LMFDB - Embedded newform 1155.3.b.a.736.16

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			736.16
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.81

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.91962i q^{2} -1.73205 q^{3} -4.52416 q^{4} +2.23607 q^{5} +5.05692i q^{6} +2.64575i q^{7} +1.53034i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.91962i q^{2} -1.73205 q^{3} -4.52416 q^{4} +2.23607 q^{5} +5.05692i q^{6} +2.64575i q^{7} +1.53034i q^{8} +3.00000 q^{9} -6.52846i q^{10} +(-0.774844 + 10.9727i) q^{11} +7.83607 q^{12} +2.60942i q^{13} +7.72458 q^{14} -3.87298 q^{15} -13.6286 q^{16} -6.81516i q^{17} -8.75885i q^{18} +3.44386i q^{19} -10.1163 q^{20} -4.58258i q^{21} +(32.0360 + 2.26225i) q^{22} +14.0821 q^{23} -2.65064i q^{24} +5.00000 q^{25} +7.61851 q^{26} -5.19615 q^{27} -11.9698i q^{28} -52.0411i q^{29} +11.3076i q^{30} -5.37851 q^{31} +45.9117i q^{32} +(1.34207 - 19.0052i) q^{33} -19.8977 q^{34} +5.91608i q^{35} -13.5725 q^{36} -12.4838 q^{37} +10.0548 q^{38} -4.51965i q^{39} +3.42196i q^{40} -65.7729i q^{41} -13.3794 q^{42} -49.2857i q^{43} +(3.50552 - 49.6421i) q^{44} +6.70820 q^{45} -41.1142i q^{46} +35.8676 q^{47} +23.6055 q^{48} -7.00000 q^{49} -14.5981i q^{50} +11.8042i q^{51} -11.8054i q^{52} +7.83995 q^{53} +15.1708i q^{54} +(-1.73260 + 24.5356i) q^{55} -4.04891 q^{56} -5.96495i q^{57} -151.940 q^{58} +23.7025 q^{59} +17.5220 q^{60} -115.788i q^{61} +15.7032i q^{62} +7.93725i q^{63} +79.5301 q^{64} +5.83484i q^{65} +(-55.4880 - 3.91833i) q^{66} +5.69186 q^{67} +30.8329i q^{68} -24.3908 q^{69} +17.2727 q^{70} -44.2393 q^{71} +4.59103i q^{72} -22.2181i q^{73} +36.4479i q^{74} -8.66025 q^{75} -15.5806i q^{76} +(-29.0310 - 2.05004i) q^{77} -13.1956 q^{78} -57.5444i q^{79} -30.4745 q^{80} +9.00000 q^{81} -192.032 q^{82} -74.5765i q^{83} +20.7323i q^{84} -15.2392i q^{85} -143.895 q^{86} +90.1378i q^{87} +(-16.7920 - 1.18578i) q^{88} -126.763 q^{89} -19.5854i q^{90} -6.90388 q^{91} -63.7094 q^{92} +9.31585 q^{93} -104.720i q^{94} +7.70071i q^{95} -79.5214i q^{96} -89.2227 q^{97} +20.4373i q^{98} +(-2.32453 + 32.9180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) $ 96 * q - 216 * q^4 + 288 * q^9	$ 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) $ 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.91962i		−	1.45981i	−0.683550	−	0.729904i	$-0.739565\pi$
$2$		−	2.91962i		−	1.45981i	0.683550	−	0.729904i	$-0.260435\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−4.52416			−1.13104
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$			5.05692i			0.842821i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			1.53034i			0.191293i
$9$	3.00000			0.333333
$10$		−	6.52846i		−	0.652846i
$11$	−0.774844	+	10.9727i	−0.0704404	+	0.997516i
$11$	−0.774844	+	10.9727i	−0.0704404	+	0.997516i
$12$	7.83607			0.653006
$13$			2.60942i			0.200725i	0.994951	+	0.100362i	$0.0320002\pi$
$13$			2.60942i			0.200725i	−0.994951	+	0.100362i	$0.968000\pi$
$14$	7.72458			0.551756
$15$	−3.87298			−0.258199
$16$	−13.6286			−0.851789
$17$		−	6.81516i		−	0.400892i	−0.979705	−	0.200446i	$-0.935761\pi$
$17$		−	6.81516i		−	0.400892i	0.979705	−	0.200446i	$-0.0642391\pi$
$18$		−	8.75885i		−	0.486603i
$19$			3.44386i			0.181256i	0.995885	+	0.0906280i	$0.0288874\pi$
$19$			3.44386i			0.181256i	−0.995885	+	0.0906280i	$0.971113\pi$
$20$	−10.1163			−0.505816
$21$		−	4.58258i		−	0.218218i
$22$	32.0360	+	2.26225i	1.45618	+	0.102829i
$23$	14.0821			0.612263			0.306132	−	0.951989i	$-0.400965\pi$
$23$	14.0821			0.612263			0.306132	+	0.951989i	$0.400965\pi$
$24$		−	2.65064i		−	0.110443i
$25$	5.00000			0.200000
$26$	7.61851			0.293019
$27$	−5.19615			−0.192450
$28$		−	11.9698i		−	0.427493i
$29$		−	52.0411i		−	1.79452i	−0.441503	−	0.897260i	$-0.645555\pi$
$29$		−	52.0411i		−	1.79452i	0.441503	−	0.897260i	$-0.354445\pi$
$30$			11.3076i			0.376921i
$31$	−5.37851			−0.173500			−0.0867501	−	0.996230i	$-0.527648\pi$
$31$	−5.37851			−0.173500			−0.0867501	+	0.996230i	$0.527648\pi$
$32$			45.9117i			1.43474i
$33$	1.34207	−	19.0052i	0.0406688	−	0.575916i
$34$	−19.8977			−0.585225
$35$			5.91608i			0.169031i
$36$	−13.5725			−0.377013
$37$	−12.4838			−0.337400			−0.168700	−	0.985667i	$-0.553957\pi$
$37$	−12.4838			−0.337400			−0.168700	+	0.985667i	$0.553957\pi$
$38$	10.0548			0.264599
$39$		−	4.51965i		−	0.115888i
$40$			3.42196i			0.0855489i
$41$		−	65.7729i		−	1.60422i	−0.597179	−	0.802108i	$-0.703712\pi$
$41$		−	65.7729i		−	1.60422i	0.597179	−	0.802108i	$-0.296288\pi$
$42$	−13.3794			−0.318556
$43$		−	49.2857i		−	1.14618i	−0.819493	−	0.573089i	$-0.805745\pi$
$43$		−	49.2857i		−	1.14618i	0.819493	−	0.573089i	$-0.194255\pi$
$44$	3.50552	−	49.6421i	0.0796709	−	1.12823i
$45$	6.70820			0.149071
$46$		−	41.1142i		−	0.893787i
$47$	35.8676			0.763140			0.381570	−	0.924340i	$-0.375384\pi$
$47$	35.8676			0.763140			0.381570	+	0.924340i	$0.375384\pi$
$48$	23.6055			0.491780
$49$	−7.00000			−0.142857
$50$		−	14.5981i		−	0.291962i
$51$			11.8042i			0.231455i
$52$		−	11.8054i		−	0.227028i
$53$	7.83995			0.147924			0.0739618	−	0.997261i	$-0.476436\pi$
$53$	7.83995			0.147924			0.0739618	+	0.997261i	$0.476436\pi$
$54$			15.1708i			0.280940i
$55$	−1.73260	+	24.5356i	−0.0315019	+	0.446103i
$56$	−4.04891			−0.0723020
$57$		−	5.96495i		−	0.104648i
$58$	−151.940			−2.61965
$59$	23.7025			0.401737			0.200869	−	0.979618i	$-0.435624\pi$
$59$	23.7025			0.401737			0.200869	+	0.979618i	$0.435624\pi$
$60$	17.5220			0.292033
$61$		−	115.788i		−	1.89816i	−0.315031	−	0.949081i	$-0.602015\pi$
$61$		−	115.788i		−	1.89816i	0.315031	−	0.949081i	$-0.397985\pi$
$62$			15.7032i			0.253277i
$63$			7.93725i			0.125988i
$64$	79.5301			1.24266
$65$			5.83484i			0.0897668i
$66$	−55.4880	−	3.91833i	−0.840727	−	0.0593686i
$67$	5.69186			0.0849532			0.0424766	−	0.999097i	$-0.486475\pi$
$67$	5.69186			0.0849532			0.0424766	+	0.999097i	$0.486475\pi$
$68$			30.8329i			0.453425i
$69$	−24.3908			−0.353490
$70$	17.2727			0.246753
$71$	−44.2393			−0.623088			−0.311544	−	0.950232i	$-0.600846\pi$
$71$	−44.2393			−0.623088			−0.311544	+	0.950232i	$0.600846\pi$
$72$			4.59103i			0.0637644i
$73$		−	22.2181i		−	0.304358i	−0.988353	−	0.152179i	$-0.951371\pi$
$73$		−	22.2181i		−	0.304358i	0.988353	−	0.152179i	$-0.0486290\pi$
$74$			36.4479i			0.492540i
$75$	−8.66025			−0.115470
$76$		−	15.5806i		−	0.205008i
$77$	−29.0310	−	2.05004i	−0.377026	−	0.0266240i
$78$	−13.1956			−0.169175
$79$		−	57.5444i		−	0.728410i	−0.931319	−	0.364205i	$-0.881341\pi$
$79$		−	57.5444i		−	0.728410i	0.931319	−	0.364205i	$-0.118659\pi$
$80$	−30.4745			−0.380931
$81$	9.00000			0.111111
$82$	−192.032			−2.34185
$83$		−	74.5765i		−	0.898512i	−0.893403	−	0.449256i	$-0.851689\pi$
$83$		−	74.5765i		−	0.898512i	0.893403	−	0.449256i	$-0.148311\pi$
$84$			20.7323i			0.246813i
$85$		−	15.2392i		−	0.179284i
$86$	−143.895			−1.67320
$87$			90.1378i			1.03607i
$88$	−16.7920	−	1.18578i	−0.190818	−	0.0134748i
$89$	−126.763			−1.42431			−0.712153	−	0.702024i	$-0.752280\pi$
$89$	−126.763			−1.42431			−0.712153	+	0.702024i	$0.752280\pi$
$90$		−	19.5854i		−	0.217615i
$91$	−6.90388			−0.0758668
$92$	−63.7094			−0.692494
$93$	9.31585			0.100170
$94$		−	104.720i		−	1.11404i
$95$			7.70071i			0.0810601i
$96$		−	79.5214i		−	0.828348i
$97$	−89.2227			−0.919821			−0.459911	−	0.887965i	$-0.652119\pi$
$97$	−89.2227			−0.919821			−0.459911	+	0.887965i	$0.652119\pi$
$98$			20.4373i			0.208544i
$99$	−2.32453	+	32.9180i	−0.0234801	+	0.332505i
$100$	−22.6208			−0.226208
$101$			51.1556i			0.506491i	0.967402	+	0.253246i	$0.0814981\pi$
$101$			51.1556i			0.506491i	−0.967402	+	0.253246i	$0.918502\pi$
$102$	34.4638			0.337880
$103$	13.7786			0.133773			0.0668863	−	0.997761i	$-0.478694\pi$
$103$	13.7786			0.133773			0.0668863	+	0.997761i	$0.478694\pi$
$104$	−3.99331			−0.0383972
$105$		−	10.2470i		−	0.0975900i
$106$		−	22.8896i		−	0.215940i
$107$			103.935i			0.971352i	0.874139	+	0.485676i	$0.161427\pi$
$107$			103.935i			0.971352i	−0.874139	+	0.485676i	$0.838573\pi$
$108$	23.5082			0.217669
$109$			94.6373i			0.868232i	0.900857	+	0.434116i	$0.142939\pi$
$109$			94.6373i			0.868232i	−0.900857	+	0.434116i	$0.857061\pi$
$110$	71.6347	+	5.05854i	0.651224	+	0.0459867i
$111$	21.6226			0.194798
$112$		−	36.0579i		−	0.321946i
$113$	160.059			1.41645			0.708224	−	0.705988i	$-0.249497\pi$
$113$	160.059			1.41645			0.708224	+	0.705988i	$0.249497\pi$
$114$	−17.4154			−0.152766
$115$	31.4884			0.273812
$116$			235.442i			2.02967i
$117$			7.82826i			0.0669082i
$118$		−	69.2022i		−	0.586459i
$119$	18.0312			0.151523
$120$		−	5.92700i		−	0.0493917i
$121$	−119.799	−	17.0042i	−0.990076	−	0.140531i
$122$	−338.056			−2.77095
$123$			113.922i			0.926195i
$124$	24.3332			0.196236
$125$	11.1803			0.0894427
$126$	23.1737			0.183919
$127$		−	17.6131i		−	0.138686i	−0.997593	−	0.0693428i	$-0.977910\pi$
$127$		−	17.6131i		−	0.138686i	0.997593	−	0.0693428i	$-0.0220902\pi$
$128$		−	48.5506i		−	0.379301i
$129$			85.3653i			0.661746i
$130$	17.0355			0.131042
$131$			89.1459i			0.680503i	0.940334	+	0.340252i	$0.110512\pi$
$131$			89.1459i			0.680503i	−0.940334	+	0.340252i	$0.889488\pi$
$132$	−6.07173	+	85.9827i	−0.0459980	+	0.651384i
$133$	−9.11161			−0.0685083
$134$		−	16.6181i		−	0.124015i
$135$	−11.6190			−0.0860663
$136$	10.4296			0.0766879
$137$	19.5103			0.142411			0.0712053	−	0.997462i	$-0.477315\pi$
$137$	19.5103			0.142411			0.0712053	+	0.997462i	$0.477315\pi$
$138$			71.2119i			0.516028i
$139$		−	227.395i		−	1.63593i	−0.575266	−	0.817967i	$-0.695101\pi$
$139$		−	227.395i		−	1.63593i	0.575266	−	0.817967i	$-0.304899\pi$
$140$		−	26.7653i		−	0.191181i
$141$	−62.1244			−0.440599
$142$			129.162i			0.909589i
$143$	−28.6323	−	2.02189i	−0.200226	−	0.0141391i
$144$	−40.8859			−0.283930
$145$		−	116.367i		−	0.802534i
$146$	−64.8684			−0.444304
$147$	12.1244			0.0824786
$148$	56.4787			0.381613
$149$			146.930i			0.986108i	0.869999	+	0.493054i	$0.164120\pi$
$149$			146.930i			0.986108i	−0.869999	+	0.493054i	$0.835880\pi$
$150$			25.2846i			0.168564i
$151$		−	262.366i		−	1.73752i	−0.495230	−	0.868762i	$-0.664916\pi$
$151$		−	262.366i		−	1.73752i	0.495230	−	0.868762i	$-0.335084\pi$
$152$	−5.27030			−0.0346730
$153$		−	20.4455i		−	0.133631i
$154$	−5.98534	+	84.7593i	−0.0388659	+	0.550385i
$155$	−12.0267			−0.0775917
$156$			20.4476i			0.131074i
$157$	−167.492			−1.06683			−0.533413	−	0.845855i	$-0.679091\pi$
$157$	−167.492			−1.06683			−0.533413	+	0.845855i	$0.679091\pi$
$158$	−168.008			−1.06334
$159$	−13.5792			−0.0854037
$160$			102.662i			0.641636i
$161$			37.2576i			0.231414i
$162$		−	26.2765i		−	0.162201i
$163$	123.785			0.759414			0.379707	−	0.925107i	$-0.376025\pi$
$163$	123.785			0.759414			0.379707	+	0.925107i	$0.376025\pi$
$164$			297.567i			1.81443i
$165$	3.00096	−	42.4970i	0.0181876	−	0.257558i
$166$	−217.735			−1.31166
$167$			268.460i			1.60755i	0.594937	+	0.803773i	$0.297177\pi$
$167$			268.460i			1.60755i	−0.594937	+	0.803773i	$0.702823\pi$
$168$	7.01292			0.0417436
$169$	162.191			0.959710
$170$	−44.4925			−0.261721
$171$			10.3316i			0.0604187i
$172$			222.976i			1.29637i
$173$		−	198.528i		−	1.14756i	−0.819010	−	0.573780i	$-0.805477\pi$
$173$		−	198.528i		−	1.14756i	0.819010	−	0.573780i	$-0.194523\pi$
$174$	263.168			1.51246
$175$			13.2288i			0.0755929i
$176$	10.5601	−	149.542i	0.0600003	−	0.849673i
$177$	−41.0539			−0.231943
$178$			370.100i			2.07921i
$179$	78.8478			0.440491			0.220245	−	0.975445i	$-0.429314\pi$
$179$	78.8478			0.440491			0.220245	+	0.975445i	$0.429314\pi$
$180$	−30.3490			−0.168605
$181$	−136.426			−0.753732			−0.376866	−	0.926268i	$-0.622998\pi$
$181$	−136.426			−0.753732			−0.376866	+	0.926268i	$0.622998\pi$
$182$			20.1567i			0.110751i
$183$			200.551i			1.09590i
$184$			21.5504i			0.117122i
$185$	−27.9146			−0.150890
$186$		−	27.1987i		−	0.146230i
$187$	74.7806	+	5.28069i	0.399896	+	0.0282390i
$188$	−162.271			−0.863141
$189$		−	13.7477i		−	0.0727393i
$190$	22.4831			0.118332
$191$	−29.5851			−0.154896			−0.0774480	−	0.996996i	$-0.524677\pi$
$191$	−29.5851			−0.154896			−0.0774480	+	0.996996i	$0.524677\pi$
$192$	−137.750			−0.717449
$193$			153.404i			0.794839i	0.917637	+	0.397420i	$0.130094\pi$
$193$			153.404i			0.794839i	−0.917637	+	0.397420i	$0.869906\pi$
$194$			260.496i			1.34276i
$195$		−	10.1062i		−	0.0518269i
$196$	31.6691			0.161577
$197$		−	150.600i		−	0.764465i	−0.924066	−	0.382232i	$-0.875155\pi$
$197$		−	150.600i		−	0.764465i	0.924066	−	0.382232i	$-0.124845\pi$
$198$	96.1080	+	6.78674i	0.485394	+	0.0342765i
$199$	−44.6275			−0.224259			−0.112129	−	0.993694i	$-0.535767\pi$
$199$	−44.6275			−0.224259			−0.112129	+	0.993694i	$0.535767\pi$
$200$			7.65172i			0.0382586i
$201$	−9.85859			−0.0490477
$202$	149.355			0.739380
$203$	137.688			0.678265
$204$		−	53.4041i		−	0.261785i
$205$		−	147.073i		−	0.717427i
$206$		−	40.2282i		−	0.195282i
$207$	42.2462			0.204088
$208$		−	35.5628i		−	0.170975i
$209$	−37.7884	−	2.66846i	−0.180806	−	0.0127677i
$210$	−29.9172			−0.142463
$211$		−	286.558i		−	1.35809i	−0.734095	−	0.679047i	$-0.762393\pi$
$211$		−	286.558i		−	1.35809i	0.734095	−	0.679047i	$-0.237607\pi$
$212$	−35.4692			−0.167307
$213$	76.6247			0.359740
$214$	303.449			1.41799
$215$		−	110.206i		−	0.512586i
$216$		−	7.95191i		−	0.0368144i
$217$		−	14.2302i		−	0.0655769i
$218$	276.305			1.26745
$219$			38.4829i			0.175721i
$220$	7.83858	−	111.003i	0.0356299	−	0.504560i
$221$	17.7836			0.0804689
$222$		−	63.1297i		−	0.284368i
$223$	209.998			0.941695			0.470848	−	0.882215i	$-0.343948\pi$
$223$	209.998			0.941695			0.470848	+	0.882215i	$0.343948\pi$
$224$	−121.471			−0.542281
$225$	15.0000			0.0666667
$226$		−	467.310i		−	2.06774i
$227$			33.2668i			0.146550i	0.997312	+	0.0732748i	$0.0233450\pi$
$227$			33.2668i			0.146550i	−0.997312	+	0.0732748i	$0.976655\pi$
$228$			26.9864i			0.118361i
$229$	375.048			1.63777			0.818883	−	0.573961i	$-0.194594\pi$
$229$	375.048			1.63777			0.818883	+	0.573961i	$0.194594\pi$
$230$		−	91.9341i		−	0.399714i
$231$	50.2831	+	3.55078i	0.217676	+	0.0153713i
$232$	79.6408			0.343279
$233$		−	124.590i		−	0.534720i	−0.963597	−	0.267360i	$-0.913849\pi$
$233$		−	124.590i		−	0.534720i	0.963597	−	0.267360i	$-0.0861513\pi$
$234$	22.8555			0.0976732
$235$	80.2023			0.341286
$236$	−107.234			−0.454381
$237$			99.6698i			0.420548i
$238$		−	52.6443i		−	0.221194i
$239$		−	370.649i		−	1.55083i	−0.631449	−	0.775417i	$-0.717540\pi$
$239$		−	370.649i		−	1.55083i	0.631449	−	0.775417i	$-0.282460\pi$
$240$	52.7834			0.219931
$241$			142.599i			0.591699i	0.955235	+	0.295849i	$0.0956026\pi$
$241$			142.599i			0.591699i	−0.955235	+	0.295849i	$0.904397\pi$
$242$	−49.6458	+	349.768i	−0.205148	+	1.44532i
$243$	−15.5885			−0.0641500
$244$			523.843i			2.14690i
$245$	−15.6525			−0.0638877
$246$	332.608			1.35207
$247$	−8.98649			−0.0363825
$248$		−	8.23097i		−	0.0331894i
$249$			129.170i			0.518756i
$250$		−	32.6423i		−	0.130569i
$251$	11.1223			0.0443121			0.0221561	−	0.999755i	$-0.492947\pi$
$251$	11.1223			0.0443121			0.0221561	+	0.999755i	$0.492947\pi$
$252$		−	35.9094i		−	0.142498i
$253$	−10.9114	+	154.518i	−0.0431280	+	0.610742i
$254$	−51.4234			−0.202454
$255$			26.3950i			0.103510i
$256$	176.371			0.688951
$257$	−391.997			−1.52528			−0.762640	−	0.646824i	$-0.776097\pi$
$257$	−391.997			−1.52528			−0.762640	+	0.646824i	$0.776097\pi$
$258$	249.234			0.966023
$259$		−	33.0291i		−	0.127525i
$260$		−	26.3978i		−	0.101530i
$261$		−	156.123i		−	0.598173i
$262$	260.272			0.993404
$263$			350.826i			1.33394i	0.745085	+	0.666970i	$0.232409\pi$
$263$			350.826i			1.33394i	−0.745085	+	0.666970i	$0.767591\pi$
$264$	29.0846	+	2.05383i	0.110169	+	0.00777965i
$265$	17.5307			0.0661534
$266$			26.6024i			0.100009i
$267$	219.560			0.822324
$268$	−25.7509			−0.0960854
$269$	−295.101			−1.09703			−0.548515	−	0.836141i	$-0.684807\pi$
$269$	−295.101			−1.09703			−0.548515	+	0.836141i	$0.684807\pi$
$270$			33.9229i			0.125640i
$271$		−	358.833i		−	1.32411i	−0.749456	−	0.662054i	$-0.769685\pi$
$271$		−	358.833i		−	1.32411i	0.749456	−	0.662054i	$-0.230315\pi$
$272$			92.8813i			0.341475i
$273$	11.9579			0.0438017
$274$		−	56.9625i		−	0.207892i
$275$	−3.87422	+	54.8634i	−0.0140881	+	0.199503i
$276$	110.348			0.399812
$277$		−	84.9118i		−	0.306541i	−0.988184	−	0.153270i	$-0.951019\pi$
$277$		−	84.9118i		−	0.306541i	0.988184	−	0.153270i	$-0.0489806\pi$
$278$	−663.905			−2.38815
$279$	−16.1355			−0.0578334
$280$	−9.05364			−0.0323344
$281$		−	141.546i		−	0.503724i	−0.967763	−	0.251862i	$-0.918957\pi$
$281$		−	141.546i		−	0.503724i	0.967763	−	0.251862i	$-0.0810429\pi$
$282$			181.380i			0.643190i
$283$		−	6.54722i		−	0.0231351i	−0.999933	−	0.0115675i	$-0.996318\pi$
$283$		−	6.54722i		−	0.0231351i	0.999933	−	0.0115675i	$-0.00368214\pi$
$284$	200.146			0.704738
$285$		−	13.3380i		−	0.0468001i
$286$	−5.90315	+	83.5954i	−0.0206404	+	0.292292i
$287$	174.019			0.606337
$288$			137.735i			0.478247i
$289$	242.554			0.839286
$290$	−339.748			−1.17155
$291$	154.538			0.531059
$292$			100.518i			0.344241i
$293$			30.7802i			0.105052i	0.998620	+	0.0525259i	$0.0167272\pi$
$293$			30.7802i			0.105052i	−0.998620	+	0.0525259i	$0.983273\pi$
$294$		−	35.3985i		−	0.120403i
$295$	53.0004			0.179662
$296$		−	19.1045i		−	0.0645423i
$297$	4.02621	−	57.0157i	0.0135563	−	0.191972i
$298$	428.980			1.43953
$299$			36.7460i			0.122896i
$300$	39.1804			0.130601
$301$	130.398			0.433215
$302$	−766.008			−2.53645
$303$		−	88.6042i		−	0.292423i
$304$		−	46.9351i		−	0.154392i
$305$		−	258.910i		−	0.848884i
$306$	−59.6930			−0.195075
$307$		−	147.680i		−	0.481043i	−0.970644	−	0.240521i	$-0.922682\pi$
$307$		−	147.680i		−	0.481043i	0.970644	−	0.240521i	$-0.0773184\pi$
$308$	131.341	+	9.27473i	0.426431	+	0.0301128i
$309$	−23.8652			−0.0772337
$310$			35.1134i			0.113269i
$311$	−87.2008			−0.280388			−0.140194	−	0.990124i	$-0.544773\pi$
$311$	−87.2008			−0.280388			−0.140194	+	0.990124i	$0.544773\pi$
$312$	6.91662			0.0221687
$313$	−481.136			−1.53718			−0.768588	−	0.639744i	$-0.779040\pi$
$313$	−481.136			−1.53718			−0.768588	+	0.639744i	$0.779040\pi$
$314$			489.012i			1.55736i
$315$			17.7482i			0.0563436i
$316$			260.340i			0.823861i
$317$	430.076			1.35671			0.678353	−	0.734736i	$-0.262694\pi$
$317$	430.076			1.35671			0.678353	+	0.734736i	$0.262694\pi$
$318$			39.6460i			0.124673i
$319$	571.030	+	40.3237i	1.79006	+	0.126407i
$320$	177.835			0.555734
$321$		−	180.020i		−	0.560811i
$322$	108.778			0.337820
$323$	23.4705			0.0726641
$324$	−40.7174			−0.125671
$325$			13.0471i			0.0401449i
$326$		−	361.403i		−	1.10860i
$327$		−	163.917i		−	0.501274i
$328$	100.655			0.306876
$329$			94.8966i			0.288440i
$330$	−124.075	−	8.76165i	−0.375985	−	0.0265504i
$331$	−255.155			−0.770860			−0.385430	−	0.922737i	$-0.625947\pi$
$331$	−255.155			−0.770860			−0.385430	+	0.922737i	$0.625947\pi$
$332$			337.396i			1.01625i
$333$	−37.4514			−0.112467
$334$	783.800			2.34671
$335$	12.7274			0.0379922
$336$			62.4542i			0.185876i
$337$		−	7.80036i		−	0.0231465i	−0.999933	−	0.0115732i	$-0.996316\pi$
$337$		−	7.80036i		−	0.0231465i	0.999933	−	0.0115732i	$-0.00368396\pi$
$338$		−	473.535i		−	1.40099i
$339$	−277.230			−0.817786
$340$			68.9444i			0.202778i
$341$	4.16750	−	59.0166i	0.0122214	−	0.173069i
$342$	30.1643			0.0881996
$343$		−	18.5203i		−	0.0539949i
$344$	75.4241			0.219256
$345$	−54.5395			−0.158086
$346$	−579.625			−1.67522
$347$			148.592i			0.428219i	0.976810	+	0.214109i	$0.0686849\pi$
$347$			148.592i			0.428219i	−0.976810	+	0.214109i	$0.931315\pi$
$348$		−	407.798i		−	1.17183i
$349$		−	366.211i		−	1.04932i	−0.851313	−	0.524658i	$-0.824193\pi$
$349$		−	366.211i		−	1.04932i	0.851313	−	0.524658i	$-0.175807\pi$
$350$	38.6229			0.110351
$351$		−	13.5589i		−	0.0386295i
$352$	−503.774	−	35.5744i	−1.43118	−	0.101064i
$353$	−557.082			−1.57813			−0.789067	−	0.614307i	$-0.789436\pi$
$353$	−557.082			−1.57813			−0.789067	+	0.614307i	$0.789436\pi$
$354$			119.862i			0.338592i
$355$	−98.9220			−0.278654
$356$	573.497			1.61095
$357$	−31.2310			−0.0874818
$358$		−	230.205i		−	0.643032i
$359$		−	190.447i		−	0.530494i	−0.964180	−	0.265247i	$-0.914547\pi$
$359$		−	190.447i		−	0.530494i	0.964180	−	0.265247i	$-0.0854535\pi$
$360$			10.2659i			0.0285163i
$361$	349.140			0.967146
$362$			398.310i			1.10030i
$363$	207.498	+	29.4522i	0.571621	+	0.0811355i
$364$	31.2342			0.0858084
$365$		−	49.6812i		−	0.136113i
$366$	585.531			1.59981
$367$	−491.882			−1.34028			−0.670139	−	0.742236i	$-0.733765\pi$
$367$	−491.882			−1.34028			−0.670139	+	0.742236i	$0.733765\pi$
$368$	−191.919			−0.521519
$369$		−	197.319i		−	0.534739i
$370$			81.5001i			0.220270i
$371$			20.7426i			0.0559098i
$372$	−42.1464			−0.113297
$373$		−	59.4250i		−	0.159316i	−0.996822	−	0.0796582i	$-0.974617\pi$
$373$		−	59.4250i		−	0.159316i	0.996822	−	0.0796582i	$-0.0253829\pi$
$374$	15.4176	−	218.331i	0.0412235	−	0.583772i
$375$	−19.3649			−0.0516398
$376$			54.8897i			0.145983i
$377$	135.797			0.360204
$378$	−40.1381			−0.106185
$379$	610.455			1.61070			0.805350	−	0.592800i	$-0.201978\pi$
$379$	610.455			1.61070			0.805350	+	0.592800i	$0.201978\pi$
$380$		−	34.8393i		−	0.0916822i
$381$			30.5067i			0.0800702i
$382$			86.3773i			0.226119i
$383$	192.955			0.503800			0.251900	−	0.967753i	$-0.418945\pi$
$383$	192.955			0.503800			0.251900	+	0.967753i	$0.418945\pi$
$384$			84.0921i			0.218990i
$385$	−64.9152	−	4.58404i	−0.168611	−	0.0119066i
$386$	447.881			1.16031
$387$		−	147.857i		−	0.382059i
$388$	403.658			1.04035
$389$	−13.4411			−0.0345530			−0.0172765	−	0.999851i	$-0.505500\pi$
$389$	−13.4411			−0.0345530			−0.0172765	+	0.999851i	$0.505500\pi$
$390$	−29.5063			−0.0756573
$391$		−	95.9715i		−	0.245451i
$392$		−	10.7124i		−	0.0273276i
$393$		−	154.405i		−	0.392889i
$394$	−439.693			−1.11597
$395$		−	128.673i		−	0.325755i
$396$	10.5166	−	148.926i	0.0265570	−	0.376077i
$397$	350.464			0.882781			0.441390	−	0.897315i	$-0.354485\pi$
$397$	350.464			0.882781			0.441390	+	0.897315i	$0.354485\pi$
$398$			130.295i			0.327375i
$399$	15.7818			0.0395533
$400$	−68.1431			−0.170358
$401$	−206.070			−0.513891			−0.256945	−	0.966426i	$-0.582716\pi$
$401$	−206.070			−0.513891			−0.256945	+	0.966426i	$0.582716\pi$
$402$			28.7833i			0.0716003i
$403$		−	14.0348i		−	0.0348258i
$404$		−	231.436i		−	0.572862i
$405$	20.1246			0.0496904
$406$		−	401.995i		−	0.990136i
$407$	9.67300	−	136.981i	0.0237666	−	0.336562i
$408$	−18.0645			−0.0442758
$409$		−	246.202i		−	0.601962i	−0.953630	−	0.300981i	$-0.902686\pi$
$409$		−	246.202i		−	0.601962i	0.953630	−	0.300981i	$-0.0973140\pi$
$410$	−429.396			−1.04731
$411$	−33.7928			−0.0822208
$412$	−62.3365			−0.151302
$413$			62.7109i			0.151842i
$414$		−	123.343i		−	0.297929i
$415$		−	166.758i		−	0.401827i
$416$	−119.803			−0.287988
$417$			393.859i			0.944506i
$418$	−7.79087	+	110.328i	−0.0186384	+	0.263942i
$419$	−66.4032			−0.158480			−0.0792401	−	0.996856i	$-0.525249\pi$
$419$	−66.4032			−0.158480			−0.0792401	+	0.996856i	$0.525249\pi$
$420$			46.3588i			0.110378i
$421$	−428.169			−1.01703			−0.508514	−	0.861054i	$-0.669805\pi$
$421$	−428.169			−1.01703			−0.508514	+	0.861054i	$0.669805\pi$
$422$	−836.639			−1.98256
$423$	107.603			0.254380
$424$			11.9978i			0.0282968i
$425$		−	34.0758i		−	0.0801784i
$426$		−	223.715i		−	0.525152i
$427$	306.346			0.717438
$428$		−	470.217i		−	1.09864i
$429$	49.5926	+	3.50202i	0.115601	+	0.00816322i
$430$	−321.759			−0.748278
$431$		−	368.429i		−	0.854825i	−0.904057	−	0.427412i	$-0.859425\pi$
$431$		−	368.429i		−	0.854825i	0.904057	−	0.427412i	$-0.140575\pi$
$432$	70.8164			0.163927
$433$	201.170			0.464597			0.232298	−	0.972645i	$-0.425375\pi$
$433$	201.170			0.464597			0.232298	+	0.972645i	$0.425375\pi$
$434$	−41.5467			−0.0957297
$435$			201.554i			0.463343i
$436$		−	428.154i		−	0.982005i
$437$			48.4967i			0.110976i
$438$	112.355			0.256519
$439$			89.4307i			0.203715i	0.994799	+	0.101857i	$0.0324785\pi$
$439$			89.4307i			0.203715i	−0.994799	+	0.101857i	$0.967521\pi$
$440$	−37.5480	−	2.65148i	−0.0853364	−	0.00602609i
$441$	−21.0000			−0.0476190
$442$		−	51.9214i		−	0.117469i
$443$	688.869			1.55501			0.777505	−	0.628877i	$-0.216485\pi$
$443$	688.869			1.55501			0.777505	+	0.628877i	$0.216485\pi$
$444$	−97.8241			−0.220324
$445$	−283.451			−0.636969
$446$		−	613.114i		−	1.37469i
$447$		−	254.490i		−	0.569330i
$448$			210.417i			0.469681i
$449$	630.673			1.40462			0.702308	−	0.711873i	$-0.252153\pi$
$449$	630.673			1.40462			0.702308	+	0.711873i	$0.252153\pi$
$450$		−	43.7942i		−	0.0973205i
$451$	721.704	+	50.9637i	1.60023	+	0.113002i
$452$	−724.131			−1.60206
$453$			454.431i			1.00316i
$454$	97.1262			0.213934
$455$	−15.4375			−0.0339287
$456$	9.12843			0.0200185
$457$		−	521.581i		−	1.14132i	−0.821188	−	0.570658i	$-0.806688\pi$
$457$		−	521.581i		−	1.14132i	0.821188	−	0.570658i	$-0.193312\pi$
$458$		−	1095.00i		−	2.39082i
$459$			35.4126i			0.0771517i
$460$	−142.459			−0.309693
$461$			805.277i			1.74681i	0.486999	+	0.873403i	$0.338092\pi$
$461$			805.277i			1.74681i	−0.486999	+	0.873403i	$0.661908\pi$
$462$	10.3669	−	146.807i	0.0224392	−	0.317765i
$463$	−394.149			−0.851295			−0.425647	−	0.904889i	$-0.639954\pi$
$463$	−394.149			−0.851295			−0.425647	+	0.904889i	$0.639954\pi$
$464$			709.248i			1.52855i
$465$	20.8309			0.0447976
$466$	−363.754			−0.780589
$467$	405.190			0.867644			0.433822	−	0.900999i	$-0.357165\pi$
$467$	405.190			0.867644			0.433822	+	0.900999i	$0.357165\pi$
$468$		−	35.4163i		−	0.0756759i
$469$			15.0593i			0.0321093i
$470$		−	234.160i		−	0.498213i
$471$	290.104			0.615932
$472$			36.2730i			0.0768495i
$473$	540.796	+	38.1887i	1.14333	+	0.0807372i
$474$	290.998			0.613919
$475$			17.2193i			0.0362512i
$476$	−81.5762			−0.171378
$477$	23.5198			0.0493079
$478$	−1082.15			−2.26392
$479$		−	636.129i		−	1.32804i	−0.747717	−	0.664018i	$-0.768850\pi$
$479$		−	636.129i		−	1.32804i	0.747717	−	0.664018i	$-0.231150\pi$
$480$		−	177.815i		−	0.370449i
$481$		−	32.5755i		−	0.0677245i
$482$	416.335			0.863766
$483$		−	64.5321i		−	0.133607i
$484$	541.991	+	76.9298i	1.11982	+	0.158946i
$485$	−199.508			−0.411357
$486$			45.5123i			0.0936467i
$487$	637.824			1.30970			0.654850	−	0.755759i	$-0.272732\pi$
$487$	637.824			1.30970			0.654850	+	0.755759i	$0.272732\pi$
$488$	177.195			0.363105
$489$	−214.401			−0.438448
$490$			45.6992i			0.0932637i
$491$			621.244i			1.26526i	0.774453	+	0.632632i	$0.218025\pi$
$491$			621.244i			1.26526i	−0.774453	+	0.632632i	$0.781975\pi$
$492$		−	515.401i		−	1.04756i
$493$	−354.668			−0.719409
$494$			26.2371i			0.0531115i
$495$	−5.19781	+	73.6069i	−0.0105006	+	0.148701i
$496$	73.3016			0.147786
$497$		−	117.046i		−	0.235505i
$498$	377.128			0.757284
$499$	11.6784			0.0234036			0.0117018	−	0.999932i	$-0.496275\pi$
$499$	11.6784			0.0234036			0.0117018	+	0.999932i	$0.496275\pi$
$500$	−50.5816			−0.101163
$501$		−	464.986i		−	0.928117i
$502$		−	32.4730i		−	0.0646872i
$503$			186.055i			0.369891i	0.982749	+	0.184946i	$0.0592109\pi$
$503$			186.055i			0.369891i	−0.982749	+	0.184946i	$0.940789\pi$
$504$	−12.1467			−0.0241007
$505$			114.387i			0.226510i
$506$	451.133	+	31.8571i	0.891566	+	0.0629586i
$507$	−280.923			−0.554089
$508$			79.6843i			0.156859i
$509$	164.289			0.322769			0.161384	−	0.986892i	$-0.448404\pi$
$509$	164.289			0.322769			0.161384	+	0.986892i	$0.448404\pi$
$510$	77.0633			0.151105
$511$	58.7836			0.115036
$512$		−	709.139i		−	1.38504i
$513$		−	17.8948i		−	0.0348827i
$514$			1144.48i			2.22662i
$515$	30.8098			0.0598249
$516$		−	386.206i		−	0.748461i
$517$	−27.7918	+	393.563i	−0.0537558	+	0.761244i
$518$	−96.4322			−0.186162
$519$			343.860i			0.662544i
$520$	−8.92932			−0.0171718
$521$	−167.948			−0.322356			−0.161178	−	0.986925i	$-0.551529\pi$
$521$	−167.948			−0.322356			−0.161178	+	0.986925i	$0.551529\pi$
$522$	−455.820			−0.873218
$523$			517.450i			0.989388i	0.869067	+	0.494694i	$0.164720\pi$
$523$			517.450i			0.989388i	−0.869067	+	0.494694i	$0.835280\pi$
$524$		−	403.310i		−	0.769676i
$525$		−	22.9129i		−	0.0436436i
$526$	1024.28			1.94730
$527$			36.6554i			0.0695549i
$528$	−18.2905	+	259.015i	−0.0346412	+	0.490559i
$529$	−330.696			−0.625134
$530$		−	51.1828i		−	0.0965713i
$531$	71.1075			0.133912
$532$	41.2224			0.0774856
$533$	171.629			0.322006
$534$		−	641.032i		−	1.20043i
$535$			232.405i			0.434402i
$536$			8.71051i			0.0162510i
$537$	−136.568			−0.254317
$538$			861.582i			1.60145i
$539$	5.42391	−	76.8087i	0.0100629	−	0.142502i
$540$	52.5660			0.0973444
$541$		−	544.683i		−	1.00681i	−0.864051	−	0.503403i	$-0.832081\pi$
$541$		−	544.683i		−	1.00681i	0.864051	−	0.503403i	$-0.167919\pi$
$542$	−1047.66			−1.93294
$543$	236.296			0.435168
$544$	312.896			0.575176
$545$			211.615i			0.388285i
$546$		−	34.9124i		−	0.0639421i
$547$			612.528i			1.11979i	0.828562	+	0.559897i	$0.189159\pi$
$547$			612.528i			1.11979i	−0.828562	+	0.559897i	$0.810841\pi$
$548$	−88.2675			−0.161072
$549$		−	347.364i		−	0.632721i
$550$	160.180	+	11.3112i	0.291236	+	0.0205659i
$551$	179.222			0.325267
$552$		−	37.3264i		−	0.0676203i
$553$	152.248			0.275313
$554$	−247.910			−0.447491
$555$	48.3496			0.0871164
$556$			1028.77i			1.85031i
$557$			610.661i			1.09634i	0.836367	+	0.548170i	$0.184675\pi$
$557$			610.661i			1.09634i	−0.836367	+	0.548170i	$0.815325\pi$
$558$			47.1095i			0.0844257i
$559$	128.607			0.230066
$560$		−	80.6280i		−	0.143979i
$561$	−129.524	−	9.14642i	−0.230880	−	0.0163038i
$562$	−413.261			−0.735340
$563$			268.050i			0.476110i	0.971252	+	0.238055i	$0.0765099\pi$
$563$			268.050i			0.476110i	−0.971252	+	0.238055i	$0.923490\pi$
$564$	281.061			0.498335
$565$	357.902			0.633455
$566$	−19.1154			−0.0337728
$567$			23.8118i			0.0419961i
$568$		−	67.7013i		−	0.119193i
$569$			32.5601i			0.0572234i	0.999591	+	0.0286117i	$0.00910863\pi$
$569$			32.5601i			0.0572234i	−0.999591	+	0.0286117i	$0.990891\pi$
$570$	−38.9419			−0.0683192
$571$			315.060i			0.551768i	0.961191	+	0.275884i	$0.0889706\pi$
$571$			315.060i			0.551768i	−0.961191	+	0.275884i	$0.911029\pi$
$572$	129.537	+	9.14737i	0.226464	+	0.0159919i
$573$	51.2430			0.0894293
$574$		−	508.068i		−	0.885135i
$575$	70.4103			0.122453
$576$	238.590			0.414219
$577$	458.959			0.795422			0.397711	−	0.917511i	$-0.369805\pi$
$577$	458.959			0.795422			0.397711	+	0.917511i	$0.369805\pi$
$578$		−	708.163i		−	1.22520i
$579$		−	265.703i		−	0.458901i
$580$			526.465i			0.907697i
$581$	197.311			0.339606
$582$		−	451.192i		−	0.775244i
$583$	−6.07474	+	86.0252i	−0.0104198	+	0.147556i
$584$	34.0014			0.0582215
$585$			17.5045i			0.0299223i
$586$	89.8664			0.153356
$587$	−44.1124			−0.0751489			−0.0375744	−	0.999294i	$-0.511963\pi$
$587$	−44.1124			−0.0751489			−0.0375744	+	0.999294i	$0.511963\pi$
$588$	−54.8525			−0.0932866
$589$		−	18.5228i		−	0.0314480i
$590$		−	154.741i		−	0.262272i
$591$			260.846i			0.441364i
$592$	170.137			0.287394
$593$			358.092i			0.603866i	0.953329	+	0.301933i	$0.0976318\pi$
$593$			358.092i			0.603866i	−0.953329	+	0.301933i	$0.902368\pi$
$594$	−166.464	−	11.7550i	−0.280242	−	0.0197895i
$595$	40.3191			0.0677631
$596$		−	664.735i		−	1.11533i
$597$	77.2971			0.129476
$598$	107.284			0.179405
$599$	935.859			1.56237			0.781184	−	0.624301i	$-0.214616\pi$
$599$	935.859			1.56237			0.781184	+	0.624301i	$0.214616\pi$
$600$		−	13.2532i		−	0.0220886i
$601$			520.391i			0.865874i	0.901424	+	0.432937i	$0.142523\pi$
$601$			520.391i			0.865874i	−0.901424	+	0.432937i	$0.857477\pi$
$602$		−	380.711i		−	0.632410i
$603$	17.0756			0.0283177
$604$			1186.99i			1.96521i
$605$	−267.879	−	38.0226i	−0.442776	−	0.0628473i
$606$	−258.690			−0.426881
$607$			525.038i			0.864972i	0.901641	+	0.432486i	$0.142364\pi$
$607$			525.038i			0.864972i	−0.901641	+	0.432486i	$0.857636\pi$
$608$	−158.114			−0.260055
$609$	−238.482			−0.391596
$610$	−755.917			−1.23921
$611$			93.5935i			0.153181i
$612$			92.4987i			0.151142i
$613$			468.054i			0.763547i	0.924256	+	0.381774i	$0.124687\pi$
$613$			468.054i			0.763547i	−0.924256	+	0.381774i	$0.875313\pi$
$614$	−431.169			−0.702230
$615$			254.737i			0.414207i
$616$	3.13728	−	44.4274i	0.00509298	−	0.0721224i
$617$	−332.221			−0.538446			−0.269223	−	0.963078i	$-0.586767\pi$
$617$	−332.221			−0.538446			−0.269223	+	0.963078i	$0.586767\pi$
$618$			69.6772i			0.112746i
$619$	118.627			0.191643			0.0958216	−	0.995399i	$-0.469452\pi$
$619$	118.627			0.191643			0.0958216	+	0.995399i	$0.469452\pi$
$620$	54.4108			0.0877593
$621$	−73.1725			−0.117830
$622$			254.593i			0.409313i
$623$		−	335.384i		−	0.538337i
$624$			61.5966i			0.0987124i
$625$	25.0000			0.0400000
$626$			1404.73i			2.24398i
$627$	65.4514	+	4.62190i	0.104388	+	0.00737146i
$628$	757.759			1.20662
$629$			85.0792i			0.135261i
$630$	51.8180			0.0822509
$631$	−439.927			−0.697190			−0.348595	−	0.937273i	$-0.613341\pi$
$631$	−439.927			−0.697190			−0.348595	+	0.937273i	$0.613341\pi$
$632$	88.0628			0.139340
$633$			496.333i			0.784096i
$634$		−	1255.66i		−	1.98053i
$635$		−	39.3840i		−	0.0620221i
$636$	61.4344			0.0965950
$637$		−	18.2659i		−	0.0286750i
$638$	117.730	−	1667.19i	0.184529	−	2.61315i
$639$	−132.718			−0.207696
$640$		−	108.562i		−	0.169629i
$641$	1132.16			1.76624			0.883120	−	0.469147i	$-0.155438\pi$
$641$	1132.16			1.76624			0.883120	+	0.469147i	$0.155438\pi$
$642$	−525.590			−0.818676
$643$	−184.573			−0.287050			−0.143525	−	0.989647i	$-0.545844\pi$
$643$	−184.573			−0.287050			−0.143525	+	0.989647i	$0.545844\pi$
$644$		−	168.559i		−	0.261738i
$645$			190.883i			0.295942i
$646$		−	68.5248i		−	0.106076i
$647$	242.405			0.374659			0.187330	−	0.982297i	$-0.440017\pi$
$647$	242.405			0.374659			0.187330	+	0.982297i	$0.440017\pi$
$648$			13.7731i			0.0212548i
$649$	−18.3657	+	260.080i	−0.0282985	+	0.400739i
$650$	38.0925			0.0586039
$651$			24.6474i			0.0378609i
$652$	−560.021			−0.858928
$653$	33.7998			0.0517607			0.0258804	−	0.999665i	$-0.491761\pi$
$653$	33.7998			0.0517607			0.0258804	+	0.999665i	$0.491761\pi$
$654$	−478.574			−0.731764
$655$			199.336i			0.304330i
$656$			896.393i			1.36645i
$657$		−	66.6543i		−	0.101453i
$658$	277.062			0.421067
$659$		−	27.9147i		−	0.0423593i	−0.999776	−	0.0211796i	$-0.993258\pi$
$659$		−	27.9147i		−	0.0423593i	0.999776	−	0.0211796i	$-0.00674219\pi$
$660$	−13.5768	+	192.263i	−0.0205709	+	0.291308i
$661$	35.2144			0.0532744			0.0266372	−	0.999645i	$-0.491520\pi$
$661$	35.2144			0.0532744			0.0266372	+	0.999645i	$0.491520\pi$
$662$			744.954i			1.12531i
$663$	−30.8021			−0.0464587
$664$	114.128			0.171879
$665$	−20.3742			−0.0306379
$666$			109.344i			0.164180i
$667$		−	732.845i		−	1.09872i
$668$		−	1214.56i		−	1.81820i
$669$	−363.727			−0.543688
$670$		−	37.1591i		−	0.0554613i
$671$	1270.50	+	89.7176i	1.89345	+	0.133707i
$672$	210.394			0.313086
$673$			1011.97i			1.50367i	0.659350	+	0.751837i	$0.270832\pi$
$673$			1011.97i			1.50367i	−0.659350	+	0.751837i	$0.729168\pi$
$674$	−22.7741			−0.0337894
$675$	−25.9808			−0.0384900
$676$	−733.778			−1.08547
$677$			596.511i			0.881110i	0.897726	+	0.440555i	$0.145218\pi$
$677$			596.511i			0.881110i	−0.897726	+	0.440555i	$0.854782\pi$
$678$			809.404i			1.19381i
$679$		−	236.061i		−	0.347660i
$680$	23.3212			0.0342959
$681$		−	57.6197i		−	0.0846104i
$682$	−172.306	−	12.1675i	−0.252648	−	0.0178409i
$683$	594.146			0.869907			0.434953	−	0.900453i	$-0.356765\pi$
$683$	594.146			0.869907			0.434953	+	0.900453i	$0.356765\pi$
$684$		−	46.7418i		−	0.0683359i
$685$	43.6263			0.0636880
$686$	−54.0721			−0.0788222
$687$	−649.603			−0.945564
$688$			671.695i			0.976302i
$689$			20.4577i			0.0296919i
$690$			159.235i			0.230775i
$691$	−698.934			−1.01148			−0.505741	−	0.862685i	$-0.668781\pi$
$691$	−698.934			−1.01148			−0.505741	+	0.862685i	$0.668781\pi$
$692$			898.171i			1.29794i
$693$	−87.0929	−	6.15013i	−0.125675	−	0.00887465i
$694$	433.831			0.625117
$695$		−	508.470i		−	0.731611i
$696$	−137.942			−0.198192
$697$	−448.253			−0.643117
$698$	−1069.20			−1.53180
$699$			215.796i			0.308721i
$700$		−	59.8490i		−	0.0854986i
$701$			274.925i			0.392190i	0.980585	+	0.196095i	$0.0628260\pi$
$701$			274.925i			0.392190i	−0.980585	+	0.196095i	$0.937174\pi$
$702$	−39.5869			−0.0563916
$703$		−	42.9925i		−	0.0611558i
$704$	−61.6234	+	872.658i	−0.0875333	+	1.23957i
$705$	−138.914			−0.197042
$706$			1626.46i			2.30377i
$707$	−135.345			−0.191436
$708$	185.734			0.262337
$709$	−1075.28			−1.51661			−0.758306	−	0.651899i	$-0.773973\pi$
$709$	−1075.28			−1.51661			−0.758306	+	0.651899i	$0.773973\pi$
$710$			288.814i			0.406781i
$711$		−	172.633i		−	0.242803i
$712$		−	193.992i		−	0.272460i
$713$	−75.7404			−0.106228
$714$			91.1826i			0.127707i
$715$	−64.0238	−	4.52109i	−0.0895438	−	0.00632321i
$716$	−356.720			−0.498213
$717$			641.984i			0.895375i
$718$	−556.033			−0.774419
$719$	−1251.05			−1.73998			−0.869992	−	0.493066i	$-0.835876\pi$
$719$	−1251.05			−1.73998			−0.869992	+	0.493066i	$0.835876\pi$
$720$	−91.4236			−0.126977
$721$			36.4547i			0.0505613i
$722$		−	1019.35i		−	1.41185i
$723$		−	246.989i		−	0.341617i
$724$	617.211			0.852501
$725$		−	260.205i		−	0.358904i
$726$	85.9891	−	605.816i	0.118442	−	0.834457i
$727$	−237.189			−0.326257			−0.163128	−	0.986605i	$-0.552158\pi$
$727$	−237.189			−0.326257			−0.163128	+	0.986605i	$0.552158\pi$
$728$		−	10.5653i		−	0.0145128i
$729$	27.0000			0.0370370
$730$	−145.050			−0.198699
$731$	−335.890			−0.459494
$732$		−	907.323i		−	1.23951i
$733$		−	1002.65i		−	1.36787i	−0.729544	−	0.683933i	$-0.760268\pi$
$733$		−	1002.65i		−	1.36787i	0.729544	−	0.683933i	$-0.239732\pi$
$734$			1436.11i			1.95655i
$735$	27.1109			0.0368856
$736$			646.531i			0.878439i
$737$	−4.41030	+	62.4550i	−0.00598413	+	0.0847421i
$738$	−576.095			−0.780616
$739$		−	740.855i		−	1.00251i	−0.865300	−	0.501255i	$-0.832872\pi$
$739$		−	740.855i		−	1.00251i	0.865300	−	0.501255i	$-0.167128\pi$
$740$	126.290			0.170663
$741$	15.5651			0.0210055
$742$	60.5603			0.0816177
$743$			805.815i			1.08454i	0.840203	+	0.542271i	$0.182436\pi$
$743$			805.815i			1.08454i	−0.840203	+	0.542271i	$0.817564\pi$
$744$			14.2565i			0.0191619i
$745$			328.546i			0.441001i
$746$	−173.498			−0.232571
$747$		−	223.729i		−	0.299504i
$748$	−338.319	−	23.8907i	−0.452299	−	0.0319394i
$749$	−274.985			−0.367137
$750$			56.5381i			0.0753842i
$751$	−567.152			−0.755195			−0.377598	−	0.925970i	$-0.623250\pi$
$751$	−567.152			−0.755195			−0.377598	+	0.925970i	$0.623250\pi$
$752$	−488.825			−0.650034
$753$	−19.2645			−0.0255836
$754$		−	396.475i		−	0.525829i
$755$		−	586.668i		−	0.777044i
$756$			62.1969i			0.0822710i
$757$	−1407.78			−1.85969			−0.929843	−	0.367957i	$-0.880057\pi$
$757$	−1407.78			−1.85969			−0.929843	+	0.367957i	$0.880057\pi$
$758$		−	1782.29i		−	2.35131i
$759$	18.8991	−	267.633i	0.0249000	−	0.352612i
$760$	−11.7847			−0.0155062
$761$			1235.66i			1.62373i	0.583847	+	0.811864i	$0.301547\pi$
$761$			1235.66i			1.62373i	−0.583847	+	0.811864i	$0.698453\pi$
$762$	89.0680			0.116887
$763$	−250.387			−0.328161
$764$	133.848			0.175194
$765$		−	45.7175i		−	0.0597614i
$766$		−	563.355i		−	0.735451i
$767$			61.8498i			0.0806385i
$768$	−305.484			−0.397766
$769$			534.890i			0.695565i	0.937575	+	0.347783i	$0.113065\pi$
$769$			534.890i			0.695565i	−0.937575	+	0.347783i	$0.886935\pi$
$770$	−13.3836	+	189.528i	−0.0173813	+	0.246140i
$771$	678.958			0.880620
$772$		−	694.024i		−	0.898995i
$773$	1049.39			1.35756			0.678781	−	0.734341i	$-0.262509\pi$
$773$	1049.39			1.35756			0.678781	+	0.734341i	$0.262509\pi$
$774$	−431.686			−0.557733
$775$	−26.8925			−0.0347001
$776$		−	136.541i		−	0.175955i
$777$			57.2080i			0.0736268i
$778$			39.2429i			0.0504407i
$779$	226.513			0.290774
$780$			45.7223i			0.0586183i
$781$	34.2785	−	485.423i	0.0438906	−	0.621541i
$782$	−280.200			−0.358312
$783$			270.413i			0.345355i
$784$	95.4003			0.121684
$785$	−374.523			−0.477099
$786$	−450.804			−0.573542
$787$		−	748.530i		−	0.951119i	−0.879684	−	0.475559i	$-0.842246\pi$
$787$		−	748.530i		−	0.951119i	0.879684	−	0.475559i	$-0.157754\pi$
$788$			681.336i			0.864640i
$789$		−	607.648i		−	0.770150i
$790$	−375.676			−0.475540
$791$			423.475i			0.535367i
$792$	−50.3759	−	3.55734i	−0.0636060	−	0.00449159i
$793$	302.139			0.381008
$794$		−	1023.22i		−	1.28869i
$795$	−30.3640			−0.0381937
$796$	201.902			0.253646
$797$	29.7801			0.0373653			0.0186826	−	0.999825i	$-0.494053\pi$
$797$	29.7801			0.0373653			0.0186826	+	0.999825i	$0.494053\pi$
$798$		−	46.0767i		−	0.0577402i
$799$		−	244.443i		−	0.305937i
$800$			229.559i			0.286948i
$801$	−380.290			−0.474769
$802$			601.646i			0.750182i
$803$	243.792	+	17.2156i	0.303602	+	0.0214391i
$804$	44.6019			0.0554749
$805$			83.3105i			0.103491i
$806$	−40.9762			−0.0508390
$807$	511.130			0.633370
$808$	−78.2858			−0.0968883
$809$			97.4368i			0.120441i	0.998185	+	0.0602205i	$0.0191804\pi$
$809$			97.4368i			0.120441i	−0.998185	+	0.0602205i	$0.980820\pi$
$810$		−	58.7561i		−	0.0725385i
$811$			1437.13i			1.77205i	0.463641	+	0.886023i	$0.346543\pi$
$811$			1437.13i			1.77205i	−0.463641	+	0.886023i	$0.653457\pi$
$812$	−622.921			−0.767144
$813$			621.518i			0.764474i
$814$	−399.931	−	28.2415i	−0.491316	−	0.0346947i
$815$	276.791			0.339620
$816$		−	160.875i		−	0.197151i
$817$	169.733			0.207752
$818$	−718.816			−0.878749
$819$	−20.7116			−0.0252889
$820$			665.380i			0.811439i
$821$			164.689i			0.200596i	0.994957	+	0.100298i	$0.0319796\pi$
$821$			164.689i			0.200596i	−0.994957	+	0.100298i	$0.968020\pi$
$822$			98.6619i			0.120027i
$823$	166.573			0.202397			0.101199	−	0.994866i	$-0.467732\pi$
$823$	166.573			0.202397			0.101199	+	0.994866i	$0.467732\pi$
$824$			21.0860i			0.0255898i
$825$	6.71035	−	95.0262i	0.00813375	−	0.115183i
$826$	183.092			0.221661
$827$		−	693.838i		−	0.838982i	−0.907760	−	0.419491i	$-0.862209\pi$
$827$		−	693.838i		−	0.838982i	0.907760	−	0.419491i	$-0.137791\pi$
$828$	−191.128			−0.230831
$829$	1400.23			1.68906			0.844529	−	0.535510i	$-0.179881\pi$
$829$	1400.23			1.68906			0.844529	+	0.535510i	$0.179881\pi$
$830$	−486.870			−0.586590
$831$			147.072i			0.176981i
$832$			207.528i			0.249432i
$833$			47.7061i			0.0572703i
$834$	1149.92			1.37880
$835$			600.295i			0.718916i
$836$	170.961	+	12.0725i	0.204498	+	0.0144408i
$837$	27.9475			0.0333901
$838$			193.872i			0.231351i
$839$	630.772			0.751814			0.375907	−	0.926657i	$-0.377331\pi$
$839$	630.772			0.751814			0.375907	+	0.926657i	$0.377331\pi$
$840$	15.6814			0.0186683
$841$	−1867.27			−2.22030
$842$			1250.09i			1.48467i
$843$			245.166i			0.290825i
$844$			1296.43i			1.53606i
$845$	362.670			0.429195
$846$		−	314.159i		−	0.371346i
$847$	44.9889	−	316.959i	0.0531156	−	0.374214i
$848$	−106.848			−0.126000
$849$			11.3401i			0.0133570i
$850$	−99.4883			−0.117045
$851$	−175.798			−0.206578
$852$	−346.662			−0.406881
$853$			683.420i			0.801196i	0.916254	+	0.400598i	$0.131198\pi$
$853$			683.420i			0.801196i	−0.916254	+	0.400598i	$0.868802\pi$
$854$		−	894.413i		−	1.04732i
$855$			23.1021i			0.0270200i
$856$	−159.056			−0.185813
$857$		−	931.942i		−	1.08745i	−0.839264	−	0.543724i	$-0.817014\pi$
$857$		−	931.942i		−	1.08745i	0.839264	−	0.543724i	$-0.182986\pi$
$858$	10.2246	−	144.791i	0.0119167	−	0.168755i
$859$	−1028.42			−1.19722			−0.598612	−	0.801039i	$-0.704281\pi$
$859$	−1028.42			−1.19722			−0.598612	+	0.801039i	$0.704281\pi$
$860$			498.590i			0.579756i
$861$	−301.409			−0.350069
$862$	−1075.67			−1.24788
$863$	1071.72			1.24185			0.620925	−	0.783870i	$-0.286757\pi$
$863$	1071.72			1.24185			0.620925	+	0.783870i	$0.286757\pi$
$864$		−	238.564i		−	0.276116i
$865$		−	443.922i		−	0.513204i
$866$		−	587.340i		−	0.678222i
$867$	−420.115			−0.484562
$868$			64.3797i			0.0741701i
$869$	631.416	+	44.5879i	0.726601	+	0.0513095i
$870$	588.461			0.676392
$871$			14.8525i			0.0170522i
$872$	−144.828			−0.166087
$873$	−267.668			−0.306607
$874$	141.592			0.162004
$875$			29.5804i			0.0338062i
$876$		−	174.103i		−	0.198747i
$877$			868.707i			0.990544i	0.868738	+	0.495272i	$0.164932\pi$
$877$			868.707i			0.990544i	−0.868738	+	0.495272i	$0.835068\pi$
$878$	261.103			0.297384
$879$		−	53.3129i		−	0.0606517i
$880$	23.6130	−	334.387i	0.0268329	−	0.379985i
$881$	−1315.49			−1.49318			−0.746589	−	0.665286i	$-0.768310\pi$
$881$	−1315.49			−1.49318			−0.746589	+	0.665286i	$0.768310\pi$
$882$			61.3119i			0.0695147i
$883$	1626.51			1.84202			0.921012	−	0.389534i	$-0.127364\pi$
$883$	1626.51			1.84202			0.921012	+	0.389534i	$0.127364\pi$
$884$	−80.4560			−0.0910135
$885$	−91.7993			−0.103728
$886$		−	2011.23i		−	2.27002i
$887$			1127.95i			1.27164i	0.771837	+	0.635820i	$0.219338\pi$
$887$			1127.95i			1.27164i	−0.771837	+	0.635820i	$0.780662\pi$
$888$			33.0900i			0.0372635i
$889$	46.5998			0.0524182
$890$			827.569i			0.929853i
$891$	−6.97360	+	98.7541i	−0.00782671	+	0.110835i
$892$	−950.064			−1.06509
$893$			123.523i			0.138324i
$894$	−743.015			−0.831112
$895$	176.309			0.196993
$896$	128.453			0.143362
$897$		−	63.6459i		−	0.0709542i
$898$		−	1841.32i		−	2.05047i
$899$			279.903i			0.311350i
$900$	−67.8624			−0.0754027
$901$		−	53.4305i		−	0.0593014i
$902$	148.794	−	2107.10i	0.164961	−	2.33603i
$903$	−225.855			−0.250117
$904$			244.945i			0.270957i
$905$	−305.057			−0.337079
$906$	1326.77			1.46442
$907$	124.779			0.137573			0.0687866	−	0.997631i	$-0.478087\pi$
$907$	124.779			0.137573			0.0687866	+	0.997631i	$0.478087\pi$
$908$		−	150.504i		−	0.165753i
$909$			153.467i			0.168830i
$910$			45.0717i			0.0495293i
$911$	731.693			0.803176			0.401588	−	0.915821i	$-0.368458\pi$
$911$	731.693			0.803176			0.401588	+	0.915821i	$0.368458\pi$
$912$			81.2940i			0.0891381i
$913$	818.304	+	57.7851i	0.896280	+	0.0632915i
$914$	−1522.82			−1.66610
$915$			448.445i			0.490104i
$916$	−1696.78			−1.85238
$917$	−235.858			−0.257206
$918$	103.391			0.112627
$919$		−	1242.36i		−	1.35186i	−0.736966	−	0.675930i	$-0.763742\pi$
$919$		−	1242.36i		−	1.35186i	0.736966	−	0.675930i	$-0.236258\pi$
$920$			48.1881i			0.0523784i
$921$			255.790i			0.277730i
$922$	2351.10			2.55000
$923$		−	115.439i		−	0.125069i
$924$	−227.489	−	16.0643i	−0.246200	−	0.0173856i
$925$	−62.4190			−0.0674800
$926$			1150.77i			1.24273i
$927$	41.3357			0.0445909
$928$	2389.29			2.57467
$929$	−472.910			−0.509053			−0.254527	−	0.967066i	$-0.581920\pi$
$929$	−472.910			−0.509053			−0.254527	+	0.967066i	$0.581920\pi$
$930$		−	60.8182i		−	0.0653959i
$931$		−	24.1070i		−	0.0258937i
$932$			563.664i			0.604790i
$933$	151.036			0.161882
$934$		−	1183.00i		−	1.26659i
$935$	167.214	+	11.8080i	0.178839	+	0.0126289i
$936$	−11.9799			−0.0127991
$937$		−	1783.75i		−	1.90368i	−0.306597	−	0.951839i	$-0.599191\pi$
$937$		−	1783.75i		−	1.90368i	0.306597	−	0.951839i	$-0.400809\pi$
$938$	43.9672			0.0468734
$939$	833.352			0.887489
$940$	−362.848			−0.386009
$941$			202.989i			0.215716i	0.994166	+	0.107858i	$0.0343992\pi$
$941$			202.989i			0.215716i	−0.994166	+	0.107858i	$0.965601\pi$
$942$		−	846.993i		−	0.899143i
$943$		−	926.217i		−	0.982202i
$944$	−323.032			−0.342195
$945$		−	30.7409i		−	0.0325300i
$946$	111.496	−	1578.92i	0.117861	−	1.66904i
$947$	1222.72			1.29115			0.645575	−	0.763697i	$-0.276618\pi$
$947$	1222.72			1.29115			0.645575	+	0.763697i	$0.276618\pi$
$948$		−	450.922i		−	0.475656i
$949$	57.9764			0.0610921
$950$	50.2738			0.0529198
$951$	−744.913			−0.783295
$952$			27.5940i			0.0289853i
$953$		−	1300.35i		−	1.36448i	−0.731128	−	0.682241i	$-0.761006\pi$
$953$		−	1300.35i		−	1.36448i	0.731128	−	0.682241i	$-0.238994\pi$
$954$		−	68.6689i		−	0.0719800i
$955$	−66.1544			−0.0692716
$956$			1676.88i			1.75406i
$957$	−989.053	−	69.8427i	−1.03349	−	0.0729809i
$958$	−1857.25			−1.93868
$959$			51.6193i			0.0538262i
$960$	−308.019			−0.320853
$961$	−932.072			−0.969898
$962$	−95.1080			−0.0988648
$963$			311.804i			0.323784i
$964$		−	645.142i		−	0.669235i
$965$			343.022i			0.355463i
$966$	−188.409			−0.195040
$967$		−	24.6565i		−	0.0254979i	−0.999919	−	0.0127490i	$-0.995942\pi$
$967$		−	24.6565i		−	0.0254979i	0.999919	−	0.0127490i	$-0.00405823\pi$
$968$	26.0223	−	183.334i	0.0268826	−	0.189395i
$969$	−40.6521			−0.0419526
$970$			582.487i			0.600502i
$971$	−1656.81			−1.70629			−0.853144	−	0.521675i	$-0.825307\pi$
$971$	−1656.81			−1.70629			−0.853144	+	0.521675i	$0.825307\pi$
$972$	70.5247			0.0725562
$973$	601.630			0.618325
$974$		−	1862.20i		−	1.91191i
$975$		−	22.5982i		−	0.0231777i
$976$			1578.03i			1.61683i
$977$	−1015.33			−1.03924			−0.519618	−	0.854399i	$-0.673926\pi$
$977$	−1015.33			−1.03924			−0.519618	+	0.854399i	$0.673926\pi$
$978$			625.969i			0.640050i
$979$	98.2218	−	1390.93i	0.100329	−	1.42077i
$980$	70.8143			0.0722595
$981$			283.912i			0.289411i
$982$	1813.80			1.84704
$983$	−222.614			−0.226464			−0.113232	−	0.993569i	$-0.536120\pi$
$983$	−222.614			−0.226464			−0.113232	+	0.993569i	$0.536120\pi$
$984$	−174.340			−0.177175
$985$		−	336.751i		−	0.341879i
$986$			1035.50i			1.05020i
$987$		−	164.366i		−	0.166531i
$988$	40.6563			0.0411501
$989$		−	694.043i		−	0.701763i
$990$	214.904	+	15.1756i	0.217075	+	0.0153289i
$991$	−684.424			−0.690640			−0.345320	−	0.938485i	$-0.612230\pi$
$991$	−684.424			−0.690640			−0.345320	+	0.938485i	$0.612230\pi$
$992$		−	246.937i		−	0.248928i
$993$	441.941			0.445056
$994$	−341.730			−0.343792
$995$	−99.7902			−0.100292
$996$		−	584.387i		−	0.586734i
$997$		−	1224.95i		−	1.22864i	−0.789057	−	0.614320i	$-0.789431\pi$
$997$		−	1224.95i		−	1.22864i	0.789057	−	0.614320i	$-0.210569\pi$
$998$		−	34.0964i		−	0.0341648i
$999$	64.8678			0.0649327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.16	✓	96
11.10	odd	2	inner	1155.3.b.a.736.81	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.16	✓	96	1.1	even	1	trivial
1155.3.b.a.736.81	yes	96	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.91962i q^{2} -1.73205 q^{3} -4.52416 q^{4} +2.23607 q^{5} +5.05692i q^{6} +2.64575i q^{7} +1.53034i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.91962i q^{2} -1.73205 q^{3} -4.52416 q^{4} +2.23607 q^{5} +5.05692i q^{6} +2.64575i q^{7} +1.53034i q^{8} +3.00000 q^{9} -6.52846i q^{10} +(-0.774844 + 10.9727i) q^{11} +7.83607 q^{12} +2.60942i q^{13} +7.72458 q^{14} -3.87298 q^{15} -13.6286 q^{16} -6.81516i q^{17} -8.75885i q^{18} +3.44386i q^{19} -10.1163 q^{20} -4.58258i q^{21} +(32.0360 + 2.26225i) q^{22} +14.0821 q^{23} -2.65064i q^{24} +5.00000 q^{25} +7.61851 q^{26} -5.19615 q^{27} -11.9698i q^{28} -52.0411i q^{29} +11.3076i q^{30} -5.37851 q^{31} +45.9117i q^{32} +(1.34207 - 19.0052i) q^{33} -19.8977 q^{34} +5.91608i q^{35} -13.5725 q^{36} -12.4838 q^{37} +10.0548 q^{38} -4.51965i q^{39} +3.42196i q^{40} -65.7729i q^{41} -13.3794 q^{42} -49.2857i q^{43} +(3.50552 - 49.6421i) q^{44} +6.70820 q^{45} -41.1142i q^{46} +35.8676 q^{47} +23.6055 q^{48} -7.00000 q^{49} -14.5981i q^{50} +11.8042i q^{51} -11.8054i q^{52} +7.83995 q^{53} +15.1708i q^{54} +(-1.73260 + 24.5356i) q^{55} -4.04891 q^{56} -5.96495i q^{57} -151.940 q^{58} +23.7025 q^{59} +17.5220 q^{60} -115.788i q^{61} +15.7032i q^{62} +7.93725i q^{63} +79.5301 q^{64} +5.83484i q^{65} +(-55.4880 - 3.91833i) q^{66} +5.69186 q^{67} +30.8329i q^{68} -24.3908 q^{69} +17.2727 q^{70} -44.2393 q^{71} +4.59103i q^{72} -22.2181i q^{73} +36.4479i q^{74} -8.66025 q^{75} -15.5806i q^{76} +(-29.0310 - 2.05004i) q^{77} -13.1956 q^{78} -57.5444i q^{79} -30.4745 q^{80} +9.00000 q^{81} -192.032 q^{82} -74.5765i q^{83} +20.7323i q^{84} -15.2392i q^{85} -143.895 q^{86} +90.1378i q^{87} +(-16.7920 - 1.18578i) q^{88} -126.763 q^{89} -19.5854i q^{90} -6.90388 q^{91} -63.7094 q^{92} +9.31585 q^{93} -104.720i q^{94} +7.70071i q^{95} -79.5214i q^{96} -89.2227 q^{97} +20.4373i q^{98} +(-2.32453 + 32.9180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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