LMFDB - Embedded newform 231.2.w.a.118.1

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			118.1
Character	$\chi$	$=$	231.118
Dual form			231.2.w.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44554 - 1.98962i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(1.57908 - 2.17341i) q^{5} +(1.98962 + 1.44554i) q^{6} +(2.53314 - 0.763690i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(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} +(2.53314 - 0.763690i) 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} +(-5.18121 - 3.93603i) 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} +(-0.228600 + 10.7081i) 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} +(2.34020 - 6.71147i) 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} +(6.14393 + 2.14231i) 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} +(5.83355 - 3.86906i) 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} +(1.60046 - 2.10678i) 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} +(-16.7362 + 5.04562i) 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} +(4.16763 - 7.72210i) 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} +(-3.09156 - 10.2546i) 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} +(-4.89260 + 6.44039i) 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	$-0.594882\pi$
$5$	1.57908	−	2.17341i	0.706184	−	0.971980i	0.999871	−	0.0160777i	$-0.00511790\pi$
$6$	1.98962	+	1.44554i	0.812259	+	0.590141i
$7$	2.53314	−	0.763690i	0.957435	−	0.288648i
$7$	2.53314	−	0.763690i	0.957435	−	0.288648i
$8$	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	−0.875320	−	0.483545i	$-0.839349\pi$
$13$	−2.47315	+	1.79685i	−0.685930	+	0.498357i	0.189390	+	0.981902i	$0.439349\pi$
$14$	−5.18121	−	3.93603i	−1.38474	−	1.05195i
$15$	−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	0.298123	−	0.954527i	$-0.403639\pi$
$17$	−2.13396	−	1.55041i	−0.517561	−	0.376030i	−0.815684	+	0.578497i	$0.803639\pi$
$18$	−2.33894	−	0.759968i	−0.551293	−	0.179126i
$19$	−2.14340	−	6.59671i	−0.491730	−	1.51339i	−0.821991	−	0.569500i	$-0.807137\pi$
$19$	−2.14340	−	6.59671i	−0.491730	−	1.51339i	0.330261	−	0.943890i	$-0.392863\pi$
$20$	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
$28$	−0.228600	+	10.7081i	−0.0432013	+	2.02363i
$29$	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	0.965121	−	0.261805i	$-0.0843179\pi$
$31$	2.32671	+	3.20245i	0.417890	+	0.575176i	−0.547230	+	0.836982i	$0.684318\pi$
$32$			0.479776i			0.0848133i
$33$	−1.51256	+	2.95164i	−0.263304	+	0.513814i
$34$			6.48696i			1.11250i
$35$	2.34020	−	6.71147i	0.395566	−	1.13445i
$36$	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	$-0.883084\pi$
$41$	−2.49284	−	7.67219i	−0.389317	−	1.19819i	0.543983	−	0.839096i	$-0.316916\pi$
$42$	6.14393	+	2.14231i	0.948029	+	0.330565i
$43$		−	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	−0.239040	−	0.971010i	$-0.576833\pi$
$47$	0.948256	−	0.308107i	0.138317	−	0.0449420i	0.377358	+	0.926068i	$0.376833\pi$
$48$	4.08143	+	1.32614i	0.589103	+	0.191411i
$49$	5.83355	−	3.86906i	0.833365	−	0.552723i
$50$	−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	0.321631	−	0.946865i	$-0.395769\pi$
$59$	0.194194	+	0.0630976i	0.0252820	+	0.00821460i	−0.296349	+	0.955080i	$0.595769\pi$
$60$	−8.79839	−	6.39240i	−1.13587	−	0.825256i
$61$	12.1551	+	8.83121i	1.55630	+	1.13072i	0.938960	+	0.344027i	$0.111791\pi$
$61$	12.1551	+	8.83121i	1.55630	+	1.13072i	0.617344	+	0.786694i	$0.288209\pi$
$62$	3.00829	−	9.25856i	0.382053	−	1.17584i
$63$	1.60046	−	2.10678i	0.201640	−	0.265429i
$64$	−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
$70$	−16.7362	+	5.04562i	−2.00035	+	0.603067i
$71$	−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	$0.424401\pi$
$73$	−4.49716	+	13.8408i	−0.526352	+	1.61995i	−0.761626	+	0.648017i	$0.775599\pi$
$74$	5.43682	−	1.76653i	0.632018	−	0.205355i
$75$	1.30324	+	1.79376i	0.150485	+	0.207125i
$76$	28.0790			3.22089
$77$	4.16763	−	7.72210i	0.474946	−	0.880015i
$78$	−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	0.365964	−	0.930629i	$-0.380739\pi$
$83$	−3.69908	−	2.68754i	−0.406027	−	0.294996i	−0.771991	+	0.635633i	$0.780739\pi$
$84$	−3.09156	−	10.2546i	−0.337317	−	1.11887i
$85$	−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	$0.386297\pi$
$89$			17.6770i			1.87375i	−0.349660	+	0.936877i	$0.613703\pi$
$90$	−5.34509	+	3.88343i	−0.563422	+	0.409350i
$91$	−4.89260	+	6.44039i	−0.512884	+	0.675137i
$92$	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	0.965492	−	0.260432i	$-0.0838650\pi$
$97$	4.13113	+	5.68602i	0.419453	+	0.577328i	−0.546039	+	0.837760i	$0.683865\pi$
$98$	−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	−0.0880761	−	0.996114i	$-0.528072\pi$
$101$	8.36217	−	6.07547i	0.832067	−	0.604532i	0.920143	+	0.391581i	$0.128072\pi$
$102$	−2.00458	−	6.16946i	−0.198483	−	0.610868i
$103$	5.56447	+	1.80801i	0.548283	+	0.178148i	0.570043	−	0.821615i	$-0.306927\pi$
$103$	5.56447	+	1.80801i	0.548283	+	0.178148i	−0.0217591	+	0.999763i	$0.506927\pi$
$104$	−9.05098	+	12.4576i	−0.887521	+	1.22157i
$105$	−0.151705	+	7.10615i	−0.0148049	+	0.693490i
$106$	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
$112$	−10.7211	−	3.73830i	−1.01305	−	0.353237i
$113$	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
$119$	−6.58964	−	2.29772i	−0.604071	−	0.210632i
$120$			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
$126$	−6.50523	−	0.138876i	−0.579532	−	0.0123721i
$127$	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	$-0.444433\pi$
$131$	3.97579			0.347367			0.173683	+	0.984802i	$0.444433\pi$
$132$	−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	−0.948563	−	0.316588i	$-0.897463\pi$
$139$	0.0580790	−	0.178749i	0.00492620	−	0.0151613i	0.953489	+	0.301427i	$0.0974628\pi$
$140$	22.9121	+	17.4057i	1.93642	+	1.47105i
$141$	−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
$147$	−4.35243	+	5.48236i	−0.358983	+	0.452178i
$148$	−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
$154$	−21.3886	+	2.87062i	−1.72354	+	0.231321i
$155$	10.6343			0.854167
$156$	7.27400	+	10.0118i	0.582386	+	0.801586i
$157$	5.84795	−	1.90012i	0.466717	−	0.151646i	−0.0662116	−	0.997806i	$-0.521091\pi$
$157$	5.84795	−	1.90012i	0.466717	−	0.151646i	0.532929	+	0.846160i	$0.321091\pi$
$158$	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
$161$	−10.8068	+	3.25802i	−0.851692	+	0.256768i
$162$	−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	$0.638740\pi$
$167$	−18.2832	+	13.2835i	−1.41480	+	1.02791i	−0.992603	+	0.121404i	$0.961260\pi$
$168$	−8.06175	+	10.6121i	−0.621977	+	0.818743i
$169$	−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	$0.0140315\pi$
$173$	2.85024	+	8.77212i	0.216699	+	0.666932i	−0.782329	+	0.622865i	$0.785969\pi$
$174$	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	−0.327871	−	0.944723i	$-0.606331\pi$
$181$	9.03991	−	12.4424i	0.671931	−	0.924834i	0.999802	+	0.0198884i	$0.00633111\pi$
$182$	19.8864	+	0.424542i	1.47408	+	0.0314692i
$183$	−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
$189$	−0.871102	+	2.49824i	−0.0633633	+	0.181720i
$190$	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
$196$	7.59857	+	27.2996i	0.542755	+	1.94997i
$197$			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	$-0.908182\pi$
$199$		−	8.02593i		−	0.568943i	0.958685	−	0.284471i	$-0.0918181\pi$
$200$	−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
$203$	13.6557	+	0.291527i	0.958443	+	0.0204612i
$204$	−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
$217$	8.33956	+	6.33535i	0.566126	+	0.430071i
$218$	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	−0.303861	−	0.952716i	$-0.598276\pi$
$223$	0.153845	−	0.0499874i	0.0103023	−	0.00334740i	0.314164	+	0.949369i	$0.398276\pi$
$224$	0.366401	+	1.21534i	0.0244812	+	0.0812033i
$225$	−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	$0.207775\pi$
$227$	−3.09289	+	9.51894i	−0.205282	+	0.631794i	−0.999702	+	0.0244244i	$0.992225\pi$
$228$	−26.7048	+	8.67690i	−1.76857	+	0.574642i
$229$	0.612988	+	0.843705i	0.0405074	+	0.0557536i	0.828790	−	0.559559i	$-0.189030\pi$
$229$	0.612988	+	0.843705i	0.0405074	+	0.0557536i	−0.788283	+	0.615313i	$0.789030\pi$
$230$	28.1861			1.85853
$231$	−1.57740	+	8.63202i	−0.103785	+	0.567945i
$232$	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
$238$	4.95402	+	16.4323i	0.321122	+	1.06515i
$239$	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	$-0.579932\pi$
$241$	−7.71499			−0.496966			−0.248483	+	0.968636i	$0.579932\pi$
$242$	−21.9593	+	15.7993i	−1.41160	+	1.01562i
$243$			1.00000i			0.0641500i
$244$	−49.2062	+	35.7504i	−3.15011	+	2.28869i
$245$	0.802563	−	18.7883i	0.0512739	−	1.20034i
$246$	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	0.987554	−	0.157283i	$-0.0502735\pi$
$251$	8.44110	+	11.6182i	0.532798	+	0.733333i	−0.454756	+	0.890616i	$0.650274\pi$
$252$	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	0.657869	−	0.753132i	$-0.271458\pi$
$257$	11.9820	+	3.89319i	0.747417	+	0.242850i	0.0895476	+	0.995983i	$0.471458\pi$
$258$	15.1910	−	20.9086i	0.945748	−	1.30171i
$259$	−0.131263	+	6.14860i	−0.00815626	+	0.382055i
$260$	−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
$266$	−14.8595	+	42.6155i	−0.911092	+	2.61292i
$267$	−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	−0.657970	−	0.753044i	$-0.728585\pi$
$269$	4.28959	−	5.90411i	0.261541	−	0.359980i	0.919511	+	0.393064i	$0.128585\pi$
$270$	3.88343	−	5.34509i	0.236338	−	0.325292i
$271$	−7.26901	+	22.3717i	−0.441561	+	1.35898i	0.444651	+	0.895704i	$0.353328\pi$
$271$	−7.26901	+	22.3717i	−0.441561	+	1.35898i	−0.886212	+	0.463281i	$0.846672\pi$
$272$	3.49797	+	10.7657i	0.212096	+	0.652764i
$273$	2.66295	−	7.63707i	0.161169	−	0.462217i
$274$			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
$280$	0.764157	−	35.7946i	0.0456671	−	2.13914i
$281$	−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	0.987929	−	0.154908i	$-0.0495082\pi$
$283$	1.64230	+	5.05449i	0.0976247	+	0.300458i	−0.890304	+	0.455366i	$0.849508\pi$
$284$	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	$0.219983\pi$
$293$	−3.89387	+	11.9841i	−0.227482	+	0.700119i	−0.998030	+	0.0627367i	$0.980017\pi$
$294$	17.1995	+	0.734696i	1.00309	+	0.0428483i
$295$	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
$301$	−8.02548	−	26.6203i	−0.462581	−	1.53437i
$302$	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	$-0.525964\pi$
$307$	−2.85519			−0.162954			−0.0814770	+	0.996675i	$0.525964\pi$
$308$	24.5170	+	25.7057i	1.39699	+	1.46472i
$309$	−5.85083			−0.332842
$310$	−15.3723	−	21.1582i	−0.873091	−	1.20171i
$311$	−27.9969	+	9.09675i	−1.58756	+	0.515829i	−0.963990	−	0.265938i	$-0.914318\pi$
$311$	−27.9969	+	9.09675i	−1.58756	+	0.515829i	−0.623570	+	0.781768i	$0.714318\pi$
$312$	4.75838	−	14.6448i	0.269390	−	0.829098i
$313$	2.22824	−	3.06691i	0.125948	−	0.173352i	−0.741387	−	0.671078i	$-0.765832\pi$
$313$	2.22824	−	3.06691i	0.125948	−	0.173352i	0.867334	+	0.497726i	$0.165832\pi$
$314$	−12.2340	−	8.88851i	−0.690404	−	0.501608i
$315$	−2.05164	−	6.80523i	−0.115597	−	0.383431i
$316$	−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
$322$	22.1039	+	16.7917i	1.23180	+	0.935767i
$323$	−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
$336$	11.3516	+	0.242337i	0.619279	+	0.0132206i
$337$	−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
$343$	11.8224	−	14.2559i	0.638351	−	0.769746i
$344$	−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	$-0.746535\pi$
$349$	−10.3439	−	31.8351i	−0.553694	−	1.70409i	0.145675	−	0.989333i	$-0.453465\pi$
$350$	−4.74993	+	13.6223i	−0.253894	+	0.728145i
$351$		−	3.05699i		−	0.163170i
$352$	1.12256	+	1.12778i	0.0598328	+	0.0601110i
$353$			17.5405i			0.933588i	0.884366	+	0.466794i	$0.154591\pi$
$353$			17.5405i			0.933588i	−0.884366	+	0.466794i	$0.845409\pi$
$354$	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
$357$	6.97715	+	0.148951i	0.369270	+	0.00788331i
$358$	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	0.301698	−	0.953404i	$-0.402447\pi$
$367$	−0.280086	−	0.0910054i	−0.0146204	−	0.00475045i	−0.316318	+	0.948653i	$0.602447\pi$
$368$	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
$371$	−10.6388	+	14.0044i	−0.552338	+	0.727072i
$372$	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
$378$	6.22976	−	1.87815i	0.320424	−	0.0966015i
$379$	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	0.552882	−	0.833259i	$-0.313528\pi$
$383$	−8.03255	−	11.0559i	−0.410444	−	0.564928i	−0.963327	+	0.268331i	$0.913528\pi$
$384$	−19.1658			−0.978053
$385$	−10.2023	−	21.2518i	−0.519957	−	1.08309i
$386$	−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
$392$	21.9238	−	27.6154i	1.10732	−	1.39479i
$393$	−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	$-0.884421\pi$
$397$		−	14.1536i		−	0.710350i	0.934800	−	0.355175i	$-0.115579\pi$
$398$	−15.9686	+	11.6018i	−0.800431	+	0.581547i
$399$	14.6130	+	11.1011i	0.731566	+	0.555752i
$400$	−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	−0.716826	−	0.697252i	$-0.754406\pi$
$409$	−5.56580	+	4.04379i	−0.275211	+	0.199953i	0.441615	+	0.897205i	$0.354406\pi$
$410$	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
$413$	0.540108	+	0.0115304i	0.0265770	+	0.000567375i
$414$	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	$-0.952225\pi$
$419$		−	6.12153i		−	0.299056i	0.988757	−	0.149528i	$-0.0477755\pi$
$420$	−27.1693	−	9.47358i	−1.32573	−	0.462264i
$421$	−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
$427$	37.5349	+	13.0879i	1.81644	+	0.633368i
$428$		−	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	0.462678	−	0.886527i	$-0.346889\pi$
$433$	6.57354	+	2.13587i	0.315904	+	0.102644i	−0.146773	+	0.989170i	$0.546889\pi$
$434$	0.549733	−	25.7506i	0.0263880	−	1.23607i
$435$	−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	$-0.402854\pi$
$439$	12.5914			0.600955			0.300478	+	0.953789i	$0.402854\pi$
$440$	−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
$448$	−11.8483	+	15.5965i	−0.559778	+	0.736866i
$449$	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
$455$	6.27184	+	20.8035i	0.294029	+	0.975283i
$456$	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	$-0.567896\pi$
$461$	−9.09026			−0.423376			−0.211688	+	0.977337i	$0.567896\pi$
$462$	19.4547	−	9.33955i	0.905112	−	0.434515i
$463$	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	−0.817848	−	0.575435i	$-0.804833\pi$
$467$	−0.385692	+	0.530860i	−0.0178477	+	0.0245653i	0.800000	+	0.600000i	$0.204833\pi$
$468$	−10.0118	−	7.27400i	−0.462796	−	0.336241i
$469$	24.7483	−	7.46113i	1.14277	−	0.344523i
$470$	−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
$476$	17.0897	−	22.4961i	0.783306	−	1.03111i
$477$	−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	0.882138	−	0.470991i	$-0.156103\pi$
$479$	15.4690	+	11.2389i	0.706795	+	0.513517i	−0.175343	+	0.984507i	$0.556103\pi$
$480$	−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
$490$	−38.5417	+	25.5625i	−1.74114	+	1.15479i
$491$	−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
$497$	−0.174886	−	0.0609804i	−0.00784470	−	0.00273534i
$498$	−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	$0.0152309\pi$
$503$	4.90894	+	15.1082i	0.218879	+	0.673640i	−0.779977	+	0.625809i	$0.784769\pi$
$504$	4.38785	−	12.5839i	0.195450	−	0.560533i
$505$		−	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	0.260354	−	0.965513i	$-0.416161\pi$
$509$	23.4296	−	7.61275i	1.03850	−	0.337429i	0.778145	+	0.628084i	$0.216161\pi$
$510$	−16.5742	−	5.38527i	−0.733917	−	0.238464i
$511$	−0.821808	+	38.4951i	−0.0363546	+	1.70292i
$512$	−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	−0.520421	−	0.853910i	$-0.674225\pi$
$521$	−32.9454	−	10.7046i	−1.44337	−	0.468978i	−0.922945	+	0.384932i	$0.874225\pi$
$522$	−10.2715	−	7.46269i	−0.449572	−	0.326633i
$523$	−25.5588	−	18.5696i	−1.11761	−	0.811990i	−0.133764	−	0.991013i	$-0.542706\pi$
$523$	−25.5588	−	18.5696i	−1.11761	−	0.811990i	−0.983845	+	0.179023i	$0.942706\pi$
$524$	−4.97356	+	15.3070i	−0.217271	+	0.668691i
$525$	4.67116	+	3.54855i	0.203866	+	0.154872i
$526$	−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
$532$	71.1280	−	21.4437i	3.08379	−	0.929702i
$533$	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
$539$	4.65989	−	22.7439i	0.200716	−	0.979649i
$540$	−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
$546$	−19.0443	+	5.74148i	−0.815020	+	0.245712i
$547$	−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
$553$	2.24505	+	1.70551i	0.0954692	+	0.0725255i
$554$	−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	0.170497	−	0.985358i	$-0.445463\pi$
$563$	27.5315	−	20.0028i	1.16031	−	0.843018i	0.989818	+	0.142340i	$0.0454627\pi$
$564$	−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
$567$	0.0564696	−	2.64515i	0.00237150	−	0.111086i
$568$	−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
$574$	−17.2820	+	49.5632i	−0.721337	+	2.06873i
$575$	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	−0.831128	−	0.556081i	$-0.812304\pi$
$577$	−1.09128	+	1.50202i	−0.0454306	+	0.0625298i	0.785697	+	0.618611i	$0.212304\pi$
$578$	−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
$581$	−11.4227	−	3.98295i	−0.473894	−	0.165241i
$582$			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	0.700298	−	0.713851i	$-0.253051\pi$
$587$	20.5275	+	6.66978i	0.847259	+	0.275291i	0.146961	+	0.989142i	$0.453051\pi$
$588$	−15.6627	−	23.6153i	−0.645919	−	0.973880i
$589$	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	$-0.599608\pi$
$593$	−14.9931			−0.615694			−0.307847	+	0.951436i	$0.599608\pi$
$594$	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	$-0.738109\pi$
$601$	7.37794	−	22.7070i	0.300952	−	0.926236i	0.981157	−	0.193214i	$-0.0618910\pi$
$602$	−41.3630	+	54.4484i	−1.68583	+	2.21915i
$603$	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	−0.522395	−	0.852703i	$-0.674961\pi$
$607$	3.13251	−	2.27591i	0.127145	−	0.0923761i	0.649540	+	0.760327i	$0.274961\pi$
$608$	3.16495	−	1.02835i	0.128356	−	0.0417053i
$609$	−13.0774	+	3.94259i	−0.529925	+	0.159762i
$610$	−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
$616$	7.94555	−	43.4806i	0.320135	−	1.75188i
$617$	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	0.258714	−	0.965954i	$-0.416701\pi$
$619$	25.7702	−	8.37324i	1.03579	−	0.336549i	0.777078	+	0.629405i	$0.216701\pi$
$620$	−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
$623$	13.4997	+	44.7781i	0.540855	+	1.79400i
$624$	−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
$630$	−10.5741	+	13.9193i	−0.421282	+	0.554556i
$631$	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	$0.504531\pi$
$643$	−24.3633	+	33.5333i	−0.960796	+	1.32242i	−0.946561	+	0.322524i	$0.895469\pi$
$644$	0.975243	−	45.6823i	0.0384300	−	1.80014i
$645$	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	$-0.917804\pi$
$647$	−23.1709	−	31.8920i	−0.910941	−	1.25380i	0.0559028	−	0.998436i	$-0.482196\pi$
$648$		−	5.03713i		−	0.197877i
$649$	0.604114	−	0.306049i	0.0237136	−	0.0120135i
$650$		−	16.6691i		−	0.653815i
$651$	−9.88912	−	3.44821i	−0.387585	−	0.135146i
$652$	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
$658$	−6.12583	−	2.13600i	−0.238810	−	0.0832698i
$659$			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	$0.0150106\pi$
$661$			2.42391i			0.0942793i	−0.998888	+	0.0471396i	$0.984989\pi$
$662$	−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
$665$	−49.2897	−	1.05225i	−1.91137	−	0.0408047i
$666$	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	0.592891	−	0.805282i	$-0.297986\pi$
$677$	0.266327	+	0.193498i	0.0102358	+	0.00743674i	−0.582656	+	0.812719i	$0.697986\pi$
$678$	−2.65177	+	8.16132i	−0.101841	+	0.313433i
$679$	14.8071	+	11.2486i	0.568244	+	0.431680i
$680$	−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
$686$	−45.4537	−	2.91463i	−1.73543	−	0.111281i
$687$	−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	$-0.913328\pi$
$691$	−24.2181	−	33.3333i	−0.921299	−	1.26806i	0.0418584	−	0.999124i	$-0.486672\pi$
$692$	−37.3387			−1.41940
$693$	−1.16725	−	8.69698i	−0.0443401	−	0.330371i
$694$	−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
$700$	22.7366	−	6.85462i	0.859362	−	0.259080i
$701$	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
$707$	16.5427	−	21.7761i	0.622154	−	0.818975i
$708$	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	0.115815	−	0.993271i	$-0.463052\pi$
$719$	−10.0370	−	3.26123i	−0.374318	−	0.121623i	−0.490133	+	0.871647i	$0.663052\pi$
$720$	−6.77656	+	9.32713i	−0.252547	+	0.347602i
$721$	15.4763	+	0.330394i	0.576368	+	0.0123045i
$722$	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	$-0.882132\pi$
$727$		−	19.5152i		−	0.723780i	0.932221	−	0.361890i	$-0.117868\pi$
$728$	−13.4136	+	38.4689i	−0.497141	+	1.42575i
$729$	−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	−0.854876	−	0.518833i	$-0.826367\pi$
$733$	3.83626	−	11.8068i	0.141696	−	0.436094i	0.996571	+	0.0827386i	$0.0263667\pi$
$734$	0.223810	+	0.688817i	0.00826099	+	0.0254247i
$735$	5.04261	+	18.1167i	0.185999	+	0.668245i
$736$		−	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
$742$	43.2423	+	0.923152i	1.58747	+	0.0338900i
$743$	−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
$756$	−8.52864	−	6.47898i	−0.310184	−	0.235638i
$757$	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	−0.944987	−	0.327106i	$-0.893926\pi$
$761$	−25.5423	+	18.5576i	−0.925908	+	0.672712i	0.0190795	+	0.999818i	$0.493926\pi$
$762$	42.7509	−	13.8906i	1.54870	−	0.503204i
$763$	8.15278	+	27.0425i	0.295150	+	0.979005i
$764$	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	$-0.850920\pi$
$769$	−49.4893			−1.78463			−0.892315	+	0.451412i	$0.850920\pi$
$770$	−27.5351	+	51.0191i	−0.992297	+	1.83860i
$771$	−12.5986			−0.453728
$772$	30.4203	+	41.8699i	1.09485	+	1.50693i
$773$	25.1807	−	8.18170i	0.905686	−	0.294275i	0.181104	−	0.983464i	$-0.442033\pi$
$773$	25.1807	−	8.18170i	0.905686	−	0.294275i	0.724582	+	0.689189i	$0.242033\pi$
$774$	−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
$777$	−1.77518	−	5.88823i	−0.0636844	−	0.211239i
$778$	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
$784$	−30.0129	−	1.28204i	−1.07189	−	0.0457870i
$785$	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	0.590575	−	0.806983i	$-0.298901\pi$
$787$	0.156727	+	0.113869i	0.00558671	+	0.00405899i	−0.584988	+	0.811042i	$0.698901\pi$
$788$	−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	$-0.548583\pi$
$797$	23.5715	−	32.4434i	0.834945	−	1.14920i	0.986982	−	0.160829i	$-0.0514167\pi$
$798$	0.963272	−	45.1216i	0.0340994	−	1.59729i
$799$	−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
$805$	−9.98367	+	28.6322i	−0.351878	+	1.00915i
$806$	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	0.883213	−	0.468972i	$-0.155375\pi$
$811$	−3.04647	−	9.37607i	−0.106976	−	0.329238i	−0.990189	+	0.139734i	$0.955375\pi$
$812$	−18.2051	+	52.2106i	−0.638875	+	1.83223i
$813$		−	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
$819$	−0.172627	+	8.08619i	−0.00603207	+	0.282554i
$820$	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	0.836510	−	0.547951i	$-0.184592\pi$
$829$	34.2970	+	11.1438i	1.19118	+	0.387039i	0.354673	+	0.934990i	$0.384592\pi$
$830$	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
$833$	−18.4472	−	0.787994i	−0.639158	−	0.0273024i
$834$	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	−0.753566	−	0.657373i	$-0.771668\pi$
$839$	−28.2941	+	9.19330i	−0.976819	+	0.317388i	−0.223254	+	0.974760i	$0.571668\pi$
$840$	10.3344	+	34.2788i	0.356570	+	1.18273i
$841$	−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
$847$	−8.27128	−	27.9032i	−0.284205	−	0.958764i
$848$	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	0.926555	−	0.376159i	$-0.122755\pi$
$853$	24.9750	+	18.1454i	0.855128	+	0.621287i	−0.0714273	+	0.997446i	$0.522755\pi$
$854$	−28.2183	−	93.5993i	−0.965612	−	3.20290i
$855$	−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	$-0.375991\pi$
$857$	22.2373			0.759612			0.379806	+	0.925066i	$0.375991\pi$
$858$	−17.6723	+	17.5905i	−0.603321	+	0.600530i
$859$		−	1.83049i		−	0.0624554i	−0.999512	−	0.0312277i	$-0.990058\pi$
$859$		−	1.83049i		−	0.0624554i	0.999512	−	0.0312277i	$-0.00994170\pi$
$860$	92.4606	−	67.1766i	3.15288	−	2.29070i
$861$	16.9954	+	12.9110i	0.579202	+	0.440005i
$862$	−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
$875$	19.7750	+	0.422163i	0.668516	+	0.0142717i
$876$	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	$-0.940352\pi$
$881$		−	11.0591i		−	0.372592i	0.982494	−	0.186296i	$-0.0596483\pi$
$882$	−16.5847	+	4.61619i	−0.558436	+	0.155435i
$883$	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	$-0.744783\pi$
$887$	8.62408	−	26.5422i	0.289568	−	0.891199i	0.984992	−	0.172600i	$-0.0552167\pi$
$888$	−3.61819	−	11.1357i	−0.121419	−	0.373688i
$889$	15.9219	−	45.6625i	0.534004	−	1.53147i
$890$		−	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
$896$	50.6965	+	1.08229i	1.69365	+	0.0361567i
$897$	−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
$910$	32.3249	−	42.5510i	1.07156	−	1.41055i
$911$	−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
$917$	10.0712	−	3.03627i	0.332581	−	0.100267i
$918$	−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
$924$	−31.2605	−	16.8714i	−1.02840	−	0.555028i
$925$	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	$-0.568896\pi$
$929$	23.7884	−	32.7419i	0.780471	−	1.07423i	0.995230	−	0.0975596i	$-0.0311037\pi$
$930$	21.1582	+	15.3723i	0.693805	+	0.504079i
$931$	−38.0267	−	30.1893i	−1.24628	−	0.989416i
$932$	−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	−0.863243	−	0.504788i	$-0.831571\pi$
$937$	−19.8943	+	14.4541i	−0.649918	+	0.472193i	0.213325	+	0.976981i	$0.431571\pi$
$938$	−50.6197	−	38.4544i	−1.65279	−	1.25558i
$939$	−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	−0.0111477	−	0.999938i	$-0.503548\pi$
$941$	−29.6202	−	21.5203i	−0.965590	−	0.701542i	−0.954442	+	0.298396i	$0.903548\pi$
$942$	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
$952$	−35.1448	−	0.750285i	−1.13905	−	0.0243169i
$953$	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
$959$	−33.5491	−	11.6981i	−1.08336	−	0.377753i
$960$	−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
$966$	−26.2110	−	9.13942i	−0.843324	−	0.294056i
$967$			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	−0.413270	−	0.910609i	$-0.635613\pi$
$971$	−6.61763	+	2.15020i	−0.212370	+	0.0690031i	0.200900	+	0.979612i	$0.435613\pi$
$972$	−3.85006	−	1.25096i	−0.123491	−	0.0401246i
$973$	0.0106133	−	0.497150i	0.000340248	−	0.0159379i
$974$	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	0.854760	−	0.519024i	$-0.173704\pi$
$983$	38.9151	+	12.6443i	1.24120	+	0.403290i	0.386441	+	0.922314i	$0.373704\pi$
$984$	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
$987$	−1.59575	+	2.10057i	−0.0507933	+	0.0668620i
$988$	−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
$994$	0.131477	+	0.436106i	0.00417021	+	0.0138325i
$995$	−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	−0.915993	−	0.401194i	$-0.868595\pi$
$997$	1.92220	−	5.91591i	0.0608765	−	0.187359i	0.976870	+	0.213835i	$0.0685955\pi$
$998$	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.118.1	✓	64
3.2	odd	2		693.2.bu.f.118.15		64
7.6	odd	2	inner	231.2.w.a.118.2	yes	64
11.7	odd	10	inner	231.2.w.a.139.2	yes	64
21.20	even	2		693.2.bu.f.118.16		64
33.29	even	10		693.2.bu.f.370.16		64
77.62	even	10	inner	231.2.w.a.139.1	yes	64
231.62	odd	10		693.2.bu.f.370.15		64

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

\(f(q)\)	\(=\)	\(q+(-1.44554 - 1.98962i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.25096 + 3.85006i) q^{4} +(1.57908 - 2.17341i) q^{5} +(1.98962 + 1.44554i) q^{6} +(2.53314 - 0.763690i) q^{7} +(4.79060 - 1.55656i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(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} +(2.53314 - 0.763690i) 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} +(-5.18121 - 3.93603i) 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} +(-0.228600 + 10.7081i) 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} +(2.34020 - 6.71147i) 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} +(6.14393 + 2.14231i) 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} +(5.83355 - 3.86906i) 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} +(1.60046 - 2.10678i) 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} +(-16.7362 + 5.04562i) 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} +(4.16763 - 7.72210i) 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} +(-3.09156 - 10.2546i) 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} +(-4.89260 + 6.44039i) 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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