LMFDB - Embedded newform 370.2.l.c.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.116304318664704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 6x^9 - 9x^8 - 2x^7 + 18x^6 - 4x^5 - 36x^4 + 48x^3 + 16x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$0.828615 - 1.14604i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.c.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +2.81361i q^{6} +(-0.712432 - 1.23397i) q^{7} +1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +2.81361i q^{6} +(-0.712432 - 1.23397i) q^{7} +1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +1.00000 q^{10} +0.135694 q^{11} +(-1.40680 + 2.43665i) q^{12} +(2.09999 - 1.21243i) q^{13} -1.42486i q^{14} +(2.43665 + 1.40680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.46516 - 1.42326i) q^{17} +(-4.25771 + 2.45819i) q^{18} +(-2.07501 + 1.19801i) q^{19} +(0.866025 + 0.500000i) q^{20} +(2.00450 - 3.47190i) q^{21} +(0.117515 + 0.0678472i) q^{22} -3.45016i q^{23} +(-2.43665 + 1.40680i) q^{24} +(0.500000 - 0.866025i) q^{25} +2.42486 q^{26} -5.39194 q^{27} +(0.712432 - 1.23397i) q^{28} -2.74145i q^{29} +(1.40680 + 2.43665i) q^{30} -4.04405i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.190895 + 0.330641i) q^{33} +(-1.42326 - 2.46516i) q^{34} +(-1.23397 - 0.712432i) q^{35} -4.91638 q^{36} +(-5.97276 - 1.15156i) q^{37} -2.39602 q^{38} +(5.90855 + 3.41131i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-0.490256 - 0.849148i) q^{41} +(3.47190 - 2.00450i) q^{42} +11.8861i q^{43} +(0.0678472 + 0.117515i) q^{44} +4.91638i q^{45} +(1.72508 - 2.98792i) q^{46} +0.163866 q^{47} -2.81361 q^{48} +(2.48488 - 4.30394i) q^{49} +(0.866025 - 0.500000i) q^{50} -8.00900i q^{51} +(2.09999 + 1.21243i) q^{52} +(0.462004 - 0.800215i) q^{53} +(-4.66956 - 2.69597i) q^{54} +(0.117515 - 0.0678472i) q^{55} +(1.23397 - 0.712432i) q^{56} +(-5.83827 - 3.37072i) q^{57} +(1.37072 - 2.37416i) q^{58} +(12.5215 + 7.22929i) q^{59} +2.81361i q^{60} +(8.11798 - 4.68692i) q^{61} +(2.02202 - 3.50225i) q^{62} +7.00517 q^{63} -1.00000 q^{64} +(1.21243 - 2.09999i) q^{65} +0.381791i q^{66} +(3.94640 + 6.83536i) q^{67} -2.84653i q^{68} +(8.40684 - 4.85369i) q^{69} +(-0.712432 - 1.23397i) q^{70} +(-2.98434 - 5.16904i) q^{71} +(-4.25771 - 2.45819i) q^{72} -9.17382 q^{73} +(-4.59679 - 3.98366i) q^{74} +2.81361 q^{75} +(-2.07501 - 1.19801i) q^{76} +(-0.0966730 - 0.167443i) q^{77} +(3.41131 + 5.90855i) q^{78} +(4.63367 - 2.67525i) q^{79} +1.00000i q^{80} +(-0.210831 - 0.365171i) q^{81} -0.980511i q^{82} +(-6.00344 + 10.3983i) q^{83} +4.00900 q^{84} -2.84653 q^{85} +(-5.94307 + 10.2937i) q^{86} +(6.67996 - 3.85668i) q^{87} +0.135694i q^{88} +(-8.45591 - 4.88202i) q^{89} +(-2.45819 + 4.25771i) q^{90} +(-2.99220 - 1.72755i) q^{91} +(2.98792 - 1.72508i) q^{92} +(9.85395 - 5.68918i) q^{93} +(0.141912 + 0.0819332i) q^{94} +(-1.19801 + 2.07501i) q^{95} +(-2.43665 - 1.40680i) q^{96} -14.5305i q^{97} +(4.30394 - 2.48488i) q^{98} +(-0.333563 + 0.577748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	1.40680	+	2.43665i	0.812218	+	1.40680i	0.911308	+	0.411725i	$0.135073\pi$
$3$	1.40680	+	2.43665i	0.812218	+	1.40680i	−0.0990900	+	0.995078i	$0.531593\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$			2.81361i			1.14865i
$7$	−0.712432	−	1.23397i	−0.269274	−	0.466396i	0.699401	−	0.714730i	$-0.253450\pi$
$7$	−0.712432	−	1.23397i	−0.269274	−	0.466396i	−0.968674	+	0.248334i	$0.920117\pi$
$8$			1.00000i			0.353553i
$9$	−2.45819	+	4.25771i	−0.819397	+	1.41924i
$10$	1.00000			0.316228
$11$	0.135694			0.0409134			0.0204567	−	0.999791i	$-0.493488\pi$
$11$	0.135694			0.0409134			0.0204567	+	0.999791i	$0.493488\pi$
$12$	−1.40680	+	2.43665i	−0.406109	+	0.703402i
$13$	2.09999	−	1.21243i	0.582433	−	0.336268i	−0.179667	−	0.983728i	$-0.557502\pi$
$13$	2.09999	−	1.21243i	0.582433	−	0.336268i	0.762100	+	0.647460i	$0.224169\pi$
$14$		−	1.42486i		−	0.380811i
$15$	2.43665	+	1.40680i	0.629142	+	0.363235i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.46516	−	1.42326i	−0.597890	−	0.345192i	0.170321	−	0.985389i	$-0.445520\pi$
$17$	−2.46516	−	1.42326i	−0.597890	−	0.345192i	−0.768211	+	0.640197i	$0.778853\pi$
$18$	−4.25771	+	2.45819i	−1.00355	+	0.579401i
$19$	−2.07501	+	1.19801i	−0.476040	+	0.274842i	−0.718765	−	0.695253i	$-0.755292\pi$
$19$	−2.07501	+	1.19801i	−0.476040	+	0.274842i	0.242725	+	0.970095i	$0.421959\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	2.00450	−	3.47190i	0.437418	−	0.757631i
$22$	0.117515	+	0.0678472i	0.0250543	+	0.0144651i
$23$		−	3.45016i		−	0.719407i	−0.933067	−	0.359704i	$-0.882878\pi$
$23$		−	3.45016i		−	0.719407i	0.933067	−	0.359704i	$-0.117122\pi$
$24$	−2.43665	+	1.40680i	−0.497380	+	0.287163i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.42486			0.475555
$27$	−5.39194			−1.03768
$28$	0.712432	−	1.23397i	0.134637	−	0.233198i
$29$		−	2.74145i		−	0.509074i	−0.967063	−	0.254537i	$-0.918077\pi$
$29$		−	2.74145i		−	0.509074i	0.967063	−	0.254537i	$-0.0819231\pi$
$30$	1.40680	+	2.43665i	0.256846	+	0.444870i
$31$		−	4.04405i		−	0.726332i	−0.931724	−	0.363166i	$-0.881696\pi$
$31$		−	4.04405i		−	0.726332i	0.931724	−	0.363166i	$-0.118304\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.190895	+	0.330641i	0.0332306	+	0.0575571i
$34$	−1.42326	−	2.46516i	−0.244088	−	0.422772i
$35$	−1.23397	−	0.712432i	−0.208579	−	0.120423i
$36$	−4.91638			−0.819397
$37$	−5.97276	−	1.15156i	−0.981916	−	0.189315i
$37$	−5.97276	−	1.15156i	−0.981916	−	0.189315i
$38$	−2.39602			−0.388685
$39$	5.90855	+	3.41131i	0.946126	+	0.546246i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−0.490256	−	0.849148i	−0.0765651	−	0.132615i	0.825201	−	0.564840i	$-0.191062\pi$
$41$	−0.490256	−	0.849148i	−0.0765651	−	0.132615i	−0.901766	+	0.432225i	$0.857729\pi$
$42$	3.47190	−	2.00450i	0.535726	−	0.309301i
$43$			11.8861i			1.81262i	0.422613	+	0.906310i	$0.361113\pi$
$43$			11.8861i			1.81262i	−0.422613	+	0.906310i	$0.638887\pi$
$44$	0.0678472	+	0.117515i	0.0102284	+	0.0177160i
$45$			4.91638i			0.732891i
$46$	1.72508	−	2.98792i	0.254349	−	0.440545i
$47$	0.163866			0.0239024			0.0119512	−	0.999929i	$-0.496196\pi$
$47$	0.163866			0.0239024			0.0119512	+	0.999929i	$0.496196\pi$
$48$	−2.81361			−0.406109
$49$	2.48488	−	4.30394i	0.354983	−	0.614849i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	8.00900i		−	1.12148i
$52$	2.09999	+	1.21243i	0.291217	+	0.168134i
$53$	0.462004	−	0.800215i	0.0634612	−	0.109918i	−0.832549	−	0.553951i	$-0.813119\pi$
$53$	0.462004	−	0.800215i	0.0634612	−	0.109918i	0.896010	+	0.444033i	$0.146453\pi$
$54$	−4.66956	−	2.69597i	−0.635447	−	0.366875i
$55$	0.117515	−	0.0678472i	0.0158457	−	0.00914852i
$56$	1.23397	−	0.712432i	0.164896	−	0.0952027i
$57$	−5.83827	−	3.37072i	−0.773297	−	0.446463i
$58$	1.37072	−	2.37416i	0.179985	−	0.311743i
$59$	12.5215	+	7.22929i	1.63016	+	0.941174i	0.984042	+	0.177937i	$0.0569424\pi$
$59$	12.5215	+	7.22929i	1.63016	+	0.941174i	0.646119	+	0.763237i	$0.276391\pi$
$60$			2.81361i			0.363235i
$61$	8.11798	−	4.68692i	1.03940	−	0.600098i	0.119737	−	0.992806i	$-0.461795\pi$
$61$	8.11798	−	4.68692i	1.03940	−	0.600098i	0.919663	+	0.392708i	$0.128462\pi$
$62$	2.02202	−	3.50225i	0.256797	−	0.444786i
$63$	7.00517			0.882569
$64$	−1.00000			−0.125000
$65$	1.21243	−	2.09999i	0.150384	−	0.260472i
$66$			0.381791i			0.0469952i
$67$	3.94640	+	6.83536i	0.482129	+	0.835073i	0.999790	−	0.0205137i	$-0.00653018\pi$
$67$	3.94640	+	6.83536i	0.482129	+	0.835073i	−0.517660	+	0.855586i	$0.673197\pi$
$68$		−	2.84653i		−	0.345192i
$69$	8.40684	−	4.85369i	1.01206	−	0.584316i
$70$	−0.712432	−	1.23397i	−0.0851519	−	0.147487i
$71$	−2.98434	−	5.16904i	−0.354177	−	0.613452i	0.632800	−	0.774315i	$-0.281905\pi$
$71$	−2.98434	−	5.16904i	−0.354177	−	0.613452i	−0.986977	+	0.160863i	$0.948572\pi$
$72$	−4.25771	−	2.45819i	−0.501776	−	0.289701i
$73$	−9.17382			−1.07371			−0.536857	−	0.843673i	$-0.680389\pi$
$73$	−9.17382			−1.07371			−0.536857	+	0.843673i	$0.680389\pi$
$74$	−4.59679	−	3.98366i	−0.534366	−	0.463091i
$75$	2.81361			0.324887
$76$	−2.07501	−	1.19801i	−0.238020	−	0.137421i
$77$	−0.0966730	−	0.167443i	−0.0110169	−	0.0190819i
$78$	3.41131	+	5.90855i	0.386254	+	0.669012i
$79$	4.63367	−	2.67525i	0.521328	−	0.300989i	−0.216150	−	0.976360i	$-0.569350\pi$
$79$	4.63367	−	2.67525i	0.521328	−	0.300989i	0.737478	+	0.675371i	$0.236017\pi$
$80$			1.00000i			0.111803i
$81$	−0.210831	−	0.365171i	−0.0234257	−	0.0405745i
$82$		−	0.980511i		−	0.108279i
$83$	−6.00344	+	10.3983i	−0.658963	+	1.14136i	0.321921	+	0.946766i	$0.395671\pi$
$83$	−6.00344	+	10.3983i	−0.658963	+	1.14136i	−0.980884	+	0.194591i	$0.937662\pi$
$84$	4.00900			0.437418
$85$	−2.84653			−0.308749
$86$	−5.94307	+	10.2937i	−0.640858	+	1.11000i
$87$	6.67996	−	3.85668i	0.716167	−	0.413479i
$88$			0.135694i			0.0144651i
$89$	−8.45591	−	4.88202i	−0.896325	−	0.517493i	−0.0203188	−	0.999794i	$-0.506468\pi$
$89$	−8.45591	−	4.88202i	−0.896325	−	0.517493i	−0.876006	+	0.482300i	$0.839801\pi$
$90$	−2.45819	+	4.25771i	−0.259116	+	0.448802i
$91$	−2.99220	−	1.72755i	−0.313668	−	0.181096i
$92$	2.98792	−	1.72508i	0.311512	−	0.179852i
$93$	9.85395	−	5.68918i	1.02181	−	0.589940i
$94$	0.141912	+	0.0819332i	0.0146372	+	0.00845076i
$95$	−1.19801	+	2.07501i	−0.122913	+	0.212892i
$96$	−2.43665	−	1.40680i	−0.248690	−	0.143581i
$97$		−	14.5305i		−	1.47535i	−0.675156	−	0.737675i	$-0.735924\pi$
$97$		−	14.5305i		−	1.47535i	0.675156	−	0.737675i	$-0.264076\pi$
$98$	4.30394	−	2.48488i	0.434764	−	0.251011i
$99$	−0.333563	+	0.577748i	−0.0335243	+	0.0580659i
$100$	1.00000			0.100000
$101$	−10.2395			−1.01886			−0.509432	−	0.860511i	$-0.670145\pi$
$101$	−10.2395			−1.01886			−0.509432	+	0.860511i	$0.670145\pi$
$102$	4.00450	−	6.93600i	0.396505	−	0.686766i
$103$			18.9067i			1.86293i	0.363826	+	0.931467i	$0.381470\pi$
$103$			18.9067i			1.86293i	−0.363826	+	0.931467i	$0.618530\pi$
$104$	1.21243	+	2.09999i	0.118889	+	0.205921i
$105$		−	4.00900i		−	0.391239i
$106$	0.800215	−	0.462004i	0.0777237	−	0.0448738i
$107$	−6.32318	−	10.9521i	−0.611285	−	1.05878i	−0.991024	−	0.133684i	$-0.957319\pi$
$107$	−6.32318	−	10.9521i	−0.611285	−	1.05878i	0.379739	−	0.925094i	$-0.376014\pi$
$108$	−2.69597	−	4.66956i	−0.259420	−	0.449329i
$109$	10.6071	+	6.12399i	1.01597	+	0.586572i	0.912935	−	0.408105i	$-0.133810\pi$
$109$	10.6071	+	6.12399i	1.01597	+	0.586572i	0.103038	+	0.994677i	$0.467144\pi$
$110$	0.135694			0.0129380
$111$	−5.59656	−	16.1736i	−0.531202	−	1.53513i
$112$	1.42486			0.134637
$113$	−4.17418	−	2.40996i	−0.392674	−	0.226710i	0.290644	−	0.956831i	$-0.406130\pi$
$113$	−4.17418	−	2.40996i	−0.392674	−	0.226710i	−0.683318	+	0.730121i	$0.739464\pi$
$114$	−3.37072	−	5.83827i	−0.315697	−	0.546804i
$115$	−1.72508	−	2.98792i	−0.160864	−	0.278625i
$116$	2.37416	−	1.37072i	0.220436	−	0.127269i
$117$			11.9216i			1.10215i
$118$	7.22929	+	12.5215i	0.665510	+	1.15270i
$119$			4.05591i			0.371805i
$120$	−1.40680	+	2.43665i	−0.128423	+	0.222435i
$121$	−10.9816			−0.998326
$122$	9.37383			0.848667
$123$	1.37939	−	2.38917i	0.124375	−	0.215424i
$124$	3.50225	−	2.02202i	0.314511	−	0.181583i
$125$		−	1.00000i		−	0.0894427i
$126$	6.06666	+	3.50259i	0.540461	+	0.312035i
$127$	−3.46769	+	6.00621i	−0.307708	+	0.532965i	−0.977860	−	0.209258i	$-0.932895\pi$
$127$	−3.46769	+	6.00621i	−0.307708	+	0.532965i	0.670153	+	0.742223i	$0.266229\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−28.9624	+	16.7215i	−2.55000	+	1.47224i
$130$	2.09999	−	1.21243i	0.184182	−	0.106337i
$131$	−16.0549	−	9.26933i	−1.40273	−	0.809865i	−0.408055	−	0.912957i	$-0.633793\pi$
$131$	−16.0549	−	9.26933i	−1.40273	−	0.809865i	−0.994672	+	0.103092i	$0.967126\pi$
$132$	−0.190895	+	0.330641i	−0.0166153	+	0.0287786i
$133$	2.95661	+	1.70700i	0.256370	+	0.148015i
$134$			7.89280i			0.681834i
$135$	−4.66956	+	2.69597i	−0.401892	+	0.232032i
$136$	1.42326	−	2.46516i	0.122044	−	0.211386i
$137$	3.81263			0.325735			0.162868	−	0.986648i	$-0.447926\pi$
$137$	3.81263			0.325735			0.162868	+	0.986648i	$0.447926\pi$
$138$	9.70738			0.826347
$139$	4.93152	−	8.54164i	0.418286	−	0.724493i	−0.577481	−	0.816404i	$-0.695964\pi$
$139$	4.93152	−	8.54164i	0.418286	−	0.724493i	0.995767	+	0.0919114i	$0.0292976\pi$
$140$		−	1.42486i		−	0.120423i
$141$	0.230528	+	0.399286i	0.0194139	+	0.0336259i
$142$		−	5.96869i		−	0.500881i
$143$	0.284957	−	0.164520i	0.0238293	−	0.0137579i
$144$	−2.45819	−	4.25771i	−0.204849	−	0.354809i
$145$	−1.37072	−	2.37416i	−0.113832	−	0.197164i
$146$	−7.94477	−	4.58691i	−0.657513	−	0.379616i
$147$	13.9830			1.15330
$148$	−1.98910	−	5.74834i	−0.163503	−	0.472511i
$149$	−8.48318			−0.694969			−0.347484	−	0.937686i	$-0.612964\pi$
$149$	−8.48318			−0.694969			−0.347484	+	0.937686i	$0.612964\pi$
$150$	2.43665	+	1.40680i	0.198952	+	0.114865i
$151$	2.94779	+	5.10573i	0.239888	+	0.415498i	0.960682	−	0.277651i	$-0.0895560\pi$
$151$	2.94779	+	5.10573i	0.239888	+	0.415498i	−0.720794	+	0.693149i	$0.756223\pi$
$152$	−1.19801	−	2.07501i	−0.0971713	−	0.168306i
$153$	12.1197	−	6.99730i	0.979819	−	0.565698i
$154$		−	0.193346i		−	0.0155803i
$155$	−2.02202	−	3.50225i	−0.162413	−	0.281307i
$156$			6.82261i			0.546246i
$157$	−8.59034	+	14.8789i	−0.685584	+	1.18747i	0.287669	+	0.957730i	$0.407120\pi$
$157$	−8.59034	+	14.8789i	−0.685584	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$158$	5.35050			0.425663
$159$	2.59980			0.206177
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−4.25738	+	2.45800i	−0.335529	+	0.193718i
$162$		−	0.421663i		−	0.0331290i
$163$	9.41656	+	5.43665i	0.737562	+	0.425832i	0.821182	−	0.570666i	$-0.193315\pi$
$163$	9.41656	+	5.43665i	0.737562	+	0.425832i	−0.0836202	+	0.996498i	$0.526648\pi$
$164$	0.490256	−	0.849148i	0.0382825	−	0.0663073i
$165$	0.330641	+	0.190895i	0.0257403	+	0.0148612i
$166$	−10.3983	+	6.00344i	−0.807062	+	0.465957i
$167$	11.8695	−	6.85285i	0.918488	−	0.530289i	0.0353354	−	0.999376i	$-0.488750\pi$
$167$	11.8695	−	6.85285i	0.918488	−	0.530289i	0.883152	+	0.469086i	$0.155417\pi$
$168$	3.47190	+	2.00450i	0.267863	+	0.154651i
$169$	−3.56002	+	6.16613i	−0.273848	+	0.474318i
$170$	−2.46516	−	1.42326i	−0.189069	−	0.109159i
$171$		−	11.7797i		−	0.900819i
$172$	−10.2937	+	5.94307i	−0.784888	+	0.453155i
$173$	−3.72448	+	6.45098i	−0.283167	+	0.490459i	−0.972163	−	0.234306i	$-0.924718\pi$
$173$	−3.72448	+	6.45098i	−0.283167	+	0.490459i	0.688996	+	0.724765i	$0.258052\pi$
$174$	7.71336			0.584748
$175$	−1.42486			−0.107710
$176$	−0.0678472	+	0.117515i	−0.00511418	+	0.00885802i
$177$			40.6808i			3.05775i
$178$	−4.88202	−	8.45591i	−0.365923	−	0.633797i
$179$		−	23.9080i		−	1.78697i	−0.449092	−	0.893486i	$-0.648252\pi$
$179$		−	23.9080i		−	1.78697i	0.449092	−	0.893486i	$-0.351748\pi$
$180$	−4.25771	+	2.45819i	−0.317351	+	0.183223i
$181$	8.02572	+	13.9010i	0.596547	+	1.03325i	0.993327	+	0.115336i	$0.0367945\pi$
$181$	8.02572	+	13.9010i	0.596547	+	1.03325i	−0.396779	+	0.917914i	$0.629872\pi$
$182$	−1.72755	−	2.99220i	−0.128054	−	0.221797i
$183$	22.8408	+	13.1871i	1.68844	+	0.974821i
$184$	3.45016			0.254349
$185$	−5.74834	+	1.98910i	−0.422627	+	0.146242i
$186$	11.3784			0.834302
$187$	−0.334509	−	0.193129i	−0.0244617	−	0.0141230i
$188$	0.0819332	+	0.141912i	0.00597559	+	0.0103500i
$189$	3.84139	+	6.65348i	0.279420	+	0.483970i
$190$	−2.07501	+	1.19801i	−0.150537	+	0.0869127i
$191$		−	1.16751i		−	0.0844777i	−0.999108	−	0.0422389i	$-0.986551\pi$
$191$		−	1.16751i		−	0.0844777i	0.999108	−	0.0422389i	$-0.0134490\pi$
$192$	−1.40680	−	2.43665i	−0.101527	−	0.175850i
$193$		−	3.22571i		−	0.232192i	−0.993238	−	0.116096i	$-0.962962\pi$
$193$		−	3.22571i		−	0.232192i	0.993238	−	0.116096i	$-0.0370380\pi$
$194$	7.26525	−	12.5838i	0.521615	−	0.903463i
$195$	6.82261			0.488577
$196$	4.96977			0.354983
$197$	1.85075	−	3.20559i	0.131860	−	0.228389i	−0.792533	−	0.609829i	$-0.791238\pi$
$197$	1.85075	−	3.20559i	0.131860	−	0.228389i	0.924394	+	0.381440i	$0.124572\pi$
$198$	−0.577748	+	0.333563i	−0.0410588	+	0.0237053i
$199$			22.9628i			1.62779i	0.581012	+	0.813895i	$0.302657\pi$
$199$			22.9628i			1.62779i	−0.581012	+	0.813895i	$0.697343\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	−11.1036	+	19.2320i	−0.783189	+	1.35652i
$202$	−8.86764	−	5.11973i	−0.623925	−	0.360223i
$203$	−3.38286	+	1.95309i	−0.237430	+	0.137080i
$204$	6.93600	−	4.00450i	0.485617	−	0.280371i
$205$	−0.849148	−	0.490256i	−0.0593070	−	0.0342409i
$206$	−9.45336	+	16.3737i	−0.658647	+	1.14081i
$207$	14.6898	+	8.48114i	1.02101	+	0.589480i
$208$			2.42486i			0.168134i
$209$	−0.281568	+	0.162563i	−0.0194764	+	0.0112447i
$210$	2.00450	−	3.47190i	0.138324	−	0.239584i
$211$	15.3087			1.05389			0.526947	−	0.849898i	$-0.323337\pi$
$211$	15.3087			1.05389			0.526947	+	0.849898i	$0.323337\pi$
$212$	0.924008			0.0634612
$213$	8.39677	−	14.5436i	0.575337	−	0.996513i
$214$		−	12.6464i		−	0.864488i
$215$	5.94307	+	10.2937i	0.405314	+	0.702025i
$216$		−	5.39194i		−	0.366875i
$217$	−4.99022	+	2.88111i	−0.338758	+	0.195582i
$218$	6.12399	+	10.6071i	0.414769	+	0.718401i
$219$	−12.9058	−	22.3534i	−0.872091	−	1.51051i
$220$	0.117515	+	0.0678472i	0.00792285	+	0.00457426i
$221$	−6.90244			−0.464308
$222$	3.24003	−	16.8050i	0.217457	−	1.12788i
$223$	−9.77305			−0.654452			−0.327226	−	0.944946i	$-0.606114\pi$
$223$	−9.77305			−0.654452			−0.327226	+	0.944946i	$0.606114\pi$
$224$	1.23397	+	0.712432i	0.0824479	+	0.0476013i
$225$	2.45819	+	4.25771i	0.163879	+	0.283847i
$226$	−2.40996	−	4.17418i	−0.160308	−	0.277662i
$227$	−9.75238	+	5.63054i	−0.647288	+	0.373712i	−0.787416	−	0.616421i	$-0.788582\pi$
$227$	−9.75238	+	5.63054i	−0.647288	+	0.373712i	0.140128	+	0.990133i	$0.455248\pi$
$228$		−	6.74145i		−	0.446463i
$229$	0.119732	+	0.207382i	0.00791212	+	0.0137042i	0.869954	−	0.493132i	$-0.164148\pi$
$229$	0.119732	+	0.207382i	0.00791212	+	0.0137042i	−0.862042	+	0.506836i	$0.830815\pi$
$230$		−	3.45016i		−	0.227497i
$231$	0.272000	−	0.471118i	0.0178963	−	0.0309973i
$232$	2.74145			0.179985
$233$	−23.8459			−1.56220			−0.781098	−	0.624408i	$-0.785340\pi$
$233$	−23.8459			−1.56220			−0.781098	+	0.624408i	$0.785340\pi$
$234$	−5.96078	+	10.3244i	−0.389668	+	0.674925i
$235$	0.141912	−	0.0819332i	0.00925735	−	0.00534473i
$236$			14.4586i			0.941174i
$237$	13.0373	+	7.52710i	0.846865	+	0.488938i
$238$	−2.02795	+	3.51252i	−0.131453	+	0.227683i
$239$	−10.4042	−	6.00686i	−0.672991	−	0.388551i	0.124218	−	0.992255i	$-0.460358\pi$
$239$	−10.4042	−	6.00686i	−0.672991	−	0.388551i	−0.797209	+	0.603704i	$0.793691\pi$
$240$	−2.43665	+	1.40680i	−0.157285	+	0.0908088i
$241$	7.10709	−	4.10328i	0.457808	−	0.264316i	−0.253314	−	0.967384i	$-0.581521\pi$
$241$	7.10709	−	4.10328i	0.457808	−	0.264316i	0.711122	+	0.703068i	$0.248187\pi$
$242$	−9.51033	−	5.49079i	−0.611347	−	0.352962i
$243$	−7.49472	+	12.9812i	−0.480786	+	0.832747i
$244$	8.11798	+	4.68692i	0.519700	+	0.300049i
$245$		−	4.96977i		−	0.317507i
$246$	2.38917	−	1.37939i	0.152328	−	0.0879465i
$247$	−2.90501	+	5.03162i	−0.184841	+	0.320154i
$248$	4.04405			0.256797
$249$	−33.7826			−2.14089
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			13.4091i			0.846375i	0.906042	+	0.423187i	$0.139089\pi$
$251$			13.4091i			0.846375i	−0.906042	+	0.423187i	$0.860911\pi$
$252$	3.50259	+	6.06666i	0.220642	+	0.382163i
$253$		−	0.468167i		−	0.0294334i
$254$	−6.00621	+	3.46769i	−0.376863	+	0.217582i
$255$	−4.00450	−	6.93600i	−0.250772	−	0.434349i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.0771	+	8.12744i	0.878108	+	0.506976i	0.870034	−	0.492991i	$-0.164097\pi$
$257$	14.0771	+	8.12744i	0.878108	+	0.506976i	0.00807398	+	0.999967i	$0.497430\pi$
$258$	−33.4429			−2.08207
$259$	2.83420	+	8.19060i	0.176109	+	0.508939i
$260$	2.42486			0.150384
$261$	11.6723	+	6.73900i	0.722497	+	0.417134i
$262$	−9.26933	−	16.0549i	−0.572661	−	0.991878i
$263$	−3.09553	−	5.36161i	−0.190878	−	0.330611i	0.754663	−	0.656112i	$-0.227800\pi$
$263$	−3.09553	−	5.36161i	−0.190878	−	0.330611i	−0.945542	+	0.325501i	$0.894467\pi$
$264$	−0.330641	+	0.190895i	−0.0203495	+	0.0117488i
$265$		−	0.924008i		−	0.0567614i
$266$	1.70700	+	2.95661i	0.104663	+	0.181281i
$267$		−	27.4722i		−	1.68127i
$268$	−3.94640	+	6.83536i	−0.241065	+	0.417536i
$269$	13.8306			0.843269			0.421634	−	0.906766i	$-0.361457\pi$
$269$	13.8306			0.843269			0.421634	+	0.906766i	$0.361457\pi$
$270$	−5.39194			−0.328143
$271$	5.32088	−	9.21603i	0.323220	−	0.559834i	−0.657930	−	0.753079i	$-0.728568\pi$
$271$	5.32088	−	9.21603i	0.323220	−	0.559834i	0.981151	+	0.193245i	$0.0619012\pi$
$272$	2.46516	−	1.42326i	0.149473	−	0.0862980i
$273$		−	9.72129i		−	0.588359i
$274$	3.30184	+	1.90632i	0.199471	+	0.115165i
$275$	0.0678472	−	0.117515i	0.00409134	−	0.00708641i
$276$	8.40684	+	4.85369i	0.506032	+	0.292158i
$277$	−17.9019	+	10.3357i	−1.07562	+	0.621011i	−0.929712	−	0.368287i	$-0.879945\pi$
$277$	−17.9019	+	10.3357i	−1.07562	+	0.621011i	−0.145911	+	0.989298i	$0.546611\pi$
$278$	8.54164	−	4.93152i	0.512294	−	0.295773i
$279$	17.2184	+	9.94104i	1.03084	+	0.595155i
$280$	0.712432	−	1.23397i	0.0425759	−	0.0737437i
$281$	−12.3130	−	7.10889i	−0.734529	−	0.424081i	0.0855476	−	0.996334i	$-0.472736\pi$
$281$	−12.3130	−	7.10889i	−0.734529	−	0.424081i	−0.820077	+	0.572253i	$0.806069\pi$
$282$			0.461056i			0.0274555i
$283$	−23.5507	+	13.5970i	−1.39994	+	0.808258i	−0.994386	−	0.105811i	$-0.966256\pi$
$283$	−23.5507	+	13.5970i	−1.39994	+	0.808258i	−0.405558	+	0.914069i	$0.632923\pi$
$284$	2.98434	−	5.16904i	0.177088	−	0.306726i
$285$	−6.74145			−0.399329
$286$	0.329041			0.0194566
$287$	−0.698547	+	1.20992i	−0.0412339	+	0.0714193i
$288$		−	4.91638i		−	0.289701i
$289$	−4.44865	−	7.70528i	−0.261685	−	0.453252i
$290$		−	2.74145i		−	0.160983i
$291$	35.4058	−	20.4416i	2.07553	−	1.19831i
$292$	−4.58691	−	7.94477i	−0.268429	−	0.464932i
$293$	−4.06312	−	7.03753i	−0.237370	−	0.411137i	0.722589	−	0.691278i	$-0.242952\pi$
$293$	−4.06312	−	7.03753i	−0.237370	−	0.411137i	−0.959959	+	0.280141i	$0.909619\pi$
$294$	12.1096	+	6.99148i	0.706246	+	0.407752i
$295$	14.4586			0.841812
$296$	1.15156	−	5.97276i	0.0669329	−	0.347160i
$297$	−0.731657			−0.0424550
$298$	−7.34665	−	4.24159i	−0.425580	−	0.245709i
$299$	−4.18308	−	7.24530i	−0.241914	−	0.419007i
$300$	1.40680	+	2.43665i	0.0812218	+	0.140680i
$301$	14.6671	−	8.46807i	0.845399	−	0.488091i
$302$			5.89559i			0.339253i
$303$	−14.4049	−	24.9500i	−0.827541	−	1.43334i
$304$		−	2.39602i		−	0.137421i
$305$	4.68692	−	8.11798i	0.268372	−	0.464834i
$306$	13.9946			0.800018
$307$	18.6234			1.06290			0.531448	−	0.847091i	$-0.321648\pi$
$307$	18.6234			1.06290			0.531448	+	0.847091i	$0.321648\pi$
$308$	0.0966730	−	0.167443i	0.00550846	−	0.00954093i
$309$	−46.0691	+	26.5980i	−2.62078	+	1.51311i
$310$		−	4.04405i		−	0.229686i
$311$	12.1810	+	7.03271i	0.690722	+	0.398789i	0.803883	−	0.594788i	$-0.202764\pi$
$311$	12.1810	+	7.03271i	0.690722	+	0.398789i	−0.113160	+	0.993577i	$0.536097\pi$
$312$	−3.41131	+	5.90855i	−0.193127	+	0.334506i
$313$	29.1305	+	16.8185i	1.64655	+	0.950637i	0.978428	+	0.206586i	$0.0662354\pi$
$313$	29.1305	+	16.8185i	1.64655	+	0.950637i	0.668123	+	0.744051i	$0.267098\pi$
$314$	−14.8789	+	8.59034i	−0.839665	+	0.484781i
$315$	6.06666	−	3.50259i	0.341817	−	0.197348i
$316$	4.63367	+	2.67525i	0.260664	+	0.150495i
$317$	14.2227	−	24.6344i	0.798825	−	1.38361i	−0.121556	−	0.992585i	$-0.538788\pi$
$317$	14.2227	−	24.6344i	0.798825	−	1.38361i	0.920381	−	0.391022i	$-0.127878\pi$
$318$	2.25149	+	1.29990i	0.126257	+	0.0728947i
$319$		−	0.371999i		−	0.0208280i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	17.7910	−	30.8148i	0.992994	−	1.71992i
$322$	−4.91600			−0.273958
$323$	6.82032			0.379493
$324$	0.210831	−	0.365171i	0.0117129	−	0.0202873i
$325$		−	2.42486i		−	0.134507i
$326$	5.43665	+	9.41656i	0.301108	+	0.521535i
$327$			34.4610i			1.90570i
$328$	0.849148	−	0.490256i	0.0468863	−	0.0270698i
$329$	−0.116744	−	0.202206i	−0.00643628	−	0.0111480i
$330$	0.190895	+	0.330641i	0.0105084	+	0.0182012i
$331$	26.5630	+	15.3361i	1.46003	+	0.842951i	0.999012	−	0.0444385i	$-0.0141499\pi$
$331$	26.5630	+	15.3361i	1.46003	+	0.842951i	0.461021	+	0.887389i	$0.347483\pi$
$332$	−12.0069			−0.658963
$333$	19.5852	−	22.5996i	1.07326	−	1.23845i
$334$	13.7057			0.749942
$335$	6.83536	+	3.94640i	0.373456	+	0.215615i
$336$	2.00450	+	3.47190i	0.109355	+	0.189408i
$337$	−8.94414	−	15.4917i	−0.487218	−	0.843887i	0.512674	−	0.858584i	$-0.328655\pi$
$337$	−8.94414	−	15.4917i	−0.487218	−	0.843887i	−0.999892	+	0.0146966i	$0.995322\pi$
$338$	−6.16613	+	3.56002i	−0.335394	+	0.193640i
$339$		−	13.5614i		−	0.736553i
$340$	−1.42326	−	2.46516i	−0.0771873	−	0.133692i
$341$		−	0.548755i		−	0.0297167i
$342$	5.88987	−	10.2015i	0.318488	−	0.551637i
$343$	−17.0553			−0.920898
$344$	−11.8861			−0.640858
$345$	4.85369	−	8.40684i	0.261314	−	0.452609i
$346$	−6.45098	+	3.72448i	−0.346807	+	0.200229i
$347$		−	1.63302i		−	0.0876649i	−0.999039	−	0.0438325i	$-0.986043\pi$
$347$		−	1.63302i		−	0.0876649i	0.999039	−	0.0438325i	$-0.0139568\pi$
$348$	6.67996	+	3.85668i	0.358084	+	0.206740i
$349$	14.4163	−	24.9697i	0.771685	−	1.33660i	−0.164954	−	0.986301i	$-0.552747\pi$
$349$	14.4163	−	24.9697i	0.771685	−	1.33660i	0.936639	−	0.350297i	$-0.113919\pi$
$350$	−1.23397	−	0.712432i	−0.0659583	−	0.0380811i
$351$	−11.3230	+	6.53736i	−0.604379	+	0.348939i
$352$	−0.117515	+	0.0678472i	−0.00626356	+	0.00361627i
$353$	−9.81009	−	5.66386i	−0.522138	−	0.301457i	0.215671	−	0.976466i	$-0.430806\pi$
$353$	−9.81009	−	5.66386i	−0.522138	−	0.301457i	−0.737809	+	0.675009i	$0.764140\pi$
$354$	−20.3404	+	35.2306i	−1.08108	+	1.87248i
$355$	−5.16904	−	2.98434i	−0.274344	−	0.158393i
$356$		−	9.76404i		−	0.517493i
$357$	−9.88285	+	5.70587i	−0.523056	+	0.301986i
$358$	11.9540	−	20.7050i	0.631790	−	1.09429i
$359$	−2.21623			−0.116968			−0.0584842	−	0.998288i	$-0.518627\pi$
$359$	−2.21623			−0.116968			−0.0584842	+	0.998288i	$0.518627\pi$
$360$	−4.91638			−0.259116
$361$	−6.62955	+	11.4827i	−0.348924	+	0.604354i
$362$			16.0514i			0.843645i
$363$	−15.4489	−	26.7583i	−0.810859	−	1.40445i
$364$		−	3.45510i		−	0.181096i
$365$	−7.94477	+	4.58691i	−0.415848	+	0.240090i
$366$	13.1871	+	22.8408i	0.689303	+	1.19391i
$367$	0.931550	+	1.61349i	0.0486265	+	0.0842236i	0.889314	−	0.457297i	$-0.151182\pi$
$367$	0.931550	+	1.61349i	0.0486265	+	0.0842236i	−0.840688	+	0.541520i	$0.817849\pi$
$368$	2.98792	+	1.72508i	0.155756	+	0.0899259i
$369$	4.82057			0.250949
$370$	−5.97276	−	1.15156i	−0.310509	−	0.0598666i
$371$	−1.31659			−0.0683537
$372$	9.85395	+	5.68918i	0.510903	+	0.294970i
$373$	−2.19037	−	3.79383i	−0.113413	−	0.196437i	0.803731	−	0.594992i	$-0.202845\pi$
$373$	−2.19037	−	3.79383i	−0.113413	−	0.196437i	−0.917144	+	0.398555i	$0.869512\pi$
$374$	−0.193129	−	0.334509i	−0.00998646	−	0.0172971i
$375$	2.43665	−	1.40680i	0.125828	−	0.0726470i
$376$			0.163866i			0.00845076i
$377$	−3.32382	−	5.75702i	−0.171185	−	0.296502i
$378$			7.68278i			0.395160i
$379$	9.65335	−	16.7201i	0.495859	−	0.858854i	−0.504129	−	0.863628i	$-0.668186\pi$
$379$	9.65335	−	16.7201i	0.495859	−	0.858854i	0.999989	+	0.00477467i	$0.00151983\pi$
$380$	−2.39602			−0.122913
$381$	−19.5134			−0.999703
$382$	0.583753	−	1.01109i	0.0298674	−	0.0517318i
$383$	−23.4066	+	13.5138i	−1.19602	+	0.690523i	−0.959666	−	0.281144i	$-0.909286\pi$
$383$	−23.4066	+	13.5138i	−1.19602	+	0.690523i	−0.236355	+	0.971667i	$0.575953\pi$
$384$		−	2.81361i		−	0.143581i
$385$	−0.167443	−	0.0966730i	−0.00853367	−	0.00492691i
$386$	1.61286	−	2.79355i	0.0820922	−	0.142188i
$387$	−50.6078	−	29.2184i	−2.57254	−	1.48526i
$388$	12.5838	−	7.26525i	0.638845	−	0.368837i
$389$	9.73946	−	5.62308i	0.493810	−	0.285101i	−0.232344	−	0.972634i	$-0.574639\pi$
$389$	9.73946	−	5.62308i	0.493810	−	0.285101i	0.726154	+	0.687532i	$0.241306\pi$
$390$	5.90855	+	3.41131i	0.299191	+	0.172738i
$391$	−4.91048	+	8.50520i	−0.248334	+	0.430126i
$392$	4.30394	+	2.48488i	0.217382	+	0.125506i
$393$		−	52.1605i		−	2.63115i
$394$	3.20559	−	1.85075i	0.161495	−	0.0932393i
$395$	2.67525	−	4.63367i	0.134606	−	0.233145i
$396$	−0.667126			−0.0335243
$397$	7.59996			0.381431			0.190715	−	0.981645i	$-0.438919\pi$
$397$	7.59996			0.381431			0.190715	+	0.981645i	$0.438919\pi$
$398$	−11.4814	+	19.8864i	−0.575511	+	0.996814i
$399$			9.60564i			0.480884i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			20.1495i			1.00622i	0.864223	+	0.503108i	$0.167810\pi$
$401$			20.1495i			1.00622i	−0.864223	+	0.503108i	$0.832190\pi$
$402$	−19.2320	+	11.1036i	−0.959206	+	0.553798i
$403$	−4.90313	−	8.49247i	−0.244242	−	0.423040i
$404$	−5.11973	−	8.86764i	−0.254716	−	0.441181i
$405$	−0.365171	−	0.210831i	−0.0181455	−	0.0104763i
$406$	−3.90619			−0.193861
$407$	−0.810471	−	0.156260i	−0.0401736	−	0.00774552i
$408$	8.00900			0.396505
$409$	16.7570	+	9.67464i	0.828579	+	0.478380i	0.853366	−	0.521313i	$-0.174557\pi$
$409$	16.7570	+	9.67464i	0.828579	+	0.478380i	−0.0247872	+	0.999693i	$0.507891\pi$
$410$	−0.490256	−	0.849148i	−0.0242120	−	0.0419364i
$411$	5.36362	+	9.29007i	0.264568	+	0.458245i
$412$	−16.3737	+	9.45336i	−0.806674	+	0.465733i
$413$		−	20.6015i		−	1.01373i
$414$	8.48114	+	14.6898i	0.416825	+	0.721963i
$415$			12.0069i			0.589395i
$416$	−1.21243	+	2.09999i	−0.0594443	+	0.102961i
$417$	27.7507			1.35896
$418$	−0.325126			−0.0159024
$419$	10.2368	−	17.7306i	0.500099	−	0.866196i	−0.499901	−	0.866082i	$-0.666630\pi$
$419$	10.2368	−	17.7306i	0.500099	−	0.866196i	1.00000		0.000113822i	$-3.62306e-5\pi$
$420$	3.47190	−	2.00450i	0.169411	−	0.0978097i
$421$		−	28.6857i		−	1.39805i	−0.715095	−	0.699027i	$-0.753616\pi$
$421$		−	28.6857i		−	1.39805i	0.715095	−	0.699027i	$-0.246384\pi$
$422$	13.2577	+	7.65434i	0.645375	+	0.372608i
$423$	−0.402815	+	0.697696i	−0.0195855	+	0.0339231i
$424$	0.800215	+	0.462004i	0.0388619	+	0.0224369i
$425$	−2.46516	+	1.42326i	−0.119578	+	0.0690384i
$426$	14.5436	−	8.39677i	0.704641	−	0.406825i
$427$	−11.5670	−	6.67821i	−0.559767	−	0.323181i
$428$	6.32318	−	10.9521i	0.305643	−	0.529389i
$429$	0.801758	+	0.462895i	0.0387093	+	0.0223488i
$430$			11.8861i			0.573201i
$431$	11.3724	−	6.56586i	0.547789	−	0.316266i	−0.200441	−	0.979706i	$-0.564237\pi$
$431$	11.3724	−	6.56586i	0.547789	−	0.316266i	0.748230	+	0.663440i	$0.230904\pi$
$432$	2.69597	−	4.66956i	0.129710	−	0.224664i
$433$	13.0628			0.627756			0.313878	−	0.949463i	$-0.398372\pi$
$433$	13.0628			0.627756			0.313878	+	0.949463i	$0.398372\pi$
$434$	−5.76221			−0.276595
$435$	3.85668	−	6.67996i	0.184914	−	0.320280i
$436$			12.2480i			0.586572i
$437$	4.13332	+	7.15911i	0.197723	+	0.342467i
$438$		−	25.8115i		−	1.23332i
$439$	28.8758	−	16.6715i	1.37817	−	0.795685i	0.386228	−	0.922403i	$-0.373778\pi$
$439$	28.8758	−	16.6715i	1.37817	−	0.795685i	0.991939	+	0.126718i	$0.0404445\pi$
$440$	0.0678472	+	0.117515i	0.00323449	+	0.00560230i
$441$	12.2166	+	21.1598i	0.581744	+	1.00761i
$442$	−5.97768	−	3.45122i	−0.284329	−	0.164158i
$443$	−12.9896			−0.617156			−0.308578	−	0.951199i	$-0.599853\pi$
$443$	−12.9896			−0.617156			−0.308578	+	0.951199i	$0.599853\pi$
$444$	11.2085	−	12.9336i	0.531930	−	0.613799i
$445$	−9.76404			−0.462860
$446$	−8.46371	−	4.88652i	−0.400768	−	0.231384i
$447$	−11.9342	−	20.6706i	−0.564466	−	0.977685i
$448$	0.712432	+	1.23397i	0.0336592	+	0.0582995i
$449$	7.61850	−	4.39854i	0.359539	−	0.207580i	−0.309339	−	0.950952i	$-0.600108\pi$
$449$	7.61850	−	4.39854i	0.359539	−	0.207580i	0.668879	+	0.743372i	$0.266775\pi$
$450$			4.91638i			0.231760i
$451$	−0.0665250	−	0.115225i	−0.00313254	−	0.00542572i
$452$		−	4.81993i		−	0.226710i
$453$	−8.29393	+	14.3655i	−0.389683	+	0.674950i
$454$	−11.2611			−0.528509
$455$	−3.45510			−0.161977
$456$	3.37072	−	5.83827i	0.157849	−	0.273402i
$457$	12.1483	−	7.01381i	0.568273	−	0.328092i	−0.188187	−	0.982133i	$-0.560261\pi$
$457$	12.1483	−	7.01381i	0.568273	−	0.328092i	0.756459	+	0.654041i	$0.226928\pi$
$458$			0.239464i			0.0111894i
$459$	13.2920	+	7.67415i	0.620419	+	0.358199i
$460$	1.72508	−	2.98792i	0.0804322	−	0.139313i
$461$	15.7345	+	9.08430i	0.732827	+	0.423098i	0.819456	−	0.573143i	$-0.194276\pi$
$461$	15.7345	+	9.08430i	0.732827	+	0.423098i	−0.0866282	+	0.996241i	$0.527609\pi$
$462$	0.471118	−	0.272000i	0.0219184	−	0.0126546i
$463$	22.4748	−	12.9759i	1.04449	−	0.603039i	0.123391	−	0.992358i	$-0.460623\pi$
$463$	22.4748	−	12.9759i	1.04449	−	0.603039i	0.921103	+	0.389319i	$0.127290\pi$
$464$	2.37416	+	1.37072i	0.110218	+	0.0636343i
$465$	5.68918	−	9.85395i	0.263829	−	0.456966i
$466$	−20.6511	−	11.9229i	−0.956646	−	0.552320i
$467$			37.6856i			1.74388i	0.489610	+	0.871941i	$0.337139\pi$
$467$			37.6856i			1.74388i	−0.489610	+	0.871941i	$0.662861\pi$
$468$	−10.3244	+	5.96078i	−0.477244	+	0.275537i
$469$	5.62308	−	9.73946i	0.259650	−	0.449726i
$470$	0.163866			0.00755859
$471$	−48.3397			−2.22737
$472$	−7.22929	+	12.5215i	−0.332755	+	0.576349i
$473$			1.61288i			0.0741605i
$474$	7.52710	+	13.0373i	0.345731	+	0.598824i
$475$			2.39602i			0.109937i
$476$	−3.51252	+	2.02795i	−0.160996	+	0.0929512i
$477$	2.27139	+	3.93416i	0.104000	+	0.180133i
$478$	−6.00686	−	10.4042i	−0.274747	−	0.475876i
$479$	7.08315	+	4.08946i	0.323637	+	0.186852i	0.653013	−	0.757347i	$-0.273505\pi$
$479$	7.08315	+	4.08946i	0.323637	+	0.186852i	−0.329375	+	0.944199i	$0.606838\pi$
$480$	−2.81361			−0.128423
$481$	−13.9389	+	4.82331i	−0.635561	+	0.219924i
$482$	8.20657			0.373799
$483$	−11.9786	−	6.91584i	−0.545045	−	0.314682i
$484$	−5.49079	−	9.51033i	−0.249582	−	0.432288i
$485$	−7.26525	−	12.5838i	−0.329898	−	0.571400i
$486$	−12.9812	+	7.49472i	−0.588841	+	0.339967i
$487$			32.8178i			1.48712i	0.668671	+	0.743558i	$0.266863\pi$
$487$			32.8178i			1.48712i	−0.668671	+	0.743558i	$0.733137\pi$
$488$	4.68692	+	8.11798i	0.212167	+	0.367484i
$489$			30.5932i			1.38347i
$490$	2.48488	−	4.30394i	0.112256	−	0.194432i
$491$	−25.5005			−1.15082			−0.575410	−	0.817865i	$-0.695158\pi$
$491$	−25.5005			−1.15082			−0.575410	+	0.817865i	$0.695158\pi$
$492$	2.75877			0.124375
$493$	−3.90180	+	6.75812i	−0.175728	+	0.304370i
$494$	−5.03162	+	2.90501i	−0.226383	+	0.130702i
$495$			0.667126i			0.0299851i
$496$	3.50225	+	2.02202i	0.157256	+	0.0907916i
$497$	−4.25228	+	7.36517i	−0.190741	+	0.330373i
$498$	−29.2566	−	16.8913i	−1.31102	−	0.756918i
$499$	−14.3171	+	8.26601i	−0.640923	+	0.370037i	−0.784970	−	0.619534i	$-0.787322\pi$
$499$	−14.3171	+	8.26601i	−0.640923	+	0.370037i	0.144047	+	0.989571i	$0.453988\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	33.3960	+	19.2812i	1.49202	+	0.861421i
$502$	−6.70455	+	11.6126i	−0.299239	+	0.518297i
$503$	14.2980	+	8.25495i	0.637516	+	0.368070i	0.783657	−	0.621194i	$-0.213352\pi$
$503$	14.2980	+	8.25495i	0.637516	+	0.368070i	−0.146141	+	0.989264i	$0.546685\pi$
$504$			7.00517i			0.312035i
$505$	−8.86764	+	5.11973i	−0.394605	+	0.227825i
$506$	0.234084	−	0.405445i	0.0104063	−	0.0180242i
$507$	−20.0330			−0.889696
$508$	−6.93538			−0.307708
$509$	5.24366	−	9.08229i	0.232421	−	0.402566i	−0.726099	−	0.687590i	$-0.758669\pi$
$509$	5.24366	−	9.08229i	0.232421	−	0.402566i	0.958520	+	0.285025i	$0.0920018\pi$
$510$		−	8.00900i		−	0.354645i
$511$	6.53572	+	11.3202i	0.289123	+	0.500776i
$512$		−	1.00000i		−	0.0441942i
$513$	11.1883	−	6.45959i	0.493977	−	0.285198i
$514$	8.12744	+	14.0771i	0.358486	+	0.620916i
$515$	9.45336	+	16.3737i	0.416565	+	0.721511i
$516$	−28.9624	−	16.7215i	−1.27500	−	0.736122i
$517$	0.0222358			0.000977928
$518$	−1.64081	+	8.51037i	−0.0720931	+	0.373924i
$519$	−20.9584			−0.919972
$520$	2.09999	+	1.21243i	0.0920908	+	0.0531686i
$521$	1.61567	+	2.79842i	0.0707837	+	0.122601i	0.899245	−	0.437445i	$-0.144117\pi$
$521$	1.61567	+	2.79842i	0.0707837	+	0.122601i	−0.828461	+	0.560046i	$0.810783\pi$
$522$	6.73900	+	11.6723i	0.294958	+	0.510883i
$523$	9.84484	−	5.68392i	0.430485	−	0.248541i	−0.269068	−	0.963121i	$-0.586716\pi$
$523$	9.84484	−	5.68392i	0.430485	−	0.248541i	0.699553	+	0.714581i	$0.253382\pi$
$524$		−	18.5387i		−	0.809865i
$525$	−2.00450	−	3.47190i	−0.0874836	−	0.151526i
$526$		−	6.19105i		−	0.269943i
$527$	−5.75574	+	9.96924i	−0.250724	+	0.434267i
$528$	−0.381791			−0.0166153
$529$	11.0964			0.482453
$530$	0.462004	−	0.800215i	0.0200682	−	0.0347591i
$531$	−61.5605	+	35.5420i	−2.67150	+	1.54239i
$532$			3.41400i			0.148015i
$533$	−2.05907	−	1.18880i	−0.0891881	−	0.0514928i
$534$	13.7361	−	23.7916i	0.594419	−	1.02956i
$535$	−10.9521	−	6.32318i	−0.473500	−	0.273375i
$536$	−6.83536	+	3.94640i	−0.295243	+	0.170458i
$537$	58.2557	−	33.6339i	2.51392	−	1.45141i
$538$	11.9777	+	6.91532i	0.516395	+	0.298141i
$539$	0.337185	−	0.584021i	0.0145236	−	0.0251556i
$540$	−4.66956	−	2.69597i	−0.200946	−	0.116016i
$541$		−	1.49314i		−	0.0641950i	−0.999485	−	0.0320975i	$-0.989781\pi$
$541$		−	1.49314i		−	0.0641950i	0.999485	−	0.0320975i	$-0.0102187\pi$
$542$	9.21603	−	5.32088i	0.395862	−	0.228551i
$543$	−22.5812	+	39.1118i	−0.969053	+	1.67845i
$544$	2.84653			0.122044
$545$	12.2480			0.524646
$546$	4.86064	−	8.41888i	0.208016	−	0.360295i
$547$			2.00176i			0.0855891i	0.999084	+	0.0427946i	$0.0136261\pi$
$547$			2.00176i			0.0855891i	−0.999084	+	0.0427946i	$0.986374\pi$
$548$	1.90632	+	3.30184i	0.0814338	+	0.141047i
$549$			46.0853i			1.96687i
$550$	0.117515	−	0.0678472i	0.00501085	−	0.00289302i
$551$	3.28428	+	5.68854i	0.139915	+	0.242340i
$552$	4.85369	+	8.40684i	0.206587	+	0.357819i
$553$	−6.60234	−	3.81186i	−0.280760	−	0.162097i
$554$	−20.6714			−0.878242
$555$	−12.9336	−	11.2085i	−0.548999	−	0.475772i
$556$	9.86304			0.418286
$557$	26.5034	+	15.3018i	1.12299	+	0.648357i	0.942162	−	0.335159i	$-0.108790\pi$
$557$	26.5034	+	15.3018i	1.12299	+	0.648357i	0.180825	+	0.983515i	$0.442123\pi$
$558$	9.94104	+	17.2184i	0.420838	+	0.728912i
$559$	14.4111	+	24.9608i	0.609526	+	1.05573i
$560$	1.23397	−	0.712432i	0.0521446	−	0.0301057i
$561$		−	1.08678i		−	0.0458838i
$562$	−7.10889	−	12.3130i	−0.299870	−	0.519391i
$563$		−	21.0846i		−	0.888610i	−0.895876	−	0.444305i	$-0.853451\pi$
$563$		−	21.0846i		−	0.888610i	0.895876	−	0.444305i	$-0.146549\pi$
$564$	−0.230528	+	0.399286i	−0.00970697	+	0.0168130i
$565$	−4.81993			−0.202776
$566$	−27.1940			−1.14305
$567$	−0.300406	+	0.520318i	−0.0126159	+	0.0218513i
$568$	5.16904	−	2.98434i	0.216888	−	0.125220i
$569$			40.6362i			1.70356i	0.523902	+	0.851779i	$0.324476\pi$
$569$			40.6362i			1.70356i	−0.523902	+	0.851779i	$0.675524\pi$
$570$	−5.83827	−	3.37072i	−0.244538	−	0.141184i
$571$	−6.07118	+	10.5156i	−0.254071	+	0.440064i	−0.964643	−	0.263561i	$-0.915103\pi$
$571$	−6.07118	+	10.5156i	−0.254071	+	0.440064i	0.710572	+	0.703625i	$0.248436\pi$
$572$	0.284957	+	0.164520i	0.0119147	+	0.00687894i
$573$	2.84481	−	1.64245i	0.118844	−	0.0686143i
$574$	−1.20992	+	0.698547i	−0.0505010	+	0.0291568i
$575$	−2.98792	−	1.72508i	−0.124605	−	0.0719407i
$576$	2.45819	−	4.25771i	0.102425	−	0.177405i
$577$	−0.653769	−	0.377454i	−0.0272168	−	0.0157136i	0.486330	−	0.873775i	$-0.338335\pi$
$577$	−0.653769	−	0.377454i	−0.0272168	−	0.0157136i	−0.513547	+	0.858062i	$0.671669\pi$
$578$		−	8.89729i		−	0.370078i
$579$	7.85995	−	4.53794i	0.326648	−	0.188591i
$580$	1.37072	−	2.37416i	0.0569162	−	0.0985818i
$581$	17.1082			0.709766
$582$	40.8831			1.69466
$583$	0.0626914	−	0.108585i	0.00259641	−	0.00449712i
$584$		−	9.17382i		−	0.379616i
$585$	5.96078	+	10.3244i	0.246448	+	0.426860i
$586$		−	8.12624i		−	0.335692i
$587$	18.0383	−	10.4144i	0.744521	−	0.429849i	−0.0791898	−	0.996860i	$-0.525233\pi$
$587$	18.0383	−	10.4144i	0.744521	−	0.429849i	0.823711	+	0.567010i	$0.191900\pi$
$588$	6.99148	+	12.1096i	0.288324	+	0.499392i
$589$	4.84480	+	8.39145i	0.199627	+	0.345763i
$590$	12.5215	+	7.22929i	0.515502	+	0.297625i
$591$	10.4146			0.428397
$592$	3.98366	−	4.59679i	0.163727	−	0.188927i
$593$	24.1914			0.993421			0.496711	−	0.867916i	$-0.334541\pi$
$593$	24.1914			0.993421			0.496711	+	0.867916i	$0.334541\pi$
$594$	−0.633634	−	0.365829i	−0.0259983	−	0.0150101i
$595$	2.02795	+	3.51252i	0.0831380	+	0.143999i
$596$	−4.24159	−	7.34665i	−0.173742	−	0.300930i
$597$	−55.9524	+	32.3041i	−2.28998	+	1.32212i
$598$		−	8.36615i		−	0.342118i
$599$	16.3882	+	28.3852i	0.669603	+	1.15979i	0.978015	+	0.208533i	$0.0668690\pi$
$599$	16.3882	+	28.3852i	0.669603	+	1.15979i	−0.308413	+	0.951253i	$0.599798\pi$
$600$			2.81361i			0.114865i
$601$	−9.68763	+	16.7795i	−0.395167	+	0.684449i	−0.993122	−	0.117080i	$-0.962647\pi$
$601$	−9.68763	+	16.7795i	−0.395167	+	0.684449i	0.597956	+	0.801529i	$0.295980\pi$
$602$	16.9361			0.690265
$603$	−38.8040			−1.58022
$604$	−2.94779	+	5.10573i	−0.119944	+	0.207749i
$605$	−9.51033	+	5.49079i	−0.386650	+	0.223233i
$606$		−	28.8098i		−	1.17032i
$607$	−13.7171	−	7.91956i	−0.556759	−	0.321445i	0.195085	−	0.980786i	$-0.437502\pi$
$607$	−13.7171	−	7.91956i	−0.556759	−	0.321445i	−0.751844	+	0.659342i	$0.770835\pi$
$608$	1.19801	−	2.07501i	0.0485857	−	0.0841528i
$609$	−9.51803	−	5.49524i	−0.385690	−	0.222678i
$610$	8.11798	−	4.68692i	0.328687	−	0.189768i
$611$	0.344118	−	0.198677i	0.0139215	−	0.00803760i
$612$	12.1197	+	6.99730i	0.489909	+	0.282849i
$613$	14.9248	−	25.8506i	0.602808	−	1.04409i	−0.389585	−	0.920990i	$-0.627382\pi$
$613$	14.9248	−	25.8506i	0.602808	−	1.04409i	0.992394	−	0.123105i	$-0.0392850\pi$
$614$	16.1284	+	9.31172i	0.650888	+	0.375791i
$615$		−	2.75877i		−	0.111244i
$616$	0.167443	−	0.0966730i	0.00674645	−	0.00389507i
$617$	18.6383	−	32.2824i	0.750349	−	1.29964i	−0.197305	−	0.980342i	$-0.563219\pi$
$617$	18.6383	−	32.2824i	0.750349	−	1.29964i	0.947654	−	0.319300i	$-0.103448\pi$
$618$	−53.1961			−2.13986
$619$	−0.794892			−0.0319494			−0.0159747	−	0.999872i	$-0.505085\pi$
$619$	−0.794892			−0.0319494			−0.0159747	+	0.999872i	$0.505085\pi$
$620$	2.02202	−	3.50225i	0.0812064	−	0.140654i
$621$			18.6030i			0.746514i
$622$	7.03271	+	12.1810i	0.281986	+	0.488414i
$623$			13.9124i			0.557390i
$624$	−5.90855	+	3.41131i	−0.236531	+	0.136562i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	16.8185	+	29.1305i	0.672202	+	1.16429i
$627$	−0.792220	−	0.457389i	−0.0316382	−	0.0182663i
$628$	−17.1807			−0.685584
$629$	13.0849	+	11.3396i	0.521728	+	0.452139i
$630$	7.00517			0.279093
$631$	−4.04038	−	2.33271i	−0.160845	−	0.0928638i	0.417417	−	0.908715i	$-0.362935\pi$
$631$	−4.04038	−	2.33271i	−0.160845	−	0.0928638i	−0.578262	+	0.815851i	$0.696269\pi$
$632$	2.67525	+	4.63367i	0.106416	+	0.184317i
$633$	21.5363	+	37.3020i	0.855991	+	1.48262i
$634$	24.6344	−	14.2227i	0.978357	−	0.564855i
$635$			6.93538i			0.275222i
$636$	1.29990	+	2.25149i	0.0515443	+	0.0892774i
$637$		−	12.0510i		−	0.477478i
$638$	0.186000	−	0.322161i	0.00736380	−	0.0127545i
$639$	29.3444			1.16084
$640$	−1.00000			−0.0395285
$641$	−1.51762	+	2.62860i	−0.0599425	+	0.103824i	−0.894439	−	0.447189i	$-0.852425\pi$
$641$	−1.51762	+	2.62860i	−0.0599425	+	0.103824i	0.834497	+	0.551013i	$0.185758\pi$
$642$	30.8148	−	17.7910i	1.21616	−	0.702153i
$643$			44.1008i			1.73916i	0.493788	+	0.869582i	$0.335612\pi$
$643$			44.1008i			1.73916i	−0.493788	+	0.869582i	$0.664388\pi$
$644$	−4.25738	−	2.45800i	−0.167764	−	0.0968588i
$645$	−16.7215	+	28.9624i	−0.658407	+	1.14039i
$646$	5.90657	+	3.41016i	0.232391	+	0.134171i
$647$	38.6108	−	22.2919i	1.51795	−	0.876386i	0.518168	−	0.855279i	$-0.326614\pi$
$647$	38.6108	−	22.2919i	1.51795	−	0.876386i	0.999777	−	0.0211074i	$-0.00671920\pi$
$648$	0.365171	−	0.210831i	0.0143453	−	0.00828224i
$649$	1.69910	+	0.980975i	0.0666955	+	0.0385067i
$650$	1.21243	−	2.09999i	0.0475555	−	0.0823685i
$651$	−14.0405	−	8.10630i	−0.550292	−	0.317711i
$652$			10.8733i			0.425832i
$653$	−11.5544	+	6.67094i	−0.452159	+	0.261054i	−0.708741	−	0.705468i	$-0.750737\pi$
$653$	−11.5544	+	6.67094i	−0.452159	+	0.261054i	0.256583	+	0.966522i	$0.417403\pi$
$654$	−17.2305	+	29.8441i	−0.673766	+	1.16700i
$655$	−18.5387			−0.724365
$656$	0.980511			0.0382825
$657$	22.5510	−	39.0595i	0.879799	−	1.52386i
$658$		−	0.233487i		−	0.00910228i
$659$	5.97659	+	10.3517i	0.232815	+	0.403247i	0.958635	−	0.284637i	$-0.0918731\pi$
$659$	5.97659	+	10.3517i	0.232815	+	0.403247i	−0.725821	+	0.687884i	$0.758540\pi$
$660$			0.381791i			0.0148612i
$661$	27.9383	−	16.1302i	1.08667	−	0.627391i	0.153984	−	0.988073i	$-0.450789\pi$
$661$	27.9383	−	16.1302i	1.08667	−	0.627391i	0.932689	+	0.360682i	$0.117456\pi$
$662$	15.3361	+	26.5630i	0.596056	+	1.03240i
$663$	−9.71037	−	16.8189i	−0.377119	−	0.653190i
$664$	−10.3983	−	6.00344i	−0.403531	−	0.232979i
$665$	3.41400			0.132389
$666$	28.2611	−	9.77920i	1.09509	−	0.378936i
$667$	−9.45842			−0.366232
$668$	11.8695	+	6.85285i	0.459244	+	0.265145i
$669$	−13.7488	−	23.8135i	−0.531558	−	0.920685i
$670$	3.94640	+	6.83536i	0.152463	+	0.264073i
$671$	1.10156	−	0.635989i	0.0425254	−	0.0245521i
$672$			4.00900i			0.154651i
$673$	2.70006	+	4.67664i	0.104080	+	0.180271i	0.913362	−	0.407149i	$-0.133477\pi$
$673$	2.70006	+	4.67664i	0.104080	+	0.180271i	−0.809282	+	0.587420i	$0.800144\pi$
$674$		−	17.8883i		−	0.689031i
$675$	−2.69597	+	4.66956i	−0.103768	+	0.179731i
$676$	−7.12004			−0.273848
$677$	−13.3269			−0.512195			−0.256097	−	0.966651i	$-0.582437\pi$
$677$	−13.3269			−0.512195			−0.256097	+	0.966651i	$0.582437\pi$
$678$	6.78069	−	11.7445i	0.260411	−	0.451045i
$679$	−17.9302	+	10.3520i	−0.688097	+	0.397273i
$680$		−	2.84653i		−	0.109159i
$681$	−27.4394	−	15.8421i	−1.05148	−	0.607071i
$682$	0.274377	−	0.475236i	0.0105065	−	0.0181977i
$683$	7.95908	+	4.59518i	0.304546	+	0.175830i	0.644483	−	0.764618i	$-0.277073\pi$
$683$	7.95908	+	4.59518i	0.304546	+	0.175830i	−0.339937	+	0.940448i	$0.610406\pi$
$684$	10.2015	−	5.88987i	0.390066	−	0.225205i
$685$	3.30184	−	1.90632i	0.126157	−	0.0728366i
$686$	−14.7703	−	8.52764i	−0.563933	−	0.325587i
$687$	−0.336879	+	0.583492i	−0.0128527	+	0.0222616i
$688$	−10.2937	−	5.94307i	−0.392444	−	0.226578i
$689$		−	2.24059i		−	0.0853598i
$690$	8.40684	−	4.85369i	0.320043	−	0.184777i
$691$	−1.39847	+	2.42223i	−0.0532005	+	0.0921459i	−0.891399	−	0.453219i	$-0.850276\pi$
$691$	−1.39847	+	2.42223i	−0.0532005	+	0.0921459i	0.838199	+	0.545365i	$0.183609\pi$
$692$	−7.44895			−0.283167
$693$	0.950563			0.0361089
$694$	0.816508	−	1.41423i	0.0309942	−	0.0536836i
$695$		−	9.86304i		−	0.374126i
$696$	3.85668	+	6.67996i	0.146187	+	0.253203i
$697$			2.79105i			0.105719i
$698$	24.9697	−	14.4163i	0.945118	−	0.545664i
$699$	−33.5465	−	58.1042i	−1.26884	−	2.19770i
$700$	−0.712432	−	1.23397i	−0.0269274	−	0.0466396i
$701$	−23.7829	−	13.7311i	−0.898268	−	0.518615i	−0.0216300	−	0.999766i	$-0.506886\pi$
$701$	−23.7829	−	13.7311i	−0.898268	−	0.518615i	−0.876638	+	0.481151i	$0.840219\pi$
$702$	−13.0747			−0.493474
$703$	13.7731	−	4.76593i	0.519463	−	0.179750i
$704$	−0.135694			−0.00511418
$705$	0.399286	+	0.230528i	0.0150380	+	0.00868218i
$706$	−5.66386	−	9.81009i	−0.213162	−	0.369208i
$707$	7.29492	+	12.6352i	0.274354	+	0.475194i
$708$	−35.2306	+	20.3404i	−1.32405	+	0.764439i
$709$		−	51.1521i		−	1.92106i	−0.278179	−	0.960529i	$-0.589731\pi$
$709$		−	51.1521i		−	1.92106i	0.278179	−	0.960529i	$-0.410269\pi$
$710$	−2.98434	−	5.16904i	−0.112000	−	0.193990i
$711$			26.3051i			0.986518i
$712$	4.88202	−	8.45591i	0.182962	−	0.316899i
$713$	−13.9526			−0.522529
$714$	−11.4117			−0.427073
$715$	0.164520	−	0.284957i	0.00615271	−	0.0106568i
$716$	20.7050	−	11.9540i	0.773781	−	0.446743i
$717$		−	33.8019i		−	1.26235i
$718$	−1.91932	−	1.10812i	−0.0716282	−	0.0413546i
$719$	21.6217	−	37.4498i	0.806352	−	1.39664i	−0.109022	−	0.994039i	$-0.534772\pi$
$719$	21.6217	−	37.4498i	0.806352	−	1.39664i	0.915374	−	0.402604i	$-0.131895\pi$
$720$	−4.25771	−	2.45819i	−0.158676	−	0.0916114i
$721$	23.3303	−	13.4697i	0.868865	−	0.501639i
$722$	−11.4827	+	6.62955i	−0.427343	+	0.246726i
$723$	19.9966	+	11.5450i	0.743680	+	0.429364i
$724$	−8.02572	+	13.9010i	−0.298274	+	0.516625i
$725$	−2.37416	−	1.37072i	−0.0881742	−	0.0509074i
$726$		−	30.8979i		−	1.14673i
$727$	−17.4389	+	10.0684i	−0.646774	+	0.373415i	−0.787219	−	0.616673i	$-0.788480\pi$
$727$	−17.4389	+	10.0684i	−0.646774	+	0.373415i	0.140445	+	0.990088i	$0.455147\pi$
$728$	1.72755	−	2.99220i	0.0640272	−	0.110898i
$729$	−43.4394			−1.60887
$730$	−9.17382			−0.339538
$731$	16.9171	−	29.3013i	0.625702	−	1.08375i
$732$			26.3743i			0.974821i
$733$	8.33337	+	14.4338i	0.307800	+	0.533125i	0.977881	−	0.209163i	$-0.0670739\pi$
$733$	8.33337	+	14.4338i	0.307800	+	0.533125i	−0.670081	+	0.742288i	$0.733741\pi$
$734$			1.86310i			0.0687683i
$735$	12.1096	−	6.99148i	0.446669	−	0.257885i
$736$	1.72508	+	2.98792i	0.0635872	+	0.110136i
$737$	0.535505	+	0.927521i	0.0197256	+	0.0341657i
$738$	4.17473	+	2.41028i	0.153674	+	0.0887238i
$739$	−23.6949			−0.871629			−0.435815	−	0.900036i	$-0.643540\pi$
$739$	−23.6949			−0.871629			−0.435815	+	0.900036i	$0.643540\pi$
$740$	−4.59679	−	3.98366i	−0.168981	−	0.146442i
$741$	−16.3471			−0.600525
$742$	−1.14020	−	0.658293i	−0.0418579	−	0.0241667i
$743$	−13.8131	−	23.9250i	−0.506754	−	0.877724i	−0.999969	−	0.00781654i	$-0.997512\pi$
$743$	−13.8131	−	23.9250i	−0.506754	−	0.877724i	0.493215	−	0.869907i	$-0.335821\pi$
$744$	5.68918	+	9.85395i	0.208575	+	0.361263i
$745$	−7.34665	+	4.24159i	−0.269160	+	0.155400i
$746$		−	4.38074i		−	0.160390i
$747$	−29.5152	−	51.1218i	−1.07990	−	1.87045i
$748$		−	0.386258i		−	0.0141230i
$749$	−9.00967	+	15.6052i	−0.329206	+	0.570202i
$750$	2.81361			0.102738
$751$	−43.9061			−1.60216			−0.801078	−	0.598560i	$-0.795740\pi$
$751$	−43.9061			−1.60216			−0.801078	+	0.598560i	$0.795740\pi$
$752$	−0.0819332	+	0.141912i	−0.00298780	+	0.00517502i
$753$	−32.6733	+	18.8640i	−1.19068	+	0.687441i
$754$		−	6.64764i		−	0.242093i
$755$	5.10573	+	2.94779i	0.185816	+	0.107281i
$756$	−3.84139	+	6.65348i	−0.139710	+	0.241985i
$757$	−46.2890	−	26.7250i	−1.68240	−	0.971335i	−0.960058	−	0.279801i	$-0.909731\pi$
$757$	−46.2890	−	26.7250i	−1.68240	−	0.971335i	−0.722344	−	0.691534i	$-0.756935\pi$
$758$	16.7201	−	9.65335i	0.607301	−	0.350625i
$759$	1.14076	−	0.658619i	0.0414070	−	0.0239064i
$760$	−2.07501	−	1.19801i	−0.0752686	−	0.0434563i
$761$	21.8105	−	37.7769i	0.790630	−	1.36941i	−0.134948	−	0.990853i	$-0.543087\pi$
$761$	21.8105	−	37.7769i	0.790630	−	1.36941i	0.925578	−	0.378558i	$-0.123580\pi$
$762$	−16.8991	−	9.75671i	−0.612190	−	0.353448i
$763$		−	17.4517i		−	0.631794i
$764$	1.01109	−	0.583753i	0.0365799	−	0.0211194i
$765$	6.99730	−	12.1197i	0.252988	−	0.438188i
$766$	−27.0276			−0.976546
$767$	35.0601			1.26595
$768$	1.40680	−	2.43665i	0.0507636	−	0.0879252i
$769$		−	0.845468i		−	0.0304884i	−0.999884	−	0.0152442i	$-0.995147\pi$
$769$		−	0.845468i		−	0.0304884i	0.999884	−	0.0152442i	$-0.00485256\pi$
$770$	−0.0966730	−	0.167443i	−0.00348385	−	0.00603421i
$771$			45.7349i			1.64710i
$772$	2.79355	−	1.61286i	0.100542	−	0.0580480i
$773$	9.74414	+	16.8773i	0.350472	+	0.607036i	0.986332	−	0.164769i	$-0.0526878\pi$
$773$	9.74414	+	16.8773i	0.350472	+	0.607036i	−0.635860	+	0.771804i	$0.719354\pi$
$774$	−29.2184	−	50.6078i	−1.05023	−	1.81906i
$775$	−3.50225	−	2.02202i	−0.125804	−	0.0726332i
$776$	14.5305			0.521615
$777$	−15.9705	+	18.4285i	−0.572939	+	0.661120i
$778$	11.2462			0.403194
$779$	2.03457	+	1.17466i	0.0728961	+	0.0420866i
$780$	3.41131	+	5.90855i	0.122144	+	0.211560i
$781$	−0.404959	−	0.701410i	−0.0144906	−	0.0250984i
$782$	−8.50520	+	4.91048i	−0.304145	+	0.175598i
$783$			14.7817i			0.528256i
$784$	2.48488	+	4.30394i	0.0887458	+	0.153712i
$785$			17.1807i			0.613205i
$786$	26.0802	−	45.1723i	0.930251	−	1.61124i
$787$	−47.9472			−1.70913			−0.854566	−	0.519343i	$-0.826177\pi$
$787$	−47.9472			−1.70913			−0.854566	+	0.519343i	$0.826177\pi$
$788$	3.70150			0.131860
$789$	8.70959	−	15.0855i	0.310070	−	0.537056i
$790$	4.63367	−	2.67525i	0.164859	−	0.0951811i
$791$			6.86773i			0.244189i
$792$	−0.577748	−	0.333563i	−0.0205294	−	0.0118526i
$793$	11.3651	−	19.6850i	0.403588	−	0.699034i
$794$	6.58176	+	3.79998i	0.233578	+	0.134856i
$795$	2.25149	−	1.29990i	0.0798521	−	0.0461026i
$796$	−19.8864	+	11.4814i	−0.704854	+	0.406947i
$797$	−37.3841	−	21.5837i	−1.32421	−	0.764534i	−0.339814	−	0.940493i	$-0.610364\pi$
$797$	−37.3841	−	21.5837i	−1.32421	−	0.764534i	−0.984398	+	0.175959i	$0.943697\pi$
$798$	−4.80282	+	8.31873i	−0.170018	+	0.294480i
$799$	−0.403958	−	0.233225i	−0.0142910	−	0.00825091i
$800$			1.00000i			0.0353553i
$801$	41.5725	−	24.0019i	1.46889	−	0.848065i
$802$	−10.0747	+	17.4500i	−0.355751	+	0.616179i
$803$	−1.24484			−0.0439294
$804$	−22.2072			−0.783189
$805$	−2.45800	+	4.25738i	−0.0866331	+	0.150053i
$806$		−	9.80626i		−	0.345411i
$807$	19.4570	+	33.7005i	0.684918	+	1.18631i
$808$		−	10.2395i		−	0.360223i
$809$	−12.4451	+	7.18518i	−0.437546	+	0.252617i	−0.702556	−	0.711628i	$-0.747958\pi$
$809$	−12.4451	+	7.18518i	−0.437546	+	0.252617i	0.265010	+	0.964246i	$0.414625\pi$
$810$	−0.210831	−	0.365171i	−0.00740786	−	0.0128308i
$811$	−2.97705	−	5.15639i	−0.104538	−	0.181065i	0.809011	−	0.587793i	$-0.200003\pi$
$811$	−2.97705	−	5.15639i	−0.104538	−	0.181065i	−0.913549	+	0.406728i	$0.866670\pi$
$812$	−3.38286	−	1.95309i	−0.118715	−	0.0685402i
$813$	29.9417			1.05010
$814$	−0.623759	−	0.540561i	−0.0218627	−	0.0189466i
$815$	10.8733			0.380875
$816$	6.93600	+	4.00450i	0.242809	+	0.140186i
$817$	−14.2397	−	24.6639i	−0.498184	−	0.862880i
$818$	9.67464	+	16.7570i	0.338266	+	0.585893i
$819$	14.7108	−	8.49329i	0.514037	−	0.296780i
$820$		−	0.980511i		−	0.0342409i
$821$	6.82863	+	11.8275i	0.238321	+	0.412784i	0.960233	−	0.279201i	$-0.0900697\pi$
$821$	6.82863	+	11.8275i	0.238321	+	0.412784i	−0.721912	+	0.691985i	$0.756736\pi$
$822$			10.7272i			0.374156i
$823$	−6.14202	+	10.6383i	−0.214097	+	0.370828i	−0.952993	−	0.302992i	$-0.902014\pi$
$823$	−6.14202	+	10.6383i	−0.214097	+	0.370828i	0.738896	+	0.673820i	$0.235348\pi$
$824$	−18.9067			−0.658647
$825$	0.381791			0.0132923
$826$	10.3008	−	17.8414i	0.358409	−	0.620783i
$827$	37.2503	−	21.5065i	1.29532	−	0.747853i	0.315727	−	0.948850i	$-0.397752\pi$
$827$	37.2503	−	21.5065i	1.29532	−	0.747853i	0.979592	+	0.200998i	$0.0644183\pi$
$828$			16.9623i			0.589480i
$829$	11.7333	+	6.77420i	0.407513	+	0.235278i	0.689720	−	0.724076i	$-0.257733\pi$
$829$	11.7333	+	6.77420i	0.407513	+	0.235278i	−0.282208	+	0.959353i	$0.591067\pi$
$830$	−6.00344	+	10.3983i	−0.208382	+	0.360929i
$831$	−50.3690	−	29.0806i	−1.74728	−	1.00879i
$832$	−2.09999	+	1.21243i	−0.0728042	+	0.0420335i
$833$	−12.2513	+	7.07328i	−0.424482	+	0.245075i
$834$	24.0328	+	13.8754i	0.832188	+	0.480464i
$835$	6.85285	−	11.8695i	0.237152	−	0.410760i
$836$	−0.281568	−	0.162563i	−0.00973822	−	0.00562236i
$837$			21.8053i			0.753701i
$838$	17.7306	−	10.2368i	0.612493	−	0.353623i
$839$	−4.93536	+	8.54829i	−0.170388	+	0.295120i	−0.938555	−	0.345129i	$-0.887835\pi$
$839$	−4.93536	+	8.54829i	−0.170388	+	0.295120i	0.768168	+	0.640249i	$0.221169\pi$
$840$	4.00900			0.138324
$841$	21.4845			0.740843
$842$	14.3428	−	24.8425i	0.494287	−	0.856130i
$843$		−	40.0032i		−	1.37778i
$844$	7.65434	+	13.2577i	0.263473	+	0.456349i
$845$			7.12004i			0.244937i
$846$	−0.697696	+	0.402815i	−0.0239873	+	0.0138491i
$847$	7.82363	+	13.5509i	0.268823	+	0.465615i
$848$	0.462004	+	0.800215i	0.0158653	+	0.0274795i
$849$	−66.2624	−	38.2566i	−2.27412	−	1.31296i
$850$	−2.84653			−0.0976350
$851$	−3.97305	+	20.6070i	−0.136194	+	0.706398i
$852$	16.7935			0.575337
$853$	25.9113	+	14.9599i	0.887186	+	0.512217i	0.873021	−	0.487683i	$-0.162158\pi$
$853$	25.9113	+	14.9599i	0.887186	+	0.512217i	0.0141647	+	0.999900i	$0.495491\pi$
$854$	−6.67821	−	11.5670i	−0.228524	−	0.395815i
$855$	−5.88987	−	10.2015i	−0.201429	−	0.348886i
$856$	10.9521	−	6.32318i	0.374334	−	0.216122i
$857$			50.3628i			1.72036i	0.509991	+	0.860180i	$0.329649\pi$
$857$			50.3628i			1.72036i	−0.509991	+	0.860180i	$0.670351\pi$
$858$	0.462895	+	0.801758i	0.0158030	+	0.0273716i
$859$		−	28.2093i		−	0.962488i	−0.876587	−	0.481244i	$-0.840185\pi$
$859$		−	28.2093i		−	0.962488i	0.876587	−	0.481244i	$-0.159815\pi$
$860$	−5.94307	+	10.2937i	−0.202657	+	0.351012i
$861$	−3.93087			−0.133964
$862$	13.1317			0.447268
$863$	3.85665	−	6.67991i	0.131282	−	0.227387i	−0.792889	−	0.609366i	$-0.791424\pi$
$863$	3.85665	−	6.67991i	0.131282	−	0.227387i	0.924171	+	0.381979i	$0.124757\pi$
$864$	4.66956	−	2.69597i	0.158862	−	0.0917188i
$865$			7.44895i			0.253272i
$866$	11.3127	+	6.53138i	0.384421	+	0.221945i
$867$	12.5167	−	21.6796i	0.425091	−	0.736279i
$868$	−4.99022	−	2.88111i	−0.169379	−	0.0977911i
$869$	0.628763	−	0.363017i	0.0213293	−	0.0123145i
$870$	6.67996	−	3.85668i	0.226472	−	0.130754i
$871$	16.5748	+	9.56948i	0.561616	+	0.324249i
$872$	−6.12399	+	10.6071i	−0.207385	+	0.359201i
$873$	61.8667	+	35.7188i	2.09387	+	1.20890i
$874$			8.26663i			0.279623i
$875$	−1.23397	+	0.712432i	−0.0417157	+	0.0240846i
$876$	12.9058	−	22.3534i	0.436045	−	0.755253i
$877$	−46.2838			−1.56289			−0.781447	−	0.623972i	$-0.785518\pi$
$877$	−46.2838			−1.56289			−0.781447	+	0.623972i	$0.785518\pi$
$878$	33.3429			1.12527
$879$	11.4320	−	19.8008i	0.385592	−	0.667866i
$880$			0.135694i			0.00457426i
$881$	8.51940	+	14.7560i	0.287026	+	0.497143i	0.973098	−	0.230390i	$-0.0740001\pi$
$881$	8.51940	+	14.7560i	0.287026	+	0.497143i	−0.686073	+	0.727533i	$0.740667\pi$
$882$			24.4333i			0.822711i
$883$	−12.7577	+	7.36566i	−0.429331	+	0.247874i	−0.699061	−	0.715062i	$-0.746399\pi$
$883$	−12.7577	+	7.36566i	−0.429331	+	0.247874i	0.269731	+	0.962936i	$0.413065\pi$
$884$	−3.45122	−	5.97768i	−0.116077	−	0.201051i
$885$	20.3404	+	35.2306i	0.683735	+	1.18426i
$886$	−11.2493	−	6.49481i	−0.377929	−	0.218198i
$887$	45.6244			1.53192			0.765958	−	0.642890i	$-0.222265\pi$
$887$	45.6244			1.53192			0.765958	+	0.642890i	$0.222265\pi$
$888$	16.1736	−	5.59656i	0.542750	−	0.187808i
$889$	9.88196			0.331430
$890$	−8.45591	−	4.88202i	−0.283443	−	0.163646i
$891$	−0.0286087	−	0.0495517i	−0.000958426	−	0.00166004i
$892$	−4.88652	−	8.46371i	−0.163613	−	0.283386i
$893$	−0.340025	+	0.196313i	−0.0113785	+	0.00656938i
$894$		−	23.8683i		−	0.798276i
$895$	−11.9540	−	20.7050i	−0.399579	−	0.692091i
$896$			1.42486i			0.0476013i
$897$	11.7695	−	20.3854i	0.392973	−	0.680650i
$898$	8.79709			0.293563
$899$	−11.0865			−0.369757
$900$	−2.45819	+	4.25771i	−0.0819397	+	0.141924i
$901$	−2.27783	+	1.31511i	−0.0758856	+	0.0438126i
$902$		−	0.133050i		−	0.00443008i
$903$	41.2675	+	23.8258i	1.37330	+	0.792873i
$904$	2.40996	−	4.17418i	0.0801542	−	0.138831i
$905$	13.9010	+	8.02572i	0.462083	+	0.266784i
$906$	−14.3655	+	8.29393i	−0.477262	+	0.275547i
$907$	−21.0518	+	12.1543i	−0.699014	+	0.403576i	−0.806980	−	0.590579i	$-0.798900\pi$
$907$	−21.0518	+	12.1543i	−0.699014	+	0.403576i	0.107966	+	0.994155i	$0.465566\pi$
$908$	−9.75238	−	5.63054i	−0.323644	−	0.186856i
$909$	25.1706	−	43.5967i	0.834855	−	1.44601i
$910$	−2.99220	−	1.72755i	−0.0991905	−	0.0572677i
$911$		−	1.13578i		−	0.0376302i	−0.999823	−	0.0188151i	$-0.994011\pi$
$911$		−	1.13578i		−	0.0376302i	0.999823	−	0.0188151i	$-0.00598938\pi$
$912$	5.83827	−	3.37072i	0.193324	−	0.111616i
$913$	−0.814634	+	1.41099i	−0.0269604	+	0.0466969i
$914$	14.0276			0.463993
$915$	26.3743			0.871907
$916$	−0.119732	+	0.207382i	−0.00395606	+	0.00685210i
$917$			26.4150i			0.872301i
$918$	7.67415	+	13.2920i	0.253285	+	0.438702i
$919$		−	22.3092i		−	0.735911i	−0.929843	−	0.367955i	$-0.880058\pi$
$919$		−	22.3092i		−	0.735911i	0.929843	−	0.367955i	$-0.119942\pi$
$920$	2.98792	−	1.72508i	0.0985089	−	0.0568741i
$921$	26.1995	+	45.3789i	0.863304	+	1.49529i
$922$	9.08430	+	15.7345i	0.299176	+	0.518187i
$923$	−12.5342	−	7.23663i	−0.412568	−	0.238196i
$924$	0.544000			0.0178963
$925$	−3.98366	+	4.59679i	−0.130982	+	0.151141i
$926$	25.9517			0.852826
$927$	−80.4993	−	46.4763i	−2.64394	−	1.52648i
$928$	1.37072	+	2.37416i	0.0449962	+	0.0779358i
$929$	19.2727	+	33.3813i	0.632318	+	1.09521i	0.987077	+	0.160249i	$0.0512296\pi$
$929$	19.2727	+	33.3813i	0.632318	+	1.09521i	−0.354759	+	0.934958i	$0.615437\pi$
$930$	9.85395	−	5.68918i	0.323124	−	0.186556i
$931$			11.9076i			0.390257i
$932$	−11.9229	−	20.6511i	−0.390549	−	0.676451i
$933$			39.5746i			1.29561i
$934$	−18.8428	+	32.6367i	−0.616556	+	1.06791i
$935$	−0.386258			−0.0126320
$936$	−11.9216			−0.389668
$937$	13.2183	−	22.8947i	0.431822	−	0.747938i	−0.565208	−	0.824948i	$-0.691204\pi$
$937$	13.2183	−	22.8947i	0.431822	−	0.747938i	0.997030	+	0.0770107i	$0.0245376\pi$
$938$	9.73946	−	5.62308i	0.318005	−	0.183600i
$939$			94.6412i			3.08850i
$940$	0.141912	+	0.0819332i	0.00462867	+	0.00267237i
$941$	11.8644	−	20.5497i	0.386768	−	0.669902i	−0.605244	−	0.796040i	$-0.706925\pi$
$941$	11.8644	−	20.5497i	0.386768	−	0.669902i	0.992013	+	0.126137i	$0.0402580\pi$
$942$	−41.8634	−	24.1698i	−1.36398	−	0.787496i
$943$	−2.92969	+	1.69146i	−0.0954039	+	0.0550815i
$944$	−12.5215	+	7.22929i	−0.407540	+	0.235293i
$945$	6.65348	+	3.84139i	0.216438	+	0.124960i
$946$	−0.806442	+	1.39680i	−0.0262197	+	0.0454139i
$947$	−21.8056	−	12.5895i	−0.708587	−	0.409103i	0.101951	−	0.994789i	$-0.467492\pi$
$947$	−21.8056	−	12.5895i	−0.708587	−	0.409103i	−0.810537	+	0.585687i	$0.800825\pi$
$948$			15.0542i			0.488938i
$949$	−19.2650	+	11.1226i	−0.625367	+	0.361056i
$950$	−1.19801	+	2.07501i	−0.0388685	+	0.0673223i
$951$	80.0341			2.59528
$952$	−4.05591			−0.131453
$953$	21.8586	−	37.8602i	0.708069	−	1.22641i	−0.257503	−	0.966277i	$-0.582900\pi$
$953$	21.8586	−	37.8602i	0.708069	−	1.22641i	0.965572	−	0.260134i	$-0.0837668\pi$
$954$			4.54278i			0.147078i
$955$	−0.583753	−	1.01109i	−0.0188898	−	0.0327181i
$956$		−	12.0137i		−	0.388551i
$957$	0.906434	−	0.523330i	0.0293009	−	0.0169169i
$958$	4.08946	+	7.08315i	0.132124	+	0.228846i
$959$	−2.71624	−	4.70466i	−0.0877119	−	0.151921i
$960$	−2.43665	−	1.40680i	−0.0786427	−	0.0454044i
$961$	14.6457			0.472441
$962$	−14.4831	−	2.79237i	−0.466955	−	0.0900296i
$963$	62.1744			2.00354
$964$	7.10709	+	4.10328i	0.228904	+	0.132158i
$965$	−1.61286	−	2.79355i	−0.0519197	−	0.0899275i
$966$	−6.91584	−	11.9786i	−0.222514	−	0.385405i
$967$	−16.2436	+	9.37825i	−0.522359	+	0.301584i	−0.737899	−	0.674911i	$-0.764182\pi$
$967$	−16.2436	+	9.37825i	−0.522359	+	0.301584i	0.215540	+	0.976495i	$0.430849\pi$
$968$		−	10.9816i		−	0.352962i
$969$	9.59485	+	16.6188i	0.308231	+	0.533872i
$970$		−	14.5305i		−	0.466546i
$971$	−5.98784	+	10.3713i	−0.192159	+	0.332829i	−0.945966	−	0.324267i	$-0.894882\pi$
$971$	−5.98784	+	10.3713i	−0.192159	+	0.332829i	0.753806	+	0.657097i	$0.228216\pi$
$972$	−14.9894			−0.480786
$973$	−14.0535			−0.450534
$974$	−16.4089	+	28.4210i	−0.525775	+	0.910669i
$975$	5.90855	−	3.41131i	0.189225	−	0.109249i
$976$			9.37383i			0.300049i
$977$	−6.81645	−	3.93548i	−0.218077	−	0.125907i	0.386982	−	0.922087i	$-0.373517\pi$
$977$	−6.81645	−	3.93548i	−0.218077	−	0.125907i	−0.605060	+	0.796180i	$0.706851\pi$
$978$	−15.2966	+	26.4945i	−0.489132	+	0.847201i
$979$	−1.14742	−	0.662464i	−0.0366717	−	0.0211724i
$980$	4.30394	−	2.48488i	0.137484	−	0.0793767i
$981$	−52.1484	+	30.1079i	−1.66497	+	0.961271i
$982$	−22.0841	−	12.7502i	−0.704731	−	0.406876i
$983$	−20.2150	+	35.0134i	−0.644759	+	1.11675i	0.339599	+	0.940570i	$0.389709\pi$
$983$	−20.2150	+	35.0134i	−0.644759	+	1.11675i	−0.984357	+	0.176184i	$0.943625\pi$
$984$	2.38917	+	1.37939i	0.0761639	+	0.0439732i
$985$		−	3.70150i		−	0.117939i
$986$	−6.75812	+	3.90180i	−0.215222	+	0.124259i
$987$	0.328471	−	0.568928i	0.0104553	−	0.0181092i
$988$	−5.81001			−0.184841
$989$	41.0091			1.30401
$990$	−0.333563	+	0.577748i	−0.0106013	+	0.0183620i
$991$		−	25.6435i		−	0.814592i	−0.913296	−	0.407296i	$-0.866472\pi$
$991$		−	25.6435i		−	0.814592i	0.913296	−	0.407296i	$-0.133528\pi$
$992$	2.02202	+	3.50225i	0.0641993	+	0.111196i
$993$			86.2997i			2.73864i
$994$	−7.36517	+	4.25228i	−0.233609	+	0.134874i
$995$	11.4814	+	19.8864i	0.363985	+	0.630440i
$996$	−16.8913	−	29.2566i	−0.535222	−	0.927031i
$997$	25.0774	+	14.4784i	0.794209	+	0.458537i	0.841442	−	0.540347i	$-0.181707\pi$
$997$	25.0774	+	14.4784i	0.794209	+	0.458537i	−0.0472332	+	0.998884i	$0.515040\pi$
$998$	−16.5320			−0.523312
$999$	32.2048	+	6.20913i	1.01892	+	0.196448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.c.101.6	yes	12
37.11	even	6	inner	370.2.l.c.11.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.c.11.6	✓	12	37.11	even	6	inner
370.2.l.c.101.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +2.81361i q^{6} +(-0.712432 - 1.23397i) q^{7} +1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +2.81361i q^{6} +(-0.712432 - 1.23397i) q^{7} +1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +1.00000 q^{10} +0.135694 q^{11} +(-1.40680 + 2.43665i) q^{12} +(2.09999 - 1.21243i) q^{13} -1.42486i q^{14} +(2.43665 + 1.40680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.46516 - 1.42326i) q^{17} +(-4.25771 + 2.45819i) q^{18} +(-2.07501 + 1.19801i) q^{19} +(0.866025 + 0.500000i) q^{20} +(2.00450 - 3.47190i) q^{21} +(0.117515 + 0.0678472i) q^{22} -3.45016i q^{23} +(-2.43665 + 1.40680i) q^{24} +(0.500000 - 0.866025i) q^{25} +2.42486 q^{26} -5.39194 q^{27} +(0.712432 - 1.23397i) q^{28} -2.74145i q^{29} +(1.40680 + 2.43665i) q^{30} -4.04405i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.190895 + 0.330641i) q^{33} +(-1.42326 - 2.46516i) q^{34} +(-1.23397 - 0.712432i) q^{35} -4.91638 q^{36} +(-5.97276 - 1.15156i) q^{37} -2.39602 q^{38} +(5.90855 + 3.41131i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-0.490256 - 0.849148i) q^{41} +(3.47190 - 2.00450i) q^{42} +11.8861i q^{43} +(0.0678472 + 0.117515i) q^{44} +4.91638i q^{45} +(1.72508 - 2.98792i) q^{46} +0.163866 q^{47} -2.81361 q^{48} +(2.48488 - 4.30394i) q^{49} +(0.866025 - 0.500000i) q^{50} -8.00900i q^{51} +(2.09999 + 1.21243i) q^{52} +(0.462004 - 0.800215i) q^{53} +(-4.66956 - 2.69597i) q^{54} +(0.117515 - 0.0678472i) q^{55} +(1.23397 - 0.712432i) q^{56} +(-5.83827 - 3.37072i) q^{57} +(1.37072 - 2.37416i) q^{58} +(12.5215 + 7.22929i) q^{59} +2.81361i q^{60} +(8.11798 - 4.68692i) q^{61} +(2.02202 - 3.50225i) q^{62} +7.00517 q^{63} -1.00000 q^{64} +(1.21243 - 2.09999i) q^{65} +0.381791i q^{66} +(3.94640 + 6.83536i) q^{67} -2.84653i q^{68} +(8.40684 - 4.85369i) q^{69} +(-0.712432 - 1.23397i) q^{70} +(-2.98434 - 5.16904i) q^{71} +(-4.25771 - 2.45819i) q^{72} -9.17382 q^{73} +(-4.59679 - 3.98366i) q^{74} +2.81361 q^{75} +(-2.07501 - 1.19801i) q^{76} +(-0.0966730 - 0.167443i) q^{77} +(3.41131 + 5.90855i) q^{78} +(4.63367 - 2.67525i) q^{79} +1.00000i q^{80} +(-0.210831 - 0.365171i) q^{81} -0.980511i q^{82} +(-6.00344 + 10.3983i) q^{83} +4.00900 q^{84} -2.84653 q^{85} +(-5.94307 + 10.2937i) q^{86} +(6.67996 - 3.85668i) q^{87} +0.135694i q^{88} +(-8.45591 - 4.88202i) q^{89} +(-2.45819 + 4.25771i) q^{90} +(-2.99220 - 1.72755i) q^{91} +(2.98792 - 1.72508i) q^{92} +(9.85395 - 5.68918i) q^{93} +(0.141912 + 0.0819332i) q^{94} +(-1.19801 + 2.07501i) q^{95} +(-2.43665 - 1.40680i) q^{96} -14.5305i q^{97} +(4.30394 - 2.48488i) q^{98} +(-0.333563 + 0.577748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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