LMFDB - Embedded newform 20.4.e.b.3.3

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			3.3
Root			$-1.76129 + 0.947553i$ of defining polynomial
Character	$\chi$	$=$	20.3
Dual form			20.4.e.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813737 - 2.70884i) q^{2} +(2.61822 - 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-0.435501 - 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(17.7783 + 17.7783i) q^{7} +(17.3744 + 14.4959i) q^{8} +13.2899i q^{9} +O(q^{10})$	\(q+(-0.813737 - 2.70884i) 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} +(17.3744 + 14.4959i) q^{8} +13.2899i q^{9} +(-29.9084 + 10.2707i) q^{10} -7.37590i q^{11} +(-5.93575 + 29.0210i) 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} +(36.0001 - 10.8144i) q^{18} -135.808 q^{19} +(52.1592 + 72.6596i) q^{20} +93.0948 q^{21} +(-19.9802 + 6.00204i) 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} +(-197.059 - 40.3050i) q^{28} +34.2890i q^{29} +(-51.4160 + 105.198i) q^{30} +187.974i q^{31} +(-179.892 - 20.1737i) 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} +(110.512 + 367.882i) q^{38} -14.0467 q^{39} +(154.380 - 200.417i) q^{40} -211.105 q^{41} +(-75.7547 - 252.179i) 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} +(-88.3159 - 219.902i) q^{48} +289.134i q^{49} +(127.767 + 329.660i) q^{50} +105.968i q^{51} +(29.7334 + 6.08147i) 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} +(92.8835 - 27.9022i) q^{58} -101.072 q^{59} +(326.803 + 53.6747i) q^{60} +232.112 q^{61} +(509.191 - 152.961i) 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} +(45.8785 - 224.309i) q^{68} -372.010i q^{69} +(-714.314 - 349.126i) q^{70} -614.600i q^{71} +(-192.649 + 230.903i) 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} +(11.4303 + 38.0504i) q^{78} +1002.91 q^{79} +(-668.522 - 255.104i) q^{80} +193.554 q^{81} +(171.784 + 571.850i) 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} +(106.920 - 128.152i) q^{88} -1049.38i q^{89} +(-136.495 - 397.478i) q^{90} -95.3802i q^{91} +(-161.060 + 787.453i) 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} +(783.218 - 235.279i) 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 $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.813737	−	2.70884i	−0.287699	−	0.957721i
$2$	−0.813737	−	2.70884i	−0.287699	−	0.957721i
$3$	2.61822	−	2.61822i	0.503877	−	0.503877i	−0.408764	−	0.912640i	$-0.634040\pi$
$3$	2.61822	−	2.61822i	0.503877	−	0.503877i	0.912640	+	0.408764i	$0.134040\pi$
$4$	−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	$-0.0125101\pi$
$7$	17.7783	+	17.7783i	0.959936	+	0.959936i	−0.0392914	+	0.999228i	$0.512510\pi$
$8$	17.3744	+	14.4959i	0.767846	+	0.640635i
$9$			13.2899i			0.492217i
$10$	−29.9084	+	10.2707i	−0.945787	+	0.324787i
$11$		−	7.37590i		−	0.202174i	−0.994878	−	0.101087i	$-0.967768\pi$
$11$		−	7.37590i		−	0.202174i	0.994878	−	0.101087i	$-0.0322321\pi$
$12$	−5.93575	+	29.0210i	−0.142792	+	0.698136i
$13$	−2.68249	−	2.68249i	−0.0572300	−	0.0572300i	0.677913	−	0.735143i	$-0.262885\pi$
$13$	−2.68249	−	2.68249i	−0.0572300	−	0.0572300i	−0.735143	+	0.677913i	$0.762885\pi$
$14$	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	−0.836571	−	0.547858i	$-0.815443\pi$
$17$	−20.2367	+	20.2367i	−0.288713	+	0.288713i	0.547858	+	0.836571i	$0.315443\pi$
$18$	36.0001	−	10.8144i	0.471406	−	0.141610i
$19$	−135.808			−1.63981			−0.819906	−	0.572498i	$-0.805975\pi$
$19$	−135.808			−1.63981			−0.819906	+	0.572498i	$0.805975\pi$
$20$	52.1592	+	72.6596i	0.583157	+	0.812359i
$21$	93.0948			0.967379
$22$	−19.9802	+	6.00204i	−0.193627	+	0.0581654i
$23$	71.0426	−	71.0426i	0.644061	−	0.644061i	−0.307490	−	0.951551i	$-0.599489\pi$
$23$	71.0426	−	71.0426i	0.644061	−	0.644061i	0.951551	+	0.307490i	$0.0994892\pi$
$24$	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
$28$	−197.059	−	40.3050i	−1.33002	−	0.272033i
$29$			34.2890i			0.219562i	0.993956	+	0.109781i	$0.0350150\pi$
$29$			34.2890i			0.219562i	−0.993956	+	0.109781i	$0.964985\pi$
$30$	−51.4160	+	105.198i	−0.312908	+	0.640213i
$31$			187.974i			1.08907i	0.838739	+	0.544533i	$0.183293\pi$
$31$			187.974i			1.08907i	−0.838739	+	0.544533i	$0.816707\pi$
$32$	−179.892	−	20.1737i	−0.993771	−	0.111445i
$33$	−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	0.121190	−	0.992629i	$-0.461329\pi$
$37$	250.679	−	250.679i	1.11382	−	1.11382i	0.992629	−	0.121190i	$-0.0386712\pi$
$38$	110.512	+	367.882i	0.471773	+	1.57048i
$39$	−14.0467			−0.0576737
$40$	154.380	−	200.417i	0.610239	−	0.792217i
$41$	−211.105			−0.804122			−0.402061	−	0.915613i	$-0.631706\pi$
$41$	−211.105			−0.804122			−0.402061	+	0.915613i	$0.631706\pi$
$42$	−75.7547	−	252.179i	−0.278314	−	0.926479i
$43$	−46.7326	+	46.7326i	−0.165736	+	0.165736i	−0.785102	−	0.619366i	$-0.787390\pi$
$43$	−46.7326	+	46.7326i	−0.165736	+	0.165736i	0.619366	+	0.785102i	$0.287390\pi$
$44$	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	$-0.386678\pi$
$47$	−189.707	−	189.707i	−0.588757	−	0.588757i	−0.937295	+	0.348538i	$0.886678\pi$
$48$	−88.3159	−	219.902i	−0.265569	−	0.661254i
$49$			289.134i			0.842956i
$50$	127.767	+	329.660i	0.361381	+	0.932418i
$51$			105.968i			0.290952i
$52$	29.7334	+	6.08147i	0.0792939	+	0.0162182i
$53$	−74.5742	−	74.5742i	−0.193275	−	0.193275i	0.603835	−	0.797109i	$-0.293639\pi$
$53$	−74.5742	−	74.5742i	−0.193275	−	0.193275i	−0.797109	+	0.603835i	$0.793639\pi$
$54$	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
$58$	92.8835	−	27.9022i	0.210279	−	0.0631679i
$59$	−101.072			−0.223024			−0.111512	−	0.993763i	$-0.535569\pi$
$59$	−101.072			−0.223024			−0.111512	+	0.993763i	$0.535569\pi$
$60$	326.803	+	53.6747i	0.703168	+	0.115489i
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	509.191	−	152.961i	1.04302	−	0.313324i
$63$	−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	$-0.235737\pi$
$67$	34.7419	+	34.7419i	0.0633493	+	0.0633493i	−0.674722	+	0.738072i	$0.735737\pi$
$68$	45.8785	−	224.309i	0.0818175	−	0.400021i
$69$		−	372.010i		−	0.649054i
$70$	−714.314	−	349.126i	−1.21967	−	0.596121i
$71$		−	614.600i		−	1.02732i	−0.857994	−	0.513660i	$-0.828289\pi$
$71$		−	614.600i		−	1.02732i	0.857994	−	0.513660i	$-0.171711\pi$
$72$	−192.649	+	230.903i	−0.315331	+	0.377946i
$73$	−37.4378	−	37.4378i	−0.0600242	−	0.0600242i	0.676457	−	0.736482i	$-0.263514\pi$
$73$	−37.4378	−	37.4378i	−0.0600242	−	0.0600242i	−0.736482	+	0.676457i	$0.763514\pi$
$74$	−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
$78$	11.4303	+	38.0504i	0.0165927	+	0.0552353i
$79$	1002.91			1.42831			0.714153	−	0.699990i	$-0.246812\pi$
$79$	1002.91			1.42831			0.714153	+	0.699990i	$0.246812\pi$
$80$	−668.522	−	255.104i	−0.934288	−	0.356518i
$81$	193.554			0.265506
$82$	171.784	+	571.850i	0.231346	+	0.770125i
$83$	423.190	−	423.190i	0.559652	−	0.559652i	−0.369556	−	0.929208i	$-0.620490\pi$
$83$	423.190	−	423.190i	0.559652	−	0.559652i	0.929208	+	0.369556i	$0.120490\pi$
$84$	−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
$88$	106.920	−	128.152i	0.129520	−	0.155239i
$89$		−	1049.38i		−	1.24982i	−0.780695	−	0.624912i	$-0.785135\pi$
$89$		−	1049.38i		−	1.24982i	0.780695	−	0.624912i	$-0.214865\pi$
$90$	−136.495	−	397.478i	−0.159865	−	0.465532i
$91$		−	95.3802i		−	0.109874i
$92$	−161.060	+	787.453i	−0.182518	+	0.892365i
$93$	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	−0.929764	−	0.368156i	$-0.879989\pi$
$97$	−536.526	+	536.526i	−0.561608	+	0.561608i	0.368156	+	0.929764i	$0.379989\pi$
$98$	783.218	−	235.279i	0.807316	−	0.242518i
$99$	98.0246			0.0995136
$100$	789.027	−	614.358i	0.789027	−	0.614358i
$101$	−1415.80			−1.39483			−0.697414	−	0.716668i	$-0.745666\pi$
$101$	−1415.80			−1.39483			−0.697414	+	0.716668i	$0.745666\pi$
$102$	287.052	−	86.2303i	0.278650	−	0.0837066i
$103$	−284.920	+	284.920i	−0.272563	+	0.272563i	−0.830131	−	0.557568i	$-0.811735\pi$
$103$	−284.920	+	284.920i	−0.272563	+	0.272563i	0.557568	+	0.830131i	$0.311735\pi$
$104$	−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	$-0.345864\pi$
$107$	−464.315	−	464.315i	−0.419505	−	0.419505i	−0.885033	+	0.465528i	$0.845864\pi$
$108$	−1169.25	−	239.150i	−1.04177	−	0.213076i
$109$			638.365i			0.560957i	0.959860	+	0.280478i	$0.0904931\pi$
$109$			638.365i			0.560957i	−0.959860	+	0.280478i	$0.909507\pi$
$110$	75.7553	+	220.601i	0.0656635	+	0.191214i
$111$		−	1312.66i		−	1.12246i
$112$	1493.18	−	599.684i	1.25976	−	0.505936i
$113$	1001.84	+	1001.84i	0.834027	+	0.834027i	0.988065	−	0.154038i	$-0.0492277\pi$
$113$	1001.84	+	1001.84i	0.834027	+	0.834027i	−0.154038	+	0.988065i	$0.549228\pi$
$114$	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
$118$	82.2456	+	273.787i	0.0641638	+	0.213594i
$119$	−719.548			−0.554293
$120$	−120.535	−	928.935i	−0.0916944	−	0.706665i
$121$	1276.60			0.959126
$122$	−188.878	−	628.756i	−0.140166	−	0.466598i
$123$	−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	$-0.349007\pi$
$127$	−619.456	−	619.456i	−0.432818	−	0.432818i	−0.889586	+	0.456768i	$0.849007\pi$
$128$	1289.83	−	658.392i	0.890674	−	0.454642i
$129$			244.712i			0.167021i
$130$	107.780	+	52.6782i	0.0727150	+	0.0355399i
$131$			1620.12i			1.08054i	0.841491	+	0.540270i	$0.181678\pi$
$131$			1620.12i			1.08054i	−0.841491	+	0.540270i	$0.818322\pi$
$132$	214.056	+	43.7815i	0.141145	+	0.0288689i
$133$	−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	−0.401379	−	0.915912i	$-0.631469\pi$
$137$	825.076	−	825.076i	0.514533	−	0.514533i	0.915912	+	0.401379i	$0.131469\pi$
$138$	−1007.72	+	302.718i	−0.621613	+	0.186733i
$139$	1264.21			0.771430			0.385715	−	0.922618i	$-0.373955\pi$
$139$	1264.21			0.771430			0.385715	+	0.922618i	$0.373955\pi$
$140$	−364.462	+	2219.06i	−0.220019	+	1.33961i
$141$	−993.387			−0.593321
$142$	−1664.86	+	500.123i	−0.983885	+	0.295559i
$143$	−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
$148$	−568.312	+	2778.58i	−0.315642	+	1.54323i
$149$			1351.49i			0.743079i	0.928417	+	0.371539i	$0.121170\pi$
$149$			1351.49i			0.743079i	−0.928417	+	0.371539i	$0.878830\pi$
$150$	1197.64	+	528.598i	0.651915	+	0.287732i
$151$			2325.64i			1.25336i	0.779275	+	0.626682i	$0.215588\pi$
$151$			2325.64i			1.25336i	−0.779275	+	0.626682i	$0.784412\pi$
$152$	−2359.57	−	1968.66i	−1.25912	−	1.05052i
$153$	−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	−0.664601	−	0.747199i	$-0.731398\pi$
$157$	162.486	−	162.486i	0.0825976	−	0.0825976i	0.747199	+	0.664601i	$0.231398\pi$
$158$	−816.105	−	2716.73i	−0.410923	−	1.36792i
$159$	−390.503			−0.194773
$160$	−147.035	+	2018.51i	−0.0726509	+	0.997357i
$161$	2526.03			1.23651
$162$	−157.502	−	524.307i	−0.0763859	−	0.254281i
$163$	932.441	−	932.441i	0.448064	−	0.448064i	−0.446647	−	0.894710i	$-0.647382\pi$
$163$	932.441	−	932.441i	0.448064	−	0.448064i	0.894710	+	0.446647i	$0.147382\pi$
$164$	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	$-0.146338\pi$
$167$	976.461	+	976.461i	0.452460	+	0.452460i	−0.443710	+	0.896170i	$0.646338\pi$
$168$	1617.46	+	1349.49i	0.742798	+	0.619737i
$169$		−	2182.61i		−	0.993449i
$170$	397.404	−	813.093i	0.179291	−	0.366831i
$171$		−	1804.87i		−	0.807143i
$172$	105.947	−	517.995i	0.0469674	−	0.229632i
$173$	761.698	+	761.698i	0.334745	+	0.334745i	0.854385	−	0.519640i	$-0.173934\pi$
$173$	761.698	+	761.698i	0.334745	+	0.334745i	−0.519640	+	0.854385i	$0.673934\pi$
$174$	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
$178$	−2842.61	+	853.921i	−1.19698	+	0.359574i
$179$	−4003.32			−1.67163			−0.835816	−	0.549009i	$-0.815005\pi$
$179$	−4003.32			−1.67163			−0.835816	+	0.549009i	$0.815005\pi$
$180$	−965.635	+	693.188i	−0.399857	+	0.287040i
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	−258.370	+	77.6144i	−0.105229	+	0.0316108i
$183$	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
$188$	2102.75	+	430.083i	0.815740	+	0.166846i
$189$			3750.78i			1.44354i
$190$	4061.80	−	1394.83i	1.55091	−	0.532589i
$191$			1458.80i			0.552644i	0.961065	+	0.276322i	$0.0891156\pi$
$191$			1458.80i			0.552644i	−0.961065	+	0.276322i	$0.910884\pi$
$192$	1559.02	+	1078.65i	0.586004	+	0.405441i
$193$	2264.70	+	2264.70i	0.844647	+	0.844647i	0.989459	−	0.144812i	$-0.0462577\pi$
$193$	2264.70	+	2264.70i	0.844647	+	0.844647i	−0.144812	+	0.989459i	$0.546258\pi$
$194$	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	−0.218902	−	0.975747i	$-0.570247\pi$
$197$	2092.70	−	2092.70i	0.756845	−	0.756845i	0.975747	+	0.218902i	$0.0702474\pi$
$198$	−79.7662	−	265.533i	−0.0286300	−	0.0953062i
$199$	−2087.70			−0.743683			−0.371842	−	0.928296i	$-0.621274\pi$
$199$	−2087.70			−0.743683			−0.371842	+	0.928296i	$0.621274\pi$
$200$	−2306.26	−	1637.43i	−0.815386	−	0.578917i
$201$	181.924			0.0638405
$202$	1152.09	+	3835.19i	0.401291	+	1.33586i
$203$	−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
$208$	−225.301	+	90.4840i	−0.0751048	+	0.0301632i
$209$			1001.70i			0.331528i
$210$	−2784.32	+	956.145i	−0.914935	+	0.314192i
$211$		−	199.597i		−	0.0651223i	−0.999470	−	0.0325611i	$-0.989634\pi$
$211$		−	199.597i		−	0.0651223i	0.999470	−	0.0325611i	$-0.0103664\pi$
$212$	826.598	+	169.067i	0.267788	+	0.0547714i
$213$	−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
$218$	1729.23	−	519.461i	0.537240	−	0.161387i
$219$	−196.041			−0.0604896
$220$	535.930	−	384.721i	0.164238	−	0.117899i
$221$	108.570			0.0330461
$222$	−3555.80	+	1068.16i	−1.07500	+	0.322930i
$223$	3340.24	−	3340.24i	1.00304	−	1.00304i	0.00304854	−	0.999995i	$-0.499030\pi$
$223$	3340.24	−	3340.24i	1.00304	−	1.00304i	0.999995	−	0.00304854i	$-0.000970381\pi$
$224$	−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	$-0.195485\pi$
$227$	824.316	+	824.316i	0.241021	+	0.241021i	−0.576251	+	0.817272i	$0.695485\pi$
$228$	806.121	−	3941.27i	0.234152	−	1.14481i
$229$		−	4512.23i		−	1.30208i	−0.759043	−	0.651041i	$-0.774333\pi$
$229$		−	4512.23i		−	1.30208i	0.759043	−	0.651041i	$-0.225667\pi$
$230$	−1395.12	+	2854.42i	−0.399962	+	0.818327i
$231$		−	686.658i		−	0.195579i
$232$	−497.050	+	595.749i	−0.140659	+	0.168590i
$233$	−292.574	−	292.574i	−0.0822625	−	0.0822625i	0.664778	−	0.747041i	$-0.268526\pi$
$233$	−292.574	−	292.574i	−0.0822625	−	0.0822625i	−0.747041	+	0.664778i	$0.768526\pi$
$234$	−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
$238$	585.522	+	1949.14i	0.159470	+	0.530858i
$239$	2925.20			0.791696			0.395848	−	0.918316i	$-0.370451\pi$
$239$	2925.20			0.791696			0.395848	+	0.918316i	$0.370451\pi$
$240$	−2418.26	+	1082.42i	−0.650407	+	0.291125i
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	−1038.81	−	3458.10i	−0.275940	−	0.918574i
$243$	−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
$248$	−2724.85	+	3265.92i	−0.697694	+	0.836235i
$249$		−	2216.01i		−	0.563991i
$250$	3627.27	−	1570.97i	0.917634	−	0.397426i
$251$		−	5268.72i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$251$		−	5268.72i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$252$	535.647	−	2618.88i	0.133899	−	0.654658i
$253$	−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	−0.504061	+	0.863668i	$0.668161\pi$
$257$	−5635.08	+	5635.08i	−1.36773	+	1.36773i	−0.863668	+	0.504061i	$0.831839\pi$
$258$	662.888	−	199.132i	0.159960	−	0.0480519i
$259$	8913.27			2.13839
$260$	54.9923	−	334.826i	0.0131172	−	0.0798654i
$261$	−455.696			−0.108072
$262$	4388.66	−	1318.35i	1.03486	−	0.310871i
$263$	−2721.99	+	2721.99i	−0.638195	+	0.638195i	−0.950110	−	0.311915i	$-0.899030\pi$
$263$	−2721.99	+	2721.99i	−0.638195	+	0.638195i	0.311915	+	0.950110i	$0.399030\pi$
$264$	−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
$268$	−385.088	−	78.7632i	−0.0877723	−	0.0179523i
$269$			603.964i			0.136893i	0.997655	+	0.0684467i	$0.0218043\pi$
$269$			603.964i			0.136893i	−0.997655	+	0.0684467i	$0.978196\pi$
$270$	−4238.40	−	2071.54i	−0.955336	−	0.466926i
$271$			4232.24i			0.948672i	0.880344	+	0.474336i	$0.157312\pi$
$271$			4232.24i			0.948672i	−0.880344	+	0.474336i	$0.842688\pi$
$272$	682.611	+	1699.67i	0.152167	+	0.378888i
$273$	−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	−0.266633	−	0.963798i	$-0.585911\pi$
$277$	3214.07	−	3214.07i	0.697165	−	0.697165i	0.963798	+	0.266633i	$0.0859113\pi$
$278$	−1028.73	−	3424.54i	−0.221940	−	0.738815i
$279$	−2498.14			−0.536056
$280$	6307.67	−	818.461i	1.34627	−	0.174687i
$281$	−7574.78			−1.60809			−0.804046	−	0.594567i	$-0.797323\pi$
$281$	−7574.78			−1.60809			−0.804046	+	0.594567i	$0.797323\pi$
$282$	808.356	+	2690.93i	0.170698	+	0.568236i
$283$	−504.094	+	504.094i	−0.105884	+	0.105884i	−0.758064	−	0.652180i	$-0.773855\pi$
$283$	−504.094	+	504.094i	−0.105884	+	0.105884i	0.652180	+	0.758064i	$0.273855\pi$
$284$	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
$288$	268.106	−	2390.73i	0.0548552	−	0.489150i
$289$			4093.95i			0.833289i
$290$	−352.170	−	1025.53i	−0.0713109	−	0.207659i
$291$			2809.49i			0.565962i
$292$	414.970	+	84.8750i	0.0831653	+	0.0170101i
$293$	−244.144	−	244.144i	−0.0486793	−	0.0486793i	0.682348	−	0.731027i	$-0.260959\pi$
$293$	−244.144	−	244.144i	−0.0486793	−	0.0486793i	−0.731027	+	0.682348i	$0.760959\pi$
$294$	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
$298$	3660.99	−	1099.76i	0.711662	−	0.213783i
$299$	−381.143			−0.0737192
$300$	457.323	−	3674.37i	0.0880118	−	0.707133i
$301$	−1661.65			−0.318192
$302$	6299.80	−	1892.46i	1.20037	−	0.360592i
$303$	−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	−0.943942	−	0.330110i	$-0.892914\pi$
$307$	−6853.22	−	6853.22i	−1.27405	−	1.27405i	−0.330110	−	0.943942i	$-0.607086\pi$
$308$	−297.286	+	1453.48i	−0.0549981	+	0.268896i
$309$			1491.97i			0.274676i
$310$	−1930.61	−	5621.99i	−0.353714	−	1.03002i
$311$		−	10802.7i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$311$		−	10802.7i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$312$	−244.053	−	203.620i	−0.0442845	−	0.0369478i
$313$	2618.43	+	2618.43i	0.472851	+	0.472851i	0.902836	−	0.429985i	$-0.141481\pi$
$313$	2618.43	+	2618.43i	0.472851	+	0.472851i	−0.429985	+	0.902836i	$0.641481\pi$
$314$	−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	−0.305138	−	0.952308i	$-0.598703\pi$
$317$	3652.64	−	3652.64i	0.647170	−	0.647170i	0.952308	+	0.305138i	$0.0987027\pi$
$318$	317.767	+	1057.81i	0.0560361	+	0.186538i
$319$	252.912			0.0443898
$320$	5587.47	−	1244.24i	0.976092	−	0.217360i
$321$	−2431.36			−0.422757
$322$	−2055.52	−	6842.61i	−0.355745	−	1.18424i
$323$	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
$328$	−3667.81	−	3060.16i	−0.617442	−	0.515149i
$329$		−	6745.31i		−	1.13034i
$330$	775.927	+	379.239i	0.129434	+	0.0632619i
$331$			7839.91i			1.30187i	0.759131	+	0.650937i	$0.225624\pi$
$331$			7839.91i			1.30187i	−0.759131	+	0.650937i	$0.774376\pi$
$332$	−959.411	+	4690.74i	−0.158598	+	0.775415i
$333$	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	−0.970204	−	0.242291i	$-0.922101\pi$
$337$	−4503.23	+	4503.23i	−0.727912	+	0.727912i	0.242291	+	0.970204i	$0.422101\pi$
$338$	−5912.34	+	1776.07i	−0.951447	+	0.285815i
$339$	5246.07			0.840494
$340$	−2525.92	−	414.862i	−0.402904	−	0.0661736i
$341$	1386.47			0.220181
$342$	−4889.10	+	1468.69i	−0.773018	+	0.232215i
$343$	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	0.922413	+	0.386205i	$0.126214\pi$
$347$	8458.77	+	8458.77i	1.30862	+	1.30862i	0.386205	+	0.922413i	$0.373786\pi$
$348$	−995.100	−	203.531i	−0.153284	−	0.0313517i
$349$		−	5515.41i		−	0.845941i	−0.906144	−	0.422970i	$-0.860987\pi$
$349$		−	5515.41i		−	0.845941i	0.906144	−	0.422970i	$-0.139013\pi$
$350$	−3589.30	+	8132.26i	−0.548160	+	1.24196i
$351$		−	565.940i		−	0.0860617i
$352$	−148.799	+	1326.86i	−0.0225314	+	0.200915i
$353$	−761.447	−	761.447i	−0.114810	−	0.114810i	0.647368	−	0.762178i	$-0.275870\pi$
$353$	−761.447	−	761.447i	−0.114810	−	0.114810i	−0.762178	+	0.647368i	$0.775870\pi$
$354$	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
$358$	3257.65	+	10844.4i	0.480928	+	1.60096i
$359$	3564.71			0.524062			0.262031	−	0.965059i	$-0.415608\pi$
$359$	3564.71			0.524062			0.262031	+	0.965059i	$0.415608\pi$
$360$	2663.51	+	2051.68i	0.389942	+	0.300370i
$361$	11584.8			1.68899
$362$	1586.78	+	5282.23i	0.230385	+	0.766928i
$363$	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	$-0.103803\pi$
$367$	4407.82	+	4407.82i	0.626939	+	0.626939i	−0.320358	+	0.947297i	$0.603803\pi$
$368$	−2396.36	−	5966.81i	−0.339453	−	0.845222i
$369$		−	2805.55i		−	0.395802i
$370$	−4922.77	+	10072.0i	−0.691683	+	1.41519i
$371$		−	2651.60i		−	0.371063i
$372$	−5455.17	−	1115.76i	−0.760316	−	0.155510i
$373$	−8371.19	−	8371.19i	−1.16205	−	1.16205i	−0.984027	−	0.178021i	$-0.943030\pi$
$373$	−8371.19	−	8371.19i	−1.16205	−	1.16205i	−0.178021	−	0.984027i	$-0.556970\pi$
$374$	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
$378$	10160.3	−	3052.15i	1.38251	−	0.415305i
$379$	−11130.1			−1.50848			−0.754240	−	0.656599i	$-0.771994\pi$
$379$	−11130.1			−1.50848			−0.754240	+	0.656599i	$0.771994\pi$
$380$	−7083.62	−	9867.74i	−0.956269	−	1.33212i
$381$	−3243.75			−0.436174
$382$	3951.66	−	1187.08i	0.529279	−	0.158995i
$383$	1006.62	−	1006.62i	0.134297	−	0.134297i	−0.636763	−	0.771060i	$-0.719727\pi$
$383$	1006.62	−	1006.62i	0.134297	−	0.134297i	0.771060	+	0.636763i	$0.219727\pi$
$384$	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
$388$	1216.35	−	5946.98i	0.159152	−	0.778124i
$389$			13548.4i			1.76589i	0.469478	+	0.882944i	$0.344442\pi$
$389$			13548.4i			1.76589i	−0.469478	+	0.882944i	$0.655558\pi$
$390$	420.115	−	144.269i	0.0545471	−	0.0187317i
$391$			2875.34i			0.371898i
$392$	−4191.26	+	5023.52i	−0.540027	+	0.647260i
$393$	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	−0.582437	−	0.812876i	$-0.697901\pi$
$397$	1822.81	−	1822.81i	0.230439	−	0.230439i	0.812876	+	0.582437i	$0.197901\pi$
$398$	1698.84	+	5655.25i	0.213957	+	0.712241i
$399$	−12643.0			−1.58632
$400$	−2558.84	+	7579.73i	−0.319855	+	0.947466i
$401$	5922.04			0.737488			0.368744	−	0.929531i	$-0.379788\pi$
$401$	5922.04			0.737488			0.368744	+	0.929531i	$0.379788\pi$
$402$	−148.038	−	492.804i	−0.0183669	−	0.0611413i
$403$	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
$408$	−1536.11	+	1841.13i	−0.186394	+	0.223406i
$409$			8533.05i			1.03162i	0.856703	+	0.515809i	$0.172509\pi$
$409$			8533.05i			1.03162i	−0.856703	+	0.515809i	$0.827491\pi$
$410$	6313.81	−	2168.18i	0.760529	−	0.261168i
$411$		−	4320.46i		−	0.518522i
$412$	645.940	−	3158.12i	0.0772408	−	0.377644i
$413$	−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
$418$	2713.46	−	815.124i	0.317511	−	0.0953804i
$419$	−7128.02			−0.831089			−0.415545	−	0.909573i	$-0.636409\pi$
$419$	−7128.02			−0.831089			−0.415545	+	0.909573i	$0.636409\pi$
$420$	4855.75	+	6764.24i	0.564134	+	0.785859i
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	−540.676	+	162.419i	−0.0623690	+	0.0187356i
$423$	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
$428$	5146.58	+	1052.65i	0.581236	+	0.118882i
$429$			103.607i			0.0116601i
$430$	917.724	−	1877.67i	0.102922	−	0.210580i
$431$			9361.72i			1.04626i	0.852253	+	0.523130i	$0.175236\pi$
$431$			9361.72i			1.04626i	−0.852253	+	0.523130i	$0.824764\pi$
$432$	8859.84	−	3558.24i	0.986734	−	0.396286i
$433$	−1769.48	−	1769.48i	−0.196388	−	0.196388i	0.602062	−	0.798450i	$-0.294346\pi$
$433$	−1769.48	−	1769.48i	−0.196388	−	0.196388i	−0.798450	+	0.602062i	$0.794346\pi$
$434$	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
$438$	159.526	+	531.044i	0.0174028	+	0.0579321i
$439$	7823.34			0.850541			0.425271	−	0.905066i	$-0.360179\pi$
$439$	7823.34			0.850541			0.425271	+	0.905066i	$0.360179\pi$
$440$	−1478.25	−	1138.69i	−0.160166	−	0.123375i
$441$	−3842.54			−0.414917
$442$	−88.3472	−	294.099i	−0.00950735	−	0.0316490i
$443$	−9066.48	+	9066.48i	−0.972374	+	0.972374i	−0.999629	−	0.0272545i	$-0.991324\pi$
$443$	−9066.48	+	9066.48i	−0.972374	+	0.972374i	0.0272545	+	0.999629i	$0.491324\pi$
$444$	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
$448$	−7324.25	+	10586.1i	−0.772407	+	1.11640i
$449$		−	3381.93i		−	0.355464i	−0.984079	−	0.177732i	$-0.943124\pi$
$449$		−	3381.93i		−	0.355464i	0.984079	−	0.177732i	$-0.0568759\pi$
$450$	−4381.13	+	1698.01i	−0.458952	+	0.177878i
$451$			1557.09i			0.162573i
$452$	−11104.6	−	2271.26i	−1.15557	−	0.236352i
$453$	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	0.0547399	−	0.998501i	$-0.482567\pi$
$457$	10289.7	−	10289.7i	1.05324	−	1.05324i	0.998501	−	0.0547399i	$-0.0174330\pi$
$458$	−12222.9	+	3671.77i	−1.24703	+	0.374608i
$459$	−4269.45			−0.434163
$460$	8867.45	+	1456.40i	0.898798	+	0.147620i
$461$	−5310.20			−0.536488			−0.268244	−	0.963351i	$-0.586443\pi$
$461$	−5310.20			−0.536488			−0.268244	+	0.963351i	$0.586443\pi$
$462$	−1860.05	+	558.759i	−0.187310	+	0.0562680i
$463$	7686.78	−	7686.78i	0.771566	−	0.771566i	−0.206814	−	0.978380i	$-0.566310\pi$
$463$	7686.78	−	7686.78i	0.771566	−	0.771566i	0.978380	+	0.206814i	$0.0663096\pi$
$464$	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	$-0.147049\pi$
$467$	4535.99	+	4535.99i	0.449466	+	0.449466i	−0.445711	+	0.895177i	$0.647049\pi$
$468$	−80.8218	+	395.153i	−0.00798288	+	0.0390298i
$469$			1235.30i			0.121623i
$470$	7622.24	+	3725.42i	0.748059	+	0.365618i
$471$		−	850.850i		−	0.0832380i
$472$	−1756.05	−	1465.12i	−0.171248	−	0.142877i
$473$	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
$478$	−2380.34	−	7923.91i	−0.227771	−	0.758224i
$479$	10969.6			1.04638			0.523189	−	0.852217i	$-0.324742\pi$
$479$	10969.6			1.04638			0.523189	+	0.852217i	$0.324742\pi$
$480$	4899.93	+	5669.87i	0.465938	+	0.539152i
$481$	−1344.89			−0.127488
$482$	−3466.03	−	11538.0i	−0.327538	−	1.09034i
$483$	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	−0.978416	−	0.206646i	$-0.933745\pi$
$487$	−12736.0	−	12736.0i	−1.18506	−	1.18506i	−0.206646	−	0.978416i	$-0.566255\pi$
$488$	4032.80	+	3364.68i	0.374091	+	0.312115i
$489$		−	4882.67i		−	0.451538i
$490$	−2969.59	−	8647.53i	−0.273781	−	0.797257i
$491$			10518.6i			0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$491$			10518.6i			0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$492$	1253.06	−	6126.46i	0.114822	−	0.561387i
$493$	−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
$498$	−6002.82	+	1803.25i	−0.540146	+	0.162260i
$499$	−2445.26			−0.219368			−0.109684	−	0.993966i	$-0.534984\pi$
$499$	−2445.26			−0.219368			−0.109684	+	0.993966i	$0.534984\pi$
$500$	−7207.14	−	8547.35i	−0.644626	−	0.764498i
$501$	5113.18			0.455968
$502$	−14272.1	+	4287.35i	−1.26892	+	0.381183i
$503$	−12216.7	+	12216.7i	−1.08293	+	1.08293i	−0.0866986	+	0.996235i	$0.527632\pi$
$503$	−12216.7	+	12216.7i	−1.08293	+	1.08293i	−0.996235	+	0.0866986i	$0.972368\pi$
$504$	−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
$508$	6866.20	+	1404.37i	0.599682	+	0.122655i
$509$		−	5615.75i		−	0.489025i	−0.969646	−	0.244512i	$-0.921372\pi$
$509$		−	5615.75i		−	0.489025i	0.969646	−	0.244512i	$-0.0786279\pi$
$510$	−1088.36	−	3169.35i	−0.0944972	−	0.275178i
$511$		−	1331.16i		−	0.115239i
$512$	−5707.93	+	10081.5i	−0.492690	+	0.870205i
$513$	−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
$518$	−7253.05	−	24144.6i	−0.615214	−	2.04798i
$519$	3988.58			0.337340
$520$	−951.740	+	123.494i	−0.0802626	+	0.0104146i
$521$	5287.10			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$521$	5287.10			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$522$	370.816	+	1234.41i	0.0310923	+	0.103503i
$523$	4328.34	−	4328.34i	0.361883	−	0.361883i	−0.502623	−	0.864506i	$-0.667631\pi$
$523$	4328.34	−	4328.34i	0.361883	−	0.361883i	0.864506	+	0.502623i	$0.167631\pi$
$524$	−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
$528$	−1621.98	+	651.409i	−0.133688	+	0.0536912i
$529$			2072.91i			0.170371i
$530$	2996.32	+	1464.47i	0.245570	+	0.120024i
$531$		−	1343.23i		−	0.109776i
$532$	26762.1	+	5473.73i	2.18098	+	0.446083i
$533$	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
$538$	1636.04	−	491.468i	0.131106	−	0.0393841i
$539$	2132.62			0.170424
$540$	−2162.54	+	13166.8i	−0.172335	+	1.04928i
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	11464.5	−	3443.93i	0.908563	−	0.272932i
$543$	−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	$-0.199037\pi$
$547$	2884.33	+	2884.33i	0.225457	+	0.225457i	−0.585335	+	0.810792i	$0.699037\pi$
$548$	−1870.52	+	9145.34i	−0.145812	+	0.712901i
$549$			3084.74i			0.239806i
$550$	2431.54	−	942.399i	0.188511	−	0.0730619i
$551$		−	4656.71i		−	0.360041i
$552$	5392.63	−	6463.44i	0.415807	−	0.498374i
$553$	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	−0.910633	−	0.413216i	$-0.864405\pi$
$557$	−6538.87	+	6538.87i	−0.497416	+	0.497416i	0.413216	+	0.910633i	$0.364405\pi$
$558$	2032.83	+	6767.07i	0.154223	+	0.513392i
$559$	250.720			0.0189702
$560$	−7349.87	−	16420.5i	−0.554622	−	1.23909i
$561$	781.612			0.0588229
$562$	6163.88	+	20518.9i	0.462647	+	1.54010i
$563$	−6499.93	+	6499.93i	−0.486571	+	0.486571i	−0.907222	−	0.420651i	$-0.861802\pi$
$563$	−6499.93	+	6499.93i	−0.486571	+	0.486571i	0.420651	+	0.907222i	$0.361802\pi$
$564$	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
$568$	8909.19	−	10678.3i	0.658136	−	0.788822i
$569$			5264.67i			0.387885i	0.981013	+	0.193942i	$0.0621275\pi$
$569$			5264.67i			0.387885i	−0.981013	+	0.193942i	$0.937872\pi$
$570$	6982.69	−	14286.7i	0.513110	−	1.04983i
$571$		−	22034.0i		−	1.61488i	−0.589952	−	0.807438i	$-0.700853\pi$
$571$		−	22034.0i		−	1.61488i	0.589952	−	0.807438i	$-0.299147\pi$
$572$	44.8563	−	219.311i	0.00327891	−	0.0160312i
$573$	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	−0.956414	−	0.292015i	$-0.905674\pi$
$577$	−9208.58	+	9208.58i	−0.664399	+	0.664399i	0.292015	+	0.956414i	$0.405674\pi$
$578$	11089.9	−	3331.40i	0.798059	−	0.239737i
$579$	11859.0			0.851196
$580$	−2491.43	+	1788.49i	−0.178363	+	0.128039i
$581$	15047.2			1.07446
$582$	7610.46	−	2286.18i	0.542034	−	0.162827i
$583$	−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	$-0.355357\pi$
$587$	−6536.20	−	6536.20i	−0.459587	−	0.459587i	−0.898520	+	0.438933i	$0.855357\pi$
$588$	−8390.94	−	1716.23i	−0.588498	−	0.120367i
$589$		−	25528.3i		−	1.78586i
$590$	3022.89	−	1038.07i	0.210933	−	0.0724351i
$591$		−	10958.3i		−	0.762713i
$592$	−8455.72	−	21054.3i	−0.587040	−	1.46170i
$593$	−11033.7	−	11033.7i	−0.764079	−	0.764079i	0.212978	−	0.977057i	$-0.431684\pi$
$593$	−11033.7	−	11033.7i	−0.764079	−	0.764079i	−0.977057	+	0.212978i	$0.931684\pi$
$594$	−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
$598$	310.150	+	1032.46i	0.0212090	+	0.0706024i
$599$	−1861.62			−0.126985			−0.0634923	−	0.997982i	$-0.520224\pi$
$599$	−1861.62			−0.126985			−0.0634923	+	0.997982i	$0.520224\pi$
$600$	−10325.4	+	1751.16i	−0.702557	+	0.119151i
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	1352.15	+	4501.15i	0.0915437	+	0.304739i
$603$	−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	$-0.259300\pi$
$607$	−617.817	−	617.817i	−0.0413121	−	0.0413121i	−0.727461	+	0.686149i	$0.759300\pi$
$608$	24430.7	+	2739.75i	1.62960	+	0.182749i
$609$			3192.13i			0.212400i
$610$	−6942.11	+	2383.95i	−0.460784	+	0.158235i
$611$			1017.77i			0.0673891i
$612$	2981.03	+	609.719i	0.196897	+	0.0402719i
$613$	5656.87	+	5656.87i	0.372722	+	0.372722i	0.868468	−	0.495745i	$-0.165105\pi$
$613$	5656.87	+	5656.87i	0.372722	+	0.372722i	−0.495745	+	0.868468i	$0.665105\pi$
$614$	−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	−0.152370	−	0.988323i	$-0.548691\pi$
$617$	12811.8	−	12811.8i	0.835953	−	0.835953i	0.988323	+	0.152370i	$0.0486907\pi$
$618$	4041.50	−	1214.07i	0.263063	−	0.0790243i
$619$	12163.2			0.789788			0.394894	−	0.918727i	$-0.370781\pi$
$619$	12163.2			0.789788			0.394894	+	0.918727i	$0.370781\pi$
$620$	−13658.1	+	9804.55i	−0.884713	+	0.635097i
$621$	14988.2			0.968530
$622$	−29262.9	+	8790.56i	−1.88639	+	0.566671i
$623$	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
$628$	−368.372	+	1801.04i	−0.0234071	+	0.114441i
$629$			10145.8i			0.643149i
$630$	4639.83	−	9493.13i	0.293421	−	0.600342i
$631$		−	3347.17i		−	0.211171i	−0.994410	−	0.105585i	$-0.966328\pi$
$631$		−	3347.17i		−	0.211171i	0.994410	−	0.105585i	$-0.0336716\pi$
$632$	17424.9	+	14538.1i	1.09672	+	0.915023i
$633$	−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
$638$	−205.804	−	685.099i	−0.0127709	−	0.0425131i
$639$	8167.95			0.505664
$640$	−7917.19	−	14123.1i	−0.488991	−	0.872289i
$641$	−24791.3			−1.52761			−0.763803	−	0.645449i	$-0.776670\pi$
$641$	−24791.3			−1.52761			−0.763803	+	0.645449i	$0.776670\pi$
$642$	1978.48	+	6586.17i	0.121627	+	0.404884i
$643$	−12922.9	+	12922.9i	−0.792583	+	0.792583i	−0.981913	−	0.189330i	$-0.939368\pi$
$643$	−12922.9	+	12922.9i	−0.792583	+	0.792583i	0.189330	+	0.981913i	$0.439368\pi$
$644$	−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	0.999585	+	0.0288113i	$0.00917218\pi$
$647$	16924.5	+	16924.5i	1.02840	+	1.02840i	0.0288113	+	0.999585i	$0.490828\pi$
$648$	3362.88	+	2805.74i	0.203868	+	0.170092i
$649$			745.493i			0.0450896i
$650$	541.575	−	1227.05i	0.0326805	−	0.0740441i
$651$			17499.4i			1.05354i
$652$	−2113.93	+	10335.4i	−0.126975	+	0.620806i
$653$	10391.0	+	10391.0i	0.622715	+	0.622715i	0.946225	−	0.323510i	$-0.104863\pi$
$653$	10391.0	+	10391.0i	0.622715	+	0.622715i	−0.323510	+	0.946225i	$0.604863\pi$
$654$	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
$658$	−18272.0	+	5488.91i	−1.08255	+	0.325197i
$659$	−773.045			−0.0456958			−0.0228479	−	0.999739i	$-0.507273\pi$
$659$	−773.045			−0.0456958			−0.0228479	+	0.999739i	$0.507273\pi$
$660$	395.899	−	2410.47i	0.0233490	−	0.142163i
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	21237.1	−	6379.62i	1.24683	−	0.374549i
$663$	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
$668$	−10823.3	−	2213.73i	−0.626896	−	0.128221i
$669$		−	17490.9i		−	1.01082i
$670$	−1395.90	−	682.254i	−0.0804900	−	0.0393400i
$671$		−	1712.04i		−	0.0984985i
$672$	−16747.0	−	1878.07i	−0.961353	−	0.107810i
$673$	−19931.6	−	19931.6i	−1.14161	−	1.14161i	−0.988155	−	0.153459i	$-0.950959\pi$
$673$	−19931.6	−	19931.6i	−1.14161	−	1.14161i	−0.153459	−	0.988155i	$-0.549041\pi$
$674$	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	−0.846120	−	0.532993i	$-0.821067\pi$
$677$	−5515.73	+	5515.73i	−0.313126	+	0.313126i	0.532993	+	0.846120i	$0.321067\pi$
$678$	−4268.92	−	14210.8i	−0.241810	−	0.804958i
$679$	−19077.0			−1.07822
$680$	931.641	+	7179.92i	0.0525394	+	0.404908i
$681$	4316.48			0.242890
$682$	−1128.22	−	3755.74i	−0.0633460	−	0.210872i
$683$	19946.1	−	19946.1i	1.11745	−	1.11745i	0.125331	−	0.992115i	$-0.460001\pi$
$683$	19946.1	−	19946.1i	1.11745	−	1.11745i	0.992115	−	0.125331i	$-0.0399992\pi$
$684$	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
$688$	1576.35	+	3925.04i	0.0873515	+	0.217501i
$689$			400.090i			0.0221222i
$690$	3820.79	+	11126.2i	0.210804	+	0.613867i
$691$			356.654i			0.0196350i	0.999952	+	0.00981748i	$0.00312505\pi$
$691$			356.654i			0.0196350i	−0.999952	+	0.00981748i	$0.996875\pi$
$692$	−8442.84	−	1726.84i	−0.463798	−	0.0948621i
$693$	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
$698$	−14940.4	+	4488.09i	−0.810175	+	0.243377i
$699$	−1532.05			−0.0829003
$700$	24949.8	+	3105.32i	1.34716	+	0.167671i
$701$	17230.0			0.928343			0.464172	−	0.885745i	$-0.346352\pi$
$701$	17230.0			0.928343			0.464172	+	0.885745i	$0.346352\pi$
$702$	−1533.04	+	460.526i	−0.0824231	+	0.0247599i
$703$	−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
$708$	599.935	−	2933.19i	0.0318460	−	0.155701i
$709$			8153.11i			0.431871i	0.976408	+	0.215935i	$0.0692801\pi$
$709$			8153.11i			0.431871i	−0.976408	+	0.215935i	$0.930720\pi$
$710$	6312.35	+	18381.7i	0.333659	+	0.971625i
$711$			13328.5i			0.703036i
$712$	15211.8	−	18232.4i	0.800681	−	0.959672i
$713$	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
$718$	−2900.74	−	9656.25i	−0.150772	−	0.501905i
$719$	−17219.3			−0.893147			−0.446573	−	0.894747i	$-0.647356\pi$
$719$	−17219.3			−0.893147			−0.446573	+	0.894747i	$0.647356\pi$
$720$	3390.29	−	8884.56i	0.175484	−	0.459872i
$721$	−10130.8			−0.523287
$722$	−9426.94	−	31381.3i	−0.485920	−	1.61758i
$723$	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	$-0.146186\pi$
$727$	8881.73	+	8881.73i	0.453102	+	0.453102i	−0.443281	+	0.896383i	$0.646186\pi$
$728$	1382.62	−	1657.17i	0.0703893	−	0.0843665i
$729$			17486.6i			0.888409i
$730$	1504.22	+	735.195i	0.0762652	+	0.0372751i
$731$		−	1891.43i		−	0.0957004i
$732$	−1377.76	+	6736.12i	−0.0695676	+	0.340129i
$733$	4401.20	+	4401.20i	0.221776	+	0.221776i	0.809246	−	0.587470i	$-0.199876\pi$
$733$	4401.20	+	4401.20i	0.221776	+	0.221776i	−0.587470	+	0.809246i	$0.699876\pi$
$734$	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
$738$	−7599.79	+	2282.98i	−0.379068	+	0.113872i
$739$	−23097.8			−1.14975			−0.574875	−	0.818241i	$-0.694949\pi$
$739$	−23097.8			−1.14975			−0.574875	+	0.818241i	$0.694949\pi$
$740$	31289.4	+	5139.03i	1.55435	+	0.255290i
$741$	1907.65			0.0945741
$742$	−7182.77	+	2157.70i	−0.355374	+	0.106754i
$743$	17404.1	−	17404.1i	0.859348	−	0.859348i	−0.131913	−	0.991261i	$-0.542112\pi$
$743$	17404.1	−	17404.1i	0.859348	−	0.859348i	0.991261	+	0.131913i	$0.0421119\pi$
$744$	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
$748$	−1654.48	−	338.395i	−0.0808739	−	0.0165414i
$749$		−	16509.4i		−	0.805396i
$750$	5383.85	−	13610.1i	0.262120	−	0.662628i
$751$		−	2347.75i		−	0.114075i	−0.998372	−	0.0570377i	$-0.981834\pi$
$751$		−	2347.75i		−	0.114075i	0.998372	−	0.0570377i	$-0.0181655\pi$
$752$	−15933.3	+	6399.05i	−0.772644	+	0.310305i
$753$	−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	−0.856307	−	0.516467i	$-0.827247\pi$
$757$	−7078.12	+	7078.12i	−0.339840	+	0.339840i	0.516467	+	0.856307i	$0.327247\pi$
$758$	9056.95	+	30149.6i	0.433989	+	1.44470i
$759$	−2743.91			−0.131222
$760$	−20966.0	+	27218.2i	−1.00068	+	1.29909i
$761$	−27017.6			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$761$	−27017.6			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$762$	2639.56	+	8786.80i	0.125487	+	0.417732i
$763$	−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
$768$	−15162.8	−	327.626i	−0.712423	−	0.0153935i
$769$			41584.0i			1.95001i	0.222183	+	0.975005i	$0.428682\pi$
$769$			41584.0i			1.95001i	−0.222183	+	0.975005i	$0.571318\pi$
$770$	−2575.11	+	5268.71i	−0.120520	+	0.246586i
$771$			29507.7i			1.37833i
$772$	−25102.5	−	5134.29i	−1.17028	−	0.239362i
$773$	−19799.8	−	19799.8i	−0.921280	−	0.921280i	0.0758404	−	0.997120i	$-0.475836\pi$
$773$	−19799.8	−	19799.8i	−0.921280	−	0.921280i	−0.997120	+	0.0758404i	$0.975836\pi$
$774$	−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
$778$	36700.5	−	11024.8i	1.69123	−	0.508045i
$779$	28669.7			1.31861
$780$	−732.665	−	1020.63i	−0.0336329	−	0.0468518i
$781$	−4533.23			−0.207697
$782$	7788.84	−	2339.77i	0.356174	−	0.106995i
$783$	−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	0.996799	+	0.0799542i	$0.0254774\pi$
$787$	23772.7	+	23772.7i	1.07675	+	1.07675i	0.0799542	+	0.996799i	$0.474523\pi$
$788$	−4744.34	+	23195.9i	−0.214480	+	1.04863i
$789$			14253.6i			0.643144i
$790$	−29995.4	+	10300.5i	−1.35087	+	0.463895i
$791$			35621.9i			1.60123i
$792$	1703.11	+	1420.96i	0.0764110	+	0.0637519i
$793$	−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	−0.485100	−	0.874459i	$-0.661217\pi$
$797$	8760.69	−	8760.69i	0.389359	−	0.389359i	0.874459	+	0.485100i	$0.161217\pi$
$798$	10288.1	+	34247.9i	0.456383	+	1.51925i
$799$	7678.08			0.339964
$800$	22614.5	+	763.592i	0.999430	+	0.0337463i
$801$	13946.1			0.615184
$802$	−4818.98	−	16041.9i	−0.212175	−	0.706308i
$803$	−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
$808$	−24598.7	−	20523.4i	−1.07101	−	0.893576i
$809$		−	27571.0i		−	1.19820i	−0.800673	−	0.599102i	$-0.795525\pi$
$809$		−	27571.0i		−	1.19820i	0.800673	−	0.599102i	$-0.204475\pi$
$810$	−5788.89	+	1987.93i	−0.251112	+	0.0862328i
$811$		−	20085.4i		−	0.869661i	−0.900512	−	0.434831i	$-0.856808\pi$
$811$		−	20085.4i		−	0.869661i	0.900512	−	0.434831i	$-0.143192\pi$
$812$	1382.02	−	6756.94i	0.0597282	−	0.292022i
$813$	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
$818$	23114.7	−	6943.65i	0.988002	−	0.296796i
$819$	1267.59			0.0540820
$820$	−11011.0	−	15338.8i	−0.468930	−	0.653236i
$821$	14867.5			0.632008			0.316004	−	0.948758i	$-0.397659\pi$
$821$	14867.5			0.632008			0.316004	+	0.948758i	$0.397659\pi$
$822$	−11703.5	+	3515.72i	−0.496600	+	0.149179i
$823$	23345.7	−	23345.7i	0.988797	−	0.988797i	−0.0111410	−	0.999938i	$-0.503546\pi$
$823$	23345.7	−	23345.7i	0.988797	−	0.988797i	0.999938	+	0.0111410i	$0.00354636\pi$
$824$	−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	$-0.281571\pi$
$827$	−3330.46	−	3330.46i	−0.140038	−	0.140038i	−0.773651	+	0.633613i	$0.781571\pi$
$828$	−10465.1	−	2140.47i	−0.439237	−	0.0898385i
$829$			11521.6i			0.482703i	0.970438	+	0.241351i	$0.0775906\pi$
$829$			11521.6i			0.482703i	−0.970438	+	0.241351i	$0.922409\pi$
$830$	−8310.51	+	17003.4i	−0.347544	+	0.711079i
$831$		−	16830.3i		−	0.702570i
$832$	1105.13	−	1597.30i	0.0460498	−	0.0665580i
$833$	−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
$838$	5800.33	+	19308.7i	0.239104	+	0.795951i
$839$	−33130.1			−1.36326			−0.681631	−	0.731696i	$-0.738729\pi$
$839$	−33130.1			−1.36326			−0.681631	+	0.731696i	$0.738729\pi$
$840$	14372.0	−	18657.8i	0.590333	−	0.766374i
$841$	23213.3			0.951792
$842$	497.388	+	1655.75i	0.0203576	+	0.0677684i
$843$	−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
$848$	−6263.43	+	2515.48i	−0.253641	+	0.101866i
$849$			2639.66i			0.106705i
$850$	−9256.82	−	4085.64i	−0.373537	−	0.164866i
$851$		−	35617.7i		−	1.43474i
$852$	17836.3	+	3648.11i	0.717208	+	0.146693i
$853$	12007.8	+	12007.8i	0.481994	+	0.481994i	0.905768	−	0.423774i	$-0.139295\pi$
$853$	12007.8	+	12007.8i	0.481994	+	0.481994i	−0.423774	+	0.905768i	$0.639295\pi$
$854$	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	−0.868736	−	0.495276i	$-0.835067\pi$
$857$	−9369.48	+	9369.48i	−0.373460	+	0.373460i	0.495276	+	0.868736i	$0.335067\pi$
$858$	280.656	−	84.3090i	0.0111672	−	0.00335462i
$859$	−17337.1			−0.688630			−0.344315	−	0.938854i	$-0.611889\pi$
$859$	−17337.1			−0.688630			−0.344315	+	0.938854i	$0.611889\pi$
$860$	−5833.11	−	958.039i	−0.231288	−	0.0379870i
$861$	−19652.8			−0.777891
$862$	25359.4	−	7617.98i	1.00203	−	0.301009i
$863$	17345.8	−	17345.8i	0.684191	−	0.684191i	−0.276751	−	0.960942i	$-0.589258\pi$
$863$	17345.8	−	17345.8i	0.684191	−	0.684191i	0.960942	+	0.276751i	$0.0892576\pi$
$864$	−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
$868$	7576.27	−	37041.8i	0.296262	−	1.44848i
$869$		−	7397.36i		−	0.288767i
$870$	−3607.12	−	1763.00i	−0.140567	−	0.0687027i
$871$		−	186.390i		−	0.00725096i
$872$	−9253.69	+	11091.2i	−0.359368	+	0.430728i
$873$	−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	−0.969836	−	0.243760i	$-0.921619\pi$
$877$	−18857.4	+	18857.4i	−0.726075	+	0.726075i	0.243760	+	0.969836i	$0.421619\pi$
$878$	−6366.14	−	21192.2i	−0.244700	−	0.814581i
$879$	−1278.44			−0.0490567
$880$	−1881.62	+	4930.95i	−0.0720789	+	0.188889i
$881$	27095.7			1.03618			0.518092	−	0.855325i	$-0.326643\pi$
$881$	27095.7			1.03618			0.518092	+	0.855325i	$0.326643\pi$
$882$	3126.82	+	10408.9i	0.119371	+	0.397374i
$883$	2484.93	−	2484.93i	0.0947049	−	0.0947049i	−0.658167	−	0.752872i	$-0.728668\pi$
$883$	2484.93	−	2484.93i	0.0947049	−	0.0947049i	0.752872	+	0.658167i	$0.228668\pi$
$884$	−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	−0.999973	−	0.00730049i	$-0.997676\pi$
$887$	−26609.3	−	26609.3i	−1.00727	−	1.00727i	−0.00730049	−	0.999973i	$-0.502324\pi$
$888$	19028.3	−	22806.7i	0.719084	−	0.861873i
$889$		−	22025.7i		−	0.830955i
$890$	10777.8	+	31385.4i	0.405926	+	1.18207i
$891$		−	1427.63i		−	0.0536785i
$892$	−7572.63	+	37024.0i	−0.284249	+	1.38975i
$893$	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
$898$	−9161.12	+	2752.00i	−0.340435	+	0.102267i
$899$	−6445.42			−0.239118
$900$	8164.73	+	10486.1i	0.302397	+	0.388372i
$901$	3018.27			0.111602
$902$	4217.90	−	1267.06i	0.155699	−	0.0467721i
$903$	−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	$-0.461309\pi$
$907$	−23802.0	−	23802.0i	−0.871369	−	0.871369i	−0.992622	+	0.121252i	$0.961309\pi$
$908$	−9136.92	−	1868.80i	−0.333942	−	0.0683022i
$909$		−	18815.8i		−	0.686558i
$910$	979.617	+	2852.67i	0.0356857	+	0.103918i
$911$			36580.4i			1.33036i	0.746681	+	0.665182i	$0.231646\pi$
$911$			36580.4i			1.33036i	−0.746681	+	0.665182i	$0.768354\pi$
$912$	11994.0	+	29864.5i	0.435483	+	1.08433i
$913$	−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
$918$	3474.21	+	11565.3i	0.124908	+	0.415807i
$919$	32910.8			1.18131			0.590657	−	0.806923i	$-0.298869\pi$
$919$	32910.8			1.18131			0.590657	+	0.806923i	$0.298869\pi$
$920$	−3270.60	−	25205.7i	−0.117205	−	0.903267i
$921$	−35886.5			−1.28393
$922$	4321.11	+	14384.5i	0.154347	+	0.513806i
$923$	−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
$928$	691.737	−	6168.30i	0.0244692	−	0.218195i
$929$		−	2662.19i		−	0.0940190i	−0.998894	−	0.0470095i	$-0.985031\pi$
$929$		−	2662.19i		−	0.0940190i	0.998894	−	0.0470095i	$-0.0149691\pi$
$930$	−19774.4	−	9664.85i	−0.697234	−	0.340777i
$931$		−	39266.6i		−	1.38229i
$932$	3242.96	+	663.293i	0.113977	+	0.0233121i
$933$	−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	0.407818	−	0.913063i	$-0.366290\pi$
$937$	37885.5	−	37885.5i	1.32088	−	1.32088i	0.913063	−	0.407818i	$-0.133710\pi$
$938$	3346.24	−	1005.21i	0.116480	−	0.0349907i
$939$	13711.2			0.476517
$940$	3889.07	−	23679.0i	0.134944	−	0.821620i
$941$	−6516.65			−0.225756			−0.112878	−	0.993609i	$-0.536007\pi$
$941$	−6516.65			−0.225756			−0.112878	+	0.993609i	$0.536007\pi$
$942$	−2304.82	+	692.368i	−0.0797188	+	0.0239475i
$943$	−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	$-0.169994\pi$
$947$	10250.1	+	10250.1i	0.351724	+	0.351724i	−0.509026	+	0.860751i	$0.669994\pi$
$948$	−5953.02	+	29105.4i	−0.203951	+	0.997152i
$949$			200.854i			0.00687037i
$950$	−17351.8	−	44770.3i	−0.592597	−	1.52899i
$951$		−	19126.8i		−	0.652187i
$952$	−12501.7	−	10430.5i	−0.425611	−	0.355099i
$953$	19249.8	+	19249.8i	0.654314	+	0.654314i	0.954029	−	0.299715i	$-0.0968914\pi$
$953$	19249.8	+	19249.8i	0.654314	+	0.654314i	−0.299715	+	0.954029i	$0.596891\pi$
$954$	−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
$958$	−8926.38	−	29715.0i	−0.301042	−	1.00214i
$959$	29336.9			0.987838
$960$	11371.5	−	17886.9i	0.382307	−	0.601352i
$961$	−5543.06			−0.186065
$962$	1094.39	+	3643.09i	0.0366782	+	0.122098i
$963$	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	$-0.278065\pi$
$967$	−3744.56	−	3744.56i	−0.124526	−	0.124526i	−0.766623	+	0.642097i	$0.778065\pi$
$968$	22180.0	+	18505.4i	0.736460	+	0.614449i
$969$		−	14391.3i		−	0.477106i
$970$	10536.2	−	21557.1i	0.348759	−	0.713564i
$971$			29491.0i			0.974677i	0.873213	+	0.487338i	$0.162032\pi$
$971$			29491.0i			0.974677i	−0.873213	+	0.487338i	$0.837968\pi$
$972$	5308.17	−	25952.6i	0.175164	−	0.856411i
$973$	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	−0.448627	−	0.893719i	$-0.648087\pi$
$977$	13592.2	−	13592.2i	0.445092	−	0.445092i	0.893719	+	0.448627i	$0.148087\pi$
$978$	−13226.4	+	3973.21i	−0.432447	+	0.129907i
$979$	−7740.14			−0.252682
$980$	−21008.3	+	15081.0i	−0.684783	+	0.491576i
$981$	−8483.78			−0.276112
$982$	28493.2	−	8559.36i	0.925921	−	0.278147i
$983$	−12087.1	+	12087.1i	−0.392185	+	0.392185i	−0.875466	−	0.483280i	$-0.839445\pi$
$983$	−12087.1	+	12087.1i	−0.392185	+	0.392185i	0.483280	+	0.875466i	$0.339445\pi$
$984$	−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
$988$	−4038.03	−	825.910i	−0.130027	−	0.0265949i
$989$			6640.01i			0.213488i
$990$	−2931.76	+	1006.78i	−0.0941187	+	0.0323207i
$991$		−	52539.6i		−	1.68413i	−0.539374	−	0.842066i	$-0.681339\pi$
$991$		−	52539.6i		−	1.68413i	0.539374	−	0.842066i	$-0.318661\pi$
$992$	3792.13	−	33814.9i	0.121371	−	1.08228i
$993$	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	−0.488966	−	0.872303i	$-0.662626\pi$
$997$	12067.7	−	12067.7i	0.383337	−	0.383337i	0.872303	+	0.488966i	$0.162626\pi$
$998$	1989.80	+	6623.82i	0.0631121	+	0.210094i
$999$	52887.0			1.67495

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.3	✓	12	1.1	even	1	trivial
20.4.e.b.3.6	yes	12	4.3	odd	2	inner
20.4.e.b.7.3	yes	12	20.7	even	4	inner
20.4.e.b.7.6	yes	12	5.2	odd	4	inner
100.4.e.e.7.1		12	5.3	odd	4
100.4.e.e.7.4		12	20.3	even	4
100.4.e.e.43.1		12	20.19	odd	2
100.4.e.e.43.4		12	5.4	even	2
180.4.k.e.127.1		12	15.2	even	4
180.4.k.e.127.4		12	60.47	odd	4
180.4.k.e.163.1		12	12.11	even	2
180.4.k.e.163.4		12	3.2	odd	2
320.4.n.k.63.3		12	8.5	even	2
320.4.n.k.63.4		12	8.3	odd	2
320.4.n.k.127.3		12	40.27	even	4
320.4.n.k.127.4		12	40.37	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.813737 - 2.70884i) q^{2} +(2.61822 - 2.61822i) q^{3} +(-6.67566 + 4.40857i) q^{4} +(-0.435501 - 11.1719i) q^{5} +(-9.22289 - 4.96181i) q^{6} +(17.7783 + 17.7783i) q^{7} +(17.3744 + 14.4959i) q^{8} +13.2899i q^{9} +O(q^{10})\)	\(q+(-0.813737 - 2.70884i) 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} +(17.3744 + 14.4959i) q^{8} +13.2899i q^{9} +(-29.9084 + 10.2707i) q^{10} -7.37590i q^{11} +(-5.93575 + 29.0210i) 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} +(36.0001 - 10.8144i) q^{18} -135.808 q^{19} +(52.1592 + 72.6596i) q^{20} +93.0948 q^{21} +(-19.9802 + 6.00204i) 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} +(-197.059 - 40.3050i) q^{28} +34.2890i q^{29} +(-51.4160 + 105.198i) q^{30} +187.974i q^{31} +(-179.892 - 20.1737i) 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} +(110.512 + 367.882i) q^{38} -14.0467 q^{39} +(154.380 - 200.417i) q^{40} -211.105 q^{41} +(-75.7547 - 252.179i) 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} +(-88.3159 - 219.902i) q^{48} +289.134i q^{49} +(127.767 + 329.660i) q^{50} +105.968i q^{51} +(29.7334 + 6.08147i) 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} +(92.8835 - 27.9022i) q^{58} -101.072 q^{59} +(326.803 + 53.6747i) q^{60} +232.112 q^{61} +(509.191 - 152.961i) 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} +(45.8785 - 224.309i) q^{68} -372.010i q^{69} +(-714.314 - 349.126i) q^{70} -614.600i q^{71} +(-192.649 + 230.903i) 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} +(11.4303 + 38.0504i) q^{78} +1002.91 q^{79} +(-668.522 - 255.104i) q^{80} +193.554 q^{81} +(171.784 + 571.850i) 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} +(106.920 - 128.152i) q^{88} -1049.38i q^{89} +(-136.495 - 397.478i) q^{90} -95.3802i q^{91} +(-161.060 + 787.453i) 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} +(783.218 - 235.279i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more