LMFDB - Embedded newform 273.2.bh.a.248.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			248.10
Character	$\chi$	$=$	273.248
Dual form			273.2.bh.a.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09109 + 0.629943i) q^{2} +(-1.60797 - 0.643773i) q^{3} +(-0.206343 + 0.357397i) q^{4} +(-2.03837 - 3.53057i) q^{5} +(2.15998 - 0.310511i) q^{6} +(-1.74546 + 1.98831i) q^{7} -3.03971i q^{8} +(2.17111 + 2.07033i) q^{9} +O(q^{10})$	\(q+(-1.09109 + 0.629943i) q^{2} +(-1.60797 - 0.643773i) q^{3} +(-0.206343 + 0.357397i) q^{4} +(-2.03837 - 3.53057i) q^{5} +(2.15998 - 0.310511i) q^{6} +(-1.74546 + 1.98831i) q^{7} -3.03971i q^{8} +(2.17111 + 2.07033i) q^{9} +(4.44811 + 2.56812i) q^{10} +(3.44076 + 1.98652i) q^{11} +(0.561875 - 0.441844i) q^{12} +1.00000i q^{13} +(0.651937 - 3.26897i) q^{14} +(1.00475 + 6.98929i) q^{15} +(1.50216 + 2.60182i) q^{16} +(-2.62470 + 4.54611i) q^{17} +(-3.67308 - 0.891248i) q^{18} +(5.30173 - 3.06096i) q^{19} +1.68242 q^{20} +(4.08666 - 2.07346i) q^{21} -5.00559 q^{22} +(0.414985 - 0.239592i) q^{23} +(-1.95688 + 4.88775i) q^{24} +(-5.80994 + 10.0631i) q^{25} +(-0.629943 - 1.09109i) q^{26} +(-2.15825 - 4.72673i) q^{27} +(-0.350452 - 1.03410i) q^{28} +1.78061i q^{29} +(-5.49913 - 6.99303i) q^{30} +(4.02710 + 2.32505i) q^{31} +(1.98694 + 1.14716i) q^{32} +(-4.25375 - 5.40933i) q^{33} -6.61365i q^{34} +(10.5778 + 2.10954i) q^{35} +(-1.18792 + 0.348750i) q^{36} +(2.92747 + 5.07053i) q^{37} +(-3.85646 + 6.67958i) q^{38} +(0.643773 - 1.60797i) q^{39} +(-10.7319 + 6.19607i) q^{40} -1.16060 q^{41} +(-3.15277 + 4.83670i) q^{42} +5.39213 q^{43} +(-1.41995 + 0.819811i) q^{44} +(2.88391 - 11.8854i) q^{45} +(-0.301858 + 0.522834i) q^{46} +(0.613160 + 1.06202i) q^{47} +(-0.740442 - 5.15068i) q^{48} +(-0.906749 - 6.94102i) q^{49} -14.6397i q^{50} +(7.14710 - 5.62029i) q^{51} +(-0.357397 - 0.206343i) q^{52} +(-1.04632 - 0.604090i) q^{53} +(5.33242 + 3.79773i) q^{54} -16.1971i q^{55} +(6.04389 + 5.30569i) q^{56} +(-10.4956 + 1.50880i) q^{57} +(-1.12168 - 1.94281i) q^{58} +(0.358619 - 0.621146i) q^{59} +(-2.70527 - 1.08310i) q^{60} +(0.520590 - 0.300563i) q^{61} -5.85859 q^{62} +(-7.90605 + 0.703165i) q^{63} -8.89922 q^{64} +(3.53057 - 2.03837i) q^{65} +(8.04881 + 3.22246i) q^{66} +(-2.10955 + 3.65385i) q^{67} +(-1.08318 - 1.87612i) q^{68} +(-0.821525 + 0.118099i) q^{69} +(-12.8702 + 4.36168i) q^{70} +2.72226i q^{71} +(6.29321 - 6.59955i) q^{72} +(9.05584 + 5.22839i) q^{73} +(-6.38829 - 3.68828i) q^{74} +(15.8206 - 12.4409i) q^{75} +2.52643i q^{76} +(-9.95552 + 3.37390i) q^{77} +(0.310511 + 2.15998i) q^{78} +(-0.460495 - 0.797600i) q^{79} +(6.12392 - 10.6069i) q^{80} +(0.427455 + 8.98984i) q^{81} +(1.26633 - 0.731115i) q^{82} -6.85477 q^{83} +(-0.102208 + 1.88840i) q^{84} +21.4005 q^{85} +(-5.88332 + 3.39673i) q^{86} +(1.14631 - 2.86316i) q^{87} +(6.03845 - 10.4589i) q^{88} +(1.74131 + 3.01603i) q^{89} +(4.34049 + 14.7847i) q^{90} +(-1.98831 - 1.74546i) q^{91} +0.197752i q^{92} +(-4.97864 - 6.33114i) q^{93} +(-1.33803 - 0.772511i) q^{94} +(-21.6138 - 12.4787i) q^{95} +(-2.45642 - 3.12374i) q^{96} +6.17977i q^{97} +(5.36180 + 7.00211i) q^{98} +(3.35751 + 11.4365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.09109	+	0.629943i	−0.771520	+	0.445437i	−0.833416	−	0.552645i	$-0.813618\pi$
$2$	−1.09109	+	0.629943i	−0.771520	+	0.445437i	0.0618968	+	0.998083i	$0.480285\pi$
$3$	−1.60797	−	0.643773i	−0.928360	−	0.371683i
$3$	−1.60797	−	0.643773i	−0.928360	−	0.371683i
$4$	−0.206343	+	0.357397i	−0.103172	+	0.178698i
$5$	−2.03837	−	3.53057i	−0.911589	−	1.57892i	−0.811820	−	0.583907i	$-0.801523\pi$
$5$	−2.03837	−	3.53057i	−0.911589	−	1.57892i	−0.0997684	−	0.995011i	$-0.531810\pi$
$6$	2.15998	−	0.310511i	0.881809	−	0.126765i
$7$	−1.74546	+	1.98831i	−0.659721	+	0.751510i
$7$	−1.74546	+	1.98831i	−0.659721	+	0.751510i
$8$		−	3.03971i		−	1.07470i
$9$	2.17111	+	2.07033i	0.723704	+	0.690111i
$10$	4.44811	+	2.56812i	1.40662	+	0.812111i
$11$	3.44076	+	1.98652i	1.03743	+	0.598959i	0.919104	−	0.394016i	$-0.128915\pi$
$11$	3.44076	+	1.98652i	1.03743	+	0.598959i	0.118324	+	0.992975i	$0.462248\pi$
$12$	0.561875	−	0.441844i	0.162199	−	0.127549i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.651937	−	3.26897i	0.174237	−	0.873669i
$15$	1.00475	+	6.98929i	0.259426	+	1.80463i
$16$	1.50216	+	2.60182i	0.375540	+	0.650454i
$17$	−2.62470	+	4.54611i	−0.636583	+	1.10259i	0.349594	+	0.936901i	$0.386319\pi$
$17$	−2.62470	+	4.54611i	−0.636583	+	1.10259i	−0.986177	+	0.165693i	$0.947014\pi$
$18$	−3.67308	−	0.891248i	−0.865753	−	0.210069i
$19$	5.30173	−	3.06096i	1.21630	−	0.702231i	0.252176	−	0.967681i	$-0.418854\pi$
$19$	5.30173	−	3.06096i	1.21630	−	0.702231i	0.964125	+	0.265450i	$0.0855206\pi$
$20$	1.68242			0.376200
$21$	4.08666	−	2.07346i	0.891782	−	0.452465i
$22$	−5.00559			−1.06719
$23$	0.414985	−	0.239592i	0.0865303	−	0.0499583i	−0.456110	−	0.889923i	$-0.650758\pi$
$23$	0.414985	−	0.239592i	0.0865303	−	0.0499583i	0.542641	+	0.839965i	$0.317424\pi$
$24$	−1.95688	+	4.88775i	−0.399447	+	0.997708i
$25$	−5.80994	+	10.0631i	−1.16199	+	2.01262i
$26$	−0.629943	−	1.09109i	−0.123542	−	0.213981i
$27$	−2.15825	−	4.72673i	−0.415356	−	0.909659i
$28$	−0.350452	−	1.03410i	−0.0662292	−	0.195426i
$29$			1.78061i			0.330651i	0.986239	+	0.165326i	$0.0528675\pi$
$29$			1.78061i			0.330651i	−0.986239	+	0.165326i	$0.947133\pi$
$30$	−5.49913	−	6.99303i	−1.00400	−	1.27675i
$31$	4.02710	+	2.32505i	0.723289	+	0.417591i	0.815962	−	0.578106i	$-0.196208\pi$
$31$	4.02710	+	2.32505i	0.723289	+	0.417591i	−0.0926732	+	0.995697i	$0.529541\pi$
$32$	1.98694	+	1.14716i	0.351245	+	0.202791i
$33$	−4.25375	−	5.40933i	−0.740483	−	0.941644i
$34$		−	6.61365i		−	1.13423i
$35$	10.5778	+	2.10954i	1.78797	+	0.356577i
$36$	−1.18792	+	0.348750i	−0.197987	+	0.0581250i
$37$	2.92747	+	5.07053i	0.481273	+	0.833590i	0.999769	−	0.0214906i	$-0.00684119\pi$
$37$	2.92747	+	5.07053i	0.481273	+	0.833590i	−0.518496	+	0.855080i	$0.673508\pi$
$38$	−3.85646	+	6.67958i	−0.625600	+	1.08357i
$39$	0.643773	−	1.60797i	0.103086	−	0.257481i
$40$	−10.7319	+	6.19607i	−1.69686	+	0.979684i
$41$	−1.16060			−0.181256			−0.0906280	−	0.995885i	$-0.528887\pi$
$41$	−1.16060			−0.181256			−0.0906280	+	0.995885i	$0.528887\pi$
$42$	−3.15277	+	4.83670i	−0.486483	+	0.746319i
$43$	5.39213			0.822292			0.411146	−	0.911570i	$-0.365129\pi$
$43$	5.39213			0.822292			0.411146	+	0.911570i	$0.365129\pi$
$44$	−1.41995	+	0.819811i	−0.214066	+	0.123591i
$45$	2.88391	−	11.8854i	0.429908	−	1.77177i
$46$	−0.301858	+	0.522834i	−0.0445066	+	0.0770876i
$47$	0.613160	+	1.06202i	0.0894385	+	0.154912i	0.907274	−	0.420540i	$-0.138159\pi$
$47$	0.613160	+	1.06202i	0.0894385	+	0.154912i	−0.817835	+	0.575452i	$0.804826\pi$
$48$	−0.740442	−	5.15068i	−0.106874	−	0.743437i
$49$	−0.906749	−	6.94102i	−0.129536	−	0.991575i
$50$		−	14.6397i		−	2.07037i
$51$	7.14710	−	5.62029i	1.00079	−	0.786997i
$52$	−0.357397	−	0.206343i	−0.0495620	−	0.0286147i
$53$	−1.04632	−	0.604090i	−0.143722	−	0.0829782i	0.426414	−	0.904528i	$-0.359777\pi$
$53$	−1.04632	−	0.604090i	−0.143722	−	0.0829782i	−0.570137	+	0.821550i	$0.693110\pi$
$54$	5.33242	+	3.79773i	0.725651	+	0.516805i
$55$		−	16.1971i		−	2.18402i
$56$	6.04389	+	5.30569i	0.807648	+	0.709002i
$57$	−10.4956	+	1.50880i	−1.39017	+	0.199846i
$58$	−1.12168	−	1.94281i	−0.147284	−	0.255104i
$59$	0.358619	−	0.621146i	0.0466882	−	0.0808663i	−0.841737	−	0.539888i	$-0.818467\pi$
$59$	0.358619	−	0.621146i	0.0466882	−	0.0808663i	0.888425	+	0.459022i	$0.151800\pi$
$60$	−2.70527	−	1.08310i	−0.349249	−	0.139827i
$61$	0.520590	−	0.300563i	0.0666547	−	0.0384831i	−0.466302	−	0.884625i	$-0.654414\pi$
$61$	0.520590	−	0.300563i	0.0666547	−	0.0384831i	0.532957	+	0.846142i	$0.321081\pi$
$62$	−5.85859			−0.744042
$63$	−7.90605	+	0.703165i	−0.996068	+	0.0885904i
$64$	−8.89922			−1.11240
$65$	3.53057	−	2.03837i	0.437913	−	0.252829i
$66$	8.04881	+	3.22246i	0.990741	+	0.396658i
$67$	−2.10955	+	3.65385i	−0.257723	+	0.446389i	−0.965631	−	0.259915i	$-0.916305\pi$
$67$	−2.10955	+	3.65385i	−0.257723	+	0.446389i	0.707909	+	0.706304i	$0.249639\pi$
$68$	−1.08318	−	1.87612i	−0.131355	−	0.227513i
$69$	−0.821525	+	0.118099i	−0.0988999	+	0.0142175i
$70$	−12.8702	+	4.36168i	−1.53829	+	0.521321i
$71$			2.72226i			0.323073i	0.986867	+	0.161537i	$0.0516450\pi$
$71$			2.72226i			0.323073i	−0.986867	+	0.161537i	$0.948355\pi$
$72$	6.29321	−	6.59955i	0.741662	−	0.777765i
$73$	9.05584	+	5.22839i	1.05991	+	0.611937i	0.925406	−	0.378977i	$-0.123724\pi$
$73$	9.05584	+	5.22839i	1.05991	+	0.611937i	0.134500	+	0.990914i	$0.457057\pi$
$74$	−6.38829	−	3.68828i	−0.742623	−	0.428754i
$75$	15.8206	−	12.4409i	1.82680	−	1.43655i
$76$			2.52643i			0.289801i
$77$	−9.95552	+	3.37390i	−1.13454	+	0.384492i
$78$	0.310511	+	2.15998i	0.0351584	+	0.244570i
$79$	−0.460495	−	0.797600i	−0.0518097	−	0.0897371i	0.838957	−	0.544197i	$-0.183166\pi$
$79$	−0.460495	−	0.797600i	−0.0518097	−	0.0897371i	−0.890767	+	0.454460i	$0.849832\pi$
$80$	6.12392	−	10.6069i	0.684675	−	1.18589i
$81$	0.427455	+	8.98984i	0.0474950	+	0.998871i
$82$	1.26633	−	0.731115i	0.139843	−	0.0807381i
$83$	−6.85477			−0.752409			−0.376204	−	0.926537i	$-0.622771\pi$
$83$	−6.85477			−0.752409			−0.376204	+	0.926537i	$0.622771\pi$
$84$	−0.102208	+	1.88840i	−0.0111518	+	0.206042i
$85$	21.4005			2.32121
$86$	−5.88332	+	3.39673i	−0.634414	+	0.366279i
$87$	1.14631	−	2.86316i	0.122897	−	0.306963i
$88$	6.03845	−	10.4589i	0.643701	−	1.11492i
$89$	1.74131	+	3.01603i	0.184578	+	0.319698i	0.943434	−	0.331560i	$-0.107575\pi$
$89$	1.74131	+	3.01603i	0.184578	+	0.319698i	−0.758856	+	0.651258i	$0.774242\pi$
$90$	4.34049	+	14.7847i	0.457528	+	1.55845i
$91$	−1.98831	−	1.74546i	−0.208431	−	0.182974i
$92$			0.197752i			0.0206171i
$93$	−4.97864	−	6.33114i	−0.516261	−	0.656509i
$94$	−1.33803	−	0.772511i	−0.138007	−	0.0796785i
$95$	−21.6138	−	12.4787i	−2.21753	−	1.28029i
$96$	−2.45642	−	3.12374i	−0.250708	−	0.318815i
$97$			6.17977i			0.627461i	0.949512	+	0.313730i	$0.101579\pi$
$97$			6.17977i			0.627461i	−0.949512	+	0.313730i	$0.898421\pi$
$98$	5.36180	+	7.00211i	0.541623	+	0.707319i
$99$	3.35751	+	11.4365i	0.337443	+	1.14941i
$100$	−2.39768	−	4.15291i	−0.239768	−	0.415291i
$101$	−7.53077	+	13.0437i	−0.749339	+	1.29789i	0.198800	+	0.980040i	$0.436296\pi$
$101$	−7.53077	+	13.0437i	−0.749339	+	1.29789i	−0.948140	+	0.317854i	$0.897038\pi$
$102$	−4.25769	+	10.6345i	−0.421574	+	1.05297i
$103$	−1.60002	+	0.923774i	−0.157655	+	0.0910222i	−0.576752	−	0.816919i	$-0.695680\pi$
$103$	−1.60002	+	0.923774i	−0.157655	+	0.0910222i	0.419097	+	0.907941i	$0.362347\pi$
$104$	3.03971			0.298068
$105$	−15.6506	−	10.2017i	−1.52734	−	0.995589i
$106$	1.52217			0.147846
$107$	10.6443	−	6.14548i	1.02902	−	0.594106i	0.112318	−	0.993672i	$-0.464173\pi$
$107$	10.6443	−	6.14548i	1.02902	−	0.594106i	0.916704	+	0.399566i	$0.130839\pi$
$108$	2.13466	+	0.203976i	0.205408	+	0.0196276i
$109$	1.25798	−	2.17888i	0.120493	−	0.208699i	−0.799469	−	0.600707i	$-0.794886\pi$
$109$	1.25798	−	2.17888i	0.120493	−	0.208699i	0.919962	+	0.392008i	$0.128219\pi$
$110$	10.2033	+	17.6726i	0.972842	+	1.68501i
$111$	−1.44300	−	10.0379i	−0.136964	−	0.952752i
$112$	−7.79517	−	1.55460i	−0.736574	−	0.146896i
$113$			11.4708i			1.07908i	0.841961	+	0.539539i	$0.181401\pi$
$113$			11.4708i			1.07908i	−0.841961	+	0.539539i	$0.818599\pi$
$114$	10.5012	−	8.25785i	0.983526	−	0.773419i
$115$	−1.69179	−	0.976755i	−0.157760	−	0.0910829i
$116$	−0.636385	−	0.367417i	−0.0590869	−	0.0341138i
$117$	−2.07033	+	2.17111i	−0.191402	+	0.200719i
$118$			0.903637i			0.0831865i
$119$	−4.45778	−	13.1538i	−0.408644	−	1.20580i
$120$	21.2454	−	3.05416i	1.93943	−	0.278805i
$121$	2.39255	+	4.14401i	0.217504	+	0.376728i
$122$	−0.378675	+	0.655884i	−0.0342836	+	0.0593809i
$123$	1.86621	+	0.747166i	0.168271	+	0.0673697i
$124$	−1.66193	+	0.959516i	−0.149246	+	0.0861670i
$125$	26.9876			2.41384
$126$	8.18328	−	5.74758i	0.729025	−	0.512035i
$127$	−9.67428			−0.858454			−0.429227	−	0.903197i	$-0.641214\pi$
$127$	−9.67428			−0.858454			−0.429227	+	0.903197i	$0.641214\pi$
$128$	5.73600	−	3.31168i	0.506995	−	0.292714i
$129$	−8.67036	−	3.47131i	−0.763383	−	0.305632i
$130$	−2.56812	+	4.44811i	−0.225239	+	0.390125i
$131$	11.0042	+	19.0598i	0.961438	+	1.66526i	0.718896	+	0.695118i	$0.244648\pi$
$131$	11.0042	+	19.0598i	0.961438	+	1.66526i	0.242542	+	0.970141i	$0.422019\pi$
$132$	2.81101	−	0.404100i	0.244667	−	0.0351724i
$133$	−3.16782	+	15.8842i	−0.274685	+	1.37734i
$134$		−	5.31559i		−	0.459197i
$135$	−12.2887	+	17.2547i	−1.05764	+	1.48505i
$136$	13.8189	+	7.97833i	1.18496	+	0.684136i
$137$	10.4974	+	6.06070i	0.896857	+	0.517801i	0.876179	−	0.481985i	$-0.160084\pi$
$137$	10.4974	+	6.06070i	0.896857	+	0.517801i	0.0206780	+	0.999786i	$0.493418\pi$
$138$	0.821964	−	0.646371i	0.0699703	−	0.0550228i
$139$			17.8189i			1.51138i	0.654932	+	0.755688i	$0.272697\pi$
$139$			17.8189i			1.51138i	−0.654932	+	0.755688i	$0.727303\pi$
$140$	−2.93659	+	3.34517i	−0.248187	+	0.282718i
$141$	−0.302238	−	2.10243i	−0.0254530	−	0.177057i
$142$	−1.71487	−	2.97024i	−0.143909	−	0.249257i
$143$	−1.98652	+	3.44076i	−0.166121	+	0.287731i
$144$	−2.12527	+	8.75880i	−0.177105	+	0.729900i
$145$	6.28657	−	3.62955i	0.522071	−	0.301418i
$146$	−13.1744			−1.09032
$147$	−3.01042	+	11.7447i	−0.248295	+	0.968684i
$148$	−2.41625			−0.198615
$149$	−15.8649	+	9.15960i	−1.29970	+	0.750384i	−0.980353	−	0.197253i	$-0.936798\pi$
$149$	−15.8649	+	9.15960i	−1.29970	+	0.750384i	−0.319350	+	0.947637i	$0.603465\pi$
$150$	−9.42467	+	23.5402i	−0.769521	+	1.92205i
$151$	11.2801	−	19.5377i	0.917963	−	1.58996i	0.115458	−	0.993312i	$-0.463167\pi$
$151$	11.2801	−	19.5377i	0.917963	−	1.58996i	0.802505	−	0.596645i	$-0.203500\pi$
$152$	−9.30442	−	16.1157i	−0.754688	−	1.30716i
$153$	−15.1105	+	4.43612i	−1.22161	+	0.358639i
$154$	8.73704	−	9.95265i	0.704051	−	0.802008i
$155$		−	18.9573i		−	1.52268i
$156$	0.441844	+	0.561875i	0.0353758	+	0.0449860i
$157$	−11.4626	−	6.61791i	−0.914812	−	0.528167i	−0.0328357	−	0.999461i	$-0.510454\pi$
$157$	−11.4626	−	6.61791i	−0.914812	−	0.528167i	−0.881976	+	0.471294i	$0.843787\pi$
$158$	1.00489	+	0.580171i	0.0799444	+	0.0461559i
$159$	1.29354	+	1.64495i	0.102585	+	0.130453i
$160$		−	9.35338i		−	0.739449i
$161$	−0.247957	+	1.24332i	−0.0195417	+	0.0979870i
$162$	−6.12948	−	9.53949i	−0.481578	−	0.749493i
$163$	4.77942	+	8.27820i	0.374353	+	0.648399i	0.990230	−	0.139444i	$-0.0445314\pi$
$163$	4.77942	+	8.27820i	0.374353	+	0.648399i	−0.615877	+	0.787842i	$0.711198\pi$
$164$	0.239483	−	0.414796i	0.0187005	−	0.0323902i
$165$	−10.4273	+	26.0444i	−0.811762	+	2.02755i
$166$	7.47920	−	4.31812i	0.580498	−	0.335151i
$167$	4.50777			0.348822			0.174411	−	0.984673i	$-0.444198\pi$
$167$	4.50777			0.348822			0.174411	+	0.984673i	$0.444198\pi$
$168$	−6.30270	−	12.4223i	−0.486264	−	0.958398i
$169$	−1.00000			−0.0769231
$170$	−23.3499	+	13.4811i	−1.79086	+	1.03395i
$171$	17.8478	+	4.33066i	1.36486	+	0.331174i
$172$	−1.11263	+	1.92713i	−0.0848371	+	0.146942i
$173$	−7.18061	−	12.4372i	−0.545931	−	0.945581i	−0.998548	−	0.0538756i	$-0.982843\pi$
$173$	−7.18061	−	12.4372i	−0.545931	−	0.945581i	0.452616	−	0.891705i	$-0.350491\pi$
$174$	0.552899	+	3.84609i	0.0419151	+	0.291571i
$175$	−9.86757	−	29.1167i	−0.745918	−	2.20102i
$176$			11.9363i			0.899732i
$177$	−0.976523	+	0.767912i	−0.0734000	+	0.0577198i
$178$	−3.79985	−	2.19385i	−0.284811	−	0.164436i
$179$	1.71706	+	0.991345i	0.128339	+	0.0740966i	0.562795	−	0.826596i	$-0.309726\pi$
$179$	1.71706	+	0.991345i	0.128339	+	0.0740966i	−0.434456	+	0.900693i	$0.643059\pi$
$180$	3.65272	+	3.48316i	0.272258	+	0.259620i
$181$			0.881907i			0.0655516i	0.999463	+	0.0327758i	$0.0104347\pi$
$181$			0.881907i			0.0655516i	−0.999463	+	0.0327758i	$0.989565\pi$
$182$	3.26897	+	0.651937i	0.242312	+	0.0483248i
$183$	−1.03059	+	0.148153i	−0.0761830	+	0.0109518i
$184$	−0.728289	−	1.26143i	−0.0536902	−	0.0929942i
$185$	11.9346	−	20.6713i	0.877446	−	1.51978i
$186$	9.42042	+	3.77160i	0.690739	+	0.276547i
$187$	−18.0619	+	10.4281i	−1.32082	+	0.762575i
$188$	−0.506085			−0.0369101
$189$	13.1653	+	3.95904i	0.957637	+	0.287977i
$190$	31.4436			2.28116
$191$	4.03878	−	2.33179i	0.292236	−	0.168723i	−0.346714	−	0.937971i	$-0.612702\pi$
$191$	4.03878	−	2.33179i	0.292236	−	0.168723i	0.638950	+	0.769248i	$0.279369\pi$
$192$	14.3096	+	5.72908i	1.03271	+	0.413461i
$193$	2.02530	−	3.50793i	0.145785	−	0.252506i	−0.783881	−	0.620911i	$-0.786763\pi$
$193$	2.02530	−	3.50793i	0.145785	−	0.252506i	0.929665	+	0.368405i	$0.120096\pi$
$194$	−3.89291	−	6.74271i	−0.279494	−	0.484098i
$195$	−6.98929	+	1.00475i	−0.500513	+	0.0719518i
$196$	2.66780	+	1.10816i	0.190557	+	0.0791545i
$197$		−	11.7757i		−	0.838983i	−0.907759	−	0.419492i	$-0.862208\pi$
$197$		−	11.7757i		−	0.838983i	0.907759	−	0.419492i	$-0.137792\pi$
$198$	−10.8677	−	10.3632i	−0.772333	−	0.736482i
$199$	4.71072	+	2.71974i	0.333934	+	0.192797i	0.657586	−	0.753379i	$-0.271577\pi$
$199$	4.71072	+	2.71974i	0.333934	+	0.192797i	−0.323652	+	0.946176i	$0.604911\pi$
$200$	30.5889	+	17.6605i	2.16297	+	1.24879i
$201$	5.74434	−	4.51719i	0.405174	−	0.318618i
$202$		−	18.9758i		−	1.33513i
$203$	−3.54041	−	3.10798i	−0.248488	−	0.218138i
$204$	0.533918	+	3.71406i	0.0373818	+	0.260036i
$205$	2.36575	+	4.09759i	0.165231	+	0.286188i
$206$	1.16385	−	2.01585i	0.0810893	−	0.140451i
$207$	1.39701	+	0.338976i	0.0970991	+	0.0235605i
$208$	−2.60182	+	1.50216i	−0.180403	+	0.104156i
$209$	24.3226			1.68243
$210$	23.5028	+	1.27206i	1.62185	+	0.0877808i
$211$	−3.86835			−0.266308			−0.133154	−	0.991095i	$-0.542510\pi$
$211$	−3.86835			−0.266308			−0.133154	+	0.991095i	$0.542510\pi$
$212$	0.431800	−	0.249300i	0.0296562	−	0.0171220i
$213$	1.75252	−	4.37731i	0.120081	−	0.299928i
$214$	−7.74261	+	13.4106i	−0.529274	+	0.916729i
$215$	−10.9912	−	19.0373i	−0.749592	−	1.29833i
$216$	−14.3679	+	6.56046i	−0.977611	+	0.446383i
$217$	−11.6521	+	3.94885i	−0.790993	+	0.268065i
$218$			3.16982i			0.214687i
$219$	−11.1956	−	14.2370i	−0.756528	−	0.962047i
$220$	5.78880	+	3.34216i	0.390281	+	0.225329i
$221$	−4.54611	−	2.62470i	−0.305805	−	0.176556i
$222$	7.89774	+	10.0432i	0.530061	+	0.674058i
$223$		−	11.6117i		−	0.777576i	−0.921327	−	0.388788i	$-0.872894\pi$
$223$		−	11.6117i		−	0.777576i	0.921327	−	0.388788i	$-0.127106\pi$
$224$	−5.74904	+	1.94833i	−0.384124	+	0.130178i
$225$	−33.4480	+	9.81964i	−2.22987	+	0.654643i
$226$	−7.22592	−	12.5157i	−0.480661	−	0.832530i
$227$	11.6549	−	20.1869i	0.773563	−	1.33985i	−0.162035	−	0.986785i	$-0.551806\pi$
$227$	11.6549	−	20.1869i	0.773563	−	1.33985i	0.935598	−	0.353066i	$-0.114861\pi$
$228$	1.62645	−	4.06241i	0.107714	−	0.269040i
$229$	7.91707	−	4.57092i	0.523174	−	0.302055i	−0.215058	−	0.976601i	$-0.568994\pi$
$229$	7.91707	−	4.57092i	0.523174	−	0.302055i	0.738232	+	0.674546i	$0.235661\pi$
$230$	2.46120			0.162287
$231$	18.1802	+	0.983982i	1.19617	+	0.0647413i
$232$	5.41254			0.355351
$233$	7.35834	−	4.24834i	0.482061	−	0.278318i	−0.239214	−	0.970967i	$-0.576890\pi$
$233$	7.35834	−	4.24834i	0.482061	−	0.278318i	0.721275	+	0.692649i	$0.243556\pi$
$234$	0.891248	−	3.67308i	0.0582627	−	0.240117i
$235$	2.49970	−	4.32960i	0.163062	−	0.282432i
$236$	0.147997	+	0.256338i	0.00963378	+	0.0166862i
$237$	0.226986	+	1.57897i	0.0147443	+	0.102565i
$238$	13.1500	+	11.5438i	0.852386	+	0.748276i
$239$			11.1177i			0.719141i	0.933118	+	0.359571i	$0.117077\pi$
$239$			11.1177i			0.719141i	−0.933118	+	0.359571i	$0.882923\pi$
$240$	−16.6755	+	13.1132i	−1.07640	+	0.846453i
$241$	−16.8355	−	9.72000i	−1.08447	−	0.626120i	−0.152372	−	0.988323i	$-0.548691\pi$
$241$	−16.8355	−	9.72000i	−1.08447	−	0.626120i	−0.932099	+	0.362203i	$0.882025\pi$
$242$	−5.22098	−	3.01434i	−0.335617	−	0.193769i
$243$	5.10009	−	14.7305i	0.327171	−	0.944965i
$244$			0.248076i			0.0158815i
$245$	−22.6575	+	17.3497i	−1.44753	+	1.10843i
$246$	−2.50689	+	0.360380i	−0.159833	+	0.0229770i
$247$	3.06096	+	5.30173i	0.194764	+	0.337341i
$248$	7.06747	−	12.2412i	0.448785	−	0.777318i
$249$	11.0222	+	4.41292i	0.698506	+	0.279657i
$250$	−29.4460	+	17.0006i	−1.86233	+	1.07522i
$251$	18.3467			1.15804			0.579018	−	0.815315i	$-0.303436\pi$
$251$	18.3467			1.15804			0.579018	+	0.815315i	$0.303436\pi$
$252$	1.38005	−	2.97069i	0.0869350	−	0.187136i
$253$	1.90382			0.119692
$254$	10.5555	−	6.09425i	0.662314	−	0.382387i
$255$	−34.4113	−	13.7771i	−2.15492	−	0.862753i
$256$	4.72688	−	8.18720i	0.295430	−	0.511700i
$257$	4.97729	+	8.62091i	0.310475	+	0.537758i	0.978465	−	0.206412i	$-0.0661787\pi$
$257$	4.97729	+	8.62091i	0.310475	+	0.537758i	−0.667991	+	0.744170i	$0.732845\pi$
$258$	11.6469	−	1.67431i	0.725104	−	0.104238i
$259$	−15.1916	−	3.02968i	−0.943957	−	0.188255i
$260$			1.68242i			0.104339i
$261$	−3.68646	+	3.86591i	−0.228186	+	0.239294i
$262$	−24.0131	−	13.8640i	−1.48354	−	0.856520i
$263$	−19.3690	−	11.1827i	−1.19434	−	0.689553i	−0.235053	−	0.971983i	$-0.575526\pi$
$263$	−19.3690	−	11.1827i	−1.19434	−	0.689553i	−0.959288	+	0.282429i	$0.908860\pi$
$264$	−16.4428	+	12.9302i	−1.01198	+	0.795798i
$265$			4.92545i			0.302568i
$266$	−6.54978	−	19.3268i	−0.401593	−	1.18500i
$267$	−0.858322	−	5.97068i	−0.0525284	−	0.365400i
$268$	−0.870583	−	1.50789i	−0.0531793	−	0.0921093i
$269$	−14.1909	+	24.5793i	−0.865232	+	1.49863i	0.00158419	+	0.999999i	$0.499496\pi$
$269$	−14.1909	+	24.5793i	−0.865232	+	1.49863i	−0.866816	+	0.498627i	$0.833838\pi$
$270$	2.53866	−	26.5677i	0.154498	−	1.61686i
$271$	5.76746	−	3.32984i	0.350348	−	0.202274i	−0.314490	−	0.949261i	$-0.601834\pi$
$271$	5.76746	−	3.32984i	0.350348	−	0.202274i	0.664839	+	0.746987i	$0.268500\pi$
$272$	−15.7709			−0.956249
$273$	2.07346	+	4.08666i	0.125491	+	0.247336i
$274$	−15.2716			−0.922591
$275$	−39.9812	+	23.0832i	−2.41096	+	1.39197i
$276$	0.127308	−	0.317979i	0.00766302	−	0.0191401i
$277$	4.49155	−	7.77958i	0.269871	−	0.467430i	−0.698957	−	0.715163i	$-0.746352\pi$
$277$	4.49155	−	7.77958i	0.269871	−	0.467430i	0.968828	+	0.247733i	$0.0796857\pi$
$278$	−11.2249	−	19.4420i	−0.673223	−	1.16606i
$279$	3.92967	+	13.3854i	0.235263	+	0.801361i
$280$	6.41239	−	32.1533i	0.383214	−	1.92153i
$281$		−	15.7713i		−	0.940839i	−0.882443	−	0.470420i	$-0.844103\pi$
$281$		−	15.7713i		−	0.940839i	0.882443	−	0.470420i	$-0.155897\pi$
$282$	1.65418	+	2.10356i	0.0985052	+	0.125265i
$283$	11.7661	+	6.79318i	0.699424	+	0.403813i	0.807133	−	0.590370i	$-0.201018\pi$
$283$	11.7661	+	6.79318i	0.699424	+	0.403813i	−0.107709	+	0.994182i	$0.534351\pi$
$284$	−0.972928	−	0.561720i	−0.0577327	−	0.0333320i
$285$	26.7208	+	33.9798i	1.58280	+	2.01279i
$286$		−	5.00559i		−	0.295987i
$287$	2.02579	−	2.30764i	0.119578	−	0.136216i
$288$	1.93887	+	6.60424i	0.114249	+	0.389159i
$289$	−5.27810	−	9.14193i	−0.310476	−	0.537761i
$290$	−4.57282	+	7.92036i	−0.268525	+	0.465100i
$291$	3.97837	−	9.93687i	0.233216	−	0.582509i
$292$	−3.73722	+	2.15769i	−0.218704	+	0.126269i
$293$	−2.31675			−0.135346			−0.0676730	−	0.997708i	$-0.521557\pi$
$293$	−2.31675			−0.135346			−0.0676730	+	0.997708i	$0.521557\pi$
$294$	−4.11382	−	14.7109i	−0.239923	−	0.857959i
$295$	−2.92400			−0.170242
$296$	15.4129	−	8.89866i	0.895859	−	0.517224i
$297$	1.96373	−	20.5509i	0.113947	−	1.19249i
$298$	11.5401	−	19.9880i	0.668498	−	1.15787i
$299$	0.239592	+	0.414985i	0.0138559	+	0.0239992i
$300$	1.18186	+	8.22130i	0.0682348	+	0.474657i
$301$	−9.41173	+	10.7212i	−0.542483	+	0.617961i
$302$			28.4233i			1.63558i
$303$	20.5064	−	16.1257i	1.17806	−	0.926396i
$304$	15.9281	+	9.19608i	0.913538	+	0.527431i
$305$	−2.12231	−	1.22532i	−0.121523	−	0.0701615i
$306$	13.6924	−	14.3590i	0.782745	−	0.820848i
$307$		−	8.37962i		−	0.478250i	−0.970989	−	0.239125i	$-0.923139\pi$
$307$		−	8.37962i		−	0.478250i	0.970989	−	0.239125i	$-0.0768606\pi$
$308$	0.848433	−	4.25425i	0.0483440	−	0.242409i
$309$	3.16749	−	0.455345i	0.180192	−	0.0259037i
$310$	11.9420	+	20.6842i	0.678260	+	1.17478i
$311$	0.605170	−	1.04819i	0.0343161	−	0.0594372i	−0.848357	−	0.529424i	$-0.822408\pi$
$311$	0.605170	−	1.04819i	0.0343161	−	0.0594372i	0.882673	+	0.469987i	$0.155741\pi$
$312$	−4.88775	−	1.95688i	−0.276715	−	0.110787i
$313$	−17.8410	+	10.3005i	−1.00843	+	0.582219i	−0.910733	−	0.412997i	$-0.864482\pi$
$313$	−17.8410	+	10.3005i	−1.00843	+	0.582219i	−0.0977007	+	0.995216i	$0.531149\pi$
$314$	16.6756			0.941061
$315$	18.5981	+	26.4795i	1.04788	+	1.49195i
$316$	0.380080			0.0213812
$317$	23.9486	−	13.8267i	1.34509	−	0.776586i	0.357538	−	0.933899i	$-0.383616\pi$
$317$	23.9486	−	13.8267i	1.34509	−	0.776586i	0.987549	+	0.157312i	$0.0502830\pi$
$318$	−2.44760	−	0.979933i	−0.137255	−	0.0549519i
$319$	−3.53722	+	6.12665i	−0.198047	+	0.343027i
$320$	18.1399	+	31.4193i	1.01405	+	1.75639i
$321$	−21.0719	+	3.02922i	−1.17612	+	0.169075i
$322$	−0.512674	−	1.51277i	−0.0285702	−	0.0843035i
$323$			32.1364i			1.78811i
$324$	−3.30114	−	1.70222i	−0.183397	−	0.0945679i
$325$	−10.0631	−	5.80994i	−0.558201	−	0.322277i
$326$	−10.4296	−	6.02153i	−0.577642	−	0.333502i
$327$	−3.42550	+	2.69372i	−0.189430	+	0.148963i
$328$			3.52790i			0.194796i
$329$	−3.18188	−	0.634567i	−0.175423	−	0.0349848i
$330$	−5.02937	−	34.9855i	−0.276858	−	1.92589i
$331$	11.2983	+	19.5693i	0.621012	+	1.07562i	0.989298	+	0.145912i	$0.0466117\pi$
$331$	11.2983	+	19.5693i	0.621012	+	1.07562i	−0.368285	+	0.929713i	$0.620055\pi$
$332$	1.41443	−	2.44987i	0.0776272	−	0.134454i
$333$	−4.14181	+	17.0695i	−0.226970	+	0.935404i
$334$	−4.91840	+	2.83964i	−0.269123	+	0.155378i
$335$	17.2002			0.939748
$336$	11.5336	+	7.51807i	0.629207	+	0.410144i
$337$	−14.6351			−0.797226			−0.398613	−	0.917119i	$-0.630508\pi$
$337$	−14.6351			−0.797226			−0.398613	+	0.917119i	$0.630508\pi$
$338$	1.09109	−	0.629943i	0.0593477	−	0.0342644i
$339$	7.38456	−	18.4446i	0.401074	−	1.00177i
$340$	−4.41584	+	7.64847i	−0.239483	+	0.414796i
$341$	9.23752	+	15.9999i	0.500240	+	0.866441i
$342$	−22.2017	+	6.51797i	−1.20053	+	0.352451i
$343$	15.3836	+	10.3124i	0.830636	+	0.556816i
$344$		−	16.3905i		−	0.883717i
$345$	2.09153	+	2.65972i	0.112604	+	0.143194i
$346$	15.6694	+	9.04675i	0.842394	+	0.486356i
$347$	10.7104	+	6.18367i	0.574966	+	0.331957i	0.759130	−	0.650939i	$-0.225624\pi$
$347$	10.7104	+	6.18367i	0.574966	+	0.331957i	−0.184164	+	0.982895i	$0.558958\pi$
$348$	0.786752	+	1.00048i	0.0421743	+	0.0536314i
$349$		−	26.7056i		−	1.42952i	−0.699372	−	0.714758i	$-0.746537\pi$
$349$		−	26.7056i		−	1.42952i	0.699372	−	0.714758i	$-0.253463\pi$
$350$	29.1083	+	25.5530i	1.55590	+	1.36587i
$351$	4.72673	−	2.15825i	0.252294	−	0.115199i
$352$	4.55772	+	7.89421i	0.242928	+	0.420763i
$353$	−15.3376	+	26.5655i	−0.816337	+	1.41394i	0.0920268	+	0.995757i	$0.470665\pi$
$353$	−15.3376	+	26.5655i	−0.816337	+	1.41394i	−0.908364	+	0.418181i	$0.862668\pi$
$354$	0.581737	−	1.45302i	0.0309190	−	0.0772270i
$355$	9.61113	−	5.54899i	0.510106	−	0.294510i
$356$	−1.43723			−0.0761728
$357$	−1.30009	+	24.0206i	−0.0688081	+	1.27131i
$358$	−2.49796			−0.132022
$359$	−24.2568	+	14.0047i	−1.28023	+	0.739139i	−0.976890	−	0.213745i	$-0.931434\pi$
$359$	−24.2568	+	14.0047i	−1.28023	+	0.739139i	−0.303336	+	0.952884i	$0.598101\pi$
$360$	−36.1281	−	8.76624i	−1.90412	−	0.462022i
$361$	9.23889	−	16.0022i	0.486257	−	0.842223i
$362$	−0.555551	−	0.962243i	−0.0291991	−	0.0505744i
$363$	−1.17933	−	8.20369i	−0.0618988	−	0.430582i
$364$	1.03410	−	0.350452i	0.0542013	−	0.0183687i
$365$		−	42.6297i		−	2.23134i
$366$	1.03114	−	0.810859i	0.0538984	−	0.0423843i
$367$	8.33427	+	4.81179i	0.435045	+	0.251174i	0.701494	−	0.712676i	$-0.252517\pi$
$367$	8.33427	+	4.81179i	0.435045	+	0.251174i	−0.266448	+	0.963849i	$0.585850\pi$
$368$	1.24675	+	0.719809i	0.0649911	+	0.0375227i
$369$	−2.51980	−	2.40284i	−0.131176	−	0.125087i
$370$			30.0724i			1.56339i
$371$	3.02742	−	1.02598i	0.157176	−	0.0532664i
$372$	3.29004	−	0.472963i	0.170580	−	0.0245220i
$373$	17.8471	+	30.9120i	0.924086	+	1.60056i	0.793025	+	0.609189i	$0.208505\pi$
$373$	17.8471	+	30.9120i	0.924086	+	1.60056i	0.131060	+	0.991374i	$0.458162\pi$
$374$	13.1382	−	22.7560i	0.679358	−	1.17668i
$375$	−43.3951	−	17.3739i	−2.24092	−	0.897184i
$376$	3.22824	−	1.86383i	0.166484	−	0.0961196i
$377$	−1.78061			−0.0917061
$378$	−16.8586	+	3.97373i	−0.867112	+	0.204387i
$379$	27.9756			1.43701			0.718504	−	0.695523i	$-0.244827\pi$
$379$	27.9756			1.43701			0.718504	+	0.695523i	$0.244827\pi$
$380$	8.91973	−	5.14981i	0.457572	−	0.264180i
$381$	15.5559	+	6.22804i	0.796954	+	0.319072i
$382$	−2.93779	+	5.08841i	−0.150311	+	0.260345i
$383$	9.67462	+	16.7569i	0.494350	+	0.856239i	0.999979	−	0.00651193i	$-0.00207283\pi$
$383$	9.67462	+	16.7569i	0.494350	+	0.856239i	−0.505629	+	0.862751i	$0.668739\pi$
$384$	−11.3553	+	1.63239i	−0.579471	+	0.0833025i
$385$	32.2049	+	28.2714i	1.64131	+	1.44084i
$386$			5.10330i			0.259751i
$387$	11.7069	+	11.1635i	0.595096	+	0.567472i
$388$	−2.20863	−	1.27515i	−0.112126	−	0.0647361i
$389$	−17.5987	−	10.1606i	−0.892291	−	0.515165i	−0.0176001	−	0.999845i	$-0.505603\pi$
$389$	−17.5987	−	10.1606i	−0.892291	−	0.515165i	−0.874691	+	0.484680i	$0.838936\pi$
$390$	6.99303	−	5.49913i	0.354106	−	0.278459i
$391$			2.51542i			0.127210i
$392$	−21.0987	+	2.75626i	−1.06565	+	0.139212i
$393$	−5.42415	−	37.7316i	−0.273612	−	1.90331i
$394$	7.41801	+	12.8484i	0.373714	+	0.647292i
$395$	−1.87732	+	3.25162i	−0.0944583	+	0.163607i
$396$	−4.78016	−	1.15987i	−0.240212	−	0.0582859i
$397$	17.1380	−	9.89460i	0.860129	−	0.496596i	−0.00392632	−	0.999992i	$-0.501250\pi$
$397$	17.1380	−	9.89460i	0.860129	−	0.496596i	0.864056	+	0.503396i	$0.167916\pi$
$398$	−6.85312			−0.343516
$399$	15.3196	−	23.5020i	0.766940	−	1.17657i
$400$	−34.9098			−1.74549
$401$	13.3689	−	7.71851i	0.667609	−	0.385444i	−0.127561	−	0.991831i	$-0.540715\pi$
$401$	13.3689	−	7.71851i	0.667609	−	0.385444i	0.795170	+	0.606387i	$0.207382\pi$
$402$	−3.42203	+	8.54729i	−0.170676	+	0.426300i
$403$	−2.32505	+	4.02710i	−0.115819	+	0.200604i
$404$	−3.10785	−	5.38295i	−0.154621	−	0.267812i
$405$	30.8679	−	19.8338i	1.53384	−	0.985551i
$406$	5.82077	+	1.16085i	0.288880	+	0.0576118i
$407$			23.2619i			1.15305i
$408$	−17.0840	−	21.7251i	−0.845786	−	1.07555i
$409$	−33.7777	−	19.5016i	−1.67020	−	0.964290i	−0.967524	−	0.252779i	$-0.918656\pi$
$409$	−33.7777	−	19.5016i	−1.67020	−	0.964290i	−0.702675	−	0.711511i	$-0.748011\pi$
$410$	−5.16250	−	2.98057i	−0.254958	−	0.147200i
$411$	−12.9778	−	16.5034i	−0.640149	−	0.814052i
$412$		−	0.762458i		−	0.0375636i
$413$	0.609076	+	1.79723i	0.0299707	+	0.0884358i
$414$	−1.73781	+	0.510184i	−0.0854086	+	0.0250742i
$415$	13.9726	+	24.2012i	0.685887	+	1.18799i
$416$	−1.14716	+	1.98694i	−0.0562442	+	0.0974178i
$417$	11.4713	−	28.6521i	0.561752	−	1.40310i
$418$	−26.5383	+	15.3219i	−1.29803	+	0.749417i
$419$	−25.2894			−1.23547			−0.617733	−	0.786388i	$-0.711949\pi$
$419$	−25.2894			−1.23547			−0.617733	+	0.786388i	$0.711949\pi$
$420$	6.87547	−	3.48842i	0.335489	−	0.170217i
$421$	−1.86934			−0.0911058			−0.0455529	−	0.998962i	$-0.514505\pi$
$421$	−1.86934			−0.0911058			−0.0455529	+	0.998962i	$0.514505\pi$
$422$	4.22073	−	2.43684i	0.205462	−	0.118623i
$423$	−0.867503	+	3.57522i	−0.0421794	+	0.173833i
$424$	−1.83626	+	3.18050i	−0.0891767	+	0.154459i
$425$	−30.4987	−	52.8253i	−1.47940	−	2.56240i
$426$	0.845291	+	5.88004i	0.0409545	+	0.284889i
$427$	−0.311056	+	1.55971i	−0.0150531	+	0.0754798i
$428$			5.07231i			0.245179i
$429$	5.40933	−	4.25375i	0.261165	−	0.205373i
$430$	23.9848	+	13.8476i	1.15665	+	0.667792i
$431$	28.9918	+	16.7385i	1.39649	+	0.806263i	0.994023	−	0.109172i	$-0.0348201\pi$
$431$	28.9918	+	16.7385i	1.39649	+	0.806263i	0.402465	+	0.915435i	$0.368153\pi$
$432$	9.05604	−	12.7157i	0.435709	−	0.611783i
$433$			13.6296i			0.654998i	0.944851	+	0.327499i	$0.106206\pi$
$433$			13.6296i			0.654998i	−0.944851	+	0.327499i	$0.893794\pi$
$434$	10.2259	−	11.6487i	0.490860	−	0.559155i
$435$	−12.4452	+	1.78907i	−0.596702	+	0.0857795i
$436$	0.519151	+	0.899196i	0.0248628	+	0.0430637i
$437$	1.46676	−	2.54050i	0.0701646	−	0.121529i
$438$	21.1839	+	8.48130i	1.01221	+	0.405252i
$439$	−31.3548	+	18.1027i	−1.49648	+	0.863994i	−0.999992	−	0.00404823i	$-0.998711\pi$
$439$	−31.3548	+	18.1027i	−1.49648	+	0.863994i	−0.496490	+	0.868042i	$0.665378\pi$
$440$	−49.2345			−2.34716
$441$	12.4016	−	16.9470i	0.590551	−	0.807001i
$442$	6.61365			0.314579
$443$	11.5323	−	6.65820i	0.547918	−	0.316341i	−0.200364	−	0.979722i	$-0.564212\pi$
$443$	11.5323	−	6.65820i	0.547918	−	0.316341i	0.748282	+	0.663381i	$0.230879\pi$
$444$	3.88526	+	1.55552i	0.184386	+	0.0738217i
$445$	7.09886	−	12.2956i	0.336518	−	0.582867i
$446$	7.31470	+	12.6694i	0.346361	+	0.599915i
$447$	31.4069	−	4.51494i	1.48550	−	0.213549i
$448$	15.5332	−	17.6944i	0.733876	−	0.835982i
$449$			7.77459i			0.366906i	0.983029	+	0.183453i	$0.0587274\pi$
$449$			7.77459i			0.366906i	−0.983029	+	0.183453i	$0.941273\pi$
$450$	30.3091	−	31.7845i	1.42878	−	1.49834i
$451$	−3.99336	−	2.30557i	−0.188040	−	0.108565i
$452$	−4.09961	−	2.36691i	−0.192830	−	0.111330i
$453$	−30.7159	+	24.1542i	−1.44316	+	1.13486i
$454$			29.3677i			1.37830i
$455$	−2.10954	+	10.5778i	−0.0988968	+	0.495893i
$456$	4.58632	+	31.9035i	0.214774	+	1.49402i
$457$	−4.36016	−	7.55202i	−0.203960	−	0.353269i	0.745841	−	0.666124i	$-0.232048\pi$
$457$	−4.36016	−	7.55202i	−0.203960	−	0.353269i	−0.949801	+	0.312855i	$0.898715\pi$
$458$	−5.75884	+	9.97460i	−0.269093	+	0.466083i
$459$	27.1530	+	2.59459i	1.26739	+	0.121105i
$460$	0.698178	−	0.403093i	0.0325527	−	0.0187943i
$461$	−40.3037			−1.87713			−0.938566	−	0.345100i	$-0.887845\pi$
$461$	−40.3037			−1.87713			−0.938566	+	0.345100i	$0.887845\pi$
$462$	−20.4561	+	10.3789i	−0.951705	+	0.482868i
$463$	−33.4254			−1.55341			−0.776706	−	0.629864i	$-0.783111\pi$
$463$	−33.4254			−1.55341			−0.776706	+	0.629864i	$0.783111\pi$
$464$	−4.63282	+	2.67476i	−0.215073	+	0.124173i
$465$	−12.2042	+	30.4827i	−0.565956	+	1.41360i
$466$	−5.35243	+	9.27067i	−0.247946	+	0.429456i
$467$	−2.15646	−	3.73509i	−0.0997888	−	0.172839i	0.811808	−	0.583924i	$-0.198483\pi$
$467$	−2.15646	−	3.73509i	−0.0997888	−	0.172839i	−0.911597	+	0.411085i	$0.865150\pi$
$468$	−0.348750	−	1.18792i	−0.0161210	−	0.0549118i
$469$	−3.58285	−	10.5721i	−0.165441	−	0.488173i
$470$			6.29867i			0.290536i
$471$	14.1710	+	18.0207i	0.652964	+	0.830349i
$472$	−1.88810	−	1.09010i	−0.0869070	−	0.0501758i
$473$	18.5530	+	10.7116i	0.853068	+	0.492519i
$474$	−1.24232	−	1.57981i	−0.0570618	−	0.0725633i
$475$			71.1359i			3.26394i
$476$	5.62095	+	1.12100i	0.257636	+	0.0513807i
$477$	−1.02100	−	3.47777i	−0.0467484	−	0.159236i
$478$	−7.00349	−	12.1304i	−0.320332	−	0.554832i
$479$	11.5911	−	20.0763i	0.529610	−	0.917312i	−0.469793	−	0.882776i	$-0.655672\pi$
$479$	11.5911	−	20.0763i	0.529610	−	0.917312i	0.999403	−	0.0345352i	$-0.0109951\pi$
$480$	−6.02145	+	15.0399i	−0.274841	+	0.686475i
$481$	−5.07053	+	2.92747i	−0.231196	+	0.133481i
$482$	24.4922			1.11559
$483$	1.19912	−	1.83958i	0.0545618	−	0.0837039i
$484$	−1.97474			−0.0897610
$485$	21.8181	−	12.5967i	0.990709	−	0.571986i
$486$	3.71474	+	19.2852i	0.168504	+	0.874793i
$487$	14.3111	−	24.7875i	0.648496	−	1.12323i	−0.334986	−	0.942223i	$-0.608732\pi$
$487$	14.3111	−	24.7875i	0.648496	−	1.12323i	0.983482	−	0.181005i	$-0.0579350\pi$
$488$	−0.913624	−	1.58244i	−0.0413578	−	0.0716338i
$489$	−2.35587	−	16.3879i	−0.106536	−	0.741088i
$490$	13.7921	−	33.2031i	0.623062	−	1.49996i
$491$		−	32.2316i		−	1.45459i	−0.686325	−	0.727295i	$-0.740777\pi$
$491$		−	32.2316i		−	1.45459i	0.686325	−	0.727295i	$-0.259223\pi$
$492$	−0.652115	+	0.512806i	−0.0293996	+	0.0231191i
$493$	−8.09486	−	4.67357i	−0.364574	−	0.210487i
$494$	−6.67958	−	3.85646i	−0.300528	−	0.173510i
$495$	33.5334	−	35.1657i	1.50721	−	1.58058i
$496$			13.9704i			0.627288i
$497$	−5.41270	−	4.75160i	−0.242793	−	0.213138i
$498$	−14.8062	+	2.12848i	−0.663481	+	0.0953794i
$499$	−3.57473	−	6.19161i	−0.160027	−	0.277174i	0.774851	−	0.632144i	$-0.217825\pi$
$499$	−3.57473	−	6.19161i	−0.160027	−	0.277174i	−0.934878	+	0.354969i	$0.884491\pi$
$500$	−5.56870	+	9.64528i	−0.249040	+	0.431350i
$501$	−7.24834	−	2.90198i	−0.323832	−	0.129651i
$502$	−20.0180	+	11.5574i	−0.893448	+	0.515832i
$503$	14.5753			0.649881			0.324940	−	0.945735i	$-0.394656\pi$
$503$	14.5753			0.649881			0.324940	+	0.945735i	$0.394656\pi$
$504$	2.13742	+	24.0321i	0.0952081	+	1.07047i
$505$	61.4021			2.73236
$506$	−2.07724	+	1.19930i	−0.0923447	+	0.0533152i
$507$	1.60797	+	0.643773i	0.0714123	+	0.0285910i
$508$	1.99622	−	3.45756i	0.0885680	−	0.153404i
$509$	−12.0120	−	20.8054i	−0.532423	−	0.922184i	−0.999283	−	0.0378526i	$-0.987948\pi$
$509$	−12.0120	−	20.8054i	−0.532423	−	0.922184i	0.466860	−	0.884331i	$-0.345385\pi$
$510$	46.2247	−	6.64508i	2.04686	−	0.294249i
$511$	−26.2023	+	8.87987i	−1.15912	+	0.392822i
$512$			25.1574i			1.11181i
$513$	−25.9108	−	18.4535i	−1.14399	−	0.814743i
$514$	−10.8614	−	6.27082i	−0.479075	−	0.276594i
$515$	6.52289	+	3.76599i	0.287433	+	0.165950i
$516$	3.02970	−	2.38248i	0.133375	−	0.104883i
$517$			4.87222i			0.214280i
$518$	18.4839	−	6.26415i	0.812137	−	0.275231i
$519$	3.53945	+	24.6212i	0.155365	+	1.08075i
$520$	−6.19607	−	10.7319i	−0.271716	−	0.470625i
$521$	−16.0382	+	27.7789i	−0.702645	+	1.21702i	0.264890	+	0.964279i	$0.414664\pi$
$521$	−16.0382	+	27.7789i	−0.702645	+	1.21702i	−0.967535	+	0.252738i	$0.918669\pi$
$522$	1.58697	−	6.54032i	0.0694596	−	0.286262i
$523$	12.4987	−	7.21615i	0.546532	−	0.315540i	−0.201190	−	0.979552i	$-0.564481\pi$
$523$	12.4987	−	7.21615i	0.546532	−	0.315540i	0.747722	+	0.664012i	$0.231148\pi$
$524$	−9.08253			−0.396772
$525$	−2.87783	+	53.1712i	−0.125599	+	2.32058i
$526$	28.1778			1.22861
$527$	−21.1399	+	12.2051i	−0.920867	+	0.531663i
$528$	7.68426	−	19.1932i	0.334415	−	0.835275i
$529$	−11.3852	+	19.7197i	−0.495008	+	0.857380i
$530$	−3.10275	−	5.37413i	−0.134775	−	0.233437i
$531$	2.06458	−	0.606117i	0.0895951	−	0.0263032i
$532$	−5.02332	−	4.40978i	−0.217789	−	0.191188i
$533$		−	1.16060i		−	0.0502714i
$534$	4.69770	+	5.97388i	0.203289	+	0.258515i
$535$	−43.3941	−	25.0536i	−1.87609	−	1.08316i
$536$	11.1066	+	6.41242i	0.479734	+	0.276975i
$537$	−2.12277	−	2.69945i	−0.0916044	−	0.116490i
$538$		−	35.7578i		−	1.54163i
$539$	10.6686	−	25.6837i	0.459529	−	1.10627i
$540$	−3.63108	−	7.95233i	−0.156257	−	0.342214i
$541$	−2.59499	−	4.49465i	−0.111567	−	0.193240i	0.804835	−	0.593498i	$-0.202254\pi$
$541$	−2.59499	−	4.49465i	−0.111567	−	0.193240i	−0.916402	+	0.400258i	$0.868920\pi$
$542$	−4.19522	+	7.26634i	−0.180200	+	0.312116i
$543$	0.567748	−	1.41808i	0.0243644	−	0.0608555i
$544$	−10.4303	+	6.02191i	−0.447193	+	0.258187i
$545$	−10.2569			−0.439359
$546$	−4.83670	−	3.15277i	−0.206992	−	0.134926i
$547$	−24.5746			−1.05073			−0.525367	−	0.850876i	$-0.676072\pi$
$547$	−24.5746			−1.05073			−0.525367	+	0.850876i	$0.676072\pi$
$548$	−4.33215	+	2.50117i	−0.185060	+	0.106845i
$549$	1.75252	+	0.425238i	0.0747959	+	0.0181487i
$550$	29.0822	−	50.3718i	1.24007	−	2.14786i
$551$	5.45037	+	9.44032i	0.232194	+	0.402171i
$552$	0.358987	+	2.49720i	0.0152795	+	0.106288i
$553$	2.38965	+	0.476572i	0.101618	+	0.0202659i
$554$			11.3177i			0.480842i
$555$	−32.4980	+	25.5555i	−1.37946	+	1.08477i
$556$	−6.36840	−	3.67680i	−0.270080	−	0.155931i
$557$	−3.07124	−	1.77318i	−0.130133	−	0.0751322i	0.433520	−	0.901144i	$-0.357271\pi$
$557$	−3.07124	−	1.77318i	−0.130133	−	0.0751322i	−0.563653	+	0.826012i	$0.690605\pi$
$558$	−12.7197	−	12.1292i	−0.538466	−	0.513471i
$559$			5.39213i			0.228063i
$560$	10.4008	+	30.6902i	0.439516	+	1.29690i
$561$	35.7563	−	5.14018i	1.50963	−	0.217019i
$562$	9.93505	+	17.2080i	0.419085	+	0.725876i
$563$	−5.07878	+	8.79670i	−0.214045	+	0.370737i	−0.952977	−	0.303044i	$-0.901997\pi$
$563$	−5.07878	+	8.79670i	−0.214045	+	0.370737i	0.738932	+	0.673780i	$0.235331\pi$
$564$	0.813768	+	0.325804i	0.0342658	+	0.0137188i
$565$	40.4983	−	23.3817i	1.70378	−	0.983675i
$566$	−17.1173			−0.719492
$567$	−18.6207	−	14.8415i	−0.781996	−	0.623284i
$568$	8.27489			0.347207
$569$	−9.05473	+	5.22775i	−0.379594	+	0.219159i	−0.677642	−	0.735392i	$-0.736998\pi$
$569$	−9.05473	+	5.22775i	−0.379594	+	0.219159i	0.298048	+	0.954551i	$0.403665\pi$
$570$	−50.5603	−	20.2425i	−2.11774	−	0.847867i
$571$	15.8385	−	27.4332i	0.662823	−	1.14804i	−0.317048	−	0.948409i	$-0.602692\pi$
$571$	15.8385	−	27.4332i	0.662823	−	1.14804i	0.979871	−	0.199633i	$-0.0639750\pi$
$572$	−0.819811	−	1.41995i	−0.0342780	−	0.0593713i
$573$	−7.99537	+	1.14938i	−0.334011	+	0.0480162i
$574$	−0.756640	+	3.79398i	−0.0315816	+	0.158358i
$575$			5.56805i			0.232204i
$576$	−19.3212	−	18.4243i	−0.805050	−	0.767681i
$577$	4.94580	+	2.85546i	0.205896	+	0.118874i	0.599403	−	0.800448i	$-0.295405\pi$
$577$	4.94580	+	2.85546i	0.205896	+	0.118874i	−0.393507	+	0.919322i	$0.628738\pi$
$578$	11.5178	+	6.64980i	0.479077	+	0.276595i
$579$	−5.51493	+	4.33680i	−0.229193	+	0.180231i
$580$			2.99573i			0.124391i
$581$	11.9647	−	13.6294i	0.496380	−	0.565443i
$582$	1.91888	+	13.3482i	0.0795403	+	0.553301i
$583$	−2.40008	−	4.15706i	−0.0994011	−	0.172168i
$584$	15.8928	−	27.5271i	0.657649	−	1.13908i
$585$	11.8854	+	2.88391i	0.491400	+	0.119235i
$586$	2.52779	−	1.45942i	0.104422	−	0.0602881i
$587$	−20.5674			−0.848908			−0.424454	−	0.905450i	$-0.639534\pi$
$587$	−20.5674			−0.848908			−0.424454	+	0.905450i	$0.639534\pi$
$588$	−3.57633	−	3.49935i	−0.147485	−	0.144311i
$589$	28.4675			1.17298
$590$	3.19035	−	1.84195i	0.131345	−	0.0758319i
$591$	−7.58087	+	18.9349i	−0.311835	+	0.778878i
$592$	−8.79505	+	15.2335i	−0.361474	+	0.626092i
$593$	−15.9774	−	27.6736i	−0.656112	−	1.13642i	−0.981614	−	0.190878i	$-0.938867\pi$
$593$	−15.9774	−	27.6736i	−0.656112	−	1.13642i	0.325502	−	0.945541i	$-0.394467\pi$
$594$	10.8033	+	23.6600i	0.443265	+	0.970783i
$595$	−37.3537	+	42.5508i	−1.53135	+	1.74441i
$596$		−	7.56009i		−	0.309673i
$597$	−5.82379	−	7.40588i	−0.238352	−	0.303102i
$598$	−0.522834	−	0.301858i	−0.0213803	−	0.0123439i
$599$	21.5906	+	12.4653i	0.882169	+	0.509320i	0.871373	−	0.490621i	$-0.163230\pi$
$599$	21.5906	+	12.4653i	0.882169	+	0.509320i	0.0107957	+	0.999942i	$0.496564\pi$
$600$	−37.8166	−	48.0899i	−1.54386	−	1.96326i
$601$		−	1.19841i		−	0.0488843i	−0.999701	−	0.0244421i	$-0.992219\pi$
$601$		−	1.19841i		−	0.0488843i	0.999701	−	0.0244421i	$-0.00778095\pi$
$602$	3.51533	−	17.6267i	0.143274	−	0.718411i
$603$	−12.1448	+	3.56545i	−0.494573	+	0.145196i
$604$	4.65515	+	8.06295i	0.189415	+	0.328077i
$605$	9.75381	−	16.8941i	0.396549	−	0.686842i
$606$	−12.2161	+	30.5125i	−0.496246	+	1.23949i
$607$	20.3275	−	11.7361i	0.825067	−	0.476353i	−0.0270936	−	0.999633i	$-0.508625\pi$
$607$	20.3275	−	11.7361i	0.825067	−	0.476353i	0.852161	+	0.523280i	$0.175292\pi$
$608$	14.0456			0.569626
$609$	3.69202	+	7.27675i	0.149608	+	0.294869i
$610$	3.08752			0.125010
$611$	−1.06202	+	0.613160i	−0.0429649	+	0.0248058i
$612$	1.53249	−	6.31580i	0.0619472	−	0.255301i
$613$	−9.87375	+	17.1018i	−0.398797	+	0.690737i	−0.993578	−	0.113151i	$-0.963906\pi$
$613$	−9.87375	+	17.1018i	−0.398797	+	0.690737i	0.594781	+	0.803888i	$0.297239\pi$
$614$	5.27868	+	9.14295i	0.213030	+	0.368979i
$615$	−1.16612	−	8.11180i	−0.0470225	−	0.327099i
$616$	10.2557	+	30.2619i	0.413213	+	1.21929i
$617$			14.9308i			0.601092i	0.953767	+	0.300546i	$0.0971688\pi$
$617$			14.9308i			0.601092i	−0.953767	+	0.300546i	$0.902831\pi$
$618$	−3.16918	+	2.49216i	−0.127483	+	0.100249i
$619$	−5.20254	−	3.00369i	−0.209108	−	0.120728i	0.391789	−	0.920055i	$-0.371856\pi$
$619$	−5.20254	−	3.00369i	−0.209108	−	0.120728i	−0.600897	+	0.799327i	$0.705190\pi$
$620$	6.77527	+	3.91170i	0.272101	+	0.157098i
$621$	−2.02813	−	1.44442i	−0.0813859	−	0.0579626i
$622$			1.52489i			0.0611426i
$623$	−9.03618	−	1.80210i	−0.362027	−	0.0721996i
$624$	5.15068	−	0.740442i	0.206192	−	0.0296414i
$625$	−25.9611	−	44.9660i	−1.03844	−	1.79864i
$626$	12.9775	−	22.4776i	0.518684	−	0.898387i
$627$	−39.1100	−	15.6583i	−1.56190	−	0.625331i
$628$	4.73044	−	2.73112i	0.188765	−	0.108984i
$629$	−30.7349			−1.22548
$630$	−36.9728	−	17.1759i	−1.47303	−	0.684305i
$631$	−37.2180			−1.48162			−0.740812	−	0.671712i	$-0.765559\pi$
$631$	−37.2180			−1.48162			−0.740812	+	0.671712i	$0.765559\pi$
$632$	−2.42447	+	1.39977i	−0.0964404	+	0.0556799i
$633$	6.22017	+	2.49034i	0.247230	+	0.0989820i
$634$	−17.4201	+	30.1725i	−0.691841	+	1.19830i
$635$	19.7198	+	34.1557i	0.782557	+	1.35543i
$636$	−0.854813	+	0.122885i	−0.0338955	+	0.00487269i
$637$	6.94102	−	0.906749i	0.275013	−	0.0359267i
$638$		−	8.91300i		−	0.352869i
$639$	−5.63599	+	5.91034i	−0.222956	+	0.233809i
$640$	−23.3842	−	13.5009i	−0.924343	−	0.533670i
$641$	25.8021	+	14.8968i	1.01912	+	0.588389i	0.913849	−	0.406054i	$-0.133096\pi$
$641$	25.8021	+	14.8968i	1.01912	+	0.588389i	0.105271	+	0.994444i	$0.466429\pi$
$642$	21.0832	−	16.5793i	0.832089	−	0.654333i
$643$		−	3.08853i		−	0.121800i	−0.998144	−	0.0608998i	$-0.980603\pi$
$643$		−	3.08853i		−	0.121800i	0.998144	−	0.0608998i	$-0.0193970\pi$
$644$	−0.393193	−	0.345169i	−0.0154940	−	0.0136015i
$645$	5.41775	+	37.6871i	0.213324	+	1.48393i
$646$	−20.2441	−	35.0638i	−0.796493	−	1.37957i
$647$	3.72461	−	6.45121i	0.146430	−	0.253623i	−0.783476	−	0.621422i	$-0.786555\pi$
$647$	3.72461	−	6.45121i	0.146430	−	0.253623i	0.929905	+	0.367799i	$0.119889\pi$
$648$	27.3265	−	1.29934i	1.07349	−	0.0510428i
$649$	2.46784	−	1.42481i	0.0968712	−	0.0559286i
$650$	14.6397			0.574217
$651$	21.2783	+	1.15166i	0.833961	+	0.0451373i
$652$	−3.94480			−0.154490
$653$	36.7497	−	21.2175i	1.43813	−	0.830304i	0.440409	−	0.897797i	$-0.354834\pi$
$653$	36.7497	−	21.2175i	1.43813	−	0.830304i	0.997720	+	0.0674935i	$0.0215002\pi$
$654$	2.04065	−	5.09697i	0.0797956	−	0.199307i
$655$	44.8612	−	77.7018i	1.75287	−	3.03606i
$656$	−1.74341	−	3.01968i	−0.0680688	−	0.117899i
$657$	8.83674	+	30.1000i	0.344754	+	1.17431i
$658$	3.87147	−	1.31203i	0.150925	−	0.0511482i
$659$			9.94881i			0.387551i	0.981046	+	0.193775i	$0.0620733\pi$
$659$			9.94881i			0.387551i	−0.981046	+	0.193775i	$0.937927\pi$
$660$	−7.15659	−	9.10076i	−0.278570	−	0.354247i
$661$	0.982661	+	0.567340i	0.0382211	+	0.0220670i	0.518989	−	0.854781i	$-0.326309\pi$
$661$	0.982661	+	0.567340i	0.0382211	+	0.0220670i	−0.480768	+	0.876848i	$0.659642\pi$
$662$	−24.6551	−	14.2346i	−0.958246	−	0.553244i
$663$	5.62029	+	7.14710i	0.218274	+	0.277570i
$664$			20.8365i			0.808614i
$665$	62.5376	−	21.1938i	2.42511	−	0.821862i
$666$	−6.23373	−	21.2335i	−0.241552	−	0.822783i
$667$	0.426620	+	0.738927i	0.0165188	+	0.0286114i
$668$	−0.930148	+	1.61106i	−0.0359885	+	0.0623339i
$669$	−7.47529	+	18.6712i	−0.289012	+	0.721870i
$670$	−18.7670	+	10.8352i	−0.725034	+	0.418599i
$671$	2.38830			0.0921992
$672$	10.4985	+	0.568222i	0.404990	+	0.0219197i
$673$	−23.1761			−0.893371			−0.446686	−	0.894691i	$-0.647396\pi$
$673$	−23.1761			−0.893371			−0.446686	+	0.894691i	$0.647396\pi$
$674$	15.9683	−	9.21930i	0.615076	−	0.355114i
$675$	60.1049	+	5.74328i	2.31344	+	0.221059i
$676$	0.206343	−	0.357397i	0.00793628	−	0.0137460i
$677$	20.0889	+	34.7951i	0.772081	+	1.33728i	0.936421	+	0.350880i	$0.114117\pi$
$677$	20.0889	+	34.7951i	0.772081	+	1.33728i	−0.164340	+	0.986404i	$0.552549\pi$
$678$	3.56179	+	24.7766i	0.136790	+	0.951541i
$679$	−12.2873	−	10.7865i	−0.471543	−	0.413949i
$680$		−	65.0513i		−	2.49460i
$681$	−31.7365	+	24.9567i	−1.21614	+	0.956344i
$682$	−20.1580	−	11.6382i	−0.771890	−	0.445651i
$683$	2.75457	+	1.59035i	0.105401	+	0.0608532i	0.551774	−	0.833994i	$-0.313951\pi$
$683$	2.75457	+	1.59035i	0.105401	+	0.0608532i	−0.446373	+	0.894847i	$0.647285\pi$
$684$	−5.23055	+	5.48516i	−0.199995	+	0.209730i
$685$		−	49.4159i		−	1.88809i
$686$	−23.2812	−	1.56097i	−0.888878	−	0.0595981i
$687$	−15.6730	+	2.25309i	−0.597963	+	0.0859608i
$688$	8.09983	+	14.0293i	0.308803	+	0.534863i
$689$	0.604090	−	1.04632i	0.0230140	−	0.0398614i
$690$	−3.95753	−	1.58446i	−0.150661	−	0.0603192i
$691$	−5.82249	+	3.36162i	−0.221498	+	0.127882i	−0.606644	−	0.794974i	$-0.707485\pi$
$691$	−5.82249	+	3.36162i	−0.221498	+	0.127882i	0.385146	+	0.922856i	$0.374151\pi$
$692$	5.92668			0.225298
$693$	−28.5996	−	13.2861i	−1.08641	−	0.504698i
$694$	−15.5814			−0.591464
$695$	62.9107	−	36.3215i	2.38634	−	1.37775i
$696$	−8.70319	−	3.48445i	−0.329893	−	0.132078i
$697$	3.04624	−	5.27624i	0.115384	−	0.199852i
$698$	16.8230	+	29.1383i	0.636760	+	1.10290i
$699$	−14.5669	+	2.09409i	−0.550972	+	0.0792056i
$700$	12.4423	+	2.48139i	0.470276	+	0.0937879i
$701$		−	26.9949i		−	1.01959i	−0.860297	−	0.509793i	$-0.829722\pi$
$701$		−	26.9949i		−	1.01959i	0.860297	−	0.509793i	$-0.170278\pi$
$702$	−3.79773	+	5.33242i	−0.143336	+	0.201259i
$703$	31.0413	+	17.9217i	1.17075	+	0.675930i
$704$	−30.6201	−	17.6785i	−1.15404	−	0.666284i
$705$	−6.80671	+	5.35262i	−0.256356	+	0.201591i
$706$		−	38.6472i		−	1.45451i
$707$	−12.7902	−	37.7407i	−0.481026	−	1.41938i
$708$	−0.0729504	−	0.507460i	−0.00274165	−	0.0190715i
$709$	−10.2526	−	17.7581i	−0.385046	−	0.666919i	0.606730	−	0.794908i	$-0.292481\pi$
$709$	−10.2526	−	17.7581i	−0.385046	−	0.666919i	−0.991776	+	0.127989i	$0.959148\pi$
$710$	−6.99110	+	12.1089i	−0.262371	+	0.454440i
$711$	0.651511	−	2.68506i	0.0244336	−	0.100697i
$712$	9.16786	−	5.29306i	0.343580	−	0.198366i
$713$	2.22825			0.0834486
$714$	−13.7131	−	27.0277i	−0.513200	−	1.01149i
$715$	16.1971			0.605738
$716$	−0.708607	+	0.409115i	−0.0264819	+	0.0152893i
$717$	7.15725	−	17.8768i	0.267292	−	0.667622i
$718$	17.6443	−	30.5608i	0.658480	−	1.14052i
$719$	−17.7125	−	30.6790i	−0.660566	−	1.14413i	−0.980467	−	0.196682i	$-0.936983\pi$
$719$	−17.7125	−	30.6790i	−0.660566	−	1.14413i	0.319902	−	0.947451i	$-0.396350\pi$
$720$	35.2556	−	10.3503i	1.31390	−	0.385734i
$721$	0.956026	−	4.79375i	0.0356043	−	0.178529i
$722$			23.2799i			0.866388i
$723$	20.8135	+	26.4677i	0.774062	+	0.984344i
$724$	−0.315191	−	0.181975i	−0.0117140	−	0.00676306i
$725$	−17.9185	−	10.3452i	−0.665476	−	0.384213i
$726$	6.45462	+	8.20808i	0.239553	+	0.304630i
$727$		−	4.04100i		−	0.149873i	−0.997188	−	0.0749363i	$-0.976125\pi$
$727$		−	4.04100i		−	0.149873i	0.997188	−	0.0749363i	$-0.0238753\pi$
$728$	−5.30569	+	6.04389i	−0.196642	+	0.224001i
$729$	−17.6839	+	20.4029i	−0.654959	+	0.755664i
$730$	26.8543	+	46.5130i	0.993922	+	1.72152i
$731$	−14.1527	+	24.5132i	−0.523457	+	0.906654i
$732$	0.159705	−	0.398898i	0.00590286	−	0.0147437i
$733$	−0.796258	+	0.459720i	−0.0294105	+	0.0169801i	−0.514633	−	0.857410i	$-0.672072\pi$
$733$	−0.796258	+	0.459720i	−0.0294105	+	0.0169801i	0.485223	+	0.874391i	$0.338739\pi$
$734$	−12.1246			−0.447528
$735$	47.6017	−	13.3115i	1.75582	−	0.491004i
$736$	1.09940			0.0405245
$737$	−14.5169	+	8.38134i	−0.534737	+	0.308731i
$738$	4.26299	+	1.03439i	0.156923	+	0.0380763i
$739$	−25.9426	+	44.9339i	−0.954313	+	1.65292i	−0.218382	+	0.975863i	$0.570078\pi$
$739$	−25.9426	+	44.9339i	−0.954313	+	1.65292i	−0.735932	+	0.677056i	$0.763256\pi$
$740$	4.92523	+	8.53075i	0.181055	+	0.313597i
$741$	−1.50880	−	10.4956i	−0.0554272	−	0.385564i
$742$	−2.65689	+	3.02655i	−0.0975373	+	0.111108i
$743$			13.6972i			0.502502i	0.967922	+	0.251251i	$0.0808420\pi$
$743$			13.6972i			0.502502i	−0.967922	+	0.251251i	$0.919158\pi$
$744$	−19.2448	+	15.1336i	−0.705550	+	0.554826i
$745$	64.6772	+	37.3414i	2.36959	+	1.36808i
$746$	−38.9456	−	22.4853i	−1.42590	−	0.823244i
$747$	−14.8825	−	14.1916i	−0.544521	−	0.519245i
$748$		−	8.60703i		−	0.314704i
$749$	−6.36004	+	31.8908i	−0.232391	+	1.16526i
$750$	58.2927	−	8.37993i	2.12855	−	0.305992i
$751$	−12.1596	−	21.0610i	−0.443710	−	0.768528i	0.554252	−	0.832349i	$-0.313004\pi$
$751$	−12.1596	−	21.0610i	−0.443710	−	0.768528i	−0.997961	+	0.0638215i	$0.979671\pi$
$752$	−1.84213	+	3.19066i	−0.0671754	+	0.116351i
$753$	−29.5010	−	11.8111i	−1.07507	−	0.430422i
$754$	1.94281	−	1.12168i	0.0707531	−	0.0408493i
$755$	−91.9724			−3.34722
$756$	−4.13152	+	3.88833i	−0.150262	+	0.141417i
$757$	−0.120656			−0.00438531			−0.00219266	−	0.999998i	$-0.500698\pi$
$757$	−0.120656			−0.00438531			−0.00219266	+	0.999998i	$0.500698\pi$
$758$	−30.5239	+	17.6230i	−1.10868	+	0.640097i
$759$	−3.06127	−	1.22563i	−0.111117	−	0.0444874i
$760$	−37.9318	+	65.6998i	−1.37593	+	2.38318i
$761$	17.0379	+	29.5104i	0.617622	+	1.06975i	0.989918	+	0.141639i	$0.0452371\pi$
$761$	17.0379	+	29.5104i	0.617622	+	1.06975i	−0.372297	+	0.928114i	$0.621430\pi$
$762$	−20.8963	+	3.00397i	−0.756992	+	0.108822i
$763$	2.13654	+	6.30440i	0.0773481	+	0.228235i
$764$			1.92460i			0.0696295i
$765$	46.4628	+	44.3061i	1.67987	+	1.60189i
$766$	−21.1118	−	12.1889i	−0.762801	−	0.440404i
$767$	0.621146	+	0.358619i	0.0224283	+	0.0129490i
$768$	−12.8714	+	10.1217i	−0.464455	+	0.365235i
$769$		−	48.2581i		−	1.74023i	−0.492849	−	0.870115i	$-0.664044\pi$
$769$		−	48.2581i		−	1.74023i	0.492849	−	0.870115i	$-0.335956\pi$
$770$	−52.9479	−	10.5595i	−1.90811	−	0.380538i
$771$	−2.45340	−	17.0664i	−0.0883569	−	0.614631i
$772$	0.835815	+	1.44767i	0.0300816	+	0.0521029i
$773$	−16.0465	+	27.7933i	−0.577152	+	0.999656i	0.418653	+	0.908146i	$0.362503\pi$
$773$	−16.0465	+	27.7933i	−0.577152	+	0.999656i	−0.995804	+	0.0915095i	$0.970831\pi$
$774$	−19.8057	−	4.80572i	−0.711901	−	0.172738i
$775$	−46.7944	+	27.0168i	−1.68091	+	0.970471i
$776$	18.7847			0.674332
$777$	22.4771	+	14.6515i	0.806361	+	0.525621i
$778$	25.6025			0.917894
$779$	−6.15321	+	3.55256i	−0.220462	+	0.127284i
$780$	1.08310	−	2.70527i	0.0387811	−	0.0968643i
$781$	−5.40784	+	9.36665i	−0.193508	+	0.335165i
$782$	−1.58457	−	2.74456i	−0.0566643	−	0.0981454i
$783$	8.41646	−	3.84301i	0.300780	−	0.137338i
$784$	16.6972	−	12.7857i	0.596328	−	0.456633i
$785$			53.9591i			1.92588i
$786$	29.6870	+	37.7518i	1.05890	+	1.34656i
$787$	−8.44483	−	4.87563i	−0.301026	−	0.173797i	0.341878	−	0.939744i	$-0.388937\pi$
$787$	−8.44483	−	4.87563i	−0.301026	−	0.173797i	−0.642904	+	0.765947i	$0.722270\pi$
$788$	4.20859	+	2.42983i	0.149925	+	0.0865592i
$789$	23.9455	+	30.4506i	0.852484	+	1.08407i
$790$		−	4.73042i		−	0.168301i
$791$	−22.8074	−	20.0217i	−0.810938	−	0.711891i
$792$	34.7636	−	10.2059i	1.23527	−	0.362650i
$793$	0.300563	+	0.520590i	0.0106733	+	0.0184867i
$794$	−12.4661	+	21.5919i	−0.442404	+	0.766267i
$795$	3.17087	−	7.91996i	0.112459	−	0.280892i
$796$	−1.94405	+	1.12240i	−0.0689050	+	0.0397823i
$797$	19.3274			0.684613			0.342306	−	0.939588i	$-0.388792\pi$
$797$	19.3274			0.684613			0.342306	+	0.939588i	$0.388792\pi$
$798$	−1.91021	+	35.2933i	−0.0676209	+	1.24937i
$799$	−6.43744			−0.227740
$800$	−23.0880	+	13.3299i	−0.816285	+	0.471282i
$801$	−2.46361	+	10.1532i	−0.0870474	+	0.358746i
$802$	−9.72445	+	16.8432i	−0.343382	+	0.594755i
$803$	20.7726	+	35.9793i	0.733051	+	1.26968i
$804$	0.429126	+	2.98510i	0.0151341	+	0.105276i
$805$	4.89504	−	1.65892i	0.172527	−	0.0584691i
$806$		−	5.85859i		−	0.206360i
$807$	38.6419	−	30.3870i	1.36026	−	1.06967i
$808$	39.6490	+	22.8914i	1.39485	+	0.805315i
$809$	16.3533	+	9.44160i	0.574953	+	0.331949i	0.759125	−	0.650945i	$-0.225627\pi$
$809$	16.3533	+	9.44160i	0.574953	+	0.331949i	−0.184172	+	0.982894i	$0.558960\pi$
$810$	−21.1856	+	41.0856i	−0.744387	+	1.44360i
$811$			23.9568i			0.841236i	0.907238	+	0.420618i	$0.138187\pi$
$811$			23.9568i			0.841236i	−0.907238	+	0.420618i	$0.861813\pi$
$812$	1.84132	−	0.624019i	0.0646177	−	0.0218988i
$813$	−11.4175	+	1.64134i	−0.400431	+	0.0575644i
$814$	−14.6537	−	25.3810i	−0.513612	−	0.889602i
$815$	19.4845	−	33.7481i	0.682512	−	1.18215i
$816$	25.3590	+	10.1529i	0.887743	+	0.355421i
$817$	28.5876	−	16.5051i	1.00015	−	0.577439i
$818$	49.1395			1.71812
$819$	−0.703165	−	7.90605i	−0.0245706	−	0.276260i
$820$	−1.95262			−0.0681885
$821$	2.33939	−	1.35065i	0.0816452	−	0.0471379i	−0.458622	−	0.888632i	$-0.651657\pi$
$821$	2.33939	−	1.35065i	0.0816452	−	0.0471379i	0.540267	+	0.841494i	$0.318323\pi$
$822$	24.5562	+	9.83144i	0.856496	+	0.342911i
$823$	−3.50931	+	6.07831i	−0.122327	+	0.211876i	−0.920685	−	0.390307i	$-0.872369\pi$
$823$	−3.50931	+	6.07831i	−0.122327	+	0.211876i	0.798358	+	0.602183i	$0.205702\pi$
$824$	2.80801	+	4.86361i	0.0978215	+	0.169432i
$825$	79.1487	−	11.3781i	2.75561	−	0.396135i
$826$	−1.79671	−	1.57726i	−0.0625155	−	0.0548799i
$827$		−	37.7335i		−	1.31212i	−0.754707	−	0.656061i	$-0.772221\pi$
$827$		−	37.7335i		−	1.31212i	0.754707	−	0.656061i	$-0.227779\pi$
$828$	−0.409413	+	0.429343i	−0.0142281	+	0.0149207i
$829$	18.0935	+	10.4463i	0.628415	+	0.362815i	0.780138	−	0.625608i	$-0.215149\pi$
$829$	18.0935	+	10.4463i	0.628415	+	0.362815i	−0.151723	+	0.988423i	$0.548482\pi$
$830$	−30.4908	−	17.6039i	−1.05835	−	0.611039i
$831$	−12.2305	+	9.61777i	−0.424273	+	0.333637i
$832$		−	8.89922i		−	0.308525i
$833$	33.9346	+	14.0959i	1.17577	+	0.488395i
$834$	5.53294	+	38.4884i	0.191590	+	1.33274i
$835$	−9.18852	−	15.9150i	−0.317982	−	0.550761i
$836$	−5.01881	+	8.69283i	−0.173579	+	0.300648i
$837$	2.29837	−	24.0530i	0.0794434	−	0.831395i
$838$	27.5931	−	15.9309i	0.953186	−	0.550322i
$839$	50.9018			1.75732			0.878662	−	0.477444i	$-0.158437\pi$
$839$	50.9018			1.75732			0.878662	+	0.477444i	$0.158437\pi$
$840$	−31.0104	+	47.5733i	−1.06996	+	1.64144i
$841$	25.8294			0.890670
$842$	2.03962	−	1.17758i	0.0702899	−	0.0405819i
$843$	−10.1532	+	25.3598i	−0.349694	+	0.873437i
$844$	0.798207	−	1.38253i	0.0274754	−	0.0475888i
$845$	2.03837	+	3.53057i	0.0701222	+	0.121455i
$846$	−1.30566	−	4.44737i	−0.0448894	−	0.152904i
$847$	−12.4157	−	2.47608i	−0.426607	−	0.0850790i
$848$		−	3.62976i		−	0.124646i
$849$	−14.5463	−	18.4979i	−0.499227	−	0.634847i
$850$	66.5539	+	38.4249i	2.28278	+	1.31796i
$851$	2.42971	+	1.40279i	0.0832895	+	0.0480872i
$852$	1.20282	+	1.52957i	0.0412078	+	0.0524023i
$853$			37.4065i			1.28078i	0.768052	+	0.640388i	$0.221226\pi$
$853$			37.4065i			1.28078i	−0.768052	+	0.640388i	$0.778774\pi$
$854$	−0.643139	−	1.89774i	−0.0220078	−	0.0649394i
$855$	−21.0909	−	71.8405i	−0.721293	−	2.45689i
$856$	−18.6805	−	32.3555i	−0.638486	−	1.10589i
$857$	−2.29740	+	3.97922i	−0.0784778	+	0.135928i	−0.902593	−	0.430494i	$-0.858339\pi$
$857$	−2.29740	+	3.97922i	−0.0784778	+	0.135928i	0.824116	+	0.566422i	$0.191673\pi$
$858$	−3.22246	+	8.04881i	−0.110013	+	0.274782i
$859$	29.5949	−	17.0866i	1.00976	−	0.582988i	0.0986421	−	0.995123i	$-0.468550\pi$
$859$	29.5949	−	17.0866i	1.00976	−	0.582988i	0.911123	+	0.412135i	$0.135217\pi$
$860$	9.07182			0.309346
$861$	−4.74299	+	2.40646i	−0.161641	+	0.0820120i
$862$	−42.1771			−1.43656
$863$	−20.7940	+	12.0054i	−0.707836	+	0.408669i	−0.810259	−	0.586072i	$-0.800674\pi$
$863$	−20.7940	+	12.0054i	−0.707836	+	0.408669i	0.102424	+	0.994741i	$0.467340\pi$
$864$	1.13400	−	11.8676i	0.0385795	−	0.403744i
$865$	−29.2735	+	50.7032i	−0.995330	+	1.72396i
$866$	−8.58589	−	14.8712i	−0.291761	−	0.505344i
$867$	2.60167	+	18.0978i	0.0883574	+	0.614634i
$868$	0.993015	−	4.97922i	0.0337051	−	0.169006i
$869$		−	3.65913i		−	0.124128i
$870$	12.4519	−	9.79182i	0.422158	−	0.331974i
$871$	−3.65385	−	2.10955i	−0.123806	−	0.0714794i
$872$	−6.62318	−	3.82389i	−0.224289	−	0.129493i
$873$	−12.7942	+	13.4170i	−0.433017	+	0.454096i
$874$			3.69590i			0.125016i
$875$	−47.1057	+	53.6597i	−1.59246	+	1.81403i
$876$	7.39839	−	1.06356i	0.249968	−	0.0359345i
$877$	10.7369	+	18.5969i	0.362560	+	0.627972i	0.988381	−	0.151994i	$-0.0485695\pi$
$877$	10.7369	+	18.5969i	0.362560	+	0.627972i	−0.625822	+	0.779966i	$0.715236\pi$
$878$	22.8073	−	39.5035i	0.769710	−	1.33318i
$879$	3.72526	+	1.49146i	0.125650	+	0.0503058i
$880$	42.1419	−	24.3306i	1.42060	−	0.820185i
$881$	−26.2116			−0.883093			−0.441546	−	0.897238i	$-0.645570\pi$
$881$	−26.2116			−0.883093			−0.441546	+	0.897238i	$0.645570\pi$
$882$	−2.85561	+	26.3031i	−0.0961536	+	0.885670i
$883$	18.0151			0.606256			0.303128	−	0.952950i	$-0.401969\pi$
$883$	18.0151			0.606256			0.303128	+	0.952950i	$0.401969\pi$
$884$	1.87612	−	1.08318i	0.0631007	−	0.0364312i
$885$	4.70169	+	1.88239i	0.158045	+	0.0632758i
$886$	−8.38858	+	14.5294i	−0.281820	+	0.488126i
$887$	14.3358	+	24.8304i	0.481350	+	0.833723i	0.999771	−	0.0214027i	$-0.00681321\pi$
$887$	14.3358	+	24.8304i	0.481350	+	0.833723i	−0.518421	+	0.855126i	$0.673480\pi$
$888$	−30.5122	+	4.38631i	−1.02392	+	0.147195i
$889$	16.8861	−	19.2355i	0.566340	−	0.645137i
$890$			17.8875i			0.599591i
$891$	−16.3878	+	31.7810i	−0.549011	+	1.06470i
$892$	4.14998	+	2.39599i	0.138952	+	0.0802238i
$893$	6.50161	+	3.75371i	0.217568	+	0.125613i
$894$	−31.4237	+	24.7108i	−1.05097	+	0.826453i
$895$		−	8.08293i		−	0.270183i
$896$	−3.42730	+	17.1853i	−0.114498	+	0.574122i
$897$	−0.118099	−	0.821525i	−0.00394322	−	0.0274299i
$898$	−4.89755	−	8.48280i	−0.163433	−	0.283075i
$899$	−4.14001	+	7.17070i	−0.138077	+	0.239156i
$900$	3.39226	−	13.9804i	0.113075	−	0.466014i
$901$	5.49253	−	3.17111i	0.182983	−	0.105645i
$902$	5.80951			0.193435
$903$	22.0358	−	11.1803i	0.733305	−	0.372058i
$904$	34.8678			1.15968
$905$	3.11363	−	1.79766i	0.103501	−	0.0597561i
$906$	18.2982	−	45.7037i	0.607916	−	1.51841i
$907$	8.02161	−	13.8938i	0.266353	−	0.461337i	−0.701564	−	0.712606i	$-0.747515\pi$
$907$	8.02161	−	13.8938i	0.266353	−	0.461337i	0.967917	+	0.251269i	$0.0808479\pi$
$908$	4.80982	+	8.33085i	0.159620	+	0.276469i
$909$	−43.3549	+	12.7281i	−1.43799	+	0.422164i
$910$	−4.36168	−	12.8702i	−0.144588	−	0.426644i
$911$		−	44.0936i		−	1.46089i	−0.682973	−	0.730444i	$-0.739313\pi$
$911$		−	44.0936i		−	1.46089i	0.682973	−	0.730444i	$-0.260687\pi$
$912$	−19.6916	−	25.0411i	−0.652055	−	0.829192i
$913$	−23.5856	−	13.6172i	−0.780570	−	0.450662i
$914$	9.51469	+	5.49331i	0.314718	+	0.181703i
$915$	2.62378	+	3.33656i	0.0867396	+	0.110303i
$916$			3.77271i			0.124654i
$917$	−57.1040	−	11.3883i	−1.88574	−	0.376076i
$918$	−31.2609	+	14.2739i	−1.03176	+	0.471109i
$919$	3.36751	+	5.83269i	0.111084	+	0.192403i	0.916208	−	0.400704i	$-0.131234\pi$
$919$	3.36751	+	5.83269i	0.111084	+	0.192403i	−0.805124	+	0.593107i	$0.797901\pi$
$920$	−2.96905	+	5.14255i	−0.0978868	+	0.169545i
$921$	−5.39458	+	13.4741i	−0.177757	+	0.443988i
$922$	43.9751	−	25.3891i	1.44824	−	0.836144i
$923$	−2.72226			−0.0896044
$924$	−4.10303	+	6.29450i	−0.134980	+	0.207074i
$925$	−68.0337			−2.23693
$926$	36.4703	−	21.0561i	1.19849	−	0.691947i
$927$	−5.38635	−	1.30696i	−0.176911	−	0.0429263i
$928$	−2.04265	+	3.53797i	−0.0670532	+	0.116140i
$929$	−12.2996	−	21.3036i	−0.403537	−	0.698947i	0.590613	−	0.806955i	$-0.298886\pi$
$929$	−12.2996	−	21.3036i	−0.403537	−	0.698947i	−0.994150	+	0.108008i	$0.965553\pi$
$930$	−5.88643	−	40.9474i	−0.193024	−	1.34272i
$931$	−26.0535	−	34.0239i	−0.853869	−	1.11509i
$932$			3.50646i			0.114858i
$933$	−1.64789	+	1.29585i	−0.0539494	+	0.0424244i
$934$	4.70579	+	2.71689i	0.153978	+	0.0888993i
$935$	73.6339	+	42.5125i	2.40809	+	1.39031i
$936$	6.59955	+	6.29321i	0.215713	+	0.205700i
$937$		−	48.7669i		−	1.59314i	−0.604543	−	0.796572i	$-0.706644\pi$
$937$		−	48.7669i		−	1.59314i	0.604543	−	0.796572i	$-0.293356\pi$
$938$	10.5690	+	9.27814i	0.345091	+	0.302942i
$939$	35.3189	−	5.07731i	1.15259	−	0.165692i
$940$	1.03159	+	1.78677i	0.0336468	+	0.0582779i
$941$	10.7108	−	18.5517i	0.349163	−	0.604767i	−0.636938	−	0.770915i	$-0.719799\pi$
$941$	10.7108	−	18.5517i	0.349163	−	0.604767i	0.986101	+	0.166147i	$0.0531328\pi$
$942$	−26.8139	−	10.7353i	−0.873643	−	0.349776i
$943$	−0.481633	+	0.278071i	−0.0156841	+	0.00905524i
$944$	2.15481			0.0701330
$945$	−12.8582	−	54.5511i	−0.418278	−	1.77455i
$946$	−26.9908			−0.877545
$947$	1.24594	−	0.719345i	0.0404877	−	0.0233756i	−0.479620	−	0.877477i	$-0.659225\pi$
$947$	1.24594	−	0.719345i	0.0404877	−	0.0233756i	0.520107	+	0.854101i	$0.325892\pi$
$948$	−0.611156	−	0.244685i	−0.0198494	−	0.00794701i
$949$	−5.22839	+	9.05584i	−0.169721	+	0.293965i
$950$	−44.8116	−	77.6159i	−1.45388	−	2.51819i
$951$	−47.4098	+	6.81545i	−1.53737	+	0.221006i
$952$	−39.9836	+	13.5503i	−1.29588	+	0.439169i
$953$			45.5963i			1.47701i	0.674249	+	0.738504i	$0.264468\pi$
$953$			45.5963i			1.47701i	−0.674249	+	0.738504i	$0.735532\pi$
$954$	3.30480	+	3.15140i	0.106997	+	0.102030i
$955$	−16.4651	−	9.50613i	−0.532798	−	0.307611i
$956$	−3.97342	−	2.29405i	−0.128509	−	0.0741950i
$957$	9.63191	−	7.57428i	0.311356	−	0.244842i
$958$			29.2069i			0.943632i
$959$	−30.3734	+	10.2935i	−0.980809	+	0.332393i
$960$	−8.94151	−	62.1992i	−0.288586	−	2.00747i
$961$	−4.68831	−	8.12038i	−0.151236	−	0.261948i
$962$	3.68828	−	6.38829i	0.118915	−	0.205967i
$963$	35.8331	+	8.69467i	1.15471	+	0.280182i
$964$	6.94779	−	4.01131i	0.223773	−	0.129196i
$965$	−16.5133			−0.531582
$966$	−0.149519	+	2.76253i	−0.00481070	+	0.0888831i
$967$	−21.5668			−0.693542			−0.346771	−	0.937950i	$-0.612722\pi$
$967$	−21.5668			−0.693542			−0.346771	+	0.937950i	$0.612722\pi$
$968$	12.5966	−	7.27265i	0.404870	−	0.233752i
$969$	20.6885	−	51.6742i	0.664611	−	1.66001i
$970$	−15.8704	+	27.4883i	−0.509568	+	0.882597i
$971$	6.44533	+	11.1636i	0.206841	+	0.358258i	0.950718	−	0.310058i	$-0.100349\pi$
$971$	6.44533	+	11.1636i	0.206841	+	0.358258i	−0.743877	+	0.668316i	$0.767015\pi$
$972$	4.21228	+	4.86230i	0.135109	+	0.155958i
$973$	−35.4294	−	31.1021i	−1.13581	−	0.997087i
$974$			36.0606i			1.15546i
$975$	12.4409	+	15.8206i	0.398426	+	0.506663i
$976$	1.56402	+	0.902986i	0.0500630	+	0.0289039i
$977$	14.2536	+	8.22933i	0.456014	+	0.263280i	0.710367	−	0.703832i	$-0.248529\pi$
$977$	14.2536	+	8.22933i	0.456014	+	0.263280i	−0.254353	+	0.967111i	$0.581862\pi$
$978$	12.8939	+	16.3967i	0.412303	+	0.524309i
$979$			13.8366i			0.442219i
$980$	−1.52553	−	11.6777i	−0.0487313	−	0.373031i
$981$	7.24223	−	2.12617i	0.231226	−	0.0678833i
$982$	20.3041	+	35.1677i	0.647929	+	1.12225i
$983$	21.4985	−	37.2366i	0.685697	−	1.18766i	−0.287520	−	0.957775i	$-0.592831\pi$
$983$	21.4985	−	37.2366i	0.685697	−	1.18766i	0.973217	−	0.229888i	$-0.0738359\pi$
$984$	2.27117	−	5.67275i	0.0724022	−	0.180841i
$985$	−41.5749	+	24.0033i	−1.32469	+	0.764807i
$986$	11.7763			0.375035
$987$	4.70783	+	3.06877i	0.149852	+	0.0976800i
$988$	−2.52643			−0.0803764
$989$	2.23765	−	1.29191i	0.0711532	−	0.0410803i
$990$	−14.4356	+	59.4932i	−0.458795	+	1.89082i
$991$	−25.5897	+	44.3227i	−0.812884	+	1.40796i	0.0979527	+	0.995191i	$0.468771\pi$
$991$	−25.5897	+	44.3227i	−0.812884	+	1.40796i	−0.910837	+	0.412766i	$0.864563\pi$
$992$	5.33441	+	9.23947i	0.169368	+	0.293353i
$993$	−5.56915	−	38.7403i	−0.176732	−	1.22939i
$994$	8.89900	+	1.77474i	0.282259	+	0.0562914i
$995$		−	22.1754i		−	0.703006i
$996$	−3.85153	+	3.02874i	−0.122040	+	0.0959692i
$997$	−23.9143	−	13.8069i	−0.757375	−	0.437270i	0.0709777	−	0.997478i	$-0.477388\pi$
$997$	−23.9143	−	13.8069i	−0.757375	−	0.437270i	−0.828352	+	0.560207i	$0.810721\pi$
$998$	7.80072	+	4.50375i	0.246928	+	0.142564i
$999$	17.6488	−	24.7808i	0.558383	−	0.784031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.248.10	yes	64
3.2	odd	2	inner	273.2.bh.a.248.23	yes	64
7.5	odd	6	inner	273.2.bh.a.131.23	yes	64
21.5	even	6	inner	273.2.bh.a.131.10	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.10	✓	64	21.5	even	6	inner
273.2.bh.a.131.23	yes	64	7.5	odd	6	inner
273.2.bh.a.248.10	yes	64	1.1	even	1	trivial
273.2.bh.a.248.23	yes	64	3.2	odd	2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09109 + 0.629943i) q^{2} +(-1.60797 - 0.643773i) q^{3} +(-0.206343 + 0.357397i) q^{4} +(-2.03837 - 3.53057i) q^{5} +(2.15998 - 0.310511i) q^{6} +(-1.74546 + 1.98831i) q^{7} -3.03971i q^{8} +(2.17111 + 2.07033i) q^{9} +O(q^{10})\)	\(q+(-1.09109 + 0.629943i) q^{2} +(-1.60797 - 0.643773i) q^{3} +(-0.206343 + 0.357397i) q^{4} +(-2.03837 - 3.53057i) q^{5} +(2.15998 - 0.310511i) q^{6} +(-1.74546 + 1.98831i) q^{7} -3.03971i q^{8} +(2.17111 + 2.07033i) q^{9} +(4.44811 + 2.56812i) q^{10} +(3.44076 + 1.98652i) q^{11} +(0.561875 - 0.441844i) q^{12} +1.00000i q^{13} +(0.651937 - 3.26897i) q^{14} +(1.00475 + 6.98929i) q^{15} +(1.50216 + 2.60182i) q^{16} +(-2.62470 + 4.54611i) q^{17} +(-3.67308 - 0.891248i) q^{18} +(5.30173 - 3.06096i) q^{19} +1.68242 q^{20} +(4.08666 - 2.07346i) q^{21} -5.00559 q^{22} +(0.414985 - 0.239592i) q^{23} +(-1.95688 + 4.88775i) q^{24} +(-5.80994 + 10.0631i) q^{25} +(-0.629943 - 1.09109i) q^{26} +(-2.15825 - 4.72673i) q^{27} +(-0.350452 - 1.03410i) q^{28} +1.78061i q^{29} +(-5.49913 - 6.99303i) q^{30} +(4.02710 + 2.32505i) q^{31} +(1.98694 + 1.14716i) q^{32} +(-4.25375 - 5.40933i) q^{33} -6.61365i q^{34} +(10.5778 + 2.10954i) q^{35} +(-1.18792 + 0.348750i) q^{36} +(2.92747 + 5.07053i) q^{37} +(-3.85646 + 6.67958i) q^{38} +(0.643773 - 1.60797i) q^{39} +(-10.7319 + 6.19607i) q^{40} -1.16060 q^{41} +(-3.15277 + 4.83670i) q^{42} +5.39213 q^{43} +(-1.41995 + 0.819811i) q^{44} +(2.88391 - 11.8854i) q^{45} +(-0.301858 + 0.522834i) q^{46} +(0.613160 + 1.06202i) q^{47} +(-0.740442 - 5.15068i) q^{48} +(-0.906749 - 6.94102i) q^{49} -14.6397i q^{50} +(7.14710 - 5.62029i) q^{51} +(-0.357397 - 0.206343i) q^{52} +(-1.04632 - 0.604090i) q^{53} +(5.33242 + 3.79773i) q^{54} -16.1971i q^{55} +(6.04389 + 5.30569i) q^{56} +(-10.4956 + 1.50880i) q^{57} +(-1.12168 - 1.94281i) q^{58} +(0.358619 - 0.621146i) q^{59} +(-2.70527 - 1.08310i) q^{60} +(0.520590 - 0.300563i) q^{61} -5.85859 q^{62} +(-7.90605 + 0.703165i) q^{63} -8.89922 q^{64} +(3.53057 - 2.03837i) q^{65} +(8.04881 + 3.22246i) q^{66} +(-2.10955 + 3.65385i) q^{67} +(-1.08318 - 1.87612i) q^{68} +(-0.821525 + 0.118099i) q^{69} +(-12.8702 + 4.36168i) q^{70} +2.72226i q^{71} +(6.29321 - 6.59955i) q^{72} +(9.05584 + 5.22839i) q^{73} +(-6.38829 - 3.68828i) q^{74} +(15.8206 - 12.4409i) q^{75} +2.52643i q^{76} +(-9.95552 + 3.37390i) q^{77} +(0.310511 + 2.15998i) q^{78} +(-0.460495 - 0.797600i) q^{79} +(6.12392 - 10.6069i) q^{80} +(0.427455 + 8.98984i) q^{81} +(1.26633 - 0.731115i) q^{82} -6.85477 q^{83} +(-0.102208 + 1.88840i) q^{84} +21.4005 q^{85} +(-5.88332 + 3.39673i) q^{86} +(1.14631 - 2.86316i) q^{87} +(6.03845 - 10.4589i) q^{88} +(1.74131 + 3.01603i) q^{89} +(4.34049 + 14.7847i) q^{90} +(-1.98831 - 1.74546i) q^{91} +0.197752i q^{92} +(-4.97864 - 6.33114i) q^{93} +(-1.33803 - 0.772511i) q^{94} +(-21.6138 - 12.4787i) q^{95} +(-2.45642 - 3.12374i) q^{96} +6.17977i q^{97} +(5.36180 + 7.00211i) q^{98} +(3.35751 + 11.4365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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