LMFDB - Embedded newform 210.2.r.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(101,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("210.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.r (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.66557 + 0.475255i$ of defining polynomial
Character	$\chi$	$=$	210.101
Dual form			210.2.r.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.475255 + 1.66557i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.421203 - 1.68006i) q^{6} +(0.0551777 + 2.64518i) q^{7} +1.00000i q^{8} +(-2.54826 - 1.58314i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.475255 + 1.66557i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.421203 - 1.68006i) q^{6} +(0.0551777 + 2.64518i) q^{7} +1.00000i q^{8} +(-2.54826 - 1.58314i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-0.167855 - 0.0969112i) q^{11} +(1.20480 + 1.24437i) q^{12} +1.54892i q^{13} +(-1.37037 - 2.26320i) q^{14} +(-1.68006 + 0.421203i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.264766 - 0.458589i) q^{17} +(2.99843 + 0.0969112i) q^{18} +(-5.53332 + 3.19467i) q^{19} +1.00000 q^{20} +(-4.43196 - 1.16523i) q^{21} +0.193822 q^{22} +(-3.68040 + 2.12488i) q^{23} +(-1.66557 - 0.475255i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.774462 - 1.34141i) q^{26} +(3.84792 - 3.49192i) q^{27} +(2.31838 + 1.27480i) q^{28} -4.87349i q^{29} +(1.24437 - 1.20480i) q^{30} +(8.02559 + 4.63357i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.241187 - 0.233517i) q^{33} +0.529533i q^{34} +(-2.26320 + 1.37037i) q^{35} +(-2.64518 + 1.41529i) q^{36} +(-0.881634 - 1.52704i) q^{37} +(3.19467 - 5.53332i) q^{38} +(-2.57984 - 0.736134i) q^{39} +(-0.866025 + 0.500000i) q^{40} +9.91573 q^{41} +(4.42080 - 1.20686i) q^{42} +11.4865 q^{43} +(-0.167855 + 0.0969112i) q^{44} +(0.0969112 - 2.99843i) q^{45} +(2.12488 - 3.68040i) q^{46} +(4.90186 + 8.49028i) q^{47} +(1.68006 - 0.421203i) q^{48} +(-6.99391 + 0.291909i) q^{49} -1.00000i q^{50} +(0.637981 + 0.658934i) q^{51} +(1.34141 + 0.774462i) q^{52} +(0.0562751 + 0.0324905i) q^{53} +(-1.58643 + 4.94805i) q^{54} -0.193822i q^{55} +(-2.64518 + 0.0551777i) q^{56} +(-2.69121 - 10.7344i) q^{57} +(2.43674 + 4.22056i) q^{58} +(6.01371 - 10.4160i) q^{59} +(-0.475255 + 1.66557i) q^{60} +(3.71180 - 2.14301i) q^{61} -9.26715 q^{62} +(4.04709 - 6.82796i) q^{63} -1.00000 q^{64} +(-1.34141 + 0.774462i) q^{65} +(-0.0921151 + 0.322825i) q^{66} +(-2.41529 + 4.18340i) q^{67} +(-0.264766 - 0.458589i) q^{68} +(-1.79001 - 7.13983i) q^{69} +(1.27480 - 2.31838i) q^{70} +6.29103i q^{71} +(1.58314 - 2.54826i) q^{72} +(-7.00763 - 4.04586i) q^{73} +(1.52704 + 0.881634i) q^{74} +(-1.20480 - 1.24437i) q^{75} +6.38933i q^{76} +(0.247085 - 0.449354i) q^{77} +(2.60228 - 0.652411i) q^{78} +(-3.38883 - 5.86962i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.98731 + 8.06854i) q^{81} +(-8.58728 + 4.95787i) q^{82} -2.11036 q^{83} +(-3.22510 + 3.25557i) q^{84} +0.529533 q^{85} +(-9.94760 + 5.74325i) q^{86} +(8.11715 + 2.31615i) q^{87} +(0.0969112 - 0.167855i) q^{88} +(8.18773 + 14.1816i) q^{89} +(1.41529 + 2.64518i) q^{90} +(-4.09717 + 0.0854660i) q^{91} +4.24976i q^{92} +(-11.5318 + 11.1651i) q^{93} +(-8.49028 - 4.90186i) q^{94} +(-5.53332 - 3.19467i) q^{95} +(-1.24437 + 1.20480i) q^{96} -8.24463i q^{97} +(5.91095 - 3.74976i) q^{98} +(0.274315 + 0.512694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.475255	+	1.66557i	−0.274389	+	0.961619i
$3$	−0.475255	+	1.66557i	−0.274389	+	0.961619i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.421203	−	1.68006i	−0.171955	−	0.685880i
$7$	0.0551777	+	2.64518i	0.0208552	+	0.999783i
$7$	0.0551777	+	2.64518i	0.0208552	+	0.999783i
$8$			1.00000i			0.353553i
$9$	−2.54826	−	1.58314i	−0.849422	−	0.527715i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−0.167855	−	0.0969112i	−0.0506102	−	0.0292198i	0.474481	−	0.880266i	$-0.342636\pi$
$11$	−0.167855	−	0.0969112i	−0.0506102	−	0.0292198i	−0.525092	+	0.851046i	$0.675969\pi$
$12$	1.20480	+	1.24437i	0.347796	+	0.359219i
$13$			1.54892i			0.429594i	0.976659	+	0.214797i	$0.0689090\pi$
$13$			1.54892i			0.429594i	−0.976659	+	0.214797i	$0.931091\pi$
$14$	−1.37037	−	2.26320i	−0.366248	−	0.604866i
$15$	−1.68006	+	0.421203i	−0.433789	+	0.108754i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.264766	−	0.458589i	0.0642153	−	0.111224i	−0.832130	−	0.554580i	$-0.812879\pi$
$17$	0.264766	−	0.458589i	0.0642153	−	0.111224i	0.896346	+	0.443356i	$0.146212\pi$
$18$	2.99843	+	0.0969112i	0.706738	+	0.0228422i
$19$	−5.53332	+	3.19467i	−1.26943	+	0.732906i	−0.974880	−	0.222729i	$-0.928503\pi$
$19$	−5.53332	+	3.19467i	−1.26943	+	0.732906i	−0.294551	+	0.955636i	$0.595170\pi$
$20$	1.00000			0.223607
$21$	−4.43196	−	1.16523i	−0.967132	−	0.254274i
$22$	0.193822			0.0413231
$23$	−3.68040	+	2.12488i	−0.767416	+	0.443068i	−0.831952	−	0.554848i	$-0.812777\pi$
$23$	−3.68040	+	2.12488i	−0.767416	+	0.443068i	0.0645362	+	0.997915i	$0.479443\pi$
$24$	−1.66557	−	0.475255i	−0.339984	−	0.0970111i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.774462	−	1.34141i	−0.151884	−	0.263072i
$27$	3.84792	−	3.49192i	0.740532	−	0.672021i
$28$	2.31838	+	1.27480i	0.438132	+	0.240915i
$29$		−	4.87349i		−	0.904984i	−0.891768	−	0.452492i	$-0.850535\pi$
$29$		−	4.87349i		−	0.904984i	0.891768	−	0.452492i	$-0.149465\pi$
$30$	1.24437	−	1.20480i	0.227190	−	0.219965i
$31$	8.02559	+	4.63357i	1.44144	+	0.832214i	0.997946	−	0.0640639i	$-0.0204062\pi$
$31$	8.02559	+	4.63357i	1.44144	+	0.832214i	0.443492	+	0.896278i	$0.353739\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.241187	−	0.233517i	0.0419852	−	0.0406502i
$34$			0.529533i			0.0908141i
$35$	−2.26320	+	1.37037i	−0.382551	+	0.231635i
$36$	−2.64518	+	1.41529i	−0.440863	+	0.235882i
$37$	−0.881634	−	1.52704i	−0.144940	−	0.251043i	0.784411	−	0.620242i	$-0.212966\pi$
$37$	−0.881634	−	1.52704i	−0.144940	−	0.251043i	−0.929350	+	0.369199i	$0.879632\pi$
$38$	3.19467	−	5.53332i	0.518243	−	0.897623i
$39$	−2.57984	−	0.736134i	−0.413106	−	0.117876i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	9.91573			1.54858			0.774289	−	0.632833i	$-0.218108\pi$
$41$	9.91573			1.54858			0.774289	+	0.632833i	$0.218108\pi$
$42$	4.42080	−	1.20686i	0.682145	−	0.186222i
$43$	11.4865			1.75168			0.875838	−	0.482606i	$-0.160310\pi$
$43$	11.4865			1.75168			0.875838	+	0.482606i	$0.160310\pi$
$44$	−0.167855	+	0.0969112i	−0.0253051	+	0.0146099i
$45$	0.0969112	−	2.99843i	0.0144467	−	0.446980i
$46$	2.12488	−	3.68040i	0.313296	−	0.542645i
$47$	4.90186	+	8.49028i	0.715010	+	1.23843i	0.962956	+	0.269660i	$0.0869114\pi$
$47$	4.90186	+	8.49028i	0.715010	+	1.23843i	−0.247945	+	0.968774i	$0.579755\pi$
$48$	1.68006	−	0.421203i	0.242495	−	0.0607954i
$49$	−6.99391	+	0.291909i	−0.999130	+	0.0417014i
$50$		−	1.00000i		−	0.141421i
$51$	0.637981	+	0.658934i	0.0893353	+	0.0922693i
$52$	1.34141	+	0.774462i	0.186020	+	0.107398i
$53$	0.0562751	+	0.0324905i	0.00772998	+	0.00446291i	0.503860	−	0.863785i	$-0.331913\pi$
$53$	0.0562751	+	0.0324905i	0.00772998	+	0.00446291i	−0.496130	+	0.868248i	$0.665246\pi$
$54$	−1.58643	+	4.94805i	−0.215886	+	0.673345i
$55$		−	0.193822i		−	0.0261350i
$56$	−2.64518	+	0.0551777i	−0.353476	+	0.00737343i
$57$	−2.69121	−	10.7344i	−0.356459	−	1.42181i
$58$	2.43674	+	4.22056i	0.319960	+	0.554187i
$59$	6.01371	−	10.4160i	0.782918	−	1.35605i	−0.147317	−	0.989089i	$-0.547064\pi$
$59$	6.01371	−	10.4160i	0.782918	−	1.35605i	0.930235	−	0.366964i	$-0.119603\pi$
$60$	−0.475255	+	1.66557i	−0.0613552	+	0.215025i
$61$	3.71180	−	2.14301i	0.475248	−	0.274384i	−0.243186	−	0.969980i	$-0.578193\pi$
$61$	3.71180	−	2.14301i	0.475248	−	0.274384i	0.718434	+	0.695595i	$0.244859\pi$
$62$	−9.26715			−1.17693
$63$	4.04709	−	6.82796i	0.509885	−	0.860242i
$64$	−1.00000			−0.125000
$65$	−1.34141	+	0.774462i	−0.166381	+	0.0960601i
$66$	−0.0921151	+	0.322825i	−0.0113386	+	0.0397371i
$67$	−2.41529	+	4.18340i	−0.295075	+	0.511084i	−0.975002	−	0.222195i	$-0.928678\pi$
$67$	−2.41529	+	4.18340i	−0.295075	+	0.511084i	0.679928	+	0.733279i	$0.262011\pi$
$68$	−0.264766	−	0.458589i	−0.0321076	−	0.0556121i
$69$	−1.79001	−	7.13983i	−0.215492	−	0.859534i
$70$	1.27480	−	2.31838i	0.152368	−	0.277099i
$71$			6.29103i			0.746608i	0.927709	+	0.373304i	$0.121775\pi$
$71$			6.29103i			0.746608i	−0.927709	+	0.373304i	$0.878225\pi$
$72$	1.58314	−	2.54826i	0.186575	−	0.300316i
$73$	−7.00763	−	4.04586i	−0.820181	−	0.473532i	0.0302980	−	0.999541i	$-0.490354\pi$
$73$	−7.00763	−	4.04586i	−0.820181	−	0.473532i	−0.850479	+	0.526009i	$0.823688\pi$
$74$	1.52704	+	0.881634i	0.177514	+	0.102488i
$75$	−1.20480	−	1.24437i	−0.139118	−	0.143687i
$76$			6.38933i			0.732906i
$77$	0.247085	−	0.449354i	0.0281580	−	0.0512086i
$78$	2.60228	−	0.652411i	0.294650	−	0.0738710i
$79$	−3.38883	−	5.86962i	−0.381273	−	0.660384i	0.609971	−	0.792423i	$-0.291181\pi$
$79$	−3.38883	−	5.86962i	−0.381273	−	0.660384i	−0.991245	+	0.132039i	$0.957848\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	3.98731	+	8.06854i	0.443034	+	0.896505i
$82$	−8.58728	+	4.95787i	−0.948306	+	0.547505i
$83$	−2.11036			−0.231642			−0.115821	−	0.993270i	$-0.536950\pi$
$83$	−2.11036			−0.231642			−0.115821	+	0.993270i	$0.536950\pi$
$84$	−3.22510	+	3.25557i	−0.351887	+	0.355212i
$85$	0.529533			0.0574359
$86$	−9.94760	+	5.74325i	−1.07268	+	0.619311i
$87$	8.11715	+	2.31615i	0.870250	+	0.248318i
$88$	0.0969112	−	0.167855i	0.0103308	−	0.0178934i
$89$	8.18773	+	14.1816i	0.867898	+	1.50324i	0.864141	+	0.503250i	$0.167863\pi$
$89$	8.18773	+	14.1816i	0.867898	+	1.50324i	0.00375740	+	0.999993i	$0.498804\pi$
$90$	1.41529	+	2.64518i	0.149185	+	0.278826i
$91$	−4.09717	+	0.0854660i	−0.429501	+	0.00895927i
$92$			4.24976i			0.443068i
$93$	−11.5318	+	11.1651i	−1.19579	+	1.15776i
$94$	−8.49028	−	4.90186i	−0.875705	−	0.505589i
$95$	−5.53332	−	3.19467i	−0.567707	−	0.327766i
$96$	−1.24437	+	1.20480i	−0.127003	+	0.122964i
$97$		−	8.24463i		−	0.837115i	−0.908190	−	0.418557i	$-0.862536\pi$
$97$		−	8.24463i		−	0.837115i	0.908190	−	0.418557i	$-0.137464\pi$
$98$	5.91095	−	3.74976i	0.597096	−	0.378783i
$99$	0.274315	+	0.512694i	0.0275697	+	0.0515277i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.22831	−	3.85955i	0.221725	−	0.384040i	−0.733607	−	0.679574i	$-0.762164\pi$
$101$	2.22831	−	3.85955i	0.221725	−	0.384040i	0.955332	+	0.295535i	$0.0954978\pi$
$102$	−0.881975	−	0.251663i	−0.0873286	−	0.0249184i
$103$	7.29356	−	4.21094i	0.718656	−	0.414916i	−0.0956021	−	0.995420i	$-0.530478\pi$
$103$	7.29356	−	4.21094i	0.718656	−	0.414916i	0.814258	+	0.580504i	$0.197144\pi$
$104$	−1.54892			−0.151884
$105$	−1.20686	−	4.42080i	−0.117777	−	0.431426i
$106$	−0.0649809			−0.00631151
$107$	−15.4270	+	8.90681i	−1.49139	+	0.861054i	−0.999951	−	0.00985883i	$-0.996862\pi$
$107$	−15.4270	+	8.90681i	−1.49139	+	0.861054i	−0.491438	+	0.870913i	$0.663528\pi$
$108$	−1.10013	−	5.07836i	−0.105860	−	0.488665i
$109$	−0.0739017	+	0.128001i	−0.00707850	+	0.0122603i	−0.869543	−	0.493857i	$-0.835587\pi$
$109$	−0.0739017	+	0.128001i	−0.00707850	+	0.0122603i	0.862464	+	0.506118i	$0.168920\pi$
$110$	0.0969112	+	0.167855i	0.00924012	+	0.0160044i
$111$	2.96239	−	0.742694i	0.281178	−	0.0704934i
$112$	2.26320	−	1.37037i	0.213852	−	0.129488i
$113$			3.44771i			0.324334i	0.986763	+	0.162167i	$0.0518483\pi$
$113$			3.44771i			0.324334i	−0.986763	+	0.162167i	$0.948152\pi$
$114$	7.69787	+	7.95069i	0.720971	+	0.744650i
$115$	−3.68040	−	2.12488i	−0.343199	−	0.198146i
$116$	−4.22056	−	2.43674i	−0.391870	−	0.226246i
$117$	2.45217	−	3.94707i	0.226703	−	0.364906i
$118$			12.0274i			1.10721i
$119$	1.22766	+	0.675050i	0.112539	+	0.0618817i
$120$	−0.421203	−	1.68006i	−0.0384504	−	0.153367i
$121$	−5.48122	−	9.49375i	−0.498292	−	0.863068i
$122$	−2.14301	+	3.71180i	−0.194019	+	0.336051i
$123$	−4.71250	+	16.5154i	−0.424912	+	1.48914i
$124$	8.02559	−	4.63357i	0.720719	−	0.416107i
$125$	−1.00000			−0.0894427
$126$	−0.0909005	+	7.93673i	−0.00809806	+	0.707060i
$127$	5.49965			0.488015			0.244007	−	0.969773i	$-0.421538\pi$
$127$	5.49965			0.488015			0.244007	+	0.969773i	$0.421538\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−5.45902	+	19.1316i	−0.480640	+	1.68444i
$130$	0.774462	−	1.34141i	0.0679248	−	0.117649i
$131$	−2.99843	−	5.19344i	−0.261974	−	0.453753i	0.704792	−	0.709414i	$-0.251040\pi$
$131$	−2.99843	−	5.19344i	−0.261974	−	0.453753i	−0.966767	+	0.255661i	$0.917707\pi$
$132$	−0.0816386	−	0.325633i	−0.00710573	−	0.0283427i
$133$	−8.75577	−	14.4603i	−0.759221	−	1.25387i
$134$		−	4.83058i		−	0.417298i
$135$	4.94805	+	1.58643i	0.425861	+	0.136539i
$136$	0.458589	+	0.264766i	0.0393237	+	0.0227035i
$137$	0.746611	+	0.431056i	0.0637872	+	0.0368276i	0.531554	−	0.847024i	$-0.321608\pi$
$137$	0.746611	+	0.431056i	0.0637872	+	0.0368276i	−0.467767	+	0.883852i	$0.654941\pi$
$138$	5.12011	+	5.28827i	0.435853	+	0.450167i
$139$			16.1843i			1.37274i	0.727254	+	0.686368i	$0.240796\pi$
$139$			16.1843i			1.37274i	−0.727254	+	0.686368i	$0.759204\pi$
$140$	0.0551777	+	2.64518i	0.00466337	+	0.223558i
$141$	−16.4708	+	4.12936i	−1.38709	+	0.347755i
$142$	−3.14552	−	5.44820i	−0.263966	−	0.457202i
$143$	0.150108	−	0.259995i	0.0125527	−	0.0217418i
$144$	−0.0969112	+	2.99843i	−0.00807593	+	0.249870i
$145$	4.22056	−	2.43674i	0.350499	−	0.202361i
$146$	8.09171			0.669675
$147$	2.83770	−	11.7876i	0.234049	−	0.972225i
$148$	−1.76327			−0.144940
$149$	11.0505	−	6.38001i	0.905292	−	0.522671i	0.0263788	−	0.999652i	$-0.491602\pi$
$149$	11.0505	−	6.38001i	0.905292	−	0.522671i	0.878913	+	0.476981i	$0.158269\pi$
$150$	1.66557	+	0.475255i	0.135993	+	0.0388044i
$151$	8.75012	−	15.1557i	0.712075	−	1.23335i	−0.252002	−	0.967727i	$-0.581089\pi$
$151$	8.75012	−	15.1557i	0.712075	−	1.23335i	0.964077	−	0.265623i	$-0.0855778\pi$
$152$	−3.19467	−	5.53332i	−0.259122	−	0.448812i
$153$	−1.40071	+	0.749442i	−0.113240	+	0.0605888i
$154$	0.0106947	+	0.512694i	0.000861802	+	0.0413141i
$155$			9.26715i			0.744355i
$156$	−1.92743	+	1.86614i	−0.154318	+	0.149411i
$157$	−2.46479	−	1.42305i	−0.196711	−	0.113571i	0.398409	−	0.917208i	$-0.369562\pi$
$157$	−2.46479	−	1.42305i	−0.196711	−	0.113571i	−0.595121	+	0.803636i	$0.702896\pi$
$158$	5.86962	+	3.38883i	0.466962	+	0.269601i
$159$	−0.0808603	+	0.0782891i	−0.00641264	+	0.00620873i
$160$			1.00000i			0.0790569i
$161$	−5.82375	−	9.61805i	−0.458976	−	0.758009i
$162$	−7.48738	−	4.99391i	−0.588264	−	0.392359i
$163$	−6.17931	−	10.7029i	−0.484001	−	0.838315i	0.515830	−	0.856691i	$-0.327484\pi$
$163$	−6.17931	−	10.7029i	−0.484001	−	0.838315i	−0.999831	+	0.0183763i	$0.994150\pi$
$164$	4.95787	−	8.58728i	0.387144	−	0.670554i
$165$	0.322825	+	0.0921151i	0.0251319	+	0.00717115i
$166$	1.82762	−	1.05518i	0.141851	−	0.0818977i
$167$	−4.99920			−0.386850			−0.193425	−	0.981115i	$-0.561960\pi$
$167$	−4.99920			−0.386850			−0.193425	+	0.981115i	$0.561960\pi$
$168$	1.16523	−	4.43196i	0.0898996	−	0.341933i
$169$	10.6008			0.815449
$170$	−0.458589	+	0.264766i	−0.0351722	+	0.0203067i
$171$	19.1580	+	0.619198i	1.46505	+	0.0473512i
$172$	5.74325	−	9.94760i	0.437919	−	0.758498i
$173$	−3.80403	−	6.58878i	−0.289215	−	0.500935i	0.684407	−	0.729100i	$-0.260061\pi$
$173$	−3.80403	−	6.58878i	−0.289215	−	0.500935i	−0.973623	+	0.228164i	$0.926728\pi$
$174$	−8.18773	+	2.05273i	−0.620710	+	0.155617i
$175$	−2.31838	−	1.27480i	−0.175253	−	0.0963660i
$176$			0.193822i			0.0146099i
$177$	14.4906	+	14.9665i	1.08918	+	1.12495i
$178$	−14.1816	−	8.18773i	−1.06295	−	0.613697i
$179$	−14.0520	−	8.11295i	−1.05030	−	0.606390i	−0.127566	−	0.991830i	$-0.540716\pi$
$179$	−14.0520	−	8.11295i	−1.05030	−	0.606390i	−0.922733	+	0.385440i	$0.874050\pi$
$180$	−2.54826	−	1.58314i	−0.189936	−	0.118001i
$181$			4.03153i			0.299661i	0.988712	+	0.149831i	$0.0478729\pi$
$181$			4.03153i			0.299661i	−0.988712	+	0.149831i	$0.952127\pi$
$182$	3.50552	−	2.12260i	0.259847	−	0.157338i
$183$	1.80529	+	7.20076i	0.133451	+	0.532295i
$184$	−2.12488	−	3.68040i	−0.156648	−	0.271322i
$185$	0.881634	−	1.52704i	0.0648190	−	0.112270i
$186$	4.40426	−	15.4351i	0.322936	−	1.13176i
$187$	−0.0888848	+	0.0513177i	−0.00649990	+	0.00375272i
$188$	9.80373			0.715010
$189$	9.44907	+	9.98575i	0.687318	+	0.726356i
$190$	6.38933			0.463531
$191$	21.8544	−	12.6176i	1.58133	−	0.912980i	0.586661	−	0.809832i	$-0.300442\pi$
$191$	21.8544	−	12.6176i	1.58133	−	0.912980i	0.994666	−	0.103147i	$-0.0328914\pi$
$192$	0.475255	−	1.66557i	0.0342986	−	0.120202i
$193$	−12.6183	+	21.8556i	−0.908286	+	1.57320i	−0.0918418	+	0.995774i	$0.529275\pi$
$193$	−12.6183	+	21.8556i	−0.908286	+	1.57320i	−0.816444	+	0.577424i	$0.804058\pi$
$194$	4.12231	+	7.14006i	0.295965	+	0.512626i
$195$	−0.652411	−	2.60228i	−0.0467201	−	0.186353i
$196$	−3.24415	+	6.20286i	−0.231725	+	0.443061i
$197$		−	14.7364i		−	1.04993i	−0.851125	−	0.524964i	$-0.824079\pi$
$197$		−	14.7364i		−	1.04993i	0.851125	−	0.524964i	$-0.175921\pi$
$198$	−0.493911	−	0.306849i	−0.0351007	−	0.0218068i
$199$	22.3991	+	12.9321i	1.58783	+	0.916734i	0.993664	+	0.112391i	$0.0358508\pi$
$199$	22.3991	+	12.9321i	1.58783	+	0.916734i	0.594165	+	0.804343i	$0.297483\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−5.81988	−	6.01103i	−0.410503	−	0.423985i
$202$			4.45663i			0.313567i
$203$	12.8912	−	0.268908i	0.904787	−	0.0188736i
$204$	0.889645	−	0.223041i	0.0622876	−	0.0156160i
$205$	4.95787	+	8.58728i	0.346272	+	0.599761i
$206$	−4.21094	+	7.29356i	−0.293390	+	0.508166i
$207$	12.7426	+	0.411849i	0.885673	+	0.0286255i
$208$	1.34141	−	0.774462i	0.0930098	−	0.0536992i
$209$	1.23840			0.0856616
$210$	3.25557	+	3.22510i	0.224656	+	0.222553i
$211$	−22.8721			−1.57458			−0.787289	−	0.616585i	$-0.788516\pi$
$211$	−22.8721			−1.57458			−0.787289	+	0.616585i	$0.788516\pi$
$212$	0.0562751	−	0.0324905i	0.00386499	−	0.00223145i
$213$	−10.4782	−	2.98985i	−0.717953	−	0.204861i
$214$	8.90681	−	15.4270i	0.608857	−	1.05457i
$215$	5.74325	+	9.94760i	0.391687	+	0.678421i
$216$	3.49192	+	3.84792i	0.237595	+	0.261818i
$217$	−11.8138	+	21.4848i	−0.801972	+	1.45848i
$218$		−	0.147803i		−	0.0100105i
$219$	10.0691	−	9.74890i	0.680405	−	0.658770i
$220$	−0.167855	−	0.0969112i	−0.0113168	−	0.00653375i
$221$	0.710319	+	0.410103i	0.0477812	+	0.0275865i
$222$	−2.19416	+	2.12439i	−0.147262	+	0.142579i
$223$			0.00626282i			0.000419390i	1.00000		0.000209695i	$6.67479e-5\pi$
$223$			0.00626282i			0.000419390i	−1.00000		0.000209695i	$0.999933\pi$
$224$	−1.27480	+	2.31838i	−0.0851763	+	0.154903i
$225$	2.64518	−	1.41529i	0.176345	−	0.0943526i
$226$	−1.72386	−	2.98581i	−0.114669	−	0.198613i
$227$	−9.41373	+	16.3051i	−0.624811	+	1.08220i	0.363766	+	0.931490i	$0.381491\pi$
$227$	−9.41373	+	16.3051i	−0.624811	+	1.08220i	−0.988577	+	0.150715i	$0.951843\pi$
$228$	−10.6419	−	3.03656i	−0.704777	−	0.201101i
$229$	6.75203	−	3.89829i	0.446187	−	0.257606i	−0.260032	−	0.965600i	$-0.583733\pi$
$229$	6.75203	−	3.89829i	0.446187	−	0.257606i	0.706218	+	0.707994i	$0.250400\pi$
$230$	4.24976			0.280221
$231$	0.631003	+	0.625096i	0.0415169	+	0.0411283i
$232$	4.87349			0.319960
$233$	11.2535	−	6.49718i	0.737238	−	0.425645i	−0.0838262	−	0.996480i	$-0.526714\pi$
$233$	11.2535	−	6.49718i	0.737238	−	0.425645i	0.821064	+	0.570836i	$0.193381\pi$
$234$	−0.150108	+	4.64434i	−0.00981287	+	0.303610i
$235$	−4.90186	+	8.49028i	−0.319762	+	0.553845i
$236$	−6.01371	−	10.4160i	−0.391459	−	0.678027i
$237$	11.3868	−	2.85477i	0.739655	−	0.185437i
$238$	−1.40071	+	0.0292184i	−0.0907944	+	0.00189395i
$239$		−	17.1710i		−	1.11070i	−0.831618	−	0.555349i	$-0.812585\pi$
$239$		−	17.1710i		−	1.11070i	0.831618	−	0.555349i	$-0.187415\pi$
$240$	1.20480	+	1.24437i	0.0777695	+	0.0803237i
$241$	7.10695	+	4.10320i	0.457799	+	0.264310i	0.711118	−	0.703072i	$-0.248189\pi$
$241$	7.10695	+	4.10320i	0.457799	+	0.264310i	−0.253319	+	0.967383i	$0.581522\pi$
$242$	9.49375	+	5.48122i	0.610281	+	0.352346i
$243$	−15.3337	+	2.80653i	−0.983659	+	0.180039i
$244$		−	4.28602i		−	0.274384i
$245$	−3.74976	−	5.91095i	−0.239563	−	0.377637i
$246$	−4.17654	−	16.6590i	−0.266286	−	1.06214i
$247$	−4.94829	−	8.57069i	−0.314852	−	0.545340i
$248$	−4.63357	+	8.02559i	−0.294232	+	0.509625i
$249$	1.00296	−	3.51495i	0.0635599	−	0.222751i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−22.9102			−1.44608			−0.723038	−	0.690808i	$-0.757255\pi$
$251$	−22.9102			−1.44608			−0.723038	+	0.690808i	$0.757255\pi$
$252$	−3.88964	−	6.91886i	−0.245025	−	0.435847i
$253$	0.823698			0.0517855
$254$	−4.76283	+	2.74982i	−0.298847	+	0.172539i
$255$	−0.251663	+	0.881975i	−0.0157598	+	0.0552314i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.54324	−	6.13707i	−0.221021	−	0.382820i	0.734097	−	0.679044i	$-0.237606\pi$
$257$	−3.54324	−	6.13707i	−0.221021	−	0.382820i	−0.955118	+	0.296225i	$0.904272\pi$
$258$	−4.83815	−	19.2980i	−0.301210	−	1.20144i
$259$	3.99063	−	2.41634i	0.247966	−	0.150144i
$260$			1.54892i			0.0960601i
$261$	−7.71544	+	12.4189i	−0.477574	+	0.768713i
$262$	5.19344	+	2.99843i	0.320852	+	0.185244i
$263$	−15.4744	−	8.93416i	−0.954194	−	0.550904i	−0.0598127	−	0.998210i	$-0.519050\pi$
$263$	−15.4744	−	8.93416i	−0.954194	−	0.550904i	−0.894381	+	0.447306i	$0.852384\pi$
$264$	0.233517	+	0.241187i	0.0143720	+	0.0148440i
$265$			0.0649809i			0.00399175i
$266$	14.8129	+	8.14514i	0.908236	+	0.499410i
$267$	−27.5117	+	6.89740i	−1.68369	+	0.422114i
$268$	2.41529	+	4.18340i	0.147537	+	0.255542i
$269$	−3.46273	+	5.99762i	−0.211126	+	0.365682i	−0.952067	−	0.305889i	$-0.901047\pi$
$269$	−3.46273	+	5.99762i	−0.211126	+	0.365682i	0.740941	+	0.671570i	$0.234380\pi$
$270$	−5.07836	+	1.10013i	−0.309059	+	0.0669520i
$271$	−14.6520	+	8.45932i	−0.890044	+	0.513867i	−0.873957	−	0.486003i	$-0.838454\pi$
$271$	−14.6520	+	8.45932i	−0.890044	+	0.513867i	−0.0160872	+	0.999871i	$0.505121\pi$
$272$	−0.529533			−0.0321076
$273$	1.80485	−	6.86476i	0.109235	−	0.415474i
$274$	−0.862112			−0.0520821
$275$	0.167855	−	0.0969112i	0.0101220	−	0.00584397i
$276$	−7.07828	−	2.01972i	−0.426062	−	0.121573i
$277$	10.6505	−	18.4471i	0.639924	−	1.10838i	−0.345525	−	0.938410i	$-0.612299\pi$
$277$	10.6505	−	18.4471i	0.639924	−	1.10838i	0.985449	−	0.169972i	$-0.0543677\pi$
$278$	−8.09216	−	14.0160i	−0.485336	−	0.840626i
$279$	−13.1157	−	24.5132i	−0.785216	−	1.46757i
$280$	−1.37037	−	2.26320i	−0.0818955	−	0.135252i
$281$			19.5927i			1.16880i	0.811464	+	0.584402i	$0.198671\pi$
$281$			19.5927i			1.16880i	−0.811464	+	0.584402i	$0.801329\pi$
$282$	12.1995	−	11.8115i	0.726467	−	0.703367i
$283$	−13.0751	−	7.54892i	−0.777235	−	0.448737i	0.0582144	−	0.998304i	$-0.481459\pi$
$283$	−13.0751	−	7.54892i	−0.777235	−	0.448737i	−0.835450	+	0.549567i	$0.814793\pi$
$284$	5.44820	+	3.14552i	0.323291	+	0.186652i
$285$	7.95069	−	7.69787i	0.470958	−	0.455982i
$286$			0.300216i			0.0177521i
$287$	0.547127	+	26.2289i	0.0322959	+	1.54824i
$288$	−1.41529	−	2.64518i	−0.0833967	−	0.155868i
$289$	8.35980	+	14.4796i	0.491753	+	0.851741i
$290$	−2.43674	+	4.22056i	−0.143091	+	0.247840i
$291$	13.7320	+	3.91830i	0.804985	+	0.229695i
$292$	−7.00763	+	4.04586i	−0.410090	+	0.236766i
$293$	−8.00534			−0.467677			−0.233839	−	0.972275i	$-0.575129\pi$
$293$	−8.00534			−0.467677			−0.233839	+	0.972275i	$0.575129\pi$
$294$	3.43628	+	11.6272i	0.200408	+	0.678113i
$295$	12.0274			0.700263
$296$	1.52704	−	0.881634i	0.0887571	−	0.0512439i
$297$	−0.984299	+	0.213231i	−0.0571148	+	0.0123729i
$298$	−6.38001	+	11.0505i	−0.369584	+	0.640138i
$299$	−3.29127	−	5.70065i	−0.190339	−	0.329677i
$300$	−1.68006	+	0.421203i	−0.0969981	+	0.0243182i
$301$	0.633799	+	30.3838i	0.0365316	+	1.75129i
$302$			17.5002i			1.00703i
$303$	5.36934	+	5.54569i	0.308461	+	0.318591i
$304$	5.53332	+	3.19467i	0.317358	+	0.183227i
$305$	3.71180	+	2.14301i	0.212537	+	0.122708i
$306$	0.838327	−	1.34939i	0.0479240	−	0.0771395i
$307$			4.33663i			0.247505i	0.992313	+	0.123752i	$0.0394928\pi$
$307$			4.33663i			0.247505i	−0.992313	+	0.123752i	$0.960507\pi$
$308$	−0.265609	−	0.438659i	−0.0151345	−	0.0249949i
$309$	3.54732	+	14.1492i	0.201800	+	0.804921i
$310$	−4.63357	−	8.02559i	−0.263169	−	0.455823i
$311$	−11.4192	+	19.7786i	−0.647523	+	1.12154i	0.336190	+	0.941794i	$0.390862\pi$
$311$	−11.4192	+	19.7786i	−0.647523	+	1.12154i	−0.983713	+	0.179748i	$0.942472\pi$
$312$	0.736134	−	2.57984i	0.0416754	−	0.146055i
$313$	21.9141	−	12.6521i	1.23866	−	0.715140i	0.269838	−	0.962906i	$-0.413030\pi$
$313$	21.9141	−	12.6521i	1.23866	−	0.715140i	0.968820	+	0.247766i	$0.0796964\pi$
$314$	2.84609			0.160614
$315$	7.93673	+	0.0909005i	0.447184	+	0.00512166i
$316$	−6.77766			−0.381273
$317$	13.0681	−	7.54489i	0.733979	−	0.423763i	−0.0858969	−	0.996304i	$-0.527376\pi$
$317$	13.0681	−	7.54489i	0.733979	−	0.423763i	0.819876	+	0.572541i	$0.194042\pi$
$318$	0.0308825	−	0.108230i	0.00173181	−	0.00606926i
$319$	−0.472296	+	0.818040i	−0.0264435	+	0.0458015i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−7.50315	−	29.9279i	−0.418785	−	1.67041i
$322$	9.85254	+	5.41760i	0.549061	+	0.301911i
$323$			3.38336i			0.188255i
$324$	8.98122	+	0.581164i	0.498956	+	0.0322869i
$325$	−1.34141	−	0.774462i	−0.0744079	−	0.0429594i
$326$	10.7029	+	6.17931i	0.592778	+	0.342241i
$327$	−0.178074	−	0.183922i	−0.00984749	−	0.0101709i
$328$			9.91573i			0.547505i
$329$	−22.1878	+	13.4348i	−1.22325	+	0.740683i
$330$	−0.325633	+	0.0816386i	−0.0179255	+	0.00449406i
$331$	−7.53086	−	13.0438i	−0.413933	−	0.716954i	0.581382	−	0.813630i	$-0.302512\pi$
$331$	−7.53086	−	13.0438i	−0.413933	−	0.716954i	−0.995316	+	0.0966768i	$0.969179\pi$
$332$	−1.05518	+	1.82762i	−0.0579104	+	0.100304i
$333$	−0.170880	+	5.28704i	−0.00936419	+	0.289728i
$334$	4.32943	−	2.49960i	0.236896	−	0.136772i
$335$	−4.83058			−0.263923
$336$	1.20686	+	4.42080i	0.0658395	+	0.241175i
$337$	14.9611			0.814983			0.407491	−	0.913209i	$-0.366404\pi$
$337$	14.9611			0.814983			0.407491	+	0.913209i	$0.366404\pi$
$338$	−9.18059	+	5.30042i	−0.499359	+	0.288305i
$339$	−5.74242	−	1.63854i	−0.311885	−	0.0889935i
$340$	0.264766	−	0.458589i	0.0143590	−	0.0248705i
$341$	−0.898091	−	1.55554i	−0.0486343	−	0.0842371i
$342$	−16.9009	+	9.04275i	−0.913896	+	0.488976i
$343$	−1.15806	−	18.4840i	−0.0625294	−	0.998043i
$344$			11.4865i			0.619311i
$345$	5.28827	−	5.12011i	0.284711	−	0.275657i
$346$	6.58878	+	3.80403i	0.354215	+	0.204506i
$347$	−3.50448	−	2.02331i	−0.188130	−	0.108617i	0.402977	−	0.915210i	$-0.367976\pi$
$347$	−3.50448	−	2.02331i	−0.188130	−	0.108617i	−0.591107	+	0.806593i	$0.701309\pi$
$348$	6.06442	−	5.87158i	0.325087	−	0.314750i
$349$			12.3695i			0.662124i	0.943609	+	0.331062i	$0.107407\pi$
$349$			12.3695i			0.662124i	−0.943609	+	0.331062i	$0.892593\pi$
$350$	2.64518	−	0.0551777i	0.141391	−	0.00294937i
$351$	5.40872	+	5.96013i	0.288696	+	0.318128i
$352$	−0.0969112	−	0.167855i	−0.00516539	−	0.00894671i
$353$	−1.83358	+	3.17585i	−0.0975914	+	0.169033i	−0.910687	−	0.413097i	$-0.864447\pi$
$353$	−1.83358	+	3.17585i	−0.0975914	+	0.169033i	0.813096	+	0.582130i	$0.197780\pi$
$354$	−20.0325	−	5.71609i	−1.06472	−	0.303807i
$355$	−5.44820	+	3.14552i	−0.289160	+	0.166947i
$356$	16.3755			0.867898
$357$	−1.70780	+	1.72393i	−0.0903861	+	0.0912401i
$358$	16.2259			0.857565
$359$	−6.34163	+	3.66134i	−0.334699	+	0.193238i	−0.657925	−	0.753083i	$-0.728566\pi$
$359$	−6.34163	+	3.66134i	−0.334699	+	0.193238i	0.323227	+	0.946322i	$0.395232\pi$
$360$	2.99843	+	0.0969112i	0.158031	+	0.00510767i
$361$	10.9118	−	18.8997i	0.574304	−	0.994723i
$362$	−2.01577	−	3.49141i	−0.105946	−	0.183504i
$363$	18.4175	−	4.61741i	0.966668	−	0.242351i
$364$	−1.97457	+	3.59099i	−0.103496	+	0.188219i
$365$		−	8.09171i		−	0.423540i
$366$	−5.16380	−	5.33340i	−0.269916	−	0.278781i
$367$	−4.12769	−	2.38312i	−0.215464	−	0.124398i	0.388384	−	0.921497i	$-0.373033\pi$
$367$	−4.12769	−	2.38312i	−0.215464	−	0.124398i	−0.603848	+	0.797100i	$0.706367\pi$
$368$	3.68040	+	2.12488i	0.191854	+	0.110767i
$369$	−25.2679	−	15.6980i	−1.31539	−	0.817207i
$370$			1.76327i			0.0916679i
$371$	−0.0828379	+	0.150650i	−0.00430073	+	0.00782138i
$372$	3.90335	+	15.5693i	0.202379	+	0.807232i
$373$	8.64813	+	14.9790i	0.447783	+	0.775584i	0.998241	−	0.0592792i	$-0.0188802\pi$
$373$	8.64813	+	14.9790i	0.447783	+	0.775584i	−0.550458	+	0.834863i	$0.685547\pi$
$374$	0.0513177	−	0.0888848i	0.00265357	−	0.00459612i
$375$	0.475255	−	1.66557i	0.0245421	−	0.0860098i
$376$	−8.49028	+	4.90186i	−0.437853	+	0.252794i
$377$	7.54866			0.388776
$378$	−13.1760	−	3.92338i	−0.677701	−	0.201797i
$379$	−8.76645			−0.450302			−0.225151	−	0.974324i	$-0.572288\pi$
$379$	−8.76645			−0.450302			−0.225151	+	0.974324i	$0.572288\pi$
$380$	−5.53332	+	3.19467i	−0.283853	+	0.163883i
$381$	−2.61374	+	9.16006i	−0.133906	+	0.469284i
$382$	−12.6176	+	21.8544i	−0.645574	+	1.11817i
$383$	−14.2377	−	24.6604i	−0.727511	−	1.26009i	−0.957932	−	0.286995i	$-0.907344\pi$
$383$	−14.2377	−	24.6604i	−0.727511	−	1.26009i	0.230422	−	0.973091i	$-0.425989\pi$
$384$	0.421203	+	1.68006i	0.0214944	+	0.0857350i
$385$	0.512694	−	0.0106947i	0.0261293	−	0.000545051i
$386$		−	25.2366i		−	1.28451i
$387$	−29.2707	−	18.1848i	−1.48791	−	0.924385i
$388$	−7.14006	−	4.12231i	−0.362481	−	0.209279i
$389$	18.2468	+	10.5348i	0.925151	+	0.534136i	0.885275	−	0.465069i	$-0.153970\pi$
$389$	18.2468	+	10.5348i	0.925151	+	0.534136i	0.0398761	+	0.999205i	$0.487304\pi$
$390$	1.86614	+	1.92743i	0.0944958	+	0.0975993i
$391$			2.25039i			0.113807i
$392$	−0.291909	−	6.99391i	−0.0147437	−	0.353246i
$393$	10.0751	−	2.52590i	0.508220	−	0.127415i
$394$	7.36822	+	12.7621i	0.371205	+	0.642947i
$395$	3.38883	−	5.86962i	0.170510	−	0.295333i
$396$	0.581164	+	0.0187836i	0.0292046	+	0.000943910i
$397$	5.71412	−	3.29905i	0.286783	−	0.165574i	−0.349707	−	0.936859i	$-0.613719\pi$
$397$	5.71412	−	3.29905i	0.286783	−	0.165574i	0.636490	+	0.771285i	$0.280386\pi$
$398$	−25.8642			−1.29646
$399$	28.2460	−	7.71101i	1.41407	−	0.386034i
$400$	1.00000			0.0500000
$401$	13.9699	−	8.06552i	0.697623	−	0.402773i	−0.108839	−	0.994059i	$-0.534713\pi$
$401$	13.9699	−	8.06552i	0.697623	−	0.402773i	0.806461	+	0.591287i	$0.201380\pi$
$402$	8.04568	+	2.29576i	0.401282	+	0.114502i
$403$	−7.17705	+	12.4310i	−0.357514	+	0.619233i
$404$	−2.22831	−	3.85955i	−0.110863	−	0.192020i
$405$	−4.99391	+	7.48738i	−0.248149	+	0.372051i
$406$	−11.0297	+	6.67850i	−0.547394	+	0.331448i
$407$			0.341761i			0.0169405i
$408$	−0.658934	+	0.637981i	−0.0326221	+	0.0315848i
$409$	−22.8659	−	13.2016i	−1.13065	−	0.652779i	−0.186549	−	0.982446i	$-0.559730\pi$
$409$	−22.8659	−	13.2016i	−1.13065	−	0.652779i	−0.944097	+	0.329666i	$0.893064\pi$
$410$	−8.58728	−	4.95787i	−0.424095	−	0.244852i
$411$	−1.07279	+	1.03867i	−0.0529166	+	0.0512339i
$412$		−	8.42187i		−	0.414916i
$413$	27.8841	+	15.3326i	1.37209	+	0.754467i
$414$	−11.2414	+	6.01464i	−0.552482	+	0.295603i
$415$	−1.05518	−	1.82762i	−0.0517966	−	0.0897144i
$416$	−0.774462	+	1.34141i	−0.0379711	+	0.0657679i
$417$	−26.9562	−	7.69169i	−1.32005	−	0.376664i
$418$	−1.07248	+	0.619198i	−0.0524568	+	0.0302860i
$419$	19.8312			0.968819			0.484409	−	0.874841i	$-0.339035\pi$
$419$	19.8312			0.968819			0.484409	+	0.874841i	$0.339035\pi$
$420$	−4.43196	−	1.16523i	−0.216257	−	0.0568575i
$421$	6.28009			0.306073			0.153036	−	0.988221i	$-0.451095\pi$
$421$	6.28009			0.306073			0.153036	+	0.988221i	$0.451095\pi$
$422$	19.8078	−	11.4360i	0.964228	−	0.556697i
$423$	0.950091	−	29.3958i	0.0461950	−	1.42927i
$424$	−0.0324905	+	0.0562751i	−0.00157788	+	0.00273296i
$425$	0.264766	+	0.458589i	0.0128431	+	0.0222448i
$426$	10.5693	−	2.64980i	0.512084	−	0.128383i
$427$	5.87345	+	9.70013i	0.284236	+	0.469422i
$428$			17.8136i			0.861054i
$429$	0.361700	+	0.373580i	0.0174631	+	0.0180366i
$430$	−9.94760	−	5.74325i	−0.479716	−	0.276964i
$431$	−3.94326	−	2.27664i	−0.189940	−	0.109662i	0.402014	−	0.915633i	$-0.368310\pi$
$431$	−3.94326	−	2.27664i	−0.189940	−	0.109662i	−0.591955	+	0.805971i	$0.701644\pi$
$432$	−4.94805	−	1.58643i	−0.238063	−	0.0763274i
$433$		−	2.62801i		−	0.126294i	−0.998004	−	0.0631471i	$-0.979886\pi$
$433$		−	2.62801i		−	0.126294i	0.998004	−	0.0631471i	$-0.0201137\pi$
$434$	−0.511340	−	24.5132i	−0.0245451	−	1.17667i
$435$	2.05273	+	8.18773i	0.0984208	+	0.392572i
$436$	0.0739017	+	0.128001i	0.00353925	+	0.00613016i
$437$	13.5765	−	23.5153i	0.649454	−	1.12489i
$438$	−3.84563	+	13.4773i	−0.183751	+	0.643972i
$439$	−5.05475	+	2.91836i	−0.241250	+	0.139286i	−0.615751	−	0.787941i	$-0.711147\pi$
$439$	−5.05475	+	2.91836i	−0.241250	+	0.139286i	0.374501	+	0.927226i	$0.377814\pi$
$440$	0.193822			0.00924012
$441$	18.2845	+	10.3285i	0.870689	+	0.491834i
$442$	−0.820205			−0.0390132
$443$	22.8164	−	13.1730i	1.08404	−	0.625870i	0.152056	−	0.988372i	$-0.451411\pi$
$443$	22.8164	−	13.1730i	1.08404	−	0.625870i	0.931983	+	0.362502i	$0.118077\pi$
$444$	0.838003	−	2.93685i	0.0397698	−	0.139377i
$445$	−8.18773	+	14.1816i	−0.388136	+	0.672271i
$446$	−0.00313141	−	0.00542376i	−0.000148277	−	0.000256823i
$447$	5.37456	+	21.4375i	0.254208	+	1.01396i
$448$	−0.0551777	−	2.64518i	−0.00260690	−	0.124973i
$449$		−	5.76638i		−	0.272132i	−0.990700	−	0.136066i	$-0.956554\pi$
$449$		−	5.76638i		−	0.272132i	0.990700	−	0.136066i	$-0.0434460\pi$
$450$	−1.58314	+	2.54826i	−0.0746302	+	0.120126i
$451$	−1.66441	−	0.960946i	−0.0783738	−	0.0452492i
$452$	2.98581	+	1.72386i	0.140441	+	0.0810834i
$453$	21.0843	+	21.7768i	0.990627	+	1.02316i
$454$		−	18.8275i		−	0.883617i
$455$	−2.12260	−	3.50552i	−0.0995091	−	0.164341i
$456$	10.7344	−	2.69121i	0.502686	−	0.126027i
$457$	0.360756	+	0.624848i	0.0168755	+	0.0292292i	0.874340	−	0.485314i	$-0.161295\pi$
$457$	0.360756	+	0.624848i	0.0168755	+	0.0292292i	−0.857464	+	0.514543i	$0.827961\pi$
$458$	−3.89829	+	6.75203i	−0.182155	+	0.315502i
$459$	−0.582557	−	2.68916i	−0.0271914	−	0.125519i
$460$	−3.68040	+	2.12488i	−0.171599	+	0.0990730i
$461$	−34.3692			−1.60073			−0.800365	−	0.599512i	$-0.795361\pi$
$461$	−34.3692			−1.60073			−0.800365	+	0.599512i	$0.795361\pi$
$462$	−0.859012	−	0.225848i	−0.0399649	−	0.0105074i
$463$	41.3815			1.92316			0.961581	−	0.274522i	$-0.0885197\pi$
$463$	41.3815			1.92316			0.961581	+	0.274522i	$0.0885197\pi$
$464$	−4.22056	+	2.43674i	−0.195935	+	0.113123i
$465$	−15.4351	−	4.40426i	−0.715786	−	0.204243i
$466$	−6.49718	+	11.2535i	−0.300976	+	0.521306i
$467$	−8.98343	−	15.5598i	−0.415704	−	0.720020i	0.579798	−	0.814760i	$-0.303131\pi$
$467$	−8.98343	−	15.5598i	−0.415704	−	0.720020i	−0.995502	+	0.0947401i	$0.969798\pi$
$468$	−2.19217	−	4.09717i	−0.101333	−	0.189392i
$469$	−11.1991	−	6.15804i	−0.517127	−	0.284352i
$470$		−	9.80373i		−	0.452212i
$471$	3.54159	−	3.42897i	0.163188	−	0.157999i
$472$	10.4160	+	6.01371i	0.479437	+	0.276803i
$473$	−1.92807	−	1.11317i	−0.0886527	−	0.0511837i
$474$	−8.43391	+	8.16573i	−0.387382	+	0.375064i
$475$		−	6.38933i		−	0.293163i
$476$	1.19844	−	0.725657i	0.0549304	−	0.0332605i
$477$	−0.0919668	−	0.171886i	−0.00421087	−	0.00787012i
$478$	8.58548	+	14.8705i	0.392691	+	0.680160i
$479$	4.50559	−	7.80391i	0.205866	−	0.356570i	−0.744542	−	0.667575i	$-0.767332\pi$
$479$	4.50559	−	7.80391i	0.205866	−	0.356570i	0.950408	+	0.311005i	$0.100666\pi$
$480$	−1.66557	−	0.475255i	−0.0760226	−	0.0216923i
$481$	2.36526	−	1.36558i	0.107847	−	0.0622652i
$482$	−8.20640			−0.373791
$483$	18.7873	−	5.12885i	0.854853	−	0.233371i
$484$	−10.9624			−0.498292
$485$	7.14006	−	4.12231i	0.324213	−	0.187185i
$486$	11.8761	−	10.0974i	0.538713	−	0.458027i
$487$	11.3648	−	19.6844i	0.514987	−	0.891984i	−0.484862	−	0.874591i	$-0.661130\pi$
$487$	11.3648	−	19.6844i	0.514987	−	0.891984i	0.999849	−	0.0173928i	$-0.00553658\pi$
$488$	2.14301	+	3.71180i	0.0970096	+	0.168025i
$489$	20.7632	−	5.20549i	0.938944	−	0.235401i
$490$	6.20286	+	3.24415i	0.280217	+	0.146556i
$491$		−	32.1654i		−	1.45160i	−0.687904	−	0.725801i	$-0.741469\pi$
$491$		−	32.1654i		−	1.45160i	0.687904	−	0.725801i	$-0.258531\pi$
$492$	11.9465	+	12.3388i	0.538589	+	0.556278i
$493$	−2.23493	−	1.29034i	−0.100656	−	0.0581138i
$494$	8.57069	+	4.94829i	0.385614	+	0.222634i
$495$	−0.306849	+	0.493911i	−0.0137918	+	0.0221996i
$496$		−	9.26715i		−	0.416107i
$497$	−16.6409	+	0.347125i	−0.746446	+	0.0155707i
$498$	0.888888	+	3.54552i	0.0398320	+	0.158878i
$499$	−10.6254	−	18.4037i	−0.475658	−	0.823864i	0.523953	−	0.851747i	$-0.324457\pi$
$499$	−10.6254	−	18.4037i	−0.475658	−	0.823864i	−0.999611	+	0.0278832i	$0.991123\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	2.37590	−	8.32653i	0.106147	−	0.372002i
$502$	19.8408	−	11.4551i	0.885537	−	0.511265i
$503$	20.9913			0.935957			0.467978	−	0.883740i	$-0.344982\pi$
$503$	20.9913			0.935957			0.467978	+	0.883740i	$0.344982\pi$
$504$	6.82796	+	4.04709i	0.304142	+	0.180272i
$505$	4.45663			0.198317
$506$	−0.713343	+	0.411849i	−0.0317120	+	0.0183089i
$507$	−5.03810	+	17.6565i	−0.223750	+	0.784151i
$508$	2.74982	−	4.76283i	0.122004	−	0.211317i
$509$	6.98403	+	12.0967i	0.309562	+	0.536177i	0.978267	−	0.207351i	$-0.0664843\pi$
$509$	6.98403	+	12.0967i	0.309562	+	0.536177i	−0.668705	+	0.743528i	$0.733151\pi$
$510$	−0.223041	−	0.889645i	−0.00987641	−	0.0393941i
$511$	10.3153	−	18.7597i	0.456324	−	0.829878i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.1363	+	31.6147i	−0.447527	+	1.39582i
$514$	6.13707	+	3.54324i	0.270695	+	0.156286i
$515$	7.29356	+	4.21094i	0.321393	+	0.185556i
$516$	13.8389	+	14.2935i	0.609226	+	0.629234i
$517$		−	1.90018i		−	0.0835699i
$518$	−2.24782	+	4.08792i	−0.0987635	+	0.179613i
$519$	12.7820	−	3.20454i	0.561066	−	0.140664i
$520$	−0.774462	−	1.34141i	−0.0339624	−	0.0588246i
$521$	−7.21208	+	12.4917i	−0.315967	+	0.547271i	−0.979643	−	0.200750i	$-0.935662\pi$
$521$	−7.21208	+	12.4917i	−0.315967	+	0.547271i	0.663676	+	0.748020i	$0.268996\pi$
$522$	0.472296	−	14.6128i	0.0206718	−	0.639586i
$523$	−25.2604	+	14.5841i	−1.10456	+	0.637717i	−0.937415	−	0.348215i	$-0.886788\pi$
$523$	−25.2604	+	14.5841i	−1.10456	+	0.637717i	−0.167144	+	0.985932i	$0.553455\pi$
$524$	−5.99687			−0.261974
$525$	3.22510	−	3.25557i	0.140755	−	0.142085i
$526$	17.8683			0.779096
$527$	4.24981	−	2.45363i	0.185125	−	0.106882i
$528$	−0.322825	−	0.0921151i	−0.0140492	−	0.00400880i
$529$	−2.46979	+	4.27779i	−0.107382	+	0.185991i
$530$	−0.0324905	−	0.0562751i	−0.00141130	−	0.00244444i
$531$	−31.8146	+	17.0223i	−1.38064	+	0.738704i
$532$	−16.9009	+	0.352549i	−0.732747	+	0.0152849i
$533$			15.3587i			0.665259i
$534$	20.3771	−	19.7292i	0.881805	−	0.853765i
$535$	−15.4270	−	8.90681i	−0.666969	−	0.385075i
$536$	−4.18340	−	2.41529i	−0.180696	−	0.104325i
$537$	20.1910	−	19.5490i	0.871306	−	0.843600i
$538$		−	6.92546i		−	0.298578i
$539$	1.20225	+	0.628790i	0.0517847	+	0.0270839i
$540$	3.84792	−	3.49192i	0.165588	−	0.150268i
$541$	12.4518	+	21.5672i	0.535345	+	0.927246i	0.999147	+	0.0413062i	$0.0131519\pi$
$541$	12.4518	+	21.5672i	0.535345	+	0.927246i	−0.463801	+	0.885939i	$0.653515\pi$
$542$	8.45932	−	14.6520i	0.363359	−	0.629356i
$543$	−6.71481	−	1.91601i	−0.288160	−	0.0822237i
$544$	0.458589	−	0.264766i	0.0196618	−	0.0113518i
$545$	−0.147803			−0.00633120
$546$	1.86933	+	6.84748i	0.0799999	+	0.293045i
$547$	−0.655376			−0.0280219			−0.0140109	−	0.999902i	$-0.504460\pi$
$547$	−0.655376			−0.0280219			−0.0140109	+	0.999902i	$0.504460\pi$
$548$	0.746611	−	0.431056i	0.0318936	−	0.0184138i
$549$	−12.8514	−	0.415364i	−0.548483	−	0.0177273i
$550$	−0.0969112	+	0.167855i	−0.00413231	+	0.00715737i
$551$	15.5692	+	26.9666i	0.663269	+	1.14882i
$552$	7.13983	−	1.79001i	0.303891	−	0.0761879i
$553$	15.3392	−	9.28792i	0.652289	−	0.394963i
$554$			21.3009i			0.904990i
$555$	2.12439	+	2.19416i	0.0901752	+	0.0931368i
$556$	14.0160	+	8.09216i	0.594412	+	0.343184i
$557$	−15.4016	−	8.89212i	−0.652587	−	0.376771i	0.136860	−	0.990590i	$-0.456299\pi$
$557$	−15.4016	−	8.89212i	−0.652587	−	0.376771i	−0.789446	+	0.613819i	$0.789632\pi$
$558$	23.6151	+	14.6712i	0.999709	+	0.621083i
$559$			17.7917i			0.752509i
$560$	2.31838	+	1.27480i	0.0979694	+	0.0538702i
$561$	−0.0432303	−	0.172433i	−0.00182519	−	0.00728013i
$562$	−9.79636	−	16.9678i	−0.413235	−	0.715743i
$563$	−10.1362	+	17.5563i	−0.427188	+	0.739912i	−0.996622	−	0.0821256i	$-0.973829\pi$
$563$	−10.1362	+	17.5563i	−0.427188	+	0.739912i	0.569434	+	0.822037i	$0.307162\pi$
$564$	−4.65927	+	16.3288i	−0.196191	+	0.687567i
$565$	−2.98581	+	1.72386i	−0.125614	+	0.0725232i
$566$	15.0978			0.634610
$567$	−21.1227	+	10.9923i	−0.887070	+	0.461634i
$568$	−6.29103			−0.263966
$569$	−38.9233	+	22.4724i	−1.63175	+	0.942092i	−0.648197	+	0.761473i	$0.724477\pi$
$569$	−38.9233	+	22.4724i	−1.63175	+	0.942092i	−0.983553	+	0.180619i	$0.942190\pi$
$570$	−3.03656	+	10.6419i	−0.127188	+	0.445740i
$571$	5.59451	−	9.68998i	0.234123	−	0.405513i	−0.724894	−	0.688860i	$-0.758111\pi$
$571$	5.59451	−	9.68998i	0.234123	−	0.405513i	0.959017	+	0.283347i	$0.0914448\pi$
$572$	−0.150108	−	0.259995i	−0.00627633	−	0.0108709i
$573$	10.6292	+	42.3967i	0.444040	+	1.77115i
$574$	−13.5883	−	22.4413i	−0.567163	−	0.936681i
$575$		−	4.24976i		−	0.177227i
$576$	2.54826	+	1.58314i	0.106178	+	0.0659644i
$577$	−8.42967	−	4.86687i	−0.350932	−	0.202611i	0.314164	−	0.949369i	$-0.398276\pi$
$577$	−8.42967	−	4.86687i	−0.350932	−	0.202611i	−0.665096	+	0.746758i	$0.731609\pi$
$578$	−14.4796	−	8.35980i	−0.602272	−	0.347722i
$579$	−30.4051	−	31.4037i	−1.26359	−	1.30509i
$580$		−	4.87349i		−	0.202361i
$581$	−0.116445	−	5.58226i	−0.00483094	−	0.231591i
$582$	−13.8514	+	3.47266i	−0.574160	+	0.143946i
$583$	−0.00629738	−	0.0109074i	−0.000260811	−	0.000451738i
$584$	4.04586	−	7.00763i	0.167419	−	0.289978i
$585$	4.64434	+	0.150108i	0.192020	+	0.00620620i
$586$	6.93283	−	4.00267i	0.286393	−	0.165349i
$587$	32.0185			1.32155			0.660773	−	0.750585i	$-0.270228\pi$
$587$	32.0185			1.32155			0.660773	+	0.750585i	$0.270228\pi$
$588$	−8.78951	−	8.35132i	−0.362473	−	0.344403i
$589$	−59.2109			−2.43974
$590$	−10.4160	+	6.01371i	−0.428822	+	0.247580i
$591$	24.5446	+	7.00357i	1.00963	+	0.288088i
$592$	−0.881634	+	1.52704i	−0.0362349	+	0.0627608i
$593$	16.2006	+	28.0603i	0.665280	+	1.15230i	0.979209	+	0.202852i	$0.0650211\pi$
$593$	16.2006	+	28.0603i	0.665280	+	1.15230i	−0.313930	+	0.949446i	$0.601646\pi$
$594$	0.745813	−	0.676813i	0.0306011	−	0.0277700i
$595$	0.0292184	+	1.40071i	0.00119784	+	0.0574234i
$596$		−	12.7600i		−	0.522671i
$597$	−32.1847	+	31.1613i	−1.31723	+	1.27535i
$598$	5.70065	+	3.29127i	0.233117	+	0.134590i
$599$	−9.13107	−	5.27183i	−0.373086	−	0.215401i	0.301720	−	0.953397i	$-0.402439\pi$
$599$	−9.13107	−	5.27183i	−0.373086	−	0.215401i	−0.674806	+	0.737996i	$0.735773\pi$
$600$	1.24437	−	1.20480i	0.0508012	−	0.0491858i
$601$		−	24.6793i		−	1.00669i	−0.864086	−	0.503344i	$-0.832103\pi$
$601$		−	24.6793i		−	1.00669i	0.864086	−	0.503344i	$-0.167897\pi$
$602$	−15.7408	−	25.9963i	−0.641547	−	1.05953i
$603$	12.7777	−	6.83667i	0.520349	−	0.278411i
$604$	−8.75012	−	15.1557i	−0.356038	−	0.616675i
$605$	5.48122	−	9.49375i	0.222843	−	0.385976i
$606$	−7.42283	−	2.11804i	−0.301532	−	0.0860393i
$607$	−11.2456	+	6.49268i	−0.456447	+	0.263530i	−0.710549	−	0.703648i	$-0.751553\pi$
$607$	−11.2456	+	6.49268i	−0.456447	+	0.263530i	0.254102	+	0.967177i	$0.418220\pi$
$608$	−6.38933			−0.259122
$609$	−5.67874	+	21.5991i	−0.230114	+	0.875239i
$610$	−4.28602			−0.173536
$611$	−13.1508	+	7.59261i	−0.532024	+	0.307164i
$612$	−0.0513177	+	1.58777i	−0.00207439	+	0.0641818i
$613$	13.3643	−	23.1477i	0.539780	−	0.934926i	−0.459136	−	0.888366i	$-0.651841\pi$
$613$	13.3643	−	23.1477i	0.539780	−	0.934926i	0.998915	−	0.0465601i	$-0.0148259\pi$
$614$	−2.16832	−	3.75563i	−0.0875061	−	0.151565i
$615$	−16.6590	+	4.17654i	−0.671755	+	0.168414i
$616$	0.449354	+	0.247085i	0.0181050	+	0.00995535i
$617$		−	13.2804i		−	0.534650i	−0.963606	−	0.267325i	$-0.913860\pi$
$617$		−	13.2804i		−	0.534650i	0.963606	−	0.267325i	$-0.0861397\pi$
$618$	−10.1467	−	10.4799i	−0.408159	−	0.421564i
$619$	8.56249	+	4.94355i	0.344155	+	0.198698i	0.662108	−	0.749408i	$-0.269662\pi$
$619$	8.56249	+	4.94355i	0.344155	+	0.198698i	−0.317953	+	0.948107i	$0.602995\pi$
$620$	8.02559	+	4.63357i	0.322315	+	0.186089i
$621$	−6.74196	+	21.0280i	−0.270546	+	0.843825i
$622$		−	22.8384i		−	0.915736i
$623$	−37.0610	+	22.4405i	−1.48482	+	0.899060i
$624$	0.652411	+	2.60228i	0.0261174	+	0.104174i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.6521	+	21.9141i	−0.505680	+	0.875864i
$627$	−0.588554	+	2.06264i	−0.0235046	+	0.0823738i
$628$	−2.46479	+	1.42305i	−0.0983557	+	0.0567857i
$629$	−0.933708			−0.0372294
$630$	−6.91886	+	3.88964i	−0.275654	+	0.154967i
$631$	−26.4695			−1.05373			−0.526867	−	0.849948i	$-0.676633\pi$
$631$	−26.4695			−1.05373			−0.526867	+	0.849948i	$0.676633\pi$
$632$	5.86962	−	3.38883i	0.233481	−	0.134800i
$633$	10.8701	−	38.0951i	0.432046	−	1.51414i
$634$	−7.54489	+	13.0681i	−0.299646	+	0.519002i
$635$	2.74982	+	4.76283i	0.109123	+	0.189007i
$636$	0.0273702	+	0.109172i	0.00108530	+	0.00432894i
$637$	−0.452145	−	10.8330i	−0.0179147	−	0.429220i
$638$		−	0.944591i		−	0.0373967i
$639$	9.95962	−	16.0312i	0.393996	−	0.634185i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	20.3632	+	11.7567i	0.804298	+	0.464362i	0.844972	−	0.534811i	$-0.179617\pi$
$641$	20.3632	+	11.7567i	0.804298	+	0.464362i	−0.0406739	+	0.999172i	$0.512950\pi$
$642$	21.4619	+	22.1667i	0.847032	+	0.874851i
$643$			20.1307i			0.793876i	0.917846	+	0.396938i	$0.129927\pi$
$643$			20.1307i			0.793876i	−0.917846	+	0.396938i	$0.870073\pi$
$644$	−11.2414	+	0.234492i	−0.442971	+	0.00924027i
$645$	−19.2980	+	4.83815i	−0.759857	+	0.190502i
$646$	−1.69168	−	2.93008i	−0.0665582	−	0.115282i
$647$	−5.16088	+	8.93890i	−0.202895	+	0.351424i	−0.949460	−	0.313888i	$-0.898368\pi$
$647$	−5.16088	+	8.93890i	−0.202895	+	0.351424i	0.746565	+	0.665312i	$0.231702\pi$
$648$	−8.06854	+	3.98731i	−0.316962	+	0.156636i
$649$	−2.01886	+	1.16559i	−0.0792473	+	0.0457535i
$650$	1.54892			0.0607538
$651$	−30.1699	−	29.8875i	−1.18245	−	1.17138i
$652$	−12.3586			−0.484001
$653$	2.88758	−	1.66715i	0.113000	−	0.0652404i	−0.442435	−	0.896801i	$-0.645885\pi$
$653$	2.88758	−	1.66715i	0.113000	−	0.0652404i	0.555435	+	0.831560i	$0.312552\pi$
$654$	0.246177	+	0.0702443i	0.00962629	+	0.00274677i
$655$	2.99843	−	5.19344i	0.117159	−	0.202925i
$656$	−4.95787	−	8.58728i	−0.193572	−	0.335277i
$657$	11.4521	+	21.4040i	0.446790	+	0.835050i
$658$	12.4978	−	22.7288i	0.487216	−	0.886059i
$659$			13.1387i			0.511809i	0.966702	+	0.255905i	$0.0823733\pi$
$659$			13.1387i			0.511809i	−0.966702	+	0.255905i	$0.917627\pi$
$660$	0.241187	−	0.233517i	0.00938818	−	0.00908965i
$661$	−0.244148	−	0.140959i	−0.00949625	−	0.00548266i	0.495244	−	0.868754i	$-0.335079\pi$
$661$	−0.244148	−	0.140959i	−0.00949625	−	0.00548266i	−0.504741	+	0.863271i	$0.668412\pi$
$662$	13.0438	+	7.53086i	0.506963	+	0.292695i
$663$	−1.02064	+	0.988184i	−0.0396383	+	0.0383779i
$664$		−	2.11036i		−	0.0818977i
$665$	8.14514	−	14.8129i	0.315855	−	0.574419i
$666$	−2.49554	−	4.66415i	−0.0967000	−	0.180732i
$667$	10.3556	+	17.9364i	0.400969	+	0.694499i
$668$	−2.49960	+	4.32943i	−0.0967124	+	0.167511i
$669$	−0.0104312	−	0.00297644i	−0.000403293	−	0.000115076i
$670$	4.18340	−	2.41529i	0.161619	−	0.0933108i
$671$	−0.830727			−0.0320699
$672$	−3.25557	−	3.22510i	−0.125586	−	0.124411i
$673$	−36.0090			−1.38805			−0.694023	−	0.719953i	$-0.744163\pi$
$673$	−36.0090			−1.38805			−0.694023	+	0.719953i	$0.744163\pi$
$674$	−12.9567	+	7.48055i	−0.499073	+	0.288140i
$675$	1.10013	+	5.07836i	0.0423442	+	0.195466i
$676$	5.30042	−	9.18059i	0.203862	−	0.353100i
$677$	2.00745	+	3.47701i	0.0771526	+	0.133632i	0.902020	−	0.431694i	$-0.142084\pi$
$677$	2.00745	+	3.47701i	0.0771526	+	0.133632i	−0.824868	+	0.565326i	$0.808750\pi$
$678$	5.79235	−	1.45219i	0.222454	−	0.0557709i
$679$	21.8085	−	0.454920i	0.836933	−	0.0174582i
$680$			0.529533i			0.0203067i
$681$	−22.6833	−	23.4283i	−0.869227	−	0.897775i
$682$	1.55554	+	0.898091i	0.0595646	+	0.0343897i
$683$	31.6027	+	18.2458i	1.20924	+	0.698156i	0.962594	−	0.270949i	$-0.0873373\pi$
$683$	31.6027	+	18.2458i	1.20924	+	0.698156i	0.246649	+	0.969105i	$0.420671\pi$
$684$	10.1152	−	16.2817i	0.386766	−	0.622547i
$685$			0.862112i			0.0329396i
$686$	10.2449	+	15.4286i	0.391153	+	0.589067i
$687$	3.28394	+	13.0987i	0.125290	+	0.499746i
$688$	−5.74325	−	9.94760i	−0.218959	−	0.379249i
$689$	−0.0503252	+	0.0871659i	−0.00191724	+	0.00332075i
$690$	−2.01972	+	7.07828i	−0.0768894	+	0.269465i
$691$	−7.57320	+	4.37239i	−0.288098	+	0.166334i	−0.637084	−	0.770795i	$-0.719860\pi$
$691$	−7.57320	+	4.37239i	−0.288098	+	0.166334i	0.348986	+	0.937128i	$0.386526\pi$
$692$	−7.60806			−0.289215
$693$	−1.34103	+	0.753900i	−0.0509415	+	0.0286383i
$694$	4.04662			0.153608
$695$	−14.0160	+	8.09216i	−0.531659	+	0.306953i
$696$	−2.31615	+	8.11715i	−0.0877935	+	0.307680i
$697$	2.62535	−	4.54724i	0.0994423	−	0.172239i
$698$	−6.18475	−	10.7123i	−0.234096	−	0.405467i
$699$	5.47327	+	21.8313i	0.207018	+	0.825734i
$700$	−2.26320	+	1.37037i	−0.0855409	+	0.0517952i
$701$			21.5875i			0.815349i	0.913127	+	0.407674i	$0.133660\pi$
$701$			21.5875i			0.815349i	−0.913127	+	0.407674i	$0.866340\pi$
$702$	−7.66415	−	2.45727i	−0.289265	−	0.0927435i
$703$	9.75673	+	5.63305i	0.367982	+	0.212455i
$704$	0.167855	+	0.0969112i	0.00632628	+	0.00365248i
$705$	−11.8115	−	12.1995i	−0.444848	−	0.459458i
$706$		−	3.66715i		−	0.138015i
$707$	10.3321	+	5.68132i	0.388580	+	0.213668i
$708$	20.2067	−	5.06598i	0.759415	−	0.190391i
$709$	2.50743	+	4.34300i	0.0941685	+	0.163105i	0.909261	−	0.416226i	$-0.136647\pi$
$709$	2.50743	+	4.34300i	0.0941685	+	0.163105i	−0.815093	+	0.579330i	$0.803314\pi$
$710$	3.14552	−	5.44820i	0.118049	−	0.204467i
$711$	−0.656831	+	20.3224i	−0.0246331	+	0.762148i
$712$	−14.1816	+	8.18773i	−0.531477	+	0.306848i
$713$	−39.3831			−1.47491
$714$	0.617028	−	2.34687i	0.0230917	−	0.0878292i
$715$	0.300216			0.0112274
$716$	−14.0520	+	8.11295i	−0.525149	+	0.303195i
$717$	28.5995	+	8.16059i	1.06807	+	0.304763i
$718$	3.66134	−	6.34163i	0.136640	−	0.236668i
$719$	17.1509	+	29.7062i	0.639619	+	1.10785i	0.985516	+	0.169580i	$0.0542412\pi$
$719$	17.1509	+	29.7062i	0.639619	+	1.10785i	−0.345897	+	0.938272i	$0.612425\pi$
$720$	−2.64518	+	1.41529i	−0.0985799	+	0.0527447i
$721$	11.5411	+	19.0604i	0.429813	+	0.709846i
$722$			21.8235i			0.812188i
$723$	−10.2118	+	9.88707i	−0.379781	+	0.367704i
$724$	3.49141	+	2.01577i	0.129757	+	0.0749154i
$725$	4.22056	+	2.43674i	0.156748	+	0.0904984i
$726$	−13.6413	+	13.2075i	−0.506277	+	0.490178i
$727$			17.4763i			0.648159i	0.946030	+	0.324080i	$0.105055\pi$
$727$			17.4763i			0.648159i	−0.946030	+	0.324080i	$0.894945\pi$
$728$	−0.0854660	−	4.09717i	−0.00316758	−	0.151851i
$729$	2.61296	−	26.8733i	0.0967764	−	0.995306i
$730$	4.04586	+	7.00763i	0.149744	+	0.259364i
$731$	3.04124	−	5.26758i	0.112484	−	0.194829i
$732$	7.13868	+	2.03696i	0.263853	+	0.0752880i
$733$	45.0320	−	25.9992i	1.66330	−	0.960304i	0.692170	−	0.721734i	$-0.256655\pi$
$733$	45.0320	−	25.9992i	1.66330	−	0.960304i	0.971125	−	0.238570i	$-0.0766786\pi$
$734$	4.76624			0.175925
$735$	11.6272	−	3.43628i	0.428876	−	0.126749i
$736$	−4.24976			−0.156648
$737$	0.810838	−	0.468137i	0.0298676	−	0.0172441i
$738$	29.7317	+	0.960946i	1.09444	+	0.0353729i
$739$	12.1033	−	20.9635i	0.445226	−	0.771155i	−0.552842	−	0.833286i	$-0.686457\pi$
$739$	12.1033	−	20.9635i	0.445226	−	0.771155i	0.998068	+	0.0621318i	$0.0197899\pi$
$740$	−0.881634	−	1.52704i	−0.0324095	−	0.0561349i
$741$	16.6268	−	4.16847i	0.610801	−	0.153133i
$742$	−0.00358550	−	0.171886i	−0.000131628	−	0.00631013i
$743$		−	48.1794i		−	1.76753i	−0.467932	−	0.883765i	$-0.655001\pi$
$743$		−	48.1794i		−	1.76753i	0.467932	−	0.883765i	$-0.344999\pi$
$744$	−11.1651	−	11.5318i	−0.409331	−	0.422775i
$745$	11.0505	+	6.38001i	0.404859	+	0.233745i
$746$	−14.9790	−	8.64813i	−0.548420	−	0.316631i
$747$	5.37774	+	3.34100i	0.196761	+	0.122241i
$748$			0.102635i			0.00375272i
$749$	−24.4113	−	40.3158i	−0.891970	−	1.47311i
$750$	0.421203	+	1.68006i	0.0153802	+	0.0613470i
$751$	−2.58147	−	4.47123i	−0.0941991	−	0.163158i	0.815075	−	0.579355i	$-0.196696\pi$
$751$	−2.58147	−	4.47123i	−0.0941991	−	0.163158i	−0.909274	+	0.416198i	$0.863362\pi$
$752$	4.90186	−	8.49028i	0.178753	−	0.309609i
$753$	10.8882	−	38.1585i	0.396787	−	1.39057i
$754$	−6.53733	+	3.77433i	−0.238076	+	0.137453i
$755$	17.5002			0.636899
$756$	13.3724	−	3.19026i	0.486351	−	0.116029i
$757$	−16.0842			−0.584591			−0.292295	−	0.956328i	$-0.594419\pi$
$757$	−16.0842			−0.584591			−0.292295	+	0.956328i	$0.594419\pi$
$758$	7.59197	−	4.38323i	0.275753	−	0.159206i
$759$	−0.391467	+	1.37193i	−0.0142094	+	0.0497979i
$760$	3.19467	−	5.53332i	0.115883	−	0.200715i
$761$	5.07895	+	8.79701i	0.184112	+	0.318891i	0.943277	−	0.332007i	$-0.107726\pi$
$761$	5.07895	+	8.79701i	0.184112	+	0.318891i	−0.759165	+	0.650898i	$0.774392\pi$
$762$	−2.31647	−	9.23972i	−0.0839168	−	0.334720i
$763$	−0.342664	−	0.188420i	−0.0124053	−	0.00682127i
$764$		−	25.2353i		−	0.912980i
$765$	−1.34939	−	0.838327i	−0.0487873	−	0.0303098i
$766$	24.6604	+	14.2377i	0.891015	+	0.514428i
$767$	16.1337	+	9.31477i	0.582552	+	0.336337i
$768$	−1.20480	−	1.24437i	−0.0434745	−	0.0449023i
$769$		−	6.68859i		−	0.241197i	−0.992701	−	0.120598i	$-0.961519\pi$
$769$		−	6.68859i		−	0.241197i	0.992701	−	0.120598i	$-0.0384813\pi$
$770$	−0.438659	+	0.265609i	−0.0158082	+	0.00957189i
$771$	11.9057	−	2.98485i	0.428773	−	0.107497i
$772$	12.6183	+	21.8556i	0.454143	+	0.786599i
$773$	13.2852	−	23.0107i	0.477836	−	0.827636i	−0.521841	−	0.853043i	$-0.674755\pi$
$773$	13.2852	−	23.0107i	0.477836	−	0.827636i	0.999677	+	0.0254064i	$0.00808799\pi$
$774$	34.4415	+	1.11317i	1.23798	+	0.0400121i
$775$	−8.02559	+	4.63357i	−0.288288	+	0.166443i
$776$	8.24463			0.295965
$777$	2.12801	+	7.79506i	0.0763421	+	0.279646i
$778$	−21.0696			−0.755382
$779$	−54.8669	+	31.6774i	−1.96581	+	1.13496i
$780$	−2.57984	−	0.736134i	−0.0923732	−	0.0263578i
$781$	0.609672	−	1.05598i	0.0218158	−	0.0377860i
$782$	−1.12519	−	1.94889i	−0.0402368	−	0.0696922i
$783$	−17.0178	−	18.7528i	−0.608168	−	0.670170i
$784$	3.74976	+	5.91095i	0.133920	+	0.211105i
$785$		−	2.84609i		−	0.101581i
$786$	−7.46232	+	7.22503i	−0.266172	+	0.257708i
$787$	25.6272	+	14.7959i	0.913510	+	0.527416i	0.881559	−	0.472074i	$-0.156494\pi$
$787$	25.6272	+	14.7959i	0.913510	+	0.527416i	0.0319515	+	0.999489i	$0.489828\pi$
$788$	−12.7621	−	7.36822i	−0.454632	−	0.262482i
$789$	22.2348	−	21.5278i	0.791580	−	0.766409i
$790$			6.77766i			0.241138i
$791$	−9.11981	+	0.190237i	−0.324263	+	0.00676405i
$792$	−0.512694	+	0.274315i	−0.0182178	+	0.00974735i
$793$	3.31936	+	5.74930i	0.117874	+	0.204164i
$794$	−3.29905	+	5.71412i	−0.117079	+	0.202786i
$795$	−0.108230	−	0.0308825i	−0.00383854	−	0.00109529i
$796$	22.3991	−	12.9321i	0.793915	−	0.458367i
$797$	34.6019			1.22566			0.612830	−	0.790215i	$-0.290031\pi$
$797$	34.6019			1.22566			0.612830	+	0.790215i	$0.290031\pi$
$798$	−20.6062	+	20.8009i	−0.729452	+	0.736344i
$799$	5.19139			0.183658
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	1.58697	−	49.1008i	0.0560727	−	1.73489i
$802$	−8.06552	+	13.9699i	−0.284803	+	0.493294i
$803$	0.784178	+	1.35824i	0.0276730	+	0.0479311i
$804$	−8.11564	+	2.03465i	−0.286217	+	0.0717567i
$805$	5.41760	−	9.85254i	0.190945	−	0.347257i
$806$		−	14.3541i		−	0.505602i
$807$	−8.34380	−	8.61783i	−0.293716	−	0.303362i
$808$	3.85955	+	2.22831i	0.135779	+	0.0783918i
$809$	14.6105	+	8.43536i	0.513677	+	0.296571i	0.734344	−	0.678778i	$-0.237490\pi$
$809$	14.6105	+	8.43536i	0.513677	+	0.296571i	−0.220667	+	0.975349i	$0.570823\pi$
$810$	0.581164	−	8.98122i	0.0204200	−	0.315568i
$811$		−	11.1600i		−	0.391880i	−0.980616	−	0.195940i	$-0.937224\pi$
$811$		−	11.1600i		−	0.391880i	0.980616	−	0.195940i	$-0.0627758\pi$
$812$	6.21274	−	11.2986i	0.218024	−	0.396503i
$813$	−7.12619	−	28.4243i	−0.249926	−	0.996883i
$814$	−0.170880	−	0.295974i	−0.00598936	−	0.0103739i
$815$	6.17931	−	10.7029i	0.216452	−	0.374906i
$816$	0.251663	−	0.881975i	0.00880998	−	0.0308753i
$817$	−63.5585	+	36.6955i	−2.22363	+	1.28381i
$818$	26.4033			0.923169
$819$	10.5760	+	6.26863i	0.369555	+	0.219044i
$820$	9.91573			0.346272
$821$	34.0899	−	19.6818i	1.18975	−	0.686901i	0.231498	−	0.972835i	$-0.425637\pi$
$821$	34.0899	−	19.6818i	1.18975	−	0.686901i	0.958249	+	0.285934i	$0.0923040\pi$
$822$	0.409723	−	1.43591i	0.0142907	−	0.0500831i
$823$	−20.3585	+	35.2620i	−0.709654	+	1.22916i	0.255332	+	0.966854i	$0.417815\pi$
$823$	−20.3585	+	35.2620i	−0.709654	+	1.22916i	−0.964986	+	0.262303i	$0.915518\pi$
$824$	4.21094	+	7.29356i	0.146695	+	0.254083i
$825$	0.0816386	+	0.325633i	0.00284229	+	0.0113371i
$826$	−31.8146	+	0.663645i	−1.10697	+	0.0230912i
$827$		−	24.7892i		−	0.862006i	−0.902350	−	0.431003i	$-0.858160\pi$
$827$		−	24.7892i		−	0.862006i	0.902350	−	0.431003i	$-0.141840\pi$
$828$	6.72798	−	10.8295i	0.233813	−	0.376351i
$829$	−0.897813	−	0.518352i	−0.0311823	−	0.0180031i	0.484328	−	0.874887i	$-0.339064\pi$
$829$	−0.897813	−	0.518352i	−0.0311823	−	0.0180031i	−0.515510	+	0.856883i	$0.672398\pi$
$830$	1.82762	+	1.05518i	0.0634377	+	0.0366258i
$831$	25.6634	+	26.5062i	0.890252	+	0.919491i
$832$		−	1.54892i		−	0.0536992i
$833$	−1.71789	+	3.28462i	−0.0595212	+	0.113805i
$834$	27.1906	−	6.81689i	0.941533	−	0.236050i
$835$	−2.49960	−	4.32943i	−0.0865022	−	0.149826i
$836$	0.619198	−	1.07248i	0.0214154	−	0.0370926i
$837$	47.0619	−	10.1951i	1.62670	−	0.352394i
$838$	−17.1743	+	9.91561i	−0.593278	+	0.342529i
$839$	19.4880			0.672801			0.336401	−	0.941719i	$-0.390790\pi$
$839$	19.4880			0.672801			0.336401	+	0.941719i	$0.390790\pi$
$840$	4.42080	−	1.20686i	0.152532	−	0.0416406i
$841$	5.24911			0.181004
$842$	−5.43872	+	3.14004i	−0.187431	+	0.108213i
$843$	−32.6331	−	9.31155i	−1.12394	−	0.320707i
$844$	−11.4360	+	19.8078i	−0.393644	+	0.681812i
$845$	5.30042	+	9.18059i	0.182340	+	0.315822i
$846$	13.8751	+	25.9326i	0.477036	+	0.891581i
$847$	24.8102	−	15.0226i	0.852488	−	0.516183i
$848$		−	0.0649809i		−	0.00223145i
$849$	18.7873	−	18.1899i	0.644778	−	0.624276i
$850$	−0.458589	−	0.264766i	−0.0157295	−	0.00908141i
$851$	6.48953	+	3.74673i	0.222458	+	0.128436i
$852$	−7.82837	+	7.57944i	−0.268196	+	0.259667i
$853$		−	3.93413i		−	0.134702i	−0.997729	−	0.0673510i	$-0.978545\pi$
$853$		−	3.93413i		−	0.134702i	0.997729	−	0.0673510i	$-0.0214547\pi$
$854$	−9.93662	−	5.46383i	−0.340024	−	0.186969i
$855$	9.04275	+	16.9009i	0.309256	+	0.577999i
$856$	−8.90681	−	15.4270i	−0.304429	−	0.527286i
$857$	4.49804	−	7.79083i	0.153650	−	0.266130i	−0.778917	−	0.627128i	$-0.784230\pi$
$857$	4.49804	−	7.79083i	0.153650	−	0.266130i	0.932567	+	0.360998i	$0.117564\pi$
$858$	−0.500032	−	0.142679i	−0.0170708	−	0.00487099i
$859$	35.2001	−	20.3228i	1.20101	−	0.693404i	0.240231	−	0.970716i	$-0.422777\pi$
$859$	35.2001	−	20.3228i	1.20101	−	0.693404i	0.960780	+	0.277312i	$0.0894435\pi$
$860$	11.4865			0.391687
$861$	−43.9461	−	11.5541i	−1.49768	−	0.393763i
$862$	4.55329			0.155086
$863$	28.7932	−	16.6238i	0.980133	−	0.565880i	0.0778229	−	0.996967i	$-0.475203\pi$
$863$	28.7932	−	16.6238i	0.980133	−	0.565880i	0.902310	+	0.431087i	$0.141870\pi$
$864$	5.07836	−	1.10013i	0.172769	−	0.0374273i
$865$	3.80403	−	6.58878i	0.129341	−	0.224025i
$866$	1.31401	+	2.27592i	0.0446517	+	0.0773391i
$867$	−28.0899	+	7.04235i	−0.953981	+	0.239171i
$868$	12.6995	+	20.9734i	0.431047	+	0.711884i
$869$			1.31366i			0.0445629i
$870$	−5.87158	−	6.06442i	−0.199065	−	0.205603i
$871$	−6.47977	−	3.74110i	−0.219559	−	0.126762i
$872$	−0.128001	−	0.0739017i	−0.00433468	−	0.00250263i
$873$	−13.0524	+	21.0095i	−0.441758	+	0.711063i
$874$			27.1531i			0.918467i
$875$	−0.0551777	−	2.64518i	−0.00186535	−	0.0894233i
$876$	−3.40825	−	13.5945i	−0.115154	−	0.459317i
$877$	−14.1314	−	24.4763i	−0.477184	−	0.826506i	0.522474	−	0.852655i	$-0.325009\pi$
$877$	−14.1314	−	24.4763i	−0.477184	−	0.826506i	−0.999658	+	0.0261486i	$0.991676\pi$
$878$	2.91836	−	5.05475i	0.0984899	−	0.170590i
$879$	3.80458	−	13.3335i	0.128325	−	0.449727i
$880$	−0.167855	+	0.0969112i	−0.00565840	+	0.00326688i
$881$	−34.2140			−1.15270			−0.576350	−	0.817203i	$-0.695523\pi$
$881$	−34.2140			−1.15270			−0.576350	+	0.817203i	$0.695523\pi$
$882$	−20.9991	+	0.197483i	−0.707076	+	0.00664960i
$883$	4.09672			0.137866			0.0689328	−	0.997621i	$-0.478041\pi$
$883$	4.09672			0.137866			0.0689328	+	0.997621i	$0.478041\pi$
$884$	0.710319	−	0.410103i	0.0238906	−	0.0137932i
$885$	−5.71609	+	20.0325i	−0.192144	+	0.673386i
$886$	−13.1730	+	22.8164i	−0.442557	+	0.766531i
$887$	0.926997	+	1.60561i	0.0311255	+	0.0539110i	0.881169	−	0.472802i	$-0.156758\pi$
$887$	0.926997	+	1.60561i	0.0311255	+	0.0539110i	−0.850043	+	0.526713i	$0.823424\pi$
$888$	0.742694	+	2.96239i	0.0249232	+	0.0994113i
$889$	0.303458	+	14.5475i	0.0101777	+	0.487909i
$890$		−	16.3755i		−	0.548907i
$891$	0.112643	−	1.74076i	0.00377367	−	0.0583177i
$892$	0.00542376	+	0.00313141i	0.000181601	+	0.000104847i
$893$	−54.2472	−	31.3196i	−1.81531	−	1.04807i
$894$	−15.3733	−	15.8782i	−0.514159	−	0.531046i
$895$		−	16.2259i		−	0.542372i
$896$	1.37037	+	2.26320i	0.0457810	+	0.0756082i
$897$	11.0590	−	2.77259i	0.369251	−	0.0925740i
$898$	2.88319	+	4.99383i	0.0962134	+	0.166646i
$899$	22.5817	−	39.1126i	0.753141	−	1.30448i
$900$	0.0969112	−	2.99843i	0.00323037	−	0.0999478i
$901$	0.0297995	−	0.0172048i	0.000992766	−	0.000573174i
$902$	1.92189			0.0639920
$903$	−50.9077	−	13.3844i	−1.69410	−	0.445406i
$904$	−3.44771			−0.114669
$905$	−3.49141	+	2.01577i	−0.116058	+	0.0670063i
$906$	−29.1479	−	8.31709i	−0.968375	−	0.276317i
$907$	−16.8711	+	29.2217i	−0.560197	+	0.970289i	0.437282	+	0.899324i	$0.355941\pi$
$907$	−16.8711	+	29.2217i	−0.560197	+	0.970289i	−0.997479	+	0.0709647i	$0.977392\pi$
$908$	9.41373	+	16.3051i	0.312406	+	0.541102i
$909$	−11.7886	+	6.30742i	−0.391002	+	0.209204i
$910$	3.59099	+	1.97457i	0.119040	+	0.0654564i
$911$			6.90180i			0.228667i	0.993442	+	0.114333i	$0.0364732\pi$
$911$			6.90180i			0.228667i	−0.993442	+	0.114333i	$0.963527\pi$
$912$	−7.95069	+	7.69787i	−0.263274	+	0.254902i
$913$	0.354234	+	0.204517i	0.0117234	+	0.00676853i
$914$	−0.624848	−	0.360756i	−0.0206682	−	0.0119328i
$915$	−5.33340	+	5.16380i	−0.176317	+	0.170710i
$916$		−	7.79658i		−	0.257606i
$917$	13.5721	−	8.21795i	0.448191	−	0.271381i
$918$	1.84909	+	2.03760i	0.0610290	+	0.0672508i
$919$	17.5128	+	30.3330i	0.577693	+	1.00059i	0.995743	+	0.0921698i	$0.0293803\pi$
$919$	17.5128	+	30.3330i	0.577693	+	1.00059i	−0.418050	+	0.908424i	$0.637286\pi$
$920$	2.12488	−	3.68040i	0.0700552	−	0.121339i
$921$	−7.22297	−	2.06101i	−0.238005	−	0.0679125i
$922$	29.7646	−	17.1846i	0.980243	−	0.565944i
$923$	−9.74433			−0.320738
$924$	0.856851	−	0.233916i	0.0281883	−	0.00769528i
$925$	1.76327			0.0579759
$926$	−35.8374	+	20.6908i	−1.17769	+	0.679940i
$927$	−25.2524	−	0.816174i	−0.829399	−	0.0268067i
$928$	2.43674	−	4.22056i	0.0799900	−	0.138547i
$929$	10.5447	+	18.2639i	0.345960	+	0.599220i	0.985528	−	0.169515i	$-0.0542201\pi$
$929$	10.5447	+	18.2639i	0.345960	+	0.599220i	−0.639568	+	0.768734i	$0.720887\pi$
$930$	15.5693	−	3.90335i	0.510538	−	0.127996i
$931$	37.7670	−	23.9584i	1.23776	−	0.785206i
$932$		−	12.9944i		−	0.425645i
$933$	−27.5157	−	28.4194i	−0.900824	−	0.930409i
$934$	15.5598	+	8.98343i	0.509131	+	0.293947i
$935$	−0.0888848	−	0.0513177i	−0.00290684	−	0.00167827i
$936$	3.94707	+	2.45217i	0.129014	+	0.0801517i
$937$		−	44.5007i		−	1.45378i	−0.686756	−	0.726888i	$-0.740966\pi$
$937$		−	44.5007i		−	1.45378i	0.686756	−	0.726888i	$-0.259034\pi$
$938$	12.7777	−	0.266540i	0.417208	−	0.00870285i
$939$	10.6582	+	42.5125i	0.347818	+	1.38734i
$940$	4.90186	+	8.49028i	0.159881	+	0.276922i
$941$	21.8197	−	37.7929i	0.711303	−	1.23201i	−0.253065	−	0.967449i	$-0.581439\pi$
$941$	21.8197	−	37.7929i	0.711303	−	1.23201i	0.964368	−	0.264564i	$-0.0852280\pi$
$942$	−1.35262	+	4.74037i	−0.0440707	+	0.154450i
$943$	−36.4938	+	21.0697i	−1.18840	+	0.686125i
$944$	−12.0274			−0.391459
$945$	−3.92338	+	13.1760i	−0.127627	+	0.428615i
$946$	2.22634			0.0723846
$947$	11.1646	−	6.44589i	0.362801	−	0.209463i	−0.307508	−	0.951546i	$-0.599495\pi$
$947$	11.1646	−	6.44589i	0.362801	−	0.209463i	0.670309	+	0.742082i	$0.266162\pi$
$948$	3.22112	−	11.2887i	0.104617	−	0.366639i
$949$	6.26672	−	10.8543i	0.203426	−	0.352345i
$950$	3.19467	+	5.53332i	0.103649	+	0.179525i
$951$	6.35586	+	25.3517i	0.206103	+	0.822084i
$952$	−0.675050	+	1.22766i	−0.0218785	+	0.0397886i
$953$			47.2228i			1.52970i	0.644211	+	0.764848i	$0.277186\pi$
$953$			47.2228i			1.52970i	−0.644211	+	0.764848i	$0.722814\pi$
$954$	0.165589	+	0.102874i	0.00536113	+	0.00333068i
$955$	21.8544	+	12.6176i	0.707191	+	0.408297i
$956$	−14.8705	−	8.58548i	−0.480946	−	0.277674i
$957$	−1.13804	−	1.17542i	−0.0367877	−	0.0379960i
$958$			9.01118i			0.291138i
$959$	−1.09902	+	1.99870i	−0.0354893	+	0.0645414i
$960$	1.68006	−	0.421203i	0.0542236	−	0.0135943i
$961$	27.4400	+	47.5275i	0.885162	+	1.53315i
$962$	−1.36558	+	2.36526i	−0.0440282	+	0.0762590i
$963$	53.4130	+	1.72634i	1.72121	+	0.0556305i
$964$	7.10695	−	4.10320i	0.228899	−	0.132155i
$965$	−25.2366			−0.812396
$966$	−13.7059	+	13.8354i	−0.440980	+	0.445146i
$967$	−7.93428			−0.255149			−0.127575	−	0.991829i	$-0.540719\pi$
$967$	−7.93428			−0.255149			−0.127575	+	0.991829i	$0.540719\pi$
$968$	9.49375	−	5.48122i	0.305141	−	0.176173i
$969$	−5.63523	−	1.60796i	−0.181030	−	0.0516551i
$970$	−4.12231	+	7.14006i	−0.132359	+	0.229253i
$971$	−16.7632	−	29.0348i	−0.537958	−	0.931770i	−0.999014	−	0.0443991i	$-0.985863\pi$
$971$	−16.7632	−	29.0348i	−0.537958	−	0.931770i	0.461056	−	0.887371i	$-0.347471\pi$
$972$	−5.23634	+	14.6827i	−0.167956	+	0.470947i
$973$	−42.8104	+	0.893014i	−1.37244	+	0.0286287i
$974$			22.7295i			0.728302i
$975$	1.92743	−	1.86614i	0.0617272	−	0.0597644i
$976$	−3.71180	−	2.14301i	−0.118812	−	0.0685961i
$977$	−11.4767	−	6.62608i	−0.367172	−	0.211987i	0.305050	−	0.952336i	$-0.401327\pi$
$977$	−11.4767	−	6.62608i	−0.367172	−	0.211987i	−0.672222	+	0.740349i	$0.734660\pi$
$978$	−15.3787	+	14.8897i	−0.491757	+	0.476120i
$979$		−	3.17393i		−	0.101439i
$980$	−6.99391	+	0.291909i	−0.223412	+	0.00932471i
$981$	0.390966	−	0.209185i	0.0124826	−	0.00667875i
$982$	16.0827	+	27.8560i	0.513219	+	0.888921i
$983$	−21.9739	+	38.0599i	−0.700858	+	1.21392i	0.267307	+	0.963611i	$0.413866\pi$
$983$	−21.9739	+	38.0599i	−0.700858	+	1.21392i	−0.968165	+	0.250311i	$0.919467\pi$
$984$	−16.5154	−	4.71250i	−0.526491	−	0.150229i
$985$	12.7621	−	7.36822i	0.406635	−	0.234771i
$986$	2.58067			0.0821853
$987$	−11.8317	−	43.3403i	−0.376607	−	1.37954i
$988$	−9.89658			−0.314852
$989$	−42.2749	+	24.4074i	−1.34426	+	0.776111i
$990$	0.0187836	−	0.581164i	0.000596981	−	0.0184706i
$991$	−5.43257	+	9.40948i	−0.172571	+	0.298902i	−0.939318	−	0.343047i	$-0.888541\pi$
$991$	−5.43257	+	9.40948i	−0.172571	+	0.298902i	0.766747	+	0.641950i	$0.221874\pi$
$992$	4.63357	+	8.02559i	0.147116	+	0.254813i
$993$	25.3045	−	6.34404i	0.803015	−	0.201322i
$994$	14.2379	−	8.62106i	0.451598	−	0.273444i
$995$			25.8642i			0.819952i
$996$	−2.54256	−	2.62606i	−0.0805640	−	0.0832100i
$997$	−34.8191	−	20.1028i	−1.10273	−	0.636662i	−0.165794	−	0.986160i	$-0.553019\pi$
$997$	−34.8191	−	20.1028i	−1.10273	−	0.636662i	−0.936937	+	0.349499i	$0.886352\pi$
$998$	18.4037	+	10.6254i	0.582560	+	0.336341i
$999$	−8.72474	−	2.79731i	−0.276039	−	0.0885030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.r.a.101.2	✓	12
3.2	odd	2		210.2.r.b.101.6	yes	12
5.2	odd	4		1050.2.u.f.899.5		12
5.3	odd	4		1050.2.u.g.899.2		12
5.4	even	2		1050.2.s.g.101.5		12
7.3	odd	6		1470.2.b.a.881.1		12
7.4	even	3		1470.2.b.b.881.6		12
7.5	odd	6		210.2.r.b.131.6	yes	12
15.2	even	4		1050.2.u.h.899.2		12
15.8	even	4		1050.2.u.e.899.5		12
15.14	odd	2		1050.2.s.f.101.1		12
21.5	even	6	inner	210.2.r.a.131.2	yes	12
21.11	odd	6		1470.2.b.a.881.7		12
21.17	even	6		1470.2.b.b.881.12		12
35.12	even	12		1050.2.u.e.299.5		12
35.19	odd	6		1050.2.s.f.551.1		12
35.33	even	12		1050.2.u.h.299.2		12
105.47	odd	12		1050.2.u.g.299.2		12
105.68	odd	12		1050.2.u.f.299.5		12
105.89	even	6		1050.2.s.g.551.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.2	✓	12	1.1	even	1	trivial
210.2.r.a.131.2	yes	12	21.5	even	6	inner
210.2.r.b.101.6	yes	12	3.2	odd	2
210.2.r.b.131.6	yes	12	7.5	odd	6
1050.2.s.f.101.1		12	15.14	odd	2
1050.2.s.f.551.1		12	35.19	odd	6
1050.2.s.g.101.5		12	5.4	even	2
1050.2.s.g.551.5		12	105.89	even	6
1050.2.u.e.299.5		12	35.12	even	12
1050.2.u.e.899.5		12	15.8	even	4
1050.2.u.f.299.5		12	105.68	odd	12
1050.2.u.f.899.5		12	5.2	odd	4
1050.2.u.g.299.2		12	105.47	odd	12
1050.2.u.g.899.2		12	5.3	odd	4
1050.2.u.h.299.2		12	35.33	even	12
1050.2.u.h.899.2		12	15.2	even	4
1470.2.b.a.881.1		12	7.3	odd	6
1470.2.b.a.881.7		12	21.11	odd	6
1470.2.b.b.881.6		12	7.4	even	3
1470.2.b.b.881.12		12	21.17	even	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.475255 + 1.66557i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.421203 - 1.68006i) q^{6} +(0.0551777 + 2.64518i) q^{7} +1.00000i q^{8} +(-2.54826 - 1.58314i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.475255 + 1.66557i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.421203 - 1.68006i) q^{6} +(0.0551777 + 2.64518i) q^{7} +1.00000i q^{8} +(-2.54826 - 1.58314i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-0.167855 - 0.0969112i) q^{11} +(1.20480 + 1.24437i) q^{12} +1.54892i q^{13} +(-1.37037 - 2.26320i) q^{14} +(-1.68006 + 0.421203i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.264766 - 0.458589i) q^{17} +(2.99843 + 0.0969112i) q^{18} +(-5.53332 + 3.19467i) q^{19} +1.00000 q^{20} +(-4.43196 - 1.16523i) q^{21} +0.193822 q^{22} +(-3.68040 + 2.12488i) q^{23} +(-1.66557 - 0.475255i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.774462 - 1.34141i) q^{26} +(3.84792 - 3.49192i) q^{27} +(2.31838 + 1.27480i) q^{28} -4.87349i q^{29} +(1.24437 - 1.20480i) q^{30} +(8.02559 + 4.63357i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.241187 - 0.233517i) q^{33} +0.529533i q^{34} +(-2.26320 + 1.37037i) q^{35} +(-2.64518 + 1.41529i) q^{36} +(-0.881634 - 1.52704i) q^{37} +(3.19467 - 5.53332i) q^{38} +(-2.57984 - 0.736134i) q^{39} +(-0.866025 + 0.500000i) q^{40} +9.91573 q^{41} +(4.42080 - 1.20686i) q^{42} +11.4865 q^{43} +(-0.167855 + 0.0969112i) q^{44} +(0.0969112 - 2.99843i) q^{45} +(2.12488 - 3.68040i) q^{46} +(4.90186 + 8.49028i) q^{47} +(1.68006 - 0.421203i) q^{48} +(-6.99391 + 0.291909i) q^{49} -1.00000i q^{50} +(0.637981 + 0.658934i) q^{51} +(1.34141 + 0.774462i) q^{52} +(0.0562751 + 0.0324905i) q^{53} +(-1.58643 + 4.94805i) q^{54} -0.193822i q^{55} +(-2.64518 + 0.0551777i) q^{56} +(-2.69121 - 10.7344i) q^{57} +(2.43674 + 4.22056i) q^{58} +(6.01371 - 10.4160i) q^{59} +(-0.475255 + 1.66557i) q^{60} +(3.71180 - 2.14301i) q^{61} -9.26715 q^{62} +(4.04709 - 6.82796i) q^{63} -1.00000 q^{64} +(-1.34141 + 0.774462i) q^{65} +(-0.0921151 + 0.322825i) q^{66} +(-2.41529 + 4.18340i) q^{67} +(-0.264766 - 0.458589i) q^{68} +(-1.79001 - 7.13983i) q^{69} +(1.27480 - 2.31838i) q^{70} +6.29103i q^{71} +(1.58314 - 2.54826i) q^{72} +(-7.00763 - 4.04586i) q^{73} +(1.52704 + 0.881634i) q^{74} +(-1.20480 - 1.24437i) q^{75} +6.38933i q^{76} +(0.247085 - 0.449354i) q^{77} +(2.60228 - 0.652411i) q^{78} +(-3.38883 - 5.86962i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.98731 + 8.06854i) q^{81} +(-8.58728 + 4.95787i) q^{82} -2.11036 q^{83} +(-3.22510 + 3.25557i) q^{84} +0.529533 q^{85} +(-9.94760 + 5.74325i) q^{86} +(8.11715 + 2.31615i) q^{87} +(0.0969112 - 0.167855i) q^{88} +(8.18773 + 14.1816i) q^{89} +(1.41529 + 2.64518i) q^{90} +(-4.09717 + 0.0854660i) q^{91} +4.24976i q^{92} +(-11.5318 + 11.1651i) q^{93} +(-8.49028 - 4.90186i) q^{94} +(-5.53332 - 3.19467i) q^{95} +(-1.24437 + 1.20480i) q^{96} -8.24463i q^{97} +(5.91095 - 3.74976i) q^{98} +(0.274315 + 0.512694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

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