LMFDB - Embedded newform 115.3.i.a.109.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(14,115)] 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("115.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 21])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.i (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:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			109.16
Character	$\chi$	$=$	115.109
Dual form			115.3.i.a.19.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18321 + 0.540352i) q^{2} +(0.134488 - 0.458024i) q^{3} +(-1.51145 - 1.74430i) q^{4} +(-2.09081 - 4.54186i) q^{5} +(0.406621 - 0.469266i) q^{6} +(1.04923 - 7.29756i) q^{7} +(-2.31167 - 7.87283i) q^{8} +(7.37958 + 4.74257i) q^{9} +(-0.0196528 - 6.50373i) q^{10} +(-11.1229 + 5.07965i) q^{11} +(-1.00221 + 0.457692i) q^{12} +(22.4127 - 3.22246i) q^{13} +(5.18471 - 8.06756i) q^{14} +(-2.36147 + 0.346815i) q^{15} +(0.205039 - 1.42608i) q^{16} +(-8.65061 + 9.98333i) q^{17} +(6.16890 + 9.59900i) q^{18} +(-5.96932 + 5.17245i) q^{19} +(-4.76224 + 10.5118i) q^{20} +(-3.20135 - 1.46201i) q^{21} -15.9054 q^{22} +(18.5664 - 13.5753i) q^{23} -3.91684 q^{24} +(-16.2570 + 18.9923i) q^{25} +(28.2601 + 8.29791i) q^{26} +(6.41157 - 5.55565i) q^{27} +(-14.3150 + 9.19971i) q^{28} +(30.9816 - 35.7547i) q^{29} +(-2.98151 - 0.865672i) q^{30} +(-5.20976 + 1.52972i) q^{31} +(-16.7311 + 26.0341i) q^{32} +(0.830708 + 5.77770i) q^{33} +(-15.6300 + 7.13796i) q^{34} +(-35.3383 + 10.4923i) q^{35} +(-2.88137 - 20.0404i) q^{36} +(16.6723 + 10.7146i) q^{37} +(-9.85787 + 2.89453i) q^{38} +(1.53828 - 10.6989i) q^{39} +(-30.9241 + 26.9599i) q^{40} +(-33.7040 + 21.6603i) q^{41} +(-2.99786 - 3.45971i) q^{42} +(57.6636 + 16.9316i) q^{43} +(25.6721 + 11.7241i) q^{44} +(6.11080 - 43.4329i) q^{45} +(29.3033 - 6.02997i) q^{46} -15.3778i q^{47} +(-0.625603 - 0.285703i) q^{48} +(-5.13841 - 1.50877i) q^{49} +(-29.4979 + 13.6873i) q^{50} +(3.40921 + 5.30483i) q^{51} +(-39.4966 - 34.2240i) q^{52} +(-8.37251 + 58.2321i) q^{53} +(10.5882 - 3.10898i) q^{54} +(46.3269 + 39.8980i) q^{55} +(-59.8780 + 8.60915i) q^{56} +(1.56630 + 3.42973i) q^{57} +(55.9777 - 25.5642i) q^{58} +(7.02361 + 48.8503i) q^{59} +(4.17420 + 3.59493i) q^{60} +(-0.0638973 - 0.217614i) q^{61} +(-6.99080 - 1.00513i) q^{62} +(42.3521 - 48.8769i) q^{63} +(-38.7120 + 24.8787i) q^{64} +(-61.4967 - 95.0579i) q^{65} +(-2.13909 + 7.28508i) q^{66} +(-4.94973 + 10.8384i) q^{67} +30.4889 q^{68} +(-3.72085 - 10.3296i) q^{69} +(-47.4820 - 6.68050i) q^{70} +(36.0043 - 78.8383i) q^{71} +(20.2783 - 69.0615i) q^{72} +(84.7567 - 73.4421i) q^{73} +(13.9370 + 21.6865i) q^{74} +(6.51257 + 10.0004i) q^{75} +(18.0446 + 2.59443i) q^{76} +(25.3986 + 86.4996i) q^{77} +(7.60129 - 11.8278i) q^{78} +(-81.0063 + 11.6469i) q^{79} +(-6.90574 + 2.05040i) q^{80} +(31.1143 + 68.1308i) q^{81} +(-51.5829 + 7.41651i) q^{82} +(-77.2113 - 49.6207i) q^{83} +(2.28849 + 7.79389i) q^{84} +(63.4297 + 18.4166i) q^{85} +(59.0789 + 51.1921i) q^{86} +(-12.2099 - 18.9989i) q^{87} +(65.7036 + 75.8260i) q^{88} +(2.85230 - 9.71406i) q^{89} +(30.6994 - 48.0880i) q^{90} -166.939i q^{91} +(-51.7416 - 11.8671i) q^{92} +2.59193i q^{93} +(8.30943 - 18.1951i) q^{94} +(35.9732 + 16.2972i) q^{95} +(9.67410 + 11.1645i) q^{96} +(97.0275 - 62.3558i) q^{97} +(-5.26453 - 4.56174i) q^{98} +(-106.173 - 15.2653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) $ 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

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 $

$2$	1.18321	+	0.540352i	0.591603	+	0.270176i	0.688638	−	0.725105i	$-0.258209\pi$
$2$	1.18321	+	0.540352i	0.591603	+	0.270176i	−0.0970357	+	0.995281i	$0.530936\pi$
$3$	0.134488	−	0.458024i	0.0448294	−	0.152675i	−0.934037	−	0.357177i	$-0.883739\pi$
$3$	0.134488	−	0.458024i	0.0448294	−	0.152675i	0.978866	+	0.204502i	$0.0655575\pi$
$4$	−1.51145	−	1.74430i	−0.377862	−	0.436076i
$5$	−2.09081	−	4.54186i	−0.418162	−	0.908373i
$5$	−2.09081	−	4.54186i	−0.418162	−	0.908373i
$6$	0.406621	−	0.469266i	0.0677702	−	0.0782110i
$7$	1.04923	−	7.29756i	0.149890	−	1.04251i	−0.766506	−	0.642237i	$-0.778006\pi$
$7$	1.04923	−	7.29756i	0.149890	−	1.04251i	0.916396	−	0.400272i	$-0.131084\pi$
$8$	−2.31167	−	7.87283i	−0.288959	−	0.984104i
$9$	7.37958	+	4.74257i	0.819954	+	0.526952i
$10$	−0.0196528	−	6.50373i	−0.00196528	−	0.650373i
$11$	−11.1229	+	5.07965i	−1.01117	+	0.461786i	−0.850923	−	0.525291i	$-0.823957\pi$
$11$	−11.1229	+	5.07965i	−1.01117	+	0.461786i	−0.160248	+	0.987077i	$0.551229\pi$
$12$	−1.00221	+	0.457692i	−0.0835171	+	0.0381410i
$13$	22.4127	−	3.22246i	1.72405	−	0.247882i	0.792083	−	0.610414i	$-0.208997\pi$
$13$	22.4127	−	3.22246i	1.72405	−	0.247882i	0.931971	+	0.362532i	$0.118088\pi$
$14$	5.18471	−	8.06756i	0.370336	−	0.576254i
$15$	−2.36147	+	0.346815i	−0.157431	+	0.0231210i
$16$	0.205039	−	1.42608i	0.0128149	−	0.0891298i
$17$	−8.65061	+	9.98333i	−0.508859	+	0.587255i	−0.950806	−	0.309786i	$-0.899742\pi$
$17$	−8.65061	+	9.98333i	−0.508859	+	0.587255i	0.441947	+	0.897041i	$0.354288\pi$
$18$	6.16890	+	9.59900i	0.342717	+	0.533278i
$19$	−5.96932	+	5.17245i	−0.314175	+	0.272234i	−0.797646	−	0.603127i	$-0.793921\pi$
$19$	−5.96932	+	5.17245i	−0.314175	+	0.272234i	0.483471	+	0.875361i	$0.339376\pi$
$20$	−4.76224	+	10.5118i	−0.238112	+	0.525590i
$21$	−3.20135	−	1.46201i	−0.152445	−	0.0696195i
$22$	−15.9054			−0.722974
$23$	18.5664	−	13.5753i	0.807235	−	0.590230i
$23$	18.5664	−	13.5753i	0.807235	−	0.590230i
$24$	−3.91684			−0.163202
$25$	−16.2570	+	18.9923i	−0.650281	+	0.759693i
$26$	28.2601	+	8.29791i	1.08693	+	0.319150i
$27$	6.41157	−	5.55565i	0.237465	−	0.205765i
$28$	−14.3150	+	9.19971i	−0.511251	+	0.328561i
$29$	30.9816	−	35.7547i	1.06833	−	1.23292i	0.0969763	−	0.995287i	$-0.469083\pi$
$29$	30.9816	−	35.7547i	1.06833	−	1.23292i	0.971355	−	0.237633i	$-0.0763717\pi$
$30$	−2.98151	−	0.865672i	−0.0993836	−	0.0288557i
$31$	−5.20976	+	1.52972i	−0.168057	+	0.0493459i	−0.364678	−	0.931134i	$-0.618821\pi$
$31$	−5.20976	+	1.52972i	−0.168057	+	0.0493459i	0.196622	+	0.980479i	$0.437003\pi$
$32$	−16.7311	+	26.0341i	−0.522846	+	0.813564i
$33$	0.830708	+	5.77770i	0.0251730	+	0.175082i
$34$	−15.6300	+	7.13796i	−0.459704	+	0.209940i
$35$	−35.3383	+	10.4923i	−1.00967	+	0.299781i
$36$	−2.88137	−	20.0404i	−0.0800381	−	0.556677i
$37$	16.6723	+	10.7146i	0.450602	+	0.289584i	0.746192	−	0.665731i	$-0.231880\pi$
$37$	16.6723	+	10.7146i	0.450602	+	0.289584i	−0.295591	+	0.955315i	$0.595516\pi$
$38$	−9.85787	+	2.89453i	−0.259418	+	0.0761719i
$39$	1.53828	−	10.6989i	0.0394430	−	0.274332i
$40$	−30.9241	+	26.9599i	−0.773101	+	0.673997i
$41$	−33.7040	+	21.6603i	−0.822049	+	0.528299i	−0.882742	−	0.469857i	$-0.844305\pi$
$41$	−33.7040	+	21.6603i	−0.822049	+	0.528299i	0.0606930	+	0.998156i	$0.480669\pi$
$42$	−2.99786	−	3.45971i	−0.0713776	−	0.0823741i
$43$	57.6636	+	16.9316i	1.34101	+	0.393757i	0.872031	−	0.489450i	$-0.162802\pi$
$43$	57.6636	+	16.9316i	1.34101	+	0.393757i	0.468983	+	0.883207i	$0.344621\pi$
$44$	25.6721	+	11.7241i	0.583457	+	0.266456i
$45$	6.11080	−	43.4329i	0.135796	−	0.965175i
$46$	29.3033	−	6.02997i	0.637028	−	0.131086i
$47$		−	15.3778i		−	0.327188i	−0.986528	−	0.163594i	$-0.947691\pi$
$47$		−	15.3778i		−	0.327188i	0.986528	−	0.163594i	$-0.0523086\pi$
$48$	−0.625603	−	0.285703i	−0.0130334	−	0.00595215i
$49$	−5.13841	−	1.50877i	−0.104866	−	0.0307913i
$50$	−29.4979	+	13.6873i	−0.589959	+	0.273746i
$51$	3.40921	+	5.30483i	0.0668472	+	0.104016i
$52$	−39.4966	−	34.2240i	−0.759550	−	0.658154i
$53$	−8.37251	+	58.2321i	−0.157972	+	1.09872i	0.744392	+	0.667743i	$0.232739\pi$
$53$	−8.37251	+	58.2321i	−0.157972	+	1.09872i	−0.902364	+	0.430975i	$0.858170\pi$
$54$	10.5882	−	3.10898i	0.196078	−	0.0575736i
$55$	46.3269	+	39.8980i	0.842307	+	0.725418i
$56$	−59.8780	+	8.60915i	−1.06925	+	0.153735i
$57$	1.56630	+	3.42973i	0.0274790	+	0.0601706i
$58$	55.9777	−	25.5642i	0.965133	−	0.440761i
$59$	7.02361	+	48.8503i	0.119044	+	0.827971i	0.958612	+	0.284716i	$0.0918992\pi$
$59$	7.02361	+	48.8503i	0.119044	+	0.827971i	−0.839568	+	0.543255i	$0.817192\pi$
$60$	4.17420	+	3.59493i	0.0695699	+	0.0599156i
$61$	−0.0638973	−	0.217614i	−0.00104750	−	0.00356745i	0.958968	−	0.283516i	$-0.0915008\pi$
$61$	−0.0638973	−	0.217614i	−0.00104750	−	0.00356745i	−0.960015	+	0.279948i	$0.909683\pi$
$62$	−6.99080	−	1.00513i	−0.112755	−	0.0162117i
$63$	42.3521	−	48.8769i	0.672256	−	0.775824i
$64$	−38.7120	+	24.8787i	−0.604874	+	0.388729i
$65$	−61.4967	−	95.0579i	−0.946102	−	1.46243i
$66$	−2.13909	+	7.28508i	−0.0324105	+	0.110380i
$67$	−4.94973	+	10.8384i	−0.0738766	+	0.161767i	−0.942967	−	0.332886i	$-0.891978\pi$
$67$	−4.94973	+	10.8384i	−0.0738766	+	0.161767i	0.869091	+	0.494653i	$0.164705\pi$
$68$	30.4889			0.448366
$69$	−3.72085	−	10.3296i	−0.0539254	−	0.149704i
$70$	−47.4820	−	6.68050i	−0.678314	−	0.0954357i
$71$	36.0043	−	78.8383i	0.507102	−	1.11040i	−0.466993	−	0.884261i	$-0.654663\pi$
$71$	36.0043	−	78.8383i	0.507102	−	1.11040i	0.974095	−	0.226138i	$-0.0726100\pi$
$72$	20.2783	−	69.0615i	0.281643	−	0.959187i
$73$	84.7567	−	73.4421i	1.16105	−	1.00606i	0.161234	−	0.986916i	$-0.448453\pi$
$73$	84.7567	−	73.4421i	1.16105	−	1.00606i	0.999817	−	0.0191401i	$-0.00609284\pi$
$74$	13.9370	+	21.6865i	0.188338	+	0.293060i
$75$	6.51257	+	10.0004i	0.0868343	+	0.133338i
$76$	18.0446	+	2.59443i	0.237429	+	0.0341372i
$77$	25.3986	+	86.4996i	0.329852	+	1.12337i
$78$	7.60129	−	11.8278i	0.0974524	−	0.151639i
$79$	−81.0063	+	11.6469i	−1.02540	+	0.147430i	−0.634434	−	0.772977i	$-0.718767\pi$
$79$	−81.0063	+	11.6469i	−1.02540	+	0.147430i	−0.390962	+	0.920407i	$0.627858\pi$
$80$	−6.90574	+	2.05040i	−0.0863218	+	0.0256300i
$81$	31.1143	+	68.1308i	0.384127	+	0.841122i
$82$	−51.5829	+	7.41651i	−0.629060	+	0.0904452i
$83$	−77.2113	−	49.6207i	−0.930256	−	0.597839i	−0.0146401	−	0.999893i	$-0.504660\pi$
$83$	−77.2113	−	49.6207i	−0.930256	−	0.597839i	−0.915616	+	0.402053i	$0.868297\pi$
$84$	2.28849	+	7.79389i	0.0272439	+	0.0927844i
$85$	63.4297	+	18.4166i	0.746232	+	0.216666i
$86$	59.0789	+	51.1921i	0.686964	+	0.595257i
$87$	−12.2099	−	18.9989i	−0.140343	−	0.218378i
$88$	65.7036	+	75.8260i	0.746632	+	0.861660i
$89$	2.85230	−	9.71406i	0.0320484	−	0.109147i	−0.941916	−	0.335850i	$-0.890977\pi$
$89$	2.85230	−	9.71406i	0.0320484	−	0.109147i	0.973964	+	0.226703i	$0.0727947\pi$
$90$	30.6994	−	48.0880i	0.341104	−	0.534311i
$91$		−	166.939i		−	1.83450i
$92$	−51.7416	−	11.8671i	−0.562409	−	0.128990i
$93$			2.59193i			0.0278702i
$94$	8.30943	−	18.1951i	0.0883982	−	0.193565i
$95$	35.9732	+	16.2972i	0.378666	+	0.171550i
$96$	9.67410	+	11.1645i	0.100772	+	0.116297i
$97$	97.0275	−	62.3558i	1.00028	−	0.642843i	0.0654225	−	0.997858i	$-0.479160\pi$
$97$	97.0275	−	62.3558i	1.00028	−	0.642843i	0.934861	+	0.355015i	$0.115524\pi$
$98$	−5.26453	−	4.56174i	−0.0537197	−	0.0465483i
$99$	−106.173	−	15.2653i	−1.07245	−	0.154195i
$100$	57.7001	−	0.348716i	0.577001	−	0.00348716i
$101$	−55.8595	−	35.8987i	−0.553064	−	0.355433i	0.234065	−	0.972221i	$-0.424797\pi$
$101$	−55.8595	−	35.8987i	−0.553064	−	0.355433i	−0.787129	+	0.616788i	$0.788434\pi$
$102$	1.16732	+	8.11887i	0.0114443	+	0.0795967i
$103$	−65.2707	−	142.923i	−0.633696	−	1.38760i	−0.905126	−	0.425143i	$-0.860224\pi$
$103$	−65.2707	−	142.923i	−0.633696	−	1.38760i	0.271430	−	0.962458i	$-0.412504\pi$
$104$	−77.1807	−	169.002i	−0.742122	−	1.62502i
$105$	0.0531738	+	17.5969i	0.000506417	+	0.167589i
$106$	−41.3722	+	64.3764i	−0.390304	+	0.607324i
$107$	−80.8763	+	23.7474i	−0.755853	+	0.221939i	−0.636884	−	0.770959i	$-0.719777\pi$
$107$	−80.8763	+	23.7474i	−0.755853	+	0.221939i	−0.118969	+	0.992898i	$0.537959\pi$
$108$	−19.3815	−	2.78664i	−0.179458	−	0.0258022i
$109$	95.6662	+	82.8953i	0.877672	+	0.760507i	0.971987	−	0.235035i	$-0.0755206\pi$
$109$	95.6662	+	82.8953i	0.877672	+	0.760507i	−0.0943149	+	0.995542i	$0.530066\pi$
$110$	33.2552	+	72.2403i	0.302320	+	0.656730i
$111$	7.14977	−	6.19531i	0.0644124	−	0.0558136i
$112$	−10.1918	−	2.99257i	−0.0909978	−	0.0267194i
$113$	−64.9400	+	142.199i	−0.574690	+	1.25840i	0.369572	+	0.929202i	$0.379504\pi$
$113$	−64.9400	+	142.199i	−0.574690	+	1.25840i	−0.944262	+	0.329194i	$0.893223\pi$
$114$			4.90442i			0.0430213i
$115$	−100.476	−	55.9427i	−0.873704	−	0.486458i
$116$	−109.194			−0.941329
$117$	180.679	+	82.5134i	1.54427	+	0.705243i
$118$	−18.0860	+	61.5951i	−0.153271	+	0.521993i
$119$	63.7775	+	73.6032i	0.535946	+	0.618514i
$120$	8.18937	+	17.7898i	0.0682447	+	0.148248i
$121$	18.6774	−	21.5549i	0.154359	−	0.178139i
$122$	0.0419846	−	0.292009i	0.000344136	−	0.00239352i
$123$	5.38814	+	18.3503i	0.0438060	+	0.149189i
$124$	10.5426	+	6.77531i	0.0850209	+	0.0546396i
$125$	120.251	+	34.1279i	0.962008	+	0.273023i
$126$	76.5220	−	34.9464i	0.607317	−	0.277352i
$127$	−175.035	+	79.9358i	−1.37823	+	0.629416i	−0.960276	−	0.279053i	$-0.909980\pi$
$127$	−175.035	+	79.9358i	−1.37823	+	0.629416i	−0.417953	+	0.908469i	$0.637252\pi$
$128$	63.2796	−	9.09823i	0.494372	−	0.0710800i
$129$	15.5101	−	24.1342i	0.120234	−	0.187087i
$130$	−21.3985	−	145.703i	−0.164604	−	1.12079i
$131$	−33.4075	+	232.354i	−0.255019	+	1.77370i	0.312090	+	0.950053i	$0.398971\pi$
$131$	−33.4075	+	232.354i	−0.255019	+	1.77370i	−0.567109	+	0.823643i	$0.691938\pi$
$132$	8.82250	−	10.1817i	0.0668371	−	0.0771341i
$133$	31.4831	+	48.9886i	0.236715	+	0.368335i
$134$	−11.7131	+	10.1495i	−0.0874111	+	0.0757422i
$135$	−38.6384	−	17.5046i	−0.286210	−	0.129664i
$136$	98.5944	+	45.0266i	0.724959	+	0.331078i
$137$	−55.0725			−0.401989			−0.200994	−	0.979592i	$-0.564417\pi$
$137$	−55.0725			−0.401989			−0.200994	+	0.979592i	$0.564417\pi$
$138$	1.17907	−	14.2326i	0.00854401	−	0.103135i
$139$	56.5226			0.406638			0.203319	−	0.979113i	$-0.434827\pi$
$139$	56.5226			0.406638			0.203319	+	0.979113i	$0.434827\pi$
$140$	71.7138	+	45.7821i	0.512242	+	0.327015i
$141$	−7.04341	−	2.06813i	−0.0499533	−	0.0146676i
$142$	85.2008	−	73.8270i	0.600006	−	0.519908i
$143$	−232.925	+	149.692i	−1.62884	+	1.04679i
$144$	8.27637	−	9.55144i	0.0574748	−	0.0663295i
$145$	−227.169	−	65.9580i	−1.56669	−	0.454883i
$146$	139.969	−	41.0986i	0.958693	−	0.281498i
$147$	−1.38211	+	2.15061i	−0.00940211	+	0.0146300i
$148$	−6.50972	−	45.2761i	−0.0439846	−	0.305919i
$149$	−229.159	+	104.653i	−1.53798	+	0.702372i	−0.990886	−	0.134700i	$-0.956993\pi$
$149$	−229.159	+	104.653i	−1.53798	+	0.702372i	−0.547093	+	0.837072i	$0.684266\pi$
$150$	2.30200	+	15.3516i	0.0153467	+	0.102344i
$151$	11.9137	+	82.8616i	0.0788987	+	0.548752i	0.990483	+	0.137638i	$0.0439511\pi$
$151$	11.9137	+	82.8616i	0.0788987	+	0.548752i	−0.911584	+	0.411114i	$0.865140\pi$
$152$	54.5209	+	35.0385i	0.358690	+	0.230516i
$153$	−111.185	+	32.6467i	−0.726696	+	0.213377i
$154$	−16.6885	+	116.071i	−0.108367	+	0.753708i
$155$	17.8404	+	20.4637i	0.115099	+	0.132024i
$156$	−20.9872	+	13.4877i	−0.134534	+	0.0864595i
$157$	110.824	+	127.898i	0.705886	+	0.814636i	0.989535	−	0.144293i	$-0.0460906\pi$
$157$	110.824	+	127.898i	0.705886	+	0.814636i	−0.283649	+	0.958928i	$0.591545\pi$
$158$	−102.140	−	29.9911i	−0.646459	−	0.189817i
$159$	25.5457	+	11.6663i	0.160665	+	0.0733731i
$160$	153.225	+	21.5580i	0.957654	+	0.134737i
$161$	−79.5861	−	149.733i	−0.494324	−	0.930020i
$162$			97.4254i			0.601392i
$163$	−111.076	−	50.7269i	−0.681450	−	0.311208i	0.0444465	−	0.999012i	$-0.485848\pi$
$163$	−111.076	−	50.7269i	−0.681450	−	0.311208i	−0.725896	+	0.687804i	$0.758575\pi$
$164$	88.7240	+	26.0517i	0.541000	+	0.158852i
$165$	24.5047	−	15.8530i	0.148513	−	0.0960790i
$166$	−64.5442	−	100.433i	−0.388820	−	0.605016i
$167$	−38.2031	−	33.1031i	−0.228761	−	0.198222i	0.532937	−	0.846155i	$-0.321088\pi$
$167$	−38.2031	−	33.1031i	−0.228761	−	0.198222i	−0.761698	+	0.647933i	$0.775634\pi$
$168$	−4.10967	+	28.5834i	−0.0244623	+	0.170139i
$169$	329.791	−	96.8353i	1.95142	−	0.572990i
$170$	65.0989	+	56.0650i	0.382935	+	0.329794i
$171$	−68.5818	+	9.86057i	−0.401063	+	0.0576642i
$172$	−57.6218	−	126.174i	−0.335010	−	0.733570i
$173$	55.2422	−	25.2283i	0.319319	−	0.145828i	−0.249306	−	0.968425i	$-0.580203\pi$
$173$	55.2422	−	25.2283i	0.319319	−	0.145828i	0.568626	+	0.822596i	$0.307475\pi$
$174$	−4.18067	−	29.0772i	−0.0240269	−	0.167110i
$175$	121.540	+	138.564i	0.694517	+	0.791795i
$176$	4.96335	+	16.9036i	0.0282008	+	0.0960432i
$177$	23.3192	+	3.35280i	0.131747	+	0.0189424i
$178$	8.62387	−	9.95248i	0.0484487	−	0.0559128i
$179$	−13.9247	+	8.94889i	−0.0777919	+	0.0499938i	−0.578959	−	0.815357i	$-0.696541\pi$
$179$	−13.9247	+	8.94889i	−0.0777919	+	0.0499938i	0.501167	+	0.865351i	$0.332904\pi$
$180$	−84.9963	+	54.9874i	−0.472202	+	0.305486i
$181$	27.6406	−	94.1353i	0.152711	−	0.520084i	−0.847227	−	0.531231i	$-0.821730\pi$
$181$	27.6406	−	94.1353i	0.152711	−	0.520084i	0.999938	+	0.0111461i	$0.00354799\pi$
$182$	90.2059	−	197.523i	0.495637	−	1.08529i
$183$	−0.108266			−0.000591618
$184$	−149.795	−	114.789i	−0.814106	−	0.623851i
$185$	13.8058	−	98.1253i	0.0746258	−	0.530407i
$186$	−1.40055	+	3.06678i	−0.00752985	+	0.0164881i
$187$	45.5078	−	154.985i	0.243357	−	0.828799i
$188$	−26.8236	+	23.2428i	−0.142679	+	0.123632i
$189$	−33.8155	−	52.6180i	−0.178918	−	0.278402i
$190$	33.7575	+	38.7212i	0.177671	+	0.203796i
$191$	−122.655	−	17.6351i	−0.642171	−	0.0923303i	−0.186467	−	0.982461i	$-0.559704\pi$
$191$	−122.655	−	17.6351i	−0.642171	−	0.0923303i	−0.455705	+	0.890131i	$0.650613\pi$
$192$	6.18874	+	21.0769i	0.0322330	+	0.109776i
$193$	−48.0186	+	74.7184i	−0.248801	+	0.387142i	−0.943081	−	0.332563i	$-0.892087\pi$
$193$	−48.0186	+	74.7184i	−0.248801	+	0.387142i	0.694280	+	0.719705i	$0.255723\pi$
$194$	148.497	−	21.3507i	0.765451	−	0.110055i
$195$	−51.8094	+	15.3828i	−0.265689	+	0.0788862i
$196$	5.13468	+	11.2434i	0.0261974	+	0.0573642i
$197$	52.3575	−	7.52788i	0.265774	−	0.0382126i	−0.00813935	−	0.999967i	$-0.502591\pi$
$197$	52.3575	−	7.52788i	0.265774	−	0.0382126i	0.273914	+	0.961754i	$0.411682\pi$
$198$	−117.375	−	75.4327i	−0.592806	−	0.380973i
$199$	−60.7947	−	207.048i	−0.305501	−	1.04044i	−0.958975	−	0.283491i	$-0.908507\pi$
$199$	−60.7947	−	207.048i	−0.305501	−	1.04044i	0.653474	−	0.756949i	$-0.273311\pi$
$200$	187.104	+	84.0848i	0.935522	+	0.420424i
$201$	4.29857	+	3.72473i	0.0213859	+	0.0185310i
$202$	−46.6953	−	72.6593i	−0.231165	−	0.359700i
$203$	−228.415	−	263.605i	−1.12520	−	1.29855i
$204$	4.10040	−	13.9647i	0.0201000	−	0.0684542i
$205$	168.847	+	107.792i	0.823642	+	0.525813i
$206$		−	204.376i		−	0.992118i
$207$	201.394	−	12.1275i	0.972918	−	0.0585870i
$208$		−	32.6230i		−	0.156841i
$209$	40.1218	−	87.8545i	0.191970	−	0.420357i
$210$	−9.44559	+	20.8495i	−0.0449790	+	0.0992831i
$211$	150.466	+	173.647i	0.713108	+	0.822970i	0.990460	−	0.137798i	$-0.0440024\pi$
$211$	150.466	+	173.647i	0.713108	+	0.822970i	−0.277353	+	0.960768i	$0.589457\pi$
$212$	114.229	−	73.4106i	0.538816	−	0.346276i
$213$	−31.2677	−	27.0936i	−0.146797	−	0.127200i
$214$	−108.525	−	15.6036i	−0.507127	−	0.0729139i
$215$	−43.6628	−	297.301i	−0.203083	−	1.38279i
$216$	−58.5602	−	37.6343i	−0.271112	−	0.174233i
$217$	5.69701	+	39.6236i	0.0262535	+	0.182597i
$218$	68.4002	+	149.776i	0.313762	+	0.687044i
$219$	−22.2395	−	48.6977i	−0.101550	−	0.222364i
$220$	−0.426408	−	141.112i	−0.00193822	−	0.641418i
$221$	−161.713	+	251.630i	−0.731731	+	1.13860i
$222$	11.8073	−	3.46693i	0.0531860	−	0.0156168i
$223$	−23.9260	−	3.44003i	−0.107291	−	0.0154262i	0.0884600	−	0.996080i	$-0.471805\pi$
$223$	−23.9260	−	3.44003i	−0.107291	−	0.0154262i	−0.195751	+	0.980654i	$0.562715\pi$
$224$	172.430	+	149.412i	0.769779	+	0.667017i
$225$	−210.043	+	63.0554i	−0.933523	+	0.280246i
$226$	−153.675	+	133.160i	−0.679976	+	0.589203i
$227$	414.487	+	121.704i	1.82594	+	0.536143i	0.999633	−	0.0270832i	$-0.00862190\pi$
$227$	414.487	+	121.704i	1.82594	+	0.536143i	0.826303	+	0.563226i	$0.190440\pi$
$228$	3.61510	−	7.91596i	0.0158557	−	0.0347191i
$229$		−	135.991i		−	0.593849i	−0.954901	−	0.296924i	$-0.904039\pi$
$229$		−	135.991i		−	0.593849i	0.954901	−	0.296924i	$-0.0959609\pi$
$230$	−88.6549	−	120.484i	−0.385456	−	0.523844i
$231$	43.0347			0.186298
$232$	−353.110	−	161.260i	−1.52203	−	0.695086i
$233$	52.6598	−	179.343i	0.226008	−	0.769712i	−0.765923	−	0.642932i	$-0.777718\pi$
$233$	52.6598	−	179.343i	0.226008	−	0.769712i	0.991931	−	0.126780i	$-0.0404641\pi$
$234$	169.194	+	195.261i	0.723052	+	0.834447i
$235$	−69.8439	+	32.1521i	−0.297208	+	0.136817i
$236$	74.5939	−	86.0860i	0.316076	−	0.364771i
$237$	−5.55979	+	38.6692i	−0.0234590	+	0.163161i
$238$	35.6903	+	121.550i	0.149959	+	0.510714i
$239$	28.9631	+	18.6135i	0.121185	+	0.0778807i	0.599829	−	0.800128i	$-0.295235\pi$
$239$	28.9631	+	18.6135i	0.121185	+	0.0778807i	−0.478644	+	0.878009i	$0.658872\pi$
$240$	0.0103911	+	3.43875i	4.32964e−5	+	0.0143281i
$241$	55.3779	−	25.2902i	0.229784	−	0.104939i	−0.297196	−	0.954816i	$-0.596052\pi$
$241$	55.3779	−	25.2902i	0.229784	−	0.104939i	0.526980	+	0.849878i	$0.323324\pi$
$242$	33.7464	−	15.4115i	0.139448	−	0.0636837i
$243$	110.966	−	15.9546i	0.456652	−	0.0656566i
$244$	−0.283008	+	0.440369i	−0.00115987	+	0.00180479i
$245$	3.89079	+	26.4925i	0.0158808	+	0.108133i
$246$	−3.54035	+	24.6237i	−0.0143917	+	0.100096i
$247$	−117.121	+	135.164i	−0.474173	+	0.547224i
$248$	24.0865	+	37.4793i	0.0971230	+	0.151126i
$249$	−33.1115	+	28.6913i	−0.132978	+	0.115226i
$250$	123.840	+	105.358i	0.495362	+	0.421432i
$251$	−125.089	−	57.1264i	−0.498364	−	0.227595i	0.150343	−	0.988634i	$-0.451962\pi$
$251$	−125.089	−	57.1264i	−0.498364	−	0.227595i	−0.648706	+	0.761039i	$0.724690\pi$
$252$	−149.269			−0.592338
$253$	−137.554	+	245.307i	−0.543692	+	0.969593i
$254$	−250.296			−0.985417
$255$	16.9658	−	26.5755i	0.0665325	−	0.104218i
$256$	256.401	+	75.2861i	1.00157	+	0.294086i
$257$	−51.6001	+	44.7118i	−0.200779	+	0.173976i	−0.749447	−	0.662064i	$-0.769680\pi$
$257$	−51.6001	+	44.7118i	−0.200779	+	0.173976i	0.548668	+	0.836040i	$0.315135\pi$
$258$	31.3926	−	20.1748i	0.121677	−	0.0781970i
$259$	95.6836	−	110.425i	0.369435	−	0.426350i
$260$	−72.8609	+	250.944i	−0.280234	+	0.965169i
$261$	398.200	−	116.922i	1.52567	−	0.447978i
$262$	−165.081	+	256.871i	−0.630080	+	0.980423i
$263$	−16.8417	−	117.136i	−0.0640367	−	0.445385i	−0.996464	−	0.0840263i	$-0.973222\pi$
$263$	−16.8417	−	117.136i	−0.0640367	−	0.445385i	0.932427	−	0.361359i	$-0.117687\pi$
$264$	43.5665	−	19.8962i	0.165025	−	0.0753643i
$265$	281.987	−	83.7253i	1.06410	−	0.315945i
$266$	10.7798	+	74.9755i	0.0405257	+	0.281863i
$267$	−4.06567	−	2.61285i	−0.0152272	−	0.00978596i
$268$	26.3867	−	7.74784i	0.0984579	−	0.0289099i
$269$	−62.8709	+	437.277i	−0.233721	+	1.62556i	0.448057	+	0.894005i	$0.352116\pi$
$269$	−62.8709	+	437.277i	−0.233721	+	1.62556i	−0.681778	+	0.731559i	$0.738793\pi$
$270$	−36.2585	−	41.5899i	−0.134291	−	0.154037i
$271$	−278.967	+	179.281i	−1.02940	+	0.661553i	−0.942342	−	0.334650i	$-0.891382\pi$
$271$	−278.967	+	179.281i	−1.02940	+	0.661553i	−0.0870546	+	0.996204i	$0.527745\pi$
$272$	12.4633	+	14.3834i	0.0458209	+	0.0528802i
$273$	−76.4623	−	22.4513i	−0.280082	−	0.0822393i
$274$	−65.1620	−	29.7585i	−0.237818	−	0.108608i
$275$	84.3506	−	293.829i	0.306730	−	1.06847i
$276$	−12.3941	+	22.1029i	−0.0449060	+	0.0800831i
$277$			47.3956i			0.171103i	0.996334	+	0.0855516i	$0.0272652\pi$
$277$			47.3956i			0.171103i	−0.996334	+	0.0855516i	$0.972735\pi$
$278$	66.8779	+	30.5421i	0.240568	+	0.109864i
$279$	−45.7007	−	13.4189i	−0.163802	−	0.0480965i
$280$	164.295	+	253.957i	0.586768	+	0.906991i
$281$	24.8507	+	38.6684i	0.0884367	+	0.137610i	0.882653	−	0.470024i	$-0.155755\pi$
$281$	24.8507	+	38.6684i	0.0884367	+	0.137610i	−0.794217	+	0.607635i	$0.792119\pi$
$282$	−7.21628	−	6.25295i	−0.0255897	−	0.0221736i
$283$	−1.71331	+	11.9163i	−0.00605408	+	0.0421071i	−0.992625	−	0.121229i	$-0.961316\pi$
$283$	−1.71331	+	11.9163i	−0.00605408	+	0.0421071i	0.986570	+	0.163336i	$0.0522255\pi$
$284$	−191.937	+	56.3577i	−0.675833	+	0.198443i
$285$	12.3025	−	14.2848i	0.0431667	−	0.0501222i
$286$	−356.484	+	51.2546i	−1.24645	+	0.179212i
$287$	122.704	+	268.684i	0.427539	+	0.936181i
$288$	−246.937	+	112.772i	−0.857419	+	0.391570i
$289$	16.2951	+	113.335i	0.0563843	+	0.392162i
$290$	−233.148	−	200.793i	−0.803957	−	0.692390i
$291$	−15.5114	−	52.8271i	−0.0533039	−	0.181536i
$292$	−256.211	−	36.8376i	−0.877434	−	0.126156i
$293$	−0.857298	+	0.989375i	−0.00292593	+	0.00337671i	−0.757211	−	0.653171i	$-0.773438\pi$
$293$	−0.857298	+	0.989375i	−0.00292593	+	0.00337671i	0.754285	+	0.656547i	$0.227984\pi$
$294$	−2.79740	+	1.79778i	−0.00951498	+	0.00611490i
$295$	207.186	−	134.037i	0.702326	−	0.454362i
$296$	45.8135	−	156.027i	0.154775	−	0.527117i
$297$	−43.0943	+	94.3633i	−0.145099	+	0.317722i
$298$	−327.692			−1.09964
$299$	372.378	−	364.089i	1.24541	−	1.21769i
$300$	7.60025	−	26.4749i	0.0253342	−	0.0882498i
$301$	184.062	−	403.039i	0.611501	−	1.33900i
$302$	−30.6780	+	104.480i	−0.101583	+	0.345960i
$303$	−23.9549	+	20.7571i	−0.0790591	+	0.0685051i
$304$	6.15236	+	9.57326i	0.0202380	+	0.0314910i
$305$	−0.854778	+	0.745203i	−0.00280255	+	0.00244329i
$306$	−149.195	−	21.4510i	−0.487565	−	0.0701012i
$307$	−51.1547	−	174.217i	−0.166628	−	0.567482i	−0.999893	−	0.0146091i	$-0.995350\pi$
$307$	−51.1547	−	174.217i	−0.166628	−	0.567482i	0.833265	−	0.552873i	$-0.186469\pi$
$308$	112.493	−	175.043i	0.365237	−	0.568320i
$309$	−74.2403	+	10.6741i	−0.240260	+	0.0345442i
$310$	10.0513	+	33.8528i	0.0324235	+	0.109203i
$311$	−145.304	−	318.171i	−0.467215	−	1.02306i	−0.985783	−	0.168021i	$-0.946262\pi$
$311$	−145.304	−	318.171i	−0.467215	−	1.02306i	0.518569	−	0.855036i	$-0.326465\pi$
$312$	−87.7870	+	12.6219i	−0.281369	+	0.0404547i
$313$	399.916	+	257.010i	1.27769	+	0.821119i	0.990601	−	0.136786i	$-0.0436771\pi$
$313$	399.916	+	257.010i	1.27769	+	0.821119i	0.287086	+	0.957905i	$0.407313\pi$
$314$	62.0178	+	211.213i	0.197509	+	0.672654i
$315$	−310.542	−	90.1651i	−0.985849	−	0.286238i
$316$	142.753	+	123.696i	0.451749	+	0.391443i
$317$	88.2076	+	137.254i	0.278257	+	0.432977i	0.952049	−	0.305944i	$-0.0989721\pi$
$317$	88.2076	+	137.254i	0.278257	+	0.432977i	−0.673792	+	0.738921i	$0.735336\pi$
$318$	23.9219	+	27.6073i	0.0752260	+	0.0868155i
$319$	−162.983	+	555.070i	−0.510920	+	1.74003i
$320$	193.935	+	123.808i	0.606046	+	0.386900i
$321$			40.2371i			0.125349i
$322$	−13.2581	−	220.170i	−0.0411743	−	0.683756i
$323$		−	104.338i		−	0.323029i
$324$	71.8133	−	157.249i	0.221646	−	0.485337i
$325$	−303.162	+	478.057i	−0.932806	+	1.47095i
$326$	−104.016	−	120.041i	−0.319067	−	0.368223i
$327$	50.8340	−	32.6690i	0.155456	−	0.0999053i
$328$	248.440	+	215.275i	0.757440	+	0.656325i
$329$	−112.221	−	16.1349i	−0.341096	−	0.0490422i
$330$	37.5603	−	5.51624i	0.113819	−	0.0167159i
$331$	393.571	+	252.933i	1.18904	+	0.764147i	0.977026	−	0.213120i	$-0.0683625\pi$
$331$	393.571	+	252.933i	1.18904	+	0.764147i	0.212010	+	0.977267i	$0.431999\pi$
$332$	30.1473	+	209.679i	0.0908051	+	0.631564i
$333$	72.2195	+	158.139i	0.216875	+	0.474891i
$334$	−27.3147	−	59.8109i	−0.0817806	−	0.179074i
$335$	59.5754	−	0.180023i	0.177837	−	0.000537383i
$336$	−2.74134	+	4.26561i	−0.00815875	+	0.0126953i
$337$	51.9693	−	15.2596i	0.154211	−	0.0452806i	−0.203716	−	0.979030i	$-0.565302\pi$
$337$	51.9693	−	15.2596i	0.154211	−	0.0452806i	0.357927	+	0.933750i	$0.383484\pi$
$338$	442.535	+	63.6270i	1.30928	+	0.188245i
$339$	56.3968	+	48.8681i	0.166362	+	0.144154i
$340$	−63.7465	−	138.476i	−0.187490	−	0.407284i
$341$	50.1771	−	43.4787i	0.147147	−	0.127503i
$342$	−86.4745	−	25.3912i	−0.252849	−	0.0742433i
$343$	133.670	−	292.697i	0.389709	−	0.853343i
$344$		−	493.116i		−	1.43348i
$345$	−39.1359	+	38.4968i	−0.113438	+	0.111585i
$346$	78.9950			0.228309
$347$	0.471708	+	0.215422i	0.00135939	+	0.000620812i	0.416095	−	0.909321i	$-0.363399\pi$
$347$	0.471708	+	0.215422i	0.00135939	+	0.000620812i	−0.414735	+	0.909942i	$0.636126\pi$
$348$	−14.6853	+	50.0136i	−0.0421992	+	0.143717i
$349$	−306.635	−	353.875i	−0.878610	−	1.01397i	−0.999772	−	0.0213370i	$-0.993208\pi$
$349$	−306.635	−	353.875i	−0.878610	−	1.01397i	0.121163	−	0.992633i	$-0.461338\pi$
$350$	68.9339	+	229.624i	0.196954	+	0.656070i
$351$	125.798	−	145.178i	0.358398	−	0.413613i
$352$	53.8538	−	374.562i	0.152994	−	1.06410i
$353$	−3.68906	−	12.5638i	−0.0104506	−	0.0355915i	0.954103	−	0.299480i	$-0.0968131\pi$
$353$	−3.68906	−	12.5638i	−0.0104506	−	0.0355915i	−0.964553	+	0.263888i	$0.914995\pi$
$354$	25.7797	+	16.5676i	0.0728241	+	0.0468012i
$355$	−433.351	+	1.30949i	−1.22071	+	0.00368870i
$356$	−21.2554	+	9.70701i	−0.0597061	+	0.0272669i
$357$	42.2894	−	19.3129i	0.118458	−	0.0540978i
$358$	−21.3114	+	3.06411i	−0.0595290	+	0.00855898i
$359$	−37.7463	+	58.7343i	−0.105143	+	0.163605i	−0.889838	−	0.456276i	$-0.849183\pi$
$359$	−37.7463	+	58.7343i	−0.105143	+	0.163605i	0.784695	+	0.619881i	$0.212819\pi$
$360$	−356.066	+	52.2932i	−0.989071	+	0.145259i
$361$	−42.4971	+	295.574i	−0.117720	+	0.818763i
$362$	83.5707	−	96.4457i	0.230858	−	0.266425i
$363$	−7.36076	−	11.4536i	−0.0202776	−	0.0315525i
$364$	−291.193	+	252.320i	−0.799981	+	0.693187i
$365$	−510.774	−	231.400i	−1.39938	−	0.633972i
$366$	−0.128101	−	0.0585018i	−0.000350003	−	0.000159841i
$367$	−278.793			−0.759655			−0.379827	−	0.925057i	$-0.624017\pi$
$367$	−278.793			−0.759655			−0.379827	+	0.925057i	$0.624017\pi$
$368$	−15.5526	−	29.2606i	−0.0422624	−	0.0795125i
$369$	−351.447			−0.952431
$370$	69.3572	−	108.642i	0.187452	−	0.293628i
$371$	416.168	+	122.198i	1.12175	+	0.329374i
$372$	4.52111	−	3.91756i	0.0121535	−	0.0105311i
$373$	414.856	−	266.612i	1.11221	−	0.714776i	0.150439	−	0.988619i	$-0.451931\pi$
$373$	414.856	−	266.612i	1.11221	−	0.714776i	0.961774	+	0.273843i	$0.0882949\pi$
$374$	137.592	−	158.789i	0.367892	−	0.424570i
$375$	31.8037	−	50.4881i	0.0848099	−	0.134635i
$376$	−121.067	+	35.5485i	−0.321987	+	0.0945438i
$377$	579.164	−	901.196i	1.53624	−	2.39044i
$378$	−11.5785	−	80.5301i	−0.0306309	−	0.213043i
$379$	−338.698	+	154.678i	−0.893662	+	0.408122i	−0.808672	−	0.588260i	$-0.799813\pi$
$379$	−338.698	+	154.678i	−0.893662	+	0.408122i	−0.0849901	+	0.996382i	$0.527086\pi$
$380$	−25.9444	−	87.3807i	−0.0682746	−	0.229949i
$381$	13.0724	+	90.9207i	0.0343108	+	0.238637i
$382$	−135.597	−	87.1426i	−0.354965	−	0.228122i
$383$	539.493	−	158.409i	1.40860	−	0.413602i	0.512970	−	0.858406i	$-0.328545\pi$
$383$	539.493	−	158.409i	1.40860	−	0.413602i	0.895627	+	0.444805i	$0.146727\pi$
$384$	4.34314	−	30.2072i	0.0113103	−	0.0786646i
$385$	339.766	−	296.211i	0.882509	−	0.769379i
$386$	−97.1900	+	62.4602i	−0.251788	+	0.161814i
$387$	345.234	+	398.422i	0.892078	+	1.02951i
$388$	−255.420	−	74.9979i	−0.658298	−	0.193294i
$389$	132.410	+	60.4695i	0.340385	+	0.155449i	0.578272	−	0.815844i	$-0.303727\pi$
$389$	132.410	+	60.4695i	0.340385	+	0.155449i	−0.237887	+	0.971293i	$0.576455\pi$
$390$	−69.6133	−	9.79427i	−0.178496	−	0.0251135i
$391$	−25.0840	+	302.789i	−0.0641535	+	0.774397i
$392$			43.9416i			0.112096i
$393$	101.931	+	46.5503i	0.259366	+	0.118449i
$394$	66.0174	+	19.3845i	0.167557	+	0.0491991i
$395$	222.267	+	343.568i	0.562702	+	0.869792i
$396$	133.847	+	208.270i	0.337998	+	0.525935i
$397$	−516.672	−	447.698i	−1.30144	−	1.12770i	−0.983757	−	0.179507i	$-0.942550\pi$
$397$	−516.672	−	447.698i	−1.30144	−	1.12770i	−0.317683	−	0.948197i	$-0.602905\pi$
$398$	39.9460	−	277.830i	0.100367	−	0.698066i
$399$	26.6721	−	7.83162i	0.0668473	−	0.0196281i
$400$	23.7512	+	27.0780i	0.0593780	+	0.0676949i
$401$	−63.0545	+	9.06587i	−0.157243	+	0.0226082i	−0.220487	−	0.975390i	$-0.570765\pi$
$401$	−63.0545	+	9.06587i	−0.157243	+	0.0226082i	0.0632436	+	0.997998i	$0.479855\pi$
$402$	3.07342	+	6.72986i	0.00764533	+	0.0167409i
$403$	−111.835	+	51.0735i	−0.277507	+	0.126733i
$404$	21.8105	+	151.695i	0.0539863	+	0.375483i
$405$	244.387	−	283.766i	0.603424	−	0.700656i
$406$	−127.823	−	435.324i	−0.314834	−	1.07223i
$407$	−239.870	−	34.4881i	−0.589361	−	0.0847373i
$408$	33.8830	−	39.1031i	0.0830467	−	0.0958410i
$409$	148.499	−	95.4344i	0.363078	−	0.233336i	−0.346364	−	0.938100i	$-0.612584\pi$
$409$	148.499	−	95.4344i	0.363078	−	0.233336i	0.709441	+	0.704764i	$0.248947\pi$
$410$	141.535	+	218.776i	0.345207	+	0.533600i
$411$	−7.40659	+	25.2245i	−0.0180209	+	0.0613735i
$412$	−150.648	+	329.873i	−0.365650	+	0.800662i
$413$	363.858			0.881011
$414$	244.844	+	94.4743i	0.591410	+	0.228199i
$415$	−63.9363	+	454.430i	−0.154063	+	1.09501i
$416$	−291.095	+	637.409i	−0.699747	+	1.53223i
$417$	7.60162	−	25.8887i	0.0182293	−	0.0620833i
$418$	94.9447	−	82.2700i	0.227140	−	0.196818i
$419$	−128.724	−	200.299i	−0.307218	−	0.478041i	0.652974	−	0.757380i	$-0.273521\pi$
$419$	−128.724	−	200.299i	−0.307218	−	0.478041i	−0.960192	+	0.279339i	$0.909885\pi$
$420$	30.6140	−	26.6895i	0.0728904	−	0.0635465i
$421$	−444.994	−	63.9805i	−1.05699	−	0.151973i	−0.408165	−	0.912908i	$-0.633831\pi$
$421$	−444.994	−	63.9805i	−1.05699	−	0.151973i	−0.648828	+	0.760935i	$0.724740\pi$
$422$	84.2015	+	286.764i	0.199530	+	0.679536i
$423$	72.9304	−	113.482i	0.172412	−	0.268279i
$424$	477.806	−	68.6981i	1.12690	−	0.162024i
$425$	−48.9736	−	326.595i	−0.115232	−	0.768458i
$426$	−22.3560	−	48.9529i	−0.0524790	−	0.114913i
$427$	−1.65510	+	0.237967i	−0.00387611	+	0.000557300i
$428$	163.663	+	105.180i	0.382390	+	0.245747i
$429$	37.2368	+	126.817i	0.0867991	+	0.295611i
$430$	108.985	−	375.361i	0.253454	−	0.872933i
$431$	−415.910	−	360.388i	−0.964989	−	0.836168i	0.0215376	−	0.999768i	$-0.493144\pi$
$431$	−415.910	−	360.388i	−0.964989	−	0.836168i	−0.986527	+	0.163600i	$0.947689\pi$
$432$	−6.60817	−	10.2825i	−0.0152967	−	0.0238021i
$433$	−72.0498	−	83.1499i	−0.166397	−	0.192032i	0.666427	−	0.745570i	$-0.267823\pi$
$433$	−72.0498	−	83.1499i	−0.166397	−	0.192032i	−0.832824	+	0.553538i	$0.813277\pi$
$434$	−14.6699	+	49.9612i	−0.0338017	+	0.115118i
$435$	−60.7620	+	95.1786i	−0.139683	+	0.218801i
$436$		−	292.163i		−	0.670099i
$437$	−40.6114	+	177.069i	−0.0929322	+	0.405192i
$438$		−	69.6365i		−	0.158988i
$439$	−68.0922	+	149.101i	−0.155108	+	0.339638i	−0.971193	−	0.238293i	$-0.923412\pi$
$439$	−68.0922	+	149.101i	−0.155108	+	0.339638i	0.816086	+	0.577931i	$0.196140\pi$
$440$	207.018	−	456.955i	0.470495	−	1.03853i
$441$	−30.7639	−	35.5034i	−0.0697593	−	0.0805066i
$442$	−327.308	+	210.348i	−0.740515	+	0.475900i
$443$	293.459	+	254.284i	0.662437	+	0.574005i	0.919837	−	0.392300i	$-0.128321\pi$
$443$	293.459	+	254.284i	0.662437	+	0.574005i	−0.257401	+	0.966305i	$0.582866\pi$
$444$	−21.6130	−	3.10748i	−0.0486780	−	0.00699884i
$445$	−50.0835	+	7.35546i	−0.112547	+	0.0165291i
$446$	−26.4505	−	16.9987i	−0.0593060	−	0.0381137i
$447$	17.1146	+	119.035i	0.0382878	+	0.266298i
$448$	140.936	+	308.607i	0.314589	+	0.688854i
$449$	−107.643	−	235.705i	−0.239739	−	0.524956i	0.751070	−	0.660223i	$-0.229538\pi$
$449$	−107.643	−	235.705i	−0.239739	−	0.524956i	−0.990809	+	0.135267i	$0.956811\pi$
$450$	−282.596	−	38.8894i	−0.627990	−	0.0864209i
$451$	264.859	−	412.129i	0.587271	−	0.913811i
$452$	346.191	−	101.651i	0.765910	−	0.224891i
$453$	39.5549	+	5.68713i	0.0873176	+	0.0125544i
$454$	424.660	+	367.970i	0.935375	+	0.810507i
$455$	−758.215	+	349.038i	−1.66641	+	0.767117i
$456$	23.3809	−	20.2596i	0.0512739	−	0.0444290i
$457$	−293.276	−	86.1137i	−0.641743	−	0.188433i	−0.0553594	−	0.998466i	$-0.517630\pi$
$457$	−293.276	−	86.1137i	−0.641743	−	0.188433i	−0.586383	+	0.810034i	$0.699449\pi$
$458$	73.4831	−	160.906i	0.160444	−	0.351322i
$459$			112.069i			0.244158i
$460$	54.2830	+	259.815i	0.118007	+	0.564816i
$461$	287.669			0.624010			0.312005	−	0.950080i	$-0.398999\pi$
$461$	287.669			0.624010			0.312005	+	0.950080i	$0.398999\pi$
$462$	50.9189	+	23.2539i	0.110214	+	0.0503331i
$463$	8.53259	−	29.0593i	0.0184289	−	0.0627632i	−0.949765	−	0.312963i	$-0.898678\pi$
$463$	8.53259	−	29.0593i	0.0184289	−	0.0627632i	0.968194	+	0.250200i	$0.0804965\pi$
$464$	−44.6365	−	51.5133i	−0.0961993	−	0.111020i
$465$	11.7722	−	5.41922i	0.0253165	−	0.0116542i
$466$	159.216	−	183.745i	0.341664	−	0.394302i
$467$	−58.4783	+	406.725i	−0.125221	+	0.870932i	0.826274	+	0.563269i	$0.190456\pi$
$467$	−58.4783	+	406.725i	−0.125221	+	0.870932i	−0.951495	+	0.307664i	$0.900453\pi$
$468$	−129.159	−	439.874i	−0.275980	−	0.939902i
$469$	73.9005	+	47.4930i	0.157570	+	0.101264i
$470$	−100.013	+	0.302217i	−0.212794	+	0.000643015i
$471$	73.4848	−	33.5594i	0.156019	−	0.0712514i
$472$	368.354	−	168.222i	0.780410	−	0.356402i
$473$	−727.392	+	104.583i	−1.53783	+	0.221106i
$474$	−27.4734	+	42.7494i	−0.0579607	+	0.0901885i
$475$	−1.19337	−	197.460i	−0.00251236	−	0.415705i
$476$	31.9899	−	222.495i	0.0672057	−	0.467426i
$477$	−337.955	+	390.021i	−0.708502	+	0.817654i
$478$	24.2115	+	37.6738i	0.0506517	+	0.0788156i
$479$	480.611	−	416.452i	1.00336	−	0.869419i	0.0119160	−	0.999929i	$-0.496207\pi$
$479$	480.611	−	416.452i	1.00336	−	0.869419i	0.991447	+	0.130510i	$0.0416615\pi$
$480$	30.4810	−	67.2813i	0.0635020	−	0.140169i
$481$	408.198	+	186.418i	0.848644	+	0.387563i
$482$	79.1891			0.164293
$483$	−79.2848	+	16.3151i	−0.164151	+	0.0337786i
$484$	−65.8282			−0.136009
$485$	−486.077	−	310.311i	−1.00222	−	0.639817i
$486$	139.917	+	41.0833i	0.287895	+	0.0845336i
$487$	−521.583	+	451.954i	−1.07101	+	0.928038i	−0.997598	−	0.0692635i	$-0.977935\pi$
$487$	−521.583	+	451.954i	−1.07101	+	0.928038i	−0.0734145	+	0.997302i	$0.523390\pi$
$488$	−1.56553	+	1.00611i	−0.00320806	+	0.00206169i
$489$	−38.1726	+	44.0535i	−0.0780625	+	0.0900890i
$490$	−9.71167	+	33.4485i	−0.0198197	+	0.0682622i
$491$	110.760	−	32.5222i	0.225581	−	0.0662366i	−0.166989	−	0.985959i	$-0.553404\pi$
$491$	110.760	−	32.5222i	0.225581	−	0.0662366i	0.392570	+	0.919722i	$0.371586\pi$
$492$	23.8646	−	37.1341i	0.0485054	−	0.0754758i
$493$	88.9411	+	618.599i	0.180408	+	1.25477i
$494$	−211.614	+	96.6409i	−0.428368	+	0.195629i
$495$	152.654	+	514.139i	0.308392	+	1.03866i
$496$	1.11330	+	7.74317i	0.00224456	+	0.0156112i
$497$	−537.551	−	345.463i	−1.08159	−	0.695097i
$498$	−54.6810	+	16.0558i	−0.109801	+	0.0322406i
$499$	−43.3802	+	301.716i	−0.0869343	+	0.604641i	0.899055	+	0.437835i	$0.144255\pi$
$499$	−43.3802	+	301.716i	−0.0869343	+	0.604641i	−0.985990	+	0.166806i	$0.946654\pi$
$500$	−122.224	−	261.337i	−0.244447	−	0.522674i
$501$	−20.2999	+	13.0460i	−0.0405188	+	0.0260398i
$502$	−117.138	−	135.184i	−0.233343	−	0.269292i
$503$	260.375	+	76.4530i	0.517644	+	0.151994i	0.530111	−	0.847928i	$-0.322150\pi$
$503$	260.375	+	76.4530i	0.517644	+	0.151994i	−0.0124670	+	0.999922i	$0.503968\pi$
$504$	−482.704	−	220.444i	−0.957746	−	0.437388i
$505$	−46.2555	+	328.764i	−0.0915951	+	0.651017i
$506$	−295.307	+	215.921i	−0.583610	+	0.426721i
$507$		−	164.075i		−	0.323620i
$508$	403.989	+	184.496i	0.795254	+	0.363180i
$509$	−78.3855	−	23.0161i	−0.153999	−	0.0452182i	0.203824	−	0.979007i	$-0.434663\pi$
$509$	−78.3855	−	23.0161i	−0.153999	−	0.0452182i	−0.357823	+	0.933789i	$0.616481\pi$
$510$	34.4341	−	22.2768i	0.0675179	−	0.0436800i
$511$	−447.019	−	695.575i	−0.874793	−	1.36120i
$512$	69.4327	+	60.1637i	0.135611	+	0.117507i
$513$	−9.53637	+	66.3269i	−0.0185894	+	0.129292i
$514$	−85.2136	+	25.0210i	−0.165785	+	0.0486789i
$515$	−512.668	+	595.275i	−0.995471	+	1.15587i
$516$	−65.5402	+	9.42326i	−0.127016	+	0.0182621i
$517$	78.1139	+	171.046i	0.151091	+	0.330842i
$518$	172.882	−	78.9524i	0.333748	−	0.152418i
$519$	−4.12575	−	28.6952i	−0.00794941	−	0.0552894i
$520$	−606.215	+	703.895i	−1.16580	+	1.35365i
$521$	105.082	+	357.878i	0.201694	+	0.686906i	0.996764	+	0.0803882i	$0.0256160\pi$
$521$	105.082	+	357.878i	0.201694	+	0.686906i	−0.795070	+	0.606518i	$0.792566\pi$
$522$	534.332	+	76.8253i	1.02362	+	0.147175i
$523$	364.533	−	420.693i	0.697003	−	0.804385i	−0.291341	−	0.956619i	$-0.594101\pi$
$523$	364.533	−	420.693i	0.697003	−	0.804385i	0.988344	+	0.152234i	$0.0486469\pi$
$524$	455.790	−	292.918i	0.869828	−	0.559005i
$525$	79.8115	−	37.0332i	0.152022	−	0.0705395i
$526$	43.3677	−	147.697i	0.0824480	−	0.280792i
$527$	29.7958	−	65.2438i	0.0565386	−	0.123802i
$528$	8.40977			0.0159276
$529$	160.423	−	504.089i	0.303257	−	0.952909i
$530$	378.890	+	53.3081i	0.714887	+	0.100581i
$531$	−179.845	+	393.805i	−0.338690	+	0.741628i
$532$	37.8660	−	128.960i	0.0711767	−	0.242406i
$533$	−685.599	+	594.075i	−1.28630	+	1.11459i
$534$	−3.39867	−	5.28843i	−0.00636455	−	0.00990343i
$535$	276.954	+	317.678i	0.517672	+	0.593790i
$536$	96.7710	+	13.9136i	0.180543	+	0.0259582i
$537$	2.22610	+	7.58139i	0.00414543	+	0.0141180i
$538$	−310.672	+	483.416i	−0.577458	+	0.898542i
$539$	64.8179	−	9.31941i	0.120256	−	0.0172902i
$540$	27.8665	+	93.8544i	0.0516046	+	0.173805i
$541$	315.410	+	690.653i	0.583014	+	1.27662i	0.939573	+	0.342349i	$0.111223\pi$
$541$	315.410	+	690.653i	0.583014	+	1.27662i	−0.356559	+	0.934273i	$0.616050\pi$
$542$	−426.949	+	61.3861i	−0.787730	+	0.113258i
$543$	−39.3989	−	25.3201i	−0.0725579	−	0.0466301i
$544$	−115.173	−	392.242i	−0.211715	−	0.721034i
$545$	176.479	−	607.821i	0.323815	−	1.11527i
$546$	−78.3389	−	67.8810i	−0.143478	−	0.124324i
$547$	332.724	+	517.728i	0.608270	+	0.946487i	0.999655	+	0.0262599i	$0.00835973\pi$
$547$	332.724	+	517.728i	0.608270	+	0.946487i	−0.391385	+	0.920227i	$0.628004\pi$
$548$	83.2392	+	96.0631i	0.151896	+	0.175298i
$549$	0.560516	−	1.90894i	0.00102098	−	0.00347712i
$550$	258.575	−	302.081i	0.470137	−	0.549239i
$551$			373.682i			0.678188i
$552$	−72.7217	+	53.1723i	−0.131742	+	0.0963265i
$553$			603.369i			1.09108i
$554$	−25.6103	+	56.0787i	−0.0462280	+	0.101225i
$555$	−43.0871	−	19.5201i	−0.0776344	−	0.0351713i
$556$	−85.4310	−	98.5927i	−0.153653	−	0.177325i
$557$	175.884	−	113.034i	0.315770	−	0.202933i	−0.373149	−	0.927771i	$-0.621722\pi$
$557$	175.884	−	113.034i	0.315770	−	0.202933i	0.688919	+	0.724838i	$0.258086\pi$
$558$	−46.8223	−	40.5718i	−0.0839110	−	0.0727093i
$559$	1346.96	+	193.663i	2.40959	+	0.346446i
$560$	7.71718	+	52.5465i	0.0137807	+	0.0938329i
$561$	−64.8668	−	41.6874i	−0.115627	−	0.0743090i
$562$	8.50892	+	59.1808i	0.0151404	+	0.105304i
$563$	−252.706	−	553.349i	−0.448856	−	0.982858i	−0.989887	−	0.141856i	$-0.954693\pi$
$563$	−252.706	−	553.349i	−0.448856	−	0.982858i	0.541031	−	0.841003i	$-0.318034\pi$
$564$	7.03830	+	15.4117i	0.0124793	+	0.0273258i
$565$	781.624	−	2.36189i	1.38341	−	0.00418034i
$566$	−8.46618	+	13.1736i	−0.0149579	+	0.0232750i
$567$	529.835	−	155.574i	0.934454	−	0.274380i
$568$	−703.911	−	101.207i	−1.23928	−	0.178182i
$569$	319.771	+	277.083i	0.561988	+	0.486965i	0.888907	−	0.458087i	$-0.151465\pi$
$569$	319.771	+	277.083i	0.561988	+	0.486965i	−0.326919	+	0.945052i	$0.606011\pi$
$570$	22.2752	−	10.2542i	0.0390793	−	0.0179898i
$571$	−187.690	+	162.635i	−0.328705	+	0.284824i	−0.803540	−	0.595250i	$-0.797053\pi$
$571$	−187.690	+	162.635i	−0.328705	+	0.284824i	0.474836	+	0.880074i	$0.342507\pi$
$572$	613.162	+	180.041i	1.07196	+	0.314756i
$573$	−24.5729	+	53.8071i	−0.0428846	+	0.0939043i
$574$			384.211i			0.669358i
$575$	−44.0082	+	573.313i	−0.0765360	+	0.997067i
$576$	−403.667			−0.700811
$577$	−591.759	−	270.247i	−1.02558	−	0.468366i	−0.169674	−	0.985500i	$-0.554272\pi$
$577$	−591.759	−	270.247i	−1.02558	−	0.468366i	−0.855904	+	0.517134i	$0.826999\pi$
$578$	−41.9602	+	142.903i	−0.0725955	+	0.247237i
$579$	27.7649	+	32.0424i	0.0479532	+	0.0553409i
$580$	228.304	+	495.945i	0.393628	+	0.855077i
$581$	−443.123	+	511.391i	−0.762690	+	0.880191i
$582$	10.1920	−	70.8869i	0.0175120	−	0.121799i
$583$	−202.672	−	690.237i	−0.347636	−	1.18394i
$584$	−774.127	−	497.501i	−1.32556	−	0.851886i
$585$	−3.00104	−	993.140i	−0.00512999	−	1.69767i
$586$	−1.54897	+	0.707391i	−0.00264329	+	0.00120715i
$587$	−327.922	+	149.757i	−0.558640	+	0.255122i	−0.674665	−	0.738124i	$-0.735712\pi$
$587$	−327.922	+	149.757i	−0.558640	+	0.255122i	0.116025	+	0.993246i	$0.462985\pi$
$588$	5.84030	−	0.839708i	0.00993248	−	0.00142808i
$589$	23.1863	−	36.0786i	0.0393656	−	0.0612540i
$590$	317.571	−	46.6397i	0.538256	−	0.0790503i
$591$	3.59351	−	24.9934i	0.00608039	−	0.0422901i
$592$	18.6983	−	21.5790i	0.0315850	−	0.0364510i
$593$	−554.899	−	863.440i	−0.935749	−	1.45605i	−0.889401	−	0.457128i	$-0.848878\pi$
$593$	−554.899	−	863.440i	−0.935749	−	1.45605i	−0.0463481	−	0.998925i	$-0.514758\pi$
$594$	−101.979	+	88.3651i	−0.171681	+	0.148763i
$595$	200.949	−	443.559i	0.337729	−	0.745477i
$596$	528.909	+	241.545i	0.887432	+	0.405276i
$597$	−103.009			−0.172544
$598$	637.335	−	229.577i	1.06578	−	0.383907i
$599$	−130.826			−0.218407			−0.109204	−	0.994019i	$-0.534830\pi$
$599$	−130.826			−0.218407			−0.109204	+	0.994019i	$0.534830\pi$
$600$	63.6762	−	74.3899i	0.106127	−	0.123983i
$601$	−791.567	−	232.425i	−1.31708	−	0.386731i	−0.453644	−	0.891183i	$-0.649876\pi$
$601$	−791.567	−	232.425i	−1.31708	−	0.386731i	−0.863439	+	0.504452i	$0.831694\pi$
$602$	435.565	−	377.420i	0.723531	−	0.626943i
$603$	−87.9288	+	56.5084i	−0.145819	+	0.0937121i
$604$	126.529	−	146.022i	0.209485	−	0.241759i
$605$	−136.950	−	39.7631i	−0.226364	−	0.0657241i
$606$	−39.5597	+	11.6158i	−0.0652800	+	0.0191679i
$607$	608.755	−	947.241i	1.00289	−	1.56053i	0.186970	−	0.982366i	$-0.440133\pi$
$607$	608.755	−	947.241i	1.00289	−	1.56053i	0.815921	−	0.578163i	$-0.196230\pi$
$608$	−34.7866	−	241.946i	−0.0572148	−	0.397938i
$609$	−151.457	+	69.1680i	−0.248697	+	0.113576i
$610$	−1.41405	+	0.419848i	−0.00231811	+	0.000688275i
$611$	−49.5544	−	344.658i	−0.0811038	−	0.564089i
$612$	224.995	+	144.596i	0.367640	+	0.236268i
$613$	−714.457	+	209.783i	−1.16551	+	0.342224i	−0.806571	−	0.591137i	$-0.798679\pi$
$613$	−714.457	+	209.783i	−1.16551	+	0.342224i	−0.358938	+	0.933362i	$0.616861\pi$
$614$	33.6119	−	233.776i	0.0547425	−	0.380743i
$615$	72.0790	−	62.8392i	0.117202	−	0.102178i
$616$	622.284	−	399.918i	1.01020	−	0.649217i
$617$	−482.903	−	557.300i	−0.782663	−	0.903241i	0.214636	−	0.976694i	$-0.431144\pi$
$617$	−482.903	−	557.300i	−0.782663	−	0.903241i	−0.997299	+	0.0734532i	$0.976598\pi$
$618$	−93.6093	−	27.4862i	−0.151471	−	0.0444760i
$619$	−957.849	−	437.435i	−1.54741	−	0.706680i	−0.555256	−	0.831679i	$-0.687380\pi$
$619$	−957.849	−	437.435i	−1.54741	−	0.706680i	−0.992157	+	0.124999i	$0.960107\pi$
$620$	8.72999	−	62.0489i	0.0140806	−	0.100079i
$621$	43.6201	−	190.187i	0.0702417	−	0.306260i
$622$		−	454.977i		−	0.731474i
$623$	−67.8962	−	31.0072i	−0.108983	−	0.0497707i
$624$	−14.9421	−	4.38740i	−0.0239457	−	0.00703109i
$625$	−96.4176	−	617.518i	−0.154268	−	0.988029i
$626$	334.307	+	520.191i	0.534036	+	0.830976i
$627$	−34.8436	−	30.1921i	−0.0555719	−	0.0481533i
$628$	55.5878	−	386.622i	0.0885156	−	0.615640i
$629$	−251.193	+	73.7568i	−0.399352	+	0.117260i
$630$	−318.715	−	274.486i	−0.505896	−	0.435692i
$631$	380.460	−	54.7019i	0.602948	−	0.0866908i	0.165921	−	0.986139i	$-0.446940\pi$
$631$	380.460	−	54.7019i	0.602948	−	0.0866908i	0.437027	+	0.899448i	$0.356031\pi$
$632$	278.954	+	610.825i	0.441383	+	0.966495i
$633$	99.7703	−	45.5636i	0.157615	−	0.0719803i
$634$	30.2024	+	210.062i	0.0476379	+	0.331329i
$635$	729.022	+	627.855i	1.14807	+	0.988747i
$636$	−18.2614	−	62.1925i	−0.0287129	−	0.0977870i
$637$	−120.028	−	17.2574i	−0.188426	−	0.0270916i
$638$	−492.776	+	568.694i	−0.772376	+	0.891370i
$639$	639.593	−	411.041i	1.00093	−	0.643257i
$640$	−173.629	−	268.385i	−0.271295	−	0.419351i
$641$	191.994	−	653.872i	0.299523	−	1.02008i	−0.662941	−	0.748672i	$-0.730692\pi$
$641$	191.994	−	653.872i	0.299523	−	1.02008i	0.962464	−	0.271410i	$-0.0874898\pi$
$642$	−21.7422	+	47.6087i	−0.0338663	+	0.0741568i
$643$	320.879			0.499034			0.249517	−	0.968370i	$-0.419728\pi$
$643$	320.879			0.499034			0.249517	+	0.968370i	$0.419728\pi$
$644$	−140.890	+	365.136i	−0.218773	+	0.566982i
$645$	−142.043	−	19.9848i	−0.220222	−	0.0309842i
$646$	56.3795	−	123.454i	0.0872747	−	0.191105i
$647$	−163.223	+	555.888i	−0.252277	+	0.859178i	0.731812	+	0.681506i	$0.238675\pi$
$647$	−163.223	+	555.888i	−0.252277	+	0.859178i	−0.984090	+	0.177672i	$0.943143\pi$
$648$	464.457	−	402.454i	0.716754	−	0.621071i
$649$	−326.265	−	507.678i	−0.502719	−	0.782247i
$650$	−617.022	+	401.826i	−0.949265	+	0.618193i
$651$	18.9147	+	2.71953i	0.0290549	+	0.00417747i
$652$	79.4031	+	270.422i	0.121784	+	0.414758i
$653$	−464.910	+	723.414i	−0.711960	+	1.10783i	0.277175	+	0.960819i	$0.410602\pi$
$653$	−464.910	+	723.414i	−0.711960	+	1.10783i	−0.989135	+	0.147012i	$0.953034\pi$
$654$	77.7998	−	11.1859i	0.118960	−	0.0171039i
$655$	1125.17	−	334.076i	1.71782	−	0.510040i
$656$	23.9786	+	52.5057i	0.0365527	+	0.0800392i
$657$	973.773	−	140.007i	1.48215	−	0.213101i
$658$	−124.061	−	79.7295i	−0.188543	−	0.121169i
$659$	304.326	+	1036.44i	0.461800	+	1.57275i	0.780667	+	0.624947i	$0.214880\pi$
$659$	304.326	+	1036.44i	0.461800	+	1.57275i	−0.318867	+	0.947800i	$0.603302\pi$
$660$	−64.6901	−	18.7826i	−0.0980152	−	0.0284584i
$661$	−28.6539	−	24.8288i	−0.0433494	−	0.0375625i	0.632917	−	0.774220i	$-0.281858\pi$
$661$	−28.6539	−	24.8288i	−0.0433494	−	0.0375625i	−0.676266	+	0.736657i	$0.736403\pi$
$662$	329.003	+	511.938i	0.496983	+	0.773320i
$663$	93.5041	+	107.909i	0.141032	+	0.162759i
$664$	−212.168	+	722.578i	−0.319530	+	1.08822i
$665$	156.674	−	245.418i	0.235601	−	0.369049i
$666$			226.134i			0.339541i
$667$	89.8369	−	1084.42i	0.134688	−	1.62582i
$668$			116.671i			0.174658i
$669$	−4.79338	+	10.4960i	−0.00716499	+	0.0156891i
$670$	70.5872	+	31.9787i	0.105354	+	0.0477294i
$671$	1.81613	+	2.09592i	0.00270660	+	0.00312358i
$672$	91.6241	−	58.8832i	0.136345	−	0.0876239i
$673$	−303.558	−	263.034i	−0.451052	−	0.390838i	0.399497	−	0.916734i	$-0.369185\pi$
$673$	−303.558	−	263.034i	−0.451052	−	0.390838i	−0.850549	+	0.525896i	$0.823730\pi$
$674$	69.7358	+	10.0265i	0.103466	+	0.0148761i
$675$	1.28178	+	212.089i	0.00189894	+	0.314206i
$676$	−667.372	−	428.894i	−0.987237	−	0.634459i
$677$	−55.3065	−	384.665i	−0.0816935	−	0.568191i	−0.989022	−	0.147769i	$-0.952791\pi$
$677$	−55.3065	−	384.665i	−0.0816935	−	0.568191i	0.907328	−	0.420423i	$-0.138118\pi$
$678$	40.3230	+	88.2951i	0.0594735	+	0.130229i
$679$	−353.241	−	773.490i	−0.520237	−	1.13916i
$680$	−1.63763	−	541.944i	−0.00240828	−	0.796977i
$681$	111.487	−	173.478i	0.163711	−	0.254739i
$682$	82.8635	−	24.3309i	0.121501	−	0.0356758i
$683$	−27.0965	−	3.89589i	−0.0396728	−	0.00570409i	0.122450	−	0.992475i	$-0.460925\pi$
$683$	−27.0965	−	3.89589i	−0.0396728	−	0.00570409i	−0.162123	+	0.986771i	$0.551834\pi$
$684$	120.858	+	104.724i	0.176692	+	0.153105i
$685$	115.146	+	250.132i	0.168096	+	0.365156i
$686$	316.318	−	274.091i	0.461106	−	0.399550i
$687$	−62.2873	−	18.2892i	−0.0906657	−	0.0266218i
$688$	35.9690	−	78.7611i	0.0522805	−	0.114478i
$689$			1332.12i			1.93341i
$690$	−67.1077	+	24.4024i	−0.0972575	+	0.0353658i
$691$	1051.13			1.52117			0.760583	−	0.649240i	$-0.224913\pi$
$691$	1051.13			1.52117			0.760583	+	0.649240i	$0.224913\pi$
$692$	−127.502	−	58.2280i	−0.184251	−	0.0841445i
$693$	−222.800	+	758.786i	−0.321500	+	1.09493i
$694$	0.441724	+	0.509776i	0.000636490	+	0.000734548i
$695$	−118.178	−	256.718i	−0.170040	−	0.369378i
$696$	−121.350	+	140.045i	−0.174353	+	0.201215i
$697$	75.3187	−	523.853i	0.108061	−	0.751582i
$698$	−171.595	−	584.398i	−0.245838	−	0.837246i
$699$	−75.0613	−	48.2389i	−0.107384	−	0.0690114i
$700$	57.9960	−	421.436i	0.0828514	−	0.602051i
$701$	630.971	−	288.155i	0.900101	−	0.411062i	0.0890428	−	0.996028i	$-0.471619\pi$
$701$	630.971	−	288.155i	0.900101	−	0.411062i	0.811058	+	0.584965i	$0.198892\pi$
$702$	227.292	−	103.801i	0.323777	−	0.147864i
$703$	−154.943	+	22.2774i	−0.220402	+	0.0316891i
$704$	304.213	−	473.365i	0.432121	−	0.672394i
$705$	5.33326	+	36.3143i	0.00756490	+	0.0515096i
$706$	2.42395	−	16.8589i	0.00343336	−	0.0238795i
$707$	−320.583	+	369.972i	−0.453441	+	0.523299i
$708$	−29.3975	−	45.7434i	−0.0415219	−	0.0646093i
$709$	96.9686	−	84.0237i	0.136768	−	0.118510i	−0.583790	−	0.811904i	$-0.698431\pi$
$709$	96.9686	−	84.0237i	0.136768	−	0.118510i	0.720558	+	0.693394i	$0.243886\pi$
$710$	−513.451	−	232.613i	−0.723170	−	0.327623i
$711$	−653.029	−	298.228i	−0.918465	−	0.419449i
$712$	−83.0707			−0.116672
$713$	−75.9601	+	99.1255i	−0.106536	+	0.139026i
$714$	60.4727			0.0846957
$715$	1166.88	+	744.936i	1.63200	+	1.04187i
$716$	36.6561	+	10.7632i	0.0511957	+	0.0150324i
$717$	12.4206	−	10.7625i	0.0173230	−	0.0150105i
$718$	−76.3988	+	49.0985i	−0.106405	+	0.0683823i
$719$	−295.830	+	341.406i	−0.411447	+	0.474835i	−0.923212	−	0.384290i	$-0.874446\pi$
$719$	−295.830	+	341.406i	−0.411447	+	0.474835i	0.511766	+	0.859125i	$0.328992\pi$
$720$	−60.6857	−	17.6199i	−0.0842856	−	0.0244721i
$721$	−1111.47	+	326.358i	−1.54157	+	0.452646i
$722$	−209.996	+	326.761i	−0.290854	+	0.452577i
$723$	−4.13588	−	28.7657i	−0.00572044	−	0.0397865i
$724$	−205.978	+	94.0670i	−0.284500	+	0.129927i
$725$	175.396	+	1169.68i	0.241925	+	1.61335i
$726$	−2.52034	−	17.5293i	−0.00347154	−	0.0241451i
$727$	54.3580	+	34.9338i	0.0747703	+	0.0480519i	0.577492	−	0.816396i	$-0.304032\pi$
$727$	54.3580	+	34.9338i	0.0747703	+	0.0480519i	−0.502722	+	0.864448i	$0.667668\pi$
$728$	−1314.28	+	385.909i	−1.80534	+	0.530095i
$729$	−88.3175	+	614.262i	−0.121149	+	0.842609i
$730$	−479.313	−	549.791i	−0.656593	−	0.753139i
$731$	−667.859	+	429.207i	−0.913623	+	0.587150i
$732$	0.163639	+	0.188849i	0.000223550	+	0.000257991i
$733$	266.100	+	78.1340i	0.363028	+	0.106595i	0.458160	−	0.888870i	$-0.348509\pi$
$733$	266.100	+	78.1340i	0.363028	+	0.106595i	−0.0951311	+	0.995465i	$0.530327\pi$
$734$	−329.870	−	150.646i	−0.449414	−	0.205240i
$735$	12.6575	+	1.78085i	0.0172211	+	0.00242292i
$736$	42.7841	+	710.488i	0.0581305	+	0.965337i
$737$		−	145.697i		−	0.197689i
$738$	−415.834	−	189.905i	−0.563460	−	0.257324i
$739$	−1376.94	−	404.306i	−1.86325	−	0.547098i	−0.999033	−	0.0439708i	$-0.985999\pi$
$739$	−1376.94	−	404.306i	−1.86325	−	0.547098i	−0.864212	−	0.503127i	$-0.832183\pi$
$740$	−192.027	+	124.230i	−0.259496	+	0.167878i
$741$	46.1573	+	71.8221i	0.0622905	+	0.0969259i
$742$	426.382	+	369.462i	0.574639	+	0.497927i
$743$	−114.648	+	797.395i	−0.154304	+	1.07321i	0.754594	+	0.656192i	$0.227834\pi$
$743$	−114.648	+	797.395i	−0.154304	+	1.07321i	−0.908898	+	0.417018i	$0.863075\pi$
$744$	20.4058	−	5.99168i	0.0274271	−	0.00805334i
$745$	954.449	+	821.998i	1.28114	+	1.10335i
$746$	634.923	−	91.2882i	0.851104	−	0.122370i
$747$	−334.457	−	732.360i	−0.447734	−	0.980401i
$748$	−339.124	+	154.873i	−0.453375	+	0.207049i
$749$	88.4404	+	615.117i	0.118078	+	0.821250i
$750$	64.9116	−	42.5525i	0.0865488	−	0.0567367i
$751$	−133.290	−	453.942i	−0.177483	−	0.604451i	−0.999393	−	0.0348338i	$-0.988910\pi$
$751$	−133.290	−	453.942i	−0.177483	−	0.604451i	0.821910	−	0.569617i	$-0.192908\pi$
$752$	−21.9300	−	3.15305i	−0.0291622	−	0.00419289i
$753$	−42.9883	+	49.6111i	−0.0570893	+	0.0658846i
$754$	1172.23	−	753.348i	1.55468	−	0.999135i
$755$	351.437	−	227.358i	0.465479	−	0.301137i
$756$	−40.6714	+	138.514i	−0.0537981	+	0.183219i
$757$	−358.868	+	785.810i	−0.474065	+	1.03806i	0.509987	+	0.860182i	$0.329650\pi$
$757$	−358.868	+	785.810i	−0.474065	+	1.03806i	−0.984053	+	0.177877i	$0.943077\pi$
$758$	−484.330			−0.638957
$759$	93.8572	+	95.9940i	0.123659	+	0.126474i
$760$	45.1471	−	320.885i	0.0594040	−	0.422217i
$761$	238.874	−	523.060i	0.313894	−	0.687333i	−0.685266	−	0.728292i	$-0.740314\pi$
$761$	238.874	−	523.060i	0.313894	−	0.687333i	0.999161	+	0.0409596i	$0.0130415\pi$
$762$	−33.6618	+	114.642i	−0.0441756	+	0.150448i
$763$	705.310	−	611.154i	0.924390	−	0.800989i
$764$	154.625	+	240.602i	0.202389	+	0.314924i
$765$	380.742	+	436.727i	0.497703	+	0.570885i
$766$	723.927	+	104.085i	0.945075	+	0.135881i
$767$	314.836	+	1072.23i	0.410477	+	1.39796i
$768$	68.9657	−	107.313i	0.0897991	−	0.139730i
$769$	−100.416	+	14.4376i	−0.130580	+	0.0187745i	−0.207295	−	0.978279i	$-0.566466\pi$
$769$	−100.416	+	14.4376i	−0.130580	+	0.0187745i	0.0767150	+	0.997053i	$0.475557\pi$
$770$	562.071	−	166.885i	0.729962	−	0.216734i
$771$	13.5395	+	29.6473i	0.0175609	+	0.0384531i
$772$	202.909	−	29.1739i	0.262836	−	0.0377901i
$773$	−262.048	−	168.408i	−0.339002	−	0.217863i	0.360052	−	0.932932i	$-0.382759\pi$
$773$	−262.048	−	168.408i	−0.339002	−	0.217863i	−0.699054	+	0.715069i	$0.746395\pi$
$774$	193.195	+	657.962i	0.249606	+	0.850081i
$775$	55.6422	−	123.814i	0.0717964	−	0.159760i
$776$	−715.212	−	619.735i	−0.921665	−	0.798627i
$777$	−37.7089	−	58.6762i	−0.0485314	−	0.0755164i
$778$	123.993	+	143.096i	0.159374	+	0.183928i
$779$	89.1536	−	303.629i	0.114446	−	0.389768i
$780$	105.140	+	67.1210i	0.134794	+	0.0860526i
$781$			1059.80i			1.35698i
$782$	−193.292	+	344.707i	−0.247177	+	0.440802i
$783$		−	401.367i		−	0.512601i
$784$	−3.20520	+	7.01841i	−0.00408827	+	0.00895206i
$785$	349.182	−	770.757i	0.444818	−	0.981857i
$786$	95.4517	+	110.157i	0.121440	+	0.140149i
$787$	−341.777	+	219.647i	−0.434278	+	0.279093i	−0.739460	−	0.673201i	$-0.764919\pi$
$787$	−341.777	+	219.647i	−0.434278	+	0.279093i	0.305182	+	0.952294i	$0.401283\pi$
$788$	−92.2666	−	79.9495i	−0.117090	−	0.101459i
$789$	−55.9163	−	8.03955i	−0.0708698	−	0.0101895i
$790$	77.3405	+	526.614i	0.0978994	+	0.666600i
$791$	969.567	+	623.103i	1.22575	+	0.787741i
$792$	125.255	+	871.169i	0.158150	+	1.09996i
$793$	−2.13337	−	4.67142i	−0.00269025	−	0.00589082i
$794$	−369.414	−	808.903i	−0.465257	−	1.01877i
$795$	−0.424309	−	140.417i	−0.000533722	−	0.176625i
$796$	−269.266	+	418.986i	−0.338274	+	0.526365i
$797$	638.975	−	187.620i	0.801725	−	0.235408i	0.144896	−	0.989447i	$-0.453715\pi$
$797$	638.975	−	187.620i	0.801725	−	0.235408i	0.656830	+	0.754039i	$0.271897\pi$
$798$	35.7904	+	5.14588i	0.0448501	+	0.00644847i
$799$	153.522	+	133.027i	0.192142	+	0.166492i
$800$	−222.450	−	740.999i	−0.278062	−	0.926249i
$801$	67.1184	−	58.1584i	0.0837933	−	0.0726073i
$802$	−79.5052	−	23.3448i	−0.0991337	−	0.0291083i
$803$	−569.678	+	1247.42i	−0.709438	+	1.55345i
$804$		−	13.1278i		−	0.0163281i
$805$	−513.668	+	674.533i	−0.638097	+	0.837929i
$806$	−159.922			−0.198414
$807$	191.828	+	87.6049i	0.237705	+	0.108556i
$808$	−153.496	+	522.758i	−0.189970	+	0.646978i
$809$	−818.902	−	945.064i	−1.01224	−	1.16819i	−0.985695	−	0.168540i	$-0.946095\pi$
$809$	−818.902	−	945.064i	−1.01224	−	1.16819i	−0.0265453	−	0.999648i	$-0.508451\pi$
$810$	442.493	−	203.698i	0.546288	−	0.251479i
$811$	−891.663	+	1029.03i	−1.09946	+	1.26885i	−0.139042	+	0.990286i	$0.544402\pi$
$811$	−891.663	+	1029.03i	−1.09946	+	1.26885i	−0.960419	+	0.278559i	$0.910143\pi$
$812$	−114.570	+	796.851i	−0.141096	+	0.981344i
$813$	44.5973	+	151.885i	0.0548553	+	0.186820i
$814$	−265.180	−	170.421i	−0.325773	−	0.209362i
$815$	1.84495	+	610.554i	0.00226375	+	0.749146i
$816$	8.26411	−	3.77409i	0.0101276	−	0.00462511i
$817$	−431.790	+	197.192i	−0.528507	+	0.241361i
$818$	227.273	−	32.6769i	0.277840	−	0.0399473i
$819$	791.721	−	1231.94i	0.966693	−	1.50420i
$820$	−67.1816	−	457.441i	−0.0819288	−	0.557855i
$821$	183.993	−	1279.70i	0.224108	−	1.55871i	−0.498155	−	0.867088i	$-0.665989\pi$
$821$	183.993	−	1279.70i	0.224108	−	1.55871i	0.722263	−	0.691619i	$-0.243102\pi$
$822$	−22.3936	+	25.8436i	−0.0272429	+	0.0314399i
$823$	−58.8076	−	91.5064i	−0.0714551	−	0.111186i	0.803687	−	0.595052i	$-0.202869\pi$
$823$	−58.8076	−	91.5064i	−0.0714551	−	0.111186i	−0.875142	+	0.483866i	$0.839232\pi$
$824$	−974.324	+	844.256i	−1.18243	+	1.02458i
$825$	−123.237	−	78.1512i	−0.149378	−	0.0947287i
$826$	430.518	+	196.611i	0.521208	+	0.238028i
$827$	91.9080			0.111134			0.0555671	−	0.998455i	$-0.482303\pi$
$827$	91.9080			0.111134			0.0555671	+	0.998455i	$0.482303\pi$
$828$	−325.551	−	332.963i	−0.393177	−	0.402129i
$829$	853.515			1.02957			0.514786	−	0.857319i	$-0.327872\pi$
$829$	853.515			1.02957			0.514786	+	0.857319i	$0.327872\pi$
$830$	−321.202	+	503.136i	−0.386990	+	0.606188i
$831$	21.7083	+	6.37414i	0.0261231	+	0.00767045i
$832$	−787.469	+	682.346i	−0.946477	+	0.820127i
$833$	59.5130	−	38.2467i	0.0714441	−	0.0459144i
$834$	22.9833	−	26.5241i	0.0275579	−	0.0318035i
$835$	−70.4746	+	242.725i	−0.0844007	+	0.290689i
$836$	−213.887	+	62.8029i	−0.255846	+	0.0751231i
$837$	−24.9041	+	38.7515i	−0.0297540	+	0.0462981i
$838$	−44.0754	−	306.551i	−0.0525960	−	0.365813i
$839$	−429.692	+	196.234i	−0.512148	+	0.233890i	−0.654688	−	0.755899i	$-0.727200\pi$
$839$	−429.692	+	196.234i	−0.512148	+	0.233890i	0.142540	+	0.989789i	$0.454473\pi$
$840$	138.414	−	41.0969i	0.164779	−	0.0489248i
$841$	−198.850	−	1383.04i	−0.236445	−	1.64451i
$842$	−491.947	−	316.155i	−0.584261	−	0.375481i
$843$	21.0532	−	6.18178i	0.0249742	−	0.00733307i
$844$	75.4716	−	524.916i	0.0894213	−	0.621939i
$845$	−1129.34	−	1295.40i	−1.33650	−	1.53302i
$846$	147.612	−	94.8643i	0.174482	−	0.112133i
$847$	−137.701	−	158.916i	−0.162575	−	0.187622i
$848$	81.3267	+	23.8797i	0.0959041	+	0.0281600i
$849$	5.22754	+	2.38734i	0.00615729	+	0.00281194i
$850$	118.530	−	412.891i	0.139447	−	0.485754i
$851$	454.998	−	27.3990i	0.534663	−	0.0321962i
$852$			95.4911i			0.112079i
$853$	748.155	+	341.671i	0.877086	+	0.400552i	0.802493	−	0.596662i	$-0.203507\pi$
$853$	748.155	+	341.671i	0.877086	+	0.400552i	0.0745938	+	0.997214i	$0.476234\pi$
$854$	−2.08691	−	0.612771i	−0.00244368	−	0.000717531i
$855$	188.177	+	290.872i	0.220090	+	0.340202i
$856$	373.919	+	581.829i	0.436821	+	0.679707i
$857$	−891.440	−	772.437i	−1.04019	−	0.901326i	−0.0449665	−	0.998988i	$-0.514318\pi$
$857$	−891.440	−	772.437i	−1.04019	−	0.901326i	−0.995220	+	0.0976621i	$0.968864\pi$
$858$	−24.4670	+	170.171i	−0.0285163	+	0.198335i
$859$	−686.923	+	201.699i	−0.799678	+	0.234807i	−0.655944	−	0.754810i	$-0.727729\pi$
$859$	−686.923	+	201.699i	−0.799678	+	0.234807i	−0.143734	+	0.989616i	$0.545911\pi$
$860$	−452.589	+	525.516i	−0.526267	+	0.611065i
$861$	139.566	−	20.0666i	0.162098	−	0.0233061i
$862$	−297.371	−	651.151i	−0.344978	−	0.755396i
$863$	1403.06	−	640.757i	1.62580	−	0.742476i	0.626479	−	0.779438i	$-0.284495\pi$
$863$	1403.06	−	640.757i	1.62580	−	0.742476i	0.999317	+	0.0369620i	$0.0117681\pi$
$864$	37.3638	+	259.871i	0.0432452	+	0.300777i
$865$	−230.084	−	198.155i	−0.265993	−	0.229081i
$866$	−40.3195	−	137.316i	−0.0465583	−	0.158563i
$867$	54.1015	+	7.77863i	0.0624008	+	0.00897189i
$868$	60.5049	−	69.8263i	0.0697061	−	0.0804451i
$869$	841.860	−	541.031i	0.968769	−	0.622590i
$870$	−123.324	+	79.7830i	−0.141751	+	0.0917045i
$871$	−76.0105	+	258.868i	−0.0872681	+	0.297208i
$872$	431.472	−	944.791i	0.494807	−	1.08348i
$873$	1011.75			1.15893
$874$	−143.731	+	187.565i	−0.164452	+	0.214605i
$875$	375.221	−	841.731i	0.428825	−	0.961978i
$876$	−51.3298	+	112.397i	−0.0585957	+	0.128307i
$877$	396.938	−	1351.85i	0.452609	−	1.54145i	−0.345196	−	0.938531i	$-0.612188\pi$
$877$	396.938	−	1351.85i	0.452609	−	1.54145i	0.797805	−	0.602915i	$-0.205994\pi$
$878$	−161.134	+	139.623i	−0.183524	+	0.159024i
$879$	0.337861	+	0.525723i	0.000384370	+	0.000598092i
$880$	66.3964	−	57.8850i	0.0754505	−	0.0657785i
$881$	632.302	+	90.9113i	0.717710	+	0.103191i	0.491487	−	0.870885i	$-0.336453\pi$
$881$	632.302	+	90.9113i	0.717710	+	0.103191i	0.226222	+	0.974076i	$0.427362\pi$
$882$	−17.2156	−	58.6311i	−0.0195189	−	0.0664752i
$883$	390.100	−	607.008i	0.441789	−	0.687438i	−0.546937	−	0.837174i	$-0.684206\pi$
$883$	390.100	−	607.008i	0.441789	−	0.687438i	0.988726	+	0.149736i	$0.0478425\pi$
$884$	683.339	−	98.2493i	0.773008	−	0.111142i
$885$	−33.5281	−	112.923i	−0.0378848	−	0.127596i
$886$	209.820	+	459.441i	0.236817	+	0.518557i
$887$	−965.187	+	138.773i	−1.08815	+	0.156452i	−0.662961	−	0.748654i	$-0.730701\pi$
$887$	−965.187	+	138.773i	−1.08815	+	0.156452i	−0.425187	+	0.905106i	$0.639792\pi$
$888$	−65.3026	−	41.9674i	−0.0735389	−	0.0472606i
$889$	399.685	+	1361.20i	0.449589	+	1.53116i
$890$	−63.2336	−	18.3597i	−0.0710490	−	0.0206289i
$891$	−692.161	−	599.761i	−0.776836	−	0.673133i
$892$	30.1624	+	46.9336i	0.0338143	+	0.0526161i
$893$	79.5409	+	91.7951i	0.0890716	+	0.102794i
$894$	−44.0706	+	150.091i	−0.0492960	+	0.167887i
$895$	69.7586	+	44.5339i	0.0779426	+	0.0497585i
$896$		−	471.333i		−	0.526042i
$897$	−116.681	−	219.524i	−0.130079	−	0.244731i
$898$		−	337.053i		−	0.375337i
$899$	−106.712	+	233.667i	−0.118701	+	0.259918i
$900$	427.456	+	271.073i	0.474952	+	0.301193i
$901$	−508.923	−	587.328i	−0.564842	−	0.651863i
$902$	536.077	−	344.516i	0.594321	−	0.381947i
$903$	−159.847	−	138.509i	−0.177018	−	0.153387i
$904$	1269.63	+	182.545i	1.40445	+	0.201930i
$905$	−485.341	+	71.2790i	−0.536288	+	0.0787614i
$906$	43.7285	+	28.1026i	0.0482654	+	0.0310183i
$907$	117.628	+	818.124i	0.129690	+	0.902011i	0.945947	+	0.324322i	$0.105136\pi$
$907$	117.628	+	818.124i	0.129690	+	0.902011i	−0.816257	+	0.577689i	$0.803955\pi$
$908$	−414.187	−	906.942i	−0.456153	−	0.998835i
$909$	−241.968	−	529.835i	−0.266191	−	0.582877i
$910$	−1085.73	+	3.28082i	−1.19311	+	0.00360530i
$911$	−121.025	+	188.319i	−0.132849	+	0.206716i	−0.901304	−	0.433187i	$-0.857389\pi$
$911$	−121.025	+	188.319i	−0.132849	+	0.206716i	0.768456	+	0.639903i	$0.221025\pi$
$912$	5.21221	−	1.53044i	0.00571514	−	0.00167812i
$913$	1110.87	+	159.719i	1.21672	+	0.174938i
$914$	−300.474	−	260.363i	−0.328747	−	0.284861i
$915$	0.226364	+	0.491730i	0.000247392	+	0.000537410i
$916$	−237.210	+	205.544i	−0.258963	+	0.224393i
$917$	1660.57	+	487.587i	1.81087	+	0.531719i
$918$	−60.5564	+	132.600i	−0.0659656	+	0.144445i
$919$			1696.94i			1.84650i	0.384194	+	0.923252i	$0.374479\pi$
$919$			1696.94i			1.84650i	−0.384194	+	0.923252i	$0.625521\pi$
$920$	−208.160	+	920.351i	−0.226261	+	1.00038i
$921$	−86.6753			−0.0941100
$922$	340.371	+	155.442i	0.369166	+	0.168592i
$923$	552.899	−	1883.00i	0.599024	−	2.04009i
$924$	−65.0448	−	75.0657i	−0.0703948	−	0.0812399i
$925$	−474.537	+	142.457i	−0.513013	+	0.154008i
$926$	25.7981	−	29.7726i	0.0278597	−	0.0321518i
$927$	196.151	−	1364.26i	0.211598	−	1.47170i
$928$	412.484	+	1404.79i	0.444487	+	1.51378i
$929$	−177.646	−	114.166i	−0.191222	−	0.122891i	0.441527	−	0.897248i	$-0.354437\pi$
$929$	−177.646	−	114.166i	−0.191222	−	0.122891i	−0.632749	+	0.774357i	$0.718073\pi$
$930$	16.8572	−	0.0509386i	0.0181260	−	5.47727e-5i
$931$	38.4769	−	17.5718i	0.0413285	−	0.0188741i
$932$	−392.421	+	179.213i	−0.421053	+	0.192288i
$933$	−165.272	+	23.7625i	−0.177140	+	0.0254689i
$934$	−288.967	+	449.641i	−0.309386	+	0.481414i
$935$	−799.070	+	117.355i	−0.854621	+	0.125513i
$936$	231.943	−	1613.20i	0.247803	−	1.72350i
$937$	−668.815	+	771.854i	−0.713784	+	0.823750i	−0.990545	−	0.137188i	$-0.956193\pi$
$937$	−668.815	+	771.854i	−0.713784	+	0.823750i	0.276761	+	0.960939i	$0.410739\pi$
$938$	61.7765	+	96.1262i	0.0658598	+	0.102480i
$939$	171.501	−	148.606i	0.182642	−	0.158260i
$940$	161.649	+	73.2329i	0.171967	+	0.0779073i
$941$	−1287.82	−	588.128i	−1.36857	−	0.625003i	−0.410582	−	0.911824i	$-0.634674\pi$
$941$	−1287.82	−	588.128i	−1.36857	−	0.625003i	−0.957984	+	0.286821i	$0.907402\pi$
$942$	105.081			0.111551
$943$	−331.718	+	859.695i	−0.351769	+	0.911660i
$944$	71.1044			0.0753224
$945$	−168.282	+	263.600i	−0.178076	+	0.278941i
$946$	−917.165	−	269.304i	−0.969519	−	0.284676i
$947$	946.355	−	820.021i	0.999318	−	0.865914i	0.00834397	−	0.999965i	$-0.497344\pi$
$947$	946.355	−	820.021i	0.999318	−	0.865914i	0.990974	+	0.134051i	$0.0427985\pi$
$948$	75.8542	−	48.7486i	0.0800150	−	0.0514225i
$949$	1662.96	−	1919.16i	1.75233	−	2.02230i
$950$	105.286	−	234.280i	0.110827	−	0.246611i
$951$	74.7284	−	21.9422i	0.0785787	−	0.0230728i
$952$	432.033	−	672.256i	0.453816	−	0.706151i
$953$	72.2388	+	502.432i	0.0758014	+	0.527211i	0.991976	+	0.126430i	$0.0403519\pi$
$953$	72.2388	+	502.432i	0.0758014	+	0.527211i	−0.916174	+	0.400781i	$0.868739\pi$
$954$	−610.619	+	278.860i	−0.640062	+	0.292306i
$955$	176.351	+	593.953i	0.184661	+	0.621940i
$956$	−11.3087	−	78.6539i	−0.0118292	−	0.0822739i
$957$	232.316	+	149.301i	0.242755	+	0.156009i
$958$	793.692	−	233.049i	0.828488	−	0.243266i
$959$	−57.7838	+	401.895i	−0.0602542	+	0.419077i
$960$	82.7889	−	72.1762i	0.0862385	−	0.0751835i
$961$	−783.643	+	503.617i	−0.815445	+	0.524055i
$962$	382.251	+	441.141i	0.397350	+	0.458566i
$963$	−709.457	−	208.315i	−0.736716	−	0.216319i
$964$	−127.815	−	58.3710i	−0.132588	−	0.0605509i
$965$	439.758	+	61.8720i	0.455708	+	0.0641160i
$966$	−102.626	−	23.5376i	−0.106238	−	0.0243661i
$967$		−	323.297i		−	0.334329i	−0.985929	−	0.167165i	$-0.946539\pi$
$967$		−	323.297i		−	0.334329i	0.985929	−	0.167165i	$-0.0534612\pi$
$968$	−212.874	−	97.2162i	−0.219911	−	0.100430i
$969$	−47.7896	−	14.0323i	−0.0493184	−	0.0144812i
$970$	−407.452	−	629.815i	−0.420053	−	0.649294i
$971$	201.785	+	313.983i	0.207811	+	0.323361i	0.929476	−	0.368882i	$-0.120259\pi$
$971$	201.785	+	313.983i	0.207811	+	0.323361i	−0.721665	+	0.692242i	$0.756623\pi$
$972$	−195.550	−	169.445i	−0.201183	−	0.174326i
$973$	59.3053	−	412.478i	0.0609510	−	0.423923i
$974$	−861.354	+	252.916i	−0.884347	+	0.259668i
$975$	178.190	+	203.149i	0.182759	+	0.208358i
$976$	−0.323436	+	0.0465031i	−0.000331390	+	4.76466e-5i
$977$	−2.43608	−	5.33427i	−0.00249343	−	0.00545985i	0.908381	−	0.418143i	$-0.137319\pi$
$977$	−2.43608	−	5.33427i	−0.00249343	−	0.00545985i	−0.910875	+	0.412683i	$0.864592\pi$
$978$	−68.9704	+	31.4977i	−0.0705219	+	0.0322063i
$979$	17.6182	+	122.537i	0.0179961	+	0.125165i
$980$	40.3303	−	46.8288i	0.0411534	−	0.0477845i
$981$	312.840	+	1065.44i	0.318899	+	1.08607i
$982$	148.626	+	21.3691i	0.151350	+	0.0217608i
$983$	930.128	−	1073.42i	0.946213	−	1.09199i	−0.0494331	−	0.998777i	$-0.515741\pi$
$983$	930.128	−	1073.42i	0.946213	−	1.09199i	0.995646	−	0.0932109i	$-0.0297131\pi$
$984$	132.013	−	84.8398i	0.134160	−	0.0862193i
$985$	−143.660	−	222.061i	−0.145848	−	0.225443i
$986$	−229.026	+	779.989i	−0.232277	+	0.791064i
$987$	−22.4825	+	49.2298i	−0.0227786	+	0.0498782i
$988$	412.790			0.417803
$989$	1300.46	−	468.442i	1.31492	−	0.473652i
$990$	−97.1950	+	690.819i	−0.0981768	+	0.697797i
$991$	109.043	−	238.772i	0.110034	−	0.240940i	−0.846602	−	0.532226i	$-0.821356\pi$
$991$	109.043	−	238.772i	0.110034	−	0.240940i	0.956636	+	0.291286i	$0.0940830\pi$
$992$	47.3400	−	161.225i	0.0477217	−	0.162525i
$993$	168.780	−	146.249i	0.169970	−	0.147280i
$994$	−449.362	−	699.220i	−0.452074	−	0.703441i
$995$	−813.272	+	709.018i	−0.817359	+	0.712581i
$996$	100.093	+	14.3911i	0.100495	+	0.0144489i
$997$	−101.714	−	346.405i	−0.102020	−	0.347448i	0.892625	−	0.450800i	$-0.148861\pi$
$997$	−101.714	−	346.405i	−0.102020	−	0.347448i	−0.994645	+	0.103352i	$0.967043\pi$
$998$	−214.360	+	333.551i	−0.214790	+	0.334220i
$999$	166.422	−	23.9279i	0.166589	−	0.0239518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.i.a.109.16	yes	220
5.4	even	2	inner	115.3.i.a.109.7	yes	220
23.19	odd	22	inner	115.3.i.a.19.7	✓	220
115.19	odd	22	inner	115.3.i.a.19.16	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.i.a.19.7	✓	220	23.19	odd	22	inner
115.3.i.a.19.16	yes	220	115.19	odd	22	inner
115.3.i.a.109.7	yes	220	5.4	even	2	inner
115.3.i.a.109.16	yes	220	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18321 + 0.540352i) q^{2} +(0.134488 - 0.458024i) q^{3} +(-1.51145 - 1.74430i) q^{4} +(-2.09081 - 4.54186i) q^{5} +(0.406621 - 0.469266i) q^{6} +(1.04923 - 7.29756i) q^{7} +(-2.31167 - 7.87283i) q^{8} +(7.37958 + 4.74257i) q^{9} +(-0.0196528 - 6.50373i) q^{10} +(-11.1229 + 5.07965i) q^{11} +(-1.00221 + 0.457692i) q^{12} +(22.4127 - 3.22246i) q^{13} +(5.18471 - 8.06756i) q^{14} +(-2.36147 + 0.346815i) q^{15} +(0.205039 - 1.42608i) q^{16} +(-8.65061 + 9.98333i) q^{17} +(6.16890 + 9.59900i) q^{18} +(-5.96932 + 5.17245i) q^{19} +(-4.76224 + 10.5118i) q^{20} +(-3.20135 - 1.46201i) q^{21} -15.9054 q^{22} +(18.5664 - 13.5753i) q^{23} -3.91684 q^{24} +(-16.2570 + 18.9923i) q^{25} +(28.2601 + 8.29791i) q^{26} +(6.41157 - 5.55565i) q^{27} +(-14.3150 + 9.19971i) q^{28} +(30.9816 - 35.7547i) q^{29} +(-2.98151 - 0.865672i) q^{30} +(-5.20976 + 1.52972i) q^{31} +(-16.7311 + 26.0341i) q^{32} +(0.830708 + 5.77770i) q^{33} +(-15.6300 + 7.13796i) q^{34} +(-35.3383 + 10.4923i) q^{35} +(-2.88137 - 20.0404i) q^{36} +(16.6723 + 10.7146i) q^{37} +(-9.85787 + 2.89453i) q^{38} +(1.53828 - 10.6989i) q^{39} +(-30.9241 + 26.9599i) q^{40} +(-33.7040 + 21.6603i) q^{41} +(-2.99786 - 3.45971i) q^{42} +(57.6636 + 16.9316i) q^{43} +(25.6721 + 11.7241i) q^{44} +(6.11080 - 43.4329i) q^{45} +(29.3033 - 6.02997i) q^{46} -15.3778i q^{47} +(-0.625603 - 0.285703i) q^{48} +(-5.13841 - 1.50877i) q^{49} +(-29.4979 + 13.6873i) q^{50} +(3.40921 + 5.30483i) q^{51} +(-39.4966 - 34.2240i) q^{52} +(-8.37251 + 58.2321i) q^{53} +(10.5882 - 3.10898i) q^{54} +(46.3269 + 39.8980i) q^{55} +(-59.8780 + 8.60915i) q^{56} +(1.56630 + 3.42973i) q^{57} +(55.9777 - 25.5642i) q^{58} +(7.02361 + 48.8503i) q^{59} +(4.17420 + 3.59493i) q^{60} +(-0.0638973 - 0.217614i) q^{61} +(-6.99080 - 1.00513i) q^{62} +(42.3521 - 48.8769i) q^{63} +(-38.7120 + 24.8787i) q^{64} +(-61.4967 - 95.0579i) q^{65} +(-2.13909 + 7.28508i) q^{66} +(-4.94973 + 10.8384i) q^{67} +30.4889 q^{68} +(-3.72085 - 10.3296i) q^{69} +(-47.4820 - 6.68050i) q^{70} +(36.0043 - 78.8383i) q^{71} +(20.2783 - 69.0615i) q^{72} +(84.7567 - 73.4421i) q^{73} +(13.9370 + 21.6865i) q^{74} +(6.51257 + 10.0004i) q^{75} +(18.0446 + 2.59443i) q^{76} +(25.3986 + 86.4996i) q^{77} +(7.60129 - 11.8278i) q^{78} +(-81.0063 + 11.6469i) q^{79} +(-6.90574 + 2.05040i) q^{80} +(31.1143 + 68.1308i) q^{81} +(-51.5829 + 7.41651i) q^{82} +(-77.2113 - 49.6207i) q^{83} +(2.28849 + 7.79389i) q^{84} +(63.4297 + 18.4166i) q^{85} +(59.0789 + 51.1921i) q^{86} +(-12.2099 - 18.9989i) q^{87} +(65.7036 + 75.8260i) q^{88} +(2.85230 - 9.71406i) q^{89} +(30.6994 - 48.0880i) q^{90} -166.939i q^{91} +(-51.7416 - 11.8671i) q^{92} +2.59193i q^{93} +(8.30943 - 18.1951i) q^{94} +(35.9732 + 16.2972i) q^{95} +(9.67410 + 11.1645i) q^{96} +(97.0275 - 62.3558i) q^{97} +(-5.26453 - 4.56174i) q^{98} +(-106.173 - 15.2653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) \) 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

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