LMFDB - Embedded newform 115.3.i.a.109.7

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)

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")

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);

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			109.7
Character	$\chi$	$=$	115.109
Dual form			115.3.i.a.19.7

$q$-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} +(-3.26287 - 3.78862i) 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} +(1.81346 + 6.24582i) 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} +(2.17410 - 0.984949i) 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} +(-1.67686 + 11.4178i) q^{20} +(-3.20135 - 1.46201i) q^{21} +15.9054 q^{22} +(-18.5664 + 13.5753i) q^{23} -3.91684 q^{24} +(-3.70736 + 24.7236i) 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} +(-3.10462 - 0.00938147i) 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} +(31.0712 - 19.8359i) 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} +(22.2845 - 34.4461i) 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} +(17.7460 - 27.2498i) 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} +(55.5374 + 25.5662i) 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} +(-5.00409 - 2.30359i) 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} +(85.3384 + 74.3989i) 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} +(-10.8254 - 5.02309i) 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} +(-6.07189 + 3.87629i) 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} +(-66.0489 - 0.199585i) 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} +(-16.2387 + 54.6920i) q^{90} -166.939i q^{91} +(51.7416 + 11.8671i) q^{92} -2.59193i q^{93} +(8.30943 - 18.1951i) q^{94} +(39.0736 + 5.73850i) 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	0.0970357	−	0.995281i	$-0.469064\pi$
$2$	−1.18321	−	0.540352i	−0.591603	−	0.270176i	−0.688638	+	0.725105i	$0.741791\pi$
$3$	−0.134488	+	0.458024i	−0.0448294	+	0.152675i	−0.978866	−	0.204502i	$-0.934442\pi$
$3$	−0.134488	+	0.458024i	−0.0448294	+	0.152675i	0.934037	+	0.357177i	$0.116261\pi$
$4$	−1.51145	−	1.74430i	−0.377862	−	0.436076i
$5$	−3.26287	−	3.78862i	−0.652574	−	0.757725i
$5$	−3.26287	−	3.78862i	−0.652574	−	0.757725i
$6$	0.406621	−	0.469266i	0.0677702	−	0.0782110i
$7$	−1.04923	+	7.29756i	−0.149890	+	1.04251i	0.766506	+	0.642237i	$0.221994\pi$
$7$	−1.04923	+	7.29756i	−0.149890	+	1.04251i	−0.916396	+	0.400272i	$0.868916\pi$
$8$	2.31167	+	7.87283i	0.288959	+	0.984104i
$9$	7.37958	+	4.74257i	0.819954	+	0.526952i
$10$	1.81346	+	6.24582i	0.181346	+	0.624582i
$11$	−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	−0.931971	−	0.362532i	$-0.881912\pi$
$13$	−22.4127	+	3.22246i	−1.72405	+	0.247882i	−0.792083	+	0.610414i	$0.791003\pi$
$14$	5.18471	−	8.06756i	0.370336	−	0.576254i
$15$	2.17410	−	0.984949i	0.144940	−	0.0656633i
$16$	0.205039	−	1.42608i	0.0128149	−	0.0891298i
$17$	8.65061	−	9.98333i	0.508859	−	0.587255i	−0.441947	−	0.897041i	$-0.645712\pi$
$17$	8.65061	−	9.98333i	0.508859	−	0.587255i	0.950806	+	0.309786i	$0.100258\pi$
$18$	−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	$0.339376\pi$
$20$	−1.67686	+	11.4178i	−0.0838428	+	0.570888i
$21$	−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
$25$	−3.70736	+	24.7236i	−0.148294	+	0.988943i
$26$	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	$-0.0763717\pi$
$30$	−3.10462	−	0.00938147i	−0.103487	−	0.000312716i
$31$	−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
$35$	31.0712	−	19.8359i	0.887750	−	0.566739i
$36$	−2.88137	−	20.0404i	−0.0800381	−	0.556677i
$37$	−16.6723	−	10.7146i	−0.450602	−	0.289584i	0.295591	−	0.955315i	$-0.404484\pi$
$37$	−16.6723	−	10.7146i	−0.450602	−	0.289584i	−0.746192	+	0.665731i	$0.768120\pi$
$38$	9.85787	−	2.89453i	0.259418	−	0.0761719i
$39$	1.53828	−	10.6989i	0.0394430	−	0.274332i
$40$	22.2845	−	34.4461i	0.557113	−	0.861152i
$41$	−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	−0.468983	−	0.883207i	$-0.655379\pi$
$43$	−57.6636	−	16.9316i	−1.34101	−	0.393757i	−0.872031	+	0.489450i	$0.837198\pi$
$44$	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	$0.0523086\pi$
$47$			15.3778i			0.327188i	−0.986528	+	0.163594i	$0.947691\pi$
$48$	0.625603	+	0.285703i	0.0130334	+	0.00595215i
$49$	−5.13841	−	1.50877i	−0.104866	−	0.0307913i
$50$	17.7460	−	27.2498i	0.354920	−	0.544996i
$51$	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	$-0.767261\pi$
$53$	8.37251	−	58.2321i	0.157972	−	1.09872i	0.902364	−	0.430975i	$-0.141830\pi$
$54$	10.5882	−	3.10898i	0.196078	−	0.0575736i
$55$	55.5374	+	25.5662i	1.00977	+	0.464839i
$56$	−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	$0.817192\pi$
$60$	−5.00409	−	2.30359i	−0.0834015	−	0.0383932i
$61$	−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
$65$	85.3384	+	74.3989i	1.31290	+	1.14460i
$66$	−2.13909	+	7.28508i	−0.0324105	+	0.110380i
$67$	4.94973	−	10.8384i	0.0738766	−	0.161767i	−0.869091	−	0.494653i	$-0.835295\pi$
$67$	4.94973	−	10.8384i	0.0738766	−	0.161767i	0.942967	+	0.332886i	$0.108022\pi$
$68$	−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	$0.551547\pi$
$73$	−84.7567	+	73.4421i	−1.16105	+	1.00606i	−0.999817	+	0.0191401i	$0.993907\pi$
$74$	13.9370	+	21.6865i	0.188338	+	0.293060i
$75$	−10.8254	−	5.02309i	−0.144339	−	0.0669745i
$76$	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	$0.627858\pi$
$80$	−6.07189	+	3.87629i	−0.0758986	+	0.0484536i
$81$	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	0.915616	−	0.402053i	$-0.131703\pi$
$83$	77.2113	+	49.6207i	0.930256	+	0.597839i	0.0146401	+	0.999893i	$0.495340\pi$
$84$	2.28849	+	7.79389i	0.0272439	+	0.0927844i
$85$	−66.0489	−	0.199585i	−0.777046	−	0.00234806i
$86$	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	$0.0727947\pi$
$90$	−16.2387	+	54.6920i	−0.180430	+	0.607688i
$91$		−	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
$95$	39.0736	+	5.73850i	0.411301	+	0.0604052i
$96$	9.67410	+	11.1645i	0.100772	+	0.116297i
$97$	−97.0275	+	62.3558i	−1.00028	+	0.642843i	−0.934861	−	0.355015i	$-0.884476\pi$
$97$	−97.0275	+	62.3558i	−1.00028	+	0.642843i	−0.0654225	+	0.997858i	$0.520840\pi$
$98$	5.26453	+	4.56174i	0.0537197	+	0.0465483i
$99$	−106.173	−	15.2653i	−1.07245	−	0.154195i
$100$	48.7289	−	30.9017i	0.487289	−	0.309017i
$101$	−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	$0.139776\pi$
$103$	65.2707	+	142.923i	0.633696	+	1.38760i	−0.271430	+	0.962458i	$0.587496\pi$
$104$	−77.1807	−	169.002i	−0.742122	−	1.62502i
$105$	4.90660	+	16.8991i	0.0467295	+	0.160944i
$106$	−41.3722	+	64.3764i	−0.390304	+	0.607324i
$107$	80.8763	−	23.7474i	0.755853	−	0.221939i	0.118969	−	0.992898i	$-0.462041\pi$
$107$	80.8763	−	23.7474i	0.755853	−	0.221939i	0.636884	+	0.770959i	$0.280223\pi$
$108$	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	$0.530066\pi$
$110$	−51.8974	−	60.2597i	−0.471794	−	0.547816i
$111$	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	$-0.620496\pi$
$113$	64.9400	−	142.199i	0.574690	−	1.25840i	0.944262	−	0.329194i	$-0.106777\pi$
$114$			4.90442i			0.0430213i
$115$	112.011	+	26.0467i	0.974013	+	0.226493i
$116$	−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
$120$	12.7801	+	14.8394i	0.106501	+	0.123662i
$121$	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
$125$	105.765	−	66.6241i	0.846120	−	0.532992i
$126$	76.5220	−	34.9464i	0.607317	−	0.277352i
$127$	175.035	−	79.9358i	1.37823	−	0.629416i	0.417953	−	0.908469i	$-0.362748\pi$
$127$	175.035	−	79.9358i	1.37823	−	0.629416i	0.960276	+	0.279053i	$0.0900204\pi$
$128$	−63.2796	+	9.09823i	−0.494372	+	0.0710800i
$129$	15.5101	−	24.1342i	0.120234	−	0.187087i
$130$	−60.7713	−	134.142i	−0.467472	−	1.03186i
$131$	−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
$135$	41.9684	+	6.16364i	0.310877	+	0.0456566i
$136$	98.5944	+	45.0266i	0.724959	+	0.331078i
$137$	55.0725			0.401989			0.200994	−	0.979592i	$-0.435583\pi$
$137$	55.0725			0.401989			0.200994	+	0.979592i	$0.435583\pi$
$138$	−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	$0.434827\pi$
$140$	−81.5624	−	24.2168i	−0.582588	−	0.172977i
$141$	−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
$145$	−236.550	−	0.714800i	−1.63138	−	0.00492966i
$146$	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	$0.684266\pi$
$150$	10.0944	+	11.7929i	0.0672963	+	0.0786191i
$151$	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
$155$	22.7943	+	14.7465i	0.147060	+	0.0951389i
$156$	−20.9872	+	13.4877i	−0.134534	+	0.0864595i
$157$	−110.824	−	127.898i	−0.705886	−	0.814636i	0.283649	−	0.958928i	$-0.408455\pi$
$157$	−110.824	−	127.898i	−0.705886	−	0.814636i	−0.989535	+	0.144293i	$0.953909\pi$
$158$	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	0.725896	−	0.687804i	$-0.241425\pi$
$163$	111.076	+	50.7269i	0.681450	+	0.311208i	−0.0444465	+	0.999012i	$0.514152\pi$
$164$	88.7240	+	26.0517i	0.541000	+	0.158852i
$165$	−19.1790	+	21.9991i	−0.116237	+	0.133328i
$166$	−64.5442	−	100.433i	−0.388820	−	0.605016i
$167$	38.2031	+	33.1031i	0.228761	+	0.198222i	0.761698	−	0.647933i	$-0.224366\pi$
$167$	38.2031	+	33.1031i	0.228761	+	0.198222i	−0.532937	+	0.846155i	$0.678912\pi$
$168$	4.10967	−	28.5834i	0.0244623	−	0.170139i
$169$	329.791	−	96.8353i	1.95142	−	0.572990i
$170$	78.0415	+	35.9258i	0.459068	+	0.211328i
$171$	−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	−0.568626	−	0.822596i	$-0.692525\pi$
$173$	−55.2422	+	25.2283i	−0.319319	+	0.145828i	0.249306	+	0.968425i	$0.419797\pi$
$174$	−4.18067	−	29.0772i	−0.0240269	−	0.167110i
$175$	−176.532	−	52.9954i	−1.00875	−	0.302831i
$176$	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	$0.332904\pi$
$180$	−66.5240	+	76.3056i	−0.369578	+	0.423920i
$181$	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
$190$	−43.1312	−	27.9033i	−0.227007	−	0.146859i
$191$	−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	−0.694280	−	0.719705i	$-0.744277\pi$
$193$	48.0186	−	74.7184i	0.248801	−	0.387142i	0.943081	+	0.332563i	$0.107913\pi$
$194$	148.497	−	21.3507i	0.765451	−	0.110055i
$195$	−45.5535	+	29.0813i	−0.233608	+	0.149135i
$196$	5.13468	+	11.2434i	0.0261974	+	0.0573642i
$197$	−52.3575	+	7.52788i	−0.265774	+	0.0382126i	−0.273914	−	0.961754i	$-0.588318\pi$
$197$	−52.3575	+	7.52788i	−0.265774	+	0.0382126i	0.00813935	+	0.999967i	$0.497409\pi$
$198$	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	$-0.273311\pi$
$200$	−203.215	+	27.9654i	−1.01607	+	0.139827i
$201$	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
$205$	192.034	+	57.0173i	0.936753	+	0.278133i
$206$		−	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
$210$	3.32593	−	22.6464i	0.0158378	−	0.107840i
$211$	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
$215$	124.002	+	273.711i	0.576751	+	1.27308i
$216$	−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
$220$	−39.3467	−	135.516i	−0.178849	−	0.615982i
$221$	−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	0.195751	−	0.980654i	$-0.437285\pi$
$223$	23.9260	+	3.44003i	0.107291	+	0.0154262i	−0.0884600	+	0.996080i	$0.528195\pi$
$224$	172.430	+	149.412i	0.769779	+	0.667017i
$225$	−144.612	+	164.867i	−0.642720	+	0.732744i
$226$	−153.675	+	133.160i	−0.679976	+	0.589203i
$227$	−414.487	−	121.704i	−1.82594	−	0.536143i	−0.826303	−	0.563226i	$-0.809560\pi$
$227$	−414.487	−	121.704i	−1.82594	−	0.536143i	−0.999633	+	0.0270832i	$0.991378\pi$
$228$	−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	$-0.0959609\pi$
$230$	−118.458	−	91.3442i	−0.515035	−	0.397149i
$231$	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	$0.222282\pi$
$233$	−52.6598	+	179.343i	−0.226008	+	0.769712i	−0.991931	+	0.126780i	$0.959536\pi$
$234$	169.194	+	195.261i	0.723052	+	0.834447i
$235$	58.2608	−	50.1758i	0.247918	−	0.213514i
$236$	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	$0.658872\pi$
$240$	−0.958838	−	3.30239i	−0.00399516	−	0.0137599i
$241$	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
$245$	11.0498	+	24.3904i	0.0451012	+	0.0995528i
$246$	−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
$250$	−161.142	+	21.6796i	−0.644568	+	0.0867186i
$251$	−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
$255$	8.97420	−	30.2252i	0.0351930	−	0.118530i
$256$	256.401	+	75.2861i	1.00157	+	0.294086i
$257$	51.6001	−	44.7118i	0.200779	−	0.173976i	−0.548668	−	0.836040i	$-0.684865\pi$
$257$	51.6001	−	44.7118i	0.200779	−	0.173976i	0.749447	+	0.662064i	$0.230320\pi$
$258$	−31.3926	+	20.1748i	−0.121677	+	0.0781970i
$259$	95.6836	−	110.425i	0.369435	−	0.426350i
$260$	0.789608	−	261.306i	0.00303695	−	1.00502i
$261$	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	$0.0267780\pi$
$263$	16.8417	+	117.136i	0.0640367	+	0.445385i	−0.932427	+	0.361359i	$0.882313\pi$
$264$	43.5665	−	19.8962i	0.165025	−	0.0753643i
$265$	−247.938	+	158.283i	−0.935614	+	0.597296i
$266$	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	$0.738793\pi$
$270$	−46.3267	−	29.9705i	−0.171580	−	0.111002i
$271$	−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	$-0.972735\pi$
$277$		−	47.3956i		−	0.171103i	0.996334	−	0.0855516i	$-0.0272652\pi$
$278$	−66.8779	−	30.5421i	−0.240568	−	0.109864i
$279$	−45.7007	−	13.4189i	−0.163802	−	0.0480965i
$280$	227.991	+	198.765i	0.814253	+	0.709874i
$281$	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	−0.986570	−	0.163336i	$-0.947774\pi$
$283$	1.71331	−	11.9163i	0.00605408	−	0.0421071i	0.992625	+	0.121229i	$0.0386836\pi$
$284$	−191.937	+	56.3577i	−0.675833	+	0.198443i
$285$	−7.88330	+	17.1249i	−0.0276607	+	0.0600873i
$286$	−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
$290$	279.501	+	128.666i	0.963796	+	0.443676i
$291$	−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	−0.754285	−	0.656547i	$-0.772016\pi$
$293$	0.857298	−	0.989375i	0.00292593	−	0.00337671i	0.757211	+	0.653171i	$0.226562\pi$
$294$	−2.79740	+	1.79778i	−0.00951498	+	0.00611490i
$295$	162.158	−	186.002i	0.549689	−	0.630515i
$296$	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
$305$	−0.615970	+	0.952131i	−0.00201958	+	0.00312174i
$306$	−149.195	−	21.4510i	−0.487565	−	0.0701012i
$307$	51.1547	+	174.217i	0.166628	+	0.567482i	0.999893	+	0.0146091i	$0.00465038\pi$
$307$	51.1547	+	174.217i	0.166628	+	0.567482i	−0.833265	+	0.552873i	$0.813531\pi$
$308$	−112.493	+	175.043i	−0.365237	+	0.568320i
$309$	−74.2403	+	10.6741i	−0.240260	+	0.0345442i
$310$	−19.0020	−	29.7651i	−0.0612969	−	0.0960165i
$311$	−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	−0.287086	−	0.957905i	$-0.592687\pi$
$313$	−399.916	−	257.010i	−1.27769	−	0.821119i	−0.990601	+	0.136786i	$0.956323\pi$
$314$	62.0178	+	211.213i	0.197509	+	0.672654i
$315$	323.366	+	0.977138i	1.02656	+	0.00310202i
$316$	142.753	+	123.696i	0.451749	+	0.391443i
$317$	−88.2076	−	137.254i	−0.278257	−	0.432977i	0.673792	−	0.738921i	$-0.264664\pi$
$317$	−88.2076	−	137.254i	−0.278257	−	0.432977i	−0.952049	+	0.305944i	$0.901028\pi$
$318$	−23.9219	−	27.6073i	−0.0752260	−	0.0868155i
$319$	−162.983	+	555.070i	−0.510920	+	1.74003i
$320$	220.568	+	65.4892i	0.689275	+	0.204654i
$321$			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
$325$	3.42110	−	566.069i	0.0105264	−	1.74175i
$326$	−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
$330$	34.5800	−	15.6660i	0.104788	−	0.0474729i
$331$	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
$335$	−57.2129	+	16.6116i	−0.170785	+	0.0495869i
$336$	−2.74134	+	4.26561i	−0.00815875	+	0.0126953i
$337$	−51.9693	+	15.2596i	−0.154211	+	0.0452806i	−0.357927	−	0.933750i	$-0.616516\pi$
$337$	−51.9693	+	15.2596i	−0.154211	+	0.0452806i	0.203716	+	0.979030i	$0.434698\pi$
$338$	−442.535	−	63.6270i	−1.30928	−	0.188245i
$339$	56.3968	+	48.8681i	0.166362	+	0.144154i
$340$	99.4814	+	115.511i	0.292592	+	0.339738i
$341$	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
$345$	−26.9942	+	47.8010i	−0.0782442	+	0.138554i
$346$	78.9950			0.228309
$347$	−0.471708	−	0.215422i	−0.00135939	−	0.000620812i	0.414735	−	0.909942i	$-0.363874\pi$
$347$	−0.471708	−	0.215422i	−0.00135939	−	0.000620812i	−0.416095	+	0.909321i	$0.636601\pi$
$348$	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	$-0.461338\pi$
$350$	180.237	+	158.094i	0.514964	+	0.451697i
$351$	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	0.964553	−	0.263888i	$-0.0850051\pi$
$353$	3.68906	+	12.5638i	0.0104506	+	0.0355915i	−0.954103	+	0.299480i	$0.903187\pi$
$354$	25.7797	+	16.5676i	0.0728241	+	0.0468012i
$355$	−416.166	+	120.833i	−1.17230	+	0.340374i
$356$	−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	$0.212819\pi$
$360$	327.813	−	148.512i	0.910593	−	0.412533i
$361$	−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
$365$	554.795	+	81.4793i	1.51999	+	0.223231i
$366$	−0.128101	−	0.0585018i	−0.000350003	−	0.000159841i
$367$	278.793			0.759655			0.379827	−	0.925057i	$-0.375983\pi$
$367$	278.793			0.759655			0.379827	+	0.925057i	$0.375983\pi$
$368$	15.5526	+	29.2606i	0.0422624	+	0.0795125i
$369$	−351.447			−0.952431
$370$	36.6871	−	123.562i	0.0991543	−	0.333952i
$371$	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	−0.961774	−	0.273843i	$-0.911705\pi$
$373$	−414.856	+	266.612i	−1.11221	+	0.714776i	−0.150439	+	0.988619i	$0.548069\pi$
$374$	137.592	−	158.789i	0.367892	−	0.424570i
$375$	16.2913	+	57.4031i	0.0434435	+	0.153075i
$376$	−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	$0.527086\pi$
$380$	−49.0480	−	76.8297i	−0.129074	−	0.202183i
$381$	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	−0.895627	−	0.444805i	$-0.853273\pi$
$383$	−539.493	+	158.409i	−1.40860	+	0.413602i	−0.512970	+	0.858406i	$0.671455\pi$
$384$	4.34314	−	30.2072i	0.0113103	−	0.0786646i
$385$	−244.842	+	378.463i	−0.635954	+	0.983020i
$386$	−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
$395$	308.439	+	268.900i	0.780858	+	0.680759i
$396$	133.847	+	208.270i	0.337998	+	0.525935i
$397$	516.672	+	447.698i	1.30144	+	1.12770i	0.983757	+	0.179507i	$0.0574503\pi$
$397$	516.672	+	447.698i	1.30144	+	1.12770i	0.317683	+	0.948197i	$0.397095\pi$
$398$	−39.9460	+	277.830i	−0.100367	+	0.698066i
$399$	26.6721	−	7.83162i	0.0668473	−	0.0196281i
$400$	34.4976	+	10.3563i	0.0862440	+	0.0258907i
$401$	−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
$405$	156.600	−	340.183i	0.386667	−	0.839957i
$406$	−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	$0.248947\pi$
$410$	−196.407	−	171.229i	−0.479041	−	0.417632i
$411$	−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	$0.909885\pi$
$420$	22.0611	−	34.1007i	0.0525263	−	0.0811921i
$421$	−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
$425$	214.753	+	250.886i	0.505301	+	0.590319i
$426$	−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
$430$	1.18109	−	390.861i	0.00274673	−	0.908979i
$431$	−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	0.832824	−	0.553538i	$-0.186723\pi$
$433$	72.0498	+	83.1499i	0.166397	+	0.192032i	−0.666427	+	0.745570i	$0.732177\pi$
$434$	−14.6699	+	49.9612i	−0.0338017	+	0.115118i
$435$	32.1406	−	108.250i	0.0738863	−	0.248850i
$436$		−	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	$0.196140\pi$
$440$	−72.8940	+	496.337i	−0.165668	+	1.12804i
$441$	−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	0.257401	−	0.966305i	$-0.417134\pi$
$443$	−293.459	−	254.284i	−0.662437	−	0.574005i	−0.919837	+	0.392300i	$0.871679\pi$
$444$	−21.6130	−	3.10748i	−0.0486780	−	0.00699884i
$445$	−46.1096	+	20.8894i	−0.103617	+	0.0469425i
$446$	−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	$0.956811\pi$
$450$	260.192	−	116.930i	0.578205	−	0.259846i
$451$	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
$455$	−632.470	+	544.701i	−1.39004	+	1.19715i
$456$	23.3809	−	20.2596i	0.0512739	−	0.0444290i
$457$	293.276	+	86.1137i	0.641743	+	0.188433i	0.586383	−	0.810034i	$-0.300551\pi$
$457$	293.276	+	86.1137i	0.641743	+	0.188433i	0.0553594	+	0.998466i	$0.482370\pi$
$458$	−73.4831	+	160.906i	−0.160444	+	0.351322i
$459$			112.069i			0.244158i
$460$	−123.866	−	234.750i	−0.269274	−	0.510327i
$461$	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	−0.968194	−	0.250200i	$-0.919504\pi$
$463$	−8.53259	+	29.0593i	−0.0184289	+	0.0627632i	0.949765	+	0.312963i	$0.101322\pi$
$464$	−44.6365	−	51.5133i	−0.0961993	−	0.111020i
$465$	−9.81984	+	8.45712i	−0.0211179	+	0.0181874i
$466$	159.216	−	183.745i	0.341664	−	0.394302i
$467$	58.4783	−	406.725i	0.125221	−	0.870932i	−0.826274	−	0.563269i	$-0.809544\pi$
$467$	58.4783	−	406.725i	0.125221	−	0.870932i	0.951495	−	0.307664i	$-0.0995472\pi$
$468$	129.159	+	439.874i	0.275980	+	0.939902i
$469$	73.9005	+	47.4930i	0.157570	+	0.101264i
$470$	−96.0470	+	27.8870i	−0.204355	+	0.0593340i
$471$	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
$475$	−105.751	−	166.759i	−0.222634	−	0.351072i
$476$	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	$0.0416615\pi$
$480$	10.7328	−	73.0799i	0.0223600	−	0.152250i
$481$	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
$485$	552.831	+	164.142i	1.13986	+	0.338437i
$486$	139.917	+	41.0833i	0.287895	+	0.0845336i
$487$	521.583	−	451.954i	1.07101	−	0.928038i	0.0734145	−	0.997302i	$-0.476610\pi$
$487$	521.583	−	451.954i	1.07101	−	0.928038i	0.997598	+	0.0692635i	$0.0220649\pi$
$488$	1.56553	−	1.00611i	0.00320806	−	0.00206169i
$489$	−38.1726	+	44.0535i	−0.0780625	+	0.0900890i
$490$	0.105247	−	34.8297i	0.000214791	−	0.0710810i
$491$	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
$495$	288.593	+	452.058i	0.583017	+	0.913248i
$496$	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	$0.946654\pi$
$500$	−276.071	−	83.7875i	−0.552142	−	0.167575i
$501$	−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	0.0124670	−	0.999922i	$-0.496032\pi$
$503$	−260.375	−	76.4530i	−0.517644	−	0.151994i	−0.530111	+	0.847928i	$0.677850\pi$
$504$	−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	$0.616481\pi$
$510$	−26.9505	+	30.9133i	−0.0528442	+	0.0606144i
$511$	−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
$515$	328.512	−	713.625i	0.637886	−	1.38568i
$516$	−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
$520$	−388.455	+	843.841i	−0.747029	+	1.62277i
$521$	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	−0.988344	−	0.152234i	$-0.951353\pi$
$523$	−364.533	+	420.693i	−0.697003	+	0.804385i	0.291341	+	0.956619i	$0.405899\pi$
$524$	455.790	−	292.918i	0.869828	−	0.559005i
$525$	48.0147	−	73.7287i	0.0914565	−	0.140436i
$526$	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
$535$	−353.859	−	228.925i	−0.661419	−	0.427898i
$536$	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
$540$	−52.6818	−	82.5217i	−0.0975589	−	0.152818i
$541$	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
$545$	1.91254	−	632.920i	0.00350925	−	1.16132i
$546$	−78.3389	−	67.8810i	−0.143478	−	0.124324i
$547$	−332.724	−	517.728i	−0.608270	−	0.946487i	−0.999655	−	0.0262599i	$-0.991640\pi$
$547$	−332.724	−	517.728i	−0.608270	−	0.946487i	0.391385	−	0.920227i	$-0.371996\pi$
$548$	−83.2392	−	96.0631i	−0.151896	−	0.175298i
$549$	0.560516	−	1.90894i	0.00102098	−	0.00347712i
$550$	−58.9671	+	393.239i	−0.107213	+	0.714981i
$551$			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
$555$	−46.8005	−	6.87330i	−0.0843252	−	0.0123843i
$556$	−85.4310	−	98.5927i	−0.153653	−	0.177325i
$557$	−175.884	+	113.034i	−0.315770	+	0.202933i	−0.688919	−	0.724838i	$-0.741914\pi$
$557$	−175.884	+	113.034i	−0.315770	+	0.202933i	0.373149	+	0.927771i	$0.378278\pi$
$558$	46.8223	+	40.5718i	0.0839110	+	0.0727093i
$559$	1346.96	+	193.663i	2.40959	+	0.346446i
$560$	−21.9167	−	48.3771i	−0.0391369	−	0.0863877i
$561$	−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	$0.0453068\pi$
$563$	252.706	+	553.349i	0.448856	+	0.982858i	−0.541031	+	0.841003i	$0.681966\pi$
$564$	7.03830	+	15.4117i	0.0124793	+	0.0273258i
$565$	−750.628	+	217.943i	−1.32855	+	0.385739i
$566$	−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	$0.606011\pi$
$570$	18.5810	−	16.0025i	0.0325983	−	0.0280746i
$571$	−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
$575$	−266.798	−	509.357i	−0.463996	−	0.885837i
$576$	−403.667			−0.700811
$577$	591.759	+	270.247i	1.02558	+	0.468366i	0.855904	−	0.517134i	$-0.173001\pi$
$577$	591.759	+	270.247i	1.02558	+	0.468366i	0.169674	+	0.985500i	$0.445728\pi$
$578$	41.9602	−	142.903i	0.0725955	−	0.247237i
$579$	27.7649	+	32.0424i	0.0479532	+	0.0553409i
$580$	356.286	+	413.696i	0.614287	+	0.713268i
$581$	−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
$585$	276.920	+	953.756i	0.473368	+	1.63035i
$586$	−1.54897	+	0.707391i	−0.00264329	+	0.00120715i
$587$	327.922	−	149.757i	0.558640	−	0.255122i	−0.116025	−	0.993246i	$-0.537015\pi$
$587$	327.922	−	149.757i	0.558640	−	0.255122i	0.674665	+	0.738124i	$0.264288\pi$
$588$	−5.84030	+	0.839708i	−0.00993248	+	0.00142808i
$589$	23.1863	−	36.0786i	0.0393656	−	0.0612540i
$590$	−292.373	+	132.456i	−0.495547	+	0.224502i
$591$	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	$0.151122\pi$
$593$	554.899	+	863.440i	0.935749	+	1.45605i	0.0463481	+	0.998925i	$0.485242\pi$
$594$	−101.979	+	88.3651i	−0.171681	+	0.148763i
$595$	70.7571	−	481.787i	0.118919	−	0.809726i
$596$	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	$0.534830\pi$
$600$	14.5211	−	96.8383i	0.0242019	−	0.161397i
$601$	−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
$605$	−142.605	−	0.430921i	−0.235711	−	0.000712265i
$606$	−39.5597	+	11.6158i	−0.0652800	+	0.0191679i
$607$	−608.755	+	947.241i	−1.00289	+	1.56053i	−0.186970	+	0.982366i	$0.559867\pi$
$607$	−608.755	+	947.241i	−1.00289	+	1.56053i	−0.815921	+	0.578163i	$0.803770\pi$
$608$	34.7866	+	241.946i	0.0572148	+	0.397938i
$609$	−151.457	+	69.1680i	−0.248697	+	0.113576i
$610$	1.24330	−	0.793725i	0.00203820	−	0.00130119i
$611$	−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	0.358938	−	0.933362i	$-0.383139\pi$
$613$	714.457	−	209.783i	1.16551	−	0.342224i	0.806571	+	0.591137i	$0.201321\pi$
$614$	33.6119	−	233.776i	0.0547425	−	0.380743i
$615$	−51.9416	+	80.2883i	−0.0844580	+	0.130550i
$616$	622.284	−	399.918i	1.01020	−	0.649217i
$617$	482.903	+	557.300i	0.782663	+	0.903241i	0.997299	−	0.0734532i	$-0.0234020\pi$
$617$	482.903	+	557.300i	0.782663	+	0.903241i	−0.214636	+	0.976694i	$0.568856\pi$
$618$	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
$625$	−597.511	−	183.318i	−0.956018	−	0.293309i
$626$	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
$630$	−382.080	−	175.887i	−0.606476	−	0.279186i
$631$	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
$635$	−873.963	−	402.322i	−1.37632	−	0.633578i
$636$	−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
$640$	240.943	+	210.056i	0.376473	+	0.328213i
$641$	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	$-0.580272\pi$
$643$	−320.879			−0.499034			−0.249517	+	0.968370i	$0.580272\pi$
$644$	−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	$-0.761325\pi$
$647$	163.223	−	555.888i	0.252277	−	0.859178i	0.984090	−	0.177672i	$-0.0568565\pi$
$648$	−464.457	+	402.454i	−0.716754	+	0.621071i
$649$	−326.265	−	507.678i	−0.502719	−	0.782247i
$650$	−309.924	+	667.927i	−0.476807	+	1.02758i
$651$	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	$-0.589398\pi$
$653$	464.910	−	723.414i	0.711960	−	1.10783i	0.989135	−	0.147012i	$-0.0469655\pi$
$654$	77.7998	−	11.1859i	0.118960	−	0.0171039i
$655$	989.307	−	631.573i	1.51039	−	0.964234i
$656$	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	$0.603302\pi$
$660$	67.3613	+	0.203551i	0.102063	+	0.000308410i
$661$	−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
$665$	−82.8743	+	279.121i	−0.124623	+	0.419731i
$666$			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
$670$	76.6708	+	11.2602i	0.114434	+	0.0168062i
$671$	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	0.850549	−	0.525896i	$-0.176270\pi$
$673$	303.558	+	263.034i	0.451052	+	0.390838i	−0.399497	+	0.916734i	$0.630815\pi$
$674$	69.7358	+	10.0265i	0.103466	+	0.0148761i
$675$	−113.586	−	179.114i	−0.168275	−	0.265354i
$676$	−667.372	−	428.894i	−0.987237	−	0.634459i
$677$	55.3065	+	384.665i	0.0816935	+	0.568191i	0.989022	+	0.147769i	$0.0472091\pi$
$677$	55.3065	+	384.665i	0.0816935	+	0.568191i	−0.907328	+	0.420423i	$0.861882\pi$
$678$	−40.3230	−	88.2951i	−0.0594735	−	0.130229i
$679$	−353.241	−	773.490i	−0.520237	−	1.13916i
$680$	−151.112	−	520.453i	−0.222224	−	0.765372i
$681$	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	0.162123	−	0.986771i	$-0.448166\pi$
$683$	27.0965	+	3.89589i	0.0396728	+	0.00570409i	−0.122450	+	0.992475i	$0.539075\pi$
$684$	120.858	+	104.724i	0.176692	+	0.153105i
$685$	−179.694	−	208.649i	−0.262327	−	0.304597i
$686$	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
$690$	57.7691	−	41.9720i	0.0837233	−	0.0608290i
$691$	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
$695$	−184.426	−	214.143i	−0.265361	−	0.308119i
$696$	−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
$700$	174.379	+	388.026i	0.249113	+	0.554322i
$701$	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
$705$	15.1464	+	33.4329i	0.0214842	+	0.0474226i
$706$	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	$0.243886\pi$
$710$	557.702	+	81.9063i	0.785496	+	0.115361i
$711$	−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
$715$	−1327.13	−	394.040i	−1.85612	−	0.551105i
$716$	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	$0.328992\pi$
$720$	−63.1916	−	0.190951i	−0.0877660	−	0.000265209i
$721$	−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
$725$	769.124	+	898.532i	1.06086	+	1.23935i
$726$	−2.52034	−	17.5293i	−0.00347154	−	0.0241451i
$727$	−54.3580	−	34.9338i	−0.0747703	−	0.0480519i	0.502722	−	0.864448i	$-0.332332\pi$
$727$	−54.3580	−	34.9338i	−0.0747703	−	0.0480519i	−0.577492	+	0.816396i	$0.695968\pi$
$728$	1314.28	−	385.909i	1.80534	−	0.530095i
$729$	−88.3175	+	614.262i	−0.121149	+	0.842609i
$730$	−612.408	−	396.191i	−0.838916	−	0.542727i
$731$	−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	0.0951311	−	0.995465i	$-0.469673\pi$
$733$	−266.100	−	78.1340i	−0.363028	−	0.106595i	−0.458160	+	0.888870i	$0.651491\pi$
$734$	−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	$-0.832183\pi$
$740$	150.294	−	172.393i	0.203100	−	0.232963i
$741$	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	$-0.772166\pi$
$743$	114.648	−	797.395i	0.154304	−	1.07321i	0.908898	−	0.417018i	$-0.136925\pi$
$744$	20.4058	−	5.99168i	0.0274271	−	0.00805334i
$745$	1144.21	+	526.727i	1.53585	+	0.707016i
$746$	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
$750$	11.7419	−	76.7227i	0.0156559	−	0.102297i
$751$	−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
$755$	275.059	−	315.503i	0.364316	−	0.417885i
$756$	−40.6714	+	138.514i	−0.0537981	+	0.183219i
$757$	358.868	−	785.810i	0.474065	−	1.03806i	−0.509987	−	0.860182i	$-0.670350\pi$
$757$	358.868	−	785.810i	0.474065	−	1.03806i	0.984053	−	0.177877i	$-0.0569228\pi$
$758$	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
$765$	−486.467	−	314.714i	−0.635904	−	0.411391i
$766$	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	$0.475557\pi$
$770$	494.202	−	315.498i	0.641820	−	0.409738i
$771$	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	0.699054	−	0.715069i	$-0.253605\pi$
$773$	262.048	+	168.408i	0.339002	+	0.217863i	−0.360052	+	0.932932i	$0.617241\pi$
$774$	193.195	+	657.962i	0.249606	+	0.850081i
$775$	−18.5058	−	134.475i	−0.0238785	−	0.173516i
$776$	−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
$780$	119.578	+	35.5042i	0.153306	+	0.0455183i
$781$			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
$785$	−122.952	+	837.185i	−0.156627	+	1.06648i
$786$	95.4517	+	110.157i	0.121440	+	0.140149i
$787$	341.777	−	219.647i	0.434278	−	0.279093i	−0.305182	−	0.952294i	$-0.598717\pi$
$787$	341.777	−	219.647i	0.434278	−	0.279093i	0.739460	+	0.673201i	$0.235081\pi$
$788$	92.2666	+	79.9495i	0.117090	+	0.101459i
$789$	−55.9163	−	8.03955i	−0.0708698	−	0.0101895i
$790$	−219.646	−	484.829i	−0.278033	−	0.613708i
$791$	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
$795$	−39.1530	−	134.849i	−0.0492490	−	0.169621i
$796$	−269.266	+	418.986i	−0.338274	+	0.526365i
$797$	−638.975	+	187.620i	−0.801725	+	0.235408i	−0.656830	−	0.754039i	$-0.728103\pi$
$797$	−638.975	+	187.620i	−0.801725	+	0.235408i	−0.144896	+	0.989447i	$0.546285\pi$
$798$	−35.7904	−	5.14588i	−0.0448501	−	0.00644847i
$799$	153.522	+	133.027i	0.192142	+	0.166492i
$800$	581.627	+	510.170i	0.727034	+	0.637712i
$801$	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
$805$	−307.604	+	790.082i	−0.382116	+	0.981468i
$806$	−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	$-0.508451\pi$
$810$	−369.108	+	317.887i	−0.455689	+	0.392453i
$811$	−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
$815$	−170.243	−	586.342i	−0.208887	−	0.719438i
$816$	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
$820$	−190.795	−	421.145i	−0.232676	−	0.513592i
$821$	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	0.875142	−	0.483866i	$-0.160768\pi$
$823$	58.8076	+	91.5064i	0.0714551	+	0.111186i	−0.803687	+	0.595052i	$0.797131\pi$
$824$	−974.324	+	844.256i	−1.18243	+	1.02458i
$825$	145.925	+	0.881913i	0.176879	+	0.00106899i
$826$	430.518	+	196.611i	0.521208	+	0.238028i
$827$	−91.9080			−0.111134			−0.0555671	−	0.998455i	$-0.517697\pi$
$827$	−91.9080			−0.111134			−0.0555671	+	0.998455i	$0.517697\pi$
$828$	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	$0.327872\pi$
$830$	−169.903	+	572.232i	−0.204702	+	0.689437i
$831$	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
$835$	0.763748	−	252.748i	0.000914668	−	0.302693i
$836$	−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	$0.454473\pi$
$840$	−121.701	+	77.6939i	−0.144882	+	0.0924928i
$841$	−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
$845$	−1442.94	−	933.493i	−1.70762	−	1.10472i
$846$	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	−0.0745938	−	0.997214i	$-0.523766\pi$
$853$	−748.155	−	341.671i	−0.877086	−	0.400552i	−0.802493	+	0.596662i	$0.796493\pi$
$854$	−2.08691	−	0.612771i	−0.00244368	−	0.000717531i
$855$	261.131	+	227.657i	0.305417	+	0.266265i
$856$	373.919	+	581.829i	0.436821	+	0.679707i
$857$	891.440	+	772.437i	1.04019	+	0.901326i	0.995220	−	0.0976621i	$-0.0311364\pi$
$857$	891.440	+	772.437i	1.04019	+	0.901326i	0.0449665	+	0.998988i	$0.485682\pi$
$858$	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	$0.545911\pi$
$860$	290.014	−	629.997i	0.337225	−	0.732555i
$861$	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	−0.999317	−	0.0369620i	$-0.988232\pi$
$863$	−1403.06	+	640.757i	−1.62580	+	0.742476i	−0.626479	+	0.779438i	$0.715505\pi$
$864$	37.3638	+	259.871i	0.0432452	+	0.300777i
$865$	275.829	+	126.975i	0.318877	+	0.146792i
$866$	−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
$870$	−96.5217	+	110.714i	−0.110944	+	0.127258i
$871$	−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	$0.387812\pi$
$877$	−396.938	+	1351.85i	−0.452609	+	1.54145i	−0.797805	+	0.602915i	$0.794006\pi$
$878$	161.134	−	139.623i	0.183524	−	0.159024i
$879$	0.337861	+	0.525723i	0.000384370	+	0.000598092i
$880$	47.8467	−	73.9585i	0.0543712	−	0.0840438i
$881$	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	−0.988726	−	0.149736i	$-0.952158\pi$
$883$	−390.100	+	607.008i	−0.441789	+	0.687438i	0.546937	+	0.837174i	$0.315794\pi$
$884$	683.339	−	98.2493i	0.773008	−	0.111142i
$885$	63.3851	+	99.2875i	0.0716215	+	0.112189i
$886$	209.820	+	459.441i	0.236817	+	0.518557i
$887$	965.187	−	138.773i	1.08815	−	0.156452i	0.425187	−	0.905106i	$-0.360208\pi$
$887$	965.187	−	138.773i	1.08815	−	0.156452i	0.662961	+	0.748654i	$0.269299\pi$
$888$	65.3026	+	41.9674i	0.0735389	+	0.0472606i
$889$	399.685	+	1361.20i	0.449589	+	1.53116i
$890$	65.8448	+	0.198968i	0.0739829	+	0.000223559i
$891$	−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
$895$	79.3386	+	23.5566i	0.0886465	+	0.0263202i
$896$		−	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
$900$	506.153	+	3.05898i	0.562392	+	0.00339887i
$901$	−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
$905$	−446.831	+	202.431i	−0.493736	+	0.223681i
$906$	43.7285	+	28.1026i	0.0482654	+	0.0310183i
$907$	−117.628	−	818.124i	−0.129690	−	0.902011i	−0.945947	−	0.324322i	$-0.894864\pi$
$907$	−117.628	−	818.124i	−0.129690	−	0.902011i	0.816257	−	0.577689i	$-0.196045\pi$
$908$	414.187	+	906.942i	0.456153	+	0.998835i
$909$	−241.968	−	529.835i	−0.266191	−	0.582877i
$910$	1042.67	−	302.737i	1.14579	−	0.332678i
$911$	−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
$915$	−0.353258	−	0.410180i	−0.000386075	−	0.000448284i
$916$	−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	$0.625521\pi$
$920$	53.8722	+	942.059i	0.0585568	+	1.02398i
$921$	−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
$925$	326.714	−	372.475i	0.353204	−	0.402676i
$926$	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	$0.718073\pi$
$930$	16.1887	−	4.70034i	0.0174072	−	0.00505413i
$931$	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
$935$	735.668	−	333.285i	0.786810	−	0.356455i
$936$	231.943	−	1613.20i	0.247803	−	1.72350i
$937$	668.815	−	771.854i	0.713784	−	0.823750i	−0.276761	−	0.960939i	$-0.589261\pi$
$937$	668.815	−	771.854i	0.713784	−	0.823750i	0.990545	+	0.137188i	$0.0438066\pi$
$938$	−61.7765	−	96.1262i	−0.0658598	−	0.102480i
$939$	171.501	−	148.606i	0.182642	−	0.158260i
$940$	−175.580	−	25.7864i	−0.186787	−	0.0274323i
$941$	−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
$945$	−89.0141	+	299.800i	−0.0941948	+	0.317249i
$946$	−917.165	−	269.304i	−0.969519	−	0.284676i
$947$	−946.355	+	820.021i	−0.999318	+	0.865914i	−0.990974	−	0.134051i	$-0.957201\pi$
$947$	−946.355	+	820.021i	−0.999318	+	0.865914i	−0.00834397	+	0.999965i	$0.502656\pi$
$948$	−75.8542	+	48.7486i	−0.0800150	+	0.0514225i
$949$	1662.96	−	1919.16i	1.75233	−	2.02230i
$950$	35.0166	+	254.453i	0.0368595	+	0.267845i
$951$	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	$-0.959648\pi$
$953$	−72.2388	−	502.432i	−0.0758014	−	0.527211i	0.916174	−	0.400781i	$-0.131261\pi$
$954$	−610.619	+	278.860i	−0.640062	+	0.292306i
$955$	333.394	+	522.234i	0.349103	+	0.546842i
$956$	−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
$960$	−59.6594	+	92.2180i	−0.0621452	+	0.0960604i
$961$	−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	$0.0534612\pi$
$967$			323.297i			0.334329i	−0.985929	+	0.167165i	$0.946539\pi$
$968$	212.874	+	97.2162i	0.219911	+	0.100430i
$969$	−47.7896	−	14.0323i	−0.0493184	−	0.0144812i
$970$	−565.418	−	492.937i	−0.582905	−	0.508182i
$971$	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
$975$	258.813	+	77.6965i	0.265450	+	0.0796887i
$976$	−0.323436	+	0.0465031i	−0.000331390	+	4.76466e-5i
$977$	2.43608	+	5.33427i	0.00249343	+	0.00545985i	0.910875	−	0.412683i	$-0.135408\pi$
$977$	2.43608	+	5.33427i	0.00249343	+	0.00545985i	−0.908381	+	0.418143i	$0.862681\pi$
$978$	68.9704	−	31.4977i	0.0705219	−	0.0322063i
$979$	17.6182	+	122.537i	0.0179961	+	0.125165i
$980$	25.8432	−	56.1391i	0.0263706	−	0.0572848i
$981$	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	$0.484259\pi$
$983$	−930.128	+	1073.42i	−0.946213	+	1.09199i	−0.995646	+	0.0932109i	$0.970287\pi$
$984$	132.013	−	84.8398i	0.134160	−	0.0862193i
$985$	199.356	+	173.801i	0.202392	+	0.176447i
$986$	−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
$995$	−586.061	+	905.898i	−0.589006	+	0.910450i
$996$	100.093	+	14.3911i	0.100495	+	0.0144489i
$997$	101.714	+	346.405i	0.102020	+	0.347448i	0.994645	−	0.103352i	$-0.0329569\pi$
$997$	101.714	+	346.405i	0.102020	+	0.347448i	−0.892625	+	0.450800i	$0.851139\pi$
$998$	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.109.7	yes	220
5.4	even	2	inner	115.3.i.a.109.16	yes	220
23.19	odd	22	inner	115.3.i.a.19.16	yes	220
115.19	odd	22	inner	115.3.i.a.19.7	✓	220

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

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} +(-3.26287 - 3.78862i) 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} +(1.81346 + 6.24582i) 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} +(2.17410 - 0.984949i) 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} +(-1.67686 + 11.4178i) q^{20} +(-3.20135 - 1.46201i) q^{21} +15.9054 q^{22} +(-18.5664 + 13.5753i) q^{23} -3.91684 q^{24} +(-3.70736 + 24.7236i) 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} +(-3.10462 - 0.00938147i) 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} +(31.0712 - 19.8359i) 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} +(22.2845 - 34.4461i) 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} +(17.7460 - 27.2498i) 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} +(55.5374 + 25.5662i) 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} +(-5.00409 - 2.30359i) 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} +(85.3384 + 74.3989i) 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} +(-10.8254 - 5.02309i) 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} +(-6.07189 + 3.87629i) 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} +(-66.0489 - 0.199585i) 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} +(-16.2387 + 54.6920i) q^{90} -166.939i q^{91} +(51.7416 + 11.8671i) q^{92} -2.59193i q^{93} +(8.30943 - 18.1951i) q^{94} +(39.0736 + 5.73850i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more