LMFDB - Embedded newform 232.3.b.c.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,3,Mod(115,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("232.115");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	232.b (of order $2$, degree $1$, 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:	$6.32154213316$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			115.2
Character	$\chi$	$=$	232.115
Dual form			232.3.b.c.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99351 + 0.160993i) q^{2} +4.31476i q^{3} +(3.94816 - 0.641884i) q^{4} -9.09838i q^{5} +(-0.694647 - 8.60151i) q^{6} +8.77758i q^{7} +(-7.76736 + 1.91523i) q^{8} -9.61712 q^{9} +O(q^{10})$	\(q+(-1.99351 + 0.160993i) q^{2} +4.31476i q^{3} +(3.94816 - 0.641884i) q^{4} -9.09838i q^{5} +(-0.694647 - 8.60151i) q^{6} +8.77758i q^{7} +(-7.76736 + 1.91523i) q^{8} -9.61712 q^{9} +(1.46478 + 18.1377i) q^{10} -1.74429i q^{11} +(2.76957 + 17.0354i) q^{12} +16.8340i q^{13} +(-1.41313 - 17.4982i) q^{14} +39.2573 q^{15} +(15.1760 - 5.06852i) q^{16} -0.967924i q^{17} +(19.1718 - 1.54829i) q^{18} +18.3924i q^{19} +(-5.84010 - 35.9219i) q^{20} -37.8731 q^{21} +(0.280820 + 3.47727i) q^{22} +33.7707i q^{23} +(-8.26375 - 33.5143i) q^{24} -57.7805 q^{25} +(-2.71016 - 33.5587i) q^{26} -2.66272i q^{27} +(5.63419 + 34.6553i) q^{28} +(-16.6970 - 23.7110i) q^{29} +(-78.2598 + 6.32017i) q^{30} -37.5606 q^{31} +(-29.4374 + 12.5474i) q^{32} +7.52620 q^{33} +(0.155829 + 1.92957i) q^{34} +79.8617 q^{35} +(-37.9700 + 6.17307i) q^{36} +31.0726 q^{37} +(-2.96106 - 36.6655i) q^{38} -72.6346 q^{39} +(17.4255 + 70.6704i) q^{40} +56.7049i q^{41} +(75.5004 - 6.09732i) q^{42} -47.3198i q^{43} +(-1.11963 - 6.88675i) q^{44} +87.5002i q^{45} +(-5.43685 - 67.3221i) q^{46} -39.7160 q^{47} +(21.8694 + 65.4806i) q^{48} -28.0459 q^{49} +(115.186 - 9.30229i) q^{50} +4.17636 q^{51} +(10.8055 + 66.4633i) q^{52} +28.9879i q^{53} +(0.428681 + 5.30817i) q^{54} -15.8702 q^{55} +(-16.8111 - 68.1786i) q^{56} -79.3588 q^{57} +(37.1030 + 44.5799i) q^{58} -4.69403 q^{59} +(154.994 - 25.1986i) q^{60} +101.994 q^{61} +(74.8774 - 6.04701i) q^{62} -84.4150i q^{63} +(56.6638 - 29.7526i) q^{64} +153.162 q^{65} +(-15.0036 + 1.21167i) q^{66} -29.6396 q^{67} +(-0.621295 - 3.82152i) q^{68} -145.712 q^{69} +(-159.205 + 12.8572i) q^{70} +59.6607i q^{71} +(74.6996 - 18.4190i) q^{72} -32.2061i q^{73} +(-61.9434 + 5.00248i) q^{74} -249.309i q^{75} +(11.8058 + 72.6162i) q^{76} +15.3107 q^{77} +(144.798 - 11.6937i) q^{78} -2.24792 q^{79} +(-46.1154 - 138.077i) q^{80} -75.0651 q^{81} +(-9.12912 - 113.042i) q^{82} +96.4157 q^{83} +(-149.529 + 24.3101i) q^{84} -8.80654 q^{85} +(7.61817 + 94.3325i) q^{86} +(102.307 - 72.0435i) q^{87} +(3.34072 + 13.5486i) q^{88} -90.5002i q^{89} +(-14.0870 - 174.433i) q^{90} -147.762 q^{91} +(21.6768 + 133.332i) q^{92} -162.065i q^{93} +(79.1742 - 6.39401i) q^{94} +167.341 q^{95} +(-54.1389 - 127.015i) q^{96} +77.5842i q^{97} +(55.9097 - 4.51520i) q^{98} +16.7751i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{4} - 184 q^{9}+O(q^{10}) $ 56 * q - 4 * q^4 - 184 * q^9	$ 56 q - 4 q^{4} - 184 q^{9} - 44 q^{16} - 12 q^{20} - 68 q^{22} - 72 q^{24} - 280 q^{25} + 116 q^{28} + 8 q^{30} + 32 q^{33} - 116 q^{34} + 96 q^{35} - 112 q^{36} - 176 q^{38} + 156 q^{42} - 424 q^{49} + 32 q^{51} - 56 q^{52} + 160 q^{54} + 32 q^{57} + 296 q^{58} + 512 q^{59} + 640 q^{62} - 304 q^{64} + 192 q^{65} + 352 q^{67} + 472 q^{74} + 44 q^{78} + 424 q^{80} + 280 q^{81} - 76 q^{82} + 128 q^{83} + 412 q^{86} - 84 q^{88} + 96 q^{91} - 92 q^{92} + 276 q^{94} + 300 q^{96}+O(q^{100}) $ 56 * q - 4 * q^4 - 184 * q^9 - 44 * q^16 - 12 * q^20 - 68 * q^22 - 72 * q^24 - 280 * q^25 + 116 * q^28 + 8 * q^30 + 32 * q^33 - 116 * q^34 + 96 * q^35 - 112 * q^36 - 176 * q^38 + 156 * q^42 - 424 * q^49 + 32 * q^51 - 56 * q^52 + 160 * q^54 + 32 * q^57 + 296 * q^58 + 512 * q^59 + 640 * q^62 - 304 * q^64 + 192 * q^65 + 352 * q^67 + 472 * q^74 + 44 * q^78 + 424 * q^80 + 280 * q^81 - 76 * q^82 + 128 * q^83 + 412 * q^86 - 84 * q^88 + 96 * q^91 - 92 * q^92 + 276 * q^94 + 300 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.99351	+	0.160993i	−0.996755	+	0.0804967i
$2$	−1.99351	+	0.160993i	−0.996755	+	0.0804967i
$3$			4.31476i			1.43825i	0.694880	+	0.719126i	$0.255458\pi$
$3$			4.31476i			1.43825i	−0.694880	+	0.719126i	$0.744542\pi$
$4$	3.94816	−	0.641884i	0.987041	−	0.160471i
$5$		−	9.09838i		−	1.81968i	−0.414963	−	0.909838i	$-0.636206\pi$
$5$		−	9.09838i		−	1.81968i	0.414963	−	0.909838i	$-0.363794\pi$
$6$	−0.694647	−	8.60151i	−0.115775	−	1.43358i
$7$			8.77758i			1.25394i	0.779043	+	0.626970i	$0.215705\pi$
$7$			8.77758i			1.25394i	−0.779043	+	0.626970i	$0.784295\pi$
$8$	−7.76736	+	1.91523i	−0.970920	+	0.239404i
$9$	−9.61712			−1.06857
$10$	1.46478	+	18.1377i	0.146478	+	1.81377i
$11$		−	1.74429i		−	0.158572i	−0.996852	−	0.0792860i	$-0.974736\pi$
$11$		−	1.74429i		−	0.158572i	0.996852	−	0.0792860i	$-0.0252640\pi$
$12$	2.76957	+	17.0354i	0.230798	+	1.41961i
$13$			16.8340i			1.29492i	0.762098	+	0.647461i	$0.224169\pi$
$13$			16.8340i			1.29492i	−0.762098	+	0.647461i	$0.775831\pi$
$14$	−1.41313	−	17.4982i	−0.100938	−	1.24987i
$15$	39.2573			2.61715
$16$	15.1760	−	5.06852i	0.948498	−	0.316783i
$17$		−	0.967924i		−	0.0569367i	−0.999595	−	0.0284684i	$-0.990937\pi$
$17$		−	0.967924i		−	0.0569367i	0.999595	−	0.0284684i	$-0.00906298\pi$
$18$	19.1718	−	1.54829i	1.06510	−	0.0860163i
$19$			18.3924i			0.968022i	0.875062	+	0.484011i	$0.160820\pi$
$19$			18.3924i			0.968022i	−0.875062	+	0.484011i	$0.839180\pi$
$20$	−5.84010	−	35.9219i	−0.292005	−	1.79609i
$21$	−37.8731			−1.80348
$22$	0.280820	+	3.47727i	0.0127645	+	0.158058i
$23$			33.7707i			1.46829i	0.678993	+	0.734145i	$0.262417\pi$
$23$			33.7707i			1.46829i	−0.678993	+	0.734145i	$0.737583\pi$
$24$	−8.26375	−	33.5143i	−0.344323	−	1.39643i
$25$	−57.7805			−2.31122
$26$	−2.71016	−	33.5587i	−0.104237	−	1.29072i
$27$		−	2.66272i		−	0.0986194i
$28$	5.63419	+	34.6553i	0.201221	+	1.23769i
$29$	−16.6970	−	23.7110i	−0.575759	−	0.817619i
$29$	−16.6970	−	23.7110i	−0.575759	−	0.817619i
$30$	−78.2598	+	6.32017i	−2.60866	+	0.210672i
$31$	−37.5606			−1.21163			−0.605816	−	0.795605i	$-0.707153\pi$
$31$	−37.5606			−1.21163			−0.605816	+	0.795605i	$0.707153\pi$
$32$	−29.4374	+	12.5474i	−0.919920	+	0.392106i
$33$	7.52620			0.228067
$34$	0.155829	+	1.92957i	0.00458322	+	0.0567519i
$35$	79.8617			2.28176
$36$	−37.9700	+	6.17307i	−1.05472	+	0.171474i
$37$	31.0726			0.839799			0.419899	−	0.907571i	$-0.362065\pi$
$37$	31.0726			0.839799			0.419899	+	0.907571i	$0.362065\pi$
$38$	−2.96106	−	36.6655i	−0.0779226	−	0.964880i
$39$	−72.6346			−1.86243
$40$	17.4255	+	70.6704i	0.435637	+	1.76676i
$41$			56.7049i			1.38305i	0.722354	+	0.691524i	$0.243060\pi$
$41$			56.7049i			1.38305i	−0.722354	+	0.691524i	$0.756940\pi$
$42$	75.5004	−	6.09732i	1.79763	−	0.145174i
$43$		−	47.3198i		−	1.10046i	−0.835013	−	0.550230i	$-0.814540\pi$
$43$		−	47.3198i		−	1.10046i	0.835013	−	0.550230i	$-0.185460\pi$
$44$	−1.11963	−	6.88675i	−0.0254462	−	0.156517i
$45$			87.5002i			1.94445i
$46$	−5.43685	−	67.3221i	−0.118192	−	1.46352i
$47$	−39.7160			−0.845020			−0.422510	−	0.906358i	$-0.638851\pi$
$47$	−39.7160			−0.845020			−0.422510	+	0.906358i	$0.638851\pi$
$48$	21.8694	+	65.4806i	0.455613	+	1.36418i
$49$	−28.0459			−0.572365
$50$	115.186	−	9.30229i	2.30372	−	0.186046i
$51$	4.17636			0.0818893
$52$	10.8055	+	66.4633i	0.207798	+	1.27814i
$53$			28.9879i			0.546942i	0.961880	+	0.273471i	$0.0881718\pi$
$53$			28.9879i			0.546942i	−0.961880	+	0.273471i	$0.911828\pi$
$54$	0.428681	+	5.30817i	0.00793854	+	0.0982994i
$55$	−15.8702			−0.288550
$56$	−16.8111	−	68.1786i	−0.300198	−	1.21748i
$57$	−79.3588			−1.39226
$58$	37.1030	+	44.5799i	0.639706	+	0.768619i
$59$	−4.69403			−0.0795598			−0.0397799	−	0.999208i	$-0.512666\pi$
$59$	−4.69403			−0.0795598			−0.0397799	+	0.999208i	$0.512666\pi$
$60$	154.994	−	25.1986i	2.58324	−	0.419977i
$61$	101.994			1.67204			0.836018	−	0.548702i	$-0.184878\pi$
$61$	101.994			1.67204			0.836018	+	0.548702i	$0.184878\pi$
$62$	74.8774	−	6.04701i	1.20770	−	0.0975324i
$63$		−	84.4150i		−	1.33992i
$64$	56.6638	−	29.7526i	0.885372	−	0.464884i
$65$	153.162			2.35634
$66$	−15.0036	+	1.21167i	−0.227327	+	0.0183586i
$67$	−29.6396			−0.442382			−0.221191	−	0.975230i	$-0.570994\pi$
$67$	−29.6396			−0.442382			−0.221191	+	0.975230i	$0.570994\pi$
$68$	−0.621295	−	3.82152i	−0.00913669	−	0.0561988i
$69$	−145.712			−2.11177
$70$	−159.205	+	12.8572i	−2.27436	+	0.183675i
$71$			59.6607i			0.840291i	0.907457	+	0.420146i	$0.138021\pi$
$71$			59.6607i			0.840291i	−0.907457	+	0.420146i	$0.861979\pi$
$72$	74.6996	−	18.4190i	1.03750	−	0.255819i
$73$		−	32.2061i		−	0.441180i	−0.975367	−	0.220590i	$-0.929202\pi$
$73$		−	32.2061i		−	0.441180i	0.975367	−	0.220590i	$-0.0707983\pi$
$74$	−61.9434	+	5.00248i	−0.837073	+	0.0676010i
$75$		−	249.309i		−	3.32412i
$76$	11.8058	+	72.6162i	0.155339	+	0.955477i
$77$	15.3107			0.198840
$78$	144.798	−	11.6937i	1.85638	−	0.149919i
$79$	−2.24792			−0.0284547			−0.0142274	−	0.999899i	$-0.504529\pi$
$79$	−2.24792			−0.0284547			−0.0142274	+	0.999899i	$0.504529\pi$
$80$	−46.1154	−	138.077i	−0.576442	−	1.72596i
$81$	−75.0651			−0.926729
$82$	−9.12912	−	113.042i	−0.111331	−	1.37856i
$83$	96.4157			1.16164			0.580818	−	0.814034i	$-0.302733\pi$
$83$	96.4157			1.16164			0.580818	+	0.814034i	$0.302733\pi$
$84$	−149.529	+	24.3101i	−1.78011	+	0.289406i
$85$	−8.80654			−0.103606
$86$	7.61817	+	94.3325i	0.0885834	+	1.09689i
$87$	102.307	−	72.0435i	1.17594	−	0.828087i
$88$	3.34072	+	13.5486i	0.0379628	+	0.153961i
$89$		−	90.5002i		−	1.01686i	−0.861105	−	0.508428i	$-0.830227\pi$
$89$		−	90.5002i		−	1.01686i	0.861105	−	0.508428i	$-0.169773\pi$
$90$	−14.0870	−	174.433i	−0.156522	−	1.93814i
$91$	−147.762			−1.62376
$92$	21.6768	+	133.332i	0.235618	+	1.44926i
$93$		−	162.065i		−	1.74263i
$94$	79.1742	−	6.39401i	0.842278	−	0.0680214i
$95$	167.341			1.76149
$96$	−54.1389	−	127.015i	−0.563947	−	1.32308i
$97$			77.5842i			0.799838i	0.916551	+	0.399919i	$0.130962\pi$
$97$			77.5842i			0.799838i	−0.916551	+	0.399919i	$0.869038\pi$
$98$	55.9097	−	4.51520i	0.570508	−	0.0460735i
$99$			16.7751i			0.169445i
$100$	−228.127	+	37.0884i	−2.28127	+	0.370884i
$101$	118.620			1.17446			0.587230	−	0.809420i	$-0.300219\pi$
$101$	118.620			1.17446			0.587230	+	0.809420i	$0.300219\pi$
$102$	−8.32561	+	0.672366i	−0.0816236	+	0.00659182i
$103$			107.532i			1.04400i	0.852946	+	0.522000i	$0.174814\pi$
$103$			107.532i			1.04400i	−0.852946	+	0.522000i	$0.825186\pi$
$104$	−32.2410	−	130.756i	−0.310009	−	1.25727i
$105$			344.584i			3.28175i
$106$	−4.66687	−	57.7877i	−0.0440270	−	0.545167i
$107$	9.27239			0.0866579			0.0433289	−	0.999061i	$-0.486204\pi$
$107$	9.27239			0.0866579			0.0433289	+	0.999061i	$0.486204\pi$
$108$	−1.70916	−	10.5129i	−0.0158256	−	0.0973413i
$109$			54.8428i			0.503145i	0.967838	+	0.251573i	$0.0809477\pi$
$109$			54.8428i			0.503145i	−0.967838	+	0.251573i	$0.919052\pi$
$110$	31.6375	−	2.55500i	0.287613	−	0.0232273i
$111$			134.070i			1.20784i
$112$	44.4894	+	133.208i	0.397226	+	1.18936i
$113$			144.241i			1.27647i	0.769841	+	0.638236i	$0.220336\pi$
$113$			144.241i			1.27647i	−0.769841	+	0.638236i	$0.779664\pi$
$114$	158.202	−	12.7762i	1.38774	−	0.112072i
$115$	307.258			2.67181
$116$	−81.1422	−	82.8972i	−0.699502	−	0.714631i
$117$		−	161.895i		−	1.38371i
$118$	9.35759	−	0.755708i	0.0793017	−	0.00640430i
$119$	8.49603			0.0713952
$120$	−304.926	+	75.1867i	−2.54105	+	0.626556i
$121$	117.957			0.974855
$122$	−203.326	+	16.4204i	−1.66661	+	0.134593i
$123$	−244.668			−1.98917
$124$	−148.295	+	24.1095i	−1.19593	+	0.194432i
$125$			298.250i			2.38600i
$126$	13.5903	+	168.282i	0.107859	+	1.33557i
$127$	61.2919			0.482613			0.241307	−	0.970449i	$-0.422424\pi$
$127$	61.2919			0.482613			0.241307	+	0.970449i	$0.422424\pi$
$128$	−108.170	+	68.4345i	−0.845077	+	0.534645i
$129$	204.173			1.58274
$130$	−305.330	+	24.6581i	−2.34869	+	0.189678i
$131$		−	92.4216i		−	0.705508i	−0.935716	−	0.352754i	$-0.885245\pi$
$131$		−	92.4216i		−	0.705508i	0.935716	−	0.352754i	$-0.114755\pi$
$132$	29.7147	−	4.83095i	0.225111	−	0.0365981i
$133$	−161.441			−1.21384
$134$	59.0868	−	4.77178i	0.440947	−	0.0356103i
$135$	−24.2265			−0.179455
$136$	1.85380	+	7.51822i	0.0136309	+	0.0552810i
$137$		−	245.355i		−	1.79091i	−0.445150	−	0.895456i	$-0.646850\pi$
$137$		−	245.355i		−	1.79091i	0.445150	−	0.895456i	$-0.353150\pi$
$138$	290.479	−	23.4587i	2.10492	−	0.169991i
$139$	59.3176			0.426745			0.213373	−	0.976971i	$-0.431555\pi$
$139$	59.3176			0.426745			0.213373	+	0.976971i	$0.431555\pi$
$140$	315.307	−	51.2620i	2.25219	−	0.366157i
$141$		−	171.365i		−	1.21535i
$142$	−9.60498	−	118.934i	−0.0676407	−	0.837564i
$143$	29.3634			0.205339
$144$	−145.949	+	48.7446i	−1.01354	+	0.338504i
$145$	−215.731	+	151.916i	−1.48780	+	1.04770i
$146$	5.18498	+	64.2032i	0.0355135	+	0.439748i
$147$		−	121.011i		−	0.823205i
$148$	122.679	−	19.9450i	0.828915	−	0.134763i
$149$		−	147.280i		−	0.988459i	−0.869331	−	0.494230i	$-0.835450\pi$
$149$		−	147.280i		−	0.988459i	0.869331	−	0.494230i	$-0.164550\pi$
$150$	40.1371	+	497.000i	0.267581	+	3.31333i
$151$		−	190.560i		−	1.26199i	−0.775789	−	0.630993i	$-0.782648\pi$
$151$		−	190.560i		−	1.26199i	0.775789	−	0.630993i	$-0.217352\pi$
$152$	−35.2257	−	142.860i	−0.231748	−	0.939872i
$153$			9.30864i			0.0608408i
$154$	−30.5220	+	2.46492i	−0.198195	+	0.0160060i
$155$			341.741i			2.20478i
$156$	−286.773	+	46.6230i	−1.83829	+	0.298865i
$157$	45.6520			0.290777			0.145388	−	0.989375i	$-0.453557\pi$
$157$	45.6520			0.290777			0.145388	+	0.989375i	$0.453557\pi$
$158$	4.48126	−	0.361901i	0.0283624	−	0.00229051i
$159$	−125.076			−0.786641
$160$	114.161	+	267.833i	0.713505	+	1.67396i
$161$	−296.425			−1.84115
$162$	149.643	−	12.0850i	0.923722	−	0.0745987i
$163$		−	64.3793i		−	0.394965i	−0.980306	−	0.197483i	$-0.936723\pi$
$163$		−	64.3793i		−	0.394965i	0.980306	−	0.197483i	$-0.0632766\pi$
$164$	36.3980	+	223.880i	0.221939	+	1.36512i
$165$		−	68.4762i		−	0.415007i
$166$	−192.206	+	15.5223i	−1.15787	+	0.0935078i
$167$		−	221.779i		−	1.32802i	−0.747723	−	0.664010i	$-0.768853\pi$
$167$		−	221.779i		−	1.32802i	0.747723	−	0.664010i	$-0.231147\pi$
$168$	294.174	−	72.5357i	1.75104	−	0.431760i
$169$	−114.383			−0.676825
$170$	17.5559	−	1.41780i	0.103270	−	0.00833997i
$171$		−	176.882i		−	1.03440i
$172$	−30.3738	−	186.826i	−0.176592	−	1.08620i
$173$			59.6822i			0.344984i	0.985011	+	0.172492i	$0.0551818\pi$
$173$			59.6822i			0.344984i	−0.985011	+	0.172492i	$0.944818\pi$
$174$	−192.352	+	160.090i	−1.10547	+	0.920059i
$175$		−	507.173i		−	2.89813i
$176$	−8.84099	−	26.4713i	−0.0502329	−	0.150405i
$177$		−	20.2536i		−	0.114427i
$178$	14.5699	+	180.413i	0.0818535	+	1.01356i
$179$	−294.772			−1.64677			−0.823386	−	0.567481i	$-0.807918\pi$
$179$	−294.772			−1.64677			−0.823386	+	0.567481i	$0.807918\pi$
$180$	56.1650	+	345.465i	0.312028	+	1.91925i
$181$			23.2086i			0.128224i	0.997943	+	0.0641121i	$0.0204215\pi$
$181$			23.2086i			0.128224i	−0.997943	+	0.0641121i	$0.979578\pi$
$182$	294.564	−	23.7887i	1.61849	−	0.130707i
$183$			440.080i			2.40481i
$184$	−64.6786	−	262.309i	−0.351514	−	1.42559i
$185$		−	282.710i		−	1.52816i
$186$	26.0914	+	323.078i	0.140276	+	1.73698i
$187$	−1.68834			−0.00902857
$188$	−156.805	+	25.4930i	−0.834069	+	0.135601i
$189$	23.3723			0.123663
$190$	−333.596	+	26.9408i	−1.75577	+	0.141794i
$191$	102.215			0.535155			0.267577	−	0.963536i	$-0.413777\pi$
$191$	102.215			0.535155			0.267577	+	0.963536i	$0.413777\pi$
$192$	128.375	+	244.490i	0.668620	+	1.27339i
$193$			106.004i			0.549246i	0.961552	+	0.274623i	$0.0885530\pi$
$193$			106.004i			0.549246i	−0.961552	+	0.274623i	$0.911447\pi$
$194$	−12.4906	−	154.665i	−0.0643843	−	0.797242i
$195$			660.857i			3.38901i
$196$	−110.730	+	18.0022i	−0.564947	+	0.0918480i
$197$		−	247.290i		−	1.25528i	−0.778504	−	0.627640i	$-0.784021\pi$
$197$		−	247.290i		−	1.25528i	0.778504	−	0.627640i	$-0.215979\pi$
$198$	−2.70068	−	33.4413i	−0.0136398	−	0.168895i
$199$			117.710i			0.591508i	0.955264	+	0.295754i	$0.0955709\pi$
$199$			117.710i			0.591508i	−0.955264	+	0.295754i	$0.904429\pi$
$200$	448.802	−	110.663i	2.24401	−	0.553315i
$201$		−	127.888i		−	0.636257i
$202$	−236.471	+	19.0971i	−1.17065	+	0.0945401i
$203$	208.125	−	146.559i	1.02525	−	0.721967i
$204$	16.4889	−	2.68074i	0.0808281	−	0.0131409i
$205$	515.923			2.51670
$206$	−17.3119	−	214.366i	−0.0840385	−	1.04061i
$207$		−	324.776i		−	1.56897i
$208$	85.3235	+	255.472i	0.410209	+	1.22823i
$209$	32.0818			0.153501
$210$	−55.4758	−	686.932i	−0.264170	−	3.27110i
$211$			117.543i			0.557077i	0.960425	+	0.278538i	$0.0898499\pi$
$211$			117.543i			0.557077i	−0.960425	+	0.278538i	$0.910150\pi$
$212$	18.6069	+	114.449i	0.0877683	+	0.539854i
$213$	−257.421			−1.20855
$214$	−18.4846	+	1.49279i	−0.0863767	+	0.00697567i
$215$	−430.533			−2.00248
$216$	5.09973	+	20.6823i	0.0236099	+	0.0957516i
$217$		−	329.691i		−	1.51931i
$218$	−8.82933	−	109.330i	−0.0405015	−	0.501512i
$219$	138.962			0.634528
$220$	−62.6583	+	10.1869i	−0.284810	+	0.0463039i
$221$	16.2940			0.0737286
$222$	−21.5845	−	267.271i	−0.0972273	−	1.20392i
$223$		−	49.2386i		−	0.220801i	−0.993887	−	0.110401i	$-0.964787\pi$
$223$		−	49.2386i		−	0.220801i	0.993887	−	0.110401i	$-0.0352134\pi$
$224$	−110.136	−	258.389i	−0.491677	−	1.15352i
$225$	555.682			2.46970
$226$	−23.2219	−	287.546i	−0.102752	−	1.27233i
$227$	242.362			1.06768			0.533838	−	0.845587i	$-0.320749\pi$
$227$	242.362			1.06768			0.533838	+	0.845587i	$0.320749\pi$
$228$	−313.321	+	50.9391i	−1.37422	+	0.223417i
$229$	−19.6984			−0.0860191			−0.0430095	−	0.999075i	$-0.513695\pi$
$229$	−19.6984			−0.0860191			−0.0430095	+	0.999075i	$0.513695\pi$
$230$	−612.522	+	49.4666i	−2.66314	+	0.215072i
$231$			66.0618i			0.285982i
$232$	175.104	+	152.193i	0.754757	+	0.656004i
$233$	3.22958			0.0138609			0.00693043	−	0.999976i	$-0.497794\pi$
$233$	3.22958			0.0138609			0.00693043	+	0.999976i	$0.497794\pi$
$234$	26.0640	+	322.738i	0.111384	+	1.37922i
$235$			361.351i			1.53766i
$236$	−18.5328	+	3.01302i	−0.0785288	+	0.0127670i
$237$		−	9.69925i		−	0.0409251i
$238$	−16.9369	+	1.36780i	−0.0711635	+	0.00574708i
$239$			433.810i			1.81510i	0.419941	+	0.907552i	$0.362051\pi$
$239$			433.810i			1.81510i	−0.419941	+	0.907552i	$0.637949\pi$
$240$	595.768	−	198.977i	2.48236	−	0.829069i
$241$	−323.772			−1.34345			−0.671726	−	0.740800i	$-0.734447\pi$
$241$	−323.772			−1.34345			−0.671726	+	0.740800i	$0.734447\pi$
$242$	−235.149	+	18.9904i	−0.971691	+	0.0784726i
$243$		−	347.852i		−	1.43149i
$244$	402.690	−	65.4684i	1.65037	−	0.268313i
$245$			255.172i			1.04152i
$246$	487.748	−	39.3899i	1.98272	−	0.160122i
$247$	−309.618			−1.25351
$248$	291.747	−	71.9372i	1.17640	−	0.290069i
$249$			416.010i			1.67072i
$250$	−48.0162	−	594.564i	−0.192065	−	2.37826i
$251$		−	218.954i		−	0.872325i	−0.899868	−	0.436163i	$-0.856337\pi$
$251$		−	218.954i		−	0.872325i	0.899868	−	0.436163i	$-0.143663\pi$
$252$	−54.1846	−	333.284i	−0.215018	−	1.32256i
$253$	58.9059			0.232830
$254$	−122.186	+	9.86759i	−0.481047	+	0.0388488i
$255$		−	37.9981i		−	0.149012i
$256$	204.620	−	153.840i	0.799297	−	0.600936i
$257$	−183.393			−0.713592			−0.356796	−	0.934182i	$-0.616131\pi$
$257$	−183.393			−0.713592			−0.356796	+	0.934182i	$0.616131\pi$
$258$	−407.022	+	32.8706i	−1.57760	+	0.127405i
$259$			272.742i			1.05306i
$260$	604.709	−	98.3123i	2.32580	−	0.378124i
$261$	160.577	+	228.031i	0.615238	+	0.873683i
$262$	14.8793	+	184.243i	0.0567911	+	0.703219i
$263$	406.786			1.54671			0.773357	−	0.633970i	$-0.218576\pi$
$263$	406.786			1.54671			0.773357	+	0.633970i	$0.218576\pi$
$264$	−58.4587	+	14.4144i	−0.221434	+	0.0546000i
$265$	263.743			0.995258
$266$	321.834	−	25.9909i	1.20990	−	0.0977102i
$267$	390.486			1.46249
$268$	−117.022	+	19.0252i	−0.436649	+	0.0709895i
$269$	−66.9942			−0.249049			−0.124525	−	0.992217i	$-0.539741\pi$
$269$	−66.9942			−0.249049			−0.124525	+	0.992217i	$0.539741\pi$
$270$	48.2957	−	3.90030i	0.178873	−	0.0144456i
$271$	414.247			1.52859			0.764294	−	0.644868i	$-0.223088\pi$
$271$	414.247			1.52859			0.764294	+	0.644868i	$0.223088\pi$
$272$	−4.90595	−	14.6892i	−0.0180366	−	0.0540044i
$273$		−	637.556i		−	2.33537i
$274$	39.5005	+	489.118i	0.144163	+	1.78510i
$275$			100.786i			0.366495i
$276$	−575.295	+	93.5303i	−2.08440	+	0.338878i
$277$			109.155i			0.394060i	0.980397	+	0.197030i	$0.0631296\pi$
$277$			109.155i			0.394060i	−0.980397	+	0.197030i	$0.936870\pi$
$278$	−118.250	+	9.54975i	−0.425361	+	0.0343516i
$279$	361.225			1.29471
$280$	−620.315	+	152.954i	−2.21541	+	0.546263i
$281$	20.1300			0.0716371			0.0358186	−	0.999358i	$-0.488596\pi$
$281$	20.1300			0.0716371			0.0358186	+	0.999358i	$0.488596\pi$
$282$	27.5886	+	341.617i	0.0978319	+	1.21141i
$283$	49.8501			0.176149			0.0880743	−	0.996114i	$-0.471929\pi$
$283$	49.8501			0.176149			0.0880743	+	0.996114i	$0.471929\pi$
$284$	38.2952	+	235.550i	0.134842	+	0.829401i
$285$			722.036i			2.53346i
$286$	−58.5363	+	4.72732i	−0.204672	+	0.0165291i
$287$	−497.732			−1.73426
$288$	283.103	−	120.670i	0.982998	−	0.418992i
$289$	288.063			0.996758
$290$	405.605	−	337.577i	1.39864	−	1.16406i
$291$	−334.757			−1.15037
$292$	−20.6726	−	127.155i	−0.0707966	−	0.435462i
$293$	−558.337			−1.90559			−0.952793	−	0.303621i	$-0.901804\pi$
$293$	−558.337			−1.90559			−0.952793	+	0.303621i	$0.901804\pi$
$294$	19.4820	+	241.237i	0.0662653	+	0.820534i
$295$			42.7081i			0.144773i
$296$	−241.352	+	59.5111i	−0.815377	+	0.201051i
$297$	−4.64457			−0.0156383
$298$	23.7112	+	293.605i	0.0795677	+	0.985252i
$299$	−568.495			−1.90132
$300$	−160.027	−	984.312i	−0.533425	−	3.28104i
$301$	415.353			1.37991
$302$	30.6789	+	379.883i	0.101586	+	1.25789i
$303$			511.818i			1.68917i
$304$	93.2224	+	279.123i	0.306653	+	0.918167i
$305$		−	927.982i		−	3.04256i
$306$	−1.49863	−	18.5569i	−0.00489748	−	0.0606434i
$307$		−	34.1166i		−	0.111129i	−0.998455	−	0.0555644i	$-0.982304\pi$
$307$		−	34.1166i		−	0.111129i	0.998455	−	0.0555644i	$-0.0176958\pi$
$308$	60.4490	−	9.82767i	0.196263	−	0.0319080i
$309$	−463.974			−1.50153
$310$	−55.0180	−	681.263i	−0.177477	−	2.19762i
$311$	158.328			0.509093			0.254547	−	0.967061i	$-0.418074\pi$
$311$	158.328			0.509093			0.254547	+	0.967061i	$0.418074\pi$
$312$	564.179	−	139.112i	1.80827	−	0.445872i
$313$	4.81090			0.0153703			0.00768514	−	0.999970i	$-0.497554\pi$
$313$	4.81090			0.0153703			0.00768514	+	0.999970i	$0.497554\pi$
$314$	−91.0077	+	7.34967i	−0.289833	+	0.0234066i
$315$	−768.040			−2.43822
$316$	−8.87517	+	1.44291i	−0.0280860	+	0.00456616i
$317$	191.615			0.604464			0.302232	−	0.953234i	$-0.402268\pi$
$317$	191.615			0.604464			0.302232	+	0.953234i	$0.402268\pi$
$318$	249.340	−	20.1364i	0.784088	−	0.0633220i
$319$	−41.3589	+	29.1245i	−0.129652	+	0.0912993i
$320$	−270.700	−	515.549i	−0.845938	−	1.61109i
$321$			40.0081i			0.124636i
$322$	590.925	−	47.7224i	1.83517	−	0.148206i
$323$	17.8025			0.0551160
$324$	−296.369	+	48.1831i	−0.914719	+	0.148713i
$325$		−	972.677i		−	2.99285i
$326$	10.3646	+	128.341i	0.0317934	+	0.393683i
$327$	−236.633			−0.723650
$328$	−108.603	−	440.448i	−0.331107	−	1.34283i
$329$		−	348.610i		−	1.05960i
$330$	11.0242	+	136.508i	0.0334067	+	0.413661i
$331$		−	380.202i		−	1.14865i	−0.818629	−	0.574323i	$-0.805266\pi$
$331$		−	380.202i		−	1.14865i	0.818629	−	0.574323i	$-0.194734\pi$
$332$	380.665	−	61.8877i	1.14658	−	0.186409i
$333$	−298.828			−0.897383
$334$	35.7050	+	442.119i	0.106901	+	1.32371i
$335$			269.672i			0.804992i
$336$	−574.761	+	191.961i	−1.71060	+	0.571312i
$337$			156.403i			0.464104i	0.972703	+	0.232052i	$0.0745439\pi$
$337$			156.403i			0.464104i	−0.972703	+	0.232052i	$0.925456\pi$
$338$	228.024	−	18.4150i	0.674628	−	0.0544822i
$339$	−622.366			−1.83589
$340$	−34.7697	+	5.65278i	−0.102264	+	0.0166258i
$341$			65.5167i			0.192131i
$342$	28.4768	+	352.616i	0.0832656	+	1.03104i
$343$			183.926i			0.536229i
$344$	90.6283	+	367.550i	0.263454	+	1.06846i
$345$			1325.74i			3.84274i
$346$	−9.60844	−	118.977i	−0.0277700	−	0.343864i
$347$	−229.602			−0.661678			−0.330839	−	0.943687i	$-0.607332\pi$
$347$	−229.602			−0.661678			−0.330839	+	0.943687i	$0.607332\pi$
$348$	357.681	−	350.109i	1.02782	−	1.00606i
$349$			249.644i			0.715312i	0.933853	+	0.357656i	$0.116424\pi$
$349$			249.644i			0.715312i	−0.933853	+	0.357656i	$0.883576\pi$
$350$	81.6515	+	1011.05i	0.233290	+	2.88873i
$351$	44.8243			0.127704
$352$	21.8863	+	51.3475i	0.0621770	+	0.145874i
$353$	203.535			0.576587			0.288294	−	0.957542i	$-0.406912\pi$
$353$	203.535			0.576587			0.288294	+	0.957542i	$0.406912\pi$
$354$	3.26070	+	40.3757i	0.00921100	+	0.114056i
$355$	542.815			1.52906
$356$	−58.0906	−	357.309i	−0.163176	−	1.00368i
$357$			36.6583i			0.102684i
$358$	587.631	−	47.4564i	1.64143	−	0.132560i
$359$	161.715			0.450458			0.225229	−	0.974306i	$-0.427687\pi$
$359$	161.715			0.450458			0.225229	+	0.974306i	$0.427687\pi$
$360$	−167.583	−	679.646i	−0.465508	−	1.88790i
$361$	22.7192			0.0629341
$362$	−3.73643	−	46.2665i	−0.0103216	−	0.127808i
$363$			508.958i			1.40209i
$364$	−583.387	+	94.8459i	−1.60271	+	0.260566i
$365$	−293.024			−0.802805
$366$	−70.8500	−	877.304i	−0.193579	−	2.39701i
$367$	159.409			0.434356			0.217178	−	0.976132i	$-0.430315\pi$
$367$	159.409			0.434356			0.217178	+	0.976132i	$0.430315\pi$
$368$	171.167	+	512.503i	0.465129	+	1.39267i
$369$		−	545.338i		−	1.47788i
$370$	45.5144	+	563.585i	0.123012	+	1.52320i
$371$	−254.444			−0.685833
$372$	−104.027	−	639.858i	−0.279642	−	1.72005i
$373$		−	142.830i		−	0.382923i	−0.981500	−	0.191462i	$-0.938677\pi$
$373$		−	142.830i		−	0.382923i	0.981500	−	0.191462i	$-0.0613227\pi$
$374$	3.36573	−	0.271812i	0.00899927	−	0.000726770i
$375$	−1286.87			−3.43167
$376$	308.488	−	76.0652i	0.820447	−	0.202301i
$377$	399.150	−	281.077i	1.05875	−	0.745563i
$378$	−46.5928	+	3.76278i	−0.123261	+	0.00995445i
$379$			158.115i			0.417190i	0.978002	+	0.208595i	$0.0668890\pi$
$379$			158.115i			0.417190i	−0.978002	+	0.208595i	$0.933111\pi$
$380$	660.690	−	107.414i	1.73866	−	0.282667i
$381$			264.459i			0.694119i
$382$	−203.766	+	16.4559i	−0.533418	+	0.0430782i
$383$			53.2261i			0.138972i	0.997583	+	0.0694858i	$0.0221359\pi$
$383$			53.2261i			0.138972i	−0.997583	+	0.0694858i	$0.977864\pi$
$384$	−295.278	−	466.727i	−0.768954	−	1.21543i
$385$		−	139.302i		−	0.361824i
$386$	−17.0660	−	211.321i	−0.0442125	−	0.547463i
$387$			455.080i			1.17592i
$388$	49.8001	+	306.315i	0.128351	+	0.789472i
$389$	388.754			0.999369			0.499684	−	0.866208i	$-0.333449\pi$
$389$	388.754			0.999369			0.499684	+	0.866208i	$0.333449\pi$
$390$	−106.394	−	1317.43i	−0.272804	−	3.37801i
$391$	32.6874			0.0835996
$392$	217.842	−	53.7143i	0.555721	−	0.137026i
$393$	398.777			1.01470
$394$	39.8121	+	492.975i	0.101046	+	1.25121i
$395$			20.4525i			0.0517784i
$396$	10.7677	+	66.2307i	0.0271910	+	0.167249i
$397$		−	672.563i		−	1.69411i	−0.531503	−	0.847056i	$-0.678373\pi$
$397$		−	672.563i		−	1.69411i	0.531503	−	0.847056i	$-0.321627\pi$
$398$	−18.9506	−	234.656i	−0.0476145	−	0.589589i
$399$		−	696.578i		−	1.74581i
$400$	−876.876	+	292.862i	−2.19219	+	0.732155i
$401$	498.847			1.24401			0.622004	−	0.783014i	$-0.286319\pi$
$401$	498.847			1.24401			0.622004	+	0.783014i	$0.286319\pi$
$402$	20.5891	+	254.945i	0.0512166	+	0.634192i
$403$		−	632.295i		−	1.56897i
$404$	468.333	−	76.1405i	1.15924	−	0.188467i
$405$			682.971i			1.68635i
$406$	−391.304	+	325.674i	−0.963802	+	0.802153i
$407$		−	54.1996i		−	0.133169i
$408$	−32.4393	+	7.99868i	−0.0795080	+	0.0196046i
$409$			588.327i			1.43845i	0.694776	+	0.719226i	$0.255503\pi$
$409$			588.327i			1.43845i	−0.694776	+	0.719226i	$0.744497\pi$
$410$	−1028.50	+	83.0602i	−2.50853	+	0.202586i
$411$	1058.65			2.57578
$412$	69.0230	+	424.553i	0.167532	+	1.03047i
$413$		−	41.2022i		−	0.0997632i
$414$	52.2869	+	647.445i	0.126297	+	1.56388i
$415$		−	877.227i		−	2.11380i
$416$	−211.223	−	495.550i	−0.507747	−	1.19123i
$417$			255.941i			0.613768i
$418$	−63.9553	+	5.16495i	−0.153003	+	0.0123563i
$419$	−128.326			−0.306267			−0.153133	−	0.988206i	$-0.548936\pi$
$419$	−128.326			−0.306267			−0.153133	+	0.988206i	$0.548936\pi$
$420$	221.183	+	1360.47i	0.526626	+	3.23922i
$421$	−146.650			−0.348337			−0.174169	−	0.984716i	$-0.555724\pi$
$421$	−146.650			−0.348337			−0.174169	+	0.984716i	$0.555724\pi$
$422$	−18.9237	−	234.323i	−0.0448428	−	0.555269i
$423$	381.953			0.902963
$424$	−55.5186	−	225.160i	−0.130940	−	0.531037i
$425$			55.9272i			0.131593i
$426$	513.172	−	41.4431i	1.20463	−	0.0972843i
$427$			895.262i			2.09663i
$428$	36.6089	−	5.95180i	0.0855349	−	0.0139061i
$429$			126.696i			0.295329i
$430$	858.273	−	69.3130i	1.99598	−	0.161193i
$431$		−	348.797i		−	0.809275i	−0.914477	−	0.404637i	$-0.867398\pi$
$431$		−	348.797i		−	0.809275i	0.914477	−	0.404637i	$-0.132602\pi$
$432$	−13.4961	−	40.4094i	−0.0312409	−	0.0935403i
$433$			180.925i			0.417841i	0.977933	+	0.208921i	$0.0669950\pi$
$433$			180.925i			0.417841i	−0.977933	+	0.208921i	$0.933005\pi$
$434$	53.0781	+	657.242i	0.122300	+	1.51438i
$435$	−655.480	−	930.828i	−1.50685	−	2.13983i
$436$	35.2027	+	216.528i	0.0807402	+	0.496625i
$437$	−621.124			−1.42134
$438$	−277.021	+	22.3719i	−0.632469	+	0.0510774i
$439$		−	414.891i		−	0.945081i	−0.881309	−	0.472541i	$-0.843337\pi$
$439$		−	414.891i		−	0.945081i	0.881309	−	0.472541i	$-0.156663\pi$
$440$	123.270	−	30.3952i	0.280159	−	0.0690799i
$441$	269.721			0.611611
$442$	−32.4823	+	2.62323i	−0.0734894	+	0.00593491i
$443$			739.497i			1.66929i	0.550786	+	0.834646i	$0.314328\pi$
$443$			739.497i			1.66929i	−0.550786	+	0.834646i	$0.685672\pi$
$444$	86.0577	+	529.332i	0.193824	+	1.19219i
$445$	−823.405			−1.85035
$446$	7.92709	+	98.1577i	0.0177738	+	0.220084i
$447$	635.479			1.42165
$448$	261.155	+	497.371i	0.582936	+	1.11020i
$449$			424.080i			0.944498i	0.881465	+	0.472249i	$0.156558\pi$
$449$			424.080i			0.944498i	−0.881465	+	0.472249i	$0.843442\pi$
$450$	−1107.76	+	89.4612i	−2.46168	+	0.198803i
$451$	98.9100			0.219313
$452$	92.5862	+	569.488i	0.204837	+	1.25993i
$453$	822.219			1.81505
$454$	−483.152	+	39.0188i	−1.06421	+	0.0859444i
$455$			1344.39i			2.95471i
$456$	616.408	−	151.990i	1.35177	−	0.333312i
$457$	−719.159			−1.57365			−0.786826	−	0.617175i	$-0.788277\pi$
$457$	−719.159			−1.57365			−0.786826	+	0.617175i	$0.788277\pi$
$458$	39.2689	−	3.17131i	0.0857399	−	0.00692425i
$459$	−2.57731			−0.00561506
$460$	1213.11	−	197.224i	2.63719	−	0.428748i
$461$	117.087			0.253985			0.126992	−	0.991904i	$-0.459468\pi$
$461$	117.087			0.253985			0.126992	+	0.991904i	$0.459468\pi$
$462$	−10.6355	−	131.695i	−0.0230206	−	0.285054i
$463$		−	400.074i		−	0.864091i	−0.901852	−	0.432046i	$-0.857792\pi$
$463$		−	400.074i		−	0.864091i	0.901852	−	0.432046i	$-0.142208\pi$
$464$	−373.573	−	275.208i	−0.805114	−	0.593120i
$465$	−1474.53			−3.17103
$466$	−6.43820	+	0.519941i	−0.0138159	+	0.00111575i
$467$			832.326i			1.78228i	0.453727	+	0.891141i	$0.350094\pi$
$467$			832.326i			1.78228i	−0.453727	+	0.891141i	$0.649906\pi$
$468$	−103.918	−	639.186i	−0.222046	−	1.36578i
$469$		−	260.164i		−	0.554721i
$470$	−58.1751	−	720.357i	−0.123777	−	1.53267i
$471$			196.977i			0.418211i
$472$	36.4602	−	8.99015i	0.0772462	−	0.0190469i
$473$	−82.5396			−0.174502
$474$	1.56151	+	19.3355i	0.00329434	+	0.0407923i
$475$		−	1062.72i		−	2.23731i
$476$	33.5437	−	5.45346i	0.0704700	−	0.0114569i
$477$		−	278.780i		−	0.584445i
$478$	−69.8405	−	864.804i	−0.146110	−	1.80921i
$479$	−343.963			−0.718086			−0.359043	−	0.933321i	$-0.616897\pi$
$479$	−343.963			−0.718086			−0.359043	+	0.933321i	$0.616897\pi$
$480$	−1155.63	+	492.576i	−2.40757	+	1.02620i
$481$			523.075i			1.08747i
$482$	645.443	−	52.1252i	1.33909	−	0.108144i
$483$		−	1279.00i		−	2.64803i
$484$	465.715	−	75.7150i	0.962221	−	0.156436i
$485$	705.891			1.45545
$486$	56.0019	+	693.446i	0.115230	+	1.42684i
$487$			816.669i			1.67694i	0.544949	+	0.838469i	$0.316549\pi$
$487$			816.669i			1.67694i	−0.544949	+	0.838469i	$0.683451\pi$
$488$	−792.226	+	195.342i	−1.62341	+	0.400292i
$489$	277.781			0.568059
$490$	−41.0810	−	508.688i	−0.0838388	−	1.03814i
$491$			642.765i			1.30909i	0.756022	+	0.654547i	$0.227140\pi$
$491$			642.765i			1.30909i	−0.756022	+	0.654547i	$0.772860\pi$
$492$	−965.989	+	157.048i	−1.96339	+	0.319204i
$493$	−22.9504	+	16.1614i	−0.0465526	+	0.0327818i
$494$	617.226	−	49.8464i	1.24945	−	0.100904i
$495$	152.626			0.308335
$496$	−570.018	+	190.377i	−1.14923	+	0.383824i
$497$	−523.676			−1.05367
$498$	−66.9749	−	829.321i	−0.134488	−	1.66530i
$499$	−688.918			−1.38060			−0.690298	−	0.723525i	$-0.742521\pi$
$499$	−688.918			−1.38060			−0.690298	+	0.723525i	$0.742521\pi$
$500$	191.442	+	1177.54i	0.382883	+	2.35508i
$501$	956.924			1.91003
$502$	35.2501	+	436.486i	0.0702193	+	0.869494i
$503$	−765.781			−1.52243			−0.761214	−	0.648501i	$-0.775396\pi$
$503$	−765.781			−1.52243			−0.761214	+	0.648501i	$0.775396\pi$
$504$	161.674	+	655.682i	0.320782	+	1.30096i
$505$		−	1079.25i		−	2.13714i
$506$	−117.430	+	9.48347i	−0.232074	+	0.0187420i
$507$		−	493.536i		−	0.973445i
$508$	241.990	−	39.3423i	0.476359	−	0.0774454i
$509$		−	343.866i		−	0.675571i	−0.941223	−	0.337785i	$-0.890322\pi$
$509$		−	343.866i		−	0.675571i	0.941223	−	0.337785i	$-0.109678\pi$
$510$	6.11744	+	75.7495i	0.0119950	+	0.148529i
$511$	282.692			0.553213
$512$	−383.145	+	339.623i	−0.748330	+	0.663326i
$513$	48.9739			0.0954657
$514$	365.596	−	29.5251i	0.711276	−	0.0574418i
$515$	978.366			1.89974
$516$	806.109	−	131.056i	1.56223	−	0.253984i
$517$			69.2763i			0.133997i
$518$	−43.9096	−	543.713i	−0.0847676	−	1.04964i
$519$	−257.514			−0.496173
$520$	−1189.67	+	293.341i	−2.28782	+	0.564117i
$521$	286.530			0.549962			0.274981	−	0.961450i	$-0.411328\pi$
$521$	286.530			0.549962			0.274981	+	0.961450i	$0.411328\pi$
$522$	−356.824	−	428.731i	−0.683570	−	0.821323i
$523$	−90.1799			−0.172428			−0.0862141	−	0.996277i	$-0.527477\pi$
$523$	−90.1799			−0.172428			−0.0862141	+	0.996277i	$0.527477\pi$
$524$	−59.3239	−	364.895i	−0.113214	−	0.696365i
$525$	2188.33			4.16824
$526$	−810.932	+	65.4899i	−1.54170	+	0.124505i
$527$			36.3558i			0.0689863i
$528$	114.217	−	38.1467i	0.216321	−	0.0722476i
$529$	−611.457			−1.15587
$530$	−525.775	+	42.4609i	−0.992028	+	0.0801150i
$531$	45.1431			0.0850152
$532$	−637.395	+	103.626i	−1.19811	+	0.194786i
$533$	−954.571			−1.79094
$534$	−778.438	+	62.8657i	−1.45775	+	0.117726i
$535$		−	84.3638i		−	0.157689i
$536$	230.221	−	56.7667i	0.429518	−	0.105908i
$537$		−	1271.87i		−	2.36847i
$538$	133.554	−	10.7856i	0.248241	−	0.0200476i
$539$			48.9202i			0.0907611i
$540$	−95.6500	+	15.5506i	−0.177130	+	0.0287974i
$541$	−717.389			−1.32604			−0.663021	−	0.748601i	$-0.730726\pi$
$541$	−717.389			−1.32604			−0.663021	+	0.748601i	$0.730726\pi$
$542$	−825.806	+	66.6911i	−1.52363	+	0.123046i
$543$	−100.139			−0.184419
$544$	12.1449	+	28.4932i	0.0223252	+	0.0523772i
$545$	498.981			0.915561
$546$	102.642	+	1270.97i	0.187990	+	2.32779i
$547$	437.691			0.800165			0.400083	−	0.916479i	$-0.368981\pi$
$547$	437.691			0.800165			0.400083	+	0.916479i	$0.368981\pi$
$548$	−157.489	−	968.701i	−0.287389	−	1.76770i
$549$	−980.890			−1.78669
$550$	−16.2259	−	200.918i	−0.0295017	−	0.365306i
$551$	436.102	−	307.098i	0.791473	−	0.557347i
$552$	1131.80	−	279.072i	2.05036	−	0.505566i
$553$		−	19.7313i		−	0.0356805i
$554$	−17.5732	−	217.601i	−0.0317205	−	0.392781i
$555$	1219.82			2.19788
$556$	234.196	−	38.0750i	0.421215	−	0.0684803i
$557$			295.234i			0.530044i	0.964242	+	0.265022i	$0.0853792\pi$
$557$			295.234i			0.530044i	−0.964242	+	0.265022i	$0.914621\pi$
$558$	−720.105	+	58.1548i	−1.29051	+	0.104220i
$559$	796.581			1.42501
$560$	1211.98	−	404.781i	2.16425	−	0.722824i
$561$		−	7.28479i		−	0.0129854i
$562$	−40.1294	+	3.24080i	−0.0714047	+	0.00576655i
$563$			775.546i			1.37752i	0.724988	+	0.688762i	$0.241845\pi$
$563$			775.546i			1.37752i	−0.724988	+	0.688762i	$0.758155\pi$
$564$	−109.996	−	676.576i	−0.195029	−	1.19960i
$565$	1312.36			2.32277
$566$	−99.3766	+	8.02553i	−0.175577	+	0.0141794i
$567$		−	658.890i		−	1.16206i
$568$	−114.264	−	463.406i	−0.201169	−	0.815856i
$569$			877.625i			1.54240i	0.636594	+	0.771199i	$0.280343\pi$
$569$			877.625i			1.54240i	−0.636594	+	0.771199i	$0.719657\pi$
$570$	−116.243	−	1439.39i	−0.203935	−	2.52524i
$571$	604.662			1.05895			0.529476	−	0.848325i	$-0.322389\pi$
$571$	604.662			1.05895			0.529476	+	0.848325i	$0.322389\pi$
$572$	115.932	−	18.8479i	0.202678	−	0.0329509i
$573$			441.031i			0.769688i
$574$	992.234	−	80.1316i	1.72863	−	0.139602i
$575$		−	1951.29i		−	3.39354i
$576$	−544.942	+	286.134i	−0.946081	+	0.496760i
$577$			338.228i			0.586184i	0.956084	+	0.293092i	$0.0946842\pi$
$577$			338.228i			0.586184i	−0.956084	+	0.293092i	$0.905316\pi$
$578$	−574.257	+	46.3763i	−0.993524	+	0.0802358i
$579$	−457.383			−0.789954
$580$	−754.230	+	738.263i	−1.30040	+	1.27287i
$581$			846.297i			1.45662i
$582$	667.342	−	53.8937i	1.14663	−	0.0926008i
$583$	50.5635			0.0867298
$584$	61.6821	+	250.157i	0.105620	+	0.428350i
$585$	−1472.98			−2.51791
$586$	1113.05	−	89.8885i	1.89940	−	0.153393i
$587$	417.867			0.711869			0.355934	−	0.934511i	$-0.384163\pi$
$587$	417.867			0.711869			0.355934	+	0.934511i	$0.384163\pi$
$588$	−77.6751	−	477.772i	−0.132101	−	0.812537i
$589$		−	690.830i		−	1.17289i
$590$	−6.87572	−	85.1390i	−0.0116538	−	0.144303i
$591$	1067.00			1.80541
$592$	471.556	−	157.492i	0.796548	−	0.266034i
$593$	−190.963			−0.322028			−0.161014	−	0.986952i	$-0.551476\pi$
$593$	−190.963			−0.322028			−0.161014	+	0.986952i	$0.551476\pi$
$594$	9.25900	−	0.747745i	0.0155875	−	0.00125883i
$595$		−	77.3001i		−	0.129916i
$596$	−94.5369	−	581.487i	−0.158619	−	0.975649i
$597$	−507.890			−0.850738
$598$	1133.30	−	91.5240i	1.89515	−	0.153050i
$599$	−924.516			−1.54343			−0.771716	−	0.635967i	$-0.780602\pi$
$599$	−924.516			−1.54343			−0.771716	+	0.635967i	$0.780602\pi$
$600$	477.484	+	1936.47i	0.795806	+	3.22745i
$601$		−	546.364i		−	0.909091i	−0.890724	−	0.454545i	$-0.849802\pi$
$601$		−	546.364i		−	0.909091i	0.890724	−	0.454545i	$-0.150198\pi$
$602$	−828.011	+	66.8691i	−1.37543	+	0.111078i
$603$	285.048			0.472716
$604$	−122.317	−	752.361i	−0.202512	−	1.24563i
$605$		−	1073.22i		−	1.77392i
$606$	−82.3993	−	1020.31i	−0.135973	−	1.68369i
$607$	736.281			1.21298			0.606492	−	0.795090i	$-0.292576\pi$
$607$	736.281			1.21298			0.606492	+	0.795090i	$0.292576\pi$
$608$	−230.777	−	541.426i	−0.379567	−	0.890503i
$609$	632.368	+	898.008i	1.03837	+	1.47456i
$610$	149.399	+	1849.94i	0.244916	+	3.03269i
$611$		−	668.578i		−	1.09424i
$612$	5.97507	+	36.7520i	0.00976318	+	0.0600523i
$613$			946.700i			1.54437i	0.635396	+	0.772186i	$0.280837\pi$
$613$			946.700i			1.54437i	−0.635396	+	0.772186i	$0.719163\pi$
$614$	5.49254	+	68.0117i	0.00894551	+	0.110768i
$615$			2226.08i			3.61965i
$616$	−118.923	+	29.3235i	−0.193058	+	0.0476030i
$617$		−	562.535i		−	0.911726i	−0.890050	−	0.455863i	$-0.849331\pi$
$617$		−	562.535i		−	0.911726i	0.890050	−	0.455863i	$-0.150669\pi$
$618$	924.937	−	74.6967i	1.49666	−	0.120869i
$619$		−	115.897i		−	0.187233i	−0.995608	−	0.0936164i	$-0.970157\pi$
$619$		−	115.897i		−	0.187233i	0.995608	−	0.0936164i	$-0.0298427\pi$
$620$	219.358	+	1349.25i	0.353803	+	2.17621i
$621$	89.9219			0.144802
$622$	−315.628	+	25.4898i	−0.507441	+	0.0409803i
$623$	794.372			1.27508
$624$	−1102.30	+	368.150i	−1.76651	+	0.589984i
$625$	1269.08			2.03052
$626$	−9.59057	+	0.774523i	−0.0153204	+	0.00123726i
$627$			138.425i			0.220773i
$628$	180.241	−	29.3033i	0.287009	−	0.0466613i
$629$		−	30.0759i		−	0.0478154i
$630$	1531.10	−	123.649i	2.43031	−	0.196269i
$631$			342.109i			0.542169i	0.962555	+	0.271085i	$0.0873824\pi$
$631$			342.109i			0.542169i	−0.962555	+	0.271085i	$0.912618\pi$
$632$	17.4604	−	4.30529i	0.0276273	−	0.00681217i
$633$	−507.170			−0.801216
$634$	−381.987	+	30.8488i	−0.602503	+	0.0486574i
$635$		−	557.657i		−	0.878200i
$636$	−493.820	+	80.2842i	−0.776446	+	0.126233i
$637$		−	472.124i		−	0.741168i
$638$	77.7605	−	64.7184i	0.121882	−	0.101440i
$639$		−	573.764i		−	0.897909i
$640$	622.643	+	984.170i	0.972880	+	1.53777i
$641$			206.481i			0.322124i	0.986944	+	0.161062i	$0.0514919\pi$
$641$			206.481i			0.322124i	−0.986944	+	0.161062i	$0.948508\pi$
$642$	−6.44104	−	79.7566i	−0.0100328	−	0.124231i
$643$	−60.9625			−0.0948095			−0.0474048	−	0.998876i	$-0.515095\pi$
$643$	−60.9625			−0.0948095			−0.0474048	+	0.998876i	$0.515095\pi$
$644$	−1170.33	+	190.270i	−1.81729	+	0.295451i
$645$		−	1857.65i		−	2.88007i
$646$	−35.4894	+	2.86608i	−0.0549371	+	0.00443665i
$647$			279.111i			0.431392i	0.976461	+	0.215696i	$0.0692020\pi$
$647$			279.111i			0.431392i	−0.976461	+	0.215696i	$0.930798\pi$
$648$	583.058	−	143.767i	0.899780	−	0.221862i
$649$			8.18776i			0.0126160i
$650$	156.595	+	1939.04i	0.240915	+	2.98314i
$651$	1422.54			2.18516
$652$	−41.3241	−	254.180i	−0.0633805	−	0.389847i
$653$	−1046.64			−1.60282			−0.801412	−	0.598113i	$-0.795917\pi$
$653$	−1046.64			−1.60282			−0.801412	+	0.598113i	$0.795917\pi$
$654$	471.731	−	38.0964i	0.721301	−	0.0582514i
$655$	−840.887			−1.28380
$656$	287.410	+	860.553i	0.438126	+	1.31182i
$657$			309.730i			0.471431i
$658$	56.1239	+	694.957i	0.0852947	+	1.05617i
$659$		−	301.454i		−	0.457441i	−0.973492	−	0.228721i	$-0.926546\pi$
$659$		−	301.454i		−	0.457441i	0.973492	−	0.228721i	$-0.0734543\pi$
$660$	−43.9538	−	270.355i	−0.0665966	−	0.409629i
$661$		−	487.334i		−	0.737268i	−0.929575	−	0.368634i	$-0.879826\pi$
$661$		−	487.334i		−	0.737268i	0.929575	−	0.368634i	$-0.120174\pi$
$662$	61.2099	+	757.935i	0.0924622	+	1.14492i
$663$			70.3048i			0.106040i
$664$	−748.896	+	184.658i	−1.12786	+	0.278100i
$665$			1468.85i			2.20880i
$666$	595.717	−	48.1094i	0.894471	−	0.0722364i
$667$	800.735	−	563.869i	1.20050	−	0.845381i
$668$	−142.357	−	875.621i	−0.213109	−	1.31081i
$669$	212.453			0.317567
$670$	−43.4155	−	537.594i	−0.0647992	−	0.802380i
$671$		−	177.908i		−	0.265138i
$672$	1114.89	−	475.208i	1.65906	−	0.707155i
$673$	1023.71			1.52111			0.760555	−	0.649274i	$-0.224927\pi$
$673$	1023.71			1.52111			0.760555	+	0.649274i	$0.224927\pi$
$674$	−25.1799	−	311.791i	−0.0373588	−	0.462598i
$675$			153.854i			0.227931i
$676$	−451.604	+	73.4209i	−0.668054	+	0.108611i
$677$	937.281			1.38446			0.692231	−	0.721676i	$-0.256628\pi$
$677$	937.281			1.38446			0.692231	+	0.721676i	$0.256628\pi$
$678$	1240.69	−	100.197i	1.82993	−	0.147783i
$679$	−681.002			−1.00295
$680$	68.4036	−	16.8666i	0.100594	−	0.0248038i
$681$			1045.73i			1.53559i
$682$	−10.5478	−	130.608i	−0.0154659	−	0.191508i
$683$	−1061.72			−1.55449			−0.777246	−	0.629197i	$-0.783384\pi$
$683$	−1061.72			−1.55449			−0.777246	+	0.629197i	$0.783384\pi$
$684$	−113.538	−	698.359i	−0.165991	−	1.02099i
$685$	−2232.33			−3.25888
$686$	−29.6109	−	366.659i	−0.0431646	−	0.534488i
$687$		−	84.9937i		−	0.123717i
$688$	−239.841	−	718.124i	−0.348607	−	1.04378i
$689$	−487.983			−0.708248
$690$	−213.436	−	2642.88i	−0.309328	−	3.83027i
$691$	−423.256			−0.612527			−0.306263	−	0.951947i	$-0.599079\pi$
$691$	−423.256			−0.612527			−0.306263	+	0.951947i	$0.599079\pi$
$692$	38.3090	+	235.635i	0.0553599	+	0.340513i
$693$	−147.245			−0.212474
$694$	457.715	−	36.9645i	0.659531	−	0.0532629i
$695$		−	539.694i		−	0.776539i
$696$	−656.676	+	755.530i	−0.943499	+	1.08553i
$697$	54.8861			0.0787462
$698$	−40.1910	−	497.667i	−0.0575802	−	0.712990i
$699$			13.9349i			0.0199354i
$700$	−325.546	−	2002.40i	−0.465066	−	2.86057i
$701$			286.253i			0.408350i	0.978934	+	0.204175i	$0.0654512\pi$
$701$			286.253i			0.408350i	−0.978934	+	0.204175i	$0.934549\pi$
$702$	−89.3576	+	7.21641i	−0.127290	+	0.0102798i
$703$			571.499i			0.812943i
$704$	−51.8972	−	98.8383i	−0.0737176	−	0.140395i
$705$	−1559.14			−2.21155
$706$	−405.750	+	32.7679i	−0.574716	+	0.0464134i
$707$			1041.20i			1.47270i
$708$	−13.0005	−	79.9645i	−0.0183622	−	0.112944i
$709$		−	574.169i		−	0.809830i	−0.914354	−	0.404915i	$-0.867301\pi$
$709$		−	574.169i		−	0.809830i	0.914354	−	0.404915i	$-0.132699\pi$
$710$	−1082.11	+	87.3897i	−1.52410	+	0.123084i
$711$	21.6186			0.0304059
$712$	173.329	+	702.947i	0.243439	+	0.987286i
$713$		−	1268.45i		−	1.77903i
$714$	−5.90174	−	73.0787i	−0.00826575	−	0.102351i
$715$		−	267.160i		−	0.373650i
$716$	−1163.81	+	189.210i	−1.62543	+	0.264259i
$717$	−1871.78			−2.61058
$718$	−322.380	+	26.0350i	−0.448997	+	0.0362604i
$719$			427.873i			0.595094i	0.954707	+	0.297547i	$0.0961685\pi$
$719$			427.873i			0.595094i	−0.954707	+	0.297547i	$0.903832\pi$
$720$	443.497	+	1327.90i	0.615968	+	1.84431i
$721$	−943.870			−1.30911
$722$	−45.2910	+	3.65764i	−0.0627299	+	0.00506599i
$723$		−	1397.00i		−	1.93222i
$724$	14.8972	+	91.6312i	0.0205762	+	0.126562i
$725$	964.762	+	1370.03i	1.33071	+	1.88970i
$726$	−81.9388	−	1014.61i	−0.112863	−	1.39754i
$727$	449.714			0.618588			0.309294	−	0.950966i	$-0.399907\pi$
$727$	449.714			0.618588			0.309294	+	0.950966i	$0.399907\pi$
$728$	1147.72	−	282.998i	1.57654	−	0.388733i
$729$	825.311			1.13211
$730$	584.145	−	47.1749i	0.800199	−	0.0646231i
$731$	−45.8020			−0.0626566
$732$	282.480	+	1737.51i	0.385902	+	2.37364i
$733$	706.434			0.963757			0.481878	−	0.876238i	$-0.339955\pi$
$733$	706.434			0.963757			0.481878	+	0.876238i	$0.339955\pi$
$734$	−317.783	+	25.6637i	−0.432946	+	0.0349642i
$735$	−1101.01			−1.49797
$736$	−423.733	−	994.122i	−0.575725	−	1.35071i
$737$			51.7001i			0.0701495i
$738$	87.7959	+	1087.14i	0.118965	+	1.47309i
$739$		−	1175.54i		−	1.59072i	−0.606138	−	0.795359i	$-0.707282\pi$
$739$		−	1175.54i		−	1.59072i	0.606138	−	0.795359i	$-0.292718\pi$
$740$	−181.467	−	1116.18i	−0.245226	−	1.50836i
$741$		−	1335.93i		−	1.80287i
$742$	507.236	−	40.9638i	0.683607	−	0.0552073i
$743$	−375.734			−0.505699			−0.252849	−	0.967506i	$-0.581368\pi$
$743$	−375.734			−0.505699			−0.252849	+	0.967506i	$0.581368\pi$
$744$	310.391	+	1258.82i	0.417193	+	1.69196i
$745$	−1340.01			−1.79868
$746$	22.9947	+	284.734i	0.0308241	+	0.381681i
$747$	−927.242			−1.24129
$748$	−6.66585	+	1.08372i	−0.00891157	+	0.00144882i
$749$			81.3892i			0.108664i
$750$	2565.40	−	207.178i	3.42053	−	0.276238i
$751$	555.158			0.739225			0.369612	−	0.929186i	$-0.379490\pi$
$751$	555.158			0.739225			0.369612	+	0.929186i	$0.379490\pi$
$752$	−602.728	+	201.301i	−0.801500	+	0.267688i
$753$	944.731			1.25462
$754$	−750.458	+	624.591i	−0.995303	+	0.828370i
$755$	−1733.79			−2.29640
$756$	92.2775	−	15.0023i	0.122060	−	0.0198443i
$757$	−1028.12			−1.35815			−0.679076	−	0.734068i	$-0.737619\pi$
$757$	−1028.12			−1.35815			−0.679076	+	0.734068i	$0.737619\pi$
$758$	−25.4555	−	315.204i	−0.0335824	−	0.415836i
$759$			254.165i			0.334868i
$760$	−1299.80	+	320.497i	−1.71026	+	0.421706i
$761$	1225.98			1.61101			0.805505	−	0.592590i	$-0.201894\pi$
$761$	1225.98			1.61101			0.805505	+	0.592590i	$0.201894\pi$
$762$	−42.5762	−	527.203i	−0.0558743	−	0.691867i
$763$	−481.387			−0.630914
$764$	403.560	−	65.6099i	0.528220	−	0.0858768i
$765$	84.6936			0.110711
$766$	−8.56905	−	106.107i	−0.0111868	−	0.138521i
$767$		−	79.0193i		−	0.103024i
$768$	663.780	+	882.886i	0.864297	+	1.14959i
$769$			483.069i			0.628179i	0.949393	+	0.314089i	$0.101699\pi$
$769$			483.069i			0.628179i	−0.949393	+	0.314089i	$0.898301\pi$
$770$	22.4268	+	277.700i	0.0291257	+	0.360650i
$771$		−	791.296i		−	1.02632i
$772$	68.0425	+	418.523i	0.0881380	+	0.542128i
$773$	778.622			1.00727			0.503636	−	0.863916i	$-0.331995\pi$
$773$	778.622			1.00727			0.503636	+	0.863916i	$0.331995\pi$
$774$	−73.2649	−	907.207i	−0.0946575	−	1.17210i
$775$	2170.27			2.80035
$776$	−148.592	−	602.625i	−0.191484	−	0.776578i
$777$	−1176.81			−1.51456
$778$	−774.986	+	62.5869i	−0.996125	+	0.0804459i
$779$	−1042.94			−1.33882
$780$	424.194	+	2609.17i	0.543838	+	3.34509i
$781$	104.066			0.133247
$782$	−65.1627	+	5.26246i	−0.0833283	+	0.00672949i
$783$	−63.1357	+	44.4595i	−0.0806331	+	0.0567810i
$784$	−425.623	+	142.151i	−0.542887	+	0.181315i
$785$		−	415.359i		−	0.529120i
$786$	−794.965	+	64.2004i	−1.01141	+	0.0816799i
$787$	1037.50			1.31829			0.659146	−	0.752015i	$-0.270918\pi$
$787$	1037.50			1.31829			0.659146	+	0.752015i	$0.270918\pi$
$788$	−158.732	−	976.341i	−0.201436	−	1.23901i
$789$			1755.18i			2.22457i
$790$	−3.29271	−	40.7722i	−0.00416799	−	0.0516104i
$791$	−1266.09			−1.60062
$792$	−32.1281	−	130.298i	−0.0405658	−	0.164518i
$793$			1716.97i			2.16516i
$794$	108.278	+	1340.76i	0.136370	+	1.68861i
$795$			1137.99i			1.43143i
$796$	75.5562	+	464.739i	0.0949199	+	0.583842i
$797$	677.091			0.849550			0.424775	−	0.905299i	$-0.360353\pi$
$797$	677.091			0.849550			0.424775	+	0.905299i	$0.360353\pi$
$798$	112.144	+	1388.63i	0.140532	+	1.74014i
$799$			38.4420i			0.0481127i
$800$	1700.91	−	724.994i	2.12614	−	0.906243i
$801$			870.351i			1.08658i
$802$	−994.456	+	80.3111i	−1.23997	+	0.100139i
$803$	−56.1769			−0.0699588
$804$	−82.0890	−	504.921i	−0.102101	−	0.628011i
$805$			2696.98i			3.35029i
$806$	101.795	+	1260.49i	0.126297	+	1.56388i
$807$		−	289.064i		−	0.358195i
$808$	−921.367	+	227.185i	−1.14031	+	0.281170i
$809$		−	828.692i		−	1.02434i	−0.858884	−	0.512171i	$-0.828841\pi$
$809$		−	828.692i		−	1.02434i	0.858884	−	0.512171i	$-0.171159\pi$
$810$	−109.954	−	1361.51i	−0.135745	−	1.68087i
$811$	589.323			0.726662			0.363331	−	0.931660i	$-0.381639\pi$
$811$	589.323			0.726662			0.363331	+	0.931660i	$0.381639\pi$
$812$	727.637	−	712.232i	0.896104	−	0.877133i
$813$			1787.38i			2.19849i
$814$	8.72578	+	108.048i	0.0107196	+	0.132736i
$815$	−585.748			−0.718709
$816$	63.3803	−	21.1680i	0.0776719	−	0.0259411i
$817$	870.325			1.06527
$818$	−94.7168	−	1172.84i	−0.115791	−	1.43378i
$819$	1421.04			1.73509
$820$	2036.95	−	331.163i	2.48408	−	0.403857i
$821$			106.761i			0.130037i	0.997884	+	0.0650187i	$0.0207107\pi$
$821$			106.761i			0.130037i	−0.997884	+	0.0650187i	$0.979289\pi$
$822$	−2110.42	+	170.435i	−2.56742	+	0.207342i
$823$	−1115.40			−1.35528			−0.677641	−	0.735393i	$-0.736998\pi$
$823$	−1115.40			−1.35528			−0.677641	+	0.735393i	$0.736998\pi$
$824$	−205.948	−	835.239i	−0.249937	−	1.01364i
$825$	−434.868			−0.527112
$826$	6.63329	+	82.1370i	0.00803061	+	0.0994395i
$827$		−	577.881i		−	0.698768i	−0.936980	−	0.349384i	$-0.886391\pi$
$827$		−	577.881i		−	0.698768i	0.936980	−	0.349384i	$-0.113609\pi$
$828$	−208.469	−	1282.27i	−0.251774	−	1.54864i
$829$	998.520			1.20449			0.602244	−	0.798312i	$-0.294274\pi$
$829$	998.520			1.20449			0.602244	+	0.798312i	$0.294274\pi$
$830$	141.228	+	1748.76i	0.170154	+	2.10694i
$831$	−470.975			−0.566757
$832$	500.855	+	953.878i	0.601989	+	1.14649i
$833$			27.1463i			0.0325886i
$834$	−41.2048	−	510.221i	−0.0494063	−	0.611776i
$835$	−2017.83			−2.41657
$836$	126.664	−	20.5928i	0.151512	−	0.0246325i
$837$			100.013i			0.119490i
$838$	255.819	−	20.6596i	0.305273	−	0.0246535i
$839$	96.6609			0.115210			0.0576048	−	0.998339i	$-0.481654\pi$
$839$	96.6609			0.115210			0.0576048	+	0.998339i	$0.481654\pi$
$840$	−659.958	−	2676.51i	−0.785664	−	3.18632i
$841$	−283.420	+	791.805i	−0.337003	+	0.941504i
$842$	292.348	−	23.6097i	0.347207	−	0.0280400i
$843$			86.8562i			0.103032i
$844$	75.4491	+	464.079i	0.0893946	+	0.549857i
$845$			1040.70i			1.23160i
$846$	−761.427	+	61.4920i	−0.900032	+	0.0726855i
$847$			1035.38i			1.22241i
$848$	146.926	+	439.920i	0.173262	+	0.518774i
$849$			215.091i			0.253346i
$850$	−9.00391	−	111.491i	−0.0105928	−	0.131166i
$851$			1049.34i			1.23307i
$852$	−1016.34	+	165.235i	−1.19289	+	0.193937i
$853$	1080.35			1.26653			0.633265	−	0.773935i	$-0.281714\pi$
$853$	1080.35			1.26653			0.633265	+	0.773935i	$0.281714\pi$
$854$	−144.131	−	1784.71i	−0.168772	−	2.08983i
$855$	−1609.34			−1.88227
$856$	−72.0220	+	17.7588i	−0.0841379	+	0.0207462i
$857$	1419.52			1.65638			0.828192	−	0.560445i	$-0.189370\pi$
$857$	1419.52			1.65638			0.828192	+	0.560445i	$0.189370\pi$
$858$	−20.3972	−	252.570i	−0.0237730	−	0.294370i
$859$		−	139.857i		−	0.162814i	−0.996681	−	0.0814071i	$-0.974059\pi$
$859$		−	139.857i		−	0.162814i	0.996681	−	0.0814071i	$-0.0259414\pi$
$860$	−1699.82	+	276.352i	−1.97653	+	0.321340i
$861$		−	2147.59i		−	2.49430i
$862$	56.1541	+	695.331i	0.0651440	+	0.806649i
$863$		−	707.643i		−	0.819981i	−0.912090	−	0.409990i	$-0.865532\pi$
$863$		−	707.643i		−	0.819981i	0.912090	−	0.409990i	$-0.134468\pi$
$864$	33.4102	+	78.3838i	0.0386692	+	0.0907220i
$865$	543.011			0.627758
$866$	−29.1278	−	360.676i	−0.0336348	−	0.416485i
$867$			1242.92i			1.43359i
$868$	−211.623	−	1301.67i	−0.243806	−	1.49962i
$869$			3.92104i			0.00451213i
$870$	1456.56	+	1750.09i	1.67421	+	2.01159i
$871$		−	498.953i		−	0.572851i
$872$	−105.037	−	425.984i	−0.120455	−	0.488514i
$873$		−	746.137i		−	0.854682i
$874$	1238.22	−	99.9969i	1.41672	−	0.114413i
$875$	−2617.91			−2.99190
$876$	548.643	−	89.1972i	0.626305	−	0.101823i
$877$			244.590i			0.278893i	0.990230	+	0.139447i	$0.0445324\pi$
$877$			244.590i			0.278893i	−0.990230	+	0.139447i	$0.955468\pi$
$878$	66.7947	+	827.089i	0.0760759	+	0.942014i
$879$		−	2409.09i		−	2.74071i
$880$	−240.846	+	80.4387i	−0.273689	+	0.0914076i
$881$			570.464i			0.647519i	0.946139	+	0.323759i	$0.104947\pi$
$881$			570.464i			0.647519i	−0.946139	+	0.323759i	$0.895053\pi$
$882$	−537.691	+	43.4232i	−0.609627	+	0.0492327i
$883$	133.952			0.151701			0.0758503	−	0.997119i	$-0.475833\pi$
$883$	133.952			0.151701			0.0758503	+	0.997119i	$0.475833\pi$
$884$	64.3315	−	10.4589i	0.0727732	−	0.0118313i
$885$	−184.275			−0.208220
$886$	−119.054	−	1474.19i	−0.134373	−	1.66388i
$887$	485.479			0.547327			0.273663	−	0.961826i	$-0.411765\pi$
$887$	485.479			0.547327			0.273663	+	0.961826i	$0.411765\pi$
$888$	−256.776	−	1041.37i	−0.289162	−	1.17272i
$889$			537.994i			0.605168i
$890$	1641.47	−	132.563i	1.84434	−	0.148947i
$891$			130.935i			0.146953i
$892$	−31.6055	−	194.402i	−0.0354322	−	0.217940i
$893$		−	730.472i		−	0.817998i
$894$	−1266.83	+	102.308i	−1.41704	+	0.114438i
$895$			2681.95i			2.99659i
$896$	−600.689	−	949.469i	−0.670412	−	1.05968i
$897$		−	2452.92i		−	2.73458i
$898$	−68.2740	−	845.407i	−0.0760290	−	0.941433i
$899$	627.150	+	890.598i	0.697608	+	0.990654i
$900$	2193.92	−	356.684i	2.43769	−	0.396315i
$901$	28.0581			0.0311411
$902$	−197.178	+	15.9239i	−0.218601	+	0.0176540i
$903$			1792.15i			1.98466i
$904$	−276.255	−	1120.37i	−0.305592	−	1.23935i
$905$	211.160			0.233326
$906$	−1639.10	+	132.372i	−1.80916	+	0.146106i
$907$			411.767i			0.453987i	0.973896	+	0.226994i	$0.0728897\pi$
$907$			411.767i			0.453987i	−0.973896	+	0.226994i	$0.927110\pi$
$908$	956.886	−	155.569i	1.05384	−	0.171331i
$909$	−1140.79			−1.25499
$910$	−216.438	−	2680.06i	−0.237844	−	2.94512i
$911$	−752.466			−0.825979			−0.412989	−	0.910736i	$-0.635515\pi$
$911$	−752.466			−0.825979			−0.412989	+	0.910736i	$0.635515\pi$
$912$	−1204.35	+	402.232i	−1.32056	+	0.441044i
$913$		−	168.177i		−	0.184203i
$914$	1433.65	−	115.780i	1.56854	−	0.126674i
$915$	4004.02			4.37597
$916$	−77.7724	+	12.6441i	−0.0849043	+	0.0138036i
$917$	811.238			0.884665
$918$	5.13790	−	0.414931i	0.00559684	−	0.000451994i
$919$			706.226i			0.768473i	0.923235	+	0.384236i	$0.125535\pi$
$919$			706.226i			0.768473i	−0.923235	+	0.384236i	$0.874465\pi$
$920$	−2386.59	+	588.470i	−2.59412	+	0.639642i
$921$	147.205			0.159831
$922$	−233.414	+	18.8503i	−0.253161	+	0.0204450i
$923$	−1004.33			−1.08811
$924$	42.4040	+	260.823i	0.0458918	+	0.282276i
$925$	−1795.39			−1.94096
$926$	64.4093	+	797.552i	0.0695565	+	0.861287i
$927$		−	1034.15i		−	1.11558i
$928$	789.028	+	488.486i	0.850246	+	0.526386i
$929$	702.732			0.756439			0.378220	−	0.925716i	$-0.376536\pi$
$929$	702.732			0.756439			0.378220	+	0.925716i	$0.376536\pi$
$930$	2939.48	−	237.389i	3.16074	−	0.255257i
$931$		−	515.831i		−	0.554062i
$932$	12.7509	−	2.07302i	0.0136812	−	0.00222427i
$933$			683.147i			0.732204i
$934$	−133.999	−	1659.25i	−0.143468	−	1.77650i
$935$			15.3612i			0.0164291i
$936$	310.065	+	1257.49i	0.331266	+	1.34348i
$937$	854.818			0.912293			0.456146	−	0.889905i	$-0.349229\pi$
$937$	854.818			0.912293			0.456146	+	0.889905i	$0.349229\pi$
$938$	41.8847	+	518.639i	0.0446532	+	0.552920i
$939$			20.7578i			0.0221063i
$940$	231.945	+	1426.67i	0.246750	+	1.51774i
$941$		−	1527.43i		−	1.62319i	−0.584217	−	0.811597i	$-0.698598\pi$
$941$		−	1527.43i		−	1.62319i	0.584217	−	0.811597i	$-0.301402\pi$
$942$	−31.7120	−	392.676i	−0.0336646	−	0.416853i
$943$	−1914.96			−2.03071
$944$	−71.2365	+	23.7918i	−0.0754624	+	0.0252032i
$945$		−	212.650i		−	0.225026i
$946$	164.543	−	13.2883i	0.173936	−	0.0140469i
$947$			919.484i			0.970944i	0.874252	+	0.485472i	$0.161352\pi$
$947$			919.484i			0.970944i	−0.874252	+	0.485472i	$0.838648\pi$
$948$	−6.22579	−	38.2942i	−0.00656729	−	0.0403947i
$949$	542.158			0.571294
$950$	171.091	+	2118.55i	0.180096	+	2.23005i
$951$			826.772i			0.869372i
$952$	−65.9917	+	16.2718i	−0.0693190	+	0.0170923i
$953$	−936.660			−0.982854			−0.491427	−	0.870919i	$-0.663525\pi$
$953$	−936.660			−0.982854			−0.491427	+	0.870919i	$0.663525\pi$
$954$	44.8818	+	555.752i	0.0470459	+	0.582549i
$955$		−	929.987i		−	0.973809i
$956$	278.455	+	1712.75i	0.291271	+	1.79158i
$957$	−125.665	−	178.453i	−0.131311	−	0.186472i
$958$	685.694	−	55.3758i	0.715755	−	0.0578035i
$959$	2153.62			2.24570
$960$	2224.47	−	1168.01i	2.31715	−	1.21667i
$961$	449.798			0.468052
$962$	−84.2117	−	1042.76i	−0.0875381	−	1.08395i
$963$	−89.1737			−0.0925999
$964$	−1278.30	+	207.824i	−1.32604	+	0.215585i
$965$	964.469			0.999450
$966$	205.911	+	2549.70i	0.213158	+	2.63944i
$967$	1259.06			1.30202			0.651012	−	0.759068i	$-0.274345\pi$
$967$	1259.06			1.30202			0.651012	+	0.759068i	$0.274345\pi$
$968$	−916.218	+	225.916i	−0.946506	+	0.233384i
$969$			76.8133i			0.0792706i
$970$	−1407.20	+	113.644i	−1.45072	+	0.117159i
$971$		−	1189.40i		−	1.22492i	−0.790500	−	0.612461i	$-0.790179\pi$
$971$		−	1189.40i		−	1.22492i	0.790500	−	0.612461i	$-0.209821\pi$
$972$	−223.281	−	1373.38i	−0.229713	−	1.41294i
$973$			520.665i			0.535113i
$974$	−131.478	−	1628.04i	−0.134988	−	1.67150i
$975$	4196.86			4.30448
$976$	1547.86	−	516.960i	1.58592	−	0.529672i
$977$	−1483.05			−1.51797			−0.758984	−	0.651109i	$-0.774304\pi$
$977$	−1483.05			−1.51797			−0.758984	+	0.651109i	$0.774304\pi$
$978$	−553.759	+	44.7209i	−0.566216	+	0.0457269i
$979$	−157.859			−0.161245
$980$	163.791	+	1007.46i	0.167134	+	1.02802i
$981$		−	527.430i		−	0.537645i
$982$	−103.481	−	1281.36i	−0.105378	−	1.30484i
$983$	504.779			0.513509			0.256754	−	0.966477i	$-0.417347\pi$
$983$	504.779			0.513509			0.256754	+	0.966477i	$0.417347\pi$
$984$	1900.42	−	468.596i	1.93133	−	0.476215i
$985$	−2249.94			−2.28420
$986$	43.1500	−	35.9129i	0.0437627	−	0.0364228i
$987$	1504.17			1.52398
$988$	−1222.42	+	198.739i	−1.23727	+	0.201152i
$989$	1598.02			1.61579
$990$	−304.261	+	24.5718i	−0.307335	+	0.0248200i
$991$		−	839.390i		−	0.847014i	−0.905893	−	0.423507i	$-0.860799\pi$
$991$		−	839.390i		−	0.847014i	0.905893	−	0.423507i	$-0.139201\pi$
$992$	1105.69	−	471.287i	1.11460	−	0.475088i
$993$	1640.48			1.65204
$994$	1043.95	−	84.3084i	1.05026	−	0.0848173i
$995$	1070.97			1.07635
$996$	267.030	+	1642.48i	0.268103	+	1.64907i
$997$	335.554			0.336563			0.168282	−	0.985739i	$-0.446178\pi$
$997$	335.554			0.336563			0.168282	+	0.985739i	$0.446178\pi$
$998$	1373.36	−	110.911i	1.37612	−	0.111134i
$999$		−	82.7376i		−	0.0828204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.3.b.c.115.2	yes	56
4.3	odd	2		928.3.b.c.463.9		56
8.3	odd	2	inner	232.3.b.c.115.56	yes	56
8.5	even	2		928.3.b.c.463.10		56
29.28	even	2	inner	232.3.b.c.115.55	yes	56
116.115	odd	2		928.3.b.c.463.47		56
232.115	odd	2	inner	232.3.b.c.115.1	✓	56
232.173	even	2		928.3.b.c.463.48		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.3.b.c.115.1	✓	56	232.115	odd	2	inner
232.3.b.c.115.2	yes	56	1.1	even	1	trivial
232.3.b.c.115.55	yes	56	29.28	even	2	inner
232.3.b.c.115.56	yes	56	8.3	odd	2	inner
928.3.b.c.463.9		56	4.3	odd	2
928.3.b.c.463.10		56	8.5	even	2
928.3.b.c.463.47		56	116.115	odd	2
928.3.b.c.463.48		56	232.173	even	2

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	232.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99351 + 0.160993i) q^{2} +4.31476i q^{3} +(3.94816 - 0.641884i) q^{4} -9.09838i q^{5} +(-0.694647 - 8.60151i) q^{6} +8.77758i q^{7} +(-7.76736 + 1.91523i) q^{8} -9.61712 q^{9} +O(q^{10})\)	\(q+(-1.99351 + 0.160993i) q^{2} +4.31476i q^{3} +(3.94816 - 0.641884i) q^{4} -9.09838i q^{5} +(-0.694647 - 8.60151i) q^{6} +8.77758i q^{7} +(-7.76736 + 1.91523i) q^{8} -9.61712 q^{9} +(1.46478 + 18.1377i) q^{10} -1.74429i q^{11} +(2.76957 + 17.0354i) q^{12} +16.8340i q^{13} +(-1.41313 - 17.4982i) q^{14} +39.2573 q^{15} +(15.1760 - 5.06852i) q^{16} -0.967924i q^{17} +(19.1718 - 1.54829i) q^{18} +18.3924i q^{19} +(-5.84010 - 35.9219i) q^{20} -37.8731 q^{21} +(0.280820 + 3.47727i) q^{22} +33.7707i q^{23} +(-8.26375 - 33.5143i) q^{24} -57.7805 q^{25} +(-2.71016 - 33.5587i) q^{26} -2.66272i q^{27} +(5.63419 + 34.6553i) q^{28} +(-16.6970 - 23.7110i) q^{29} +(-78.2598 + 6.32017i) q^{30} -37.5606 q^{31} +(-29.4374 + 12.5474i) q^{32} +7.52620 q^{33} +(0.155829 + 1.92957i) q^{34} +79.8617 q^{35} +(-37.9700 + 6.17307i) q^{36} +31.0726 q^{37} +(-2.96106 - 36.6655i) q^{38} -72.6346 q^{39} +(17.4255 + 70.6704i) q^{40} +56.7049i q^{41} +(75.5004 - 6.09732i) q^{42} -47.3198i q^{43} +(-1.11963 - 6.88675i) q^{44} +87.5002i q^{45} +(-5.43685 - 67.3221i) q^{46} -39.7160 q^{47} +(21.8694 + 65.4806i) q^{48} -28.0459 q^{49} +(115.186 - 9.30229i) q^{50} +4.17636 q^{51} +(10.8055 + 66.4633i) q^{52} +28.9879i q^{53} +(0.428681 + 5.30817i) q^{54} -15.8702 q^{55} +(-16.8111 - 68.1786i) q^{56} -79.3588 q^{57} +(37.1030 + 44.5799i) q^{58} -4.69403 q^{59} +(154.994 - 25.1986i) q^{60} +101.994 q^{61} +(74.8774 - 6.04701i) q^{62} -84.4150i q^{63} +(56.6638 - 29.7526i) q^{64} +153.162 q^{65} +(-15.0036 + 1.21167i) q^{66} -29.6396 q^{67} +(-0.621295 - 3.82152i) q^{68} -145.712 q^{69} +(-159.205 + 12.8572i) q^{70} +59.6607i q^{71} +(74.6996 - 18.4190i) q^{72} -32.2061i q^{73} +(-61.9434 + 5.00248i) q^{74} -249.309i q^{75} +(11.8058 + 72.6162i) q^{76} +15.3107 q^{77} +(144.798 - 11.6937i) q^{78} -2.24792 q^{79} +(-46.1154 - 138.077i) q^{80} -75.0651 q^{81} +(-9.12912 - 113.042i) q^{82} +96.4157 q^{83} +(-149.529 + 24.3101i) q^{84} -8.80654 q^{85} +(7.61817 + 94.3325i) q^{86} +(102.307 - 72.0435i) q^{87} +(3.34072 + 13.5486i) q^{88} -90.5002i q^{89} +(-14.0870 - 174.433i) q^{90} -147.762 q^{91} +(21.6768 + 133.332i) q^{92} -162.065i q^{93} +(79.1742 - 6.39401i) q^{94} +167.341 q^{95} +(-54.1389 - 127.015i) q^{96} +77.5842i q^{97} +(55.9097 - 4.51520i) q^{98} +16.7751i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{4} - 184 q^{9}+O(q^{10}) \) 56 * q - 4 * q^4 - 184 * q^9	\( 56 q - 4 q^{4} - 184 q^{9} - 44 q^{16} - 12 q^{20} - 68 q^{22} - 72 q^{24} - 280 q^{25} + 116 q^{28} + 8 q^{30} + 32 q^{33} - 116 q^{34} + 96 q^{35} - 112 q^{36} - 176 q^{38} + 156 q^{42} - 424 q^{49} + 32 q^{51} - 56 q^{52} + 160 q^{54} + 32 q^{57} + 296 q^{58} + 512 q^{59} + 640 q^{62} - 304 q^{64} + 192 q^{65} + 352 q^{67} + 472 q^{74} + 44 q^{78} + 424 q^{80} + 280 q^{81} - 76 q^{82} + 128 q^{83} + 412 q^{86} - 84 q^{88} + 96 q^{91} - 92 q^{92} + 276 q^{94} + 300 q^{96}+O(q^{100}) \) 56 * q - 4 * q^4 - 184 * q^9 - 44 * q^16 - 12 * q^20 - 68 * q^22 - 72 * q^24 - 280 * q^25 + 116 * q^28 + 8 * q^30 + 32 * q^33 - 116 * q^34 + 96 * q^35 - 112 * q^36 - 176 * q^38 + 156 * q^42 - 424 * q^49 + 32 * q^51 - 56 * q^52 + 160 * q^54 + 32 * q^57 + 296 * q^58 + 512 * q^59 + 640 * q^62 - 304 * q^64 + 192 * q^65 + 352 * q^67 + 472 * q^74 + 44 * q^78 + 424 * q^80 + 280 * q^81 - 76 * q^82 + 128 * q^83 + 412 * q^86 - 84 * q^88 + 96 * q^91 - 92 * q^92 + 276 * q^94 + 300 * q^96

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