LMFDB - Embedded newform 241.4.i.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,4,Mod(4,241)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("241.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	241.i (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.2194603114$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	241.4
Dual form			241.4.i.a.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.60313 + 2.08027i) q^{2} +(2.14174 + 1.23654i) q^{3} +(4.65504 - 8.06276i) q^{4} +19.0905i q^{5} -10.2893 q^{6} +(-0.517826 + 1.93255i) q^{7} +5.45061i q^{8} +(-10.4420 - 18.0860i) q^{9} +O(q^{10})$	\(q+(-3.60313 + 2.08027i) q^{2} +(2.14174 + 1.23654i) q^{3} +(4.65504 - 8.06276i) q^{4} +19.0905i q^{5} -10.2893 q^{6} +(-0.517826 + 1.93255i) q^{7} +5.45061i q^{8} +(-10.4420 - 18.0860i) q^{9} +(-39.7135 - 68.7857i) q^{10} +(-11.8601 + 44.2626i) q^{11} +(19.9398 - 11.5122i) q^{12} +(-18.6946 - 69.7692i) q^{13} +(-2.15444 - 8.04046i) q^{14} +(-23.6062 + 40.8871i) q^{15} +(25.9016 + 44.8628i) q^{16} +(-69.1782 + 69.1782i) q^{17} +(75.2475 + 43.4441i) q^{18} +(20.7187 - 77.3232i) q^{19} +(153.923 + 88.8672i) q^{20} +(-3.49872 + 3.49872i) q^{21} +(-49.3445 - 184.156i) q^{22} +(36.5446 + 36.5446i) q^{23} +(-6.73988 + 11.6738i) q^{24} -239.449 q^{25} +(212.498 + 212.498i) q^{26} -118.420i q^{27} +(13.1712 + 13.1712i) q^{28} +(-193.452 + 111.689i) q^{29} -196.429i q^{30} +(31.7931 + 8.51893i) q^{31} +(-224.416 - 129.567i) q^{32} +(-80.1336 + 80.1336i) q^{33} +(105.349 - 393.167i) q^{34} +(-36.8935 - 9.88558i) q^{35} -194.431 q^{36} +(-67.7932 + 253.008i) q^{37} +(86.2009 + 321.706i) q^{38} +(46.2331 - 172.544i) q^{39} -104.055 q^{40} -365.105i q^{41} +(5.32808 - 19.8847i) q^{42} +(325.811 - 325.811i) q^{43} +(301.669 + 301.669i) q^{44} +(345.272 - 199.343i) q^{45} +(-207.698 - 55.6525i) q^{46} -610.320i q^{47} +128.113i q^{48} +(293.580 + 169.499i) q^{49} +(862.766 - 498.118i) q^{50} +(-233.703 + 62.6206i) q^{51} +(-649.556 - 174.048i) q^{52} +(143.068 + 82.6001i) q^{53} +(246.346 + 426.684i) q^{54} +(-844.996 - 226.416i) q^{55} +(-10.5336 - 2.82247i) q^{56} +(139.987 - 139.987i) q^{57} +(464.688 - 804.863i) q^{58} +(-187.767 + 108.407i) q^{59} +(219.775 + 380.662i) q^{60} -173.040i q^{61} +(-132.276 + 35.4433i) q^{62} +(40.3593 - 10.8142i) q^{63} +663.711 q^{64} +(1331.93 - 356.890i) q^{65} +(122.032 - 455.431i) q^{66} +(-307.832 + 177.727i) q^{67} +(235.740 + 879.794i) q^{68} +(33.0805 + 123.458i) q^{69} +(153.497 - 41.1293i) q^{70} +(98.7791 + 26.4678i) q^{71} +(98.5797 - 56.9150i) q^{72} +(-332.959 - 332.959i) q^{73} +(-282.056 - 1052.65i) q^{74} +(-512.838 - 296.087i) q^{75} +(-526.992 - 526.992i) q^{76} +(-79.3983 - 45.8406i) q^{77} +(192.355 + 717.877i) q^{78} -520.343i q^{79} +(-856.456 + 494.475i) q^{80} +(-135.502 + 234.696i) q^{81} +(759.516 + 1315.52i) q^{82} +(368.330 + 637.965i) q^{83} +(11.9227 + 44.4961i) q^{84} +(-1320.65 - 1320.65i) q^{85} +(-496.165 + 1851.71i) q^{86} -552.432 q^{87} +(-241.258 - 64.6449i) q^{88} +(-1314.91 - 352.328i) q^{89} +(-829.372 + 1436.52i) q^{90} +144.513 q^{91} +(464.767 - 124.534i) q^{92} +(57.5587 + 57.5587i) q^{93} +(1269.63 + 2199.06i) q^{94} +(1476.14 + 395.531i) q^{95} +(-320.428 - 554.998i) q^{96} +(-859.561 + 1488.80i) q^{97} -1410.41 q^{98} +(924.375 - 247.686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{2} - 6 q^{3} + 490 q^{4} - 168 q^{6} - 48 q^{7} + 1110 q^{9}+O(q^{10}) $ 240 * q - 6 * q^2 - 6 * q^3 + 490 * q^4 - 168 * q^6 - 48 * q^7 + 1110 * q^9	\( 240 q - 6 q^{2} - 6 q^{3} + 490 q^{4} - 168 q^{6} - 48 q^{7} + 1110 q^{9} - 30 q^{10} + 124 q^{11} - 54 q^{12} - 12 q^{13} + 176 q^{14} - 68 q^{15} - 2134 q^{16} + 244 q^{17} - 168 q^{18} + 422 q^{19} + 378 q^{20} - 198 q^{21} - 382 q^{22} + 256 q^{23} - 876 q^{24} - 6856 q^{25} + 158 q^{26} - 76 q^{28} - 486 q^{29} - 1172 q^{31} - 132 q^{32} + 466 q^{33} + 116 q^{34} + 676 q^{35} + 10348 q^{36} + 28 q^{37} - 194 q^{38} - 646 q^{39} - 708 q^{40} + 664 q^{42} + 638 q^{43} + 904 q^{44} - 624 q^{45} + 984 q^{46} - 4782 q^{49} + 6024 q^{50} + 54 q^{51} - 1580 q^{52} - 294 q^{53} - 2006 q^{54} + 172 q^{55} + 3268 q^{56} + 1550 q^{57} - 2628 q^{58} - 972 q^{59} + 276 q^{60} + 4742 q^{62} + 1564 q^{63} - 19920 q^{64} + 1140 q^{65} - 2884 q^{66} - 546 q^{67} + 5230 q^{68} - 6138 q^{69} + 1920 q^{70} + 1460 q^{71} + 9612 q^{72} + 2798 q^{73} - 5346 q^{74} - 1002 q^{75} + 4076 q^{76} - 54 q^{77} + 836 q^{78} + 4362 q^{80} - 5156 q^{81} - 362 q^{82} - 1052 q^{83} + 3832 q^{84} - 2088 q^{85} + 10678 q^{86} + 1436 q^{87} + 5326 q^{88} - 2070 q^{89} + 194 q^{90} - 1752 q^{91} - 4014 q^{92} - 618 q^{93} + 1206 q^{94} + 1140 q^{95} + 11508 q^{96} - 1352 q^{97} + 8460 q^{98} + 5686 q^{99}+O(q^{100}) \) 240 * q - 6 * q^2 - 6 * q^3 + 490 * q^4 - 168 * q^6 - 48 * q^7 + 1110 * q^9 - 30 * q^10 + 124 * q^11 - 54 * q^12 - 12 * q^13 + 176 * q^14 - 68 * q^15 - 2134 * q^16 + 244 * q^17 - 168 * q^18 + 422 * q^19 + 378 * q^20 - 198 * q^21 - 382 * q^22 + 256 * q^23 - 876 * q^24 - 6856 * q^25 + 158 * q^26 - 76 * q^28 - 486 * q^29 - 1172 * q^31 - 132 * q^32 + 466 * q^33 + 116 * q^34 + 676 * q^35 + 10348 * q^36 + 28 * q^37 - 194 * q^38 - 646 * q^39 - 708 * q^40 + 664 * q^42 + 638 * q^43 + 904 * q^44 - 624 * q^45 + 984 * q^46 - 4782 * q^49 + 6024 * q^50 + 54 * q^51 - 1580 * q^52 - 294 * q^53 - 2006 * q^54 + 172 * q^55 + 3268 * q^56 + 1550 * q^57 - 2628 * q^58 - 972 * q^59 + 276 * q^60 + 4742 * q^62 + 1564 * q^63 - 19920 * q^64 + 1140 * q^65 - 2884 * q^66 - 546 * q^67 + 5230 * q^68 - 6138 * q^69 + 1920 * q^70 + 1460 * q^71 + 9612 * q^72 + 2798 * q^73 - 5346 * q^74 - 1002 * q^75 + 4076 * q^76 - 54 * q^77 + 836 * q^78 + 4362 * q^80 - 5156 * q^81 - 362 * q^82 - 1052 * q^83 + 3832 * q^84 - 2088 * q^85 + 10678 * q^86 + 1436 * q^87 + 5326 * q^88 - 2070 * q^89 + 194 * q^90 - 1752 * q^91 - 4014 * q^92 - 618 * q^93 + 1206 * q^94 + 1140 * q^95 + 11508 * q^96 - 1352 * q^97 + 8460 * q^98 + 5686 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	−3.60313	+	2.08027i	−1.27390	+	0.735486i	−0.975720	−	0.219024i	$-0.929713\pi$
$2$	−3.60313	+	2.08027i	−1.27390	+	0.735486i	−0.298180	+	0.954510i	$0.596379\pi$
$3$	2.14174	+	1.23654i	0.412179	+	0.237972i	0.691725	−	0.722161i	$-0.256851\pi$
$3$	2.14174	+	1.23654i	0.412179	+	0.237972i	−0.279547	+	0.960132i	$0.590184\pi$
$4$	4.65504	−	8.06276i	0.581880	−	1.00785i
$5$			19.0905i			1.70751i	0.520675	+	0.853755i	$0.325680\pi$
$5$			19.0905i			1.70751i	−0.520675	+	0.853755i	$0.674320\pi$
$6$	−10.2893			−0.700099
$7$	−0.517826	+	1.93255i	−0.0279600	+	0.104348i	−0.978496	−	0.206267i	$-0.933868\pi$
$7$	−0.517826	+	1.93255i	−0.0279600	+	0.104348i	0.950536	+	0.310615i	$0.100535\pi$
$8$			5.45061i			0.240885i
$9$	−10.4420	−	18.0860i	−0.386739	−	0.669852i
$10$	−39.7135	−	68.7857i	−1.25585	−	2.17520i
$11$	−11.8601	+	44.2626i	−0.325087	+	1.21324i	0.589137	+	0.808033i	$0.299468\pi$
$11$	−11.8601	+	44.2626i	−0.325087	+	1.21324i	−0.914224	+	0.405209i	$0.867199\pi$
$12$	19.9398	−	11.5122i	0.479677	−	0.276942i
$13$	−18.6946	−	69.7692i	−0.398842	−	1.48850i	−0.815136	−	0.579269i	$-0.803338\pi$
$13$	−18.6946	−	69.7692i	−0.398842	−	1.48850i	0.416294	−	0.909230i	$-0.363329\pi$
$14$	−2.15444	−	8.04046i	−0.0411284	−	0.153493i
$15$	−23.6062	+	40.8871i	−0.406339	+	0.703800i
$16$	25.9016	+	44.8628i	0.404712	+	0.700981i
$17$	−69.1782	+	69.1782i	−0.986951	+	0.986951i	−0.999916	−	0.0129647i	$-0.995873\pi$
$17$	−69.1782	+	69.1782i	−0.986951	+	0.986951i	0.0129647	+	0.999916i	$0.495873\pi$
$18$	75.2475	+	43.4441i	0.985333	+	0.568882i
$19$	20.7187	−	77.3232i	0.250168	−	0.933640i	−0.720547	−	0.693406i	$-0.756109\pi$
$19$	20.7187	−	77.3232i	0.250168	−	0.933640i	0.970715	−	0.240234i	$-0.0772242\pi$
$20$	153.923	+	88.8672i	1.72091	+	0.993565i
$21$	−3.49872	+	3.49872i	−0.0363564	+	0.0363564i
$22$	−49.3445	−	184.156i	−0.478194	−	1.78465i
$23$	36.5446	+	36.5446i	0.331308	+	0.331308i	0.853083	−	0.521775i	$-0.174730\pi$
$23$	36.5446	+	36.5446i	0.331308	+	0.331308i	−0.521775	+	0.853083i	$0.674730\pi$
$24$	−6.73988	+	11.6738i	−0.0573238	+	0.0992878i
$25$	−239.449			−1.91559
$26$	212.498	+	212.498i	1.60286	+	1.60286i
$27$		−	118.420i		−	0.844075i
$28$	13.1712	+	13.1712i	0.0888974	+	0.0888974i
$29$	−193.452	+	111.689i	−1.23873	+	0.715179i	−0.968834	−	0.247712i	$-0.920321\pi$
$29$	−193.452	+	111.689i	−1.23873	+	0.715179i	−0.269892	+	0.962891i	$0.586988\pi$
$30$		−	196.429i		−	1.19543i
$31$	31.7931	+	8.51893i	0.184200	+	0.0493563i	0.349740	−	0.936847i	$-0.386270\pi$
$31$	31.7931	+	8.51893i	0.184200	+	0.0493563i	−0.165540	+	0.986203i	$0.552937\pi$
$32$	−224.416	−	129.567i	−1.23974	−	0.715763i
$33$	−80.1336	+	80.1336i	−0.422711	+	0.422711i
$34$	105.349	−	393.167i	0.531388	−	1.98317i
$35$	−36.8935	−	9.88558i	−0.178175	−	0.0477420i
$36$	−194.431			−0.900142
$37$	−67.7932	+	253.008i	−0.301220	+	1.12417i	0.634931	+	0.772569i	$0.281029\pi$
$37$	−67.7932	+	253.008i	−0.301220	+	1.12417i	−0.936151	+	0.351599i	$0.885638\pi$
$38$	86.2009	+	321.706i	0.367990	+	1.37336i
$39$	46.2331	−	172.544i	0.189826	−	0.708441i
$40$	−104.055			−0.411314
$41$		−	365.105i		−	1.39073i	−0.718659	−	0.695363i	$-0.755244\pi$
$41$		−	365.105i		−	1.39073i	0.718659	−	0.695363i	$-0.244756\pi$
$42$	5.32808	−	19.8847i	0.0195748	−	0.0730540i
$43$	325.811	−	325.811i	1.15548	−	1.15548i	0.170044	−	0.985436i	$-0.445609\pi$
$43$	325.811	−	325.811i	1.15548	−	1.15548i	0.985436	−	0.170044i	$-0.0543911\pi$
$44$	301.669	+	301.669i	1.03360	+	1.03360i
$45$	345.272	−	199.343i	1.14378	−	0.660361i
$46$	−207.698	−	55.6525i	−0.665725	−	0.178381i
$47$		−	610.320i		−	1.89413i	−0.321037	−	0.947067i	$-0.604031\pi$
$47$		−	610.320i		−	1.89413i	0.321037	−	0.947067i	$-0.395969\pi$
$48$			128.113i			0.385240i
$49$	293.580	+	169.499i	0.855919	+	0.494165i
$50$	862.766	−	498.118i	2.44027	−	1.40889i
$51$	−233.703	+	62.6206i	−0.641667	+	0.171934i
$52$	−649.556	−	174.048i	−1.73225	−	0.464156i
$53$	143.068	+	82.6001i	0.370790	+	0.214075i	0.673803	−	0.738911i	$-0.264659\pi$
$53$	143.068	+	82.6001i	0.370790	+	0.214075i	−0.303014	+	0.952986i	$0.597993\pi$
$54$	246.346	+	426.684i	0.620805	+	1.07527i
$55$	−844.996	−	226.416i	−2.07162	−	0.555090i
$56$	−10.5336	−	2.82247i	−0.0251359	−	0.00673515i
$57$	139.987	−	139.987i	0.325294	−	0.325294i
$58$	464.688	−	804.863i	1.05201	−	1.82213i
$59$	−187.767	+	108.407i	−0.414324	+	0.239210i	−0.692646	−	0.721278i	$-0.743555\pi$
$59$	−187.767	+	108.407i	−0.414324	+	0.239210i	0.278322	+	0.960488i	$0.410222\pi$
$60$	219.775	+	380.662i	0.472881	+	0.819053i
$61$		−	173.040i		−	0.363206i	−0.983372	−	0.181603i	$-0.941872\pi$
$61$		−	173.040i		−	0.363206i	0.983372	−	0.181603i	$-0.0581285\pi$
$62$	−132.276	+	35.4433i	−0.270953	+	0.0726017i
$63$	40.3593	−	10.8142i	0.0807110	−	0.0216264i
$64$	663.711			1.29631
$65$	1331.93	−	356.890i	2.54163	−	0.681027i
$66$	122.032	−	455.431i	0.227593	−	0.849390i
$67$	−307.832	+	177.727i	−0.561309	+	0.324072i	−0.753671	−	0.657252i	$-0.771719\pi$
$67$	−307.832	+	177.727i	−0.561309	+	0.324072i	0.192362	+	0.981324i	$0.438385\pi$
$68$	235.740	+	879.794i	0.420407	+	1.56898i
$69$	33.0805	+	123.458i	0.0577163	+	0.215400i
$70$	153.497	−	41.1293i	0.262091	−	0.0702271i
$71$	98.7791	+	26.4678i	0.165112	+	0.0442415i	0.340428	−	0.940271i	$-0.389428\pi$
$71$	98.7791	+	26.4678i	0.165112	+	0.0442415i	−0.175316	+	0.984512i	$0.556095\pi$
$72$	98.5797	−	56.9150i	0.161357	−	0.0931597i
$73$	−332.959	−	332.959i	−0.533834	−	0.533834i	0.387877	−	0.921711i	$-0.373208\pi$
$73$	−332.959	−	332.959i	−0.533834	−	0.533834i	−0.921711	+	0.387877i	$0.873208\pi$
$74$	−282.056	−	1052.65i	−0.443086	−	1.65362i
$75$	−512.838	−	296.087i	−0.789566	−	0.455856i
$76$	−526.992	−	526.992i	−0.795397	−	0.795397i
$77$	−79.3983	−	45.8406i	−0.117510	−	0.0678445i
$78$	192.355	+	717.877i	0.279229	+	1.04210i
$79$		−	520.343i		−	0.741052i	−0.928822	−	0.370526i	$-0.879177\pi$
$79$		−	520.343i		−	0.741052i	0.928822	−	0.370526i	$-0.120823\pi$
$80$	−856.456	+	494.475i	−1.19693	+	0.691050i
$81$	−135.502	+	234.696i	−0.185873	+	0.321942i
$82$	759.516	+	1315.52i	1.02286	+	1.77165i
$83$	368.330	+	637.965i	0.487101	+	0.843684i	0.999890	−	0.0148305i	$-0.00472088\pi$
$83$	368.330	+	637.965i	0.487101	+	0.843684i	−0.512789	+	0.858515i	$0.671388\pi$
$84$	11.9227	+	44.4961i	0.0154866	+	0.0577967i
$85$	−1320.65	−	1320.65i	−1.68523	−	1.68523i
$86$	−496.165	+	1851.71i	−0.622126	+	2.32181i
$87$	−552.432			−0.680769
$88$	−241.258	−	64.6449i	−0.292252	−	0.0783087i
$89$	−1314.91	−	352.328i	−1.56606	−	0.419626i	−0.631487	−	0.775386i	$-0.717555\pi$
$89$	−1314.91	−	352.328i	−1.56606	−	0.419626i	−0.934577	+	0.355760i	$0.884222\pi$
$90$	−829.372	+	1436.52i	−0.971373	+	1.68247i
$91$	144.513			0.166474
$92$	464.767	−	124.534i	0.526688	−	0.141126i
$93$	57.5587	+	57.5587i	0.0641780	+	0.0641780i
$94$	1269.63	+	2199.06i	1.39311	+	2.41294i
$95$	1476.14	+	395.531i	1.59420	+	0.427165i
$96$	−320.428	−	554.998i	−0.340662	−	0.590044i
$97$	−859.561	+	1488.80i	−0.899744	+	1.55840i	−0.0719236	+	0.997410i	$0.522914\pi$
$97$	−859.561	+	1488.80i	−0.899744	+	1.55840i	−0.827821	+	0.560993i	$0.810420\pi$
$98$	−1410.41			−1.45381
$99$	924.375	−	247.686i	0.938416	−	0.251448i
$100$	−1114.64	+	1930.62i	−1.11464	+	1.93062i
$101$	−373.371	+	373.371i	−0.367840	+	0.367840i	−0.866689	−	0.498849i	$-0.833756\pi$
$101$	−373.371	+	373.371i	−0.367840	+	0.367840i	0.498849	+	0.866689i	$0.333756\pi$
$102$	711.796	−	711.796i	0.690964	−	0.690964i
$103$	−858.568	−	858.568i	−0.821332	−	0.821332i	0.164967	−	0.986299i	$-0.447248\pi$
$103$	−858.568	−	858.568i	−0.821332	−	0.821332i	−0.986299	+	0.164967i	$0.947248\pi$
$104$	380.285	−	101.897i	0.358557	−	0.0960752i
$105$	−66.7926	−	66.7926i	−0.0620789	−	0.0620789i
$106$	−687.322			−0.629798
$107$	−470.651	+	815.191i	−0.425229	+	0.736519i	−0.996442	−	0.0842835i	$-0.973140\pi$
$107$	−470.651	+	815.191i	−0.425229	+	0.736519i	0.571213	+	0.820802i	$0.306473\pi$
$108$	−954.795	−	551.251i	−0.850697	−	0.491150i
$109$	−241.951	−	902.973i	−0.212612	−	0.793479i	−0.986994	−	0.160760i	$-0.948606\pi$
$109$	−241.951	−	902.973i	−0.212612	−	0.793479i	0.774382	−	0.632719i	$-0.218061\pi$
$110$	3515.64	−	942.013i	3.04730	−	0.816522i
$111$	−458.049	+	458.049i	−0.391676	+	0.391676i
$112$	−100.112	+	26.8250i	−0.0844618	+	0.0226315i
$113$	1101.52	−	635.965i	0.917014	−	0.529438i	0.0343328	−	0.999410i	$-0.489069\pi$
$113$	1101.52	−	635.965i	0.917014	−	0.529438i	0.882681	+	0.469972i	$0.155736\pi$
$114$	−213.181	+	795.603i	−0.175143	+	0.653641i
$115$	−697.657	+	697.657i	−0.565712	+	0.565712i
$116$			2079.67i			1.66459i
$117$	−1066.64	+	1066.64i	−0.842826	+	0.842826i
$118$	451.032	−	781.210i	0.351872	−	0.609460i
$119$	−97.8683	−	169.513i	−0.0753913	−	0.130582i
$120$	−222.859	−	128.668i	−0.169535	−	0.0978811i
$121$	−665.832	−	384.418i	−0.500250	−	0.288819i
$122$	359.970	+	623.487i	0.267133	+	0.462687i
$123$	451.465	−	781.961i	0.330953	−	0.573228i
$124$	216.684	−	216.684i	0.156926	−	0.156926i
$125$		−	2184.89i		−	1.56338i
$126$	−122.923	+	122.923i	−0.0869117	+	0.0869117i
$127$	−222.234	+	829.388i	−0.155276	+	0.579498i	0.843806	+	0.536649i	$0.180310\pi$
$127$	−222.234	+	829.388i	−0.155276	+	0.579498i	−0.999082	+	0.0428490i	$0.986357\pi$
$128$	−596.106	+	344.162i	−0.411631	+	0.237655i
$129$	1100.68	−	294.926i	0.751236	−	0.201293i
$130$	−4056.70	+	4056.70i	−2.73689	+	2.73689i
$131$	−159.994	+	42.8702i	−0.106708	+	0.0285923i	−0.311778	−	0.950155i	$-0.600924\pi$
$131$	−159.994	+	42.8702i	−0.106708	+	0.0285923i	0.205070	+	0.978747i	$0.434258\pi$
$132$	273.073	+	1019.12i	0.180060	+	0.671995i
$133$	138.703	+	80.0800i	0.0904289	+	0.0522091i
$134$	739.440	−	1280.75i	0.476701	−	0.825670i
$135$	2260.71			1.44127
$136$	−377.063	−	377.063i	−0.237742	−	0.237742i
$137$	2872.90	−	769.791i	1.79159	−	0.480056i	0.798977	−	0.601361i	$-0.205375\pi$
$137$	2872.90	−	769.791i	1.79159	−	0.480056i	0.992615	+	0.121305i	$0.0387080\pi$
$138$	−376.019	−	376.019i	−0.231948	−	0.231948i
$139$	−1467.96	+	1467.96i	−0.895761	+	0.895761i	−0.995058	−	0.0992971i	$-0.968341\pi$
$139$	−1467.96	+	1467.96i	−0.895761	+	0.895761i	0.0992971	+	0.995058i	$0.468341\pi$
$140$	−251.446	+	251.446i	−0.151793	+	0.151793i
$141$	754.683	−	1307.15i	0.450750	−	0.780722i
$142$	−410.974	+	110.120i	−0.242875	+	0.0650780i
$143$	3309.88			1.93557
$144$	540.926	−	936.911i	0.313036	−	0.542194i
$145$	−2132.21	−	3693.10i	−1.22118	−	2.11514i
$146$	1892.34	+	507.050i	1.07268	+	0.287423i
$147$	419.182	+	726.045i	0.235194	+	0.407369i
$148$	1724.36	+	1724.36i	0.957713	+	0.957713i
$149$	−2728.95	+	731.221i	−1.50043	+	0.402040i	−0.913245	−	0.407411i	$-0.866432\pi$
$149$	−2728.95	+	731.221i	−1.50043	+	0.402040i	−0.587188	+	0.809451i	$0.699765\pi$
$150$	2463.77			1.34110
$151$	−227.545	+	394.119i	−0.122631	+	0.212404i	−0.920805	−	0.390024i	$-0.872467\pi$
$151$	−227.545	+	394.119i	−0.122631	+	0.212404i	0.798173	+	0.602428i	$0.205800\pi$
$152$	421.459	+	112.930i	0.224900	+	0.0602618i
$153$	1973.51	+	528.801i	1.04280	+	0.279418i
$154$	381.443			0.199595
$155$	−162.631	+	606.947i	−0.0842764	+	0.314524i
$156$	−1175.97	−	1175.97i	−0.603543	−	0.603543i
$157$	601.563	+	2245.06i	0.305796	+	1.14125i	0.932258	+	0.361794i	$0.117836\pi$
$157$	601.563	+	2245.06i	0.305796	+	1.14125i	−0.626462	+	0.779452i	$0.715498\pi$
$158$	1082.45	+	1874.86i	0.545033	+	0.944026i
$159$	204.276	+	353.817i	0.101888	+	0.176475i
$160$	2473.50	−	4284.23i	1.22217	−	2.11686i
$161$	−89.5482	+	51.7007i	−0.0438347	+	0.0253080i
$162$		−	1127.52i		−	0.546829i
$163$	821.537	+	3066.02i	0.394771	+	1.47331i	0.822169	+	0.569243i	$0.192764\pi$
$163$	821.537	+	3066.02i	0.394771	+	1.47331i	−0.427398	+	0.904064i	$0.640570\pi$
$164$	−2943.75	−	1699.58i	−1.40164	−	0.809235i
$165$	−1529.79	−	1529.79i	−0.721784	−	0.721784i
$166$	−2654.28	−	1532.45i	−1.24104	−	0.716513i
$167$	−309.159	−	1153.80i	−0.143254	−	0.534631i	−0.999827	−	0.0186052i	$-0.994077\pi$
$167$	−309.159	−	1153.80i	−0.143254	−	0.534631i	0.856573	−	0.516026i	$-0.172589\pi$
$168$	−19.0702	−	19.0702i	−0.00875772	−	0.00875772i
$169$	−2615.59	+	1510.11i	−1.19053	+	0.687352i
$170$	7505.78	+	2011.17i	3.38628	+	0.907350i
$171$	−1614.81	+	432.687i	−0.722150	+	0.193500i
$172$	−1110.27	−	4143.60i	−0.492195	−	1.83690i
$173$	−468.124	−	1747.06i	−0.205727	−	0.767784i	−0.989227	−	0.146392i	$-0.953234\pi$
$173$	−468.124	−	1747.06i	−0.205727	−	0.767784i	0.783500	−	0.621392i	$-0.213433\pi$
$174$	1990.48	−	1149.21i	0.867231	−	0.500696i
$175$	123.993	−	462.748i	0.0535599	−	0.199888i
$176$	−2292.94	+	614.391i	−0.982027	+	0.263133i
$177$	−536.198			−0.227701
$178$	5470.72	−	1465.87i	2.30364	−	0.617258i
$179$	−2724.44	+	730.012i	−1.13762	+	0.304825i	−0.777995	−	0.628271i	$-0.783763\pi$
$179$	−2724.44	+	730.012i	−1.13762	+	0.304825i	−0.359628	+	0.933096i	$0.617096\pi$
$180$		−	3711.79i		−	1.53700i
$181$	−790.627	−	1369.41i	−0.324679	−	0.562360i	0.656768	−	0.754092i	$-0.271923\pi$
$181$	−790.627	−	1369.41i	−0.324679	−	0.562360i	−0.981447	+	0.191732i	$0.938590\pi$
$182$	−520.700	+	300.626i	−0.212071	+	0.122439i
$183$	213.971	−	370.608i	0.0864326	−	0.149706i
$184$	−199.191	+	199.191i	−0.0798072	+	0.0798072i
$185$	−4830.05	−	1294.21i	−1.91953	−	0.514336i
$186$	−327.129	−	87.6540i	−0.128958	−	0.0345543i
$187$	−2241.54	−	3882.46i	−0.876566	−	1.51826i
$188$	−4920.86	−	2841.06i	−1.90899	−	1.10216i
$189$	228.854	+	61.3212i	0.0880776	+	0.0236003i
$190$	−6141.55	+	1645.62i	−2.34502	+	0.628348i
$191$	−3144.89	+	1815.70i	−1.19139	+	0.687851i	−0.958623	−	0.284680i	$-0.908113\pi$
$191$	−3144.89	+	1815.70i	−1.19139	+	0.687851i	−0.232771	+	0.972532i	$0.574779\pi$
$192$	1421.50	+	820.702i	0.534312	+	0.308485i
$193$		−	219.201i		−	0.0817534i	−0.999164	−	0.0408767i	$-0.986985\pi$
$193$		−	219.201i		−	0.0817534i	0.999164	−	0.0408767i	$-0.0130151\pi$
$194$		−	7152.47i		−	2.64700i
$195$	3293.96	+	882.615i	1.20967	+	0.324130i
$196$	2733.25	−	1578.04i	0.996083	−	0.575089i
$197$	−1467.96	−	1467.96i	−0.530902	−	0.530902i	0.389939	−	0.920841i	$-0.372496\pi$
$197$	−1467.96	−	1467.96i	−0.530902	−	0.530902i	−0.920841	+	0.389939i	$0.872496\pi$
$198$	−2815.39	+	2815.39i	−1.01051	+	1.01051i
$199$	−647.693	+	2417.22i	−0.230722	+	0.861068i	0.749308	+	0.662221i	$0.230386\pi$
$199$	−647.693	+	2417.22i	−0.230722	+	0.861068i	−0.980031	+	0.198846i	$0.936281\pi$
$200$		−	1305.14i		−	0.461438i
$201$	−879.064			−0.308480
$202$	568.593	−	2122.02i	0.198050	−	0.739132i
$203$	−115.671	−	431.691i	−0.0399928	−	0.149255i
$204$	−583.003	+	2175.79i	−0.200090	+	0.746746i
$205$	6970.05			2.37468
$206$	4879.58	+	1307.48i	1.65037	+	0.442216i
$207$	279.349	−	1042.54i	0.0937975	−	0.350057i
$208$	2645.82	−	2645.82i	0.881994	−	0.881994i
$209$	3176.80	+	1834.13i	1.05141	+	0.607029i
$210$	379.609	+	101.716i	0.124740	+	0.0334241i
$211$			824.238i			0.268923i	0.990919	+	0.134462i	$0.0429305\pi$
$211$			824.238i			0.268923i	−0.990919	+	0.134462i	$0.957069\pi$
$212$	1331.97	−	769.013i	0.431510	−	0.249132i
$213$	178.831	+	178.831i	0.0575273	+	0.0575273i
$214$		−	3916.32i		−	1.25100i
$215$	6219.91	+	6219.91i	1.97300	+	1.97300i
$216$	645.464			0.203325
$217$	−32.9266	+	57.0305i	−0.0103005	+	0.0178409i
$218$	2750.21	+	2750.21i	0.854439	+	0.854439i
$219$	−301.397	−	1124.83i	−0.0929977	−	0.347072i
$220$	−5759.03	+	5759.03i	−1.76488	+	1.76488i
$221$	6119.76	+	3533.25i	1.86271	+	1.07544i
$222$	697.545	−	2603.28i	0.210884	−	0.787029i
$223$	−4205.95	−	2428.30i	−1.26301	−	0.729199i	−0.289354	−	0.957222i	$-0.593440\pi$
$223$	−4205.95	−	2428.30i	−1.26301	−	0.729199i	−0.973656	+	0.228024i	$0.926774\pi$
$224$	366.604	−	366.604i	0.109351	−	0.109351i
$225$	2500.32	+	4330.67i	0.740834	+	1.28316i
$226$	−2645.96	+	4582.93i	−0.778789	+	1.34890i
$227$	−530.165	−	1978.60i	−0.155015	−	0.578522i	−0.999104	−	0.0423199i	$-0.986525\pi$
$227$	−530.165	−	1978.60i	−0.155015	−	0.578522i	0.844090	−	0.536202i	$-0.180142\pi$
$228$	−477.038	−	1780.33i	−0.138564	−	0.517128i
$229$	−295.412	+	170.556i	−0.0852461	+	0.0492169i	−0.542017	−	0.840367i	$-0.682339\pi$
$229$	−295.412	+	170.556i	−0.0852461	+	0.0492169i	0.456771	+	0.889584i	$0.349006\pi$
$230$	1062.44	−	3965.06i	0.304587	−	1.13673i
$231$	−113.367	−	196.358i	−0.0322901	−	0.0559281i
$232$	−608.775	−	1054.43i	−0.172276	−	0.298391i
$233$		−	3153.68i		−	0.886714i	−0.896345	−	0.443357i	$-0.853787\pi$
$233$		−	3153.68i		−	0.886714i	0.896345	−	0.443357i	$-0.146213\pi$
$234$	1624.34	−	6062.12i	0.453789	−	1.69356i
$235$	11651.3			3.23425
$236$			2018.56i			0.556766i
$237$	643.423	−	1114.44i	0.176349	−	0.305446i
$238$	705.264	+	407.185i	0.192082	+	0.110899i
$239$	−3960.96	+	2286.86i	−1.07202	+	0.618932i	−0.928733	−	0.370749i	$-0.879101\pi$
$239$	−3960.96	+	2286.86i	−1.07202	+	0.618932i	−0.143288	+	0.989681i	$0.545768\pi$
$240$	−2445.75			−0.657801
$241$	−1767.98	−	3297.24i	−0.472555	−	0.881301i
$241$	−1767.98	−	3297.24i	−0.472555	−	0.881301i
$242$	3198.77			0.849690
$243$	−3349.41	+	1933.78i	−0.884216	+	0.510502i
$244$	−1395.18	−	805.509i	−0.366055	−	0.211342i
$245$	−3235.82	+	5604.60i	−0.843792	+	1.46149i
$246$			3756.68i			0.973646i
$247$	−5782.11			−1.48950
$248$	−46.4334	+	173.292i	−0.0118892	+	0.0443711i
$249$			1821.81i			0.463665i
$250$	4545.17	+	7872.46i	1.14985	+	1.99159i
$251$	−1290.27	−	2234.81i	−0.324466	−	0.561992i	0.656938	−	0.753945i	$-0.271851\pi$
$251$	−1290.27	−	2234.81i	−0.324466	−	0.561992i	−0.981404	+	0.191953i	$0.938518\pi$
$252$	100.681	−	375.748i	0.0251680	−	0.0939281i
$253$	−2050.98	+	1184.14i	−0.509661	+	0.294253i
$254$	−924.612	−	3450.70i	−0.228407	−	0.852426i
$255$	−1195.46	−	4461.52i	−0.293579	−	1.09565i
$256$	−1222.94	+	2118.20i	−0.298571	+	0.517139i
$257$	726.386	+	1258.14i	0.176306	+	0.305371i	0.940613	−	0.339482i	$-0.110252\pi$
$257$	726.386	+	1258.14i	0.176306	+	0.305371i	−0.764306	+	0.644853i	$0.776918\pi$
$258$	−3352.37	+	3352.37i	−0.808951	+	0.808951i
$259$	−453.846	−	262.028i	−0.108883	−	0.0628634i
$260$	3322.67	−	12400.4i	0.792552	−	2.95784i
$261$	4040.03	+	2332.51i	0.958127	+	0.553175i
$262$	487.297	−	487.297i	0.114906	−	0.114906i
$263$	−1192.30	−	4449.72i	−0.279545	−	1.04328i	−0.952734	−	0.303805i	$-0.901743\pi$
$263$	−1192.30	−	4449.72i	−0.279545	−	1.04328i	0.673189	−	0.739470i	$-0.264924\pi$
$264$	−436.777	−	436.777i	−0.101825	−	0.101825i
$265$	−1576.88	+	2731.24i	−0.365536	+	0.633127i
$266$	−666.352			−0.153596
$267$	−2380.53	−	2380.53i	−0.545640	−	0.545640i
$268$			3309.31i			0.754284i
$269$	−6.11976	−	6.11976i	−0.00138709	−	0.00138709i	0.706413	−	0.707800i	$-0.250312\pi$
$269$	−6.11976	−	6.11976i	−0.00138709	−	0.00138709i	−0.707800	+	0.706413i	$0.750312\pi$
$270$	−8145.64	+	4702.89i	−1.83603	+	1.06003i
$271$			5576.21i			1.24993i	0.780653	+	0.624965i	$0.214887\pi$
$271$			5576.21i			1.24993i	−0.780653	+	0.624965i	$0.785113\pi$
$272$	−4895.35	−	1311.71i	−1.09127	−	0.292404i
$273$	309.510	+	178.696i	0.0686169	+	0.0396160i
$274$	−8750.05	+	8750.05i	−1.92923	+	1.92923i
$275$	2839.89	−	10598.6i	0.622734	−	2.32408i
$276$	1149.40	+	307.982i	0.250674	+	0.0671678i
$277$	5997.98			1.30102			0.650512	−	0.759496i	$-0.274555\pi$
$277$	5997.98			1.30102			0.650512	+	0.759496i	$0.274555\pi$
$278$	2235.50	−	8343.00i	0.482289	−	1.79993i
$279$	−177.909	−	663.964i	−0.0381760	−	0.142475i
$280$	53.8825	−	201.092i	0.0115003	−	0.0429198i
$281$	−6239.97			−1.32472			−0.662359	−	0.749187i	$-0.730444\pi$
$281$	−6239.97			−1.32472			−0.662359	+	0.749187i	$0.730444\pi$
$282$			6279.77i			1.32608i
$283$	−1903.62	+	7104.41i	−0.399854	+	1.49227i	0.413500	+	0.910504i	$0.364306\pi$
$283$	−1903.62	+	7104.41i	−0.399854	+	1.49227i	−0.813353	+	0.581770i	$0.802360\pi$
$284$	673.224	−	673.224i	0.140664	−	0.140664i
$285$	2672.43	+	2672.43i	0.555443	+	0.555443i
$286$	−11925.9	+	6885.45i	−2.46572	+	1.42358i
$287$	705.584	+	189.061i	0.145120	+	0.0388847i
$288$			5411.72i			1.10725i
$289$		−	4658.24i		−	0.948146i
$290$	15365.3	+	8871.14i	3.11131	+	1.79631i
$291$	−3681.92	+	2125.76i	−0.741711	+	0.428227i
$292$	−4234.50	+	1134.63i	−0.848649	+	0.227395i
$293$	−142.457	−	38.1711i	−0.0284041	−	0.00761085i	0.244589	−	0.969627i	$-0.421347\pi$
$293$	−142.457	−	38.1711i	−0.0284041	−	0.00761085i	−0.272993	+	0.962016i	$0.588014\pi$
$294$	−3020.74	−	1744.02i	−0.599228	−	0.345964i
$295$	−2069.55	−	3584.57i	−0.408454	−	0.707463i
$296$	−1379.05	−	369.514i	−0.270795	−	0.0725594i
$297$	5241.59	+	1404.48i	1.02407	+	0.274398i
$298$	8311.64	−	8311.64i	1.61571	−	1.61571i
$299$	1866.50	−	3232.88i	0.361012	−	0.625291i
$300$	−4774.56	+	2756.60i	−0.918865	+	0.530507i
$301$	460.933	+	798.360i	0.0882650	+	0.152879i
$302$		−	1893.42i		−	0.360774i
$303$	−1261.35	+	337.979i	−0.239151	+	0.0640804i
$304$	4005.58	−	1073.29i	0.755711	−	0.202492i
$305$	3303.43			0.620177
$306$	−8210.87	+	2200.10i	−1.53394	+	0.411017i
$307$	1424.03	−	5314.55i	0.264735	−	0.988004i	−0.697677	−	0.716412i	$-0.745783\pi$
$307$	1424.03	−	5314.55i	0.264735	−	0.988004i	0.962412	−	0.271592i	$-0.0875502\pi$
$308$	−739.204	+	426.780i	−0.136753	+	0.0789546i
$309$	−777.182	−	2900.48i	−0.143082	−	0.533989i
$310$	−676.633	−	2525.23i	−0.123968	−	0.462656i
$311$	1436.25	−	384.842i	0.261872	−	0.0701685i	−0.125494	−	0.992094i	$-0.540052\pi$
$311$	1436.25	−	384.842i	0.261872	−	0.0701685i	0.387366	+	0.921926i	$0.373385\pi$
$312$	940.472	+	251.999i	0.170653	+	0.0457263i
$313$	4209.15	−	2430.16i	0.760113	−	0.438852i	−0.0692231	−	0.997601i	$-0.522052\pi$
$313$	4209.15	−	2430.16i	0.760113	−	0.438852i	0.829336	+	0.558750i	$0.188719\pi$
$314$	−6837.85	−	6837.85i	−1.22892	−	1.22892i
$315$	206.450	+	770.481i	0.0369274	+	0.137815i
$316$	−4195.40	−	2422.21i	−0.746866	−	0.431203i
$317$	531.359	+	531.359i	0.0941455	+	0.0941455i	0.752611	−	0.658465i	$-0.228794\pi$
$317$	531.359	+	531.359i	0.0941455	+	0.0941455i	−0.658465	+	0.752611i	$0.728794\pi$
$318$	−1472.07	−	849.899i	−0.259589	−	0.149874i
$319$	−2649.30	−	9887.31i	−0.464991	−	1.73537i
$320$			12670.6i			2.21346i
$321$	−2016.03	+	1163.95i	−0.350541	+	0.202385i
$322$	215.103	−	372.569i	0.0372273	−	0.0644796i
$323$	3915.80	+	6782.36i	0.674554	+	1.16836i
$324$	1261.53	+	2185.03i	0.216312	+	0.374663i
$325$	4476.40	+	16706.2i	0.764019	+	2.85136i
$326$	−9338.24	−	9338.24i	−1.58650	−	1.58650i
$327$	598.363	−	2233.12i	0.101191	−	0.377651i
$328$	1990.04			0.335005
$329$	1179.48	+	316.039i	0.197649	+	0.0529599i
$330$	8694.43	+	2329.67i	1.45034	+	0.388618i
$331$	289.055	−	500.659i	0.0479998	−	0.0831380i	−0.841027	−	0.540993i	$-0.818049\pi$
$331$	289.055	−	500.659i	0.0479998	−	0.0831380i	0.889027	+	0.457855i	$0.151382\pi$
$332$	6858.35			1.13374
$333$	5283.79	−	1415.79i	0.869519	−	0.232987i
$334$	3514.15	+	3514.15i	0.575705	+	0.575705i
$335$	−3392.91	−	5876.69i	−0.553356	−	0.958441i
$336$	−247.585	−	66.3402i	−0.0401990	−	0.0107713i
$337$	−1876.11	−	3249.52i	−0.303259	−	0.525260i	0.673613	−	0.739084i	$-0.264741\pi$
$337$	−1876.11	−	3249.52i	−0.303259	−	0.525260i	−0.976872	+	0.213824i	$0.931408\pi$
$338$	6282.88	−	10882.3i	1.01108	−	1.75124i
$339$	3145.57			0.503965
$340$	−16795.7	+	4500.41i	−2.67905	+	0.717850i
$341$	−754.139	+	1306.21i	−0.119762	+	0.207434i
$342$	4918.27	−	4918.27i	0.777631	−	0.777631i
$343$	−964.840	+	964.840i	−0.151885	+	0.151885i
$344$	1775.87	+	1775.87i	0.278338	+	0.278338i
$345$	−2356.88	+	631.524i	−0.367798	+	0.0985511i
$346$	5321.07	+	5321.07i	0.826770	+	0.826770i
$347$	1389.16			0.214911			0.107455	−	0.994210i	$-0.465730\pi$
$347$	1389.16			0.214911			0.107455	+	0.994210i	$0.465730\pi$
$348$	−2571.59	+	4454.12i	−0.396126	+	0.686110i
$349$	−467.816	−	270.094i	−0.0717524	−	0.0414263i	0.463695	−	0.885995i	$-0.346524\pi$
$349$	−467.816	−	270.094i	−0.0717524	−	0.0414263i	−0.535447	+	0.844569i	$0.679857\pi$
$350$	515.877	+	1925.28i	0.0787851	+	0.294030i
$351$	−8262.09	+	2213.82i	−1.25640	+	0.336653i
$352$	8396.57	−	8396.57i	1.27142	−	1.27142i
$353$	−8283.83	+	2219.65i	−1.24902	+	0.334674i	−0.821958	−	0.569549i	$-0.807118\pi$
$353$	−8283.83	+	2219.65i	−1.24902	+	0.334674i	−0.427062	+	0.904222i	$0.640451\pi$
$354$	1931.99	−	1115.43i	0.290068	−	0.167471i
$355$	−505.284	+	1885.75i	−0.0755428	+	0.281930i
$356$	−8961.67	+	8961.67i	−1.33418	+	1.33418i
$357$		−	484.071i		−	0.0717640i
$358$	8297.90	−	8297.90i	1.22502	−	1.22502i
$359$	−5744.51	+	9949.78i	−0.844522	+	1.46276i	0.0415130	+	0.999138i	$0.486782\pi$
$359$	−5744.51	+	9949.78i	−0.844522	+	1.46276i	−0.886035	+	0.463618i	$0.846551\pi$
$360$	1086.54	+	1881.94i	0.159071	+	0.275519i
$361$	390.449	+	225.426i	0.0569251	+	0.0328657i
$362$	5697.47	+	3289.43i	0.827216	+	0.477594i
$363$	−950.695	−	1646.65i	−0.137462	−	0.238090i
$364$	672.714	−	1165.18i	0.0968676	−	0.167780i
$365$	6356.36	−	6356.36i	0.911527	−	0.911527i
$366$			1780.47i			0.254280i
$367$	4269.34	−	4269.34i	0.607242	−	0.607242i	−0.334982	−	0.942224i	$-0.608730\pi$
$367$	4269.34	−	4269.34i	0.607242	−	0.607242i	0.942224	+	0.334982i	$0.108730\pi$
$368$	−692.932	+	2586.06i	−0.0981565	+	0.366325i
$369$	−6603.28	+	3812.41i	−0.931580	+	0.537848i
$370$	20095.6	−	5384.61i	2.82357	−	0.756574i
$371$	−233.713	+	233.713i	−0.0327056	+	0.0327056i
$372$	732.020	−	196.144i	0.102025	−	0.0273376i
$373$	624.367	+	2330.17i	0.0866716	+	0.323463i	0.995625	−	0.0934339i	$-0.0297844\pi$
$373$	624.367	+	2330.17i	0.0866716	+	0.323463i	−0.908954	+	0.416897i	$0.863118\pi$
$374$	16153.1	+	9326.02i	2.23331	+	1.28940i
$375$	2701.70	−	4679.48i	0.372041	−	0.644393i
$376$	3326.61			0.456269
$377$	11409.0	+	11409.0i	1.55860	+	1.55860i
$378$	−952.155	+	255.129i	−0.129560	+	0.0347154i
$379$	604.025	+	604.025i	0.0818646	+	0.0818646i	0.746853	−	0.664989i	$-0.231564\pi$
$379$	604.025	+	604.025i	0.0818646	+	0.0818646i	−0.664989	+	0.746853i	$0.731564\pi$
$380$	10060.6	−	10060.6i	1.35815	−	1.35815i
$381$	−1501.54	+	1501.54i	−0.201906	+	0.201906i
$382$	7554.30	−	13084.4i	1.01181	−	1.75251i
$383$	−4399.58	+	1178.86i	−0.586966	+	0.157277i	−0.540066	−	0.841622i	$-0.681601\pi$
$383$	−4399.58	+	1178.86i	−0.586966	+	0.157277i	−0.0469000	+	0.998900i	$0.514934\pi$
$384$	−1702.27			−0.226221
$385$	875.123	−	1515.76i	0.115845	−	0.200650i
$386$	455.996	+	789.809i	0.0601285	+	0.104146i
$387$	−9294.71	−	2490.51i	−1.22087	−	0.327131i
$388$	8002.58	+	13860.9i	1.04709	+	1.81361i
$389$	4961.14	+	4961.14i	0.646632	+	0.646632i	0.952178	−	0.305545i	$-0.0988387\pi$
$389$	4961.14	+	4961.14i	0.646632	+	0.646632i	−0.305545	+	0.952178i	$0.598839\pi$
$390$	−13704.7	+	3672.15i	−1.77939	+	0.476786i
$391$	−5056.18			−0.653970
$392$	−923.871	+	1600.19i	−0.119037	+	0.206178i
$393$	−395.676	−	106.021i	−0.0507869	−	0.0136083i
$394$	8343.00	+	2235.50i	1.06679	+	0.285845i
$395$	9933.62			1.26535
$396$	2305.97	−	8606.00i	0.292625	−	1.09209i
$397$	289.451	+	289.451i	0.0365922	+	0.0365922i	0.725166	−	0.688574i	$-0.241763\pi$
$397$	289.451	+	289.451i	0.0365922	+	0.0365922i	−0.688574	+	0.725166i	$0.741763\pi$
$398$	−2694.75	−	10057.0i	−0.339386	−	1.26661i
$399$	198.044	+	343.022i	0.0248486	+	0.0430390i
$400$	−6202.10	−	10742.4i	−0.775263	−	1.34279i
$401$	−3248.02	+	5625.73i	−0.404485	+	0.700588i	−0.994261	−	0.106978i	$-0.965882\pi$
$401$	−3248.02	+	5625.73i	−0.404485	+	0.700588i	0.589777	+	0.807566i	$0.299216\pi$
$402$	3167.38	−	1828.69i	0.392972	−	0.226883i
$403$		−	2377.44i		−	0.293867i
$404$	1272.35	+	4748.46i	0.156687	+	0.584764i
$405$	−4480.47	−	2586.80i	−0.549719	−	0.317381i
$406$	1314.81	+	1314.81i	0.160722	+	0.160722i
$407$	−10394.7	−	6001.40i	−1.26596	−	0.730905i
$408$	−341.321	−	1273.83i	−0.0414164	−	0.154568i
$409$	−1735.07	−	1735.07i	−0.209764	−	0.209764i	0.594403	−	0.804167i	$-0.297388\pi$
$409$	−1735.07	−	1735.07i	−0.209764	−	0.209764i	−0.804167	+	0.594403i	$0.797388\pi$
$410$	−25114.0	+	14499.6i	−3.02510	+	1.74654i
$411$	7104.89	+	1903.75i	0.852696	+	0.228479i
$412$	−10919.1	+	2925.76i	−1.30569	+	0.349859i
$413$	−112.272	−	419.005i	−0.0133766	−	0.0499223i
$414$	1162.24	+	4337.54i	0.137973	+	0.514924i
$415$	−12179.1	+	7031.61i	−1.44060	+	0.831731i
$416$	−4844.40	+	18079.5i	−0.570953	+	2.13082i
$417$	−4959.18	+	1328.81i	−0.582379	+	0.156048i
$418$	−15261.9			−1.78585
$419$	14880.3	−	3987.17i	1.73497	−	0.464883i	0.753648	−	0.657278i	$-0.228292\pi$
$419$	14880.3	−	3987.17i	1.73497	−	0.464883i	0.981318	+	0.192395i	$0.0616256\pi$
$420$	−849.454	+	227.611i	−0.0986884	+	0.0264435i
$421$		−	5293.51i		−	0.612803i	−0.951902	−	0.306402i	$-0.900875\pi$
$421$		−	5293.51i		−	0.612803i	0.951902	−	0.306402i	$-0.0991250\pi$
$422$	−1714.64	−	2969.84i	−0.197789	−	0.342581i
$423$	−11038.2	+	6372.93i	−1.26879	+	0.732535i
$424$	−450.221	+	779.806i	−0.0515676	+	0.0893177i
$425$	16564.6	−	16564.6i	1.89060	−	1.89060i
$426$	−1016.37	−	272.335i	−0.115594	−	0.0309734i
$427$	334.410	+	89.6048i	0.0378998	+	0.0101552i
$428$	4381.79	+	7589.49i	0.494864	+	0.857130i
$429$	7088.92	+	4092.79i	0.797800	+	0.460610i
$430$	−35350.2	−	9472.06i	−3.96451	−	1.06229i
$431$	−8127.45	+	2177.74i	−0.908319	+	0.243383i	−0.682585	−	0.730806i	$-0.739144\pi$
$431$	−8127.45	+	2177.74i	−0.908319	+	0.243383i	−0.225733	+	0.974189i	$0.572478\pi$
$432$	5312.67	−	3067.27i	0.591681	−	0.341607i
$433$	−5382.28	−	3107.46i	−0.597358	−	0.344885i	0.170644	−	0.985333i	$-0.445415\pi$
$433$	−5382.28	−	3107.46i	−0.597358	−	0.344885i	−0.768002	+	0.640448i	$0.778749\pi$
$434$		−	273.985i		−	0.0303034i
$435$		−	10546.2i		−	1.16242i
$436$	−8406.75	−	2252.58i	−0.923418	−	0.247429i
$437$	3582.91	−	2068.59i	0.392205	−	0.226440i
$438$	3425.92	+	3425.92i	0.373737	+	0.373737i
$439$	−1113.66	+	1113.66i	−0.121076	+	0.121076i	−0.765048	−	0.643973i	$-0.777285\pi$
$439$	−1113.66	+	1113.66i	−0.121076	+	0.121076i	0.643973	+	0.765048i	$0.277285\pi$
$440$	1234.11	−	4605.75i	0.133713	−	0.499024i
$441$		−	7079.58i		−	0.764451i
$442$	−29400.4			−3.16388
$443$	−4219.18	+	15746.2i	−0.452504	+	1.68877i	0.242819	+	0.970072i	$0.421928\pi$
$443$	−4219.18	+	15746.2i	−0.452504	+	1.68877i	−0.695323	+	0.718697i	$0.744739\pi$
$444$	1560.90	+	5825.37i	0.166841	+	0.622658i
$445$	6726.13	−	25102.3i	0.716515	−	2.67407i
$446$	20206.1			2.14526
$447$	−6748.90	−	1808.36i	−0.714121	−	0.191348i
$448$	−343.687	+	1282.66i	−0.0362448	+	0.135267i
$449$	1225.53	−	1225.53i	0.128811	−	0.128811i	−0.639762	−	0.768573i	$-0.720967\pi$
$449$	1225.53	−	1225.53i	0.128811	−	0.128811i	0.768573	+	0.639762i	$0.220967\pi$
$450$	−18017.9	−	10402.7i	−1.88750	−	1.08975i
$451$	16160.5	+	4330.18i	1.68729	+	0.452107i
$452$		−	11841.8i		−	1.23228i
$453$	−974.685	+	562.735i	−0.101092	+	0.0583655i
$454$	6026.28	+	6026.28i	0.622968	+	0.622968i
$455$			2758.84i			0.284255i
$456$	763.016	+	763.016i	0.0783585	+	0.0783585i
$457$	12672.8			1.29717			0.648587	−	0.761141i	$-0.275360\pi$
$457$	12672.8			1.29717			0.648587	+	0.761141i	$0.275360\pi$
$458$	709.605	−	1229.07i	0.0723966	−	0.125395i
$459$	8192.11	+	8192.11i	0.833061	+	0.833061i
$460$	2377.42	+	8872.66i	0.240974	+	0.899326i
$461$	−2911.67	+	2911.67i	−0.294165	+	0.294165i	−0.838723	−	0.544558i	$-0.816697\pi$
$461$	−2911.67	+	2911.67i	−0.294165	+	0.294165i	0.544558	+	0.838723i	$0.316697\pi$
$462$	816.954	+	471.669i	0.0822687	+	0.0474979i
$463$	−2531.69	+	9448.39i	−0.254120	+	0.948389i	0.714458	+	0.699678i	$0.246673\pi$
$463$	−2531.69	+	9448.39i	−0.254120	+	0.948389i	−0.968578	+	0.248710i	$0.919993\pi$
$464$	−10021.4	−	5785.85i	−1.00265	−	0.578883i
$465$	−1098.83	+	1098.83i	−0.109585	+	0.109585i
$466$	6560.50	+	11363.1i	0.652166	+	1.12958i
$467$	7442.07	−	12890.0i	0.737426	−	1.27726i	−0.216225	−	0.976343i	$-0.569375\pi$
$467$	7442.07	−	12890.0i	0.737426	−	1.27726i	0.953651	−	0.300915i	$-0.0972921\pi$
$468$	3634.80	+	13565.3i	0.359015	+	1.33986i
$469$	−184.064	−	686.934i	−0.0181221	−	0.0676326i
$470$	−41981.3	+	24237.9i	−4.12011	+	2.37875i
$471$	−1487.71	+	5552.21i	−0.145541	+	0.543168i
$472$	−590.885	−	1023.44i	−0.0576222	−	0.0998046i
$473$	10557.1	+	18285.4i	1.02625	+	1.77751i
$474$			5353.97i			0.518810i
$475$	−4961.07	+	18515.0i	−0.479220	+	1.78847i
$476$	−1822.32			−0.175475
$477$		−	3450.03i		−	0.331165i
$478$	9514.57	−	16479.7i	0.910431	−	1.57691i
$479$	9792.02	+	5653.43i	0.934048	+	0.539273i	0.888089	−	0.459671i	$-0.152033\pi$
$479$	9792.02	+	5653.43i	0.934048	+	0.539273i	0.0459583	+	0.998943i	$0.485366\pi$
$480$	10595.2	−	6117.15i	1.00751	−	0.581684i
$481$	18919.5			1.79346
$482$	13229.4	+	8202.50i	1.25017	+	0.775132i
$483$	−255.719			−0.0240903
$484$	−6198.95	+	3578.96i	−0.582170	+	0.336116i
$485$	−28422.1	−	16409.5i	−2.66099	−	1.53632i
$486$	8045.57	−	13935.3i	0.750935	−	1.30066i
$487$		−	9605.67i		−	0.893788i	−0.894587	−	0.446894i	$-0.852530\pi$
$487$		−	9605.67i		−	0.893788i	0.894587	−	0.446894i	$-0.147470\pi$
$488$	943.175			0.0874909
$489$	−2031.72	+	7582.48i	−0.187889	+	0.701210i
$490$		−	26925.5i		−	2.48239i
$491$	1075.03	+	1862.01i	0.0988097	+	0.171143i	0.911192	−	0.411981i	$-0.135163\pi$
$491$	1075.03	+	1862.01i	0.0988097	+	0.171143i	−0.812383	+	0.583125i	$0.801830\pi$
$492$	−4203.18	−	7280.11i	−0.385150	−	0.667099i
$493$	5656.16	−	21109.1i	0.516716	−	1.92841i
$494$	20833.7	−	12028.3i	1.89747	−	1.09551i
$495$	4728.45	+	17646.8i	0.429350	+	1.60236i
$496$	441.307	+	1646.98i	0.0399502	+	0.149096i
$497$	−102.301	+	177.190i	−0.00923303	+	0.0159921i
$498$	−3789.86	−	6564.23i	−0.341019	−	0.590663i
$499$	−3052.76	+	3052.76i	−0.273869	+	0.273869i	−0.830655	−	0.556787i	$-0.812034\pi$
$499$	−3052.76	+	3052.76i	−0.273869	+	0.273869i	0.556787	+	0.830655i	$0.312034\pi$
$500$	−17616.3	−	10170.8i	−1.57565	−	0.909700i
$501$	764.572	−	2853.42i	0.0681808	−	0.254454i
$502$	9298.02	+	5368.21i	0.826675	+	0.477281i
$503$	−1287.31	+	1287.31i	−0.114112	+	0.114112i	−0.761857	−	0.647745i	$-0.775712\pi$
$503$	−1287.31	+	1287.31i	−0.114112	+	0.114112i	0.647745	+	0.761857i	$0.275712\pi$
$504$	58.9442	+	219.983i	0.00520949	+	0.0194421i
$505$	−7127.86	−	7127.86i	−0.628091	−	0.628091i
$506$	4926.64	−	8533.19i	0.432838	−	0.749697i
$507$	−7469.24			−0.654281
$508$	5652.65	+	5652.65i	0.493692	+	0.493692i
$509$			15258.3i			1.32871i	0.747418	+	0.664354i	$0.231293\pi$
$509$			15258.3i			1.32871i	−0.747418	+	0.664354i	$0.768707\pi$
$510$	13588.6	+	13588.6i	1.17983	+	1.17983i
$511$	815.875	−	471.046i	0.0706305	−	0.0407786i
$512$		−	15682.8i		−	1.35369i
$513$	−9156.65	−	2453.52i	−0.788062	−	0.211161i
$514$	−5234.53	−	3022.16i	−0.449193	−	0.259342i
$515$	16390.5	−	16390.5i	1.40243	−	1.40243i
$516$	2745.79	−	10247.4i	0.234257	−	0.874258i
$517$	27014.3	+	7238.46i	2.29804	+	0.615759i
$518$	2180.35			0.184941
$519$	1157.70	−	4320.61i	0.0979144	−	0.365422i
$520$	1945.27	+	7259.84i	0.164049	+	0.612241i
$521$	514.244	−	1919.18i	0.0432427	−	0.161384i	−0.940928	−	0.338606i	$-0.890045\pi$
$521$	514.244	−	1919.18i	0.0432427	−	0.161384i	0.984171	+	0.177222i	$0.0567112\pi$
$522$	−19409.0			−1.62741
$523$			1145.90i			0.0958065i	0.998852	+	0.0479032i	$0.0152539\pi$
$523$			1145.90i			0.0958065i	−0.998852	+	0.0479032i	$0.984746\pi$
$524$	−399.125	+	1489.55i	−0.0332745	+	0.124182i
$525$	837.766	−	837.766i	0.0696440	−	0.0696440i
$526$	13552.6	+	13552.6i	1.12343	+	1.12343i
$527$	−2788.71	+	1610.06i	−0.230509	+	0.133084i
$528$	−5670.61	−	1519.43i	−0.467389	−	0.125237i
$529$		−	9495.98i		−	0.780470i
$530$		−	13121.3i		−	1.07539i
$531$	3921.30	+	2263.96i	0.320471	+	0.185024i
$532$	1291.33	−	745.551i	0.105237	−	0.0607589i
$533$	−25473.1	+	6825.48i	−2.07009	+	0.554680i
$534$	13529.5	+	3625.21i	1.09640	+	0.293780i
$535$	−15562.4	−	8984.98i	−1.25761	−	0.726083i
$536$	−968.721	−	1677.87i	−0.0780642	−	0.135211i
$537$	−6737.75	−	1805.37i	−0.541444	−	0.145079i
$538$	34.7810	+	9.31955i	0.00278720	+	0.000746829i
$539$	−10984.3	+	10984.3i	−0.877790	+	0.877790i
$540$	10523.7	−	18227.6i	0.838644	−	1.45257i
$541$	−1480.49	+	854.763i	−0.117655	+	0.0679281i	−0.557673	−	0.830061i	$-0.688306\pi$
$541$	−1480.49	+	854.763i	−0.117655	+	0.0679281i	0.440018	+	0.897989i	$0.354972\pi$
$542$	−11600.0	−	20091.8i	−0.919306	−	1.59228i
$543$		−	3910.56i		−	0.309057i
$544$	24487.9	−	6561.52i	1.92998	−	0.517137i
$545$	17238.3	−	4618.98i	1.35487	−	0.363037i
$546$	−1486.94			−0.116548
$547$	6676.83	−	1789.05i	0.521903	−	0.139843i	0.0117562	−	0.999931i	$-0.496258\pi$
$547$	6676.83	−	1789.05i	0.521903	−	0.139843i	0.510147	+	0.860087i	$0.329591\pi$
$548$	7166.81	−	26746.9i	0.558669	−	2.08498i
$549$	−3129.61	+	1806.88i	−0.243294	+	0.140466i
$550$	11815.5	+	44096.0i	0.916025	+	3.41865i
$551$	4628.11	+	17272.4i	0.357830	+	1.33544i
$552$	−672.922	+	180.309i	−0.0518867	+	0.0139030i
$553$	1005.59	+	269.447i	0.0773274	+	0.0207198i
$554$	−21611.5	+	12477.4i	−1.65737	+	0.956884i
$555$	−8744.40	−	8744.40i	−0.668791	−	0.668791i
$556$	5002.40	+	18669.2i	0.381563	+	1.42401i
$557$	21192.7	+	12235.6i	1.61214	+	0.930772i	0.988872	+	0.148767i	$0.0475304\pi$
$557$	21192.7	+	12235.6i	1.61214	+	0.930772i	0.623272	+	0.782005i	$0.285803\pi$
$558$	2022.25	+	2022.25i	0.153421	+	0.153421i
$559$	−28822.5	−	16640.6i	−2.18079	−	1.25908i
$560$	−512.104	−	1911.20i	−0.0386435	−	0.144219i
$561$		−	11087.0i		−	0.834391i
$562$	22483.4	−	12980.8i	1.68756	−	0.974311i
$563$	6178.40	−	10701.3i	0.462502	−	0.801076i	−0.536583	−	0.843847i	$-0.680285\pi$
$563$	6178.40	−	10701.3i	0.462502	−	0.801076i	0.999085	+	0.0427711i	$0.0136186\pi$
$564$	−7026.15	−	12169.6i	−0.524564	−	0.908572i
$565$	12140.9	+	21028.7i	0.904021	+	1.56581i
$566$	−7920.09	−	29558.2i	−0.588174	−	2.19509i
$567$	−383.396	−	383.396i	−0.0283970	−	0.0283970i
$568$	−144.266	+	538.406i	−0.0106571	+	0.0397729i
$569$	12714.9			0.936797			0.468399	−	0.883517i	$-0.344831\pi$
$569$	12714.9			0.936797			0.468399	+	0.883517i	$0.344831\pi$
$570$	−15188.5	−	4069.75i	−1.11610	−	0.299058i
$571$	13512.8	+	3620.74i	0.990354	+	0.265364i	0.717399	−	0.696662i	$-0.245332\pi$
$571$	13512.8	+	3620.74i	0.990354	+	0.265364i	0.272955	+	0.962027i	$0.411999\pi$
$572$	15407.6	−	26686.8i	1.12627	−	1.95075i
$573$	−8980.73			−0.654756
$574$	−2935.61	+	786.594i	−0.213467	+	0.0571983i
$575$	−8750.57	−	8750.57i	−0.634651	−	0.634651i
$576$	−6930.44	−	12003.9i	−0.501334	−	0.868335i
$577$	−8.76456	−	2.34846i	−0.000632363	−	0.000169441i	0.258503	−	0.966010i	$-0.416771\pi$
$577$	−8.76456	−	2.34846i	−0.000632363	−	0.000169441i	−0.259135	+	0.965841i	$0.583438\pi$
$578$	9690.39	+	16784.3i	0.697348	+	1.20784i
$579$	271.050	−	469.472i	0.0194550	−	0.0336970i
$580$	−39702.1			−2.84231
$581$	−1423.63	+	381.461i	−0.101656	+	0.0272387i
$582$	8844.29	−	15318.8i	0.629910	−	1.09104i
$583$	−5352.89	+	5352.89i	−0.380264	+	0.380264i
$584$	1814.83	−	1814.83i	0.128593	−	0.128593i
$585$	−20362.7	−	20362.7i	−1.43913	−	1.43913i
$586$	592.696	−	158.812i	0.0417816	−	0.0111954i
$587$	7618.38	+	7618.38i	0.535680	+	0.535680i	0.922257	−	0.386577i	$-0.126343\pi$
$587$	7618.38	+	7618.38i	0.535680	+	0.535680i	−0.386577	+	0.922257i	$0.626343\pi$
$588$	7805.24			0.547419
$589$	1317.42	−	2281.84i	0.0921621	−	0.159629i
$590$	14913.7	+	8610.45i	1.04066	+	0.600825i
$591$	−1328.81	−	4959.18i	−0.0924870	−	0.345166i
$592$	−13106.6	+	3511.90i	−0.909928	+	0.243814i
$593$	9763.63	−	9763.63i	0.676128	−	0.676128i	−0.282993	−	0.959122i	$-0.591327\pi$
$593$	9763.63	−	9763.63i	0.676128	−	0.676128i	0.959122	+	0.282993i	$0.0913275\pi$
$594$	−21807.8	+	5843.39i	−1.50637	+	0.403632i
$595$	3236.09	−	1868.36i	0.222969	−	0.128731i
$596$	−6807.72	+	25406.7i	−0.467877	+	1.74614i
$597$	−4376.18	+	4376.18i	−0.300008	+	0.300008i
$598$			15531.3i			1.06208i
$599$	10590.2	−	10590.2i	0.722375	−	0.722375i	−0.246713	−	0.969089i	$-0.579351\pi$
$599$	10590.2	−	10590.2i	0.722375	−	0.722375i	0.969089	+	0.246713i	$0.0793506\pi$
$600$	1613.86	−	2795.28i	0.109809	−	0.190195i
$601$	2069.53	+	3584.53i	0.140462	+	0.243288i	0.927671	−	0.373399i	$-0.121808\pi$
$601$	2069.53	+	3584.53i	0.140462	+	0.243288i	−0.787208	+	0.616687i	$0.788474\pi$
$602$	−3321.61	−	1917.73i	−0.224881	−	0.129835i
$603$	6428.74	+	3711.64i	0.434160	+	0.250663i
$604$	2118.46	+	3669.28i	0.142713	+	0.247187i
$605$	7338.76	−	12711.1i	0.493162	−	0.854181i
$606$	3841.73	−	3841.73i	0.257524	−	0.257524i
$607$			27905.8i			1.86600i	0.359878	+	0.933000i	$0.382818\pi$
$607$			27905.8i			1.86600i	−0.359878	+	0.933000i	$0.617182\pi$
$608$	−14668.1	+	14668.1i	−0.978408	+	0.978408i
$609$	286.064	−	1067.60i	0.0190343	−	0.0710369i
$610$	−11902.7	+	6872.03i	−0.790043	+	0.456132i
$611$	−42581.5	+	11409.7i	−2.81942	+	0.755460i
$612$	13450.4	−	13450.4i	0.888397	−	0.888397i
$613$	7078.49	−	1896.68i	0.466391	−	0.124969i	−0.0179680	−	0.999839i	$-0.505720\pi$
$613$	7078.49	−	1896.68i	0.466391	−	0.124969i	0.484359	+	0.874870i	$0.339053\pi$
$614$	5924.73	+	22111.4i	0.389418	+	1.45333i
$615$	14928.1	+	8618.72i	0.978793	+	0.565106i
$616$	249.859	−	432.769i	0.0163427	−	0.0283064i
$617$	1090.08			0.0711262			0.0355631	−	0.999367i	$-0.488678\pi$
$617$	1090.08			0.0711262			0.0355631	+	0.999367i	$0.488678\pi$
$618$	8834.07	+	8834.07i	0.575014	+	0.575014i
$619$	28504.1	−	7637.66i	1.85085	−	0.495935i	0.851268	−	0.524732i	$-0.175834\pi$
$619$	28504.1	−	7637.66i	1.85085	−	0.495935i	0.999585	+	0.0287972i	$0.00916770\pi$
$620$	4136.62	+	4136.62i	0.267953	+	0.267953i
$621$	4327.63	−	4327.63i	0.279649	−	0.279649i
$622$	−4374.42	+	4374.42i	−0.281991	+	0.281991i
$623$	1361.79	−	2358.68i	0.0875743	−	0.151683i
$624$	8938.33	−	2395.02i	0.573429	−	0.153650i
$625$	11779.7			0.753900
$626$	−10110.8	+	17512.3i	−0.645539	+	1.11811i
$627$	4535.93	+	7856.46i	0.288911	+	0.500409i
$628$	20901.7	+	5600.60i	1.32814	+	0.355873i
$629$	−12812.8	−	22192.4i	−0.812209	−	1.40679i
$630$	−2346.67	−	2346.67i	−0.148403	−	0.148403i
$631$	6193.07	−	1659.43i	0.390717	−	0.104692i	−0.0581119	−	0.998310i	$-0.518508\pi$
$631$	6193.07	−	1659.43i	0.390717	−	0.104692i	0.448829	+	0.893618i	$0.351841\pi$
$632$	2836.18			0.178509
$633$	−1019.20	+	1765.31i	−0.0639961	+	0.110845i
$634$	−3019.93	−	809.187i	−0.189175	−	0.0506892i
$635$	−15833.5	−	4242.56i	−0.989499	−	0.265135i
$636$	3803.65			0.237146
$637$	6337.41	−	23651.5i	0.394188	−	1.47113i
$638$	30114.0	+	30114.0i	1.86869	+	1.86869i
$639$	−552.751	−	2062.89i	−0.0342198	−	0.127710i
$640$	−6570.23	−	11380.0i	−0.405799	−	0.702864i
$641$	7908.27	+	13697.5i	0.487298	+	0.844025i	0.999893	−	0.0146057i	$-0.00464929\pi$
$641$	7908.27	+	13697.5i	0.487298	+	0.844025i	−0.512596	+	0.858630i	$0.671316\pi$
$642$	4842.67	−	8387.76i	0.297703	−	0.515636i
$643$	−17717.3	+	10229.1i	−1.08663	+	0.627365i	−0.932677	−	0.360713i	$-0.882533\pi$
$643$	−17717.3	+	10229.1i	−1.08663	+	0.627365i	−0.153952	+	0.988078i	$0.549200\pi$
$644$			962.675i			0.0589048i
$645$	5630.31	+	21012.6i	0.343710	+	1.28274i
$646$	−28218.3	−	16291.8i	−1.71863	−	0.992250i
$647$	−14595.2	−	14595.2i	−0.886857	−	0.886857i	0.107363	−	0.994220i	$-0.465759\pi$
$647$	−14595.2	−	14595.2i	−0.886857	−	0.886857i	−0.994220	+	0.107363i	$0.965759\pi$
$648$	−1279.23	−	738.567i	−0.0775511	−	0.0447741i
$649$	−2571.44	−	9596.75i	−0.155528	−	0.580440i
$650$	−50882.4	−	50882.4i	−3.07042	−	3.07042i
$651$	−141.041	+	81.4299i	−0.00849127	+	0.00490244i
$652$	28544.8	+	7648.57i	1.71457	+	0.459419i
$653$	3832.51	−	1026.92i	0.229675	−	0.0615412i	−0.142146	−	0.989846i	$-0.545400\pi$
$653$	3832.51	−	1026.92i	0.229675	−	0.0615412i	0.371821	+	0.928305i	$0.378734\pi$
$654$	2489.51	+	9290.98i	0.148849	+	0.555514i
$655$	−818.416	−	3054.37i	−0.0488216	−	0.182205i
$656$	16379.6	−	9456.78i	0.974873	−	0.562843i
$657$	−2545.15	+	9498.63i	−0.151135	+	0.564044i
$658$	−4907.25	+	1314.89i	−0.290736	+	0.0779026i
$659$	−16998.4			−1.00480			−0.502402	−	0.864634i	$-0.667550\pi$
$659$	−16998.4			−1.00480			−0.502402	+	0.864634i	$0.667550\pi$
$660$	−19455.6	+	5213.12i	−1.14744	+	0.307455i
$661$	−27709.5	+	7424.74i	−1.63052	+	0.436897i	−0.954068	−	0.299589i	$-0.903151\pi$
$661$	−27709.5	+	7424.74i	−1.63052	+	0.436897i	−0.676453	+	0.736486i	$0.736484\pi$
$662$			2405.25i			0.141213i
$663$	8737.98	+	15134.6i	0.511848	+	0.886546i
$664$	−3477.30	+	2007.62i	−0.203231	+	0.117336i
$665$	−1528.77	+	2647.91i	−0.0891477	+	0.154408i
$666$	−16093.0	+	16093.0i	−0.936321	+	0.936321i
$667$	−11151.3	−	2987.97i	−0.647344	−	0.173455i
$668$	−10741.9	−	2878.29i	−0.622182	−	0.166713i
$669$	−6005.38	−	10401.6i	−0.347057	−	0.601121i
$670$	24450.2	+	14116.3i	1.40984	+	0.813972i
$671$	7659.21	+	2052.28i	0.440656	+	0.118073i
$672$	1238.49	−	331.852i	0.0710949	−	0.0190498i
$673$	15172.7	−	8759.96i	0.869040	−	0.501741i	0.00201118	−	0.999998i	$-0.499360\pi$
$673$	15172.7	−	8759.96i	0.869040	−	0.501741i	0.867029	+	0.498257i	$0.166026\pi$
$674$	13519.7	+	7805.63i	0.772643	+	0.446086i
$675$			28355.6i			1.61690i
$676$			28118.5i			1.59983i
$677$	2085.93	+	558.922i	0.118418	+	0.0317299i	0.317541	−	0.948245i	$-0.397143\pi$
$677$	2085.93	+	558.922i	0.118418	+	0.0317299i	−0.199124	+	0.979974i	$0.563810\pi$
$678$	−11333.9	+	6543.64i	−0.642001	+	0.370659i
$679$	−2432.09	−	2432.09i	−0.137460	−	0.137460i
$680$	7198.34	−	7198.34i	0.405947	−	0.405947i
$681$	1311.14	−	4893.23i	0.0737781	−	0.275344i
$682$		−	6275.25i		−	0.352334i
$683$	−4749.39			−0.266077			−0.133038	−	0.991111i	$-0.542473\pi$
$683$	−4749.39			−0.266077			−0.133038	+	0.991111i	$0.542473\pi$
$684$	−4028.35	+	15034.0i	−0.225187	+	0.840409i
$685$	14695.7	+	54845.2i	0.819700	+	3.05916i
$686$	1469.32	−	5483.57i	0.0817767	−	0.305195i
$687$	−843.595			−0.0468489
$688$	23055.8	+	6177.78i	1.27761	+	0.342334i
$689$	3088.35	−	11525.9i	0.170765	−	0.637302i
$690$	7178.41	−	7178.41i	0.396054	−	0.396054i
$691$	−9761.19	−	5635.63i	−0.537385	−	0.310259i	0.206633	−	0.978418i	$-0.433749\pi$
$691$	−9761.19	−	5635.63i	−0.537385	−	0.310259i	−0.744019	+	0.668159i	$0.767083\pi$
$692$	−16265.3	−	4358.27i	−0.893516	−	0.239417i
$693$			1914.66i			0.104952i
$694$	−5005.32	+	2889.82i	−0.273774	+	0.158064i
$695$	−28024.2	−	28024.2i	−1.52952	−	1.52952i
$696$		−	3011.09i		−	0.163987i
$697$	25257.3	+	25257.3i	1.37258	+	1.37258i
$698$	2247.47			0.121874
$699$	3899.64	−	6754.37i	0.211013	−	0.365485i
$700$	−3153.83	−	3153.83i	−0.170291	−	0.170291i
$701$	1220.20	+	4553.86i	0.0657438	+	0.245359i	0.990975	−	0.134044i	$-0.0427962\pi$
$701$	1220.20	+	4553.86i	0.0657438	+	0.245359i	−0.925232	+	0.379403i	$0.876130\pi$
$702$	25164.1	−	25164.1i	1.35293	−	1.35293i
$703$	18158.8	+	10484.0i	0.974213	+	0.562462i
$704$	−7871.69	+	29377.5i	−0.421414	+	1.57274i
$705$	24954.2	+	14407.3i	1.33309	+	0.769660i
$706$	25230.3	−	25230.3i	1.34498	−	1.34498i
$707$	−528.219	−	914.902i	−0.0280986	−	0.0486682i
$708$	−2496.02	+	4323.23i	−0.132495	+	0.229487i
$709$	−1327.07	−	4952.71i	−0.0702953	−	0.262345i	0.921830	−	0.387594i	$-0.126694\pi$
$709$	−1327.07	−	4952.71i	−0.0702953	−	0.262345i	−0.992125	+	0.125249i	$0.960027\pi$
$710$	−2102.25	−	7845.72i	−0.111121	−	0.414711i
$711$	−9410.91	+	5433.39i	−0.496395	+	0.286594i
$712$	1920.40	−	7167.04i	0.101082	−	0.377242i
$713$	850.545	+	1473.19i	0.0446749	+	0.0773791i
$714$	1007.00	+	1744.17i	0.0527814	+	0.0914201i
$715$			63187.5i			3.30500i
$716$	−6796.47	+	25364.8i	−0.354743	+	1.32392i
$717$	−11311.1			−0.589153
$718$		−	47800.5i		−	2.48454i
$719$	−6670.15	+	11553.0i	−0.345973	+	0.599243i	−0.985530	−	0.169501i	$-0.945784\pi$
$719$	−6670.15	+	11553.0i	−0.345973	+	0.599243i	0.639557	+	0.768744i	$0.279118\pi$
$720$	17886.1	+	10326.6i	0.925802	+	0.534512i
$721$	2103.82	−	1214.64i	0.108669	−	0.0627400i
$722$	−1875.79			−0.0966892
$723$	290.591	−	9248.01i	0.0149477	−	0.475708i
$724$	−14721.6			−0.755696
$725$	46321.8	−	26743.9i	2.37289	−	1.36999i
$726$	6850.96	+	3955.40i	0.350224	+	0.202202i
$727$	1310.45	−	2269.76i	0.0668526	−	0.115792i	−0.830662	−	0.556778i	$-0.812038\pi$
$727$	1310.45	−	2269.76i	0.0668526	−	0.115792i	0.897514	+	0.440985i	$0.145371\pi$
$728$			787.685i			0.0401010i
$729$	−2247.68			−0.114194
$730$	−9679.87	+	36125.8i	−0.490778	+	1.83161i
$731$			45078.0i			2.28081i
$732$	−1992.08	−	3450.39i	−0.100587	−	0.174221i
$733$	−6181.99	−	10707.5i	−0.311510	−	0.539551i	0.667179	−	0.744897i	$-0.267501\pi$
$733$	−6181.99	−	10707.5i	−0.311510	−	0.539551i	−0.978689	+	0.205346i	$0.934168\pi$
$734$	−6501.62	+	24264.4i	−0.326947	+	1.22018i
$735$	−13860.6	+	8002.42i	−0.695586	+	0.401597i
$736$	−3466.24	−	12936.2i	−0.173597	−	0.647873i
$737$	−4215.73	−	15733.3i	−0.210703	−	0.786356i
$738$	15861.7	−	27473.2i	0.791160	−	1.37033i
$739$	−18658.0	−	32316.5i	−0.928747	−	1.60864i	−0.785421	−	0.618962i	$-0.787553\pi$
$739$	−18658.0	−	32316.5i	−0.928747	−	1.60864i	−0.143326	−	0.989675i	$-0.545780\pi$
$740$	−32919.0	+	32919.0i	−1.63530	+	1.63530i
$741$	−12383.8	−	7149.79i	−0.613941	−	0.354459i
$742$	355.913	−	1328.29i	0.0176091	−	0.0657182i
$743$	4265.40	+	2462.63i	0.210609	+	0.121595i	0.601594	−	0.798802i	$-0.294532\pi$
$743$	4265.40	+	2462.63i	0.210609	+	0.121595i	−0.390986	+	0.920397i	$0.627866\pi$
$744$	−313.730	+	313.730i	−0.0154595	+	0.0154595i
$745$	−13959.4	−	52097.2i	−0.686487	−	2.56200i
$746$	−7097.05	−	7097.05i	−0.348313	−	0.348313i
$747$	7692.16	−	13323.2i	0.376762	−	0.652571i
$748$	−41737.8			−2.04022
$749$	−1331.69	−	1331.69i	−0.0649649	−	0.0649649i
$750$			22481.1i			1.09452i
$751$	4419.57	+	4419.57i	0.214743	+	0.214743i	0.806279	−	0.591536i	$-0.201478\pi$
$751$	4419.57	+	4419.57i	0.214743	+	0.214743i	−0.591536	+	0.806279i	$0.701478\pi$
$752$	27380.7	−	15808.2i	1.32775	−	0.766578i
$753$		−	6381.86i		−	0.308855i
$754$	−64841.7	−	17374.3i	−3.13183	−	0.839170i
$755$	−7523.95	−	4343.95i	−0.362681	−	0.209394i
$756$	1559.74	−	1559.74i	0.0750360	−	0.0750360i
$757$	−3443.98	+	12853.1i	−0.165355	+	0.617113i	0.832640	+	0.553815i	$0.186829\pi$
$757$	−3443.98	+	12853.1i	−0.165355	+	0.617113i	−0.997995	+	0.0632982i	$0.979838\pi$
$758$	−3432.92	−	919.847i	−0.164498	−	0.0440770i
$759$	−5856.91			−0.280095
$760$	−2155.89	+	8045.88i	−0.102898	+	0.384019i
$761$	−1367.64	−	5104.12i	−0.0651472	−	0.243133i	0.925672	−	0.378327i	$-0.123501\pi$
$761$	−1367.64	−	5104.12i	−0.0651472	−	0.243133i	−0.990819	+	0.135195i	$0.956834\pi$
$762$	2286.63	−	8533.83i	0.108709	−	0.405706i
$763$	1870.33			0.0887426
$764$			33808.6i			1.60099i
$765$	−10095.1	+	37675.4i	−0.477110	+	1.78060i
$766$	13399.9	−	13399.9i	0.632061	−	0.632061i
$767$	11073.7	+	11073.7i	0.521314	+	0.521314i
$768$	−5238.47	+	3024.43i	−0.246129	+	0.142103i
$769$	5922.93	+	1587.04i	0.277746	+	0.0744217i	0.395003	−	0.918680i	$-0.370744\pi$
$769$	5922.93	+	1587.04i	0.277746	+	0.0744217i	−0.117257	+	0.993102i	$0.537410\pi$
$770$			7281.96i			0.340810i
$771$			3592.81i			0.167824i
$772$	−1767.36	−	1020.39i	−0.0823948	−	0.0475707i
$773$	−30826.5	+	17797.7i	−1.43435	+	0.828122i	−0.997449	−	0.0713870i	$-0.977257\pi$
$773$	−30826.5	+	17797.7i	−1.43435	+	0.828122i	−0.436901	+	0.899509i	$0.643924\pi$
$774$	38671.0	−	10361.9i	1.79587	−	0.481201i
$775$	−7612.82	−	2039.85i	−0.352852	−	0.0945465i
$776$	−8114.89	−	4685.13i	−0.375396	−	0.216735i
$777$	−648.014	−	1122.39i	−0.0299194	−	0.0518219i
$778$	−28196.2	−	7555.14i	−1.29933	−	0.348155i
$779$	−28231.1	−	7564.49i	−1.29844	−	0.347915i
$780$	22449.8	−	22449.8i	1.03056	−	1.03056i
$781$	−2343.06	+	4058.30i	−0.107351	+	0.185938i
$782$	18218.1	−	10518.2i	0.833091	−	0.480986i
$783$	13226.3	+	22908.6i	0.603664	+	1.04558i
$784$			17561.1i			0.799977i
$785$	−42859.5	+	11484.2i	−1.94869	+	0.522150i
$786$	1646.23	−	441.105i	0.0747060	−	0.0200174i
$787$	6479.34			0.293474			0.146737	−	0.989176i	$-0.453123\pi$
$787$	6479.34			0.293474			0.146737	+	0.989176i	$0.453123\pi$
$788$	−18669.2	+	5002.40i	−0.843988	+	0.226146i
$789$	2948.64	−	11004.5i	0.133047	−	0.496540i
$790$	−35792.2	+	20664.6i	−1.61193	+	0.930650i
$791$	658.638	+	2458.07i	0.0296062	+	0.110492i
$792$	1350.04	+	5038.41i	0.0605701	+	0.226051i
$793$	−12072.9	+	3234.92i	−0.540631	+	0.144862i
$794$	−1645.06	−	440.793i	−0.0735278	−	0.0197017i
$795$	−6754.55	+	3899.74i	−0.301332	+	0.173974i
$796$	16474.5	+	16474.5i	0.733570	+	0.733570i
$797$	−3188.88	−	11901.1i	−0.141727	−	0.528931i	−0.999879	−	0.0155363i	$-0.995054\pi$
$797$	−3188.88	−	11901.1i	−0.141727	−	0.528931i	0.858153	−	0.513395i	$-0.171612\pi$
$798$	−1427.15	−	823.968i	−0.0633092	−	0.0365516i
$799$	42220.8	+	42220.8i	1.86942	+	1.86942i
$800$	53736.3	+	31024.6i	2.37483	+	1.37111i
$801$	7357.99	+	27460.4i	0.324571	+	1.21132i
$802$		−	27027.0i		−	1.18997i
$803$	18686.5	−	10788.7i	0.821212	−	0.474127i
$804$	−4092.08	+	7087.69i	−0.179498	+	0.310900i
$805$	−986.995	−	1709.52i	−0.0432136	−	0.0748482i
$806$	4945.70	+	8566.21i	0.216135	+	0.374357i
$807$	−5.53965	−	20.6743i	−0.000241642	−	0.000901819i
$808$	−2035.10	−	2035.10i	−0.0886072	−	0.0886072i
$809$	−6451.16	+	24076.1i	−0.280360	+	1.04632i	0.671804	+	0.740729i	$0.265520\pi$
$809$	−6451.16	+	24076.1i	−0.280360	+	1.04632i	−0.952164	+	0.305588i	$0.901147\pi$
$810$	21525.0			0.933716
$811$	−1782.15	−	477.527i	−0.0771639	−	0.0206760i	0.220031	−	0.975493i	$-0.429384\pi$
$811$	−1782.15	−	477.527i	−0.0771639	−	0.0206760i	−0.297194	+	0.954817i	$0.596051\pi$
$812$	−4019.08	−	1076.91i	−0.173697	−	0.0465420i
$813$	−6895.19	+	11942.8i	−0.297448	+	0.515194i
$814$	49938.1			2.15028
$815$	−58531.9	+	15683.6i	−2.51569	+	0.674076i
$816$	−8862.62	−	8862.62i	−0.380213	−	0.380213i
$817$	−18442.4	−	31943.1i	−0.789739	−	1.36787i
$818$	9861.09	+	2642.27i	0.421497	+	0.112940i
$819$	−1509.00	−	2613.67i	−0.0643819	−	0.111513i
$820$	32445.8	−	56197.8i	1.38178	−	2.39331i
$821$	−25481.1			−1.08319			−0.541593	−	0.840641i	$-0.682178\pi$
$821$	−25481.1			−1.08319			−0.541593	+	0.840641i	$0.682178\pi$
$822$	−29560.1	+	7920.62i	−1.25429	+	0.336087i
$823$	−16687.6	+	28903.7i	−0.706794	+	1.22420i	0.259246	+	0.965811i	$0.416526\pi$
$823$	−16687.6	+	28903.7i	−0.706794	+	1.22420i	−0.966040	+	0.258392i	$0.916807\pi$
$824$	4679.72	−	4679.72i	0.197847	−	0.197847i
$825$	19187.9	−	19187.9i	0.809742	−	0.809742i
$826$	1276.17	+	1276.17i	0.0537576	+	0.0537576i
$827$	8111.62	−	2173.50i	0.341075	−	0.0913907i	−0.0842160	−	0.996448i	$-0.526839\pi$
$827$	8111.62	−	2173.50i	0.341075	−	0.0913907i	0.425291	+	0.905057i	$0.360172\pi$
$828$	−7105.40	−	7105.40i	−0.298224	−	0.298224i
$829$	31388.2			1.31503			0.657514	−	0.753443i	$-0.271608\pi$
$829$	31388.2			1.31503			0.657514	+	0.753443i	$0.271608\pi$
$830$	29255.3	−	50671.6i	1.22345	−	2.11908i
$831$	12846.1	+	7416.72i	0.536254	+	0.309607i
$832$	−12407.8	−	46306.5i	−0.517023	−	1.92956i
$833$	−32034.9	+	8583.74i	−1.33247	+	0.357033i
$834$	15104.3	−	15104.3i	0.627121	−	0.627121i
$835$	22026.6	−	5902.01i	0.912888	−	0.244608i
$836$	29576.2	−	17075.8i	1.22358	−	0.706436i
$837$	1008.82	−	3764.95i	0.0416604	−	0.155479i
$838$	−45321.3	+	45321.3i	−1.86826	+	1.86826i
$839$		−	19441.4i		−	0.799990i	−0.916517	−	0.399995i	$-0.869012\pi$
$839$		−	19441.4i		−	0.799990i	0.916517	−	0.399995i	$-0.130988\pi$
$840$	364.060	−	364.060i	0.0149539	−	0.0149539i
$841$	12754.5	−	22091.5i	0.522961	−	0.905796i
$842$	11011.9	+	19073.2i	0.450708	+	0.780649i
$843$	−13364.4	−	7715.95i	−0.546020	−	0.315245i
$844$	6645.63	+	3836.86i	0.271033	+	0.156481i
$845$	−28828.9	−	49933.1i	−1.17366	−	2.03284i
$846$	26514.8	−	45925.0i	1.07754	−	1.86635i
$847$	1087.69	−	1087.69i	0.0441247	−	0.0441247i
$848$			8557.89i			0.346555i
$849$	−12861.9	+	12861.9i	−0.519930	+	0.519930i
$850$	−25225.7	+	94143.5i	−1.01792	+	3.79894i
$851$	−11723.5	+	6768.59i	−0.472242	+	0.272649i
$852$	2274.34	−	609.407i	0.0914525	−	0.0245046i
$853$	656.594	−	656.594i	0.0263556	−	0.0263556i	−0.693806	−	0.720162i	$-0.744068\pi$
$853$	656.594	−	656.594i	0.0263556	−	0.0263556i	0.720162	+	0.693806i	$0.244068\pi$
$854$	−1391.32	+	372.804i	−0.0557496	+	0.0149380i
$855$	−8260.24	−	30827.6i	−0.330403	−	1.23308i
$856$	−4443.29	−	2565.33i	−0.177416	−	0.102431i
$857$	2636.93	−	4567.30i	0.105106	−	0.182049i	−0.808675	−	0.588255i	$-0.799815\pi$
$857$	2636.93	−	4567.30i	0.105106	−	0.182049i	0.913782	+	0.406206i	$0.133148\pi$
$858$	−34056.4			−1.35509
$859$	−13671.1	−	13671.1i	−0.543017	−	0.543017i	0.381395	−	0.924412i	$-0.375444\pi$
$859$	−13671.1	−	13671.1i	−0.543017	−	0.543017i	−0.924412	+	0.381395i	$0.875444\pi$
$860$	79103.5	−	21195.7i	3.13652	−	0.840428i
$861$	1277.40	+	1277.40i	0.0505618	+	0.0505618i
$862$	24754.0	−	24754.0i	0.978101	−	0.978101i
$863$	17638.3	−	17638.3i	0.695731	−	0.695731i	−0.267756	−	0.963487i	$-0.586282\pi$
$863$	17638.3	−	17638.3i	0.695731	−	0.695731i	0.963487	+	0.267756i	$0.0862820\pi$
$864$	−15343.4	+	26575.5i	−0.604157	+	1.04643i
$865$	33352.4	−	8936.74i	1.31100	−	0.351281i
$866$	25857.4			1.01463
$867$	5760.08	−	9976.76i	0.225632	−	0.390806i
$868$	306.549	+	530.958i	0.0119873	+	0.0207626i
$869$	23031.7	+	6171.32i	0.899076	+	0.240907i
$870$	21939.0	+	37999.4i	0.854944	+	1.48081i
$871$	18154.7	+	18154.7i	0.706255	+	0.706255i
$872$	4921.76	−	1318.78i	0.191137	−	0.0512151i
$873$	35902.0			1.39187
$874$	−8606.46	+	14906.8i	−0.333087	+	0.576923i
$875$	4222.42	+	1131.39i	0.163136	+	0.0437121i
$876$	−10472.2	−	2806.03i	−0.403909	−	0.108227i
$877$	45128.4			1.73760			0.868801	−	0.495161i	$-0.164891\pi$
$877$	45128.4			1.73760			0.868801	+	0.495161i	$0.164891\pi$
$878$	1695.96	−	6329.40i	0.0651888	−	0.243288i
$879$	−257.905	−	257.905i	−0.00989640	−	0.00989640i
$880$	−11729.1	−	43773.5i	−0.449303	−	1.67682i
$881$	−6827.26	−	11825.2i	−0.261085	−	0.452213i	0.705445	−	0.708764i	$-0.250747\pi$
$881$	−6827.26	−	11825.2i	−0.261085	−	0.452213i	−0.966531	+	0.256551i	$0.917414\pi$
$882$	14727.4	+	25508.7i	0.562243	+	0.973834i
$883$	16423.1	−	28445.7i	0.625914	−	1.08411i	−0.362450	−	0.932003i	$-0.618060\pi$
$883$	16423.1	−	28445.7i	0.625914	−	1.08411i	0.988363	−	0.152111i	$-0.0486071\pi$
$884$	56975.4	−	32894.8i	2.16775	−	1.25155i
$885$		−	10236.3i		−	0.388802i
$886$	−17554.1	−	65512.7i	−0.665621	−	2.48413i
$887$	12441.1	+	7182.86i	0.470948	+	0.271902i	0.716636	−	0.697447i	$-0.245681\pi$
$887$	12441.1	+	7182.86i	0.470948	+	0.271902i	−0.245689	+	0.969349i	$0.579014\pi$
$888$	−2496.65	−	2496.65i	−0.0943491	−	0.0943491i
$889$	−1487.76	−	858.957i	−0.0561280	−	0.0324055i
$890$	27984.3	+	104439.i	1.05397	+	3.93348i
$891$	−8781.17	−	8781.17i	−0.330169	−	0.330169i
$892$	−39157.7	+	22607.7i	−1.46984	+	0.848612i
$893$	−47191.9	−	12645.0i	−1.76844	−	0.473852i
$894$	28079.0	−	7523.76i	1.05045	−	0.281468i
$895$	−13936.3	−	52011.1i	−0.520492	−	1.94250i
$896$	−356.432	−	1330.22i	−0.0132897	−	0.0495978i
$897$	7995.14	−	4616.00i	0.297603	−	0.171821i
$898$	−1866.31	+	6965.15i	−0.0693535	+	0.258831i
$899$	−7101.90	+	1902.95i	−0.263472	+	0.0705972i
$900$	46556.2			1.72431
$901$	−15611.3	+	4183.03i	−0.577233	+	0.154669i
$902$	−67236.2	+	18015.9i	−2.48195	+	0.665037i
$903$			2279.84i			0.0840182i
$904$	3466.40	+	6003.97i	0.127534	+	0.220895i
$905$	26142.7	−	15093.5i	0.960236	−	0.554392i
$906$	2341.28	−	4055.21i	0.0858540	−	0.148704i
$907$	1829.78	−	1829.78i	0.0669867	−	0.0669867i	−0.672820	−	0.739806i	$-0.734917\pi$
$907$	1829.78	−	1829.78i	0.0669867	−	0.0669867i	0.739806	+	0.672820i	$0.234917\pi$
$908$	−18420.9	−	4935.88i	−0.673260	−	0.180400i
$909$	10651.5	+	2854.07i	0.388656	+	0.104140i
$910$	−5739.12	−	9940.45i	−0.209066	−	0.362113i
$911$	−20032.5	−	11565.8i	−0.728549	−	0.420628i	0.0893424	−	0.996001i	$-0.471523\pi$
$911$	−20032.5	−	11565.8i	−0.728549	−	0.420628i	−0.817891	+	0.575373i	$0.804857\pi$
$912$	9906.10	+	2654.33i	0.359675	+	0.0963747i
$913$	−32606.4	+	8736.86i	−1.18194	+	0.316701i
$914$	−45661.7	+	26362.8i	−1.65247	+	0.954053i
$915$	7075.11	+	4084.82i	0.255624	+	0.147585i
$916$			3175.78i			0.114553i
$917$		−	331.396i		−	0.0119342i
$918$	−46559.0	−	12475.5i	−1.67394	−	0.448531i
$919$	−40634.0	+	23460.1i	−1.45853	+	0.842085i	−0.998939	−	0.0460443i	$-0.985338\pi$
$919$	−40634.0	+	23460.1i	−1.45853	+	0.842085i	−0.459594	+	0.888129i	$0.652005\pi$
$920$	−3802.66	−	3802.66i	−0.136272	−	0.136272i
$921$	9621.54	−	9621.54i	0.344235	−	0.344235i
$922$	4434.07	−	16548.2i	0.158382	−	0.591090i
$923$		−	7386.54i		−	0.263414i
$924$	−2110.91			−0.0751558
$925$	16233.0	−	60582.4i	0.577014	−	2.15345i
$926$	−10533.2	−	39310.4i	−0.373803	−	1.39505i
$927$	−6562.93	+	24493.2i	−0.232529	+	0.867812i
$928$	57884.9			2.04759
$929$	−14687.6	−	3935.53i	−0.518713	−	0.138989i	−0.0100419	−	0.999950i	$-0.503196\pi$
$929$	−14687.6	−	3935.53i	−0.518713	−	0.138989i	−0.508671	+	0.860961i	$0.669863\pi$
$930$	1673.36	−	6245.07i	0.0590018	−	0.220198i
$931$	19188.8	−	19188.8i	0.675496	−	0.675496i
$932$	−25427.4	−	14680.5i	−0.893670	−	0.515961i
$933$	3551.95	+	951.743i	0.124636	+	0.0333962i
$934$			61926.0i			2.16947i
$935$	74118.4	−	42792.3i	2.59244	−	1.49675i
$936$	−5813.82	−	5813.82i	−0.203024	−	0.203024i
$937$			524.483i			0.0182861i	0.999958	+	0.00914307i	$0.00291037\pi$
$937$			524.483i			0.0182861i	−0.999958	+	0.00914307i	$0.997090\pi$
$938$	2092.21	+	2092.21i	0.0728286	+	0.0728286i
$939$	12019.9			0.417737
$940$	54237.4	−	93941.9i	1.88195	−	3.25963i
$941$	14968.8	+	14968.8i	0.518565	+	0.518565i	0.917137	−	0.398572i	$-0.130494\pi$
$941$	14968.8	+	14968.8i	0.518565	+	0.518565i	−0.398572	+	0.917137i	$0.630494\pi$
$942$	−6189.67	−	23100.2i	−0.214087	−	0.798985i
$943$	13342.6	−	13342.6i	0.460759	−	0.460759i
$944$	−9726.90	−	5615.83i	−0.335364	−	0.193622i
$945$	−1170.65	+	4368.94i	−0.0402978	+	0.150393i
$946$	−76077.0	−	43923.1i	−2.61467	−	1.50958i
$947$	17620.1	−	17620.1i	0.604620	−	0.604620i	−0.336915	−	0.941535i	$-0.609384\pi$
$947$	17620.1	−	17620.1i	0.604620	−	0.604620i	0.941535	+	0.336915i	$0.109384\pi$
$948$	−5990.31	−	10375.5i	−0.205228	−	0.355466i
$949$	−17005.7	+	29454.8i	−0.581696	+	1.00753i
$950$	−20640.7	−	77032.2i	−0.704919	−	2.63080i
$951$	480.991	+	1795.08i	0.0164008	+	0.0612087i
$952$	923.948	−	533.442i	0.0314552	−	0.0181607i
$953$	9409.41	−	35116.4i	0.319833	−	1.19363i	−0.599573	−	0.800320i	$-0.704663\pi$
$953$	9409.41	−	35116.4i	0.319833	−	1.19363i	0.919405	−	0.393311i	$-0.128671\pi$
$954$	7176.98	+	12430.9i	0.243568	+	0.421871i
$955$	−34662.8	−	60037.6i	−1.17451	−	2.03432i
$956$			42581.7i			1.44057i
$957$	6551.91	−	24452.0i	0.221309	−	0.825938i
$958$	−47042.6			−1.58651
$959$			5950.65i			0.200372i
$960$	−15667.7	+	27137.2i	−0.526741	+	0.912342i
$961$	−24861.5	−	14353.8i	−0.834532	−	0.481817i
$962$	−68169.4	+	39357.6i	−2.28469	+	1.31907i
$963$	19658.1			0.657811
$964$	−34814.8	−	1093.95i	−1.16319	−	0.0365496i
$965$	4184.66			0.139595
$966$	921.390	−	531.965i	0.0306886	−	0.0177181i
$967$	6708.09	+	3872.92i	0.223079	+	0.128795i	0.607375	−	0.794415i	$-0.292222\pi$
$967$	6708.09	+	3872.92i	0.223079	+	0.128795i	−0.384296	+	0.923210i	$0.625556\pi$
$968$	2095.32	−	3629.19i	0.0695723	−	0.120503i
$969$			19368.1i			0.642099i
$970$	136545.			4.51978
$971$	2459.50	−	9178.96i	0.0812863	−	0.303365i	−0.913299	−	0.407290i	$-0.866474\pi$
$971$	2459.50	−	9178.96i	0.0812863	−	0.303365i	0.994585	+	0.103926i	$0.0331404\pi$
$972$			36007.3i			1.18820i
$973$	−2076.76	−	3597.06i	−0.0684255	−	0.118516i
$974$	19982.4	+	34610.5i	0.657368	+	1.13860i
$975$	−11070.5	+	41315.6i	−0.363629	+	1.35708i
$976$	7763.07	−	4482.01i	0.254600	−	0.146994i
$977$	1879.66	+	7014.98i	0.0615513	+	0.229713i	0.989848	−	0.142127i	$-0.0453940\pi$
$977$	1879.66	+	7014.98i	0.0615513	+	0.229713i	−0.928297	+	0.371839i	$0.878727\pi$
$978$	−8453.05	−	31547.2i	−0.276379	−	1.03146i
$979$	31189.9	−	54022.5i	1.01822	−	1.76360i
$980$	30125.7	+	52179.3i	0.981970	+	1.70082i
$981$	−13804.7	+	13804.7i	−0.449288	+	0.449288i
$982$	−7746.97	−	4472.72i	−0.251747	−	0.145346i
$983$	−8609.57	+	32131.4i	−0.279352	+	1.04255i	0.673517	+	0.739172i	$0.264783\pi$
$983$	−8609.57	+	32131.4i	−0.279352	+	1.04255i	−0.952869	+	0.303383i	$0.901884\pi$
$984$	4262.16	+	2460.76i	0.138082	+	0.0797218i
$985$	28024.1	−	28024.1i	0.906521	−	0.906521i
$986$	23532.7	+	87825.2i	0.760074	+	2.83664i
$987$	2135.34	+	2135.34i	0.0688639	+	0.0688639i
$988$	−26915.9	+	46619.7i	−0.866710	+	1.50119i
$989$	23813.3			0.765640
$990$	−53747.4	−	53747.4i	−1.72546	−	1.72546i
$991$			15257.1i			0.489059i	0.969642	+	0.244530i	$0.0786335\pi$
$991$			15257.1i			0.489059i	−0.969642	+	0.244530i	$0.921366\pi$
$992$	−6031.12	−	6031.12i	−0.193032	−	0.193032i
$993$	1238.17	−	714.855i	0.0395690	−	0.0228452i
$994$		−	851.253i		−	0.0271631i
$995$	−46146.1	−	12364.8i	−1.47028	−	0.393961i
$996$	14688.8	+	8480.60i	0.467303	+	0.269797i
$997$	17582.5	−	17582.5i	0.558520	−	0.558520i	−0.370366	−	0.928886i	$-0.620768\pi$
$997$	17582.5	−	17582.5i	0.558520	−	0.558520i	0.928886	+	0.370366i	$0.120768\pi$
$998$	4648.94	−	17350.1i	0.147454	−	0.550308i
$999$	29961.3	+	8028.10i	0.948881	+	0.254252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.4.i.a.4.9	✓	240
241.181	even	12	inner	241.4.i.a.181.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.4.i.a.4.9	✓	240	1.1	even	1	trivial
241.4.i.a.181.9	yes	240	241.181	even	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	241.i (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.60313 + 2.08027i) q^{2} +(2.14174 + 1.23654i) q^{3} +(4.65504 - 8.06276i) q^{4} +19.0905i q^{5} -10.2893 q^{6} +(-0.517826 + 1.93255i) q^{7} +5.45061i q^{8} +(-10.4420 - 18.0860i) q^{9} +O(q^{10})\)	\(q+(-3.60313 + 2.08027i) q^{2} +(2.14174 + 1.23654i) q^{3} +(4.65504 - 8.06276i) q^{4} +19.0905i q^{5} -10.2893 q^{6} +(-0.517826 + 1.93255i) q^{7} +5.45061i q^{8} +(-10.4420 - 18.0860i) q^{9} +(-39.7135 - 68.7857i) q^{10} +(-11.8601 + 44.2626i) q^{11} +(19.9398 - 11.5122i) q^{12} +(-18.6946 - 69.7692i) q^{13} +(-2.15444 - 8.04046i) q^{14} +(-23.6062 + 40.8871i) q^{15} +(25.9016 + 44.8628i) q^{16} +(-69.1782 + 69.1782i) q^{17} +(75.2475 + 43.4441i) q^{18} +(20.7187 - 77.3232i) q^{19} +(153.923 + 88.8672i) q^{20} +(-3.49872 + 3.49872i) q^{21} +(-49.3445 - 184.156i) q^{22} +(36.5446 + 36.5446i) q^{23} +(-6.73988 + 11.6738i) q^{24} -239.449 q^{25} +(212.498 + 212.498i) q^{26} -118.420i q^{27} +(13.1712 + 13.1712i) q^{28} +(-193.452 + 111.689i) q^{29} -196.429i q^{30} +(31.7931 + 8.51893i) q^{31} +(-224.416 - 129.567i) q^{32} +(-80.1336 + 80.1336i) q^{33} +(105.349 - 393.167i) q^{34} +(-36.8935 - 9.88558i) q^{35} -194.431 q^{36} +(-67.7932 + 253.008i) q^{37} +(86.2009 + 321.706i) q^{38} +(46.2331 - 172.544i) q^{39} -104.055 q^{40} -365.105i q^{41} +(5.32808 - 19.8847i) q^{42} +(325.811 - 325.811i) q^{43} +(301.669 + 301.669i) q^{44} +(345.272 - 199.343i) q^{45} +(-207.698 - 55.6525i) q^{46} -610.320i q^{47} +128.113i q^{48} +(293.580 + 169.499i) q^{49} +(862.766 - 498.118i) q^{50} +(-233.703 + 62.6206i) q^{51} +(-649.556 - 174.048i) q^{52} +(143.068 + 82.6001i) q^{53} +(246.346 + 426.684i) q^{54} +(-844.996 - 226.416i) q^{55} +(-10.5336 - 2.82247i) q^{56} +(139.987 - 139.987i) q^{57} +(464.688 - 804.863i) q^{58} +(-187.767 + 108.407i) q^{59} +(219.775 + 380.662i) q^{60} -173.040i q^{61} +(-132.276 + 35.4433i) q^{62} +(40.3593 - 10.8142i) q^{63} +663.711 q^{64} +(1331.93 - 356.890i) q^{65} +(122.032 - 455.431i) q^{66} +(-307.832 + 177.727i) q^{67} +(235.740 + 879.794i) q^{68} +(33.0805 + 123.458i) q^{69} +(153.497 - 41.1293i) q^{70} +(98.7791 + 26.4678i) q^{71} +(98.5797 - 56.9150i) q^{72} +(-332.959 - 332.959i) q^{73} +(-282.056 - 1052.65i) q^{74} +(-512.838 - 296.087i) q^{75} +(-526.992 - 526.992i) q^{76} +(-79.3983 - 45.8406i) q^{77} +(192.355 + 717.877i) q^{78} -520.343i q^{79} +(-856.456 + 494.475i) q^{80} +(-135.502 + 234.696i) q^{81} +(759.516 + 1315.52i) q^{82} +(368.330 + 637.965i) q^{83} +(11.9227 + 44.4961i) q^{84} +(-1320.65 - 1320.65i) q^{85} +(-496.165 + 1851.71i) q^{86} -552.432 q^{87} +(-241.258 - 64.6449i) q^{88} +(-1314.91 - 352.328i) q^{89} +(-829.372 + 1436.52i) q^{90} +144.513 q^{91} +(464.767 - 124.534i) q^{92} +(57.5587 + 57.5587i) q^{93} +(1269.63 + 2199.06i) q^{94} +(1476.14 + 395.531i) q^{95} +(-320.428 - 554.998i) q^{96} +(-859.561 + 1488.80i) q^{97} -1410.41 q^{98} +(924.375 - 247.686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{2} - 6 q^{3} + 490 q^{4} - 168 q^{6} - 48 q^{7} + 1110 q^{9}+O(q^{10}) \) 240 * q - 6 * q^2 - 6 * q^3 + 490 * q^4 - 168 * q^6 - 48 * q^7 + 1110 * q^9	\( 240 q - 6 q^{2} - 6 q^{3} + 490 q^{4} - 168 q^{6} - 48 q^{7} + 1110 q^{9} - 30 q^{10} + 124 q^{11} - 54 q^{12} - 12 q^{13} + 176 q^{14} - 68 q^{15} - 2134 q^{16} + 244 q^{17} - 168 q^{18} + 422 q^{19} + 378 q^{20} - 198 q^{21} - 382 q^{22} + 256 q^{23} - 876 q^{24} - 6856 q^{25} + 158 q^{26} - 76 q^{28} - 486 q^{29} - 1172 q^{31} - 132 q^{32} + 466 q^{33} + 116 q^{34} + 676 q^{35} + 10348 q^{36} + 28 q^{37} - 194 q^{38} - 646 q^{39} - 708 q^{40} + 664 q^{42} + 638 q^{43} + 904 q^{44} - 624 q^{45} + 984 q^{46} - 4782 q^{49} + 6024 q^{50} + 54 q^{51} - 1580 q^{52} - 294 q^{53} - 2006 q^{54} + 172 q^{55} + 3268 q^{56} + 1550 q^{57} - 2628 q^{58} - 972 q^{59} + 276 q^{60} + 4742 q^{62} + 1564 q^{63} - 19920 q^{64} + 1140 q^{65} - 2884 q^{66} - 546 q^{67} + 5230 q^{68} - 6138 q^{69} + 1920 q^{70} + 1460 q^{71} + 9612 q^{72} + 2798 q^{73} - 5346 q^{74} - 1002 q^{75} + 4076 q^{76} - 54 q^{77} + 836 q^{78} + 4362 q^{80} - 5156 q^{81} - 362 q^{82} - 1052 q^{83} + 3832 q^{84} - 2088 q^{85} + 10678 q^{86} + 1436 q^{87} + 5326 q^{88} - 2070 q^{89} + 194 q^{90} - 1752 q^{91} - 4014 q^{92} - 618 q^{93} + 1206 q^{94} + 1140 q^{95} + 11508 q^{96} - 1352 q^{97} + 8460 q^{98} + 5686 q^{99}+O(q^{100}) \) 240 * q - 6 * q^2 - 6 * q^3 + 490 * q^4 - 168 * q^6 - 48 * q^7 + 1110 * q^9 - 30 * q^10 + 124 * q^11 - 54 * q^12 - 12 * q^13 + 176 * q^14 - 68 * q^15 - 2134 * q^16 + 244 * q^17 - 168 * q^18 + 422 * q^19 + 378 * q^20 - 198 * q^21 - 382 * q^22 + 256 * q^23 - 876 * q^24 - 6856 * q^25 + 158 * q^26 - 76 * q^28 - 486 * q^29 - 1172 * q^31 - 132 * q^32 + 466 * q^33 + 116 * q^34 + 676 * q^35 + 10348 * q^36 + 28 * q^37 - 194 * q^38 - 646 * q^39 - 708 * q^40 + 664 * q^42 + 638 * q^43 + 904 * q^44 - 624 * q^45 + 984 * q^46 - 4782 * q^49 + 6024 * q^50 + 54 * q^51 - 1580 * q^52 - 294 * q^53 - 2006 * q^54 + 172 * q^55 + 3268 * q^56 + 1550 * q^57 - 2628 * q^58 - 972 * q^59 + 276 * q^60 + 4742 * q^62 + 1564 * q^63 - 19920 * q^64 + 1140 * q^65 - 2884 * q^66 - 546 * q^67 + 5230 * q^68 - 6138 * q^69 + 1920 * q^70 + 1460 * q^71 + 9612 * q^72 + 2798 * q^73 - 5346 * q^74 - 1002 * q^75 + 4076 * q^76 - 54 * q^77 + 836 * q^78 + 4362 * q^80 - 5156 * q^81 - 362 * q^82 - 1052 * q^83 + 3832 * q^84 - 2088 * q^85 + 10678 * q^86 + 1436 * q^87 + 5326 * q^88 - 2070 * q^89 + 194 * q^90 - 1752 * q^91 - 4014 * q^92 - 618 * q^93 + 1206 * q^94 + 1140 * q^95 + 11508 * q^96 - 1352 * q^97 + 8460 * q^98 + 5686 * q^99

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