LMFDB - Embedded newform 210.3.k.b.83.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(83,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.8
Character	$\chi$	$=$	210.83
Dual form			210.3.k.b.167.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-0.199427 + 2.99336i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 + 2.79394i) q^{6} +(-5.12625 - 4.76671i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-0.199427 + 2.99336i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 + 2.79394i) q^{6} +(-5.12625 - 4.76671i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +(-1.95750 - 6.79472i) q^{10} +6.70149i q^{11} +(-5.98673 - 0.398853i) q^{12} +(-16.0066 + 16.0066i) q^{13} +(-0.359544 - 9.89296i) q^{14} +(8.11250 - 12.6169i) q^{15} -4.00000 q^{16} +(7.21482 - 7.21482i) q^{17} +(-7.72655 - 10.1144i) q^{18} -8.06294 q^{19} +(4.83722 - 8.75222i) q^{20} +(15.2908 - 14.3941i) q^{21} +(-6.70149 + 6.70149i) q^{22} +(11.7195 - 11.7195i) q^{23} +(-5.58788 - 6.38558i) q^{24} +(13.3006 + 21.1682i) q^{25} -32.0132 q^{26} +(5.35279 - 26.4641i) q^{27} +(9.53342 - 10.2525i) q^{28} +6.17789 q^{29} +(20.7294 - 4.50445i) q^{30} +41.4735i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-20.0600 - 1.33645i) q^{33} +14.4296 q^{34} +(10.9042 + 33.2581i) q^{35} +(2.38782 - 17.8409i) q^{36} +(-37.8620 + 37.8620i) q^{37} +(-8.06294 - 8.06294i) q^{38} +(-44.7214 - 51.1057i) q^{39} +(13.5894 - 3.91499i) q^{40} +74.2121 q^{41} +(29.6849 + 0.896672i) q^{42} +(-42.3069 - 42.3069i) q^{43} -13.4030 q^{44} +(36.1493 + 26.7998i) q^{45} +23.4390 q^{46} +(-39.4156 + 39.4156i) q^{47} +(0.797706 - 11.9735i) q^{48} +(3.55696 + 48.8707i) q^{49} +(-7.86757 + 34.4688i) q^{50} +(20.1578 + 23.0354i) q^{51} +(-32.0132 - 32.0132i) q^{52} +(-44.4204 + 44.4204i) q^{53} +(31.8169 - 21.1113i) q^{54} +(16.2083 - 29.3264i) q^{55} +(19.7859 - 0.719089i) q^{56} +(1.60796 - 24.1353i) q^{57} +(6.17789 + 6.17789i) q^{58} +51.9749i q^{59} +(25.2339 + 16.2250i) q^{60} -15.0083i q^{61} +(-41.4735 + 41.4735i) q^{62} +(40.0375 + 48.6415i) q^{63} -8.00000i q^{64} +(108.760 - 31.3328i) q^{65} +(-18.7235 - 21.3964i) q^{66} +(-38.7098 + 38.7098i) q^{67} +(14.4296 + 14.4296i) q^{68} +(32.7435 + 37.4179i) q^{69} +(-22.3538 + 44.1623i) q^{70} -128.871i q^{71} +(20.2287 - 15.4531i) q^{72} +(54.2081 - 54.2081i) q^{73} -75.7239 q^{74} +(-66.0167 + 35.5921i) q^{75} -16.1259i q^{76} +(31.9440 - 34.3535i) q^{77} +(6.38427 - 95.8271i) q^{78} +25.7821i q^{79} +(17.5044 + 9.67445i) q^{80} +(78.1491 + 21.3005i) q^{81} +(74.2121 + 74.2121i) q^{82} +(-27.7179 - 27.7179i) q^{83} +(28.7883 + 30.5816i) q^{84} +(-49.0227 + 14.1230i) q^{85} -84.6139i q^{86} +(-1.23203 + 18.4927i) q^{87} +(-13.4030 - 13.4030i) q^{88} +32.5020i q^{89} +(9.34946 + 62.9491i) q^{90} +(158.353 - 5.75508i) q^{91} +(23.4390 + 23.4390i) q^{92} +(-124.145 - 8.27091i) q^{93} -78.8312 q^{94} +(35.2843 + 19.5011i) q^{95} +(12.7712 - 11.1758i) q^{96} +(56.7224 + 56.7224i) q^{97} +(-45.3138 + 52.4277i) q^{98} +(8.00099 - 59.7803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9	$ 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9} - 8 q^{14} - 4 q^{15} - 128 q^{16} - 4 q^{18} + 12 q^{21} - 40 q^{22} - 24 q^{23} + 16 q^{25} - 8 q^{28} + 112 q^{29} + 28 q^{30} - 128 q^{32} + 48 q^{35} - 40 q^{36} + 32 q^{37} - 64 q^{39} - 20 q^{42} - 32 q^{43} - 80 q^{44} - 48 q^{46} + 8 q^{50} + 84 q^{51} + 136 q^{53} + 340 q^{57} + 112 q^{58} + 64 q^{60} + 168 q^{63} + 200 q^{65} + 32 q^{67} - 72 q^{72} + 64 q^{74} - 88 q^{77} - 4 q^{78} + 76 q^{81} - 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} - 48 q^{92} - 388 q^{93} - 544 q^{95} - 128 q^{98} - 160 q^{99}+O(q^{100}) $ 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9 - 8 * q^14 - 4 * q^15 - 128 * q^16 - 4 * q^18 + 12 * q^21 - 40 * q^22 - 24 * q^23 + 16 * q^25 - 8 * q^28 + 112 * q^29 + 28 * q^30 - 128 * q^32 + 48 * q^35 - 40 * q^36 + 32 * q^37 - 64 * q^39 - 20 * q^42 - 32 * q^43 - 80 * q^44 - 48 * q^46 + 8 * q^50 + 84 * q^51 + 136 * q^53 + 340 * q^57 + 112 * q^58 + 64 * q^60 + 168 * q^63 + 200 * q^65 + 32 * q^67 - 72 * q^72 + 64 * q^74 - 88 * q^77 - 4 * q^78 + 76 * q^81 - 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 - 48 * q^92 - 388 * q^93 - 544 * q^95 - 128 * q^98 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−0.199427	+	2.99336i	−0.0664755	+	0.997788i
$3$	−0.199427	+	2.99336i	−0.0664755	+	0.997788i
$4$			2.00000i			0.500000i
$5$	−4.37611	−	2.41861i	−0.875222	−	0.483722i
$5$	−4.37611	−	2.41861i	−0.875222	−	0.483722i
$6$	−3.19279	+	2.79394i	−0.532132	+	0.465656i
$7$	−5.12625	−	4.76671i	−0.732322	−	0.680959i
$7$	−5.12625	−	4.76671i	−0.732322	−	0.680959i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−8.92046	−	1.19391i	−0.991162	−	0.132657i
$10$	−1.95750	−	6.79472i	−0.195750	−	0.679472i
$11$			6.70149i			0.609226i	0.952476	+	0.304613i	$0.0985271\pi$
$11$			6.70149i			0.609226i	−0.952476	+	0.304613i	$0.901473\pi$
$12$	−5.98673	−	0.398853i	−0.498894	−	0.0332378i
$13$	−16.0066	+	16.0066i	−1.23128	+	1.23128i	−0.267802	+	0.963474i	$0.586297\pi$
$13$	−16.0066	+	16.0066i	−1.23128	+	1.23128i	−0.963474	+	0.267802i	$0.913703\pi$
$14$	−0.359544	−	9.89296i	−0.0256817	−	0.706640i
$15$	8.11250	−	12.6169i	0.540833	−	0.841130i
$16$	−4.00000			−0.250000
$17$	7.21482	−	7.21482i	0.424401	−	0.424401i	−0.462315	−	0.886716i	$-0.652981\pi$
$17$	7.21482	−	7.21482i	0.424401	−	0.424401i	0.886716	+	0.462315i	$0.152981\pi$
$18$	−7.72655	−	10.1144i	−0.429253	−	0.561909i
$19$	−8.06294			−0.424365			−0.212183	−	0.977230i	$-0.568057\pi$
$19$	−8.06294			−0.424365			−0.212183	+	0.977230i	$0.568057\pi$
$20$	4.83722	−	8.75222i	0.241861	−	0.437611i
$21$	15.2908	−	14.3941i	0.728134	−	0.685435i
$22$	−6.70149	+	6.70149i	−0.304613	+	0.304613i
$23$	11.7195	−	11.7195i	0.509543	−	0.509543i	−0.404843	−	0.914386i	$-0.632674\pi$
$23$	11.7195	−	11.7195i	0.509543	−	0.509543i	0.914386	+	0.404843i	$0.132674\pi$
$24$	−5.58788	−	6.38558i	−0.232828	−	0.266066i
$25$	13.3006	+	21.1682i	0.532025	+	0.846728i
$26$	−32.0132			−1.23128
$27$	5.35279	−	26.4641i	0.198252	−	0.980151i
$28$	9.53342	−	10.2525i	0.340479	−	0.366161i
$29$	6.17789			0.213031			0.106515	−	0.994311i	$-0.466031\pi$
$29$	6.17789			0.213031			0.106515	+	0.994311i	$0.466031\pi$
$30$	20.7294	−	4.50445i	0.690982	−	0.150148i
$31$			41.4735i			1.33785i	0.743328	+	0.668927i	$0.233246\pi$
$31$			41.4735i			1.33785i	−0.743328	+	0.668927i	$0.766754\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−20.0600	−	1.33645i	−0.607879	−	0.0404986i
$34$	14.4296			0.424401
$35$	10.9042	+	33.2581i	0.311549	+	0.950230i
$36$	2.38782	−	17.8409i	0.0663285	−	0.495581i
$37$	−37.8620	+	37.8620i	−1.02330	+	1.02330i	−0.0235744	+	0.999722i	$0.507505\pi$
$37$	−37.8620	+	37.8620i	−1.02330	+	1.02330i	−0.999722	+	0.0235744i	$0.992495\pi$
$38$	−8.06294	−	8.06294i	−0.212183	−	0.212183i
$39$	−44.7214	−	51.1057i	−1.14670	−	1.31040i
$40$	13.5894	−	3.91499i	0.339736	−	0.0978748i
$41$	74.2121			1.81005			0.905025	−	0.425358i	$-0.139852\pi$
$41$	74.2121			1.81005			0.905025	+	0.425358i	$0.139852\pi$
$42$	29.6849	+	0.896672i	0.706784	+	0.0213493i
$43$	−42.3069	−	42.3069i	−0.983882	−	0.983882i	0.0159899	−	0.999872i	$-0.494910\pi$
$43$	−42.3069	−	42.3069i	−0.983882	−	0.983882i	−0.999872	+	0.0159899i	$0.994910\pi$
$44$	−13.4030			−0.304613
$45$	36.1493	+	26.7998i	0.803317	+	0.595551i
$46$	23.4390			0.509543
$47$	−39.4156	+	39.4156i	−0.838630	+	0.838630i	−0.988679	−	0.150049i	$-0.952057\pi$
$47$	−39.4156	+	39.4156i	−0.838630	+	0.838630i	0.150049	+	0.988679i	$0.452057\pi$
$48$	0.797706	−	11.9735i	0.0166189	−	0.249447i
$49$	3.55696	+	48.8707i	0.0725910	+	0.997362i
$50$	−7.86757	+	34.4688i	−0.157351	+	0.689377i
$51$	20.1578	+	23.0354i	0.395250	+	0.451675i
$52$	−32.0132	−	32.0132i	−0.615638	−	0.615638i
$53$	−44.4204	+	44.4204i	−0.838121	+	0.838121i	−0.988611	−	0.150491i	$-0.951915\pi$
$53$	−44.4204	+	44.4204i	−0.838121	+	0.838121i	0.150491	+	0.988611i	$0.451915\pi$
$54$	31.8169	−	21.1113i	0.589201	−	0.390950i
$55$	16.2083	−	29.3264i	0.294696	−	0.533208i
$56$	19.7859	−	0.719089i	0.353320	−	0.0128409i
$57$	1.60796	−	24.1353i	0.0282099	−	0.423427i
$58$	6.17789	+	6.17789i	0.106515	+	0.106515i
$59$			51.9749i			0.880931i	0.897769	+	0.440466i	$0.145187\pi$
$59$			51.9749i			0.880931i	−0.897769	+	0.440466i	$0.854813\pi$
$60$	25.2339	+	16.2250i	0.420565	+	0.270417i
$61$		−	15.0083i		−	0.246038i	−0.992404	−	0.123019i	$-0.960742\pi$
$61$		−	15.0083i		−	0.246038i	0.992404	−	0.123019i	$-0.0392576\pi$
$62$	−41.4735	+	41.4735i	−0.668927	+	0.668927i
$63$	40.0375	+	48.6415i	0.635516	+	0.772088i
$64$		−	8.00000i		−	0.125000i
$65$	108.760	−	31.3328i	1.67323	−	0.482043i
$66$	−18.7235	−	21.3964i	−0.283690	−	0.324189i
$67$	−38.7098	+	38.7098i	−0.577758	+	0.577758i	−0.934285	−	0.356527i	$-0.883961\pi$
$67$	−38.7098	+	38.7098i	−0.577758	+	0.577758i	0.356527	+	0.934285i	$0.383961\pi$
$68$	14.4296	+	14.4296i	0.212201	+	0.212201i
$69$	32.7435	+	37.4179i	0.474544	+	0.542288i
$70$	−22.3538	+	44.1623i	−0.319340	+	0.630890i
$71$		−	128.871i		−	1.81508i	−0.419962	−	0.907542i	$-0.637957\pi$
$71$		−	128.871i		−	1.81508i	0.419962	−	0.907542i	$-0.362043\pi$
$72$	20.2287	−	15.4531i	0.280955	−	0.214626i
$73$	54.2081	−	54.2081i	0.742576	−	0.742576i	−0.230497	−	0.973073i	$-0.574035\pi$
$73$	54.2081	−	54.2081i	0.742576	−	0.742576i	0.973073	+	0.230497i	$0.0740352\pi$
$74$	−75.7239			−1.02330
$75$	−66.0167	+	35.5921i	−0.880222	+	0.474562i
$76$		−	16.1259i		−	0.212183i
$77$	31.9440	−	34.3535i	0.414858	−	0.446150i
$78$	6.38427	−	95.8271i	0.0818497	−	1.22855i
$79$			25.7821i			0.326355i	0.986597	+	0.163178i	$0.0521743\pi$
$79$			25.7821i			0.326355i	−0.986597	+	0.163178i	$0.947826\pi$
$80$	17.5044	+	9.67445i	0.218805	+	0.120931i
$81$	78.1491	+	21.3005i	0.964804	+	0.262969i
$82$	74.2121	+	74.2121i	0.905025	+	0.905025i
$83$	−27.7179	−	27.7179i	−0.333950	−	0.333950i	0.520134	−	0.854084i	$-0.325882\pi$
$83$	−27.7179	−	27.7179i	−0.333950	−	0.333950i	−0.854084	+	0.520134i	$0.825882\pi$
$84$	28.7883	+	30.5816i	0.342718	+	0.364067i
$85$	−49.0227	+	14.1230i	−0.576737	+	0.166153i
$86$		−	84.6139i		−	0.983882i
$87$	−1.23203	+	18.4927i	−0.0141613	+	0.212559i
$88$	−13.4030	−	13.4030i	−0.152307	−	0.152307i
$89$			32.5020i			0.365191i	0.983188	+	0.182595i	$0.0584498\pi$
$89$			32.5020i			0.365191i	−0.983188	+	0.182595i	$0.941550\pi$
$90$	9.34946	+	62.9491i	0.103883	+	0.699434i
$91$	158.353	−	5.75508i	1.74014	−	0.0632426i
$92$	23.4390	+	23.4390i	0.254772	+	0.254772i
$93$	−124.145	−	8.27091i	−1.33489	−	0.0889345i
$94$	−78.8312			−0.838630
$95$	35.2843	+	19.5011i	0.371414	+	0.205275i
$96$	12.7712	−	11.1758i	0.133033	−	0.116414i
$97$	56.7224	+	56.7224i	0.584767	+	0.584767i	0.936210	−	0.351442i	$-0.114309\pi$
$97$	56.7224	+	56.7224i	0.584767	+	0.584767i	−0.351442	+	0.936210i	$0.614309\pi$
$98$	−45.3138	+	52.4277i	−0.462385	+	0.534976i
$99$	8.00099	−	59.7803i	0.0808181	−	0.603842i
$100$	−42.3364	+	26.6013i	−0.423364	+	0.266013i
$101$	−63.3063			−0.626795			−0.313398	−	0.949622i	$-0.601467\pi$
$101$	−63.3063			−0.626795			−0.313398	+	0.949622i	$0.601467\pi$
$102$	−2.87765	+	43.1932i	−0.0282123	+	0.423463i
$103$	41.4114	−	41.4114i	0.402052	−	0.402052i	−0.476904	−	0.878956i	$-0.658241\pi$
$103$	41.4114	−	41.4114i	0.402052	−	0.402052i	0.878956	+	0.476904i	$0.158241\pi$
$104$		−	64.0263i		−	0.615638i
$105$	−101.728	+	26.0078i	−0.968839	+	0.247693i
$106$	−88.8408			−0.838121
$107$	−3.96732	−	3.96732i	−0.0370777	−	0.0370777i	0.688325	−	0.725403i	$-0.258346\pi$
$107$	−3.96732	−	3.96732i	−0.0370777	−	0.0370777i	−0.725403	+	0.688325i	$0.758346\pi$
$108$	52.9282	+	10.7056i	0.490076	+	0.0991258i
$109$		−	108.319i		−	0.993756i	−0.867820	−	0.496878i	$-0.834480\pi$
$109$		−	108.319i		−	0.993756i	0.867820	−	0.496878i	$-0.165520\pi$
$110$	45.5347	−	13.1181i	0.413952	−	0.119256i
$111$	−105.784	−	120.885i	−0.953009	−	1.08906i
$112$	20.5050	+	19.0668i	0.183080	+	0.170240i
$113$	17.5503	−	17.5503i	0.155312	−	0.155312i	−0.625174	−	0.780486i	$-0.714972\pi$
$113$	17.5503	−	17.5503i	0.155312	−	0.155312i	0.780486	+	0.625174i	$0.214972\pi$
$114$	25.7433	−	22.5274i	0.225818	−	0.197608i
$115$	−79.6307	+	22.9409i	−0.692441	+	0.199486i
$116$			12.3558i			0.106515i
$117$	161.897	−	123.676i	1.38373	−	1.05706i
$118$	−51.9749	+	51.9749i	−0.440466	+	0.440466i
$119$	−71.3760	+	2.59405i	−0.599798	+	0.0217987i
$120$	9.00890	+	41.4589i	0.0750742	+	0.345491i
$121$	76.0901			0.628844
$122$	15.0083	−	15.0083i	0.123019	−	0.123019i
$123$	−14.7999	+	222.144i	−0.120324	+	1.80605i
$124$	−82.9469			−0.668927
$125$	−7.00734	−	124.803i	−0.0560587	−	0.998427i
$126$	−8.60403	+	88.6790i	−0.0682860	+	0.703802i
$127$	−95.1373	+	95.1373i	−0.749113	+	0.749113i	−0.974313	−	0.225200i	$-0.927696\pi$
$127$	−95.1373	+	95.1373i	−0.749113	+	0.749113i	0.225200	+	0.974313i	$0.427696\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	135.077	−	118.203i	1.04711	−	0.916302i
$130$	140.093	+	77.4274i	1.07764	+	0.595596i
$131$	70.4896			0.538088			0.269044	−	0.963128i	$-0.413292\pi$
$131$	70.4896			0.538088			0.269044	+	0.963128i	$0.413292\pi$
$132$	2.67291	−	40.1200i	0.0202493	−	0.303939i
$133$	41.3327	+	38.4337i	0.310772	+	0.288975i
$134$	−77.4196			−0.577758
$135$	−87.4307	+	102.863i	−0.647635	+	0.761951i
$136$			28.8593i			0.212201i
$137$	33.6211	+	33.6211i	0.245409	+	0.245409i	0.819084	−	0.573674i	$-0.194482\pi$
$137$	33.6211	+	33.6211i	0.245409	+	0.245409i	−0.573674	+	0.819084i	$0.694482\pi$
$138$	−4.67436	+	70.1614i	−0.0338722	+	0.508416i
$139$	−116.378			−0.837250			−0.418625	−	0.908159i	$-0.637488\pi$
$139$	−116.378			−0.837250			−0.418625	+	0.908159i	$0.637488\pi$
$140$	−66.5161	+	21.8084i	−0.475115	+	0.155775i
$141$	−110.125	−	125.846i	−0.781026	−	0.892523i
$142$	128.871	−	128.871i	0.907542	−	0.907542i
$143$	−107.268	−	107.268i	−0.750125	−	0.750125i
$144$	35.6818	+	4.77565i	0.247791	+	0.0331642i
$145$	−27.0351	−	14.9419i	−0.186449	−	0.103048i
$146$	108.416			0.742576
$147$	−146.997	+	0.901155i	−0.999981	+	0.00613030i
$148$	−75.7239	−	75.7239i	−0.511648	−	0.511648i
$149$	129.115			0.866546			0.433273	−	0.901263i	$-0.357359\pi$
$149$	129.115			0.866546			0.433273	+	0.901263i	$0.357359\pi$
$150$	−101.609	−	30.4245i	−0.677392	−	0.202830i
$151$	−51.7299			−0.342582			−0.171291	−	0.985220i	$-0.554794\pi$
$151$	−51.7299			−0.342582			−0.171291	+	0.985220i	$0.554794\pi$
$152$	16.1259	−	16.1259i	0.106091	−	0.106091i
$153$	−72.9734	+	55.7456i	−0.476950	+	0.364351i
$154$	66.2976	−	2.40948i	0.430504	−	0.0156460i
$155$	100.308	−	181.492i	0.647150	−	1.17092i
$156$	102.211	−	89.4428i	0.655201	−	0.573351i
$157$	−38.1320	−	38.1320i	−0.242879	−	0.242879i	0.575161	−	0.818040i	$-0.304939\pi$
$157$	−38.1320	−	38.1320i	−0.242879	−	0.242879i	−0.818040	+	0.575161i	$0.804939\pi$
$158$	−25.7821	+	25.7821i	−0.163178	+	0.163178i
$159$	−124.108	−	141.825i	−0.780552	−	0.891981i
$160$	7.82998	+	27.1789i	0.0489374	+	0.169868i
$161$	−115.941	+	4.21368i	−0.720128	+	0.0261719i
$162$	56.8487	+	99.4496i	0.350918	+	0.613887i
$163$	−61.7109	−	61.7109i	−0.378594	−	0.378594i	0.492001	−	0.870595i	$-0.336266\pi$
$163$	−61.7109	−	61.7109i	−0.378594	−	0.378594i	−0.870595	+	0.492001i	$0.836266\pi$
$164$			148.424i			0.905025i
$165$	84.5523	+	54.3658i	0.512438	+	0.329490i
$166$		−	55.4357i		−	0.333950i
$167$	−162.253	+	162.253i	−0.971575	+	0.971575i	−0.999607	−	0.0280316i	$-0.991076\pi$
$167$	−162.253	+	162.253i	−0.971575	+	0.971575i	0.0280316	+	0.999607i	$0.491076\pi$
$168$	−1.79334	+	59.3699i	−0.0106747	+	0.353392i
$169$		−	343.421i		−	2.03208i
$170$	−63.1457	−	34.8997i	−0.371445	−	0.205292i
$171$	71.9251	+	9.62645i	0.420615	+	0.0562950i
$172$	84.6139	−	84.6139i	0.491941	−	0.491941i
$173$	−90.7208	−	90.7208i	−0.524398	−	0.524398i	0.394499	−	0.918896i	$-0.370918\pi$
$173$	−90.7208	−	90.7208i	−0.524398	−	0.524398i	−0.918896	+	0.394499i	$0.870918\pi$
$174$	−19.7247	+	17.2606i	−0.113360	+	0.0991991i
$175$	32.7203	−	171.914i	0.186973	−	0.982365i
$176$		−	26.8060i		−	0.152307i
$177$	−155.580	−	10.3652i	−0.878983	−	0.0585604i
$178$	−32.5020	+	32.5020i	−0.182595	+	0.182595i
$179$	−23.3548			−0.130474			−0.0652369	−	0.997870i	$-0.520780\pi$
$179$	−23.3548			−0.130474			−0.0652369	+	0.997870i	$0.520780\pi$
$180$	−53.5996	+	72.2985i	−0.297776	+	0.401659i
$181$			132.268i			0.730762i	0.930858	+	0.365381i	$0.119061\pi$
$181$			132.268i			0.730762i	−0.930858	+	0.365381i	$0.880939\pi$
$182$	164.108	+	152.597i	0.901690	+	0.838448i
$183$	44.9254	+	2.99306i	0.245494	+	0.0163555i
$184$			46.8780i			0.254772i
$185$	257.261	−	74.1147i	1.39060	−	0.400620i
$186$	−115.874	−	132.416i	−0.622980	−	0.711915i
$187$	48.3500	+	48.3500i	0.258556	+	0.258556i
$188$	−78.8312	−	78.8312i	−0.419315	−	0.419315i
$189$	−153.586	+	110.146i	−0.812626	+	0.582785i
$190$	15.7832	+	54.7854i	0.0830693	+	0.288344i
$191$			137.668i			0.720774i	0.932803	+	0.360387i	$0.117355\pi$
$191$			137.668i			0.720774i	−0.932803	+	0.360387i	$0.882645\pi$
$192$	23.9469	+	1.59541i	0.124724	+	0.00830944i
$193$	188.004	+	188.004i	0.974116	+	0.974116i	0.999673	−	0.0255577i	$-0.00813615\pi$
$193$	188.004	+	188.004i	0.974116	+	0.974116i	−0.0255577	+	0.999673i	$0.508136\pi$
$194$			113.445i			0.584767i
$195$	72.1009	+	331.808i	0.369748	+	1.70158i
$196$	−97.7415	+	7.11392i	−0.498681	+	0.0362955i
$197$	2.30427	+	2.30427i	0.0116968	+	0.0116968i	0.712931	−	0.701234i	$-0.247367\pi$
$197$	2.30427	+	2.30427i	0.0116968	+	0.0116968i	−0.701234	+	0.712931i	$0.747367\pi$
$198$	67.7813	−	51.7793i	0.342330	−	0.261512i
$199$	−266.282			−1.33810			−0.669051	−	0.743217i	$-0.733299\pi$
$199$	−266.282			−1.33810			−0.669051	+	0.743217i	$0.733299\pi$
$200$	−68.9377	−	15.7351i	−0.344688	−	0.0786757i
$201$	−108.153	−	123.592i	−0.538073	−	0.614887i
$202$	−63.3063	−	63.3063i	−0.313398	−	0.313398i
$203$	−31.6694	−	29.4482i	−0.156007	−	0.145065i
$204$	−46.0708	+	40.3155i	−0.225837	+	0.197625i
$205$	−324.760	−	179.490i	−1.58419	−	0.875562i
$206$	82.8227			0.402052
$207$	−118.535	+	90.5512i	−0.572634	+	0.437446i
$208$	64.0263	−	64.0263i	0.307819	−	0.307819i
$209$		−	54.0337i		−	0.258534i
$210$	−127.736	−	75.7203i	−0.608266	−	0.360573i
$211$	104.157			0.493637			0.246819	−	0.969062i	$-0.420615\pi$
$211$	104.157			0.493637			0.246819	+	0.969062i	$0.420615\pi$
$212$	−88.8408	−	88.8408i	−0.419060	−	0.419060i
$213$	385.758	+	25.7003i	1.81107	+	0.120659i
$214$		−	7.93464i		−	0.0370777i
$215$	82.8157	+	287.464i	0.385189	+	1.33704i
$216$	42.2226	+	63.6337i	0.195475	+	0.294601i
$217$	197.692	−	212.604i	0.911023	−	0.979740i
$218$	108.319	−	108.319i	0.496878	−	0.496878i
$219$	151.454	+	173.075i	0.691570	+	0.790297i
$220$	58.6529	+	32.4166i	0.266604	+	0.147348i
$221$			230.969i			1.04511i
$222$	15.1014	−	226.669i	0.0680242	−	1.02103i
$223$	−2.59750	+	2.59750i	−0.0116480	+	0.0116480i	−0.712907	−	0.701259i	$-0.752622\pi$
$223$	−2.59750	+	2.59750i	−0.0116480	+	0.0116480i	0.701259	+	0.712907i	$0.252622\pi$
$224$	1.43818	+	39.5719i	0.00642044	+	0.176660i
$225$	−93.3748	−	204.710i	−0.414999	−	0.909822i
$226$	35.1005			0.155312
$227$	−60.1162	+	60.1162i	−0.264829	+	0.264829i	−0.827013	−	0.562183i	$-0.809961\pi$
$227$	−60.1162	+	60.1162i	−0.264829	+	0.264829i	0.562183	+	0.827013i	$0.309961\pi$
$228$	48.2706	+	3.21593i	0.211713	+	0.0141050i
$229$	345.368			1.50816			0.754078	−	0.656785i	$-0.228084\pi$
$229$	345.368			1.50816			0.754078	+	0.656785i	$0.228084\pi$
$230$	−102.572	−	56.6898i	−0.445963	−	0.246477i
$231$	96.4621	+	102.471i	0.417585	+	0.443598i
$232$	−12.3558	+	12.3558i	−0.0532577	+	0.0532577i
$233$	−258.641	+	258.641i	−1.11005	+	1.11005i	−0.116904	+	0.993143i	$0.537297\pi$
$233$	−258.641	+	258.641i	−1.11005	+	1.11005i	−0.993143	+	0.116904i	$0.962703\pi$
$234$	285.572	+	38.2209i	1.22039	+	0.163337i
$235$	267.818	−	77.1559i	1.13965	−	0.328323i
$236$	−103.950			−0.440466
$237$	−77.1751	−	5.14163i	−0.325633	−	0.0216946i
$238$	−73.9700	−	68.7819i	−0.310798	−	0.289000i
$239$	209.847			0.878022			0.439011	−	0.898482i	$-0.355329\pi$
$239$	209.847			0.878022			0.439011	+	0.898482i	$0.355329\pi$
$240$	−32.4500	+	50.4678i	−0.135208	+	0.210282i
$241$			174.145i			0.722592i	0.932451	+	0.361296i	$0.117666\pi$
$241$			174.145i			0.722592i	−0.932451	+	0.361296i	$0.882334\pi$
$242$	76.0901	+	76.0901i	0.314422	+	0.314422i
$243$	−79.3451	+	229.681i	−0.326523	+	0.945189i
$244$	30.0166			0.123019
$245$	102.634	−	222.466i	0.418913	−	0.908026i
$246$	−236.944	+	207.344i	−0.963185	+	0.842861i
$247$	129.060	−	129.060i	0.522511	−	0.522511i
$248$	−82.9469	−	82.9469i	−0.334464	−	0.334464i
$249$	88.4973	−	77.4420i	0.355411	−	0.311012i
$250$	117.796	−	131.811i	0.471184	−	0.527243i
$251$	425.295			1.69440			0.847202	−	0.531271i	$-0.178285\pi$
$251$	425.295			1.69440			0.847202	+	0.531271i	$0.178285\pi$
$252$	−97.2831	+	80.0750i	−0.386044	+	0.317758i
$253$	78.5381	+	78.5381i	0.310427	+	0.310427i
$254$	−190.275			−0.749113
$255$	−32.4988	−	149.559i	−0.127446	−	0.586507i
$256$	16.0000			0.0625000
$257$	24.8379	−	24.8379i	0.0966454	−	0.0966454i	−0.657131	−	0.753776i	$-0.728230\pi$
$257$	24.8379	−	24.8379i	0.0966454	−	0.0966454i	0.753776	+	0.657131i	$0.228230\pi$
$258$	253.280	+	16.8743i	0.981706	+	0.0654041i
$259$	374.567	−	13.6131i	1.44620	−	0.0525601i
$260$	62.6656	+	217.520i	0.241022	+	0.836617i
$261$	−55.1096	−	7.37586i	−0.211148	−	0.0282600i
$262$	70.4896	+	70.4896i	0.269044	+	0.269044i
$263$	220.211	−	220.211i	0.837302	−	0.837302i	−0.151201	−	0.988503i	$-0.548314\pi$
$263$	220.211	−	220.211i	0.837302	−	0.837302i	0.988503	+	0.151201i	$0.0483140\pi$
$264$	42.7929	−	37.4471i	0.162094	−	0.141845i
$265$	301.824	−	86.9527i	1.13896	−	0.328124i
$266$	2.89899	+	79.7664i	0.0108984	+	0.299874i
$267$	−97.2902	−	6.48175i	−0.364383	−	0.0242762i
$268$	−77.4196	−	77.4196i	−0.288879	−	0.288879i
$269$			251.260i			0.934053i	0.884243	+	0.467026i	$0.154675\pi$
$269$			251.260i			0.934053i	−0.884243	+	0.467026i	$0.845325\pi$
$270$	−190.294	+	15.4326i	−0.704793	+	0.0571579i
$271$		−	101.261i		−	0.373657i	−0.982393	−	0.186829i	$-0.940179\pi$
$271$		−	101.261i		−	0.373657i	0.982393	−	0.186829i	$-0.0598209\pi$
$272$	−28.8593	+	28.8593i	−0.106100	+	0.106100i
$273$	−14.3527	+	475.155i	−0.0525738	+	1.74049i
$274$			67.2421i			0.245409i
$275$	−141.858	+	89.1340i	−0.515849	+	0.324124i
$276$	−74.8358	+	65.4871i	−0.271144	+	0.237272i
$277$	−298.311	+	298.311i	−1.07693	+	1.07693i	−0.0801518	+	0.996783i	$0.525541\pi$
$277$	−298.311	+	298.311i	−1.07693	+	1.07693i	−0.996783	+	0.0801518i	$0.974459\pi$
$278$	−116.378	−	116.378i	−0.418625	−	0.418625i
$279$	49.5157	−	369.962i	0.177476	−	1.32603i
$280$	−88.3245	−	44.7077i	−0.315445	−	0.159670i
$281$		−	105.319i		−	0.374801i	−0.982284	−	0.187400i	$-0.939994\pi$
$281$		−	105.319i		−	0.374801i	0.982284	−	0.187400i	$-0.0600062\pi$
$282$	15.7210	−	235.970i	0.0557483	−	0.836775i
$283$	−205.970	+	205.970i	−0.727811	+	0.727811i	−0.970183	−	0.242372i	$-0.922074\pi$
$283$	−205.970	+	205.970i	−0.727811	+	0.727811i	0.242372	+	0.970183i	$0.422074\pi$
$284$	257.742			0.907542
$285$	−65.4106	+	101.730i	−0.229511	+	0.356946i
$286$		−	214.536i		−	0.750125i
$287$	−380.430	−	353.747i	−1.32554	−	1.23257i
$288$	30.9062	+	40.4575i	0.107313	+	0.140477i
$289$			184.893i			0.639767i
$290$	−12.0932	−	41.9770i	−0.0417007	−	0.144748i
$291$	−181.103	+	158.479i	−0.622346	+	0.544601i
$292$	108.416	+	108.416i	0.371288	+	0.371288i
$293$	123.123	+	123.123i	0.420216	+	0.420216i	0.885278	−	0.465062i	$-0.153968\pi$
$293$	123.123	+	123.123i	0.420216	+	0.420216i	−0.465062	+	0.885278i	$0.653968\pi$
$294$	−147.898	−	146.096i	−0.503056	−	0.496925i
$295$	125.707	−	227.448i	0.426126	−	0.771010i
$296$		−	151.448i		−	0.511648i
$297$	177.349	+	35.8717i	0.597134	+	0.120780i
$298$	129.115	+	129.115i	0.433273	+	0.433273i
$299$			375.178i			1.25478i
$300$	−71.1843	−	132.033i	−0.237281	−	0.440111i
$301$	15.2112	+	418.541i	0.0505356	+	1.39050i
$302$	−51.7299	−	51.7299i	−0.171291	−	0.171291i
$303$	12.6250	−	189.499i	0.0416665	−	0.625409i
$304$	32.2518			0.106091
$305$	−36.2993	+	65.6780i	−0.119014	+	0.215338i
$306$	−128.719	−	17.2277i	−0.420650	−	0.0562998i
$307$	−234.650	−	234.650i	−0.764331	−	0.764331i	0.212771	−	0.977102i	$-0.431751\pi$
$307$	−234.650	−	234.650i	−0.764331	−	0.764331i	−0.977102	+	0.212771i	$0.931751\pi$
$308$	68.7071	+	63.8881i	0.223075	+	0.207429i
$309$	115.701	+	132.218i	0.374436	+	0.427889i
$310$	281.801	−	81.1842i	0.909034	−	0.261884i
$311$	−312.785			−1.00574			−0.502870	−	0.864362i	$-0.667723\pi$
$311$	−312.785			−1.00574			−0.502870	+	0.864362i	$0.667723\pi$
$312$	191.654	+	12.7685i	0.614276	+	0.0409248i
$313$	240.526	−	240.526i	0.768452	−	0.768452i	−0.209382	−	0.977834i	$-0.567145\pi$
$313$	240.526	−	240.526i	0.768452	−	0.768452i	0.977834	+	0.209382i	$0.0671451\pi$
$314$		−	76.2640i		−	0.242879i
$315$	−57.5634	−	309.696i	−0.182741	−	0.983161i
$316$	−51.5641			−0.163178
$317$	170.827	+	170.827i	0.538887	+	0.538887i	0.923202	−	0.384315i	$-0.125562\pi$
$317$	170.827	+	170.827i	0.538887	+	0.538887i	−0.384315	+	0.923202i	$0.625562\pi$
$318$	17.7172	−	265.933i	0.0557145	−	0.836267i
$319$			41.4010i			0.129784i
$320$	−19.3489	+	35.0089i	−0.0604653	+	0.109403i
$321$	12.6668	−	11.0844i	0.0394605	−	0.0345310i
$322$	−120.154	−	111.727i	−0.373150	−	0.346978i
$323$	−58.1727	+	58.1727i	−0.180101	+	0.180101i
$324$	−42.6010	+	156.298i	−0.131485	+	0.482402i
$325$	−551.728	−	125.933i	−1.69763	−	0.387486i
$326$		−	123.422i		−	0.378594i
$327$	324.240	+	21.6018i	0.991558	+	0.0660605i
$328$	−148.424	+	148.424i	−0.452513	+	0.452513i
$329$	389.937	−	14.1717i	1.18522	−	0.0430749i
$330$	30.1865	+	138.918i	0.0914743	+	0.420964i
$331$	−421.233			−1.27261			−0.636303	−	0.771439i	$-0.719537\pi$
$331$	−421.233			−1.27261			−0.636303	+	0.771439i	$0.719537\pi$
$332$	55.4357	−	55.4357i	0.166975	−	0.166975i
$333$	382.950	−	292.542i	1.15000	−	0.878505i
$334$	−324.506			−0.971575
$335$	263.022	−	75.7743i	0.785141	−	0.226192i
$336$	−61.1632	+	57.5765i	−0.182033	+	0.171359i
$337$	159.190	−	159.190i	0.472375	−	0.472375i	−0.430307	−	0.902682i	$-0.641595\pi$
$337$	159.190	−	159.190i	0.472375	−	0.472375i	0.902682	+	0.430307i	$0.141595\pi$
$338$	343.421	−	343.421i	1.01604	−	1.01604i
$339$	49.0343	+	56.0343i	0.144644	+	0.165293i
$340$	−28.2460	−	98.0454i	−0.0830764	−	0.288369i
$341$	−277.934			−0.815056
$342$	62.2987	+	81.5516i	0.182160	+	0.238455i
$343$	214.719	−	267.479i	0.626002	−	0.779821i
$344$	169.228			0.491941
$345$	−52.7899	−	242.939i	−0.153014	−	0.704170i
$346$		−	181.442i		−	0.524398i
$347$	−280.509	−	280.509i	−0.808384	−	0.808384i	0.176005	−	0.984389i	$-0.443682\pi$
$347$	−280.509	−	280.509i	−0.808384	−	0.808384i	−0.984389	+	0.176005i	$0.943682\pi$
$348$	−36.9853	−	2.46407i	−0.106280	−	0.00708066i
$349$	−504.442			−1.44539			−0.722697	−	0.691165i	$-0.757098\pi$
$349$	−504.442			−1.44539			−0.722697	+	0.691165i	$0.757098\pi$
$350$	204.634	−	139.194i	0.584669	−	0.397696i
$351$	337.920	+	509.279i	0.962734	+	1.45094i
$352$	26.8060	−	26.8060i	0.0761533	−	0.0761533i
$353$	−205.433	−	205.433i	−0.581964	−	0.581964i	0.353479	−	0.935443i	$-0.384999\pi$
$353$	−205.433	−	205.433i	−0.581964	−	0.581964i	−0.935443	+	0.353479i	$0.884999\pi$
$354$	−145.215	−	165.945i	−0.410211	−	0.468772i
$355$	−311.689	+	563.953i	−0.877996	+	1.58860i
$356$	−65.0039			−0.182595
$357$	6.46933	−	214.172i	0.0181214	−	0.599920i
$358$	−23.3548	−	23.3548i	−0.0652369	−	0.0652369i
$359$	−428.176			−1.19269			−0.596346	−	0.802727i	$-0.703381\pi$
$359$	−428.176			−1.19269			−0.596346	+	0.802727i	$0.703381\pi$
$360$	−125.898	+	18.6989i	−0.349717	+	0.0519415i
$361$	−295.989			−0.819914
$362$	−132.268	+	132.268i	−0.365381	+	0.365381i
$363$	−15.1744	+	227.765i	−0.0418027	+	0.627453i
$364$	11.5102	+	316.705i	0.0316213	+	0.870069i
$365$	−368.329	+	106.112i	−1.00912	+	0.290718i
$366$	41.9323	+	47.9184i	0.114569	+	0.130925i
$367$	−152.654	−	152.654i	−0.415952	−	0.415952i	0.467854	−	0.883806i	$-0.345027\pi$
$367$	−152.654	−	152.654i	−0.415952	−	0.415952i	−0.883806	+	0.467854i	$0.845027\pi$
$368$	−46.8780	+	46.8780i	−0.127386	+	0.127386i
$369$	−662.006	−	88.6027i	−1.79405	−	0.240116i
$370$	331.376	+	183.147i	0.895611	+	0.494991i
$371$	439.449	−	15.9711i	1.18450	−	0.0430488i
$372$	16.5418	−	248.290i	0.0444673	−	0.667447i
$373$	382.613	+	382.613i	1.02577	+	1.02577i	0.999659	+	0.0261145i	$0.00831345\pi$
$373$	382.613	+	382.613i	1.02577	+	1.02577i	0.0261145	+	0.999659i	$0.491687\pi$
$374$			96.7001i			0.258556i
$375$	374.980	+	3.91361i	0.999946	+	0.0104363i
$376$		−	157.662i		−	0.419315i
$377$	−98.8869	+	98.8869i	−0.262299	+	0.262299i
$378$	−263.733	−	43.4400i	−0.697706	−	0.114921i
$379$			726.851i			1.91781i	0.283721	+	0.958907i	$0.408431\pi$
$379$			726.851i			1.91781i	−0.283721	+	0.958907i	$0.591569\pi$
$380$	−39.0022	+	70.5686i	−0.102637	+	0.185707i
$381$	−265.808	−	303.753i	−0.697658	−	0.797253i
$382$	−137.668	+	137.668i	−0.360387	+	0.360387i
$383$	−465.105	−	465.105i	−1.21437	−	1.21437i	−0.969573	−	0.244801i	$-0.921277\pi$
$383$	−465.105	−	465.105i	−1.21437	−	1.21437i	−0.244801	−	0.969573i	$-0.578723\pi$
$384$	22.3515	+	25.5423i	0.0582070	+	0.0665165i
$385$	−222.878	+	73.0745i	−0.578905	+	0.189804i
$386$			376.009i			0.974116i
$387$	326.886	+	427.908i	0.844668	+	1.10571i
$388$	−113.445	+	113.445i	−0.292384	+	0.292384i
$389$	−120.366			−0.309424			−0.154712	−	0.987960i	$-0.549445\pi$
$389$	−120.366			−0.309424			−0.154712	+	0.987960i	$0.549445\pi$
$390$	−259.707	+	403.908i	−0.665915	+	1.03566i
$391$		−	169.108i		−	0.432502i
$392$	−104.855	−	90.6275i	−0.267488	−	0.231193i
$393$	−14.0575	+	211.001i	−0.0357697	+	0.536898i
$394$			4.60854i			0.0116968i
$395$	62.3568	−	112.825i	0.157865	−	0.285633i
$396$	119.561	+	16.0020i	0.301921	+	0.0404090i
$397$	312.868	+	312.868i	0.788080	+	0.788080i	0.981179	−	0.193100i	$-0.0618541\pi$
$397$	312.868	+	312.868i	0.788080	+	0.788080i	−0.193100	+	0.981179i	$0.561854\pi$
$398$	−266.282	−	266.282i	−0.669051	−	0.669051i
$399$	−123.289	+	116.059i	−0.308995	+	0.290875i
$400$	−53.2025	−	84.6728i	−0.133006	−	0.211682i
$401$			641.900i			1.60075i	0.599501	+	0.800374i	$0.295366\pi$
$401$			641.900i			1.60075i	−0.599501	+	0.800374i	$0.704634\pi$
$402$	15.4395	−	231.745i	0.0384068	−	0.576480i
$403$	−663.849	−	663.849i	−1.64727	−	1.64727i
$404$		−	126.613i		−	0.313398i
$405$	−290.471	−	282.226i	−0.717213	−	0.696854i
$406$	−2.22122	−	61.1176i	−0.00547100	−	0.150536i
$407$	−253.732	−	253.732i	−0.623419	−	0.623419i
$408$	−86.3864	−	5.75531i	−0.211731	−	0.0141061i
$409$	−134.590			−0.329071			−0.164535	−	0.986371i	$-0.552612\pi$
$409$	−134.590			−0.329071			−0.164535	+	0.986371i	$0.552612\pi$
$410$	−145.270	−	504.250i	−0.354317	−	1.22988i
$411$	−107.345	+	93.9351i	−0.261180	+	0.228553i
$412$	82.8227	+	82.8227i	0.201026	+	0.201026i
$413$	247.749	−	266.437i	0.599878	−	0.645125i
$414$	−209.087	−	27.9841i	−0.505040	−	0.0675945i
$415$	54.2576	+	188.335i	0.130741	+	0.453819i
$416$	128.053			0.307819
$417$	23.2088	−	348.361i	0.0556566	−	0.835398i
$418$	54.0337	−	54.0337i	0.129267	−	0.129267i
$419$		−	268.374i		−	0.640510i	−0.947331	−	0.320255i	$-0.896231\pi$
$419$		−	268.374i		−	0.640510i	0.947331	−	0.320255i	$-0.103769\pi$
$420$	−52.0155	−	203.456i	−0.123846	−	0.484419i
$421$	−28.9266			−0.0687092			−0.0343546	−	0.999410i	$-0.510938\pi$
$421$	−28.9266			−0.0687092			−0.0343546	+	0.999410i	$0.510938\pi$
$422$	104.157	+	104.157i	0.246819	+	0.246819i
$423$	398.664	−	304.546i	0.942468	−	0.719968i
$424$		−	177.682i		−	0.419060i
$425$	248.687	+	56.7631i	0.585145	+	0.133560i
$426$	360.057	+	411.458i	0.845205	+	0.965864i
$427$	−71.5403	+	76.9365i	−0.167542	+	0.180179i
$428$	7.93464	−	7.93464i	0.0185389	−	0.0185389i
$429$	342.484	−	299.700i	0.798331	−	0.698601i
$430$	−204.648	+	370.279i	−0.475926	+	0.861115i
$431$			276.630i			0.641833i	0.947107	+	0.320917i	$0.103991\pi$
$431$			276.630i			0.641833i	−0.947107	+	0.320917i	$0.896009\pi$
$432$	−21.4112	+	105.856i	−0.0495629	+	0.245038i
$433$	−249.817	+	249.817i	−0.576945	+	0.576945i	−0.934060	−	0.357116i	$-0.883760\pi$
$433$	−249.817	+	249.817i	−0.576945	+	0.576945i	0.357116	+	0.934060i	$0.383760\pi$
$434$	410.296	−	14.9116i	0.945381	−	0.0343584i
$435$	50.1181	−	77.9461i	0.115214	−	0.179186i
$436$	216.639			0.496878
$437$	−94.4936	+	94.4936i	−0.216233	+	0.216233i
$438$	−21.6210	+	324.529i	−0.0493631	+	0.740934i
$439$	519.817			1.18409			0.592047	−	0.805903i	$-0.298320\pi$
$439$	519.817			1.18409			0.592047	+	0.805903i	$0.298320\pi$
$440$	26.2363	+	91.0695i	0.0596279	+	0.206976i
$441$	26.6177	−	440.196i	0.0603575	−	0.998177i
$442$	−230.969	+	230.969i	−0.522555	+	0.522555i
$443$	388.588	−	388.588i	0.877173	−	0.877173i	−0.116068	−	0.993241i	$-0.537029\pi$
$443$	388.588	−	388.588i	0.877173	−	0.877173i	0.993241	+	0.116068i	$0.0370290\pi$
$444$	241.771	−	211.568i	0.544529	−	0.476504i
$445$	78.6096	−	142.232i	0.176651	−	0.319623i
$446$	−5.19500			−0.0116480
$447$	−25.7490	+	386.489i	−0.0576041	+	0.864629i
$448$	−38.1337	+	41.0100i	−0.0851198	+	0.0915402i
$449$	−283.968			−0.632445			−0.316223	−	0.948685i	$-0.602415\pi$
$449$	−283.968			−0.632445			−0.316223	+	0.948685i	$0.602415\pi$
$450$	111.335	−	298.085i	0.247411	−	0.662410i
$451$			497.331i			1.10273i
$452$	35.1005	+	35.1005i	0.0776560	+	0.0776560i
$453$	10.3163	−	154.846i	0.0227733	−	0.341824i
$454$	−120.232			−0.264829
$455$	−706.887	−	357.808i	−1.55360	−	0.786392i
$456$	45.0547	+	51.4866i	0.0988042	+	0.112909i
$457$	−201.368	+	201.368i	−0.440630	+	0.440630i	−0.892224	−	0.451594i	$-0.850856\pi$
$457$	−201.368	+	201.368i	−0.440630	+	0.440630i	0.451594	+	0.892224i	$0.350856\pi$
$458$	345.368	+	345.368i	0.754078	+	0.754078i
$459$	−152.314	−	229.553i	−0.331839	−	0.500116i
$460$	−45.8817	−	159.261i	−0.0997429	−	0.346220i
$461$	553.509			1.20067			0.600335	−	0.799749i	$-0.295034\pi$
$461$	553.509			1.20067			0.600335	+	0.799749i	$0.295034\pi$
$462$	−6.00904	+	198.933i	−0.0130066	+	0.430592i
$463$	574.866	+	574.866i	1.24161	+	1.24161i	0.959333	+	0.282278i	$0.0910902\pi$
$463$	574.866	+	574.866i	1.24161	+	1.24161i	0.282278	+	0.959333i	$0.408910\pi$
$464$	−24.7116			−0.0532577
$465$	523.269	+	336.453i	1.12531	+	0.723556i
$466$	−517.282			−1.11005
$467$	628.925	−	628.925i	1.34673	−	1.34673i	0.457549	−	0.889184i	$-0.348727\pi$
$467$	628.925	−	628.925i	1.34673	−	1.34673i	0.889184	−	0.457549i	$-0.151273\pi$
$468$	247.351	+	323.793i	0.528528	+	0.691865i
$469$	382.955	−	13.9179i	0.816534	−	0.0296757i
$470$	344.974	+	190.662i	0.733987	+	0.405664i
$471$	121.748	−	106.538i	0.258487	−	0.226196i
$472$	−103.950	−	103.950i	−0.220233	−	0.220233i
$473$	283.519	−	283.519i	0.599407	−	0.599407i
$474$	−72.0335	−	82.3167i	−0.151969	−	0.173664i
$475$	−107.242	−	170.678i	−0.225773	−	0.359322i
$476$	−5.18810	−	142.752i	−0.0108994	−	0.299899i
$477$	449.284	−	343.216i	0.941896	−	0.719531i
$478$	209.847	+	209.847i	0.439011	+	0.439011i
$479$		−	229.796i		−	0.479742i	−0.970805	−	0.239871i	$-0.922895\pi$
$479$		−	229.796i		−	0.479742i	0.970805	−	0.239871i	$-0.0771051\pi$
$480$	−82.9178	+	18.0178i	−0.172745	+	0.0375371i
$481$		−	1212.08i		−	2.51992i
$482$	−174.145	+	174.145i	−0.361296	+	0.361296i
$483$	10.5085	−	347.893i	0.0217568	−	0.720275i
$484$			152.180i			0.314422i
$485$	−111.034	−	385.413i	−0.228936	−	0.794666i
$486$	−309.026	+	150.336i	−0.635856	+	0.309333i
$487$	58.0212	−	58.0212i	0.119140	−	0.119140i	−0.645023	−	0.764163i	$-0.723152\pi$
$487$	58.0212	−	58.0212i	0.119140	−	0.119140i	0.764163	+	0.645023i	$0.223152\pi$
$488$	30.0166	+	30.0166i	0.0615095	+	0.0615095i
$489$	197.030	−	172.416i	0.402924	−	0.352590i
$490$	325.100	−	119.833i	0.663470	−	0.244557i
$491$		−	105.182i		−	0.214221i	−0.994247	−	0.107110i	$-0.965840\pi$
$491$		−	105.182i		−	0.214221i	0.994247	−	0.107110i	$-0.0341598\pi$
$492$	−444.287	−	29.5997i	−0.903023	−	0.0601620i
$493$	44.5724	−	44.5724i	0.0904105	−	0.0904105i
$494$	258.120			0.522511
$495$	−179.599	+	242.254i	−0.362825	+	0.489402i
$496$		−	165.894i		−	0.334464i
$497$	−614.290	+	660.625i	−1.23600	+	1.32923i
$498$	165.939	+	11.0554i	0.333211	+	0.0221995i
$499$		−	29.9809i		−	0.0600819i	−0.999549	−	0.0300409i	$-0.990436\pi$
$499$		−	29.9809i		−	0.0600819i	0.999549	−	0.0300409i	$-0.00956377\pi$
$500$	249.607	−	14.0147i	0.499214	−	0.0280293i
$501$	−453.325	−	518.040i	−0.904840	−	1.03401i
$502$	425.295	+	425.295i	0.847202	+	0.847202i
$503$	−159.113	−	159.113i	−0.316328	−	0.316328i	0.531027	−	0.847355i	$-0.321806\pi$
$503$	−159.113	−	159.113i	−0.316328	−	0.316328i	−0.847355	+	0.531027i	$0.821806\pi$
$504$	−177.358	−	17.2081i	−0.351901	−	0.0341430i
$505$	277.035	+	153.113i	0.548585	+	0.303195i
$506$			157.076i			0.310427i
$507$	1027.99	+	68.4873i	2.02758	+	0.135084i
$508$	−190.275	−	190.275i	−0.374556	−	0.374556i
$509$			782.408i			1.53715i	0.639761	+	0.768574i	$0.279033\pi$
$509$			782.408i			1.53715i	−0.639761	+	0.768574i	$0.720967\pi$
$510$	117.060	−	182.058i	0.229530	−	0.356977i
$511$	−536.278	+	19.4902i	−1.04947	+	0.0381413i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−43.1592	+	213.378i	−0.0841311	+	0.415942i
$514$	49.6757			0.0966454
$515$	−281.379	+	81.0626i	−0.546366	+	0.157403i
$516$	236.406	+	270.154i	0.458151	+	0.523555i
$517$	−264.143	−	264.143i	−0.510915	−	0.510915i
$518$	388.180	+	360.954i	0.749383	+	0.696822i
$519$	289.653	−	253.468i	0.558097	−	0.488378i
$520$	−154.855	+	280.186i	−0.297798	+	0.538819i
$521$	−224.244			−0.430411			−0.215205	−	0.976569i	$-0.569042\pi$
$521$	−224.244			−0.430411			−0.215205	+	0.976569i	$0.569042\pi$
$522$	−47.7337	−	62.4855i	−0.0914439	−	0.119704i
$523$	278.114	−	278.114i	0.531767	−	0.531767i	−0.389331	−	0.921098i	$-0.627294\pi$
$523$	278.114	−	278.114i	0.531767	−	0.531767i	0.921098	+	0.389331i	$0.127294\pi$
$524$			140.979i			0.269044i
$525$	508.076	+	132.228i	0.967763	+	0.251863i
$526$	440.421			0.837302
$527$	299.224	+	299.224i	0.567787	+	0.567787i
$528$	80.2400	+	5.34582i	0.151970	+	0.0101247i
$529$			254.307i			0.480731i
$530$	388.777	+	214.871i	0.733541	+	0.405418i
$531$	62.0535	−	463.640i	0.116862	−	0.873146i
$532$	−76.8674	+	82.6654i	−0.144488	+	0.155386i
$533$	−1187.88	+	1187.88i	−2.22867	+	2.22867i
$534$	−90.8084	−	103.772i	−0.170053	−	0.194329i
$535$	7.76601	+	26.9568i	0.0145159	+	0.0503866i
$536$		−	154.839i		−	0.288879i
$537$	4.65757	−	69.9095i	0.00867331	−	0.130185i
$538$	−251.260	+	251.260i	−0.467026	+	0.467026i
$539$	−327.507	+	23.8369i	−0.607619	+	0.0442243i
$540$	−205.727	−	174.861i	−0.380975	−	0.323817i
$541$	135.498			0.250458			0.125229	−	0.992128i	$-0.460033\pi$
$541$	135.498			0.250458			0.125229	+	0.992128i	$0.460033\pi$
$542$	101.261	−	101.261i	0.186829	−	0.186829i
$543$	−395.926	−	26.3777i	−0.729146	−	0.0485778i
$544$	−57.7186			−0.106100
$545$	−261.983	+	474.018i	−0.480702	+	0.869757i
$546$	−489.507	+	460.802i	−0.896533	+	0.843960i
$547$	−15.9985	+	15.9985i	−0.0292477	+	0.0292477i	−0.721579	−	0.692332i	$-0.756584\pi$
$547$	−15.9985	+	15.9985i	−0.0292477	+	0.0292477i	0.692332	+	0.721579i	$0.256584\pi$
$548$	−67.2421	+	67.2421i	−0.122705	+	0.122705i
$549$	−17.9186	+	133.881i	−0.0326387	+	0.243864i
$550$	−230.993	−	52.7244i	−0.419986	−	0.0958626i
$551$	−49.8120			−0.0904028
$552$	−140.323	−	9.34871i	−0.254208	−	0.0169361i
$553$	122.896	−	132.165i	0.222234	−	0.238997i
$554$	−596.622			−1.07693
$555$	170.547	+	784.858i	0.307293	+	1.41416i
$556$		−	232.756i		−	0.418625i
$557$	502.514	+	502.514i	0.902180	+	0.902180i	0.995625	−	0.0934442i	$-0.0297877\pi$
$557$	502.514	+	502.514i	0.902180	+	0.902180i	−0.0934442	+	0.995625i	$0.529788\pi$
$558$	419.478	−	320.447i	0.751753	−	0.574277i
$559$	1354.38			2.42286
$560$	−43.6169	−	133.032i	−0.0778873	−	0.237558i
$561$	−154.372	+	135.087i	−0.275172	+	0.240797i
$562$	105.319	−	105.319i	0.187400	−	0.187400i
$563$	502.281	+	502.281i	0.892150	+	0.892150i	0.994725	−	0.102575i	$-0.0327081\pi$
$563$	502.281	+	502.281i	0.892150	+	0.892150i	−0.102575	+	0.994725i	$0.532708\pi$
$564$	251.691	−	220.249i	0.446261	−	0.390513i
$565$	−119.249	+	34.3546i	−0.211060	+	0.0608046i
$566$	−411.941			−0.727811
$567$	−299.079	−	481.706i	−0.527476	−	0.849570i
$568$	257.742	+	257.742i	0.453771	+	0.453771i
$569$	359.729			0.632212			0.316106	−	0.948724i	$-0.397624\pi$
$569$	359.729			0.632212			0.316106	+	0.948724i	$0.397624\pi$
$570$	−167.140	+	36.3191i	−0.293229	+	0.0637178i
$571$	583.678			1.02220			0.511102	−	0.859520i	$-0.329238\pi$
$571$	583.678			1.02220			0.511102	+	0.859520i	$0.329238\pi$
$572$	214.536	−	214.536i	0.375063	−	0.375063i
$573$	−412.090	−	27.4546i	−0.719180	−	0.0479138i
$574$	−26.6825	−	734.177i	−0.0464852	−	1.27905i
$575$	403.958	+	92.2040i	0.702535	+	0.160355i
$576$	−9.55130	+	71.3637i	−0.0165821	+	0.123895i
$577$	−194.662	−	194.662i	−0.337369	−	0.337369i	0.518007	−	0.855376i	$-0.326674\pi$
$577$	−194.662	−	194.662i	−0.337369	−	0.337369i	−0.855376	+	0.518007i	$0.826674\pi$
$578$	−184.893	+	184.893i	−0.319884	+	0.319884i
$579$	−600.258	+	525.272i	−1.03672	+	0.907206i
$580$	29.8838	−	54.0702i	0.0515238	−	0.0932245i
$581$	9.96580	+	274.212i	0.0171528	+	0.471965i
$582$	−339.582	−	22.6239i	−0.583474	−	0.0388727i
$583$	−297.683	−	297.683i	−0.510605	−	0.510605i
$584$			216.832i			0.371288i
$585$	−1007.60	+	149.653i	−1.72239	+	0.255817i
$586$			246.246i			0.420216i
$587$	−505.473	+	505.473i	−0.861113	+	0.861113i	−0.991467	−	0.130355i	$-0.958388\pi$
$587$	−505.473	+	505.473i	−0.861113	+	0.861113i	0.130355	+	0.991467i	$0.458388\pi$
$588$	−1.80231	−	293.994i	−0.00306515	−	0.499991i
$589$		−	334.398i		−	0.567739i
$590$	353.155	−	101.741i	0.598568	−	0.172442i
$591$	−7.35705	+	6.43798i	−0.0124485	+	0.0108934i
$592$	151.448	−	151.448i	0.255824	−	0.255824i
$593$	−78.0986	−	78.0986i	−0.131701	−	0.131701i	0.638183	−	0.769884i	$-0.279686\pi$
$593$	−78.0986	−	78.0986i	−0.131701	−	0.131701i	−0.769884	+	0.638183i	$0.779686\pi$
$594$	141.477	+	213.220i	0.238177	+	0.358957i
$595$	318.623	+	161.279i	0.535501	+	0.271057i
$596$			258.231i			0.433273i
$597$	53.1037	−	797.080i	0.0889510	−	1.33514i
$598$	−375.178	+	375.178i	−0.627388	+	0.627388i
$599$	−516.399			−0.862102			−0.431051	−	0.902328i	$-0.641857\pi$
$599$	−516.399			−0.862102			−0.431051	+	0.902328i	$0.641857\pi$
$600$	60.8490	−	203.218i	0.101415	−	0.338696i
$601$			894.037i			1.48758i	0.668412	+	0.743791i	$0.266974\pi$
$601$			894.037i			1.48758i	−0.668412	+	0.743791i	$0.733026\pi$
$602$	−403.330	+	433.752i	−0.669983	+	0.720519i
$603$	391.525	−	299.093i	0.649296	−	0.496008i
$604$		−	103.460i		−	0.171291i
$605$	−332.978	−	184.032i	−0.550377	−	0.304186i
$606$	202.124	−	176.874i	0.333538	−	0.291871i
$607$	71.3484	+	71.3484i	0.117543	+	0.117543i	0.763431	−	0.645889i	$-0.223513\pi$
$607$	71.3484	+	71.3484i	0.117543	+	0.117543i	−0.645889	+	0.763431i	$0.723513\pi$
$608$	32.2518	+	32.2518i	0.0530457	+	0.0530457i
$609$	94.4649	−	88.9254i	0.155115	−	0.146019i
$610$	−101.977	+	29.3787i	−0.167176	+	0.0481618i
$611$		−	1261.82i		−	2.06517i
$612$	−111.491	−	145.947i	−0.182175	−	0.238475i
$613$	−32.1532	−	32.1532i	−0.0524522	−	0.0524522i	0.680394	−	0.732846i	$-0.261809\pi$
$613$	−32.1532	−	32.1532i	−0.0524522	−	0.0524522i	−0.732846	+	0.680394i	$0.761809\pi$
$614$		−	469.299i		−	0.764331i
$615$	602.045	−	936.330i	0.978935	−	1.52249i
$616$	4.81896	+	132.595i	0.00782299	+	0.215252i
$617$	771.937	+	771.937i	1.25111	+	1.25111i	0.955221	+	0.295892i	$0.0956170\pi$
$617$	771.937	+	771.937i	1.25111	+	1.25111i	0.295892	+	0.955221i	$0.404383\pi$
$618$	−16.5170	+	247.919i	−0.0267266	+	0.401163i
$619$	−245.518			−0.396636			−0.198318	−	0.980138i	$-0.563548\pi$
$619$	−245.518			−0.396636			−0.198318	+	0.980138i	$0.563548\pi$
$620$	362.985	+	200.616i	0.585459	+	0.323575i
$621$	−247.414	−	372.878i	−0.398412	−	0.600447i
$622$	−312.785	−	312.785i	−0.502870	−	0.502870i
$623$	154.927	−	166.613i	0.248680	−	0.267437i
$624$	178.886	+	204.423i	0.286676	+	0.327600i
$625$	−271.186	+	563.101i	−0.433898	+	0.900962i
$626$	481.051			0.768452
$627$	161.743	+	10.7758i	0.257963	+	0.0171862i
$628$	76.2640	−	76.2640i	0.121440	−	0.121440i
$629$			546.335i			0.868577i
$630$	252.132	−	367.259i	0.400210	−	0.582951i
$631$	405.528			0.642675			0.321337	−	0.946965i	$-0.395868\pi$
$631$	405.528			0.642675			0.321337	+	0.946965i	$0.395868\pi$
$632$	−51.5641	−	51.5641i	−0.0815888	−	0.0815888i
$633$	−20.7718	+	311.781i	−0.0328148	+	0.492545i
$634$			341.654i			0.538887i
$635$	646.431	−	186.231i	1.01800	−	0.293277i
$636$	283.650	−	248.216i	0.445991	−	0.390276i
$637$	−839.188	−	725.319i	−1.31741	−	1.13865i
$638$	−41.4010	+	41.4010i	−0.0648919	+	0.0648919i
$639$	−153.861	+	1149.59i	−0.240783	+	1.79904i
$640$	−54.3578	+	15.6600i	−0.0849340	+	0.0244687i
$641$		−	891.470i		−	1.39075i	−0.718648	−	0.695374i	$-0.755239\pi$
$641$		−	891.470i		−	1.39075i	0.718648	−	0.695374i	$-0.244761\pi$
$642$	23.7513	+	1.58238i	0.0369957	+	0.00246476i
$643$	−319.764	+	319.764i	−0.497300	+	0.497300i	−0.910596	−	0.413297i	$-0.864377\pi$
$643$	−319.764	+	319.764i	−0.497300	+	0.497300i	0.413297	+	0.910596i	$0.364377\pi$
$644$	−8.42736	−	231.881i	−0.0130860	−	0.360064i
$645$	−876.999	+	190.570i	−1.35969	+	0.295457i
$646$	−116.345			−0.180101
$647$	185.628	−	185.628i	0.286906	−	0.286906i	−0.548950	−	0.835855i	$-0.684972\pi$
$647$	185.628	−	185.628i	0.286906	−	0.286906i	0.835855	+	0.548950i	$0.184972\pi$
$648$	−198.899	+	113.697i	−0.306943	+	0.175459i
$649$	−348.309			−0.536686
$650$	−425.795	−	677.661i	−0.655070	−	1.04256i
$651$	596.975	+	634.163i	0.917012	+	0.974137i
$652$	123.422	−	123.422i	0.189297	−	0.189297i
$653$	−528.502	+	528.502i	−0.809345	+	0.809345i	−0.984535	−	0.175190i	$-0.943946\pi$
$653$	−528.502	+	528.502i	−0.809345	+	0.809345i	0.175190	+	0.984535i	$0.443946\pi$
$654$	302.638	+	345.841i	0.462749	+	0.528809i
$655$	−308.470	−	170.487i	−0.470947	−	0.260285i
$656$	−296.848			−0.452513
$657$	−548.280	+	418.841i	−0.834521	+	0.637505i
$658$	404.109	+	375.765i	0.614147	+	0.571072i
$659$	101.666			0.154274			0.0771369	−	0.997021i	$-0.475422\pi$
$659$	101.666			0.154274			0.0771369	+	0.997021i	$0.475422\pi$
$660$	−108.732	+	169.105i	−0.164745	+	0.256219i
$661$			563.886i			0.853080i	0.904469	+	0.426540i	$0.140268\pi$
$661$			563.886i			0.853080i	−0.904469	+	0.426540i	$0.859732\pi$
$662$	−421.233	−	421.233i	−0.636303	−	0.636303i
$663$	−691.375	−	46.0614i	−1.04280	−	0.0694742i
$664$	110.871			0.166975
$665$	−87.9201	−	268.158i	−0.132211	−	0.403245i
$666$	675.492	+	90.4078i	1.01425	+	0.135747i
$667$	72.4017	−	72.4017i	0.108548	−	0.108548i
$668$	−324.506	−	324.506i	−0.485788	−	0.485788i
$669$	−7.25725	−	8.29327i	−0.0108479	−	0.0123965i
$670$	338.796	+	187.248i	0.505666	+	0.279475i
$671$	100.578			0.149893
$672$	−118.740	−	3.58669i	−0.176696	−	0.00533733i
$673$	−835.168	−	835.168i	−1.24096	−	1.24096i	−0.959602	−	0.281361i	$-0.909214\pi$
$673$	−835.168	−	835.168i	−1.24096	−	1.24096i	−0.281361	−	0.959602i	$-0.590786\pi$
$674$	318.381			0.472375
$675$	631.393	−	238.680i	0.935397	−	0.353600i
$676$	686.843			1.01604
$677$	710.321	−	710.321i	1.04922	−	1.04922i	0.0504936	−	0.998724i	$-0.483921\pi$
$677$	710.321	−	710.321i	1.04922	−	1.04922i	0.998724	−	0.0504936i	$-0.0160794\pi$
$678$	−6.99998	+	105.069i	−0.0103245	+	0.154969i
$679$	−20.3942	−	561.153i	−0.0300357	−	0.826440i
$680$	69.7994	−	126.291i	0.102646	−	0.185723i
$681$	−167.961	−	191.938i	−0.246639	−	0.281848i
$682$	−277.934	−	277.934i	−0.407528	−	0.407528i
$683$	228.514	−	228.514i	0.334573	−	0.334573i	−0.519747	−	0.854320i	$-0.673974\pi$
$683$	228.514	−	228.514i	0.334573	−	0.334573i	0.854320	+	0.519747i	$0.173974\pi$
$684$	−19.2529	+	143.850i	−0.0281475	+	0.210307i
$685$	−65.8131	−	228.446i	−0.0960775	−	0.333497i
$686$	482.197	−	52.7601i	0.702912	−	0.0769097i
$687$	−68.8755	+	1033.81i	−0.100255	+	1.50482i
$688$	169.228	+	169.228i	0.245971	+	0.245971i
$689$		−	1422.04i		−	2.06391i
$690$	190.149	−	295.729i	0.275578	−	0.428592i
$691$			334.468i			0.484034i	0.970272	+	0.242017i	$0.0778090\pi$
$691$			334.468i			0.484034i	−0.970272	+	0.242017i	$0.922191\pi$
$692$	181.442	−	181.442i	0.262199	−	0.262199i
$693$	−325.971	+	268.311i	−0.470376	+	0.387173i
$694$		−	561.019i		−	0.808384i
$695$	509.282	+	281.473i	0.732780	+	0.404997i
$696$	−34.5213	−	39.4494i	−0.0495995	−	0.0566802i
$697$	535.427	−	535.427i	0.768188	−	0.768188i
$698$	−504.442	−	504.442i	−0.722697	−	0.722697i
$699$	−722.627	−	825.787i	−1.03380	−	1.18138i
$700$	343.828	+	65.4405i	0.491183	+	0.0934865i
$701$		−	786.818i		−	1.12242i	−0.827673	−	0.561211i	$-0.810336\pi$
$701$		−	786.818i		−	1.12242i	0.827673	−	0.561211i	$-0.189664\pi$
$702$	−171.360	+	847.199i	−0.244102	+	1.20684i
$703$	305.279	−	305.279i	0.434252	−	0.434252i
$704$	53.6119			0.0761533
$705$	177.546	+	817.063i	0.251838	+	1.15896i
$706$		−	410.867i		−	0.581964i
$707$	324.524	+	301.763i	0.459016	+	0.426821i
$708$	20.7304	−	311.160i	0.0292802	−	0.439491i
$709$		−	1314.72i		−	1.85434i	−0.374647	−	0.927168i	$-0.622236\pi$
$709$		−	1314.72i		−	1.85434i	0.374647	−	0.927168i	$-0.377764\pi$
$710$	−875.642	+	252.264i	−1.23330	+	0.355302i
$711$	30.7815	−	229.988i	0.0432933	−	0.323471i
$712$	−65.0039	−	65.0039i	−0.0912976	−	0.0912976i
$713$	486.048	+	486.048i	0.681695	+	0.681695i
$714$	220.641	−	207.702i	0.309021	−	0.290900i
$715$	209.977	+	728.855i	0.293673	+	1.01938i
$716$		−	46.7096i		−	0.0652369i
$717$	−41.8491	+	628.149i	−0.0583670	+	0.876080i
$718$	−428.176	−	428.176i	−0.596346	−	0.596346i
$719$		−	678.749i		−	0.944018i	−0.881594	−	0.472009i	$-0.843529\pi$
$719$		−	678.749i		−	0.944018i	0.881594	−	0.472009i	$-0.156471\pi$
$720$	−144.597	−	107.199i	−0.200829	−	0.148888i
$721$	−409.681	+	14.8892i	−0.568212	+	0.0206508i
$722$	−295.989	−	295.989i	−0.409957	−	0.409957i
$723$	−521.279	−	34.7291i	−0.720994	−	0.0480347i
$724$	−264.536			−0.365381
$725$	82.1698	+	130.775i	0.113338	+	0.180379i
$726$	−242.940	+	212.591i	−0.334628	+	0.292825i
$727$	−167.875	−	167.875i	−0.230915	−	0.230915i	0.582160	−	0.813074i	$-0.302208\pi$
$727$	−167.875	−	167.875i	−0.230915	−	0.230915i	−0.813074	+	0.582160i	$0.802208\pi$
$728$	−305.195	+	328.215i	−0.419224	+	0.450845i
$729$	−671.695	−	283.313i	−0.921393	−	0.388633i
$730$	−474.441	−	262.216i	−0.649919	−	0.359201i
$731$	−610.474			−0.835122
$732$	−5.98611	+	89.8507i	−0.00817775	+	0.122747i
$733$	138.636	−	138.636i	0.189135	−	0.189135i	−0.606187	−	0.795322i	$-0.707302\pi$
$733$	138.636	−	138.636i	0.189135	−	0.189135i	0.795322	+	0.606187i	$0.207302\pi$
$734$		−	305.309i		−	0.415952i
$735$	645.455	+	351.586i	0.878170	+	0.478348i
$736$	−93.7560			−0.127386
$737$	−259.413	−	259.413i	−0.351985	−	0.351985i
$738$	−573.403	−	750.608i	−0.776969	−	1.01708i
$739$			467.931i			0.633195i	0.948560	+	0.316598i	$0.102540\pi$
$739$			467.931i			0.633195i	−0.948560	+	0.316598i	$0.897460\pi$
$740$	148.229	+	514.523i	0.200310	+	0.695301i
$741$	360.586	+	412.062i	0.486621	+	0.556089i
$742$	455.420	+	423.478i	0.613774	+	0.570725i
$743$	164.867	−	164.867i	0.221893	−	0.221893i	−0.587402	−	0.809295i	$-0.699849\pi$
$743$	164.867	−	164.867i	0.221893	−	0.221893i	0.809295	+	0.587402i	$0.199849\pi$
$744$	264.832	−	231.749i	0.355957	−	0.311490i
$745$	−565.023	−	312.280i	−0.758419	−	0.419168i
$746$			765.227i			1.02577i
$747$	214.163	+	280.349i	0.286698	+	0.375299i
$748$	−96.7001	+	96.7001i	−0.129278	+	0.129278i
$749$	1.42643	+	39.2485i	0.00190444	+	0.0524013i
$750$	371.066	+	378.893i	0.494755	+	0.505191i
$751$	661.864			0.881310			0.440655	−	0.897677i	$-0.354746\pi$
$751$	661.864			0.881310			0.440655	+	0.897677i	$0.354746\pi$
$752$	157.662	−	157.662i	0.209657	−	0.209657i
$753$	−84.8152	+	1273.06i	−0.112636	+	1.69066i
$754$	−197.774			−0.262299
$755$	226.376	+	125.114i	0.299835	+	0.165715i
$756$	−220.293	−	307.173i	−0.291393	−	0.406313i
$757$	846.245	−	846.245i	1.11789	−	1.11789i	0.125843	−	0.992050i	$-0.459837\pi$
$757$	846.245	−	846.245i	1.11789	−	1.11789i	0.992050	−	0.125843i	$-0.0401635\pi$
$758$	−726.851	+	726.851i	−0.958907	+	0.958907i
$759$	−250.756	+	219.430i	−0.330376	+	0.289105i
$760$	−109.571	+	31.5664i	−0.144172	+	0.0415347i
$761$	29.8430			0.0392155			0.0196078	−	0.999808i	$-0.493758\pi$
$761$	29.8430			0.0392155			0.0196078	+	0.999808i	$0.493758\pi$
$762$	37.9458	−	569.561i	0.0497976	−	0.747456i
$763$	−516.327	+	555.273i	−0.676707	+	0.727750i
$764$	−275.336			−0.360387
$765$	454.166	−	67.4547i	0.593682	−	0.0881761i
$766$		−	930.211i		−	1.21437i
$767$	−831.941	−	831.941i	−1.08467	−	1.08467i
$768$	−3.19082	+	47.8938i	−0.00415472	+	0.0623618i
$769$	−331.944			−0.431656			−0.215828	−	0.976431i	$-0.569245\pi$
$769$	−331.944			−0.431656			−0.215828	+	0.976431i	$0.569245\pi$
$770$	−295.953	−	149.804i	−0.384354	−	0.194551i
$771$	69.3954	+	79.3021i	0.0900071	+	0.102856i
$772$	−376.009	+	376.009i	−0.487058	+	0.487058i
$773$	−221.297	−	221.297i	−0.286284	−	0.286284i	0.549325	−	0.835609i	$-0.314885\pi$
$773$	−221.297	−	221.297i	−0.286284	−	0.286284i	−0.835609	+	0.549325i	$0.814885\pi$
$774$	−101.022	+	754.795i	−0.130519	+	0.975187i
$775$	−877.919	+	551.624i	−1.13280	+	0.711772i
$776$	−226.890			−0.292384
$777$	−33.9498	+	1123.93i	−0.0436934	+	1.44650i
$778$	−120.366	−	120.366i	−0.154712	−	0.154712i
$779$	−598.367			−0.768123
$780$	−663.615	+	144.202i	−0.850789	+	0.184874i
$781$	863.627			1.10580
$782$	169.108	−	169.108i	0.216251	−	0.216251i
$783$	33.0689	−	163.492i	0.0422336	−	0.208802i
$784$	−14.2278	−	195.483i	−0.0181478	−	0.249340i
$785$	74.6433	+	259.096i	0.0950870	+	0.330059i
$786$	−225.058	+	196.943i	−0.286334	+	0.250564i
$787$	866.889	+	866.889i	1.10151	+	1.10151i	0.994229	+	0.107282i	$0.0342149\pi$
$787$	866.889	+	866.889i	1.10151	+	1.10151i	0.107282	+	0.994229i	$0.465785\pi$
$788$	−4.60854	+	4.60854i	−0.00584840	+	0.00584840i
$789$	615.254	+	703.086i	0.779790	+	0.891110i
$790$	175.182	−	50.4683i	0.221749	−	0.0638839i
$791$	−173.624	+	6.31010i	−0.219500	+	0.00797737i
$792$	103.559	+	135.563i	0.130756	+	0.171165i
$793$	240.232	+	240.232i	0.302941	+	0.302941i
$794$			625.735i			0.788080i
$795$	200.089	+	920.810i	0.251685	+	1.15825i
$796$		−	532.564i		−	0.669051i
$797$	258.945	−	258.945i	0.324900	−	0.324900i	−0.525743	−	0.850643i	$-0.676213\pi$
$797$	258.945	−	258.945i	0.324900	−	0.324900i	0.850643	+	0.525743i	$0.176213\pi$
$798$	−239.348	−	7.22982i	−0.299935	−	0.00905992i
$799$			568.753i			0.711831i
$800$	31.4703	−	137.875i	0.0393379	−	0.172344i
$801$	38.8045	−	289.932i	0.0484451	−	0.361963i
$802$	−641.900	+	641.900i	−0.800374	+	0.800374i
$803$	363.275	+	363.275i	0.452397	+	0.452397i
$804$	247.185	−	216.306i	0.307443	−	0.269037i
$805$	517.560	+	261.976i	0.642931	+	0.325436i
$806$		−	1327.70i		−	1.64727i
$807$	−752.113	−	50.1080i	−0.931987	−	0.0620916i
$808$	126.613	−	126.613i	0.156699	−	0.156699i
$809$	1378.37			1.70380			0.851898	−	0.523707i	$-0.175451\pi$
$809$	1378.37			1.70380			0.851898	+	0.523707i	$0.175451\pi$
$810$	−8.24578	−	572.697i	−0.0101800	−	0.707033i
$811$			1011.53i			1.24726i	0.781720	+	0.623630i	$0.214343\pi$
$811$			1011.53i			1.24726i	−0.781720	+	0.623630i	$0.785657\pi$
$812$	58.8964	−	63.3388i	0.0725325	−	0.0780035i
$813$	303.111	+	20.1941i	0.372831	+	0.0248391i
$814$		−	507.463i		−	0.623419i
$815$	120.799	+	419.308i	0.148219	+	0.514488i
$816$	−80.6310	−	92.1417i	−0.0988126	−	0.112919i
$817$	341.118	+	341.118i	0.417526	+	0.417526i
$818$	−134.590	−	134.590i	−0.164535	−	0.164535i
$819$	−1419.45	−	137.721i	−1.73315	−	0.168158i
$820$	358.980	−	649.520i	0.437781	−	0.792097i
$821$		−	423.217i		−	0.515490i	−0.966213	−	0.257745i	$-0.917021\pi$
$821$		−	423.217i		−	0.515490i	0.966213	−	0.257745i	$-0.0829794\pi$
$822$	−201.280	−	13.4099i	−0.244866	−	0.0163137i
$823$	−538.152	−	538.152i	−0.653891	−	0.653891i	0.300037	−	0.953928i	$-0.403001\pi$
$823$	−538.152	−	538.152i	−0.653891	−	0.653891i	−0.953928	+	0.300037i	$0.903001\pi$
$824$			165.645i			0.201026i
$825$	−238.520	−	442.410i	−0.289116	−	0.536254i
$826$	514.186	−	18.6873i	0.622502	−	0.0226238i
$827$	632.746	+	632.746i	0.765110	+	0.765110i	0.977241	−	0.212131i	$-0.0680404\pi$
$827$	632.746	+	632.746i	0.765110	+	0.765110i	−0.212131	+	0.977241i	$0.568040\pi$
$828$	−181.102	−	237.071i	−0.218723	−	0.286317i
$829$	−376.988			−0.454750			−0.227375	−	0.973807i	$-0.573014\pi$
$829$	−376.988			−0.454750			−0.227375	+	0.973807i	$0.573014\pi$
$830$	−134.077	+	242.593i	−0.161539	+	0.292280i
$831$	−833.462	−	952.444i	−1.00296	−	1.14614i
$832$	128.053	+	128.053i	0.153909	+	0.153909i
$833$	378.256	+	326.931i	0.454089	+	0.392474i
$834$	371.570	−	325.152i	0.445528	−	0.389871i
$835$	1102.46	−	317.610i	1.32032	−	0.380371i
$836$	108.067			0.129267
$837$	1097.56	+	221.999i	1.31130	+	0.265232i
$838$	268.374	−	268.374i	0.320255	−	0.320255i
$839$			30.3808i			0.0362107i	0.999836	+	0.0181054i	$0.00576343\pi$
$839$			30.3808i			0.0362107i	−0.999836	+	0.0181054i	$0.994237\pi$
$840$	151.441	−	255.472i	0.180286	−	0.304133i
$841$	−802.834			−0.954618
$842$	−28.9266	−	28.9266i	−0.0343546	−	0.0343546i
$843$	315.258	+	21.0034i	0.373972	+	0.0249151i
$844$			208.315i			0.246819i
$845$	−830.603	+	1502.85i	−0.982962	+	1.77852i
$846$	703.210	+	94.1175i	0.831218	+	0.111250i
$847$	−390.057	−	362.699i	−0.460516	−	0.428216i
$848$	177.682	−	177.682i	0.209530	−	0.209530i
$849$	−575.469	−	657.621i	−0.677819	−	0.774583i
$850$	191.923	+	305.450i	0.225792	+	0.359353i
$851$			887.446i			1.04283i
$852$	−51.4006	+	771.515i	−0.0603293	+	0.905534i
$853$	396.677	−	396.677i	0.465038	−	0.465038i	−0.435265	−	0.900303i	$-0.643345\pi$
$853$	396.677	−	396.677i	0.465038	−	0.465038i	0.900303	+	0.435265i	$0.143345\pi$
$854$	−148.477	+	5.39616i	−0.173860	+	0.00631868i
$855$	−291.469	−	216.085i	−0.340900	−	0.252731i
$856$	15.8693			0.0185389
$857$	−303.815	+	303.815i	−0.354510	+	0.354510i	−0.861785	−	0.507274i	$-0.830653\pi$
$857$	−303.815	+	303.815i	−0.354510	+	0.354510i	0.507274	+	0.861785i	$0.330653\pi$
$858$	642.184	+	42.7841i	0.748466	+	0.0498650i
$859$	−139.382			−0.162261			−0.0811304	−	0.996703i	$-0.525853\pi$
$859$	−139.382			−0.162261			−0.0811304	+	0.996703i	$0.525853\pi$
$860$	−574.928	+	165.631i	−0.668520	+	0.192595i
$861$	1134.76	−	1068.22i	1.31796	−	1.24067i
$862$	−276.630	+	276.630i	−0.320917	+	0.320917i
$863$	698.585	−	698.585i	0.809484	−	0.809484i	−0.175072	−	0.984556i	$-0.556016\pi$
$863$	698.585	−	698.585i	0.809484	−	0.809484i	0.984556	+	0.175072i	$0.0560158\pi$
$864$	−127.267	+	84.4452i	−0.147300	+	0.0977375i
$865$	177.586	+	616.422i	0.205301	+	0.712627i
$866$	−499.634			−0.576945
$867$	−553.451	−	36.8725i	−0.638352	−	0.0425288i
$868$	425.207	+	395.384i	0.489870	+	0.455512i
$869$	−172.778			−0.198824
$870$	128.064	−	27.8280i	0.147200	−	0.0319862i
$871$		−	1239.22i		−	1.42276i
$872$	216.639	+	216.639i	0.248439	+	0.248439i
$873$	−438.268	−	573.712i	−0.502026	−	0.657172i
$874$	−188.987			−0.216233
$875$	−558.980	+	673.176i	−0.638835	+	0.769344i
$876$	−346.150	+	302.908i	−0.395148	+	0.345785i
$877$	122.285	−	122.285i	0.139435	−	0.139435i	−0.633944	−	0.773379i	$-0.718565\pi$
$877$	122.285	−	122.285i	0.139435	−	0.139435i	0.773379	+	0.633944i	$0.218565\pi$
$878$	519.817	+	519.817i	0.592047	+	0.592047i
$879$	−393.107	+	343.999i	−0.447220	+	0.391352i
$880$	−64.8332	+	117.306i	−0.0736741	+	0.133302i
$881$	75.7345			0.0859643			0.0429821	−	0.999076i	$-0.486314\pi$
$881$	75.7345			0.0859643			0.0429821	+	0.999076i	$0.486314\pi$
$882$	466.814	−	413.578i	0.529267	−	0.468910i
$883$	−1004.90	−	1004.90i	−1.13805	−	1.13805i	−0.988799	−	0.149255i	$-0.952313\pi$
$883$	−1004.90	−	1004.90i	−1.13805	−	1.13805i	−0.149255	−	0.988799i	$-0.547687\pi$
$884$	−461.939			−0.522555
$885$	655.765	+	421.647i	0.740978	+	0.476437i
$886$	777.176			0.877173
$887$	265.442	−	265.442i	0.299258	−	0.299258i	−0.541465	−	0.840723i	$-0.682130\pi$
$887$	265.442	−	265.442i	0.299258	−	0.299258i	0.840723	+	0.541465i	$0.182130\pi$
$888$	453.339	+	30.2027i	0.510517	+	0.0340121i
$889$	941.190	−	34.2061i	1.05871	−	0.0384770i
$890$	220.842	−	63.6224i	0.248137	−	0.0714859i
$891$	−142.745	+	523.716i	−0.160208	+	0.587784i
$892$	−5.19500	−	5.19500i	−0.00582399	−	0.00582399i
$893$	317.806	−	317.806i	0.355885	−	0.355885i
$894$	−412.238	+	360.740i	−0.461117	+	0.403512i
$895$	102.203	+	56.4862i	0.114193	+	0.0631131i
$896$	−79.1437	+	2.87635i	−0.0883300	+	0.00321022i
$897$	−1123.05	−	74.8205i	−1.25200	−	0.0834119i
$898$	−283.968	−	283.968i	−0.316223	−	0.316223i
$899$			256.218i			0.285004i
$900$	409.420	−	186.750i	0.454911	−	0.207499i
$901$			640.970i			0.711399i
$902$	−497.331	+	497.331i	−0.551365	+	0.551365i
$903$	−1255.88	−	37.9355i	−1.39079	−	0.0420105i
$904$			70.2011i			0.0776560i
$905$	319.905	−	578.819i	0.353486	−	0.639579i
$906$	165.163	−	144.530i	0.182299	−	0.159525i
$907$	149.728	−	149.728i	0.165081	−	0.165081i	−0.619732	−	0.784813i	$-0.712759\pi$
$907$	149.728	−	149.728i	0.165081	−	0.165081i	0.784813	+	0.619732i	$0.212759\pi$
$908$	−120.232	−	120.232i	−0.132415	−	0.132415i
$909$	564.721	+	75.5822i	0.621255	+	0.0831487i
$910$	−349.079	−	1064.70i	−0.383603	−	1.17000i
$911$		−	1426.12i		−	1.56544i	−0.622373	−	0.782721i	$-0.713831\pi$
$911$		−	1426.12i		−	1.56544i	0.622373	−	0.782721i	$-0.286169\pi$
$912$	−6.43186	+	96.5413i	−0.00705248	+	0.105857i
$913$	185.751	−	185.751i	0.203451	−	0.203451i
$914$	−402.736			−0.440630
$915$	−189.359	−	121.755i	−0.206950	−	0.133066i
$916$			690.735i			0.754078i
$917$	−361.347	−	336.003i	−0.394054	−	0.366416i
$918$	77.2389	−	381.867i	0.0841382	−	0.415977i
$919$		−	816.634i		−	0.888612i	−0.895875	−	0.444306i	$-0.853450\pi$
$919$		−	816.634i		−	0.888612i	0.895875	−	0.444306i	$-0.146550\pi$
$920$	113.380	−	205.143i	0.123239	−	0.222982i
$921$	749.187	−	655.596i	0.813450	−	0.711831i
$922$	553.509	+	553.509i	0.600335	+	0.600335i
$923$	2062.78	+	2062.78i	2.23487	+	2.23487i
$924$	−204.942	+	192.924i	−0.221799	+	0.208792i
$925$	−1305.06	−	297.882i	−1.41087	−	0.322034i
$926$			1149.73i			1.24161i
$927$	−418.850	+	319.967i	−0.451834	+	0.345164i
$928$	−24.7116	−	24.7116i	−0.0266288	−	0.0266288i
$929$			238.799i			0.257050i	0.991706	+	0.128525i	$0.0410242\pi$
$929$			238.799i			0.257050i	−0.991706	+	0.128525i	$0.958976\pi$
$930$	186.815	+	859.722i	0.200877	+	0.924432i
$931$	−28.6796	−	394.042i	−0.0308051	−	0.423246i
$932$	−517.282	−	517.282i	−0.555024	−	0.555024i
$933$	62.3777	−	936.280i	0.0668571	−	1.00352i
$934$	1257.85			1.34673
$935$	−94.6450	−	328.525i	−0.101225	−	0.351364i
$936$	−76.4418	+	571.144i	−0.0816686	+	0.610197i
$937$	397.595	+	397.595i	0.424328	+	0.424328i	0.886691	−	0.462363i	$-0.152998\pi$
$937$	397.595	+	397.595i	0.424328	+	0.424328i	−0.462363	+	0.886691i	$0.652998\pi$
$938$	396.873	+	369.037i	0.423105	+	0.393429i
$939$	672.013	+	767.948i	0.715669	+	0.817836i
$940$	154.312	+	535.636i	0.164161	+	0.569825i
$941$	64.3259			0.0683591			0.0341796	−	0.999416i	$-0.489118\pi$
$941$	64.3259			0.0683591			0.0341796	+	0.999416i	$0.489118\pi$
$942$	228.286	+	15.2091i	0.242342	+	0.0161455i
$943$	869.728	−	869.728i	0.922299	−	0.922299i
$944$		−	207.900i		−	0.220233i
$945$	938.512	−	110.547i	0.993134	−	0.116981i
$946$	567.039			0.599407
$947$	−74.9155	−	74.9155i	−0.0791083	−	0.0791083i	0.666445	−	0.745554i	$-0.267815\pi$
$947$	−74.9155	−	74.9155i	−0.0791083	−	0.0791083i	−0.745554	+	0.666445i	$0.767815\pi$
$948$	10.2833	−	154.350i	0.0108473	−	0.162817i
$949$			1735.37i			1.82863i
$950$	63.4358	−	277.920i	0.0667745	−	0.292548i
$951$	−545.416	+	477.281i	−0.573518	+	0.501872i
$952$	137.564	−	147.940i	0.144500	−	0.155399i
$953$	445.618	−	445.618i	0.467595	−	0.467595i	−0.433540	−	0.901134i	$-0.642736\pi$
$953$	445.618	−	445.618i	0.467595	−	0.467595i	0.901134	+	0.433540i	$0.142736\pi$
$954$	792.500	+	106.068i	0.830713	+	0.111183i
$955$	332.965	−	602.449i	0.348655	−	0.630837i
$956$			419.695i			0.439011i
$957$	−123.928	−	8.25647i	−0.129497	−	0.00862745i
$958$	229.796	−	229.796i	0.239871	−	0.239871i
$959$	−12.0883	−	332.612i	−0.0126051	−	0.346832i
$960$	−100.936	−	64.9000i	−0.105141	−	0.0676041i
$961$	−759.049			−0.789853
$962$	1212.08	−	1212.08i	1.25996	−	1.25996i
$963$	30.6537	+	40.1269i	0.0318314	+	0.0416687i
$964$	−348.289			−0.361296
$965$	−368.018	−	1277.44i	−0.381366	−	1.32377i
$966$	358.401	−	337.384i	0.371016	−	0.349259i
$967$	−1035.26	+	1035.26i	−1.07059	+	1.07059i	−0.0732796	+	0.997311i	$0.523347\pi$
$967$	−1035.26	+	1035.26i	−1.07059	+	1.07059i	−0.997311	+	0.0732796i	$0.976653\pi$
$968$	−152.180	+	152.180i	−0.157211	+	0.157211i
$969$	−162.531	−	185.733i	−0.167731	−	0.191675i
$970$	274.379	−	496.447i	0.282865	−	0.511801i
$971$	−1533.72			−1.57952			−0.789762	−	0.613413i	$-0.789796\pi$
$971$	−1533.72			−1.57952			−0.789762	+	0.613413i	$0.789796\pi$
$972$	−459.362	−	158.690i	−0.472595	−	0.163262i
$973$	596.582	+	554.739i	0.613137	+	0.570133i
$974$	116.042			0.119140
$975$	486.993	−	1626.41i	0.499480	−	1.66811i
$976$			60.0333i			0.0615095i
$977$	975.493	+	975.493i	0.998458	+	0.998458i	0.999999	−	0.00154127i	$-0.000490601\pi$
$977$	975.493	+	975.493i	0.998458	+	0.998458i	−0.00154127	+	0.999999i	$0.500491\pi$
$978$	369.446	+	24.6136i	0.377757	+	0.0251672i
$979$	−217.811			−0.222484
$980$	444.933	+	205.267i	0.454013	+	0.209456i
$981$	−129.324	+	966.259i	−0.131829	+	0.984973i
$982$	105.182	−	105.182i	0.107110	−	0.107110i
$983$	−518.969	−	518.969i	−0.527944	−	0.527944i	0.392015	−	0.919959i	$-0.371778\pi$
$983$	−518.969	−	518.969i	−0.527944	−	0.527944i	−0.919959	+	0.392015i	$0.871778\pi$
$984$	−414.688	−	473.887i	−0.421431	−	0.481593i
$985$	−4.51060	−	15.6569i	−0.00457928	−	0.0158953i
$986$	89.1447			0.0904105
$987$	−35.3429	+	1170.05i	−0.0358084	+	1.18546i
$988$	258.120	+	258.120i	0.261255	+	0.261255i
$989$	−991.632			−1.00266
$990$	−421.853	+	62.6553i	−0.426114	+	0.0632882i
$991$	398.566			0.402185			0.201093	−	0.979572i	$-0.435551\pi$
$991$	398.566			0.402185			0.201093	+	0.979572i	$0.435551\pi$
$992$	165.894	−	165.894i	0.167232	−	0.167232i
$993$	84.0050	−	1260.90i	0.0845972	−	1.26979i
$994$	−1274.92	+	46.3348i	−1.28261	+	0.0466145i
$995$	1165.28	+	644.033i	1.17114	+	0.647270i
$996$	154.884	+	176.995i	0.155506	+	0.177705i
$997$	1068.24	+	1068.24i	1.07146	+	1.07146i	0.997242	+	0.0742170i	$0.0236457\pi$
$997$	1068.24	+	1068.24i	1.07146	+	1.07146i	0.0742170	+	0.997242i	$0.476354\pi$
$998$	29.9809	−	29.9809i	0.0300409	−	0.0300409i
$999$	799.315	+	1204.65i	0.800115	+	1.20586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.k.b.83.8	yes	32
3.2	odd	2		210.3.k.a.83.1	✓	32
5.2	odd	4		210.3.k.a.167.16	yes	32
7.6	odd	2	inner	210.3.k.b.83.9	yes	32
15.2	even	4	inner	210.3.k.b.167.9	yes	32
21.20	even	2		210.3.k.a.83.16	yes	32
35.27	even	4		210.3.k.a.167.1	yes	32
105.62	odd	4	inner	210.3.k.b.167.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.k.a.83.1	✓	32	3.2	odd	2
210.3.k.a.83.16	yes	32	21.20	even	2
210.3.k.a.167.1	yes	32	35.27	even	4
210.3.k.a.167.16	yes	32	5.2	odd	4
210.3.k.b.83.8	yes	32	1.1	even	1	trivial
210.3.k.b.83.9	yes	32	7.6	odd	2	inner
210.3.k.b.167.8	yes	32	105.62	odd	4	inner
210.3.k.b.167.9	yes	32	15.2	even	4	inner

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.199427 + 2.99336i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 + 2.79394i) q^{6} +(-5.12625 - 4.76671i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.199427 + 2.99336i) q^{3} +2.00000i q^{4} +(-4.37611 - 2.41861i) q^{5} +(-3.19279 + 2.79394i) q^{6} +(-5.12625 - 4.76671i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-8.92046 - 1.19391i) q^{9} +(-1.95750 - 6.79472i) q^{10} +6.70149i q^{11} +(-5.98673 - 0.398853i) q^{12} +(-16.0066 + 16.0066i) q^{13} +(-0.359544 - 9.89296i) q^{14} +(8.11250 - 12.6169i) q^{15} -4.00000 q^{16} +(7.21482 - 7.21482i) q^{17} +(-7.72655 - 10.1144i) q^{18} -8.06294 q^{19} +(4.83722 - 8.75222i) q^{20} +(15.2908 - 14.3941i) q^{21} +(-6.70149 + 6.70149i) q^{22} +(11.7195 - 11.7195i) q^{23} +(-5.58788 - 6.38558i) q^{24} +(13.3006 + 21.1682i) q^{25} -32.0132 q^{26} +(5.35279 - 26.4641i) q^{27} +(9.53342 - 10.2525i) q^{28} +6.17789 q^{29} +(20.7294 - 4.50445i) q^{30} +41.4735i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-20.0600 - 1.33645i) q^{33} +14.4296 q^{34} +(10.9042 + 33.2581i) q^{35} +(2.38782 - 17.8409i) q^{36} +(-37.8620 + 37.8620i) q^{37} +(-8.06294 - 8.06294i) q^{38} +(-44.7214 - 51.1057i) q^{39} +(13.5894 - 3.91499i) q^{40} +74.2121 q^{41} +(29.6849 + 0.896672i) q^{42} +(-42.3069 - 42.3069i) q^{43} -13.4030 q^{44} +(36.1493 + 26.7998i) q^{45} +23.4390 q^{46} +(-39.4156 + 39.4156i) q^{47} +(0.797706 - 11.9735i) q^{48} +(3.55696 + 48.8707i) q^{49} +(-7.86757 + 34.4688i) q^{50} +(20.1578 + 23.0354i) q^{51} +(-32.0132 - 32.0132i) q^{52} +(-44.4204 + 44.4204i) q^{53} +(31.8169 - 21.1113i) q^{54} +(16.2083 - 29.3264i) q^{55} +(19.7859 - 0.719089i) q^{56} +(1.60796 - 24.1353i) q^{57} +(6.17789 + 6.17789i) q^{58} +51.9749i q^{59} +(25.2339 + 16.2250i) q^{60} -15.0083i q^{61} +(-41.4735 + 41.4735i) q^{62} +(40.0375 + 48.6415i) q^{63} -8.00000i q^{64} +(108.760 - 31.3328i) q^{65} +(-18.7235 - 21.3964i) q^{66} +(-38.7098 + 38.7098i) q^{67} +(14.4296 + 14.4296i) q^{68} +(32.7435 + 37.4179i) q^{69} +(-22.3538 + 44.1623i) q^{70} -128.871i q^{71} +(20.2287 - 15.4531i) q^{72} +(54.2081 - 54.2081i) q^{73} -75.7239 q^{74} +(-66.0167 + 35.5921i) q^{75} -16.1259i q^{76} +(31.9440 - 34.3535i) q^{77} +(6.38427 - 95.8271i) q^{78} +25.7821i q^{79} +(17.5044 + 9.67445i) q^{80} +(78.1491 + 21.3005i) q^{81} +(74.2121 + 74.2121i) q^{82} +(-27.7179 - 27.7179i) q^{83} +(28.7883 + 30.5816i) q^{84} +(-49.0227 + 14.1230i) q^{85} -84.6139i q^{86} +(-1.23203 + 18.4927i) q^{87} +(-13.4030 - 13.4030i) q^{88} +32.5020i q^{89} +(9.34946 + 62.9491i) q^{90} +(158.353 - 5.75508i) q^{91} +(23.4390 + 23.4390i) q^{92} +(-124.145 - 8.27091i) q^{93} -78.8312 q^{94} +(35.2843 + 19.5011i) q^{95} +(12.7712 - 11.1758i) q^{96} +(56.7224 + 56.7224i) q^{97} +(-45.3138 + 52.4277i) q^{98} +(8.00099 - 59.7803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9	\( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9} - 8 q^{14} - 4 q^{15} - 128 q^{16} - 4 q^{18} + 12 q^{21} - 40 q^{22} - 24 q^{23} + 16 q^{25} - 8 q^{28} + 112 q^{29} + 28 q^{30} - 128 q^{32} + 48 q^{35} - 40 q^{36} + 32 q^{37} - 64 q^{39} - 20 q^{42} - 32 q^{43} - 80 q^{44} - 48 q^{46} + 8 q^{50} + 84 q^{51} + 136 q^{53} + 340 q^{57} + 112 q^{58} + 64 q^{60} + 168 q^{63} + 200 q^{65} + 32 q^{67} - 72 q^{72} + 64 q^{74} - 88 q^{77} - 4 q^{78} + 76 q^{81} - 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} - 48 q^{92} - 388 q^{93} - 544 q^{95} - 128 q^{98} - 160 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9 - 8 * q^14 - 4 * q^15 - 128 * q^16 - 4 * q^18 + 12 * q^21 - 40 * q^22 - 24 * q^23 + 16 * q^25 - 8 * q^28 + 112 * q^29 + 28 * q^30 - 128 * q^32 + 48 * q^35 - 40 * q^36 + 32 * q^37 - 64 * q^39 - 20 * q^42 - 32 * q^43 - 80 * q^44 - 48 * q^46 + 8 * q^50 + 84 * q^51 + 136 * q^53 + 340 * q^57 + 112 * q^58 + 64 * q^60 + 168 * q^63 + 200 * q^65 + 32 * q^67 - 72 * q^72 + 64 * q^74 - 88 * q^77 - 4 * q^78 + 76 * q^81 - 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 - 48 * q^92 - 388 * q^93 - 544 * q^95 - 128 * q^98 - 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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