
$664$	−4.21040	−	7.29263i	−0.163395	−	0.283009i
$665$	1.90667	+	3.04101i	0.0739376	+	0.117925i
$666$	0.0159372	−	6.43713i	0.000617554	−	0.249434i
$667$	−41.7266	+	72.2726i	−1.61566	+	2.79841i
$668$	−4.20095	+	7.27625i	−0.162539	+	0.281527i
$669$	−29.6208	−	29.6942i	−1.14521	−	1.14805i
$670$	−4.78573	−	8.28913i	−0.184889	−	0.320237i
$671$	8.83255	−	15.2984i	0.340977	−	0.590589i
$672$	−3.35237	−	3.12436i	−0.129320	−	0.120525i
$673$	−5.72198	−	9.91077i	−0.220566	−	0.382032i	0.734414	−	0.678702i	$-0.237457\pi$
$673$	−5.72198	−	9.91077i	−0.220566	−	0.382032i	−0.954980	+	0.296670i	$0.904124\pi$
$674$	−15.9279	+	27.5879i	−0.613518	+	1.06264i
$675$	−1.32621	−	5.02406i	−0.0510460	−	0.193376i
$676$	−6.80282	−	11.7828i	−0.261647	−	0.453186i
$677$	24.3889			0.937342			0.468671	−	0.883373i	$-0.344733\pi$
$677$	24.3889			0.937342			0.468671	+	0.883373i	$0.344733\pi$
$678$	−6.96242	+	25.8560i	−0.267390	+	0.992996i
$679$	11.5870	−	21.8722i	0.444668	−	0.839377i
$680$	0.765442	−	1.32578i	0.0293534	−	0.0508415i
$681$	4.24324	−	15.7579i	0.162601	−	0.603846i
$682$	−11.0376	+	19.1177i	−0.422652	+	0.732055i
$683$	−4.97150	−	8.61090i	−0.190229	−	0.329487i	0.755097	−	0.655613i	$-0.227590\pi$
$683$	−4.97150	−	8.61090i	−0.190229	−	0.329487i	−0.945326	+	0.326126i	$0.894256\pi$
$684$	−0.0100763	+	4.06988i	−0.000385277	+	0.155616i
$685$	1.64180			0.0627298
$686$	−18.4098	+	2.01993i	−0.702889	+	0.0771213i
$687$	10.1165	+	10.1416i	0.385968	+	0.386925i
$688$	−4.60472	−	7.97561i	−0.175553	−	0.304067i
$689$	−12.1557			−0.463094
$690$	−3.91314	+	14.5321i	−0.148971	+	0.553226i
$691$	9.85219			0.374795			0.187397	−	0.982284i	$-0.439995\pi$
$691$	9.85219			0.374795			0.187397	+	0.982284i	$0.439995\pi$
$692$	−1.66675			−0.0633603
$693$	−28.7804	+	17.9458i	−1.09328	+	0.681704i
$694$	−8.25454			−0.313338
$695$	−3.08238			−0.116921
$696$	−11.7485	−	11.7776i	−0.445326	−	0.446430i
$697$	5.18552			0.196416
$698$	0.793152	+	1.37378i	0.0300212	+	0.0519983i
$699$	−5.56668	+	20.6727i	−0.210551	+	0.781915i
$700$	−2.64400	+	0.0963576i	−0.0999337	+	0.00364197i
$701$	−2.41415			−0.0911813			−0.0455906	−	0.998960i	$-0.514517\pi$
$701$	−2.41415			−0.0911813			−0.0455906	+	0.998960i	$0.514517\pi$
$702$	6.84070	+	25.9144i	0.258186	+	0.978077i
$703$	1.45547	+	2.52095i	0.0548942	+	0.0950795i
$704$	−2.13657	+	3.70065i	−0.0805250	+	0.139473i
$705$	12.3766	+	12.4073i	0.466129	+	0.467284i
$706$	6.36496	−	11.0244i	0.239549	−	0.414910i
$707$	−0.0293326	+	0.00106900i	−0.00110317	+	4.02037e-5i
$708$	19.2842	−	5.14161i	0.724745	−	0.193233i
$709$	24.4454			0.918067			0.459033	−	0.888419i	$-0.348196\pi$
$709$	24.4454			0.918067			0.459033	+	0.888419i	$0.348196\pi$
$710$	3.63657	+	6.29872i	0.136478	+	0.236387i
$711$	−16.7723	+	9.62819i	−0.629009	+	0.361085i
$712$	−6.50852	+	11.2731i	−0.243917	+	0.422477i
$713$	22.4438	+	38.8737i	0.840526	+	1.45583i
$714$	1.57618	−	6.83603i	0.0589872	−	0.255832i
$715$	11.0206	−	19.0882i	0.412146	−	0.713857i
$716$	10.7128	+	18.5550i	0.400354	+	0.693434i
$717$	6.07186	−	22.5488i	0.226758	−	0.842100i
$718$	−0.786031	+	1.36145i	−0.0293344	+	0.0508087i
$719$	17.8331	−	30.8879i	0.665064	−	1.15192i	−0.314204	−	0.949356i	$-0.601738\pi$
$719$	17.8331	−	30.8879i	0.665064	−	1.15192i	0.979268	−	0.202569i	$-0.0649291\pi$
$720$	−2.59435	−	1.50643i	−0.0966859	−	0.0561412i
$721$	10.7500	−	20.2922i	0.400350	−	0.755720i
$722$	8.57978	+	14.8606i	0.319306	+	0.553055i
$723$	6.75732	−	25.0944i	0.251308	−	0.933270i
$724$	19.7789			0.735075
$725$	−9.60452			−0.356703
$726$	8.88027	+	8.90228i	0.329578	+	0.330395i
$727$	−22.5812	−	39.1118i	−0.837492	−	1.45058i	−0.891986	−	0.452064i	$-0.850688\pi$
$727$	−22.5812	−	39.1118i	−0.837492	−	1.45058i	0.0544941	−	0.998514i	$-0.482645\pi$
$728$	13.6379	−	0.497019i	0.505454	−	0.0184207i
$729$	0.200539	−	26.9993i	0.00742739	−	0.999972i
$730$	−1.83021	+	3.17001i	−0.0677390	+	0.117327i
$731$	7.04929	−	12.2097i	0.260727	−	0.451593i
$732$	6.91859	−	1.84465i	0.255718	−	0.0681804i
$733$	−7.52546	−	13.0345i	−0.277959	−	0.481439i	0.692918	−	0.721016i	$-0.256325\pi$
$733$	−7.52546	−	13.0345i	−0.277959	−	0.481439i	−0.970877	+	0.239577i	$0.922991\pi$
$734$	14.5348	−	25.1750i	0.536489	−	0.929226i
$735$	−11.4567	+	3.96798i	−0.422585	+	0.146361i
$736$	4.34447	+	7.52485i	0.160139	+	0.277370i
$737$	−20.4501	+	35.4206i	−0.753289	+	1.30473i
$738$	0.0251588	−	10.1618i	0.000926109	−	0.374061i
$739$	7.91265	+	13.7051i	0.291071	+	0.504150i	0.974063	−	0.226275i	$-0.0726549\pi$
$739$	7.91265	+	13.7051i	0.291071	+	0.504150i	−0.682992	+	0.730426i	$0.739322\pi$
$740$	−2.14572			−0.0788781
$741$	−8.55965	−	8.58087i	−0.314447	−	0.315226i
$742$	2.91881	−	5.50968i	0.107153	−	0.202267i
$743$	−4.93045	+	8.53979i	−0.180881	+	0.313294i	−0.942181	−	0.335105i	$-0.891228\pi$
$743$	−4.93045	+	8.53979i	−0.180881	+	0.313294i	0.761300	+	0.648400i	$0.224561\pi$
$744$	−8.64583	+	2.30518i	−0.316971	+	0.0845118i
$745$	−6.99840	+	12.1216i	−0.256401	+	0.444100i
$746$	14.4271	+	24.9884i	0.528212	+	0.914891i
$747$	−21.8466	−	12.6853i	−0.799324	−	0.464132i
$748$	−6.54168			−0.239187
$749$	31.6645	−	1.15398i	1.15700	−	0.0421655i
$750$	−1.67359	+	0.446216i	−0.0611107	+	0.0162935i
$751$	−23.2284	−	40.2328i	−0.847617	−	1.46812i	−0.883329	−	0.468754i	$-0.844703\pi$
$751$	−23.2284	−	40.2328i	−0.847617	−	1.46812i	0.0357115	−	0.999362i	$-0.488630\pi$
$752$	10.1180			0.368964
$753$	40.8173	−	10.8828i	1.48747	−	0.396592i
$754$	49.5407			1.80417
$755$	−21.8021			−0.793461
$756$	−13.3886	−	3.12193i	−0.486937	−	0.113543i
$757$	−14.1617			−0.514715			−0.257357	−	0.966316i	$-0.582852\pi$
$757$	−14.1617			−0.514715			−0.257357	+	0.966316i	$0.582852\pi$
$758$	−28.2079			−1.02456
$759$	62.1387	−	16.5676i	2.25549	−	0.601366i
$760$	1.35663			0.0492102
$761$	7.52932	+	13.0412i	0.272938	+	0.472742i	0.969613	−	0.244645i	$-0.0786714\pi$
$761$	7.52932	+	13.0412i	0.272938	+	0.472742i	−0.696675	+	0.717387i	$0.745338\pi$
$762$	16.5228	−	4.40534i	0.598556	−	0.159589i
$763$	−10.4889	+	19.7994i	−0.379725	+	0.716787i
$764$	0.0842687			0.00304874
$765$	0.0113706	−	4.59264i	0.000411104	−	0.166047i
$766$	3.59518	+	6.22704i	0.129899	+	0.224992i
$767$	−29.7174	+	51.4720i	−1.07303	+	1.85855i
$768$	−1.67359	+	0.446216i	−0.0603903	+	0.0161014i
$769$	7.96647	−	13.7983i	0.287278	−	0.497580i	−0.685881	−	0.727714i	$-0.740583\pi$
$769$	7.96647	−	13.7983i	0.287278	−	0.497580i	0.973159	+	0.230133i	$0.0739163\pi$
$770$	6.00566	+	9.57862i	0.216429	+	0.345189i
$771$	−11.5104	−	11.5389i	−0.414535	−	0.415563i
$772$	10.5925			0.381234
$773$	−5.05712	−	8.75918i	−0.181892	−	0.315046i	0.760633	−	0.649182i	$-0.224889\pi$
$773$	−5.05712	−	8.75918i	−0.181892	−	0.315046i	−0.942525	+	0.334136i	$0.891555\pi$
$774$	−23.8926	−	13.8734i	−0.858800	−	0.498667i
$775$	−2.58302	+	4.47393i	−0.0927850	+	0.160708i
$776$	−4.67765	−	8.10193i	−0.167918	−	0.290842i
$777$	−9.40244	+	2.87753i	−0.337311	+	0.103231i
$778$	18.6082	−	32.2303i	0.667135	−	1.15551i
$779$	2.29764	+	3.97963i	0.0823215	+	0.142585i
$780$	8.63247	−	2.30161i	0.309092	−	0.0824110i
$781$	15.5396	−	26.9153i	0.556049	−	0.963105i
$782$	−6.65089	+	11.5197i	−0.237835	+	0.411943i
$783$	−48.1577	−	13.0957i	−1.72102	−	0.468002i
$784$	−3.04944	+	6.30087i	−0.108909	+	0.225031i
$785$	3.09509	+	5.36086i	0.110469	+	0.191337i
$786$	7.74976	+	7.76897i	0.276425	+	0.277110i
$787$	31.4844			1.12230			0.561148	−	0.827715i	$-0.310360\pi$
$787$	31.4844			1.12230			0.561148	+	0.827715i	$0.310360\pi$
$788$	−17.9858			−0.640718
$789$	−6.38609	+	23.7158i	−0.227351	+	0.844303i
$790$	3.22323	+	5.58279i	0.114677	+	0.198627i
$791$	40.8755	−	1.48966i	1.45337	−	0.0529663i
$792$	−0.0317385	+	12.8194i	−0.00112778	+	0.455517i
$793$	−10.6617	+	18.4666i	−0.378608	+	0.655768i
$794$	−4.61549	+	7.99427i	−0.163798	+	0.283706i
$795$	1.06133	−	3.94141i	0.0376415	−	0.139787i
$796$	11.6593	+	20.1945i	0.413252	+	0.715774i
$797$	−4.18225	+	7.24386i	−0.148143	+	0.256591i	−0.930541	−	0.366188i	$-0.880663\pi$
$797$	−4.18225	+	7.24386i	−0.148143	+	0.256591i	0.782398	+	0.622778i	$0.213996\pi$
$798$	5.94470	−	1.81932i	0.210440	−	0.0644032i
$799$	7.74471	+	13.4142i	0.273988	+	0.474562i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−0.0966834	+	39.0510i	−0.00341614	+	1.37980i
$802$	−6.38363	−	11.0568i	−0.225414	−	0.390428i
$803$	15.6414			0.551975
$804$	−16.0187	+	4.27094i	−0.564935	+	0.150625i
$805$	22.9735	−	0.837246i	0.809711	−	0.0295090i
$806$	13.3234	−	23.0768i	0.469297	−	0.812846i
$807$	10.6098	+	10.6361i	0.373484	+	0.374410i
$808$	−0.00554702	+	0.00960773i	−0.000195144	+	0.000337999i
$809$	12.8189	+	22.2030i	0.450688	+	0.780615i	0.998429	−	0.0560330i	$-0.0178452\pi$
$809$	12.8189	+	22.2030i	0.450688	+	0.780615i	−0.547740	+	0.836648i	$0.684512\pi$
$810$	−8.99989	−	0.0445646i	−0.316224	−	0.00156584i
$811$	35.8157			1.25766			0.628830	−	0.777543i	$-0.283534\pi$
$811$	35.8157			1.25766			0.628830	+	0.777543i	$0.283534\pi$
$812$	−11.8957	+	22.4549i	−0.417456	+	0.788011i
$813$	−11.6862	+	43.3987i	−0.409854	+	1.52206i
$814$	4.58447	+	7.94054i	0.160686	+	0.278316i
$815$	−4.84952			−0.169871
$816$	−1.87262	−	1.87726i	−0.0655548	−	0.0657173i
$817$	12.4938			0.437103
$818$	−13.6602			−0.477617
$819$	34.7405	−	21.6622i	1.21393	−	0.756939i
$820$	−3.38728			−0.118289
$821$	−20.4554			−0.713899			−0.356950	−	0.934124i	$-0.616183\pi$
$821$	−20.4554			−0.713899			−0.356950	+	0.934124i	$0.616183\pi$
$822$	0.739397	−	2.74587i	0.0257894	−	0.0957731i
$823$	−2.29872			−0.0801284			−0.0400642	−	0.999197i	$-0.512756\pi$
$823$	−2.29872			−0.0801284			−0.0400642	+	0.999197i	$0.512756\pi$
$824$	−4.33975	−	7.51666i	−0.151182	−	0.261855i
$825$	5.22702	+	5.23998i	0.181981	+	0.182433i
$826$	−16.1945	−	25.8291i	−0.563479	−	0.898710i
$827$	12.5820			0.437520			0.218760	−	0.975779i	$-0.429799\pi$
$827$	12.5820			0.437520			0.218760	+	0.975779i	$0.429799\pi$
$828$	22.5422	+	13.0893i	0.783396	+	0.454884i
$829$	−25.6282	−	44.3893i	−0.890103	−	1.54170i	−0.839751	−	0.542972i	$-0.817299\pi$
$829$	−25.6282	−	44.3893i	−0.890103	−	1.54170i	−0.0503516	−	0.998732i	$-0.516034\pi$
$830$	−4.21040	+	7.29263i	−0.146145	+	0.253131i
$831$	−6.79129	+	25.2205i	−0.235587	+	0.874890i
$832$	2.57903	−	4.46702i	0.0894119	−	0.154866i
$833$	−10.6878	+	0.780044i	−0.370309	+	0.0270269i
$834$	−1.38817	+	5.15520i	−0.0480685	+	0.178510i
$835$	8.40189			0.290759
$836$	−2.89854	−	5.02041i	−0.100248	−	0.173635i
$837$	−19.0516	+	18.9107i	−0.658521	+	0.653648i
$838$	14.0027	−	24.2535i	0.483716	−	0.837822i
$839$	−22.1590	−	38.3805i	−0.765013	−	1.32504i	−0.940240	−	0.340514i	$-0.889399\pi$
$839$	−22.1590	−	38.3805i	−0.765013	−	1.32504i	0.175226	−	0.984528i	$-0.443934\pi$
$840$	−1.02959	+	4.46542i	−0.0355242	+	0.154072i
$841$	−31.6234	+	54.7733i	−1.09046	+	1.88874i
$842$	7.73475	+	13.3970i	0.266557	+	0.461690i
$843$	17.9424	+	17.9869i	0.617968	+	0.619500i
$844$	−2.29045	+	3.96718i	−0.0788406	+	0.136556i
$845$	−6.80282	+	11.7828i	−0.234024	+	0.405341i
$846$	26.3247	−	15.1118i	0.905063	−	0.519555i
$847$	8.99150	−	16.9728i	0.308952	−	0.583192i
$848$	−1.17832	−	2.04090i	−0.0404635	−	0.0700849i
$849$	19.8758	−	5.29935i	0.682136	−	0.181873i
$850$	−1.53088			−0.0525089
$851$	18.6440			0.639109
$852$	12.1722	−	3.24539i	0.417013	−	0.111185i
$853$	23.0872	+	39.9882i	0.790490	+	1.36917i	0.925664	+	0.378346i	$0.123507\pi$
$853$	23.0872	+	39.9882i	0.790490	+	1.36917i	−0.135174	+	0.990822i	$0.543159\pi$
$854$	−5.81010	−	9.26671i	−0.198818	−	0.317100i
$855$	3.52966	−	2.02621i	0.120712	−	0.0692951i
$856$	5.98800	−	10.3715i	0.204666	−	0.354491i
$857$	−17.6402	+	30.5538i	−0.602578	+	1.04370i	0.389851	+	0.920878i	$0.372527\pi$
$857$	−17.6402	+	30.5538i	−0.602578	+	1.04370i	−0.992429	+	0.122818i	$0.960807\pi$
$858$	−26.9613	−	27.0281i	−0.920444	−	0.922726i
$859$	15.8174	+	27.3966i	0.539683	+	0.934759i	0.998921	+	0.0464451i	$0.0147893\pi$
$859$	15.8174	+	27.3966i	0.539683	+	0.934759i	−0.459238	+	0.888313i	$0.651877\pi$
$860$	−4.60472	+	7.97561i	−0.157020	+	0.271966i
$861$	−14.8429	+	4.54253i	−0.505845	+	0.154809i
$862$	−14.0831	−	24.3926i	−0.479672	−	0.830816i
$863$	6.73299	−	11.6619i	0.229193	−	0.396975i	−0.728376	−	0.685178i	$-0.759724\pi$
$863$	6.73299	−	11.6619i	0.229193	−	0.396975i	0.957569	+	0.288203i	$0.0930578\pi$
$864$	−3.68785	+	3.66056i	−0.125463	+	0.124535i
$865$	0.833374	+	1.44345i	0.0283356	+	0.0490786i
$866$	21.0723			0.716066
$867$	−6.60063	+	24.5125i	−0.224169	+	0.832487i
$868$	7.26060	+	11.5802i	0.246441	+	0.393056i
$869$	13.7733	−	23.8560i	0.467227	−	0.809261i
$870$	−4.32548	+	16.0633i	−0.146647	+	0.544598i
$871$	24.6851	−	42.7559i	0.836424	−	1.44873i
$872$	4.23436	+	7.33412i	0.143393	+	0.248365i
$873$	−24.2710	−	14.0931i	−0.821448	−	0.476979i
$874$	−11.7877			−0.398725
$875$	1.40545	+	2.24159i	0.0475128	+	0.0757795i
$876$	4.47752	+	4.48862i	0.151281	+	0.151656i
$877$	10.5356	+	18.2482i	0.355761	+	0.616197i	0.987248	−	0.159190i	$-0.0508882\pi$
$877$	10.5356	+	18.2482i	0.355761	+	0.616197i	−0.631487	+	0.775387i	$0.717555\pi$
$878$	12.5687			0.424174
$879$	−11.4562	+	42.5444i	−0.386408	+	1.43499i
$880$	4.27314			0.144047
$881$	−17.0942			−0.575918			−0.287959	−	0.957643i	$-0.592977\pi$
$881$	−17.0942			−0.575918			−0.287959	+	0.957643i	$0.592977\pi$
$882$	1.47676	+	20.9480i	0.0497249	+	0.705356i
$883$	26.3481			0.886684			0.443342	−	0.896353i	$-0.353793\pi$
$883$	26.3481			0.886684			0.443342	+	0.896353i	$0.353793\pi$
$884$	7.89640			0.265585
$885$	−14.0949	−	14.1298i	−0.473794	−	0.474968i
$886$	14.3908			0.483469
$887$	8.80208	+	15.2456i	0.295545	+	0.511899i	0.975111	−	0.221715i	$-0.0711655\pi$
$887$	8.80208	+	15.2456i	0.295545	+	0.511899i	−0.679567	+	0.733614i	$0.737832\pi$
$888$	−0.966342	+	3.58866i	−0.0324283	+	0.120428i
$889$	−13.8755	−	22.1304i	−0.465369	−	0.742231i
$890$	13.0170			0.436332
$891$	19.0640	+	33.4006i	0.638667	+	1.11896i
$892$	12.1076	+	20.9711i	0.405394	+	0.702163i
$893$	−6.86317	+	11.8874i	−0.229667	+	0.397795i
$894$	17.1213	+	17.1637i	0.572621	+	0.574040i
$895$	10.7128	−	18.5550i	0.358088	−	0.620226i
$896$	1.40545	+	2.24159i	0.0469527	+	0.0748862i
$897$	−75.0071	+	19.9986i	−2.50441	+	0.667734i
$898$	11.2511			0.375454
$899$	24.8087	+	42.9699i	0.827417	+	1.43313i
$900$	−0.00742745	+	2.99999i	−0.000247582	+	0.0999997i
$901$	1.80386	−	3.12438i	0.0600954	−	0.104088i
$902$	7.23715	+	12.5351i	0.240971	+	0.417373i
$903$	−9.48195	+	41.1240i	−0.315539	+	1.36852i
$904$	7.72987	−	13.3885i	0.257092	−	0.445296i
$905$	−9.88943	−	17.1290i	−0.328736	−	0.569387i
$906$	−9.81878	+	36.4636i	−0.326207	+	1.21142i
$907$	0.389288	−	0.674267i	0.0129261	−	0.0223887i	−0.859490	−	0.511153i	$-0.829219\pi$
$907$	0.389288	−	0.674267i	0.0129261	−	0.0223887i	0.872416	+	0.488764i	$0.162552\pi$
$908$	−4.71096	+	8.15962i	−0.156339	+	0.270787i
$909$	−8.24005e−5		0.0332820i	−2.73305e−6		0.00110390i
$910$	−7.24938	−	11.5623i	−0.240315	−	0.383285i
$911$	9.28698	+	16.0855i	0.307691	+	0.532937i	0.977857	−	0.209275i	$-0.0671103\pi$
$911$	9.28698	+	16.0855i	0.307691	+	0.532937i	−0.670166	+	0.742212i	$0.733777\pi$
$912$	0.610970	−	2.26893i	0.0202312	−	0.0751319i
$913$	35.9833			1.19087
$914$	−4.96710			−0.164297
$915$	−5.05681	−	5.06935i	−0.167173	−	0.167587i
$916$	−4.13516	−	7.16232i	−0.136630	−	0.236650i
$917$	7.84684	−	14.8121i	0.259125	−	0.489137i
$918$	−7.67596	−	2.08735i	−0.253344	−	0.0688928i
$919$	−4.87601	+	8.44549i	−0.160845	+	0.278591i	−0.935172	−	0.354194i	$-0.884755\pi$
$919$	−4.87601	+	8.44549i	−0.160845	+	0.278591i	0.774327	+	0.632785i	$0.218088\pi$
$920$	4.34447	−	7.52485i	0.143233	−	0.248087i
$921$	−12.5799	+	3.35408i	−0.414521	+	0.110521i
$922$	−10.1629	−	17.6027i	−0.334698	−	0.579715i
$923$	−18.7577	+	32.4892i	−0.617416	+	1.06940i
$924$	18.7247	−	5.73052i	0.615998	−	0.188520i
$925$	1.07286	+	1.85825i	0.0352754	+	0.0610987i
$926$	8.34268	−	14.4499i	0.274157	−	0.474855i
$927$	−22.5177	−	13.0750i	−0.739577	−	0.429440i
$928$	4.80226	+	8.31776i	0.157642	+	0.273044i
$929$	4.90416			0.160900			0.0804501	−	0.996759i	$-0.474364\pi$
$929$	4.90416			0.160900			0.0804501	+	0.996759i	$0.474364\pi$
$930$	6.31925	+	6.33492i	0.207217	+	0.207730i
$931$	−5.33426	−	7.85669i	−0.174823	−	0.257493i
$932$	6.18028	−	10.7046i	0.202442	−	0.350639i
$933$	41.0983	−	10.9577i	1.34550	−	0.358740i
$934$	−17.1435	+	29.6935i	−0.560954	+	0.971600i
$935$	3.27084	+	5.66526i	0.106968	+	0.185274i
$936$	0.0383113	−	15.4741i	0.00125224	−	0.505788i
$937$	39.6506			1.29533			0.647665	−	0.761925i	$-0.275746\pi$
$937$	39.6506			1.29533			0.647665	+	0.761925i	$0.275746\pi$
$938$	13.4522	+	21.4553i	0.439229	+	0.700540i
$939$	31.9824	−	8.52725i	1.04371	−	0.278276i
$940$	−5.05898	−	8.76241i	−0.165006	−	0.285798i
$941$	−11.0259			−0.359436			−0.179718	−	0.983718i	$-0.557518\pi$
$941$	−11.0259			−0.359436			−0.179718	+	0.983718i	$0.557518\pi$
$942$	10.3598	−	2.76216i	0.337541	−	0.0899961i
$943$	29.4319			0.958433
$944$	−11.5227			−0.375031
$945$	3.99061	+	13.1558i	0.129815	+	0.427958i
$946$	39.3532			1.27948
$947$	−29.3024			−0.952200			−0.476100	−	0.879391i	$-0.657950\pi$
$947$	−29.3024			−0.952200			−0.476100	+	0.879391i	$0.657950\pi$
$948$	10.7887	−	2.87651i	0.350401	−	0.0934248i
$949$	−18.8806			−0.612892
$950$	−0.678316	−	1.17488i	−0.0220075	−	0.0381180i
$951$	−1.67448	+	0.446455i	−0.0542988	+	0.0144773i
$952$	−1.89608	+	3.57912i	−0.0614522	+	0.116000i
$953$	42.5425			1.37809			0.689043	−	0.724721i	$-0.258031\pi$
$953$	42.5425			1.37809			0.689043	+	0.724721i	$0.258031\pi$
$954$	−6.11394	−	3.55009i	−0.197946	−	0.114939i
$955$	−0.0421344	−	0.0729789i	−0.00136344	−	0.00236154i
$956$	−6.74114	+	11.6760i	−0.218024	+	0.377629i
$957$	68.6864	−	18.3134i	2.22032	−	0.591987i
$958$	−10.0398	+	17.3895i	−0.324372	+	0.561829i
$959$	−4.34090	+	0.158200i	−0.140175	+	0.00510853i
$960$	1.22323	+	1.22626i	0.0394795	+	0.0395774i
$961$	−4.31194			−0.139095
$962$	−5.53387	−	9.58495i	−0.178419	−	0.309031i
$963$	0.0889512	−	35.9279i	0.00286641	−	1.15776i
$964$	−7.50216	+	12.9941i	−0.241628	+	0.418513i
$965$	−5.29627	−	9.17342i	−0.170493	−	0.295303i
$966$	8.94606	−	38.7998i	0.287835	−	1.24836i
$967$	−21.6984	+	37.5827i	−0.697772	+	1.20858i	0.271465	+	0.962448i	$0.412492\pi$
$967$	−21.6984	+	37.5827i	−0.697772	+	1.20858i	−0.969237	+	0.246129i	$0.920841\pi$
$968$	−3.62985	−	6.28709i	−0.116668	−	0.202075i
$969$	3.47578	−	0.926722i	0.111658	−	0.0297706i
$970$	−4.67765	+	8.10193i	−0.150190	+	0.260137i
$971$	−12.7923	+	22.1570i	−0.410525	+	0.711050i	−0.994947	−	0.100399i	$-0.967988\pi$
$971$	−12.7923	+	22.1570i	−0.410525	+	0.711050i	0.584422	+	0.811450i	$0.301321\pi$
$972$	−4.12771	+	15.0320i	−0.132396	+	0.482153i
$973$	8.14979	−	0.297010i	0.261270	−	0.00952172i
$974$	7.56980	+	13.1113i	0.242552	+	0.420113i
$975$	−6.30949	−	6.32513i	−0.202065	−	0.202566i
$976$	−4.13399			−0.132326
$977$	−32.2662			−1.03229			−0.516143	−	0.856502i	$-0.672633\pi$
$977$	−32.2662			−1.03229			−0.516143	+	0.856502i	$0.672633\pi$
$978$	−2.18402	+	8.11071i	−0.0698373	+	0.259352i
$979$	−27.8118	−	48.1715i	−0.888869	−	1.53957i
$980$	6.98143	−	0.509538i	0.223014	−	0.0162766i
$981$	21.9709	+	12.7575i	0.701475	+	0.407316i
$982$	12.5900	−	21.8064i	0.401762	−	0.695871i
$983$	−26.5965	+	46.0665i	−0.848297	+	1.46929i	0.0344304	+	0.999407i	$0.489038\pi$
$983$	−26.5965	+	46.0665i	−0.848297	+	1.46929i	−0.882727	+	0.469886i	$0.844295\pi$
$984$	−1.52549	+	5.66514i	−0.0486308	+	0.180598i
$985$	8.99291	+	15.5762i	0.286538	+	0.496298i
$986$	−7.35170	+	12.7335i	−0.234126	+	0.405518i
$987$	−33.9191	−	31.6122i	−1.07966	−	1.00623i
$988$	3.49880	+	6.06009i	0.111312	+	0.192797i
$989$	40.0102	−	69.2997i	1.27225	−	2.20360i
$990$	11.1178	−	6.38220i	0.353346	−	0.202840i
$991$	−17.7897	−	30.8126i	−0.565108	−	0.978795i	−0.997040	−	0.0768890i	$-0.975501\pi$
$991$	−17.7897	−	30.8126i	−0.565108	−	0.978795i	0.431932	−	0.901906i	$-0.357832\pi$
$992$	5.16605			0.164022
$993$	6.69611	−	1.78534i	0.212495	−	0.0566560i
$994$	−10.2220	−	16.3034i	−0.324222	−	0.517112i
$995$	11.6593	−	20.1945i	0.369624	−	0.640208i
$996$	10.3006	+	10.3261i	0.326386	+	0.327195i
$997$	−12.3661	+	21.4188i	−0.391640	+	0.678340i	−0.992666	−	0.120889i	$-0.961425\pi$
$997$	−12.3661	+	21.4188i	−0.391640	+	0.678340i	0.601026	+	0.799229i	$0.294759\pi$
$998$	−1.23811	−	2.14447i	−0.0391917	−	0.0678820i
$999$	2.84568	+	10.7802i	0.0900333	+	0.341071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.121.2	✓	12
3.2	odd	2		1890.2.i.g.1171.4		12
7.4	even	3		630.2.l.g.571.5	yes	12
9.2	odd	6		1890.2.l.g.1801.3		12
9.7	even	3		630.2.l.g.331.5	yes	12
21.11	odd	6		1890.2.l.g.361.3		12
63.11	odd	6		1890.2.i.g.991.4		12
63.25	even	3	inner	630.2.i.g.151.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.2	✓	12	1.1	even	1	trivial
630.2.i.g.151.2	yes	12	63.25	even	3	inner
630.2.l.g.331.5	yes	12	9.7	even	3
630.2.l.g.571.5	yes	12	7.4	even	3
1890.2.i.g.991.4		12	63.11	odd	6
1890.2.i.g.1171.4		12	3.2	odd	2
1890.2.l.g.361.3		12	21.11	odd	6
1890.2.l.g.1801.3		12	9.2	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.67359 + 0.446216i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67359 + 0.446216i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.60178 - 1.49356i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.67359 + 0.446216i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67359 + 0.446216i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.60178 - 1.49356i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.13657 + 3.70065i) q^{11} +(-1.67359 + 0.446216i) q^{12} +(2.57903 - 4.46702i) q^{13} +(1.40545 + 2.24159i) q^{14} +(1.22323 + 1.22626i) q^{15} +1.00000 q^{16} +(0.765442 + 1.32578i) q^{17} +(2.60178 - 1.49356i) q^{18} +(-0.678316 + 1.17488i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.35237 - 3.12436i) q^{21} +(-2.13657 + 3.70065i) q^{22} +(4.34447 + 7.52485i) q^{23} +(-1.67359 + 0.446216i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.57903 - 4.46702i) q^{26} +(-3.68785 + 3.66056i) q^{27} +(1.40545 + 2.24159i) q^{28} +(4.80226 + 8.31776i) q^{29} +(1.22323 + 1.22626i) q^{30} +5.16605 q^{31} +1.00000 q^{32} +(1.92444 - 7.14672i) q^{33} +(0.765442 + 1.32578i) q^{34} +(1.23855 - 2.33795i) q^{35} +(2.60178 - 1.49356i) q^{36} +(1.07286 - 1.85825i) q^{37} +(-0.678316 + 1.17488i) q^{38} +(-2.32298 + 8.62674i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.69364 - 2.93347i) q^{41} +(-3.35237 - 3.12436i) q^{42} +(-4.60472 - 7.97561i) q^{43} +(-2.13657 + 3.70065i) q^{44} +(-2.59435 - 1.50643i) q^{45} +(4.34447 + 7.52485i) q^{46} +10.1180 q^{47} +(-1.67359 + 0.446216i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.87262 - 1.87726i) q^{51} +(2.57903 - 4.46702i) q^{52} +(-1.17832 - 2.04090i) q^{53} +(-3.68785 + 3.66056i) q^{54} +4.27314 q^{55} +(1.40545 + 2.24159i) q^{56} +(0.610970 - 2.26893i) q^{57} +(4.80226 + 8.31776i) q^{58} -11.5227 q^{59} +(1.22323 + 1.22626i) q^{60} -4.13399 q^{61} +5.16605 q^{62} +(7.00462 + 3.73300i) q^{63} +1.00000 q^{64} -5.15806 q^{65} +(1.92444 - 7.14672i) q^{66} +9.57147 q^{67} +(0.765442 + 1.32578i) q^{68} +(-10.6286 - 10.6549i) q^{69} +(1.23855 - 2.33795i) q^{70} -7.27314 q^{71} +(2.60178 - 1.49356i) q^{72} +(-1.83021 - 3.17001i) q^{73} +(1.07286 - 1.85825i) q^{74} +(0.450358 - 1.67248i) q^{75} +(-0.678316 + 1.17488i) q^{76} +(-11.2982 + 0.411749i) q^{77} +(-2.32298 + 8.62674i) q^{78} -6.44646 q^{79} +(-0.500000 - 0.866025i) q^{80} +(4.53854 - 7.77185i) q^{81} +(1.69364 - 2.93347i) q^{82} +(-4.21040 - 7.29263i) q^{83} +(-3.35237 - 3.12436i) q^{84} +(0.765442 - 1.32578i) q^{85} +(-4.60472 - 7.97561i) q^{86} +(-11.7485 - 11.7776i) q^{87} +(-2.13657 + 3.70065i) q^{88} +(-6.50852 + 11.2731i) q^{89} +(-2.59435 - 1.50643i) q^{90} +(13.6379 - 0.497019i) q^{91} +(4.34447 + 7.52485i) q^{92} +(-8.64583 + 2.30518i) q^{93} +10.1180 q^{94} +1.35663 q^{95} +(-1.67359 + 0.446216i) q^{96} +(-4.67765 - 8.10193i) q^{97} +(-3.04944 + 6.30087i) q^{98} +(-0.0317385 + 12.8194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

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