LMFDB - Embedded newform 1155.3.b.a.736.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,3,Mod(736,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.736");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1155.b (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:	$31.4714705336$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			736.19
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.78

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81721i q^{2} -1.73205 q^{3} -3.93666 q^{4} -2.23607 q^{5} +4.87955i q^{6} +2.64575i q^{7} -0.178435i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.81721i q^{2} -1.73205 q^{3} -3.93666 q^{4} -2.23607 q^{5} +4.87955i q^{6} +2.64575i q^{7} -0.178435i q^{8} +3.00000 q^{9} +6.29947i q^{10} +(10.0297 - 4.51714i) q^{11} +6.81850 q^{12} +17.9645i q^{13} +7.45363 q^{14} +3.87298 q^{15} -16.2493 q^{16} -30.4206i q^{17} -8.45162i q^{18} -7.14756i q^{19} +8.80264 q^{20} -4.58258i q^{21} +(-12.7257 - 28.2558i) q^{22} +12.7880 q^{23} +0.309058i q^{24} +5.00000 q^{25} +50.6098 q^{26} -5.19615 q^{27} -10.4154i q^{28} -3.50507i q^{29} -10.9110i q^{30} -11.9905 q^{31} +45.0640i q^{32} +(-17.3720 + 7.82392i) q^{33} -85.7013 q^{34} -5.91608i q^{35} -11.8100 q^{36} -14.3400 q^{37} -20.1362 q^{38} -31.1155i q^{39} +0.398993i q^{40} -35.1217i q^{41} -12.9101 q^{42} -74.7913i q^{43} +(-39.4837 + 17.7825i) q^{44} -6.70820 q^{45} -36.0264i q^{46} -88.0629 q^{47} +28.1447 q^{48} -7.00000 q^{49} -14.0860i q^{50} +52.6901i q^{51} -70.7202i q^{52} +16.0668 q^{53} +14.6386i q^{54} +(-22.4272 + 10.1006i) q^{55} +0.472095 q^{56} +12.3799i q^{57} -9.87451 q^{58} -32.8995 q^{59} -15.2466 q^{60} +64.9712i q^{61} +33.7797i q^{62} +7.93725i q^{63} +61.9574 q^{64} -40.1699i q^{65} +(22.0416 + 48.9405i) q^{66} -40.9161 q^{67} +119.756i q^{68} -22.1494 q^{69} -16.6668 q^{70} +70.8583 q^{71} -0.535305i q^{72} +38.2254i q^{73} +40.3986i q^{74} -8.66025 q^{75} +28.1375i q^{76} +(11.9512 + 26.5362i) q^{77} -87.6587 q^{78} +101.763i q^{79} +36.3346 q^{80} +9.00000 q^{81} -98.9451 q^{82} +56.6589i q^{83} +18.0401i q^{84} +68.0226i q^{85} -210.703 q^{86} +6.07096i q^{87} +(-0.806016 - 1.78965i) q^{88} -104.100 q^{89} +18.8984i q^{90} -47.5296 q^{91} -50.3419 q^{92} +20.7682 q^{93} +248.092i q^{94} +15.9824i q^{95} -78.0532i q^{96} +30.1713 q^{97} +19.7205i q^{98} +(30.0892 - 13.5514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) $ 96 * q - 216 * q^4 + 288 * q^9	$ 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) $ 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$		−	2.81721i		−	1.40860i	−0.709900	−	0.704302i	$-0.751260\pi$
$2$		−	2.81721i		−	1.40860i	0.709900	−	0.704302i	$-0.248740\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.93666			−0.984166
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$			4.87955i			0.813258i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$		−	0.178435i		−	0.0223044i
$9$	3.00000			0.333333
$10$			6.29947i			0.629947i
$11$	10.0297	−	4.51714i	0.911793	−	0.410649i
$11$	10.0297	−	4.51714i	0.911793	−	0.410649i
$12$	6.81850			0.568208
$13$			17.9645i			1.38189i	0.722909	+	0.690943i	$0.242804\pi$
$13$			17.9645i			1.38189i	−0.722909	+	0.690943i	$0.757196\pi$
$14$	7.45363			0.532402
$15$	3.87298			0.258199
$16$	−16.2493			−1.01558
$17$		−	30.4206i		−	1.78945i	−0.446618	−	0.894725i	$-0.647372\pi$
$17$		−	30.4206i		−	1.78945i	0.446618	−	0.894725i	$-0.352628\pi$
$18$		−	8.45162i		−	0.469535i
$19$		−	7.14756i		−	0.376187i	−0.982151	−	0.188094i	$-0.939769\pi$
$19$		−	7.14756i		−	0.376187i	0.982151	−	0.188094i	$-0.0602308\pi$
$20$	8.80264			0.440132
$21$		−	4.58258i		−	0.218218i
$22$	−12.7257	−	28.2558i	−0.578442	−	1.28436i
$23$	12.7880			0.555999			0.277999	−	0.960581i	$-0.410329\pi$
$23$	12.7880			0.555999			0.277999	+	0.960581i	$0.410329\pi$
$24$			0.309058i			0.0128774i
$25$	5.00000			0.200000
$26$	50.6098			1.94653
$27$	−5.19615			−0.192450
$28$		−	10.4154i		−	0.371980i
$29$		−	3.50507i		−	0.120864i	−0.998172	−	0.0604322i	$-0.980752\pi$
$29$		−	3.50507i		−	0.120864i	0.998172	−	0.0604322i	$-0.0192479\pi$
$30$		−	10.9110i		−	0.363700i
$31$	−11.9905			−0.386790			−0.193395	−	0.981121i	$-0.561950\pi$
$31$	−11.9905			−0.386790			−0.193395	+	0.981121i	$0.561950\pi$
$32$			45.0640i			1.40825i
$33$	−17.3720	+	7.82392i	−0.526424	+	0.237088i
$34$	−85.7013			−2.52063
$35$		−	5.91608i		−	0.169031i
$36$	−11.8100			−0.328055
$37$	−14.3400			−0.387566			−0.193783	−	0.981044i	$-0.562076\pi$
$37$	−14.3400			−0.387566			−0.193783	+	0.981044i	$0.562076\pi$
$38$	−20.1362			−0.529899
$39$		−	31.1155i		−	0.797832i
$40$			0.398993i			0.00997482i
$41$		−	35.1217i		−	0.856627i	−0.903630	−	0.428313i	$-0.859108\pi$
$41$		−	35.1217i		−	0.856627i	0.903630	−	0.428313i	$-0.140892\pi$
$42$	−12.9101			−0.307383
$43$		−	74.7913i		−	1.73933i	−0.493640	−	0.869667i	$-0.664334\pi$
$43$		−	74.7913i		−	1.73933i	0.493640	−	0.869667i	$-0.335666\pi$
$44$	−39.4837	+	17.7825i	−0.897356	+	0.404147i
$45$	−6.70820			−0.149071
$46$		−	36.0264i		−	0.783182i
$47$	−88.0629			−1.87368			−0.936839	−	0.349760i	$-0.886263\pi$
$47$	−88.0629			−1.87368			−0.936839	+	0.349760i	$0.886263\pi$
$48$	28.1447			0.586347
$49$	−7.00000			−0.142857
$50$		−	14.0860i		−	0.281721i
$51$			52.6901i			1.03314i
$52$		−	70.7202i		−	1.36000i
$53$	16.0668			0.303146			0.151573	−	0.988446i	$-0.451566\pi$
$53$	16.0668			0.303146			0.151573	+	0.988446i	$0.451566\pi$
$54$			14.6386i			0.271086i
$55$	−22.4272	+	10.1006i	−0.407766	+	0.183648i
$56$	0.472095			0.00843026
$57$			12.3799i			0.217192i
$58$	−9.87451			−0.170250
$59$	−32.8995			−0.557619			−0.278809	−	0.960346i	$-0.589940\pi$
$59$	−32.8995			−0.557619			−0.278809	+	0.960346i	$0.589940\pi$
$60$	−15.2466			−0.254110
$61$			64.9712i			1.06510i	0.846398	+	0.532551i	$0.178766\pi$
$61$			64.9712i			1.06510i	−0.846398	+	0.532551i	$0.821234\pi$
$62$			33.7797i			0.544834i
$63$			7.93725i			0.125988i
$64$	61.9574			0.968084
$65$		−	40.1699i		−	0.617998i
$66$	22.0416	+	48.9405i	0.333964	+	0.741523i
$67$	−40.9161			−0.610688			−0.305344	−	0.952242i	$-0.598771\pi$
$67$	−40.9161			−0.610688			−0.305344	+	0.952242i	$0.598771\pi$
$68$			119.756i			1.76112i
$69$	−22.1494			−0.321006
$70$	−16.6668			−0.238098
$71$	70.8583			0.998004			0.499002	−	0.866601i	$-0.333700\pi$
$71$	70.8583			0.998004			0.499002	+	0.866601i	$0.333700\pi$
$72$		−	0.535305i		−	0.00743479i
$73$			38.2254i			0.523636i	0.965117	+	0.261818i	$0.0843220\pi$
$73$			38.2254i			0.523636i	−0.965117	+	0.261818i	$0.915678\pi$
$74$			40.3986i			0.545927i
$75$	−8.66025			−0.115470
$76$			28.1375i			0.370230i
$77$	11.9512	+	26.5362i	0.155211	+	0.344626i
$78$	−87.6587			−1.12383
$79$			101.763i			1.28814i	0.764968	+	0.644068i	$0.222755\pi$
$79$			101.763i			1.28814i	−0.764968	+	0.644068i	$0.777245\pi$
$80$	36.3346			0.454183
$81$	9.00000			0.111111
$82$	−98.9451			−1.20665
$83$			56.6589i			0.682637i	0.939948	+	0.341319i	$0.110873\pi$
$83$			56.6589i			0.682637i	−0.939948	+	0.341319i	$0.889127\pi$
$84$			18.0401i			0.214763i
$85$			68.0226i			0.800266i
$86$	−210.703			−2.45003
$87$			6.07096i			0.0697811i
$88$	−0.806016	−	1.78965i	−0.00915927	−	0.0203370i
$89$	−104.100			−1.16966			−0.584829	−	0.811157i	$-0.698838\pi$
$89$	−104.100			−1.16966			−0.584829	+	0.811157i	$0.698838\pi$
$90$			18.8984i			0.209982i
$91$	−47.5296			−0.522304
$92$	−50.3419			−0.547195
$93$	20.7682			0.223313
$94$			248.092i			2.63927i
$95$			15.9824i			0.168236i
$96$		−	78.0532i		−	0.813054i
$97$	30.1713			0.311045			0.155522	−	0.987832i	$-0.450294\pi$
$97$	30.1713			0.311045			0.155522	+	0.987832i	$0.450294\pi$
$98$			19.7205i			0.201229i
$99$	30.0892	−	13.5514i	0.303931	−	0.136883i
$100$	−19.6833			−0.196833
$101$		−	109.652i		−	1.08567i	−0.839840	−	0.542834i	$-0.817351\pi$
$101$		−	109.652i		−	1.08567i	0.839840	−	0.542834i	$-0.182649\pi$
$102$	148.439			1.45528
$103$	−138.100			−1.34078			−0.670390	−	0.742009i	$-0.733873\pi$
$103$	−138.100			−1.34078			−0.670390	+	0.742009i	$0.733873\pi$
$104$	3.20550			0.0308221
$105$			10.2470i			0.0975900i
$106$		−	45.2634i		−	0.427013i
$107$			44.8371i			0.419038i	0.977805	+	0.209519i	$0.0671899\pi$
$107$			44.8371i			0.419038i	−0.977805	+	0.209519i	$0.932810\pi$
$108$	20.4555			0.189403
$109$		−	198.548i		−	1.82154i	−0.412915	−	0.910770i	$-0.635489\pi$
$109$		−	198.548i		−	1.82154i	0.412915	−	0.910770i	$-0.364511\pi$
$110$	28.4556	+	63.1820i	0.258687	+	0.574381i
$111$	24.8375			0.223761
$112$		−	42.9917i		−	0.383855i
$113$	−126.902			−1.12303			−0.561514	−	0.827467i	$-0.689781\pi$
$113$	−126.902			−1.12303			−0.561514	+	0.827467i	$0.689781\pi$
$114$	34.8768			0.305937
$115$	−28.5948			−0.248650
$116$			13.7983i			0.118951i
$117$			53.8935i			0.460629i
$118$			92.6847i			0.785464i
$119$	80.4855			0.676349
$120$		−	0.691076i		−	0.00575896i
$121$	80.1909	−	90.6114i	0.662735	−	0.748854i
$122$	183.037			1.50031
$123$			60.8326i			0.494574i
$124$	47.2025			0.380666
$125$	−11.1803			−0.0894427
$126$	22.3609			0.177467
$127$		−	153.997i		−	1.21257i	−0.795246	−	0.606287i	$-0.792658\pi$
$127$		−	153.997i		−	1.21257i	0.795246	−	0.606287i	$-0.207342\pi$
$128$			5.70920i			0.0446032i
$129$			129.542i			1.00420i
$130$	−113.167			−0.870515
$131$			64.1006i			0.489317i	0.969609	+	0.244659i	$0.0786759\pi$
$131$			64.1006i			0.489317i	−0.969609	+	0.244659i	$0.921324\pi$
$132$	68.3877	−	30.8001i	0.518089	−	0.233334i
$133$	18.9107			0.142185
$134$			115.269i			0.860217i
$135$	11.6190			0.0860663
$136$	−5.42811			−0.0399126
$137$	−228.951			−1.67118			−0.835589	−	0.549355i	$-0.814874\pi$
$137$	−228.951			−1.67118			−0.835589	+	0.549355i	$0.814874\pi$
$138$			62.3995i			0.452171i
$139$			150.523i			1.08290i	0.840734	+	0.541449i	$0.182124\pi$
$139$			150.523i			1.08290i	−0.840734	+	0.541449i	$0.817876\pi$
$140$			23.2896i			0.166354i
$141$	152.529			1.08177
$142$		−	199.622i		−	1.40579i
$143$	81.1483	+	180.179i	0.567470	+	1.25999i
$144$	−48.7480			−0.338528
$145$			7.83757i			0.0540522i
$146$	107.689			0.737596
$147$	12.1244			0.0824786
$148$	56.4515			0.381429
$149$			178.634i			1.19888i	0.800418	+	0.599442i	$0.204611\pi$
$149$			178.634i			1.19888i	−0.800418	+	0.599442i	$0.795389\pi$
$150$			24.3977i			0.162652i
$151$			163.025i			1.07964i	0.841782	+	0.539818i	$0.181507\pi$
$151$			163.025i			1.07964i	−0.841782	+	0.539818i	$0.818493\pi$
$152$	−1.27537			−0.00839062
$153$		−	91.2619i		−	0.596483i
$154$	74.7579	−	33.6691i	0.485441	−	0.218631i
$155$	26.8116			0.172978
$156$			122.491i			0.785199i
$157$	−104.064			−0.662831			−0.331415	−	0.943485i	$-0.607526\pi$
$157$	−104.064			−0.662831			−0.331415	+	0.943485i	$0.607526\pi$
$158$	286.687			1.81447
$159$	−27.8284			−0.175022
$160$		−	100.766i		−	0.629789i
$161$			33.8338i			0.210148i
$162$		−	25.3549i		−	0.156512i
$163$	−292.311			−1.79332			−0.896660	−	0.442720i	$-0.854014\pi$
$163$	−292.311			−1.79332			−0.896660	+	0.442720i	$0.854014\pi$
$164$			138.262i			0.843063i
$165$	38.8450	−	17.4948i	0.235424	−	0.106029i
$166$	159.620			0.961566
$167$		−	299.120i		−	1.79114i	−0.444920	−	0.895570i	$-0.646768\pi$
$167$		−	299.120i		−	1.79114i	0.444920	−	0.895570i	$-0.353232\pi$
$168$	−0.817692			−0.00486721
$169$	−153.724			−0.909609
$170$	191.634			1.12726
$171$		−	21.4427i		−	0.125396i
$172$			294.428i			1.71179i
$173$			164.904i			0.953201i	0.879120	+	0.476601i	$0.158131\pi$
$173$			164.904i			0.953201i	−0.879120	+	0.476601i	$0.841869\pi$
$174$	17.1032			0.0982940
$175$			13.2288i			0.0755929i
$176$	−162.976	+	73.4006i	−0.926003	+	0.417049i
$177$	56.9836			0.321941
$178$			293.270i			1.64758i
$179$	87.0228			0.486161			0.243080	−	0.970006i	$-0.421842\pi$
$179$	87.0228			0.486161			0.243080	+	0.970006i	$0.421842\pi$
$180$	26.4079			0.146711
$181$	261.759			1.44618			0.723092	−	0.690751i	$-0.242720\pi$
$181$	261.759			1.44618			0.723092	+	0.690751i	$0.242720\pi$
$182$			133.901i			0.735719i
$183$		−	112.533i		−	0.614936i
$184$		−	2.28182i		−	0.0124012i
$185$	32.0651			0.173325
$186$		−	58.5082i		−	0.314560i
$187$	−137.414	−	305.111i	−0.734836	−	1.63161i
$188$	346.674			1.84401
$189$		−	13.7477i		−	0.0727393i
$190$	45.0258			0.236978
$191$	298.539			1.56303			0.781517	−	0.623884i	$-0.214446\pi$
$191$	298.539			1.56303			0.781517	+	0.623884i	$0.214446\pi$
$192$	−107.313			−0.558924
$193$		−	208.048i		−	1.07797i	−0.842316	−	0.538985i	$-0.818808\pi$
$193$		−	208.048i		−	1.07797i	0.842316	−	0.538985i	$-0.181192\pi$
$194$		−	84.9989i		−	0.438139i
$195$			69.5763i			0.356801i
$196$	27.5566			0.140595
$197$		−	274.427i		−	1.39303i	−0.717541	−	0.696516i	$-0.754732\pi$
$197$		−	274.427i		−	1.39303i	0.717541	−	0.696516i	$-0.245268\pi$
$198$	−38.1772	−	84.7675i	−0.192814	−	0.428119i
$199$	109.085			0.548166			0.274083	−	0.961706i	$-0.411626\pi$
$199$	109.085			0.548166			0.274083	+	0.961706i	$0.411626\pi$
$200$		−	0.892175i		−	0.00446087i
$201$	70.8687			0.352581
$202$	−308.914			−1.52928
$203$	9.27354			0.0456825
$204$		−	207.423i		−	1.01678i
$205$			78.5345i			0.383095i
$206$			389.057i			1.88863i
$207$	38.3639			0.185333
$208$		−	291.912i		−	1.40342i
$209$	−32.2865	−	71.6880i	−0.154481	−	0.343005i
$210$	28.8678			0.137466
$211$		−	286.697i		−	1.35875i	−0.733791	−	0.679376i	$-0.762251\pi$
$211$		−	286.697i		−	1.35875i	0.733791	−	0.679376i	$-0.237749\pi$
$212$	−63.2494			−0.298346
$213$	−122.730			−0.576198
$214$	126.315			0.590259
$215$			167.238i			0.777853i
$216$			0.927175i			0.00429248i
$217$		−	31.7239i		−	0.146193i
$218$	−559.350			−2.56583
$219$		−	66.2084i		−	0.302321i
$220$	88.2881	−	39.7628i	0.401310	−	0.180740i
$221$	546.492			2.47282
$222$		−	69.9725i		−	0.315191i
$223$	−317.428			−1.42344			−0.711721	−	0.702462i	$-0.752084\pi$
$223$	−317.428			−1.42344			−0.711721	+	0.702462i	$0.752084\pi$
$224$	−119.228			−0.532269
$225$	15.0000			0.0666667
$226$			357.510i			1.58190i
$227$			150.894i			0.664732i	0.943150	+	0.332366i	$0.107847\pi$
$227$			150.894i			0.664732i	−0.943150	+	0.332366i	$0.892153\pi$
$228$		−	48.7356i		−	0.213753i
$229$	−395.000			−1.72489			−0.862444	−	0.506152i	$-0.831068\pi$
$229$	−395.000			−1.72489			−0.862444	+	0.506152i	$0.831068\pi$
$230$			80.5575i			0.350250i
$231$	−20.7001	−	45.9620i	−0.0896110	−	0.198970i
$232$	−0.625427			−0.00269581
$233$			181.844i			0.780447i	0.920720	+	0.390223i	$0.127602\pi$
$233$			181.844i			0.780447i	−0.920720	+	0.390223i	$0.872398\pi$
$234$	151.829			0.648843
$235$	196.915			0.837935
$236$	129.514			0.548789
$237$		−	176.258i		−	0.743706i
$238$		−	226.744i		−	0.952707i
$239$		−	201.246i		−	0.842033i	−0.907053	−	0.421017i	$-0.861673\pi$
$239$		−	201.246i		−	0.842033i	0.907053	−	0.421017i	$-0.138327\pi$
$240$	−62.9334			−0.262223
$241$			281.288i			1.16717i	0.812052	+	0.583585i	$0.198350\pi$
$241$			281.288i			1.16717i	−0.812052	+	0.583585i	$0.801650\pi$
$242$	−255.271	−	225.914i	−1.05484	−	0.933531i
$243$	−15.5885			−0.0641500
$244$		−	255.770i		−	1.04824i
$245$	15.6525			0.0638877
$246$	171.378			0.696659
$247$	128.402			0.519848
$248$			2.13952i			0.00862711i
$249$		−	98.1361i		−	0.394121i
$250$			31.4973i			0.125989i
$251$	−322.926			−1.28656			−0.643278	−	0.765633i	$-0.722426\pi$
$251$	−322.926			−1.28656			−0.643278	+	0.765633i	$0.722426\pi$
$252$		−	31.2463i		−	0.123993i
$253$	128.260	−	57.7651i	0.506956	−	0.228321i
$254$	−433.842			−1.70804
$255$		−	117.819i		−	0.462034i
$256$	263.914			1.03091
$257$	−146.111			−0.568523			−0.284262	−	0.958747i	$-0.591748\pi$
$257$	−146.111			−0.568523			−0.284262	+	0.958747i	$0.591748\pi$
$258$	364.948			1.41453
$259$		−	37.9399i		−	0.146486i
$260$			158.135i			0.608213i
$261$		−	10.5152i		−	0.0402882i
$262$	180.585			0.689255
$263$			65.4490i			0.248855i	0.992229	+	0.124428i	$0.0397095\pi$
$263$			65.4490i			0.248855i	−0.992229	+	0.124428i	$0.960291\pi$
$264$	1.39606	+	3.09977i	0.00528811	+	0.0117416i
$265$	−35.9264			−0.135571
$266$		−	53.2753i		−	0.200283i
$267$	180.306			0.675302
$268$	161.073			0.601018
$269$	211.202			0.785138			0.392569	−	0.919723i	$-0.371586\pi$
$269$	211.202			0.785138			0.392569	+	0.919723i	$0.371586\pi$
$270$		−	32.7330i		−	0.121233i
$271$		−	535.425i		−	1.97574i	−0.155284	−	0.987870i	$-0.549629\pi$
$271$		−	535.425i		−	1.97574i	0.155284	−	0.987870i	$-0.450371\pi$
$272$			494.315i			1.81734i
$273$	82.3238			0.301552
$274$			645.004i			2.35403i
$275$	50.1486	−	22.5857i	0.182359	−	0.0821298i
$276$	87.1948			0.315923
$277$			21.4126i			0.0773018i	0.999253	+	0.0386509i	$0.0123060\pi$
$277$			21.4126i			0.0773018i	−0.999253	+	0.0386509i	$0.987694\pi$
$278$	424.054			1.52537
$279$	−35.9715			−0.128930
$280$	−1.05564			−0.00377013
$281$		−	187.396i		−	0.666890i	−0.942769	−	0.333445i	$-0.891789\pi$
$281$		−	187.396i		−	0.666890i	0.942769	−	0.333445i	$-0.108211\pi$
$282$		−	429.707i		−	1.52378i
$283$		−	451.900i		−	1.59682i	−0.602115	−	0.798410i	$-0.705675\pi$
$283$		−	451.900i		−	1.59682i	0.602115	−	0.798410i	$-0.294325\pi$
$284$	−278.945			−0.982201
$285$		−	27.6824i		−	0.0971311i
$286$	507.602	−	228.612i	1.77483	−	0.799341i
$287$	92.9233			0.323774
$288$			135.192i			0.469417i
$289$	−636.416			−2.20213
$290$	22.0801			0.0761382
$291$	−52.2583			−0.179582
$292$		−	150.481i		−	0.515345i
$293$			141.359i			0.482454i	0.970469	+	0.241227i	$0.0775499\pi$
$293$			141.359i			0.482454i	−0.970469	+	0.241227i	$0.922450\pi$
$294$		−	34.1568i		−	0.116180i
$295$	73.5655			0.249375
$296$			2.55875i			0.00864442i
$297$	−52.1160	+	23.4718i	−0.175475	+	0.0790295i
$298$	503.249			1.68875
$299$			229.730i			0.768327i
$300$	34.0925			0.113642
$301$	197.879			0.657406
$302$	459.276			1.52078
$303$			189.924i			0.626810i
$304$			116.143i			0.382050i
$305$		−	145.280i		−	0.476328i
$306$	−257.104			−0.840209
$307$		−	199.832i		−	0.650920i	−0.945556	−	0.325460i	$-0.894481\pi$
$307$		−	199.832i		−	0.650920i	0.945556	−	0.325460i	$-0.105519\pi$
$308$	−47.0480	−	104.464i	−0.152753	−	0.339169i
$309$	239.197			0.774099
$310$		−	75.5338i		−	0.243657i
$311$	−312.502			−1.00483			−0.502415	−	0.864627i	$-0.667555\pi$
$311$	−312.502			−1.00483			−0.502415	+	0.864627i	$0.667555\pi$
$312$	−5.55209			−0.0177951
$313$	−357.725			−1.14289			−0.571446	−	0.820639i	$-0.693617\pi$
$313$	−357.725			−1.14289			−0.571446	+	0.820639i	$0.693617\pi$
$314$			293.171i			0.933666i
$315$		−	17.7482i		−	0.0563436i
$316$		−	400.606i		−	1.26774i
$317$	−335.388			−1.05801			−0.529003	−	0.848620i	$-0.677434\pi$
$317$	−335.388			−1.05801			−0.529003	+	0.848620i	$0.677434\pi$
$318$			78.3985i			0.246536i
$319$	−15.8329	−	35.1549i	−0.0496329	−	0.110203i
$320$	−138.541			−0.432941
$321$		−	77.6601i		−	0.241932i
$322$	95.3169			0.296015
$323$	−217.433			−0.673168
$324$	−35.4300			−0.109352
$325$			89.8226i			0.276377i
$326$			823.502i			2.52608i
$327$			343.895i			1.05167i
$328$	−6.26694			−0.0191065
$329$		−	232.993i		−	0.708184i
$330$	−49.2865	−	109.434i	−0.149353	−	0.331619i
$331$	−215.780			−0.651903			−0.325951	−	0.945387i	$-0.605685\pi$
$331$	−215.780			−0.651903			−0.325951	+	0.945387i	$0.605685\pi$
$332$		−	223.047i		−	0.671828i
$333$	−43.0199			−0.129189
$334$	−842.685			−2.52301
$335$	91.4911			0.273108
$336$			74.4638i			0.221619i
$337$			292.278i			0.867294i	0.901083	+	0.433647i	$0.142774\pi$
$337$			292.278i			0.867294i	−0.901083	+	0.433647i	$0.857226\pi$
$338$			433.072i			1.28128i
$339$	219.801			0.648380
$340$		−	267.782i		−	0.787595i
$341$	−120.261	+	54.1628i	−0.352673	+	0.158835i
$342$	−60.4085			−0.176633
$343$		−	18.5203i		−	0.0539949i
$344$	−13.3454			−0.0387947
$345$	49.5276			0.143558
$346$	464.568			1.34268
$347$		−	315.208i		−	0.908380i	−0.890905	−	0.454190i	$-0.849929\pi$
$347$		−	315.208i		−	0.908380i	0.890905	−	0.454190i	$-0.150071\pi$
$348$		−	23.8993i		−	0.0686762i
$349$			252.089i			0.722318i	0.932504	+	0.361159i	$0.117619\pi$
$349$			252.089i			0.722318i	−0.932504	+	0.361159i	$0.882381\pi$
$350$	37.2682			0.106480
$351$		−	93.3464i		−	0.265944i
$352$	203.561	+	451.980i	0.578297	+	1.28403i
$353$	−244.994			−0.694035			−0.347017	−	0.937859i	$-0.612805\pi$
$353$	−244.994			−0.694035			−0.347017	+	0.937859i	$0.612805\pi$
$354$		−	160.535i		−	0.453488i
$355$	−158.444			−0.446321
$356$	409.805			1.15114
$357$	−139.405			−0.390490
$358$		−	245.161i		−	0.684808i
$359$		−	365.062i		−	1.01689i	−0.861095	−	0.508444i	$-0.830221\pi$
$359$		−	365.062i		−	1.01689i	0.861095	−	0.508444i	$-0.169779\pi$
$360$			1.19698i			0.00332494i
$361$	309.912			0.858483
$362$		−	737.431i		−	2.03710i
$363$	−138.895	+	156.944i	−0.382630	+	0.432351i
$364$	187.108			0.514033
$365$		−	85.4747i		−	0.234177i
$366$	−317.030			−0.866202
$367$	−68.8031			−0.187474			−0.0937371	−	0.995597i	$-0.529881\pi$
$367$	−68.8031			−0.187474			−0.0937371	+	0.995597i	$0.529881\pi$
$368$	−207.796			−0.564663
$369$		−	105.365i		−	0.285542i
$370$		−	90.3341i		−	0.244146i
$371$			42.5087i			0.114579i
$372$	−81.7572			−0.219777
$373$		−	363.034i		−	0.973281i	−0.873602	−	0.486640i	$-0.838222\pi$
$373$		−	363.034i		−	0.973281i	0.873602	−	0.486640i	$-0.161778\pi$
$374$	−859.561	+	387.125i	−2.29829	+	1.03509i
$375$	19.3649			0.0516398
$376$			15.7135i			0.0417912i
$377$	62.9669			0.167021
$378$	−38.7302			−0.102461
$379$	111.650			0.294591			0.147295	−	0.989093i	$-0.452943\pi$
$379$	111.650			0.294591			0.147295	+	0.989093i	$0.452943\pi$
$380$		−	62.9174i		−	0.165572i
$381$			266.731i			0.700080i
$382$		−	841.048i		−	2.20170i
$383$	244.790			0.639140			0.319570	−	0.947563i	$-0.396462\pi$
$383$	244.790			0.639140			0.319570	+	0.947563i	$0.396462\pi$
$384$		−	9.88863i		−	0.0257516i
$385$	−26.7238	−	59.3367i	−0.0694124	−	0.154121i
$386$	−586.115			−1.51843
$387$		−	224.374i		−	0.579778i
$388$	−118.774			−0.306119
$389$	413.922			1.06407			0.532033	−	0.846724i	$-0.321428\pi$
$389$	413.922			1.06407			0.532033	+	0.846724i	$0.321428\pi$
$390$	196.011			0.502592
$391$		−	389.019i		−	0.994932i
$392$			1.24904i			0.00318634i
$393$		−	111.025i		−	0.282508i
$394$	−773.119			−1.96223
$395$		−	227.548i		−	0.576072i
$396$	−118.451	+	53.3474i	−0.299119	+	0.134716i
$397$	750.862			1.89134			0.945671	−	0.325126i	$-0.105407\pi$
$397$	750.862			1.89134			0.945671	+	0.325126i	$0.105407\pi$
$398$		−	307.315i		−	0.772149i
$399$	−32.7542			−0.0820908
$400$	−81.2467			−0.203117
$401$	335.954			0.837790			0.418895	−	0.908035i	$-0.362418\pi$
$401$	335.954			0.837790			0.418895	+	0.908035i	$0.362418\pi$
$402$		−	199.652i		−	0.496646i
$403$		−	215.403i		−	0.534500i
$404$			431.664i			1.06848i
$405$	−20.1246			−0.0496904
$406$		−	26.1255i		−	0.0643485i
$407$	−143.826	+	64.7756i	−0.353380	+	0.159154i
$408$	9.40176			0.0230435
$409$			388.850i			0.950734i	0.879788	+	0.475367i	$0.157685\pi$
$409$			388.850i			0.950734i	−0.879788	+	0.475367i	$0.842315\pi$
$410$	221.248			0.539629
$411$	396.556			0.964855
$412$	543.654			1.31955
$413$		−	87.0439i		−	0.210760i
$414$		−	108.079i		−	0.261061i
$415$		−	126.693i		−	0.305285i
$416$	−809.554			−1.94604
$417$		−	260.713i		−	0.625211i
$418$	−201.960	+	90.9578i	−0.483158	+	0.217602i
$419$	515.798			1.23102			0.615511	−	0.788129i	$-0.288950\pi$
$419$	515.798			1.23102			0.615511	+	0.788129i	$0.288950\pi$
$420$		−	40.3388i		−	0.0960447i
$421$	−675.252			−1.60392			−0.801961	−	0.597376i	$-0.796210\pi$
$421$	−675.252			−1.60392			−0.801961	+	0.597376i	$0.796210\pi$
$422$	−807.684			−1.91394
$423$	−264.189			−0.624560
$424$		−	2.86687i		−	0.00676149i
$425$		−	152.103i		−	0.357890i
$426$			345.756i			0.811634i
$427$	−171.898			−0.402570
$428$		−	176.509i		−	0.412403i
$429$	−140.553	−	312.080i	−0.327629	−	0.727458i
$430$	471.146			1.09569
$431$			126.588i			0.293709i	0.989158	+	0.146854i	$0.0469149\pi$
$431$			126.588i			0.293709i	−0.989158	+	0.146854i	$0.953085\pi$
$432$	84.4340			0.195449
$433$	10.1859			0.0235241			0.0117621	−	0.999931i	$-0.496256\pi$
$433$	10.1859			0.0235241			0.0117621	+	0.999931i	$0.496256\pi$
$434$	−89.3728			−0.205928
$435$		−	13.5751i		−	0.0312071i
$436$			781.616i			1.79270i
$437$		−	91.4028i		−	0.209160i
$438$	−186.523			−0.425851
$439$		−	75.4857i		−	0.171949i	−0.996297	−	0.0859746i	$-0.972600\pi$
$439$		−	75.4857i		−	0.171949i	0.996297	−	0.0859746i	$-0.0274004\pi$
$440$	1.80231	+	4.00179i	0.00409615	+	0.00909497i
$441$	−21.0000			−0.0476190
$442$		−	1539.58i		−	3.48322i
$443$	6.27059			0.0141548			0.00707741	−	0.999975i	$-0.497747\pi$
$443$	6.27059			0.0141548			0.00707741	+	0.999975i	$0.497747\pi$
$444$	−97.7769			−0.220218
$445$	232.774			0.523087
$446$			894.259i			2.00507i
$447$		−	309.403i		−	0.692176i
$448$			163.924i			0.365902i
$449$	−607.460			−1.35292			−0.676458	−	0.736481i	$-0.736486\pi$
$449$	−607.460			−1.35292			−0.676458	+	0.736481i	$0.736486\pi$
$450$		−	42.2581i		−	0.0939069i
$451$	−158.650	−	352.261i	−0.351773	−	0.781067i
$452$	499.571			1.10524
$453$		−	282.368i		−	0.623329i
$454$	425.101			0.936345
$455$	106.280			0.233581
$456$	2.20901			0.00484433
$457$		−	71.7177i		−	0.156931i	−0.996917	−	0.0784657i	$-0.974998\pi$
$457$		−	71.7177i		−	0.156931i	0.996917	−	0.0784657i	$-0.0250021\pi$
$458$			1112.80i			2.42969i
$459$			158.070i			0.344380i
$460$	112.568			0.244713
$461$		−	373.566i		−	0.810339i	−0.914242	−	0.405169i	$-0.867213\pi$
$461$		−	373.566i		−	0.810339i	0.914242	−	0.405169i	$-0.132787\pi$
$462$	−129.484	+	58.3166i	−0.280269	+	0.126226i
$463$	608.399			1.31404			0.657018	−	0.753875i	$-0.271818\pi$
$463$	608.399			1.31404			0.657018	+	0.753875i	$0.271818\pi$
$464$			56.9551i			0.122748i
$465$	−46.4390			−0.0998688
$466$	512.293			1.09934
$467$	−65.2688			−0.139762			−0.0698809	−	0.997555i	$-0.522262\pi$
$467$	−65.2688			−0.139762			−0.0698809	+	0.997555i	$0.522262\pi$
$468$		−	212.161i		−	0.453335i
$469$		−	108.254i		−	0.230818i
$470$		−	554.750i		−	1.18032i
$471$	180.245			0.382686
$472$			5.87042i			0.0124373i
$473$	−337.843	−	750.137i	−0.714256	−	1.58591i
$474$	−496.556			−1.04759
$475$		−	35.7378i		−	0.0752374i
$476$	−316.844			−0.665639
$477$	48.2003			0.101049
$478$	−566.952			−1.18609
$479$			356.904i			0.745103i	0.928012	+	0.372551i	$0.121517\pi$
$479$			356.904i			0.745103i	−0.928012	+	0.372551i	$0.878483\pi$
$480$			174.532i			0.363609i
$481$		−	257.610i		−	0.535572i
$482$	792.446			1.64408
$483$		−	58.6019i		−	0.121329i
$484$	−315.684	+	356.706i	−0.652241	+	0.736997i
$485$	−67.4651			−0.139103
$486$			43.9159i			0.0903620i
$487$	177.072			0.363598			0.181799	−	0.983336i	$-0.441808\pi$
$487$	177.072			0.363598			0.181799	+	0.983336i	$0.441808\pi$
$488$	11.5931			0.0237564
$489$	506.298			1.03537
$490$		−	44.0963i		−	0.0899924i
$491$			116.915i			0.238116i	0.992887	+	0.119058i	$0.0379874\pi$
$491$			116.915i			0.238116i	−0.992887	+	0.119058i	$0.962013\pi$
$492$		−	239.477i		−	0.486742i
$493$	−106.626			−0.216281
$494$		−	361.736i		−	0.732260i
$495$	−67.2815	+	30.3019i	−0.135922	+	0.0612160i
$496$	194.838			0.392818
$497$			187.473i			0.377210i
$498$	−276.470			−0.555160
$499$	156.669			0.313967			0.156983	−	0.987601i	$-0.449823\pi$
$499$	156.669			0.313967			0.156983	+	0.987601i	$0.449823\pi$
$500$	44.0132			0.0880264
$501$			518.092i			1.03412i
$502$			909.749i			1.81225i
$503$		−	583.422i		−	1.15989i	−0.814657	−	0.579943i	$-0.803075\pi$
$503$		−	583.422i		−	1.15989i	0.814657	−	0.579943i	$-0.196925\pi$
$504$	1.41628			0.00281009
$505$			245.190i			0.485525i
$506$	−162.736	−	361.335i	−0.321613	−	0.714101i
$507$	266.258			0.525163
$508$			606.234i			1.19337i
$509$	550.167			1.08088			0.540439	−	0.841383i	$-0.318258\pi$
$509$	550.167			1.08088			0.540439	+	0.841383i	$0.318258\pi$
$510$	−331.920			−0.650823
$511$	−101.135			−0.197916
$512$		−	720.663i		−	1.40754i
$513$			37.1398i			0.0723972i
$514$			411.624i			0.800824i
$515$	308.802			0.599615
$516$		−	509.965i		−	0.988303i
$517$	−883.247	+	397.793i	−1.70841	+	0.769425i
$518$	−106.885			−0.206341
$519$		−	285.622i		−	0.550331i
$520$	−7.16771			−0.0137841
$521$	−164.014			−0.314806			−0.157403	−	0.987534i	$-0.550312\pi$
$521$	−164.014			−0.314806			−0.157403	+	0.987534i	$0.550312\pi$
$522$	−29.6235			−0.0567501
$523$			275.295i			0.526377i	0.964744	+	0.263189i	$0.0847741\pi$
$523$			275.295i			0.526377i	−0.964744	+	0.263189i	$0.915226\pi$
$524$		−	252.342i		−	0.481569i
$525$		−	22.9129i		−	0.0436436i
$526$	184.383			0.350539
$527$			364.759i			0.692142i
$528$	282.283	−	127.133i	0.534628	−	0.240783i
$529$	−365.468			−0.690865
$530$			101.212i			0.190966i
$531$	−98.6985			−0.185873
$532$	−74.4449			−0.139934
$533$	630.944			1.18376
$534$		−	507.959i		−	0.951233i
$535$		−	100.259i		−	0.187400i
$536$			7.30086i			0.0136210i
$537$	−150.728			−0.280685
$538$		−	595.000i		−	1.10595i
$539$	−70.2081	+	31.6200i	−0.130256	+	0.0586642i
$540$	−45.7399			−0.0847035
$541$			680.457i			1.25778i	0.777496	+	0.628888i	$0.216490\pi$
$541$			680.457i			1.25778i	−0.777496	+	0.628888i	$0.783510\pi$
$542$	−1508.41			−2.78304
$543$	−453.381			−0.834955
$544$	1370.88			2.51999
$545$			443.966i			0.814617i
$546$		−	231.923i		−	0.424768i
$547$			594.563i			1.08695i	0.839425	+	0.543476i	$0.182892\pi$
$547$			594.563i			1.08695i	−0.839425	+	0.543476i	$0.817108\pi$
$548$	901.304			1.64472
$549$			194.914i			0.355034i
$550$	−63.6286	−	141.279i	−0.115688	−	0.256871i
$551$	−25.0527			−0.0454677
$552$			3.95223i			0.00715984i
$553$	−269.239			−0.486870
$554$	60.3237			0.108888
$555$	−55.5384			−0.100069
$556$		−	592.557i		−	1.06575i
$557$		−	707.951i		−	1.27101i	−0.772098	−	0.635504i	$-0.780792\pi$
$557$		−	707.951i		−	1.27101i	0.772098	−	0.635504i	$-0.219208\pi$
$558$			101.339i			0.181611i
$559$	1343.59			2.40356
$560$			96.1324i			0.171665i
$561$	238.009	+	528.467i	0.424258	+	0.942010i
$562$	−527.934			−0.939385
$563$		−	667.042i		−	1.18480i	−0.805644	−	0.592400i	$-0.798181\pi$
$563$		−	667.042i		−	1.18480i	0.805644	−	0.592400i	$-0.201819\pi$
$564$	−600.457			−1.06464
$565$	283.762			0.502233
$566$	−1273.10			−2.24929
$567$			23.8118i			0.0419961i
$568$		−	12.6436i		−	0.0222598i
$569$		−	175.813i		−	0.308986i	−0.987994	−	0.154493i	$-0.950626\pi$
$569$		−	175.813i		−	0.308986i	0.987994	−	0.154493i	$-0.0493744\pi$
$570$	−77.9870			−0.136819
$571$		−	618.364i		−	1.08295i	−0.840717	−	0.541475i	$-0.817866\pi$
$571$		−	618.364i		−	1.08295i	0.840717	−	0.541475i	$-0.182134\pi$
$572$	−319.453	−	709.305i	−0.558485	−	1.24004i
$573$	−517.086			−0.902418
$574$		−	261.784i		−	0.456070i
$575$	63.9399			0.111200
$576$	185.872			0.322695
$577$	705.802			1.22323			0.611614	−	0.791157i	$-0.290521\pi$
$577$	705.802			1.22323			0.611614	+	0.791157i	$0.290521\pi$
$578$			1792.92i			3.10193i
$579$			360.350i			0.622366i
$580$		−	30.8539i		−	0.0531963i
$581$	−149.905			−0.258013
$582$			147.222i			0.252959i
$583$	161.145	−	72.5758i	0.276407	−	0.124487i
$584$	6.82075			0.0116794
$585$		−	120.510i		−	0.205999i
$586$	398.238			0.679587
$587$	678.178			1.15533			0.577664	−	0.816275i	$-0.303964\pi$
$587$	678.178			1.15533			0.577664	+	0.816275i	$0.303964\pi$
$588$	−47.7295			−0.0811726
$589$			85.7027i			0.145506i
$590$		−	207.249i		−	0.351270i
$591$			475.322i			0.804268i
$592$	233.015			0.393606
$593$			476.359i			0.803303i	0.915793	+	0.401652i	$0.131564\pi$
$593$			476.359i			0.803303i	−0.915793	+	0.401652i	$0.868436\pi$
$594$	66.1248	+	146.822i	0.111321	+	0.247174i
$595$	−179.971			−0.302472
$596$		−	703.221i		−	1.17990i
$597$	−188.941			−0.316484
$598$	647.197			1.08227
$599$	168.928			0.282017			0.141009	−	0.990008i	$-0.454965\pi$
$599$	168.928			0.282017			0.141009	+	0.990008i	$0.454965\pi$
$600$			1.54529i			0.00257549i
$601$			592.489i			0.985838i	0.870075	+	0.492919i	$0.164070\pi$
$601$			592.489i			0.985838i	−0.870075	+	0.492919i	$0.835930\pi$
$602$		−	557.467i		−	0.926025i
$603$	−122.748			−0.203563
$604$		−	641.775i		−	1.06254i
$605$	−179.312	+	202.613i	−0.296384	+	0.334898i
$606$	535.054			0.882928
$607$			191.087i			0.314805i	0.987535	+	0.157402i	$0.0503120\pi$
$607$			191.087i			0.314805i	−0.987535	+	0.157402i	$0.949688\pi$
$608$	322.098			0.529766
$609$	−16.0622			−0.0263748
$610$	−409.284			−0.670957
$611$		−	1582.01i		−	2.58921i
$612$			359.267i			0.587038i
$613$		−	501.012i		−	0.817311i	−0.912689	−	0.408655i	$-0.865998\pi$
$613$		−	501.012i		−	0.817311i	0.912689	−	0.408655i	$-0.134002\pi$
$614$	−562.970			−0.916889
$615$		−	136.026i		−	0.221180i
$616$	4.73498	−	2.13252i	0.00768666	−	0.00346188i
$617$	−374.764			−0.607397			−0.303699	−	0.952768i	$-0.598222\pi$
$617$	−374.764			−0.607397			−0.303699	+	0.952768i	$0.598222\pi$
$618$		−	673.867i		−	1.09040i
$619$	187.335			0.302642			0.151321	−	0.988485i	$-0.451647\pi$
$619$	187.335			0.302642			0.151321	+	0.988485i	$0.451647\pi$
$620$	−105.548			−0.170239
$621$	−66.4483			−0.107002
$622$			880.383i			1.41541i
$623$		−	275.421i		−	0.442089i
$624$			505.606i			0.810265i
$625$	25.0000			0.0400000
$626$			1007.79i			1.60988i
$627$	55.9219	+	124.167i	0.0891896	+	0.198034i
$628$	409.667			0.652335
$629$			436.231i			0.693530i
$630$	−50.0005			−0.0793659
$631$	481.681			0.763361			0.381681	−	0.924294i	$-0.375345\pi$
$631$	481.681			0.763361			0.381681	+	0.924294i	$0.375345\pi$
$632$	18.1580			0.0287311
$633$			496.573i			0.784476i
$634$			944.858i			1.49031i
$635$			344.348i			0.542280i
$636$	109.551			0.172250
$637$		−	125.752i		−	0.197412i
$638$	−99.0386	+	44.6046i	−0.155233	+	0.0699131i
$639$	212.575			0.332668
$640$		−	12.7662i		−	0.0199471i
$641$	−330.034			−0.514874			−0.257437	−	0.966295i	$-0.582878\pi$
$641$	−330.034			−0.514874			−0.257437	+	0.966295i	$0.582878\pi$
$642$	−218.785			−0.340786
$643$	388.572			0.604311			0.302156	−	0.953259i	$-0.402294\pi$
$643$	388.572			0.604311			0.302156	+	0.953259i	$0.402294\pi$
$644$		−	133.192i		−	0.206820i
$645$		−	289.666i		−	0.449094i
$646$			612.555i			0.948227i
$647$	808.882			1.25020			0.625102	−	0.780543i	$-0.285057\pi$
$647$	808.882			1.25020			0.625102	+	0.780543i	$0.285057\pi$
$648$		−	1.60591i		−	0.00247826i
$649$	−329.973	+	148.612i	−0.508433	+	0.228986i
$650$	253.049			0.389306
$651$			54.9474i			0.0844045i
$652$	1150.73			1.76492
$653$	572.165			0.876210			0.438105	−	0.898924i	$-0.355650\pi$
$653$	572.165			0.876210			0.438105	+	0.898924i	$0.355650\pi$
$654$	968.823			1.48138
$655$		−	143.333i		−	0.218829i
$656$			570.704i			0.869976i
$657$			114.676i			0.174545i
$658$	−656.388			−0.997551
$659$			301.078i			0.456871i	0.973559	+	0.228435i	$0.0733610\pi$
$659$			301.078i			0.456871i	−0.973559	+	0.228435i	$0.926639\pi$
$660$	−152.920	+	68.8712i	−0.231696	+	0.104350i
$661$	−353.235			−0.534395			−0.267198	−	0.963642i	$-0.586098\pi$
$661$	−353.235			−0.534395			−0.267198	+	0.963642i	$0.586098\pi$
$662$			607.897i			0.918273i
$663$	−946.552			−1.42768
$664$	10.1099			0.0152258
$665$	−42.2855			−0.0635872
$666$			121.196i			0.181976i
$667$		−	44.8227i		−	0.0672005i
$668$			1177.54i			1.76278i
$669$	549.801			0.821825
$670$		−	257.749i		−	0.384701i
$671$	293.484	+	651.643i	0.437383	+	0.971152i
$672$	206.509			0.307306
$673$			1088.23i			1.61699i	0.588503	+	0.808495i	$0.299717\pi$
$673$			1088.23i			1.61699i	−0.588503	+	0.808495i	$0.700283\pi$
$674$	823.409			1.22167
$675$	−25.9808			−0.0384900
$676$	605.159			0.895205
$677$			211.906i			0.313008i	0.987677	+	0.156504i	$0.0500224\pi$
$677$			211.906i			0.313008i	−0.987677	+	0.156504i	$0.949978\pi$
$678$		−	619.225i		−	0.913311i
$679$			79.8258i			0.117564i
$680$	12.1376			0.0178494
$681$		−	261.357i		−	0.383783i
$682$	152.588	+	338.801i	0.223736	+	0.496776i
$683$	996.085			1.45840			0.729198	−	0.684302i	$-0.239893\pi$
$683$	996.085			1.45840			0.729198	+	0.684302i	$0.239893\pi$
$684$			84.4125i			0.123410i
$685$	511.951			0.747374
$686$	−52.1754			−0.0760575
$687$	684.159			0.995865
$688$			1215.31i			1.76644i
$689$			288.632i			0.418914i
$690$		−	139.530i		−	0.202217i
$691$	405.344			0.586605			0.293302	−	0.956020i	$-0.405246\pi$
$691$	405.344			0.586605			0.293302	+	0.956020i	$0.405246\pi$
$692$		−	649.171i		−	0.938108i
$693$	35.8537	+	79.6085i	0.0517369	+	0.114875i
$694$	−888.006			−1.27955
$695$		−	336.579i		−	0.484286i
$696$	1.08327			0.00155642
$697$	−1068.42			−1.53289
$698$	710.187			1.01746
$699$		−	314.963i		−	0.450591i
$700$		−	52.0771i		−	0.0743959i
$701$			249.714i			0.356225i	0.984010	+	0.178113i	$0.0569992\pi$
$701$			249.714i			0.356225i	−0.984010	+	0.178113i	$0.943001\pi$
$702$	−262.976			−0.374610
$703$			102.496i			0.145797i
$704$	621.416	−	279.870i	0.882693	−	0.397543i
$705$	−341.066			−0.483782
$706$			690.200i			0.977620i
$707$	290.113			0.410344
$708$	−224.325			−0.316844
$709$	1067.72			1.50595			0.752975	−	0.658050i	$-0.228618\pi$
$709$	1067.72			1.50595			0.752975	+	0.658050i	$0.228618\pi$
$710$			446.369i			0.628689i
$711$			305.288i			0.429379i
$712$			18.5750i			0.0260885i
$713$	−153.334			−0.215055
$714$			392.733i			0.550046i
$715$	−181.453	−	402.893i	−0.253780	−	0.563487i
$716$	−342.579			−0.478463
$717$			348.568i			0.486148i
$718$	−1028.46			−1.43239
$719$	1009.20			1.40362			0.701808	−	0.712367i	$-0.252377\pi$
$719$	1009.20			1.40362			0.701808	+	0.712367i	$0.252377\pi$
$720$	109.004			0.151394
$721$		−	365.379i		−	0.506767i
$722$		−	873.088i		−	1.20926i
$723$		−	487.205i		−	0.673865i
$724$	−1030.46			−1.42329
$725$		−	17.5253i		−	0.0241729i
$726$	442.143	+	391.295i	0.609012	+	0.538974i
$727$	1013.00			1.39339			0.696695	−	0.717367i	$-0.254653\pi$
$727$	1013.00			1.39339			0.696695	+	0.717367i	$0.254653\pi$
$728$			8.48095i			0.0116497i
$729$	27.0000			0.0370370
$730$	−240.800			−0.329863
$731$	−2275.20			−3.11245
$732$			443.006i			0.605199i
$733$		−	465.649i		−	0.635265i	−0.948214	−	0.317633i	$-0.897112\pi$
$733$		−	465.649i		−	0.635265i	0.948214	−	0.317633i	$-0.102888\pi$
$734$			193.833i			0.264077i
$735$	−27.1109			−0.0368856
$736$			576.278i			0.782986i
$737$	−410.377	+	184.824i	−0.556821	+	0.250778i
$738$	−296.835			−0.402216
$739$			393.093i			0.531925i	0.963983	+	0.265963i	$0.0856897\pi$
$739$			393.093i			0.531925i	−0.963983	+	0.265963i	$0.914310\pi$
$740$	−126.229			−0.170580
$741$	−222.399			−0.300134
$742$	119.756			0.161396
$743$			71.5252i			0.0962654i	0.998841	+	0.0481327i	$0.0153270\pi$
$743$			71.5252i			0.0962654i	−0.998841	+	0.0481327i	$0.984673\pi$
$744$		−	3.70576i		−	0.00498087i
$745$		−	399.437i		−	0.536157i
$746$	−1022.74			−1.37097
$747$			169.977i			0.227546i
$748$	540.954	+	1201.12i	0.723200	+	1.60577i
$749$	−118.628			−0.158382
$750$		−	54.5550i		−	0.0727400i
$751$	−756.656			−1.00753			−0.503766	−	0.863840i	$-0.668052\pi$
$751$	−756.656			−1.00753			−0.503766	+	0.863840i	$0.668052\pi$
$752$	1430.96			1.90288
$753$	559.324			0.742794
$754$		−	177.391i		−	0.235266i
$755$		−	364.535i		−	0.482828i
$756$			54.1202i			0.0715875i
$757$	−288.841			−0.381560			−0.190780	−	0.981633i	$-0.561102\pi$
$757$	−288.841			−0.381560			−0.190780	+	0.981633i	$0.561102\pi$
$758$		−	314.541i		−	0.414962i
$759$	−222.153	+	100.052i	−0.292691	+	0.131821i
$760$	2.85182			0.00375240
$761$		−	855.683i		−	1.12442i	−0.826995	−	0.562210i	$-0.809951\pi$
$761$		−	855.683i		−	1.12442i	0.826995	−	0.562210i	$-0.190049\pi$
$762$	751.436			0.986136
$763$	525.308			0.688477
$764$	−1175.25			−1.53828
$765$			204.068i			0.266755i
$766$		−	689.626i		−	0.900295i
$767$		−	591.024i		−	0.770565i
$768$	−457.112			−0.595198
$769$			677.890i			0.881522i	0.897625	+	0.440761i	$0.145291\pi$
$769$			677.890i			0.881522i	−0.897625	+	0.440761i	$0.854709\pi$
$770$	−167.164	+	75.2864i	−0.217096	+	0.0977746i
$771$	253.071			0.328237
$772$			819.015i			1.06090i
$773$	997.874			1.29091			0.645455	−	0.763798i	$-0.276668\pi$
$773$	997.874			1.29091			0.645455	+	0.763798i	$0.276668\pi$
$774$	−632.108			−0.816677
$775$	−59.9525			−0.0773580
$776$		−	5.38362i		−	0.00693765i
$777$			65.7139i			0.0845739i
$778$		−	1166.10i		−	1.49885i
$779$	−251.034			−0.322252
$780$		−	273.898i		−	0.351152i
$781$	710.689	−	320.077i	0.909973	−	0.409829i
$782$	−1095.95			−1.40147
$783$			18.2129i			0.0232604i
$784$	113.745			0.145083
$785$	232.695			0.296427
$786$	−312.782			−0.397941
$787$		−	541.217i		−	0.687697i	−0.939025	−	0.343848i	$-0.888269\pi$
$787$		−	541.217i		−	0.687697i	0.939025	−	0.343848i	$-0.111731\pi$
$788$			1080.33i			1.37097i
$789$		−	113.361i		−	0.143677i
$790$	−641.051			−0.811458
$791$		−	335.751i		−	0.424464i
$792$	−2.41805	−	5.36896i	−0.00305309	−	0.00677899i
$793$	−1167.18			−1.47185
$794$		−	2115.34i		−	2.66415i
$795$	62.2263			0.0782721
$796$	−429.431			−0.539487
$797$	638.655			0.801324			0.400662	−	0.916226i	$-0.368780\pi$
$797$	638.655			0.801324			0.400662	+	0.916226i	$0.368780\pi$
$798$			92.2754i			0.115633i
$799$			2678.93i			3.35285i
$800$			225.320i			0.281650i
$801$	−312.299			−0.389886
$802$		−	946.451i		−	1.18011i
$803$	172.670	+	383.391i	0.215031	+	0.477448i
$804$	−278.986			−0.346998
$805$		−	75.6547i		−	0.0939810i
$806$	−606.836			−0.752899
$807$	−365.813			−0.453300
$808$	−19.5658			−0.0242151
$809$		−	657.857i		−	0.813173i	−0.913612	−	0.406587i	$-0.866719\pi$
$809$		−	657.857i		−	0.813173i	0.913612	−	0.406587i	$-0.133281\pi$
$810$			56.6952i			0.0699941i
$811$		−	757.424i		−	0.933939i	−0.884273	−	0.466969i	$-0.845346\pi$
$811$		−	757.424i		−	0.933939i	0.884273	−	0.466969i	$-0.154654\pi$
$812$	−36.5068			−0.0449591
$813$			927.384i			1.14069i
$814$	182.486	+	405.187i	0.224185	+	0.497773i
$815$	653.628			0.801997
$816$		−	856.179i		−	1.04924i
$817$	−534.575			−0.654315
$818$	1095.47			1.33921
$819$	−142.589			−0.174101
$820$		−	309.164i		−	0.377029i
$821$			829.383i			1.01021i	0.863058	+	0.505105i	$0.168546\pi$
$821$			829.383i			1.01021i	−0.863058	+	0.505105i	$0.831454\pi$
$822$		−	1117.18i		−	1.35910i
$823$	−1200.92			−1.45920			−0.729599	−	0.683875i	$-0.760293\pi$
$823$	−1200.92			−1.45920			−0.729599	+	0.683875i	$0.760293\pi$
$824$			24.6419i			0.0299052i
$825$	−86.8600	+	39.1196i	−0.105285	+	0.0474177i
$826$	−245.221			−0.296877
$827$		−	1257.92i		−	1.52107i	−0.649299	−	0.760533i	$-0.724938\pi$
$827$		−	1257.92i		−	1.52107i	0.649299	−	0.760533i	$-0.275062\pi$
$828$	−151.026			−0.182398
$829$	1115.37			1.34544			0.672720	−	0.739897i	$-0.265126\pi$
$829$	1115.37			1.34544			0.672720	+	0.739897i	$0.265126\pi$
$830$	−356.921			−0.430025
$831$		−	37.0877i		−	0.0446302i
$832$			1113.03i			1.33778i
$833$			212.945i			0.255636i
$834$	−734.483			−0.880675
$835$			668.854i			0.801022i
$836$	127.101	+	282.212i	0.152035	+	0.337574i
$837$	62.3045			0.0744378
$838$		−	1453.11i		−	1.73402i
$839$	−366.627			−0.436981			−0.218490	−	0.975839i	$-0.570113\pi$
$839$	−366.627			−0.436981			−0.218490	+	0.975839i	$0.570113\pi$
$840$	1.82841			0.00217668
$841$	828.714			0.985392
$842$			1902.32i			2.25929i
$843$			324.580i			0.385029i
$844$			1128.63i			1.33724i
$845$	343.737			0.406789
$846$			744.275i			0.879757i
$847$	239.735	+	212.165i	0.283040	+	0.250490i
$848$	−261.074			−0.307871
$849$			782.713i			0.921924i
$850$	−428.507			−0.504125
$851$	−183.379			−0.215486
$852$	483.147			0.567074
$853$			1428.45i			1.67462i	0.546729	+	0.837310i	$0.315873\pi$
$853$			1428.45i			1.67462i	−0.546729	+	0.837310i	$0.684127\pi$
$854$			484.271i			0.567062i
$855$			47.9473i			0.0560787i
$856$	8.00051			0.00934639
$857$		−	1.81683i		−	0.00211999i	−0.999999	−	0.00105999i	$-0.999663\pi$
$857$		−	1.81683i		−	0.00211999i	0.999999	−	0.00105999i	$-0.000337407\pi$
$858$	−879.193	+	395.967i	−1.02470	+	0.461500i
$859$	−637.516			−0.742161			−0.371080	−	0.928601i	$-0.621013\pi$
$859$	−637.516			−0.742161			−0.371080	+	0.928601i	$0.621013\pi$
$860$		−	658.361i		−	0.765537i
$861$	−160.948			−0.186931
$862$	356.626			0.413719
$863$	246.245			0.285337			0.142668	−	0.989771i	$-0.454432\pi$
$863$	246.245			0.285337			0.142668	+	0.989771i	$0.454432\pi$
$864$		−	234.160i		−	0.271018i
$865$		−	368.736i		−	0.426285i
$866$		−	28.6959i		−	0.0331362i
$867$	1102.30			1.27140
$868$			124.886i			0.143878i
$869$	459.677	+	1020.65i	0.528972	+	1.17451i
$870$	−38.2438			−0.0439584
$871$		−	735.037i		−	0.843900i
$872$	−35.4279			−0.0406283
$873$	90.5140			0.103682
$874$	−257.501			−0.294623
$875$		−	29.5804i		−	0.0338062i
$876$			260.640i			0.297534i
$877$		−	32.5000i		−	0.0370582i	−0.999828	−	0.0185291i	$-0.994102\pi$
$877$		−	32.5000i		−	0.0370582i	0.999828	−	0.0185291i	$-0.00589833\pi$
$878$	−212.659			−0.242208
$879$		−	244.841i		−	0.278545i
$880$	364.426	−	164.129i	0.414121	−	0.186510i
$881$	916.511			1.04031			0.520154	−	0.854072i	$-0.325875\pi$
$881$	916.511			1.04031			0.520154	+	0.854072i	$0.325875\pi$
$882$			59.1614i			0.0670764i
$883$	−956.269			−1.08298			−0.541488	−	0.840708i	$-0.682139\pi$
$883$	−956.269			−1.08298			−0.541488	+	0.840708i	$0.682139\pi$
$884$	−2151.36			−2.43366
$885$	−127.419			−0.143977
$886$		−	17.6655i		−	0.0199385i
$887$			252.970i			0.285197i	0.989781	+	0.142599i	$0.0455458\pi$
$887$			252.970i			0.285197i	−0.989781	+	0.142599i	$0.954454\pi$
$888$		−	4.43188i		−	0.00499086i
$889$	407.438			0.458310
$890$		−	655.772i		−	0.736822i
$891$	90.2675	−	40.6543i	0.101310	−	0.0456277i
$892$	1249.61			1.40090
$893$			629.434i			0.704854i
$894$	−871.652			−0.975002
$895$	−194.589			−0.217418
$896$	−15.1051			−0.0168584
$897$		−	397.904i		−	0.443594i
$898$			1711.34i			1.90572i
$899$			42.0275i			0.0467492i
$900$	−59.0499			−0.0656110
$901$		−	488.761i		−	0.542465i
$902$	−992.393	+	446.949i	−1.10021	+	0.495509i
$903$	−342.737			−0.379554
$904$			22.6438i			0.0250484i
$905$	−585.312			−0.646753
$906$	−795.489			−0.878023
$907$	1264.42			1.39407			0.697036	−	0.717036i	$-0.254502\pi$
$907$	1264.42			1.39407			0.697036	+	0.717036i	$0.254502\pi$
$908$		−	594.020i		−	0.654207i
$909$		−	328.957i		−	0.361889i
$910$		−	299.412i		−	0.329024i
$911$	−587.851			−0.645281			−0.322640	−	0.946522i	$-0.604570\pi$
$911$	−587.851			−0.645281			−0.322640	+	0.946522i	$0.604570\pi$
$912$		−	201.166i		−	0.220576i
$913$	255.936	+	568.273i	0.280324	+	0.622424i
$914$	−202.044			−0.221054
$915$			251.632i			0.275008i
$916$	1554.98			1.69758
$917$	−169.594			−0.184945
$918$	445.317			0.485095
$919$		−	1315.97i		−	1.43196i	−0.698120	−	0.715981i	$-0.745980\pi$
$919$		−	1315.97i		−	1.43196i	0.698120	−	0.715981i	$-0.254020\pi$
$920$			5.10231i			0.00554599i
$921$			346.120i			0.375809i
$922$	−1052.41			−1.14145
$923$			1272.93i			1.37913i
$924$	81.4895	+	180.937i	0.0881921	+	0.195819i
$925$	−71.6998			−0.0775132
$926$		−	1713.99i		−	1.85096i
$927$	−414.301			−0.446926
$928$	157.953			0.170207
$929$	−97.8069			−0.105282			−0.0526410	−	0.998614i	$-0.516764\pi$
$929$	−97.8069			−0.105282			−0.0526410	+	0.998614i	$0.516764\pi$
$930$			130.828i			0.140676i
$931$			50.0329i			0.0537410i
$932$		−	715.859i		−	0.768089i
$933$	541.269			0.580139
$934$			183.876i			0.196869i
$935$	307.268	+	682.249i	0.328629	+	0.729678i
$936$	9.61649			0.0102740
$937$			112.303i			0.119854i	0.998203	+	0.0599269i	$0.0190868\pi$
$937$			112.303i			0.119854i	−0.998203	+	0.0599269i	$0.980913\pi$
$938$	−304.973			−0.325131
$939$	619.599			0.659849
$940$	−775.186			−0.824666
$941$		−	1512.97i		−	1.60783i	−0.594742	−	0.803917i	$-0.702746\pi$
$941$		−	1512.97i		−	1.60783i	0.594742	−	0.803917i	$-0.297254\pi$
$942$		−	507.788i		−	0.539053i
$943$		−	449.135i		−	0.476284i
$944$	534.595			0.566308
$945$			30.7409i			0.0325300i
$946$	−2113.29	+	951.774i	−2.23392	+	1.00610i
$947$	1267.20			1.33812			0.669061	−	0.743207i	$-0.266696\pi$
$947$	1267.20			1.33812			0.669061	+	0.743207i	$0.266696\pi$
$948$			693.869i			0.731930i
$949$	−686.701			−0.723605
$950$	−100.681			−0.105980
$951$	580.909			0.610840
$952$		−	14.3614i		−	0.0150855i
$953$			1026.87i			1.07751i	0.842463	+	0.538755i	$0.181105\pi$
$953$			1026.87i			1.07751i	−0.842463	+	0.538755i	$0.818895\pi$
$954$		−	135.790i		−	0.142338i
$955$	−667.555			−0.699010
$956$			792.237i			0.828700i
$957$	27.4234	+	60.8901i	0.0286556	+	0.0636260i
$958$	1005.47			1.04956
$959$		−	605.749i		−	0.631646i
$960$	239.960			0.249958
$961$	−817.228			−0.850393
$962$	−725.742			−0.754409
$963$			134.511i			0.139679i
$964$		−	1107.34i		−	1.14869i
$965$			465.210i			0.482082i
$966$	−165.094			−0.170904
$967$		−	1392.54i		−	1.44006i	−0.693940	−	0.720032i	$-0.744127\pi$
$967$		−	1392.54i		−	1.44006i	0.693940	−	0.720032i	$-0.255873\pi$
$968$	−16.1682	−	14.3089i	−0.0167027	−	0.0147819i
$969$	376.605			0.388654
$970$			190.063i			0.195942i
$971$	−652.774			−0.672270			−0.336135	−	0.941814i	$-0.609120\pi$
$971$	−652.774			−0.672270			−0.336135	+	0.941814i	$0.609120\pi$
$972$	61.3665			0.0631343
$973$	−398.246			−0.409297
$974$		−	498.850i		−	0.512166i
$975$		−	155.577i		−	0.159566i
$976$		−	1055.74i		−	1.08170i
$977$	1298.76			1.32933			0.664665	−	0.747141i	$-0.268574\pi$
$977$	1298.76			1.32933			0.664665	+	0.747141i	$0.268574\pi$
$978$		−	1426.35i		−	1.45843i
$979$	−1044.09	+	470.232i	−1.06649	+	0.480319i
$980$	−61.6185			−0.0628760
$981$		−	595.643i		−	0.607180i
$982$	329.373			0.335411
$983$	−847.451			−0.862107			−0.431054	−	0.902326i	$-0.641858\pi$
$983$	−847.451			−0.862107			−0.431054	+	0.902326i	$0.641858\pi$
$984$	10.8547			0.0110312
$985$			613.638i			0.622983i
$986$			300.389i			0.304654i
$987$			403.555i			0.408870i
$988$	−505.477			−0.511616
$989$		−	956.430i		−	0.967067i
$990$	85.3668	+	189.546i	0.0862291	+	0.191460i
$991$	1293.66			1.30540			0.652702	−	0.757615i	$-0.273635\pi$
$991$	1293.66			1.30540			0.652702	+	0.757615i	$0.273635\pi$
$992$		−	540.340i		−	0.544698i
$993$	373.742			0.376376
$994$	528.151			0.531339
$995$	−243.922			−0.245147
$996$			386.329i			0.387880i
$997$			734.756i			0.736967i	0.929634	+	0.368484i	$0.120123\pi$
$997$			734.756i			0.736967i	−0.929634	+	0.368484i	$0.879877\pi$
$998$		−	441.370i		−	0.442255i
$999$	74.5126			0.0745872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.19	✓	96
11.10	odd	2	inner	1155.3.b.a.736.78	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.19	✓	96	1.1	even	1	trivial
1155.3.b.a.736.78	yes	96	11.10	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1155.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.81721i q^{2} -1.73205 q^{3} -3.93666 q^{4} -2.23607 q^{5} +4.87955i q^{6} +2.64575i q^{7} -0.178435i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.81721i q^{2} -1.73205 q^{3} -3.93666 q^{4} -2.23607 q^{5} +4.87955i q^{6} +2.64575i q^{7} -0.178435i q^{8} +3.00000 q^{9} +6.29947i q^{10} +(10.0297 - 4.51714i) q^{11} +6.81850 q^{12} +17.9645i q^{13} +7.45363 q^{14} +3.87298 q^{15} -16.2493 q^{16} -30.4206i q^{17} -8.45162i q^{18} -7.14756i q^{19} +8.80264 q^{20} -4.58258i q^{21} +(-12.7257 - 28.2558i) q^{22} +12.7880 q^{23} +0.309058i q^{24} +5.00000 q^{25} +50.6098 q^{26} -5.19615 q^{27} -10.4154i q^{28} -3.50507i q^{29} -10.9110i q^{30} -11.9905 q^{31} +45.0640i q^{32} +(-17.3720 + 7.82392i) q^{33} -85.7013 q^{34} -5.91608i q^{35} -11.8100 q^{36} -14.3400 q^{37} -20.1362 q^{38} -31.1155i q^{39} +0.398993i q^{40} -35.1217i q^{41} -12.9101 q^{42} -74.7913i q^{43} +(-39.4837 + 17.7825i) q^{44} -6.70820 q^{45} -36.0264i q^{46} -88.0629 q^{47} +28.1447 q^{48} -7.00000 q^{49} -14.0860i q^{50} +52.6901i q^{51} -70.7202i q^{52} +16.0668 q^{53} +14.6386i q^{54} +(-22.4272 + 10.1006i) q^{55} +0.472095 q^{56} +12.3799i q^{57} -9.87451 q^{58} -32.8995 q^{59} -15.2466 q^{60} +64.9712i q^{61} +33.7797i q^{62} +7.93725i q^{63} +61.9574 q^{64} -40.1699i q^{65} +(22.0416 + 48.9405i) q^{66} -40.9161 q^{67} +119.756i q^{68} -22.1494 q^{69} -16.6668 q^{70} +70.8583 q^{71} -0.535305i q^{72} +38.2254i q^{73} +40.3986i q^{74} -8.66025 q^{75} +28.1375i q^{76} +(11.9512 + 26.5362i) q^{77} -87.6587 q^{78} +101.763i q^{79} +36.3346 q^{80} +9.00000 q^{81} -98.9451 q^{82} +56.6589i q^{83} +18.0401i q^{84} +68.0226i q^{85} -210.703 q^{86} +6.07096i q^{87} +(-0.806016 - 1.78965i) q^{88} -104.100 q^{89} +18.8984i q^{90} -47.5296 q^{91} -50.3419 q^{92} +20.7682 q^{93} +248.092i q^{94} +15.9824i q^{95} -78.0532i q^{96} +30.1713 q^{97} +19.7205i q^{98} +(30.0892 - 13.5514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 96 * q - 216 * q^4 + 288 * q^9	\( 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) \) 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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