LMFDB - Embedded newform 1155.3.b.a.736.9

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			736.9
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.88

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57619i q^{2} -1.73205 q^{3} -8.78910 q^{4} +2.23607 q^{5} +6.19413i q^{6} +2.64575i q^{7} +17.1267i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.57619i q^{2} -1.73205 q^{3} -8.78910 q^{4} +2.23607 q^{5} +6.19413i q^{6} +2.64575i q^{7} +17.1267i q^{8} +3.00000 q^{9} -7.99659i q^{10} +(-7.82898 - 7.72703i) q^{11} +15.2232 q^{12} -4.15358i q^{13} +9.46170 q^{14} -3.87298 q^{15} +26.0919 q^{16} -22.8459i q^{17} -10.7286i q^{18} -34.4563i q^{19} -19.6530 q^{20} -4.58258i q^{21} +(-27.6333 + 27.9979i) q^{22} -10.0287 q^{23} -29.6643i q^{24} +5.00000 q^{25} -14.8540 q^{26} -5.19615 q^{27} -23.2538i q^{28} +9.36715i q^{29} +13.8505i q^{30} +1.45445 q^{31} -24.8026i q^{32} +(13.5602 + 13.3836i) q^{33} -81.7011 q^{34} +5.91608i q^{35} -26.3673 q^{36} +33.5415 q^{37} -123.222 q^{38} +7.19421i q^{39} +38.2965i q^{40} +5.68138i q^{41} -16.3881 q^{42} +51.8723i q^{43} +(68.8097 + 67.9137i) q^{44} +6.70820 q^{45} +35.8645i q^{46} +2.85278 q^{47} -45.1925 q^{48} -7.00000 q^{49} -17.8809i q^{50} +39.5702i q^{51} +36.5062i q^{52} -76.0550 q^{53} +18.5824i q^{54} +(-17.5061 - 17.2782i) q^{55} -45.3130 q^{56} +59.6801i q^{57} +33.4987 q^{58} +20.8061 q^{59} +34.0400 q^{60} +109.170i q^{61} -5.20137i q^{62} +7.93725i q^{63} +15.6688 q^{64} -9.28769i q^{65} +(47.8623 - 48.4938i) q^{66} -31.7208 q^{67} +200.795i q^{68} +17.3702 q^{69} +21.1570 q^{70} -119.688 q^{71} +51.3801i q^{72} +68.8555i q^{73} -119.951i q^{74} -8.66025 q^{75} +302.840i q^{76} +(20.4438 - 20.7135i) q^{77} +25.7278 q^{78} +13.4901i q^{79} +58.3433 q^{80} +9.00000 q^{81} +20.3177 q^{82} -116.301i q^{83} +40.2767i q^{84} -51.0850i q^{85} +185.505 q^{86} -16.2244i q^{87} +(132.339 - 134.085i) q^{88} -56.6702 q^{89} -23.9898i q^{90} +10.9893 q^{91} +88.1434 q^{92} -2.51918 q^{93} -10.2021i q^{94} -77.0466i q^{95} +42.9594i q^{96} -34.8154 q^{97} +25.0333i q^{98} +(-23.4869 - 23.1811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.57619i		−	1.78809i	−0.447974	−	0.894046i	$-0.647854\pi$
$2$		−	3.57619i		−	1.78809i	0.447974	−	0.894046i	$-0.352146\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−8.78910			−2.19728
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$			6.19413i			1.03236i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			17.1267i			2.14084i
$9$	3.00000			0.333333
$10$		−	7.99659i		−	0.799659i
$11$	−7.82898	−	7.72703i	−0.711726	−	0.702458i
$11$	−7.82898	−	7.72703i	−0.711726	−	0.702458i
$12$	15.2232			1.26860
$13$		−	4.15358i		−	0.319506i	−0.987157	−	0.159753i	$-0.948930\pi$
$13$		−	4.15358i		−	0.319506i	0.987157	−	0.159753i	$-0.0510698\pi$
$14$	9.46170			0.675836
$15$	−3.87298			−0.258199
$16$	26.0919			1.63074
$17$		−	22.8459i		−	1.34388i	−0.740608	−	0.671938i	$-0.765462\pi$
$17$		−	22.8459i		−	1.34388i	0.740608	−	0.671938i	$-0.234538\pi$
$18$		−	10.7286i		−	0.596031i
$19$		−	34.4563i		−	1.81349i	−0.421680	−	0.906745i	$-0.638559\pi$
$19$		−	34.4563i		−	1.81349i	0.421680	−	0.906745i	$-0.361441\pi$
$20$	−19.6530			−0.982651
$21$		−	4.58258i		−	0.218218i
$22$	−27.6333	+	27.9979i	−1.25606	+	1.27263i
$23$	−10.0287			−0.436031			−0.218015	−	0.975945i	$-0.569958\pi$
$23$	−10.0287			−0.436031			−0.218015	+	0.975945i	$0.569958\pi$
$24$		−	29.6643i		−	1.23601i
$25$	5.00000			0.200000
$26$	−14.8540			−0.571307
$27$	−5.19615			−0.192450
$28$		−	23.2538i		−	0.830492i
$29$			9.36715i			0.323005i	0.986872	+	0.161503i	$0.0516340\pi$
$29$			9.36715i			0.323005i	−0.986872	+	0.161503i	$0.948366\pi$
$30$			13.8505i			0.461684i
$31$	1.45445			0.0469177			0.0234588	−	0.999725i	$-0.492532\pi$
$31$	1.45445			0.0469177			0.0234588	+	0.999725i	$0.492532\pi$
$32$		−	24.8026i		−	0.775082i
$33$	13.5602	+	13.3836i	0.410915	+	0.405564i
$34$	−81.7011			−2.40297
$35$			5.91608i			0.169031i
$36$	−26.3673			−0.732425
$37$	33.5415			0.906527			0.453263	−	0.891377i	$-0.350260\pi$
$37$	33.5415			0.906527			0.453263	+	0.891377i	$0.350260\pi$
$38$	−123.222			−3.24269
$39$			7.19421i			0.184467i
$40$			38.2965i			0.957413i
$41$			5.68138i			0.138570i	0.997597	+	0.0692851i	$0.0220718\pi$
$41$			5.68138i			0.138570i	−0.997597	+	0.0692851i	$0.977928\pi$
$42$	−16.3881			−0.390194
$43$			51.8723i			1.20633i	0.797615	+	0.603167i	$0.206095\pi$
$43$			51.8723i			1.20633i	−0.797615	+	0.603167i	$0.793905\pi$
$44$	68.8097	+	67.9137i	1.56386	+	1.54349i
$45$	6.70820			0.149071
$46$			35.8645i			0.779664i
$47$	2.85278			0.0606974			0.0303487	−	0.999539i	$-0.490338\pi$
$47$	2.85278			0.0606974			0.0303487	+	0.999539i	$0.490338\pi$
$48$	−45.1925			−0.941511
$49$	−7.00000			−0.142857
$50$		−	17.8809i		−	0.357619i
$51$			39.5702i			0.775887i
$52$			36.5062i			0.702043i
$53$	−76.0550			−1.43500			−0.717500	−	0.696559i	$-0.754714\pi$
$53$	−76.0550			−1.43500			−0.717500	+	0.696559i	$0.754714\pi$
$54$			18.5824i			0.344119i
$55$	−17.5061	−	17.2782i	−0.318293	−	0.314149i
$56$	−45.3130			−0.809161
$57$			59.6801i			1.04702i
$58$	33.4987			0.577563
$59$	20.8061			0.352645			0.176323	−	0.984332i	$-0.443580\pi$
$59$	20.8061			0.352645			0.176323	+	0.984332i	$0.443580\pi$
$60$	34.0400			0.567334
$61$			109.170i			1.78967i	0.446394	+	0.894836i	$0.352708\pi$
$61$			109.170i			1.78967i	−0.446394	+	0.894836i	$0.647292\pi$
$62$		−	5.20137i		−	0.0838931i
$63$			7.93725i			0.125988i
$64$	15.6688			0.244826
$65$		−	9.28769i		−	0.142888i
$66$	47.8623	−	48.4938i	0.725186	−	0.734754i
$67$	−31.7208			−0.473445			−0.236722	−	0.971577i	$-0.576073\pi$
$67$	−31.7208			−0.473445			−0.236722	+	0.971577i	$0.576073\pi$
$68$			200.795i			2.95287i
$69$	17.3702			0.251743
$70$	21.1570			0.302243
$71$	−119.688			−1.68574			−0.842871	−	0.538115i	$-0.819137\pi$
$71$	−119.688			−1.68574			−0.842871	+	0.538115i	$0.819137\pi$
$72$			51.3801i			0.713613i
$73$			68.8555i			0.943226i	0.881806	+	0.471613i	$0.156328\pi$
$73$			68.8555i			0.943226i	−0.881806	+	0.471613i	$0.843672\pi$
$74$		−	119.951i		−	1.62095i
$75$	−8.66025			−0.115470
$76$			302.840i			3.98474i
$77$	20.4438	−	20.7135i	0.265504	−	0.269007i
$78$	25.7278			0.329844
$79$			13.4901i			0.170761i	0.996348	+	0.0853803i	$0.0272105\pi$
$79$			13.4901i			0.170761i	−0.996348	+	0.0853803i	$0.972789\pi$
$80$	58.3433			0.729291
$81$	9.00000			0.111111
$82$	20.3177			0.247776
$83$		−	116.301i		−	1.40122i	−0.713546	−	0.700609i	$-0.752912\pi$
$83$		−	116.301i		−	1.40122i	0.713546	−	0.700609i	$-0.247088\pi$
$84$			40.2767i			0.479485i
$85$		−	51.0850i		−	0.600999i
$86$	185.505			2.15704
$87$		−	16.2244i		−	0.186487i
$88$	132.339	−	134.085i	1.50385	−	1.52369i
$89$	−56.6702			−0.636744			−0.318372	−	0.947966i	$-0.603136\pi$
$89$	−56.6702			−0.636744			−0.318372	+	0.947966i	$0.603136\pi$
$90$		−	23.9898i		−	0.266553i
$91$	10.9893			0.120762
$92$	88.1434			0.958080
$93$	−2.51918			−0.0270879
$94$		−	10.2021i		−	0.108533i
$95$		−	77.0466i		−	0.811017i
$96$			42.9594i			0.447494i
$97$	−34.8154			−0.358922			−0.179461	−	0.983765i	$-0.557435\pi$
$97$	−34.8154			−0.358922			−0.179461	+	0.983765i	$0.557435\pi$
$98$			25.0333i			0.255442i
$99$	−23.4869	−	23.1811i	−0.237242	−	0.234153i
$100$	−43.9455			−0.439455
$101$			87.9846i			0.871135i	0.900156	+	0.435567i	$0.143452\pi$
$101$			87.9846i			0.871135i	−0.900156	+	0.435567i	$0.856548\pi$
$102$	141.511			1.38736
$103$	−43.0653			−0.418110			−0.209055	−	0.977904i	$-0.567039\pi$
$103$	−43.0653			−0.418110			−0.209055	+	0.977904i	$0.567039\pi$
$104$	71.1372			0.684012
$105$		−	10.2470i		−	0.0975900i
$106$			271.987i			2.56591i
$107$		−	90.1036i		−	0.842090i	−0.907040	−	0.421045i	$-0.861663\pi$
$107$		−	90.1036i		−	0.842090i	0.907040	−	0.421045i	$-0.138337\pi$
$108$	45.6695			0.422866
$109$		−	35.0148i		−	0.321237i	−0.987017	−	0.160618i	$-0.948651\pi$
$109$		−	35.0148i		−	0.321237i	0.987017	−	0.160618i	$-0.0513489\pi$
$110$	−61.7899	+	62.6052i	−0.561727	+	0.569138i
$111$	−58.0956			−0.523384
$112$			69.0327i			0.616363i
$113$	−83.2259			−0.736512			−0.368256	−	0.929724i	$-0.620045\pi$
$113$	−83.2259			−0.736512			−0.368256	+	0.929724i	$0.620045\pi$
$114$	213.427			1.87217
$115$	−22.4249			−0.194999
$116$		−	82.3288i		−	0.709731i
$117$		−	12.4607i		−	0.106502i
$118$		−	74.4063i		−	0.630562i
$119$	60.4445			0.507937
$120$		−	66.3315i		−	0.552762i
$121$	1.58591	+	120.990i	0.0131067	+	0.999914i
$122$	390.412			3.20010
$123$		−	9.84043i		−	0.0800035i
$124$	−12.7833			−0.103091
$125$	11.1803			0.0894427
$126$	28.3851			0.225279
$127$			24.2929i			0.191283i	0.995416	+	0.0956415i	$0.0304902\pi$
$127$			24.2929i			0.191283i	−0.995416	+	0.0956415i	$0.969510\pi$
$128$		−	155.245i		−	1.21285i
$129$		−	89.8455i		−	0.696477i
$130$	−33.2145			−0.255496
$131$			220.451i			1.68283i	0.540388	+	0.841416i	$0.318277\pi$
$131$			220.451i			1.68283i	−0.540388	+	0.841416i	$0.681723\pi$
$132$	−119.182	−	117.630i	−0.902893	−	0.891136i
$133$	91.1628			0.685435
$134$			113.439i			0.846563i
$135$	−11.6190			−0.0860663
$136$	391.275			2.87702
$137$	209.751			1.53103			0.765516	−	0.643417i	$-0.222484\pi$
$137$	209.751			1.53103			0.765516	+	0.643417i	$0.222484\pi$
$138$		−	62.1192i		−	0.450139i
$139$			170.361i			1.22562i	0.790231	+	0.612809i	$0.209961\pi$
$139$			170.361i			1.22562i	−0.790231	+	0.612809i	$0.790039\pi$
$140$		−	51.9970i		−	0.371407i
$141$	−4.94116			−0.0350437
$142$			428.026i			3.01426i
$143$	−32.0949	+	32.5183i	−0.224440	+	0.227401i
$144$	78.2757			0.543581
$145$			20.9456i			0.144452i
$146$	246.240			1.68658
$147$	12.1244			0.0824786
$148$	−294.800			−1.99189
$149$			31.5925i			0.212030i	0.994365	+	0.106015i	$0.0338092\pi$
$149$			31.5925i			0.212030i	−0.994365	+	0.106015i	$0.966191\pi$
$150$			30.9707i			0.206471i
$151$		−	128.997i		−	0.854286i	−0.904184	−	0.427143i	$-0.859520\pi$
$151$		−	128.997i		−	0.854286i	0.904184	−	0.427143i	$-0.140480\pi$
$152$	590.123			3.88239
$153$		−	68.5377i		−	0.447959i
$154$	−74.0755	−	73.1109i	−0.481009	−	0.474746i
$155$	3.25224			0.0209822
$156$		−	63.2307i		−	0.405325i
$157$	−20.3248			−0.129457			−0.0647287	−	0.997903i	$-0.520618\pi$
$157$	−20.3248			−0.129457			−0.0647287	+	0.997903i	$0.520618\pi$
$158$	48.2430			0.305336
$159$	131.731			0.828497
$160$		−	55.4604i		−	0.346627i
$161$		−	26.5335i		−	0.164804i
$162$		−	32.1857i		−	0.198677i
$163$	−200.790			−1.23184			−0.615920	−	0.787809i	$-0.711215\pi$
$163$	−200.790			−1.23184			−0.615920	+	0.787809i	$0.711215\pi$
$164$		−	49.9342i		−	0.304477i
$165$	30.3215	+	29.9267i	0.183767	+	0.181374i
$166$	−415.914			−2.50551
$167$		−	135.858i		−	0.813520i	−0.913535	−	0.406760i	$-0.866659\pi$
$167$		−	135.858i		−	0.813520i	0.913535	−	0.406760i	$-0.133341\pi$
$168$	78.4845			0.467169
$169$	151.748			0.897916
$170$	−182.689			−1.07464
$171$		−	103.369i		−	0.604496i
$172$		−	455.911i		−	2.65065i
$173$		−	56.7631i		−	0.328110i	−0.986451	−	0.164055i	$-0.947542\pi$
$173$		−	56.7631i		−	0.328110i	0.986451	−	0.164055i	$-0.0524575\pi$
$174$	−58.0214			−0.333456
$175$			13.2288i			0.0755929i
$176$	−204.273	−	201.613i	−1.16064	−	1.14553i
$177$	−36.0372			−0.203600
$178$			202.663i			1.13856i
$179$	−175.290			−0.979275			−0.489637	−	0.871926i	$-0.662871\pi$
$179$	−175.290			−0.979275			−0.489637	+	0.871926i	$0.662871\pi$
$180$	−58.9591			−0.327550
$181$	−102.038			−0.563745			−0.281873	−	0.959452i	$-0.590956\pi$
$181$	−102.038			−0.563745			−0.281873	+	0.959452i	$0.590956\pi$
$182$		−	39.2999i		−	0.215934i
$183$		−	189.088i		−	1.03327i
$184$		−	171.759i		−	0.933472i
$185$	75.0011			0.405411
$186$			9.00904i			0.0484357i
$187$	−176.531	+	178.860i	−0.944016	+	0.956471i
$188$	−25.0734			−0.133369
$189$		−	13.7477i		−	0.0727393i
$190$	−275.533			−1.45017
$191$	9.78313			0.0512206			0.0256103	−	0.999672i	$-0.491847\pi$
$191$	9.78313			0.0512206			0.0256103	+	0.999672i	$0.491847\pi$
$192$	−27.1392			−0.141350
$193$		−	154.161i		−	0.798763i	−0.916785	−	0.399382i	$-0.869225\pi$
$193$		−	154.161i		−	0.798763i	0.916785	−	0.399382i	$-0.130775\pi$
$194$			124.506i			0.641786i
$195$			16.0867i			0.0824961i
$196$	61.5237			0.313896
$197$			212.710i			1.07975i	0.841746	+	0.539874i	$0.181528\pi$
$197$			212.710i			1.07975i	−0.841746	+	0.539874i	$0.818472\pi$
$198$	−82.8999	+	83.9937i	−0.418686	+	0.424210i
$199$	−336.294			−1.68992			−0.844959	−	0.534832i	$-0.820375\pi$
$199$	−336.294			−1.68992			−0.844959	+	0.534832i	$0.820375\pi$
$200$			85.6336i			0.428168i
$201$	54.9420			0.273343
$202$	314.649			1.55767
$203$	−24.7831			−0.122084
$204$		−	347.787i		−	1.70484i
$205$			12.7039i			0.0619704i
$206$			154.009i			0.747619i
$207$	−30.0861			−0.145344
$208$		−	108.375i		−	0.521033i
$209$	−266.245	+	269.758i	−1.27390	+	1.29071i
$210$	−36.6450			−0.174500
$211$		−	234.007i		−	1.10904i	−0.832171	−	0.554519i	$-0.812902\pi$
$211$		−	234.007i		−	1.10904i	0.832171	−	0.554519i	$-0.187098\pi$
$212$	668.455			3.15309
$213$	207.305			0.973264
$214$	−322.227			−1.50573
$215$			115.990i			0.539489i
$216$		−	88.9930i		−	0.412005i
$217$			3.84811i			0.0177332i
$218$	−125.220			−0.574401
$219$		−	119.261i		−	0.544572i
$220$	153.863	+	151.860i	0.699378	+	0.690271i
$221$	−94.8922			−0.429377
$222$			207.761i			0.935858i
$223$	297.680			1.33489			0.667443	−	0.744661i	$-0.267389\pi$
$223$	297.680			1.33489			0.667443	+	0.744661i	$0.267389\pi$
$224$	65.6216			0.292953
$225$	15.0000			0.0666667
$226$			297.631i			1.31695i
$227$		−	97.5496i		−	0.429734i	−0.976643	−	0.214867i	$-0.931068\pi$
$227$		−	97.5496i		−	0.429734i	0.976643	−	0.214867i	$-0.0689318\pi$
$228$		−	524.534i		−	2.30059i
$229$	−394.529			−1.72283			−0.861417	−	0.507898i	$-0.830423\pi$
$229$	−394.529			−1.72283			−0.861417	+	0.507898i	$0.830423\pi$
$230$			80.1955i			0.348676i
$231$	−35.4097	+	35.8769i	−0.153289	+	0.155311i
$232$	−160.428			−0.691502
$233$		−	270.109i		−	1.15927i	−0.814877	−	0.579633i	$-0.803196\pi$
$233$		−	270.109i		−	1.15927i	0.814877	−	0.579633i	$-0.196804\pi$
$234$	−44.5619			−0.190436
$235$	6.37901			0.0271447
$236$	−182.867			−0.774859
$237$		−	23.3655i		−	0.0985887i
$238$		−	216.161i		−	0.908239i
$239$		−	214.503i		−	0.897501i	−0.893657	−	0.448750i	$-0.851869\pi$
$239$		−	214.503i		−	0.897501i	0.893657	−	0.448750i	$-0.148131\pi$
$240$	−101.054			−0.421056
$241$			277.056i			1.14961i	0.818290	+	0.574806i	$0.194922\pi$
$241$			277.056i			1.14961i	−0.818290	+	0.574806i	$0.805078\pi$
$242$	432.681	−	5.67150i	1.78794	−	0.0234359i
$243$	−15.5885			−0.0641500
$244$		−	959.507i		−	3.93240i
$245$	−15.6525			−0.0638877
$246$	−35.1912			−0.143054
$247$	−143.117			−0.579421
$248$			24.9099i			0.100443i
$249$			201.439i			0.808993i
$250$		−	39.9830i		−	0.159932i
$251$	165.948			0.661146			0.330573	−	0.943780i	$-0.392758\pi$
$251$	165.948			0.661146			0.330573	+	0.943780i	$0.392758\pi$
$252$		−	69.7613i		−	0.276831i
$253$	78.5146	+	77.4922i	0.310334	+	0.306293i
$254$	86.8761			0.342032
$255$			88.4817i			0.346987i
$256$	−492.510			−1.92387
$257$	−262.729			−1.02229			−0.511145	−	0.859494i	$-0.670779\pi$
$257$	−262.729			−1.02229			−0.511145	+	0.859494i	$0.670779\pi$
$258$	−321.304			−1.24537
$259$			88.7425i			0.342635i
$260$			81.6304i			0.313963i
$261$			28.1014i			0.107668i
$262$	788.374			3.00906
$263$			248.672i			0.945521i	0.881191	+	0.472761i	$0.156743\pi$
$263$			248.672i			0.945521i	−0.881191	+	0.472761i	$0.843257\pi$
$264$	−229.217	+	232.242i	−0.868248	+	0.879703i
$265$	−170.064			−0.641751
$266$		−	326.015i		−	1.22562i
$267$	98.1556			0.367624
$268$	278.797			1.04029
$269$	108.382			0.402906			0.201453	−	0.979498i	$-0.435434\pi$
$269$	108.382			0.402906			0.201453	+	0.979498i	$0.435434\pi$
$270$			41.5515i			0.153895i
$271$		−	50.8562i		−	0.187661i	−0.995588	−	0.0938306i	$-0.970089\pi$
$271$		−	50.8562i		−	0.187661i	0.995588	−	0.0938306i	$-0.0299112\pi$
$272$		−	596.093i		−	2.19152i
$273$	−19.0341			−0.0697220
$274$		−	750.109i		−	2.73763i
$275$	−39.1449	−	38.6352i	−0.142345	−	0.140492i
$276$	−152.669			−0.553148
$277$		−	449.565i		−	1.62298i	−0.584368	−	0.811488i	$-0.698658\pi$
$277$		−	449.565i		−	1.62298i	0.584368	−	0.811488i	$-0.301342\pi$
$278$	609.242			2.19152
$279$	4.36334			0.0156392
$280$	−101.323			−0.361868
$281$			467.477i			1.66362i	0.555060	+	0.831810i	$0.312695\pi$
$281$			467.477i			1.66362i	−0.555060	+	0.831810i	$0.687305\pi$
$282$			17.6705i			0.0626614i
$283$			48.2005i			0.170320i	0.996367	+	0.0851598i	$0.0271401\pi$
$283$			48.2005i			0.170320i	−0.996367	+	0.0851598i	$0.972860\pi$
$284$	1051.95			3.70404
$285$			133.449i			0.468241i
$286$	116.291	+	114.777i	0.406614	+	0.401319i
$287$	−15.0315			−0.0523746
$288$		−	74.4079i		−	0.258361i
$289$	−232.935			−0.806002
$290$	74.9053			0.258294
$291$	60.3021			0.207224
$292$		−	605.178i		−	2.07253i
$293$		−	144.820i		−	0.494267i	−0.968981	−	0.247134i	$-0.920511\pi$
$293$		−	144.820i		−	0.494267i	0.968981	−	0.247134i	$-0.0794886\pi$
$294$		−	43.3589i		−	0.147479i
$295$	46.5238			0.157708
$296$			574.456i			1.94073i
$297$	40.6806	+	40.1508i	0.136972	+	0.135188i
$298$	112.981			0.379130
$299$			41.6551i			0.139315i
$300$	76.1159			0.253720
$301$	−137.241			−0.455951
$302$	−461.318			−1.52754
$303$		−	152.394i		−	0.502950i
$304$		−	899.031i		−	2.95734i
$305$			244.112i			0.800366i
$306$	−245.103			−0.800991
$307$			423.108i			1.37820i	0.724665	+	0.689101i	$0.241994\pi$
$307$			423.108i			1.37820i	−0.724665	+	0.689101i	$0.758006\pi$
$308$	−179.683	+	182.053i	−0.583385	+	0.591082i
$309$	74.5913			0.241396
$310$		−	11.6306i		−	0.0375182i
$311$	265.503			0.853708			0.426854	−	0.904321i	$-0.359622\pi$
$311$	265.503			0.853708			0.426854	+	0.904321i	$0.359622\pi$
$312$	−123.213			−0.394914
$313$	430.578			1.37565			0.687824	−	0.725878i	$-0.258566\pi$
$313$	430.578			1.37565			0.687824	+	0.725878i	$0.258566\pi$
$314$			72.6853i			0.231482i
$315$			17.7482i			0.0563436i
$316$		−	118.566i		−	0.375208i
$317$	200.764			0.633326			0.316663	−	0.948538i	$-0.397438\pi$
$317$	200.764			0.633326			0.316663	+	0.948538i	$0.397438\pi$
$318$		−	471.095i		−	1.48143i
$319$	72.3803	−	73.3352i	0.226897	−	0.229891i
$320$	35.0366			0.109489
$321$			156.064i			0.486181i
$322$	−94.8886			−0.294685
$323$	−787.185			−2.43710
$324$	−79.1019			−0.244142
$325$		−	20.7679i		−	0.0639012i
$326$			718.062i			2.20264i
$327$			60.6475i			0.185466i
$328$	−97.3033			−0.296656
$329$			7.54775i			0.0229415i
$330$	107.023	−	108.435i	0.324313	−	0.328592i
$331$	−237.769			−0.718335			−0.359167	−	0.933273i	$-0.616939\pi$
$331$	−237.769			−0.718335			−0.359167	+	0.933273i	$0.616939\pi$
$332$			1022.18i			3.07886i
$333$	100.624			0.302176
$334$	−485.853			−1.45465
$335$	−70.9299			−0.211731
$336$		−	119.568i		−	0.355858i
$337$			337.399i			1.00118i	0.865683	+	0.500592i	$0.166884\pi$
$337$			337.399i			1.00118i	−0.865683	+	0.500592i	$0.833116\pi$
$338$		−	542.678i		−	1.60556i
$339$	144.151			0.425226
$340$			448.991i			1.32056i
$341$	−11.3868	−	11.2386i	−0.0333925	−	0.0329577i
$342$	−369.666			−1.08090
$343$		−	18.5203i		−	0.0539949i
$344$	−888.403			−2.58257
$345$	38.8410			0.112583
$346$	−202.995			−0.586692
$347$		−	682.353i		−	1.96643i	−0.182437	−	0.983217i	$-0.558399\pi$
$347$		−	682.353i		−	1.96643i	0.182437	−	0.983217i	$-0.441601\pi$
$348$			142.598i			0.409763i
$349$			468.842i			1.34339i	0.740829	+	0.671693i	$0.234433\pi$
$349$			468.842i			1.34339i	−0.740829	+	0.671693i	$0.765567\pi$
$350$	47.3085			0.135167
$351$			21.5826i			0.0614890i
$352$	−191.651	+	194.179i	−0.544462	+	0.551646i
$353$	406.302			1.15100			0.575498	−	0.817803i	$-0.304808\pi$
$353$	406.302			1.15100			0.575498	+	0.817803i	$0.304808\pi$
$354$			128.876i			0.364055i
$355$	−267.630			−0.753887
$356$	498.080			1.39910
$357$	−104.693			−0.293258
$358$			626.870i			1.75103i
$359$			523.086i			1.45706i	0.685012	+	0.728532i	$0.259797\pi$
$359$			523.086i			1.45706i	−0.685012	+	0.728532i	$0.740203\pi$
$360$			114.890i			0.319138i
$361$	−826.237			−2.28874
$362$			364.907i			1.00803i
$363$	−2.74687	−	209.560i	−0.00756714	−	0.577301i
$364$	−96.5864			−0.265347
$365$			153.966i			0.421823i
$366$	−676.214			−1.84758
$367$	1.02479			0.00279235			0.00139617	−	0.999999i	$-0.499556\pi$
$367$	1.02479			0.00279235			0.00139617	+	0.999999i	$0.499556\pi$
$368$	−261.668			−0.711055
$369$			17.0441i			0.0461900i
$370$		−	268.218i		−	0.724913i
$371$		−	201.223i		−	0.542379i
$372$	22.1413			0.0595196
$373$		−	214.772i		−	0.575795i	−0.957661	−	0.287898i	$-0.907044\pi$
$373$		−	214.772i		−	0.575795i	0.957661	−	0.287898i	$-0.0929563\pi$
$374$	639.637	+	631.307i	1.71026	+	1.68799i
$375$	−19.3649			−0.0516398
$376$			48.8588i			0.129943i
$377$	38.9072			0.103202
$378$	−49.1644			−0.130065
$379$	−240.901			−0.635624			−0.317812	−	0.948154i	$-0.602948\pi$
$379$	−240.901			−0.635624			−0.317812	+	0.948154i	$0.602948\pi$
$380$			677.171i			1.78203i
$381$		−	42.0766i		−	0.110437i
$382$		−	34.9863i		−	0.0915871i
$383$	501.684			1.30988			0.654941	−	0.755680i	$-0.272694\pi$
$383$	501.684			1.30988			0.654941	+	0.755680i	$0.272694\pi$
$384$			268.893i			0.700241i
$385$	45.7137	−	46.3169i	0.118737	−	0.120304i
$386$	−551.309			−1.42826
$387$			155.617i			0.402111i
$388$	305.996			0.788650
$389$	−122.273			−0.314327			−0.157163	−	0.987573i	$-0.550235\pi$
$389$	−122.273			−0.314327			−0.157163	+	0.987573i	$0.550235\pi$
$390$	57.5292			0.147511
$391$			229.115i			0.585971i
$392$		−	119.887i		−	0.305834i
$393$		−	381.832i		−	0.971583i
$394$	760.692			1.93069
$395$			30.1647i			0.0763664i
$396$	206.429	+	203.741i	0.521286	+	0.514498i
$397$	−498.744			−1.25628			−0.628141	−	0.778100i	$-0.716184\pi$
$397$	−498.744			−1.25628			−0.628141	+	0.778100i	$0.716184\pi$
$398$			1202.65i			3.02173i
$399$	−157.899			−0.395736
$400$	130.460			0.326149
$401$	−215.530			−0.537481			−0.268740	−	0.963213i	$-0.586607\pi$
$401$	−215.530			−0.537481			−0.268740	+	0.963213i	$0.586607\pi$
$402$		−	196.483i		−	0.488763i
$403$		−	6.04117i		−	0.0149905i
$404$		−	773.306i		−	1.91412i
$405$	20.1246			0.0496904
$406$			88.6291i			0.218298i
$407$	−262.596	−	259.176i	−0.645198	−	0.636797i
$408$	−677.708			−1.66105
$409$			381.480i			0.932715i	0.884596	+	0.466357i	$0.154434\pi$
$409$			381.480i			0.932715i	−0.884596	+	0.466357i	$0.845566\pi$
$410$	45.4317			0.110809
$411$	−363.300			−0.883941
$412$	378.505			0.918702
$413$			55.0477i			0.133287i
$414$			107.594i			0.259888i
$415$		−	260.057i		−	0.626644i
$416$	−103.020			−0.247644
$417$		−	295.074i		−	0.707611i
$418$	964.704	+	952.141i	2.30790	+	2.27785i
$419$	−634.739			−1.51489			−0.757445	−	0.652899i	$-0.773552\pi$
$419$	−634.739			−1.51489			−0.757445	+	0.652899i	$0.773552\pi$
$420$			90.0615i			0.214432i
$421$	639.239			1.51838			0.759191	−	0.650868i	$-0.225595\pi$
$421$	639.239			1.51838			0.759191	+	0.650868i	$0.225595\pi$
$422$	−836.852			−1.98306
$423$	8.55834			0.0202325
$424$		−	1302.57i		−	3.07210i
$425$		−	114.229i		−	0.268775i
$426$		−	741.362i		−	1.74029i
$427$	−288.837			−0.676433
$428$			791.930i			1.85030i
$429$	55.5899	−	56.3234i	0.129580	−	0.131290i
$430$	414.802			0.964656
$431$		−	641.601i		−	1.48863i	−0.667827	−	0.744317i	$-0.732775\pi$
$431$		−	641.601i		−	1.48863i	0.667827	−	0.744317i	$-0.267225\pi$
$432$	−135.578			−0.313837
$433$	−122.617			−0.283181			−0.141591	−	0.989925i	$-0.545222\pi$
$433$	−122.617			−0.283181			−0.141591	+	0.989925i	$0.545222\pi$
$434$	13.7615			0.0317086
$435$		−	36.2788i		−	0.0833995i
$436$			307.749i			0.705846i
$437$			345.552i			0.790737i
$438$	−426.500			−0.973745
$439$		−	467.357i		−	1.06460i	−0.846557	−	0.532298i	$-0.821329\pi$
$439$		−	467.357i		−	1.06460i	0.846557	−	0.532298i	$-0.178671\pi$
$440$	295.918	−	299.823i	0.672542	−	0.681415i
$441$	−21.0000			−0.0476190
$442$			339.352i			0.767765i
$443$	−73.4797			−0.165868			−0.0829342	−	0.996555i	$-0.526429\pi$
$443$	−73.4797			−0.165868			−0.0829342	+	0.996555i	$0.526429\pi$
$444$	510.608			1.15002
$445$	−126.718			−0.284760
$446$		−	1064.56i		−	2.38690i
$447$		−	54.7199i		−	0.122416i
$448$			41.4558i			0.0925354i
$449$	428.949			0.955343			0.477671	−	0.878539i	$-0.341481\pi$
$449$	428.949			0.955343			0.477671	+	0.878539i	$0.341481\pi$
$450$		−	53.6428i		−	0.119206i
$451$	43.9002	−	44.4794i	0.0973396	−	0.0986239i
$452$	731.481			1.61832
$453$			223.430i			0.493223i
$454$	−348.855			−0.768404
$455$	24.5729			0.0540064
$456$	−1022.12			−2.24150
$457$		−	170.321i		−	0.372694i	−0.982484	−	0.186347i	$-0.940335\pi$
$457$		−	170.321i		−	0.372694i	0.982484	−	0.186347i	$-0.0596649\pi$
$458$			1410.91i			3.08059i
$459$			118.711i			0.258629i
$460$	197.095			0.428466
$461$		−	642.133i		−	1.39291i	−0.717599	−	0.696456i	$-0.754759\pi$
$461$		−	642.133i		−	1.39291i	0.717599	−	0.696456i	$-0.245241\pi$
$462$	128.302	+	126.632i	0.277711	+	0.274095i
$463$	60.3132			0.130266			0.0651330	−	0.997877i	$-0.479253\pi$
$463$	60.3132			0.130266			0.0651330	+	0.997877i	$0.479253\pi$
$464$			244.407i			0.526739i
$465$	−5.63305			−0.0121141
$466$	−965.960			−2.07288
$467$	−8.64546			−0.0185128			−0.00925638	−	0.999957i	$-0.502946\pi$
$467$	−8.64546			−0.0185128			−0.00925638	+	0.999957i	$0.502946\pi$
$468$			109.519i			0.234014i
$469$		−	83.9253i		−	0.178945i
$470$		−	22.8125i		−	0.0485373i
$471$	35.2036			0.0747422
$472$			356.340i			0.754957i
$473$	400.819	−	406.108i	0.847398	−	0.858578i
$474$	−83.5594			−0.176286
$475$		−	172.281i		−	0.362698i
$476$	−531.253			−1.11608
$477$	−228.165			−0.478333
$478$	−767.101			−1.60481
$479$		−	819.445i		−	1.71074i	−0.518017	−	0.855371i	$-0.673329\pi$
$479$		−	819.445i		−	1.71074i	0.518017	−	0.855371i	$-0.326671\pi$
$480$			96.0602i			0.200125i
$481$		−	139.317i		−	0.289641i
$482$	990.805			2.05561
$483$			45.9573i			0.0951497i
$484$	−13.9387	−	1063.39i	−0.0287990	−	2.19709i
$485$	−77.8497			−0.160515
$486$			55.7472i			0.114706i
$487$	−419.832			−0.862079			−0.431039	−	0.902333i	$-0.641853\pi$
$487$	−419.832			−0.862079			−0.431039	+	0.902333i	$0.641853\pi$
$488$	−1869.72			−3.83140
$489$	347.778			0.711203
$490$			55.9762i			0.114237i
$491$		−	350.300i		−	0.713442i	−0.934211	−	0.356721i	$-0.883895\pi$
$491$		−	350.300i		−	0.713442i	0.934211	−	0.356721i	$-0.116105\pi$
$492$			86.4886i			0.175790i
$493$	214.001			0.434079
$494$			511.813i			1.03606i
$495$	−52.5184	−	51.8345i	−0.106098	−	0.104716i
$496$	37.9493			0.0765107
$497$		−	316.664i		−	0.637151i
$498$	720.385			1.44656
$499$	107.548			0.215528			0.107764	−	0.994177i	$-0.465631\pi$
$499$	107.548			0.215528			0.107764	+	0.994177i	$0.465631\pi$
$500$	−98.2651			−0.196530
$501$			235.313i			0.469686i
$502$		−	593.460i		−	1.18219i
$503$		−	746.064i		−	1.48323i	−0.670827	−	0.741614i	$-0.734061\pi$
$503$		−	746.064i		−	1.48323i	0.670827	−	0.741614i	$-0.265939\pi$
$504$	−135.939			−0.269720
$505$			196.740i			0.389583i
$506$	277.126	−	280.783i	0.547681	−	0.554907i
$507$	−262.835			−0.518412
$508$		−	213.513i		−	0.420301i
$509$	876.809			1.72261			0.861305	−	0.508088i	$-0.169648\pi$
$509$	876.809			1.72261			0.861305	+	0.508088i	$0.169648\pi$
$510$	316.427			0.620445
$511$	−182.174			−0.356506
$512$			1140.33i			2.22720i
$513$			179.040i			0.349006i
$514$			939.567i			1.82795i
$515$	−96.2969			−0.186984
$516$			789.661i			1.53035i
$517$	−22.3344	−	22.0435i	−0.0431999	−	0.0426374i
$518$	317.359			0.612663
$519$			98.3166i			0.189435i
$520$	159.068			0.305899
$521$	−832.161			−1.59724			−0.798619	−	0.601837i	$-0.794436\pi$
$521$	−832.161			−1.59724			−0.798619	+	0.601837i	$0.794436\pi$
$522$	100.496			0.192521
$523$			456.844i			0.873507i	0.899581	+	0.436754i	$0.143872\pi$
$523$			456.844i			0.873507i	−0.899581	+	0.436754i	$0.856128\pi$
$524$		−	1937.57i		−	3.69765i
$525$		−	22.9129i		−	0.0436436i
$526$	889.298			1.69068
$527$		−	33.2281i		−	0.0630515i
$528$	353.811	+	349.204i	0.670097	+	0.661371i
$529$	−428.425			−0.809877
$530$			608.181i			1.14751i
$531$	62.4182			0.117548
$532$	−801.239			−1.50609
$533$	23.5981			0.0442740
$534$		−	351.023i		−	0.657346i
$535$		−	201.478i		−	0.376594i
$536$		−	543.273i		−	1.01357i
$537$	303.611			0.565384
$538$		−	387.593i		−	0.720433i
$539$	54.8029	+	54.0892i	0.101675	+	0.100351i
$540$	102.120			0.189111
$541$			466.236i			0.861804i	0.902399	+	0.430902i	$0.141804\pi$
$541$			466.236i			0.861804i	−0.902399	+	0.430902i	$0.858196\pi$
$542$	−181.871			−0.335556
$543$	176.735			0.325479
$544$	−566.638			−1.04161
$545$		−	78.2955i		−	0.143662i
$546$			68.0695i			0.124669i
$547$			665.010i			1.21574i	0.794036	+	0.607871i	$0.207976\pi$
$547$			665.010i			1.21574i	−0.794036	+	0.607871i	$0.792024\pi$
$548$	−1843.53			−3.36410
$549$			327.510i			0.596558i
$550$	−138.167	+	139.989i	−0.251212	+	0.254526i
$551$	322.757			0.585766
$552$			297.495i			0.538940i
$553$	−35.6914			−0.0645414
$554$	−1607.73			−2.90203
$555$	−129.906			−0.234064
$556$		−	1497.32i		−	2.69302i
$557$		−	532.059i		−	0.955222i	−0.878571	−	0.477611i	$-0.841503\pi$
$557$		−	532.059i		−	0.955222i	0.878571	−	0.477611i	$-0.158497\pi$
$558$		−	15.6041i		−	0.0279644i
$559$	215.456			0.385431
$560$			154.362i			0.275646i
$561$	305.761	−	309.795i	0.545028	−	0.552219i
$562$	1671.79			2.97471
$563$			253.490i			0.450248i	0.974330	+	0.225124i	$0.0722787\pi$
$563$			253.490i			0.450248i	−0.974330	+	0.225124i	$0.927721\pi$
$564$	43.4284			0.0770006
$565$	−186.099			−0.329378
$566$	172.374			0.304547
$567$			23.8118i			0.0419961i
$568$		−	2049.86i		−	3.60891i
$569$		−	346.979i		−	0.609805i	−0.952384	−	0.304903i	$-0.901376\pi$
$569$		−	346.979i		−	0.609805i	0.952384	−	0.304903i	$-0.0986239\pi$
$570$	477.237			0.837258
$571$			212.339i			0.371872i	0.982562	+	0.185936i	$0.0595318\pi$
$571$			212.339i			0.371872i	−0.982562	+	0.185936i	$0.940468\pi$
$572$	282.085	−	285.807i	0.493156	−	0.499662i
$573$	−16.9449			−0.0295722
$574$			53.7555i			0.0936506i
$575$	−50.1436			−0.0872062
$576$	47.0065			0.0816085
$577$	552.271			0.957141			0.478571	−	0.878049i	$-0.341155\pi$
$577$	552.271			0.957141			0.478571	+	0.878049i	$0.341155\pi$
$578$			833.017i			1.44121i
$579$			267.015i			0.461166i
$580$		−	184.093i		−	0.317401i
$581$	307.704			0.529611
$582$		−	215.651i		−	0.370535i
$583$	595.433	+	587.679i	1.02133	+	1.00803i
$584$	−1179.27			−2.01930
$585$		−	27.8631i		−	0.0476292i
$586$	−517.904			−0.883795
$587$	−516.194			−0.879377			−0.439688	−	0.898150i	$-0.644911\pi$
$587$	−516.194			−0.879377			−0.439688	+	0.898150i	$0.644911\pi$
$588$	−106.562			−0.181228
$589$		−	50.1149i		−	0.0850847i
$590$		−	166.378i		−	0.281996i
$591$		−	368.425i		−	0.623393i
$592$	875.162			1.47831
$593$		−	345.257i		−	0.582220i	−0.956690	−	0.291110i	$-0.905975\pi$
$593$		−	345.257i		−	0.582220i	0.956690	−	0.291110i	$-0.0940246\pi$
$594$	143.587	−	145.481i	0.241729	−	0.244918i
$595$	135.158			0.227156
$596$		−	277.670i		−	0.465889i
$597$	582.478			0.975674
$598$	148.966			0.249107
$599$	−118.104			−0.197168			−0.0985842	−	0.995129i	$-0.531431\pi$
$599$	−118.104			−0.197168			−0.0985842	+	0.995129i	$0.531431\pi$
$600$		−	148.322i		−	0.247203i
$601$			75.6580i			0.125887i	0.998017	+	0.0629435i	$0.0200488\pi$
$601$			75.6580i			0.125887i	−0.998017	+	0.0629435i	$0.979951\pi$
$602$			490.800i			0.815283i
$603$	−95.1624			−0.157815
$604$			1133.77i			1.87710i
$605$	3.54620	+	270.541i	0.00586148	+	0.447175i
$606$	−544.988			−0.899321
$607$		−	618.092i		−	1.01827i	−0.860686	−	0.509136i	$-0.829965\pi$
$607$		−	618.092i		−	1.01827i	0.860686	−	0.509136i	$-0.170035\pi$
$608$	−854.607			−1.40560
$609$	42.9257			0.0704855
$610$	872.988			1.43113
$611$		−	11.8493i		−	0.0193932i
$612$			602.384i			0.984288i
$613$		−	985.131i		−	1.60706i	−0.595261	−	0.803532i	$-0.702951\pi$
$613$		−	985.131i		−	1.60706i	0.595261	−	0.803532i	$-0.297049\pi$
$614$	1513.11			2.46435
$615$		−	22.0039i		−	0.0357787i
$616$	354.755	+	350.135i	0.575901	+	0.568401i
$617$	364.161			0.590213			0.295106	−	0.955464i	$-0.404645\pi$
$617$	364.161			0.590213			0.295106	+	0.955464i	$0.404645\pi$
$618$		−	266.752i		−	0.431638i
$619$	−979.707			−1.58273			−0.791363	−	0.611347i	$-0.790628\pi$
$619$	−979.707			−1.58273			−0.791363	+	0.611347i	$0.790628\pi$
$620$	−28.5843			−0.0461037
$621$	52.1107			0.0839142
$622$		−	949.489i		−	1.52651i
$623$		−	149.935i		−	0.240666i
$624$			187.711i			0.300818i
$625$	25.0000			0.0400000
$626$		−	1539.83i		−	2.45978i
$627$	461.150	−	467.234i	0.735486	−	0.745190i
$628$	178.637			0.284453
$629$		−	766.285i		−	1.21826i
$630$	63.4710			0.100748
$631$	1072.67			1.69995			0.849977	−	0.526820i	$-0.176616\pi$
$631$	1072.67			1.69995			0.849977	+	0.526820i	$0.176616\pi$
$632$	−231.041			−0.365571
$633$			405.312i			0.640303i
$634$		−	717.971i		−	1.13245i
$635$			54.3207i			0.0855444i
$636$	−1157.80			−1.82044
$637$			29.0751i			0.0456437i
$638$	−262.260	−	258.845i	−0.411066	−	0.405713i
$639$	−359.063			−0.561914
$640$		−	347.139i		−	0.542404i
$641$	−1001.76			−1.56281			−0.781403	−	0.624027i	$-0.785496\pi$
$641$	−1001.76			−1.56281			−0.781403	+	0.624027i	$0.785496\pi$
$642$	558.114			0.869336
$643$	−70.7747			−0.110070			−0.0550348	−	0.998484i	$-0.517527\pi$
$643$	−70.7747			−0.110070			−0.0550348	+	0.998484i	$0.517527\pi$
$644$			233.205i			0.362120i
$645$		−	200.901i		−	0.311474i
$646$			2815.12i			4.35777i
$647$	−587.221			−0.907605			−0.453803	−	0.891102i	$-0.649933\pi$
$647$	−587.221			−0.907605			−0.453803	+	0.891102i	$0.649933\pi$
$648$			154.140i			0.237871i
$649$	−162.890	−	160.769i	−0.250987	−	0.247718i
$650$	−74.2699			−0.114261
$651$		−	6.66512i		−	0.0102383i
$652$	1764.76			2.70669
$653$	−747.737			−1.14508			−0.572540	−	0.819877i	$-0.694042\pi$
$653$	−747.737			−1.14508			−0.572540	+	0.819877i	$0.694042\pi$
$654$	216.887			0.331631
$655$			492.943i			0.752585i
$656$			148.238i			0.225972i
$657$			206.566i			0.314409i
$658$	26.9921			0.0410215
$659$			317.711i			0.482111i	0.970511	+	0.241055i	$0.0774936\pi$
$659$			317.711i			0.482111i	−0.970511	+	0.241055i	$0.922506\pi$
$660$	−266.499	−	263.029i	−0.403786	−	0.398528i
$661$	596.054			0.901746			0.450873	−	0.892588i	$-0.351113\pi$
$661$	596.054			0.901746			0.450873	+	0.892588i	$0.351113\pi$
$662$			850.305i			1.28445i
$663$	164.358			0.247901
$664$	1991.86			2.99978
$665$	203.846			0.306536
$666$		−	359.852i		−	0.540318i
$667$		−	93.9404i		−	0.140840i
$668$			1194.07i			1.78753i
$669$	−515.596			−0.770697
$670$			253.658i			0.378595i
$671$	843.560	−	854.690i	1.25717	−	1.27376i
$672$	−113.660			−0.169137
$673$		−	778.735i		−	1.15711i	−0.815643	−	0.578555i	$-0.803617\pi$
$673$		−	778.735i		−	1.15711i	0.815643	−	0.578555i	$-0.196383\pi$
$674$	1206.60			1.79021
$675$	−25.9808			−0.0384900
$676$	−1333.73			−1.97297
$677$		−	871.699i		−	1.28759i	−0.765198	−	0.643796i	$-0.777359\pi$
$677$		−	871.699i		−	1.28759i	0.765198	−	0.643796i	$-0.222641\pi$
$678$		−	515.512i		−	0.760343i
$679$		−	92.1130i		−	0.135660i
$680$	874.918			1.28664
$681$			168.961i			0.248107i
$682$	−40.1912	+	40.7215i	−0.0589314	+	0.0597089i
$683$	−1148.30			−1.68126			−0.840630	−	0.541611i	$-0.817815\pi$
$683$	−1148.30			−1.68126			−0.840630	+	0.541611i	$0.817815\pi$
$684$			908.520i			1.32825i
$685$	469.018			0.684698
$686$	−66.2319			−0.0965479
$687$	683.344			0.994679
$688$			1353.45i			1.96722i
$689$			315.901i			0.458491i
$690$		−	138.903i		−	0.201308i
$691$	−77.8168			−0.112615			−0.0563074	−	0.998413i	$-0.517933\pi$
$691$	−77.8168			−0.112615			−0.0563074	+	0.998413i	$0.517933\pi$
$692$			498.897i			0.720949i
$693$	61.3314	−	62.1406i	0.0885013	−	0.0896690i
$694$	−2440.22			−3.51617
$695$			380.939i			0.548113i
$696$	277.870			0.399239
$697$	129.796			0.186221
$698$	1676.67			2.40210
$699$			467.843i			0.669303i
$700$		−	116.269i		−	0.166098i
$701$			522.176i			0.744902i	0.928052	+	0.372451i	$0.121483\pi$
$701$			522.176i			0.744902i	−0.928052	+	0.372451i	$0.878517\pi$
$702$	77.1835			0.109948
$703$		−	1155.72i		−	1.64398i
$704$	−122.671	−	121.074i	−0.174249	−	0.171980i
$705$	−11.0488			−0.0156720
$706$		−	1453.01i		−	2.05809i
$707$	−232.785			−0.329258
$708$	316.734			0.447365
$709$	−1301.14			−1.83518			−0.917591	−	0.397527i	$-0.869869\pi$
$709$	−1301.14			−1.83518			−0.917591	+	0.397527i	$0.869869\pi$
$710$			957.094i			1.34802i
$711$			40.4703i			0.0569202i
$712$		−	970.574i		−	1.36317i
$713$	−14.5862			−0.0204576
$714$			374.402i			0.524372i
$715$	−71.7663	+	72.7131i	−0.100372	+	0.101697i
$716$	1540.64			2.15174
$717$			371.530i			0.518172i
$718$	1870.65			2.60537
$719$	1010.40			1.40528			0.702642	−	0.711544i	$-0.252004\pi$
$719$	1010.40			1.40528			0.702642	+	0.711544i	$0.252004\pi$
$720$	175.030			0.243097
$721$		−	113.940i		−	0.158031i
$722$			2954.78i			4.09249i
$723$		−	479.876i		−	0.663729i
$724$	896.822			1.23870
$725$			46.8357i			0.0646010i
$726$	−749.426	+	9.82332i	−1.03227	+	0.0135307i
$727$	−301.912			−0.415284			−0.207642	−	0.978205i	$-0.566579\pi$
$727$	−301.912			−0.415284			−0.207642	+	0.978205i	$0.566579\pi$
$728$			188.211i			0.258532i
$729$	27.0000			0.0370370
$730$	550.609			0.754259
$731$	1185.07			1.62116
$732$			1661.91i			2.27037i
$733$		−	83.5411i		−	0.113972i	−0.998375	−	0.0569858i	$-0.981851\pi$
$733$		−	83.5411i		−	0.113972i	0.998375	−	0.0569858i	$-0.0181490\pi$
$734$		−	3.66484i		−	0.00499297i
$735$	27.1109			0.0368856
$736$			248.738i			0.337960i
$737$	248.342	+	245.108i	0.336963	+	0.332575i
$738$	60.9530			0.0825921
$739$		−	396.215i		−	0.536151i	−0.963398	−	0.268075i	$-0.913612\pi$
$739$		−	396.215i		−	0.536151i	0.963398	−	0.268075i	$-0.0863876\pi$
$740$	−659.192			−0.890800
$741$	247.886			0.334529
$742$	−719.609			−0.969824
$743$		−	357.422i		−	0.481052i	−0.970643	−	0.240526i	$-0.922680\pi$
$743$		−	357.422i		−	0.481052i	0.970643	−	0.240526i	$-0.0773200\pi$
$744$		−	43.1452i		−	0.0579909i
$745$			70.6431i			0.0948229i
$746$	−768.063			−1.02957
$747$		−	348.903i		−	0.467073i
$748$	1551.55	−	1572.02i	2.07426	−	2.10163i
$749$	238.392			0.318280
$750$			69.2525i			0.0923367i
$751$	1393.20			1.85513			0.927566	−	0.373659i	$-0.121897\pi$
$751$	1393.20			1.85513			0.927566	+	0.373659i	$0.121897\pi$
$752$	74.4345			0.0989820
$753$	−287.430			−0.381713
$754$		−	139.139i		−	0.184535i
$755$		−	288.447i		−	0.382049i
$756$			120.830i			0.159828i
$757$	591.851			0.781838			0.390919	−	0.920425i	$-0.372157\pi$
$757$	591.851			0.781838			0.390919	+	0.920425i	$0.372157\pi$
$758$			861.508i			1.13655i
$759$	−135.991	−	134.220i	−0.179172	−	0.176838i
$760$	1319.56			1.73626
$761$			441.539i			0.580209i	0.956995	+	0.290104i	$0.0936900\pi$
$761$			441.539i			0.580209i	−0.956995	+	0.290104i	$0.906310\pi$
$762$	−150.474			−0.197472
$763$	92.6405			0.121416
$764$	−85.9849			−0.112546
$765$		−	153.255i		−	0.200333i
$766$		−	1794.12i		−	2.34219i
$767$		−	86.4197i		−	0.112672i
$768$	853.053			1.11075
$769$			994.821i			1.29366i	0.762636	+	0.646828i	$0.223905\pi$
$769$			994.821i			1.29366i	−0.762636	+	0.646828i	$0.776095\pi$
$770$	−165.638	−	163.481i	−0.215114	−	0.212313i
$771$	455.060			0.590220
$772$			1354.94i			1.75510i
$773$	791.691			1.02418			0.512090	−	0.858932i	$-0.328871\pi$
$773$	791.691			1.02418			0.512090	+	0.858932i	$0.328871\pi$
$774$	556.515			0.719012
$775$	7.27224			0.00938353
$776$		−	596.274i		−	0.768394i
$777$		−	153.706i		−	0.197820i
$778$			437.272i			0.562046i
$779$	195.759			0.251295
$780$		−	141.388i		−	0.181267i
$781$	937.033	+	924.831i	1.19979	+	1.18416i
$782$	819.357			1.04777
$783$		−	48.6731i		−	0.0621623i
$784$	−182.643			−0.232963
$785$	−45.4476			−0.0578951
$786$	−1365.50			−1.73728
$787$		−	1287.84i		−	1.63639i	−0.574943	−	0.818193i	$-0.694976\pi$
$787$		−	1287.84i		−	1.63639i	0.574943	−	0.818193i	$-0.305024\pi$
$788$		−	1869.53i		−	2.37251i
$789$		−	430.713i		−	0.545897i
$790$	107.875			0.136550
$791$		−	220.195i		−	0.278376i
$792$	397.016	−	402.254i	0.501283	−	0.507897i
$793$	453.447			0.571812
$794$			1783.60i			2.24635i
$795$	294.560			0.370515
$796$	2955.72			3.71321
$797$	−613.983			−0.770368			−0.385184	−	0.922840i	$-0.625862\pi$
$797$	−613.983			−0.770368			−0.385184	+	0.922840i	$0.625862\pi$
$798$			564.675i			0.707612i
$799$		−	65.1743i		−	0.0815698i
$800$		−	124.013i		−	0.155016i
$801$	−170.011			−0.212248
$802$			770.775i			0.961065i
$803$	532.049	−	539.068i	0.662576	−	0.671318i
$804$	−482.891			−0.600611
$805$		−	59.3307i		−	0.0737027i
$806$	−21.6043			−0.0268044
$807$	−187.723			−0.232618
$808$	−1506.89			−1.86496
$809$			382.751i			0.473116i	0.971617	+	0.236558i	$0.0760193\pi$
$809$			382.751i			0.473116i	−0.971617	+	0.236558i	$0.923981\pi$
$810$		−	71.9693i		−	0.0888510i
$811$		−	86.0932i		−	0.106157i	−0.998590	−	0.0530784i	$-0.983097\pi$
$811$		−	86.0932i		−	0.106157i	0.998590	−	0.0530784i	$-0.0169033\pi$
$812$	217.822			0.268253
$813$			88.0855i			0.108346i
$814$	−926.862	+	939.091i	−1.13865	+	1.15367i
$815$	−448.980			−0.550895
$816$			1032.46i			1.26527i
$817$	1787.33			2.18767
$818$	1364.24			1.66778
$819$	32.9680			0.0402540
$820$		−	111.656i		−	0.136166i
$821$		−	851.989i		−	1.03775i	−0.854851	−	0.518873i	$-0.826352\pi$
$821$		−	851.989i		−	1.03775i	0.854851	−	0.518873i	$-0.173648\pi$
$822$			1299.23i			1.58057i
$823$	70.9655			0.0862278			0.0431139	−	0.999070i	$-0.486272\pi$
$823$	70.9655			0.0862278			0.0431139	+	0.999070i	$0.486272\pi$
$824$		−	737.567i		−	0.895106i
$825$	67.8010	+	66.9181i	0.0821830	+	0.0811128i
$826$	196.861			0.238330
$827$		−	1019.63i		−	1.23293i	−0.787382	−	0.616466i	$-0.788564\pi$
$827$		−	1019.63i		−	1.23293i	0.787382	−	0.616466i	$-0.211436\pi$
$828$	264.430			0.319360
$829$	−1105.52			−1.33356			−0.666782	−	0.745253i	$-0.732329\pi$
$829$	−1105.52			−1.33356			−0.666782	+	0.745253i	$0.732329\pi$
$830$	−930.012			−1.12050
$831$			778.669i			0.937026i
$832$		−	65.0818i		−	0.0782233i
$833$			159.921i			0.191982i
$834$	−1055.24			−1.26527
$835$		−	303.787i		−	0.363817i
$836$	2340.05	−	2370.93i	2.79911	−	2.83604i
$837$	−7.55753			−0.00902931
$838$			2269.94i			2.70876i
$839$	−1120.51			−1.33553			−0.667763	−	0.744374i	$-0.732748\pi$
$839$	−1120.51			−1.33553			−0.667763	+	0.744374i	$0.732748\pi$
$840$	175.497			0.208925
$841$	753.257			0.895668
$842$		−	2286.04i		−	2.71501i
$843$		−	809.695i		−	0.960492i
$844$			2056.71i			2.43686i
$845$	339.318			0.401560
$846$		−	30.6062i		−	0.0361776i
$847$	−320.108	+	4.19592i	−0.377932	+	0.00495386i
$848$	−1984.42			−2.34012
$849$		−	83.4857i		−	0.0983341i
$850$	−408.506			−0.480595
$851$	−336.378			−0.395274
$852$	−1822.03			−2.13853
$853$			788.755i			0.924684i	0.886702	+	0.462342i	$0.152991\pi$
$853$			788.755i			0.924684i	−0.886702	+	0.462342i	$0.847009\pi$
$854$			1032.93i			1.20952i
$855$		−	231.140i		−	0.270339i
$856$	1543.18			1.80278
$857$			612.702i			0.714938i	0.933925	+	0.357469i	$0.116360\pi$
$857$			612.702i			0.714938i	−0.933925	+	0.357469i	$0.883640\pi$
$858$	−201.423	−	198.800i	−0.234758	−	0.231701i
$859$	−451.038			−0.525073			−0.262537	−	0.964922i	$-0.584559\pi$
$859$	−451.038			−0.525073			−0.262537	+	0.964922i	$0.584559\pi$
$860$		−	1019.45i		−	1.18541i
$861$	26.0353			0.0302385
$862$	−2294.48			−2.66181
$863$	−1324.46			−1.53471			−0.767356	−	0.641222i	$-0.778428\pi$
$863$	−1324.46			−1.53471			−0.767356	+	0.641222i	$0.778428\pi$
$864$			128.878i			0.149165i
$865$		−	126.926i		−	0.146735i
$866$			438.503i			0.506354i
$867$	403.454			0.465345
$868$		−	33.8214i		−	0.0389647i
$869$	104.238	−	105.614i	0.119952	−	0.121535i
$870$	−129.740			−0.149126
$871$			131.755i			0.151269i
$872$	599.689			0.687717
$873$	−104.446			−0.119641
$874$	1235.76			1.41391
$875$			29.5804i			0.0338062i
$876$			1048.20i			1.19657i
$877$			674.684i			0.769309i	0.923061	+	0.384654i	$0.125679\pi$
$877$			674.684i			0.769309i	−0.923061	+	0.384654i	$0.874321\pi$
$878$	−1671.36			−1.90360
$879$			250.836i			0.285365i
$880$	−456.768	−	450.820i	−0.519055	−	0.512296i
$881$	1595.82			1.81137			0.905686	−	0.423949i	$-0.139356\pi$
$881$	1595.82			1.81137			0.905686	+	0.423949i	$0.139356\pi$
$882$			75.0999i			0.0851473i
$883$	258.515			0.292769			0.146384	−	0.989228i	$-0.453236\pi$
$883$	258.515			0.292769			0.146384	+	0.989228i	$0.453236\pi$
$884$	834.018			0.943459
$885$	−80.5815			−0.0910526
$886$			262.777i			0.296588i
$887$			1179.39i			1.32964i	0.747005	+	0.664819i	$0.231491\pi$
$887$			1179.39i			1.32964i	−0.747005	+	0.664819i	$0.768509\pi$
$888$		−	994.986i		−	1.12048i
$889$	−64.2731			−0.0722982
$890$			453.168i			0.509178i
$891$	−70.4608	−	69.5433i	−0.0790806	−	0.0780508i
$892$	−2616.34			−2.93311
$893$		−	98.2962i		−	0.110074i
$894$	−195.688			−0.218891
$895$	−391.961			−0.437945
$896$	410.740			0.458415
$897$		−	72.1487i		−	0.0804333i
$898$		−	1534.00i		−	1.70824i
$899$			13.6240i			0.0151546i
$900$	−131.837			−0.146485
$901$			1737.54i			1.92846i
$902$	−159.067	−	156.995i	−0.176349	−	0.174052i
$903$	237.709			0.263243
$904$		−	1425.39i		−	1.57675i
$905$	−228.164			−0.252115
$906$	799.026			0.881928
$907$	235.668			0.259832			0.129916	−	0.991525i	$-0.458529\pi$
$907$	235.668			0.259832			0.129916	+	0.991525i	$0.458529\pi$
$908$			857.373i			0.944244i
$909$			263.954i			0.290378i
$910$		−	87.8773i		−	0.0965685i
$911$	535.753			0.588093			0.294047	−	0.955791i	$-0.404998\pi$
$911$	535.753			0.588093			0.294047	+	0.955791i	$0.404998\pi$
$912$			1557.17i			1.70742i
$913$	−898.662	+	910.519i	−0.984296	+	0.997283i
$914$	−609.100			−0.666412
$915$		−	422.814i		−	0.462091i
$916$	3467.56			3.78554
$917$	−583.258			−0.636051
$918$	424.532			0.462453
$919$		−	82.4629i		−	0.0897311i	−0.998993	−	0.0448655i	$-0.985714\pi$
$919$		−	82.4629i		−	0.0897311i	0.998993	−	0.0448655i	$-0.0142859\pi$
$920$		−	384.065i		−	0.417461i
$921$		−	732.844i		−	0.795705i
$922$	−2296.39			−2.49066
$923$			497.133i			0.538605i
$924$	311.220	−	315.326i	0.336818	−	0.341262i
$925$	167.707			0.181305
$926$		−	215.691i		−	0.232928i
$927$	−129.196			−0.139370
$928$	232.330			0.250355
$929$	−979.404			−1.05426			−0.527128	−	0.849786i	$-0.676731\pi$
$929$	−979.404			−1.05426			−0.527128	+	0.849786i	$0.676731\pi$
$930$			20.1448i			0.0216611i
$931$			241.194i			0.259070i
$932$			2374.02i			2.54723i
$933$	−459.865			−0.492889
$934$			30.9178i			0.0331025i
$935$	−394.735	+	399.943i	−0.422177	+	0.427747i
$936$	213.412			0.228004
$937$			508.830i			0.543041i	0.962433	+	0.271521i	$0.0875265\pi$
$937$			508.830i			0.543041i	−0.962433	+	0.271521i	$0.912473\pi$
$938$	−300.133			−0.319971
$939$	−745.782			−0.794230
$940$	−56.0658			−0.0596444
$941$		−	1116.71i		−	1.18673i	−0.804934	−	0.593365i	$-0.797799\pi$
$941$		−	1116.71i		−	1.18673i	0.804934	−	0.593365i	$-0.202201\pi$
$942$		−	125.895i		−	0.133646i
$943$		−	56.9769i		−	0.0604209i
$944$	542.870			0.575074
$945$		−	30.7409i		−	0.0325300i
$946$	−1452.32	−	1433.40i	−1.53522	−	1.51523i
$947$	−1226.74			−1.29540			−0.647699	−	0.761896i	$-0.724268\pi$
$947$	−1226.74			−1.29540			−0.647699	+	0.761896i	$0.724268\pi$
$948$			205.362i			0.216626i
$949$	285.997			0.301367
$950$	−616.111			−0.648537
$951$	−347.734			−0.365651
$952$			1035.22i			1.08741i
$953$		−	1445.95i		−	1.51726i	−0.651523	−	0.758629i	$-0.725870\pi$
$953$		−	1445.95i		−	1.51726i	0.651523	−	0.758629i	$-0.274130\pi$
$954$			815.960i			0.855304i
$955$	21.8757			0.0229065
$956$			1885.29i			1.97206i
$957$	−125.366	+	127.020i	−0.130999	+	0.132728i
$958$	−2930.49			−3.05896
$959$			554.950i			0.578675i
$960$	−60.6851			−0.0632137
$961$	−958.885			−0.997799
$962$	−498.225			−0.517905
$963$		−	270.311i		−	0.280697i
$964$		−	2435.08i		−	2.52601i
$965$		−	344.715i		−	0.357218i
$966$	164.352			0.170137
$967$		−	39.9448i		−	0.0413080i	−0.999787	−	0.0206540i	$-0.993425\pi$
$967$		−	39.9448i		−	0.0413080i	0.999787	−	0.0206540i	$-0.00657484\pi$
$968$	−2072.15	+	27.1614i	−2.14066	+	0.0280593i
$969$	1363.44			1.40706
$970$			278.405i			0.287015i
$971$	109.458			0.112727			0.0563635	−	0.998410i	$-0.482049\pi$
$971$	109.458			0.112727			0.0563635	+	0.998410i	$0.482049\pi$
$972$	137.009			0.140955
$973$	−450.733			−0.463240
$974$			1501.40i			1.54148i
$975$			35.9711i			0.0368934i
$976$			2848.45i			2.91850i
$977$	707.098			0.723744			0.361872	−	0.932228i	$-0.382138\pi$
$977$	707.098			0.723744			0.361872	+	0.932228i	$0.382138\pi$
$978$		−	1243.72i		−	1.27170i
$979$	443.670	+	437.892i	0.453187	+	0.447285i
$980$	137.571			0.140379
$981$		−	105.044i		−	0.107079i
$982$	−1252.74			−1.27570
$983$	−1067.27			−1.08573			−0.542864	−	0.839821i	$-0.682660\pi$
$983$	−1067.27			−1.08573			−0.542864	+	0.839821i	$0.682660\pi$
$984$	168.534			0.171275
$985$			475.635i			0.482878i
$986$		−	765.306i		−	0.776173i
$987$		−	13.0731i		−	0.0132453i
$988$	1257.87			1.27315
$989$		−	520.213i		−	0.525999i
$990$	−185.370	+	187.816i	−0.187242	+	0.189713i
$991$	−866.343			−0.874210			−0.437105	−	0.899410i	$-0.643996\pi$
$991$	−866.343			−0.874210			−0.437105	+	0.899410i	$0.643996\pi$
$992$		−	36.0741i		−	0.0363650i
$993$	411.828			0.414731
$994$	−1132.45			−1.13928
$995$	−751.975			−0.755754
$996$		−	1770.47i		−	1.77758i
$997$		−	690.996i		−	0.693075i	−0.938036	−	0.346538i	$-0.887357\pi$
$997$		−	690.996i		−	0.693075i	0.938036	−	0.346538i	$-0.112643\pi$
$998$		−	384.613i		−	0.385384i
$999$	−174.287			−0.174461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.9	✓	96
11.10	odd	2	inner	1155.3.b.a.736.88	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.9	✓	96	1.1	even	1	trivial
1155.3.b.a.736.88	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)

\(f(q)\)	\(=\)	\(q-3.57619i q^{2} -1.73205 q^{3} -8.78910 q^{4} +2.23607 q^{5} +6.19413i q^{6} +2.64575i q^{7} +17.1267i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.57619i q^{2} -1.73205 q^{3} -8.78910 q^{4} +2.23607 q^{5} +6.19413i q^{6} +2.64575i q^{7} +17.1267i q^{8} +3.00000 q^{9} -7.99659i q^{10} +(-7.82898 - 7.72703i) q^{11} +15.2232 q^{12} -4.15358i q^{13} +9.46170 q^{14} -3.87298 q^{15} +26.0919 q^{16} -22.8459i q^{17} -10.7286i q^{18} -34.4563i q^{19} -19.6530 q^{20} -4.58258i q^{21} +(-27.6333 + 27.9979i) q^{22} -10.0287 q^{23} -29.6643i q^{24} +5.00000 q^{25} -14.8540 q^{26} -5.19615 q^{27} -23.2538i q^{28} +9.36715i q^{29} +13.8505i q^{30} +1.45445 q^{31} -24.8026i q^{32} +(13.5602 + 13.3836i) q^{33} -81.7011 q^{34} +5.91608i q^{35} -26.3673 q^{36} +33.5415 q^{37} -123.222 q^{38} +7.19421i q^{39} +38.2965i q^{40} +5.68138i q^{41} -16.3881 q^{42} +51.8723i q^{43} +(68.8097 + 67.9137i) q^{44} +6.70820 q^{45} +35.8645i q^{46} +2.85278 q^{47} -45.1925 q^{48} -7.00000 q^{49} -17.8809i q^{50} +39.5702i q^{51} +36.5062i q^{52} -76.0550 q^{53} +18.5824i q^{54} +(-17.5061 - 17.2782i) q^{55} -45.3130 q^{56} +59.6801i q^{57} +33.4987 q^{58} +20.8061 q^{59} +34.0400 q^{60} +109.170i q^{61} -5.20137i q^{62} +7.93725i q^{63} +15.6688 q^{64} -9.28769i q^{65} +(47.8623 - 48.4938i) q^{66} -31.7208 q^{67} +200.795i q^{68} +17.3702 q^{69} +21.1570 q^{70} -119.688 q^{71} +51.3801i q^{72} +68.8555i q^{73} -119.951i q^{74} -8.66025 q^{75} +302.840i q^{76} +(20.4438 - 20.7135i) q^{77} +25.7278 q^{78} +13.4901i q^{79} +58.3433 q^{80} +9.00000 q^{81} +20.3177 q^{82} -116.301i q^{83} +40.2767i q^{84} -51.0850i q^{85} +185.505 q^{86} -16.2244i q^{87} +(132.339 - 134.085i) q^{88} -56.6702 q^{89} -23.9898i q^{90} +10.9893 q^{91} +88.1434 q^{92} -2.51918 q^{93} -10.2021i q^{94} -77.0466i q^{95} +42.9594i q^{96} -34.8154 q^{97} +25.0333i q^{98} +(-23.4869 - 23.1811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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