LMFDB - Embedded newform 1155.3.b.a.736.10

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			736.10
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.87

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57202i q^{2} +1.73205 q^{3} -8.75932 q^{4} -2.23607 q^{5} -6.18692i q^{6} -2.64575i q^{7} +17.0004i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.57202i q^{2} +1.73205 q^{3} -8.75932 q^{4} -2.23607 q^{5} -6.18692i q^{6} -2.64575i q^{7} +17.0004i q^{8} +3.00000 q^{9} +7.98728i q^{10} +(10.8321 - 1.91459i) q^{11} -15.1716 q^{12} -0.386402i q^{13} -9.45067 q^{14} -3.87298 q^{15} +25.6884 q^{16} -28.5488i q^{17} -10.7161i q^{18} -25.6789i q^{19} +19.5864 q^{20} -4.58258i q^{21} +(-6.83895 - 38.6925i) q^{22} -9.17999 q^{23} +29.4455i q^{24} +5.00000 q^{25} -1.38023 q^{26} +5.19615 q^{27} +23.1750i q^{28} -7.84295i q^{29} +13.8344i q^{30} -4.66759 q^{31} -23.7580i q^{32} +(18.7617 - 3.31616i) q^{33} -101.977 q^{34} +5.91608i q^{35} -26.2780 q^{36} -45.3161 q^{37} -91.7256 q^{38} -0.669267i q^{39} -38.0140i q^{40} +66.3063i q^{41} -16.3690 q^{42} +26.3628i q^{43} +(-94.8818 + 16.7705i) q^{44} -6.70820 q^{45} +32.7911i q^{46} -7.97229 q^{47} +44.4936 q^{48} -7.00000 q^{49} -17.8601i q^{50} -49.4481i q^{51} +3.38462i q^{52} +19.9017 q^{53} -18.5608i q^{54} +(-24.2213 + 4.28115i) q^{55} +44.9788 q^{56} -44.4772i q^{57} -28.0152 q^{58} -92.9919 q^{59} +33.9247 q^{60} -23.2655i q^{61} +16.6727i q^{62} -7.93725i q^{63} +17.8897 q^{64} +0.864021i q^{65} +(-11.8454 - 67.0173i) q^{66} +10.5415 q^{67} +250.069i q^{68} -15.9002 q^{69} +21.1324 q^{70} -18.3575 q^{71} +51.0012i q^{72} -5.14836i q^{73} +161.870i q^{74} +8.66025 q^{75} +224.930i q^{76} +(-5.06552 - 28.6590i) q^{77} -2.39064 q^{78} -134.399i q^{79} -57.4411 q^{80} +9.00000 q^{81} +236.847 q^{82} +34.9717i q^{83} +40.1403i q^{84} +63.8372i q^{85} +94.1683 q^{86} -13.5844i q^{87} +(32.5487 + 184.150i) q^{88} -44.6559 q^{89} +23.9618i q^{90} -1.02232 q^{91} +80.4105 q^{92} -8.08450 q^{93} +28.4772i q^{94} +57.4198i q^{95} -41.1500i q^{96} -109.303 q^{97} +25.0041i q^{98} +(32.4963 - 5.74376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) $ 96 * q - 216 * q^4 + 288 * q^9	$ 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) $ 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	3.57202i		−	1.78601i	−0.450047	−	0.893005i	$-0.648593\pi$
$2$		−	3.57202i		−	1.78601i	0.450047	−	0.893005i	$-0.351407\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−8.75932			−2.18983
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		−	6.18692i		−	1.03115i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$			17.0004i			2.12505i
$9$	3.00000			0.333333
$10$			7.98728i			0.798728i
$11$	10.8321	−	1.91459i	0.984736	−	0.174053i
$11$	10.8321	−	1.91459i	0.984736	−	0.174053i
$12$	−15.1716			−1.26430
$13$		−	0.386402i		−	0.0297232i	−0.999890	−	0.0148616i	$-0.995269\pi$
$13$		−	0.386402i		−	0.0297232i	0.999890	−	0.0148616i	$-0.00473077\pi$
$14$	−9.45067			−0.675048
$15$	−3.87298			−0.258199
$16$	25.6884			1.60553
$17$		−	28.5488i		−	1.67934i	−0.543094	−	0.839672i	$-0.682747\pi$
$17$		−	28.5488i		−	1.67934i	0.543094	−	0.839672i	$-0.317253\pi$
$18$		−	10.7161i		−	0.595337i
$19$		−	25.6789i		−	1.35152i	−0.737121	−	0.675761i	$-0.763815\pi$
$19$		−	25.6789i		−	1.35152i	0.737121	−	0.675761i	$-0.236185\pi$
$20$	19.5864			0.979322
$21$		−	4.58258i		−	0.218218i
$22$	−6.83895	−	38.6925i	−0.310861	−	1.75875i
$23$	−9.17999			−0.399130			−0.199565	−	0.979885i	$-0.563953\pi$
$23$	−9.17999			−0.399130			−0.199565	+	0.979885i	$0.563953\pi$
$24$			29.4455i			1.22690i
$25$	5.00000			0.200000
$26$	−1.38023			−0.0530859
$27$	5.19615			0.192450
$28$			23.1750i			0.827678i
$29$		−	7.84295i		−	0.270447i	−0.990815	−	0.135223i	$-0.956825\pi$
$29$		−	7.84295i		−	0.270447i	0.990815	−	0.135223i	$-0.0431752\pi$
$30$			13.8344i			0.461146i
$31$	−4.66759			−0.150567			−0.0752837	−	0.997162i	$-0.523986\pi$
$31$	−4.66759			−0.150567			−0.0752837	+	0.997162i	$0.523986\pi$
$32$		−	23.7580i		−	0.742437i
$33$	18.7617	−	3.31616i	0.568538	−	0.100490i
$34$	−101.977			−2.99932
$35$			5.91608i			0.169031i
$36$	−26.2780			−0.729943
$37$	−45.3161			−1.22476			−0.612380	−	0.790564i	$-0.709788\pi$
$37$	−45.3161			−1.22476			−0.612380	+	0.790564i	$0.709788\pi$
$38$	−91.7256			−2.41383
$39$		−	0.669267i		−	0.0171607i
$40$		−	38.0140i		−	0.950350i
$41$			66.3063i			1.61723i	0.588340	+	0.808614i	$0.299782\pi$
$41$			66.3063i			1.61723i	−0.588340	+	0.808614i	$0.700218\pi$
$42$	−16.3690			−0.389739
$43$			26.3628i			0.613087i	0.951857	+	0.306544i	$0.0991725\pi$
$43$			26.3628i			0.613087i	−0.951857	+	0.306544i	$0.900827\pi$
$44$	−94.8818	+	16.7705i	−2.15641	+	0.381148i
$45$	−6.70820			−0.149071
$46$			32.7911i			0.712850i
$47$	−7.97229			−0.169623			−0.0848116	−	0.996397i	$-0.527029\pi$
$47$	−7.97229			−0.169623			−0.0848116	+	0.996397i	$0.527029\pi$
$48$	44.4936			0.926951
$49$	−7.00000			−0.142857
$50$		−	17.8601i		−	0.357202i
$51$		−	49.4481i		−	0.969570i
$52$			3.38462i			0.0650888i
$53$	19.9017			0.375504			0.187752	−	0.982216i	$-0.439880\pi$
$53$	19.9017			0.375504			0.187752	+	0.982216i	$0.439880\pi$
$54$		−	18.5608i		−	0.343718i
$55$	−24.2213	+	4.28115i	−0.440387	+	0.0778391i
$56$	44.9788			0.803193
$57$		−	44.4772i		−	0.780302i
$58$	−28.0152			−0.483020
$59$	−92.9919			−1.57613			−0.788067	−	0.615590i	$-0.788918\pi$
$59$	−92.9919			−1.57613			−0.788067	+	0.615590i	$0.788918\pi$
$60$	33.9247			0.565412
$61$		−	23.2655i		−	0.381402i	−0.981648	−	0.190701i	$-0.938924\pi$
$61$		−	23.2655i		−	0.381402i	0.981648	−	0.190701i	$-0.0610761\pi$
$62$			16.6727i			0.268915i
$63$		−	7.93725i		−	0.125988i
$64$	17.8897			0.279527
$65$			0.864021i			0.0132926i
$66$	−11.8454	−	67.0173i	−0.179476	−	1.01541i
$67$	10.5415			0.157336			0.0786680	−	0.996901i	$-0.474933\pi$
$67$	10.5415			0.157336			0.0786680	+	0.996901i	$0.474933\pi$
$68$			250.069i			3.67748i
$69$	−15.9002			−0.230438
$70$	21.1324			0.301891
$71$	−18.3575			−0.258556			−0.129278	−	0.991608i	$-0.541266\pi$
$71$	−18.3575			−0.258556			−0.129278	+	0.991608i	$0.541266\pi$
$72$			51.0012i			0.708349i
$73$		−	5.14836i		−	0.0705254i	−0.999378	−	0.0352627i	$-0.988773\pi$
$73$		−	5.14836i		−	0.0705254i	0.999378	−	0.0352627i	$-0.0112268\pi$
$74$			161.870i			2.18743i
$75$	8.66025			0.115470
$76$			224.930i			2.95960i
$77$	−5.06552	−	28.6590i	−0.0657860	−	0.372195i
$78$	−2.39064			−0.0306492
$79$		−	134.399i		−	1.70126i	−0.525768	−	0.850628i	$-0.676222\pi$
$79$		−	134.399i		−	1.70126i	0.525768	−	0.850628i	$-0.323778\pi$
$80$	−57.4411			−0.718013
$81$	9.00000			0.111111
$82$	236.847			2.88838
$83$			34.9717i			0.421346i	0.977557	+	0.210673i	$0.0675655\pi$
$83$			34.9717i			0.421346i	−0.977557	+	0.210673i	$0.932435\pi$
$84$			40.1403i			0.477860i
$85$			63.8372i			0.751025i
$86$	94.1683			1.09498
$87$		−	13.5844i		−	0.156142i
$88$	32.5487	+	184.150i	0.369872	+	2.09261i
$89$	−44.6559			−0.501752			−0.250876	−	0.968019i	$-0.580719\pi$
$89$	−44.6559			−0.501752			−0.250876	+	0.968019i	$0.580719\pi$
$90$			23.9618i			0.266243i
$91$	−1.02232			−0.0112343
$92$	80.4105			0.874027
$93$	−8.08450			−0.0869301
$94$			28.4772i			0.302948i
$95$			57.4198i			0.604419i
$96$		−	41.1500i		−	0.428646i
$97$	−109.303			−1.12683			−0.563417	−	0.826173i	$-0.690513\pi$
$97$	−109.303			−1.12683			−0.563417	+	0.826173i	$0.690513\pi$
$98$			25.0041i			0.255144i
$99$	32.4963	−	5.74376i	0.328245	−	0.0580178i
$100$	−43.7966			−0.437966
$101$		−	70.7620i		−	0.700614i	−0.936635	−	0.350307i	$-0.886077\pi$
$101$		−	70.7620i		−	0.700614i	0.936635	−	0.350307i	$-0.113923\pi$
$102$	−176.629			−1.73166
$103$	70.6813			0.686227			0.343113	−	0.939294i	$-0.388519\pi$
$103$	70.6813			0.686227			0.343113	+	0.939294i	$0.388519\pi$
$104$	6.56898			0.0631633
$105$			10.2470i			0.0975900i
$106$		−	71.0892i		−	0.670653i
$107$			152.290i			1.42327i	0.702551	+	0.711633i	$0.252044\pi$
$107$			152.290i			1.42327i	−0.702551	+	0.711633i	$0.747956\pi$
$108$	−45.5148			−0.421433
$109$		−	117.905i		−	1.08169i	−0.841121	−	0.540846i	$-0.818104\pi$
$109$		−	117.905i		−	1.08169i	0.841121	−	0.540846i	$-0.181896\pi$
$110$	15.2923	+	86.5190i	0.139021	+	0.786536i
$111$	−78.4898			−0.707115
$112$		−	67.9652i		−	0.606832i
$113$	−155.278			−1.37414			−0.687069	−	0.726592i	$-0.741103\pi$
$113$	−155.278			−1.37414			−0.687069	+	0.726592i	$0.741103\pi$
$114$	−158.873			−1.39363
$115$	20.5271			0.178496
$116$			68.6989i			0.592232i
$117$		−	1.15921i		−	0.00990774i
$118$			332.169i			2.81499i
$119$	−75.5332			−0.634732
$120$		−	65.8422i		−	0.548685i
$121$	113.669	−	41.4780i	0.939411	−	0.342794i
$122$	−83.1049			−0.681187
$123$			114.846i			0.933707i
$124$	40.8849			0.329717
$125$	−11.1803			−0.0894427
$126$	−28.3520			−0.225016
$127$			150.544i			1.18539i	0.805428	+	0.592694i	$0.201936\pi$
$127$			150.544i			1.18539i	−0.805428	+	0.592694i	$0.798064\pi$
$128$		−	158.934i		−	1.24167i
$129$			45.6616i			0.353966i
$130$	3.08630			0.0237408
$131$		−	191.469i		−	1.46159i	−0.682595	−	0.730797i	$-0.739149\pi$
$131$		−	191.469i		−	1.46159i	0.682595	−	0.730797i	$-0.260851\pi$
$132$	−164.340	+	29.0473i	−1.24500	+	0.220056i
$133$	−67.9401			−0.510827
$134$		−	37.6545i		−	0.281004i
$135$	−11.6190			−0.0860663
$136$	485.341			3.56869
$137$	−10.3177			−0.0753119			−0.0376559	−	0.999291i	$-0.511989\pi$
$137$	−10.3177			−0.0753119			−0.0376559	+	0.999291i	$0.511989\pi$
$138$			56.7958i			0.411564i
$139$			221.518i			1.59366i	0.604206	+	0.796828i	$0.293490\pi$
$139$			221.518i			1.59366i	−0.604206	+	0.796828i	$0.706510\pi$
$140$		−	51.8208i		−	0.370149i
$141$	−13.8084			−0.0979319
$142$			65.5733i			0.461784i
$143$	−0.739800	−	4.18554i	−0.00517343	−	0.0292695i
$144$	77.0653			0.535175
$145$			17.5374i			0.120947i
$146$	−18.3900			−0.125959
$147$	−12.1244			−0.0824786
$148$	396.938			2.68202
$149$		−	85.7817i		−	0.575716i	−0.957673	−	0.287858i	$-0.907057\pi$
$149$		−	85.7817i		−	0.575716i	0.957673	−	0.287858i	$-0.0929432\pi$
$150$		−	30.9346i		−	0.206231i
$151$		−	137.485i		−	0.910500i	−0.890364	−	0.455250i	$-0.849550\pi$
$151$		−	137.485i		−	0.910500i	0.890364	−	0.455250i	$-0.150450\pi$
$152$	436.552			2.87205
$153$		−	85.6465i		−	0.559781i
$154$	−102.371	+	18.0942i	−0.664744	+	0.117494i
$155$	10.4370			0.0673358
$156$			5.86233i			0.0375790i
$157$	−158.470			−1.00936			−0.504682	−	0.863305i	$-0.668390\pi$
$157$	−158.470			−1.00936			−0.504682	+	0.863305i	$0.668390\pi$
$158$	−480.076			−3.03846
$159$	34.4707			0.216797
$160$			53.1245i			0.332028i
$161$			24.2880i			0.150857i
$162$		−	32.1482i		−	0.198446i
$163$	−79.0019			−0.484674			−0.242337	−	0.970192i	$-0.577914\pi$
$163$	−79.0019			−0.484674			−0.242337	+	0.970192i	$0.577914\pi$
$164$		−	580.798i		−	3.54145i
$165$	−41.9525	+	7.41517i	−0.254258	+	0.0449404i
$166$	124.920			0.752528
$167$		−	107.298i		−	0.642504i	−0.946994	−	0.321252i	$-0.895896\pi$
$167$		−	107.298i		−	0.642504i	0.946994	−	0.321252i	$-0.104104\pi$
$168$	77.9056			0.463724
$169$	168.851			0.999117
$170$	228.028			1.34134
$171$		−	77.0368i		−	0.450507i
$172$		−	230.920i		−	1.34256i
$173$		−	64.1829i		−	0.371000i	−0.982644	−	0.185500i	$-0.940610\pi$
$173$		−	64.1829i		−	0.371000i	0.982644	−	0.185500i	$-0.0593904\pi$
$174$	−48.5237			−0.278872
$175$		−	13.2288i		−	0.0755929i
$176$	278.259	−	49.1827i	1.58102	−	0.279447i
$177$	−161.067			−0.909981
$178$			159.512i			0.896134i
$179$	−334.855			−1.87070			−0.935349	−	0.353726i	$-0.884915\pi$
$179$	−334.855			−1.87070			−0.935349	+	0.353726i	$0.884915\pi$
$180$	58.7593			0.326441
$181$	266.646			1.47318			0.736591	−	0.676339i	$-0.236434\pi$
$181$	266.646			1.47318			0.736591	+	0.676339i	$0.236434\pi$
$182$			3.65176i			0.0200646i
$183$		−	40.2971i		−	0.220202i
$184$		−	156.063i		−	0.848170i
$185$	101.330			0.547729
$186$			28.8780i			0.155258i
$187$	−54.6593	−	309.244i	−0.292296	−	1.65371i
$188$	69.8318			0.371446
$189$		−	13.7477i		−	0.0727393i
$190$	205.105			1.07950
$191$	−237.192			−1.24184			−0.620922	−	0.783872i	$-0.713242\pi$
$191$	−237.192			−1.24184			−0.620922	+	0.783872i	$0.713242\pi$
$192$	30.9859			0.161385
$193$			246.851i			1.27902i	0.768782	+	0.639511i	$0.220863\pi$
$193$			246.851i			1.27902i	−0.768782	+	0.639511i	$0.779137\pi$
$194$			390.432i			2.01254i
$195$			1.49653i			0.00767450i
$196$	61.3152			0.312833
$197$			78.2249i			0.397081i	0.980093	+	0.198540i	$0.0636201\pi$
$197$			78.2249i			0.397081i	−0.980093	+	0.198540i	$0.936380\pi$
$198$	−20.5168	−	116.077i	−0.103620	−	0.586249i
$199$	306.035			1.53787			0.768933	−	0.639329i	$-0.220788\pi$
$199$	306.035			1.53787			0.768933	+	0.639329i	$0.220788\pi$
$200$			85.0019i			0.425010i
$201$	18.2584			0.0908380
$202$	−252.763			−1.25130
$203$	−20.7505			−0.102219
$204$			433.131i			2.12319i
$205$		−	148.265i		−	0.723246i
$206$		−	252.475i		−	1.22561i
$207$	−27.5400			−0.133043
$208$		−	9.92605i		−	0.0477214i
$209$	−49.1646	−	278.157i	−0.235237	−	1.33089i
$210$	36.6023			0.174297
$211$			75.4775i			0.357713i	0.983875	+	0.178857i	$0.0572399\pi$
$211$			75.4775i			0.357713i	−0.983875	+	0.178857i	$0.942760\pi$
$212$	−174.325			−0.822289
$213$	−31.7961			−0.149277
$214$	543.981			2.54197
$215$		−	58.9489i		−	0.274181i
$216$			88.3366i			0.408966i
$217$			12.3493i			0.0569091i
$218$	−421.157			−1.93191
$219$		−	8.91721i		−	0.0407179i
$220$	212.162	−	37.5000i	0.964374	−	0.170454i
$221$	−11.0313			−0.0499155
$222$			280.367i			1.26291i
$223$	251.949			1.12982			0.564909	−	0.825153i	$-0.308911\pi$
$223$	251.949			1.12982			0.564909	+	0.825153i	$0.308911\pi$
$224$	−62.8577			−0.280615
$225$	15.0000			0.0666667
$226$			554.655i			2.45422i
$227$		−	313.697i		−	1.38192i	−0.722891	−	0.690962i	$-0.757187\pi$
$227$		−	313.697i		−	1.38192i	0.722891	−	0.690962i	$-0.242813\pi$
$228$			389.590i			1.70873i
$229$	411.724			1.79792			0.898961	−	0.438028i	$-0.144323\pi$
$229$	411.724			1.79792			0.898961	+	0.438028i	$0.144323\pi$
$230$		−	73.3231i		−	0.318796i
$231$	−8.77375	−	49.6389i	−0.0379816	−	0.214887i
$232$	133.333			0.574712
$233$			109.526i			0.470069i	0.971987	+	0.235035i	$0.0755204\pi$
$233$			109.526i			0.470069i	−0.971987	+	0.235035i	$0.924480\pi$
$234$	−4.14070			−0.0176953
$235$	17.8266			0.0758578
$236$	814.546			3.45146
$237$		−	232.786i		−	0.982220i
$238$			269.806i			1.13364i
$239$			108.982i			0.455992i	0.973662	+	0.227996i	$0.0732174\pi$
$239$			108.982i			0.455992i	−0.973662	+	0.227996i	$0.926783\pi$
$240$	−99.4908			−0.414545
$241$		−	380.879i		−	1.58041i	−0.612841	−	0.790206i	$-0.709973\pi$
$241$		−	380.879i		−	1.58041i	0.612841	−	0.790206i	$-0.290027\pi$
$242$	−148.160	−	406.027i	−0.612233	−	1.67780i
$243$	15.5885			0.0641500
$244$			203.790i			0.835205i
$245$	15.6525			0.0638877
$246$	410.232			1.66761
$247$	−9.92238			−0.0401716
$248$		−	79.3508i		−	0.319963i
$249$			60.5728i			0.243264i
$250$			39.9364i			0.159746i
$251$	207.914			0.828341			0.414170	−	0.910199i	$-0.364072\pi$
$251$	207.914			0.828341			0.414170	+	0.910199i	$0.364072\pi$
$252$			69.5250i			0.275893i
$253$	−99.4385	+	17.5759i	−0.393038	+	0.0694700i
$254$	537.747			2.11711
$255$			110.569i			0.433605i
$256$	−496.158			−1.93812
$257$	−5.35835			−0.0208496			−0.0104248	−	0.999946i	$-0.503318\pi$
$257$	−5.35835			−0.0208496			−0.0104248	+	0.999946i	$0.503318\pi$
$258$	163.104			0.632187
$259$			119.895i			0.462916i
$260$		−	7.56823i		−	0.0291086i
$261$		−	23.5288i		−	0.0901488i
$262$	−683.930			−2.61042
$263$		−	165.180i		−	0.628063i	−0.949413	−	0.314031i	$-0.898320\pi$
$263$		−	165.180i		−	0.628063i	0.949413	−	0.314031i	$-0.101680\pi$
$264$	56.3761	+	318.957i	0.213546	+	1.20817i
$265$	−44.5015			−0.167930
$266$			242.683i			0.912343i
$267$	−77.3463			−0.289687
$268$	−92.3365			−0.344539
$269$	−55.4173			−0.206012			−0.103006	−	0.994681i	$-0.532846\pi$
$269$	−55.4173			−0.206012			−0.103006	+	0.994681i	$0.532846\pi$
$270$			41.5031i			0.153715i
$271$		−	147.875i		−	0.545663i	−0.962062	−	0.272831i	$-0.912040\pi$
$271$		−	147.875i		−	0.545663i	0.962062	−	0.272831i	$-0.0879601\pi$
$272$		−	733.375i		−	2.69623i
$273$	−1.77072			−0.00648614
$274$			36.8551i			0.134508i
$275$	54.1605	−	9.57294i	0.196947	−	0.0348107i
$276$	139.275			0.504620
$277$		−	401.172i		−	1.44827i	−0.689656	−	0.724137i	$-0.742238\pi$
$277$		−	401.172i		−	1.44827i	0.689656	−	0.724137i	$-0.257762\pi$
$278$	791.267			2.84629
$279$	−14.0028			−0.0501891
$280$	−100.576			−0.359199
$281$			174.453i			0.620828i	0.950602	+	0.310414i	$0.100468\pi$
$281$			174.453i			0.620828i	−0.950602	+	0.310414i	$0.899532\pi$
$282$			49.3239i			0.174907i
$283$			331.805i			1.17246i	0.810146	+	0.586228i	$0.199388\pi$
$283$			331.805i			1.17246i	−0.810146	+	0.586228i	$0.800612\pi$
$284$	160.799			0.566194
$285$			99.4541i			0.348962i
$286$	−14.9508	+	2.64258i	−0.0522756	+	0.00923979i
$287$	175.430			0.611255
$288$		−	71.2739i		−	0.247479i
$289$	−526.037			−1.82020
$290$	62.6438			0.216013
$291$	−189.318			−0.650578
$292$			45.0961i			0.154439i
$293$		−	249.876i		−	0.852821i	−0.904530	−	0.426410i	$-0.859778\pi$
$293$		−	249.876i		−	0.852821i	0.904530	−	0.426410i	$-0.140222\pi$
$294$			43.3084i			0.147308i
$295$	207.936			0.704868
$296$		−	770.391i		−	2.60267i
$297$	56.2852	−	9.94849i	0.189513	−	0.0334966i
$298$	−306.414			−1.02823
$299$			3.54716i			0.0118634i
$300$	−75.8579			−0.252860
$301$	69.7493			0.231725
$302$	−491.101			−1.62616
$303$		−	122.563i		−	0.404500i
$304$		−	659.651i		−	2.16990i
$305$			52.0233i			0.170568i
$306$	−305.931			−0.999775
$307$			256.640i			0.835961i	0.908456	+	0.417980i	$0.137262\pi$
$307$			256.640i			0.835961i	−0.908456	+	0.417980i	$0.862738\pi$
$308$	44.3706	+	251.034i	0.144060	+	0.815045i
$309$	122.424			0.396193
$310$		−	37.2813i		−	0.120262i
$311$	−12.0006			−0.0385870			−0.0192935	−	0.999814i	$-0.506142\pi$
$311$	−12.0006			−0.0385870			−0.0192935	+	0.999814i	$0.506142\pi$
$312$	11.3778			0.0364673
$313$	195.751			0.625402			0.312701	−	0.949852i	$-0.398766\pi$
$313$	195.751			0.625402			0.312701	+	0.949852i	$0.398766\pi$
$314$			566.059i			1.80274i
$315$			17.7482i			0.0563436i
$316$			1177.25i			3.72546i
$317$	318.599			1.00504			0.502522	−	0.864564i	$-0.332406\pi$
$317$	318.599			1.00504			0.502522	+	0.864564i	$0.332406\pi$
$318$		−	123.130i		−	0.387202i
$319$	−15.0160	−	84.9556i	−0.0470722	−	0.266318i
$320$	−40.0026			−0.125008
$321$			263.773i			0.821723i
$322$	86.7571			0.269432
$323$	−733.104			−2.26967
$324$	−78.8339			−0.243314
$325$		−	1.93201i		−	0.00594464i
$326$			282.196i			0.865633i
$327$		−	204.217i		−	0.624516i
$328$	−1127.23			−3.43669
$329$			21.0927i			0.0641115i
$330$	26.4871	+	149.855i	0.0802640	+	0.454107i
$331$	−278.465			−0.841283			−0.420642	−	0.907227i	$-0.638195\pi$
$331$	−278.465			−0.841283			−0.420642	+	0.907227i	$0.638195\pi$
$332$		−	306.328i		−	0.922676i
$333$	−135.948			−0.408253
$334$	−383.271			−1.14752
$335$	−23.5715			−0.0703628
$336$		−	117.719i		−	0.350355i
$337$			17.3136i			0.0513757i	0.999670	+	0.0256878i	$0.00817759\pi$
$337$			17.3136i			0.0513757i	−0.999670	+	0.0256878i	$0.991822\pi$
$338$		−	603.138i		−	1.78443i
$339$	−268.949			−0.793359
$340$		−	559.170i		−	1.64462i
$341$	−50.5598	+	8.93651i	−0.148269	+	0.0262068i
$342$	−275.177			−0.804611
$343$			18.5203i			0.0539949i
$344$	−448.177			−1.30284
$345$	35.5539			0.103055
$346$	−229.263			−0.662609
$347$			47.3741i			0.136525i	0.997667	+	0.0682624i	$0.0217455\pi$
$347$			47.3741i			0.136525i	−0.997667	+	0.0682624i	$0.978255\pi$
$348$			118.990i			0.341925i
$349$		−	487.599i		−	1.39713i	−0.715545	−	0.698566i	$-0.753822\pi$
$349$		−	487.599i		−	1.39713i	0.715545	−	0.698566i	$-0.246178\pi$
$350$	−47.2534			−0.135010
$351$		−	2.00780i		−	0.00572023i
$352$	−45.4868	−	257.349i	−0.129224	−	0.731105i
$353$	88.6338			0.251087			0.125544	−	0.992088i	$-0.459932\pi$
$353$	88.6338			0.251087			0.125544	+	0.992088i	$0.459932\pi$
$354$			575.333i			1.62523i
$355$	41.0486			0.115630
$356$	391.156			1.09875
$357$	−130.827			−0.366463
$358$			1196.11i			3.34108i
$359$			152.957i			0.426064i	0.977045	+	0.213032i	$0.0683339\pi$
$359$			152.957i			0.426064i	−0.977045	+	0.213032i	$0.931666\pi$
$360$		−	114.042i		−	0.316783i
$361$	−298.407			−0.826613
$362$		−	952.464i		−	2.63112i
$363$	196.880	−	71.8420i	0.542369	−	0.197912i
$364$	8.95485			0.0246012
$365$			11.5121i			0.0315399i
$366$	−143.942			−0.393284
$367$	−245.716			−0.669526			−0.334763	−	0.942302i	$-0.608656\pi$
$367$	−245.716			−0.669526			−0.334763	+	0.942302i	$0.608656\pi$
$368$	−235.819			−0.640814
$369$			198.919i			0.539076i
$370$		−	361.952i		−	0.978250i
$371$		−	52.6549i		−	0.141927i
$372$	70.8148			0.190362
$373$		−	461.159i		−	1.23635i	−0.786040	−	0.618176i	$-0.787872\pi$
$373$		−	461.159i		−	1.23635i	0.786040	−	0.618176i	$-0.212128\pi$
$374$	−1104.63	+	195.244i	−2.95354	+	0.522043i
$375$	−19.3649			−0.0516398
$376$		−	135.532i		−	0.360457i
$377$	−3.03053			−0.00803854
$378$	−49.1071			−0.129913
$379$	−14.1767			−0.0374056			−0.0187028	−	0.999825i	$-0.505954\pi$
$379$	−14.1767			−0.0374056			−0.0187028	+	0.999825i	$0.505954\pi$
$380$		−	502.959i		−	1.32358i
$381$			260.750i			0.684384i
$382$			847.255i			2.21795i
$383$	−200.520			−0.523551			−0.261776	−	0.965129i	$-0.584308\pi$
$383$	−200.520			−0.523551			−0.261776	+	0.965129i	$0.584308\pi$
$384$		−	275.282i		−	0.716881i
$385$	11.3269	+	64.0836i	0.0294204	+	0.166451i
$386$	881.758			2.28435
$387$			79.0883i			0.204362i
$388$	957.419			2.46757
$389$	304.029			0.781566			0.390783	−	0.920483i	$-0.372204\pi$
$389$	304.029			0.781566			0.390783	+	0.920483i	$0.372204\pi$
$390$	5.34563			0.0137067
$391$			262.078i			0.670277i
$392$		−	119.003i		−	0.303578i
$393$		−	331.634i		−	0.843852i
$394$	279.421			0.709190
$395$			300.526i			0.760825i
$396$	−284.645	+	50.3115i	−0.718802	+	0.127049i
$397$	−536.681			−1.35184			−0.675921	−	0.736974i	$-0.736254\pi$
$397$	−536.681			−1.35184			−0.675921	+	0.736974i	$0.736254\pi$
$398$		−	1093.16i		−	2.74664i
$399$	−117.676			−0.294926
$400$	128.442			0.321105
$401$	−471.418			−1.17561			−0.587804	−	0.809004i	$-0.700007\pi$
$401$	−471.418			−1.17561			−0.587804	+	0.809004i	$0.700007\pi$
$402$		−	65.2195i		−	0.162238i
$403$			1.80356i			0.00447535i
$404$			619.827i			1.53423i
$405$	−20.1246			−0.0496904
$406$			74.1212i			0.182564i
$407$	−490.869	+	86.7617i	−1.20607	+	0.213174i
$408$	840.636			2.06038
$409$		−	680.533i		−	1.66390i	−0.554854	−	0.831948i	$-0.687226\pi$
$409$		−	680.533i		−	1.66390i	0.554854	−	0.831948i	$-0.312774\pi$
$410$	−529.607			−1.29172
$411$	−17.8708			−0.0434813
$412$	−619.120			−1.50272
$413$			246.033i			0.595722i
$414$			98.3733i			0.237617i
$415$		−	78.1991i		−	0.188432i
$416$	−9.18013			−0.0220676
$417$			383.681i			0.920098i
$418$	−993.581	+	175.617i	−2.37699	+	0.420136i
$419$	−200.588			−0.478730			−0.239365	−	0.970930i	$-0.576939\pi$
$419$	−200.588			−0.478730			−0.239365	+	0.970930i	$0.576939\pi$
$420$		−	89.7563i		−	0.213706i
$421$	378.429			0.898880			0.449440	−	0.893310i	$-0.351624\pi$
$421$	378.429			0.898880			0.449440	+	0.893310i	$0.351624\pi$
$422$	269.607			0.638880
$423$	−23.9169			−0.0565410
$424$			338.336i			0.797963i
$425$		−	142.744i		−	0.335869i
$426$			113.576i			0.266611i
$427$	−61.5548			−0.144156
$428$		−	1333.95i		−	3.11671i
$429$	−1.28137	−	7.24957i	−0.00298688	−	0.0168988i
$430$	−210.567			−0.489690
$431$		−	271.599i		−	0.630161i	−0.949065	−	0.315081i	$-0.897968\pi$
$431$		−	271.599i		−	0.630161i	0.949065	−	0.315081i	$-0.102032\pi$
$432$	133.481			0.308984
$433$	313.129			0.723161			0.361581	−	0.932341i	$-0.382237\pi$
$433$	313.129			0.723161			0.361581	+	0.932341i	$0.382237\pi$
$434$	44.1119			0.101640
$435$			30.3756i			0.0698290i
$436$			1032.76i			2.36872i
$437$			235.732i			0.539433i
$438$	−31.8525			−0.0727225
$439$		−	507.983i		−	1.15714i	−0.815634	−	0.578568i	$-0.803612\pi$
$439$		−	507.983i		−	1.15714i	0.815634	−	0.578568i	$-0.196388\pi$
$440$	−72.7812	−	411.772i	−0.165412	−	0.935844i
$441$	−21.0000			−0.0476190
$442$			39.4041i			0.0891496i
$443$	−130.757			−0.295163			−0.147582	−	0.989050i	$-0.547149\pi$
$443$	−130.757			−0.295163			−0.147582	+	0.989050i	$0.547149\pi$
$444$	687.517			1.54846
$445$	99.8537			0.224390
$446$		−	899.968i		−	2.01787i
$447$		−	148.578i		−	0.332390i
$448$		−	47.3317i		−	0.105651i
$449$	521.863			1.16228			0.581139	−	0.813804i	$-0.302607\pi$
$449$	521.863			1.16228			0.581139	+	0.813804i	$0.302607\pi$
$450$		−	53.5803i		−	0.119067i
$451$	126.949	+	718.237i	0.281484	+	1.59254i
$452$	1360.13			3.00913
$453$		−	238.132i		−	0.525677i
$454$	−1120.53			−2.46813
$455$	2.28598			0.00502414
$456$	756.130			1.65818
$457$		−	155.334i		−	0.339898i	−0.985453	−	0.169949i	$-0.945640\pi$
$457$		−	155.334i		−	0.339898i	0.985453	−	0.169949i	$-0.0543604\pi$
$458$		−	1470.69i		−	3.21111i
$459$		−	148.344i		−	0.323190i
$460$	−179.803			−0.390877
$461$			544.919i			1.18204i	0.806658	+	0.591018i	$0.201274\pi$
$461$			544.919i			1.18204i	−0.806658	+	0.591018i	$0.798726\pi$
$462$	−177.311	+	31.3400i	−0.383790	+	0.0678355i
$463$	765.119			1.65252			0.826262	−	0.563286i	$-0.190463\pi$
$463$	765.119			1.65252			0.826262	+	0.563286i	$0.190463\pi$
$464$		−	201.473i		−	0.434209i
$465$	18.0775			0.0388763
$466$	391.230			0.839548
$467$	609.112			1.30431			0.652154	−	0.758087i	$-0.273866\pi$
$467$	609.112			1.30431			0.652154	+	0.758087i	$0.273866\pi$
$468$			10.1539i			0.0216963i
$469$		−	27.8902i		−	0.0594674i
$470$		−	63.6769i		−	0.135483i
$471$	−274.479			−0.582757
$472$		−	1580.90i		−	3.34936i
$473$	50.4738	+	285.564i	0.106710	+	0.603729i
$474$	−831.517			−1.75425
$475$		−	128.395i		−	0.270304i
$476$	661.619			1.38996
$477$	59.7051			0.125168
$478$	389.286			0.814407
$479$		−	410.748i		−	0.857512i	−0.903420	−	0.428756i	$-0.858952\pi$
$479$		−	410.748i		−	0.857512i	0.903420	−	0.428756i	$-0.141048\pi$
$480$			92.0143i			0.191696i
$481$			17.5102i			0.0364038i
$482$	−1360.51			−2.82263
$483$			42.0680i			0.0870973i
$484$	−995.661	+	363.319i	−2.05715	+	0.750660i
$485$	244.409			0.503935
$486$		−	55.6823i		−	0.114573i
$487$	721.235			1.48097			0.740487	−	0.672070i	$-0.234595\pi$
$487$	721.235			1.48097			0.740487	+	0.672070i	$0.234595\pi$
$488$	395.523			0.810497
$489$	−136.835			−0.279827
$490$		−	55.9109i		−	0.114104i
$491$		−	236.412i		−	0.481491i	−0.970588	−	0.240746i	$-0.922608\pi$
$491$		−	236.412i		−	0.481491i	0.970588	−	0.240746i	$-0.0773919\pi$
$492$		−	1005.97i		−	2.04466i
$493$	−223.907			−0.454173
$494$			35.4429i			0.0717468i
$495$	−72.6639	+	12.8434i	−0.146796	+	0.0259464i
$496$	−119.903			−0.241740
$497$			48.5693i			0.0977250i
$498$	216.367			0.434472
$499$	858.075			1.71959			0.859795	−	0.510640i	$-0.170591\pi$
$499$	858.075			1.71959			0.859795	+	0.510640i	$0.170591\pi$
$500$	97.9322			0.195864
$501$		−	185.846i		−	0.370950i
$502$		−	742.671i		−	1.47942i
$503$		−	699.111i		−	1.38988i	−0.719067	−	0.694941i	$-0.755430\pi$
$503$		−	699.111i		−	1.38988i	0.719067	−	0.694941i	$-0.244570\pi$
$504$	134.936			0.267731
$505$			158.229i			0.313324i
$506$	62.7815	+	355.196i	0.124074	+	0.701969i
$507$	292.458			0.576840
$508$		−	1318.66i		−	2.59580i
$509$	341.178			0.670290			0.335145	−	0.942167i	$-0.391215\pi$
$509$	341.178			0.670290			0.335145	+	0.942167i	$0.391215\pi$
$510$	394.955			0.774422
$511$	−13.6213			−0.0266561
$512$			1136.55i			2.21982i
$513$		−	133.432i		−	0.260101i
$514$			19.1401i			0.0372376i
$515$	−158.048			−0.306890
$516$		−	399.965i		−	0.775126i
$517$	−86.3566	+	15.2636i	−0.167034	+	0.0295235i
$518$	428.268			0.826772
$519$		−	111.168i		−	0.214197i
$520$	−14.6887			−0.0282475
$521$	516.493			0.991349			0.495675	−	0.868508i	$-0.334921\pi$
$521$	516.493			0.991349			0.495675	+	0.868508i	$0.334921\pi$
$522$	−84.0455			−0.161007
$523$		−	713.239i		−	1.36375i	−0.731471	−	0.681873i	$-0.761166\pi$
$523$		−	713.239i		−	1.36375i	0.731471	−	0.681873i	$-0.238834\pi$
$524$			1677.14i			3.20064i
$525$		−	22.9129i		−	0.0436436i
$526$	−590.028			−1.12173
$527$			133.254i			0.252854i
$528$	481.960	−	85.1870i	0.912802	−	0.161339i
$529$	−444.728			−0.840695
$530$			158.960i			0.299925i
$531$	−278.976			−0.525378
$532$	595.109			1.11863
$533$	25.6209			0.0480692
$534$			276.283i			0.517383i
$535$		−	340.530i		−	0.636504i
$536$			179.210i			0.334347i
$537$	−579.986			−1.08005
$538$			197.952i			0.367940i
$539$	−75.8247	+	13.4021i	−0.140677	+	0.0248648i
$540$	101.774			0.188471
$541$			351.042i			0.648877i	0.945907	+	0.324438i	$0.105175\pi$
$541$			351.042i			0.648877i	−0.945907	+	0.324438i	$0.894825\pi$
$542$	−528.211			−0.974559
$543$	461.844			0.850542
$544$	−678.263			−1.24681
$545$			263.643i			0.483748i
$546$			6.32503i			0.0115843i
$547$			251.618i			0.459996i	0.973191	+	0.229998i	$0.0738719\pi$
$547$			251.618i			0.459996i	−0.973191	+	0.229998i	$0.926128\pi$
$548$	90.3763			0.164920
$549$		−	69.7965i		−	0.127134i
$550$	−34.1947	−	193.462i	−0.0621722	−	0.351750i
$551$	−201.399			−0.365515
$552$		−	270.310i		−	0.489691i
$553$	−355.587			−0.643014
$554$	−1432.99			−2.58663
$555$	175.509			0.316232
$556$		−	1940.35i		−	3.48984i
$557$			168.565i			0.302631i	0.988486	+	0.151315i	$0.0483509\pi$
$557$			168.565i			0.302631i	−0.988486	+	0.151315i	$0.951649\pi$
$558$			50.0182i			0.0896383i
$559$	10.1866			0.0182229
$560$			151.975i			0.271383i
$561$	−94.6727	−	535.626i	−0.168757	−	0.954770i
$562$	623.148			1.10880
$563$			733.907i			1.30356i	0.758406	+	0.651782i	$0.225978\pi$
$563$			733.907i			1.30356i	−0.758406	+	0.651782i	$0.774022\pi$
$564$	120.952			0.214454
$565$	347.211			0.614533
$566$	1185.21			2.09402
$567$		−	23.8118i		−	0.0419961i
$568$		−	312.084i		−	0.549444i
$569$			297.909i			0.523566i	0.965127	+	0.261783i	$0.0843104\pi$
$569$			297.909i			0.523566i	−0.965127	+	0.261783i	$0.915690\pi$
$570$	355.252			0.623249
$571$		−	17.4540i		−	0.0305674i	−0.999883	−	0.0152837i	$-0.995135\pi$
$571$		−	17.4540i		−	0.0305674i	0.999883	−	0.0152837i	$-0.00486514\pi$
$572$	6.48015	+	36.6625i	0.0113289	+	0.0640953i
$573$	−410.829			−0.716979
$574$		−	626.640i		−	1.09171i
$575$	−45.8999			−0.0798260
$576$	53.6691			0.0931756
$577$	199.511			0.345773			0.172887	−	0.984942i	$-0.444691\pi$
$577$	199.511			0.345773			0.172887	+	0.984942i	$0.444691\pi$
$578$			1879.01i			3.25089i
$579$			427.559i			0.738444i
$580$		−	153.615i		−	0.264854i
$581$	92.5264			0.159254
$582$			676.248i			1.16194i
$583$	215.577	−	38.1036i	0.369772	−	0.0653577i
$584$	87.5240			0.149870
$585$			2.59206i			0.00443087i
$586$	−892.564			−1.52315
$587$	−845.891			−1.44104			−0.720521	−	0.693433i	$-0.756097\pi$
$587$	−845.891			−1.44104			−0.720521	+	0.693433i	$0.756097\pi$
$588$	106.201			0.180614
$589$			119.859i			0.203495i
$590$		−	742.752i		−	1.25890i
$591$			135.490i			0.229255i
$592$	−1164.10			−1.96638
$593$		−	80.7486i		−	0.136170i	−0.997680	−	0.0680849i	$-0.978311\pi$
$593$		−	80.7486i		−	0.136170i	0.997680	−	0.0680849i	$-0.0216889\pi$
$594$	−35.5362	−	201.052i	−0.0598253	−	0.338471i
$595$	168.897			0.283861
$596$			751.390i			1.26072i
$597$	530.069			0.887888
$598$	12.6705			0.0211882
$599$	740.175			1.23568			0.617842	−	0.786302i	$-0.288007\pi$
$599$	740.175			1.23568			0.617842	+	0.786302i	$0.288007\pi$
$600$			147.228i			0.245379i
$601$			199.786i			0.332423i	0.986090	+	0.166211i	$0.0531534\pi$
$601$			199.786i			0.332423i	−0.986090	+	0.166211i	$0.946847\pi$
$602$		−	249.146i		−	0.413863i
$603$	31.6245			0.0524453
$604$			1204.28i			1.99384i
$605$	−254.171	+	92.7477i	−0.420117	+	0.153302i
$606$	−437.799			−0.722440
$607$		−	789.302i		−	1.30033i	−0.759792	−	0.650167i	$-0.774699\pi$
$607$		−	789.302i		−	1.30033i	0.759792	−	0.650167i	$-0.225301\pi$
$608$	−610.079			−1.00342
$609$	−35.9409			−0.0590163
$610$	185.828			0.304636
$611$			3.08051i			0.00504174i
$612$			750.206i			1.22583i
$613$			578.702i			0.944049i	0.881585	+	0.472025i	$0.156477\pi$
$613$			578.702i			0.944049i	−0.881585	+	0.472025i	$0.843523\pi$
$614$	916.723			1.49303
$615$		−	256.803i		−	0.417566i
$616$	487.215	−	86.1159i	0.790933	−	0.139798i
$617$	−1006.92			−1.63196			−0.815979	−	0.578082i	$-0.803801\pi$
$617$	−1006.92			−1.63196			−0.815979	+	0.578082i	$0.803801\pi$
$618$		−	437.300i		−	0.707605i
$619$	1029.84			1.66371			0.831854	−	0.554995i	$-0.187280\pi$
$619$	1029.84			1.66371			0.831854	+	0.554995i	$0.187280\pi$
$620$	−91.4215			−0.147454
$621$	−47.7006			−0.0768126
$622$			42.8662i			0.0689167i
$623$			118.148i			0.189644i
$624$		−	17.1924i		−	0.0275520i
$625$	25.0000			0.0400000
$626$		−	699.225i		−	1.11697i
$627$	−85.1555	−	481.781i	−0.135814	−	0.768391i
$628$	1388.09			2.21034
$629$			1293.72i			2.05679i
$630$	63.3971			0.100630
$631$	−1075.51			−1.70446			−0.852228	−	0.523171i	$-0.824749\pi$
$631$	−1075.51			−1.70446			−0.852228	+	0.523171i	$0.824749\pi$
$632$	2284.84			3.61525
$633$			130.731i			0.206526i
$634$		−	1138.04i		−	1.79502i
$635$		−	336.627i		−	0.530121i
$636$	−301.940			−0.474749
$637$			2.70481i			0.00424617i
$638$	−303.463	+	53.6375i	−0.475647	+	0.0840713i
$639$	−55.0725			−0.0861854
$640$			355.388i			0.555294i
$641$	−681.591			−1.06332			−0.531662	−	0.846956i	$-0.678432\pi$
$641$	−681.591			−1.06332			−0.531662	+	0.846956i	$0.678432\pi$
$642$	942.203			1.46761
$643$	−596.596			−0.927832			−0.463916	−	0.885879i	$-0.653556\pi$
$643$	−596.596			−0.927832			−0.463916	+	0.885879i	$0.653556\pi$
$644$		−	212.746i		−	0.330351i
$645$		−	102.102i		−	0.158298i
$646$			2618.66i			4.05365i
$647$	224.351			0.346756			0.173378	−	0.984855i	$-0.444532\pi$
$647$	224.351			0.346756			0.173378	+	0.984855i	$0.444532\pi$
$648$			153.003i			0.236116i
$649$	−1007.30	+	178.041i	−1.55208	+	0.274332i
$650$	−6.90117			−0.0106172
$651$			21.3896i			0.0328565i
$652$	692.003			1.06135
$653$	−763.887			−1.16981			−0.584906	−	0.811101i	$-0.698869\pi$
$653$	−763.887			−1.16981			−0.584906	+	0.811101i	$0.698869\pi$
$654$	−729.466			−1.11539
$655$			428.137i			0.653645i
$656$			1703.30i			2.59650i
$657$		−	15.4451i		−	0.0235085i
$658$	75.3435			0.114504
$659$			224.413i			0.340535i	0.985398	+	0.170268i	$0.0544632\pi$
$659$			224.413i			0.340535i	−0.985398	+	0.170268i	$0.945537\pi$
$660$	367.476	−	64.9518i	0.556781	−	0.0984119i
$661$	1136.45			1.71929			0.859646	−	0.510890i	$-0.170684\pi$
$661$	1136.45			1.71929			0.859646	+	0.510890i	$0.170684\pi$
$662$			994.681i			1.50254i
$663$	−19.1068			−0.0288187
$664$	−594.532			−0.895380
$665$	151.919			0.228449
$666$			485.610i			0.729144i
$667$			71.9982i			0.107943i
$668$			939.859i			1.40698i
$669$	436.389			0.652301
$670$			84.1980i			0.125669i
$671$	−44.5439	−	252.014i	−0.0663843	−	0.375580i
$672$	−108.873			−0.162013
$673$		−	870.414i		−	1.29333i	−0.762772	−	0.646667i	$-0.776162\pi$
$673$		−	870.414i		−	1.29333i	0.762772	−	0.646667i	$-0.223838\pi$
$674$	61.8445			0.0917575
$675$	25.9808			0.0384900
$676$	−1479.02			−2.18790
$677$		−	285.534i		−	0.421764i	−0.977511	−	0.210882i	$-0.932366\pi$
$677$		−	285.534i		−	0.421764i	0.977511	−	0.210882i	$-0.0676336\pi$
$678$			960.690i			1.41695i
$679$			289.188i			0.425903i
$680$	−1085.26			−1.59597
$681$		−	543.339i		−	0.797854i
$682$	31.9214	+	180.601i	0.0468056	+	0.264810i
$683$	500.810			0.733250			0.366625	−	0.930369i	$-0.380513\pi$
$683$	500.810			0.733250			0.366625	+	0.930369i	$0.380513\pi$
$684$			674.790i			0.986535i
$685$	23.0711			0.0336805
$686$	66.1547			0.0964355
$687$	713.127			1.03803
$688$			677.217i			0.984328i
$689$		−	7.69005i		−	0.0111612i
$690$		−	126.999i		−	0.184057i
$691$	−980.701			−1.41925			−0.709624	−	0.704580i	$-0.751135\pi$
$691$	−980.701			−1.41925			−0.709624	+	0.704580i	$0.751135\pi$
$692$			562.199i			0.812426i
$693$	−15.1966	−	85.9771i	−0.0219287	−	0.124065i
$694$	169.221			0.243835
$695$		−	495.330i		−	0.712705i
$696$	230.940			0.331810
$697$	1892.97			2.71588
$698$	−1741.71			−2.49529
$699$			189.705i			0.271395i
$700$			115.875i			0.165536i
$701$		−	1236.61i		−	1.76407i	−0.471182	−	0.882036i	$-0.656172\pi$
$701$		−	1236.61i		−	1.76407i	0.471182	−	0.882036i	$-0.343828\pi$
$702$	−7.17191			−0.0102164
$703$			1163.67i			1.65529i
$704$	193.783	−	34.2514i	0.275260	−	0.0486526i
$705$	30.8765			0.0437965
$706$		−	316.602i		−	0.448444i
$707$	−187.219			−0.264807
$708$	1410.83			1.99270
$709$	371.247			0.523620			0.261810	−	0.965119i	$-0.415681\pi$
$709$	371.247			0.523620			0.261810	+	0.965119i	$0.415681\pi$
$710$		−	146.626i		−	0.206516i
$711$		−	403.198i		−	0.567085i
$712$		−	759.168i		−	1.06625i
$713$	42.8484			0.0600960
$714$			467.317i			0.654506i
$715$	1.65424	+	9.35916i	0.00231363	+	0.0130897i
$716$	2933.10			4.09651
$717$			188.763i			0.263267i
$718$	546.365			0.760955
$719$	818.248			1.13804			0.569018	−	0.822325i	$-0.307323\pi$
$719$	818.248			1.13804			0.569018	+	0.822325i	$0.307323\pi$
$720$	−172.323			−0.239338
$721$		−	187.005i		−	0.259369i
$722$			1065.92i			1.47634i
$723$		−	659.703i		−	0.912452i
$724$	−2335.64			−3.22602
$725$		−	39.2147i		−	0.0540893i
$726$	−256.621	−	703.259i	−0.353473	−	0.968676i
$727$	−510.939			−0.702805			−0.351402	−	0.936225i	$-0.614295\pi$
$727$	−510.939			−0.702805			−0.351402	+	0.936225i	$0.614295\pi$
$728$		−	17.3799i		−	0.0238735i
$729$	27.0000			0.0370370
$730$	41.1213			0.0563306
$731$	752.626			1.02958
$732$			352.975i			0.482206i
$733$		−	331.247i		−	0.451906i	−0.974138	−	0.225953i	$-0.927450\pi$
$733$		−	331.247i		−	0.451906i	0.974138	−	0.225953i	$-0.0725495\pi$
$734$			877.702i			1.19578i
$735$	27.1109			0.0368856
$736$			218.098i			0.296329i
$737$	114.187	−	20.1827i	0.154934	−	0.0273849i
$738$	710.542			0.962795
$739$			155.758i			0.210769i	0.994432	+	0.105384i	$0.0336073\pi$
$739$			155.758i			0.210769i	−0.994432	+	0.105384i	$0.966393\pi$
$740$	−887.581			−1.19943
$741$	−17.1861			−0.0231931
$742$	−188.084			−0.253483
$743$			533.474i			0.718000i	0.933338	+	0.359000i	$0.116882\pi$
$743$			533.474i			0.718000i	−0.933338	+	0.359000i	$0.883118\pi$
$744$		−	137.440i		−	0.184731i
$745$			191.814i			0.257468i
$746$	−1647.27			−2.20814
$747$			104.915i			0.140449i
$748$	478.778	+	2708.77i	0.640078	+	3.62135i
$749$	402.920			0.537944
$750$			69.1719i			0.0922291i
$751$	389.125			0.518143			0.259071	−	0.965858i	$-0.416584\pi$
$751$	389.125			0.518143			0.259071	+	0.965858i	$0.416584\pi$
$752$	−204.795			−0.272334
$753$	360.117			0.478243
$754$			10.8251i			0.0143569i
$755$			307.427i			0.407188i
$756$			120.421i			0.159287i
$757$	706.018			0.932653			0.466326	−	0.884613i	$-0.345577\pi$
$757$	706.018			0.932653			0.466326	+	0.884613i	$0.345577\pi$
$758$			50.6396i			0.0668068i
$759$	−172.233	+	30.4424i	−0.226920	+	0.0401085i
$760$	−976.159			−1.28442
$761$			574.200i			0.754534i	0.926105	+	0.377267i	$0.123136\pi$
$761$			574.200i			0.754534i	−0.926105	+	0.377267i	$0.876864\pi$
$762$	931.405			1.22232
$763$	−311.946			−0.408841
$764$	2077.64			2.71943
$765$			191.512i			0.250342i
$766$			716.262i			0.935068i
$767$			35.9322i			0.0468477i
$768$	−859.370			−1.11897
$769$			466.203i			0.606245i	0.952952	+	0.303123i	$0.0980292\pi$
$769$			466.203i			0.606245i	−0.952952	+	0.303123i	$0.901971\pi$
$770$	228.908	−	40.4598i	0.297283	−	0.0525451i
$771$	−9.28094			−0.0120375
$772$		−	2162.25i		−	2.80084i
$773$	−1346.23			−1.74156			−0.870780	−	0.491672i	$-0.836386\pi$
$773$	−1346.23			−1.74156			−0.870780	+	0.491672i	$0.836386\pi$
$774$	282.505			0.364993
$775$	−23.3379			−0.0301135
$776$		−	1858.19i		−	2.39458i
$777$			207.665i			0.267264i
$778$		−	1086.00i		−	1.39588i
$779$	1702.68			2.18572
$780$		−	13.1086i		−	0.0168059i
$781$	−198.850	+	35.1470i	−0.254610	+	0.0450026i
$782$	936.148			1.19712
$783$		−	40.7532i		−	0.0520475i
$784$	−179.819			−0.229361
$785$	354.350			0.451402
$786$	−1184.60			−1.50713
$787$		−	1255.19i		−	1.59490i	−0.603386	−	0.797449i	$-0.706182\pi$
$787$		−	1255.19i		−	1.59490i	0.603386	−	0.797449i	$-0.293818\pi$
$788$		−	685.197i		−	0.869540i
$789$		−	286.101i		−	0.362612i
$790$	1073.48			1.35884
$791$			410.826i			0.519376i
$792$	97.6462	+	552.450i	0.123291	+	0.697537i
$793$	−8.98984			−0.0113365
$794$			1917.03i			2.41440i
$795$	−77.0789			−0.0969546
$796$	−2680.66			−3.36767
$797$	1136.12			1.42549			0.712745	−	0.701423i	$-0.247451\pi$
$797$	1136.12			1.42549			0.712745	+	0.701423i	$0.247451\pi$
$798$			420.340i			0.526741i
$799$			227.600i			0.284856i
$800$		−	118.790i		−	0.148487i
$801$	−133.968			−0.167251
$802$			1683.92i			2.09965i
$803$	−9.85698	−	55.7675i	−0.0122752	−	0.0694489i
$804$	−159.931			−0.198920
$805$		−	54.3095i		−	0.0674653i
$806$	6.44237			0.00799301
$807$	−95.9856			−0.118941
$808$	1202.98			1.48884
$809$			1023.98i			1.26574i	0.774258	+	0.632870i	$0.218123\pi$
$809$			1023.98i			1.26574i	−0.774258	+	0.632870i	$0.781877\pi$
$810$			71.8855i			0.0887475i
$811$			470.032i			0.579570i	0.957092	+	0.289785i	$0.0935839\pi$
$811$			470.032i			0.579570i	−0.957092	+	0.289785i	$0.906416\pi$
$812$	181.760			0.223843
$813$		−	256.126i		−	0.315038i
$814$	309.914	+	1753.39i	0.380730	+	2.15404i
$815$	176.654			0.216753
$816$		−	1270.24i		−	1.55667i
$817$	676.967			0.828601
$818$	−2430.88			−2.97173
$819$	−3.06697			−0.00374477
$820$			1298.70i			1.58379i
$821$			1263.22i			1.53863i	0.638869	+	0.769315i	$0.279403\pi$
$821$			1263.22i			1.53863i	−0.638869	+	0.769315i	$0.720597\pi$
$822$			63.8349i			0.0776581i
$823$	−1460.71			−1.77486			−0.887432	−	0.460938i	$-0.847513\pi$
$823$	−1460.71			−1.77486			−0.887432	+	0.460938i	$0.847513\pi$
$824$			1201.61i			1.45826i
$825$	93.8087	−	16.5808i	0.113708	−	0.0200980i
$826$	878.836			1.06397
$827$		−	1084.96i		−	1.31192i	−0.754796	−	0.655960i	$-0.772264\pi$
$827$		−	1084.96i		−	1.31192i	0.754796	−	0.655960i	$-0.227736\pi$
$828$	241.231			0.291342
$829$	1319.98			1.59226			0.796130	−	0.605126i	$-0.206877\pi$
$829$	1319.98			1.59226			0.796130	+	0.605126i	$0.206877\pi$
$830$	−279.329			−0.336541
$831$		−	694.850i		−	0.836161i
$832$		−	6.91261i		−	0.00830843i
$833$			199.842i			0.239906i
$834$	1370.52			1.64330
$835$			239.926i			0.287337i
$836$	430.648	+	2436.46i	0.515130	+	2.91443i
$837$	−24.2535			−0.0289767
$838$			716.503i			0.855016i
$839$	117.117			0.139591			0.0697955	−	0.997561i	$-0.477765\pi$
$839$	117.117			0.139591			0.0697955	+	0.997561i	$0.477765\pi$
$840$	−174.202			−0.207383
$841$	779.488			0.926859
$842$		−	1351.75i		−	1.60541i
$843$			302.161i			0.358435i
$844$		−	661.132i		−	0.783332i
$845$	−377.562			−0.446818
$846$			85.4315i			0.100983i
$847$	−109.741	−	300.739i	−0.129564	−	0.355064i
$848$	511.243			0.602881
$849$			574.703i			0.676918i
$850$	−509.885			−0.599865
$851$	416.001			0.488838
$852$	278.512			0.326892
$853$			247.192i			0.289791i	0.989447	+	0.144896i	$0.0462847\pi$
$853$			247.192i			0.289791i	−0.989447	+	0.144896i	$0.953715\pi$
$854$			219.875i			0.257465i
$855$			172.259i			0.201473i
$856$	−2588.98			−3.02451
$857$			172.122i			0.200843i	0.994945	+	0.100421i	$0.0320191\pi$
$857$			172.122i			0.200843i	−0.994945	+	0.100421i	$0.967981\pi$
$858$	−25.8956	+	4.57708i	−0.0301814	+	0.00533460i
$859$	1303.73			1.51773			0.758867	−	0.651246i	$-0.225753\pi$
$859$	1303.73			1.51773			0.758867	+	0.651246i	$0.225753\pi$
$860$			516.352i			0.600410i
$861$	303.854			0.352908
$862$	−970.158			−1.12547
$863$	321.665			0.372729			0.186365	−	0.982481i	$-0.440329\pi$
$863$	321.665			0.372729			0.186365	+	0.982481i	$0.440329\pi$
$864$		−	123.450i		−	0.142882i
$865$			143.517i			0.165916i
$866$		−	1118.50i		−	1.29157i
$867$	−911.122			−1.05089
$868$		−	108.171i		−	0.124621i
$869$	−257.319	−	1455.83i	−0.296109	−	1.67529i
$870$	108.502			0.124715
$871$		−	4.07326i		−	0.00467653i
$872$	2004.42			2.29865
$873$	−327.909			−0.375611
$874$	842.040			0.963433
$875$			29.5804i			0.0338062i
$876$			78.1087i			0.0891652i
$877$			1122.43i			1.27985i	0.768436	+	0.639927i	$0.221035\pi$
$877$			1122.43i			1.27985i	−0.768436	+	0.639927i	$0.778965\pi$
$878$	−1814.53			−2.06666
$879$		−	432.799i		−	0.492376i
$880$	−622.207	+	109.976i	−0.707054	+	0.124973i
$881$	−407.912			−0.463010			−0.231505	−	0.972834i	$-0.574365\pi$
$881$	−407.912			−0.463010			−0.231505	+	0.972834i	$0.574365\pi$
$882$			75.0124i			0.0850481i
$883$	785.366			0.889429			0.444715	−	0.895672i	$-0.353305\pi$
$883$	785.366			0.889429			0.444715	+	0.895672i	$0.353305\pi$
$884$	96.6269			0.109306
$885$	360.156			0.406956
$886$			467.068i			0.527165i
$887$			654.563i			0.737952i	0.929439	+	0.368976i	$0.120291\pi$
$887$			654.563i			0.737952i	−0.929439	+	0.368976i	$0.879709\pi$
$888$		−	1334.36i		−	1.50265i
$889$	398.302			0.448034
$890$		−	356.679i		−	0.400763i
$891$	97.4889	−	17.2313i	0.109415	−	0.0193393i
$892$	−2206.91			−2.47411
$893$			204.720i			0.229249i
$894$	−530.724			−0.593652
$895$	748.758			0.836602
$896$	−420.501			−0.469309
$897$			6.14387i			0.00684935i
$898$		−	1864.10i		−	2.07584i
$899$			36.6077i			0.0407204i
$900$	−131.390			−0.145989
$901$		−	568.170i		−	0.630600i
$902$	2565.56	−	453.465i	2.84430	−	0.502733i
$903$	120.809			0.133787
$904$		−	2639.78i		−	2.92011i
$905$	−596.238			−0.658827
$906$	−850.612			−0.938865
$907$	1281.73			1.41315			0.706576	−	0.707637i	$-0.250239\pi$
$907$	1281.73			1.41315			0.706576	+	0.707637i	$0.250239\pi$
$908$			2747.77i			3.02618i
$909$		−	212.286i		−	0.233538i
$910$		−	8.16558i		−	0.00897316i
$911$	1180.00			1.29528			0.647642	−	0.761945i	$-0.275755\pi$
$911$	1180.00			1.29528			0.647642	+	0.761945i	$0.275755\pi$
$912$		−	1142.55i		−	1.25280i
$913$	66.9564	+	378.817i	0.0733367	+	0.414914i
$914$	−554.855			−0.607062
$915$			90.1069i			0.0984775i
$916$	−3606.43			−3.93715
$917$	−506.579			−0.552431
$918$	−529.888			−0.577220
$919$		−	779.846i		−	0.848581i	−0.905526	−	0.424291i	$-0.860524\pi$
$919$		−	779.846i		−	0.848581i	0.905526	−	0.424291i	$-0.139476\pi$
$920$			348.968i			0.379313i
$921$			444.514i			0.482642i
$922$	1946.46			2.11113
$923$			7.09337i			0.00768512i
$924$	76.8521	+	434.803i	0.0831732	+	0.470566i
$925$	−226.581			−0.244952
$926$		−	2733.02i		−	2.95142i
$927$	212.044			0.228742
$928$	−186.333			−0.200790
$929$	1372.20			1.47707			0.738537	−	0.674213i	$-0.235517\pi$
$929$	1372.20			1.47707			0.738537	+	0.674213i	$0.235517\pi$
$930$		−	64.5732i		−	0.0694335i
$931$			179.752i			0.193075i
$932$		−	959.375i		−	1.02937i
$933$	−20.7856			−0.0222782
$934$		−	2175.76i		−	2.32951i
$935$	122.222	+	691.490i	0.130719	+	0.739562i
$936$	19.7069			0.0210544
$937$		−	1439.55i		−	1.53634i	−0.640249	−	0.768168i	$-0.721169\pi$
$937$		−	1439.55i		−	1.53634i	0.640249	−	0.768168i	$-0.278831\pi$
$938$	−99.6244			−0.106209
$939$	339.050			0.361076
$940$	−156.149			−0.166116
$941$		−	1503.26i		−	1.59752i	−0.601652	−	0.798759i	$-0.705490\pi$
$941$		−	1503.26i		−	1.59752i	0.601652	−	0.798759i	$-0.294510\pi$
$942$			980.443i			1.04081i
$943$		−	608.691i		−	0.645484i
$944$	−2388.81			−2.53052
$945$			30.7409i			0.0325300i
$946$	1020.04	−	180.293i	1.07827	−	0.190585i
$947$	−309.670			−0.327001			−0.163500	−	0.986543i	$-0.552278\pi$
$947$	−309.670			−0.327001			−0.163500	+	0.986543i	$0.552278\pi$
$948$			2039.05i			2.15090i
$949$	−1.98933			−0.00209624
$950$	−458.628			−0.482766
$951$	551.830			0.580263
$952$		−	1284.09i		−	1.34884i
$953$			119.904i			0.125817i	0.998019	+	0.0629086i	$0.0200377\pi$
$953$			119.904i			0.125817i	−0.998019	+	0.0629086i	$0.979962\pi$
$954$		−	213.268i		−	0.223551i
$955$	530.378			0.555370
$956$		−	954.610i		−	0.998546i
$957$	−26.0085	−	147.147i	−0.0271771	−	0.153759i
$958$	−1467.20			−1.53152
$959$			27.2981i			0.0284652i
$960$	−69.2865			−0.0721735
$961$	−939.214			−0.977329
$962$	62.5469			0.0650175
$963$			456.869i			0.474422i
$964$			3336.25i			3.46084i
$965$		−	551.976i		−	0.571996i
$966$	150.268			0.155557
$967$			129.352i			0.133767i	0.997761	+	0.0668833i	$0.0213055\pi$
$967$			129.352i			0.133767i	−0.997761	+	0.0668833i	$0.978694\pi$
$968$	705.142	+	1932.41i	0.728453	+	1.99629i
$969$	−1269.77			−1.31040
$970$		−	873.032i		−	0.900033i
$971$	371.852			0.382958			0.191479	−	0.981497i	$-0.438672\pi$
$971$	371.852			0.382958			0.191479	+	0.981497i	$0.438672\pi$
$972$	−136.544			−0.140478
$973$	586.082			0.602345
$974$		−	2576.26i		−	2.64503i
$975$		−	3.34634i		−	0.00343214i
$976$		−	597.654i		−	0.612351i
$977$	−1582.50			−1.61976			−0.809879	−	0.586596i	$-0.800468\pi$
$977$	−1582.50			−1.61976			−0.809879	+	0.586596i	$0.800468\pi$
$978$			488.778i			0.499773i
$979$	−483.717	+	85.4977i	−0.494093	+	0.0873317i
$980$	−137.105			−0.139903
$981$		−	353.714i		−	0.360564i
$982$	−844.469			−0.859948
$983$	−630.322			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$983$	−630.322			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$984$	−1952.43			−1.98417
$985$		−	174.916i		−	0.177580i
$986$			799.801i			0.811157i
$987$			36.5336i			0.0370148i
$988$	86.9133			0.0879690
$989$		−	242.010i		−	0.244701i
$990$	45.8770	+	259.557i	0.0463405	+	0.262179i
$991$	−1370.75			−1.38320			−0.691598	−	0.722283i	$-0.743093\pi$
$991$	−1370.75			−1.38320			−0.691598	+	0.722283i	$0.743093\pi$
$992$			110.893i			0.111787i
$993$	−482.315			−0.485715
$994$	173.491			0.174538
$995$	−684.316			−0.687755
$996$		−	530.576i		−	0.532707i
$997$			217.483i			0.218137i	0.994034	+	0.109068i	$0.0347868\pi$
$997$			217.483i			0.218137i	−0.994034	+	0.109068i	$0.965213\pi$
$998$		−	3065.06i		−	3.07120i
$999$	−235.469			−0.235705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.10	✓	96
11.10	odd	2	inner	1155.3.b.a.736.87	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.10	✓	96	1.1	even	1	trivial
1155.3.b.a.736.87	yes	96	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1155.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.57202i q^{2} +1.73205 q^{3} -8.75932 q^{4} -2.23607 q^{5} -6.18692i q^{6} -2.64575i q^{7} +17.0004i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.57202i q^{2} +1.73205 q^{3} -8.75932 q^{4} -2.23607 q^{5} -6.18692i q^{6} -2.64575i q^{7} +17.0004i q^{8} +3.00000 q^{9} +7.98728i q^{10} +(10.8321 - 1.91459i) q^{11} -15.1716 q^{12} -0.386402i q^{13} -9.45067 q^{14} -3.87298 q^{15} +25.6884 q^{16} -28.5488i q^{17} -10.7161i q^{18} -25.6789i q^{19} +19.5864 q^{20} -4.58258i q^{21} +(-6.83895 - 38.6925i) q^{22} -9.17999 q^{23} +29.4455i q^{24} +5.00000 q^{25} -1.38023 q^{26} +5.19615 q^{27} +23.1750i q^{28} -7.84295i q^{29} +13.8344i q^{30} -4.66759 q^{31} -23.7580i q^{32} +(18.7617 - 3.31616i) q^{33} -101.977 q^{34} +5.91608i q^{35} -26.2780 q^{36} -45.3161 q^{37} -91.7256 q^{38} -0.669267i q^{39} -38.0140i q^{40} +66.3063i q^{41} -16.3690 q^{42} +26.3628i q^{43} +(-94.8818 + 16.7705i) q^{44} -6.70820 q^{45} +32.7911i q^{46} -7.97229 q^{47} +44.4936 q^{48} -7.00000 q^{49} -17.8601i q^{50} -49.4481i q^{51} +3.38462i q^{52} +19.9017 q^{53} -18.5608i q^{54} +(-24.2213 + 4.28115i) q^{55} +44.9788 q^{56} -44.4772i q^{57} -28.0152 q^{58} -92.9919 q^{59} +33.9247 q^{60} -23.2655i q^{61} +16.6727i q^{62} -7.93725i q^{63} +17.8897 q^{64} +0.864021i q^{65} +(-11.8454 - 67.0173i) q^{66} +10.5415 q^{67} +250.069i q^{68} -15.9002 q^{69} +21.1324 q^{70} -18.3575 q^{71} +51.0012i q^{72} -5.14836i q^{73} +161.870i q^{74} +8.66025 q^{75} +224.930i q^{76} +(-5.06552 - 28.6590i) q^{77} -2.39064 q^{78} -134.399i q^{79} -57.4411 q^{80} +9.00000 q^{81} +236.847 q^{82} +34.9717i q^{83} +40.1403i q^{84} +63.8372i q^{85} +94.1683 q^{86} -13.5844i q^{87} +(32.5487 + 184.150i) q^{88} -44.6559 q^{89} +23.9618i q^{90} -1.02232 q^{91} +80.4105 q^{92} -8.08450 q^{93} +28.4772i q^{94} +57.4198i q^{95} -41.1500i q^{96} -109.303 q^{97} +25.0041i q^{98} +(32.4963 - 5.74376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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