LMFDB - Embedded newform 1050.3.c.c.449.19

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:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.19
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-2.05675 - 2.18398i) q^{3} +2.00000 q^{4} +(-2.90869 - 3.08861i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-0.539533 + 8.98381i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-2.05675 - 2.18398i) q^{3} +2.00000 q^{4} +(-2.90869 - 3.08861i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-0.539533 + 8.98381i) q^{9} -10.4995i q^{11} +(-4.11351 - 4.36796i) q^{12} +4.25324i q^{13} +3.74166i q^{14} +4.00000 q^{16} +3.70274 q^{17} +(-0.763014 + 12.7050i) q^{18} +7.95778 q^{19} +(5.77827 - 5.44166i) q^{21} -14.8485i q^{22} +2.84656 q^{23} +(-5.81738 - 6.17723i) q^{24} +6.01499i q^{26} +(20.7301 - 17.2992i) q^{27} +5.29150i q^{28} -43.7226i q^{29} +49.6484 q^{31} +5.65685 q^{32} +(-22.9306 + 21.5948i) q^{33} +5.23646 q^{34} +(-1.07907 + 17.9676i) q^{36} +4.01613i q^{37} +11.2540 q^{38} +(9.28899 - 8.74787i) q^{39} -29.9759i q^{41} +(8.17170 - 7.69567i) q^{42} -6.84221i q^{43} -20.9989i q^{44} +4.02565 q^{46} -1.10933 q^{47} +(-8.22701 - 8.73592i) q^{48} -7.00000 q^{49} +(-7.61561 - 8.08670i) q^{51} +8.50648i q^{52} -57.7890 q^{53} +(29.3169 - 24.4647i) q^{54} +7.48331i q^{56} +(-16.3672 - 17.3796i) q^{57} -61.8331i q^{58} -91.4315i q^{59} +105.146 q^{61} +70.2135 q^{62} +(-23.7689 - 1.42747i) q^{63} +8.00000 q^{64} +(-32.4288 + 30.5396i) q^{66} +94.2973i q^{67} +7.40547 q^{68} +(-5.85468 - 6.21684i) q^{69} -22.1757i q^{71} +(-1.52603 + 25.4101i) q^{72} -117.450i q^{73} +5.67967i q^{74} +15.9156 q^{76} +27.7789 q^{77} +(13.1366 - 12.3714i) q^{78} -29.1891 q^{79} +(-80.4178 - 9.69412i) q^{81} -42.3924i q^{82} +108.374 q^{83} +(11.5565 - 10.8833i) q^{84} -9.67635i q^{86} +(-95.4893 + 89.9266i) q^{87} -29.6969i q^{88} -114.722i q^{89} -11.2530 q^{91} +5.69313 q^{92} +(-102.115 - 108.431i) q^{93} -1.56884 q^{94} +(-11.6348 - 12.3545i) q^{96} -134.697i q^{97} -9.89949 q^{98} +(94.3251 + 5.66480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * 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
$3$	−2.05675	−	2.18398i	−0.685584	−	0.727993i
$3$	−2.05675	−	2.18398i	−0.685584	−	0.727993i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−2.90869	−	3.08861i	−0.484781	−	0.514769i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	−0.539533	+	8.98381i	−0.0599481	+	0.998201i
$10$		0			0
$11$		−	10.4995i		−	0.954496i	−0.878769	−	0.477248i	$-0.841634\pi$
$11$		−	10.4995i		−	0.954496i	0.878769	−	0.477248i	$-0.158366\pi$
$12$	−4.11351	−	4.36796i	−0.342792	−	0.363997i
$13$			4.25324i			0.327172i	0.986529	+	0.163586i	$0.0523062\pi$
$13$			4.25324i			0.327172i	−0.986529	+	0.163586i	$0.947694\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	3.70274			0.217808			0.108904	−	0.994052i	$-0.465266\pi$
$17$	3.70274			0.217808			0.108904	+	0.994052i	$0.465266\pi$
$18$	−0.763014	+	12.7050i	−0.0423897	+	0.705835i
$19$	7.95778			0.418831			0.209415	−	0.977827i	$-0.432844\pi$
$19$	7.95778			0.418831			0.209415	+	0.977827i	$0.432844\pi$
$20$		0			0
$21$	5.77827	−	5.44166i	0.275156	−	0.259127i
$22$		−	14.8485i		−	0.674930i
$23$	2.84656			0.123764			0.0618818	−	0.998083i	$-0.480290\pi$
$23$	2.84656			0.123764			0.0618818	+	0.998083i	$0.480290\pi$
$24$	−5.81738	−	6.17723i	−0.242391	−	0.257384i
$25$		0			0
$26$			6.01499i			0.231346i
$27$	20.7301	−	17.2992i	0.767783	−	0.640710i
$28$			5.29150i			0.188982i
$29$		−	43.7226i		−	1.50768i	−0.657060	−	0.753838i	$-0.728200\pi$
$29$		−	43.7226i		−	1.50768i	0.657060	−	0.753838i	$-0.271800\pi$
$30$		0			0
$31$	49.6484			1.60156			0.800781	−	0.598957i	$-0.204418\pi$
$31$	49.6484			1.60156			0.800781	+	0.598957i	$0.204418\pi$
$32$	5.65685			0.176777
$33$	−22.9306	+	21.5948i	−0.694866	+	0.654387i
$34$	5.23646			0.154013
$35$		0			0
$36$	−1.07907	+	17.9676i	−0.0299740	+	0.499101i
$37$			4.01613i			0.108544i	0.998526	+	0.0542721i	$0.0172838\pi$
$37$			4.01613i			0.108544i	−0.998526	+	0.0542721i	$0.982716\pi$
$38$	11.2540			0.296158
$39$	9.28899	−	8.74787i	0.238179	−	0.224304i
$40$		0			0
$41$		−	29.9759i		−	0.731120i	−0.930788	−	0.365560i	$-0.880877\pi$
$41$		−	29.9759i		−	0.731120i	0.930788	−	0.365560i	$-0.119123\pi$
$42$	8.17170	−	7.69567i	0.194564	−	0.183230i
$43$		−	6.84221i		−	0.159121i	−0.996830	−	0.0795606i	$-0.974648\pi$
$43$		−	6.84221i		−	0.159121i	0.996830	−	0.0795606i	$-0.0253517\pi$
$44$		−	20.9989i		−	0.477248i
$45$		0			0
$46$	4.02565			0.0875141
$47$	−1.10933			−0.0236029			−0.0118014	−	0.999930i	$-0.503757\pi$
$47$	−1.10933			−0.0236029			−0.0118014	+	0.999930i	$0.503757\pi$
$48$	−8.22701	−	8.73592i	−0.171396	−	0.181998i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−7.61561	−	8.08670i	−0.149326	−	0.158563i
$52$			8.50648i			0.163586i
$53$	−57.7890			−1.09036			−0.545180	−	0.838319i	$-0.683539\pi$
$53$	−57.7890			−1.09036			−0.545180	+	0.838319i	$0.683539\pi$
$54$	29.3169	−	24.4647i	0.542905	−	0.453050i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−16.3672	−	17.3796i	−0.287144	−	0.304906i
$58$		−	61.8331i		−	1.06609i
$59$		−	91.4315i		−	1.54969i	−0.632154	−	0.774843i	$-0.717829\pi$
$59$		−	91.4315i		−	1.54969i	0.632154	−	0.774843i	$-0.282171\pi$
$60$		0			0
$61$	105.146			1.72370			0.861850	−	0.507164i	$-0.169306\pi$
$61$	105.146			1.72370			0.861850	+	0.507164i	$0.169306\pi$
$62$	70.2135			1.13248
$63$	−23.7689	−	1.42747i	−0.377285	−	0.0226582i
$64$	8.00000			0.125000
$65$		0			0
$66$	−32.4288	+	30.5396i	−0.491345	+	0.462722i
$67$			94.2973i			1.40742i	0.710486	+	0.703712i	$0.248475\pi$
$67$			94.2973i			1.40742i	−0.710486	+	0.703712i	$0.751525\pi$
$68$	7.40547			0.108904
$69$	−5.85468	−	6.21684i	−0.0848504	−	0.0900991i
$70$		0			0
$71$		−	22.1757i		−	0.312335i	−0.987731	−	0.156167i	$-0.950086\pi$
$71$		−	22.1757i		−	0.312335i	0.987731	−	0.156167i	$-0.0499139\pi$
$72$	−1.52603	+	25.4101i	−0.0211948	+	0.352918i
$73$		−	117.450i		−	1.60890i	−0.594017	−	0.804452i	$-0.702459\pi$
$73$		−	117.450i		−	1.60890i	0.594017	−	0.804452i	$-0.297541\pi$
$74$			5.67967i			0.0767523i
$75$		0			0
$76$	15.9156			0.209415
$77$	27.7789			0.360765
$78$	13.1366	−	12.3714i	0.168418	−	0.158607i
$79$	−29.1891			−0.369482			−0.184741	−	0.982787i	$-0.559145\pi$
$79$	−29.1891			−0.369482			−0.184741	+	0.982787i	$0.559145\pi$
$80$		0			0
$81$	−80.4178	−	9.69412i	−0.992812	−	0.119680i
$82$		−	42.3924i		−	0.516980i
$83$	108.374			1.30571			0.652854	−	0.757484i	$-0.273571\pi$
$83$	108.374			1.30571			0.652854	+	0.757484i	$0.273571\pi$
$84$	11.5565	−	10.8833i	0.137578	−	0.129563i
$85$		0			0
$86$		−	9.67635i		−	0.112516i
$87$	−95.4893	+	89.9266i	−1.09758	+	1.03364i
$88$		−	29.6969i		−	0.337465i
$89$		−	114.722i		−	1.28901i	−0.764601	−	0.644503i	$-0.777064\pi$
$89$		−	114.722i		−	1.28901i	0.764601	−	0.644503i	$-0.222936\pi$
$90$		0			0
$91$	−11.2530			−0.123660
$92$	5.69313			0.0618818
$93$	−102.115	−	108.431i	−1.09801	−	1.16593i
$94$	−1.56884			−0.0166897
$95$		0			0
$96$	−11.6348	−	12.3545i	−0.121195	−	0.128692i
$97$		−	134.697i		−	1.38863i	−0.719669	−	0.694317i	$-0.755707\pi$
$97$		−	134.697i		−	1.38863i	0.719669	−	0.694317i	$-0.244293\pi$
$98$	−9.89949			−0.101015
$99$	94.3251	+	5.66480i	0.952779	+	0.0572202i
$100$		0			0
$101$			38.1420i			0.377643i	0.982011	+	0.188822i	$0.0604668\pi$
$101$			38.1420i			0.377643i	−0.982011	+	0.188822i	$0.939533\pi$
$102$	−10.7701	−	11.4363i	−0.105589	−	0.112121i
$103$			24.3910i			0.236806i	0.992966	+	0.118403i	$0.0377774\pi$
$103$			24.3910i			0.236806i	−0.992966	+	0.118403i	$0.962223\pi$
$104$			12.0300i			0.115673i
$105$		0			0
$106$	−81.7260			−0.771000
$107$	−33.9052			−0.316871			−0.158435	−	0.987369i	$-0.550645\pi$
$107$	−33.9052			−0.316871			−0.158435	+	0.987369i	$0.550645\pi$
$108$	41.4603	−	34.5983i	0.383892	−	0.320355i
$109$	24.4736			0.224528			0.112264	−	0.993678i	$-0.464190\pi$
$109$	24.4736			0.224528			0.112264	+	0.993678i	$0.464190\pi$
$110$		0			0
$111$	8.77115	−	8.26020i	0.0790194	−	0.0744162i
$112$			10.5830i			0.0944911i
$113$	−223.285			−1.97597			−0.987987	−	0.154540i	$-0.950610\pi$
$113$	−223.285			−1.97597			−0.987987	+	0.154540i	$0.950610\pi$
$114$	−23.1467	−	24.5785i	−0.203041	−	0.215601i
$115$		0			0
$116$		−	87.4452i		−	0.753838i
$117$	−38.2103	−	2.29476i	−0.326584	−	0.0196134i
$118$		−	129.304i		−	1.09579i
$119$			9.79652i			0.0823237i
$120$		0			0
$121$	10.7615			0.0889379
$122$	148.698			1.21884
$123$	−65.4668	+	61.6531i	−0.532250	+	0.501244i
$124$	99.2968			0.800781
$125$		0			0
$126$	−33.6144	−	2.01875i	−0.266781	−	0.0160218i
$127$		−	177.867i		−	1.40053i	−0.713883	−	0.700265i	$-0.753065\pi$
$127$		−	177.867i		−	1.40053i	0.713883	−	0.700265i	$-0.246935\pi$
$128$	11.3137			0.0883883
$129$	−14.9432	+	14.0727i	−0.115839	+	0.109091i
$130$		0			0
$131$			105.991i			0.809090i	0.914518	+	0.404545i	$0.132570\pi$
$131$			105.991i			0.809090i	−0.914518	+	0.404545i	$0.867430\pi$
$132$	−45.8612	+	43.1896i	−0.347433	+	0.327194i
$133$			21.0543i			0.158303i
$134$			133.357i			0.995198i
$135$		0			0
$136$	10.4729			0.0770067
$137$	119.161			0.869792			0.434896	−	0.900481i	$-0.356785\pi$
$137$	119.161			0.869792			0.434896	+	0.900481i	$0.356785\pi$
$138$	−8.27977	−	8.79194i	−0.0599983	−	0.0637097i
$139$	258.103			1.85685			0.928426	−	0.371517i	$-0.121162\pi$
$139$	258.103			1.85685			0.928426	+	0.371517i	$0.121162\pi$
$140$		0			0
$141$	2.28163	+	2.42276i	0.0161817	+	0.0171827i
$142$		−	31.3612i		−	0.220854i
$143$	44.6567			0.312285
$144$	−2.15813	+	35.9353i	−0.0149870	+	0.249550i
$145$		0			0
$146$		−	166.099i		−	1.13767i
$147$	14.3973	+	15.2879i	0.0979406	+	0.103999i
$148$			8.03227i			0.0542721i
$149$		−	66.2196i		−	0.444427i	−0.974998	−	0.222213i	$-0.928672\pi$
$149$		−	66.2196i		−	0.444427i	0.974998	−	0.222213i	$-0.0713282\pi$
$150$		0			0
$151$	−160.306			−1.06163			−0.530815	−	0.847487i	$-0.678114\pi$
$151$	−160.306			−1.06163			−0.530815	+	0.847487i	$0.678114\pi$
$152$	22.5080			0.148079
$153$	−1.99775	+	33.2647i	−0.0130572	+	0.217416i
$154$	39.2854			0.255100
$155$		0			0
$156$	18.5780	−	17.4957i	0.119090	−	0.112152i
$157$			188.012i			1.19753i	0.800926	+	0.598764i	$0.204341\pi$
$157$			188.012i			1.19753i	−0.800926	+	0.598764i	$0.795659\pi$
$158$	−41.2796			−0.261263
$159$	118.858	+	126.210i	0.747533	+	0.793774i
$160$		0			0
$161$			7.53130i			0.0467783i
$162$	−113.728	−	13.7096i	−0.702024	−	0.0846269i
$163$			252.814i			1.55100i	0.631345	+	0.775502i	$0.282503\pi$
$163$			252.814i			1.55100i	−0.631345	+	0.775502i	$0.717497\pi$
$164$		−	59.9518i		−	0.365560i
$165$		0			0
$166$	153.264			0.923275
$167$	−122.360			−0.732692			−0.366346	−	0.930479i	$-0.619391\pi$
$167$	−122.360			−0.732692			−0.366346	+	0.930479i	$0.619391\pi$
$168$	16.3434	−	15.3913i	0.0972822	−	0.0916151i
$169$	150.910			0.892958
$170$		0			0
$171$	−4.29348	+	71.4912i	−0.0251081	+	0.418077i
$172$		−	13.6844i		−	0.0795606i
$173$	−18.2273			−0.105360			−0.0526801	−	0.998611i	$-0.516776\pi$
$173$	−18.2273			−0.105360			−0.0526801	+	0.998611i	$0.516776\pi$
$174$	−135.042	+	127.175i	−0.776105	+	0.730893i
$175$		0			0
$176$		−	41.9978i		−	0.238624i
$177$	−199.685	+	188.052i	−1.12816	+	1.06244i
$178$		−	162.241i		−	0.911466i
$179$		−	183.782i		−	1.02672i	−0.858174	−	0.513359i	$-0.828401\pi$
$179$		−	183.782i		−	1.02672i	0.858174	−	0.513359i	$-0.171599\pi$
$180$		0			0
$181$	203.653			1.12515			0.562577	−	0.826745i	$-0.309810\pi$
$181$	203.653			1.12515			0.562577	+	0.826745i	$0.309810\pi$
$182$	−15.9142			−0.0874405
$183$	−216.259	−	229.636i	−1.18174	−	1.25484i
$184$	8.05130			0.0437571
$185$		0			0
$186$	−144.412	−	153.345i	−0.776407	−	0.824434i
$187$		−	38.8767i		−	0.207897i
$188$	−2.21867			−0.0118014
$189$	45.7693	+	54.8468i	0.242165	+	0.290195i
$190$		0			0
$191$			179.246i			0.938461i	0.883076	+	0.469230i	$0.155469\pi$
$191$			179.246i			0.938461i	−0.883076	+	0.469230i	$0.844531\pi$
$192$	−16.4540	−	17.4718i	−0.0856980	−	0.0909991i
$193$			175.142i			0.907472i	0.891136	+	0.453736i	$0.149909\pi$
$193$			175.142i			0.907472i	−0.891136	+	0.453736i	$0.850091\pi$
$194$		−	190.491i		−	0.981912i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	274.883			1.39535			0.697674	−	0.716416i	$-0.254219\pi$
$197$	274.883			1.39535			0.697674	+	0.716416i	$0.254219\pi$
$198$	133.396	+	8.01123i	0.673717	+	0.0404608i
$199$	42.6607			0.214375			0.107188	−	0.994239i	$-0.465815\pi$
$199$	42.6607			0.214375			0.107188	+	0.994239i	$0.465815\pi$
$200$		0			0
$201$	205.943	−	193.946i	1.02459	−	0.964907i
$202$			53.9409i			0.267034i
$203$	115.679			0.569848
$204$	−15.2312	−	16.1734i	−0.0746629	−	0.0792814i
$205$		0			0
$206$			34.4941i			0.167447i
$207$	−1.53581	+	25.5730i	−0.00741939	+	0.123541i
$208$			17.0130i			0.0817931i
$209$		−	83.5523i		−	0.399772i
$210$		0			0
$211$	232.969			1.10412			0.552059	−	0.833805i	$-0.313842\pi$
$211$	232.969			1.10412			0.552059	+	0.833805i	$0.313842\pi$
$212$	−115.578			−0.545180
$213$	−48.4314	+	45.6100i	−0.227377	+	0.214132i
$214$	−47.9492			−0.224062
$215$		0			0
$216$	58.6337	−	48.9294i	0.271452	−	0.226525i
$217$			131.357i			0.605333i
$218$	34.6109			0.158765
$219$	−256.508	+	241.566i	−1.17127	+	1.10304i
$220$		0			0
$221$			15.7486i			0.0712608i
$222$	12.4043	−	11.6817i	0.0558752	−	0.0526202i
$223$			355.681i			1.59498i	0.603331	+	0.797491i	$0.293840\pi$
$223$			355.681i			1.59498i	−0.603331	+	0.797491i	$0.706160\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−315.773			−1.39722
$227$	−285.817			−1.25910			−0.629552	−	0.776958i	$-0.716762\pi$
$227$	−285.817			−1.25910			−0.629552	+	0.776958i	$0.716762\pi$
$228$	−32.7344	−	34.7593i	−0.143572	−	0.152453i
$229$	−424.265			−1.85268			−0.926342	−	0.376682i	$-0.877065\pi$
$229$	−424.265			−1.85268			−0.926342	+	0.376682i	$0.877065\pi$
$230$		0			0
$231$	−57.1344	−	60.6686i	−0.247335	−	0.262635i
$232$		−	123.666i		−	0.533044i
$233$	−102.687			−0.440716			−0.220358	−	0.975419i	$-0.570723\pi$
$233$	−102.687			−0.440716			−0.220358	+	0.975419i	$0.570723\pi$
$234$	−54.0376	−	3.24528i	−0.230930	−	0.0138687i
$235$		0			0
$236$		−	182.863i		−	0.774843i
$237$	60.0348	+	63.7484i	0.253311	+	0.268981i
$238$			13.8544i			0.0582116i
$239$			189.780i			0.794057i	0.917806	+	0.397029i	$0.129959\pi$
$239$			189.780i			0.794057i	−0.917806	+	0.397029i	$0.870041\pi$
$240$		0			0
$241$	−214.128			−0.888499			−0.444249	−	0.895903i	$-0.646530\pi$
$241$	−214.128			−0.888499			−0.444249	+	0.895903i	$0.646530\pi$
$242$	15.2190			0.0628886
$243$	144.228	+	195.569i	0.593530	+	0.804812i
$244$	210.291			0.861850
$245$		0			0
$246$	−92.5840	+	87.1906i	−0.376358	+	0.354433i
$247$			33.8464i			0.137030i
$248$	140.427			0.566238
$249$	−222.898	−	236.686i	−0.895173	−	0.950547i
$250$		0			0
$251$			181.164i			0.721768i	0.932611	+	0.360884i	$0.117525\pi$
$251$			181.164i			0.721768i	−0.932611	+	0.360884i	$0.882475\pi$
$252$	−47.5379	−	2.85494i	−0.188642	−	0.0113291i
$253$		−	29.8874i		−	0.118132i
$254$		−	251.542i		−	0.990324i
$255$		0			0
$256$	16.0000			0.0625000
$257$	276.740			1.07681			0.538405	−	0.842686i	$-0.319027\pi$
$257$	276.740			1.07681			0.538405	+	0.842686i	$0.319027\pi$
$258$	−21.1329	+	19.9019i	−0.0819106	+	0.0771390i
$259$	−10.6257			−0.0410258
$260$		0			0
$261$	392.796	+	23.5898i	1.50496	+	0.0903822i
$262$			149.894i			0.572113i
$263$	−43.4119			−0.165064			−0.0825321	−	0.996588i	$-0.526301\pi$
$263$	−43.4119			−0.165064			−0.0825321	+	0.996588i	$0.526301\pi$
$264$	−64.8575	+	61.0793i	−0.245672	+	0.231361i
$265$		0			0
$266$			29.7753i			0.111937i
$267$	−250.550	+	235.954i	−0.938388	+	0.883723i
$268$			188.595i			0.703712i
$269$			166.942i			0.620602i	0.950638	+	0.310301i	$0.100430\pi$
$269$			166.942i			0.620602i	−0.950638	+	0.310301i	$0.899570\pi$
$270$		0			0
$271$	403.869			1.49029			0.745146	−	0.666902i	$-0.232380\pi$
$271$	403.869			1.49029			0.745146	+	0.666902i	$0.232380\pi$
$272$	14.8109			0.0544520
$273$	23.1447	+	24.5764i	0.0847791	+	0.0900233i
$274$	168.520			0.615036
$275$		0			0
$276$	−11.7094	−	12.4337i	−0.0424252	−	0.0450495i
$277$		−	116.712i		−	0.421343i	−0.977557	−	0.210671i	$-0.932435\pi$
$277$		−	116.712i		−	0.421343i	0.977557	−	0.210671i	$-0.0675650\pi$
$278$	365.012			1.31299
$279$	−26.7869	+	446.032i	−0.0960105	+	1.59868i
$280$		0			0
$281$			492.295i			1.75194i	0.482367	+	0.875969i	$0.339777\pi$
$281$			492.295i			1.75194i	−0.482367	+	0.875969i	$0.660223\pi$
$282$	3.22671	+	3.42630i	0.0114422	+	0.0121500i
$283$		−	108.656i		−	0.383942i	−0.981401	−	0.191971i	$-0.938512\pi$
$283$		−	108.656i		−	0.383942i	0.981401	−	0.191971i	$-0.0614879\pi$
$284$		−	44.3515i		−	0.156167i
$285$		0			0
$286$	63.1541			0.220819
$287$	79.3088			0.276337
$288$	−3.05206	+	50.8201i	−0.0105974	+	0.176459i
$289$	−275.290			−0.952560
$290$		0			0
$291$	−294.177	+	277.039i	−1.01092	+	0.952026i
$292$		−	234.900i		−	0.804452i
$293$	396.582			1.35352			0.676761	−	0.736203i	$-0.263383\pi$
$293$	396.582			1.35352			0.676761	+	0.736203i	$0.263383\pi$
$294$	20.3608	+	21.6203i	0.0692545	+	0.0735384i
$295$		0			0
$296$			11.3593i			0.0383762i
$297$	−181.632	−	217.655i	−0.611555	−	0.732846i
$298$		−	93.6487i		−	0.314257i
$299$			12.1071i			0.0404921i
$300$		0			0
$301$	18.1028			0.0601422
$302$	−226.707			−0.750686
$303$	83.3013	−	78.4486i	0.274922	−	0.258906i
$304$	31.8311			0.104708
$305$		0			0
$306$	−2.82524	+	47.0434i	−0.00923281	+	0.153736i
$307$		−	24.9415i		−	0.0812426i	−0.999175	−	0.0406213i	$-0.987066\pi$
$307$		−	24.9415i		−	0.0812426i	0.999175	−	0.0406213i	$-0.0129337\pi$
$308$	55.5579			0.180383
$309$	53.2694	−	50.1662i	0.172393	−	0.162350i
$310$		0			0
$311$			173.045i			0.556413i	0.960521	+	0.278207i	$0.0897400\pi$
$311$			173.045i			0.556413i	−0.960521	+	0.278207i	$0.910260\pi$
$312$	26.2732	−	24.7427i	0.0842091	−	0.0793036i
$313$			288.216i			0.920818i	0.887707	+	0.460409i	$0.152297\pi$
$313$			288.216i			0.920818i	−0.887707	+	0.460409i	$0.847703\pi$
$314$			265.889i			0.846780i
$315$		0			0
$316$	−58.3782			−0.184741
$317$	517.337			1.63198			0.815988	−	0.578068i	$-0.196193\pi$
$317$	517.337			1.63198			0.815988	+	0.578068i	$0.196193\pi$
$318$	168.090	+	178.488i	0.528586	+	0.561283i
$319$	−459.063			−1.43907
$320$		0			0
$321$	69.7346	+	74.0482i	0.217242	+	0.230680i
$322$			10.6509i			0.0330772i
$323$	29.4656			0.0912246
$324$	−160.836	−	19.3882i	−0.496406	−	0.0598402i
$325$		0			0
$326$			357.533i			1.09673i
$327$	−50.3361	−	53.4498i	−0.153933	−	0.163455i
$328$		−	84.7847i		−	0.258490i
$329$		−	2.93502i		−	0.00892104i
$330$		0			0
$331$	−368.507			−1.11332			−0.556658	−	0.830742i	$-0.687916\pi$
$331$	−368.507			−1.11332			−0.556658	+	0.830742i	$0.687916\pi$
$332$	216.748			0.652854
$333$	−36.0802	−	2.16683i	−0.108349	−	0.00650701i
$334$	−173.043			−0.518092
$335$		0			0
$336$	23.1131	−	21.7666i	0.0687889	−	0.0647816i
$337$		−	249.469i		−	0.740264i	−0.928979	−	0.370132i	$-0.879312\pi$
$337$		−	249.469i		−	0.740264i	0.928979	−	0.370132i	$-0.120688\pi$
$338$	213.419			0.631417
$339$	459.242	+	487.650i	1.35470	+	1.43849i
$340$		0			0
$341$		−	521.281i		−	1.52868i
$342$	−6.07190	+	101.104i	−0.0177541	+	0.295625i
$343$		−	18.5203i		−	0.0539949i
$344$		−	19.3527i		−	0.0562578i
$345$		0			0
$346$	−25.7773			−0.0745009
$347$	277.849			0.800718			0.400359	−	0.916358i	$-0.368885\pi$
$347$	277.849			0.800718			0.400359	+	0.916358i	$0.368885\pi$
$348$	−190.979	+	179.853i	−0.548789	+	0.516819i
$349$	−212.724			−0.609525			−0.304763	−	0.952428i	$-0.598577\pi$
$349$	−212.724			−0.609525			−0.304763	+	0.952428i	$0.598577\pi$
$350$		0			0
$351$	73.5775	+	88.1703i	0.209623	+	0.251198i
$352$		−	59.3939i		−	0.168733i
$353$	−312.301			−0.884706			−0.442353	−	0.896841i	$-0.645856\pi$
$353$	−312.301			−0.884706			−0.442353	+	0.896841i	$0.645856\pi$
$354$	−282.397	+	265.946i	−0.797730	+	0.751259i
$355$		0			0
$356$		−	229.443i		−	0.644503i
$357$	21.3954	−	20.1490i	0.0599311	−	0.0564398i
$358$		−	259.908i		−	0.725999i
$359$			444.359i			1.23777i	0.785483	+	0.618884i	$0.212415\pi$
$359$			444.359i			1.23777i	−0.785483	+	0.618884i	$0.787585\pi$
$360$		0			0
$361$	−297.674			−0.824581
$362$	288.009			0.795605
$363$	−22.1337	−	23.5029i	−0.0609744	−	0.0647462i
$364$	−22.5060			−0.0618298
$365$		0			0
$366$	−305.836	−	324.754i	−0.835617	−	0.887307i
$367$			21.3612i			0.0582048i	0.999576	+	0.0291024i	$0.00926489\pi$
$367$			21.3612i			0.0582048i	−0.999576	+	0.0291024i	$0.990735\pi$
$368$	11.3863			0.0309409
$369$	269.298	+	16.1730i	0.729805	+	0.0438292i
$370$		0			0
$371$		−	152.895i		−	0.412117i
$372$	−204.229	−	216.862i	−0.549003	−	0.582963i
$373$			182.853i			0.490222i	0.969495	+	0.245111i	$0.0788243\pi$
$373$			182.853i			0.490222i	−0.969495	+	0.245111i	$0.921176\pi$
$374$		−	54.9800i		−	0.147005i
$375$		0			0
$376$	−3.13767			−0.00834487
$377$	185.963			0.493270
$378$	64.7275	+	77.5651i	0.171237	+	0.205199i
$379$	−527.027			−1.39057			−0.695287	−	0.718733i	$-0.744723\pi$
$379$	−527.027			−1.39057			−0.695287	+	0.718733i	$0.744723\pi$
$380$		0			0
$381$	−388.459	+	365.829i	−1.01958	+	0.960182i
$382$			253.492i			0.663592i
$383$	−179.373			−0.468338			−0.234169	−	0.972196i	$-0.575237\pi$
$383$	−179.373			−0.468338			−0.234169	+	0.972196i	$0.575237\pi$
$384$	−23.2695	−	24.7089i	−0.0605977	−	0.0643461i
$385$		0			0
$386$			247.688i			0.641680i
$387$	61.4691	+	3.69160i	0.158835	+	0.00953901i
$388$		−	269.395i		−	0.694317i
$389$		−	565.905i		−	1.45477i	−0.686230	−	0.727385i	$-0.740736\pi$
$389$		−	565.905i		−	1.45477i	0.686230	−	0.727385i	$-0.259264\pi$
$390$		0			0
$391$	10.5401			0.0269567
$392$	−19.7990			−0.0505076
$393$	231.482	−	217.997i	0.589012	−	0.554700i
$394$	388.744			0.986659
$395$		0			0
$396$	188.650	+	11.3296i	0.476390	+	0.0286101i
$397$		−	210.208i		−	0.529490i	−0.964318	−	0.264745i	$-0.914712\pi$
$397$		−	210.208i		−	0.529490i	0.964318	−	0.264745i	$-0.0852878\pi$
$398$	60.3313			0.151586
$399$	45.9822	−	43.3035i	0.115244	−	0.108530i
$400$		0			0
$401$		−	592.469i		−	1.47748i	−0.673991	−	0.738739i	$-0.735421\pi$
$401$		−	592.469i		−	1.47748i	0.673991	−	0.738739i	$-0.264579\pi$
$402$	291.248	−	274.282i	0.724498	−	0.682292i
$403$			211.167i			0.523987i
$404$			76.2839i			0.188822i
$405$		0			0
$406$	163.595			0.402943
$407$	42.1672			0.103605
$408$	−21.5402	−	22.8726i	−0.0527946	−	0.0560604i
$409$	−250.632			−0.612793			−0.306397	−	0.951904i	$-0.599123\pi$
$409$	−250.632			−0.612793			−0.306397	+	0.951904i	$0.599123\pi$
$410$		0			0
$411$	−245.086	−	260.246i	−0.596316	−	0.633202i
$412$			48.7820i			0.118403i
$413$	241.905			0.585726
$414$	−2.17197	+	36.1657i	−0.00524630	+	0.0873567i
$415$		0			0
$416$			24.0600i			0.0578365i
$417$	−530.853	−	563.691i	−1.27303	−	1.35178i
$418$		−	118.161i		−	0.282681i
$419$		−	215.898i		−	0.515271i	−0.966242	−	0.257635i	$-0.917057\pi$
$419$		−	215.898i		−	0.515271i	0.966242	−	0.257635i	$-0.0829433\pi$
$420$		0			0
$421$	−674.017			−1.60099			−0.800495	−	0.599340i	$-0.795430\pi$
$421$	−674.017			−1.60099			−0.800495	+	0.599340i	$0.795430\pi$
$422$	329.468			0.780729
$423$	0.598522	−	9.96605i	0.00141495	−	0.0235604i
$424$	−163.452			−0.385500
$425$		0			0
$426$	−68.4923	+	64.5023i	−0.160780	+	0.151414i
$427$			278.189i			0.651497i
$428$	−67.8104			−0.158435
$429$	−91.8478	−	97.5294i	−0.214098	−	0.227341i
$430$		0			0
$431$		−	309.009i		−	0.716958i	−0.933538	−	0.358479i	$-0.883295\pi$
$431$		−	309.009i		−	0.716958i	0.933538	−	0.358479i	$-0.116705\pi$
$432$	82.9206	−	69.1966i	0.191946	−	0.160177i
$433$		−	26.5043i		−	0.0612110i	−0.999532	−	0.0306055i	$-0.990256\pi$
$433$		−	26.5043i		−	0.0612110i	0.999532	−	0.0306055i	$-0.00974355\pi$
$434$			185.767i			0.428035i
$435$		0			0
$436$	48.9472			0.112264
$437$	22.6523			0.0518360
$438$	−362.758	+	341.626i	−0.828214	+	0.779967i
$439$	−118.098			−0.269016			−0.134508	−	0.990912i	$-0.542945\pi$
$439$	−118.098			−0.269016			−0.134508	+	0.990912i	$0.542945\pi$
$440$		0			0
$441$	3.77673	−	62.8867i	0.00856401	−	0.142600i
$442$			22.2719i			0.0503890i
$443$	467.265			1.05477			0.527387	−	0.849625i	$-0.323172\pi$
$443$	467.265			1.05477			0.527387	+	0.849625i	$0.323172\pi$
$444$	17.5423	−	16.5204i	0.0395097	−	0.0372081i
$445$		0			0
$446$			503.009i			1.12782i
$447$	−144.622	+	136.197i	−0.323540	+	0.304692i
$448$			21.1660i			0.0472456i
$449$		−	226.411i		−	0.504257i	−0.967694	−	0.252128i	$-0.918870\pi$
$449$		−	226.411i		−	0.504257i	0.967694	−	0.252128i	$-0.0811305\pi$
$450$		0			0
$451$	−314.731			−0.697851
$452$	−446.570			−0.987987
$453$	329.710	+	350.106i	0.727838	+	0.772860i
$454$	−404.206			−0.890322
$455$		0			0
$456$	−46.2934	−	49.1570i	−0.101521	−	0.107800i
$457$		−	348.845i		−	0.763337i	−0.924299	−	0.381668i	$-0.875350\pi$
$457$		−	348.845i		−	0.763337i	0.924299	−	0.381668i	$-0.124650\pi$
$458$	−600.001			−1.31005
$459$	76.7583	−	64.0542i	0.167229	−	0.139552i
$460$		0			0
$461$			316.335i			0.686192i	0.939300	+	0.343096i	$0.111476\pi$
$461$			316.335i			0.686192i	−0.939300	+	0.343096i	$0.888524\pi$
$462$	−80.8003	−	85.7984i	−0.174892	−	0.185711i
$463$		−	897.150i		−	1.93769i	−0.247671	−	0.968844i	$-0.579665\pi$
$463$		−	897.150i		−	1.93769i	0.247671	−	0.968844i	$-0.420335\pi$
$464$		−	174.890i		−	0.376919i
$465$		0			0
$466$	−145.221			−0.311633
$467$	−366.255			−0.784272			−0.392136	−	0.919907i	$-0.628264\pi$
$467$	−366.255			−0.784272			−0.392136	+	0.919907i	$0.628264\pi$
$468$	−76.4207	−	4.58953i	−0.163292	−	0.00980668i
$469$	−249.487			−0.531956
$470$		0			0
$471$	410.614	−	386.694i	0.871792	−	0.821006i
$472$		−	258.607i		−	0.547897i
$473$	−71.8395			−0.151880
$474$	84.9020	+	90.1539i	0.179118	+	0.190198i
$475$		0			0
$476$			19.5930i			0.0411618i
$477$	31.1791	−	519.166i	0.0653649	−	1.08840i
$478$			268.389i			0.561483i
$479$		−	58.3478i		−	0.121812i	−0.998144	−	0.0609058i	$-0.980601\pi$
$479$		−	58.3478i		−	0.121812i	0.998144	−	0.0609058i	$-0.0193989\pi$
$480$		0			0
$481$	−17.0816			−0.0355127
$482$	−302.823			−0.628263
$483$	16.4482	−	15.4900i	0.0340543	−	0.0320704i
$484$	21.5230			0.0444689
$485$		0			0
$486$	203.969	+	276.577i	0.419689	+	0.569088i
$487$			806.802i			1.65668i	0.560227	+	0.828339i	$0.310714\pi$
$487$			806.802i			1.65668i	−0.560227	+	0.828339i	$0.689286\pi$
$488$	297.397			0.609420
$489$	552.140	−	519.975i	1.12912	−	1.06334i
$490$		0			0
$491$			646.450i			1.31660i	0.752756	+	0.658300i	$0.228724\pi$
$491$			646.450i			1.31660i	−0.752756	+	0.658300i	$0.771276\pi$
$492$	−130.934	+	123.306i	−0.266125	+	0.250622i
$493$		−	161.893i		−	0.328384i
$494$			47.8660i			0.0968947i
$495$		0			0
$496$	198.594			0.400390
$497$	58.6715			0.118051
$498$	−315.226	−	334.725i	−0.632983	−	0.672138i
$499$	887.133			1.77782			0.888911	−	0.458080i	$-0.151463\pi$
$499$	887.133			1.77782			0.888911	+	0.458080i	$0.151463\pi$
$500$		0			0
$501$	251.664	+	267.231i	0.502323	+	0.533395i
$502$			256.204i			0.510367i
$503$	709.850			1.41123			0.705616	−	0.708594i	$-0.250670\pi$
$503$	709.850			1.41123			0.705616	+	0.708594i	$0.250670\pi$
$504$	−67.2287	−	4.03749i	−0.133390	−	0.00801090i
$505$		0			0
$506$		−	42.2671i		−	0.0835319i
$507$	−310.384	−	329.584i	−0.612198	−	0.650067i
$508$		−	355.735i		−	0.700265i
$509$			121.075i			0.237868i	0.992902	+	0.118934i	$0.0379477\pi$
$509$			121.075i			0.237868i	−0.992902	+	0.118934i	$0.962052\pi$
$510$		0			0
$511$	310.744			0.608109
$512$	22.6274			0.0441942
$513$	164.966	−	137.663i	0.321571	−	0.268349i
$514$	391.370			0.761419
$515$		0			0
$516$	−29.8865	+	28.1455i	−0.0579196	+	0.0545455i
$517$			11.6474i			0.0225288i
$518$	−15.0270			−0.0290096
$519$	37.4891	+	39.8081i	0.0722333	+	0.0767015i
$520$		0			0
$521$		−	563.114i		−	1.08083i	−0.841398	−	0.540417i	$-0.818267\pi$
$521$		−	563.114i		−	1.08083i	0.841398	−	0.540417i	$-0.181733\pi$
$522$	555.497	+	33.3610i	1.06417	+	0.0639099i
$523$			414.766i			0.793051i	0.918024	+	0.396525i	$0.129784\pi$
$523$			414.766i			0.793051i	−0.918024	+	0.396525i	$0.870216\pi$
$524$			211.982i			0.404545i
$525$		0			0
$526$	−61.3937			−0.116718
$527$	183.835			0.348833
$528$	−91.7224	+	86.3791i	−0.173717	+	0.163597i
$529$	−520.897			−0.984683
$530$		0			0
$531$	821.403	+	49.3303i	1.54690	+	0.0929007i
$532$			42.1086i			0.0791515i
$533$	127.495			0.239202
$534$	−354.331	+	333.689i	−0.663541	+	0.624887i
$535$		0			0
$536$			266.713i			0.497599i
$537$	−401.377	+	377.995i	−0.747443	+	0.703901i
$538$			236.091i			0.438832i
$539$			73.4962i			0.136357i
$540$		0			0
$541$	146.103			0.270060			0.135030	−	0.990841i	$-0.456887\pi$
$541$	146.103			0.270060			0.135030	+	0.990841i	$0.456887\pi$
$542$	571.157			1.05380
$543$	−418.864	−	444.774i	−0.771389	−	0.819105i
$544$	20.9458			0.0385034
$545$		0			0
$546$	32.7315	+	34.7562i	0.0599479	+	0.0636561i
$547$			144.077i			0.263396i	0.991290	+	0.131698i	$0.0420428\pi$
$547$			144.077i			0.263396i	−0.991290	+	0.131698i	$0.957957\pi$
$548$	238.323			0.434896
$549$	−56.7295	+	944.609i	−0.103332	+	1.72060i
$550$		0			0
$551$		−	347.935i		−	0.631461i
$552$	−16.5595	−	17.5839i	−0.0299992	−	0.0318548i
$553$		−	77.2271i		−	0.139651i
$554$		−	165.056i		−	0.297934i
$555$		0			0
$556$	516.205			0.928426
$557$	−383.039			−0.687682			−0.343841	−	0.939028i	$-0.611728\pi$
$557$	−383.039			−0.687682			−0.343841	+	0.939028i	$0.611728\pi$
$558$	−37.8825	+	630.785i	−0.0678897	+	1.13044i
$559$	29.1016			0.0520601
$560$		0			0
$561$	−84.9059	+	79.9598i	−0.151347	+	0.142531i
$562$			696.210i			1.23881i
$563$	−727.247			−1.29174			−0.645868	−	0.763449i	$-0.723504\pi$
$563$	−727.247			−1.29174			−0.645868	+	0.763449i	$0.723504\pi$
$564$	4.56325	+	4.84553i	0.00809087	+	0.00859136i
$565$		0			0
$566$		−	153.662i		−	0.271488i
$567$	25.6482	−	212.766i	0.0452350	−	0.375248i
$568$		−	62.7225i		−	0.110427i
$569$		−	236.225i		−	0.415158i	−0.978218	−	0.207579i	$-0.933442\pi$
$569$		−	236.225i		−	0.415158i	0.978218	−	0.207579i	$-0.0665585\pi$
$570$		0			0
$571$	398.093			0.697186			0.348593	−	0.937274i	$-0.386660\pi$
$571$	398.093			0.697186			0.348593	+	0.937274i	$0.386660\pi$
$572$	89.3134			0.156142
$573$	391.470	−	368.665i	0.683193	−	0.643394i
$574$	112.160			0.195400
$575$		0			0
$576$	−4.31626	+	71.8705i	−0.00749351	+	0.124775i
$577$			99.6832i			0.172761i	0.996262	+	0.0863806i	$0.0275301\pi$
$577$			99.6832i			0.172761i	−0.996262	+	0.0863806i	$0.972470\pi$
$578$	−389.318			−0.673561
$579$	382.507	−	360.224i	0.660634	−	0.622149i
$580$		0			0
$581$			286.730i			0.493511i
$582$	−416.028	+	391.793i	−0.714825	+	0.673184i
$583$			606.753i			1.04074i
$584$		−	332.199i		−	0.568834i
$585$		0			0
$586$	560.852			0.957085
$587$	249.784			0.425526			0.212763	−	0.977104i	$-0.431754\pi$
$587$	249.784			0.425526			0.212763	+	0.977104i	$0.431754\pi$
$588$	28.7945	+	30.5757i	0.0489703	+	0.0519995i
$589$	395.091			0.670783
$590$		0			0
$591$	−565.367	−	600.340i	−0.956628	−	1.01580i
$592$			16.0645i			0.0271360i
$593$	854.348			1.44072			0.720361	−	0.693599i	$-0.243976\pi$
$593$	854.348			1.44072			0.720361	+	0.693599i	$0.243976\pi$
$594$	−256.866	−	307.811i	−0.432434	−	0.518200i
$595$		0			0
$596$		−	132.439i		−	0.222213i
$597$	−87.7425	−	93.1701i	−0.146972	−	0.156064i
$598$			17.1221i			0.0286322i
$599$			780.767i			1.30345i	0.758455	+	0.651725i	$0.225954\pi$
$599$			780.767i			1.30345i	−0.758455	+	0.651725i	$0.774046\pi$
$600$		0			0
$601$	−361.598			−0.601660			−0.300830	−	0.953678i	$-0.597264\pi$
$601$	−361.598			−0.601660			−0.300830	+	0.953678i	$0.597264\pi$
$602$	25.6012			0.0425269
$603$	−847.150	−	50.8765i	−1.40489	−	0.0843723i
$604$	−320.613			−0.530815
$605$		0			0
$606$	117.806	−	110.943i	0.194399	−	0.183074i
$607$			652.157i			1.07439i	0.843457	+	0.537197i	$0.180517\pi$
$607$			652.157i			1.07439i	−0.843457	+	0.537197i	$0.819483\pi$
$608$	45.0160			0.0740395
$609$	−237.923	−	252.641i	−0.390679	−	0.414845i
$610$		0			0
$611$		−	4.71827i		−	0.00772220i
$612$	−3.99549	+	66.5294i	−0.00652858	+	0.108708i
$613$		−	12.0837i		−	0.0197124i	−0.999951	−	0.00985620i	$-0.996863\pi$
$613$		−	12.0837i		−	0.0197124i	0.999951	−	0.00985620i	$-0.00313738\pi$
$614$		−	35.2726i		−	0.0574472i
$615$		0			0
$616$	78.5707			0.127550
$617$	−523.595			−0.848615			−0.424307	−	0.905518i	$-0.639482\pi$
$617$	−523.595			−0.848615			−0.424307	+	0.905518i	$0.639482\pi$
$618$	75.3343	−	70.9458i	0.121900	−	0.114799i
$619$	318.836			0.515082			0.257541	−	0.966267i	$-0.417088\pi$
$619$	318.836			0.515082			0.257541	+	0.966267i	$0.417088\pi$
$620$		0			0
$621$	59.0097	−	49.2432i	0.0950237	−	0.0792966i
$622$			244.722i			0.393444i
$623$	303.525			0.487199
$624$	37.1560	−	34.9915i	0.0595448	−	0.0560761i
$625$		0			0
$626$			407.599i			0.651117i
$627$	−182.477	+	171.847i	−0.291031	+	0.274077i
$628$			376.024i			0.598764i
$629$			14.8707i			0.0236418i
$630$		0			0
$631$	−906.187			−1.43611			−0.718056	−	0.695985i	$-0.754968\pi$
$631$	−906.187			−1.43611			−0.718056	+	0.695985i	$0.754968\pi$
$632$	−82.5593			−0.130632
$633$	−479.159	−	508.799i	−0.756965	−	0.803790i
$634$	731.624			1.15398
$635$		0			0
$636$	237.716	+	252.420i	0.373767	+	0.396887i
$637$		−	29.7727i		−	0.0467389i
$638$	−649.214			−1.01758
$639$	199.223	+	11.9645i	0.311773	+	0.0187238i
$640$		0			0
$641$		−	456.311i		−	0.711873i	−0.934510	−	0.355937i	$-0.884162\pi$
$641$		−	456.311i		−	0.711873i	0.934510	−	0.355937i	$-0.115838\pi$
$642$	98.6196	+	104.720i	0.153613	+	0.163115i
$643$			713.329i			1.10938i	0.832058	+	0.554688i	$0.187163\pi$
$643$			713.329i			1.10938i	−0.832058	+	0.554688i	$0.812837\pi$
$644$			15.0626i			0.0233891i
$645$		0			0
$646$	41.6706			0.0645056
$647$	−990.731			−1.53127			−0.765634	−	0.643276i	$-0.777575\pi$
$647$	−990.731			−1.53127			−0.765634	+	0.643276i	$0.777575\pi$
$648$	−227.456	−	27.4191i	−0.351012	−	0.0423134i
$649$	−959.981			−1.47917
$650$		0			0
$651$	286.882	−	270.170i	0.440679	−	0.415007i
$652$			505.627i			0.775502i
$653$	−915.043			−1.40129			−0.700646	−	0.713509i	$-0.747105\pi$
$653$	−915.043			−1.40129			−0.700646	+	0.713509i	$0.747105\pi$
$654$	−71.1860	−	75.5894i	−0.108847	−	0.115580i
$655$		0			0
$656$		−	119.904i		−	0.182780i
$657$	1055.15	+	63.3681i	1.60601	+	0.0964507i
$658$		−	4.15075i		−	0.00630813i
$659$		−	148.607i		−	0.225503i	−0.993623	−	0.112752i	$-0.964034\pi$
$659$		−	148.607i		−	0.225503i	0.993623	−	0.112752i	$-0.0359664\pi$
$660$		0			0
$661$	−154.606			−0.233898			−0.116949	−	0.993138i	$-0.537311\pi$
$661$	−154.606			−0.233898			−0.116949	+	0.993138i	$0.537311\pi$
$662$	−521.148			−0.787233
$663$	34.3947	−	32.3910i	0.0518774	−	0.0488553i
$664$	306.527			0.461638
$665$		0			0
$666$	−51.0251	−	3.06437i	−0.0766143	−	0.00460115i
$667$		−	124.459i		−	0.186595i
$668$	−244.719			−0.366346
$669$	776.800	−	731.548i	1.16114	−	1.09350i
$670$		0			0
$671$		−	1103.97i		−	1.64526i
$672$	32.6868	−	30.7827i	0.0486411	−	0.0458075i
$673$		−	859.143i		−	1.27659i	−0.769793	−	0.638293i	$-0.779641\pi$
$673$		−	859.143i		−	1.27659i	0.769793	−	0.638293i	$-0.220359\pi$
$674$		−	352.803i		−	0.523446i
$675$		0			0
$676$	301.820			0.446479
$677$	547.092			0.808112			0.404056	−	0.914734i	$-0.367600\pi$
$677$	547.092			0.808112			0.404056	+	0.914734i	$0.367600\pi$
$678$	649.466	+	689.641i	0.957915	+	1.01717i
$679$	356.376			0.524854
$680$		0			0
$681$	587.855	+	624.218i	0.863223	+	0.916620i
$682$		−	737.203i		−	1.08094i
$683$	83.7756			0.122658			0.0613291	−	0.998118i	$-0.480466\pi$
$683$	83.7756			0.122658			0.0613291	+	0.998118i	$0.480466\pi$
$684$	−8.58696	+	142.982i	−0.0125540	+	0.209039i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	872.608	+	926.586i	1.27017	+	1.34874i
$688$		−	27.3688i		−	0.0397803i
$689$		−	245.791i		−	0.356735i
$690$		0			0
$691$	−1021.46			−1.47823			−0.739116	−	0.673578i	$-0.764757\pi$
$691$	−1021.46			−1.47823			−0.739116	+	0.673578i	$0.764757\pi$
$692$	−36.4546			−0.0526801
$693$	−14.9876	+	249.561i	−0.0216272	+	0.360117i
$694$	392.938			0.566193
$695$		0			0
$696$	−270.084	+	254.351i	−0.388052	+	0.365447i
$697$		−	110.993i		−	0.159244i
$698$	−300.838			−0.431000
$699$	211.201	+	224.266i	0.302148	+	0.320838i
$700$		0			0
$701$			1194.70i			1.70428i	0.523310	+	0.852142i	$0.324697\pi$
$701$			1194.70i			1.70428i	−0.523310	+	0.852142i	$0.675303\pi$
$702$	104.054	+	124.692i	0.148226	+	0.177624i
$703$			31.9595i			0.0454616i
$704$		−	83.9956i		−	0.119312i
$705$		0			0
$706$	−441.661			−0.625582
$707$	−100.914			−0.142736
$708$	−399.369	+	376.104i	−0.564081	+	0.531220i
$709$	1127.65			1.59048			0.795238	−	0.606298i	$-0.207346\pi$
$709$	1127.65			1.59048			0.795238	+	0.606298i	$0.207346\pi$
$710$		0			0
$711$	15.7485	−	262.229i	0.0221498	−	0.368818i
$712$		−	324.482i		−	0.455733i
$713$	141.327			0.198215
$714$	30.2577	−	28.4950i	0.0423777	−	0.0399090i
$715$		0			0
$716$		−	367.565i		−	0.513359i
$717$	414.475	−	390.330i	0.578068	−	0.544393i
$718$			628.418i			0.875234i
$719$			85.5636i			0.119004i	0.998228	+	0.0595018i	$0.0189512\pi$
$719$			85.5636i			0.119004i	−0.998228	+	0.0595018i	$0.981049\pi$
$720$		0			0
$721$	−64.5325			−0.0895041
$722$	−420.974			−0.583067
$723$	440.409	+	467.652i	0.609141	+	0.646821i
$724$	407.306			0.562577
$725$		0			0
$726$	−31.3018	−	33.2381i	−0.0431154	−	0.0457825i
$727$		−	106.746i		−	0.146830i	−0.997301	−	0.0734151i	$-0.976610\pi$
$727$		−	106.746i		−	0.146830i	0.997301	−	0.0734151i	$-0.0233898\pi$
$728$	−31.8283			−0.0437203
$729$	130.478	−	717.228i	0.178982	−	0.983852i
$730$		0			0
$731$		−	25.3349i		−	0.0346579i
$732$	−432.517	−	459.272i	−0.590871	−	0.627421i
$733$		−	1125.65i		−	1.53567i	−0.640648	−	0.767835i	$-0.721334\pi$
$733$		−	1125.65i		−	1.53567i	0.640648	−	0.767835i	$-0.278666\pi$
$734$			30.2092i			0.0411570i
$735$		0			0
$736$	16.1026			0.0218785
$737$	990.071			1.34338
$738$	380.845	+	22.8721i	0.516050	+	0.0309919i
$739$	754.785			1.02136			0.510680	−	0.859771i	$-0.329394\pi$
$739$	754.785			1.02136			0.510680	+	0.859771i	$0.329394\pi$
$740$		0			0
$741$	73.9198	−	69.6136i	0.0997568	−	0.0939455i
$742$		−	216.227i		−	0.291411i
$743$	−1033.99			−1.39164			−0.695822	−	0.718214i	$-0.744960\pi$
$743$	−1033.99			−1.39164			−0.695822	+	0.718214i	$0.744960\pi$
$744$	−288.824	−	306.690i	−0.388204	−	0.412217i
$745$		0			0
$746$			258.593i			0.346639i
$747$	−58.4712	+	973.610i	−0.0782747	+	1.30336i
$748$		−	77.7534i		−	0.103948i
$749$		−	89.7047i		−	0.119766i
$750$		0			0
$751$	898.534			1.19645			0.598225	−	0.801328i	$-0.295873\pi$
$751$	898.534			1.19645			0.598225	+	0.801328i	$0.295873\pi$
$752$	−4.43734			−0.00590071
$753$	395.658	−	372.609i	0.525442	−	0.494833i
$754$	262.991			0.348795
$755$		0			0
$756$	91.5385	+	109.694i	0.121083	+	0.145097i
$757$		−	977.654i		−	1.29148i	−0.763555	−	0.645742i	$-0.776548\pi$
$757$		−	977.654i		−	1.29148i	0.763555	−	0.645742i	$-0.223452\pi$
$758$	−745.329			−0.983284
$759$	−65.2734	+	61.4709i	−0.0859992	+	0.0809894i
$760$		0			0
$761$		−	1131.97i		−	1.48747i	−0.668472	−	0.743737i	$-0.733051\pi$
$761$		−	1131.97i		−	1.48747i	0.668472	−	0.743737i	$-0.266949\pi$
$762$	−549.363	+	517.361i	−0.720949	+	0.678951i
$763$			64.7510i			0.0848637i
$764$			358.492i			0.469230i
$765$		0			0
$766$	−253.672			−0.331165
$767$	388.880			0.507015
$768$	−32.9081	−	34.9437i	−0.0428490	−	0.0454996i
$769$	−99.2202			−0.129025			−0.0645125	−	0.997917i	$-0.520549\pi$
$769$	−99.2202			−0.129025			−0.0645125	+	0.997917i	$0.520549\pi$
$770$		0			0
$771$	−569.186	−	604.395i	−0.738244	−	0.783910i
$772$			350.284i			0.453736i
$773$	77.6933			0.100509			0.0502544	−	0.998736i	$-0.483997\pi$
$773$	77.6933			0.100509			0.0502544	+	0.998736i	$0.483997\pi$
$774$	86.9305	+	5.22070i	0.112313	+	0.00674510i
$775$		0			0
$776$		−	380.982i		−	0.490956i
$777$	21.8544	+	23.2063i	0.0281267	+	0.0298665i
$778$		−	800.311i		−	1.02868i
$779$		−	238.542i		−	0.306215i
$780$		0			0
$781$	−232.833			−0.298122
$782$	14.9059			0.0190613
$783$	−756.364	−	906.376i	−0.965982	−	1.15757i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	327.365	−	308.294i	0.416494	−	0.392232i
$787$		−	53.9577i		−	0.0685612i	−0.999412	−	0.0342806i	$-0.989086\pi$
$787$		−	53.9577i		−	0.0685612i	0.999412	−	0.0342806i	$-0.0109140\pi$
$788$	549.767			0.697674
$789$	89.2876	+	94.8107i	0.113166	+	0.120166i
$790$		0			0
$791$		−	590.756i		−	0.746848i
$792$	266.792	+	16.0225i	0.336858	+	0.0202304i
$793$			447.210i			0.563947i
$794$		−	297.278i		−	0.374406i
$795$		0			0
$796$	85.3214			0.107188
$797$	580.476			0.728326			0.364163	−	0.931335i	$-0.381355\pi$
$797$	580.476			0.728326			0.364163	+	0.931335i	$0.381355\pi$
$798$	65.0286	−	61.2404i	0.0814895	−	0.0767424i
$799$	−4.10757			−0.00514089
$800$		0			0
$801$	1030.64	+	61.8961i	1.28669	+	0.0772735i
$802$		−	837.878i		−	1.04474i
$803$	−1233.16			−1.53569
$804$	411.887	−	387.893i	0.512297	−	0.482454i
$805$		0			0
$806$			298.635i			0.370515i
$807$	364.598	−	343.358i	0.451794	−	0.425475i
$808$			107.882i			0.133517i
$809$			498.810i			0.616576i	0.951293	+	0.308288i	$0.0997560\pi$
$809$			498.810i			0.616576i	−0.951293	+	0.308288i	$0.900244\pi$
$810$		0			0
$811$	1457.86			1.79761			0.898804	−	0.438351i	$-0.144437\pi$
$811$	1457.86			1.79761			0.898804	+	0.438351i	$0.144437\pi$
$812$	231.358			0.284924
$813$	−830.659	−	882.042i	−1.02172	−	1.08492i
$814$	59.6334			0.0732597
$815$		0			0
$816$	−30.4625	−	32.3468i	−0.0373314	−	0.0396407i
$817$		−	54.4488i		−	0.0666448i
$818$	−354.448			−0.433310
$819$	6.07137	−	101.095i	0.00741315	−	0.123437i
$820$		0			0
$821$			932.133i			1.13536i	0.823248	+	0.567682i	$0.192160\pi$
$821$			932.133i			1.13536i	−0.823248	+	0.567682i	$0.807840\pi$
$822$	−346.604	−	368.044i	−0.421659	−	0.447742i
$823$		−	1301.33i		−	1.58121i	−0.612328	−	0.790604i	$-0.709767\pi$
$823$		−	1301.33i		−	1.58121i	0.612328	−	0.790604i	$-0.290233\pi$
$824$			68.9881i			0.0837235i
$825$		0			0
$826$	342.105			0.414171
$827$	−982.931			−1.18855			−0.594275	−	0.804262i	$-0.702561\pi$
$827$	−982.931			−1.18855			−0.594275	+	0.804262i	$0.702561\pi$
$828$	−3.07163	+	51.1460i	−0.00370970	+	0.0617705i
$829$	−951.503			−1.14777			−0.573886	−	0.818935i	$-0.694565\pi$
$829$	−951.503			−1.14777			−0.573886	+	0.818935i	$0.694565\pi$
$830$		0			0
$831$	−254.897	+	240.048i	−0.306735	+	0.288866i
$832$			34.0259i			0.0408966i
$833$	−25.9191			−0.0311154
$834$	−750.740	−	797.179i	−0.900168	−	0.955850i
$835$		0			0
$836$		−	167.105i		−	0.199886i
$837$	1029.22	−	858.876i	1.22965	−	1.02614i
$838$		−	305.326i		−	0.364351i
$839$			288.034i			0.343306i	0.985157	+	0.171653i	$0.0549108\pi$
$839$			288.034i			0.343306i	−0.985157	+	0.171653i	$0.945089\pi$
$840$		0			0
$841$	−1070.67			−1.27309
$842$	−953.204			−1.13207
$843$	1075.16	−	1012.53i	1.27540	−	1.20110i
$844$	465.937			0.552059
$845$		0			0
$846$	0.846438	−	14.0941i	0.00100052	−	0.0166597i
$847$			28.4722i			0.0336154i
$848$	−231.156			−0.272590
$849$	−237.301	+	223.478i	−0.279507	+	0.263224i
$850$		0			0
$851$			11.4322i			0.0134338i
$852$	−96.8628	+	91.2201i	−0.113689	+	0.107066i
$853$			880.826i			1.03262i	0.856401	+	0.516310i	$0.172695\pi$
$853$			880.826i			1.03262i	−0.856401	+	0.516310i	$0.827305\pi$
$854$			393.419i			0.460678i
$855$		0			0
$856$	−95.8984			−0.112031
$857$	−499.910			−0.583326			−0.291663	−	0.956521i	$-0.594209\pi$
$857$	−499.910			−0.583326			−0.291663	+	0.956521i	$0.594209\pi$
$858$	−129.892	−	137.927i	−0.151390	−	0.160754i
$859$	−138.926			−0.161730			−0.0808652	−	0.996725i	$-0.525768\pi$
$859$	−138.926			−0.161730			−0.0808652	+	0.996725i	$0.525768\pi$
$860$		0			0
$861$	−163.119	−	173.209i	−0.189453	−	0.201172i
$862$		−	437.005i		−	0.506966i
$863$	503.960			0.583963			0.291982	−	0.956424i	$-0.405685\pi$
$863$	503.960			0.583963			0.291982	+	0.956424i	$0.405685\pi$
$864$	117.267	−	97.8588i	0.135726	−	0.113263i
$865$		0			0
$866$		−	37.4828i		−	0.0432827i
$867$	566.203	+	601.227i	0.653060	+	0.693457i
$868$			262.715i			0.302667i
$869$			306.470i			0.352669i
$870$		0			0
$871$	−401.069			−0.460470
$872$	69.2217			0.0793827
$873$	1210.10	+	72.6737i	1.38614	+	0.0832459i
$874$	32.0352			0.0366536
$875$		0			0
$876$	−513.017	+	483.132i	−0.585636	+	0.551520i
$877$		−	433.319i		−	0.494092i	−0.969004	−	0.247046i	$-0.920540\pi$
$877$		−	433.319i		−	0.494092i	0.969004	−	0.247046i	$-0.0794599\pi$
$878$	−167.016			−0.190223
$879$	−815.671	−	866.127i	−0.927954	−	0.985355i
$880$		0			0
$881$		−	930.356i		−	1.05602i	−0.849237	−	0.528012i	$-0.822938\pi$
$881$		−	930.356i		−	1.05602i	0.849237	−	0.528012i	$-0.177062\pi$
$882$	5.34110	−	88.9352i	0.00605567	−	0.100834i
$883$		−	11.6086i		−	0.0131468i	−0.999978	−	0.00657338i	$-0.997908\pi$
$883$		−	11.6086i		−	0.0131468i	0.999978	−	0.00657338i	$-0.00209239\pi$
$884$			31.4973i			0.0356304i
$885$		0			0
$886$	660.812			0.745837
$887$	74.3001			0.0837656			0.0418828	−	0.999123i	$-0.486664\pi$
$887$	74.3001			0.0837656			0.0418828	+	0.999123i	$0.486664\pi$
$888$	24.8086	−	23.3634i	0.0279376	−	0.0263101i
$889$	470.593			0.529351
$890$		0			0
$891$	−101.783	+	844.343i	−0.114235	+	0.947635i
$892$			711.362i			0.797491i
$893$	−8.82784			−0.00988560
$894$	−204.527	+	192.612i	−0.228777	+	0.215450i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	26.4417	−	24.9014i	0.0294779	−	0.0277607i
$898$		−	320.194i		−	0.356563i
$899$		−	2170.76i		−	2.41464i
$900$		0			0
$901$	−213.978			−0.237489
$902$	−445.097			−0.493455
$903$	−37.2330	−	39.5361i	−0.0412325	−	0.0437831i
$904$	−631.545			−0.698612
$905$		0			0
$906$	466.281	+	495.124i	0.514659	+	0.546495i
$907$		−	927.337i		−	1.02242i	−0.859455	−	0.511211i	$-0.829197\pi$
$907$		−	927.337i		−	1.02242i	0.859455	−	0.511211i	$-0.170803\pi$
$908$	−571.634			−0.629552
$909$	−342.660	−	20.5788i	−0.376964	−	0.0226390i
$910$		0			0
$911$			1331.44i			1.46152i	0.682636	+	0.730758i	$0.260833\pi$
$911$			1331.44i			1.46152i	−0.682636	+	0.730758i	$0.739167\pi$
$912$	−65.4688	−	69.5185i	−0.0717859	−	0.0762264i
$913$		−	1137.87i		−	1.24629i
$914$		−	493.341i		−	0.539761i
$915$		0			0
$916$	−848.530			−0.926342
$917$	−280.425			−0.305807
$918$	108.553	−	90.5863i	0.118249	−	0.0986779i
$919$	60.3397			0.0656580			0.0328290	−	0.999461i	$-0.489548\pi$
$919$	60.3397			0.0656580			0.0328290	+	0.999461i	$0.489548\pi$
$920$		0			0
$921$	−54.4716	+	51.2984i	−0.0591440	+	0.0556986i
$922$			447.365i			0.485211i
$923$	94.3188			0.102187
$924$	−114.269	−	121.337i	−0.123668	−	0.131317i
$925$		0			0
$926$		−	1268.76i		−	1.37015i
$927$	−219.124	−	13.1597i	−0.236380	−	0.0141960i
$928$		−	247.332i		−	0.266522i
$929$		−	76.2234i		−	0.0820488i	−0.999158	−	0.0410244i	$-0.986938\pi$
$929$		−	76.2234i		−	0.0820488i	0.999158	−	0.0410244i	$-0.0130621\pi$
$930$		0			0
$931$	−55.7045			−0.0598329
$932$	−205.374			−0.220358
$933$	377.926	−	355.910i	0.405065	−	0.381468i
$934$	−517.963			−0.554564
$935$		0			0
$936$	−108.075	−	6.49057i	−0.115465	−	0.00693437i
$937$			275.139i			0.293638i	0.989163	+	0.146819i	$0.0469035\pi$
$937$			275.139i			0.293638i	−0.989163	+	0.146819i	$0.953096\pi$
$938$	−352.828			−0.376150
$939$	629.458	−	592.789i	0.670349	−	0.631298i
$940$		0			0
$941$			497.628i			0.528829i	0.964409	+	0.264414i	$0.0851787\pi$
$941$			497.628i			0.528829i	−0.964409	+	0.264414i	$0.914821\pi$
$942$	580.696	−	546.868i	0.616450	−	0.580539i
$943$		−	85.3284i		−	0.0904861i
$944$		−	365.726i		−	0.387422i
$945$		0			0
$946$	−101.596			−0.107396
$947$	−1193.87			−1.26069			−0.630344	−	0.776316i	$-0.717086\pi$
$947$	−1193.87			−1.26069			−0.630344	+	0.776316i	$0.717086\pi$
$948$	120.070	+	127.497i	0.126656	+	0.134490i
$949$	499.543			0.526389
$950$		0			0
$951$	−1064.03	−	1129.85i	−1.11886	−	1.18807i
$952$			27.7087i			0.0291058i
$953$	1054.39			1.10639			0.553196	−	0.833051i	$-0.313408\pi$
$953$	1054.39			1.10639			0.553196	+	0.833051i	$0.313408\pi$
$954$	44.0939	−	734.211i	0.0462200	−	0.769614i
$955$		0			0
$956$			379.559i			0.397029i
$957$	944.180	+	1002.58i	0.986604	+	1.04763i
$958$		−	82.5162i		−	0.0861339i
$959$			315.272i			0.328750i
$960$		0			0
$961$	1503.97			1.56500
$962$	−24.1570			−0.0251112
$963$	18.2930	−	304.598i	0.0189958	−	0.316301i
$964$	−428.256			−0.444249
$965$		0			0
$966$	23.2613	−	21.9062i	0.0240800	−	0.0226772i
$967$		−	1124.72i		−	1.16310i	−0.813509	−	0.581552i	$-0.802446\pi$
$967$		−	1124.72i		−	1.16310i	0.813509	−	0.581552i	$-0.197554\pi$
$968$	30.4381			0.0314443
$969$	−60.6034	−	64.3522i	−0.0625422	−	0.0664109i
$970$		0			0
$971$			181.104i			0.186512i	0.995642	+	0.0932562i	$0.0297276\pi$
$971$			181.104i			0.186512i	−0.995642	+	0.0932562i	$0.970272\pi$
$972$	288.456	+	391.139i	0.296765	+	0.402406i
$973$			682.875i			0.701824i
$974$			1140.99i			1.17145i
$975$		0			0
$976$	420.583			0.430925
$977$	−678.890			−0.694872			−0.347436	−	0.937704i	$-0.612948\pi$
$977$	−678.890			−0.694872			−0.347436	+	0.937704i	$0.612948\pi$
$978$	780.844	−	735.356i	0.798409	−	0.751898i
$979$	−1204.51			−1.23035
$980$		0			0
$981$	−13.2043	+	219.866i	−0.0134600	+	0.224124i
$982$			914.219i			0.930976i
$983$	−710.487			−0.722774			−0.361387	−	0.932416i	$-0.617697\pi$
$983$	−710.487			−0.722774			−0.361387	+	0.932416i	$0.617697\pi$
$984$	−185.168	+	174.381i	−0.188179	+	0.177217i
$985$		0			0
$986$		−	228.952i		−	0.232202i
$987$	−6.41003	+	6.03662i	−0.00649446	+	0.00611613i
$988$			67.6927i			0.0685149i
$989$		−	19.4768i		−	0.0196934i
$990$		0			0
$991$	−753.180			−0.760020			−0.380010	−	0.924982i	$-0.624079\pi$
$991$	−753.180			−0.760020			−0.380010	+	0.924982i	$0.624079\pi$
$992$	280.854			0.283119
$993$	757.929	+	804.813i	0.763272	+	0.810486i
$994$	82.9741			0.0834749
$995$		0			0
$996$	−445.796	−	473.372i	−0.447587	−	0.475273i
$997$			1097.84i			1.10114i	0.834789	+	0.550570i	$0.185590\pi$
$997$			1097.84i			1.10114i	−0.834789	+	0.550570i	$0.814410\pi$
$998$	1254.60			1.25711
$999$	69.4757	+	83.2551i	0.0695453	+	0.0833384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.19		32
3.2	odd	2	inner	1050.3.c.c.449.13		32
5.2	odd	4		1050.3.e.d.701.10		16
5.3	odd	4		210.3.e.a.71.7	✓	16
5.4	even	2	inner	1050.3.c.c.449.14		32
15.2	even	4		1050.3.e.d.701.2		16
15.8	even	4		210.3.e.a.71.15	yes	16
15.14	odd	2	inner	1050.3.c.c.449.20		32
20.3	even	4		1680.3.l.c.1121.4		16
60.23	odd	4		1680.3.l.c.1121.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.7	✓	16	5.3	odd	4
210.3.e.a.71.15	yes	16	15.8	even	4
1050.3.c.c.449.13		32	3.2	odd	2	inner
1050.3.c.c.449.14		32	5.4	even	2	inner
1050.3.c.c.449.19		32	1.1	even	1	trivial
1050.3.c.c.449.20		32	15.14	odd	2	inner
1050.3.e.d.701.2		16	15.2	even	4
1050.3.e.d.701.10		16	5.2	odd	4
1680.3.l.c.1121.3		16	60.23	odd	4
1680.3.l.c.1121.4		16	20.3	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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-2.05675 - 2.18398i) q^{3} +2.00000 q^{4} +(-2.90869 - 3.08861i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-0.539533 + 8.98381i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-2.05675 - 2.18398i) q^{3} +2.00000 q^{4} +(-2.90869 - 3.08861i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-0.539533 + 8.98381i) q^{9} -10.4995i q^{11} +(-4.11351 - 4.36796i) q^{12} +4.25324i q^{13} +3.74166i q^{14} +4.00000 q^{16} +3.70274 q^{17} +(-0.763014 + 12.7050i) q^{18} +7.95778 q^{19} +(5.77827 - 5.44166i) q^{21} -14.8485i q^{22} +2.84656 q^{23} +(-5.81738 - 6.17723i) q^{24} +6.01499i q^{26} +(20.7301 - 17.2992i) q^{27} +5.29150i q^{28} -43.7226i q^{29} +49.6484 q^{31} +5.65685 q^{32} +(-22.9306 + 21.5948i) q^{33} +5.23646 q^{34} +(-1.07907 + 17.9676i) q^{36} +4.01613i q^{37} +11.2540 q^{38} +(9.28899 - 8.74787i) q^{39} -29.9759i q^{41} +(8.17170 - 7.69567i) q^{42} -6.84221i q^{43} -20.9989i q^{44} +4.02565 q^{46} -1.10933 q^{47} +(-8.22701 - 8.73592i) q^{48} -7.00000 q^{49} +(-7.61561 - 8.08670i) q^{51} +8.50648i q^{52} -57.7890 q^{53} +(29.3169 - 24.4647i) q^{54} +7.48331i q^{56} +(-16.3672 - 17.3796i) q^{57} -61.8331i q^{58} -91.4315i q^{59} +105.146 q^{61} +70.2135 q^{62} +(-23.7689 - 1.42747i) q^{63} +8.00000 q^{64} +(-32.4288 + 30.5396i) q^{66} +94.2973i q^{67} +7.40547 q^{68} +(-5.85468 - 6.21684i) q^{69} -22.1757i q^{71} +(-1.52603 + 25.4101i) q^{72} -117.450i q^{73} +5.67967i q^{74} +15.9156 q^{76} +27.7789 q^{77} +(13.1366 - 12.3714i) q^{78} -29.1891 q^{79} +(-80.4178 - 9.69412i) q^{81} -42.3924i q^{82} +108.374 q^{83} +(11.5565 - 10.8833i) q^{84} -9.67635i q^{86} +(-95.4893 + 89.9266i) q^{87} -29.6969i q^{88} -114.722i q^{89} -11.2530 q^{91} +5.69313 q^{92} +(-102.115 - 108.431i) q^{93} -1.56884 q^{94} +(-11.6348 - 12.3545i) q^{96} -134.697i q^{97} -9.89949 q^{98} +(94.3251 + 5.66480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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