LMFDB - Embedded newform 20.4.e.b.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,4,Mod(3,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("20.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	20.e (of order $4$, degree $2$, 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:	$1.18003820011$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.6
Root			$1.76129 - 0.947553i$ of defining polynomial
Character	$\chi$	$=$	20.7
Dual form			20.4.e.b.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70884 - 0.813737i) q^{2} +(-2.61822 - 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 + 17.7783i) q^{7} +(14.4959 - 17.3744i) q^{8} -13.2899i q^{9} +O(q^{10})$	\(q+(2.70884 - 0.813737i) q^{2} +(-2.61822 - 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 + 17.7783i) q^{7} +(14.4959 - 17.3744i) q^{8} -13.2899i q^{9} +(7.91125 + 30.6172i) q^{10} -7.37590i q^{11} +(-29.0210 - 5.93575i) q^{12} +(-2.68249 + 2.68249i) q^{13} +(-33.6917 + 62.6254i) q^{14} +(30.3906 - 28.1101i) q^{15} +(25.1290 - 58.8603i) q^{16} +(-20.2367 - 20.2367i) q^{17} +(-10.8144 - 36.0001i) q^{18} +135.808 q^{19} +(46.3447 + 76.4995i) q^{20} +93.0948 q^{21} +(-6.00204 - 19.9802i) q^{22} +(-71.0426 - 71.0426i) q^{23} +(-83.4434 + 7.53642i) q^{24} +(-124.621 - 9.73070i) q^{25} +(-5.08361 + 9.44930i) q^{26} +(-105.488 + 105.488i) q^{27} +(-40.3050 + 197.059i) q^{28} -34.2890i q^{29} +(59.4491 - 100.876i) q^{30} +187.974i q^{31} +(20.1737 - 179.892i) q^{32} +(-19.3117 + 19.3117i) q^{33} +(-71.2855 - 38.3507i) q^{34} +(-190.874 - 206.359i) q^{35} +(-58.5893 - 88.7186i) q^{36} +(250.679 + 250.679i) q^{37} +(367.882 - 110.512i) q^{38} +14.0467 q^{39} +(187.791 + 169.513i) q^{40} -211.105 q^{41} +(252.179 - 75.7547i) q^{42} +(46.7326 + 46.7326i) q^{43} +(-32.5172 - 49.2390i) q^{44} +(148.472 + 5.78774i) q^{45} +(-250.253 - 134.633i) q^{46} +(189.707 - 189.707i) q^{47} +(-219.902 + 88.3159i) q^{48} -289.134i q^{49} +(-345.496 + 75.0495i) q^{50} +105.968i q^{51} +(-6.08147 + 29.7334i) q^{52} +(-74.5742 + 74.5742i) q^{53} +(-199.910 + 371.589i) q^{54} +(82.4025 + 3.21221i) q^{55} +(51.1739 + 566.598i) q^{56} +(-355.575 - 355.575i) q^{57} +(-27.9022 - 92.8835i) q^{58} +101.072 q^{59} +(78.9520 - 321.633i) q^{60} +232.112 q^{61} +(152.961 + 509.191i) q^{62} +(236.271 + 236.271i) q^{63} +(-91.7370 - 503.715i) q^{64} +(-28.8002 - 31.1367i) q^{65} +(-36.5978 + 68.0271i) q^{66} +(-34.7419 + 34.7419i) q^{67} +(-224.309 - 45.8785i) q^{68} +372.010i q^{69} +(-684.969 - 403.672i) q^{70} -614.600i q^{71} +(-230.903 - 192.649i) q^{72} +(-37.4378 + 37.4378i) q^{73} +(883.036 + 475.063i) q^{74} +(300.807 + 351.761i) q^{75} +(906.607 - 598.718i) q^{76} +(131.131 + 131.131i) q^{77} +(38.0504 - 11.4303i) q^{78} -1002.91 q^{79} +(646.635 + 306.371i) q^{80} +193.554 q^{81} +(-571.850 + 171.784i) q^{82} +(-423.190 - 423.190i) q^{83} +(621.470 - 410.415i) q^{84} +(234.895 - 217.269i) q^{85} +(164.619 + 88.5632i) q^{86} +(-89.7761 + 89.7761i) q^{87} +(-128.152 - 106.920i) q^{88} +1049.38i q^{89} +(406.898 - 105.139i) q^{90} -95.3802i q^{91} +(-787.453 - 161.060i) q^{92} +(492.156 - 492.156i) q^{93} +(359.514 - 668.257i) q^{94} +(-59.1444 + 1517.22i) q^{95} +(-523.815 + 418.177i) q^{96} +(-536.526 - 536.526i) q^{97} +(-235.279 - 783.218i) q^{98} -98.0246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8	$ 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8} - 110 q^{10} - 80 q^{12} + 116 q^{13} + 312 q^{16} - 332 q^{17} + 198 q^{18} + 140 q^{20} - 144 q^{21} + 360 q^{22} + 340 q^{25} - 164 q^{26} - 880 q^{28} - 1240 q^{30} - 376 q^{32} + 80 q^{33} + 460 q^{36} + 508 q^{37} + 1600 q^{38} + 1420 q^{40} - 656 q^{41} + 1160 q^{42} + 1180 q^{45} - 1432 q^{46} - 2720 q^{48} - 1570 q^{50} - 932 q^{52} - 644 q^{53} + 2048 q^{56} - 960 q^{57} + 1576 q^{58} + 3280 q^{60} - 896 q^{61} + 2440 q^{62} - 2740 q^{65} - 1680 q^{66} - 844 q^{68} - 3040 q^{70} - 3036 q^{72} + 1436 q^{73} + 800 q^{76} + 3120 q^{77} + 3720 q^{78} + 1840 q^{80} + 5988 q^{81} - 1352 q^{82} + 500 q^{85} - 2552 q^{86} - 2400 q^{88} - 750 q^{90} - 1840 q^{92} - 3280 q^{93} + 1088 q^{96} - 4772 q^{97} + 1698 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8 - 110 * q^10 - 80 * q^12 + 116 * q^13 + 312 * q^16 - 332 * q^17 + 198 * q^18 + 140 * q^20 - 144 * q^21 + 360 * q^22 + 340 * q^25 - 164 * q^26 - 880 * q^28 - 1240 * q^30 - 376 * q^32 + 80 * q^33 + 460 * q^36 + 508 * q^37 + 1600 * q^38 + 1420 * q^40 - 656 * q^41 + 1160 * q^42 + 1180 * q^45 - 1432 * q^46 - 2720 * q^48 - 1570 * q^50 - 932 * q^52 - 644 * q^53 + 2048 * q^56 - 960 * q^57 + 1576 * q^58 + 3280 * q^60 - 896 * q^61 + 2440 * q^62 - 2740 * q^65 - 1680 * q^66 - 844 * q^68 - 3040 * q^70 - 3036 * q^72 + 1436 * q^73 + 800 * q^76 + 3120 * q^77 + 3720 * q^78 + 1840 * q^80 + 5988 * q^81 - 1352 * q^82 + 500 * q^85 - 2552 * q^86 - 2400 * q^88 - 750 * q^90 - 1840 * q^92 - 3280 * q^93 + 1088 * q^96 - 4772 * q^97 + 1698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.70884	−	0.813737i	0.957721	−	0.287699i
$2$	2.70884	−	0.813737i	0.957721	−	0.287699i
$3$	−2.61822	−	2.61822i	−0.503877	−	0.503877i	0.408764	−	0.912640i	$-0.365960\pi$
$3$	−2.61822	−	2.61822i	−0.503877	−	0.503877i	−0.912640	+	0.408764i	$0.865960\pi$
$4$	6.67566	−	4.40857i	0.834458	−	0.551071i
$5$	−0.435501	+	11.1719i	−0.0389524	+	0.999241i
$5$	−0.435501	+	11.1719i	−0.0389524	+	0.999241i
$6$	−9.22289	−	4.96181i	−0.627538	−	0.337608i
$7$	−17.7783	+	17.7783i	−0.959936	+	0.959936i	−0.999228	−	0.0392914i	$-0.987490\pi$
$7$	−17.7783	+	17.7783i	−0.959936	+	0.959936i	0.0392914	+	0.999228i	$0.487490\pi$
$8$	14.4959	−	17.3744i	0.640635	−	0.767846i
$9$		−	13.2899i		−	0.492217i
$10$	7.91125	+	30.6172i	0.250176	+	0.968200i
$11$		−	7.37590i		−	0.202174i	−0.994878	−	0.101087i	$-0.967768\pi$
$11$		−	7.37590i		−	0.202174i	0.994878	−	0.101087i	$-0.0322321\pi$
$12$	−29.0210	−	5.93575i	−0.698136	−	0.142792i
$13$	−2.68249	+	2.68249i	−0.0572300	+	0.0572300i	−0.735143	−	0.677913i	$-0.762885\pi$
$13$	−2.68249	+	2.68249i	−0.0572300	+	0.0572300i	0.677913	+	0.735143i	$0.262885\pi$
$14$	−33.6917	+	62.6254i	−0.643178	+	1.19552i
$15$	30.3906	−	28.1101i	0.523121	−	0.483867i
$16$	25.1290	−	58.8603i	0.392641	−	0.919692i
$17$	−20.2367	−	20.2367i	−0.288713	−	0.288713i	0.547858	−	0.836571i	$-0.315443\pi$
$17$	−20.2367	−	20.2367i	−0.288713	−	0.288713i	−0.836571	+	0.547858i	$0.815443\pi$
$18$	−10.8144	−	36.0001i	−0.141610	−	0.471406i
$19$	135.808			1.63981			0.819906	−	0.572498i	$-0.194025\pi$
$19$	135.808			1.63981			0.819906	+	0.572498i	$0.194025\pi$
$20$	46.3447	+	76.4995i	0.518149	+	0.855290i
$21$	93.0948			0.967379
$22$	−6.00204	−	19.9802i	−0.0581654	−	0.193627i
$23$	−71.0426	−	71.0426i	−0.644061	−	0.644061i	0.307490	−	0.951551i	$-0.400511\pi$
$23$	−71.0426	−	71.0426i	−0.644061	−	0.644061i	−0.951551	+	0.307490i	$0.900511\pi$
$24$	−83.4434	+	7.53642i	−0.709700	+	0.0640985i
$25$	−124.621	−	9.73070i	−0.996965	−	0.0778456i
$26$	−5.08361	+	9.44930i	−0.0383453	+	0.0712754i
$27$	−105.488	+	105.488i	−0.751893	+	0.751893i
$28$	−40.3050	+	197.059i	−0.272033	+	1.33002i
$29$		−	34.2890i		−	0.219562i	−0.993956	−	0.109781i	$-0.964985\pi$
$29$		−	34.2890i		−	0.219562i	0.993956	−	0.109781i	$-0.0350150\pi$
$30$	59.4491	−	100.876i	0.361796	−	0.613911i
$31$			187.974i			1.08907i	0.838739	+	0.544533i	$0.183293\pi$
$31$			187.974i			1.08907i	−0.838739	+	0.544533i	$0.816707\pi$
$32$	20.1737	−	179.892i	0.111445	−	0.993771i
$33$	−19.3117	+	19.3117i	−0.101871	+	0.101871i
$34$	−71.2855	−	38.3507i	−0.359569	−	0.193444i
$35$	−190.874	−	206.359i	−0.921816	−	0.996600i
$36$	−58.5893	−	88.7186i	−0.271247	−	0.410734i
$37$	250.679	+	250.679i	1.11382	+	1.11382i	0.992629	+	0.121190i	$0.0386712\pi$
$37$	250.679	+	250.679i	1.11382	+	1.11382i	0.121190	+	0.992629i	$0.461329\pi$
$38$	367.882	−	110.512i	1.57048	−	0.471773i
$39$	14.0467			0.0576737
$40$	187.791	+	169.513i	0.742309	+	0.670058i
$41$	−211.105			−0.804122			−0.402061	−	0.915613i	$-0.631706\pi$
$41$	−211.105			−0.804122			−0.402061	+	0.915613i	$0.631706\pi$
$42$	252.179	−	75.7547i	0.926479	−	0.278314i
$43$	46.7326	+	46.7326i	0.165736	+	0.165736i	0.785102	−	0.619366i	$-0.212610\pi$
$43$	46.7326	+	46.7326i	0.165736	+	0.165736i	−0.619366	+	0.785102i	$0.712610\pi$
$44$	−32.5172	−	49.2390i	−0.111412	−	0.168706i
$45$	148.472	+	5.78774i	0.491843	+	0.0191730i
$46$	−250.253	−	134.633i	−0.802126	−	0.431535i
$47$	189.707	−	189.707i	0.588757	−	0.588757i	−0.348538	−	0.937295i	$-0.613322\pi$
$47$	189.707	−	189.707i	0.588757	−	0.588757i	0.937295	+	0.348538i	$0.113322\pi$
$48$	−219.902	+	88.3159i	−0.661254	+	0.265569i
$49$		−	289.134i		−	0.842956i
$50$	−345.496	+	75.0495i	−0.977211	+	0.212272i
$51$			105.968i			0.290952i
$52$	−6.08147	+	29.7334i	−0.0162182	+	0.0792939i
$53$	−74.5742	+	74.5742i	−0.193275	+	0.193275i	−0.797109	−	0.603835i	$-0.793639\pi$
$53$	−74.5742	+	74.5742i	−0.193275	+	0.193275i	0.603835	+	0.797109i	$0.293639\pi$
$54$	−199.910	+	371.589i	−0.503784	+	0.936423i
$55$	82.4025	+	3.21221i	0.202021	+	0.00787517i
$56$	51.1739	+	566.598i	0.122114	+	1.35205i
$57$	−355.575	−	355.575i	−0.826263	−	0.826263i
$58$	−27.9022	−	92.8835i	−0.0631679	−	0.210279i
$59$	101.072			0.223024			0.111512	−	0.993763i	$-0.464431\pi$
$59$	101.072			0.223024			0.111512	+	0.993763i	$0.464431\pi$
$60$	78.9520	−	321.633i	0.169878	−	0.692044i
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	152.961	+	509.191i	0.313324	+	1.04302i
$63$	236.271	+	236.271i	0.472497	+	0.472497i
$64$	−91.7370	−	503.715i	−0.179174	−	0.983817i
$65$	−28.8002	−	31.1367i	−0.0549573	−	0.0594158i
$66$	−36.5978	+	68.0271i	−0.0682557	+	0.126872i
$67$	−34.7419	+	34.7419i	−0.0633493	+	0.0633493i	−0.738072	−	0.674722i	$-0.764263\pi$
$67$	−34.7419	+	34.7419i	−0.0633493	+	0.0633493i	0.674722	+	0.738072i	$0.264263\pi$
$68$	−224.309	−	45.8785i	−0.400021	−	0.0818175i
$69$			372.010i			0.649054i
$70$	−684.969	−	403.672i	−1.16956	−	0.689258i
$71$		−	614.600i		−	1.02732i	−0.857994	−	0.513660i	$-0.828289\pi$
$71$		−	614.600i		−	1.02732i	0.857994	−	0.513660i	$-0.171711\pi$
$72$	−230.903	−	192.649i	−0.377946	−	0.315331i
$73$	−37.4378	+	37.4378i	−0.0600242	+	0.0600242i	−0.736482	−	0.676457i	$-0.763514\pi$
$73$	−37.4378	+	37.4378i	−0.0600242	+	0.0600242i	0.676457	+	0.736482i	$0.263514\pi$
$74$	883.036	+	475.063i	1.38717	+	0.746283i
$75$	300.807	+	351.761i	0.463123	+	0.541572i
$76$	906.607	−	598.718i	1.36836	−	0.903654i
$77$	131.131	+	131.131i	0.194074	+	0.194074i
$78$	38.0504	−	11.4303i	0.0552353	−	0.0165927i
$79$	−1002.91			−1.42831			−0.714153	−	0.699990i	$-0.753188\pi$
$79$	−1002.91			−1.42831			−0.714153	+	0.699990i	$0.753188\pi$
$80$	646.635	+	306.371i	0.903700	+	0.428167i
$81$	193.554			0.265506
$82$	−571.850	+	171.784i	−0.770125	+	0.231346i
$83$	−423.190	−	423.190i	−0.559652	−	0.559652i	0.369556	−	0.929208i	$-0.379510\pi$
$83$	−423.190	−	423.190i	−0.559652	−	0.559652i	−0.929208	+	0.369556i	$0.879510\pi$
$84$	621.470	−	410.415i	0.807237	−	0.533095i
$85$	234.895	−	217.269i	0.299740	−	0.277248i
$86$	164.619	+	88.5632i	0.206411	+	0.111047i
$87$	−89.7761	+	89.7761i	−0.110632	+	0.110632i
$88$	−128.152	−	106.920i	−0.155239	−	0.129520i
$89$			1049.38i			1.24982i	0.780695	+	0.624912i	$0.214865\pi$
$89$			1049.38i			1.24982i	−0.780695	+	0.624912i	$0.785135\pi$
$90$	406.898	−	105.139i	0.476564	−	0.123141i
$91$		−	95.3802i		−	0.109874i
$92$	−787.453	−	161.060i	−0.892365	−	0.182518i
$93$	492.156	−	492.156i	0.548755	−	0.548755i
$94$	359.514	−	668.257i	0.394479	−	0.733249i
$95$	−59.1444	+	1517.22i	−0.0638746	+	1.63857i
$96$	−523.815	+	418.177i	−0.556892	+	0.444583i
$97$	−536.526	−	536.526i	−0.561608	−	0.561608i	0.368156	−	0.929764i	$-0.379989\pi$
$97$	−536.526	−	536.526i	−0.561608	−	0.561608i	−0.929764	+	0.368156i	$0.879989\pi$
$98$	−235.279	−	783.218i	−0.242518	−	0.807316i
$99$	−98.0246			−0.0995136
$100$	−874.824	+	484.440i	−0.874824	+	0.484440i
$101$	−1415.80			−1.39483			−0.697414	−	0.716668i	$-0.745666\pi$
$101$	−1415.80			−1.39483			−0.697414	+	0.716668i	$0.745666\pi$
$102$	86.2303	+	287.052i	0.0837066	+	0.278650i
$103$	284.920	+	284.920i	0.272563	+	0.272563i	0.830131	−	0.557568i	$-0.188265\pi$
$103$	284.920	+	284.920i	0.272563	+	0.272563i	−0.557568	+	0.830131i	$0.688265\pi$
$104$	7.72143	+	85.4919i	0.00728027	+	0.0806074i
$105$	−40.5429	+	1040.04i	−0.0376817	+	0.966645i
$106$	−141.326	+	262.694i	−0.129498	+	0.240708i
$107$	464.315	−	464.315i	0.419505	−	0.419505i	−0.465528	−	0.885033i	$-0.654136\pi$
$107$	464.315	−	464.315i	0.419505	−	0.419505i	0.885033	+	0.465528i	$0.154136\pi$
$108$	−239.150	+	1169.25i	−0.213076	+	1.04177i
$109$		−	638.365i		−	0.560957i	−0.959860	−	0.280478i	$-0.909507\pi$
$109$		−	638.365i		−	0.560957i	0.959860	−	0.280478i	$-0.0904931\pi$
$110$	225.829	−	58.3525i	0.195745	−	0.0505791i
$111$		−	1312.66i		−	1.12246i
$112$	599.684	+	1493.18i	0.505936	+	1.25976i
$113$	1001.84	−	1001.84i	0.834027	−	0.834027i	−0.154038	−	0.988065i	$-0.549228\pi$
$113$	1001.84	−	1001.84i	0.834027	−	0.834027i	0.988065	+	0.154038i	$0.0492277\pi$
$114$	−1252.54	−	673.852i	−1.02905	−	0.553614i
$115$	824.616	−	762.738i	0.668660	−	0.618484i
$116$	−151.165	−	228.902i	−0.120994	−	0.183216i
$117$	35.6500	+	35.6500i	0.0281696	+	0.0281696i
$118$	273.787	−	82.2456i	0.213594	−	0.0641638i
$119$	719.548			0.554293
$120$	−47.8561	−	935.500i	−0.0364053	−	0.711659i
$121$	1276.60			0.959126
$122$	628.756	−	188.878i	0.466598	−	0.140166i
$123$	552.718	+	552.718i	0.405178	+	0.405178i
$124$	828.695	+	1254.85i	0.600153	+	0.908780i
$125$	162.982	−	1388.01i	0.116621	−	0.993177i
$126$	832.282	+	447.758i	0.588457	+	0.316583i
$127$	619.456	−	619.456i	0.432818	−	0.432818i	−0.456768	−	0.889586i	$-0.650993\pi$
$127$	619.456	−	619.456i	0.432818	−	0.432818i	0.889586	+	0.456768i	$0.150993\pi$
$128$	−658.392	−	1289.83i	−0.454642	−	0.890674i
$129$		−	244.712i		−	0.167021i
$130$	−103.352	−	60.9086i	−0.0697277	−	0.0410926i
$131$			1620.12i			1.08054i	0.841491	+	0.540270i	$0.181678\pi$
$131$			1620.12i			1.08054i	−0.841491	+	0.540270i	$0.818322\pi$
$132$	−43.7815	+	214.056i	−0.0288689	+	0.141145i
$133$	−2414.43	+	2414.43i	−1.57412	+	1.57412i
$134$	−65.8397	+	122.381i	−0.0424454	+	0.0788965i
$135$	−1132.55	−	1224.43i	−0.722034	−	0.780611i
$136$	−644.950	+	58.2504i	−0.406647	+	0.0367274i
$137$	825.076	+	825.076i	0.514533	+	0.514533i	0.915912	−	0.401379i	$-0.131469\pi$
$137$	825.076	+	825.076i	0.514533	+	0.514533i	−0.401379	+	0.915912i	$0.631469\pi$
$138$	302.718	+	1007.72i	0.186733	+	0.621613i
$139$	−1264.21			−0.771430			−0.385715	−	0.922618i	$-0.626045\pi$
$139$	−1264.21			−0.771430			−0.385715	+	0.922618i	$0.626045\pi$
$140$	−2183.96	−	536.101i	−1.31841	−	0.323634i
$141$	−993.387			−0.593321
$142$	−500.123	−	1664.86i	−0.295559	−	0.983885i
$143$	19.7858	+	19.7858i	0.0115704	+	0.0115704i
$144$	−782.244	−	333.961i	−0.452688	−	0.193264i
$145$	383.072	+	14.9329i	0.219396	+	0.00855247i
$146$	−70.9487	+	131.878i	−0.0402175	+	0.0747553i
$147$	−757.016	+	757.016i	−0.424746	+	0.424746i
$148$	2778.58	+	568.312i	1.54323	+	0.315642i
$149$		−	1351.49i		−	0.743079i	−0.928417	−	0.371539i	$-0.878830\pi$
$149$		−	1351.49i		−	0.743079i	0.928417	−	0.371539i	$-0.121170\pi$
$150$	1101.08	+	708.089i	0.599352	+	0.385435i
$151$			2325.64i			1.25336i	0.779275	+	0.626682i	$0.215588\pi$
$151$			2325.64i			1.25336i	−0.779275	+	0.626682i	$0.784412\pi$
$152$	1968.66	−	2359.57i	1.05052	−	1.25912i
$153$	−268.943	+	268.943i	−0.142109	+	0.142109i
$154$	461.918	+	248.507i	0.241704	+	0.130034i
$155$	−2100.01	−	81.8626i	−1.08824	−	0.0424217i
$156$	93.7712	−	61.9260i	0.0481263	−	0.0317823i
$157$	162.486	+	162.486i	0.0825976	+	0.0825976i	0.747199	−	0.664601i	$-0.231398\pi$
$157$	162.486	+	162.486i	0.0825976	+	0.0825976i	−0.664601	+	0.747199i	$0.731398\pi$
$158$	−2716.73	+	816.105i	−1.36792	+	0.410923i
$159$	390.503			0.194773
$160$	2000.94	+	303.721i	0.988675	+	0.150070i
$161$	2526.03			1.23651
$162$	524.307	−	157.502i	0.254281	−	0.0763859i
$163$	−932.441	−	932.441i	−0.448064	−	0.448064i	0.446647	−	0.894710i	$-0.352618\pi$
$163$	−932.441	−	932.441i	−0.448064	−	0.448064i	−0.894710	+	0.446647i	$0.852618\pi$
$164$	−1409.26	+	930.670i	−0.671006	+	0.443129i
$165$	−207.337	−	224.158i	−0.0978255	−	0.105762i
$166$	−1490.72	−	801.990i	−0.697002	−	0.374979i
$167$	−976.461	+	976.461i	−0.452460	+	0.452460i	−0.896170	−	0.443710i	$-0.853662\pi$
$167$	−976.461	+	976.461i	−0.452460	+	0.452460i	0.443710	+	0.896170i	$0.353662\pi$
$168$	1349.49	−	1617.46i	0.619737	−	0.742798i
$169$			2182.61i			0.993449i
$170$	459.494	−	779.689i	0.207303	−	0.351761i
$171$		−	1804.87i		−	0.807143i
$172$	517.995	+	105.947i	0.229632	+	0.0469674i
$173$	761.698	−	761.698i	0.334745	−	0.334745i	−0.519640	−	0.854385i	$-0.673934\pi$
$173$	761.698	−	761.698i	0.334745	−	0.334745i	0.854385	+	0.519640i	$0.173934\pi$
$174$	−170.135	+	316.244i	−0.0741260	+	0.137784i
$175$	2388.54	−	2042.54i	1.03175	−	0.882296i
$176$	−434.148	−	185.349i	−0.185938	−	0.0793818i
$177$	−264.628	−	264.628i	−0.112376	−	0.112376i
$178$	853.921	+	2842.61i	0.359574	+	1.19698i
$179$	4003.32			1.67163			0.835816	−	0.549009i	$-0.184995\pi$
$179$	4003.32			1.67163			0.835816	+	0.549009i	$0.184995\pi$
$180$	1016.67	−	615.914i	0.420988	−	0.255042i
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	−77.6144	−	258.370i	−0.0316108	−	0.105229i
$183$	−607.721	−	607.721i	−0.245487	−	0.245487i
$184$	−2264.15	+	204.493i	−0.907147	+	0.0819315i
$185$	−2909.72	+	2691.38i	−1.15636	+	1.06959i
$186$	932.688	−	1733.66i	0.367677	−	0.683430i
$187$	−149.264	+	149.264i	−0.0583704	+	0.0583704i
$188$	430.083	−	2102.75i	0.166846	−	0.815740i
$189$		−	3750.78i		−	1.44354i
$190$	1074.41	+	4158.05i	0.410241	+	1.58767i
$191$			1458.80i			0.552644i	0.961065	+	0.276322i	$0.0891156\pi$
$191$			1458.80i			0.552644i	−0.961065	+	0.276322i	$0.910884\pi$
$192$	−1078.65	+	1559.02i	−0.405441	+	0.586004i
$193$	2264.70	−	2264.70i	0.844647	−	0.844647i	−0.144812	−	0.989459i	$-0.546258\pi$
$193$	2264.70	−	2264.70i	0.844647	−	0.844647i	0.989459	+	0.144812i	$0.0462577\pi$
$194$	−1889.96	−	1016.77i	−0.699438	−	0.376289i
$195$	−6.11736	+	156.928i	−0.00224653	+	0.0576300i
$196$	−1274.67	−	1930.16i	−0.464529	−	0.703411i
$197$	2092.70	+	2092.70i	0.756845	+	0.756845i	0.975747	−	0.218902i	$-0.0702474\pi$
$197$	2092.70	+	2092.70i	0.756845	+	0.756845i	−0.218902	+	0.975747i	$0.570247\pi$
$198$	−265.533	+	79.7662i	−0.0953062	+	0.0286300i
$199$	2087.70			0.743683			0.371842	−	0.928296i	$-0.378726\pi$
$199$	2087.70			0.743683			0.371842	+	0.928296i	$0.378726\pi$
$200$	−1975.56	+	2024.15i	−0.698464	+	0.715645i
$201$	181.924			0.0638405
$202$	−3835.19	+	1152.09i	−1.33586	+	0.401291i
$203$	609.599	+	609.599i	0.210766	+	0.210766i
$204$	467.169	+	707.409i	0.160335	+	0.242787i
$205$	91.9363	−	2358.43i	0.0313225	−	0.803512i
$206$	1003.65	+	539.954i	0.339456	+	0.182623i
$207$	−944.145	+	944.145i	−0.317018	+	0.317018i
$208$	90.4840	+	225.301i	0.0301632	+	0.0751048i
$209$		−	1001.70i		−	0.331528i
$210$	736.496	+	2850.30i	0.242015	+	0.936617i
$211$		−	199.597i		−	0.0651223i	−0.999470	−	0.0325611i	$-0.989634\pi$
$211$		−	199.597i		−	0.0651223i	0.999470	−	0.0325611i	$-0.0103664\pi$
$212$	−169.067	+	826.598i	−0.0547714	+	0.267788i
$213$	−1609.16	+	1609.16i	−0.517642	+	0.517642i
$214$	879.926	−	1635.59i	0.281077	−	0.522460i
$215$	−542.442	+	501.738i	−0.172066	+	0.159155i
$216$	303.641	+	3361.92i	0.0956489	+	1.05903i
$217$	−3341.84	−	3341.84i	−1.04543	−	1.04543i
$218$	−519.461	−	1729.23i	−0.161387	−	0.537240i
$219$	196.041			0.0604896
$220$	564.252	−	341.834i	0.172918	−	0.104756i
$221$	108.570			0.0330461
$222$	−1068.16	−	3555.80i	−0.322930	−	1.07500i
$223$	−3340.24	−	3340.24i	−1.00304	−	1.00304i	−0.999995	−	0.00304854i	$-0.999030\pi$
$223$	−3340.24	−	3340.24i	−1.00304	−	1.00304i	−0.00304854	−	0.999995i	$-0.500970\pi$
$224$	2839.51	+	3556.82i	0.846976	+	1.06094i
$225$	−129.320	+	1656.19i	−0.0383169	+	0.490723i
$226$	1898.59	−	3529.06i	0.558816	−	1.03871i
$227$	−824.316	+	824.316i	−0.241021	+	0.241021i	−0.817272	−	0.576251i	$-0.804515\pi$
$227$	−824.316	+	824.316i	−0.241021	+	0.241021i	0.576251	+	0.817272i	$0.304515\pi$
$228$	−3941.27	−	806.121i	−1.14481	−	0.234152i
$229$			4512.23i			1.30208i	0.759043	+	0.651041i	$0.225667\pi$
$229$			4512.23i			1.30208i	−0.759043	+	0.651041i	$0.774333\pi$
$230$	1613.09	−	2737.16i	0.462452	−	0.784708i
$231$		−	686.658i		−	0.195579i
$232$	−595.749	−	497.050i	−0.168590	−	0.140659i
$233$	−292.574	+	292.574i	−0.0822625	+	0.0822625i	−0.747041	−	0.664778i	$-0.768526\pi$
$233$	−292.574	+	292.574i	−0.0822625	+	0.0822625i	0.664778	+	0.747041i	$0.268526\pi$
$234$	125.580	+	67.5605i	0.0350829	+	0.0188742i
$235$	2036.76	+	2201.99i	0.565376	+	0.611243i
$236$	674.720	−	445.581i	0.186104	−	0.122902i
$237$	2625.84	+	2625.84i	0.719690	+	0.719690i
$238$	1949.14	−	585.522i	0.530858	−	0.159470i
$239$	−2925.20			−0.791696			−0.395848	−	0.918316i	$-0.629549\pi$
$239$	−2925.20			−0.791696			−0.395848	+	0.918316i	$0.629549\pi$
$240$	−890.885	−	2495.18i	−0.239610	−	0.671096i
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	3458.10	−	1038.81i	0.918574	−	0.275940i
$243$	2341.40	+	2341.40i	0.618111	+	0.618111i
$244$	1549.50	−	1023.28i	0.406544	−	0.268480i
$245$	3230.16	+	125.918i	0.842316	+	0.0328351i
$246$	1947.00	+	1047.46i	0.504617	+	0.271478i
$247$	−364.304	+	364.304i	−0.0938465	+	0.0938465i
$248$	3265.92	+	2724.85i	0.836235	+	0.697694i
$249$			2216.01i			0.563991i
$250$	−687.978	−	3892.52i	−0.174046	−	0.984737i
$251$		−	5268.72i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$251$		−	5268.72i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$252$	2618.88	+	535.647i	0.654658	+	0.133899i
$253$	−524.003	+	524.003i	−0.130213	+	0.130213i
$254$	1173.94	−	2182.08i	0.289997	−	0.539040i
$255$	−1183.86	−	46.1493i	−0.290731	−	0.0113333i
$256$	−2833.07	−	2958.20i	−0.691667	−	0.722217i
$257$	−5635.08	−	5635.08i	−1.36773	−	1.36773i	−0.863668	−	0.504061i	$-0.831839\pi$
$257$	−5635.08	−	5635.08i	−1.36773	−	1.36773i	−0.504061	−	0.863668i	$-0.668161\pi$
$258$	−199.132	−	662.888i	−0.0480519	−	0.159960i
$259$	−8913.27			−2.13839
$260$	−329.529	−	80.8902i	−0.0786020	−	0.0192946i
$261$	−455.696			−0.108072
$262$	1318.35	+	4388.66i	0.310871	+	1.03486i
$263$	2721.99	+	2721.99i	0.638195	+	0.638195i	0.950110	−	0.311915i	$-0.100970\pi$
$263$	2721.99	+	2721.99i	0.638195	+	0.638195i	−0.311915	+	0.950110i	$0.600970\pi$
$264$	55.5878	+	615.470i	0.0129591	+	0.143483i
$265$	−800.655	−	865.609i	−0.185599	−	0.200656i
$266$	−4575.60	+	8505.01i	−1.05469	+	1.96044i
$267$	2747.51	−	2747.51i	0.629757	−	0.629757i
$268$	−78.7632	+	385.088i	−0.0179523	+	0.0877723i
$269$		−	603.964i		−	0.136893i	−0.997655	−	0.0684467i	$-0.978196\pi$
$269$		−	603.964i		−	0.136893i	0.997655	−	0.0684467i	$-0.0218043\pi$
$270$	−4064.28	−	2395.20i	−0.916089	−	0.539878i
$271$			4232.24i			0.948672i	0.880344	+	0.474336i	$0.157312\pi$
$271$			4232.24i			0.948672i	−0.880344	+	0.474336i	$0.842688\pi$
$272$	−1699.67	+	682.611i	−0.378888	+	0.152167i
$273$	−249.726	+	249.726i	−0.0553631	+	0.0553631i
$274$	2906.40	+	1563.61i	0.640810	+	0.344748i
$275$	−71.7727	+	919.189i	−0.0157384	+	0.201561i
$276$	1640.03	+	2483.41i	0.357675	+	0.541609i
$277$	3214.07	+	3214.07i	0.697165	+	0.697165i	0.963798	−	0.266633i	$-0.0859113\pi$
$277$	3214.07	+	3214.07i	0.697165	+	0.697165i	−0.266633	+	0.963798i	$0.585911\pi$
$278$	−3424.54	+	1028.73i	−0.738815	+	0.221940i
$279$	2498.14			0.536056
$280$	−6352.24	+	324.953i	−1.35578	+	0.0693559i
$281$	−7574.78			−1.60809			−0.804046	−	0.594567i	$-0.797323\pi$
$281$	−7574.78			−1.60809			−0.804046	+	0.594567i	$0.797323\pi$
$282$	−2690.93	+	808.356i	−0.568236	+	0.170698i
$283$	504.094	+	504.094i	0.105884	+	0.105884i	0.758064	−	0.652180i	$-0.226145\pi$
$283$	504.094	+	504.094i	0.105884	+	0.105884i	−0.652180	+	0.758064i	$0.726145\pi$
$284$	−2709.51	−	4102.87i	−0.566126	−	0.857255i
$285$	4127.28	−	3817.58i	0.857821	−	0.793451i
$286$	69.6971	+	37.4962i	0.0144101	+	0.00775244i
$287$	3753.08	−	3753.08i	0.771906	−	0.771906i
$288$	−2390.73	−	268.106i	−0.489150	−	0.0548552i
$289$		−	4093.95i		−	0.833289i
$290$	1049.83	−	271.269i	0.212580	−	0.0549291i
$291$			2809.49i			0.565962i
$292$	−84.8750	+	414.970i	−0.0170101	+	0.0831653i
$293$	−244.144	+	244.144i	−0.0486793	+	0.0486793i	−0.731027	−	0.682348i	$-0.760959\pi$
$293$	−244.144	+	244.144i	−0.0486793	+	0.0486793i	0.682348	+	0.731027i	$0.260959\pi$
$294$	−1434.63	+	2666.65i	−0.284589	+	0.528987i
$295$	−44.0167	+	1129.16i	−0.00868730	+	0.222854i
$296$	7989.20	−	721.566i	1.56879	−	0.141690i
$297$	778.066	+	778.066i	0.152013	+	0.152013i
$298$	−1099.76	−	3660.99i	−0.213783	−	0.711662i
$299$	381.143			0.0737192
$300$	3558.85	+	1022.11i	0.684902	+	0.196705i
$301$	−1661.65			−0.318192
$302$	1892.46	+	6299.80i	0.360592	+	1.20037i
$303$	3706.88	+	3706.88i	0.702822	+	0.702822i
$304$	3412.71	−	7993.69i	0.643857	−	1.50812i
$305$	−101.085	+	2593.13i	−0.0189774	+	0.486826i
$306$	−509.676	+	947.373i	−0.0952164	+	0.176986i
$307$	6853.22	−	6853.22i	1.27405	−	1.27405i	0.330110	−	0.943942i	$-0.392914\pi$
$307$	6853.22	−	6853.22i	1.27405	−	1.27405i	0.943942	−	0.330110i	$-0.107086\pi$
$308$	1453.48	+	297.286i	0.268896	+	0.0549981i
$309$		−	1491.97i		−	0.274676i
$310$	−5755.22	+	1487.11i	−1.05443	+	0.272458i
$311$		−	10802.7i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$311$		−	10802.7i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$312$	203.620	−	244.053i	0.0369478	−	0.0442845i
$313$	2618.43	−	2618.43i	0.472851	−	0.472851i	−0.429985	−	0.902836i	$-0.641481\pi$
$313$	2618.43	−	2618.43i	0.472851	−	0.472851i	0.902836	+	0.429985i	$0.141481\pi$
$314$	572.372	+	307.929i	0.102869	+	0.0553422i
$315$	−2742.48	+	2536.68i	−0.490543	+	0.453733i
$316$	−6695.09	+	4421.40i	−1.19186	+	0.787098i
$317$	3652.64	+	3652.64i	0.647170	+	0.647170i	0.952308	−	0.305138i	$-0.0987027\pi$
$317$	3652.64	+	3652.64i	0.647170	+	0.647170i	−0.305138	+	0.952308i	$0.598703\pi$
$318$	1057.81	−	317.767i	0.186538	−	0.0560361i
$319$	−252.912			−0.0443898
$320$	5667.38	−	805.504i	0.990050	−	0.140716i
$321$	−2431.36			−0.422757
$322$	6842.61	−	2055.52i	1.18424	−	0.355745i
$323$	−2748.30	−	2748.30i	−0.473436	−	0.473436i
$324$	1292.10	−	853.296i	0.221554	−	0.146313i
$325$	360.397	−	308.192i	0.0615115	−	0.0526012i
$326$	−3284.60	−	1767.07i	−0.558028	−	0.300212i
$327$	−1671.38	+	1671.38i	−0.282653	+	0.282653i
$328$	−3060.16	+	3667.81i	−0.515149	+	0.617442i
$329$			6745.31i			1.13034i
$330$	−744.050	−	438.491i	−0.124117	−	0.0731458i
$331$			7839.91i			1.30187i	0.759131	+	0.650937i	$0.225624\pi$
$331$			7839.91i			1.30187i	−0.759131	+	0.650937i	$0.774376\pi$
$332$	−4690.74	−	959.411i	−0.775415	−	0.158598i
$333$	3331.48	−	3331.48i	0.548241	−	0.548241i
$334$	−1850.50	+	3439.66i	−0.303158	+	0.563503i
$335$	−373.002	−	403.262i	−0.0608336	−	0.0657688i
$336$	2339.38	−	5479.59i	0.379832	−	0.889691i
$337$	−4503.23	−	4503.23i	−0.727912	−	0.727912i	0.242291	−	0.970204i	$-0.422101\pi$
$337$	−4503.23	−	4503.23i	−0.727912	−	0.727912i	−0.970204	+	0.242291i	$0.922101\pi$
$338$	1776.07	+	5912.34i	0.285815	+	0.951447i
$339$	−5246.07			−0.840494
$340$	610.235	−	2485.96i	0.0973371	−	0.396530i
$341$	1386.47			0.220181
$342$	−1468.69	−	4889.10i	−0.232215	−	0.773018i
$343$	−957.648	−	957.648i	−0.150753	−	0.150753i
$344$	1489.38	−	134.517i	0.233436	−	0.0210834i
$345$	−4156.04	−	162.011i	−0.648562	−	0.0252822i
$346$	1443.50	−	2683.14i	0.224286	−	0.416898i
$347$	−8458.77	+	8458.77i	−1.30862	+	1.30862i	−0.386205	+	0.922413i	$0.626214\pi$
$347$	−8458.77	+	8458.77i	−1.30862	+	1.30862i	−0.922413	+	0.386205i	$0.873786\pi$
$348$	−203.531	+	995.100i	−0.0313517	+	0.153284i
$349$			5515.41i			0.845941i	0.906144	+	0.422970i	$0.139013\pi$
$349$			5515.41i			0.845941i	−0.906144	+	0.422970i	$0.860987\pi$
$350$	4808.07	−	7476.57i	0.734292	−	1.14183i
$351$		−	565.940i		−	0.0860617i
$352$	−1326.86	−	148.799i	−0.200915	−	0.0225314i
$353$	−761.447	+	761.447i	−0.114810	+	0.114810i	−0.762178	−	0.647368i	$-0.775870\pi$
$353$	−761.447	+	761.447i	−0.114810	+	0.114810i	0.647368	+	0.762178i	$0.275870\pi$
$354$	−932.172	−	501.497i	−0.139956	−	0.0752946i
$355$	6866.23	+	267.659i	1.02654	+	0.0400165i
$356$	4626.28	+	7005.33i	0.688742	+	1.04293i
$357$	−1883.93	−	1883.93i	−0.279295	−	0.279295i
$358$	10844.4	−	3257.65i	1.60096	−	0.480928i
$359$	−3564.71			−0.524062			−0.262031	−	0.965059i	$-0.584392\pi$
$359$	−3564.71			−0.524062			−0.262031	+	0.965059i	$0.584392\pi$
$360$	2252.80	−	2495.71i	0.329814	−	0.365377i
$361$	11584.8			1.68899
$362$	−5282.23	+	1586.78i	−0.766928	+	0.230385i
$363$	−3342.41	−	3342.41i	−0.483281	−	0.483281i
$364$	−420.491	−	636.726i	−0.0605486	−	0.0916855i
$365$	−401.946	−	434.554i	−0.0576405	−	0.0623167i
$366$	−2140.75	−	1151.70i	−0.305734	−	0.164481i
$367$	−4407.82	+	4407.82i	−0.626939	+	0.626939i	−0.947297	−	0.320358i	$-0.896197\pi$
$367$	−4407.82	+	4407.82i	−0.626939	+	0.626939i	0.320358	+	0.947297i	$0.396197\pi$
$368$	−5966.81	+	2396.36i	−0.845222	+	0.339453i
$369$			2805.55i			0.395802i
$370$	−5691.90	+	9658.26i	−0.799750	+	1.35705i
$371$		−	2651.60i		−	0.371063i
$372$	1115.76	−	5455.17i	0.155510	−	0.760316i
$373$	−8371.19	+	8371.19i	−1.16205	+	1.16205i	−0.178021	+	0.984027i	$0.556970\pi$
$373$	−8371.19	+	8371.19i	−1.16205	+	1.16205i	−0.984027	+	0.178021i	$0.943030\pi$
$374$	−282.871	+	525.794i	−0.0391094	+	0.0726957i
$375$	−4060.83	+	3207.38i	−0.559201	+	0.441676i
$376$	−546.061	−	6046.00i	−0.0748962	−	0.829252i
$377$	91.9800	+	91.9800i	0.0125656	+	0.0125656i
$378$	−3052.15	−	10160.3i	−0.415305	−	1.38251i
$379$	11130.1			1.50848			0.754240	−	0.656599i	$-0.228006\pi$
$379$	11130.1			1.50848			0.754240	+	0.656599i	$0.228006\pi$
$380$	6293.97	+	10389.2i	0.849667	+	1.40252i
$381$	−3243.75			−0.436174
$382$	1187.08	+	3951.66i	0.158995	+	0.529279i
$383$	−1006.62	−	1006.62i	−0.134297	−	0.134297i	0.636763	−	0.771060i	$-0.280273\pi$
$383$	−1006.62	−	1006.62i	−0.134297	−	0.134297i	−0.771060	+	0.636763i	$0.780273\pi$
$384$	−1653.25	+	5100.88i	−0.219706	+	0.677873i
$385$	−1522.08	+	1407.87i	−0.201487	+	0.186367i
$386$	4291.85	−	7977.60i	0.565932	−	1.05194i
$387$	621.069	−	621.069i	0.0815781	−	0.0815781i
$388$	−5946.98	−	1216.35i	−0.778124	−	0.159152i
$389$		−	13548.4i		−	1.76589i	−0.469478	−	0.882944i	$-0.655558\pi$
$389$		−	13548.4i		−	1.76589i	0.469478	−	0.882944i	$-0.344442\pi$
$390$	111.127	+	430.071i	0.0144286	+	0.0558397i
$391$			2875.34i			0.371898i
$392$	−5023.52	−	4191.26i	−0.647260	−	0.540027i
$393$	4241.84	−	4241.84i	0.544459	−	0.544459i
$394$	7371.69	+	3965.88i	0.942590	+	0.507102i
$395$	436.768	−	11204.4i	0.0556359	−	1.42722i
$396$	−654.379	+	432.148i	−0.0830399	+	0.0548391i
$397$	1822.81	+	1822.81i	0.230439	+	0.230439i	0.812876	−	0.582437i	$-0.197901\pi$
$397$	1822.81	+	1822.81i	0.230439	+	0.230439i	−0.582437	+	0.812876i	$0.697901\pi$
$398$	5655.25	−	1698.84i	0.712241	−	0.213957i
$399$	12643.0			1.58632
$400$	−3704.34	+	7090.69i	−0.463043	+	0.886336i
$401$	5922.04			0.737488			0.368744	−	0.929531i	$-0.379788\pi$
$401$	5922.04			0.737488			0.368744	+	0.929531i	$0.379788\pi$
$402$	492.804	−	148.038i	0.0611413	−	0.0183669i
$403$	−504.238	−	504.238i	−0.0623273	−	0.0623273i
$404$	−9451.43	+	6241.67i	−1.16393	+	0.768650i
$405$	−84.2929	+	2162.36i	−0.0103421	+	0.265305i
$406$	2147.36	+	1155.25i	0.262492	+	0.141218i
$407$	1848.98	−	1848.98i	0.225186	−	0.225186i
$408$	1841.13	+	1536.11i	0.223406	+	0.186394i
$409$		−	8533.05i		−	1.03162i	−0.856703	−	0.515809i	$-0.827491\pi$
$409$		−	8533.05i		−	1.03162i	0.856703	−	0.515809i	$-0.172509\pi$
$410$	−1670.10	−	6463.43i	−0.201172	−	0.778552i
$411$		−	4320.46i		−	0.518522i
$412$	3158.12	+	645.940i	0.377644	+	0.0772408i
$413$	−1796.88	+	1796.88i	−0.214088	+	0.214088i
$414$	−1789.26	+	3325.83i	−0.212408	+	0.394820i
$415$	4912.12	−	4543.52i	0.581027	−	0.537428i
$416$	428.443	+	536.674i	0.0504955	+	0.0632515i
$417$	3309.98	+	3309.98i	0.388706	+	0.388706i
$418$	−815.124	−	2713.46i	−0.0953804	−	0.317511i
$419$	7128.02			0.831089			0.415545	−	0.909573i	$-0.363591\pi$
$419$	7128.02			0.831089			0.415545	+	0.909573i	$0.363591\pi$
$420$	4314.45	+	7121.71i	0.501247	+	0.827390i
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	−162.419	−	540.676i	−0.0187356	−	0.0623690i
$423$	−2521.17	−	2521.17i	−0.289796	−	0.289796i
$424$	214.658	+	2376.70i	0.0245866	+	0.272223i
$425$	2325.00	+	2718.83i	0.265362	+	0.310312i
$426$	−3049.53	+	5668.39i	−0.346831	+	0.644682i
$427$	−4126.56	+	4126.56i	−0.467677	+	0.467677i
$428$	1052.65	−	5146.58i	0.118882	−	0.581236i
$429$		−	103.607i		−	0.0116601i
$430$	−1061.11	+	1800.53i	−0.119003	+	0.201929i
$431$			9361.72i			1.04626i	0.852253	+	0.523130i	$0.175236\pi$
$431$			9361.72i			1.04626i	−0.852253	+	0.523130i	$0.824764\pi$
$432$	3558.24	+	8859.84i	0.396286	+	0.986734i
$433$	−1769.48	+	1769.48i	−0.196388	+	0.196388i	−0.798450	−	0.602062i	$-0.794346\pi$
$433$	−1769.48	+	1769.48i	−0.196388	+	0.196388i	0.602062	+	0.798450i	$0.294346\pi$
$434$	−11771.9	−	6333.15i	−1.30200	−	0.700463i
$435$	−963.868	−	1042.06i	−0.106239	−	0.114858i
$436$	−2814.28	−	4261.51i	−0.309127	−	0.468095i
$437$	−9648.13	−	9648.13i	−1.05614	−	1.05614i
$438$	531.044	−	159.526i	0.0579321	−	0.0174028i
$439$	−7823.34			−0.850541			−0.425271	−	0.905066i	$-0.639821\pi$
$439$	−7823.34			−0.850541			−0.425271	+	0.905066i	$0.639821\pi$
$440$	1250.31	−	1385.13i	0.135469	−	0.150076i
$441$	−3842.54			−0.414917
$442$	294.099	−	88.3472i	0.0316490	−	0.00950735i
$443$	9066.48	+	9066.48i	0.972374	+	0.972374i	0.999629	−	0.0272545i	$-0.00867646\pi$
$443$	9066.48	+	9066.48i	0.972374	+	0.972374i	−0.0272545	+	0.999629i	$0.508676\pi$
$444$	−5786.97	−	8762.91i	−0.618553	−	0.936642i
$445$	−11723.5	−	457.007i	−1.24888	−	0.0486836i
$446$	−11766.3	−	6330.10i	−1.24921	−	0.672061i
$447$	−3538.51	+	3538.51i	−0.374420	+	0.374420i
$448$	10586.1	+	7324.25i	1.11640	+	0.772407i
$449$			3381.93i			0.355464i	0.984079	+	0.177732i	$0.0568759\pi$
$449$			3381.93i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$450$	997.396	+	4591.59i	0.104484	+	0.480999i
$451$			1557.09i			0.162573i
$452$	2271.26	−	11104.6i	0.236352	−	1.15557i
$453$	6089.04	−	6089.04i	0.631541	−	0.631541i
$454$	−1562.17	+	2903.72i	−0.161489	+	0.300173i
$455$	1065.57	+	41.5382i	0.109791	+	0.00427987i
$456$	−11332.3	+	1023.50i	−1.16378	+	0.105110i
$457$	10289.7	+	10289.7i	1.05324	+	1.05324i	0.998501	+	0.0547399i	$0.0174330\pi$
$457$	10289.7	+	10289.7i	1.05324	+	1.05324i	0.0547399	+	0.998501i	$0.482567\pi$
$458$	3671.77	+	12222.9i	0.374608	+	1.24703i
$459$	4269.45			0.434163
$460$	2142.28	−	8727.16i	0.217140	−	0.884579i
$461$	−5310.20			−0.536488			−0.268244	−	0.963351i	$-0.586443\pi$
$461$	−5310.20			−0.536488			−0.268244	+	0.963351i	$0.586443\pi$
$462$	−558.759	−	1860.05i	−0.0562680	−	0.187310i
$463$	−7686.78	−	7686.78i	−0.771566	−	0.771566i	0.206814	−	0.978380i	$-0.433690\pi$
$463$	−7686.78	−	7686.78i	−0.771566	−	0.771566i	−0.978380	+	0.206814i	$0.933690\pi$
$464$	−2018.26	−	861.648i	−0.201930	−	0.0862091i
$465$	5283.96	+	5712.63i	0.526963	+	0.569714i
$466$	−554.459	+	1030.62i	−0.0551176	+	0.102451i
$467$	−4535.99	+	4535.99i	−0.449466	+	0.449466i	−0.895177	−	0.445711i	$-0.852951\pi$
$467$	−4535.99	+	4535.99i	−0.449466	+	0.449466i	0.445711	+	0.895177i	$0.352951\pi$
$468$	395.153	+	80.8218i	0.0390298	+	0.00798288i
$469$		−	1235.30i		−	0.121623i
$470$	7309.10	+	4307.47i	0.717327	+	0.422742i
$471$		−	850.850i		−	0.0832380i
$472$	1465.12	−	1756.05i	0.142877	−	0.171248i
$473$	344.695	−	344.695i	0.0335076	−	0.0335076i
$474$	9249.72	+	4976.24i	0.896316	+	0.482208i
$475$	−16924.5	−	1321.51i	−1.63484	−	0.127652i
$476$	4803.46	−	3172.18i	0.462534	−	0.305455i
$477$	991.080	+	991.080i	0.0951330	+	0.0951330i
$478$	−7923.91	+	2380.34i	−0.758224	+	0.227771i
$479$	−10969.6			−1.04638			−0.523189	−	0.852217i	$-0.675258\pi$
$479$	−10969.6			−1.04638			−0.523189	+	0.852217i	$0.675258\pi$
$480$	−4443.69	−	6034.10i	−0.422553	−	0.573787i
$481$	−1344.89			−0.127488
$482$	11538.0	−	3466.03i	1.09034	−	0.327538i
$483$	−6613.70	−	6613.70i	−0.623051	−	0.623051i
$484$	8522.13	−	5627.97i	0.800350	−	0.528547i
$485$	6227.65	−	5760.33i	0.583058	−	0.539306i
$486$	8247.77	+	4437.20i	0.769808	+	0.414147i
$487$	12736.0	−	12736.0i	1.18506	−	1.18506i	0.206646	−	0.978416i	$-0.433745\pi$
$487$	12736.0	−	12736.0i	1.18506	−	1.18506i	0.978416	−	0.206646i	$-0.0662547\pi$
$488$	3364.68	−	4032.80i	0.312115	−	0.374091i
$489$			4882.67i			0.451538i
$490$	8852.46	−	2287.41i	0.816150	−	0.210887i
$491$			10518.6i			0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$491$			10518.6i			0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$492$	6126.46	+	1253.06i	0.561387	+	0.114822i
$493$	−693.897	+	693.897i	−0.0633905	+	0.0633905i
$494$	−690.394	+	1283.29i	−0.0628792	+	0.116878i
$495$	42.6898	−	1095.12i	0.00387629	−	0.0994380i
$496$	11064.2	+	4723.59i	1.00161	+	0.427612i
$497$	10926.5	+	10926.5i	0.986161	+	0.986161i
$498$	1803.25	+	6002.82i	0.162260	+	0.540146i
$499$	2445.26			0.219368			0.109684	−	0.993966i	$-0.465016\pi$
$499$	2445.26			0.219368			0.109684	+	0.993966i	$0.465016\pi$
$500$	−5031.11	−	9984.38i	−0.449996	−	0.893031i
$501$	5113.18			0.455968
$502$	−4287.35	−	14272.1i	−0.381183	−	1.26892i
$503$	12216.7	+	12216.7i	1.08293	+	1.08293i	0.996235	+	0.0866986i	$0.0276317\pi$
$503$	12216.7	+	12216.7i	1.08293	+	1.08293i	0.0866986	+	0.996235i	$0.472368\pi$
$504$	7530.01	−	680.093i	0.665502	−	0.0601066i
$505$	616.584	−	15817.1i	0.0543319	−	1.39377i
$506$	−993.041	+	1845.84i	−0.0872452	+	0.162169i
$507$	5714.55	−	5714.55i	0.500576	−	0.500576i
$508$	1404.37	−	6866.20i	0.122655	−	0.599682i
$509$			5615.75i			0.489025i	0.969646	+	0.244512i	$0.0786279\pi$
$509$			5615.75i			0.489025i	−0.969646	+	0.244512i	$0.921372\pi$
$510$	−3244.45	+	838.342i	−0.281700	+	0.0727890i
$511$		−	1331.16i		−	0.115239i
$512$	−10081.5	−	5707.93i	−0.870205	−	0.492690i
$513$	−14326.0	+	14326.0i	−1.23296	+	1.23296i
$514$	−19850.0	−	10679.1i	−1.70340	−	0.916408i
$515$	−3307.17	+	3059.00i	−0.282973	+	0.261739i
$516$	−1078.83	−	1633.62i	−0.0920406	−	0.139372i
$517$	−1399.26	−	1399.26i	−0.119031	−	0.119031i
$518$	−24144.6	+	7253.05i	−2.04798	+	0.615214i
$519$	−3988.58			−0.337340
$520$	−958.465	+	49.0309i	−0.0808298	+	0.00413490i
$521$	5287.10			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$521$	5287.10			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$522$	−1234.41	+	370.816i	−0.103503	+	0.0310923i
$523$	−4328.34	−	4328.34i	−0.361883	−	0.361883i	0.502623	−	0.864506i	$-0.332369\pi$
$523$	−4328.34	−	4328.34i	−0.361883	−	0.361883i	−0.864506	+	0.502623i	$0.832369\pi$
$524$	7142.43	+	10815.4i	0.595455	+	0.901666i
$525$	−11601.5	−	905.878i	−0.964443	−	0.0753062i
$526$	9588.45	+	5158.47i	0.794821	+	0.427605i
$527$	3803.97	−	3803.97i	0.314428	−	0.314428i
$528$	651.409	+	1621.98i	0.0536912	+	0.133688i
$529$		−	2072.91i		−	0.170371i
$530$	−2873.23	−	1693.28i	−0.235481	−	0.138776i
$531$		−	1343.23i		−	0.109776i
$532$	−5473.73	+	26762.1i	−0.446083	+	2.18098i
$533$	566.287	−	566.287i	0.0460199	−	0.0460199i
$534$	5206.83	−	9678.34i	0.421951	−	0.784312i
$535$	4985.05	+	5389.47i	0.402846	+	0.435527i
$536$	100.003	+	1107.23i	0.00805871	+	0.0892262i
$537$	−10481.6	−	10481.6i	−0.842297	−	0.842297i
$538$	−491.468	−	1636.04i	−0.0393841	−	0.131106i
$539$	−2132.62			−0.170424
$540$	−12958.5	−	3180.96i	−1.03268	−	0.253494i
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	3443.93	+	11464.5i	0.272932	+	0.908563i
$543$	5105.52	+	5105.52i	0.403497	+	0.403497i
$544$	−4048.67	+	3232.17i	−0.319090	+	0.254739i
$545$	7131.72	+	278.009i	0.560531	+	0.0218506i
$546$	−473.258	+	879.681i	−0.0370945	+	0.0689503i
$547$	−2884.33	+	2884.33i	−0.225457	+	0.225457i	−0.810792	−	0.585335i	$-0.800963\pi$
$547$	−2884.33	+	2884.33i	−0.225457	+	0.225457i	0.585335	+	0.810792i	$0.300963\pi$
$548$	9145.34	+	1870.52i	0.712901	+	0.145812i
$549$		−	3084.74i		−	0.239806i
$550$	553.557	+	2548.34i	0.0429159	+	0.197567i
$551$		−	4656.71i		−	0.360041i
$552$	6463.44	+	5392.63i	0.498374	+	0.415807i
$553$	17830.0	−	17830.0i	1.37108	−	1.37108i
$554$	11321.8	+	6091.00i	0.868263	+	0.467115i
$555$	14664.9	+	571.666i	1.12160	+	0.0437223i
$556$	−8439.43	+	5573.35i	−0.643726	+	0.425113i
$557$	−6538.87	−	6538.87i	−0.497416	−	0.497416i	0.413216	−	0.910633i	$-0.364405\pi$
$557$	−6538.87	−	6538.87i	−0.497416	−	0.497416i	−0.910633	+	0.413216i	$0.864405\pi$
$558$	6767.07	−	2032.83i	0.513392	−	0.154223i
$559$	−250.720			−0.0189702
$560$	−16942.8	+	6049.30i	−1.27851	+	0.456481i
$561$	781.612			0.0588229
$562$	−20518.9	+	6163.88i	−1.54010	+	0.462647i
$563$	6499.93	+	6499.93i	0.486571	+	0.486571i	0.907222	−	0.420651i	$-0.138198\pi$
$563$	6499.93	+	6499.93i	0.486571	+	0.486571i	−0.420651	+	0.907222i	$0.638198\pi$
$564$	−6631.52	+	4379.42i	−0.495102	+	0.326962i
$565$	10756.1	+	11628.7i	0.800907	+	0.865882i
$566$	1775.71	+	955.311i	0.131870	+	0.0709447i
$567$	−3441.05	+	3441.05i	−0.254869	+	0.254869i
$568$	−10678.3	−	8909.19i	−0.788822	−	0.658136i
$569$		−	5264.67i		−	0.387885i	−0.981013	−	0.193942i	$-0.937872\pi$
$569$		−	5264.67i		−	0.387885i	0.981013	−	0.193942i	$-0.0621275\pi$
$570$	8073.66	−	13699.7i	0.593278	−	1.00670i
$571$		−	22034.0i		−	1.61488i	−0.589952	−	0.807438i	$-0.700853\pi$
$571$		−	22034.0i		−	1.61488i	0.589952	−	0.807438i	$-0.299147\pi$
$572$	219.311	+	44.8563i	0.0160312	+	0.00327891i
$573$	3819.46	−	3819.46i	0.278464	−	0.278464i
$574$	7112.48	−	13220.5i	0.517194	−	0.961348i
$575$	8162.08	+	9544.67i	0.591969	+	0.692244i
$576$	−6694.29	+	1219.17i	−0.484251	+	0.0881924i
$577$	−9208.58	−	9208.58i	−0.664399	−	0.664399i	0.292015	−	0.956414i	$-0.405674\pi$
$577$	−9208.58	−	9208.58i	−0.664399	−	0.664399i	−0.956414	+	0.292015i	$0.905674\pi$
$578$	−3331.40	−	11089.9i	−0.239737	−	0.798059i
$579$	−11859.0			−0.851196
$580$	2623.09	−	1589.11i	0.187789	−	0.113766i
$581$	15047.2			1.07446
$582$	2286.18	+	7610.46i	0.162827	+	0.542034i
$583$	550.052	+	550.052i	0.0390751	+	0.0390751i
$584$	107.763	+	1193.15i	0.00763572	+	0.0845429i
$585$	−413.802	+	382.751i	−0.0292455	+	0.0270509i
$586$	−462.679	+	860.016i	−0.0326162	+	0.0606262i
$587$	6536.20	−	6536.20i	0.459587	−	0.459587i	−0.438933	−	0.898520i	$-0.644643\pi$
$587$	6536.20	−	6536.20i	0.459587	−	0.459587i	0.898520	+	0.438933i	$0.144643\pi$
$588$	−1716.23	+	8390.94i	−0.120367	+	0.588498i
$589$			25528.3i			1.78586i
$590$	799.602	+	3094.53i	0.0557951	+	0.215932i
$591$		−	10958.3i		−	0.762713i
$592$	21054.3	−	8455.72i	1.46170	−	0.587040i
$593$	−11033.7	+	11033.7i	−0.764079	+	0.764079i	−0.977057	−	0.212978i	$-0.931684\pi$
$593$	−11033.7	+	11033.7i	−0.764079	+	0.764079i	0.212978	+	0.977057i	$0.431684\pi$
$594$	2740.80	+	1474.52i	0.189321	+	0.101852i
$595$	−313.364	+	8038.68i	−0.0215910	+	0.553872i
$596$	−5958.16	−	9022.12i	−0.409489	−	0.620068i
$597$	−5466.05	−	5466.05i	−0.374725	−	0.374725i
$598$	1032.46	−	310.150i	0.0706024	−	0.0212090i
$599$	1861.62			0.126985			0.0634923	−	0.997982i	$-0.479776\pi$
$599$	1861.62			0.126985			0.0634923	+	0.997982i	$0.479776\pi$
$600$	10472.1	−	127.230i	0.712537	−	0.00865692i
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	−4501.15	+	1352.15i	−0.304739	+	0.0915437i
$603$	461.715	+	461.715i	0.0311816	+	0.0311816i
$604$	10252.8	+	15525.2i	0.690693	+	1.04588i
$605$	−555.959	+	14261.9i	−0.0373602	+	0.958398i
$606$	13057.8	+	7024.94i	0.875308	+	0.470905i
$607$	617.817	−	617.817i	0.0413121	−	0.0413121i	−0.686149	−	0.727461i	$-0.740700\pi$
$607$	617.817	−	617.817i	0.0413121	−	0.0413121i	0.727461	+	0.686149i	$0.240700\pi$
$608$	2739.75	−	24430.7i	0.182749	−	1.62960i
$609$		−	3192.13i		−	0.212400i
$610$	1836.30	+	7106.63i	0.121884	+	0.471703i
$611$			1017.77i			0.0673891i
$612$	−609.719	+	2981.03i	−0.0402719	+	0.196897i
$613$	5656.87	−	5656.87i	0.372722	−	0.372722i	−0.495745	−	0.868468i	$-0.665105\pi$
$613$	5656.87	−	5656.87i	0.372722	−	0.372722i	0.868468	+	0.495745i	$0.165105\pi$
$614$	12987.6	−	24141.0i	0.853642	−	1.58673i
$615$	−6415.60	+	5934.18i	−0.420654	+	0.389088i
$616$	4179.17	−	377.453i	0.273350	−	0.0246884i
$617$	12811.8	+	12811.8i	0.835953	+	0.835953i	0.988323	−	0.152370i	$-0.0486907\pi$
$617$	12811.8	+	12811.8i	0.835953	+	0.835953i	−0.152370	+	0.988323i	$0.548691\pi$
$618$	−1214.07	−	4041.50i	−0.0790243	−	0.263063i
$619$	−12163.2			−0.789788			−0.394894	−	0.918727i	$-0.629219\pi$
$619$	−12163.2			−0.789788			−0.394894	+	0.918727i	$0.629219\pi$
$620$	−14379.9	+	8711.57i	−0.931468	+	0.564299i
$621$	14988.2			0.968530
$622$	−8790.56	−	29262.9i	−0.566671	−	1.88639i
$623$	−18656.2	−	18656.2i	−1.19975	−	1.19975i
$624$	352.980	−	826.794i	0.0226450	−	0.0530421i
$625$	15435.6	+	2425.29i	0.987880	+	0.155219i
$626$	4962.20	−	9223.62i	0.316820	−	0.588898i
$627$	−2622.68	+	2622.68i	−0.167049	+	0.167049i
$628$	1801.04	+	368.372i	0.114441	+	0.0234071i
$629$		−	10145.8i		−	0.643149i
$630$	−5364.75	+	9103.13i	−0.339264	+	0.575679i
$631$		−	3347.17i		−	0.211171i	−0.994410	−	0.105585i	$-0.966328\pi$
$631$		−	3347.17i		−	0.211171i	0.994410	−	0.105585i	$-0.0336716\pi$
$632$	−14538.1	+	17424.9i	−0.915023	+	1.09672i
$633$	−522.588	+	522.588i	−0.0328136	+	0.0328136i
$634$	12866.7	+	6922.14i	0.805998	+	0.433617i
$635$	6650.70	+	7190.25i	0.415630	+	0.449349i
$636$	2606.87	−	1721.56i	0.162530	−	0.107334i
$637$	775.600	+	775.600i	0.0482424	+	0.0482424i
$638$	−685.099	+	205.804i	−0.0425131	+	0.0127709i
$639$	−8167.95			−0.505664
$640$	14696.6	−	6793.74i	0.907708	−	0.419603i
$641$	−24791.3			−1.52761			−0.763803	−	0.645449i	$-0.776670\pi$
$641$	−24791.3			−1.52761			−0.763803	+	0.645449i	$0.776670\pi$
$642$	−6586.17	+	1978.48i	−0.404884	+	0.121627i
$643$	12922.9	+	12922.9i	0.792583	+	0.792583i	0.981913	−	0.189330i	$-0.0606316\pi$
$643$	12922.9	+	12922.9i	0.792583	+	0.792583i	−0.189330	+	0.981913i	$0.560632\pi$
$644$	16862.9	−	11136.2i	1.03182	−	0.681408i
$645$	2733.89	+	106.572i	0.166894	+	0.00650587i
$646$	−9681.12	−	5208.33i	−0.589626	−	0.317212i
$647$	−16924.5	+	16924.5i	−1.02840	+	1.02840i	−0.0288113	+	0.999585i	$0.509172\pi$
$647$	−16924.5	+	16924.5i	−1.02840	+	1.02840i	−0.999585	+	0.0288113i	$0.990828\pi$
$648$	2805.74	−	3362.88i	0.170092	−	0.203868i
$649$		−	745.493i		−	0.0450896i
$650$	725.472	−	1128.11i	0.0437774	−	0.0680741i
$651$			17499.4i			1.05354i
$652$	−10335.4	−	2113.93i	−0.620806	−	0.126975i
$653$	10391.0	−	10391.0i	0.622715	−	0.622715i	−0.323510	−	0.946225i	$-0.604863\pi$
$653$	10391.0	−	10391.0i	0.622715	−	0.622715i	0.946225	+	0.323510i	$0.104863\pi$
$654$	−3167.44	+	5887.57i	−0.189384	+	0.352022i
$655$	−18099.8	−	705.565i	−1.07972	−	0.0420896i
$656$	−5304.85	+	12425.7i	−0.315731	+	0.739545i
$657$	497.543	+	497.543i	0.0295449	+	0.0295449i
$658$	5488.91	+	18272.0i	0.325197	+	1.08255i
$659$	773.045			0.0456958			0.0228479	−	0.999739i	$-0.492727\pi$
$659$	773.045			0.0456958			0.0228479	+	0.999739i	$0.492727\pi$
$660$	−2372.33	−	582.342i	−0.139913	−	0.0343449i
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	6379.62	+	21237.1i	0.374549	+	1.24683i
$663$	−284.260	−	284.260i	−0.0166512	−	0.0166512i
$664$	−13487.2	+	1218.13i	−0.788259	+	0.0711938i
$665$	−25922.1	−	28025.1i	−1.51161	−	1.63424i
$666$	6313.51	−	11735.4i	0.367333	−	0.682790i
$667$	−2435.98	+	2435.98i	−0.141411	+	0.141411i
$668$	−2213.73	+	10823.3i	−0.128221	+	0.626896i
$669$			17490.9i			1.01082i
$670$	−1338.55	−	788.848i	−0.0771833	−	0.0454864i
$671$		−	1712.04i		−	0.0984985i
$672$	1878.07	−	16747.0i	0.107810	−	0.961353i
$673$	−19931.6	+	19931.6i	−1.14161	+	1.14161i	−0.153459	+	0.988155i	$0.549041\pi$
$673$	−19931.6	+	19931.6i	−1.14161	+	1.14161i	−0.988155	+	0.153459i	$0.950959\pi$
$674$	−15863.0	−	8534.10i	−0.906557	−	0.487717i
$675$	14172.4	−	12119.5i	0.808143	−	0.691080i
$676$	9622.18	+	14570.4i	0.547462	+	0.828992i
$677$	−5515.73	−	5515.73i	−0.313126	−	0.313126i	0.532993	−	0.846120i	$-0.321067\pi$
$677$	−5515.73	−	5515.73i	−0.313126	−	0.313126i	−0.846120	+	0.532993i	$0.821067\pi$
$678$	−14210.8	+	4268.92i	−0.804958	+	0.241810i
$679$	19077.0			1.07822
$680$	−369.889	−	7230.65i	−0.0208597	−	0.407769i
$681$	4316.48			0.242890
$682$	3755.74	−	1128.22i	0.210872	−	0.0633460i
$683$	−19946.1	−	19946.1i	−1.11745	−	1.11745i	−0.992115	−	0.125331i	$-0.960001\pi$
$683$	−19946.1	−	19946.1i	−1.11745	−	1.11745i	−0.125331	−	0.992115i	$-0.539999\pi$
$684$	−7956.88	−	12048.7i	−0.444794	−	0.673527i
$685$	−9576.95	+	8858.31i	−0.534185	+	0.494100i
$686$	−3373.39	−	1814.85i	−0.187750	−	0.101007i
$687$	11814.0	−	11814.0i	0.656089	−	0.656089i
$688$	3925.04	−	1576.35i	0.217501	−	0.0873515i
$689$		−	400.090i		−	0.0221222i
$690$	−11389.9	+	2943.06i	−0.628415	+	0.162378i
$691$			356.654i			0.0196350i	0.999952	+	0.00981748i	$0.00312505\pi$
$691$			356.654i			0.0196350i	−0.999952	+	0.00981748i	$0.996875\pi$
$692$	1726.84	−	8442.84i	0.0948621	−	0.463798i
$693$	1742.71	−	1742.71i	0.0955267	−	0.0955267i
$694$	−16030.3	+	29796.7i	−0.876802	+	1.62978i
$695$	550.564	−	14123.6i	0.0300490	−	0.770845i
$696$	258.416	+	2861.19i	0.0140736	+	0.155823i
$697$	4272.07	+	4272.07i	0.232161	+	0.232161i
$698$	4488.09	+	14940.4i	0.243377	+	0.810175i
$699$	1532.05			0.0829003
$700$	6940.35	−	24165.4i	0.374744	−	1.30481i
$701$	17230.0			0.928343			0.464172	−	0.885745i	$-0.346352\pi$
$701$	17230.0			0.928343			0.464172	+	0.885745i	$0.346352\pi$
$702$	−460.526	−	1533.04i	−0.0247599	−	0.0824231i
$703$	34044.1	+	34044.1i	1.82646	+	1.82646i
$704$	−3715.35	+	676.643i	−0.198903	+	0.0362243i
$705$	432.621	−	11098.0i	0.0231113	−	0.592871i
$706$	−1443.02	+	2682.26i	−0.0769248	+	0.142986i
$707$	25170.5	−	25170.5i	1.33895	−	1.33895i
$708$	−2933.19	−	599.935i	−0.155701	−	0.0318460i
$709$		−	8153.11i		−	0.431871i	−0.976408	−	0.215935i	$-0.930720\pi$
$709$		−	8153.11i		−	0.431871i	0.976408	−	0.215935i	$-0.0692801\pi$
$710$	18817.3	−	4862.26i	0.994651	−	0.257010i
$711$			13328.5i			0.703036i
$712$	18232.4	+	15211.8i	0.959672	+	0.800681i
$713$	13354.1	−	13354.1i	0.701425	−	0.701425i
$714$	−6636.31	−	3570.26i	−0.347840	−	0.187134i
$715$	−229.661	+	212.427i	−0.0120124	+	0.0111110i
$716$	26724.8	−	17648.9i	1.39491	−	0.921189i
$717$	7658.81	+	7658.81i	0.398917	+	0.398917i
$718$	−9656.25	+	2900.74i	−0.501905	+	0.150772i
$719$	17219.3			0.893147			0.446573	−	0.894747i	$-0.352644\pi$
$719$	17219.3			0.893147			0.446573	+	0.894747i	$0.352644\pi$
$720$	4071.63	−	8593.68i	0.210751	−	0.444816i
$721$	−10130.8			−0.523287
$722$	31381.3	−	9426.94i	1.61758	−	0.485920i
$723$	−11152.0	−	11152.0i	−0.573649	−	0.573649i
$724$	−13017.5	+	8596.70i	−0.668221	+	0.441290i
$725$	−333.656	+	4273.12i	−0.0170920	+	0.218896i
$726$	−11773.9	−	6334.22i	−0.601888	−	0.323809i
$727$	−8881.73	+	8881.73i	−0.453102	+	0.453102i	−0.896383	−	0.443281i	$-0.853814\pi$
$727$	−8881.73	+	8881.73i	−0.453102	+	0.453102i	0.443281	+	0.896383i	$0.353814\pi$
$728$	−1657.17	−	1382.62i	−0.0843665	−	0.0703893i
$729$		−	17486.6i		−	0.888409i
$730$	−1442.42	−	850.061i	−0.0731320	−	0.0430989i
$731$		−	1891.43i		−	0.0957004i
$732$	−6736.12	−	1377.76i	−0.340129	−	0.0695676i
$733$	4401.20	−	4401.20i	0.221776	−	0.221776i	−0.587470	−	0.809246i	$-0.699876\pi$
$733$	4401.20	−	4401.20i	0.221776	−	0.221776i	0.809246	+	0.587470i	$0.199876\pi$
$734$	−8353.30	+	15526.9i	−0.420062	+	0.780802i
$735$	−8127.59	−	8786.95i	−0.407878	−	0.440968i
$736$	−14213.2	+	11346.8i	−0.711826	+	0.568271i
$737$	256.253	+	256.253i	0.0128076	+	0.0128076i
$738$	2282.98	+	7599.79i	0.113872	+	0.379068i
$739$	23097.8			1.14975			0.574875	−	0.818241i	$-0.305051\pi$
$739$	23097.8			1.14975			0.574875	+	0.818241i	$0.305051\pi$
$740$	−7559.18	+	30794.4i	−0.375515	+	1.52976i
$741$	1907.65			0.0945741
$742$	−2157.70	−	7182.77i	−0.106754	−	0.355374i
$743$	−17404.1	−	17404.1i	−0.859348	−	0.859348i	0.131913	−	0.991261i	$-0.457888\pi$
$743$	−17404.1	−	17404.1i	−0.859348	−	0.859348i	−0.991261	+	0.131913i	$0.957888\pi$
$744$	−1416.65	−	15685.1i	−0.0698075	−	0.772911i
$745$	15098.7	+	588.577i	0.742515	+	0.0289447i
$746$	−15864.3	+	29488.2i	−0.778597	+	1.44724i
$747$	−5624.13	+	5624.13i	−0.275470	+	0.275470i
$748$	−338.395	+	1654.48i	−0.0165414	+	0.0808739i
$749$			16509.4i			0.805396i
$750$	−8390.19	+	11992.7i	−0.408488	+	0.583884i
$751$		−	2347.75i		−	0.114075i	−0.998372	−	0.0570377i	$-0.981834\pi$
$751$		−	2347.75i		−	0.114075i	0.998372	−	0.0570377i	$-0.0181655\pi$
$752$	−6399.05	−	15933.3i	−0.310305	−	0.772644i
$753$	−13794.7	+	13794.7i	−0.667604	+	0.667604i
$754$	324.007	+	174.312i	0.0156494	+	0.00841919i
$755$	−25981.7	−	1012.82i	−1.25241	−	0.0488215i
$756$	−16535.6	−	25038.9i	−0.795493	−	1.20457i
$757$	−7078.12	−	7078.12i	−0.339840	−	0.339840i	0.516467	−	0.856307i	$-0.327247\pi$
$757$	−7078.12	−	7078.12i	−0.339840	−	0.339840i	−0.856307	+	0.516467i	$0.827247\pi$
$758$	30149.6	−	9056.95i	1.44470	−	0.433989i
$759$	2743.91			0.131222
$760$	25503.5	+	23021.2i	1.21725	+	1.09877i
$761$	−27017.6			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$761$	−27017.6			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$762$	−8786.80	+	2639.56i	−0.417732	+	0.125487i
$763$	11349.0	+	11349.0i	0.538483	+	0.538483i
$764$	6431.22	+	9738.45i	0.304546	+	0.461158i
$765$	−2887.47	−	3121.72i	−0.136466	−	0.147537i
$766$	−3545.90	−	1907.65i	−0.167257	−	0.0899821i
$767$	−271.124	+	271.124i	−0.0127636	+	0.0127636i
$768$	−327.626	+	15162.8i	−0.0153935	+	0.712423i
$769$		−	41584.0i		−	1.95001i	−0.222183	−	0.975005i	$-0.571318\pi$
$769$		−	41584.0i		−	1.95001i	0.222183	−	0.975005i	$-0.428682\pi$
$770$	−2977.45	+	5052.26i	−0.139350	+	0.236456i
$771$			29507.7i			1.37833i
$772$	5134.29	−	25102.5i	0.239362	−	1.17028i
$773$	−19799.8	+	19799.8i	−0.921280	+	0.921280i	−0.997120	−	0.0758404i	$-0.975836\pi$
$773$	−19799.8	+	19799.8i	−0.921280	+	0.921280i	0.0758404	+	0.997120i	$0.475836\pi$
$774$	1176.99	−	2187.77i	0.0546591	−	0.101599i
$775$	1829.12	−	23425.4i	0.0847790	−	1.08576i
$776$	−17099.2	+	1544.36i	−0.791014	+	0.0714426i
$777$	23336.9	+	23336.9i	1.07749	+	1.07749i
$778$	−11024.8	−	36700.5i	−0.508045	−	1.69123i
$779$	−28669.7			−1.31861
$780$	650.991	+	1074.57i	0.0298836	+	0.0493278i
$781$	−4533.23			−0.207697
$782$	2339.77	+	7788.84i	0.106995	+	0.356174i
$783$	3617.07	+	3617.07i	0.165087	+	0.165087i
$784$	−17018.5	−	7265.64i	−0.775260	−	0.330979i
$785$	−1886.04	+	1744.51i	−0.0857523	+	0.0793176i
$786$	8038.74	−	14942.2i	0.364799	−	0.678081i
$787$	−23772.7	+	23772.7i	−1.07675	+	1.07675i	−0.0799542	+	0.996799i	$0.525477\pi$
$787$	−23772.7	+	23772.7i	−1.07675	+	1.07675i	−0.996799	+	0.0799542i	$0.974523\pi$
$788$	23195.9	+	4744.34i	1.04863	+	0.214480i
$789$		−	14253.6i		−	0.643144i
$790$	−7934.27	−	30706.3i	−0.357327	−	1.38289i
$791$			35621.9i			1.60123i
$792$	−1420.96	+	1703.11i	−0.0637519	+	0.0764110i
$793$	−622.640	+	622.640i	−0.0278822	+	0.0278822i
$794$	6420.99	+	3454.42i	0.286993	+	0.154399i
$795$	−170.064	+	4362.65i	−0.00758687	+	0.194625i
$796$	13936.8	−	9203.77i	0.620573	−	0.409823i
$797$	8760.69	+	8760.69i	0.389359	+	0.389359i	0.874459	−	0.485100i	$-0.161217\pi$
$797$	8760.69	+	8760.69i	0.389359	+	0.389359i	−0.485100	+	0.874459i	$0.661217\pi$
$798$	34247.9	−	10288.1i	1.51925	−	0.456383i
$799$	−7678.08			−0.339964
$800$	−4264.54	+	22221.9i	−0.188468	+	0.982079i
$801$	13946.1			0.615184
$802$	16041.9	−	4818.98i	0.706308	−	0.212175i
$803$	276.138	+	276.138i	0.0121353	+	0.0121353i
$804$	1214.46	−	802.025i	0.0532722	−	0.0351806i
$805$	−1100.09	+	28220.4i	−0.0481652	+	1.23558i
$806$	−1776.22	−	955.585i	−0.0776236	−	0.0417606i
$807$	−1581.31	+	1581.31i	−0.0689774	+	0.0689774i
$808$	−20523.4	+	24598.7i	−0.893576	+	1.07101i
$809$			27571.0i			1.19820i	0.800673	+	0.599102i	$0.204475\pi$
$809$			27571.0i			1.19820i	−0.800673	+	0.599102i	$0.795525\pi$
$810$	1531.25	+	5926.08i	0.0664231	+	0.257063i
$811$		−	20085.4i		−	0.869661i	−0.900512	−	0.434831i	$-0.856808\pi$
$811$		−	20085.4i		−	0.869661i	0.900512	−	0.434831i	$-0.143192\pi$
$812$	6756.94	+	1382.02i	0.292022	+	0.0597282i
$813$	11080.9	−	11080.9i	0.478014	−	0.478014i
$814$	3504.02	−	6513.18i	0.150879	−	0.280451i
$815$	10823.2	−	10011.0i	0.465177	−	0.430271i
$816$	6237.33	+	2662.88i	0.267586	+	0.114239i
$817$	6346.65	+	6346.65i	0.271776	+	0.271776i
$818$	−6943.65	−	23114.7i	−0.296796	−	0.988002i
$819$	−1267.59			−0.0540820
$820$	−9783.57	−	16149.4i	−0.416655	−	0.687758i
$821$	14867.5			0.632008			0.316004	−	0.948758i	$-0.397659\pi$
$821$	14867.5			0.632008			0.316004	+	0.948758i	$0.397659\pi$
$822$	−3515.72	−	11703.5i	−0.149179	−	0.496600i
$823$	−23345.7	−	23345.7i	−0.988797	−	0.988797i	0.0111410	−	0.999938i	$-0.496454\pi$
$823$	−23345.7	−	23345.7i	−0.988797	−	0.988797i	−0.999938	+	0.0111410i	$0.996454\pi$
$824$	9080.48	−	820.128i	0.383900	−	0.0346730i
$825$	2594.56	−	2218.72i	0.109492	−	0.0936316i
$826$	−3405.27	+	6329.64i	−0.143444	+	0.266630i
$827$	3330.46	−	3330.46i	0.140038	−	0.140038i	−0.633613	−	0.773651i	$-0.718429\pi$
$827$	3330.46	−	3330.46i	0.140038	−	0.140038i	0.773651	+	0.633613i	$0.218429\pi$
$828$	−2140.47	+	10465.1i	−0.0898385	+	0.439237i
$829$		−	11521.6i		−	0.482703i	−0.970438	−	0.241351i	$-0.922409\pi$
$829$		−	11521.6i		−	0.482703i	0.970438	−	0.241351i	$-0.0775906\pi$
$830$	9608.93	−	16304.8i	0.401844	−	0.681867i
$831$		−	16830.3i		−	0.702570i
$832$	1597.30	+	1105.13i	0.0665580	+	0.0460498i
$833$	−5851.12	+	5851.12i	−0.243372	+	0.243372i
$834$	11659.7	+	6272.76i	0.484102	+	0.260441i
$835$	−10483.6	−	11334.1i	−0.434492	−	0.469741i
$836$	−4416.09	−	6687.04i	−0.182696	−	0.276646i
$837$	−19828.9	−	19828.9i	−0.818861	−	0.818861i
$838$	19308.7	−	5800.33i	0.795951	−	0.239104i
$839$	33130.1			1.36326			0.681631	−	0.731696i	$-0.261271\pi$
$839$	33130.1			1.36326			0.681631	+	0.731696i	$0.261271\pi$
$840$	17482.4	+	15780.8i	0.718094	+	0.648200i
$841$	23213.3			0.951792
$842$	−1655.75	+	497.388i	−0.0677684	+	0.0203576i
$843$	19832.5	+	19832.5i	0.810280	+	0.810280i
$844$	−879.936	−	1332.44i	−0.0358870	−	0.0543418i
$845$	−24383.8	−	950.528i	−0.992695	−	0.0386972i
$846$	−8881.03	−	4777.89i	−0.360918	−	0.194169i
$847$	−22695.7	+	22695.7i	−0.920699	+	0.920699i
$848$	2515.48	+	6263.43i	0.101866	+	0.253641i
$849$		−	2639.66i		−	0.106705i
$850$	8510.46	+	5472.95i	0.343419	+	0.220848i
$851$		−	35617.7i		−	1.43474i
$852$	−3648.11	+	17836.3i	−0.146693	+	0.717208i
$853$	12007.8	−	12007.8i	0.481994	−	0.481994i	−0.423774	−	0.905768i	$-0.639295\pi$
$853$	12007.8	−	12007.8i	0.481994	−	0.481994i	0.905768	+	0.423774i	$0.139295\pi$
$854$	−7820.26	+	14536.1i	−0.313354	+	0.582454i
$855$	20163.7	+	786.020i	0.806531	+	0.0314401i
$856$	−1336.51	−	14797.8i	−0.0533655	−	0.590864i
$857$	−9369.48	−	9369.48i	−0.373460	−	0.373460i	0.495276	−	0.868736i	$-0.335067\pi$
$857$	−9369.48	−	9369.48i	−0.373460	−	0.373460i	−0.868736	+	0.495276i	$0.835067\pi$
$858$	−84.3090	−	280.656i	−0.00335462	−	0.0111672i
$859$	17337.1			0.688630			0.344315	−	0.938854i	$-0.388111\pi$
$859$	17337.1			0.688630			0.344315	+	0.938854i	$0.388111\pi$
$860$	−1409.21	+	5740.83i	−0.0558765	+	0.227629i
$861$	−19652.8			−0.777891
$862$	7617.98	+	25359.4i	0.301009	+	1.00203i
$863$	−17345.8	−	17345.8i	−0.684191	−	0.684191i	0.276751	−	0.960942i	$-0.410742\pi$
$863$	−17345.8	−	17345.8i	−0.684191	−	0.684191i	−0.960942	+	0.276751i	$0.910742\pi$
$864$	16848.3	+	21104.4i	0.663414	+	0.831004i
$865$	8177.86	+	8841.30i	0.321451	+	0.347530i
$866$	−3353.36	+	6233.15i	−0.131584	+	0.244586i
$867$	−10718.9	+	10718.9i	−0.419875	+	0.419875i
$868$	−37041.8	−	7576.27i	−1.44848	−	0.296262i
$869$			7397.36i			0.288767i
$870$	−3458.93	−	2038.45i	−0.134792	−	0.0794367i
$871$		−	186.390i		−	0.00725096i
$872$	−11091.2	−	9253.69i	−0.430728	−	0.359368i
$873$	−7130.35	+	7130.35i	−0.276433	+	0.276433i
$874$	−33986.3	−	18284.2i	−1.31534	−	0.707636i
$875$	21778.8	+	27573.9i	0.841438	+	1.06533i
$876$	1308.70	−	864.260i	0.0504760	−	0.0333341i
$877$	−18857.4	−	18857.4i	−0.726075	−	0.726075i	0.243760	−	0.969836i	$-0.421619\pi$
$877$	−18857.4	−	18857.4i	−0.726075	−	0.726075i	−0.969836	+	0.243760i	$0.921619\pi$
$878$	−21192.2	+	6366.14i	−0.814581	+	0.244700i
$879$	1278.44			0.0490567
$880$	2259.76	−	4769.51i	0.0865643	−	0.182705i
$881$	27095.7			1.03618			0.518092	−	0.855325i	$-0.326643\pi$
$881$	27095.7			1.03618			0.518092	+	0.855325i	$0.326643\pi$
$882$	−10408.9	+	3126.82i	−0.397374	+	0.119371i
$883$	−2484.93	−	2484.93i	−0.0947049	−	0.0947049i	0.658167	−	0.752872i	$-0.271332\pi$
$883$	−2484.93	−	2484.93i	−0.0947049	−	0.0947049i	−0.752872	+	0.658167i	$0.771332\pi$
$884$	724.775	−	478.638i	0.0275756	−	0.0182108i
$885$	3071.63	−	2841.13i	0.116668	−	0.107914i
$886$	31937.4	+	17182.0i	1.21101	+	0.651511i
$887$	26609.3	−	26609.3i	1.00727	−	1.00727i	0.00730049	−	0.999973i	$-0.497676\pi$
$887$	26609.3	−	26609.3i	1.00727	−	1.00727i	0.999973	−	0.00730049i	$-0.00232384\pi$
$888$	−22806.7	−	19028.3i	−0.861873	−	0.719084i
$889$			22025.7i			0.830955i
$890$	−32129.1	+	8301.92i	−1.21008	+	0.312675i
$891$		−	1427.63i		−	0.0536785i
$892$	−37024.0	−	7572.63i	−1.38975	−	0.284249i
$893$	25763.6	−	25763.6i	0.965451	−	0.965451i
$894$	−6705.85	+	12464.7i	−0.250869	+	0.466310i
$895$	−1743.45	+	44724.5i	−0.0651141	+	1.67036i
$896$	34636.1	+	11225.9i	1.29142	+	0.418563i
$897$	−997.915	−	997.915i	−0.0371454	−	0.0371454i
$898$	2752.00	+	9161.12i	0.102267	+	0.340435i
$899$	6445.42			0.239118
$900$	6438.14	+	11626.3i	0.238450	+	0.430603i
$901$	3018.27			0.111602
$902$	1267.06	+	4217.90i	0.0467721	+	0.155699i
$903$	4350.56	+	4350.56i	0.160330	+	0.160330i
$904$	−2883.74	−	31928.9i	−0.106097	−	1.17471i
$905$	849.225	−	21785.1i	0.0311925	−	0.800177i
$906$	11539.4	−	21449.1i	0.423146	−	0.786534i
$907$	23802.0	−	23802.0i	0.871369	−	0.871369i	−0.121252	−	0.992622i	$-0.538691\pi$
$907$	23802.0	−	23802.0i	0.871369	−	0.871369i	0.992622	+	0.121252i	$0.0386910\pi$
$908$	−1868.80	+	9136.92i	−0.0683022	+	0.333942i
$909$			18815.8i			0.686558i
$910$	2920.27	−	754.577i	0.106380	−	0.0274879i
$911$			36580.4i			1.33036i	0.746681	+	0.665182i	$0.231646\pi$
$911$			36580.4i			1.33036i	−0.746681	+	0.665182i	$0.768354\pi$
$912$	−29864.5	+	11994.0i	−1.08433	+	0.435483i
$913$	−3121.41	+	3121.41i	−0.113147	+	0.113147i
$914$	36246.2	+	19500.0i	1.31173	+	0.705694i
$915$	7054.04	−	6524.71i	0.254863	−	0.235738i
$916$	19892.5	+	30122.2i	0.717540	+	1.08653i
$917$	−28803.0	−	28803.0i	−1.03725	−	1.03725i
$918$	11565.3	−	3474.21i	0.415807	−	0.124908i
$919$	−32910.8			−1.18131			−0.590657	−	0.806923i	$-0.701131\pi$
$919$	−32910.8			−1.18131			−0.590657	+	0.806923i	$0.701131\pi$
$920$	−1298.52	−	25383.8i	−0.0465337	−	0.909650i
$921$	−35886.5			−1.28393
$922$	−14384.5	+	4321.11i	−0.513806	+	0.154347i
$923$	1648.66	+	1648.66i	0.0587935	+	0.0587935i
$924$	−3027.18	−	4583.90i	−0.107778	−	0.163203i
$925$	−28800.5	−	33679.0i	−1.02373	−	1.19715i
$926$	−27077.3	−	14567.3i	−0.960924	−	0.516966i
$927$	3786.55	−	3786.55i	0.134160	−	0.134160i
$928$	−6168.30	−	691.737i	−0.218195	−	0.0244692i
$929$			2662.19i			0.0940190i	0.998894	+	0.0470095i	$0.0149691\pi$
$929$			2662.19i			0.0940190i	−0.998894	+	0.0470095i	$0.985031\pi$
$930$	18962.0	+	11174.9i	0.668590	+	0.394020i
$931$		−	39266.6i		−	1.38229i
$932$	−663.293	+	3242.96i	−0.0233121	+	0.113977i
$933$	−28283.9	+	28283.9i	−0.992468	+	0.992468i
$934$	−8596.18	+	15978.4i	−0.301152	+	0.559774i
$935$	−1602.55	−	1732.56i	−0.0560524	−	0.0605998i
$936$	1136.17	−	102.617i	0.0396763	−	0.00358347i
$937$	37885.5	+	37885.5i	1.32088	+	1.32088i	0.913063	+	0.407818i	$0.133710\pi$
$937$	37885.5	+	37885.5i	1.32088	+	1.32088i	0.407818	+	0.913063i	$0.366290\pi$
$938$	−1005.21	−	3346.24i	−0.0349907	−	0.116480i
$939$	−13711.2			−0.476517
$940$	23304.4	+	5720.57i	0.808621	+	0.198494i
$941$	−6516.65			−0.225756			−0.112878	−	0.993609i	$-0.536007\pi$
$941$	−6516.65			−0.225756			−0.112878	+	0.993609i	$0.536007\pi$
$942$	−692.368	−	2304.82i	−0.0239475	−	0.0797188i
$943$	14997.4	+	14997.4i	0.517904	+	0.517904i
$944$	2539.83	−	5949.10i	0.0875681	−	0.205113i
$945$	41903.1	+	1633.47i	1.44244	+	0.0562293i
$946$	653.234	−	1214.22i	0.0224508	−	0.0417310i
$947$	−10250.1	+	10250.1i	−0.351724	+	0.351724i	−0.860751	−	0.509026i	$-0.830006\pi$
$947$	−10250.1	+	10250.1i	−0.351724	+	0.351724i	0.509026	+	0.860751i	$0.330006\pi$
$948$	29105.4	+	5953.02i	0.997152	+	0.203951i
$949$		−	200.854i		−	0.00687037i
$950$	−46921.1	+	10192.3i	−1.60244	+	0.348086i
$951$		−	19126.8i		−	0.652187i
$952$	10430.5	−	12501.7i	0.355099	−	0.425611i
$953$	19249.8	−	19249.8i	0.654314	−	0.654314i	−0.299715	−	0.954029i	$-0.596891\pi$
$953$	19249.8	−	19249.8i	0.654314	−	0.654314i	0.954029	+	0.299715i	$0.0968914\pi$
$954$	3491.16	+	1878.20i	0.118481	+	0.0637411i
$955$	−16297.5	−	635.308i	−0.552225	−	0.0215268i
$956$	−19527.7	+	12896.0i	−0.660637	+	0.436281i
$957$	662.180	+	662.180i	0.0223670	+	0.0223670i
$958$	−29715.0	+	8926.38i	−1.00214	+	0.301042i
$959$	−29336.9			−0.987838
$960$	−16947.4	−	12729.5i	−0.569766	−	0.427960i
$961$	−5543.06			−0.186065
$962$	−3643.09	+	1094.39i	−0.122098	+	0.0366782i
$963$	−6170.68	−	6170.68i	−0.206487	−	0.206487i
$964$	28434.3	−	18777.8i	0.950007	−	0.627379i
$965$	24314.7	+	26287.2i	0.811105	+	0.876907i
$966$	−23297.3	−	12533.7i	−0.775960	−	0.417457i
$967$	3744.56	−	3744.56i	0.124526	−	0.124526i	−0.642097	−	0.766623i	$-0.721935\pi$
$967$	3744.56	−	3744.56i	0.124526	−	0.124526i	0.766623	+	0.642097i	$0.221935\pi$
$968$	18505.4	−	22180.0i	0.614449	−	0.736460i
$969$			14391.3i			0.477106i
$970$	12182.3	−	20671.5i	0.403248	−	0.684250i
$971$			29491.0i			0.974677i	0.873213	+	0.487338i	$0.162032\pi$
$971$			29491.0i			0.974677i	−0.873213	+	0.487338i	$0.837968\pi$
$972$	25952.6	+	5308.17i	0.856411	+	0.175164i
$973$	22475.4	−	22475.4i	0.740524	−	0.740524i
$974$	24136.1	−	44863.7i	0.794016	−	1.47590i
$975$	−1750.51	−	136.684i	−0.0574987	−	0.00448965i
$976$	5832.75	−	13662.2i	0.191293	−	0.448070i
$977$	13592.2	+	13592.2i	0.445092	+	0.445092i	0.893719	−	0.448627i	$-0.148087\pi$
$977$	13592.2	+	13592.2i	0.445092	+	0.445092i	−0.448627	+	0.893719i	$0.648087\pi$
$978$	3973.21	+	13226.4i	0.129907	+	0.432447i
$979$	7740.14			0.252682
$980$	22118.6	−	13399.8i	0.720972	−	0.436777i
$981$	−8483.78			−0.276112
$982$	8559.36	+	28493.2i	0.278147	+	0.925921i
$983$	12087.1	+	12087.1i	0.392185	+	0.392185i	0.875466	−	0.483280i	$-0.160555\pi$
$983$	12087.1	+	12087.1i	0.392185	+	0.392185i	−0.483280	+	0.875466i	$0.660555\pi$
$984$	17615.3	−	1590.97i	0.570686	−	0.0515430i
$985$	−24290.7	+	22467.9i	−0.785752	+	0.726790i
$986$	−1315.01	+	2444.31i	−0.0424730	+	0.0789478i
$987$	17660.7	−	17660.7i	0.569551	−	0.569551i
$988$	−825.910	+	4038.03i	−0.0265949	+	0.130027i
$989$		−	6640.01i		−	0.213488i
$990$	−775.497	−	3001.24i	−0.0248959	−	0.0963491i
$991$		−	52539.6i		−	1.68413i	−0.539374	−	0.842066i	$-0.681339\pi$
$991$		−	52539.6i		−	1.68413i	0.539374	−	0.842066i	$-0.318661\pi$
$992$	33814.9	+	3792.13i	1.08228	+	0.121371i
$993$	20526.6	−	20526.6i	0.655984	−	0.655984i
$994$	38489.6	+	20706.9i	1.22818	+	0.660749i
$995$	−909.194	+	23323.5i	−0.0289682	+	0.743119i
$996$	9769.43	+	14793.3i	0.310799	+	0.470627i
$997$	12067.7	+	12067.7i	0.383337	+	0.383337i	0.872303	−	0.488966i	$-0.162626\pi$
$997$	12067.7	+	12067.7i	0.383337	+	0.383337i	−0.488966	+	0.872303i	$0.662626\pi$
$998$	6623.82	−	1989.80i	0.210094	−	0.0631121i
$999$	−52887.0			−1.67495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.4.e.b.7.6	yes	12
3.2	odd	2		180.4.k.e.127.1		12
4.3	odd	2	inner	20.4.e.b.7.3	yes	12
5.2	odd	4		100.4.e.e.43.4		12
5.3	odd	4	inner	20.4.e.b.3.3	✓	12
5.4	even	2		100.4.e.e.7.1		12
8.3	odd	2		320.4.n.k.127.3		12
8.5	even	2		320.4.n.k.127.4		12
12.11	even	2		180.4.k.e.127.4		12
15.8	even	4		180.4.k.e.163.4		12
20.3	even	4	inner	20.4.e.b.3.6	yes	12
20.7	even	4		100.4.e.e.43.1		12
20.19	odd	2		100.4.e.e.7.4		12
40.3	even	4		320.4.n.k.63.4		12
40.13	odd	4		320.4.n.k.63.3		12
60.23	odd	4		180.4.k.e.163.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.3	✓	12	5.3	odd	4	inner
20.4.e.b.3.6	yes	12	20.3	even	4	inner
20.4.e.b.7.3	yes	12	4.3	odd	2	inner
20.4.e.b.7.6	yes	12	1.1	even	1	trivial
100.4.e.e.7.1		12	5.4	even	2
100.4.e.e.7.4		12	20.19	odd	2
100.4.e.e.43.1		12	20.7	even	4
100.4.e.e.43.4		12	5.2	odd	4
180.4.k.e.127.1		12	3.2	odd	2
180.4.k.e.127.4		12	12.11	even	2
180.4.k.e.163.1		12	60.23	odd	4
180.4.k.e.163.4		12	15.8	even	4
320.4.n.k.63.3		12	40.13	odd	4
320.4.n.k.63.4		12	40.3	even	4
320.4.n.k.127.3		12	8.3	odd	2
320.4.n.k.127.4		12	8.5	even	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70884 - 0.813737i) q^{2} +(-2.61822 - 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 + 17.7783i) q^{7} +(14.4959 - 17.3744i) q^{8} -13.2899i q^{9} +O(q^{10})\)	\(q+(2.70884 - 0.813737i) q^{2} +(-2.61822 - 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(-17.7783 + 17.7783i) q^{7} +(14.4959 - 17.3744i) q^{8} -13.2899i q^{9} +(7.91125 + 30.6172i) q^{10} -7.37590i q^{11} +(-29.0210 - 5.93575i) q^{12} +(-2.68249 + 2.68249i) q^{13} +(-33.6917 + 62.6254i) q^{14} +(30.3906 - 28.1101i) q^{15} +(25.1290 - 58.8603i) q^{16} +(-20.2367 - 20.2367i) q^{17} +(-10.8144 - 36.0001i) q^{18} +135.808 q^{19} +(46.3447 + 76.4995i) q^{20} +93.0948 q^{21} +(-6.00204 - 19.9802i) q^{22} +(-71.0426 - 71.0426i) q^{23} +(-83.4434 + 7.53642i) q^{24} +(-124.621 - 9.73070i) q^{25} +(-5.08361 + 9.44930i) q^{26} +(-105.488 + 105.488i) q^{27} +(-40.3050 + 197.059i) q^{28} -34.2890i q^{29} +(59.4491 - 100.876i) q^{30} +187.974i q^{31} +(20.1737 - 179.892i) q^{32} +(-19.3117 + 19.3117i) q^{33} +(-71.2855 - 38.3507i) q^{34} +(-190.874 - 206.359i) q^{35} +(-58.5893 - 88.7186i) q^{36} +(250.679 + 250.679i) q^{37} +(367.882 - 110.512i) q^{38} +14.0467 q^{39} +(187.791 + 169.513i) q^{40} -211.105 q^{41} +(252.179 - 75.7547i) q^{42} +(46.7326 + 46.7326i) q^{43} +(-32.5172 - 49.2390i) q^{44} +(148.472 + 5.78774i) q^{45} +(-250.253 - 134.633i) q^{46} +(189.707 - 189.707i) q^{47} +(-219.902 + 88.3159i) q^{48} -289.134i q^{49} +(-345.496 + 75.0495i) q^{50} +105.968i q^{51} +(-6.08147 + 29.7334i) q^{52} +(-74.5742 + 74.5742i) q^{53} +(-199.910 + 371.589i) q^{54} +(82.4025 + 3.21221i) q^{55} +(51.1739 + 566.598i) q^{56} +(-355.575 - 355.575i) q^{57} +(-27.9022 - 92.8835i) q^{58} +101.072 q^{59} +(78.9520 - 321.633i) q^{60} +232.112 q^{61} +(152.961 + 509.191i) q^{62} +(236.271 + 236.271i) q^{63} +(-91.7370 - 503.715i) q^{64} +(-28.8002 - 31.1367i) q^{65} +(-36.5978 + 68.0271i) q^{66} +(-34.7419 + 34.7419i) q^{67} +(-224.309 - 45.8785i) q^{68} +372.010i q^{69} +(-684.969 - 403.672i) q^{70} -614.600i q^{71} +(-230.903 - 192.649i) q^{72} +(-37.4378 + 37.4378i) q^{73} +(883.036 + 475.063i) q^{74} +(300.807 + 351.761i) q^{75} +(906.607 - 598.718i) q^{76} +(131.131 + 131.131i) q^{77} +(38.0504 - 11.4303i) q^{78} -1002.91 q^{79} +(646.635 + 306.371i) q^{80} +193.554 q^{81} +(-571.850 + 171.784i) q^{82} +(-423.190 - 423.190i) q^{83} +(621.470 - 410.415i) q^{84} +(234.895 - 217.269i) q^{85} +(164.619 + 88.5632i) q^{86} +(-89.7761 + 89.7761i) q^{87} +(-128.152 - 106.920i) q^{88} +1049.38i q^{89} +(406.898 - 105.139i) q^{90} -95.3802i q^{91} +(-787.453 - 161.060i) q^{92} +(492.156 - 492.156i) q^{93} +(359.514 - 668.257i) q^{94} +(-59.1444 + 1517.22i) q^{95} +(-523.815 + 418.177i) q^{96} +(-536.526 - 536.526i) q^{97} +(-235.279 - 783.218i) q^{98} -98.0246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8	\( 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8} - 110 q^{10} - 80 q^{12} + 116 q^{13} + 312 q^{16} - 332 q^{17} + 198 q^{18} + 140 q^{20} - 144 q^{21} + 360 q^{22} + 340 q^{25} - 164 q^{26} - 880 q^{28} - 1240 q^{30} - 376 q^{32} + 80 q^{33} + 460 q^{36} + 508 q^{37} + 1600 q^{38} + 1420 q^{40} - 656 q^{41} + 1160 q^{42} + 1180 q^{45} - 1432 q^{46} - 2720 q^{48} - 1570 q^{50} - 932 q^{52} - 644 q^{53} + 2048 q^{56} - 960 q^{57} + 1576 q^{58} + 3280 q^{60} - 896 q^{61} + 2440 q^{62} - 2740 q^{65} - 1680 q^{66} - 844 q^{68} - 3040 q^{70} - 3036 q^{72} + 1436 q^{73} + 800 q^{76} + 3120 q^{77} + 3720 q^{78} + 1840 q^{80} + 5988 q^{81} - 1352 q^{82} + 500 q^{85} - 2552 q^{86} - 2400 q^{88} - 750 q^{90} - 1840 q^{92} - 3280 q^{93} + 1088 q^{96} - 4772 q^{97} + 1698 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8 - 110 * q^10 - 80 * q^12 + 116 * q^13 + 312 * q^16 - 332 * q^17 + 198 * q^18 + 140 * q^20 - 144 * q^21 + 360 * q^22 + 340 * q^25 - 164 * q^26 - 880 * q^28 - 1240 * q^30 - 376 * q^32 + 80 * q^33 + 460 * q^36 + 508 * q^37 + 1600 * q^38 + 1420 * q^40 - 656 * q^41 + 1160 * q^42 + 1180 * q^45 - 1432 * q^46 - 2720 * q^48 - 1570 * q^50 - 932 * q^52 - 644 * q^53 + 2048 * q^56 - 960 * q^57 + 1576 * q^58 + 3280 * q^60 - 896 * q^61 + 2440 * q^62 - 2740 * q^65 - 1680 * q^66 - 844 * q^68 - 3040 * q^70 - 3036 * q^72 + 1436 * q^73 + 800 * q^76 + 3120 * q^77 + 3720 * q^78 + 1840 * q^80 + 5988 * q^81 - 1352 * q^82 + 500 * q^85 - 2552 * q^86 - 2400 * q^88 - 750 * q^90 - 1840 * q^92 - 3280 * q^93 + 1088 * q^96 - 4772 * q^97 + 1698 * q^98

Introduction

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