LMFDB - Embedded newform 1155.3.b.a.736.15

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			736.15
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.82

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.94196i q^{2} +1.73205 q^{3} -4.65512 q^{4} -2.23607 q^{5} -5.09562i q^{6} +2.64575i q^{7} +1.92733i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.94196i q^{2} +1.73205 q^{3} -4.65512 q^{4} -2.23607 q^{5} -5.09562i q^{6} +2.64575i q^{7} +1.92733i q^{8} +3.00000 q^{9} +6.57842i q^{10} +(7.11471 - 8.38933i) q^{11} -8.06290 q^{12} +20.3376i q^{13} +7.78369 q^{14} -3.87298 q^{15} -12.9503 q^{16} +19.5005i q^{17} -8.82587i q^{18} +12.3126i q^{19} +10.4092 q^{20} +4.58258i q^{21} +(-24.6811 - 20.9312i) q^{22} +17.2403 q^{23} +3.33824i q^{24} +5.00000 q^{25} +59.8324 q^{26} +5.19615 q^{27} -12.3163i q^{28} +14.2937i q^{29} +11.3942i q^{30} +16.4718 q^{31} +45.8087i q^{32} +(12.3230 - 14.5308i) q^{33} +57.3696 q^{34} -5.91608i q^{35} -13.9654 q^{36} -42.7746 q^{37} +36.2233 q^{38} +35.2258i q^{39} -4.30964i q^{40} +40.8148i q^{41} +13.4817 q^{42} +25.1559i q^{43} +(-33.1198 + 39.0533i) q^{44} -6.70820 q^{45} -50.7203i q^{46} +20.5703 q^{47} -22.4307 q^{48} -7.00000 q^{49} -14.7098i q^{50} +33.7758i q^{51} -94.6740i q^{52} -34.3023 q^{53} -15.2869i q^{54} +(-15.9090 + 18.7591i) q^{55} -5.09924 q^{56} +21.3261i q^{57} +42.0513 q^{58} +96.8211 q^{59} +18.0292 q^{60} +2.50933i q^{61} -48.4594i q^{62} +7.93725i q^{63} +82.9659 q^{64} -45.4763i q^{65} +(-42.7489 - 36.2539i) q^{66} +81.6940 q^{67} -90.7770i q^{68} +29.8611 q^{69} -17.4049 q^{70} -5.87211 q^{71} +5.78199i q^{72} -14.8139i q^{73} +125.841i q^{74} +8.66025 q^{75} -57.3168i q^{76} +(22.1961 + 18.8237i) q^{77} +103.633 q^{78} -9.16500i q^{79} +28.9579 q^{80} +9.00000 q^{81} +120.075 q^{82} -74.5065i q^{83} -21.3324i q^{84} -43.6044i q^{85} +74.0076 q^{86} +24.7573i q^{87} +(16.1690 + 13.7124i) q^{88} +79.2208 q^{89} +19.7353i q^{90} -53.8082 q^{91} -80.2557 q^{92} +28.5300 q^{93} -60.5170i q^{94} -27.5319i q^{95} +79.3430i q^{96} -143.797 q^{97} +20.5937i q^{98} +(21.3441 - 25.1680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.94196i		−	1.47098i	−0.677536	−	0.735490i	$-0.736952\pi$
$2$		−	2.94196i		−	1.47098i	0.677536	−	0.735490i	$-0.263048\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−4.65512			−1.16378
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		−	5.09562i		−	0.849270i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			1.92733i			0.240916i
$9$	3.00000			0.333333
$10$			6.57842i			0.657842i
$11$	7.11471	−	8.38933i	0.646792	−	0.762667i
$11$	7.11471	−	8.38933i	0.646792	−	0.762667i
$12$	−8.06290			−0.671908
$13$			20.3376i			1.56443i	0.623008	+	0.782216i	$0.285910\pi$
$13$			20.3376i			1.56443i	−0.623008	+	0.782216i	$0.714090\pi$
$14$	7.78369			0.555978
$15$	−3.87298			−0.258199
$16$	−12.9503			−0.809397
$17$			19.5005i			1.14709i	0.819175	+	0.573543i	$0.194431\pi$
$17$			19.5005i			1.14709i	−0.819175	+	0.573543i	$0.805569\pi$
$18$		−	8.82587i		−	0.490326i
$19$			12.3126i			0.648034i	0.946051	+	0.324017i	$0.105034\pi$
$19$			12.3126i			0.648034i	−0.946051	+	0.324017i	$0.894966\pi$
$20$	10.4092			0.520458
$21$			4.58258i			0.218218i
$22$	−24.6811	−	20.9312i	−1.12187	−	0.951417i
$23$	17.2403			0.749579			0.374790	−	0.927110i	$-0.377715\pi$
$23$	17.2403			0.749579			0.374790	+	0.927110i	$0.377715\pi$
$24$			3.33824i			0.139093i
$25$	5.00000			0.200000
$26$	59.8324			2.30125
$27$	5.19615			0.192450
$28$		−	12.3163i		−	0.439867i
$29$			14.2937i			0.492885i	0.969157	+	0.246442i	$0.0792616\pi$
$29$			14.2937i			0.492885i	−0.969157	+	0.246442i	$0.920738\pi$
$30$			11.3942i			0.379805i
$31$	16.4718			0.531349			0.265674	−	0.964063i	$-0.414405\pi$
$31$	16.4718			0.531349			0.265674	+	0.964063i	$0.414405\pi$
$32$			45.8087i			1.43152i
$33$	12.3230	−	14.5308i	0.373425	−	0.440326i
$34$	57.3696			1.68734
$35$		−	5.91608i		−	0.169031i
$36$	−13.9654			−0.387927
$37$	−42.7746			−1.15607			−0.578035	−	0.816012i	$-0.696180\pi$
$37$	−42.7746			−1.15607			−0.578035	+	0.816012i	$0.696180\pi$
$38$	36.2233			0.953244
$39$			35.2258i			0.903225i
$40$		−	4.30964i		−	0.107741i
$41$			40.8148i			0.995483i	0.867325	+	0.497741i	$0.165837\pi$
$41$			40.8148i			0.995483i	−0.867325	+	0.497741i	$0.834163\pi$
$42$	13.4817			0.320994
$43$			25.1559i			0.585021i	0.956262	+	0.292511i	$0.0944907\pi$
$43$			25.1559i			0.585021i	−0.956262	+	0.292511i	$0.905509\pi$
$44$	−33.1198	+	39.0533i	−0.752723	+	0.887576i
$45$	−6.70820			−0.149071
$46$		−	50.7203i		−	1.10262i
$47$	20.5703			0.437666			0.218833	−	0.975762i	$-0.429775\pi$
$47$	20.5703			0.437666			0.218833	+	0.975762i	$0.429775\pi$
$48$	−22.4307			−0.467305
$49$	−7.00000			−0.142857
$50$		−	14.7098i		−	0.294196i
$51$			33.7758i			0.662271i
$52$		−	94.6740i		−	1.82065i
$53$	−34.3023			−0.647213			−0.323606	−	0.946192i	$-0.604895\pi$
$53$	−34.3023			−0.647213			−0.323606	+	0.946192i	$0.604895\pi$
$54$		−	15.2869i		−	0.283090i
$55$	−15.9090	+	18.7591i	−0.289254	+	0.341075i
$56$	−5.09924			−0.0910578
$57$			21.3261i			0.374143i
$58$	42.0513			0.725023
$59$	96.8211			1.64104			0.820518	−	0.571621i	$-0.193685\pi$
$59$	96.8211			1.64104			0.820518	+	0.571621i	$0.193685\pi$
$60$	18.0292			0.300487
$61$			2.50933i			0.0411365i	0.999788	+	0.0205682i	$0.00654754\pi$
$61$			2.50933i			0.0411365i	−0.999788	+	0.0205682i	$0.993452\pi$
$62$		−	48.4594i		−	0.781603i
$63$			7.93725i			0.125988i
$64$	82.9659			1.29634
$65$		−	45.4763i		−	0.699635i
$66$	−42.7489	−	36.2539i	−0.647710	−	0.549301i
$67$	81.6940			1.21931			0.609657	−	0.792665i	$-0.291307\pi$
$67$	81.6940			1.21931			0.609657	+	0.792665i	$0.291307\pi$
$68$		−	90.7770i		−	1.33496i
$69$	29.8611			0.432770
$70$	−17.4049			−0.248641
$71$	−5.87211			−0.0827058			−0.0413529	−	0.999145i	$-0.513167\pi$
$71$	−5.87211			−0.0827058			−0.0413529	+	0.999145i	$0.513167\pi$
$72$			5.78199i			0.0803055i
$73$		−	14.8139i		−	0.202931i	−0.994839	−	0.101465i	$-0.967647\pi$
$73$		−	14.8139i		−	0.202931i	0.994839	−	0.101465i	$-0.0323531\pi$
$74$			125.841i			1.70055i
$75$	8.66025			0.115470
$76$		−	57.3168i		−	0.754169i
$77$	22.1961	+	18.8237i	0.288261	+	0.244464i
$78$	103.633			1.32862
$79$		−	9.16500i		−	0.116013i	−0.998316	−	0.0580063i	$-0.981526\pi$
$79$		−	9.16500i		−	0.116013i	0.998316	−	0.0580063i	$-0.0184744\pi$
$80$	28.9579			0.361973
$81$	9.00000			0.111111
$82$	120.075			1.46433
$83$		−	74.5065i		−	0.897669i	−0.893615	−	0.448835i	$-0.851839\pi$
$83$		−	74.5065i		−	0.897669i	0.893615	−	0.448835i	$-0.148161\pi$
$84$		−	21.3324i		−	0.253958i
$85$		−	43.6044i		−	0.512993i
$86$	74.0076			0.860554
$87$			24.7573i			0.284567i
$88$	16.1690	+	13.7124i	0.183739	+	0.155823i
$89$	79.2208			0.890121			0.445061	−	0.895500i	$-0.353182\pi$
$89$	79.2208			0.890121			0.445061	+	0.895500i	$0.353182\pi$
$90$			19.7353i			0.219281i
$91$	−53.8082			−0.591299
$92$	−80.2557			−0.872345
$93$	28.5300			0.306774
$94$		−	60.5170i		−	0.643798i
$95$		−	27.5319i		−	0.289810i
$96$			79.3430i			0.826490i
$97$	−143.797			−1.48245			−0.741223	−	0.671259i	$-0.765754\pi$
$97$	−143.797			−1.48245			−0.741223	+	0.671259i	$0.765754\pi$
$98$			20.5937i			0.210140i
$99$	21.3441	−	25.1680i	0.215597	−	0.254222i
$100$	−23.2756			−0.232756
$101$		−	139.494i		−	1.38113i	−0.723271	−	0.690564i	$-0.757362\pi$
$101$		−	139.494i		−	1.38113i	0.723271	−	0.690564i	$-0.242638\pi$
$102$	99.3670			0.974186
$103$	185.615			1.80209			0.901045	−	0.433726i	$-0.142801\pi$
$103$	185.615			1.80209			0.901045	+	0.433726i	$0.142801\pi$
$104$	−39.1973			−0.376897
$105$		−	10.2470i		−	0.0975900i
$106$			100.916i			0.952036i
$107$		−	7.05172i		−	0.0659039i	−0.999457	−	0.0329519i	$-0.989509\pi$
$107$		−	7.05172i		−	0.0659039i	0.999457	−	0.0329519i	$-0.0104908\pi$
$108$	−24.1887			−0.223969
$109$			56.7327i			0.520483i	0.965544	+	0.260242i	$0.0838022\pi$
$109$			56.7327i			0.520483i	−0.965544	+	0.260242i	$0.916198\pi$
$110$	55.1886	+	46.8035i	0.501714	+	0.425487i
$111$	−74.0877			−0.667457
$112$		−	34.2634i		−	0.305923i
$113$	104.189			0.922024			0.461012	−	0.887394i	$-0.347486\pi$
$113$	104.189			0.922024			0.461012	+	0.887394i	$0.347486\pi$
$114$	62.7406			0.550356
$115$	−38.5505			−0.335222
$116$		−	66.5386i		−	0.573609i
$117$			61.0128i			0.521477i
$118$		−	284.844i		−	2.41393i
$119$	−51.5934			−0.433558
$120$		−	7.46452i		−	0.0622043i
$121$	−19.7618	−	119.375i	−0.163321	−	0.986573i
$122$	7.38233			0.0605109
$123$			70.6933i			0.574742i
$124$	−76.6783			−0.618373
$125$	−11.1803			−0.0894427
$126$	23.3511			0.185326
$127$			105.292i			0.829073i	0.910033	+	0.414537i	$0.136056\pi$
$127$			105.292i			0.829073i	−0.910033	+	0.414537i	$0.863944\pi$
$128$		−	60.8474i		−	0.475370i
$129$			43.5713i			0.337762i
$130$	−133.789			−1.02915
$131$			186.383i			1.42277i	0.702800	+	0.711387i	$0.251933\pi$
$131$			186.383i			1.42277i	−0.702800	+	0.711387i	$0.748067\pi$
$132$	−57.3652	+	67.6424i	−0.434585	+	0.512442i
$133$	−32.5762			−0.244934
$134$		−	240.340i		−	1.79359i
$135$	−11.6190			−0.0860663
$136$	−37.5839			−0.276352
$137$	−133.767			−0.976400			−0.488200	−	0.872732i	$-0.662346\pi$
$137$	−133.767			−0.976400			−0.488200	+	0.872732i	$0.662346\pi$
$138$		−	87.8501i		−	0.636595i
$139$			146.253i			1.05218i	0.850428	+	0.526091i	$0.176343\pi$
$139$			146.253i			1.05218i	−0.850428	+	0.526091i	$0.823657\pi$
$140$			27.5401i			0.196715i
$141$	35.6288			0.252687
$142$			17.2755i			0.121658i
$143$	170.619	+	144.696i	1.19314	+	1.01186i
$144$	−38.8510			−0.269799
$145$		−	31.9616i		−	0.220425i
$146$	−43.5820			−0.298507
$147$	−12.1244			−0.0824786
$148$	199.121			1.34541
$149$		−	167.637i		−	1.12508i	−0.826770	−	0.562540i	$-0.809824\pi$
$149$		−	167.637i		−	1.12508i	0.826770	−	0.562540i	$-0.190176\pi$
$150$		−	25.4781i		−	0.169854i
$151$		−	194.087i		−	1.28535i	−0.766140	−	0.642673i	$-0.777825\pi$
$151$		−	194.087i		−	1.28535i	0.766140	−	0.642673i	$-0.222175\pi$
$152$	−23.7305			−0.156122
$153$			58.5014i			0.382362i
$154$	55.3787	−	65.3000i	0.359602	−	0.424026i
$155$	−36.8321			−0.237626
$156$		−	163.980i		−	1.05115i
$157$	12.2165			0.0778121			0.0389060	−	0.999243i	$-0.487613\pi$
$157$	12.2165			0.0778121			0.0389060	+	0.999243i	$0.487613\pi$
$158$	−26.9630			−0.170652
$159$	−59.4133			−0.373668
$160$		−	102.431i		−	0.640196i
$161$			45.6136i			0.283314i
$162$		−	26.4776i		−	0.163442i
$163$	114.396			0.701815			0.350907	−	0.936410i	$-0.385873\pi$
$163$	114.396			0.701815			0.350907	+	0.936410i	$0.385873\pi$
$164$		−	189.998i		−	1.15852i
$165$	−27.5551	+	32.4918i	−0.167001	+	0.196920i
$166$	−219.195			−1.32045
$167$			273.424i			1.63727i	0.574313	+	0.818636i	$0.305269\pi$
$167$			273.424i			1.63727i	−0.574313	+	0.818636i	$0.694731\pi$
$168$	−8.83214			−0.0525723
$169$	−244.618			−1.44744
$170$	−128.282			−0.754601
$171$			36.9379i			0.216011i
$172$		−	117.104i		−	0.680836i
$173$			303.803i			1.75609i	0.478579	+	0.878045i	$0.341152\pi$
$173$			303.803i			1.75609i	−0.478579	+	0.878045i	$0.658848\pi$
$174$	72.8350			0.418592
$175$			13.2288i			0.0755929i
$176$	−92.1379	+	108.645i	−0.523511	+	0.617300i
$177$	167.699			0.947452
$178$		−	233.064i		−	1.30935i
$179$	96.0045			0.536338			0.268169	−	0.963372i	$-0.413581\pi$
$179$	96.0045			0.536338			0.268169	+	0.963372i	$0.413581\pi$
$180$	31.2275			0.173486
$181$	−175.608			−0.970212			−0.485106	−	0.874455i	$-0.661219\pi$
$181$	−175.608			−0.970212			−0.485106	+	0.874455i	$0.661219\pi$
$182$			158.302i			0.869789i
$183$			4.34628i			0.0237502i
$184$			33.2278i			0.180586i
$185$	95.6469			0.517010
$186$		−	83.9341i		−	0.451259i
$187$	163.596	+	138.740i	0.874844	+	0.741926i
$188$	−95.7572			−0.509347
$189$			13.7477i			0.0727393i
$190$	−80.9977			−0.426304
$191$	−308.588			−1.61565			−0.807823	−	0.589425i	$-0.799354\pi$
$191$	−308.588			−1.61565			−0.807823	+	0.589425i	$0.799354\pi$
$192$	143.701			0.748444
$193$		−	348.522i		−	1.80581i	−0.429837	−	0.902907i	$-0.641429\pi$
$193$		−	348.522i		−	1.80581i	0.429837	−	0.902907i	$-0.358571\pi$
$194$			423.046i			2.18065i
$195$		−	78.7672i		−	0.403934i
$196$	32.5858			0.166254
$197$			373.949i			1.89822i	0.314949	+	0.949109i	$0.398013\pi$
$197$			373.949i			1.89822i	−0.314949	+	0.949109i	$0.601987\pi$
$198$	−74.0432	−	62.7935i	−0.373956	−	0.317139i
$199$	−30.5948			−0.153743			−0.0768713	−	0.997041i	$-0.524493\pi$
$199$	−30.5948			−0.153743			−0.0768713	+	0.997041i	$0.524493\pi$
$200$			9.63666i			0.0481833i
$201$	141.498			0.703971
$202$	−410.386			−2.03161
$203$	−37.8175			−0.186293
$204$		−	157.230i		−	0.770737i
$205$		−	91.2647i		−	0.445194i
$206$		−	546.072i		−	2.65084i
$207$	51.7210			0.249860
$208$		−	263.379i		−	1.26625i
$209$	103.295	+	87.6009i	0.494234	+	0.419143i
$210$	−30.1461			−0.143553
$211$		−	10.0859i		−	0.0478006i	−0.999714	−	0.0239003i	$-0.992392\pi$
$211$		−	10.0859i		−	0.0478006i	0.999714	−	0.0239003i	$-0.00760843\pi$
$212$	159.681			0.753213
$213$	−10.1708			−0.0477502
$214$	−20.7459			−0.0969432
$215$		−	56.2503i		−	0.261629i
$216$			10.0147i			0.0463644i
$217$			43.5803i			0.200831i
$218$	166.905			0.765620
$219$		−	25.6585i		−	0.117162i
$220$	74.0581	−	87.3259i	0.336628	−	0.396936i
$221$	−396.593			−1.79454
$222$			217.963i			0.981816i
$223$	31.4952			0.141234			0.0706171	−	0.997503i	$-0.477503\pi$
$223$	31.4952			0.141234			0.0706171	+	0.997503i	$0.477503\pi$
$224$	−121.198			−0.541064
$225$	15.0000			0.0666667
$226$		−	306.519i		−	1.35628i
$227$		−	297.260i		−	1.30952i	−0.755839	−	0.654758i	$-0.772771\pi$
$227$		−	297.260i		−	1.30952i	0.755839	−	0.654758i	$-0.227229\pi$
$228$		−	99.2756i		−	0.435420i
$229$	−371.131			−1.62066			−0.810330	−	0.585973i	$-0.800712\pi$
$229$	−371.131			−1.62066			−0.810330	+	0.585973i	$0.800712\pi$
$230$			113.414i			0.493105i
$231$	38.4448	+	32.6037i	0.166428	+	0.141142i
$232$	−27.5486			−0.118744
$233$		−	78.8708i		−	0.338501i	−0.985573	−	0.169251i	$-0.945865\pi$
$233$		−	78.8708i		−	0.338501i	0.985573	−	0.169251i	$-0.0541347\pi$
$234$	179.497			0.767082
$235$	−45.9966			−0.195730
$236$	−450.714			−1.90980
$237$		−	15.8742i		−	0.0669799i
$238$			151.786i			0.637755i
$239$		−	183.702i		−	0.768627i	−0.923203	−	0.384314i	$-0.874438\pi$
$239$		−	183.702i		−	0.768627i	0.923203	−	0.384314i	$-0.125562\pi$
$240$	50.1565			0.208985
$241$			301.377i			1.25053i	0.780414	+	0.625263i	$0.215008\pi$
$241$			301.377i			1.25053i	−0.780414	+	0.625263i	$0.784992\pi$
$242$	−351.197	+	58.1385i	−1.45123	+	0.240242i
$243$	15.5885			0.0641500
$244$		−	11.6812i		−	0.0478738i
$245$	15.6525			0.0638877
$246$	207.977			0.845434
$247$	−250.410			−1.01380
$248$			31.7466i			0.128011i
$249$		−	129.049i		−	0.518270i
$250$			32.8921i			0.131568i
$251$	−223.382			−0.889969			−0.444985	−	0.895538i	$-0.646791\pi$
$251$	−223.382			−0.889969			−0.444985	+	0.895538i	$0.646791\pi$
$252$		−	36.9489i		−	0.146622i
$253$	122.660	−	144.635i	0.484822	−	0.571679i
$254$	309.766			1.21955
$255$		−	75.5250i		−	0.296176i
$256$	152.853			0.597082
$257$	426.693			1.66028			0.830142	−	0.557552i	$-0.188259\pi$
$257$	426.693			1.66028			0.830142	+	0.557552i	$0.188259\pi$
$258$	128.185			0.496841
$259$		−	113.171i		−	0.436953i
$260$			211.697i			0.814221i
$261$			42.8810i			0.164295i
$262$	548.332			2.09287
$263$			423.216i			1.60919i	0.593827	+	0.804593i	$0.297617\pi$
$263$			423.216i			1.60919i	−0.593827	+	0.804593i	$0.702383\pi$
$264$	28.0056	+	23.7506i	0.106082	+	0.0899643i
$265$	76.7022			0.289442
$266$			95.8378i			0.360293i
$267$	137.214			0.513912
$268$	−380.295			−1.41901
$269$	−471.055			−1.75113			−0.875567	−	0.483096i	$-0.839512\pi$
$269$	−471.055			−1.75113			−0.875567	+	0.483096i	$0.839512\pi$
$270$			34.1825i			0.126602i
$271$		−	462.016i		−	1.70485i	−0.522846	−	0.852427i	$-0.675130\pi$
$271$		−	462.016i		−	1.70485i	0.522846	−	0.852427i	$-0.324870\pi$
$272$		−	252.538i		−	0.928448i
$273$	−93.1986			−0.341387
$274$			393.536i			1.43626i
$275$	35.5735	−	41.9467i	0.129358	−	0.152533i
$276$	−139.007			−0.503649
$277$			199.780i			0.721226i	0.932715	+	0.360613i	$0.117433\pi$
$277$			199.780i			0.721226i	−0.932715	+	0.360613i	$0.882567\pi$
$278$	430.271			1.54774
$279$	49.4155			0.177116
$280$	11.4022			0.0407223
$281$			207.876i			0.739772i	0.929077	+	0.369886i	$0.120603\pi$
$281$			207.876i			0.739772i	−0.929077	+	0.369886i	$0.879397\pi$
$282$		−	104.819i		−	0.371697i
$283$		−	155.650i		−	0.550000i	−0.961444	−	0.275000i	$-0.911322\pi$
$283$		−	155.650i		−	0.550000i	0.961444	−	0.275000i	$-0.0886779\pi$
$284$	27.3354			0.0962513
$285$		−	47.6867i		−	0.167322i
$286$	425.690	−	501.954i	1.48843	−	1.75508i
$287$	−107.986			−0.376257
$288$			137.426i			0.477174i
$289$	−91.2682			−0.315807
$290$	−94.0296			−0.324240
$291$	−249.064			−0.855891
$292$			68.9606i			0.236167i
$293$			53.6749i			0.183191i	0.995796	+	0.0915954i	$0.0291966\pi$
$293$			53.6749i			0.183191i	−0.995796	+	0.0915954i	$0.970803\pi$
$294$			35.6693i			0.121324i
$295$	−216.499			−0.733894
$296$		−	82.4408i		−	0.278516i
$297$	36.9691	−	43.5923i	0.124475	−	0.146775i
$298$	−493.180			−1.65497
$299$			350.627i			1.17266i
$300$	−40.3145			−0.134382
$301$	−66.5563			−0.221117
$302$	−570.997			−1.89072
$303$		−	241.611i		−	0.797395i
$304$		−	159.453i		−	0.524517i
$305$		−	5.61102i		−	0.0183968i
$306$	172.109			0.562447
$307$			56.7128i			0.184732i	0.995725	+	0.0923661i	$0.0294430\pi$
$307$			56.7128i			0.184732i	−0.995725	+	0.0923661i	$0.970557\pi$
$308$	−103.325	−	87.6268i	−0.335472	−	0.284503i
$309$	321.495			1.04044
$310$			108.359i			0.349544i
$311$	408.153			1.31239			0.656194	−	0.754592i	$-0.272165\pi$
$311$	408.153			1.31239			0.656194	+	0.754592i	$0.272165\pi$
$312$	−67.8917			−0.217602
$313$	84.5231			0.270042			0.135021	−	0.990843i	$-0.456890\pi$
$313$	84.5231			0.270042			0.135021	+	0.990843i	$0.456890\pi$
$314$		−	35.9404i		−	0.114460i
$315$		−	17.7482i		−	0.0563436i
$316$			42.6642i			0.135013i
$317$	131.336			0.414309			0.207154	−	0.978308i	$-0.433580\pi$
$317$	131.336			0.414309			0.207154	+	0.978308i	$0.433580\pi$
$318$			174.791i			0.549658i
$319$	119.914	+	101.695i	0.375907	+	0.318794i
$320$	−185.517			−0.579742
$321$		−	12.2139i		−	0.0380496i
$322$	134.193			0.416749
$323$	−240.102			−0.743351
$324$	−41.8961			−0.129309
$325$			101.688i			0.312886i
$326$		−	336.548i		−	1.03235i
$327$			98.2639i			0.300501i
$328$	−78.6636			−0.239828
$329$			54.4239i			0.165422i
$330$	95.5894	+	81.0661i	0.289665	+	0.245655i
$331$	24.4564			0.0738863			0.0369431	−	0.999317i	$-0.488238\pi$
$331$	24.4564			0.0738863			0.0369431	+	0.999317i	$0.488238\pi$
$332$			346.837i			1.04469i
$333$	−128.324			−0.385357
$334$	804.403			2.40839
$335$	−182.673			−0.545294
$336$		−	59.3459i		−	0.176625i
$337$			509.292i			1.51125i	0.655004	+	0.755626i	$0.272667\pi$
$337$			509.292i			1.51125i	−0.655004	+	0.755626i	$0.727333\pi$
$338$			719.657i			2.12916i
$339$	180.460			0.532331
$340$			202.983i			0.597010i
$341$	117.192	−	138.188i	0.343672	−	0.405242i
$342$	108.670			0.317748
$343$		−	18.5203i		−	0.0539949i
$344$	−48.4838			−0.140941
$345$	−66.7715			−0.193540
$346$	893.777			2.58317
$347$			291.684i			0.840587i	0.907388	+	0.420294i	$0.138073\pi$
$347$			291.684i			0.840587i	−0.907388	+	0.420294i	$0.861927\pi$
$348$		−	115.248i		−	0.331173i
$349$			39.3523i			0.112757i	0.998409	+	0.0563786i	$0.0179554\pi$
$349$			39.3523i			0.112757i	−0.998409	+	0.0563786i	$0.982045\pi$
$350$	38.9184			0.111196
$351$			105.677i			0.301075i
$352$	384.304	+	325.916i	1.09177	+	0.925896i
$353$	−396.357			−1.12282			−0.561412	−	0.827536i	$-0.689742\pi$
$353$	−396.357			−1.12282			−0.561412	+	0.827536i	$0.689742\pi$
$354$		−	493.364i		−	1.39368i
$355$	13.1304			0.0369871
$356$	−368.782			−1.03590
$357$	−89.3624			−0.250315
$358$		−	282.441i		−	0.788942i
$359$			202.451i			0.563932i	0.959424	+	0.281966i	$0.0909865\pi$
$359$			202.451i			0.563932i	−0.959424	+	0.281966i	$0.909014\pi$
$360$		−	12.9289i		−	0.0359137i
$361$	209.399			0.580052
$362$			516.632i			1.42716i
$363$	−34.2285	−	206.764i	−0.0942934	−	0.569598i
$364$	250.484			0.688142
$365$			33.1250i			0.0907534i
$366$	12.7866			0.0349360
$367$	−214.380			−0.584142			−0.292071	−	0.956397i	$-0.594344\pi$
$367$	−214.380			−0.584142			−0.292071	+	0.956397i	$0.594344\pi$
$368$	−223.268			−0.606707
$369$			122.444i			0.331828i
$370$		−	281.389i		−	0.760511i
$371$		−	90.7553i		−	0.244623i
$372$	−132.811			−0.357018
$373$		−	110.927i		−	0.297391i	−0.988883	−	0.148695i	$-0.952493\pi$
$373$		−	110.927i		−	0.297391i	0.988883	−	0.148695i	$-0.0475074\pi$
$374$	408.168	−	481.292i	1.09136	−	1.28688i
$375$	−19.3649			−0.0516398
$376$			39.6458i			0.105441i
$377$	−290.699			−0.771084
$378$	40.4452			0.106998
$379$	−202.144			−0.533361			−0.266680	−	0.963785i	$-0.585927\pi$
$379$	−202.144			−0.533361			−0.266680	+	0.963785i	$0.585927\pi$
$380$			128.164i			0.337275i
$381$			182.372i			0.478666i
$382$			907.854i			2.37658i
$383$	563.686			1.47177			0.735883	−	0.677109i	$-0.236767\pi$
$383$	563.686			1.47177			0.735883	+	0.677109i	$0.236767\pi$
$384$		−	105.391i		−	0.274455i
$385$	−49.6320	−	42.0912i	−0.128914	−	0.109328i
$386$	−1025.34			−2.65631
$387$			75.4677i			0.195007i
$388$	669.393			1.72524
$389$	563.168			1.44773			0.723867	−	0.689940i	$-0.242363\pi$
$389$	563.168			1.44773			0.723867	+	0.689940i	$0.242363\pi$
$390$	−231.730			−0.594179
$391$			336.194i			0.859832i
$392$		−	13.4913i		−	0.0344166i
$393$			322.826i			0.821439i
$394$	1100.14			2.79224
$395$			20.4936i			0.0518824i
$396$	−99.3594	+	117.160i	−0.250908	+	0.295859i
$397$	272.484			0.686359			0.343179	−	0.939270i	$-0.388496\pi$
$397$	272.484			0.686359			0.343179	+	0.939270i	$0.388496\pi$
$398$			90.0086i			0.226152i
$399$	−56.4236			−0.141413
$400$	−64.7517			−0.161879
$401$	466.992			1.16457			0.582284	−	0.812985i	$-0.302159\pi$
$401$	466.992			1.16457			0.582284	+	0.812985i	$0.302159\pi$
$402$		−	416.282i		−	1.03553i
$403$			334.997i			0.831259i
$404$			649.361i			1.60733i
$405$	−20.1246			−0.0496904
$406$			111.257i			0.274033i
$407$	−304.329	+	358.850i	−0.747736	+	0.881696i
$408$	−65.0971			−0.159552
$409$			258.163i			0.631206i	0.948891	+	0.315603i	$0.102207\pi$
$409$			258.163i			0.631206i	−0.948891	+	0.315603i	$0.897793\pi$
$410$	−268.497			−0.654870
$411$	−231.691			−0.563725
$412$	−864.061			−2.09724
$413$			256.165i			0.620253i
$414$		−	152.161i		−	0.367538i
$415$			166.602i			0.401450i
$416$	−931.639			−2.23952
$417$			253.318i			0.607477i
$418$	257.718	−	303.889i	0.616551	−	0.727008i
$419$	−335.879			−0.801620			−0.400810	−	0.916161i	$-0.631271\pi$
$419$	−335.879			−0.801620			−0.400810	+	0.916161i	$0.631271\pi$
$420$			47.7008i			0.113573i
$421$	−339.073			−0.805398			−0.402699	−	0.915332i	$-0.631928\pi$
$421$	−339.073			−0.805398			−0.402699	+	0.915332i	$0.631928\pi$
$422$	−29.6724			−0.0703137
$423$	61.7109			0.145889
$424$		−	66.1118i		−	0.155924i
$425$			97.5023i			0.229417i
$426$			29.9220i			0.0702395i
$427$	−6.63905			−0.0155481
$428$			32.8266i			0.0766976i
$429$	295.521	+	250.621i	0.688859	+	0.584198i
$430$	−165.486			−0.384851
$431$		−	570.699i		−	1.32413i	−0.749448	−	0.662063i	$-0.769681\pi$
$431$		−	570.699i		−	1.32413i	0.749448	−	0.662063i	$-0.230319\pi$
$432$	−67.2920			−0.155768
$433$	−178.571			−0.412404			−0.206202	−	0.978509i	$-0.566110\pi$
$433$	−178.571			−0.412404			−0.206202	+	0.978509i	$0.566110\pi$
$434$	128.212			0.295418
$435$		−	55.3591i		−	0.127262i
$436$		−	264.097i		−	0.605728i
$437$			212.274i			0.485753i
$438$	−75.4862			−0.172343
$439$		−	346.150i		−	0.788498i	−0.919004	−	0.394249i	$-0.871005\pi$
$439$		−	346.150i		−	0.788498i	0.919004	−	0.394249i	$-0.128995\pi$
$440$	−36.1550	−	30.6619i	−0.0821705	−	0.0696860i
$441$	−21.0000			−0.0476190
$442$			1166.76i			2.63973i
$443$	364.201			0.822123			0.411062	−	0.911608i	$-0.365158\pi$
$443$	364.201			0.822123			0.411062	+	0.911608i	$0.365158\pi$
$444$	344.887			0.776773
$445$	−177.143			−0.398074
$446$		−	92.6576i		−	0.207752i
$447$		−	290.355i		−	0.649565i
$448$			219.507i			0.489971i
$449$	−262.050			−0.583629			−0.291815	−	0.956475i	$-0.594259\pi$
$449$	−262.050			−0.583629			−0.291815	+	0.956475i	$0.594259\pi$
$450$		−	44.1294i		−	0.0980653i
$451$	342.409	+	290.385i	0.759222	+	0.643870i
$452$	−485.011			−1.07303
$453$		−	336.169i		−	0.742095i
$454$	−874.526			−1.92627
$455$	120.319			0.264437
$456$	−41.1025			−0.0901371
$457$			144.287i			0.315727i	0.987461	+	0.157864i	$0.0504606\pi$
$457$			144.287i			0.315727i	−0.987461	+	0.157864i	$0.949539\pi$
$458$			1091.85i			2.38396i
$459$			101.327i			0.220757i
$460$	179.457			0.390124
$461$		−	40.1459i		−	0.0870843i	−0.999052	−	0.0435422i	$-0.986136\pi$
$461$		−	40.1459i		−	0.0870843i	0.999052	−	0.0435422i	$-0.0138643\pi$
$462$	95.9187	−	113.103i	0.207616	−	0.244811i
$463$	−6.41580			−0.0138570			−0.00692851	−	0.999976i	$-0.502205\pi$
$463$	−6.41580			−0.0138570			−0.00692851	+	0.999976i	$0.502205\pi$
$464$		−	185.108i		−	0.398939i
$465$	−63.7951			−0.137194
$466$	−232.034			−0.497928
$467$	−221.902			−0.475166			−0.237583	−	0.971367i	$-0.576355\pi$
$467$	−221.902			−0.475166			−0.237583	+	0.971367i	$0.576355\pi$
$468$		−	284.022i		−	0.606884i
$469$			216.142i			0.460857i
$470$			135.320i			0.287915i
$471$	21.1596			0.0449248
$472$			186.606i			0.395352i
$473$	211.041	+	178.977i	0.446176	+	0.378387i
$474$	−46.7014			−0.0985261
$475$			61.5632i			0.129607i
$476$	240.173			0.504566
$477$	−102.907			−0.215738
$478$	−540.443			−1.13063
$479$		−	831.078i		−	1.73503i	−0.497414	−	0.867514i	$-0.665717\pi$
$479$		−	831.078i		−	1.73503i	0.497414	−	0.867514i	$-0.334283\pi$
$480$		−	177.416i		−	0.369617i
$481$		−	869.933i		−	1.80859i
$482$	886.638			1.83950
$483$			79.0051i			0.163572i
$484$	91.9937	+	555.706i	0.190070	+	1.14815i
$485$	321.541			0.662970
$486$		−	45.8606i		−	0.0943634i
$487$	−145.686			−0.299149			−0.149575	−	0.988750i	$-0.547790\pi$
$487$	−145.686			−0.299149			−0.149575	+	0.988750i	$0.547790\pi$
$488$	−4.83630			−0.00991045
$489$	198.139			0.405193
$490$		−	46.0489i		−	0.0939774i
$491$		−	5.93335i		−	0.0120842i	−0.999982	−	0.00604211i	$-0.998077\pi$
$491$		−	5.93335i		−	0.0120842i	0.999982	−	0.00604211i	$-0.00192327\pi$
$492$		−	329.086i		−	0.668873i
$493$	−278.733			−0.565381
$494$			736.695i			1.49129i
$495$	−47.7269	+	56.2774i	−0.0964180	+	0.113692i
$496$	−213.316			−0.430072
$497$		−	15.5361i		−	0.0312598i
$498$	−379.657			−0.762364
$499$	−586.679			−1.17571			−0.587854	−	0.808967i	$-0.700027\pi$
$499$	−586.679			−1.17571			−0.587854	+	0.808967i	$0.700027\pi$
$500$	52.0458			0.104092
$501$			473.585i			0.945279i
$502$			657.182i			1.30913i
$503$		−	274.049i		−	0.544828i	−0.962180	−	0.272414i	$-0.912178\pi$
$503$		−	274.049i		−	0.544828i	0.962180	−	0.272414i	$-0.0878221\pi$
$504$	−15.2977			−0.0303526
$505$			311.918i			0.617660i
$506$	−425.510	−	360.860i	−0.840928	−	0.713162i
$507$	−423.691			−0.835683
$508$		−	490.148i		−	0.964859i
$509$	219.788			0.431804			0.215902	−	0.976415i	$-0.430731\pi$
$509$	219.788			0.431804			0.215902	+	0.976415i	$0.430731\pi$
$510$	−222.191			−0.435669
$511$	39.1940			0.0767006
$512$		−	693.077i		−	1.35367i
$513$			63.9784i			0.124714i
$514$		−	1255.31i		−	2.44224i
$515$	−415.048			−0.805919
$516$		−	202.830i		−	0.393081i
$517$	146.352	−	172.571i	0.283079	−	0.333793i
$518$	−332.944			−0.642749
$519$			526.203i			1.01388i
$520$	87.6478			0.168554
$521$	839.697			1.61170			0.805851	−	0.592118i	$-0.201708\pi$
$521$	839.697			1.61170			0.805851	+	0.592118i	$0.201708\pi$
$522$	126.154			0.241674
$523$		−	69.2977i		−	0.132500i	−0.997803	−	0.0662502i	$-0.978896\pi$
$523$		−	69.2977i		−	0.132500i	0.997803	−	0.0662502i	$-0.0211036\pi$
$524$		−	867.637i		−	1.65580i
$525$			22.9129i			0.0436436i
$526$	1245.08			2.36708
$527$			321.208i			0.609503i
$528$	−159.588	+	188.178i	−0.302249	+	0.356398i
$529$	−231.771			−0.438131
$530$		−	225.655i		−	0.425763i
$531$	290.463			0.547012
$532$	151.646			0.285049
$533$	−830.075			−1.55736
$534$		−	403.679i		−	0.755953i
$535$			15.7681i			0.0294731i
$536$			157.451i			0.293753i
$537$	166.285			0.309655
$538$			1385.82i			2.57588i
$539$	−49.8030	+	58.7253i	−0.0923988	+	0.108952i
$540$	54.0876			0.100162
$541$			571.881i			1.05708i	0.848908	+	0.528541i	$0.177261\pi$
$541$			571.881i			1.05708i	−0.848908	+	0.528541i	$0.822739\pi$
$542$	−1359.23			−2.50781
$543$	−304.163			−0.560152
$544$	−893.291			−1.64208
$545$		−	126.858i		−	0.232767i
$546$			274.186i			0.502173i
$547$		−	347.939i		−	0.636086i	−0.948076	−	0.318043i	$-0.896974\pi$
$547$		−	347.939i		−	0.636086i	0.948076	−	0.318043i	$-0.103026\pi$
$548$	622.700			1.13631
$549$			7.52798i			0.0137122i
$550$	−123.405	−	104.656i	−0.224373	−	0.190283i
$551$	−175.993			−0.319406
$552$			57.5522i			0.104261i
$553$	24.2483			0.0438487
$554$	587.743			1.06091
$555$	165.665			0.298496
$556$		−	680.826i		−	1.22451i
$557$		−	589.513i		−	1.05837i	−0.848506	−	0.529186i	$-0.822497\pi$
$557$		−	589.513i		−	1.05837i	0.848506	−	0.529186i	$-0.177503\pi$
$558$		−	145.378i		−	0.260534i
$559$	−511.611			−0.915225
$560$			76.6153i			0.136813i
$561$	283.356	+	240.305i	0.505092	+	0.428351i
$562$	611.562			1.08819
$563$			359.032i			0.637713i	0.947803	+	0.318856i	$0.103299\pi$
$563$			359.032i			0.637713i	−0.947803	+	0.318856i	$0.896701\pi$
$564$	−165.856			−0.294072
$565$	−232.973			−0.412342
$566$	−457.916			−0.809039
$567$			23.8118i			0.0419961i
$568$		−	11.3175i		−	0.0199252i
$569$		−	130.752i		−	0.229793i	−0.993377	−	0.114896i	$-0.963346\pi$
$569$		−	130.752i		−	0.229793i	0.993377	−	0.114896i	$-0.0366536\pi$
$570$	−140.292			−0.246127
$571$		−	363.004i		−	0.635734i	−0.948135	−	0.317867i	$-0.897033\pi$
$571$		−	363.004i		−	0.635734i	0.948135	−	0.317867i	$-0.102967\pi$
$572$	−794.251	−	673.578i	−1.38855	−	1.17758i
$573$	−534.491			−0.932794
$574$			317.690i			0.553466i
$575$	86.2016			0.149916
$576$	248.898			0.432114
$577$	−468.332			−0.811667			−0.405833	−	0.913947i	$-0.633019\pi$
$577$	−468.332			−0.811667			−0.405833	+	0.913947i	$0.633019\pi$
$578$			268.507i			0.464545i
$579$		−	603.658i		−	1.04259i
$580$			148.785i			0.256526i
$581$	197.126			0.339287
$582$			732.737i			1.25900i
$583$	−244.051	+	287.773i	−0.418612	+	0.493607i
$584$	28.5514			0.0488893
$585$		−	136.429i		−	0.233212i
$586$	157.909			0.269470
$587$	651.090			1.10918			0.554591	−	0.832123i	$-0.312875\pi$
$587$	651.090			1.10918			0.554591	+	0.832123i	$0.312875\pi$
$588$	56.4403			0.0959869
$589$			202.812i			0.344332i
$590$			636.930i			1.07954i
$591$			647.698i			1.09594i
$592$	553.946			0.935719
$593$			287.827i			0.485374i	0.970105	+	0.242687i	$0.0780287\pi$
$593$			287.827i			0.485374i	−0.970105	+	0.242687i	$0.921971\pi$
$594$	−128.247	−	108.762i	−0.215903	−	0.183100i
$595$	115.366			0.193893
$596$			780.369i			1.30934i
$597$	−52.9917			−0.0887634
$598$	1031.53			1.72497
$599$	−84.1192			−0.140433			−0.0702163	−	0.997532i	$-0.522369\pi$
$599$	−84.1192			−0.140433			−0.0702163	+	0.997532i	$0.522369\pi$
$600$			16.6912i			0.0278186i
$601$			526.558i			0.876136i	0.898942	+	0.438068i	$0.144337\pi$
$601$			526.558i			0.876136i	−0.898942	+	0.438068i	$0.855663\pi$
$602$			195.806i			0.325259i
$603$	245.082			0.406438
$604$			903.500i			1.49586i
$605$	44.1888	+	266.931i	0.0730394	+	0.441209i
$606$	−710.809			−1.17295
$607$		−	997.207i		−	1.64284i	−0.570321	−	0.821422i	$-0.693181\pi$
$607$		−	997.207i		−	1.64284i	0.570321	−	0.821422i	$-0.306819\pi$
$608$	−564.026			−0.927675
$609$	−65.5017			−0.107556
$610$	−16.5074			−0.0270613
$611$			418.351i			0.684699i
$612$		−	272.331i		−	0.444985i
$613$			107.985i			0.176158i	0.996113	+	0.0880791i	$0.0280728\pi$
$613$			107.985i			0.176158i	−0.996113	+	0.0880791i	$0.971927\pi$
$614$	166.847			0.271737
$615$		−	158.075i		−	0.257033i
$616$	−36.2796	+	42.7792i	−0.0588954	+	0.0694468i
$617$	399.289			0.647147			0.323573	−	0.946203i	$-0.395116\pi$
$617$	399.289			0.647147			0.323573	+	0.946203i	$0.395116\pi$
$618$		−	945.825i		−	1.53046i
$619$	746.420			1.20585			0.602924	−	0.797798i	$-0.294002\pi$
$619$	746.420			1.20585			0.602924	+	0.797798i	$0.294002\pi$
$620$	171.458			0.276545
$621$	89.5833			0.144257
$622$		−	1200.77i		−	1.93050i
$623$			209.598i			0.336434i
$624$		−	456.186i		−	0.731067i
$625$	25.0000			0.0400000
$626$		−	248.663i		−	0.397226i
$627$	178.912	+	151.729i	0.285346	+	0.241992i
$628$	−56.8692			−0.0905561
$629$		−	834.124i		−	1.32611i
$630$	−52.2146			−0.0828803
$631$	709.666			1.12467			0.562334	−	0.826910i	$-0.309903\pi$
$631$	709.666			1.12467			0.562334	+	0.826910i	$0.309903\pi$
$632$	17.6640			0.0279494
$633$		−	17.4694i		−	0.0275977i
$634$		−	386.385i		−	0.609440i
$635$		−	235.441i		−	0.370773i
$636$	276.576			0.434868
$637$		−	142.363i		−	0.223490i
$638$	299.183	−	352.783i	0.468939	−	0.552951i
$639$	−17.6163			−0.0275686
$640$			136.059i			0.212592i
$641$	−575.621			−0.898004			−0.449002	−	0.893531i	$-0.648220\pi$
$641$	−575.621			−0.898004			−0.449002	+	0.893531i	$0.648220\pi$
$642$	−35.9329			−0.0559702
$643$	309.929			0.482005			0.241002	−	0.970525i	$-0.422524\pi$
$643$	309.929			0.482005			0.241002	+	0.970525i	$0.422524\pi$
$644$		−	212.337i		−	0.329715i
$645$		−	97.4284i		−	0.151052i
$646$			706.371i			1.09345i
$647$	−294.944			−0.455863			−0.227932	−	0.973677i	$-0.573196\pi$
$647$	−294.944			−0.455863			−0.227932	+	0.973677i	$0.573196\pi$
$648$			17.3460i			0.0267685i
$649$	688.854	−	812.265i	1.06141	−	1.25156i
$650$	299.162			0.460249
$651$			75.4834i			0.115950i
$652$	−532.526			−0.816757
$653$	195.516			0.299413			0.149706	−	0.988731i	$-0.452167\pi$
$653$	195.516			0.299413			0.149706	+	0.988731i	$0.452167\pi$
$654$	289.088			0.442031
$655$		−	416.766i		−	0.636284i
$656$		−	528.566i		−	0.805741i
$657$		−	44.4418i		−	0.0676436i
$658$	160.113			0.243333
$659$		−	1190.81i		−	1.80700i	−0.428586	−	0.903501i	$-0.640988\pi$
$659$		−	1190.81i		−	1.80700i	0.428586	−	0.903501i	$-0.359012\pi$
$660$	128.272	−	151.253i	0.194352	−	0.229171i
$661$	381.403			0.577009			0.288505	−	0.957478i	$-0.406842\pi$
$661$	381.403			0.577009			0.288505	+	0.957478i	$0.406842\pi$
$662$		−	71.9496i		−	0.108685i
$663$	−686.919			−1.03608
$664$	143.599			0.216263
$665$	72.8426			0.109538
$666$			377.523i			0.566851i
$667$			246.427i			0.369456i
$668$		−	1272.82i		−	1.90542i
$669$	54.5513			0.0815416
$670$			537.418i			0.802116i
$671$	21.0516	+	17.8531i	0.0313734	+	0.0266067i
$672$	−209.922			−0.312384
$673$			200.235i			0.297525i	0.988873	+	0.148763i	$0.0475290\pi$
$673$			200.235i			0.297525i	−0.988873	+	0.148763i	$0.952471\pi$
$674$	1498.31			2.22302
$675$	25.9808			0.0384900
$676$	1138.73			1.68451
$677$		−	905.067i		−	1.33688i	−0.743767	−	0.668439i	$-0.766963\pi$
$677$		−	905.067i		−	1.33688i	0.743767	−	0.668439i	$-0.233037\pi$
$678$		−	530.906i		−	0.783048i
$679$		−	380.452i		−	0.560312i
$680$	84.0400			0.123588
$681$		−	514.869i		−	0.756049i
$682$	−406.542	−	344.775i	−0.596103	−	0.505534i
$683$	524.476			0.767901			0.383950	−	0.923354i	$-0.374563\pi$
$683$	524.476			0.767901			0.383950	+	0.923354i	$0.374563\pi$
$684$		−	171.950i		−	0.251390i
$685$	299.112			0.436659
$686$	−54.4858			−0.0794254
$687$	−642.818			−0.935689
$688$		−	325.778i		−	0.473514i
$689$		−	697.626i		−	1.01252i
$690$			196.439i			0.284694i
$691$	798.817			1.15603			0.578015	−	0.816026i	$-0.303827\pi$
$691$	798.817			1.15603			0.578015	+	0.816026i	$0.303827\pi$
$692$		−	1414.24i		−	2.04370i
$693$	66.5883	+	56.4712i	0.0960870	+	0.0814881i
$694$	858.122			1.23649
$695$		−	327.032i		−	0.470550i
$696$	−47.7156			−0.0685569
$697$	−795.908			−1.14190
$698$	115.773			0.165864
$699$		−	136.608i		−	0.195434i
$700$		−	61.5814i		−	0.0879735i
$701$		−	1244.02i		−	1.77463i	−0.461160	−	0.887317i	$-0.652567\pi$
$701$		−	1244.02i		−	1.77463i	0.461160	−	0.887317i	$-0.347433\pi$
$702$	310.898			0.442875
$703$		−	526.668i		−	0.749172i
$704$	590.278	−	696.029i	0.838463	−	0.988677i
$705$	−79.6685			−0.113005
$706$			1166.07i			1.65165i
$707$	369.066			0.522018
$708$	−780.659			−1.10263
$709$	−885.894			−1.24950			−0.624749	−	0.780826i	$-0.714799\pi$
$709$	−885.894			−1.24950			−0.624749	+	0.780826i	$0.714799\pi$
$710$		−	38.6292i		−	0.0544073i
$711$		−	27.4950i		−	0.0386709i
$712$			152.685i			0.214445i
$713$	283.979			0.398288
$714$			262.900i			0.368208i
$715$	−381.516	−	323.550i	−0.533588	−	0.452518i
$716$	−446.912			−0.624179
$717$		−	318.181i		−	0.443767i
$718$	595.604			0.829532
$719$	−958.692			−1.33337			−0.666684	−	0.745340i	$-0.732287\pi$
$719$	−958.692			−1.33337			−0.666684	+	0.745340i	$0.732287\pi$
$720$	86.8736			0.120658
$721$			491.092i			0.681126i
$722$		−	616.042i		−	0.853244i
$723$			522.000i			0.721992i
$724$	817.478			1.12911
$725$			71.4683i			0.0985769i
$726$	−608.291	+	100.699i	−0.837867	+	0.138704i
$727$	−1383.64			−1.90322			−0.951612	−	0.307302i	$-0.900574\pi$
$727$	−1383.64			−1.90322			−0.951612	+	0.307302i	$0.900574\pi$
$728$		−	103.706i		−	0.142454i
$729$	27.0000			0.0370370
$730$	97.4523			0.133496
$731$	−490.552			−0.671070
$732$		−	20.2324i		−	0.0276399i
$733$			324.213i			0.442309i	0.975239	+	0.221155i	$0.0709825\pi$
$733$			324.213i			0.442309i	−0.975239	+	0.221155i	$0.929017\pi$
$734$			630.698i			0.859261i
$735$	27.1109			0.0368856
$736$			789.757i			1.07304i
$737$	581.229	−	685.358i	0.788642	−	0.929930i
$738$	360.226			0.488112
$739$		−	126.970i		−	0.171813i	−0.996303	−	0.0859064i	$-0.972621\pi$
$739$		−	126.970i		−	0.171813i	0.996303	−	0.0859064i	$-0.0273786\pi$
$740$	−445.247			−0.601686
$741$	−433.722			−0.585320
$742$	−266.998			−0.359836
$743$		−	224.468i		−	0.302111i	−0.988525	−	0.151055i	$-0.951733\pi$
$743$		−	224.468i		−	0.302111i	0.988525	−	0.151055i	$-0.0482672\pi$
$744$			54.9868i			0.0739070i
$745$			374.847i			0.503151i
$746$	−326.342			−0.437456
$747$		−	223.520i		−	0.299223i
$748$	−761.558	−	645.852i	−1.01813	−	0.863438i
$749$	18.6571			0.0249093
$750$			56.9708i			0.0759610i
$751$	−925.128			−1.23186			−0.615931	−	0.787800i	$-0.711220\pi$
$751$	−925.128			−1.23186			−0.615931	+	0.787800i	$0.711220\pi$
$752$	−266.393			−0.354246
$753$	−386.910			−0.513824
$754$			855.223i			1.13425i
$755$			433.993i			0.574825i
$756$		−	63.9973i		−	0.0846525i
$757$	−776.679			−1.02600			−0.512998	−	0.858390i	$-0.671465\pi$
$757$	−776.679			−1.02600			−0.512998	+	0.858390i	$0.671465\pi$
$758$			594.698i			0.784562i
$759$	212.453	−	250.515i	0.279912	−	0.330059i
$760$	53.0631			0.0698199
$761$			681.248i			0.895201i	0.894234	+	0.447600i	$0.147721\pi$
$761$			681.248i			0.895201i	−0.894234	+	0.447600i	$0.852279\pi$
$762$	536.530			0.704107
$763$	−150.101			−0.196724
$764$	1436.52			1.88026
$765$		−	130.813i		−	0.170998i
$766$		−	1658.34i		−	2.16494i
$767$			1969.11i			2.56729i
$768$	264.749			0.344726
$769$		−	888.690i		−	1.15564i	−0.816163	−	0.577822i	$-0.803903\pi$
$769$		−	888.690i		−	1.15564i	0.816163	−	0.577822i	$-0.196097\pi$
$770$	−123.831	+	146.015i	−0.160819	+	0.189630i
$771$	739.054			0.958565
$772$			1622.41i			2.10157i
$773$	686.960			0.888694			0.444347	−	0.895855i	$-0.353436\pi$
$773$	686.960			0.888694			0.444347	+	0.895855i	$0.353436\pi$
$774$	222.023			0.286851
$775$	82.3591			0.106270
$776$		−	277.145i		−	0.357146i
$777$		−	196.018i		−	0.252275i
$778$		−	1656.82i		−	2.12959i
$779$	−502.538			−0.645107
$780$			366.671i			0.470091i
$781$	−41.7784	+	49.2631i	−0.0534934	+	0.0630769i
$782$	989.069			1.26479
$783$			74.2720i			0.0948557i
$784$	90.6524			0.115628
$785$	−27.3169			−0.0347986
$786$	949.739			1.20832
$787$		−	135.323i		−	0.171948i	−0.996297	−	0.0859742i	$-0.972600\pi$
$787$		−	135.323i		−	0.171948i	0.996297	−	0.0859742i	$-0.0274003\pi$
$788$		−	1740.78i		−	2.20911i
$789$			733.032i			0.929064i
$790$	60.2912			0.0763180
$791$			275.657i			0.348492i
$792$	48.5071	+	41.1372i	0.0612463	+	0.0519409i
$793$	−51.0337			−0.0643552
$794$		−	801.638i		−	1.00962i
$795$	132.852			0.167110
$796$	142.422			0.178923
$797$	−1156.16			−1.45063			−0.725317	−	0.688415i	$-0.758307\pi$
$797$	−1156.16			−1.45063			−0.725317	+	0.688415i	$0.758307\pi$
$798$			165.996i			0.208015i
$799$			401.131i			0.502041i
$800$			229.044i			0.286304i
$801$	237.662			0.296707
$802$		−	1373.87i		−	1.71306i
$803$	−124.279	−	105.397i	−0.154768	−	0.131254i
$804$	−658.691			−0.819267
$805$		−	101.995i		−	0.126702i
$806$	985.548			1.22276
$807$	−815.892			−1.01102
$808$	268.851			0.332737
$809$		−	43.3491i		−	0.0535835i	−0.999641	−	0.0267918i	$-0.991471\pi$
$809$		−	43.3491i		−	0.0535835i	0.999641	−	0.0267918i	$-0.00852910\pi$
$810$			59.2058i			0.0730935i
$811$		−	476.841i		−	0.587967i	−0.955810	−	0.293983i	$-0.905019\pi$
$811$		−	476.841i		−	0.587967i	0.955810	−	0.293983i	$-0.0949811\pi$
$812$	176.045			0.216804
$813$		−	800.235i		−	0.984298i
$814$	1055.72	+	895.322i	1.29696	+	1.09990i
$815$	−255.797			−0.313861
$816$		−	437.408i		−	0.536040i
$817$	−309.736			−0.379114
$818$	759.506			0.928491
$819$	−161.425			−0.197100
$820$			424.848i			0.518107i
$821$		−	1320.96i		−	1.60896i	−0.593978	−	0.804481i	$-0.702443\pi$
$821$		−	1320.96i		−	1.60896i	0.593978	−	0.804481i	$-0.297557\pi$
$822$			681.625i			0.829227i
$823$	−151.589			−0.184191			−0.0920956	−	0.995750i	$-0.529357\pi$
$823$	−151.589			−0.184191			−0.0920956	+	0.995750i	$0.529357\pi$
$824$			357.742i			0.434153i
$825$	61.6152	−	72.6538i	0.0746851	−	0.0880652i
$826$	753.625			0.912380
$827$		−	610.784i		−	0.738554i	−0.929319	−	0.369277i	$-0.879605\pi$
$827$		−	610.784i		−	0.738554i	0.929319	−	0.369277i	$-0.120395\pi$
$828$	−240.767			−0.290782
$829$	487.749			0.588358			0.294179	−	0.955750i	$-0.404954\pi$
$829$	487.749			0.588358			0.294179	+	0.955750i	$0.404954\pi$
$830$	490.135			0.590524
$831$			346.029i			0.416400i
$832$			1687.33i			2.02804i
$833$		−	136.503i		−	0.163869i
$834$	745.251			0.893586
$835$		−	611.396i		−	0.732210i
$836$	−480.850	−	407.792i	−0.575179	−	0.487790i
$837$	85.5901			0.102258
$838$			988.141i			1.17917i
$839$	−1540.06			−1.83559			−0.917797	−	0.397050i	$-0.870034\pi$
$839$	−1540.06			−1.83559			−0.917797	+	0.397050i	$0.870034\pi$
$840$	19.7493			0.0235110
$841$	636.691			0.757065
$842$			997.538i			1.18472i
$843$			360.052i			0.427108i
$844$			46.9512i			0.0556294i
$845$	546.983			0.647317
$846$		−	181.551i		−	0.214599i
$847$	315.837	−	52.2849i	0.372890	−	0.0617296i
$848$	444.226			0.523852
$849$		−	269.594i		−	0.317543i
$850$	286.848			0.337468
$851$	−737.447			−0.866566
$852$	47.3462			0.0555707
$853$		−	1422.25i		−	1.66735i	−0.552258	−	0.833673i	$-0.686234\pi$
$853$		−	1422.25i		−	1.66735i	0.552258	−	0.833673i	$-0.313766\pi$
$854$			19.5318i			0.0228710i
$855$		−	82.5957i		−	0.0966032i
$856$	13.5910			0.0158773
$857$		−	280.876i		−	0.327743i	−0.986482	−	0.163872i	$-0.947602\pi$
$857$		−	280.876i		−	0.327743i	0.986482	−	0.163872i	$-0.0523983\pi$
$858$	737.317	−	869.410i	0.859343	−	1.01330i
$859$	−619.467			−0.721149			−0.360575	−	0.932730i	$-0.617419\pi$
$859$	−619.467			−0.721149			−0.360575	+	0.932730i	$0.617419\pi$
$860$			261.852i			0.304479i
$861$	−187.037			−0.217232
$862$	−1678.97			−1.94776
$863$	1179.46			1.36670			0.683348	−	0.730092i	$-0.260523\pi$
$863$	1179.46			1.36670			0.683348	+	0.730092i	$0.260523\pi$
$864$			238.029i			0.275497i
$865$		−	679.325i		−	0.785347i
$866$			525.348i			0.606638i
$867$	−158.081			−0.182331
$868$		−	202.872i		−	0.233723i
$869$	−76.8883	−	65.2063i	−0.0884790	−	0.0750360i
$870$	−162.864			−0.187200
$871$			1661.46i			1.90753i
$872$	−109.343			−0.125393
$873$	−431.392			−0.494149
$874$	624.501			0.714532
$875$		−	29.5804i		−	0.0338062i
$876$			119.443i			0.136351i
$877$			315.705i			0.359983i	0.983668	+	0.179992i	$0.0576071\pi$
$877$			315.705i			0.359983i	−0.983668	+	0.179992i	$0.942393\pi$
$878$	−1018.36			−1.15986
$879$			92.9676i			0.105765i
$880$	206.027	−	242.937i	0.234121	−	0.276065i
$881$	153.680			0.174438			0.0872188	−	0.996189i	$-0.472202\pi$
$881$	153.680			0.174438			0.0872188	+	0.996189i	$0.472202\pi$
$882$			61.7811i			0.0700466i
$883$	961.469			1.08887			0.544433	−	0.838804i	$-0.316745\pi$
$883$	961.469			1.08887			0.544433	+	0.838804i	$0.316745\pi$
$884$	1846.19			2.08845
$885$	−374.987			−0.423714
$886$		−	1071.46i		−	1.20933i
$887$		−	165.941i		−	0.187082i	−0.995615	−	0.0935409i	$-0.970181\pi$
$887$		−	165.941i		−	0.187082i	0.995615	−	0.0935409i	$-0.0298186\pi$
$888$		−	142.792i		−	0.160801i
$889$	−278.577			−0.313360
$890$			521.147i			0.585559i
$891$	64.0324	−	75.5040i	0.0718657	−	0.0847407i
$892$	−146.614			−0.164365
$893$			253.275i			0.283623i
$894$	−854.214			−0.955496
$895$	−214.673			−0.239858
$896$	160.987			0.179673
$897$			607.303i			0.677038i
$898$			770.939i			0.858507i
$899$			235.442i			0.261894i
$900$	−69.8268			−0.0775853
$901$		−	668.910i		−	0.742409i
$902$	854.302	−	1007.35i	0.947119	−	1.11680i
$903$	−115.279			−0.127662
$904$			200.806i			0.222131i
$905$	392.672			0.433892
$906$	−988.996			−1.09161
$907$	−105.814			−0.116664			−0.0583318	−	0.998297i	$-0.518578\pi$
$907$	−105.814			−0.116664			−0.0583318	+	0.998297i	$0.518578\pi$
$908$			1383.78i			1.52399i
$909$		−	418.482i		−	0.460376i
$910$		−	353.973i		−	0.388982i
$911$	722.962			0.793591			0.396796	−	0.917907i	$-0.370122\pi$
$911$	722.962			0.793591			0.396796	+	0.917907i	$0.370122\pi$
$912$		−	276.181i		−	0.302830i
$913$	−625.060	−	530.092i	−0.684622	−	0.580605i
$914$	424.487			0.464428
$915$		−	9.71857i		−	0.0106214i
$916$	1727.66			1.88609
$917$	−493.124			−0.537758
$918$	298.101			0.324729
$919$			896.160i			0.975147i	0.873082	+	0.487573i	$0.162118\pi$
$919$			896.160i			0.975147i	−0.873082	+	0.487573i	$0.837882\pi$
$920$		−	74.2996i		−	0.0807605i
$921$			98.2294i			0.106655i
$922$	−118.107			−0.128099
$923$		−	119.425i		−	0.129387i
$924$	−178.965	−	151.774i	−0.193685	−	0.164258i
$925$	−213.873			−0.231214
$926$			18.8750i			0.0203834i
$927$	556.846			0.600697
$928$	−654.774			−0.705575
$929$	−960.562			−1.03397			−0.516987	−	0.855993i	$-0.672947\pi$
$929$	−960.562			−1.03397			−0.516987	+	0.855993i	$0.672947\pi$
$930$			187.682i			0.201809i
$931$		−	86.1885i		−	0.0925763i
$932$			367.153i			0.393941i
$933$	706.941			0.757708
$934$			652.827i			0.698959i
$935$	−365.812	−	310.232i	−0.391242	−	0.331799i
$936$	−117.592			−0.125632
$937$			37.1392i			0.0396363i	0.999804	+	0.0198182i	$0.00630873\pi$
$937$			37.1392i			0.0396363i	−0.999804	+	0.0198182i	$0.993691\pi$
$938$	635.881			0.677911
$939$	146.398			0.155909
$940$	214.120			0.227787
$941$			1103.70i			1.17291i	0.809983	+	0.586453i	$0.199476\pi$
$941$			1103.70i			1.17291i	−0.809983	+	0.586453i	$0.800524\pi$
$942$		−	62.2506i		−	0.0660835i
$943$			703.660i			0.746193i
$944$	−1253.87			−1.32825
$945$		−	30.7409i		−	0.0325300i
$946$	526.543	−	620.875i	0.556599	−	0.656316i
$947$	−351.162			−0.370815			−0.185408	−	0.982662i	$-0.559361\pi$
$947$	−351.162			−0.370815			−0.185408	+	0.982662i	$0.559361\pi$
$948$			73.8965i			0.0779499i
$949$	301.280			0.317471
$950$	181.116			0.190649
$951$	227.480			0.239201
$952$		−	99.4375i		−	0.104451i
$953$		−	519.178i		−	0.544783i	−0.962187	−	0.272391i	$-0.912185\pi$
$953$		−	519.178i		−	0.544783i	0.962187	−	0.272391i	$-0.0878145\pi$
$954$			302.747i			0.317345i
$955$	690.025			0.722539
$956$			855.154i			0.894513i
$957$	207.698	+	176.141i	0.217030	+	0.184056i
$958$	−2445.00			−2.55219
$959$		−	353.914i		−	0.369044i
$960$	−321.326			−0.334714
$961$	−689.679			−0.717668
$962$	−2559.31			−2.66040
$963$		−	21.1551i		−	0.0219680i
$964$		−	1402.95i		−	1.45534i
$965$			779.319i			0.807584i
$966$	232.430			0.240610
$967$		−	23.3950i		−	0.0241934i	−0.999927	−	0.0120967i	$-0.996149\pi$
$967$		−	23.3950i		−	0.0241934i	0.999927	−	0.0120967i	$-0.00385059\pi$
$968$	230.076	−	38.0876i	0.237682	−	0.0393467i
$969$	−415.869			−0.429174
$970$		−	945.959i		−	0.975215i
$971$	1713.20			1.76437			0.882183	−	0.470907i	$-0.156073\pi$
$971$	1713.20			1.76437			0.882183	+	0.470907i	$0.156073\pi$
$972$	−72.5661			−0.0746565
$973$	−386.950			−0.397687
$974$			428.601i			0.440042i
$975$			176.129i			0.180645i
$976$		−	32.4966i		−	0.0332957i
$977$	721.333			0.738315			0.369157	−	0.929367i	$-0.379646\pi$
$977$	721.333			0.738315			0.369157	+	0.929367i	$0.379646\pi$
$978$		−	582.918i		−	0.596030i
$979$	563.633	−	664.610i	0.575723	−	0.678866i
$980$	−72.8641			−0.0743512
$981$			170.198i			0.173494i
$982$	−17.4557			−0.0177756
$983$	1631.94			1.66016			0.830081	−	0.557643i	$-0.188294\pi$
$983$	1631.94			1.66016			0.830081	+	0.557643i	$0.188294\pi$
$984$	−136.249			−0.138465
$985$		−	836.175i		−	0.848909i
$986$			820.021i			0.831664i
$987$			94.2650i			0.0955066i
$988$	1165.69			1.17985
$989$			433.696i			0.438520i
$990$	165.566	+	140.411i	0.167238	+	0.141829i
$991$	−741.332			−0.748065			−0.374032	−	0.927416i	$-0.622025\pi$
$991$	−741.332			−0.748065			−0.374032	+	0.927416i	$0.622025\pi$
$992$			754.553i			0.760638i
$993$	42.3596			0.0426583
$994$	−45.7067			−0.0459826
$995$	68.4120			0.0687558
$996$			600.739i			0.603152i
$997$			302.029i			0.302938i	0.988462	+	0.151469i	$0.0484003\pi$
$997$			302.029i			0.302938i	−0.988462	+	0.151469i	$0.951600\pi$
$998$			1725.98i			1.72944i
$999$	−222.263			−0.222486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.15	✓	96
11.10	odd	2	inner	1155.3.b.a.736.82	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.15	✓	96	1.1	even	1	trivial
1155.3.b.a.736.82	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)

\(f(q)\)	\(=\)	\(q-2.94196i q^{2} +1.73205 q^{3} -4.65512 q^{4} -2.23607 q^{5} -5.09562i q^{6} +2.64575i q^{7} +1.92733i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.94196i q^{2} +1.73205 q^{3} -4.65512 q^{4} -2.23607 q^{5} -5.09562i q^{6} +2.64575i q^{7} +1.92733i q^{8} +3.00000 q^{9} +6.57842i q^{10} +(7.11471 - 8.38933i) q^{11} -8.06290 q^{12} +20.3376i q^{13} +7.78369 q^{14} -3.87298 q^{15} -12.9503 q^{16} +19.5005i q^{17} -8.82587i q^{18} +12.3126i q^{19} +10.4092 q^{20} +4.58258i q^{21} +(-24.6811 - 20.9312i) q^{22} +17.2403 q^{23} +3.33824i q^{24} +5.00000 q^{25} +59.8324 q^{26} +5.19615 q^{27} -12.3163i q^{28} +14.2937i q^{29} +11.3942i q^{30} +16.4718 q^{31} +45.8087i q^{32} +(12.3230 - 14.5308i) q^{33} +57.3696 q^{34} -5.91608i q^{35} -13.9654 q^{36} -42.7746 q^{37} +36.2233 q^{38} +35.2258i q^{39} -4.30964i q^{40} +40.8148i q^{41} +13.4817 q^{42} +25.1559i q^{43} +(-33.1198 + 39.0533i) q^{44} -6.70820 q^{45} -50.7203i q^{46} +20.5703 q^{47} -22.4307 q^{48} -7.00000 q^{49} -14.7098i q^{50} +33.7758i q^{51} -94.6740i q^{52} -34.3023 q^{53} -15.2869i q^{54} +(-15.9090 + 18.7591i) q^{55} -5.09924 q^{56} +21.3261i q^{57} +42.0513 q^{58} +96.8211 q^{59} +18.0292 q^{60} +2.50933i q^{61} -48.4594i q^{62} +7.93725i q^{63} +82.9659 q^{64} -45.4763i q^{65} +(-42.7489 - 36.2539i) q^{66} +81.6940 q^{67} -90.7770i q^{68} +29.8611 q^{69} -17.4049 q^{70} -5.87211 q^{71} +5.78199i q^{72} -14.8139i q^{73} +125.841i q^{74} +8.66025 q^{75} -57.3168i q^{76} +(22.1961 + 18.8237i) q^{77} +103.633 q^{78} -9.16500i q^{79} +28.9579 q^{80} +9.00000 q^{81} +120.075 q^{82} -74.5065i q^{83} -21.3324i q^{84} -43.6044i q^{85} +74.0076 q^{86} +24.7573i q^{87} +(16.1690 + 13.7124i) q^{88} +79.2208 q^{89} +19.7353i q^{90} -53.8082 q^{91} -80.2557 q^{92} +28.5300 q^{93} -60.5170i q^{94} -27.5319i q^{95} +79.3430i q^{96} -143.797 q^{97} +20.5937i q^{98} +(21.3441 - 25.1680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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