LMFDB - Embedded newform 380.2.bj.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14173 + 0.834541i) q^{2} +(-2.50164 - 1.75167i) q^{3} +(0.607081 - 1.90564i) q^{4} +(2.16402 - 0.563029i) q^{5} +(4.31804 - 0.0877964i) q^{6} +(0.675461 - 0.180989i) q^{7} +(0.897212 + 2.68235i) q^{8} +(2.16382 + 5.94503i) q^{9} +O(q^{10})$	\(q+(-1.14173 + 0.834541i) q^{2} +(-2.50164 - 1.75167i) q^{3} +(0.607081 - 1.90564i) q^{4} +(2.16402 - 0.563029i) q^{5} +(4.31804 - 0.0877964i) q^{6} +(0.675461 - 0.180989i) q^{7} +(0.897212 + 2.68235i) q^{8} +(2.16382 + 5.94503i) q^{9} +(-2.00085 + 2.44879i) q^{10} +(2.67109 - 1.54215i) q^{11} +(-4.85675 + 3.70382i) q^{12} +(-2.35452 + 1.64865i) q^{13} +(-0.620149 + 0.770341i) q^{14} +(-6.39986 - 2.38216i) q^{15} +(-3.26290 - 2.31375i) q^{16} +(4.93433 - 2.30092i) q^{17} +(-7.43186 - 4.98181i) q^{18} +(4.23631 - 1.02651i) q^{19} +(0.240809 - 4.46565i) q^{20} +(-2.00680 - 0.730414i) q^{21} +(-1.76266 + 3.98985i) q^{22} +(-5.86180 + 0.512841i) q^{23} +(2.45409 - 8.28191i) q^{24} +(4.36600 - 2.43682i) q^{25} +(1.31235 - 3.84726i) q^{26} +(2.62938 - 9.81300i) q^{27} +(0.0651600 - 1.39706i) q^{28} +(-2.34879 - 6.45324i) q^{29} +(9.29490 - 2.62117i) q^{30} +(3.20498 + 1.85040i) q^{31} +(5.65627 - 0.0813539i) q^{32} +(-9.38346 - 0.820946i) q^{33} +(-3.71345 + 6.74492i) q^{34} +(1.35981 - 0.771969i) q^{35} +(12.6427 - 0.514327i) q^{36} +(4.28677 - 4.28677i) q^{37} +(-3.98004 + 4.70736i) q^{38} +8.77807 q^{39} +(3.45183 + 5.29952i) q^{40} +(0.0276960 + 0.157072i) q^{41} +(2.90078 - 0.840821i) q^{42} +(0.221939 - 2.53677i) q^{43} +(-1.31722 - 6.02634i) q^{44} +(8.02977 + 11.6469i) q^{45} +(6.26459 - 5.47744i) q^{46} +(-8.92943 - 4.16386i) q^{47} +(4.10969 + 11.5037i) q^{48} +(-5.63869 + 3.25550i) q^{49} +(-2.95115 + 6.42578i) q^{50} +(-16.3744 - 2.88725i) q^{51} +(1.71235 + 5.48773i) q^{52} +(-0.974074 - 11.1337i) q^{53} +(5.18731 + 13.3981i) q^{54} +(4.91202 - 4.84116i) q^{55} +(1.09151 + 1.64944i) q^{56} +(-12.3958 - 4.85266i) q^{57} +(8.06717 + 5.40768i) q^{58} +(-3.73037 - 1.35774i) q^{59} +(-8.42476 + 10.7496i) q^{60} +(-1.11880 - 0.938789i) q^{61} +(-5.20344 + 0.562041i) q^{62} +(2.53756 + 3.62401i) q^{63} +(-6.39002 + 4.81327i) q^{64} +(-4.16700 + 4.89339i) q^{65} +(11.3985 - 6.89359i) q^{66} +(14.1231 + 6.58573i) q^{67} +(-1.38917 - 10.7999i) q^{68} +(15.5625 + 8.98500i) q^{69} +(-0.908293 + 2.01620i) q^{70} +(3.88690 + 4.63223i) q^{71} +(-14.0053 + 11.1381i) q^{72} +(-2.89514 + 4.13469i) q^{73} +(-1.31683 + 8.47181i) q^{74} +(-15.1907 - 1.55173i) q^{75} +(0.615635 - 8.69603i) q^{76} +(1.52510 - 1.52510i) q^{77} +(-10.0222 + 7.32567i) q^{78} +(-0.681245 - 3.86353i) q^{79} +(-8.36371 - 3.16991i) q^{80} +(-9.22761 + 7.74289i) q^{81} +(-0.162704 - 0.156220i) q^{82} +(0.189756 + 0.708179i) q^{83} +(-2.61019 + 3.38081i) q^{84} +(9.38253 - 7.75741i) q^{85} +(1.86365 + 3.08152i) q^{86} +(-5.42812 + 20.2580i) q^{87} +(6.53313 + 5.78116i) q^{88} +(-11.5536 - 2.03722i) q^{89} +(-18.8876 - 6.59640i) q^{90} +(-1.29200 + 1.53974i) q^{91} +(-2.58130 + 11.4818i) q^{92} +(-4.77644 - 10.2431i) q^{93} +(13.6699 - 2.69798i) q^{94} +(8.58951 - 4.60655i) q^{95} +(-14.2925 - 9.70440i) q^{96} +(2.04801 - 0.955003i) q^{97} +(3.72099 - 8.42261i) q^{98} +(14.9479 + 12.5428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.14173	+	0.834541i	−0.807323	+	0.590110i
$2$	−1.14173	+	0.834541i	−0.807323	+	0.590110i
$3$	−2.50164	−	1.75167i	−1.44432	−	1.01133i	−0.992892	−	0.119022i	$-0.962024\pi$
$3$	−2.50164	−	1.75167i	−1.44432	−	1.01133i	−0.451433	−	0.892305i	$-0.649087\pi$
$4$	0.607081	−	1.90564i	0.303541	−	0.952818i
$5$	2.16402	−	0.563029i	0.967781	−	0.251794i
$5$	2.16402	−	0.563029i	0.967781	−	0.251794i
$6$	4.31804	−	0.0877964i	1.76283	−	0.0358427i
$7$	0.675461	−	0.180989i	0.255300	−	0.0684075i	−0.128899	−	0.991658i	$-0.541144\pi$
$7$	0.675461	−	0.180989i	0.255300	−	0.0684075i	0.384199	+	0.923250i	$0.374478\pi$
$8$	0.897212	+	2.68235i	0.317212	+	0.948355i
$9$	2.16382	+	5.94503i	0.721272	+	1.98168i
$10$	−2.00085	+	2.44879i	−0.632725	+	0.774376i
$11$	2.67109	−	1.54215i	0.805363	−	0.464977i	−0.0399797	−	0.999200i	$-0.512729\pi$
$11$	2.67109	−	1.54215i	0.805363	−	0.464977i	0.845343	+	0.534224i	$0.179396\pi$
$12$	−4.85675	+	3.70382i	−1.40202	+	1.06920i
$13$	−2.35452	+	1.64865i	−0.653027	+	0.457254i	−0.852555	−	0.522638i	$-0.824948\pi$
$13$	−2.35452	+	1.64865i	−0.653027	+	0.457254i	0.199528	+	0.979892i	$0.436059\pi$
$14$	−0.620149	+	0.770341i	−0.165742	+	0.205882i
$15$	−6.39986	−	2.38216i	−1.65244	−	0.615070i
$16$	−3.26290	−	2.31375i	−0.815726	−	0.578438i
$17$	4.93433	−	2.30092i	1.19675	−	0.558054i	0.280964	−	0.959718i	$-0.409346\pi$
$17$	4.93433	−	2.30092i	1.19675	−	0.558054i	0.915787	+	0.401664i	$0.131568\pi$
$18$	−7.43186	−	4.98181i	−1.75171	−	1.17422i
$19$	4.23631	−	1.02651i	0.971875	−	0.235497i
$19$	4.23631	−	1.02651i	0.971875	−	0.235497i
$20$	0.240809	−	4.46565i	0.0538465	−	0.998549i
$21$	−2.00680	−	0.730414i	−0.437919	−	0.159389i
$22$	−1.76266	+	3.98985i	−0.375801	+	0.850639i
$23$	−5.86180	+	0.512841i	−1.22227	+	0.106935i	−0.679964	−	0.733246i	$-0.738005\pi$
$23$	−5.86180	+	0.512841i	−1.22227	+	0.106935i	−0.542307	+	0.840181i	$0.682449\pi$
$24$	2.45409	−	8.28191i	0.500939	−	1.69054i
$25$	4.36600	−	2.43682i	0.873199	−	0.487364i
$26$	1.31235	−	3.84726i	0.257373	−	0.754510i
$27$	2.62938	−	9.81300i	0.506025	−	1.88851i
$28$	0.0651600	−	1.39706i	0.0123141	−	0.264019i
$29$	−2.34879	−	6.45324i	−0.436159	−	1.19834i	−0.941971	−	0.335693i	$-0.891029\pi$
$29$	−2.34879	−	6.45324i	−0.436159	−	1.19834i	0.505812	−	0.862643i	$-0.331193\pi$
$30$	9.29490	−	2.62117i	1.69701	−	0.478559i
$31$	3.20498	+	1.85040i	0.575631	+	0.332341i	0.759395	−	0.650630i	$-0.225495\pi$
$31$	3.20498	+	1.85040i	0.575631	+	0.332341i	−0.183764	+	0.982970i	$0.558828\pi$
$32$	5.65627	−	0.0813539i	0.999897	−	0.0143815i
$33$	−9.38346	−	0.820946i	−1.63345	−	0.142908i
$34$	−3.71345	+	6.74492i	−0.636851	+	1.15674i
$35$	1.35981	−	0.771969i	0.229850	−	0.130487i
$36$	12.6427	−	0.514327i	2.10711	−	0.0857212i
$37$	4.28677	−	4.28677i	0.704740	−	0.704740i	−0.260684	−	0.965424i	$-0.583948\pi$
$37$	4.28677	−	4.28677i	0.704740	−	0.704740i	0.965424	+	0.260684i	$0.0839480\pi$
$38$	−3.98004	+	4.70736i	−0.645648	+	0.763635i
$39$	8.77807			1.40562
$40$	3.45183	+	5.29952i	0.545782	+	0.837927i
$41$	0.0276960	+	0.157072i	0.00432540	+	0.0245305i	0.986894	−	0.161369i	$-0.0515911\pi$
$41$	0.0276960	+	0.157072i	0.00432540	+	0.0245305i	−0.982569	+	0.185900i	$0.940480\pi$
$42$	2.90078	−	0.840821i	0.447599	−	0.129742i
$43$	0.221939	−	2.53677i	0.0338453	−	0.386854i	−0.960313	−	0.278924i	$-0.910022\pi$
$43$	0.221939	−	2.53677i	0.0338453	−	0.386854i	0.994159	−	0.107930i	$-0.0344222\pi$
$44$	−1.31722	−	6.02634i	−0.198578	−	0.908505i
$45$	8.02977	+	11.6469i	1.19701	+	1.73622i
$46$	6.26459	−	5.47744i	0.923664	−	0.807605i
$47$	−8.92943	−	4.16386i	−1.30249	−	0.607361i	−0.357333	−	0.933977i	$-0.616314\pi$
$47$	−8.92943	−	4.16386i	−1.30249	−	0.607361i	−0.945157	+	0.326616i	$0.894092\pi$
$48$	4.10969	+	11.5037i	0.593183	+	1.66042i
$49$	−5.63869	+	3.25550i	−0.805527	+	0.465071i
$50$	−2.95115	+	6.42578i	−0.417356	+	0.908743i
$51$	−16.3744	−	2.88725i	−2.29287	−	0.404295i
$52$	1.71235	+	5.48773i	0.237460	+	0.761011i
$53$	−0.974074	−	11.1337i	−0.133799	−	1.52933i	−0.705405	−	0.708805i	$-0.749235\pi$
$53$	−0.974074	−	11.1337i	−0.133799	−	1.52933i	0.571605	−	0.820529i	$-0.306321\pi$
$54$	5.18731	+	13.3981i	0.705904	+	1.82325i
$55$	4.91202	−	4.84116i	0.662337	−	0.652782i
$56$	1.09151	+	1.64944i	0.145859	+	0.220416i
$57$	−12.3958	−	4.85266i	−1.64187	−	0.642750i
$58$	8.06717	+	5.40768i	1.05927	+	0.710063i
$59$	−3.73037	−	1.35774i	−0.485652	−	0.176763i	0.0875773	−	0.996158i	$-0.472088\pi$
$59$	−3.73037	−	1.35774i	−0.485652	−	0.176763i	−0.573230	+	0.819395i	$0.694310\pi$
$60$	−8.42476	+	10.7496i	−1.08763	+	1.38777i
$61$	−1.11880	−	0.938789i	−0.143248	−	0.120200i	0.568348	−	0.822788i	$-0.307583\pi$
$61$	−1.11880	−	0.938789i	−0.143248	−	0.120200i	−0.711596	+	0.702589i	$0.752027\pi$
$62$	−5.20344	+	0.562041i	−0.660838	+	0.0713793i
$63$	2.53756	+	3.62401i	0.319702	+	0.456582i
$64$	−6.39002	+	4.81327i	−0.798753	+	0.601659i
$65$	−4.16700	+	4.89339i	−0.516853	+	0.606951i
$66$	11.3985	−	6.89359i	1.40305	−	0.848542i
$67$	14.1231	+	6.58573i	1.72542	+	0.804575i	0.992211	+	0.124569i	$0.0397548\pi$
$67$	14.1231	+	6.58573i	1.72542	+	0.804575i	0.733206	+	0.680006i	$0.238023\pi$
$68$	−1.38917	−	10.7999i	−0.168462	−	1.30968i
$69$	15.5625	+	8.98500i	1.87350	+	1.08167i
$70$	−0.908293	+	2.01620i	−0.108562	+	0.240982i
$71$	3.88690	+	4.63223i	0.461290	+	0.549744i	0.945676	−	0.325110i	$-0.105401\pi$
$71$	3.88690	+	4.63223i	0.461290	+	0.549744i	−0.484386	+	0.874854i	$0.660957\pi$
$72$	−14.0053	+	11.1381i	−1.65054	+	1.31263i
$73$	−2.89514	+	4.13469i	−0.338851	+	0.483929i	−0.952026	−	0.306018i	$-0.901003\pi$
$73$	−2.89514	+	4.13469i	−0.338851	+	0.483929i	0.613175	+	0.789947i	$0.289892\pi$
$74$	−1.31683	+	8.47181i	−0.153079	+	0.984827i
$75$	−15.1907	−	1.55173i	−1.75407	−	0.179179i
$76$	0.615635	−	8.69603i	0.0706182	−	0.997503i
$77$	1.52510	−	1.52510i	0.173802	−	0.173802i
$78$	−10.0222	+	7.32567i	−1.13479	+	0.829468i
$79$	−0.681245	−	3.86353i	−0.0766461	−	0.434682i	−0.998849	−	0.0479742i	$-0.984723\pi$
$79$	−0.681245	−	3.86353i	−0.0766461	−	0.434682i	0.922202	−	0.386707i	$-0.126388\pi$
$80$	−8.36371	−	3.16991i	−0.935092	−	0.354406i
$81$	−9.22761	+	7.74289i	−1.02529	+	0.860321i
$82$	−0.162704	−	0.156220i	−0.0179677	−	0.0172516i
$83$	0.189756	+	0.708179i	0.0208284	+	0.0777327i	0.975558	−	0.219743i	$-0.0705219\pi$
$83$	0.189756	+	0.708179i	0.0208284	+	0.0777327i	−0.954729	+	0.297476i	$0.903855\pi$
$84$	−2.61019	+	3.38081i	−0.284795	+	0.368876i
$85$	9.38253	−	7.75741i	1.01768	−	0.841410i
$86$	1.86365	+	3.08152i	0.200962	+	0.332289i
$87$	−5.42812	+	20.2580i	−0.581955	+	2.17189i
$88$	6.53313	+	5.78116i	0.696434	+	0.616274i
$89$	−11.5536	−	2.03722i	−1.22468	−	0.215945i	−0.476343	−	0.879260i	$-0.658038\pi$
$89$	−11.5536	−	2.03722i	−1.22468	−	0.215945i	−0.748340	+	0.663315i	$0.769149\pi$
$90$	−18.8876	−	6.59640i	−1.99093	−	0.695322i
$91$	−1.29200	+	1.53974i	−0.135438	+	0.161409i
$92$	−2.58130	+	11.4818i	−0.269119	+	1.19706i
$93$	−4.77644	−	10.2431i	−0.495293	−	1.06216i
$94$	13.6699	−	2.69798i	1.40994	−	0.278276i
$95$	8.58951	−	4.60655i	0.881265	−	0.472622i
$96$	−14.2925	−	9.70440i	−1.45872	−	0.990451i
$97$	2.04801	−	0.955003i	0.207944	−	0.0969658i	−0.315856	−	0.948807i	$-0.602292\pi$
$97$	2.04801	−	0.955003i	0.207944	−	0.0969658i	0.523800	+	0.851841i	$0.324514\pi$
$98$	3.72099	−	8.42261i	0.375877	−	0.850812i
$99$	14.9479	+	12.5428i	1.50232	+	1.26060i
$100$	−1.99317	−	9.79935i	−0.199317	−	0.979935i
$101$	1.40638	−	7.97599i	0.139940	−	0.793641i	−0.831351	−	0.555748i	$-0.812432\pi$
$101$	1.40638	−	7.97599i	0.139940	−	0.793641i	0.971291	−	0.237893i	$-0.0764568\pi$
$102$	21.1046	−	10.3687i	2.08967	−	1.02665i
$103$	12.2072	+	3.27091i	1.20281	+	0.322293i	0.803938	−	0.594713i	$-0.202734\pi$
$103$	12.2072	+	3.27091i	1.20281	+	0.322293i	0.398874	+	0.917006i	$0.369401\pi$
$104$	−6.53478	−	4.83647i	−0.640787	−	0.474254i
$105$	−4.75400	−	0.450748i	−0.463943	−	0.0439885i
$106$	10.4037	+	11.8988i	1.01049	+	1.15571i
$107$	4.05644	−	1.08692i	0.392151	−	0.105077i	−0.0573551	−	0.998354i	$-0.518267\pi$
$107$	4.05644	−	1.08692i	0.392151	−	0.105077i	0.449506	+	0.893277i	$0.351600\pi$
$108$	−17.1038	−	10.9679i	−1.64581	−	1.05539i
$109$	2.19842	+	2.61997i	0.210570	+	0.250948i	0.860984	−	0.508632i	$-0.169849\pi$
$109$	2.19842	+	2.61997i	0.210570	+	0.250948i	−0.650413	+	0.759580i	$0.725404\pi$
$110$	−1.56804	+	9.62657i	−0.149507	+	0.917857i
$111$	−18.2330	+	3.21497i	−1.73060	+	0.305151i
$112$	−2.62273	−	0.972300i	−0.247825	−	0.0918737i
$113$	10.8211	+	10.8211i	1.01796	+	1.01796i	0.999836	+	0.0181256i	$0.00576988\pi$
$113$	10.8211	+	10.8211i	1.01796	+	1.01796i	0.0181256	+	0.999836i	$0.494230\pi$
$114$	18.2024	−	4.80442i	1.70481	−	0.449975i
$115$	−12.3963	+	4.41017i	−1.15596	+	0.411250i
$116$	−13.7234	+	0.558294i	−1.27419	+	0.0518363i
$117$	−14.8961	−	10.4303i	−1.37714	−	0.964284i
$118$	5.39215	−	1.56297i	0.496388	−	0.143883i
$119$	2.91651	−	2.44724i	0.267356	−	0.224338i
$120$	0.647753	−	19.3040i	0.0591315	−	1.76220i
$121$	−0.743525	+	1.28782i	−0.0675932	+	0.117075i
$122$	2.06083	+	0.138152i	0.186579	+	0.0125077i
$123$	0.205853	−	0.441453i	0.0185611	−	0.0398045i
$124$	5.47187	−	4.98419i	0.491388	−	0.447593i
$125$	8.07612	−	7.73151i	0.722350	−	0.691528i
$126$	−5.92159	−	2.01993i	−0.527537	−	0.179950i
$127$	−13.0886	+	9.16471i	−1.16142	+	0.813237i	−0.985250	−	0.171122i	$-0.945261\pi$
$127$	−13.0886	+	9.16471i	−1.16142	+	0.813237i	−0.176173	+	0.984359i	$0.556372\pi$
$128$	3.27878	−	10.8282i	0.289806	−	0.957085i
$129$	−4.99880	+	5.95734i	−0.440120	+	0.524514i
$130$	0.673840	−	9.06445i	0.0590997	−	0.795005i
$131$	−1.59843	+	4.39166i	−0.139656	+	0.383701i	−0.989728	−	0.142966i	$-0.954336\pi$
$131$	−1.59843	+	4.39166i	−0.139656	+	0.383701i	0.850072	+	0.526667i	$0.176558\pi$
$132$	−7.26095	+	17.3831i	−0.631984	+	1.51300i
$133$	2.67567	−	1.46009i	0.232010	−	0.126606i
$134$	−21.6208	+	4.26724i	−1.86776	+	0.368634i
$135$	0.165045	−	22.7160i	0.0142048	−	1.95508i
$136$	10.5990	+	11.1712i	0.908858	+	0.957923i
$137$	11.7905	−	1.03154i	1.00733	−	0.0881300i	0.428469	−	0.903556i	$-0.359053\pi$
$137$	11.7905	−	1.03154i	1.00733	−	0.0881300i	0.578861	+	0.815426i	$0.303497\pi$
$138$	−25.2665	+	2.72911i	−2.15082	+	0.232318i
$139$	−1.46026	+	8.28157i	−0.123858	+	0.702433i	0.858122	+	0.513446i	$0.171631\pi$
$139$	−1.46026	+	8.28157i	−0.123858	+	0.702433i	−0.981980	+	0.188987i	$0.939480\pi$
$140$	−0.645577	−	3.05996i	−0.0545612	−	0.258613i
$141$	15.0445	+	26.0579i	1.26698	+	2.19447i
$142$	−8.30356	−	2.04496i	−0.696820	−	0.171609i
$143$	−3.74666	+	8.03474i	−0.313311	+	0.671898i
$144$	6.69502	−	24.4046i	0.557918	−	2.03372i
$145$	−8.71620	−	12.6425i	−0.723841	−	1.04990i
$146$	−0.145109	−	7.13680i	−0.0120093	−	0.590646i
$147$	19.8085	+	1.73302i	1.63378	+	0.142937i
$148$	−5.56661	−	10.7714i	−0.457572	−	0.885407i
$149$	7.62455	−	1.34441i	0.624627	−	0.110139i	0.147629	−	0.989043i	$-0.452836\pi$
$149$	7.62455	−	1.34441i	0.624627	−	0.110139i	0.476998	+	0.878904i	$0.341725\pi$
$150$	18.6386	−	10.9056i	1.52183	−	0.890437i
$151$		−	18.3490i		−	1.49322i	−0.665263	−	0.746609i	$-0.731680\pi$
$151$		−	18.3490i		−	1.49322i	0.665263	−	0.746609i	$-0.268320\pi$
$152$	6.55431	+	10.4423i	0.531625	+	0.846980i
$153$	24.3560	+	24.3560i	1.96907	+	1.96907i
$154$	−0.468490	+	3.01401i	−0.0377520	+	0.242876i
$155$	7.97748	+	2.19980i	0.640766	+	0.176692i
$156$	5.32901	−	16.7278i	0.426662	−	1.33930i
$157$	−1.14040	+	13.0349i	−0.0910141	+	1.04030i	0.804110	+	0.594480i	$0.202642\pi$
$157$	−1.14040	+	13.0349i	−0.0910141	+	1.04030i	−0.895125	+	0.445816i	$0.852913\pi$
$158$	4.00208	+	3.84257i	0.318388	+	0.305699i
$159$	−17.0658	+	29.5589i	−1.35341	+	2.34417i
$160$	12.1945	−	3.36070i	0.964059	−	0.265686i
$161$	−3.86660	+	1.40733i	−0.304731	+	0.110913i
$162$	4.07366	−	16.5411i	0.320057	−	1.29959i
$163$	16.6724	+	4.46736i	1.30588	+	0.349910i	0.843672	−	0.536860i	$-0.180389\pi$
$163$	16.6724	+	4.46736i	1.30588	+	0.349910i	0.462211	+	0.886770i	$0.347056\pi$
$164$	0.316136	+	0.0425769i	0.0246861	+	0.00332470i
$165$	−20.7682	+	3.50662i	−1.61681	+	0.272990i
$166$	−0.807654	−	0.650188i	−0.0626861	−	0.0504643i
$167$	−0.661437	−	7.56026i	−0.0511835	−	0.585030i	−0.977873	−	0.209201i	$-0.932914\pi$
$167$	−0.661437	−	7.56026i	−0.0511835	−	0.585030i	0.926689	−	0.375829i	$-0.122642\pi$
$168$	0.158707	−	6.03827i	0.0122445	−	0.465863i
$169$	−1.62055	+	4.45242i	−0.124658	+	0.342494i
$170$	−4.23840	+	16.6870i	−0.325071	+	1.27983i
$171$	15.2692	+	22.9638i	1.16766	+	1.75609i
$172$	−4.69943	−	1.96296i	−0.358328	−	0.149674i
$173$	−0.143529	−	0.307798i	−0.0109123	−	0.0234015i	0.900776	−	0.434284i	$-0.142998\pi$
$173$	−0.143529	−	0.307798i	−0.0109123	−	0.0234015i	−0.911688	+	0.410882i	$0.865221\pi$
$174$	−10.7087	−	27.6591i	−0.811826	−	2.09683i
$175$	2.50802	−	2.43617i	0.189589	−	0.184157i
$176$	−12.2837	−	1.14834i	−0.925916	−	0.0865594i
$177$	6.95373	+	9.93096i	0.522675	+	0.746457i
$178$	14.8912	−	7.31604i	1.11615	−	0.548360i
$179$	1.18503	+	2.05254i	0.0885737	+	0.153414i	0.906908	−	0.421328i	$-0.138436\pi$
$179$	1.18503	+	2.05254i	0.0885737	+	0.153414i	−0.818335	+	0.574742i	$0.805102\pi$
$180$	27.0695	−	8.23122i	2.01764	−	0.613519i
$181$	−1.16892	+	0.425453i	−0.0868853	+	0.0316237i	−0.385097	−	0.922876i	$-0.625832\pi$
$181$	−1.16892	+	0.425453i	−0.0868853	+	0.0316237i	0.298212	+	0.954500i	$0.403610\pi$
$182$	0.190130	−	2.83620i	0.0140934	−	0.210233i
$183$	1.15440	+	4.30829i	0.0853360	+	0.318478i
$184$	−6.63490	−	15.2633i	−0.489131	−	1.12522i
$185$	6.86309	−	11.6902i	0.504585	−	0.859484i
$186$	14.0017	+	7.70869i	1.02665	+	0.565229i
$187$	9.63167	−	13.7555i	0.704337	−	1.00590i
$188$	−13.3557	+	14.4884i	−0.974064	+	1.05668i
$189$		−	7.10419i		−	0.516754i
$190$	−5.96252	+	12.4277i	−0.432567	+	0.901602i
$191$		−	0.709917i		−	0.0513678i	−0.999670	−	0.0256839i	$-0.991824\pi$
$191$		−	0.709917i		−	0.0513678i	0.999670	−	0.0256839i	$-0.00817634\pi$
$192$	24.4168	−	0.847889i	1.76213	−	0.0611911i
$193$	2.81357	−	4.01819i	0.202525	−	0.289236i	−0.705023	−	0.709185i	$-0.749063\pi$
$193$	2.81357	−	4.01819i	0.202525	−	0.289236i	0.907548	+	0.419949i	$0.137952\pi$
$194$	−1.54128	+	2.79950i	−0.110657	+	0.200993i
$195$	18.9960	−	4.94231i	1.36033	−	0.353926i
$196$	2.78065	+	12.7216i	0.198618	+	0.908689i
$197$	1.08817	+	4.06111i	0.0775291	+	0.289342i	0.993795	−	0.111228i	$-0.0354785\pi$
$197$	1.08817	+	4.06111i	0.0775291	+	0.289342i	−0.916266	+	0.400571i	$0.868812\pi$
$198$	−27.5339	−	1.84579i	−1.95675	−	0.131174i
$199$	2.37065	−	0.862845i	0.168051	−	0.0611654i	−0.256625	−	0.966511i	$-0.582610\pi$
$199$	2.37065	−	0.862845i	0.168051	−	0.0611654i	0.424675	+	0.905346i	$0.360388\pi$
$200$	10.4536	+	9.52480i	0.739183	+	0.673505i
$201$	−23.7951	−	41.2143i	−1.67837	−	2.90703i
$202$	5.05059	+	10.2801i	0.355358	+	0.723304i
$203$	−2.75448	−	3.93381i	−0.193327	−	0.276099i
$204$	−15.4426	+	29.4509i	−1.08120	+	2.06197i
$205$	0.148371	+	0.324314i	0.0103627	+	0.0226511i
$206$	−16.6670	+	6.45294i	−1.16125	+	0.449597i
$207$	−15.7327	−	33.7389i	−1.09350	−	2.34502i
$208$	11.4972	+	0.0683827i	0.797185	+	0.00474149i
$209$	9.73252	−	9.27492i	0.673212	−	0.641560i
$210$	5.80394	−	3.45278i	0.400510	−	0.238264i
$211$	−7.16301	+	19.6802i	−0.493122	+	1.35484i	0.404686	+	0.914456i	$0.367381\pi$
$211$	−7.16301	+	19.6802i	−0.493122	+	1.35484i	−0.897808	+	0.440386i	$0.854842\pi$
$212$	−21.8082	−	4.90284i	−1.49779	−	0.336728i
$213$	−1.60951	−	18.3967i	−0.110282	−	1.26052i
$214$	−3.72427	+	4.62623i	−0.254586	+	0.316243i
$215$	−0.947996	−	5.61459i	−0.0646528	−	0.382912i
$216$	28.6810	−	1.75140i	1.95150	−	0.119168i
$217$	2.49974	+	0.669803i	0.169693	+	0.0454692i
$218$	−4.69647	−	1.15662i	−0.318085	−	0.0783364i
$219$	14.4852	−	5.27219i	0.978821	−	0.356262i
$220$	−6.24349	−	12.2995i	−0.420936	−	0.829232i
$221$	−7.82458	+	13.5526i	−0.526338	+	0.911644i
$222$	18.1341	−	18.8868i	1.21708	−	1.26760i
$223$	1.88924	−	21.5942i	0.126513	−	1.44605i	−0.622044	−	0.782982i	$-0.713698\pi$
$223$	1.88924	−	21.5942i	0.126513	−	1.44605i	0.748558	−	0.663070i	$-0.230747\pi$
$224$	3.80587	−	1.07868i	0.254290	−	0.0720720i
$225$	23.9342	+	20.6832i	1.59561	+	1.37888i
$226$	−21.3854	−	3.32408i	−1.42253	−	0.221115i
$227$	−19.6323	−	19.6323i	−1.30304	−	1.30304i	−0.926330	−	0.376713i	$-0.877054\pi$
$227$	−19.6323	−	19.6323i	−1.30304	−	1.30304i	−0.376713	−	0.926330i	$-0.622946\pi$
$228$	−16.7727	+	20.6760i	−1.11080	+	1.36930i
$229$		−	6.30888i		−	0.416903i	−0.978033	−	0.208451i	$-0.933158\pi$
$229$		−	6.30888i		−	0.416903i	0.978033	−	0.208451i	$-0.0668423\pi$
$230$	10.4728	−	15.3805i	0.690554	−	1.01416i
$231$	−6.48674	+	1.14379i	−0.426796	+	0.0752557i
$232$	15.2025	−	12.0902i	0.998093	−	0.793760i
$233$	−24.9020	−	2.17864i	−1.63139	−	0.142728i	−0.765659	−	0.643246i	$-0.777587\pi$
$233$	−24.9020	−	2.17864i	−1.63139	−	0.142728i	−0.865726	+	0.500518i	$0.833143\pi$
$234$	25.7118	−	0.522784i	1.68083	−	0.0341755i
$235$	−21.6679	−	3.98316i	−1.41346	−	0.259833i
$236$	−4.85200	+	6.28447i	−0.315838	+	0.409084i
$237$	−5.06340	+	10.8585i	−0.328903	+	0.705336i
$238$	−1.28753	+	5.22803i	−0.0834583	+	0.338883i
$239$	1.76969	+	3.06519i	0.114471	+	0.198270i	0.917568	−	0.397578i	$-0.130149\pi$
$239$	1.76969	+	3.06519i	0.114471	+	0.198270i	−0.803097	+	0.595848i	$0.796816\pi$
$240$	15.3704	+	22.5804i	0.992155	+	1.45756i
$241$	−0.839877	+	4.76318i	−0.0541013	+	0.306823i	−0.999836	−	0.0181165i	$-0.994233\pi$
$241$	−0.839877	+	4.76318i	−0.0541013	+	0.306823i	0.945735	+	0.324940i	$0.105344\pi$
$242$	−0.225839	−	2.09084i	−0.0145175	−	0.134405i
$243$	6.28568	−	0.549926i	0.403227	−	0.0352778i
$244$	−2.46820	+	1.56211i	−0.158010	+	0.100004i
$245$	−10.3693	+	10.2197i	−0.662471	+	0.652914i
$246$	0.133383	+	0.675811i	0.00850418	+	0.0430881i
$247$	−8.28212	+	9.40113i	−0.526979	+	0.598180i
$248$	−2.08787	+	10.2571i	−0.132580	+	0.651325i
$249$	0.765794	−	2.10400i	0.0485302	−	0.133336i
$250$	−2.76845	+	15.5671i	−0.175092	+	0.984552i
$251$	7.98040	−	9.51067i	0.503718	−	0.600308i	−0.452933	−	0.891545i	$-0.649622\pi$
$251$	7.98040	−	9.51067i	0.503718	−	0.600308i	0.956651	+	0.291237i	$0.0940667\pi$
$252$	8.44655	−	2.63560i	0.532083	−	0.166027i
$253$	−14.8665	+	10.4096i	−0.934650	+	0.654449i
$254$	7.29524	−	21.3866i	0.457744	−	1.34191i
$255$	−37.0602	+	2.97119i	−2.32080	+	0.186063i
$256$	5.29309	+	15.0991i	0.330818	+	0.943695i
$257$	−8.84265	+	18.9631i	−0.551589	+	1.18289i	0.410928	+	0.911668i	$0.365205\pi$
$257$	−8.84265	+	18.9631i	−0.551589	+	1.18289i	−0.962518	+	0.271219i	$0.912573\pi$
$258$	0.735620	−	10.9734i	0.0457977	−	0.683171i
$259$	2.11969	−	3.67140i	0.131711	−	0.228130i
$260$	6.79532	+	10.9115i	0.421428	+	0.676701i
$261$	33.2824	−	27.9272i	2.06013	−	1.72865i
$262$	−1.84005	−	6.34803i	−0.113678	−	0.392183i
$263$	12.7330	+	8.91576i	0.785152	+	0.549769i	0.895993	−	0.444069i	$-0.146465\pi$
$263$	12.7330	+	8.91576i	0.785152	+	0.549769i	−0.110841	+	0.993838i	$0.535354\pi$
$264$	−6.21688	−	25.9063i	−0.382623	−	1.59442i
$265$	−8.37653	−	23.5452i	−0.514566	−	1.44637i
$266$	−1.83638	+	3.89998i	−0.112596	+	0.239123i
$267$	25.3346	+	25.3346i	1.55045	+	1.55045i
$268$	21.1239	−	22.9155i	1.29035	−	1.39979i
$269$	−28.5686	+	5.03741i	−1.74186	+	0.307136i	−0.951987	−	0.306140i	$-0.900963\pi$
$269$	−28.5686	+	5.03741i	−1.74186	+	0.307136i	−0.789869	+	0.613276i	$0.789851\pi$
$270$	18.7690	+	26.0732i	1.14224	+	1.58676i
$271$	10.5546	+	12.5784i	0.641144	+	0.764085i	0.984550	−	0.175101i	$-0.0560253\pi$
$271$	10.5546	+	12.5784i	0.641144	+	0.764085i	−0.343407	+	0.939187i	$0.611581\pi$
$272$	−21.4240	−	3.90916i	−1.29902	−	0.237027i
$273$	5.92925	−	1.58874i	0.358854	−	0.0961548i
$274$	−12.6007	+	11.0174i	−0.761235	+	0.665585i
$275$	7.90401	−	13.2420i	0.476630	−	0.798522i
$276$	26.5698	−	24.2018i	1.59932	−	1.45678i
$277$	8.65110	+	2.31806i	0.519795	+	0.139279i	0.509172	−	0.860665i	$-0.329952\pi$
$277$	8.65110	+	2.31806i	0.519795	+	0.139279i	0.0106230	+	0.999944i	$0.496619\pi$
$278$	−5.24409	−	10.6739i	−0.314519	−	0.640180i
$279$	−4.06568	+	23.0576i	−0.243406	+	1.38042i
$280$	3.29073	+	2.95487i	0.196659	+	0.176587i
$281$	1.91639	+	1.60804i	0.114322	+	0.0959276i	0.698157	−	0.715945i	$-0.254004\pi$
$281$	1.91639	+	1.60804i	0.114322	+	0.0959276i	−0.583835	+	0.811873i	$0.698448\pi$
$282$	−38.9232	−	17.1957i	−2.31784	−	1.02399i
$283$	6.95871	−	3.24490i	0.413652	−	0.192889i	−0.204640	−	0.978837i	$-0.565602\pi$
$283$	6.95871	−	3.24490i	0.413652	−	0.192889i	0.618293	+	0.785948i	$0.287825\pi$
$284$	11.1870	−	4.59488i	0.663827	−	0.272656i
$285$	−29.5571	−	3.52205i	−1.75081	−	0.208628i
$286$	−2.42766	−	12.3002i	−0.143550	−	0.727327i
$287$	0.0471360	+	0.101083i	0.00278235	+	0.00596676i
$288$	12.7228	+	33.4507i	0.749697	+	1.97110i
$289$	8.12603	−	9.68422i	0.478002	−	0.569660i
$290$	20.5022	+	7.16029i	1.20393	+	0.420467i
$291$	−6.79624	−	1.19836i	−0.398403	−	0.0702492i
$292$	6.12163	+	8.02718i	0.358241	+	0.469755i
$293$	4.38318	−	16.3582i	0.256068	−	0.955659i	−0.711425	−	0.702762i	$-0.751950\pi$
$293$	4.38318	−	16.3582i	0.256068	−	0.955659i	0.967493	−	0.252897i	$-0.0813833\pi$
$294$	−24.0622	+	14.5524i	−1.40334	+	0.848714i
$295$	−8.83705	−	0.837881i	−0.514513	−	0.0487833i
$296$	15.3448	+	7.65248i	0.891896	+	0.444792i
$297$	−8.10983	−	30.2663i	−0.470580	−	1.75623i
$298$	−7.58318	+	7.89795i	−0.439282	+	0.457516i
$299$	12.9562	−	10.8716i	0.749279	−	0.628720i
$300$	−12.1790	+	28.0059i	−0.703156	+	1.61692i
$301$	−0.309217	−	1.75366i	−0.0178230	−	0.101079i
$302$	15.3130	+	20.9495i	0.881163	+	1.20551i
$303$	−17.4896	+	17.4896i	−1.00475	+	1.00475i
$304$	−16.1977	−	6.45238i	−0.929004	−	0.370069i
$305$	−2.94969	−	1.40164i	−0.168898	−	0.0802577i
$306$	−48.1340	−	7.48182i	−2.75164	−	0.427707i
$307$	−9.56107	+	13.6546i	−0.545679	+	0.779311i	−0.993380	−	0.114873i	$-0.963354\pi$
$307$	−9.56107	+	13.6546i	−0.545679	+	0.779311i	0.447701	+	0.894183i	$0.352243\pi$
$308$	−1.98043	−	3.83215i	−0.112846	−	0.218357i
$309$	−24.8085	−	29.5657i	−1.41131	−	1.68193i
$310$	−10.9439	+	4.14596i	−0.621573	+	0.235475i
$311$	7.09443	+	4.09597i	0.402288	+	0.232261i	0.687471	−	0.726212i	$-0.258721\pi$
$311$	7.09443	+	4.09597i	0.402288	+	0.232261i	−0.285183	+	0.958473i	$0.592054\pi$
$312$	7.87579	+	23.5459i	0.445879	+	1.33302i
$313$	10.7656	+	5.02006i	0.608505	+	0.283751i	0.702345	−	0.711837i	$-0.252136\pi$
$313$	10.7656	+	5.02006i	0.608505	+	0.283751i	−0.0938399	+	0.995587i	$0.529914\pi$
$314$	−9.57611	−	15.8340i	−0.540411	−	0.893563i
$315$	7.53176	+	6.41372i	0.424367	+	0.361372i
$316$	−7.77607	−	1.04727i	−0.437438	−	0.0589137i
$317$	11.0106	+	15.7248i	0.618419	+	0.883193i	0.999139	−	0.0414971i	$-0.0132127\pi$
$317$	11.0106	+	15.7248i	0.618419	+	0.883193i	−0.380720	+	0.924690i	$0.624324\pi$
$318$	−5.18359	−	47.9903i	−0.290681	−	2.69116i
$319$	−16.2257	−	13.6150i	−0.908465	−	0.762293i
$320$	−11.1181	+	14.0138i	−0.621523	+	0.783396i
$321$	−12.0517	−	4.38646i	−0.672660	−	0.244828i
$322$	3.24013	−	4.83362i	0.180565	−	0.269367i
$323$	18.5414	−	14.8125i	1.03167	−	0.824190i
$324$	9.15322	+	22.2850i	0.508512	+	1.23806i
$325$	−6.26236	+	12.9356i	−0.347373	+	0.717536i
$326$	−22.7635	+	8.81331i	−1.26075	+	0.488124i
$327$	−0.910332	−	10.4051i	−0.0503415	−	0.575406i
$328$	−0.396473	+	0.215217i	−0.0218916	+	0.0118834i
$329$	−6.78509	−	1.19640i	−0.374074	−	0.0659594i
$330$	20.7852	−	21.3356i	1.14419	−	1.17448i
$331$	−16.6569	+	9.61686i	−0.915545	+	0.528590i	−0.882211	−	0.470854i	$-0.843946\pi$
$331$	−16.6569	+	9.61686i	−0.915545	+	0.528590i	−0.0333340	+	0.999444i	$0.510613\pi$
$332$	1.46473	+	0.0683162i	0.0803874	+	0.00374934i
$333$	34.7608	+	16.2092i	1.90488	+	0.888259i
$334$	7.06453	+	8.07975i	0.386554	+	0.442104i
$335$	34.2708	+	6.29993i	1.87241	+	0.344202i
$336$	4.85799	+	7.02650i	0.265025	+	0.383327i
$337$	−2.43032	+	27.7787i	−0.132388	+	1.51320i	0.581848	+	0.813297i	$0.302330\pi$
$337$	−2.43032	+	27.7787i	−0.132388	+	1.51320i	−0.714236	+	0.699905i	$0.753226\pi$
$338$	−1.86550	−	6.43586i	−0.101470	−	0.350065i
$339$	−8.11553	−	46.0254i	−0.440775	−	2.49976i
$340$	−9.08685	−	22.5891i	−0.492804	−	1.22506i
$341$	11.4144			0.618123
$342$	−36.5975	−	13.4756i	−1.97897	−	0.728679i
$343$	−6.68081	+	6.68081i	−0.360730	+	0.360730i
$344$	7.00364	−	1.68070i	0.377611	−	0.0906174i
$345$	38.7364	+	10.6816i	2.08550	+	0.575079i
$346$	0.420741	+	0.231641i	0.0226192	+	0.0124531i
$347$	−1.12261	−	0.0982158i	−0.0602650	−	0.00527250i	0.0569834	−	0.998375i	$-0.481852\pi$
$347$	−1.12261	−	0.0982158i	−0.0602650	−	0.00527250i	−0.117248	+	0.993103i	$0.537407\pi$
$348$	35.3091	+	22.6423i	1.89277	+	1.21375i
$349$	−10.5407	−	6.08566i	−0.564229	−	0.325758i	0.190612	−	0.981665i	$-0.438953\pi$
$349$	−10.5407	−	6.08566i	−0.564229	−	0.325758i	−0.754841	+	0.655908i	$0.772286\pi$
$350$	−0.830389	+	4.87449i	−0.0443862	+	0.260553i
$351$	9.98730	+	27.4399i	0.533082	+	1.46463i
$352$	14.9829	−	8.94014i	0.798593	−	0.476511i
$353$	−6.92806	+	25.8559i	−0.368743	+	1.37617i	0.493532	+	0.869728i	$0.335706\pi$
$353$	−6.92806	+	25.8559i	−0.368743	+	1.37617i	−0.862275	+	0.506440i	$0.830961\pi$
$354$	−16.2271	−	5.53527i	−0.862459	−	0.294196i
$355$	11.0194	+	7.83581i	0.584850	+	0.415882i
$356$	−10.8962	+	20.7803i	−0.577497	+	1.10135i
$357$	−11.5828	+	1.01337i	−0.613028	+	0.0536330i
$358$	−3.06592	−	1.35448i	−0.162039	−	0.0715865i
$359$	−11.9095	−	4.33470i	−0.628558	−	0.228776i	0.00804545	−	0.999968i	$-0.497439\pi$
$359$	−11.9095	−	4.33470i	−0.628558	−	0.228776i	−0.636604	+	0.771191i	$0.719661\pi$
$360$	−24.0367	+	31.9884i	−1.26684	+	1.68594i
$361$	16.8926	−	8.69718i	0.889083	−	0.457747i
$362$	0.979532	−	1.46126i	0.0514831	−	0.0768024i
$363$	4.11587	−	1.91926i	0.216027	−	0.100735i
$364$	2.14985	+	3.39683i	0.112683	+	0.178042i
$365$	−3.93720	+	10.5776i	−0.206083	+	0.553658i
$366$	−4.91346	−	3.95550i	−0.256831	−	0.206757i
$367$	−25.2387	+	17.6724i	−1.31745	+	0.922490i	−0.999670	−	0.0256746i	$-0.991827\pi$
$367$	−25.2387	+	17.6724i	−1.31745	+	0.922490i	−0.317781	+	0.948164i	$0.602938\pi$
$368$	20.3131	+	11.8894i	1.05889	+	0.619779i
$369$	−0.873869	+	0.504529i	−0.0454918	+	0.0262647i
$370$	1.92022	+	19.0746i	0.0998272	+	0.991641i
$371$	−2.67303	−	7.34409i	−0.138777	−	0.381286i
$372$	−22.4193	+	2.88376i	−1.16239	+	0.149516i
$373$	11.6329	−	3.11703i	0.602329	−	0.161394i	0.0552472	−	0.998473i	$-0.482405\pi$
$373$	11.6329	−	3.11703i	0.602329	−	0.161394i	0.547082	+	0.837079i	$0.315739\pi$
$374$	0.482754	+	23.7430i	0.0249626	+	1.22772i
$375$	−33.7466	+	5.19480i	−1.74267	+	0.268258i
$376$	3.15735	−	27.6877i	0.162828	−	1.42789i
$377$	16.1694	+	11.3220i	0.832768	+	0.583111i
$378$	5.92874	+	8.11104i	0.304941	+	0.417187i
$379$	22.2847			1.14469			0.572345	−	0.820013i	$-0.306034\pi$
$379$	22.2847			1.14469			0.572345	+	0.820013i	$0.306034\pi$
$380$	−3.56387	−	19.1650i	−0.182823	−	0.983146i
$381$	48.7965			2.49992
$382$	0.592455	+	0.810531i	0.0303126	+	0.0414704i
$383$	10.3111	+	7.21993i	0.526874	+	0.368921i	0.806543	−	0.591175i	$-0.201336\pi$
$383$	10.3111	+	7.21993i	0.526874	+	0.368921i	−0.279669	+	0.960096i	$0.590225\pi$
$384$	−27.1698	+	21.3449i	−1.38650	+	1.08925i
$385$	2.44168	−	4.15904i	0.124440	−	0.211964i
$386$	0.141020	+	6.93572i	0.00717775	+	0.353019i
$387$	15.5614	−	4.16967i	0.791032	−	0.211956i
$388$	−0.576580	−	4.48253i	−0.0292714	−	0.227566i
$389$	9.20845	+	25.3000i	0.466887	+	1.28276i	0.920214	+	0.391417i	$0.128015\pi$
$389$	9.20845	+	25.3000i	0.466887	+	1.28276i	−0.453327	+	0.891344i	$0.649763\pi$
$390$	−17.5636	+	21.4957i	−0.889369	+	1.08848i
$391$	−27.7441	+	16.0181i	−1.40308	+	0.810068i
$392$	−13.7915	−	12.2041i	−0.696575	−	0.616399i
$393$	11.6914	−	8.18644i	0.589755	−	0.412951i
$394$	−4.63156	−	3.72856i	−0.233335	−	0.187842i
$395$	−3.64951	−	7.97722i	−0.183627	−	0.401377i
$396$	32.9766	−	20.8708i	1.65713	−	1.04880i
$397$	−27.7178	+	12.9250i	−1.39111	+	0.648688i	−0.966495	−	0.256684i	$-0.917370\pi$
$397$	−27.7178	+	12.9250i	−1.39111	+	0.648688i	−0.424620	+	0.905372i	$0.639592\pi$
$398$	−1.98655	+	2.96354i	−0.0995768	+	0.148549i
$399$	−9.25118	−	1.03427i	−0.463138	−	0.0517783i
$400$	−19.8840	−	2.15073i	−0.994201	−	0.107537i
$401$	−2.34995	−	0.855311i	−0.117351	−	0.0427122i	0.282677	−	0.959215i	$-0.408777\pi$
$401$	−2.34995	−	0.855311i	−0.117351	−	0.0427122i	−0.400028	+	0.916503i	$0.631000\pi$
$402$	61.5625	+	27.1975i	3.07046	+	1.35649i
$403$	−10.5969	+	0.927105i	−0.527867	+	0.0461824i
$404$	−14.3456	−	7.52213i	−0.713718	−	0.374240i
$405$	−15.6093	+	21.9512i	−0.775632	+	1.09076i
$406$	6.42779	+	2.19261i	0.319006	+	0.108817i
$407$	4.83948	−	18.0612i	0.239884	−	0.895260i
$408$	−6.94668	−	46.5123i	−0.343912	−	2.30270i
$409$	11.6527	+	32.0156i	0.576190	+	1.58307i	0.794548	+	0.607201i	$0.207708\pi$
$409$	11.6527	+	32.0156i	0.576190	+	1.58307i	−0.218358	+	0.975869i	$0.570070\pi$
$410$	−0.440053	−	0.246456i	−0.0217327	−	0.0121716i
$411$	−31.3025	−	18.0725i	−1.54404	−	0.891452i
$412$	13.6439	−	21.2768i	0.672189	−	1.04823i
$413$	−2.76545	−	0.241946i	−0.136079	−	0.0119054i
$414$	46.1190	+	25.3910i	2.26662	+	1.24790i
$415$	0.809362	+	1.42568i	0.0397300	+	0.0699837i
$416$	−13.1837	+	9.51678i	−0.646383	+	0.466599i
$417$	18.1596	−	18.1596i	0.889281	−	0.889281i
$418$	−3.37157	+	18.7116i	−0.164909	+	0.915215i
$419$	−10.2081			−0.498699			−0.249350	−	0.968414i	$-0.580217\pi$
$419$	−10.2081			−0.498699			−0.249350	+	0.968414i	$0.580217\pi$
$420$	−3.74503	+	8.78576i	−0.182739	+	0.428701i
$421$	−1.72627	−	9.79015i	−0.0841331	−	0.477143i	−0.997540	−	0.0700956i	$-0.977670\pi$
$421$	−1.72627	−	9.79015i	−0.0841331	−	0.477143i	0.913407	−	0.407047i	$-0.133442\pi$
$422$	−8.24575	−	28.4473i	−0.401397	−	1.38479i
$423$	5.43266	−	62.0956i	0.264145	−	3.01919i
$424$	28.9906	−	12.6021i	1.40791	−	0.612013i
$425$	15.9364	−	22.0699i	0.773027	−	1.07055i
$426$	17.1905	+	19.6609i	0.832881	+	0.952572i
$427$	−0.925620	−	0.431624i	−0.0447939	−	0.0208877i
$428$	0.391315	−	8.38995i	0.0189149	−	0.405544i
$429$	23.4470	−	13.5371i	1.13203	−	0.653579i
$430$	5.76796	+	5.61919i	0.278156	+	0.270981i
$431$	5.66314	+	0.998564i	0.272784	+	0.0480991i	0.308367	−	0.951268i	$-0.400218\pi$
$431$	5.66314	+	0.998564i	0.272784	+	0.0480991i	−0.0355829	+	0.999367i	$0.511329\pi$
$432$	−31.2843	+	25.9351i	−1.50517	+	1.24780i
$433$	0.821788	+	9.39308i	0.0394926	+	0.451403i	0.990036	+	0.140812i	$0.0449713\pi$
$433$	0.821788	+	9.39308i	0.0394926	+	0.451403i	−0.950544	+	0.310591i	$0.899473\pi$
$434$	−3.41300	+	1.32140i	−0.163829	+	0.0634294i
$435$	−0.340720	+	46.8950i	−0.0163363	+	2.24844i
$436$	6.32734	−	2.59885i	0.303025	−	0.124462i
$437$	−24.3060	+	8.18973i	−1.16271	+	0.391768i
$438$	−12.1383	+	18.1079i	−0.579991	+	0.865230i
$439$	−14.0185	−	5.10232i	−0.669067	−	0.243520i	−0.0149209	−	0.999889i	$-0.504750\pi$
$439$	−14.0185	−	5.10232i	−0.669067	−	0.243520i	−0.654146	+	0.756368i	$0.726972\pi$
$440$	17.3928	+	8.83222i	0.829170	+	0.421060i
$441$	−31.5551	−	26.4779i	−1.50262	−	1.26085i
$442$	−2.37665	−	22.0033i	−0.113045	−	1.04659i
$443$	4.52306	+	6.45960i	0.214897	+	0.306905i	0.912099	−	0.409970i	$-0.134461\pi$
$443$	4.52306	+	6.45960i	0.214897	+	0.306905i	−0.697202	+	0.716875i	$0.745572\pi$
$444$	−4.94234	+	36.6972i	−0.234553	+	1.74157i
$445$	−26.1494	+	2.09645i	−1.23960	+	0.0993812i
$446$	15.8642	+	26.2313i	0.751192	+	1.24209i
$447$	−21.4289	−	9.99245i	−1.01355	−	0.472626i
$448$	−3.44506	+	4.40771i	−0.162764	+	0.208244i
$449$	24.4536	+	14.1183i	1.15404	+	0.666285i	0.949868	−	0.312651i	$-0.101217\pi$
$449$	24.4536	+	14.1183i	1.15404	+	0.666285i	0.204171	+	0.978935i	$0.434550\pi$
$450$	−44.5872	−	3.64048i	−2.10186	−	0.171614i
$451$	0.316208	+	0.376842i	0.0148896	+	0.0177448i
$452$	27.1903	−	14.0518i	1.27893	−	0.660940i
$453$	−32.1414	+	45.9026i	−1.51013	+	2.15669i
$454$	38.7987	+	6.03077i	1.82091	+	0.283038i
$455$	−1.92900	+	4.05948i	−0.0904327	+	0.190311i
$456$	1.89485	−	37.6038i	0.0887346	−	1.76096i
$457$	17.7687	−	17.7687i	0.831184	−	0.831184i	−0.156495	−	0.987679i	$-0.550020\pi$
$457$	17.7687	−	17.7687i	0.831184	−	0.831184i	0.987679	+	0.156495i	$0.0500195\pi$
$458$	5.26502	+	7.20302i	0.246018	+	0.336575i
$459$	−9.60463	−	54.4706i	−0.448306	−	2.54247i
$460$	0.878595	+	26.3002i	0.0409647	+	1.22626i
$461$	−1.19837	+	1.00555i	−0.0558135	+	0.0468331i	−0.670268	−	0.742119i	$-0.733821\pi$
$461$	−1.19837	+	1.00555i	−0.0558135	+	0.0468331i	0.614454	+	0.788953i	$0.289376\pi$
$462$	6.45155	−	6.71935i	0.300153	−	0.312612i
$463$	−10.1095	−	37.7292i	−0.469828	−	1.75342i	−0.640364	−	0.768072i	$-0.721216\pi$
$463$	−10.1095	−	37.7292i	−0.469828	−	1.75342i	0.170535	−	0.985352i	$-0.445450\pi$
$464$	−7.26734	+	26.4908i	−0.337378	+	1.22981i
$465$	−16.1035	−	19.4770i	−0.746781	−	0.903226i
$466$	30.2495	−	18.2943i	1.40128	−	0.847469i
$467$	4.76888	−	17.7977i	0.220677	−	0.823580i	−0.763413	−	0.645911i	$-0.776478\pi$
$467$	4.76888	−	17.7977i	0.220677	−	0.823580i	0.984090	−	0.177669i	$-0.0568556\pi$
$468$	−28.9195	+	22.0544i	−1.33681	+	1.01947i
$469$	10.7316	+	1.89227i	0.495539	+	0.0873768i
$470$	28.0629	−	13.5350i	1.29445	−	0.624325i
$471$	25.6857	−	30.6110i	1.18353	−	1.41048i
$472$	0.295014	−	11.2243i	0.0135791	−	0.516642i
$473$	−3.31927	−	7.11820i	−0.152620	−	0.327295i
$474$	−3.28085	−	16.6231i	−0.150694	−	0.763523i
$475$	15.9943	−	14.8048i	0.733868	−	0.679292i
$476$	−2.89300	−	7.04348i	−0.132600	−	0.322837i
$477$	64.0826	−	29.8822i	2.93414	−	1.36821i
$478$	−4.57852	−	2.02273i	−0.209417	−	0.0925175i
$479$	30.9017	+	25.9296i	1.41193	+	1.18475i	0.955498	+	0.294997i	$0.0953187\pi$
$479$	30.9017	+	25.9296i	1.41193	+	1.18475i	0.456436	+	0.889756i	$0.349126\pi$
$480$	−36.3931	−	12.9535i	−1.66111	−	0.591242i
$481$	−3.02589	+	17.1607i	−0.137969	+	0.782460i
$482$	−3.01616	−	6.13917i	−0.137382	−	0.279631i
$483$	12.1380	+	3.25238i	0.552300	+	0.147988i
$484$	2.00274	+	2.19870i	0.0910337	+	0.0999410i
$485$	3.89425	−	3.21974i	0.176829	−	0.146201i
$486$	−6.71760	+	5.87353i	−0.304716	+	0.266429i
$487$	11.4525	−	3.06868i	0.518961	−	0.139055i	0.0101748	−	0.999948i	$-0.496761\pi$
$487$	11.4525	−	3.06868i	0.518961	−	0.139055i	0.508786	+	0.860893i	$0.330095\pi$
$488$	1.51436	−	3.84332i	0.0685517	−	0.173979i
$489$	−33.8831	−	40.3803i	−1.53225	−	1.82606i
$490$	3.31014	−	20.3218i	0.149537	−	0.918043i
$491$	18.9630	−	3.34369i	0.855790	−	0.150899i	0.271494	−	0.962440i	$-0.412482\pi$
$491$	18.9630	−	3.34369i	0.855790	−	0.150899i	0.584295	+	0.811541i	$0.301371\pi$
$492$	−0.716279	−	0.660278i	−0.0322924	−	0.0297676i
$493$	−26.4381	−	26.4381i	−1.19071	−	1.19071i
$494$	1.61029	−	17.6453i	0.0724503	−	0.793900i
$495$	39.4095	+	18.7268i	1.77133	+	0.841705i
$496$	−6.17618	−	13.4532i	−0.277319	−	0.604066i
$497$	3.46383	+	2.42540i	0.155374	+	0.108794i
$498$	0.881548	+	3.04128i	0.0395031	+	0.136283i
$499$	−19.2890	+	16.1854i	−0.863495	+	0.724558i	−0.962718	−	0.270507i	$-0.912809\pi$
$499$	−19.2890	+	16.1854i	−0.863495	+	0.724558i	0.0992229	+	0.995065i	$0.468364\pi$
$500$	−9.83060	−	20.0838i	−0.439638	−	0.898175i
$501$	−11.5884	+	20.0717i	−0.517731	+	0.896737i
$502$	−1.17439	+	17.5186i	−0.0524156	+	0.781892i
$503$	−11.1617	+	23.9363i	−0.497675	+	1.06727i	0.483713	+	0.875227i	$0.339288\pi$
$503$	−11.1617	+	23.9363i	−0.497675	+	1.06727i	−0.981387	+	0.192040i	$0.938490\pi$
$504$	−7.44414	+	10.0581i	−0.331589	+	0.448025i
$505$	−1.44727	−	18.0521i	−0.0644028	−	0.803306i
$506$	8.28622	−	24.2917i	0.368368	−	1.07990i
$507$	11.8532	−	8.29970i	0.526419	−	0.368603i
$508$	9.51879	+	30.5058i	0.422328	+	1.35348i
$509$	6.47122	−	7.71210i	0.286832	−	0.341833i	−0.603318	−	0.797501i	$-0.706155\pi$
$509$	6.47122	−	7.71210i	0.286832	−	0.341833i	0.890150	+	0.455668i	$0.150600\pi$
$510$	39.8330	−	34.3205i	1.76384	−	1.51974i
$511$	−1.20722	+	3.31681i	−0.0534043	+	0.146727i
$512$	−18.6441	−	12.8218i	−0.823961	−	0.566647i
$513$	1.06578	−	44.2699i	0.0470553	−	1.95457i
$514$	−5.72962	−	29.0303i	−0.252723	−	1.28047i
$515$	28.2583	+	0.205313i	1.24521	+	0.00904718i
$516$	8.31784	+	13.1425i	0.366173	+	0.578566i
$517$	−30.2726	+	2.64851i	−1.33139	+	0.116481i
$518$	0.643836	+	5.96071i	0.0282885	+	0.261898i
$519$	−0.180103	+	1.02142i	−0.00790566	+	0.0448352i
$520$	−16.8645	−	6.78695i	−0.739556	−	0.297628i
$521$	4.46702	+	7.73711i	0.195704	+	0.338969i	0.947131	−	0.320847i	$-0.103968\pi$
$521$	4.46702	+	7.73711i	0.195704	+	0.338969i	−0.751427	+	0.659816i	$0.770634\pi$
$522$	−14.6930	+	59.6608i	−0.643094	+	2.61128i
$523$	−14.6603	+	31.4392i	−0.641052	+	1.37474i	0.270166	+	0.962814i	$0.412922\pi$
$523$	−14.6603	+	31.4392i	−0.641052	+	1.37474i	−0.911217	+	0.411926i	$0.864856\pi$
$524$	7.39852	+	5.71212i	0.323206	+	0.249535i
$525$	−10.5416	+	1.70121i	−0.460071	+	0.0742470i
$526$	−21.9782	+	0.446872i	−0.958295	+	0.0194845i
$527$	20.0720	+	1.75608i	0.874352	+	0.0764959i
$528$	28.7179	+	24.3897i	1.24978	+	1.06142i
$529$	11.4472	−	2.01844i	0.497703	−	0.0877584i
$530$	29.2131	+	19.8916i	1.26894	+	0.864037i
$531$		−	25.1151i		−	1.08990i
$532$	−1.15805	−	5.98526i	−0.0502079	−	0.259494i
$533$	−0.324168	−	0.324168i	−0.0140413	−	0.0140413i
$534$	−50.0679	−	7.78241i	−2.16665	−	0.336778i
$535$	8.16626	−	4.63602i	0.353058	−	0.200432i
$536$	−4.99380	+	43.7921i	−0.215699	+	1.89153i
$537$	0.630838	−	7.21052i	0.0272227	−	0.311157i
$538$	28.4136	−	29.5930i	1.22500	−	1.27584i
$539$	−10.0410	+	17.3914i	−0.432495	+	0.749103i
$540$	−43.1882	−	14.1050i	−1.85852	−	0.606981i
$541$	−22.8138	+	8.30355i	−0.980843	+	0.356998i	−0.782168	−	0.623068i	$-0.785886\pi$
$541$	−22.8138	+	8.30355i	−0.980843	+	0.356998i	−0.198675	+	0.980065i	$0.563664\pi$
$542$	−22.5476	−	5.55292i	−0.968504	−	0.238518i
$543$	3.66948	+	0.983234i	0.157472	+	0.0421946i
$544$	27.7227	−	13.4160i	1.18860	−	0.575208i
$545$	6.23255	+	4.43191i	0.266973	+	0.189842i
$546$	−5.44372	+	6.76211i	−0.232970	+	0.289391i
$547$	−2.42378	−	27.7039i	−0.103633	−	1.18453i	−0.852831	−	0.522187i	$-0.825116\pi$
$547$	−2.42378	−	27.7039i	−0.103633	−	1.18453i	0.749198	−	0.662346i	$-0.230439\pi$
$548$	5.19206	−	23.0946i	0.221794	−	0.986554i
$549$	3.16024	−	8.68270i	0.134876	−	0.370568i
$550$	2.02676	+	21.7150i	0.0864215	+	0.925929i
$551$	−16.5745	−	24.9269i	−0.706096	−	1.06192i
$552$	−10.1381	+	49.8055i	−0.431506	+	2.11986i
$553$	−1.15941	−	2.48637i	−0.0493033	−	0.105731i
$554$	−11.8117	+	4.57312i	−0.501832	+	0.194293i
$555$	−37.6465	+	17.2230i	−1.59800	+	0.731074i
$556$	14.8952	+	7.81032i	0.631695	+	0.331231i
$557$	−10.7057	−	15.2894i	−0.453616	−	0.647831i	0.525581	−	0.850744i	$-0.323848\pi$
$557$	−10.7057	−	15.2894i	−0.453616	−	0.647831i	−0.979197	+	0.202913i	$0.934959\pi$
$558$	−14.6006	−	29.7185i	−0.618094	−	1.25808i
$559$	3.65970	+	6.33879i	0.154789	+	0.268102i
$560$	−6.22308	−	0.627406i	−0.262973	−	0.0265127i
$561$	−48.1900	+	17.5397i	−2.03458	+	0.740528i
$562$	−3.52997	−	0.236638i	−0.148903	−	0.00998197i
$563$	−10.9476	−	40.8569i	−0.461386	−	1.72191i	−0.668603	−	0.743620i	$-0.733107\pi$
$563$	−10.9476	−	40.8569i	−0.461386	−	1.72191i	0.207217	−	0.978295i	$-0.433559\pi$
$564$	58.7902	−	12.8502i	2.47551	−	0.541089i
$565$	29.5097	+	17.3245i	1.24148	+	0.728846i
$566$	−5.23694	+	9.51212i	−0.220125	+	0.399824i
$567$	−4.83152	+	6.90012i	−0.202905	+	0.289778i
$568$	−8.93789	+	14.5821i	−0.375026	+	0.611852i
$569$			44.9255i			1.88337i	0.336489	+	0.941687i	$0.390761\pi$
$569$			44.9255i			1.88337i	−0.336489	+	0.941687i	$0.609239\pi$
$570$	36.6854	−	20.6454i	1.53658	−	0.864739i
$571$			17.2217i			0.720704i	0.932816	+	0.360352i	$0.117343\pi$
$571$			17.2217i			0.720704i	−0.932816	+	0.360352i	$0.882657\pi$
$572$	13.0368	+	12.0175i	0.545094	+	0.502477i
$573$	−1.24354	+	1.77596i	−0.0519496	+	0.0741918i
$574$	−0.138175	−	0.0760727i	−0.00576730	−	0.00317521i
$575$	−24.3429	+	16.5232i	−1.01517	+	0.689065i
$576$	−42.4419	−	27.5739i	−1.76841	−	1.14891i
$577$	−0.270071	−	1.00792i	−0.0112432	−	0.0419601i	0.960076	−	0.279738i	$-0.0902476\pi$
$577$	−0.270071	−	1.00792i	−0.0112432	−	0.0419601i	−0.971320	+	0.237778i	$0.923581\pi$
$578$	−1.19582	+	17.8382i	−0.0497396	+	0.741973i
$579$	−14.0771	+	5.12364i	−0.585024	+	0.212931i
$580$	−29.3835	+	8.93486i	−1.22008	+	0.371000i
$581$	0.256345	+	0.444003i	0.0106350	+	0.0184204i
$582$	8.75954	−	4.30354i	0.363094	−	0.178388i
$583$	−19.7717	−	28.2370i	−0.818862	−	1.16946i
$584$	−13.6883	−	4.05610i	−0.566424	−	0.167842i
$585$	−38.1080	−	14.1846i	−1.57557	−	0.586459i
$586$	8.64724	+	22.3346i	0.357214	+	0.922633i
$587$	2.33482	+	5.00703i	0.0963682	+	0.206662i	0.948582	−	0.316531i	$-0.102518\pi$
$587$	2.33482	+	5.00703i	0.0963682	+	0.206662i	−0.852214	+	0.523194i	$0.824740\pi$
$588$	15.3279	−	36.6958i	0.632112	−	1.51331i
$589$	15.4767	+	4.54891i	0.637707	+	0.187435i
$590$	10.7887	−	6.41825i	0.444166	−	0.264235i
$591$	4.39151	−	12.0656i	0.180643	−	0.496312i
$592$	−23.9058	+	4.06879i	−0.982524	+	0.167226i
$593$	−0.00859331	−	0.0982220i	−0.000352885	−	0.00403349i	0.996016	−	0.0891723i	$-0.0284222\pi$
$593$	−0.00859331	−	0.0982220i	−0.000352885	−	0.00403349i	−0.996369	+	0.0851388i	$0.972867\pi$
$594$	34.5177	+	27.7879i	1.41628	+	1.14015i
$595$	4.93352	−	6.93797i	0.202255	−	0.284429i
$596$	2.06676	−	15.3458i	0.0846576	−	0.628588i
$597$	−7.44193	−	1.99406i	−0.304578	−	0.0816114i
$598$	−5.71971	+	23.2249i	−0.233896	+	0.949737i
$599$	16.9154	−	6.15671i	0.691146	−	0.251556i	0.0275200	−	0.999621i	$-0.491239\pi$
$599$	16.9154	−	6.15671i	0.691146	−	0.251556i	0.663626	+	0.748065i	$0.269017\pi$
$600$	−9.46695	−	42.1390i	−0.386487	−	1.72032i
$601$	−6.09299	+	10.5534i	−0.248538	+	0.430481i	−0.963120	−	0.269071i	$-0.913284\pi$
$601$	−6.09299	+	10.5534i	−0.248538	+	0.430481i	0.714582	+	0.699552i	$0.246617\pi$
$602$	1.81654	+	1.74415i	0.0740368	+	0.0710861i
$603$	−8.59251	+	98.2129i	−0.349914	+	3.99954i
$604$	−34.9665	−	11.1393i	−1.42277	−	0.453253i
$605$	−0.883923	+	3.20550i	−0.0359366	+	0.130322i
$606$	5.37255	−	34.5641i	0.218245	−	1.40407i
$607$	30.8833	+	30.8833i	1.25351	+	1.25351i	0.954134	+	0.299380i	$0.0967798\pi$
$607$	30.8833	+	30.8833i	1.25351	+	1.25351i	0.299380	+	0.954134i	$0.403220\pi$
$608$	23.8782	−	6.15083i	0.968388	−	0.249449i
$609$			14.6659i			0.594294i
$610$	4.53746	−	0.861343i	0.183717	−	0.0348748i
$611$	27.8893	−	4.91764i	1.12828	−	0.198946i
$612$	61.1998	−	31.6276i	2.47385	−	1.27847i
$613$	−1.47387	−	0.128947i	−0.0595292	−	0.00520813i	0.0573522	−	0.998354i	$-0.481734\pi$
$613$	−1.47387	−	0.128947i	−0.0595292	−	0.00520813i	−0.116881	+	0.993146i	$0.537290\pi$
$614$	−0.479216	−	23.5690i	−0.0193396	−	0.951166i
$615$	0.196919	−	1.07122i	0.00794056	−	0.0431956i
$616$	5.45920	+	2.72252i	0.219958	+	0.109694i
$617$	16.0880	−	34.5008i	0.647677	−	1.38895i	−0.258484	−	0.966016i	$-0.583223\pi$
$617$	16.0880	−	34.5008i	0.647677	−	1.38895i	0.906161	−	0.422932i	$-0.138999\pi$
$618$	52.9984	+	13.0522i	2.13191	+	0.525035i
$619$	−12.7137	−	22.0207i	−0.511005	−	0.885086i	−0.999919	−	0.0127543i	$-0.995940\pi$
$619$	−12.7137	−	22.0207i	−0.511005	−	0.885086i	0.488914	−	0.872332i	$-0.337393\pi$
$620$	9.03500	−	13.8667i	0.362854	−	0.556901i
$621$	−10.3804	+	58.8703i	−0.416552	+	2.36238i
$622$	−11.5182	+	1.24411i	−0.461836	+	0.0498844i
$623$	−8.17275	+	0.715023i	−0.327434	+	0.0286468i
$624$	−28.6420	−	20.3103i	−1.14660	−	0.813063i
$625$	13.1238	−	21.2783i	0.524954	−	0.851131i
$626$	−16.4808	+	3.25276i	−0.658704	+	0.130006i
$627$	−40.5939	+	6.15439i	−1.62116	+	0.245783i
$628$	24.1474	+	10.0864i	0.963587	+	0.402492i
$629$	11.2888	−	31.0158i	0.450116	−	1.23668i
$630$	−13.9517	−	1.03715i	−0.555851	−	0.0413212i
$631$	16.6534	−	19.8467i	0.662960	−	0.790084i	−0.324848	−	0.945766i	$-0.605313\pi$
$631$	16.6534	−	19.8467i	0.662960	−	0.790084i	0.987807	+	0.155682i	$0.0497575\pi$
$632$	9.75214	−	5.29375i	0.387919	−	0.210574i
$633$	52.3926	−	36.6857i	2.08242	−	1.45812i
$634$	−25.6941	−	8.76461i	−1.02044	−	0.348087i
$635$	−23.1640	+	27.2019i	−0.919234	+	1.07947i
$636$	45.9681	+	50.4659i	1.82275	+	2.00110i
$637$	7.90922	−	16.9614i	0.313375	−	0.672035i
$638$	29.8876	+	2.00357i	1.18326	+	0.0793222i
$639$	−19.1282	+	33.1310i	−0.756700	+	1.31064i
$640$	0.998782	−	25.2785i	0.0394803	−	0.999220i
$641$	28.3099	−	23.7548i	1.11817	−	0.938259i	0.119662	−	0.992815i	$-0.461819\pi$
$641$	28.3099	−	23.7548i	1.11817	−	0.938259i	0.998511	+	0.0545561i	$0.0173744\pi$
$642$	17.4204	−	5.04950i	0.687529	−	0.199288i
$643$	32.6552	+	22.8654i	1.28780	+	0.901724i	0.998458	−	0.0555036i	$-0.0176764\pi$
$643$	32.6552	+	22.8654i	1.28780	+	0.901724i	0.289337	+	0.957227i	$0.406565\pi$
$644$	0.334514	+	8.22270i	0.0131817	+	0.324020i
$645$	−7.46336	+	15.7063i	−0.293870	+	0.618434i
$646$	−8.80761	+	32.3854i	−0.346531	+	1.27419i
$647$	−27.4995	−	27.4995i	−1.08112	−	1.08112i	−0.996406	−	0.0847097i	$-0.973004\pi$
$647$	−27.4995	−	27.4995i	−1.08112	−	1.08112i	−0.0847097	−	0.996406i	$-0.526996\pi$
$648$	−29.0483	−	17.8047i	−1.14112	−	0.699435i
$649$	−12.0580	+	2.12615i	−0.473317	+	0.0834586i
$650$	−3.64535	−	19.9951i	−0.142982	−	0.784272i
$651$	−5.08019	−	6.05433i	−0.199108	−	0.237288i
$652$	18.6347	−	29.0595i	0.729790	−	1.13806i
$653$	−8.06409	+	2.16077i	−0.315572	+	0.0845574i	−0.413129	−	0.910673i	$-0.635564\pi$
$653$	−8.06409	+	2.16077i	−0.315572	+	0.0845574i	0.0975564	+	0.995230i	$0.468897\pi$
$654$	9.72288	+	11.1201i	0.380195	+	0.434831i
$655$	−0.986413	+	10.4036i	−0.0385424	+	0.406503i
$656$	0.273056	−	0.576593i	0.0106611	−	0.0225122i
$657$	−30.8454	−	8.26501i	−1.20339	−	0.322449i
$658$	8.74517	−	4.29648i	0.340922	−	0.167494i
$659$	0.873533	−	4.95405i	0.0340280	−	0.192982i	−0.963055	−	0.269304i	$-0.913206\pi$
$659$	0.873533	−	4.95405i	0.0340280	−	0.192982i	0.997083	+	0.0763215i	$0.0243175\pi$
$660$	−5.92568	+	41.7055i	−0.230657	+	1.62339i
$661$	−20.8595	−	17.5032i	−0.811341	−	0.680796i	0.139587	−	0.990210i	$-0.455423\pi$
$661$	−20.8595	−	17.5032i	−0.811341	−	0.680796i	−0.950927	+	0.309414i	$0.899867\pi$
$662$	10.9920	−	24.8807i	0.427214	−	0.967015i
$663$	43.3139	−	20.1976i	1.68217	−	0.784411i
$664$	−1.72933	+	1.14438i	−0.0671111	+	0.0444105i
$665$	4.96815	−	4.66615i	0.192656	−	0.180946i
$666$	−53.2145	+	10.5028i	−2.06202	+	0.406975i
$667$	17.0776	+	36.6231i	0.661248	+	1.41805i
$668$	−14.8087	−	3.32923i	−0.572964	−	0.128812i
$669$	−42.5521	+	50.7116i	−1.64516	+	1.96062i
$670$	−44.3854	+	21.4076i	−1.71476	+	0.827047i
$671$	−4.43618	−	0.782219i	−0.171257	−	0.0301972i
$672$	−11.4104	−	3.96816i	−0.440166	−	0.153075i
$673$	−7.95864	+	29.7020i	−0.306783	+	1.14493i	0.624617	+	0.780931i	$0.285255\pi$
$673$	−7.95864	+	29.7020i	−0.306783	+	1.14493i	−0.931400	+	0.363998i	$0.881411\pi$
$674$	−20.4077	−	33.7439i	−0.786075	−	1.29977i
$675$	−12.4326	−	49.2508i	−0.478531	−	1.89567i
$676$	7.50089	+	5.79116i	0.288496	+	0.222737i
$677$	−8.33961	−	31.1238i	−0.320517	−	1.19619i	−0.918742	−	0.394858i	$-0.870794\pi$
$677$	−8.33961	−	31.1238i	−0.320517	−	1.19619i	0.598225	−	0.801328i	$-0.295873\pi$
$678$	47.6759	+	45.7758i	1.83098	+	1.75801i
$679$	1.21051	−	1.01574i	0.0464550	−	0.0389803i
$680$	29.2262	+	18.2072i	1.12077	+	0.698214i
$681$	14.7237	+	83.5024i	0.564215	+	3.19982i
$682$	−13.0321	+	9.52577i	−0.499025	+	0.364761i
$683$	−30.6571	+	30.6571i	−1.17306	+	1.17306i	−0.191586	+	0.981476i	$0.561363\pi$
$683$	−30.6571	+	30.6571i	−1.17306	+	1.17306i	−0.981476	+	0.191586i	$0.938637\pi$
$684$	53.0303	−	15.1566i	2.02767	−	0.579528i
$685$	24.9341	−	8.87066i	0.952684	−	0.338931i
$686$	2.05225	−	13.2031i	0.0783552	−	0.504095i
$687$	−11.0511	+	15.7826i	−0.421625	+	0.602143i
$688$	−6.59363	+	7.76373i	−0.251380	+	0.295989i
$689$	20.6491	+	24.6087i	0.786669	+	0.937516i
$690$	−53.1406	+	20.1316i	−2.02303	+	0.766398i
$691$	23.7325	+	13.7020i	0.902828	+	0.521248i	0.878117	−	0.478447i	$-0.158800\pi$
$691$	23.7325	+	13.7020i	0.902828	+	0.521248i	0.0247114	+	0.999695i	$0.492133\pi$
$692$	−0.673686	+	0.0866550i	−0.0256097	+	0.00329413i
$693$	12.3668	+	5.76675i	0.469777	+	0.219061i
$694$	1.36368	−	0.824731i	0.0517647	−	0.0313063i
$695$	1.50272	+	18.7437i	0.0570014	+	0.710988i
$696$	−59.2093	+	3.61560i	−2.24432	+	0.137049i
$697$	0.498071	+	0.711319i	0.0188658	+	0.0269431i
$698$	17.1133	−	1.84846i	0.647748	−	0.0699654i
$699$	58.4797	+	49.0703i	2.21191	+	1.85601i
$700$	−3.11989	−	6.25834i	−0.117921	−	0.236543i
$701$	−6.28068	−	2.28598i	−0.237218	−	0.0863402i	0.220676	−	0.975347i	$-0.429174\pi$
$701$	−6.28068	−	2.28598i	−0.237218	−	0.0863402i	−0.457894	+	0.889007i	$0.651396\pi$
$702$	−34.3025	−	22.9940i	−1.29466	−	0.867854i
$703$	13.7597	−	22.5605i	0.518956	−	0.850884i
$704$	−9.64551	+	22.7111i	−0.363529	+	0.855956i
$705$	47.2281	+	47.9194i	1.77871	+	1.80475i
$706$	−13.6678	−	35.3021i	−0.514396	−	1.32861i
$707$	−0.493612	−	5.64201i	−0.0185642	−	0.212190i
$708$	23.1463	−	7.22239i	0.869891	−	0.271434i
$709$	20.0308	+	3.53197i	0.752273	+	0.132646i	0.536620	−	0.843824i	$-0.319701\pi$
$709$	20.0308	+	3.53197i	0.752273	+	0.132646i	0.215653	+	0.976470i	$0.430812\pi$
$710$	−19.1205	+	0.249809i	−0.717579	+	0.00937515i
$711$	21.4948	−	12.4100i	0.806116	−	0.465411i
$712$	−4.90152	−	32.8187i	−0.183692	−	1.22993i
$713$	−19.7359	−	9.20301i	−0.739116	−	0.344655i
$714$	12.3787	−	10.8233i	0.463262	−	0.405053i
$715$	−3.58407	+	19.4968i	−0.134036	+	0.729140i
$716$	4.63081	−	1.01219i	0.173061	−	0.0378272i
$717$	0.942070	−	10.7679i	0.0351823	−	0.402135i
$718$	17.2149	−	4.98991i	0.642453	−	0.186222i
$719$	−3.57813	−	20.2926i	−0.133442	−	0.756785i	−0.975932	−	0.218074i	$-0.930023\pi$
$719$	−3.57813	−	20.2926i	−0.133442	−	0.756785i	0.842491	−	0.538711i	$-0.181089\pi$
$720$	0.747667	−	56.5816i	0.0278639	−	2.10867i
$721$	8.83750			0.329126
$722$	−12.0285	+	24.0274i	−0.447656	+	0.894206i
$723$	10.4446	−	10.4446i	0.388439	−	0.388439i
$724$	0.101128	+	2.48583i	0.00375839	+	0.0923850i
$725$	−25.9802	−	22.4513i	−0.964879	−	0.833819i
$726$	−3.09750	+	5.62614i	−0.114959	+	0.208806i
$727$	−4.98669	−	0.436279i	−0.184946	−	0.0161807i	−0.00569368	−	0.999984i	$-0.501812\pi$
$727$	−4.98669	−	0.436279i	−0.184946	−	0.0161807i	−0.179253	+	0.983803i	$0.557368\pi$
$728$	−5.28933	−	2.08412i	−0.196036	−	0.0772426i
$729$	14.6081	+	8.43397i	0.541039	+	0.312369i
$730$	−4.33225	−	15.3625i	−0.160344	−	0.568592i
$731$	−4.74178	−	13.0279i	−0.175381	−	0.481856i
$732$	8.91086	+	0.415610i	0.329355	+	0.0153614i
$733$	−1.94139	+	7.24536i	−0.0717068	+	0.267614i	−0.992466	−	0.122517i	$-0.960903\pi$
$733$	−1.94139	+	7.24536i	−0.0717068	+	0.267614i	0.920760	+	0.390130i	$0.127570\pi$
$734$	14.0674	−	41.2398i	0.519239	−	1.52219i
$735$	43.8419	−	7.40249i	1.61713	−	0.273045i
$736$	−33.1142	+	3.37765i	−1.22061	+	0.124502i
$737$	47.8804	−	4.18899i	1.76370	−	0.154303i
$738$	0.576670	−	1.30531i	0.0212275	−	0.0480493i
$739$	−20.0011	−	7.27981i	−0.735753	−	0.267792i	−0.0531548	−	0.998586i	$-0.516928\pi$
$739$	−20.0011	−	7.27981i	−0.735753	−	0.267792i	−0.682598	+	0.730794i	$0.739150\pi$
$740$	−18.1109	−	20.1755i	−0.665770	−	0.741666i
$741$	37.1866	−	9.01074i	1.36608	−	0.331018i
$742$	9.18082	+	6.15420i	0.337039	+	0.225928i
$743$	−30.1007	+	14.0362i	−1.10429	+	0.514938i	−0.887279	−	0.461232i	$-0.847408\pi$
$743$	−30.1007	+	14.0362i	−1.10429	+	0.514938i	−0.217008	+	0.976170i	$0.569630\pi$
$744$	23.1901	−	22.0023i	0.850191	−	0.806644i
$745$	15.7428	−	7.20219i	0.576770	−	0.263868i
$746$	−10.6803	+	13.2669i	−0.391034	+	0.485737i
$747$	−3.79955	+	2.66047i	−0.139018	+	0.0973416i
$748$	−20.3657	−	26.7051i	−0.744643	−	0.976437i
$749$	2.54325	−	1.46834i	0.0929282	−	0.0536521i
$750$	34.1942	−	34.0940i	1.24859	−	1.24494i
$751$	3.32296	+	9.12976i	0.121257	+	0.333150i	0.985439	−	0.170029i	$-0.0543861\pi$
$751$	3.32296	+	9.12976i	0.121257	+	0.333150i	−0.864183	+	0.503178i	$0.832164\pi$
$752$	19.5017	+	34.2468i	0.711155	+	1.24885i
$753$	−36.6237	+	9.81328i	−1.33464	+	0.357616i
$754$	−27.9097	+	0.567474i	−1.01641	+	0.0206662i
$755$	−10.3310	−	39.7076i	−0.375984	−	1.44511i
$756$	−13.5380	−	4.31282i	−0.492372	−	0.156856i
$757$	−10.4363	−	7.30758i	−0.379314	−	0.265599i	0.368334	−	0.929693i	$-0.379928\pi$
$757$	−10.4363	−	7.30758i	−0.379314	−	0.265599i	−0.747648	+	0.664095i	$0.768817\pi$
$758$	−25.4431	+	18.5975i	−0.924135	+	0.675493i
$759$	55.4250			2.01180
$760$	20.0630	+	18.9070i	0.727761	+	0.685831i
$761$	−21.4425			−0.777290			−0.388645	−	0.921388i	$-0.627057\pi$
$761$	−21.4425			−0.777290			−0.388645	+	0.921388i	$0.627057\pi$
$762$	−55.7123	+	40.7227i	−2.01824	+	1.47523i
$763$	1.95913	+	1.37180i	0.0709254	+	0.0496625i
$764$	−1.35284	−	0.430977i	−0.0489442	−	0.0155922i
$765$	66.4201	+	38.9938i	2.40142	+	1.40982i
$766$	−17.7978	+	0.361874i	−0.643061	+	0.0130750i
$767$	11.0217	−	2.95325i	0.397970	−	0.106636i
$768$	13.2072	−	47.0444i	0.476575	−	1.69757i
$769$	−9.24379	−	25.3971i	−0.333340	−	0.915843i	−0.987237	−	0.159260i	$-0.949089\pi$
$769$	−9.24379	−	25.3971i	−0.333340	−	0.915843i	0.653897	−	0.756584i	$-0.273133\pi$
$770$	0.683155	+	6.78617i	0.0246192	+	0.244557i
$771$	55.3383	−	31.9496i	1.99296	−	1.15064i
$772$	−5.94915	−	7.80101i	−0.214115	−	0.280764i
$773$	−6.39911	+	4.48071i	−0.230160	+	0.161160i	−0.682968	−	0.730448i	$-0.739311\pi$
$773$	−6.39911	+	4.48071i	−0.230160	+	0.161160i	0.452808	+	0.891608i	$0.350422\pi$
$774$	−14.2871	+	17.7473i	−0.513541	+	0.637913i
$775$	18.5020	+	0.268870i	0.664612	+	0.00965810i
$776$	4.39915	+	4.63664i	0.157920	+	0.166446i
$777$	−11.7338	+	5.47156i	−0.420947	+	0.196291i
$778$	−31.6274	−	21.2009i	−1.13390	−	0.760088i
$779$	0.278564	+	0.636975i	0.00998060	+	0.0228220i
$780$	2.11384	−	39.1998i	0.0756875	−	1.40358i
$781$	17.5259	+	6.37889i	0.627125	+	0.228255i
$782$	18.3084	−	41.4418i	0.654709	−	1.48196i
$783$	−69.5015	+	6.08059i	−2.48378	+	0.217303i
$784$	25.9309	+	2.42415i	0.926104	+	0.0865769i
$785$	4.87116	+	28.8499i	0.173859	+	1.02970i
$786$	−6.51652	+	19.1037i	−0.232436	+	0.681405i
$787$	−2.83584	+	10.5835i	−0.101087	+	0.377261i	−0.997872	−	0.0652056i	$-0.979230\pi$
$787$	−2.83584	+	10.5835i	−0.101087	+	0.377261i	0.896785	+	0.442466i	$0.145896\pi$
$788$	8.39962	+	0.391766i	0.299224	+	0.0139561i
$789$	−16.2360	−	44.6081i	−0.578018	−	1.58809i
$790$	10.8241	+	6.06214i	0.385103	+	0.215681i
$791$	9.26772	+	5.35072i	0.329522	+	0.190250i
$792$	−20.2327	+	51.3490i	−0.718938	+	1.82461i
$793$	4.18199	+	0.365877i	0.148507	+	0.0129927i
$794$	20.8597	−	37.8885i	0.740282	−	1.34461i
$795$	−20.2883	+	73.5746i	−0.719552	+	2.60942i
$796$	−0.205093	−	5.04141i	−0.00726935	−	0.178688i
$797$	−26.2634	+	26.2634i	−0.930298	+	0.930298i	−0.997724	−	0.0674265i	$-0.978521\pi$
$797$	−26.2634	+	26.2634i	−0.930298	+	0.930298i	0.0674265	+	0.997724i	$0.478521\pi$
$798$	11.4255	−	6.53964i	0.404457	−	0.231501i
$799$	−53.6415			−1.89770
$800$	24.4970	−	14.1385i	0.866100	−	0.499871i
$801$	−12.8886	−	73.0949i	−0.455396	−	2.58268i
$802$	3.39679	−	0.984597i	0.119945	−	0.0347673i
$803$	−1.35685	+	15.5089i	−0.0478822	+	0.547296i
$804$	−92.9850	+	20.3243i	−3.27933	+	0.716784i
$805$	−7.57505	+	5.22250i	−0.266985	+	0.184069i
$806$	11.3250	−	9.90202i	0.398907	−	0.348784i
$807$	80.2922	+	37.4409i	2.82642	+	1.31798i
$808$	22.6562	−	3.38374i	0.797044	−	0.119040i
$809$	−5.63654	+	3.25426i	−0.198170	+	0.114414i	−0.595802	−	0.803132i	$-0.703166\pi$
$809$	−5.63654	+	3.25426i	−0.198170	+	0.114414i	0.397631	+	0.917545i	$0.369832\pi$
$810$	−0.497630	−	38.0889i	−0.0174849	−	1.33831i
$811$	−10.3397	−	1.82317i	−0.363076	−	0.0640201i	−0.0108657	−	0.999941i	$-0.503459\pi$
$811$	−10.3397	−	1.82317i	−0.363076	−	0.0640201i	−0.352210	+	0.935921i	$0.614570\pi$
$812$	−9.16860	+	2.86090i	−0.321755	+	0.100398i
$813$	−4.37048	−	49.9549i	−0.153280	−	1.75199i
$814$	9.54745	+	24.6597i	0.334638	+	0.864322i
$815$	38.5947	+	0.280413i	1.35191	+	0.00982245i
$816$	46.7477	+	47.3071i	1.63650	+	1.65608i
$817$	−1.66381	−	10.9744i	−0.0582093	−	0.383944i
$818$	−40.0226	−	26.8284i	−1.39936	−	0.938033i
$819$	−11.9495	−	4.34926i	−0.417549	−	0.151975i
$820$	0.708098	−	0.0858564i	0.0247279	−	0.00299824i
$821$	11.4055	+	9.57035i	0.398055	+	0.334008i	0.819741	−	0.572734i	$-0.194117\pi$
$821$	11.4055	+	9.57035i	0.398055	+	0.334008i	−0.421686	+	0.906742i	$0.638562\pi$
$822$	50.8212	−	5.48937i	1.77259	−	0.191464i
$823$	−18.9503	−	27.0639i	−0.660567	−	0.943387i	−0.999996	−	0.00275550i	$-0.999123\pi$
$823$	−18.9503	−	27.0639i	−0.660567	−	0.943387i	0.339430	−	0.940631i	$-0.389766\pi$
$824$	2.17872	+	35.6787i	0.0758991	+	1.24293i
$825$	−42.9686	+	19.2815i	−1.49598	+	0.671297i
$826$	3.35931	−	2.03165i	0.116885	−	0.0706902i
$827$	−13.1536	−	6.13364i	−0.457397	−	0.213288i	0.180243	−	0.983622i	$-0.442311\pi$
$827$	−13.1536	−	6.13364i	−0.457397	−	0.213288i	−0.637640	+	0.770335i	$0.720089\pi$
$828$	−73.8452	+	9.49858i	−2.56630	+	0.330098i
$829$	13.2198	+	7.63244i	0.459142	+	0.265086i	0.711683	−	0.702500i	$-0.247933\pi$
$829$	13.2198	+	7.63244i	0.459142	+	0.265086i	−0.252542	+	0.967586i	$0.581266\pi$
$830$	−2.11386	−	0.952288i	−0.0733730	−	0.0330544i
$831$	−17.5815	−	20.9528i	−0.609896	−	0.726846i
$832$	7.11002	−	21.8679i	0.246496	−	0.758133i
$833$	−20.3325	+	29.0379i	−0.704480	+	1.00610i
$834$	−5.57838	+	35.8883i	−0.193163	+	1.24271i
$835$	−5.68801	−	15.9882i	−0.196842	−	0.553293i
$836$	−11.7662	−	24.1773i	−0.406943	−	0.836189i
$837$	26.5851	−	26.5851i	0.918914	−	0.918914i
$838$	11.6549	−	8.51909i	0.402611	−	0.294287i
$839$	8.99773	+	51.0287i	0.310636	+	1.76171i	0.595710	+	0.803200i	$0.296871\pi$
$839$	8.99773	+	51.0287i	0.310636	+	1.76171i	−0.285074	+	0.958506i	$0.592018\pi$
$840$	−3.05628	−	13.1563i	−0.105452	−	0.453936i
$841$	−13.9122	+	11.6737i	−0.479732	+	0.402543i
$842$	10.1412	+	9.73704i	0.349489	+	0.335561i
$843$	−1.97736	−	7.37962i	−0.0681040	−	0.254168i
$844$	33.1548	+	25.5976i	1.14124	+	0.881105i
$845$	−1.00006	+	10.5476i	−0.0344032	+	0.362847i
$846$	45.6187	+	75.4300i	1.56840	+	2.59334i
$847$	−0.269140	+	1.00444i	−0.00924776	+	0.0345131i
$848$	−22.5824	+	38.5820i	−0.775482	+	1.32491i
$849$	−23.0922	−	4.07178i	−0.792522	−	0.139743i
$850$	0.223240	+	38.4973i	0.00765705	+	1.32045i
$851$	−22.9298	+	27.3266i	−0.786022	+	0.936745i
$852$	−36.0346	−	8.10119i	−1.23453	−	0.277542i
$853$	6.23998	+	13.3817i	0.213653	+	0.458180i	0.983702	−	0.179804i	$-0.0575463\pi$
$853$	6.23998	+	13.3817i	0.213653	+	0.458180i	−0.770050	+	0.637984i	$0.779769\pi$
$854$	1.41701	−	0.279672i	0.0484892	−	0.00957017i
$855$	45.9722	+	41.0972i	1.57222	+	1.40550i
$856$	6.55499	+	9.90560i	0.224045	+	0.338567i
$857$	−25.4611	+	11.8727i	−0.869733	+	0.405563i	−0.805657	−	0.592382i	$-0.798188\pi$
$857$	−25.4611	+	11.8727i	−0.869733	+	0.405563i	−0.0640758	+	0.997945i	$0.520410\pi$
$858$	−15.4728	+	35.0232i	−0.528232	+	1.19567i
$859$	−21.8878	−	18.3660i	−0.746802	−	0.626641i	0.187853	−	0.982197i	$-0.439847\pi$
$859$	−21.8878	−	18.3660i	−0.746802	−	0.626641i	−0.934655	+	0.355556i	$0.884292\pi$
$860$	−11.2749	−	1.60198i	−0.384470	−	0.0546270i
$861$	0.0591473	−	0.335441i	0.00201574	−	0.0114318i
$862$	−7.29910	+	3.58603i	−0.248608	+	0.122141i
$863$	19.8184	+	5.31032i	0.674626	+	0.180765i	0.579838	−	0.814732i	$-0.303116\pi$
$863$	19.8184	+	5.31032i	0.674626	+	0.180765i	0.0947881	+	0.995497i	$0.469783\pi$
$864$	14.0742	−	55.7189i	0.478813	−	1.89559i
$865$	−0.483899	−	0.585272i	−0.0164531	−	0.0198999i
$866$	−8.77718	−	10.0385i	−0.298261	−	0.341123i
$867$	−37.2920	+	9.99236i	−1.26650	+	0.339358i
$868$	2.79395	−	4.35697i	0.0948328	−	0.147885i
$869$	−7.77783	−	9.26926i	−0.263845	−	0.314438i
$870$	−38.7468	−	53.8256i	−1.31364	−	1.82486i
$871$	−44.1109	+	7.77794i	−1.49464	+	0.263545i
$872$	−5.05524	+	8.24760i	−0.171192	+	0.279299i
$873$	10.1090	+	10.1090i	0.342139	+	0.342139i
$874$	20.9161	−	29.6348i	0.707498	−	1.00241i
$875$	4.05578	−	6.68403i	0.137110	−	0.225961i
$876$	−1.25317	−	30.8042i	−0.0423407	−	1.04078i
$877$	10.1966	+	7.13973i	0.344314	+	0.241091i	0.732923	−	0.680311i	$-0.238155\pi$
$877$	10.1966	+	7.13973i	0.344314	+	0.241091i	−0.388609	+	0.921403i	$0.627044\pi$
$878$	20.2634	−	5.87357i	0.683857	−	0.198223i
$879$	−39.6194	+	33.2446i	−1.33633	+	1.12131i
$880$	−27.2287	+	4.43103i	−0.917879	+	0.149370i
$881$	6.98604	−	12.1002i	0.235366	−	0.407665i	−0.724013	−	0.689786i	$-0.757705\pi$
$881$	6.98604	−	12.1002i	0.235366	−	0.407665i	0.959379	+	0.282121i	$0.0910379\pi$
$882$	58.1242	+	3.89647i	1.95714	+	0.131201i
$883$	15.3978	−	33.0207i	0.518177	−	1.11123i	−0.456931	−	0.889502i	$-0.651051\pi$
$883$	15.3978	−	33.0207i	0.518177	−	1.11123i	0.975108	−	0.221732i	$-0.0711709\pi$
$884$	21.0761	+	23.1383i	0.708867	+	0.778226i
$885$	20.6395	+	17.5757i	0.693788	+	0.590800i
$886$	−10.5549	−	3.60042i	−0.354599	−	0.120958i
$887$	−27.2989	+	19.1149i	−0.916609	+	0.641816i	−0.933707	−	0.358038i	$-0.883446\pi$
$887$	−27.2989	+	19.1149i	−0.916609	+	0.641816i	0.0170986	+	0.999854i	$0.494557\pi$
$888$	−24.9825	−	46.0227i	−0.838358	−	1.54442i
$889$	−7.18210	+	8.55930i	−0.240880	+	0.287070i
$890$	28.1058	−	24.2163i	0.942110	−	0.811732i
$891$	−12.7071	+	34.9123i	−0.425702	+	1.16961i
$892$	−40.0037	−	16.7096i	−1.33942	−	0.559480i
$893$	−42.1020	−	8.47328i	−1.40889	−	0.283547i
$894$	32.8050	−	6.47463i	1.09716	−	0.216544i
$895$	3.72008	+	3.77454i	0.124349	+	0.126169i
$896$	0.254907	−	7.90744i	0.00851583	−	0.264169i
$897$	−51.4554	+	4.50176i	−1.71804	+	0.150309i
$898$	−39.7017	+	4.28831i	−1.32486	+	0.143103i
$899$	4.41323	−	25.0287i	0.147190	−	0.834754i
$900$	53.9446	−	33.0535i	1.79815	−	1.10178i
$901$	−30.4242	−	52.6962i	−1.01358	−	1.75556i
$902$	−0.675513	−	0.166362i	−0.0224921	−	0.00553925i
$903$	−2.29828	+	4.92868i	−0.0764820	+	0.164016i
$904$	−19.3171	+	38.7347i	−0.642479	+	1.28830i
$905$	−2.29003	+	1.57883i	−0.0761233	+	0.0524820i
$906$	−1.61097	−	79.2316i	−0.0535211	−	2.63229i
$907$	11.9560	+	1.04601i	0.396992	+	0.0347323i	0.283904	−	0.958853i	$-0.408370\pi$
$907$	11.9560	+	1.04601i	0.396992	+	0.0347323i	0.113088	+	0.993585i	$0.463926\pi$
$908$	−49.3305	+	25.4937i	−1.63709	+	0.846037i
$909$	50.4607	−	8.89758i	1.67367	−	0.295114i
$910$	−1.18542	−	6.24464i	−0.0392962	−	0.207008i
$911$			38.2598i			1.26760i	0.773495	+	0.633802i	$0.218507\pi$
$911$			38.2598i			1.26760i	−0.773495	+	0.633802i	$0.781493\pi$
$912$	29.2186	+	44.5147i	0.967523	+	1.47403i
$913$	1.59897	+	1.59897i	0.0529183	+	0.0529183i
$914$	−5.45828	+	35.1157i	−0.180544	+	1.16152i
$915$	4.92385	+	8.67328i	0.162777	+	0.286730i
$916$	−12.0224	−	3.83001i	−0.397233	−	0.126547i
$917$	−0.284836	+	3.25569i	−0.00940612	+	0.107512i
$918$	56.4238	+	54.1751i	1.86226	+	1.78804i
$919$	7.10139	−	12.3000i	0.234253	−	0.405739i	−0.724802	−	0.688957i	$-0.758069\pi$
$919$	7.10139	−	12.3000i	0.234253	−	0.405739i	0.959055	+	0.283219i	$0.0914022\pi$
$920$	−22.9518	−	29.2945i	−0.756697	−	0.965810i
$921$	47.8368	−	17.4112i	1.57628	−	0.573718i
$922$	0.529036	−	2.14815i	0.0174229	−	0.0707456i
$923$	−16.7887	−	4.49853i	−0.552608	−	0.148071i
$924$	−1.75834	+	13.0557i	−0.0578450	+	0.429503i
$925$	8.26994	−	29.1621i	0.271914	−	0.958843i
$926$	43.0289	+	34.6396i	1.41402	+	1.13833i
$927$	6.96847	+	79.6499i	0.228875	+	2.61605i
$928$	−13.8104	−	36.3102i	−0.453348	−	1.19194i
$929$	5.01672	−	13.7833i	0.164593	−	0.452216i	−0.829787	−	0.558079i	$-0.811538\pi$
$929$	5.01672	−	13.7833i	0.164593	−	0.452216i	0.994381	+	0.105863i	$0.0337606\pi$
$930$	34.6402	+	8.79843i	1.13590	+	0.288512i
$931$	−20.5454	+	19.5794i	−0.673349	+	0.641690i
$932$	−19.2693	+	46.1316i	−0.631185	+	1.51109i
$933$	−10.5729	−	22.6738i	−0.346143	−	0.742305i
$934$	9.40816	+	24.2999i	0.307844	+	0.795119i
$935$	13.0984	−	35.1900i	0.428365	−	1.15084i
$936$	14.6129	−	49.3147i	0.477638	−	1.61190i
$937$	20.3054	+	28.9991i	0.663347	+	0.947358i	0.999984	+	0.00572334i	$0.00182180\pi$
$937$	20.3054	+	28.9991i	0.663347	+	0.947358i	−0.336636	+	0.941635i	$0.609289\pi$
$938$	−13.8317	+	6.79550i	−0.451622	+	0.221881i
$939$	−18.1381	−	31.4161i	−0.591914	−	1.02523i
$940$	−20.7446	+	38.8730i	−0.676615	+	1.26790i
$941$	−9.02669	+	3.28545i	−0.294262	+	0.107103i	−0.484933	−	0.874551i	$-0.661156\pi$
$941$	−9.02669	+	3.28545i	−0.294262	+	0.107103i	0.190671	+	0.981654i	$0.438934\pi$
$942$	−3.77989	+	56.3852i	−0.123155	+	1.83713i
$943$	−0.242902	−	0.906522i	−0.00790997	−	0.0295204i
$944$	9.03035	+	13.0613i	0.293913	+	0.425110i
$945$	−3.99987	−	15.3736i	−0.130116	−	0.500104i
$946$	9.73014	+	5.35698i	0.316354	+	0.174170i
$947$	−14.1992	+	20.2785i	−0.461412	+	0.658964i	−0.980674	−	0.195651i	$-0.937318\pi$
$947$	−14.1992	+	20.2785i	−0.461412	+	0.658964i	0.519262	+	0.854615i	$0.326207\pi$
$948$	17.6185	+	16.2410i	0.572221	+	0.527483i
$949$		−	14.5083i		−	0.470960i
$950$	−5.90587	+	30.2510i	−0.191612	+	0.981471i
$951$		−	58.6249i		−	1.90104i
$952$	9.18109	+	5.62741i	0.297561	+	0.182385i
$953$	−4.76042	+	6.79858i	−0.154205	+	0.220228i	−0.888820	−	0.458257i	$-0.848474\pi$
$953$	−4.76042	+	6.79858i	−0.154205	+	0.220228i	0.734615	+	0.678484i	$0.237363\pi$
$954$	−48.2269	+	87.5969i	−1.56140	+	2.83605i
$955$	−0.399704	−	1.53628i	−0.0129341	−	0.0497128i
$956$	6.91548	−	1.51156i	0.223662	−	0.0488874i
$957$	16.7420	+	62.4819i	0.541192	+	2.01975i
$958$	−56.9206	−	3.81578i	−1.83902	−	0.123282i
$959$	7.77733	−	2.83072i	0.251143	−	0.0914086i
$960$	52.3612	−	15.5822i	1.68995	−	0.502915i
$961$	−8.65207	−	14.9858i	−0.279099	−	0.483414i
$962$	−10.8666	−	22.1181i	−0.350352	−	0.713115i
$963$	15.2392	+	21.7638i	0.491075	+	0.701328i
$964$	8.56702	+	4.49214i	0.275925	+	0.144682i
$965$	3.82627	−	10.2796i	0.123172	−	0.330911i
$966$	−16.5726	+	6.41637i	−0.533214	+	0.206443i
$967$	10.7766	+	23.1105i	0.346552	+	0.743183i	0.999904	−	0.0138711i	$-0.00441546\pi$
$967$	10.7766	+	23.1105i	0.346552	+	0.743183i	−0.653352	+	0.757055i	$0.726638\pi$
$968$	−4.12149	−	0.838945i	−0.132470	−	0.0269647i
$969$	−72.3307	+	4.57715i	−2.32360	+	0.147039i
$970$	−1.75916	+	6.92597i	−0.0564833	+	0.222380i
$971$	10.1897	−	27.9960i	0.327003	−	0.898434i	−0.661863	−	0.749625i	$-0.730234\pi$
$971$	10.1897	−	27.9960i	0.327003	−	0.898434i	0.988866	−	0.148809i	$-0.0475440\pi$
$972$	2.76796	−	12.3121i	0.0887824	−	0.394910i
$973$	0.512523	+	5.85817i	0.0164307	+	0.187804i
$974$	−10.5146	+	13.0611i	−0.336911	+	0.418506i
$975$	38.3250	−	21.3906i	1.22738	−	0.685046i
$976$	1.47843	+	5.65182i	0.0473233	+	0.180910i
$977$	22.1658	+	5.93932i	0.709148	+	0.190016i	0.595324	−	0.803485i	$-0.297024\pi$
$977$	22.1658	+	5.93932i	0.709148	+	0.190016i	0.113823	+	0.993501i	$0.463690\pi$
$978$	72.3842	+	17.8264i	2.31459	+	0.570026i
$979$	−34.0025	+	12.3759i	−1.08672	+	0.395535i
$980$	13.1801	+	25.9643i	0.421022	+	0.829401i
$981$	−10.8189	+	18.7388i	−0.345420	+	0.598284i
$982$	−18.8602	+	19.6430i	−0.601852	+	0.626834i
$983$	−1.68910	+	19.3065i	−0.0538738	+	0.615781i	0.920484	+	0.390779i	$0.127794\pi$
$983$	−1.68910	+	19.3065i	−0.0538738	+	0.615781i	−0.974358	+	0.225002i	$0.927761\pi$
$984$	1.36883	+	0.156093i	0.0436365	+	0.00497607i
$985$	4.64136	+	8.17567i	0.147886	+	0.260499i
$986$	52.2487	+	8.12140i	1.66394	+	0.258638i
$987$	14.8782	+	14.8782i	0.473578	+	0.473578i
$988$	12.8872	+	21.4900i	0.409997	+	0.683687i
$989$			14.9839i			0.476460i
$990$	−60.6232	+	11.5081i	−1.92673	+	0.365750i
$991$	41.0625	−	7.24043i	1.30439	−	0.230000i	0.522087	−	0.852892i	$-0.325154\pi$
$991$	41.0625	−	7.24043i	1.30439	−	0.230000i	0.782308	+	0.622892i	$0.214043\pi$
$992$	18.2788	+	10.2056i	0.580351	+	0.324028i
$993$	58.5152	+	5.11941i	1.85692	+	0.162460i
$994$	−5.97885	+	0.121565i	−0.189638	+	0.00385580i
$995$	4.64433	−	3.20196i	0.147235	−	0.101509i
$996$	−3.54456	−	2.73662i	−0.112314	−	0.0867133i
$997$	−13.4577	+	28.8602i	−0.426211	+	0.914012i	0.569544	+	0.821961i	$0.307120\pi$
$997$	−13.4577	+	28.8602i	−0.426211	+	0.914012i	−0.995754	+	0.0920507i	$0.970658\pi$
$998$	8.51540	−	34.5768i	0.269550	−	1.09451i
$999$	−30.7945	−	53.3376i	−0.974294	−	1.68753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.11	yes	672
4.3	odd	2	inner	380.2.bj.a.23.6	✓	672
5.2	odd	4	inner	380.2.bj.a.327.19	yes	672
19.5	even	9	inner	380.2.bj.a.43.24	yes	672
20.7	even	4	inner	380.2.bj.a.327.24	yes	672
76.43	odd	18	inner	380.2.bj.a.43.19	yes	672
95.62	odd	36	inner	380.2.bj.a.347.6	yes	672
380.347	even	36	inner	380.2.bj.a.347.11	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.6	✓	672	4.3	odd	2	inner
380.2.bj.a.23.11	yes	672	1.1	even	1	trivial
380.2.bj.a.43.19	yes	672	76.43	odd	18	inner
380.2.bj.a.43.24	yes	672	19.5	even	9	inner
380.2.bj.a.327.19	yes	672	5.2	odd	4	inner
380.2.bj.a.327.24	yes	672	20.7	even	4	inner
380.2.bj.a.347.6	yes	672	95.62	odd	36	inner
380.2.bj.a.347.11	yes	672	380.347	even	36	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14173 + 0.834541i) q^{2} +(-2.50164 - 1.75167i) q^{3} +(0.607081 - 1.90564i) q^{4} +(2.16402 - 0.563029i) q^{5} +(4.31804 - 0.0877964i) q^{6} +(0.675461 - 0.180989i) q^{7} +(0.897212 + 2.68235i) q^{8} +(2.16382 + 5.94503i) q^{9} +O(q^{10})\)	\(q+(-1.14173 + 0.834541i) q^{2} +(-2.50164 - 1.75167i) q^{3} +(0.607081 - 1.90564i) q^{4} +(2.16402 - 0.563029i) q^{5} +(4.31804 - 0.0877964i) q^{6} +(0.675461 - 0.180989i) q^{7} +(0.897212 + 2.68235i) q^{8} +(2.16382 + 5.94503i) q^{9} +(-2.00085 + 2.44879i) q^{10} +(2.67109 - 1.54215i) q^{11} +(-4.85675 + 3.70382i) q^{12} +(-2.35452 + 1.64865i) q^{13} +(-0.620149 + 0.770341i) q^{14} +(-6.39986 - 2.38216i) q^{15} +(-3.26290 - 2.31375i) q^{16} +(4.93433 - 2.30092i) q^{17} +(-7.43186 - 4.98181i) q^{18} +(4.23631 - 1.02651i) q^{19} +(0.240809 - 4.46565i) q^{20} +(-2.00680 - 0.730414i) q^{21} +(-1.76266 + 3.98985i) q^{22} +(-5.86180 + 0.512841i) q^{23} +(2.45409 - 8.28191i) q^{24} +(4.36600 - 2.43682i) q^{25} +(1.31235 - 3.84726i) q^{26} +(2.62938 - 9.81300i) q^{27} +(0.0651600 - 1.39706i) q^{28} +(-2.34879 - 6.45324i) q^{29} +(9.29490 - 2.62117i) q^{30} +(3.20498 + 1.85040i) q^{31} +(5.65627 - 0.0813539i) q^{32} +(-9.38346 - 0.820946i) q^{33} +(-3.71345 + 6.74492i) q^{34} +(1.35981 - 0.771969i) q^{35} +(12.6427 - 0.514327i) q^{36} +(4.28677 - 4.28677i) q^{37} +(-3.98004 + 4.70736i) q^{38} +8.77807 q^{39} +(3.45183 + 5.29952i) q^{40} +(0.0276960 + 0.157072i) q^{41} +(2.90078 - 0.840821i) q^{42} +(0.221939 - 2.53677i) q^{43} +(-1.31722 - 6.02634i) q^{44} +(8.02977 + 11.6469i) q^{45} +(6.26459 - 5.47744i) q^{46} +(-8.92943 - 4.16386i) q^{47} +(4.10969 + 11.5037i) q^{48} +(-5.63869 + 3.25550i) q^{49} +(-2.95115 + 6.42578i) q^{50} +(-16.3744 - 2.88725i) q^{51} +(1.71235 + 5.48773i) q^{52} +(-0.974074 - 11.1337i) q^{53} +(5.18731 + 13.3981i) q^{54} +(4.91202 - 4.84116i) q^{55} +(1.09151 + 1.64944i) q^{56} +(-12.3958 - 4.85266i) q^{57} +(8.06717 + 5.40768i) q^{58} +(-3.73037 - 1.35774i) q^{59} +(-8.42476 + 10.7496i) q^{60} +(-1.11880 - 0.938789i) q^{61} +(-5.20344 + 0.562041i) q^{62} +(2.53756 + 3.62401i) q^{63} +(-6.39002 + 4.81327i) q^{64} +(-4.16700 + 4.89339i) q^{65} +(11.3985 - 6.89359i) q^{66} +(14.1231 + 6.58573i) q^{67} +(-1.38917 - 10.7999i) q^{68} +(15.5625 + 8.98500i) q^{69} +(-0.908293 + 2.01620i) q^{70} +(3.88690 + 4.63223i) q^{71} +(-14.0053 + 11.1381i) q^{72} +(-2.89514 + 4.13469i) q^{73} +(-1.31683 + 8.47181i) q^{74} +(-15.1907 - 1.55173i) q^{75} +(0.615635 - 8.69603i) q^{76} +(1.52510 - 1.52510i) q^{77} +(-10.0222 + 7.32567i) q^{78} +(-0.681245 - 3.86353i) q^{79} +(-8.36371 - 3.16991i) q^{80} +(-9.22761 + 7.74289i) q^{81} +(-0.162704 - 0.156220i) q^{82} +(0.189756 + 0.708179i) q^{83} +(-2.61019 + 3.38081i) q^{84} +(9.38253 - 7.75741i) q^{85} +(1.86365 + 3.08152i) q^{86} +(-5.42812 + 20.2580i) q^{87} +(6.53313 + 5.78116i) q^{88} +(-11.5536 - 2.03722i) q^{89} +(-18.8876 - 6.59640i) q^{90} +(-1.29200 + 1.53974i) q^{91} +(-2.58130 + 11.4818i) q^{92} +(-4.77644 - 10.2431i) q^{93} +(13.6699 - 2.69798i) q^{94} +(8.58951 - 4.60655i) q^{95} +(-14.2925 - 9.70440i) q^{96} +(2.04801 - 0.955003i) q^{97} +(3.72099 - 8.42261i) q^{98} +(14.9479 + 12.5428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

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