LMFDB - Embedded newform 1155.3.b.a.736.17

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			736.17
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.80

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.91387i q^{2} -1.73205 q^{3} -4.49063 q^{4} +2.23607 q^{5} +5.04697i q^{6} -2.64575i q^{7} +1.42964i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.91387i q^{2} -1.73205 q^{3} -4.49063 q^{4} +2.23607 q^{5} +5.04697i q^{6} -2.64575i q^{7} +1.42964i q^{8} +3.00000 q^{9} -6.51561i q^{10} +(3.40000 + 10.4614i) q^{11} +7.77800 q^{12} +8.89625i q^{13} -7.70937 q^{14} -3.87298 q^{15} -13.7968 q^{16} -21.0532i q^{17} -8.74161i q^{18} +13.7552i q^{19} -10.0414 q^{20} +4.58258i q^{21} +(30.4830 - 9.90716i) q^{22} -36.8321 q^{23} -2.47621i q^{24} +5.00000 q^{25} +25.9225 q^{26} -5.19615 q^{27} +11.8811i q^{28} +22.1928i q^{29} +11.2854i q^{30} +31.0516 q^{31} +45.9205i q^{32} +(-5.88898 - 18.1196i) q^{33} -61.3462 q^{34} -5.91608i q^{35} -13.4719 q^{36} -50.4911 q^{37} +40.0809 q^{38} -15.4088i q^{39} +3.19677i q^{40} +60.1812i q^{41} +13.3530 q^{42} +25.9562i q^{43} +(-15.2682 - 46.9781i) q^{44} +6.70820 q^{45} +107.324i q^{46} -87.0343 q^{47} +23.8967 q^{48} -7.00000 q^{49} -14.5693i q^{50} +36.4652i q^{51} -39.9498i q^{52} -64.9447 q^{53} +15.1409i q^{54} +(7.60264 + 23.3923i) q^{55} +3.78247 q^{56} -23.8247i q^{57} +64.6670 q^{58} -20.6811 q^{59} +17.3921 q^{60} +35.9600i q^{61} -90.4803i q^{62} -7.93725i q^{63} +78.6192 q^{64} +19.8926i q^{65} +(-52.7981 + 17.1597i) q^{66} +117.174 q^{67} +94.5421i q^{68} +63.7950 q^{69} -17.2387 q^{70} +15.3591 q^{71} +4.28891i q^{72} +131.484i q^{73} +147.125i q^{74} -8.66025 q^{75} -61.7696i q^{76} +(27.6781 - 8.99556i) q^{77} -44.8991 q^{78} -62.8679i q^{79} -30.8505 q^{80} +9.00000 q^{81} +175.360 q^{82} -47.1957i q^{83} -20.5787i q^{84} -47.0763i q^{85} +75.6330 q^{86} -38.4391i q^{87} +(-14.9559 + 4.86077i) q^{88} +150.401 q^{89} -19.5468i q^{90} +23.5373 q^{91} +165.399 q^{92} -53.7830 q^{93} +253.607i q^{94} +30.7576i q^{95} -79.5366i q^{96} -30.9484 q^{97} +20.3971i q^{98} +(10.2000 + 31.3841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.91387i		−	1.45693i	−0.685081	−	0.728467i	$-0.740233\pi$
$2$		−	2.91387i		−	1.45693i	0.685081	−	0.728467i	$-0.259767\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−4.49063			−1.12266
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$			5.04697i			0.841162i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$			1.42964i			0.178705i
$9$	3.00000			0.333333
$10$		−	6.51561i		−	0.651561i
$11$	3.40000	+	10.4614i	0.309091	+	0.951032i
$11$	3.40000	+	10.4614i	0.309091	+	0.951032i
$12$	7.77800			0.648167
$13$			8.89625i			0.684327i	0.939640	+	0.342163i	$0.111160\pi$
$13$			8.89625i			0.684327i	−0.939640	+	0.342163i	$0.888840\pi$
$14$	−7.70937			−0.550669
$15$	−3.87298			−0.258199
$16$	−13.7968			−0.862297
$17$		−	21.0532i		−	1.23842i	−0.785225	−	0.619211i	$-0.787453\pi$
$17$		−	21.0532i		−	1.23842i	0.785225	−	0.619211i	$-0.212547\pi$
$18$		−	8.74161i		−	0.485645i
$19$			13.7552i			0.723958i	0.932186	+	0.361979i	$0.117899\pi$
$19$			13.7552i			0.723958i	−0.932186	+	0.361979i	$0.882101\pi$
$20$	−10.0414			−0.502068
$21$			4.58258i			0.218218i
$22$	30.4830	−	9.90716i	1.38559	−	0.450326i
$23$	−36.8321			−1.60139			−0.800697	−	0.599069i	$-0.795537\pi$
$23$	−36.8321			−1.60139			−0.800697	+	0.599069i	$0.795537\pi$
$24$		−	2.47621i		−	0.103175i
$25$	5.00000			0.200000
$26$	25.9225			0.997019
$27$	−5.19615			−0.192450
$28$			11.8811i			0.424325i
$29$			22.1928i			0.765269i	0.923900	+	0.382635i	$0.124983\pi$
$29$			22.1928i			0.765269i	−0.923900	+	0.382635i	$0.875017\pi$
$30$			11.2854i			0.376179i
$31$	31.0516			1.00166			0.500832	−	0.865544i	$-0.333027\pi$
$31$	31.0516			1.00166			0.500832	+	0.865544i	$0.333027\pi$
$32$			45.9205i			1.43501i
$33$	−5.88898	−	18.1196i	−0.178454	−	0.549079i
$34$	−61.3462			−1.80430
$35$		−	5.91608i		−	0.169031i
$36$	−13.4719			−0.374219
$37$	−50.4911			−1.36463			−0.682313	−	0.731061i	$-0.739026\pi$
$37$	−50.4911			−1.36463			−0.682313	+	0.731061i	$0.739026\pi$
$38$	40.0809			1.05476
$39$		−	15.4088i		−	0.395096i
$40$			3.19677i			0.0799192i
$41$			60.1812i			1.46783i	0.679240	+	0.733917i	$0.262310\pi$
$41$			60.1812i			1.46783i	−0.679240	+	0.733917i	$0.737690\pi$
$42$	13.3530			0.317929
$43$			25.9562i			0.603633i	0.953366	+	0.301816i	$0.0975930\pi$
$43$			25.9562i			0.603633i	−0.953366	+	0.301816i	$0.902407\pi$
$44$	−15.2682	−	46.9781i	−0.347004	−	1.06768i
$45$	6.70820			0.149071
$46$			107.324i			2.33313i
$47$	−87.0343			−1.85179			−0.925897	−	0.377775i	$-0.876689\pi$
$47$	−87.0343			−1.85179			−0.925897	+	0.377775i	$0.876689\pi$
$48$	23.8967			0.497847
$49$	−7.00000			−0.142857
$50$		−	14.5693i		−	0.291387i
$51$			36.4652i			0.715003i
$52$		−	39.9498i		−	0.768265i
$53$	−64.9447			−1.22537			−0.612686	−	0.790327i	$-0.709911\pi$
$53$	−64.9447			−1.22537			−0.612686	+	0.790327i	$0.709911\pi$
$54$			15.1409i			0.280387i
$55$	7.60264	+	23.3923i	0.138230	+	0.425315i
$56$	3.78247			0.0675440
$57$		−	23.8247i		−	0.417977i
$58$	64.6670			1.11495
$59$	−20.6811			−0.350526			−0.175263	−	0.984522i	$-0.556078\pi$
$59$	−20.6811			−0.350526			−0.175263	+	0.984522i	$0.556078\pi$
$60$	17.3921			0.289869
$61$			35.9600i			0.589509i	0.955573	+	0.294754i	$0.0952378\pi$
$61$			35.9600i			0.589509i	−0.955573	+	0.294754i	$0.904762\pi$
$62$		−	90.4803i		−	1.45936i
$63$		−	7.93725i		−	0.125988i
$64$	78.6192			1.22843
$65$			19.8926i			0.306040i
$66$	−52.7981	+	17.1597i	−0.799972	+	0.259996i
$67$	117.174			1.74886			0.874432	−	0.485148i	$-0.161234\pi$
$67$	117.174			1.74886			0.874432	+	0.485148i	$0.161234\pi$
$68$			94.5421i			1.39032i
$69$	63.7950			0.924566
$70$	−17.2387			−0.246267
$71$	15.3591			0.216325			0.108163	−	0.994133i	$-0.465503\pi$
$71$	15.3591			0.216325			0.108163	+	0.994133i	$0.465503\pi$
$72$			4.28891i			0.0595682i
$73$			131.484i			1.80115i	0.434697	+	0.900577i	$0.356855\pi$
$73$			131.484i			1.80115i	−0.434697	+	0.900577i	$0.643145\pi$
$74$			147.125i			1.98817i
$75$	−8.66025			−0.115470
$76$		−	61.7696i		−	0.812757i
$77$	27.6781	−	8.99556i	0.359456	−	0.116825i
$78$	−44.8991			−0.575629
$79$		−	62.8679i		−	0.795796i	−0.917430	−	0.397898i	$-0.869740\pi$
$79$		−	62.8679i		−	0.795796i	0.917430	−	0.397898i	$-0.130260\pi$
$80$	−30.8505			−0.385631
$81$	9.00000			0.111111
$82$	175.360			2.13854
$83$		−	47.1957i		−	0.568622i	−0.958732	−	0.284311i	$-0.908235\pi$
$83$		−	47.1957i		−	0.568622i	0.958732	−	0.284311i	$-0.0917649\pi$
$84$		−	20.5787i		−	0.244984i
$85$		−	47.0763i		−	0.553839i
$86$	75.6330			0.879453
$87$		−	38.4391i		−	0.441829i
$88$	−14.9559	+	4.86077i	−0.169954	+	0.0552360i
$89$	150.401			1.68990			0.844948	−	0.534848i	$-0.179631\pi$
$89$	150.401			1.68990			0.844948	+	0.534848i	$0.179631\pi$
$90$		−	19.5468i		−	0.217187i
$91$	23.5373			0.258651
$92$	165.399			1.79782
$93$	−53.7830			−0.578311
$94$			253.607i			2.69794i
$95$			30.7576i			0.323764i
$96$		−	79.5366i		−	0.828506i
$97$	−30.9484			−0.319056			−0.159528	−	0.987193i	$-0.550997\pi$
$97$	−30.9484			−0.319056			−0.159528	+	0.987193i	$0.550997\pi$
$98$			20.3971i			0.208133i
$99$	10.2000	+	31.3841i	0.103030	+	0.317011i
$100$	−22.4532			−0.224532
$101$			65.0414i			0.643974i	0.946744	+	0.321987i	$0.104351\pi$
$101$			65.0414i			0.643974i	−0.946744	+	0.321987i	$0.895649\pi$
$102$	106.255			1.04171
$103$	−154.940			−1.50427			−0.752136	−	0.659008i	$-0.770976\pi$
$103$	−154.940			−1.50427			−0.752136	+	0.659008i	$0.770976\pi$
$104$	−12.7184			−0.122292
$105$			10.2470i			0.0975900i
$106$			189.240i			1.78529i
$107$			18.3813i			0.171788i	0.996304	+	0.0858940i	$0.0273746\pi$
$107$			18.3813i			0.171788i	−0.996304	+	0.0858940i	$0.972625\pi$
$108$	23.3340			0.216056
$109$		−	38.0457i		−	0.349043i	−0.984653	−	0.174521i	$-0.944162\pi$
$109$		−	38.0457i		−	0.349043i	0.984653	−	0.174521i	$-0.0558378\pi$
$110$	68.1621	−	22.1531i	0.619656	−	0.201392i
$111$	87.4532			0.787867
$112$			36.5028i			0.325918i
$113$	171.735			1.51978			0.759890	−	0.650052i	$-0.225253\pi$
$113$	171.735			1.51978			0.759890	+	0.650052i	$0.225253\pi$
$114$	−69.4221			−0.608966
$115$	−82.3590			−0.716165
$116$		−	99.6598i		−	0.859136i
$117$			26.6887i			0.228109i
$118$			60.2619i			0.510694i
$119$	−55.7015			−0.468079
$120$		−	5.53696i		−	0.0461414i
$121$	−97.8800	+	71.1373i	−0.808925	+	0.587911i
$122$	104.783			0.858876
$123$		−	104.237i		−	0.847454i
$124$	−139.441			−1.12453
$125$	11.1803			0.0894427
$126$	−23.1281			−0.183556
$127$			111.131i			0.875051i	0.899206	+	0.437525i	$0.144145\pi$
$127$			111.131i			0.875051i	−0.899206	+	0.437525i	$0.855855\pi$
$128$		−	45.4043i		−	0.354721i
$129$		−	44.9575i		−	0.348508i
$130$	57.9645			0.445881
$131$		−	252.596i		−	1.92821i	−0.265513	−	0.964107i	$-0.585541\pi$
$131$		−	252.596i		−	1.92821i	0.265513	−	0.964107i	$-0.414459\pi$
$132$	26.4452	+	81.3685i	0.200343	+	0.616428i
$133$	36.3928			0.273630
$134$		−	341.429i		−	2.54798i
$135$	−11.6190			−0.0860663
$136$	30.0984			0.221312
$137$	143.758			1.04933			0.524664	−	0.851309i	$-0.324191\pi$
$137$	143.758			1.04933			0.524664	+	0.851309i	$0.324191\pi$
$138$		−	185.890i		−	1.34703i
$139$		−	96.0141i		−	0.690749i	−0.938465	−	0.345374i	$-0.887752\pi$
$139$		−	96.0141i		−	0.690749i	0.938465	−	0.345374i	$-0.112248\pi$
$140$			26.5669i			0.189764i
$141$	150.748			1.06913
$142$		−	44.7543i		−	0.315171i
$143$	−93.0668	+	30.2473i	−0.650817	+	0.211519i
$144$	−41.3903			−0.287432
$145$			49.6246i			0.342239i
$146$	383.128			2.62416
$147$	12.1244			0.0824786
$148$	226.737			1.53201
$149$			50.8167i			0.341051i	0.985353	+	0.170526i	$0.0545466\pi$
$149$			50.8167i			0.341051i	−0.985353	+	0.170526i	$0.945453\pi$
$150$			25.2348i			0.168232i
$151$			288.544i			1.91089i	0.295172	+	0.955444i	$0.404623\pi$
$151$			288.544i			1.91089i	−0.295172	+	0.955444i	$0.595377\pi$
$152$	−19.6650			−0.129375
$153$		−	63.1595i		−	0.412807i
$154$	−26.2119	−	80.6505i	−0.170207	−	0.523705i
$155$	69.4335			0.447958
$156$			69.1950i			0.443558i
$157$	4.58898			0.0292292			0.0146146	−	0.999893i	$-0.495348\pi$
$157$	4.58898			0.0292292			0.0146146	+	0.999893i	$0.495348\pi$
$158$	−183.189			−1.15942
$159$	112.488			0.707469
$160$			102.681i			0.641758i
$161$			97.4485i			0.605270i
$162$		−	26.2248i		−	0.161882i
$163$	72.2133			0.443027			0.221513	−	0.975157i	$-0.428900\pi$
$163$	72.2133			0.443027			0.221513	+	0.975157i	$0.428900\pi$
$164$		−	270.251i		−	1.64787i
$165$	−13.1682	−	40.5167i	−0.0798070	−	0.245556i
$166$	−137.522			−0.828446
$167$		−	59.0967i		−	0.353872i	−0.984222	−	0.176936i	$-0.943381\pi$
$167$		−	59.0967i		−	0.353872i	0.984222	−	0.176936i	$-0.0566186\pi$
$168$	−6.55142			−0.0389966
$169$	89.8568			0.531697
$170$	−137.174			−0.806907
$171$			41.2656i			0.241319i
$172$		−	116.560i		−	0.677673i
$173$			12.1886i			0.0704541i	0.999379	+	0.0352271i	$0.0112154\pi$
$173$			12.1886i			0.0704541i	−0.999379	+	0.0352271i	$0.988785\pi$
$174$	−112.006			−0.643715
$175$		−	13.2288i		−	0.0755929i
$176$	−46.9090	−	144.333i	−0.266528	−	0.820072i
$177$	35.8207			0.202377
$178$		−	438.248i		−	2.46207i
$179$	−42.1448			−0.235446			−0.117723	−	0.993046i	$-0.537559\pi$
$179$	−42.1448			−0.235446			−0.117723	+	0.993046i	$0.537559\pi$
$180$	−30.1241			−0.167356
$181$	−55.6996			−0.307733			−0.153866	−	0.988092i	$-0.549173\pi$
$181$	−55.6996			−0.307733			−0.153866	+	0.988092i	$0.549173\pi$
$182$		−	68.5845i		−	0.376838i
$183$		−	62.2846i		−	0.340353i
$184$		−	52.6565i		−	0.286177i
$185$	−112.902			−0.610279
$186$			156.716i			0.842562i
$187$	220.245	−	71.5808i	1.17778	−	0.382785i
$188$	390.839			2.07893
$189$			13.7477i			0.0727393i
$190$	89.6235			0.471703
$191$	53.2840			0.278974			0.139487	−	0.990224i	$-0.455455\pi$
$191$	53.2840			0.278974			0.139487	+	0.990224i	$0.455455\pi$
$192$	−136.173			−0.709232
$193$			154.234i			0.799142i	0.916702	+	0.399571i	$0.130841\pi$
$193$			154.234i			0.799142i	−0.916702	+	0.399571i	$0.869159\pi$
$194$			90.1796i			0.464843i
$195$		−	34.4550i		−	0.176692i
$196$	31.4344			0.160380
$197$		−	378.159i		−	1.91959i	−0.280708	−	0.959793i	$-0.590569\pi$
$197$		−	378.159i		−	1.91959i	0.280708	−	0.959793i	$-0.409431\pi$
$198$	91.4491	−	29.7215i	0.461864	−	0.150109i
$199$	−346.128			−1.73934			−0.869669	−	0.493636i	$-0.835667\pi$
$199$	−346.128			−1.73934			−0.869669	+	0.493636i	$0.835667\pi$
$200$			7.14819i			0.0357409i
$201$	−202.951			−1.00971
$202$	189.522			0.938228
$203$	58.7167			0.289245
$204$		−	163.752i		−	0.802704i
$205$			134.569i			0.656435i
$206$			451.475i			2.19163i
$207$	−110.496			−0.533798
$208$		−	122.739i		−	0.590093i
$209$	−143.898	+	46.7677i	−0.688508	+	0.223769i
$210$	29.8583			0.142182
$211$			293.063i			1.38892i	0.719529	+	0.694462i	$0.244358\pi$
$211$			293.063i			1.38892i	−0.719529	+	0.694462i	$0.755642\pi$
$212$	291.643			1.37567
$213$	−26.6027			−0.124895
$214$	53.5608			0.250284
$215$			58.0399i			0.269953i
$216$		−	7.42862i		−	0.0343917i
$217$		−	82.1548i		−	0.378594i
$218$	−110.860			−0.508532
$219$		−	227.737i		−	1.03990i
$220$	−34.1406	−	105.046i	−0.155185	−	0.477483i
$221$	187.294			0.847485
$222$		−	254.827i		−	1.14787i
$223$	−329.653			−1.47826			−0.739132	−	0.673561i	$-0.764764\pi$
$223$	−329.653			−1.47826			−0.739132	+	0.673561i	$0.764764\pi$
$224$	121.494			0.542385
$225$	15.0000			0.0666667
$226$		−	500.414i		−	2.21422i
$227$		−	261.772i		−	1.15318i	−0.817034	−	0.576589i	$-0.804383\pi$
$227$		−	261.772i		−	1.15318i	0.817034	−	0.576589i	$-0.195617\pi$
$228$			106.988i			0.469246i
$229$	−380.156			−1.66007			−0.830036	−	0.557710i	$-0.811680\pi$
$229$	−380.156			−1.66007			−0.830036	+	0.557710i	$0.811680\pi$
$230$			239.983i			1.04341i
$231$	−47.9400	+	15.5808i	−0.207532	+	0.0674492i
$232$	−31.7277			−0.136757
$233$		−	4.48400i		−	0.0192446i	−0.999954	−	0.00962232i	$-0.996937\pi$
$233$		−	4.48400i		−	0.0192446i	0.999954	−	0.00962232i	$-0.00306293\pi$
$234$	77.7675			0.332340
$235$	−194.615			−0.828148
$236$	92.8710			0.393521
$237$			108.890i			0.459453i
$238$			162.307i			0.681961i
$239$			187.815i			0.785838i	0.919573	+	0.392919i	$0.128535\pi$
$239$			187.815i			0.785838i	−0.919573	+	0.392919i	$0.871465\pi$
$240$	53.4346			0.222644
$241$			324.314i			1.34570i	0.739778	+	0.672851i	$0.234931\pi$
$241$			324.314i			1.34570i	−0.739778	+	0.672851i	$0.765069\pi$
$242$	207.285	+	285.209i	0.856548	+	1.17855i
$243$	−15.5885			−0.0641500
$244$		−	161.483i		−	0.661817i
$245$	−15.6525			−0.0638877
$246$	−303.732			−1.23468
$247$	−122.370			−0.495424
$248$			44.3925i			0.179002i
$249$			81.7453i			0.328294i
$250$		−	32.5780i		−	0.130312i
$251$	−369.440			−1.47187			−0.735936	−	0.677051i	$-0.763257\pi$
$251$	−369.440			−1.47187			−0.735936	+	0.677051i	$0.763257\pi$
$252$			35.6433i			0.141442i
$253$	−125.229	−	385.313i	−0.494977	−	1.52298i
$254$	323.822			1.27489
$255$			81.5386i			0.319759i
$256$	182.175			0.711621
$257$	76.1233			0.296200			0.148100	−	0.988972i	$-0.452684\pi$
$257$	76.1233			0.296200			0.148100	+	0.988972i	$0.452684\pi$
$258$	−131.000			−0.507753
$259$			133.587i			0.515780i
$260$		−	89.3304i		−	0.343579i
$261$			66.5784i			0.255090i
$262$	−736.032			−2.80928
$263$			107.233i			0.407732i	0.978999	+	0.203866i	$0.0653507\pi$
$263$			107.233i			0.407732i	−0.978999	+	0.203866i	$0.934649\pi$
$264$	25.9045	−	8.41910i	0.0981230	−	0.0318905i
$265$	−145.221			−0.548003
$266$		−	106.044i		−	0.398662i
$267$	−260.502			−0.975662
$268$	−526.185			−1.96338
$269$	67.6226			0.251385			0.125693	−	0.992069i	$-0.459885\pi$
$269$	67.6226			0.251385			0.125693	+	0.992069i	$0.459885\pi$
$270$			33.8561i			0.125393i
$271$		−	185.448i		−	0.684309i	−0.939644	−	0.342154i	$-0.888843\pi$
$271$		−	185.448i		−	0.684309i	0.939644	−	0.342154i	$-0.111157\pi$
$272$			290.465i			1.06789i
$273$	−40.7677			−0.149332
$274$		−	418.892i		−	1.52880i
$275$	17.0000	+	52.3068i	0.0618182	+	0.190206i
$276$	−286.480			−1.03797
$277$			265.925i			0.960019i	0.877263	+	0.480010i	$0.159367\pi$
$277$			265.925i			0.960019i	−0.877263	+	0.480010i	$0.840633\pi$
$278$	−279.772			−1.00638
$279$	93.1548			0.333888
$280$	8.45785			0.0302066
$281$			80.3577i			0.285970i	0.989725	+	0.142985i	$0.0456701\pi$
$281$			80.3577i			0.285970i	−0.989725	+	0.142985i	$0.954330\pi$
$282$		−	439.260i		−	1.55766i
$283$			248.450i			0.877917i	0.898507	+	0.438958i	$0.144652\pi$
$283$			248.450i			0.877917i	−0.898507	+	0.438958i	$0.855348\pi$
$284$	−68.9720			−0.242859
$285$		−	53.2737i		−	0.186925i
$286$	88.1366	+	271.185i	0.308170	+	0.948198i
$287$	159.224			0.554789
$288$			137.761i			0.478338i
$289$	−154.236			−0.533689
$290$	144.600			0.498620
$291$	53.6042			0.184207
$292$		−	590.447i		−	2.02208i
$293$		−	287.335i		−	0.980665i	−0.871535	−	0.490333i	$-0.836875\pi$
$293$		−	287.335i		−	0.980665i	0.871535	−	0.490333i	$-0.163125\pi$
$294$		−	35.3288i		−	0.120166i
$295$	−46.2443			−0.156760
$296$		−	72.1840i		−	0.243865i
$297$	−17.6669	−	54.3588i	−0.0594846	−	0.183026i
$298$	148.073			0.496889
$299$		−	327.667i		−	1.09588i
$300$	38.8900			0.129633
$301$	68.6737			0.228152
$302$	840.780			2.78404
$303$		−	112.655i		−	0.371799i
$304$		−	189.777i		−	0.624267i
$305$			80.4091i			0.263636i
$306$	−184.039			−0.601433
$307$			272.810i			0.888632i	0.895870	+	0.444316i	$0.146553\pi$
$307$			272.810i			0.888632i	−0.895870	+	0.444316i	$0.853447\pi$
$308$	−124.292	+	40.3958i	−0.403547	+	0.131155i
$309$	268.364			0.868492
$310$		−	202.320i		−	0.652645i
$311$	−357.641			−1.14997			−0.574986	−	0.818163i	$-0.694993\pi$
$311$	−357.641			−1.14997			−0.574986	+	0.818163i	$0.694993\pi$
$312$	22.0289			0.0706056
$313$	332.086			1.06098			0.530489	−	0.847692i	$-0.322008\pi$
$313$	332.086			1.06098			0.530489	+	0.847692i	$0.322008\pi$
$314$		−	13.3717i		−	0.0425850i
$315$		−	17.7482i		−	0.0563436i
$316$			282.317i			0.893407i
$317$	37.3900			0.117950			0.0589748	−	0.998259i	$-0.481217\pi$
$317$	37.3900			0.117950			0.0589748	+	0.998259i	$0.481217\pi$
$318$		−	327.774i		−	1.03074i
$319$	−232.167	+	75.4556i	−0.727796	+	0.236538i
$320$	175.798			0.549369
$321$		−	31.8374i		−	0.0991819i
$322$	283.952			0.881839
$323$	289.591			0.896566
$324$	−40.4157			−0.124740
$325$			44.4812i			0.136865i
$326$		−	210.420i		−	0.645461i
$327$			65.8970i			0.201520i
$328$	−86.0373			−0.262309
$329$			230.271i			0.699913i
$330$	−118.060	+	38.3703i	−0.357758	+	0.116274i
$331$	345.893			1.04499			0.522497	−	0.852641i	$-0.325001\pi$
$331$	345.893			1.04499			0.522497	+	0.852641i	$0.325001\pi$
$332$			211.938i			0.638368i
$333$	−151.473			−0.454875
$334$	−172.200			−0.515569
$335$	262.009			0.782116
$336$		−	63.2247i		−	0.188169i
$337$			169.271i			0.502288i	0.967950	+	0.251144i	$0.0808068\pi$
$337$			169.271i			0.502288i	−0.967950	+	0.251144i	$0.919193\pi$
$338$		−	261.831i		−	0.774647i
$339$	−297.454			−0.877445
$340$			211.402i			0.621772i
$341$	105.576	+	324.842i	0.309606	+	0.952616i
$342$	120.243			0.351586
$343$			18.5203i			0.0539949i
$344$	−37.1080			−0.107872
$345$	142.650			0.413478
$346$	35.5159			0.102647
$347$			451.984i			1.30255i	0.758843	+	0.651273i	$0.225765\pi$
$347$			451.984i			1.30255i	−0.758843	+	0.651273i	$0.774235\pi$
$348$			172.616i			0.496022i
$349$		−	483.860i		−	1.38642i	−0.720736	−	0.693210i	$-0.756196\pi$
$349$		−	483.860i		−	1.38642i	0.720736	−	0.693210i	$-0.243804\pi$
$350$	−38.5469			−0.110134
$351$		−	46.2263i		−	0.131699i
$352$	−480.390	+	156.130i	−1.36475	+	0.443550i
$353$	−531.865			−1.50670			−0.753350	−	0.657620i	$-0.771563\pi$
$353$	−531.865			−1.50670			−0.753350	+	0.657620i	$0.771563\pi$
$354$		−	104.377i		−	0.294849i
$355$	34.3439			0.0967435
$356$	−675.395			−1.89718
$357$	96.4778			0.270246
$358$			122.804i			0.343029i
$359$			549.517i			1.53069i	0.643622	+	0.765344i	$0.277431\pi$
$359$			549.517i			1.53069i	−0.643622	+	0.765344i	$0.722569\pi$
$360$			9.59030i			0.0266397i
$361$	171.794			0.475885
$362$			162.301i			0.448346i
$363$	169.533	−	123.213i	0.467033	−	0.339431i
$364$	−105.697			−0.290377
$365$			294.008i			0.805500i
$366$	−181.489			−0.495872
$367$	304.285			0.829114			0.414557	−	0.910023i	$-0.363937\pi$
$367$	304.285			0.829114			0.414557	+	0.910023i	$0.363937\pi$
$368$	508.163			1.38088
$369$			180.544i			0.489278i
$370$			328.980i			0.889136i
$371$			171.828i			0.463147i
$372$	241.519			0.649246
$373$		−	402.611i		−	1.07939i	−0.841862	−	0.539693i	$-0.818540\pi$
$373$		−	402.611i		−	1.07939i	0.841862	−	0.539693i	$-0.181460\pi$
$374$	−208.577	−	641.764i	−0.557693	−	1.71595i
$375$	−19.3649			−0.0516398
$376$		−	124.428i		−	0.330924i
$377$	−197.433			−0.523694
$378$	40.0591			0.105976
$379$	−659.453			−1.73998			−0.869991	−	0.493067i	$-0.835876\pi$
$379$	−659.453			−1.73998			−0.869991	+	0.493067i	$0.835876\pi$
$380$		−	138.121i		−	0.363476i
$381$		−	192.485i		−	0.505211i
$382$		−	155.263i		−	0.406447i
$383$	−398.990			−1.04175			−0.520875	−	0.853633i	$-0.674394\pi$
$383$	−398.990			−1.04175			−0.520875	+	0.853633i	$0.674394\pi$
$384$			78.6425i			0.204798i
$385$	61.8902	−	20.1147i	0.160754	−	0.0522459i
$386$	449.419			1.16430
$387$			77.8686i			0.201211i
$388$	138.978			0.358191
$389$	386.465			0.993483			0.496742	−	0.867899i	$-0.334530\pi$
$389$	386.465			0.993483			0.496742	+	0.867899i	$0.334530\pi$
$390$	−100.397			−0.257429
$391$			775.432i			1.98320i
$392$		−	10.0075i		−	0.0255292i
$393$			437.509i			1.11326i
$394$	−1101.90			−2.79671
$395$		−	140.577i		−	0.355891i
$396$	−45.8045	−	140.934i	−0.115668	−	0.355895i
$397$	−118.763			−0.299151			−0.149575	−	0.988750i	$-0.547791\pi$
$397$	−118.763			−0.299151			−0.149575	+	0.988750i	$0.547791\pi$
$398$			1008.57i			2.53410i
$399$	−63.0343			−0.157981
$400$	−68.9838			−0.172459
$401$	−351.419			−0.876358			−0.438179	−	0.898888i	$-0.644376\pi$
$401$	−351.419			−0.876358			−0.438179	+	0.898888i	$0.644376\pi$
$402$			591.373i			1.47108i
$403$			276.243i			0.685466i
$404$		−	292.077i		−	0.722963i
$405$	20.1246			0.0496904
$406$		−	171.093i		−	0.421411i
$407$	−171.670	−	528.206i	−0.421794	−	1.29780i
$408$	−52.1320			−0.127774
$409$			112.845i			0.275904i	0.990439	+	0.137952i	$0.0440519\pi$
$409$			112.845i			0.275904i	−0.990439	+	0.137952i	$0.955948\pi$
$410$	392.117			0.956383
$411$	−248.996			−0.605830
$412$	695.779			1.68878
$413$			54.7169i			0.132487i
$414$			321.971i			0.777709i
$415$		−	105.533i		−	0.254296i
$416$	−408.520			−0.982019
$417$			166.301i			0.398804i
$418$	136.275	+	419.300i	0.326017	+	1.00311i
$419$	−8.96589			−0.0213983			−0.0106992	−	0.999943i	$-0.503406\pi$
$419$	−8.96589			−0.0213983			−0.0106992	+	0.999943i	$0.503406\pi$
$420$		−	46.0153i		−	0.109560i
$421$	−297.996			−0.707829			−0.353914	−	0.935278i	$-0.615150\pi$
$421$	−297.996			−0.707829			−0.353914	+	0.935278i	$0.615150\pi$
$422$	853.947			2.02357
$423$	−261.103			−0.617265
$424$		−	92.8474i		−	0.218980i
$425$		−	105.266i		−	0.247684i
$426$			77.5168i			0.181964i
$427$	95.1413			0.222813
$428$		−	82.5437i		−	0.192859i
$429$	161.196	−	52.3898i	0.375749	−	0.122121i
$430$	169.121			0.393304
$431$		−	555.943i		−	1.28989i	−0.764229	−	0.644945i	$-0.776880\pi$
$431$		−	555.943i		−	1.28989i	0.764229	−	0.644945i	$-0.223120\pi$
$432$	71.6900			0.165949
$433$	478.108			1.10418			0.552088	−	0.833786i	$-0.313831\pi$
$433$	478.108			1.10418			0.552088	+	0.833786i	$0.313831\pi$
$434$	−239.388			−0.551586
$435$		−	85.9524i		−	0.197592i
$436$			170.849i			0.391856i
$437$		−	506.633i		−	1.15934i
$438$	−663.597			−1.51506
$439$			476.563i			1.08556i	0.839874	+	0.542782i	$0.182629\pi$
$439$			476.563i			1.08556i	−0.839874	+	0.542782i	$0.817371\pi$
$440$	−33.4425	+	10.8690i	−0.0760057	+	0.0247023i
$441$	−21.0000			−0.0476190
$442$		−	545.751i		−	1.23473i
$443$	314.073			0.708968			0.354484	−	0.935062i	$-0.384657\pi$
$443$	314.073			0.708968			0.354484	+	0.935062i	$0.384657\pi$
$444$	−392.720			−0.884505
$445$	336.306			0.755745
$446$			960.565i			2.15373i
$447$		−	88.0170i		−	0.196906i
$448$		−	208.007i		−	0.464301i
$449$	196.704			0.438093			0.219047	−	0.975714i	$-0.429705\pi$
$449$	196.704			0.438093			0.219047	+	0.975714i	$0.429705\pi$
$450$		−	43.7080i		−	0.0971290i
$451$	−629.577	+	204.616i	−1.39596	+	0.453694i
$452$	−771.199			−1.70619
$453$		−	499.773i		−	1.10325i
$454$	−762.768			−1.68011
$455$	52.6309			0.115672
$456$	34.0607			0.0746945
$457$		−	322.483i		−	0.705653i	−0.935689	−	0.352826i	$-0.885221\pi$
$457$		−	322.483i		−	0.705653i	0.935689	−	0.352826i	$-0.114779\pi$
$458$			1107.73i			2.41862i
$459$			109.395i			0.238334i
$460$	369.844			0.804009
$461$		−	65.1094i		−	0.141235i	−0.997503	−	0.0706176i	$-0.977503\pi$
$461$		−	65.1094i		−	0.141235i	0.997503	−	0.0706176i	$-0.0224970\pi$
$462$	45.4003	+	139.691i	0.0982691	+	0.302361i
$463$	14.0408			0.0303257			0.0151629	−	0.999885i	$-0.495173\pi$
$463$	14.0408			0.0303257			0.0151629	+	0.999885i	$0.495173\pi$
$464$		−	306.189i		−	0.659890i
$465$	−120.262			−0.258629
$466$	−13.0658			−0.0280382
$467$	−390.618			−0.836440			−0.418220	−	0.908346i	$-0.637346\pi$
$467$	−390.618			−0.836440			−0.418220	+	0.908346i	$0.637346\pi$
$468$		−	119.849i		−	0.256088i
$469$		−	310.013i		−	0.661009i
$470$			567.082i			1.20656i
$471$	−7.94834			−0.0168755
$472$		−	29.5664i		−	0.0626407i
$473$	−271.537	+	88.2512i	−0.574074	+	0.186578i
$474$	317.292			0.669393
$475$			68.7760i			0.144792i
$476$	250.135			0.525493
$477$	−194.834			−0.408457
$478$	547.269			1.14491
$479$		−	584.912i		−	1.22111i	−0.791974	−	0.610555i	$-0.790946\pi$
$479$		−	584.912i		−	1.22111i	0.791974	−	0.610555i	$-0.209054\pi$
$480$		−	177.849i		−	0.370519i
$481$		−	449.182i		−	0.933850i
$482$	945.009			1.96060
$483$		−	168.786i		−	0.349453i
$484$	439.543	−	319.451i	0.908147	−	0.660023i
$485$	−69.2027			−0.142686
$486$			45.4227i			0.0934624i
$487$	−738.716			−1.51687			−0.758435	−	0.651748i	$-0.774036\pi$
$487$	−738.716			−1.51687			−0.758435	+	0.651748i	$0.774036\pi$
$488$	−51.4098			−0.105348
$489$	−125.077			−0.255782
$490$			45.6093i			0.0930801i
$491$		−	548.700i		−	1.11751i	−0.829331	−	0.558757i	$-0.811278\pi$
$491$		−	548.700i		−	1.11751i	0.829331	−	0.558757i	$-0.188722\pi$
$492$			468.089i			0.951401i
$493$	467.229			0.947726
$494$			356.569i			0.721800i
$495$	22.8079	+	70.1769i	0.0460766	+	0.141772i
$496$	−428.411			−0.863732
$497$		−	40.6363i		−	0.0817632i
$498$	238.195			0.478303
$499$	−950.752			−1.90531			−0.952657	−	0.304048i	$-0.901662\pi$
$499$	−950.752			−1.90531			−0.952657	+	0.304048i	$0.901662\pi$
$500$	−50.2068			−0.100414
$501$			102.358i			0.204308i
$502$			1076.50i			2.14442i
$503$			656.805i			1.30578i	0.757455	+	0.652888i	$0.226443\pi$
$503$			656.805i			1.30578i	−0.757455	+	0.652888i	$0.773557\pi$
$504$	11.3474			0.0225147
$505$			145.437i			0.287994i
$506$	−1122.75	+	364.901i	−2.21888	+	0.721149i
$507$	−155.636			−0.306975
$508$		−	499.050i		−	0.982383i
$509$	−356.993			−0.701362			−0.350681	−	0.936495i	$-0.614050\pi$
$509$	−356.993			−0.701362			−0.350681	+	0.936495i	$0.614050\pi$
$510$	237.593			0.465868
$511$	347.874			0.680772
$512$		−	712.451i		−	1.39151i
$513$		−	71.4741i		−	0.139326i
$514$		−	221.813i		−	0.431543i
$515$	−346.456			−0.672731
$516$			201.887i			0.391255i
$517$	−295.917	−	910.497i	−0.572373	−	1.76112i
$518$	389.255			0.751457
$519$		−	21.1112i		−	0.0406767i
$520$	−28.4392			−0.0546908
$521$	43.8023			0.0840735			0.0420367	−	0.999116i	$-0.486615\pi$
$521$	43.8023			0.0840735			0.0420367	+	0.999116i	$0.486615\pi$
$522$	194.001			0.371649
$523$		−	972.600i		−	1.85966i	−0.367994	−	0.929828i	$-0.619955\pi$
$523$		−	972.600i		−	1.85966i	0.367994	−	0.929828i	$-0.380045\pi$
$524$			1134.32i			2.16473i
$525$			22.9129i			0.0436436i
$526$	312.464			0.594039
$527$		−	653.735i		−	1.24048i
$528$	81.2488	+	249.992i	0.153880	+	0.473469i
$529$	827.602			1.56446
$530$			423.154i			0.798404i
$531$	−62.0432			−0.116842
$532$	−163.427			−0.307193
$533$	−535.387			−1.00448
$534$			759.068i			1.42148i
$535$			41.1019i			0.0768259i
$536$			167.516i			0.312530i
$537$	72.9970			0.135935
$538$		−	197.043i		−	0.366252i
$539$	−23.8000	−	73.2295i	−0.0441559	−	0.135862i
$540$	52.1764			0.0966230
$541$		−	640.265i		−	1.18348i	−0.806128	−	0.591742i	$-0.798441\pi$
$541$		−	640.265i		−	1.18348i	0.806128	−	0.591742i	$-0.201559\pi$
$542$	−540.370			−0.996993
$543$	96.4746			0.177670
$544$	966.772			1.77715
$545$		−	85.0727i		−	0.156097i
$546$			118.792i			0.217567i
$547$			345.169i			0.631022i	0.948922	+	0.315511i	$0.102176\pi$
$547$			345.169i			0.631022i	−0.948922	+	0.315511i	$0.897824\pi$
$548$	−645.564			−1.17804
$549$			107.880i			0.196503i
$550$	152.415	−	49.5358i	0.277118	−	0.0900651i
$551$	−305.267			−0.554023
$552$			91.2038i			0.165224i
$553$	−166.333			−0.300783
$554$	774.872			1.39869
$555$	195.551			0.352345
$556$			431.164i			0.775475i
$557$			756.763i			1.35864i	0.733841	+	0.679321i	$0.237726\pi$
$557$			756.763i			1.35864i	−0.733841	+	0.679321i	$0.762274\pi$
$558$		−	271.441i		−	0.486453i
$559$	−230.913			−0.413082
$560$			81.6227i			0.145755i
$561$	−381.475	+	123.982i	−0.679991	+	0.221001i
$562$	234.152			0.416640
$563$		−	733.565i		−	1.30296i	−0.758667	−	0.651478i	$-0.774149\pi$
$563$		−	733.565i		−	1.30296i	0.758667	−	0.651478i	$-0.225851\pi$
$564$	−676.953			−1.20027
$565$	384.011			0.679666
$566$	723.952			1.27907
$567$		−	23.8118i		−	0.0419961i
$568$			21.9579i			0.0386583i
$569$			99.8631i			0.175506i	0.996142	+	0.0877532i	$0.0279687\pi$
$569$			99.8631i			0.175506i	−0.996142	+	0.0877532i	$0.972031\pi$
$570$	−155.233			−0.272338
$571$		−	1120.33i		−	1.96204i	−0.193896	−	0.981022i	$-0.562112\pi$
$571$		−	1120.33i		−	1.96204i	0.193896	−	0.981022i	$-0.437888\pi$
$572$	417.929	−	135.829i	0.730645	−	0.237464i
$573$	−92.2906			−0.161066
$574$		−	463.959i		−	0.808291i
$575$	−184.160			−0.320279
$576$	235.858			0.409475
$577$	259.217			0.449249			0.224624	−	0.974445i	$-0.427884\pi$
$577$	259.217			0.449249			0.224624	+	0.974445i	$0.427884\pi$
$578$			449.424i			0.777550i
$579$		−	267.142i		−	0.461385i
$580$		−	222.846i		−	0.384217i
$581$	−124.868			−0.214919
$582$		−	156.196i		−	0.268377i
$583$	−220.812	−	679.410i	−0.378752	−	1.16537i
$584$	−187.975			−0.321875
$585$			59.6779i			0.102013i
$586$	−837.256			−1.42876
$587$	649.652			1.10673			0.553366	−	0.832938i	$-0.313343\pi$
$587$	649.652			1.10673			0.553366	+	0.832938i	$0.313343\pi$
$588$	−54.4460			−0.0925953
$589$			427.121i			0.725163i
$590$			134.750i			0.228389i
$591$			654.990i			1.10827i
$592$	696.614			1.17671
$593$		−	475.879i		−	0.802494i	−0.915970	−	0.401247i	$-0.868577\pi$
$593$		−	475.879i		−	0.802494i	0.915970	−	0.401247i	$-0.131423\pi$
$594$	−158.394	+	51.4791i	−0.266657	+	0.0866652i
$595$	−124.552			−0.209332
$596$		−	228.199i		−	0.382884i
$597$	599.511			1.00421
$598$	−954.780			−1.59662
$599$	−341.850			−0.570701			−0.285350	−	0.958423i	$-0.592110\pi$
$599$	−341.850			−0.570701			−0.285350	+	0.958423i	$0.592110\pi$
$600$		−	12.3810i		−	0.0206350i
$601$			419.930i			0.698719i	0.936989	+	0.349360i	$0.113601\pi$
$601$			419.930i			0.698719i	−0.936989	+	0.349360i	$0.886399\pi$
$602$		−	200.106i		−	0.332402i
$603$	351.522			0.582955
$604$		−	1295.75i		−	2.14527i
$605$	−218.866	+	159.068i	−0.361762	+	0.262922i
$606$	−328.262			−0.541686
$607$			613.413i			1.01056i	0.862954	+	0.505282i	$0.168612\pi$
$607$			613.413i			1.01056i	−0.862954	+	0.505282i	$0.831388\pi$
$608$	−631.646			−1.03889
$609$	−101.700			−0.166995
$610$	234.302			0.384101
$611$		−	774.279i		−	1.26723i
$612$			283.626i			0.463441i
$613$		−	14.2440i		−	0.0232365i	−0.999933	−	0.0116183i	$-0.996302\pi$
$613$		−	14.2440i		−	0.0232365i	0.999933	−	0.0116183i	$-0.00369829\pi$
$614$	794.932			1.29468
$615$		−	233.081i		−	0.378993i
$616$	12.8604	+	39.5697i	0.0208773	+	0.0642366i
$617$	−327.214			−0.530331			−0.265166	−	0.964203i	$-0.585427\pi$
$617$	−327.214			−0.530331			−0.265166	+	0.964203i	$0.585427\pi$
$618$		−	781.977i		−	1.26534i
$619$	−791.809			−1.27917			−0.639587	−	0.768719i	$-0.720895\pi$
$619$	−791.809			−1.27917			−0.639587	+	0.768719i	$0.720895\pi$
$620$	−311.800			−0.502904
$621$	191.385			0.308189
$622$			1042.12i			1.67543i
$623$		−	397.923i		−	0.638721i
$624$			212.591i			0.340690i
$625$	25.0000			0.0400000
$626$		−	967.655i		−	1.54577i
$627$	249.239	−	81.0041i	0.397510	−	0.129193i
$628$	−20.6074			−0.0328143
$629$			1063.00i			1.68998i
$630$	−51.7160			−0.0820890
$631$	−101.790			−0.161316			−0.0806579	−	0.996742i	$-0.525702\pi$
$631$	−101.790			−0.161316			−0.0806579	+	0.996742i	$0.525702\pi$
$632$	89.8783			0.142213
$633$		−	507.600i		−	0.801896i
$634$		−	108.950i		−	0.171845i
$635$			248.497i			0.391335i
$636$	−505.140			−0.794245
$637$		−	62.2737i		−	0.0977610i
$638$	219.868	+	676.504i	0.344620	+	1.06035i
$639$	46.0772			0.0721083
$640$		−	101.527i		−	0.158636i
$641$	572.449			0.893056			0.446528	−	0.894770i	$-0.352660\pi$
$641$	572.449			0.893056			0.446528	+	0.894770i	$0.352660\pi$
$642$	−92.7699			−0.144501
$643$	673.375			1.04724			0.523619	−	0.851952i	$-0.324581\pi$
$643$	673.375			1.04724			0.523619	+	0.851952i	$0.324581\pi$
$644$		−	437.605i		−	0.679511i
$645$		−	100.528i		−	0.155857i
$646$		−	843.829i		−	1.30624i
$647$	−772.639			−1.19419			−0.597093	−	0.802172i	$-0.703678\pi$
$647$	−772.639			−1.19419			−0.597093	+	0.802172i	$0.703678\pi$
$648$			12.8667i			0.0198561i
$649$	−70.3157	−	216.352i	−0.108345	−	0.333362i
$650$	129.613			0.199404
$651$			142.296i			0.218581i
$652$	−324.283			−0.497367
$653$	985.297			1.50888			0.754439	−	0.656370i	$-0.227909\pi$
$653$	985.297			1.50888			0.754439	+	0.656370i	$0.227909\pi$
$654$	192.015			0.293601
$655$		−	564.822i		−	0.862324i
$656$		−	830.305i		−	1.26571i
$657$			394.453i			0.600384i
$658$	670.980			1.01973
$659$		−	303.792i		−	0.460990i	−0.973074	−	0.230495i	$-0.925966\pi$
$659$		−	303.792i		−	0.460990i	0.973074	−	0.230495i	$-0.0740345\pi$
$660$	59.1333	+	181.945i	0.0895960	+	0.275675i
$661$	816.691			1.23554			0.617769	−	0.786359i	$-0.288036\pi$
$661$	816.691			1.23554			0.617769	+	0.786359i	$0.288036\pi$
$662$		−	1007.89i		−	1.52249i
$663$	−324.403			−0.489296
$664$	67.4727			0.101616
$665$	81.3769			0.122371
$666$			441.374i			0.662723i
$667$		−	817.407i		−	1.22550i
$668$			265.381i			0.397278i
$669$	570.975			0.853476
$670$		−	763.459i		−	1.13949i
$671$	−376.191	+	122.264i	−0.560642	+	0.182212i
$672$	−210.434			−0.313146
$673$			367.197i			0.545612i	0.962069	+	0.272806i	$0.0879518\pi$
$673$			367.197i			0.545612i	−0.962069	+	0.272806i	$0.912048\pi$
$674$	493.234			0.731801
$675$	−25.9808			−0.0384900
$676$	−403.514			−0.596914
$677$			913.759i			1.34972i	0.737947	+	0.674859i	$0.235795\pi$
$677$			913.759i			1.34972i	−0.737947	+	0.674859i	$0.764205\pi$
$678$			866.742i			1.27838i
$679$			81.8818i			0.120592i
$680$	67.3021			0.0989737
$681$			453.402i			0.665788i
$682$	946.547	−	307.633i	1.38790	−	0.451075i
$683$	37.3304			0.0546565			0.0273283	−	0.999627i	$-0.491300\pi$
$683$	37.3304			0.0546565			0.0273283	+	0.999627i	$0.491300\pi$
$684$		−	185.309i		−	0.270919i
$685$	321.453			0.469274
$686$	53.9656			0.0786671
$687$	658.450			0.958443
$688$		−	358.111i		−	0.520511i
$689$		−	577.764i		−	0.838555i
$690$		−	415.663i		−	0.602411i
$691$	616.926			0.892802			0.446401	−	0.894833i	$-0.352705\pi$
$691$	616.926			0.892802			0.446401	+	0.894833i	$0.352705\pi$
$692$		−	54.7343i		−	0.0790959i
$693$	83.0344	−	26.9867i	0.119819	−	0.0389418i
$694$	1317.02			1.89772
$695$		−	214.694i		−	0.308912i
$696$	54.9540			0.0789568
$697$	1267.00			1.81780
$698$	−1409.91			−2.01992
$699$			7.76652i			0.0111109i
$700$			59.4055i			0.0848650i
$701$		−	1019.28i		−	1.45404i	−0.686615	−	0.727021i	$-0.740904\pi$
$701$		−	1019.28i		−	1.45404i	0.686615	−	0.727021i	$-0.259096\pi$
$702$	−134.697			−0.191876
$703$		−	694.516i		−	0.987931i
$704$	267.306	+	822.464i	0.379695	+	1.16827i
$705$	337.083			0.478131
$706$			1549.78i			2.19516i
$707$	172.083			0.243399
$708$	−160.857			−0.227200
$709$	196.219			0.276754			0.138377	−	0.990380i	$-0.455811\pi$
$709$	196.219			0.276754			0.138377	+	0.990380i	$0.455811\pi$
$710$		−	100.074i		−	0.140949i
$711$		−	188.604i		−	0.265265i
$712$			215.019i			0.301992i
$713$	−1143.69			−1.60406
$714$		−	281.124i		−	0.393730i
$715$	−208.104	+	67.6349i	−0.291054	+	0.0945943i
$716$	189.257			0.264325
$717$		−	325.306i		−	0.453704i
$718$	1601.22			2.23011
$719$	−1179.32			−1.64022			−0.820109	−	0.572207i	$-0.806087\pi$
$719$	−1179.32			−1.64022			−0.820109	+	0.572207i	$0.806087\pi$
$720$	−92.5514			−0.128544
$721$			409.933i			0.568561i
$722$		−	500.586i		−	0.693333i
$723$		−	561.729i		−	0.776942i
$724$	250.127			0.345479
$725$			110.964i			0.153054i
$726$	−359.028	−	493.997i	−0.494528	−	0.680437i
$727$	−435.623			−0.599206			−0.299603	−	0.954064i	$-0.596854\pi$
$727$	−435.623			−0.599206			−0.299603	+	0.954064i	$0.596854\pi$
$728$			33.6498i			0.0462222i
$729$	27.0000			0.0370370
$730$	856.699			1.17356
$731$	546.461			0.747552
$732$			279.697i			0.382100i
$733$			908.697i			1.23970i	0.784722	+	0.619848i	$0.212806\pi$
$733$			908.697i			1.23970i	−0.784722	+	0.619848i	$0.787194\pi$
$734$		−	886.646i		−	1.20796i
$735$	27.1109			0.0368856
$736$		−	1691.35i		−	2.29802i
$737$	398.392	+	1225.80i	0.540558	+	1.66323i
$738$	526.080			0.712846
$739$			444.123i			0.600979i	0.953785	+	0.300489i	$0.0971500\pi$
$739$			444.123i			0.600979i	−0.953785	+	0.300489i	$0.902850\pi$
$740$	507.000			0.685135
$741$	211.951			0.286033
$742$	500.683			0.674775
$743$		−	652.102i		−	0.877661i	−0.898570	−	0.438830i	$-0.855393\pi$
$743$		−	652.102i		−	0.877661i	0.898570	−	0.438830i	$-0.144607\pi$
$744$		−	76.8901i		−	0.103347i
$745$			113.629i			0.152523i
$746$	−1173.16			−1.57259
$747$		−	141.587i		−	0.189541i
$748$	−989.038	+	321.443i	−1.32224	+	0.429737i
$749$	48.6324			0.0649298
$750$			56.4268i			0.0752358i
$751$	888.507			1.18310			0.591549	−	0.806269i	$-0.298517\pi$
$751$	888.507			1.18310			0.591549	+	0.806269i	$0.298517\pi$
$752$	1200.79			1.59680
$753$	639.888			0.849785
$754$			575.293i			0.762988i
$755$			645.204i			0.854575i
$756$		−	61.7360i		−	0.0816614i
$757$	−1144.68			−1.51212			−0.756062	−	0.654500i	$-0.772879\pi$
$757$	−1144.68			−1.51212			−0.756062	+	0.654500i	$0.772879\pi$
$758$			1921.56i			2.53504i
$759$	216.903	+	667.382i	0.285775	+	0.879292i
$760$	−43.9722			−0.0578581
$761$		−	1297.28i		−	1.70470i	−0.522971	−	0.852350i	$-0.675177\pi$
$761$		−	1297.28i		−	1.70470i	0.522971	−	0.852350i	$-0.324823\pi$
$762$	−560.877			−0.736059
$763$	−100.659			−0.131926
$764$	−239.279			−0.313192
$765$		−	141.229i		−	0.184613i
$766$			1162.61i			1.51776i
$767$		−	183.984i		−	0.239875i
$768$	−315.536			−0.410854
$769$		−	330.557i		−	0.429852i	−0.976630	−	0.214926i	$-0.931049\pi$
$769$		−	330.557i		−	0.429852i	0.976630	−	0.214926i	$-0.0689511\pi$
$770$	−58.6116	−	180.340i	−0.0761189	−	0.234208i
$771$	−131.849			−0.171011
$772$		−	692.610i		−	0.897163i
$773$	−272.145			−0.352063			−0.176032	−	0.984384i	$-0.556326\pi$
$773$	−272.145			−0.352063			−0.176032	+	0.984384i	$0.556326\pi$
$774$	226.899			0.293151
$775$	155.258			0.200333
$776$		−	44.2450i		−	0.0570168i
$777$		−	231.379i		−	0.297786i
$778$		−	1126.11i		−	1.44744i
$779$	−827.804			−1.06265
$780$			154.725i			0.198365i
$781$	52.2209	+	160.677i	0.0668641	+	0.205732i
$782$	2259.51			2.88940
$783$		−	115.317i		−	0.147276i
$784$	96.5773			0.123185
$785$	10.2613			0.0130717
$786$	1274.84			1.62194
$787$		−	1065.43i		−	1.35379i	−0.736078	−	0.676896i	$-0.763324\pi$
$787$		−	1065.43i		−	1.35379i	0.736078	−	0.676896i	$-0.236676\pi$
$788$			1698.17i			2.15504i
$789$		−	185.734i		−	0.235404i
$790$	−409.623			−0.518510
$791$		−	454.368i		−	0.574423i
$792$	−44.8678	+	14.5823i	−0.0566513	+	0.0184120i
$793$	−319.909			−0.403417
$794$			346.060i			0.435843i
$795$	251.530			0.316390
$796$	1554.33			1.95268
$797$	764.179			0.958819			0.479409	−	0.877591i	$-0.340851\pi$
$797$	764.179			0.958819			0.479409	+	0.877591i	$0.340851\pi$
$798$			183.674i			0.230167i
$799$			1832.35i			2.29330i
$800$			229.602i			0.287003i
$801$	451.202			0.563299
$802$			1023.99i			1.27680i
$803$	−1375.50	+	447.047i	−1.71295	+	0.556720i
$804$	911.379			1.13356
$805$			217.901i			0.270685i
$806$	804.935			0.998679
$807$	−117.126			−0.145137
$808$	−92.9856			−0.115081
$809$		−	674.045i		−	0.833183i	−0.909094	−	0.416592i	$-0.863224\pi$
$809$		−	674.045i		−	0.833183i	0.909094	−	0.416592i	$-0.136776\pi$
$810$		−	58.6405i		−	0.0723957i
$811$		−	262.280i		−	0.323403i	−0.986840	−	0.161701i	$-0.948302\pi$
$811$		−	262.280i		−	0.323403i	0.986840	−	0.161701i	$-0.0516981\pi$
$812$	−263.675			−0.324723
$813$			321.205i			0.395086i
$814$	−1539.12	+	500.224i	−1.89081	+	0.614526i
$815$	161.474			0.198127
$816$		−	503.101i		−	0.616545i
$817$	−357.033			−0.437005
$818$	328.814			0.401974
$819$	70.6118			0.0862171
$820$		−	604.301i		−	0.736952i
$821$		−	472.015i		−	0.574927i	−0.957792	−	0.287464i	$-0.907188\pi$
$821$		−	472.015i		−	0.574927i	0.957792	−	0.287464i	$-0.0928121\pi$
$822$			725.542i			0.882655i
$823$	−242.270			−0.294375			−0.147187	−	0.989109i	$-0.547022\pi$
$823$	−242.270			−0.294375			−0.147187	+	0.989109i	$0.547022\pi$
$824$		−	221.508i		−	0.268820i
$825$	−29.4449	−	90.5980i	−0.0356908	−	0.109816i
$826$	159.438			0.193024
$827$		−	331.447i		−	0.400782i	−0.979716	−	0.200391i	$-0.935779\pi$
$827$		−	331.447i		−	0.400782i	0.979716	−	0.200391i	$-0.0642213\pi$
$828$	496.198			0.599273
$829$	281.631			0.339724			0.169862	−	0.985468i	$-0.445668\pi$
$829$	281.631			0.339724			0.169862	+	0.985468i	$0.445668\pi$
$830$	−307.508			−0.370492
$831$		−	460.596i		−	0.554267i
$832$			699.416i			0.840645i
$833$			147.372i			0.176917i
$834$	484.580			0.581031
$835$		−	132.144i		−	0.158257i
$836$	646.193	−	210.017i	0.772959	−	0.251216i
$837$	−161.349			−0.192770
$838$			26.1254i			0.0311759i
$839$	−60.0178			−0.0715349			−0.0357674	−	0.999360i	$-0.511388\pi$
$839$	−60.0178			−0.0715349			−0.0357674	+	0.999360i	$0.511388\pi$
$840$	−14.6494			−0.0174398
$841$	348.479			0.414363
$842$			868.321i			1.03126i
$843$		−	139.184i		−	0.165105i
$844$		−	1316.04i		−	1.55929i
$845$	200.926			0.237782
$846$			760.820i			0.899314i
$847$	188.212	+	258.966i	0.222210	+	0.305745i
$848$	896.026			1.05663
$849$		−	430.329i		−	0.506866i
$850$	−306.731			−0.360860
$851$	1859.69			2.18530
$852$	119.463			0.140215
$853$		−	743.851i		−	0.872041i	−0.899937	−	0.436020i	$-0.856388\pi$
$853$		−	743.851i		−	0.872041i	0.899937	−	0.436020i	$-0.143612\pi$
$854$		−	277.229i		−	0.324625i
$855$			92.2727i			0.107921i
$856$	−26.2786			−0.0306993
$857$		−	188.038i		−	0.219415i	−0.993964	−	0.109707i	$-0.965009\pi$
$857$		−	188.038i		−	0.219415i	0.993964	−	0.109707i	$-0.0349913\pi$
$858$	−152.657	−	469.705i	−0.177922	−	0.547442i
$859$	874.909			1.01852			0.509260	−	0.860613i	$-0.329919\pi$
$859$	874.909			1.01852			0.509260	+	0.860613i	$0.329919\pi$
$860$		−	260.636i		−	0.303065i
$861$	−275.785			−0.320308
$862$	−1619.94			−1.87929
$863$	−395.827			−0.458664			−0.229332	−	0.973348i	$-0.573654\pi$
$863$	−395.827			−0.458664			−0.229332	+	0.973348i	$0.573654\pi$
$864$		−	238.610i		−	0.276169i
$865$			27.2545i			0.0315080i
$866$		−	1393.14i		−	1.60871i
$867$	267.145			0.308125
$868$			368.927i			0.425031i
$869$	657.683	−	213.751i	0.756828	−	0.245974i
$870$	−250.454			−0.287878
$871$			1042.41i			1.19679i
$872$	54.3915			0.0623756
$873$	−92.8452			−0.106352
$874$	−1476.26			−1.68909
$875$		−	29.5804i		−	0.0338062i
$876$			1022.68i			1.16745i
$877$			788.354i			0.898922i	0.893300	+	0.449461i	$0.148384\pi$
$877$			788.354i			0.898922i	−0.893300	+	0.449461i	$0.851616\pi$
$878$	1388.64			1.58160
$879$			497.679i			0.566187i
$880$	−104.892	−	322.738i	−0.119195	−	0.366748i
$881$	−604.250			−0.685868			−0.342934	−	0.939359i	$-0.611421\pi$
$881$	−604.250			−0.685868			−0.342934	+	0.939359i	$0.611421\pi$
$882$			61.1912i			0.0693778i
$883$	−1654.46			−1.87368			−0.936842	−	0.349753i	$-0.886265\pi$
$883$	−1654.46			−1.87368			−0.936842	+	0.349753i	$0.886265\pi$
$884$	−841.070			−0.951436
$885$	80.0974			0.0905055
$886$		−	915.167i		−	1.03292i
$887$			1534.14i			1.72958i	0.502131	+	0.864792i	$0.332550\pi$
$887$			1534.14i			1.72958i	−0.502131	+	0.864792i	$0.667450\pi$
$888$			125.026i			0.140796i
$889$	294.026			0.330738
$890$		−	979.953i		−	1.10107i
$891$	30.6000	+	94.1522i	0.0343435	+	0.105670i
$892$	1480.35			1.65958
$893$		−	1197.18i		−	1.34062i
$894$	−256.470			−0.286879
$895$	−94.2387			−0.105295
$896$	−120.128			−0.134072
$897$			567.536i			0.632705i
$898$		−	573.169i		−	0.638273i
$899$			689.122i			0.766543i
$900$	−67.3595			−0.0748439
$901$			1367.29i			1.51753i
$902$	596.225	+	1834.50i	0.661003	+	2.03382i
$903$	−118.946			−0.131723
$904$			245.519i			0.271592i
$905$	−124.548			−0.137622
$906$	−1456.27			−1.60737
$907$	−1181.75			−1.30292			−0.651462	−	0.758681i	$-0.725844\pi$
$907$	−1181.75			−1.30292			−0.651462	+	0.758681i	$0.725844\pi$
$908$			1175.52i			1.29463i
$909$			195.124i			0.214658i
$910$		−	153.360i		−	0.168527i
$911$	1010.06			1.10874			0.554370	−	0.832270i	$-0.312959\pi$
$911$	1010.06			1.10874			0.554370	+	0.832270i	$0.312959\pi$
$912$			328.704i			0.360421i
$913$	493.731	−	160.465i	0.540778	−	0.175756i
$914$	−939.674			−1.02809
$915$		−	139.273i		−	0.152211i
$916$	1707.14			1.86369
$917$	−668.307			−0.728797
$918$	318.764			0.347238
$919$			992.708i			1.08020i	0.841599	+	0.540102i	$0.181615\pi$
$919$			992.708i			1.08020i	−0.841599	+	0.540102i	$0.818385\pi$
$920$		−	117.744i		−	0.127982i
$921$		−	472.521i		−	0.513052i
$922$	−189.720			−0.205770
$923$			136.638i			0.148037i
$924$	215.281	−	69.9675i	0.232988	−	0.0757224i
$925$	−252.456			−0.272925
$926$		−	40.9131i		−	0.0441826i
$927$	−464.820			−0.501424
$928$	−1019.10			−1.09817
$929$	−1267.93			−1.36484			−0.682419	−	0.730961i	$-0.739072\pi$
$929$	−1267.93			−1.36484			−0.682419	+	0.730961i	$0.739072\pi$
$930$			350.429i			0.376805i
$931$		−	96.2864i		−	0.103423i
$932$			20.1360i			0.0216051i
$933$	619.453			0.663937
$934$			1138.21i			1.21864i
$935$	492.482	−	160.060i	0.526719	−	0.171187i
$936$	−38.1552			−0.0407641
$937$			361.875i			0.386206i	0.981179	+	0.193103i	$0.0618551\pi$
$937$			361.875i			0.386206i	−0.981179	+	0.193103i	$0.938145\pi$
$938$	−903.337			−0.963046
$939$	−575.190			−0.612556
$940$	873.943			0.929727
$941$			150.032i			0.159439i	0.996817	+	0.0797193i	$0.0254024\pi$
$941$			150.032i			0.159439i	−0.996817	+	0.0797193i	$0.974598\pi$
$942$			23.1604i			0.0245864i
$943$		−	2216.60i		−	2.35058i
$944$	285.331			0.302258
$945$			30.7409i			0.0325300i
$946$	257.152	+	791.224i	0.271831	+	0.836389i
$947$	1526.76			1.61221			0.806104	−	0.591774i	$-0.201572\pi$
$947$	1526.76			1.61221			0.806104	+	0.591774i	$0.201572\pi$
$948$		−	488.987i		−	0.515809i
$949$	−1169.72			−1.23258
$950$	200.404			0.210952
$951$	−64.7614			−0.0680982
$952$		−	79.6329i		−	0.0836480i
$953$			1094.63i			1.14861i	0.818640	+	0.574307i	$0.194729\pi$
$953$			1094.63i			1.14861i	−0.818640	+	0.574307i	$0.805271\pi$
$954$			567.721i			0.595095i
$955$	119.147			0.124761
$956$		−	843.409i		−	0.882227i
$957$	402.125	−	130.693i	0.420193	−	0.136565i
$958$	−1704.36			−1.77908
$959$		−	380.348i		−	0.396609i
$960$	−304.491			−0.317178
$961$	3.20200			0.00333195
$962$	−1308.86			−1.36056
$963$			55.1440i			0.0572627i
$964$		−	1456.38i		−	1.51076i
$965$			344.878i			0.357387i
$966$	−491.820			−0.509130
$967$		−	755.720i		−	0.781510i	−0.920495	−	0.390755i	$-0.872214\pi$
$967$		−	755.720i		−	0.781510i	0.920495	−	0.390755i	$-0.127786\pi$
$968$	−101.701	−	139.933i	−0.105063	−	0.144559i
$969$	−501.586			−0.517632
$970$			201.648i			0.207884i
$971$	−954.755			−0.983270			−0.491635	−	0.870801i	$-0.663601\pi$
$971$	−954.755			−0.983270			−0.491635	+	0.870801i	$0.663601\pi$
$972$	70.0020			0.0720185
$973$	−254.029			−0.261078
$974$			2152.52i			2.20998i
$975$		−	77.0438i		−	0.0790193i
$976$		−	496.132i		−	0.508332i
$977$	−770.551			−0.788690			−0.394345	−	0.918962i	$-0.629029\pi$
$977$	−770.551			−0.788690			−0.394345	+	0.918962i	$0.629029\pi$
$978$			364.458i			0.372657i
$979$	511.363	+	1573.40i	0.522332	+	1.60715i
$980$	70.2895			0.0717240
$981$		−	114.137i		−	0.116348i
$982$	−1598.84			−1.62815
$983$	428.799			0.436215			0.218107	−	0.975925i	$-0.430012\pi$
$983$	428.799			0.436215			0.218107	+	0.975925i	$0.430012\pi$
$984$	149.021			0.151444
$985$		−	845.588i		−	0.858465i
$986$		−	1361.44i		−	1.38078i
$987$		−	398.841i		−	0.404095i
$988$	549.517			0.556192
$989$		−	956.021i		−	0.966654i
$990$	204.486	−	66.4593i	0.206552	−	0.0671306i
$991$	1507.85			1.52154			0.760771	−	0.649020i	$-0.224821\pi$
$991$	1507.85			1.52154			0.760771	+	0.649020i	$0.224821\pi$
$992$			1425.90i			1.43740i
$993$	−599.104			−0.603328
$994$	−118.409			−0.119124
$995$	−773.966			−0.777855
$996$		−	367.088i		−	0.368562i
$997$			1363.05i			1.36715i	0.729880	+	0.683576i	$0.239576\pi$
$997$			1363.05i			1.36715i	−0.729880	+	0.683576i	$0.760424\pi$
$998$			2770.37i			2.77592i
$999$	262.360			0.262622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.17	✓	96
11.10	odd	2	inner	1155.3.b.a.736.80	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.17	✓	96	1.1	even	1	trivial
1155.3.b.a.736.80	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)

\(f(q)\)	\(=\)	\(q-2.91387i q^{2} -1.73205 q^{3} -4.49063 q^{4} +2.23607 q^{5} +5.04697i q^{6} -2.64575i q^{7} +1.42964i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.91387i q^{2} -1.73205 q^{3} -4.49063 q^{4} +2.23607 q^{5} +5.04697i q^{6} -2.64575i q^{7} +1.42964i q^{8} +3.00000 q^{9} -6.51561i q^{10} +(3.40000 + 10.4614i) q^{11} +7.77800 q^{12} +8.89625i q^{13} -7.70937 q^{14} -3.87298 q^{15} -13.7968 q^{16} -21.0532i q^{17} -8.74161i q^{18} +13.7552i q^{19} -10.0414 q^{20} +4.58258i q^{21} +(30.4830 - 9.90716i) q^{22} -36.8321 q^{23} -2.47621i q^{24} +5.00000 q^{25} +25.9225 q^{26} -5.19615 q^{27} +11.8811i q^{28} +22.1928i q^{29} +11.2854i q^{30} +31.0516 q^{31} +45.9205i q^{32} +(-5.88898 - 18.1196i) q^{33} -61.3462 q^{34} -5.91608i q^{35} -13.4719 q^{36} -50.4911 q^{37} +40.0809 q^{38} -15.4088i q^{39} +3.19677i q^{40} +60.1812i q^{41} +13.3530 q^{42} +25.9562i q^{43} +(-15.2682 - 46.9781i) q^{44} +6.70820 q^{45} +107.324i q^{46} -87.0343 q^{47} +23.8967 q^{48} -7.00000 q^{49} -14.5693i q^{50} +36.4652i q^{51} -39.9498i q^{52} -64.9447 q^{53} +15.1409i q^{54} +(7.60264 + 23.3923i) q^{55} +3.78247 q^{56} -23.8247i q^{57} +64.6670 q^{58} -20.6811 q^{59} +17.3921 q^{60} +35.9600i q^{61} -90.4803i q^{62} -7.93725i q^{63} +78.6192 q^{64} +19.8926i q^{65} +(-52.7981 + 17.1597i) q^{66} +117.174 q^{67} +94.5421i q^{68} +63.7950 q^{69} -17.2387 q^{70} +15.3591 q^{71} +4.28891i q^{72} +131.484i q^{73} +147.125i q^{74} -8.66025 q^{75} -61.7696i q^{76} +(27.6781 - 8.99556i) q^{77} -44.8991 q^{78} -62.8679i q^{79} -30.8505 q^{80} +9.00000 q^{81} +175.360 q^{82} -47.1957i q^{83} -20.5787i q^{84} -47.0763i q^{85} +75.6330 q^{86} -38.4391i q^{87} +(-14.9559 + 4.86077i) q^{88} +150.401 q^{89} -19.5468i q^{90} +23.5373 q^{91} +165.399 q^{92} -53.7830 q^{93} +253.607i q^{94} +30.7576i q^{95} -79.5366i q^{96} -30.9484 q^{97} +20.3971i q^{98} +(10.2000 + 31.3841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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