LMFDB - Embedded newform 1155.3.b.a.736.13

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			736.13
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.84

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.25995i q^{2} +1.73205 q^{3} -6.62729 q^{4} +2.23607 q^{5} -5.64640i q^{6} +2.64575i q^{7} +8.56486i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.25995i q^{2} +1.73205 q^{3} -6.62729 q^{4} +2.23607 q^{5} -5.64640i q^{6} +2.64575i q^{7} +8.56486i q^{8} +3.00000 q^{9} -7.28948i q^{10} +(-6.99198 + 8.49189i) q^{11} -11.4788 q^{12} +11.8404i q^{13} +8.62503 q^{14} +3.87298 q^{15} +1.41185 q^{16} +0.714799i q^{17} -9.77986i q^{18} +9.50856i q^{19} -14.8191 q^{20} +4.58258i q^{21} +(27.6832 + 22.7935i) q^{22} +5.30292 q^{23} +14.8348i q^{24} +5.00000 q^{25} +38.5992 q^{26} +5.19615 q^{27} -17.5342i q^{28} -18.2527i q^{29} -12.6257i q^{30} +15.1227 q^{31} +29.6569i q^{32} +(-12.1105 + 14.7084i) q^{33} +2.33021 q^{34} +5.91608i q^{35} -19.8819 q^{36} +21.2978 q^{37} +30.9975 q^{38} +20.5082i q^{39} +19.1516i q^{40} +34.2854i q^{41} +14.9390 q^{42} +60.6984i q^{43} +(46.3379 - 56.2783i) q^{44} +6.70820 q^{45} -17.2873i q^{46} +69.4507 q^{47} +2.44540 q^{48} -7.00000 q^{49} -16.2998i q^{50} +1.23807i q^{51} -78.4699i q^{52} +76.9151 q^{53} -16.9392i q^{54} +(-15.6345 + 18.9885i) q^{55} -22.6605 q^{56} +16.4693i q^{57} -59.5031 q^{58} -90.6691 q^{59} -25.6674 q^{60} +117.263i q^{61} -49.2993i q^{62} +7.93725i q^{63} +102.327 q^{64} +26.4760i q^{65} +(47.9487 + 39.4795i) q^{66} -64.3561 q^{67} -4.73719i q^{68} +9.18492 q^{69} +19.2861 q^{70} +116.263 q^{71} +25.6946i q^{72} +57.1670i q^{73} -69.4298i q^{74} +8.66025 q^{75} -63.0161i q^{76} +(-22.4674 - 18.4990i) q^{77} +66.8558 q^{78} -78.9922i q^{79} +3.15699 q^{80} +9.00000 q^{81} +111.769 q^{82} +50.1381i q^{83} -30.3701i q^{84} +1.59834i q^{85} +197.874 q^{86} -31.6147i q^{87} +(-72.7318 - 59.8853i) q^{88} +72.2902 q^{89} -21.8684i q^{90} -31.3268 q^{91} -35.1440 q^{92} +26.1933 q^{93} -226.406i q^{94} +21.2618i q^{95} +51.3672i q^{96} -53.1639 q^{97} +22.8197i q^{98} +(-20.9759 + 25.4757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.25995i		−	1.62998i	−0.579477	−	0.814988i	$-0.696743\pi$
$2$		−	3.25995i		−	1.62998i	0.579477	−	0.814988i	$-0.303257\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−6.62729			−1.65682
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$		−	5.64640i		−	0.941067i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			8.56486i			1.07061i
$9$	3.00000			0.333333
$10$		−	7.28948i		−	0.728948i
$11$	−6.99198	+	8.49189i	−0.635634	+	0.771990i
$11$	−6.99198	+	8.49189i	−0.635634	+	0.771990i
$12$	−11.4788			−0.956567
$13$			11.8404i			0.910801i	0.890287	+	0.455401i	$0.150504\pi$
$13$			11.8404i			0.910801i	−0.890287	+	0.455401i	$0.849496\pi$
$14$	8.62503			0.616073
$15$	3.87298			0.258199
$16$	1.41185			0.0882406
$17$			0.714799i			0.0420470i	0.999779	+	0.0210235i	$0.00669248\pi$
$17$			0.714799i			0.0420470i	−0.999779	+	0.0210235i	$0.993308\pi$
$18$		−	9.77986i		−	0.543326i
$19$			9.50856i			0.500451i	0.968188	+	0.250225i	$0.0805047\pi$
$19$			9.50856i			0.500451i	−0.968188	+	0.250225i	$0.919495\pi$
$20$	−14.8191			−0.740954
$21$			4.58258i			0.218218i
$22$	27.6832	+	22.7935i	1.25833	+	1.03607i
$23$	5.30292			0.230562			0.115281	−	0.993333i	$-0.463223\pi$
$23$	5.30292			0.230562			0.115281	+	0.993333i	$0.463223\pi$
$24$			14.8348i			0.618115i
$25$	5.00000			0.200000
$26$	38.5992			1.48458
$27$	5.19615			0.192450
$28$		−	17.5342i		−	0.626220i
$29$		−	18.2527i		−	0.629405i	−0.949190	−	0.314702i	$-0.898095\pi$
$29$		−	18.2527i		−	0.629405i	0.949190	−	0.314702i	$-0.101905\pi$
$30$		−	12.6257i		−	0.420858i
$31$	15.1227			0.487829			0.243914	−	0.969797i	$-0.421568\pi$
$31$	15.1227			0.487829			0.243914	+	0.969797i	$0.421568\pi$
$32$			29.6569i			0.926777i
$33$	−12.1105	+	14.7084i	−0.366984	+	0.445709i
$34$	2.33021			0.0685357
$35$			5.91608i			0.169031i
$36$	−19.8819			−0.552275
$37$	21.2978			0.575616			0.287808	−	0.957688i	$-0.407074\pi$
$37$	21.2978			0.575616			0.287808	+	0.957688i	$0.407074\pi$
$38$	30.9975			0.815723
$39$			20.5082i			0.525851i
$40$			19.1516i			0.478790i
$41$			34.2854i			0.836230i	0.908394	+	0.418115i	$0.137309\pi$
$41$			34.2854i			0.836230i	−0.908394	+	0.418115i	$0.862691\pi$
$42$	14.9390			0.355690
$43$			60.6984i			1.41159i	0.708416	+	0.705796i	$0.249410\pi$
$43$			60.6984i			1.41159i	−0.708416	+	0.705796i	$0.750590\pi$
$44$	46.3379	−	56.2783i	1.05313	−	1.27905i
$45$	6.70820			0.149071
$46$		−	17.2873i		−	0.375810i
$47$	69.4507			1.47767			0.738837	−	0.673884i	$-0.235375\pi$
$47$	69.4507			1.47767			0.738837	+	0.673884i	$0.235375\pi$
$48$	2.44540			0.0509458
$49$	−7.00000			−0.142857
$50$		−	16.2998i		−	0.325995i
$51$			1.23807i			0.0242759i
$52$		−	78.4699i		−	1.50904i
$53$	76.9151			1.45123			0.725615	−	0.688101i	$-0.241556\pi$
$53$	76.9151			1.45123			0.725615	+	0.688101i	$0.241556\pi$
$54$		−	16.9392i		−	0.313689i
$55$	−15.6345	+	18.9885i	−0.284264	+	0.345245i
$56$	−22.6605			−0.404651
$57$			16.4693i			0.288935i
$58$	−59.5031			−1.02591
$59$	−90.6691			−1.53676			−0.768382	−	0.639991i	$-0.778938\pi$
$59$	−90.6691			−1.53676			−0.768382	+	0.639991i	$0.778938\pi$
$60$	−25.6674			−0.427790
$61$			117.263i			1.92235i	0.275947	+	0.961173i	$0.411008\pi$
$61$			117.263i			1.92235i	−0.275947	+	0.961173i	$0.588992\pi$
$62$		−	49.2993i		−	0.795149i
$63$			7.93725i			0.125988i
$64$	102.327			1.59886
$65$			26.4760i			0.407323i
$66$	47.9487	+	39.4795i	0.726495	+	0.598175i
$67$	−64.3561			−0.960539			−0.480270	−	0.877121i	$-0.659461\pi$
$67$	−64.3561			−0.960539			−0.480270	+	0.877121i	$0.659461\pi$
$68$		−	4.73719i		−	0.0696645i
$69$	9.18492			0.133115
$70$	19.2861			0.275516
$71$	116.263			1.63751			0.818754	−	0.574145i	$-0.194665\pi$
$71$	116.263			1.63751			0.818754	+	0.574145i	$0.194665\pi$
$72$			25.6946i			0.356869i
$73$			57.1670i			0.783110i	0.920155	+	0.391555i	$0.128063\pi$
$73$			57.1670i			0.783110i	−0.920155	+	0.391555i	$0.871937\pi$
$74$		−	69.4298i		−	0.938240i
$75$	8.66025			0.115470
$76$		−	63.0161i		−	0.829159i
$77$	−22.4674	−	18.4990i	−0.291785	−	0.240247i
$78$	66.8558			0.857125
$79$		−	78.9922i		−	0.999902i	−0.866054	−	0.499951i	$-0.833351\pi$
$79$		−	78.9922i		−	0.999902i	0.866054	−	0.499951i	$-0.166649\pi$
$80$	3.15699			0.0394624
$81$	9.00000			0.111111
$82$	111.769			1.36303
$83$			50.1381i			0.604073i	0.953296	+	0.302036i	$0.0976664\pi$
$83$			50.1381i			0.604073i	−0.953296	+	0.302036i	$0.902334\pi$
$84$		−	30.3701i		−	0.361549i
$85$			1.59834i			0.0188040i
$86$	197.874			2.30086
$87$		−	31.6147i		−	0.363387i
$88$	−72.7318	−	59.8853i	−0.826498	−	0.680514i
$89$	72.2902			0.812249			0.406125	−	0.913818i	$-0.366880\pi$
$89$	72.2902			0.812249			0.406125	+	0.913818i	$0.366880\pi$
$90$		−	21.8684i		−	0.242983i
$91$	−31.3268			−0.344251
$92$	−35.1440			−0.382000
$93$	26.1933			0.281648
$94$		−	226.406i		−	2.40857i
$95$			21.2618i			0.223808i
$96$			51.3672i			0.535075i
$97$	−53.1639			−0.548082			−0.274041	−	0.961718i	$-0.588360\pi$
$97$	−53.1639			−0.548082			−0.274041	+	0.961718i	$0.588360\pi$
$98$			22.8197i			0.232854i
$99$	−20.9759	+	25.4757i	−0.211878	+	0.257330i
$100$	−33.1365			−0.331365
$101$		−	36.0469i		−	0.356900i	−0.983949	−	0.178450i	$-0.942892\pi$
$101$		−	36.0469i		−	0.356900i	0.983949	−	0.178450i	$-0.0571082\pi$
$102$	4.03605			0.0395691
$103$	1.48598			0.0144270			0.00721349	−	0.999974i	$-0.497704\pi$
$103$	1.48598			0.0144270			0.00721349	+	0.999974i	$0.497704\pi$
$104$	−101.411			−0.975110
$105$			10.2470i			0.0975900i
$106$		−	250.740i		−	2.36547i
$107$		−	60.2073i		−	0.562685i	−0.959607	−	0.281342i	$-0.909220\pi$
$107$		−	60.2073i		−	0.562685i	0.959607	−	0.281342i	$-0.0907797\pi$
$108$	−34.4364			−0.318856
$109$		−	102.947i		−	0.944468i	−0.881473	−	0.472234i	$-0.843448\pi$
$109$		−	102.947i		−	0.944468i	0.881473	−	0.472234i	$-0.156552\pi$
$110$	61.9015	+	50.9679i	0.562741	+	0.463344i
$111$	36.8889			0.332332
$112$			3.73540i			0.0333518i
$113$	−68.8910			−0.609655			−0.304827	−	0.952408i	$-0.598599\pi$
$113$	−68.8910			−0.609655			−0.304827	+	0.952408i	$0.598599\pi$
$114$	53.6892			0.470958
$115$	11.8577			0.103110
$116$			120.966i			1.04281i
$117$			35.5213i			0.303600i
$118$			295.577i			2.50489i
$119$	−1.89118			−0.0158923
$120$			33.1715i			0.276430i
$121$	−23.2245	−	118.750i	−0.191938	−	0.981407i
$122$	382.272			3.13338
$123$			59.3841i			0.482797i
$124$	−100.222			−0.808246
$125$	11.1803			0.0894427
$126$	25.8751			0.205358
$127$		−	4.54268i		−	0.0357691i	−0.999840	−	0.0178846i	$-0.994307\pi$
$127$		−	4.54268i		−	0.0357691i	0.999840	−	0.0178846i	$-0.00569313\pi$
$128$		−	214.955i		−	1.67934i
$129$			105.133i			0.814983i
$130$	86.3104			0.663927
$131$			70.1980i			0.535863i	0.963438	+	0.267931i	$0.0863401\pi$
$131$			70.1980i			0.535863i	−0.963438	+	0.267931i	$0.913660\pi$
$132$	80.2596	−	97.4768i	0.608027	−	0.738461i
$133$	−25.1573			−0.189153
$134$			209.798i			1.56566i
$135$	11.6190			0.0860663
$136$	−6.12215			−0.0450158
$137$	57.1217			0.416947			0.208473	−	0.978028i	$-0.433151\pi$
$137$	57.1217			0.416947			0.208473	+	0.978028i	$0.433151\pi$
$138$		−	29.9424i		−	0.216974i
$139$		−	118.088i		−	0.849558i	−0.905297	−	0.424779i	$-0.860352\pi$
$139$		−	118.088i		−	0.849558i	0.905297	−	0.424779i	$-0.139648\pi$
$140$		−	39.2076i		−	0.280054i
$141$	120.292			0.853135
$142$		−	379.012i		−	2.66910i
$143$	−100.548	−	82.7879i	−0.703130	−	0.578937i
$144$	4.23555			0.0294135
$145$		−	40.8144i		−	0.281478i
$146$	186.362			1.27645
$147$	−12.1244			−0.0824786
$148$	−141.147			−0.953694
$149$			108.058i			0.725221i	0.931941	+	0.362610i	$0.118114\pi$
$149$			108.058i			0.725221i	−0.931941	+	0.362610i	$0.881886\pi$
$150$		−	28.2320i		−	0.188213i
$151$		−	15.9008i		−	0.105303i	−0.998613	−	0.0526516i	$-0.983233\pi$
$151$		−	15.9008i		−	0.105303i	0.998613	−	0.0526516i	$-0.0167673\pi$
$152$	−81.4395			−0.535786
$153$			2.14440i			0.0140157i
$154$	−60.3060	+	73.2428i	−0.391597	+	0.475603i
$155$	33.8154			0.218164
$156$		−	135.914i		−	0.871243i
$157$	−57.6377			−0.367119			−0.183560	−	0.983009i	$-0.558762\pi$
$157$	−57.6377			−0.367119			−0.183560	+	0.983009i	$0.558762\pi$
$158$	−257.511			−1.62982
$159$	133.221			0.837868
$160$			66.3147i			0.414467i
$161$			14.0302i			0.0871441i
$162$		−	29.3396i		−	0.181109i
$163$	−306.244			−1.87880			−0.939398	−	0.342827i	$-0.888615\pi$
$163$	−306.244			−1.87880			−0.939398	+	0.342827i	$0.888615\pi$
$164$		−	227.219i		−	1.38548i
$165$	−27.0798	+	32.8890i	−0.164120	+	0.199327i
$166$	163.448			0.984625
$167$			282.882i			1.69391i	0.531668	+	0.846953i	$0.321565\pi$
$167$			282.882i			1.69391i	−0.531668	+	0.846953i	$0.678435\pi$
$168$	−39.2491			−0.233626
$169$	28.8045			0.170441
$170$	5.21051			0.0306501
$171$			28.5257i			0.166817i
$172$		−	402.266i		−	2.33876i
$173$			205.611i			1.18850i	0.804279	+	0.594251i	$0.202552\pi$
$173$			205.611i			1.18850i	−0.804279	+	0.594251i	$0.797448\pi$
$174$	−103.062			−0.592312
$175$			13.2288i			0.0755929i
$176$	−9.87162	+	11.9893i	−0.0560888	+	0.0681209i
$177$	−157.044			−0.887252
$178$		−	235.663i		−	1.32395i
$179$	−337.861			−1.88749			−0.943745	−	0.330674i	$-0.892724\pi$
$179$	−337.861			−1.88749			−0.943745	+	0.330674i	$0.892724\pi$
$180$	−44.4572			−0.246985
$181$	−57.0926			−0.315429			−0.157714	−	0.987485i	$-0.550413\pi$
$181$	−57.0926			−0.315429			−0.157714	+	0.987485i	$0.550413\pi$
$182$			102.124i			0.561120i
$183$			203.106i			1.10987i
$184$			45.4187i			0.246841i
$185$	47.6233			0.257423
$186$		−	85.3888i		−	0.459080i
$187$	−6.07000	−	4.99786i	−0.0324599	−	0.0267265i
$188$	−460.270			−2.44824
$189$			13.7477i			0.0727393i
$190$	69.3125			0.364802
$191$	63.7145			0.333584			0.166792	−	0.985992i	$-0.446659\pi$
$191$	63.7145			0.333584			0.166792	+	0.985992i	$0.446659\pi$
$192$	177.236			0.923105
$193$		−	164.827i		−	0.854024i	−0.904246	−	0.427012i	$-0.859566\pi$
$193$		−	164.827i		−	0.854024i	0.904246	−	0.427012i	$-0.140434\pi$
$194$			173.312i			0.893360i
$195$			45.8577i			0.235168i
$196$	46.3911			0.236689
$197$		−	344.225i		−	1.74734i	−0.486523	−	0.873668i	$-0.661735\pi$
$197$		−	344.225i		−	1.74734i	0.486523	−	0.873668i	$-0.338265\pi$
$198$	83.0495	+	68.3806i	0.419442	+	0.345356i
$199$	149.135			0.749423			0.374711	−	0.927142i	$-0.377742\pi$
$199$	149.135			0.749423			0.374711	+	0.927142i	$0.377742\pi$
$200$			42.8243i			0.214121i
$201$	−111.468			−0.554568
$202$	−117.511			−0.581738
$203$	48.2922			0.237893
$204$		−	8.20505i		−	0.0402208i
$205$			76.6645i			0.373973i
$206$		−	4.84422i		−	0.0235156i
$207$	15.9088			0.0768539
$208$			16.7169i			0.0803697i
$209$	−80.7457	−	66.4837i	−0.386343	−	0.318104i
$210$	33.4046			0.159069
$211$			314.317i			1.48965i	0.667257	+	0.744827i	$0.267468\pi$
$211$			314.317i			1.48965i	−0.667257	+	0.744827i	$0.732532\pi$
$212$	−509.739			−2.40443
$213$	201.374			0.945416
$214$	−196.273			−0.917163
$215$			135.726i			0.631283i
$216$			44.5043i			0.206038i
$217$			40.0109i			0.184382i
$218$	−335.602			−1.53946
$219$			99.0162i			0.452129i
$220$	103.615	−	125.842i	0.470976	−	0.572009i
$221$	−8.46352			−0.0382965
$222$		−	120.256i		−	0.541693i
$223$	−369.689			−1.65780			−0.828900	−	0.559397i	$-0.811033\pi$
$223$	−369.689			−1.65780			−0.828900	+	0.559397i	$0.811033\pi$
$224$	−78.4647			−0.350289
$225$	15.0000			0.0666667
$226$			224.581i			0.993723i
$227$		−	154.248i		−	0.679507i	−0.940514	−	0.339754i	$-0.889656\pi$
$227$		−	154.248i		−	0.679507i	0.940514	−	0.339754i	$-0.110344\pi$
$228$		−	109.147i		−	0.478715i
$229$	131.904			0.575999			0.288000	−	0.957631i	$-0.407010\pi$
$229$	131.904			0.575999			0.288000	+	0.957631i	$0.407010\pi$
$230$		−	38.6555i		−	0.168067i
$231$	−38.9147	−	32.0413i	−0.168462	−	0.138707i
$232$	156.332			0.673845
$233$			65.4028i			0.280699i	0.990102	+	0.140349i	$0.0448226\pi$
$233$			65.4028i			0.280699i	−0.990102	+	0.140349i	$0.955177\pi$
$234$	115.798			0.494862
$235$	155.296			0.660836
$236$	600.891			2.54615
$237$		−	136.819i		−	0.577293i
$238$			6.16516i			0.0259040i
$239$			275.468i			1.15259i	0.817243	+	0.576293i	$0.195501\pi$
$239$			275.468i			1.15259i	−0.817243	+	0.576293i	$0.804499\pi$
$240$	5.46807			0.0227836
$241$		−	4.09092i		−	0.0169748i	−0.999964	−	0.00848739i	$-0.997298\pi$
$241$		−	4.09092i		−	0.0169748i	0.999964	−	0.00848739i	$-0.00270165\pi$
$242$	−387.120	+	75.7108i	−1.59967	+	0.312855i
$243$	15.5885			0.0641500
$244$		−	777.137i		−	3.18499i
$245$	−15.6525			−0.0638877
$246$	193.589			0.786948
$247$	−112.585			−0.455811
$248$			129.524i			0.522273i
$249$			86.8417i			0.348762i
$250$		−	36.4474i		−	0.145790i
$251$	−9.82343			−0.0391372			−0.0195686	−	0.999809i	$-0.506229\pi$
$251$	−9.82343			−0.0391372			−0.0195686	+	0.999809i	$0.506229\pi$
$252$		−	52.6025i		−	0.208740i
$253$	−37.0779	+	45.0318i	−0.146553	+	0.177991i
$254$	−14.8089			−0.0583028
$255$			2.76841i			0.0108565i
$256$	−291.434			−1.13841
$257$	−103.472			−0.402615			−0.201308	−	0.979528i	$-0.564519\pi$
$257$	−103.472			−0.402615			−0.201308	+	0.979528i	$0.564519\pi$
$258$	342.728			1.32840
$259$			56.3487i			0.217562i
$260$		−	175.464i		−	0.674862i
$261$		−	54.7582i		−	0.209802i
$262$	228.842			0.873444
$263$		−	385.813i		−	1.46697i	−0.679705	−	0.733485i	$-0.737892\pi$
$263$		−	385.813i		−	1.46697i	0.679705	−	0.733485i	$-0.262108\pi$
$264$	−125.975	−	103.724i	−0.477179	−	0.392895i
$265$	171.987			0.649009
$266$			82.0116i			0.308314i
$267$	125.210			0.468952
$268$	426.507			1.59144
$269$	88.0610			0.327364			0.163682	−	0.986513i	$-0.447663\pi$
$269$	88.0610			0.327364			0.163682	+	0.986513i	$0.447663\pi$
$270$		−	37.8772i		−	0.140286i
$271$		−	254.661i		−	0.939709i	−0.882744	−	0.469855i	$-0.844306\pi$
$271$		−	254.661i		−	0.939709i	0.882744	−	0.469855i	$-0.155694\pi$
$272$			1.00919i			0.00371026i
$273$	−54.2596			−0.198753
$274$		−	186.214i		−	0.679614i
$275$	−34.9599	+	42.4595i	−0.127127	+	0.154398i
$276$	−60.8712			−0.220548
$277$		−	322.903i		−	1.16572i	−0.812574	−	0.582858i	$-0.801934\pi$
$277$		−	322.903i		−	1.16572i	0.812574	−	0.582858i	$-0.198066\pi$
$278$	−384.963			−1.38476
$279$	45.3681			0.162610
$280$	−50.6704			−0.180966
$281$			365.333i			1.30012i	0.759884	+	0.650059i	$0.225256\pi$
$281$			365.333i			1.30012i	−0.759884	+	0.650059i	$0.774744\pi$
$282$		−	392.147i		−	1.39059i
$283$			30.2357i			0.106840i	0.998572	+	0.0534199i	$0.0170122\pi$
$283$			30.2357i			0.106840i	−0.998572	+	0.0534199i	$0.982988\pi$
$284$	−770.509			−2.71306
$285$			36.8265i			0.129216i
$286$	−269.885	+	327.780i	−0.943653	+	1.14609i
$287$	−90.7107			−0.316065
$288$			88.9706i			0.308926i
$289$	288.489			0.998232
$290$	−133.053			−0.458803
$291$	−92.0826			−0.316435
$292$		−	378.863i		−	1.29748i
$293$			166.153i			0.567074i	0.958961	+	0.283537i	$0.0915080\pi$
$293$			166.153i			0.567074i	−0.958961	+	0.283537i	$0.908492\pi$
$294$			39.5248i			0.134438i
$295$	−202.742			−0.687262
$296$			182.412i			0.616258i
$297$	−36.3314	+	44.1252i	−0.122328	+	0.148570i
$298$	352.264			1.18209
$299$			62.7888i			0.209996i
$300$	−57.3940			−0.191313
$301$	−160.593			−0.533531
$302$	−51.8358			−0.171642
$303$		−	62.4350i		−	0.206056i
$304$			13.4247i			0.0441601i
$305$			262.208i			0.859699i
$306$	6.99064			0.0228452
$307$		−	275.260i		−	0.896612i	−0.893880	−	0.448306i	$-0.852027\pi$
$307$		−	275.260i		−	0.896612i	0.893880	−	0.448306i	$-0.147973\pi$
$308$	148.898	+	122.599i	0.483436	+	0.398047i
$309$	2.57379			0.00832942
$310$		−	110.236i		−	0.355602i
$311$	4.61508			0.0148395			0.00741974	−	0.999972i	$-0.497638\pi$
$311$	4.61508			0.0148395			0.00741974	+	0.999972i	$0.497638\pi$
$312$	−175.650			−0.562980
$313$	191.204			0.610874			0.305437	−	0.952212i	$-0.401197\pi$
$313$	191.204			0.610874			0.305437	+	0.952212i	$0.401197\pi$
$314$			187.896i			0.598396i
$315$			17.7482i			0.0563436i
$316$			523.505i			1.65666i
$317$	227.156			0.716581			0.358291	−	0.933610i	$-0.383360\pi$
$317$	227.156			0.716581			0.358291	+	0.933610i	$0.383360\pi$
$318$		−	434.294i		−	1.36570i
$319$	155.000	+	127.623i	0.485894	+	0.400071i
$320$	228.811			0.715034
$321$		−	104.282i		−	0.324866i
$322$	45.7378			0.142043
$323$	−6.79672			−0.0210425
$324$	−59.6456			−0.184092
$325$			59.2021i			0.182160i
$326$			998.341i			3.06239i
$327$		−	178.309i		−	0.545289i
$328$	−293.650			−0.895273
$329$			183.749i			0.558508i
$330$	107.216	+	88.2789i	0.324898	+	0.267512i
$331$	−215.320			−0.650515			−0.325257	−	0.945626i	$-0.605451\pi$
$331$	−215.320			−0.650515			−0.325257	+	0.945626i	$0.605451\pi$
$332$		−	332.280i		−	1.00084i
$333$	63.8934			0.191872
$334$	922.183			2.76103
$335$	−143.905			−0.429566
$336$			6.46991i			0.0192557i
$337$		−	10.2677i		−	0.0304679i	−0.999884	−	0.0152339i	$-0.995151\pi$
$337$		−	10.2677i		−	0.0304679i	0.999884	−	0.0152339i	$-0.00484930\pi$
$338$		−	93.9014i		−	0.277815i
$339$	−119.323			−0.351984
$340$		−	10.5927i		−	0.0311549i
$341$	−105.737	+	128.420i	−0.310081	+	0.376599i
$342$	92.9924			0.271908
$343$		−	18.5203i		−	0.0539949i
$344$	−519.873			−1.51126
$345$	20.5381			0.0595308
$346$	670.282			1.93723
$347$			89.6958i			0.258489i	0.991613	+	0.129245i	$0.0412553\pi$
$347$			89.6958i			0.258489i	−0.991613	+	0.129245i	$0.958745\pi$
$348$			209.520i			0.602068i
$349$			421.491i			1.20771i	0.797094	+	0.603855i	$0.206369\pi$
$349$			421.491i			1.20771i	−0.797094	+	0.603855i	$0.793631\pi$
$350$	43.1251			0.123215
$351$			61.5246i			0.175284i
$352$	−251.843	−	207.360i	−0.715463	−	0.589091i
$353$	89.5009			0.253544			0.126772	−	0.991932i	$-0.459538\pi$
$353$	89.5009			0.253544			0.126772	+	0.991932i	$0.459538\pi$
$354$			511.955i			1.44620i
$355$	259.972			0.732316
$356$	−479.088			−1.34575
$357$	−3.27562			−0.00917541
$358$			1101.41i			3.07656i
$359$			242.680i			0.675989i	0.941148	+	0.337995i	$0.109749\pi$
$359$			242.680i			0.675989i	−0.941148	+	0.337995i	$0.890251\pi$
$360$			57.4548i			0.159597i
$361$	270.587			0.749549
$362$			186.119i			0.514142i
$363$	−40.2260	−	205.681i	−0.110816	−	0.566616i
$364$	207.612			0.570362
$365$			127.829i			0.350217i
$366$	662.115			1.80906
$367$	151.072			0.411640			0.205820	−	0.978590i	$-0.434014\pi$
$367$	151.072			0.411640			0.205820	+	0.978590i	$0.434014\pi$
$368$	7.48693			0.0203449
$369$			102.856i			0.278743i
$370$		−	155.250i		−	0.419594i
$371$			203.498i			0.548513i
$372$	−173.590			−0.466641
$373$			340.987i			0.914174i	0.889422	+	0.457087i	$0.151107\pi$
$373$			340.987i			0.914174i	−0.889422	+	0.457087i	$0.848893\pi$
$374$	−16.2928	+	19.7879i	−0.0435636	+	0.0529089i
$375$	19.3649			0.0516398
$376$			594.835i			1.58201i
$377$	216.120			0.573263
$378$	44.8169			0.118563
$379$	182.264			0.480909			0.240454	−	0.970660i	$-0.422704\pi$
$379$	182.264			0.480909			0.240454	+	0.970660i	$0.422704\pi$
$380$		−	140.908i		−	0.370811i
$381$		−	7.86815i		−	0.0206513i
$382$		−	207.706i		−	0.543733i
$383$	687.344			1.79463			0.897316	−	0.441389i	$-0.145514\pi$
$383$	687.344			1.79463			0.897316	+	0.441389i	$0.145514\pi$
$384$		−	372.313i		−	0.969565i
$385$	−50.2387	−	41.3651i	−0.130490	−	0.107442i
$386$	−537.327			−1.39204
$387$			182.095i			0.470530i
$388$	352.333			0.908074
$389$	−418.402			−1.07558			−0.537792	−	0.843077i	$-0.680741\pi$
$389$	−418.402			−1.07558			−0.537792	+	0.843077i	$0.680741\pi$
$390$	149.494			0.383318
$391$			3.79052i			0.00969443i
$392$		−	59.9540i		−	0.152944i
$393$			121.587i			0.309381i
$394$	−1122.16			−2.84812
$395$		−	176.632i		−	0.447170i
$396$	139.014	−	168.835i	0.351045	−	0.426351i
$397$	14.2376			0.0358629			0.0179314	−	0.999839i	$-0.494292\pi$
$397$	14.2376			0.0358629			0.0179314	+	0.999839i	$0.494292\pi$
$398$		−	486.173i		−	1.22154i
$399$	−43.5737			−0.109207
$400$	7.05925			0.0176481
$401$	714.683			1.78225			0.891125	−	0.453757i	$-0.149917\pi$
$401$	714.683			1.78225			0.891125	+	0.453757i	$0.149917\pi$
$402$			363.381i			0.903932i
$403$			179.059i			0.444315i
$404$			238.893i			0.591320i
$405$	20.1246			0.0496904
$406$		−	157.430i		−	0.387759i
$407$	−148.914	+	180.859i	−0.365881	+	0.444370i
$408$	−10.6039			−0.0259899
$409$		−	258.746i		−	0.632630i	−0.948654	−	0.316315i	$-0.897554\pi$
$409$		−	258.746i		−	0.632630i	0.948654	−	0.316315i	$-0.102446\pi$
$410$	249.923			0.609568
$411$	98.9377			0.240724
$412$	−9.84802			−0.0239030
$413$		−	239.888i		−	0.580843i
$414$		−	51.8618i		−	0.125270i
$415$			112.112i			0.270150i
$416$	−351.150			−0.844110
$417$		−	204.535i		−	0.490492i
$418$	−216.734	+	263.227i	−0.518502	+	0.629730i
$419$	624.763			1.49108			0.745540	−	0.666461i	$-0.232192\pi$
$419$	624.763			1.49108			0.745540	+	0.666461i	$0.232192\pi$
$420$		−	67.9096i		−	0.161689i
$421$	−549.214			−1.30455			−0.652274	−	0.757984i	$-0.726185\pi$
$421$	−549.214			−1.30455			−0.652274	+	0.757984i	$0.726185\pi$
$422$	1024.66			2.42810
$423$	208.352			0.492558
$424$			658.767i			1.55370i
$425$			3.57400i			0.00840940i
$426$		−	656.468i		−	1.54101i
$427$	−310.249			−0.726578
$428$			399.011i			0.932269i
$429$	−174.153	−	143.393i	−0.405952	−	0.334249i
$430$	442.460			1.02898
$431$			399.513i			0.926944i	0.886112	+	0.463472i	$0.153396\pi$
$431$			399.513i			0.926944i	−0.886112	+	0.463472i	$0.846604\pi$
$432$	7.33619			0.0169819
$433$	231.226			0.534009			0.267004	−	0.963695i	$-0.413966\pi$
$433$	231.226			0.534009			0.267004	+	0.963695i	$0.413966\pi$
$434$	130.434			0.300538
$435$		−	70.6925i		−	0.162512i
$436$			682.260i			1.56482i
$437$			50.4231i			0.115385i
$438$	322.788			0.736959
$439$		−	308.759i		−	0.703322i	−0.936127	−	0.351661i	$-0.885617\pi$
$439$		−	308.759i		−	0.703322i	0.936127	−	0.351661i	$-0.114383\pi$
$440$	−162.633	−	133.908i	−0.369621	−	0.304335i
$441$	−21.0000			−0.0476190
$442$			27.5907i			0.0624224i
$443$	165.492			0.373571			0.186786	−	0.982401i	$-0.440193\pi$
$443$	165.492			0.373571			0.186786	+	0.982401i	$0.440193\pi$
$444$	−244.473			−0.550615
$445$	161.646			0.363249
$446$			1205.17i			2.70217i
$447$			187.162i			0.418706i
$448$			270.733i			0.604314i
$449$	−586.467			−1.30616			−0.653081	−	0.757288i	$-0.726524\pi$
$449$	−586.467			−1.30616			−0.653081	+	0.757288i	$0.726524\pi$
$450$		−	48.8993i		−	0.108665i
$451$	−291.148	−	239.723i	−0.645561	−	0.531536i
$452$	456.561			1.01009
$453$		−	27.5409i		−	0.0607968i
$454$	−502.842			−1.10758
$455$	−70.0489			−0.153954
$456$	−141.057			−0.309336
$457$			347.355i			0.760076i	0.924971	+	0.380038i	$0.124089\pi$
$457$			347.355i			0.760076i	−0.924971	+	0.380038i	$0.875911\pi$
$458$		−	430.000i		−	0.938865i
$459$			3.71421i			0.00809195i
$460$	−78.5844			−0.170836
$461$		−	177.402i		−	0.384820i	−0.981315	−	0.192410i	$-0.938370\pi$
$461$		−	177.402i		−	0.384820i	0.981315	−	0.192410i	$-0.0616303\pi$
$462$	−104.453	+	126.860i	−0.226089	+	0.274589i
$463$	−530.403			−1.14558			−0.572790	−	0.819702i	$-0.694139\pi$
$463$	−530.403			−1.14558			−0.572790	+	0.819702i	$0.694139\pi$
$464$		−	25.7701i		−	0.0555391i
$465$	58.5699			0.125957
$466$	213.210			0.457532
$467$	−562.622			−1.20476			−0.602379	−	0.798210i	$-0.705780\pi$
$467$	−562.622			−1.20476			−0.602379	+	0.798210i	$0.705780\pi$
$468$		−	235.410i		−	0.503012i
$469$		−	170.270i		−	0.363050i
$470$		−	506.259i		−	1.07715i
$471$	−99.8315			−0.211956
$472$		−	776.568i		−	1.64527i
$473$	−515.445	−	424.402i	−1.08973	−	0.897256i
$474$	−446.022			−0.940975
$475$			47.5428i			0.100090i
$476$	12.5334			0.0263307
$477$	230.745			0.483743
$478$	898.012			1.87869
$479$			715.033i			1.49276i	0.665519	+	0.746381i	$0.268210\pi$
$479$			715.033i			1.49276i	−0.665519	+	0.746381i	$0.731790\pi$
$480$			114.861i			0.239293i
$481$			252.175i			0.524272i
$482$	−13.3362			−0.0276685
$483$			24.3010i			0.0503127i
$484$	153.916	+	786.993i	0.318008	+	1.62602i
$485$	−118.878			−0.245110
$486$		−	50.8176i		−	0.104563i
$487$	−742.123			−1.52387			−0.761933	−	0.647655i	$-0.775750\pi$
$487$	−742.123			−1.52387			−0.761933	+	0.647655i	$0.775750\pi$
$488$	−1004.34			−2.05808
$489$	−530.430			−1.08472
$490$			51.0263i			0.104135i
$491$		−	339.593i		−	0.691635i	−0.938302	−	0.345818i	$-0.887602\pi$
$491$		−	339.593i		−	0.691635i	0.938302	−	0.345818i	$-0.112398\pi$
$492$		−	393.556i		−	0.799910i
$493$	13.0470			0.0264646
$494$			367.023i			0.742962i
$495$	−46.9036	+	56.9654i	−0.0947548	+	0.115082i
$496$	21.3510			0.0430463
$497$			307.603i			0.618920i
$498$	283.100			0.568473
$499$	587.144			1.17664			0.588320	−	0.808628i	$-0.299789\pi$
$499$	587.144			1.17664			0.588320	+	0.808628i	$0.299789\pi$
$500$	−74.0954			−0.148191
$501$			489.966i			0.977977i
$502$			32.0239i			0.0637927i
$503$			349.582i			0.694993i	0.937681	+	0.347497i	$0.112968\pi$
$503$			349.582i			0.694993i	−0.937681	+	0.347497i	$0.887032\pi$
$504$	−67.9814			−0.134884
$505$		−	80.6032i		−	0.159610i
$506$	146.802	+	120.872i	0.290122	+	0.238878i
$507$	49.8909			0.0984041
$508$			30.1057i			0.0592631i
$509$	202.587			0.398010			0.199005	−	0.979998i	$-0.436229\pi$
$509$	202.587			0.398010			0.199005	+	0.979998i	$0.436229\pi$
$510$	9.02487			0.0176958
$511$	−151.250			−0.295988
$512$			90.2402i			0.176250i
$513$			49.4080i			0.0963118i
$514$			337.314i			0.656254i
$515$	3.32275			0.00645194
$516$		−	696.746i		−	1.35028i
$517$	−485.598	+	589.768i	−0.939260	+	1.14075i
$518$	183.694			0.354622
$519$			356.129i			0.686182i
$520$	−226.763			−0.436083
$521$	−288.271			−0.553304			−0.276652	−	0.960970i	$-0.589225\pi$
$521$	−288.271			−0.553304			−0.276652	+	0.960970i	$0.589225\pi$
$522$	−178.509			−0.341972
$523$		−	609.078i		−	1.16459i	−0.812979	−	0.582293i	$-0.802156\pi$
$523$		−	609.078i		−	1.16459i	0.812979	−	0.582293i	$-0.197844\pi$
$524$		−	465.223i		−	0.887830i
$525$			22.9129i			0.0436436i
$526$	−1257.73			−2.39113
$527$			10.8097i			0.0205117i
$528$	−17.0982	+	20.7660i	−0.0323829	+	0.0393296i
$529$	−500.879			−0.946841
$530$		−	560.671i		−	1.05787i
$531$	−272.007			−0.512255
$532$	166.725			0.313392
$533$	−405.954			−0.761639
$534$		−	408.180i		−	0.764381i
$535$		−	134.628i		−	0.251640i
$536$		−	551.201i		−	1.02836i
$537$	−585.192			−1.08974
$538$		−	287.075i		−	0.533596i
$539$	48.9438	−	59.4433i	0.0908049	−	0.110284i
$540$	−77.0022			−0.142597
$541$		−	636.893i		−	1.17725i	−0.808406	−	0.588625i	$-0.799669\pi$
$541$		−	636.893i		−	1.17725i	0.808406	−	0.588625i	$-0.200331\pi$
$542$	−830.184			−1.53170
$543$	−98.8873			−0.182113
$544$	−21.1987			−0.0389682
$545$		−	230.196i		−	0.422379i
$546$			176.884i			0.323963i
$547$			196.340i			0.358939i	0.983764	+	0.179469i	$0.0574381\pi$
$547$			196.340i			0.358939i	−0.983764	+	0.179469i	$0.942562\pi$
$548$	−378.562			−0.690807
$549$			351.789i			0.640782i
$550$	138.416	+	113.968i	0.251665	+	0.207214i
$551$	173.557			0.314986
$552$			78.6675i			0.142514i
$553$	208.994			0.377927
$554$	−1052.65			−1.90009
$555$	82.4860			0.148623
$556$			782.607i			1.40757i
$557$		−	72.6355i		−	0.130405i	−0.997872	−	0.0652024i	$-0.979231\pi$
$557$		−	72.6355i		−	0.130405i	0.997872	−	0.0652024i	$-0.0207693\pi$
$558$		−	147.898i		−	0.265050i
$559$	−718.695			−1.28568
$560$			8.35262i			0.0149154i
$561$	−10.5135	−	8.65655i	−0.0187407	−	0.0154306i
$562$	1190.97			2.11916
$563$		−	632.420i		−	1.12330i	−0.827373	−	0.561652i	$-0.810166\pi$
$563$		−	632.420i		−	1.12330i	0.827373	−	0.561652i	$-0.189834\pi$
$564$	−797.211			−1.41349
$565$	−154.045			−0.272646
$566$	98.5669			0.174146
$567$			23.8118i			0.0419961i
$568$			995.776i			1.75313i
$569$		−	190.350i		−	0.334535i	−0.985912	−	0.167267i	$-0.946506\pi$
$569$		−	190.350i		−	0.334535i	0.985912	−	0.167267i	$-0.0534943\pi$
$570$	120.053			0.210619
$571$			561.099i			0.982660i	0.870973	+	0.491330i	$0.163489\pi$
$571$			561.099i			0.982660i	−0.870973	+	0.491330i	$0.836511\pi$
$572$	666.358	+	548.660i	1.16496	+	0.959196i
$573$	110.357			0.192595
$574$			295.713i			0.515179i
$575$	26.5146			0.0461123
$576$	306.982			0.532955
$577$	812.560			1.40825			0.704125	−	0.710076i	$-0.251340\pi$
$577$	812.560			1.40825			0.704125	+	0.710076i	$0.251340\pi$
$578$		−	940.461i		−	1.62709i
$579$		−	285.488i		−	0.493071i
$580$			270.489i			0.466360i
$581$	−132.653			−0.228318
$582$			300.185i			0.515782i
$583$	−537.789	+	653.155i	−0.922451	+	1.12033i
$584$	−489.627			−0.838403
$585$			79.4279i			0.135774i
$586$	541.650			0.924318
$587$	−364.939			−0.621701			−0.310851	−	0.950459i	$-0.600614\pi$
$587$	−364.939			−0.621701			−0.310851	+	0.950459i	$0.600614\pi$
$588$	80.3517			0.136652
$589$			143.795i			0.244134i
$590$			660.931i			1.12022i
$591$		−	596.215i		−	1.00882i
$592$	30.0693			0.0507927
$593$		−	417.866i		−	0.704665i	−0.935875	−	0.352332i	$-0.885389\pi$
$593$		−	417.866i		−	0.704665i	0.935875	−	0.352332i	$-0.114611\pi$
$594$	143.846	+	118.439i	0.242165	+	0.199392i
$595$	−4.22881			−0.00710724
$596$		−	716.131i		−	1.20156i
$597$	258.310			0.432679
$598$	204.688			0.342288
$599$	1132.05			1.88990			0.944952	−	0.327209i	$-0.106108\pi$
$599$	1132.05			1.88990			0.944952	+	0.327209i	$0.106108\pi$
$600$			74.1738i			0.123623i
$601$		−	657.422i		−	1.09388i	−0.837172	−	0.546940i	$-0.815793\pi$
$601$		−	657.422i		−	1.09388i	0.837172	−	0.546940i	$-0.184207\pi$
$602$			523.525i			0.869644i
$603$	−193.068			−0.320180
$604$			105.379i			0.174469i
$605$	−51.9316	−	265.534i	−0.0858373	−	0.438899i
$606$	−203.535			−0.335867
$607$		−	678.467i		−	1.11774i	−0.829256	−	0.558869i	$-0.811236\pi$
$607$		−	678.467i		−	1.11774i	0.829256	−	0.558869i	$-0.188764\pi$
$608$	−281.994			−0.463806
$609$	83.6445			0.137347
$610$	854.786			1.40129
$611$			822.325i			1.34587i
$612$		−	14.2116i		−	0.0232215i
$613$		−	30.6052i		−	0.0499269i	−0.999688	−	0.0249635i	$-0.992053\pi$
$613$		−	30.6052i		−	0.0499269i	0.999688	−	0.0249635i	$-0.00794694\pi$
$614$	−897.334			−1.46146
$615$			132.787i			0.215914i
$616$	158.442	−	192.430i	0.257210	−	0.312387i
$617$	871.930			1.41318			0.706588	−	0.707625i	$-0.250233\pi$
$617$	871.930			1.41318			0.706588	+	0.707625i	$0.250233\pi$
$618$		−	8.39044i		−	0.0135768i
$619$	675.320			1.09099			0.545493	−	0.838115i	$-0.316342\pi$
$619$	675.320			1.09099			0.545493	+	0.838115i	$0.316342\pi$
$620$	−224.104			−0.361459
$621$	27.5548			0.0443716
$622$		−	15.0449i		−	0.0241880i
$623$			191.262i			0.307001i
$624$			28.9545i			0.0464015i
$625$	25.0000			0.0400000
$626$		−	623.314i		−	0.995710i
$627$	−139.856	−	115.153i	−0.223055	−	0.183657i
$628$	381.982			0.608252
$629$			15.2236i			0.0242029i
$630$	57.8584			0.0918388
$631$	435.147			0.689614			0.344807	−	0.938674i	$-0.387944\pi$
$631$	435.147			0.689614			0.344807	+	0.938674i	$0.387944\pi$
$632$	676.557			1.07050
$633$			544.413i			0.860053i
$634$		−	740.519i		−	1.16801i
$635$		−	10.1577i		−	0.0159964i
$636$	−882.894			−1.38820
$637$		−	82.8829i		−	0.130114i
$638$	416.044	−	505.294i	0.652107	−	0.791996i
$639$	348.789			0.545836
$640$		−	480.654i		−	0.751022i
$641$	349.206			0.544784			0.272392	−	0.962186i	$-0.412185\pi$
$641$	349.206			0.544784			0.272392	+	0.962186i	$0.412185\pi$
$642$	−339.955			−0.529524
$643$	−1140.87			−1.77429			−0.887144	−	0.461493i	$-0.847314\pi$
$643$	−1140.87			−1.77429			−0.887144	+	0.461493i	$0.847314\pi$
$644$		−	92.9823i		−	0.144382i
$645$			235.084i			0.364471i
$646$			22.1570i			0.0342987i
$647$	830.684			1.28390			0.641950	−	0.766746i	$-0.278125\pi$
$647$	830.684			1.28390			0.641950	+	0.766746i	$0.278125\pi$
$648$			77.0837i			0.118956i
$649$	633.957	−	769.953i	0.976820	−	1.18637i
$650$	192.996			0.296917
$651$			69.3009i			0.106453i
$652$	2029.57			3.11283
$653$	551.009			0.843812			0.421906	−	0.906640i	$-0.361361\pi$
$653$	551.009			0.843812			0.421906	+	0.906640i	$0.361361\pi$
$654$	−581.280			−0.888808
$655$			156.968i			0.239645i
$656$			48.4059i			0.0737894i
$657$			171.501i			0.261037i
$658$	599.014			0.910355
$659$		−	193.074i		−	0.292980i	−0.989212	−	0.146490i	$-0.953202\pi$
$659$		−	193.074i		−	0.292980i	0.989212	−	0.146490i	$-0.0467976\pi$
$660$	179.466	−	217.965i	0.271918	−	0.330250i
$661$	−1047.86			−1.58527			−0.792634	−	0.609698i	$-0.791291\pi$
$661$	−1047.86			−1.58527			−0.792634	+	0.609698i	$0.791291\pi$
$662$			701.934i			1.06032i
$663$	−14.6593			−0.0221105
$664$	−429.425			−0.646725
$665$	−56.2534			−0.0845916
$666$		−	208.289i		−	0.312747i
$667$		−	96.7928i		−	0.145117i
$668$		−	1874.74i		−	2.80650i
$669$	−640.321			−0.957131
$670$			469.123i			0.700183i
$671$	−995.786	−	819.901i	−1.48403	−	1.22191i
$672$	−135.905			−0.202239
$673$			164.660i			0.244666i	0.992489	+	0.122333i	$0.0390376\pi$
$673$			164.660i			0.244666i	−0.992489	+	0.122333i	$0.960962\pi$
$674$	−33.4721			−0.0496619
$675$	25.9808			0.0384900
$676$	−190.896			−0.282391
$677$		−	1335.05i		−	1.97201i	−0.166727	−	0.986003i	$-0.553320\pi$
$677$		−	1335.05i		−	1.97201i	0.166727	−	0.986003i	$-0.446680\pi$
$678$			388.986i			0.573726i
$679$		−	140.658i		−	0.207155i
$680$	−13.6896			−0.0201317
$681$		−	267.166i		−	0.392314i
$682$	418.644	+	344.699i	0.613848	+	0.505424i
$683$	−226.154			−0.331118			−0.165559	−	0.986200i	$-0.552943\pi$
$683$	−226.154			−0.331118			−0.165559	+	0.986200i	$0.552943\pi$
$684$		−	189.048i		−	0.276386i
$685$	127.728			0.186464
$686$	−60.3752			−0.0880105
$687$	228.464			0.332553
$688$			85.6971i			0.124560i
$689$			910.707i			1.32178i
$690$		−	66.9533i		−	0.0970338i
$691$	−514.860			−0.745094			−0.372547	−	0.928013i	$-0.621516\pi$
$691$	−514.860			−0.745094			−0.372547	+	0.928013i	$0.621516\pi$
$692$		−	1362.64i		−	1.96914i
$693$	−67.4023	−	55.4971i	−0.0972616	−	0.0800824i
$694$	292.404			0.421332
$695$		−	264.054i		−	0.379934i
$696$	270.775			0.389045
$697$	−24.5072			−0.0351610
$698$	1374.04			1.96854
$699$			113.281i			0.162062i
$700$		−	87.6709i		−	0.125244i
$701$		−	1123.33i		−	1.60247i	−0.598350	−	0.801235i	$-0.704177\pi$
$701$		−	1123.33i		−	1.60247i	0.598350	−	0.801235i	$-0.295823\pi$
$702$	200.567			0.285708
$703$			202.511i			0.288067i
$704$	−715.471	+	868.953i	−1.01629	+	1.23431i
$705$	268.981			0.381534
$706$		−	291.769i		−	0.413270i
$707$	95.3710			0.134895
$708$	1040.77			1.47002
$709$	−849.866			−1.19868			−0.599341	−	0.800494i	$-0.704571\pi$
$709$	−849.866			−1.19868			−0.599341	+	0.800494i	$0.704571\pi$
$710$		−	847.497i		−	1.19366i
$711$		−	236.977i		−	0.333301i
$712$			619.155i			0.869599i
$713$	80.1944			0.112475
$714$			10.6784i			0.0149557i
$715$	−224.831	−	185.119i	−0.314449	−	0.258908i
$716$	2239.10			3.12724
$717$			477.124i			0.665445i
$718$	791.126			1.10185
$719$	171.596			0.238659			0.119330	−	0.992855i	$-0.461925\pi$
$719$	171.596			0.238659			0.119330	+	0.992855i	$0.461925\pi$
$720$	9.47098			0.0131541
$721$			3.93153i			0.00545289i
$722$		−	882.102i		−	1.22175i
$723$		−	7.08568i		−	0.00980039i
$724$	378.370			0.522610
$725$		−	91.2637i		−	0.125881i
$726$	−670.512	+	131.135i	−0.923570	+	0.180627i
$727$	550.052			0.756605			0.378303	−	0.925682i	$-0.376508\pi$
$727$	550.052			0.756605			0.378303	+	0.925682i	$0.376508\pi$
$728$		−	268.310i		−	0.368557i
$729$	27.0000			0.0370370
$730$	416.718			0.570846
$731$	−43.3872			−0.0593532
$732$		−	1346.04i		−	1.83885i
$733$		−	719.483i		−	0.981559i	−0.871284	−	0.490780i	$-0.836712\pi$
$733$		−	719.483i		−	0.981559i	0.871284	−	0.490780i	$-0.163288\pi$
$734$		−	492.488i		−	0.670964i
$735$	−27.1109			−0.0368856
$736$			157.268i			0.213679i
$737$	449.977	−	546.506i	0.610552	−	0.741527i
$738$	335.306			0.454345
$739$			784.036i			1.06094i	0.847703	+	0.530471i	$0.177985\pi$
$739$			784.036i			1.06094i	−0.847703	+	0.530471i	$0.822015\pi$
$740$	−315.614			−0.426505
$741$	−195.004			−0.263163
$742$	663.395			0.894063
$743$		−	1364.56i		−	1.83655i	−0.395940	−	0.918276i	$-0.629581\pi$
$743$		−	1364.56i		−	1.83655i	0.395940	−	0.918276i	$-0.370419\pi$
$744$			224.342i			0.301534i
$745$			241.625i			0.324328i
$746$	1111.60			1.49008
$747$			150.414i			0.201358i
$748$	40.2277	+	33.1223i	0.0537803	+	0.0442811i
$749$	159.293			0.212675
$750$		−	63.1287i		−	0.0841716i
$751$	−561.098			−0.747134			−0.373567	−	0.927603i	$-0.621865\pi$
$751$	−561.098			−0.747134			−0.373567	+	0.927603i	$0.621865\pi$
$752$	98.0539			0.130391
$753$	−17.0147			−0.0225958
$754$		−	704.541i		−	0.934404i
$755$		−	35.5552i		−	0.0470930i
$756$		−	91.1102i		−	0.120516i
$757$	1015.88			1.34199			0.670993	−	0.741463i	$-0.265868\pi$
$757$	1015.88			1.34199			0.670993	+	0.741463i	$0.265868\pi$
$758$		−	594.173i		−	0.783870i
$759$	−64.2208	+	77.9974i	−0.0846124	+	0.102763i
$760$	−182.104			−0.239611
$761$			380.426i			0.499903i	0.968258	+	0.249951i	$0.0804146\pi$
$761$			380.426i			0.499903i	−0.968258	+	0.249951i	$0.919585\pi$
$762$	−25.6498			−0.0336611
$763$	272.372			0.356975
$764$	−422.254			−0.552689
$765$			4.79502i			0.00626800i
$766$		−	2240.71i		−	2.92521i
$767$		−	1073.56i		−	1.39969i
$768$	−504.778			−0.657263
$769$		−	258.509i		−	0.336163i	−0.985773	−	0.168081i	$-0.946243\pi$
$769$		−	258.509i		−	0.336163i	0.985773	−	0.168081i	$-0.0537572\pi$
$770$	−134.848	+	163.776i	−0.175128	+	0.212696i
$771$	−179.219			−0.232450
$772$			1092.35i			1.41497i
$773$	−934.303			−1.20867			−0.604336	−	0.796730i	$-0.706562\pi$
$773$	−934.303			−1.20867			−0.604336	+	0.796730i	$0.706562\pi$
$774$	593.622			0.766954
$775$	75.6134			0.0975657
$776$		−	455.341i		−	0.586780i
$777$			97.5987i			0.125610i
$778$			1363.97i			1.75318i
$779$	−326.005			−0.418492
$780$		−	303.913i		−	0.389632i
$781$	−812.909	+	987.293i	−1.04086	+	1.26414i
$782$	12.3569			0.0158017
$783$		−	94.8440i		−	0.121129i
$784$	−9.88295			−0.0126058
$785$	−128.882			−0.164181
$786$	396.367			0.504283
$787$			602.118i			0.765080i	0.923939	+	0.382540i	$0.124951\pi$
$787$			602.118i			0.765080i	−0.923939	+	0.382540i	$0.875049\pi$
$788$			2281.28i			2.89503i
$789$		−	668.248i		−	0.846956i
$790$	−575.812			−0.728876
$791$		−	182.268i		−	0.230428i
$792$	−218.196	−	179.656i	−0.275499	−	0.226838i
$793$	−1388.44			−1.75087
$794$		−	46.4138i		−	0.0584557i
$795$	297.891			0.374706
$796$	−988.362			−1.24166
$797$	−39.9447			−0.0501189			−0.0250594	−	0.999686i	$-0.507978\pi$
$797$	−39.9447			−0.0501189			−0.0250594	+	0.999686i	$0.507978\pi$
$798$			142.048i			0.178005i
$799$			49.6433i			0.0621318i
$800$			148.284i			0.185355i
$801$	216.870			0.270750
$802$		−	2329.83i		−	2.90503i
$803$	−485.456	−	399.711i	−0.604553	−	0.497772i
$804$	738.732			0.918821
$805$			31.3725i			0.0389720i
$806$	583.724			0.724223
$807$	152.526			0.189004
$808$	308.736			0.382099
$809$		−	538.906i		−	0.666139i	−0.942902	−	0.333069i	$-0.891916\pi$
$809$		−	538.906i		−	0.666139i	0.942902	−	0.333069i	$-0.108084\pi$
$810$		−	65.6053i		−	0.0809942i
$811$		−	747.119i		−	0.921232i	−0.887599	−	0.460616i	$-0.847628\pi$
$811$		−	747.119i		−	0.921232i	0.887599	−	0.460616i	$-0.152372\pi$
$812$	−320.047			−0.394146
$813$		−	441.086i		−	0.542541i
$814$	589.590	+	485.452i	0.724313	+	0.596378i
$815$	−684.782			−0.840224
$816$			1.74797i			0.00214212i
$817$	−577.155			−0.706432
$818$	−843.499			−1.03117
$819$	−93.9804			−0.114750
$820$		−	508.078i		−	0.619608i
$821$		−	477.472i		−	0.581574i	−0.956788	−	0.290787i	$-0.906083\pi$
$821$		−	477.472i		−	0.581574i	0.956788	−	0.290787i	$-0.0939171\pi$
$822$		−	322.532i		−	0.392375i
$823$	−150.719			−0.183134			−0.0915668	−	0.995799i	$-0.529187\pi$
$823$	−150.719			−0.183134			−0.0915668	+	0.995799i	$0.529187\pi$
$824$			12.7272i			0.0154456i
$825$	−60.5523	+	73.5420i	−0.0733967	+	0.0891418i
$826$	−782.024			−0.946760
$827$		−	1258.20i		−	1.52140i	−0.649103	−	0.760701i	$-0.724856\pi$
$827$		−	1258.20i		−	1.52140i	0.649103	−	0.760701i	$-0.275144\pi$
$828$	−105.432			−0.127333
$829$	−305.944			−0.369051			−0.184526	−	0.982828i	$-0.559075\pi$
$829$	−305.944			−0.369051			−0.184526	+	0.982828i	$0.559075\pi$
$830$	365.480			0.440338
$831$		−	559.285i		−	0.673026i
$832$			1211.60i			1.45625i
$833$		−	5.00360i		−	0.00600672i
$834$	−666.775			−0.799491
$835$			632.544i			0.757538i
$836$	535.126	+	440.607i	0.640102	+	0.527042i
$837$	78.5798			0.0938827
$838$		−	2036.70i		−	2.43043i
$839$	925.604			1.10322			0.551611	−	0.834101i	$-0.314013\pi$
$839$	925.604			1.10322			0.551611	+	0.834101i	$0.314013\pi$
$840$	−87.7637			−0.104481
$841$	507.838			0.603850
$842$			1790.41i			2.12638i
$843$			632.775i			0.750623i
$844$		−	2083.07i		−	2.46810i
$845$	64.4089			0.0762235
$846$		−	679.218i		−	0.802858i
$847$	314.184	−	61.4463i	0.370937	−	0.0725458i
$848$	108.593			0.128057
$849$			52.3697i			0.0616840i
$850$	11.6511			0.0137071
$851$	112.940			0.132715
$852$	−1334.56			−1.56639
$853$		−	1249.50i		−	1.46483i	−0.680858	−	0.732415i	$-0.738393\pi$
$853$		−	1249.50i		−	1.46483i	0.680858	−	0.732415i	$-0.261607\pi$
$854$			1011.40i			1.18431i
$855$			63.7854i			0.0746028i
$856$	515.667			0.602414
$857$			1327.44i			1.54894i	0.632612	+	0.774469i	$0.281983\pi$
$857$			1327.44i			1.54894i	−0.632612	+	0.774469i	$0.718017\pi$
$858$	−467.454	+	567.732i	−0.544818	+	0.661693i
$859$	589.495			0.686258			0.343129	−	0.939288i	$-0.388513\pi$
$859$	589.495			0.686258			0.343129	+	0.939288i	$0.388513\pi$
$860$		−	899.495i		−	1.04592i
$861$	−157.115			−0.182480
$862$	1302.39			1.51090
$863$	456.664			0.529159			0.264579	−	0.964364i	$-0.414767\pi$
$863$	456.664			0.529159			0.264579	+	0.964364i	$0.414767\pi$
$864$			154.102i			0.178358i
$865$			459.760i			0.531515i
$866$		−	753.785i		−	0.870422i
$867$	499.678			0.576330
$868$		−	265.164i		−	0.305488i
$869$	670.794	+	552.312i	0.771914	+	0.635572i
$870$	−230.454			−0.264890
$871$		−	762.004i		−	0.874861i
$872$	881.726			1.01115
$873$	−159.492			−0.182694
$874$	164.377			0.188074
$875$			29.5804i			0.0338062i
$876$		−	656.210i		−	0.749098i
$877$			50.3291i			0.0573878i	0.999588	+	0.0286939i	$0.00913481\pi$
$877$			50.3291i			0.0573878i	−0.999588	+	0.0286939i	$0.990865\pi$
$878$	−1006.54			−1.14640
$879$			287.785i			0.327401i
$880$	−22.0736	+	26.8088i	−0.0250837	+	0.0304646i
$881$	192.520			0.218524			0.109262	−	0.994013i	$-0.465151\pi$
$881$	192.520			0.218524			0.109262	+	0.994013i	$0.465151\pi$
$882$			68.4590i			0.0776179i
$883$	−913.532			−1.03458			−0.517289	−	0.855811i	$-0.673059\pi$
$883$	−913.532			−1.03458			−0.517289	+	0.855811i	$0.673059\pi$
$884$	56.0903			0.0634505
$885$	−351.160			−0.396791
$886$		−	539.496i		−	0.608912i
$887$			1484.18i			1.67326i	0.547771	+	0.836628i	$0.315476\pi$
$887$			1484.18i			1.67326i	−0.547771	+	0.836628i	$0.684524\pi$
$888$			315.948i			0.355797i
$889$	12.0188			0.0135195
$890$		−	526.957i		−	0.592087i
$891$	−62.9278	+	76.4270i	−0.0706260	+	0.0857767i
$892$	2450.04			2.74668
$893$			660.376i			0.739503i
$894$	610.138			0.682481
$895$	−755.480			−0.844111
$896$	568.717			0.634729
$897$			108.753i			0.121241i
$898$			1911.85i			2.12901i
$899$		−	276.030i		−	0.307042i
$900$	−99.4094			−0.110455
$901$			54.9789i			0.0610199i
$902$	−781.485	+	949.129i	−0.866391	+	1.05225i
$903$	−278.155			−0.308034
$904$		−	590.041i		−	0.652701i
$905$	−127.663			−0.141064
$906$	−89.7822			−0.0990973
$907$	−932.895			−1.02855			−0.514275	−	0.857625i	$-0.671939\pi$
$907$	−932.895			−1.02855			−0.514275	+	0.857625i	$0.671939\pi$
$908$			1022.25i			1.12582i
$909$		−	108.141i		−	0.118967i
$910$			228.356i			0.250941i
$911$	502.091			0.551142			0.275571	−	0.961281i	$-0.411133\pi$
$911$	502.091			0.551142			0.275571	+	0.961281i	$0.411133\pi$
$912$			23.2522i			0.0254958i
$913$	−425.767	−	350.564i	−0.466338	−	0.383969i
$914$	1132.36			1.23891
$915$			454.158i			0.496347i
$916$	−874.165			−0.954329
$917$	−185.727			−0.202537
$918$	12.1081			0.0131897
$919$			532.086i			0.578984i	0.957180	+	0.289492i	$0.0934864\pi$
$919$			532.086i			0.578984i	−0.957180	+	0.289492i	$0.906514\pi$
$920$			101.559i			0.110391i
$921$		−	476.764i		−	0.517659i
$922$	−578.322			−0.627247
$923$			1376.60i			1.49144i
$924$	257.899	+	212.347i	0.279112	+	0.229813i
$925$	106.489			0.115123
$926$			1729.09i			1.86727i
$927$	4.45794			0.00480899
$928$	541.319			0.583318
$929$	1099.03			1.18302			0.591510	−	0.806298i	$-0.298532\pi$
$929$	1099.03			1.18302			0.591510	+	0.806298i	$0.298532\pi$
$930$		−	190.935i		−	0.205307i
$931$		−	66.5600i		−	0.0714930i
$932$		−	433.444i		−	0.465068i
$933$	7.99355			0.00856758
$934$			1834.12i			1.96373i
$935$	−13.5729	−	11.1756i	−0.0145165	−	0.0119525i
$936$	−304.234			−0.325037
$937$		−	1167.21i		−	1.24568i	−0.782348	−	0.622842i	$-0.785978\pi$
$937$		−	1167.21i		−	1.24568i	0.782348	−	0.622842i	$-0.214022\pi$
$938$	−555.073			−0.591763
$939$	331.174			0.352688
$940$	−1029.20			−1.09489
$941$			1057.61i			1.12392i	0.827166	+	0.561958i	$0.189952\pi$
$941$			1057.61i			1.12392i	−0.827166	+	0.561958i	$0.810048\pi$
$942$			325.446i			0.345484i
$943$			181.813i			0.192802i
$944$	−128.011			−0.135605
$945$			30.7409i			0.0325300i
$946$	−1383.53	+	1680.33i	−1.46251	+	1.77624i
$947$	59.2468			0.0625626			0.0312813	−	0.999511i	$-0.490041\pi$
$947$	59.2468			0.0625626			0.0312813	+	0.999511i	$0.490041\pi$
$948$			906.737i			0.956473i
$949$	−676.882			−0.713258
$950$	154.987			0.163145
$951$	393.446			0.413718
$952$		−	16.1977i		−	0.0170144i
$953$		−	231.973i		−	0.243414i	−0.992566	−	0.121707i	$-0.961163\pi$
$953$		−	231.973i		−	0.243414i	0.992566	−	0.121707i	$-0.0388368\pi$
$954$		−	752.219i		−	0.788490i
$955$	142.470			0.149183
$956$		−	1825.61i		−	1.90963i
$957$	268.468	+	221.049i	0.280531	+	0.230981i
$958$	2330.97			2.43317
$959$			151.130i			0.157591i
$960$	396.312			0.412825
$961$	−732.304			−0.762023
$962$	822.078			0.854551
$963$		−	180.622i		−	0.187562i
$964$			27.1117i			0.0281242i
$965$		−	368.563i		−	0.381931i
$966$	79.2202			0.0820085
$967$		−	90.1447i		−	0.0932210i	−0.998913	−	0.0466105i	$-0.985158\pi$
$967$		−	90.1447i		−	0.0932210i	0.998913	−	0.0466105i	$-0.0148420\pi$
$968$	1017.08	−	198.915i	1.05070	−	0.205490i
$969$	−11.7723			−0.0121489
$970$			387.537i			0.399523i
$971$	−276.170			−0.284418			−0.142209	−	0.989837i	$-0.545421\pi$
$971$	−276.170			−0.284418			−0.142209	+	0.989837i	$0.545421\pi$
$972$	−103.309			−0.106285
$973$	312.433			0.321103
$974$			2419.29i			2.48387i
$975$			102.541i			0.105170i
$976$			165.558i			0.169629i
$977$	−101.200			−0.103582			−0.0517911	−	0.998658i	$-0.516493\pi$
$977$	−101.200			−0.103582			−0.0517911	+	0.998658i	$0.516493\pi$
$978$			1729.18i			1.76807i
$979$	−505.451	+	613.880i	−0.516293	+	0.627048i
$980$	103.734			0.105851
$981$		−	308.841i		−	0.314823i
$982$	−1107.06			−1.12735
$983$	−1714.69			−1.74435			−0.872173	−	0.489198i	$-0.837290\pi$
$983$	−1714.69			−1.74435			−0.872173	+	0.489198i	$0.837290\pi$
$984$	−508.616			−0.516886
$985$		−	769.711i		−	0.781432i
$986$		−	42.5327i		−	0.0431367i
$987$			318.263i			0.322455i
$988$	746.136			0.755199
$989$			321.879i			0.325459i
$990$	185.704	+	152.904i	0.187580	+	0.154448i
$991$	345.608			0.348746			0.174373	−	0.984680i	$-0.444210\pi$
$991$	345.608			0.348746			0.174373	+	0.984680i	$0.444210\pi$
$992$			448.491i			0.452108i
$993$	−372.946			−0.375575
$994$	1002.77			1.00882
$995$	333.476			0.335152
$996$		−	575.525i		−	0.577837i
$997$		−	1286.97i		−	1.29085i	−0.763825	−	0.645424i	$-0.776681\pi$
$997$		−	1286.97i		−	1.29085i	0.763825	−	0.645424i	$-0.223319\pi$
$998$		−	1914.06i		−	1.91790i
$999$	110.667			0.110777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.13	✓	96
11.10	odd	2	inner	1155.3.b.a.736.84	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.13	✓	96	1.1	even	1	trivial
1155.3.b.a.736.84	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)

\(f(q)\)	\(=\)	\(q-3.25995i q^{2} +1.73205 q^{3} -6.62729 q^{4} +2.23607 q^{5} -5.64640i q^{6} +2.64575i q^{7} +8.56486i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.25995i q^{2} +1.73205 q^{3} -6.62729 q^{4} +2.23607 q^{5} -5.64640i q^{6} +2.64575i q^{7} +8.56486i q^{8} +3.00000 q^{9} -7.28948i q^{10} +(-6.99198 + 8.49189i) q^{11} -11.4788 q^{12} +11.8404i q^{13} +8.62503 q^{14} +3.87298 q^{15} +1.41185 q^{16} +0.714799i q^{17} -9.77986i q^{18} +9.50856i q^{19} -14.8191 q^{20} +4.58258i q^{21} +(27.6832 + 22.7935i) q^{22} +5.30292 q^{23} +14.8348i q^{24} +5.00000 q^{25} +38.5992 q^{26} +5.19615 q^{27} -17.5342i q^{28} -18.2527i q^{29} -12.6257i q^{30} +15.1227 q^{31} +29.6569i q^{32} +(-12.1105 + 14.7084i) q^{33} +2.33021 q^{34} +5.91608i q^{35} -19.8819 q^{36} +21.2978 q^{37} +30.9975 q^{38} +20.5082i q^{39} +19.1516i q^{40} +34.2854i q^{41} +14.9390 q^{42} +60.6984i q^{43} +(46.3379 - 56.2783i) q^{44} +6.70820 q^{45} -17.2873i q^{46} +69.4507 q^{47} +2.44540 q^{48} -7.00000 q^{49} -16.2998i q^{50} +1.23807i q^{51} -78.4699i q^{52} +76.9151 q^{53} -16.9392i q^{54} +(-15.6345 + 18.9885i) q^{55} -22.6605 q^{56} +16.4693i q^{57} -59.5031 q^{58} -90.6691 q^{59} -25.6674 q^{60} +117.263i q^{61} -49.2993i q^{62} +7.93725i q^{63} +102.327 q^{64} +26.4760i q^{65} +(47.9487 + 39.4795i) q^{66} -64.3561 q^{67} -4.73719i q^{68} +9.18492 q^{69} +19.2861 q^{70} +116.263 q^{71} +25.6946i q^{72} +57.1670i q^{73} -69.4298i q^{74} +8.66025 q^{75} -63.0161i q^{76} +(-22.4674 - 18.4990i) q^{77} +66.8558 q^{78} -78.9922i q^{79} +3.15699 q^{80} +9.00000 q^{81} +111.769 q^{82} +50.1381i q^{83} -30.3701i q^{84} +1.59834i q^{85} +197.874 q^{86} -31.6147i q^{87} +(-72.7318 - 59.8853i) q^{88} +72.2902 q^{89} -21.8684i q^{90} -31.3268 q^{91} -35.1440 q^{92} +26.1933 q^{93} -226.406i q^{94} +21.2618i q^{95} +51.3672i q^{96} -53.1639 q^{97} +22.8197i q^{98} +(-20.9759 + 25.4757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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