LMFDB - Embedded newform 207.3.j.a.10.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,3,Mod(10,207)] 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("207.10"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	207.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.64034147226$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	207.10
Dual form			207.3.j.a.145.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.881085 + 1.01683i) q^{2} +(0.311634 - 2.16747i) q^{4} +(2.08252 + 0.951056i) q^{5} +(-2.90589 + 9.89656i) q^{7} +(7.00598 - 4.50247i) q^{8} +(0.867820 + 2.95552i) q^{10} +(6.07406 + 5.26321i) q^{11} +(14.4927 - 4.25543i) q^{13} +(-12.6234 + 5.76492i) q^{14} +(2.34688 + 0.689107i) q^{16} +(13.1674 - 1.89318i) q^{17} +(26.2733 + 3.77753i) q^{19} +(2.71037 - 4.21741i) q^{20} +10.8136i q^{22} +(-22.1459 + 6.20960i) q^{23} +(-12.9391 - 14.9325i) q^{25} +(17.0963 + 10.9871i) q^{26} +(20.5449 + 9.38253i) q^{28} +(-0.753370 - 5.23980i) q^{29} +(-29.7398 + 19.1126i) q^{31} +(-12.4713 - 27.3082i) q^{32} +(13.5266 + 11.7209i) q^{34} +(-15.4638 + 17.8461i) q^{35} +(-32.5376 + 14.8594i) q^{37} +(19.3079 + 30.0437i) q^{38} +(18.8722 - 2.71342i) q^{40} +(-7.60347 + 16.6493i) q^{41} +(8.28150 - 12.8863i) q^{43} +(13.3007 - 11.5251i) q^{44} +(-25.8265 - 17.0473i) q^{46} -72.6550 q^{47} +(-48.2763 - 31.0253i) q^{49} +(3.78334 - 26.3137i) q^{50} +(-4.70709 - 32.7385i) q^{52} +(25.8947 - 88.1894i) q^{53} +(7.64377 + 16.7375i) q^{55} +(24.2004 + 82.4189i) q^{56} +(4.66419 - 5.38276i) q^{58} +(71.1561 - 20.8933i) q^{59} +(-15.2916 - 23.7942i) q^{61} +(-45.6374 - 13.4004i) q^{62} +(20.8438 - 45.6417i) q^{64} +(34.2285 + 4.92131i) q^{65} +(-5.29481 + 4.58798i) q^{67} -29.1298i q^{68} -31.7713 q^{70} +(-18.7368 - 21.6234i) q^{71} +(-1.65454 + 11.5076i) q^{73} +(-43.7778 - 19.9926i) q^{74} +(16.3753 - 55.7692i) q^{76} +(-69.7382 + 44.8180i) q^{77} +(5.91331 + 20.1389i) q^{79} +(4.23206 + 3.66710i) q^{80} +(-23.6287 + 6.93802i) q^{82} +(15.0149 - 6.85707i) q^{83} +(29.2218 + 8.58031i) q^{85} +(20.3998 - 2.93305i) q^{86} +(66.2522 + 9.52563i) q^{88} +(-21.3179 + 33.1714i) q^{89} +155.794i q^{91} +(6.55766 + 49.9356i) q^{92} +(-64.0153 - 73.8775i) q^{94} +(51.1221 + 32.8542i) q^{95} +(-77.7143 - 35.4909i) q^{97} +(-10.9882 - 76.4246i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 11 q^{2} - 23 q^{4} + 11 q^{5} - 11 q^{7} - 10 q^{8} - 11 q^{10} + 11 q^{11} - 11 q^{13} + 11 q^{14} + 73 q^{16} - 44 q^{17} + 22 q^{19} - 77 q^{20} - 36 q^{23} - 152 q^{25} + 186 q^{26} - 275 q^{28}+ \cdots - 77 q^{98}+O(q^{100}) $ 30 * q + 11 * q^2 - 23 * q^4 + 11 * q^5 - 11 * q^7 - 10 * q^8 - 11 * q^10 + 11 * q^11 - 11 * q^13 + 11 * q^14 + 73 * q^16 - 44 * q^17 + 22 * q^19 - 77 * q^20 - 36 * q^23 - 152 * q^25 + 186 * q^26 - 275 * q^28 + 88 * q^29 - 110 * q^31 + 147 * q^32 + 231 * q^34 - 209 * q^35 + 341 * q^37 - 374 * q^38 + 429 * q^40 - 77 * q^41 + 77 * q^43 - 110 * q^44 - 99 * q^46 + 110 * q^47 - 422 * q^49 + 396 * q^50 - 472 * q^52 + 187 * q^53 - 165 * q^55 - 176 * q^56 - 13 * q^58 + q^59 + 297 * q^61 - 82 * q^62 + 386 * q^64 - 220 * q^65 + 11 * q^67 - 198 * q^70 + 176 * q^71 - 121 * q^73 + 352 * q^74 + 110 * q^76 - 110 * q^77 + 33 * q^79 + 242 * q^80 + 96 * q^82 + 154 * q^83 + 275 * q^85 - 143 * q^86 + 429 * q^88 - 121 * q^89 - 166 * q^92 - 295 * q^94 + 154 * q^95 + 154 * q^97 - 77 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$	0.881085	+	1.01683i	0.440542	+	0.508413i	0.931985	−	0.362497i	$-0.118076\pi$
$2$	0.881085	+	1.01683i	0.440542	+	0.508413i	−0.491443	+	0.870910i	$0.663530\pi$
$3$		0			0
$3$		0			0
$4$	0.311634	−	2.16747i	0.0779086	−	0.541866i
$5$	2.08252	+	0.951056i	0.416505	+	0.190211i	0.612634	−	0.790367i	$-0.290110\pi$
$5$	2.08252	+	0.951056i	0.416505	+	0.190211i	−0.196129	+	0.980578i	$0.562837\pi$
$6$		0			0
$7$	−2.90589	+	9.89656i	−0.415128	+	1.41379i	0.441222	+	0.897398i	$0.354545\pi$
$7$	−2.90589	+	9.89656i	−0.415128	+	1.41379i	−0.856349	+	0.516397i	$0.827273\pi$
$8$	7.00598	−	4.50247i	0.875748	−	0.562809i
$9$		0			0
$10$	0.867820	+	2.95552i	0.0867820	+	0.295552i
$11$	6.07406	+	5.26321i	0.552188	+	0.478473i	0.885691	−	0.464276i	$-0.153685\pi$
$11$	6.07406	+	5.26321i	0.552188	+	0.478473i	−0.333503	+	0.942749i	$0.608231\pi$
$12$		0			0
$13$	14.4927	−	4.25543i	1.11482	−	0.327341i	0.328096	−	0.944644i	$-0.393593\pi$
$13$	14.4927	−	4.25543i	1.11482	−	0.327341i	0.786725	+	0.617303i	$0.211775\pi$
$14$	−12.6234	+	5.76492i	−0.901673	+	0.411780i
$15$		0			0
$16$	2.34688	+	0.689107i	0.146680	+	0.0430692i
$17$	13.1674	−	1.89318i	0.774550	−	0.111364i	0.256305	−	0.966596i	$-0.417495\pi$
$17$	13.1674	−	1.89318i	0.774550	−	0.111364i	0.518245	+	0.855232i	$0.326586\pi$
$18$		0			0
$19$	26.2733	+	3.77753i	1.38280	+	0.198817i	0.793243	−	0.608906i	$-0.208391\pi$
$19$	26.2733	+	3.77753i	1.38280	+	0.198817i	0.589562	+	0.807723i	$0.299300\pi$
$20$	2.71037	−	4.21741i	0.135518	−	0.210871i
$21$		0			0
$22$			10.8136i			0.491527i
$23$	−22.1459	+	6.20960i	−0.962865	+	0.269982i
$23$	−22.1459	+	6.20960i	−0.962865	+	0.269982i
$24$		0			0
$25$	−12.9391	−	14.9325i	−0.517565	−	0.597302i
$26$	17.0963	+	10.9871i	0.657551	+	0.422582i
$27$		0			0
$28$	20.5449	+	9.38253i	0.733746	+	0.335090i
$29$	−0.753370	−	5.23980i	−0.0259783	−	0.180683i	0.972701	−	0.232062i	$-0.0745473\pi$
$29$	−0.753370	−	5.23980i	−0.0259783	−	0.180683i	−0.998679	+	0.0513794i	$0.983638\pi$
$30$		0			0
$31$	−29.7398	+	19.1126i	−0.959347	+	0.616535i	−0.923817	−	0.382834i	$-0.874948\pi$
$31$	−29.7398	+	19.1126i	−0.959347	+	0.616535i	−0.0355297	+	0.999369i	$0.511312\pi$
$32$	−12.4713	−	27.3082i	−0.389727	−	0.853382i
$33$		0			0
$34$	13.5266	+	11.7209i	0.397841	+	0.344731i
$35$	−15.4638	+	17.8461i	−0.441822	+	0.509890i
$36$		0			0
$37$	−32.5376	+	14.8594i	−0.879393	+	0.401605i	−0.803356	−	0.595499i	$-0.796954\pi$
$37$	−32.5376	+	14.8594i	−0.879393	+	0.401605i	−0.0760377	+	0.997105i	$0.524227\pi$
$38$	19.3079	+	30.0437i	0.508103	+	0.790624i
$39$		0			0
$40$	18.8722	−	2.71342i	0.471806	−	0.0678354i
$41$	−7.60347	+	16.6493i	−0.185451	+	0.406080i	−0.979407	−	0.201894i	$-0.935290\pi$
$41$	−7.60347	+	16.6493i	−0.185451	+	0.406080i	0.793957	+	0.607974i	$0.208018\pi$
$42$		0			0
$43$	8.28150	−	12.8863i	0.192593	−	0.299681i	−0.731505	−	0.681836i	$-0.761182\pi$
$43$	8.28150	−	12.8863i	0.192593	−	0.299681i	0.924098	+	0.382155i	$0.124818\pi$
$44$	13.3007	−	11.5251i	0.302289	−	0.261935i
$45$		0			0
$46$	−25.8265	−	17.0473i	−0.561446	−	0.370595i
$47$	−72.6550			−1.54585			−0.772926	−	0.634496i	$-0.781208\pi$
$47$	−72.6550			−1.54585			−0.772926	+	0.634496i	$0.781208\pi$
$48$		0			0
$49$	−48.2763	−	31.0253i	−0.985231	−	0.633170i
$50$	3.78334	−	26.3137i	0.0756667	−	0.526274i
$51$		0			0
$52$	−4.70709	−	32.7385i	−0.0905209	−	0.629587i
$53$	25.8947	−	88.1894i	0.488580	−	1.66395i	−0.233668	−	0.972316i	$-0.575073\pi$
$53$	25.8947	−	88.1894i	0.488580	−	1.66395i	0.722248	−	0.691634i	$-0.243109\pi$
$54$		0			0
$55$	7.64377	+	16.7375i	0.138978	+	0.304319i
$56$	24.2004	+	82.4189i	0.432149	+	1.47177i
$57$		0			0
$58$	4.66419	−	5.38276i	0.0804170	−	0.0928062i
$59$	71.1561	−	20.8933i	1.20604	−	0.354124i	0.383878	−	0.923384i	$-0.374588\pi$
$59$	71.1561	−	20.8933i	1.20604	−	0.354124i	0.822158	+	0.569260i	$0.192770\pi$
$60$		0			0
$61$	−15.2916	−	23.7942i	−0.250682	−	0.390069i	0.692992	−	0.720945i	$-0.256292\pi$
$61$	−15.2916	−	23.7942i	−0.250682	−	0.390069i	−0.943674	+	0.330876i	$0.892656\pi$
$62$	−45.6374	−	13.4004i	−0.736087	−	0.216135i
$63$		0			0
$64$	20.8438	−	45.6417i	0.325685	−	0.713151i
$65$	34.2285	+	4.92131i	0.526592	+	0.0757125i
$66$		0			0
$67$	−5.29481	+	4.58798i	−0.0790270	+	0.0684773i	−0.693479	−	0.720477i	$-0.743923\pi$
$67$	−5.29481	+	4.58798i	−0.0790270	+	0.0684773i	0.614452	+	0.788955i	$0.289377\pi$
$68$		−	29.1298i		−	0.428379i
$69$		0			0
$70$	−31.7713			−0.453876
$71$	−18.7368	−	21.6234i	−0.263899	−	0.304556i	0.608300	−	0.793707i	$-0.291852\pi$
$71$	−18.7368	−	21.6234i	−0.263899	−	0.304556i	−0.872199	+	0.489152i	$0.837306\pi$
$72$		0			0
$73$	−1.65454	+	11.5076i	−0.0226649	+	0.157638i	−0.998011	−	0.0630439i	$-0.979919\pi$
$73$	−1.65454	+	11.5076i	−0.0226649	+	0.157638i	0.975346	+	0.220682i	$0.0708283\pi$
$74$	−43.7778	−	19.9926i	−0.591592	−	0.270171i
$75$		0			0
$76$	16.3753	−	55.7692i	0.215465	−	0.733806i
$77$	−69.7382	+	44.8180i	−0.905691	+	0.582053i
$78$		0			0
$79$	5.91331	+	20.1389i	0.0748520	+	0.254922i	0.988415	−	0.151774i	$-0.0484987\pi$
$79$	5.91331	+	20.1389i	0.0748520	+	0.254922i	−0.913563	+	0.406697i	$0.866681\pi$
$80$	4.23206	+	3.66710i	0.0529007	+	0.0458387i
$81$		0			0
$82$	−23.6287	+	6.93802i	−0.288155	+	0.0846100i
$83$	15.0149	−	6.85707i	0.180902	−	0.0826153i	−0.322905	−	0.946431i	$-0.604659\pi$
$83$	15.0149	−	6.85707i	0.180902	−	0.0826153i	0.503807	+	0.863816i	$0.331932\pi$
$84$		0			0
$85$	29.2218	+	8.58031i	0.343786	+	0.100945i
$86$	20.3998	−	2.93305i	0.237207	−	0.0341052i
$87$		0			0
$88$	66.2522	+	9.52563i	0.752866	+	0.108246i
$89$	−21.3179	+	33.1714i	−0.239527	+	0.372712i	−0.940117	−	0.340853i	$-0.889284\pi$
$89$	−21.3179	+	33.1714i	−0.239527	+	0.372712i	0.700589	+	0.713565i	$0.252921\pi$
$90$		0			0
$91$			155.794i			1.71202i
$92$	6.55766	+	49.9356i	0.0712789	+	0.542778i
$93$		0			0
$94$	−64.0153	−	73.8775i	−0.681013	−	0.785931i
$95$	51.1221	+	32.8542i	0.538127	+	0.345833i
$96$		0			0
$97$	−77.7143	−	35.4909i	−0.801178	−	0.365886i	−0.0276260	−	0.999618i	$-0.508795\pi$
$97$	−77.7143	−	35.4909i	−0.801178	−	0.365886i	−0.773552	+	0.633732i	$0.781522\pi$
$98$	−10.9882	−	76.4246i	−0.112124	−	0.779842i
$99$		0			0
$100$	−36.3981	+	23.3916i	−0.363981	+	0.233916i
$101$	−9.02736	−	19.7672i	−0.0893798	−	0.195715i	0.859663	−	0.510861i	$-0.170673\pi$
$101$	−9.02736	−	19.7672i	−0.0893798	−	0.195715i	−0.949043	+	0.315147i	$0.897946\pi$
$102$		0			0
$103$	−76.0694	−	65.9145i	−0.738538	−	0.639947i	0.202097	−	0.979365i	$-0.435224\pi$
$103$	−76.0694	−	65.9145i	−0.738538	−	0.639947i	−0.940635	+	0.339419i	$0.889770\pi$
$104$	82.3755	−	95.0664i	0.792072	−	0.914100i
$105$		0			0
$106$	112.489	−	51.3719i	1.06121	−	0.484640i
$107$	−28.2516	−	43.9603i	−0.264033	−	0.410844i	0.683771	−	0.729697i	$-0.260339\pi$
$107$	−28.2516	−	43.9603i	−0.264033	−	0.410844i	−0.947804	+	0.318853i	$0.896702\pi$
$108$		0			0
$109$	69.0753	−	9.93152i	0.633718	−	0.0911149i	0.182033	−	0.983292i	$-0.441732\pi$
$109$	69.0753	−	9.93152i	0.633718	−	0.0911149i	0.451685	+	0.892177i	$0.350823\pi$
$110$	−10.2843	+	22.5196i	−0.0934940	+	0.204723i
$111$		0			0
$112$	−13.6396	+	21.2236i	−0.121782	+	0.189496i
$113$	−94.9959	+	82.3144i	−0.840672	+	0.728446i	−0.964564	−	0.263850i	$-0.915008\pi$
$113$	−94.9959	+	82.3144i	−0.840672	+	0.728446i	0.123892	+	0.992296i	$0.460462\pi$
$114$		0			0
$115$	−52.0250	−	8.13037i	−0.452391	−	0.0706989i
$116$	−11.5919			−0.0999299
$117$		0			0
$118$	83.9395	+	53.9446i	0.711352	+	0.457158i
$119$	−19.5270	+	135.813i	−0.164092	+	1.14129i
$120$		0			0
$121$	−8.02718	−	55.8303i	−0.0663403	−	0.461407i
$122$	10.7214	−	36.5137i	0.0878801	−	0.299292i
$123$		0			0
$124$	32.1579	+	70.4160i	0.259338	+	0.567871i
$125$	−28.8694	−	98.3201i	−0.230955	−	0.786561i
$126$		0			0
$127$	−24.0577	+	27.7640i	−0.189430	+	0.218614i	−0.842518	−	0.538668i	$-0.818928\pi$
$127$	−24.0577	+	27.7640i	−0.189430	+	0.218614i	0.653088	+	0.757282i	$0.273473\pi$
$128$	−50.4456	+	14.8122i	−0.394106	+	0.115720i
$129$		0			0
$130$	25.1541	+	39.1405i	0.193493	+	0.301081i
$131$	98.3863	+	28.8888i	0.751040	+	0.220525i	0.634779	−	0.772693i	$-0.281091\pi$
$131$	98.3863	+	28.8888i	0.751040	+	0.220525i	0.116261	+	0.993219i	$0.462909\pi$
$132$		0			0
$133$	−113.732	+	249.038i	−0.855127	+	1.87247i
$134$	−9.33036	−	1.34150i	−0.0696295	−	0.0100112i
$135$		0			0
$136$	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	$0.767818\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	5.47855	−	38.1042i	0.0385814	−	0.268339i
$143$	110.427	+	50.4302i	0.772215	+	0.352659i
$144$		0			0
$145$	3.41444	−	11.6285i	0.0235479	−	0.0801966i
$146$	−13.1590	+	8.45677i	−0.0901301	+	0.0579231i
$147$		0			0
$148$	22.0674	+	75.1547i	0.149104	+	0.507802i
$149$	45.4620	+	39.3930i	0.305114	+	0.264383i	0.793937	−	0.608000i	$-0.208028\pi$
$149$	45.4620	+	39.3930i	0.305114	+	0.264383i	−0.488823	+	0.872383i	$0.662574\pi$
$150$		0			0
$151$	77.6109	−	22.7886i	0.513979	−	0.150918i	−0.0144495	−	0.999896i	$-0.504600\pi$
$151$	77.6109	−	22.7886i	0.513979	−	0.150918i	0.528429	+	0.848978i	$0.322781\pi$
$152$	201.078	−	91.8295i	1.32288	−	0.604141i
$153$		0			0
$154$	−107.017	−	31.4232i	−0.694919	−	0.204047i
$155$	−80.1108	+	11.5182i	−0.516844	+	0.0743110i
$156$		0			0
$157$	−121.801	−	17.5123i	−0.775799	−	0.111543i	−0.256968	−	0.966420i	$-0.582724\pi$
$157$	−121.801	−	17.5123i	−0.775799	−	0.111543i	−0.518831	+	0.854877i	$0.673633\pi$
$158$	−15.2676	+	23.7569i	−0.0966304	+	0.150360i
$159$		0			0
$160$		−	68.7309i		−	0.429568i
$161$	2.89995	−	237.213i	0.0180121	−	1.47337i
$162$		0			0
$163$	198.855	+	229.491i	1.21997	+	1.40792i	0.884935	+	0.465715i	$0.154203\pi$
$163$	198.855	+	229.491i	1.21997	+	1.40792i	0.335035	+	0.942206i	$0.391252\pi$
$164$	33.7172	+	21.6688i	0.205593	+	0.132127i
$165$		0			0
$166$	20.2018	+	9.22587i	0.121698	+	0.0555776i
$167$	−32.2123	−	224.041i	−0.192888	−	1.34157i	−0.824315	−	0.566131i	$-0.808440\pi$
$167$	−32.2123	−	224.041i	−0.192888	−	1.34157i	0.631427	−	0.775435i	$-0.282469\pi$
$168$		0			0
$169$	49.7572	−	31.9770i	0.294421	−	0.189213i
$170$	17.0222	+	37.2735i	0.100131	+	0.219256i
$171$		0			0
$172$	−25.3497	−	21.9657i	−0.147382	−	0.127707i
$173$	−46.5540	+	53.7262i	−0.269098	+	0.310556i	−0.874175	−	0.485611i	$-0.838597\pi$
$173$	−46.5540	+	53.7262i	−0.269098	+	0.310556i	0.605077	+	0.796167i	$0.293143\pi$
$174$		0			0
$175$	185.381	−	84.6605i	1.05932	−	0.483774i
$176$	10.6282	+	16.5378i	0.0603875	+	0.0939648i
$177$		0			0
$178$	−52.5124	+	7.55015i	−0.295014	+	0.0424166i
$179$	11.2744	−	24.6875i	0.0629854	−	0.137919i	−0.875522	−	0.483179i	$-0.839482\pi$
$179$	11.2744	−	24.6875i	0.0629854	−	0.137919i	0.938507	+	0.345260i	$0.112209\pi$
$180$		0			0
$181$	112.540	−	175.116i	0.621768	−	0.967490i	−0.377373	−	0.926061i	$-0.623173\pi$
$181$	112.540	−	175.116i	0.621768	−	0.967490i	0.999141	−	0.0414292i	$-0.0131911\pi$
$182$	−158.415	+	137.267i	−0.870412	+	0.754216i
$183$		0			0
$184$	−127.195	+	143.216i	−0.691279	+	0.778346i
$185$	−81.8923			−0.442661
$186$		0			0
$187$	89.9436	+	57.8032i	0.480982	+	0.309108i
$188$	−22.6418	+	157.477i	−0.120435	+	0.837645i
$189$		0			0
$190$	11.6359	+	80.9296i	0.0612417	+	0.425945i
$191$	−66.9746	+	228.094i	−0.350652	+	1.19421i	0.575734	+	0.817637i	$0.304716\pi$
$191$	−66.9746	+	228.094i	−0.350652	+	1.19421i	−0.926386	+	0.376575i	$0.877102\pi$
$192$		0			0
$193$	−8.07013	−	17.6711i	−0.0418141	−	0.0915602i	0.887572	−	0.460669i	$-0.152390\pi$
$193$	−8.07013	−	17.6711i	−0.0418141	−	0.0915602i	−0.929386	+	0.369108i	$0.879663\pi$
$194$	−32.3848	−	110.292i	−0.166932	−	0.568518i
$195$		0			0
$196$	−82.2908	+	94.9687i	−0.419851	+	0.484534i
$197$	273.025	−	80.1673i	1.38591	−	0.406941i	0.498089	−	0.867126i	$-0.334035\pi$
$197$	273.025	−	80.1673i	1.38591	−	0.406941i	0.887823	+	0.460185i	$0.152217\pi$
$198$		0			0
$199$	−124.453	−	193.653i	−0.625393	−	0.973131i	−0.998963	−	0.0455287i	$-0.985503\pi$
$199$	−124.453	−	193.653i	−0.625393	−	0.973131i	0.373570	−	0.927602i	$-0.378134\pi$
$200$	−157.885	−	46.3591i	−0.789423	−	0.231796i
$201$		0			0
$202$	12.1459	−	26.5958i	0.0601282	−	0.131662i
$203$	54.0453	+	7.77054i	0.266233	+	0.0382785i
$204$		0			0
$205$	−31.6688	+	27.4412i	−0.154482	+	0.133859i
$206$		−	135.426i		−	0.657406i
$207$		0			0
$208$	36.9451			0.177621
$209$	139.704	+	161.227i	0.668439	+	0.771420i
$210$		0			0
$211$	−44.6752	+	310.723i	−0.211731	+	1.47262i	0.555643	+	0.831421i	$0.312472\pi$
$211$	−44.6752	+	310.723i	−0.211731	+	1.47262i	−0.767374	+	0.641200i	$0.778437\pi$
$212$	−183.078	−	83.6088i	−0.863574	−	0.394381i
$213$		0			0
$214$	19.8079	−	67.4597i	0.0925605	−	0.315232i
$215$	29.5020	−	18.9598i	0.137219	−	0.0881850i
$216$		0			0
$217$	−102.728	−	349.860i	−0.473402	−	1.61226i
$218$	70.9598	+	61.4870i	0.325504	+	0.282051i
$219$		0			0
$220$	38.6601	−	11.3516i	0.175728	−	0.0515983i
$221$	182.774	−	83.4701i	0.827031	−	0.377693i
$222$		0			0
$223$	−151.479	−	44.4783i	−0.679278	−	0.199454i	−0.0761477	−	0.997097i	$-0.524262\pi$
$223$	−151.479	−	44.4783i	−0.679278	−	0.199454i	−0.603131	+	0.797642i	$0.706080\pi$
$224$	306.498	−	44.0677i	1.36829	−	0.196731i
$225$		0			0
$226$	−167.399	−	24.0683i	−0.740703	−	0.106497i
$227$	29.5680	−	46.0087i	0.130256	−	0.202682i	−0.769999	−	0.638045i	$-0.779744\pi$
$227$	29.5680	−	46.0087i	0.130256	−	0.202682i	0.900255	+	0.435363i	$0.143380\pi$
$228$		0			0
$229$		−	173.588i		−	0.758025i	−0.925391	−	0.379013i	$-0.876264\pi$
$229$		−	173.588i		−	0.758025i	0.925391	−	0.379013i	$-0.123736\pi$
$230$	−37.5713	−	60.0639i	−0.163353	−	0.261148i
$231$		0			0
$232$	−28.8702	−	33.3180i	−0.124440	−	0.143612i
$233$	−296.516	−	190.559i	−1.27260	−	0.817852i	−0.282646	−	0.959224i	$-0.591212\pi$
$233$	−296.516	−	190.559i	−1.27260	−	0.817852i	−0.989956	+	0.141372i	$0.954848\pi$
$234$		0			0
$235$	−151.306	−	69.0990i	−0.643854	−	0.294038i
$236$	−23.1109	−	160.740i	−0.0979274	−	0.681100i
$237$		0			0
$238$	−155.303	+	99.8072i	−0.652534	+	0.419358i
$239$	54.3419	+	118.992i	0.227372	+	0.497875i	0.988592	−	0.150619i	$-0.0481266\pi$
$239$	54.3419	+	118.992i	0.227372	+	0.497875i	−0.761220	+	0.648494i	$0.775399\pi$
$240$		0			0
$241$	42.3937	+	36.7343i	0.175907	+	0.152425i	0.738365	−	0.674402i	$-0.235598\pi$
$241$	42.3937	+	36.7343i	0.175907	+	0.152425i	−0.562457	+	0.826826i	$0.690144\pi$
$242$	49.6971	−	57.3535i	0.205360	−	0.236998i
$243$		0			0
$244$	−56.3386	+	25.7290i	−0.230896	+	0.105447i
$245$	−71.0297	−	110.524i	−0.289917	−	0.451120i
$246$		0			0
$247$	396.845	−	57.0578i	1.60666	−	0.231003i
$248$	−122.302	+	267.805i	−0.493155	+	1.07986i
$249$		0			0
$250$	74.5381	−	115.983i	0.298152	−	0.463934i
$251$	−148.924	+	129.043i	−0.593321	+	0.514116i	−0.898959	−	0.438032i	$-0.855676\pi$
$251$	−148.924	+	129.043i	−0.593321	+	0.514116i	0.305638	+	0.952148i	$0.401130\pi$
$252$		0			0
$253$	−167.198	−	78.8410i	−0.660862	−	0.311624i
$254$	−49.4280			−0.194599
$255$		0			0
$256$	−228.351	−	146.752i	−0.891997	−	0.573251i
$257$	−19.8378	+	137.975i	−0.0771901	+	0.536869i	0.914132	+	0.405416i	$0.132873\pi$
$257$	−19.8378	+	137.975i	−0.0771901	+	0.536869i	−0.991322	+	0.131453i	$0.958036\pi$
$258$		0			0
$259$	−52.5064	−	365.190i	−0.202727	−	1.41000i
$260$	21.3336	−	72.6554i	0.0820521	−	0.279444i
$261$		0			0
$262$	57.3118	+	125.495i	0.218747	+	0.478989i
$263$	−80.6330	−	274.611i	−0.306589	−	1.04415i	−0.958320	−	0.285697i	$-0.907775\pi$
$263$	−80.6330	−	274.611i	−0.306589	−	1.04415i	0.651731	−	0.758451i	$-0.274043\pi$
$264$		0			0
$265$	137.799	−	159.029i	0.519998	−	0.600110i
$266$	−353.436	+	103.778i	−1.32871	+	0.390144i
$267$		0			0
$268$	8.29424	+	12.9061i	0.0309487	+	0.0481571i
$269$	−443.025	−	130.084i	−1.64693	−	0.483583i	−0.678862	−	0.734266i	$-0.737527\pi$
$269$	−443.025	−	130.084i	−1.64693	−	0.483583i	−0.968069	+	0.250683i	$0.919345\pi$
$270$		0			0
$271$	−48.8346	+	106.933i	−0.180201	+	0.394586i	−0.978079	−	0.208233i	$-0.933229\pi$
$271$	−48.8346	+	106.933i	−0.180201	+	0.394586i	0.797878	+	0.602819i	$0.205956\pi$
$272$	32.2068	+	4.63065i	0.118408	+	0.0170244i
$273$		0			0
$274$	−185.676	+	160.889i	−0.677651	+	0.587188i
$275$		−	158.803i		−	0.577464i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−27.9872	+	194.655i	−0.0999542	+	0.695197i
$281$	431.727	+	197.163i	1.53640	+	0.701649i	0.990666	−	0.136312i	$-0.0435250\pi$
$281$	431.727	+	197.163i	1.53640	+	0.701649i	0.545730	+	0.837961i	$0.316252\pi$
$282$		0			0
$283$	−68.5475	+	233.451i	−0.242217	+	0.824917i	0.745208	+	0.666832i	$0.232350\pi$
$283$	−68.5475	+	233.451i	−0.242217	+	0.824917i	−0.987426	+	0.158085i	$0.949468\pi$
$284$	−52.7071	+	33.8728i	−0.185588	+	0.119270i
$285$		0			0
$286$	46.0166	+	156.718i	0.160897	+	0.547965i
$287$	−142.676	−	123.629i	−0.497128	−	0.430764i
$288$		0			0
$289$	−107.498	+	31.5644i	−0.371967	+	0.109219i
$290$	14.8326	−	6.77381i	0.0511468	−	0.0233580i
$291$		0			0
$292$	24.4267	+	7.17232i	0.0836530	+	0.0245627i
$293$	228.098	−	32.7955i	0.778491	−	0.111930i	0.258396	−	0.966039i	$-0.416806\pi$
$293$	228.098	−	32.7955i	0.778491	−	0.111930i	0.520094	+	0.854109i	$0.325897\pi$
$294$		0			0
$295$	168.055	+	24.1627i	0.569678	+	0.0819073i
$296$	−161.054	+	250.604i	−0.544100	+	0.846636i
$297$		0			0
$298$			80.9355i			0.271596i
$299$	−294.529	+	184.234i	−0.985046	+	0.616168i
$300$		0			0
$301$	103.465	+	119.405i	0.343736	+	0.396693i
$302$	91.5538	+	58.8381i	0.303158	+	0.194828i
$303$		0			0
$304$	59.0572	+	26.9705i	0.194267	+	0.0887189i
$305$	−9.21550	−	64.0952i	−0.0302148	−	0.210148i
$306$		0			0
$307$	30.9820	−	19.9109i	0.100919	−	0.0648565i	−0.489208	−	0.872167i	$-0.662714\pi$
$307$	30.9820	−	19.9109i	0.100919	−	0.0648565i	0.590127	+	0.807311i	$0.299078\pi$
$308$	75.4087	+	165.122i	0.244834	+	0.536111i
$309$		0			0
$310$	−82.2965	−	71.3103i	−0.265472	−	0.230033i
$311$	33.0792	−	38.1754i	0.106364	−	0.122750i	−0.700071	−	0.714073i	$-0.746848\pi$
$311$	33.0792	−	38.1754i	0.106364	−	0.122750i	0.806435	+	0.591322i	$0.201394\pi$
$312$		0			0
$313$	379.824	−	173.460i	1.21349	−	0.554184i	0.297248	−	0.954800i	$-0.403931\pi$
$313$	379.824	−	173.460i	1.21349	−	0.554184i	0.916246	+	0.400616i	$0.131204\pi$
$314$	−89.5097	−	139.280i	−0.285063	−	0.443566i
$315$		0			0
$316$	45.4931	−	6.54092i	0.143966	−	0.0206991i
$317$	85.0163	−	186.160i	0.268190	−	0.587254i	−0.726842	−	0.686804i	$-0.759013\pi$
$317$	85.0163	−	186.160i	0.268190	−	0.587254i	0.995033	+	0.0995498i	$0.0317403\pi$
$318$		0			0
$319$	23.0022	−	35.7921i	0.0721071	−	0.112201i
$320$	86.8156	−	75.2261i	0.271299	−	0.235082i
$321$		0			0
$322$	243.759	−	206.056i	0.757016	−	0.639925i
$323$	353.101			1.09319
$324$		0			0
$325$	−251.067	−	161.351i	−0.772514	−	0.496465i
$326$	−58.1443	+	404.402i	−0.178357	+	1.24050i
$327$		0			0
$328$	21.6931	+	150.879i	0.0661376	+	0.459997i
$329$	211.128	−	719.035i	0.641726	−	2.18552i
$330$		0			0
$331$	71.1293	+	155.751i	0.214892	+	0.470548i	0.986125	−	0.166005i	$-0.0530868\pi$
$331$	71.1293	+	155.751i	0.214892	+	0.470548i	−0.771233	+	0.636553i	$0.780360\pi$
$332$	−10.1833	−	34.6812i	−0.0306726	−	0.104461i
$333$		0			0
$334$	199.429	−	230.154i	0.597094	−	0.689083i
$335$	−15.3900	+	4.51891i	−0.0459403	+	0.0134893i
$336$		0			0
$337$	228.387	+	355.377i	0.677706	+	1.05453i	0.994367	+	0.105993i	$0.0338020\pi$
$337$	228.387	+	355.377i	0.677706	+	1.05453i	−0.316661	+	0.948539i	$0.602562\pi$
$338$	76.3553	+	22.4199i	0.225903	+	0.0663312i
$339$		0			0
$340$	27.7040	−	60.6634i	0.0814825	−	0.178422i
$341$	−281.235	−	40.4354i	−0.824735	−	0.118579i
$342$		0			0
$343$	65.3709	−	56.6442i	0.190586	−	0.165143i
$344$		−	127.568i		−	0.370838i
$345$		0			0
$346$	−95.6482			−0.276440
$347$	102.928	+	118.785i	0.296623	+	0.342321i	0.884424	−	0.466685i	$-0.154552\pi$
$347$	102.928	+	118.785i	0.296623	+	0.342321i	−0.587801	+	0.809006i	$0.700006\pi$
$348$		0			0
$349$	26.1822	−	182.101i	0.0750206	−	0.521779i	−0.917311	−	0.398172i	$-0.869645\pi$
$349$	26.1822	−	182.101i	0.0750206	−	0.521779i	0.992331	−	0.123607i	$-0.0394463\pi$
$350$	249.421	+	113.907i	0.712632	+	0.325448i
$351$		0			0
$352$	67.9777	−	231.511i	0.193118	−	0.657701i
$353$	−191.548	+	123.101i	−0.542630	+	0.348727i	−0.783067	−	0.621938i	$-0.786346\pi$
$353$	−191.548	+	123.101i	−0.542630	+	0.348727i	0.240437	+	0.970665i	$0.422709\pi$
$354$		0			0
$355$	−18.4547	−	62.8511i	−0.0519852	−	0.177045i
$356$	65.2544	+	56.5432i	0.183299	+	0.158829i
$357$		0			0
$358$	35.0366	−	10.2877i	0.0978675	−	0.0287365i
$359$	49.1496	−	22.4459i	0.136907	−	0.0625233i	−0.345784	−	0.938314i	$-0.612387\pi$
$359$	49.1496	−	22.4459i	0.136907	−	0.0625233i	0.482690	+	0.875791i	$0.339660\pi$
$360$		0			0
$361$	329.639	+	96.7908i	0.913128	+	0.268119i
$362$	277.220	−	39.8582i	0.765800	−	0.110105i
$363$		0			0
$364$	337.677	+	48.5506i	0.927684	+	0.133381i
$365$	−14.3900	+	22.3912i	−0.0394246	+	0.0613458i
$366$		0			0
$367$			503.890i			1.37300i	0.727131	+	0.686499i	$0.240853\pi$
$367$			503.890i			1.37300i	−0.727131	+	0.686499i	$0.759147\pi$
$368$	−56.2529	−	0.687697i	−0.152861	−	0.00186874i
$369$		0			0
$370$	−72.1541	−	83.2703i	−0.195011	−	0.225055i
$371$	797.525	+	512.538i	2.14966	+	1.38150i
$372$		0			0
$373$	297.027	+	135.648i	0.796318	+	0.363666i	0.771664	−	0.636030i	$-0.219424\pi$
$373$	297.027	+	135.648i	0.796318	+	0.363666i	0.0246535	+	0.999696i	$0.492152\pi$
$374$	20.4721	+	142.387i	0.0547382	+	0.380713i
$375$		0			0
$376$	−509.020	+	327.127i	−1.35378	+	0.870019i
$377$	−33.2160	−	72.7329i	−0.0881061	−	0.192925i
$378$		0			0
$379$	266.695	+	231.092i	0.703680	+	0.609742i	0.931406	−	0.363983i	$-0.118583\pi$
$379$	266.695	+	231.092i	0.703680	+	0.609742i	−0.227725	+	0.973725i	$0.573129\pi$
$380$	87.1417	−	100.567i	0.229320	−	0.264650i
$381$		0			0
$382$	−290.943	+	132.869i	−0.761630	+	0.347825i
$383$	290.623	+	452.218i	0.758806	+	1.18072i	0.978719	+	0.205205i	$0.0657863\pi$
$383$	290.623	+	452.218i	0.758806	+	1.18072i	−0.219913	+	0.975519i	$0.570577\pi$
$384$		0			0
$385$	−187.856	+	27.0096i	−0.487938	+	0.0701548i
$386$	10.8580	−	23.7757i	0.0281295	−	0.0615950i
$387$		0			0
$388$	−101.144	+	157.383i	−0.260680	+	0.405626i
$389$	−10.6600	+	9.23695i	−0.0274036	+	0.0237454i	−0.668455	−	0.743753i	$-0.733044\pi$
$389$	−10.6600	+	9.23695i	−0.0274036	+	0.0237454i	0.641051	+	0.767498i	$0.278499\pi$
$390$		0			0
$391$	−279.847	+	123.690i	−0.715721	+	0.316343i
$392$	−477.914			−1.21917
$393$		0			0
$394$	322.074	+	206.984i	0.817447	+	0.525341i
$395$	−6.83861	+	47.5635i	−0.0173129	+	0.120414i
$396$		0			0
$397$	−20.9638	−	145.807i	−0.0528056	−	0.367271i	−0.999041	−	0.0437913i	$-0.986056\pi$
$397$	−20.9638	−	145.807i	−0.0528056	−	0.367271i	0.946235	−	0.323480i	$-0.104853\pi$
$398$	87.2576	−	297.172i	0.219240	−	0.746663i
$399$		0			0
$400$	−20.0765	−	43.9614i	−0.0501912	−	0.109903i
$401$	−93.4983	−	318.426i	−0.233163	−	0.794080i	−0.990072	−	0.140560i	$-0.955110\pi$
$401$	−93.4983	−	318.426i	−0.233163	−	0.794080i	0.756909	−	0.653520i	$-0.226708\pi$
$402$		0			0
$403$	−349.676	+	403.548i	−0.867683	+	1.00136i
$404$	−45.6579	+	13.4064i	−0.113015	+	0.0331841i
$405$		0			0
$406$	39.7172	+	61.8011i	0.0978256	+	0.152220i
$407$	−275.843	−	80.9949i	−0.677748	−	0.199005i
$408$		0			0
$409$	305.548	−	669.057i	0.747061	−	1.63584i	−0.0245148	−	0.999699i	$-0.507804\pi$
$409$	305.548	−	669.057i	0.747061	−	1.63584i	0.771576	−	0.636137i	$-0.219469\pi$
$410$	−55.8058	−	8.02367i	−0.136112	−	0.0195699i
$411$		0			0
$412$	−166.573	+	144.337i	−0.404304	+	0.350331i
$413$			764.915i			1.85209i
$414$		0			0
$415$	37.7903			0.0910610
$416$	−296.950	−	342.699i	−0.713823	−	0.823795i
$417$		0			0
$418$	−40.8487	+	284.109i	−0.0977241	+	0.679686i
$419$	259.291	+	118.414i	0.618832	+	0.282611i	0.700059	−	0.714085i	$-0.253157\pi$
$419$	259.291	+	118.414i	0.618832	+	0.282611i	−0.0812277	+	0.996696i	$0.525884\pi$
$420$		0			0
$421$	165.419	−	563.364i	0.392918	−	1.33816i	−0.491263	−	0.871011i	$-0.663465\pi$
$421$	165.419	−	563.364i	0.392918	−	1.33816i	0.884181	−	0.467145i	$-0.154717\pi$
$422$	−355.314	+	228.346i	−0.841976	+	0.541105i
$423$		0			0
$424$	−215.652	−	734.444i	−0.508614	−	1.73218i
$425$	−198.644	−	172.126i	−0.467398	−	0.405003i
$426$		0			0
$427$	279.917	−	82.1910i	0.655543	−	0.192485i
$428$	−104.087	+	47.5347i	−0.243193	+	0.111062i
$429$		0			0
$430$	45.2725	+	13.2932i	0.105285	+	0.0309145i
$431$	638.587	−	91.8149i	1.48164	−	0.213028i	0.646436	−	0.762968i	$-0.276259\pi$
$431$	638.587	−	91.8149i	1.48164	−	0.213028i	0.835204	+	0.549941i	$0.185350\pi$
$432$		0			0
$433$	−86.2796	−	12.4051i	−0.199260	−	0.0286493i	0.0419621	−	0.999119i	$-0.486639\pi$
$433$	−86.2796	−	12.4051i	−0.199260	−	0.0286493i	−0.241222	+	0.970470i	$0.577548\pi$
$434$	265.235	−	412.714i	0.611140	−	0.950953i
$435$		0			0
$436$		−	152.813i		−	0.350489i
$437$	−605.303	+	79.4898i	−1.38513	+	0.181899i
$438$		0			0
$439$	166.005	+	191.579i	0.378142	+	0.436400i	0.912636	−	0.408773i	$-0.134043\pi$
$439$	166.005	+	191.579i	0.378142	+	0.436400i	−0.534494	+	0.845172i	$0.679498\pi$
$440$	128.912	+	82.8469i	0.292983	+	0.188289i
$441$		0			0
$442$	245.914	+	112.305i	0.556366	+	0.254084i
$443$	−100.645	−	700.000i	−0.227189	−	1.58014i	−0.709865	−	0.704337i	$-0.751244\pi$
$443$	−100.645	−	700.000i	−0.227189	−	1.58014i	0.482676	−	0.875799i	$-0.339665\pi$
$444$		0			0
$445$	−75.9429	+	48.8056i	−0.170658	+	0.109675i
$446$	−88.2392	−	193.217i	−0.197846	−	0.433222i
$447$		0			0
$448$	391.126	+	338.912i	0.873048	+	0.756501i
$449$	−268.808	+	310.221i	−0.598681	+	0.690915i	−0.971514	−	0.236984i	$-0.923841\pi$
$449$	−268.808	+	310.221i	−0.598681	+	0.690915i	0.372832	+	0.927899i	$0.378387\pi$
$450$		0			0
$451$	−133.813	+	61.1102i	−0.296702	+	0.135499i
$452$	148.810	+	231.552i	0.329225	+	0.512284i
$453$		0			0
$454$	72.8348	−	10.4721i	0.160429	−	0.0230662i
$455$	−148.168	+	324.444i	−0.325645	+	0.713063i
$456$		0			0
$457$	−418.002	+	650.423i	−0.914664	+	1.42325i	−0.00866652	+	0.999962i	$0.502759\pi$
$457$	−418.002	+	650.423i	−0.914664	+	1.42325i	−0.905998	+	0.423283i	$0.860878\pi$
$458$	176.509	−	152.946i	0.385390	−	0.333942i
$459$		0			0
$460$	−33.8351	+	110.229i	−0.0735545	+	0.239628i
$461$	−378.361			−0.820739			−0.410369	−	0.911919i	$-0.634600\pi$
$461$	−378.361			−0.820739			−0.410369	+	0.911919i	$0.634600\pi$
$462$		0			0
$463$	−97.0838	−	62.3919i	−0.209684	−	0.134756i	0.431584	−	0.902073i	$-0.357955\pi$
$463$	−97.0838	−	62.3919i	−0.209684	−	0.134756i	−0.641268	+	0.767317i	$0.721591\pi$
$464$	1.84271	−	12.8164i	0.00397137	−	0.0276215i
$465$		0			0
$466$	−67.4902	−	469.405i	−0.144829	−	1.00731i
$467$	1.77496	−	6.04497i	0.00380078	−	0.0129443i	−0.957571	−	0.288198i	$-0.906944\pi$
$467$	1.77496	−	6.04497i	0.00380078	−	0.0129443i	0.961372	+	0.275254i	$0.0887620\pi$
$468$		0			0
$469$	−30.0191	−	65.7326i	−0.0640066	−	0.140155i
$470$	−63.0515	−	214.734i	−0.134152	−	0.456880i
$471$		0			0
$472$	404.447	−	466.757i	0.856879	−	0.988892i
$473$	118.125	−	34.6848i	0.249737	−	0.0733293i
$474$		0			0
$475$	−283.545	−	441.205i	−0.596938	−	0.928853i
$476$	288.285	+	84.6480i	0.605640	+	0.177832i
$477$		0			0
$478$	−73.1145	+	160.098i	−0.152959	+	0.334934i
$479$	−176.586	−	25.3892i	−0.368655	−	0.0530046i	−0.0445023	−	0.999009i	$-0.514170\pi$
$479$	−176.586	−	25.3892i	−0.368655	−	0.0530046i	−0.324153	+	0.946005i	$0.605079\pi$
$480$		0			0
$481$	−408.323	+	353.814i	−0.848905	+	0.735580i
$482$			75.4731i			0.156583i
$483$		0			0
$484$	−123.512			−0.255190
$485$	−128.088	−	147.821i	−0.264099	−	0.304786i
$486$		0			0
$487$	−20.8008	+	144.672i	−0.0427120	+	0.297069i	0.957257	+	0.289238i	$0.0934018\pi$
$487$	−20.8008	+	144.672i	−0.0427120	+	0.297069i	−0.999969	+	0.00783097i	$0.997507\pi$
$488$	−214.266	−	97.8519i	−0.439069	−	0.200516i
$489$		0			0
$490$	49.8009	−	169.606i	0.101634	−	0.346135i
$491$	−269.661	+	173.301i	−0.549208	+	0.352954i	−0.785631	−	0.618696i	$-0.787661\pi$
$491$	−269.661	+	173.301i	−0.549208	+	0.352954i	0.236423	+	0.971650i	$0.424025\pi$
$492$		0			0
$493$	−19.8398	−	67.5681i	−0.0402430	−	0.137055i
$494$	407.672	+	353.250i	0.825248	+	0.715081i
$495$		0			0
$496$	−82.9663	+	24.3611i	−0.167271	+	0.0491152i
$497$	268.445	−	122.595i	0.540131	−	0.246669i
$498$		0			0
$499$	−397.621	−	116.752i	−0.796836	−	0.233972i	−0.142122	−	0.989849i	$-0.545393\pi$
$499$	−397.621	−	116.752i	−0.796836	−	0.233972i	−0.654714	+	0.755877i	$0.727211\pi$
$500$	−222.102	+	31.9335i	−0.444204	+	0.0638669i
$501$		0			0
$502$	−262.429	−	37.7316i	−0.522767	−	0.0751625i
$503$	−387.279	+	602.617i	−0.769938	+	1.19805i	0.205691	+	0.978617i	$0.434056\pi$
$503$	−387.279	+	602.617i	−0.769938	+	1.19805i	−0.975628	+	0.219430i	$0.929580\pi$
$504$		0			0
$505$		−	49.7511i		−	0.0985170i
$506$	−67.1481	−	239.477i	−0.132704	−	0.473275i
$507$		0			0
$508$	52.6804	+	60.7964i	0.103701	+	0.119678i
$509$	168.764	+	108.458i	0.331560	+	0.213080i	0.695819	−	0.718217i	$-0.255042\pi$
$509$	168.764	+	108.458i	0.331560	+	0.213080i	−0.364260	+	0.931297i	$0.618678\pi$
$510$		0			0
$511$	−109.078	−	49.8141i	−0.213459	−	0.0974835i
$512$	−22.0461	−	153.334i	−0.0430588	−	0.299481i
$513$		0			0
$514$	−157.776	+	101.396i	−0.306957	+	0.197269i
$515$	−95.7278	−	209.615i	−0.185879	−	0.407019i
$516$		0			0
$517$	−441.311	−	382.399i	−0.853600	−	0.739649i
$518$	325.072	−	375.153i	0.627552	−	0.724234i
$519$		0			0
$520$	261.962	−	119.634i	0.503774	−	0.230066i
$521$	−347.311	−	540.427i	−0.666624	−	1.03729i	−0.995669	−	0.0929733i	$-0.970363\pi$
$521$	−347.311	−	540.427i	−0.666624	−	1.03729i	0.329044	−	0.944315i	$-0.393273\pi$
$522$		0			0
$523$	177.710	−	25.5509i	0.339790	−	0.0488545i	0.0296924	−	0.999559i	$-0.490547\pi$
$523$	177.710	−	25.5509i	0.339790	−	0.0488545i	0.310098	+	0.950705i	$0.399638\pi$
$524$	93.2761	−	204.246i	0.178008	−	0.389783i
$525$		0			0
$526$	208.187	−	323.945i	0.395793	−	0.615865i
$527$	−355.410	+	307.965i	−0.674403	+	0.584373i
$528$		0			0
$529$	451.882	−	275.034i	0.854219	−	0.519914i
$530$	283.118			0.534185
$531$		0			0
$532$	504.339	+	324.119i	0.948006	+	0.609246i
$533$	−39.3448	+	273.649i	−0.0738176	+	0.513412i
$534$		0			0
$535$	−17.0258	−	118.417i	−0.0318239	−	0.221340i
$536$	−16.4381	+	55.9831i	−0.0306681	+	0.104446i
$537$		0			0
$538$	−258.070	−	565.094i	−0.479683	−	1.05036i
$539$	−129.941	−	442.538i	−0.241078	−	0.821035i
$540$		0			0
$541$	−527.967	+	609.307i	−0.975910	+	1.12626i	0.0160703	+	0.999871i	$0.494884\pi$
$541$	−527.967	+	609.307i	−0.975910	+	1.12626i	−0.991981	+	0.126390i	$0.959661\pi$
$542$	−151.760	+	44.5606i	−0.279999	+	0.0822152i
$543$		0			0
$544$	−215.913	−	335.967i	−0.396899	−	0.617586i
$545$	153.296	+	45.0118i	0.281278	+	0.0825905i
$546$		0			0
$547$	−57.4155	+	125.722i	−0.104964	+	0.229840i	−0.954826	−	0.297166i	$-0.903958\pi$
$547$	−57.4155	+	125.722i	−0.104964	+	0.229840i	0.849861	+	0.527006i	$0.176686\pi$
$548$	395.788	+	56.9057i	0.722240	+	0.103842i
$549$		0			0
$550$	161.475	−	139.919i	0.293590	−	0.254397i
$551$		−	140.513i		−	0.255014i
$552$		0			0
$553$	−216.489			−0.391481
$554$	−284.126	−	327.899i	−0.512862	−	0.591875i
$555$		0			0
$556$	46.8084	−	325.560i	0.0841878	−	0.585539i
$557$	−94.7549	−	43.2731i	−0.170117	−	0.0776896i	0.328537	−	0.944491i	$-0.393445\pi$
$557$	−94.7549	−	43.2731i	−0.170117	−	0.0776896i	−0.498653	+	0.866802i	$0.666172\pi$
$558$		0			0
$559$	65.1845	−	221.998i	0.116609	−	0.397134i
$560$	−48.5896	+	31.2266i	−0.0867671	+	0.0557618i
$561$		0			0
$562$	179.908	+	612.709i	0.320120	+	1.09023i
$563$	165.885	+	143.740i	0.294645	+	0.255311i	0.789620	−	0.613596i	$-0.210277\pi$
$563$	165.885	+	143.740i	0.294645	+	0.255311i	−0.494975	+	0.868907i	$0.664823\pi$
$564$		0			0
$565$	−276.117	+	81.0752i	−0.488702	+	0.143496i
$566$	−297.776	+	135.990i	−0.526106	+	0.240264i
$567$		0			0
$568$	−228.629	−	67.1315i	−0.402515	−	0.118189i
$569$	865.074	−	124.379i	1.52034	−	0.218592i	0.669023	−	0.743242i	$-0.266713\pi$
$569$	865.074	−	124.379i	1.52034	−	0.218592i	0.851318	+	0.524650i	$0.175804\pi$
$570$		0			0
$571$	147.961	+	21.2736i	0.259127	+	0.0372568i	0.270654	−	0.962677i	$-0.412760\pi$
$571$	147.961	+	21.2736i	0.259127	+	0.0372568i	−0.0115270	+	0.999934i	$0.503669\pi$
$572$	143.718	−	223.630i	0.251256	−	0.390962i
$573$		0			0
$574$		−	254.004i		−	0.442516i
$575$	379.274	+	250.348i	0.659606	+	0.435388i
$576$		0			0
$577$	−554.057	−	639.416i	−0.960238	−	1.10817i	−0.994070	−	0.108746i	$-0.965317\pi$
$577$	−554.057	−	639.416i	−0.960238	−	1.10817i	0.0338319	−	0.999428i	$-0.489229\pi$
$578$	−126.811	−	81.4962i	−0.219396	−	0.140997i
$579$		0			0
$580$	−24.1403	−	11.0245i	−0.0416213	−	0.0190078i
$581$	24.2298	+	168.522i	0.0417036	+	0.290055i
$582$		0			0
$583$	621.445	−	399.379i	1.06594	−	0.685041i
$584$	40.2209	+	88.0714i	0.0688714	+	0.150807i
$585$		0			0
$586$	234.321	+	203.040i	0.399865	+	0.346485i
$587$	488.077	−	563.271i	0.831477	−	0.959576i	−0.168180	−	0.985756i	$-0.553789\pi$
$587$	488.077	−	563.271i	0.831477	−	0.959576i	0.999657	+	0.0261807i	$0.00833452\pi$
$588$		0			0
$589$	−853.560	+	389.808i	−1.44917	+	0.661813i
$590$	123.501	+	192.172i	0.209325	+	0.325715i
$591$		0			0
$592$	−86.6016	+	12.4514i	−0.146286	+	0.0210328i
$593$	−268.581	+	588.110i	−0.452919	+	0.991754i	0.536126	+	0.844138i	$0.319887\pi$
$593$	−268.581	+	588.110i	−0.452919	+	0.991754i	−0.989045	+	0.147616i	$0.952840\pi$
$594$		0			0
$595$	−169.831	+	264.262i	−0.285430	+	0.444138i
$596$	99.5505	−	86.2610i	0.167031	−	0.144733i
$597$		0			0
$598$	−446.839	−	137.159i	−0.747222	−	0.229362i
$599$	385.426			0.643449			0.321724	−	0.946833i	$-0.395738\pi$
$599$	385.426			0.643449			0.321724	+	0.946833i	$0.395738\pi$
$600$		0			0
$601$	804.595	+	517.082i	1.33876	+	0.860369i	0.996846	−	0.0793627i	$-0.0252885\pi$
$601$	804.595	+	517.082i	1.33876	+	0.860369i	0.341914	+	0.939731i	$0.388925\pi$
$602$	−30.2525	+	210.411i	−0.0502534	+	0.349520i
$603$		0			0
$604$	−25.2073	−	175.321i	−0.0417339	−	0.290266i
$605$	36.3809	−	123.902i	0.0601338	−	0.204797i
$606$		0			0
$607$	−69.1866	−	151.498i	−0.113981	−	0.249584i	0.844041	−	0.536279i	$-0.180171\pi$
$607$	−69.1866	−	151.498i	−0.113981	−	0.249584i	−0.958022	+	0.286695i	$0.907443\pi$
$608$	−224.503	−	764.588i	−0.369249	−	1.25755i
$609$		0			0
$610$	57.0541	−	65.8439i	0.0935312	−	0.107941i
$611$	−1052.97	+	309.179i	−1.72335	+	0.506021i
$612$		0			0
$613$	437.247	+	680.370i	0.713291	+	1.10990i	0.988893	+	0.148630i	$0.0474864\pi$
$613$	437.247	+	680.370i	0.713291	+	1.10990i	−0.275602	+	0.961272i	$0.588877\pi$
$614$	47.5438	+	13.9601i	0.0774329	+	0.0227363i
$615$		0			0
$616$	−286.793	+	627.989i	−0.465573	+	1.01946i
$617$	985.450	+	141.686i	1.59716	+	0.229637i	0.882666	−	0.470000i	$-0.155746\pi$
$617$	985.450	+	141.686i	1.59716	+	0.229637i	0.714498	+	0.699638i	$0.246655\pi$
$618$		0			0
$619$	50.4021	−	43.6736i	0.0814250	−	0.0705552i	−0.613197	−	0.789930i	$-0.710117\pi$
$619$	50.4021	−	43.6736i	0.0814250	−	0.0705552i	0.694622	+	0.719375i	$0.255572\pi$
$620$			177.227i			0.285850i
$621$		0			0
$622$	67.9633			0.109266
$623$	−266.335	−	307.367i	−0.427504	−	0.493366i
$624$		0			0
$625$	−36.9117	+	256.727i	−0.0590588	+	0.410763i
$626$	511.035	+	233.382i	0.816351	+	0.372815i
$627$		0			0
$628$	−75.9145	+	258.541i	−0.120883	+	0.411689i
$629$	−400.302	+	257.258i	−0.636410	+	0.408996i
$630$		0			0
$631$	236.205	+	804.440i	0.374334	+	1.27486i	0.904319	+	0.426858i	$0.140379\pi$
$631$	236.205	+	804.440i	0.374334	+	1.27486i	−0.529985	+	0.848007i	$0.677802\pi$
$632$	132.103	+	114.468i	0.209024	+	0.181120i
$633$		0			0
$634$	264.199	−	77.5757i	0.416717	−	0.122359i
$635$	−76.5058	+	34.9390i	−0.120482	+	0.0550221i
$636$		0			0
$637$	−831.679	−	244.203i	−1.30562	−	0.383364i
$638$	56.6612	−	8.14664i	0.0888106	−	0.0127690i
$639$		0			0
$640$	−119.141	−	17.1299i	−0.186158	−	0.0267655i
$641$	−182.159	+	283.445i	−0.284179	+	0.442192i	−0.953769	−	0.300539i	$-0.902833\pi$
$641$	−182.159	+	283.445i	−0.284179	+	0.442192i	0.669590	+	0.742731i	$0.266470\pi$
$642$		0			0
$643$		−	661.045i		−	1.02806i	−0.857771	−	0.514032i	$-0.828151\pi$
$643$		−	661.045i		−	1.02806i	0.857771	−	0.514032i	$-0.171849\pi$
$644$	−513.247	−	80.2092i	−0.796967	−	0.124548i
$645$		0			0
$646$	311.112	+	359.043i	0.481598	+	0.555794i
$647$	327.556	+	210.507i	0.506268	+	0.325359i	0.768719	−	0.639587i	$-0.220894\pi$
$647$	327.556	+	210.507i	0.506268	+	0.325359i	−0.262451	+	0.964945i	$0.584531\pi$
$648$		0			0
$649$	542.173	+	247.602i	0.835397	+	0.381513i
$650$	−57.1455	−	397.456i	−0.0879161	−	0.611470i
$651$		0			0
$652$	559.384	−	359.494i	0.857951	−	0.551372i
$653$	503.194	+	1101.84i	0.770589	+	1.68735i	0.725352	+	0.688378i	$0.241677\pi$
$653$	503.194	+	1101.84i	0.770589	+	1.68735i	0.0452364	+	0.998976i	$0.485596\pi$
$654$		0			0
$655$	177.417	+	153.732i	0.270865	+	0.234706i
$656$	−29.3176	+	33.8343i	−0.0446915	+	0.0515767i
$657$		0			0
$658$	917.155	−	418.851i	1.39385	−	0.636551i
$659$	−428.607	−	666.925i	−0.650390	−	1.01203i	−0.997250	−	0.0741096i	$-0.976389\pi$
$659$	−428.607	−	666.925i	−0.650390	−	1.01203i	0.346860	−	0.937917i	$-0.387248\pi$
$660$		0			0
$661$	940.233	−	135.185i	1.42244	−	0.204516i	0.612241	−	0.790671i	$-0.290268\pi$
$661$	940.233	−	135.185i	1.42244	−	0.204516i	0.810199	+	0.586155i	$0.199359\pi$
$662$	−95.7012	+	209.556i	−0.144564	+	0.316550i
$663$		0			0
$664$	74.3203	−	115.645i	0.111928	−	0.174164i
$665$	−473.699	+	410.462i	−0.712329	+	0.617236i
$666$		0			0
$667$	49.2211	+	111.362i	0.0737948	+	0.166960i
$668$	−495.641			−0.741977
$669$		0			0
$670$	−18.1548	−	11.6674i	−0.0270968	−	0.0174140i
$671$	32.3517	−	225.011i	0.0482141	−	0.335336i
$672$		0			0
$673$	41.2573	+	286.951i	0.0613035	+	0.426375i	0.997242	+	0.0742130i	$0.0236445\pi$
$673$	41.2573	+	286.951i	0.0613035	+	0.426375i	−0.935939	+	0.352162i	$0.885446\pi$
$674$	−160.128	+	545.347i	−0.237579	+	0.809121i
$675$		0			0
$676$	−53.8030	−	117.812i	−0.0795902	−	0.174278i
$677$	−25.2455	−	85.9784i	−0.0372903	−	0.126999i	0.938744	−	0.344614i	$-0.111990\pi$
$677$	−25.2455	−	85.9784i	−0.0372903	−	0.126999i	−0.976035	+	0.217615i	$0.930172\pi$
$678$		0			0
$679$	577.068	−	665.972i	0.849879	−	0.980812i
$680$	243.360	−	71.4570i	0.357883	−	0.105084i
$681$		0			0
$682$	−206.676	−	321.594i	−0.303044	−	0.471545i
$683$	−1190.84	−	349.662i	−1.74354	−	0.511951i	−0.754087	−	0.656774i	$-0.771920\pi$
$683$	−1190.84	−	349.662i	−1.74354	−	0.511951i	−0.989457	+	0.144824i	$0.953739\pi$
$684$		0			0
$685$	−173.667	+	380.277i	−0.253528	+	0.555148i
$686$	115.195	+	16.5625i	0.167922	+	0.0241436i
$687$		0			0
$688$	28.3157	−	24.5357i	0.0411566	−	0.0356624i
$689$		−	1388.29i		−	2.01494i
$690$		0			0
$691$	−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
$693$		0			0
$694$	−30.0957	+	209.320i	−0.0433655	+	0.301614i
$695$	312.801	+	142.851i	0.450073	+	0.205542i
$696$		0			0
$697$	−68.5976	+	233.622i	−0.0984183	+	0.335182i
$698$	208.234	−	133.824i	0.298329	−	0.191725i
$699$		0			0
$700$	−125.728	−	428.189i	−0.179611	−	0.611699i
$701$	−473.583	−	410.362i	−0.675582	−	0.585395i	0.248017	−	0.968756i	$-0.420221\pi$
$701$	−473.583	−	410.362i	−0.675582	−	0.585395i	−0.923599	+	0.383360i	$0.874767\pi$
$702$		0			0
$703$	−911.001	+	267.494i	−1.29588	+	0.380503i
$704$	366.828	−	167.525i	0.521063	−	0.237962i
$705$		0			0
$706$	−293.942	−	86.3093i	−0.416349	−	0.122251i
$707$	221.860	−	31.8986i	0.313804	−	0.0451182i
$708$		0			0
$709$	−375.851	−	54.0392i	−0.530114	−	0.0762189i	−0.127940	−	0.991782i	$-0.540836\pi$
$709$	−375.851	−	54.0392i	−0.530114	−	0.0762189i	−0.402174	+	0.915563i	$0.631745\pi$
$710$	47.6484	−	74.1424i	0.0671105	−	0.104426i
$711$		0			0
$712$			328.381i			0.461210i
$713$	539.932	−	607.937i	0.757268	−	0.852647i
$714$		0			0
$715$	182.004	+	210.044i	0.254551	+	0.293768i
$716$	−49.9957	−	32.1303i	−0.0698265	−	0.0448747i
$717$		0			0
$718$	66.1285	+	30.1999i	0.0921009	+	0.0420611i
$719$	−15.7988	−	109.883i	−0.0219733	−	0.152828i	0.975881	−	0.218304i	$-0.0700524\pi$
$719$	−15.7988	−	109.883i	−0.0219733	−	0.152828i	−0.997854	+	0.0654762i	$0.979143\pi$
$720$		0			0
$721$	873.377	−	561.285i	1.21134	−	0.778481i
$722$	192.021	+	420.467i	0.265957	+	0.582364i
$723$		0			0
$724$	−344.486	−	298.499i	−0.475809	−	0.412291i
$725$	−68.4957	+	79.0482i	−0.0944768	+	0.109032i
$726$		0			0
$727$	121.194	−	55.3476i	0.166705	−	0.0761315i	−0.330315	−	0.943871i	$-0.607155\pi$
$727$	121.194	−	55.3476i	0.166705	−	0.0761315i	0.497020	+	0.867739i	$0.334428\pi$
$728$	701.456	+	1091.49i	0.963539	+	1.49930i
$729$		0			0
$730$	−35.4468	+	5.09648i	−0.0485572	+	0.00698148i
$731$	84.6495	−	185.356i	0.115800	−	0.253566i
$732$		0			0
$733$	−721.336	+	1122.42i	−0.984087	+	1.53127i	−0.143459	+	0.989656i	$0.545822\pi$
$733$	−721.336	+	1122.42i	−0.984087	+	1.53127i	−0.840628	+	0.541613i	$0.817814\pi$
$734$	−512.369	+	443.970i	−0.698050	+	0.604864i
$735$		0			0
$736$	445.760	+	527.324i	0.605652	+	0.716473i
$737$	−56.3085			−0.0764023
$738$		0			0
$739$	−316.334	−	203.296i	−0.428057	−	0.275096i	0.308822	−	0.951120i	$-0.400065\pi$
$739$	−316.334	−	203.296i	−0.428057	−	0.275096i	−0.736880	+	0.676024i	$0.763702\pi$
$740$	−25.5205	+	177.499i	−0.0344871	+	0.239863i
$741$		0			0
$742$	181.525	+	1262.53i	0.244643	+	1.70153i
$743$	−389.916	+	1327.93i	−0.524786	+	1.78726i	0.0869720	+	0.996211i	$0.472281\pi$
$743$	−389.916	+	1327.93i	−0.524786	+	1.78726i	−0.611758	+	0.791045i	$0.709537\pi$
$744$		0			0
$745$	57.2106	+	125.274i	0.0767928	+	0.168153i
$746$	123.776	+	421.541i	0.165919	+	0.565069i
$747$		0			0
$748$	153.316	−	176.936i	0.204968	−	0.236546i
$749$	517.152	−	151.849i	0.690456	−	0.202736i
$750$		0			0
$751$	383.108	+	596.128i	0.510131	+	0.793779i	0.996811	−	0.0798013i	$-0.0254286\pi$
$751$	383.108	+	596.128i	0.510131	+	0.793779i	−0.486680	+	0.873580i	$0.661792\pi$
$752$	−170.513	−	50.0671i	−0.226746	−	0.0665786i
$753$		0			0
$754$	44.6906	−	97.8587i	0.0592713	−	0.129786i
$755$	183.300	+	26.3545i	0.242781	+	0.0349066i
$756$		0			0
$757$	−90.7661	+	78.6493i	−0.119902	+	0.103896i	−0.712748	−	0.701420i	$-0.752550\pi$
$757$	−90.7661	+	78.6493i	−0.119902	+	0.103896i	0.592846	+	0.805316i	$0.298004\pi$
$758$			474.794i			0.626378i
$759$		0			0
$760$	506.085			0.665902
$761$	550.928	+	635.804i	0.723952	+	0.835485i	0.991776	−	0.127983i	$-0.0408501\pi$
$761$	550.928	+	635.804i	0.723952	+	0.835485i	−0.267824	+	0.963468i	$0.586305\pi$
$762$		0			0
$763$	−102.437	+	712.468i	−0.134256	+	0.933772i
$764$	473.515	+	216.247i	0.619784	+	0.283046i
$765$		0			0
$766$	−203.764	+	693.955i	−0.266010	+	0.905946i
$767$	942.333	−	605.601i	1.22860	−	0.789570i
$768$		0			0
$769$	−301.597	−	1027.15i	−0.392194	−	1.33569i	−0.885016	−	0.465560i	$-0.845853\pi$
$769$	−301.597	−	1027.15i	−0.392194	−	1.33569i	0.492823	−	0.870130i	$-0.335965\pi$
$770$	−192.981	−	167.219i	−0.250625	−	0.217168i
$771$		0			0
$772$	−40.8165	+	11.9848i	−0.0528711	+	0.0155243i
$773$	622.782	−	284.415i	0.805669	−	0.367937i	0.0303761	−	0.999539i	$-0.490330\pi$
$773$	622.782	−	284.415i	0.805669	−	0.367937i	0.775293	+	0.631602i	$0.217602\pi$
$774$		0			0
$775$	670.206	+	196.790i	0.864782	+	0.253923i
$776$	−704.262	+	101.258i	−0.907554	+	0.130487i
$777$		0			0
$778$	−18.7848	−	2.70084i	−0.0241449	−	0.00347152i
$779$	−262.661	+	408.709i	−0.337178	+	0.524659i
$780$		0			0
$781$		−	229.958i		−	0.294440i
$782$	−372.340	−	175.574i	−0.476139	−	0.224520i
$783$		0			0
$784$	−91.9191	−	106.080i	−0.117244	−	0.135307i
$785$	−236.997	−	152.309i	−0.301907	−	0.194024i
$786$		0			0
$787$	155.189	+	70.8725i	0.197191	+	0.0900540i	0.511563	−	0.859246i	$-0.329067\pi$
$787$	155.189	+	70.8725i	0.197191	+	0.0900540i	−0.314372	+	0.949300i	$0.601794\pi$
$788$	−88.6759	−	616.754i	−0.112533	−	0.782683i
$789$		0			0
$790$	−54.3893	+	34.9539i	−0.0688472	+	0.0442454i
$791$	−538.582	−	1179.33i	−0.680887	−	1.49094i
$792$		0			0
$793$	−322.871	−	279.770i	−0.407152	−	0.352799i
$794$	129.789	−	149.785i	0.163462	−	0.188646i
$795$		0			0
$796$	−458.520	+	209.399i	−0.576030	+	0.263064i
$797$	−165.608	−	257.691i	−0.207789	−	0.323327i	0.721679	−	0.692228i	$-0.243371\pi$
$797$	−165.608	−	257.691i	−0.207789	−	0.323327i	−0.929469	+	0.368901i	$0.879734\pi$
$798$		0			0
$799$	−956.675	+	137.549i	−1.19734	+	0.172152i
$800$	−246.414	+	539.572i	−0.308018	+	0.674465i
$801$		0			0
$802$	241.404	−	375.632i	0.301002	−	0.468369i
$803$	−70.6166	+	61.1896i	−0.0879409	+	0.0762012i
$804$		0			0
$805$	231.642	−	491.243i	0.287754	−	0.610240i
$806$	−718.433			−0.891356
$807$		0			0
$808$	−152.247	−	97.8430i	−0.188424	−	0.121093i
$809$	44.2504	−	307.768i	0.0546976	−	0.380430i	−0.944024	−	0.329877i	$-0.892993\pi$
$809$	44.2504	−	307.768i	0.0546976	−	0.380430i	0.998721	−	0.0505528i	$-0.0160983\pi$
$810$		0			0
$811$	−196.465	−	1366.44i	−0.242250	−	1.68489i	−0.640773	−	0.767730i	$-0.721386\pi$
$811$	−196.465	−	1366.44i	−0.242250	−	1.68489i	0.398523	−	0.917158i	$-0.369523\pi$
$812$	33.6847	−	114.720i	0.0414837	−	0.141280i
$813$		0			0
$814$	−160.684	−	351.848i	−0.197400	−	0.432246i
$815$	195.861	+	667.043i	0.240321	+	0.818457i
$816$		0			0
$817$	266.261	−	307.281i	0.325900	−	0.376109i
$818$	949.529	−	278.807i	1.16079	−	0.340840i
$819$		0			0
$820$	49.6087	+	77.1927i	0.0604984	+	0.0941374i
$821$	1195.09	+	350.909i	1.45565	+	0.427416i	0.911404	−	0.411512i	$-0.134999\pi$
$821$	1195.09	+	350.909i	1.45565	+	0.427416i	0.544242	+	0.838928i	$0.316817\pi$
$822$		0			0
$823$	177.663	−	389.027i	0.215872	−	0.472694i	−0.770455	−	0.637495i	$-0.779971\pi$
$823$	177.663	−	389.027i	0.215872	−	0.472694i	0.986327	+	0.164801i	$0.0526981\pi$
$824$	−829.719	−	119.296i	−1.00694	−	0.144776i
$825$		0			0
$826$	−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	$0.878772\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	107.858	−	750.170i	0.129637	−	0.901646i
$833$	−694.408	−	317.126i	−0.833623	−	0.380703i
$834$		0			0
$835$	145.993	−	497.207i	0.174842	−	0.595458i
$836$	392.990	−	252.559i	0.470084	−	0.302104i
$837$		0			0
$838$	108.050	+	367.986i	0.128939	+	0.439124i
$839$	−960.771	−	832.513i	−1.14514	−	0.992268i	−0.999996	−	0.00285681i	$-0.999091\pi$
$839$	−960.771	−	832.513i	−1.14514	−	0.992268i	−0.145142	−	0.989411i	$-0.546364\pi$
$840$		0			0
$841$	780.046	−	229.042i	0.927522	−	0.272345i
$842$	718.591	−	328.169i	0.853433	−	0.389750i
$843$		0			0
$844$	659.559	+	193.664i	0.781468	+	0.229460i
$845$	134.032	−	19.2709i	0.158618	−	0.0228058i
$846$		0			0
$847$	575.854	+	82.7953i	0.679875	+	0.0977512i
$848$	121.544	−	189.126i	0.143330	−	0.223026i
$849$		0			0
$850$		−	353.644i		−	0.416052i
$851$	628.303	−	531.120i	0.738311	−	0.624113i
$852$		0			0
$853$	−120.587	−	139.165i	−0.141368	−	0.163147i	0.680650	−	0.732608i	$-0.261697\pi$
$853$	−120.587	−	139.165i	−0.141368	−	0.163147i	−0.822018	+	0.569461i	$0.807152\pi$
$854$	330.205	+	212.210i	0.386656	+	0.248489i
$855$		0			0
$856$	−395.860	−	180.783i	−0.462453	−	0.211195i
$857$	142.527	+	991.300i	0.166310	+	1.15671i	0.886431	+	0.462861i	$0.153177\pi$
$857$	142.527	+	991.300i	0.166310	+	1.15671i	−0.720121	+	0.693849i	$0.755914\pi$
$858$		0			0
$859$	−1050.84	+	675.333i	−1.22333	+	0.786185i	−0.982839	−	0.184467i	$-0.940944\pi$
$859$	−1050.84	+	675.333i	−1.22333	+	0.786185i	−0.240489	+	0.970652i	$0.577308\pi$
$860$	−31.9008	−	69.8531i	−0.0370940	−	0.0812245i
$861$		0			0
$862$	656.009	+	568.435i	0.761031	+	0.659437i
$863$	243.431	−	280.935i	0.282076	−	0.325533i	−0.596976	−	0.802259i	$-0.703631\pi$
$863$	243.431	−	280.935i	0.282076	−	0.325533i	0.879052	+	0.476726i	$0.158177\pi$
$864$		0			0
$865$	−148.046	+	67.6105i	−0.171152	+	0.0781625i
$866$	−63.4058	−	98.6613i	−0.0732168	−	0.113928i
$867$		0			0
$868$	−790.324	+	113.631i	−0.910512	+	0.130912i
$869$	−70.0773	+	153.448i	−0.0806413	+	0.176580i
$870$		0			0
$871$	−57.2122	+	89.0238i	−0.0656856	+	0.102209i
$872$	439.224	−	380.590i	0.503697	−	0.436456i
$873$		0			0
$874$	−614.150	−	545.450i	−0.702689	−	0.624085i
$875$	1056.92			1.20791
$876$		0			0
$877$	195.815	+	125.842i	0.223278	+	0.143492i	0.647498	−	0.762067i	$-0.275815\pi$
$877$	195.815	+	125.842i	0.223278	+	0.143492i	−0.424220	+	0.905559i	$0.639452\pi$
$878$	−48.5389	+	337.595i	−0.0552835	+	0.384505i
$879$		0			0
$880$	6.40509	+	44.5484i	0.00727851	+	0.0506232i
$881$	107.057	−	364.604i	0.121518	−	0.413853i	−0.876155	−	0.482029i	$-0.839900\pi$
$881$	107.057	−	364.604i	0.121518	−	0.413853i	0.997673	+	0.0681764i	$0.0217181\pi$
$882$		0			0
$883$	65.8746	+	144.245i	0.0746031	+	0.163358i	0.943259	−	0.332058i	$-0.107743\pi$
$883$	65.8746	+	144.245i	0.0746031	+	0.163358i	−0.868656	+	0.495416i	$0.835016\pi$
$884$	−123.960	−	422.168i	−0.140226	−	0.477566i
$885$		0			0
$886$	623.102	−	719.098i	0.703275	−	0.811623i
$887$	−937.152	+	275.173i	−1.05654	+	0.310229i	−0.763457	−	0.645858i	$-0.776500\pi$
$887$	−937.152	+	275.173i	−1.05654	+	0.310229i	−0.293084	+	0.956087i	$0.594682\pi$
$888$		0			0
$889$	−204.859	−	318.767i	−0.230438	−	0.358569i
$890$	−116.539	−	34.2189i	−0.130943	−	0.0384482i
$891$		0			0
$892$	−143.611	+	314.465i	−0.160999	+	0.352539i
$893$	−1908.89	−	274.457i	−2.13761	−	0.307342i
$894$		0			0
$895$	46.9583	−	40.6896i	0.0524674	−	0.0454633i
$896$		−	542.281i		−	0.605224i
$897$		0			0
$898$	−552.283			−0.615015
$899$	122.551	+	141.432i	0.136319	+	0.157321i
$900$		0			0
$901$	174.007	−	1210.24i	0.193126	−	1.34322i
$902$	−180.039	−	82.2209i	−0.199599	−	0.0911540i
$903$		0			0
$904$	−294.921	+	1004.41i	−0.326240	+	1.11107i
$905$	400.912	−	257.651i	0.442997	−	0.284697i
$906$		0			0
$907$	−265.774	−	905.144i	−0.293026	−	0.997954i	−0.966055	−	0.258338i	$-0.916825\pi$
$907$	−265.774	−	905.144i	−0.293026	−	0.997954i	0.673029	−	0.739616i	$-0.264993\pi$
$908$	−90.5079	−	78.4256i	−0.0996783	−	0.0863718i
$909$		0			0
$910$	−460.452	+	135.201i	−0.505991	+	0.148572i
$911$	−250.275	+	114.297i	−0.274725	+	0.125463i	−0.548014	−	0.836469i	$-0.684616\pi$
$911$	−250.275	+	114.297i	−0.274725	+	0.125463i	0.273288	+	0.961932i	$0.411889\pi$
$912$		0			0
$913$	127.292	+	37.3762i	0.139421	+	0.0409378i
$914$	−1029.66	+	148.043i	−1.12654	+	0.161973i
$915$		0			0
$916$	−376.246	−	54.0959i	−0.410748	−	0.0590567i
$917$	−571.800	+	889.738i	−0.623555	+	0.970271i
$918$		0			0
$919$			412.424i			0.448775i	0.974500	+	0.224388i	$0.0720382\pi$
$919$			412.424i			0.448775i	−0.974500	+	0.224388i	$0.927962\pi$
$920$	−401.093	+	177.280i	−0.435971	+	0.192696i
$921$		0			0
$922$	−333.368	−	384.727i	−0.361570	−	0.417274i
$923$	−363.564	−	233.648i	−0.393894	−	0.253140i
$924$		0			0
$925$	642.896	+	293.601i	0.695023	+	0.317406i
$926$	−22.0973	−	153.690i	−0.0238631	−	0.165972i
$927$		0			0
$928$	−133.694	+	85.9201i	−0.144067	+	0.0925863i
$929$	135.394	+	296.471i	0.145741	+	0.319129i	0.968398	−	0.249409i	$-0.0802365\pi$
$929$	135.394	+	296.471i	0.145741	+	0.319129i	−0.822657	+	0.568538i	$0.807509\pi$
$930$		0			0
$931$	−1151.18	−	997.502i	−1.23650	−	1.07143i
$932$	−505.436	+	583.304i	−0.542313	+	0.625863i
$933$		0			0
$934$	7.71057	−	3.52130i	0.00825543	−	0.00377013i
$935$	132.335	+	205.918i	0.141535	+	0.220233i
$936$		0			0
$937$	1031.01	−	148.237i	1.10033	−	0.158204i	0.431860	−	0.901941i	$-0.357857\pi$
$937$	1031.01	−	148.237i	1.10033	−	0.158204i	0.668473	+	0.743736i	$0.266948\pi$
$938$	40.3893	−	88.4402i	0.0430589	−	0.0942859i
$939$		0			0
$940$	−196.922	+	306.416i	−0.209491	+	0.325975i
$941$	873.960	−	757.291i	0.928757	−	0.804772i	−0.0522722	−	0.998633i	$-0.516646\pi$
$941$	873.960	−	757.291i	0.928757	−	0.804772i	0.981029	+	0.193860i	$0.0621009\pi$
$942$		0			0
$943$	65.0004	−	415.928i	0.0689294	−	0.441069i
$944$	181.393			0.192153
$945$		0			0
$946$	139.347	+	89.5529i	0.147301	+	0.0946648i
$947$	−13.9968	+	97.3500i	−0.0147802	+	0.102798i	−0.995876	−	0.0907237i	$-0.971082\pi$
$947$	−13.9968	+	97.3500i	−0.0147802	+	0.102798i	0.981096	+	0.193522i	$0.0619911\pi$
$948$		0			0
$949$	24.9910	+	173.816i	0.0263341	+	0.183157i
$950$	198.801	−	677.056i	0.209265	−	0.712690i
$951$		0			0
$952$	474.688	+	1039.42i	0.498622	+	1.09183i
$953$	189.567	+	645.605i	0.198916	+	0.677445i	0.997174	+	0.0751296i	$0.0239370\pi$
$953$	189.567	+	645.605i	0.198916	+	0.677445i	−0.798258	+	0.602316i	$0.794245\pi$
$954$		0			0
$955$	−356.407	+	411.315i	−0.373201	+	0.430697i
$956$	274.846	−	80.7021i	0.287496	−	0.0844164i
$957$		0			0
$958$	−129.771	−	201.927i	−0.135460	−	0.210780i
$959$	−1807.15	−	530.627i	−1.88441	−	0.553313i
$960$		0			0
$961$	119.948	−	262.650i	0.124816	−	0.273309i
$962$	−719.535	−	103.453i	−0.747957	−	0.107540i
$963$		0			0
$964$	92.8317	−	80.4391i	0.0962985	−	0.0834431i
$965$		−	44.4756i		−	0.0460888i
$966$		0			0
$967$	−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
$969$		0			0
$970$	37.4523	−	260.486i	0.0386106	−	0.268543i
$971$	801.065	+	365.834i	0.824989	+	0.376760i	0.782741	−	0.622347i	$-0.213821\pi$
$971$	801.065	+	365.834i	0.824989	+	0.376760i	0.0422481	+	0.999107i	$0.486548\pi$
$972$		0			0
$973$	−436.474	+	1486.49i	−0.448586	+	1.52774i
$974$	−165.434	+	106.318i	−0.169850	+	0.109156i
$975$		0			0
$976$	−19.4909	−	66.3798i	−0.0199702	−	0.0680121i
$977$	1045.41	+	905.852i	1.07002	+	0.927177i	0.997533	−	0.0701920i	$-0.0223612\pi$
$977$	1045.41	+	905.852i	1.07002	+	0.927177i	0.0724862	+	0.997369i	$0.476907\pi$
$978$		0			0
$979$	−304.074	+	89.2843i	−0.310597	+	0.0911995i
$980$	−261.693	+	119.511i	−0.267034	+	0.121950i
$981$		0			0
$982$	−413.811	−	121.506i	−0.421396	−	0.123733i
$983$	−585.631	+	84.2010i	−0.595759	+	0.0856572i	−0.433597	−	0.901107i	$-0.642756\pi$
$983$	−585.631	+	84.2010i	−0.595759	+	0.0856572i	−0.162162	+	0.986764i	$0.551847\pi$
$984$		0			0
$985$	644.824	+	92.7116i	0.654643	+	0.0941235i
$986$	51.2245	−	79.7069i	0.0519518	−	0.0808386i
$987$		0			0
$988$		−	877.930i		−	0.888593i
$989$	−103.383	+	336.803i	−0.104533	+	0.340549i
$990$		0			0
$991$	−1200.52	−	1385.48i	−1.21143	−	1.39806i	−0.892967	−	0.450123i	$-0.851380\pi$
$991$	−1200.52	−	1385.48i	−1.21143	−	1.39806i	−0.318459	−	0.947937i	$-0.603165\pi$
$992$	892.823	+	573.782i	0.900023	+	0.578410i
$993$		0			0
$994$	361.180	+	164.946i	0.363360	+	0.165941i
$995$	−75.0018	−	521.649i	−0.0753787	−	0.524270i
$996$		0			0
$997$	−179.201	+	115.166i	−0.179740	+	0.115512i	−0.627417	−	0.778683i	$-0.715888\pi$
$997$	−179.201	+	115.166i	−0.179740	+	0.115512i	0.447677	+	0.894195i	$0.352252\pi$
$998$	−231.621	−	507.180i	−0.232086	−	0.508196i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.3.j.a.10.2		30
3.2	odd	2		23.3.d.a.10.2	yes	30
12.11	even	2		368.3.p.a.33.1		30
23.7	odd	22	inner	207.3.j.a.145.2		30
69.50	odd	22		529.3.b.b.528.18		30
69.53	even	22		23.3.d.a.7.2	✓	30
69.65	even	22		529.3.b.b.528.17		30
276.191	odd	22		368.3.p.a.145.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.7.2	✓	30	69.53	even	22
23.3.d.a.10.2	yes	30	3.2	odd	2
207.3.j.a.10.2		30	1.1	even	1	trivial
207.3.j.a.145.2		30	23.7	odd	22	inner
368.3.p.a.33.1		30	12.11	even	2
368.3.p.a.145.1		30	276.191	odd	22
529.3.b.b.528.17		30	69.65	even	22
529.3.b.b.528.18		30	69.50	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	207.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.881085 + 1.01683i) q^{2} +(0.311634 - 2.16747i) q^{4} +(2.08252 + 0.951056i) q^{5} +(-2.90589 + 9.89656i) q^{7} +(7.00598 - 4.50247i) q^{8} +(0.867820 + 2.95552i) q^{10} +(6.07406 + 5.26321i) q^{11} +(14.4927 - 4.25543i) q^{13} +(-12.6234 + 5.76492i) q^{14} +(2.34688 + 0.689107i) q^{16} +(13.1674 - 1.89318i) q^{17} +(26.2733 + 3.77753i) q^{19} +(2.71037 - 4.21741i) q^{20} +10.8136i q^{22} +(-22.1459 + 6.20960i) q^{23} +(-12.9391 - 14.9325i) q^{25} +(17.0963 + 10.9871i) q^{26} +(20.5449 + 9.38253i) q^{28} +(-0.753370 - 5.23980i) q^{29} +(-29.7398 + 19.1126i) q^{31} +(-12.4713 - 27.3082i) q^{32} +(13.5266 + 11.7209i) q^{34} +(-15.4638 + 17.8461i) q^{35} +(-32.5376 + 14.8594i) q^{37} +(19.3079 + 30.0437i) q^{38} +(18.8722 - 2.71342i) q^{40} +(-7.60347 + 16.6493i) q^{41} +(8.28150 - 12.8863i) q^{43} +(13.3007 - 11.5251i) q^{44} +(-25.8265 - 17.0473i) q^{46} -72.6550 q^{47} +(-48.2763 - 31.0253i) q^{49} +(3.78334 - 26.3137i) q^{50} +(-4.70709 - 32.7385i) q^{52} +(25.8947 - 88.1894i) q^{53} +(7.64377 + 16.7375i) q^{55} +(24.2004 + 82.4189i) q^{56} +(4.66419 - 5.38276i) q^{58} +(71.1561 - 20.8933i) q^{59} +(-15.2916 - 23.7942i) q^{61} +(-45.6374 - 13.4004i) q^{62} +(20.8438 - 45.6417i) q^{64} +(34.2285 + 4.92131i) q^{65} +(-5.29481 + 4.58798i) q^{67} -29.1298i q^{68} -31.7713 q^{70} +(-18.7368 - 21.6234i) q^{71} +(-1.65454 + 11.5076i) q^{73} +(-43.7778 - 19.9926i) q^{74} +(16.3753 - 55.7692i) q^{76} +(-69.7382 + 44.8180i) q^{77} +(5.91331 + 20.1389i) q^{79} +(4.23206 + 3.66710i) q^{80} +(-23.6287 + 6.93802i) q^{82} +(15.0149 - 6.85707i) q^{83} +(29.2218 + 8.58031i) q^{85} +(20.3998 - 2.93305i) q^{86} +(66.2522 + 9.52563i) q^{88} +(-21.3179 + 33.1714i) q^{89} +155.794i q^{91} +(6.55766 + 49.9356i) q^{92} +(-64.0153 - 73.8775i) q^{94} +(51.1221 + 32.8542i) q^{95} +(-77.7143 - 35.4909i) q^{97} +(-10.9882 - 76.4246i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 11 q^{2} - 23 q^{4} + 11 q^{5} - 11 q^{7} - 10 q^{8} - 11 q^{10} + 11 q^{11} - 11 q^{13} + 11 q^{14} + 73 q^{16} - 44 q^{17} + 22 q^{19} - 77 q^{20} - 36 q^{23} - 152 q^{25} + 186 q^{26} - 275 q^{28}+ \cdots - 77 q^{98}+O(q^{100}) \) 30 * q + 11 * q^2 - 23 * q^4 + 11 * q^5 - 11 * q^7 - 10 * q^8 - 11 * q^10 + 11 * q^11 - 11 * q^13 + 11 * q^14 + 73 * q^16 - 44 * q^17 + 22 * q^19 - 77 * q^20 - 36 * q^23 - 152 * q^25 + 186 * q^26 - 275 * q^28 + 88 * q^29 - 110 * q^31 + 147 * q^32 + 231 * q^34 - 209 * q^35 + 341 * q^37 - 374 * q^38 + 429 * q^40 - 77 * q^41 + 77 * q^43 - 110 * q^44 - 99 * q^46 + 110 * q^47 - 422 * q^49 + 396 * q^50 - 472 * q^52 + 187 * q^53 - 165 * q^55 - 176 * q^56 - 13 * q^58 + q^59 + 297 * q^61 - 82 * q^62 + 386 * q^64 - 220 * q^65 + 11 * q^67 - 198 * q^70 + 176 * q^71 - 121 * q^73 + 352 * q^74 + 110 * q^76 - 110 * q^77 + 33 * q^79 + 242 * q^80 + 96 * q^82 + 154 * q^83 + 275 * q^85 - 143 * q^86 + 429 * q^88 - 121 * q^89 - 166 * q^92 - 295 * q^94 + 154 * q^95 + 154 * q^97 - 77 * q^98

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