LMFDB - Embedded newform 23.3.d.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,3,Mod(5,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	23.7
Dual form			23.3.d.a.10.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.881085 + 1.01683i) q^{2} +(2.64748 - 1.70143i) q^{3} +(0.311634 + 2.16747i) q^{4} +(-2.08252 + 0.951056i) q^{5} +(-0.602595 + 4.19114i) q^{6} +(-2.90589 - 9.89656i) q^{7} +(-7.00598 - 4.50247i) q^{8} +(0.375553 - 0.822346i) q^{9} +(0.867820 - 2.95552i) q^{10} +(-6.07406 + 5.26321i) q^{11} +(4.51285 + 5.20810i) q^{12} +(14.4927 + 4.25543i) q^{13} +(12.6234 + 5.76492i) q^{14} +(-3.89528 + 6.06118i) q^{15} +(2.34688 - 0.689107i) q^{16} +(-13.1674 - 1.89318i) q^{17} +(0.505289 + 1.10643i) q^{18} +(26.2733 - 3.77753i) q^{19} +(-2.71037 - 4.21741i) q^{20} +(-24.5316 - 21.2568i) q^{21} -10.8136i q^{22} +(22.1459 + 6.20960i) q^{23} -26.2089 q^{24} +(-12.9391 + 14.9325i) q^{25} +(-17.0963 + 10.9871i) q^{26} +(3.62597 + 25.2192i) q^{27} +(20.5449 - 9.38253i) q^{28} +(0.753370 - 5.23980i) q^{29} +(-2.73109 - 9.30124i) q^{30} +(-29.7398 - 19.1126i) q^{31} +(12.4713 - 27.3082i) q^{32} +(-7.12598 + 24.2689i) q^{33} +(13.5266 - 11.7209i) q^{34} +(15.4638 + 17.8461i) q^{35} +(1.89944 + 0.557726i) q^{36} +(-32.5376 - 14.8594i) q^{37} +(-19.3079 + 30.0437i) q^{38} +(45.6095 - 13.3921i) q^{39} +(18.8722 + 2.71342i) q^{40} +(7.60347 + 16.6493i) q^{41} +(43.2289 - 6.21538i) q^{42} +(8.28150 + 12.8863i) q^{43} +(-13.3007 - 11.5251i) q^{44} +2.06973i q^{45} +(-25.8265 + 17.0473i) q^{46} +72.6550 q^{47} +(5.04086 - 5.81747i) q^{48} +(-48.2763 + 31.0253i) q^{49} +(-3.78334 - 26.3137i) q^{50} +(-38.0815 + 17.3912i) q^{51} +(-4.70709 + 32.7385i) q^{52} +(-25.8947 - 88.1894i) q^{53} +(-28.8383 - 18.5333i) q^{54} +(7.64377 - 16.7375i) q^{55} +(-24.2004 + 82.4189i) q^{56} +(63.1309 - 54.7032i) q^{57} +(4.66419 + 5.38276i) q^{58} +(-71.1561 - 20.8933i) q^{59} +(-14.3513 - 6.55402i) q^{60} +(-15.2916 + 23.7942i) q^{61} +(45.6374 - 13.4004i) q^{62} +(-9.22972 - 1.32703i) q^{63} +(20.8438 + 45.6417i) q^{64} +(-34.2285 + 4.92131i) q^{65} +(-18.3986 - 28.6288i) q^{66} +(-5.29481 - 4.58798i) q^{67} -29.1298i q^{68} +(69.1961 - 21.2400i) q^{69} -31.7713 q^{70} +(18.7368 - 21.6234i) q^{71} +(-6.33371 + 4.07043i) q^{72} +(-1.65454 - 11.5076i) q^{73} +(43.7778 - 19.9926i) q^{74} +(-8.84937 + 61.5487i) q^{75} +(16.3753 + 55.7692i) q^{76} +(69.7382 + 44.8180i) q^{77} +(-26.5683 + 58.1765i) q^{78} +(5.91331 - 20.1389i) q^{79} +(-4.23206 + 3.66710i) q^{80} +(57.8367 + 66.7471i) q^{81} +(-23.6287 - 6.93802i) q^{82} +(-15.0149 - 6.85707i) q^{83} +(38.4285 - 59.7959i) q^{84} +(29.2218 - 8.58031i) q^{85} +(-20.3998 - 2.93305i) q^{86} +(-6.92065 - 15.1541i) q^{87} +(66.2522 - 9.52563i) q^{88} +(21.3179 + 33.1714i) q^{89} +(-2.10455 - 1.82360i) q^{90} -155.794i q^{91} +(-6.55766 + 49.9356i) q^{92} -111.254 q^{93} +(-64.0153 + 73.8775i) q^{94} +(-51.1221 + 32.8542i) q^{95} +(-13.4457 - 93.5171i) q^{96} +(-77.7143 + 35.4909i) q^{97} +(10.9882 - 76.4246i) q^{98} +(2.04705 + 6.97160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18}+ \cdots - 242 q^{99}+O(q^{100}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.881085	+	1.01683i	−0.440542	+	0.508413i	−0.931985	−	0.362497i	$-0.881924\pi$
$2$	−0.881085	+	1.01683i	−0.440542	+	0.508413i	0.491443	+	0.870910i	$0.336470\pi$
$3$	2.64748	−	1.70143i	0.882494	−	0.567145i	−0.0190563	−	0.999818i	$-0.506066\pi$
$3$	2.64748	−	1.70143i	0.882494	−	0.567145i	0.901551	+	0.432674i	$0.142430\pi$
$4$	0.311634	+	2.16747i	0.0779086	+	0.541866i
$5$	−2.08252	+	0.951056i	−0.416505	+	0.190211i	−0.612634	−	0.790367i	$-0.709890\pi$
$5$	−2.08252	+	0.951056i	−0.416505	+	0.190211i	0.196129	+	0.980578i	$0.437163\pi$
$6$	−0.602595	+	4.19114i	−0.100432	+	0.698523i
$7$	−2.90589	−	9.89656i	−0.415128	−	1.41379i	−0.856349	−	0.516397i	$-0.827273\pi$
$7$	−2.90589	−	9.89656i	−0.415128	−	1.41379i	0.441222	−	0.897398i	$-0.354545\pi$
$8$	−7.00598	−	4.50247i	−0.875748	−	0.562809i
$9$	0.375553	−	0.822346i	0.0417281	−	0.0913718i
$10$	0.867820	−	2.95552i	0.0867820	−	0.295552i
$11$	−6.07406	+	5.26321i	−0.552188	+	0.478473i	−0.885691	−	0.464276i	$-0.846315\pi$
$11$	−6.07406	+	5.26321i	−0.552188	+	0.478473i	0.333503	+	0.942749i	$0.391769\pi$
$12$	4.51285	+	5.20810i	0.376071	+	0.434008i
$13$	14.4927	+	4.25543i	1.11482	+	0.327341i	0.786725	−	0.617303i	$-0.211775\pi$
$13$	14.4927	+	4.25543i	1.11482	+	0.327341i	0.328096	+	0.944644i	$0.393593\pi$
$14$	12.6234	+	5.76492i	0.901673	+	0.411780i
$15$	−3.89528	+	6.06118i	−0.259686	+	0.404079i
$16$	2.34688	−	0.689107i	0.146680	−	0.0430692i
$17$	−13.1674	−	1.89318i	−0.774550	−	0.111364i	−0.256305	−	0.966596i	$-0.582505\pi$
$17$	−13.1674	−	1.89318i	−0.774550	−	0.111364i	−0.518245	+	0.855232i	$0.673414\pi$
$18$	0.505289	+	1.10643i	0.0280716	+	0.0614683i
$19$	26.2733	−	3.77753i	1.38280	−	0.198817i	0.589562	−	0.807723i	$-0.299300\pi$
$19$	26.2733	−	3.77753i	1.38280	−	0.198817i	0.793243	+	0.608906i	$0.208391\pi$
$20$	−2.71037	−	4.21741i	−0.135518	−	0.210871i
$21$	−24.5316	−	21.2568i	−1.16817	−	1.01223i
$22$		−	10.8136i		−	0.491527i
$23$	22.1459	+	6.20960i	0.962865	+	0.269982i
$23$	22.1459	+	6.20960i	0.962865	+	0.269982i
$24$	−26.2089			−1.09204
$25$	−12.9391	+	14.9325i	−0.517565	+	0.597302i
$26$	−17.0963	+	10.9871i	−0.657551	+	0.422582i
$27$	3.62597	+	25.2192i	0.134295	+	0.934044i
$28$	20.5449	−	9.38253i	0.733746	−	0.335090i
$29$	0.753370	−	5.23980i	0.0259783	−	0.180683i	−0.972701	−	0.232062i	$-0.925453\pi$
$29$	0.753370	−	5.23980i	0.0259783	−	0.180683i	0.998679	+	0.0513794i	$0.0163618\pi$
$30$	−2.73109	−	9.30124i	−0.0910363	−	0.310041i
$31$	−29.7398	−	19.1126i	−0.959347	−	0.616535i	−0.0355297	−	0.999369i	$-0.511312\pi$
$31$	−29.7398	−	19.1126i	−0.959347	−	0.616535i	−0.923817	+	0.382834i	$0.874948\pi$
$32$	12.4713	−	27.3082i	0.389727	−	0.853382i
$33$	−7.12598	+	24.2689i	−0.215939	+	0.735420i
$34$	13.5266	−	11.7209i	0.397841	−	0.344731i
$35$	15.4638	+	17.8461i	0.441822	+	0.509890i
$36$	1.89944	+	0.557726i	0.0527623	+	0.0154924i
$37$	−32.5376	−	14.8594i	−0.879393	−	0.401605i	−0.0760377	−	0.997105i	$-0.524227\pi$
$37$	−32.5376	−	14.8594i	−0.879393	−	0.401605i	−0.803356	+	0.595499i	$0.796954\pi$
$38$	−19.3079	+	30.0437i	−0.508103	+	0.790624i
$39$	45.6095	−	13.3921i	1.16947	−	0.343388i
$40$	18.8722	+	2.71342i	0.471806	+	0.0678354i
$41$	7.60347	+	16.6493i	0.185451	+	0.406080i	0.979407	−	0.201894i	$-0.0647097\pi$
$41$	7.60347	+	16.6493i	0.185451	+	0.406080i	−0.793957	+	0.607974i	$0.791982\pi$
$42$	43.2289	−	6.21538i	1.02926	−	0.147985i
$43$	8.28150	+	12.8863i	0.192593	+	0.299681i	0.924098	−	0.382155i	$-0.124818\pi$
$43$	8.28150	+	12.8863i	0.192593	+	0.299681i	−0.731505	+	0.681836i	$0.761182\pi$
$44$	−13.3007	−	11.5251i	−0.302289	−	0.261935i
$45$			2.06973i			0.0459939i
$46$	−25.8265	+	17.0473i	−0.561446	+	0.370595i
$47$	72.6550			1.54585			0.772926	−	0.634496i	$-0.218792\pi$
$47$	72.6550			1.54585			0.772926	+	0.634496i	$0.218792\pi$
$48$	5.04086	−	5.81747i	0.105018	−	0.121197i
$49$	−48.2763	+	31.0253i	−0.985231	+	0.633170i
$50$	−3.78334	−	26.3137i	−0.0756667	−	0.526274i
$51$	−38.0815	+	17.3912i	−0.746695	+	0.341004i
$52$	−4.70709	+	32.7385i	−0.0905209	+	0.629587i
$53$	−25.8947	−	88.1894i	−0.488580	−	1.66395i	−0.722248	−	0.691634i	$-0.756891\pi$
$53$	−25.8947	−	88.1894i	−0.488580	−	1.66395i	0.233668	−	0.972316i	$-0.424927\pi$
$54$	−28.8383	−	18.5333i	−0.534043	−	0.343209i
$55$	7.64377	−	16.7375i	0.138978	−	0.304319i
$56$	−24.2004	+	82.4189i	−0.432149	+	1.47177i
$57$	63.1309	−	54.7032i	1.10756	−	0.959706i
$58$	4.66419	+	5.38276i	0.0804170	+	0.0928062i
$59$	−71.1561	−	20.8933i	−1.20604	−	0.354124i	−0.383878	−	0.923384i	$-0.625412\pi$
$59$	−71.1561	−	20.8933i	−1.20604	−	0.354124i	−0.822158	+	0.569260i	$0.807230\pi$
$60$	−14.3513	−	6.55402i	−0.239188	−	0.109234i
$61$	−15.2916	+	23.7942i	−0.250682	+	0.390069i	−0.943674	−	0.330876i	$-0.892656\pi$
$61$	−15.2916	+	23.7942i	−0.250682	+	0.390069i	0.692992	+	0.720945i	$0.256292\pi$
$62$	45.6374	−	13.4004i	0.736087	−	0.216135i
$63$	−9.22972	−	1.32703i	−0.146503	−	0.0210640i
$64$	20.8438	+	45.6417i	0.325685	+	0.713151i
$65$	−34.2285	+	4.92131i	−0.526592	+	0.0757125i
$66$	−18.3986	−	28.6288i	−0.278767	−	0.433770i
$67$	−5.29481	−	4.58798i	−0.0790270	−	0.0684773i	0.614452	−	0.788955i	$-0.289377\pi$
$67$	−5.29481	−	4.58798i	−0.0790270	−	0.0684773i	−0.693479	+	0.720477i	$0.743923\pi$
$68$		−	29.1298i		−	0.428379i
$69$	69.1961	−	21.2400i	1.00284	−	0.307826i
$70$	−31.7713			−0.453876
$71$	18.7368	−	21.6234i	0.263899	−	0.304556i	−0.608300	−	0.793707i	$-0.708148\pi$
$71$	18.7368	−	21.6234i	0.263899	−	0.304556i	0.872199	+	0.489152i	$0.162694\pi$
$72$	−6.33371	+	4.07043i	−0.0879682	+	0.0565337i
$73$	−1.65454	−	11.5076i	−0.0226649	−	0.157638i	0.975346	−	0.220682i	$-0.0708283\pi$
$73$	−1.65454	−	11.5076i	−0.0226649	−	0.157638i	−0.998011	+	0.0630439i	$0.979919\pi$
$74$	43.7778	−	19.9926i	0.591592	−	0.270171i
$75$	−8.84937	+	61.5487i	−0.117992	+	0.820650i
$76$	16.3753	+	55.7692i	0.215465	+	0.733806i
$77$	69.7382	+	44.8180i	0.905691	+	0.582053i
$78$	−26.5683	+	58.1765i	−0.340619	+	0.745853i
$79$	5.91331	−	20.1389i	0.0748520	−	0.254922i	−0.913563	−	0.406697i	$-0.866681\pi$
$79$	5.91331	−	20.1389i	0.0748520	−	0.254922i	0.988415	+	0.151774i	$0.0484987\pi$
$80$	−4.23206	+	3.66710i	−0.0529007	+	0.0458387i
$81$	57.8367	+	66.7471i	0.714033	+	0.824038i
$82$	−23.6287	−	6.93802i	−0.288155	−	0.0846100i
$83$	−15.0149	−	6.85707i	−0.180902	−	0.0826153i	0.322905	−	0.946431i	$-0.395341\pi$
$83$	−15.0149	−	6.85707i	−0.180902	−	0.0826153i	−0.503807	+	0.863816i	$0.668068\pi$
$84$	38.4285	−	59.7959i	0.457482	−	0.711855i
$85$	29.2218	−	8.58031i	0.343786	−	0.100945i
$86$	−20.3998	−	2.93305i	−0.237207	−	0.0341052i
$87$	−6.92065	−	15.1541i	−0.0795477	−	0.174185i
$88$	66.2522	−	9.52563i	0.752866	−	0.108246i
$89$	21.3179	+	33.1714i	0.239527	+	0.372712i	0.940117	−	0.340853i	$-0.110716\pi$
$89$	21.3179	+	33.1714i	0.239527	+	0.372712i	−0.700589	+	0.713565i	$0.747079\pi$
$90$	−2.10455	−	1.82360i	−0.0233839	−	0.0202623i
$91$		−	155.794i		−	1.71202i
$92$	−6.55766	+	49.9356i	−0.0712789	+	0.542778i
$93$	−111.254			−1.19628
$94$	−64.0153	+	73.8775i	−0.681013	+	0.785931i
$95$	−51.1221	+	32.8542i	−0.538127	+	0.345833i
$96$	−13.4457	−	93.5171i	−0.140060	−	0.974136i
$97$	−77.7143	+	35.4909i	−0.801178	+	0.365886i	−0.773552	−	0.633732i	$-0.781522\pi$
$97$	−77.7143	+	35.4909i	−0.801178	+	0.365886i	−0.0276260	+	0.999618i	$0.508795\pi$
$98$	10.9882	−	76.4246i	0.112124	−	0.779842i
$99$	2.04705	+	6.97160i	0.0206772	+	0.0704202i
$100$	−36.3981	−	23.3916i	−0.363981	−	0.233916i
$101$	9.02736	−	19.7672i	0.0893798	−	0.195715i	−0.859663	−	0.510861i	$-0.829327\pi$
$101$	9.02736	−	19.7672i	0.0893798	−	0.195715i	0.949043	+	0.315147i	$0.102054\pi$
$102$	15.8692	−	54.0454i	0.155580	−	0.529857i
$103$	−76.0694	+	65.9145i	−0.738538	+	0.639947i	−0.940635	−	0.339419i	$-0.889770\pi$
$103$	−76.0694	+	65.9145i	−0.738538	+	0.639947i	0.202097	+	0.979365i	$0.435224\pi$
$104$	−82.3755	−	95.0664i	−0.792072	−	0.914100i
$105$	71.3041	+	20.9368i	0.679087	+	0.199398i
$106$	112.489	+	51.3719i	1.06121	+	0.484640i
$107$	28.2516	−	43.9603i	0.264033	−	0.410844i	−0.683771	−	0.729697i	$-0.739661\pi$
$107$	28.2516	−	43.9603i	0.264033	−	0.410844i	0.947804	+	0.318853i	$0.103298\pi$
$108$	−53.5318	+	15.7183i	−0.495665	+	0.145540i
$109$	69.0753	+	9.93152i	0.633718	+	0.0911149i	0.451685	−	0.892177i	$-0.350823\pi$
$109$	69.0753	+	9.93152i	0.633718	+	0.0911149i	0.182033	+	0.983292i	$0.441732\pi$
$110$	10.2843	+	22.5196i	0.0934940	+	0.204723i
$111$	−111.425	+	16.0205i	−1.00383	+	0.144329i
$112$	−13.6396	−	21.2236i	−0.121782	−	0.189496i
$113$	94.9959	+	82.3144i	0.840672	+	0.728446i	0.964564	−	0.263850i	$-0.0849923\pi$
$113$	94.9959	+	82.3144i	0.840672	+	0.728446i	−0.123892	+	0.992296i	$0.539538\pi$
$114$			112.391i			0.985889i
$115$	−52.0250	+	8.13037i	−0.452391	+	0.0706989i
$116$	11.5919			0.0999299
$117$	8.94221	−	10.3199i	0.0764291	−	0.0882039i
$118$	83.9395	−	53.9446i	0.711352	−	0.457158i
$119$	19.5270	+	135.813i	0.164092	+	1.14129i
$120$	54.5806	−	24.9261i	0.454838	−	0.207718i
$121$	−8.02718	+	55.8303i	−0.0663403	+	0.461407i
$122$	−10.7214	−	36.5137i	−0.0878801	−	0.299292i
$123$	48.4577	+	31.1419i	0.393965	+	0.253186i
$124$	32.1579	−	70.4160i	0.259338	−	0.567871i
$125$	28.8694	−	98.3201i	0.230955	−	0.786561i
$126$	9.48153	−	8.21579i	0.0752502	−	0.0652047i
$127$	−24.0577	−	27.7640i	−0.189430	−	0.218614i	0.653088	−	0.757282i	$-0.273473\pi$
$127$	−24.0577	−	27.7640i	−0.189430	−	0.218614i	−0.842518	+	0.538668i	$0.818928\pi$
$128$	50.4456	+	14.8122i	0.394106	+	0.115720i
$129$	43.8503	+	20.0257i	0.339925	+	0.155238i
$130$	25.1541	−	39.1405i	0.193493	−	0.301081i
$131$	−98.3863	+	28.8888i	−0.751040	+	0.220525i	−0.634779	−	0.772693i	$-0.718909\pi$
$131$	−98.3863	+	28.8888i	−0.751040	+	0.220525i	−0.116261	+	0.993219i	$0.537091\pi$
$132$	−54.8226	−	7.88231i	−0.415323	−	0.0597144i
$133$	−113.732	−	249.038i	−0.855127	−	1.87247i
$134$	9.33036	−	1.34150i	0.0696295	−	0.0100112i
$135$	−31.5360	−	49.0710i	−0.233600	−	0.363489i
$136$	83.7263	+	72.5492i	0.615634	+	0.533450i
$137$			182.604i			1.33287i	0.745561	+	0.666437i	$0.232182\pi$
$137$			182.604i			1.33287i	−0.745561	+	0.666437i	$0.767818\pi$
$138$	−39.3703	+	89.0746i	−0.285292	+	0.645468i
$139$	150.203			1.08060			0.540298	−	0.841473i	$-0.318311\pi$
$139$	150.203			1.08060			0.540298	+	0.841473i	$0.318311\pi$
$140$	−33.8619	+	39.0787i	−0.241870	+	0.279133i
$141$	192.353	−	123.618i	1.36421	−	0.876722i
$142$	5.47855	+	38.1042i	0.0385814	+	0.268339i
$143$	−110.427	+	50.4302i	−0.772215	+	0.352659i
$144$	0.314694	−	2.18875i	0.00218538	−	0.0151996i
$145$	3.41444	+	11.6285i	0.0235479	+	0.0801966i
$146$	13.1590	+	8.45677i	0.0901301	+	0.0579231i
$147$	−75.0232	+	164.278i	−0.510362	+	1.11754i
$148$	22.0674	−	75.1547i	0.149104	−	0.507802i
$149$	−45.4620	+	39.3930i	−0.305114	+	0.264383i	−0.793937	−	0.608000i	$-0.791972\pi$
$149$	−45.4620	+	39.3930i	−0.305114	+	0.264383i	0.488823	+	0.872383i	$0.337426\pi$
$150$	−54.7873	−	63.2279i	−0.365249	−	0.421520i
$151$	77.6109	+	22.7886i	0.513979	+	0.150918i	0.528429	−	0.848978i	$-0.322781\pi$
$151$	77.6109	+	22.7886i	0.513979	+	0.150918i	−0.0144495	+	0.999896i	$0.504600\pi$
$152$	−201.078	−	91.8295i	−1.32288	−	0.604141i
$153$	−6.50189	+	10.1171i	−0.0424960	+	0.0661251i
$154$	−107.017	+	31.4232i	−0.694919	+	0.204047i
$155$	80.1108	+	11.5182i	0.516844	+	0.0743110i
$156$	43.2405	+	94.6835i	0.277183	+	0.606945i
$157$	−121.801	+	17.5123i	−0.775799	+	0.111543i	−0.518831	−	0.854877i	$-0.673633\pi$
$157$	−121.801	+	17.5123i	−0.775799	+	0.111543i	−0.256968	+	0.966420i	$0.582724\pi$
$158$	15.2676	+	23.7569i	0.0966304	+	0.150360i
$159$	−218.604	−	189.422i	−1.37487	−	1.19133i
$160$			68.7309i			0.429568i
$161$	−2.89995	−	237.213i	−0.0180121	−	1.47337i
$162$	−118.829			−0.733514
$163$	198.855	−	229.491i	1.21997	−	1.40792i	0.335035	−	0.942206i	$-0.391252\pi$
$163$	198.855	−	229.491i	1.21997	−	1.40792i	0.884935	−	0.465715i	$-0.154203\pi$
$164$	−33.7172	+	21.6688i	−0.205593	+	0.132127i
$165$	−8.24104	−	57.3177i	−0.0499457	−	0.347380i
$166$	20.2018	−	9.22587i	0.121698	−	0.0555776i
$167$	32.2123	−	224.041i	0.192888	−	1.34157i	−0.631427	−	0.775435i	$-0.717531\pi$
$167$	32.2123	−	224.041i	0.192888	−	1.34157i	0.824315	−	0.566131i	$-0.191560\pi$
$168$	76.1602	+	259.378i	0.453335	+	1.54392i
$169$	49.7572	+	31.9770i	0.294421	+	0.189213i
$170$	−17.0222	+	37.2735i	−0.100131	+	0.219256i
$171$	6.76057	−	23.0244i	0.0395355	−	0.134646i
$172$	−25.3497	+	21.9657i	−0.147382	+	0.127707i
$173$	46.5540	+	53.7262i	0.269098	+	0.310556i	0.874175	−	0.485611i	$-0.161403\pi$
$173$	46.5540	+	53.7262i	0.269098	+	0.310556i	−0.605077	+	0.796167i	$0.706857\pi$
$174$	21.5068	+	6.31496i	0.123602	+	0.0362929i
$175$	185.381	+	84.6605i	1.05932	+	0.483774i
$176$	−10.6282	+	16.5378i	−0.0603875	+	0.0939648i
$177$	−223.933	+	65.7527i	−1.26516	+	0.371484i
$178$	−52.5124	−	7.55015i	−0.295014	−	0.0424166i
$179$	−11.2744	−	24.6875i	−0.0629854	−	0.137919i	0.875522	−	0.483179i	$-0.160518\pi$
$179$	−11.2744	−	24.6875i	−0.0629854	−	0.137919i	−0.938507	+	0.345260i	$0.887791\pi$
$180$	−4.48606	+	0.644998i	−0.0249226	+	0.00358332i
$181$	112.540	+	175.116i	0.621768	+	0.967490i	0.999141	+	0.0414292i	$0.0131911\pi$
$181$	112.540	+	175.116i	0.621768	+	0.967490i	−0.377373	+	0.926061i	$0.623173\pi$
$182$	158.415	+	137.267i	0.870412	+	0.754216i
$183$			89.0125i			0.486407i
$184$	−127.195	−	143.216i	−0.691279	−	0.778346i
$185$	81.8923			0.442661
$186$	98.0245	−	113.126i	0.527013	−	0.608206i
$187$	89.9436	−	57.8032i	0.480982	−	0.309108i
$188$	22.6418	+	157.477i	0.120435	+	0.837645i
$189$	239.047	−	109.169i	1.26480	−	0.577614i
$190$	11.6359	−	80.9296i	0.0612417	−	0.425945i
$191$	66.9746	+	228.094i	0.350652	+	1.19421i	0.926386	+	0.376575i	$0.122898\pi$
$191$	66.9746	+	228.094i	0.350652	+	1.19421i	−0.575734	+	0.817637i	$0.695284\pi$
$192$	132.840	+	85.3711i	0.691875	+	0.444641i
$193$	−8.07013	+	17.6711i	−0.0418141	+	0.0915602i	−0.929386	−	0.369108i	$-0.879663\pi$
$193$	−8.07013	+	17.6711i	−0.0418141	+	0.0915602i	0.887572	+	0.460669i	$0.152390\pi$
$194$	32.3848	−	110.292i	0.166932	−	0.568518i
$195$	−82.2460	+	71.2666i	−0.421775	+	0.365470i
$196$	−82.2908	−	94.9687i	−0.419851	−	0.484534i
$197$	−273.025	−	80.1673i	−1.38591	−	0.406941i	−0.498089	−	0.867126i	$-0.665965\pi$
$197$	−273.025	−	80.1673i	−1.38591	−	0.406941i	−0.887823	+	0.460185i	$0.847783\pi$
$198$	−8.89252	−	4.06108i	−0.0449117	−	0.0205105i
$199$	−124.453	+	193.653i	−0.625393	+	0.973131i	0.373570	+	0.927602i	$0.378134\pi$
$199$	−124.453	+	193.653i	−0.625393	+	0.973131i	−0.998963	+	0.0455287i	$0.985503\pi$
$200$	157.885	−	46.3591i	0.789423	−	0.231796i
$201$	−21.8241	−	3.13783i	−0.108577	−	0.0156111i
$202$	12.1459	+	26.5958i	0.0601282	+	0.131662i
$203$	−54.0453	+	7.77054i	−0.266233	+	0.0382785i
$204$	−49.5624	−	77.1206i	−0.242953	−	0.378042i
$205$	−31.6688	−	27.4412i	−0.154482	−	0.133859i
$206$		−	135.426i		−	0.657406i
$207$	13.4234	−	15.8796i	0.0648473	−	0.0767129i
$208$	36.9451			0.177621
$209$	−139.704	+	161.227i	−0.668439	+	0.771420i
$210$	−84.1140	+	54.0568i	−0.400543	+	0.257413i
$211$	−44.6752	−	310.723i	−0.211731	−	1.47262i	−0.767374	−	0.641200i	$-0.778437\pi$
$211$	−44.6752	−	310.723i	−0.211731	−	1.47262i	0.555643	−	0.831421i	$-0.312472\pi$
$212$	183.078	−	83.6088i	0.863574	−	0.394381i
$213$	12.8146	−	89.1272i	0.0601622	−	0.418437i
$214$	19.8079	+	67.4597i	0.0925605	+	0.315232i
$215$	−29.5020	−	18.9598i	−0.137219	−	0.0881850i
$216$	88.1452	−	193.011i	0.408080	−	0.893570i
$217$	−102.728	+	349.860i	−0.473402	+	1.61226i
$218$	−70.9598	+	61.4870i	−0.325504	+	0.282051i
$219$	−23.9598	−	27.6510i	−0.109405	−	0.126260i
$220$	38.6601	+	11.3516i	0.175728	+	0.0515983i
$221$	−182.774	−	83.4701i	−0.827031	−	0.377693i
$222$	81.8848	−	127.415i	0.368850	−	0.573942i
$223$	−151.479	+	44.4783i	−0.679278	+	0.199454i	−0.603131	−	0.797642i	$-0.706080\pi$
$223$	−151.479	+	44.4783i	−0.679278	+	0.199454i	−0.0761477	+	0.997097i	$0.524262\pi$
$224$	−306.498	−	44.0677i	−1.36829	−	0.196731i
$225$	7.42040	+	16.2484i	0.0329795	+	0.0722151i
$226$	−167.399	+	24.0683i	−0.740703	+	0.106497i
$227$	−29.5680	−	46.0087i	−0.130256	−	0.202682i	0.769999	−	0.638045i	$-0.220256\pi$
$227$	−29.5680	−	46.0087i	−0.130256	−	0.202682i	−0.900255	+	0.435363i	$0.856620\pi$
$228$	138.241	+	119.787i	0.606321	+	0.525380i
$229$			173.588i			0.758025i	0.925391	+	0.379013i	$0.123736\pi$
$229$			173.588i			0.758025i	−0.925391	+	0.379013i	$0.876264\pi$
$230$	37.5713	−	60.0639i	0.163353	−	0.261148i
$231$	260.886			1.12938
$232$	−28.8702	+	33.3180i	−0.124440	+	0.143612i
$233$	296.516	−	190.559i	1.27260	−	0.817852i	0.282646	−	0.959224i	$-0.408788\pi$
$233$	296.516	−	190.559i	1.27260	−	0.817852i	0.989956	+	0.141372i	$0.0451515\pi$
$234$	2.61466	+	18.1853i	0.0111737	+	0.0777151i
$235$	−151.306	+	69.0990i	−0.643854	+	0.294038i
$236$	23.1109	−	160.740i	0.0979274	−	0.681100i
$237$	−18.6096	−	63.3784i	−0.0785215	−	0.267420i
$238$	−155.303	−	99.8072i	−0.652534	−	0.419358i
$239$	−54.3419	+	118.992i	−0.227372	+	0.497875i	−0.988592	−	0.150619i	$-0.951873\pi$
$239$	−54.3419	+	118.992i	−0.227372	+	0.497875i	0.761220	+	0.648494i	$0.224601\pi$
$240$	−4.96497	+	16.9091i	−0.0206874	+	0.0704548i
$241$	42.3937	−	36.7343i	0.175907	−	0.152425i	−0.562457	−	0.826826i	$-0.690144\pi$
$241$	42.3937	−	36.7343i	0.175907	−	0.152425i	0.738365	+	0.674402i	$0.235598\pi$
$242$	−49.6971	−	57.3535i	−0.205360	−	0.236998i
$243$	46.6692	+	13.7033i	0.192054	+	0.0563922i
$244$	−56.3386	−	25.7290i	−0.230896	−	0.105447i
$245$	71.0297	−	110.524i	0.289917	−	0.451120i
$246$	−74.3613	+	21.8344i	−0.302282	+	0.0887579i
$247$	396.845	+	57.0578i	1.60666	+	0.231003i
$248$	122.302	+	267.805i	0.493155	+	1.07986i
$249$	−51.4185	+	7.39287i	−0.206500	+	0.0296902i
$250$	74.5381	+	115.983i	0.298152	+	0.463934i
$251$	148.924	+	129.043i	0.593321	+	0.514116i	0.898959	−	0.438032i	$-0.144324\pi$
$251$	148.924	+	129.043i	0.593321	+	0.514116i	−0.305638	+	0.952148i	$0.598870\pi$
$252$		−	20.4186i		−	0.0810264i
$253$	−167.198	+	78.8410i	−0.660862	+	0.311624i
$254$	49.4280			0.194599
$255$	62.7655	−	72.4352i	0.246139	−	0.284060i
$256$	−228.351	+	146.752i	−0.891997	+	0.573251i
$257$	19.8378	+	137.975i	0.0771901	+	0.536869i	0.991322	+	0.131453i	$0.0419642\pi$
$257$	19.8378	+	137.975i	0.0771901	+	0.536869i	−0.914132	+	0.405416i	$0.867127\pi$
$258$	−58.9985	+	26.9437i	−0.228676	+	0.104433i
$259$	−52.5064	+	365.190i	−0.202727	+	1.41000i
$260$	−21.3336	−	72.6554i	−0.0820521	−	0.279444i
$261$	−4.02600	−	2.58735i	−0.0154253	−	0.00991324i
$262$	57.3118	−	125.495i	0.218747	−	0.478989i
$263$	80.6330	−	274.611i	0.306589	−	1.04415i	−0.651731	−	0.758451i	$-0.725957\pi$
$263$	80.6330	−	274.611i	0.306589	−	1.04415i	0.958320	−	0.285697i	$-0.0922251\pi$
$264$	159.194	−	137.943i	0.603009	−	0.522510i
$265$	137.799	+	159.029i	0.519998	+	0.600110i
$266$	353.436	+	103.778i	1.32871	+	0.390144i
$267$	112.878	+	51.5496i	0.422763	+	0.193069i
$268$	8.29424	−	12.9061i	0.0309487	−	0.0481571i
$269$	443.025	−	130.084i	1.64693	−	0.483583i	0.678862	−	0.734266i	$-0.262473\pi$
$269$	443.025	−	130.084i	1.64693	−	0.483583i	0.968069	+	0.250683i	$0.0806552\pi$
$270$	77.6827	+	11.1691i	0.287714	+	0.0413670i
$271$	−48.8346	−	106.933i	−0.180201	−	0.394586i	0.797878	−	0.602819i	$-0.205956\pi$
$271$	−48.8346	−	106.933i	−0.180201	−	0.394586i	−0.978079	+	0.208233i	$0.933229\pi$
$272$	−32.2068	+	4.63065i	−0.118408	+	0.0170244i
$273$	−265.072	−	412.461i	−0.970961	−	1.51085i
$274$	−185.676	−	160.889i	−0.677651	−	0.587188i
$275$		−	158.803i		−	0.577464i
$276$	67.6008	+	143.361i	0.244931	+	0.519424i
$277$	−322.473			−1.16416			−0.582081	−	0.813131i	$-0.697761\pi$
$277$	−322.473			−1.16416			−0.582081	+	0.813131i	$0.697761\pi$
$278$	−132.342	+	152.730i	−0.476049	+	0.549390i
$279$	−26.8860	+	17.2786i	−0.0963656	+	0.0619304i
$280$	−27.9872	−	194.655i	−0.0999542	−	0.695197i
$281$	−431.727	+	197.163i	−1.53640	+	0.701649i	−0.990666	−	0.136312i	$-0.956475\pi$
$281$	−431.727	+	197.163i	−1.53640	+	0.701649i	−0.545730	+	0.837961i	$0.683748\pi$
$282$	−43.7815	+	304.507i	−0.155254	+	1.07981i
$283$	−68.5475	−	233.451i	−0.242217	−	0.824917i	−0.987426	−	0.158085i	$-0.949468\pi$
$283$	−68.5475	−	233.451i	−0.242217	−	0.824917i	0.745208	−	0.666832i	$-0.232350\pi$
$284$	52.7071	+	33.8728i	0.185588	+	0.119270i
$285$	−79.4456	+	173.962i	−0.278757	+	0.610392i
$286$	46.0166	−	156.718i	0.160897	−	0.547965i
$287$	142.676	−	123.629i	0.497128	−	0.430764i
$288$	−17.7732	−	20.5114i	−0.0617125	−	0.0712200i
$289$	−107.498	−	31.5644i	−0.371967	−	0.109219i
$290$	−14.8326	−	6.77381i	−0.0511468	−	0.0233580i
$291$	−145.362	+	226.187i	−0.499525	+	0.777276i
$292$	24.4267	−	7.17232i	0.0836530	−	0.0245627i
$293$	−228.098	−	32.7955i	−0.778491	−	0.111930i	−0.258396	−	0.966039i	$-0.583194\pi$
$293$	−228.098	−	32.7955i	−0.778491	−	0.111930i	−0.520094	+	0.854109i	$0.674103\pi$
$294$	−100.940	−	221.028i	−0.343334	−	0.751797i
$295$	168.055	−	24.1627i	0.569678	−	0.0819073i
$296$	161.054	+	250.604i	0.544100	+	0.846636i
$297$	−154.758	−	134.099i	−0.521072	−	0.451511i
$298$		−	80.9355i		−	0.271596i
$299$	294.529	+	184.234i	0.985046	+	0.616168i
$300$	−136.163			−0.453875
$301$	103.465	−	119.405i	0.343736	−	0.396693i
$302$	−91.5538	+	58.8381i	−0.303158	+	0.194828i
$303$	−9.73274	−	67.6927i	−0.0321213	−	0.223408i
$304$	59.0572	−	26.9705i	0.194267	−	0.0887189i
$305$	9.21550	−	64.0952i	0.0302148	−	0.210148i
$306$	−4.55865	−	15.5253i	−0.0148976	−	0.0507364i
$307$	30.9820	+	19.9109i	0.100919	+	0.0648565i	0.590127	−	0.807311i	$-0.299078\pi$
$307$	30.9820	+	19.9109i	0.100919	+	0.0648565i	−0.489208	+	0.872167i	$0.662714\pi$
$308$	−75.4087	+	165.122i	−0.244834	+	0.536111i
$309$	−89.2433	+	303.935i	−0.288813	+	0.983607i
$310$	−82.2965	+	71.3103i	−0.265472	+	0.230033i
$311$	−33.0792	−	38.1754i	−0.106364	−	0.122750i	0.700071	−	0.714073i	$-0.253152\pi$
$311$	−33.0792	−	38.1754i	−0.106364	−	0.122750i	−0.806435	+	0.591322i	$0.798606\pi$
$312$	−379.837	−	111.530i	−1.21743	−	0.357468i
$313$	379.824	+	173.460i	1.21349	+	0.554184i	0.916246	−	0.400616i	$-0.131204\pi$
$313$	379.824	+	173.460i	1.21349	+	0.554184i	0.297248	+	0.954800i	$0.403931\pi$
$314$	89.5097	−	139.280i	0.285063	−	0.443566i
$315$	20.4832	−	6.01440i	0.0650260	−	0.0190933i
$316$	45.4931	+	6.54092i	0.143966	+	0.0206991i
$317$	−85.0163	−	186.160i	−0.268190	−	0.587254i	0.726842	−	0.686804i	$-0.240987\pi$
$317$	−85.0163	−	186.160i	−0.268190	−	0.587254i	−0.995033	+	0.0995498i	$0.968260\pi$
$318$	385.218	−	55.3860i	1.21138	−	0.174170i
$319$	23.0022	+	35.7921i	0.0721071	+	0.112201i
$320$	−86.8156	−	75.2261i	−0.271299	−	0.235082i
$321$		−	164.452i		−	0.512312i
$322$	243.759	+	206.056i	0.757016	+	0.639925i
$323$	−353.101			−1.09319
$324$	−126.648	+	146.160i	−0.390889	+	0.451110i
$325$	−251.067	+	161.351i	−0.772514	+	0.496465i
$326$	58.1443	+	404.402i	0.178357	+	1.24050i
$327$	199.773	−	91.2335i	0.610928	−	0.279001i
$328$	21.6931	−	150.879i	0.0661376	−	0.459997i
$329$	−211.128	−	719.035i	−0.641726	−	2.18552i
$330$	65.5432	+	42.1220i	0.198616	+	0.127643i
$331$	71.1293	−	155.751i	0.214892	−	0.470548i	−0.771233	−	0.636553i	$-0.780360\pi$
$331$	71.1293	−	155.751i	0.214892	−	0.470548i	0.986125	+	0.166005i	$0.0530868\pi$
$332$	10.1833	−	34.6812i	0.0306726	−	0.104461i
$333$	−24.4391	+	21.1766i	−0.0733908	+	0.0635935i
$334$	199.429	+	230.154i	0.597094	+	0.689083i
$335$	15.3900	+	4.51891i	0.0459403	+	0.0134893i
$336$	−72.2211	−	32.9823i	−0.214944	−	0.0981616i
$337$	228.387	−	355.377i	0.677706	−	1.05453i	−0.316661	−	0.948539i	$-0.602562\pi$
$337$	228.387	−	355.377i	0.677706	−	1.05453i	0.994367	−	0.105993i	$-0.0338020\pi$
$338$	−76.3553	+	22.4199i	−0.225903	+	0.0663312i
$339$	391.552	+	56.2967i	1.15502	+	0.166067i
$340$	27.7040	+	60.6634i	0.0814825	+	0.178422i
$341$	281.235	−	40.4354i	0.824735	−	0.118579i
$342$	17.4552	+	27.1608i	0.0510385	+	0.0794175i
$343$	65.3709	+	56.6442i	0.190586	+	0.165143i
$344$		−	127.568i		−	0.370838i
$345$	−123.902	+	110.042i	−0.359136	+	0.318963i
$346$	−95.6482			−0.276440
$347$	−102.928	+	118.785i	−0.296623	+	0.342321i	−0.884424	−	0.466685i	$-0.845448\pi$
$347$	−102.928	+	118.785i	−0.296623	+	0.342321i	0.587801	+	0.809006i	$0.299994\pi$
$348$	30.6893	−	19.7228i	0.0881876	−	0.0566747i
$349$	26.1822	+	182.101i	0.0750206	+	0.521779i	0.992331	+	0.123607i	$0.0394463\pi$
$349$	26.1822	+	182.101i	0.0750206	+	0.521779i	−0.917311	+	0.398172i	$0.869645\pi$
$350$	−249.421	+	113.907i	−0.712632	+	0.325448i
$351$	−54.7686	+	380.924i	−0.156036	+	1.08525i
$352$	67.9777	+	231.511i	0.193118	+	0.657701i
$353$	191.548	+	123.101i	0.542630	+	0.348727i	0.783067	−	0.621938i	$-0.213654\pi$
$353$	191.548	+	123.101i	0.542630	+	0.348727i	−0.240437	+	0.970665i	$0.577291\pi$
$354$	130.445	−	285.635i	0.368489	−	0.806878i
$355$	−18.4547	+	62.8511i	−0.0519852	+	0.177045i
$356$	−65.2544	+	56.5432i	−0.183299	+	0.158829i
$357$	282.774	+	326.339i	0.792084	+	0.914114i
$358$	35.0366	+	10.2877i	0.0978675	+	0.0287365i
$359$	−49.1496	−	22.4459i	−0.136907	−	0.0625233i	0.345784	−	0.938314i	$-0.387613\pi$
$359$	−49.1496	−	22.4459i	−0.136907	−	0.0625233i	−0.482690	+	0.875791i	$0.660340\pi$
$360$	9.31888	−	14.5005i	0.0258858	−	0.0402791i
$361$	329.639	−	96.7908i	0.913128	−	0.268119i
$362$	−277.220	−	39.8582i	−0.765800	−	0.110105i
$363$	73.7397	+	161.467i	0.203140	+	0.444814i
$364$	337.677	−	48.5506i	0.927684	−	0.133381i
$365$	14.3900	+	22.3912i	0.0394246	+	0.0613458i
$366$	−90.5102	−	78.4276i	−0.247296	−	0.214283i
$367$		−	503.890i		−	1.37300i	−0.727131	−	0.686499i	$-0.759147\pi$
$367$		−	503.890i		−	1.37300i	0.727131	−	0.686499i	$-0.240853\pi$
$368$	56.2529	−	0.687697i	0.152861	−	0.00186874i
$369$	16.5470			0.0448428
$370$	−72.1541	+	83.2703i	−0.195011	+	0.225055i
$371$	−797.525	+	512.538i	−2.14966	+	1.38150i
$372$	−34.6707	−	241.140i	−0.0932007	−	0.648225i
$373$	297.027	−	135.648i	0.796318	−	0.363666i	0.0246535	−	0.999696i	$-0.492152\pi$
$373$	297.027	−	135.648i	0.796318	−	0.363666i	0.771664	+	0.636030i	$0.219424\pi$
$374$	−20.4721	+	142.387i	−0.0547382	+	0.380713i
$375$	−90.8539	−	309.420i	−0.242277	−	0.825120i
$376$	−509.020	−	327.127i	−1.35378	−	0.870019i
$377$	33.2160	−	72.7329i	0.0881061	−	0.192925i
$378$	−99.6146	+	339.256i	−0.263531	+	0.897503i
$379$	266.695	−	231.092i	0.703680	−	0.609742i	−0.227725	−	0.973725i	$-0.573129\pi$
$379$	266.695	−	231.092i	0.703680	−	0.609742i	0.931406	+	0.363983i	$0.118583\pi$
$380$	−87.1417	−	100.567i	−0.229320	−	0.264650i
$381$	−110.931	−	32.5722i	−0.291157	−	0.0854915i
$382$	−290.943	−	132.869i	−0.761630	−	0.347825i
$383$	−290.623	+	452.218i	−0.758806	+	1.18072i	0.219913	+	0.975519i	$0.429423\pi$
$383$	−290.623	+	452.218i	−0.758806	+	1.18072i	−0.978719	+	0.205205i	$0.934214\pi$
$384$	158.756	−	46.6149i	0.413427	−	0.121393i
$385$	−187.856	−	27.0096i	−0.487938	−	0.0701548i
$386$	−10.8580	−	23.7757i	−0.0281295	−	0.0615950i
$387$	13.7071	−	1.97079i	0.0354189	−	0.00509247i
$388$	−101.144	−	157.383i	−0.260680	−	0.405626i
$389$	10.6600	+	9.23695i	0.0274036	+	0.0237454i	0.668455	−	0.743753i	$-0.266956\pi$
$389$	10.6600	+	9.23695i	0.0274036	+	0.0237454i	−0.641051	+	0.767498i	$0.721501\pi$
$390$		−	146.422i		−	0.375441i
$391$	−279.847	−	123.690i	−0.715721	−	0.316343i
$392$	477.914			1.21917
$393$	−211.324	+	243.880i	−0.537719	+	0.620561i
$394$	322.074	−	206.984i	0.817447	−	0.525341i
$395$	6.83861	+	47.5635i	0.0173129	+	0.120414i
$396$	−14.4728	+	6.60949i	−0.0365474	+	0.0166906i
$397$	−20.9638	+	145.807i	−0.0528056	+	0.367271i	0.946235	+	0.323480i	$0.104853\pi$
$397$	−20.9638	+	145.807i	−0.0528056	+	0.367271i	−0.999041	+	0.0437913i	$0.986056\pi$
$398$	−87.2576	−	297.172i	−0.219240	−	0.746663i
$399$	−724.825	−	465.817i	−1.81661	−	1.16746i
$400$	−20.0765	+	43.9614i	−0.0501912	+	0.109903i
$401$	93.4983	−	318.426i	0.233163	−	0.794080i	−0.756909	−	0.653520i	$-0.773292\pi$
$401$	93.4983	−	318.426i	0.233163	−	0.794080i	0.990072	−	0.140560i	$-0.0448903\pi$
$402$	22.4195	−	19.4266i	0.0557699	−	0.0483249i
$403$	−349.676	−	403.548i	−0.867683	−	1.00136i
$404$	45.6579	+	13.4064i	0.113015	+	0.0331841i
$405$	−183.926	−	83.9964i	−0.454140	−	0.207399i
$406$	39.7172	−	61.8011i	0.0978256	−	0.152220i
$407$	275.843	−	80.9949i	0.677748	−	0.199005i
$408$	345.102	+	49.6181i	0.845837	+	0.121613i
$409$	305.548	+	669.057i	0.747061	+	1.63584i	0.771576	+	0.636137i	$0.219469\pi$
$409$	305.548	+	669.057i	0.747061	+	1.63584i	−0.0245148	+	0.999699i	$0.507804\pi$
$410$	55.8058	−	8.02367i	0.136112	−	0.0195699i
$411$	310.688	+	483.441i	0.755933	+	1.17625i
$412$	−166.573	−	144.337i	−0.404304	−	0.350331i
$413$			764.915i			1.85209i
$414$	4.31960	+	27.6405i	0.0104338	+	0.0667645i
$415$	37.7903			0.0910610
$416$	296.950	−	342.699i	0.713823	−	0.823795i
$417$	397.660	−	255.560i	0.953621	−	0.612855i
$418$	−40.8487	−	284.109i	−0.0977241	−	0.679686i
$419$	−259.291	+	118.414i	−0.618832	+	0.282611i	−0.700059	−	0.714085i	$-0.746843\pi$
$419$	−259.291	+	118.414i	−0.618832	+	0.282611i	0.0812277	+	0.996696i	$0.474116\pi$
$420$	−23.1589	+	161.074i	−0.0551403	+	0.383509i
$421$	165.419	+	563.364i	0.392918	+	1.33816i	0.884181	+	0.467145i	$0.154717\pi$
$421$	165.419	+	563.364i	0.392918	+	1.33816i	−0.491263	+	0.871011i	$0.663465\pi$
$422$	355.314	+	228.346i	0.841976	+	0.541105i
$423$	27.2858	−	59.7476i	0.0645055	−	0.141247i
$424$	−215.652	+	734.444i	−0.508614	+	1.73218i
$425$	198.644	−	172.126i	0.467398	−	0.405003i
$426$	79.3361	+	91.5588i	0.186235	+	0.214927i
$427$	279.917	+	82.1910i	0.655543	+	0.192485i
$428$	104.087	+	47.5347i	0.243193	+	0.111062i
$429$	−206.549	+	321.397i	−0.481467	+	0.749177i
$430$	45.2725	−	13.2932i	0.105285	−	0.0309145i
$431$	−638.587	−	91.8149i	−1.48164	−	0.213028i	−0.646436	−	0.762968i	$-0.723741\pi$
$431$	−638.587	−	91.8149i	−1.48164	−	0.213028i	−0.835204	+	0.549941i	$0.814650\pi$
$432$	25.8885	+	56.6878i	0.0599270	+	0.131222i
$433$	−86.2796	+	12.4051i	−0.199260	+	0.0286493i	−0.241222	−	0.970470i	$-0.577548\pi$
$433$	−86.2796	+	12.4051i	−0.199260	+	0.0286493i	0.0419621	+	0.999119i	$0.486639\pi$
$434$	−265.235	−	412.714i	−0.611140	−	0.950953i
$435$	28.8248	+	24.9768i	0.0662639	+	0.0574180i
$436$			152.813i			0.350489i
$437$	605.303	+	79.4898i	1.38513	+	0.181899i
$438$	49.2269			0.112390
$439$	166.005	−	191.579i	0.378142	−	0.436400i	−0.534494	−	0.845172i	$-0.679498\pi$
$439$	166.005	−	191.579i	0.378142	−	0.436400i	0.912636	+	0.408773i	$0.134043\pi$
$440$	−128.912	+	82.8469i	−0.292983	+	0.188289i
$441$	7.38323	+	51.3515i	0.0167420	+	0.116443i
$442$	245.914	−	112.305i	0.556366	−	0.254084i
$443$	100.645	−	700.000i	0.227189	−	1.58014i	−0.482676	−	0.875799i	$-0.660335\pi$
$443$	100.645	−	700.000i	0.227189	−	1.58014i	0.709865	−	0.704337i	$-0.248756\pi$
$444$	−69.4477	−	236.517i	−0.156414	−	0.532696i
$445$	−75.9429	−	48.8056i	−0.170658	−	0.109675i
$446$	88.2392	−	193.217i	0.197846	−	0.433222i
$447$	−53.3352	+	181.643i	−0.119318	+	0.406360i
$448$	391.126	−	338.912i	0.873048	−	0.756501i
$449$	268.808	+	310.221i	0.598681	+	0.690915i	0.971514	−	0.236984i	$-0.0761588\pi$
$449$	268.808	+	310.221i	0.598681	+	0.690915i	−0.372832	+	0.927899i	$0.621613\pi$
$450$	−23.0598	−	6.77097i	−0.0512440	−	0.0150466i
$451$	−133.813	−	61.1102i	−0.296702	−	0.135499i
$452$	−148.810	+	231.552i	−0.329225	+	0.512284i
$453$	244.247	−	71.7173i	0.539176	−	0.158316i
$454$	72.8348	+	10.4721i	0.160429	+	0.0230662i
$455$	148.168	+	324.444i	0.325645	+	0.713063i
$456$	−688.594	+	99.0048i	−1.51007	+	0.217116i
$457$	−418.002	−	650.423i	−0.914664	−	1.42325i	−0.905998	−	0.423283i	$-0.860878\pi$
$457$	−418.002	−	650.423i	−0.914664	−	1.42325i	−0.00866652	−	0.999962i	$-0.502759\pi$
$458$	−176.509	−	152.946i	−0.385390	−	0.333942i
$459$		−	338.935i		−	0.738420i
$460$	−33.8351	−	110.229i	−0.0735545	−	0.239628i
$461$	378.361			0.820739			0.410369	−	0.911919i	$-0.365400\pi$
$461$	378.361			0.820739			0.410369	+	0.911919i	$0.365400\pi$
$462$	−229.862	+	265.275i	−0.497538	+	0.574189i
$463$	−97.0838	+	62.3919i	−0.209684	+	0.134756i	−0.641268	−	0.767317i	$-0.721591\pi$
$463$	−97.0838	+	62.3919i	−0.209684	+	0.134756i	0.431584	+	0.902073i	$0.357955\pi$
$464$	−1.84271	−	12.8164i	−0.00397137	−	0.0276215i
$465$	231.690	−	105.809i	0.498257	−	0.227546i
$466$	−67.4902	+	469.405i	−0.144829	+	1.00731i
$467$	−1.77496	−	6.04497i	−0.00380078	−	0.0129443i	0.957571	−	0.288198i	$-0.0930562\pi$
$467$	−1.77496	−	6.04497i	−0.00380078	−	0.0129443i	−0.961372	+	0.275254i	$0.911238\pi$
$468$	25.1546	+	16.1659i	0.0537492	+	0.0345425i
$469$	−30.0191	+	65.7326i	−0.0640066	+	0.140155i
$470$	63.0515	−	214.734i	0.134152	−	0.456880i
$471$	−292.669	+	253.599i	−0.621377	+	0.538427i
$472$	404.447	+	466.757i	0.856879	+	0.988892i
$473$	−118.125	−	34.6848i	−0.249737	−	0.0733293i
$474$	80.8415	+	36.9191i	0.170552	+	0.0778883i
$475$	−283.545	+	441.205i	−0.596938	+	0.928853i
$476$	−288.285	+	84.6480i	−0.605640	+	0.177832i
$477$	−82.2470	−	11.8253i	−0.172426	−	0.0247911i
$478$	−73.1145	−	160.098i	−0.152959	−	0.334934i
$479$	176.586	−	25.3892i	0.368655	−	0.0530046i	0.0445023	−	0.999009i	$-0.485830\pi$
$479$	176.586	−	25.3892i	0.368655	−	0.0530046i	0.324153	+	0.946005i	$0.394921\pi$
$480$	116.941	+	181.964i	0.243627	+	0.379091i
$481$	−408.323	−	353.814i	−0.848905	−	0.735580i
$482$			75.4731i			0.156583i
$483$	−411.279	−	623.083i	−0.851510	−	1.29003i
$484$	−123.512			−0.255190
$485$	128.088	−	147.821i	0.264099	−	0.304786i
$486$	−55.0534	+	35.3807i	−0.113279	+	0.0727998i
$487$	−20.8008	−	144.672i	−0.0427120	−	0.297069i	−0.999969	−	0.00783097i	$-0.997507\pi$
$487$	−20.8008	−	144.672i	−0.0427120	−	0.297069i	0.957257	−	0.289238i	$-0.0934018\pi$
$488$	214.266	−	97.8519i	0.439069	−	0.200516i
$489$	136.002	−	945.912i	0.278122	−	1.93438i
$490$	49.8009	+	169.606i	0.101634	+	0.346135i
$491$	269.661	+	173.301i	0.549208	+	0.352954i	0.785631	−	0.618696i	$-0.212339\pi$
$491$	269.661	+	173.301i	0.549208	+	0.352954i	−0.236423	+	0.971650i	$0.575975\pi$
$492$	−52.3979	+	114.735i	−0.106500	+	0.233202i
$493$	−19.8398	+	67.5681i	−0.0402430	+	0.137055i
$494$	−407.672	+	353.250i	−0.825248	+	0.715081i
$495$	−10.8934	−	12.5717i	−0.0220069	−	0.0253973i
$496$	−82.9663	−	24.3611i	−0.167271	−	0.0491152i
$497$	−268.445	−	122.595i	−0.540131	−	0.246669i
$498$	37.7868	−	58.7975i	0.0758772	−	0.118067i
$499$	−397.621	+	116.752i	−0.796836	+	0.233972i	−0.654714	−	0.755877i	$-0.727211\pi$
$499$	−397.621	+	116.752i	−0.796836	+	0.233972i	−0.142122	+	0.989849i	$0.545393\pi$
$500$	222.102	+	31.9335i	0.444204	+	0.0638669i
$501$	−295.910	−	647.953i	−0.590639	−	1.29332i
$502$	−262.429	+	37.7316i	−0.522767	+	0.0751625i
$503$	387.279	+	602.617i	0.769938	+	1.19805i	0.975628	+	0.219430i	$0.0704196\pi$
$503$	387.279	+	602.617i	0.769938	+	1.19805i	−0.205691	+	0.978617i	$0.565944\pi$
$504$	58.6883	+	50.8537i	0.116445	+	0.100900i
$505$			49.7511i			0.0985170i
$506$	67.1481	−	239.477i	0.132704	−	0.473275i
$507$	186.138			0.367136
$508$	52.6804	−	60.7964i	0.103701	−	0.119678i
$509$	−168.764	+	108.458i	−0.331560	+	0.213080i	−0.695819	−	0.718217i	$-0.744958\pi$
$509$	−168.764	+	108.458i	−0.331560	+	0.213080i	0.364260	+	0.931297i	$0.381322\pi$
$510$	18.3523	+	127.643i	0.0359849	+	0.250281i
$511$	−109.078	+	49.8141i	−0.213459	+	0.0974835i
$512$	22.0461	−	153.334i	0.0430588	−	0.299481i
$513$	190.533	+	648.894i	0.371408	+	1.26490i
$514$	−157.776	−	101.396i	−0.306957	−	0.197269i
$515$	95.7278	−	209.615i	0.185879	−	0.407019i
$516$	−29.7399	+	101.285i	−0.0576354	+	0.196288i
$517$	−441.311	+	382.399i	−0.853600	+	0.739649i
$518$	−325.072	−	375.153i	−0.627552	−	0.724234i
$519$	214.663	+	63.0306i	0.413608	+	0.121446i
$520$	261.962	+	119.634i	0.503774	+	0.230066i
$521$	347.311	−	540.427i	0.666624	−	1.03729i	−0.329044	−	0.944315i	$-0.606727\pi$
$521$	347.311	−	540.427i	0.666624	−	1.03729i	0.995669	−	0.0929733i	$-0.0296371\pi$
$522$	6.17814	−	1.81407i	0.0118355	−	0.00347522i
$523$	177.710	+	25.5509i	0.339790	+	0.0488545i	0.310098	−	0.950705i	$-0.399638\pi$
$523$	177.710	+	25.5509i	0.339790	+	0.0488545i	0.0296924	+	0.999559i	$0.490547\pi$
$524$	−93.2761	−	204.246i	−0.178008	−	0.389783i
$525$	634.836	−	91.2757i	1.20921	−	0.173858i
$526$	208.187	+	323.945i	0.395793	+	0.615865i
$527$	355.410	+	307.965i	0.674403	+	0.584373i
$528$			61.8668i			0.117172i
$529$	451.882	+	275.034i	0.854219	+	0.519914i
$530$	−283.118			−0.534185
$531$	−43.9044	+	50.6684i	−0.0826826	+	0.0954208i
$532$	504.339	−	324.119i	0.948006	−	0.609246i
$533$	39.3448	+	273.649i	0.0738176	+	0.513412i
$534$	−151.872	+	69.3575i	−0.284404	+	0.129883i
$535$	−17.0258	+	118.417i	−0.0318239	+	0.221340i
$536$	16.4381	+	55.9831i	0.0306681	+	0.104446i
$537$	−71.8528	−	46.1770i	−0.133804	−	0.0859907i
$538$	−258.070	+	565.094i	−0.479683	+	1.05036i
$539$	129.941	−	442.538i	0.241078	−	0.821035i
$540$	96.5321	−	83.6455i	0.178763	−	0.154899i
$541$	−527.967	−	609.307i	−0.975910	−	1.12626i	−0.991981	−	0.126390i	$-0.959661\pi$
$541$	−527.967	−	609.307i	−0.975910	−	1.12626i	0.0160703	−	0.999871i	$-0.494884\pi$
$542$	151.760	+	44.5606i	0.279999	+	0.0822152i
$543$	595.896	+	272.137i	1.09741	+	0.501172i
$544$	−215.913	+	335.967i	−0.396899	+	0.617586i
$545$	−153.296	+	45.0118i	−0.281278	+	0.0825905i
$546$	652.952	+	93.8804i	1.19588	+	0.171942i
$547$	−57.4155	−	125.722i	−0.104964	−	0.229840i	0.849861	−	0.527006i	$-0.176686\pi$
$547$	−57.4155	−	125.722i	−0.104964	−	0.229840i	−0.954826	+	0.297166i	$0.903958\pi$
$548$	−395.788	+	56.9057i	−0.722240	+	0.103842i
$549$	13.8243	+	21.5110i	0.0251808	+	0.0391821i
$550$	161.475	+	139.919i	0.293590	+	0.254397i
$551$		−	140.513i		−	0.255014i
$552$	−580.419	−	162.747i	−1.05148	−	0.294831i
$553$	−216.489			−0.391481
$554$	284.126	−	327.899i	0.512862	−	0.591875i
$555$	216.809	−	139.334i	0.390646	−	0.251053i
$556$	46.8084	+	325.560i	0.0841878	+	0.585539i
$557$	94.7549	−	43.2731i	0.170117	−	0.0776896i	−0.328537	−	0.944491i	$-0.606555\pi$
$557$	94.7549	−	43.2731i	0.170117	−	0.0776896i	0.498653	+	0.866802i	$0.333828\pi$
$558$	6.11953	−	42.5623i	0.0109669	−	0.0762765i
$559$	65.1845	+	221.998i	0.116609	+	0.397134i
$560$	48.5896	+	31.2266i	0.0867671	+	0.0557618i
$561$	139.776	−	306.066i	0.249155	−	0.545572i
$562$	179.908	−	612.709i	0.320120	−	1.09023i
$563$	−165.885	+	143.740i	−0.294645	+	0.255311i	−0.789620	−	0.613596i	$-0.789723\pi$
$563$	−165.885	+	143.740i	−0.294645	+	0.255311i	0.494975	+	0.868907i	$0.335177\pi$
$564$	327.881	+	378.395i	0.581349	+	0.670913i
$565$	−276.117	−	81.0752i	−0.488702	−	0.143496i
$566$	297.776	+	135.990i	0.526106	+	0.240264i
$567$	492.500	−	766.345i	0.868606	−	1.35158i
$568$	−228.629	+	67.1315i	−0.402515	+	0.118189i
$569$	−865.074	−	124.379i	−1.52034	−	0.218592i	−0.669023	−	0.743242i	$-0.733287\pi$
$569$	−865.074	−	124.379i	−1.52034	−	0.218592i	−0.851318	+	0.524650i	$0.824196\pi$
$570$	−106.890	−	234.057i	−0.187527	−	0.410627i
$571$	147.961	−	21.2736i	0.259127	−	0.0372568i	−0.0115270	−	0.999934i	$-0.503669\pi$
$571$	147.961	−	21.2736i	0.259127	−	0.0372568i	0.270654	+	0.962677i	$0.412760\pi$
$572$	−143.718	−	223.630i	−0.251256	−	0.390962i
$573$	565.402	+	489.923i	0.986739	+	0.855014i
$574$			254.004i			0.442516i
$575$	−379.274	+	250.348i	−0.659606	+	0.435388i
$576$	45.3612			0.0787521
$577$	−554.057	+	639.416i	−0.960238	+	1.10817i	0.0338319	+	0.999428i	$0.489229\pi$
$577$	−554.057	+	639.416i	−0.960238	+	1.10817i	−0.994070	+	0.108746i	$0.965317\pi$
$578$	126.811	−	81.4962i	0.219396	−	0.140997i
$579$	8.70071	+	60.5148i	0.0150271	+	0.104516i
$580$	−24.1403	+	11.0245i	−0.0416213	+	0.0190078i
$581$	−24.2298	+	168.522i	−0.0417036	+	0.290055i
$582$	−101.917	−	347.098i	−0.175115	−	0.596388i
$583$	621.445	+	399.379i	1.06594	+	0.685041i
$584$	−40.2209	+	88.0714i	−0.0688714	+	0.150807i
$585$	−8.80758	+	29.9959i	−0.0150557	+	0.0512750i
$586$	234.321	−	203.040i	0.399865	−	0.346485i
$587$	−488.077	−	563.271i	−0.831477	−	0.959576i	0.168180	−	0.985756i	$-0.446211\pi$
$587$	−488.077	−	563.271i	−0.831477	−	0.959576i	−0.999657	+	0.0261807i	$0.991665\pi$
$588$	−379.447	−	111.416i	−0.645317	−	0.189482i
$589$	−853.560	−	389.808i	−1.44917	−	0.661813i
$590$	−123.501	+	192.172i	−0.209325	+	0.325715i
$591$	−859.227	+	252.292i	−1.45385	+	0.426890i
$592$	−86.6016	−	12.4514i	−0.146286	−	0.0210328i
$593$	268.581	+	588.110i	0.452919	+	0.991754i	0.989045	+	0.147616i	$0.0471601\pi$
$593$	268.581	+	588.110i	0.452919	+	0.991754i	−0.536126	+	0.844138i	$0.680113\pi$
$594$	272.710	−	39.2098i	0.459108	−	0.0660098i
$595$	−169.831	−	264.262i	−0.285430	−	0.444138i
$596$	−99.5505	−	86.2610i	−0.167031	−	0.144733i
$597$			724.442i			1.21347i
$598$	−446.839	+	137.159i	−0.747222	+	0.229362i
$599$	−385.426			−0.643449			−0.321724	−	0.946833i	$-0.604262\pi$
$599$	−385.426			−0.643449			−0.321724	+	0.946833i	$0.604262\pi$
$600$	339.120	−	391.365i	0.565200	−	0.652276i
$601$	804.595	−	517.082i	1.33876	−	0.860369i	0.341914	−	0.939731i	$-0.388925\pi$
$601$	804.595	−	517.082i	1.33876	−	0.860369i	0.996846	+	0.0793627i	$0.0252885\pi$
$602$	30.2525	+	210.411i	0.0502534	+	0.349520i
$603$	−5.76139	+	2.63114i	−0.00955454	+	0.00436341i
$604$	−25.2073	+	175.321i	−0.0417339	+	0.290266i
$605$	−36.3809	−	123.902i	−0.0601338	−	0.204797i
$606$	77.4071	+	49.7465i	0.127734	+	0.0820900i
$607$	−69.1866	+	151.498i	−0.113981	+	0.249584i	−0.958022	−	0.286695i	$-0.907443\pi$
$607$	−69.1866	+	151.498i	−0.113981	+	0.249584i	0.844041	+	0.536279i	$0.180171\pi$
$608$	224.503	−	764.588i	0.369249	−	1.25755i
$609$	−129.863	+	112.527i	−0.213240	+	0.184773i
$610$	57.0541	+	65.8439i	0.0935312	+	0.107941i
$611$	1052.97	+	309.179i	1.72335	+	0.506021i
$612$	−23.9548	−	10.9398i	−0.0391418	−	0.0178754i
$613$	437.247	−	680.370i	0.713291	−	1.10990i	−0.275602	−	0.961272i	$-0.588877\pi$
$613$	437.247	−	680.370i	0.713291	−	1.10990i	0.988893	−	0.148630i	$-0.0474864\pi$
$614$	−47.5438	+	13.9601i	−0.0774329	+	0.0227363i
$615$	−130.532	−	18.7677i	−0.212247	−	0.0305165i
$616$	−286.793	−	627.989i	−0.465573	−	1.01946i
$617$	−985.450	+	141.686i	−1.59716	+	0.229637i	−0.882666	−	0.470000i	$-0.844254\pi$
$617$	−985.450	+	141.686i	−1.59716	+	0.229637i	−0.714498	+	0.699638i	$0.753345\pi$
$618$	−230.418	−	358.537i	−0.372844	−	0.580157i
$619$	50.4021	+	43.6736i	0.0814250	+	0.0705552i	0.694622	−	0.719375i	$-0.255572\pi$
$619$	50.4021	+	43.6736i	0.0814250	+	0.0705552i	−0.613197	+	0.789930i	$0.710117\pi$
$620$			177.227i			0.285850i
$621$	−76.3006	+	581.018i	−0.122867	+	0.935616i
$622$	67.9633			0.109266
$623$	266.335	−	307.367i	0.427504	−	0.493366i
$624$	97.8114	−	62.8596i	0.156749	−	0.100737i
$625$	−36.9117	−	256.727i	−0.0590588	−	0.410763i
$626$	−511.035	+	233.382i	−0.816351	+	0.372815i
$627$	−95.5467	+	664.542i	−0.152387	+	1.05988i
$628$	−75.9145	−	258.541i	−0.120883	−	0.411689i
$629$	400.302	+	257.258i	0.636410	+	0.408996i
$630$	−11.9318	+	26.1270i	−0.0189394	+	0.0414715i
$631$	236.205	−	804.440i	0.374334	−	1.27486i	−0.529985	−	0.848007i	$-0.677802\pi$
$631$	236.205	−	804.440i	0.374334	−	1.27486i	0.904319	−	0.426858i	$-0.140379\pi$
$632$	−132.103	+	114.468i	−0.209024	+	0.181120i
$633$	−646.951	−	746.622i	−1.02204	−	1.17950i
$634$	264.199	+	77.5757i	0.416717	+	0.122359i
$635$	76.5058	+	34.9390i	0.120482	+	0.0550221i
$636$	342.440	−	532.848i	0.538428	−	0.837811i
$637$	−831.679	+	244.203i	−1.30562	+	0.383364i
$638$	−56.6612	−	8.14664i	−0.0888106	−	0.0127690i
$639$	−10.7453	−	23.5289i	−0.0168158	−	0.0368214i
$640$	−119.141	+	17.1299i	−0.186158	+	0.0267655i
$641$	182.159	+	283.445i	0.284179	+	0.442192i	0.953769	−	0.300539i	$-0.0971666\pi$
$641$	182.159	+	283.445i	0.284179	+	0.442192i	−0.669590	+	0.742731i	$0.733530\pi$
$642$	167.219	+	144.896i	0.260466	+	0.225695i
$643$			661.045i			1.02806i	0.857771	+	0.514032i	$0.171849\pi$
$643$			661.045i			1.02806i	−0.857771	+	0.514032i	$0.828151\pi$
$644$	513.247	−	80.2092i	0.796967	−	0.124548i
$645$	−110.365			−0.171108
$646$	311.112	−	359.043i	0.481598	−	0.555794i
$647$	−327.556	+	210.507i	−0.506268	+	0.325359i	−0.768719	−	0.639587i	$-0.779106\pi$
$647$	−327.556	+	210.507i	−0.506268	+	0.325359i	0.262451	+	0.964945i	$0.415469\pi$
$648$	−104.676	−	728.037i	−0.161537	−	1.12351i
$649$	542.173	−	247.602i	0.835397	−	0.381513i
$650$	57.1455	−	397.456i	0.0879161	−	0.611470i
$651$	323.293	+	1101.03i	0.496610	+	1.69130i
$652$	559.384	+	359.494i	0.857951	+	0.551372i
$653$	−503.194	+	1101.84i	−0.770589	+	1.68735i	−0.0452364	+	0.998976i	$0.514404\pi$
$653$	−503.194	+	1101.84i	−0.770589	+	1.68735i	−0.725352	+	0.688378i	$0.758323\pi$
$654$	−83.2488	+	283.519i	−0.127292	+	0.433516i
$655$	177.417	−	153.732i	0.270865	−	0.234706i
$656$	29.3176	+	33.8343i	0.0446915	+	0.0515767i
$657$	−10.0846	−	2.96110i	−0.0153494	−	0.00450700i
$658$	917.155	+	418.851i	1.39385	+	0.636551i
$659$	428.607	−	666.925i	0.650390	−	1.01203i	−0.346860	−	0.937917i	$-0.612752\pi$
$659$	428.607	−	666.925i	0.650390	−	1.01203i	0.997250	−	0.0741096i	$-0.0236115\pi$
$660$	121.666	−	35.7243i	0.184342	−	0.0541278i
$661$	940.233	+	135.185i	1.42244	+	0.204516i	0.810199	−	0.586155i	$-0.199359\pi$
$661$	940.233	+	135.185i	1.42244	+	0.204516i	0.612241	+	0.790671i	$0.290268\pi$
$662$	95.7012	+	209.556i	0.144564	+	0.316550i
$663$	−625.910	+	89.9922i	−0.944057	+	0.135735i
$664$	74.3203	+	115.645i	0.111928	+	0.174164i
$665$	473.699	+	410.462i	0.712329	+	0.617236i
$666$		−	43.5088i		−	0.0653285i
$667$	49.2211	−	111.362i	0.0737948	−	0.166960i
$668$	495.641			0.741977
$669$	−325.361	+	375.487i	−0.486340	+	0.561266i
$670$	−18.1548	+	11.6674i	−0.0270968	+	0.0174140i
$671$	−32.3517	−	225.011i	−0.0482141	−	0.335336i
$672$	−886.426	+	404.817i	−1.31909	+	0.602406i
$673$	41.2573	−	286.951i	0.0613035	−	0.426375i	−0.935939	−	0.352162i	$-0.885446\pi$
$673$	41.2573	−	286.951i	0.0613035	−	0.426375i	0.997242	−	0.0742130i	$-0.0236445\pi$
$674$	160.128	+	545.347i	0.237579	+	0.809121i
$675$	−423.504	−	272.169i	−0.627413	−	0.403214i
$676$	−53.8030	+	117.812i	−0.0795902	+	0.174278i
$677$	25.2455	−	85.9784i	0.0372903	−	0.126999i	−0.938744	−	0.344614i	$-0.888010\pi$
$677$	25.2455	−	85.9784i	0.0372903	−	0.126999i	0.976035	+	0.217615i	$0.0698278\pi$
$678$	−402.235	+	348.539i	−0.593267	+	0.514069i
$679$	577.068	+	665.972i	0.849879	+	0.980812i
$680$	−243.360	−	71.4570i	−0.357883	−	0.105084i
$681$	−156.562	−	71.4993i	−0.229900	−	0.104992i
$682$	−206.676	+	321.594i	−0.303044	+	0.471545i
$683$	1190.84	−	349.662i	1.74354	−	0.511951i	0.754087	−	0.656774i	$-0.228080\pi$
$683$	1190.84	−	349.662i	1.74354	−	0.511951i	0.989457	+	0.144824i	$0.0462615\pi$
$684$	52.0114	+	7.47811i	0.0760401	+	0.0109329i
$685$	−173.667	−	380.277i	−0.253528	−	0.555148i
$686$	−115.195	+	16.5625i	−0.167922	+	0.0241436i
$687$	295.348	+	459.571i	0.429910	+	0.668953i
$688$	28.3157	+	24.5357i	0.0411566	+	0.0356624i
$689$		−	1388.29i		−	2.01494i
$690$	−2.72550	−	222.943i	−0.00395000	−	0.323106i
$691$	−99.4743			−0.143957			−0.0719785	−	0.997406i	$-0.522931\pi$
$691$	−99.4743			−0.143957			−0.0719785	+	0.997406i	$0.522931\pi$
$692$	−101.942	+	117.647i	−0.147315	+	0.170010i
$693$	63.0463	−	40.5174i	0.0909760	−	0.0584667i
$694$	−30.0957	−	209.320i	−0.0433655	−	0.301614i
$695$	−312.801	+	142.851i	−0.450073	+	0.205542i
$696$	−19.7450	+	137.329i	−0.0283692	+	0.197312i
$697$	−68.5976	−	233.622i	−0.0984183	−	0.335182i
$698$	−208.234	−	133.824i	−0.298329	−	0.191725i
$699$	460.798	−	1009.01i	0.659224	−	1.44350i
$700$	−125.728	+	428.189i	−0.179611	+	0.611699i
$701$	473.583	−	410.362i	0.675582	−	0.585395i	−0.248017	−	0.968756i	$-0.579779\pi$
$701$	473.583	−	410.362i	0.675582	−	0.585395i	0.923599	+	0.383360i	$0.125233\pi$
$702$	−339.078	−	391.316i	−0.483017	−	0.557431i
$703$	−911.001	−	267.494i	−1.29588	−	0.380503i
$704$	−366.828	−	167.525i	−0.521063	−	0.237962i
$705$	−283.012	+	440.375i	−0.401435	+	0.624646i
$706$	−293.942	+	86.3093i	−0.416349	+	0.122251i
$707$	−221.860	−	31.8986i	−0.313804	−	0.0451182i
$708$	−212.302	−	464.877i	−0.299862	−	0.656606i
$709$	−375.851	+	54.0392i	−0.530114	+	0.0762189i	−0.402174	−	0.915563i	$-0.631745\pi$
$709$	−375.851	+	54.0392i	−0.530114	+	0.0762189i	−0.127940	+	0.991782i	$0.540836\pi$
$710$	−47.6484	−	74.1424i	−0.0671105	−	0.104426i
$711$	−14.3404	−	12.4260i	−0.0201693	−	0.0174768i
$712$		−	328.381i		−	0.461210i
$713$	−539.932	−	607.937i	−0.757268	−	0.852647i
$714$	−580.978			−0.813694
$715$	182.004	−	210.044i	0.254551	−	0.293768i
$716$	49.9957	−	32.1303i	0.0698265	−	0.0448747i
$717$	58.5880	+	407.489i	0.0817127	+	0.568324i
$718$	66.1285	−	30.1999i	0.0921009	−	0.0420611i
$719$	15.7988	−	109.883i	0.0219733	−	0.152828i	−0.975881	−	0.218304i	$-0.929948\pi$
$719$	15.7988	−	109.883i	0.0219733	−	0.152828i	0.997854	+	0.0654762i	$0.0208567\pi$
$720$	1.42626	+	4.85741i	0.00198092	+	0.00674640i
$721$	873.377	+	561.285i	1.21134	+	0.778481i
$722$	−192.021	+	420.467i	−0.265957	+	0.582364i
$723$	49.7355	−	169.384i	0.0687904	−	0.234279i
$724$	−344.486	+	298.499i	−0.475809	+	0.412291i
$725$	68.4957	+	79.0482i	0.0944768	+	0.109032i
$726$	−229.155	−	67.2860i	−0.315641	−	0.0926805i
$727$	121.194	+	55.3476i	0.166705	+	0.0761315i	0.497020	−	0.867739i	$-0.334428\pi$
$727$	121.194	+	55.3476i	0.166705	+	0.0761315i	−0.330315	+	0.943871i	$0.607155\pi$
$728$	−701.456	+	1091.49i	−0.963539	+	1.49930i
$729$	−615.803	+	180.816i	−0.844723	+	0.248033i
$730$	−35.4468	−	5.09648i	−0.0485572	−	0.00698148i
$731$	−84.6495	−	185.356i	−0.115800	−	0.253566i
$732$	−192.932	+	27.7394i	−0.263568	+	0.0378953i
$733$	−721.336	−	1122.42i	−0.984087	−	1.53127i	−0.840628	−	0.541613i	$-0.817814\pi$
$733$	−721.336	−	1122.42i	−0.984087	−	1.53127i	−0.143459	−	0.989656i	$-0.545822\pi$
$734$	512.369	+	443.970i	0.698050	+	0.604864i
$735$		−	413.464i		−	0.562536i
$736$	445.760	−	527.324i	0.605652	−	0.716473i
$737$	56.3085			0.0764023
$738$	−14.5793	+	16.8254i	−0.0197551	+	0.0227987i
$739$	−316.334	+	203.296i	−0.428057	+	0.275096i	−0.736880	−	0.676024i	$-0.763702\pi$
$739$	−316.334	+	203.296i	−0.428057	+	0.275096i	0.308822	+	0.951120i	$0.400065\pi$
$740$	25.5205	+	177.499i	0.0344871	+	0.239863i
$741$	1147.72	−	524.147i	1.54888	−	0.707351i
$742$	181.525	−	1262.53i	0.244643	−	1.70153i
$743$	389.916	+	1327.93i	0.524786	+	1.78726i	0.611758	+	0.791045i	$0.290463\pi$
$743$	389.916	+	1327.93i	0.524786	+	1.78726i	−0.0869720	+	0.996211i	$0.527719\pi$
$744$	779.446	+	500.919i	1.04764	+	0.673279i
$745$	57.2106	−	125.274i	0.0767928	−	0.168153i
$746$	−123.776	+	421.541i	−0.165919	+	0.565069i
$747$	−11.2778	+	9.77225i	−0.0150974	+	0.0130820i
$748$	153.316	+	176.936i	0.204968	+	0.236546i
$749$	−517.152	−	151.849i	−0.690456	−	0.202736i
$750$	394.676	+	180.243i	0.526235	+	0.240324i
$751$	383.108	−	596.128i	0.510131	−	0.793779i	−0.486680	−	0.873580i	$-0.661792\pi$
$751$	383.108	−	596.128i	0.510131	−	0.793779i	0.996811	+	0.0798013i	$0.0254286\pi$
$752$	170.513	−	50.0671i	0.226746	−	0.0665786i
$753$	613.831	+	88.2556i	0.815181	+	0.117205i
$754$	44.6906	+	97.8587i	0.0592713	+	0.129786i
$755$	−183.300	+	26.3545i	−0.242781	+	0.0349066i
$756$	311.115	+	484.105i	0.411528	+	0.640350i
$757$	−90.7661	−	78.6493i	−0.119902	−	0.103896i	0.592846	−	0.805316i	$-0.298004\pi$
$757$	−90.7661	−	78.6493i	−0.119902	−	0.103896i	−0.712748	+	0.701420i	$0.752550\pi$
$758$			474.794i			0.626378i
$759$	−308.511	+	493.206i	−0.406471	+	0.649811i
$760$	506.085			0.665902
$761$	−550.928	+	635.804i	−0.723952	+	0.835485i	−0.991776	−	0.127983i	$-0.959150\pi$
$761$	−550.928	+	635.804i	−0.723952	+	0.835485i	0.267824	+	0.963468i	$0.413695\pi$
$762$	130.860	−	84.0985i	0.171732	−	0.110366i
$763$	−102.437	−	712.468i	−0.134256	−	0.933772i
$764$	−473.515	+	216.247i	−0.619784	+	0.283046i
$765$	3.91836	−	27.2528i	0.00512204	−	0.0356246i
$766$	−203.764	−	693.955i	−0.266010	−	0.905946i
$767$	−942.333	−	605.601i	−1.22860	−	0.789570i
$768$	−354.866	+	777.049i	−0.462065	+	1.01178i
$769$	−301.597	+	1027.15i	−0.392194	+	1.33569i	0.492823	+	0.870130i	$0.335965\pi$
$769$	−301.597	+	1027.15i	−0.392194	+	1.33569i	−0.885016	+	0.465560i	$0.845853\pi$
$770$	192.981	−	167.219i	0.250625	−	0.217168i
$771$	287.276	+	331.534i	0.372602	+	0.430006i
$772$	−40.8165	−	11.9848i	−0.0528711	−	0.0155243i
$773$	−622.782	−	284.415i	−0.805669	−	0.367937i	−0.0303761	−	0.999539i	$-0.509670\pi$
$773$	−622.782	−	284.415i	−0.805669	−	0.367937i	−0.775293	+	0.631602i	$0.782398\pi$
$774$	−10.0732	+	15.6742i	−0.0130145	+	0.0202509i
$775$	670.206	−	196.790i	0.864782	−	0.253923i
$776$	704.262	+	101.258i	0.907554	+	0.130487i
$777$	482.337	+	1056.17i	0.620768	+	1.35929i
$778$	−18.7848	+	2.70084i	−0.0241449	+	0.00347152i
$779$	262.661	+	408.709i	0.337178	+	0.524659i
$780$	−180.099	−	156.056i	−0.230896	−	0.200072i
$781$			229.958i			0.294440i
$782$	372.340	−	175.574i	0.476139	−	0.224520i
$783$	134.875			0.172255
$784$	−91.9191	+	106.080i	−0.117244	+	0.135307i
$785$	236.997	−	152.309i	0.301907	−	0.194024i
$786$	−61.7900	−	429.759i	−0.0786132	−	0.546767i
$787$	155.189	−	70.8725i	0.197191	−	0.0900540i	−0.314372	−	0.949300i	$-0.601794\pi$
$787$	155.189	−	70.8725i	0.197191	−	0.0900540i	0.511563	+	0.859246i	$0.329067\pi$
$788$	88.6759	−	616.754i	0.112533	−	0.782683i
$789$	−253.758	−	864.219i	−0.321619	−	1.09533i
$790$	−54.3893	−	34.9539i	−0.0688472	−	0.0442454i
$791$	538.582	−	1179.33i	0.680887	−	1.49094i
$792$	17.0479	−	58.0596i	0.0215251	−	0.0733076i
$793$	−322.871	+	279.770i	−0.407152	+	0.352799i
$794$	−129.789	−	149.785i	−0.163462	−	0.188646i
$795$	635.399	+	186.570i	0.799244	+	0.234679i
$796$	−458.520	−	209.399i	−0.576030	−	0.263064i
$797$	165.608	−	257.691i	0.207789	−	0.323327i	−0.721679	−	0.692228i	$-0.756629\pi$
$797$	165.608	−	257.691i	0.207789	−	0.323327i	0.929469	+	0.368901i	$0.120266\pi$
$798$	1112.29	−	326.597i	1.39384	−	0.409270i
$799$	−956.675	−	137.549i	−1.19734	−	0.172152i
$800$	246.414	+	539.572i	0.308018	+	0.674465i
$801$	35.2844	−	5.07313i	0.0440504	−	0.00633349i
$802$	241.404	+	375.632i	0.301002	+	0.468369i
$803$	70.6166	+	61.1896i	0.0879409	+	0.0762012i
$804$		−	48.2808i		−	0.0600507i
$805$	231.642	+	491.243i	0.287754	+	0.610240i
$806$	718.433			0.891356
$807$	951.571	−	1098.17i	1.17915	−	1.36081i
$808$	−152.247	+	97.8430i	−0.188424	+	0.121093i
$809$	−44.2504	−	307.768i	−0.0546976	−	0.380430i	−0.998721	−	0.0505528i	$-0.983902\pi$
$809$	−44.2504	−	307.768i	−0.0546976	−	0.380430i	0.944024	−	0.329877i	$-0.107007\pi$
$810$	247.465	−	113.013i	0.305512	−	0.139523i
$811$	−196.465	+	1366.44i	−0.242250	+	1.68489i	0.398523	+	0.917158i	$0.369523\pi$
$811$	−196.465	+	1366.44i	−0.242250	+	1.68489i	−0.640773	+	0.767730i	$0.721386\pi$
$812$	−33.6847	−	114.720i	−0.0414837	−	0.141280i
$813$	−311.228	−	200.014i	−0.382814	−	0.246020i
$814$	−160.684	+	351.848i	−0.197400	+	0.432246i
$815$	−195.861	+	667.043i	−0.240321	+	0.818457i
$816$	−77.3883	+	67.0574i	−0.0948387	+	0.0821782i
$817$	266.261	+	307.281i	0.325900	+	0.376109i
$818$	−949.529	−	278.807i	−1.16079	−	0.340840i
$819$	−128.116	−	58.5087i	−0.156430	−	0.0714392i
$820$	49.6087	−	77.1927i	0.0604984	−	0.0941374i
$821$	−1195.09	+	350.909i	−1.45565	+	0.427416i	−0.911404	−	0.411512i	$-0.865001\pi$
$821$	−1195.09	+	350.909i	−1.45565	+	0.427416i	−0.544242	+	0.838928i	$0.683183\pi$
$822$	−765.318	−	110.036i	−0.931044	−	0.133864i
$823$	177.663	+	389.027i	0.215872	+	0.472694i	0.986327	−	0.164801i	$-0.0526981\pi$
$823$	177.663	+	389.027i	0.215872	+	0.472694i	−0.770455	+	0.637495i	$0.779971\pi$
$824$	829.719	−	119.296i	1.00694	−	0.144776i
$825$	−270.192	−	420.427i	−0.327506	−	0.509609i
$826$	−777.786	−	673.955i	−0.941629	−	0.815926i
$827$			614.807i			0.743419i	0.928349	+	0.371709i	$0.121228\pi$
$827$			614.807i			0.743419i	−0.928349	+	0.371709i	$0.878772\pi$
$828$	38.6016	+	24.1461i	0.0466203	+	0.0291620i
$829$	517.712			0.624502			0.312251	−	0.950000i	$-0.398917\pi$
$829$	517.712			0.624502			0.312251	+	0.950000i	$0.398917\pi$
$830$	−33.2965	+	38.4262i	−0.0401162	+	0.0462966i
$831$	−853.741	+	548.666i	−1.02737	+	0.660248i
$832$	107.858	+	750.170i	0.129637	+	0.901646i
$833$	694.408	−	317.126i	0.833623	−	0.380703i
$834$	−90.5115	+	629.521i	−0.108527	+	0.754822i
$835$	145.993	+	497.207i	0.174842	+	0.595458i
$836$	−392.990	−	252.559i	−0.470084	−	0.302104i
$837$	374.168	−	819.315i	0.447035	−	0.978870i
$838$	108.050	−	367.986i	0.128939	−	0.439124i
$839$	960.771	−	832.513i	1.14514	−	0.992268i	0.145142	−	0.989411i	$-0.453636\pi$
$839$	960.771	−	832.513i	1.14514	−	0.992268i	0.999996	−	0.00285681i	$-0.000909352\pi$
$840$	−405.288	−	467.728i	−0.482486	−	0.556818i
$841$	780.046	+	229.042i	0.927522	+	0.272345i
$842$	−718.591	−	328.169i	−0.853433	−	0.389750i
$843$	−807.531	+	1256.54i	−0.957925	+	1.49056i
$844$	659.559	−	193.664i	0.781468	−	0.229460i
$845$	−134.032	−	19.2709i	−0.158618	−	0.0228058i
$846$	36.7118	+	80.3876i	0.0433946	+	0.0950208i
$847$	575.854	−	82.7953i	0.679875	−	0.0977512i
$848$	−121.544	−	189.126i	−0.143330	−	0.223026i
$849$	−578.681	−	501.430i	−0.681603	−	0.590612i
$850$			353.644i			0.416052i
$851$	−628.303	−	531.120i	−0.738311	−	0.624113i
$852$	197.173			0.231424
$853$	−120.587	+	139.165i	−0.141368	+	0.163147i	−0.822018	−	0.569461i	$-0.807152\pi$
$853$	−120.587	+	139.165i	−0.141368	+	0.163147i	0.680650	+	0.732608i	$0.261697\pi$
$854$	−330.205	+	212.210i	−0.386656	+	0.248489i
$855$	7.81845	+	54.3785i	0.00914439	+	0.0636006i
$856$	−395.860	+	180.783i	−0.462453	+	0.211195i
$857$	−142.527	+	991.300i	−0.166310	+	1.15671i	0.720121	+	0.693849i	$0.244086\pi$
$857$	−142.527	+	991.300i	−0.166310	+	1.15671i	−0.886431	+	0.462861i	$0.846823\pi$
$858$	−144.817	−	493.202i	−0.168785	−	0.574828i
$859$	−1050.84	−	675.333i	−1.22333	−	0.786185i	−0.240489	−	0.970652i	$-0.577308\pi$
$859$	−1050.84	−	675.333i	−1.22333	−	0.786185i	−0.982839	+	0.184467i	$0.940944\pi$
$860$	31.9008	−	69.8531i	0.0370940	−	0.0812245i
$861$	167.385	−	570.060i	0.194407	−	0.662091i
$862$	656.009	−	568.435i	0.761031	−	0.659437i
$863$	−243.431	−	280.935i	−0.282076	−	0.325533i	0.596976	−	0.802259i	$-0.296369\pi$
$863$	−243.431	−	280.935i	−0.282076	−	0.325533i	−0.879052	+	0.476726i	$0.841823\pi$
$864$	733.912	+	215.496i	0.849435	+	0.249417i
$865$	−148.046	−	67.6105i	−0.171152	−	0.0781625i
$866$	63.4058	−	98.6613i	0.0732168	−	0.113928i
$867$	−338.305	+	99.3352i	−0.390201	+	0.114573i
$868$	−790.324	−	113.631i	−0.910512	−	0.130912i
$869$	70.0773	+	153.448i	0.0806413	+	0.176580i
$870$	−50.7942	+	7.30310i	−0.0583841	+	0.00839437i
$871$	−57.2122	−	89.0238i	−0.0656856	−	0.102209i
$872$	−439.224	−	380.590i	−0.503697	−	0.436456i
$873$			77.2368i			0.0884728i
$874$	−614.150	+	545.450i	−0.702689	+	0.624085i
$875$	−1056.92			−1.20791
$876$	52.4660	−	60.5489i	0.0598926	−	0.0691198i
$877$	195.815	−	125.842i	0.223278	−	0.143492i	−0.424220	−	0.905559i	$-0.639452\pi$
$877$	195.815	−	125.842i	0.223278	−	0.143492i	0.647498	+	0.762067i	$0.275815\pi$
$878$	48.5389	+	337.595i	0.0552835	+	0.384505i
$879$	−659.684	+	301.268i	−0.750494	+	0.342739i
$880$	6.40509	−	44.5484i	0.00727851	−	0.0506232i
$881$	−107.057	−	364.604i	−0.121518	−	0.413853i	0.876155	−	0.482029i	$-0.160100\pi$
$881$	−107.057	−	364.604i	−0.121518	−	0.413853i	−0.997673	+	0.0681764i	$0.978282\pi$
$882$	−58.7208	−	37.7376i	−0.0665769	−	0.0427864i
$883$	65.8746	−	144.245i	0.0746031	−	0.163358i	−0.868656	−	0.495416i	$-0.835016\pi$
$883$	65.8746	−	144.245i	0.0746031	−	0.163358i	0.943259	+	0.332058i	$0.107743\pi$
$884$	123.960	−	422.168i	0.140226	−	0.477566i
$885$	403.812	−	349.905i	0.456284	−	0.395373i
$886$	623.102	+	719.098i	0.703275	+	0.811623i
$887$	937.152	+	275.173i	1.05654	+	0.310229i	0.763457	−	0.645858i	$-0.223500\pi$
$887$	937.152	+	275.173i	1.05654	+	0.310229i	0.293084	+	0.956087i	$0.405318\pi$
$888$	852.773	+	389.448i	0.960330	+	0.438568i
$889$	−204.859	+	318.767i	−0.230438	+	0.358569i
$890$	116.539	−	34.2189i	0.130943	−	0.0384482i
$891$	−702.608	−	101.020i	−0.788561	−	0.113378i
$892$	−143.611	−	314.465i	−0.160999	−	0.352539i
$893$	1908.89	−	274.457i	2.13761	−	0.307342i
$894$	−137.706	−	214.275i	−0.154034	−	0.239682i
$895$	46.9583	+	40.6896i	0.0524674	+	0.0454633i
$896$		−	542.281i		−	0.605224i
$897$	1093.22	−	13.3647i	1.21875	−	0.0148994i
$898$	−552.283			−0.615015
$899$	−122.551	+	141.432i	−0.136319	+	0.157321i
$900$	−32.9054	+	21.1470i	−0.0365616	+	0.0234967i
$901$	174.007	+	1210.24i	0.193126	+	1.34322i
$902$	180.039	−	82.2209i	0.199599	−	0.0911540i
$903$	70.7619	−	492.160i	0.0783631	−	0.545027i
$904$	−294.921	−	1004.41i	−0.326240	−	1.11107i
$905$	−400.912	−	257.651i	−0.442997	−	0.284697i
$906$	−142.278	+	311.545i	−0.157040	+	0.343869i
$907$	−265.774	+	905.144i	−0.293026	+	0.997954i	0.673029	+	0.739616i	$0.264993\pi$
$907$	−265.774	+	905.144i	−0.293026	+	0.997954i	−0.966055	+	0.258338i	$0.916825\pi$
$908$	90.5079	−	78.4256i	0.0996783	−	0.0863718i
$909$	−12.8652	−	14.8472i	−0.0141531	−	0.0163336i
$910$	−460.452	−	135.201i	−0.505991	−	0.148572i
$911$	250.275	+	114.297i	0.274725	+	0.125463i	0.548014	−	0.836469i	$-0.315384\pi$
$911$	250.275	+	114.297i	0.274725	+	0.125463i	−0.273288	+	0.961932i	$0.588111\pi$
$912$	110.464	−	171.886i	0.121123	−	0.188471i
$913$	127.292	−	37.3762i	0.139421	−	0.0409378i
$914$	1029.66	+	148.043i	1.12654	+	0.161973i
$915$	−84.6559	−	185.371i	−0.0925201	−	0.202591i
$916$	−376.246	+	54.0959i	−0.410748	+	0.0590567i
$917$	571.800	+	889.738i	0.623555	+	0.970271i
$918$	344.638	+	298.630i	0.375422	+	0.325305i
$919$		−	412.424i		−	0.448775i	−0.974500	−	0.224388i	$-0.927962\pi$
$919$		−	412.424i		−	0.448775i	0.974500	−	0.224388i	$-0.0720382\pi$
$920$	401.093	+	177.280i	0.435971	+	0.192696i
$921$	115.902			0.125843
$922$	−333.368	+	384.727i	−0.361570	+	0.417274i
$923$	363.564	−	233.648i	0.393894	−	0.253140i
$924$	81.3010	+	565.461i	0.0879881	+	0.611971i
$925$	642.896	−	293.601i	0.695023	−	0.317406i
$926$	22.0973	−	153.690i	0.0238631	−	0.165972i
$927$	25.6365	+	87.3098i	0.0276553	+	0.0941853i
$928$	−133.694	−	85.9201i	−0.144067	−	0.0925863i
$929$	−135.394	+	296.471i	−0.145741	+	0.319129i	−0.968398	−	0.249409i	$-0.919764\pi$
$929$	−135.394	+	296.471i	−0.145741	+	0.319129i	0.822657	+	0.568538i	$0.192491\pi$
$930$	−96.5487	+	328.815i	−0.103816	+	0.353564i
$931$	−1151.18	+	997.502i	−1.23650	+	1.07143i
$932$	505.436	+	583.304i	0.542313	+	0.625863i
$933$	−152.529	−	44.7867i	−0.163483	−	0.0480029i
$934$	7.71057	+	3.52130i	0.00825543	+	0.00377013i
$935$	−132.335	+	205.918i	−0.141535	+	0.220233i
$936$	−109.114	+	32.0387i	−0.116575	+	0.0342294i
$937$	1031.01	+	148.237i	1.10033	+	0.158204i	0.668473	−	0.743736i	$-0.266948\pi$
$937$	1031.01	+	148.237i	1.10033	+	0.158204i	0.431860	+	0.901941i	$0.357857\pi$
$938$	−40.3893	−	88.4402i	−0.0430589	−	0.0942859i
$939$	1300.71	−	187.013i	1.38520	−	0.199162i
$940$	−196.922	−	306.416i	−0.209491	−	0.325975i
$941$	−873.960	−	757.291i	−0.928757	−	0.804772i	0.0522722	−	0.998633i	$-0.483354\pi$
$941$	−873.960	−	757.291i	−0.928757	−	0.804772i	−0.981029	+	0.193860i	$0.937899\pi$
$942$		−	521.035i		−	0.553116i
$943$	65.0004	+	415.928i	0.0689294	+	0.441069i
$944$	−181.393			−0.192153
$945$	−393.994	+	454.694i	−0.416925	+	0.481157i
$946$	139.347	−	89.5529i	0.147301	−	0.0946648i
$947$	13.9968	+	97.3500i	0.0147802	+	0.102798i	0.995876	−	0.0907237i	$-0.0289180\pi$
$947$	13.9968	+	97.3500i	0.0147802	+	0.102798i	−0.981096	+	0.193522i	$0.938009\pi$
$948$	131.571	−	60.0865i	0.138788	−	0.0633824i
$949$	24.9910	−	173.816i	0.0263341	−	0.183157i
$950$	−198.801	−	677.056i	−0.209265	−	0.712690i
$951$	−541.817	−	348.205i	−0.569734	−	0.366146i
$952$	474.688	−	1039.42i	0.498622	−	1.09183i
$953$	−189.567	+	645.605i	−0.198916	+	0.677445i	0.798258	+	0.602316i	$0.205755\pi$
$953$	−189.567	+	645.605i	−0.198916	+	0.677445i	−0.997174	+	0.0751296i	$0.976063\pi$
$954$	84.4909	−	73.2118i	0.0885649	−	0.0767420i
$955$	−356.407	−	411.315i	−0.373201	−	0.430697i
$956$	−274.846	−	80.7021i	−0.287496	−	0.0844164i
$957$	121.796	+	55.6222i	0.127268	+	0.0581214i
$958$	−129.771	+	201.927i	−0.135460	+	0.210780i
$959$	1807.15	−	530.627i	1.88441	−	0.553313i
$960$	−357.835	−	51.4489i	−0.372745	−	0.0535926i
$961$	119.948	+	262.650i	0.124816	+	0.273309i
$962$	719.535	−	103.453i	0.747957	−	0.107540i
$963$	−25.5406	−	39.7420i	−0.0265219	−	0.0412689i
$964$	92.8317	+	80.4391i	0.0962985	+	0.0834431i
$965$		−	44.4756i		−	0.0460888i
$966$	995.939	+	130.789i	1.03099	+	0.135392i
$967$	−441.665			−0.456738			−0.228369	−	0.973575i	$-0.573339\pi$
$967$	−441.665			−0.456738			−0.228369	+	0.973575i	$0.573339\pi$
$968$	307.613	−	355.004i	0.317782	−	0.366739i
$969$	−934.830	+	600.779i	−0.964737	+	0.619999i
$970$	37.4523	+	260.486i	0.0386106	+	0.268543i
$971$	−801.065	+	365.834i	−0.824989	+	0.376760i	−0.782741	−	0.622347i	$-0.786179\pi$
$971$	−801.065	+	365.834i	−0.824989	+	0.376760i	−0.0422481	+	0.999107i	$0.513452\pi$
$972$	−15.1577	+	105.424i	−0.0155944	+	0.108461i
$973$	−436.474	−	1486.49i	−0.448586	−	1.52774i
$974$	165.434	+	106.318i	0.169850	+	0.109156i
$975$	−390.168	+	854.348i	−0.400172	+	0.876254i
$976$	−19.4909	+	66.3798i	−0.0199702	+	0.0680121i
$977$	−1045.41	+	905.852i	−1.07002	+	0.927177i	−0.997533	−	0.0701920i	$-0.977639\pi$
$977$	−1045.41	+	905.852i	−1.07002	+	0.927177i	−0.0724862	+	0.997369i	$0.523093\pi$
$978$	841.999	+	971.719i	0.860940	+	0.993578i
$979$	−304.074	−	89.2843i	−0.310597	−	0.0911995i
$980$	261.693	+	119.511i	0.267034	+	0.121950i
$981$	34.1086	−	53.0740i	0.0347692	−	0.0541019i
$982$	−413.811	+	121.506i	−0.421396	+	0.123733i
$983$	585.631	+	84.2010i	0.595759	+	0.0856572i	0.433597	−	0.901107i	$-0.357244\pi$
$983$	585.631	+	84.2010i	0.595759	+	0.0856572i	0.162162	+	0.986764i	$0.448153\pi$
$984$	−199.279	−	436.359i	−0.202519	−	0.443454i
$985$	644.824	−	92.7116i	0.654643	−	0.0941235i
$986$	−51.2245	−	79.7069i	−0.0519518	−	0.0808386i
$987$	−1782.35	−	1544.41i	−1.80582	−	1.56476i
$988$			877.930i			0.888593i
$989$	103.383	+	336.803i	0.104533	+	0.340549i
$990$	22.3812			0.0226073
$991$	−1200.52	+	1385.48i	−1.21143	+	1.39806i	−0.318459	+	0.947937i	$0.603165\pi$
$991$	−1200.52	+	1385.48i	−1.21143	+	1.39806i	−0.892967	+	0.450123i	$0.851380\pi$
$992$	−892.823	+	573.782i	−0.900023	+	0.578410i
$993$	−76.6872	−	533.371i	−0.0772278	−	0.537131i
$994$	361.180	−	164.946i	0.363360	−	0.165941i
$995$	75.0018	−	521.649i	0.0753787	−	0.524270i
$996$	−32.0476	−	109.144i	−0.0321763	−	0.109582i
$997$	−179.201	−	115.166i	−0.179740	−	0.115512i	0.447677	−	0.894195i	$-0.352252\pi$
$997$	−179.201	−	115.166i	−0.179740	−	0.115512i	−0.627417	+	0.778683i	$0.715888\pi$
$998$	231.621	−	507.180i	0.232086	−	0.508196i
$999$	256.762	−	874.451i	0.257019	−	0.875326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.7.2	✓	30
3.2	odd	2		207.3.j.a.145.2		30
4.3	odd	2		368.3.p.a.145.1		30
23.6	even	11		529.3.b.b.528.17		30
23.10	odd	22	inner	23.3.d.a.10.2	yes	30
23.17	odd	22		529.3.b.b.528.18		30
69.56	even	22		207.3.j.a.10.2		30
92.79	even	22		368.3.p.a.33.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.7.2	✓	30	1.1	even	1	trivial
23.3.d.a.10.2	yes	30	23.10	odd	22	inner
207.3.j.a.10.2		30	69.56	even	22
207.3.j.a.145.2		30	3.2	odd	2
368.3.p.a.33.1		30	92.79	even	22
368.3.p.a.145.1		30	4.3	odd	2
529.3.b.b.528.17		30	23.6	even	11
529.3.b.b.528.18		30	23.17	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.881085 + 1.01683i) q^{2} +(2.64748 - 1.70143i) q^{3} +(0.311634 + 2.16747i) q^{4} +(-2.08252 + 0.951056i) q^{5} +(-0.602595 + 4.19114i) q^{6} +(-2.90589 - 9.89656i) q^{7} +(-7.00598 - 4.50247i) q^{8} +(0.375553 - 0.822346i) q^{9} +(0.867820 - 2.95552i) q^{10} +(-6.07406 + 5.26321i) q^{11} +(4.51285 + 5.20810i) q^{12} +(14.4927 + 4.25543i) q^{13} +(12.6234 + 5.76492i) q^{14} +(-3.89528 + 6.06118i) q^{15} +(2.34688 - 0.689107i) q^{16} +(-13.1674 - 1.89318i) q^{17} +(0.505289 + 1.10643i) q^{18} +(26.2733 - 3.77753i) q^{19} +(-2.71037 - 4.21741i) q^{20} +(-24.5316 - 21.2568i) q^{21} -10.8136i q^{22} +(22.1459 + 6.20960i) q^{23} -26.2089 q^{24} +(-12.9391 + 14.9325i) q^{25} +(-17.0963 + 10.9871i) q^{26} +(3.62597 + 25.2192i) q^{27} +(20.5449 - 9.38253i) q^{28} +(0.753370 - 5.23980i) q^{29} +(-2.73109 - 9.30124i) q^{30} +(-29.7398 - 19.1126i) q^{31} +(12.4713 - 27.3082i) q^{32} +(-7.12598 + 24.2689i) q^{33} +(13.5266 - 11.7209i) q^{34} +(15.4638 + 17.8461i) q^{35} +(1.89944 + 0.557726i) q^{36} +(-32.5376 - 14.8594i) q^{37} +(-19.3079 + 30.0437i) q^{38} +(45.6095 - 13.3921i) q^{39} +(18.8722 + 2.71342i) q^{40} +(7.60347 + 16.6493i) q^{41} +(43.2289 - 6.21538i) q^{42} +(8.28150 + 12.8863i) q^{43} +(-13.3007 - 11.5251i) q^{44} +2.06973i q^{45} +(-25.8265 + 17.0473i) q^{46} +72.6550 q^{47} +(5.04086 - 5.81747i) q^{48} +(-48.2763 + 31.0253i) q^{49} +(-3.78334 - 26.3137i) q^{50} +(-38.0815 + 17.3912i) q^{51} +(-4.70709 + 32.7385i) q^{52} +(-25.8947 - 88.1894i) q^{53} +(-28.8383 - 18.5333i) q^{54} +(7.64377 - 16.7375i) q^{55} +(-24.2004 + 82.4189i) q^{56} +(63.1309 - 54.7032i) q^{57} +(4.66419 + 5.38276i) q^{58} +(-71.1561 - 20.8933i) q^{59} +(-14.3513 - 6.55402i) q^{60} +(-15.2916 + 23.7942i) q^{61} +(45.6374 - 13.4004i) q^{62} +(-9.22972 - 1.32703i) q^{63} +(20.8438 + 45.6417i) q^{64} +(-34.2285 + 4.92131i) q^{65} +(-18.3986 - 28.6288i) q^{66} +(-5.29481 - 4.58798i) q^{67} -29.1298i q^{68} +(69.1961 - 21.2400i) q^{69} -31.7713 q^{70} +(18.7368 - 21.6234i) q^{71} +(-6.33371 + 4.07043i) q^{72} +(-1.65454 - 11.5076i) q^{73} +(43.7778 - 19.9926i) q^{74} +(-8.84937 + 61.5487i) q^{75} +(16.3753 + 55.7692i) q^{76} +(69.7382 + 44.8180i) q^{77} +(-26.5683 + 58.1765i) q^{78} +(5.91331 - 20.1389i) q^{79} +(-4.23206 + 3.66710i) q^{80} +(57.8367 + 66.7471i) q^{81} +(-23.6287 - 6.93802i) q^{82} +(-15.0149 - 6.85707i) q^{83} +(38.4285 - 59.7959i) q^{84} +(29.2218 - 8.58031i) q^{85} +(-20.3998 - 2.93305i) q^{86} +(-6.92065 - 15.1541i) q^{87} +(66.2522 - 9.52563i) q^{88} +(21.3179 + 33.1714i) q^{89} +(-2.10455 - 1.82360i) q^{90} -155.794i q^{91} +(-6.55766 + 49.9356i) q^{92} -111.254 q^{93} +(-64.0153 + 73.8775i) q^{94} +(-51.1221 + 32.8542i) q^{95} +(-13.4457 - 93.5171i) q^{96} +(-77.7143 + 35.4909i) q^{97} +(10.9882 - 76.4246i) q^{98} +(2.04705 + 6.97160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18}+ \cdots - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

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