LMFDB - Embedded newform 384.2.v.a.157.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			157.17
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.112149 - 1.40976i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.97485 - 0.316205i) q^{4} +(-3.03042 + 1.61979i) q^{5} +(-1.39198 - 0.249789i) q^{6} +(0.773129 + 3.88678i) q^{7} +(-0.667250 + 2.74860i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(0.112149 - 1.40976i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.97485 - 0.316205i) q^{4} +(-3.03042 + 1.61979i) q^{5} +(-1.39198 - 0.249789i) q^{6} +(0.773129 + 3.88678i) q^{7} +(-0.667250 + 2.74860i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.94366 + 4.45382i) q^{10} +(3.11939 - 3.80098i) q^{11} +(-0.508251 + 1.93434i) q^{12} +(-1.46409 + 2.73913i) q^{13} +(5.56613 - 0.654029i) q^{14} +(1.31496 + 3.17459i) q^{15} +(3.80003 + 1.24891i) q^{16} +(-1.58108 + 3.81705i) q^{17} +(-0.385024 + 1.36079i) q^{18} +(0.563036 + 1.85608i) q^{19} +(6.49679 - 2.24061i) q^{20} +(3.94385 - 0.388435i) q^{21} +(-5.00864 - 4.82386i) q^{22} +(-5.28927 + 3.53418i) q^{23} +(2.66996 + 0.933446i) q^{24} +(3.78186 - 5.65995i) q^{25} +(3.69731 + 2.37121i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-0.297790 - 7.92026i) q^{28} +(3.53190 - 2.89856i) q^{29} +(4.62288 - 1.49775i) q^{30} +(-6.59692 + 6.59692i) q^{31} +(2.18683 - 5.21706i) q^{32} +(-3.47693 - 3.47693i) q^{33} +(5.20381 + 2.65701i) q^{34} +(-8.63868 - 10.5263i) q^{35} +(1.87521 + 0.695403i) q^{36} +(-0.317475 - 0.0963051i) q^{37} +(2.67977 - 0.585589i) q^{38} +(2.58243 + 1.72553i) q^{39} +(-2.43011 - 9.41020i) q^{40} +(0.356442 + 0.533453i) q^{41} +(-0.105303 - 5.60344i) q^{42} +(0.577366 + 5.86210i) q^{43} +(-7.36220 + 6.51999i) q^{44} +(3.28820 - 0.997463i) q^{45} +(4.38915 + 7.85295i) q^{46} +(-5.75850 - 2.38525i) q^{47} +(1.61537 - 3.65932i) q^{48} +(-8.04219 + 3.33118i) q^{49} +(-7.55504 - 5.96626i) q^{50} +(3.64370 + 1.94760i) q^{51} +(3.75748 - 4.94640i) q^{52} +(-7.52112 - 6.17242i) q^{53} +(1.31650 + 0.516551i) q^{54} +(-3.29624 + 16.5713i) q^{55} +(-11.1991 - 0.468435i) q^{56} +(1.90233 - 0.378397i) q^{57} +(-3.69017 - 5.30420i) q^{58} +(3.25378 + 6.08740i) q^{59} +(-1.59302 - 6.68513i) q^{60} +(8.53974 + 0.841091i) q^{61} +(8.56024 + 10.0399i) q^{62} -3.96293i q^{63} +(-7.10956 - 3.66800i) q^{64} -10.6722i q^{65} +(-5.29157 + 4.51170i) q^{66} +(6.73188 + 0.663033i) q^{67} +(4.32935 - 7.03815i) q^{68} +(2.99872 + 5.61021i) q^{69} +(-15.8083 + 10.9980i) q^{70} +(16.2505 - 3.23243i) q^{71} +(1.19065 - 2.56561i) q^{72} +(-0.0908179 + 0.456572i) q^{73} +(-0.171371 + 0.436763i) q^{74} +(-5.26201 - 4.31842i) q^{75} +(-0.525007 - 3.84351i) q^{76} +(17.1853 + 9.18573i) q^{77} +(2.72219 - 3.44709i) q^{78} +(-8.39175 + 3.47598i) q^{79} +(-13.5387 + 2.37053i) q^{80} +(0.923880 + 0.382683i) q^{81} +(0.792015 - 0.442671i) q^{82} +(-14.8410 + 4.50197i) q^{83} +(-7.91131 - 0.479966i) q^{84} +(-1.39151 - 14.1283i) q^{85} +(8.32890 - 0.156522i) q^{86} +(-2.53841 - 3.79900i) q^{87} +(8.36596 + 11.1101i) q^{88} +(4.76310 + 3.18260i) q^{89} +(-1.03742 - 4.74743i) q^{90} +(-11.7783 - 3.57291i) q^{91} +(11.5630 - 5.30696i) q^{92} +(5.91854 + 7.21177i) q^{93} +(-4.00843 + 7.85060i) q^{94} +(-4.71270 - 4.71270i) q^{95} +(-4.97759 - 2.68767i) q^{96} +(-2.35610 + 2.35610i) q^{97} +(3.79425 + 11.7111i) q^{98} +(-3.80098 + 3.11939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.112149	−	1.40976i	0.0793010	−	0.996851i
$2$	0.112149	−	1.40976i	0.0793010	−	0.996851i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	−1.97485	−	0.316205i	−0.987423	−	0.158103i
$5$	−3.03042	+	1.61979i	−1.35524	+	0.724393i	−0.979331	−	0.202262i	$-0.935171\pi$
$5$	−3.03042	+	1.61979i	−1.35524	+	0.724393i	−0.375913	+	0.926655i	$0.622671\pi$
$6$	−1.39198	−	0.249789i	−0.568273	−	0.101976i
$7$	0.773129	+	3.88678i	0.292215	+	1.46907i	0.796032	+	0.605255i	$0.206929\pi$
$7$	0.773129	+	3.88678i	0.292215	+	1.46907i	−0.503816	+	0.863811i	$0.668071\pi$
$8$	−0.667250	+	2.74860i	−0.235908	+	0.971775i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	1.94366	+	4.45382i	0.614640	+	1.40842i
$11$	3.11939	−	3.80098i	0.940530	−	1.14604i	−0.0485733	−	0.998820i	$-0.515467\pi$
$11$	3.11939	−	3.80098i	0.940530	−	1.14604i	0.989104	−	0.147220i	$-0.0470326\pi$
$12$	−0.508251	+	1.93434i	−0.146720	+	0.558397i
$13$	−1.46409	+	2.73913i	−0.406067	+	0.759697i	−0.998961	−	0.0455835i	$-0.985485\pi$
$13$	−1.46409	+	2.73913i	−0.406067	+	0.759697i	0.592894	+	0.805281i	$0.297985\pi$
$14$	5.56613	−	0.654029i	1.48761	−	0.174797i
$15$	1.31496	+	3.17459i	0.339521	+	0.819676i
$16$	3.80003	+	1.24891i	0.950007	+	0.312228i
$17$	−1.58108	+	3.81705i	−0.383467	+	0.925771i	0.607823	+	0.794073i	$0.292043\pi$
$17$	−1.58108	+	3.81705i	−0.383467	+	0.925771i	−0.991290	+	0.131699i	$0.957957\pi$
$18$	−0.385024	+	1.36079i	−0.0907511	+	0.320742i
$19$	0.563036	+	1.85608i	0.129169	+	0.425814i	0.997540	−	0.0701018i	$-0.0223324\pi$
$19$	0.563036	+	1.85608i	0.129169	+	0.425814i	−0.868371	+	0.495916i	$0.834832\pi$
$20$	6.49679	−	2.24061i	1.45273	−	0.501015i
$21$	3.94385	−	0.388435i	0.860618	−	0.0847635i
$22$	−5.00864	−	4.82386i	−1.06785	−	1.02845i
$23$	−5.28927	+	3.53418i	−1.10289	+	0.736927i	−0.967248	−	0.253832i	$-0.918309\pi$
$23$	−5.28927	+	3.53418i	−1.10289	+	0.736927i	−0.135640	+	0.990758i	$0.543309\pi$
$24$	2.66996	+	0.933446i	0.545003	+	0.190539i
$25$	3.78186	−	5.65995i	0.756371	−	1.13199i
$26$	3.69731	+	2.37121i	0.725103	+	0.465032i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	−0.297790	−	7.92026i	−0.0562769	−	1.49679i
$29$	3.53190	−	2.89856i	0.655857	−	0.538248i	−0.246551	−	0.969130i	$-0.579297\pi$
$29$	3.53190	−	2.89856i	0.655857	−	0.538248i	0.902409	+	0.430882i	$0.141797\pi$
$30$	4.62288	−	1.49775i	0.844019	−	0.273451i
$31$	−6.59692	+	6.59692i	−1.18484	+	1.18484i	−0.206368	+	0.978475i	$0.566164\pi$
$31$	−6.59692	+	6.59692i	−1.18484	+	1.18484i	−0.978475	+	0.206368i	$0.933836\pi$
$32$	2.18683	−	5.21706i	0.386581	−	0.922255i
$33$	−3.47693	−	3.47693i	−0.605255	−	0.605255i
$34$	5.20381	+	2.65701i	0.892447	+	0.455674i
$35$	−8.63868	−	10.5263i	−1.46020	−	1.77926i
$36$	1.87521	+	0.695403i	0.312535	+	0.115900i
$37$	−0.317475	−	0.0963051i	−0.0521926	−	0.0158325i	0.264080	−	0.964501i	$-0.414932\pi$
$37$	−0.317475	−	0.0963051i	−0.0521926	−	0.0158325i	−0.316273	+	0.948668i	$0.602432\pi$
$38$	2.67977	−	0.585589i	0.434716	−	0.0949950i
$39$	2.58243	+	1.72553i	0.413520	+	0.276305i
$40$	−2.43011	−	9.41020i	−0.384234	−	1.48788i
$41$	0.356442	+	0.533453i	0.0556669	+	0.0833113i	0.858259	−	0.513217i	$-0.171546\pi$
$41$	0.356442	+	0.533453i	0.0556669	+	0.0833113i	−0.802592	+	0.596528i	$0.796546\pi$
$42$	−0.105303	−	5.60344i	−0.0162486	−	0.864629i
$43$	0.577366	+	5.86210i	0.0880476	+	0.893962i	0.933181	+	0.359407i	$0.117021\pi$
$43$	0.577366	+	5.86210i	0.0880476	+	0.893962i	−0.845134	+	0.534555i	$0.820479\pi$
$44$	−7.36220	+	6.51999i	−1.10989	+	0.982925i
$45$	3.28820	−	0.997463i	0.490175	−	0.148693i
$46$	4.38915	+	7.85295i	0.647146	+	1.15785i
$47$	−5.75850	−	2.38525i	−0.839963	−	0.347924i	−0.0791242	−	0.996865i	$-0.525212\pi$
$47$	−5.75850	−	2.38525i	−0.839963	−	0.347924i	−0.760839	+	0.648941i	$0.775212\pi$
$48$	1.61537	−	3.65932i	0.233158	−	0.528177i
$49$	−8.04219	+	3.33118i	−1.14888	+	0.475883i
$50$	−7.55504	−	5.96626i	−1.06844	−	0.843757i
$51$	3.64370	+	1.94760i	0.510220	+	0.272718i
$52$	3.75748	−	4.94640i	0.521069	−	0.685942i
$53$	−7.52112	−	6.17242i	−1.03311	−	0.847848i	−0.0445957	−	0.999005i	$-0.514200\pi$
$53$	−7.52112	−	6.17242i	−1.03311	−	0.847848i	−0.988510	+	0.151157i	$0.951700\pi$
$54$	1.31650	+	0.516551i	0.179153	+	0.0702937i
$55$	−3.29624	+	16.5713i	−0.444465	+	2.23448i
$56$	−11.1991	−	0.468435i	−1.49654	−	0.0625972i
$57$	1.90233	−	0.378397i	0.251970	−	0.0501199i
$58$	−3.69017	−	5.30420i	−0.484543	−	0.696476i
$59$	3.25378	+	6.08740i	0.423606	+	0.792512i	0.999690	−	0.0248787i	$-0.00791996\pi$
$59$	3.25378	+	6.08740i	0.423606	+	0.792512i	−0.576084	+	0.817390i	$0.695420\pi$
$60$	−1.59302	−	6.68513i	−0.205658	−	0.863046i
$61$	8.53974	+	0.841091i	1.09340	+	0.107691i	0.628603	−	0.777726i	$-0.283627\pi$
$61$	8.53974	+	0.841091i	1.09340	+	0.107691i	0.464798	+	0.885417i	$0.346127\pi$
$62$	8.56024	+	10.0399i	1.08715	+	1.27507i
$63$		−	3.96293i		−	0.499282i
$64$	−7.10956	−	3.66800i	−0.888695	−	0.458500i
$65$		−	10.6722i		−	1.32373i
$66$	−5.29157	+	4.51170i	−0.651347	+	0.555352i
$67$	6.73188	+	0.663033i	0.822431	+	0.0810023i	0.500473	−	0.865752i	$-0.333159\pi$
$67$	6.73188	+	0.663033i	0.822431	+	0.0810023i	0.321957	+	0.946754i	$0.395659\pi$
$68$	4.32935	−	7.03815i	0.525011	−	0.853501i
$69$	2.99872	+	5.61021i	0.361003	+	0.675390i
$70$	−15.8083	+	10.9980i	−1.88946	+	1.31451i
$71$	16.2505	−	3.23243i	1.92858	−	0.383619i	0.928665	−	0.370919i	$-0.120957\pi$
$71$	16.2505	−	3.23243i	1.92858	−	0.383619i	0.999919	−	0.0127000i	$-0.00404264\pi$
$72$	1.19065	−	2.56561i	0.140320	−	0.302360i
$73$	−0.0908179	+	0.456572i	−0.0106294	+	0.0534378i	−0.985736	−	0.168299i	$-0.946173\pi$
$73$	−0.0908179	+	0.456572i	−0.0106294	+	0.0534378i	0.975107	+	0.221737i	$0.0711726\pi$
$74$	−0.171371	+	0.436763i	−0.0199215	+	0.0507727i
$75$	−5.26201	−	4.31842i	−0.607604	−	0.498648i
$76$	−0.525007	−	3.84351i	−0.0602224	−	0.440881i
$77$	17.1853	+	9.18573i	1.95844	+	1.04681i
$78$	2.72219	−	3.44709i	0.308228	−	0.390306i
$79$	−8.39175	+	3.47598i	−0.944146	+	0.391078i	−0.801028	−	0.598627i	$-0.795713\pi$
$79$	−8.39175	+	3.47598i	−0.944146	+	0.391078i	−0.143119	+	0.989706i	$0.545713\pi$
$80$	−13.5387	+	2.37053i	−1.51367	+	0.265033i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	0.792015	−	0.442671i	0.0874634	−	0.0488849i
$83$	−14.8410	+	4.50197i	−1.62901	+	0.494156i	−0.966880	−	0.255230i	$-0.917849\pi$
$83$	−14.8410	+	4.50197i	−1.62901	+	0.494156i	−0.662133	+	0.749386i	$0.730349\pi$
$84$	−7.91131	−	0.479966i	−0.863195	−	0.0523686i
$85$	−1.39151	−	14.1283i	−0.150931	−	1.53243i
$86$	8.32890	−	0.156522i	0.898129	−	0.0168782i
$87$	−2.53841	−	3.79900i	−0.272146	−	0.407296i
$88$	8.36596	+	11.1101i	0.891814	+	1.18434i
$89$	4.76310	+	3.18260i	0.504888	+	0.337355i	0.781789	−	0.623543i	$-0.214307\pi$
$89$	4.76310	+	3.18260i	0.504888	+	0.337355i	−0.276901	+	0.960898i	$0.589307\pi$
$90$	−1.03742	−	4.74743i	−0.109353	−	0.500423i
$91$	−11.7783	−	3.57291i	−1.23470	−	0.374543i
$92$	11.5630	−	5.30696i	1.20553	−	0.553288i
$93$	5.91854	+	7.21177i	0.613724	+	0.747825i
$94$	−4.00843	+	7.85060i	−0.413438	+	0.809727i
$95$	−4.71270	−	4.71270i	−0.483513	−	0.483513i
$96$	−4.97759	−	2.68767i	−0.508024	−	0.274309i
$97$	−2.35610	+	2.35610i	−0.239226	+	0.239226i	−0.816530	−	0.577304i	$-0.804105\pi$
$97$	−2.35610	+	2.35610i	−0.239226	+	0.239226i	0.577304	+	0.816530i	$0.304105\pi$
$98$	3.79425	+	11.7111i	0.383277	+	1.18300i
$99$	−3.80098	+	3.11939i	−0.382013	+	0.313510i
$100$	−9.25829	+	9.98168i	−0.925829	+	0.998168i
$101$	3.25209	−	10.7207i	0.323595	−	1.06675i	−0.632713	−	0.774387i	$-0.718059\pi$
$101$	3.25209	−	10.7207i	0.323595	−	1.06675i	0.956308	−	0.292362i	$-0.0944414\pi$
$102$	3.15428	−	4.91832i	0.312320	−	0.486986i
$103$	3.85971	−	5.77646i	0.380308	−	0.569172i	−0.591096	−	0.806601i	$-0.701305\pi$
$103$	3.85971	−	5.77646i	0.380308	−	0.569172i	0.971405	+	0.237429i	$0.0763047\pi$
$104$	−6.55184	−	5.85188i	−0.642460	−	0.573824i
$105$	−11.3223	+	7.56533i	−1.10495	+	0.738301i
$106$	−9.54512	+	9.91074i	−0.927104	+	0.962617i
$107$	−7.53122	+	0.741760i	−0.728070	+	0.0717087i	−0.455259	−	0.890359i	$-0.650453\pi$
$107$	−7.53122	+	0.741760i	−0.728070	+	0.0717087i	−0.272811	+	0.962068i	$0.587953\pi$
$108$	0.875857	−	1.79802i	0.0842794	−	0.173015i
$109$	−2.82201	−	9.30292i	−0.270299	−	0.891058i	−0.982049	−	0.188625i	$-0.939597\pi$
$109$	−2.82201	−	9.30292i	−0.270299	−	0.891058i	0.711750	−	0.702433i	$-0.247903\pi$
$110$	22.9919	+	6.50536i	2.19219	+	0.620262i
$111$	−0.126959	+	0.306507i	−0.0120505	+	0.0290924i
$112$	−1.91634	+	15.7355i	−0.181077	+	1.48686i
$113$	−0.841191	−	2.03081i	−0.0791326	−	0.191043i	0.879362	−	0.476154i	$-0.157970\pi$
$113$	−0.841191	−	2.03081i	−0.0791326	−	0.191043i	−0.958494	+	0.285111i	$0.907970\pi$
$114$	−0.320105	−	2.72427i	−0.0299806	−	0.255151i
$115$	10.3041	−	19.2775i	0.960859	−	1.79764i
$116$	−7.89150	+	4.60739i	−0.732707	+	0.427786i
$117$	1.97034	−	2.40086i	0.182158	−	0.221960i
$118$	8.94668	−	3.90436i	0.823608	−	0.359425i
$119$	−16.0584	−	3.19422i	−1.47207	−	0.292814i
$120$	−9.60308	+	1.49605i	−0.876637	+	0.136570i
$121$	−2.57091	−	12.9248i	−0.233719	−	1.17499i
$122$	2.14346	−	11.9446i	0.194059	−	1.08142i
$123$	0.565822	−	0.302438i	0.0510184	−	0.0272699i
$124$	15.1139	−	10.9419i	1.35727	−	0.982613i
$125$	−0.608656	+	6.17979i	−0.0544398	+	0.552737i
$126$	−5.58678	−	0.444437i	−0.497710	−	0.0395936i
$127$	−6.54334			−0.580627			−0.290314	−	0.956932i	$-0.593760\pi$
$127$	−6.54334			−0.580627			−0.290314	+	0.956932i	$0.593760\pi$
$128$	−5.96832	+	9.61141i	−0.527530	+	0.849536i
$129$	5.89046			0.518626
$130$	−15.0453	−	1.19688i	−1.31956	−	0.104973i
$131$	−0.244148	+	2.47888i	−0.0213313	+	0.216581i	0.978610	+	0.205725i	$0.0659554\pi$
$131$	−0.244148	+	2.47888i	−0.0213313	+	0.216581i	−0.999941	+	0.0108552i	$0.996545\pi$
$132$	5.76697	+	7.96582i	0.501950	+	0.693335i
$133$	−6.77888	+	3.62339i	−0.587804	+	0.314188i
$134$	1.68969	−	9.41598i	0.145967	−	0.813417i
$135$	−0.670361	−	3.37013i	−0.0576955	−	0.290055i
$136$	−9.43656	−	6.89266i	−0.809179	−	0.591041i
$137$	20.0229	+	3.98281i	1.71067	+	0.340274i	0.950802	−	0.309800i	$-0.100262\pi$
$137$	20.0229	+	3.98281i	1.71067	+	0.340274i	0.759871	+	0.650074i	$0.225262\pi$
$138$	8.24535	−	3.59830i	0.701891	−	0.306307i
$139$	1.38164	−	1.68353i	0.117189	−	0.142796i	−0.711111	−	0.703079i	$-0.751808\pi$
$139$	1.38164	−	1.68353i	0.117189	−	0.142796i	0.828301	+	0.560284i	$0.189308\pi$
$140$	13.7316	+	23.5193i	1.16053	+	1.98775i
$141$	−2.93819	+	5.49697i	−0.247441	+	0.462929i
$142$	−2.73448	−	23.2719i	−0.229472	−	1.95293i
$143$	5.84430	+	14.1094i	0.488725	+	1.17989i
$144$	−3.48336	−	1.96626i	−0.290280	−	0.163855i
$145$	−6.00808	+	14.5048i	−0.498944	+	1.20456i
$146$	0.633472	+	0.179235i	0.0524265	+	0.0148336i
$147$	2.52687	+	8.32998i	0.208413	+	0.687045i
$148$	0.596513	+	0.290575i	0.0490330	+	0.0238851i
$149$	−10.2821	+	1.01270i	−0.842343	+	0.0829636i	−0.509978	−	0.860187i	$-0.670347\pi$
$149$	−10.2821	+	1.01270i	−0.842343	+	0.0829636i	−0.332365	+	0.943151i	$0.607847\pi$
$150$	−6.67806	+	6.93386i	−0.545261	+	0.566147i
$151$	19.9349	−	13.3201i	1.62228	−	1.08397i	0.689041	−	0.724722i	$-0.258032\pi$
$151$	19.9349	−	13.3201i	1.62228	−	1.08397i	0.933241	−	0.359252i	$-0.116968\pi$
$152$	−5.47730	+	0.309089i	−0.444268	+	0.0250704i
$153$	2.29537	−	3.43526i	0.185569	−	0.277724i
$154$	14.8770	−	23.1970i	1.19882	−	1.86926i
$155$	9.30579	−	30.6771i	0.747459	−	2.46404i
$156$	−4.55428	−	4.22422i	−0.364634	−	0.338209i
$157$	9.12020	−	7.48476i	0.727872	−	0.597349i	−0.195750	−	0.980654i	$-0.562714\pi$
$157$	9.12020	−	7.48476i	0.727872	−	0.597349i	0.923622	+	0.383305i	$0.125214\pi$
$158$	3.95917	+	12.2202i	0.314975	+	0.972186i
$159$	−6.87990	+	6.87990i	−0.545612	+	0.545612i
$160$	1.82353	+	19.3521i	0.144163	+	1.52992i
$161$	−17.8259	−	17.8259i	−1.40487	−	1.40487i
$162$	0.643104	−	1.25953i	0.0505270	−	0.0989581i
$163$	2.50825	+	3.05631i	0.196461	+	0.239389i	0.861918	−	0.507048i	$-0.169263\pi$
$163$	2.50825	+	3.05631i	0.196461	+	0.239389i	−0.665457	+	0.746436i	$0.731763\pi$
$164$	−0.535237	−	1.16620i	−0.0417950	−	0.0910646i
$165$	16.1684	+	4.90464i	1.25871	+	0.381826i
$166$	4.68230	+	21.4272i	0.363417	+	1.66307i
$167$	7.44578	+	4.97511i	0.576172	+	0.384986i	0.809243	−	0.587474i	$-0.199878\pi$
$167$	7.44578	+	4.97511i	0.576172	+	0.384986i	−0.233071	+	0.972460i	$0.574878\pi$
$168$	−1.56388	+	11.0992i	−0.120656	+	0.856323i
$169$	1.86317	+	2.78843i	0.143321	+	0.214494i
$170$	−20.0735	+	0.377234i	−1.53957	+	0.0289325i
$171$	−0.190114	−	1.93026i	−0.0145384	−	0.147611i
$172$	0.713417	−	11.7593i	0.0543975	−	0.896639i
$173$	−12.4758	+	3.78448i	−0.948514	+	0.287729i	−0.726385	−	0.687289i	$-0.758801\pi$
$173$	−12.4758	+	3.78448i	−0.948514	+	0.287729i	−0.222130	+	0.975017i	$0.571301\pi$
$174$	−5.64036	+	3.15250i	−0.427594	+	0.238990i
$175$	24.9228	+	10.3234i	1.88399	+	0.780374i
$176$	16.6009	−	10.5480i	1.25134	−	0.795086i
$177$	6.37701	−	2.64144i	0.479326	−	0.198543i
$178$	5.02088	−	6.35791i	0.376331	−	0.476545i
$179$	−1.20157	−	0.642251i	−0.0898093	−	0.0480041i	0.425881	−	0.904779i	$-0.359964\pi$
$179$	−1.20157	−	0.642251i	−0.0898093	−	0.0480041i	−0.515690	+	0.856775i	$0.672464\pi$
$180$	−6.80908	+	0.930091i	−0.507519	+	0.0693249i
$181$	10.8891	+	8.93646i	0.809381	+	0.664242i	0.945200	−	0.326492i	$-0.105866\pi$
$181$	10.8891	+	8.93646i	0.809381	+	0.664242i	−0.135819	+	0.990734i	$0.543366\pi$
$182$	−6.35787	+	16.2039i	−0.471277	+	1.20111i
$183$	1.67408	−	8.41617i	0.123752	−	0.622141i
$184$	−6.18476	−	16.8962i	−0.455946	−	1.24561i
$185$	1.11808	−	0.222399i	0.0822027	−	0.0163511i
$186$	10.8306	−	7.53494i	0.794139	−	0.552488i
$187$	9.57657	+	17.9165i	0.700308	+	1.31018i
$188$	10.6179	+	6.53136i	0.774391	+	0.476349i
$189$	−3.94385	−	0.388435i	−0.286873	−	0.0282545i
$190$	−7.17230	+	6.11525i	−0.520333	+	0.443647i
$191$			14.2417i			1.03049i	0.857043	+	0.515246i	$0.172299\pi$
$191$			14.2417i			1.03049i	−0.857043	+	0.515246i	$0.827701\pi$
$192$	−4.34719	+	6.71579i	−0.313732	+	0.484671i
$193$			7.53512i			0.542390i	0.962524	+	0.271195i	$0.0874188\pi$
$193$			7.53512i			0.542390i	−0.962524	+	0.271195i	$0.912581\pi$
$194$	3.05730	+	3.58577i	0.219502	+	0.257443i
$195$	−10.6208	−	1.04606i	−0.760574	−	0.0749100i
$196$	16.9354	−	4.03559i	1.20967	−	0.288257i
$197$	3.60650	+	6.74729i	0.256953	+	0.480725i	0.977011	−	0.213189i	$-0.0683850\pi$
$197$	3.60650	+	6.74729i	0.256953	+	0.480725i	−0.720058	+	0.693914i	$0.755885\pi$
$198$	3.97131	+	5.70831i	0.282229	+	0.405672i
$199$	5.90194	−	1.17397i	0.418378	−	0.0832205i	0.0185876	−	0.999827i	$-0.494083\pi$
$199$	5.90194	−	1.17397i	0.418378	−	0.0832205i	0.399790	+	0.916607i	$0.369083\pi$
$200$	13.0335	+	14.1714i	0.921605	+	1.00207i
$201$	1.31968	−	6.63448i	0.0930831	−	0.467960i
$202$	−14.7489	−	5.78697i	−1.03773	−	0.407170i
$203$	13.9967	+	11.4868i	0.982374	+	0.806213i
$204$	−6.57990	−	4.99836i	−0.460685	−	0.349955i
$205$	−1.94425	−	1.03922i	−0.135792	−	0.0725825i
$206$	−7.71057	−	6.08909i	−0.537221	−	0.424247i
$207$	5.87712	−	2.43438i	0.408488	−	0.169201i
$208$	−8.98453	+	8.58023i	−0.622965	+	0.594932i
$209$	8.81126	+	3.64974i	0.609488	+	0.252458i
$210$	9.39552	+	16.8102i	0.648352	+	1.16001i
$211$	4.55140	−	1.38065i	0.313331	−	0.0950480i	−0.129702	−	0.991553i	$-0.541402\pi$
$211$	4.55140	−	1.38065i	0.313331	−	0.0950480i	0.443034	+	0.896505i	$0.353902\pi$
$212$	12.9013	+	14.5678i	0.886065	+	1.00052i
$213$	−1.62404	−	16.4891i	−0.111277	−	1.12982i
$214$	0.201088	+	10.7004i	0.0137461	+	0.731464i
$215$	−11.2450	−	16.8294i	−0.766906	−	1.14776i
$216$	−2.43655	−	1.43639i	−0.165786	−	0.0977342i
$217$	−30.7411	−	20.5405i	−2.08684	−	1.39438i
$218$	−13.4314	+	2.93505i	−0.909687	+	0.198786i
$219$	0.445472	+	0.135133i	0.0301022	+	0.00913141i
$220$	11.7495	−	31.6835i	0.792152	−	2.13610i
$221$	−8.14055	−	9.91929i	−0.547593	−	0.667244i
$222$	0.417863	+	0.213357i	0.0280451	+	0.0143196i
$223$	5.15254	+	5.15254i	0.345039	+	0.345039i	0.858258	−	0.513219i	$-0.171547\pi$
$223$	5.15254	+	5.15254i	0.345039	+	0.345039i	−0.513219	+	0.858258i	$0.671547\pi$
$224$	21.9683	+	4.46629i	1.46782	+	0.298416i
$225$	−4.81339	+	4.81339i	−0.320893	+	0.320893i
$226$	−2.95730	+	0.958124i	−0.196717	+	0.0637335i
$227$	8.44431	−	6.93006i	0.560468	−	0.459965i	−0.311004	−	0.950409i	$-0.600665\pi$
$227$	8.44431	−	6.93006i	0.560468	−	0.459965i	0.871473	+	0.490444i	$0.163165\pi$
$228$	−3.87646	+	0.145749i	−0.256725	+	0.00965246i
$229$	6.56004	−	21.6255i	0.433499	−	1.42906i	−0.419791	−	0.907621i	$-0.637897\pi$
$229$	6.56004	−	21.6255i	0.433499	−	1.42906i	0.853291	−	0.521436i	$-0.174603\pi$
$230$	−26.0211	−	16.6882i	−1.71578	−	1.10039i
$231$	10.8259	−	16.2022i	0.712295	−	1.06602i
$232$	5.61030	+	11.6418i	0.368334	+	0.764323i
$233$	−15.7096	+	10.4968i	−1.02917	+	0.687669i	−0.950975	−	0.309269i	$-0.899916\pi$
$233$	−15.7096	+	10.4968i	−1.02917	+	0.687669i	−0.0781950	+	0.996938i	$0.524916\pi$
$234$	−3.16367	−	3.04696i	−0.206816	−	0.199186i
$235$	21.3143	−	2.09927i	1.39039	−	0.136941i
$236$	−4.50085	−	13.0505i	−0.292980	−	0.849517i
$237$	2.63670	+	8.69205i	0.171272	+	0.564609i
$238$	−6.30401	+	22.2803i	−0.408629	+	1.44422i
$239$	−3.64813	+	8.80737i	−0.235978	+	0.569701i	−0.996860	−	0.0791894i	$-0.974767\pi$
$239$	−3.64813	+	8.80737i	−0.235978	+	0.569701i	0.760882	+	0.648891i	$0.224767\pi$
$240$	1.03209	+	13.7058i	0.0666214	+	0.884707i
$241$	−5.81152	−	14.0303i	−0.374353	−	0.903768i	−0.993002	−	0.118100i	$-0.962320\pi$
$241$	−5.81152	−	14.0303i	−0.374353	−	0.903768i	0.618649	−	0.785668i	$-0.287680\pi$
$242$	−18.5092	+	2.17486i	−1.18982	+	0.139805i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	−16.5987	−	4.36133i	−1.06262	−	0.279206i
$245$	18.9754	−	23.1216i	1.21229	−	1.47718i
$246$	−0.362909	−	0.831590i	−0.0231382	−	0.0530203i
$247$	−5.90838	−	1.17525i	−0.375941	−	0.0747793i
$248$	−13.7305	−	22.5341i	−0.871886	−	1.43091i
$249$	3.02562	+	15.2108i	0.191741	+	0.963947i
$250$	8.64375	+	1.55111i	0.546679	+	0.0981010i
$251$	2.79922	−	1.49622i	0.176685	−	0.0944403i	−0.380683	−	0.924706i	$-0.624311\pi$
$251$	2.79922	−	1.49622i	0.176685	−	0.0944403i	0.557368	+	0.830265i	$0.311811\pi$
$252$	−1.25310	+	7.82617i	−0.0789378	+	0.493002i
$253$	−3.06593	+	31.1289i	−0.192753	+	1.95706i
$254$	−0.733826	+	9.22453i	−0.0460443	+	0.578799i
$255$	−14.1966			−0.889028
$256$	12.8804	+	9.49181i	0.805027	+	0.593238i
$257$	16.9581			1.05782			0.528909	−	0.848679i	$-0.322601\pi$
$257$	16.9581			1.05782			0.528909	+	0.848679i	$0.322601\pi$
$258$	0.660607	−	8.30414i	0.0411276	−	0.516993i
$259$	0.128867	−	1.30841i	0.00800744	−	0.0813009i
$260$	−3.37461	+	21.0760i	−0.209285	+	1.30708i
$261$	−4.02952	+	2.15382i	−0.249421	+	0.133318i
$262$	3.46724	+	0.622193i	0.214207	+	0.0384392i
$263$	3.35563	+	16.8699i	0.206917	+	1.04024i	0.934971	+	0.354723i	$0.115425\pi$
$263$	3.35563	+	16.8699i	0.206917	+	1.04024i	−0.728054	+	0.685519i	$0.759575\pi$
$264$	11.8766	−	7.23669i	0.730957	−	0.445387i
$265$	32.7902	+	6.52237i	2.01429	+	0.400666i
$266$	4.34787	+	9.96295i	0.266585	+	0.610868i
$267$	3.63414	−	4.42822i	0.222406	−	0.271003i
$268$	−13.0848	−	3.43804i	−0.799280	−	0.210012i
$269$	−1.09856	+	2.05526i	−0.0669804	+	0.125312i	−0.913183	−	0.407550i	$-0.866383\pi$
$269$	−1.09856	+	2.05526i	−0.0669804	+	0.125312i	0.846203	+	0.532861i	$0.178883\pi$
$270$	−4.82625	+	0.567092i	−0.293716	+	0.0345121i
$271$	8.94061	+	21.5845i	0.543103	+	1.31117i	0.922523	+	0.385943i	$0.126124\pi$
$271$	8.94061	+	21.5845i	0.543103	+	1.31117i	−0.379419	+	0.925225i	$0.623876\pi$
$272$	−10.7753	+	12.5303i	−0.653348	+	0.759760i
$273$	−4.71019	+	11.3714i	−0.285074	+	0.688228i
$274$	7.86034	−	27.7808i	0.474861	−	1.67830i
$275$	−9.71630	−	32.0303i	−0.585915	−	1.93150i
$276$	−4.14803	−	12.0275i	−0.249682	−	0.723971i
$277$	28.0411	−	2.76181i	1.68483	−	0.165941i	0.790230	−	0.612811i	$-0.209961\pi$
$277$	28.0411	−	2.76181i	1.68483	−	0.165941i	0.894599	+	0.446870i	$0.147461\pi$
$278$	−2.21843	−	2.13659i	−0.133053	−	0.128144i
$279$	7.75716	−	5.18317i	0.464409	−	0.310308i
$280$	34.6966	−	16.7206i	2.07352	−	0.999247i
$281$	−12.1494	+	18.1828i	−0.724771	+	1.08470i	0.267852	+	0.963460i	$0.413686\pi$
$281$	−12.1494	+	18.1828i	−0.724771	+	1.08470i	−0.992624	+	0.121237i	$0.961314\pi$
$282$	7.41990	+	4.75863i	0.441849	+	0.283372i
$283$	−5.44067	+	17.9355i	−0.323414	+	1.06615i	0.633003	+	0.774150i	$0.281822\pi$
$283$	−5.44067	+	17.9355i	−0.323414	+	1.06615i	−0.956417	+	0.292005i	$0.905678\pi$
$284$	−33.1144	+	1.24505i	−1.96498	+	0.0738802i
$285$	−5.15193	+	4.22808i	−0.305174	+	0.250450i
$286$	20.5463	−	6.65671i	1.21493	−	0.393620i
$287$	−1.79784	+	1.79784i	−0.106123	+	0.106123i
$288$	−3.16261	+	4.69019i	−0.186359	+	0.276372i
$289$	−0.0492813	−	0.0492813i	−0.00289890	−	0.00289890i
$290$	19.7745	+	10.0966i	1.16120	+	0.592895i
$291$	2.11382	+	2.57569i	0.123914	+	0.150990i
$292$	0.323722	−	0.872943i	0.0189444	−	0.0510851i
$293$	−15.8404	−	4.80514i	−0.925408	−	0.280720i	−0.208609	−	0.977999i	$-0.566894\pi$
$293$	−15.8404	−	4.80514i	−0.925408	−	0.280720i	−0.716799	+	0.697280i	$0.754394\pi$
$294$	12.0267	−	2.62809i	0.701409	−	0.153273i
$295$	−19.7206	−	13.1769i	−1.14818	−	0.767189i
$296$	0.476539	−	0.808352i	0.0276983	−	0.0469845i
$297$	2.73180	+	4.08843i	0.158515	+	0.237235i
$298$	0.274539	+	14.6089i	0.0159036	+	0.846270i
$299$	−1.93657	−	19.6623i	−0.111995	−	1.13710i
$300$	9.02614	+	10.1921i	0.521125	+	0.588440i
$301$	−22.3383	+	6.77626i	−1.28756	+	0.390577i
$302$	−16.5425	−	29.5973i	−0.951912	−	1.70313i
$303$	−10.3503	−	4.28724i	−0.594610	−	0.246295i
$304$	−0.178530	+	7.75634i	−0.0102394	+	0.444857i
$305$	−27.2414	+	11.2837i	−1.55984	+	0.646105i
$306$	−4.58547	−	3.62117i	−0.262134	−	0.207009i
$307$	−19.9299	−	10.6527i	−1.13746	−	0.607984i	−0.208446	−	0.978034i	$-0.566840\pi$
$307$	−19.9299	−	10.6527i	−1.13746	−	0.607984i	−0.929012	+	0.370050i	$0.879340\pi$
$308$	−31.0337	−	23.5745i	−1.76831	−	1.34328i
$309$	−5.37033	−	4.40732i	−0.305507	−	0.250723i
$310$	−42.2037	−	16.5593i	−2.39701	−	0.940506i
$311$	−3.48987	+	17.5448i	−0.197892	+	0.994872i	0.746333	+	0.665572i	$0.231812\pi$
$311$	−3.48987	+	17.5448i	−0.197892	+	0.994872i	−0.944226	+	0.329299i	$0.893188\pi$
$312$	−6.46590	+	5.94670i	−0.366059	+	0.336666i
$313$	−16.5352	+	3.28906i	−0.934627	+	0.185909i	−0.638835	−	0.769343i	$-0.720583\pi$
$313$	−16.5352	+	3.28906i	−0.934627	+	0.185909i	−0.295792	+	0.955252i	$0.595583\pi$
$314$	−9.52889	−	13.6967i	−0.537747	−	0.772950i
$315$	6.41912	+	12.0093i	0.361677	+	0.676649i
$316$	17.6715	−	4.21100i	0.994102	−	0.236887i
$317$	23.6912	+	2.33338i	1.33063	+	0.131056i	0.738209	−	0.674573i	$-0.235672\pi$
$317$	23.6912	+	2.33338i	1.33063	+	0.131056i	0.592422	+	0.805628i	$0.298172\pi$
$318$	8.92744	+	10.4706i	0.500626	+	0.587161i
$319$		−	22.4664i		−	1.25788i
$320$	27.4863	−	0.400435i	1.53653	−	0.0223850i
$321$			7.56766i			0.422386i
$322$	−27.1293	+	23.1310i	−1.51186	+	1.28904i
$323$	−7.97496	−	0.785465i	−0.443739	−	0.0437045i
$324$	−1.70351	−	1.04788i	−0.0946396	−	0.0582153i
$325$	9.96632	+	18.6457i	0.552832	+	1.03428i
$326$	4.58996	−	3.19327i	0.254214	−	0.176859i
$327$	−9.53473	+	1.89658i	−0.527272	+	0.104881i
$328$	−1.70408	+	0.623768i	−0.0940922	+	0.0344418i
$329$	4.81888	−	24.2261i	0.265673	−	1.33563i
$330$	8.72764	−	22.2436i	0.480441	−	1.22447i
$331$	7.24573	+	5.94642i	0.398261	+	0.326845i	0.812114	−	0.583499i	$-0.198317\pi$
$331$	7.24573	+	5.94642i	0.398261	+	0.326845i	−0.413852	+	0.910344i	$0.635817\pi$
$332$	30.7323	−	4.19790i	1.68665	−	0.230389i
$333$	0.292587	+	0.156391i	0.0160337	+	0.00857017i
$334$	7.84875	−	9.93881i	0.429464	−	0.543827i
$335$	−21.4744	+	8.89499i	−1.17327	+	0.485985i
$336$	15.4718	+	3.44946i	0.844059	+	0.188183i
$337$	−22.4917	−	9.31638i	−1.22520	−	0.507495i	−0.326142	−	0.945321i	$-0.605749\pi$
$337$	−22.4917	−	9.31638i	−1.22520	−	0.507495i	−0.899060	+	0.437825i	$0.855749\pi$
$338$	4.13997	−	2.31390i	0.225184	−	0.125860i
$339$	−2.10349	+	0.638086i	−0.114246	+	0.0346561i
$340$	−1.71941	+	28.3412i	−0.0932481	+	1.53702i
$341$	4.49644	+	45.6531i	0.243496	+	2.47226i
$342$	−2.74252	+	0.0515391i	−0.148299	+	0.00278692i
$343$	−3.75344	−	5.61742i	−0.202667	−	0.303312i
$344$	−16.4978	−	2.32454i	−0.889501	−	0.125331i
$345$	−18.1747	−	12.1440i	−0.978495	−	0.653810i
$346$	3.93607	+	18.0122i	0.211604	+	0.968344i
$347$	20.3095	+	6.16081i	1.09027	+	0.330730i	0.783713	−	0.621123i	$-0.213323\pi$
$347$	20.3095	+	6.16081i	1.09027	+	0.330730i	0.306556	+	0.951853i	$0.400823\pi$
$348$	3.81171	+	8.30510i	0.204329	+	0.445200i
$349$	−2.19514	−	2.67478i	−0.117503	−	0.143178i	0.710937	−	0.703256i	$-0.248271\pi$
$349$	−2.19514	−	2.67478i	−0.117503	−	0.143178i	−0.828440	+	0.560078i	$0.810771\pi$
$350$	17.3486	−	33.9775i	0.927319	−	1.81617i
$351$	−2.19618	−	2.19618i	−0.117223	−	0.117223i
$352$	−13.0084	−	24.5862i	−0.693350	−	1.31045i
$353$	5.64140	−	5.64140i	0.300261	−	0.300261i	−0.540855	−	0.841116i	$-0.681899\pi$
$353$	5.64140	−	5.64140i	0.300261	−	0.300261i	0.841116	+	0.540855i	$0.181899\pi$
$354$	−3.00863	−	9.28629i	−0.159907	−	0.493561i
$355$	−44.0101	+	36.1181i	−2.33581	+	1.91695i
$356$	−8.40004	−	7.79127i	−0.445201	−	0.412936i
$357$	−4.75284	+	15.6680i	−0.251547	+	0.829239i
$358$	−1.04017	+	1.62189i	−0.0549749	+	0.0857197i
$359$	−8.54691	+	12.7913i	−0.451088	+	0.675102i	−0.985413	−	0.170178i	$-0.945566\pi$
$359$	−8.54691	+	12.7913i	−0.451088	+	0.675102i	0.534325	+	0.845279i	$0.320566\pi$
$360$	0.547576	+	9.70348i	0.0288598	+	0.511418i
$361$	12.6699	−	8.46575i	0.666837	−	0.445566i
$362$	13.8195	−	14.3488i	0.726335	−	0.754157i
$363$	−13.1146	+	1.29167i	−0.688338	+	0.0677953i
$364$	22.1306	+	10.7803i	1.15996	+	0.565042i
$365$	−0.464336	−	1.53071i	−0.0243045	−	0.0801211i
$366$	−11.6770	−	3.30391i	−0.610369	−	0.172698i
$367$	−2.55715	+	6.17350i	−0.133482	+	0.322254i	−0.976462	−	0.215692i	$-0.930799\pi$
$367$	−2.55715	+	6.17350i	−0.133482	+	0.322254i	0.842980	+	0.537946i	$0.180799\pi$
$368$	−24.5132	+	6.82413i	−1.27784	+	0.355733i
$369$	−0.245521	−	0.592741i	−0.0127813	−	0.0308569i
$370$	−0.188139	−	1.60116i	−0.00978088	−	0.0832405i
$371$	18.1761	−	34.0050i	0.943655	−	1.76545i
$372$	−9.40781	−	16.1136i	−0.487772	−	0.835451i
$373$	13.5289	−	16.4850i	0.700501	−	0.853562i	−0.294267	−	0.955723i	$-0.595076\pi$
$373$	13.5289	−	16.4850i	0.700501	−	0.853562i	0.994768	+	0.102161i	$0.0325756\pi$
$374$	26.3320	−	11.4914i	1.36159	−	0.594204i
$375$	6.09037	+	1.21145i	0.314505	+	0.0625590i
$376$	10.3984	−	14.2362i	0.536259	−	0.734177i
$377$	2.76848	+	13.9181i	0.142584	+	0.716818i
$378$	−0.989897	+	5.51631i	−0.0509148	+	0.283729i
$379$	8.14340	−	4.35274i	0.418298	−	0.223585i	−0.248800	−	0.968555i	$-0.580036\pi$
$379$	8.14340	−	4.35274i	0.418298	−	0.223585i	0.667098	+	0.744970i	$0.267536\pi$
$380$	7.81667	+	10.7970i	0.400987	+	0.553876i
$381$	−0.641359	+	6.51183i	−0.0328578	+	0.333611i
$382$	20.0773	+	1.59718i	1.02725	+	0.0817190i
$383$	2.19487			0.112153			0.0560763	−	0.998426i	$-0.482141\pi$
$383$	2.19487			0.112153			0.0560763	+	0.998426i	$0.482141\pi$
$384$	8.98013	+	6.88167i	0.458265	+	0.351179i
$385$	−66.9576			−3.41247
$386$	10.6227	+	0.845053i	0.540682	+	0.0430121i
$387$	0.577366	−	5.86210i	0.0293492	−	0.297987i
$388$	5.39795	−	3.90792i	0.274039	−	0.198395i
$389$	−30.3141	+	16.2032i	−1.53699	+	0.821536i	−0.999760	−	0.0219032i	$-0.993027\pi$
$389$	−30.3141	+	16.2032i	−1.53699	+	0.821536i	−0.537225	+	0.843439i	$0.680527\pi$
$390$	−2.66581	+	14.8555i	−0.134988	+	0.752238i
$391$	−5.12741	−	25.7772i	−0.259304	−	1.30361i
$392$	−3.78993	−	24.3275i	−0.191420	−	1.22872i
$393$	2.44301	+	0.485945i	0.123234	+	0.0245127i
$394$	9.91653	−	4.32760i	0.499587	−	0.218021i
$395$	19.8002	−	24.1266i	0.996254	−	1.21394i
$396$	8.49272	−	4.95842i	0.426775	−	0.249170i
$397$	7.17569	−	13.4248i	0.360138	−	0.673770i	−0.634973	−	0.772534i	$-0.718989\pi$
$397$	7.17569	−	13.4248i	0.360138	−	0.673770i	0.995111	+	0.0987641i	$0.0314889\pi$
$398$	−0.993120	−	8.45198i	−0.0497806	−	0.423660i
$399$	2.94149	+	7.10139i	0.147259	+	0.355514i
$400$	21.4399	−	16.7848i	1.07200	−	0.839238i
$401$	−1.94083	+	4.68557i	−0.0969202	+	0.233986i	−0.964902	−	0.262610i	$-0.915417\pi$
$401$	−1.94083	+	4.68557i	−0.0969202	+	0.233986i	0.867982	+	0.496596i	$0.165417\pi$
$402$	−9.20502	−	2.60448i	−0.459105	−	0.129900i
$403$	−8.41129	−	27.7283i	−0.418996	−	1.38125i
$404$	−9.81231	+	20.1434i	−0.488181	+	1.00217i
$405$	−3.41961	+	0.336802i	−0.169922	+	0.0167358i
$406$	17.7633	−	18.4437i	0.881577	−	0.915346i
$407$	−1.35638	+	0.906306i	−0.0672334	+	0.0449239i
$408$	−7.78442	+	8.71553i	−0.385386	+	0.431483i
$409$	16.6464	−	24.9130i	0.823110	−	1.23187i	−0.146984	−	0.989139i	$-0.546957\pi$
$409$	16.6464	−	24.9130i	0.823110	−	1.23187i	0.970093	−	0.242732i	$-0.0780434\pi$
$410$	−1.68310	+	2.62438i	−0.0831224	+	0.129609i
$411$	5.92622	−	19.5361i	0.292319	−	0.963645i
$412$	−9.44888	+	10.1872i	−0.465513	+	0.501885i
$413$	−21.1448	+	17.3531i	−1.04047	+	0.853889i
$414$	−2.77278	−	8.55834i	−0.136275	−	0.420619i
$415$	37.6822	−	37.6822i	1.84975	−	1.84975i
$416$	11.0885	+	13.6283i	0.543657	+	0.668182i
$417$	−1.54000	−	1.54000i	−0.0754143	−	0.0754143i
$418$	6.13343	−	12.0124i	0.299996	−	0.587548i
$419$	13.4388	+	16.3752i	0.656526	+	0.799980i	0.989741	−	0.142871i	$-0.0456335\pi$
$419$	13.4388	+	16.3752i	0.656526	+	0.799980i	−0.333215	+	0.942851i	$0.608133\pi$
$420$	24.7520	−	11.3602i	1.20778	−	0.554320i
$421$	−33.4882	−	10.1585i	−1.63211	−	0.495096i	−0.664448	−	0.747334i	$-0.731333\pi$
$421$	−33.4882	−	10.1585i	−1.63211	−	0.495096i	−0.967665	+	0.252238i	$0.918833\pi$
$422$	−1.43595	−	6.57122i	−0.0699012	−	0.319882i
$423$	5.18251	+	3.46284i	0.251982	+	0.168369i
$424$	21.9840	−	16.5540i	1.06764	−	0.803932i
$425$	15.6249	+	23.3844i	0.757920	+	1.13431i
$426$	−23.4278	+	0.440270i	−1.13508	+	0.0213311i
$427$	3.33318	+	33.8424i	0.161304	+	1.63775i
$428$	15.1075	+	0.916549i	0.730251	+	0.0443031i
$429$	14.6143	−	4.43320i	0.705585	−	0.214037i
$430$	−24.9865	+	13.9654i	−1.20496	+	0.673472i
$431$	10.8187	+	4.48127i	0.521120	+	0.215855i	0.627709	−	0.778448i	$-0.283993\pi$
$431$	10.8187	+	4.48127i	0.521120	+	0.215855i	−0.106589	+	0.994303i	$0.533993\pi$
$432$	−2.29823	+	3.27386i	−0.110573	+	0.157514i
$433$	19.6416	−	8.13583i	0.943916	−	0.390983i	0.142975	−	0.989726i	$-0.454333\pi$
$433$	19.6416	−	8.13583i	0.943916	−	0.390983i	0.800941	+	0.598743i	$0.204333\pi$
$434$	−32.4048	+	41.0339i	−1.55548	+	1.96969i
$435$	13.8460	+	7.40086i	0.663867	+	0.354844i
$436$	2.63140	+	19.2642i	0.126021	+	0.922586i
$437$	−9.53776	−	7.82744i	−0.456253	−	0.374437i
$438$	0.240463	−	0.612854i	0.0114898	−	0.0292833i
$439$	−4.32040	+	21.7201i	−0.206202	+	1.03665i	0.729534	+	0.683944i	$0.239737\pi$
$439$	−4.32040	+	21.7201i	−0.206202	+	1.03665i	−0.935736	+	0.352701i	$0.885263\pi$
$440$	−43.3485	−	20.1172i	−2.06656	−	0.959052i
$441$	8.53754	−	1.69822i	0.406550	−	0.0808678i
$442$	−14.8968	+	10.3638i	−0.708567	+	0.492955i
$443$	6.47234	+	12.1089i	0.307510	+	0.575311i	0.987445	−	0.157961i	$-0.0504921\pi$
$443$	6.47234	+	12.1089i	0.307510	+	0.575311i	−0.679935	+	0.733272i	$0.737992\pi$
$444$	0.347644	−	0.565159i	0.0164985	−	0.0268213i
$445$	−19.5894	−	1.92938i	−0.928624	−	0.0914615i
$446$	7.84169	−	6.68599i	0.371315	−	0.316591i
$447$			10.3319i			0.488680i
$448$	8.76011	−	30.4691i	0.413876	−	1.43953i
$449$		−	26.3185i		−	1.24205i	−0.783791	−	0.621024i	$-0.786717\pi$
$449$		−	26.3185i		−	1.24205i	0.783791	−	0.621024i	$-0.213283\pi$
$450$	6.24591	+	7.32554i	0.294435	+	0.345329i
$451$	3.13953	+	0.309216i	0.147834	+	0.0145604i
$452$	1.01907	+	4.27653i	0.0479329	+	0.201151i
$453$	−11.3020	−	21.1445i	−0.531014	−	0.993457i
$454$	−8.82271	−	12.6816i	−0.414070	−	0.595179i
$455$	41.4806	−	8.25101i	1.94464	−	0.386813i
$456$	−0.229269	+	5.48122i	−0.0107365	+	0.256682i
$457$	0.886544	−	4.45696i	0.0414708	−	0.208488i	−0.954494	−	0.298229i	$-0.903604\pi$
$457$	0.886544	−	4.45696i	0.0414708	−	0.208488i	0.995965	+	0.0897414i	$0.0286040\pi$
$458$	−29.7511	−	11.6734i	−1.39018	−	0.545460i
$459$	−3.19373	−	2.62103i	−0.149071	−	0.122339i
$460$	−26.4446	+	34.8120i	−1.23299	+	1.62312i
$461$	−22.6519	−	12.1077i	−1.05500	−	0.563911i	−0.149724	−	0.988728i	$-0.547839\pi$
$461$	−22.6519	−	12.1077i	−1.05500	−	0.563911i	−0.905279	+	0.424817i	$0.860339\pi$
$462$	−21.6271	−	17.0790i	−1.00618	−	0.794589i
$463$	5.71450	−	2.36702i	0.265575	−	0.110005i	−0.245922	−	0.969290i	$-0.579091\pi$
$463$	5.71450	−	2.36702i	0.265575	−	0.110005i	0.511498	+	0.859285i	$0.329091\pi$
$464$	17.0414	−	6.60356i	0.791125	−	0.306563i
$465$	−29.6172	−	12.2679i	−1.37347	−	0.568908i
$466$	13.0362	+	23.3240i	0.603889	+	1.08046i
$467$	−13.5391	+	4.10703i	−0.626514	+	0.190051i	−0.587547	−	0.809190i	$-0.699906\pi$
$467$	−13.5391	+	4.10703i	−0.626514	+	0.190051i	−0.0389661	+	0.999241i	$0.512406\pi$
$468$	−4.65028	+	4.11831i	−0.214959	+	0.190369i
$469$	2.62755	+	26.6780i	0.121329	+	1.23187i
$470$	−0.569104	−	30.2834i	−0.0262508	−	1.39687i
$471$	−6.55478	−	9.80992i	−0.302028	−	0.452017i
$472$	−18.9029	+	4.88152i	−0.870076	+	0.224690i
$473$	24.0828	+	16.0916i	1.10733	+	0.739892i
$474$	12.5494	−	2.74232i	0.576413	−	0.125959i
$475$	12.6346	+	3.83268i	0.579717	+	0.175855i
$476$	30.7029	+	11.3858i	1.40726	+	0.521870i
$477$	6.17242	+	7.52112i	0.282616	+	0.344368i
$478$	12.0071	+	6.13072i	0.549194	+	0.280413i
$479$	−18.3092	−	18.3092i	−0.836567	−	0.836567i	0.151838	−	0.988405i	$-0.451481\pi$
$479$	−18.3092	−	18.3092i	−0.836567	−	0.836567i	−0.988405	+	0.151838i	$0.951481\pi$
$480$	19.4377	+	0.0820838i	0.887204	+	0.00374659i
$481$	0.728605	−	0.728605i	0.0332216	−	0.0332216i
$482$	−20.4310	+	6.61937i	−0.930608	+	0.301504i
$483$	−19.4873	+	15.9928i	−0.886701	+	0.727697i
$484$	0.990249	+	26.3375i	0.0450113	+	1.19716i
$485$	3.32358	−	10.9564i	0.150916	−	0.497503i
$486$	−1.19043	−	0.763462i	−0.0539990	−	0.0346314i
$487$	14.8200	−	22.1796i	0.671556	−	1.00505i	−0.326648	−	0.945146i	$-0.605919\pi$
$487$	14.8200	−	22.1796i	0.671556	−	1.00505i	0.998204	−	0.0599086i	$-0.0190809\pi$
$488$	−8.00995	+	22.9111i	−0.362594	+	1.03714i
$489$	3.28745	−	2.19660i	0.148663	−	0.0993337i
$490$	−30.4678	−	29.3438i	−1.37639	−	1.32562i
$491$	−41.6677	+	4.10391i	−1.88044	+	0.185207i	−0.972343	−	0.233556i	$-0.924964\pi$
$491$	−41.6677	+	4.10391i	−1.88044	+	0.185207i	−0.908095	+	0.418763i	$0.862464\pi$
$492$	−1.21304	+	0.418352i	−0.0546882	+	0.0188608i
$493$	5.47974	+	18.0643i	0.246795	+	0.813574i
$494$	−2.31944	+	8.19759i	−0.104356	+	0.368827i
$495$	6.46581	−	15.6099i	0.290617	−	0.701611i
$496$	−33.3075	+	16.8295i	−1.49555	+	0.755667i
$497$	25.1275	+	60.6632i	1.12712	+	2.72112i
$498$	21.7829	−	2.55953i	0.976116	−	0.114695i
$499$	−13.5054	+	25.2669i	−0.604586	+	1.13110i	0.374418	+	0.927260i	$0.377842\pi$
$499$	−13.5054	+	25.2669i	−0.604586	+	1.13110i	−0.979004	+	0.203841i	$0.934658\pi$
$500$	3.15608	−	12.0117i	0.141144	−	0.537178i
$501$	5.68097	−	6.92228i	0.253807	−	0.309265i
$502$	−1.79538	−	4.11403i	−0.0801315	−	0.183618i
$503$	9.68469	+	1.92640i	0.431819	+	0.0858941i	0.406214	−	0.913778i	$-0.366849\pi$
$503$	9.68469	+	1.92640i	0.431819	+	0.0858941i	0.0256051	+	0.999672i	$0.491849\pi$
$504$	10.8925	+	2.64426i	0.485190	+	0.117785i
$505$	7.51011	+	37.7559i	0.334196	+	1.68012i
$506$	43.5404	+	7.81328i	1.93561	+	0.347343i
$507$	2.95762	−	1.58088i	0.131353	−	0.0702095i
$508$	12.9221	+	2.06904i	0.573324	+	0.0917987i
$509$	−1.03108	+	10.4687i	−0.0457018	+	0.464018i	0.944912	+	0.327326i	$0.106147\pi$
$509$	−1.03108	+	10.4687i	−0.0457018	+	0.464018i	−0.990613	+	0.136693i	$0.956353\pi$
$510$	−1.59213	+	20.0139i	−0.0705009	+	0.886228i
$511$	−1.84481			−0.0816096
$512$	14.8257	−	17.0938i	0.655209	−	0.755447i
$513$	−1.93960			−0.0856354
$514$	1.90183	−	23.9068i	0.0838860	−	1.05449i
$515$	−2.33986	+	23.7570i	−0.103107	+	1.04686i
$516$	−11.6328	−	1.86260i	−0.512103	−	0.0819962i
$517$	−27.0293	+	14.4474i	−1.18875	+	0.635398i
$518$	−1.83010	−	0.328409i	−0.0804098	−	0.0144295i
$519$	2.54342	+	12.7866i	0.111644	+	0.561271i
$520$	29.3336	+	7.12104i	1.28637	+	0.312278i
$521$	19.6768	+	3.91397i	0.862058	+	0.171474i	0.606270	−	0.795259i	$-0.292665\pi$
$521$	19.6768	+	3.91397i	0.862058	+	0.171474i	0.255788	+	0.966733i	$0.417665\pi$
$522$	2.58447	+	5.92220i	0.113119	+	0.259208i
$523$	−3.68223	+	4.48681i	−0.161012	+	0.196194i	−0.847267	−	0.531167i	$-0.821754\pi$
$523$	−3.68223	+	4.48681i	−0.161012	+	0.196194i	0.686255	+	0.727361i	$0.259254\pi$
$524$	1.26599	−	4.81820i	0.0553050	−	0.210484i
$525$	12.7165	−	23.7910i	0.554995	−	1.03832i
$526$	24.1588	−	2.83870i	1.05338	−	0.123773i
$527$	−14.7506	−	35.6110i	−0.642545	−	1.55124i
$528$	−8.87004	−	17.5548i	−0.386019	−	0.763975i
$529$	6.68423	−	16.1372i	0.290619	−	0.701616i
$530$	12.8724	−	45.4948i	0.559139	−	1.97617i
$531$	−2.00367	−	6.60521i	−0.0869518	−	0.286642i
$532$	14.5330	−	5.01211i	0.630085	−	0.217303i
$533$	−1.98306	+	0.195314i	−0.0858958	+	0.00846000i
$534$	−5.83516	−	5.61989i	−0.252512	−	0.243196i
$535$	21.6212	−	14.4469i	0.934768	−	0.624592i
$536$	−6.31426	+	18.0608i	−0.272734	+	0.780109i
$537$	−0.756932	+	1.13283i	−0.0326640	+	0.0488852i
$538$	2.77423	+	1.77920i	0.119605	+	0.0767068i
$539$	−12.4249	+	40.9595i	−0.535179	+	1.76425i
$540$	0.258206	+	6.86746i	0.0111114	+	0.295528i
$541$	19.4978	−	16.0014i	0.838274	−	0.687954i	−0.113906	−	0.993492i	$-0.536336\pi$
$541$	19.4978	−	16.0014i	0.838274	−	0.687954i	0.952180	+	0.305538i	$0.0988362\pi$
$542$	31.4317	−	10.1834i	1.35011	−	0.437416i
$543$	9.96075	−	9.96075i	0.427457	−	0.427457i
$544$	16.4563	+	16.5958i	0.705556	+	0.711541i
$545$	23.6207	+	23.6207i	1.01180	+	1.01180i
$546$	15.5027	+	7.91552i	0.663454	+	0.338753i
$547$	−13.5279	−	16.4838i	−0.578413	−	0.704798i	0.398805	−	0.917036i	$-0.369425\pi$
$547$	−13.5279	−	16.4838i	−0.578413	−	0.704798i	−0.977218	+	0.212237i	$0.931925\pi$
$548$	−38.2828	−	14.1968i	−1.63536	−	0.606456i
$549$	−8.21156	−	2.49095i	−0.350461	−	0.106311i
$550$	−46.2448	+	10.1055i	−1.97188	+	0.430899i
$551$	7.36854	+	4.92350i	0.313910	+	0.209748i
$552$	−17.4211	+	4.49886i	−0.741491	+	0.191484i
$553$	−19.9983	−	29.9295i	−0.850413	−	1.27273i
$554$	−0.748716	−	39.8410i	−0.0318099	−	1.69268i
$555$	−0.111738	−	1.13449i	−0.00474300	−	0.0481565i
$556$	−3.26087	+	2.88784i	−0.138292	+	0.122472i
$557$	−16.8799	+	5.12046i	−0.715224	+	0.216961i	−0.626865	−	0.779128i	$-0.715662\pi$
$557$	−16.8799	+	5.12046i	−0.715224	+	0.216961i	−0.0883590	+	0.996089i	$0.528162\pi$
$558$	−6.43707	−	11.5170i	−0.272503	−	0.487554i
$559$	−16.9024	−	7.00118i	−0.714893	−	0.296119i
$560$	−19.6809	−	50.7891i	−0.831668	−	2.14623i
$561$	18.7689	−	7.77433i	0.792424	−	0.328233i
$562$	24.2709	+	19.1669i	1.02381	+	0.808507i
$563$	18.3826	+	9.82572i	0.774735	+	0.414105i	0.810858	−	0.585243i	$-0.199001\pi$
$563$	18.3826	+	9.82572i	0.774735	+	0.414105i	−0.0361230	+	0.999347i	$0.511501\pi$
$564$	7.54065	−	9.92660i	0.317519	−	0.417985i
$565$	5.83866	+	4.79166i	0.245634	+	0.201587i
$566$	24.6746	+	9.68148i	1.03715	+	0.406943i
$567$	−0.773129	+	3.88678i	−0.0324684	+	0.163230i
$568$	−1.95851	+	46.8230i	−0.0821774	+	1.96465i
$569$	10.0642	−	2.00189i	0.421911	−	0.0839234i	0.0204316	−	0.999791i	$-0.493496\pi$
$569$	10.0642	−	2.00189i	0.421911	−	0.0839234i	0.401480	+	0.915868i	$0.368496\pi$
$570$	5.38280	+	7.73716i	0.225461	+	0.324074i
$571$	14.7179	+	27.5352i	0.615924	+	1.15231i	0.975666	+	0.219261i	$0.0703645\pi$
$571$	14.7179	+	27.5352i	0.615924	+	1.15231i	−0.359742	+	0.933052i	$0.617135\pi$
$572$	−7.08013	−	29.7119i	−0.296035	−	1.24232i
$573$	14.1731	+	1.39593i	0.592090	+	0.0583157i
$574$	2.33290	+	2.73615i	0.0973732	+	0.114205i
$575$			43.3027i			1.80585i
$576$	6.25736	+	4.98452i	0.260723	+	0.207689i
$577$			42.1383i			1.75424i	0.480271	+	0.877120i	$0.340538\pi$
$577$			42.1383i			1.75424i	−0.480271	+	0.877120i	$0.659462\pi$
$578$	−0.0750016	+	0.0639479i	−0.00311966	+	0.00265988i
$579$	7.49883	+	0.738571i	0.311641	+	0.0306940i
$580$	16.4515	−	26.7449i	0.683112	−	1.11052i
$581$	−28.9722	−	54.2032i	−1.20197	−	2.24873i
$582$	3.86817	−	2.69111i	0.160341	−	0.111550i
$583$	−46.9226	+	9.33348i	−1.94333	+	0.386553i
$584$	−1.19433	−	0.554269i	−0.0494219	−	0.0229358i
$585$	−2.08205	+	10.4672i	−0.0860821	+	0.432764i
$586$	−8.55058	+	21.7923i	−0.353221	+	0.900233i
$587$	−18.4775	−	15.1641i	−0.762647	−	0.625888i	0.170510	−	0.985356i	$-0.445458\pi$
$587$	−18.4775	−	15.1641i	−0.762647	−	0.625888i	−0.933158	+	0.359467i	$0.882958\pi$
$588$	−2.35620	−	17.2494i	−0.0971679	−	0.711354i
$589$	−15.9587	−	8.53012i	−0.657568	−	0.351477i
$590$	−20.7879	+	26.3236i	−0.855825	+	1.08373i
$591$	7.06830	−	2.92779i	0.290751	−	0.120433i
$592$	−1.08614	−	0.762461i	−0.0446400	−	0.0313370i
$593$	34.8776	+	14.4468i	1.43225	+	0.593258i	0.957906	−	0.287081i	$-0.0926850\pi$
$593$	34.8776	+	14.4468i	1.43225	+	0.593258i	0.474345	+	0.880339i	$0.342685\pi$
$594$	6.07008	−	3.39268i	0.249058	−	0.139203i
$595$	53.8377	−	16.3315i	2.20713	−	0.669526i
$596$	20.6258	+	1.25133i	0.844866	+	0.0512566i
$597$	−0.589825	−	5.98859i	−0.0241399	−	0.245097i
$598$	−27.9364	+	0.524996i	−1.14240	+	0.0214687i
$599$	13.4565	+	20.1390i	0.549816	+	0.822858i	0.997451	−	0.0713588i	$-0.0227335\pi$
$599$	13.4565	+	20.1390i	0.549816	+	0.822858i	−0.447635	+	0.894216i	$0.647734\pi$
$600$	15.3807	−	11.5817i	0.627913	−	0.472820i
$601$	12.9972	+	8.68443i	0.530166	+	0.354245i	0.791662	−	0.610959i	$-0.209216\pi$
$601$	12.9972	+	8.68443i	0.530166	+	0.354245i	−0.261497	+	0.965204i	$0.584216\pi$
$602$	7.04768	+	32.2516i	0.287242	+	1.31448i
$603$	−6.47318	−	1.96362i	−0.263608	−	0.0799647i
$604$	−43.5803	+	20.0016i	−1.77326	+	0.813854i
$605$	28.7265	+	35.0033i	1.16790	+	1.42309i
$606$	−7.20475	+	14.1106i	−0.292673	+	0.573206i
$607$	11.9928	+	11.9928i	0.486773	+	0.486773i	0.907286	−	0.420514i	$-0.138150\pi$
$607$	11.9928	+	11.9928i	0.486773	+	0.486773i	−0.420514	+	0.907286i	$0.638150\pi$
$608$	10.9146	+	1.12155i	0.442644	+	0.0454848i
$609$	12.8034	−	12.8034i	0.518819	−	0.518819i
$610$	12.8523	+	39.6692i	0.520374	+	1.60616i
$611$	14.9645	−	12.2810i	0.605398	−	0.496837i
$612$	−5.61924	+	6.05830i	−0.227144	+	0.244892i
$613$	−2.57914	+	8.50228i	−0.104170	+	0.343404i	−0.993495	−	0.113872i	$-0.963675\pi$
$613$	−2.57914	+	8.50228i	−0.104170	+	0.343404i	0.889325	+	0.457276i	$0.151175\pi$
$614$	−17.2529	+	26.9016i	−0.696270	+	1.08566i
$615$	−1.22479	+	1.83303i	−0.0493883	+	0.0739148i
$616$	−36.7147	+	41.1062i	−1.47928	+	1.65622i
$617$	3.92837	−	2.62485i	0.158150	−	0.105673i	−0.473977	−	0.880537i	$-0.657182\pi$
$617$	3.92837	−	2.62485i	0.158150	−	0.105673i	0.632127	+	0.774865i	$0.282182\pi$
$618$	−6.81553	+	7.07660i	−0.274161	+	0.284663i
$619$	−32.7139	+	3.22204i	−1.31488	+	0.129505i	−0.731024	−	0.682351i	$-0.760957\pi$
$619$	−32.7139	+	3.22204i	−1.31488	+	0.129505i	−0.583858	+	0.811856i	$0.698457\pi$
$620$	−28.0777	+	57.6399i	−1.12763	+	2.31488i
$621$	−1.84660	−	6.08743i	−0.0741016	−	0.244280i
$622$	24.3425	+	6.88750i	0.976045	+	0.276163i
$623$	−8.68759	+	20.9737i	−0.348061	+	0.840294i
$624$	7.65828	+	9.78228i	0.306577	+	0.391604i
$625$	4.85945	+	11.7318i	0.194378	+	0.469270i
$626$	2.78239	+	23.6796i	0.111207	+	0.946427i
$627$	4.49582	−	8.41109i	0.179546	−	0.335907i
$628$	−20.3777	+	11.8974i	−0.813159	+	0.474757i
$629$	0.869554	−	1.05955i	0.0346714	−	0.0422472i
$630$	17.6502	−	7.70259i	0.703200	−	0.306878i
$631$	−30.7366	−	6.11390i	−1.22361	−	0.243390i	−0.459322	−	0.888270i	$-0.651908\pi$
$631$	−30.7366	−	6.11390i	−1.22361	−	0.243390i	−0.764284	+	0.644879i	$0.776908\pi$
$632$	−3.95466	−	25.3849i	−0.157308	−	1.00976i
$633$	−0.927889	−	4.66481i	−0.0368803	−	0.185410i
$634$	5.94644	−	33.1372i	0.236163	−	1.31605i
$635$	19.8290	−	10.5988i	0.786892	−	0.420602i
$636$	15.7622	−	11.4113i	0.625012	−	0.452487i
$637$	2.64998	−	26.9057i	0.104996	−	1.06604i
$638$	−31.6722	−	2.51958i	−1.25392	−	0.0997510i
$639$	−16.5689			−0.655456
$640$	2.51804	−	38.7940i	0.0995341	−	1.53347i
$641$	7.62310			0.301094			0.150547	−	0.988603i	$-0.451896\pi$
$641$	7.62310			0.301094			0.150547	+	0.988603i	$0.451896\pi$
$642$	10.6686	+	0.848703i	0.421055	+	0.0334956i
$643$	−0.830626	+	8.43348i	−0.0327567	+	0.332584i	0.964815	+	0.262931i	$0.0846892\pi$
$643$	−0.830626	+	8.43348i	−0.0327567	+	0.332584i	−0.997571	+	0.0696530i	$0.977811\pi$
$644$	29.5667	+	40.8399i	1.16509	+	1.60932i
$645$	−17.8506	+	9.54133i	−0.702865	+	0.375689i
$646$	−2.00170	+	11.1547i	−0.0787558	+	0.438876i
$647$	−4.61588	−	23.2056i	−0.181469	−	0.912306i	−0.958988	−	0.283446i	$-0.908522\pi$
$647$	−4.61588	−	23.2056i	−0.181469	−	0.912306i	0.777519	−	0.628859i	$-0.216478\pi$
$648$	−1.66830	+	2.28403i	−0.0655370	+	0.0897250i
$649$	33.2879	+	6.62138i	1.30666	+	0.259912i
$650$	27.4036	−	11.9590i	1.07486	−	0.469072i
$651$	−23.4548	+	28.5797i	−0.919265	+	1.12013i
$652$	−3.98698	−	6.82886i	−0.156142	−	0.267439i
$653$	9.60407	−	17.9679i	0.375836	−	0.703140i	−0.620898	−	0.783891i	$-0.713232\pi$
$653$	9.60407	−	17.9679i	0.375836	−	0.703140i	0.996734	+	0.0807512i	$0.0257319\pi$
$654$	1.60441	+	13.6544i	0.0627374	+	0.533928i
$655$	−3.27540	−	7.90751i	−0.127980	−	0.308972i
$656$	0.688253	+	2.47230i	0.0268718	+	0.0965271i
$657$	0.178146	−	0.430082i	0.00695013	−	0.0167791i
$658$	−33.6126	−	9.51039i	−1.31036	−	0.370753i
$659$	−3.93281	−	12.9647i	−0.153201	−	0.505035i	0.846422	−	0.532513i	$-0.178752\pi$
$659$	−3.93281	−	12.9647i	−0.153201	−	0.505035i	−0.999622	+	0.0274784i	$0.991252\pi$
$660$	−30.3793	−	14.7985i	−1.18251	−	0.576029i
$661$	6.63488	−	0.653479i	0.258067	−	0.0254174i	0.0318438	−	0.999493i	$-0.489862\pi$
$661$	6.63488	−	0.653479i	0.258067	−	0.0254174i	0.226223	+	0.974075i	$0.427362\pi$
$662$	9.19562	−	9.54786i	0.357398	−	0.371088i
$663$	−10.6694	+	7.12909i	−0.414367	+	0.276871i
$664$	−2.47144	−	43.7959i	−0.0959106	−	1.69961i
$665$	14.6737	−	21.9608i	0.569022	−	0.851602i
$666$	0.253287	−	0.394938i	0.00981467	−	0.0153035i
$667$	−8.43716	+	27.8136i	−0.326688	+	1.07695i
$668$	−13.1311	−	12.1795i	−0.508058	−	0.471238i
$669$	5.63276	−	4.62269i	0.217775	−	0.178723i
$670$	10.1315	+	31.2713i	0.391413	+	1.20812i
$671$	29.8357	−	29.8357i	1.15179	−	1.15179i
$672$	6.59805	−	21.4247i	0.254525	−	0.826477i
$673$	−3.28057	−	3.28057i	−0.126457	−	0.126457i	0.641046	−	0.767503i	$-0.278501\pi$
$673$	−3.28057	−	3.28057i	−0.126457	−	0.126457i	−0.767503	+	0.641046i	$0.778501\pi$
$674$	−15.6563	+	30.6631i	−0.603057	+	1.18110i
$675$	4.31842	+	5.26201i	0.166216	+	0.202535i
$676$	−2.79775	−	6.09586i	−0.107606	−	0.234456i
$677$	−4.52887	−	1.37382i	−0.174059	−	0.0528001i	0.202052	−	0.979375i	$-0.435239\pi$
$677$	−4.52887	−	1.37382i	−0.174059	−	0.0528001i	−0.376111	+	0.926575i	$0.622739\pi$
$678$	0.663645	+	3.03697i	0.0254871	+	0.116634i
$679$	−10.9792	−	7.33608i	−0.421344	−	0.281533i
$680$	39.7614	+	5.60238i	1.52478	+	0.214841i
$681$	−6.06901	−	9.08291i	−0.232565	−	0.348058i
$682$	64.8642	−	1.21897i	2.48378	−	0.0466766i
$683$	−2.16487	−	21.9803i	−0.0828363	−	0.841051i	−0.943389	−	0.331689i	$-0.892381\pi$
$683$	−2.16487	−	21.9803i	−0.0828363	−	0.841051i	0.860552	−	0.509362i	$-0.170119\pi$
$684$	−0.234912	+	3.87208i	−0.00898210	+	0.148053i
$685$	−67.1291	+	20.3634i	−2.56487	+	0.778045i
$686$	−8.34016	+	4.66146i	−0.318429	+	0.177975i
$687$	−20.8784	−	8.64812i	−0.796561	−	0.329946i
$688$	−5.12724	+	22.9972i	−0.195474	+	0.876761i
$689$	27.9187	−	11.5643i	1.06362	−	0.440565i
$690$	−19.1584	+	24.2601i	−0.729346	+	0.923566i
$691$	−12.3044	−	6.57684i	−0.468081	−	0.250195i	0.220454	−	0.975397i	$-0.429246\pi$
$691$	−12.3044	−	6.57684i	−0.468081	−	0.250195i	−0.688536	+	0.725203i	$0.741746\pi$
$692$	25.8344	−	3.52886i	0.982075	−	0.134147i
$693$	−15.0630	−	12.3619i	−0.572197	−	0.469590i
$694$	10.9629	−	27.9405i	0.416148	−	1.06061i
$695$	−1.45997	+	7.33979i	−0.0553800	+	0.278414i
$696$	12.1357	−	4.44218i	0.460001	−	0.168381i
$697$	−2.59978	+	0.517128i	−0.0984737	+	0.0195876i
$698$	−4.01698	+	2.79464i	−0.152045	+	0.105779i
$699$	8.90646	+	16.6628i	0.336873	+	0.630246i
$700$	−45.9545	−	28.2678i	−1.73692	−	1.06842i
$701$	8.43955	+	0.831223i	0.318758	+	0.0313949i	0.256131	−	0.966642i	$-0.417552\pi$
$701$	8.43955	+	0.831223i	0.318758	+	0.0313949i	0.0626268	+	0.998037i	$0.480052\pi$
$702$	−3.34238	+	2.84978i	−0.126150	+	0.107558i
$703$		−	0.643483i		−	0.0242694i
$704$	−36.1195	+	15.5814i	−1.36130	+	0.587246i
$705$		−	21.4174i		−	0.806626i
$706$	−7.32034	−	8.58569i	−0.275505	−	0.323127i
$707$	44.1833	+	4.35167i	1.66168	+	0.163662i
$708$	−13.4288	+	3.20000i	−0.504687	+	0.120263i
$709$	10.5262	+	19.6931i	0.395320	+	0.739591i	0.998307	−	0.0581595i	$-0.0185232\pi$
$709$	10.5262	+	19.6931i	0.395320	+	0.739591i	−0.602988	+	0.797750i	$0.706023\pi$
$710$	45.9822	+	66.0942i	1.72568	+	2.48047i
$711$	8.90864	−	1.77204i	0.334100	−	0.0664566i
$712$	−11.9259	+	10.9683i	−0.446941	+	0.411053i
$713$	11.5782	−	58.2076i	0.433607	−	2.17989i
$714$	21.5551	+	8.45751i	0.806680	+	0.316514i
$715$	−40.5650	−	33.2908i	−1.51704	−	1.24501i
$716$	2.16983	+	1.64829i	0.0810902	+	0.0615994i
$717$	8.40738	+	4.49384i	0.313979	+	0.167825i
$718$	17.0742	+	13.4836i	0.637204	+	0.503204i
$719$	11.7867	−	4.88220i	0.439569	−	0.182075i	−0.151913	−	0.988394i	$-0.548543\pi$
$719$	11.7867	−	4.88220i	0.439569	−	0.182075i	0.591482	+	0.806318i	$0.298543\pi$
$720$	13.7410	+	0.316281i	0.512096	+	0.0117871i
$721$	25.4359	+	10.5359i	0.947283	+	0.392377i
$722$	−10.5138	−	18.8109i	−0.391282	−	0.700070i
$723$	−14.5323	+	4.40833i	−0.540463	+	0.163948i
$724$	−18.6786	−	21.0913i	−0.694183	−	0.783853i
$725$	−3.04853	−	30.9523i	−0.113220	−	1.14954i
$726$	0.350168	+	18.6333i	0.0129959	+	0.691546i
$727$	−9.06912	−	13.5729i	−0.336355	−	0.503391i	0.624281	−	0.781200i	$-0.285392\pi$
$727$	−9.06912	−	13.5729i	−0.336355	−	0.503391i	−0.960636	+	0.277809i	$0.910392\pi$
$728$	17.6796	−	29.9898i	0.655249	−	1.11150i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−2.21001	+	0.482935i	−0.0817961	+	0.0178742i
$731$	−23.2888	−	7.06458i	−0.861368	−	0.261293i
$732$	−5.96729	+	16.0913i	−0.220557	+	0.594751i
$733$	−2.12734	−	2.59217i	−0.0785750	−	0.0957439i	0.732239	−	0.681048i	$-0.238475\pi$
$733$	−2.12734	−	2.59217i	−0.0785750	−	0.0957439i	−0.810814	+	0.585304i	$0.800975\pi$
$734$	8.41637	+	4.29731i	0.310654	+	0.158617i
$735$	−21.1503	−	21.1503i	−0.780141	−	0.780141i
$736$	6.87126	+	35.3231i	0.253278	+	1.30203i
$737$	23.5195	−	23.5195i	0.866353	−	0.866353i
$738$	−0.863157	+	0.279651i	−0.0317733	+	0.0102941i
$739$	1.74797	−	1.43452i	0.0643001	−	0.0527697i	−0.601694	−	0.798726i	$-0.705507\pi$
$739$	1.74797	−	1.43452i	0.0643001	−	0.0527697i	0.665994	+	0.745957i	$0.268007\pi$
$740$	−2.27835	+	0.0856626i	−0.0837539	+	0.00314902i
$741$	−1.74871	+	5.76473i	−0.0642406	+	0.211773i
$742$	−45.9005	−	29.4375i	−1.68506	−	1.08069i
$743$	24.3180	−	36.3944i	0.892140	−	1.33518i	−0.0495751	−	0.998770i	$-0.515787\pi$
$743$	24.3180	−	36.3944i	0.892140	−	1.33518i	0.941715	−	0.336411i	$-0.109213\pi$
$744$	−23.7714	+	11.4556i	−0.871501	+	0.419984i
$745$	29.5187	−	19.7238i	1.08148	−	0.722624i
$746$	−21.7227	−	20.9213i	−0.795324	−	0.765983i
$747$	15.4341	−	1.52013i	0.564706	−	0.0556187i
$748$	−13.2470	−	38.4105i	−0.484357	−	1.40443i
$749$	−8.70566	−	28.6987i	−0.318098	−	1.04863i
$750$	2.39088	−	8.45010i	0.0873026	−	0.308554i
$751$	−14.5646	+	35.1620i	−0.531469	+	1.28308i	0.399081	+	0.916916i	$0.369329\pi$
$751$	−14.5646	+	35.1620i	−0.531469	+	1.28308i	−0.930550	+	0.366165i	$0.880671\pi$
$752$	−18.9035	−	16.2559i	−0.689339	−	0.592791i
$753$	−1.21464	−	2.93240i	−0.0442639	−	0.106863i
$754$	19.9316	−	2.34200i	0.725867	−	0.0852905i
$755$	−38.8354	+	72.6559i	−1.41336	+	2.64422i
$756$	7.66566	+	2.01416i	0.278797	+	0.0732544i
$757$	1.89541	−	2.30957i	0.0688900	−	0.0839426i	−0.737425	−	0.675429i	$-0.763959\pi$
$757$	1.89541	−	2.30957i	0.0688900	−	0.0839426i	0.806315	+	0.591486i	$0.201459\pi$
$758$	−5.22304	−	11.9684i	−0.189710	−	0.434712i
$759$	30.6785	+	6.10233i	1.11356	+	0.221500i
$760$	16.0979	−	9.80876i	0.583931	−	0.355801i
$761$	−4.89708	−	24.6193i	−0.177519	−	0.892449i	−0.962157	−	0.272495i	$-0.912151\pi$
$761$	−4.89708	−	24.6193i	−0.177519	−	0.892449i	0.784638	−	0.619954i	$-0.212849\pi$
$762$	9.10818	+	1.63445i	0.329955	+	0.0592100i
$763$	33.9766	−	18.1609i	1.23004	−	0.657468i
$764$	4.50329	−	28.1251i	0.162923	−	1.01753i
$765$	−1.39151	+	14.1283i	−0.0503103	+	0.510809i
$766$	0.246152	−	3.09424i	0.00889382	−	0.111799i
$767$	−21.4380			−0.774081
$768$	10.7086	−	11.8881i	0.386414	−	0.428973i
$769$	−10.4538			−0.376972			−0.188486	−	0.982076i	$-0.560358\pi$
$769$	−10.4538			−0.376972			−0.188486	+	0.982076i	$0.560358\pi$
$770$	−7.50920	+	94.3941i	−0.270613	+	3.40173i
$771$	1.66218	−	16.8764i	0.0598621	−	0.607790i
$772$	2.38264	−	14.8807i	0.0857532	−	0.535568i
$773$	26.6680	−	14.2543i	0.959180	−	0.512693i	0.0839875	−	0.996467i	$-0.473234\pi$
$773$	26.6680	−	14.2543i	0.959180	−	0.512693i	0.875193	+	0.483774i	$0.160734\pi$
$774$	−8.19940	−	1.47137i	−0.294721	−	0.0528875i
$775$	12.3896	+	62.2868i	0.445048	+	2.23741i
$776$	−4.90386	−	8.04808i	−0.176038	−	0.288909i
$777$	−1.28948	−	0.256494i	−0.0462599	−	0.00920167i
$778$	19.4430	+	44.5527i	0.697064	+	1.59729i
$779$	−0.789442	+	0.961938i	−0.0282847	+	0.0344650i
$780$	20.6437	+	5.42417i	0.739165	+	0.194217i
$781$	38.4053	−	71.8513i	1.37425	−	2.57104i
$782$	−36.9147	+	4.33753i	−1.32007	+	0.155110i
$783$	1.74849	+	4.22122i	0.0624859	+	0.150854i
$784$	−34.7209	+	2.61460i	−1.24003	+	0.0933786i
$785$	−15.5143	+	37.4548i	−0.553728	+	1.33682i
$786$	0.959047	−	3.38956i	0.0342081	−	0.120902i
$787$	−5.22975	−	17.2402i	−0.186421	−	0.614546i	−0.999476	−	0.0323604i	$-0.989698\pi$
$787$	−5.22975	−	17.2402i	−0.186421	−	0.614546i	0.813056	−	0.582186i	$-0.197802\pi$
$788$	−4.98876	−	14.4653i	−0.177717	−	0.515303i
$789$	17.1176	−	1.68593i	0.609402	−	0.0600208i
$790$	−31.7921	−	30.6192i	−1.13111	−	1.08938i
$791$	7.24299	−	4.83961i	0.257531	−	0.172077i
$792$	−6.03773	−	12.5288i	−0.214541	−	0.445191i
$793$	−14.8068	+	22.1600i	−0.525806	+	0.786924i
$794$	−18.1210	−	11.6216i	−0.643089	−	0.412434i
$795$	9.70497	−	31.9930i	0.344200	−	1.13467i
$796$	−12.0266	+	0.452183i	−0.426273	+	0.0160272i
$797$	−36.4993	+	29.9542i	−1.29287	+	1.06103i	−0.298573	+	0.954387i	$0.596511\pi$
$797$	−36.4993	+	29.9542i	−1.29287	+	1.06103i	−0.994297	+	0.106644i	$0.965989\pi$
$798$	10.3411	−	3.35039i	0.366073	−	0.118602i
$799$	18.2092	−	18.2092i	0.644197	−	0.644197i
$800$	−21.2580	−	32.1076i	−0.751584	−	1.13517i
$801$	−4.05069	−	4.05069i	−0.143124	−	0.143124i
$802$	6.38786	+	3.26158i	0.225563	+	0.115170i
$803$	1.45213	+	1.76942i	0.0512445	+	0.0624416i
$804$	−4.70402	+	12.6848i	−0.165898	+	0.447358i
$805$	82.8940	+	25.1456i	2.92163	+	0.886266i
$806$	−40.0336	+	8.74821i	−1.41012	+	0.308143i
$807$	1.93769	+	1.29472i	0.0682099	+	0.0455764i
$808$	27.2969	+	16.0921i	0.960302	+	0.566116i
$809$	−9.98348	−	14.9413i	−0.351001	−	0.525309i	0.613394	−	0.789777i	$-0.289804\pi$
$809$	−9.98348	−	14.9413i	−0.351001	−	0.525309i	−0.964395	+	0.264468i	$0.914804\pi$
$810$	0.0913056	+	4.85860i	0.00320815	+	0.170714i
$811$	1.57845	+	16.0263i	0.0554270	+	0.562760i	0.982291	+	0.187362i	$0.0599939\pi$
$811$	1.57845	+	16.0263i	0.0554270	+	0.562760i	−0.926864	+	0.375398i	$0.877506\pi$
$812$	−24.0091	−	27.1104i	−0.842554	−	0.951389i
$813$	22.3569	−	6.78190i	0.784092	−	0.237852i
$814$	1.12556	+	2.01381i	0.0394508	+	0.0705842i
$815$	−12.5516	−	5.19906i	−0.439665	−	0.182115i
$816$	11.4138	+	11.9516i	0.399562	+	0.418389i
$817$	−10.5555	+	4.37221i	−0.369289	+	0.152964i
$818$	−33.2545	−	26.2613i	−1.16272	−	0.918206i
$819$	10.8550	+	5.80210i	0.379303	+	0.202742i
$820$	3.51099	+	2.66709i	0.122609	+	0.0931387i
$821$	−24.2234	−	19.8797i	−0.845403	−	0.693805i	0.108442	−	0.994103i	$-0.465414\pi$
$821$	−24.2234	−	19.8797i	−0.845403	−	0.693805i	−0.953845	+	0.300298i	$0.902914\pi$
$822$	−26.8766	−	10.5455i	−0.937429	−	0.367816i
$823$	4.64390	−	23.3464i	0.161876	−	0.813806i	−0.811457	−	0.584412i	$-0.801325\pi$
$823$	4.64390	−	23.3464i	0.161876	−	0.813806i	0.973334	−	0.229395i	$-0.0736746\pi$
$824$	13.3018	+	14.4631i	0.463389	+	0.503847i
$825$	−32.8285	+	6.52999i	−1.14294	+	0.227345i
$826$	22.0923	+	31.7552i	0.768690	+	1.10490i
$827$	10.1389	+	18.9685i	0.352564	+	0.659600i	0.994216	−	0.107395i	$-0.0342510\pi$
$827$	10.1389	+	18.9685i	0.352564	+	0.659600i	−0.641653	+	0.766995i	$0.721751\pi$
$828$	−12.3762	+	2.94915i	−0.430101	+	0.102490i
$829$	−19.6712	−	1.93744i	−0.683207	−	0.0672900i	−0.249542	−	0.968364i	$-0.580280\pi$
$829$	−19.6712	−	1.93744i	−0.683207	−	0.0672900i	−0.433665	+	0.901074i	$0.642780\pi$
$830$	−48.8969	−	57.3489i	−1.69724	−	1.99061i
$831$		−	28.1768i		−	0.977443i
$832$	20.4562	−	14.1037i	0.709190	−	0.488957i
$833$		−	35.9643i		−	1.24609i
$834$	−2.34374	+	1.99833i	−0.0811572	+	0.0691964i
$835$	−30.6225	−	3.01605i	−1.05973	−	0.104375i
$836$	−16.2468	−	9.99385i	−0.561908	−	0.345644i
$837$	−4.39788	−	8.22785i	−0.152013	−	0.284396i
$838$	24.5922	−	17.1090i	0.849524	−	0.591020i
$839$	20.7114	−	4.11975i	0.715036	−	0.142229i	0.175851	−	0.984417i	$-0.443732\pi$
$839$	20.7114	−	4.11975i	0.715036	−	0.142229i	0.539185	+	0.842187i	$0.318732\pi$
$840$	−13.2392	−	36.1684i	−0.456797	−	1.24793i
$841$	−1.58492	+	7.96796i	−0.0546526	+	0.274757i
$842$	−18.0767	+	46.0710i	−0.622965	+	1.58771i
$843$	16.9044	+	13.8731i	0.582220	+	0.477815i
$844$	−9.42488	+	1.28740i	−0.324418	+	0.0443141i
$845$	−10.1629	−	5.43216i	−0.349613	−	0.186872i
$846$	5.46299	−	6.91774i	0.187821	−	0.237837i
$847$	48.2484	−	19.9851i	1.65783	−	0.686697i
$848$	−20.8717	−	32.8486i	−0.716736	−	1.12803i
$849$	17.3158	+	7.17246i	0.594278	+	0.246158i
$850$	34.7186	−	19.4049i	1.19084	−	0.665581i
$851$	2.01957	−	0.612630i	0.0692300	−	0.0210007i
$852$	−2.00673	+	33.0770i	−0.0687493	+	1.13320i
$853$	−1.88024	−	19.0904i	−0.0643782	−	0.653642i	−0.972179	−	0.234240i	$-0.924740\pi$
$853$	−1.88024	−	19.0904i	−0.0643782	−	0.653642i	0.907801	−	0.419402i	$-0.137760\pi$
$854$	48.0834	−	0.903612i	1.64538	−	0.0309210i
$855$	3.70274	+	5.54155i	0.126631	+	0.189517i
$856$	2.98640	−	21.1952i	0.102073	−	0.724438i
$857$	−8.78248	−	5.86827i	−0.300004	−	0.200456i	0.396453	−	0.918055i	$-0.370241\pi$
$857$	−8.78248	−	5.86827i	−0.300004	−	0.200456i	−0.696457	+	0.717599i	$0.745241\pi$
$858$	−4.61077	−	21.0998i	−0.157409	−	0.720336i
$859$	6.95408	+	2.10950i	0.237270	+	0.0719751i	0.406680	−	0.913570i	$-0.366686\pi$
$859$	6.95408	+	2.10950i	0.237270	+	0.0719751i	−0.169410	+	0.985546i	$0.554186\pi$
$860$	16.8857	+	36.7912i	0.575797	+	1.25457i
$861$	1.61296	+	1.96540i	0.0549696	+	0.0669807i
$862$	7.53082	−	14.7493i	0.256501	−	0.502362i
$863$	−6.69088	−	6.69088i	−0.227760	−	0.227760i	0.583996	−	0.811756i	$-0.301488\pi$
$863$	−6.69088	−	6.69088i	−0.227760	−	0.227760i	−0.811756	+	0.583996i	$0.801488\pi$
$864$	4.35761	+	3.60710i	0.148249	+	0.122716i
$865$	31.6767	−	31.6767i	1.07704	−	1.07704i
$866$	−9.26678	−	28.6024i	−0.314898	−	0.971949i
$867$	−0.0538744	+	0.0442136i	−0.00182967	+	0.00150157i
$868$	54.2138	+	50.2848i	1.84014	+	1.70678i
$869$	−12.9650	+	42.7398i	−0.439807	+	1.44985i
$870$	11.9863	−	18.6896i	0.406372	−	0.633637i
$871$	−11.6722	+	17.4687i	−0.395499	+	0.591906i
$872$	27.4529	−	1.54919i	0.929674	−	0.0524624i
$873$	2.77048	−	1.85118i	0.0937666	−	0.0626528i
$874$	−12.1045	+	12.5681i	−0.409439	+	0.425123i
$875$	−24.4901	+	2.41206i	−0.827915	+	0.0815425i
$876$	−0.837009	−	0.407726i	−0.0282799	−	0.0137758i
$877$	7.63406	+	25.1661i	0.257784	+	0.849799i	0.986327	+	0.164799i	$0.0526977\pi$
$877$	7.63406	+	25.1661i	0.257784	+	0.849799i	−0.728543	+	0.685000i	$0.759802\pi$
$878$	30.1357	+	8.52662i	1.01703	+	0.287759i
$879$	−6.33464	+	15.2932i	−0.213662	+	0.515826i
$880$	−33.2220	+	58.8548i	−1.11991	+	1.98400i
$881$	−17.7308	−	42.8060i	−0.597367	−	1.44217i	−0.876255	−	0.481847i	$-0.839966\pi$
$881$	−17.7308	−	42.8060i	−0.597367	−	1.44217i	0.278889	−	0.960323i	$-0.410034\pi$
$882$	−1.43661	−	12.2263i	−0.0483733	−	0.411682i
$883$	11.9146	−	22.2907i	0.400959	−	0.750142i	−0.597710	−	0.801712i	$-0.703923\pi$
$883$	11.9146	−	22.2907i	0.400959	−	0.750142i	0.998669	+	0.0515702i	$0.0164226\pi$
$884$	12.9398	+	22.1631i	0.435212	+	0.745427i
$885$	−15.0464	+	18.3341i	−0.505780	+	0.616295i
$886$	17.7965	−	7.76645i	0.597885	−	0.260919i
$887$	−47.0054	−	9.34995i	−1.57829	−	0.313941i	−0.673296	−	0.739373i	$-0.735122\pi$
$887$	−47.0054	−	9.34995i	−1.57829	−	0.313941i	−0.904990	+	0.425432i	$0.860122\pi$
$888$	−0.757750	−	0.553477i	−0.0254284	−	0.0185735i
$889$	−5.05884	−	25.4325i	−0.169668	−	0.852979i
$890$	−4.91688	+	27.3999i	−0.164814	+	0.918447i
$891$	4.33651	−	2.31791i	0.145279	−	0.0776530i
$892$	−8.54620	−	11.8047i	−0.286148	−	0.395251i
$893$	1.18497	−	12.0312i	0.0396536	−	0.402609i
$894$	14.5654	+	1.15870i	0.487141	+	0.0387529i
$895$	4.68156			0.156487
$896$	−41.9717	−	15.7667i	−1.40218	−	0.526729i
$897$	−19.7575			−0.659683
$898$	−37.1028	−	2.95159i	−1.23814	−	0.0984957i
$899$	−4.17812	+	42.4212i	−0.139348	+	1.41483i
$900$	11.0277	−	7.98368i	0.367591	−	0.266123i
$901$	35.4519	−	18.9495i	1.18108	−	0.631298i
$902$	0.788014	−	4.39130i	0.0262380	−	0.146214i
$903$	4.55409	+	22.8949i	0.151551	+	0.761896i
$904$	6.14317	−	0.957034i	0.204319	−	0.0318305i
$905$	−47.4738	−	9.44312i	−1.57808	−	0.313900i
$906$	−31.0762	+	13.5618i	−1.03244	+	0.450559i
$907$	−2.43981	+	2.97291i	−0.0810124	+	0.0987139i	−0.811939	−	0.583742i	$-0.801588\pi$
$907$	−2.43981	+	2.97291i	−0.0810124	+	0.0987139i	0.730927	+	0.682456i	$0.239088\pi$
$908$	−18.8675	+	11.0157i	−0.626141	+	0.365568i
$909$	−5.28110	+	9.88025i	−0.175163	+	0.327707i
$910$	−6.97995	−	59.4031i	−0.231383	−	1.96919i
$911$	9.54304	+	23.0389i	0.316175	+	0.763314i	0.999450	+	0.0331533i	$0.0105550\pi$
$911$	9.54304	+	23.0389i	0.316175	+	0.763314i	−0.683275	+	0.730161i	$0.739445\pi$
$912$	7.70150	+	0.937925i	0.255022	+	0.0310578i
$913$	−29.1829	+	70.4539i	−0.965815	+	2.33168i
$914$	−6.18382	−	1.74966i	−0.204543	−	0.0578735i
$915$	8.55929	+	28.2162i	0.282961	+	0.932798i
$916$	−19.7932	+	40.6328i	−0.653985	+	1.34255i
$917$	−9.82362	+	0.967542i	−0.324405	+	0.0319511i
$918$	−4.05319	+	4.20845i	−0.133775	+	0.138899i
$919$	−38.4431	+	25.6868i	−1.26812	+	0.847330i	−0.993457	−	0.114210i	$-0.963566\pi$
$919$	−38.4431	+	25.6868i	−1.26812	+	0.847330i	−0.274663	+	0.961541i	$0.588566\pi$
$920$	46.1108	+	41.1846i	1.52023	+	1.35782i
$921$	−12.5549	+	18.7897i	−0.413698	+	0.619143i
$922$	−19.6093	+	30.5759i	−0.645798	+	1.00696i
$923$	−14.9383	+	49.2449i	−0.491699	+	1.62091i
$924$	−26.5028	+	28.5736i	−0.871877	+	0.940001i
$925$	−1.74573	+	1.43268i	−0.0573992	+	0.0471063i
$926$	−2.69606	−	8.32153i	−0.0885981	−	0.273463i
$927$	−4.91248	+	4.91248i	−0.161347	+	0.161347i
$928$	−7.39827	−	24.7648i	−0.242860	−	0.812945i
$929$	21.6707	+	21.6707i	0.710993	+	0.710993i	0.966743	−	0.255750i	$-0.0823224\pi$
$929$	21.6707	+	21.6707i	0.710993	+	0.710993i	−0.255750	+	0.966743i	$0.582322\pi$
$930$	−20.6163	+	40.3774i	−0.676034	+	1.32403i
$931$	−10.7110	−	13.0514i	−0.351039	−	0.427742i
$932$	34.3432	−	15.7621i	1.12495	−	0.516306i
$933$	17.1182	+	5.19275i	0.560425	+	0.170003i
$934$	4.27154	+	19.5474i	0.139769	+	0.639612i
$935$	−58.0420	−	38.7824i	−1.89818	−	1.26832i
$936$	5.28430	+	7.01764i	0.172723	+	0.229379i
$937$	27.0512	+	40.4850i	0.883724	+	1.32259i	0.945879	+	0.324519i	$0.105203\pi$
$937$	27.0512	+	40.4850i	0.883724	+	1.32259i	−0.0621554	+	0.998066i	$0.519797\pi$
$938$	37.9042	−	0.712318i	1.23762	−	0.0232580i
$939$	1.65249	+	16.7780i	0.0539270	+	0.547530i
$940$	−42.7562	−	2.59394i	−1.39455	−	0.0846051i
$941$	−11.9893	+	3.63693i	−0.390841	+	0.118560i	−0.479588	−	0.877494i	$-0.659214\pi$
$941$	−11.9893	+	3.63693i	−0.390841	+	0.118560i	0.0887466	+	0.996054i	$0.471714\pi$
$942$	−14.5647	+	8.14050i	−0.474545	+	0.265232i
$943$	−3.77063	−	1.56185i	−0.122789	−	0.0508607i
$944$	4.76183	+	27.1960i	0.154985	+	0.885154i
$945$	12.5807	−	5.21109i	0.409250	−	0.169517i
$946$	25.3861	−	32.1463i	0.825374	−	1.04517i
$947$	47.3358	+	25.3015i	1.53821	+	0.822189i	0.999790	−	0.0204893i	$-0.00652241\pi$
$947$	47.3358	+	25.3015i	1.53821	+	0.822189i	0.538417	+	0.842678i	$0.319022\pi$
$948$	−2.45861	−	17.9992i	−0.0798520	−	0.584587i
$949$	−1.11764	−	0.917227i	−0.0362803	−	0.0297744i
$950$	6.82011	−	17.3820i	0.221274	−	0.563946i
$951$	4.64429	−	23.3484i	0.150601	−	0.757124i
$952$	19.4946	−	42.0068i	0.631824	−	1.36145i
$953$	−27.8657	+	5.54283i	−0.902657	+	0.179550i	−0.624536	−	0.780996i	$-0.714712\pi$
$953$	−27.8657	+	5.54283i	−0.902657	+	0.179550i	−0.278122	+	0.960546i	$0.589712\pi$
$954$	11.2952	−	7.85815i	0.365696	−	0.254417i
$955$	−23.0686	−	43.1582i	−0.746481	−	1.39657i
$956$	9.98943	−	16.2396i	0.323081	−	0.525227i
$957$	−22.3582	−	2.20209i	−0.722739	−	0.0711836i
$958$	−27.8649	+	23.7582i	−0.900273	+	0.767592i
$959$			80.9039i			2.61252i
$960$	2.29562	−	27.3932i	0.0740910	−	0.884112i
$961$		−	56.0387i		−	1.80770i
$962$	−0.945447	−	1.10887i	−0.0304824	−	0.0357514i
$963$	7.53122	+	0.741760i	0.242690	+	0.0239029i
$964$	7.04042	+	29.5452i	0.226757	+	0.951587i
$965$	−12.2053	−	22.8346i	−0.392903	−	0.735071i
$966$	20.3605	+	29.2659i	0.655089	+	0.941616i
$967$	41.5375	−	8.26232i	1.33576	−	0.265698i	0.525010	−	0.851096i	$-0.324062\pi$
$967$	41.5375	−	8.26232i	1.33576	−	0.265698i	0.810746	+	0.585398i	$0.199062\pi$
$968$	37.2406	+	1.55770i	1.19696	+	0.0500664i
$969$	−1.56337	+	7.85957i	−0.0502226	+	0.252486i
$970$	−15.0731	−	5.91419i	−0.483968	−	0.189893i
$971$	−16.5360	−	13.5708i	−0.530666	−	0.435507i	0.330518	−	0.943800i	$-0.392777\pi$
$971$	−16.5360	−	13.5708i	−0.530666	−	0.435507i	−0.861184	+	0.508293i	$0.830277\pi$
$972$	−1.20980	+	1.59260i	−0.0388045	+	0.0510827i
$973$	7.61172	+	4.06855i	0.244021	+	0.130432i
$974$	−29.6059	−	23.3800i	−0.948634	−	0.749143i
$975$	19.5328	−	8.09074i	0.625549	−	0.259111i
$976$	31.4008	+	13.8616i	1.00511	+	0.443698i
$977$	−52.1123	−	21.5856i	−1.66722	−	0.690586i	−0.668627	−	0.743598i	$-0.733118\pi$
$977$	−52.1123	−	21.5856i	−1.66722	−	0.690586i	−0.998594	+	0.0530121i	$0.983118\pi$
$978$	−2.72800	−	4.88085i	−0.0872317	−	0.156073i
$979$	26.9550	−	8.17671i	0.861485	−	0.261329i
$980$	−44.7846	+	39.6614i	−1.43059	+	1.26694i
$981$	0.952876	+	9.67471i	0.0304230	+	0.308890i
$982$	1.11255	+	59.2017i	0.0355030	+	1.88920i
$983$	28.3864	+	42.4832i	0.905384	+	1.35500i	0.934702	+	0.355433i	$0.115667\pi$
$983$	28.3864	+	42.4832i	0.905384	+	1.35500i	−0.0293174	+	0.999570i	$0.509333\pi$
$984$	0.453735	+	1.75702i	0.0144646	+	0.0560116i
$985$	−21.8584	−	14.6053i	−0.696467	−	0.465365i
$986$	26.0808	−	5.69923i	0.830583	−	0.181501i
$987$	−23.6371	−	7.17025i	−0.752379	−	0.228232i
$988$	11.2965	+	4.18920i	0.359390	+	0.133276i
$989$	−23.7715	−	28.9657i	−0.755891	−	0.921056i
$990$	−21.2810	−	10.8659i	−0.676355	−	0.345340i
$991$	−39.5360	−	39.5360i	−1.25590	−	1.25590i	−0.953032	−	0.302871i	$-0.902055\pi$
$991$	−39.5360	−	39.5360i	−1.25590	−	1.25590i	−0.302871	−	0.953032i	$-0.597945\pi$
$992$	19.9902	+	48.8429i	0.634689	+	1.55076i
$993$	6.62799	−	6.62799i	0.210333	−	0.210333i
$994$	88.3386	−	28.6205i	2.80193	−	0.907787i
$995$	−15.9838	+	13.1175i	−0.506720	+	0.415854i
$996$	−1.16539	−	30.9957i	−0.0369269	−	0.982138i
$997$	−8.15483	+	26.8829i	−0.258266	+	0.851389i	0.727908	+	0.685675i	$0.240493\pi$
$997$	−8.15483	+	26.8829i	−0.258266	+	0.851389i	−0.986174	+	0.165714i	$0.947007\pi$
$998$	34.1056	+	21.8731i	1.07959	+	0.692379i
$999$	0.184316	−	0.275849i	0.00583151	−	0.00872748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.17	✓	512
128.53	even	32	inner	384.2.v.a.181.17	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.17	✓	512	1.1	even	1	trivial
384.2.v.a.181.17	yes	512	128.53	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.112149 - 1.40976i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.97485 - 0.316205i) q^{4} +(-3.03042 + 1.61979i) q^{5} +(-1.39198 - 0.249789i) q^{6} +(0.773129 + 3.88678i) q^{7} +(-0.667250 + 2.74860i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(0.112149 - 1.40976i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.97485 - 0.316205i) q^{4} +(-3.03042 + 1.61979i) q^{5} +(-1.39198 - 0.249789i) q^{6} +(0.773129 + 3.88678i) q^{7} +(-0.667250 + 2.74860i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.94366 + 4.45382i) q^{10} +(3.11939 - 3.80098i) q^{11} +(-0.508251 + 1.93434i) q^{12} +(-1.46409 + 2.73913i) q^{13} +(5.56613 - 0.654029i) q^{14} +(1.31496 + 3.17459i) q^{15} +(3.80003 + 1.24891i) q^{16} +(-1.58108 + 3.81705i) q^{17} +(-0.385024 + 1.36079i) q^{18} +(0.563036 + 1.85608i) q^{19} +(6.49679 - 2.24061i) q^{20} +(3.94385 - 0.388435i) q^{21} +(-5.00864 - 4.82386i) q^{22} +(-5.28927 + 3.53418i) q^{23} +(2.66996 + 0.933446i) q^{24} +(3.78186 - 5.65995i) q^{25} +(3.69731 + 2.37121i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-0.297790 - 7.92026i) q^{28} +(3.53190 - 2.89856i) q^{29} +(4.62288 - 1.49775i) q^{30} +(-6.59692 + 6.59692i) q^{31} +(2.18683 - 5.21706i) q^{32} +(-3.47693 - 3.47693i) q^{33} +(5.20381 + 2.65701i) q^{34} +(-8.63868 - 10.5263i) q^{35} +(1.87521 + 0.695403i) q^{36} +(-0.317475 - 0.0963051i) q^{37} +(2.67977 - 0.585589i) q^{38} +(2.58243 + 1.72553i) q^{39} +(-2.43011 - 9.41020i) q^{40} +(0.356442 + 0.533453i) q^{41} +(-0.105303 - 5.60344i) q^{42} +(0.577366 + 5.86210i) q^{43} +(-7.36220 + 6.51999i) q^{44} +(3.28820 - 0.997463i) q^{45} +(4.38915 + 7.85295i) q^{46} +(-5.75850 - 2.38525i) q^{47} +(1.61537 - 3.65932i) q^{48} +(-8.04219 + 3.33118i) q^{49} +(-7.55504 - 5.96626i) q^{50} +(3.64370 + 1.94760i) q^{51} +(3.75748 - 4.94640i) q^{52} +(-7.52112 - 6.17242i) q^{53} +(1.31650 + 0.516551i) q^{54} +(-3.29624 + 16.5713i) q^{55} +(-11.1991 - 0.468435i) q^{56} +(1.90233 - 0.378397i) q^{57} +(-3.69017 - 5.30420i) q^{58} +(3.25378 + 6.08740i) q^{59} +(-1.59302 - 6.68513i) q^{60} +(8.53974 + 0.841091i) q^{61} +(8.56024 + 10.0399i) q^{62} -3.96293i q^{63} +(-7.10956 - 3.66800i) q^{64} -10.6722i q^{65} +(-5.29157 + 4.51170i) q^{66} +(6.73188 + 0.663033i) q^{67} +(4.32935 - 7.03815i) q^{68} +(2.99872 + 5.61021i) q^{69} +(-15.8083 + 10.9980i) q^{70} +(16.2505 - 3.23243i) q^{71} +(1.19065 - 2.56561i) q^{72} +(-0.0908179 + 0.456572i) q^{73} +(-0.171371 + 0.436763i) q^{74} +(-5.26201 - 4.31842i) q^{75} +(-0.525007 - 3.84351i) q^{76} +(17.1853 + 9.18573i) q^{77} +(2.72219 - 3.44709i) q^{78} +(-8.39175 + 3.47598i) q^{79} +(-13.5387 + 2.37053i) q^{80} +(0.923880 + 0.382683i) q^{81} +(0.792015 - 0.442671i) q^{82} +(-14.8410 + 4.50197i) q^{83} +(-7.91131 - 0.479966i) q^{84} +(-1.39151 - 14.1283i) q^{85} +(8.32890 - 0.156522i) q^{86} +(-2.53841 - 3.79900i) q^{87} +(8.36596 + 11.1101i) q^{88} +(4.76310 + 3.18260i) q^{89} +(-1.03742 - 4.74743i) q^{90} +(-11.7783 - 3.57291i) q^{91} +(11.5630 - 5.30696i) q^{92} +(5.91854 + 7.21177i) q^{93} +(-4.00843 + 7.85060i) q^{94} +(-4.71270 - 4.71270i) q^{95} +(-4.97759 - 2.68767i) q^{96} +(-2.35610 + 2.35610i) q^{97} +(3.79425 + 11.7111i) q^{98} +(-3.80098 + 3.11939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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