LMFDB - Embedded newform 196.6.d.b.195.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.9
Character	$\chi$	$=$	196.195
Dual form			196.6.d.b.195.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23262 - 4.64222i) q^{2} -8.56469 q^{3} +(-11.1004 + 30.0130i) q^{4} +54.9613i q^{5} +(27.6864 + 39.7592i) q^{6} +(175.210 - 45.4904i) q^{8} -169.646 q^{9} +O(q^{10})$	\(q+(-3.23262 - 4.64222i) q^{2} -8.56469 q^{3} +(-11.1004 + 30.0130i) q^{4} +54.9613i q^{5} +(27.6864 + 39.7592i) q^{6} +(175.210 - 45.4904i) q^{8} -169.646 q^{9} +(255.142 - 177.669i) q^{10} -525.582i q^{11} +(95.0711 - 257.052i) q^{12} -1005.77i q^{13} -470.727i q^{15} +(-777.564 - 666.311i) q^{16} +1342.87i q^{17} +(548.401 + 787.534i) q^{18} -47.0786 q^{19} +(-1649.56 - 610.090i) q^{20} +(-2439.87 + 1699.01i) q^{22} +798.379i q^{23} +(-1500.62 + 389.612i) q^{24} +104.255 q^{25} +(-4669.01 + 3251.28i) q^{26} +3534.19 q^{27} -600.350 q^{29} +(-2185.22 + 1521.68i) q^{30} +5238.56 q^{31} +(-579.589 + 5763.55i) q^{32} +4501.45i q^{33} +(6233.89 - 4340.99i) q^{34} +(1883.13 - 5091.59i) q^{36} -13219.8 q^{37} +(152.187 + 218.549i) q^{38} +8614.13i q^{39} +(2500.21 + 9629.78i) q^{40} +3464.72i q^{41} +11552.1i q^{43} +(15774.3 + 5834.15i) q^{44} -9323.97i q^{45} +(3706.25 - 2580.86i) q^{46} +3589.67 q^{47} +(6659.60 + 5706.74i) q^{48} +(-337.016 - 483.973i) q^{50} -11501.3i q^{51} +(30186.3 + 11164.4i) q^{52} -2690.17 q^{53} +(-11424.7 - 16406.5i) q^{54} +28886.7 q^{55} +403.214 q^{57} +(1940.70 + 2786.95i) q^{58} +8262.55 q^{59} +(14127.9 + 5225.23i) q^{60} -12997.7i q^{61} +(-16934.3 - 24318.6i) q^{62} +(28629.2 - 15940.8i) q^{64} +55278.6 q^{65} +(20896.7 - 14551.5i) q^{66} +55772.7i q^{67} +(-40303.6 - 14906.3i) q^{68} -6837.87i q^{69} +37357.0i q^{71} +(-29723.7 + 7717.27i) q^{72} -49193.1i q^{73} +(42734.4 + 61369.0i) q^{74} -892.910 q^{75} +(522.589 - 1412.97i) q^{76} +(39988.7 - 27846.2i) q^{78} +108641. i q^{79} +(36621.3 - 42736.0i) q^{80} +10954.8 q^{81} +(16084.0 - 11200.1i) q^{82} +71003.7 q^{83} -73805.9 q^{85} +(53627.3 - 37343.5i) q^{86} +5141.81 q^{87} +(-23909.0 - 92087.4i) q^{88} +69993.0i q^{89} +(-43283.9 + 30140.8i) q^{90} +(-23961.8 - 8862.29i) q^{92} -44866.7 q^{93} +(-11604.0 - 16664.0i) q^{94} -2587.50i q^{95} +(4964.00 - 49363.0i) q^{96} +110504. i q^{97} +89163.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−3.23262	−	4.64222i	−0.571452	−	0.820636i
$2$	−3.23262	−	4.64222i	−0.571452	−	0.820636i
$3$	−8.56469			−0.549425			−0.274713	−	0.961526i	$-0.588583\pi$
$3$	−8.56469			−0.549425			−0.274713	+	0.961526i	$0.588583\pi$
$4$	−11.1004	+	30.0130i	−0.346886	+	0.937907i
$5$			54.9613i			0.983178i	0.870827	+	0.491589i	$0.163584\pi$
$5$			54.9613i			0.983178i	−0.870827	+	0.491589i	$0.836416\pi$
$6$	27.6864	+	39.7592i	0.313970	+	0.450878i
$7$		0			0
$7$		0			0
$8$	175.210	−	45.4904i	0.967909	−	0.251302i
$9$	−169.646			−0.698132
$10$	255.142	−	177.669i	0.806831	−	0.561839i
$11$		−	525.582i		−	1.30966i	−0.755775	−	0.654831i	$-0.772740\pi$
$11$		−	525.582i		−	1.30966i	0.755775	−	0.654831i	$-0.227260\pi$
$12$	95.0711	−	257.052i	0.190588	−	0.515310i
$13$		−	1005.77i		−	1.65060i	−0.564696	−	0.825299i	$-0.691007\pi$
$13$		−	1005.77i		−	1.65060i	0.564696	−	0.825299i	$-0.308993\pi$
$14$		0			0
$15$		−	470.727i		−	0.540183i
$16$	−777.564	−	666.311i	−0.759340	−	0.650694i
$17$			1342.87i			1.12697i	0.826127	+	0.563484i	$0.190539\pi$
$17$			1342.87i			1.12697i	−0.826127	+	0.563484i	$0.809461\pi$
$18$	548.401	+	787.534i	0.398949	+	0.572912i
$19$	−47.0786			−0.0299185			−0.0149592	−	0.999888i	$-0.504762\pi$
$19$	−47.0786			−0.0299185			−0.0149592	+	0.999888i	$0.504762\pi$
$20$	−1649.56	−	610.090i	−0.922130	−	0.341051i
$21$		0			0
$22$	−2439.87	+	1699.01i	−1.07476	+	0.748408i
$23$			798.379i			0.314695i	0.987543	+	0.157347i	$0.0502943\pi$
$23$			798.379i			0.314695i	−0.987543	+	0.157347i	$0.949706\pi$
$24$	−1500.62	+	389.612i	−0.531794	+	0.138071i
$25$	104.255			0.0333615
$26$	−4669.01	+	3251.28i	−1.35454	+	0.943237i
$27$	3534.19			0.932996
$28$		0			0
$29$	−600.350			−0.132559			−0.0662795	−	0.997801i	$-0.521113\pi$
$29$	−600.350			−0.132559			−0.0662795	+	0.997801i	$0.521113\pi$
$30$	−2185.22	+	1521.68i	−0.443293	+	0.308688i
$31$	5238.56			0.979057			0.489529	−	0.871987i	$-0.337169\pi$
$31$	5238.56			0.979057			0.489529	+	0.871987i	$0.337169\pi$
$32$	−579.589	+	5763.55i	−0.100056	+	0.994982i
$33$			4501.45i			0.719561i
$34$	6233.89	−	4340.99i	0.924831	−	0.644008i
$35$		0			0
$36$	1883.13	−	5091.59i	0.242172	−	0.654783i
$37$	−13219.8			−1.58752			−0.793760	−	0.608231i	$-0.791879\pi$
$37$	−13219.8			−1.58752			−0.793760	+	0.608231i	$0.791879\pi$
$38$	152.187	+	218.549i	0.0170970	+	0.0245522i
$39$			8614.13i			0.906880i
$40$	2500.21	+	9629.78i	0.247074	+	0.951626i
$41$			3464.72i			0.321891i	0.986963	+	0.160946i	$0.0514543\pi$
$41$			3464.72i			0.321891i	−0.986963	+	0.160946i	$0.948546\pi$
$42$		0			0
$43$			11552.1i			0.952773i	0.879236	+	0.476387i	$0.158054\pi$
$43$			11552.1i			0.952773i	−0.879236	+	0.476387i	$0.841946\pi$
$44$	15774.3	+	5834.15i	1.22834	+	0.454303i
$45$		−	9323.97i		−	0.686388i
$46$	3706.25	−	2580.86i	0.258250	−	0.179833i
$47$	3589.67			0.237033			0.118517	−	0.992952i	$-0.462186\pi$
$47$	3589.67			0.237033			0.118517	+	0.992952i	$0.462186\pi$
$48$	6659.60	+	5706.74i	0.417201	+	0.357508i
$49$		0			0
$50$	−337.016	−	483.973i	−0.0190645	−	0.0273777i
$51$		−	11501.3i		−	0.619185i
$52$	30186.3	+	11164.4i	1.54811	+	0.572569i
$53$	−2690.17			−0.131550			−0.0657748	−	0.997834i	$-0.520952\pi$
$53$	−2690.17			−0.131550			−0.0657748	+	0.997834i	$0.520952\pi$
$54$	−11424.7	−	16406.5i	−0.533162	−	0.765650i
$55$	28886.7			1.28763
$56$		0			0
$57$	403.214			0.0164380
$58$	1940.70	+	2786.95i	0.0757510	+	0.108783i
$59$	8262.55			0.309018			0.154509	−	0.987991i	$-0.450620\pi$
$59$	8262.55			0.309018			0.154509	+	0.987991i	$0.450620\pi$
$60$	14127.9	+	5225.23i	0.506641	+	0.187382i
$61$		−	12997.7i		−	0.447240i	−0.974676	−	0.223620i	$-0.928213\pi$
$61$		−	12997.7i		−	0.447240i	0.974676	−	0.223620i	$-0.0717875\pi$
$62$	−16934.3	−	24318.6i	−0.559484	−	0.803449i
$63$		0			0
$64$	28629.2	−	15940.8i	0.873695	−	0.486474i
$65$	55278.6			1.62283
$66$	20896.7	−	14551.5i	0.590498	−	0.411194i
$67$			55772.7i			1.51787i	0.651166	+	0.758936i	$0.274280\pi$
$67$			55772.7i			1.51787i	−0.651166	+	0.758936i	$0.725720\pi$
$68$	−40303.6	−	14906.3i	−1.05699	−	0.390930i
$69$		−	6837.87i		−	0.172901i
$70$		0			0
$71$			37357.0i			0.879480i	0.898125	+	0.439740i	$0.144929\pi$
$71$			37357.0i			0.879480i	−0.898125	+	0.439740i	$0.855071\pi$
$72$	−29723.7	+	7717.27i	−0.675728	+	0.175442i
$73$		−	49193.1i		−	1.08043i	−0.841527	−	0.540216i	$-0.818343\pi$
$73$		−	49193.1i		−	1.08043i	0.841527	−	0.540216i	$-0.181657\pi$
$74$	42734.4	+	61369.0i	0.907191	+	1.30278i
$75$	−892.910			−0.0183297
$76$	522.589	−	1412.97i	0.0103783	−	0.0280608i
$77$		0			0
$78$	39988.7	−	27846.2i	0.744218	−	0.518238i
$79$			108641.i			1.95850i	0.202645	+	0.979252i	$0.435046\pi$
$79$			108641.i			1.95850i	−0.202645	+	0.979252i	$0.564954\pi$
$80$	36621.3	−	42736.0i	0.639748	−	0.746566i
$81$	10954.8			0.185520
$82$	16084.0	−	11200.1i	0.264155	−	0.183945i
$83$	71003.7			1.13132			0.565661	−	0.824638i	$-0.308621\pi$
$83$	71003.7			1.13132			0.565661	+	0.824638i	$0.308621\pi$
$84$		0			0
$85$	−73805.9			−1.10801
$86$	53627.3	−	37343.5i	0.781880	−	0.544464i
$87$	5141.81			0.0728312
$88$	−23909.0	−	92087.4i	−0.329120	−	1.26763i
$89$			69993.0i			0.936655i	0.883555	+	0.468328i	$0.155143\pi$
$89$			69993.0i			0.936655i	−0.883555	+	0.468328i	$0.844857\pi$
$90$	−43283.9	+	30140.8i	−0.563274	+	0.392237i
$91$		0			0
$92$	−23961.8	−	8862.29i	−0.295155	−	0.109163i
$93$	−44866.7			−0.537919
$94$	−11604.0	−	16664.0i	−0.135453	−	0.194518i
$95$		−	2587.50i		−	0.0294152i
$96$	4964.00	−	49363.0i	0.0549736	−	0.546668i
$97$			110504.i			1.19247i	0.802809	+	0.596236i	$0.203338\pi$
$97$			110504.i			1.19247i	−0.802809	+	0.596236i	$0.796662\pi$
$98$		0			0
$99$			89163.0i			0.914317i
$100$	−1157.26	+	3129.00i	−0.0115726	+	0.0312900i
$101$			55545.6i			0.541809i	0.962606	+	0.270904i	$0.0873227\pi$
$101$			55545.6i			0.541809i	−0.962606	+	0.270904i	$0.912677\pi$
$102$	−53391.4	+	37179.2i	−0.508125	+	0.353834i
$103$	117652.			1.09271			0.546355	−	0.837554i	$-0.316015\pi$
$103$	117652.			1.09271			0.546355	+	0.837554i	$0.316015\pi$
$104$	−45753.0	−	176222.i	−0.414798	−	1.59763i
$105$		0			0
$106$	8696.29	+	12488.3i	0.0751743	+	0.107954i
$107$		−	150598.i		−	1.27163i	−0.771843	−	0.635813i	$-0.780665\pi$
$107$		−	150598.i		−	1.27163i	0.771843	−	0.635813i	$-0.219335\pi$
$108$	−39230.7	+	106072.i	−0.323643	+	0.875064i
$109$	58261.5			0.469695			0.234847	−	0.972032i	$-0.424541\pi$
$109$	58261.5			0.469695			0.234847	+	0.972032i	$0.424541\pi$
$110$	−93379.7	−	134098.i	−0.735818	−	1.05668i
$111$	113223.			0.872223
$112$		0			0
$113$	−60945.6			−0.449000			−0.224500	−	0.974474i	$-0.572075\pi$
$113$	−60945.6			−0.449000			−0.224500	+	0.974474i	$0.572075\pi$
$114$	−1303.44	−	1871.81i	−0.00939351	−	0.0134896i
$115$	−43880.0			−0.309401
$116$	6664.09	−	18018.3i	0.0459829	−	0.124328i
$117$			170625.i			1.15234i
$118$	−26709.7	−	38356.5i	−0.176589	−	0.253591i
$119$		0			0
$120$	−21413.6	−	82476.1i	−0.135749	−	0.522848i
$121$	−115186.			−0.715214
$122$	−60338.0	+	42016.5i	−0.367021	+	0.255576i
$123$		−	29674.3i		−	0.176855i
$124$	−58149.9	+	157225.i	−0.339621	+	0.918265i
$125$			177484.i			1.01598i
$126$		0			0
$127$			49258.1i			0.270999i	0.990777	+	0.135500i	$0.0432639\pi$
$127$			49258.1i			0.270999i	−0.990777	+	0.135500i	$0.956736\pi$
$128$	−166548.	−	81372.7i	−0.898492	−	0.438989i
$129$		−	98940.1i		−	0.523478i
$130$	−178695.	−	256615.i	−0.927370	−	1.33175i
$131$	148451.			0.755799			0.377899	−	0.925847i	$-0.376646\pi$
$131$	148451.			0.755799			0.377899	+	0.925847i	$0.376646\pi$
$132$	−135102.	−	49967.7i	−0.674882	−	0.249606i
$133$		0			0
$134$	258909.	−	180292.i	1.24562	−	0.867390i
$135$			194243.i			0.917301i
$136$	61087.8	+	235285.i	0.283209	+	1.09080i
$137$	−267905.			−1.21949			−0.609747	−	0.792596i	$-0.708729\pi$
$137$	−267905.			−1.21949			−0.609747	+	0.792596i	$0.708729\pi$
$138$	−31742.9	+	22104.2i	−0.141889	+	0.0988047i
$139$	−181033.			−0.794732			−0.397366	−	0.917660i	$-0.630076\pi$
$139$	−181033.			−0.794732			−0.397366	+	0.917660i	$0.630076\pi$
$140$		0			0
$141$	−30744.4			−0.130232
$142$	173419.	−	120761.i	0.721733	−	0.502580i
$143$	−528616.			−2.16173
$144$	131911.	+	113037.i	0.530120	+	0.454270i
$145$		−	32996.0i		−	0.130329i
$146$	−228365.	+	159023.i	−0.886640	+	0.617414i
$147$		0			0
$148$	146744.	−	396765.i	0.550688	−	1.48895i
$149$	66115.0			0.243969			0.121984	−	0.992532i	$-0.461074\pi$
$149$	66115.0			0.243969			0.121984	+	0.992532i	$0.461074\pi$
$150$	2886.44	+	4145.08i	0.0104745	+	0.0150420i
$151$		−	167175.i		−	0.596664i	−0.954462	−	0.298332i	$-0.903570\pi$
$151$		−	167175.i		−	0.596664i	0.954462	−	0.298332i	$-0.0964303\pi$
$152$	−8248.66	+	2141.63i	−0.0289584	+	0.00751857i
$153$		−	227813.i		−	0.786773i
$154$		0			0
$155$			287918.i			0.962587i
$156$	−258536.	−	95619.9i	−0.850569	−	0.314584i
$157$			388142.i			1.25673i	0.777919	+	0.628365i	$0.216275\pi$
$157$			388142.i			1.25673i	−0.777919	+	0.628365i	$0.783725\pi$
$158$	504333.	−	351194.i	1.60722	−	1.11919i
$159$	23040.5			0.0722767
$160$	−316772.	−	31855.0i	−0.978244	−	0.0983733i
$161$		0			0
$162$	−35412.6	−	50854.5i	−0.106016	−	0.152244i
$163$		−	290546.i		−	0.856538i	−0.903651	−	0.428269i	$-0.859124\pi$
$163$		−	290546.i		−	0.856538i	0.903651	−	0.428269i	$-0.140876\pi$
$164$	−103987.	−	38459.7i	−0.301904	−	0.111660i
$165$	−247406.			−0.707457
$166$	−229528.	−	329615.i	−0.646495	−	0.928402i
$167$	556102.			1.54299			0.771496	−	0.636234i	$-0.219509\pi$
$167$	556102.			1.54299			0.771496	+	0.636234i	$0.219509\pi$
$168$		0			0
$169$	−640285.			−1.72447
$170$	238586.	+	342623.i	0.633174	+	0.909273i
$171$	7986.70			0.0208871
$172$	−346713.	−	128232.i	−0.893613	−	0.330504i
$173$		−	46934.5i		−	0.119228i	−0.998222	−	0.0596139i	$-0.981013\pi$
$173$		−	46934.5i		−	0.119228i	0.998222	−	0.0596139i	$-0.0189869\pi$
$174$	−16621.5	−	23869.4i	−0.0416195	−	0.0597679i
$175$		0			0
$176$	−350201.	+	408674.i	−0.852189	+	0.994479i
$177$	−70766.2			−0.169782
$178$	324923.	−	226261.i	0.768653	−	0.535253i
$179$			32119.9i			0.0749276i	0.999298	+	0.0374638i	$0.0119279\pi$
$179$			32119.9i			0.0749276i	−0.999298	+	0.0374638i	$0.988072\pi$
$180$	279841.	+	103499.i	0.643768	+	0.238098i
$181$			512222.i			1.16215i	0.813851	+	0.581074i	$0.197367\pi$
$181$			512222.i			1.16215i	−0.813851	+	0.581074i	$0.802633\pi$
$182$		0			0
$183$			111321.i			0.245725i
$184$	36318.6	+	139884.i	0.0790833	+	0.304596i
$185$		−	726575.i		−	1.56081i
$186$	145037.	+	208281.i	0.307395	+	0.441435i
$187$	705789.			1.47595
$188$	−39846.6	+	107737.i	−0.0822236	+	0.222315i
$189$		0			0
$190$	−12011.7	+	8364.41i	−0.0241392	+	0.0168094i
$191$		−	4220.21i		−	0.00837049i	−0.999991	−	0.00418524i	$-0.998668\pi$
$191$		−	4220.21i		−	0.00837049i	0.999991	−	0.00418524i	$-0.00133221\pi$
$192$	−245201.	+	136528.i	−0.480030	+	0.267281i
$193$	17136.0			0.0331143			0.0165571	−	0.999863i	$-0.494729\pi$
$193$	17136.0			0.0331143			0.0165571	+	0.999863i	$0.494729\pi$
$194$	512983.	−	357217.i	0.978586	−	0.681440i
$195$	−473444.			−0.891624
$196$		0			0
$197$	958831.			1.76026			0.880129	−	0.474734i	$-0.157456\pi$
$197$	958831.			1.76026			0.880129	+	0.474734i	$0.157456\pi$
$198$	413914.	−	288230.i	0.750321	−	0.522488i
$199$	57018.5			0.102066			0.0510332	−	0.998697i	$-0.483749\pi$
$199$	57018.5			0.102066			0.0510332	+	0.998697i	$0.483749\pi$
$200$	18266.5	−	4742.60i	0.0322909	−	0.00838380i
$201$		−	477676.i		−	0.833957i
$202$	257855.	−	179558.i	0.444628	−	0.309617i
$203$		0			0
$204$	345188.	+	127668.i	0.580738	+	0.214787i
$205$	−190426.			−0.316476
$206$	−380323.	−	546164.i	−0.624431	−	0.896717i
$207$		−	135442.i		−	0.219699i
$208$	−670157.	+	782053.i	−1.07403	+	1.25337i
$209$			24743.7i			0.0391831i
$210$		0			0
$211$		−	96012.1i		−	0.148464i	−0.997241	−	0.0742318i	$-0.976350\pi$
$211$		−	96012.1i		−	0.148464i	0.997241	−	0.0742318i	$-0.0236505\pi$
$212$	29861.8	−	80740.1i	0.0456327	−	0.123381i
$213$		−	319951.i		−	0.483208i
$214$	−699108.	+	486826.i	−1.04354	+	0.726673i
$215$	−634918.			−0.936745
$216$	619226.	−	160772.i	0.903056	−	0.234463i
$217$		0			0
$218$	−188337.	−	270463.i	−0.268408	−	0.385448i
$219$			421324.i			0.593616i
$220$	−320653.	+	866977.i	−0.446661	+	1.20768i
$221$	1.35062e6			1.86017
$222$	−366007.	−	525606.i	−0.498433	−	0.715778i
$223$	−618991.			−0.833532			−0.416766	−	0.909014i	$-0.636837\pi$
$223$	−618991.			−0.833532			−0.416766	+	0.909014i	$0.636837\pi$
$224$		0			0
$225$	−17686.4			−0.0232907
$226$	197014.	+	282923.i	0.256582	+	0.368465i
$227$	1.31750e6			1.69702			0.848508	−	0.529182i	$-0.177501\pi$
$227$	1.31750e6			1.69702			0.848508	+	0.529182i	$0.177501\pi$
$228$	−4475.82	+	12101.7i	−0.00570210	+	0.0154173i
$229$		−	33059.7i		−	0.0416591i	−0.999783	−	0.0208296i	$-0.993369\pi$
$229$		−	33059.7i		−	0.0416591i	0.999783	−	0.0208296i	$-0.00663073\pi$
$230$	141847.	+	203700.i	0.176808	+	0.253906i
$231$		0			0
$232$	−105187.	+	27310.2i	−0.128305	+	0.0333123i
$233$	762869.			0.920578			0.460289	−	0.887769i	$-0.347746\pi$
$233$	762869.			0.920578			0.460289	+	0.887769i	$0.347746\pi$
$234$	792080.	−	551567.i	0.945647	−	0.658504i
$235$			197293.i			0.233046i
$236$	−91717.2	+	247984.i	−0.107194	+	0.289830i
$237$		−	930473.i		−	1.07605i
$238$		0			0
$239$		−	1.17736e6i		−	1.33326i	−0.745387	−	0.666632i	$-0.767735\pi$
$239$		−	1.17736e6i		−	1.33326i	0.745387	−	0.666632i	$-0.232265\pi$
$240$	−313650.	+	366020.i	−0.351494	+	0.410182i
$241$			1.28491e6i			1.42504i	0.701649	+	0.712522i	$0.252447\pi$
$241$			1.28491e6i			1.42504i	−0.701649	+	0.712522i	$0.747553\pi$
$242$	372352.	+	534718.i	0.408710	+	0.586930i
$243$	−952632.			−1.03493
$244$	390099.	+	144279.i	0.419470	+	0.155141i
$245$		0			0
$246$	−137754.	+	95925.6i	−0.145134	+	0.101064i
$247$			47350.4i			0.0493834i
$248$	917850.	−	238305.i	0.947638	−	0.246039i
$249$	−608125.			−0.621576
$250$	823919.	−	573738.i	0.833748	−	0.580582i
$251$	1.48159e6			1.48437			0.742186	−	0.670194i	$-0.233789\pi$
$251$	1.48159e6			1.48437			0.742186	+	0.670194i	$0.233789\pi$
$252$		0			0
$253$	419614.			0.412144
$254$	228667.	−	159233.i	0.222392	−	0.154863i
$255$	632125.			0.608769
$256$	160637.	+	1.03620e6i	0.153195	+	0.988196i
$257$			1.11479e6i			1.05283i	0.850227	+	0.526415i	$0.176464\pi$
$257$			1.11479e6i			1.05283i	−0.850227	+	0.526415i	$0.823536\pi$
$258$	−459301.	+	319836.i	−0.429584	+	0.299142i
$259$		0			0
$260$	−613612.	+	1.65908e6i	−0.562937	+	1.52207i
$261$	101847.			0.0925437
$262$	−479887.	−	689144.i	−0.431903	−	0.620236i
$263$			1.60568e6i			1.43143i	0.698395	+	0.715713i	$0.253898\pi$
$263$			1.60568e6i			1.43143i	−0.698395	+	0.715713i	$0.746102\pi$
$264$	204773.	+	788700.i	0.180827	+	0.696470i
$265$		−	147855.i		−	0.129337i
$266$		0			0
$267$		−	599469.i		−	0.514622i
$268$	−1.67391e6	−	619097.i	−1.42362	−	0.526528i
$269$			812107.i			0.684278i	0.939649	+	0.342139i	$0.111151\pi$
$269$			812107.i			0.684278i	−0.939649	+	0.342139i	$0.888849\pi$
$270$	901720.	−	627915.i	0.752770	−	0.524193i
$271$	−1.84581e6			−1.52673			−0.763366	−	0.645966i	$-0.776455\pi$
$271$	−1.84581e6			−1.52673			−0.763366	+	0.645966i	$0.776455\pi$
$272$	894769.	−	1.04417e6i	0.733311	−	0.855752i
$273$		0			0
$274$	866035.	+	1.24367e6i	0.696882	+	1.00076i
$275$		−	54794.5i		−	0.0436923i
$276$	205225.	+	75902.8i	0.162165	+	0.0599770i
$277$	−470388.			−0.368347			−0.184173	−	0.982894i	$-0.558961\pi$
$277$	−470388.			−0.368347			−0.184173	+	0.982894i	$0.558961\pi$
$278$	585211.	+	840394.i	0.454151	+	0.652185i
$279$	−888702.			−0.683511
$280$		0			0
$281$	115672.			0.0873901			0.0436950	−	0.999045i	$-0.486087\pi$
$281$	115672.			0.0873901			0.0436950	+	0.999045i	$0.486087\pi$
$282$	99384.9	+	142722.i	0.0744213	+	0.106873i
$283$	−1.19333e6			−0.885717			−0.442859	−	0.896591i	$-0.646036\pi$
$283$	−1.19333e6			−0.885717			−0.442859	+	0.896591i	$0.646036\pi$
$284$	−1.12120e6	−	414676.i	−0.824871	−	0.305079i
$285$			22161.2i			0.0161615i
$286$	1.70881e6	+	2.45395e6i	1.23532	+	1.77399i
$287$		0			0
$288$	98325.0	−	977764.i	0.0698526	−	0.694629i
$289$	−383443.			−0.270058
$290$	−153175.	+	106663.i	−0.106953	+	0.0744767i
$291$		−	946432.i		−	0.655174i
$292$	1.47643e6	+	546061.i	1.01334	+	0.374786i
$293$		−	2.48950e6i		−	1.69411i	−0.531503	−	0.847056i	$-0.678373\pi$
$293$		−	2.48950e6i		−	1.69411i	0.531503	−	0.847056i	$-0.321627\pi$
$294$		0			0
$295$			454120.i			0.303820i
$296$	−2.31624e6	+	601373.i	−1.53657	+	0.398946i
$297$		−	1.85751e6i		−	1.22191i
$298$	−213724.	−	306920.i	−0.139416	−	0.200209i
$299$	802988.			0.519435
$300$	9911.62	−	26798.9i	0.00635830	−	0.0171915i
$301$		0			0
$302$	−776065.	+	540414.i	−0.489644	+	0.340965i
$303$		−	475731.i		−	0.297683i
$304$	36606.7	+	31369.0i	0.0227183	+	0.0194678i
$305$	714369.			0.439717
$306$	−1.05756e6	+	736431.i	−0.645654	+	0.449603i
$307$	−1.47151e6			−0.891079			−0.445540	−	0.895262i	$-0.646988\pi$
$307$	−1.47151e6			−0.891079			−0.445540	+	0.895262i	$0.646988\pi$
$308$		0			0
$309$	−1.00765e6			−0.600362
$310$	1.33658e6	−	930730.i	0.789933	−	0.550072i
$311$	1.15068e6			0.674613			0.337307	−	0.941395i	$-0.390484\pi$
$311$	1.15068e6			0.674613			0.337307	+	0.941395i	$0.390484\pi$
$312$	391861.	+	1.50928e6i	0.227900	+	0.877777i
$313$		−	1.28904e6i		−	0.743713i	−0.928290	−	0.371856i	$-0.878721\pi$
$313$		−	1.28904e6i		−	0.743713i	0.928290	−	0.371856i	$-0.121279\pi$
$314$	1.80184e6	−	1.25472e6i	1.03132	−	0.718160i
$315$		0			0
$316$	−3.26063e6	−	1.20595e6i	−1.83690	−	0.679378i
$317$	−266679.			−0.149053			−0.0745265	−	0.997219i	$-0.523745\pi$
$317$	−266679.			−0.149053			−0.0745265	+	0.997219i	$0.523745\pi$
$318$	−74481.0	−	106959.i	−0.0413026	−	0.0593128i
$319$			315533.i			0.173607i
$320$	876126.	+	1.57350e6i	0.478290	+	0.858998i
$321$			1.28982e6i			0.698663i
$322$		0			0
$323$		−	63220.5i		−	0.0337172i
$324$	−121602.	+	328786.i	−0.0643544	+	0.174001i
$325$		−	104857.i		−	0.0550665i
$326$	−1.34878e6	+	939226.i	−0.702905	+	0.489470i
$327$	−498992.			−0.258062
$328$	157612.	+	607055.i	0.0808917	+	0.311561i
$329$		0			0
$330$	799768.	+	1.14851e6i	0.404277	+	0.580564i
$331$		−	88764.5i		−	0.0445317i	−0.999752	−	0.0222659i	$-0.992912\pi$
$331$		−	88764.5i		−	0.0445317i	0.999752	−	0.0222659i	$-0.00708803\pi$
$332$	−788166.	+	2.13104e6i	−0.392439	+	1.06107i
$333$	2.24268e6			1.10830
$334$	−1.79767e6	−	2.58155e6i	−0.881745	−	1.26623i
$335$	−3.06534e6			−1.49234
$336$		0			0
$337$	2.73985e6			1.31417			0.657086	−	0.753816i	$-0.271789\pi$
$337$	2.73985e6			1.31417			0.657086	+	0.753816i	$0.271789\pi$
$338$	2.06980e6	+	2.97234e6i	0.985453	+	1.41516i
$339$	521980.			0.246692
$340$	819272.	−	2.21514e6i	0.384353	−	1.03921i
$341$		−	2.75330e6i		−	1.28223i
$342$	−25818.0	−	37076.0i	−0.0119359	−	0.0171407i
$343$		0			0
$344$	525510.	+	2.02404e6i	0.239433	+	0.922198i
$345$	375818.			0.169993
$346$	−217880.	+	151721.i	−0.0978425	+	0.0681329i
$347$		−	1.96156e6i		−	0.874536i	−0.899331	−	0.437268i	$-0.855946\pi$
$347$		−	1.96156e6i		−	0.874536i	0.899331	−	0.437268i	$-0.144054\pi$
$348$	−57075.9	+	154321.i	−0.0252641	+	0.0683090i
$349$			16825.6i			0.00739446i	0.999993	+	0.00369723i	$0.00117687\pi$
$349$			16825.6i			0.00739446i	−0.999993	+	0.00369723i	$0.998823\pi$
$350$		0			0
$351$		−	3.55459e6i		−	1.54000i
$352$	3.02922e6	+	304622.i	1.30309	+	0.131040i
$353$			2.01608e6i			0.861134i	0.902559	+	0.430567i	$0.141686\pi$
$353$			2.01608e6i			0.861134i	−0.902559	+	0.430567i	$0.858314\pi$
$354$	228760.	+	328512.i	0.0970224	+	0.139329i
$355$	−2.05319e6			−0.864685
$356$	−2.10070e6	−	776948.i	−0.878496	−	0.324913i
$357$		0			0
$358$	149108.	−	103831.i	0.0614882	−	0.0428175i
$359$		−	880940.i		−	0.360753i	−0.983598	−	0.180377i	$-0.942268\pi$
$359$		−	880940.i		−	0.360753i	0.983598	−	0.180377i	$-0.0577317\pi$
$360$	−424152.	−	1.63365e6i	−0.172490	−	0.664361i
$361$	−2.47388e6			−0.999105
$362$	2.37784e6	−	1.65582e6i	0.953700	−	0.664111i
$363$	986532.			0.392957
$364$		0			0
$365$	2.70372e6			1.06226
$366$	516776.	−	359858.i	0.201651	−	0.140420i
$367$	1.67655e6			0.649758			0.324879	−	0.945756i	$-0.394676\pi$
$367$	1.67655e6			0.649758			0.324879	+	0.945756i	$0.394676\pi$
$368$	531969.	−	620791.i	0.204770	−	0.238960i
$369$		−	587777.i		−	0.224722i
$370$	−3.37292e6	+	2.34874e6i	−1.28086	+	0.891930i
$371$		0			0
$372$	498036.	−	1.34659e6i	0.186596	−	0.504518i
$373$	−166508.			−0.0619675			−0.0309837	−	0.999520i	$-0.509864\pi$
$373$	−166508.			−0.0619675			−0.0309837	+	0.999520i	$0.509864\pi$
$374$	−2.28155e6	−	3.27643e6i	−0.843433	−	1.21122i
$375$		−	1.52010e6i		−	0.558204i
$376$	628946.	−	163296.i	0.229427	−	0.0595668i
$377$			603815.i			0.218802i
$378$		0			0
$379$		−	2.67656e6i		−	0.957147i	−0.878047	−	0.478574i	$-0.841154\pi$
$379$		−	2.67656e6i		−	0.957147i	0.878047	−	0.478574i	$-0.158846\pi$
$380$	77658.8	+	28722.2i	0.0275887	+	0.0102037i
$381$		−	421880.i		−	0.148894i
$382$	−19591.1	+	13642.3i	−0.00686912	+	0.00478333i
$383$	4.48421e6			1.56203			0.781015	−	0.624512i	$-0.214702\pi$
$383$	4.48421e6			1.56203			0.781015	+	0.624512i	$0.214702\pi$
$384$	1.42643e6	+	696932.i	0.493654	+	0.241192i
$385$		0			0
$386$	−55394.0	−	79548.8i	−0.0189232	−	0.0271747i
$387$		−	1.95977e6i		−	0.665161i
$388$	−3.31656e6	−	1.22663e6i	−1.11843	−	0.413652i
$389$	−2.27740e6			−0.763073			−0.381536	−	0.924354i	$-0.624605\pi$
$389$	−2.27740e6			−0.763073			−0.381536	+	0.924354i	$0.624605\pi$
$390$	1.53046e6	+	2.19783e6i	0.509520	+	0.731699i
$391$	−1.07212e6			−0.354651
$392$		0			0
$393$	−1.27144e6			−0.415255
$394$	−3.09954e6	−	4.45110e6i	−1.00590	−	1.44453i
$395$	−5.97103e6			−1.92556
$396$	−2.67605e6	−	989741.i	−0.857544	−	0.317164i
$397$			652519.i			0.207786i	0.994588	+	0.103893i	$0.0331300\pi$
$397$			652519.i			0.207786i	−0.994588	+	0.103893i	$0.966870\pi$
$398$	−184319.	−	264692.i	−0.0583261	−	0.0837594i
$399$		0			0
$400$	−81064.8	−	69466.1i	−0.0253327	−	0.0217081i
$401$	−299794.			−0.0931026			−0.0465513	−	0.998916i	$-0.514823\pi$
$401$	−299794.			−0.0931026			−0.0465513	+	0.998916i	$0.514823\pi$
$402$	−2.21748e6	+	1.54415e6i	−0.684375	+	0.476566i
$403$		−	5.26880e6i		−	1.61603i
$404$	−1.66709e6	−	616575.i	−0.508166	−	0.187946i
$405$			602089.i			0.182399i
$406$		0			0
$407$			6.94807e6i			2.07911i
$408$	−523198.	−	2.01514e6i	−0.155602	−	0.599314i
$409$			1.40471e6i			0.415220i	0.978212	+	0.207610i	$0.0665684\pi$
$409$			1.40471e6i			0.415220i	−0.978212	+	0.207610i	$0.933432\pi$
$410$	615574.	+	883997.i	0.180851	+	0.259712i
$411$	2.29452e6			0.670021
$412$	−1.30597e6	+	3.53108e6i	−0.379046	+	1.02486i
$413$		0			0
$414$	−628751.	+	437832.i	−0.180292	+	0.125547i
$415$			3.90246e6i			1.11229i
$416$	5.79682e6	+	582935.i	1.64231	+	0.165153i
$417$	1.55049e6			0.436646
$418$	114866.	−	79986.9i	0.0321551	−	0.0223913i
$419$	2.63281e6			0.732630			0.366315	−	0.930491i	$-0.380619\pi$
$419$	2.63281e6			0.732630			0.366315	+	0.930491i	$0.380619\pi$
$420$		0			0
$421$	−2.29645e6			−0.631469			−0.315735	−	0.948848i	$-0.602251\pi$
$421$	−2.29645e6			−0.631469			−0.315735	+	0.948848i	$0.602251\pi$
$422$	−445709.	+	310371.i	−0.121835	+	0.0848398i
$423$	−608973.			−0.165481
$424$	−471345.	+	122377.i	−0.127328	+	0.0330586i
$425$			140001.i			0.0375974i
$426$	−1.48528e6	+	1.03428e6i	−0.396538	+	0.276130i
$427$		0			0
$428$	4.51990e6	+	1.67169e6i	1.19267	+	0.441109i
$429$	4.52744e6			1.18771
$430$	2.05245e6	+	2.94743e6i	0.535305	+	0.768727i
$431$			2.52971e6i			0.655961i	0.944684	+	0.327981i	$0.106368\pi$
$431$			2.52971e6i			0.655961i	−0.944684	+	0.327981i	$0.893632\pi$
$432$	−2.74806e6	−	2.35487e6i	−0.708462	−	0.607095i
$433$		−	506501.i		−	0.129826i	−0.997891	−	0.0649128i	$-0.979323\pi$
$433$		−	506501.i		−	0.129826i	0.997891	−	0.0649128i	$-0.0206769\pi$
$434$		0			0
$435$			282600.i			0.0716061i
$436$	−646724.	+	1.74861e6i	−0.162931	+	0.440530i
$437$		−	37586.6i		−	0.00941520i
$438$	1.95588e6	−	1.36198e6i	0.487143	−	0.339223i
$439$	−495283.			−0.122657			−0.0613285	−	0.998118i	$-0.519534\pi$
$439$	−495283.			−0.122657			−0.0613285	+	0.998118i	$0.519534\pi$
$440$	5.06124e6	−	1.31407e6i	1.24631	−	0.323584i
$441$		0			0
$442$	−4.36605e6	−	6.26988e6i	−1.06300	−	1.52652i
$443$			250211.i			0.0605755i	0.999541	+	0.0302877i	$0.00964236\pi$
$443$			250211.i			0.0605755i	−0.999541	+	0.0302877i	$0.990358\pi$
$444$	−1.25682e6	+	3.39817e6i	−0.302562	+	0.818065i
$445$	−3.84691e6			−0.920899
$446$	2.00096e6	+	2.87349e6i	0.476323	+	0.684026i
$447$	−566254.			−0.134043
$448$		0			0
$449$	−5.81736e6			−1.36179			−0.680894	−	0.732382i	$-0.738409\pi$
$449$	−5.81736e6			−1.36179			−0.680894	+	0.732382i	$0.738409\pi$
$450$	57173.4	+	82104.2i	0.0133095	+	0.0191132i
$451$	1.82100e6			0.421568
$452$	676517.	−	1.82916e6i	0.155752	−	0.421120i
$453$			1.43181e6i			0.327822i
$454$	−4.25898e6	−	6.11612e6i	−0.969763	−	1.39263i
$455$		0			0
$456$	70647.2	−	18342.4i	0.0159105	−	0.00413089i
$457$	−5.24207e6			−1.17412			−0.587059	−	0.809544i	$-0.699714\pi$
$457$	−5.24207e6			−1.17412			−0.587059	+	0.809544i	$0.699714\pi$
$458$	−153470.	+	106869.i	−0.0341870	+	0.0238062i
$459$			4.74595e6i			1.05146i
$460$	487083.	−	1.31697e6i	0.107327	−	0.290189i
$461$			2.57206e6i			0.563674i	0.959462	+	0.281837i	$0.0909438\pi$
$461$			2.57206e6i			0.563674i	−0.959462	+	0.281837i	$0.909056\pi$
$462$		0			0
$463$		−	1.72459e6i		−	0.373881i	−0.982371	−	0.186940i	$-0.940143\pi$
$463$		−	1.72459e6i		−	0.373881i	0.982371	−	0.186940i	$-0.0598571\pi$
$464$	466810.	+	400019.i	0.100657	+	0.0862553i
$465$		−	2.46593e6i		−	0.528870i
$466$	−2.46607e6	−	3.54141e6i	−0.526066	−	0.755459i
$467$	−958306.			−0.203335			−0.101667	−	0.994818i	$-0.532418\pi$
$467$	−958306.			−0.203335			−0.101667	+	0.994818i	$0.532418\pi$
$468$	−5.12098e6	−	1.89400e6i	−1.08078	−	0.399729i
$469$		0			0
$470$	915876.	−	637772.i	0.191246	−	0.133174i
$471$		−	3.32432e6i		−	0.690479i
$472$	1.44768e6	−	375867.i	0.299101	−	0.0776567i
$473$	6.07158e6			1.24781
$474$	−4.31946e6	+	3.00787e6i	−0.883046	+	0.614911i
$475$	−4908.17			−0.000998127
$476$		0			0
$477$	456376.			0.0918390
$478$	−5.46558e6	+	3.80597e6i	−1.09412	+	0.761896i
$479$	−9.16761e6			−1.82565			−0.912825	−	0.408351i	$-0.866104\pi$
$479$	−9.16761e6			−1.82565			−0.912825	+	0.408351i	$0.866104\pi$
$480$	2.71306e6	+	272828.i	0.537472	+	0.0540488i
$481$			1.32961e7i			2.62036i
$482$	5.96481e6	−	4.15361e6i	1.16944	−	0.814344i
$483$		0			0
$484$	1.27860e6	−	3.45708e6i	0.248098	−	0.670804i
$485$	−6.07344e6			−1.17241
$486$	3.07949e6	+	4.42232e6i	0.591410	+	0.849297i
$487$			3.84357e6i			0.734365i	0.930149	+	0.367183i	$0.119678\pi$
$487$			3.84357e6i			0.734365i	−0.930149	+	0.367183i	$0.880322\pi$
$488$	−591270.	−	2.27732e6i	−0.112392	−	0.432888i
$489$			2.48844e6i			0.470603i
$490$		0			0
$491$			8.08747e6i			1.51394i	0.653449	+	0.756971i	$0.273322\pi$
$491$			8.08747e6i			1.51394i	−0.653449	+	0.756971i	$0.726678\pi$
$492$	890615.	+	329395.i	0.165874	+	0.0613485i
$493$		−	806191.i		−	0.149390i
$494$	219811.	−	153066.i	0.0405258	−	0.0282202i
$495$	−4.90051e6			−0.898936
$496$	−4.07332e6	−	3.49051e6i	−0.743437	−	0.637067i
$497$		0			0
$498$	1.96584e6	+	2.82305e6i	0.355201	+	0.510088i
$499$		−	1.60743e6i		−	0.288988i	−0.989506	−	0.144494i	$-0.953845\pi$
$499$		−	1.60743e6i		−	0.288988i	0.989506	−	0.144494i	$-0.0461554\pi$
$500$	−5.32684e6	−	1.97014e6i	−0.952893	−	0.352429i
$501$	−4.76285e6			−0.847759
$502$	−4.78940e6	−	6.87784e6i	−0.848247	−	1.21813i
$503$	9.86993e6			1.73938			0.869689	−	0.493600i	$-0.164319\pi$
$503$	9.86993e6			1.73938			0.869689	+	0.493600i	$0.164319\pi$
$504$		0			0
$505$	−3.05286e6			−0.532694
$506$	−1.35645e6	−	1.94794e6i	−0.235520	−	0.338220i
$507$	5.48384e6			0.947469
$508$	−1.47838e6	−	546782.i	−0.254172	−	0.0940058i
$509$		−	5.18693e6i		−	0.887394i	−0.896177	−	0.443697i	$-0.853667\pi$
$509$		−	5.18693e6i		−	0.887394i	0.896177	−	0.443697i	$-0.146333\pi$
$510$	−2.04342e6	−	2.93446e6i	−0.347882	−	0.499577i
$511$		0			0
$512$	4.29098e6	−	4.09534e6i	0.723405	−	0.690423i
$513$	−166385.			−0.0279139
$514$	5.17508e6	−	3.60368e6i	0.863991	−	0.601642i
$515$			6.46629e6i			1.07433i
$516$	2.96949e6	+	1.09827e6i	0.490973	+	0.181587i
$517$		−	1.88667e6i		−	0.310433i
$518$		0			0
$519$			401980.i			0.0655067i
$520$	9.68537e6	−	2.51465e6i	1.57075	−	0.407820i
$521$		−	3.11549e6i		−	0.502843i	−0.967878	−	0.251422i	$-0.919102\pi$
$521$		−	3.11549e6i		−	0.502843i	0.967878	−	0.251422i	$-0.0808980\pi$
$522$	−329232.	−	472796.i	−0.0528842	−	0.0759446i
$523$	9.96967e6			1.59377			0.796887	−	0.604128i	$-0.206479\pi$
$523$	9.96967e6			1.59377			0.796887	+	0.604128i	$0.206479\pi$
$524$	−1.64786e6	+	4.45548e6i	−0.262176	+	0.708869i
$525$		0			0
$526$	7.45390e6	−	5.19054e6i	1.17468	−	0.817990i
$527$			7.03471e6i			1.10337i
$528$	2.99936e6	−	3.50017e6i	0.468214	−	0.546392i
$529$	5.79893e6			0.900967
$530$	−686376.	+	477959.i	−0.106138	+	0.0739097i
$531$	−1.40171e6			−0.215735
$532$		0			0
$533$	3.48472e6			0.531313
$534$	−2.78286e6	+	1.93785e6i	−0.422317	+	0.294082i
$535$	8.27706e6			1.25023
$536$	2.53713e6	+	9.77195e6i	0.381443	+	1.46916i
$537$		−	275097.i		−	0.0411671i
$538$	3.76998e6	−	2.62523e6i	0.561543	−	0.391032i
$539$		0			0
$540$	−5.82984e6	−	2.15617e6i	−0.860344	−	0.318199i
$541$	9.11479e6			1.33892			0.669458	−	0.742850i	$-0.266526\pi$
$541$	9.11479e6			1.33892			0.669458	+	0.742850i	$0.266526\pi$
$542$	5.96679e6	+	8.56863e6i	0.872453	+	1.25289i
$543$		−	4.38702e6i		−	0.638514i
$544$	−7.73970e6	−	778313.i	−1.12131	−	0.112761i
$545$			3.20213e6i			0.461793i
$546$		0			0
$547$			7.96828e6i			1.13867i	0.822107	+	0.569333i	$0.192799\pi$
$547$			7.96828e6i			1.13867i	−0.822107	+	0.569333i	$0.807201\pi$
$548$	2.97384e6	−	8.04064e6i	0.423025	−	1.14377i
$549$			2.20500e6i			0.312233i
$550$	−254368.	+	177130.i	−0.0358555	+	0.0249680i
$551$	28263.6			0.00396597
$552$	−311058.	−	1.19807e6i	−0.0434504	−	0.167353i
$553$		0			0
$554$	1.52058e6	+	2.18364e6i	0.210492	+	0.302278i
$555$			6.22289e6i			0.857551i
$556$	2.00953e6	−	5.43335e6i	0.275681	−	0.745385i
$557$	754870.			0.103094			0.0515471	−	0.998671i	$-0.483585\pi$
$557$	754870.			0.103094			0.0515471	+	0.998671i	$0.483585\pi$
$558$	2.87283e6	+	4.12555e6i	0.390594	+	0.560914i
$559$	1.16188e7			1.57265
$560$		0			0
$561$	−6.04487e6			−0.810923
$562$	−373923.	−	536974.i	−0.0499392	−	0.0717154i
$563$	5.83089e6			0.775289			0.387645	−	0.921809i	$-0.373289\pi$
$563$	5.83089e6			0.775289			0.387645	+	0.921809i	$0.373289\pi$
$564$	341273.	−	922732.i	0.0451757	−	0.122146i
$565$		−	3.34965e6i		−	0.441446i
$566$	3.85759e6	+	5.53971e6i	0.506145	+	0.726851i
$567$		0			0
$568$	1.69939e6	+	6.54533e6i	0.221015	+	0.851256i
$569$	7.32494e6			0.948470			0.474235	−	0.880398i	$-0.342725\pi$
$569$	7.32494e6			0.948470			0.474235	+	0.880398i	$0.342725\pi$
$570$	102877.	−	71638.6i	0.0132627	−	0.00923549i
$571$			6.48463e6i			0.832329i	0.909289	+	0.416164i	$0.136626\pi$
$571$			6.48463e6i			0.832329i	−0.909289	+	0.416164i	$0.863374\pi$
$572$	5.86783e6	−	1.58654e7i	0.749872	−	2.02750i
$573$			36144.8i			0.00459896i
$574$		0			0
$575$			83234.9i			0.0104987i
$576$	−4.85684e6	+	2.70429e6i	−0.609954	+	0.339623i
$577$		−	2.08701e6i		−	0.260966i	−0.991451	−	0.130483i	$-0.958347\pi$
$577$		−	2.08701e6i		−	0.260966i	0.991451	−	0.130483i	$-0.0416529\pi$
$578$	1.23953e6	+	1.78003e6i	0.154325	+	0.221619i
$579$	−146764.			−0.0181938
$580$	990310.	+	366267.i	0.122237	+	0.0452093i
$581$		0			0
$582$	−4.39354e6	+	3.05945e6i	−0.537660	+	0.374400i
$583$			1.41390e6i			0.172286i
$584$	−2.23782e6	−	8.61913e6i	−0.271514	−	1.04576i
$585$	−9.37779e6			−1.13295
$586$	−1.15568e7	+	8.04759e6i	−1.39025	+	0.968104i
$587$	8.74889e6			1.04799			0.523996	−	0.851721i	$-0.324441\pi$
$587$	8.74889e6			1.04799			0.523996	+	0.851721i	$0.324441\pi$
$588$		0			0
$589$	−246624.			−0.0292919
$590$	2.10813e6	−	1.46800e6i	0.249325	−	0.173618i
$591$	−8.21209e6			−0.967131
$592$	1.02792e7	+	8.80846e6i	1.20547	+	1.03299i
$593$			3.65382e6i			0.426689i	0.976977	+	0.213344i	$0.0684356\pi$
$593$			3.65382e6i			0.426689i	−0.976977	+	0.213344i	$0.931564\pi$
$594$	−8.62295e6	+	6.00461e6i	−1.00274	+	0.698262i
$595$		0			0
$596$	−733899.	+	1.98431e6i	−0.0846293	+	0.228820i
$597$	−488346.			−0.0560779
$598$	−2.59575e6	−	3.72764e6i	−0.296832	−	0.426267i
$599$		−	7.00652e6i		−	0.797876i	−0.916978	−	0.398938i	$-0.869379\pi$
$599$		−	7.00652e6i		−	0.797876i	0.916978	−	0.398938i	$-0.130621\pi$
$600$	−156447.	+	40618.9i	−0.0177414	+	0.00460627i
$601$			1.24584e7i			1.40694i	0.710723	+	0.703472i	$0.248368\pi$
$601$			1.24584e7i			1.40694i	−0.710723	+	0.703472i	$0.751632\pi$
$602$		0			0
$603$		−	9.46162e6i		−	1.05967i
$604$	5.01744e6	+	1.85571e6i	0.559616	+	0.206975i
$605$		−	6.33077e6i		−	0.703182i
$606$	−2.20844e6	+	1.53786e6i	−0.244290	+	0.170112i
$607$	8.20968e6			0.904387			0.452194	−	0.891920i	$-0.350642\pi$
$607$	8.20968e6			0.904387			0.452194	+	0.891920i	$0.350642\pi$
$608$	27286.3	−	271340.i	0.00299354	−	0.0297684i
$609$		0			0
$610$	−2.30928e6	−	3.31625e6i	−0.251277	−	0.360847i
$611$		−	3.61039e6i		−	0.391247i
$612$	6.83735e6	+	2.52880e6i	0.737920	+	0.272920i
$613$	1.13043e7			1.21504			0.607520	−	0.794304i	$-0.292164\pi$
$613$	1.13043e7			1.21504			0.607520	+	0.794304i	$0.292164\pi$
$614$	4.75682e6	+	6.83105e6i	0.509209	+	0.731252i
$615$	1.63094e6			0.173880
$616$		0			0
$617$	8.66997e6			0.916864			0.458432	−	0.888729i	$-0.348411\pi$
$617$	8.66997e6			0.916864			0.458432	+	0.888729i	$0.348411\pi$
$618$	3.25735e6	+	4.67773e6i	0.343078	+	0.492679i
$619$	1.19172e6			0.125011			0.0625056	−	0.998045i	$-0.480091\pi$
$619$	1.19172e6			0.125011			0.0625056	+	0.998045i	$0.480091\pi$
$620$	−8.64130e6	−	3.19600e6i	−0.902818	−	0.333908i
$621$			2.82162e6i			0.293609i
$622$	−3.71972e6	−	5.34172e6i	−0.385509	−	0.553612i
$623$		0			0
$624$	5.73969e6	−	6.69804e6i	0.590101	−	0.688630i
$625$	−9.42896e6			−0.965525
$626$	−5.98400e6	+	4.16697e6i	−0.610317	+	0.424996i
$627$		−	211922.i		−	0.0215282i
$628$	−1.16493e7	−	4.30852e6i	−1.17870	−	0.435942i
$629$		−	1.77524e7i		−	1.78908i
$630$		0			0
$631$		−	351151.i		−	0.0351092i	−0.999846	−	0.0175546i	$-0.994412\pi$
$631$		−	351151.i		−	0.0351092i	0.999846	−	0.0175546i	$-0.00558809\pi$
$632$	4.94211e6	+	1.90349e7i	0.492175	+	1.89565i
$633$			822314.i			0.0815696i
$634$	862071.	+	1.23798e6i	0.0851766	+	0.122318i
$635$	−2.70729e6			−0.266440
$636$	−255757.	+	691514.i	−0.0250718	+	0.0677888i
$637$		0			0
$638$	1.46477e6	−	1.02000e6i	0.142468	−	0.0992083i
$639$		−	6.33747e6i		−	0.613993i
$640$	4.47235e6	−	9.15369e6i	0.431604	−	0.883378i
$641$	−1.04424e7			−1.00382			−0.501908	−	0.864921i	$-0.667368\pi$
$641$	−1.04424e7			−1.00382			−0.501908	+	0.864921i	$0.667368\pi$
$642$	5.98764e6	−	4.16951e6i	0.573348	−	0.399252i
$643$	−2.01326e7			−1.92032			−0.960159	−	0.279456i	$-0.909846\pi$
$643$	−2.01326e7			−1.92032			−0.960159	+	0.279456i	$0.909846\pi$
$644$		0			0
$645$	5.43788e6			0.514671
$646$	−293483.	+	204368.i	−0.0276695	+	0.0192678i
$647$	−2.91740e6			−0.273991			−0.136995	−	0.990572i	$-0.543745\pi$
$647$	−2.91740e6			−0.273991			−0.136995	+	0.990572i	$0.543745\pi$
$648$	1.91939e6	−	498338.i	0.179567	−	0.0466215i
$649$		−	4.34265e6i		−	0.404709i
$650$	−486767.	+	338961.i	−0.0451895	+	0.0314678i
$651$		0			0
$652$	8.72018e6	+	3.22517e6i	0.803353	+	0.297121i
$653$	−1.80660e6			−0.165797			−0.0828987	−	0.996558i	$-0.526418\pi$
$653$	−1.80660e6			−0.165797			−0.0828987	+	0.996558i	$0.526418\pi$
$654$	1.61305e6	+	2.31643e6i	0.147470	+	0.211775i
$655$			8.15909e6i			0.743085i
$656$	2.30858e6	−	2.69405e6i	0.209453	−	0.244425i
$657$			8.34542e6i			0.754283i
$658$		0			0
$659$			1.63666e7i			1.46807i	0.679113	+	0.734034i	$0.262365\pi$
$659$			1.63666e7i			1.46807i	−0.679113	+	0.734034i	$0.737635\pi$
$660$	2.74629e6	−	7.42539e6i	0.245407	−	0.663529i
$661$			1.17490e6i			0.104591i	0.998632	+	0.0522957i	$0.0166538\pi$
$661$			1.17490e6i			0.104591i	−0.998632	+	0.0522957i	$0.983346\pi$
$662$	−412064.	+	286942.i	−0.0365443	+	0.0254477i
$663$	−1.15677e7			−1.02203
$664$	1.24406e7	−	3.22999e6i	1.09502	−	0.284303i
$665$		0			0
$666$	−7.24973e6	−	1.04110e7i	−0.633339	−	0.909509i
$667$		−	479307.i		−	0.0417156i
$668$	−6.17293e6	+	1.66903e7i	−0.535242	+	1.44718i
$669$	5.30147e6			0.457963
$670$	9.90908e6	+	1.42300e7i	0.852799	+	1.22467i
$671$	−6.83135e6			−0.585733
$672$		0			0
$673$	−1.58661e7			−1.35031			−0.675154	−	0.737677i	$-0.735923\pi$
$673$	−1.58661e7			−1.35031			−0.675154	+	0.737677i	$0.735923\pi$
$674$	−8.85689e6	−	1.27190e7i	−0.750985	−	1.07846i
$675$	368456.			0.0311262
$676$	7.10739e6	−	1.92169e7i	0.598196	−	1.61740i
$677$		−	1.76918e7i		−	1.48355i	−0.670651	−	0.741773i	$-0.733985\pi$
$677$		−	1.76918e7i		−	1.48355i	0.670651	−	0.741773i	$-0.266015\pi$
$678$	−1.68736e6	−	2.42314e6i	−0.140972	−	0.202444i
$679$		0			0
$680$	−1.29315e7	+	3.35746e6i	−1.07245	+	0.278445i
$681$	−1.12840e7			−0.932384
$682$	−1.27814e7	+	8.90036e6i	−1.05225	+	0.732735i
$683$		−	3.18958e6i		−	0.261627i	−0.991407	−	0.130813i	$-0.958241\pi$
$683$		−	3.18958e6i		−	0.261627i	0.991407	−	0.130813i	$-0.0417589\pi$
$684$	−88655.2	+	239705.i	−0.00724543	+	0.0195901i
$685$		−	1.47244e7i		−	1.19898i
$686$		0			0
$687$			283146.i			0.0228886i
$688$	7.69728e6	−	8.98249e6i	0.619964	−	0.723479i
$689$			2.70570e6i			0.217136i
$690$	−1.21488e6	−	1.74463e6i	−0.0971426	−	0.139502i
$691$	−2.37212e6			−0.188991			−0.0944954	−	0.995525i	$-0.530124\pi$
$691$	−2.37212e6			−0.188991			−0.0944954	+	0.995525i	$0.530124\pi$
$692$	1.40865e6	+	520990.i	0.111825	+	0.0413584i
$693$		0			0
$694$	−9.10598e6	+	6.34097e6i	−0.717675	+	0.499755i
$695$		−	9.94981e6i		−	0.781363i
$696$	900897.	−	233903.i	0.0704940	−	0.0183026i
$697$	−4.65267e6			−0.362761
$698$	78108.0	−	54390.7i	0.00606816	−	0.00422558i
$699$	−6.53374e6			−0.505789
$700$		0			0
$701$	1.76418e6			0.135597			0.0677983	−	0.997699i	$-0.478403\pi$
$701$	1.76418e6			0.135597			0.0677983	+	0.997699i	$0.478403\pi$
$702$	−1.65012e7	+	1.14906e7i	−1.26378	+	0.880037i
$703$	622368.			0.0474962
$704$	−8.37819e6	−	1.50470e7i	−0.637116	−	1.14424i
$705$		−	1.68975e6i		−	0.128041i
$706$	9.35907e6	−	6.51721e6i	0.706677	−	0.492096i
$707$		0			0
$708$	785529.	−	2.12391e6i	0.0588951	−	0.159240i
$709$	−1.26071e7			−0.941888			−0.470944	−	0.882163i	$-0.656087\pi$
$709$	−1.26071e7			−0.941888			−0.470944	+	0.882163i	$0.656087\pi$
$710$	6.63718e6	+	9.53135e6i	0.494126	+	0.709592i
$711$		−	1.84305e7i		−	1.36729i
$712$	3.18401e6	+	1.22635e7i	0.235383	+	0.906597i
$713$			4.18236e6i			0.308104i
$714$		0			0
$715$		−	2.90534e7i		−	2.12536i
$716$	−964016.	−	356542.i	−0.0702751	−	0.0259913i
$717$			1.00838e7i			0.732529i
$718$	−4.08952e6	+	2.84774e6i	−0.296047	+	0.206153i
$719$	1.04868e7			0.756520			0.378260	−	0.925699i	$-0.376523\pi$
$719$	1.04868e7			0.756520			0.378260	+	0.925699i	$0.376523\pi$
$720$	−6.21266e6	+	7.24999e6i	−0.446628	+	0.521202i
$721$		0			0
$722$	7.99712e6	+	1.14843e7i	0.570940	+	0.819901i
$723$		−	1.10048e7i		−	0.782955i
$724$	−1.53733e7	−	5.68584e6i	−1.08999	−	0.403133i
$725$	−62589.3			−0.00442237
$726$	−3.18908e6	−	4.57969e6i	−0.224556	−	0.322474i
$727$	−1.88450e7			−1.32239			−0.661196	−	0.750213i	$-0.729951\pi$
$727$	−1.88450e7			−1.32239			−0.661196	+	0.750213i	$0.729951\pi$
$728$		0			0
$729$	5.49698e6			0.383094
$730$	−8.74009e6	−	1.25512e7i	−0.607028	−	0.871725i
$731$	−1.55130e7			−1.07375
$732$	−3.34108e6	−	1.23570e6i	−0.230467	−	0.0852386i
$733$			1.38347e7i			0.951066i	0.879698	+	0.475533i	$0.157745\pi$
$733$			1.38347e7i			0.951066i	−0.879698	+	0.475533i	$0.842255\pi$
$734$	−5.41965e6	−	7.78292e6i	−0.371305	−	0.533215i
$735$		0			0
$736$	−4.60150e6	−	462732.i	−0.313116	−	0.0314873i
$737$	2.93132e7			1.98790
$738$	−2.72859e6	+	1.90006e6i	−0.184415	+	0.128418i
$739$		−	8.84502e6i		−	0.595782i	−0.954600	−	0.297891i	$-0.903717\pi$
$739$		−	8.84502e6i		−	0.595782i	0.954600	−	0.297891i	$-0.0962832\pi$
$740$	2.18067e7	+	8.06524e6i	1.46390	+	0.541425i
$741$		−	405541.i		−	0.0271325i
$742$		0			0
$743$		−	1.25478e7i		−	0.833865i	−0.908937	−	0.416933i	$-0.863105\pi$
$743$		−	1.25478e7i		−	0.833865i	0.908937	−	0.416933i	$-0.136895\pi$
$744$	−7.86110e6	+	2.04101e6i	−0.520656	+	0.135180i
$745$			3.63376e6i			0.239865i
$746$	538258.	+	772967.i	0.0354114	+	0.0508527i
$747$	−1.20455e7			−0.789811
$748$	−7.83451e6	+	2.11829e7i	−0.511986	+	1.38430i
$749$		0			0
$750$	−7.05662e6	+	4.91389e6i	−0.458082	+	0.318987i
$751$			1.98408e7i			1.28369i	0.766834	+	0.641845i	$0.221831\pi$
$751$			1.98408e7i			1.28369i	−0.766834	+	0.641845i	$0.778169\pi$
$752$	−2.79120e6	−	2.39183e6i	−0.179989	−	0.154236i
$753$	−1.26893e7			−0.815551
$754$	2.80304e6	−	1.95190e6i	0.179556	−	0.125035i
$755$	9.18818e6			0.586627
$756$		0			0
$757$	2.81038e7			1.78248			0.891241	−	0.453530i	$-0.149835\pi$
$757$	2.81038e7			1.78248			0.891241	+	0.453530i	$0.149835\pi$
$758$	−1.24252e7	+	8.65229e6i	−0.785469	+	0.546963i
$759$	−3.59387e6			−0.226442
$760$	−117707.	−	453357.i	−0.00739209	−	0.0284712i
$761$			1.88493e7i			1.17987i	0.807452	+	0.589934i	$0.200846\pi$
$761$			1.88493e7i			1.17987i	−0.807452	+	0.589934i	$0.799154\pi$
$762$	−1.95846e6	+	1.36378e6i	−0.122188	+	0.0850856i
$763$		0			0
$764$	126661.	+	46845.8i	0.00785074	+	0.00290361i
$765$	1.25209e7			0.773537
$766$	−1.44958e7	−	2.08167e7i	−0.892625	−	1.28186i
$767$		−	8.31024e6i		−	0.510065i
$768$	−1.37580e6	−	8.87472e6i	−0.0841692	−	0.542940i
$769$		−	1.42553e6i		−	0.0869279i	−0.999055	−	0.0434639i	$-0.986161\pi$
$769$		−	1.42553e6i		−	0.0869279i	0.999055	−	0.0434639i	$-0.0138394\pi$
$770$		0			0
$771$		−	9.54780e6i		−	0.578452i
$772$	−190215.	+	514302.i	−0.0114869	+	0.0310581i
$773$			2.42045e7i			1.45696i	0.685067	+	0.728480i	$0.259773\pi$
$773$			2.42045e7i			1.45696i	−0.685067	+	0.728480i	$0.740227\pi$
$774$	−9.09766e6	+	6.33518e6i	−0.545855	+	0.380108i
$775$	546145.			0.0326628
$776$	5.02687e6	+	1.93614e7i	0.299670	+	1.15420i
$777$		0			0
$778$	7.36198e6	+	1.05722e7i	0.436059	+	0.626205i
$779$		−	163114.i		−	0.00963050i
$780$	5.25539e6	−	1.42095e7i	0.309292	−	0.836261i
$781$	1.96342e7			1.15182
$782$	3.46575e6	+	4.97701e6i	0.202666	+	0.291039i
$783$	−2.12175e6			−0.123677
$784$		0			0
$785$	−2.13328e7			−1.23559
$786$	4.11008e6	+	5.90230e6i	0.237298	+	0.340773i
$787$	−41394.8			−0.00238237			−0.00119118	−	0.999999i	$-0.500379\pi$
$787$	−41394.8			−0.00238237			−0.00119118	+	0.999999i	$0.500379\pi$
$788$	−1.06434e7	+	2.87774e7i	−0.610609	+	1.65096i
$789$		−	1.37521e7i		−	0.786461i
$790$	1.93021e7	+	2.77188e7i	1.10036	+	1.58018i
$791$		0			0
$792$	4.05606e6	+	1.56223e7i	0.229769	+	0.884975i
$793$	−1.30727e7			−0.738214
$794$	3.02914e6	−	2.10935e6i	0.170517	−	0.118740i
$795$			1.26633e6i			0.0710608i
$796$	−632926.	+	1.71130e6i	−0.0354054	+	0.0957289i
$797$		−	1.28311e7i		−	0.715512i	−0.933815	−	0.357756i	$-0.883542\pi$
$797$		−	1.28311e7i		−	0.715512i	0.933815	−	0.357756i	$-0.116458\pi$
$798$		0			0
$799$			4.82046e6i			0.267129i
$800$	−60424.9	+	600878.i	−0.00333804	+	0.0331941i
$801$		−	1.18740e7i		−	0.653909i
$802$	969119.	+	1.39171e6i	0.0532036	+	0.0764033i
$803$	−2.58550e7			−1.41500
$804$	1.43365e7	+	5.30237e6i	0.782174	+	0.289288i
$805$		0			0
$806$	−2.44589e7	+	1.70320e7i	−1.32617	+	0.923483i
$807$		−	6.95545e6i		−	0.375960i
$808$	2.52679e6	+	9.73215e6i	0.136157	+	0.524421i
$809$	−3.03498e6			−0.163036			−0.0815182	−	0.996672i	$-0.525977\pi$
$809$	−3.03498e6			−0.163036			−0.0815182	+	0.996672i	$0.525977\pi$
$810$	2.79503e6	−	1.94632e6i	0.149683	−	0.104232i
$811$	−2.07140e7			−1.10589			−0.552945	−	0.833218i	$-0.686496\pi$
$811$	−2.07140e7			−1.10589			−0.552945	+	0.833218i	$0.686496\pi$
$812$		0			0
$813$	1.58088e7			0.838825
$814$	3.22545e7	−	2.24605e7i	1.70620	−	1.18811i
$815$	1.59688e7			0.842129
$816$	−7.66342e6	+	8.94298e6i	−0.402900	+	0.470172i
$817$		−	543857.i		−	0.0285055i
$818$	6.52096e6	−	4.54089e6i	0.340744	−	0.237278i
$819$		0			0
$820$	2.11379e6	−	5.71525e6i	0.109781	−	0.296825i
$821$	3.27252e6			0.169443			0.0847217	−	0.996405i	$-0.473000\pi$
$821$	3.27252e6			0.169443			0.0847217	+	0.996405i	$0.473000\pi$
$822$	−7.41732e6	−	1.06517e7i	−0.382884	−	0.549843i
$823$			1.71790e6i			0.0884095i	0.999022	+	0.0442047i	$0.0140754\pi$
$823$			1.71790e6i			0.0884095i	−0.999022	+	0.0442047i	$0.985925\pi$
$824$	2.06138e7	−	5.35203e6i	1.05764	−	0.274600i
$825$			469298.i			0.0240057i
$826$		0			0
$827$		−	2.41034e7i		−	1.22550i	−0.790275	−	0.612752i	$-0.790063\pi$
$827$		−	2.41034e7i		−	1.22550i	0.790275	−	0.612752i	$-0.209937\pi$
$828$	4.06502e6	+	1.50345e6i	0.206057	+	0.0762104i
$829$			1.15482e7i			0.583618i	0.956477	+	0.291809i	$0.0942572\pi$
$829$			1.15482e7i			0.583618i	−0.956477	+	0.291809i	$0.905743\pi$
$830$	1.81161e7	−	1.26152e7i	0.912785	−	0.635620i
$831$	4.02873e6			0.202379
$832$	−1.60328e7	−	2.87945e7i	−0.802973	−	1.44212i
$833$		0			0
$834$	−5.01215e6	−	7.19772e6i	−0.249522	−	0.358327i
$835$			3.05641e7i			1.51704i
$836$	−742633.	−	274664.i	−0.0367501	−	0.0135921i
$837$	1.85141e7			0.913457
$838$	−8.51088e6	−	1.22221e7i	−0.418663	−	0.601223i
$839$	−1.35657e7			−0.665332			−0.332666	−	0.943045i	$-0.607948\pi$
$839$	−1.35657e7			−0.665332			−0.332666	+	0.943045i	$0.607948\pi$
$840$		0			0
$841$	−2.01507e7			−0.982428
$842$	7.42355e6	+	1.06606e7i	0.360854	+	0.518206i
$843$	−990694.			−0.0480143
$844$	2.88161e6	+	1.06577e6i	0.139245	+	0.0514999i
$845$		−	3.51909e7i		−	1.69546i
$846$	1.96858e6	+	2.82698e6i	0.0945641	+	0.135799i
$847$		0			0
$848$	2.09178e6	+	1.79249e6i	0.0998909	+	0.0855986i
$849$	1.02205e7			0.486635
$850$	649913.	−	452569.i	0.0308538	−	0.0214851i
$851$		−	1.05544e7i		−	0.499584i
$852$	9.60270e6	+	3.55157e6i	0.453205	+	0.167618i
$853$		−	1.43938e7i		−	0.677335i	−0.940906	−	0.338668i	$-0.890024\pi$
$853$		−	1.43938e7i		−	0.677335i	0.940906	−	0.338668i	$-0.109976\pi$
$854$		0			0
$855$			438960.i			0.0205357i
$856$	−6.85076e6	−	2.63863e7i	−0.319562	−	1.23082i
$857$		−	2.48025e7i		−	1.15357i	−0.816897	−	0.576784i	$-0.804308\pi$
$857$		−	2.48025e7i		−	1.15357i	0.816897	−	0.576784i	$-0.195692\pi$
$858$	−1.46355e7	−	2.10173e7i	−0.678717	−	0.974674i
$859$	−9.36134e6			−0.432868			−0.216434	−	0.976297i	$-0.569443\pi$
$859$	−9.36134e6			−0.432868			−0.216434	+	0.976297i	$0.569443\pi$
$860$	7.04782e6	−	1.90558e7i	0.324944	−	0.878580i
$861$		0			0
$862$	1.17435e7	−	8.17760e6i	0.538305	−	0.374850i
$863$		−	3.34039e7i		−	1.52676i	−0.645950	−	0.763380i	$-0.723539\pi$
$863$		−	3.34039e7i		−	1.52676i	0.645950	−	0.763380i	$-0.276461\pi$
$864$	−2.04838e6	+	2.03695e7i	−0.0933523	+	0.928314i
$865$	2.57958e6			0.117222
$866$	−2.35129e6	+	1.63732e6i	−0.106540	+	0.0741890i
$867$	3.28408e6			0.148377
$868$		0			0
$869$	5.70996e7			2.56498
$870$	1.31189e6	−	913540.i	0.0587625	−	0.0409194i
$871$	5.60947e7			2.50540
$872$	1.02080e7	−	2.65034e6i	0.454622	−	0.118035i
$873$		−	1.87466e7i		−	0.832503i
$874$	−174485.	+	121503.i	−0.00772645	+	0.00538033i
$875$		0			0
$876$	−1.26452e7	−	4.67684e6i	−0.556757	−	0.205917i
$877$	1.74511e7			0.766167			0.383084	−	0.923714i	$-0.374862\pi$
$877$	1.74511e7			0.766167			0.383084	+	0.923714i	$0.374862\pi$
$878$	1.60106e6	+	2.29921e6i	0.0700925	+	0.100657i
$879$			2.13218e7i			0.930788i
$880$	−2.24613e7	−	1.92475e7i	−0.977749	−	0.837853i
$881$			3.98953e7i			1.73174i	0.500271	+	0.865869i	$0.333234\pi$
$881$			3.98953e7i			1.73174i	−0.500271	+	0.865869i	$0.666766\pi$
$882$		0			0
$883$			1.52150e7i			0.656706i	0.944555	+	0.328353i	$0.106494\pi$
$883$			1.52150e7i			0.656706i	−0.944555	+	0.328353i	$0.893506\pi$
$884$	−1.49924e7	+	4.05363e7i	−0.645268	+	1.74467i
$885$		−	3.88940e6i		−	0.166926i
$886$	1.16153e6	−	808836.i	0.0497104	−	0.0346160i
$887$	2.46799e7			1.05325			0.526627	−	0.850096i	$-0.323456\pi$
$887$	2.46799e7			1.05325			0.526627	+	0.850096i	$0.323456\pi$
$888$	1.98378e7	−	5.15057e6i	0.844233	−	0.219191i
$889$		0			0
$890$	1.24356e7	+	1.78582e7i	0.526249	+	0.755722i
$891$		−	5.75764e6i		−	0.242969i
$892$	6.87102e6	−	1.85778e7i	0.289141	−	0.781776i
$893$	−168997.			−0.00709168
$894$	1.83048e6	+	2.62867e6i	0.0765988	+	0.110000i
$895$	−1.76535e6			−0.0736671
$896$		0			0
$897$	−6.87734e6			−0.285391
$898$	1.88053e7	+	2.70054e7i	0.778196	+	1.11753i
$899$	−3.14497e6			−0.129783
$900$	196325.	−	530823.i	0.00807924	−	0.0218446i
$901$		−	3.61255e6i		−	0.148252i
$902$	−5.88659e6	−	8.45347e6i	−0.240906	−	0.345954i
$903$		0			0
$904$	−1.06783e7	+	2.77244e6i	−0.434591	+	0.112834i
$905$	−2.81524e7			−1.14260
$906$	6.64675e6	−	4.62848e6i	0.269023	−	0.187335i
$907$			6.32324e6i			0.255224i	0.991824	+	0.127612i	$0.0407312\pi$
$907$			6.32324e6i			0.255224i	−0.991824	+	0.127612i	$0.959269\pi$
$908$	−1.46247e7	+	3.95422e7i	−0.588671	+	1.59164i
$909$		−	9.42309e6i		−	0.378254i
$910$		0			0
$911$			2.11360e6i			0.0843774i	0.999110	+	0.0421887i	$0.0134331\pi$
$911$			2.11360e6i			0.0843774i	−0.999110	+	0.0421887i	$0.986567\pi$
$912$	−313525.	−	268666.i	−0.0124820	−	0.0106961i
$913$		−	3.73183e7i		−	1.48165i
$914$	1.69456e7	+	2.43348e7i	0.670952	+	0.963524i
$915$	−6.11835e6			−0.241591
$916$	992221.	+	366974.i	0.0390724	+	0.0144510i
$917$		0			0
$918$	2.20317e7	−	1.53419e7i	0.862864	−	0.600857i
$919$		−	1.15307e7i		−	0.450368i	−0.974316	−	0.225184i	$-0.927702\pi$
$919$		−	1.15307e7i		−	0.450368i	0.974316	−	0.225184i	$-0.0722983\pi$
$920$	−7.68822e6	+	1.99612e6i	−0.299472	+	0.0777530i
$921$	1.26030e7			0.489581
$922$	1.19400e7	−	8.31448e6i	0.462571	−	0.322113i
$923$	3.75726e7			1.45167
$924$		0			0
$925$	−1.37822e6			−0.0529621
$926$	−8.00592e6	+	5.57494e6i	−0.306820	+	0.213655i
$927$	−1.99591e7			−0.762856
$928$	347956.	−	3.46014e6i	0.0132634	−	0.131894i
$929$			3.28513e7i			1.24886i	0.781082	+	0.624429i	$0.214668\pi$
$929$			3.28513e7i			1.24886i	−0.781082	+	0.624429i	$0.785332\pi$
$930$	−1.14474e7	+	7.97142e6i	−0.434009	+	0.302223i
$931$		0			0
$932$	−8.46812e6	+	2.28960e7i	−0.319336	+	0.863416i
$933$	−9.85525e6			−0.370650
$934$	3.09784e6	+	4.44867e6i	0.116196	+	0.166864i
$935$			3.87911e7i			1.45112i
$936$	7.76182e6	+	2.98953e7i	0.289584	+	1.11536i
$937$		−	4.13580e7i		−	1.53890i	−0.638707	−	0.769450i	$-0.720531\pi$
$937$		−	4.13580e7i		−	1.53890i	0.638707	−	0.769450i	$-0.279469\pi$
$938$		0			0
$939$			1.10402e7i			0.408615i
$940$	−5.92135e6	−	2.19002e6i	−0.218575	−	0.0808404i
$941$			8.21905e6i			0.302585i	0.988489	+	0.151293i	$0.0483436\pi$
$941$			8.21905e6i			0.302585i	−0.988489	+	0.151293i	$0.951656\pi$
$942$	−1.54322e7	+	1.07463e7i	−0.566631	+	0.394575i
$943$	−2.76616e6			−0.101297
$944$	−6.42466e6	−	5.50542e6i	−0.234650	−	0.201076i
$945$		0			0
$946$	−1.96271e7	−	2.81856e7i	−0.713063	−	1.02400i
$947$			3.56997e7i			1.29357i	0.762672	+	0.646785i	$0.223887\pi$
$947$			3.56997e7i			1.29357i	−0.762672	+	0.646785i	$0.776113\pi$
$948$	2.79263e7	+	1.03286e7i	1.00924	+	0.373267i
$949$	−4.94771e7			−1.78336
$950$	15866.2	+	22784.8i	0.000570381	+	0.000819098i
$951$	2.28402e6			0.0818935
$952$		0			0
$953$	−4.96767e7			−1.77182			−0.885912	−	0.463853i	$-0.846466\pi$
$953$	−4.96767e7			−1.77182			−0.885912	+	0.463853i	$0.846466\pi$
$954$	−1.47529e6	−	2.11860e6i	−0.0524816	−	0.0753664i
$955$	231948.			0.00822968
$956$	3.53363e7	+	1.30692e7i	1.25048	+	0.462491i
$957$		−	2.70244e6i		−	0.0953843i
$958$	2.96354e7	+	4.25581e7i	1.04327	+	1.49819i
$959$		0			0
$960$	−7.50375e6	−	1.34765e7i	−0.262785	−	0.471955i
$961$	−1.18660e6			−0.0414471
$962$	6.17232e7	−	4.29811e7i	2.15036	−	1.49741i
$963$			2.55483e7i			0.887763i
$964$	−3.85639e7	−	1.42629e7i	−1.33656	−	0.494328i
$965$			941814.i			0.0325572i
$966$		0			0
$967$			2.53358e7i			0.871303i	0.900115	+	0.435651i	$0.143482\pi$
$967$			2.53358e7i			0.871303i	−0.900115	+	0.435651i	$0.856518\pi$
$968$	−2.01817e7	+	5.23986e6i	−0.692262	+	0.179734i
$969$			541464.i			0.0185251i
$970$	1.96331e7	+	2.81942e7i	0.669977	+	0.962123i
$971$	−1.86858e7			−0.636008			−0.318004	−	0.948089i	$-0.603013\pi$
$971$	−1.86858e7			−0.636008			−0.318004	+	0.948089i	$0.603013\pi$
$972$	1.05745e7	−	2.85914e7i	0.359001	−	0.970665i
$973$		0			0
$974$	1.78427e7	−	1.24248e7i	0.602646	−	0.419654i
$975$			898064.i			0.0302549i
$976$	−8.66048e6	+	1.01065e7i	−0.291016	+	0.339607i
$977$	5.81534e6			0.194912			0.0974561	−	0.995240i	$-0.468929\pi$
$977$	5.81534e6			0.194912			0.0974561	+	0.995240i	$0.468929\pi$
$978$	1.15519e7	−	8.04418e6i	0.386194	−	0.268927i
$979$	3.67871e7			1.22670
$980$		0			0
$981$	−9.88384e6			−0.327909
$982$	3.75438e7	−	2.61437e7i	1.24239	−	0.865145i
$983$	−2.91262e7			−0.961392			−0.480696	−	0.876887i	$-0.659616\pi$
$983$	−2.91262e7			−0.961392			−0.480696	+	0.876887i	$0.659616\pi$
$984$	−1.34990e6	−	5.19924e6i	−0.0444440	−	0.171180i
$985$			5.26986e7i			1.73065i
$986$	−3.74252e6	+	2.60611e6i	−0.122595	+	0.0853690i
$987$		0			0
$988$	−1.42113e6	−	525606.i	−0.0463171	−	0.0171304i
$989$	−9.22295e6			−0.299833
$990$	1.58415e7	+	2.27493e7i	0.513698	+	0.737699i
$991$		−	3.72612e7i		−	1.20524i	−0.798029	−	0.602619i	$-0.794124\pi$
$991$		−	3.72612e7i		−	1.20524i	0.798029	−	0.602619i	$-0.205876\pi$
$992$	−3.03621e6	+	3.01927e7i	−0.0979610	+	0.974144i
$993$			760241.i			0.0244668i
$994$		0			0
$995$			3.13381e6i			0.100350i
$996$	6.75040e6	−	1.82517e7i	0.215616	−	0.582981i
$997$			4.74646e7i			1.51228i	0.654411	+	0.756139i	$0.272917\pi$
$997$			4.74646e7i			1.51228i	−0.654411	+	0.756139i	$0.727083\pi$
$998$	−7.46202e6	+	5.19620e6i	−0.237154	+	0.165143i
$999$	−4.67211e7			−1.48115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.b.195.9		36
4.3	odd	2	inner	196.6.d.b.195.12		36
7.2	even	3		28.6.f.a.3.7	✓	36
7.3	odd	6		28.6.f.a.19.17	yes	36
7.6	odd	2	inner	196.6.d.b.195.10		36
28.3	even	6		28.6.f.a.19.7	yes	36
28.23	odd	6		28.6.f.a.3.17	yes	36
28.27	even	2	inner	196.6.d.b.195.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.7	✓	36	7.2	even	3
28.6.f.a.3.17	yes	36	28.23	odd	6
28.6.f.a.19.7	yes	36	28.3	even	6
28.6.f.a.19.17	yes	36	7.3	odd	6
196.6.d.b.195.9		36	1.1	even	1	trivial
196.6.d.b.195.10		36	7.6	odd	2	inner
196.6.d.b.195.11		36	28.27	even	2	inner
196.6.d.b.195.12		36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23262 - 4.64222i) q^{2} -8.56469 q^{3} +(-11.1004 + 30.0130i) q^{4} +54.9613i q^{5} +(27.6864 + 39.7592i) q^{6} +(175.210 - 45.4904i) q^{8} -169.646 q^{9} +O(q^{10})\)	\(q+(-3.23262 - 4.64222i) q^{2} -8.56469 q^{3} +(-11.1004 + 30.0130i) q^{4} +54.9613i q^{5} +(27.6864 + 39.7592i) q^{6} +(175.210 - 45.4904i) q^{8} -169.646 q^{9} +(255.142 - 177.669i) q^{10} -525.582i q^{11} +(95.0711 - 257.052i) q^{12} -1005.77i q^{13} -470.727i q^{15} +(-777.564 - 666.311i) q^{16} +1342.87i q^{17} +(548.401 + 787.534i) q^{18} -47.0786 q^{19} +(-1649.56 - 610.090i) q^{20} +(-2439.87 + 1699.01i) q^{22} +798.379i q^{23} +(-1500.62 + 389.612i) q^{24} +104.255 q^{25} +(-4669.01 + 3251.28i) q^{26} +3534.19 q^{27} -600.350 q^{29} +(-2185.22 + 1521.68i) q^{30} +5238.56 q^{31} +(-579.589 + 5763.55i) q^{32} +4501.45i q^{33} +(6233.89 - 4340.99i) q^{34} +(1883.13 - 5091.59i) q^{36} -13219.8 q^{37} +(152.187 + 218.549i) q^{38} +8614.13i q^{39} +(2500.21 + 9629.78i) q^{40} +3464.72i q^{41} +11552.1i q^{43} +(15774.3 + 5834.15i) q^{44} -9323.97i q^{45} +(3706.25 - 2580.86i) q^{46} +3589.67 q^{47} +(6659.60 + 5706.74i) q^{48} +(-337.016 - 483.973i) q^{50} -11501.3i q^{51} +(30186.3 + 11164.4i) q^{52} -2690.17 q^{53} +(-11424.7 - 16406.5i) q^{54} +28886.7 q^{55} +403.214 q^{57} +(1940.70 + 2786.95i) q^{58} +8262.55 q^{59} +(14127.9 + 5225.23i) q^{60} -12997.7i q^{61} +(-16934.3 - 24318.6i) q^{62} +(28629.2 - 15940.8i) q^{64} +55278.6 q^{65} +(20896.7 - 14551.5i) q^{66} +55772.7i q^{67} +(-40303.6 - 14906.3i) q^{68} -6837.87i q^{69} +37357.0i q^{71} +(-29723.7 + 7717.27i) q^{72} -49193.1i q^{73} +(42734.4 + 61369.0i) q^{74} -892.910 q^{75} +(522.589 - 1412.97i) q^{76} +(39988.7 - 27846.2i) q^{78} +108641. i q^{79} +(36621.3 - 42736.0i) q^{80} +10954.8 q^{81} +(16084.0 - 11200.1i) q^{82} +71003.7 q^{83} -73805.9 q^{85} +(53627.3 - 37343.5i) q^{86} +5141.81 q^{87} +(-23909.0 - 92087.4i) q^{88} +69993.0i q^{89} +(-43283.9 + 30140.8i) q^{90} +(-23961.8 - 8862.29i) q^{92} -44866.7 q^{93} +(-11604.0 - 16664.0i) q^{94} -2587.50i q^{95} +(4964.00 - 49363.0i) q^{96} +110504. i q^{97} +89163.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

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