LMFDB - Embedded newform 201.3.c.a.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.4
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.48861i q^{2} +(2.56342 + 1.55849i) q^{3} -8.17041 q^{4} -4.65961i q^{5} +(5.43698 - 8.94276i) q^{6} -13.4680 q^{7} +14.5490i q^{8} +(4.14220 + 7.99013i) q^{9} +O(q^{10})$	\(q-3.48861i q^{2} +(2.56342 + 1.55849i) q^{3} -8.17041 q^{4} -4.65961i q^{5} +(5.43698 - 8.94276i) q^{6} -13.4680 q^{7} +14.5490i q^{8} +(4.14220 + 7.99013i) q^{9} -16.2556 q^{10} -16.1705i q^{11} +(-20.9442 - 12.7335i) q^{12} +3.95086 q^{13} +46.9847i q^{14} +(7.26196 - 11.9445i) q^{15} +18.0740 q^{16} -4.42122i q^{17} +(27.8745 - 14.4505i) q^{18} -22.7582 q^{19} +38.0709i q^{20} +(-34.5242 - 20.9898i) q^{21} -56.4125 q^{22} +0.463943i q^{23} +(-22.6744 + 37.2950i) q^{24} +3.28807 q^{25} -13.7830i q^{26} +(-1.83437 + 26.9376i) q^{27} +110.039 q^{28} -49.1798i q^{29} +(-41.6698 - 25.3342i) q^{30} +51.3504 q^{31} -4.85735i q^{32} +(25.2016 - 41.4517i) q^{33} -15.4239 q^{34} +62.7557i q^{35} +(-33.8435 - 65.2827i) q^{36} +27.0084 q^{37} +79.3944i q^{38} +(10.1277 + 6.15738i) q^{39} +67.7924 q^{40} +13.8546i q^{41} +(-73.2254 + 120.441i) q^{42} -11.4932 q^{43} +132.119i q^{44} +(37.2309 - 19.3010i) q^{45} +1.61852 q^{46} -65.3258i q^{47} +(46.3312 + 28.1682i) q^{48} +132.388 q^{49} -11.4708i q^{50} +(6.89044 - 11.3334i) q^{51} -32.2801 q^{52} +10.2225i q^{53} +(93.9749 + 6.39941i) q^{54} -75.3481 q^{55} -195.946i q^{56} +(-58.3387 - 35.4685i) q^{57} -171.569 q^{58} -1.70030i q^{59} +(-59.3332 + 97.5916i) q^{60} -29.9771 q^{61} -179.142i q^{62} +(-55.7873 - 107.611i) q^{63} +55.3506 q^{64} -18.4094i q^{65} +(-144.609 - 87.9185i) q^{66} -8.18535 q^{67} +36.1232i q^{68} +(-0.723052 + 1.18928i) q^{69} +218.930 q^{70} -80.0169i q^{71} +(-116.248 + 60.2647i) q^{72} -21.0900 q^{73} -94.2217i q^{74} +(8.42870 + 5.12444i) q^{75} +185.944 q^{76} +217.785i q^{77} +(21.4807 - 35.3316i) q^{78} -89.2542 q^{79} -84.2177i q^{80} +(-46.6843 + 66.1935i) q^{81} +48.3334 q^{82} -51.8823i q^{83} +(282.077 + 171.496i) q^{84} -20.6012 q^{85} +40.0951i q^{86} +(76.6463 - 126.068i) q^{87} +235.264 q^{88} -0.0561552i q^{89} +(-67.3338 - 129.884i) q^{90} -53.2103 q^{91} -3.79061i q^{92} +(131.632 + 80.0292i) q^{93} -227.896 q^{94} +106.044i q^{95} +(7.57015 - 12.4514i) q^{96} +46.4301 q^{97} -461.850i q^{98} +(129.204 - 66.9814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	3.48861i		−	1.74431i	−0.489233	−	0.872153i	$-0.662723\pi$
$2$		−	3.48861i		−	1.74431i	0.489233	−	0.872153i	$-0.337277\pi$
$3$	2.56342	+	1.55849i	0.854472	+	0.519498i
$3$	2.56342	+	1.55849i	0.854472	+	0.519498i
$4$	−8.17041			−2.04260
$5$		−	4.65961i		−	0.931921i	−0.884805	−	0.465961i	$-0.845709\pi$
$5$		−	4.65961i		−	0.931921i	0.884805	−	0.465961i	$-0.154291\pi$
$6$	5.43698	−	8.94276i	0.906163	−	1.49046i
$7$	−13.4680			−1.92400			−0.962002	−	0.273041i	$-0.911970\pi$
$7$	−13.4680			−1.92400			−0.962002	+	0.273041i	$0.911970\pi$
$8$			14.5490i			1.81862i
$9$	4.14220	+	7.99013i	0.460245	+	0.887792i
$10$	−16.2556			−1.62556
$11$		−	16.1705i		−	1.47004i	−0.678044	−	0.735022i	$-0.737172\pi$
$11$		−	16.1705i		−	1.47004i	0.678044	−	0.735022i	$-0.262828\pi$
$12$	−20.9442	−	12.7335i	−1.74535	−	1.06113i
$13$	3.95086			0.303912			0.151956	−	0.988387i	$-0.451443\pi$
$13$	3.95086			0.303912			0.151956	+	0.988387i	$0.451443\pi$
$14$			46.9847i			3.35605i
$15$	7.26196	−	11.9445i	0.484131	−	0.796300i
$16$	18.0740			1.12962
$17$		−	4.42122i		−	0.260072i	−0.991509	−	0.130036i	$-0.958491\pi$
$17$		−	4.42122i		−	0.260072i	0.991509	−	0.130036i	$-0.0415093\pi$
$18$	27.8745	−	14.4505i	1.54858	−	0.802807i
$19$	−22.7582			−1.19780			−0.598899	−	0.800824i	$-0.704395\pi$
$19$	−22.7582			−1.19780			−0.598899	+	0.800824i	$0.704395\pi$
$20$			38.0709i			1.90355i
$21$	−34.5242	−	20.9898i	−1.64401	−	0.999516i
$22$	−56.4125			−2.56421
$23$			0.463943i			0.0201714i	0.999949	+	0.0100857i	$0.00321044\pi$
$23$			0.463943i			0.0201714i	−0.999949	+	0.0100857i	$0.996790\pi$
$24$	−22.6744	+	37.2950i	−0.944768	+	1.55396i
$25$	3.28807			0.131523
$26$		−	13.7830i		−	0.530116i
$27$	−1.83437	+	26.9376i	−0.0679397	+	0.997689i
$28$	110.039			3.92998
$29$		−	49.1798i		−	1.69586i	−0.530112	−	0.847928i	$-0.677850\pi$
$29$		−	49.1798i		−	1.69586i	0.530112	−	0.847928i	$-0.322150\pi$
$30$	−41.6698	−	25.3342i	−1.38899	−	0.844472i
$31$	51.3504			1.65646			0.828232	−	0.560385i	$-0.189347\pi$
$31$	51.3504			1.65646			0.828232	+	0.560385i	$0.189347\pi$
$32$		−	4.85735i		−	0.151792i
$33$	25.2016	−	41.4517i	0.763684	−	1.25611i
$34$	−15.4239			−0.453645
$35$			62.7557i			1.79302i
$36$	−33.8435	−	65.2827i	−0.940097	−	1.81341i
$37$	27.0084			0.729955			0.364978	−	0.931016i	$-0.381077\pi$
$37$	27.0084			0.729955			0.364978	+	0.931016i	$0.381077\pi$
$38$			79.3944i			2.08933i
$39$	10.1277	+	6.15738i	0.259684	+	0.157882i
$40$	67.7924			1.69481
$41$			13.8546i			0.337917i	0.985623	+	0.168959i	$0.0540405\pi$
$41$			13.8546i			0.337917i	−0.985623	+	0.168959i	$0.945960\pi$
$42$	−73.2254	+	120.441i	−1.74346	+	2.86765i
$43$	−11.4932			−0.267283			−0.133641	−	0.991030i	$-0.542667\pi$
$43$	−11.4932			−0.267283			−0.133641	+	0.991030i	$0.542667\pi$
$44$			132.119i			3.00272i
$45$	37.2309	−	19.3010i	0.827352	−	0.428912i
$46$	1.61852			0.0351851
$47$		−	65.3258i		−	1.38991i	−0.719053	−	0.694956i	$-0.755424\pi$
$47$		−	65.3258i		−	1.38991i	0.719053	−	0.694956i	$-0.244576\pi$
$48$	46.3312	+	28.1682i	0.965233	+	0.586837i
$49$	132.388			2.70179
$50$		−	11.4708i		−	0.229416i
$51$	6.89044	−	11.3334i	0.135107	−	0.222224i
$52$	−32.2801			−0.620772
$53$			10.2225i			0.192878i	0.995339	+	0.0964389i	$0.0307452\pi$
$53$			10.2225i			0.192878i	−0.995339	+	0.0964389i	$0.969255\pi$
$54$	93.9749	+	6.39941i	1.74028	+	0.118508i
$55$	−75.3481			−1.36996
$56$		−	195.946i		−	3.49903i
$57$	−58.3387	−	35.4685i	−1.02349	−	0.622254i
$58$	−171.569			−2.95809
$59$		−	1.70030i		−	0.0288186i	−0.999896	−	0.0144093i	$-0.995413\pi$
$59$		−	1.70030i		−	0.0288186i	0.999896	−	0.0144093i	$-0.00458678\pi$
$60$	−59.3332	+	97.5916i	−0.988887	+	1.62653i
$61$	−29.9771			−0.491428			−0.245714	−	0.969342i	$-0.579022\pi$
$61$	−29.9771			−0.491428			−0.245714	+	0.969342i	$0.579022\pi$
$62$		−	179.142i		−	2.88938i
$63$	−55.7873	−	107.611i	−0.885513	−	1.70812i
$64$	55.3506			0.864853
$65$		−	18.4094i		−	0.283222i
$66$	−144.609	−	87.9185i	−2.19104	−	1.33210i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$			36.1232i			0.531224i
$69$	−0.723052	+	1.18928i	−0.0104790	+	0.0172359i
$70$	218.930			3.12758
$71$		−	80.0169i		−	1.12700i	−0.826117	−	0.563499i	$-0.809455\pi$
$71$		−	80.0169i		−	1.12700i	0.826117	−	0.563499i	$-0.190545\pi$
$72$	−116.248	+	60.2647i	−1.61456	+	0.837010i
$73$	−21.0900			−0.288904			−0.144452	−	0.989512i	$-0.546142\pi$
$73$	−21.0900			−0.288904			−0.144452	+	0.989512i	$0.546142\pi$
$74$		−	94.2217i		−	1.27327i
$75$	8.42870	+	5.12444i	0.112383	+	0.0683259i
$76$	185.944			2.44663
$77$			217.785i			2.82837i
$78$	21.4807	−	35.3316i	0.275394	−	0.452969i
$79$	−89.2542			−1.12980			−0.564900	−	0.825159i	$-0.691085\pi$
$79$	−89.2542			−1.12980			−0.564900	+	0.825159i	$0.691085\pi$
$80$		−	84.2177i		−	1.05272i
$81$	−46.6843	+	66.1935i	−0.576350	+	0.817203i
$82$	48.3334			0.589431
$83$		−	51.8823i		−	0.625088i	−0.949903	−	0.312544i	$-0.898819\pi$
$83$		−	51.8823i		−	0.625088i	0.949903	−	0.312544i	$-0.101181\pi$
$84$	282.077	+	171.496i	3.35806	+	2.04161i
$85$	−20.6012			−0.242366
$86$			40.0951i			0.466223i
$87$	76.6463	−	126.068i	0.880993	−	1.44906i
$88$	235.264			2.67345
$89$		−	0.0561552i		−	0.000630957i	−1.00000		0.000315479i	$-0.999900\pi$
$89$		−	0.0561552i		−	0.000630957i	1.00000		0.000315479i	$-0.000100420\pi$
$90$	−67.3338	−	129.884i	−0.748153	−	1.44316i
$91$	−53.2103			−0.584728
$92$		−	3.79061i		−	0.0412022i
$93$	131.632	+	80.0292i	1.41540	+	0.860529i
$94$	−227.896			−2.42443
$95$			106.044i			1.11625i
$96$	7.57015	−	12.4514i	0.0788557	−	0.129702i
$97$	46.4301			0.478661			0.239331	−	0.970938i	$-0.423072\pi$
$97$	46.4301			0.478661			0.239331	+	0.970938i	$0.423072\pi$
$98$		−	461.850i		−	4.71276i
$99$	129.204	−	66.9814i	1.30509	−	0.676580i
$100$	−26.8649			−0.268649
$101$		−	11.5347i		−	0.114205i	−0.998368	−	0.0571026i	$-0.981814\pi$
$101$		−	11.5347i		−	0.114205i	0.998368	−	0.0571026i	$-0.0181862\pi$
$102$	−39.5379	−	24.0381i	−0.387627	−	0.235667i
$103$	−71.7774			−0.696868			−0.348434	−	0.937333i	$-0.613287\pi$
$103$	−71.7774			−0.696868			−0.348434	+	0.937333i	$0.613287\pi$
$104$			57.4808i			0.552700i
$105$	−97.8043	+	160.869i	−0.931470	+	1.53209i
$106$	35.6624			0.336438
$107$			72.5709i			0.678232i	0.940744	+	0.339116i	$0.110128\pi$
$107$			72.5709i			0.678232i	−0.940744	+	0.339116i	$0.889872\pi$
$108$	14.9876	−	220.091i	0.138774	−	2.03788i
$109$	157.193			1.44214			0.721070	−	0.692862i	$-0.243650\pi$
$109$	157.193			1.44214			0.721070	+	0.692862i	$0.243650\pi$
$110$			262.860i			2.38964i
$111$	69.2336	+	42.0923i	0.623726	+	0.379210i
$112$	−243.421			−2.17340
$113$			59.6586i			0.527952i	0.964529	+	0.263976i	$0.0850340\pi$
$113$			59.6586i			0.527952i	−0.964529	+	0.263976i	$0.914966\pi$
$114$	−123.736	+	203.521i	−1.08540	+	1.78527i
$115$	2.16179			0.0187982
$116$			401.819i			3.46396i
$117$	16.3652	+	31.5679i	0.139874	+	0.269811i
$118$	−5.93168			−0.0502685
$119$			59.5452i			0.500380i
$120$	173.780	+	105.654i	1.44817	+	0.880449i
$121$	−140.484			−1.16103
$122$			104.579i			0.857201i
$123$	−21.5923	+	35.5151i	−0.175547	+	0.288741i
$124$	−419.554			−3.38350
$125$		−	131.811i		−	1.05449i
$126$	−375.414	+	194.620i	−2.97948	+	1.54461i
$127$	194.930			1.53488			0.767440	−	0.641121i	$-0.221530\pi$
$127$	194.930			1.53488			0.767440	+	0.641121i	$0.221530\pi$
$128$		−	212.526i		−	1.66036i
$129$	−29.4617	−	17.9120i	−0.228385	−	0.138853i
$130$	−64.2234			−0.494026
$131$			101.314i			0.773387i	0.922208	+	0.386693i	$0.126383\pi$
$131$			101.314i			0.773387i	−0.922208	+	0.386693i	$0.873617\pi$
$132$	−205.907	+	338.677i	−1.55990	+	2.56574i
$133$	306.508			2.30457
$134$			28.5555i			0.213101i
$135$	125.519	+	8.54745i	0.929768	+	0.0633144i
$136$	64.3241			0.472972
$137$			137.312i			1.00228i	0.865366	+	0.501140i	$0.167086\pi$
$137$			137.312i			1.00228i	−0.865366	+	0.501140i	$0.832914\pi$
$138$	4.14893	+	2.52245i	0.0300647	+	0.0182786i
$139$	−268.683			−1.93297			−0.966484	−	0.256725i	$-0.917356\pi$
$139$	−268.683			−1.93297			−0.966484	+	0.256725i	$0.917356\pi$
$140$		−	512.740i		−	3.66243i
$141$	101.810	−	167.457i	0.722055	−	1.18764i
$142$	−279.148			−1.96583
$143$		−	63.8872i		−	0.446764i
$144$	74.8661	+	144.414i	0.519904	+	1.00287i
$145$	−229.158			−1.58040
$146$			73.5748i			0.503937i
$147$	339.365	+	206.326i	2.30861	+	1.40358i
$148$	−220.669			−1.49101
$149$			9.88786i			0.0663614i	0.999449	+	0.0331807i	$0.0105637\pi$
$149$			9.88786i			0.0663614i	−0.999449	+	0.0331807i	$0.989436\pi$
$150$	17.8772	−	29.4045i	0.119181	−	0.196030i
$151$	−18.5227			−0.122667			−0.0613334	−	0.998117i	$-0.519535\pi$
$151$	−18.5227			−0.122667			−0.0613334	+	0.998117i	$0.519535\pi$
$152$		−	331.108i		−	2.17834i
$153$	35.3261	−	18.3136i	0.230890	−	0.119697i
$154$	759.766			4.93354
$155$		−	239.273i		−	1.54369i
$156$	−82.7474	−	50.3083i	−0.530432	−	0.322489i
$157$	36.6341			0.233338			0.116669	−	0.993171i	$-0.462778\pi$
$157$	36.6341			0.233338			0.116669	+	0.993171i	$0.462778\pi$
$158$			311.373i			1.97072i
$159$	−15.9317	+	26.2046i	−0.100200	+	0.164809i
$160$	−22.6334			−0.141458
$161$		−	6.24840i		−	0.0388099i
$162$	230.923	+	162.864i	1.42545	+	1.00533i
$163$	209.403			1.28468			0.642342	−	0.766418i	$-0.277963\pi$
$163$	209.403			1.28468			0.642342	+	0.766418i	$0.277963\pi$
$164$		−	113.198i		−	0.690231i
$165$	−193.148	−	117.429i	−1.17060	−	0.711693i
$166$	−180.997			−1.09035
$167$		−	51.6124i		−	0.309056i	−0.987988	−	0.154528i	$-0.950614\pi$
$167$		−	51.6124i		−	0.309056i	0.987988	−	0.154528i	$-0.0493857\pi$
$168$	305.380	−	502.291i	1.81774	−	2.98982i
$169$	−153.391			−0.907637
$170$			71.8694i			0.422761i
$171$	−94.2690	−	181.841i	−0.551280	−	1.06340i
$172$	93.9038			0.545952
$173$			174.739i			1.01005i	0.863105	+	0.505025i	$0.168517\pi$
$173$			174.739i			1.01005i	−0.863105	+	0.505025i	$0.831483\pi$
$174$	−439.803	−	267.389i	−2.52761	−	1.53672i
$175$	−44.2839			−0.253051
$176$		−	292.265i		−	1.66060i
$177$	2.64990	−	4.35857i	0.0149712	−	0.0246247i
$178$	−0.195904			−0.00110058
$179$			76.3183i			0.426359i	0.977013	+	0.213180i	$0.0683820\pi$
$179$			76.3183i			0.426359i	−0.977013	+	0.213180i	$0.931618\pi$
$180$	−304.191	+	157.697i	−1.68995	+	0.876096i
$181$	183.539			1.01403			0.507014	−	0.861938i	$-0.330749\pi$
$181$	183.539			1.01403			0.507014	+	0.861938i	$0.330749\pi$
$182$			185.630i			1.01994i
$183$	−76.8438	−	46.7191i	−0.419912	−	0.255296i
$184$	−6.74988			−0.0366842
$185$		−	125.848i		−	0.680261i
$186$	279.191	−	459.214i	1.50103	−	2.46889i
$187$	−71.4933			−0.382317
$188$			533.739i			2.83904i
$189$	24.7054	−	362.797i	0.130716	−	1.91956i
$190$	369.947			1.94709
$191$		−	133.318i		−	0.698001i	−0.937123	−	0.349000i	$-0.886521\pi$
$191$		−	133.318i		−	0.698001i	0.937123	−	0.349000i	$-0.113479\pi$
$192$	141.887	+	86.2635i	0.738992	+	0.449289i
$193$	111.968			0.580147			0.290073	−	0.957004i	$-0.406320\pi$
$193$	111.968			0.580147			0.290073	+	0.957004i	$0.406320\pi$
$194$		−	161.977i		−	0.834931i
$195$	28.6910	−	47.1910i	0.147133	−	0.242005i
$196$	−1081.66			−5.51869
$197$			113.137i			0.574302i	0.957885	+	0.287151i	$0.0927081\pi$
$197$			113.137i			0.574302i	−0.957885	+	0.287151i	$0.907292\pi$
$198$	−233.672	−	450.743i	−1.18016	−	2.27648i
$199$	−310.393			−1.55976			−0.779882	−	0.625927i	$-0.784721\pi$
$199$	−310.393			−1.55976			−0.779882	+	0.625927i	$0.784721\pi$
$200$			47.8380i			0.239190i
$201$	−20.9825	−	12.7568i	−0.104390	−	0.0634667i
$202$	−40.2402			−0.199209
$203$			662.355i			3.26283i
$204$	−56.2978	+	92.5988i	−0.275969	+	0.453916i
$205$	64.5570			0.314912
$206$			250.404i			1.21555i
$207$	−3.70696	+	1.92175i	−0.0179080	+	0.00928379i
$208$	71.4078			0.343307
$209$			368.011i			1.76082i
$210$	561.210	+	341.201i	2.67243	+	1.62477i
$211$	203.165			0.962869			0.481434	−	0.876482i	$-0.340116\pi$
$211$	203.165			0.962869			0.481434	+	0.876482i	$0.340116\pi$
$212$		−	83.5222i		−	0.393973i
$213$	124.706	−	205.117i	0.585473	−	0.962988i
$214$	253.172			1.18304
$215$			53.5536i			0.249086i
$216$	−391.914	−	26.6882i	−1.81442	−	0.123556i
$217$	−691.589			−3.18704
$218$		−	548.386i		−	2.51553i
$219$	−54.0624	−	32.8686i	−0.246860	−	0.150085i
$220$	615.625			2.79829
$221$		−	17.4676i		−	0.0790390i
$222$	146.844	−	241.529i	0.661458	−	1.08797i
$223$	65.4803			0.293634			0.146817	−	0.989164i	$-0.453097\pi$
$223$	65.4803			0.293634			0.146817	+	0.989164i	$0.453097\pi$
$224$			65.4190i			0.292049i
$225$	13.6199	+	26.2721i	0.0605327	+	0.116765i
$226$	208.126			0.920910
$227$			298.365i			1.31438i	0.753724	+	0.657191i	$0.228256\pi$
$227$			298.365i			1.31438i	−0.753724	+	0.657191i	$0.771744\pi$
$228$	476.651	+	289.792i	2.09057	+	1.27102i
$229$	−95.0193			−0.414931			−0.207466	−	0.978242i	$-0.566522\pi$
$229$	−95.0193			−0.414931			−0.207466	+	0.978242i	$0.566522\pi$
$230$		−	7.54165i		−	0.0327898i
$231$	−339.416	+	558.272i	−1.46933	+	2.41676i
$232$	715.515			3.08411
$233$		−	408.782i		−	1.75443i	−0.480099	−	0.877214i	$-0.659399\pi$
$233$		−	408.782i		−	1.75443i	0.480099	−	0.877214i	$-0.340601\pi$
$234$	110.128	−	57.0920i	0.470632	−	0.243983i
$235$	−304.393			−1.29529
$236$			13.8921i			0.0588650i
$237$	−228.796	−	139.102i	−0.965382	−	0.586928i
$238$	207.730			0.872815
$239$		−	287.733i		−	1.20390i	−0.798532	−	0.601952i	$-0.794390\pi$
$239$		−	287.733i		−	1.20390i	0.798532	−	0.601952i	$-0.205610\pi$
$240$	131.253	−	215.885i	0.546886	−	0.899521i
$241$	59.9989			0.248958			0.124479	−	0.992222i	$-0.460274\pi$
$241$	59.9989			0.248958			0.124479	+	0.992222i	$0.460274\pi$
$242$			490.095i			2.02519i
$243$	−222.833	+	96.9242i	−0.917010	+	0.398865i
$244$	244.925			1.00379
$245$		−	616.875i		−	2.51786i
$246$	123.899	+	75.3272i	0.503653	+	0.306208i
$247$	−89.9143			−0.364026
$248$			747.094i			3.01248i
$249$	80.8582	−	132.996i	0.324732	−	0.534120i
$250$	−459.838			−1.83935
$251$		−	94.4140i		−	0.376151i	−0.982155	−	0.188076i	$-0.939775\pi$
$251$		−	94.4140i		−	0.376151i	0.982155	−	0.188076i	$-0.0602250\pi$
$252$	455.805	+	879.229i	1.80875	+	3.48900i
$253$	7.50218			0.0296529
$254$		−	680.034i		−	2.67730i
$255$	−52.8093	−	32.1067i	−0.207095	−	0.125909i
$256$	−520.019			−2.03132
$257$			79.6147i			0.309785i	0.987931	+	0.154892i	$0.0495031\pi$
$257$			79.6147i			0.309785i	−0.987931	+	0.154892i	$0.950497\pi$
$258$	−62.4880	+	102.781i	−0.242202	+	0.398374i
$259$	−363.749			−1.40444
$260$			150.413i			0.578510i
$261$	392.953	−	203.713i	1.50557	−	0.780508i
$262$	353.444			1.34902
$263$			133.487i			0.507555i	0.967263	+	0.253778i	$0.0816731\pi$
$263$			133.487i			0.507555i	−0.967263	+	0.253778i	$0.918327\pi$
$264$	603.078	+	366.656i	2.28439	+	1.38885i
$265$	47.6329			0.179747
$266$		−	1069.29i		−	4.01988i
$267$	0.0875174	−	0.143949i	0.000327781	−	0.000539135i
$268$	66.8777			0.249544
$269$			286.780i			1.06610i	0.846085	+	0.533049i	$0.178954\pi$
$269$			286.780i			1.06610i	−0.846085	+	0.533049i	$0.821046\pi$
$270$	29.8187	−	437.886i	0.110440	−	1.62180i
$271$	49.5153			0.182713			0.0913567	−	0.995818i	$-0.470880\pi$
$271$	49.5153			0.182713			0.0913567	+	0.995818i	$0.470880\pi$
$272$		−	79.9092i		−	0.293784i
$273$	−136.400	−	82.9278i	−0.499634	−	0.303765i
$274$	479.030			1.74828
$275$		−	53.1697i		−	0.193345i
$276$	5.90763	−	9.71690i	0.0214045	−	0.0352062i
$277$	447.313			1.61485			0.807424	−	0.589972i	$-0.200861\pi$
$277$	447.313			1.61485			0.807424	+	0.589972i	$0.200861\pi$
$278$			937.330i			3.37169i
$279$	212.704	+	410.296i	0.762379	+	1.47060i
$280$	−913.030			−3.26082
$281$		−	171.252i		−	0.609439i	−0.952442	−	0.304719i	$-0.901437\pi$
$281$		−	171.252i		−	0.609439i	0.952442	−	0.304719i	$-0.0985627\pi$
$282$	−584.193	−	355.175i	−2.07161	−	1.25949i
$283$	45.7487			0.161656			0.0808282	−	0.996728i	$-0.474244\pi$
$283$	45.7487			0.161656			0.0808282	+	0.996728i	$0.474244\pi$
$284$			653.771i			2.30201i
$285$	−165.269	+	271.835i	−0.579891	+	0.953808i
$286$	−222.878			−0.779293
$287$		−	186.594i		−	0.650155i
$288$	38.8109	−	20.1201i	0.134760	−	0.0698616i
$289$	269.453			0.932363
$290$			799.445i			2.75671i
$291$	119.020	+	72.3610i	0.409002	+	0.248663i
$292$	172.314			0.590116
$293$		−	326.487i		−	1.11429i	−0.830415	−	0.557146i	$-0.811897\pi$
$293$		−	326.487i		−	1.11429i	0.830415	−	0.557146i	$-0.188103\pi$
$294$	719.790	−	1183.91i	2.44826	−	4.02692i
$295$	−7.92272			−0.0268567
$296$			392.943i			1.32751i
$297$	435.594	+	29.6627i	1.46665	+	0.0998743i
$298$	34.4949			0.115755
$299$			1.83297i			0.00613034i
$300$	−68.8660	−	41.8688i	−0.229553	−	0.139563i
$301$	154.790			0.514253
$302$			64.6185i			0.213969i
$303$	17.9768	−	29.5683i	0.0593293	−	0.0975851i
$304$	−411.331			−1.35306
$305$			139.682i			0.457972i
$306$	−63.8890	−	123.239i	−0.208788	−	0.402742i
$307$	153.276			0.499271			0.249636	−	0.968340i	$-0.419689\pi$
$307$	153.276			0.499271			0.249636	+	0.968340i	$0.419689\pi$
$308$		−	1779.39i		−	5.77724i
$309$	−183.995	−	111.865i	−0.595455	−	0.362021i
$310$	−834.729			−2.69267
$311$		−	605.132i		−	1.94576i	−0.231308	−	0.972881i	$-0.574300\pi$
$311$		−	605.132i		−	1.94576i	0.231308	−	0.972881i	$-0.425700\pi$
$312$	−89.5834	+	147.347i	−0.287126	+	0.472267i
$313$	529.560			1.69188			0.845942	−	0.533275i	$-0.179039\pi$
$313$	529.560			1.69188			0.845942	+	0.533275i	$0.179039\pi$
$314$		−	127.802i		−	0.407013i
$315$	−501.426	+	259.947i	−1.59183	+	0.825228i
$316$	729.244			2.30773
$317$		−	431.867i		−	1.36235i	−0.732118	−	0.681177i	$-0.761468\pi$
$317$		−	431.867i		−	1.36235i	0.732118	−	0.681177i	$-0.238532\pi$
$318$	91.4176	+	55.5796i	0.287477	+	0.174779i
$319$	−795.261			−2.49298
$320$		−	257.912i		−	0.805974i
$321$	−113.101	+	186.029i	−0.352340	+	0.579531i
$322$	−21.7982			−0.0676964
$323$			100.619i			0.311514i
$324$	381.430	−	540.828i	1.17725	−	1.66922i
$325$	12.9907			0.0399714
$326$		−	730.527i		−	2.24088i
$327$	402.952	+	244.985i	1.23227	+	0.749188i
$328$	−201.570			−0.614543
$329$			879.810i			2.67420i
$330$	−409.666	+	673.820i	−1.24141	+	2.04188i
$331$	−159.136			−0.480772			−0.240386	−	0.970677i	$-0.577274\pi$
$331$	−159.136			−0.480772			−0.240386	+	0.970677i	$0.577274\pi$
$332$			423.900i			1.27681i
$333$	111.874	+	215.800i	0.335958	+	0.648049i
$334$	−180.055			−0.539088
$335$			38.1405i			0.113852i
$336$	−623.990	−	379.370i	−1.85711	−	1.12908i
$337$	−138.903			−0.412175			−0.206088	−	0.978534i	$-0.566073\pi$
$337$	−138.903			−0.412175			−0.206088	+	0.978534i	$0.566073\pi$
$338$			535.121i			1.58320i
$339$	−92.9775	+	152.930i	−0.274270	+	0.451120i
$340$	168.320			0.495059
$341$		−	830.360i		−	2.43507i
$342$	−634.372	+	328.868i	−1.85489	+	0.961602i
$343$	−1123.07			−3.27426
$344$		−	167.213i		−	0.486085i
$345$	5.54157	+	3.36914i	0.0160625	+	0.00976561i
$346$	609.595			1.76183
$347$			346.794i			0.999405i	0.866197	+	0.499703i	$0.166557\pi$
$347$			346.794i			0.999405i	−0.866197	+	0.499703i	$0.833443\pi$
$348$	−626.232	+	1030.03i	−1.79952	+	2.95986i
$349$	−298.699			−0.855872			−0.427936	−	0.903809i	$-0.640759\pi$
$349$	−298.699			−0.855872			−0.427936	+	0.903809i	$0.640759\pi$
$350$			154.489i			0.441398i
$351$	−7.24734	+	106.427i	−0.0206477	+	0.303210i
$352$	−78.5457			−0.223141
$353$		−	271.786i		−	0.769933i	−0.922930	−	0.384967i	$-0.874213\pi$
$353$		−	271.786i		−	0.769933i	0.922930	−	0.384967i	$-0.125787\pi$
$354$	−15.2054	−	9.24448i	−0.0429530	−	0.0261143i
$355$	−372.847			−1.05027
$356$			0.458811i			0.00128880i
$357$	−92.8007	+	152.639i	−0.259946	+	0.427560i
$358$	266.245			0.743701
$359$			446.377i			1.24339i	0.783260	+	0.621695i	$0.213555\pi$
$359$			446.377i			1.24339i	−0.783260	+	0.621695i	$0.786445\pi$
$360$	280.810	+	541.670i	0.780027	+	1.50464i
$361$	156.935			0.434722
$362$		−	640.297i		−	1.76877i
$363$	−360.120	−	218.944i	−0.992066	−	0.603151i
$364$	434.750			1.19437
$365$			98.2711i			0.269236i
$366$	−162.985	+	268.078i	−0.445314	+	0.732454i
$367$	64.5579			0.175907			0.0879535	−	0.996125i	$-0.471967\pi$
$367$	64.5579			0.175907			0.0879535	+	0.996125i	$0.471967\pi$
$368$			8.38530i			0.0227862i
$369$	−110.700	+	57.3886i	−0.300000	+	0.155525i
$370$	−439.036			−1.18658
$371$		−	137.677i		−	0.371098i
$372$	−1075.49	−	653.872i	−2.89111	−	1.75772i
$373$	−185.801			−0.498126			−0.249063	−	0.968487i	$-0.580123\pi$
$373$	−185.801			−0.498126			−0.249063	+	0.968487i	$0.580123\pi$
$374$			249.412i			0.666878i
$375$	205.427	−	337.887i	0.547805	−	0.901032i
$376$	950.422			2.52772
$377$		−	194.302i		−	0.515391i
$378$	−1265.66	−	86.1874i	−3.34830	−	0.228009i
$379$	−333.548			−0.880075			−0.440037	−	0.897979i	$-0.645035\pi$
$379$	−333.548			−0.880075			−0.440037	+	0.897979i	$0.645035\pi$
$380$		−	866.424i		−	2.28006i
$381$	499.686	+	303.797i	1.31151	+	0.797366i
$382$	−465.095			−1.21753
$383$		−	511.557i		−	1.33566i	−0.744315	−	0.667829i	$-0.767224\pi$
$383$		−	511.557i		−	1.33566i	0.744315	−	0.667829i	$-0.232776\pi$
$384$	331.220	−	544.793i	0.862553	−	1.41873i
$385$	1014.79			2.63582
$386$		−	390.614i		−	1.01195i
$387$	−47.6070	−	91.8318i	−0.123015	−	0.237291i
$388$	−379.353			−0.977715
$389$		−	468.711i		−	1.20491i	−0.798152	−	0.602457i	$-0.794189\pi$
$389$		−	468.711i		−	1.20491i	0.798152	−	0.602457i	$-0.205811\pi$
$390$	−164.631	−	100.092i	−0.422131	−	0.256645i
$391$	2.05119			0.00524602
$392$			1926.11i			4.91353i
$393$	−157.897	+	259.709i	−0.401773	+	0.660837i
$394$	394.693			1.00176
$395$			415.889i			1.05288i
$396$	−1055.65	+	547.266i	−2.66579	+	1.38198i
$397$	142.475			0.358880			0.179440	−	0.983769i	$-0.442571\pi$
$397$	142.475			0.358880			0.179440	+	0.983769i	$0.442571\pi$
$398$			1082.84i			2.72071i
$399$	785.707	+	477.690i	1.96919	+	1.19722i
$400$	59.4287			0.148572
$401$			92.5996i			0.230922i	0.993312	+	0.115461i	$0.0368345\pi$
$401$			92.5996i			0.230922i	−0.993312	+	0.115461i	$0.963166\pi$
$402$	−44.5036	+	73.1997i	−0.110705	+	0.182089i
$403$	202.878			0.503419
$404$			94.2434i			0.233276i
$405$	308.435	+	217.531i	0.761569	+	0.537112i
$406$	2310.70			5.69138
$407$		−	436.738i		−	1.07307i
$408$	164.890	+	100.249i	0.404141	+	0.245708i
$409$	22.3970			0.0547604			0.0273802	−	0.999625i	$-0.491284\pi$
$409$	22.3970			0.0547604			0.0273802	+	0.999625i	$0.491284\pi$
$410$		−	225.214i		−	0.549304i
$411$	−214.000	+	351.989i	−0.520682	+	0.856420i
$412$	586.451			1.42343
$413$			22.8997i			0.0554471i
$414$	6.70422	+	12.9322i	0.0161938	+	0.0312371i
$415$	−241.751			−0.582533
$416$		−	19.1907i		−	0.0461315i
$417$	−688.745	−	418.740i	−1.65167	−	1.00417i
$418$	1283.85			3.07140
$419$			109.399i			0.261095i	0.991442	+	0.130548i	$0.0416736\pi$
$419$			109.399i			0.261095i	−0.991442	+	0.130548i	$0.958326\pi$
$420$	799.102	−	1314.37i	1.90262	−	3.12944i
$421$	327.119			0.777005			0.388502	−	0.921448i	$-0.372993\pi$
$421$	327.119			0.777005			0.388502	+	0.921448i	$0.372993\pi$
$422$		−	708.765i		−	1.67954i
$423$	521.962	−	270.593i	1.23395	−	0.639699i
$424$	−148.727			−0.350771
$425$		−	14.5373i		−	0.0342054i
$426$	−715.572	−	435.050i	−1.67975	−	1.02124i
$427$	403.733			0.945510
$428$		−	592.934i		−	1.38536i
$429$	99.5678	−	163.770i	0.232093	−	0.381747i
$430$	186.828			0.434483
$431$			55.9545i			0.129825i	0.997891	+	0.0649124i	$0.0206768\pi$
$431$			55.9545i			0.129825i	−0.997891	+	0.0649124i	$0.979323\pi$
$432$	−33.1544	+	486.870i	−0.0767463	+	1.12701i
$433$	−617.801			−1.42679			−0.713396	−	0.700762i	$-0.752844\pi$
$433$	−617.801			−1.42679			−0.713396	+	0.700762i	$0.752844\pi$
$434$			2412.68i			5.55918i
$435$	−587.428	−	357.142i	−1.35041	−	0.821016i
$436$	−1284.33			−2.94572
$437$		−	10.5585i		−	0.0241613i
$438$	−114.666	+	188.603i	−0.261794	+	0.430600i
$439$	105.870			0.241162			0.120581	−	0.992704i	$-0.461524\pi$
$439$	105.870			0.241162			0.120581	+	0.992704i	$0.461524\pi$
$440$		−	1096.24i		−	2.49144i
$441$	548.377	+	1057.80i	1.24349	+	2.39863i
$442$	−60.9377			−0.137868
$443$			793.729i			1.79171i	0.444344	+	0.895856i	$0.353437\pi$
$443$			793.729i			1.79171i	−0.444344	+	0.895856i	$0.646563\pi$
$444$	−565.667	−	343.912i	−1.27403	−	0.774576i
$445$	−0.261661			−0.000588002
$446$		−	228.435i		−	0.512187i
$447$	−15.4101	+	25.3467i	−0.0344746	+	0.0567040i
$448$	−745.463			−1.66398
$449$		−	609.154i		−	1.35669i	−0.734743	−	0.678345i	$-0.762697\pi$
$449$		−	609.154i		−	1.35669i	0.734743	−	0.678345i	$-0.237303\pi$
$450$	91.6533	−	47.5144i	0.203674	−	0.105588i
$451$	224.036			0.496753
$452$		−	487.435i		−	1.07840i
$453$	−47.4814	−	28.8675i	−0.104815	−	0.0637251i
$454$	1040.88			2.29269
$455$			247.939i			0.544921i
$456$	516.029	−	848.767i	1.13164	−	1.86133i
$457$	−248.790			−0.544399			−0.272199	−	0.962241i	$-0.587751\pi$
$457$	−248.790			−0.544399			−0.272199	+	0.962241i	$0.587751\pi$
$458$			331.485i			0.723767i
$459$	119.097	+	8.11016i	0.259471	+	0.0176692i
$460$	−17.6627			−0.0383972
$461$			535.148i			1.16084i	0.814317	+	0.580421i	$0.197112\pi$
$461$			535.148i			1.16084i	−0.814317	+	0.580421i	$0.802888\pi$
$462$	1947.60	+	1184.09i	4.21557	+	2.56296i
$463$	691.457			1.49343			0.746714	−	0.665145i	$-0.231630\pi$
$463$	691.457			1.49343			0.746714	+	0.665145i	$0.231630\pi$
$464$		−	888.876i		−	1.91568i
$465$	372.905	−	613.355i	0.801945	−	1.31904i
$466$	−1426.08			−3.06026
$467$		−	277.450i		−	0.594111i	−0.954860	−	0.297056i	$-0.903995\pi$
$467$		−	277.450i		−	0.594111i	0.954860	−	0.297056i	$-0.0960047\pi$
$468$	−133.711	−	257.922i	−0.285707	−	0.551116i
$469$	110.241			0.235055
$470$			1061.91i			2.25938i
$471$	93.9084	+	57.0940i	0.199381	+	0.121219i
$472$	24.7376			0.0524101
$473$			185.850i			0.392917i
$474$	−485.273	+	798.179i	−1.02378	+	1.68392i
$475$	−74.8306			−0.157538
$476$		−	486.509i		−	1.02208i
$477$	−81.6793	+	42.3437i	−0.171235	+	0.0887710i
$478$	−1003.79			−2.09998
$479$		−	609.745i		−	1.27295i	−0.771296	−	0.636477i	$-0.780391\pi$
$479$		−	609.745i		−	1.27295i	0.771296	−	0.636477i	$-0.219609\pi$
$480$	−58.0187	−	35.2739i	−0.120872	−	0.0734873i
$481$	106.706			0.221842
$482$		−	209.313i		−	0.434259i
$483$	9.73808	−	16.0172i	0.0201617	−	0.0331620i
$484$	1147.82			2.37152
$485$		−	216.346i		−	0.446074i
$486$	338.131	+	777.379i	0.695742	+	1.59955i
$487$	202.064			0.414915			0.207458	−	0.978244i	$-0.433481\pi$
$487$	202.064			0.414915			0.207458	+	0.978244i	$0.433481\pi$
$488$		−	436.136i		−	0.893721i
$489$	536.788	+	326.354i	1.09773	+	0.667390i
$490$	−2152.04			−4.39192
$491$		−	172.832i		−	0.351999i	−0.984390	−	0.176000i	$-0.943684\pi$
$491$		−	172.832i		−	0.351999i	0.984390	−	0.176000i	$-0.0563158\pi$
$492$	176.418	−	290.173i	0.358573	−	0.589783i
$493$	−217.435			−0.441044
$494$			313.676i			0.634972i
$495$	−312.107	−	602.041i	−0.630519	−	1.21624i
$496$	928.107			1.87118
$497$			1077.67i			2.16835i
$498$	−463.971	−	282.083i	−0.931669	−	0.566432i
$499$	237.404			0.475760			0.237880	−	0.971295i	$-0.423548\pi$
$499$	237.404			0.475760			0.237880	+	0.971295i	$0.423548\pi$
$500$			1076.95i			2.15391i
$501$	80.4375	−	132.304i	0.160554	−	0.264080i
$502$	−329.374			−0.656123
$503$			183.508i			0.364826i	0.983222	+	0.182413i	$0.0583908\pi$
$503$			183.508i			0.364826i	−0.983222	+	0.182413i	$0.941609\pi$
$504$	1565.63	−	811.647i	3.10641	−	1.61041i
$505$	−53.7472			−0.106430
$506$		−	26.1722i		−	0.0517237i
$507$	−393.204	−	239.058i	−0.775551	−	0.471515i
$508$	−1592.66			−3.13515
$509$		−	161.372i		−	0.317037i	−0.987356	−	0.158519i	$-0.949328\pi$
$509$		−	161.372i		−	0.317037i	0.987356	−	0.158519i	$-0.0506718\pi$
$510$	−112.008	+	184.231i	−0.219623	+	0.361238i
$511$	284.041			0.555853
$512$			964.039i			1.88289i
$513$	41.7469	−	613.051i	0.0813781	−	1.19503i
$514$	277.745			0.540360
$515$			334.455i			0.649426i
$516$	240.714	+	146.348i	0.466501	+	0.283621i
$517$	−1056.35			−2.04323
$518$			1268.98i			2.44977i
$519$	−272.329	+	447.927i	−0.524718	+	0.863059i
$520$	267.838			0.515073
$521$		−	361.755i		−	0.694348i	−0.937801	−	0.347174i	$-0.887141\pi$
$521$		−	361.755i		−	0.694348i	0.937801	−	0.347174i	$-0.112859\pi$
$522$	−710.674	−	1370.86i	−1.36145	−	2.62617i
$523$	26.6385			0.0509341			0.0254671	−	0.999676i	$-0.491893\pi$
$523$	26.6385			0.0509341			0.0254671	+	0.999676i	$0.491893\pi$
$524$		−	827.775i		−	1.57972i
$525$	−113.518	−	69.0161i	−0.216225	−	0.131459i
$526$	465.684			0.885332
$527$		−	227.031i		−	0.430800i
$528$	455.493	−	749.197i	0.862676	−	1.41893i
$529$	528.785			0.999593
$530$		−	166.173i		−	0.313534i
$531$	13.5856	−	7.04298i	0.0255849	−	0.0132636i
$532$	−2504.30			−4.70732
$533$			54.7376i			0.102697i
$534$	−0.502182	−	0.305314i	−0.000940417	−	0.000571750i
$535$	338.152			0.632059
$536$		−	119.088i		−	0.222180i
$537$	−118.942	+	195.636i	−0.221493	+	0.364312i
$538$	1000.46			1.85960
$539$		−	2140.78i		−	3.97176i
$540$	−1025.54	−	69.8362i	−1.89915	−	0.129326i
$541$	123.648			0.228555			0.114277	−	0.993449i	$-0.463545\pi$
$541$	123.648			0.228555			0.114277	+	0.993449i	$0.463545\pi$
$542$		−	172.740i		−	0.318708i
$543$	470.487	+	286.044i	0.866458	+	0.526785i
$544$	−21.4754			−0.0394769
$545$		−	732.459i		−	1.34396i
$546$	−289.303	+	475.847i	−0.529859	+	0.871514i
$547$	−308.956			−0.564819			−0.282410	−	0.959294i	$-0.591134\pi$
$547$	−308.956			−0.564819			−0.282410	+	0.959294i	$0.591134\pi$
$548$		−	1121.90i		−	2.04726i
$549$	−124.171	−	239.521i	−0.226177	−	0.436286i
$550$	−185.489			−0.337252
$551$			1119.24i			2.03129i
$552$	−17.3028	−	10.5196i	−0.0313456	−	0.0190573i
$553$	1202.08			2.17374
$554$		−	1560.50i		−	2.81679i
$555$	196.134	−	322.601i	0.353394	−	0.581264i
$556$	2195.25			3.94829
$557$			936.150i			1.68070i	0.542044	+	0.840350i	$0.317651\pi$
$557$			936.150i			1.68070i	−0.542044	+	0.840350i	$0.682349\pi$
$558$	1431.36	−	742.041i	2.56517	−	1.32982i
$559$	−45.4078			−0.0812304
$560$			1134.25i			2.02544i
$561$	−183.267	−	111.422i	−0.326679	−	0.198613i
$562$	−597.433			−1.06305
$563$			779.875i			1.38521i	0.721316	+	0.692606i	$0.243538\pi$
$563$			779.875i			1.38521i	−0.721316	+	0.692606i	$0.756462\pi$
$564$	−831.828	+	1368.19i	−1.47487	+	2.42588i
$565$	277.986			0.492010
$566$		−	159.600i		−	0.281978i
$567$	628.746	−	891.496i	1.10890	−	1.57230i
$568$	1164.16			2.04958
$569$		−	528.856i		−	0.929448i	−0.885456	−	0.464724i	$-0.846154\pi$
$569$		−	528.856i		−	0.929448i	0.885456	−	0.464724i	$-0.153846\pi$
$570$	948.328	+	576.559i	1.66373	+	1.01151i
$571$	803.247			1.40674			0.703369	−	0.710825i	$-0.251678\pi$
$571$	803.247			1.40674			0.703369	+	0.710825i	$0.251678\pi$
$572$			521.985i			0.912562i
$573$	207.775	−	341.750i	0.362610	−	0.596422i
$574$	−650.955			−1.13407
$575$			1.52548i			0.00265301i
$576$	229.273	+	442.258i	0.398044	+	0.767809i
$577$	800.725			1.38774			0.693869	−	0.720101i	$-0.255905\pi$
$577$	800.725			1.38774			0.693869	+	0.720101i	$0.255905\pi$
$578$		−	940.016i		−	1.62633i
$579$	287.021	+	174.502i	0.495719	+	0.301385i
$580$	1872.32			3.22814
$581$			698.753i			1.20267i
$582$	252.439	−	415.214i	0.433745	−	0.713425i
$583$	165.303			0.283539
$584$		−	306.837i		−	0.525406i
$585$	147.094	−	76.2556i	0.251442	−	0.130351i
$586$	−1138.99			−1.94366
$587$			605.804i			1.03203i	0.856578	+	0.516017i	$0.172586\pi$
$587$			605.804i			1.03203i	−0.856578	+	0.516017i	$0.827414\pi$
$588$	−2772.75	−	1685.77i	−4.71557	−	2.86695i
$589$	−1168.64			−1.98411
$590$			27.6393i			0.0468462i
$591$	−176.324	+	290.018i	−0.298348	+	0.490725i
$592$	488.149			0.824576
$593$			602.083i			1.01532i	0.861558	+	0.507659i	$0.169489\pi$
$593$			602.083i			1.01532i	−0.861558	+	0.507659i	$0.830511\pi$
$594$	103.481	−	1519.62i	0.174211	−	2.55828i
$595$	277.457			0.466314
$596$		−	80.7879i		−	0.135550i
$597$	−795.666	−	483.745i	−1.33277	−	0.810294i
$598$	6.39453			0.0106932
$599$			238.624i			0.398370i	0.979962	+	0.199185i	$0.0638295\pi$
$599$			238.624i			0.398370i	−0.979962	+	0.199185i	$0.936171\pi$
$600$	−74.5552	+	122.629i	−0.124259	+	0.204381i
$601$	57.4075			0.0955199			0.0477600	−	0.998859i	$-0.484792\pi$
$601$	57.4075			0.0955199			0.0477600	+	0.998859i	$0.484792\pi$
$602$		−	540.003i		−	0.897015i
$603$	−33.9054	−	65.4020i	−0.0562278	−	0.108461i
$604$	151.338			0.250560
$605$			654.602i			1.08199i
$606$	−103.152	−	62.7140i	−0.170218	−	0.103488i
$607$	633.695			1.04398			0.521989	−	0.852952i	$-0.325190\pi$
$607$	633.695			1.04398			0.521989	+	0.852952i	$0.325190\pi$
$608$			110.545i			0.181817i
$609$	−1032.28	+	1697.89i	−1.69503	+	2.78800i
$610$	487.295			0.798844
$611$		−	258.093i		−	0.422411i
$612$	−288.629	+	149.630i	−0.471616	+	0.244493i
$613$	−510.791			−0.833264			−0.416632	−	0.909075i	$-0.636790\pi$
$613$	−510.791			−0.833264			−0.416632	+	0.909075i	$0.636790\pi$
$614$		−	534.721i		−	0.870882i
$615$	165.487	+	100.612i	0.269084	+	0.163596i
$616$	−3168.54			−5.14373
$617$		−	144.884i		−	0.234820i	−0.993084	−	0.117410i	$-0.962541\pi$
$617$		−	144.884i		−	0.234820i	0.993084	−	0.117410i	$-0.0374592\pi$
$618$	−390.252	+	641.889i	−0.631476	+	1.03865i
$619$	−435.866			−0.704145			−0.352073	−	0.935973i	$-0.614523\pi$
$619$	−435.866			−0.704145			−0.352073	+	0.935973i	$0.614523\pi$
$620$			1954.96i			3.15315i
$621$	−12.4975	−	0.851043i	−0.0201248	−	0.00137044i
$622$	−2111.07			−3.39400
$623$			0.756300i			0.00121396i
$624$	183.048	+	111.288i	0.293346	+	0.178347i
$625$	−531.987			−0.851179
$626$		−	1847.43i		−	2.95116i
$627$	−573.542	+	943.364i	−0.914740	+	1.50457i
$628$	−299.316			−0.476617
$629$		−	119.410i		−	0.189841i
$630$	906.854	+	1749.28i	1.43945	+	2.77664i
$631$	−254.879			−0.403929			−0.201964	−	0.979393i	$-0.564733\pi$
$631$	−254.879			−0.403929			−0.201964	+	0.979393i	$0.564733\pi$
$632$		−	1298.56i		−	2.05468i
$633$	520.797	+	316.632i	0.822745	+	0.500208i
$634$	−1506.61			−2.37636
$635$		−	908.296i		−	1.43039i
$636$	130.169	−	214.102i	0.204668	−	0.336639i
$637$	523.046			0.821108
$638$			2774.36i			4.34852i
$639$	639.345	−	331.446i	1.00054	−	0.518695i
$640$	−990.288			−1.54732
$641$		−	763.805i		−	1.19158i	−0.803139	−	0.595792i	$-0.796838\pi$
$641$		−	763.805i		−	1.19158i	0.803139	−	0.595792i	$-0.203162\pi$
$642$	648.984	+	394.566i	1.01088	+	0.614589i
$643$	952.001			1.48056			0.740281	−	0.672297i	$-0.234692\pi$
$643$	952.001			1.48056			0.740281	+	0.672297i	$0.234692\pi$
$644$			51.0520i			0.0792733i
$645$	−83.4628	+	137.280i	−0.129400	+	0.212837i
$646$	351.020			0.543375
$647$			783.627i			1.21117i	0.795781	+	0.605585i	$0.207061\pi$
$647$			783.627i			1.21117i	−0.795781	+	0.605585i	$0.792939\pi$
$648$	−963.045	−	679.208i	−1.48618	−	1.04816i
$649$	−27.4946			−0.0423646
$650$		−	45.3196i		−	0.0697224i
$651$	−1772.83	−	1077.84i	−2.72324	−	1.65566i
$652$	−1710.91			−2.62410
$653$		−	42.6346i		−	0.0652904i	−0.999467	−	0.0326452i	$-0.989607\pi$
$653$		−	42.6346i		−	0.0652904i	0.999467	−	0.0326452i	$-0.0103931\pi$
$654$	854.656	−	1405.74i	1.30681	−	2.14945i
$655$	472.082			0.720735
$656$			250.408i			0.381720i
$657$	−87.3590	−	168.512i	−0.132967	−	0.256487i
$658$	3069.32			4.66462
$659$		−	725.673i		−	1.10117i	−0.834778	−	0.550586i	$-0.814404\pi$
$659$		−	725.673i		−	1.10117i	0.834778	−	0.550586i	$-0.185596\pi$
$660$	1578.10	+	959.447i	2.39106	+	1.45371i
$661$	428.406			0.648118			0.324059	−	0.946037i	$-0.394952\pi$
$661$	428.406			0.648118			0.324059	+	0.946037i	$0.394952\pi$
$662$			555.162i			0.838614i
$663$	27.2231	−	44.7768i	0.0410606	−	0.0675366i
$664$	754.834			1.13680
$665$		−	1428.21i		−	2.14768i
$666$	752.843	−	390.285i	1.13040	−	0.586014i
$667$	22.8166			0.0342078
$668$			421.694i			0.631279i
$669$	167.853	+	102.051i	0.250902	+	0.152542i
$670$	133.057			0.198593
$671$			484.744i			0.722421i
$672$	−101.955	+	167.696i	−0.151719	+	0.249548i
$673$	−214.662			−0.318962			−0.159481	−	0.987201i	$-0.550982\pi$
$673$	−214.662			−0.318962			−0.159481	+	0.987201i	$0.550982\pi$
$674$			484.579i			0.718960i
$675$	−6.03155	+	88.5729i	−0.00893563	+	0.131219i
$676$	1253.27			1.85394
$677$		−	21.1813i		−	0.0312870i	−0.999878	−	0.0156435i	$-0.995020\pi$
$677$		−	21.1813i		−	0.0312870i	0.999878	−	0.0156435i	$-0.00497969\pi$
$678$	533.513	+	324.362i	0.786892	+	0.478411i
$679$	−625.323			−0.920946
$680$		−	299.725i		−	0.440772i
$681$	−464.999	+	764.833i	−0.682819	+	1.12310i
$682$	−2896.81			−4.24751
$683$			734.706i			1.07570i	0.843039	+	0.537852i	$0.180764\pi$
$683$			734.706i			1.07570i	−0.843039	+	0.537852i	$0.819236\pi$
$684$	770.216	+	1485.71i	1.12605	+	2.17210i
$685$	639.822			0.934046
$686$			3917.96i			5.71131i
$687$	−243.574	−	148.087i	−0.354547	−	0.215556i
$688$	−207.727			−0.301929
$689$			40.3877i			0.0586179i
$690$	11.7536	−	19.3324i	0.0170342	−	0.0280180i
$691$	45.8955			0.0664190			0.0332095	−	0.999448i	$-0.489427\pi$
$691$	45.8955			0.0664190			0.0332095	+	0.999448i	$0.489427\pi$
$692$		−	1427.69i		−	2.06313i
$693$	−1740.13	+	902.108i	−2.51101	+	1.30174i
$694$	1209.83			1.74327
$695$			1251.96i			1.80137i
$696$	1834.16	+	1115.12i	2.63529	+	1.60219i
$697$	61.2543			0.0878828
$698$			1042.05i			1.49290i
$699$	637.083	−	1047.88i	0.911421	−	1.49911i
$700$	361.818			0.516882
$701$		−	1273.53i		−	1.81673i	−0.418177	−	0.908366i	$-0.637331\pi$
$701$		−	1273.53i		−	1.81673i	0.418177	−	0.908366i	$-0.362669\pi$
$702$	371.281	+	25.2831i	0.528891	+	0.0360159i
$703$	−614.661			−0.874340
$704$		−	895.045i		−	1.27137i
$705$	−780.285	−	474.394i	−1.10679	−	0.672899i
$706$	−948.158			−1.34300
$707$			155.350i			0.219731i
$708$	−21.6508	+	35.6113i	−0.0305802	+	0.0502985i
$709$	222.314			0.313561			0.156780	−	0.987634i	$-0.449889\pi$
$709$	222.314			0.313561			0.156780	+	0.987634i	$0.449889\pi$
$710$			1300.72i			1.83200i
$711$	−369.709	−	713.153i	−0.519984	−	1.00303i
$712$	0.816999			0.00114747
$713$			23.8236i			0.0334133i
$714$	532.498	+	323.746i	0.745796	+	0.453425i
$715$	−297.689			−0.416349
$716$		−	623.552i		−	0.870883i
$717$	448.430	−	737.580i	0.625425	−	1.02870i
$718$	1557.24			2.16885
$719$		−	295.961i		−	0.411629i	−0.978591	−	0.205815i	$-0.934016\pi$
$719$		−	295.961i		−	0.411629i	0.978591	−	0.205815i	$-0.0659844\pi$
$720$	672.910	−	348.847i	0.934598	−	0.484509i
$721$	966.701			1.34078
$722$		−	547.484i		−	0.758288i
$723$	153.802	+	93.5078i	0.212728	+	0.129333i
$724$	−1499.59			−2.07126
$725$		−	161.707i		−	0.223044i
$726$	−763.810	+	1256.32i	−1.05208	+	1.73047i
$727$	−1210.32			−1.66482			−0.832408	−	0.554164i	$-0.813038\pi$
$727$	−1210.32			−1.66482			−0.832408	+	0.554164i	$0.813038\pi$
$728$		−	774.154i		−	1.06340i
$729$	−722.270	−	98.8272i	−0.990768	−	0.135565i
$730$	342.830			0.469630
$731$			50.8138i			0.0695127i
$732$	627.846	+	381.714i	0.857713	+	0.521468i
$733$	540.143			0.736894			0.368447	−	0.929649i	$-0.379890\pi$
$733$	540.143			0.736894			0.368447	+	0.929649i	$0.379890\pi$
$734$		−	225.217i		−	0.306836i
$735$	961.396	−	1581.31i	1.30802	−	2.15144i
$736$	2.25354			0.00306187
$737$			132.361i			0.179594i
$738$	200.207	+	386.190i	0.271283	+	0.523292i
$739$	1390.45			1.88153			0.940763	−	0.339064i	$-0.110110\pi$
$739$	1390.45			1.88153			0.940763	+	0.339064i	$0.110110\pi$
$740$			1028.23i			1.38950i
$741$	−230.488	−	140.131i	−0.311050	−	0.189110i
$742$	−480.302			−0.647308
$743$		−	361.919i		−	0.487105i	−0.969888	−	0.243552i	$-0.921687\pi$
$743$		−	361.919i		−	0.487105i	0.969888	−	0.243552i	$-0.0783128\pi$
$744$	−1164.34	+	1915.11i	−1.56497	+	2.57408i
$745$	46.0735			0.0618436
$746$			648.188i			0.868884i
$747$	414.547	−	214.907i	0.554948	−	0.287694i
$748$	584.130			0.780922
$749$		−	977.387i		−	1.30492i
$750$	−1178.76	−	716.655i	−1.57168	−	0.955540i
$751$	398.697			0.530888			0.265444	−	0.964126i	$-0.414481\pi$
$751$	398.697			0.530888			0.265444	+	0.964126i	$0.414481\pi$
$752$		−	1180.70i		−	1.57008i
$753$	147.144	−	242.022i	0.195410	−	0.321411i
$754$	−677.845			−0.898999
$755$			86.3085i			0.114316i
$756$	−201.853	+	2964.20i	−0.267001	+	3.92090i
$757$	−1297.38			−1.71385			−0.856924	−	0.515442i	$-0.827628\pi$
$757$	−1297.38			−1.71385			−0.856924	+	0.515442i	$0.827628\pi$
$758$			1163.62i			1.53512i
$759$	19.2312	+	11.6921i	0.0253376	+	0.0154046i
$760$	−1542.83			−2.03004
$761$			94.6838i			0.124420i	0.998063	+	0.0622101i	$0.0198149\pi$
$761$			94.6838i			0.124420i	−0.998063	+	0.0622101i	$0.980185\pi$
$762$	1059.83	−	1743.21i	1.39085	−	2.28768i
$763$	−2117.08			−2.77469
$764$			1089.26i			1.42574i
$765$	−85.3341	−	164.606i	−0.111548	−	0.215171i
$766$	−1784.62			−2.32980
$767$		−	6.71763i		−	0.00875832i
$768$	−1333.02	−	810.445i	−1.73571	−	1.05527i
$769$	1068.31			1.38923			0.694613	−	0.719384i	$-0.255576\pi$
$769$	1068.31			1.38923			0.694613	+	0.719384i	$0.255576\pi$
$770$		−	3540.21i		−	4.59767i
$771$	−124.079	+	204.086i	−0.160933	+	0.264703i
$772$	−914.828			−1.18501
$773$			554.285i			0.717057i	0.933519	+	0.358529i	$0.116721\pi$
$773$			554.285i			0.717057i	−0.933519	+	0.358529i	$0.883279\pi$
$774$	−320.365	+	166.082i	−0.413909	+	0.214576i
$775$	168.844			0.217863
$776$			675.510i			0.870502i
$777$	−932.441	−	566.901i	−1.20005	−	0.729602i
$778$	−1635.15			−2.10174
$779$		−	315.306i		−	0.404757i
$780$	−234.417	+	385.570i	−0.300535	+	0.494321i
$781$	−1293.91			−1.65674
$782$		−	7.15582i		−	0.00915067i
$783$	1324.79	+	90.2140i	1.69194	+	0.115216i
$784$	2392.78			3.05201
$785$		−	170.700i		−	0.217453i
$786$	906.024	+	550.840i	1.15270	+	0.700814i
$787$	−498.855			−0.633869			−0.316935	−	0.948447i	$-0.602654\pi$
$787$	−498.855			−0.633869			−0.316935	+	0.948447i	$0.602654\pi$
$788$		−	924.379i		−	1.17307i
$789$	−208.039	+	342.183i	−0.263674	+	0.433692i
$790$	1450.88			1.83655
$791$		−	803.484i		−	1.01578i
$792$	974.509	+	1879.79i	1.23044	+	2.37347i
$793$	−118.435			−0.149351
$794$		−	497.041i		−	0.625996i
$795$	122.103	+	74.2355i	0.153589	+	0.0933780i
$796$	2536.04			3.18598
$797$			1139.70i			1.42999i	0.699131	+	0.714993i	$0.253570\pi$
$797$			1139.70i			1.42999i	−0.699131	+	0.714993i	$0.746430\pi$
$798$	1666.48	−	2741.03i	2.08832	−	3.43487i
$799$	−288.820			−0.361477
$800$		−	15.9713i		−	0.0199642i
$801$	0.448687	−	0.232606i	0.000560159	−	0.000290395i
$802$	323.044			0.402798
$803$			341.035i			0.424701i
$804$	171.435	+	104.228i	0.213228	+	0.129637i
$805$	−29.1151			−0.0361678
$806$		−	707.763i		−	0.878118i
$807$	−446.945	+	735.137i	−0.553835	+	0.910950i
$808$	167.818			0.207696
$809$		−	467.918i		−	0.578390i	−0.957270	−	0.289195i	$-0.906612\pi$
$809$		−	467.918i		−	0.578390i	0.957270	−	0.289195i	$-0.0933877\pi$
$810$	758.880	−	1076.01i	0.936889	−	1.32841i
$811$	−1513.76			−1.86654			−0.933268	−	0.359182i	$-0.883056\pi$
$811$	−1513.76			−1.86654			−0.933268	+	0.359182i	$0.883056\pi$
$812$		−	5411.72i		−	6.66467i
$813$	126.928	+	77.1693i	0.156123	+	0.0949192i
$814$	−1523.61			−1.87176
$815$		−	975.738i		−	1.19722i
$816$	124.538	−	204.840i	0.152620	−	0.251030i
$817$	261.563			0.320151
$818$		−	78.1345i		−	0.0955189i
$819$	−220.408	−	425.157i	−0.269118	−	0.519117i
$820$	−527.458			−0.643241
$821$			767.783i			0.935180i	0.883945	+	0.467590i	$0.154878\pi$
$821$			767.783i			0.935180i	−0.883945	+	0.467590i	$0.845122\pi$
$822$	1227.95	+	746.564i	1.49386	+	0.908229i
$823$	373.901			0.454314			0.227157	−	0.973858i	$-0.427057\pi$
$823$	373.901			0.454314			0.227157	+	0.973858i	$0.427057\pi$
$824$		−	1044.29i		−	1.26734i
$825$	82.8646	−	136.296i	0.100442	−	0.165207i
$826$	79.8881			0.0967168
$827$		−	3.15478i		−	0.00381473i	−0.999998	−	0.00190736i	$-0.999393\pi$
$827$		−	3.15478i		−	0.00381473i	0.999998	−	0.00190736i	$-0.000607133\pi$
$828$	30.2874	−	15.7015i	0.0365790	−	0.0189631i
$829$	663.788			0.800709			0.400354	−	0.916360i	$-0.368887\pi$
$829$	663.788			0.800709			0.400354	+	0.916360i	$0.368887\pi$
$830$			843.376i			1.01612i
$831$	1146.65	+	697.134i	1.37984	+	0.838909i
$832$	218.682			0.262839
$833$		−	585.316i		−	0.702661i
$834$	−1460.82	+	2402.77i	−1.75158	+	2.88101i
$835$	−240.493			−0.288016
$836$		−	3006.80i		−	3.59665i
$837$	−94.1957	+	1383.26i	−0.112540	+	1.65264i
$838$	381.651			0.455430
$839$			690.063i			0.822483i	0.911526	+	0.411242i	$0.134905\pi$
$839$			690.063i			0.822483i	−0.911526	+	0.411242i	$0.865095\pi$
$840$	−2340.48	−	1422.95i	−2.78628	−	1.69399i
$841$	−1577.65			−1.87592
$842$		−	1141.19i		−	1.35533i
$843$	266.895	−	438.991i	0.316602	−	0.520748i
$844$	−1659.94			−1.96676
$845$			714.740i			0.845847i
$846$	−943.993	−	1820.92i	−1.11583	−	2.15239i
$847$	1892.05			2.23382
$848$			184.762i			0.217880i
$849$	117.273	+	71.2991i	0.138131	+	0.0839801i
$850$	−50.7150			−0.0596647
$851$			12.5303i			0.0147242i
$852$	−1018.90	+	1675.89i	−1.19589	+	1.96700i
$853$	229.993			0.269629			0.134814	−	0.990871i	$-0.456956\pi$
$853$	229.993			0.269629			0.134814	+	0.990871i	$0.456956\pi$
$854$		−	1408.47i		−	1.64926i
$855$	−847.306	+	439.256i	−0.991002	+	0.513750i
$856$	−1055.83			−1.23345
$857$			1030.79i			1.20279i	0.798953	+	0.601393i	$0.205387\pi$
$857$			1030.79i			1.20279i	−0.798953	+	0.601393i	$0.794613\pi$
$858$	−571.329	−	347.353i	−0.665884	−	0.404841i
$859$	−206.184			−0.240028			−0.120014	−	0.992772i	$-0.538294\pi$
$859$	−206.184			−0.240028			−0.120014	+	0.992772i	$0.538294\pi$
$860$		−	437.555i		−	0.508785i
$861$	290.806	−	478.319i	0.337754	−	0.555539i
$862$	195.203			0.226454
$863$		−	936.971i		−	1.08571i	−0.839825	−	0.542857i	$-0.817343\pi$
$863$		−	936.971i		−	1.08571i	0.839825	−	0.542857i	$-0.182657\pi$
$864$	130.846	+	8.91019i	0.151442	+	0.0103127i
$865$	814.213			0.941286
$866$			2155.27i			2.48876i
$867$	690.720	+	419.940i	0.796678	+	0.484360i
$868$	5650.57			6.50987
$869$			1443.28i			1.66086i
$870$	−1245.93	+	2049.31i	−1.43210	+	2.35553i
$871$	−32.3392			−0.0371288
$872$			2287.00i			2.62270i
$873$	192.323	+	370.983i	0.220301	+	0.424952i
$874$	−36.8345			−0.0421447
$875$			1775.24i			2.02884i
$876$	441.712	+	268.550i	0.504238	+	0.306564i
$877$	1165.25			1.32868			0.664340	−	0.747430i	$-0.268713\pi$
$877$	1165.25			1.32868			0.664340	+	0.747430i	$0.268713\pi$
$878$		−	369.339i		−	0.420659i
$879$	508.828	−	836.923i	0.578872	−	0.952131i
$880$	−1361.84			−1.54755
$881$			1259.72i			1.42988i	0.699188	+	0.714938i	$0.253545\pi$
$881$			1259.72i			1.42988i	−0.699188	+	0.714938i	$0.746455\pi$
$882$	3690.24	−	1913.08i	4.18395	−	2.16902i
$883$	−157.970			−0.178901			−0.0894507	−	0.995991i	$-0.528511\pi$
$883$	−157.970			−0.178901			−0.0894507	+	0.995991i	$0.528511\pi$
$884$			142.718i			0.161445i
$885$	−20.3092	−	12.3475i	−0.0229483	−	0.0139520i
$886$	2769.01			3.12530
$887$		−	1320.42i		−	1.48863i	−0.667827	−	0.744317i	$-0.732775\pi$
$887$		−	1320.42i		−	1.48863i	0.667827	−	0.744317i	$-0.267225\pi$
$888$	−612.399	+	1007.28i	−0.689639	+	1.13432i
$889$	−2625.32			−2.95312
$890$			0.912834i			0.00102566i
$891$	1070.38	+	754.908i	1.20132	+	0.847259i
$892$	−535.001			−0.599777
$893$			1486.70i			1.66483i
$894$	88.4247	+	53.7600i	0.0989091	+	0.0601343i
$895$	355.613			0.397333
$896$			2862.31i			3.19454i
$897$	−2.85667	+	4.69867i	−0.00318470	+	0.00523820i
$898$	−2125.10			−2.36648
$899$		−	2525.40i		−	2.80912i
$900$	−111.280	−	214.654i	−0.123644	−	0.238505i
$901$	45.1960			0.0501621
$902$		−	781.574i		−	0.866490i
$903$	396.792	+	241.239i	0.439415	+	0.267153i
$904$	−867.970			−0.960144
$905$		−	855.220i		−	0.944994i
$906$	−100.707	+	165.644i	−0.111156	+	0.182830i
$907$	1027.65			1.13302			0.566512	−	0.824054i	$-0.308293\pi$
$907$	1027.65			1.13302			0.566512	+	0.824054i	$0.308293\pi$
$908$		−	2437.76i		−	2.68476i
$909$	92.1639	−	47.7791i	0.101390	−	0.0525623i
$910$	864.963			0.950508
$911$			1158.96i			1.27218i	0.771613	+	0.636092i	$0.219450\pi$
$911$			1158.96i			1.27218i	−0.771613	+	0.636092i	$0.780550\pi$
$912$	−1054.41	−	641.057i	−1.15615	−	0.702913i
$913$	−838.962			−0.918907
$914$			867.932i			0.949598i
$915$	−217.693	+	358.062i	−0.237915	+	0.391324i
$916$	776.347			0.847540
$917$		−	1364.50i		−	1.48800i
$918$	28.2932	−	415.484i	0.0308205	−	0.452597i
$919$	48.1601			0.0524049			0.0262025	−	0.999657i	$-0.491659\pi$
$919$	48.1601			0.0524049			0.0262025	+	0.999657i	$0.491659\pi$
$920$			31.4518i			0.0341867i
$921$	392.911	+	238.880i	0.426613	+	0.259370i
$922$	1866.92			2.02486
$923$		−	316.135i		−	0.342508i
$924$	2773.17	−	4561.32i	3.00126	−	4.93649i
$925$	88.8055			0.0960059
$926$		−	2412.23i		−	2.60500i
$927$	−297.317	−	573.511i	−0.320730	−	0.618674i
$928$	−238.884			−0.257418
$929$			686.177i			0.738619i	0.929307	+	0.369309i	$0.120406\pi$
$929$			686.177i			0.738619i	−0.929307	+	0.369309i	$0.879594\pi$
$930$	−2139.76	−	1300.92i	−2.30081	−	1.39884i
$931$	−3012.91			−3.23621
$932$			3339.92i			3.58360i
$933$	943.093	−	1551.20i	1.01082	−	1.66260i
$934$	−967.915			−1.03631
$935$			333.130i			0.356289i
$936$	−459.279	+	238.097i	−0.490683	+	0.254377i
$937$	1243.11			1.32669			0.663347	−	0.748312i	$-0.269135\pi$
$937$	1243.11			1.32669			0.663347	+	0.748312i	$0.269135\pi$
$938$		−	384.587i		−	0.410007i
$939$	1357.48	+	825.315i	1.44567	+	0.878929i
$940$	2487.01			2.64576
$941$			1069.00i			1.13603i	0.823019	+	0.568014i	$0.192288\pi$
$941$			1069.00i			1.13603i	−0.823019	+	0.568014i	$0.807712\pi$
$942$	199.179	−	327.610i	0.211442	−	0.347781i
$943$	−6.42775			−0.00681628
$944$		−	30.7312i		−	0.0325542i
$945$	−1690.49	−	115.117i	−1.78888	−	0.121817i
$946$	648.358			0.685368
$947$			1369.14i			1.44577i	0.690970	+	0.722884i	$0.257184\pi$
$947$			1369.14i			1.44577i	−0.690970	+	0.722884i	$0.742816\pi$
$948$	1869.35	+	1136.52i	1.97189	+	1.19886i
$949$	−83.3235			−0.0878014
$950$			261.055i			0.274795i
$951$	673.061	−	1107.05i	0.707740	−	1.16409i
$952$	−866.320			−0.910000
$953$		−	1467.20i		−	1.53956i	−0.638307	−	0.769782i	$-0.720365\pi$
$953$		−	1467.20i		−	1.53956i	0.638307	−	0.769782i	$-0.279635\pi$
$954$	147.721	+	284.947i	0.154844	+	0.298687i
$955$	−621.210			−0.650482
$956$			2350.90i			2.45910i
$957$	−2038.58	−	1239.41i	−2.13018	−	1.29510i
$958$	−2127.16			−2.22042
$959$		−	1849.33i		−	1.92839i
$960$	401.954	−	661.135i	0.418702	−	0.688683i
$961$	1675.86			1.74387
$962$		−	372.256i		−	0.386961i
$963$	−579.851	+	300.603i	−0.602129	+	0.312153i
$964$	−490.216			−0.508523
$965$		−	521.728i		−	0.540651i
$966$	−55.8779	−	33.9724i	−0.0578447	−	0.0351681i
$967$	−752.558			−0.778240			−0.389120	−	0.921187i	$-0.627221\pi$
$967$	−752.558			−0.778240			−0.389120	+	0.921187i	$0.627221\pi$
$968$		−	2043.90i		−	2.11147i
$969$	−156.814	+	257.928i	−0.161831	+	0.266180i
$970$	−754.748			−0.778090
$971$			1227.74i			1.26441i	0.774801	+	0.632206i	$0.217850\pi$
$971$			1227.74i			1.26441i	−0.774801	+	0.632206i	$0.782150\pi$
$972$	1820.64	−	791.911i	1.87309	−	0.814723i
$973$	3618.63			3.71904
$974$		−	704.922i		−	0.723739i
$975$	33.3006	+	20.2459i	0.0341545	+	0.0207651i
$976$	−541.806			−0.555129
$977$		−	15.7798i		−	0.0161513i	−0.999967	−	0.00807563i	$-0.997429\pi$
$977$		−	15.7798i		−	0.0161513i	0.999967	−	0.00807563i	$-0.00257058\pi$
$978$	1138.52	−	1872.65i	1.16413	−	1.91477i
$979$	−0.908056			−0.000927534
$980$			5040.13i			5.14299i
$981$	651.126	+	1255.99i	0.663737	+	1.28032i
$982$	−602.943			−0.613995
$983$			1219.82i			1.24092i	0.784238	+	0.620460i	$0.213054\pi$
$983$			1219.82i			1.24092i	−0.784238	+	0.620460i	$0.786946\pi$
$984$	−516.708	−	314.146i	−0.525110	−	0.319254i
$985$	527.176			0.535204
$986$			758.546i			0.769316i
$987$	−1371.18	+	2255.32i	−1.38924	+	2.28503i
$988$	734.637			0.743560
$989$		−	5.33217i		−	0.00539147i
$990$	−2100.29	+	1088.82i	−2.12150	+	1.09982i
$991$	−1618.62			−1.63332			−0.816662	−	0.577116i	$-0.804178\pi$
$991$	−1618.62			−1.63332			−0.816662	+	0.577116i	$0.804178\pi$
$992$		−	249.427i		−	0.251439i
$993$	−407.931	−	248.012i	−0.410806	−	0.249760i
$994$	3759.57			3.78227
$995$			1446.31i			1.45358i
$996$	−660.645	+	1086.63i	−0.663298	+	1.09100i
$997$	518.409			0.519969			0.259985	−	0.965613i	$-0.416282\pi$
$997$	518.409			0.519969			0.259985	+	0.965613i	$0.416282\pi$
$998$		−	828.211i		−	0.829871i
$999$	−49.5433	+	727.541i	−0.0495929	+	0.728269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.4	✓	44
3.2	odd	2	inner	201.3.c.a.68.41	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.4	✓	44	1.1	even	1	trivial
201.3.c.a.68.41	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.48861i q^{2} +(2.56342 + 1.55849i) q^{3} -8.17041 q^{4} -4.65961i q^{5} +(5.43698 - 8.94276i) q^{6} -13.4680 q^{7} +14.5490i q^{8} +(4.14220 + 7.99013i) q^{9} +O(q^{10})\)	\(q-3.48861i q^{2} +(2.56342 + 1.55849i) q^{3} -8.17041 q^{4} -4.65961i q^{5} +(5.43698 - 8.94276i) q^{6} -13.4680 q^{7} +14.5490i q^{8} +(4.14220 + 7.99013i) q^{9} -16.2556 q^{10} -16.1705i q^{11} +(-20.9442 - 12.7335i) q^{12} +3.95086 q^{13} +46.9847i q^{14} +(7.26196 - 11.9445i) q^{15} +18.0740 q^{16} -4.42122i q^{17} +(27.8745 - 14.4505i) q^{18} -22.7582 q^{19} +38.0709i q^{20} +(-34.5242 - 20.9898i) q^{21} -56.4125 q^{22} +0.463943i q^{23} +(-22.6744 + 37.2950i) q^{24} +3.28807 q^{25} -13.7830i q^{26} +(-1.83437 + 26.9376i) q^{27} +110.039 q^{28} -49.1798i q^{29} +(-41.6698 - 25.3342i) q^{30} +51.3504 q^{31} -4.85735i q^{32} +(25.2016 - 41.4517i) q^{33} -15.4239 q^{34} +62.7557i q^{35} +(-33.8435 - 65.2827i) q^{36} +27.0084 q^{37} +79.3944i q^{38} +(10.1277 + 6.15738i) q^{39} +67.7924 q^{40} +13.8546i q^{41} +(-73.2254 + 120.441i) q^{42} -11.4932 q^{43} +132.119i q^{44} +(37.2309 - 19.3010i) q^{45} +1.61852 q^{46} -65.3258i q^{47} +(46.3312 + 28.1682i) q^{48} +132.388 q^{49} -11.4708i q^{50} +(6.89044 - 11.3334i) q^{51} -32.2801 q^{52} +10.2225i q^{53} +(93.9749 + 6.39941i) q^{54} -75.3481 q^{55} -195.946i q^{56} +(-58.3387 - 35.4685i) q^{57} -171.569 q^{58} -1.70030i q^{59} +(-59.3332 + 97.5916i) q^{60} -29.9771 q^{61} -179.142i q^{62} +(-55.7873 - 107.611i) q^{63} +55.3506 q^{64} -18.4094i q^{65} +(-144.609 - 87.9185i) q^{66} -8.18535 q^{67} +36.1232i q^{68} +(-0.723052 + 1.18928i) q^{69} +218.930 q^{70} -80.0169i q^{71} +(-116.248 + 60.2647i) q^{72} -21.0900 q^{73} -94.2217i q^{74} +(8.42870 + 5.12444i) q^{75} +185.944 q^{76} +217.785i q^{77} +(21.4807 - 35.3316i) q^{78} -89.2542 q^{79} -84.2177i q^{80} +(-46.6843 + 66.1935i) q^{81} +48.3334 q^{82} -51.8823i q^{83} +(282.077 + 171.496i) q^{84} -20.6012 q^{85} +40.0951i q^{86} +(76.6463 - 126.068i) q^{87} +235.264 q^{88} -0.0561552i q^{89} +(-67.3338 - 129.884i) q^{90} -53.2103 q^{91} -3.79061i q^{92} +(131.632 + 80.0292i) q^{93} -227.896 q^{94} +106.044i q^{95} +(7.57015 - 12.4514i) q^{96} +46.4301 q^{97} -461.850i q^{98} +(129.204 - 66.9814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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