LMFDB - Embedded newform 231.2.w.a.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.2
Character	$\chi$	$=$	231.118
Dual form			231.2.w.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44554 - 1.98962i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(-1.57908 + 2.17341i) q^{5} +(-1.98962 - 1.44554i) q^{6} +(1.60046 + 2.10678i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.44554 - 1.98962i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(-1.57908 + 2.17341i) q^{5} +(-1.98962 - 1.44554i) q^{6} +(1.60046 + 2.10678i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +6.60689 q^{10} +(2.35064 - 2.33976i) q^{11} +4.04819i q^{12} +(2.47315 - 1.79685i) q^{13} +(1.87815 - 6.22976i) q^{14} +(-0.830170 + 2.55500i) q^{15} +(-3.47187 - 2.52246i) q^{16} +(2.13396 + 1.55041i) q^{17} +(-2.33894 - 0.759968i) q^{18} +(2.14340 + 6.59671i) q^{19} +(-6.39240 - 8.79839i) q^{20} +(2.17316 + 1.50909i) q^{21} +(-8.05320 - 1.29465i) q^{22} -4.26616 q^{23} +(4.07512 - 2.96075i) q^{24} +(-0.685154 - 2.10869i) q^{25} +(-7.15011 - 2.32321i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-10.1133 + 3.52639i) q^{28} +(4.90988 + 1.59532i) q^{29} +(6.28353 - 2.04164i) q^{30} +(-2.32671 - 3.20245i) q^{31} +0.479776i q^{32} +(1.51256 - 2.95164i) q^{33} -6.48696i q^{34} +(-7.10615 + 0.151705i) q^{35} +(1.25096 + 3.85006i) q^{36} +(-0.718304 + 2.21071i) q^{37} +(10.0266 - 13.8004i) q^{38} +(1.79685 - 2.47315i) q^{39} +(-4.18167 + 12.8699i) q^{40} +(2.49284 + 7.67219i) q^{41} +(-0.138876 - 6.50523i) q^{42} -10.5088i q^{43} +(6.06767 + 11.9770i) q^{44} +2.68649i q^{45} +(6.16692 + 8.48804i) q^{46} +(-0.948256 + 0.308107i) q^{47} +(-4.08143 - 1.32614i) q^{48} +(-1.87703 + 6.74365i) q^{49} +(-3.20507 + 4.41139i) q^{50} +(2.50862 + 0.815099i) q^{51} +(3.82417 + 11.7696i) q^{52} +(-5.37779 + 3.90719i) q^{53} -2.45931 q^{54} +(1.37343 + 8.80357i) q^{55} +(10.9465 + 7.60151i) q^{56} +(4.07699 + 5.61150i) q^{57} +(-3.92337 - 12.0749i) q^{58} +(-0.194194 - 0.0630976i) q^{59} +(-8.79839 - 6.39240i) q^{60} +(-12.1551 - 8.83121i) q^{61} +(-3.00829 + 9.25856i) q^{62} +(2.53314 + 0.763690i) q^{63} +(-5.98917 + 4.35138i) q^{64} +8.21255i q^{65} +(-8.05911 + 1.25729i) q^{66} +9.76985 q^{67} +(-8.63867 + 6.27636i) q^{68} +(-4.05736 + 1.31832i) q^{69} +(10.5741 + 13.9193i) q^{70} +(-0.0566342 - 0.0411472i) q^{71} +(2.96075 - 4.07512i) q^{72} +(4.49716 - 13.8408i) q^{73} +(5.43682 - 1.76653i) q^{74} +(-1.30324 - 1.79376i) q^{75} -28.0790 q^{76} +(8.69148 + 1.20757i) q^{77} -7.51807 q^{78} +(0.626363 + 0.862114i) q^{79} +(10.9647 - 3.56265i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6612 - 16.0503i) q^{82} +(3.69908 + 2.68754i) q^{83} +(-8.52864 + 6.47898i) q^{84} +(-6.73937 + 2.18975i) q^{85} +(-20.9086 + 15.1910i) q^{86} +5.16255 q^{87} +(7.61898 - 14.8678i) q^{88} -17.6770i q^{89} +(5.34509 - 3.88343i) q^{90} +(7.74376 + 2.33459i) q^{91} +(5.33679 - 16.4250i) q^{92} +(-3.20245 - 2.32671i) q^{93} +(1.98376 + 1.44129i) q^{94} +(-17.7220 - 5.75822i) q^{95} +(0.148259 + 0.456295i) q^{96} +(-4.13113 - 5.68602i) q^{97} +(16.1306 - 6.01366i) q^{98} +(0.526429 - 3.27458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.44554	−	1.98962i	−1.02215	−	1.40687i	−0.910682	−	0.413107i	$-0.864444\pi$
$2$	−1.44554	−	1.98962i	−1.02215	−	1.40687i	−0.111472	−	0.993768i	$-0.535556\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−1.25096	+	3.85006i	−0.625480	+	1.92503i
$5$	−1.57908	+	2.17341i	−0.706184	+	0.971980i	0.293686	+	0.955902i	$0.405118\pi$
$5$	−1.57908	+	2.17341i	−0.706184	+	0.971980i	−0.999871	+	0.0160777i	$0.994882\pi$
$6$	−1.98962	−	1.44554i	−0.812259	−	0.590141i
$7$	1.60046	+	2.10678i	0.604919	+	0.796287i
$7$	1.60046	+	2.10678i	0.604919	+	0.796287i
$8$	4.79060	−	1.55656i	1.69373	−	0.550327i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	6.60689			2.08928
$11$	2.35064	−	2.33976i	0.708744	−	0.705465i
$11$	2.35064	−	2.33976i	0.708744	−	0.705465i
$12$			4.04819i			1.16861i
$13$	2.47315	−	1.79685i	0.685930	−	0.498357i	−0.189390	−	0.981902i	$-0.560651\pi$
$13$	2.47315	−	1.79685i	0.685930	−	0.498357i	0.875320	+	0.483545i	$0.160651\pi$
$14$	1.87815	−	6.22976i	0.501956	−	1.66497i
$15$	−0.830170	+	2.55500i	−0.214349	+	0.659698i
$16$	−3.47187	−	2.52246i	−0.867968	−	0.630615i
$17$	2.13396	+	1.55041i	0.517561	+	0.376030i	0.815684	−	0.578497i	$-0.196361\pi$
$17$	2.13396	+	1.55041i	0.517561	+	0.376030i	−0.298123	+	0.954527i	$0.596361\pi$
$18$	−2.33894	−	0.759968i	−0.551293	−	0.179126i
$19$	2.14340	+	6.59671i	0.491730	+	1.51339i	0.821991	+	0.569500i	$0.192863\pi$
$19$	2.14340	+	6.59671i	0.491730	+	1.51339i	−0.330261	+	0.943890i	$0.607137\pi$
$20$	−6.39240	−	8.79839i	−1.42938	−	1.96738i
$21$	2.17316	+	1.50909i	0.474223	+	0.329311i
$22$	−8.05320	−	1.29465i	−1.71695	−	0.276020i
$23$	−4.26616			−0.889556			−0.444778	−	0.895641i	$-0.646717\pi$
$23$	−4.26616			−0.889556			−0.444778	+	0.895641i	$0.646717\pi$
$24$	4.07512	−	2.96075i	0.831831	−	0.604361i
$25$	−0.685154	−	2.10869i	−0.137031	−	0.421737i
$26$	−7.15011	−	2.32321i	−1.40225	−	0.455619i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−10.1133	+	3.52639i	−1.91124	+	0.666424i
$29$	4.90988	+	1.59532i	0.911741	+	0.296243i	0.727075	−	0.686559i	$-0.240879\pi$
$29$	4.90988	+	1.59532i	0.911741	+	0.296243i	0.184667	+	0.982801i	$0.440879\pi$
$30$	6.28353	−	2.04164i	1.14721	−	0.372751i
$31$	−2.32671	−	3.20245i	−0.417890	−	0.575176i	0.547230	−	0.836982i	$-0.315682\pi$
$31$	−2.32671	−	3.20245i	−0.417890	−	0.575176i	−0.965121	+	0.261805i	$0.915682\pi$
$32$			0.479776i			0.0848133i
$33$	1.51256	−	2.95164i	0.263304	−	0.513814i
$34$		−	6.48696i		−	1.11250i
$35$	−7.10615	+	0.151705i	−1.20116	+	0.0256428i
$36$	1.25096	+	3.85006i	0.208493	+	0.641676i
$37$	−0.718304	+	2.21071i	−0.118089	+	0.363439i	−0.992579	−	0.121604i	$-0.961196\pi$
$37$	−0.718304	+	2.21071i	−0.118089	+	0.363439i	0.874490	+	0.485043i	$0.161196\pi$
$38$	10.0266	−	13.8004i	1.62653	−	2.23872i
$39$	1.79685	−	2.47315i	0.287727	−	0.396022i
$40$	−4.18167	+	12.8699i	−0.661180	+	2.03490i
$41$	2.49284	+	7.67219i	0.389317	+	1.19819i	0.933300	+	0.359098i	$0.116916\pi$
$41$	2.49284	+	7.67219i	0.389317	+	1.19819i	−0.543983	+	0.839096i	$0.683084\pi$
$42$	−0.138876	−	6.50523i	−0.0214290	−	1.00378i
$43$		−	10.5088i		−	1.60258i	−0.598277	−	0.801290i	$-0.704148\pi$
$43$		−	10.5088i		−	1.60258i	0.598277	−	0.801290i	$-0.295852\pi$
$44$	6.06767	+	11.9770i	0.914736	+	1.80561i
$45$			2.68649i			0.400478i
$46$	6.16692	+	8.48804i	0.909263	+	1.25149i
$47$	−0.948256	+	0.308107i	−0.138317	+	0.0449420i	−0.377358	−	0.926068i	$-0.623167\pi$
$47$	−0.948256	+	0.308107i	−0.138317	+	0.0449420i	0.239040	+	0.971010i	$0.423167\pi$
$48$	−4.08143	−	1.32614i	−0.589103	−	0.191411i
$49$	−1.87703	+	6.74365i	−0.268147	+	0.963378i
$50$	−3.20507	+	4.41139i	−0.453265	+	0.623865i
$51$	2.50862	+	0.815099i	0.351277	+	0.114137i
$52$	3.82417	+	11.7696i	0.530317	+	1.63215i
$53$	−5.37779	+	3.90719i	−0.738696	+	0.536694i	−0.892302	−	0.451438i	$-0.850911\pi$
$53$	−5.37779	+	3.90719i	−0.738696	+	0.536694i	0.153607	+	0.988132i	$0.450911\pi$
$54$	−2.45931			−0.334669
$55$	1.37343	+	8.80357i	0.185193	+	1.18707i
$56$	10.9465	+	7.60151i	1.46279	+	1.01579i
$57$	4.07699	+	5.61150i	0.540011	+	0.743261i
$58$	−3.92337	−	12.0749i	−0.515164	−	1.58551i
$59$	−0.194194	−	0.0630976i	−0.0252820	−	0.00821460i	0.296349	−	0.955080i	$-0.404231\pi$
$59$	−0.194194	−	0.0630976i	−0.0252820	−	0.00821460i	−0.321631	+	0.946865i	$0.604231\pi$
$60$	−8.79839	−	6.39240i	−1.13587	−	0.825256i
$61$	−12.1551	−	8.83121i	−1.55630	−	1.13072i	−0.938960	−	0.344027i	$-0.888209\pi$
$61$	−12.1551	−	8.83121i	−1.55630	−	1.13072i	−0.617344	−	0.786694i	$-0.711791\pi$
$62$	−3.00829	+	9.25856i	−0.382053	+	1.17584i
$63$	2.53314	+	0.763690i	0.319145	+	0.0962159i
$64$	−5.98917	+	4.35138i	−0.748646	+	0.543923i
$65$			8.21255i			1.01864i
$66$	−8.05911	+	1.25729i	−0.992008	+	0.154762i
$67$	9.76985			1.19358			0.596788	−	0.802399i	$-0.296443\pi$
$67$	9.76985			1.19358			0.596788	+	0.802399i	$0.296443\pi$
$68$	−8.63867	+	6.27636i	−1.04759	+	0.761121i
$69$	−4.05736	+	1.31832i	−0.488449	+	0.158707i
$70$	10.5741	+	13.9193i	1.26385	+	1.66367i
$71$	−0.0566342	−	0.0411472i	−0.00672124	−	0.00488327i	0.584420	−	0.811452i	$-0.301322\pi$
$71$	−0.0566342	−	0.0411472i	−0.00672124	−	0.00488327i	−0.591141	+	0.806568i	$0.701322\pi$
$72$	2.96075	−	4.07512i	0.348928	−	0.480258i
$73$	4.49716	−	13.8408i	0.526352	−	1.61995i	−0.235274	−	0.971929i	$-0.575599\pi$
$73$	4.49716	−	13.8408i	0.526352	−	1.61995i	0.761626	−	0.648017i	$-0.224401\pi$
$74$	5.43682	−	1.76653i	0.632018	−	0.205355i
$75$	−1.30324	−	1.79376i	−0.150485	−	0.207125i
$76$	−28.0790			−3.22089
$77$	8.69148	+	1.20757i	0.990486	+	0.137615i
$78$	−7.51807			−0.851254
$79$	0.626363	+	0.862114i	0.0704713	+	0.0969954i	0.842798	−	0.538230i	$-0.180907\pi$
$79$	0.626363	+	0.862114i	0.0704713	+	0.0969954i	−0.772326	+	0.635226i	$0.780907\pi$
$80$	10.9647	−	3.56265i	1.22589	−	0.398316i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	11.6612	−	16.0503i	1.28777	−	1.77246i
$83$	3.69908	+	2.68754i	0.406027	+	0.294996i	0.771991	−	0.635633i	$-0.219261\pi$
$83$	3.69908	+	2.68754i	0.406027	+	0.294996i	−0.365964	+	0.930629i	$0.619261\pi$
$84$	−8.52864	+	6.47898i	−0.930551	+	0.706915i
$85$	−6.73937	+	2.18975i	−0.730987	+	0.237512i
$86$	−20.9086	+	15.1910i	−2.25463	+	1.63808i
$87$	5.16255			0.553483
$88$	7.61898	−	14.8678i	0.812186	−	1.58491i
$89$		−	17.6770i		−	1.87375i	−0.349660	−	0.936877i	$-0.613703\pi$
$89$		−	17.6770i		−	1.87375i	0.349660	−	0.936877i	$-0.386297\pi$
$90$	5.34509	−	3.88343i	0.563422	−	0.409350i
$91$	7.74376	+	2.33459i	0.811767	+	0.244732i
$92$	5.33679	−	16.4250i	0.556399	−	1.71242i
$93$	−3.20245	−	2.32671i	−0.332078	−	0.241269i
$94$	1.98376	+	1.44129i	0.204609	+	0.148657i
$95$	−17.7220	−	5.75822i	−1.81824	−	0.590781i
$96$	0.148259	+	0.456295i	0.0151316	+	0.0465704i
$97$	−4.13113	−	5.68602i	−0.419453	−	0.577328i	0.546039	−	0.837760i	$-0.316135\pi$
$97$	−4.13113	−	5.68602i	−0.419453	−	0.577328i	−0.965492	+	0.260432i	$0.916135\pi$
$98$	16.1306	−	6.01366i	1.62944	−	0.607472i
$99$	0.526429	−	3.27458i	0.0529081	−	0.329108i
$100$	8.97566			0.897566
$101$	−8.36217	+	6.07547i	−0.832067	+	0.604532i	−0.920143	−	0.391581i	$-0.871928\pi$
$101$	−8.36217	+	6.07547i	−0.832067	+	0.604532i	0.0880761	+	0.996114i	$0.471928\pi$
$102$	−2.00458	−	6.16946i	−0.198483	−	0.610868i
$103$	−5.56447	−	1.80801i	−0.548283	−	0.178148i	0.0217591	−	0.999763i	$-0.493073\pi$
$103$	−5.56447	−	1.80801i	−0.548283	−	0.178148i	−0.570043	+	0.821615i	$0.693073\pi$
$104$	9.05098	−	12.4576i	0.887521	−	1.22157i
$105$	−6.71147	+	2.34020i	−0.654973	+	0.228380i
$106$	15.5477	+	5.05174i	1.51012	+	0.490668i
$107$	−0.542665	+	0.176323i	−0.0524614	+	0.0170458i	−0.335130	−	0.942172i	$-0.608780\pi$
$107$	−0.542665	+	0.176323i	−0.0524614	+	0.0170458i	0.282669	+	0.959218i	$0.408780\pi$
$108$	2.37947	+	3.27506i	0.228964	+	0.315142i
$109$			10.6755i			1.02253i	0.859424	+	0.511264i	$0.170823\pi$
$109$			10.6755i			1.02253i	−0.859424	+	0.511264i	$0.829177\pi$
$110$	15.5304	−	15.4586i	1.48077	−	1.47392i
$111$			2.32448i			0.220630i
$112$	−0.242337	−	11.3516i	−0.0228987	−	1.07262i
$113$	1.07826	+	3.31854i	0.101434	+	0.312182i	0.988877	−	0.148736i	$-0.0475203\pi$
$113$	1.07826	+	3.31854i	0.101434	+	0.312182i	−0.887443	+	0.460918i	$0.847520\pi$
$114$	5.27128	−	16.2233i	0.493701	−	1.51946i
$115$	6.73659	−	9.27212i	0.628190	−	0.864630i
$116$	−12.2841	+	16.9076i	−1.14055	+	1.56983i
$117$	0.944661	−	2.90737i	0.0873339	−	0.268786i
$118$	0.155176	+	0.477584i	0.0142851	+	0.0439651i
$119$	0.148951	+	6.97715i	0.0136543	+	0.639595i
$120$			13.5322i			1.23531i
$121$	0.0510122	−	10.9999i	0.00463747	−	0.999989i
$122$			36.9500i			3.34529i
$123$	4.74167	+	6.52635i	0.427542	+	0.588461i
$124$	15.2402	−	4.95185i	1.36861	−	0.444689i
$125$	−7.11004	−	2.31019i	−0.635942	−	0.206630i
$126$	−2.14231	−	6.14393i	−0.190852	−	0.547345i
$127$	10.7435	−	14.7871i	0.953330	−	1.31215i	0.00329842	−	0.999995i	$-0.498950\pi$
$127$	10.7435	−	14.7871i	0.953330	−	1.31215i	0.950032	−	0.312152i	$-0.101050\pi$
$128$	18.2278	+	5.92257i	1.61113	+	0.523486i
$129$	−3.24740	−	9.99448i	−0.285918	−	0.879965i
$130$	16.3399	−	11.8716i	1.43310	−	1.04121i
$131$	−3.97579			−0.347367			−0.173683	−	0.984802i	$-0.555567\pi$
$131$	−3.97579			−0.347367			−0.173683	+	0.984802i	$0.555567\pi$
$132$	9.47181	+	9.51584i	0.824415	+	0.828247i
$133$	−10.4674	+	15.0735i	−0.907637	+	1.30704i
$134$	−14.1227	−	19.4383i	−1.22002	−	1.67921i
$135$	0.830170	+	2.55500i	0.0714496	+	0.219899i
$136$	12.6362	+	4.10576i	1.08355	+	0.352066i
$137$	−10.8644	−	7.89345i	−0.928208	−	0.674383i	0.0173453	−	0.999850i	$-0.494479\pi$
$137$	−10.8644	−	7.89345i	−0.928208	−	0.674383i	−0.945553	+	0.325467i	$0.894479\pi$
$138$	8.48804	+	6.16692i	0.722550	+	0.524963i
$139$	−0.0580790	+	0.178749i	−0.00492620	+	0.0151613i	−0.953489	−	0.301427i	$-0.902537\pi$
$139$	−0.0580790	+	0.178749i	−0.00492620	+	0.0151613i	0.948563	+	0.316588i	$0.102537\pi$
$140$	8.30544	−	27.5489i	0.701938	−	2.32831i
$141$	−0.806634	+	0.586054i	−0.0679309	+	0.0493547i
$142$			0.172161i			0.0144474i
$143$	1.60929	−	10.0103i	0.134575	−	0.837107i
$144$	−4.29147			−0.357622
$145$	−11.2203	+	8.15206i	−0.931799	+	0.676992i
$146$	−34.0388	+	11.0599i	−2.81707	+	0.915323i
$147$	0.298741	+	6.99362i	0.0246397	+	0.576824i
$148$	−7.61281	−	5.53103i	−0.625769	−	0.454648i
$149$	2.06650	−	2.84429i	0.169294	−	0.233014i	−0.715937	−	0.698165i	$-0.754000\pi$
$149$	2.06650	−	2.84429i	0.169294	−	0.233014i	0.885231	+	0.465152i	$0.154000\pi$
$150$	−1.68500	+	5.18591i	−0.137580	+	0.423427i
$151$	−13.5785	+	4.41192i	−1.10500	+	0.359037i	−0.804026	−	0.594595i	$-0.797313\pi$
$151$	−13.5785	+	4.41192i	−1.10500	+	0.359037i	−0.300977	+	0.953632i	$0.597313\pi$
$152$	20.5363	+	28.2659i	1.66572	+	2.29266i
$153$	2.63772			0.213247
$154$	−10.1613	−	19.0383i	−0.818822	−	1.53415i
$155$	10.6343			0.854167
$156$	7.27400	+	10.0118i	0.582386	+	0.801586i
$157$	−5.84795	+	1.90012i	−0.466717	+	0.151646i	−0.532929	−	0.846160i	$-0.678909\pi$
$157$	−5.84795	+	1.90012i	−0.466717	+	0.151646i	0.0662116	+	0.997806i	$0.478909\pi$
$158$	0.809846	−	2.49245i	0.0644279	−	0.198289i
$159$	−3.90719	+	5.37779i	−0.309860	+	0.426486i
$160$	−1.04275	−	0.757604i	−0.0824368	−	0.0598938i
$161$	−6.82784	−	8.98785i	−0.538109	−	0.708342i
$162$	−2.33894	+	0.759968i	−0.183764	+	0.0597087i
$163$	0.861818	−	0.626148i	0.0675028	−	0.0490437i	−0.553522	−	0.832834i	$-0.686717\pi$
$163$	0.861818	−	0.626148i	0.0675028	−	0.0490437i	0.621025	+	0.783791i	$0.286717\pi$
$164$	−32.6568			−2.55007
$165$	4.02667	+	7.94828i	0.313475	+	0.618773i
$166$		−	11.2447i		−	0.872760i
$167$	18.2832	−	13.2835i	1.41480	−	1.02791i	0.422194	−	0.906506i	$-0.361260\pi$
$167$	18.2832	−	13.2835i	1.41480	−	1.02791i	0.992603	−	0.121404i	$-0.0387398\pi$
$168$	12.7597	+	3.84681i	0.984435	+	0.296788i
$169$	−1.12940	+	3.47595i	−0.0868773	+	0.267381i
$170$	14.0988	+	10.2434i	1.08133	+	0.785633i
$171$	5.61150	+	4.07699i	0.429122	+	0.311775i
$172$	40.4595	+	13.1461i	3.08501	+	1.00238i
$173$	−2.85024	−	8.77212i	−0.216699	−	0.666932i	−0.999029	−	0.0440669i	$-0.985969\pi$
$173$	−2.85024	−	8.77212i	−0.216699	−	0.666932i	0.782329	−	0.622865i	$-0.214031\pi$
$174$	−7.46269	−	10.2715i	−0.565745	−	0.778682i
$175$	3.34597	−	4.81834i	0.252932	−	0.364232i
$176$	−14.0631	+	2.19396i	−1.06004	+	0.165376i
$177$	−0.204188			−0.0153477
$178$	−35.1704	+	25.5528i	−2.63614	+	1.91527i
$179$	5.74302	+	17.6752i	0.429254	+	1.32111i	0.898862	+	0.438232i	$0.144395\pi$
$179$	5.74302	+	17.6752i	0.429254	+	1.32111i	−0.469608	+	0.882875i	$0.655605\pi$
$180$	−10.3431	−	3.36069i	−0.770931	−	0.250491i
$181$	−9.03991	+	12.4424i	−0.671931	+	0.924834i	−0.999802	−	0.0198884i	$-0.993669\pi$
$181$	−9.03991	+	12.4424i	−0.671931	+	0.924834i	0.327871	+	0.944723i	$0.393669\pi$
$182$	−6.54900	−	18.7819i	−0.485444	−	1.39221i
$183$	−14.2892	−	4.64284i	−1.05629	−	0.343209i
$184$	−20.4374	+	6.64053i	−1.50667	+	0.489546i
$185$	−3.67053	−	5.05206i	−0.269863	−	0.371435i
$186$			9.73502i			0.713807i
$187$	8.64376	−	1.34850i	0.632095	−	0.0986121i
$188$		−	4.03627i		−	0.294375i
$189$	2.64515	−	0.0564696i	0.192406	−	0.00410756i
$190$	14.1612	+	43.5838i	1.02736	+	3.16190i
$191$	2.34249	−	7.20943i	0.169496	−	0.521656i	−0.829843	−	0.557997i	$-0.811570\pi$
$191$	2.34249	−	7.20943i	0.169496	−	0.521656i	0.999339	+	0.0363406i	$0.0115701\pi$
$192$	−4.35138	+	5.98917i	−0.314034	+	0.432231i
$193$	7.51453	−	10.3429i	0.540908	−	0.744496i	−0.447836	−	0.894116i	$-0.647805\pi$
$193$	7.51453	−	10.3429i	0.540908	−	0.744496i	0.988744	+	0.149620i	$0.0478050\pi$
$194$	−5.34129	+	16.4388i	−0.383482	+	1.18024i
$195$	2.53782	+	7.81060i	0.181737	+	0.559329i
$196$	−23.6153	−	15.6627i	−1.68681	−	1.11876i
$197$			3.77253i			0.268781i	0.990928	+	0.134391i	$0.0429077\pi$
$197$			3.77253i			0.268781i	−0.990928	+	0.134391i	$0.957092\pi$
$198$	−7.27615	+	3.68616i	−0.517093	+	0.261964i
$199$			8.02593i			0.568943i	0.958685	+	0.284471i	$0.0918181\pi$
$199$			8.02593i			0.568943i	−0.958685	+	0.284471i	$0.908182\pi$
$200$	−6.56459	−	9.03538i	−0.464186	−	0.638898i
$201$	9.29168	−	3.01905i	0.655384	−	0.212947i
$202$	24.1758	+	7.85519i	1.70100	+	0.552689i
$203$	4.49711	+	12.8973i	0.315635	+	0.905211i
$204$	−6.27636	+	8.63867i	−0.439433	+	0.604828i
$205$	−20.6112	−	6.69699i	−1.43955	−	0.467738i
$206$	4.44644	+	13.6847i	0.309798	+	0.953461i
$207$	−3.45140	+	2.50759i	−0.239889	+	0.174289i
$208$	−13.1190			−0.909636
$209$	20.4731	+	10.4914i	1.41616	+	0.725708i
$210$	14.3578	+	9.97042i	0.990786	+	0.688025i
$211$	−2.52551	−	3.47607i	−0.173864	−	0.239303i	0.713188	−	0.700973i	$-0.247250\pi$
$211$	−2.52551	−	3.47607i	−0.173864	−	0.239303i	−0.887052	+	0.461670i	$0.847250\pi$
$212$	−8.31551	−	25.5925i	−0.571112	−	1.75770i
$213$	−0.0665775	−	0.0216323i	−0.00456181	−	0.00148222i
$214$	1.13526	+	0.824816i	0.0776049	+	0.0563833i
$215$	22.8400	+	16.5942i	1.55767	+	1.13172i
$216$	1.55656	−	4.79060i	0.105910	−	0.325959i
$217$	3.02302	−	10.0273i	0.205216	−	0.680696i
$218$	21.2402	−	15.4319i	1.43857	−	1.04518i
$219$		−	14.5531i		−	0.983407i
$220$	−35.6124	−	5.72513i	−2.40099	−	0.385988i
$221$	8.06347			0.542408
$222$	4.62484	−	3.36014i	0.310399	−	0.225518i
$223$	−0.153845	+	0.0499874i	−0.0103023	+	0.00334740i	−0.314164	−	0.949369i	$-0.601724\pi$
$223$	−0.153845	+	0.0499874i	−0.0103023	+	0.00334740i	0.303861	+	0.952716i	$0.401724\pi$
$224$	−1.01078	+	0.767865i	−0.0675358	+	0.0513051i
$225$	−1.79376	−	1.30324i	−0.119584	−	0.0868826i
$226$	5.04397	−	6.94243i	0.335520	−	0.461804i
$227$	3.09289	−	9.51894i	0.205282	−	0.631794i	−0.794419	−	0.607370i	$-0.792225\pi$
$227$	3.09289	−	9.51894i	0.205282	−	0.631794i	0.999702	−	0.0244244i	$-0.00777530\pi$
$228$	−26.7048	+	8.67690i	−1.76857	+	0.574642i
$229$	−0.612988	−	0.843705i	−0.0405074	−	0.0557536i	0.788283	−	0.615313i	$-0.210970\pi$
$229$	−0.612988	−	0.843705i	−0.0405074	−	0.0557536i	−0.828790	+	0.559559i	$0.810970\pi$
$230$	−28.1861			−1.85853
$231$	8.63925	−	1.53735i	0.568421	−	0.101150i
$232$	26.0044			1.70727
$233$	10.6331	+	14.6352i	0.696599	+	0.958786i	0.999982	+	0.00591774i	$0.00188369\pi$
$233$	10.6331	+	14.6352i	0.696599	+	0.958786i	−0.303383	+	0.952869i	$0.598116\pi$
$234$	−7.15011	+	2.32321i	−0.467417	+	0.151873i
$235$	0.827725	−	2.54747i	0.0539948	−	0.166179i
$236$	0.485859	−	0.668727i	0.0316267	−	0.0435304i
$237$	0.862114	+	0.626363i	0.0560003	+	0.0406866i
$238$	13.6666	−	10.3821i	0.885873	−	0.672974i
$239$	13.3060	−	4.32337i	0.860692	−	0.279656i	0.154775	−	0.987950i	$-0.450535\pi$
$239$	13.3060	−	4.32337i	0.860692	−	0.279656i	0.705918	+	0.708294i	$0.250535\pi$
$240$	9.32713	−	6.77656i	0.602064	−	0.437425i
$241$	7.71499			0.496966			0.248483	−	0.968636i	$-0.420068\pi$
$241$	7.71499			0.496966			0.248483	+	0.968636i	$0.420068\pi$
$242$	−21.9593	+	15.7993i	−1.41160	+	1.01562i
$243$		−	1.00000i		−	0.0641500i
$244$	49.2062	−	35.7504i	3.15011	−	2.28869i
$245$	−11.6928	−	14.7283i	−0.747023	−	0.940956i
$246$	6.13067	−	18.8683i	0.390877	−	1.20300i
$247$	17.1543	+	12.4633i	1.09150	+	0.793022i
$248$	−16.1311	−	11.7200i	−1.02433	−	0.744218i
$249$	4.34853	+	1.41292i	0.275577	+	0.0895404i
$250$	5.68147	+	17.4858i	0.359328	+	1.10590i
$251$	−8.44110	−	11.6182i	−0.532798	−	0.733333i	0.454756	−	0.890616i	$-0.349726\pi$
$251$	−8.44110	−	11.6182i	−0.532798	−	0.733333i	−0.987554	+	0.157283i	$0.949726\pi$
$252$	−6.10910	+	8.79738i	−0.384837	+	0.554183i
$253$	−10.0282	+	9.98180i	−0.630468	+	0.627551i
$254$	−44.9510			−2.82048
$255$	−5.73285	+	4.16516i	−0.359005	+	0.260832i
$256$	−9.99011	−	30.7464i	−0.624382	−	1.92165i
$257$	−11.9820	−	3.89319i	−0.747417	−	0.242850i	−0.0895476	−	0.995983i	$-0.528542\pi$
$257$	−11.9820	−	3.89319i	−0.747417	−	0.242850i	−0.657869	+	0.753132i	$0.728542\pi$
$258$	−15.1910	+	20.9086i	−0.945748	+	1.30171i
$259$	−5.80710	+	2.02486i	−0.360836	+	0.125819i
$260$	−31.6188	−	10.2736i	−1.96091	−	0.637140i
$261$	4.90988	−	1.59532i	0.303914	−	0.0987476i
$262$	5.74719	+	7.91032i	0.355062	+	0.488701i
$263$		−	3.92323i		−	0.241917i	−0.992658	−	0.120958i	$-0.961403\pi$
$263$		−	3.92323i		−	0.241917i	0.992658	−	0.120958i	$-0.0385967\pi$
$264$	2.65169	−	16.4945i	0.163200	−	1.01517i
$265$		−	17.8579i		−	1.09700i
$266$	45.1216	−	0.963272i	2.76658	−	0.0590620i
$267$	−5.46248	−	16.8118i	−0.334298	−	1.02886i
$268$	−12.2217	+	37.6145i	−0.746558	+	2.29767i
$269$	−4.28959	+	5.90411i	−0.261541	+	0.359980i	−0.919511	−	0.393064i	$-0.871415\pi$
$269$	−4.28959	+	5.90411i	−0.261541	+	0.359980i	0.657970	+	0.753044i	$0.271415\pi$
$270$	3.88343	−	5.34509i	0.236338	−	0.325292i
$271$	7.26901	−	22.3717i	0.441561	−	1.35898i	−0.444651	−	0.895704i	$-0.646672\pi$
$271$	7.26901	−	22.3717i	0.441561	−	1.35898i	0.886212	−	0.463281i	$-0.153328\pi$
$272$	−3.49797	−	10.7657i	−0.212096	−	0.652764i
$273$	8.08619	−	0.172627i	0.489398	−	0.0104479i
$274$			33.0264i			1.99520i
$275$	−6.54437	−	3.35366i	−0.394641	−	0.202233i
$276$		−	17.2702i		−	1.03955i
$277$	−7.73078	−	10.6405i	−0.464497	−	0.639326i	0.510936	−	0.859619i	$-0.329299\pi$
$277$	−7.73078	−	10.6405i	−0.464497	−	0.639326i	−0.975434	+	0.220293i	$0.929299\pi$
$278$	0.439598	−	0.142834i	0.0263654	−	0.00856662i
$279$	−3.76470	−	1.22323i	−0.225387	−	0.0732326i
$280$	−33.8066	+	11.7879i	−2.02033	+	0.704462i
$281$	−11.4851	+	15.8079i	−0.685144	+	0.943020i	−0.999981	−	0.00612545i	$-0.998050\pi$
$281$	−11.4851	+	15.8079i	−0.685144	+	0.943020i	0.314837	+	0.949146i	$0.398050\pi$
$282$	2.33205	+	0.757730i	0.138872	+	0.0451221i
$283$	−1.64230	−	5.05449i	−0.0976247	−	0.300458i	0.890304	−	0.455366i	$-0.150492\pi$
$283$	−1.64230	−	5.05449i	−0.0976247	−	0.300458i	−0.987929	+	0.154908i	$0.950492\pi$
$284$	0.229266	−	0.166572i	0.0136044	−	0.00988420i
$285$	−18.6340			−1.10378
$286$	−22.2431	+	11.2685i	−1.31526	+	0.666322i
$287$	−12.1739	+	17.5309i	−0.718602	+	1.03482i
$288$	0.282006	+	0.388147i	0.0166173	+	0.0228718i
$289$	−3.10329	−	9.55093i	−0.182546	−	0.561820i
$290$	32.4390	+	10.5401i	1.90489	+	0.618935i
$291$	−5.68602	−	4.13113i	−0.333320	−	0.242171i
$292$	47.6622	+	34.6286i	2.78922	+	2.02649i
$293$	3.89387	−	11.9841i	0.227482	−	0.700119i	−0.770548	−	0.637382i	$-0.780017\pi$
$293$	3.89387	−	11.9841i	0.227482	−	0.700119i	0.998030	−	0.0627367i	$-0.0199828\pi$
$294$	13.4828	−	10.7040i	0.786334	−	0.624268i
$295$	0.443785	−	0.322429i	0.0258381	−	0.0187725i
$296$			11.7087i			0.680555i
$297$	−0.511237	−	3.27699i	−0.0296650	−	0.190150i
$298$	−8.64628			−0.500866
$299$	−10.5509	+	7.66566i	−0.610173	+	0.443316i
$300$	8.53636	−	2.77363i	0.492847	−	0.160136i
$301$	22.1397	−	16.8190i	1.27611	−	0.969430i
$302$	28.4064	+	20.6384i	1.63460	+	1.18761i
$303$	−6.07547	+	8.36217i	−0.349027	+	0.480394i
$304$	9.19834	−	28.3096i	0.527561	−	1.62367i
$305$	38.3877	−	12.4729i	2.19807	−	0.714198i
$306$	−3.81294	−	5.24806i	−0.217971	−	0.300012i
$307$	2.85519			0.162954			0.0814770	−	0.996675i	$-0.474036\pi$
$307$	2.85519			0.162954			0.0814770	+	0.996675i	$0.474036\pi$
$308$	−15.5219	+	31.9521i	−0.884442	+	1.82064i
$309$	−5.85083			−0.332842
$310$	−15.3723	−	21.1582i	−0.873091	−	1.20171i
$311$	27.9969	−	9.09675i	1.58756	−	0.515829i	0.623570	−	0.781768i	$-0.285682\pi$
$311$	27.9969	−	9.09675i	1.58756	−	0.515829i	0.963990	+	0.265938i	$0.0856817\pi$
$312$	4.75838	−	14.6448i	0.269390	−	0.829098i
$313$	−2.22824	+	3.06691i	−0.125948	+	0.173352i	−0.867334	−	0.497726i	$-0.834168\pi$
$313$	−2.22824	+	3.06691i	−0.125948	+	0.173352i	0.741387	+	0.671078i	$0.234168\pi$
$314$	12.2340	+	8.88851i	0.690404	+	0.501608i
$315$	−5.65983	+	4.29962i	−0.318895	+	0.242256i
$316$	−4.10274	+	1.33306i	−0.230797	+	0.0749906i
$317$	−2.63800	+	1.91662i	−0.148165	+	0.107648i	−0.659398	−	0.751794i	$-0.729189\pi$
$317$	−2.63800	+	1.91662i	−0.148165	+	0.107648i	0.511233	+	0.859442i	$0.329189\pi$
$318$	16.3478			0.916737
$319$	15.2740	−	7.73794i	0.855180	−	0.433241i
$320$		−	19.8881i		−	1.11178i
$321$	−0.461619	+	0.335386i	−0.0257650	+	0.0187194i
$322$	−8.01248	+	26.5771i	−0.446518	+	1.48109i
$323$	−5.65369	+	17.4003i	−0.314580	+	0.968177i
$324$	3.27506	+	2.37947i	0.181948	+	0.132193i
$325$	−5.48349	−	3.98399i	−0.304169	−	0.220992i
$326$	−2.49159	−	0.809568i	−0.137997	−	0.0448378i
$327$	3.29891	+	10.1530i	0.182430	+	0.561463i
$328$	23.8844	+	32.8741i	1.31880	+	1.81517i
$329$	−2.16676	−	1.50465i	−0.119457	−	0.0829541i
$330$	9.99335	−	19.5011i	0.550116	−	1.07350i
$331$	20.2863			1.11504			0.557518	−	0.830165i	$-0.311754\pi$
$331$	20.2863			1.11504			0.557518	+	0.830165i	$0.311754\pi$
$332$	−14.9746	+	10.8797i	−0.821837	+	0.597100i
$333$	0.718304	+	2.21071i	0.0393628	+	0.121146i
$334$	−52.8584	−	17.1747i	−2.89228	−	0.939759i
$335$	−15.4273	+	21.2339i	−0.842885	+	1.16013i
$336$	−3.73830	−	10.7211i	−0.203941	−	0.584884i
$337$	−29.7629	−	9.67055i	−1.62129	−	0.526788i	−0.649043	−	0.760752i	$-0.724830\pi$
$337$	−29.7629	−	9.67055i	−1.62129	−	0.526788i	−0.972245	+	0.233964i	$0.924830\pi$
$338$	8.54843	−	2.77755i	0.464973	−	0.151079i
$339$	2.05097	+	2.82292i	0.111394	+	0.153320i
$340$		−	28.6862i		−	1.55573i
$341$	−12.9622	−	2.08384i	−0.701944	−	0.112846i
$342$		−	17.0582i		−	0.922404i
$343$	−17.2115	+	6.83848i	−0.929333	+	0.369243i
$344$	−16.3576	−	50.3435i	−0.881942	−	2.71434i
$345$	3.54164	−	10.9000i	0.190675	−	0.586838i
$346$	−13.3331	+	18.3514i	−0.716790	+	0.986576i
$347$	7.96036	−	10.9565i	0.427334	−	0.588175i	−0.540005	−	0.841662i	$-0.681577\pi$
$347$	7.96036	−	10.9565i	0.427334	−	0.588175i	0.967339	+	0.253487i	$0.0815775\pi$
$348$	−6.45814	+	19.8761i	−0.346193	+	1.06547i
$349$	10.3439	+	31.8351i	0.553694	+	1.70409i	0.699368	+	0.714761i	$0.253465\pi$
$349$	10.3439	+	31.8351i	0.553694	+	1.70409i	−0.145675	+	0.989333i	$0.546535\pi$
$350$	−14.4234	+	0.307917i	−0.770964	+	0.0164588i
$351$		−	3.05699i		−	0.163170i
$352$	1.12256	+	1.12778i	0.0598328	+	0.0601110i
$353$		−	17.5405i		−	0.933588i	−0.884366	−	0.466794i	$-0.845409\pi$
$353$		−	17.5405i		−	0.933588i	0.884366	−	0.466794i	$-0.154591\pi$
$354$	0.295163	+	0.406257i	0.0156877	+	0.0215923i
$355$	0.178859	−	0.0581150i	0.00949287	−	0.00308442i
$356$	68.0573	+	22.1132i	3.60703	+	1.17200i
$357$	2.29772	+	6.58964i	0.121608	+	0.348761i
$358$	26.8652	−	36.9767i	1.41987	−	1.95428i
$359$	31.4281	+	10.2116i	1.65871	+	0.538949i	0.980602	−	0.196010i	$-0.0627984\pi$
$359$	31.4281	+	10.2116i	1.65871	+	0.538949i	0.678112	+	0.734958i	$0.262798\pi$
$360$	4.18167	+	12.8699i	0.220393	+	0.678301i
$361$	−23.5511	+	17.1109i	−1.23953	+	0.900574i
$362$	37.8232			1.98794
$363$	−3.35063	−	10.4773i	−0.175863	−	0.549914i
$364$	−18.6754	+	26.8935i	−0.978859	+	1.40960i
$365$	22.9805	+	31.6299i	1.20285	+	1.65558i
$366$	11.4182	+	35.1415i	0.596838	+	1.83688i
$367$	0.280086	+	0.0910054i	0.0146204	+	0.00475045i	0.316318	−	0.948653i	$-0.397553\pi$
$367$	0.280086	+	0.0910054i	0.0146204	+	0.00475045i	−0.301698	+	0.953404i	$0.597553\pi$
$368$	14.8116	+	10.7612i	0.772106	+	0.560968i
$369$	6.52635	+	4.74167i	0.339748	+	0.246842i
$370$	−4.74576	+	14.6059i	−0.246720	+	0.759327i
$371$	−16.8385	−	5.07648i	−0.874213	−	0.263558i
$372$	12.9641	−	9.41898i	0.672158	−	0.488351i
$373$			26.8956i			1.39260i	0.717751	+	0.696299i	$0.245171\pi$
$373$			26.8956i			1.39260i	−0.717751	+	0.696299i	$0.754829\pi$
$374$	−15.1779	−	15.2485i	−0.784833	−	0.788481i
$375$	−7.47594			−0.386056
$376$	−4.06312	+	2.95203i	−0.209540	+	0.152239i
$377$	15.0094	−	4.87686i	0.773025	−	0.251171i
$378$	−3.93603	−	5.18121i	−0.202448	−	0.266493i
$379$	8.92049	+	6.48111i	0.458215	+	0.332912i	0.792831	−	0.609442i	$-0.208607\pi$
$379$	8.92049	+	6.48111i	0.458215	+	0.332912i	−0.334616	+	0.942355i	$0.608607\pi$
$380$	44.3390	−	61.0273i	2.27454	−	3.13064i
$381$	5.64819	−	17.3833i	0.289365	−	0.890575i
$382$	−17.7302	+	5.76089i	−0.907156	+	0.294753i
$383$	8.03255	+	11.0559i	0.410444	+	0.564928i	0.963327	−	0.268331i	$-0.0864721\pi$
$383$	8.03255	+	11.0559i	0.410444	+	0.564928i	−0.552882	+	0.833259i	$0.686472\pi$
$384$	19.1658			0.978053
$385$	−16.3491	+	16.9833i	−0.833225	+	0.865550i
$386$	−31.4410			−1.60030
$387$	−6.17693	−	8.50181i	−0.313991	−	0.432171i
$388$	27.0594	−	8.79213i	1.37373	−	0.446353i
$389$	−7.65575	+	23.5620i	−0.388162	+	1.19464i	0.545998	+	0.837786i	$0.316150\pi$
$389$	−7.65575	+	23.5620i	−0.388162	+	1.19464i	−0.934160	+	0.356854i	$0.883850\pi$
$390$	11.8716	−	16.3399i	0.601142	−	0.827401i
$391$	−9.10381	−	6.61430i	−0.460399	−	0.334500i
$392$	1.50480	+	35.2278i	0.0760037	+	1.77927i
$393$	−3.78120	+	1.22859i	−0.190737	+	0.0619741i
$394$	7.50590	−	5.45335i	0.378142	−	0.274736i
$395$	−2.86280			−0.144043
$396$	11.9488	+	6.12315i	0.600449	+	0.307700i
$397$			14.1536i			0.710350i	0.934800	+	0.355175i	$0.115579\pi$
$397$			14.1536i			0.710350i	−0.934800	+	0.355175i	$0.884421\pi$
$398$	15.9686	−	11.6018i	0.800431	−	0.581547i
$399$	−5.29710	+	17.5703i	−0.265187	+	0.879617i
$400$	−2.94031	+	9.04936i	−0.147016	+	0.452468i
$401$	−7.65280	−	5.56009i	−0.382163	−	0.277657i	0.380074	−	0.924956i	$-0.375899\pi$
$401$	−7.65280	−	5.56009i	−0.382163	−	0.277657i	−0.762236	+	0.647299i	$0.775899\pi$
$402$	−19.4383	−	14.1227i	−0.969494	−	0.704379i
$403$	−11.5086	−	3.73939i	−0.573287	−	0.186272i
$404$	−12.9302	−	39.7950i	−0.643301	−	1.97988i
$405$	1.57908	+	2.17341i	0.0784649	+	0.107998i
$406$	19.1599	−	27.5911i	0.950890	−	1.36932i
$407$	3.48407	+	6.87725i	0.172699	+	0.340893i
$408$	13.2865			0.657781
$409$	5.56580	−	4.04379i	0.275211	−	0.199953i	−0.441615	−	0.897205i	$-0.645594\pi$
$409$	5.56580	−	4.04379i	0.275211	−	0.199953i	0.716826	+	0.697252i	$0.245594\pi$
$410$	16.4700	+	50.6893i	0.813393	+	2.50337i
$411$	−12.7719	−	4.14983i	−0.629990	−	0.204696i
$412$	13.9219	−	19.1618i	0.685881	−	0.944034i
$413$	−0.177869	−	0.510110i	−0.00875234	−	0.0251009i
$414$	9.97829	+	3.24214i	0.490406	+	0.159343i
$415$	−11.6823	+	3.79580i	−0.573460	+	0.186328i
$416$	0.862087	+	1.18656i	0.0422673	+	0.0581760i
$417$			0.187948i			0.00920384i
$418$	−8.72081	−	55.8996i	−0.426549	−	2.73414i
$419$			6.12153i			0.299056i	0.988757	+	0.149528i	$0.0477755\pi$
$419$			6.12153i			0.299056i	−0.988757	+	0.149528i	$0.952225\pi$
$420$	−0.614130	−	28.7671i	−0.0299665	−	1.40369i
$421$	−2.31603	−	7.12801i	−0.112876	−	0.347398i	0.878622	−	0.477518i	$-0.158464\pi$
$421$	−2.31603	−	7.12801i	−0.112876	−	0.347398i	−0.991498	+	0.130120i	$0.958464\pi$
$422$	−3.26532	+	10.0496i	−0.158954	+	0.489209i
$423$	−0.586054	+	0.806634i	−0.0284949	+	0.0392199i
$424$	−19.6810	+	27.0886i	−0.955795	+	1.31554i
$425$	1.80724	−	5.56212i	0.0876641	−	0.269802i
$426$	0.0532006	+	0.163734i	0.00257758	+	0.00793296i
$427$	−0.848430	−	39.7422i	−0.0410584	−	1.92326i
$428$		−	2.30987i		−	0.111652i
$429$	−1.56285	−	10.0177i	−0.0754549	−	0.483659i
$430$		−	69.4306i		−	3.34824i
$431$	−18.9604	−	26.0967i	−0.913289	−	1.25703i	−0.966031	−	0.258427i	$-0.916796\pi$
$431$	−18.9604	−	26.0967i	−0.913289	−	1.25703i	0.0527417	−	0.998608i	$-0.483204\pi$
$432$	−4.08143	+	1.32614i	−0.196368	+	0.0638038i
$433$	−6.57354	−	2.13587i	−0.315904	−	0.102644i	0.146773	−	0.989170i	$-0.453111\pi$
$433$	−6.57354	−	2.13587i	−0.315904	−	0.102644i	−0.462678	+	0.886527i	$0.653111\pi$
$434$	−24.3204	+	8.48020i	−1.16742	+	0.407062i
$435$	−8.15206	+	11.2203i	−0.390861	+	0.537975i
$436$	−41.1013	−	13.3546i	−1.96840	−	0.639571i
$437$	−9.14410	−	28.1426i	−0.437421	−	1.34624i
$438$	−28.9552	+	21.0372i	−1.38353	+	1.00519i
$439$	−12.5914			−0.600955			−0.300478	−	0.953789i	$-0.597146\pi$
$439$	−12.5914			−0.600955			−0.300478	+	0.953789i	$0.597146\pi$
$440$	20.2828	+	40.0365i	0.966946	+	1.90867i
$441$	2.44527	+	6.55901i	0.116441	+	0.312334i
$442$	−11.6561	−	16.0432i	−0.554424	−	0.763099i
$443$	−11.7559	−	36.1808i	−0.558537	−	1.71900i	−0.686413	−	0.727211i	$-0.740816\pi$
$443$	−11.7559	−	36.1808i	−0.558537	−	1.71900i	0.127876	−	0.991790i	$-0.459184\pi$
$444$	−8.94939	−	2.90783i	−0.424719	−	0.138000i
$445$	38.4193	+	27.9133i	1.82125	+	1.32322i
$446$	0.321846	+	0.233835i	0.0152399	+	0.0110724i
$447$	1.08642	−	3.34367i	0.0513860	−	0.158150i
$448$	−18.7529	−	5.65361i	−0.885989	−	0.267108i
$449$	2.04009	−	1.48221i	0.0962777	−	0.0699499i	−0.538605	−	0.842558i	$-0.681048\pi$
$449$	2.04009	−	1.48221i	0.0962777	−	0.0699499i	0.634883	+	0.772609i	$0.281048\pi$
$450$			5.45278i			0.257047i
$451$	23.8109	+	12.2019i	1.12121	+	0.574564i
$452$	−14.1254			−0.664405
$453$	−11.5506	+	8.39197i	−0.542693	+	0.394289i
$454$	−23.4100	+	7.60637i	−1.09869	+	0.356984i
$455$	−17.3020	+	13.1439i	−0.811131	+	0.616195i
$456$	28.2659	+	20.5363i	1.32367	+	0.961703i
$457$	−24.6830	+	33.9732i	−1.15462	+	1.58920i	−0.425261	+	0.905071i	$0.639818\pi$
$457$	−24.6830	+	33.9732i	−1.15462	+	1.58920i	−0.729361	+	0.684129i	$0.760182\pi$
$458$	−0.792553	+	2.43923i	−0.0370336	+	0.113978i
$459$	2.50862	−	0.815099i	0.117092	−	0.0380456i
$460$	27.2710	+	37.5353i	1.27152	+	1.75009i
$461$	9.09026			0.423376			0.211688	−	0.977337i	$-0.432104\pi$
$461$	9.09026			0.423376			0.211688	+	0.977337i	$0.432104\pi$
$462$	−15.5472	−	14.9665i	−0.723319	−	0.696305i
$463$	13.4108			0.623251			0.311625	−	0.950205i	$-0.399127\pi$
$463$	13.4108			0.623251			0.311625	+	0.950205i	$0.399127\pi$
$464$	−13.0223	−	17.9237i	−0.604547	−	0.832087i
$465$	10.1138	−	3.28618i	0.469017	−	0.152393i
$466$	13.7479	−	42.3118i	0.636860	−	1.96005i
$467$	0.385692	−	0.530860i	0.0178477	−	0.0245653i	−0.800000	−	0.600000i	$-0.795167\pi$
$467$	0.385692	−	0.530860i	0.0178477	−	0.0245653i	0.817848	+	0.575435i	$0.195167\pi$
$468$	10.0118	+	7.27400i	0.462796	+	0.336241i
$469$	15.6363	+	20.5829i	0.722017	+	0.950430i
$470$	−6.26502	+	2.03563i	−0.288984	+	0.0938966i
$471$	−4.97457	+	3.61423i	−0.229216	+	0.166535i
$472$	−1.02852			−0.0473415
$473$	−24.5881	−	24.7024i	−1.13056	−	1.13582i
$474$		−	2.62072i		−	0.120373i
$475$	12.4418	−	9.03952i	0.570871	−	0.414762i
$476$	−27.0488	−	8.15467i	−1.23978	−	0.373769i
$477$	−2.05413	+	6.32197i	−0.0940522	+	0.289463i
$478$	−27.8363	−	20.2242i	−1.27320	−	0.925034i
$479$	−15.4690	−	11.2389i	−0.706795	−	0.513517i	0.175343	−	0.984507i	$-0.443897\pi$
$479$	−15.4690	−	11.2389i	−0.706795	−	0.513517i	−0.882138	+	0.470991i	$0.843897\pi$
$480$	−1.22583	−	0.398296i	−0.0559512	−	0.0181796i
$481$	2.19585	+	6.75812i	0.100122	+	0.308144i
$482$	−11.1524	−	15.3499i	−0.507976	−	0.699169i
$483$	−9.27106	−	6.43804i	−0.421848	−	0.292941i
$484$	42.2864	+	13.9568i	1.92211	+	0.634400i
$485$	18.8814			0.857362
$486$	−1.98962	+	1.44554i	−0.0902510	+	0.0655712i
$487$	6.15033	+	18.9288i	0.278698	+	0.857745i	0.988217	+	0.153059i	$0.0489123\pi$
$487$	6.15033	+	18.9288i	0.278698	+	0.857745i	−0.709519	+	0.704686i	$0.751088\pi$
$488$	−71.9766	−	23.3866i	−3.25823	−	1.05866i
$489$	0.626148	−	0.861818i	0.0283154	−	0.0389728i
$490$	−12.4013	+	44.5545i	−0.560235	+	2.01277i
$491$	−20.5775	−	6.68604i	−0.928650	−	0.301737i	−0.194639	−	0.980875i	$-0.562354\pi$
$491$	−20.5775	−	6.68604i	−0.928650	−	0.301737i	−0.734010	+	0.679138i	$0.762354\pi$
$492$	−31.0585	+	10.0915i	−1.40022	+	0.454960i
$493$	8.00408	+	11.0167i	0.360485	+	0.496166i
$494$		−	52.1468i		−	2.34620i
$495$	6.28574	+	6.31496i	0.282523	+	0.283836i
$496$			16.9875i			0.762763i
$497$	−0.00395308	−	0.185170i	−0.000177320	−	0.00830602i
$498$	−3.47481	−	10.6944i	−0.155710	−	0.479226i
$499$	−6.94222	+	21.3659i	−0.310776	+	0.956471i	0.666682	+	0.745342i	$0.267714\pi$
$499$	−6.94222	+	21.3659i	−0.310776	+	0.956471i	−0.977458	+	0.211129i	$0.932286\pi$
$500$	17.7888	−	24.4841i	0.795537	−	1.09496i
$501$	13.2835	−	18.2832i	0.593464	−	0.816833i
$502$	−10.9138	+	33.5892i	−0.487106	+	1.49916i
$503$	−4.90894	−	15.1082i	−0.218879	−	0.673640i	−0.998855	−	0.0478310i	$-0.984769\pi$
$503$	−4.90894	−	15.1082i	−0.218879	−	0.673640i	0.779977	−	0.625809i	$-0.215231\pi$
$504$	13.3240	−	0.284445i	0.593496	−	0.0126702i
$505$		−	27.7681i		−	1.23566i
$506$	34.3562	+	5.52318i	1.52732	+	0.245535i
$507$			3.65483i			0.162317i
$508$	43.4917	+	59.8612i	1.92963	+	2.65591i
$509$	−23.4296	+	7.61275i	−1.03850	+	0.337429i	−0.778145	−	0.628084i	$-0.783839\pi$
$509$	−23.4296	+	7.61275i	−1.03850	+	0.337429i	−0.260354	+	0.965513i	$0.583839\pi$
$510$	16.5742	+	5.38527i	0.733917	+	0.238464i
$511$	36.3571	−	12.6772i	1.60834	−	0.560808i
$512$	−24.2017	+	33.3108i	−1.06957	+	1.47214i
$513$	6.59671	+	2.14340i	0.291252	+	0.0946335i
$514$	9.57455	+	29.4674i	0.422315	+	1.29975i
$515$	12.7163	−	9.23891i	0.560346	−	0.407115i
$516$	42.5417			1.87279
$517$	−1.50811	+	2.94294i	−0.0663266	+	0.129430i
$518$	12.4231	+	8.62691i	0.545841	+	0.379045i
$519$	−5.42147	−	7.46201i	−0.237976	−	0.327546i
$520$	12.7833	+	39.3430i	0.560586	+	1.72531i
$521$	32.9454	+	10.7046i	1.44337	+	0.468978i	0.922945	−	0.384932i	$-0.125775\pi$
$521$	32.9454	+	10.7046i	1.44337	+	0.468978i	0.520421	+	0.853910i	$0.325775\pi$
$522$	−10.2715	−	7.46269i	−0.449572	−	0.326633i
$523$	25.5588	+	18.5696i	1.11761	+	0.811990i	0.983845	−	0.179023i	$-0.0572936\pi$
$523$	25.5588	+	18.5696i	1.11761	+	0.811990i	0.133764	+	0.991013i	$0.457294\pi$
$524$	4.97356	−	15.3070i	0.217271	−	0.668691i
$525$	1.69326	−	5.61648i	0.0738998	−	0.245123i
$526$	−7.80574	+	5.67120i	−0.340346	+	0.247276i
$527$		−	10.4413i		−	0.454828i
$528$	−12.6968	+	6.43231i	−0.552558	+	0.279930i
$529$	−4.79988			−0.208691
$530$	−35.5304	+	25.8144i	−1.54334	+	1.12131i
$531$	−0.194194	+	0.0630976i	−0.00842732	+	0.00273820i
$532$	−44.9395	−	59.1563i	−1.94837	−	2.56475i
$533$	19.9510	+	14.4952i	0.864172	+	0.627858i
$534$	−25.5528	+	35.1704i	−1.10578	+	1.52197i
$535$	0.473688	−	1.45786i	0.0204793	−	0.0630289i
$536$	46.8034	−	15.2073i	2.02160	−	0.656857i
$537$	10.9239	+	15.0354i	0.471400	+	0.648827i
$538$	17.9477			0.773782
$539$	11.3663	+	20.2437i	0.489582	+	0.871957i
$540$	−10.8754			−0.468003
$541$	4.29539	+	5.91210i	0.184673	+	0.254181i	0.891309	−	0.453397i	$-0.149788\pi$
$541$	4.29539	+	5.91210i	0.184673	+	0.254181i	−0.706636	+	0.707578i	$0.749788\pi$
$542$	−55.0189	+	17.8767i	−2.36326	+	0.767871i
$543$	−4.75256	+	14.6269i	−0.203952	+	0.627700i
$544$	−0.743851	+	1.02382i	−0.0318923	+	0.0438960i
$545$	−23.2023	−	16.8574i	−0.993876	−	0.722093i
$546$	−12.0324	−	15.8389i	−0.514939	−	0.677843i
$547$	−14.1327	+	4.59200i	−0.604272	+	0.196340i	−0.595145	−	0.803618i	$-0.702905\pi$
$547$	−14.1327	+	4.59200i	−0.604272	+	0.196340i	−0.00912718	+	0.999958i	$0.502905\pi$
$548$	43.9812	−	31.9542i	1.87878	−	1.36501i
$549$	−15.0246			−0.641232
$550$	2.78767	+	17.8687i	0.118866	+	0.761924i
$551$			35.8085i			1.52549i
$552$	−17.3851	+	12.6310i	−0.739960	+	0.537613i
$553$	−0.813812	+	2.69939i	−0.0346068	+	0.114790i
$554$	−9.99539	+	30.7626i	−0.424663	+	1.30698i
$555$	−5.05206	−	3.67053i	−0.214448	−	0.155806i
$556$	−0.615539	−	0.447215i	−0.0261047	−	0.0189662i
$557$	−9.18542	−	2.98453i	−0.389199	−	0.126458i	0.107880	−	0.994164i	$-0.465594\pi$
$557$	−9.18542	−	2.98453i	−0.389199	−	0.126458i	−0.497078	+	0.867706i	$0.665594\pi$
$558$	3.00829	+	9.25856i	0.127351	+	0.391946i
$559$	−18.8828	−	25.9899i	−0.798657	−	1.09926i
$560$	25.0543	+	17.3983i	1.05874	+	0.735212i
$561$	7.80400	−	3.95357i	0.329485	−	0.166920i
$562$	48.0540			2.02703
$563$	−27.5315	+	20.0028i	−1.16031	+	0.843018i	−0.989818	−	0.142340i	$-0.954537\pi$
$563$	−27.5315	+	20.0028i	−1.16031	+	0.843018i	−0.170497	+	0.985358i	$0.554537\pi$
$564$	−1.24728	−	3.83872i	−0.0525198	−	0.161639i
$565$	−8.91522	−	2.89673i	−0.375066	−	0.121866i
$566$	−7.68249	+	10.5740i	−0.322919	+	0.444460i
$567$	2.49824	−	0.871102i	0.104916	−	0.0365828i
$568$	−0.335359	−	0.108965i	−0.0140714	−	0.00457207i
$569$	−4.46863	+	1.45195i	−0.187335	+	0.0608688i	−0.401182	−	0.915998i	$-0.631401\pi$
$569$	−4.46863	+	1.45195i	−0.187335	+	0.0608688i	0.213847	+	0.976867i	$0.431401\pi$
$570$	26.9363	+	37.0746i	1.12824	+	1.55288i
$571$			17.5936i			0.736271i	0.929772	+	0.368136i	$0.120004\pi$
$571$			17.5936i			0.736271i	−0.929772	+	0.368136i	$0.879996\pi$
$572$	36.5273	+	18.7184i	1.52728	+	0.782655i
$573$		−	7.58045i		−	0.316678i
$574$	52.4778	−	1.12032i	2.19038	−	0.0467611i
$575$	2.92297	+	8.99599i	0.121896	+	0.375159i
$576$	−2.28766	+	7.04069i	−0.0953191	+	0.293362i
$577$	1.09128	−	1.50202i	0.0454306	−	0.0625298i	−0.785697	−	0.618611i	$-0.787696\pi$
$577$	1.09128	−	1.50202i	0.0454306	−	0.0625298i	0.831128	+	0.556081i	$0.187696\pi$
$578$	−14.5168	+	19.9807i	−0.603819	+	0.831086i
$579$	3.95062	−	12.1588i	0.164182	−	0.505301i
$580$	−17.3497	−	53.3969i	−0.720407	−	2.21719i
$581$	0.258197	+	12.0945i	0.0107118	+	0.501763i
$582$			17.2848i			0.716476i
$583$	−3.49933	+	21.7671i	−0.144928	+	0.901503i
$584$		−	73.3059i		−	3.03342i
$585$	4.82722	+	6.64409i	0.199581	+	0.274699i
$586$	−29.4726	+	9.57623i	−1.21750	+	0.395590i
$587$	−20.5275	−	6.66978i	−0.847259	−	0.275291i	−0.146961	−	0.989142i	$-0.546949\pi$
$587$	−20.5275	−	6.66978i	−0.847259	−	0.275291i	−0.700298	+	0.713851i	$0.746949\pi$
$588$	−27.2996	−	7.59857i	−1.12582	−	0.313360i
$589$	16.1385	−	22.2128i	0.664977	−	0.915262i
$590$	−1.28302	−	0.416879i	−0.0528211	−	0.0171626i
$591$	1.16577	+	3.58789i	0.0479536	+	0.147586i
$592$	8.07030	−	5.86342i	0.331687	−	0.240985i
$593$	14.9931			0.615694			0.307847	−	0.951436i	$-0.400392\pi$
$593$	14.9931			0.615694			0.307847	+	0.951436i	$0.400392\pi$
$594$	−5.78094	+	5.75420i	−0.237195	+	0.236098i
$595$	−15.3994	−	10.6937i	−0.631315	−	0.438400i
$596$	8.36558	+	11.5142i	0.342668	+	0.471642i
$597$	2.48015	+	7.63311i	0.101506	+	0.312402i
$598$	30.5035	+	9.91119i	1.24738	+	0.405299i
$599$	−34.8547	−	25.3234i	−1.42413	−	1.03469i	−0.991073	−	0.133319i	$-0.957436\pi$
$599$	−34.8547	−	25.3234i	−1.42413	−	1.03469i	−0.433052	−	0.901369i	$-0.642564\pi$
$600$	−9.03538	−	6.56459i	−0.368868	−	0.267998i
$601$	−7.37794	+	22.7070i	−0.300952	+	0.926236i	0.680204	+	0.733023i	$0.261891\pi$
$601$	−7.37794	+	22.7070i	−0.300952	+	0.926236i	−0.981157	+	0.193214i	$0.938109\pi$
$602$	−65.4674	−	19.7371i	−2.66825	−	0.804425i
$603$	7.90397	−	5.74257i	0.321875	−	0.233856i
$604$		−	57.7971i		−	2.35173i
$605$	23.8267	+	17.4805i	0.968694	+	0.710684i
$606$	25.4199			1.03261
$607$	−3.13251	+	2.27591i	−0.127145	+	0.0923761i	−0.649540	−	0.760327i	$-0.725039\pi$
$607$	−3.13251	+	2.27591i	−0.127145	+	0.0923761i	0.522395	+	0.852703i	$0.325039\pi$
$608$	−3.16495	+	1.02835i	−0.128356	+	0.0417053i
$609$	8.26248	+	10.8763i	0.334812	+	0.440732i
$610$	−80.3076	−	58.3469i	−3.25156	−	2.36240i
$611$	−1.79156	+	2.46587i	−0.0724788	+	0.0997585i
$612$	−3.29968	+	10.1554i	−0.133382	+	0.410506i
$613$	5.84418	−	1.89889i	0.236044	−	0.0766954i	−0.188606	−	0.982053i	$-0.560397\pi$
$613$	5.84418	−	1.89889i	0.236044	−	0.0766954i	0.424650	+	0.905357i	$0.360397\pi$
$614$	−4.12730	−	5.68074i	−0.166564	−	0.229256i
$615$	−21.6719			−0.873896
$616$	43.5170	−	7.74383i	1.75335	−	0.312008i
$617$	11.1535			0.449023			0.224511	−	0.974471i	$-0.427921\pi$
$617$	11.1535			0.449023			0.224511	+	0.974471i	$0.427921\pi$
$618$	8.45763	+	11.6409i	0.340216	+	0.468267i
$619$	−25.7702	+	8.37324i	−1.03579	+	0.336549i	−0.777078	−	0.629405i	$-0.783299\pi$
$619$	−25.7702	+	8.37324i	−1.03579	+	0.336549i	−0.258714	+	0.965954i	$0.583299\pi$
$620$	−13.3031	+	40.9427i	−0.534264	+	1.64430i
$621$	−2.50759	+	3.45140i	−0.100626	+	0.138500i
$622$	−58.5699	−	42.5535i	−2.34844	−	1.70624i
$623$	37.2414	−	28.2913i	1.49205	−	1.13347i
$624$	−12.4769	+	4.05398i	−0.499475	+	0.162289i
$625$	25.2171	−	18.3213i	1.00868	−	0.732851i
$626$	9.32301			0.372623
$627$	22.7131	+	3.65141i	0.907075	+	0.145823i
$628$		−	24.8919i		−	0.993296i
$629$	−4.96035	+	3.60390i	−0.197782	+	0.143697i
$630$	16.7362	+	5.04562i	0.666784	+	0.201022i
$631$	11.4727	−	35.3094i	0.456721	−	1.40564i	−0.412381	−	0.911011i	$-0.635303\pi$
$631$	11.4727	−	35.3094i	0.456721	−	1.40564i	0.869102	−	0.494632i	$-0.164697\pi$
$632$	4.34258	+	3.15507i	0.172739	+	0.125502i
$633$	−3.47607	−	2.52551i	−0.138161	−	0.100380i
$634$	7.62670	+	2.47806i	0.302895	+	0.0984165i
$635$	15.1738	+	46.7001i	0.602153	+	1.85324i
$636$	−15.8170	−	21.7703i	−0.627187	−	0.863249i
$637$	7.47515	+	20.0508i	0.296176	+	0.794442i
$638$	−37.4748	−	19.2040i	−1.48364	−	0.760292i
$639$	−0.0700037			−0.00276930
$640$	−41.6553	+	30.2643i	−1.64657	+	1.19630i
$641$	−4.64925	−	14.3089i	−0.183634	−	0.565169i	0.816288	−	0.577646i	$-0.196028\pi$
$641$	−4.64925	−	14.3089i	−0.183634	−	0.565169i	−0.999922	+	0.0124768i	$0.996028\pi$
$642$	1.33458	+	0.433632i	0.0526717	+	0.0171141i
$643$	24.3633	−	33.5333i	0.960796	−	1.32242i	0.0142347	−	0.999899i	$-0.495469\pi$
$643$	24.3633	−	33.5333i	0.960796	−	1.32242i	0.946561	−	0.322524i	$-0.104531\pi$
$644$	43.1451	−	15.0441i	1.70016	−	0.592822i
$645$	26.8500	+	8.72410i	1.05722	+	0.343511i
$646$	42.7926	−	13.9042i	1.68365	−	0.547052i
$647$	23.1709	+	31.8920i	0.910941	+	1.25380i	0.966844	+	0.255367i	$0.0821963\pi$
$647$	23.1709	+	31.8920i	0.910941	+	1.25380i	−0.0559028	+	0.998436i	$0.517804\pi$
$648$		−	5.03713i		−	0.197877i
$649$	−0.604114	+	0.306049i	−0.0237136	+	0.0120135i
$650$			16.6691i			0.653815i
$651$	−0.223532	−	10.4707i	−0.00876090	−	0.410378i
$652$	1.33260	+	4.10134i	0.0521888	+	0.160621i
$653$	7.38578	−	22.7311i	0.289028	−	0.889536i	−0.696134	−	0.717911i	$-0.745098\pi$
$653$	7.38578	−	22.7311i	0.289028	−	0.889536i	0.985162	−	0.171625i	$-0.0549017\pi$
$654$	15.4319	−	21.2402i	0.603436	−	0.830558i
$655$	6.27808	−	8.64104i	0.245305	−	0.337633i
$656$	10.6980	−	32.9249i	0.417685	−	1.28550i
$657$	−4.49716	−	13.8408i	−0.175451	−	0.539982i
$658$	0.138467	+	6.48607i	0.00539801	+	0.252854i
$659$			3.29585i			0.128388i	0.997937	+	0.0641940i	$0.0204476\pi$
$659$			3.29585i			0.128388i	−0.997937	+	0.0641940i	$0.979552\pi$
$660$	−35.6386	+	5.55991i	−1.38723	+	0.216419i
$661$		−	2.42391i		−	0.0942793i	−0.998888	−	0.0471396i	$-0.984989\pi$
$661$		−	2.42391i		−	0.0942793i	0.998888	−	0.0471396i	$-0.0150106\pi$
$662$	−29.3248	−	40.3621i	−1.13974	−	1.56872i
$663$	7.66881	−	2.49175i	0.297832	−	0.0967715i
$664$	21.9041	+	7.11708i	0.850045	+	0.276196i
$665$	−16.2321	−	46.5521i	−0.629454	−	1.80521i
$666$	3.36014	−	4.62484i	0.130203	−	0.179209i
$667$	−20.9463	−	6.80587i	−0.811045	−	0.263524i
$668$	28.2708	+	87.0086i	1.09383	+	3.36646i
$669$	−0.130869	+	0.0950817i	−0.00505968	+	0.00367607i
$670$	64.5483			2.49372
$671$	−49.2352	+	7.68111i	−1.90071	+	0.296526i
$672$	−0.724028	+	1.04263i	−0.0279300	+	0.0402204i
$673$	−21.7158	−	29.8892i	−0.837083	−	1.15215i	−0.986563	−	0.163381i	$-0.947760\pi$
$673$	−21.7158	−	29.8892i	−0.837083	−	1.15215i	0.149480	−	0.988765i	$-0.452240\pi$
$674$	23.7829	+	73.1961i	0.916081	+	2.81941i
$675$	−2.10869	−	0.685154i	−0.0811633	−	0.0263716i
$676$	−11.9698	−	8.69655i	−0.460376	−	0.334483i
$677$	−0.266327	−	0.193498i	−0.0102358	−	0.00743674i	0.582656	−	0.812719i	$-0.302014\pi$
$677$	−0.266327	−	0.193498i	−0.0102358	−	0.00743674i	−0.592891	+	0.805282i	$0.702014\pi$
$678$	2.65177	−	8.16132i	0.101841	−	0.313433i
$679$	5.36745	−	17.8037i	0.205984	−	0.683242i
$680$	−28.8771	+	20.9804i	−1.10739	+	0.804563i
$681$		−	10.0088i		−	0.383538i
$682$	14.5914	+	28.8022i	0.558735	+	1.10289i
$683$	11.5321			0.441262			0.220631	−	0.975357i	$-0.429188\pi$
$683$	11.5321			0.441262			0.220631	+	0.975357i	$0.429188\pi$
$684$	−22.7164	+	16.5044i	−0.868584	+	0.631063i
$685$	34.3114	−	11.1485i	1.31097	−	0.425961i
$686$	38.4860	+	24.3590i	1.46940	+	0.930031i
$687$	−0.843705	−	0.612988i	−0.0321894	−	0.0233869i
$688$	−26.5081	+	36.4852i	−1.01061	+	1.39099i
$689$	−6.27945	+	19.3262i	−0.239228	+	0.736268i
$690$	−26.8065	+	8.70997i	−1.02051	+	0.331583i
$691$	24.2181	+	33.3333i	0.921299	+	1.26806i	0.963158	+	0.268936i	$0.0866722\pi$
$691$	24.2181	+	33.3333i	0.921299	+	1.26806i	−0.0418584	+	0.999124i	$0.513328\pi$
$692$	37.3387			1.41940
$693$	7.74134	−	4.13178i	0.294069	−	0.156953i
$694$	−33.3063			−1.26429
$695$	−0.296784	−	0.408488i	−0.0112576	−	0.0154948i
$696$	24.7317	−	8.03581i	0.937452	−	0.304597i
$697$	−6.57542	+	20.2371i	−0.249062	+	0.766533i
$698$	48.3873	−	66.5994i	1.83149	−	2.52082i
$699$	14.6352	+	10.6331i	0.553556	+	0.402182i
$700$	14.3652	+	18.9097i	0.542955	+	0.714721i
$701$	6.76427	−	2.19785i	0.255483	−	0.0830115i	−0.178475	−	0.983944i	$-0.557116\pi$
$701$	6.76427	−	2.19785i	0.255483	−	0.0830115i	0.433958	+	0.900933i	$0.357116\pi$
$702$	−6.08225	+	4.41901i	−0.229560	+	0.166785i
$703$	−16.1231			−0.608093
$704$	−3.89716	+	24.2418i	−0.146880	+	0.913646i
$705$		−	2.67857i		−	0.100881i
$706$	−34.8990	+	25.3556i	−1.31344	+	0.954271i
$707$	−26.1830	−	7.89366i	−0.984714	−	0.296872i
$708$	0.255431	−	0.786136i	0.00959969	−	0.0295448i
$709$	−12.7647	−	9.27407i	−0.479387	−	0.348295i	0.321701	−	0.946841i	$-0.395745\pi$
$709$	−12.7647	−	9.27407i	−0.479387	−	0.348295i	−0.801088	+	0.598546i	$0.795745\pi$
$710$	−0.374176	−	0.271855i	−0.0140426	−	0.0102025i
$711$	1.01348	+	0.329298i	0.0380083	+	0.0123496i
$712$	−27.5152	−	84.6831i	−1.03118	−	3.17364i
$713$	9.92613	+	13.6621i	0.371737	+	0.511652i
$714$	9.78943	−	14.0972i	0.366360	−	0.527575i
$715$	19.2154	+	19.3047i	0.718616	+	0.721957i
$716$	−75.2349			−2.81166
$717$	11.3187	−	8.22355i	0.422706	−	0.307114i
$718$	−25.1135	−	77.2915i	−0.937228	−	2.88449i
$719$	10.0370	+	3.26123i	0.374318	+	0.121623i	0.490133	−	0.871647i	$-0.336948\pi$
$719$	10.0370	+	3.26123i	0.374318	+	0.121623i	−0.115815	+	0.993271i	$0.536948\pi$
$720$	6.77656	−	9.32713i	0.252547	−	0.347602i
$721$	−5.09667	−	14.6168i	−0.189810	−	0.544356i
$722$	68.0884	+	22.1233i	2.53399	+	0.823343i
$723$	7.33739	−	2.38406i	0.272880	−	0.0886642i
$724$	−36.5953	−	50.3691i	−1.36005	−	1.87195i
$725$		−	11.4464i		−	0.425109i
$726$	−16.0023	+	21.8119i	−0.593902	+	0.809514i
$727$			19.5152i			0.723780i	0.932221	+	0.361890i	$0.117868\pi$
$727$			19.5152i			0.723780i	−0.932221	+	0.361890i	$0.882132\pi$
$728$	40.7312	−	0.869544i	1.50960	−	0.0322274i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	29.7122	−	91.4448i	1.09970	−	3.38452i
$731$	16.2930	−	22.4254i	0.602618	−	0.829432i
$732$	35.7504	−	49.2062i	1.32137	−	1.81871i
$733$	−3.83626	+	11.8068i	−0.141696	+	0.436094i	−0.996571	−	0.0827386i	$-0.973633\pi$
$733$	−3.83626	+	11.8068i	−0.141696	+	0.436094i	0.854876	+	0.518833i	$0.173633\pi$
$734$	−0.223810	−	0.688817i	−0.00826099	−	0.0254247i
$735$	−15.6718	−	10.3942i	−0.578062	−	0.383395i
$736$		−	2.04680i		−	0.0754462i
$737$	22.9654	−	22.8591i	0.845941	−	0.842027i
$738$		−	19.8393i		−	0.730293i
$739$	11.9182	+	16.4040i	0.438419	+	0.603433i	0.969860	−	0.243663i	$-0.0783491\pi$
$739$	11.9182	+	16.4040i	0.438419	+	0.603433i	−0.531441	+	0.847096i	$0.678349\pi$
$740$	24.0424	−	7.81185i	0.883817	−	0.287169i
$741$	20.1661	+	6.55235i	0.740819	+	0.240707i
$742$	14.2406	+	40.8406i	0.522788	+	1.49931i
$743$	−22.7996	+	31.3810i	−0.836436	+	1.15126i	0.150255	+	0.988647i	$0.451991\pi$
$743$	−22.7996	+	31.3810i	−0.836436	+	1.15126i	−0.986691	+	0.162608i	$0.948009\pi$
$744$	−18.9633	−	6.16155i	−0.695228	−	0.225893i
$745$	2.91866	+	8.98271i	0.106931	+	0.329101i
$746$	53.5120	−	38.8787i	1.95921	−	1.42345i
$747$	4.57232			0.167292
$748$	−5.62120	+	34.9659i	−0.205531	+	1.27848i
$749$	−1.23999	−	0.861077i	−0.0453082	−	0.0314631i
$750$	10.8068	+	14.8743i	0.394609	+	0.543132i
$751$	5.62466	+	17.3109i	0.205247	+	0.631684i	0.999703	+	0.0243632i	$0.00775583\pi$
$751$	5.62466	+	17.3109i	0.205247	+	0.631684i	−0.794456	+	0.607321i	$0.792244\pi$
$752$	4.06941	+	1.32223i	0.148396	+	0.0482168i
$753$	−11.6182	−	8.44110i	−0.423390	−	0.307611i
$754$	−31.3999	−	22.8134i	−1.14352	−	0.830814i
$755$	11.8526	−	36.4784i	0.431359	−	1.32759i
$756$	−3.09156	+	10.2546i	−0.112439	+	0.372957i
$757$	8.40592	−	6.10726i	0.305518	−	0.221972i	−0.424453	−	0.905450i	$-0.639533\pi$
$757$	8.40592	−	6.10726i	0.305518	−	0.221972i	0.729971	+	0.683478i	$0.239533\pi$
$758$		−	27.1171i		−	0.984939i
$759$	−6.45284	+	12.5921i	−0.234223	+	0.457066i
$760$	−93.8618			−3.40473
$761$	25.5423	−	18.5576i	0.925908	−	0.672712i	−0.0190795	−	0.999818i	$-0.506074\pi$
$761$	25.5423	−	18.5576i	0.925908	−	0.672712i	0.944987	+	0.327106i	$0.106074\pi$
$762$	−42.7509	+	13.8906i	−1.54870	+	0.503204i
$763$	−22.4909	+	17.0858i	−0.814226	+	0.618546i
$764$	24.8264	+	18.0374i	0.898187	+	0.652571i
$765$	−4.16516	+	5.73285i	−0.150592	+	0.207272i
$766$	10.3856	−	31.9635i	0.375246	−	1.15489i
$767$	−0.593650	+	0.192888i	−0.0214354	+	0.00696480i
$768$	−19.0023	−	26.1544i	−0.685687	−	0.943767i
$769$	49.4893			1.78463			0.892315	−	0.451412i	$-0.149080\pi$
$769$	49.4893			1.78463			0.892315	+	0.451412i	$0.149080\pi$
$770$	57.4237	+	7.97827i	2.06940	+	0.287517i
$771$	−12.5986			−0.453728
$772$	30.4203	+	41.8699i	1.09485	+	1.50693i
$773$	−25.1807	+	8.18170i	−0.905686	+	0.294275i	−0.724582	−	0.689189i	$-0.757967\pi$
$773$	−25.1807	+	8.18170i	−0.905686	+	0.294275i	−0.181104	+	0.983464i	$0.557967\pi$
$774$	−7.98636	+	24.5795i	−0.287064	+	0.883491i
$775$	−5.15880	+	7.10048i	−0.185309	+	0.255057i
$776$	−28.6412	−	20.8091i	−1.02816	−	0.747002i
$777$	−4.89717	+	3.72025i	−0.175685	+	0.133463i
$778$	57.9461	−	18.8278i	2.07747	−	0.675011i
$779$	−45.2680	+	32.8892i	−1.62190	+	1.17838i
$780$	−33.2460			−1.19040
$781$	−0.229401	+	0.0357885i	−0.00820862	+	0.00128061i
$782$			27.6744i			0.989634i
$783$	4.17659	−	3.03447i	0.149259	−	0.108443i
$784$	23.5274	−	18.6783i	0.840264	−	0.667083i
$785$	5.10463	−	15.7104i	0.182192	−	0.560730i
$786$	7.91032	+	5.74719i	0.282152	+	0.204995i
$787$	−0.156727	−	0.113869i	−0.00558671	−	0.00405899i	0.584988	−	0.811042i	$-0.301099\pi$
$787$	−0.156727	−	0.113869i	−0.00558671	−	0.00405899i	−0.590575	+	0.806983i	$0.701099\pi$
$788$	−14.5244	−	4.71928i	−0.517412	−	0.168117i
$789$	−1.21234	−	3.73121i	−0.0431606	−	0.132835i
$790$	4.13831	+	5.69589i	0.147234	+	0.202651i
$791$	−5.26572	+	7.58286i	−0.187227	+	0.269616i
$792$	−2.57517	−	16.5066i	−0.0915046	−	0.586537i
$793$	−45.9299			−1.63102
$794$	28.1604	−	20.4597i	0.999374	−	0.726087i
$795$	−5.51839	−	16.9839i	−0.195717	−	0.602356i
$796$	−30.9003	−	10.0401i	−1.09523	−	0.355862i
$797$	−23.5715	+	32.4434i	−0.834945	+	1.14920i	0.152037	+	0.988375i	$0.451417\pi$
$797$	−23.5715	+	32.4434i	−0.834945	+	1.14920i	−0.986982	+	0.160829i	$0.948583\pi$
$798$	42.6155	−	14.8595i	1.50857	−	0.526019i
$799$	−2.50123	−	0.812699i	−0.0884872	−	0.0287512i
$800$	1.01170	−	0.328721i	0.0357689	−	0.0116220i
$801$	−10.3903	−	14.3010i	−0.367122	−	0.505300i
$802$			23.2635i			0.821464i
$803$	−21.8131	−	43.0571i	−0.769766	−	1.51945i
$804$			39.5502i			1.39483i
$805$	30.3160	−	0.647197i	1.06850	−	0.0228107i
$806$	9.19630	+	28.3033i	0.323926	+	0.996941i
$807$	−2.25517	+	6.94070i	−0.0793857	+	0.244324i
$808$	−30.6030	+	42.1214i	−1.07661	+	1.48182i
$809$	−18.5406	+	25.5189i	−0.651852	+	0.897197i	−0.999178	−	0.0405472i	$-0.987090\pi$
$809$	−18.5406	+	25.5189i	−0.651852	+	0.897197i	0.347326	+	0.937745i	$0.387090\pi$
$810$	2.04164	−	6.28353i	0.0717360	−	0.220781i
$811$	3.04647	+	9.37607i	0.106976	+	0.329238i	0.990189	−	0.139734i	$-0.0446246\pi$
$811$	3.04647	+	9.37607i	0.106976	+	0.329238i	−0.883213	+	0.468972i	$0.844625\pi$
$812$	−55.2809	+	1.18016i	−1.93998	+	0.0414154i
$813$		−	23.5230i		−	0.824988i
$814$	8.64675	−	16.8734i	0.303068	−	0.591411i
$815$			2.86182i			0.100245i
$816$	−6.65354	−	9.15781i	−0.232921	−	0.320588i
$817$	69.3236	−	22.5246i	2.42533	−	0.788037i
$818$	−16.0912	−	5.22836i	−0.562616	−	0.182805i
$819$	7.63707	−	2.66295i	0.266861	−	0.0930509i
$820$	51.5676	−	70.9767i	1.80082	−	2.47861i
$821$	0.208305	+	0.0676823i	0.00726988	+	0.00236213i	0.312650	−	0.949869i	$-0.398783\pi$
$821$	0.208305	+	0.0676823i	0.00726988	+	0.00236213i	−0.305380	+	0.952231i	$0.598783\pi$
$822$	10.2057	+	31.4099i	0.355965	+	1.09555i
$823$	3.15735	−	2.29395i	0.110058	−	0.0799621i	−0.531395	−	0.847124i	$-0.678332\pi$
$823$	3.15735	−	2.29395i	0.110058	−	0.0799621i	0.641453	+	0.767162i	$0.278332\pi$
$824$	−29.4714			−1.02668
$825$	−7.26041	−	1.16720i	−0.252775	−	0.0406367i
$826$	−0.757808	+	1.09128i	−0.0263675	+	0.0379704i
$827$	5.43703	+	7.48344i	0.189064	+	0.260225i	0.893018	−	0.450021i	$-0.148584\pi$
$827$	5.43703	+	7.48344i	0.189064	+	0.260225i	−0.703954	+	0.710246i	$0.748584\pi$
$828$	−5.33679	−	16.4250i	−0.185466	−	0.570807i
$829$	−34.2970	−	11.1438i	−1.19118	−	0.387039i	−0.354673	−	0.934990i	$-0.615408\pi$
$829$	−34.2970	−	11.1438i	−1.19118	−	0.387039i	−0.836510	+	0.547951i	$0.815408\pi$
$830$	24.4394	+	17.7563i	0.848305	+	0.616330i
$831$	−10.6405	−	7.73078i	−0.369115	−	0.268178i
$832$	−6.99334	+	21.5233i	−0.242451	+	0.746186i
$833$	−14.4609	+	11.4805i	−0.501041	+	0.397775i
$834$	0.373945	−	0.271687i	0.0129486	−	0.00940774i
$835$			60.7126i			2.10105i
$836$	−66.0037	+	65.6983i	−2.28279	+	2.27222i
$837$	−3.95844			−0.136824
$838$	12.1795	−	8.84894i	0.420735	−	0.305682i
$839$	28.2941	−	9.19330i	0.976819	−	0.317388i	0.223254	−	0.974760i	$-0.428332\pi$
$839$	28.2941	−	9.19330i	0.976819	−	0.317388i	0.753566	+	0.657373i	$0.228332\pi$
$840$	−28.5093	+	21.6578i	−0.983664	+	0.747264i
$841$	−1.89964	−	1.38017i	−0.0655047	−	0.0475920i
$842$	−10.8341	+	14.9119i	−0.373368	+	0.513897i
$843$	−6.03808	+	18.5833i	−0.207963	+	0.640043i
$844$	16.5424	−	5.37495i	0.569413	−	0.185013i
$845$	−5.77126	−	7.94345i	−0.198537	−	0.273263i
$846$	2.45206			0.0843037
$847$	23.2560	−	17.4974i	0.799084	−	0.601219i
$848$	28.5267			0.979611
$849$	−3.12384	−	4.29960i	−0.107210	−	0.147562i
$850$	−13.6790	+	4.44456i	−0.469184	+	0.152447i
$851$	3.06440	−	9.43126i	0.105046	−	0.323299i
$852$	0.166572	−	0.229266i	0.00570665	−	0.00785453i
$853$	−24.9750	−	18.1454i	−0.855128	−	0.621287i	0.0714273	−	0.997446i	$-0.477245\pi$
$853$	−24.9750	−	18.1454i	−0.855128	−	0.621287i	−0.926555	+	0.376159i	$0.877245\pi$
$854$	−77.8454	+	59.1371i	−2.66382	+	2.02363i
$855$	−17.7220	+	5.75822i	−0.606079	+	0.196927i
$856$	−2.32523	+	1.68938i	−0.0794749	+	0.0577419i
$857$	−22.2373			−0.759612			−0.379806	−	0.925066i	$-0.624009\pi$
$857$	−22.2373			−0.759612			−0.379806	+	0.925066i	$0.624009\pi$
$858$	−17.6723	+	17.5905i	−0.603321	+	0.600530i
$859$			1.83049i			0.0624554i	0.999512	+	0.0312277i	$0.00994170\pi$
$859$			1.83049i			0.0624554i	−0.999512	+	0.0312277i	$0.990058\pi$
$860$	−92.4606	+	67.1766i	−3.15288	+	2.29070i
$861$	−6.16070	+	20.4348i	−0.209956	+	0.696417i
$862$	−24.5145	+	75.4479i	−0.834968	+	2.56977i
$863$	−9.15075	−	6.64841i	−0.311495	−	0.226314i	0.421043	−	0.907041i	$-0.361664\pi$
$863$	−9.15075	−	6.64841i	−0.311495	−	0.226314i	−0.732538	+	0.680726i	$0.761664\pi$
$864$	0.388147	+	0.282006i	0.0132050	+	0.00959402i
$865$	23.5662	+	7.65711i	0.801274	+	0.260350i
$866$	5.25277	+	16.1664i	0.178496	+	0.549355i
$867$	−5.90280	−	8.12451i	−0.200470	−	0.275923i
$868$	34.8239	+	24.1825i	1.18200	+	0.820809i
$869$	3.48950	+	0.560979i	0.118373	+	0.0190299i
$870$	34.1084			1.15638
$871$	24.1623	−	17.5550i	0.818710	−	0.594827i
$872$	16.6171	+	51.1420i	0.562724	+	1.73189i
$873$	−6.68432	−	2.17187i	−0.226230	−	0.0735065i
$874$	−42.7750	+	58.8747i	−1.44689	+	1.99147i
$875$	−6.51231	−	18.6767i	−0.220156	−	0.631387i
$876$	56.0303	+	18.2053i	1.89309	+	0.615102i
$877$	19.7581	−	6.41979i	0.667183	−	0.216781i	0.0442074	−	0.999022i	$-0.485924\pi$
$877$	19.7581	−	6.41979i	0.667183	−	0.216781i	0.622975	+	0.782242i	$0.285924\pi$
$878$	18.2014	+	25.0521i	0.614269	+	0.845469i
$879$		−	12.6008i		−	0.425016i
$880$	17.4383	−	34.0293i	0.587845	−	1.14713i
$881$			11.0591i			0.372592i	0.982494	+	0.186296i	$0.0596483\pi$
$881$			11.0591i			0.372592i	−0.982494	+	0.186296i	$0.940352\pi$
$882$	9.51521	−	14.3465i	0.320394	−	0.483072i
$883$	6.60030	+	20.3136i	0.222118	+	0.683608i	0.998571	+	0.0534339i	$0.0170166\pi$
$883$	6.60030	+	20.3136i	0.222118	+	0.683608i	−0.776454	+	0.630174i	$0.782983\pi$
$884$	−10.0871	+	31.0448i	−0.339265	+	1.04415i
$885$	0.322429	−	0.443785i	0.0108383	−	0.0149177i
$886$	−54.9925	+	75.6906i	−1.84751	+	2.54288i
$887$	−8.62408	+	26.5422i	−0.289568	+	0.891199i	0.695424	+	0.718600i	$0.255217\pi$
$887$	−8.62408	+	26.5422i	−0.289568	+	0.891199i	−0.984992	+	0.172600i	$0.944783\pi$
$888$	3.61819	+	11.1357i	0.121419	+	0.373688i
$889$	48.3478	−	1.03215i	1.62153	−	0.0346171i
$890$		−	116.790i		−	3.91480i
$891$	−1.49886	−	2.95862i	−0.0502137	−	0.0991174i
$892$		−	0.654846i		−	0.0219259i
$893$	−4.06499	−	5.59497i	−0.136030	−	0.187229i
$894$	−8.22310	+	2.67185i	−0.275022	+	0.0893600i
$895$	−47.4842	−	15.4285i	−1.58722	−	0.515719i
$896$	16.6954	+	47.8808i	0.557754	+	1.59959i
$897$	−7.66566	+	10.5509i	−0.255949	+	0.352283i
$898$	−5.89808	−	1.91640i	−0.196821	−	0.0639511i
$899$	−6.31496	−	19.4355i	−0.210616	−	0.648209i
$900$	7.26146	−	5.27576i	0.242049	−	0.175859i
$901$	−17.5337			−0.584133
$902$	−10.1426	−	65.0130i	−0.337711	−	2.16470i
$903$	15.8588	−	22.8374i	0.527748	−	0.759980i
$904$	10.3310	+	14.2194i	0.343604	+	0.472931i
$905$	−12.7677	−	39.2949i	−0.424412	−	1.30621i
$906$	33.3937	+	10.8503i	1.10943	+	0.360476i
$907$	13.2683	+	9.64000i	0.440568	+	0.320091i	0.785860	−	0.618404i	$-0.212220\pi$
$907$	13.2683	+	9.64000i	0.440568	+	0.320091i	−0.345293	+	0.938495i	$0.612220\pi$
$908$	32.7794	+	23.8156i	1.08782	+	0.790349i
$909$	−3.19407	+	9.83032i	−0.105940	+	0.326051i
$910$	51.1622	+	15.4244i	1.69601	+	0.511314i
$911$	−28.9893	+	21.0619i	−0.960457	+	0.697813i	−0.953257	−	0.302161i	$-0.902292\pi$
$911$	−28.9893	+	21.0619i	−0.960457	+	0.697813i	−0.00720031	+	0.999974i	$0.502292\pi$
$912$		−	29.7665i		−	0.985666i
$913$	14.9834	−	2.33754i	0.495879	−	0.0773612i
$914$	103.274			3.41601
$915$	32.6545	−	23.7249i	1.07953	−	0.784322i
$916$	4.01514	−	1.30460i	0.132664	−	0.0431051i
$917$	−6.36312	−	8.37612i	−0.210129	−	0.276604i
$918$	−5.24806	−	3.81294i	−0.173212	−	0.125846i
$919$	27.0888	−	37.2845i	0.893576	−	1.22990i	−0.0788964	−	0.996883i	$-0.525140\pi$
$919$	27.0888	−	37.2845i	0.893576	−	1.22990i	0.972472	−	0.233019i	$-0.0748604\pi$
$920$	17.8397	−	54.9049i	0.588157	−	1.81016i
$921$	2.71544	−	0.882301i	0.0894769	−	0.0290728i
$922$	−13.1404	−	18.0862i	−0.432755	−	0.595636i
$923$	−0.214000			−0.00704391
$924$	−4.88847	+	35.1848i	−0.160819	+	1.15749i
$925$	5.15385			0.169458
$926$	−19.3859	−	26.6823i	−0.637059	−	0.876836i
$927$	−5.56447	+	1.80801i	−0.182761	+	0.0593827i
$928$	−0.765395	+	2.35564i	−0.0251253	+	0.0773278i
$929$	−23.7884	+	32.7419i	−0.780471	+	1.07423i	0.214758	+	0.976667i	$0.431104\pi$
$929$	−23.7884	+	32.7419i	−0.780471	+	1.07423i	−0.995230	+	0.0975596i	$0.968896\pi$
$930$	−21.1582	−	15.3723i	−0.693805	−	0.504079i
$931$	−48.5091	+	2.07213i	−1.58982	+	0.0679112i
$932$	−69.6481	+	22.6300i	−2.28140	+	0.741272i
$933$	23.8156	−	17.3030i	0.779688	−	0.566476i
$934$	−1.61374			−0.0528033
$935$	−10.7183	+	20.9158i	−0.350526	+	0.684021i
$936$		−	15.3984i		−	0.503314i
$937$	19.8943	−	14.4541i	0.649918	−	0.472193i	−0.213325	−	0.976981i	$-0.568429\pi$
$937$	19.8943	−	14.4541i	0.649918	−	0.472193i	0.863243	+	0.504788i	$0.168429\pi$
$938$	18.3492	−	60.8638i	0.599123	−	1.98727i
$939$	−1.17146	+	3.60537i	−0.0382290	+	0.117657i
$940$	8.77248	+	6.37358i	0.286127	+	0.207883i
$941$	29.6202	+	21.5203i	0.965590	+	0.701542i	0.954442	−	0.298396i	$-0.0964515\pi$
$941$	29.6202	+	21.5203i	0.965590	+	0.701542i	0.0111477	+	0.999938i	$0.496452\pi$
$942$	14.3819	+	4.67297i	0.468588	+	0.152253i
$943$	−10.6349	−	32.7308i	−0.346319	−	1.06586i
$944$	0.515056	+	0.708914i	0.0167637	+	0.0230732i
$945$	−4.05416	+	5.83817i	−0.131882	+	0.189916i
$946$	−13.6052	+	84.6296i	−0.442344	+	2.75154i
$947$	14.3694			0.466944			0.233472	−	0.972364i	$-0.424991\pi$
$947$	14.3694			0.466944			0.233472	+	0.972364i	$0.424991\pi$
$948$	−3.49000	+	2.53564i	−0.113350	+	0.0823536i
$949$	−13.7477	−	42.3112i	−0.446271	−	1.37348i
$950$	−35.9705	−	11.6875i	−1.16704	−	0.379193i
$951$	−1.91662	+	2.63800i	−0.0621507	+	0.0855431i
$952$	11.5739	+	33.1929i	0.375113	+	1.07579i
$953$	22.2166	+	7.21861i	0.719666	+	0.233834i	0.645878	−	0.763440i	$-0.276491\pi$
$953$	22.2166	+	7.21861i	0.719666	+	0.233834i	0.0737875	+	0.997274i	$0.476491\pi$
$954$	15.5477	−	5.05174i	0.503374	−	0.163556i
$955$	11.9701	+	16.4754i	0.387343	+	0.533132i
$956$			56.6372i			1.83178i
$957$	12.1353	−	12.0791i	0.392278	−	0.390463i
$958$			47.0237i			1.51927i
$959$	−0.758338	−	35.5221i	−0.0244880	−	1.14707i
$960$	−6.14576	−	18.9147i	−0.198354	−	0.610470i
$961$	4.73746	−	14.5804i	0.152821	−	0.470335i
$962$	10.2719	−	14.1381i	0.331180	−	0.455830i
$963$	−0.335386	+	0.461619i	−0.0108077	+	0.0148755i
$964$	−9.65114	+	29.7031i	−0.310842	+	0.956674i
$965$	10.6133	+	32.6644i	0.341654	+	1.05150i
$966$	0.592468	+	27.7524i	0.0190623	+	0.892918i
$967$			26.8562i			0.863636i	0.901961	+	0.431818i	$0.142128\pi$
$967$			26.8562i			0.863636i	−0.901961	+	0.431818i	$0.857872\pi$
$968$	−16.8776	−	52.7754i	−0.542466	−	1.69627i
$969$			18.2957i			0.587743i
$970$	−27.2940	−	37.5669i	−0.876356	−	1.20620i
$971$	6.61763	−	2.15020i	0.212370	−	0.0690031i	−0.200900	−	0.979612i	$-0.564387\pi$
$971$	6.61763	−	2.15020i	0.212370	−	0.0690031i	0.413270	+	0.910609i	$0.364387\pi$
$972$	3.85006	+	1.25096i	0.123491	+	0.0401246i
$973$	−0.469538	+	0.163722i	−0.0150527	+	0.00524867i
$974$	28.7705	−	39.5992i	0.921867	−	1.26884i
$975$	−6.44622	−	2.09451i	−0.206444	−	0.0670779i
$976$	19.9246	+	61.3216i	0.637771	+	1.96286i
$977$	9.75213	−	7.08534i	0.311998	−	0.226680i	−0.420755	−	0.907174i	$-0.638235\pi$
$977$	9.75213	−	7.08534i	0.311998	−	0.226680i	0.732753	+	0.680494i	$0.238235\pi$
$978$	−2.61982			−0.0837725
$979$	−41.3599	−	41.5522i	−1.32187	−	1.32801i
$980$	71.3319	−	26.5933i	2.27862	−	0.849491i
$981$	6.27491	+	8.63667i	0.200342	+	0.275748i
$982$	16.4430	+	50.6064i	0.524718	+	1.61492i
$983$	−38.9151	−	12.6443i	−1.24120	−	0.403290i	−0.386441	−	0.922314i	$-0.626296\pi$
$983$	−38.9151	−	12.6443i	−1.24120	−	0.403290i	−0.854760	+	0.519024i	$0.826296\pi$
$984$	32.8741	+	23.8844i	1.04799	+	0.761407i
$985$	−8.19925	−	5.95711i	−0.261250	−	0.189809i
$986$	10.3487	−	31.8502i	0.329571	−	1.01432i
$987$	−2.52568	−	0.761441i	−0.0803931	−	0.0242369i
$988$	−69.4438	+	50.4539i	−2.20930	+	1.60515i
$989$			44.8323i			1.42558i
$990$	3.47806	−	21.6348i	0.110540	−	0.687599i
$991$	−61.2430			−1.94545			−0.972725	−	0.231963i	$-0.925485\pi$
$991$	−61.2430			−1.94545			−0.972725	+	0.231963i	$0.925485\pi$
$992$	1.53646	−	1.11630i	0.0487826	−	0.0354426i
$993$	19.2934	−	6.26881i	0.612258	−	0.198935i
$994$	−0.362704	+	0.275537i	−0.0115043	+	0.00873950i
$995$	−17.4437	−	12.6736i	−0.553001	−	0.401779i
$996$	−10.8797	+	14.9746i	−0.344736	+	0.474488i
$997$	−1.92220	+	5.91591i	−0.0608765	+	0.187359i	−0.976870	−	0.213835i	$-0.931405\pi$
$997$	−1.92220	+	5.91591i	−0.0608765	+	0.187359i	0.915993	+	0.401194i	$0.131405\pi$
$998$	52.5454	−	17.0730i	1.66330	−	0.540438i
$999$	1.36630	+	1.88055i	0.0432277	+	0.0594978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.118.2	yes	64
3.2	odd	2		693.2.bu.f.118.16		64
7.6	odd	2	inner	231.2.w.a.118.1	✓	64
11.7	odd	10	inner	231.2.w.a.139.1	yes	64
21.20	even	2		693.2.bu.f.118.15		64
33.29	even	10		693.2.bu.f.370.15		64
77.62	even	10	inner	231.2.w.a.139.2	yes	64
231.62	odd	10		693.2.bu.f.370.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.118.1	✓	64	7.6	odd	2	inner
231.2.w.a.118.2	yes	64	1.1	even	1	trivial
231.2.w.a.139.1	yes	64	11.7	odd	10	inner
231.2.w.a.139.2	yes	64	77.62	even	10	inner
693.2.bu.f.118.15		64	21.20	even	2
693.2.bu.f.118.16		64	3.2	odd	2
693.2.bu.f.370.15		64	33.29	even	10
693.2.bu.f.370.16		64	231.62	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44554 - 1.98962i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(-1.57908 + 2.17341i) q^{5} +(-1.98962 - 1.44554i) q^{6} +(1.60046 + 2.10678i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.44554 - 1.98962i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(-1.57908 + 2.17341i) q^{5} +(-1.98962 - 1.44554i) q^{6} +(1.60046 + 2.10678i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +6.60689 q^{10} +(2.35064 - 2.33976i) q^{11} +4.04819i q^{12} +(2.47315 - 1.79685i) q^{13} +(1.87815 - 6.22976i) q^{14} +(-0.830170 + 2.55500i) q^{15} +(-3.47187 - 2.52246i) q^{16} +(2.13396 + 1.55041i) q^{17} +(-2.33894 - 0.759968i) q^{18} +(2.14340 + 6.59671i) q^{19} +(-6.39240 - 8.79839i) q^{20} +(2.17316 + 1.50909i) q^{21} +(-8.05320 - 1.29465i) q^{22} -4.26616 q^{23} +(4.07512 - 2.96075i) q^{24} +(-0.685154 - 2.10869i) q^{25} +(-7.15011 - 2.32321i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-10.1133 + 3.52639i) q^{28} +(4.90988 + 1.59532i) q^{29} +(6.28353 - 2.04164i) q^{30} +(-2.32671 - 3.20245i) q^{31} +0.479776i q^{32} +(1.51256 - 2.95164i) q^{33} -6.48696i q^{34} +(-7.10615 + 0.151705i) q^{35} +(1.25096 + 3.85006i) q^{36} +(-0.718304 + 2.21071i) q^{37} +(10.0266 - 13.8004i) q^{38} +(1.79685 - 2.47315i) q^{39} +(-4.18167 + 12.8699i) q^{40} +(2.49284 + 7.67219i) q^{41} +(-0.138876 - 6.50523i) q^{42} -10.5088i q^{43} +(6.06767 + 11.9770i) q^{44} +2.68649i q^{45} +(6.16692 + 8.48804i) q^{46} +(-0.948256 + 0.308107i) q^{47} +(-4.08143 - 1.32614i) q^{48} +(-1.87703 + 6.74365i) q^{49} +(-3.20507 + 4.41139i) q^{50} +(2.50862 + 0.815099i) q^{51} +(3.82417 + 11.7696i) q^{52} +(-5.37779 + 3.90719i) q^{53} -2.45931 q^{54} +(1.37343 + 8.80357i) q^{55} +(10.9465 + 7.60151i) q^{56} +(4.07699 + 5.61150i) q^{57} +(-3.92337 - 12.0749i) q^{58} +(-0.194194 - 0.0630976i) q^{59} +(-8.79839 - 6.39240i) q^{60} +(-12.1551 - 8.83121i) q^{61} +(-3.00829 + 9.25856i) q^{62} +(2.53314 + 0.763690i) q^{63} +(-5.98917 + 4.35138i) q^{64} +8.21255i q^{65} +(-8.05911 + 1.25729i) q^{66} +9.76985 q^{67} +(-8.63867 + 6.27636i) q^{68} +(-4.05736 + 1.31832i) q^{69} +(10.5741 + 13.9193i) q^{70} +(-0.0566342 - 0.0411472i) q^{71} +(2.96075 - 4.07512i) q^{72} +(4.49716 - 13.8408i) q^{73} +(5.43682 - 1.76653i) q^{74} +(-1.30324 - 1.79376i) q^{75} -28.0790 q^{76} +(8.69148 + 1.20757i) q^{77} -7.51807 q^{78} +(0.626363 + 0.862114i) q^{79} +(10.9647 - 3.56265i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6612 - 16.0503i) q^{82} +(3.69908 + 2.68754i) q^{83} +(-8.52864 + 6.47898i) q^{84} +(-6.73937 + 2.18975i) q^{85} +(-20.9086 + 15.1910i) q^{86} +5.16255 q^{87} +(7.61898 - 14.8678i) q^{88} -17.6770i q^{89} +(5.34509 - 3.88343i) q^{90} +(7.74376 + 2.33459i) q^{91} +(5.33679 - 16.4250i) q^{92} +(-3.20245 - 2.32671i) q^{93} +(1.98376 + 1.44129i) q^{94} +(-17.7220 - 5.75822i) q^{95} +(0.148259 + 0.456295i) q^{96} +(-4.13113 - 5.68602i) q^{97} +(16.1306 - 6.01366i) q^{98} +(0.526429 - 3.27458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Introduction

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