LMFDB - Embedded newform 1050.3.c.b.449.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.3
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.16802 - 2.07357i) q^{3} +2.00000 q^{4} +(3.06604 + 2.93247i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(0.400623 + 8.99108i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.16802 - 2.07357i) q^{3} +2.00000 q^{4} +(3.06604 + 2.93247i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(0.400623 + 8.99108i) q^{9} +21.5844i q^{11} +(-4.33604 - 4.14714i) q^{12} +15.4777i q^{13} -3.74166i q^{14} +4.00000 q^{16} -20.3523 q^{17} +(-0.566566 - 12.7153i) q^{18} +5.86900 q^{19} +(5.48615 - 5.73604i) q^{21} -30.5249i q^{22} -11.3900 q^{23} +(6.13209 + 5.86494i) q^{24} -21.8887i q^{26} +(17.7751 - 20.3236i) q^{27} +5.29150i q^{28} +3.43729i q^{29} -21.0811 q^{31} -5.65685 q^{32} +(44.7567 - 46.7954i) q^{33} +28.7825 q^{34} +(0.801245 + 17.9822i) q^{36} -58.9411i q^{37} -8.30001 q^{38} +(32.0940 - 33.5559i) q^{39} +36.1742i q^{41} +(-7.75859 + 8.11199i) q^{42} -50.1346i q^{43} +43.1688i q^{44} +16.1079 q^{46} -36.7558 q^{47} +(-8.67208 - 8.29428i) q^{48} -7.00000 q^{49} +(44.1242 + 42.2019i) q^{51} +30.9554i q^{52} +40.9385 q^{53} +(-25.1377 + 28.7419i) q^{54} -7.48331i q^{56} +(-12.7241 - 12.1698i) q^{57} -4.86107i q^{58} -110.141i q^{59} -41.5100 q^{61} +29.8132 q^{62} +(-23.7882 + 1.05995i) q^{63} +8.00000 q^{64} +(-63.2955 + 66.1786i) q^{66} +109.401i q^{67} -40.7046 q^{68} +(24.6938 + 23.6180i) q^{69} +14.3549i q^{71} +(-1.13313 - 25.4306i) q^{72} -19.2937i q^{73} +83.3553i q^{74} +11.7380 q^{76} -57.1069 q^{77} +(-45.3878 + 47.4552i) q^{78} +122.271 q^{79} +(-80.6790 + 7.20406i) q^{81} -51.1580i q^{82} -74.4062 q^{83} +(10.9723 - 11.4721i) q^{84} +70.9010i q^{86} +(7.12747 - 7.45212i) q^{87} -61.0498i q^{88} -92.0314i q^{89} -40.9501 q^{91} -22.7800 q^{92} +(45.7042 + 43.7131i) q^{93} +51.9805 q^{94} +(12.2642 + 11.7299i) q^{96} -5.71291i q^{97} +9.89949 q^{98} +(-194.067 + 8.64719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.16802	−	2.07357i	−0.722673	−	0.691190i
$3$	−2.16802	−	2.07357i	−0.722673	−	0.691190i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	3.06604	+	2.93247i	0.511007	+	0.488745i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.82843			−0.353553
$9$	0.400623	+	8.99108i	0.0445136	+	0.999009i
$10$		0			0
$11$			21.5844i			1.96222i	0.193461	+	0.981108i	$0.438029\pi$
$11$			21.5844i			1.96222i	−0.193461	+	0.981108i	$0.561971\pi$
$12$	−4.33604	−	4.14714i	−0.361337	−	0.345595i
$13$			15.4777i			1.19059i	0.803507	+	0.595295i	$0.202965\pi$
$13$			15.4777i			1.19059i	−0.803507	+	0.595295i	$0.797035\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−20.3523			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$17$	−20.3523			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$18$	−0.566566	−	12.7153i	−0.0314759	−	0.706406i
$19$	5.86900			0.308895			0.154447	−	0.988001i	$-0.450640\pi$
$19$	5.86900			0.308895			0.154447	+	0.988001i	$0.450640\pi$
$20$		0			0
$21$	5.48615	−	5.73604i	0.261245	−	0.273145i
$22$		−	30.5249i		−	1.38750i
$23$	−11.3900			−0.495218			−0.247609	−	0.968860i	$-0.579645\pi$
$23$	−11.3900			−0.495218			−0.247609	+	0.968860i	$0.579645\pi$
$24$	6.13209	+	5.86494i	0.255504	+	0.244372i
$25$		0			0
$26$		−	21.8887i		−	0.841875i
$27$	17.7751	−	20.3236i	0.658336	−	0.752724i
$28$			5.29150i			0.188982i
$29$			3.43729i			0.118527i	0.998242	+	0.0592637i	$0.0188753\pi$
$29$			3.43729i			0.118527i	−0.998242	+	0.0592637i	$0.981125\pi$
$30$		0			0
$31$	−21.0811			−0.680035			−0.340018	−	0.940419i	$-0.610433\pi$
$31$	−21.0811			−0.680035			−0.340018	+	0.940419i	$0.610433\pi$
$32$	−5.65685			−0.176777
$33$	44.7567	−	46.7954i	1.35626	−	1.41804i
$34$	28.7825			0.846544
$35$		0			0
$36$	0.801245	+	17.9822i	0.0222568	+	0.499504i
$37$		−	58.9411i		−	1.59300i	−0.604636	−	0.796502i	$-0.706682\pi$
$37$		−	58.9411i		−	1.59300i	0.604636	−	0.796502i	$-0.293318\pi$
$38$	−8.30001			−0.218421
$39$	32.0940	−	33.5559i	0.822924	−	0.860408i
$40$		0			0
$41$			36.1742i			0.882297i	0.897434	+	0.441149i	$0.145429\pi$
$41$			36.1742i			0.882297i	−0.897434	+	0.441149i	$0.854571\pi$
$42$	−7.75859	+	8.11199i	−0.184728	+	0.193143i
$43$		−	50.1346i		−	1.16592i	−0.812501	−	0.582960i	$-0.801894\pi$
$43$		−	50.1346i		−	1.16592i	0.812501	−	0.582960i	$-0.198106\pi$
$44$			43.1688i			0.981108i
$45$		0			0
$46$	16.1079			0.350172
$47$	−36.7558			−0.782037			−0.391019	−	0.920383i	$-0.627877\pi$
$47$	−36.7558			−0.782037			−0.391019	+	0.920383i	$0.627877\pi$
$48$	−8.67208	−	8.29428i	−0.180668	−	0.172797i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	44.1242	+	42.2019i	0.865181	+	0.827488i
$52$			30.9554i			0.595295i
$53$	40.9385			0.772424			0.386212	−	0.922410i	$-0.373783\pi$
$53$	40.9385			0.772424			0.386212	+	0.922410i	$0.373783\pi$
$54$	−25.1377	+	28.7419i	−0.465514	+	0.532257i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	−12.7241	−	12.1698i	−0.223230	−	0.213505i
$58$		−	4.86107i		−	0.0838115i
$59$		−	110.141i		−	1.86680i	−0.358834	−	0.933402i	$-0.616825\pi$
$59$		−	110.141i		−	1.86680i	0.358834	−	0.933402i	$-0.383175\pi$
$60$		0			0
$61$	−41.5100			−0.680492			−0.340246	−	0.940336i	$-0.610510\pi$
$61$	−41.5100			−0.680492			−0.340246	+	0.940336i	$0.610510\pi$
$62$	29.8132			0.480857
$63$	−23.7882	+	1.05995i	−0.377590	+	0.0168246i
$64$	8.00000			0.125000
$65$		0			0
$66$	−63.2955	+	66.1786i	−0.959023	+	1.00271i
$67$			109.401i			1.63286i	0.577447	+	0.816428i	$0.304049\pi$
$67$			109.401i			1.63286i	−0.577447	+	0.816428i	$0.695951\pi$
$68$	−40.7046			−0.598597
$69$	24.6938	+	23.6180i	0.357881	+	0.342289i
$70$		0			0
$71$			14.3549i			0.202181i	0.994877	+	0.101091i	$0.0322332\pi$
$71$			14.3549i			0.202181i	−0.994877	+	0.101091i	$0.967767\pi$
$72$	−1.13313	−	25.4306i	−0.0157379	−	0.353203i
$73$		−	19.2937i		−	0.264297i	−0.991230	−	0.132148i	$-0.957812\pi$
$73$		−	19.2937i		−	0.264297i	0.991230	−	0.132148i	$-0.0421876\pi$
$74$			83.3553i			1.12642i
$75$		0			0
$76$	11.7380			0.154447
$77$	−57.1069			−0.741648
$78$	−45.3878	+	47.4552i	−0.581895	+	0.608400i
$79$	122.271			1.54774			0.773868	−	0.633347i	$-0.218319\pi$
$79$	122.271			1.54774			0.773868	+	0.633347i	$0.218319\pi$
$80$		0			0
$81$	−80.6790	+	7.20406i	−0.996037	+	0.0889390i
$82$		−	51.1580i		−	0.623878i
$83$	−74.4062			−0.896461			−0.448230	−	0.893918i	$-0.647946\pi$
$83$	−74.4062			−0.896461			−0.448230	+	0.893918i	$0.647946\pi$
$84$	10.9723	−	11.4721i	0.130623	−	0.136572i
$85$		0			0
$86$			70.9010i			0.824430i
$87$	7.12747	−	7.45212i	0.0819249	−	0.0856566i
$88$		−	61.0498i		−	0.693748i
$89$		−	92.0314i		−	1.03406i	−0.855967	−	0.517030i	$-0.827038\pi$
$89$		−	92.0314i		−	1.03406i	0.855967	−	0.517030i	$-0.172962\pi$
$90$		0			0
$91$	−40.9501			−0.450001
$92$	−22.7800			−0.247609
$93$	45.7042	+	43.7131i	0.491443	+	0.470033i
$94$	51.9805			0.552984
$95$		0			0
$96$	12.2642	+	11.7299i	0.127752	+	0.122186i
$97$		−	5.71291i		−	0.0588960i	−0.999566	−	0.0294480i	$-0.990625\pi$
$97$		−	5.71291i		−	0.0588960i	0.999566	−	0.0294480i	$-0.00937494\pi$
$98$	9.89949			0.101015
$99$	−194.067	+	8.64719i	−1.96027	+	0.0873453i
$100$		0			0
$101$		−	70.4373i		−	0.697399i	−0.937235	−	0.348699i	$-0.886623\pi$
$101$		−	70.4373i		−	0.697399i	0.937235	−	0.348699i	$-0.113377\pi$
$102$	−62.4011	−	59.6825i	−0.611775	−	0.585123i
$103$		−	160.976i		−	1.56287i	−0.623985	−	0.781436i	$-0.714487\pi$
$103$		−	160.976i		−	1.56287i	0.623985	−	0.781436i	$-0.285513\pi$
$104$		−	43.7775i		−	0.420937i
$105$		0			0
$106$	−57.8957			−0.546186
$107$	−59.6176			−0.557174			−0.278587	−	0.960411i	$-0.589866\pi$
$107$	−59.6176			−0.557174			−0.278587	+	0.960411i	$0.589866\pi$
$108$	35.5501	−	40.6471i	0.329168	−	0.376362i
$109$	136.100			1.24862			0.624311	−	0.781176i	$-0.285380\pi$
$109$	136.100			1.24862			0.624311	+	0.781176i	$0.285380\pi$
$110$		0			0
$111$	−122.219	+	127.786i	−1.10107	+	1.15122i
$112$			10.5830i			0.0944911i
$113$	11.2386			0.0994565			0.0497282	−	0.998763i	$-0.484164\pi$
$113$	11.2386			0.0994565			0.0497282	+	0.998763i	$0.484164\pi$
$114$	17.9946	+	17.2107i	0.157847	+	0.150971i
$115$		0			0
$116$			6.87459i			0.0592637i
$117$	−139.161	+	6.20071i	−1.18941	+	0.0529975i
$118$			155.763i			1.32003i
$119$		−	53.8471i		−	0.452497i
$120$		0			0
$121$	−344.885			−2.85029
$122$	58.7040			0.481181
$123$	75.0097	−	78.4264i	0.609835	−	0.637613i
$124$	−42.1622			−0.340018
$125$		0			0
$126$	33.6415	−	1.49899i	0.266996	−	0.0118968i
$127$			99.4974i			0.783444i	0.920084	+	0.391722i	$0.128121\pi$
$127$			99.4974i			0.783444i	−0.920084	+	0.391722i	$0.871879\pi$
$128$	−11.3137			−0.0883883
$129$	−103.958	+	108.693i	−0.805872	+	0.842580i
$130$		0			0
$131$			61.1500i			0.466794i	0.972382	+	0.233397i	$0.0749841\pi$
$131$			61.1500i			0.466794i	−0.972382	+	0.233397i	$0.925016\pi$
$132$	89.5134	−	93.5907i	0.678132	−	0.709021i
$133$			15.5279i			0.116751i
$134$		−	154.717i		−	1.15460i
$135$		0			0
$136$	57.5650			0.423272
$137$	185.256			1.35223			0.676115	−	0.736796i	$-0.263662\pi$
$137$	185.256			1.35223			0.676115	+	0.736796i	$0.263662\pi$
$138$	−34.9222	−	33.4008i	−0.253060	−	0.242035i
$139$	−214.966			−1.54652			−0.773259	−	0.634090i	$-0.781375\pi$
$139$	−214.966			−1.54652			−0.773259	+	0.634090i	$0.781375\pi$
$140$		0			0
$141$	79.6872	+	76.2156i	0.565158	+	0.540536i
$142$		−	20.3008i		−	0.142964i
$143$	−334.076			−2.33620
$144$	1.60249	+	35.9643i	0.0111284	+	0.249752i
$145$		0			0
$146$			27.2854i			0.186886i
$147$	15.1761	+	14.5150i	0.103239	+	0.0987414i
$148$		−	117.882i		−	0.796502i
$149$		−	190.863i		−	1.28096i	−0.767975	−	0.640480i	$-0.778736\pi$
$149$		−	190.863i		−	1.28096i	0.767975	−	0.640480i	$-0.221264\pi$
$150$		0			0
$151$	−228.832			−1.51544			−0.757720	−	0.652579i	$-0.773687\pi$
$151$	−228.832			−1.51544			−0.757720	+	0.652579i	$0.773687\pi$
$152$	−16.6000			−0.109211
$153$	−8.15359	−	182.989i	−0.0532915	−	1.19601i
$154$	80.7613			0.524424
$155$		0			0
$156$	64.1881	−	67.1118i	0.411462	−	0.430204i
$157$			162.693i			1.03626i	0.855302	+	0.518130i	$0.173372\pi$
$157$			162.693i			1.03626i	−0.855302	+	0.518130i	$0.826628\pi$
$158$	−172.917			−1.09441
$159$	−88.7554	−	84.8887i	−0.558210	−	0.533891i
$160$		0			0
$161$		−	30.1351i		−	0.187175i
$162$	114.097	−	10.1881i	0.704305	−	0.0628894i
$163$			165.314i			1.01420i	0.861888	+	0.507099i	$0.169282\pi$
$163$			165.314i			1.01420i	−0.861888	+	0.507099i	$0.830718\pi$
$164$			72.3484i			0.441149i
$165$		0			0
$166$	105.226			0.633893
$167$	−284.970			−1.70641			−0.853203	−	0.521578i	$-0.825343\pi$
$167$	−284.970			−1.70641			−0.853203	+	0.521578i	$0.825343\pi$
$168$	−15.5172	+	16.2240i	−0.0923641	+	0.0965713i
$169$	−70.5585			−0.417506
$170$		0			0
$171$	2.35125	+	52.7686i	0.0137500	+	0.308588i
$172$		−	100.269i		−	0.582960i
$173$	−99.5549			−0.575462			−0.287731	−	0.957711i	$-0.592901\pi$
$173$	−99.5549			−0.575462			−0.287731	+	0.957711i	$0.592901\pi$
$174$	−10.0798	+	10.5389i	−0.0579296	+	0.0605683i
$175$		0			0
$176$			86.3375i			0.490554i
$177$	−228.386	+	238.789i	−1.29032	+	1.34909i
$178$			130.152i			0.731191i
$179$		−	12.5355i		−	0.0700305i	−0.999387	−	0.0350153i	$-0.988852\pi$
$179$		−	12.5355i		−	0.0700305i	0.999387	−	0.0350153i	$-0.0111480\pi$
$180$		0			0
$181$	273.269			1.50977			0.754886	−	0.655856i	$-0.227692\pi$
$181$	273.269			1.50977			0.754886	+	0.655856i	$0.227692\pi$
$182$	57.9122			0.318199
$183$	89.9946	+	86.0739i	0.491774	+	0.470349i
$184$	32.2158			0.175086
$185$		0			0
$186$	−64.6355	−	61.8196i	−0.347503	−	0.332364i
$187$		−	439.292i		−	2.34915i
$188$	−73.5115			−0.391019
$189$	53.7711	+	47.0284i	0.284503	+	0.248828i
$190$		0			0
$191$		−	342.054i		−	1.79086i	−0.445204	−	0.895429i	$-0.646869\pi$
$191$		−	342.054i		−	1.79086i	0.445204	−	0.895429i	$-0.353131\pi$
$192$	−17.3442	−	16.5886i	−0.0903342	−	0.0863987i
$193$			165.170i			0.855801i	0.903826	+	0.427901i	$0.140747\pi$
$193$			165.170i			0.855801i	−0.903826	+	0.427901i	$0.859253\pi$
$194$			8.07927i			0.0416457i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	30.6180			0.155421			0.0777107	−	0.996976i	$-0.475239\pi$
$197$	30.6180			0.155421			0.0777107	+	0.996976i	$0.475239\pi$
$198$	274.452	−	12.2290i	1.38612	−	0.0617625i
$199$	95.5834			0.480319			0.240159	−	0.970733i	$-0.422800\pi$
$199$	95.5834			0.480319			0.240159	+	0.970733i	$0.422800\pi$
$200$		0			0
$201$	226.851	−	237.184i	1.12861	−	1.18002i
$202$			99.6133i			0.493135i
$203$	−9.09422			−0.0447991
$204$	88.2484	+	84.4038i	0.432590	+	0.413744i
$205$		0			0
$206$			227.654i			1.10512i
$207$	−4.56309	−	102.408i	−0.0220439	−	0.494727i
$208$			61.9107i			0.297648i
$209$			126.679i			0.606118i
$210$		0			0
$211$	−219.336			−1.03951			−0.519754	−	0.854316i	$-0.673976\pi$
$211$	−219.336			−1.03951			−0.519754	+	0.854316i	$0.673976\pi$
$212$	81.8769			0.386212
$213$	29.7658	−	31.1216i	0.139746	−	0.146111i
$214$	84.3121			0.393982
$215$		0			0
$216$	−50.2755	+	57.4837i	−0.232757	+	0.266128i
$217$		−	55.7753i		−	0.257029i
$218$	−192.474			−0.882909
$219$	−40.0068	+	41.8291i	−0.182679	+	0.191000i
$220$		0			0
$221$		−	315.006i		−	1.42537i
$222$	172.843	−	180.716i	0.778572	−	0.814036i
$223$			129.309i			0.579863i	0.957047	+	0.289931i	$0.0936325\pi$
$223$			129.309i			0.579863i	−0.957047	+	0.289931i	$0.906368\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−15.8938			−0.0703263
$227$	28.0990			0.123784			0.0618920	−	0.998083i	$-0.480287\pi$
$227$	28.0990			0.123784			0.0618920	+	0.998083i	$0.480287\pi$
$228$	−25.4482	−	24.3395i	−0.111615	−	0.106752i
$229$	−112.434			−0.490980			−0.245490	−	0.969399i	$-0.578949\pi$
$229$	−112.434			−0.490980			−0.245490	+	0.969399i	$0.578949\pi$
$230$		0			0
$231$	123.809	+	118.415i	0.535969	+	0.512619i
$232$		−	9.72213i		−	0.0419058i
$233$	86.1561			0.369769			0.184884	−	0.982760i	$-0.440809\pi$
$233$	86.1561			0.369769			0.184884	+	0.982760i	$0.440809\pi$
$234$	196.803	−	8.76912i	0.841040	−	0.0374749i
$235$		0			0
$236$		−	220.283i		−	0.933402i
$237$	−265.086	−	253.538i	−1.11851	−	1.06978i
$238$			76.1514i			0.319964i
$239$			167.453i			0.700639i	0.936630	+	0.350320i	$0.113927\pi$
$239$			167.453i			0.700639i	−0.936630	+	0.350320i	$0.886073\pi$
$240$		0			0
$241$	207.471			0.860875			0.430437	−	0.902621i	$-0.358359\pi$
$241$	207.471			0.860875			0.430437	+	0.902621i	$0.358359\pi$
$242$	487.741			2.01546
$243$	189.852	+	151.675i	0.781283	+	0.624177i
$244$	−83.0200			−0.340246
$245$		0			0
$246$	−106.080	+	110.912i	−0.431218	+	0.450860i
$247$			90.8384i			0.367767i
$248$	59.6263			0.240429
$249$	161.314	+	154.286i	0.647848	+	0.619624i
$250$		0			0
$251$		−	334.951i		−	1.33446i	−0.744850	−	0.667232i	$-0.767479\pi$
$251$		−	334.951i		−	1.33446i	0.744850	−	0.667232i	$-0.232521\pi$
$252$	−47.5763	+	2.11990i	−0.188795	+	0.00841228i
$253$		−	245.846i		−	0.971724i
$254$		−	140.711i		−	0.553979i
$255$		0			0
$256$	16.0000			0.0625000
$257$	508.318			1.97789			0.988945	−	0.148286i	$-0.0473755\pi$
$257$	508.318			1.97789			0.988945	+	0.148286i	$0.0473755\pi$
$258$	147.018	−	153.715i	0.569838	−	0.595794i
$259$	155.944			0.602099
$260$		0			0
$261$	−30.9050	+	1.37706i	−0.118410	+	0.00527608i
$262$		−	86.4791i		−	0.330073i
$263$	−183.740			−0.698632			−0.349316	−	0.937005i	$-0.613586\pi$
$263$	−183.740			−0.698632			−0.349316	+	0.937005i	$0.613586\pi$
$264$	−126.591	+	132.357i	−0.479512	+	0.501353i
$265$		0			0
$266$		−	21.9598i		−	0.0825555i
$267$	−190.833	+	199.526i	−0.714732	+	0.747288i
$268$			218.803i			0.816428i
$269$		−	104.569i		−	0.388732i	−0.980929	−	0.194366i	$-0.937735\pi$
$269$		−	104.569i		−	0.388732i	0.980929	−	0.194366i	$-0.0622649\pi$
$270$		0			0
$271$	47.7128			0.176062			0.0880309	−	0.996118i	$-0.471943\pi$
$271$	47.7128			0.176062			0.0880309	+	0.996118i	$0.471943\pi$
$272$	−81.4092			−0.299299
$273$	88.7806	+	84.9128i	0.325204	+	0.311036i
$274$	−261.991			−0.956171
$275$		0			0
$276$	49.3875	+	47.2359i	0.178940	+	0.171145i
$277$			91.1196i			0.328952i	0.986381	+	0.164476i	$0.0525933\pi$
$277$			91.1196i			0.328952i	−0.986381	+	0.164476i	$0.947407\pi$
$278$	304.008			1.09355
$279$	−8.44556	−	189.542i	−0.0302708	−	0.679361i
$280$		0			0
$281$			57.4942i			0.204606i	0.994753	+	0.102303i	$0.0326211\pi$
$281$			57.4942i			0.204606i	−0.994753	+	0.102303i	$0.967379\pi$
$282$	−112.695	−	107.785i	−0.399627	−	0.382217i
$283$			181.851i			0.642583i	0.946980	+	0.321291i	$0.104117\pi$
$283$			181.851i			0.642583i	−0.946980	+	0.321291i	$0.895883\pi$
$284$			28.7097i			0.101091i
$285$		0			0
$286$	472.455			1.65194
$287$	−95.7079			−0.333477
$288$	−2.26626	−	50.8612i	−0.00786897	−	0.176601i
$289$	125.216			0.433274
$290$		0			0
$291$	−11.8461	+	12.3857i	−0.0407083	+	0.0425625i
$292$		−	38.5873i		−	0.132148i
$293$	137.935			0.470768			0.235384	−	0.971902i	$-0.424365\pi$
$293$	137.935			0.470768			0.235384	+	0.971902i	$0.424365\pi$
$294$	−21.4623	−	20.5273i	−0.0730010	−	0.0698207i
$295$		0			0
$296$			166.711i			0.563212i
$297$	438.671	+	383.664i	1.47701	+	1.29180i
$298$			269.921i			0.905775i
$299$		−	176.291i		−	0.589601i
$300$		0			0
$301$	132.644			0.440676
$302$	323.617			1.07158
$303$	−146.057	+	152.709i	−0.482035	+	0.503991i
$304$	23.4760			0.0772236
$305$		0			0
$306$	11.5309	+	258.786i	0.0376827	+	0.845705i
$307$			263.303i			0.857665i	0.903384	+	0.428833i	$0.141075\pi$
$307$			263.303i			0.857665i	−0.903384	+	0.428833i	$0.858925\pi$
$308$	−114.214			−0.370824
$309$	−333.795	+	348.999i	−1.08024	+	1.12945i
$310$		0			0
$311$			236.151i			0.759329i	0.925124	+	0.379664i	$0.123961\pi$
$311$			236.151i			0.759329i	−0.925124	+	0.379664i	$0.876039\pi$
$312$	−90.7756	+	94.9105i	−0.290948	+	0.304200i
$313$		−	554.176i		−	1.77053i	−0.465088	−	0.885264i	$-0.653977\pi$
$313$		−	554.176i		−	1.77053i	0.465088	−	0.885264i	$-0.346023\pi$
$314$		−	230.082i		−	0.732746i
$315$		0			0
$316$	244.542			0.773868
$317$	−185.897			−0.586427			−0.293213	−	0.956047i	$-0.594725\pi$
$317$	−185.897			−0.586427			−0.293213	+	0.956047i	$0.594725\pi$
$318$	125.519	+	120.051i	0.394714	+	0.377518i
$319$	−74.1918			−0.232576
$320$		0			0
$321$	129.252	+	123.621i	0.402655	+	0.385113i
$322$			42.6175i			0.132352i
$323$	−119.448			−0.369807
$324$	−161.358	+	14.4081i	−0.498019	+	0.0444695i
$325$		0			0
$326$		−	233.790i		−	0.717147i
$327$	−295.067	−	282.212i	−0.902345	−	0.863034i
$328$		−	102.316i		−	0.311939i
$329$		−	97.2466i		−	0.295582i
$330$		0			0
$331$	334.725			1.01125			0.505627	−	0.862752i	$-0.331261\pi$
$331$	334.725			1.01125			0.505627	+	0.862752i	$0.331261\pi$
$332$	−148.812			−0.448230
$333$	529.944	−	23.6131i	1.59142	−	0.0709103i
$334$	403.008			1.20661
$335$		0			0
$336$	21.9446	−	22.9442i	0.0653113	−	0.0682862i
$337$			616.673i			1.82989i	0.403578	+	0.914945i	$0.367766\pi$
$337$			616.673i			1.82989i	−0.403578	+	0.914945i	$0.632234\pi$
$338$	99.7847			0.295221
$339$	−24.3655	−	23.3040i	−0.0718745	−	0.0687433i
$340$		0			0
$341$		−	455.022i		−	1.33438i
$342$	−3.32517	−	74.6261i	−0.00972273	−	0.218205i
$343$		−	18.5203i		−	0.0539949i
$344$			141.802i			0.412215i
$345$		0			0
$346$	140.792			0.406913
$347$	−178.599			−0.514696			−0.257348	−	0.966319i	$-0.582849\pi$
$347$	−178.599			−0.514696			−0.257348	+	0.966319i	$0.582849\pi$
$348$	14.2549	−	14.9042i	0.0409624	−	0.0428283i
$349$	304.258			0.871799			0.435900	−	0.899995i	$-0.356430\pi$
$349$	304.258			0.871799			0.435900	+	0.899995i	$0.356430\pi$
$350$		0			0
$351$	314.561	+	275.117i	0.896187	+	0.783808i
$352$		−	122.100i		−	0.346874i
$353$	−62.3918			−0.176747			−0.0883737	−	0.996087i	$-0.528167\pi$
$353$	−62.3918			−0.176747			−0.0883737	+	0.996087i	$0.528167\pi$
$354$	322.986	−	337.698i	0.912391	−	0.953950i
$355$		0			0
$356$		−	184.063i		−	0.517030i
$357$	−111.656	+	116.742i	−0.312761	+	0.327008i
$358$			17.7278i			0.0495190i
$359$			234.476i			0.653136i	0.945174	+	0.326568i	$0.105892\pi$
$359$			234.476i			0.653136i	−0.945174	+	0.326568i	$0.894108\pi$
$360$		0			0
$361$	−326.555			−0.904584
$362$	−386.460			−1.06757
$363$	747.718	+	715.144i	2.05983	+	1.97009i
$364$	−81.9002			−0.225000
$365$		0			0
$366$	−127.272	−	121.727i	−0.347736	−	0.332587i
$367$			437.328i			1.19163i	0.803122	+	0.595815i	$0.203171\pi$
$367$			437.328i			1.19163i	−0.803122	+	0.595815i	$0.796829\pi$
$368$	−45.5600			−0.123804
$369$	−325.245	+	14.4922i	−0.881423	+	0.0392742i
$370$		0			0
$371$			108.313i			0.291949i
$372$	91.4084	+	87.4262i	0.245722	+	0.235017i
$373$		−	192.812i		−	0.516923i	−0.966022	−	0.258462i	$-0.916784\pi$
$373$		−	192.812i		−	0.516923i	0.966022	−	0.258462i	$-0.0832156\pi$
$374$			621.252i			1.66110i
$375$		0			0
$376$	103.961			0.276492
$377$	−53.2013			−0.141118
$378$	−76.0438	−	66.5082i	−0.201174	−	0.175948i
$379$	−254.123			−0.670509			−0.335255	−	0.942128i	$-0.608822\pi$
$379$	−254.123			−0.670509			−0.335255	+	0.942128i	$0.608822\pi$
$380$		0			0
$381$	206.315	−	215.712i	0.541509	−	0.566174i
$382$			483.737i			1.26633i
$383$	−283.574			−0.740401			−0.370201	−	0.928952i	$-0.620711\pi$
$383$	−283.574			−0.740401			−0.370201	+	0.928952i	$0.620711\pi$
$384$	24.5283	+	23.4598i	0.0638759	+	0.0610931i
$385$		0			0
$386$		−	233.585i		−	0.605143i
$387$	450.764	−	20.0850i	1.16476	−	0.0518993i
$388$		−	11.4258i		−	0.0294480i
$389$			267.701i			0.688178i	0.938937	+	0.344089i	$0.111812\pi$
$389$			267.701i			0.688178i	−0.938937	+	0.344089i	$0.888188\pi$
$390$		0			0
$391$	231.813			0.592872
$392$	19.7990			0.0505076
$393$	126.799	−	132.574i	0.322643	−	0.337339i
$394$	−43.3004			−0.109899
$395$		0			0
$396$	−388.134	+	17.2944i	−0.980136	+	0.0436727i
$397$		−	194.275i		−	0.489359i	−0.969604	−	0.244679i	$-0.921317\pi$
$397$		−	194.275i		−	0.489359i	0.969604	−	0.244679i	$-0.0786827\pi$
$398$	−135.175			−0.339637
$399$	32.1982	−	33.6648i	0.0806972	−	0.0843729i
$400$		0			0
$401$		−	48.6208i		−	0.121249i	−0.998161	−	0.0606245i	$-0.980691\pi$
$401$		−	48.6208i		−	0.121249i	0.998161	−	0.0606245i	$-0.0193092\pi$
$402$	−320.816	+	335.429i	−0.798050	+	0.834401i
$403$		−	326.286i		−	0.809643i
$404$		−	140.875i		−	0.348699i
$405$		0			0
$406$	12.8612			0.0316778
$407$	1272.21			3.12582
$408$	−124.802	−	119.365i	−0.305888	−	0.292561i
$409$	−324.450			−0.793276			−0.396638	−	0.917975i	$-0.629823\pi$
$409$	−324.450			−0.793276			−0.396638	+	0.917975i	$0.629823\pi$
$410$		0			0
$411$	−401.638	−	384.140i	−0.977221	−	0.934648i
$412$		−	321.952i		−	0.781436i
$413$	291.407			0.705585
$414$	6.45319	+	144.827i	0.0155874	+	0.349825i
$415$		0			0
$416$		−	87.5550i		−	0.210469i
$417$	466.051	+	445.747i	1.11763	+	1.06894i
$418$		−	179.151i		−	0.428590i
$419$		−	588.706i		−	1.40503i	−0.711670	−	0.702514i	$-0.752061\pi$
$419$		−	588.706i		−	1.40503i	0.711670	−	0.702514i	$-0.247939\pi$
$420$		0			0
$421$	−231.638			−0.550210			−0.275105	−	0.961414i	$-0.588713\pi$
$421$	−231.638			−0.550210			−0.275105	+	0.961414i	$0.588713\pi$
$422$	310.188			0.735043
$423$	−14.7252	−	330.474i	−0.0348113	−	0.781262i
$424$	−115.791			−0.273093
$425$		0			0
$426$	−42.0952	+	44.0126i	−0.0988150	+	0.103316i
$427$		−	109.825i		−	0.257202i
$428$	−119.235			−0.278587
$429$	724.283	+	692.730i	1.68831	+	1.61475i
$430$		0			0
$431$		−	644.009i		−	1.49422i	−0.664701	−	0.747110i	$-0.731441\pi$
$431$		−	644.009i		−	1.49422i	0.664701	−	0.747110i	$-0.268559\pi$
$432$	71.1003	−	81.2942i	0.164584	−	0.188181i
$433$		−	107.672i		−	0.248665i	−0.992241	−	0.124332i	$-0.960321\pi$
$433$		−	107.672i		−	0.248665i	0.992241	−	0.124332i	$-0.0396789\pi$
$434$			78.8782i			0.181747i
$435$		0			0
$436$	272.199			0.624311
$437$	−66.8479			−0.152970
$438$	56.5781	−	59.1552i	0.129174	−	0.135058i
$439$	−486.128			−1.10735			−0.553677	−	0.832731i	$-0.686776\pi$
$439$	−486.128			−1.10735			−0.553677	+	0.832731i	$0.686776\pi$
$440$		0			0
$441$	−2.80436	−	62.9376i	−0.00635909	−	0.142716i
$442$			445.486i			1.00789i
$443$	−312.569			−0.705574			−0.352787	−	0.935704i	$-0.614766\pi$
$443$	−312.569			−0.705574			−0.352787	+	0.935704i	$0.614766\pi$
$444$	−244.437	+	255.571i	−0.550534	+	0.575611i
$445$		0			0
$446$		−	182.871i		−	0.410025i
$447$	−395.767	+	413.795i	−0.885386	+	0.925715i
$448$			21.1660i			0.0472456i
$449$			398.630i			0.887817i	0.896072	+	0.443909i	$0.146409\pi$
$449$			398.630i			0.887817i	−0.896072	+	0.443909i	$0.853591\pi$
$450$		0			0
$451$	−780.797			−1.73126
$452$	22.4772			0.0497282
$453$	496.111	+	474.498i	1.09517	+	1.04746i
$454$	−39.7380			−0.0875286
$455$		0			0
$456$	35.9892	+	34.4213i	0.0789237	+	0.0754853i
$457$		−	704.328i		−	1.54120i	−0.637319	−	0.770600i	$-0.719957\pi$
$457$		−	704.328i		−	1.54120i	0.637319	−	0.770600i	$-0.280043\pi$
$458$	159.006			0.347175
$459$	−361.764	+	413.631i	−0.788156	+	0.901157i
$460$		0			0
$461$			178.771i			0.387789i	0.981022	+	0.193895i	$0.0621120\pi$
$461$			178.771i			0.387789i	−0.981022	+	0.193895i	$0.937888\pi$
$462$	−175.092	−	167.464i	−0.378987	−	0.362477i
$463$			333.207i			0.719670i	0.933016	+	0.359835i	$0.117167\pi$
$463$			333.207i			0.719670i	−0.933016	+	0.359835i	$0.882833\pi$
$464$			13.7492i			0.0296318i
$465$		0			0
$466$	−121.843			−0.261466
$467$	−609.720			−1.30561			−0.652805	−	0.757526i	$-0.726408\pi$
$467$	−609.720			−1.30561			−0.652805	+	0.757526i	$0.726408\pi$
$468$	−278.322	+	12.4014i	−0.594705	+	0.0264987i
$469$	−289.449			−0.617161
$470$		0			0
$471$	337.355	−	352.721i	0.716252	−	0.748877i
$472$			311.527i			0.660015i
$473$	1082.12			2.28779
$474$	374.889	+	358.556i	0.790904	+	0.756448i
$475$		0			0
$476$		−	107.694i		−	0.226248i
$477$	16.4009	+	368.081i	0.0343834	+	0.771658i
$478$		−	236.814i		−	0.495427i
$479$		−	857.088i		−	1.78933i	−0.446739	−	0.894664i	$-0.647415\pi$
$479$		−	857.088i		−	1.78933i	0.446739	−	0.894664i	$-0.352585\pi$
$480$		0			0
$481$	912.272			1.89661
$482$	−293.408			−0.608730
$483$	−62.4873	+	65.3335i	−0.129373	+	0.135266i
$484$	−689.771			−1.42515
$485$		0			0
$486$	−268.491	−	214.501i	−0.552451	−	0.441360i
$487$		−	661.830i		−	1.35899i	−0.733678	−	0.679497i	$-0.762198\pi$
$487$		−	661.830i		−	1.35899i	0.733678	−	0.679497i	$-0.237802\pi$
$488$	117.408			0.240590
$489$	342.791	−	358.405i	0.701004	−	0.732934i
$490$		0			0
$491$			775.502i			1.57943i	0.613471	+	0.789717i	$0.289773\pi$
$491$			775.502i			1.57943i	−0.613471	+	0.789717i	$0.710227\pi$
$492$	150.019	−	156.853i	0.304917	−	0.318806i
$493$		−	69.9568i		−	0.141900i
$494$		−	128.465i		−	0.260050i
$495$		0			0
$496$	−84.3243			−0.170009
$497$	−37.9794			−0.0764173
$498$	−228.133	−	218.194i	−0.458098	−	0.438141i
$499$	329.020			0.659359			0.329679	−	0.944093i	$-0.393059\pi$
$499$	329.020			0.659359			0.329679	+	0.944093i	$0.393059\pi$
$500$		0			0
$501$	617.821	+	590.905i	1.23317	+	1.17945i
$502$			473.692i			0.943609i
$503$	−428.007			−0.850909			−0.425454	−	0.904980i	$-0.639886\pi$
$503$	−428.007			−0.850909			−0.425454	+	0.904980i	$0.639886\pi$
$504$	67.2831	−	2.99798i	0.133498	−	0.00594838i
$505$		0			0
$506$			347.679i			0.687113i
$507$	152.972	+	146.308i	0.301720	+	0.288576i
$508$			198.995i			0.391722i
$509$		−	129.534i		−	0.254488i	−0.991871	−	0.127244i	$-0.959387\pi$
$509$		−	129.534i		−	0.254488i	0.991871	−	0.127244i	$-0.0406131\pi$
$510$		0			0
$511$	51.0463			0.0998948
$512$	−22.6274			−0.0441942
$513$	104.322	−	119.279i	0.203356	−	0.232512i
$514$	−718.870			−1.39858
$515$		0			0
$516$	−207.915	+	217.386i	−0.402936	+	0.421290i
$517$		−	793.350i		−	1.53453i
$518$	−220.538			−0.425748
$519$	215.837	+	206.434i	0.415871	+	0.397753i
$520$		0			0
$521$			323.415i			0.620758i	0.950613	+	0.310379i	$0.100456\pi$
$521$			323.415i			0.620758i	−0.950613	+	0.310379i	$0.899544\pi$
$522$	43.7062	−	1.94745i	0.0837284	−	0.00373075i
$523$			156.308i			0.298869i	0.988772	+	0.149434i	$0.0477453\pi$
$523$			156.308i			0.298869i	−0.988772	+	0.149434i	$0.952255\pi$
$524$			122.300i			0.233397i
$525$		0			0
$526$	259.848			0.494007
$527$	429.049			0.814134
$528$	179.027	−	187.181i	0.339066	−	0.354510i
$529$	−399.268			−0.754760
$530$		0			0
$531$	990.290	−	44.1251i	1.86495	−	0.0830982i
$532$			31.0558i			0.0583756i
$533$	−559.892			−1.05045
$534$	269.879	−	282.172i	0.505392	−	0.528412i
$535$		0			0
$536$		−	309.434i		−	0.577302i
$537$	−25.9931	+	27.1771i	−0.0484044	+	0.0506092i
$538$			147.883i			0.274875i
$539$		−	151.091i		−	0.280317i
$540$		0			0
$541$	5.36672			0.00992000			0.00496000	−	0.999988i	$-0.498421\pi$
$541$	5.36672			0.00992000			0.00496000	+	0.999988i	$0.498421\pi$
$542$	−67.4760			−0.124495
$543$	−592.452	−	566.642i	−1.09107	−	1.04354i
$544$	115.130			0.211636
$545$		0			0
$546$	−125.555	−	120.085i	−0.229954	−	0.219936i
$547$			131.066i			0.239608i	0.992798	+	0.119804i	$0.0382267\pi$
$547$			131.066i			0.239608i	−0.992798	+	0.119804i	$0.961773\pi$
$548$	370.511			0.676115
$549$	−16.6299	−	373.220i	−0.0302912	−	0.679818i
$550$		0			0
$551$			20.1735i			0.0366125i
$552$	−69.8445	−	66.8017i	−0.126530	−	0.121018i
$553$			323.499i			0.584989i
$554$		−	128.863i		−	0.232604i
$555$		0			0
$556$	−429.932			−0.773259
$557$	−527.699			−0.947395			−0.473698	−	0.880688i	$-0.657081\pi$
$557$	−527.699			−0.947395			−0.473698	+	0.880688i	$0.657081\pi$
$558$	11.9438	+	268.052i	0.0214047	+	0.480381i
$559$	775.967			1.38813
$560$		0			0
$561$	−910.902	+	952.393i	−1.62371	+	1.69767i
$562$		−	81.3090i		−	0.144678i
$563$	−1029.77			−1.82907			−0.914534	−	0.404508i	$-0.867443\pi$
$563$	−1029.77			−1.82907			−0.914534	+	0.404508i	$0.867443\pi$
$564$	159.374	+	152.431i	0.282579	+	0.270268i
$565$		0			0
$566$		−	257.176i		−	0.454375i
$567$	−19.0601	−	213.457i	−0.0336158	−	0.376467i
$568$		−	40.6017i		−	0.0714818i
$569$		−	853.166i		−	1.49941i	−0.661771	−	0.749706i	$-0.730195\pi$
$569$		−	853.166i		−	1.49941i	0.661771	−	0.749706i	$-0.269805\pi$
$570$		0			0
$571$	−680.521			−1.19181			−0.595903	−	0.803057i	$-0.703206\pi$
$571$	−680.521			−1.19181			−0.595903	+	0.803057i	$0.703206\pi$
$572$	−668.152			−1.16810
$573$	−709.272	+	741.580i	−1.23782	+	1.29421i
$574$	135.351			0.235804
$575$		0			0
$576$	3.20498	+	71.9286i	0.00556420	+	0.124876i
$577$		−	680.596i		−	1.17954i	−0.807570	−	0.589771i	$-0.799218\pi$
$577$		−	680.596i		−	1.17954i	0.807570	−	0.589771i	$-0.200782\pi$
$578$	−177.083			−0.306371
$579$	342.491	−	358.091i	0.591521	−	0.618465i
$580$		0			0
$581$		−	196.860i		−	0.338830i
$582$	16.7529	−	17.5160i	0.0287851	−	0.0300963i
$583$			883.631i			1.51566i
$584$			54.5707i			0.0934431i
$585$		0			0
$586$	−195.070			−0.332883
$587$	−85.5232			−0.145695			−0.0728477	−	0.997343i	$-0.523209\pi$
$587$	−85.5232			−0.145695			−0.0728477	+	0.997343i	$0.523209\pi$
$588$	30.3523	+	29.0300i	0.0516195	+	0.0493707i
$589$	−123.725			−0.210059
$590$		0			0
$591$	−66.3804	−	63.4885i	−0.112319	−	0.107426i
$592$		−	235.765i		−	0.398251i
$593$	920.751			1.55270			0.776350	−	0.630302i	$-0.217069\pi$
$593$	920.751			1.55270			0.776350	+	0.630302i	$0.217069\pi$
$594$	−620.375	−	542.582i	−1.04440	−	0.913438i
$595$		0			0
$596$		−	381.726i		−	0.640480i
$597$	−207.227	−	198.199i	−0.347113	−	0.331991i
$598$			249.313i			0.416911i
$599$			305.908i			0.510697i	0.966849	+	0.255349i	$0.0821902\pi$
$599$			305.908i			0.510697i	−0.966849	+	0.255349i	$0.917810\pi$
$600$		0			0
$601$	−448.975			−0.747047			−0.373524	−	0.927621i	$-0.621851\pi$
$601$	−448.975			−0.747047			−0.373524	+	0.927621i	$0.621851\pi$
$602$	−187.586			−0.311605
$603$	−983.636	+	43.8286i	−1.63124	+	0.0726843i
$604$	−457.663			−0.757720
$605$		0			0
$606$	206.555	−	215.964i	0.340850	−	0.356376i
$607$		−	595.850i		−	0.981630i	−0.871264	−	0.490815i	$-0.836699\pi$
$607$		−	595.850i		−	0.981630i	0.871264	−	0.490815i	$-0.163301\pi$
$608$	−33.2001			−0.0546053
$609$	19.7165	+	18.8575i	0.0323751	+	0.0309647i
$610$		0			0
$611$		−	568.894i		−	0.931086i
$612$	−16.3072	−	365.978i	−0.0266457	−	0.598004i
$613$		−	1060.26i		−	1.72963i	−0.502094	−	0.864813i	$-0.667437\pi$
$613$		−	1060.26i		−	1.72963i	0.502094	−	0.864813i	$-0.332563\pi$
$614$		−	372.367i		−	0.606461i
$615$		0			0
$616$	161.523			0.262212
$617$	670.881			1.08733			0.543664	−	0.839303i	$-0.317037\pi$
$617$	670.881			1.08733			0.543664	+	0.839303i	$0.317037\pi$
$618$	472.057	−	493.559i	0.763846	−	0.798639i
$619$	−594.860			−0.961002			−0.480501	−	0.876994i	$-0.659545\pi$
$619$	−594.860			−0.961002			−0.480501	+	0.876994i	$0.659545\pi$
$620$		0			0
$621$	−202.458	+	231.485i	−0.326019	+	0.372762i
$622$		−	333.968i		−	0.536927i
$623$	243.492			0.390838
$624$	128.376	−	134.224i	0.205731	−	0.215102i
$625$		0			0
$626$			783.723i			1.25195i
$627$	262.677	−	274.642i	0.418942	−	0.438025i
$628$			325.386i			0.518130i
$629$			1199.59i			1.90713i
$630$		0			0
$631$	−899.137			−1.42494			−0.712470	−	0.701703i	$-0.752423\pi$
$631$	−899.137			−1.42494			−0.712470	+	0.701703i	$0.752423\pi$
$632$	−345.835			−0.547207
$633$	475.525	+	454.809i	0.751225	+	0.718497i
$634$	262.899			0.414666
$635$		0			0
$636$	−177.511	−	169.777i	−0.279105	−	0.266946i
$637$		−	108.344i		−	0.170084i
$638$	104.923			0.164456
$639$	−129.066	+	5.75088i	−0.201981	+	0.00899981i
$640$		0			0
$641$			642.796i			1.00280i	0.865215	+	0.501401i	$0.167182\pi$
$641$			642.796i			1.00280i	−0.865215	+	0.501401i	$0.832818\pi$
$642$	−182.790	−	174.827i	−0.284720	−	0.272316i
$643$		−	149.781i		−	0.232941i	−0.993194	−	0.116470i	$-0.962842\pi$
$643$		−	149.781i		−	0.232941i	0.993194	−	0.116470i	$-0.0371580\pi$
$644$		−	60.2702i		−	0.0935873i
$645$		0			0
$646$	168.924			0.261493
$647$	956.646			1.47859			0.739294	−	0.673383i	$-0.235160\pi$
$647$	956.646			1.47859			0.739294	+	0.673383i	$0.235160\pi$
$648$	228.195	−	20.3762i	0.352152	−	0.0314447i
$649$	2377.33			3.66307
$650$		0			0
$651$	−115.654	+	120.922i	−0.177656	+	0.185748i
$652$			330.629i			0.507099i
$653$	−1008.83			−1.54492			−0.772461	−	0.635062i	$-0.780974\pi$
$653$	−1008.83			−1.54492			−0.772461	+	0.635062i	$0.780974\pi$
$654$	417.288	+	399.108i	0.638055	+	0.610257i
$655$		0			0
$656$			144.697i			0.220574i
$657$	173.471	−	7.72948i	0.264035	−	0.0117648i
$658$			137.527i			0.209008i
$659$			236.530i			0.358922i	0.983765	+	0.179461i	$0.0574354\pi$
$659$			236.530i			0.358922i	−0.983765	+	0.179461i	$0.942565\pi$
$660$		0			0
$661$	317.576			0.480448			0.240224	−	0.970717i	$-0.422779\pi$
$661$	317.576			0.480448			0.240224	+	0.970717i	$0.422779\pi$
$662$	−473.373			−0.715065
$663$	−653.188	+	682.940i	−0.985200	+	1.03008i
$664$	210.453			0.316947
$665$		0			0
$666$	−749.454	+	33.3940i	−1.12531	+	0.0501412i
$667$		−	39.1508i		−	0.0586968i
$668$	−569.940			−0.853203
$669$	268.132	−	280.345i	0.400795	−	0.419051i
$670$		0			0
$671$		−	895.968i		−	1.33527i
$672$	−31.0343	+	32.4480i	−0.0461821	+	0.0482856i
$673$		−	910.481i		−	1.35287i	−0.736503	−	0.676435i	$-0.763524\pi$
$673$		−	910.481i		−	1.35287i	0.736503	−	0.676435i	$-0.236476\pi$
$674$		−	872.107i		−	1.29393i
$675$		0			0
$676$	−141.117			−0.208753
$677$	276.295			0.408117			0.204059	−	0.978959i	$-0.434587\pi$
$677$	276.295			0.408117			0.204059	+	0.978959i	$0.434587\pi$
$678$	34.4580	+	32.9568i	0.0508230	+	0.0486088i
$679$	15.1149			0.0222606
$680$		0			0
$681$	−60.9192	−	58.2652i	−0.0894555	−	0.0855583i
$682$			643.498i			0.943546i
$683$	−52.2298			−0.0764711			−0.0382356	−	0.999269i	$-0.512174\pi$
$683$	−52.2298			−0.0764711			−0.0382356	+	0.999269i	$0.512174\pi$
$684$	4.70250	+	105.537i	0.00687501	+	0.154294i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	243.760	+	233.140i	0.354818	+	0.339360i
$688$		−	200.538i		−	0.291480i
$689$			633.632i			0.919641i
$690$		0			0
$691$	340.120			0.492215			0.246107	−	0.969243i	$-0.420848\pi$
$691$	340.120			0.492215			0.246107	+	0.969243i	$0.420848\pi$
$692$	−199.110			−0.287731
$693$	−22.8783	−	513.453i	−0.0330134	−	0.740913i
$694$	252.578			0.363945
$695$		0			0
$696$	−20.1595	+	21.0778i	−0.0289648	+	0.0302842i
$697$		−	736.228i		−	1.05628i
$698$	−430.286			−0.616455
$699$	−186.788	−	178.651i	−0.267222	−	0.255580i
$700$		0			0
$701$			945.305i			1.34851i	0.738499	+	0.674255i	$0.235535\pi$
$701$			945.305i			1.34851i	−0.738499	+	0.674255i	$0.764465\pi$
$702$	−444.857	−	389.074i	−0.633700	−	0.554236i
$703$		−	345.925i		−	0.492070i
$704$			172.675i			0.245277i
$705$		0			0
$706$	88.2353			0.124979
$707$	186.360			0.263592
$708$	−456.772	+	477.577i	−0.645158	+	0.674544i
$709$	549.256			0.774691			0.387346	−	0.921935i	$-0.373392\pi$
$709$	549.256			0.774691			0.387346	+	0.921935i	$0.373392\pi$
$710$		0			0
$711$	48.9846	+	1099.35i	0.0688953	+	1.54620i
$712$			260.304i			0.365596i
$713$	240.114			0.336765
$714$	157.905	−	165.098i	0.221156	−	0.231229i
$715$		0			0
$716$		−	25.0709i		−	0.0350153i
$717$	347.225	−	363.041i	0.484275	−	0.506333i
$718$		−	331.599i		−	0.461837i
$719$		−	460.758i		−	0.640832i	−0.947277	−	0.320416i	$-0.896177\pi$
$719$		−	460.758i		−	0.640832i	0.947277	−	0.320416i	$-0.103823\pi$
$720$		0			0
$721$	425.902			0.590710
$722$	461.818			0.639638
$723$	−449.801	−	430.205i	−0.622131	−	0.595028i
$724$	546.538			0.754886
$725$		0			0
$726$	−1057.43	−	1011.37i	−1.45652	−	1.39307i
$727$		−	830.945i		−	1.14298i	−0.820610	−	0.571489i	$-0.806366\pi$
$727$		−	830.945i		−	1.14298i	0.820610	−	0.571489i	$-0.193634\pi$
$728$	115.824			0.159099
$729$	−97.0941	−	722.505i	−0.133188	−	0.991091i
$730$		0			0
$731$			1020.35i			1.39583i
$732$	179.989	+	172.148i	0.245887	+	0.235175i
$733$			357.586i			0.487838i	0.969796	+	0.243919i	$0.0784332\pi$
$733$			357.586i			0.487838i	−0.969796	+	0.243919i	$0.921567\pi$
$734$		−	618.476i		−	0.842610i
$735$		0			0
$736$	64.4316			0.0875429
$737$	−2361.36			−3.20402
$738$	459.966	−	20.4951i	0.623260	−	0.0277711i
$739$	−1194.69			−1.61663			−0.808313	−	0.588753i	$-0.799619\pi$
$739$	−1194.69			−1.61663			−0.808313	+	0.588753i	$0.799619\pi$
$740$		0			0
$741$	188.360	−	196.940i	0.254197	−	0.265775i
$742$		−	153.178i		−	0.206439i
$743$	1281.79			1.72516			0.862578	−	0.505924i	$-0.168849\pi$
$743$	1281.79			1.72516			0.862578	+	0.505924i	$0.168849\pi$
$744$	−129.271	−	123.639i	−0.173751	−	0.166182i
$745$		0			0
$746$			272.678i			0.365520i
$747$	−29.8088	−	668.992i	−0.0399047	−	0.895572i
$748$		−	878.584i		−	1.17458i
$749$		−	157.733i		−	0.210592i
$750$		0			0
$751$	140.864			0.187569			0.0937846	−	0.995593i	$-0.470103\pi$
$751$	140.864			0.187569			0.0937846	+	0.995593i	$0.470103\pi$
$752$	−147.023			−0.195509
$753$	−694.543	+	726.180i	−0.922368	+	0.964382i
$754$	75.2380			0.0997852
$755$		0			0
$756$	107.542	+	94.0568i	0.142252	+	0.124414i
$757$			1205.54i			1.59252i	0.604954	+	0.796260i	$0.293191\pi$
$757$			1205.54i			1.59252i	−0.604954	+	0.796260i	$0.706809\pi$
$758$	359.384			0.474122
$759$	−509.779	+	532.999i	−0.671646	+	0.702239i
$760$		0			0
$761$			619.622i			0.814221i	0.913379	+	0.407110i	$0.133464\pi$
$761$			619.622i			0.814221i	−0.913379	+	0.407110i	$0.866536\pi$
$762$	−291.773	+	305.063i	−0.382904	+	0.400346i
$763$			360.086i			0.471935i
$764$		−	684.108i		−	0.895429i
$765$		0			0
$766$	401.034			0.523543
$767$	1704.73			2.22260
$768$	−34.6883	−	33.1771i	−0.0451671	−	0.0431994i
$769$	18.6417			0.0242415			0.0121208	−	0.999927i	$-0.496142\pi$
$769$	18.6417			0.0242415			0.0121208	+	0.999927i	$0.496142\pi$
$770$		0			0
$771$	−1102.04	−	1054.03i	−1.42937	−	1.36710i
$772$			330.339i			0.427901i
$773$	−923.108			−1.19419			−0.597094	−	0.802171i	$-0.703678\pi$
$773$	−923.108			−1.19419			−0.597094	+	0.802171i	$0.703678\pi$
$774$	−637.476	+	28.4045i	−0.823613	+	0.0366984i
$775$		0			0
$776$			16.1585i			0.0208229i
$777$	−338.089	−	323.360i	−0.435121	−	0.416164i
$778$		−	378.587i		−	0.486616i
$779$			212.306i			0.272537i
$780$		0			0
$781$	−309.841			−0.396723
$782$	−327.833			−0.419224
$783$	69.8580	+	61.0981i	0.0892184	+	0.0780308i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−179.320	+	187.488i	−0.228143	+	0.238535i
$787$		−	937.629i		−	1.19140i	−0.803208	−	0.595698i	$-0.796875\pi$
$787$		−	937.629i		−	1.19140i	0.803208	−	0.595698i	$-0.203125\pi$
$788$	61.2360			0.0777107
$789$	398.352	+	380.998i	0.504883	+	0.482887i
$790$		0			0
$791$			29.7345i			0.0375910i
$792$	548.904	−	24.4579i	0.693060	−	0.0308812i
$793$		−	642.479i		−	0.810188i
$794$			274.747i			0.346029i
$795$		0			0
$796$	191.167			0.240159
$797$	−1269.26			−1.59255			−0.796276	−	0.604933i	$-0.793200\pi$
$797$	−1269.26			−1.59255			−0.796276	+	0.604933i	$0.793200\pi$
$798$	−45.5351	+	47.6092i	−0.0570615	+	0.0596607i
$799$	748.064			0.936251
$800$		0			0
$801$	827.461	−	36.8698i	1.03304	−	0.0460298i
$802$			68.7602i			0.0857359i
$803$	416.442			0.518608
$804$	453.702	−	474.369i	0.564307	−	0.590011i
$805$		0			0
$806$			461.438i			0.572504i
$807$	−216.831	+	226.707i	−0.268687	+	0.280926i
$808$			199.227i			0.246568i
$809$		−	184.116i		−	0.227584i	−0.993505	−	0.113792i	$-0.963700\pi$
$809$		−	184.116i		−	0.227584i	0.993505	−	0.113792i	$-0.0362998\pi$
$810$		0			0
$811$	−1513.33			−1.86601			−0.933004	−	0.359866i	$-0.882822\pi$
$811$	−1513.33			−1.86601			−0.933004	+	0.359866i	$0.882822\pi$
$812$	−18.1884			−0.0223996
$813$	−103.442	−	98.9357i	−0.127235	−	0.121692i
$814$	−1799.17			−2.21029
$815$		0			0
$816$	176.497	+	168.808i	0.216295	+	0.206872i
$817$		−	294.240i		−	0.360146i
$818$	458.841			0.560931
$819$	−16.4055	−	368.185i	−0.0200312	−	0.449555i
$820$		0			0
$821$			373.901i			0.455422i	0.973729	+	0.227711i	$0.0731241\pi$
$821$			373.901i			0.455422i	−0.973729	+	0.227711i	$0.926876\pi$
$822$	568.002	+	543.256i	0.690999	+	0.660896i
$823$			1175.55i			1.42837i	0.699958	+	0.714184i	$0.253202\pi$
$823$			1175.55i			1.42837i	−0.699958	+	0.714184i	$0.746798\pi$
$824$			455.308i			0.552559i
$825$		0			0
$826$	−412.111			−0.498924
$827$	−309.851			−0.374668			−0.187334	−	0.982296i	$-0.559985\pi$
$827$	−309.851			−0.374668			−0.187334	+	0.982296i	$0.559985\pi$
$828$	−9.12619	−	204.817i	−0.0110220	−	0.247363i
$829$	−1268.28			−1.52989			−0.764943	−	0.644098i	$-0.777233\pi$
$829$	−1268.28			−1.52989			−0.764943	+	0.644098i	$0.777233\pi$
$830$		0			0
$831$	188.943	−	197.549i	0.227368	−	0.237725i
$832$			123.821i			0.148824i
$833$	142.466			0.171028
$834$	−659.095	−	630.381i	−0.790282	−	0.755853i
$835$		0			0
$836$			253.357i			0.303059i
$837$	−374.718	+	428.443i	−0.447691	+	0.511879i
$838$			832.556i			0.993504i
$839$			785.235i			0.935917i	0.883750	+	0.467959i	$0.155010\pi$
$839$			785.235i			0.935917i	−0.883750	+	0.467959i	$0.844990\pi$
$840$		0			0
$841$	829.185			0.985951
$842$	327.586			0.389057
$843$	119.218	−	124.649i	0.141421	−	0.147863i
$844$	−438.673			−0.519754
$845$		0			0
$846$	20.8246	+	467.361i	0.0246153	+	0.552436i
$847$		−	912.481i		−	1.07731i
$848$	163.754			0.193106
$849$	377.080	−	394.256i	0.444147	−	0.464377i
$850$		0			0
$851$			671.340i			0.788883i
$852$	59.5316	−	62.2433i	0.0698728	−	0.0730555i
$853$		−	922.834i		−	1.08187i	−0.841065	−	0.540934i	$-0.818071\pi$
$853$		−	922.834i		−	1.08187i	0.841065	−	0.540934i	$-0.181929\pi$
$854$			155.316i			0.181869i
$855$		0			0
$856$	168.624			0.196991
$857$	−78.6000			−0.0917153			−0.0458576	−	0.998948i	$-0.514602\pi$
$857$	−78.6000			−0.0917153			−0.0458576	+	0.998948i	$0.514602\pi$
$858$	−1024.29	−	979.668i	−1.19381	−	1.14180i
$859$	1397.46			1.62685			0.813425	−	0.581669i	$-0.197600\pi$
$859$	1397.46			1.62685			0.813425	+	0.581669i	$0.197600\pi$
$860$		0			0
$861$	207.497	+	198.457i	0.240995	+	0.230496i
$862$			910.766i			1.05657i
$863$	136.180			0.157799			0.0788993	−	0.996883i	$-0.474859\pi$
$863$	136.180			0.157799			0.0788993	+	0.996883i	$0.474859\pi$
$864$	−100.551	+	114.967i	−0.116378	+	0.133064i
$865$		0			0
$866$			152.271i			0.175833i
$867$	−271.472	−	259.645i	−0.313116	−	0.299475i
$868$		−	111.551i		−	0.128515i
$869$			2639.15i			3.03699i
$870$		0			0
$871$	−1693.28			−1.94406
$872$	−384.948			−0.441454
$873$	51.3652	−	2.28872i	0.0588376	−	0.00262167i
$874$	94.5372			0.108166
$875$		0			0
$876$	−80.0135	+	83.6581i	−0.0913396	+	0.0955002i
$877$			732.352i			0.835065i	0.908662	+	0.417532i	$0.137105\pi$
$877$			732.352i			0.835065i	−0.908662	+	0.417532i	$0.862895\pi$
$878$	687.489			0.783018
$879$	−299.046	−	286.018i	−0.340212	−	0.325390i
$880$		0			0
$881$			936.339i			1.06281i	0.847117	+	0.531407i	$0.178337\pi$
$881$			936.339i			1.06281i	−0.847117	+	0.531407i	$0.821663\pi$
$882$	3.96596	+	89.0071i	0.00449655	+	0.100915i
$883$		−	579.650i		−	0.656456i	−0.944599	−	0.328228i	$-0.893549\pi$
$883$		−	579.650i		−	0.656456i	0.944599	−	0.328228i	$-0.106451\pi$
$884$		−	630.013i		−	0.712684i
$885$		0			0
$886$	442.040			0.498916
$887$	−1141.28			−1.28667			−0.643335	−	0.765585i	$-0.722450\pi$
$887$	−1141.28			−1.28667			−0.643335	+	0.765585i	$0.722450\pi$
$888$	345.686	−	361.432i	0.389286	−	0.407018i
$889$	−263.245			−0.296114
$890$		0			0
$891$	−155.495	−	1741.41i	−0.174518	−	1.95444i
$892$			258.619i			0.289931i
$893$	−215.719			−0.241567
$894$	559.700	−	585.194i	0.626062	−	0.654579i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	−365.551	+	382.202i	−0.407526	+	0.426089i
$898$		−	563.748i		−	0.627782i
$899$		−	72.4619i		−	0.0806028i
$900$		0			0
$901$	−833.192			−0.924742
$902$	1104.21			1.22418
$903$	−287.574	−	275.046i	−0.318465	−	0.304591i
$904$	−31.7875			−0.0351632
$905$		0			0
$906$	−701.608	−	671.042i	−0.774401	−	0.740664i
$907$			632.857i			0.697748i	0.937170	+	0.348874i	$0.113436\pi$
$907$			632.857i			0.697748i	−0.937170	+	0.348874i	$0.886564\pi$
$908$	56.1980			0.0618920
$909$	633.307	−	28.2188i	0.696707	−	0.0310437i
$910$		0			0
$911$		−	962.509i		−	1.05654i	−0.849076	−	0.528271i	$-0.822841\pi$
$911$		−	962.509i		−	1.05654i	0.849076	−	0.528271i	$-0.177159\pi$
$912$	−50.8964	−	48.6791i	−0.0558075	−	0.0533762i
$913$		−	1606.01i		−	1.75905i
$914$			996.070i			1.08979i
$915$		0			0
$916$	−224.869			−0.245490
$917$	−161.788			−0.176431
$918$	511.611	−	584.963i	0.557310	−	0.637215i
$919$	−895.701			−0.974647			−0.487323	−	0.873222i	$-0.662027\pi$
$919$	−895.701			−0.974647			−0.487323	+	0.873222i	$0.662027\pi$
$920$		0			0
$921$	545.977	−	570.847i	0.592809	−	0.619812i
$922$		−	252.820i		−	0.274208i
$923$	−222.180			−0.240715
$924$	247.618	+	236.830i	0.267985	+	0.256310i
$925$		0			0
$926$		−	471.226i		−	0.508883i
$927$	1447.35	−	64.4906i	1.56132	−	0.0695691i
$928$		−	19.4443i		−	0.0209529i
$929$		−	446.813i		−	0.480961i	−0.970654	−	0.240480i	$-0.922695\pi$
$929$		−	446.813i		−	0.480961i	0.970654	−	0.240480i	$-0.0773050\pi$
$930$		0			0
$931$	−41.0830			−0.0441278
$932$	172.312			0.184884
$933$	489.676	−	511.981i	0.524840	−	0.548747i
$934$	862.274			0.923205
$935$		0			0
$936$	393.607	−	17.5382i	0.420520	−	0.0187374i
$937$			365.622i			0.390205i	0.980783	+	0.195102i	$0.0625039\pi$
$937$			365.622i			0.390205i	−0.980783	+	0.195102i	$0.937496\pi$
$938$	409.342			0.436399
$939$	−1149.12	+	1201.46i	−1.22377	+	1.27951i
$940$		0			0
$941$			1434.12i			1.52404i	0.647556	+	0.762018i	$0.275791\pi$
$941$			1434.12i			1.52404i	−0.647556	+	0.762018i	$0.724209\pi$
$942$	−477.092	+	498.823i	−0.506467	+	0.529536i
$943$		−	412.024i		−	0.436929i
$944$		−	440.566i		−	0.466701i
$945$		0			0
$946$	−1530.35			−1.61771
$947$	−795.408			−0.839924			−0.419962	−	0.907542i	$-0.637957\pi$
$947$	−795.408			−0.839924			−0.419962	+	0.907542i	$0.637957\pi$
$948$	−530.172	−	507.075i	−0.559254	−	0.534889i
$949$	298.621			0.314669
$950$		0			0
$951$	403.029	+	385.471i	0.423795	+	0.405332i
$952$			152.303i			0.159982i
$953$	−602.632			−0.632352			−0.316176	−	0.948700i	$-0.602399\pi$
$953$	−602.632			−0.632352			−0.316176	+	0.948700i	$0.602399\pi$
$954$	−23.1943	−	520.545i	−0.0243127	−	0.545645i
$955$		0			0
$956$			334.906i			0.350320i
$957$	160.849	+	153.842i	0.168077	+	0.160754i
$958$			1212.11i			1.26525i
$959$			490.140i			0.511095i
$960$		0			0
$961$	−516.588			−0.537552
$962$	−1290.15			−1.34111
$963$	−23.8842	−	536.027i	−0.0248018	−	0.556622i
$964$	414.942			0.430437
$965$		0			0
$966$	88.3703	−	92.3956i	0.0914807	−	0.0956476i
$967$			911.816i			0.942933i	0.881884	+	0.471467i	$0.156275\pi$
$967$			911.816i			0.942933i	−0.881884	+	0.471467i	$0.843725\pi$
$968$	975.483			1.00773
$969$	258.965	+	247.683i	0.267250	+	0.255607i
$970$		0			0
$971$		−	220.137i		−	0.226711i	−0.993554	−	0.113356i	$-0.963840\pi$
$971$		−	220.137i		−	0.226711i	0.993554	−	0.113356i	$-0.0361599\pi$
$972$	379.704	+	303.350i	0.390642	+	0.312088i
$973$		−	568.747i		−	0.584529i
$974$			935.969i			0.960954i
$975$		0			0
$976$	−166.040			−0.170123
$977$	936.742			0.958794			0.479397	−	0.877598i	$-0.340855\pi$
$977$	936.742			0.958794			0.479397	+	0.877598i	$0.340855\pi$
$978$	−484.779	+	506.861i	−0.495684	+	0.518263i
$979$	1986.44			2.02905
$980$		0			0
$981$	54.5246	+	1223.68i	0.0555806	+	1.24738i
$982$		−	1096.73i		−	1.11683i
$983$	1229.46			1.25072			0.625361	−	0.780335i	$-0.284952\pi$
$983$	1229.46			1.25072			0.625361	+	0.780335i	$0.284952\pi$
$984$	−212.159	+	221.823i	−0.215609	+	0.225430i
$985$		0			0
$986$			98.9339i			0.100339i
$987$	−201.648	+	210.833i	−0.204303	+	0.213609i
$988$			181.677i			0.183883i
$989$			571.033i			0.577384i
$990$		0			0
$991$	808.810			0.816156			0.408078	−	0.912947i	$-0.366199\pi$
$991$	808.810			0.816156			0.408078	+	0.912947i	$0.366199\pi$
$992$	119.253			0.120214
$993$	−725.691	−	694.076i	−0.730807	−	0.698969i
$994$	53.7110			0.0540352
$995$		0			0
$996$	322.628	+	308.573i	0.323924	+	0.309812i
$997$			1221.16i			1.22483i	0.790535	+	0.612417i	$0.209803\pi$
$997$			1221.16i			1.22483i	−0.790535	+	0.612417i	$0.790197\pi$
$998$	−465.304			−0.466237
$999$	−1197.89	−	1047.68i	−1.19909	−	1.04873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.3		32
3.2	odd	2	inner	1050.3.c.b.449.29		32
5.2	odd	4		1050.3.e.c.701.2	yes	16
5.3	odd	4		1050.3.e.b.701.15	yes	16
5.4	even	2	inner	1050.3.c.b.449.30		32
15.2	even	4		1050.3.e.c.701.10	yes	16
15.8	even	4		1050.3.e.b.701.7	✓	16
15.14	odd	2	inner	1050.3.c.b.449.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.3		32	1.1	even	1	trivial
1050.3.c.b.449.4		32	15.14	odd	2	inner
1050.3.c.b.449.29		32	3.2	odd	2	inner
1050.3.c.b.449.30		32	5.4	even	2	inner
1050.3.e.b.701.7	✓	16	15.8	even	4
1050.3.e.b.701.15	yes	16	5.3	odd	4
1050.3.e.c.701.2	yes	16	5.2	odd	4
1050.3.e.c.701.10	yes	16	15.2	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.16802 - 2.07357i) q^{3} +2.00000 q^{4} +(3.06604 + 2.93247i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(0.400623 + 8.99108i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.16802 - 2.07357i) q^{3} +2.00000 q^{4} +(3.06604 + 2.93247i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(0.400623 + 8.99108i) q^{9} +21.5844i q^{11} +(-4.33604 - 4.14714i) q^{12} +15.4777i q^{13} -3.74166i q^{14} +4.00000 q^{16} -20.3523 q^{17} +(-0.566566 - 12.7153i) q^{18} +5.86900 q^{19} +(5.48615 - 5.73604i) q^{21} -30.5249i q^{22} -11.3900 q^{23} +(6.13209 + 5.86494i) q^{24} -21.8887i q^{26} +(17.7751 - 20.3236i) q^{27} +5.29150i q^{28} +3.43729i q^{29} -21.0811 q^{31} -5.65685 q^{32} +(44.7567 - 46.7954i) q^{33} +28.7825 q^{34} +(0.801245 + 17.9822i) q^{36} -58.9411i q^{37} -8.30001 q^{38} +(32.0940 - 33.5559i) q^{39} +36.1742i q^{41} +(-7.75859 + 8.11199i) q^{42} -50.1346i q^{43} +43.1688i q^{44} +16.1079 q^{46} -36.7558 q^{47} +(-8.67208 - 8.29428i) q^{48} -7.00000 q^{49} +(44.1242 + 42.2019i) q^{51} +30.9554i q^{52} +40.9385 q^{53} +(-25.1377 + 28.7419i) q^{54} -7.48331i q^{56} +(-12.7241 - 12.1698i) q^{57} -4.86107i q^{58} -110.141i q^{59} -41.5100 q^{61} +29.8132 q^{62} +(-23.7882 + 1.05995i) q^{63} +8.00000 q^{64} +(-63.2955 + 66.1786i) q^{66} +109.401i q^{67} -40.7046 q^{68} +(24.6938 + 23.6180i) q^{69} +14.3549i q^{71} +(-1.13313 - 25.4306i) q^{72} -19.2937i q^{73} +83.3553i q^{74} +11.7380 q^{76} -57.1069 q^{77} +(-45.3878 + 47.4552i) q^{78} +122.271 q^{79} +(-80.6790 + 7.20406i) q^{81} -51.1580i q^{82} -74.4062 q^{83} +(10.9723 - 11.4721i) q^{84} +70.9010i q^{86} +(7.12747 - 7.45212i) q^{87} -61.0498i q^{88} -92.0314i q^{89} -40.9501 q^{91} -22.7800 q^{92} +(45.7042 + 43.7131i) q^{93} +51.9805 q^{94} +(12.2642 + 11.7299i) q^{96} -5.71291i q^{97} +9.89949 q^{98} +(-194.067 + 8.64719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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