LMFDB - Embedded newform 375.3.p.a.14.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(14,375)] 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("375.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([25, 43])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.p (of order $50$, degree $20$, 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:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$1960$
Relative dimension:	$98$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			14.4
Character	$\chi$	$=$	375.14
Dual form			375.3.p.a.134.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60052 - 3.40129i) q^{2} +(2.98667 + 0.282520i) q^{3} +(-6.45738 + 7.80563i) q^{4} +(-3.91956 - 3.10436i) q^{5} +(-3.81930 - 10.6107i) q^{6} +(-11.0932 - 3.60439i) q^{7} +(22.3206 + 5.73095i) q^{8} +(8.84036 + 1.68759i) q^{9} +(-4.28549 + 18.3001i) q^{10} +(1.91142 - 0.899444i) q^{11} +(-21.4913 + 21.4885i) q^{12} +(-1.81735 + 14.3858i) q^{13} +(5.49532 + 43.4999i) q^{14} +(-10.8294 - 10.3791i) q^{15} +(-8.63901 - 45.2873i) q^{16} +(2.62788 + 3.17656i) q^{17} +(-8.40925 - 32.7696i) q^{18} +(0.141484 + 2.24882i) q^{19} +(49.5416 - 10.5486i) q^{20} +(-32.1133 - 13.8991i) q^{21} +(-6.11854 - 5.06169i) q^{22} +(-15.1956 - 8.35385i) q^{23} +(65.0451 + 23.4225i) q^{24} +(5.72585 + 24.3355i) q^{25} +(51.8390 - 16.8435i) q^{26} +(25.9265 + 7.53784i) q^{27} +(99.7673 - 63.3143i) q^{28} +(-33.7328 + 21.4075i) q^{29} +(-17.9695 + 53.4457i) q^{30} +(35.5800 + 43.0088i) q^{31} +(-65.6343 + 47.6861i) q^{32} +(5.96288 - 2.14633i) q^{33} +(6.59840 - 14.0223i) q^{34} +(32.2910 + 48.5648i) q^{35} +(-70.2583 + 58.1072i) q^{36} +(13.3991 - 2.55602i) q^{37} +(7.42245 - 4.08053i) q^{38} +(-9.49210 + 42.4522i) q^{39} +(-69.6959 - 91.7540i) q^{40} +(12.8524 + 23.3784i) q^{41} +(4.12310 + 131.472i) q^{42} +(16.1269 - 22.1968i) q^{43} +(-5.32201 + 20.7279i) q^{44} +(-29.4114 - 34.0583i) q^{45} +(-4.09292 + 65.0551i) q^{46} +(47.2209 - 12.1243i) q^{47} +(-13.0073 - 137.699i) q^{48} +(70.4249 + 51.1666i) q^{49} +(73.6075 - 58.4248i) q^{50} +(6.95115 + 10.2297i) q^{51} +(-100.555 - 107.080i) q^{52} +(-70.3159 - 27.8401i) q^{53} +(-15.8576 - 100.248i) q^{54} +(-10.2841 - 2.40831i) q^{55} +(-226.949 - 144.026i) q^{56} +(-0.212772 + 6.75646i) q^{57} +(126.803 + 80.4718i) q^{58} +(-71.8385 + 76.5002i) q^{59} +(150.944 - 17.5086i) q^{60} +(-79.9690 - 43.9634i) q^{61} +(89.3387 - 189.854i) q^{62} +(-91.9849 - 50.5848i) q^{63} +(105.639 + 58.0754i) q^{64} +(51.7820 - 50.7443i) q^{65} +(-16.8440 - 16.8462i) q^{66} +(-0.790803 - 0.501859i) q^{67} -41.7642 q^{68} +(-43.0241 - 29.2432i) q^{69} +(113.500 - 187.560i) q^{70} +(28.8297 + 112.284i) q^{71} +(187.651 + 88.3316i) q^{72} +(-0.816947 - 0.869960i) q^{73} +(-30.1394 - 41.4833i) q^{74} +(10.2260 + 74.2996i) q^{75} +(-18.4671 - 13.4171i) q^{76} +(-24.4456 + 3.08820i) q^{77} +(159.584 - 35.6604i) q^{78} +(-1.30598 + 20.7579i) q^{79} +(-106.727 + 204.325i) q^{80} +(75.3041 + 29.8378i) q^{81} +(58.9460 - 81.1322i) q^{82} +(5.05282 + 80.3122i) q^{83} +(315.859 - 160.912i) q^{84} +(-0.438924 - 20.6086i) q^{85} +(-101.309 - 19.3257i) q^{86} +(-106.797 + 54.4069i) q^{87} +(47.8186 - 9.12189i) q^{88} +(-70.8597 - 75.4579i) q^{89} +(-68.7683 + 154.548i) q^{90} +(72.0122 - 153.034i) q^{91} +(163.331 - 64.6673i) q^{92} +(94.1147 + 138.505i) q^{93} +(-116.816 - 141.207i) q^{94} +(6.42661 - 9.25361i) q^{95} +(-209.500 + 123.880i) q^{96} +(-62.9349 + 39.9397i) q^{97} +(61.3158 - 321.429i) q^{98} +(18.4155 - 4.72574i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) $ 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{43}{50}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.60052	−	3.40129i	−0.800262	−	1.70064i	−0.709428	−	0.704777i	$-0.751047\pi$
$2$	−1.60052	−	3.40129i	−0.800262	−	1.70064i	−0.0908336	−	0.995866i	$-0.528953\pi$
$3$	2.98667	+	0.282520i	0.995556	+	0.0941733i
$3$	2.98667	+	0.282520i	0.995556	+	0.0941733i
$4$	−6.45738	+	7.80563i	−1.61434	+	1.95141i
$5$	−3.91956	−	3.10436i	−0.783911	−	0.620873i
$5$	−3.91956	−	3.10436i	−0.783911	−	0.620873i
$6$	−3.81930	−	10.6107i	−0.636550	−	1.76845i
$7$	−11.0932	−	3.60439i	−1.58474	−	0.514913i	−0.621466	−	0.783441i	$-0.713463\pi$
$7$	−11.0932	−	3.60439i	−1.58474	−	0.514913i	−0.963272	+	0.268529i	$0.913463\pi$
$8$	22.3206	+	5.73095i	2.79007	+	0.716369i
$9$	8.84036	+	1.68759i	0.982263	+	0.187510i
$10$	−4.28549	+	18.3001i	−0.428549	+	1.83001i
$11$	1.91142	−	0.899444i	0.173765	−	0.0817677i	−0.336929	−	0.941530i	$-0.609388\pi$
$11$	1.91142	−	0.899444i	0.173765	−	0.0817677i	0.510694	+	0.859762i	$0.329388\pi$
$12$	−21.4913	+	21.4885i	−1.79094	+	1.79071i
$13$	−1.81735	+	14.3858i	−0.139796	+	1.10660i	0.753601	+	0.657332i	$0.228315\pi$
$13$	−1.81735	+	14.3858i	−0.139796	+	1.10660i	−0.893397	+	0.449268i	$0.851685\pi$
$14$	5.49532	+	43.4999i	0.392523	+	3.10714i
$15$	−10.8294	−	10.3791i	−0.721958	−	0.691937i
$16$	−8.63901	−	45.2873i	−0.539938	−	2.83046i
$17$	2.62788	+	3.17656i	0.154581	+	0.186856i	0.842118	−	0.539293i	$-0.181308\pi$
$17$	2.62788	+	3.17656i	0.154581	+	0.186856i	−0.687537	+	0.726149i	$0.741308\pi$
$18$	−8.40925	−	32.7696i	−0.467181	−	1.82054i
$19$	0.141484	+	2.24882i	0.00744653	+	0.118359i	0.999994	−	0.00350044i	$-0.00111423\pi$
$19$	0.141484	+	2.24882i	0.00744653	+	0.118359i	−0.992547	+	0.121860i	$0.961114\pi$
$20$	49.5416	−	10.5486i	2.47708	−	0.527428i
$21$	−32.1133	−	13.8991i	−1.52920	−	0.661864i
$22$	−6.11854	−	5.06169i	−0.278115	−	0.230077i
$23$	−15.1956	−	8.35385i	−0.660678	−	0.363211i	0.115874	−	0.993264i	$-0.463033\pi$
$23$	−15.1956	−	8.35385i	−0.660678	−	0.363211i	−0.776552	+	0.630053i	$0.783033\pi$
$24$	65.0451	+	23.4225i	2.71021	+	0.975936i
$25$	5.72585	+	24.3355i	0.229034	+	0.973418i
$26$	51.8390	−	16.8435i	1.99381	−	0.647827i
$27$	25.9265	+	7.53784i	0.960239	+	0.279179i
$28$	99.7673	−	63.3143i	3.56312	−	2.26122i
$29$	−33.7328	+	21.4075i	−1.16320	+	0.738190i	−0.970032	−	0.242976i	$-0.921876\pi$
$29$	−33.7328	+	21.4075i	−1.16320	+	0.738190i	−0.193169	+	0.981166i	$0.561876\pi$
$30$	−17.9695	+	53.4457i	−0.598983	+	1.78152i
$31$	35.5800	+	43.0088i	1.14774	+	1.38738i	0.909257	+	0.416234i	$0.136650\pi$
$31$	35.5800	+	43.0088i	1.14774	+	1.38738i	0.238484	+	0.971147i	$0.423350\pi$
$32$	−65.6343	+	47.6861i	−2.05107	+	1.49019i
$33$	5.96288	−	2.14633i	0.180693	−	0.0650402i
$34$	6.59840	−	14.0223i	0.194071	−	0.412421i
$35$	32.2910	+	48.5648i	0.922599	+	1.38757i
$36$	−70.2583	+	58.1072i	−1.95162	+	1.61409i
$37$	13.3991	−	2.55602i	0.362138	−	0.0690816i	−0.00310109	−	0.999995i	$-0.500987\pi$
$37$	13.3991	−	2.55602i	0.362138	−	0.0690816i	0.365239	+	0.930914i	$0.380987\pi$
$38$	7.42245	−	4.08053i	0.195328	−	0.107382i
$39$	−9.49210	+	42.4522i	−0.243387	+	1.08852i
$40$	−69.6959	−	91.7540i	−1.74240	−	2.29385i
$41$	12.8524	+	23.3784i	0.313472	+	0.570204i	0.985368	−	0.170442i	$-0.0545196\pi$
$41$	12.8524	+	23.3784i	0.313472	+	0.570204i	−0.671895	+	0.740646i	$0.734520\pi$
$42$	4.12310	+	131.472i	0.0981689	+	3.13030i
$43$	16.1269	−	22.1968i	0.375044	−	0.516204i	−0.579219	−	0.815172i	$-0.696642\pi$
$43$	16.1269	−	22.1968i	0.375044	−	0.516204i	0.954263	+	0.298968i	$0.0966424\pi$
$44$	−5.32201	+	20.7279i	−0.120955	+	0.471088i
$45$	−29.4114	−	34.0583i	−0.653587	−	0.756851i
$46$	−4.09292	+	65.0551i	−0.0889766	+	1.41424i
$47$	47.2209	−	12.1243i	1.00470	−	0.257963i	0.289722	−	0.957111i	$-0.406437\pi$
$47$	47.2209	−	12.1243i	1.00470	−	0.257963i	0.714977	+	0.699148i	$0.246437\pi$
$48$	−13.0073	−	137.699i	−0.270985	−	2.86872i
$49$	70.4249	+	51.1666i	1.43724	+	1.04422i
$50$	73.6075	−	58.4248i	1.47215	−	1.16850i
$51$	6.95115	+	10.2297i	0.136297	+	0.200583i
$52$	−100.555	−	107.080i	−1.93375	−	2.05923i
$53$	−70.3159	−	27.8401i	−1.32672	−	0.525284i	−0.405414	−	0.914133i	$-0.632873\pi$
$53$	−70.3159	−	27.8401i	−1.32672	−	0.525284i	−0.921301	+	0.388849i	$0.872873\pi$
$54$	−15.8576	−	100.248i	−0.293659	−	1.85644i
$55$	−10.2841	−	2.40831i	−0.186984	−	0.0437874i
$56$	−226.949	−	144.026i	−4.05267	−	2.57190i
$57$	−0.212772	+	6.75646i	−0.00373284	+	0.118534i
$58$	126.803	+	80.4718i	2.18626	+	1.38744i
$59$	−71.8385	+	76.5002i	−1.21760	+	1.29661i	−0.275494	+	0.961303i	$0.588841\pi$
$59$	−71.8385	+	76.5002i	−1.21760	+	1.29661i	−0.942107	+	0.335311i	$0.891159\pi$
$60$	150.944	−	17.5086i	2.51574	−	0.291809i
$61$	−79.9690	−	43.9634i	−1.31097	−	0.720711i	−0.335749	−	0.941952i	$-0.608989\pi$
$61$	−79.9690	−	43.9634i	−1.31097	−	0.720711i	−0.975219	+	0.221241i	$0.928989\pi$
$62$	89.3387	−	189.854i	1.44095	−	3.06217i
$63$	−91.9849	−	50.5848i	−1.46008	−	0.802933i
$64$	105.639	+	58.0754i	1.65061	+	0.907428i
$65$	51.7820	−	50.7443i	0.796646	−	0.780681i
$66$	−16.8440	−	16.8462i	−0.255212	−	0.255246i
$67$	−0.790803	−	0.501859i	−0.0118030	−	0.00749043i	0.529912	−	0.848053i	$-0.322225\pi$
$67$	−0.790803	−	0.501859i	−0.0118030	−	0.00749043i	−0.541715	+	0.840562i	$0.682225\pi$
$68$	−41.7642			−0.614180
$69$	−43.0241	−	29.2432i	−0.623537	−	0.423815i
$70$	113.500	−	187.560i	1.62143	−	2.67943i
$71$	28.8297	+	112.284i	0.406052	+	1.58147i	0.762395	+	0.647112i	$0.224023\pi$
$71$	28.8297	+	112.284i	0.406052	+	1.58147i	−0.356344	+	0.934355i	$0.615977\pi$
$72$	187.651	+	88.3316i	2.60626	+	1.22683i
$73$	−0.816947	−	0.869960i	−0.0111911	−	0.0119173i	0.723349	−	0.690483i	$-0.242602\pi$
$73$	−0.816947	−	0.869960i	−0.0111911	−	0.0119173i	−0.734540	+	0.678566i	$0.762602\pi$
$74$	−30.1394	−	41.4833i	−0.407289	−	0.560585i
$75$	10.2260	+	74.2996i	0.136346	+	0.990661i
$76$	−18.4671	−	13.4171i	−0.242988	−	0.176541i
$77$	−24.4456	+	3.08820i	−0.317475	+	0.0401065i
$78$	159.584	−	35.6604i	2.04595	−	0.457185i
$79$	−1.30598	+	20.7579i	−0.0165313	+	0.262758i	0.981076	+	0.193623i	$0.0620239\pi$
$79$	−1.30598	+	20.7579i	−0.0165313	+	0.262758i	−0.997607	+	0.0691350i	$0.977976\pi$
$80$	−106.727	+	204.325i	−1.33409	+	2.55406i
$81$	75.3041	+	29.8378i	0.929680	+	0.368367i
$82$	58.9460	−	81.1322i	0.718853	−	0.989417i
$83$	5.05282	+	80.3122i	0.0608773	+	0.967617i	0.903357	+	0.428889i	$0.141095\pi$
$83$	5.05282	+	80.3122i	0.0608773	+	0.967617i	−0.842480	+	0.538728i	$0.818905\pi$
$84$	315.859	−	160.912i	3.76023	−	1.91562i
$85$	−0.438924	−	20.6086i	−0.00516381	−	0.242454i
$86$	−101.309	−	19.3257i	−1.17801	−	0.224718i
$87$	−106.797	+	54.4069i	−1.22755	+	0.625367i
$88$	47.8186	−	9.12189i	0.543393	−	0.103658i
$89$	−70.8597	−	75.4579i	−0.796176	−	0.847842i	0.194943	−	0.980814i	$-0.437548\pi$
$89$	−70.8597	−	75.4579i	−0.796176	−	0.847842i	−0.991120	+	0.132973i	$0.957548\pi$
$90$	−68.7683	+	154.548i	−0.764093	+	1.71720i
$91$	72.0122	−	153.034i	0.791343	−	1.68169i
$92$	163.331	−	64.6673i	1.77534	−	0.702905i
$93$	94.1147	+	138.505i	1.01199	+	1.48930i
$94$	−116.816	−	141.207i	−1.24273	−	1.50220i
$95$	6.42661	−	9.25361i	0.0676486	−	0.0974065i
$96$	−209.500	+	123.880i	−2.18229	+	1.29041i
$97$	−62.9349	+	39.9397i	−0.648814	+	0.411750i	−0.819105	−	0.573644i	$-0.805529\pi$
$97$	−62.9349	+	39.9397i	−0.648814	+	0.411750i	0.170291	+	0.985394i	$0.445529\pi$
$98$	61.3158	−	321.429i	0.625671	−	3.27988i
$99$	18.4155	−	4.72574i	0.186015	−	0.0477347i
$100$	−226.928	−	112.449i	−2.26928	−	1.12449i
$101$	−89.7182	−	29.1512i	−0.888299	−	0.288626i	−0.170900	−	0.985288i	$-0.554667\pi$
$101$	−89.7182	−	29.1512i	−0.888299	−	0.288626i	−0.717399	+	0.696663i	$0.754667\pi$
$102$	23.6688	−	40.0158i	0.232047	−	0.392312i
$103$	−144.789	−	119.780i	−1.40572	−	1.16291i	−0.964047	−	0.265731i	$-0.914387\pi$
$103$	−144.789	−	119.780i	−1.40572	−	1.16291i	−0.441668	−	0.897178i	$-0.645613\pi$
$104$	−123.009	+	310.684i	−1.18278	+	2.98735i
$105$	82.7218	+	154.170i	0.787827	+	1.46828i
$106$	17.8504	+	283.723i	0.168400	+	2.67664i
$107$	17.4467	+	53.6954i	0.163053	+	0.501826i	0.998888	−	0.0471555i	$-0.0150156\pi$
$107$	17.4467	+	53.6954i	0.163053	+	0.501826i	−0.835834	+	0.548982i	$0.815016\pi$
$108$	−226.255	+	153.698i	−2.09495	+	1.42313i
$109$	13.0437	+	68.3777i	0.119667	+	0.627318i	0.990697	+	0.136088i	$0.0434528\pi$
$109$	13.0437	+	68.3777i	0.119667	+	0.627318i	−0.871029	+	0.491231i	$0.836547\pi$
$110$	8.26862	+	38.8338i	0.0751692	+	0.353034i
$111$	40.7408	−	3.84846i	0.367035	−	0.0346708i
$112$	−67.3990	+	533.518i	−0.601776	+	4.76355i
$113$	−41.3575	−	38.8373i	−0.365996	−	0.343693i	0.479628	−	0.877472i	$-0.340772\pi$
$113$	−41.3575	−	38.8373i	−0.365996	−	0.343693i	−0.845624	+	0.533779i	$0.820772\pi$
$114$	23.3212	−	10.0902i	0.204572	−	0.0885104i
$115$	33.6266	+	79.9161i	0.292405	+	0.694922i
$116$	50.7266	−	401.542i	0.437298	−	3.46157i
$117$	−40.3433	+	124.109i	−0.344815	+	1.06076i
$118$	375.178	+	121.903i	3.17948	+	1.03308i
$119$	−17.7019	−	44.7100i	−0.148756	−	0.375714i
$120$	−182.236	−	293.729i	−1.51863	−	2.44774i
$121$	−74.2838	+	89.7937i	−0.613916	+	0.742097i
$122$	−21.5396	+	342.362i	−0.176554	+	2.80625i
$123$	31.7809	+	73.4544i	0.258381	+	0.597190i
$124$	−565.464			−4.56020
$125$	53.1033	−	113.159i	0.424826	−	0.905275i
$126$	−24.8293	+	393.829i	−0.197058	+	3.12563i
$127$	−130.338	+	61.3324i	−1.02628	+	0.482933i	−0.863830	−	0.503784i	$-0.831941\pi$
$127$	−130.338	+	61.3324i	−1.02628	+	0.482933i	−0.162454	+	0.986716i	$0.551941\pi$
$128$	8.07732	−	128.385i	0.0631041	−	1.00301i
$129$	54.4367	−	61.7382i	0.421990	−	0.478591i
$130$	−255.474	−	94.9079i	−1.96519	−	0.730061i
$131$	−30.8269	−	77.8598i	−0.235320	−	0.594350i	0.763346	−	0.645990i	$-0.223555\pi$
$131$	−30.8269	−	77.8598i	−0.235320	−	0.594350i	−0.998666	+	0.0516400i	$0.983555\pi$
$132$	−21.7511	+	60.4037i	−0.164781	+	0.457604i
$133$	6.53613	−	25.4565i	0.0491438	−	0.191403i
$134$	−0.441267	+	3.49299i	−0.00329303	+	0.0260671i
$135$	−78.2200	−	110.030i	−0.579408	−	0.815038i
$136$	40.4511	+	85.9629i	0.297434	+	0.632080i
$137$	74.7952	+	70.2373i	0.545950	+	0.512681i	0.907715	−	0.419588i	$-0.137826\pi$
$137$	74.7952	+	70.2373i	0.545950	+	0.512681i	−0.361764	+	0.932270i	$0.617826\pi$
$138$	−30.6036	+	193.142i	−0.221765	+	1.39958i
$139$	−136.351	+	17.2252i	−0.980945	+	0.123922i	−0.599419	−	0.800436i	$-0.704602\pi$
$139$	−136.351	+	17.2252i	−0.980945	+	0.123922i	−0.381527	+	0.924358i	$0.624602\pi$
$140$	−587.594	−	61.5501i	−4.19710	−	0.439644i
$141$	144.458	−	22.8703i	1.02453	−	0.162201i
$142$	335.768	−	277.771i	2.36456	−	1.95614i
$143$	9.46552	+	29.1319i	0.0661924	+	0.203719i
$144$	0.0541761	−	414.935i	0.000376223	−	2.88149i
$145$	198.674	+	20.8110i	1.37017	+	0.143524i
$146$	−1.65144	+	4.17106i	−0.0113112	+	0.0285689i
$147$	195.880	+	172.714i	1.33252	+	1.17493i
$148$	−66.5719	+	121.094i	−0.449810	+	0.818201i
$149$	100.840	+	32.7649i	0.676778	+	0.219899i	0.627184	−	0.778871i	$-0.284207\pi$
$149$	100.840	+	32.7649i	0.676778	+	0.219899i	0.0495938	+	0.998769i	$0.484207\pi$
$150$	236.347	−	153.700i	1.57565	−	1.02467i
$151$	46.0635	+	141.769i	0.305057	+	0.938868i	0.979656	+	0.200684i	$0.0643164\pi$
$151$	46.0635	+	141.769i	0.305057	+	0.938868i	−0.674599	+	0.738184i	$0.735684\pi$
$152$	−9.72990	+	51.0059i	−0.0640125	+	0.335565i
$153$	17.8707	+	32.5167i	0.116802	+	0.212527i
$154$	49.6296	+	78.2038i	0.322270	+	0.507817i
$155$	−5.94279	−	279.029i	−0.0383406	−	1.80018i
$156$	−270.072	−	348.222i	−1.73123	−	2.23219i
$157$	93.3184	+	128.442i	0.594385	+	0.818100i	0.995180	−	0.0980675i	$-0.0312661\pi$
$157$	93.3184	+	128.442i	0.594385	+	0.818100i	−0.400795	+	0.916168i	$0.631266\pi$
$158$	72.6938	−	28.7815i	0.460087	−	0.182162i
$159$	−202.145	−	103.015i	−1.27135	−	0.647891i
$160$	405.292	+	16.8443i	2.53308	+	0.105277i
$161$	138.457	+	147.441i	0.859980	+	0.915786i
$162$	−19.0393	−	303.887i	−0.117526	−	1.87585i
$163$	−66.7008	−	121.328i	−0.409208	−	0.744346i	0.588744	−	0.808320i	$-0.299623\pi$
$163$	−66.7008	−	121.328i	−0.409208	−	0.744346i	−0.997952	+	0.0639736i	$0.979623\pi$
$164$	−265.475	−	50.6421i	−1.61875	−	0.308794i
$165$	−30.0348	−	10.0983i	−0.182029	−	0.0612017i
$166$	265.078	−	145.728i	1.59685	−	0.877878i
$167$	−5.48623	−	87.2012i	−0.0328517	−	0.522163i	−0.979698	−	0.200477i	$-0.935751\pi$
$167$	−5.48623	−	87.2012i	−0.0328517	−	0.522163i	0.946847	−	0.321685i	$-0.104249\pi$
$168$	−637.132	−	494.277i	−3.79245	−	2.94212i
$169$	−39.9581	−	10.2595i	−0.236438	−	0.0607070i
$170$	−69.3932	+	34.4774i	−0.408195	+	0.202808i
$171$	−2.54431	+	20.1192i	−0.0148790	+	0.117656i
$172$	69.1223	+	269.214i	0.401874	+	1.56520i
$173$	65.1636	−	8.23208i	0.376668	−	0.0475843i	0.0652799	−	0.997867i	$-0.479206\pi$
$173$	65.1636	−	8.23208i	0.376668	−	0.0475843i	0.311388	+	0.950283i	$0.399206\pi$
$174$	355.984	+	276.167i	2.04589	+	1.58717i
$175$	24.1966	−	290.595i	0.138266	−	1.66055i
$176$	−57.2461	−	78.7926i	−0.325262	−	0.447685i
$177$	−236.171	+	208.185i	−1.33430	+	1.17619i
$178$	−143.241	+	361.786i	−0.804727	+	2.03251i
$179$	61.6251	+	240.014i	0.344274	+	1.34086i	0.871191	+	0.490943i	$0.163348\pi$
$179$	61.6251	+	240.014i	0.344274	+	1.34086i	−0.526917	+	0.849917i	$0.676652\pi$
$180$	455.767	−	9.64746i	2.53204	−	0.0535970i
$181$	161.125	−	253.893i	0.890194	−	1.40272i	−0.0249904	−	0.999688i	$-0.507956\pi$
$181$	161.125	−	253.893i	0.890194	−	1.40272i	0.915185	−	0.403034i	$-0.132044\pi$
$182$	−635.769			−3.49323
$183$	−226.420	−	153.897i	−1.23727	−	0.840966i
$184$	−291.299	−	273.548i	−1.58315	−	1.48667i
$185$	−60.4534	−	31.5773i	−0.326775	−	0.170688i
$186$	320.463	−	541.792i	1.72292	−	2.91286i
$187$	7.88010	+	3.70809i	0.0421396	+	0.0198294i
$188$	−210.286	+	446.880i	−1.11854	+	2.37702i
$189$	−260.437	−	177.067i	−1.37797	−	0.936865i
$190$	−41.7601	−	7.04813i	−0.219790	−	0.0370954i
$191$	−8.75142	+	9.31932i	−0.0458190	+	0.0487923i	−0.751470	−	0.659768i	$-0.770655\pi$
$191$	−8.75142	+	9.31932i	−0.0458190	+	0.0487923i	0.705651	+	0.708560i	$0.250655\pi$
$192$	299.100	+	203.297i	1.55781	+	1.05884i
$193$			17.2040i			0.0891396i	0.999006	+	0.0445698i	$0.0141917\pi$
$193$			17.2040i			0.0891396i	−0.999006	+	0.0445698i	$0.985808\pi$
$194$	236.575	+	150.135i	1.21946	+	0.773893i
$195$	168.992	−	136.927i	0.866625	−	0.702189i
$196$	−854.148	+	219.308i	−4.35790	+	1.11892i
$197$	−184.990	−	73.2426i	−0.939034	−	0.371790i	−0.151777	−	0.988415i	$-0.548499\pi$
$197$	−184.990	−	73.2426i	−0.939034	−	0.371790i	−0.787257	+	0.616625i	$0.788499\pi$
$198$	−45.5481	−	55.0728i	−0.230041	−	0.278145i
$199$	97.8166	−	71.0679i	0.491541	−	0.357125i	−0.314236	−	0.949345i	$-0.601748\pi$
$199$	97.8166	−	71.0679i	0.491541	−	0.357125i	0.805777	+	0.592220i	$0.201748\pi$
$200$	−11.6609	+	575.996i	−0.0583047	+	2.87998i
$201$	−2.22008	−	1.72230i	−0.0110452	−	0.00856867i
$202$	44.4445	+	351.815i	0.220022	+	1.74166i
$203$	451.365	−	115.891i	2.22347	−	0.570890i
$204$	−124.736	−	11.7992i	−0.611450	−	0.0578393i
$205$	22.1994	−	131.531i	0.108290	−	0.641616i
$206$	−175.667	+	684.178i	−0.852753	+	3.32125i
$207$	−120.237	−	99.4950i	−0.580854	−	0.480652i
$208$	667.194	−	41.9763i	3.20766	−	0.201809i
$209$	2.29313	+	4.17118i	0.0109719	+	0.0199578i
$210$	391.977	−	528.113i	1.86656	−	2.51482i
$211$	10.7431	−	56.3171i	0.0509150	−	0.266906i	−0.947722	−	0.319097i	$-0.896620\pi$
$211$	10.7431	−	56.3171i	0.0509150	−	0.266906i	0.998637	+	0.0521911i	$0.0166205\pi$
$212$	671.366	−	369.087i	3.16682	−	1.74097i
$213$	54.3821	+	343.500i	0.255315	+	1.61268i
$214$	154.710	−	145.282i	0.722942	−	0.678888i
$215$	−132.117	+	36.9378i	−0.614498	+	0.171804i
$216$	535.495	+	316.832i	2.47914	+	1.46682i
$217$	−239.674	−	605.348i	−1.10449	−	2.78962i
$218$	211.695	−	153.806i	0.971080	−	0.705531i
$219$	−2.19417	−	2.82909i	−0.0100190	−	0.0129182i
$220$	85.2068	−	64.7226i	0.387303	−	0.294194i
$221$	−50.4731	+	32.0312i	−0.228385	+	0.144938i
$222$	−78.2964	−	132.412i	−0.352687	−	0.596449i
$223$	263.524	+	50.2699i	1.18172	+	0.225426i	0.740553	−	0.671998i	$-0.234564\pi$
$223$	263.524	+	50.2699i	1.18172	+	0.225426i	0.441170	+	0.897424i	$0.354564\pi$
$224$	899.971	−	292.418i	4.01773	−	1.30544i
$225$	9.55046	+	224.797i	0.0424465	+	0.999099i
$226$	−65.9031	+	202.829i	−0.291607	+	0.897473i
$227$	80.2781	+	44.1333i	0.353648	+	0.194420i	0.648668	−	0.761071i	$-0.275326\pi$
$227$	80.2781	+	44.1333i	0.353648	+	0.194420i	−0.295020	+	0.955491i	$0.595326\pi$
$228$	−51.3645	−	45.2899i	−0.225283	−	0.198640i
$229$	2.81250	+	1.11355i	0.0122817	+	0.00486266i	0.374257	−	0.927325i	$-0.377898\pi$
$229$	2.81250	+	1.11355i	0.0122817	+	0.00486266i	−0.361976	+	0.932188i	$0.617898\pi$
$230$	217.997	−	242.281i	0.947814	−	1.05340i
$231$	−73.8834	+	2.31705i	−0.319841	+	0.0100305i
$232$	−875.622	+	284.507i	−3.77423	+	1.22632i
$233$	196.601	+	237.650i	0.843783	+	1.01996i	0.999483	+	0.0321537i	$0.0102366\pi$
$233$	196.601	+	237.650i	0.843783	+	1.01996i	−0.155700	+	0.987804i	$0.549763\pi$
$234$	486.700	−	61.4200i	2.07992	−	0.262479i
$235$	−222.723	−	99.0690i	−0.947757	−	0.421570i
$236$	−133.244	−	1054.74i	−0.564594	−	4.46922i
$237$	−9.76504	+	61.6280i	−0.0412027	+	0.260034i
$238$	−123.739	+	131.769i	−0.519912	+	0.553650i
$239$	−237.115	+	111.578i	−0.992114	+	0.466853i	−0.852147	−	0.523303i	$-0.824700\pi$
$239$	−237.115	+	111.578i	−0.992114	+	0.466853i	−0.139967	+	0.990156i	$0.544700\pi$
$240$	−376.484	+	580.097i	−1.56868	+	2.41707i
$241$	−27.1145	−	3.42536i	−0.112508	−	0.0142131i	0.0688774	−	0.997625i	$-0.478058\pi$
$241$	−27.1145	−	3.42536i	−0.112508	−	0.0142131i	−0.181386	+	0.983412i	$0.558058\pi$
$242$	424.307	+	108.944i	1.75334	+	0.450180i
$243$	216.479	+	110.390i	0.890858	+	0.454281i
$244$	859.552	−	340.321i	3.52276	−	1.39476i
$245$	−117.194	−	419.175i	−0.478344	−	1.71092i
$246$	198.974	−	225.661i	0.808835	−	0.917323i
$247$	−32.6083	−	2.05154i	−0.132017	−	0.00830582i
$248$	547.685	+	1163.89i	2.20841	+	4.69310i
$249$	−7.59872	+	241.293i	−0.0305169	+	0.969050i
$250$	−469.881	+	0.494727i	−1.87952	+	0.00197891i
$251$			226.537i			0.902538i	0.892388	+	0.451269i	$0.149028\pi$
$251$			226.537i			0.902538i	−0.892388	+	0.451269i	$0.850972\pi$
$252$	988.828	−	391.355i	3.92392	−	1.55300i
$253$	−36.5589	−	2.30009i	−0.144502	−	0.00909128i
$254$	417.218	+	345.153i	1.64259	+	1.35887i
$255$	4.51141	−	61.6750i	0.0176918	−	0.241863i
$256$	−1.26514	+	0.500904i	−0.00494195	+	0.00195665i
$257$	67.1464	−	206.655i	0.261270	−	0.804106i	−0.731259	−	0.682100i	$-0.761067\pi$
$257$	67.1464	−	206.655i	0.261270	−	0.804106i	0.992529	−	0.122007i	$-0.0389330\pi$
$258$	−297.117	−	86.3414i	−1.15161	−	0.334657i
$259$	−157.852	−	19.9413i	−0.609465	−	0.0769934i
$260$	61.7152	+	731.866i	0.237366	+	2.81487i
$261$	−334.338	+	132.323i	−1.28099	+	0.506985i
$262$	−215.484	+	229.468i	−0.822460	+	0.875831i
$263$	−392.567	−	49.5927i	−1.49265	−	0.188566i	−0.663747	−	0.747957i	$-0.731035\pi$
$263$	−392.567	−	49.5927i	−1.49265	−	0.188566i	−0.828903	+	0.559392i	$0.811035\pi$
$264$	145.395	−	13.7343i	0.550740	−	0.0520240i
$265$	189.182	+	327.407i	0.713893	+	1.23550i
$266$	−97.0462	+	18.5126i	−0.364835	+	0.0695961i
$267$	−190.316	−	245.387i	−0.712794	−	0.919052i
$268$	9.02384	−	2.93202i	0.0336710	−	0.0109404i
$269$	−85.5332	+	5.38129i	−0.317967	+	0.0200048i	−0.220972	−	0.975280i	$-0.570923\pi$
$269$	−85.5332	+	5.38129i	−0.317967	+	0.0200048i	−0.0969949	+	0.995285i	$0.530923\pi$
$270$	−249.051	+	442.155i	−0.922411	+	1.63761i
$271$	−238.731	−	94.5204i	−0.880928	−	0.348784i	−0.116268	−	0.993218i	$-0.537093\pi$
$271$	−238.731	−	94.5204i	−0.880928	−	0.348784i	−0.764660	+	0.644434i	$0.777093\pi$
$272$	121.155	−	146.452i	0.445424	−	0.538425i
$273$	258.311	−	436.716i	0.946196	−	1.59969i
$274$	119.186	−	366.816i	0.434985	−	1.33875i
$275$	32.8329	+	41.3651i	0.119392	+	0.150419i
$276$	506.085	−	146.995i	1.83364	−	0.532592i
$277$	43.6999	+	8.33621i	0.157761	+	0.0300946i	0.265657	−	0.964068i	$-0.414411\pi$
$277$	43.6999	+	8.33621i	0.157761	+	0.0300946i	−0.107895	+	0.994162i	$0.534411\pi$
$278$	276.821	+	436.201i	0.995761	+	1.56907i
$279$	241.959	+	440.258i	0.867236	+	1.57798i
$280$	442.431	+	1269.05i	1.58011	+	4.53233i
$281$	31.6521	−	26.1849i	0.112641	−	0.0931846i	−0.579398	−	0.815044i	$-0.696712\pi$
$281$	31.6521	−	26.1849i	0.112641	−	0.0931846i	0.692039	+	0.721860i	$0.256712\pi$
$282$	−308.997	−	454.740i	−1.09574	−	1.61255i
$283$	−124.103	−	313.448i	−0.438526	−	1.10759i	−0.966120	−	0.258094i	$-0.916906\pi$
$283$	−124.103	−	313.448i	−0.438526	−	1.10759i	0.527594	−	0.849497i	$-0.323094\pi$
$284$	−1062.61	−	500.028i	−3.74159	−	1.76066i
$285$	21.8085	−	25.8218i	0.0765210	−	0.0906029i
$286$	83.9361	−	78.8212i	0.293483	−	0.275599i
$287$	−58.3087	−	305.665i	−0.203166	−	1.06503i
$288$	−660.706	+	310.799i	−2.29412	+	1.07916i
$289$	50.9684	−	267.186i	0.176361	−	0.924518i
$290$	−247.199	−	709.057i	−0.852410	−	2.44503i
$291$	−199.250	+	101.506i	−0.684706	+	0.348819i
$292$	12.0659	−	0.759124i	0.0413217	−	0.00259974i
$293$	−124.159	−	90.2066i	−0.423750	−	0.307872i	0.355395	−	0.934716i	$-0.384346\pi$
$293$	−124.159	−	90.2066i	−0.423750	−	0.307872i	−0.779145	+	0.626844i	$0.784346\pi$
$294$	273.940	−	942.677i	0.931768	−	3.20639i
$295$	519.060	−	76.8342i	1.75952	−	0.260455i
$296$	313.725	+	19.7379i	1.05988	+	0.0666820i
$297$	56.3361	−	8.91145i	0.189684	−	0.0300049i
$298$	−49.9540	−	395.427i	−0.167631	−	1.32693i
$299$	147.793	−	203.419i	0.494290	−	0.680331i
$300$	−645.988	−	399.961i	−2.15329	−	1.33320i
$301$	−258.904	+	188.105i	−0.860147	+	0.624933i
$302$	408.471	−	383.580i	1.35255	−	1.27013i
$303$	−259.723	−	112.412i	−0.857170	−	0.370997i
$304$	100.621	−	25.8350i	0.330990	−	0.0849837i
$305$	176.965	+	420.570i	0.580213	+	1.37892i
$306$	81.9962	−	112.827i	0.267961	−	0.368716i
$307$			70.9486i			0.231103i	0.993301	+	0.115551i	$0.0368635\pi$
$307$			70.9486i			0.231103i	−0.993301	+	0.115551i	$0.963136\pi$
$308$	133.749	−	210.755i	0.434251	−	0.684270i
$309$	−398.596	−	398.648i	−1.28995	−	1.29012i
$310$	−939.545	+	466.805i	−3.03079	+	1.50582i
$311$	−115.545	+	210.176i	−0.371528	+	0.675808i	−0.994303	−	0.106594i	$-0.966005\pi$
$311$	−115.545	+	210.176i	−0.371528	+	0.675808i	0.622774	+	0.782402i	$0.286005\pi$
$312$	−455.161	+	893.159i	−1.45885	+	2.86269i
$313$	79.6885	+	37.4986i	0.254596	+	0.119804i	0.548842	−	0.835926i	$-0.315069\pi$
$313$	79.6885	+	37.4986i	0.254596	+	0.119804i	−0.294247	+	0.955730i	$0.595069\pi$
$314$	287.509	−	522.977i	0.915633	−	1.66553i
$315$	203.507	+	483.824i	0.646053	+	1.53595i
$316$	−153.595	−	144.236i	−0.486061	−	0.456442i
$317$	165.462	−	260.726i	0.521962	−	0.822481i	−0.476427	−	0.879214i	$-0.658068\pi$
$317$	165.462	−	260.726i	0.521962	−	0.822481i	0.998389	+	0.0567331i	$0.0180684\pi$
$318$	−26.8444	+	852.430i	−0.0844164	+	2.68060i
$319$	−45.2226	+	71.2595i	−0.141764	+	0.223384i
$320$	−233.770	−	555.571i	−0.730531	−	1.73616i
$321$	36.9375	+	165.299i	0.115070	+	0.514951i
$322$	279.887	−	706.915i	0.869216	−	2.19539i
$323$	−6.77172	+	6.35906i	−0.0209651	+	0.0196875i
$324$	−719.170	+	395.122i	−2.21966	+	1.21951i
$325$	−360.491	+	38.1450i	−1.10920	+	0.117369i
$326$	−305.916	+	421.058i	−0.938394	+	1.29159i
$327$	19.6393	+	207.907i	0.0600589	+	0.635800i
$328$	152.892	+	595.475i	0.466134	+	1.81547i
$329$	−567.529	−	35.7059i	−1.72501	−	0.108529i
$330$	13.7243	+	118.320i	0.0415888	+	0.358544i
$331$	−103.055	−	26.4601i	−0.311346	−	0.0799400i	0.0897840	−	0.995961i	$-0.471382\pi$
$331$	−103.055	−	26.4601i	−0.311346	−	0.0799400i	−0.401130	+	0.916021i	$0.631382\pi$
$332$	−659.515	−	479.166i	−1.98649	−	1.44327i
$333$	122.767	+	0.0160291i	0.368669	+	4.81353e-5i
$334$	−287.815	+	158.228i	−0.861723	+	0.473736i
$335$	1.54165	+	4.42200i	0.00460193	+	0.0132000i
$336$	−352.028	+	1574.40i	−1.04770	+	4.68571i
$337$	−172.770	−	314.268i	−0.512671	−	0.932545i	−0.998295	−	0.0583773i	$-0.981407\pi$
$337$	−172.770	−	314.268i	−0.512671	−	0.932545i	0.485623	−	0.874168i	$-0.338593\pi$
$338$	29.0584	+	152.329i	0.0859715	+	0.450679i
$339$	−112.549	−	127.679i	−0.332003	−	0.376633i
$340$	163.697	+	129.651i	0.481463	+	0.381327i
$341$	106.692	+	50.2055i	0.312880	+	0.147230i
$342$	72.5034	−	23.5473i	0.211998	−	0.0688518i
$343$	−260.868	−	359.054i	−0.760549	−	1.04681i
$344$	487.171	−	403.023i	1.41619	−	1.17158i
$345$	77.8537	+	248.183i	0.225663	+	0.719371i
$346$	−132.296	−	208.465i	−0.382357	−	0.602499i
$347$	119.171	+	187.783i	0.343431	+	0.541161i	0.971513	−	0.236987i	$-0.0761597\pi$
$347$	119.171	+	187.783i	0.343431	+	0.541161i	−0.628082	+	0.778147i	$0.716160\pi$
$348$	264.947	−	1184.94i	0.761343	−	3.40501i
$349$	26.8462	+	82.6240i	0.0769232	+	0.236745i	0.982123	−	0.188242i	$-0.0602788\pi$
$349$	26.8462	+	82.6240i	0.0769232	+	0.236745i	−0.905200	+	0.424987i	$0.860279\pi$
$350$	−1027.13	+	382.806i	−2.93464	+	1.09373i
$351$	−155.555	+	359.274i	−0.443177	+	1.02357i
$352$	−82.5635	+	150.182i	−0.234555	+	0.426655i
$353$	381.017	−	460.570i	1.07937	−	1.30473i	0.129673	−	0.991557i	$-0.458607\pi$
$353$	381.017	−	460.570i	1.07937	−	1.30473i	0.949695	−	0.313175i	$-0.101393\pi$
$354$	1086.09	+	470.079i	3.06806	+	1.32791i
$355$	235.571	−	529.602i	0.663581	−	1.49184i
$356$	1046.56	−	65.8443i	2.93979	−	0.184956i
$357$	−40.2383	−	138.535i	−0.112712	−	0.388053i
$358$	717.724	−	593.753i	2.00482	−	1.65853i
$359$	182.962	−	34.9019i	0.509644	−	0.0972198i	0.0738555	−	0.997269i	$-0.476470\pi$
$359$	182.962	−	34.9019i	0.509644	−	0.0972198i	0.435788	+	0.900049i	$0.356470\pi$
$360$	−461.294	−	928.757i	−1.28137	−	2.57988i
$361$	353.116	−	44.6090i	0.978161	−	0.123571i
$362$	−1121.45	−	141.672i	−3.09792	−	0.391358i
$363$	−247.229	+	247.197i	−0.681073	+	0.680984i
$364$	729.514	+	1550.30i	2.00416	+	4.25906i
$365$	0.501398	+	5.94596i	0.00137369	+	0.0162903i
$366$	−161.056	+	1016.44i	−0.440043	+	2.77715i
$367$	−71.0302	+	276.644i	−0.193543	+	0.753800i	0.795473	+	0.605989i	$0.207223\pi$
$367$	−71.0302	+	276.644i	−0.193543	+	0.753800i	−0.989016	+	0.147810i	$0.952777\pi$
$368$	−247.048	+	760.336i	−0.671327	+	2.06613i
$369$	74.1666	+	228.363i	0.200993	+	0.618869i
$370$	−10.6462	+	256.160i	−0.0287735	+	0.692323i
$371$	679.680	+	562.280i	1.83202	+	1.51558i
$372$	−1688.85	−	159.755i	−4.53993	−	0.429449i
$373$	188.799	−	88.8421i	0.506163	−	0.238182i	−0.155703	−	0.987804i	$-0.549764\pi$
$373$	188.799	−	88.8421i	0.506163	−	0.238182i	0.661867	+	0.749621i	$0.269764\pi$
$374$		−	32.7374i		−	0.0875331i
$375$	190.572	−	322.967i	0.508191	−	0.861244i
$376$	1123.48			2.98798
$377$	−246.660	−	524.179i	−0.654270	−	1.39039i
$378$	−185.421	+	1169.22i	−0.490533	+	3.09318i
$379$	319.876	−	386.664i	0.844001	−	1.02022i	−0.155474	−	0.987840i	$-0.549691\pi$
$379$	319.876	−	386.664i	0.844001	−	1.02022i	0.999476	−	0.0323822i	$-0.0103094\pi$
$380$	30.7312	+	109.918i	0.0808716	+	0.289258i
$381$	−406.604	+	146.356i	−1.06720	+	0.384138i
$382$	45.7046	+	14.8503i	0.119645	+	0.0388752i
$383$	41.4187	+	10.6345i	0.108143	+	0.0277663i	0.302373	−	0.953190i	$-0.402221\pi$
$383$	41.4187	+	10.6345i	0.108143	+	0.0277663i	−0.194231	+	0.980956i	$0.562221\pi$
$384$	60.3957	−	381.162i	0.157280	−	0.992610i
$385$	105.403	+	63.7837i	0.273774	+	0.165672i
$386$	58.5156	−	27.5353i	0.151595	−	0.0713351i
$387$	180.027	−	169.012i	0.465185	−	0.436724i
$388$	94.6400	−	749.153i	0.243918	−	1.93081i
$389$	50.9499	+	403.310i	0.130977	+	1.03679i	0.911396	+	0.411530i	$0.135006\pi$
$389$	50.9499	+	403.310i	0.130977	+	1.03679i	−0.780419	+	0.625256i	$0.784994\pi$
$390$	−736.203	−	355.635i	−1.88770	−	0.911884i
$391$	−13.3957	−	70.2226i	−0.0342600	−	0.179597i
$392$	1278.69	+	1545.67i	3.26197	+	3.94304i
$393$	−70.0727	−	241.251i	−0.178302	−	0.613869i
$394$	46.9614	+	746.429i	0.119191	+	1.89449i
$395$	69.5589	−	77.3075i	0.176099	−	0.195715i
$396$	−82.0286	+	174.261i	−0.207143	+	0.440052i
$397$	−352.133	−	291.309i	−0.886984	−	0.733777i	0.0777585	−	0.996972i	$-0.475224\pi$
$397$	−352.133	−	291.309i	−0.886984	−	0.733777i	−0.964743	+	0.263195i	$0.915224\pi$
$398$	−398.280	−	218.956i	−1.00070	−	0.550142i
$399$	26.7132	−	74.1836i	0.0669504	−	0.185924i
$400$	1052.62	−	469.543i	2.63155	−	1.17386i
$401$	87.0291	−	28.2775i	0.217030	−	0.0705174i	−0.198484	−	0.980104i	$-0.563602\pi$
$401$	87.0291	−	28.2775i	0.217030	−	0.0705174i	0.415514	+	0.909587i	$0.363602\pi$
$402$	−2.30475	+	10.3077i	−0.00573322	+	0.0256411i
$403$	−683.377	+	433.685i	−1.69573	+	1.07614i
$404$	806.888	−	512.067i	1.99725	−	1.26749i
$405$	−202.532	−	350.722i	−0.500078	−	0.865980i
$406$	−1116.60	−	1349.74i	−2.75024	−	3.32447i
$407$	23.3123	−	16.9374i	0.0572784	−	0.0416152i
$408$	96.5276	+	268.171i	0.236587	+	0.657281i
$409$	−71.0945	+	151.083i	−0.173825	+	0.369397i	−0.972688	−	0.232116i	$-0.925435\pi$
$409$	−71.0945	+	151.083i	−0.173825	+	0.369397i	0.798863	+	0.601513i	$0.205435\pi$
$410$	−482.906	+	135.012i	−1.17782	+	0.329299i
$411$	203.545	+	230.907i	0.495243	+	0.561817i
$412$	1869.91	−	356.705i	4.53862	−	0.865788i
$413$	1072.65	−	589.696i	2.59722	−	1.42783i
$414$	−145.969	+	568.204i	−0.352582	+	1.37247i
$415$	229.513	−	330.474i	0.553045	−	0.796323i
$416$	−566.723	−	1030.86i	−1.36231	−	2.47804i
$417$	−412.103	+	12.9239i	−0.988256	+	0.0309926i
$418$	10.5172	−	14.4757i	0.0251607	−	0.0346308i
$419$	−153.952	+	599.603i	−0.367427	+	1.43103i	0.469119	+	0.883135i	$0.344572\pi$
$419$	−153.952	+	599.603i	−0.367427	+	1.43103i	−0.836546	+	0.547897i	$0.815428\pi$
$420$	−1737.56	−	349.837i	−4.13705	−	0.832945i
$421$	−29.8037	+	473.716i	−0.0707926	+	1.12522i	0.788939	+	0.614471i	$0.210630\pi$
$421$	−29.8037	+	473.716i	−0.0707926	+	1.12522i	−0.859732	+	0.510745i	$0.829370\pi$
$422$	−208.745	+	53.5967i	−0.494657	+	0.127006i
$423$	437.910	−	27.4936i	1.03525	−	0.0649966i
$424$	−1409.94	−	1024.38i	−3.32534	−	2.41600i
$425$	−62.2561	+	82.1391i	−0.146485	+	0.193268i
$426$	1081.30	−	734.750i	2.53827	−	1.72476i
$427$	728.649	+	775.932i	1.70644	+	1.81717i
$428$	−531.786	−	210.549i	−1.24249	−	0.491937i
$429$	20.0400	+	89.6814i	0.0467133	+	0.209048i
$430$	337.093	+	390.249i	0.783936	+	0.907555i
$431$	−58.9175	−	37.3902i	−0.136700	−	0.0867522i	0.465718	−	0.884933i	$-0.345796\pi$
$431$	−58.9175	−	37.3902i	−0.136700	−	0.0867522i	−0.602418	+	0.798181i	$0.705796\pi$
$432$	117.389	−	1239.26i	0.271734	−	2.86865i
$433$	71.2499	+	45.2165i	0.164549	+	0.104426i	0.615551	−	0.788097i	$-0.288933\pi$
$433$	71.2499	+	45.2165i	0.164549	+	0.104426i	−0.451002	+	0.892523i	$0.648933\pi$
$434$	−1675.36	+	1784.07i	−3.86027	+	4.11077i
$435$	587.495	+	118.285i	1.35056	+	0.271920i
$436$	−617.960	−	339.726i	−1.41734	−	0.779188i
$437$	16.6364	−	35.3542i	0.0380696	−	0.0809020i
$438$	−6.11071	+	11.9910i	−0.0139514	+	0.0273767i
$439$	269.326	+	148.063i	0.613498	+	0.337273i	0.758023	−	0.652228i	$-0.226165\pi$
$439$	269.326	+	148.063i	0.613498	+	0.337273i	−0.144525	+	0.989501i	$0.546165\pi$
$440$	−215.745	−	112.693i	−0.490331	−	0.256120i
$441$	536.233	+	571.180i	1.21595	+	1.29519i
$442$	189.731	+	120.407i	0.429255	+	0.272414i
$443$	562.832			1.27050			0.635251	−	0.772306i	$-0.280897\pi$
$443$	562.832			1.27050			0.635251	+	0.772306i	$0.280897\pi$
$444$	−233.039	+	342.859i	−0.524864	+	0.772205i
$445$	43.4898	+	515.736i	0.0977299	+	1.15896i
$446$	−250.794	−	976.780i	−0.562319	−	2.19009i
$447$	291.919	+	126.347i	0.653062	+	0.282656i
$448$	−962.542	−	1025.00i	−2.14853	−	2.28795i
$449$	−74.4730	−	102.503i	−0.165864	−	0.228292i	0.717992	−	0.696052i	$-0.245061\pi$
$449$	−74.4730	−	102.503i	−0.165864	−	0.228292i	−0.883856	+	0.467759i	$0.845061\pi$
$450$	749.314	−	392.277i	1.66514	−	0.871727i
$451$	45.5937	+	33.1258i	0.101095	+	0.0734497i
$452$	570.211	−	72.0344i	1.26153	−	0.159368i
$453$	97.5239	+	436.431i	0.215285	+	0.963423i
$454$	21.6228	−	343.685i	0.0476274	−	0.757016i
$455$	−757.328	+	376.272i	−1.66446	+	0.826972i
$456$	−43.4702	+	149.589i	−0.0953293	+	0.328046i
$457$	38.8497	−	53.4720i	0.0850103	−	0.117007i	−0.764394	−	0.644750i	$-0.776962\pi$
$457$	38.8497	−	53.4720i	0.0850103	−	0.117007i	0.849404	+	0.527743i	$0.176962\pi$
$458$	−0.713980	−	11.3484i	−0.00155891	−	0.0247781i
$459$	44.1871	+	102.165i	0.0962683	+	0.222582i
$460$	−840.935	−	253.571i	−1.82812	−	0.551242i
$461$	−33.7942	−	6.44659i	−0.0733063	−	0.0139839i	0.150598	−	0.988595i	$-0.451880\pi$
$461$	−33.7942	−	6.44659i	−0.0733063	−	0.0139839i	−0.223904	+	0.974611i	$0.571880\pi$
$462$	126.133	+	247.590i	0.273015	+	0.535909i
$463$	−298.023	+	56.8509i	−0.643678	+	0.122788i	−0.498877	−	0.866673i	$-0.666254\pi$
$463$	−298.023	+	56.8509i	−0.643678	+	0.122788i	−0.144801	+	0.989461i	$0.546254\pi$
$464$	1260.91	+	1342.73i	2.71747	+	2.89381i
$465$	61.0820	−	835.045i	0.131359	−	1.79579i
$466$	493.651	−	1049.06i	1.05934	−	2.25121i
$467$	−692.063	+	274.007i	−1.48193	+	0.586739i	−0.963340	−	0.268282i	$-0.913544\pi$
$467$	−692.063	+	274.007i	−1.48193	+	0.586739i	−0.518593	+	0.855021i	$0.673544\pi$
$468$	−708.236	−	1116.32i	−1.51332	−	2.38531i
$469$	6.96361	+	8.41756i	0.0148478	+	0.0179479i
$470$	19.5114	+	916.107i	0.0415135	+	1.94916i
$471$	242.424	+	409.977i	0.514700	+	0.870439i
$472$	−2041.90	+	1295.83i	−4.32605	+	2.74540i
$473$	10.8605	−	56.9325i	0.0229608	−	0.120365i
$474$	225.244	−	65.4234i	0.475197	−	0.138024i
$475$	−53.9161	+	16.3195i	−0.113507	+	0.0343569i
$476$	463.297	+	150.534i	0.973314	+	0.316249i
$477$	−574.636	−	364.780i	−1.20469	−	0.764739i
$478$	759.017	+	627.914i	1.58790	+	1.31363i
$479$	82.1608	−	207.514i	0.171526	−	0.433224i	−0.818429	−	0.574607i	$-0.805155\pi$
$479$	82.1608	−	207.514i	0.171526	−	0.433224i	0.989955	+	0.141383i	$0.0451549\pi$
$480$	1205.71	+	164.811i	2.51191	+	0.343357i
$481$	12.4195	+	197.402i	0.0258202	+	0.410400i
$482$	31.7468	+	97.7067i	0.0658648	+	0.202711i
$483$	371.869	+	479.475i	0.769915	+	0.992703i
$484$	−221.218	−	1159.66i	−0.457061	−	2.39600i
$485$	370.665	+	38.8269i	0.764257	+	0.0800554i
$486$	28.9901	−	912.988i	0.0596504	−	1.87858i
$487$	−108.183	+	856.360i	−0.222142	+	1.75844i	0.348564	+	0.937285i	$0.386669\pi$
$487$	−108.183	+	856.360i	−0.222142	+	1.75844i	−0.570707	+	0.821154i	$0.693331\pi$
$488$	−1533.00	−	1439.59i	−3.14140	−	2.94997i
$489$	−164.936	−	381.212i	−0.337292	−	0.779574i
$490$	−1238.16	+	1069.51i	−2.52686	+	2.18268i
$491$	76.3250	−	604.175i	0.155448	−	1.23050i	−0.700582	−	0.713572i	$-0.747076\pi$
$491$	76.3250	−	604.175i	0.155448	−	1.23050i	0.856030	−	0.516926i	$-0.172924\pi$
$492$	−778.579	−	226.253i	−1.58248	−	0.459864i
$493$	−156.648	−	50.8980i	−0.317744	−	0.103241i
$494$	45.2125	+	114.194i	0.0915232	+	0.231161i
$495$	−86.8510	−	38.6456i	−0.175457	−	0.0780720i
$496$	1640.38	−	1982.87i	3.30721	−	3.99773i
$497$	84.9033	−	1349.50i	0.170832	−	2.71529i
$498$	832.870	−	360.350i	1.67243	−	0.723595i
$499$	210.501			0.421847			0.210923	−	0.977503i	$-0.432353\pi$
$499$	210.501			0.421847			0.210923	+	0.977503i	$0.432353\pi$
$500$	540.372	+	1145.22i	1.08074	+	2.29044i
$501$	8.25051	−	261.991i	0.0164681	−	0.522936i
$502$	770.517	−	362.578i	1.53490	−	0.722267i
$503$	−3.55104	+	56.4421i	−0.00705971	+	0.112211i	−0.999978	−	0.00658576i	$-0.997904\pi$
$503$	−3.55104	+	56.4421i	−0.00705971	+	0.112211i	0.992919	+	0.118797i	$0.0379037\pi$
$504$	−1763.26	−	1656.24i	−3.49853	−	3.28620i
$505$	261.160	+	392.778i	0.517148	+	0.777778i
$506$	50.6902	+	128.029i	0.100178	+	0.253021i
$507$	−116.443	−	41.9306i	−0.229670	−	0.0827034i
$508$	362.904	−	1413.42i	0.714378	−	2.78232i
$509$	72.6918	−	575.415i	0.142813	−	1.13048i	−0.743943	−	0.668243i	$-0.767047\pi$
$509$	72.6918	−	575.415i	0.142813	−	1.13048i	0.886756	−	0.462238i	$-0.152953\pi$
$510$	−216.995	+	83.3677i	−0.425480	+	0.163466i
$511$	5.92685	+	12.5952i	0.0115985	+	0.0246481i
$512$	−371.367	−	348.737i	−0.725326	−	0.681127i
$513$	−13.2831	+	59.3705i	−0.0258930	+	0.115732i
$514$	−810.364	+	102.373i	−1.57658	+	0.199169i
$515$	195.668	+	918.960i	0.379938	+	1.78439i
$516$	130.387	+	823.580i	0.252688	+	1.59609i
$517$	79.3536	−	65.6470i	0.153489	−	0.126977i
$518$	184.819	+	568.815i	0.356794	+	1.09810i
$519$	196.948	−	6.17646i	0.379476	−	0.0119007i
$520$	1446.62	−	835.882i	2.78196	−	1.60747i
$521$	40.0759	−	101.220i	0.0769212	−	0.194281i	−0.886228	−	0.463250i	$-0.846683\pi$
$521$	40.0759	−	101.220i	0.0769212	−	0.194281i	0.963149	+	0.268970i	$0.0866831\pi$
$522$	985.184	+	925.392i	1.88733	+	1.77278i
$523$	−377.643	+	686.931i	−0.722072	+	1.31344i	0.219163	+	0.975688i	$0.429667\pi$
$523$	−377.643	+	686.931i	−0.722072	+	1.31344i	−0.941234	+	0.337755i	$0.890333\pi$
$524$	806.806	+	262.147i	1.53971	+	0.500281i
$525$	154.366	−	861.076i	0.294031	−	1.64014i
$526$	459.634	+	1414.61i	0.873829	+	2.68937i
$527$	−43.1201	+	226.044i	−0.0818219	+	0.428925i
$528$	−148.715	−	251.500i	−0.281657	−	0.476326i
$529$	−122.333	−	192.766i	−0.231253	−	0.364397i
$530$	810.815	−	1167.48i	1.52984	−	2.20280i
$531$	−764.179	+	555.056i	−1.43913	+	1.04530i
$532$	156.498	+	215.401i	0.294169	+	0.404889i
$533$	−359.674	+	142.405i	−0.674810	+	0.267176i
$534$	−530.026	+	1040.07i	−0.992558	+	1.94769i
$535$	98.3067	−	264.623i	0.183751	−	0.494623i
$536$	−14.7751	−	15.7338i	−0.0275654	−	0.0293542i
$537$	116.245	+	734.252i	0.216471	+	1.36732i
$538$	155.201	+	282.310i	0.288478	+	0.524740i
$539$	180.633	+	34.4575i	0.335126	+	0.0639287i
$540$	1363.95	+	99.9496i	2.52584	+	0.185092i
$541$	811.151	−	445.934i	1.49935	−	0.824277i	0.500221	−	0.865898i	$-0.333252\pi$
$541$	811.151	−	445.934i	1.49935	−	0.824277i	0.999133	+	0.0416204i	$0.0132520\pi$
$542$	60.6042	+	963.276i	0.111816	+	1.77726i
$543$	552.957	−	712.772i	1.01834	−	1.31266i
$544$	−323.956	−	83.1779i	−0.595508	−	0.152901i
$545$	161.144	−	308.503i	0.295676	−	0.566060i
$546$	−1898.83	−	179.617i	−3.47771	−	0.328969i
$547$	3.24118	+	12.6236i	0.00592537	+	0.0230778i	0.971477	−	0.237133i	$-0.0762078\pi$
$547$	3.24118	+	12.6236i	0.00592537	+	0.0230778i	−0.965552	+	0.260211i	$0.916208\pi$
$548$	−1031.23	+	130.274i	−1.88180	+	0.237727i
$549$	−632.764	−	523.607i	−1.15257	−	0.953746i
$550$	88.1448	−	177.880i	0.160263	−	0.323418i
$551$	−52.9144	−	72.8304i	−0.0960333	−	0.132179i
$552$	−792.731	−	899.295i	−1.43611	−	1.62916i
$553$	89.3069	−	225.564i	0.161495	−	0.407891i
$554$	−41.5890	−	161.978i	−0.0750703	−	0.292380i
$555$	−171.633	−	111.390i	−0.309249	−	0.200703i
$556$	746.019	−	1175.54i	1.34176	−	2.11428i
$557$	83.9097			0.150646			0.0753229	−	0.997159i	$-0.476001\pi$
$557$	83.9097			0.150646			0.0753229	+	0.997159i	$0.476001\pi$
$558$	1110.18	−	1527.61i	1.98957	−	2.73766i
$559$	290.010	+	272.338i	0.518802	+	0.487187i
$560$	1920.41	−	1881.92i	3.42930	−	3.36057i
$561$	22.4876	+	13.3011i	0.0400849	+	0.0237097i
$562$	−139.722	−	65.7483i	−0.248616	−	0.116990i
$563$	−387.557	+	823.602i	−0.688379	+	1.46288i	0.188452	+	0.982082i	$0.439653\pi$
$563$	−387.557	+	823.602i	−0.688379	+	1.46288i	−0.876831	+	0.480798i	$0.840347\pi$
$564$	−754.305	+	1275.27i	−1.33742	+	2.26112i
$565$	41.5381	+	280.614i	0.0735188	+	0.496662i
$566$	−867.498	+	923.791i	−1.53268	+	1.63214i
$567$	−727.814	−	602.420i	−1.28362	−	1.06247i
$568$			2671.47i			4.70329i
$569$	−788.104	−	500.146i	−1.38507	−	0.878991i	−0.386015	−	0.922492i	$-0.626149\pi$
$569$	−788.104	−	500.146i	−1.38507	−	0.878991i	−0.999053	+	0.0435010i	$0.986149\pi$
$570$	−122.732	−	32.8485i	−0.215320	−	0.0576289i
$571$	−676.710	+	173.750i	−1.18513	+	0.304290i	−0.789285	−	0.614027i	$-0.789549\pi$
$571$	−676.710	+	173.750i	−1.18513	+	0.304290i	−0.395846	+	0.918317i	$0.629549\pi$
$572$	−288.515	−	114.231i	−0.504397	−	0.199705i
$573$	−28.7705	+	25.3613i	−0.0502103	+	0.0442605i
$574$	−946.329	+	687.549i	−1.64866	+	1.19782i
$575$	116.287	−	417.625i	0.202238	−	0.726304i
$576$	835.878	+	691.682i	1.45118	+	1.20084i
$577$	7.72578	+	61.1559i	0.0133896	+	0.105989i	0.997393	−	0.0721596i	$-0.0229891\pi$
$577$	7.72578	+	61.1559i	0.0133896	+	0.105989i	−0.984004	+	0.178149i	$0.942989\pi$
$578$	−990.352	+	254.279i	−1.71341	+	0.439929i
$579$	−4.86046	+	51.3825i	−0.00839457	+	0.0887435i
$580$	−1445.36	+	1416.39i	−2.49200	+	2.44206i
$581$	233.425	−	909.129i	0.401764	−	1.56477i
$582$	664.156	+	515.241i	1.14116	+	0.885295i
$583$	−159.444	+	10.0313i	−0.273488	+	0.0172064i
$584$	−13.2490	−	24.0999i	−0.0226867	−	0.0412670i
$585$	543.407	−	361.211i	0.928901	−	0.617455i
$586$	−108.100	+	566.677i	−0.184470	+	0.967026i
$587$	652.090	−	358.490i	1.11089	−	0.610715i	0.182826	−	0.983145i	$-0.441475\pi$
$587$	652.090	−	358.490i	1.11089	−	0.610715i	0.928060	+	0.372430i	$0.121475\pi$
$588$	−2613.01	+	413.686i	−4.44390	+	0.703548i
$589$	−91.6852	+	86.0982i	−0.155663	+	0.146177i
$590$	−1092.10	−	1642.50i	−1.85102	−	2.78389i
$591$	−531.810	−	271.014i	−0.899848	−	0.458569i
$592$	−231.510	−	584.728i	−0.391065	−	0.987717i
$593$	100.672	−	73.1422i	0.169767	−	0.123343i	−0.499658	−	0.866223i	$-0.666541\pi$
$593$	100.672	−	73.1422i	0.169767	−	0.123343i	0.669424	+	0.742880i	$0.266541\pi$
$594$	−120.478	−	177.352i	−0.202824	−	0.298573i
$595$	−69.4123	+	230.196i	−0.116659	+	0.386885i
$596$	−906.912	+	575.544i	−1.52166	+	0.965678i
$597$	312.224	−	184.621i	0.522988	−	0.309248i
$598$	−928.432	−	177.108i	−1.55256	−	0.296167i
$599$	−672.811	+	218.610i	−1.12322	+	0.364958i	−0.810997	−	0.585050i	$-0.801075\pi$
$599$	−672.811	+	218.610i	−1.12322	+	0.364958i	−0.312227	+	0.950008i	$0.601075\pi$
$600$	−197.558	+	1717.02i	−0.329263	+	2.86169i
$601$	32.0887	−	98.7590i	0.0533922	−	0.164324i	−0.920805	−	0.390024i	$-0.872467\pi$
$601$	32.0887	−	98.7590i	0.0533922	−	0.164324i	0.974197	+	0.225699i	$0.0724667\pi$
$602$	1054.18	+	579.541i	1.75113	+	0.962692i
$603$	−6.14406	−	5.77116i	−0.0101891	−	0.00957075i
$604$	−1404.05	−	555.901i	−2.32458	−	0.920366i
$605$	569.912	−	121.348i	0.942003	−	0.200574i
$606$	33.3464	+	1063.31i	0.0550270	+	1.75464i
$607$	−347.498	+	112.909i	−0.572484	+	0.186011i	−0.580931	−	0.813953i	$-0.697311\pi$
$607$	−347.498	+	112.909i	−0.572484	+	0.186011i	0.00844691	+	0.999964i	$0.497311\pi$
$608$	−116.524	−	140.853i	−0.191651	−	0.231666i
$609$	1380.82	−	218.608i	2.26735	−	0.358962i
$610$	1147.24	−	1275.04i	1.88072	−	2.09023i
$611$	88.6004	+	701.344i	0.145009	+	1.14786i
$612$	−369.211	−	70.4807i	−0.603286	−	0.115165i
$613$	274.058	−	291.842i	0.447076	−	0.476087i	−0.465469	−	0.885064i	$-0.654114\pi$
$613$	274.058	−	291.842i	0.447076	−	0.476087i	0.912545	+	0.408977i	$0.134114\pi$
$614$	241.317	−	113.555i	0.393024	−	0.184943i
$615$	103.462	−	386.568i	0.168231	−	0.628566i
$616$	−563.339	−	71.1662i	−0.914511	−	0.115530i
$617$	484.382	+	124.368i	0.785061	+	0.201569i	0.619883	−	0.784694i	$-0.287180\pi$
$617$	484.382	+	124.368i	0.785061	+	0.201569i	0.165178	+	0.986264i	$0.447180\pi$
$618$	−717.953	+	1993.78i	−1.16174	+	3.22619i
$619$	988.620	−	391.422i	1.59712	−	0.632346i	0.610014	−	0.792390i	$-0.291164\pi$
$619$	988.620	−	391.422i	1.59712	−	0.632346i	0.987110	+	0.160044i	$0.0511637\pi$
$620$	2216.37	+	1755.41i	3.57479	+	2.83130i
$621$	−330.998	−	331.128i	−0.533008	−	0.533217i
$622$	899.803	+	56.6108i	1.44663	+	0.0910141i
$623$	514.079	+	1092.47i	0.825166	+	1.75357i
$624$	2004.55	+	63.1264i	3.21241	+	0.101164i
$625$	−559.429	+	278.683i	−0.895087	+	0.445892i
$626$		−	331.061i		−	0.528851i
$627$	5.67037	+	13.1058i	0.00904365	+	0.0209024i
$628$	−1605.16	−	100.988i	−2.55599	−	0.160809i
$629$	43.3306	+	35.8462i	0.0688880	+	0.0569891i
$630$	1319.91	−	1466.56i	2.09509	−	2.32787i
$631$	346.423	−	137.159i	0.549007	−	0.217367i	−0.0772119	−	0.997015i	$-0.524602\pi$
$631$	346.423	−	137.159i	0.549007	−	0.217367i	0.626218	+	0.779648i	$0.284602\pi$
$632$	−148.113	+	455.844i	−0.234356	+	0.721272i
$633$	47.9967	−	165.165i	0.0758241	−	0.260925i
$634$	−1151.63	−	145.485i	−1.81645	−	0.229471i
$635$	701.266	+	164.221i	1.10436	+	0.258615i
$636$	2109.42	−	912.665i	3.31670	−	1.43501i
$637$	−864.060	+	920.130i	−1.35645	+	1.44447i
$638$	314.754	+	39.7626i	0.493344	+	0.0623239i
$639$	65.3756	+	1041.29i	0.102309	+	1.62955i
$640$	−430.214	+	478.139i	−0.672210	+	0.747092i
$641$	420.895	−	80.2901i	0.656623	−	0.125258i	0.151706	−	0.988426i	$-0.451523\pi$
$641$	420.895	−	80.2901i	0.656623	−	0.125258i	0.504917	+	0.863168i	$0.331523\pi$
$642$	503.111	−	390.201i	0.783662	−	0.607789i
$643$	−908.209	+	295.095i	−1.41246	+	0.458935i	−0.913197	−	0.407519i	$-0.866394\pi$
$643$	−908.209	+	295.095i	−1.41246	+	0.458935i	−0.499258	+	0.866453i	$0.666394\pi$
$644$	−2044.94	+	128.657i	−3.17538	+	0.199778i
$645$	−405.026	+	72.9951i	−0.627947	+	0.113171i
$646$	32.4673	+	12.8547i	0.0502590	+	0.0198989i
$647$	−632.566	+	764.641i	−0.977690	+	1.18182i	0.00563765	+	0.999984i	$0.498205\pi$
$647$	−632.566	+	764.641i	−0.977690	+	1.18182i	−0.983328	+	0.181841i	$0.941795\pi$
$648$	1509.83	+	1097.56i	2.32999	+	1.69377i
$649$	−68.5056	+	210.838i	−0.105556	+	0.324867i
$650$	706.717	+	1165.08i	1.08726	+	1.79243i
$651$	−544.804	−	1875.68i	−0.836873	−	2.88124i
$652$	1377.76	+	262.821i	2.11312	+	0.403100i
$653$	−416.176	−	655.788i	−0.637329	−	1.00427i	−0.997450	−	0.0713646i	$-0.977265\pi$
$653$	−416.176	−	655.788i	−0.637329	−	1.00427i	0.360121	−	0.932906i	$-0.382735\pi$
$654$	675.717	−	399.558i	1.03321	−	0.610945i
$655$	−120.877	+	400.874i	−0.184546	+	0.612021i
$656$	947.711	−	784.014i	1.44468	−	1.19514i
$657$	−5.75398	−	9.06943i	−0.00875795	−	0.0138043i
$658$	786.898	+	1987.48i	1.19589	+	3.02048i
$659$	−379.091	−	178.387i	−0.575251	−	0.270693i	0.116069	−	0.993241i	$-0.462971\pi$
$659$	−379.091	−	178.387i	−0.575251	−	0.270693i	−0.691320	+	0.722548i	$0.742971\pi$
$660$	272.770	−	169.232i	0.413287	−	0.256413i
$661$	−236.826	+	222.395i	−0.358285	+	0.336452i	−0.842697	−	0.538388i	$-0.819034\pi$
$661$	−236.826	+	222.395i	−0.358285	+	0.336452i	0.484412	+	0.874840i	$0.339034\pi$
$662$	74.9442	+	392.871i	0.113209	+	0.593461i
$663$	−159.796	+	81.4069i	−0.241019	+	0.122786i
$664$	−347.484	+	1821.57i	−0.523319	+	2.74333i
$665$	−104.645	+	79.4878i	−0.157361	+	0.119531i
$666$	−196.436	−	417.590i	−0.294950	−	0.627012i
$667$	691.426	−	43.5008i	1.03662	−	0.0652186i
$668$	716.087	+	520.267i	1.07199	+	0.778844i
$669$	772.857	+	224.590i	1.15524	+	0.335711i
$670$	12.5731	−	12.3211i	0.0187658	−	0.0183897i
$671$	−192.397	−	12.1046i	−0.286731	−	0.0180396i
$672$	2770.53	−	619.097i	4.12281	−	0.921275i
$673$	105.408	+	834.387i	0.156623	+	1.23980i	0.852918	+	0.522045i	$0.174831\pi$
$673$	105.408	+	834.387i	0.156623	+	1.23980i	−0.696294	+	0.717756i	$0.745169\pi$
$674$	−792.392	+	1090.63i	−1.17566	+	1.61815i
$675$	−34.9856	+	674.093i	−0.0518306	+	0.998656i
$676$	338.106	−	245.648i	0.500157	−	0.363385i
$677$	−184.529	+	173.285i	−0.272569	+	0.255959i	−0.808762	−	0.588136i	$-0.799862\pi$
$677$	−184.529	+	173.285i	−0.272569	+	0.255959i	0.536193	+	0.844095i	$0.319862\pi$
$678$	−254.134	+	587.164i	−0.374829	+	0.866023i
$679$	842.106	−	216.216i	1.24021	−	0.318433i
$680$	108.310	−	462.511i	0.159279	−	0.680163i
$681$	227.296	+	154.492i	0.333767	+	0.226860i
$682$		−	443.246i		−	0.649921i
$683$	650.845	−	1025.57i	0.952921	−	1.50156i	0.0901739	−	0.995926i	$-0.471258\pi$
$683$	650.845	−	1025.57i	0.952921	−	1.50156i	0.862747	−	0.505636i	$-0.168742\pi$
$684$	−140.613	−	149.777i	−0.205575	−	0.218973i
$685$	−75.1217	−	507.491i	−0.109667	−	0.740862i
$686$	−803.721	+	1461.96i	−1.17161	+	2.13114i
$687$	8.08541	+	4.12039i	0.0117692	+	0.00599765i
$688$	−1144.55	−	538.585i	−1.66359	−	0.782828i
$689$	528.290	−	960.956i	0.766749	−	1.39471i
$690$	719.535	−	662.025i	1.04280	−	0.959457i
$691$	470.148	+	441.498i	0.680388	+	0.638927i	0.945626	−	0.325256i	$-0.105451\pi$
$691$	470.148	+	441.498i	0.680388	+	0.638927i	−0.265238	+	0.964183i	$0.585451\pi$
$692$	−356.530	+	561.801i	−0.515216	+	0.811851i
$693$	−221.320	−	13.9533i	−0.319365	−	0.0201346i
$694$	447.968	−	705.884i	0.645486	−	1.01712i
$695$	587.910	+	355.769i	0.845914	+	0.511898i
$696$	−2695.57	+	602.347i	−3.87295	+	0.865441i
$697$	−40.4883	+	102.262i	−0.0580893	+	0.146717i
$698$	238.060	−	223.553i	0.341060	−	0.320277i
$699$	520.042	+	765.326i	0.743980	+	1.09489i
$700$	2112.03	+	2065.35i	3.01719	+	2.95051i
$701$	−215.305	+	296.342i	−0.307140	+	0.422742i	−0.934487	−	0.355998i	$-0.884141\pi$
$701$	−215.305	+	296.342i	−0.307140	+	0.422742i	0.627347	+	0.778740i	$0.284141\pi$
$702$	1470.96	−	45.9385i	2.09539	−	0.0654395i
$703$	7.64380	+	29.7706i	0.0108731	+	0.0423480i
$704$	254.155	+	15.9901i	0.361016	+	0.0227132i
$705$	−637.210	−	358.810i	−0.903845	−	0.508950i
$706$	−2176.36	−	558.794i	−3.08266	−	0.791493i
$707$	890.186	+	646.758i	1.25910	+	0.914792i
$708$	−99.9720	−	3187.79i	−0.141203	−	4.50253i
$709$	−705.655	+	387.937i	−0.995283	+	0.547161i	−0.894177	−	0.447714i	$-0.852238\pi$
$709$	−705.655	+	387.937i	−0.995283	+	0.547161i	−0.101106	+	0.994876i	$0.532238\pi$
$710$	−2178.37	+	46.3951i	−3.06812	+	0.0653452i
$711$	−46.5760	+	181.303i	−0.0655078	+	0.254998i
$712$	−1149.18	−	2090.36i	−1.61402	−	2.93590i
$713$	−181.370	−	950.774i	−0.254376	−	1.33348i
$714$	−406.795	+	358.590i	−0.569740	+	0.502228i
$715$	53.3353	−	143.568i	0.0745948	−	0.200795i
$716$	−2271.40	−	1068.84i	−3.17234	−	1.49279i
$717$	−739.707	+	266.256i	−1.03167	+	0.371348i
$718$	−411.547	−	566.445i	−0.573185	−	0.788921i
$719$	152.110	−	125.836i	0.211557	−	0.175016i	−0.525610	−	0.850726i	$-0.676163\pi$
$719$	152.110	−	125.836i	0.211557	−	0.175016i	0.737167	+	0.675710i	$0.236163\pi$
$720$	−1288.32	+	1626.19i	−1.78934	+	2.25860i
$721$	1174.43	+	1850.61i	1.62889	+	2.56673i
$722$	−716.899	−	1129.65i	−0.992935	−	1.56461i
$723$	−80.0144	−	17.8908i	−0.110670	−	0.0247453i
$724$	941.346	+	2897.17i	1.30020	+	4.00161i
$725$	−714.111	−	698.328i	−0.984980	−	0.963211i
$726$	1236.49	+	445.253i	1.70315	+	0.613297i
$727$	−247.460	+	450.128i	−0.340385	+	0.619159i	−0.989994	−	0.141110i	$-0.954933\pi$
$727$	−247.460	+	450.128i	−0.340385	+	0.619159i	0.649608	+	0.760269i	$0.274933\pi$
$728$	2484.38	−	3003.10i	3.41261	−	4.12514i
$729$	615.362	+	390.859i	0.844118	+	0.536157i
$730$	19.4214	−	11.2220i	0.0266047	−	0.0153727i
$731$	112.889	−	7.10236i	0.154431	−	0.00971595i
$732$	2663.34	−	773.584i	3.63845	−	1.05681i
$733$	123.175	−	101.899i	0.168043	−	0.139017i	−0.549602	−	0.835427i	$-0.685220\pi$
$733$	123.175	−	101.899i	0.168043	−	0.139017i	0.717644	+	0.696410i	$0.245220\pi$
$734$	1054.63	−	201.182i	1.43683	−	0.274090i
$735$	−231.595	−	1285.05i	−0.315096	−	1.74836i
$736$	1395.72	−	176.320i	1.89635	−	0.239565i
$737$	−1.96295	−	0.247978i	−0.00266343	−	0.000336469i
$738$	658.022	−	617.762i	0.891628	−	0.837076i
$739$	−390.822	−	830.540i	−0.528853	−	1.12387i	−0.973610	−	0.228219i	$-0.926710\pi$
$739$	−390.822	−	830.540i	−0.528853	−	1.12387i	0.444757	−	0.895651i	$-0.353290\pi$
$740$	636.851	−	267.971i	0.860610	−	0.362123i
$741$	−96.8105	−	15.3398i	−0.130648	−	0.0207014i
$742$	824.632	−	3211.73i	1.11136	−	4.32848i
$743$	91.4092	−	281.329i	0.123027	−	0.378639i	−0.870509	−	0.492152i	$-0.836210\pi$
$743$	91.4092	−	281.329i	0.123027	−	0.378639i	0.993536	+	0.113513i	$0.0362104\pi$
$744$	1306.93	+	3630.88i	1.75663	+	4.88022i
$745$	−293.534	−	441.468i	−0.394005	−	0.592574i
$746$	−604.355	−	499.966i	−0.810127	−	0.670195i
$747$	−90.8650	+	718.516i	−0.121640	+	0.961869i
$748$	−79.8288	+	37.5646i	−0.106723	+	0.0502201i
$749$		−	658.537i		−	0.879221i
$750$	−1403.52	−	131.273i	−1.87136	−	0.175031i
$751$	410.848			0.547068			0.273534	−	0.961862i	$-0.411807\pi$
$751$	410.848			0.547068			0.273534	+	0.961862i	$0.411807\pi$
$752$	−957.016	−	2033.76i	−1.27263	−	2.70447i
$753$	−64.0012	+	676.591i	−0.0849950	+	0.898527i
$754$	−1388.10	+	1677.92i	−1.84098	+	2.22536i
$755$	259.554	−	698.670i	0.343780	−	0.925390i
$756$	3063.86	−	889.484i	4.05273	−	1.17657i
$757$	−598.228	−	194.376i	−0.790262	−	0.256772i	−0.114046	−	0.993475i	$-0.536381\pi$
$757$	−598.228	−	194.376i	−0.790262	−	0.256772i	−0.676216	+	0.736704i	$0.736381\pi$
$758$	−1827.13	−	469.126i	−2.41046	−	0.618900i
$759$	−108.540	−	17.1982i	−0.143003	−	0.0226591i
$760$	196.478	−	169.715i	0.258523	−	0.223310i
$761$	−38.0254	+	17.8934i	−0.0499677	+	0.0235130i	−0.450601	−	0.892726i	$-0.648790\pi$
$761$	−38.0254	+	17.8934i	−0.0499677	+	0.0235130i	0.400633	+	0.916239i	$0.368790\pi$
$762$	1148.58	+	1148.73i	1.50732	+	1.50752i
$763$	101.763	−	805.540i	0.133373	−	1.05575i
$764$	−16.2319	−	128.489i	−0.0212460	−	0.168179i
$765$	30.8985	−	182.928i	0.0403902	−	0.239122i
$766$	−30.1206	−	157.898i	−0.0393219	−	0.206133i
$767$	−969.962	−	1172.48i	−1.26462	−	1.52866i
$768$	−3.92006	+	1.13861i	−0.00510425	+	0.00148256i
$769$	−67.2628	−	1069.11i	−0.0874679	−	1.39026i	−0.759869	−	0.650076i	$-0.774737\pi$
$769$	−67.2628	−	1069.11i	−0.0874679	−	1.39026i	0.672402	−	0.740187i	$-0.265263\pi$
$770$	48.2468	−	460.593i	0.0626582	−	0.598172i
$771$	258.928	−	598.241i	0.335834	−	0.775928i
$772$	−134.288	−	111.092i	−0.173948	−	0.143902i
$773$	−527.398	−	289.939i	−0.682274	−	0.375083i	0.102614	−	0.994721i	$-0.467279\pi$
$773$	−527.398	−	289.939i	−0.682274	−	0.375083i	−0.784888	+	0.619638i	$0.787279\pi$
$774$	−862.995	−	341.814i	−1.11498	−	0.441621i
$775$	−842.913	+	1112.12i	−1.08763	+	1.43499i
$776$	−1633.64	+	530.801i	−2.10520	+	0.684022i
$777$	−465.816	−	104.154i	−0.599506	−	0.134047i
$778$	1290.23	−	818.803i	1.65839	−	1.05245i
$779$	−50.7554	+	32.2104i	−0.0651546	+	0.0413484i
$780$	−22.4440	+	2203.28i	−0.0287744	+	2.82471i
$781$	156.099	+	188.691i	0.199870	+	0.241602i
$782$	−217.407	+	157.955i	−0.278014	+	0.201989i
$783$	−1035.94	+	300.748i	−1.32304	+	0.384097i
$784$	1708.80	−	3631.38i	2.17959	−	4.63186i
$785$	32.9631	−	793.129i	0.0419912	−	1.01036i
$786$	−708.410	+	624.465i	−0.901284	+	0.794485i
$787$	−890.056	+	169.787i	−1.13095	+	0.215740i	−0.718692	−	0.695329i	$-0.755259\pi$
$787$	−890.056	+	169.787i	−1.13095	+	0.215740i	−0.412255	+	0.911068i	$0.635259\pi$
$788$	1766.25	−	971.006i	2.24144	−	1.23224i
$789$	−1158.46	−	259.025i	−1.46826	−	0.328295i
$790$	−374.276	−	112.857i	−0.473767	−	0.142857i
$791$	318.801	+	579.897i	0.403036	+	0.733119i
$792$	438.128	+	0.0572043i	0.553192	+	7.22277e-5i
$793$	777.780	−	1070.52i	0.980807	−	1.34997i
$794$	−427.230	+	1663.95i	−0.538073	+	2.09566i
$795$	472.524	+	1031.30i	0.594370	+	1.29724i
$796$	−76.9090	+	1222.43i	−0.0966193	+	1.53572i
$797$	444.809	−	114.207i	0.558104	−	0.143297i	0.0409067	−	0.999163i	$-0.486975\pi$
$797$	444.809	−	114.207i	0.558104	−	0.143297i	0.517197	+	0.855866i	$0.326975\pi$
$798$	−295.075	+	27.8734i	−0.369768	+	0.0349290i
$799$	162.604	+	118.139i	0.203509	+	0.147858i
$800$	−1536.28	−	1324.20i	−1.92034	−	1.65525i
$801$	−499.084	−	786.657i	−0.623076	−	0.982094i
$802$	−235.472	−	250.752i	−0.293606	−	0.312658i
$803$	−2.34401	−	0.928058i	−0.00291906	−	0.00115574i
$804$	27.7796	−	6.20756i	0.0345517	−	0.00772085i
$805$	−84.9772	−	1007.73i	−0.105562	−	1.25183i
$806$	2568.85	+	1630.24i	3.18716	+	2.02263i
$807$	−256.979	−	8.09270i	−0.318438	−	0.0100281i
$808$	−1835.50	−	1164.84i	−2.27166	−	1.44164i
$809$	−227.546	+	242.312i	−0.281269	+	0.299521i	−0.854054	−	0.520185i	$-0.825863\pi$
$809$	−227.546	+	242.312i	−0.281269	+	0.299521i	0.572785	+	0.819706i	$0.305863\pi$
$810$	−868.750	+	1250.21i	−1.07253	+	1.54347i
$811$	−601.604	−	330.734i	−0.741805	−	0.407811i	0.0655713	−	0.997848i	$-0.479113\pi$
$811$	−601.604	−	330.734i	−0.741805	−	0.407811i	−0.807376	+	0.590037i	$0.799113\pi$
$812$	−2010.03	+	4271.54i	−2.47541	+	5.26051i
$813$	−686.307	−	349.747i	−0.844166	−	0.430194i
$814$	−94.9208	−	52.1831i	−0.116610	−	0.0641071i
$815$	−115.210	+	682.617i	−0.141362	+	0.837567i
$816$	403.226	−	403.174i	0.494150	−	0.494085i
$817$	52.1983	+	33.1261i	0.0638903	+	0.0405460i
$818$	627.667			0.767319
$819$	894.871	−	1231.35i	1.09264	−	1.50348i
$820$	883.334	+	1022.63i	1.07724	+	1.24711i
$821$	340.391	+	1325.74i	0.414605	+	1.61478i	0.742348	+	0.670014i	$0.233712\pi$
$821$	340.391	+	1325.74i	0.414605	+	1.61478i	−0.327743	+	0.944767i	$0.606288\pi$
$822$	459.601	−	1061.89i	0.559126	−	1.29183i
$823$	−250.049	−	266.275i	−0.303826	−	0.323542i	0.558879	−	0.829249i	$-0.311232\pi$
$823$	−250.049	−	266.275i	−0.303826	−	0.323542i	−0.862705	+	0.505707i	$0.831232\pi$
$824$	−2545.32	−	3503.33i	−3.08898	−	4.25161i
$825$	86.3744	+	132.820i	0.104696	+	0.160994i
$826$	−3722.53	−	2704.58i	−4.50670	−	3.27431i
$827$	534.021	−	67.4626i	0.645733	−	0.0815750i	0.204356	−	0.978897i	$-0.434490\pi$
$827$	534.021	−	67.4626i	0.645733	−	0.0815750i	0.441377	+	0.897322i	$0.354490\pi$
$828$	1553.04	−	296.047i	1.87565	−	0.357545i
$829$	−37.6422	+	598.306i	−0.0454068	+	0.721721i	0.907800	+	0.419403i	$0.137760\pi$
$829$	−37.6422	+	598.306i	−0.0454068	+	0.721721i	−0.953207	+	0.302318i	$0.902240\pi$
$830$	−1491.38	−	251.710i	−1.79684	−	0.303264i
$831$	128.162	+	37.2436i	0.154226	+	0.0448178i
$832$	−1027.44	+	1414.15i	−1.23491	+	1.69971i
$833$	22.5340	+	358.168i	0.0270517	+	0.429974i
$834$	703.538	+	1380.99i	0.843571	+	1.65587i
$835$	−249.200	+	358.821i	−0.298444	+	0.429726i
$836$	−47.3663	−	9.03561i	−0.0566583	−	0.0108081i
$837$	598.269	+	1383.26i	0.714778	+	1.65264i
$838$	2285.82	−	436.044i	2.72771	−	0.520339i
$839$	658.009	+	700.708i	0.784278	+	0.835171i	0.989648	−	0.143513i	$-0.0458400\pi$
$839$	658.009	+	700.708i	0.784278	+	0.835171i	−0.205371	+	0.978684i	$0.565840\pi$
$840$	962.860	+	3915.24i	1.14626	+	4.66099i
$841$	321.542	−	683.312i	0.382333	−	0.812499i
$842$	1658.95	−	656.823i	1.97024	−	0.780075i
$843$	101.932	−	69.2632i	0.120916	−	0.0821627i
$844$	370.219	+	447.517i	0.438648	+	0.530234i
$845$	124.769	+	164.257i	0.147655	+	0.194387i
$846$	−794.400	−	1445.45i	−0.939007	−	1.70858i
$847$	1147.69	−	728.348i	1.35501	−	0.859916i
$848$	−653.340	+	3424.93i	−0.770448	+	4.03883i
$849$	−282.099	−	971.227i	−0.332272	−	1.14397i
$850$	379.021	+	80.2854i	0.445907	+	0.0944534i
$851$	−224.960	−	73.0940i	−0.264348	−	0.0858919i
$852$	−3032.40	−	1793.63i	−3.55916	−	2.10519i
$853$	−641.731	−	530.886i	−0.752322	−	0.622375i	0.180141	−	0.983641i	$-0.442345\pi$
$853$	−641.731	−	530.886i	−0.752322	−	0.622375i	−0.932463	+	0.361266i	$0.882345\pi$
$854$	1472.95	−	3720.24i	1.72476	−	4.35626i
$855$	72.4299	−	70.9599i	0.0847133	−	0.0829940i
$856$	81.6946	+	1298.50i	0.0954377	+	1.51694i
$857$	431.519	+	1328.08i	0.503523	+	1.54968i	0.803240	+	0.595656i	$0.203108\pi$
$857$	431.519	+	1328.08i	0.503523	+	1.54968i	−0.299717	+	0.954028i	$0.596892\pi$
$858$	272.958	−	211.699i	0.318132	−	0.246736i
$859$	148.940	+	780.773i	0.173388	+	0.908933i	0.957526	+	0.288346i	$0.0931054\pi$
$859$	148.940	+	780.773i	0.173388	+	0.908933i	−0.784138	+	0.620586i	$0.786895\pi$
$860$	564.808	−	1269.78i	0.656754	−	1.47649i
$861$	−87.7922	−	929.393i	−0.101965	−	1.07943i
$862$	−32.8759	+	260.239i	−0.0381391	+	0.301902i
$863$	−473.507	−	444.653i	−0.548676	−	0.515241i	0.359883	−	0.932997i	$-0.382817\pi$
$863$	−473.507	−	444.653i	−0.548676	−	0.515241i	−0.908559	+	0.417757i	$0.862817\pi$
$864$	−2061.11	+	741.591i	−2.38555	+	0.858323i
$865$	−280.968	−	170.025i	−0.324818	−	0.196561i
$866$	39.7573	−	314.711i	0.0459091	−	0.363408i
$867$	227.711	−	783.596i	0.262642	−	0.903801i
$868$	6272.79	+	2038.15i	7.22671	+	2.34810i
$869$	16.1743	+	40.8516i	0.0186126	+	0.0470099i
$870$	−537.978	−	2187.56i	−0.618366	−	2.51443i
$871$	8.65681	−	10.4643i	0.00993893	−	0.0120141i
$872$	−100.725	+	1600.98i	−0.115511	+	1.83599i
$873$	−623.770	+	246.874i	−0.714513	+	0.282788i
$874$	−146.877			−0.168051
$875$	−996.954	+	1063.89i	−1.13938	+	1.21587i
$876$	36.2514	+	1.14161i	0.0413828	+	0.00130321i
$877$	−740.226	+	348.324i	−0.844043	+	0.397176i	−0.798652	−	0.601793i	$-0.794453\pi$
$877$	−740.226	+	348.324i	−0.844043	+	0.397176i	−0.0453907	+	0.998969i	$0.514453\pi$
$878$	72.5426	−	1153.03i	0.0826226	−	1.31325i
$879$	−345.336	−	304.494i	−0.392873	−	0.346410i
$880$	−20.2212	+	486.545i	−0.0229787	+	0.552892i
$881$	168.918	+	426.638i	0.191734	+	0.484265i	0.993562	−	0.113290i	$-0.0361389\pi$
$881$	168.918	+	426.638i	0.191734	+	0.484265i	−0.801828	+	0.597555i	$0.796139\pi$
$882$	1084.49	−	2738.07i	1.22958	−	3.10439i
$883$	−103.131	+	401.668i	−0.116796	+	0.454890i	−0.999898	−	0.0142911i	$-0.995451\pi$
$883$	−103.131	+	401.668i	−0.116796	+	0.454890i	0.883102	+	0.469181i	$0.155451\pi$
$884$	75.9002	−	600.812i	0.0858600	−	0.679652i
$885$	1571.97	−	82.8335i	1.77623	−	0.0935972i
$886$	−900.827	−	1914.35i	−1.01673	−	2.16067i
$887$	1093.29	+	1026.66i	1.23257	+	1.15746i	0.981903	+	0.189384i	$0.0606489\pi$
$887$	1093.29	+	1026.66i	1.23257	+	1.15746i	0.250664	+	0.968074i	$0.419351\pi$
$888$	931.415	+	147.584i	1.04889	+	0.166198i
$889$	1666.93	−	210.582i	1.87506	−	0.236875i
$890$	1684.56	−	973.369i	1.89276	−	1.09367i
$891$	170.775	−	10.6995i	0.191667	−	0.0120084i
$892$	−2094.06	+	1732.36i	−2.34761	+	1.94211i
$893$	33.9463	+	104.476i	0.0380138	+	0.116994i
$894$	−37.4801	−	1195.12i	−0.0419240	−	1.33682i
$895$	503.547	−	1132.06i	0.562623	−	1.26487i
$896$	−552.353	+	1395.09i	−0.616466	+	1.55702i
$897$	498.877	−	565.791i	0.556162	−	0.630759i
$898$	−229.447	+	417.363i	−0.255509	+	0.464770i
$899$	−2120.92	−	689.130i	−2.35920	−	0.766552i
$900$	−1816.36	−	1377.05i	−2.01817	−	1.53006i
$901$	−96.3461	−	296.523i	−0.106932	−	0.329104i
$902$	39.6964	−	208.096i	0.0440094	−	0.230705i
$903$	−826.404	+	488.661i	−0.915176	+	0.541153i
$904$	−700.550	−	1103.89i	−0.774945	−	1.22112i
$905$	−1419.71	+	494.956i	−1.56875	+	0.546912i
$906$	1328.34	−	1030.22i	1.46616	−	1.13711i
$907$	−310.763	−	427.729i	−0.342627	−	0.471586i	0.602579	−	0.798059i	$-0.294140\pi$
$907$	−310.763	−	427.729i	−0.342627	−	0.471586i	−0.945207	+	0.326473i	$0.894140\pi$
$908$	−862.875	+	341.636i	−0.950302	+	0.376251i
$909$	−743.946	−	409.114i	−0.818423	−	0.450071i
$910$	2491.93	+	1973.66i	2.73839	+	2.16885i
$911$	837.215	+	891.543i	0.919007	+	0.978643i	0.999836	−	0.0180854i	$-0.00575706\pi$
$911$	837.215	+	891.543i	0.919007	+	0.978643i	−0.0808299	+	0.996728i	$0.525757\pi$
$912$	307.820	−	48.7333i	0.337522	−	0.0534356i
$913$	81.8944	+	148.965i	0.0896981	+	0.163160i
$914$	−244.054	−	46.5557i	−0.267017	−	0.0509362i
$915$	409.716	+	1306.10i	0.447777	+	1.42743i
$916$	−26.8533	+	14.7628i	−0.0293159	+	0.0161165i
$917$	61.3307	+	974.824i	0.0668819	+	1.06306i
$918$	276.771	−	313.811i	0.301494	−	0.341842i
$919$	−908.741	−	233.325i	−0.988837	−	0.253890i	−0.280569	−	0.959834i	$-0.590523\pi$
$919$	−908.741	−	233.325i	−0.988837	−	0.253890i	−0.708268	+	0.705944i	$0.750523\pi$
$920$	292.571	+	1976.49i	0.318012	+	2.14835i
$921$	−20.0444	+	211.900i	−0.0217637	+	0.230076i
$922$	32.1617	+	125.262i	0.0348826	+	0.135859i
$923$	−1667.69	+	210.678i	−1.80682	+	0.228254i
$924$	459.007	−	591.668i	0.496761	−	0.640334i
$925$	138.923	+	311.438i	0.150187	+	0.336690i
$926$	670.359	+	922.670i	0.723930	+	0.996404i
$927$	−1077.85	−	1303.24i	−1.16273	−	1.40587i
$928$	1193.19	−	3013.65i	1.28576	−	3.24747i
$929$	398.618	+	1552.51i	0.429083	+	1.67117i	0.704391	+	0.709812i	$0.251220\pi$
$929$	398.618	+	1552.51i	0.429083	+	1.67117i	−0.275309	+	0.961356i	$0.588780\pi$
$930$	−2937.99	+	1128.75i	−3.15913	+	1.21371i
$931$	−105.101	+	165.612i	−0.112890	+	0.177887i
$932$	−3124.54			−3.35251
$933$	−404.474	+	595.082i	−0.433520	+	0.637816i
$934$	2039.64	+	1915.35i	2.18377	+	2.05070i
$935$	−19.3752	−	38.9968i	−0.0207222	−	0.0417078i
$936$	−1611.75	+	2538.98i	−1.72195	+	2.71258i
$937$	−685.812	−	322.719i	−0.731923	−	0.344417i	0.0234381	−	0.999725i	$-0.492539\pi$
$937$	−685.812	−	322.719i	−0.731923	−	0.344417i	−0.755362	+	0.655308i	$0.772539\pi$
$938$	17.4851	−	37.1578i	0.0186408	−	0.0396138i
$939$	227.409	+	134.509i	0.242182	+	0.143247i
$940$	2211.50	−	1098.77i	2.35266	−	1.16890i
$941$	19.7422	−	21.0234i	0.0209801	−	0.0223415i	−0.718393	−	0.695637i	$-0.755122\pi$
$941$	19.7422	−	21.0234i	0.0209801	−	0.0223415i	0.739373	+	0.673296i	$0.235122\pi$
$942$	1006.44	−	1480.73i	1.06841	−	1.57190i
$943$		−	462.615i		−	0.490578i
$944$	4085.10	+	2592.48i	4.32744	+	2.74628i
$945$	471.116	+	1502.52i	0.498536	+	1.58997i
$946$	−211.026	+	54.1823i	−0.223072	+	0.0572752i
$947$	790.815	+	313.106i	0.835074	+	0.330629i	0.746455	−	0.665436i	$-0.231755\pi$
$947$	790.815	+	313.106i	0.835074	+	0.330629i	0.0886193	+	0.996066i	$0.471755\pi$
$948$	−417.989	−	474.178i	−0.440916	−	0.500187i
$949$	13.9998	−	10.1714i	0.0147521	−	0.0107180i
$950$	141.801	+	157.264i	0.149265	+	0.165541i
$951$	567.840	−	731.957i	0.597098	−	0.769671i
$952$	−138.887	−	1099.40i	−0.145889	−	1.15483i
$953$	−1174.61	+	301.589i	−1.23254	+	0.316463i	−0.808129	−	0.589006i	$-0.799519\pi$
$953$	−1174.61	+	301.589i	−1.23254	+	0.316463i	−0.424413	+	0.905469i	$0.639519\pi$
$954$	−321.004	+	2538.34i	−0.336482	+	2.66074i
$955$	63.2323	−	9.36001i	0.0662118	−	0.00980105i
$956$	660.207	−	2571.34i	0.690593	−	2.68968i
$957$	−155.197	+	200.052i	−0.162170	+	0.209041i
$958$	−837.316	+	52.6795i	−0.874025	+	0.0549890i
$959$	−576.552	−	1048.74i	−0.601202	−	1.09358i
$960$	−541.233	−	1725.35i	−0.563785	−	1.79724i
$961$	−403.749	+	2116.53i	−0.420134	+	2.20242i
$962$	651.544	−	358.189i	0.677281	−	0.372338i
$963$	63.6195	+	504.130i	0.0660639	+	0.523499i
$964$	201.826	−	189.527i	0.209363	−	0.196605i
$965$	53.4073	−	67.4319i	0.0553444	−	0.0698776i
$966$	1035.65	−	2032.25i	1.07210	−	2.10377i
$967$	105.996	+	267.715i	0.109613	+	0.276851i	0.974221	−	0.225596i	$-0.0724330\pi$
$967$	105.996	+	267.715i	0.109613	+	0.276851i	−0.864608	+	0.502447i	$0.832433\pi$
$968$	−2172.66	+	1578.53i	−2.24448	+	1.63071i
$969$	−22.0214	+	17.0793i	−0.0227259	+	0.0176257i
$970$	−461.196	−	1322.88i	−0.475460	−	1.36379i
$971$	164.460	−	104.369i	0.169371	−	0.107486i	−0.448439	−	0.893813i	$-0.648020\pi$
$971$	164.460	−	104.369i	0.169371	−	0.107486i	0.617810	+	0.786327i	$0.288020\pi$
$972$	−2259.55	+	976.919i	−2.32464	+	1.00506i
$973$	1574.65	+	300.381i	1.61835	+	0.308717i
$974$	3085.88	−	1002.66i	3.16825	−	1.02943i
$975$	−1087.44	+	12.0805i	−1.11533	+	0.0123902i
$976$	−1300.13	+	4001.38i	−1.33210	+	4.09978i
$977$	1334.78	+	733.803i	1.36621	+	0.751078i	0.984859	−	0.173355i	$-0.0554607\pi$
$977$	1334.78	+	733.803i	1.36621	+	0.751078i	0.381346	+	0.924432i	$0.375461\pi$
$978$	−1032.63	+	1171.13i	−1.05586	+	1.19748i
$979$	−203.313	−	80.4971i	−0.207674	−	0.0822238i
$980$	4028.69	+	1792.00i	4.11091	+	1.82857i
$981$	−0.0817987	+	626.496i	−8.33829e−5	+	0.638630i
$982$	−2177.13	+	707.393i	−2.21704	+	0.720359i
$983$	−18.2691	−	22.0836i	−0.0185850	−	0.0224655i	0.761139	−	0.648589i	$-0.224641\pi$
$983$	−18.2691	−	22.0836i	−0.0185850	−	0.0224655i	−0.779724	+	0.626124i	$0.784641\pi$
$984$	288.404	+	1821.68i	0.293093	+	1.85130i
$985$	497.706	+	861.353i	0.505285	+	0.874470i
$986$	77.6001	+	614.268i	0.0787019	+	0.622990i
$987$	−1684.93	−	266.980i	−1.70713	−	0.270496i
$988$	226.578	−	241.281i	0.229330	−	0.244211i
$989$	−430.486	+	202.572i	−0.435274	+	0.204825i
$990$	7.56227	+	357.259i	0.00763866	+	0.360867i
$991$	1123.55	+	141.937i	1.13375	+	0.143226i	0.669735	−	0.742600i	$-0.266408\pi$
$991$	1123.55	+	141.937i	1.13375	+	0.143226i	0.464017	+	0.885826i	$0.346408\pi$
$992$	−4386.19	−	1126.18i	−4.42156	−	1.13526i
$993$	−300.317	−	108.143i	−0.302434	−	0.108905i
$994$	−4725.92	+	1871.13i	−4.75445	+	1.88242i
$995$	−604.018	−	25.1035i	−0.607054	−	0.0252297i
$996$	−1834.38	−	1617.44i	−1.84175	−	1.62393i
$997$	1921.16	+	120.869i	1.92695	+	0.121233i	0.979852	−	0.199725i	$-0.0640050\pi$
$997$	1921.16	+	120.869i	1.92695	+	0.121233i	0.947093	+	0.320958i	$0.104005\pi$
$998$	−336.913	−	715.976i	−0.337588	−	0.717411i
$999$	366.659	+	34.7319i	0.367026	+	0.0347667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.p.a.14.4	✓	1960
3.2	odd	2	inner	375.3.p.a.14.95	yes	1960
125.9	even	50	inner	375.3.p.a.134.95	yes	1960
375.134	odd	50	inner	375.3.p.a.134.4	yes	1960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.p.a.14.4	✓	1960	1.1	even	1	trivial
375.3.p.a.14.95	yes	1960	3.2	odd	2	inner
375.3.p.a.134.4	yes	1960	375.134	odd	50	inner
375.3.p.a.134.95	yes	1960	125.9	even	50	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.p (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60052 - 3.40129i) q^{2} +(2.98667 + 0.282520i) q^{3} +(-6.45738 + 7.80563i) q^{4} +(-3.91956 - 3.10436i) q^{5} +(-3.81930 - 10.6107i) q^{6} +(-11.0932 - 3.60439i) q^{7} +(22.3206 + 5.73095i) q^{8} +(8.84036 + 1.68759i) q^{9} +(-4.28549 + 18.3001i) q^{10} +(1.91142 - 0.899444i) q^{11} +(-21.4913 + 21.4885i) q^{12} +(-1.81735 + 14.3858i) q^{13} +(5.49532 + 43.4999i) q^{14} +(-10.8294 - 10.3791i) q^{15} +(-8.63901 - 45.2873i) q^{16} +(2.62788 + 3.17656i) q^{17} +(-8.40925 - 32.7696i) q^{18} +(0.141484 + 2.24882i) q^{19} +(49.5416 - 10.5486i) q^{20} +(-32.1133 - 13.8991i) q^{21} +(-6.11854 - 5.06169i) q^{22} +(-15.1956 - 8.35385i) q^{23} +(65.0451 + 23.4225i) q^{24} +(5.72585 + 24.3355i) q^{25} +(51.8390 - 16.8435i) q^{26} +(25.9265 + 7.53784i) q^{27} +(99.7673 - 63.3143i) q^{28} +(-33.7328 + 21.4075i) q^{29} +(-17.9695 + 53.4457i) q^{30} +(35.5800 + 43.0088i) q^{31} +(-65.6343 + 47.6861i) q^{32} +(5.96288 - 2.14633i) q^{33} +(6.59840 - 14.0223i) q^{34} +(32.2910 + 48.5648i) q^{35} +(-70.2583 + 58.1072i) q^{36} +(13.3991 - 2.55602i) q^{37} +(7.42245 - 4.08053i) q^{38} +(-9.49210 + 42.4522i) q^{39} +(-69.6959 - 91.7540i) q^{40} +(12.8524 + 23.3784i) q^{41} +(4.12310 + 131.472i) q^{42} +(16.1269 - 22.1968i) q^{43} +(-5.32201 + 20.7279i) q^{44} +(-29.4114 - 34.0583i) q^{45} +(-4.09292 + 65.0551i) q^{46} +(47.2209 - 12.1243i) q^{47} +(-13.0073 - 137.699i) q^{48} +(70.4249 + 51.1666i) q^{49} +(73.6075 - 58.4248i) q^{50} +(6.95115 + 10.2297i) q^{51} +(-100.555 - 107.080i) q^{52} +(-70.3159 - 27.8401i) q^{53} +(-15.8576 - 100.248i) q^{54} +(-10.2841 - 2.40831i) q^{55} +(-226.949 - 144.026i) q^{56} +(-0.212772 + 6.75646i) q^{57} +(126.803 + 80.4718i) q^{58} +(-71.8385 + 76.5002i) q^{59} +(150.944 - 17.5086i) q^{60} +(-79.9690 - 43.9634i) q^{61} +(89.3387 - 189.854i) q^{62} +(-91.9849 - 50.5848i) q^{63} +(105.639 + 58.0754i) q^{64} +(51.7820 - 50.7443i) q^{65} +(-16.8440 - 16.8462i) q^{66} +(-0.790803 - 0.501859i) q^{67} -41.7642 q^{68} +(-43.0241 - 29.2432i) q^{69} +(113.500 - 187.560i) q^{70} +(28.8297 + 112.284i) q^{71} +(187.651 + 88.3316i) q^{72} +(-0.816947 - 0.869960i) q^{73} +(-30.1394 - 41.4833i) q^{74} +(10.2260 + 74.2996i) q^{75} +(-18.4671 - 13.4171i) q^{76} +(-24.4456 + 3.08820i) q^{77} +(159.584 - 35.6604i) q^{78} +(-1.30598 + 20.7579i) q^{79} +(-106.727 + 204.325i) q^{80} +(75.3041 + 29.8378i) q^{81} +(58.9460 - 81.1322i) q^{82} +(5.05282 + 80.3122i) q^{83} +(315.859 - 160.912i) q^{84} +(-0.438924 - 20.6086i) q^{85} +(-101.309 - 19.3257i) q^{86} +(-106.797 + 54.4069i) q^{87} +(47.8186 - 9.12189i) q^{88} +(-70.8597 - 75.4579i) q^{89} +(-68.7683 + 154.548i) q^{90} +(72.0122 - 153.034i) q^{91} +(163.331 - 64.6673i) q^{92} +(94.1147 + 138.505i) q^{93} +(-116.816 - 141.207i) q^{94} +(6.42661 - 9.25361i) q^{95} +(-209.500 + 123.880i) q^{96} +(-62.9349 + 39.9397i) q^{97} +(61.3158 - 321.429i) q^{98} +(18.4155 - 4.72574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) \) 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

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