LMFDB - Embedded newform 325.3.bm.a.6.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(6,325)] 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("325.6"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([24, 25])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.bm (of order $60$, degree $16$, 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:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$1088$
Relative dimension:	$68$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			6.5
Character	$\chi$	$=$	325.6
Dual form			325.3.bm.a.271.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.90131 + 1.88413i) q^{2} +(-0.428913 - 4.08083i) q^{3} +(3.24070 - 7.27873i) q^{4} +(-2.87751 + 4.08900i) q^{5} +(8.93325 + 11.0316i) q^{6} +(3.13792 - 11.7109i) q^{7} +(2.14713 + 13.5565i) q^{8} +(-7.66591 + 1.62944i) q^{9} +(0.644328 - 17.2851i) q^{10} +(-11.2248 - 17.2847i) q^{11} +(-31.0933 - 10.1028i) q^{12} +(12.8246 + 2.12857i) q^{13} +(12.9608 + 39.8892i) q^{14} +(17.9207 + 9.98882i) q^{15} +(-10.4464 - 11.6018i) q^{16} +(19.4329 + 2.04248i) q^{17} +(19.1711 - 19.1711i) q^{18} +(-3.43568 - 4.24271i) q^{19} +(20.4376 + 34.1959i) q^{20} +(-49.1361 - 7.78239i) q^{21} +(65.1333 + 28.9992i) q^{22} +(-0.844542 + 3.97326i) q^{23} +(54.4008 - 14.5766i) q^{24} +(-8.43987 - 23.5323i) q^{25} +(-41.2185 + 17.9875i) q^{26} +(-1.47446 - 4.53792i) q^{27} +(-75.0713 - 60.7916i) q^{28} +(3.15321 + 30.0008i) q^{29} +(-70.8139 + 4.78440i) q^{30} +(-8.31173 + 1.31645i) q^{31} +(-0.863560 - 0.231390i) q^{32} +(-65.7215 + 53.2202i) q^{33} +(-60.2293 + 30.6883i) q^{34} +(38.8564 + 46.5292i) q^{35} +(-12.9827 + 61.0786i) q^{36} +(1.90164 - 36.2855i) q^{37} +(17.9618 + 5.83615i) q^{38} +(3.18571 - 53.2478i) q^{39} +(-61.6109 - 30.2293i) q^{40} +(-57.6009 - 3.01874i) q^{41} +(157.222 - 69.9998i) q^{42} +(-14.0764 + 8.12700i) q^{43} +(-162.187 + 25.6879i) q^{44} +(15.3960 - 36.0346i) q^{45} +(-5.03587 - 13.1189i) q^{46} +(15.3312 + 2.42823i) q^{47} +(-42.8646 + 47.6060i) q^{48} +(-84.8630 - 48.9957i) q^{49} +(68.8247 + 52.3727i) q^{50} -80.1786i q^{51} +(57.0538 - 86.4485i) q^{52} +(-11.7339 + 8.52520i) q^{53} +(12.8279 + 10.3878i) q^{54} +(102.977 + 3.83861i) q^{55} +(165.496 + 17.3943i) q^{56} +(-15.8402 + 15.8402i) q^{57} +(-65.6740 - 81.1006i) q^{58} +(-39.5348 - 25.6742i) q^{59} +(130.782 - 98.0695i) q^{60} +(26.5815 - 29.5218i) q^{61} +(21.6345 - 19.4798i) q^{62} +(-4.97285 + 94.8876i) q^{63} +(62.3323 - 20.2530i) q^{64} +(-45.6065 + 46.3146i) q^{65} +(90.4045 - 278.236i) q^{66} +(-12.9714 + 33.7917i) q^{67} +(77.8430 - 134.828i) q^{68} +(16.5764 + 1.74225i) q^{69} +(-200.402 - 61.7849i) q^{70} +(-30.0399 + 11.5312i) q^{71} +(-38.5492 - 100.424i) q^{72} +(-38.8195 + 76.1875i) q^{73} +(62.8495 + 108.858i) q^{74} +(-92.4114 + 44.5350i) q^{75} +(-42.0156 + 11.2580i) q^{76} +(-237.642 + 77.2144i) q^{77} +(91.0833 + 160.491i) q^{78} +(-90.2677 + 65.5833i) q^{79} +(77.4995 - 9.33071i) q^{80} +(-82.3226 + 36.6524i) q^{81} +(172.806 - 99.7695i) q^{82} +(128.231 - 20.3098i) q^{83} +(-215.881 + 332.428i) q^{84} +(-64.2701 + 73.5840i) q^{85} +(25.5276 - 50.1007i) q^{86} +(121.076 - 25.7355i) q^{87} +(210.218 - 189.281i) q^{88} +(-31.2480 - 48.1176i) q^{89} +(23.2256 + 133.556i) q^{90} +(65.1699 - 143.508i) q^{91} +(26.1834 + 19.0233i) q^{92} +(8.93722 + 33.3541i) q^{93} +(-49.0558 + 21.8410i) q^{94} +(27.2347 - 1.84006i) q^{95} +(-0.573873 + 3.62329i) q^{96} +(-12.2995 + 4.72135i) q^{97} +(338.528 - 17.7415i) q^{98} +(114.213 + 114.213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1088 q - 16 q^{2} - 6 q^{3} - 18 q^{4} - 6 q^{5} - 28 q^{6} - 32 q^{7} - 44 q^{8} + 378 q^{9} - 54 q^{10} - 12 q^{11} + 44 q^{13} - 24 q^{14} + 54 q^{15} - 382 q^{16} - 66 q^{17} - 500 q^{18} + 48 q^{19}+ \cdots - 792 q^{99}+O(q^{100}) $ 1088 * q - 16 * q^2 - 6 * q^3 - 18 * q^4 - 6 * q^5 - 28 * q^6 - 32 * q^7 - 44 * q^8 + 378 * q^9 - 54 * q^10 - 12 * q^11 + 44 * q^13 - 24 * q^14 + 54 * q^15 - 382 * q^16 - 66 * q^17 - 500 * q^18 + 48 * q^19 - 66 * q^20 + 42 * q^21 + 196 * q^22 - 18 * q^23 - 36 * q^24 - 12 * q^26 - 76 * q^28 + 94 * q^29 - 216 * q^30 - 12 * q^31 - 152 * q^32 - 222 * q^33 + 64 * q^34 - 82 * q^35 - 126 * q^36 - 210 * q^37 - 288 * q^39 - 432 * q^40 - 462 * q^41 + 222 * q^42 - 48 * q^43 + 36 * q^44 - 458 * q^45 - 396 * q^46 - 186 * q^47 - 334 * q^48 - 48 * q^49 + 106 * q^50 - 122 * q^52 + 12 * q^53 - 940 * q^54 + 130 * q^55 + 714 * q^56 - 252 * q^57 - 312 * q^58 - 132 * q^59 + 132 * q^60 + 294 * q^61 + 198 * q^62 + 1192 * q^63 + 338 * q^65 + 384 * q^66 - 236 * q^67 - 236 * q^68 - 648 * q^69 - 1114 * q^70 - 92 * q^71 + 546 * q^72 + 928 * q^73 + 164 * q^74 + 132 * q^75 + 620 * q^76 - 1742 * q^78 + 216 * q^79 - 540 * q^80 + 806 * q^81 + 3132 * q^82 + 874 * q^83 + 496 * q^84 + 514 * q^85 - 276 * q^86 + 74 * q^87 - 2394 * q^88 - 672 * q^89 + 308 * q^91 + 1960 * q^92 + 1008 * q^93 + 474 * q^94 + 2328 * q^95 - 1626 * q^96 + 632 * q^97 + 84 * q^98 - 792 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−2.90131	+	1.88413i	−1.45066	+	0.942067i	−0.451906	+	0.892065i	$0.649256\pi$
$2$	−2.90131	+	1.88413i	−1.45066	+	0.942067i	−0.998749	+	0.0500013i	$0.984077\pi$
$3$	−0.428913	−	4.08083i	−0.142971	−	1.36028i	−0.797078	−	0.603876i	$-0.793622\pi$
$3$	−0.428913	−	4.08083i	−0.142971	−	1.36028i	0.654107	−	0.756402i	$-0.273045\pi$
$4$	3.24070	−	7.27873i	0.810175	−	1.81968i
$5$	−2.87751	+	4.08900i	−0.575502	+	0.817800i
$5$	−2.87751	+	4.08900i	−0.575502	+	0.817800i
$6$	8.93325	+	11.0316i	1.48887	+	1.83861i
$7$	3.13792	−	11.7109i	0.448275	−	1.67298i	−0.258868	−	0.965913i	$-0.583350\pi$
$7$	3.13792	−	11.7109i	0.448275	−	1.67298i	0.707143	−	0.707071i	$-0.249984\pi$
$8$	2.14713	+	13.5565i	0.268392	+	1.69456i
$9$	−7.66591	+	1.62944i	−0.851768	+	0.181049i
$10$	0.644328	−	17.2851i	0.0644328	−	1.72851i
$11$	−11.2248	−	17.2847i	−1.02044	−	1.57133i	−0.803638	−	0.595119i	$-0.797105\pi$
$11$	−11.2248	−	17.2847i	−1.02044	−	1.57133i	−0.216799	−	0.976216i	$-0.569562\pi$
$12$	−31.0933	−	10.1028i	−2.59111	−	0.841901i
$13$	12.8246	+	2.12857i	0.986504	+	0.163736i
$13$	12.8246	+	2.12857i	0.986504	+	0.163736i
$14$	12.9608	+	39.8892i	0.925770	+	2.84923i
$15$	17.9207	+	9.98882i	1.19472	+	0.665921i
$16$	−10.4464	−	11.6018i	−0.652897	−	0.725116i
$17$	19.4329	+	2.04248i	1.14311	+	0.120146i	0.657098	−	0.753805i	$-0.271784\pi$
$17$	19.4329	+	2.04248i	1.14311	+	0.120146i	0.486014	+	0.873951i	$0.338450\pi$
$18$	19.1711	−	19.1711i	1.06506	−	1.06506i
$19$	−3.43568	−	4.24271i	−0.180825	−	0.223301i	0.678671	−	0.734442i	$-0.262556\pi$
$19$	−3.43568	−	4.24271i	−0.180825	−	0.223301i	−0.859497	+	0.511142i	$0.829223\pi$
$20$	20.4376	+	34.1959i	1.02188	+	1.70979i
$21$	−49.1361	−	7.78239i	−2.33981	−	0.370590i
$22$	65.1333	+	28.9992i	2.96060	+	1.31815i
$23$	−0.844542	+	3.97326i	−0.0367192	+	0.172750i	−0.992686	−	0.120724i	$-0.961478\pi$
$23$	−0.844542	+	3.97326i	−0.0367192	+	0.172750i	0.955967	+	0.293475i	$0.0948116\pi$
$24$	54.4008	−	14.5766i	2.26670	−	0.607360i
$25$	−8.43987	−	23.5323i	−0.337595	−	0.941292i
$26$	−41.2185	+	17.9875i	−1.58533	+	0.691828i
$27$	−1.47446	−	4.53792i	−0.0546096	−	0.168071i
$28$	−75.0713	−	60.7916i	−2.68112	−	2.17113i
$29$	3.15321	+	30.0008i	0.108731	+	1.03451i	0.903790	+	0.427977i	$0.140774\pi$
$29$	3.15321	+	30.0008i	0.108731	+	1.03451i	−0.795058	+	0.606533i	$0.792560\pi$
$30$	−70.8139	+	4.78440i	−2.36046	+	0.159480i
$31$	−8.31173	+	1.31645i	−0.268120	+	0.0424661i	−0.289047	−	0.957315i	$-0.593338\pi$
$31$	−8.31173	+	1.31645i	−0.268120	+	0.0424661i	0.0209266	+	0.999781i	$0.493338\pi$
$32$	−0.863560	−	0.231390i	−0.0269862	−	0.00723094i
$33$	−65.7215	+	53.2202i	−1.99156	+	1.61273i
$34$	−60.2293	+	30.6883i	−1.77145	+	0.902598i
$35$	38.8564	+	46.5292i	1.11018	+	1.32940i
$36$	−12.9827	+	61.0786i	−0.360630	+	1.69663i
$37$	1.90164	−	36.2855i	0.0513957	−	0.980689i	−0.844258	−	0.535937i	$-0.819958\pi$
$37$	1.90164	−	36.2855i	0.0513957	−	0.980689i	0.895654	−	0.444752i	$-0.146708\pi$
$38$	17.9618	+	5.83615i	0.472679	+	0.153583i
$39$	3.18571	−	53.2478i	0.0816850	−	1.36533i
$40$	−61.6109	−	30.2293i	−1.54027	−	0.755732i
$41$	−57.6009	−	3.01874i	−1.40490	−	0.0736277i	−0.665251	−	0.746620i	$-0.731675\pi$
$41$	−57.6009	−	3.01874i	−1.40490	−	0.0736277i	−0.739650	+	0.672992i	$0.765009\pi$
$42$	157.222	−	69.9998i	3.74338	−	1.66666i
$43$	−14.0764	+	8.12700i	−0.327357	+	0.189000i	−0.654667	−	0.755917i	$-0.727191\pi$
$43$	−14.0764	+	8.12700i	−0.327357	+	0.189000i	0.327310	+	0.944917i	$0.393858\pi$
$44$	−162.187	+	25.6879i	−3.68606	+	0.583815i
$45$	15.3960	−	36.0346i	0.342132	−	0.800770i
$46$	−5.03587	−	13.1189i	−0.109475	−	0.285193i
$47$	15.3312	+	2.42823i	0.326196	+	0.0516644i	0.317385	−	0.948297i	$-0.397195\pi$
$47$	15.3312	+	2.42823i	0.326196	+	0.0516644i	0.00881133	+	0.999961i	$0.497195\pi$
$48$	−42.8646	+	47.6060i	−0.893013	+	0.991792i
$49$	−84.8630	−	48.9957i	−1.73190	−	0.999912i
$50$	68.8247	+	52.3727i	1.37649	+	1.04745i
$51$		−	80.1786i		−	1.57213i
$52$	57.0538	−	86.4485i	1.09719	−	1.66247i
$53$	−11.7339	+	8.52520i	−0.221395	+	0.160853i	−0.692954	−	0.720981i	$-0.743691\pi$
$53$	−11.7339	+	8.52520i	−0.221395	+	0.160853i	0.471559	+	0.881834i	$0.343691\pi$
$54$	12.8279	+	10.3878i	0.237554	+	0.192367i
$55$	102.977	+	3.83861i	1.87230	+	0.0697930i
$56$	165.496	+	17.3943i	2.95528	+	0.310613i
$57$	−15.8402	+	15.8402i	−0.277898	+	0.277898i
$58$	−65.6740	−	81.1006i	−1.13231	−	1.39829i
$59$	−39.5348	−	25.6742i	−0.670082	−	0.435156i	0.164250	−	0.986419i	$-0.447480\pi$
$59$	−39.5348	−	25.6742i	−0.670082	−	0.435156i	−0.834332	+	0.551263i	$0.814146\pi$
$60$	130.782	−	98.0695i	2.17969	−	1.63449i
$61$	26.5815	−	29.5218i	0.435762	−	0.483963i	−0.484763	−	0.874645i	$-0.661094\pi$
$61$	26.5815	−	29.5218i	0.435762	−	0.483963i	0.920526	+	0.390682i	$0.127761\pi$
$62$	21.6345	−	19.4798i	0.348944	−	0.314191i
$63$	−4.97285	+	94.8876i	−0.0789341	+	1.50615i
$64$	62.3323	−	20.2530i	0.973943	−	0.316453i
$65$	−45.6065	+	46.3146i	−0.701639	+	0.712533i
$66$	90.4045	−	278.236i	1.36976	−	4.21570i
$67$	−12.9714	+	33.7917i	−0.193603	+	0.504354i	−0.995678	−	0.0928694i	$-0.970396\pi$
$67$	−12.9714	+	33.7917i	−0.193603	+	0.504354i	0.802075	+	0.597223i	$0.203729\pi$
$68$	77.8430	−	134.828i	1.14475	−	1.98276i
$69$	16.5764	+	1.74225i	0.240238	+	0.0252501i
$70$	−200.402	−	61.7849i	−2.86288	−	0.882641i
$71$	−30.0399	+	11.5312i	−0.423098	+	0.162412i	−0.560595	−	0.828090i	$-0.689427\pi$
$71$	−30.0399	+	11.5312i	−0.423098	+	0.162412i	0.137497	+	0.990502i	$0.456094\pi$
$72$	−38.5492	−	100.424i	−0.535406	−	1.39478i
$73$	−38.8195	+	76.1875i	−0.531774	+	1.04366i	0.456320	+	0.889815i	$0.349167\pi$
$73$	−38.8195	+	76.1875i	−0.531774	+	1.04366i	−0.988094	+	0.153849i	$0.950833\pi$
$74$	62.8495	+	108.858i	0.849317	+	1.47106i
$75$	−92.4114	+	44.5350i	−1.23215	+	0.593800i
$76$	−42.0156	+	11.2580i	−0.552837	+	0.148132i
$77$	−237.642	+	77.2144i	−3.08625	+	1.00278i
$78$	91.0833	+	160.491i	1.16773	+	2.05758i
$79$	−90.2677	+	65.5833i	−1.14263	+	0.830169i	−0.987483	−	0.157723i	$-0.949585\pi$
$79$	−90.2677	+	65.5833i	−1.14263	+	0.830169i	−0.155146	+	0.987892i	$0.549585\pi$
$80$	77.4995	−	9.33071i	0.968743	−	0.116634i
$81$	−82.3226	+	36.6524i	−1.01633	+	0.452498i
$82$	172.806	−	99.7695i	2.10739	−	1.21670i
$83$	128.231	−	20.3098i	1.54495	−	0.244696i	0.674993	−	0.737825i	$-0.264147\pi$
$83$	128.231	−	20.3098i	1.54495	−	0.244696i	0.869956	+	0.493129i	$0.164147\pi$
$84$	−215.881	+	332.428i	−2.57001	+	3.95748i
$85$	−64.2701	+	73.5840i	−0.756119	+	0.865694i
$86$	25.5276	−	50.1007i	0.296832	−	0.582566i
$87$	121.076	−	25.7355i	1.39168	−	0.295810i
$88$	210.218	−	189.281i	2.38884	−	2.15092i
$89$	−31.2480	−	48.1176i	−0.351101	−	0.540648i	0.618360	−	0.785895i	$-0.287797\pi$
$89$	−31.2480	−	48.1176i	−0.351101	−	0.540648i	−0.969460	+	0.245248i	$0.921131\pi$
$90$	23.2256	+	133.556i	0.258063	+	1.48395i
$91$	65.1699	−	143.508i	0.716152	−	1.57701i
$92$	26.1834	+	19.0233i	0.284602	+	0.206775i
$93$	8.93722	+	33.3541i	0.0960991	+	0.358647i
$94$	−49.0558	+	21.8410i	−0.521870	+	0.232351i
$95$	27.2347	−	1.84006i	0.286681	−	0.0193690i
$96$	−0.573873	+	3.62329i	−0.00597784	+	0.0377426i
$97$	−12.2995	+	4.72135i	−0.126799	+	0.0486738i	−0.420940	−	0.907088i	$-0.638300\pi$
$97$	−12.2995	+	4.72135i	−0.126799	+	0.0486738i	0.294141	+	0.955762i	$0.404967\pi$
$98$	338.528	−	17.7415i	3.45437	−	0.181036i
$99$	114.213	+	114.213i	1.15366	+	1.15366i
$100$	−198.636	−	14.8296i	−1.98636	−	0.148296i
$101$	62.7915	+	36.2527i	0.621698	+	0.358937i	0.777530	−	0.628846i	$-0.216472\pi$
$101$	62.7915	+	36.2527i	0.621698	+	0.358937i	−0.155832	+	0.987784i	$0.549806\pi$
$102$	151.067	+	232.623i	1.48105	+	2.28062i
$103$	−18.8159	−	25.8979i	−0.182679	−	0.251436i	0.707850	−	0.706363i	$-0.249665\pi$
$103$	−18.8159	−	25.8979i	−0.182679	−	0.251436i	−0.890529	+	0.454927i	$0.849665\pi$
$104$	−1.31983	+	178.426i	−0.0126907	+	1.71564i
$105$	173.212	−	178.524i	1.64964	−	1.70022i
$106$	17.9812	−	46.8426i	0.169634	−	0.441911i
$107$	51.0191	−	88.3677i	0.476814	−	0.825866i	−0.522833	−	0.852435i	$-0.675125\pi$
$107$	51.0191	−	88.3677i	0.476814	−	0.825866i	0.999647	+	0.0265688i	$0.00845811\pi$
$108$	−37.8086	−	3.97384i	−0.350079	−	0.0367948i
$109$	48.2014	+	94.6006i	0.442215	+	0.867895i	0.999299	+	0.0374391i	$0.0119200\pi$
$109$	48.2014	+	94.6006i	0.442215	+	0.867895i	−0.557084	+	0.830456i	$0.688080\pi$
$110$	−306.000	+	182.885i	−2.78181	+	1.66259i
$111$	−148.891	+	7.80303i	−1.34136	+	0.0702976i
$112$	−168.648	+	85.9303i	−1.50578	+	0.767235i
$113$	−6.80250	+	1.44592i	−0.0601991	+	0.0127957i	−0.237913	−	0.971287i	$-0.576463\pi$
$113$	−6.80250	+	1.44592i	−0.0601991	+	0.0127957i	0.177714	+	0.984082i	$0.443130\pi$
$114$	16.1123	−	75.8024i	0.141336	−	0.664933i
$115$	−13.8165	−	14.8864i	−0.120143	−	0.129447i
$116$	228.586	+	74.2722i	1.97057	+	0.640278i
$117$	−101.780	+	4.57943i	−0.869917	+	0.0391404i
$118$	163.076			1.38200
$119$	84.8983	−	221.168i	0.713431	−	1.85855i
$120$	−96.9349	+	264.389i	−0.807791	+	2.20324i
$121$	−123.549	+	277.495i	−1.02107	+	2.29335i
$122$	−21.4983	+	135.735i	−0.176216	+	1.11258i
$123$	12.3868	+	236.355i	0.100706	+	1.92158i
$124$	−17.3537	+	64.7651i	−0.139950	+	0.522299i
$125$	120.509	+	33.2038i	0.964075	+	0.265630i
$126$	−164.353	−	284.668i	−1.30439	−	2.25927i
$127$	10.6530	−	50.1184i	0.0838819	−	0.394633i	−0.916098	−	0.400954i	$-0.868679\pi$
$127$	10.6530	−	50.1184i	0.0838819	−	0.394633i	0.999980	+	0.00632082i	$0.00201199\pi$
$128$	−140.436	+	173.424i	−1.09715	+	1.35487i
$129$	39.2025	+	53.9576i	0.303895	+	0.418276i
$130$	45.0557	−	220.302i	0.346582	−	1.69463i
$131$	80.3982	+	58.4127i	0.613726	+	0.445898i	0.850725	−	0.525612i	$-0.176164\pi$
$131$	80.3982	+	58.4127i	0.613726	+	0.445898i	−0.236998	+	0.971510i	$0.576164\pi$
$132$	174.392	+	650.840i	1.32115	+	4.93060i
$133$	−60.4668	+	26.9216i	−0.454638	+	0.202418i
$134$	−26.0340	−	122.480i	−0.194283	−	0.914031i
$135$	22.7983	+	7.02884i	0.168876	+	0.0520655i
$136$	14.0362	+	267.827i	0.103208	+	1.96932i
$137$	−209.429	−	136.005i	−1.52868	−	0.992737i	−0.988506	−	0.151184i	$-0.951692\pi$
$137$	−209.429	−	136.005i	−1.52868	−	0.992737i	−0.540175	−	0.841553i	$-0.681642\pi$
$138$	−51.3761	+	26.1774i	−0.372290	+	0.189691i
$139$	16.6296	−	18.4690i	0.119637	−	0.132871i	−0.680351	−	0.732887i	$-0.738173\pi$
$139$	16.6296	−	18.4690i	0.119637	−	0.132871i	0.799988	+	0.600016i	$0.204839\pi$
$140$	464.595	−	132.038i	3.31854	−	0.943132i
$141$	3.33343	−	63.6057i	0.0236414	−	0.451104i
$142$	65.4288	−	90.0550i	0.460766	−	0.634190i
$143$	−107.162	−	245.561i	−0.749381	−	1.71721i
$144$	98.9853	+	71.9170i	0.687398	+	0.499424i
$145$	−131.747	−	73.4341i	−0.908598	−	0.506442i
$146$	−30.9201	−	294.185i	−0.211781	−	2.01496i
$147$	−163.544	+	367.327i	−1.11255	+	2.49882i
$148$	−257.950	−	131.432i	−1.74290	−	0.888054i
$149$	119.767	+	32.0915i	0.803806	+	0.215379i	0.637255	−	0.770653i	$-0.280070\pi$
$149$	119.767	+	32.0915i	0.803806	+	0.215379i	0.166552	+	0.986033i	$0.446737\pi$
$150$	184.204	−	303.325i	1.22803	−	2.02217i
$151$	109.137	+	109.137i	0.722760	+	0.722760i	0.969167	−	0.246406i	$-0.0792498\pi$
$151$	109.137	+	109.137i	0.722760	+	0.722760i	−0.246406	+	0.969167i	$0.579250\pi$
$152$	50.1394	−	55.6854i	0.329864	−	0.366351i
$153$	−152.299	+	16.0073i	−0.995419	+	0.104623i
$154$	543.990	−	671.771i	3.53240	−	4.36215i
$155$	18.5341	−	37.7748i	0.119575	−	0.243708i
$156$	−377.253	−	195.748i	−2.41829	−	1.25480i
$157$	210.367			1.33992			0.669958	−	0.742399i	$-0.266312\pi$
$157$	210.367			1.33992			0.669958	+	0.742399i	$0.266312\pi$
$158$	138.327	−	360.354i	0.875487	−	2.28072i
$159$	39.8228	+	44.2277i	0.250458	+	0.278161i
$160$	3.43106	−	2.86527i	0.0214441	−	0.0179079i
$161$	43.8803	+	22.3581i	0.272548	+	0.138870i
$162$	169.785	−	261.447i	1.04806	−	1.61387i
$163$	130.722	+	84.8922i	0.801978	+	0.520811i	0.879341	−	0.476192i	$-0.157983\pi$
$163$	130.722	+	84.8922i	0.801978	+	0.520811i	−0.0773629	+	0.997003i	$0.524650\pi$
$164$	−208.640	+	409.479i	−1.27219	+	2.49682i
$165$	−28.5033	−	421.877i	−0.172747	−	2.55683i
$166$	−333.771	+	300.529i	−2.01067	+	1.81041i
$167$	−104.343	−	40.0533i	−0.624805	−	0.239840i	0.0253054	−	0.999680i	$-0.491944\pi$
$167$	−104.343	−	40.0533i	−0.624805	−	0.239840i	−0.650111	+	0.759839i	$0.725278\pi$
$168$		−	682.822i		−	4.06442i
$169$	159.938	+	54.5959i	0.946381	+	0.323052i
$170$	47.8256	−	334.584i	0.281327	−	1.96814i
$171$	33.2509	+	26.9260i	0.194450	+	0.157462i
$172$	13.5369	+	128.795i	0.0787031	+	0.748810i
$173$	−143.625	−	129.320i	−0.830200	−	0.747516i	0.139914	−	0.990164i	$-0.455317\pi$
$173$	−143.625	−	129.320i	−0.830200	−	0.747516i	−0.970114	+	0.242648i	$0.921984\pi$
$174$	−302.790	+	302.790i	−1.74017	+	1.74017i
$175$	−302.068	+	24.9958i	−1.72610	+	0.142833i
$176$	−83.2760	+	310.790i	−0.473159	+	1.76585i
$177$	−87.8152	+	172.347i	−0.496131	+	0.973712i
$178$	181.320	+	80.7289i	1.01865	+	0.453533i
$179$	168.843	−	17.7462i	0.943259	−	0.0991405i	0.379602	−	0.925150i	$-0.376061\pi$
$179$	168.843	−	17.7462i	0.943259	−	0.0991405i	0.563657	+	0.826009i	$0.309394\pi$
$180$	−212.393	−	228.841i	−1.17996	−	1.27134i
$181$	197.734	−	272.157i	1.09245	−	1.50363i	0.247425	−	0.968907i	$-0.420416\pi$
$181$	197.734	−	272.157i	1.09245	−	1.50363i	0.845027	−	0.534724i	$-0.179584\pi$
$182$	81.3094	+	539.149i	0.446755	+	2.96236i
$183$	−131.875	−	95.8125i	−0.720626	−	0.523565i
$184$	−55.6767	−	2.91789i	−0.302591	−	0.0158581i
$185$	142.899	+	112.188i	0.772430	+	0.606420i
$186$	−88.7733	−	79.9318i	−0.477276	−	0.429741i
$187$	−182.827	−	358.818i	−0.977685	−	1.91881i
$188$	67.3584	−	103.723i	0.358289	−	0.551717i
$189$	−57.7698	+	3.02759i	−0.305660	+	0.0160190i
$190$	−75.5493	+	56.6523i	−0.397628	+	0.298170i
$191$	−120.439	+	25.6001i	−0.630572	+	0.134032i	−0.512101	−	0.858925i	$-0.671133\pi$
$191$	−120.439	+	25.6001i	−0.630572	+	0.134032i	−0.118471	+	0.992958i	$0.537799\pi$
$192$	−109.384	−	245.681i	−0.569710	−	1.27959i
$193$	−61.0552	+	16.3597i	−0.316348	+	0.0847653i	−0.413499	−	0.910504i	$-0.635694\pi$
$193$	−61.0552	+	16.3597i	−0.316348	+	0.0847653i	0.0971511	+	0.995270i	$0.469027\pi$
$194$	26.7892	−	36.8721i	0.138088	−	0.190062i
$195$	208.564	+	166.248i	1.06956	+	0.852552i
$196$	−631.642	+	458.915i	−3.22266	+	2.34140i
$197$	−14.2881	−	11.5702i	−0.0725282	−	0.0587322i	0.592371	−	0.805665i	$-0.298192\pi$
$197$	−14.2881	−	11.5702i	−0.0725282	−	0.0587322i	−0.664899	+	0.746933i	$0.731525\pi$
$198$	−546.559	−	116.175i	−2.76040	−	0.586740i
$199$	−67.0299	+	38.6997i	−0.336833	+	0.194471i	−0.658871	−	0.752256i	$-0.728966\pi$
$199$	−67.0299	+	38.6997i	−0.336833	+	0.194471i	0.322037	+	0.946727i	$0.395632\pi$
$200$	300.893	−	164.942i	1.50447	−	0.824709i
$201$	143.462	+	38.4405i	0.713741	+	0.191246i
$202$	−250.482	+	13.1272i	−1.24001	+	0.0649863i
$203$	361.230	+	57.2133i	1.77946	+	0.281839i
$204$	−583.598	−	259.835i	−2.86078	−	1.27370i
$205$	178.091	−	226.844i	0.868736	−	1.10656i
$206$	103.386	+	39.6862i	0.501874	+	0.192651i
$207$		−	31.8348i		−	0.153791i
$208$	−109.274	−	171.024i	−0.525358	−	0.822232i
$209$	−34.7691	+	107.008i	−0.166359	+	0.512001i
$210$	−166.179	+	844.306i	−0.791328	+	4.02051i
$211$	−264.501	−	56.2215i	−1.25356	−	0.266453i	−0.467162	−	0.884172i	$-0.654723\pi$
$211$	−264.501	−	56.2215i	−1.25356	−	0.266453i	−0.786399	+	0.617719i	$0.788057\pi$
$212$	24.0265	+	113.036i	0.113333	+	0.533188i
$213$	59.9416	+	117.642i	0.281416	+	0.552310i
$214$	18.4742	+	352.509i	0.0863281	+	1.64724i
$215$	7.27360	−	80.9438i	0.0338307	−	0.376483i
$216$	58.3523	−	29.7320i	0.270150	−	0.137648i
$217$	−10.6648	+	101.469i	−0.0491465	+	0.467597i
$218$	−318.087	−	183.648i	−1.45912	−	0.842421i
$219$	327.559	+	125.738i	1.49570	+	0.574146i
$220$	361.657	−	737.099i	1.64389	−	3.35045i
$221$	244.871	+	67.5582i	1.10801	+	0.305693i
$222$	417.276	−	303.169i	1.87962	−	1.36563i
$223$	81.5212	−	52.9405i	0.365566	−	0.237401i	−0.348764	−	0.937211i	$-0.613398\pi$
$223$	81.5212	−	52.9405i	0.365566	−	0.237401i	0.714330	+	0.699809i	$0.246732\pi$
$224$	−5.41957	+	9.38696i	−0.0241945	+	0.0419061i
$225$	103.044	+	166.644i	0.457972	+	0.740641i
$226$	17.0119	−	17.0119i	0.0752737	−	0.0752737i
$227$	−13.1918	−	251.715i	−0.0581137	−	1.10888i	−0.859635	−	0.510909i	$-0.829309\pi$
$227$	−13.1918	−	251.715i	−0.0581137	−	1.10888i	0.801521	−	0.597967i	$-0.204025\pi$
$228$	63.9632	+	166.630i	0.280540	+	0.730833i
$229$	−79.3411	−	12.5664i	−0.346468	−	0.0548751i	−0.0192243	−	0.999815i	$-0.506120\pi$
$229$	−79.3411	−	12.5664i	−0.346468	−	0.0548751i	−0.327243	+	0.944940i	$0.606120\pi$
$230$	68.1339	+	17.1581i	0.296234	+	0.0746003i
$231$	417.027	+	936.657i	1.80531	+	4.05479i
$232$	−399.935	+	107.162i	−1.72386	+	0.461906i
$233$	41.5235	−	57.1523i	0.178213	−	0.245289i	−0.710560	−	0.703636i	$-0.751558\pi$
$233$	41.5235	−	57.1523i	0.178213	−	0.245289i	0.888773	+	0.458348i	$0.151558\pi$
$234$	286.668	−	205.054i	1.22508	−	0.876299i
$235$	−54.0448	+	55.7022i	−0.229978	+	0.237031i
$236$	−314.996	+	204.561i	−1.33473	+	0.866784i
$237$	306.352	+	340.238i	1.29262	+	1.43560i
$238$	170.393	+	801.635i	0.715936	+	3.36822i
$239$	252.966	+	128.893i	1.05844	+	0.539300i	0.894453	−	0.447163i	$-0.147566\pi$
$239$	252.966	+	128.893i	1.05844	+	0.539300i	0.163984	+	0.986463i	$0.447566\pi$
$240$	−71.3176	−	312.260i	−0.297157	−	1.30108i
$241$	−295.742	−	192.057i	−1.22715	−	0.796917i	−0.242274	−	0.970208i	$-0.577893\pi$
$241$	−295.742	−	192.057i	−1.22715	−	0.796917i	−0.984871	+	0.173290i	$0.944560\pi$
$242$	−164.385	−	1037.88i	−0.679275	−	4.28877i
$243$	163.410	+	283.034i	0.672469	+	1.16475i
$244$	−128.738	−	289.151i	−0.527616	−	1.18504i
$245$	444.538	−	206.019i	1.81444	−	0.840896i
$246$	−481.262	−	662.400i	−1.95635	−	2.69268i
$247$	−35.0302	−	61.7240i	−0.141823	−	0.249895i
$248$	−35.6928	−	109.851i	−0.143923	−	0.442948i
$249$	−137.881	−	514.577i	−0.553737	−	2.06658i
$250$	−412.196	+	130.721i	−1.64878	+	0.522885i
$251$	−305.002	+	176.093i	−1.21515	+	0.701566i	−0.963876	−	0.266350i	$-0.914182\pi$
$251$	−305.002	+	176.093i	−1.21515	+	0.701566i	−0.251272	+	0.967916i	$0.580849\pi$
$252$	674.546	+	343.698i	2.67677	+	1.36388i
$253$	78.1563	−	30.0014i	0.308918	−	0.118583i
$254$	63.5221	+	165.481i	0.250087	+	0.651499i
$255$	327.850	+	230.715i	1.28569	+	0.904763i
$256$	53.2911	−	507.031i	0.208168	−	1.98059i
$257$	−52.0184	−	30.0328i	−0.202406	−	0.116859i	0.395371	−	0.918521i	$-0.370616\pi$
$257$	−52.0184	−	30.0328i	−0.202406	−	0.116859i	−0.597777	+	0.801662i	$0.703949\pi$
$258$	−215.402	−	82.6850i	−0.834891	−	0.320484i
$259$	−418.968	−	136.131i	−1.61764	−	0.525602i
$260$	189.315	+	482.049i	0.728134	+	1.85404i
$261$	−73.0567	−	224.845i	−0.279911	−	0.861477i
$262$	−343.317	−	17.9925i	−1.31037	−	0.0686737i
$263$	−26.9518	−	29.9330i	−0.102478	−	0.113814i	0.689724	−	0.724073i	$-0.257732\pi$
$263$	−26.9518	−	29.9330i	−0.102478	−	0.113814i	−0.792202	+	0.610259i	$0.791065\pi$
$264$	−862.591	−	776.680i	−3.26739	−	2.94197i
$265$	−1.09505	−	72.5114i	−0.00413225	−	0.273628i
$266$	124.709	−	192.035i	0.468832	−	0.721937i
$267$	−182.957	+	148.156i	−0.685234	+	0.554891i
$268$	203.924	+	203.924i	0.760912	+	0.760912i
$269$	−21.5566	+	205.097i	−0.0801361	+	0.762444i	0.878487	+	0.477766i	$0.158553\pi$
$269$	−21.5566	+	205.097i	−0.0801361	+	0.762444i	−0.958623	+	0.284678i	$0.908113\pi$
$270$	−79.3883	+	22.5622i	−0.294031	+	0.0835638i
$271$	177.844	−	219.619i	0.656252	−	0.810404i	−0.335023	−	0.942210i	$-0.608744\pi$
$271$	177.844	−	219.619i	0.656252	−	0.810404i	0.991276	+	0.131806i	$0.0420776\pi$
$272$	−179.307	−	246.794i	−0.659215	−	0.907332i
$273$	−613.583	−	204.395i	−2.24756	−	0.748700i
$274$	863.871			3.15281
$275$	−312.012	+	410.026i	−1.13459	+	1.49100i
$276$	66.4007	−	115.009i	0.240582	−	0.416701i
$277$	74.8740	+	67.4169i	0.270303	+	0.243382i	0.793124	−	0.609061i	$-0.208453\pi$
$277$	74.8740	+	67.4169i	0.270303	+	0.243382i	−0.522820	+	0.852443i	$0.675120\pi$
$278$	−13.4495	+	84.9167i	−0.0483795	+	0.305456i
$279$	61.5719	−	23.6352i	0.220688	−	0.0847141i
$280$	−547.341	+	626.661i	−1.95479	+	2.23807i
$281$	−72.0196	−	454.714i	−0.256297	−	1.61820i	−0.694618	−	0.719379i	$-0.744426\pi$
$281$	−72.0196	−	454.714i	−0.256297	−	1.61820i	0.438320	−	0.898819i	$-0.355574\pi$
$282$	110.170	+	190.821i	0.390675	+	0.676669i
$283$	−48.8851	−	109.798i	−0.172739	−	0.387978i	0.806342	−	0.591450i	$-0.201444\pi$
$283$	−48.8851	−	109.798i	−0.172739	−	0.387978i	−0.979081	+	0.203472i	$0.934777\pi$
$284$	−13.4175	+	256.022i	−0.0472449	+	0.901486i
$285$	−19.1903	−	110.351i	−0.0673342	−	0.387196i
$286$	773.579	+	510.543i	2.70482	+	1.78511i
$287$	−216.099	+	665.085i	−0.752959	+	2.31737i
$288$	6.99701	+	0.366698i	0.0242952	+	0.00127326i
$289$	90.7820	+	19.2963i	0.314124	+	0.0667692i
$290$	520.598	−	35.1731i	1.79517	−	0.121287i
$291$	24.5425	+	48.1674i	0.0843385	+	0.165524i
$292$	428.746	+	529.458i	1.46831	+	1.81321i
$293$	151.593	−	565.752i	0.517382	−	1.93089i	0.228287	−	0.973594i	$-0.426688\pi$
$293$	151.593	−	565.752i	0.517382	−	1.93089i	0.289095	−	0.957300i	$-0.406646\pi$
$294$	−217.599	−	1373.87i	−0.740134	−	4.67302i
$295$	218.744	−	87.7801i	0.741504	−	0.297560i
$296$	495.987	−	52.1303i	1.67563	−	0.176116i
$297$	−61.8860	+	76.4228i	−0.208370	+	0.257316i
$298$	−407.946	+	132.550i	−1.36895	+	0.444798i
$299$	−19.2882	+	49.1576i	−0.0645091	+	0.164407i
$300$	24.6807	+	816.962i	0.0822690	+	2.72321i
$301$	51.0038	+	190.349i	0.169448	+	0.632387i
$302$	−522.268	−	111.012i	−1.72936	−	0.367588i
$303$	121.009	−	271.791i	0.399370	−	0.896999i
$304$	−13.3330	+	84.1811i	−0.0438585	+	0.276912i
$305$	44.2259	+	193.641i	0.145003	+	0.634888i
$306$	411.707	−	333.394i	1.34545	−	1.08952i
$307$	217.104	+	217.104i	0.707180	+	0.707180i	0.965941	−	0.258761i	$-0.0833142\pi$
$307$	217.104	+	217.104i	0.707180	+	0.707180i	−0.258761	+	0.965941i	$0.583314\pi$
$308$	−208.102	+	1979.96i	−0.675656	+	6.42843i
$309$	−97.6147	+	87.8927i	−0.315905	+	0.284442i
$310$	17.3994	+	144.517i	0.0561272	+	0.466184i
$311$	−166.569	+	54.1216i	−0.535592	+	0.174024i	−0.564310	−	0.825563i	$-0.690858\pi$
$311$	−166.569	+	54.1216i	−0.535592	+	0.174024i	0.0287177	+	0.999588i	$0.490858\pi$
$312$	728.693	−	71.1433i	2.33556	−	0.228023i
$313$	102.294	−	314.829i	0.326819	−	1.00585i	−0.643794	−	0.765199i	$-0.722641\pi$
$313$	102.294	−	314.829i	0.326819	−	1.00585i	0.970613	−	0.240646i	$-0.0773594\pi$
$314$	−610.340	+	396.359i	−1.94376	+	1.26229i
$315$	−373.686	−	293.374i	−1.18631	−	0.931347i
$316$	184.833	+	869.570i	0.584914	+	2.75181i
$317$	−471.162	+	74.6248i	−1.48632	+	0.235409i	−0.846199	−	0.532867i	$-0.821114\pi$
$317$	−471.162	+	74.6248i	−1.48632	+	0.235409i	−0.640118	+	0.768277i	$0.721114\pi$
$318$	−198.869	−	53.2868i	−0.625374	−	0.167569i
$319$	483.160	−	391.255i	1.51461	−	1.22651i
$320$	−96.5474	+	313.155i	−0.301711	+	0.978610i
$321$	−382.497	−	170.299i	−1.19158	−	0.530525i
$322$	−169.436	+	17.8084i	−0.526199	+	0.0553057i
$323$	−58.0996	−	89.4656i	−0.179875	−	0.276983i
$324$			717.983i			2.21600i
$325$	−58.1475	−	319.756i	−0.178915	−	0.983864i
$326$	−539.215			−1.65403
$327$	365.375	−	237.277i	1.11735	−	0.725619i
$328$	−82.7535	−	787.347i	−0.252297	−	2.40045i
$329$	76.5449	−	171.923i	0.232659	−	0.522561i
$330$	877.569	+	1170.29i	2.65930	+	3.54634i
$331$	−102.701	−	126.825i	−0.310275	−	0.383158i	0.598025	−	0.801478i	$-0.295952\pi$
$331$	−102.701	−	126.825i	−0.310275	−	0.383158i	−0.908300	+	0.418320i	$0.862619\pi$
$332$	267.728	−	999.175i	0.806410	−	3.00956i
$333$	44.5472	+	281.260i	0.133775	+	0.844625i
$334$	378.196	−	80.3880i	1.13232	−	0.240683i
$335$	−100.849	−	150.276i	−0.301042	−	0.448586i
$336$	423.003	+	651.367i	1.25894	+	1.93859i
$337$	122.789	+	39.8964i	0.364358	+	0.118387i	0.485474	−	0.874251i	$-0.338647\pi$
$337$	122.789	+	39.8964i	0.364358	+	0.118387i	−0.121116	+	0.992638i	$0.538647\pi$
$338$	−566.897	+	142.946i	−1.67721	+	0.422916i
$339$	8.81822	+	27.1397i	0.0260125	+	0.0800581i
$340$	327.318	+	706.269i	0.962699	+	2.07726i
$341$	116.052	+	128.889i	0.340328	+	0.377973i
$342$	−147.203	−	15.4717i	−0.430419	−	0.0452389i
$343$	−420.001	+	420.001i	−1.22449	+	1.22449i
$344$	−140.397	−	173.376i	−0.408132	−	0.504001i
$345$	−54.8230	+	62.7678i	−0.158907	+	0.181936i
$346$	660.356	+	104.590i	1.90854	+	0.302284i
$347$	−519.971	−	231.506i	−1.49848	−	0.667165i	−0.516521	−	0.856275i	$-0.672773\pi$
$347$	−519.971	−	231.506i	−1.49848	−	0.667165i	−0.981956	+	0.189110i	$0.939440\pi$
$348$	205.049	−	964.679i	0.589221	−	2.77207i
$349$	−507.312	+	135.934i	−1.45362	+	0.389496i	−0.897280	−	0.441461i	$-0.854460\pi$
$349$	−507.312	+	135.934i	−1.45362	+	0.389496i	−0.556337	+	0.830957i	$0.687794\pi$
$350$	829.296	−	641.656i	2.36942	−	1.83330i
$351$	−9.25001	−	61.3353i	−0.0263533	−	0.174744i
$352$	5.69378	+	17.5237i	0.0161755	+	0.0497831i
$353$	306.969	+	248.579i	0.869601	+	0.704189i	0.956407	−	0.292036i	$-0.0943327\pi$
$353$	306.969	+	248.579i	0.869601	+	0.704189i	−0.0868059	+	0.996225i	$0.527666\pi$
$354$	−69.9456	−	665.488i	−0.197586	−	1.87991i
$355$	39.2889	−	156.015i	0.110673	−	0.439478i
$356$	−451.501	+	71.5107i	−1.26826	+	0.200873i
$357$	−938.962	−	251.594i	−2.63015	−	0.704745i
$358$	−456.431	+	369.611i	−1.27495	+	1.03243i
$359$	−38.3375	+	19.5339i	−0.106790	+	0.0544120i	−0.506569	−	0.862199i	$-0.669087\pi$
$359$	−38.3375	+	19.5339i	−0.106790	+	0.0544120i	0.399780	+	0.916611i	$0.369087\pi$
$360$	521.560	+	131.344i	1.44878	+	0.364843i
$361$	68.8594	−	323.958i	0.190746	−	0.897391i
$362$	−60.9067	+	1162.17i	−0.168251	+	3.21041i
$363$	1185.40	+	385.161i	3.26558	+	1.06105i
$364$	−833.357	−	939.419i	−2.28944	−	2.58082i
$365$	−199.827	−	377.963i	−0.547473	−	1.03552i
$366$	563.133	+	29.5125i	1.53861	+	0.0806353i
$367$	−88.0880	+	39.2193i	−0.240022	+	0.106865i	−0.523223	−	0.852196i	$-0.675270\pi$
$367$	−88.0880	+	39.2193i	−0.240022	+	0.106865i	0.283201	+	0.959061i	$0.408604\pi$
$368$	54.9195	−	31.7078i	0.149238	−	0.0861625i
$369$	446.482	−	70.7159i	1.20998	−	0.191642i
$370$	−625.973	−	56.2498i	−1.69182	−	0.152027i
$371$	63.0175	+	164.166i	0.169858	+	0.442496i
$372$	271.739	+	43.0392i	0.730480	+	0.115697i
$373$	246.477	−	273.741i	0.660797	−	0.733889i	−0.315834	−	0.948815i	$-0.602284\pi$
$373$	246.477	−	273.741i	0.660797	−	0.733889i	0.976631	+	0.214925i	$0.0689508\pi$
$374$	1206.50	+	696.573i	3.22594	+	1.86249i
$375$	83.8111	−	506.020i	0.223496	−	1.34939i
$376$			213.051i			0.566626i
$377$	−23.4202	+	391.459i	−0.0621226	+	1.03835i
$378$	161.904	−	117.630i	0.428317	−	0.311190i
$379$	−285.539	−	231.225i	−0.753402	−	0.610093i	0.173745	−	0.984791i	$-0.444413\pi$
$379$	−285.539	−	231.225i	−0.753402	−	0.610093i	−0.927147	+	0.374698i	$0.877746\pi$
$380$	74.8661	−	204.197i	0.197016	−	0.537360i
$381$	−209.094	−	21.9767i	−0.548804	−	0.0576816i
$382$	301.197	−	301.197i	0.788475	−	0.788475i
$383$	56.8987	+	70.2640i	0.148560	+	0.183457i	0.845994	−	0.533193i	$-0.179008\pi$
$383$	56.8987	+	70.2640i	0.148560	+	0.183457i	−0.697433	+	0.716650i	$0.745675\pi$
$384$	767.947	+	498.711i	1.99986	+	1.29873i
$385$	368.086	−	1193.90i	0.956068	−	3.10104i
$386$	146.316	−	162.501i	0.379058	−	0.420986i
$387$	94.6657	−	85.2374i	0.244614	−	0.220252i
$388$	−5.49368	+	104.826i	−0.0141590	+	0.270169i
$389$	481.173	−	156.343i	1.23695	−	0.401909i	0.383722	−	0.923449i	$-0.374642\pi$
$389$	481.173	−	156.343i	1.23695	−	0.401909i	0.853227	+	0.521540i	$0.174642\pi$
$390$	−918.341	−	89.3744i	−2.35472	−	0.229165i
$391$	−24.5272	+	75.4871i	−0.0627295	+	0.193062i
$392$	481.996	−	1255.64i	1.22958	−	3.20317i
$393$	203.889	−	353.146i	0.518801	−	0.898589i
$394$	63.2540	+	6.64826i	0.160543	+	0.0168738i
$395$	−8.42407	−	557.822i	−0.0213267	−	1.41221i
$396$	1201.45	−	461.195i	3.03397	−	1.16463i
$397$	164.278	+	427.960i	0.413799	+	1.07798i	0.969173	+	0.246383i	$0.0792421\pi$
$397$	164.278	+	427.960i	0.413799	+	1.07798i	−0.555373	+	0.831601i	$0.687425\pi$
$398$	121.559	−	238.573i	0.305425	−	0.599430i
$399$	135.797	+	235.208i	0.340344	+	0.589494i
$400$	−184.852	+	343.745i	−0.462131	+	0.859362i
$401$	325.576	−	87.2378i	0.811910	−	0.217551i	0.171103	−	0.985253i	$-0.445267\pi$
$401$	325.576	−	87.2378i	0.811910	−	0.217551i	0.640806	+	0.767702i	$0.278600\pi$
$402$	−488.655	+	158.774i	−1.21556	+	0.394959i
$403$	−109.396	−	0.809212i	−0.271455	−	0.00200797i
$404$	467.362	−	339.558i	1.15684	−	0.840491i
$405$	87.0125	−	442.085i	0.214846	−	1.09157i
$406$	−1155.84	+	514.613i	−2.84689	+	1.26752i
$407$	−648.529	+	374.428i	−1.59344	+	0.919972i
$408$	1086.94	−	172.154i	2.66407	−	0.421947i
$409$	−221.374	+	340.886i	−0.541257	+	0.833463i	−0.998436	−	0.0559120i	$-0.982193\pi$
$409$	−221.374	+	340.886i	−0.541257	+	0.833463i	0.457179	+	0.889375i	$0.348860\pi$
$410$	−89.2930	+	993.692i	−0.217788	+	2.42364i
$411$	−465.187	+	912.980i	−1.13184	+	2.22136i
$412$	−249.481	+	53.0288i	−0.605536	+	0.128711i
$413$	−424.725	+	382.424i	−1.02839	+	0.925966i
$414$	59.9810	+	92.3626i	0.144882	+	0.223098i
$415$	−285.939	+	582.777i	−0.689009	+	1.40428i
$416$	−10.5822	−	4.80562i	−0.0254381	−	0.0115520i
$417$	−82.5017	−	59.9410i	−0.197846	−	0.143743i
$418$	−100.742	−	375.974i	−0.241009	−	0.899459i
$419$	−119.635	+	53.2648i	−0.285525	+	0.127124i	−0.544502	−	0.838760i	$-0.683281\pi$
$419$	−119.635	+	53.2648i	−0.285525	+	0.127124i	0.258977	+	0.965883i	$0.416615\pi$
$420$	−738.098	−	1839.30i	−1.75738	−	4.37929i
$421$	51.8337	−	327.265i	0.123120	−	0.777351i	−0.846437	−	0.532488i	$-0.821257\pi$
$421$	51.8337	−	327.265i	0.123120	−	0.777351i	0.969558	−	0.244863i	$-0.0787430\pi$
$422$	873.329	−	335.240i	2.06950	−	0.794407i
$423$	−121.484	+	6.36673i	−0.287197	+	0.0150514i
$424$	−140.766	−	140.766i	−0.331995	−	0.331995i
$425$	−115.947	−	474.539i	−0.272816	−	1.11656i
$426$	−395.563	−	228.378i	−0.928551	−	0.536099i
$427$	−262.315	−	403.930i	−0.614321	−	0.945972i
$428$	−477.867	−	657.728i	−1.11651	−	1.53675i
$429$	−956.131	+	542.633i	−2.22874	+	1.26488i
$430$	131.406	+	248.548i	0.305595	+	0.578018i
$431$	173.068	−	450.859i	0.401551	−	1.04608i	−0.572531	−	0.819883i	$-0.694039\pi$
$431$	173.068	−	450.859i	0.401551	−	1.04608i	0.974082	−	0.226193i	$-0.0726281\pi$
$432$	−37.2455	+	64.5111i	−0.0862165	+	0.149331i
$433$	425.896	+	44.7634i	0.983593	+	0.103380i	0.582650	−	0.812723i	$-0.302016\pi$
$433$	425.896	+	44.7634i	0.983593	+	0.103380i	0.400943	+	0.916103i	$0.368683\pi$
$434$	−160.239	−	314.486i	−0.369213	−	0.724622i
$435$	−243.165	+	569.133i	−0.558999	+	1.30835i
$436$	844.778	−	44.2730i	1.93757	−	0.101543i
$437$	19.7590	−	10.0677i	0.0452150	−	0.0230382i
$438$	−1187.26	+	252.359i	−2.71063	+	0.576163i
$439$	57.6894	−	271.407i	0.131411	−	0.618240i	−0.862313	−	0.506376i	$-0.830985\pi$
$439$	57.6894	−	271.407i	0.131411	−	0.618240i	0.993724	−	0.111864i	$-0.0356820\pi$
$440$	169.067	+	1404.24i	0.384242	+	3.19146i
$441$	730.388	+	237.317i	1.65621	+	0.538135i
$442$	−837.736	+	265.362i	−1.89533	+	0.600367i
$443$	−175.650			−0.396500			−0.198250	−	0.980151i	$-0.563526\pi$
$443$	−175.650			−0.396500			−0.198250	+	0.980151i	$0.563526\pi$
$444$	−425.714	+	1109.02i	−0.958816	+	2.49780i
$445$	286.669	+	10.6860i	0.644201	+	0.0240136i
$446$	−136.771	+	307.194i	−0.306662	+	0.688775i
$447$	79.5905	−	502.514i	0.178055	−	1.12419i
$448$	−41.5866	−	793.519i	−0.0928272	−	1.77125i
$449$	−181.741	+	678.265i	−0.404767	+	1.51061i	0.399717	+	0.916639i	$0.369108\pi$
$449$	−181.741	+	678.265i	−0.404767	+	1.51061i	−0.804484	+	0.593974i	$0.797558\pi$
$450$	−612.942	−	289.338i	−1.36209	−	0.642974i
$451$	594.381	+	1029.50i	1.31792	+	2.28270i
$452$	−11.5204	+	54.1993i	−0.0254877	+	0.119910i
$453$	398.559	−	492.179i	0.879821	−	1.08649i
$454$	512.538	+	705.448i	1.12894	+	1.55385i
$455$	399.276	+	679.424i	0.877529	+	1.49324i
$456$	−248.748	−	180.726i	−0.545501	−	0.396329i
$457$	134.284	+	501.156i	0.293839	+	1.09662i	0.942135	+	0.335233i	$0.108815\pi$
$457$	134.284	+	501.156i	0.293839	+	1.09662i	−0.648297	+	0.761388i	$0.724518\pi$
$458$	253.870	−	113.030i	0.554301	−	0.246791i
$459$	−19.3844	−	91.1965i	−0.0422319	−	0.198685i
$460$	−153.129	+	52.3240i	−0.332890	+	0.113748i
$461$	−2.15829	−	41.1826i	−0.00468175	−	0.0893332i	0.995289	−	0.0969502i	$-0.0309087\pi$
$461$	−2.15829	−	41.1826i	−0.00468175	−	0.0893332i	−0.999971	+	0.00761698i	$0.997575\pi$
$462$	−2974.71	−	1931.80i	−6.43877	−	4.18139i
$463$	76.2206	−	38.8363i	0.164623	−	0.0838797i	−0.369737	−	0.929136i	$-0.620552\pi$
$463$	76.2206	−	38.8363i	0.164623	−	0.0838797i	0.534361	+	0.845257i	$0.320552\pi$
$464$	315.125	−	349.982i	0.679149	−	0.754271i
$465$	−162.102	−	59.4326i	−0.348607	−	0.127812i
$466$	−12.7902	+	244.052i	−0.0274469	+	0.523718i
$467$	368.026	−	506.545i	0.788065	−	1.08468i	−0.206281	−	0.978493i	$-0.566136\pi$
$467$	368.026	−	506.545i	0.788065	−	1.08468i	0.994346	−	0.106186i	$-0.0338639\pi$
$468$	−296.507	+	755.672i	−0.633562	+	1.61468i
$469$	355.028	+	257.943i	0.756989	+	0.549984i
$470$	51.8505	−	263.437i	0.110320	−	0.560504i
$471$	−90.2290	−	858.472i	−0.191569	−	1.82266i
$472$	263.165	−	591.079i	0.557554	−	1.25229i
$473$	298.477	+	152.082i	0.631030	+	0.321526i
$474$	−1529.88	−	409.929i	−3.22758	−	0.864829i
$475$	−70.8440	+	116.657i	−0.149145	+	0.245594i
$476$	−1334.69	−	1334.69i	−2.80397	−	2.80397i
$477$	76.0600	−	84.4732i	0.159455	−	0.177093i
$478$	−976.785	+	102.664i	−2.04348	+	0.214779i
$479$	202.172	−	249.662i	0.422072	−	0.521215i	−0.521111	−	0.853489i	$-0.674482\pi$
$479$	202.172	−	249.662i	0.422072	−	0.521215i	0.943183	+	0.332274i	$0.107816\pi$
$480$	−13.1643	−	12.7726i	−0.0274257	−	0.0266096i
$481$	101.624	−	461.298i	0.211276	−	0.959039i
$482$	1219.90			2.53091
$483$	72.4189	−	188.658i	0.149936	−	0.390596i
$484$	1619.43	+	1798.56i	3.34593	+	3.71603i
$485$	16.0865	−	63.8786i	0.0331679	−	0.131709i
$486$	−1007.38	−	513.285i	−2.07279	−	1.05614i
$487$	461.926	−	711.304i	0.948514	−	1.46058i	0.0618954	−	0.998083i	$-0.480285\pi$
$487$	461.926	−	711.304i	0.948514	−	1.46058i	0.886619	−	0.462501i	$-0.153048\pi$
$488$	457.285	+	296.964i	0.937060	+	0.608534i
$489$	290.362	−	569.868i	0.593788	−	1.16537i
$490$	−901.574	+	1435.29i	−1.83995	+	2.92917i
$491$	476.368	−	428.924i	0.970200	−	0.873572i	−0.0218058	−	0.999762i	$-0.506942\pi$
$491$	476.368	−	428.924i	0.970200	−	0.873572i	0.992006	+	0.126190i	$0.0402749\pi$
$492$	1760.50	+	675.794i	3.57826	+	1.37357i
$493$			589.444i			1.19563i
$494$	217.930	+	113.079i	0.441153	+	0.228905i
$495$	−795.664	+	138.368i	−1.60740	+	0.279531i
$496$	102.100	+	82.6793i	0.205848	+	0.166692i
$497$	40.7782	+	387.978i	0.0820486	+	0.780640i
$498$	1369.57	+	1233.16i	2.75013	+	2.47623i
$499$	−52.4981	+	52.4981i	−0.105207	+	0.105207i	−0.757751	−	0.652544i	$-0.773702\pi$
$499$	−52.4981	+	52.4981i	−0.105207	+	0.105207i	0.652544	+	0.757751i	$0.273702\pi$
$500$	632.216	−	769.552i	1.26443	−	1.53910i
$501$	−118.697	+	442.984i	−0.236920	+	0.884199i
$502$	553.124	−	1085.57i	1.10184	−	2.16248i
$503$	−674.761	−	300.423i	−1.34147	−	0.597262i	−0.394595	−	0.918855i	$-0.629115\pi$
$503$	−674.761	−	300.423i	−1.34147	−	0.597262i	−0.946878	+	0.321593i	$0.895782\pi$
$504$	−1297.02	+	136.322i	−2.57345	+	0.270481i
$505$	−328.920	+	152.437i	−0.651327	+	0.301855i
$506$	−170.229	+	234.300i	−0.336421	+	0.463044i
$507$	154.197	−	676.099i	0.304136	−	1.33353i
$508$	−330.275	−	239.959i	−0.650149	−	0.472361i
$509$	276.619	+	14.4970i	0.543457	+	0.0284814i	0.322090	−	0.946709i	$-0.395615\pi$
$509$	276.619	+	14.4970i	0.543457	+	0.0284814i	0.221367	+	0.975191i	$0.428948\pi$
$510$	−1385.89	−	51.6613i	−2.71744	−	0.101297i
$511$	770.411	+	693.681i	1.50765	+	1.35750i
$512$	395.460	+	776.134i	0.772383	+	1.51589i
$513$	−14.1873	+	21.8465i	−0.0276556	+	0.0425859i
$514$	207.507	−	10.8750i	0.403711	−	0.0211576i
$515$	160.040	−	2.41688i	0.310757	−	0.00469296i
$516$	519.786	−	110.484i	1.00734	−	0.214116i
$517$	−130.119	−	292.252i	−0.251681	−	0.565284i
$518$	1472.05	−	394.433i	2.84179	−	0.761455i
$519$	−466.132	+	641.575i	−0.898135	+	1.23618i
$520$	−725.787	−	518.820i	−1.39574	−	0.997730i
$521$	147.094	−	106.870i	0.282331	−	0.205125i	−0.437603	−	0.899168i	$-0.644172\pi$
$521$	147.094	−	106.870i	0.282331	−	0.205125i	0.719933	+	0.694043i	$0.244172\pi$
$522$	635.599	+	514.698i	1.21762	+	0.986012i
$523$	207.346	+	44.0728i	0.396455	+	0.0842692i	0.401825	−	0.915716i	$-0.368376\pi$
$523$	207.346	+	44.0728i	0.396455	+	0.0842692i	−0.00536989	+	0.999986i	$0.501709\pi$
$524$	685.717	−	395.899i	1.30862	−	0.755532i
$525$	231.565	+	1221.97i	0.441075	+	2.32756i
$526$	134.593	+	36.0642i	0.255881	+	0.0685631i
$527$	−164.210	+	8.60588i	−0.311594	+	0.0163299i
$528$	1304.00	+	206.534i	2.46970	+	0.391162i
$529$	468.192	+	208.453i	0.885051	+	0.394050i
$530$	139.798	+	208.315i	0.263770	+	0.393047i
$531$	344.905	+	132.397i	0.649539	+	0.249334i
$532$			527.366i			0.991290i
$533$	−732.281	−	161.321i	−1.37388	−	0.302667i
$534$	251.671	−	774.563i	0.471293	−	1.45049i
$535$	214.528	+	462.896i	0.400986	+	0.865227i
$536$	−485.948	−	103.291i	−0.906620	−	0.192708i
$537$	−144.838	−	681.410i	−0.269717	−	1.26892i
$538$	−323.889	−	635.667i	−0.602023	−	1.18154i
$539$	105.696	+	2016.80i	0.196096	+	3.74174i
$540$	125.044	−	143.165i	0.231562	−	0.265119i
$541$	88.9616	−	45.3282i	0.164439	−	0.0837859i	−0.369834	−	0.929098i	$-0.620585\pi$
$541$	88.9616	−	45.3282i	0.164439	−	0.0837859i	0.534273	+	0.845312i	$0.320585\pi$
$542$	−102.189	+	972.267i	−0.188541	+	1.79385i
$543$	−1195.44	−	690.187i	−2.20154	−	1.27106i
$544$	−16.3089	−	6.26039i	−0.0299795	−	0.0115081i
$545$	−525.522	−	75.1185i	−0.964260	−	0.137832i
$546$	2165.30	−	563.058i	3.96576	−	1.03124i
$547$	−177.737	+	129.133i	−0.324930	+	0.236076i	−0.738276	−	0.674498i	$-0.764360\pi$
$547$	−177.737	+	129.133i	−0.324930	+	0.236076i	0.413346	+	0.910574i	$0.364360\pi$
$548$	−1668.64	+	1083.63i	−3.04496	+	1.97742i
$549$	−155.668	+	269.624i	−0.283547	+	0.491119i
$550$	132.701	−	1777.49i	0.241275	−	3.23179i
$551$	116.451	−	116.451i	0.211345	−	0.211345i
$552$	11.9730	+	228.459i	0.0216903	+	0.413875i
$553$	484.786	+	1262.91i	0.876647	+	2.28374i
$554$	−344.255	−	54.5247i	−0.621399	−	0.0984200i
$555$	396.528	−	631.268i	0.714465	−	1.13742i
$556$	−80.5396	−	180.895i	−0.144855	−	0.325350i
$557$	−248.724	+	66.6453i	−0.446541	+	0.119650i	−0.475081	−	0.879942i	$-0.657581\pi$
$557$	−248.724	+	66.6453i	−0.446541	+	0.119650i	0.0285392	+	0.999593i	$0.490914\pi$
$558$	−134.107	+	184.583i	−0.240336	+	0.330794i
$559$	−197.822	+	74.2626i	−0.353886	+	0.132849i
$560$	133.916	−	936.866i	0.239136	−	1.67298i
$561$	−1385.86	+	899.989i	−2.47034	+	1.60426i
$562$	1065.69	+	1183.57i	1.89625	+	2.10600i
$563$	19.0833	+	89.7796i	0.0338956	+	0.159466i	0.991840	−	0.127487i	$-0.0406910\pi$
$563$	19.0833	+	89.7796i	0.0338956	+	0.159466i	−0.957945	+	0.286953i	$0.907358\pi$
$564$	−452.166	−	230.390i	−0.801713	−	0.408493i
$565$	13.6619	−	31.9761i	0.0241804	−	0.0565948i
$566$	348.705	+	226.451i	0.616086	+	0.400091i
$567$	170.910	+	1079.08i	0.301428	+	1.90314i
$568$	−220.823	−	382.476i	−0.388773	−	0.673374i
$569$	−28.7893	−	64.6619i	−0.0505964	−	0.113641i	0.886479	−	0.462770i	$-0.153144\pi$
$569$	−28.7893	−	64.6619i	−0.0505964	−	0.113641i	−0.937075	+	0.349128i	$0.886478\pi$
$570$	263.593	+	284.005i	0.462443	+	0.498255i
$571$	−226.730	−	312.068i	−0.397076	−	0.546528i	0.562931	−	0.826504i	$-0.309674\pi$
$571$	−226.730	−	312.068i	−0.397076	−	0.546528i	−0.960007	+	0.279976i	$0.909674\pi$
$572$	−2134.65	−	15.7902i	−3.73191	−	0.0276052i
$573$	156.128	+	480.512i	0.272474	+	0.838590i
$574$	−626.138	−	2336.78i	−1.09083	−	4.07104i
$575$	100.628	−	13.6598i	0.175005	−	0.0237561i
$576$	−444.833	+	256.825i	−0.772280	+	0.445876i
$577$	455.963	+	232.325i	0.790231	+	0.402643i	0.802027	−	0.597288i	$-0.203755\pi$
$577$	455.963	+	232.325i	0.790231	+	0.402643i	−0.0117964	+	0.999930i	$0.503755\pi$
$578$	−299.744	+	115.061i	−0.518587	+	0.199067i
$579$	92.9486	+	242.139i	0.160533	+	0.418203i
$580$	−961.459	+	720.971i	−1.65769	+	1.24305i
$581$	164.533	−	1565.43i	0.283189	−	2.69437i
$582$	−161.959	−	93.5072i	−0.278280	−	0.160665i
$583$	279.067	+	107.124i	0.478673	+	0.183745i
$584$	−1116.19	−	362.671i	−1.91128	−	0.621011i
$585$	274.148	−	429.357i	0.468630	−	0.733944i
$586$	626.134	+	1927.04i	1.06849	+	3.28847i
$587$	−33.4871	−	1.75498i	−0.0570478	−	0.00298975i	0.0237907	−	0.999717i	$-0.492426\pi$
$587$	−33.4871	−	1.75498i	−0.0570478	−	0.00298975i	−0.0808385	+	0.996727i	$0.525760\pi$
$588$	2143.67	+	2380.79i	3.64571	+	4.04897i
$589$	34.1418	+	30.7414i	0.0579656	+	0.0521925i
$590$	−469.254	+	666.820i	−0.795346	+	1.13020i
$591$	−41.0879	+	63.2698i	−0.0695227	+	0.107056i
$592$	−440.844	+	356.989i	−0.744669	+	0.603021i
$593$	524.343	+	524.343i	0.884222	+	0.884222i	0.993960	−	0.109739i	$-0.0350015\pi$
$593$	524.343	+	524.343i	0.884222	+	0.884222i	−0.109739	+	0.993960i	$0.535001\pi$
$594$	35.5597	−	338.328i	0.0598648	−	0.569575i
$595$	660.059	+	983.561i	1.10934	+	1.65304i
$596$	621.715	−	767.754i	1.04315	−	1.28818i
$597$	186.677	+	256.939i	0.312692	+	0.430383i
$598$	−36.6583	−	178.963i	−0.0613016	−	0.299269i
$599$	−1080.05			−1.80310			−0.901548	−	0.432680i	$-0.857568\pi$
$599$	−1080.05			−1.80310			−0.901548	+	0.432680i	$0.857568\pi$
$600$	−802.157	−	1157.15i	−1.33693	−	1.92858i
$601$	295.972	−	512.638i	0.492466	−	0.852976i	−0.507497	−	0.861654i	$-0.669429\pi$
$601$	295.972	−	512.638i	0.492466	−	0.852976i	0.999962	+	0.00867802i	$0.00276233\pi$
$602$	−506.620	−	456.163i	−0.841561	−	0.757745i
$603$	44.3762	−	280.180i	0.0735924	−	0.464644i
$604$	1148.06	−	440.698i	1.90076	−	0.729632i
$605$	−779.166	−	1303.69i	−1.28788	−	2.15486i
$606$	161.005	+	1016.55i	0.265685	+	1.67747i
$607$	−372.249	−	644.754i	−0.613260	−	1.06220i	−0.990687	−	0.136159i	$-0.956524\pi$
$607$	−372.249	−	644.754i	−0.613260	−	1.06220i	0.377427	−	0.926039i	$-0.376809\pi$
$608$	1.98519	+	4.45882i	0.00326512	+	0.00733358i
$609$	78.5415	−	1498.66i	0.128968	−	2.46086i
$610$	−493.159	−	478.485i	−0.808457	−	0.784402i
$611$	191.448	+	63.7745i	0.313335	+	0.104377i
$612$	−377.043	+	1160.42i	−0.616084	+	1.89611i
$613$	770.212	+	40.3651i	1.25646	+	0.0658484i	0.668914	−	0.743340i	$-0.266760\pi$
$613$	770.212	+	40.3651i	1.25646	+	0.0658484i	0.587549	+	0.809189i	$0.300093\pi$
$614$	−1038.94	−	220.834i	−1.69209	−	0.359664i
$615$	−1002.10	−	629.463i	−1.62943	−	1.02352i
$616$	−1557.00	−	3055.79i	−2.52760	−	4.96070i
$617$	199.941	+	246.906i	0.324053	+	0.400173i	0.912974	−	0.408019i	$-0.133780\pi$
$617$	199.941	+	246.906i	0.324053	+	0.400173i	−0.588920	+	0.808191i	$0.700447\pi$
$618$	117.609	−	438.923i	0.190306	−	0.710232i
$619$	56.0885	+	354.129i	0.0906114	+	0.572098i	0.990665	+	0.136319i	$0.0435271\pi$
$619$	56.0885	+	354.129i	0.0906114	+	0.572098i	−0.900054	+	0.435779i	$0.856473\pi$
$620$	−214.889	−	257.322i	−0.346595	−	0.415035i
$621$	19.2756	−	2.02594i	0.0310396	−	0.00326239i
$622$	381.297	−	470.862i	0.613017	−	0.757013i
$623$	−661.554	+	214.952i	−1.06188	+	0.345027i
$624$	−651.053	+	519.286i	−1.04335	+	0.832188i
$625$	−482.537	+	397.219i	−0.772060	+	0.635550i
$626$	296.393	+	1106.15i	0.473472	+	1.76702i
$627$	451.596	+	95.9897i	0.720249	+	0.153094i
$628$	681.736	−	1531.20i	1.08557	−	2.43822i
$629$	111.067	−	701.249i	0.176577	−	1.11486i
$630$	1636.94	+	147.095i	2.59831	+	0.233484i
$631$	−681.607	+	551.954i	−1.08020	+	0.874730i	−0.992600	−	0.121426i	$-0.961253\pi$
$631$	−681.607	+	551.954i	−1.08020	+	0.874730i	−0.0876007	+	0.996156i	$0.527920\pi$
$632$	−1082.90	−	1082.90i	−1.71344	−	1.71344i
$633$	−115.983	+	1103.50i	−0.183227	+	1.74329i
$634$	1226.39	−	1104.24i	1.93436	−	1.74171i
$635$	174.280	+	187.776i	0.274457	+	0.295711i
$636$	450.975	−	146.531i	0.709080	−	0.230394i
$637$	−984.040	−	808.985i	−1.54480	−	1.26999i
$638$	−664.621	+	2045.49i	−1.04173	+	3.20610i
$639$	211.494	−	137.346i	0.330976	−	0.214939i
$640$	−305.024	−	1073.27i	−0.476600	−	1.67698i
$641$	−68.5207	−	322.365i	−0.106897	−	0.502909i	−0.998723	−	0.0505303i	$-0.983909\pi$
$641$	−68.5207	−	322.365i	−0.106897	−	0.502909i	0.891826	−	0.452379i	$-0.149424\pi$
$642$	1430.61	−	226.586i	2.22836	−	0.352938i
$643$	335.566	+	89.9147i	0.521876	+	0.139836i	0.510134	−	0.860095i	$-0.329596\pi$
$643$	335.566	+	89.9147i	0.521876	+	0.139836i	0.0117418	+	0.999931i	$0.496262\pi$
$644$	304.942	−	246.937i	0.473512	−	0.383442i
$645$	−333.438	+	5.03549i	−0.516958	+	0.00780696i
$646$	337.130	+	150.100i	0.521874	+	0.232353i
$647$	586.392	−	61.6323i	0.906325	−	0.0952586i	0.360116	−	0.932908i	$-0.382737\pi$
$647$	586.392	−	61.6323i	0.906325	−	0.0952586i	0.546209	+	0.837649i	$0.316070\pi$
$648$	−673.635	−	1037.31i	−1.03956	−	1.60078i
$649$			971.535i			1.49697i
$650$	771.167	+	818.154i	1.18641	+	1.25870i
$651$	418.651			0.643089
$652$	1041.54	−	676.384i	1.59745	−	1.03740i
$653$	24.8507	+	236.439i	0.0380562	+	0.362081i	0.996933	+	0.0782584i	$0.0249359\pi$
$653$	24.8507	+	236.439i	0.0380562	+	0.362081i	−0.958877	+	0.283822i	$0.908397\pi$
$654$	−613.004	+	1376.83i	−0.937316	+	2.10525i
$655$	−470.196	+	160.665i	−0.717857	+	0.245290i
$656$	566.697	+	699.812i	0.863867	+	1.06679i
$657$	173.444	−	647.301i	0.263994	−	0.985237i
$658$	101.845	+	643.022i	0.154779	+	0.977237i
$659$	853.797	−	181.480i	1.29559	−	0.275387i	0.492016	−	0.870586i	$-0.336260\pi$
$659$	853.797	−	181.480i	1.29559	−	0.275387i	0.803578	+	0.595199i	$0.202927\pi$
$660$	−3163.10	−	1159.71i	−4.79257	−	1.75713i
$661$	−117.080	−	180.288i	−0.177126	−	0.272750i	0.738945	−	0.673765i	$-0.235324\pi$
$661$	−117.080	−	180.288i	−0.177126	−	0.272750i	−0.916071	+	0.401015i	$0.868657\pi$
$662$	536.924	+	174.457i	0.811063	+	0.263530i
$663$	170.665	−	1028.25i	0.257414	−	1.55091i
$664$	550.658	+	1694.75i	0.829303	+	2.55233i
$665$	63.9116	−	324.716i	0.0961076	−	0.488295i
$666$	−659.177	−	732.090i	−0.989755	−	1.09923i
$667$	−121.864	−	12.8084i	−0.182705	−	0.0192030i
$668$	−629.680	+	629.680i	−0.942635	+	0.942635i
$669$	−251.007	−	309.968i	−0.375197	−	0.463330i
$670$	575.735	+	245.985i	0.859306	+	0.367142i
$671$	−808.646	−	128.077i	−1.20514	−	0.190875i
$672$	40.6312	+	18.0902i	0.0604630	+	0.0269199i
$673$	127.786	−	601.186i	0.189875	−	0.893293i	−0.775281	−	0.631617i	$-0.782392\pi$
$673$	127.786	−	601.186i	0.189875	−	0.893293i	0.965156	−	0.261676i	$-0.0842751\pi$
$674$	−431.418	+	115.598i	−0.640086	+	0.171511i
$675$	−94.3433	+	72.9968i	−0.139768	+	0.108143i
$676$	915.701	−	987.220i	1.35459	−	1.46038i
$677$	−90.2047	−	277.622i	−0.133242	−	0.410076i	0.862071	−	0.506788i	$-0.169167\pi$
$677$	−90.2047	−	277.622i	−0.133242	−	0.410076i	−0.995312	+	0.0967121i	$0.969167\pi$
$678$	−76.7192	−	62.1260i	−0.113155	−	0.0916313i
$679$	16.6962	+	158.854i	0.0245894	+	0.233953i
$680$	−1135.54	−	713.282i	−1.66991	−	1.04894i
$681$	−1021.55	+	161.797i	−1.50007	+	0.237588i
$682$	−579.546	−	155.289i	−0.849775	−	0.227696i
$683$	−28.9458	+	23.4398i	−0.0423803	+	0.0343189i	−0.650277	−	0.759698i	$-0.725347\pi$
$683$	−28.9458	+	23.4398i	−0.0423803	+	0.0343189i	0.607896	+	0.794016i	$0.292014\pi$
$684$	303.743	−	154.765i	0.444069	−	0.226265i
$685$	1158.76	−	465.001i	1.69162	−	0.678833i
$686$	427.216	−	2009.89i	0.622764	−	2.92987i
$687$	−17.2509	+	329.168i	−0.0251106	+	0.479138i
$688$	241.335	+	78.4145i	0.350777	+	0.113975i
$689$	−168.629	+	84.3554i	−0.244744	+	0.122432i
$690$	40.7957	−	285.403i	0.0591242	−	0.413627i
$691$	−430.796	−	22.5771i	−0.623439	−	0.0326731i	−0.261999	−	0.965068i	$-0.584382\pi$
$691$	−430.796	−	22.5771i	−0.623439	−	0.0326731i	−0.361441	+	0.932395i	$0.617715\pi$
$692$	−1406.73	+	626.317i	−2.03285	+	0.905083i
$693$	1695.92	−	979.141i	2.44722	−	1.41290i
$694$	1944.79	−	308.024i	2.80229	−	0.443839i
$695$	27.6681	+	121.143i	0.0398102	+	0.174307i
$696$	608.848	+	1586.10i	0.874782	+	2.27889i
$697$	−1113.19	−	176.312i	−1.59711	−	0.252958i
$698$	1215.75	−	1350.23i	1.74177	−	1.93443i
$699$	−251.039	−	144.937i	−0.359140	−	0.207350i
$700$	−796.973	+	2279.67i	−1.13853	+	3.25668i
$701$		−	982.596i		−	1.40171i	−0.713306	−	0.700853i	$-0.752803\pi$
$701$		−	982.596i		−	1.40171i	0.713306	−	0.700853i	$-0.247197\pi$
$702$	142.401	+	160.524i	0.202850	+	0.228667i
$703$	−160.482	+	116.597i	−0.228282	+	0.165857i
$704$	−1049.74	−	850.059i	−1.49110	−	1.20747i
$705$	250.492	+	196.656i	0.355308	+	0.278945i
$706$	−1358.97	−	142.833i	−1.92489	−	0.202314i
$707$	621.586	−	621.586i	0.879188	−	0.879188i
$708$	969.885	+	1197.71i	1.36989	+	1.69168i
$709$	473.434	+	307.452i	0.667749	+	0.433641i	0.833495	−	0.552527i	$-0.186336\pi$
$709$	473.434	+	307.452i	0.667749	+	0.433641i	−0.165746	+	0.986168i	$0.553003\pi$
$710$	179.963	+	526.672i	0.253469	+	0.741792i
$711$	585.120	−	649.842i	0.822954	−	0.913983i
$712$	585.212	−	526.927i	0.821927	−	0.740066i
$713$	1.78902	−	34.1364i	0.00250914	−	0.0478772i
$714$	3198.26	−	1039.18i	4.47935	−	1.45543i
$715$	1312.46	+	268.421i	1.83561	+	0.375414i
$716$	418.001	−	1286.48i	0.583801	−	1.79675i
$717$	417.489	−	1087.60i	0.582273	−	1.51687i
$718$	74.4244	−	128.907i	0.103655	−	0.179536i
$719$	428.486	+	45.0357i	0.595947	+	0.0626366i	0.397700	−	0.917516i	$-0.369808\pi$
$719$	428.486	+	45.0357i	0.595947	+	0.0626366i	0.198247	+	0.980152i	$0.436475\pi$
$720$	−578.900	+	197.809i	−0.804028	+	0.274735i
$721$	−362.331	+	139.086i	−0.502539	+	0.192907i
$722$	410.598	+	1069.64i	0.568695	+	1.48150i
$723$	−656.906	+	1289.25i	−0.908583	+	1.78319i
$724$	−1340.16	−	2321.23i	−1.85105	−	3.20612i
$725$	679.375	−	327.405i	0.937069	−	0.451593i
$726$	−4164.92	+	1115.99i	−5.73681	+	1.53717i
$727$	−240.269	+	78.0683i	−0.330494	+	0.107384i	−0.469564	−	0.882898i	$-0.655589\pi$
$727$	−240.269	+	78.0683i	−0.330494	+	0.107384i	0.139069	+	0.990283i	$0.455589\pi$
$728$	2085.39	+	575.344i	2.86454	+	0.790307i
$729$	428.799	−	311.541i	0.588201	−	0.427353i
$730$	1291.90	+	720.088i	1.76972	+	0.986422i
$731$	−290.144	+	129.181i	−0.396914	+	0.176718i
$732$	−1124.76	+	649.380i	−1.53656	+	0.887131i
$733$	357.931	−	56.6908i	0.488310	−	0.0773408i	0.0925757	−	0.995706i	$-0.470490\pi$
$733$	357.931	−	56.6908i	0.488310	−	0.0773408i	0.395735	+	0.918365i	$0.370490\pi$
$734$	181.676	−	279.757i	0.247515	−	0.381140i
$735$	−1031.40	−	1725.72i	−1.40326	−	2.34792i
$736$	1.64869	−	3.23573i	0.00224006	−	0.00439637i
$737$	729.681	−	155.098i	0.990069	−	0.210446i
$738$	−1162.15	+	1046.40i	−1.57472	+	1.41789i
$739$	381.494	+	587.449i	0.516230	+	0.794925i	0.996622	−	0.0821294i	$-0.0261721\pi$
$739$	381.494	+	587.449i	0.516230	+	0.794925i	−0.480391	+	0.877054i	$0.659505\pi$
$740$	1279.68	−	676.560i	1.72930	−	0.914271i
$741$	−236.860	+	169.427i	−0.319650	+	0.228646i
$742$	−492.144	−	357.564i	−0.663267	−	0.481892i
$743$	−45.7236	−	170.643i	−0.0615392	−	0.229667i	0.928306	−	0.371817i	$-0.121265\pi$
$743$	−45.7236	−	170.643i	−0.0615392	−	0.229667i	−0.989845	+	0.142150i	$0.954598\pi$
$744$	−432.975	+	192.773i	−0.581956	+	0.259103i
$745$	−475.853	+	397.384i	−0.638730	+	0.533402i
$746$	−199.343	+	1258.60i	−0.267216	+	1.68714i
$747$	−949.912	+	364.637i	−1.27164	+	0.488135i
$748$	−3204.23	+	167.927i	−4.28373	+	0.224501i
$749$	−874.770	−	874.770i	−1.16792	−	1.16792i
$750$	710.248	+	1626.03i	0.946997	+	2.16804i
$751$	−830.993	−	479.774i	−1.10652	−	0.638847i	−0.168591	−	0.985686i	$-0.553922\pi$
$751$	−830.993	−	479.774i	−1.10652	−	0.638847i	−0.937925	+	0.346839i	$0.887255\pi$
$752$	−131.983	−	203.237i	−0.175510	−	0.270262i
$753$	849.426	+	1169.14i	1.12806	+	1.55264i
$754$	−669.611	−	1179.87i	−0.888078	−	1.56481i
$755$	−760.303	+	132.218i	−1.00702	+	0.175124i
$756$	−165.178	+	430.302i	−0.218489	+	0.569183i
$757$	336.025	−	582.013i	0.443891	−	0.768842i	−0.554083	−	0.832461i	$-0.686931\pi$
$757$	336.025	−	582.013i	0.443891	−	0.768842i	0.997974	+	0.0636196i	$0.0202644\pi$
$758$	1264.10	+	132.862i	1.66767	+	0.175280i
$759$	−155.953	−	306.075i	−0.205472	−	0.403261i
$760$	83.4212	+	365.255i	0.109765	+	0.480599i
$761$	−678.126	+	35.5391i	−0.891098	+	0.0467005i	−0.492387	−	0.870376i	$-0.663876\pi$
$761$	−678.126	+	35.5391i	−0.891098	+	0.0467005i	−0.398711	+	0.917077i	$0.630542\pi$
$762$	648.054	−	330.200i	0.850465	−	0.433334i
$763$	1259.11	−	267.632i	1.65021	−	0.350762i
$764$	−203.971	+	959.607i	−0.266977	+	1.25603i
$765$	372.788	−	668.812i	0.487305	−	0.874265i
$766$	−297.467	−	96.6530i	−0.388339	−	0.126179i
$767$	−452.367	−	413.413i	−0.589788	−	0.539000i
$768$	−2091.97			−2.72391
$769$	40.0013	−	104.207i	0.0520172	−	0.135510i	−0.905110	−	0.425178i	$-0.860212\pi$
$769$	40.0013	−	104.207i	0.0520172	−	0.135510i	0.957127	+	0.289668i	$0.0935449\pi$
$770$	1181.54	+	4157.40i	1.53446	+	5.39923i
$771$	−100.248	+	225.160i	−0.130023	+	0.292036i
$772$	−78.7838	+	497.422i	−0.102052	+	0.644328i
$773$	71.4788	+	1363.90i	0.0924693	+	1.76442i	0.514173	+	0.857686i	$0.328099\pi$
$773$	71.4788	+	1363.90i	0.0924693	+	1.76442i	−0.421704	+	0.906734i	$0.638568\pi$
$774$	−114.056	+	425.663i	−0.147359	+	0.549952i
$775$	101.129	+	184.483i	0.130489	+	0.238043i
$776$	−90.4137	−	156.601i	−0.116513	−	0.201806i
$777$	−375.827	+	1768.13i	−0.483690	+	2.27558i
$778$	−1101.46	+	1360.19i	−1.41576	+	1.74832i
$779$	185.091	+	254.756i	0.237600	+	0.327029i
$780$	1885.96	−	979.320i	2.41790	−	1.25554i
$781$	536.506	+	389.795i	0.686948	+	0.499097i
$782$	−71.0666	−	265.224i	−0.0908780	−	0.339161i
$783$	131.492	−	58.5440i	0.167933	−	0.0747688i
$784$	318.068	+	1496.39i	0.405699	+	1.90867i
$785$	−605.333	+	860.190i	−0.771124	+	1.09578i
$786$	73.8289	+	1408.74i	0.0939298	+	1.79229i
$787$	172.187	+	111.820i	0.218789	+	0.142083i	0.649380	−	0.760464i	$-0.275028\pi$
$787$	172.187	+	111.820i	0.218789	+	0.142083i	−0.430591	+	0.902547i	$0.641695\pi$
$788$	−130.520	+	66.5033i	−0.165634	+	0.0843950i
$789$	−110.592	+	122.824i	−0.140167	+	0.155671i
$790$	1075.45	+	1602.54i	1.36133	+	2.02853i
$791$	−4.41276	+	84.2005i	−0.00557871	+	0.106448i
$792$	−1303.09	+	1793.55i	−1.64532	+	2.26459i
$793$	403.735	−	322.023i	0.509124	−	0.406082i
$794$	−1282.96	−	932.122i	−1.61581	−	1.17396i
$795$	−295.437	+	35.5698i	−0.371619	+	0.0447419i
$796$	64.4611	+	613.307i	0.0809813	+	0.770486i
$797$	−278.802	+	626.200i	−0.349815	+	0.785697i	0.649857	+	0.760057i	$0.274829\pi$
$797$	−278.802	+	626.200i	−0.349815	+	0.785697i	−0.999671	+	0.0256397i	$0.991838\pi$
$798$	−837.154	−	426.551i	−1.04906	−	0.534525i
$799$	292.971	+	78.5013i	0.366672	+	0.0982495i
$800$	1.84319	+	22.2744i	0.00230399	+	0.0278430i
$801$	317.949	+	317.949i	0.396940	+	0.396940i
$802$	−780.229	+	866.532i	−0.972854	+	1.08046i
$803$	1752.62	−	184.208i	2.18259	−	0.229399i
$804$	744.716	−	919.647i	0.926263	−	1.14384i
$805$	−217.688	+	115.091i	−0.270420	+	0.142970i
$806$	318.918	−	203.770i	0.395679	−	0.252816i
$807$	846.215			1.04859
$808$	−356.637	+	929.071i	−0.441382	+	1.14984i
$809$	−826.486	−	917.905i	−1.02161	−	1.13462i	−0.990833	−	0.135091i	$-0.956867\pi$
$809$	−826.486	−	917.905i	−1.02161	−	1.13462i	−0.0307807	−	0.999526i	$-0.509799\pi$
$810$	580.496	+	1446.57i	0.716662	+	1.78589i
$811$	198.485	+	101.133i	0.244741	+	0.124702i	0.572059	−	0.820213i	$-0.306145\pi$
$811$	198.485	+	101.133i	0.244741	+	0.124702i	−0.327318	+	0.944914i	$0.606145\pi$
$812$	1587.08	−	2443.89i	1.95453	−	3.00972i
$813$	−972.510	−	631.556i	−1.19620	−	0.776821i
$814$	1176.11	−	2308.25i	1.44485	−	2.83569i
$815$	−723.279	+	290.246i	−0.887459	+	0.356130i
$816$	−930.220	+	837.573i	−1.13997	+	1.02644i
$817$	82.8424	+	31.8002i	0.101398	+	0.0389232i
$818$		−	1406.12i		−	1.71897i
$819$	−265.749	+	1206.31i	−0.324480	+	1.47290i
$820$	−1074.00	−	2031.41i	−1.30975	−	2.47733i
$821$	117.356	+	95.0333i	0.142943	+	0.115753i	0.698125	−	0.715976i	$-0.254018\pi$
$821$	117.356	+	95.0333i	0.142943	+	0.115753i	−0.555182	+	0.831729i	$0.687351\pi$
$822$	−370.525	−	3525.31i	−0.450761	−	4.28870i
$823$	362.067	+	326.007i	0.439936	+	0.396120i	0.859114	−	0.511784i	$-0.171015\pi$
$823$	362.067	+	326.007i	0.439936	+	0.396120i	−0.419178	+	0.907904i	$0.637682\pi$
$824$	310.684	−	310.684i	0.377044	−	0.377044i
$825$	1807.07	+	1097.41i	2.19039	+	1.33019i
$826$	511.721	−	1909.77i	0.619517	−	2.31207i
$827$	349.956	−	686.828i	0.423164	−	0.830505i	−0.576744	−	0.816925i	$-0.695677\pi$
$827$	349.956	−	686.828i	0.423164	−	0.830505i	0.999908	−	0.0135804i	$-0.00432291\pi$
$828$	−231.717	−	103.167i	−0.279851	−	0.124598i
$829$	−1537.33	+	161.580i	−1.85444	+	0.194909i	−0.965018	−	0.262185i	$-0.915557\pi$
$829$	−1537.33	+	161.580i	−1.85444	+	0.194909i	−0.889419	+	0.457094i	$0.848890\pi$
$830$	−268.433	−	2229.57i	−0.323413	−	2.68622i
$831$	243.003	−	334.464i	0.292422	−	0.402484i
$832$	842.494	−	127.057i	1.01261	−	0.152713i
$833$	−1549.06	−	1125.46i	−1.85962	−	1.35109i
$834$	352.300	+	18.4632i	0.422422	+	0.0221382i
$835$	464.025	−	311.403i	0.555718	−	0.372937i
$836$	666.208	+	599.857i	0.796900	+	0.717532i
$837$	18.2292	+	35.7769i	0.0217793	+	0.0427442i
$838$	246.740	−	379.946i	0.294439	−	0.453396i
$839$	−1546.51	+	81.0489i	−1.84327	+	0.0966018i	−0.941788	−	0.336209i	$-0.890855\pi$
$839$	−1546.51	+	81.0489i	−1.84327	+	0.0966018i	−0.901485	+	0.432810i	$0.857522\pi$
$840$	2792.06	+	1964.83i	3.32388	+	2.33908i
$841$	−67.4831	+	14.3440i	−0.0802416	+	0.0170559i
$842$	466.225	+	1047.16i	0.553712	+	1.24366i
$843$	−1824.72	+	488.932i	−2.16456	+	0.579991i
$844$	−1266.39	+	1743.04i	−1.50046	+	2.06521i
$845$	−683.467	+	496.888i	−0.808837	+	0.588033i
$846$	340.469	−	247.365i	0.402445	−	0.292393i
$847$	2862.03	+	2317.63i	3.37902	+	2.73628i
$848$	221.485	+	47.0781i	0.261185	+	0.0555166i
$849$	−427.099	+	246.586i	−0.503061	+	0.290443i
$850$	1230.49	+	1158.33i	1.44764	+	1.36274i
$851$	142.566	+	38.2004i	0.167527	+	0.0448888i
$852$	1050.54	−	55.0564i	1.23303	−	0.0646201i
$853$	−770.907	−	122.100i	−0.903760	−	0.143142i	−0.312778	−	0.949826i	$-0.601260\pi$
$853$	−770.907	−	122.100i	−0.903760	−	0.143142i	−0.590982	+	0.806685i	$0.701260\pi$
$854$	1522.12	+	677.690i	1.78234	+	0.793548i
$855$	−205.780	+	58.4829i	−0.240679	+	0.0684011i
$856$	1307.50	+	501.902i	1.52745	+	0.586334i
$857$			111.321i			0.129896i	0.997889	+	0.0649480i	$0.0206882\pi$
$857$			111.321i			0.129896i	−0.997889	+	0.0649480i	$0.979312\pi$
$858$	1751.64	−	3375.82i	2.04154	−	3.93453i
$859$	343.736	−	1057.91i	0.400159	−	1.23156i	−0.524712	−	0.851280i	$-0.675827\pi$
$859$	343.736	−	1057.91i	0.400159	−	1.23156i	0.924871	−	0.380282i	$-0.124173\pi$
$860$	−565.597	−	315.257i	−0.657671	−	0.366578i
$861$	2806.79	+	596.602i	3.25992	+	0.692917i
$862$	347.353	+	1634.17i	0.402961	+	1.89578i
$863$	−530.204	−	1040.58i	−0.614373	−	1.20578i	−0.963250	−	0.268607i	$-0.913437\pi$
$863$	−530.204	−	1040.58i	−0.614373	−	1.20578i	0.348876	−	0.937169i	$-0.386563\pi$
$864$	0.223254	+	4.25994i	0.000258396	+	0.00493048i
$865$	942.072	−	215.161i	1.08910	−	0.248741i
$866$	−1320.00	+	672.572i	−1.52424	+	0.776642i
$867$	39.8074	−	378.743i	0.0459140	−	0.436843i
$868$	704.001	+	406.455i	0.811062	+	0.468267i
$869$	2146.82	+	824.089i	2.47045	+	0.948318i
$870$	−366.827	−	2109.39i	−0.421640	−	2.42458i
$871$	−238.281	+	405.753i	−0.273571	+	0.465848i
$872$	−1178.96	+	856.561i	−1.35201	+	0.982295i
$873$	86.5941	−	56.2349i	0.0991914	−	0.0644156i
$874$	−38.3580	+	66.4381i	−0.0438879	+	0.0760161i
$875$	766.995	−	1307.08i	0.876565	−	1.49381i
$876$	1976.73	−	1976.73i	2.25655	−	2.25655i
$877$	0.654450	+	12.4876i	0.000746237	+	0.0142390i	0.998977	−	0.0452151i	$-0.0143973\pi$
$877$	0.654450	+	12.4876i	0.000746237	+	0.0142390i	−0.998231	+	0.0594541i	$0.981064\pi$
$878$	343.993	+	896.131i	0.391791	+	1.02065i
$879$	−2373.76	−	375.967i	−2.70052	−	0.427721i
$880$	−1031.19	−	1234.82i	−1.17181	−	1.40320i
$881$	462.077	+	1037.84i	0.524492	+	1.17803i	0.960549	+	0.278109i	$0.0897077\pi$
$881$	462.077	+	1037.84i	0.524492	+	1.17803i	−0.436058	+	0.899919i	$0.643626\pi$
$882$	−2566.22	+	687.617i	−2.90955	+	0.779611i
$883$	567.693	−	781.363i	0.642914	−	0.884896i	−0.355852	−	0.934542i	$-0.615809\pi$
$883$	567.693	−	781.363i	0.642914	−	0.884896i	0.998767	+	0.0496464i	$0.0158094\pi$
$884$	1285.29	−	1563.41i	1.45395	−	1.76857i
$885$	−452.038	−	855.007i	−0.510778	−	0.966109i
$886$	509.614	−	330.947i	0.575185	−	0.373530i
$887$	−887.549	−	985.723i	−1.00062	−	1.11130i	−0.993784	−	0.111323i	$-0.964491\pi$
$887$	−887.549	−	985.723i	−1.00062	−	1.11130i	−0.00683412	−	0.999977i	$-0.502175\pi$
$888$	−425.470	−	2001.68i	−0.479133	−	2.25414i
$889$	−553.503	−	282.024i	−0.622613	−	0.317237i
$890$	−851.851	+	509.120i	−0.957136	+	0.572045i
$891$	1557.58	+	1011.50i	1.74813	+	1.13525i
$892$	−121.154	−	764.936i	−0.135823	−	0.857551i
$893$	−42.3709	−	73.3886i	−0.0474479	−	0.0821821i
$894$	715.887	+	1607.91i	0.800769	+	1.79856i
$895$	−413.285	+	741.466i	−0.461770	+	0.828453i
$896$	1590.27	+	2188.82i	1.77485	+	2.44287i
$897$	208.877	+	57.6277i	0.232862	+	0.0642450i
$898$	−750.656	−	2310.28i	−0.835920	−	2.57270i
$899$	−65.7031	−	245.207i	−0.0730847	−	0.272756i
$900$	1546.89	−	209.984i	1.71877	−	0.233315i
$901$	−245.437	+	141.703i	−0.272405	+	0.157273i
$902$	−3664.20	−	1867.00i	−4.06230	−	2.06985i
$903$	754.905	−	289.781i	0.835997	−	0.320909i
$904$	−34.2074	−	89.1133i	−0.0378401	−	0.0985767i
$905$	543.870	+	1591.67i	0.600962	+	1.75875i
$906$	−229.012	+	2178.90i	−0.252773	+	2.40497i
$907$	1199.33	+	692.432i	1.32230	+	0.763431i	0.984095	−	0.177640i	$-0.0568464\pi$
$907$	1199.33	+	692.432i	1.32230	+	0.763431i	0.338207	+	0.941072i	$0.390180\pi$
$908$	−1874.92	−	719.713i	−2.06489	−	0.792635i
$909$	−540.425	−	175.595i	−0.594527	−	0.193174i
$910$	−2438.55	−	1218.93i	−2.67972	−	1.33949i
$911$	334.342	+	1029.00i	0.367005	+	1.12953i	0.948716	+	0.316130i	$0.102384\pi$
$911$	334.342	+	1029.00i	0.367005	+	1.12953i	−0.581711	+	0.813396i	$0.697616\pi$
$912$	349.248	+	18.3033i	0.382947	+	0.0200694i
$913$	−1790.41	−	1988.46i	−1.96102	−	2.17794i
$914$	−1333.84	−	1201.00i	−1.45935	−	1.31400i
$915$	771.248	−	263.534i	0.842894	−	0.288015i
$916$	−348.588	+	536.779i	−0.380555	+	0.586003i
$917$	936.347	−	758.239i	1.02110	−	0.826869i
$918$	228.067	+	228.067i	0.248439	+	0.248439i
$919$	42.2984	−	402.442i	0.0460265	−	0.437913i	−0.947106	−	0.320920i	$-0.896008\pi$
$919$	42.2984	−	402.442i	0.0460265	−	0.437913i	0.993133	−	0.116993i	$-0.0373255\pi$
$920$	172.142	−	219.266i	0.187110	−	0.238333i
$921$	792.848	−	979.086i	0.860856	−	1.06307i
$922$	83.8554	+	115.417i	0.0909494	+	0.125181i
$923$	−409.794	+	83.9411i	−0.443980	+	0.0909438i
$924$	8169.14			8.84106
$925$	−869.931	+	261.495i	−0.940465	+	0.282697i
$926$	−147.967	+	256.286i	−0.159791	+	0.276767i
$927$	186.440	+	167.872i	0.201122	+	0.181091i
$928$	4.21890	−	26.6371i	0.00454623	−	0.0287038i
$929$	1623.48	−	623.197i	1.74756	−	0.670825i	0.747582	−	0.664170i	$-0.231215\pi$
$929$	1623.48	−	623.197i	1.74756	−	0.670825i	0.999978	−	0.00665553i	$-0.00211854\pi$
$930$	582.287	−	132.989i	0.626116	−	0.142999i
$931$	83.6876	+	528.383i	0.0898900	+	0.567543i
$932$	−281.431	−	487.452i	−0.301964	−	0.523017i
$933$	292.305	+	656.527i	0.313296	+	0.703674i
$934$	−113.361	+	2163.06i	−0.121371	+	2.31591i
$935$	1993.30	+	284.923i	2.13187	+	0.304731i
$936$	−280.617	−	1369.95i	−0.299804	−	1.46362i
$937$	−386.652	+	1189.99i	−0.412648	+	1.27000i	0.501689	+	0.865048i	$0.332712\pi$
$937$	−386.652	+	1189.99i	−0.412648	+	1.27000i	−0.914337	+	0.404953i	$0.867288\pi$
$938$	−1516.04	−	79.4525i	−1.61625	−	0.0847042i
$939$	−1328.64	−	282.412i	−1.41495	−	0.300758i
$940$	230.298	+	573.892i	0.244998	+	0.610523i
$941$	209.119	+	410.420i	0.222231	+	0.436153i	0.975022	−	0.222106i	$-0.0712932\pi$
$941$	209.119	+	410.420i	0.222231	+	0.436153i	−0.752792	+	0.658259i	$0.771293\pi$
$942$	1879.26	+	2320.69i	1.99497	+	2.46358i
$943$	60.6406	−	226.314i	0.0643061	−	0.239994i
$944$	115.126	+	726.879i	0.121956	+	0.769999i
$945$	153.853	−	244.933i	0.162808	−	0.259188i
$946$	−1152.52	+	121.134i	−1.21831	+	0.128049i
$947$	676.108	−	834.923i	0.713947	−	0.881651i	−0.283049	−	0.959105i	$-0.591346\pi$
$947$	676.108	−	834.923i	0.713947	−	0.881651i	0.996996	+	0.0774545i	$0.0246792\pi$
$948$	3469.30	−	1127.24i	3.65959	−	1.18907i
$949$	−660.013	+	894.441i	−0.695483	+	0.942509i
$950$	−14.2574	−	471.939i	−0.0150078	−	0.496778i
$951$	506.619	+	1890.73i	0.532722	+	1.98815i
$952$	3180.54	+	676.045i	3.34090	+	0.710131i
$953$	−60.3880	+	135.634i	−0.0633663	+	0.142323i	−0.942453	−	0.334339i	$-0.891487\pi$
$953$	−60.3880	+	135.634i	−0.0633663	+	0.142323i	0.879087	+	0.476662i	$0.158154\pi$
$954$	−61.5149	+	388.390i	−0.0644811	+	0.407118i
$955$	241.886	−	566.141i	0.253284	−	0.592817i
$956$	1757.96	−	1423.57i	1.83887	−	1.48909i
$957$	−1803.88	−	1803.88i	−1.88493	−	1.88493i
$958$	−116.168	+	1105.27i	−0.121261	+	1.15372i
$959$	−2249.91	+	2025.83i	−2.34610	+	2.11244i
$960$	1319.35	+	259.678i	1.37432	+	0.270497i
$961$	−846.614	+	275.081i	−0.880971	+	0.286245i
$962$	574.304	+	1529.84i	0.596989	+	1.59027i
$963$	−247.118	+	760.552i	−0.256613	+	0.789773i
$964$	−2356.34	+	1530.23i	−2.44434	+	1.58737i
$965$	108.792	−	296.730i	0.112738	−	0.307492i
$966$	145.347	+	683.802i	0.150462	+	0.707869i
$967$	23.7704	−	3.76485i	0.0245815	−	0.00389333i	−0.144132	−	0.989559i	$-0.546039\pi$
$967$	23.7704	−	3.76485i	0.0245815	−	0.00389333i	0.168713	+	0.985665i	$0.446039\pi$
$968$	−4027.14	−	1079.07i	−4.16026	−	1.11474i
$969$	−340.175	+	275.468i	−0.351057	+	0.284281i
$970$	73.6840	+	215.641i	0.0759629	+	0.222310i
$971$	94.5271	+	42.0862i	0.0973503	+	0.0433431i	0.454834	−	0.890576i	$-0.349699\pi$
$971$	94.5271	+	42.0862i	0.0973503	+	0.0433431i	−0.357484	+	0.933919i	$0.616365\pi$
$972$	2589.69	−	272.188i	2.66429	−	0.280029i
$973$	−164.106	−	252.701i	−0.168660	−	0.259714i
$974$			2934.05i			3.01237i
$975$	−1279.93	+	374.438i	−1.31275	+	0.384039i
$976$	−620.187			−0.635437
$977$	−50.8382	+	33.0147i	−0.0520350	+	0.0337919i	−0.570394	−	0.821371i	$-0.693210\pi$
$977$	−50.8382	+	33.0147i	−0.0520350	+	0.0337919i	0.518359	+	0.855163i	$0.326543\pi$
$978$	231.276	+	2200.45i	0.236479	+	2.24994i
$979$	−480.946	+	1080.22i	−0.491262	+	1.10339i
$980$	−58.9468	−	3903.32i	−0.0601498	−	3.98298i
$981$	−523.653	−	646.658i	−0.533796	−	0.659183i
$982$	−573.943	+	2141.98i	−0.584463	+	2.18125i
$983$	29.8862	+	188.694i	0.0304030	+	0.191957i	0.998215	−	0.0597156i	$-0.0190194\pi$
$983$	29.8862	+	188.694i	0.0304030	+	0.191957i	−0.967812	+	0.251673i	$0.919019\pi$
$984$	−3177.54	+	675.407i	−3.22921	+	0.686389i
$985$	88.4248	−	25.1304i	0.0897713	−	0.0255131i
$986$	−1110.59	−	1710.16i	−1.12636	−	1.73444i
$987$	−734.419	−	238.627i	−0.744092	−	0.241770i
$988$	−562.795	+	54.9464i	−0.569630	+	0.0556137i
$989$	−20.4026	−	62.7927i	−0.0206295	−	0.0634911i
$990$	2047.77	−	1900.59i	2.06845	−	1.91978i
$991$	−674.992	−	749.655i	−0.681123	−	0.756463i	0.299130	−	0.954212i	$-0.403304\pi$
$991$	−674.992	−	749.655i	−0.681123	−	0.756463i	−0.980253	+	0.197749i	$0.936637\pi$
$992$	7.48229	+	0.786420i	0.00754263	+	0.000792762i
$993$	−473.503	+	473.503i	−0.476841	+	0.476841i
$994$	−849.313	−	1048.81i	−0.854440	−	1.05515i
$995$	34.6360	−	385.444i	0.0348100	−	0.387381i
$996$	−4192.30	−	663.995i	−4.20914	−	0.666662i
$997$	−796.714	−	354.720i	−0.799111	−	0.355787i	−0.0337843	−	0.999429i	$-0.510756\pi$
$997$	−796.714	−	354.720i	−0.799111	−	0.355787i	−0.765327	+	0.643642i	$0.777423\pi$
$998$	53.3998	−	251.227i	0.0535069	−	0.251730i
$999$	−167.465	+	44.8720i	−0.167632	+	0.0449169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.bm.a.6.5	✓	1088
13.11	odd	12	inner	325.3.bm.a.206.64	yes	1088
25.21	even	5	inner	325.3.bm.a.71.64	yes	1088
325.271	odd	60	inner	325.3.bm.a.271.5	yes	1088

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.bm.a.6.5	✓	1088	1.1	even	1	trivial
325.3.bm.a.71.64	yes	1088	25.21	even	5	inner
325.3.bm.a.206.64	yes	1088	13.11	odd	12	inner
325.3.bm.a.271.5	yes	1088	325.271	odd	60	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.bm (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.90131 + 1.88413i) q^{2} +(-0.428913 - 4.08083i) q^{3} +(3.24070 - 7.27873i) q^{4} +(-2.87751 + 4.08900i) q^{5} +(8.93325 + 11.0316i) q^{6} +(3.13792 - 11.7109i) q^{7} +(2.14713 + 13.5565i) q^{8} +(-7.66591 + 1.62944i) q^{9} +(0.644328 - 17.2851i) q^{10} +(-11.2248 - 17.2847i) q^{11} +(-31.0933 - 10.1028i) q^{12} +(12.8246 + 2.12857i) q^{13} +(12.9608 + 39.8892i) q^{14} +(17.9207 + 9.98882i) q^{15} +(-10.4464 - 11.6018i) q^{16} +(19.4329 + 2.04248i) q^{17} +(19.1711 - 19.1711i) q^{18} +(-3.43568 - 4.24271i) q^{19} +(20.4376 + 34.1959i) q^{20} +(-49.1361 - 7.78239i) q^{21} +(65.1333 + 28.9992i) q^{22} +(-0.844542 + 3.97326i) q^{23} +(54.4008 - 14.5766i) q^{24} +(-8.43987 - 23.5323i) q^{25} +(-41.2185 + 17.9875i) q^{26} +(-1.47446 - 4.53792i) q^{27} +(-75.0713 - 60.7916i) q^{28} +(3.15321 + 30.0008i) q^{29} +(-70.8139 + 4.78440i) q^{30} +(-8.31173 + 1.31645i) q^{31} +(-0.863560 - 0.231390i) q^{32} +(-65.7215 + 53.2202i) q^{33} +(-60.2293 + 30.6883i) q^{34} +(38.8564 + 46.5292i) q^{35} +(-12.9827 + 61.0786i) q^{36} +(1.90164 - 36.2855i) q^{37} +(17.9618 + 5.83615i) q^{38} +(3.18571 - 53.2478i) q^{39} +(-61.6109 - 30.2293i) q^{40} +(-57.6009 - 3.01874i) q^{41} +(157.222 - 69.9998i) q^{42} +(-14.0764 + 8.12700i) q^{43} +(-162.187 + 25.6879i) q^{44} +(15.3960 - 36.0346i) q^{45} +(-5.03587 - 13.1189i) q^{46} +(15.3312 + 2.42823i) q^{47} +(-42.8646 + 47.6060i) q^{48} +(-84.8630 - 48.9957i) q^{49} +(68.8247 + 52.3727i) q^{50} -80.1786i q^{51} +(57.0538 - 86.4485i) q^{52} +(-11.7339 + 8.52520i) q^{53} +(12.8279 + 10.3878i) q^{54} +(102.977 + 3.83861i) q^{55} +(165.496 + 17.3943i) q^{56} +(-15.8402 + 15.8402i) q^{57} +(-65.6740 - 81.1006i) q^{58} +(-39.5348 - 25.6742i) q^{59} +(130.782 - 98.0695i) q^{60} +(26.5815 - 29.5218i) q^{61} +(21.6345 - 19.4798i) q^{62} +(-4.97285 + 94.8876i) q^{63} +(62.3323 - 20.2530i) q^{64} +(-45.6065 + 46.3146i) q^{65} +(90.4045 - 278.236i) q^{66} +(-12.9714 + 33.7917i) q^{67} +(77.8430 - 134.828i) q^{68} +(16.5764 + 1.74225i) q^{69} +(-200.402 - 61.7849i) q^{70} +(-30.0399 + 11.5312i) q^{71} +(-38.5492 - 100.424i) q^{72} +(-38.8195 + 76.1875i) q^{73} +(62.8495 + 108.858i) q^{74} +(-92.4114 + 44.5350i) q^{75} +(-42.0156 + 11.2580i) q^{76} +(-237.642 + 77.2144i) q^{77} +(91.0833 + 160.491i) q^{78} +(-90.2677 + 65.5833i) q^{79} +(77.4995 - 9.33071i) q^{80} +(-82.3226 + 36.6524i) q^{81} +(172.806 - 99.7695i) q^{82} +(128.231 - 20.3098i) q^{83} +(-215.881 + 332.428i) q^{84} +(-64.2701 + 73.5840i) q^{85} +(25.5276 - 50.1007i) q^{86} +(121.076 - 25.7355i) q^{87} +(210.218 - 189.281i) q^{88} +(-31.2480 - 48.1176i) q^{89} +(23.2256 + 133.556i) q^{90} +(65.1699 - 143.508i) q^{91} +(26.1834 + 19.0233i) q^{92} +(8.93722 + 33.3541i) q^{93} +(-49.0558 + 21.8410i) q^{94} +(27.2347 - 1.84006i) q^{95} +(-0.573873 + 3.62329i) q^{96} +(-12.2995 + 4.72135i) q^{97} +(338.528 - 17.7415i) q^{98} +(114.213 + 114.213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1088 q - 16 q^{2} - 6 q^{3} - 18 q^{4} - 6 q^{5} - 28 q^{6} - 32 q^{7} - 44 q^{8} + 378 q^{9} - 54 q^{10} - 12 q^{11} + 44 q^{13} - 24 q^{14} + 54 q^{15} - 382 q^{16} - 66 q^{17} - 500 q^{18} + 48 q^{19}+ \cdots - 792 q^{99}+O(q^{100}) \) 1088 * q - 16 * q^2 - 6 * q^3 - 18 * q^4 - 6 * q^5 - 28 * q^6 - 32 * q^7 - 44 * q^8 + 378 * q^9 - 54 * q^10 - 12 * q^11 + 44 * q^13 - 24 * q^14 + 54 * q^15 - 382 * q^16 - 66 * q^17 - 500 * q^18 + 48 * q^19 - 66 * q^20 + 42 * q^21 + 196 * q^22 - 18 * q^23 - 36 * q^24 - 12 * q^26 - 76 * q^28 + 94 * q^29 - 216 * q^30 - 12 * q^31 - 152 * q^32 - 222 * q^33 + 64 * q^34 - 82 * q^35 - 126 * q^36 - 210 * q^37 - 288 * q^39 - 432 * q^40 - 462 * q^41 + 222 * q^42 - 48 * q^43 + 36 * q^44 - 458 * q^45 - 396 * q^46 - 186 * q^47 - 334 * q^48 - 48 * q^49 + 106 * q^50 - 122 * q^52 + 12 * q^53 - 940 * q^54 + 130 * q^55 + 714 * q^56 - 252 * q^57 - 312 * q^58 - 132 * q^59 + 132 * q^60 + 294 * q^61 + 198 * q^62 + 1192 * q^63 + 338 * q^65 + 384 * q^66 - 236 * q^67 - 236 * q^68 - 648 * q^69 - 1114 * q^70 - 92 * q^71 + 546 * q^72 + 928 * q^73 + 164 * q^74 + 132 * q^75 + 620 * q^76 - 1742 * q^78 + 216 * q^79 - 540 * q^80 + 806 * q^81 + 3132 * q^82 + 874 * q^83 + 496 * q^84 + 514 * q^85 - 276 * q^86 + 74 * q^87 - 2394 * q^88 - 672 * q^89 + 308 * q^91 + 1960 * q^92 + 1008 * q^93 + 474 * q^94 + 2328 * q^95 - 1626 * q^96 + 632 * q^97 + 84 * q^98 - 792 * q^99

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