LMFDB - Embedded newform 1050.3.c.c.449.21

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			449.21
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-0.396304 - 2.97371i) q^{3} +2.00000 q^{4} +(-0.560459 - 4.20546i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.68589 + 2.35699i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-0.396304 - 2.97371i) q^{3} +2.00000 q^{4} +(-0.560459 - 4.20546i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.68589 + 2.35699i) q^{9} -2.01787i q^{11} +(-0.792609 - 5.94742i) q^{12} +11.6017i q^{13} +3.74166i q^{14} +4.00000 q^{16} -17.3916 q^{17} +(-12.2837 + 3.33328i) q^{18} -36.1315 q^{19} +(7.86769 - 1.04852i) q^{21} -2.85370i q^{22} -32.2831 q^{23} +(-1.12092 - 8.41092i) q^{24} +16.4072i q^{26} +(10.4512 + 24.8952i) q^{27} +5.29150i q^{28} +46.1442i q^{29} +34.0124 q^{31} +5.65685 q^{32} +(-6.00057 + 0.799692i) q^{33} -24.5954 q^{34} +(-17.3718 + 4.71398i) q^{36} -31.4813i q^{37} -51.0976 q^{38} +(34.4999 - 4.59779i) q^{39} -32.1651i q^{41} +(11.1266 - 1.48284i) q^{42} -51.7542i q^{43} -4.03575i q^{44} -45.6552 q^{46} -92.3399 q^{47} +(-1.58522 - 11.8948i) q^{48} -7.00000 q^{49} +(6.89236 + 51.7175i) q^{51} +23.2033i q^{52} -18.3315 q^{53} +(14.7803 + 35.2071i) q^{54} +7.48331i q^{56} +(14.3191 + 107.445i) q^{57} +65.2577i q^{58} +45.4634i q^{59} +28.1445 q^{61} +48.1007 q^{62} +(-6.23600 - 22.9807i) q^{63} +8.00000 q^{64} +(-8.48608 + 1.13094i) q^{66} +33.7430i q^{67} -34.7832 q^{68} +(12.7939 + 96.0005i) q^{69} +25.2759i q^{71} +(-24.5674 + 6.66657i) q^{72} +48.5331i q^{73} -44.5212i q^{74} -72.2630 q^{76} +5.33879 q^{77} +(48.7903 - 6.50225i) q^{78} -32.9331 q^{79} +(69.8892 - 40.9450i) q^{81} -45.4883i q^{82} -82.4176 q^{83} +(15.7354 - 2.09705i) q^{84} -73.1915i q^{86} +(137.219 - 18.2871i) q^{87} -5.70741i q^{88} +48.8676i q^{89} -30.6951 q^{91} -64.5661 q^{92} +(-13.4792 - 101.143i) q^{93} -130.588 q^{94} +(-2.24184 - 16.8218i) q^{96} +14.5167i q^{97} -9.89949 q^{98} +(4.75610 + 17.5270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.396304	−	2.97371i	−0.132101	−	0.991236i
$3$	−0.396304	−	2.97371i	−0.132101	−	0.991236i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−0.560459	−	4.20546i	−0.0934098	−	0.700910i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	−8.68589	+	2.35699i	−0.965098	+	0.261888i
$10$		0			0
$11$		−	2.01787i		−	0.183443i	−0.995785	−	0.0917215i	$-0.970763\pi$
$11$		−	2.01787i		−	0.183443i	0.995785	−	0.0917215i	$-0.0292369\pi$
$12$	−0.792609	−	5.94742i	−0.0660507	−	0.495618i
$13$			11.6017i			0.892435i	0.894925	+	0.446218i	$0.147229\pi$
$13$			11.6017i			0.892435i	−0.894925	+	0.446218i	$0.852771\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−17.3916			−1.02303			−0.511517	−	0.859273i	$-0.670916\pi$
$17$	−17.3916			−1.02303			−0.511517	+	0.859273i	$0.670916\pi$
$18$	−12.2837	+	3.33328i	−0.682428	+	0.185182i
$19$	−36.1315			−1.90166			−0.950829	−	0.309718i	$-0.899766\pi$
$19$	−36.1315			−1.90166			−0.950829	+	0.309718i	$0.899766\pi$
$20$		0			0
$21$	7.86769	−	1.04852i	0.374652	−	0.0499297i
$22$		−	2.85370i		−	0.129714i
$23$	−32.2831			−1.40361			−0.701806	−	0.712368i	$-0.747623\pi$
$23$	−32.2831			−1.40361			−0.701806	+	0.712368i	$0.747623\pi$
$24$	−1.12092	−	8.41092i	−0.0467049	−	0.350455i
$25$		0			0
$26$			16.4072i			0.631047i
$27$	10.4512	+	24.8952i	0.387083	+	0.922045i
$28$			5.29150i			0.188982i
$29$			46.1442i			1.59118i	0.605837	+	0.795589i	$0.292839\pi$
$29$			46.1442i			1.59118i	−0.605837	+	0.795589i	$0.707161\pi$
$30$		0			0
$31$	34.0124			1.09717			0.548586	−	0.836094i	$-0.315166\pi$
$31$	34.0124			1.09717			0.548586	+	0.836094i	$0.315166\pi$
$32$	5.65685			0.176777
$33$	−6.00057	+	0.799692i	−0.181835	+	0.0242331i
$34$	−24.5954			−0.723394
$35$		0			0
$36$	−17.3718	+	4.71398i	−0.482549	+	0.130944i
$37$		−	31.4813i		−	0.850845i	−0.904995	−	0.425423i	$-0.860125\pi$
$37$		−	31.4813i		−	0.850845i	0.904995	−	0.425423i	$-0.139875\pi$
$38$	−51.0976			−1.34467
$39$	34.4999	−	4.59779i	0.884614	−	0.117892i
$40$		0			0
$41$		−	32.1651i		−	0.784514i	−0.919856	−	0.392257i	$-0.871694\pi$
$41$		−	32.1651i		−	0.784514i	0.919856	−	0.392257i	$-0.128306\pi$
$42$	11.1266	−	1.48284i	0.264919	−	0.0353056i
$43$		−	51.7542i		−	1.20359i	−0.798652	−	0.601793i	$-0.794453\pi$
$43$		−	51.7542i		−	1.20359i	0.798652	−	0.601793i	$-0.205547\pi$
$44$		−	4.03575i		−	0.0917215i
$45$		0			0
$46$	−45.6552			−0.992503
$47$	−92.3399			−1.96468			−0.982339	−	0.187110i	$-0.940088\pi$
$47$	−92.3399			−1.96468			−0.982339	+	0.187110i	$0.940088\pi$
$48$	−1.58522	−	11.8948i	−0.0330254	−	0.247809i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	6.89236	+	51.7175i	0.135144	+	1.01407i
$52$			23.2033i			0.446218i
$53$	−18.3315			−0.345877			−0.172939	−	0.984933i	$-0.555326\pi$
$53$	−18.3315			−0.345877			−0.172939	+	0.984933i	$0.555326\pi$
$54$	14.7803	+	35.2071i	0.273709	+	0.651984i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	14.3191	+	107.445i	0.251212	+	1.88499i
$58$			65.2577i			1.12513i
$59$			45.4634i			0.770566i	0.922798	+	0.385283i	$0.125896\pi$
$59$			45.4634i			0.770566i	−0.922798	+	0.385283i	$0.874104\pi$
$60$		0			0
$61$	28.1445			0.461385			0.230693	−	0.973027i	$-0.425901\pi$
$61$	28.1445			0.461385			0.230693	+	0.973027i	$0.425901\pi$
$62$	48.1007			0.775818
$63$	−6.23600	−	22.9807i	−0.0989842	−	0.364773i
$64$	8.00000			0.125000
$65$		0			0
$66$	−8.48608	+	1.13094i	−0.128577	+	0.0171354i
$67$			33.7430i			0.503626i	0.967776	+	0.251813i	$0.0810268\pi$
$67$			33.7430i			0.503626i	−0.967776	+	0.251813i	$0.918973\pi$
$68$	−34.7832			−0.511517
$69$	12.7939	+	96.0005i	0.185419	+	1.39131i
$70$		0			0
$71$			25.2759i			0.355999i	0.984031	+	0.177999i	$0.0569625\pi$
$71$			25.2759i			0.355999i	−0.984031	+	0.177999i	$0.943038\pi$
$72$	−24.5674	+	6.66657i	−0.341214	+	0.0925912i
$73$			48.5331i			0.664837i	0.943132	+	0.332418i	$0.107865\pi$
$73$			48.5331i			0.664837i	−0.943132	+	0.332418i	$0.892135\pi$
$74$		−	44.5212i		−	0.601638i
$75$		0			0
$76$	−72.2630			−0.950829
$77$	5.33879			0.0693349
$78$	48.7903	−	6.50225i	0.625517	−	0.0833622i
$79$	−32.9331			−0.416875			−0.208437	−	0.978036i	$-0.566838\pi$
$79$	−32.9331			−0.416875			−0.208437	+	0.978036i	$0.566838\pi$
$80$		0			0
$81$	69.8892	−	40.9450i	0.862830	−	0.505494i
$82$		−	45.4883i		−	0.554735i
$83$	−82.4176			−0.992983			−0.496492	−	0.868041i	$-0.665379\pi$
$83$	−82.4176			−0.992983			−0.496492	+	0.868041i	$0.665379\pi$
$84$	15.7354	−	2.09705i	0.187326	−	0.0249648i
$85$		0			0
$86$		−	73.1915i		−	0.851064i
$87$	137.219	−	18.2871i	1.57723	−	0.210197i
$88$		−	5.70741i		−	0.0648569i
$89$			48.8676i			0.549075i	0.961576	+	0.274537i	$0.0885247\pi$
$89$			48.8676i			0.549075i	−0.961576	+	0.274537i	$0.911475\pi$
$90$		0			0
$91$	−30.6951			−0.337309
$92$	−64.5661			−0.701806
$93$	−13.4792	−	101.143i	−0.144938	−	1.08756i
$94$	−130.588			−1.38924
$95$		0			0
$96$	−2.24184	−	16.8218i	−0.0233525	−	0.175227i
$97$			14.5167i			0.149657i	0.997196	+	0.0748283i	$0.0238409\pi$
$97$			14.5167i			0.149657i	−0.997196	+	0.0748283i	$0.976159\pi$
$98$	−9.89949			−0.101015
$99$	4.75610	+	17.5270i	0.0480414	+	0.177041i
$100$		0			0
$101$			68.8829i			0.682009i	0.940062	+	0.341004i	$0.110767\pi$
$101$			68.8829i			0.682009i	−0.940062	+	0.341004i	$0.889233\pi$
$102$	9.74727	+	73.1396i	0.0955615	+	0.717055i
$103$		−	43.5237i		−	0.422560i	−0.977426	−	0.211280i	$-0.932237\pi$
$103$		−	43.5237i		−	0.422560i	0.977426	−	0.211280i	$-0.0677632\pi$
$104$			32.8144i			0.315523i
$105$		0			0
$106$	−25.9247			−0.244572
$107$	207.704			1.94116			0.970579	−	0.240781i	$-0.0774037\pi$
$107$	207.704			1.94116			0.970579	+	0.240781i	$0.0774037\pi$
$108$	20.9025	+	49.7904i	0.193542	+	0.461022i
$109$	151.884			1.39343			0.696715	−	0.717348i	$-0.254644\pi$
$109$	151.884			1.39343			0.696715	+	0.717348i	$0.254644\pi$
$110$		0			0
$111$	−93.6161	+	12.4762i	−0.843389	+	0.112398i
$112$			10.5830i			0.0944911i
$113$	38.2266			0.338289			0.169144	−	0.985591i	$-0.445900\pi$
$113$	38.2266			0.338289			0.169144	+	0.985591i	$0.445900\pi$
$114$	20.2502	+	151.949i	0.177633	+	1.33289i
$115$		0			0
$116$			92.2883i			0.795589i
$117$	−27.3450	−	100.771i	−0.233718	−	0.861288i
$118$			64.2949i			0.544872i
$119$		−	46.0138i		−	0.386671i
$120$		0			0
$121$	116.928			0.966349
$122$	39.8023			0.326248
$123$	−95.6495	+	12.7472i	−0.777638	+	0.103635i
$124$	68.0247			0.548586
$125$		0			0
$126$	−8.81904	−	32.4996i	−0.0699924	−	0.257933i
$127$		−	101.520i		−	0.799371i	−0.916652	−	0.399685i	$-0.869119\pi$
$127$		−	101.520i		−	0.799371i	0.916652	−	0.399685i	$-0.130881\pi$
$128$	11.3137			0.0883883
$129$	−153.902	+	20.5104i	−1.19304	+	0.158996i
$130$		0			0
$131$			224.148i			1.71105i	0.517758	+	0.855527i	$0.326767\pi$
$131$			224.148i			1.71105i	−0.517758	+	0.855527i	$0.673233\pi$
$132$	−12.0011	+	1.59938i	−0.0909177	+	0.0121165i
$133$		−	95.5949i		−	0.718759i
$134$			47.7198i			0.356118i
$135$		0			0
$136$	−49.1908			−0.361697
$137$	−122.440			−0.893726			−0.446863	−	0.894602i	$-0.647459\pi$
$137$	−122.440			−0.893726			−0.446863	+	0.894602i	$0.647459\pi$
$138$	18.0933	+	135.765i	0.131111	+	0.983805i
$139$	−132.544			−0.953551			−0.476776	−	0.879025i	$-0.658195\pi$
$139$	−132.544			−0.953551			−0.476776	+	0.879025i	$0.658195\pi$
$140$		0			0
$141$	36.5947	+	274.592i	0.259537	+	1.94746i
$142$			35.7455i			0.251729i
$143$	23.4107			0.163711
$144$	−34.7435	+	9.42795i	−0.241275	+	0.0654719i
$145$		0			0
$146$			68.6361i			0.470111i
$147$	2.77413	+	20.8160i	0.0188716	+	0.141605i
$148$		−	62.9626i		−	0.425423i
$149$		−	11.7097i		−	0.0785885i	−0.999228	−	0.0392943i	$-0.987489\pi$
$149$		−	11.7097i		−	0.0785885i	0.999228	−	0.0392943i	$-0.0125110\pi$
$150$		0			0
$151$	−73.1995			−0.484765			−0.242382	−	0.970181i	$-0.577929\pi$
$151$	−73.1995			−0.484765			−0.242382	+	0.970181i	$0.577929\pi$
$152$	−102.195			−0.672337
$153$	151.061	−	40.9917i	0.987329	−	0.267920i
$154$	7.55019			0.0490272
$155$		0			0
$156$	68.9999	−	9.19557i	0.442307	−	0.0589460i
$157$		−	290.488i		−	1.85024i	−0.379675	−	0.925120i	$-0.623964\pi$
$157$		−	290.488i		−	1.85024i	0.379675	−	0.925120i	$-0.376036\pi$
$158$	−46.5745			−0.294775
$159$	7.26485	+	54.5125i	0.0456909	+	0.342846i
$160$		0			0
$161$		−	85.4130i		−	0.530515i
$162$	98.8383	−	57.9050i	0.610113	−	0.357439i
$163$			22.7666i			0.139672i	0.997558	+	0.0698361i	$0.0222476\pi$
$163$			22.7666i			0.139672i	−0.997558	+	0.0698361i	$0.977752\pi$
$164$		−	64.3301i		−	0.392257i
$165$		0			0
$166$	−116.556			−0.702145
$167$	−235.762			−1.41175			−0.705874	−	0.708338i	$-0.749445\pi$
$167$	−235.762			−1.41175			−0.705874	+	0.708338i	$0.749445\pi$
$168$	22.2532	−	2.96567i	0.132460	−	0.0176528i
$169$	34.4016			0.203560
$170$		0			0
$171$	313.834	−	85.1615i	1.83529	−	0.498020i
$172$		−	103.508i		−	0.601793i
$173$	−136.011			−0.786189			−0.393095	−	0.919498i	$-0.628596\pi$
$173$	−136.011			−0.786189			−0.393095	+	0.919498i	$0.628596\pi$
$174$	194.057	−	25.8619i	1.11527	−	0.148632i
$175$		0			0
$176$		−	8.07149i		−	0.0458607i
$177$	135.195	−	18.0173i	0.763813	−	0.101793i
$178$			69.1093i			0.388254i
$179$		−	12.3778i		−	0.0691495i	−0.999402	−	0.0345748i	$-0.988992\pi$
$179$		−	12.3778i		−	0.0691495i	0.999402	−	0.0345748i	$-0.0110077\pi$
$180$		0			0
$181$	−55.8191			−0.308393			−0.154196	−	0.988040i	$-0.549279\pi$
$181$	−55.8191			−0.308393			−0.154196	+	0.988040i	$0.549279\pi$
$182$	−43.4094			−0.238513
$183$	−11.1538	−	83.6935i	−0.0609496	−	0.457342i
$184$	−91.3103			−0.496252
$185$		0			0
$186$	−19.0625	−	143.038i	−0.102487	−	0.769019i
$187$			35.0940i			0.187668i
$188$	−184.680			−0.982339
$189$	−65.8665	+	27.6514i	−0.348500	+	0.146304i
$190$		0			0
$191$		−	198.559i		−	1.03958i	−0.854295	−	0.519788i	$-0.826011\pi$
$191$		−	198.559i		−	1.03958i	0.854295	−	0.519788i	$-0.173989\pi$
$192$	−3.17044	−	23.7897i	−0.0165127	−	0.123905i
$193$			44.6577i			0.231387i	0.993285	+	0.115694i	$0.0369091\pi$
$193$			44.6577i			0.231387i	−0.993285	+	0.115694i	$0.963091\pi$
$194$			20.5297i			0.105823i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	0.952715			0.00483612			0.00241806	−	0.999997i	$-0.499230\pi$
$197$	0.952715			0.00483612			0.00241806	+	0.999997i	$0.499230\pi$
$198$	6.72614	+	24.7869i	0.0339704	+	0.125187i
$199$	131.143			0.659011			0.329505	−	0.944154i	$-0.393118\pi$
$199$	131.143			0.659011			0.329505	+	0.944154i	$0.393118\pi$
$200$		0			0
$201$	100.342	−	13.3725i	0.499213	−	0.0665298i
$202$			97.4151i			0.482253i
$203$	−122.086			−0.601409
$204$	13.7847	+	103.435i	0.0675722	+	0.507034i
$205$		0			0
$206$		−	61.5518i		−	0.298795i
$207$	280.407	−	76.0908i	1.35462	−	0.367588i
$208$			46.4066i			0.223109i
$209$			72.9087i			0.348846i
$210$		0			0
$211$	−101.671			−0.481855			−0.240928	−	0.970543i	$-0.577452\pi$
$211$	−101.671			−0.481855			−0.240928	+	0.970543i	$0.577452\pi$
$212$	−36.6630			−0.172939
$213$	75.1632	−	10.0170i	0.352879	−	0.0470279i
$214$	293.738			1.37261
$215$		0			0
$216$	29.5606	+	70.4143i	0.136855	+	0.325992i
$217$			89.9882i			0.414692i
$218$	214.796			0.985304
$219$	144.323	−	19.2339i	0.659010	−	0.0878259i
$220$		0			0
$221$		−	201.771i		−	0.912992i
$222$	−132.393	+	17.6440i	−0.596366	+	0.0794773i
$223$		−	368.065i		−	1.65051i	−0.564757	−	0.825257i	$-0.691030\pi$
$223$		−	368.065i		−	1.65051i	0.564757	−	0.825257i	$-0.308970\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	54.0606			0.239206
$227$	−311.633			−1.37283			−0.686415	−	0.727210i	$-0.740817\pi$
$227$	−311.633			−1.37283			−0.686415	+	0.727210i	$0.740817\pi$
$228$	28.6381	+	214.889i	0.125606	+	0.942496i
$229$	121.083			0.528748			0.264374	−	0.964420i	$-0.414835\pi$
$229$	121.083			0.528748			0.264374	+	0.964420i	$0.414835\pi$
$230$		0			0
$231$	−2.11579	−	15.8760i	−0.00915925	−	0.0687273i
$232$			130.515i			0.562566i
$233$	−188.437			−0.808744			−0.404372	−	0.914595i	$-0.632510\pi$
$233$	−188.437			−0.808744			−0.404372	+	0.914595i	$0.632510\pi$
$234$	−38.6716	−	142.511i	−0.165263	−	0.609022i
$235$		0			0
$236$			90.9268i			0.385283i
$237$	13.0515	+	97.9335i	0.0550698	+	0.413221i
$238$		−	65.0733i		−	0.273417i
$239$		−	242.788i		−	1.01585i	−0.861402	−	0.507924i	$-0.830413\pi$
$239$		−	242.788i		−	1.01585i	0.861402	−	0.507924i	$-0.169587\pi$
$240$		0			0
$241$	−217.929			−0.904272			−0.452136	−	0.891949i	$-0.649338\pi$
$241$	−217.929			−0.904272			−0.452136	+	0.891949i	$0.649338\pi$
$242$	165.361			0.683312
$243$	−149.456	−	191.603i	−0.615045	−	0.788492i
$244$	56.2890			0.230693
$245$		0			0
$246$	−135.269	+	18.0272i	−0.549873	+	0.0732813i
$247$		−	419.185i		−	1.69711i
$248$	96.2015			0.387909
$249$	32.6625	+	245.086i	0.131175	+	0.984281i
$250$		0			0
$251$		−	44.7224i		−	0.178177i	−0.996024	−	0.0890885i	$-0.971605\pi$
$251$		−	44.7224i		−	0.178177i	0.996024	−	0.0890885i	$-0.0283954\pi$
$252$	−12.4720	−	45.9614i	−0.0494921	−	0.182386i
$253$			65.1431i			0.257483i
$254$		−	143.571i		−	0.565241i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−163.933			−0.637872			−0.318936	−	0.947776i	$-0.603325\pi$
$257$	−163.933			−0.637872			−0.318936	+	0.947776i	$0.603325\pi$
$258$	−217.650	+	29.0061i	−0.843606	+	0.112427i
$259$	83.2916			0.321589
$260$		0			0
$261$	−108.761	−	400.803i	−0.416710	−	1.53564i
$262$			316.993i			1.20990i
$263$	516.880			1.96532			0.982662	−	0.185404i	$-0.0593592\pi$
$263$	516.880			1.96532			0.982662	+	0.185404i	$0.0593592\pi$
$264$	−16.9722	+	2.26187i	−0.0642885	+	0.00856769i
$265$		0			0
$266$		−	135.192i		−	0.508239i
$267$	145.318	−	19.3665i	0.544263	−	0.0725336i
$268$			67.4859i			0.251813i
$269$		−	425.762i		−	1.58276i	−0.611325	−	0.791380i	$-0.709363\pi$
$269$		−	425.762i		−	1.58276i	0.611325	−	0.791380i	$-0.290637\pi$
$270$		0			0
$271$	−38.4253			−0.141791			−0.0708953	−	0.997484i	$-0.522586\pi$
$271$	−38.4253			−0.141791			−0.0708953	+	0.997484i	$0.522586\pi$
$272$	−69.5663			−0.255759
$273$	12.1646	+	91.2783i	0.0445590	+	0.334353i
$274$	−173.157			−0.631960
$275$		0			0
$276$	25.5878	+	192.001i	0.0927096	+	0.695655i
$277$			365.774i			1.32048i	0.751053	+	0.660242i	$0.229546\pi$
$277$			365.774i			1.32048i	−0.751053	+	0.660242i	$0.770454\pi$
$278$	−187.445			−0.674263
$279$	−295.427	+	80.1667i	−1.05888	+	0.287336i
$280$		0			0
$281$			402.773i			1.43336i	0.697404	+	0.716678i	$0.254338\pi$
$281$			402.773i			1.43336i	−0.697404	+	0.716678i	$0.745662\pi$
$282$	51.7527	+	388.331i	0.183520	+	1.37706i
$283$		−	390.233i		−	1.37892i	−0.724326	−	0.689458i	$-0.757849\pi$
$283$		−	390.233i		−	1.37892i	0.724326	−	0.689458i	$-0.242151\pi$
$284$			50.5518i			0.177999i
$285$		0			0
$286$	33.1077			0.115761
$287$	85.1008			0.296518
$288$	−49.1348	+	13.3331i	−0.170607	+	0.0462956i
$289$	13.4671			0.0465989
$290$		0			0
$291$	43.1684	−	5.75302i	0.148345	−	0.0197698i
$292$			97.0662i			0.332418i
$293$	22.6093			0.0771650			0.0385825	−	0.999255i	$-0.487716\pi$
$293$	22.6093			0.0771650			0.0385825	+	0.999255i	$0.487716\pi$
$294$	3.92321	+	29.4382i	0.0133443	+	0.100130i
$295$		0			0
$296$		−	89.0425i		−	0.300819i
$297$	50.2354	−	21.0893i	0.169143	−	0.0710077i
$298$		−	16.5600i		−	0.0555705i
$299$		−	374.537i		−	1.25263i
$300$		0			0
$301$	136.929			0.454913
$302$	−103.520			−0.342780
$303$	204.838	−	27.2986i	0.676032	−	0.0900944i
$304$	−144.526			−0.475414
$305$		0			0
$306$	213.633	−	57.9711i	0.698147	−	0.189448i
$307$		−	332.914i		−	1.08441i	−0.840246	−	0.542206i	$-0.817589\pi$
$307$		−	332.914i		−	1.08441i	0.840246	−	0.542206i	$-0.182411\pi$
$308$	10.6776			0.0346675
$309$	−129.427	+	17.2486i	−0.418857	+	0.0558208i
$310$		0			0
$311$		−	145.028i		−	0.466328i	−0.972437	−	0.233164i	$-0.925092\pi$
$311$		−	145.028i		−	0.466328i	0.972437	−	0.233164i	$-0.0749080\pi$
$312$	97.5806	−	13.0045i	0.312758	−	0.0416811i
$313$			345.934i			1.10522i	0.833440	+	0.552611i	$0.186368\pi$
$313$			345.934i			1.10522i	−0.833440	+	0.552611i	$0.813632\pi$
$314$		−	410.812i		−	1.30832i
$315$		0			0
$316$	−65.8662			−0.208437
$317$	−155.393			−0.490199			−0.245099	−	0.969498i	$-0.578821\pi$
$317$	−155.393			−0.490199			−0.245099	+	0.969498i	$0.578821\pi$
$318$	10.2741	+	77.0924i	0.0323083	+	0.242429i
$319$	93.1131			0.291890
$320$		0			0
$321$	−82.3140	−	617.651i	−0.256430	−	1.92415i
$322$		−	120.792i		−	0.375131i
$323$	628.384			1.94546
$324$	139.778	−	81.8901i	0.431415	−	0.252747i
$325$		0			0
$326$			32.1968i			0.0987632i
$327$	−60.1923	−	451.659i	−0.184074	−	1.38122i
$328$		−	90.9765i		−	0.277367i
$329$		−	244.308i		−	0.742578i
$330$		0			0
$331$	142.477			0.430443			0.215221	−	0.976565i	$-0.430953\pi$
$331$	142.477			0.430443			0.215221	+	0.976565i	$0.430953\pi$
$332$	−164.835			−0.496492
$333$	74.2010	+	273.443i	0.222826	+	0.821149i
$334$	−333.418			−0.998256
$335$		0			0
$336$	31.4708	−	4.19409i	0.0936630	−	0.0124824i
$337$			226.965i			0.673487i	0.941596	+	0.336743i	$0.109325\pi$
$337$			226.965i			0.673487i	−0.941596	+	0.336743i	$0.890675\pi$
$338$	48.6512			0.143938
$339$	−15.1494	−	113.675i	−0.0446884	−	0.335324i
$340$		0			0
$341$		−	68.6326i		−	0.201269i
$342$	443.828	−	120.437i	1.29774	−	0.352154i
$343$		−	18.5203i		−	0.0539949i
$344$		−	146.383i		−	0.425532i
$345$		0			0
$346$	−192.348			−0.555920
$347$	91.8895			0.264811			0.132406	−	0.991196i	$-0.457730\pi$
$347$	91.8895			0.264811			0.132406	+	0.991196i	$0.457730\pi$
$348$	274.439	−	36.5743i	0.788617	−	0.105098i
$349$	−442.343			−1.26746			−0.633729	−	0.773555i	$-0.718476\pi$
$349$	−442.343			−1.26746			−0.633729	+	0.773555i	$0.718476\pi$
$350$		0			0
$351$	−288.826	+	121.252i	−0.822865	+	0.345447i
$352$		−	11.4148i		−	0.0324284i
$353$	88.1350			0.249674			0.124837	−	0.992177i	$-0.460159\pi$
$353$	88.1350			0.249674			0.124837	+	0.992177i	$0.460159\pi$
$354$	191.194	−	25.4804i	0.540097	−	0.0719784i
$355$		0			0
$356$			97.7353i			0.274537i
$357$	−136.832	+	18.2355i	−0.383282	+	0.0510797i
$358$		−	17.5048i		−	0.0488961i
$359$			21.1772i			0.0589894i	0.999565	+	0.0294947i	$0.00938981\pi$
$359$			21.1772i			0.0589894i	−0.999565	+	0.0294947i	$0.990610\pi$
$360$		0			0
$361$	944.484			2.61630
$362$	−78.9401			−0.218067
$363$	−46.3392	−	347.710i	−0.127656	−	0.957880i
$364$	−61.3902			−0.168654
$365$		0			0
$366$	−15.7738	−	118.360i	−0.0430979	−	0.323389i
$367$			306.468i			0.835064i	0.908662	+	0.417532i	$0.137105\pi$
$367$			306.468i			0.835064i	−0.908662	+	0.417532i	$0.862895\pi$
$368$	−129.132			−0.350903
$369$	75.8126	+	279.382i	0.205454	+	0.757133i
$370$		0			0
$371$		−	48.5006i		−	0.130729i
$372$	−26.9585	−	202.286i	−0.0724691	−	0.543779i
$373$			536.875i			1.43934i	0.694315	+	0.719671i	$0.255708\pi$
$373$			536.875i			1.43934i	−0.694315	+	0.719671i	$0.744292\pi$
$374$			49.6304i			0.132702i
$375$		0			0
$376$	−261.177			−0.694619
$377$	−535.349			−1.42002
$378$	−93.1493	+	39.1050i	−0.246427	+	0.103452i
$379$	−457.399			−1.20686			−0.603429	−	0.797417i	$-0.706199\pi$
$379$	−457.399			−1.20686			−0.603429	+	0.797417i	$0.706199\pi$
$380$		0			0
$381$	−301.891	+	40.2329i	−0.792365	+	0.105598i
$382$		−	280.805i		−	0.735092i
$383$	−274.471			−0.716633			−0.358317	−	0.933600i	$-0.616649\pi$
$383$	−274.471			−0.716633			−0.358317	+	0.933600i	$0.616649\pi$
$384$	−4.48367	−	33.6437i	−0.0116762	−	0.0876137i
$385$		0			0
$386$			63.1556i			0.163615i
$387$	121.984	+	449.531i	0.315204	+	1.16158i
$388$			29.0334i			0.0748283i
$389$		−	507.661i		−	1.30504i	−0.757771	−	0.652521i	$-0.773712\pi$
$389$		−	507.661i		−	1.30504i	0.757771	−	0.652521i	$-0.226288\pi$
$390$		0			0
$391$	561.454			1.43594
$392$	−19.7990			−0.0505076
$393$	666.551	−	88.8309i	1.69606	−	0.226033i
$394$	1.34734			0.00341965
$395$		0			0
$396$	9.51220	+	35.0540i	0.0240207	+	0.0885203i
$397$			552.511i			1.39171i	0.718180	+	0.695857i	$0.244975\pi$
$397$			552.511i			1.39171i	−0.718180	+	0.695857i	$0.755025\pi$
$398$	185.464			0.465991
$399$	−284.271	+	37.8847i	−0.712460	+	0.0949491i
$400$		0			0
$401$			240.320i			0.599302i	0.954049	+	0.299651i	$0.0968702\pi$
$401$			240.320i			0.599302i	−0.954049	+	0.299651i	$0.903130\pi$
$402$	141.905	−	18.9116i	0.352997	−	0.0470437i
$403$			394.600i			0.979155i
$404$			137.766i			0.341004i
$405$		0			0
$406$	−172.656			−0.425260
$407$	−63.5252			−0.156082
$408$	19.4945	+	146.279i	0.0477807	+	0.358527i
$409$	441.083			1.07844			0.539222	−	0.842164i	$-0.318719\pi$
$409$	441.083			1.07844			0.539222	+	0.842164i	$0.318719\pi$
$410$		0			0
$411$	48.5237	+	364.102i	0.118063	+	0.885894i
$412$		−	87.0474i		−	0.211280i
$413$	−120.285			−0.291247
$414$	396.556	−	107.609i	0.957864	−	0.259924i
$415$		0			0
$416$			65.6289i			0.157762i
$417$	52.5276	+	394.146i	0.125966	+	0.945195i
$418$			103.109i			0.246671i
$419$		−	412.950i		−	0.985561i	−0.870154	−	0.492780i	$-0.835981\pi$
$419$		−	412.950i		−	0.985561i	0.870154	−	0.492780i	$-0.164019\pi$
$420$		0			0
$421$	−147.333			−0.349959			−0.174980	−	0.984572i	$-0.555986\pi$
$421$	−147.333			−0.349959			−0.174980	+	0.984572i	$0.555986\pi$
$422$	−143.785			−0.340723
$423$	802.053	−	217.644i	1.89611	−	0.514525i
$424$	−51.8493			−0.122286
$425$		0			0
$426$	106.297	−	14.1661i	0.249523	−	0.0332538i
$427$			74.4633i			0.174387i
$428$	415.408			0.970579
$429$	−9.27775	−	69.6165i	−0.0216265	−	0.162276i
$430$		0			0
$431$		−	50.5951i		−	0.117390i	−0.998276	−	0.0586950i	$-0.981306\pi$
$431$		−	50.5951i		−	0.117390i	0.998276	−	0.0586950i	$-0.0186939\pi$
$432$	41.8050	+	99.5808i	0.0967708	+	0.230511i
$433$			653.464i			1.50915i	0.656211	+	0.754577i	$0.272158\pi$
$433$			653.464i			1.50915i	−0.656211	+	0.754577i	$0.727842\pi$
$434$			127.263i			0.293232i
$435$		0			0
$436$	303.768			0.696715
$437$	1166.44			2.66919
$438$	204.104	−	27.2008i	0.465991	−	0.0621023i
$439$	760.655			1.73270			0.866350	−	0.499438i	$-0.166460\pi$
$439$	760.655			1.73270			0.866350	+	0.499438i	$0.166460\pi$
$440$		0			0
$441$	60.8012	−	16.4989i	0.137871	−	0.0374125i
$442$		−	285.347i		−	0.645583i
$443$	−543.566			−1.22701			−0.613506	−	0.789690i	$-0.710241\pi$
$443$	−543.566			−1.22701			−0.613506	+	0.789690i	$0.710241\pi$
$444$	−187.232	+	24.9523i	−0.421694	+	0.0561990i
$445$		0			0
$446$		−	520.522i		−	1.16709i
$447$	−34.8212	+	4.64060i	−0.0778998	+	0.0103817i
$448$			21.1660i			0.0472456i
$449$		−	691.105i		−	1.53921i	−0.638521	−	0.769604i	$-0.720454\pi$
$449$		−	691.105i		−	1.53921i	0.638521	−	0.769604i	$-0.279546\pi$
$450$		0			0
$451$	−64.9050			−0.143914
$452$	76.4532			0.169144
$453$	29.0093	+	217.674i	0.0640381	+	0.480516i
$454$	−440.715			−0.970738
$455$		0			0
$456$	40.5004	+	303.899i	0.0888167	+	0.666445i
$457$		−	32.4937i		−	0.0711022i	−0.999368	−	0.0355511i	$-0.988681\pi$
$457$		−	32.4937i		−	0.0711022i	0.999368	−	0.0355511i	$-0.0113186\pi$
$458$	171.238			0.373882
$459$	−181.764	−	432.967i	−0.395999	−	0.943283i
$460$		0			0
$461$			18.9876i			0.0411879i	0.999788	+	0.0205940i	$0.00655573\pi$
$461$			18.9876i			0.0411879i	−0.999788	+	0.0205940i	$0.993444\pi$
$462$	−2.99217	−	22.4521i	−0.00647656	−	0.0485975i
$463$			772.969i			1.66948i	0.550645	+	0.834740i	$0.314382\pi$
$463$			772.969i			1.66948i	−0.550645	+	0.834740i	$0.685618\pi$
$464$			184.577i			0.397795i
$465$		0			0
$466$	−266.491			−0.571868
$467$	−335.729			−0.718905			−0.359453	−	0.933163i	$-0.617037\pi$
$467$	−335.729			−0.718905			−0.359453	+	0.933163i	$0.617037\pi$
$468$	−54.6899	−	201.541i	−0.116859	−	0.430644i
$469$	−89.2755			−0.190353
$470$		0			0
$471$	−863.826	+	115.122i	−1.83402	+	0.244419i
$472$			128.590i			0.272436i
$473$	−104.433			−0.220790
$474$	18.4577	+	138.499i	0.0389402	+	0.292192i
$475$		0			0
$476$		−	92.0276i		−	0.193335i
$477$	159.225	−	43.2071i	0.333806	−	0.0905809i
$478$		−	343.353i		−	0.718313i
$479$			937.543i			1.95729i	0.205551	+	0.978646i	$0.434101\pi$
$479$			937.543i			1.95729i	−0.205551	+	0.978646i	$0.565899\pi$
$480$		0			0
$481$	365.235			0.759324
$482$	−308.199			−0.639417
$483$	−253.993	+	33.8495i	−0.525866	+	0.0700819i
$484$	233.856			0.483174
$485$		0			0
$486$	−211.363	−	270.968i	−0.434903	−	0.557548i
$487$		−	752.244i		−	1.54465i	−0.635228	−	0.772325i	$-0.719094\pi$
$487$		−	752.244i		−	1.54465i	0.635228	−	0.772325i	$-0.280906\pi$
$488$	79.6046			0.163124
$489$	67.7012	−	9.02249i	0.138448	−	0.0184509i
$490$		0			0
$491$			854.568i			1.74047i	0.492641	+	0.870233i	$0.336032\pi$
$491$			854.568i			1.74047i	−0.492641	+	0.870233i	$0.663968\pi$
$492$	−191.299	+	25.4943i	−0.388819	+	0.0518177i
$493$		−	802.520i		−	1.62783i
$494$		−	592.817i		−	1.20003i
$495$		0			0
$496$	136.049			0.274293
$497$	−66.8738			−0.134555
$498$	46.1917	+	346.604i	0.0927544	+	0.695992i
$499$	364.673			0.730807			0.365404	−	0.930849i	$-0.380931\pi$
$499$	364.673			0.730807			0.365404	+	0.930849i	$0.380931\pi$
$500$		0			0
$501$	93.4334	+	701.087i	0.186494	+	1.39937i
$502$		−	63.2471i		−	0.125990i
$503$	−251.341			−0.499683			−0.249842	−	0.968287i	$-0.580379\pi$
$503$	−251.341			−0.499683			−0.249842	+	0.968287i	$0.580379\pi$
$504$	−17.6381	−	64.9992i	−0.0349962	−	0.128967i
$505$		0			0
$506$			92.1263i			0.182068i
$507$	−13.6335	−	102.300i	−0.0268905	−	0.201776i
$508$		−	203.040i		−	0.399685i
$509$			377.854i			0.742345i	0.928564	+	0.371173i	$0.121044\pi$
$509$			377.854i			0.742345i	−0.928564	+	0.371173i	$0.878956\pi$
$510$		0			0
$511$	−128.406			−0.251285
$512$	22.6274			0.0441942
$513$	−377.619	−	899.501i	−0.736100	−	1.75341i
$514$	−231.836			−0.451043
$515$		0			0
$516$	−307.804	+	41.0209i	−0.596519	+	0.0794978i
$517$			186.330i			0.360406i
$518$	117.792			0.227398
$519$	53.9017	+	404.456i	0.103857	+	0.779299i
$520$		0			0
$521$			959.258i			1.84119i	0.390524	+	0.920593i	$0.372294\pi$
$521$			959.258i			1.84119i	−0.390524	+	0.920593i	$0.627706\pi$
$522$	−153.812	−	566.821i	−0.294658	−	1.08586i
$523$		−	372.766i		−	0.712745i	−0.934344	−	0.356372i	$-0.884013\pi$
$523$		−	372.766i		−	0.712745i	0.934344	−	0.356372i	$-0.115987\pi$
$524$			448.296i			0.855527i
$525$		0			0
$526$	730.979			1.38969
$527$	−591.529			−1.12245
$528$	−24.0023	+	3.19877i	−0.0454588	+	0.00605827i
$529$	513.197			0.970126
$530$		0			0
$531$	−107.157	−	394.890i	−0.201802	−	0.743672i
$532$		−	191.190i		−	0.359379i
$533$	373.168			0.700128
$534$	205.511	−	27.3883i	0.384852	−	0.0512890i
$535$		0			0
$536$			95.4395i			0.178059i
$537$	−36.8079	+	4.90536i	−0.0685435	+	0.00913475i
$538$		−	602.119i		−	1.11918i
$539$			14.1251i			0.0262061i
$540$		0			0
$541$	−425.367			−0.786262			−0.393131	−	0.919483i	$-0.628608\pi$
$541$	−425.367			−0.786262			−0.393131	+	0.919483i	$0.628608\pi$
$542$	−54.3415			−0.100261
$543$	22.1213	+	165.990i	0.0407391	+	0.305690i
$544$	−98.3816			−0.180849
$545$		0			0
$546$	17.2033	+	129.087i	0.0315080	+	0.236423i
$547$			163.904i			0.299641i	0.988713	+	0.149821i	$0.0478696\pi$
$547$			163.904i			0.299641i	−0.988713	+	0.149821i	$0.952130\pi$
$548$	−244.881			−0.446863
$549$	−244.460	+	66.3362i	−0.445282	+	0.120831i
$550$		0			0
$551$		−	1667.26i		−	3.02588i
$552$	36.1867	+	271.530i	0.0655556	+	0.491903i
$553$		−	87.1328i		−	0.157564i
$554$			517.283i			0.933723i
$555$		0			0
$556$	−265.087			−0.476776
$557$	−706.900			−1.26912			−0.634560	−	0.772873i	$-0.718819\pi$
$557$	−706.900			−1.26912			−0.634560	+	0.772873i	$0.718819\pi$
$558$	−417.797	+	113.373i	−0.748741	+	0.203177i
$559$	600.435			1.07412
$560$		0			0
$561$	104.359	−	13.9079i	0.186024	−	0.0247913i
$562$			569.607i			1.01354i
$563$	456.163			0.810237			0.405118	−	0.914264i	$-0.367230\pi$
$563$	456.163			0.810237			0.405118	+	0.914264i	$0.367230\pi$
$564$	73.1894	+	549.184i	0.129768	+	0.973730i
$565$		0			0
$566$		−	551.873i		−	0.975040i
$567$	108.330	+	184.909i	0.191059	+	0.326119i
$568$			71.4911i			0.125865i
$569$		−	429.044i		−	0.754032i	−0.926207	−	0.377016i	$-0.876950\pi$
$569$		−	429.044i		−	0.754032i	0.926207	−	0.377016i	$-0.123050\pi$
$570$		0			0
$571$	−739.819			−1.29566			−0.647828	−	0.761787i	$-0.724322\pi$
$571$	−739.819			−1.29566			−0.647828	+	0.761787i	$0.724322\pi$
$572$	46.8213			0.0818555
$573$	−590.457	+	78.6899i	−1.03047	+	0.137330i
$574$	120.351			0.209670
$575$		0			0
$576$	−69.4871	+	18.8559i	−0.120637	+	0.0327359i
$577$			826.999i			1.43327i	0.697446	+	0.716637i	$0.254320\pi$
$577$			826.999i			1.43327i	−0.697446	+	0.716637i	$0.745680\pi$
$578$	19.0453			0.0329504
$579$	132.799	−	17.6981i	0.229359	−	0.0305666i
$580$		0			0
$581$		−	218.057i		−	0.375312i
$582$	61.0493	−	8.13601i	0.104896	−	0.0139794i
$583$			36.9906i			0.0634488i
$584$			137.272i			0.235055i
$585$		0			0
$586$	31.9744			0.0545639
$587$	419.920			0.715366			0.357683	−	0.933843i	$-0.383567\pi$
$587$	419.920			0.715366			0.357683	+	0.933843i	$0.383567\pi$
$588$	5.54826	+	41.6319i	0.00943582	+	0.0708026i
$589$	−1228.92			−2.08645
$590$		0			0
$591$	−0.377565	−	2.83310i	−0.000638858	−	0.00479374i
$592$		−	125.925i		−	0.212711i
$593$	−831.323			−1.40189			−0.700947	−	0.713213i	$-0.747239\pi$
$593$	−831.323			−1.40189			−0.700947	+	0.713213i	$0.747239\pi$
$594$	71.0435	−	29.8248i	0.119602	−	0.0502100i
$595$		0			0
$596$		−	23.4194i		−	0.0392943i
$597$	−51.9726	−	389.982i	−0.0870563	−	0.653235i
$598$		−	529.675i		−	0.885745i
$599$			902.352i			1.50643i	0.657774	+	0.753216i	$0.271498\pi$
$599$			902.352i			1.50643i	−0.657774	+	0.753216i	$0.728502\pi$
$600$		0			0
$601$	−149.891			−0.249403			−0.124702	−	0.992194i	$-0.539797\pi$
$601$	−149.891			−0.249403			−0.124702	+	0.992194i	$0.539797\pi$
$602$	193.647			0.321672
$603$	−79.5318	−	293.088i	−0.131893	−	0.486049i
$604$	−146.399			−0.242382
$605$		0			0
$606$	289.684	−	38.6060i	0.478027	−	0.0637063i
$607$		−	14.9805i		−	0.0246795i	−0.999924	−	0.0123398i	$-0.996072\pi$
$607$		−	14.9805i		−	0.0246795i	0.999924	−	0.0123398i	$-0.00392797\pi$
$608$	−204.391			−0.336169
$609$	48.3832	+	363.048i	0.0794470	+	0.596138i
$610$		0			0
$611$		−	1071.30i		−	1.75335i
$612$	302.123	−	81.9835i	0.493664	−	0.133960i
$613$			289.923i			0.472958i	0.971637	+	0.236479i	$0.0759935\pi$
$613$			289.923i			0.472958i	−0.971637	+	0.236479i	$0.924006\pi$
$614$		−	470.812i		−	0.766795i
$615$		0			0
$616$	15.1004			0.0245136
$617$	1118.36			1.81257			0.906287	−	0.422662i	$-0.138904\pi$
$617$	1118.36			1.81257			0.906287	+	0.422662i	$0.138904\pi$
$618$	−183.037	+	24.3933i	−0.296177	+	0.0394713i
$619$	963.589			1.55669			0.778343	−	0.627839i	$-0.216060\pi$
$619$	963.589			1.55669			0.778343	+	0.627839i	$0.216060\pi$
$620$		0			0
$621$	−337.398	−	803.694i	−0.543315	−	1.29419i
$622$		−	205.101i		−	0.329744i
$623$	−129.292			−0.207531
$624$	138.000	−	18.3911i	0.221153	−	0.0294730i
$625$		0			0
$626$			489.225i			0.781509i
$627$	216.809	−	28.8941i	0.345788	−	0.0460830i
$628$		−	580.975i		−	0.925120i
$629$			547.509i			0.870444i
$630$		0			0
$631$	408.113			0.646772			0.323386	−	0.946267i	$-0.395179\pi$
$631$	408.113			0.646772			0.323386	+	0.946267i	$0.395179\pi$
$632$	−93.1489			−0.147388
$633$	40.2928	+	302.341i	0.0636538	+	0.477632i
$634$	−219.759			−0.346623
$635$		0			0
$636$	14.5297	+	109.025i	0.0228454	+	0.171423i
$637$		−	81.2116i		−	0.127491i
$638$	131.682			0.206398
$639$	−59.5750	−	219.544i	−0.0932316	−	0.343574i
$640$		0			0
$641$			548.724i			0.856044i	0.903768	+	0.428022i	$0.140789\pi$
$641$			548.724i			0.856044i	−0.903768	+	0.428022i	$0.859211\pi$
$642$	−116.410	−	873.491i	−0.181323	−	1.36058i
$643$		−	106.614i		−	0.165807i	−0.996558	−	0.0829033i	$-0.973581\pi$
$643$		−	106.614i		−	0.165807i	0.996558	−	0.0829033i	$-0.0264193\pi$
$644$		−	170.826i		−	0.265258i
$645$		0			0
$646$	888.669			1.37565
$647$	−316.788			−0.489625			−0.244813	−	0.969570i	$-0.578726\pi$
$647$	−316.788			−0.489625			−0.244813	+	0.969570i	$0.578726\pi$
$648$	197.677	−	115.810i	0.305056	−	0.178719i
$649$	91.7393			0.141355
$650$		0			0
$651$	267.599	−	35.6627i	0.411058	−	0.0547815i
$652$			45.5332i			0.0698361i
$653$	−407.664			−0.624293			−0.312147	−	0.950034i	$-0.601048\pi$
$653$	−407.664			−0.624293			−0.312147	+	0.950034i	$0.601048\pi$
$654$	−85.1247	−	638.742i	−0.130160	−	0.976669i
$655$		0			0
$656$		−	128.660i		−	0.196128i
$657$	−114.392	−	421.553i	−0.174112	−	0.641633i
$658$		−	345.504i		−	0.525082i
$659$		−	442.719i		−	0.671804i	−0.941897	−	0.335902i	$-0.890959\pi$
$659$		−	442.719i		−	0.671804i	0.941897	−	0.335902i	$-0.109041\pi$
$660$		0			0
$661$	300.069			0.453962			0.226981	−	0.973899i	$-0.427114\pi$
$661$	300.069			0.453962			0.226981	+	0.973899i	$0.427114\pi$
$662$	201.492			0.304369
$663$	−600.009	+	79.9628i	−0.904990	+	0.120608i
$664$	−233.112			−0.351073
$665$		0			0
$666$	104.936	+	386.706i	0.157562	+	0.580640i
$667$		−	1489.68i		−	2.23340i
$668$	−471.524			−0.705874
$669$	−1094.52	+	145.866i	−1.63605	+	0.218035i
$670$		0			0
$671$		−	56.7920i		−	0.0846378i
$672$	44.5064	−	5.93134i	0.0662298	−	0.00882640i
$673$			199.000i			0.295691i	0.989011	+	0.147845i	$0.0472338\pi$
$673$			199.000i			0.295691i	−0.989011	+	0.147845i	$0.952766\pi$
$674$			320.977i			0.476227i
$675$		0			0
$676$	68.8031			0.101780
$677$	235.136			0.347321			0.173660	−	0.984806i	$-0.444441\pi$
$677$	235.136			0.347321			0.173660	+	0.984806i	$0.444441\pi$
$678$	−21.4245	−	160.760i	−0.0315995	−	0.237110i
$679$	−38.4075			−0.0565648
$680$		0			0
$681$	123.501	+	926.704i	0.181353	+	1.36080i
$682$		−	97.0612i		−	0.142318i
$683$	−698.860			−1.02322			−0.511610	−	0.859218i	$-0.670951\pi$
$683$	−698.860			−1.02322			−0.511610	+	0.859218i	$0.670951\pi$
$684$	627.668	−	170.323i	0.917643	−	0.249010i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−47.9859	−	360.067i	−0.0698484	−	0.524114i
$688$		−	207.017i		−	0.300897i
$689$		−	212.676i		−	0.308673i
$690$		0			0
$691$	326.641			0.472708			0.236354	−	0.971667i	$-0.424047\pi$
$691$	326.641			0.472708			0.236354	+	0.971667i	$0.424047\pi$
$692$	−272.022			−0.393095
$693$	−46.3721	+	12.5835i	−0.0669150	+	0.0181580i
$694$	129.951			0.187250
$695$		0			0
$696$	388.115	−	51.7238i	0.557636	−	0.0743159i
$697$			559.401i			0.802584i
$698$	−625.567			−0.896228
$699$	74.6785	+	560.358i	0.106836	+	0.801656i
$700$		0			0
$701$		−	482.417i		−	0.688185i	−0.938936	−	0.344092i	$-0.888187\pi$
$701$		−	482.417i		−	0.688185i	0.938936	−	0.344092i	$-0.111813\pi$
$702$	−408.461	+	171.476i	−0.581853	+	0.244268i
$703$			1137.47i			1.61802i
$704$		−	16.1430i		−	0.0229304i
$705$		0			0
$706$	124.642			0.176546
$707$	−182.247			−0.257775
$708$	270.390	−	36.0347i	0.381906	−	0.0508964i
$709$	415.186			0.585594			0.292797	−	0.956175i	$-0.405414\pi$
$709$	415.186			0.585594			0.292797	+	0.956175i	$0.405414\pi$
$710$		0			0
$711$	286.053	−	77.6229i	0.402325	−	0.109174i
$712$			138.219i			0.194127i
$713$	−1098.02			−1.54000
$714$	−193.509	+	25.7888i	−0.271021	+	0.0361188i
$715$		0			0
$716$		−	24.7555i		−	0.0345748i
$717$	−721.979	+	96.2178i	−1.00694	+	0.134195i
$718$			29.9491i			0.0417118i
$719$			1341.45i			1.86571i	0.360249	+	0.932856i	$0.382692\pi$
$719$			1341.45i			1.86571i	−0.360249	+	0.932856i	$0.617308\pi$
$720$		0			0
$721$	115.153			0.159713
$722$	1335.70			1.85000
$723$	86.3664	+	648.059i	0.119456	+	0.896347i
$724$	−111.638			−0.154196
$725$		0			0
$726$	−65.5335	−	491.737i	−0.0902665	−	0.677323i
$727$		−	5.22241i		−	0.00718351i	−0.999994	−	0.00359175i	$-0.998857\pi$
$727$		−	5.22241i		−	0.00718351i	0.999994	−	0.00359175i	$-0.00114329\pi$
$728$	−86.8188			−0.119257
$729$	−510.543	+	520.372i	−0.700333	+	0.713816i
$730$		0			0
$731$			900.088i			1.23131i
$732$	−22.3076	−	167.387i	−0.0304748	−	0.228671i
$733$		−	163.268i		−	0.222739i	−0.993779	−	0.111370i	$-0.964476\pi$
$733$		−	163.268i		−	0.222739i	0.993779	−	0.111370i	$-0.0355237\pi$
$734$			433.412i			0.590479i
$735$		0			0
$736$	−182.621			−0.248126
$737$	68.0890			0.0923867
$738$	107.215	+	395.106i	0.145278	+	0.535374i
$739$	995.463			1.34704			0.673520	−	0.739169i	$-0.264781\pi$
$739$	995.463			1.34704			0.673520	+	0.739169i	$0.264781\pi$
$740$		0			0
$741$	−1246.53	+	166.125i	−1.68223	+	0.224190i
$742$		−	68.5902i		−	0.0924396i
$743$	1330.52			1.79074			0.895371	−	0.445321i	$-0.146911\pi$
$743$	1330.52			1.79074			0.895371	+	0.445321i	$0.146911\pi$
$744$	−38.1251	−	286.075i	−0.0512434	−	0.384510i
$745$		0			0
$746$			759.256i			1.01777i
$747$	715.870	−	194.257i	0.958327	−	0.260050i
$748$			70.1880i			0.0938342i
$749$			549.533i			0.733689i
$750$		0			0
$751$	−1291.88			−1.72021			−0.860107	−	0.510113i	$-0.829603\pi$
$751$	−1291.88			−1.72021			−0.860107	+	0.510113i	$0.829603\pi$
$752$	−369.359			−0.491169
$753$	−132.991	+	17.7237i	−0.176615	+	0.0235374i
$754$	−757.098			−1.00411
$755$		0			0
$756$	−131.733	+	55.3028i	−0.174250	+	0.0731519i
$757$			608.247i			0.803497i	0.915750	+	0.401748i	$0.131597\pi$
$757$			608.247i			0.803497i	−0.915750	+	0.401748i	$0.868403\pi$
$758$	−646.860			−0.853378
$759$	193.717	−	25.8165i	0.255226	−	0.0340138i
$760$		0			0
$761$			19.5785i			0.0257273i	0.999917	+	0.0128637i	$0.00409475\pi$
$761$			19.5785i			0.0257273i	−0.999917	+	0.0128637i	$0.995905\pi$
$762$	−426.939	+	56.8979i	−0.560287	+	0.0746691i
$763$			401.847i			0.526667i
$764$		−	397.118i		−	0.519788i
$765$		0			0
$766$	−388.160			−0.506736
$767$	−527.451			−0.687680
$768$	−6.34087	−	47.5793i	−0.00825634	−	0.0619523i
$769$	−1084.91			−1.41081			−0.705405	−	0.708804i	$-0.749235\pi$
$769$	−1084.91			−1.41081			−0.705405	+	0.708804i	$0.749235\pi$
$770$		0			0
$771$	64.9674	+	487.489i	0.0842638	+	0.632282i
$772$			89.3154i			0.115694i
$773$	−564.003			−0.729628			−0.364814	−	0.931080i	$-0.618867\pi$
$773$	−564.003			−0.729628			−0.364814	+	0.931080i	$0.618867\pi$
$774$	172.512	+	635.733i	0.222883	+	0.821361i
$775$		0			0
$776$			41.0594i			0.0529116i
$777$	−33.0088	−	247.685i	−0.0424824	−	0.318771i
$778$		−	717.941i		−	0.922804i
$779$			1162.17i			1.49188i
$780$		0			0
$781$	51.0036			0.0653055
$782$	794.015			1.01536
$783$	−1148.77	+	482.264i	−1.46714	+	0.615918i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	942.645	−	125.626i	1.19929	−	0.159829i
$787$		−	1360.30i		−	1.72846i	−0.503094	−	0.864232i	$-0.667805\pi$
$787$		−	1360.30i		−	1.72846i	0.503094	−	0.864232i	$-0.332195\pi$
$788$	1.90543			0.00241806
$789$	−204.842	−	1537.05i	−0.259622	−	1.94810i
$790$		0			0
$791$			101.138i			0.127861i
$792$	13.4523	+	49.5739i	0.0169852	+	0.0625933i
$793$			326.523i			0.411756i
$794$			781.368i			0.984091i
$795$		0			0
$796$	262.286			0.329505
$797$	81.4055			0.102140			0.0510700	−	0.998695i	$-0.483737\pi$
$797$	81.4055			0.102140			0.0510700	+	0.998695i	$0.483737\pi$
$798$	−402.021	+	53.5770i	−0.503785	+	0.0671392i
$799$	1605.94			2.00993
$800$		0			0
$801$	−115.180	−	424.459i	−0.143796	−	0.529911i
$802$			339.864i			0.423770i
$803$	97.9336			0.121960
$804$	200.683	−	26.7450i	0.249606	−	0.0332649i
$805$		0			0
$806$			558.048i			0.692367i
$807$	−1266.09	+	168.731i	−1.56889	+	0.209085i
$808$			194.830i			0.241127i
$809$			907.697i			1.12200i	0.827816	+	0.560999i	$0.189583\pi$
$809$			907.697i			1.12200i	−0.827816	+	0.560999i	$0.810417\pi$
$810$		0			0
$811$	−451.340			−0.556523			−0.278261	−	0.960505i	$-0.589758\pi$
$811$	−451.340			−0.556523			−0.278261	+	0.960505i	$0.589758\pi$
$812$	−244.172			−0.300704
$813$	15.2281	+	114.266i	0.0187307	+	0.140548i
$814$	−89.8382			−0.110366
$815$		0			0
$816$	27.5694	+	206.870i	0.0337861	+	0.253517i
$817$			1869.96i			2.28881i
$818$	623.786			0.762574
$819$	266.614	−	72.3480i	0.325536	−	0.0883370i
$820$		0			0
$821$		−	248.662i		−	0.302878i	−0.988467	−	0.151439i	$-0.951609\pi$
$821$		−	248.662i		−	0.302878i	0.988467	−	0.151439i	$-0.0483906\pi$
$822$	68.6229	+	514.918i	0.0834828	+	0.626421i
$823$		−	596.005i		−	0.724186i	−0.932142	−	0.362093i	$-0.882062\pi$
$823$		−	596.005i		−	0.724186i	0.932142	−	0.362093i	$-0.117938\pi$
$824$		−	123.104i		−	0.149398i
$825$		0			0
$826$	−170.108			−0.205942
$827$	758.271			0.916894			0.458447	−	0.888722i	$-0.348406\pi$
$827$	758.271			0.916894			0.458447	+	0.888722i	$0.348406\pi$
$828$	560.814	−	152.182i	0.677312	−	0.183794i
$829$	−509.182			−0.614212			−0.307106	−	0.951675i	$-0.599361\pi$
$829$	−509.182			−0.614212			−0.307106	+	0.951675i	$0.599361\pi$
$830$		0			0
$831$	1087.71	−	144.958i	1.30891	−	0.174438i
$832$			92.8133i			0.111554i
$833$	121.741			0.146148
$834$	74.2853	+	557.407i	0.0890711	+	0.668353i
$835$		0			0
$836$			145.817i			0.174423i
$837$	355.472	+	846.745i	0.424697	+	1.01164i
$838$		−	584.000i		−	0.696897i
$839$		−	766.956i		−	0.914131i	−0.889433	−	0.457065i	$-0.848901\pi$
$839$		−	766.956i		−	0.914131i	0.889433	−	0.457065i	$-0.151099\pi$
$840$		0			0
$841$	−1288.28			−1.53185
$842$	−208.360			−0.247459
$843$	1197.73	−	159.621i	1.42079	−	0.189348i
$844$	−203.343			−0.240928
$845$		0			0
$846$	1134.27	−	307.795i	1.34075	−	0.363824i
$847$			309.363i			0.365245i
$848$	−73.3260			−0.0864693
$849$	−1160.44	+	154.651i	−1.36683	+	0.182157i
$850$		0			0
$851$			1016.31i			1.19426i
$852$	150.326	−	20.0339i	0.176439	−	0.0235140i
$853$			735.107i			0.861790i	0.902402	+	0.430895i	$0.141802\pi$
$853$			735.107i			0.861790i	−0.902402	+	0.430895i	$0.858198\pi$
$854$			105.307i			0.123310i
$855$		0			0
$856$	587.476			0.686303
$857$	514.911			0.600830			0.300415	−	0.953809i	$-0.402875\pi$
$857$	514.911			0.600830			0.300415	+	0.953809i	$0.402875\pi$
$858$	−13.1207	−	98.4526i	−0.0152922	−	0.114747i
$859$	−1414.99			−1.64726			−0.823628	−	0.567131i	$-0.808053\pi$
$859$	−1414.99			−1.64726			−0.823628	+	0.567131i	$0.808053\pi$
$860$		0			0
$861$	−33.7258	−	253.065i	−0.0391705	−	0.293920i
$862$		−	71.5523i		−	0.0830073i
$863$	−249.645			−0.289276			−0.144638	−	0.989485i	$-0.546202\pi$
$863$	−249.645			−0.289276			−0.144638	+	0.989485i	$0.546202\pi$
$864$	59.1212	+	140.829i	0.0684273	+	0.162996i
$865$		0			0
$866$			924.138i			1.06713i
$867$	−5.33707	−	40.0472i	−0.00615579	−	0.0461906i
$868$			179.976i			0.207346i
$869$			66.4548i			0.0764728i
$870$		0			0
$871$	−391.474			−0.449454
$872$	429.593			0.492652
$873$	−34.2156	−	126.090i	−0.0391932	−	0.144433i
$874$	1649.59			1.88740
$875$		0			0
$876$	288.646	−	38.4677i	0.329505	−	0.0439130i
$877$		−	767.333i		−	0.874952i	−0.899230	−	0.437476i	$-0.855872\pi$
$877$		−	767.333i		−	0.874952i	0.899230	−	0.437476i	$-0.144128\pi$
$878$	1075.73			1.22520
$879$	−8.96018	−	67.2336i	−0.0101936	−	0.0764887i
$880$		0			0
$881$		−	1200.08i		−	1.36217i	−0.732203	−	0.681087i	$-0.761508\pi$
$881$		−	1200.08i		−	1.36217i	0.732203	−	0.681087i	$-0.238492\pi$
$882$	85.9859	−	23.3330i	0.0974897	−	0.0264546i
$883$		−	370.168i		−	0.419217i	−0.977785	−	0.209608i	$-0.932781\pi$
$883$		−	370.168i		−	0.419217i	0.977785	−	0.209608i	$-0.0672189\pi$
$884$		−	403.542i		−	0.456496i
$885$		0			0
$886$	−768.718			−0.867628
$887$	797.714			0.899339			0.449670	−	0.893195i	$-0.351542\pi$
$887$	797.714			0.899339			0.449670	+	0.893195i	$0.351542\pi$
$888$	−264.786	+	35.2879i	−0.298183	+	0.0397387i
$889$	268.597			0.302134
$890$		0			0
$891$	−82.6219	−	141.028i	−0.0927294	−	0.158280i
$892$		−	736.129i		−	0.825257i
$893$	3336.38			3.73614
$894$	−49.2446	+	6.56280i	−0.0550835	+	0.00734094i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	−1113.76	+	148.431i	−1.24165	+	0.165475i
$898$		−	977.369i		−	1.08838i
$899$			1569.47i			1.74580i
$900$		0			0
$901$	318.814			0.353844
$902$	−91.7895			−0.101762
$903$	−54.2655	−	407.186i	−0.0600947	−	0.450926i
$904$	108.121			0.119603
$905$		0			0
$906$	41.0253	+	307.837i	0.0452818	+	0.339776i
$907$			60.6349i			0.0668522i	0.999441	+	0.0334261i	$0.0106418\pi$
$907$			60.6349i			0.0668522i	−0.999441	+	0.0334261i	$0.989358\pi$
$908$	−623.265			−0.686415
$909$	−162.356	−	598.309i	−0.178610	−	0.658206i
$910$		0			0
$911$			1640.58i			1.80085i	0.435009	+	0.900426i	$0.356745\pi$
$911$			1640.58i			1.80085i	−0.435009	+	0.900426i	$0.643255\pi$
$912$	57.2763	+	429.778i	0.0628029	+	0.471248i
$913$			166.308i			0.182156i
$914$		−	45.9530i		−	0.0502768i
$915$		0			0
$916$	242.167			0.264374
$917$	−593.040			−0.646718
$918$	−257.053	−	612.308i	−0.280014	−	0.667002i
$919$	−904.955			−0.984717			−0.492358	−	0.870393i	$-0.663865\pi$
$919$	−904.955			−0.984717			−0.492358	+	0.870393i	$0.663865\pi$
$920$		0			0
$921$	−989.990	+	131.935i	−1.07491	+	0.143252i
$922$			26.8526i			0.0291243i
$923$	−293.242			−0.317706
$924$	−4.23157	−	31.7520i	−0.00457962	−	0.0343636i
$925$		0			0
$926$			1093.14i			1.18050i
$927$	102.585	+	378.042i	0.110663	+	0.407812i
$928$			261.031i			0.281283i
$929$			320.892i			0.345417i	0.984973	+	0.172709i	$0.0552519\pi$
$929$			320.892i			0.345417i	−0.984973	+	0.172709i	$0.944748\pi$
$930$		0			0
$931$	252.920			0.271665
$932$	−376.875			−0.404372
$933$	−431.271	+	57.4753i	−0.462242	+	0.0616027i
$934$	−474.792			−0.508343
$935$		0			0
$936$	−77.3432	−	285.022i	−0.0826317	−	0.304511i
$937$			862.831i			0.920845i	0.887700	+	0.460422i	$0.152302\pi$
$937$			862.831i			0.920845i	−0.887700	+	0.460422i	$0.847698\pi$
$938$	−126.255			−0.134600
$939$	1028.71	−	137.095i	1.09554	−	0.146001i
$940$		0			0
$941$			1297.26i			1.37859i	0.724479	+	0.689297i	$0.242080\pi$
$941$			1297.26i			1.37859i	−0.724479	+	0.689297i	$0.757920\pi$
$942$	−1221.63	+	162.806i	−1.29685	+	0.172831i
$943$			1038.39i			1.10115i
$944$			181.854i			0.192641i
$945$		0			0
$946$	−147.691			−0.156122
$947$	969.136			1.02337			0.511687	−	0.859172i	$-0.329021\pi$
$947$	969.136			1.02337			0.511687	+	0.859172i	$0.329021\pi$
$948$	26.1031	+	195.867i	0.0275349	+	0.206611i
$949$	−563.064			−0.593324
$950$		0			0
$951$	61.5829	+	462.094i	0.0647560	+	0.485903i
$952$		−	130.147i		−	0.136709i
$953$	1341.41			1.40756			0.703782	−	0.710416i	$-0.251493\pi$
$953$	1341.41			1.40756			0.703782	+	0.710416i	$0.251493\pi$
$954$	225.179	−	61.1041i	0.236036	−	0.0640504i
$955$		0			0
$956$		−	485.575i		−	0.507924i
$957$	−36.9011	−	276.891i	−0.0385592	−	0.289332i
$958$			1325.89i			1.38401i
$959$		−	323.947i		−	0.337797i
$960$		0			0
$961$	195.840			0.203788
$962$	516.520			0.536923
$963$	−1804.09	+	489.556i	−1.87341	+	0.508365i
$964$	−435.859			−0.452136
$965$		0			0
$966$	−359.201	+	47.8705i	−0.371843	+	0.0495554i
$967$			454.329i			0.469834i	0.972015	+	0.234917i	$0.0754818\pi$
$967$			454.329i			0.469834i	−0.972015	+	0.234917i	$0.924518\pi$
$968$	330.723			0.341656
$969$	−249.031	−	1868.63i	−0.256998	−	1.92841i
$970$		0			0
$971$		−	1594.23i		−	1.64185i	−0.571037	−	0.820924i	$-0.693459\pi$
$971$		−	1594.23i		−	1.64185i	0.571037	−	0.820924i	$-0.306541\pi$
$972$	−298.912	−	383.207i	−0.307523	−	0.394246i
$973$		−	350.677i		−	0.360408i
$974$		−	1063.83i		−	1.09223i
$975$		0			0
$976$	112.578			0.115346
$977$	544.109			0.556918			0.278459	−	0.960448i	$-0.410176\pi$
$977$	544.109			0.556918			0.278459	+	0.960448i	$0.410176\pi$
$978$	95.7439	−	12.7597i	0.0978977	−	0.0130468i
$979$	98.6087			0.100724
$980$		0			0
$981$	−1319.25	+	357.989i	−1.34480	+	0.364922i
$982$			1208.54i			1.23069i
$983$	−605.161			−0.615627			−0.307813	−	0.951447i	$-0.599597\pi$
$983$	−605.161			−0.615627			−0.307813	+	0.951447i	$0.599597\pi$
$984$	−270.538	+	36.0544i	−0.274937	+	0.0366406i
$985$		0			0
$986$		−	1134.93i		−	1.15105i
$987$	−726.502	+	96.8205i	−0.736071	+	0.0980957i
$988$		−	838.370i		−	0.848553i
$989$			1670.79i			1.68937i
$990$		0			0
$991$	−1002.42			−1.01152			−0.505761	−	0.862674i	$-0.668788\pi$
$991$	−1002.42			−1.01152			−0.505761	+	0.862674i	$0.668788\pi$
$992$	192.403			0.193955
$993$	−56.4641	−	423.684i	−0.0568621	−	0.426670i
$994$	−94.5738			−0.0951446
$995$		0			0
$996$	65.3249	+	490.172i	0.0655873	+	0.492141i
$997$			9.04315i			0.00907036i	0.999990	+	0.00453518i	$0.00144360\pi$
$997$			9.04315i			0.00907036i	−0.999990	+	0.00453518i	$0.998556\pi$
$998$	515.725			0.516759
$999$	783.733	−	329.019i	0.784517	−	0.329348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.21		32
3.2	odd	2	inner	1050.3.c.c.449.11		32
5.2	odd	4		210.3.e.a.71.9	yes	16
5.3	odd	4		1050.3.e.d.701.8		16
5.4	even	2	inner	1050.3.c.c.449.12		32
15.2	even	4		210.3.e.a.71.1	✓	16
15.8	even	4		1050.3.e.d.701.16		16
15.14	odd	2	inner	1050.3.c.c.449.22		32
20.7	even	4		1680.3.l.c.1121.15		16
60.47	odd	4		1680.3.l.c.1121.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.1	✓	16	15.2	even	4
210.3.e.a.71.9	yes	16	5.2	odd	4
1050.3.c.c.449.11		32	3.2	odd	2	inner
1050.3.c.c.449.12		32	5.4	even	2	inner
1050.3.c.c.449.21		32	1.1	even	1	trivial
1050.3.c.c.449.22		32	15.14	odd	2	inner
1050.3.e.d.701.8		16	5.3	odd	4
1050.3.e.d.701.16		16	15.8	even	4
1680.3.l.c.1121.15		16	20.7	even	4
1680.3.l.c.1121.16		16	60.47	odd	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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-0.396304 - 2.97371i) q^{3} +2.00000 q^{4} +(-0.560459 - 4.20546i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.68589 + 2.35699i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-0.396304 - 2.97371i) q^{3} +2.00000 q^{4} +(-0.560459 - 4.20546i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.68589 + 2.35699i) q^{9} -2.01787i q^{11} +(-0.792609 - 5.94742i) q^{12} +11.6017i q^{13} +3.74166i q^{14} +4.00000 q^{16} -17.3916 q^{17} +(-12.2837 + 3.33328i) q^{18} -36.1315 q^{19} +(7.86769 - 1.04852i) q^{21} -2.85370i q^{22} -32.2831 q^{23} +(-1.12092 - 8.41092i) q^{24} +16.4072i q^{26} +(10.4512 + 24.8952i) q^{27} +5.29150i q^{28} +46.1442i q^{29} +34.0124 q^{31} +5.65685 q^{32} +(-6.00057 + 0.799692i) q^{33} -24.5954 q^{34} +(-17.3718 + 4.71398i) q^{36} -31.4813i q^{37} -51.0976 q^{38} +(34.4999 - 4.59779i) q^{39} -32.1651i q^{41} +(11.1266 - 1.48284i) q^{42} -51.7542i q^{43} -4.03575i q^{44} -45.6552 q^{46} -92.3399 q^{47} +(-1.58522 - 11.8948i) q^{48} -7.00000 q^{49} +(6.89236 + 51.7175i) q^{51} +23.2033i q^{52} -18.3315 q^{53} +(14.7803 + 35.2071i) q^{54} +7.48331i q^{56} +(14.3191 + 107.445i) q^{57} +65.2577i q^{58} +45.4634i q^{59} +28.1445 q^{61} +48.1007 q^{62} +(-6.23600 - 22.9807i) q^{63} +8.00000 q^{64} +(-8.48608 + 1.13094i) q^{66} +33.7430i q^{67} -34.7832 q^{68} +(12.7939 + 96.0005i) q^{69} +25.2759i q^{71} +(-24.5674 + 6.66657i) q^{72} +48.5331i q^{73} -44.5212i q^{74} -72.2630 q^{76} +5.33879 q^{77} +(48.7903 - 6.50225i) q^{78} -32.9331 q^{79} +(69.8892 - 40.9450i) q^{81} -45.4883i q^{82} -82.4176 q^{83} +(15.7354 - 2.09705i) q^{84} -73.1915i q^{86} +(137.219 - 18.2871i) q^{87} -5.70741i q^{88} +48.8676i q^{89} -30.6951 q^{91} -64.5661 q^{92} +(-13.4792 - 101.143i) q^{93} -130.588 q^{94} +(-2.24184 - 16.8218i) q^{96} +14.5167i q^{97} -9.89949 q^{98} +(4.75610 + 17.5270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more