LMFDB - Embedded newform 630.2.bk.c.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

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.bk (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.546603 - 1.64354i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.64354 + 0.546603i) q^{6} +(-0.852286 + 2.50472i) q^{7} +1.00000i q^{8} +(-2.40245 + 1.79673i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.546603 - 1.64354i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.64354 + 0.546603i) q^{6} +(-0.852286 + 2.50472i) q^{7} +1.00000i q^{8} +(-2.40245 + 1.79673i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-1.52837 + 0.882407i) q^{11} +(0.546603 + 1.64354i) q^{12} +(-1.79971 + 1.03906i) q^{13} +(2.50472 + 0.852286i) q^{14} +(-1.69665 - 0.348398i) q^{15} +1.00000 q^{16} +(-0.861240 + 1.49171i) q^{17} +(1.79673 + 2.40245i) q^{18} +(-6.79557 + 3.92342i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.58247 + 0.0316804i) q^{21} +(0.882407 + 1.52837i) q^{22} +(-6.19453 - 3.57642i) q^{23} +(1.64354 - 0.546603i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.03906 + 1.79971i) q^{26} +(4.26618 + 2.96642i) q^{27} +(0.852286 - 2.50472i) q^{28} +(5.62132 + 3.24547i) q^{29} +(-0.348398 + 1.69665i) q^{30} +4.88768i q^{31} -1.00000i q^{32} +(2.28569 + 2.02962i) q^{33} +(1.49171 + 0.861240i) q^{34} +(1.74301 + 1.99046i) q^{35} +(2.40245 - 1.79673i) q^{36} +(-5.24042 - 9.07668i) q^{37} +(3.92342 + 6.79557i) q^{38} +(2.69147 + 2.38994i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-3.17762 - 5.50380i) q^{41} +(0.0316804 - 4.58247i) q^{42} +(1.94221 - 3.36401i) q^{43} +(1.52837 - 0.882407i) q^{44} +(0.354788 + 2.97895i) q^{45} +(-3.57642 + 6.19453i) q^{46} +12.0224 q^{47} +(-0.546603 - 1.64354i) q^{48} +(-5.54722 - 4.26947i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.92244 + 0.600108i) q^{51} +(1.79971 - 1.03906i) q^{52} +(4.34949 + 2.51118i) q^{53} +(2.96642 - 4.26618i) q^{54} +1.76481i q^{55} +(-2.50472 - 0.852286i) q^{56} +(10.1628 + 9.02424i) q^{57} +(3.24547 - 5.62132i) q^{58} -8.50907 q^{59} +(1.69665 + 0.348398i) q^{60} +6.93320i q^{61} +4.88768 q^{62} +(-2.45272 - 7.54878i) q^{63} -1.00000 q^{64} +2.07813i q^{65} +(2.02962 - 2.28569i) q^{66} +4.25239 q^{67} +(0.861240 - 1.49171i) q^{68} +(-2.49203 + 12.1358i) q^{69} +(1.99046 - 1.74301i) q^{70} +7.97609i q^{71} +(-1.79673 - 2.40245i) q^{72} +(-9.43511 - 5.44736i) q^{73} +(-9.07668 + 5.24042i) q^{74} +(-1.15005 + 1.29514i) q^{75} +(6.79557 - 3.92342i) q^{76} +(-0.907568 - 4.58021i) q^{77} +(2.38994 - 2.69147i) q^{78} -11.6744 q^{79} +(0.500000 - 0.866025i) q^{80} +(2.54353 - 8.63310i) q^{81} +(-5.50380 + 3.17762i) q^{82} +(-5.77748 + 10.0069i) q^{83} +(-4.58247 - 0.0316804i) q^{84} +(0.861240 + 1.49171i) q^{85} +(-3.36401 - 1.94221i) q^{86} +(2.26143 - 11.0128i) q^{87} +(-0.882407 - 1.52837i) q^{88} +(-4.36194 - 7.55510i) q^{89} +(2.97895 - 0.354788i) q^{90} +(-1.06869 - 5.39334i) q^{91} +(6.19453 + 3.57642i) q^{92} +(8.03310 - 2.67162i) q^{93} -12.0224i q^{94} +7.84685i q^{95} +(-1.64354 + 0.546603i) q^{96} +(5.31507 + 3.06866i) q^{97} +(-4.26947 + 5.54722i) q^{98} +(2.08640 - 4.86601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.546603	−	1.64354i	−0.315582	−	0.948898i
$3$	−0.546603	−	1.64354i	−0.315582	−	0.948898i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.64354	+	0.546603i	−0.670973	+	0.223150i
$7$	−0.852286	+	2.50472i	−0.322134	+	0.946694i
$7$	−0.852286	+	2.50472i	−0.322134	+	0.946694i
$8$			1.00000i			0.353553i
$9$	−2.40245	+	1.79673i	−0.800817	+	0.598910i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−1.52837	+	0.882407i	−0.460822	+	0.266056i	−0.712390	−	0.701784i	$-0.752387\pi$
$11$	−1.52837	+	0.882407i	−0.460822	+	0.266056i	0.251568	+	0.967840i	$0.419054\pi$
$12$	0.546603	+	1.64354i	0.157791	+	0.474449i
$13$	−1.79971	+	1.03906i	−0.499150	+	0.288184i	−0.728362	−	0.685192i	$-0.759718\pi$
$13$	−1.79971	+	1.03906i	−0.499150	+	0.288184i	0.229213	+	0.973376i	$0.426385\pi$
$14$	2.50472	+	0.852286i	0.669414	+	0.227783i
$15$	−1.69665	−	0.348398i	−0.438073	−	0.0899559i
$16$	1.00000			0.250000
$17$	−0.861240	+	1.49171i	−0.208881	+	0.361793i	−0.951362	−	0.308074i	$-0.900316\pi$
$17$	−0.861240	+	1.49171i	−0.208881	+	0.361793i	0.742481	+	0.669867i	$0.233649\pi$
$18$	1.79673	+	2.40245i	0.423493	+	0.566263i
$19$	−6.79557	+	3.92342i	−1.55901	+	0.900095i	−0.561659	+	0.827369i	$0.689837\pi$
$19$	−6.79557	+	3.92342i	−1.55901	+	0.900095i	−0.997352	+	0.0727261i	$0.976830\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	4.58247	+	0.0316804i	0.999976	+	0.00691322i
$22$	0.882407	+	1.52837i	0.188130	+	0.325851i
$23$	−6.19453	−	3.57642i	−1.29165	−	0.745734i	−0.312703	−	0.949851i	$-0.601234\pi$
$23$	−6.19453	−	3.57642i	−1.29165	−	0.745734i	−0.978947	+	0.204117i	$0.934568\pi$
$24$	1.64354	−	0.546603i	0.335486	−	0.111575i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.03906	+	1.79971i	0.203777	+	0.352952i
$27$	4.26618	+	2.96642i	0.821027	+	0.570889i
$28$	0.852286	−	2.50472i	0.161067	−	0.473347i
$29$	5.62132	+	3.24547i	1.04385	+	0.602669i	0.920922	−	0.389747i	$-0.127437\pi$
$29$	5.62132	+	3.24547i	1.04385	+	0.602669i	0.122931	+	0.992415i	$0.460771\pi$
$30$	−0.348398	+	1.69665i	−0.0636084	+	0.309764i
$31$			4.88768i			0.877854i	0.898523	+	0.438927i	$0.144641\pi$
$31$			4.88768i			0.877854i	−0.898523	+	0.438927i	$0.855359\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.28569	+	2.02962i	0.397887	+	0.353311i
$34$	1.49171	+	0.861240i	0.255826	+	0.147701i
$35$	1.74301	+	1.99046i	0.294622	+	0.336449i
$36$	2.40245	−	1.79673i	0.400408	−	0.299455i
$37$	−5.24042	−	9.07668i	−0.861520	−	1.49220i	−0.870461	−	0.492237i	$-0.836179\pi$
$37$	−5.24042	−	9.07668i	−0.861520	−	1.49220i	0.00894096	−	0.999960i	$-0.497154\pi$
$38$	3.92342	+	6.79557i	0.636463	+	1.10239i
$39$	2.69147	+	2.38994i	0.430980	+	0.382697i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−3.17762	−	5.50380i	−0.496261	−	0.859549i	0.503730	−	0.863861i	$-0.331961\pi$
$41$	−3.17762	−	5.50380i	−0.496261	−	0.859549i	−0.999991	+	0.00431191i	$0.998627\pi$
$42$	0.0316804	−	4.58247i	0.00488838	−	0.707090i
$43$	1.94221	−	3.36401i	0.296184	−	0.513006i	−0.679075	−	0.734069i	$-0.737619\pi$
$43$	1.94221	−	3.36401i	0.296184	−	0.513006i	0.975260	+	0.221062i	$0.0709524\pi$
$44$	1.52837	−	0.882407i	0.230411	−	0.133028i
$45$	0.354788	+	2.97895i	0.0528887	+	0.444075i
$46$	−3.57642	+	6.19453i	−0.527314	+	0.913334i
$47$	12.0224			1.75365			0.876826	−	0.480808i	$-0.159657\pi$
$47$	12.0224			1.75365			0.876826	+	0.480808i	$0.159657\pi$
$48$	−0.546603	−	1.64354i	−0.0788954	−	0.237225i
$49$	−5.54722	−	4.26947i	−0.792459	−	0.609925i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	2.92244	+	0.600108i	0.409224	+	0.0840320i
$52$	1.79971	−	1.03906i	0.249575	−	0.144092i
$53$	4.34949	+	2.51118i	0.597449	+	0.344937i	0.768037	−	0.640405i	$-0.221234\pi$
$53$	4.34949	+	2.51118i	0.597449	+	0.344937i	−0.170588	+	0.985342i	$0.554567\pi$
$54$	2.96642	−	4.26618i	0.403679	−	0.580554i
$55$			1.76481i			0.237968i
$56$	−2.50472	−	0.852286i	−0.334707	−	0.113892i
$57$	10.1628	+	9.02424i	1.34609	+	1.19529i
$58$	3.24547	−	5.62132i	0.426151	−	0.738115i
$59$	−8.50907			−1.10779			−0.553893	−	0.832588i	$-0.686858\pi$
$59$	−8.50907			−1.10779			−0.553893	+	0.832588i	$0.686858\pi$
$60$	1.69665	+	0.348398i	0.219036	+	0.0449780i
$61$			6.93320i			0.887705i	0.896100	+	0.443853i	$0.146389\pi$
$61$			6.93320i			0.887705i	−0.896100	+	0.443853i	$0.853611\pi$
$62$	4.88768			0.620736
$63$	−2.45272	−	7.54878i	−0.309014	−	0.951057i
$64$	−1.00000			−0.125000
$65$			2.07813i			0.257760i
$66$	2.02962	−	2.28569i	0.249829	−	0.281349i
$67$	4.25239			0.519512			0.259756	−	0.965674i	$-0.416358\pi$
$67$	4.25239			0.519512			0.259756	+	0.965674i	$0.416358\pi$
$68$	0.861240	−	1.49171i	0.104441	−	0.180897i
$69$	−2.49203	+	12.1358i	−0.300005	+	1.46098i
$70$	1.99046	−	1.74301i	0.237906	−	0.208329i
$71$			7.97609i			0.946588i	0.880905	+	0.473294i	$0.156935\pi$
$71$			7.97609i			0.946588i	−0.880905	+	0.473294i	$0.843065\pi$
$72$	−1.79673	−	2.40245i	−0.211747	−	0.283131i
$73$	−9.43511	−	5.44736i	−1.10430	−	0.637566i	−0.166950	−	0.985965i	$-0.553392\pi$
$73$	−9.43511	−	5.44736i	−1.10430	−	0.637566i	−0.937346	+	0.348400i	$0.886725\pi$
$74$	−9.07668	+	5.24042i	−1.05514	+	0.609187i
$75$	−1.15005	+	1.29514i	−0.132796	+	0.149550i
$76$	6.79557	−	3.92342i	0.779505	−	0.450048i
$77$	−0.907568	−	4.58021i	−0.103427	−	0.521963i
$78$	2.38994	−	2.69147i	0.270607	−	0.304749i
$79$	−11.6744			−1.31347			−0.656737	−	0.754119i	$-0.728064\pi$
$79$	−11.6744			−1.31347			−0.656737	+	0.754119i	$0.728064\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	2.54353	−	8.63310i	0.282614	−	0.959234i
$82$	−5.50380	+	3.17762i	−0.607793	+	0.350910i
$83$	−5.77748	+	10.0069i	−0.634161	+	1.09840i	0.352531	+	0.935800i	$0.385321\pi$
$83$	−5.77748	+	10.0069i	−0.634161	+	1.09840i	−0.986692	+	0.162599i	$0.948012\pi$
$84$	−4.58247	−	0.0316804i	−0.499988	−	0.00345661i
$85$	0.861240	+	1.49171i	0.0934146	+	0.161799i
$86$	−3.36401	−	1.94221i	−0.362750	−	0.209434i
$87$	2.26143	−	11.0128i	0.242451	−	1.18070i
$88$	−0.882407	−	1.52837i	−0.0940649	−	0.162925i
$89$	−4.36194	−	7.55510i	−0.462364	−	0.800839i	0.536714	−	0.843764i	$-0.319665\pi$
$89$	−4.36194	−	7.55510i	−0.462364	−	0.800839i	−0.999078	+	0.0429257i	$0.986332\pi$
$90$	2.97895	−	0.354788i	0.314009	−	0.0373980i
$91$	−1.06869	−	5.39334i	−0.112029	−	0.565376i
$92$	6.19453	+	3.57642i	0.645825	+	0.372867i
$93$	8.03310	−	2.67162i	0.832994	−	0.277034i
$94$		−	12.0224i		−	1.24002i
$95$			7.84685i			0.805070i
$96$	−1.64354	+	0.546603i	−0.167743	+	0.0557875i
$97$	5.31507	+	3.06866i	0.539664	+	0.311575i	0.744943	−	0.667128i	$-0.232477\pi$
$97$	5.31507	+	3.06866i	0.539664	+	0.311575i	−0.205279	+	0.978704i	$0.565810\pi$
$98$	−4.26947	+	5.54722i	−0.431282	+	0.560353i
$99$	2.08640	−	4.86601i	0.209691	−	0.489053i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.03604	+	5.25858i	0.302098	+	0.523249i	0.976611	−	0.215014i	$-0.0689798\pi$
$101$	3.03604	+	5.25858i	0.302098	+	0.523249i	−0.674513	+	0.738263i	$0.735646\pi$
$102$	0.600108	−	2.92244i	0.0594196	−	0.289365i
$103$	−15.8719	−	9.16364i	−1.56390	−	0.902920i	−0.996856	−	0.0792358i	$-0.974752\pi$
$103$	−15.8719	−	9.16364i	−1.56390	−	0.902920i	−0.567048	−	0.823685i	$-0.691915\pi$
$104$	−1.03906	−	1.79971i	−0.101888	−	0.176476i
$105$	2.31867	−	3.95269i	0.226279	−	0.385743i
$106$	2.51118	−	4.34949i	0.243907	−	0.422460i
$107$	1.63586	−	0.944465i	0.158145	−	0.0913048i	−0.418839	−	0.908060i	$-0.637563\pi$
$107$	1.63586	−	0.944465i	0.158145	−	0.0913048i	0.576984	+	0.816756i	$0.304230\pi$
$108$	−4.26618	−	2.96642i	−0.410514	−	0.285444i
$109$	3.31820	−	5.74730i	0.317826	−	0.550491i	−0.662208	−	0.749320i	$-0.730380\pi$
$109$	3.31820	−	5.74730i	0.317826	−	0.550491i	0.980034	+	0.198829i	$0.0637138\pi$
$110$	1.76481			0.168268
$111$	−12.0535	+	13.5742i	−1.14406	+	1.28841i
$112$	−0.852286	+	2.50472i	−0.0805335	+	0.236674i
$113$	11.9525	−	6.90075i	1.12439	−	0.649168i	0.181874	−	0.983322i	$-0.441784\pi$
$113$	11.9525	−	6.90075i	1.12439	−	0.649168i	0.942519	+	0.334154i	$0.108450\pi$
$114$	9.02424	−	10.1628i	0.845197	−	0.951832i
$115$	−6.19453	+	3.57642i	−0.577643	+	0.333502i
$116$	−5.62132	−	3.24547i	−0.521926	−	0.301334i
$117$	2.45680	−	5.72989i	0.227131	−	0.529728i
$118$			8.50907i			0.783323i
$119$	−3.00229	−	3.42853i	−0.275220	−	0.314293i
$120$	0.348398	−	1.69665i	0.0318042	−	0.154882i
$121$	−3.94271	+	6.82898i	−0.358429	+	0.620817i
$122$	6.93320			0.627702
$123$	−7.30882	+	8.23095i	−0.659014	+	0.742159i
$124$		−	4.88768i		−	0.438927i
$125$	−1.00000			−0.0894427
$126$	−7.54878	+	2.45272i	−0.672499	+	0.218506i
$127$	−2.81109			−0.249444			−0.124722	−	0.992192i	$-0.539804\pi$
$127$	−2.81109			−0.249444			−0.124722	+	0.992192i	$0.539804\pi$
$128$			1.00000i			0.0883883i
$129$	−6.59050	−	1.35332i	−0.580261	−	0.119153i
$130$	2.07813			0.182264
$131$	−8.54952	+	14.8082i	−0.746975	+	1.29380i	0.202291	+	0.979326i	$0.435161\pi$
$131$	−8.54952	+	14.8082i	−0.746975	+	1.29380i	−0.949266	+	0.314474i	$0.898172\pi$
$132$	−2.28569	−	2.02962i	−0.198943	−	0.176656i
$133$	−4.03530	−	20.3649i	−0.349905	−	1.76586i
$134$		−	4.25239i		−	0.367350i
$135$	4.70209	−	2.21141i	0.404692	−	0.190328i
$136$	−1.49171	−	0.861240i	−0.127913	−	0.0738507i
$137$	7.22017	−	4.16857i	0.616861	−	0.356145i	−0.158785	−	0.987313i	$-0.550758\pi$
$137$	7.22017	−	4.16857i	0.616861	−	0.356145i	0.775646	+	0.631168i	$0.217424\pi$
$138$	12.1358	+	2.49203i	1.03307	+	0.212136i
$139$	−8.22347	+	4.74782i	−0.697505	+	0.402705i	−0.806418	−	0.591346i	$-0.798597\pi$
$139$	−8.22347	+	4.74782i	−0.697505	+	0.402705i	0.108912	+	0.994051i	$0.465263\pi$
$140$	−1.74301	−	1.99046i	−0.147311	−	0.168225i
$141$	−6.57150	−	19.7594i	−0.553420	−	1.66404i
$142$	7.97609			0.669339
$143$	1.83375	−	3.17615i	0.153346	−	0.265603i
$144$	−2.40245	+	1.79673i	−0.200204	+	0.149727i
$145$	5.62132	−	3.24547i	0.466825	−	0.269522i
$146$	−5.44736	+	9.43511i	−0.450827	+	0.780855i
$147$	−3.98492	+	11.4508i	−0.328671	+	0.944444i
$148$	5.24042	+	9.07668i	0.430760	+	0.746098i
$149$	3.98762	+	2.30225i	0.326679	+	0.188608i	0.654365	−	0.756178i	$-0.272936\pi$
$149$	3.98762	+	2.30225i	0.326679	+	0.188608i	−0.327687	+	0.944786i	$0.606269\pi$
$150$	1.29514	+	1.15005i	0.105748	+	0.0939009i
$151$	−2.54672	−	4.41105i	−0.207249	−	0.358966i	0.743598	−	0.668627i	$-0.233118\pi$
$151$	−2.54672	−	4.41105i	−0.207249	−	0.358966i	−0.950847	+	0.309661i	$0.899784\pi$
$152$	−3.92342	−	6.79557i	−0.318232	−	0.551193i
$153$	−0.611116	−	5.13118i	−0.0494058	−	0.414831i
$154$	−4.58021	+	0.907568i	−0.369084	+	0.0731339i
$155$	4.23286	+	2.44384i	0.339991	+	0.196294i
$156$	−2.69147	−	2.38994i	−0.215490	−	0.191348i
$157$		−	4.84681i		−	0.386818i	−0.981118	−	0.193409i	$-0.938046\pi$
$157$		−	4.84681i		−	0.386818i	0.981118	−	0.193409i	$-0.0619544\pi$
$158$			11.6744i			0.928767i
$159$	1.74978	−	8.52119i	0.138767	−	0.675774i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	14.2374	−	12.4674i	1.12207	−	0.982571i
$162$	−8.63310	−	2.54353i	−0.678281	−	0.199838i
$163$	−0.203760	−	0.352922i	−0.0159597	−	0.0276430i	0.857935	−	0.513758i	$-0.171747\pi$
$163$	−0.203760	−	0.352922i	−0.0159597	−	0.0276430i	−0.873895	+	0.486115i	$0.838414\pi$
$164$	3.17762	+	5.50380i	0.248131	+	0.429775i
$165$	2.90054	−	0.964654i	0.225807	−	0.0750982i
$166$	10.0069	+	5.77748i	0.776685	+	0.448420i
$167$	−4.29226	−	7.43442i	−0.332145	−	0.575293i	0.650787	−	0.759260i	$-0.274439\pi$
$167$	−4.29226	−	7.43442i	−0.332145	−	0.575293i	−0.982932	+	0.183968i	$0.941106\pi$
$168$	−0.0316804	+	4.58247i	−0.00244419	+	0.353545i
$169$	−4.34070	+	7.51831i	−0.333900	+	0.578331i
$170$	1.49171	−	0.861240i	0.114409	−	0.0660541i
$171$	9.27668	−	21.6356i	0.709406	−	1.65452i
$172$	−1.94221	+	3.36401i	−0.148092	+	0.256503i
$173$	−10.5609			−0.802928			−0.401464	−	0.915875i	$-0.631499\pi$
$173$	−10.5609			−0.802928			−0.401464	+	0.915875i	$0.631499\pi$
$174$	−11.0128	−	2.26143i	−0.834882	−	0.171438i
$175$	2.59529	−	0.514257i	0.196186	−	0.0388742i
$176$	−1.52837	+	0.882407i	−0.115206	+	0.0665140i
$177$	4.65109	+	13.9850i	0.349597	+	1.05118i
$178$	−7.55510	+	4.36194i	−0.566278	+	0.326941i
$179$	−0.503264	−	0.290560i	−0.0376157	−	0.0217175i	0.481074	−	0.876680i	$-0.340247\pi$
$179$	−0.503264	−	0.290560i	−0.0376157	−	0.0217175i	−0.518690	+	0.854962i	$0.673580\pi$
$180$	−0.354788	−	2.97895i	−0.0264444	−	0.222038i
$181$			15.6386i			1.16241i	0.813757	+	0.581206i	$0.197419\pi$
$181$			15.6386i			1.16241i	−0.813757	+	0.581206i	$0.802581\pi$
$182$	−5.39334	+	1.06869i	−0.399781	+	0.0792166i
$183$	11.3950	−	3.78971i	0.842342	−	0.280143i
$184$	3.57642	−	6.19453i	0.263657	−	0.456667i
$185$	−10.4808			−0.770567
$186$	−2.67162	−	8.03310i	−0.195893	−	0.589016i
$187$		−	3.03986i		−	0.222296i
$188$	−12.0224			−0.876826
$189$	−11.0661	+	8.15734i	−0.804938	+	0.593359i
$190$	7.84685			0.569270
$191$		−	17.0990i		−	1.23724i	−0.785690	−	0.618620i	$-0.787692\pi$
$191$		−	17.0990i		−	1.23724i	0.785690	−	0.618620i	$-0.212308\pi$
$192$	0.546603	+	1.64354i	0.0394477	+	0.118612i
$193$	0.814513			0.0586299			0.0293150	−	0.999570i	$-0.490667\pi$
$193$	0.814513			0.0586299			0.0293150	+	0.999570i	$0.490667\pi$
$194$	3.06866	−	5.31507i	0.220317	−	0.381600i
$195$	3.41548	−	1.13591i	0.244588	−	0.0813442i
$196$	5.54722	+	4.26947i	0.396230	+	0.304962i
$197$			15.4752i			1.10256i	0.834320	+	0.551280i	$0.185860\pi$
$197$			15.4752i			1.10256i	−0.834320	+	0.551280i	$0.814140\pi$
$198$	−4.86601	−	2.08640i	−0.345813	−	0.148274i
$199$	−7.51013	−	4.33598i	−0.532379	−	0.307369i	0.209606	−	0.977786i	$-0.432782\pi$
$199$	−7.51013	−	4.33598i	−0.532379	−	0.307369i	−0.741985	+	0.670417i	$0.766115\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−2.32437	−	6.98897i	−0.163948	−	0.492964i
$202$	5.25858	−	3.03604i	0.369993	−	0.213615i
$203$	−12.9200	+	11.3137i	−0.906803	+	0.794069i
$204$	−2.92244	−	0.600108i	−0.204612	−	0.0420160i
$205$	−6.35524			−0.443869
$206$	−9.16364	+	15.8719i	−0.638461	+	1.10585i
$207$	21.3079	−	2.53774i	1.48100	−	0.176385i
$208$	−1.79971	+	1.03906i	−0.124787	+	0.0720460i
$209$	6.92412	−	11.9929i	0.478951	−	0.829568i
$210$	−3.95269	−	2.31867i	−0.272762	−	0.160003i
$211$	11.5037	+	19.9250i	0.791946	+	1.37169i	0.924760	+	0.380550i	$0.124265\pi$
$211$	11.5037	+	19.9250i	0.791946	+	1.37169i	−0.132814	+	0.991141i	$0.542401\pi$
$212$	−4.34949	−	2.51118i	−0.298724	−	0.172469i
$213$	13.1090	−	4.35976i	0.898216	−	0.298726i
$214$	−0.944465	−	1.63586i	−0.0645623	−	0.111825i
$215$	−1.94221	−	3.36401i	−0.132458	−	0.229423i
$216$	−2.96642	+	4.26618i	−0.201840	+	0.290277i
$217$	−12.2423	−	4.16570i	−0.831059	−	0.282786i
$218$	−5.74730	−	3.31820i	−0.389256	−	0.224737i
$219$	−3.79570	+	18.4845i	−0.256490	+	1.24907i
$220$		−	1.76481i		−	0.118984i
$221$		−	3.57953i		−	0.240785i
$222$	13.5742	+	12.0535i	0.911040	+	0.808975i
$223$	7.09528	+	4.09646i	0.475135	+	0.274320i	0.718387	−	0.695644i	$-0.244881\pi$
$223$	7.09528	+	4.09646i	0.475135	+	0.274320i	−0.243252	+	0.969963i	$0.578214\pi$
$224$	2.50472	+	0.852286i	0.167353	+	0.0569458i
$225$	2.75724	+	1.18222i	0.183816	+	0.0788145i
$226$	−6.90075	−	11.9525i	−0.459031	−	0.795066i
$227$	4.97492	+	8.61681i	0.330197	+	0.571918i	0.982550	−	0.185997i	$-0.0595515\pi$
$227$	4.97492	+	8.61681i	0.330197	+	0.571918i	−0.652353	+	0.757915i	$0.726218\pi$
$228$	−10.1628	−	9.02424i	−0.673047	−	0.597645i
$229$	2.88702	+	1.66682i	0.190780	+	0.110147i	0.592348	−	0.805683i	$-0.298201\pi$
$229$	2.88702	+	1.66682i	0.190780	+	0.110147i	−0.401568	+	0.915829i	$0.631535\pi$
$230$	3.57642	+	6.19453i	0.235822	+	0.408455i
$231$	−7.03168	+	3.99518i	−0.462651	+	0.262864i
$232$	−3.24547	+	5.62132i	−0.213076	+	0.369058i
$233$	17.9721	−	10.3762i	1.17739	−	0.679766i	0.221980	−	0.975051i	$-0.428748\pi$
$233$	17.9721	−	10.3762i	1.17739	−	0.679766i	0.955409	+	0.295285i	$0.0954146\pi$
$234$	−5.72989	−	2.45680i	−0.374574	−	0.160606i
$235$	6.01122	−	10.4117i	0.392129	−	0.679187i
$236$	8.50907			0.553893
$237$	6.38128	+	19.1874i	0.414508	+	1.24635i
$238$	−3.42853	+	3.00229i	−0.222238	+	0.194610i
$239$	13.5359	−	7.81497i	0.875567	−	0.505509i	0.00637252	−	0.999980i	$-0.497972\pi$
$239$	13.5359	−	7.81497i	0.875567	−	0.505509i	0.869194	+	0.494471i	$0.164638\pi$
$240$	−1.69665	−	0.348398i	−0.109518	−	0.0224890i
$241$	17.0167	−	9.82459i	1.09614	−	0.632857i	0.160936	−	0.986965i	$-0.448549\pi$
$241$	17.0167	−	9.82459i	1.09614	−	0.632857i	0.935205	+	0.354107i	$0.115215\pi$
$242$	6.82898	+	3.94271i	0.438984	+	0.253447i
$243$	−15.5792	+	0.538492i	−0.999403	+	0.0345443i
$244$		−	6.93320i		−	0.443853i
$245$	−6.47108	+	2.66929i	−0.413422	+	0.170535i
$246$	8.23095	+	7.30882i	0.524786	+	0.465993i
$247$	8.15337	−	14.1220i	0.518786	−	0.898564i
$248$	−4.88768			−0.310368
$249$	19.6047	+	4.02572i	1.24240	+	0.255120i
$250$			1.00000i			0.0632456i
$251$	4.91923			0.310499			0.155250	−	0.987875i	$-0.450382\pi$
$251$	4.91923			0.310499			0.155250	+	0.987875i	$0.450382\pi$
$252$	2.45272	+	7.54878i	0.154507	+	0.475529i
$253$	12.6234			0.793628
$254$			2.81109i			0.176384i
$255$	1.98093	−	2.23086i	0.124051	−	0.139702i
$256$	1.00000			0.0625000
$257$	6.90748	−	11.9641i	0.430877	−	0.746300i	−0.566072	−	0.824356i	$-0.691538\pi$
$257$	6.90748	−	11.9641i	0.430877	−	0.746300i	0.996949	+	0.0780552i	$0.0248710\pi$
$258$	−1.35332	+	6.59050i	−0.0842542	+	0.410307i
$259$	27.2009	−	5.38985i	1.69018	−	0.334909i
$260$		−	2.07813i		−	0.128880i
$261$	−19.3362	+	2.30291i	−1.19688	+	0.142547i
$262$	14.8082	+	8.54952i	0.914854	+	0.528191i
$263$	−21.5810	+	12.4598i	−1.33074	+	0.768305i	−0.985414	−	0.170176i	$-0.945566\pi$
$263$	−21.5810	+	12.4598i	−1.33074	+	0.768305i	−0.345330	+	0.938481i	$0.612233\pi$
$264$	−2.02962	+	2.28569i	−0.124914	+	0.140674i
$265$	4.34949	−	2.51118i	0.267187	−	0.154261i
$266$	−20.3649	+	4.03530i	−1.24865	+	0.247420i
$267$	−10.0329	+	11.2987i	−0.614001	+	0.691467i
$268$	−4.25239			−0.259756
$269$	8.99870	−	15.5862i	0.548660	−	0.950308i	−0.449706	−	0.893176i	$-0.648471\pi$
$269$	8.99870	−	15.5862i	0.548660	−	0.950308i	0.998367	−	0.0571312i	$-0.0181953\pi$
$270$	−2.21141	−	4.70209i	−0.134582	−	0.286160i
$271$	0.247998	−	0.143182i	0.0150648	−	0.00869766i	−0.492449	−	0.870341i	$-0.663898\pi$
$271$	0.247998	−	0.143182i	0.0150648	−	0.00869766i	0.507513	+	0.861644i	$0.330565\pi$
$272$	−0.861240	+	1.49171i	−0.0522203	+	0.0904483i
$273$	−8.28003	+	4.70445i	−0.501130	+	0.284727i
$274$	−4.16857	−	7.22017i	−0.251832	−	0.436187i
$275$	1.52837	+	0.882407i	0.0921644	+	0.0532112i
$276$	2.49203	−	12.1358i	0.150003	−	0.730492i
$277$	−6.27436	−	10.8675i	−0.376990	−	0.652965i	0.613633	−	0.789591i	$-0.289707\pi$
$277$	−6.27436	−	10.8675i	−0.376990	−	0.652965i	−0.990623	+	0.136626i	$0.956374\pi$
$278$	4.74782	+	8.22347i	0.284755	+	0.493211i
$279$	−8.78184	−	11.7424i	−0.525755	−	0.703000i
$280$	−1.99046	+	1.74301i	−0.118953	+	0.104164i
$281$	−2.38434	−	1.37660i	−0.142238	−	0.0821209i	0.427192	−	0.904161i	$-0.359503\pi$
$281$	−2.38434	−	1.37660i	−0.142238	−	0.0821209i	−0.569430	+	0.822040i	$0.692836\pi$
$282$	−19.7594	+	6.57150i	−1.17665	+	0.391327i
$283$			18.0647i			1.07384i	0.843634	+	0.536919i	$0.180412\pi$
$283$			18.0647i			1.07384i	−0.843634	+	0.536919i	$0.819588\pi$
$284$		−	7.97609i		−	0.473294i
$285$	12.8966	−	4.28911i	0.763929	−	0.254065i
$286$	−3.17615	−	1.83375i	−0.187810	−	0.108432i
$287$	16.4937	−	3.26823i	0.973593	−	0.192917i
$288$	1.79673	+	2.40245i	0.105873	+	0.141566i
$289$	7.01653	+	12.1530i	0.412737	+	0.714882i
$290$	−3.24547	−	5.62132i	−0.190581	−	0.330095i
$291$	2.13823	−	10.4129i	0.125345	−	0.610414i
$292$	9.43511	+	5.44736i	0.552148	+	0.318783i
$293$	−5.02230	−	8.69888i	−0.293406	−	0.508194i	0.681207	−	0.732091i	$-0.261455\pi$
$293$	−5.02230	−	8.69888i	−0.293406	−	0.508194i	−0.974613	+	0.223897i	$0.928122\pi$
$294$	11.4508	+	3.98492i	0.667823	+	0.232405i
$295$	−4.25453	+	7.36907i	−0.247709	+	0.429044i
$296$	9.07668	−	5.24042i	0.527571	−	0.304593i
$297$	−9.13792	−	0.769295i	−0.530236	−	0.0446390i
$298$	2.30225	−	3.98762i	0.133366	−	0.230997i
$299$	14.8645			0.859635
$300$	1.15005	−	1.29514i	0.0663979	−	0.0747751i
$301$	6.77057	+	7.73178i	0.390249	+	0.445653i
$302$	−4.41105	+	2.54672i	−0.253827	+	0.146547i
$303$	6.98318	−	7.86422i	0.401173	−	0.451788i
$304$	−6.79557	+	3.92342i	−0.389753	+	0.225024i
$305$	6.00433	+	3.46660i	0.343807	+	0.198497i
$306$	−5.13118	+	0.611116i	−0.293330	+	0.0349352i
$307$			28.7798i			1.64255i	0.570535	+	0.821274i	$0.306736\pi$
$307$			28.7798i			1.64255i	−0.570535	+	0.821274i	$0.693264\pi$
$308$	0.907568	+	4.58021i	0.0517135	+	0.260982i
$309$	−6.38518	+	31.0950i	−0.363240	+	1.76893i
$310$	2.44384	−	4.23286i	0.138801	−	0.240410i
$311$	−27.0587			−1.53436			−0.767178	−	0.641435i	$-0.778340\pi$
$311$	−27.0587			−1.53436			−0.767178	+	0.641435i	$0.778340\pi$
$312$	−2.38994	+	2.69147i	−0.135304	+	0.152374i
$313$			29.8779i			1.68880i	0.535714	+	0.844400i	$0.320043\pi$
$313$			29.8779i			1.68880i	−0.535714	+	0.844400i	$0.679957\pi$
$314$	−4.84681			−0.273521
$315$	−7.76380	−	1.65027i	−0.437441	−	0.0929823i
$316$	11.6744			0.656737
$317$			2.50188i			0.140520i	0.997529	+	0.0702599i	$0.0223829\pi$
$317$			2.50188i			0.140520i	−0.997529	+	0.0702599i	$0.977617\pi$
$318$	−8.52119	−	1.74978i	−0.477844	−	0.0981228i
$319$	−11.4553			−0.641374
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−2.44643	−	2.17236i	−0.136547	−	0.121249i
$322$	−12.4674	−	14.2374i	−0.694782	−	0.793421i
$323$		−	13.5160i		−	0.752052i
$324$	−2.54353	+	8.63310i	−0.141307	+	0.479617i
$325$	1.79971	+	1.03906i	0.0998299	+	0.0576368i
$326$	−0.352922	+	0.203760i	−0.0195465	+	0.0112852i
$327$	−11.2597	−	2.31211i	−0.622661	−	0.127860i
$328$	5.50380	−	3.17762i	0.303897	−	0.175455i
$329$	−10.2466	+	30.1128i	−0.564911	+	1.66017i
$330$	−0.964654	−	2.90054i	−0.0531024	−	0.159670i
$331$	22.7722			1.25168			0.625838	−	0.779953i	$-0.284757\pi$
$331$	22.7722			1.25168			0.625838	+	0.779953i	$0.284757\pi$
$332$	5.77748	−	10.0069i	0.317081	−	0.549200i
$333$	28.8982	+	12.3906i	1.58361	+	0.679003i
$334$	−7.43442	+	4.29226i	−0.406793	+	0.234862i
$335$	2.12619	−	3.68268i	0.116166	−	0.201206i
$336$	4.58247	+	0.0316804i	0.249994	+	0.00172830i
$337$	−6.91370	−	11.9749i	−0.376613	−	0.652313i	0.613954	−	0.789342i	$-0.289578\pi$
$337$	−6.91370	−	11.9749i	−0.376613	−	0.652313i	−0.990567	+	0.137029i	$0.956245\pi$
$338$	7.51831	+	4.34070i	0.408942	+	0.236103i
$339$	−17.8749	−	15.8724i	−0.970832	−	0.862069i
$340$	−0.861240	−	1.49171i	−0.0467073	−	0.0808994i
$341$	−4.31293	−	7.47021i	−0.233558	−	0.404534i
$342$	−21.6356	−	9.27668i	−1.16992	−	0.501626i
$343$	15.4216	−	10.2554i	0.832690	−	0.553739i
$344$	3.36401	+	1.94221i	0.181375	+	0.104717i
$345$	9.26394	+	8.22609i	0.498754	+	0.442878i
$346$			10.5609i			0.567756i
$347$		−	5.16857i		−	0.277463i	−0.990330	−	0.138732i	$-0.955697\pi$
$347$		−	5.16857i		−	0.277463i	0.990330	−	0.138732i	$-0.0443025\pi$
$348$	−2.26143	+	11.0128i	−0.121225	+	0.590351i
$349$	−6.38127	−	3.68423i	−0.341582	−	0.197212i	0.319390	−	0.947623i	$-0.396522\pi$
$349$	−6.38127	−	3.68423i	−0.341582	−	0.197212i	−0.660971	+	0.750411i	$0.729855\pi$
$350$	−0.514257	−	2.59529i	−0.0274882	−	0.138724i
$351$	−10.7602	−	0.905870i	−0.574337	−	0.0483517i
$352$	0.882407	+	1.52837i	0.0470325	+	0.0814626i
$353$	4.06250	+	7.03645i	0.216225	+	0.374512i	0.953651	−	0.300916i	$-0.0972922\pi$
$353$	4.06250	+	7.03645i	0.216225	+	0.374512i	−0.737426	+	0.675428i	$0.763959\pi$
$354$	13.9850	−	4.65109i	0.743294	−	0.247202i
$355$	6.90750	+	3.98805i	0.366612	+	0.211663i
$356$	4.36194	+	7.55510i	0.231182	+	0.400419i
$357$	−3.99386	+	6.80843i	−0.211378	+	0.360340i
$358$	−0.290560	+	0.503264i	−0.0153566	+	0.0265983i
$359$	−14.8774	+	8.58944i	−0.785197	+	0.453333i	−0.838269	−	0.545257i	$-0.816432\pi$
$359$	−14.8774	+	8.58944i	−0.785197	+	0.453333i	0.0530722	+	0.998591i	$0.483099\pi$
$360$	−2.97895	+	0.354788i	−0.157004	+	0.0186990i
$361$	21.2865	−	36.8693i	1.12034	−	1.94049i
$362$	15.6386			0.821949
$363$	13.3788	+	2.74727i	0.702205	+	0.144194i
$364$	1.06869	+	5.39334i	0.0560146	+	0.282688i
$365$	−9.43511	+	5.44736i	−0.493856	+	0.285128i
$366$	−3.78971	−	11.3950i	−0.198091	−	0.595626i
$367$	−11.3900	+	6.57603i	−0.594554	+	0.343266i	−0.766896	−	0.641771i	$-0.778200\pi$
$367$	−11.3900	+	6.57603i	−0.594554	+	0.343266i	0.172342	+	0.985037i	$0.444867\pi$
$368$	−6.19453	−	3.57642i	−0.322912	−	0.186434i
$369$	17.5229	+	7.51328i	0.912207	+	0.391126i
$370$			10.4808i			0.544873i
$371$	−9.99681	+	8.75400i	−0.519009	+	0.454485i
$372$	−8.03310	+	2.67162i	−0.416497	+	0.138517i
$373$	−6.98405	+	12.0967i	−0.361620	+	0.626345i	−0.988228	−	0.152990i	$-0.951110\pi$
$373$	−6.98405	+	12.0967i	−0.361620	+	0.626345i	0.626607	+	0.779335i	$0.284443\pi$
$374$	−3.03986			−0.157187
$375$	0.546603	+	1.64354i	0.0282265	+	0.0848721i
$376$			12.0224i			0.620010i
$377$	−13.4890			−0.694718
$378$	8.15734	+	11.0661i	0.419568	+	0.569177i
$379$	18.2898			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$379$	18.2898			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$380$		−	7.84685i		−	0.402535i
$381$	1.53655	+	4.62015i	0.0787200	+	0.236697i
$382$	−17.0990			−0.874861
$383$	8.09287	−	14.0173i	0.413526	−	0.716248i	−0.581746	−	0.813370i	$-0.697630\pi$
$383$	8.09287	−	14.0173i	0.413526	−	0.716248i	0.995272	+	0.0971219i	$0.0309637\pi$
$384$	1.64354	−	0.546603i	0.0838716	−	0.0278937i
$385$	−4.42036	−	1.50413i	−0.225282	−	0.0766574i
$386$		−	0.814513i		−	0.0414576i
$387$	1.37815	+	11.5715i	0.0700552	+	0.588212i
$388$	−5.31507	−	3.06866i	−0.269832	−	0.155788i
$389$	3.60907	−	2.08370i	0.182987	−	0.105648i	−0.405708	−	0.914003i	$-0.632975\pi$
$389$	3.60907	−	2.08370i	0.182987	−	0.105648i	0.588695	+	0.808355i	$0.299642\pi$
$390$	−1.13591	−	3.41548i	−0.0575191	−	0.172950i
$391$	10.6700	−	6.16030i	0.539603	−	0.311540i
$392$	4.26947	−	5.54722i	0.215641	−	0.280177i
$393$	29.0111	+	5.95727i	1.46342	+	0.300505i
$394$	15.4752			0.779628
$395$	−5.83721	+	10.1103i	−0.293702	+	0.508707i
$396$	−2.08640	+	4.86601i	−0.104845	+	0.244526i
$397$	−16.3535	+	9.44168i	−0.820757	+	0.473865i	−0.850678	−	0.525688i	$-0.823808\pi$
$397$	−16.3535	+	9.44168i	−0.820757	+	0.473865i	0.0299201	+	0.999552i	$0.490475\pi$
$398$	−4.33598	+	7.51013i	−0.217343	+	0.376449i
$399$	−31.2648	+	17.7637i	−1.56520	+	0.889296i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	3.81763	+	2.20411i	0.190643	+	0.110068i	0.592284	−	0.805730i	$-0.298226\pi$
$401$	3.81763	+	2.20411i	0.190643	+	0.110068i	−0.401640	+	0.915797i	$0.631560\pi$
$402$	−6.98897	+	2.32437i	−0.348578	+	0.115929i
$403$	−5.07861	−	8.79641i	−0.252983	−	0.438180i
$404$	−3.03604	−	5.25858i	−0.151049	−	0.261624i
$405$	−6.20472	−	6.51931i	−0.308315	−	0.323947i
$406$	11.3137	+	12.9200i	0.561492	+	0.641207i
$407$	16.0187	+	9.24838i	0.794015	+	0.458425i
$408$	−0.600108	+	2.92244i	−0.0297098	+	0.144683i
$409$			36.9170i			1.82543i	0.408599	+	0.912714i	$0.366017\pi$
$409$			36.9170i			1.82543i	−0.408599	+	0.912714i	$0.633983\pi$
$410$			6.35524i			0.313863i
$411$	−10.7978	−	9.58809i	−0.532615	−	0.472946i
$412$	15.8719	+	9.16364i	0.781952	+	0.451460i
$413$	7.25216	−	21.3128i	0.356856	−	1.04873i
$414$	−2.53774	−	21.3079i	−0.124723	−	1.04723i
$415$	5.77748	+	10.0069i	0.283605	+	0.491219i
$416$	1.03906	+	1.79971i	0.0509442	+	0.0882380i
$417$	12.2982	+	10.9204i	0.602246	+	0.534776i
$418$	−11.9929	−	6.92412i	−0.586593	−	0.338670i
$419$	−10.6989	−	18.5311i	−0.522677	−	0.905304i	−0.999652	−	0.0263867i	$-0.991600\pi$
$419$	−10.6989	−	18.5311i	−0.522677	−	0.905304i	0.476974	−	0.878917i	$-0.341733\pi$
$420$	−2.31867	+	3.95269i	−0.113139	+	0.192872i
$421$	−12.6605	+	21.9286i	−0.617033	+	1.06873i	0.372991	+	0.927835i	$0.378332\pi$
$421$	−12.6605	+	21.9286i	−0.617033	+	1.06873i	−0.990024	+	0.140898i	$0.955001\pi$
$422$	19.9250	−	11.5037i	0.969932	−	0.559991i
$423$	−28.8833	+	21.6011i	−1.40435	+	1.05028i
$424$	−2.51118	+	4.34949i	−0.121954	+	0.211230i
$425$	1.72248			0.0835525
$426$	−4.35976	−	13.1090i	−0.211231	−	0.635134i
$427$	−17.3657	−	5.90907i	−0.840385	−	0.285960i
$428$	−1.63586	+	0.944465i	−0.0790723	+	0.0456524i
$429$	−6.22247	−	1.27775i	−0.300424	−	0.0616904i
$430$	−3.36401	+	1.94221i	−0.162227	+	0.0936617i
$431$	22.1285	+	12.7759i	1.06589	+	0.615393i	0.927056	−	0.374922i	$-0.122331\pi$
$431$	22.1285	+	12.7759i	1.06589	+	0.615393i	0.138836	+	0.990315i	$0.455664\pi$
$432$	4.26618	+	2.96642i	0.205257	+	0.142722i
$433$			3.82288i			0.183716i	0.995772	+	0.0918579i	$0.0292806\pi$
$433$			3.82288i			0.183716i	−0.995772	+	0.0918579i	$0.970719\pi$
$434$	−4.16570	+	12.2423i	−0.199960	+	0.587647i
$435$	−8.40669	−	7.46488i	−0.403070	−	0.357914i
$436$	−3.31820	+	5.74730i	−0.158913	+	0.275246i
$437$	56.1272			2.68493
$438$	18.4845	+	3.79570i	0.883225	+	0.181366i
$439$		−	3.14023i		−	0.149875i	−0.997188	−	0.0749376i	$-0.976124\pi$
$439$		−	3.14023i		−	0.149875i	0.997188	−	0.0749376i	$-0.0238758\pi$
$440$	−1.76481			−0.0841342
$441$	20.9980	+	0.290348i	0.999904	+	0.0138261i
$442$	−3.57953			−0.170261
$443$		−	30.4394i		−	1.44622i	−0.690733	−	0.723110i	$-0.742712\pi$
$443$		−	30.4394i		−	1.44622i	0.690733	−	0.723110i	$-0.257288\pi$
$444$	12.0535	−	13.5742i	0.572032	−	0.644203i
$445$	−8.72387			−0.413551
$446$	4.09646	−	7.09528i	0.193973	−	0.335971i
$447$	1.60420	−	7.81223i	0.0758760	−	0.369506i
$448$	0.852286	−	2.50472i	0.0402667	−	0.118337i
$449$		−	23.6834i		−	1.11769i	−0.829273	−	0.558844i	$-0.811245\pi$
$449$		−	23.6834i		−	1.11769i	0.829273	−	0.558844i	$-0.188755\pi$
$450$	1.18222	−	2.75724i	0.0557303	−	0.129977i
$451$	9.71319	+	5.60791i	0.457376	+	0.264066i
$452$	−11.9525	+	6.90075i	−0.562196	+	0.324584i
$453$	−5.85769	+	6.59673i	−0.275218	+	0.309942i
$454$	8.61681	−	4.97492i	0.404407	−	0.233484i
$455$	−5.20512	−	1.77116i	−0.244020	−	0.0830332i
$456$	−9.02424	+	10.1628i	−0.422599	+	0.475916i
$457$	−8.67786			−0.405933			−0.202967	−	0.979186i	$-0.565058\pi$
$457$	−8.67786			−0.405933			−0.202967	+	0.979186i	$0.565058\pi$
$458$	1.66682	−	2.88702i	0.0778856	−	0.134902i
$459$	−8.09926	+	3.80911i	−0.378041	+	0.177794i
$460$	6.19453	−	3.57642i	0.288822	−	0.166751i
$461$	14.9611	−	25.9133i	0.696807	−	1.20690i	−0.272761	−	0.962082i	$-0.587937\pi$
$461$	14.9611	−	25.9133i	0.696807	−	1.20690i	0.969568	−	0.244823i	$-0.0787298\pi$
$462$	3.99518	+	7.03168i	0.185873	+	0.327143i
$463$	−15.7628	−	27.3020i	−0.732559	−	1.26883i	−0.955786	−	0.294063i	$-0.904992\pi$
$463$	−15.7628	−	27.3020i	−0.732559	−	1.26883i	0.223227	−	0.974767i	$-0.428341\pi$
$464$	5.62132	+	3.24547i	0.260963	+	0.150667i
$465$	1.70286	−	8.29268i	0.0789681	−	0.384564i
$466$	−10.3762	−	17.9721i	−0.480667	−	0.832540i
$467$	−15.6065	−	27.0312i	−0.722181	−	1.25085i	−0.960124	−	0.279574i	$-0.909807\pi$
$467$	−15.6065	−	27.0312i	−0.722181	−	1.25085i	0.237944	−	0.971279i	$-0.423527\pi$
$468$	−2.45680	+	5.72989i	−0.113565	+	0.264864i
$469$	−3.62425	+	10.6510i	−0.167352	+	0.491819i
$470$	−10.4117	−	6.01122i	−0.480257	−	0.277277i
$471$	−7.96593	+	2.64928i	−0.367051	+	0.122073i
$472$		−	8.50907i		−	0.391662i
$473$			6.85528i			0.315206i
$474$	19.1874	−	6.38128i	0.881305	−	0.293102i
$475$	6.79557	+	3.92342i	0.311802	+	0.180019i
$476$	3.00229	+	3.42853i	0.137610	+	0.157146i
$477$	−14.9613	+	1.78188i	−0.685033	+	0.0815865i
$478$	−7.81497	−	13.5359i	−0.357449	−	0.619119i
$479$	14.7833	+	25.6054i	0.675465	+	1.16994i	0.976333	+	0.216274i	$0.0693905\pi$
$479$	14.7833	+	25.6054i	0.675465	+	1.16994i	−0.300867	+	0.953666i	$0.597276\pi$
$480$	−0.348398	+	1.69665i	−0.0159021	+	0.0774411i
$481$	18.8625	+	10.8903i	0.860055	+	0.496553i
$482$	−9.82459	−	17.0167i	−0.447498	−	0.775089i
$483$	−28.2729	−	16.5850i	−1.28646	−	0.754646i
$484$	3.94271	−	6.82898i	0.179214	−	0.310408i
$485$	5.31507	−	3.06866i	0.241345	−	0.139341i
$486$	0.538492	+	15.5792i	0.0244265	+	0.706685i
$487$	9.02713	−	15.6354i	0.409058	−	0.708509i	−0.585726	−	0.810509i	$-0.699191\pi$
$487$	9.02713	−	15.6354i	0.409058	−	0.708509i	0.994784	+	0.101999i	$0.0325240\pi$
$488$	−6.93320			−0.313851
$489$	−0.468666	+	0.527796i	−0.0211938	+	0.0238677i
$490$	2.66929	+	6.47108i	0.120586	+	0.292334i
$491$	−8.24376	+	4.75953i	−0.372035	+	0.214795i	−0.674347	−	0.738414i	$-0.735575\pi$
$491$	−8.24376	+	4.75953i	−0.372035	+	0.214795i	0.302312	+	0.953209i	$0.402242\pi$
$492$	7.30882	−	8.23095i	0.329507	−	0.371080i
$493$	−9.68261	+	5.59026i	−0.436083	+	0.251772i
$494$	−14.1220	−	8.15337i	−0.635381	−	0.366837i
$495$	−3.17089	−	4.23988i	−0.142521	−	0.190568i
$496$			4.88768i			0.219463i
$497$	−19.9779	−	6.79791i	−0.896129	−	0.304928i
$498$	4.02572	−	19.6047i	0.180397	−	0.878509i
$499$	−5.26991	+	9.12775i	−0.235914	+	0.408614i	−0.959538	−	0.281580i	$-0.909142\pi$
$499$	−5.26991	+	9.12775i	−0.235914	+	0.408614i	0.723624	+	0.690194i	$0.242475\pi$
$500$	1.00000			0.0447214
$501$	−9.87260	+	11.1182i	−0.441075	+	0.496724i
$502$		−	4.91923i		−	0.219556i
$503$	16.8262			0.750245			0.375122	−	0.926975i	$-0.377601\pi$
$503$	16.8262			0.750245			0.375122	+	0.926975i	$0.377601\pi$
$504$	7.54878	−	2.45272i	0.336250	−	0.109253i
$505$	6.07209			0.270204
$506$		−	12.6234i		−	0.561180i
$507$	14.7293	+	3.02458i	0.654150	+	0.134326i
$508$	2.81109			0.124722
$509$	−4.58691	+	7.94476i	−0.203311	+	0.352145i	−0.949593	−	0.313484i	$-0.898504\pi$
$509$	−4.58691	+	7.94476i	−0.203311	+	0.352145i	0.746282	+	0.665630i	$0.231837\pi$
$510$	−2.23086	−	1.98093i	−0.0987840	−	0.0877171i
$511$	21.6855	−	18.9896i	0.959311	−	0.840049i
$512$		−	1.00000i		−	0.0441942i
$513$	−40.6297	−	3.42050i	−1.79384	−	0.151019i
$514$	−11.9641	−	6.90748i	−0.527714	−	0.304676i
$515$	−15.8719	+	9.16364i	−0.699399	+	0.403798i
$516$	6.59050	+	1.35332i	0.290131	+	0.0595767i
$517$	−18.3748	+	10.6087i	−0.808122	+	0.466569i
$518$	−5.38985	−	27.2009i	−0.236816	−	1.19514i
$519$	5.77261	+	17.3572i	0.253389	+	0.761897i
$520$	−2.07813			−0.0911318
$521$	7.22962	−	12.5221i	0.316736	−	0.548602i	−0.663069	−	0.748558i	$-0.730747\pi$
$521$	7.22962	−	12.5221i	0.316736	−	0.548602i	0.979805	+	0.199956i	$0.0640799\pi$
$522$	2.30291	+	19.3362i	0.100796	+	0.846321i
$523$	23.7011	−	13.6839i	1.03638	−	0.598353i	0.117573	−	0.993064i	$-0.462489\pi$
$523$	23.7011	−	13.6839i	1.03638	−	0.598353i	0.918805	+	0.394711i	$0.129155\pi$
$524$	8.54952	−	14.8082i	0.373488	−	0.646900i
$525$	−2.26380	−	3.98437i	−0.0988002	−	0.173892i
$526$	12.4598	+	21.5810i	0.543274	+	0.940978i
$527$	−7.29101	−	4.20947i	−0.317601	−	0.183367i
$528$	2.28569	+	2.02962i	0.0994717	+	0.0883278i
$529$	14.0815	+	24.3899i	0.612239	+	1.06043i
$530$	−2.51118	−	4.34949i	−0.109079	−	0.188930i
$531$	20.4426	−	15.2885i	0.887134	−	0.663464i
$532$	4.03530	+	20.3649i	0.174952	+	0.882929i
$533$	11.4376	+	6.60350i	0.495417	+	0.286029i
$534$	11.2987	+	10.0329i	0.488941	+	0.434164i
$535$		−	1.88893i		−	0.0816655i
$536$			4.25239i			0.183675i
$537$	−0.202461	+	0.985956i	−0.00873683	+	0.0425471i
$538$	−15.5862	−	8.99870i	−0.671969	−	0.387961i
$539$	12.2456	+	1.63045i	0.527457	+	0.0702284i
$540$	−4.70209	+	2.21141i	−0.202346	+	0.0951640i
$541$	−5.30916	−	9.19574i	−0.228259	−	0.395356i	0.729033	−	0.684478i	$-0.239970\pi$
$541$	−5.30916	−	9.19574i	−0.228259	−	0.395356i	−0.957292	+	0.289122i	$0.906637\pi$
$542$	−0.143182	−	0.247998i	−0.00615018	−	0.0106524i
$543$	25.7027	−	8.54813i	1.10301	−	0.366836i
$544$	1.49171	+	0.861240i	0.0639566	+	0.0369254i
$545$	−3.31820	−	5.74730i	−0.142136	−	0.246187i
$546$	4.70445	+	8.28003i	0.201332	+	0.354352i
$547$	15.7759	−	27.3247i	0.674529	−	1.16832i	−0.302077	−	0.953284i	$-0.597680\pi$
$547$	15.7759	−	27.3247i	0.674529	−	1.16832i	0.976606	−	0.215036i	$-0.0689868\pi$
$548$	−7.22017	+	4.16857i	−0.308430	+	0.178072i
$549$	−12.4571	−	16.6567i	−0.531655	−	0.710889i
$550$	0.882407	−	1.52837i	0.0376260	−	0.0651701i
$551$	−50.9334			−2.16984
$552$	−12.1358	−	2.49203i	−0.516536	−	0.106068i
$553$	9.94995	−	29.2411i	0.423115	−	1.24346i
$554$	−10.8675	+	6.27436i	−0.461716	+	0.266572i
$555$	5.72887	+	17.2257i	0.243177	+	0.731190i
$556$	8.22347	−	4.74782i	0.348753	−	0.201352i
$557$	−33.3462	−	19.2524i	−1.41292	−	0.815752i	−0.417262	−	0.908786i	$-0.637010\pi$
$557$	−33.3462	−	19.2524i	−1.41292	−	0.815752i	−0.995663	+	0.0930341i	$0.970343\pi$
$558$	−11.7424	+	8.78184i	−0.497096	+	0.371765i
$559$			8.07231i			0.341422i
$560$	1.74301	+	1.99046i	0.0736554	+	0.0841123i
$561$	−4.99613	+	1.66160i	−0.210937	+	0.0701527i
$562$	−1.37660	+	2.38434i	−0.0580682	+	0.100577i
$563$	15.3918			0.648689			0.324344	−	0.945939i	$-0.394856\pi$
$563$	15.3918			0.648689			0.324344	+	0.945939i	$0.394856\pi$
$564$	6.57150	+	19.7594i	0.276710	+	0.832019i
$565$		−	13.8015i		−	0.580634i
$566$	18.0647			0.759318
$567$	19.4557	+	13.7287i	0.817061	+	0.576551i
$568$	−7.97609			−0.334669
$569$		−	3.97024i		−	0.166441i	−0.996531	−	0.0832206i	$-0.973479\pi$
$569$		−	3.97024i		−	0.166441i	0.996531	−	0.0832206i	$-0.0265206\pi$
$570$	−4.28911	−	12.8966i	−0.179651	−	0.540180i
$571$	−32.6966			−1.36831			−0.684155	−	0.729337i	$-0.739829\pi$
$571$	−32.6966			−1.36831			−0.684155	+	0.729337i	$0.739829\pi$
$572$	−1.83375	+	3.17615i	−0.0766731	+	0.132802i
$573$	−28.1029	+	9.34637i	−1.17402	+	0.390450i
$574$	−3.26823	−	16.4937i	−0.136413	−	0.688434i
$575$			7.15283i			0.298294i
$576$	2.40245	−	1.79673i	0.100102	−	0.0748637i
$577$	−24.1173	−	13.9241i	−1.00402	−	0.579668i	−0.0945813	−	0.995517i	$-0.530151\pi$
$577$	−24.1173	−	13.9241i	−1.00402	−	0.579668i	−0.909434	+	0.415849i	$0.863485\pi$
$578$	12.1530	−	7.01653i	0.505498	−	0.291849i
$579$	−0.445215	−	1.33868i	−0.0185025	−	0.0556338i
$580$	−5.62132	+	3.24547i	−0.233413	+	0.134761i
$581$	−20.1404	−	22.9997i	−0.835563	−	0.954188i
$582$	−10.4129	−	2.13823i	−0.431628	−	0.0886324i
$583$	−8.86354			−0.367090
$584$	5.44736	−	9.43511i	0.225414	−	0.390428i
$585$	−3.73383	−	4.99259i	−0.154375	−	0.206418i
$586$	−8.69888	+	5.02230i	−0.359348	+	0.207469i
$587$	−13.5554	+	23.4786i	−0.559490	+	0.969065i	0.438049	+	0.898951i	$0.355670\pi$
$587$	−13.5554	+	23.4786i	−0.559490	+	0.969065i	−0.997539	+	0.0701141i	$0.977664\pi$
$588$	3.98492	−	11.4508i	0.164335	−	0.472222i
$589$	−19.1764	−	33.2146i	−0.790152	−	1.36858i
$590$	7.36907	+	4.25453i	0.303380	+	0.175156i
$591$	25.4341	−	8.45878i	1.04622	−	0.347948i
$592$	−5.24042	−	9.07668i	−0.215380	−	0.373049i
$593$	10.1795	+	17.6314i	0.418022	+	0.724035i	0.995740	−	0.0922009i	$-0.0293902\pi$
$593$	10.1795	+	17.6314i	0.418022	+	0.724035i	−0.577719	+	0.816236i	$0.696057\pi$
$594$	−0.769295	+	9.13792i	−0.0315646	+	0.374933i
$595$	−4.47034	+	0.885797i	−0.183266	+	0.0363141i
$596$	−3.98762	−	2.30225i	−0.163339	−	0.0943040i
$597$	−3.02129	+	14.7133i	−0.123653	+	0.602174i
$598$		−	14.8645i		−	0.607854i
$599$		−	14.5125i		−	0.592966i	−0.955038	−	0.296483i	$-0.904186\pi$
$599$		−	14.5125i		−	0.592966i	0.955038	−	0.296483i	$-0.0958138\pi$
$600$	−1.29514	−	1.15005i	−0.0528740	−	0.0469504i
$601$	−0.0811489	−	0.0468513i	−0.00331013	−	0.00191111i	0.498344	−	0.866979i	$-0.333942\pi$
$601$	−0.0811489	−	0.0468513i	−0.00331013	−	0.00191111i	−0.501654	+	0.865068i	$0.667275\pi$
$602$	7.73178	−	6.77057i	0.315124	−	0.275948i
$603$	−10.2161	+	7.64039i	−0.416034	+	0.311141i
$604$	2.54672	+	4.41105i	0.103625	+	0.179483i
$605$	3.94271	+	6.82898i	0.160294	+	0.277638i
$606$	−7.86422	−	6.98318i	−0.319462	−	0.283672i
$607$	−22.4938	−	12.9868i	−0.912997	−	0.527119i	−0.0316028	−	0.999501i	$-0.510061\pi$
$607$	−22.4938	−	12.9868i	−0.912997	−	0.527119i	−0.881394	+	0.472381i	$0.843394\pi$
$608$	3.92342	+	6.79557i	0.159116	+	0.275597i
$609$	25.6567	+	15.0503i	1.03966	+	0.609871i
$610$	3.46660	−	6.00433i	0.140358	−	0.243108i
$611$	−21.6369	+	12.4921i	−0.875335	+	0.505375i
$612$	0.611116	+	5.13118i	0.0247029	+	0.207416i
$613$	−15.6051	+	27.0288i	−0.630284	+	1.09168i	0.357210	+	0.934024i	$0.383728\pi$
$613$	−15.6051	+	27.0288i	−0.630284	+	1.09168i	−0.987494	+	0.157659i	$0.949605\pi$
$614$	28.7798			1.16146
$615$	3.47380	+	10.4451i	0.140077	+	0.421187i
$616$	4.58021	−	0.907568i	0.184542	−	0.0365670i
$617$	3.21109	−	1.85393i	0.129274	−	0.0746362i	−0.433969	−	0.900928i	$-0.642887\pi$
$617$	3.21109	−	1.85393i	0.129274	−	0.0746362i	0.563242	+	0.826292i	$0.309554\pi$
$618$	31.0950	+	6.38518i	1.25082	+	0.256850i
$619$	−11.2200	+	6.47787i	−0.450970	+	0.260368i	−0.708240	−	0.705972i	$-0.750510\pi$
$619$	−11.2200	+	6.47787i	−0.450970	+	0.260368i	0.257270	+	0.966340i	$0.417177\pi$
$620$	−4.23286	−	2.44384i	−0.169996	−	0.0981470i
$621$	−15.8179	−	33.6333i	−0.634749	−	1.34966i
$622$			27.0587i			1.08495i
$623$	22.6410	−	4.48631i	0.907093	−	0.179740i
$624$	2.69147	+	2.38994i	0.107745	+	0.0956742i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	29.8779			1.19416
$627$	−23.4956	−	4.82469i	−0.938324	−	0.192680i
$628$			4.84681i			0.193409i
$629$	18.0530			0.719822
$630$	−1.65027	+	7.76380i	−0.0657484	+	0.309317i
$631$	−17.8680			−0.711312			−0.355656	−	0.934617i	$-0.615743\pi$
$631$	−17.8680			−0.711312			−0.355656	+	0.934617i	$0.615743\pi$
$632$		−	11.6744i		−	0.464383i
$633$	26.4595	−	29.7978i	1.05167	−	1.18436i
$634$	2.50188			0.0993625
$635$	−1.40555	+	2.43448i	−0.0557774	+	0.0966094i
$636$	−1.74978	+	8.52119i	−0.0693833	+	0.337887i
$637$	14.4196	+	1.91991i	0.571326	+	0.0760694i
$638$			11.4553i			0.453520i
$639$	−14.3309	−	19.1622i	−0.566921	−	0.758043i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−35.5095	+	20.5014i	−1.40254	+	0.809757i	−0.994653	−	0.103276i	$-0.967068\pi$
$641$	−35.5095	+	20.5014i	−1.40254	+	0.809757i	−0.407887	+	0.913032i	$0.633734\pi$
$642$	−2.17236	+	2.44643i	−0.0857360	+	0.0965530i
$643$	28.4023	−	16.3981i	1.12008	−	0.646677i	0.178657	−	0.983911i	$-0.442825\pi$
$643$	28.4023	−	16.3981i	1.12008	−	0.646677i	0.941421	+	0.337234i	$0.109491\pi$
$644$	−14.2374	+	12.4674i	−0.561033	+	0.491285i
$645$	−4.46726	+	5.03088i	−0.175898	+	0.198091i
$646$	−13.5160			−0.531781
$647$	−1.81054	+	3.13595i	−0.0711797	+	0.123287i	−0.899419	−	0.437088i	$-0.856010\pi$
$647$	−1.81054	+	3.13595i	−0.0711797	+	0.123287i	0.828239	+	0.560375i	$0.189343\pi$
$648$	8.63310	+	2.54353i	0.339140	+	0.0999192i
$649$	13.0050	−	7.50847i	0.510493	−	0.294733i
$650$	1.03906	−	1.79971i	0.0407554	−	0.0705904i
$651$	−0.154843	+	22.3976i	−0.00606879	+	0.877833i
$652$	0.203760	+	0.352922i	0.00797984	+	0.0138215i
$653$	−2.29323	−	1.32400i	−0.0897412	−	0.0518121i	0.454458	−	0.890768i	$-0.349833\pi$
$653$	−2.29323	−	1.32400i	−0.0897412	−	0.0518121i	−0.544199	+	0.838956i	$0.683166\pi$
$654$	−2.31211	+	11.2597i	−0.0904107	+	0.440288i
$655$	8.54952	+	14.8082i	0.334058	+	0.578605i
$656$	−3.17762	−	5.50380i	−0.124065	−	0.214887i
$657$	32.4548	−	3.86532i	1.26618	−	0.150801i
$658$	30.1128	+	10.2466i	1.17392	+	0.399452i
$659$	−11.8954	−	6.86782i	−0.463380	−	0.267532i	0.250085	−	0.968224i	$-0.419542\pi$
$659$	−11.8954	−	6.86782i	−0.463380	−	0.267532i	−0.713464	+	0.700692i	$0.752875\pi$
$660$	−2.90054	+	0.964654i	−0.112904	+	0.0375491i
$661$			21.1787i			0.823754i	0.911239	+	0.411877i	$0.135127\pi$
$661$			21.1787i			0.823754i	−0.911239	+	0.411877i	$0.864873\pi$
$662$		−	22.7722i		−	0.885068i
$663$	−5.88310	+	1.95658i	−0.228481	+	0.0759874i
$664$	−10.0069	−	5.77748i	−0.388343	−	0.224210i
$665$	−19.6541	−	6.68776i	−0.762155	−	0.259340i
$666$	12.3906	−	28.8982i	0.480128	−	1.11978i
$667$	−23.2143	−	40.2083i	−0.898861	−	1.55687i
$668$	4.29226	+	7.43442i	0.166073	+	0.287646i
$669$	2.85440	−	13.9005i	0.110357	−	0.537425i
$670$	−3.68268	−	2.12619i	−0.142274	−	0.0821420i
$671$	−6.11791	−	10.5965i	−0.236179	−	0.409074i
$672$	0.0316804	−	4.58247i	0.00122210	−	0.176772i
$673$	−12.7400	+	22.0663i	−0.491089	+	0.850591i	−0.999947	−	0.0102589i	$-0.996734\pi$
$673$	−12.7400	+	22.0663i	−0.491089	+	0.850591i	0.508858	+	0.860850i	$0.330068\pi$
$674$	−11.9749	+	6.91370i	−0.461255	+	0.266306i
$675$	0.435907	−	5.17784i	0.0167781	−	0.199295i
$676$	4.34070	−	7.51831i	0.166950	−	0.289166i
$677$	−4.69172			−0.180317			−0.0901587	−	0.995927i	$-0.528737\pi$
$677$	−4.69172			−0.180317			−0.0901587	+	0.995927i	$0.528737\pi$
$678$	−15.8724	+	17.8749i	−0.609575	+	0.686482i
$679$	−12.2161	+	10.6974i	−0.468810	+	0.410528i
$680$	−1.49171	+	0.861240i	−0.0572045	+	0.0330270i
$681$	11.4428	−	12.8865i	0.438488	−	0.493810i
$682$	−7.47021	+	4.31293i	−0.286049	+	0.165150i
$683$	11.5223	+	6.65242i	0.440890	+	0.254548i	0.703975	−	0.710225i	$-0.251407\pi$
$683$	11.5223	+	6.65242i	0.440890	+	0.254548i	−0.263085	+	0.964773i	$0.584740\pi$
$684$	−9.27668	+	21.6356i	−0.354703	+	0.827259i
$685$		−	8.33714i		−	0.318546i
$686$	−10.2554	−	15.4216i	−0.391553	−	0.588801i
$687$	1.16144	−	5.65603i	0.0443115	−	0.215791i
$688$	1.94221	−	3.36401i	0.0740461	−	0.128252i
$689$	−10.4371			−0.397622
$690$	8.22609	−	9.26394i	0.313162	−	0.352672i
$691$			31.6667i			1.20466i	0.798248	+	0.602328i	$0.205760\pi$
$691$			31.6667i			1.20466i	−0.798248	+	0.602328i	$0.794240\pi$
$692$	10.5609			0.401464
$693$	10.4098	+	9.37307i	0.395435	+	0.356053i
$694$	−5.16857			−0.196196
$695$			9.49564i			0.360190i
$696$	11.0128	+	2.26143i	0.417441	+	0.0857192i
$697$	10.9468			0.414639
$698$	−3.68423	+	6.38127i	−0.139450	+	0.241535i
$699$	−26.8773	−	23.8662i	−1.01659	−	0.902701i
$700$	−2.59529	+	0.514257i	−0.0980928	+	0.0194371i
$701$		−	4.16751i		−	0.157405i	−0.996898	−	0.0787023i	$-0.974922\pi$
$701$		−	4.16751i		−	0.157405i	0.996898	−	0.0787023i	$-0.0250776\pi$
$702$	−0.905870	+	10.7602i	−0.0341898	+	0.406117i
$703$	71.2233	+	41.1208i	2.68624	+	1.55090i
$704$	1.52837	−	0.882407i	0.0576028	−	0.0332570i
$705$	−20.3979	−	4.18859i	−0.768228	−	0.157751i
$706$	7.03645	−	4.06250i	0.264820	−	0.152894i
$707$	−15.7588	+	3.12261i	−0.592672	+	0.117438i
$708$	−4.65109	−	13.9850i	−0.174799	−	0.525588i
$709$	45.1598			1.69601			0.848006	−	0.529987i	$-0.177803\pi$
$709$	45.1598			1.69601			0.848006	+	0.529987i	$0.177803\pi$
$710$	3.98805	−	6.90750i	0.149669	−	0.259234i
$711$	28.0472	−	20.9758i	1.05185	−	0.786653i
$712$	7.55510	−	4.36194i	0.283139	−	0.163471i
$713$	17.4804	−	30.2769i	0.654645	−	1.13388i
$714$	6.80843	+	3.99386i	0.254799	+	0.149466i
$715$	−1.83375	−	3.17615i	−0.0685785	−	0.118781i
$716$	0.503264	+	0.290560i	0.0188079	+	0.0108587i
$717$	−20.2430	−	17.9752i	−0.755989	−	0.671295i
$718$	8.58944	+	14.8774i	0.320555	+	0.555218i
$719$	−4.50906	−	7.80992i	−0.168160	−	0.291261i	0.769613	−	0.638510i	$-0.220449\pi$
$719$	−4.50906	−	7.80992i	−0.168160	−	0.291261i	−0.937773	+	0.347249i	$0.887116\pi$
$720$	0.354788	+	2.97895i	0.0132222	+	0.111019i
$721$	36.4797	−	31.9446i	1.35858	−	1.18968i
$722$	−36.8693	−	21.2865i	−1.37213	−	0.792202i
$723$	−25.4485	−	22.5975i	−0.946439	−	0.840409i
$724$		−	15.6386i		−	0.581206i
$725$		−	6.49094i		−	0.241067i
$726$	2.74727	−	13.3788i	0.101961	−	0.496534i
$727$	17.0192	+	9.82602i	0.631206	+	0.364427i	0.781219	−	0.624257i	$-0.214598\pi$
$727$	17.0192	+	9.82602i	0.631206	+	0.364427i	−0.150013	+	0.988684i	$0.547932\pi$
$728$	5.39334	−	1.06869i	0.199891	−	0.0396083i
$729$	9.40065	+	25.3106i	0.348172	+	0.937431i
$730$	5.44736	+	9.43511i	0.201616	+	0.349209i
$731$	3.34542	+	5.79443i	0.123735	+	0.214315i
$732$	−11.3950	+	3.78971i	−0.421171	+	0.140072i
$733$	−34.1513	−	19.7173i	−1.26141	−	0.728274i	−0.288061	−	0.957612i	$-0.593011\pi$
$733$	−34.1513	−	19.7173i	−1.26141	−	0.728274i	−0.973347	+	0.229338i	$0.926344\pi$
$734$	6.57603	+	11.3900i	0.242726	+	0.420413i
$735$	7.92421	+	9.17644i	0.292289	+	0.338478i
$736$	−3.57642	+	6.19453i	−0.131828	+	0.228334i
$737$	−6.49924	+	3.75234i	−0.239403	+	0.138219i
$738$	7.51328	−	17.5229i	0.276568	−	0.645028i
$739$	16.3564	−	28.3302i	0.601681	−	1.04214i	−0.390886	−	0.920439i	$-0.627831\pi$
$739$	16.3564	−	28.3302i	0.601681	−	1.04214i	0.992567	−	0.121702i	$-0.0388354\pi$
$740$	10.4808			0.385284
$741$	−27.6668	−	5.68123i	−1.01637	−	0.208705i
$742$	8.75400	+	9.99681i	0.321370	+	0.366994i
$743$	25.7477	−	14.8655i	0.944593	−	0.545361i	0.0531960	−	0.998584i	$-0.483059\pi$
$743$	25.7477	−	14.8655i	0.944593	−	0.545361i	0.891397	+	0.453223i	$0.149726\pi$
$744$	2.67162	+	8.03310i	0.0979465	+	0.294508i
$745$	3.98762	−	2.30225i	0.146095	−	0.0843480i
$746$	12.0967	+	6.98405i	0.442893	+	0.255704i
$747$	−4.09957	−	34.4216i	−0.149995	−	1.25942i
$748$			3.03986i			0.111148i
$749$	0.971395	+	4.90232i	0.0354940	+	0.179127i
$750$	1.64354	−	0.546603i	0.0600136	−	0.0199591i
$751$	−4.05528	+	7.02395i	−0.147979	+	0.256308i	−0.930480	−	0.366341i	$-0.880610\pi$
$751$	−4.05528	+	7.02395i	−0.147979	+	0.256308i	0.782501	+	0.622649i	$0.213944\pi$
$752$	12.0224			0.438413
$753$	−2.68887	−	8.08496i	−0.0979878	−	0.294632i
$754$			13.4890i			0.491240i
$755$	−5.09344			−0.185369
$756$	11.0661	−	8.15734i	0.402469	−	0.296680i
$757$	−44.6682			−1.62349			−0.811747	−	0.584010i	$-0.801483\pi$
$757$	−44.6682			−1.62349			−0.811747	+	0.584010i	$0.801483\pi$
$758$		−	18.2898i		−	0.664314i
$759$	−6.90000	−	20.7471i	−0.250454	−	0.753072i
$760$	−7.84685			−0.284635
$761$	−7.25578	+	12.5674i	−0.263022	+	0.455567i	−0.967043	−	0.254612i	$-0.918052\pi$
$761$	−7.25578	+	12.5674i	−0.263022	+	0.455567i	0.704022	+	0.710178i	$0.251386\pi$
$762$	4.62015	−	1.53655i	0.167370	−	0.0556635i
$763$	11.5673	+	13.2095i	0.418764	+	0.478216i
$764$			17.0990i			0.618620i
$765$	−4.74929	−	2.03635i	−0.171711	−	0.0736243i
$766$	−14.0173	−	8.09287i	−0.506464	−	0.292407i
$767$	15.3139	−	8.84146i	0.552951	−	0.319247i
$768$	−0.546603	−	1.64354i	−0.0197238	−	0.0593062i
$769$	14.5008	−	8.37203i	0.522912	−	0.301903i	−0.215213	−	0.976567i	$-0.569045\pi$
$769$	14.5008	−	8.37203i	0.522912	−	0.301903i	0.738125	+	0.674664i	$0.235711\pi$
$770$	−1.50413	+	4.42036i	−0.0542050	+	0.159299i
$771$	−23.4391	−	4.81310i	−0.844140	−	0.173340i
$772$	−0.814513			−0.0293150
$773$	−17.7940	+	30.8201i	−0.640005	+	1.10852i	0.345426	+	0.938446i	$0.387734\pi$
$773$	−17.7940	+	30.8201i	−0.640005	+	1.10852i	−0.985431	+	0.170075i	$0.945599\pi$
$774$	11.5715	−	1.37815i	0.415928	−	0.0495365i
$775$	4.23286	−	2.44384i	0.152049	−	0.0877854i
$776$	−3.06866	+	5.31507i	−0.110158	+	0.190800i
$777$	−23.7265	−	41.7596i	−0.851184	−	1.49812i
$778$	−2.08370	−	3.60907i	−0.0747042	−	0.129392i
$779$	43.1875	+	24.9343i	1.54735	+	0.893365i
$780$	−3.41548	+	1.13591i	−0.122294	+	0.0406721i
$781$	−7.03816	−	12.1905i	−0.251845	−	0.436209i
$782$	−6.16030	−	10.6700i	−0.220292	−	0.381557i
$783$	14.3541	+	30.5210i	0.512975	+	1.09073i
$784$	−5.54722	−	4.26947i	−0.198115	−	0.152481i
$785$	−4.19746	−	2.42341i	−0.149814	−	0.0864950i
$786$	5.95727	−	29.0111i	0.212489	−	1.03479i
$787$			2.94121i			0.104843i	0.998625	+	0.0524215i	$0.0166939\pi$
$787$			2.94121i			0.104843i	−0.998625	+	0.0524215i	$0.983306\pi$
$788$		−	15.4752i		−	0.551280i
$789$	32.2745	+	28.6587i	1.14900	+	1.02028i
$790$	10.1103	+	5.83721i	0.359710	+	0.207679i
$791$	7.09752	+	35.8189i	0.252359	+	1.27357i
$792$	4.86601	+	2.08640i	0.172906	+	0.0741368i
$793$	−7.20403	−	12.4777i	−0.255823	−	0.443098i
$794$	9.44168	+	16.3535i	0.335073	+	0.580363i
$795$	−6.50467	−	5.77595i	−0.230697	−	0.204852i
$796$	7.51013	+	4.33598i	0.266190	+	0.153685i
$797$	−2.92189	−	5.06085i	−0.103499	−	0.179265i	0.809625	−	0.586947i	$-0.199670\pi$
$797$	−2.92189	−	5.06085i	−0.103499	−	0.179265i	−0.913124	+	0.407682i	$0.866337\pi$
$798$	17.7637	+	31.2648i	0.628827	+	1.10676i
$799$	−10.3542	+	17.9340i	−0.366305	+	0.634459i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	24.0538	+	10.3135i	0.849899	+	0.364410i
$802$	2.20411	−	3.81763i	0.0778298	−	0.134805i
$803$	19.2272			0.678512
$804$	2.32437	+	6.98897i	0.0819742	+	0.246482i
$805$	−3.67839	−	18.5637i	−0.129646	−	0.654284i
$806$	−8.79641	+	5.07861i	−0.309840	+	0.178886i
$807$	−30.5353	−	6.27025i	−1.07489	−	0.220723i
$808$	−5.25858	+	3.03604i	−0.184996	+	0.106808i
$809$	5.11072	+	2.95068i	0.179683	+	0.103740i	0.587144	−	0.809483i	$-0.300252\pi$
$809$	5.11072	+	2.95068i	0.179683	+	0.103740i	−0.407460	+	0.913223i	$0.633586\pi$
$810$	−6.51931	+	6.20472i	−0.229065	+	0.218012i
$811$			14.0694i			0.494044i	0.969010	+	0.247022i	$0.0794520\pi$
$811$			14.0694i			0.494044i	−0.969010	+	0.247022i	$0.920548\pi$
$812$	12.9200	−	11.3137i	0.453402	−	0.397035i
$813$	−0.370881	−	0.329331i	−0.0130074	−	0.0115501i
$814$	9.24838	−	16.0187i	0.324155	−	0.561454i
$815$	−0.407519			−0.0142748
$816$	2.92244	+	0.600108i	0.102306	+	0.0210080i
$817$			30.4805i			1.06638i
$818$	36.9170			1.29077
$819$	12.2578	+	11.0371i	0.428324	+	0.385667i
$820$	6.35524			0.221935
$821$			31.3884i			1.09546i	0.836654	+	0.547731i	$0.184508\pi$
$821$			31.3884i			1.09546i	−0.836654	+	0.547731i	$0.815492\pi$
$822$	−9.58809	+	10.7978i	−0.334423	+	0.376616i
$823$	10.2553			0.357478			0.178739	−	0.983897i	$-0.442798\pi$
$823$	10.2553			0.357478			0.178739	+	0.983897i	$0.442798\pi$
$824$	9.16364	−	15.8719i	0.319231	−	0.552924i
$825$	0.614858	−	2.99427i	0.0214066	−	0.104247i
$826$	−21.3128	−	7.25216i	−0.741568	−	0.252335i
$827$			53.6894i			1.86696i	0.358625	+	0.933482i	$0.383246\pi$
$827$			53.6894i			1.86696i	−0.358625	+	0.933482i	$0.616754\pi$
$828$	−21.3079	+	2.53774i	−0.740501	+	0.0881926i
$829$	−26.9613	−	15.5661i	−0.936406	−	0.540634i	−0.0475739	−	0.998868i	$-0.515149\pi$
$829$	−26.9613	−	15.5661i	−0.936406	−	0.540634i	−0.888832	+	0.458234i	$0.848482\pi$
$830$	10.0069	−	5.77748i	0.347344	−	0.200539i
$831$	−14.4316	+	16.2524i	−0.500627	+	0.563789i
$832$	1.79971	−	1.03906i	0.0623937	−	0.0360230i
$833$	11.1463	−	4.59780i	0.386197	−	0.159304i
$834$	10.9204	−	12.2982i	0.378143	−	0.425852i
$835$	−8.58453			−0.297080
$836$	−6.92412	+	11.9929i	−0.239476	+	0.414784i
$837$	−14.4989	+	20.8517i	−0.501157	+	0.720742i
$838$	−18.5311	+	10.6989i	−0.640147	+	0.369589i
$839$	26.3146	−	45.5783i	0.908482	−	1.57354i	0.0923091	−	0.995730i	$-0.470575\pi$
$839$	26.3146	−	45.5783i	0.908482	−	1.57354i	0.816173	−	0.577807i	$-0.196091\pi$
$840$	3.95269	+	2.31867i	0.136381	+	0.0800017i
$841$	6.56615	+	11.3729i	0.226419	+	0.392169i
$842$	21.9286	+	12.6605i	0.755708	+	0.436308i
$843$	−0.959207	+	4.67120i	−0.0330368	+	0.160885i
$844$	−11.5037	−	19.9250i	−0.395973	−	0.685846i
$845$	4.34070	+	7.51831i	0.149325	+	0.258638i
$846$	21.6011	+	28.8833i	0.742660	+	0.993028i
$847$	−13.7443	−	15.6956i	−0.472261	−	0.539308i
$848$	4.34949	+	2.51118i	0.149362	+	0.0862343i
$849$	29.6901	−	9.87425i	1.01896	−	0.338883i
$850$		−	1.72248i		−	0.0590806i
$851$			74.9677i			2.56986i
$852$	−13.1090	+	4.35976i	−0.449108	+	0.149363i
$853$	−8.49076	−	4.90215i	−0.290718	−	0.167846i	0.347547	−	0.937662i	$-0.387015\pi$
$853$	−8.49076	−	4.90215i	−0.290718	−	0.167846i	−0.638266	+	0.769816i	$0.720348\pi$
$854$	−5.90907	+	17.3657i	−0.202204	+	0.594242i
$855$	−14.0987	−	18.8517i	−0.482164	−	0.644713i
$856$	0.944465	+	1.63586i	0.0322811	+	0.0559126i
$857$	11.7593	+	20.3678i	0.401691	+	0.695750i	0.993930	−	0.110013i	$-0.0350892\pi$
$857$	11.7593	+	20.3678i	0.401691	+	0.695750i	−0.592239	+	0.805762i	$0.701756\pi$
$858$	−1.27775	+	6.22247i	−0.0436217	+	0.212432i
$859$	40.4491	+	23.3533i	1.38011	+	0.796804i	0.992171	−	0.124883i	$-0.0398555\pi$
$859$	40.4491	+	23.3533i	1.38011	+	0.796804i	0.387934	+	0.921687i	$0.373189\pi$
$860$	1.94221	+	3.36401i	0.0662288	+	0.114712i
$861$	−14.3870	−	25.3217i	−0.490307	−	0.862960i
$862$	12.7759	−	22.1285i	0.435149	−	0.753700i
$863$	−46.9624	+	27.1137i	−1.59862	+	0.922962i	−0.606864	+	0.794806i	$0.707573\pi$
$863$	−46.9624	+	27.1137i	−1.59862	+	0.922962i	−0.991754	+	0.128156i	$0.959094\pi$
$864$	2.96642	−	4.26618i	0.100920	−	0.145139i
$865$	−5.28044	+	9.14598i	−0.179540	+	0.310973i
$866$	3.82288			0.129907
$867$	16.1387	−	18.1748i	0.548098	−	0.617249i
$868$	12.2423	+	4.16570i	0.415529	+	0.141393i
$869$	17.8429	−	10.3016i	0.605278	−	0.349458i
$870$	−7.46488	+	8.40669i	−0.253083	+	0.285014i
$871$	−7.65306	+	4.41850i	−0.259314	+	0.149715i
$872$	5.74730	+	3.31820i	0.194628	+	0.112369i
$873$	−18.2827	+	2.17745i	−0.618777	+	0.0736955i
$874$		−	56.1272i		−	1.89853i
$875$	0.852286	−	2.50472i	0.0288125	−	0.0846749i
$876$	3.79570	−	18.4845i	0.128245	−	0.624535i
$877$	−11.7991	+	20.4366i	−0.398426	+	0.690094i	−0.993532	−	0.113553i	$-0.963777\pi$
$877$	−11.7991	+	20.4366i	−0.398426	+	0.690094i	0.595106	+	0.803647i	$0.297110\pi$
$878$	−3.14023			−0.105978
$879$	−11.5518	+	13.0092i	−0.389631	+	0.438789i
$880$			1.76481i			0.0594919i
$881$	−20.2179			−0.681159			−0.340580	−	0.940216i	$-0.610623\pi$
$881$	−20.2179			−0.681159			−0.340580	+	0.940216i	$0.610623\pi$
$882$	0.290348	−	20.9980i	0.00977654	−	0.707039i
$883$	23.0406			0.775379			0.387689	−	0.921790i	$-0.373273\pi$
$883$	23.0406			0.775379			0.387689	+	0.921790i	$0.373273\pi$
$884$			3.57953i			0.120393i
$885$	14.4369	+	2.96454i	0.485291	+	0.0996520i
$886$	−30.4394			−1.02263
$887$	−12.0971	+	20.9528i	−0.406181	+	0.703527i	−0.994458	−	0.105133i	$-0.966473\pi$
$887$	−12.0971	+	20.9528i	−0.406181	+	0.703527i	0.588277	+	0.808660i	$0.299806\pi$
$888$	−13.5742	−	12.0535i	−0.455520	−	0.404488i
$889$	2.39586	−	7.04100i	0.0803545	−	0.236147i
$890$			8.72387i			0.292425i
$891$	3.73045	+	15.4390i	0.124975	+	0.517227i
$892$	−7.09528	−	4.09646i	−0.237568	−	0.137160i
$893$	−81.6993	+	47.1691i	−2.73396	+	1.57845i
$894$	−7.81223	−	1.60420i	−0.261280	−	0.0536525i
$895$	−0.503264	+	0.290560i	−0.0168223	+	0.00971234i
$896$	−2.50472	−	0.852286i	−0.0836767	−	0.0284729i
$897$	−8.12497	−	24.4304i	−0.271285	−	0.815706i
$898$	−23.6834			−0.790325
$899$	−15.8628	+	27.4752i	−0.529055	+	0.916350i
$900$	−2.75724	−	1.18222i	−0.0919079	−	0.0394073i
$901$	−7.49191	+	4.32546i	−0.249592	+	0.144102i
$902$	5.60791	−	9.71319i	0.186723	−	0.323414i
$903$	9.00669	−	15.3539i	0.299724	−	0.510946i
$904$	6.90075	+	11.9525i	0.229516	+	0.397533i
$905$	13.5435	+	7.81932i	0.450200	+	0.259923i
$906$	6.59673	+	5.85769i	0.219162	+	0.194609i
$907$	−20.0257	−	34.6855i	−0.664942	−	1.15171i	−0.979301	−	0.202409i	$-0.935123\pi$
$907$	−20.0257	−	34.6855i	−0.664942	−	1.15171i	0.314359	−	0.949304i	$-0.398211\pi$
$908$	−4.97492	−	8.61681i	−0.165098	−	0.285959i
$909$	−16.7422	−	7.17853i	−0.555304	−	0.238097i
$910$	−1.77116	+	5.20512i	−0.0587133	+	0.172548i
$911$	−0.337824	−	0.195043i	−0.0111926	−	0.00646205i	0.494393	−	0.869238i	$-0.335390\pi$
$911$	−0.337824	−	0.195043i	−0.0111926	−	0.00646205i	−0.505586	+	0.862776i	$0.668724\pi$
$912$	10.1628	+	9.02424i	0.336523	+	0.298822i
$913$		−	20.3924i		−	0.674889i
$914$			8.67786i			0.287038i
$915$	2.41551	−	11.7632i	0.0798543	−	0.388880i
$916$	−2.88702	−	1.66682i	−0.0953900	−	0.0550734i
$917$	−29.8037	−	34.0350i	−0.984206	−	1.12393i
$918$	3.80911	+	8.09926i	0.125719	+	0.267315i
$919$	27.1206	+	46.9743i	0.894627	+	1.54954i	0.834265	+	0.551363i	$0.185892\pi$
$919$	27.1206	+	46.9743i	0.894627	+	1.54954i	0.0603619	+	0.998177i	$0.480775\pi$
$920$	−3.57642	−	6.19453i	−0.117911	−	0.204228i
$921$	47.3007	−	15.7311i	1.55861	−	0.518358i
$922$	−25.9133	−	14.9611i	−0.853411	−	0.492717i
$923$	−8.28766	−	14.3546i	−0.272792	−	0.472489i
$924$	7.03168	−	3.99518i	0.231325	−	0.131432i
$925$	−5.24042	+	9.07668i	−0.172304	+	0.298439i
$926$	−27.3020	+	15.7628i	−0.897198	+	0.517998i
$927$	54.5960	−	6.50231i	1.79317	−	0.213564i
$928$	3.24547	−	5.62132i	0.106538	−	0.184529i
$929$	17.1351			0.562184			0.281092	−	0.959681i	$-0.409303\pi$
$929$	17.1351			0.562184			0.281092	+	0.959681i	$0.409303\pi$
$930$	−8.29268	−	1.70286i	−0.271928	−	0.0558389i
$931$	54.4474	+	7.24942i	1.78444	+	0.237590i
$932$	−17.9721	+	10.3762i	−0.588695	+	0.339883i
$933$	14.7903	+	44.4720i	0.484214	+	1.45595i
$934$	−27.0312	+	15.6065i	−0.884487	+	0.510659i
$935$	−2.63259	−	1.51993i	−0.0860950	−	0.0497070i
$936$	5.72989	+	2.45680i	0.187287	+	0.0803029i
$937$			6.23344i			0.203638i	0.994803	+	0.101819i	$0.0324662\pi$
$937$			6.23344i			0.203638i	−0.994803	+	0.101819i	$0.967534\pi$
$938$	10.6510	+	3.62425i	0.347768	+	0.118336i
$939$	49.1055	−	16.3314i	1.60250	−	0.532954i
$940$	−6.01122	+	10.4117i	−0.196064	+	0.339593i
$941$	28.8454			0.940335			0.470167	−	0.882577i	$-0.344194\pi$
$941$	28.8454			0.940335			0.470167	+	0.882577i	$0.344194\pi$
$942$	2.64928	+	7.96593i	0.0863183	+	0.259544i
$943$			45.4580i			1.48032i
$944$	−8.50907			−0.276947
$945$	1.53143	+	13.6622i	0.0498175	+	0.444430i
$946$	6.85528			0.222884
$947$			10.7256i			0.348537i	0.984698	+	0.174268i	$0.0557560\pi$
$947$			10.7256i			0.348537i	−0.984698	+	0.174268i	$0.944244\pi$
$948$	−6.38128	−	19.1874i	−0.207254	−	0.623177i
$949$	22.6406			0.734945
$950$	3.92342	−	6.79557i	0.127293	−	0.220477i
$951$	4.11195	−	1.36754i	0.133339	−	0.0443454i
$952$	3.42853	−	3.00229i	0.111119	−	0.0973048i
$953$			23.9523i			0.775891i	0.921682	+	0.387946i	$0.126815\pi$
$953$			23.9523i			0.775891i	−0.921682	+	0.387946i	$0.873185\pi$
$954$	1.78188	+	14.9613i	0.0576903	+	0.484392i
$955$	−14.8082	−	8.54950i	−0.479181	−	0.276655i
$956$	−13.5359	+	7.81497i	−0.437783	+	0.252754i
$957$	6.26151	+	18.8273i	0.202406	+	0.608599i
$958$	25.6054	−	14.7833i	0.827273	−	0.477626i
$959$	4.28743	+	21.6373i	0.138448	+	0.698705i
$960$	1.69665	+	0.348398i	0.0547591	+	0.0112445i
$961$	7.11057			0.229373
$962$	10.8903	−	18.8625i	0.351116	−	0.608151i
$963$	−2.23313	+	5.20823i	−0.0719615	+	0.167833i
$964$	−17.0167	+	9.82459i	−0.548071	+	0.316429i
$965$	0.407256	−	0.705389i	0.0131100	−	0.0227073i
$966$	−16.5850	+	28.2729i	−0.533615	+	0.909667i
$967$	−22.5636	−	39.0812i	−0.725595	−	1.25677i	−0.958729	−	0.284323i	$-0.908231\pi$
$967$	−22.5636	−	39.0812i	−0.725595	−	1.25677i	0.233133	−	0.972445i	$-0.425102\pi$
$968$	−6.82898	−	3.94271i	−0.219492	−	0.126724i
$969$	−22.2142	+	7.38791i	−0.713621	+	0.237334i
$970$	−3.06866	−	5.31507i	−0.0985287	−	0.170657i
$971$	6.67403	+	11.5598i	0.214180	+	0.370971i	0.953019	−	0.302912i	$-0.0979588\pi$
$971$	6.67403	+	11.5598i	0.214180	+	0.370971i	−0.738839	+	0.673882i	$0.764625\pi$
$972$	15.5792	−	0.538492i	0.499702	−	0.0172721i
$973$	−4.88320	−	24.6440i	−0.156548	−	0.790049i
$974$	−15.6354	−	9.02713i	−0.500992	−	0.289248i
$975$	0.724014	−	3.52585i	0.0231870	−	0.112918i
$976$			6.93320i			0.221926i
$977$			52.1043i			1.66696i	0.552546	+	0.833482i	$0.313656\pi$
$977$			52.1043i			1.66696i	−0.552546	+	0.833482i	$0.686344\pi$
$978$	0.527796	+	0.468666i	0.0168770	+	0.0149863i
$979$	13.3333	+	7.69801i	0.426136	+	0.246030i
$980$	6.47108	−	2.66929i	0.206711	−	0.0852674i
$981$	2.35452	+	19.7695i	0.0751741	+	0.631192i
$982$	4.75953	+	8.24376i	0.151883	+	0.263069i
$983$	18.3720	+	31.8213i	0.585977	+	1.01494i	0.994753	+	0.102307i	$0.0326226\pi$
$983$	18.3720	+	31.8213i	0.585977	+	1.01494i	−0.408776	+	0.912635i	$0.634044\pi$
$984$	−8.23095	−	7.30882i	−0.262393	−	0.232997i
$985$	13.4019	+	7.73758i	0.427020	+	0.246540i
$986$	5.59026	+	9.68261i	0.178030	+	0.308357i
$987$	55.0924	+	0.380875i	1.75361	+	0.0121234i
$988$	−8.15337	+	14.1220i	−0.259393	+	0.449282i
$989$	−24.0622	+	13.8923i	−0.765133	+	0.441750i
$990$	−4.23988	+	3.17089i	−0.134752	+	0.100778i
$991$	−13.8366	+	23.9658i	−0.439536	+	0.761298i	−0.997654	−	0.0684637i	$-0.978190\pi$
$991$	−13.8366	+	23.9658i	−0.439536	+	0.761298i	0.558118	+	0.829762i	$0.311524\pi$
$992$	4.88768			0.155184
$993$	−12.4474	−	37.4271i	−0.395006	−	1.18771i
$994$	−6.79791	+	19.9779i	−0.215617	+	0.633659i
$995$	−7.51013	+	4.33598i	−0.238087	+	0.137460i
$996$	−19.6047	−	4.02572i	−0.621199	−	0.127560i
$997$	−24.1902	+	13.9662i	−0.766111	+	0.442314i	−0.831485	−	0.555546i	$-0.812509\pi$
$997$	−24.1902	+	13.9662i	−0.766111	+	0.442314i	0.0653746	+	0.997861i	$0.479176\pi$
$998$	9.12775	+	5.26991i	0.288934	+	0.166816i
$999$	4.56868	−	54.2681i	0.144547	−	1.71697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.3	yes	32
3.2	odd	2		1890.2.bk.c.521.11		32
7.5	odd	6		630.2.t.c.551.1	yes	32
9.4	even	3		1890.2.t.c.1151.12		32
9.5	odd	6		630.2.t.c.311.1	✓	32
21.5	even	6		1890.2.t.c.1601.12		32
63.5	even	6	inner	630.2.bk.c.131.11	yes	32
63.40	odd	6		1890.2.bk.c.341.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.1	✓	32	9.5	odd	6
630.2.t.c.551.1	yes	32	7.5	odd	6
630.2.bk.c.101.3	yes	32	1.1	even	1	trivial
630.2.bk.c.131.11	yes	32	63.5	even	6	inner
1890.2.t.c.1151.12		32	9.4	even	3
1890.2.t.c.1601.12		32	21.5	even	6
1890.2.bk.c.341.11		32	63.40	odd	6
1890.2.bk.c.521.11		32	3.2	odd	2

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.546603 - 1.64354i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.64354 + 0.546603i) q^{6} +(-0.852286 + 2.50472i) q^{7} +1.00000i q^{8} +(-2.40245 + 1.79673i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.546603 - 1.64354i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.64354 + 0.546603i) q^{6} +(-0.852286 + 2.50472i) q^{7} +1.00000i q^{8} +(-2.40245 + 1.79673i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-1.52837 + 0.882407i) q^{11} +(0.546603 + 1.64354i) q^{12} +(-1.79971 + 1.03906i) q^{13} +(2.50472 + 0.852286i) q^{14} +(-1.69665 - 0.348398i) q^{15} +1.00000 q^{16} +(-0.861240 + 1.49171i) q^{17} +(1.79673 + 2.40245i) q^{18} +(-6.79557 + 3.92342i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.58247 + 0.0316804i) q^{21} +(0.882407 + 1.52837i) q^{22} +(-6.19453 - 3.57642i) q^{23} +(1.64354 - 0.546603i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.03906 + 1.79971i) q^{26} +(4.26618 + 2.96642i) q^{27} +(0.852286 - 2.50472i) q^{28} +(5.62132 + 3.24547i) q^{29} +(-0.348398 + 1.69665i) q^{30} +4.88768i q^{31} -1.00000i q^{32} +(2.28569 + 2.02962i) q^{33} +(1.49171 + 0.861240i) q^{34} +(1.74301 + 1.99046i) q^{35} +(2.40245 - 1.79673i) q^{36} +(-5.24042 - 9.07668i) q^{37} +(3.92342 + 6.79557i) q^{38} +(2.69147 + 2.38994i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-3.17762 - 5.50380i) q^{41} +(0.0316804 - 4.58247i) q^{42} +(1.94221 - 3.36401i) q^{43} +(1.52837 - 0.882407i) q^{44} +(0.354788 + 2.97895i) q^{45} +(-3.57642 + 6.19453i) q^{46} +12.0224 q^{47} +(-0.546603 - 1.64354i) q^{48} +(-5.54722 - 4.26947i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.92244 + 0.600108i) q^{51} +(1.79971 - 1.03906i) q^{52} +(4.34949 + 2.51118i) q^{53} +(2.96642 - 4.26618i) q^{54} +1.76481i q^{55} +(-2.50472 - 0.852286i) q^{56} +(10.1628 + 9.02424i) q^{57} +(3.24547 - 5.62132i) q^{58} -8.50907 q^{59} +(1.69665 + 0.348398i) q^{60} +6.93320i q^{61} +4.88768 q^{62} +(-2.45272 - 7.54878i) q^{63} -1.00000 q^{64} +2.07813i q^{65} +(2.02962 - 2.28569i) q^{66} +4.25239 q^{67} +(0.861240 - 1.49171i) q^{68} +(-2.49203 + 12.1358i) q^{69} +(1.99046 - 1.74301i) q^{70} +7.97609i q^{71} +(-1.79673 - 2.40245i) q^{72} +(-9.43511 - 5.44736i) q^{73} +(-9.07668 + 5.24042i) q^{74} +(-1.15005 + 1.29514i) q^{75} +(6.79557 - 3.92342i) q^{76} +(-0.907568 - 4.58021i) q^{77} +(2.38994 - 2.69147i) q^{78} -11.6744 q^{79} +(0.500000 - 0.866025i) q^{80} +(2.54353 - 8.63310i) q^{81} +(-5.50380 + 3.17762i) q^{82} +(-5.77748 + 10.0069i) q^{83} +(-4.58247 - 0.0316804i) q^{84} +(0.861240 + 1.49171i) q^{85} +(-3.36401 - 1.94221i) q^{86} +(2.26143 - 11.0128i) q^{87} +(-0.882407 - 1.52837i) q^{88} +(-4.36194 - 7.55510i) q^{89} +(2.97895 - 0.354788i) q^{90} +(-1.06869 - 5.39334i) q^{91} +(6.19453 + 3.57642i) q^{92} +(8.03310 - 2.67162i) q^{93} -12.0224i q^{94} +7.84685i q^{95} +(-1.64354 + 0.546603i) q^{96} +(5.31507 + 3.06866i) q^{97} +(-4.26947 + 5.54722i) q^{98} +(2.08640 - 4.86601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

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