LMFDB - Embedded newform 380.2.bj.a.23.6

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			23.6
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37318 + 0.338181i) q^{2} +(2.50164 + 1.75167i) q^{3} +(1.77127 - 0.928769i) q^{4} +(2.16402 - 0.563029i) q^{5} +(-4.02760 - 1.55936i) q^{6} +(-0.675461 + 0.180989i) q^{7} +(-2.11818 + 1.87438i) q^{8} +(2.16382 + 5.94503i) q^{9} +O(q^{10})$	\(q+(-1.37318 + 0.338181i) q^{2} +(2.50164 + 1.75167i) q^{3} +(1.77127 - 0.928769i) q^{4} +(2.16402 - 0.563029i) q^{5} +(-4.02760 - 1.55936i) q^{6} +(-0.675461 + 0.180989i) q^{7} +(-2.11818 + 1.87438i) q^{8} +(2.16382 + 5.94503i) q^{9} +(-2.78120 + 1.50497i) q^{10} +(-2.67109 + 1.54215i) q^{11} +(6.05798 + 0.779227i) q^{12} +(-2.35452 + 1.64865i) q^{13} +(0.866325 - 0.476959i) q^{14} +(6.39986 + 2.38216i) q^{15} +(2.27478 - 3.29020i) q^{16} +(4.93433 - 2.30092i) q^{17} +(-4.98181 - 7.43186i) q^{18} +(-4.23631 + 1.02651i) q^{19} +(3.31014 - 3.00715i) q^{20} +(-2.00680 - 0.730414i) q^{21} +(3.14637 - 3.02097i) q^{22} +(5.86180 - 0.512841i) q^{23} +(-8.58224 + 0.978670i) q^{24} +(4.36600 - 2.43682i) q^{25} +(2.67565 - 3.06016i) q^{26} +(-2.62938 + 9.81300i) q^{27} +(-1.02833 + 0.947928i) q^{28} +(-2.34879 - 6.45324i) q^{29} +(-9.59378 - 1.10683i) q^{30} +(-3.20498 - 1.85040i) q^{31} +(-2.01101 + 5.28733i) q^{32} +(-9.38346 - 0.820946i) q^{33} +(-5.99762 + 4.82828i) q^{34} +(-1.35981 + 0.771969i) q^{35} +(9.35426 + 8.52056i) q^{36} +(4.28677 - 4.28677i) q^{37} +(5.47008 - 2.84222i) q^{38} -8.77807 q^{39} +(-3.52847 + 5.24880i) q^{40} +(0.0276960 + 0.157072i) q^{41} +(3.00271 + 0.324333i) q^{42} +(-0.221939 + 2.53677i) q^{43} +(-3.29891 + 5.21239i) q^{44} +(8.02977 + 11.6469i) q^{45} +(-7.87590 + 2.68658i) q^{46} +(8.92943 + 4.16386i) q^{47} +(11.4540 - 4.24624i) q^{48} +(-5.63869 + 3.25550i) q^{49} +(-5.17123 + 4.82269i) q^{50} +(16.3744 + 2.88725i) q^{51} +(-2.63927 + 5.10701i) q^{52} +(-0.974074 - 11.1337i) q^{53} +(0.292061 - 14.3643i) q^{54} +(-4.91202 + 4.84116i) q^{55} +(1.09151 - 1.64944i) q^{56} +(-12.3958 - 4.85266i) q^{57} +(5.40768 + 8.06717i) q^{58} +(3.73037 + 1.35774i) q^{59} +(13.5483 - 1.72455i) q^{60} +(-1.11880 - 0.938789i) q^{61} +(5.02679 + 1.45707i) q^{62} +(-2.53756 - 3.62401i) q^{63} +(0.973407 - 7.94056i) q^{64} +(-4.16700 + 4.89339i) q^{65} +(13.1628 - 2.04600i) q^{66} +(-14.1231 - 6.58573i) q^{67} +(6.60300 - 8.65839i) q^{68} +(15.5625 + 8.98500i) q^{69} +(1.60621 - 1.51992i) q^{70} +(-3.88690 - 4.63223i) q^{71} +(-15.7266 - 8.53686i) q^{72} +(-2.89514 + 4.13469i) q^{73} +(-4.43682 + 7.33622i) q^{74} +(15.1907 + 1.55173i) q^{75} +(-6.55024 + 5.75276i) q^{76} +(1.52510 - 1.52510i) q^{77} +(12.0539 - 2.96858i) q^{78} +(0.681245 + 3.86353i) q^{79} +(3.07019 - 8.40083i) q^{80} +(-9.22761 + 7.74289i) q^{81} +(-0.0911505 - 0.206323i) q^{82} +(-0.189756 - 0.708179i) q^{83} +(-4.23296 + 0.570091i) q^{84} +(9.38253 - 7.75741i) q^{85} +(-0.553125 - 3.55851i) q^{86} +(5.42812 - 20.2580i) q^{87} +(2.76728 - 8.27320i) q^{88} +(-11.5536 - 2.03722i) q^{89} +(-14.9651 - 13.2778i) q^{90} +(1.29200 - 1.53974i) q^{91} +(9.90651 - 6.35264i) 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} +(6.64201 - 6.37729i) 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 $

$2$	−1.37318	+	0.338181i	−0.970988	+	0.239130i
$2$	−1.37318	+	0.338181i	−0.970988	+	0.239130i
$3$	2.50164	+	1.75167i	1.44432	+	1.01133i	0.992892	+	0.119022i	$0.0379760\pi$
$3$	2.50164	+	1.75167i	1.44432	+	1.01133i	0.451433	+	0.892305i	$0.350913\pi$
$4$	1.77127	−	0.928769i	0.885634	−	0.464384i
$5$	2.16402	−	0.563029i	0.967781	−	0.251794i
$5$	2.16402	−	0.563029i	0.967781	−	0.251794i
$6$	−4.02760	−	1.55936i	−1.64426	−	0.636605i
$7$	−0.675461	+	0.180989i	−0.255300	+	0.0684075i	−0.384199	−	0.923250i	$-0.625522\pi$
$7$	−0.675461	+	0.180989i	−0.255300	+	0.0684075i	0.128899	+	0.991658i	$0.458856\pi$
$8$	−2.11818	+	1.87438i	−0.748891	+	0.662693i
$9$	2.16382	+	5.94503i	0.721272	+	1.98168i
$10$	−2.78120	+	1.50497i	−0.879492	+	0.475915i
$11$	−2.67109	+	1.54215i	−0.805363	+	0.464977i	−0.845343	−	0.534224i	$-0.820604\pi$
$11$	−2.67109	+	1.54215i	−0.805363	+	0.464977i	0.0399797	+	0.999200i	$0.487271\pi$
$12$	6.05798	+	0.779227i	1.74879	+	0.224944i
$13$	−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	$0.436059\pi$
$14$	0.866325	−	0.476959i	0.231535	−	0.127473i
$15$	6.39986	+	2.38216i	1.65244	+	0.615070i
$16$	2.27478	−	3.29020i	0.568694	−	0.822549i
$17$	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	$0.131568\pi$
$18$	−4.98181	−	7.43186i	−1.17422	−	1.75171i
$19$	−4.23631	+	1.02651i	−0.971875	+	0.235497i
$19$	−4.23631	+	1.02651i	−0.971875	+	0.235497i
$20$	3.31014	−	3.00715i	0.740170	−	0.672420i
$21$	−2.00680	−	0.730414i	−0.437919	−	0.159389i
$22$	3.14637	−	3.02097i	0.670808	−	0.644073i
$23$	5.86180	−	0.512841i	1.22227	−	0.106935i	0.542307	−	0.840181i	$-0.317551\pi$
$23$	5.86180	−	0.512841i	1.22227	−	0.106935i	0.679964	+	0.733246i	$0.261995\pi$
$24$	−8.58224	+	0.978670i	−1.75184	+	0.199770i
$25$	4.36600	−	2.43682i	0.873199	−	0.487364i
$26$	2.67565	−	3.06016i	0.524738	−	0.600147i
$27$	−2.62938	+	9.81300i	−0.506025	+	1.88851i
$28$	−1.02833	+	0.947928i	−0.194335	+	0.179141i
$29$	−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	$-0.331193\pi$
$30$	−9.59378	−	1.10683i	−1.75158	−	0.202078i
$31$	−3.20498	−	1.85040i	−0.575631	−	0.332341i	0.183764	−	0.982970i	$-0.441172\pi$
$31$	−3.20498	−	1.85040i	−0.575631	−	0.332341i	−0.759395	+	0.650630i	$0.774505\pi$
$32$	−2.01101	+	5.28733i	−0.355499	+	0.934677i
$33$	−9.38346	−	0.820946i	−1.63345	−	0.142908i
$34$	−5.99762	+	4.82828i	−1.02858	+	0.828043i
$35$	−1.35981	+	0.771969i	−0.229850	+	0.130487i
$36$	9.35426	+	8.52056i	1.55904	+	1.42009i
$37$	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	$0.0839480\pi$
$38$	5.47008	−	2.84222i	0.887364	−	0.461069i
$39$	−8.77807			−1.40562
$40$	−3.52847	+	5.24880i	−0.557900	+	0.829908i
$41$	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	$0.940480\pi$
$42$	3.00271	+	0.324333i	0.463329	+	0.0500457i
$43$	−0.221939	+	2.53677i	−0.0338453	+	0.386854i	0.960313	+	0.278924i	$0.0899778\pi$
$43$	−0.221939	+	2.53677i	−0.0338453	+	0.386854i	−0.994159	+	0.107930i	$0.965578\pi$
$44$	−3.29891	+	5.21239i	−0.497329	+	0.785797i
$45$	8.02977	+	11.6469i	1.19701	+	1.73622i
$46$	−7.87590	+	2.68658i	−1.16124	+	0.396114i
$47$	8.92943	+	4.16386i	1.30249	+	0.607361i	0.945157	−	0.326616i	$-0.105908\pi$
$47$	8.92943	+	4.16386i	1.30249	+	0.607361i	0.357333	+	0.933977i	$0.383686\pi$
$48$	11.4540	−	4.24624i	1.65325	−	0.612892i
$49$	−5.63869	+	3.25550i	−0.805527	+	0.465071i
$50$	−5.17123	+	4.82269i	−0.731322	+	0.682032i
$51$	16.3744	+	2.88725i	2.29287	+	0.404295i
$52$	−2.63927	+	5.10701i	−0.366001	+	0.708215i
$53$	−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	$-0.306321\pi$
$54$	0.292061	−	14.3643i	0.0397445	−	1.95473i
$55$	−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
$58$	5.40768	+	8.06717i	0.710063	+	1.05927i
$59$	3.73037	+	1.35774i	0.485652	+	0.176763i	0.573230	−	0.819395i	$-0.305690\pi$
$59$	3.73037	+	1.35774i	0.485652	+	0.176763i	−0.0875773	+	0.996158i	$0.527912\pi$
$60$	13.5483	−	1.72455i	1.74908	−	0.222639i
$61$	−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	$0.752027\pi$
$62$	5.02679	+	1.45707i	0.638403	+	0.185048i
$63$	−2.53756	−	3.62401i	−0.319702	−	0.456582i
$64$	0.973407	−	7.94056i	0.121676	−	0.992570i
$65$	−4.16700	+	4.89339i	−0.516853	+	0.606951i
$66$	13.1628	−	2.04600i	1.62023	−	0.251845i
$67$	−14.1231	−	6.58573i	−1.72542	−	0.804575i	−0.992211	−	0.124569i	$-0.960245\pi$
$67$	−14.1231	−	6.58573i	−1.72542	−	0.804575i	−0.733206	−	0.680006i	$-0.761977\pi$
$68$	6.60300	−	8.65839i	0.800732	−	1.04998i
$69$	15.5625	+	8.98500i	1.87350	+	1.08167i
$70$	1.60621	−	1.51992i	0.191978	−	0.181665i
$71$	−3.88690	−	4.63223i	−0.461290	−	0.549744i	0.484386	−	0.874854i	$-0.339043\pi$
$71$	−3.88690	−	4.63223i	−0.461290	−	0.549744i	−0.945676	+	0.325110i	$0.894599\pi$
$72$	−15.7266	−	8.53686i	−1.85340	−	1.00608i
$73$	−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	$0.289892\pi$
$74$	−4.43682	+	7.33622i	−0.515770	+	0.852819i
$75$	15.1907	+	1.55173i	1.75407	+	0.179179i
$76$	−6.55024	+	5.75276i	−0.751365	+	0.659887i
$77$	1.52510	−	1.52510i	0.173802	−	0.173802i
$78$	12.0539	−	2.96858i	1.36484	−	0.336125i
$79$	0.681245	+	3.86353i	0.0766461	+	0.434682i	0.998849	+	0.0479742i	$0.0152765\pi$
$79$	0.681245	+	3.86353i	0.0766461	+	0.434682i	−0.922202	+	0.386707i	$0.873612\pi$
$80$	3.07019	−	8.40083i	0.343258	−	0.939241i
$81$	−9.22761	+	7.74289i	−1.02529	+	0.860321i
$82$	−0.0911505	−	0.206323i	−0.0100659	−	0.0227845i
$83$	−0.189756	−	0.708179i	−0.0208284	−	0.0777327i	0.954729	−	0.297476i	$-0.0961448\pi$
$83$	−0.189756	−	0.708179i	−0.0208284	−	0.0777327i	−0.975558	+	0.219743i	$0.929478\pi$
$84$	−4.23296	+	0.570091i	−0.461854	+	0.0622020i
$85$	9.38253	−	7.75741i	1.01768	−	0.841410i
$86$	−0.553125	−	3.55851i	−0.0596450	−	0.383724i
$87$	5.42812	−	20.2580i	0.581955	−	2.17189i
$88$	2.76728	−	8.27320i	0.294993	−	0.881926i
$89$	−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	$0.769149\pi$
$90$	−14.9651	−	13.2778i	−1.57746	−	1.39960i
$91$	1.29200	−	1.53974i	0.135438	−	0.161409i
$92$	9.90651	−	6.35264i	1.03283	−	0.662308i
$93$	−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	$0.324514\pi$
$98$	6.64201	−	6.37729i	0.670944	−	0.644204i
$99$	−14.9479	−	12.5428i	−1.50232	−	1.26060i
$100$	5.47011	−	8.37126i	0.547011	−	0.837126i
$101$	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	$-0.0764568\pi$
$102$	−23.4615	+	1.57278i	−2.32303	+	0.155729i
$103$	−12.2072	−	3.27091i	−1.20281	−	0.322293i	−0.398874	−	0.917006i	$-0.630599\pi$
$103$	−12.2072	−	3.27091i	−1.20281	−	0.322293i	−0.803938	+	0.594713i	$0.797266\pi$
$104$	1.89711	−	7.90542i	0.186027	−	0.775190i
$105$	−4.75400	−	0.450748i	−0.463943	−	0.0439885i
$106$	5.10279	+	14.9592i	0.495627	+	1.45297i
$107$	−4.05644	+	1.08692i	−0.392151	+	0.105077i	−0.449506	−	0.893277i	$-0.648400\pi$
$107$	−4.05644	+	1.08692i	−0.392151	+	0.105077i	0.0573551	+	0.998354i	$0.481733\pi$
$108$	4.45666	+	19.8235i	0.428843	+	1.90752i
$109$	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	$0.725404\pi$
$110$	5.10792	−	8.30895i	0.487021	−	0.792227i
$111$	18.2330	−	3.21497i	1.73060	−	0.305151i
$112$	−0.941033	+	2.63411i	−0.0889193	+	0.248900i
$113$	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	$0.494230\pi$
$114$	18.6628	+	2.47156i	1.74793	+	0.231483i
$115$	12.3963	−	4.41017i	1.15596	−	0.411250i
$116$	−10.1539	−	9.24894i	−0.942766	−	0.858742i
$117$	−14.8961	−	10.4303i	−1.37714	−	0.964284i
$118$	−5.58164	−	0.602892i	−0.513832	−	0.0555007i
$119$	−2.91651	+	2.44724i	−0.267356	+	0.224338i
$120$	−18.0211	+	6.94992i	−1.64510	+	0.634438i
$121$	−0.743525	+	1.28782i	−0.0675932	+	0.117075i
$122$	1.85380	+	0.910771i	0.167836	+	0.0824573i
$123$	−0.205853	+	0.441453i	−0.0185611	+	0.0398045i
$124$	−7.39547	−	0.300861i	−0.664132	−	0.0270181i
$125$	8.07612	−	7.73151i	0.722350	−	0.691528i
$126$	4.71011	+	4.11828i	0.419610	+	0.366885i
$127$	13.0886	−	9.16471i	1.16142	−	0.813237i	0.176173	−	0.984359i	$-0.443628\pi$
$127$	13.0886	−	9.16471i	1.16142	−	0.813237i	0.985250	+	0.171122i	$0.0547394\pi$
$128$	1.34868	+	11.2330i	0.119207	+	0.992869i
$129$	−4.99880	+	5.95734i	−0.440120	+	0.524514i
$130$	4.06721	−	8.12873i	0.356718	−	0.712936i
$131$	1.59843	−	4.39166i	0.139656	−	0.383701i	−0.850072	−	0.526667i	$-0.823442\pi$
$131$	1.59843	−	4.39166i	0.139656	−	0.383701i	0.989728	+	0.142966i	$0.0456639\pi$
$132$	−17.3831	+	7.26095i	−1.51300	+	0.631984i
$133$	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
$136$	−6.13903	+	14.1226i	−0.526418	+	1.21100i
$137$	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	$0.303497\pi$
$138$	−24.4087	−	7.07513i	−2.07781	−	0.602275i
$139$	1.46026	−	8.28157i	0.123858	−	0.702433i	−0.858122	−	0.513446i	$-0.828369\pi$
$139$	1.46026	−	8.28157i	0.123858	−	0.702433i	0.981980	−	0.188987i	$-0.0605204\pi$
$140$	−1.69161	+	2.63031i	−0.142967	+	0.222302i
$141$	15.0445	+	26.0579i	1.26698	+	2.19447i
$142$	6.90396	+	5.04642i	0.579367	+	0.423486i
$143$	3.74666	−	8.03474i	0.313311	−	0.671898i
$144$	24.4825	+	6.40425i	2.04021	+	0.533687i
$145$	−8.71620	−	12.6425i	−0.723841	−	1.04990i
$146$	2.57729	−	6.65677i	0.213298	−	0.550918i
$147$	−19.8085	−	1.73302i	−1.63378	−	0.142937i
$148$	3.61160	−	11.5744i	0.296871	−	0.951412i
$149$	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	$0.341725\pi$
$150$	−21.3843	+	3.00638i	−1.74602	+	0.245470i
$151$			18.3490i			1.49322i	0.665263	+	0.746609i	$0.268320\pi$
$151$			18.3490i			1.49322i	−0.665263	+	0.746609i	$0.731680\pi$
$152$	7.04921	−	10.1148i	0.571767	−	0.820416i
$153$	24.3560	+	24.3560i	1.96907	+	1.96907i
$154$	−1.57849	+	2.61001i	−0.127198	+	0.210320i
$155$	−7.97748	−	2.19980i	−0.640766	−	0.176692i
$156$	−15.5483	+	8.15280i	−1.24486	+	0.652747i
$157$	−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	$0.852913\pi$
$158$	−2.24205	−	5.07496i	−0.178368	−	0.403742i
$159$	17.0658	−	29.5589i	1.35341	−	2.34417i
$160$	−1.37494	+	12.5742i	−0.108699	+	0.994075i
$161$	−3.86660	+	1.40733i	−0.304731	+	0.110913i
$162$	10.0527	−	13.7530i	0.789816	−	1.08054i
$163$	−16.6724	−	4.46736i	−1.30588	−	0.349910i	−0.462211	−	0.886770i	$-0.652944\pi$
$163$	−16.6724	−	4.46736i	−1.30588	−	0.349910i	−0.843672	+	0.536860i	$0.819611\pi$
$164$	0.194941	+	0.252493i	0.0152223	+	0.0197164i
$165$	−20.7682	+	3.50662i	−1.61681	+	0.272990i
$166$	0.500062	+	0.908288i	0.0388123	+	0.0704968i
$167$	0.661437	+	7.56026i	0.0511835	+	0.585030i	0.977873	+	0.209201i	$0.0670864\pi$
$167$	0.661437	+	7.56026i	0.0511835	+	0.585030i	−0.926689	+	0.375829i	$0.877358\pi$
$168$	5.61984	−	2.21435i	0.433580	−	0.170840i
$169$	−1.62055	+	4.45242i	−0.124658	+	0.342494i
$170$	−10.2605	+	13.8253i	−0.786946	+	1.06036i
$171$	−15.2692	−	22.9638i	−1.16766	−	1.75609i
$172$	1.96296	+	4.69943i	0.149674	+	0.358328i
$173$	−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	$0.865221\pi$
$174$	−0.602933	+	29.6537i	−0.0457082	+	2.24804i
$175$	−2.50802	+	2.43617i	−0.189589	+	0.184157i
$176$	−1.00214	+	12.2965i	−0.0755393	+	0.926881i
$177$	6.95373	+	9.93096i	0.522675	+	0.746457i
$178$	16.5542	−	1.10974i	1.24079	−	0.0831788i
$179$	−1.18503	−	2.05254i	−0.0885737	−	0.153414i	0.818335	−	0.574742i	$-0.194898\pi$
$179$	−1.18503	−	2.05254i	−0.0885737	−	0.153414i	−0.906908	+	0.421328i	$0.861564\pi$
$180$	25.0402	+	13.1720i	1.86638	+	0.981781i
$181$	−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	$0.403610\pi$
$182$	−1.25344	+	2.55128i	−0.0929112	+	0.189114i
$183$	−1.15440	−	4.30829i	−0.0853360	−	0.318478i
$184$	−11.4551	+	12.0735i	−0.844483	+	0.890073i
$185$	6.86309	−	11.6902i	0.504585	−	0.859484i
$186$	10.0229	+	12.4504i	0.734918	+	0.912905i
$187$	−9.63167	+	13.7555i	−0.704337	+	1.00590i
$188$	19.6837	−	0.918063i	1.43558	−	0.0669566i
$189$		−	7.10419i		−	0.516754i
$190$	10.2371	−	9.23044i	0.742680	−	0.669647i
$191$			0.709917i			0.0513678i	0.999670	+	0.0256839i	$0.00817634\pi$
$191$			0.709917i			0.0513678i	−0.999670	+	0.0256839i	$0.991824\pi$
$192$	16.3444	−	18.1594i	1.17955	−	1.31054i
$193$	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	$0.137952\pi$
$194$	−2.48933	+	2.00399i	−0.178724	+	0.143878i
$195$	−18.9960	+	4.94231i	−1.36033	+	0.353926i
$196$	−6.96402	+	11.0034i	−0.497430	+	0.785957i
$197$	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	$0.868812\pi$
$198$	24.7679	+	12.1684i	1.76018	+	0.864773i
$199$	−2.37065	+	0.862845i	−0.168051	+	0.0611654i	−0.424675	−	0.905346i	$-0.639612\pi$
$199$	−2.37065	+	0.862845i	−0.168051	+	0.0611654i	0.256625	+	0.966511i	$0.417390\pi$
$200$	−4.68046	+	13.3452i	−0.330959	+	0.943645i
$201$	−23.7951	−	41.2143i	−1.67837	−	2.90703i
$202$	0.766105	+	11.4281i	0.0539030	+	0.804079i
$203$	2.75448	+	3.93381i	0.193327	+	0.276099i
$204$	31.6850	−	10.0939i	2.21839	−	0.706717i
$205$	0.148371	+	0.324314i	0.0103627	+	0.0226511i
$206$	17.8689	+	0.363319i	1.24499	+	0.0253137i
$207$	15.7327	+	33.7389i	1.09350	+	2.34502i
$208$	0.0683827	+	11.4972i	0.00474149	+	0.797185i
$209$	9.73252	−	9.27492i	0.673212	−	0.641560i
$210$	6.68055	−	0.988751i	0.461002	−	0.0682303i
$211$	7.16301	−	19.6802i	0.493122	−	1.35484i	−0.404686	−	0.914456i	$-0.632619\pi$
$211$	7.16301	−	19.6802i	0.493122	−	1.35484i	0.897808	−	0.440386i	$-0.145158\pi$
$212$	−12.0660	−	18.8161i	−0.828696	−	1.29230i
$213$	−1.60951	−	18.3967i	−0.110282	−	1.26052i
$214$	5.20266	−	2.86435i	0.355647	−	0.195803i
$215$	0.947996	+	5.61459i	0.0646528	+	0.382912i
$216$	−12.8238	−	25.7142i	−0.872546	−	1.74963i
$217$	2.49974	+	0.669803i	0.169693	+	0.0454692i
$218$	−3.90486	−	2.85424i	−0.264470	−	0.193314i
$219$	−14.4852	+	5.27219i	−0.978821	+	0.356262i
$220$	−4.20419	+	13.1371i	−0.283446	+	0.885704i
$221$	−7.82458	+	13.5526i	−0.526338	+	0.911644i
$222$	−23.9500	+	10.5808i	−1.60742	+	0.710135i
$223$	−1.88924	+	21.5942i	−0.126513	+	1.44605i	0.622044	+	0.782982i	$0.286302\pi$
$223$	−1.88924	+	21.5942i	−0.126513	+	1.44605i	−0.748558	+	0.663070i	$0.769253\pi$
$224$	0.401406	−	3.93536i	0.0268201	−	0.262942i
$225$	23.9342	+	20.6832i	1.59561	+	1.37888i
$226$	−18.5188	−	11.1998i	−1.23185	−	0.745003i
$227$	19.6323	+	19.6323i	1.30304	+	1.30304i	0.926330	+	0.376713i	$0.122946\pi$
$227$	19.6323	+	19.6323i	1.30304	+	1.30304i	0.376713	+	0.926330i	$0.377054\pi$
$228$	−26.4633	+	2.91750i	−1.75258	+	0.193216i
$229$		−	6.30888i		−	0.416903i	−0.978033	−	0.208451i	$-0.933158\pi$
$229$		−	6.30888i		−	0.416903i	0.978033	−	0.208451i	$-0.0668423\pi$
$230$	−15.5310	+	10.2482i	−1.02408	+	0.675745i
$231$	6.48674	−	1.14379i	0.426796	−	0.0752557i
$232$	17.0710	+	9.26663i	1.12077	+	0.608384i
$233$	−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	$0.833143\pi$
$234$	23.9824	+	9.28520i	1.56778	+	0.606992i
$235$	21.6679	+	3.98316i	1.41346	+	0.259833i
$236$	7.86851	−	1.05972i	0.512196	−	0.0689821i
$237$	−5.06340	+	10.8585i	−0.328903	+	0.705336i
$238$	3.17729	−	4.34682i	0.205953	−	0.281762i
$239$	−1.76969	−	3.06519i	−0.114471	−	0.198270i	0.803097	−	0.595848i	$-0.203184\pi$
$239$	−1.76969	−	3.06519i	−0.114471	−	0.198270i	−0.917568	+	0.397578i	$0.869851\pi$
$240$	22.3960	−	15.6379i	1.44566	−	1.00942i
$241$	−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	$0.105344\pi$
$242$	0.585479	−	2.01986i	0.0376360	−	0.129842i
$243$	−6.28568	+	0.549926i	−0.403227	+	0.0352778i
$244$	−2.85362	−	0.623735i	−0.182684	−	0.0399305i
$245$	−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
$248$	10.2571	−	2.08787i	0.651325	−	0.132580i
$249$	0.765794	−	2.10400i	0.0485302	−	0.133336i
$250$	−8.47534	+	13.3480i	−0.536028	+	0.844200i
$251$	−7.98040	+	9.51067i	−0.503718	+	0.600308i	−0.956651	−	0.291237i	$-0.905933\pi$
$251$	−7.98040	+	9.51067i	−0.503718	+	0.600308i	0.452933	+	0.891545i	$0.350378\pi$
$252$	−7.86057	−	4.06229i	−0.495169	−	0.255900i
$253$	−14.8665	+	10.4096i	−0.934650	+	0.654449i
$254$	−14.8737	+	17.0111i	−0.933258	+	1.06737i
$255$	37.0602	−	2.97119i	2.32080	−	0.186063i
$256$	−5.65078	−	14.9689i	−0.353174	−	0.935558i
$257$	−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	$0.912573\pi$
$258$	4.84961	−	9.87102i	0.301924	−	0.614543i
$259$	−2.11969	+	3.67140i	−0.131711	+	0.228130i
$260$	−2.83604	+	12.5377i	−0.175884	+	0.777554i
$261$	33.2824	−	27.9272i	2.06013	−	1.72865i
$262$	−0.709767	+	6.57111i	−0.0438496	+	0.405965i
$263$	−12.7330	−	8.91576i	−0.785152	−	0.549769i	0.110841	−	0.993838i	$-0.464646\pi$
$263$	−12.7330	−	8.91576i	−0.785152	−	0.549769i	−0.895993	+	0.444069i	$0.853535\pi$
$264$	21.4147	−	15.8492i	1.31798	−	0.975453i
$265$	−8.37653	−	23.5452i	−0.514566	−	1.44637i
$266$	−3.18042	+	2.90983i	−0.195004	+	0.178413i
$267$	−25.3346	−	25.3346i	−1.55045	−	1.55045i
$268$	−31.1325	+	1.45205i	−1.90172	+	0.0886979i
$269$	−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	$0.789851\pi$
$270$	−7.45547	−	31.2490i	−0.453726	−	1.90176i
$271$	−10.5546	−	12.5784i	−0.641144	−	0.764085i	0.343407	−	0.939187i	$-0.388419\pi$
$271$	−10.5546	−	12.5784i	−0.641144	−	0.764085i	−0.984550	+	0.175101i	$0.943975\pi$
$272$	3.65404	−	21.4690i	0.221559	−	1.30175i
$273$	5.92925	−	1.58874i	0.358854	−	0.0961548i
$274$	−15.8417	+	5.40381i	−0.957031	+	0.326456i
$275$	−7.90401	+	13.2420i	−0.476630	+	0.798522i
$276$	35.9103	+	1.46090i	2.16155	+	0.0879356i
$277$	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	$0.496619\pi$
$278$	0.795457	+	11.8659i	0.0477083	+	0.711672i
$279$	4.06568	−	23.0576i	0.243406	−	1.38042i
$280$	1.43337	−	4.18398i	0.0856601	−	0.250040i
$281$	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	$0.698448\pi$
$282$	−29.4712	−	30.6945i	−1.75498	−	1.82783i
$283$	−6.95871	+	3.24490i	−0.413652	+	0.192889i	−0.618293	−	0.785948i	$-0.712175\pi$
$283$	−6.95871	+	3.24490i	−0.413652	+	0.192889i	0.204640	+	0.978837i	$0.434398\pi$
$284$	−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
$288$	−35.7848	−	0.514691i	−2.10864	−	0.0303285i
$289$	8.12603	−	9.68422i	0.478002	−	0.569660i
$290$	16.2444	+	14.4129i	0.953904	+	0.846353i
$291$	6.79624	+	1.19836i	0.398403	+	0.0702492i
$292$	−1.28790	+	10.0126i	−0.0753686	+	0.585941i
$293$	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	$-0.0813833\pi$
$294$	27.7869	−	4.31911i	1.62056	−	0.251896i
$295$	8.83705	+	0.837881i	0.514513	+	0.0487833i
$296$	−1.04514	+	17.1152i	−0.0607473	+	0.994800i
$297$	−8.10983	−	30.2663i	−0.470580	−	1.75623i
$298$	−10.0152	+	4.42460i	−0.580168	+	0.256310i
$299$	−12.9562	+	10.8716i	−0.749279	+	0.628720i
$300$	28.3479	−	11.3601i	1.63667	−	0.655875i
$301$	−0.309217	−	1.75366i	−0.0178230	−	0.101079i
$302$	−6.20527	−	25.1965i	−0.357073	−	1.44990i
$303$	17.4896	−	17.4896i	1.00475	−	1.00475i
$304$	−6.25925	+	16.2733i	−0.358992	+	0.933341i
$305$	−2.94969	−	1.40164i	−0.168898	−	0.0802577i
$306$	−41.6820	−	25.2085i	−2.38280	−	1.44108i
$307$	9.56107	−	13.6546i	0.545679	−	0.779311i	−0.447701	−	0.894183i	$-0.647757\pi$
$307$	9.56107	−	13.6546i	0.545679	−	0.779311i	0.993380	+	0.114873i	$0.0366460\pi$
$308$	1.28490	−	4.11783i	0.0732138	−	0.234635i
$309$	−24.8085	−	29.5657i	−1.41131	−	1.68193i
$310$	11.6985	+	0.322903i	0.664429	+	0.0183397i
$311$	−7.09443	−	4.09597i	−0.402288	−	0.232261i	0.285183	−	0.958473i	$-0.407946\pi$
$311$	−7.09443	−	4.09597i	−0.402288	−	0.232261i	−0.687471	+	0.726212i	$0.741279\pi$
$312$	18.5936	−	16.4534i	1.05265	−	0.931493i
$313$	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	$0.529914\pi$
$314$	−2.84216	−	18.2849i	−0.160392	−	1.03188i
$315$	−7.53176	−	6.41372i	−0.424367	−	0.361372i
$316$	4.79500	+	6.21063i	0.269740	+	0.349375i
$317$	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	$0.624324\pi$
$318$	−13.4383	+	46.3611i	−0.753580	+	2.59980i
$319$	16.2257	+	13.6150i	0.908465	+	0.762293i
$320$	−2.36429	−	17.7316i	−0.132168	−	0.991227i
$321$	−12.0517	−	4.38646i	−0.672660	−	0.244828i
$322$	4.83362	−	3.24013i	0.269367	−	0.180565i
$323$	−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
$326$	24.4050	+	0.496215i	1.35167	+	0.0274828i
$327$	0.910332	+	10.4051i	0.0503415	+	0.575406i
$328$	−0.353078	−	0.280795i	−0.0194955	−	0.0155043i
$329$	−6.78509	−	1.19640i	−0.374074	−	0.0659594i
$330$	27.3327	−	11.8386i	1.50462	−	0.651696i
$331$	16.6569	−	9.61686i	0.915545	−	0.528590i	0.0333340	−	0.999444i	$-0.489387\pi$
$331$	16.6569	−	9.61686i	0.915545	−	0.528590i	0.882211	+	0.470854i	$0.156054\pi$
$332$	−0.993843	−	1.07813i	−0.0545442	−	0.0591703i
$333$	34.7608	+	16.2092i	1.90488	+	0.888259i
$334$	−3.46501	−	10.1579i	−0.189597	−	0.555818i
$335$	−34.2708	−	6.29993i	−1.87241	−	0.344202i
$336$	−6.96822	+	4.94123i	−0.380148	+	0.269566i
$337$	−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	$0.753226\pi$
$338$	0.719587	−	6.66203i	0.0391404	−	0.362366i
$339$	8.11553	+	46.0254i	0.440775	+	2.49976i
$340$	9.41412	−	22.4547i	0.510553	−	1.21777i
$341$	11.4144			0.618123
$342$	28.7333	+	26.3698i	1.55372	+	1.42591i
$343$	6.68081	−	6.68081i	0.360730	−	0.360730i
$344$	−4.28476	−	5.78935i	−0.231019	−	0.312141i
$345$	38.7364	+	10.6816i	2.08550	+	0.575079i
$346$	0.301183	+	0.374125i	0.0161917	+	0.0201131i
$347$	1.12261	+	0.0982158i	0.0602650	+	0.00527250i	0.117248	−	0.993103i	$-0.462593\pi$
$347$	1.12261	+	0.0982158i	0.0602650	+	0.00527250i	−0.0569834	+	0.998375i	$0.518148\pi$
$348$	−9.20036	−	40.9238i	−0.493191	−	2.19375i
$349$	−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	$0.772286\pi$
$350$	2.62011	−	4.19348i	0.140051	−	0.224151i
$351$	−9.98730	−	27.4399i	−0.533082	−	1.46463i
$352$	−2.78230	−	17.2242i	−0.148297	−	0.918053i
$353$	−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	$0.830961\pi$
$354$	−12.9072	−	11.2854i	−0.686011	−	0.599813i
$355$	−11.0194	−	7.83581i	−0.584850	−	0.415882i
$356$	−22.3567	+	7.12220i	−1.18490	+	0.377476i
$357$	−11.5828	+	1.01337i	−0.613028	+	0.0536330i
$358$	2.32140	+	2.41776i	0.122690	+	0.127783i
$359$	11.9095	+	4.33470i	0.628558	+	0.228776i	0.636604	−	0.771191i	$-0.280339\pi$
$359$	11.9095	+	4.33470i	0.628558	+	0.228776i	−0.00804545	+	0.999968i	$0.502561\pi$
$360$	−38.8392	−	9.61944i	−2.04701	−	0.506989i
$361$	16.8926	−	8.69718i	0.889083	−	0.457747i
$362$	1.46126	−	0.979532i	0.0768024	−	0.0514831i
$363$	−4.11587	+	1.91926i	−0.216027	+	0.100735i
$364$	0.858409	−	3.92727i	0.0449929	−	0.205845i
$365$	−3.93720	+	10.5776i	−0.206083	+	0.553658i
$366$	3.04219	+	5.52568i	0.159018	+	0.288832i
$367$	25.2387	−	17.6724i	1.31745	−	0.922490i	0.317781	−	0.948164i	$-0.397062\pi$
$367$	25.2387	−	17.6724i	1.31745	−	0.922490i	0.999670	+	0.0256746i	$0.00817336\pi$
$368$	11.6469	−	20.4531i	0.607139	−	1.06619i
$369$	−0.873869	+	0.504529i	−0.0454918	+	0.0262647i
$370$	−5.47087	+	18.3738i	−0.284417	+	0.955209i
$371$	2.67303	+	7.34409i	0.138777	+	0.381286i
$372$	−17.9738	−	13.7071i	−0.931899	−	0.710678i
$373$	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	$0.315739\pi$
$374$	8.57422	−	22.1460i	0.443363	−	1.14514i
$375$	33.7466	−	5.19480i	1.74267	−	0.268258i
$376$	−26.7188	+	7.91731i	−1.37792	+	0.408304i
$377$	16.1694	+	11.3220i	0.832768	+	0.583111i
$378$	2.40250	+	9.75536i	0.123571	+	0.501761i
$379$	−22.2847			−1.14469			−0.572345	−	0.820013i	$-0.693966\pi$
$379$	−22.2847			−1.14469			−0.572345	+	0.820013i	$0.693966\pi$
$380$	−10.9359	+	16.1371i	−0.561000	+	0.827816i
$381$	48.7965			2.49992
$382$	−0.240080	−	0.974846i	−0.0122836	−	0.0498775i
$383$	−10.3111	−	7.21993i	−0.526874	−	0.368921i	0.279669	−	0.960096i	$-0.409775\pi$
$383$	−10.3111	−	7.21993i	−0.526874	−	0.368921i	−0.806543	+	0.591175i	$0.798664\pi$
$384$	−16.3027	+	30.4635i	−0.831942	+	1.55458i
$385$	2.44168	−	4.15904i	0.124440	−	0.211964i
$386$	−2.50467	+	6.46921i	−0.127484	+	0.329274i
$387$	−15.5614	+	4.16967i	−0.791032	+	0.211956i
$388$	2.74060	−	3.59369i	0.139133	−	0.182442i
$389$	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	$0.649763\pi$
$390$	24.4136	−	13.2108i	1.23623	−	0.668954i
$391$	27.7441	−	16.0181i	1.40308	−	0.810068i
$392$	5.84174	−	17.4648i	0.295052	−	0.882105i
$393$	11.6914	−	8.18644i	0.589755	−	0.412951i
$394$	−2.86765	−	5.20866i	−0.144470	−	0.262408i
$395$	3.64951	+	7.97722i	0.183627	+	0.401377i
$396$	−38.1261	−	8.33347i	−1.91591	−	0.418772i
$397$	−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	$0.639592\pi$
$398$	2.96354	−	1.98655i	0.148549	−	0.0995768i
$399$	9.25118	+	1.03427i	0.463138	+	0.0517783i
$400$	1.91406	−	19.9082i	0.0957030	−	0.995410i
$401$	−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	$0.631000\pi$
$402$	46.6129	+	48.5477i	2.32484	+	2.42134i
$403$	10.5969	−	0.927105i	0.527867	−	0.0461824i
$404$	−4.91677	−	15.4338i	−0.244619	−	0.767861i
$405$	−15.6093	+	21.9512i	−0.775632	+	1.09076i
$406$	−5.11275	−	4.47033i	−0.253741	−	0.221859i
$407$	−4.83948	+	18.0612i	−0.239884	+	0.895260i
$408$	−40.0958	+	24.5761i	−1.98504	+	1.21670i
$409$	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	$0.570070\pi$
$410$	−0.313418	−	0.395166i	−0.0154786	−	0.0195159i
$411$	31.3025	+	18.0725i	1.54404	+	0.891452i
$412$	−24.6602	+	5.54402i	−1.21492	+	0.273134i
$413$	−2.76545	−	0.241946i	−0.136079	−	0.0119054i
$414$	−33.0138	−	41.0092i	−1.62254	−	2.01549i
$415$	−0.809362	−	1.42568i	−0.0397300	−	0.0699837i
$416$	−3.98202	−	15.7646i	−0.195235	−	0.772923i
$417$	18.1596	−	18.1596i	0.889281	−	0.889281i
$418$	−10.2279	+	16.0275i	−0.500265	+	0.783932i
$419$	10.2081			0.498699			0.249350	−	0.968414i	$-0.419783\pi$
$419$	10.2081			0.498699			0.249350	+	0.968414i	$0.419783\pi$
$420$	−8.83925	+	3.61697i	−0.431311	+	0.176490i
$421$	−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	$-0.133442\pi$
$422$	−3.18066	+	29.4469i	−0.154832	+	1.43345i
$423$	−5.43266	+	62.0956i	−0.264145	+	3.01919i
$424$	22.9321	+	21.7575i	1.11368	+	1.05664i
$425$	15.9364	−	22.0699i	0.773027	−	1.07055i
$426$	8.43158	+	24.7178i	0.408511	+	1.19758i
$427$	0.925620	+	0.431624i	0.0447939	+	0.0208877i
$428$	−6.17554	+	5.69272i	−0.298506	+	0.275168i
$429$	23.4470	−	13.5371i	1.13203	−	0.653579i
$430$	−3.20052	−	7.38927i	−0.154343	−	0.356342i
$431$	−5.66314	−	0.998564i	−0.272784	−	0.0480991i	0.0355829	−	0.999367i	$-0.488671\pi$
$431$	−5.66314	−	0.998564i	−0.272784	−	0.0480991i	−0.308367	+	0.951268i	$0.599782\pi$
$432$	26.3054	+	30.9736i	1.26562	+	1.49022i
$433$	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	$0.899473\pi$
$434$	−3.65912	−	0.0743990i	−0.175643	−	0.00357126i
$435$	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
$438$	18.1079	−	12.1383i	0.865230	−	0.579991i
$439$	14.0185	+	5.10232i	0.669067	+	0.243520i	0.654146	−	0.756368i	$-0.273028\pi$
$439$	14.0185	+	5.10232i	0.669067	+	0.243520i	0.0149209	+	0.999889i	$0.495250\pi$
$440$	1.33040	−	19.4615i	0.0634243	−	0.927788i
$441$	−31.5551	−	26.4779i	−1.50262	−	1.26085i
$442$	6.16137	−	21.2563i	0.293066	−	1.01106i
$443$	−4.52306	−	6.45960i	−0.214897	−	0.306905i	0.697202	−	0.716875i	$-0.254428\pi$
$443$	−4.52306	−	6.45960i	−0.214897	−	0.306905i	−0.912099	+	0.409970i	$0.865539\pi$
$444$	29.3095	−	22.6288i	1.39097	−	1.07391i
$445$	−26.1494	+	2.09645i	−1.23960	+	0.0993812i
$446$	−4.70845	−	30.2917i	−0.222952	−	1.43435i
$447$	21.4289	+	9.99245i	1.01355	+	0.472626i
$448$	0.779657	+	5.53971i	0.0368353	+	0.261727i
$449$	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	$0.434550\pi$
$450$	−39.8607	−	20.3077i	−1.87905	−	0.957315i
$451$	−0.316208	−	0.376842i	−0.0148896	−	0.0177448i
$452$	29.2173	+	9.11674i	1.37427	+	0.428816i
$453$	−32.1414	+	45.9026i	−1.51013	+	2.15669i
$454$	−33.5981	−	20.3195i	−1.57684	−	0.953642i
$455$	1.92900	−	4.05948i	0.0904327	−	0.190311i
$456$	35.3524	−	12.9557i	1.65553	−	0.606704i
$457$	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	$0.0500195\pi$
$458$	2.13354	+	8.66326i	0.0996939	+	0.404807i
$459$	9.60463	+	54.4706i	0.448306	+	2.54247i
$460$	17.8612	−	19.3249i	0.832783	−	0.901029i
$461$	−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	$0.289376\pi$
$462$	−8.52068	+	3.76432i	−0.396418	+	0.175132i
$463$	10.1095	+	37.7292i	0.469828	+	1.75342i	0.640364	+	0.768072i	$0.278784\pi$
$463$	10.1095	+	37.7292i	0.469828	+	1.75342i	−0.170535	+	0.985352i	$0.554550\pi$
$464$	−26.5754	−	6.95171i	−1.23373	−	0.322725i
$465$	−16.1035	−	19.4770i	−0.746781	−	0.903226i
$466$	34.9318	−	5.42971i	1.61819	−	0.251526i
$467$	−4.76888	+	17.7977i	−0.220677	+	0.823580i	0.763413	+	0.645911i	$0.223522\pi$
$467$	−4.76888	+	17.7977i	−0.220677	+	0.823580i	−0.984090	+	0.177669i	$0.943144\pi$
$468$	−36.0723	−	4.63991i	−1.66744	−	0.214480i
$469$	10.7316	+	1.89227i	0.495539	+	0.0873768i
$470$	−31.1010	+	1.85804i	−1.43458	+	0.0857051i
$471$	−25.6857	+	30.6110i	−1.18353	+	1.41048i
$472$	−10.4465	+	4.11617i	−0.480840	+	0.189462i
$473$	−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
$478$	3.46669	+	3.61059i	0.158563	+	0.165145i
$479$	−30.9017	−	25.9296i	−1.41193	−	1.18475i	−0.955498	−	0.294997i	$-0.904681\pi$
$479$	−30.9017	−	25.9296i	−1.41193	−	1.18475i	−0.456436	−	0.889756i	$-0.650874\pi$
$480$	−25.4654	+	29.0476i	−1.16233	+	1.32584i
$481$	−3.02589	+	17.1607i	−0.137969	+	0.782460i
$482$	−0.457511	−	6.82475i	−0.0208390	−	0.310859i
$483$	−12.1380	−	3.25238i	−0.552300	−	0.147988i
$484$	−0.120892	+	2.97164i	−0.00549508	+	0.135075i
$485$	3.89425	−	3.21974i	0.176829	−	0.146201i
$486$	8.44542	−	2.88085i	0.383092	−	0.130678i
$487$	−11.4525	+	3.06868i	−0.518961	+	0.139055i	−0.508786	−	0.860893i	$-0.669905\pi$
$487$	−11.4525	+	3.06868i	−0.518961	+	0.139055i	−0.0101748	+	0.999948i	$0.503239\pi$
$488$	4.12948	−	0.108537i	0.186933	−	0.00491324i
$489$	−33.8831	−	40.3803i	−1.53225	−	1.82606i
$490$	10.7829	−	17.5403i	0.487120	−	0.792388i
$491$	−18.9630	+	3.34369i	−0.855790	+	0.150899i	−0.584295	−	0.811541i	$-0.698629\pi$
$491$	−18.9630	+	3.34369i	−0.855790	+	0.150899i	−0.271494	+	0.962440i	$0.587518\pi$
$492$	0.0453872	+	0.973121i	0.00204621	+	0.0438717i
$493$	−26.4381	−	26.4381i	−1.19071	−	1.19071i
$494$	−8.19359	+	15.7103i	−0.368647	+	0.706842i
$495$	−39.4095	−	18.7268i	−1.77133	−	0.841705i
$496$	−13.3788	+	6.33577i	−0.600725	+	0.284485i
$497$	3.46383	+	2.42540i	0.155374	+	0.108794i
$498$	−0.340043	+	3.14816i	−0.0152377	+	0.141072i
$499$	19.2890	−	16.1854i	0.863495	−	0.724558i	−0.0992229	−	0.995065i	$-0.531636\pi$
$499$	19.2890	−	16.1854i	0.863495	−	0.724558i	0.962718	+	0.270507i	$0.0871912\pi$
$500$	7.12418	−	21.1954i	0.318603	−	0.947888i
$501$	−11.5884	+	20.0717i	−0.517731	+	0.896737i
$502$	7.74223	−	15.7587i	0.345553	−	0.703346i
$503$	11.1617	−	23.9363i	0.497675	−	1.06727i	−0.483713	−	0.875227i	$-0.660712\pi$
$503$	11.1617	−	23.9363i	0.497675	−	1.06727i	0.981387	−	0.192040i	$-0.0615102\pi$
$504$	12.1678	+	2.91997i	0.541996	+	0.130066i
$505$	−1.44727	−	18.0521i	−0.0644028	−	0.803306i
$506$	16.8941	−	19.3219i	0.751035	−	0.858964i
$507$	−11.8532	+	8.29970i	−0.526419	+	0.368603i
$508$	14.6715	−	28.3894i	0.650941	−	1.25958i
$509$	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	$0.150600\pi$
$510$	−49.8856	+	16.6130i	−2.20897	+	0.735637i
$511$	1.20722	−	3.31681i	0.0534043	−	0.146727i
$512$	12.8218	+	18.6441i	0.566647	+	0.823961i
$513$	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
$516$	−3.32122	+	15.1948i	−0.146209	+	0.668912i
$517$	−30.2726	+	2.64851i	−1.33139	+	0.116481i
$518$	1.66912	−	5.75835i	0.0733369	−	0.253007i
$519$	0.180103	−	1.02142i	0.00790566	−	0.0448352i
$520$	−0.345596	−	18.1756i	−0.0151554	−	0.797055i
$521$	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	$0.770634\pi$
$522$	−36.2584	+	49.6047i	−1.58699	+	2.17114i
$523$	14.6603	−	31.4392i	0.641052	−	1.37474i	−0.270166	−	0.962814i	$-0.587078\pi$
$523$	14.6603	−	31.4392i	0.641052	−	1.37474i	0.911217	−	0.411926i	$-0.135144\pi$
$524$	−1.24758	−	9.26337i	−0.0545009	−	0.404672i
$525$	−10.5416	+	1.70121i	−0.460071	+	0.0742470i
$526$	20.4999	+	7.93691i	0.893839	+	0.346066i
$527$	−20.0720	−	1.75608i	−0.874352	−	0.0764959i
$528$	−24.0463	+	29.0059i	−1.04648	+	1.26232i
$529$	11.4472	−	2.01844i	0.497703	−	0.0877584i
$530$	19.4650	+	29.4991i	0.845507	+	1.28136i
$531$			25.1151i			1.08990i
$532$	3.38325	−	5.07129i	0.146682	−	0.219868i
$533$	−0.324168	−	0.324168i	−0.0140413	−	0.0140413i
$534$	43.3567	+	26.2213i	1.87623	+	1.13471i
$535$	−8.16626	+	4.63602i	−0.353058	+	0.200432i
$536$	42.2596	−	12.5223i	1.82534	−	0.540883i
$537$	0.630838	−	7.21052i	0.0272227	−	0.311157i
$538$	37.5263	−	16.5786i	1.61787	−	0.714755i
$539$	10.0410	−	17.3914i	0.432495	−	0.749103i
$540$	20.8056	+	40.3894i	0.895329	+	1.73808i
$541$	−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	$0.563664\pi$
$542$	18.7471	+	13.7032i	0.805258	+	0.588601i
$543$	−3.66948	−	0.983234i	−0.157472	−	0.0421946i
$544$	2.24274	+	30.7166i	0.0961565	+	1.31696i
$545$	6.23255	+	4.43191i	0.266973	+	0.189842i
$546$	−7.60467	+	4.18679i	−0.325450	+	0.179178i
$547$	2.42378	+	27.7039i	0.103633	+	1.18453i	0.852831	+	0.522187i	$0.174884\pi$
$547$	2.42378	+	27.7039i	0.103633	+	1.18453i	−0.749198	+	0.662346i	$0.769561\pi$
$548$	19.9261	−	12.7778i	0.851200	−	0.545839i
$549$	3.16024	−	8.68270i	0.134876	−	0.370568i
$550$	6.37548	−	20.8567i	0.271851	−	0.889332i
$551$	16.5745	+	24.9269i	0.706096	+	1.06192i
$552$	−49.8055	+	10.1381i	−2.11986	+	0.431506i
$553$	−1.15941	−	2.48637i	−0.0493033	−	0.105731i
$554$	−12.6635	−	0.257480i	−0.538020	−	0.0109393i
$555$	37.6465	−	17.2230i	1.59800	−	0.731074i
$556$	−5.10514	−	16.0251i	−0.216506	−	0.679616i
$557$	−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	$0.934959\pi$
$558$	2.21472	+	33.0373i	0.0937565	+	1.39858i
$559$	−3.65970	−	6.33879i	−0.154789	−	0.268102i
$560$	−0.553337	+	6.23010i	−0.0233828	+	0.263270i
$561$	−48.1900	+	17.5397i	−2.03458	+	0.740528i
$562$	−3.17536	−	1.56005i	−0.133944	−	0.0658067i
$563$	10.9476	+	40.8569i	0.461386	+	1.72191i	0.668603	+	0.743620i	$0.266893\pi$
$563$	10.9476	+	40.8569i	0.461386	+	1.72191i	−0.207217	+	0.978295i	$0.566441\pi$
$564$	50.8497	+	32.1826i	2.14116	+	1.35513i
$565$	29.5097	+	17.3245i	1.24148	+	0.728846i
$566$	8.45822	−	6.80914i	0.355526	−	0.286210i
$567$	4.83152	−	6.90012i	0.202905	−	0.289778i
$568$	16.9157	+	2.52639i	0.709768	+	0.106005i
$569$			44.9255i			1.88337i	0.336489	+	0.941687i	$0.390761\pi$
$569$			44.9255i			1.88337i	−0.336489	+	0.941687i	$0.609239\pi$
$570$	41.7784	−	5.15921i	1.74990	−	0.216095i
$571$		−	17.2217i		−	0.720704i	−0.932816	−	0.360352i	$-0.882657\pi$
$571$		−	17.2217i		−	0.720704i	0.932816	−	0.360352i	$-0.117343\pi$
$572$	−0.826077	−	17.7114i	−0.0345400	−	0.740553i
$573$	−1.24354	+	1.77596i	−0.0519496	+	0.0741918i
$574$	0.0989108	+	0.122866i	0.00412846	+	0.00512831i
$575$	24.3429	−	16.5232i	1.01517	−	0.689065i
$576$	49.3132	−	11.3950i	2.05471	−	0.474790i
$577$	−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	$0.923581\pi$
$578$	−7.88351	+	16.0463i	−0.327911	+	0.667437i
$579$	14.0771	−	5.12364i	0.585024	−	0.212931i
$580$	−27.1807	−	14.2980i	−1.12862	−	0.593691i
$581$	0.256345	+	0.444003i	0.0106350	+	0.0184204i
$582$	−9.73775	+	0.652789i	−0.403643	+	0.0270590i
$583$	19.7717	+	28.2370i	0.818862	+	1.16946i
$584$	−1.61753	−	14.1846i	−0.0669341	−	0.586964i
$585$	−38.1080	−	14.1846i	−1.57557	−	0.586459i
$586$	−0.486865	+	23.9452i	−0.0201122	+	0.989166i
$587$	−2.33482	−	5.00703i	−0.0963682	−	0.206662i	0.852214	−	0.523194i	$-0.175260\pi$
$587$	−2.33482	−	5.00703i	−0.0963682	−	0.206662i	−0.948582	+	0.316531i	$0.897482\pi$
$588$	−36.6958	+	15.3279i	−1.51331	+	0.632112i
$589$	15.4767	+	4.54891i	0.637707	+	0.187435i
$590$	−12.4183	+	1.83796i	−0.511251	+	0.0756675i
$591$	−4.39151	+	12.0656i	−0.180643	+	0.496312i
$592$	−4.35287	−	23.8558i	−0.178902	−	0.980465i
$593$	−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	$0.972867\pi$
$594$	21.3718	+	38.8186i	0.876894	+	1.59275i
$595$	−4.93352	+	6.93797i	−0.202255	+	0.284429i
$596$	12.2565	−	9.46276i	0.502044	−	0.387610i
$597$	−7.44193	−	1.99406i	−0.304578	−	0.0816114i
$598$	14.1147	−	19.3102i	0.577195	−	0.789654i
$599$	−16.9154	+	6.15671i	−0.691146	+	0.251556i	−0.663626	−	0.748065i	$-0.730983\pi$
$599$	−16.9154	+	6.15671i	−0.691146	+	0.251556i	−0.0275200	+	0.999621i	$0.508761\pi$
$600$	−35.0852	+	25.1862i	−1.43235	+	1.02822i
$601$	−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	$0.246617\pi$
$602$	1.01767	+	2.30352i	0.0414770	+	0.0938847i
$603$	8.59251	−	98.2129i	0.349914	−	3.99954i
$604$	17.0420	+	32.5010i	0.693428	+	1.32245i
$605$	−0.883923	+	3.20550i	−0.0359366	+	0.130322i
$606$	−18.1018	+	29.9310i	−0.735334	+	1.21587i
$607$	−30.8833	−	30.8833i	−1.25351	−	1.25351i	−0.954134	−	0.299380i	$-0.903220\pi$
$607$	−30.8833	−	30.8833i	−1.25351	−	1.25351i	−0.299380	−	0.954134i	$-0.596780\pi$
$608$	3.09176	−	24.4631i	0.125387	−	0.992108i
$609$			14.6659i			0.594294i
$610$	4.52447	+	0.927183i	0.183190	+	0.0375406i
$611$	−27.8893	+	4.91764i	−1.12828	+	0.198946i
$612$	65.7621	+	20.5199i	2.65828	+	0.829468i
$613$	−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	$0.537290\pi$
$614$	−8.51138	+	21.9837i	−0.343491	+	0.887189i
$615$	−0.196919	+	1.07122i	−0.00794056	+	0.0431956i
$616$	−0.371828	+	6.08907i	−0.0149814	+	0.245336i
$617$	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	$-0.138999\pi$
$618$	44.0652	+	32.2093i	1.77256	+	1.29565i
$619$	12.7137	+	22.0207i	0.511005	+	0.885086i	0.999919	+	0.0127543i	$0.00405992\pi$
$619$	12.7137	+	22.0207i	0.511005	+	0.885086i	−0.488914	+	0.872332i	$0.662607\pi$
$620$	−16.1734	+	3.51279i	−0.649538	+	0.141077i
$621$	−10.3804	+	58.8703i	−0.416552	+	2.36238i
$622$	11.1271	+	3.22532i	0.446157	+	0.129324i
$623$	8.17275	−	0.715023i	0.327434	−	0.0286468i
$624$	−19.9682	+	28.8816i	−0.799366	+	1.15619i
$625$	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
$628$	10.0864	+	24.1474i	0.402492	+	0.963587i
$629$	11.2888	−	31.0158i	0.450116	−	1.23668i
$630$	12.5115	+	6.26012i	0.498470	+	0.249409i
$631$	−16.6534	+	19.8467i	−0.662960	+	0.790084i	−0.987807	−	0.155682i	$-0.950243\pi$
$631$	−16.6534	+	19.8467i	−0.662960	+	0.790084i	0.324848	+	0.945766i	$0.394687\pi$
$632$	−8.68473	−	6.90677i	−0.345460	−	0.274736i
$633$	52.3926	−	36.6857i	2.08242	−	1.45812i
$634$	−20.4374	−	17.8695i	−0.811675	−	0.709687i
$635$	23.1640	−	27.2019i	0.919234	−	1.07947i
$636$	2.77478	−	68.2068i	0.110027	−	2.70458i
$637$	7.90922	−	16.9614i	0.313375	−	0.672035i
$638$	−26.8852	−	13.2087i	−1.06440	−	0.522936i
$639$	19.1282	−	33.1310i	0.756700	−	1.31064i
$640$	9.24310	+	23.5492i	0.365366	+	0.930864i
$641$	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	$0.0173744\pi$
$642$	18.0326	+	1.94776i	0.711690	+	0.0768720i
$643$	−32.6552	−	22.8654i	−1.28780	−	0.901724i	−0.289337	−	0.957227i	$-0.593435\pi$
$643$	−32.6552	−	22.8654i	−1.28780	−	0.901724i	−0.998458	+	0.0555036i	$0.982324\pi$
$644$	−5.54170	+	6.08393i	−0.218374	+	0.239741i
$645$	−7.46336	+	15.7063i	−0.293870	+	0.618434i
$646$	20.4515	−	26.6107i	0.804653	−	1.04698i
$647$	27.4995	+	27.4995i	1.08112	+	1.08112i	0.996406	+	0.0847097i	$0.0269963\pi$
$647$	27.4995	+	27.4995i	1.08112	+	1.08112i	0.0847097	+	0.996406i	$0.473004\pi$
$648$	5.03268	−	33.6969i	0.197702	−	1.32374i
$649$	−12.0580	+	2.12615i	−0.473317	+	0.0834586i
$650$	4.22482	−	19.8807i	0.165711	−	0.779786i
$651$	5.08019	+	6.05433i	0.199108	+	0.237288i
$652$	−33.6804	+	7.57192i	−1.31903	+	0.296539i
$653$	−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	$0.468897\pi$
$654$	−4.76887	−	13.9803i	−0.186478	−	0.546674i
$655$	0.986413	−	10.4036i	0.0385424	−	0.406503i
$656$	0.579800	+	0.266178i	0.0226374	+	0.0103925i
$657$	−30.8454	−	8.26501i	−1.20339	−	0.322449i
$658$	9.72178	−	0.651718i	0.378994	−	0.0254066i
$659$	−0.873533	+	4.95405i	−0.0340280	+	0.192982i	−0.997083	−	0.0763215i	$-0.975682\pi$
$659$	−0.873533	+	4.95405i	−0.0340280	+	0.192982i	0.963055	+	0.269304i	$0.0867936\pi$
$660$	−33.5293	+	25.5000i	−1.30513	+	0.992588i
$661$	−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	$0.899867\pi$
$662$	−19.6207	+	18.8387i	−0.762581	+	0.732189i
$663$	−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
$668$	8.19331	+	12.7769i	0.317009	+	0.494354i
$669$	−42.5521	+	50.7116i	−1.64516	+	1.96062i
$670$	49.1906	−	2.93876i	1.90040	−	0.113534i
$671$	4.43618	+	0.782219i	0.171257	+	0.0301972i
$672$	7.89762	−	9.14173i	0.304657	−	0.352650i
$673$	−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	$0.881411\pi$
$674$	−6.05694	−	38.9671i	−0.233305	−	1.50096i
$675$	12.4326	+	49.2508i	0.478531	+	1.89567i
$676$	1.26484	+	9.39154i	0.0486478	+	0.361213i
$677$	−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	$-0.295873\pi$
$678$	−26.7090	−	60.4569i	−1.02575	−	2.32183i
$679$	−1.21051	+	1.01574i	−0.0464550	+	0.0389803i
$680$	−5.33359	+	34.0180i	−0.204534	+	1.30453i
$681$	14.7237	+	83.5024i	0.564215	+	3.19982i
$682$	−15.6740	+	3.86012i	−0.600190	+	0.147812i
$683$	30.6571	−	30.6571i	1.17306	−	1.17306i	0.191586	−	0.981476i	$-0.438637\pi$
$683$	30.6571	−	30.6571i	1.17306	−	1.17306i	0.981476	−	0.191586i	$-0.0613630\pi$
$684$	−48.3739	−	26.4935i	−1.84962	−	1.01300i
$685$	24.9341	−	8.87066i	0.952684	−	0.338931i
$686$	−6.91465	+	11.4333i	−0.264003	+	0.436525i
$687$	11.0511	−	15.7826i	0.421625	−	0.602143i
$688$	7.84161	+	6.50081i	0.298959	+	0.247841i
$689$	20.6491	+	24.6087i	0.786669	+	0.937516i
$690$	−56.8045	−	1.56793i	−2.16251	−	0.0596899i
$691$	−23.7325	−	13.7020i	−0.902828	−	0.521248i	−0.0247114	−	0.999695i	$-0.507867\pi$
$691$	−23.7325	−	13.7020i	−0.902828	−	0.521248i	−0.878117	+	0.478447i	$0.841200\pi$
$692$	−0.540101	−	0.411888i	−0.0205316	−	0.0156576i
$693$	12.3668	+	5.76675i	0.469777	+	0.219061i
$694$	−1.57477	+	0.244778i	−0.0597774	+	0.00929163i
$695$	−1.50272	−	18.7437i	−0.0570014	−	0.710988i
$696$	26.4734	+	53.0846i	1.00347	+	2.01216i
$697$	0.498071	+	0.711319i	0.0188658	+	0.0269431i
$698$	16.5323	+	4.79207i	0.625758	+	0.181383i
$699$	−58.4797	−	49.0703i	−2.21191	−	1.85601i
$700$	−2.17974	+	6.64449i	−0.0823863	+	0.251138i
$701$	−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	$0.651396\pi$
$702$	22.9940	+	34.3025i	0.867854	+	1.29466i
$703$	−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
$706$	0.769539	−	37.8478i	0.0289620	−	1.42442i
$707$	0.493612	+	5.64201i	0.0185642	+	0.212190i
$708$	21.5405	+	11.1320i	0.809541	+	0.418365i
$709$	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	$0.430812\pi$
$710$	17.7816	+	7.03345i	0.667332	+	0.263961i
$711$	−21.4948	+	12.4100i	−0.806116	+	0.465411i
$712$	28.2912	−	17.3407i	1.06026	−	0.649870i
$713$	−19.7359	−	9.20301i	−0.739116	−	0.344655i
$714$	15.5626	−	5.30863i	0.582417	−	0.198670i
$715$	3.58407	−	19.4968i	0.134036	−	0.729140i
$716$	−4.00535	−	2.53497i	−0.149687	−	0.0947365i
$717$	0.942070	−	10.7679i	0.0351823	−	0.402135i
$718$	−17.8198	−	1.92478i	−0.665029	−	0.0718320i
$719$	3.57813	+	20.2926i	0.133442	+	0.756785i	0.975932	+	0.218074i	$0.0699775\pi$
$719$	3.57813	+	20.2926i	0.133442	+	0.756785i	−0.842491	+	0.538711i	$0.818911\pi$
$720$	56.5865	+	0.0745664i	2.10886	+	0.00277892i
$721$	8.83750			0.329126
$722$	−20.2554	+	17.6556i	−0.753827	+	0.657073i
$723$	−10.4446	+	10.4446i	−0.388439	+	0.388439i
$724$	−1.67533	+	1.83925i	−0.0622630	+	0.0683552i
$725$	−25.9802	−	22.4513i	−0.964879	−	0.833819i
$726$	5.00279	−	4.02741i	0.185671	−	0.149471i
$727$	4.98669	+	0.436279i	0.184946	+	0.0161807i	0.179253	−	0.983803i	$-0.442632\pi$
$727$	4.98669	+	0.436279i	0.184946	+	0.0161807i	0.00569368	+	0.999984i	$0.498188\pi$
$728$	0.149373	+	5.68316i	0.00553613	+	0.210632i
$729$	14.6081	+	8.43397i	0.541039	+	0.312369i
$730$	1.82936	−	15.8565i	0.0677075	−	0.586875i
$731$	4.74178	+	13.0279i	0.175381	+	0.481856i
$732$	−6.04616	−	6.55896i	−0.223473	−	0.242426i
$733$	−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	$0.127570\pi$
$734$	−28.6810	+	32.8027i	−1.05863	+	1.21077i
$735$	−43.8419	+	7.40249i	−1.61713	+	0.273045i
$736$	−9.07656	+	32.0246i	−0.334566	+	1.18044i
$737$	47.8804	−	4.18899i	1.76370	−	0.154303i
$738$	1.02936	−	0.988337i	0.0378913	−	0.0363812i
$739$	20.0011	+	7.27981i	0.735753	+	0.267792i	0.682598	−	0.730794i	$-0.260850\pi$
$739$	20.0011	+	7.27981i	0.735753	+	0.267792i	0.0531548	+	0.998586i	$0.483072\pi$
$740$	1.29884	−	27.0808i	0.0477462	−	0.995509i
$741$	37.1866	−	9.01074i	1.36608	−	0.331018i
$742$	−6.15420	−	9.18082i	−0.225928	−	0.337039i
$743$	30.1007	−	14.0362i	1.10429	−	0.514938i	0.217008	−	0.976170i	$-0.430370\pi$
$743$	30.1007	−	14.0362i	1.10429	−	0.514938i	0.887279	+	0.461232i	$0.152592\pi$
$744$	29.3168	+	12.7439i	1.07481	+	0.467215i
$745$	15.7428	−	7.20219i	0.576770	−	0.263868i
$746$	−14.9200	+	8.21428i	−0.546260	+	0.300746i
$747$	3.79955	−	2.66047i	0.139018	−	0.0973416i
$748$	−4.28463	+	33.3102i	−0.156662	+	1.21794i
$749$	2.54325	−	1.46834i	0.0929282	−	0.0536521i
$750$	−44.5836	+	18.5459i	−1.62796	+	0.677200i
$751$	−3.32296	−	9.12976i	−0.121257	−	0.333150i	0.864183	−	0.503178i	$-0.167836\pi$
$751$	−3.32296	−	9.12976i	−0.121257	−	0.333150i	−0.985439	+	0.170029i	$0.945614\pi$
$752$	34.0124	−	19.9077i	1.24030	−	0.725960i
$753$	−36.6237	+	9.81328i	−1.33464	+	0.357616i
$754$	−26.0325	−	10.0789i	−0.948047	−	0.367053i
$755$	10.3310	+	39.7076i	0.375984	+	1.44511i
$756$	−6.59815	−	12.5834i	−0.239972	−	0.457654i
$757$	−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	$0.768817\pi$
$758$	30.6010	−	7.53627i	1.11148	−	0.273730i
$759$	−55.4250			−2.01180
$760$	9.55975	−	25.8575i	0.346769	−	0.937951i
$761$	−21.4425			−0.777290			−0.388645	−	0.921388i	$-0.627057\pi$
$761$	−21.4425			−0.777290			−0.388645	+	0.921388i	$0.627057\pi$
$762$	−67.0066	+	16.5020i	−2.42739	+	0.597806i
$763$	−1.95913	−	1.37180i	−0.0709254	−	0.0496625i
$764$	0.659349	+	1.25745i	0.0238544	+	0.0454930i
$765$	66.4201	+	38.9938i	2.40142	+	1.40982i
$766$	16.6007	+	6.42726i	0.599808	+	0.232226i
$767$	−11.0217	+	2.95325i	−0.397970	+	0.106636i
$768$	12.0844	−	47.3452i	0.436057	−	1.70842i
$769$	−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	$-0.273133\pi$
$770$	−1.94637	+	6.53685i	−0.0701423	+	0.235572i
$771$	−55.3383	+	31.9496i	−1.99296	+	1.15064i
$772$	1.25161	−	9.73045i	0.0450464	−	0.350206i
$773$	−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	$0.350422\pi$
$774$	19.9586	−	10.9883i	0.717397	−	0.394966i
$775$	−18.5020	−	0.268870i	−0.664612	−	0.00965810i
$776$	−2.54803	+	5.86162i	−0.0914688	+	0.210420i
$777$	−11.7338	+	5.47156i	−0.420947	+	0.196291i
$778$	−21.2009	−	31.6274i	−0.760088	−	1.13390i
$779$	−0.278564	−	0.636975i	−0.00998060	−	0.0228220i
$780$	−29.0567	+	26.3970i	−1.04040	+	0.945165i
$781$	17.5259	+	6.37889i	0.627125	+	0.228255i
$782$	−32.6807	+	31.3782i	−1.16866	+	1.12208i
$783$	69.5015	−	6.08059i	2.48378	−	0.217303i
$784$	−2.11553	+	25.9579i	−0.0755547	+	0.927068i
$785$	4.87116	+	28.8499i	0.173859	+	1.02970i
$786$	−13.2860	+	15.1953i	−0.473896	+	0.541998i
$787$	2.83584	−	10.5835i	0.101087	−	0.377261i	−0.896785	−	0.442466i	$-0.854104\pi$
$787$	2.83584	−	10.5835i	0.101087	−	0.377261i	0.997872	+	0.0652056i	$0.0207703\pi$
$788$	5.69928	+	6.18266i	0.203028	+	0.220248i
$789$	−16.2360	−	44.6081i	−0.578018	−	1.58809i
$790$	−7.70920	−	9.71999i	−0.274281	−	0.345822i
$791$	−9.26772	−	5.35072i	−0.329522	−	0.190250i
$792$	55.1723	−	1.45012i	1.96046	−	0.0515277i
$793$	4.18199	+	0.365877i	0.148507	+	0.0129927i
$794$	33.6906	−	27.1220i	1.19563	−	0.962525i
$795$	20.2883	−	73.5746i	0.719552	−	2.60942i
$796$	−3.39766	+	3.73011i	−0.120427	+	0.132210i
$797$	−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	$0.478521\pi$
$798$	−13.0533	+	1.70833i	−0.462083	+	0.0604742i
$799$	53.6415			1.89770
$800$	4.10422	+	27.9849i	0.145106	+	0.989416i
$801$	−12.8886	−	73.0949i	−0.455396	−	2.58268i
$802$	3.51616	+	0.379792i	0.124160	+	0.0134109i
$803$	1.35685	−	15.5089i	0.0478822	−	0.547296i
$804$	−80.4259	−	50.9014i	−2.83640	−	1.79515i
$805$	−7.57505	+	5.22250i	−0.266985	+	0.184069i
$806$	−14.2379	+	4.85674i	−0.501509	+	0.171071i
$807$	−80.2922	−	37.4409i	−2.82642	−	1.31798i
$808$	11.9711	+	19.5307i	0.421140	+	0.687088i
$809$	−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	$0.369832\pi$
$810$	14.0110	−	35.4218i	0.492295	−	1.24460i
$811$	10.3397	+	1.82317i	0.363076	+	0.0640201i	0.352210	−	0.935921i	$-0.385430\pi$
$811$	10.3397	+	1.82317i	0.363076	+	0.0640201i	0.0108657	+	0.999941i	$0.496541\pi$
$812$	8.53252	+	4.40955i	0.299433	+	0.154745i
$813$	−4.37048	−	49.9549i	−0.153280	−	1.75199i
$814$	0.537549	−	26.4380i	0.0188411	−	0.926650i
$815$	−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
$818$	−26.8284	−	40.0226i	−0.938033	−	1.39936i
$819$	11.9495	+	4.34926i	0.417549	+	0.151975i
$820$	0.564018	+	0.436644i	0.0196963	+	0.0152483i
$821$	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	$0.638562\pi$
$822$	−49.0959	−	14.2310i	−1.71242	−	0.496363i
$823$	18.9503	+	27.0639i	0.660567	+	0.943387i	0.999996	+	0.00275550i	$0.000877103\pi$
$823$	18.9503	+	27.0639i	0.660567	+	0.943387i	−0.339430	+	0.940631i	$0.610234\pi$
$824$	31.9881	−	15.9526i	1.11436	−	0.555733i
$825$	−42.9686	+	19.2815i	−1.49598	+	0.671297i
$826$	3.87930	−	0.602988i	0.134978	−	0.0209806i
$827$	13.1536	+	6.13364i	0.457397	+	0.213288i	0.637640	−	0.770335i	$-0.279911\pi$
$827$	13.1536	+	6.13364i	0.457397	+	0.213288i	−0.180243	+	0.983622i	$0.557689\pi$
$828$	59.2025	+	45.1486i	2.05743	+	1.56902i
$829$	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	$0.581266\pi$
$830$	1.59354	+	1.68401i	0.0553125	+	0.0584527i
$831$	17.5815	+	20.9528i	0.609896	+	0.726846i
$832$	10.7993	+	20.3010i	0.374399	+	0.703812i
$833$	−20.3325	+	29.0379i	−0.704480	+	1.00610i
$834$	−18.7953	+	31.0778i	−0.650827	+	1.07613i
$835$	5.68801	+	15.9882i	0.196842	+	0.553293i
$836$	8.62463	−	25.4676i	0.298289	−	0.880816i
$837$	26.5851	−	26.5851i	0.918914	−	0.918914i
$838$	−14.0176	+	3.45219i	−0.484231	+	0.119254i
$839$	−8.99773	−	51.0287i	−0.310636	−	1.76171i	−0.595710	−	0.803200i	$-0.703129\pi$
$839$	−8.99773	−	51.0287i	−0.310636	−	1.76171i	0.285074	−	0.958506i	$-0.407982\pi$
$840$	10.9147	−	7.95603i	0.376594	−	0.274509i
$841$	−13.9122	+	11.6737i	−0.479732	+	0.402543i
$842$	5.68132	+	12.8599i	0.195791	+	0.443181i
$843$	1.97736	+	7.37962i	0.0681040	+	0.254168i
$844$	−5.59076	−	41.5117i	−0.192442	−	1.42889i
$845$	−1.00006	+	10.5476i	−0.0344032	+	0.362847i
$846$	−13.5395	−	87.1058i	−0.465497	−	2.99476i
$847$	0.269140	−	1.00444i	0.00924776	−	0.0345131i
$848$	−38.8479	−	22.1218i	−1.33404	−	0.759667i
$849$	−23.0922	−	4.07178i	−0.792522	−	0.139743i
$850$	−14.4199	+	35.6953i	−0.494600	+	1.22434i
$851$	22.9298	−	27.3266i	0.786022	−	0.936745i
$852$	−19.9372	−	31.0907i	−0.683037	−	1.06515i
$853$	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	$0.520410\pi$
$858$	−27.6191	+	26.5183i	−0.942899	+	0.905320i
$859$	21.8878	+	18.3660i	0.746802	+	0.626641i	0.934655	−	0.355556i	$-0.115708\pi$
$859$	21.8878	+	18.3660i	0.746802	+	0.626641i	−0.187853	+	0.982197i	$0.560153\pi$
$860$	6.89381	+	9.06447i	0.235077	+	0.309096i
$861$	0.0591473	−	0.335441i	0.00201574	−	0.0114318i
$862$	8.11422	−	0.543952i	0.276371	−	0.0185271i
$863$	−19.8184	−	5.31032i	−0.674626	−	0.180765i	−0.0947881	−	0.995497i	$-0.530217\pi$
$863$	−19.8184	−	5.31032i	−0.674626	−	0.180765i	−0.579838	+	0.814732i	$0.696884\pi$
$864$	−46.5968	−	33.6364i	−1.58526	−	1.14433i
$865$	−0.483899	−	0.585272i	−0.0164531	−	0.0198999i
$866$	−4.30503	−	12.6205i	−0.146291	−	0.428863i
$867$	37.2920	−	9.99236i	1.26650	−	0.339358i
$868$	5.04980	−	1.13528i	0.171401	−	0.0385339i
$869$	−7.77783	−	9.26926i	−0.263845	−	0.314438i
$870$	15.3911	+	64.5107i	0.521808	+	2.18712i
$871$	44.1109	−	7.77794i	1.49464	−	0.263545i
$872$	−9.56748	−	1.42892i	−0.323996	−	0.0483892i
$873$	10.1090	+	10.1090i	0.342139	+	0.342139i
$874$	30.6069	−	19.4658i	1.03530	−	0.658441i
$875$	−4.05578	+	6.68403i	−0.137110	+	0.225961i
$876$	−20.7606	+	22.7919i	−0.701435	+	0.770067i
$877$	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	$0.627044\pi$
$878$	−20.9755	−	2.26563i	−0.707889	−	0.0764614i
$879$	39.6194	−	33.2446i	1.33633	−	1.12131i
$880$	4.75461	+	27.1741i	0.160278	+	0.916038i
$881$	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	$0.0910379\pi$
$882$	52.2853	+	25.6877i	1.76054	+	0.864949i
$883$	−15.3978	+	33.0207i	−0.518177	+	1.11123i	0.456931	+	0.889502i	$0.348949\pi$
$883$	−15.3978	+	33.0207i	−0.518177	+	1.11123i	−0.975108	+	0.221732i	$0.928829\pi$
$884$	−1.27222	+	31.2724i	−0.0427894	+	1.05181i
$885$	20.6395	+	17.5757i	0.693788	+	0.590800i
$886$	8.39550	+	7.34060i	0.282052	+	0.246612i
$887$	27.2989	−	19.1149i	0.916609	−	0.641816i	−0.0170986	−	0.999854i	$-0.505443\pi$
$887$	27.2989	−	19.1149i	0.916609	−	0.641816i	0.933707	+	0.358038i	$0.116554\pi$
$888$	−32.5947	+	40.9854i	−1.09381	+	1.37538i
$889$	−7.18210	+	8.55930i	−0.240880	+	0.287070i
$890$	35.1989	−	11.7220i	1.17987	−	0.392923i
$891$	12.7071	−	34.9123i	0.425702	−	1.16961i
$892$	16.7096	+	40.0037i	0.559480	+	1.33942i
$893$	−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
$896$	−2.94404	−	7.34338i	−0.0983534	−	0.245325i
$897$	−51.4554	+	4.50176i	−1.71804	+	0.150309i
$898$	−38.3539	−	11.1173i	−1.27989	−	0.370989i
$899$	−4.41323	+	25.0287i	−0.147190	+	0.834754i
$900$	61.6037	+	14.4061i	2.05346	+	0.480204i
$901$	−30.4242	−	52.6962i	−1.01358	−	1.75556i
$902$	0.561652	+	0.410538i	0.0187010	+	0.0136694i
$903$	2.29828	−	4.92868i	0.0764820	−	0.164016i
$904$	−43.2038	−	2.63823i	−1.43694	−	0.0877463i
$905$	−2.29003	+	1.57883i	−0.0761233	+	0.0524820i
$906$	28.6126	−	73.9023i	0.950590	−	2.45524i
$907$	−11.9560	−	1.04601i	−0.396992	−	0.0347323i	−0.113088	−	0.993585i	$-0.536074\pi$
$907$	−11.9560	−	1.04601i	−0.396992	−	0.0347323i	−0.283904	+	0.958853i	$0.591630\pi$
$908$	53.0080	+	16.5402i	1.75913	+	0.548906i
$909$	50.4607	−	8.89758i	1.67367	−	0.295114i
$910$	−1.27603	+	6.22676i	−0.0422999	+	0.206415i
$911$		−	38.2598i		−	1.26760i	−0.773495	−	0.633802i	$-0.781493\pi$
$911$		−	38.2598i		−	1.26760i	0.773495	−	0.633802i	$-0.218507\pi$
$912$	−44.1639	+	29.7460i	−1.46241	+	0.984988i
$913$	1.59897	+	1.59897i	0.0529183	+	0.0529183i
$914$	−18.3906	+	30.4087i	−0.608308	+	1.00583i
$915$	−4.92385	−	8.67328i	−0.162777	−	0.286730i
$916$	−5.85950	−	11.1747i	−0.193603	−	0.369223i
$917$	−0.284836	+	3.25569i	−0.00940612	+	0.107512i
$918$	−31.6098	−	71.5500i	−1.04328	−	2.36150i
$919$	−7.10139	+	12.3000i	−0.234253	+	0.405739i	−0.959055	−	0.283219i	$-0.908598\pi$
$919$	−7.10139	+	12.3000i	−0.234253	+	0.405739i	0.724802	+	0.688957i	$0.241931\pi$
$920$	−17.9914	+	32.5770i	−0.593159	+	1.07403i
$921$	47.8368	−	17.4112i	1.57628	−	0.573718i
$922$	1.30552	−	1.78607i	0.0429951	−	0.0588211i
$923$	16.7887	+	4.49853i	0.552608	+	0.148071i
$924$	10.4274	−	8.05064i	0.343038	−	0.264847i
$925$	8.26994	−	29.1621i	0.271914	−	0.958843i
$926$	−26.6415	−	48.3903i	−0.875494	−	1.59020i
$927$	−6.96847	−	79.6499i	−0.228875	−	2.61605i
$928$	38.8438	+	0.558689i	1.27511	+	0.0183399i
$929$	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	$0.0337606\pi$
$930$	28.6998	+	21.2997i	0.941104	+	0.698443i
$931$	20.5454	−	19.5794i	0.673349	−	0.641690i
$932$	−46.1316	+	19.2693i	−1.51109	+	0.631185i
$933$	−10.5729	−	22.6738i	−0.346143	−	0.742305i
$934$	0.529707	−	26.0523i	0.0173326	−	0.852456i
$935$	−13.0984	+	35.1900i	−0.428365	+	1.15084i
$936$	51.1030	−	5.82749i	1.67035	−	0.190478i
$937$	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	$0.609289\pi$
$938$	−15.3764	+	1.03078i	−0.502056	+	0.0336563i
$939$	18.1381	+	31.4161i	0.591914	+	1.02523i
$940$	42.0790	−	13.0692i	1.37247	−	0.426270i
$941$	−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	$0.438934\pi$
$942$	24.9191	−	50.7209i	0.811908	−	1.65258i
$943$	0.242902	+	0.906522i	0.00790997	+	0.0295204i
$944$	12.9530	−	9.18508i	0.421584	−	0.298949i
$945$	−3.99987	−	15.3736i	−0.130116	−	0.500104i
$946$	6.96521	+	8.65209i	0.226459	+	0.281304i
$947$	14.1992	−	20.2785i	0.461412	−	0.658964i	−0.519262	−	0.854615i	$-0.673793\pi$
$947$	14.1992	−	20.2785i	0.461412	−	0.658964i	0.980674	+	0.195651i	$0.0626819\pi$
$948$	1.11640	+	23.9361i	0.0362589	+	0.777407i
$949$		−	14.5083i		−	0.470960i
$950$	16.9564	−	25.7387i	0.550138	−	0.835074i
$951$			58.6249i			1.90104i
$952$	1.59064	−	10.6503i	0.0515531	−	0.345180i
$953$	−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	$0.237363\pi$
$954$	−77.8916	+	62.7053i	−2.52183	+	2.03016i
$955$	0.399704	+	1.53628i	0.0129341	+	0.0497128i
$956$	−5.98144	−	3.78564i	−0.193454	−	0.122436i
$957$	16.7420	+	62.4819i	0.541192	+	2.01975i
$958$	51.2026	+	25.1557i	1.65428	+	0.812745i
$959$	−7.77733	+	2.83072i	−0.251143	+	0.0914086i
$960$	25.1453	−	48.4996i	0.811562	−	1.56532i
$961$	−8.65207	−	14.9858i	−0.279099	−	0.483414i
$962$	−1.64831	−	24.5881i	−0.0531436	−	0.792752i
$963$	−15.2392	−	21.7638i	−0.491075	−	0.701328i
$964$	2.93625	+	9.21692i	0.0945701	+	0.296857i
$965$	3.82627	−	10.2796i	0.123172	−	0.330911i
$966$	17.7676	+	0.361260i	0.571665	+	0.0116234i
$967$	−10.7766	−	23.1105i	−0.346552	−	0.743183i	0.653352	−	0.757055i	$-0.273362\pi$
$967$	−10.7766	−	23.1105i	−0.346552	−	0.743183i	−0.999904	+	0.0138711i	$0.995585\pi$
$968$	−0.838945	−	4.12149i	−0.0269647	−	0.132470i
$969$	−72.3307	+	4.57715i	−2.32360	+	0.147039i
$970$	−4.25866	+	5.73825i	−0.136737	+	0.184244i
$971$	−10.1897	+	27.9960i	−0.327003	+	0.898434i	0.661863	+	0.749625i	$0.269766\pi$
$971$	−10.1897	+	27.9960i	−0.327003	+	0.898434i	−0.988866	+	0.148809i	$0.952456\pi$
$972$	−10.6229	+	6.81201i	−0.340729	+	0.218495i
$973$	0.512523	+	5.85817i	0.0164307	+	0.187804i
$974$	14.6886	−	8.08686i	0.470652	−	0.259120i
$975$	−38.3250	+	21.3906i	−1.22738	+	0.685046i
$976$	−5.63383	+	1.54555i	−0.180334	+	0.0494719i
$977$	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	$0.463690\pi$
$978$	60.1835	+	43.9909i	1.92446	+	1.40667i
$979$	34.0025	−	12.3759i	1.08672	−	0.395535i
$980$	−8.87507	+	27.7326i	−0.283504	+	0.885884i
$981$	−10.8189	+	18.7388i	−0.345420	+	0.598284i
$982$	24.9090	−	11.0044i	0.794877	−	0.351166i
$983$	1.68910	−	19.3065i	0.0538738	−	0.615781i	−0.920484	−	0.390779i	$-0.872206\pi$
$983$	1.68910	−	19.3065i	0.0538738	−	0.615781i	0.974358	−	0.225002i	$-0.0722388\pi$
$984$	−0.391416	−	1.32092i	−0.0124779	−	0.0421095i
$985$	4.64136	+	8.17567i	0.147886	+	0.260499i
$986$	45.2452	+	27.3635i	1.44090	+	0.871431i
$987$	−14.8782	−	14.8782i	−0.473578	−	0.473578i
$988$	5.93837	−	24.3441i	0.188925	−	0.774489i
$989$			14.9839i			0.476460i
$990$	60.4496	+	12.3877i	1.92121	+	0.393708i
$991$	−41.0625	+	7.24043i	−1.30439	+	0.230000i	−0.782308	−	0.622892i	$-0.785957\pi$
$991$	−41.0625	+	7.24043i	−1.30439	+	0.230000i	−0.522087	+	0.852892i	$0.674846\pi$
$992$	16.2289	−	13.2246i	0.515268	−	0.419882i
$993$	58.5152	+	5.11941i	1.85692	+	0.162460i
$994$	−5.57670	−	2.15912i	−0.176882	−	0.0684832i
$995$	−4.64433	+	3.20196i	−0.147235	+	0.101509i
$996$	−0.597705	−	4.43799i	−0.0189390	−	0.140623i
$997$	−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	$0.970658\pi$
$998$	−21.0138	+	28.7487i	−0.665179	+	0.910025i
$999$	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.23.6	✓	672
4.3	odd	2	inner	380.2.bj.a.23.11	yes	672
5.2	odd	4	inner	380.2.bj.a.327.24	yes	672
19.5	even	9	inner	380.2.bj.a.43.19	yes	672
20.7	even	4	inner	380.2.bj.a.327.19	yes	672
76.43	odd	18	inner	380.2.bj.a.43.24	yes	672
95.62	odd	36	inner	380.2.bj.a.347.11	yes	672
380.347	even	36	inner	380.2.bj.a.347.6	yes	672

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

\(f(q)\)	\(=\)	\(q+(-1.37318 + 0.338181i) q^{2} +(2.50164 + 1.75167i) q^{3} +(1.77127 - 0.928769i) q^{4} +(2.16402 - 0.563029i) q^{5} +(-4.02760 - 1.55936i) q^{6} +(-0.675461 + 0.180989i) q^{7} +(-2.11818 + 1.87438i) q^{8} +(2.16382 + 5.94503i) q^{9} +O(q^{10})\)	\(q+(-1.37318 + 0.338181i) q^{2} +(2.50164 + 1.75167i) q^{3} +(1.77127 - 0.928769i) q^{4} +(2.16402 - 0.563029i) q^{5} +(-4.02760 - 1.55936i) q^{6} +(-0.675461 + 0.180989i) q^{7} +(-2.11818 + 1.87438i) q^{8} +(2.16382 + 5.94503i) q^{9} +(-2.78120 + 1.50497i) q^{10} +(-2.67109 + 1.54215i) q^{11} +(6.05798 + 0.779227i) q^{12} +(-2.35452 + 1.64865i) q^{13} +(0.866325 - 0.476959i) q^{14} +(6.39986 + 2.38216i) q^{15} +(2.27478 - 3.29020i) q^{16} +(4.93433 - 2.30092i) q^{17} +(-4.98181 - 7.43186i) q^{18} +(-4.23631 + 1.02651i) q^{19} +(3.31014 - 3.00715i) q^{20} +(-2.00680 - 0.730414i) q^{21} +(3.14637 - 3.02097i) q^{22} +(5.86180 - 0.512841i) q^{23} +(-8.58224 + 0.978670i) q^{24} +(4.36600 - 2.43682i) q^{25} +(2.67565 - 3.06016i) q^{26} +(-2.62938 + 9.81300i) q^{27} +(-1.02833 + 0.947928i) q^{28} +(-2.34879 - 6.45324i) q^{29} +(-9.59378 - 1.10683i) q^{30} +(-3.20498 - 1.85040i) q^{31} +(-2.01101 + 5.28733i) q^{32} +(-9.38346 - 0.820946i) q^{33} +(-5.99762 + 4.82828i) q^{34} +(-1.35981 + 0.771969i) q^{35} +(9.35426 + 8.52056i) q^{36} +(4.28677 - 4.28677i) q^{37} +(5.47008 - 2.84222i) q^{38} -8.77807 q^{39} +(-3.52847 + 5.24880i) q^{40} +(0.0276960 + 0.157072i) q^{41} +(3.00271 + 0.324333i) q^{42} +(-0.221939 + 2.53677i) q^{43} +(-3.29891 + 5.21239i) q^{44} +(8.02977 + 11.6469i) q^{45} +(-7.87590 + 2.68658i) q^{46} +(8.92943 + 4.16386i) q^{47} +(11.4540 - 4.24624i) q^{48} +(-5.63869 + 3.25550i) q^{49} +(-5.17123 + 4.82269i) q^{50} +(16.3744 + 2.88725i) q^{51} +(-2.63927 + 5.10701i) q^{52} +(-0.974074 - 11.1337i) q^{53} +(0.292061 - 14.3643i) q^{54} +(-4.91202 + 4.84116i) q^{55} +(1.09151 - 1.64944i) q^{56} +(-12.3958 - 4.85266i) q^{57} +(5.40768 + 8.06717i) q^{58} +(3.73037 + 1.35774i) q^{59} +(13.5483 - 1.72455i) q^{60} +(-1.11880 - 0.938789i) q^{61} +(5.02679 + 1.45707i) q^{62} +(-2.53756 - 3.62401i) q^{63} +(0.973407 - 7.94056i) q^{64} +(-4.16700 + 4.89339i) q^{65} +(13.1628 - 2.04600i) q^{66} +(-14.1231 - 6.58573i) q^{67} +(6.60300 - 8.65839i) q^{68} +(15.5625 + 8.98500i) q^{69} +(1.60621 - 1.51992i) q^{70} +(-3.88690 - 4.63223i) q^{71} +(-15.7266 - 8.53686i) q^{72} +(-2.89514 + 4.13469i) q^{73} +(-4.43682 + 7.33622i) q^{74} +(15.1907 + 1.55173i) q^{75} +(-6.55024 + 5.75276i) q^{76} +(1.52510 - 1.52510i) q^{77} +(12.0539 - 2.96858i) q^{78} +(0.681245 + 3.86353i) q^{79} +(3.07019 - 8.40083i) q^{80} +(-9.22761 + 7.74289i) q^{81} +(-0.0911505 - 0.206323i) q^{82} +(-0.189756 - 0.708179i) q^{83} +(-4.23296 + 0.570091i) q^{84} +(9.38253 - 7.75741i) q^{85} +(-0.553125 - 3.55851i) q^{86} +(5.42812 - 20.2580i) q^{87} +(2.76728 - 8.27320i) q^{88} +(-11.5536 - 2.03722i) q^{89} +(-14.9651 - 13.2778i) q^{90} +(1.29200 - 1.53974i) q^{91} +(9.90651 - 6.35264i) 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} +(6.64201 - 6.37729i) 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

Introduction

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