LMFDB - Embedded newform 152.4.t.a.101.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,4,Mod(5,152)] 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("152.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, 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:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	152.101
Dual form			152.4.t.a.149.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96760 + 2.03189i) q^{2} +(-1.12968 + 3.10377i) q^{3} +(-0.257137 - 7.99587i) q^{4} +(2.27970 - 0.401972i) q^{5} +(-4.08375 - 8.40233i) q^{6} +(3.20168 - 5.54548i) q^{7} +(16.7526 + 15.2102i) q^{8} +(12.3260 + 10.3428i) q^{9} +(-3.66876 + 5.42300i) q^{10} +(-9.01975 + 5.20756i) q^{11} +(25.1078 + 8.23466i) q^{12} +(16.3784 + 44.9994i) q^{13} +(4.96817 + 17.4167i) q^{14} +(-1.32770 + 7.52974i) q^{15} +(-63.8678 + 4.11207i) q^{16} +(-9.18576 + 7.70777i) q^{17} +(-45.2679 + 4.69472i) q^{18} +(23.1416 + 79.5202i) q^{19} +(-3.80031 - 18.1248i) q^{20} +(13.5950 + 16.2019i) q^{21} +(7.16605 - 28.5735i) q^{22} +(24.0217 - 136.234i) q^{23} +(-66.1339 + 34.8137i) q^{24} +(-112.426 + 40.9198i) q^{25} +(-123.660 - 55.2614i) q^{26} +(-123.258 + 71.1630i) q^{27} +(-45.1642 - 24.1743i) q^{28} +(-118.661 + 141.415i) q^{29} +(-12.6872 - 17.5132i) q^{30} +(-2.16068 + 3.74241i) q^{31} +(117.311 - 137.863i) q^{32} +(-5.97362 - 33.8781i) q^{33} +(2.41254 - 33.8302i) q^{34} +(5.06974 - 13.9290i) q^{35} +(79.5298 - 101.217i) q^{36} +372.850i q^{37} +(-207.110 - 109.442i) q^{38} -158.170 q^{39} +(44.3050 + 27.9404i) q^{40} +(-62.2220 - 22.6470i) q^{41} +(-59.6699 - 4.25524i) q^{42} +(-168.958 + 29.7919i) q^{43} +(43.9582 + 70.7817i) q^{44} +(32.2571 + 18.6236i) q^{45} +(229.546 + 316.862i) q^{46} +(60.5211 + 50.7833i) q^{47} +(59.3871 - 202.876i) q^{48} +(150.998 + 261.537i) q^{49} +(138.065 - 308.951i) q^{50} +(-13.5462 - 37.2178i) q^{51} +(355.597 - 142.531i) q^{52} +(316.894 + 55.8770i) q^{53} +(97.9265 - 390.466i) q^{54} +(-18.4690 + 15.4973i) q^{55} +(137.984 - 44.2033i) q^{56} +(-272.955 - 18.0061i) q^{57} +(-53.8620 - 519.353i) q^{58} +(-55.5836 - 66.2420i) q^{59} +(60.5482 + 8.67991i) q^{60} +(691.438 + 121.919i) q^{61} +(-3.35282 - 11.7538i) q^{62} +(96.8195 - 35.2394i) q^{63} +(49.3023 + 509.621i) q^{64} +(55.4263 + 96.0012i) q^{65} +(80.5901 + 54.5206i) q^{66} +(197.722 - 235.636i) q^{67} +(63.9923 + 71.4662i) q^{68} +(395.700 + 228.458i) q^{69} +(18.3270 + 37.7078i) q^{70} +(68.5839 + 388.959i) q^{71} +(49.1785 + 360.749i) q^{72} +(-408.524 - 148.691i) q^{73} +(-757.589 - 733.618i) q^{74} -395.171i q^{75} +(629.882 - 205.485i) q^{76} +66.6918i q^{77} +(311.214 - 321.383i) q^{78} +(271.509 + 98.8213i) q^{79} +(-143.946 + 35.0473i) q^{80} +(-6.19131 - 35.1127i) q^{81} +(168.444 - 81.8681i) q^{82} +(-870.671 - 502.682i) q^{83} +(126.052 - 112.870i) q^{84} +(-17.8424 + 21.2638i) q^{85} +(271.908 - 401.923i) q^{86} +(-304.870 - 528.050i) q^{87} +(-230.313 - 49.9515i) q^{88} +(1305.85 - 475.291i) q^{89} +(-101.310 + 28.8990i) q^{90} +(301.982 + 53.2475i) q^{91} +(-1095.48 - 157.043i) q^{92} +(-9.17470 - 10.9340i) q^{93} +(-222.267 + 23.0513i) q^{94} +(84.7208 + 171.980i) q^{95} +(295.371 + 519.846i) q^{96} +(582.397 - 488.689i) q^{97} +(-828.518 - 207.787i) q^{98} +(-165.038 - 29.1007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) $ 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.96760	+	2.03189i	−0.695650	+	0.718381i
$2$	−1.96760	+	2.03189i	−0.695650	+	0.718381i
$3$	−1.12968	+	3.10377i	−0.217407	+	0.597320i	−0.999672	−	0.0256259i	$-0.991842\pi$
$3$	−1.12968	+	3.10377i	−0.217407	+	0.597320i	0.782265	+	0.622946i	$0.214064\pi$
$4$	−0.257137	−	7.99587i	−0.0321422	−	0.999483i
$5$	2.27970	−	0.401972i	0.203902	−	0.0359535i	−0.0707641	−	0.997493i	$-0.522544\pi$
$5$	2.27970	−	0.401972i	0.203902	−	0.0359535i	0.274666	+	0.961540i	$0.411433\pi$
$6$	−4.08375	−	8.40233i	−0.277864	−	0.571706i
$7$	3.20168	−	5.54548i	0.172875	−	0.299428i	−0.766549	−	0.642186i	$-0.778028\pi$
$7$	3.20168	−	5.54548i	0.172875	−	0.299428i	0.939424	+	0.342758i	$0.111361\pi$
$8$	16.7526	+	15.2102i	0.740369	+	0.672200i
$9$	12.3260	+	10.3428i	0.456519	+	0.383065i
$10$	−3.66876	+	5.42300i	−0.116016	+	0.171490i
$11$	−9.01975	+	5.20756i	−0.247233	+	0.142740i	−0.618496	−	0.785788i	$-0.712258\pi$
$11$	−9.01975	+	5.20756i	−0.247233	+	0.142740i	0.371264	+	0.928527i	$0.378925\pi$
$12$	25.1078	+	8.23466i	0.603999	+	0.198095i
$13$	16.3784	+	44.9994i	0.349428	+	0.960044i	0.982551	+	0.185994i	$0.0595504\pi$
$13$	16.3784	+	44.9994i	0.349428	+	0.960044i	−0.633123	+	0.774051i	$0.718227\pi$
$14$	4.96817	+	17.4167i	0.0948429	+	0.332487i
$15$	−1.32770	+	7.52974i	−0.0228540	+	0.129611i
$16$	−63.8678	+	4.11207i	−0.997934	+	0.0642511i
$17$	−9.18576	+	7.70777i	−0.131051	+	0.109965i	−0.705957	−	0.708254i	$-0.749483\pi$
$17$	−9.18576	+	7.70777i	−0.131051	+	0.109965i	0.574906	+	0.818219i	$0.305039\pi$
$18$	−45.2679	+	4.69472i	−0.592764	+	0.0614754i
$19$	23.1416	+	79.5202i	0.279424	+	0.960168i
$19$	23.1416	+	79.5202i	0.279424	+	0.960168i
$20$	−3.80031	−	18.1248i	−0.0424887	−	0.202641i
$21$	13.5950	+	16.2019i	0.141270	+	0.168359i
$22$	7.16605	−	28.5735i	0.0694458	−	0.276904i
$23$	24.0217	−	136.234i	0.217777	−	1.23507i	−0.658246	−	0.752803i	$-0.728701\pi$
$23$	24.0217	−	136.234i	0.217777	−	1.23507i	0.876023	−	0.482270i	$-0.160187\pi$
$24$	−66.1339	+	34.8137i	−0.562480	+	0.296097i
$25$	−112.426	+	40.9198i	−0.899409	+	0.327358i
$26$	−123.660	−	55.2614i	−0.932757	−	0.416833i
$27$	−123.258	+	71.1630i	−0.878556	+	0.507234i
$28$	−45.1642	−	24.1743i	−0.304830	−	0.163161i
$29$	−118.661	+	141.415i	−0.759821	+	0.905520i	−0.997837	−	0.0657416i	$-0.979059\pi$
$29$	−118.661	+	141.415i	−0.759821	+	0.905520i	0.238015	+	0.971261i	$0.423503\pi$
$30$	−12.6872	−	17.5132i	−0.0772120	−	0.106582i
$31$	−2.16068	+	3.74241i	−0.0125184	+	0.0216825i	−0.872217	−	0.489120i	$-0.837318\pi$
$31$	−2.16068	+	3.74241i	−0.0125184	+	0.0216825i	0.859698	+	0.510802i	$0.170652\pi$
$32$	117.311	−	137.863i	0.648056	−	0.761593i
$33$	−5.97362	−	33.8781i	−0.0315113	−	0.178710i
$34$	2.41254	−	33.8302i	0.0121690	−	0.170642i
$35$	5.06974	−	13.9290i	0.0244841	−	0.0672694i
$36$	79.5298	−	101.217i	0.368193	−	0.468596i
$37$			372.850i			1.65665i	0.560246	+	0.828326i	$0.310707\pi$
$37$			372.850i			1.65665i	−0.560246	+	0.828326i	$0.689293\pi$
$38$	−207.110	−	109.442i	−0.884147	−	0.467208i
$39$	−158.170			−0.649422
$40$	44.3050	+	27.9404i	0.175131	+	0.110444i
$41$	−62.2220	−	22.6470i	−0.237011	−	0.0862649i	0.220784	−	0.975323i	$-0.429138\pi$
$41$	−62.2220	−	22.6470i	−0.237011	−	0.0862649i	−0.457795	+	0.889058i	$0.651361\pi$
$42$	−59.6699	−	4.25524i	−0.219220	−	0.0156333i
$43$	−168.958	+	29.7919i	−0.599208	+	0.105656i	−0.465021	−	0.885300i	$-0.653953\pi$
$43$	−168.958	+	29.7919i	−0.599208	+	0.105656i	−0.134187	+	0.990956i	$0.542842\pi$
$44$	43.9582	+	70.7817i	0.150613	+	0.242517i
$45$	32.2571	+	18.6236i	0.106858	+	0.0616943i
$46$	229.546	+	316.862i	0.735756	+	1.01562i
$47$	60.5211	+	50.7833i	0.187828	+	0.157606i	0.731853	−	0.681463i	$-0.238656\pi$
$47$	60.5211	+	50.7833i	0.187828	+	0.157606i	−0.544025	+	0.839069i	$0.683100\pi$
$48$	59.3871	−	202.876i	0.178579	−	0.610054i
$49$	150.998	+	261.537i	0.440229	+	0.762498i
$50$	138.065	−	308.951i	0.390506	−	0.873845i
$51$	−13.5462	−	37.2178i	−0.0371930	−	0.102187i
$52$	355.597	−	142.531i	0.948317	−	0.380105i
$53$	316.894	+	55.8770i	0.821298	+	0.144817i	0.568480	−	0.822697i	$-0.307532\pi$
$53$	316.894	+	55.8770i	0.821298	+	0.144817i	0.252818	+	0.967514i	$0.418643\pi$
$54$	97.9265	−	390.466i	0.246780	−	0.983995i
$55$	−18.4690	+	15.4973i	−0.0452793	+	0.0379938i
$56$	137.984	−	44.2033i	0.329267	−	0.105481i
$57$	−272.955	−	18.0061i	−0.634276	−	0.0418414i
$58$	−53.8620	−	519.353i	−0.121938	−	1.17577i
$59$	−55.5836	−	66.2420i	−0.122650	−	0.146169i	0.701225	−	0.712940i	$-0.252637\pi$
$59$	−55.5836	−	66.2420i	−0.122650	−	0.146169i	−0.823875	+	0.566771i	$0.808192\pi$
$60$	60.5482	+	8.67991i	0.130279	+	0.0186762i
$61$	691.438	+	121.919i	1.45130	+	0.255904i	0.843049	−	0.537837i	$-0.180759\pi$
$61$	691.438	+	121.919i	1.45130	+	0.255904i	0.608255	+	0.793741i	$0.291870\pi$
$62$	−3.35282	−	11.7538i	−0.00686787	−	0.0240764i
$63$	96.8195	−	35.2394i	0.193621	−	0.0704722i
$64$	49.3023	+	509.621i	0.0962936	+	0.995353i
$65$	55.4263	+	96.0012i	0.105766	+	0.183192i
$66$	80.5901	+	54.5206i	0.150302	+	0.101682i
$67$	197.722	−	235.636i	0.360531	−	0.429664i	−0.555038	−	0.831825i	$-0.687296\pi$
$67$	197.722	−	235.636i	0.360531	−	0.429664i	0.915569	+	0.402161i	$0.131741\pi$
$68$	63.9923	+	71.4662i	0.114121	+	0.127449i
$69$	395.700	+	228.458i	0.690387	+	0.398595i
$70$	18.3270	+	37.7078i	0.0312927	+	0.0643848i
$71$	68.5839	+	388.959i	0.114640	+	0.650154i	0.986928	+	0.161162i	$0.0515241\pi$
$71$	68.5839	+	388.959i	0.114640	+	0.650154i	−0.872288	+	0.488992i	$0.837365\pi$
$72$	49.1785	+	360.749i	0.0804963	+	0.590482i
$73$	−408.524	−	148.691i	−0.654988	−	0.238396i	−0.00691684	−	0.999976i	$-0.502202\pi$
$73$	−408.524	−	148.691i	−0.654988	−	0.238396i	−0.648071	+	0.761580i	$0.724424\pi$
$74$	−757.589	−	733.618i	−1.19011	−	1.15245i
$75$		−	395.171i		−	0.608405i
$76$	629.882	−	205.485i	0.950690	−	0.310141i
$77$			66.6918i			0.0987044i
$78$	311.214	−	321.383i	0.451770	−	0.466532i
$79$	271.509	+	98.8213i	0.386673	+	0.140738i	0.528039	−	0.849220i	$-0.322927\pi$
$79$	271.509	+	98.8213i	0.386673	+	0.140738i	−0.141366	+	0.989957i	$0.545150\pi$
$80$	−143.946	+	35.0473i	−0.201171	+	0.0489801i
$81$	−6.19131	−	35.1127i	−0.00849288	−	0.0481655i
$82$	168.444	−	81.8681i	0.226848	−	0.110254i
$83$	−870.671	−	502.682i	−1.15143	−	0.664778i	−0.202194	−	0.979346i	$-0.564807\pi$
$83$	−870.671	−	502.682i	−1.15143	−	0.664778i	−0.949235	+	0.314568i	$0.898140\pi$
$84$	126.052	−	112.870i	0.163731	−	0.146608i
$85$	−17.8424	+	21.2638i	−0.0227681	+	0.0271339i
$86$	271.908	−	401.923i	0.340937	−	0.503959i
$87$	−304.870	−	528.050i	−0.375695	−	0.650723i
$88$	−230.313	−	49.9515i	−0.278993	−	0.0605096i
$89$	1305.85	−	475.291i	1.55528	−	0.566076i	0.585632	−	0.810577i	$-0.300846\pi$
$89$	1305.85	−	475.291i	1.55528	−	0.566076i	0.969649	+	0.244501i	$0.0786242\pi$
$90$	−101.310	+	28.8990i	−0.118656	+	0.0338469i
$91$	301.982	+	53.2475i	0.347871	+	0.0613391i
$92$	−1095.48	−	157.043i	−1.24143	−	0.177966i
$93$	−9.17470	−	10.9340i	−0.0102298	−	0.0121914i
$94$	−222.267	+	23.0513i	−0.243884	+	0.0252931i
$95$	84.7208	+	171.980i	0.0914965	+	0.185734i
$96$	295.371	+	519.846i	0.314023	+	0.552672i
$97$	582.397	−	488.689i	0.609624	−	0.511535i	−0.284899	−	0.958558i	$-0.591960\pi$
$97$	582.397	−	488.689i	0.609624	−	0.511535i	0.894523	+	0.447023i	$0.147516\pi$
$98$	−828.518	−	207.787i	−0.854009	−	0.214180i
$99$	−165.038	−	29.1007i	−0.167545	−	0.0295427i
$100$	356.098	+	888.422i	0.356098	+	0.888422i
$101$	167.461	+	460.094i	0.164980	+	0.453278i	0.994442	−	0.105284i	$-0.0335753\pi$
$101$	167.461	+	460.094i	0.164980	+	0.453278i	−0.829462	+	0.558562i	$0.811353\pi$
$102$	102.276	+	45.7052i	0.0992824	+	0.0443676i
$103$	324.366	+	561.818i	0.310298	+	0.537452i	0.978427	−	0.206593i	$-0.0662377\pi$
$103$	324.366	+	561.818i	0.310298	+	0.537452i	−0.668129	+	0.744046i	$0.732904\pi$
$104$	−410.065	+	1002.98i	−0.386637	+	0.945673i
$105$	37.5052	+	31.4706i	0.0348584	+	0.0292496i
$106$	−737.056	+	533.951i	−0.675370	+	0.489263i
$107$	−1418.40	−	818.913i	−1.28151	−	0.739881i	−0.304387	−	0.952548i	$-0.598452\pi$
$107$	−1418.40	−	818.913i	−1.28151	−	0.739881i	−0.977125	+	0.212667i	$0.931785\pi$
$108$	600.704	+	967.255i	0.535211	+	0.861798i
$109$	412.234	−	72.6880i	0.362246	−	0.0638738i	0.0104371	−	0.999946i	$-0.496678\pi$
$109$	412.234	−	72.6880i	0.362246	−	0.0638738i	0.351809	+	0.936072i	$0.385567\pi$
$110$	4.85068	−	68.0194i	0.00420449	−	0.0589582i
$111$	−1157.24	−	421.200i	−0.989552	−	0.360167i
$112$	−181.681	+	367.343i	−0.153279	+	0.309916i
$113$	−939.119			−0.781813			−0.390906	−	0.920430i	$-0.627838\pi$
$113$	−939.119			−0.781813			−0.390906	+	0.920430i	$0.627838\pi$
$114$	573.651	−	519.185i	0.471292	−	0.426545i
$115$		−	320.227i		−	0.259664i
$116$	1161.25	+	912.436i	0.929474	+	0.730323i
$117$	−263.537	+	724.061i	−0.208239	+	0.572132i
$118$	243.962	+	17.3977i	0.190327	+	0.0135728i
$119$	13.3334	+	75.6173i	0.0102712	+	0.0582507i
$120$	−136.771	+	105.949i	−0.104045	+	0.0805978i
$121$	−611.263	+	1058.74i	−0.459251	+	0.795446i
$122$	−1608.20	+	1165.04i	−1.19344	+	0.864569i
$123$	140.582	−	167.539i	0.103055	−	0.122817i
$124$	30.4794	+	16.3142i	0.0220737	+	0.0118150i
$125$	−490.440	+	283.156i	−0.350930	+	0.202610i
$126$	−118.899	+	266.063i	−0.0840664	+	0.188117i
$127$	1695.20	−	617.002i	1.18445	−	0.431103i	0.326675	−	0.945137i	$-0.394072\pi$
$127$	1695.20	−	617.002i	1.18445	−	0.431103i	0.857770	+	0.514034i	$0.171849\pi$
$128$	−1132.50	−	902.551i	−0.782029	−	0.623242i
$129$	98.4015	−	558.063i	0.0671610	−	0.380889i
$130$	−304.120	−	76.2714i	−0.205178	−	0.0514573i
$131$	−694.621	−	827.817i	−0.463277	−	0.552112i	0.482936	−	0.875656i	$-0.339570\pi$
$131$	−694.621	−	827.817i	−0.463277	−	0.552112i	−0.946213	+	0.323543i	$0.895126\pi$
$132$	−269.348	+	56.4756i	−0.177604	+	0.0372391i
$133$	515.070	+	126.267i	0.335806	+	0.0823214i
$134$	89.7489	+	865.385i	0.0578591	+	0.557895i
$135$	−252.385	+	211.776i	−0.160903	+	0.135013i
$136$	−271.122	−	10.5913i	−0.170945	−	0.00667793i
$137$	−86.9872	+	493.329i	−0.0542469	+	0.307649i	−0.999843	−	0.0176921i	$-0.994368\pi$
$137$	−86.9872	+	493.329i	−0.0542469	+	0.307649i	0.945597	+	0.325341i	$0.105479\pi$
$138$	−1242.78	+	354.506i	−0.766611	+	0.218678i
$139$	−377.522	−	1037.23i	−0.230367	−	0.632928i	0.769617	−	0.638505i	$-0.220447\pi$
$139$	−377.522	−	1037.23i	−0.230367	−	0.632928i	−0.999984	+	0.00557713i	$0.998225\pi$
$140$	−112.678	−	36.9553i	−0.0680216	−	0.0223092i
$141$	−225.989	+	130.475i	−0.134977	+	0.0779287i
$142$	−925.266	−	625.958i	−0.546807	−	0.369924i
$143$	−382.066	−	320.592i	−0.223426	−	0.187477i
$144$	−829.765	−	609.883i	−0.480188	−	0.352942i
$145$	−213.666	+	370.081i	−0.122373	+	0.211956i
$146$	1105.93	−	537.512i	0.626901	−	0.304690i
$147$	−982.329	+	173.211i	−0.551164	+	0.0971851i
$148$	2981.26	−	95.8736i	1.65580	−	0.0532484i
$149$	946.057	−	2599.27i	0.520161	−	1.42913i	−0.350180	−	0.936682i	$-0.613880\pi$
$149$	946.057	−	2599.27i	0.520161	−	1.42913i	0.870341	−	0.492449i	$-0.163898\pi$
$150$	802.942	+	777.536i	0.437066	+	0.423237i
$151$	−390.565			−0.210488			−0.105244	−	0.994446i	$-0.533562\pi$
$151$	−390.565			−0.210488			−0.105244	+	0.994446i	$0.533562\pi$
$152$	−821.831	+	1684.16i	−0.438548	+	0.898708i
$153$	−192.943			−0.101951
$154$	−135.510	−	131.222i	−0.0709073	−	0.0686637i
$155$	−3.42136	+	9.40010i	−0.00177297	+	0.00487119i
$156$	40.6714	+	1264.70i	0.0208738	+	0.649086i
$157$	−583.673	+	102.917i	−0.296702	+	0.0523165i	−0.320017	−	0.947412i	$-0.603689\pi$
$157$	−583.673	+	102.917i	−0.296702	+	0.0523165i	0.0233158	+	0.999728i	$0.492578\pi$
$158$	−735.014	+	357.236i	−0.370092	+	0.179875i
$159$	−531.418	+	920.443i	−0.265058	+	0.459094i
$160$	212.016	−	361.441i	0.104758	−	0.178590i
$161$	−678.571	−	569.388i	−0.332167	−	0.278721i
$162$	83.5270	+	56.5075i	0.0405093	+	0.0274052i
$163$	894.532	−	516.459i	0.429848	−	0.248173i	−0.269434	−	0.963019i	$-0.586837\pi$
$163$	894.532	−	516.459i	0.429848	−	0.248173i	0.699282	+	0.714846i	$0.253503\pi$
$164$	−165.082	+	503.342i	−0.0786023	+	0.239661i
$165$	−27.2361	−	74.8305i	−0.0128505	−	0.0353063i
$166$	2734.52	−	780.031i	1.27855	−	0.364712i
$167$	426.453	−	2418.53i	0.197604	−	1.12067i	−0.711057	−	0.703134i	$-0.751783\pi$
$167$	426.453	−	2418.53i	0.197604	−	1.12067i	0.908661	−	0.417534i	$-0.137106\pi$
$168$	−18.6810	+	478.206i	−0.00857900	+	0.219610i
$169$	−73.6903	+	61.8335i	−0.0335413	+	0.0281445i
$170$	−8.09894	−	78.0924i	−0.00365389	−	0.0352318i
$171$	−537.214	+	1219.52i	−0.240244	+	0.545372i
$172$	281.658	+	1343.31i	0.124862	+	0.595502i
$173$	279.219	+	332.760i	0.122709	+	0.146239i	0.823901	−	0.566733i	$-0.191793\pi$
$173$	279.219	+	332.760i	0.122709	+	0.146239i	−0.701192	+	0.712972i	$0.747349\pi$
$174$	1672.80	+	419.527i	0.728819	+	0.182783i
$175$	−133.033	+	754.469i	−0.0574650	+	0.325900i
$176$	554.658	−	369.685i	0.237551	−	0.158330i
$177$	268.391	−	97.6864i	0.113975	−	0.0414834i
$178$	−1603.65	+	3588.53i	−0.675273	+	1.51107i
$179$	2699.08	−	1558.31i	1.12703	−	0.650692i	0.183845	−	0.982955i	$-0.441146\pi$
$179$	2699.08	−	1558.31i	1.12703	−	0.650692i	0.943187	+	0.332264i	$0.107812\pi$
$180$	140.617	−	262.712i	0.0582278	−	0.108785i
$181$	1213.71	−	1446.44i	0.498421	−	0.593996i	−0.456917	−	0.889509i	$-0.651046\pi$
$181$	1213.71	−	1446.44i	0.498421	−	0.593996i	0.955338	+	0.295514i	$0.0954908\pi$
$182$	−702.371	+	508.823i	−0.286061	+	0.207233i
$183$	−1159.51	+	2008.33i	−0.468380	+	0.811258i
$184$	2474.56	−	1916.90i	0.991451	−	0.768020i
$185$	149.875	+	849.984i	0.0595624	+	0.337795i
$186$	40.2687	+	2.87169i	0.0158744	+	0.00113206i
$187$	42.7147	−	117.358i	0.0167038	−	0.0458933i
$188$	390.494	−	496.977i	0.151488	−	0.192797i
$189$			911.366i			0.350752i
$190$	−516.139	−	166.243i	−0.197077	−	0.0634766i
$191$	4251.89			1.61076			0.805382	−	0.592757i	$-0.201960\pi$
$191$	4251.89			1.61076			0.805382	+	0.592757i	$0.201960\pi$
$192$	−1637.44	−	422.685i	−0.615479	−	0.158878i
$193$	2274.75	+	827.943i	0.848396	+	0.308791i	0.729386	−	0.684102i	$-0.239806\pi$
$193$	2274.75	+	827.943i	0.848396	+	0.308791i	0.119010	+	0.992893i	$0.462028\pi$
$194$	−152.960	+	2144.91i	−0.0566078	+	0.793791i
$195$	−360.579	+	63.5798i	−0.132418	+	0.0233490i
$196$	2052.39	−	1274.61i	0.747955	−	0.464510i
$197$	−2555.64	−	1475.50i	−0.924274	−	0.533630i	−0.0392780	−	0.999228i	$-0.512506\pi$
$197$	−2555.64	−	1475.50i	−0.924274	−	0.533630i	−0.884996	+	0.465598i	$0.845839\pi$
$198$	383.857	−	278.081i	0.137776	−	0.0998097i
$199$	−1014.16	−	850.978i	−0.361264	−	0.303137i	0.444030	−	0.896012i	$-0.353548\pi$
$199$	−1014.16	−	850.978i	−0.361264	−	0.303137i	−0.805294	+	0.592875i	$0.797993\pi$
$200$	−2505.83	−	1024.50i	−0.885945	−	0.362217i
$201$	507.996	+	879.875i	0.178265	+	0.308764i
$202$	−1264.35	−	565.018i	−0.440394	−	0.196805i
$203$	404.298	+	1110.80i	0.139784	+	0.384053i
$204$	−294.105	+	117.883i	−0.100939	+	0.0404583i
$205$	−150.951	−	26.6167i	−0.0514285	−	0.00906824i
$206$	−1779.77	−	446.356i	−0.601955	−	0.150966i
$207$	1705.12	−	1430.77i	0.572532	−	0.480411i
$208$	−1231.09	−	2806.66i	−0.410390	−	0.935610i
$209$	−622.838	−	596.741i	−0.206137	−	0.197500i
$210$	−137.740	+	14.2849i	−0.0452616	+	0.00469407i
$211$	3163.36	+	3769.94i	1.03211	+	1.23002i	0.972769	+	0.231779i	$0.0744545\pi$
$211$	3163.36	+	3769.94i	1.03211	+	1.23002i	0.0593378	+	0.998238i	$0.481101\pi$
$212$	365.300	−	2548.21i	0.118344	−	0.825528i
$213$	−1284.71	−	226.530i	−0.413273	−	0.0728712i
$214$	4454.77	−	1270.74i	1.42300	−	0.405915i
$215$	−373.198	+	135.833i	−0.118381	+	0.0430872i
$216$	−3147.30	−	682.604i	−0.991419	−	0.215025i
$217$	13.8357	+	23.9641i	0.00432823	+	0.00749671i
$218$	−663.416	+	980.634i	−0.206111	+	0.304665i
$219$	923.001	−	1099.99i	0.284797	−	0.339408i
$220$	128.664	+	143.691i	0.0394296	+	0.0440347i
$221$	−497.293	−	287.112i	−0.151365	−	0.0873904i
$222$	3132.81	−	1522.63i	0.947119	−	0.460325i
$223$	−627.710	−	3559.92i	−0.188496	−	1.06901i	−0.921381	−	0.388661i	$-0.872938\pi$
$223$	−627.710	−	3559.92i	−0.188496	−	1.06901i	0.732885	−	0.680353i	$-0.238173\pi$
$224$	−388.925	−	1091.94i	−0.116010	−	0.325706i
$225$	−1808.99	−	658.418i	−0.535997	−	0.195087i
$226$	1847.81	−	1908.18i	0.543868	−	0.561639i
$227$			2343.14i			0.685110i	0.939498	+	0.342555i	$0.111292\pi$
$227$			2343.14i			0.685110i	−0.939498	+	0.342555i	$0.888708\pi$
$228$	−73.7872	+	2187.14i	−0.0214328	+	0.635293i
$229$		−	3431.46i		−	0.990206i	−0.868834	−	0.495103i	$-0.835130\pi$
$229$		−	3431.46i		−	0.990206i	0.868834	−	0.495103i	$-0.164870\pi$
$230$	650.666	+	630.077i	0.186537	+	0.180635i
$231$	−206.996	−	75.3403i	−0.0589581	−	0.0214590i
$232$	−4138.83	+	564.218i	−1.17124	+	0.159667i
$233$	21.2293	+	120.397i	0.00596899	+	0.0338518i	0.987647	−	0.156697i	$-0.0500845\pi$
$233$	21.2293	+	120.397i	0.00596899	+	0.0338518i	−0.981678	+	0.190548i	$0.938973\pi$
$234$	−952.677	−	1960.14i	−0.266147	−	0.547599i
$235$	158.383	+	91.4426i	0.0439650	+	0.0253832i
$236$	−515.370	+	461.473i	−0.142151	+	0.127285i
$237$	−613.436	+	731.065i	−0.168131	+	0.200370i
$238$	−179.881	−	121.692i	−0.0489913	−	0.0331435i
$239$	1786.24	+	3093.86i	0.483441	+	0.837345i	0.999819	−	0.0190158i	$-0.00605329\pi$
$239$	1786.24	+	3093.86i	0.483441	+	0.837345i	−0.516378	+	0.856361i	$0.672720\pi$
$240$	53.8342	−	486.367i	0.0144791	−	0.130812i
$241$	343.624	−	125.069i	0.0918456	−	0.0334291i	−0.295689	−	0.955284i	$-0.595549\pi$
$241$	343.624	−	125.069i	0.0918456	−	0.0334291i	0.387534	+	0.921855i	$0.373327\pi$
$242$	−948.519	−	3325.19i	−0.251955	−	0.883269i
$243$	−3668.45	−	646.846i	−0.968440	−	0.170762i
$244$	797.055	−	5559.99i	0.209124	−	1.45878i
$245$	449.361	+	535.528i	0.117178	+	0.139647i
$246$	63.8121	+	615.295i	0.0165387	+	0.159471i
$247$	−3199.34	+	2343.78i	−0.824165	+	0.603769i
$248$	−93.1199	+	29.8310i	−0.0238432	+	0.00763819i
$249$	2543.79	−	2134.49i	0.647413	−	0.543244i
$250$	389.647	−	1553.66i	0.0985738	−	0.393047i
$251$	2049.61	+	361.401i	0.515418	+	0.0908822i	0.425306	−	0.905049i	$-0.360166\pi$
$251$	2049.61	+	361.401i	0.515418	+	0.0908822i	0.0901121	+	0.995932i	$0.471277\pi$
$252$	−306.666	−	765.094i	−0.0766592	−	0.191256i
$253$	492.775	+	1353.89i	0.122452	+	0.336435i
$254$	−2081.79	+	4658.46i	−0.514263	+	1.15078i
$255$	−45.8416	−	79.4000i	−0.0112577	−	0.0194989i
$256$	4062.18	−	525.257i	0.991744	−	0.128237i
$257$	−1983.10	−	1664.02i	−0.481332	−	0.403886i	0.369576	−	0.929201i	$-0.379503\pi$
$257$	−1983.10	−	1664.02i	−0.481332	−	0.403886i	−0.850908	+	0.525315i	$0.823947\pi$
$258$	940.307	+	1297.98i	0.226903	+	0.313213i
$259$	2067.63	+	1193.75i	0.496048	+	0.286393i
$260$	753.361	−	467.867i	0.179698	−	0.111600i
$261$	−2925.24	+	515.798i	−0.693746	+	0.122326i
$262$	3048.77	+	217.417i	0.718906	+	0.0512674i
$263$	−4354.18	−	1584.79i	−1.02088	−	0.371568i	−0.223276	−	0.974755i	$-0.571675\pi$
$263$	−4354.18	−	1584.79i	−1.02088	−	0.371568i	−0.797600	+	0.603187i	$0.793897\pi$
$264$	415.217	−	658.407i	0.0967986	−	0.153493i
$265$	744.884			0.172671
$266$	−1270.01	+	798.122i	−0.292742	+	0.183970i
$267$			4589.98i			1.05207i
$268$	−1934.95	−	1520.37i	−0.441030	−	0.346534i
$269$	−1016.30	+	2792.27i	−0.230353	+	0.632890i	−0.999984	−	0.00559857i	$-0.998218\pi$
$269$	−1016.30	+	2792.27i	−0.230353	+	0.632890i	0.769631	+	0.638489i	$0.220440\pi$
$270$	66.2861	−	929.508i	0.0149409	−	0.209511i
$271$	714.429	+	4051.73i	0.160142	+	0.908210i	0.953933	+	0.300019i	$0.0969931\pi$
$271$	714.429	+	4051.73i	0.160142	+	0.908210i	−0.793791	+	0.608190i	$0.791896\pi$
$272$	554.979	−	530.051i	0.123715	−	0.118158i
$273$	−506.410	+	877.128i	−0.112269	+	0.194455i
$274$	−831.234	−	1147.42i	−0.183273	−	0.252986i
$275$	800.964	−	954.552i	0.175636	−	0.209315i
$276$	1724.97	−	3222.71i	0.376199	−	0.702842i
$277$	−952.258	+	549.787i	−0.206555	+	0.119254i	−0.599709	−	0.800218i	$-0.704717\pi$
$277$	−952.258	+	549.787i	−0.206555	+	0.119254i	0.393155	+	0.919472i	$0.371384\pi$
$278$	2850.35	+	1273.77i	0.614938	+	0.274805i
$279$	−65.3395	+	23.7816i	−0.0140207	+	0.00510311i
$280$	296.794	−	156.236i	0.0633458	−	0.0333460i
$281$	−61.8297	+	350.654i	−0.0131262	+	0.0744421i	−0.990667	−	0.136303i	$-0.956478\pi$
$281$	−61.8297	+	350.654i	−0.0131262	+	0.0744421i	0.977541	+	0.210745i	$0.0675890\pi$
$282$	179.545	−	715.905i	0.0379139	−	0.151176i
$283$	4257.88	+	5074.35i	0.894363	+	1.06586i	0.997463	+	0.0711896i	$0.0226795\pi$
$283$	4257.88	+	5074.35i	0.894363	+	1.06586i	−0.103100	+	0.994671i	$0.532876\pi$
$284$	3092.43	−	648.404i	0.646133	−	0.135478i
$285$	−629.492	+	68.6718i	−0.130835	+	0.0142729i
$286$	1403.16	−	145.521i	0.290107	−	0.0300869i
$287$	−324.803	+	272.542i	−0.0668033	+	0.0560546i
$288$	2871.86	−	485.986i	0.587589	−	0.0994341i
$289$	−828.165	+	4696.76i	−0.168566	+	0.955986i
$290$	−331.554	−	1162.32i	−0.0671364	−	0.235357i
$291$	858.856	+	2359.69i	0.173014	+	0.475352i
$292$	−1083.86	+	3304.74i	−0.217220	+	0.662312i
$293$	4259.31	−	2459.12i	0.849255	−	0.490318i	−0.0111442	−	0.999938i	$-0.503547\pi$
$293$	4259.31	−	2459.12i	0.849255	−	0.490318i	0.860400	+	0.509620i	$0.170214\pi$
$294$	1580.88	−	2336.79i	0.313601	−	0.463553i
$295$	−153.341	−	128.669i	−0.0302640	−	0.0253945i
$296$	−5671.11	+	6246.22i	−1.11360	+	1.22653i
$297$	741.171	−	1283.75i	0.144805	−	0.250810i
$298$	3419.97	+	7036.60i	0.664810	+	1.36785i
$299$	6523.86	−	1150.33i	1.26182	−	0.222493i
$300$	−3159.73	+	101.613i	−0.608091	+	0.0195554i
$301$	−375.741	+	1032.34i	−0.0719513	+	0.197685i
$302$	768.473	−	793.584i	0.146426	−	0.151211i
$303$	−1617.20			−0.306620
$304$	−1805.00	−	4983.62i	−0.340538	−	0.940231i
$305$	1625.28			0.305125
$306$	379.635	−	392.039i	0.0709224	−	0.0732399i
$307$	−3469.90	+	9533.47i	−0.645074	+	1.77233i	−0.00990698	+	0.999951i	$0.503154\pi$
$307$	−3469.90	+	9533.47i	−0.645074	+	1.77233i	−0.635167	+	0.772375i	$0.719069\pi$
$308$	533.259	−	17.1489i	0.0986534	−	0.00317257i
$309$	−2110.18	+	372.082i	−0.388492	+	0.0685016i
$310$	−12.3681	−	25.4474i	−0.00226600	−	0.00466231i
$311$	−3043.34	+	5271.22i	−0.554894	+	0.961105i	0.443017	+	0.896513i	$0.353908\pi$
$311$	−3043.34	+	5271.22i	−0.554894	+	0.961105i	−0.997912	+	0.0645921i	$0.979425\pi$
$312$	−2649.76	−	2405.79i	−0.480812	−	0.436541i
$313$	−6286.96	−	5275.39i	−1.13534	−	0.952660i	−0.136060	−	0.990701i	$-0.543444\pi$
$313$	−6286.96	−	5275.39i	−1.13534	−	0.952660i	−0.999276	+	0.0380407i	$0.987888\pi$
$314$	939.315	−	1388.46i	0.168817	−	0.249539i
$315$	206.554	−	119.254i	0.0369460	−	0.0213308i
$316$	720.347	−	2196.36i	0.128236	−	0.390997i
$317$	−262.123	−	720.178i	−0.0464426	−	0.127600i	0.914303	−	0.405031i	$-0.132739\pi$
$317$	−262.123	−	720.178i	−0.0464426	−	0.127600i	−0.960746	+	0.277431i	$0.910517\pi$
$318$	−824.621	−	2890.84i	−0.145417	−	0.509781i
$319$	333.868	−	1893.46i	0.0585989	−	0.332331i
$320$	317.248	+	1141.96i	0.0554209	+	0.199493i
$321$	4144.05	−	3477.27i	0.720555	−	0.604618i
$322$	2492.09	−	258.454i	0.431300	−	0.0447300i
$323$	−825.497	−	552.084i	−0.142204	−	0.0951045i
$324$	−279.164	+	58.5337i	−0.0478677	+	0.0100366i
$325$	−3682.73	−	4388.90i	−0.628557	−	0.749085i
$326$	−710.692	+	2833.77i	−0.120741	+	0.481436i
$327$	−240.085	+	1361.59i	−0.0406017	+	0.230264i
$328$	−697.919	−	1325.80i	−0.117488	−	0.223187i
$329$	475.387	−	173.027i	0.0796624	−	0.0289948i
$330$	205.637	+	91.8954i	0.0343028	+	0.0153293i
$331$	−6688.49	+	3861.60i	−1.11067	+	0.641247i	−0.939004	−	0.343907i	$-0.888249\pi$
$331$	−6688.49	+	3861.60i	−1.11067	+	0.641247i	−0.171669	+	0.985155i	$0.554916\pi$
$332$	−3795.50	+	7091.03i	−0.627425	+	1.17220i
$333$	−3856.29	+	4595.75i	−0.634606	+	0.756293i
$334$	4075.10	+	5625.20i	0.667604	+	0.921548i
$335$	356.027	−	616.657i	0.0580652	−	0.100572i
$336$	−934.905	−	978.874i	−0.151795	−	0.158934i
$337$	−994.304	−	5638.98i	−0.160722	−	0.911498i	−0.953367	−	0.301815i	$-0.902408\pi$
$337$	−994.304	−	5638.98i	−0.160722	−	0.911498i	0.792645	−	0.609684i	$-0.208703\pi$
$338$	19.3539	−	271.394i	0.00311454	−	0.0436742i
$339$	1060.90	−	2914.80i	0.169971	−	0.466992i
$340$	174.610	+	137.198i	0.0278517	+	0.0218841i
$341$		−	45.0075i		−	0.00714749i
$342$	−1420.90	−	3491.07i	−0.224659	−	0.551975i
$343$	4130.15			0.650167
$344$	−3283.64	−	2070.79i	−0.514657	−	0.324563i
$345$	993.910	+	361.754i	0.155102	+	0.0564526i
$346$	−1225.52	−	87.3958i	−0.190417	−	0.0135793i
$347$	2996.53	−	528.369i	0.463579	−	0.0817416i	0.0630198	−	0.998012i	$-0.479927\pi$
$347$	2996.53	−	528.369i	0.463579	−	0.0817416i	0.400560	+	0.916271i	$0.368816\pi$
$348$	−4143.82	+	2573.48i	−0.638311	+	0.396416i
$349$	−5319.62	−	3071.28i	−0.815910	−	0.471066i	0.0330939	−	0.999452i	$-0.489464\pi$
$349$	−5319.62	−	3071.28i	−0.815910	−	0.471066i	−0.849004	+	0.528386i	$0.822797\pi$
$350$	−1271.24	−	1754.80i	−0.194145	−	0.267994i
$351$	−5221.06	−	4380.99i	−0.793959	−	0.666211i
$352$	−340.184	+	1854.39i	−0.0515109	+	0.280794i
$353$	5822.80	+	10085.4i	0.877950	+	1.52065i	0.853587	+	0.520950i	$0.174422\pi$
$353$	5822.80	+	10085.4i	0.877950	+	1.52065i	0.0243625	+	0.999703i	$0.492244\pi$
$354$	−329.598	+	737.548i	−0.0494856	+	0.110735i
$355$	312.701	+	859.139i	0.0467505	+	0.128446i
$356$	−4136.15	−	10319.2i	−0.615774	−	1.53628i
$357$	−249.761	−	44.0396i	−0.0370273	−	0.00652891i
$358$	−2144.38	+	8550.36i	−0.316575	+	1.26229i
$359$	4876.25	−	4091.66i	0.716877	−	0.601531i	−0.209643	−	0.977778i	$-0.567230\pi$
$359$	4876.25	−	4091.66i	0.716877	−	0.601531i	0.926519	+	0.376247i	$0.122786\pi$
$360$	257.123	+	802.630i	0.0376432	+	0.117506i
$361$	−5787.93	+	3680.46i	−0.843845	+	0.536588i
$362$	550.920	+	5312.13i	0.0799882	+	0.771269i
$363$	−2595.54	−	3093.25i	−0.375291	−	0.447255i
$364$	348.109	−	2428.30i	0.0501260	−	0.349663i
$365$	−991.079	−	174.754i	−0.142125	−	0.0250604i
$366$	−1799.26	−	6307.58i	−0.256964	−	0.900826i
$367$	−156.118	+	56.8222i	−0.0222051	+	0.00808200i	−0.353099	−	0.935586i	$-0.614872\pi$
$367$	−156.118	+	56.8222i	−0.0222051	+	0.00808200i	0.330894	+	0.943668i	$0.392650\pi$
$368$	−974.007	+	8799.71i	−0.137972	+	1.24651i
$369$	−532.717	−	922.693i	−0.0751549	−	0.130172i
$370$	−2021.97	−	1367.90i	−0.284100	−	0.192199i
$371$	1324.46	−	1578.43i	0.185344	−	0.220884i
$372$	−85.0675	+	76.1712i	−0.0118563	+	0.0106164i
$373$	−4191.16	−	2419.77i	−0.581797	−	0.335900i	0.180050	−	0.983657i	$-0.442374\pi$
$373$	−4191.16	−	2419.77i	−0.581797	−	0.335900i	−0.761847	+	0.647757i	$0.775707\pi$
$374$	154.412	+	317.704i	0.0213489	+	0.0439253i
$375$	−324.809	−	1842.09i	−0.0447282	−	0.253666i
$376$	241.468	+	1771.29i	0.0331190	+	0.242945i
$377$	−8307.06	−	3023.52i	−1.13484	−	0.413049i
$378$	−1851.79	−	1793.20i	−0.251973	−	0.244001i
$379$			460.797i			0.0624526i	0.999512	+	0.0312263i	$0.00994126\pi$
$379$			460.797i			0.0624526i	−0.999512	+	0.0312263i	$0.990059\pi$
$380$	1353.34	−	721.638i	0.182697	−	0.0974191i
$381$			5958.51i			0.801217i
$382$	−8365.99	+	8639.36i	−1.12053	+	1.15714i
$383$	7587.57	+	2761.65i	1.01229	+	0.368443i	0.794311	−	0.607511i	$-0.207832\pi$
$383$	7587.57	+	2761.65i	1.01229	+	0.368443i	0.217977	+	0.975954i	$0.430054\pi$
$384$	4080.67	−	2495.42i	0.542293	−	0.331625i
$385$	26.8082	+	152.037i	0.00354876	+	0.0201260i
$386$	−6158.08	+	2992.99i	−0.812016	+	0.394661i
$387$	−2390.71	−	1380.28i	−0.314023	−	0.181301i
$388$	−4057.25	−	4531.11i	−0.530865	−	0.592867i
$389$	8677.39	−	10341.3i	1.13101	−	1.34788i	0.201320	−	0.979526i	$-0.435477\pi$
$389$	8677.39	−	10341.3i	1.13101	−	1.34788i	0.929685	−	0.368354i	$-0.120079\pi$
$390$	580.287	−	857.756i	0.0753435	−	0.111370i
$391$	829.400	+	1436.56i	0.107275	+	0.185806i
$392$	−1448.39	+	6678.15i	−0.186620	+	0.860452i
$393$	3354.05	−	1220.77i	0.430507	−	0.156692i
$394$	8026.52	−	2289.59i	1.02632	−	0.292761i
$395$	658.682	+	116.143i	0.0839035	+	0.0147944i
$396$	−190.248	+	1327.11i	−0.0241422	+	0.168408i
$397$	4422.16	+	5270.13i	0.559048	+	0.666248i	0.969345	−	0.245705i	$-0.0790193\pi$
$397$	4422.16	+	5270.13i	0.559048	+	0.666248i	−0.410297	+	0.911952i	$0.634575\pi$
$398$	3724.54	−	386.271i	0.469081	−	0.0486483i
$399$	−973.767	+	1456.01i	−0.122179	+	0.182687i
$400$	7012.14	−	3075.76i	0.876518	−	0.384470i
$401$	3933.83	−	3300.88i	0.489891	−	0.411067i	−0.364096	−	0.931361i	$-0.618622\pi$
$401$	3933.83	−	3300.88i	0.489891	−	0.411067i	0.853987	+	0.520294i	$0.174178\pi$
$402$	−2787.34	−	699.047i	−0.345821	−	0.0867296i
$403$	−203.795	−	35.9345i	−0.0251904	−	0.00444175i
$404$	3635.79	−	1457.30i	0.447741	−	0.179464i
$405$	−28.2286	−	77.5575i	−0.00346343	−	0.00951571i
$406$	−3052.51	−	1364.11i	−0.373137	−	0.166748i
$407$	−1941.64	−	3363.01i	−0.236470	−	0.409578i
$408$	339.154	−	829.535i	0.0411535	−	0.100657i
$409$	3604.19	+	3024.28i	0.435736	+	0.365626i	0.834111	−	0.551597i	$-0.185981\pi$
$409$	3604.19	+	3024.28i	0.435736	+	0.365626i	−0.398375	+	0.917223i	$0.630426\pi$
$410$	351.092	−	254.344i	0.0422907	−	0.0306370i
$411$	−1432.91	−	827.291i	−0.171971	−	0.0992878i
$412$	4408.82	−	2738.05i	0.527201	−	0.327413i
$413$	−545.305	+	96.1520i	−0.0649702	+	0.0114560i
$414$	−447.831	+	6279.78i	−0.0531635	+	0.745494i
$415$	−2186.93	−	795.977i	−0.258680	−	0.0941518i
$416$	8125.11	+	3020.92i	0.957612	+	0.356041i
$417$	3645.81			0.428144
$418$	2438.00	−	91.3913i	0.285279	−	0.0106940i
$419$		−	13826.6i		−	1.61210i	−0.591844	−	0.806052i	$-0.701600\pi$
$419$		−	13826.6i		−	1.61210i	0.591844	−	0.806052i	$-0.298400\pi$
$420$	241.990	−	307.978i	0.0281141	−	0.0357805i
$421$	4047.27	−	11119.8i	0.468532	−	1.28728i	−0.450387	−	0.892833i	$-0.648714\pi$
$421$	4047.27	−	11119.8i	0.468532	−	1.28728i	0.918919	−	0.394447i	$-0.129064\pi$
$422$	−13884.3	−	990.133i	−1.60161	−	0.114215i
$423$	220.746	+	1251.91i	0.0253736	+	0.143901i
$424$	4458.92	+	5756.10i	0.510718	+	0.659295i
$425$	717.320	−	1242.43i	0.0818709	−	0.141805i
$426$	2988.08	−	2164.68i	0.339843	−	0.246195i
$427$	2889.87	−	3444.01i	0.327518	−	0.390321i
$428$	−6183.19	+	11551.9i	−0.698308	+	1.30463i
$429$	1426.65	−	823.679i	0.160558	−	0.0926983i
$430$	458.306	−	1025.56i	0.0513988	−	0.115016i
$431$	−6523.82	+	2374.48i	−0.729098	+	0.265370i	−0.679783	−	0.733413i	$-0.737926\pi$
$431$	−6523.82	+	2374.48i	−0.729098	+	0.265370i	−0.0493152	+	0.998783i	$0.515704\pi$
$432$	7579.58	−	5051.87i	0.844150	−	0.562634i
$433$	679.053	−	3851.10i	0.0753653	−	0.427418i	−0.923657	−	0.383219i	$-0.874815\pi$
$433$	679.053	−	3851.10i	0.0753653	−	0.427418i	0.999023	−	0.0441988i	$-0.0140735\pi$
$434$	−75.9153	−	19.0391i	−0.00839643	−	0.00210577i
$435$	−907.271	−	1081.24i	−0.100001	−	0.119176i
$436$	−687.204	−	3277.48i	−0.0754842	−	0.360006i
$437$	11389.2	−	1242.46i	1.24673	−	0.136007i
$438$	418.964	+	4039.77i	0.0457051	+	0.440702i
$439$	11084.3	−	9300.85i	1.20507	−	1.01117i	0.205600	−	0.978636i	$-0.434085\pi$
$439$	11084.3	−	9300.85i	1.20507	−	1.01117i	0.999470	−	0.0325383i	$-0.0103591\pi$
$440$	−545.122	−	21.2950i	−0.0590628	−	0.00230728i
$441$	−843.803	+	4785.45i	−0.0911136	+	0.516731i
$442$	1561.85	−	445.523i	0.168076	−	0.0479443i
$443$	−5519.43	−	15164.5i	−0.591955	−	1.62638i	−0.766872	−	0.641799i	$-0.778188\pi$
$443$	−5519.43	−	15164.5i	−0.591955	−	1.62638i	0.174918	−	0.984583i	$-0.444034\pi$
$444$	−3070.29	+	9361.43i	−0.328175	+	1.00062i
$445$	2785.89	−	1608.43i	0.296773	−	0.171342i
$446$	8468.44	+	5729.05i	0.899086	+	0.608247i
$447$	6998.79	+	5872.68i	0.740562	+	0.621405i
$448$	2983.94	+	1358.24i	0.314683	+	0.143238i
$449$	−8484.89	+	14696.3i	−0.891819	+	1.54468i	−0.0541261	+	0.998534i	$0.517237\pi$
$449$	−8484.89	+	14696.3i	−0.891819	+	1.54468i	−0.837693	+	0.546142i	$0.816096\pi$
$450$	4897.19	−	2380.16i	0.513013	−	0.249338i
$451$	679.162	−	119.755i	0.0709102	−	0.0125034i
$452$	241.482	+	7509.07i	0.0251292	+	0.781409i
$453$	441.212	−	1212.22i	0.0457615	−	0.125729i
$454$	−4761.01	−	4610.36i	−0.492170	−	0.476597i
$455$	709.830			0.0731370
$456$	−4298.84	−	4453.33i	−0.441473	−	0.457339i
$457$	16446.8			1.68348			0.841738	−	0.539887i	$-0.181533\pi$
$457$	16446.8			1.68348			0.841738	+	0.539887i	$0.181533\pi$
$458$	6972.34	+	6751.73i	0.711345	+	0.688837i
$459$	583.710	−	1603.73i	0.0593579	−	0.163084i
$460$	−2560.49	+	82.3423i	−0.259530	+	0.00834615i
$461$	−10128.0	+	1785.84i	−1.02323	+	0.180423i	−0.659990	−	0.751274i	$-0.729440\pi$
$461$	−10128.0	+	1785.84i	−1.02323	+	0.180423i	−0.363237	+	0.931697i	$0.618329\pi$
$462$	560.367	−	272.353i	0.0564299	−	0.0274264i
$463$	3383.41	−	5860.23i	0.339612	−	0.588225i	−0.644748	−	0.764395i	$-0.723038\pi$
$463$	3383.41	−	5860.23i	0.339612	−	0.588225i	0.984360	+	0.176170i	$0.0563710\pi$
$464$	6997.11	−	9519.79i	0.700071	−	0.952468i
$465$	−25.3107	−	21.2382i	−0.00252420	−	0.00211806i
$466$	−286.404	−	193.757i	−0.0284708	−	0.0192610i
$467$	8313.90	−	4800.03i	0.823815	−	0.475630i	−0.0279153	−	0.999610i	$-0.508887\pi$
$467$	8313.90	−	4800.03i	0.823815	−	0.475630i	0.851730	+	0.523981i	$0.175554\pi$
$468$	5857.26	+	1921.02i	0.578530	+	0.189742i
$469$	−673.671	−	1850.89i	−0.0663267	−	0.182231i
$470$	−497.435	+	141.895i	−0.0488191	+	0.0139258i
$471$	339.931	−	1927.85i	0.0332552	−	0.188600i
$472$	76.3781	−	1955.16i	0.00744827	−	0.190665i
$473$	1368.82	−	1148.58i	0.133062	−	0.111652i
$474$	−278.448	−	2684.87i	−0.0269821	−	0.260169i
$475$	−5855.67	−	7993.20i	−0.565635	−	0.772112i
$476$	601.197	−	126.056i	0.0578904	−	0.0121382i
$477$	3328.12	+	3966.30i	0.319464	+	0.380722i
$478$	−9800.99	−	2458.03i	−0.937839	−	0.235204i
$479$	1526.60	−	8657.76i	0.145620	−	0.825852i	−0.821247	−	0.570573i	$-0.806721\pi$
$479$	1526.60	−	8657.76i	0.145620	−	0.825852i	0.966867	−	0.255280i	$-0.0821676\pi$
$480$	882.320	+	1066.36i	0.0839004	+	0.101401i
$481$	−16778.0	+	6106.70i	−1.59046	+	0.578880i
$482$	−421.987	+	944.291i	−0.0398776	+	0.0892351i
$483$	2533.81	−	1462.90i	0.238701	−	0.137814i
$484$	8622.71	+	4615.33i	0.809796	+	0.433446i
$485$	1131.25	−	1348.17i	0.105912	−	0.126221i
$486$	8532.34	−	6181.14i	0.796368	−	0.576918i
$487$	−7798.05	+	13506.6i	−0.725592	+	1.25676i	0.233138	+	0.972444i	$0.425101\pi$
$487$	−7798.05	+	13506.6i	−0.725592	+	1.25676i	−0.958730	+	0.284319i	$0.908233\pi$
$488$	9729.00	+	12559.3i	0.902482	+	1.16503i
$489$	592.432	+	3359.85i	0.0547867	+	0.310711i
$490$	−1972.29	−	140.650i	−0.181835	−	0.0129672i
$491$	1358.99	−	3733.81i	0.124910	−	0.343186i	−0.861438	−	0.507863i	$-0.830436\pi$
$491$	1358.99	−	3733.81i	0.124910	−	0.343186i	0.986348	+	0.164676i	$0.0526580\pi$
$492$	−1375.77	−	1080.99i	−0.126066	−	0.0990546i
$493$		−	2213.62i		−	0.202224i
$494$	1532.71	−	11112.3i	0.139595	−	1.01208i
$495$	−387.934			−0.0352249
$496$	122.609	−	247.905i	0.0110994	−	0.0224420i
$497$	2376.55	+	864.992i	0.214492	+	0.0780688i
$498$	−668.097	+	9368.50i	−0.0601168	+	0.842997i
$499$	−6223.29	+	1097.33i	−0.558302	+	0.0984437i	−0.445677	−	0.895194i	$-0.647037\pi$
$499$	−6223.29	+	1097.33i	−0.558302	+	0.0984437i	−0.112625	+	0.993638i	$0.535926\pi$
$500$	2390.19	+	3848.68i	0.213785	+	0.344237i
$501$	7024.80	+	4055.77i	0.626437	+	0.361674i
$502$	−4767.12	+	3453.48i	−0.423839	+	0.307045i
$503$	340.781	+	285.949i	0.0302081	+	0.0253476i	0.657767	−	0.753222i	$-0.271501\pi$
$503$	340.781	+	285.949i	0.0302081	+	0.0253476i	−0.627559	+	0.778569i	$0.715946\pi$
$504$	2157.98	+	882.286i	0.190722	+	0.0779765i
$505$	566.704	+	981.560i	0.0499366	+	0.0864928i
$506$	−3720.53	−	1662.64i	−0.326873	−	0.146074i
$507$	−108.670	−	298.569i	−0.00951917	−	0.0261537i
$508$	−5369.36	−	13395.9i	−0.468951	−	1.16998i
$509$	10774.7	+	1899.87i	0.938269	+	0.165442i	0.621814	−	0.783165i	$-0.286396\pi$
$509$	10774.7	+	1899.87i	0.938269	+	0.165442i	0.316456	+	0.948607i	$0.397507\pi$
$510$	251.530	+	63.0821i	0.0218391	+	0.00547710i
$511$	−2132.52	+	1789.40i	−0.184613	+	0.154909i
$512$	−6925.47	+	9287.39i	−0.597784	+	0.801657i
$513$	−8511.29	−	8154.67i	−0.732520	−	0.701827i
$514$	7283.04	−	755.322i	0.624982	−	0.0648168i
$515$	965.291	+	1150.39i	0.0825938	+	0.0984314i
$516$	−4487.50	−	643.307i	−0.382851	−	0.0548837i
$517$	−810.343	−	142.885i	−0.0689339	−	0.0121549i
$518$	−6493.82	+	1852.38i	−0.550815	+	0.157122i
$519$	−1348.24	+	490.718i	−0.114029	+	0.0415032i
$520$	−531.656	+	2451.32i	−0.0448358	+	0.206726i
$521$	−6479.17	−	11222.2i	−0.544832	−	0.943677i	−0.998617	−	0.0525658i	$-0.983260\pi$
$521$	−6479.17	−	11222.2i	−0.544832	−	0.943677i	0.453785	−	0.891111i	$-0.350073\pi$
$522$	4707.64	−	6958.64i	0.394727	−	0.583470i
$523$	−8107.13	+	9661.70i	−0.677821	+	0.807795i	−0.989826	−	0.142285i	$-0.954555\pi$
$523$	−8107.13	+	9661.70i	−0.677821	+	0.807795i	0.312005	+	0.950080i	$0.398999\pi$
$524$	−6440.50	+	5766.96i	−0.536936	+	0.480784i
$525$	−2191.41	−	1265.21i	−0.182173	−	0.105178i
$526$	11787.4	−	5728.98i	0.977100	−	0.474896i
$527$	−8.99814	−	51.0310i	−0.000743767	−	0.00421811i
$528$	520.831	+	2139.15i	0.0429285	+	0.176316i
$529$	−6549.30	−	2383.75i	−0.538284	−	0.195919i
$530$	−1465.63	+	1513.52i	−0.120119	+	0.124044i
$531$		−	1391.39i		−	0.113712i
$532$	877.172	−	4150.90i	0.0714854	−	0.338279i
$533$		−	3170.87i		−	0.257684i
$534$	−9326.33	−	9031.23i	−0.755786	−	0.731872i
$535$	−3562.70	−	1296.72i	−0.287904	−	0.104789i
$536$	6896.42	−	940.143i	0.555747	−	0.0757612i
$537$	1787.55	+	10137.7i	0.143647	+	0.814663i
$538$	−3673.90	−	7559.06i	−0.294411	−	0.605751i
$539$	−2723.94	−	1572.67i	−0.217678	−	0.125676i
$540$	1758.23	+	1963.58i	0.140115	+	0.156480i
$541$	−8713.40	+	10384.2i	−0.692455	+	0.825236i	−0.991650	−	0.128956i	$-0.958837\pi$
$541$	−8713.40	+	10384.2i	−0.692455	+	0.825236i	0.299195	+	0.954192i	$0.403282\pi$
$542$	−9638.36	−	6520.52i	−0.763843	−	0.516753i
$543$	3118.32	+	5401.08i	0.246445	+	0.426856i
$544$	−14.9712	+	2170.58i	−0.00117994	+	0.171071i
$545$	910.549	−	331.413i	0.0715663	−	0.0260480i
$546$	−785.815	−	2754.80i	−0.0615930	−	0.215924i
$547$	−17541.9	−	3093.11i	−1.37118	−	0.241777i	−0.560934	−	0.827861i	$-0.689558\pi$
$547$	−17541.9	−	3093.11i	−1.37118	−	0.241777i	−0.810250	+	0.586084i	$0.800669\pi$
$548$	3966.96	+	568.685i	0.309234	+	0.0443303i
$549$	7261.69	+	8654.15i	0.564520	+	0.672769i
$550$	363.569	+	3505.64i	0.0281866	+	0.271784i
$551$	−13991.4	−	6163.39i	−1.08176	−	0.476532i
$552$	3154.15	+	9845.93i	0.243206	+	0.759186i
$553$	1417.30	−	1189.25i	0.108987	−	0.0914507i
$554$	756.554	−	3016.64i	0.0580197	−	0.231344i
$555$	−2807.46	−	495.031i	−0.214721	−	0.0378611i
$556$	−8196.51	+	3285.33i	−0.625197	+	0.250592i
$557$	8201.83	+	22534.3i	0.623918	+	1.71420i	0.697187	+	0.716889i	$0.254435\pi$
$557$	8201.83	+	22534.3i	0.623918	+	1.71420i	−0.0732685	+	0.997312i	$0.523343\pi$
$558$	80.2401	−	179.555i	0.00608751	−	0.0136222i
$559$	−4107.89	−	7115.08i	−0.310815	−	0.538347i
$560$	−266.516	+	910.461i	−0.0201113	+	0.0687035i
$561$	315.997	+	265.153i	0.0237814	+	0.0199550i
$562$	−590.833	−	815.575i	−0.0443466	−	0.0612153i
$563$	−5934.48	−	3426.27i	−0.444242	−	0.256484i	0.261153	−	0.965297i	$-0.415897\pi$
$563$	−5934.48	−	3426.27i	−0.444242	−	0.256484i	−0.705396	+	0.708814i	$0.749231\pi$
$564$	1101.37	+	1773.43i	0.0822269	+	0.132402i
$565$	−2140.90	+	377.499i	−0.159413	+	0.0281089i
$566$	−18688.3	−	1332.72i	−1.38786	−	0.0989725i
$567$	−214.539	−	78.0859i	−0.0158903	−	0.00578359i
$568$	−4767.16	+	7559.26i	−0.352158	+	0.558415i
$569$	21088.0			1.55370			0.776849	−	0.629687i	$-0.216817\pi$
$569$	21088.0			1.55370			0.776849	+	0.629687i	$0.216817\pi$
$570$	1099.05	−	1414.17i	0.0807617	−	0.103918i
$571$			22271.6i			1.63229i	0.577850	+	0.816143i	$0.303892\pi$
$571$			22271.6i			1.63229i	−0.577850	+	0.816143i	$0.696108\pi$
$572$	−2465.16	+	3137.39i	−0.180199	+	0.229337i
$573$	−4803.26	+	13196.9i	−0.350191	+	0.962141i
$574$	85.3060	−	1196.22i	0.00620314	−	0.0869846i
$575$	2873.98	+	16299.2i	0.208441	+	1.18213i
$576$	−4663.18	+	6791.51i	−0.337325	+	0.491284i
$577$	11448.4	−	19829.2i	0.826002	−	1.43068i	−0.0751483	−	0.997172i	$-0.523943\pi$
$577$	11448.4	−	19829.2i	0.826002	−	1.43068i	0.901151	−	0.433506i	$-0.142724\pi$
$578$	−7913.79	−	10924.1i	−0.569499	−	0.786126i
$579$	−5139.48	+	6124.99i	−0.368894	+	0.439630i
$580$	3014.06	+	1613.29i	0.215779	+	0.115497i
$581$	−5575.23	+	3218.86i	−0.398106	+	0.229846i
$582$	−6484.50	−	2897.81i	−0.461841	−	0.206388i
$583$	−3149.29	+	1146.25i	−0.223723	+	0.0814284i
$584$	−4582.25	−	8704.67i	−0.324683	−	0.616784i
$585$	−309.731	+	1756.57i	−0.0218903	+	0.124146i
$586$	−3383.96	+	13493.0i	−0.238550	+	0.951178i
$587$	−9876.57	−	11770.4i	−0.694463	−	0.827628i	0.297425	−	0.954745i	$-0.403872\pi$
$587$	−9876.57	−	11770.4i	−0.694463	−	0.827628i	−0.991888	+	0.127117i	$0.959428\pi$
$588$	1637.57	+	7810.03i	0.114851	+	0.547756i
$589$	−347.599	−	85.2125i	−0.0243168	−	0.00596115i
$590$	563.153	−	58.4045i	0.0392960	−	0.00407538i
$591$	7466.66	−	6265.27i	0.519691	−	0.436073i
$592$	−1533.19	−	23813.1i	−0.106442	−	1.65323i
$593$	1498.51	−	8498.48i	0.103771	−	0.588517i	−0.887932	−	0.459974i	$-0.847859\pi$
$593$	1498.51	−	8498.48i	0.103771	−	0.588517i	0.991704	−	0.128543i	$-0.0410302\pi$
$594$	1150.10	+	4031.87i	0.0794433	+	0.278501i
$595$	60.7921	+	167.025i	0.00418862	+	0.0115082i
$596$	−21026.7	−	6896.18i	−1.44511	−	0.473957i
$597$	3786.91	−	2186.37i	0.259611	−	0.149886i
$598$	−10499.0	+	15519.1i	−0.717951	+	1.06125i
$599$	16744.5	+	14050.3i	1.14217	+	0.958395i	0.999508	−	0.0313766i	$-0.00998912\pi$
$599$	16744.5	+	14050.3i	1.14217	+	0.958395i	0.142663	+	0.989771i	$0.454434\pi$
$600$	6010.61	−	6620.15i	0.408970	−	0.450444i
$601$	−4575.24	+	7924.55i	−0.310529	+	0.537852i	−0.978477	−	0.206356i	$-0.933839\pi$
$601$	−4575.24	+	7924.55i	−0.310529	+	0.537852i	0.667948	+	0.744208i	$0.267173\pi$
$602$	−1358.29	−	2794.69i	−0.0919599	−	0.189208i
$603$	4874.25	−	859.461i	0.329179	−	0.0580431i
$604$	100.429	+	3122.90i	0.00676554	+	0.210379i
$605$	−967.910	+	2659.31i	−0.0650432	+	0.178705i
$606$	3182.00	−	3285.97i	0.213300	−	0.220270i
$607$	−15137.7			−1.01223			−0.506113	−	0.862467i	$-0.668918\pi$
$607$	−15137.7			−1.01223			−0.506113	+	0.862467i	$0.668918\pi$
$608$	13677.7	+	6138.19i	0.912339	+	0.409435i
$609$	−3904.38			−0.259792
$610$	−3197.89	+	3302.38i	−0.212260	+	0.219196i
$611$	−1293.97	+	3555.16i	−0.0856769	+	0.235395i
$612$	49.6129	+	1542.75i	0.00327694	+	0.101899i
$613$	8044.55	−	1418.47i	0.530043	−	0.0934608i	0.0977791	−	0.995208i	$-0.468826\pi$
$613$	8044.55	−	1418.47i	0.530043	−	0.0934608i	0.432264	+	0.901747i	$0.357715\pi$
$614$	−12543.6	−	25808.5i	−0.824459	−	1.69633i
$615$	253.138	−	438.447i	0.0165976	−	0.0287478i
$616$	−1014.39	+	1117.26i	−0.0663491	+	0.0730777i
$617$	−19665.2	−	16501.1i	−1.28313	−	1.07668i	−0.992804	−	0.119748i	$-0.961791\pi$
$617$	−19665.2	−	16501.1i	−1.28313	−	1.07668i	−0.290327	−	0.956927i	$-0.593764\pi$
$618$	3395.95	−	5019.76i	0.221044	−	0.326738i
$619$	−5369.39	+	3100.02i	−0.348650	+	0.201293i	−0.664090	−	0.747652i	$-0.731181\pi$
$619$	−5369.39	+	3100.02i	−0.348650	+	0.201293i	0.315441	+	0.948945i	$0.397848\pi$
$620$	76.0417	+	24.9396i	0.00492566	+	0.00161548i
$621$	6733.93	+	18501.3i	0.435142	+	1.19554i
$622$	−4722.47	−	16555.4i	−0.304427	−	1.06722i
$623$	1545.21	−	8763.31i	0.0993699	−	0.563554i
$624$	10102.0	−	650.406i	0.648080	−	0.0417261i
$625$	10452.1	−	8770.35i	0.668934	−	0.561302i
$626$	23089.2	−	2394.57i	1.47417	−	0.152886i
$627$	2555.75	−	1259.02i	0.162786	−	0.0801919i
$628$	972.997	+	4640.51i	0.0618261	+	0.294867i
$629$	−2873.84	−	3424.91i	−0.182174	−	0.217107i
$630$	−164.104	+	654.337i	−0.0103779	+	0.0413800i
$631$	1749.77	−	9923.44i	0.110392	−	0.626063i	−0.878537	−	0.477674i	$-0.841480\pi$
$631$	1749.77	−	9923.44i	0.110392	−	0.626063i	0.988929	−	0.148389i	$-0.0474089\pi$
$632$	3045.41	+	5785.22i	0.191677	+	0.364120i
$633$	−15274.6	+	5559.50i	−0.959100	+	0.349084i
$634$	1979.07	+	884.413i	0.123973	+	0.0554015i
$635$	3616.52	−	2088.00i	0.226011	−	0.130488i
$636$	7496.39	+	4012.47i	0.467376	+	0.250165i
$637$	−9295.88	+	11078.4i	−0.578204	+	0.689077i
$638$	3190.38	+	4403.95i	0.197976	+	0.273282i
$639$	−3177.54	+	5503.66i	−0.196716	+	0.340722i
$640$	−2944.55	−	1602.31i	−0.181865	−	0.0989637i
$641$	3504.11	+	19872.8i	0.215919	+	1.22454i	0.879305	+	0.476260i	$0.158008\pi$
$641$	3504.11	+	19872.8i	0.215919	+	1.22454i	−0.663386	+	0.748278i	$0.730881\pi$
$642$	−1088.39	+	15262.1i	−0.0669085	+	0.938235i
$643$	−5616.97	+	15432.5i	−0.344497	+	0.946498i	0.639575	+	0.768729i	$0.279110\pi$
$643$	−5616.97	+	15432.5i	−0.344497	+	0.946498i	−0.984072	+	0.177769i	$0.943112\pi$
$644$	−4378.27	+	5572.17i	−0.267900	+	0.340954i
$645$		−	1311.77i		−	0.0800788i
$646$	2746.02	−	591.041i	0.167245	−	0.0359972i
$647$	18674.5			1.13473			0.567365	−	0.823466i	$-0.307963\pi$
$647$	18674.5			1.13473			0.567365	+	0.823466i	$0.307963\pi$
$648$	430.348	−	682.401i	0.0260890	−	0.0413692i
$649$	846.310	+	308.032i	0.0511873	+	0.0186307i
$650$	16163.9	+	1152.70i	0.975384	+	0.0695577i
$651$	−90.0087	+	15.8710i	−0.00541892	+	0.000955502i
$652$	−4359.55	−	7019.76i	−0.261861	−	0.421649i
$653$	9579.79	+	5530.90i	0.574099	+	0.331456i	0.758785	−	0.651342i	$-0.225794\pi$
$653$	9579.79	+	5530.90i	0.574099	+	0.331456i	−0.184686	+	0.982798i	$0.559127\pi$
$654$	−2294.21	−	3166.89i	−0.137172	−	0.189350i
$655$	−1916.28	−	1607.95i	−0.114314	−	0.0959205i
$656$	4067.11	+	1190.55i	0.242064	+	0.0708584i
$657$	−3497.60	−	6058.02i	−0.207693	−	0.359735i
$658$	−583.798	+	1306.38i	−0.0345879	+	0.0773982i
$659$	−3203.72	−	8802.15i	−0.189377	−	0.520308i	0.808275	−	0.588806i	$-0.200402\pi$
$659$	−3203.72	−	8802.15i	−0.189377	−	0.520308i	−0.997651	+	0.0684977i	$0.978179\pi$
$660$	−591.331	+	237.018i	−0.0348750	+	0.0139786i
$661$	4018.63	+	708.593i	0.236470	+	0.0416960i	0.290627	−	0.956836i	$-0.406136\pi$
$661$	4018.63	+	708.593i	0.236470	+	0.0416960i	−0.0541571	+	0.998532i	$0.517247\pi$
$662$	5313.90	−	21188.3i	0.311980	−	1.24397i
$663$	1452.91	−	1219.14i	0.0851077	−	0.0714138i
$664$	−6940.17	−	21664.3i	−0.405619	−	1.26617i
$665$	1224.96	+	80.8071i	0.0714314	+	0.00471213i
$666$	−1750.43	−	16878.1i	−0.101843	−	0.982004i
$667$	16415.0	+	19562.6i	0.952911	+	1.13564i
$668$	−19447.9	−	2787.96i	−1.12644	−	0.161481i
$669$	11758.3	+	2073.30i	0.679523	+	0.119818i
$670$	552.460	+	1936.74i	0.0318558	+	0.111676i
$671$	−6871.50	+	2501.02i	−0.395337	+	0.143891i
$672$	3828.48	+	26.4063i	0.219772	+	0.00151584i
$673$	9211.78	+	15955.3i	0.527620	+	0.913864i	0.999482	+	0.0321919i	$0.0102488\pi$
$673$	9211.78	+	15955.3i	0.527620	+	0.913864i	−0.471862	+	0.881672i	$0.656418\pi$
$674$	13414.2	+	9074.92i	0.766609	+	0.518624i
$675$	10945.4	−	13044.3i	0.624134	−	0.743814i
$676$	513.361	+	573.318i	0.0292081	+	0.0326194i
$677$	6018.07	+	3474.53i	0.341644	+	0.197248i	0.660999	−	0.750387i	$-0.270133\pi$
$677$	6018.07	+	3474.53i	0.341644	+	0.197248i	−0.319355	+	0.947635i	$0.603466\pi$
$678$	3835.13	+	7890.79i	0.217238	+	0.446967i
$679$	−845.365	−	4794.30i	−0.0477793	−	0.270970i
$680$	−622.334	+	84.8385i	−0.0350962	+	0.00478442i
$681$	−7272.57	−	2647.00i	−0.409230	−	0.148947i
$682$	91.4503	+	88.5566i	0.00513462	+	0.00497215i
$683$		−	2788.15i		−	0.156202i	−0.996945	−	0.0781008i	$-0.975114\pi$
$683$		−	2788.15i		−	0.156202i	0.996945	−	0.0781008i	$-0.0248856\pi$
$684$	9889.22	+	3981.91i	0.552812	+	0.222591i
$685$			1159.61i			0.0646807i
$686$	−8126.47	+	8392.01i	−0.452289	+	0.467067i
$687$	10650.4	+	3876.45i	0.591470	+	0.215278i
$688$	10668.5	−	2597.51i	0.591181	−	0.143938i
$689$	2675.80	+	15175.2i	0.147953	+	0.839086i
$690$	−2690.66	+	1307.73i	−0.148451	+	0.0721513i
$691$	25175.4	+	14535.0i	1.38599	+	0.800201i	0.992860	−	0.119282i	$-0.0380593\pi$
$691$	25175.4	+	14535.0i	1.38599	+	0.800201i	0.393129	+	0.919483i	$0.371393\pi$
$692$	2588.91	−	2318.16i	0.142219	−	0.127346i
$693$	−689.777	+	822.044i	−0.0378102	+	0.0450604i
$694$	−4822.37	+	7128.23i	−0.263767	+	0.389890i
$695$	−1277.57	−	2212.82i	−0.0697283	−	0.120773i
$696$	2924.34	−	13483.3i	0.159263	−	0.734317i
$697$	746.114	−	271.563i	0.0405468	−	0.0147578i
$698$	16707.4	−	4765.83i	0.905993	−	0.258437i
$699$	−397.667	−	70.1193i	−0.0215181	−	0.00379422i
$700$	6066.84	+	869.714i	0.327579	+	0.0469601i
$701$	3283.02	+	3912.55i	0.176887	+	0.210806i	0.847202	−	0.531271i	$-0.178285\pi$
$701$	3283.02	+	3912.55i	0.176887	+	0.210806i	−0.670315	+	0.742077i	$0.733841\pi$
$702$	19174.6	−	1988.60i	1.03091	−	0.106916i
$703$	−29649.1	+	8628.36i	−1.59066	+	0.462908i
$704$	−3098.57	−	4339.91i	−0.165883	−	0.232339i
$705$	−462.738	+	388.284i	−0.0247202	+	0.0207427i
$706$	−31949.3	−	8012.68i	−1.70315	−	0.427140i
$707$	3087.60	+	544.427i	0.164245	+	0.0289608i
$708$	−850.101	−	2120.90i	−0.0451254	−	0.112582i
$709$	−8006.48	−	21997.6i	−0.424104	−	1.16522i	−0.949338	−	0.314258i	$-0.898244\pi$
$709$	−8006.48	−	21997.6i	−0.424104	−	1.16522i	0.525234	−	0.850958i	$-0.323978\pi$
$710$	−2360.94	−	1055.06i	−0.124795	−	0.0557688i
$711$	2324.54	+	4026.23i	0.122612	+	0.212370i
$712$	29105.7	+	11899.8i	1.53200	+	0.626355i
$713$	457.939	+	384.257i	0.0240532	+	0.0201831i
$714$	580.912	−	420.834i	0.0304483	−	0.0220579i
$715$	−999.863	−	577.271i	−0.0522976	−	0.0301940i
$716$	−13154.1	−	21180.8i	−0.686581	−	1.10553i
$717$	−11620.5	+	2049.01i	−0.605266	+	0.106725i
$718$	−1280.69	+	17958.7i	−0.0665669	+	0.933446i
$719$	−21610.8	−	7865.68i	−1.12093	−	0.407984i	−0.285936	−	0.958249i	$-0.592305\pi$
$719$	−21610.8	−	7865.68i	−1.12093	−	0.407984i	−0.834990	+	0.550265i	$0.814527\pi$
$720$	−2136.77	−	1056.81i	−0.110601	−	0.0547011i
$721$	4154.07			0.214571
$722$	3910.03	−	19002.1i	0.201546	−	0.979479i
$723$			1207.82i			0.0621289i
$724$	−11877.6	−	9332.72i	−0.609709	−	0.479072i
$725$	7553.95	−	20754.3i	0.386961	−	1.06317i
$726$	11392.1	+	812.408i	0.582371	+	0.0415307i
$727$	2728.62	+	15474.8i	0.139201	+	0.789446i	0.971842	+	0.235633i	$0.0757165\pi$
$727$	2728.62	+	15474.8i	0.139201	+	0.789446i	−0.832641	+	0.553813i	$0.813172\pi$
$728$	4249.09	+	5485.22i	0.216321	+	0.279253i
$729$	6633.16	−	11489.0i	0.336999	−	0.583700i
$730$	2305.12	−	1669.92i	0.116872	−	0.0846663i
$731$	1322.38	−	1575.96i	0.0669085	−	0.0797384i
$732$	16356.5	+	8754.88i	0.825893	+	0.442062i
$733$	−25763.8	+	14874.7i	−1.29824	+	0.749538i	−0.980100	−	0.198506i	$-0.936391\pi$
$733$	−25763.8	+	14874.7i	−1.29824	+	0.749538i	−0.318138	+	0.948044i	$0.603058\pi$
$734$	191.720	−	429.017i	0.00964103	−	0.0215740i
$735$	−2169.79	+	789.737i	−0.108889	+	0.0396325i
$736$	−15963.6	−	19293.3i	−0.799491	−	0.966253i
$737$	−556.316	+	3155.03i	−0.0278048	+	0.157689i
$738$	2922.98	+	733.065i	0.145795	+	0.0365644i
$739$	1434.57	+	1709.65i	0.0714092	+	0.0851021i	0.800566	−	0.599244i	$-0.204532\pi$
$739$	1434.57	+	1709.65i	0.0714092	+	0.0851021i	−0.729157	+	0.684346i	$0.760088\pi$
$740$	6757.82	−	1416.94i	0.335706	−	0.0703891i
$741$	−3660.31	−	12577.7i	−0.181464	−	0.623554i
$742$	601.192	+	5796.87i	0.0297445	+	0.286806i
$743$	16449.1	−	13802.5i	0.812194	−	0.681511i	−0.138937	−	0.990301i	$-0.544368\pi$
$743$	16449.1	−	13802.5i	0.812194	−	0.681511i	0.951130	+	0.308790i	$0.0999240\pi$
$744$	12.6071	−	322.722i	0.000621233	−	0.0159026i
$745$	1111.89	−	6305.84i	0.0546798	−	0.310105i
$746$	13163.2	−	3754.85i	0.646031	−	0.184282i
$747$	−5532.79	−	15201.2i	−0.270996	−	0.744555i
$748$	−949.359	−	311.364i	−0.0464064	−	0.0152200i
$749$	−9082.53	+	5243.80i	−0.443082	+	0.255813i
$750$	4382.01	+	2964.50i	0.213344	+	0.144331i
$751$	10276.9	+	8623.37i	0.499348	+	0.419003i	0.857362	−	0.514713i	$-0.172102\pi$
$751$	10276.9	+	8623.37i	0.499348	+	0.419003i	−0.358014	+	0.933716i	$0.616546\pi$
$752$	−4074.17	−	2994.55i	−0.197566	−	0.145213i
$753$	−3437.10	+	5953.23i	−0.166341	+	0.288111i
$754$	22488.4	−	10929.9i	1.08618	−	0.527911i
$755$	−890.369	+	156.996i	−0.0429190	+	0.00756778i
$756$	7287.16	−	234.346i	0.350571	−	0.0112739i
$757$	13768.3	−	37828.0i	0.661052	−	1.81622i	0.0889592	−	0.996035i	$-0.471646\pi$
$757$	13768.3	−	37828.0i	0.661052	−	1.81622i	0.572092	−	0.820189i	$-0.306132\pi$
$758$	−936.288	−	906.662i	−0.0448648	−	0.0434452i
$759$	−4758.83			−0.227582
$760$	−1196.54	+	4169.73i	−0.0571093	+	0.199016i
$761$	−3509.29			−0.167164			−0.0835819	−	0.996501i	$-0.526636\pi$
$761$	−3509.29			−0.167164			−0.0835819	+	0.996501i	$0.526636\pi$
$762$	−12107.0	−	11723.9i	−0.575579	−	0.557367i
$763$	916.753	−	2518.76i	0.0434976	−	0.119509i
$764$	−1093.32	−	33997.5i	−0.0517734	−	1.60993i
$765$	−439.852	+	77.5578i	−0.0207881	+	0.00366550i
$766$	−20540.6	+	9983.28i	−0.968881	+	0.470901i
$767$	2070.48	−	3586.17i	0.0974713	−	0.168825i
$768$	−2958.68	+	13201.4i	−0.139013	+	0.620268i
$769$	−17642.9	−	14804.1i	−0.827331	−	0.694213i	0.127346	−	0.991858i	$-0.459354\pi$
$769$	−17642.9	−	14804.1i	−0.827331	−	0.694213i	−0.954677	+	0.297645i	$0.903799\pi$
$770$	−361.670	−	244.676i	−0.0169269	−	0.0114513i
$771$	7404.99	−	4275.27i	0.345894	−	0.199702i
$772$	6035.20	−	18401.5i	0.281362	−	0.857882i
$773$	−9049.96	−	24864.6i	−0.421092	−	1.15694i	−0.951082	−	0.308938i	$-0.900026\pi$
$773$	−9049.96	−	24864.6i	−0.421092	−	1.15694i	0.529990	−	0.848004i	$-0.322196\pi$
$774$	7508.53	−	2141.83i	0.348693	−	0.0994659i
$775$	89.7786	−	509.160i	0.00416122	−	0.0235994i
$776$	17189.7	+	671.513i	0.795201	+	0.0310643i
$777$	−6040.87	+	5068.89i	−0.278913	+	0.234035i
$778$	3938.79	+	37979.0i	0.181507	+	1.75015i
$779$	360.972	−	5471.99i	0.0166023	−	0.251675i
$780$	601.094	+	2866.79i	0.0275931	+	0.131600i
$781$	−2644.13	−	3151.16i	−0.121145	−	0.144375i
$782$	−4550.86	−	1141.33i	−0.208105	−	0.0521915i
$783$	4562.42	−	25874.8i	0.208235	−	1.18096i
$784$	−10719.4	−	16082.9i	−0.488310	−	0.732638i
$785$	−1289.23	+	469.240i	−0.0586172	+	0.0213349i
$786$	−4118.94	+	9217.04i	−0.186918	+	0.418271i
$787$	−19175.6	+	11071.1i	−0.868536	+	0.501450i	−0.866862	−	0.498549i	$-0.833866\pi$
$787$	−19175.6	+	11071.1i	−0.868536	+	0.501450i	−0.00167470	+	0.999999i	$0.500533\pi$
$788$	−11140.8	+	20814.0i	−0.503646	+	0.940948i
$789$	9837.65	−	11724.1i	0.443891	−	0.529008i
$790$	−1532.01	+	1109.84i	−0.0689955	+	0.0499829i
$791$	−3006.76	+	5207.86i	−0.135156	+	0.234096i
$792$	−2322.20	−	2997.77i	−0.104187	−	0.134496i
$793$	5838.38	+	33111.1i	0.261446	+	1.48274i
$794$	−19409.3	−	1384.14i	−0.867521	−	0.0618657i
$795$	−841.479	+	2311.94i	−0.0375399	+	0.103140i
$796$	−6543.53	+	8327.87i	−0.291368	+	0.370821i
$797$			17353.6i			0.771263i	0.922653	+	0.385631i	$0.126016\pi$
$797$			17353.6i			0.771263i	−0.922653	+	0.385631i	$0.873984\pi$
$798$	−1042.48	−	4843.43i	−0.0462449	−	0.214857i
$799$	−947.359			−0.0419464
$800$	−7547.46	+	20299.7i	−0.333554	+	0.897130i
$801$	21011.8	+	7647.66i	0.926859	+	0.337349i
$802$	−1033.18	+	14487.9i	−0.0454897	+	0.637887i
$803$	4459.10	−	786.259i	0.195963	−	0.0345535i
$804$	6904.74	−	4288.12i	0.302875	−	0.188097i
$805$	−1775.81	−	1025.27i	−0.0777505	−	0.0448893i
$806$	474.001	−	343.384i	0.0207146	−	0.0150064i
$807$	−7518.45	−	6308.72i	−0.327958	−	0.275189i
$808$	−4192.70	+	10254.9i	−0.182548	+	0.446493i
$809$	4890.64	+	8470.84i	0.212541	+	0.368132i	0.952509	−	0.304510i	$-0.0984927\pi$
$809$	4890.64	+	8470.84i	0.212541	+	0.368132i	−0.739968	+	0.672642i	$0.765159\pi$
$810$	213.131	+	95.2443i	0.00924524	+	0.00413154i
$811$	9115.54	+	25044.7i	0.394685	+	1.08439i	0.964837	+	0.262850i	$0.0846623\pi$
$811$	9115.54	+	25044.7i	0.394685	+	1.08439i	−0.570151	+	0.821540i	$0.693115\pi$
$812$	8777.84	−	3518.34i	0.379362	−	0.152056i
$813$	−13382.7	−	2359.73i	−0.577308	−	0.101795i
$814$	10653.6	+	2671.86i	0.458734	+	0.115048i
$815$	1831.66	−	1536.95i	0.0787242	−	0.0660575i
$816$	1018.20	+	2321.31i	0.0436817	+	0.0995860i
$817$	−6279.04	−	12746.2i	−0.268881	−	0.545817i
$818$	−13236.6	+	1372.76i	−0.565778	+	0.0586767i
$819$	3171.50	+	3779.65i	0.135313	+	0.161260i
$820$	−174.008	+	1213.83i	−0.00741053	+	0.0516934i
$821$	−5158.05	−	909.503i	−0.219266	−	0.0386625i	0.0629359	−	0.998018i	$-0.479954\pi$
$821$	−5158.05	−	909.503i	−0.219266	−	0.0386625i	−0.282202	+	0.959355i	$0.591065\pi$
$822$	4500.35	−	1283.74i	0.190958	−	0.0544715i
$823$	30382.4	−	11058.3i	1.28683	−	0.468369i	0.394146	−	0.919048i	$-0.371040\pi$
$823$	30382.4	−	11058.3i	1.28683	−	0.468369i	0.892686	+	0.450679i	$0.148818\pi$
$824$	−3111.36	+	14345.6i	−0.131540	+	0.606496i
$825$	2057.87	+	3564.34i	0.0868436	+	0.150418i
$826$	877.569	−	1297.19i	0.0369668	−	0.0546427i
$827$	1401.86	−	1670.67i	0.0589450	−	0.0702479i	−0.735766	−	0.677236i	$-0.763178\pi$
$827$	1401.86	−	1670.67i	0.0589450	−	0.0702479i	0.794711	+	0.606988i	$0.207622\pi$
$828$	−11878.7	−	13266.0i	−0.498566	−	0.556795i
$829$	987.095	+	569.900i	0.0413549	+	0.0238763i	0.520535	−	0.853840i	$-0.325733\pi$
$829$	987.095	+	569.900i	0.0413549	+	0.0238763i	−0.479180	+	0.877717i	$0.659066\pi$
$830$	5920.33	−	2877.43i	0.247587	−	0.120334i
$831$	−630.663	−	3576.67i	−0.0263267	−	0.149306i
$832$	−22125.1	+	10565.4i	−0.921935	+	0.440250i
$833$	−3402.90	−	1238.56i	−0.141541	−	0.0515167i
$834$	−7173.48	+	7407.88i	−0.297838	+	0.307570i
$835$		−	5684.94i		−	0.235611i
$836$	−4611.31	+	5133.57i	−0.190772	+	0.212378i
$837$		−	615.043i		−	0.0253990i
$838$	28094.0	+	27205.1i	1.15811	+	1.12146i
$839$	18106.2	+	6590.13i	0.745049	+	0.271176i	0.686521	−	0.727110i	$-0.259137\pi$
$839$	18106.2	+	6590.13i	0.745049	+	0.271176i	0.0585284	+	0.998286i	$0.481359\pi$
$840$	149.638	+	1097.67i	0.00614645	+	0.0450873i
$841$	−1682.58	−	9542.41i	−0.0689895	−	0.391259i
$842$	14630.8	+	30102.8i	0.598824	+	1.23208i
$843$	−1018.50	−	588.031i	−0.0416121	−	0.0240247i
$844$	29330.5	−	26263.2i	1.19621	−	1.07111i
$845$	−143.136	+	170.583i	−0.00582725	+	0.00694465i
$846$	−2978.08	−	2014.72i	−0.121027	−	0.0818766i
$847$	3914.14	+	6779.49i	0.158786	+	0.275025i
$848$	−20469.1	−	2265.65i	−0.828906	−	0.0917485i
$849$	−20559.6	+	7483.09i	−0.831100	+	0.302496i
$850$	1113.09	+	3902.12i	0.0449162	+	0.157461i
$851$	50794.7	+	8956.47i	2.04609	+	0.360780i
$852$	−1480.95	+	10330.7i	−0.0595501	+	0.415402i
$853$	−29656.2	−	35342.9i	−1.19040	−	1.41866i	−0.884465	−	0.466607i	$-0.845476\pi$
$853$	−29656.2	−	35342.9i	−1.19040	−	1.41866i	−0.305933	−	0.952053i	$-0.598968\pi$
$854$	1311.75	+	12648.3i	0.0525611	+	0.506810i
$855$	−734.473	+	2996.07i	−0.0293783	+	0.119840i
$856$	−11306.1	−	35293.0i	−0.451444	−	1.40922i
$857$	8971.00	−	7527.56i	0.357577	−	0.300043i	−0.446247	−	0.894910i	$-0.647240\pi$
$857$	8971.00	−	7527.56i	0.357577	−	0.300043i	0.803824	+	0.594867i	$0.202795\pi$
$858$	−1133.45	+	4519.47i	−0.0450996	+	0.179827i
$859$	−6874.27	−	1212.12i	−0.273046	−	0.0481455i	0.0354483	−	0.999372i	$-0.488714\pi$
$859$	−6874.27	−	1212.12i	−0.273046	−	0.0481455i	−0.308495	+	0.951226i	$0.599825\pi$
$860$	1182.07	+	2949.12i	0.0468699	+	0.116935i
$861$	−478.984	−	1316.00i	−0.0189591	−	0.0520896i
$862$	8011.57	−	17927.7i	0.316560	−	0.708375i
$863$	−6922.43	−	11990.0i	−0.273050	−	0.472936i	0.696591	−	0.717468i	$-0.254699\pi$
$863$	−6922.43	−	11990.0i	−0.273050	−	0.472936i	−0.969641	+	0.244532i	$0.921366\pi$
$864$	−4648.72	+	25340.9i	−0.183047	+	0.997818i
$865$	770.295	+	646.354i	0.0302784	+	0.0254066i
$866$	6488.90	+	8957.16i	0.254621	+	0.351474i
$867$	−13642.1	−	7876.25i	−0.534382	−	0.308526i
$868$	188.056	−	116.790i	0.00735372	−	0.00456695i
$869$	−2963.56	+	522.556i	−0.115687	+	0.0203987i
$870$	3982.11	+	283.977i	0.155179	+	0.0110663i
$871$	13841.8	+	5038.02i	0.538476	+	0.195989i
$872$	8011.60	+	5052.43i	0.311132	+	0.196212i
$873$	12233.0			0.474256
$874$	−19884.8	+	25586.3i	−0.769582	+	0.990239i
$875$			3626.30i			0.140104i
$876$	−9032.71	−	7097.34i	−0.348387	−	0.273741i
$877$	7793.55	−	21412.6i	0.300079	−	0.824461i	−0.694406	−	0.719584i	$-0.744333\pi$
$877$	7793.55	−	21412.6i	0.300079	−	0.824461i	0.994485	−	0.104878i	$-0.0334451\pi$
$878$	−2911.18	+	40822.4i	−0.111899	+	1.56912i
$879$	2820.87	+	15997.9i	0.108243	+	0.613875i
$880$	1115.85	−	1065.73i	0.0427446	−	0.0408246i
$881$	19408.8	−	33617.1i	0.742225	−	1.28557i	−0.209255	−	0.977861i	$-0.567104\pi$
$881$	19408.8	−	33617.1i	0.742225	−	1.28557i	0.951480	−	0.307710i	$-0.0995628\pi$
$882$	−8063.23	−	11130.3i	−0.307827	−	0.424918i
$883$	10160.6	−	12108.9i	0.387238	−	0.461493i	−0.536847	−	0.843680i	$-0.680385\pi$
$883$	10160.6	−	12108.9i	0.387238	−	0.461493i	0.924085	+	0.382187i	$0.124829\pi$
$884$	−2167.84	+	4050.12i	−0.0824800	+	0.154095i
$885$	572.583	−	330.581i	0.0217482	−	0.0125563i
$886$	41672.6	+	18622.8i	1.58016	+	0.706144i
$887$	−48823.3	+	17770.2i	−1.84817	+	0.672678i	−0.862006	+	0.506898i	$0.830792\pi$
$887$	−48823.3	+	17770.2i	−1.84817	+	0.672678i	−0.986163	+	0.165780i	$0.946986\pi$
$888$	−12980.3	−	24658.0i	−0.490529	−	0.931834i
$889$	2005.92	−	11376.1i	0.0756764	−	0.429182i
$890$	−2213.35	+	8825.37i	−0.0833613	+	0.332390i
$891$	238.695	+	284.466i	0.00897485	+	0.0106958i
$892$	−28303.3	+	5934.48i	−1.06240	+	0.222759i
$893$	−2637.74	+	5987.86i	−0.0988450	+	0.224385i
$894$	−25703.4	+	2665.69i	−0.961578	+	0.0997250i
$895$	5526.68	−	4637.43i	0.206410	−	0.173198i
$896$	−8630.98	+	3390.57i	−0.321809	+	0.126419i
$897$	−3799.50	+	21548.0i	−0.141429	+	0.802083i
$898$	−13166.3	−	46156.6i	−0.489272	−	1.71522i
$899$	−272.844	−	749.632i	−0.0101222	−	0.0278105i
$900$	−4799.47	+	14633.7i	−0.177758	+	0.541990i
$901$	−3341.60	+	1929.28i	−0.123557	+	0.0713358i
$902$	−1092.99	+	1615.61i	−0.0403465	+	0.0596385i
$903$	−2779.67	−	2332.42i	−0.102438	−	0.0859559i
$904$	−15732.7	−	14284.1i	−0.578830	−	0.525535i
$905$	2185.46	−	3785.32i	0.0802730	−	0.139037i
$906$	1594.97	+	3281.66i	0.0584871	+	0.120337i
$907$	26506.9	−	4673.88i	0.970393	−	0.171106i	0.334086	−	0.942543i	$-0.391572\pi$
$907$	26506.9	−	4673.88i	0.970393	−	0.171106i	0.636307	+	0.771436i	$0.280461\pi$
$908$	18735.5	−	602.510i	0.684756	−	0.0220209i
$909$	−2694.52	+	7403.13i	−0.0983185	+	0.270128i
$910$	−1396.66	+	1442.30i	−0.0508778	+	0.0525402i
$911$	−19109.5			−0.694978			−0.347489	−	0.937684i	$-0.612966\pi$
$911$	−19109.5			−0.694978			−0.347489	+	0.937684i	$0.612966\pi$
$912$	17507.0	+	27.5975i	0.635654	+	0.00100202i
$913$	10471.0			0.379561
$914$	−32360.6	+	33418.0i	−1.17111	+	1.20938i
$915$	−1836.04	+	5044.48i	−0.0663361	+	0.182257i
$916$	−27437.5	+	882.356i	−0.989695	+	0.0318274i
$917$	−6814.60	+	1201.60i	−0.245407	+	0.0432718i
$918$	2110.10	+	4341.53i	0.0758644	+	0.156091i
$919$	10526.7	−	18232.7i	0.377849	−	0.654453i	−0.612900	−	0.790160i	$-0.709997\pi$
$919$	10526.7	−	18232.7i	0.377849	−	0.654453i	0.990749	+	0.135707i	$0.0433307\pi$
$920$	4870.70	−	5364.65i	0.174546	−	0.192247i
$921$	−25669.8	−	21539.5i	−0.918402	−	0.770631i
$922$	16299.2	−	24092.8i	0.582196	−	0.860578i
$923$	−16379.6	+	9456.76i	−0.584118	+	0.337241i
$924$	−549.185	+	1674.48i	−0.0195529	+	0.0596174i
$925$	−15256.9	−	41918.1i	−0.542319	−	1.49001i
$926$	5250.16	+	18405.3i	0.186319	+	0.653169i
$927$	−1812.61	+	10279.8i	−0.0642221	+	0.364222i
$928$	5575.66	+	32948.4i	0.197231	+	1.16550i
$929$	14404.9	−	12087.2i	0.508730	−	0.426875i	−0.351952	−	0.936018i	$-0.614482\pi$
$929$	14404.9	−	12087.2i	0.508730	−	0.426875i	0.860682	+	0.509143i	$0.170038\pi$
$930$	92.9548	−	9.64032i	0.00327753	−	0.000339912i
$931$	−17303.1	+	18059.8i	−0.609116	+	0.635754i
$932$	957.220	−	200.705i	0.0336425	−	0.00705398i
$933$	−12922.6	−	15400.6i	−0.453450	−	0.540400i
$934$	−6605.27	+	26337.4i	−0.231404	+	0.922685i
$935$	50.2020	−	284.710i	0.00175592	−	0.00995829i
$936$	−15428.0	+	8121.50i	−0.538761	+	0.283611i
$937$	−10300.3	+	3748.98i	−0.359119	+	0.130709i	−0.515278	−	0.857023i	$-0.672311\pi$
$937$	−10300.3	+	3748.98i	−0.359119	+	0.130709i	0.156159	+	0.987732i	$0.450089\pi$
$938$	5086.32	+	2272.99i	0.177051	+	0.0791212i
$939$	23475.8	−	13553.8i	0.815872	−	0.471044i
$940$	690.437	−	1289.92i	0.0239570	−	0.0447582i
$941$	−24746.6	+	29491.9i	−0.857297	+	1.02169i	0.142195	+	0.989839i	$0.454584\pi$
$941$	−24746.6	+	29491.9i	−0.857297	+	1.02169i	−0.999493	+	0.0318487i	$0.989861\pi$
$942$	3248.32	+	4483.92i	0.112352	+	0.155089i
$943$	−4579.95	+	7932.71i	−0.158159	+	0.273939i
$944$	3822.39	+	4002.16i	0.131788	+	0.137987i
$945$	366.343	+	2077.64i	0.0126107	+	0.0715191i
$946$	−359.506	+	5041.22i	−0.0123557	+	0.173260i
$947$	−5536.17	+	15210.5i	−0.189970	+	0.521938i	−0.997713	−	0.0675973i	$-0.978467\pi$
$947$	−5536.17	+	15210.5i	−0.189970	+	0.521938i	0.807743	+	0.589535i	$0.200689\pi$
$948$	6003.23	+	4716.97i	0.205671	+	0.161603i
$949$		−	20818.6i		−	0.712119i
$950$	27762.9	+	3829.31i	0.948155	+	0.130778i
$951$	2531.38			0.0863150
$952$	−926.782	+	1469.59i	−0.0315517	+	0.0500313i
$953$	7873.89	+	2865.86i	0.267639	+	0.0974128i	0.472354	−	0.881409i	$-0.343404\pi$
$953$	7873.89	+	2865.86i	0.267639	+	0.0974128i	−0.204715	+	0.978822i	$0.565627\pi$
$954$	−14607.5	−	1041.70i	−0.495738	−	0.0353527i
$955$	9693.01	−	1709.14i	0.328438	−	0.0579125i
$956$	24278.8	−	15078.1i	0.821374	−	0.510106i
$957$	5499.70	+	3175.25i	0.185768	+	0.107253i
$958$	14587.9	+	20136.8i	0.491976	+	0.679115i
$959$	2457.24	+	2061.87i	0.0827408	+	0.0694278i
$960$	−3902.77	−	305.388i	−0.131210	−	0.0102670i
$961$	14886.2	+	25783.6i	0.499687	+	0.865483i
$962$	20604.2	−	46106.5i	0.690547	−	1.54525i
$963$	−9013.39	−	24764.1i	−0.301612	−	0.828672i
$964$	−1088.39	−	2715.41i	−0.0363639	−	0.0907237i
$965$	5518.56	+	973.070i	0.184092	+	0.0324604i
$966$	−2013.08	+	8026.82i	−0.0670493	+	0.267349i
$967$	−192.341	+	161.394i	−0.00639636	+	0.00536718i	−0.645980	−	0.763354i	$-0.723551\pi$
$967$	−192.341	+	161.394i	−0.00639636	+	0.00536718i	0.639584	+	0.768721i	$0.279107\pi$
$968$	−26343.8	+	8439.26i	−0.874714	+	0.280215i
$969$	2646.08	−	1938.47i	0.0877239	−	0.0642649i
$970$	513.490	+	4951.23i	0.0169971	+	0.163891i
$971$	9596.74	+	11436.9i	0.317172	+	0.377991i	0.900950	−	0.433922i	$-0.142871\pi$
$971$	9596.74	+	11436.9i	0.317172	+	0.377991i	−0.583778	+	0.811913i	$0.698426\pi$
$972$	−4228.80	+	29498.7i	−0.139546	+	0.973428i
$973$	−6960.66	−	1227.35i	−0.229341	−	0.0404390i
$974$	−12100.5	−	42420.3i	−0.398076	−	1.39552i
$975$	17782.4	−	6472.27i	0.584096	−	0.212593i
$976$	−44661.9	−	4943.46i	−1.46475	−	0.162127i
$977$	1660.01	+	2875.22i	0.0543587	+	0.0941521i	0.891924	−	0.452185i	$-0.149355\pi$
$977$	1660.01	+	2875.22i	0.0543587	+	0.0941521i	−0.837566	+	0.546337i	$0.816022\pi$
$978$	−7992.51	−	5407.07i	−0.261321	−	0.176788i
$979$	−9303.36	+	11087.3i	−0.303715	+	0.361953i
$980$	4166.46	−	3730.73i	0.135809	−	0.121606i
$981$	5832.99	+	3367.68i	0.189840	+	0.109604i
$982$	4912.73	+	10107.9i	0.159645	+	0.328470i
$983$	5846.84	+	33159.1i	0.189710	+	1.07590i	0.919752	+	0.392499i	$0.128389\pi$
$983$	5846.84	+	33159.1i	0.189710	+	1.07590i	−0.730042	+	0.683402i	$0.760500\pi$
$984$	4903.41	−	668.448i	0.158857	−	0.0216558i
$985$	−6419.20	−	2336.40i	−0.207647	−	0.0755774i
$986$	4497.82	+	4355.50i	0.145274	+	0.140677i
$987$			1670.95i			0.0538876i
$988$	19563.2	+	24978.8i	0.629947	+	0.804333i
$989$			23733.5i			0.763074i
$990$	763.298	−	788.239i	0.0245042	−	0.0253049i
$991$	24521.9	+	8925.25i	0.786039	+	0.286095i	0.703688	−	0.710509i	$-0.251535\pi$
$991$	24521.9	+	8925.25i	0.786039	+	0.286095i	0.0823504	+	0.996603i	$0.473757\pi$
$992$	262.469	+	736.904i	0.00840062	+	0.0235854i
$993$	−4429.66	−	25121.9i	−0.141562	−	0.802838i
$994$	−6433.65	+	3126.92i	−0.205295	+	0.0997786i
$995$	−2654.04	−	1532.31i	−0.0845614	−	0.0488216i
$996$	−17721.2	−	19790.9i	−0.563773	−	0.629618i
$997$	24179.4	−	28815.9i	0.768074	−	0.915355i	−0.230255	−	0.973130i	$-0.573956\pi$
$997$	24179.4	−	28815.9i	0.768074	−	0.915355i	0.998330	+	0.0577751i	$0.0184006\pi$
$998$	10015.3	−	14804.1i	0.317663	−	0.469556i
$999$	−26533.1	−	45956.7i	−0.840311	−	1.45546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.t.a.101.15	yes	348
8.5	even	2	inner	152.4.t.a.101.12	✓	348
19.16	even	9	inner	152.4.t.a.149.12	yes	348
152.149	even	18	inner	152.4.t.a.149.15	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.t.a.101.12	✓	348	8.5	even	2	inner
152.4.t.a.101.15	yes	348	1.1	even	1	trivial
152.4.t.a.149.12	yes	348	19.16	even	9	inner
152.4.t.a.149.15	yes	348	152.149	even	18	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96760 + 2.03189i) q^{2} +(-1.12968 + 3.10377i) q^{3} +(-0.257137 - 7.99587i) q^{4} +(2.27970 - 0.401972i) q^{5} +(-4.08375 - 8.40233i) q^{6} +(3.20168 - 5.54548i) q^{7} +(16.7526 + 15.2102i) q^{8} +(12.3260 + 10.3428i) q^{9} +(-3.66876 + 5.42300i) q^{10} +(-9.01975 + 5.20756i) q^{11} +(25.1078 + 8.23466i) q^{12} +(16.3784 + 44.9994i) q^{13} +(4.96817 + 17.4167i) q^{14} +(-1.32770 + 7.52974i) q^{15} +(-63.8678 + 4.11207i) q^{16} +(-9.18576 + 7.70777i) q^{17} +(-45.2679 + 4.69472i) q^{18} +(23.1416 + 79.5202i) q^{19} +(-3.80031 - 18.1248i) q^{20} +(13.5950 + 16.2019i) q^{21} +(7.16605 - 28.5735i) q^{22} +(24.0217 - 136.234i) q^{23} +(-66.1339 + 34.8137i) q^{24} +(-112.426 + 40.9198i) q^{25} +(-123.660 - 55.2614i) q^{26} +(-123.258 + 71.1630i) q^{27} +(-45.1642 - 24.1743i) q^{28} +(-118.661 + 141.415i) q^{29} +(-12.6872 - 17.5132i) q^{30} +(-2.16068 + 3.74241i) q^{31} +(117.311 - 137.863i) q^{32} +(-5.97362 - 33.8781i) q^{33} +(2.41254 - 33.8302i) q^{34} +(5.06974 - 13.9290i) q^{35} +(79.5298 - 101.217i) q^{36} +372.850i q^{37} +(-207.110 - 109.442i) q^{38} -158.170 q^{39} +(44.3050 + 27.9404i) q^{40} +(-62.2220 - 22.6470i) q^{41} +(-59.6699 - 4.25524i) q^{42} +(-168.958 + 29.7919i) q^{43} +(43.9582 + 70.7817i) q^{44} +(32.2571 + 18.6236i) q^{45} +(229.546 + 316.862i) q^{46} +(60.5211 + 50.7833i) q^{47} +(59.3871 - 202.876i) q^{48} +(150.998 + 261.537i) q^{49} +(138.065 - 308.951i) q^{50} +(-13.5462 - 37.2178i) q^{51} +(355.597 - 142.531i) q^{52} +(316.894 + 55.8770i) q^{53} +(97.9265 - 390.466i) q^{54} +(-18.4690 + 15.4973i) q^{55} +(137.984 - 44.2033i) q^{56} +(-272.955 - 18.0061i) q^{57} +(-53.8620 - 519.353i) q^{58} +(-55.5836 - 66.2420i) q^{59} +(60.5482 + 8.67991i) q^{60} +(691.438 + 121.919i) q^{61} +(-3.35282 - 11.7538i) q^{62} +(96.8195 - 35.2394i) q^{63} +(49.3023 + 509.621i) q^{64} +(55.4263 + 96.0012i) q^{65} +(80.5901 + 54.5206i) q^{66} +(197.722 - 235.636i) q^{67} +(63.9923 + 71.4662i) q^{68} +(395.700 + 228.458i) q^{69} +(18.3270 + 37.7078i) q^{70} +(68.5839 + 388.959i) q^{71} +(49.1785 + 360.749i) q^{72} +(-408.524 - 148.691i) q^{73} +(-757.589 - 733.618i) q^{74} -395.171i q^{75} +(629.882 - 205.485i) q^{76} +66.6918i q^{77} +(311.214 - 321.383i) q^{78} +(271.509 + 98.8213i) q^{79} +(-143.946 + 35.0473i) q^{80} +(-6.19131 - 35.1127i) q^{81} +(168.444 - 81.8681i) q^{82} +(-870.671 - 502.682i) q^{83} +(126.052 - 112.870i) q^{84} +(-17.8424 + 21.2638i) q^{85} +(271.908 - 401.923i) q^{86} +(-304.870 - 528.050i) q^{87} +(-230.313 - 49.9515i) q^{88} +(1305.85 - 475.291i) q^{89} +(-101.310 + 28.8990i) q^{90} +(301.982 + 53.2475i) q^{91} +(-1095.48 - 157.043i) q^{92} +(-9.17470 - 10.9340i) q^{93} +(-222.267 + 23.0513i) q^{94} +(84.7208 + 171.980i) q^{95} +(295.371 + 519.846i) q^{96} +(582.397 - 488.689i) q^{97} +(-828.518 - 207.787i) q^{98} +(-165.038 - 29.1007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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