LMFDB - Embedded newform 200.6.f.c.149.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.7
Root			$-3.90102 - 0.884346i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.c.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.01667 - 4.78536i) q^{2} -25.4343 q^{3} +(-13.7994 + 28.8717i) q^{4} +(76.7270 + 121.712i) q^{6} -56.4938i q^{7} +(179.790 - 21.0614i) q^{8} +403.904 q^{9} +O(q^{10})$	\(q+(-3.01667 - 4.78536i) q^{2} -25.4343 q^{3} +(-13.7994 + 28.8717i) q^{4} +(76.7270 + 121.712i) q^{6} -56.4938i q^{7} +(179.790 - 21.0614i) q^{8} +403.904 q^{9} +261.019i q^{11} +(350.978 - 734.333i) q^{12} -720.631 q^{13} +(-270.343 + 170.423i) q^{14} +(-643.154 - 796.825i) q^{16} -1876.44i q^{17} +(-1218.45 - 1932.83i) q^{18} -1992.33i q^{19} +1436.88i q^{21} +(1249.07 - 787.408i) q^{22} -2570.29i q^{23} +(-4572.83 + 535.682i) q^{24} +(2173.91 + 3448.48i) q^{26} -4092.49 q^{27} +(1631.07 + 779.581i) q^{28} +1700.16i q^{29} -7734.68 q^{31} +(-1872.91 + 5481.48i) q^{32} -6638.83i q^{33} +(-8979.46 + 5660.61i) q^{34} +(-5573.63 + 11661.4i) q^{36} +12228.1 q^{37} +(-9534.02 + 6010.20i) q^{38} +18328.8 q^{39} +14979.3 q^{41} +(6876.00 - 4334.60i) q^{42} -18113.9 q^{43} +(-7536.06 - 3601.90i) q^{44} +(-12299.8 + 7753.73i) q^{46} +2141.03i q^{47} +(16358.2 + 20266.7i) q^{48} +13615.4 q^{49} +47726.0i q^{51} +(9944.27 - 20805.9i) q^{52} -1605.71 q^{53} +(12345.7 + 19584.1i) q^{54} +(-1189.84 - 10157.0i) q^{56} +50673.5i q^{57} +(8135.87 - 5128.81i) q^{58} +2680.90i q^{59} -44521.9i q^{61} +(23333.0 + 37013.2i) q^{62} -22818.1i q^{63} +(31880.8 - 7573.26i) q^{64} +(-31769.2 + 20027.2i) q^{66} -12486.0 q^{67} +(54176.2 + 25893.8i) q^{68} +65373.7i q^{69} +8189.38 q^{71} +(72617.9 - 8506.79i) q^{72} +41082.7i q^{73} +(-36888.2 - 58516.0i) q^{74} +(57522.0 + 27492.9i) q^{76} +14746.0 q^{77} +(-55291.8 - 87709.7i) q^{78} -46325.9 q^{79} +5940.95 q^{81} +(-45187.8 - 71681.6i) q^{82} -61655.4 q^{83} +(-41485.3 - 19828.1i) q^{84} +(54643.7 + 86681.7i) q^{86} -43242.3i q^{87} +(5497.42 + 46928.5i) q^{88} -53205.4 q^{89} +40711.2i q^{91} +(74208.8 + 35468.5i) q^{92} +196726. q^{93} +(10245.6 - 6458.79i) q^{94} +(47636.2 - 139418. i) q^{96} -39211.8i q^{97} +(-41073.3 - 65154.8i) q^{98} +105427. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9	$ 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28} + 7160 q^{31} + 14792 q^{32} - 21132 q^{34} + 18344 q^{36} - 3608 q^{37} - 16884 q^{38} + 44904 q^{39} + 11608 q^{41} - 49444 q^{42} - 51772 q^{43} - 72296 q^{44} - 28516 q^{46} - 85048 q^{48} - 18756 q^{49} - 111624 q^{52} + 928 q^{53} + 100584 q^{54} - 53624 q^{56} + 152344 q^{58} + 228648 q^{62} + 11264 q^{64} - 56688 q^{66} - 161604 q^{67} + 359040 q^{68} - 200312 q^{71} + 563448 q^{72} - 78876 q^{74} - 153872 q^{76} + 26008 q^{77} - 624640 q^{78} - 282080 q^{79} + 65172 q^{81} - 410576 q^{82} - 99092 q^{83} + 297128 q^{84} + 27452 q^{86} - 464496 q^{88} + 3160 q^{89} - 519244 q^{92} + 293472 q^{93} - 148820 q^{94} + 395168 q^{96} + 663674 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−3.01667	−	4.78536i	−0.533277	−	0.845941i
$2$	−3.01667	−	4.78536i	−0.533277	−	0.845941i
$3$	−25.4343			−1.63161			−0.815806	−	0.578326i	$-0.803706\pi$
$3$	−25.4343			−1.63161			−0.815806	+	0.578326i	$0.803706\pi$
$4$	−13.7994	+	28.8717i	−0.431231	+	0.902242i
$5$		0			0
$5$		0			0
$6$	76.7270	+	121.712i	0.870101	+	1.38025i
$7$		−	56.4938i		−	0.435769i	−0.975975	−	0.217884i	$-0.930084\pi$
$7$		−	56.4938i		−	0.435769i	0.975975	−	0.217884i	$-0.0699156\pi$
$8$	179.790	−	21.0614i	0.993208	−	0.116349i
$9$	403.904			1.66216
$10$		0			0
$11$			261.019i			0.650414i	0.945643	+	0.325207i	$0.105434\pi$
$11$			261.019i			0.650414i	−0.945643	+	0.325207i	$0.894566\pi$
$12$	350.978	−	734.333i	0.703602	−	1.47211i
$13$	−720.631			−1.18265			−0.591323	−	0.806435i	$-0.701394\pi$
$13$	−720.631			−1.18265			−0.591323	+	0.806435i	$0.701394\pi$
$14$	−270.343	+	170.423i	−0.368634	+	0.232385i
$15$		0			0
$16$	−643.154	−	796.825i	−0.628080	−	0.778149i
$17$		−	1876.44i		−	1.57476i	−0.616471	−	0.787378i	$-0.711438\pi$
$17$		−	1876.44i		−	1.57476i	0.616471	−	0.787378i	$-0.288562\pi$
$18$	−1218.45	−	1932.83i	−0.886391	−	1.40609i
$19$		−	1992.33i		−	1.26613i	−0.774100	−	0.633063i	$-0.781797\pi$
$19$		−	1992.33i		−	1.26613i	0.774100	−	0.633063i	$-0.218203\pi$
$20$		0			0
$21$			1436.88i			0.711005i
$22$	1249.07	−	787.408i	0.550212	−	0.346851i
$23$		−	2570.29i		−	1.01313i	−0.862203	−	0.506563i	$-0.830916\pi$
$23$		−	2570.29i		−	1.01313i	0.862203	−	0.506563i	$-0.169084\pi$
$24$	−4572.83	+	535.682i	−1.62053	+	0.189836i
$25$		0			0
$26$	2173.91	+	3448.48i	0.630678	+	1.00045i
$27$	−4092.49			−1.08038
$28$	1631.07	+	779.581i	0.393169	+	0.187917i
$29$			1700.16i			0.375400i	0.982226	+	0.187700i	$0.0601032\pi$
$29$			1700.16i			0.375400i	−0.982226	+	0.187700i	$0.939897\pi$
$30$		0			0
$31$	−7734.68			−1.44557			−0.722783	−	0.691075i	$-0.757137\pi$
$31$	−7734.68			−1.44557			−0.722783	+	0.691075i	$0.757137\pi$
$32$	−1872.91	+	5481.48i	−0.323327	+	0.946287i
$33$		−	6638.83i		−	1.06122i
$34$	−8979.46	+	5660.61i	−1.33215	+	0.839781i
$35$		0			0
$36$	−5573.63	+	11661.4i	−0.716774	+	1.49967i
$37$	12228.1			1.46844			0.734218	−	0.678913i	$-0.237549\pi$
$37$	12228.1			1.46844			0.734218	+	0.678913i	$0.237549\pi$
$38$	−9534.02	+	6010.20i	−1.07107	+	0.675196i
$39$	18328.8			1.92962
$40$		0			0
$41$	14979.3			1.39166			0.695830	−	0.718206i	$-0.255037\pi$
$41$	14979.3			1.39166			0.695830	+	0.718206i	$0.255037\pi$
$42$	6876.00	−	4334.60i	0.601468	−	0.379163i
$43$	−18113.9			−1.49397			−0.746984	−	0.664842i	$-0.768499\pi$
$43$	−18113.9			−1.49397			−0.746984	+	0.664842i	$0.768499\pi$
$44$	−7536.06	−	3601.90i	−0.586831	−	0.280479i
$45$		0			0
$46$	−12299.8	+	7753.73i	−0.857044	+	0.540277i
$47$			2141.03i			0.141377i	0.997498	+	0.0706885i	$0.0225196\pi$
$47$			2141.03i			0.141377i	−0.997498	+	0.0706885i	$0.977480\pi$
$48$	16358.2	+	20266.7i	1.02478	+	1.26964i
$49$	13615.4			0.810106
$50$		0			0
$51$			47726.0i			2.56939i
$52$	9944.27	−	20805.9i	0.509993	−	1.06703i
$53$	−1605.71			−0.0785192			−0.0392596	−	0.999229i	$-0.512500\pi$
$53$	−1605.71			−0.0785192			−0.0392596	+	0.999229i	$0.512500\pi$
$54$	12345.7	+	19584.1i	0.576144	+	0.913941i
$55$		0			0
$56$	−1189.84	−	10157.0i	−0.0507012	−	0.432809i
$57$			50673.5i			2.06583i
$58$	8135.87	−	5128.81i	0.317566	−	0.200192i
$59$			2680.90i			0.100265i	0.998743	+	0.0501327i	$0.0159644\pi$
$59$			2680.90i			0.100265i	−0.998743	+	0.0501327i	$0.984036\pi$
$60$		0			0
$61$		−	44521.9i		−	1.53197i	−0.642860	−	0.765984i	$-0.722252\pi$
$61$		−	44521.9i		−	1.53197i	0.642860	−	0.765984i	$-0.277748\pi$
$62$	23333.0	+	37013.2i	0.770887	+	1.22286i
$63$		−	22818.1i		−	0.724316i
$64$	31880.8	−	7573.26i	0.972926	−	0.231117i
$65$		0			0
$66$	−31769.2	+	20027.2i	−0.897732	+	0.565926i
$67$	−12486.0			−0.339809			−0.169905	−	0.985461i	$-0.554346\pi$
$67$	−12486.0			−0.339809			−0.169905	+	0.985461i	$0.554346\pi$
$68$	54176.2	+	25893.8i	1.42081	+	0.679083i
$69$			65373.7i			1.65303i
$70$		0			0
$71$	8189.38			0.192799			0.0963996	−	0.995343i	$-0.469267\pi$
$71$	8189.38			0.192799			0.0963996	+	0.995343i	$0.469267\pi$
$72$	72617.9	−	8506.79i	1.65087	−	0.193390i
$73$			41082.7i			0.902302i	0.892448	+	0.451151i	$0.148986\pi$
$73$			41082.7i			0.902302i	−0.892448	+	0.451151i	$0.851014\pi$
$74$	−36888.2	−	58516.0i	−0.783084	−	1.24221i
$75$		0			0
$76$	57522.0	+	27492.9i	1.14235	+	0.545993i
$77$	14746.0			0.283430
$78$	−55291.8	−	87709.7i	−1.02902	−	1.63234i
$79$	−46325.9			−0.835134			−0.417567	−	0.908646i	$-0.637117\pi$
$79$	−46325.9			−0.835134			−0.417567	+	0.908646i	$0.637117\pi$
$80$		0			0
$81$	5940.95			0.100611
$82$	−45187.8	−	71681.6i	−0.742141	−	1.17726i
$83$	−61655.4			−0.982372			−0.491186	−	0.871055i	$-0.663436\pi$
$83$	−61655.4			−0.982372			−0.491186	+	0.871055i	$0.663436\pi$
$84$	−41485.3	−	19828.1i	−0.641499	−	0.306608i
$85$		0			0
$86$	54643.7	+	86681.7i	0.796699	+	1.26381i
$87$		−	43242.3i		−	0.612507i
$88$	5497.42	+	46928.5i	0.0756750	+	0.645997i
$89$	−53205.4			−0.712001			−0.356000	−	0.934486i	$-0.615860\pi$
$89$	−53205.4			−0.712001			−0.356000	+	0.934486i	$0.615860\pi$
$90$		0			0
$91$			40711.2i			0.515360i
$92$	74208.8	+	35468.5i	0.914084	+	0.436891i
$93$	196726.			2.35860
$94$	10245.6	−	6458.79i	0.119597	−	0.0753931i
$95$		0			0
$96$	47636.2	−	139418.i	0.527545	−	1.54397i
$97$		−	39211.8i		−	0.423143i	−0.977363	−	0.211571i	$-0.932142\pi$
$97$		−	39211.8i		−	0.423143i	0.977363	−	0.211571i	$-0.0678581\pi$
$98$	−41073.3	−	65154.8i	−0.432011	−	0.685301i
$99$			105427.i			1.08109i
$100$		0			0
$101$			41893.0i			0.408637i	0.978904	+	0.204319i	$0.0654979\pi$
$101$			41893.0i			0.408637i	−0.978904	+	0.204319i	$0.934502\pi$
$102$	228386.	−	143974.i	2.17355	−	1.37020i
$103$			118358.i			1.09927i	0.835405	+	0.549635i	$0.185233\pi$
$103$			118358.i			1.09927i	−0.835405	+	0.549635i	$0.814767\pi$
$104$	−129562.	+	15177.5i	−1.17461	+	0.137600i
$105$		0			0
$106$	4843.88	+	7683.88i	0.0418725	+	0.0664226i
$107$	−147978.			−1.24951			−0.624754	−	0.780822i	$-0.714801\pi$
$107$	−147978.			−1.24951			−0.624754	+	0.780822i	$0.714801\pi$
$108$	56473.9	−	118157.i	0.465895	−	0.974768i
$109$			126538.i			1.02013i	0.860135	+	0.510066i	$0.170379\pi$
$109$			126538.i			1.02013i	−0.860135	+	0.510066i	$0.829621\pi$
$110$		0			0
$111$	−311014.			−2.39592
$112$	−45015.7	+	36334.2i	−0.339093	+	0.273697i
$113$			221898.i			1.63478i	0.576088	+	0.817388i	$0.304579\pi$
$113$			221898.i			1.63478i	−0.576088	+	0.817388i	$0.695421\pi$
$114$	242491.	−	152865.i	1.74757	−	1.10166i
$115$		0			0
$116$	−49086.5	−	23461.1i	−0.338701	−	0.161884i
$117$	−291066.			−1.96574
$118$	12829.1	−	8087.40i	0.0848185	−	0.0534692i
$119$	−106007.			−0.686229
$120$		0			0
$121$	92920.2			0.576961
$122$	−213054.	+	134308.i	−1.29595	+	0.816963i
$123$	−380989.			−2.27065
$124$	106734.	−	223313.i	0.623373	−	1.30425i
$125$		0			0
$126$	−109193.	+	68834.7i	−0.612728	+	0.386261i
$127$			237825.i			1.30842i	0.756312	+	0.654212i	$0.226999\pi$
$127$			237825.i			1.30842i	−0.756312	+	0.654212i	$0.773001\pi$
$128$	−132415.	−	129715.i	−0.714351	−	0.699788i
$129$	460715.			2.43758
$130$		0			0
$131$		−	151213.i		−	0.769856i	−0.922947	−	0.384928i	$-0.874226\pi$
$131$		−	151213.i		−	0.769856i	0.922947	−	0.384928i	$-0.125774\pi$
$132$	191675.	+	91611.9i	0.957480	+	0.457633i
$133$	−112554.			−0.551738
$134$	37666.1	+	59749.9i	0.181213	+	0.287458i
$135$		0			0
$136$	−39520.5	−	337366.i	−0.183221	−	1.56406i
$137$			163216.i			0.742954i	0.928442	+	0.371477i	$0.121148\pi$
$137$			163216.i			0.742954i	−0.928442	+	0.371477i	$0.878852\pi$
$138$	312837.	−	197211.i	1.39836	−	0.881522i
$139$		−	7490.33i		−	0.0328824i	−0.999865	−	0.0164412i	$-0.994766\pi$
$139$		−	7490.33i		−	0.0328824i	0.999865	−	0.0164412i	$-0.00523364\pi$
$140$		0			0
$141$		−	54455.7i		−	0.230672i
$142$	−24704.7	−	39189.2i	−0.102815	−	0.163097i
$143$		−	188098.i		−	0.769209i
$144$	−259772.	−	321841.i	−1.04397	−	1.29341i
$145$		0			0
$146$	196596.	−	123933.i	0.763294	−	0.481177i
$147$	−346300.			−1.32178
$148$	−168741.	+	353047.i	−0.633236	+	1.32488i
$149$			35543.3i			0.131157i	0.997847	+	0.0655786i	$0.0208893\pi$
$149$			35543.3i			0.131157i	−0.997847	+	0.0655786i	$0.979111\pi$
$150$		0			0
$151$	549802.			1.96229			0.981147	−	0.193263i	$-0.0619070\pi$
$151$	549802.			1.96229			0.981147	+	0.193263i	$0.0619070\pi$
$152$	−41961.3	−	358201.i	−0.147312	−	1.25753i
$153$		−	757903.i		−	2.61749i
$154$	−44483.7	−	70564.7i	−0.151147	−	0.239765i
$155$		0			0
$156$	−252926.	+	529183.i	−0.832111	+	1.74098i
$157$	−252420.			−0.817287			−0.408643	−	0.912694i	$-0.633998\pi$
$157$	−252420.			−0.817287			−0.408643	+	0.912694i	$0.633998\pi$
$158$	139750.	+	221686.i	0.445358	+	0.706474i
$159$	40840.0			0.128113
$160$		0			0
$161$	−145206.			−0.441488
$162$	−17921.9	−	28429.6i	−0.0536533	−	0.0851106i
$163$	383218.			1.12974			0.564868	−	0.825182i	$-0.308927\pi$
$163$	383218.			1.12974			0.564868	+	0.825182i	$0.308927\pi$
$164$	−206706.	+	432480.i	−0.600127	+	1.25561i
$165$		0			0
$166$	185994.	+	295043.i	0.523876	+	0.831028i
$167$			108418.i			0.300821i	0.988624	+	0.150411i	$0.0480596\pi$
$167$			108418.i			0.300821i	−0.988624	+	0.150411i	$0.951940\pi$
$168$	30262.8	+	258337.i	0.0827247	+	0.706176i
$169$	148016.			0.398650
$170$		0			0
$171$		−	804710.i		−	2.10450i
$172$	249961.	−	522980.i	0.644245	−	1.34792i
$173$	−305932.			−0.777157			−0.388579	−	0.921416i	$-0.627034\pi$
$173$	−305932.			−0.777157			−0.388579	+	0.921416i	$0.627034\pi$
$174$	−206930.	+	130448.i	−0.518144	+	0.326636i
$175$		0			0
$176$	207986.	−	167875.i	0.506119	−	0.408512i
$177$		−	68186.9i		−	0.163594i
$178$	160503.	+	254607.i	0.379694	+	0.602311i
$179$		−	209868.i		−	0.489568i	−0.969578	−	0.244784i	$-0.921283\pi$
$179$		−	209868.i		−	0.489568i	0.969578	−	0.244784i	$-0.0787170\pi$
$180$		0			0
$181$		−	212990.i		−	0.483239i	−0.970371	−	0.241620i	$-0.922321\pi$
$181$		−	212990.i		−	0.483239i	0.970371	−	0.241620i	$-0.0776786\pi$
$182$	194818.	−	122812.i	0.435964	−	0.274830i
$183$			1.13239e6i			2.49958i
$184$	−54134.0	−	462113.i	−0.117876	−	1.00624i
$185$		0			0
$186$	−593458.	−	941406.i	−1.25779	−	1.99524i
$187$	489787.			1.02424
$188$	−61815.3	−	29545.0i	−0.127556	−	0.0609662i
$189$			231201.i			0.470798i
$190$		0			0
$191$	−177246.			−0.351555			−0.175777	−	0.984430i	$-0.556244\pi$
$191$	−177246.			−0.351555			−0.175777	+	0.984430i	$0.556244\pi$
$192$	−810867.	+	192621.i	−1.58744	+	0.377094i
$193$		−	758117.i		−	1.46502i	−0.680758	−	0.732509i	$-0.738349\pi$
$193$		−	758117.i		−	1.46502i	0.680758	−	0.732509i	$-0.261651\pi$
$194$	−187643.	+	118289.i	−0.357954	+	0.225652i
$195$		0			0
$196$	−187885.	+	393101.i	−0.349343	+	0.730911i
$197$	−353509.			−0.648985			−0.324492	−	0.945888i	$-0.605193\pi$
$197$	−353509.			−0.648985			−0.324492	+	0.945888i	$0.605193\pi$
$198$	504505.	−	318037.i	0.914539	−	0.576521i
$199$	−233027.			−0.417132			−0.208566	−	0.978008i	$-0.566880\pi$
$199$	−233027.			−0.417132			−0.208566	+	0.978008i	$0.566880\pi$
$200$		0			0
$201$	317572.			0.554437
$202$	200473.	−	126377.i	0.345683	−	0.217917i
$203$	96048.4			0.163587
$204$	−1.37793e6	−	658590.i	−2.31821	−	1.10800i
$205$		0			0
$206$	566385.	−	357047.i	0.929917	−	0.586215i
$207$		−	1.03815e6i		−	1.68397i
$208$	463476.	+	574217.i	0.742795	+	0.920274i
$209$	520035.			0.823507
$210$		0			0
$211$			401222.i			0.620410i	0.950670	+	0.310205i	$0.100398\pi$
$211$			401222.i			0.620410i	−0.950670	+	0.310205i	$0.899602\pi$
$212$	22157.8	−	46359.5i	0.0338599	−	0.0708433i
$213$	−208291.			−0.314573
$214$	446402.	+	708130.i	0.666334	+	1.05701i
$215$		0			0
$216$	−735789.	+	86193.6i	−1.07305	+	0.125702i
$217$			436961.i			0.629932i
$218$	605533.	−	381725.i	0.862971	−	0.544013i
$219$		−	1.04491e6i		−	1.47221i
$220$		0			0
$221$			1.35222e6i			1.86238i
$222$	938226.	+	1.48831e6i	1.27769	+	2.02681i
$223$			475659.i			0.640521i	0.947330	+	0.320260i	$0.103770\pi$
$223$			475659.i			0.640521i	−0.947330	+	0.320260i	$0.896230\pi$
$224$	309670.	+	105808.i	0.412362	+	0.140896i
$225$		0			0
$226$	1.06186e6	−	669395.i	1.38292	−	0.871789i
$227$	−28559.0			−0.0367856			−0.0183928	−	0.999831i	$-0.505855\pi$
$227$	−28559.0			−0.0367856			−0.0183928	+	0.999831i	$0.505855\pi$
$228$	−1.46303e6	−	699264.i	−1.86388	−	0.890849i
$229$			969736.i			1.22198i	0.791638	+	0.610991i	$0.209229\pi$
$229$			969736.i			1.22198i	−0.791638	+	0.610991i	$0.790771\pi$
$230$		0			0
$231$	−375053.			−0.462448
$232$	35807.7	+	305671.i	0.0436774	+	0.372850i
$233$			16005.7i			0.0193146i	0.999953	+	0.00965728i	$0.00307406\pi$
$233$			16005.7i			0.0193146i	−0.999953	+	0.00965728i	$0.996926\pi$
$234$	878050.	+	1.39286e6i	1.04829	+	1.66290i
$235$		0			0
$236$	−77402.3	−	36994.8i	−0.0904636	−	0.0432375i
$237$	1.17827e6			1.36261
$238$	319790.	+	507284.i	0.365950	+	0.580509i
$239$	−1.26598e6			−1.43361			−0.716807	−	0.697272i	$-0.754397\pi$
$239$	−1.26598e6			−1.43361			−0.716807	+	0.697272i	$0.754397\pi$
$240$		0			0
$241$	414590.			0.459807			0.229904	−	0.973213i	$-0.426159\pi$
$241$	414590.			0.459807			0.229904	+	0.973213i	$0.426159\pi$
$242$	−280310.	−	444657.i	−0.307680	−	0.488075i
$243$	843371.			0.916227
$244$	1.28543e6	+	614376.i	1.38220	+	0.660632i
$245$		0			0
$246$	1.14932e6	+	1.82317e6i	1.21089	+	1.92083i
$247$			1.43573e6i			1.49738i
$248$	−1.39062e6	+	162903.i	−1.43575	+	0.168190i
$249$	1.56816e6			1.60285
$250$		0			0
$251$		−	184150.i		−	0.184496i	−0.995736	−	0.0922479i	$-0.970595\pi$
$251$		−	184150.i		−	0.184496i	0.995736	−	0.0922479i	$-0.0294052\pi$
$252$	658798.	+	314876.i	0.653508	+	0.312348i
$253$	670895.			0.658951
$254$	1.13808e6	−	717440.i	1.10685	−	0.697752i
$255$		0			0
$256$	−221283.	+	1.02496e6i	−0.211032	+	0.977479i
$257$		−	846268.i		−	0.799236i	−0.916682	−	0.399618i	$-0.869143\pi$
$257$		−	846268.i		−	0.799236i	0.916682	−	0.399618i	$-0.130857\pi$
$258$	−1.38983e6	−	2.20469e6i	−1.29990	−	2.06204i
$259$		−	690813.i		−	0.639899i
$260$		0			0
$261$			686701.i			0.623974i
$262$	−723607.	+	456159.i	−0.651253	+	0.410547i
$263$			1.53385e6i			1.36740i	0.729765	+	0.683698i	$0.239629\pi$
$263$			1.53385e6i			1.36740i	−0.729765	+	0.683698i	$0.760371\pi$
$264$	−139823.	−	1.19360e6i	−0.123472	−	1.05402i
$265$		0			0
$266$	339539.	+	538613.i	0.294229	+	0.466738i
$267$	1.35324e6			1.16171
$268$	172299.	−	360492.i	0.146536	−	0.306590i
$269$			646714.i			0.544918i	0.962167	+	0.272459i	$0.0878370\pi$
$269$			646714.i			0.544918i	−0.962167	+	0.272459i	$0.912163\pi$
$270$		0			0
$271$	−1.58318e6			−1.30950			−0.654752	−	0.755844i	$-0.727227\pi$
$271$	−1.58318e6			−1.30950			−0.654752	+	0.755844i	$0.727227\pi$
$272$	−1.49520e6	+	1.20684e6i	−1.22539	+	0.989072i
$273$		−	1.03546e6i		−	0.840867i
$274$	781049.	−	492369.i	0.628495	−	0.396200i
$275$		0			0
$276$	−1.88745e6	−	902117.i	−1.49143	−	0.712837i
$277$	1.62475e6			1.27229			0.636147	−	0.771568i	$-0.280527\pi$
$277$	1.62475e6			1.27229			0.636147	+	0.771568i	$0.280527\pi$
$278$	−35844.0	+	22595.9i	−0.0278166	+	0.0175355i
$279$	−3.12407e6			−2.40276
$280$		0			0
$281$	−1.48375e6			−1.12097			−0.560487	−	0.828163i	$-0.689386\pi$
$281$	−1.48375e6			−1.12097			−0.560487	+	0.828163i	$0.689386\pi$
$282$	−260590.	+	164275.i	−0.195135	+	0.123012i
$283$	−1.18244e6			−0.877634			−0.438817	−	0.898577i	$-0.644602\pi$
$283$	−1.18244e6			−0.877634			−0.438817	+	0.898577i	$0.644602\pi$
$284$	−113008.	+	236442.i	−0.0831410	+	0.173951i
$285$		0			0
$286$	−900118.	+	567430.i	−0.650705	+	0.410202i
$287$		−	846241.i		−	0.606442i
$288$	−756478.	+	2.21399e6i	−0.537421	+	1.57288i
$289$	−2.10118e6			−1.47985
$290$		0			0
$291$			997325.i			0.690405i
$292$	−1.18613e6	−	566916.i	−0.814094	−	0.389101i
$293$	887981.			0.604275			0.302137	−	0.953264i	$-0.402300\pi$
$293$	887981.			0.604275			0.302137	+	0.953264i	$0.402300\pi$
$294$	1.04467e6	+	1.65717e6i	0.704874	+	1.11815i
$295$		0			0
$296$	2.19849e6	−	257541.i	1.45846	−	0.170851i
$297$		−	1.06822e6i		−	0.702697i
$298$	170088.	−	107223.i	0.110951	−	0.0699432i
$299$			1.85223e6i			1.19817i
$300$		0			0
$301$			1.02332e6i			0.651024i
$302$	−1.65857e6	−	2.63100e6i	−1.04645	−	1.65998i
$303$		−	1.06552e6i		−	0.666738i
$304$	−1.58754e6	+	1.28137e6i	−0.985235	+	0.795228i
$305$		0			0
$306$	−3.62684e6	+	2.28635e6i	−2.21424	+	1.39585i
$307$	1.47690e6			0.894346			0.447173	−	0.894447i	$-0.352431\pi$
$307$	1.47690e6			0.894346			0.447173	+	0.894447i	$0.352431\pi$
$308$	−203485.	+	425741.i	−0.122224	+	0.255722i
$309$		−	3.01035e6i		−	1.79358i
$310$		0			0
$311$	364521.			0.213708			0.106854	−	0.994275i	$-0.465922\pi$
$311$	364521.			0.213708			0.106854	+	0.994275i	$0.465922\pi$
$312$	3.29533e6	−	386029.i	1.91651	−	0.224509i
$313$		−	324246.i		−	0.187074i	−0.995616	−	0.0935371i	$-0.970183\pi$
$313$		−	324246.i		−	0.187074i	0.995616	−	0.0935371i	$-0.0298174\pi$
$314$	761468.	+	1.20792e6i	0.435840	+	0.691376i
$315$		0			0
$316$	639269.	−	1.33751e6i	0.360136	−	0.753493i
$317$	−1.55670e6			−0.870074			−0.435037	−	0.900413i	$-0.643265\pi$
$317$	−1.55670e6			−0.870074			−0.435037	+	0.900413i	$0.643265\pi$
$318$	−123201.	−	195434.i	−0.0683197	−	0.108376i
$319$	−443773.			−0.244165
$320$		0			0
$321$	3.76373e6			2.03871
$322$	438038.	+	694862.i	0.235436	+	0.373473i
$323$	−3.73849e6			−1.99384
$324$	−81981.6	+	171526.i	−0.0433864	+	0.0907751i
$325$		0			0
$326$	−1.15604e6	−	1.83384e6i	−0.602462	−	0.955689i
$327$		−	3.21842e6i		−	1.66446i
$328$	2.69314e6	−	315486.i	1.38221	−	0.161918i
$329$	120955.			0.0616077
$330$		0			0
$331$			558769.i			0.280325i	0.990128	+	0.140163i	$0.0447626\pi$
$331$			558769.i			0.280325i	−0.990128	+	0.140163i	$0.955237\pi$
$332$	850807.	−	1.78010e6i	0.423629	−	0.886336i
$333$	4.93899e6			2.44077
$334$	518818.	−	327060.i	0.254477	−	0.160421i
$335$		0			0
$336$	1.14494e6	−	924136.i	0.553268	−	0.446568i
$337$			2.18320e6i			1.04717i	0.851972	+	0.523587i	$0.175407\pi$
$337$			2.18320e6i			1.04717i	−0.851972	+	0.523587i	$0.824593\pi$
$338$	−446516.	−	708310.i	−0.212591	−	0.337234i
$339$		−	5.64384e6i		−	2.66732i
$340$		0			0
$341$		−	2.01890e6i		−	0.940216i
$342$	−3.85083e6	+	2.42755e6i	−1.78028	+	1.12228i
$343$		−	1.71868e6i		−	0.788787i
$344$	−3.25670e6	+	381505.i	−1.48382	+	0.173822i
$345$		0			0
$346$	922895.	+	1.46399e6i	0.414440	+	0.657429i
$347$	2.53924e6			1.13209			0.566043	−	0.824375i	$-0.308473\pi$
$347$	2.53924e6			1.13209			0.566043	+	0.824375i	$0.308473\pi$
$348$	1.24848e6	+	596718.i	0.552629	+	0.264132i
$349$			2.58452e6i			1.13584i	0.823085	+	0.567918i	$0.192251\pi$
$349$			2.58452e6i			1.13584i	−0.823085	+	0.567918i	$0.807749\pi$
$350$		0			0
$351$	2.94918e6			1.27771
$352$	−1.43077e6	−	488865.i	−0.615479	−	0.210297i
$353$		−	284338.i		−	0.121450i	−0.998155	−	0.0607250i	$-0.980659\pi$
$353$		−	284338.i		−	0.121450i	0.998155	−	0.0607250i	$-0.0193413\pi$
$354$	−326299.	+	205697.i	−0.138391	+	0.0872410i
$355$		0			0
$356$	734202.	−	1.53613e6i	0.307037	−	0.642397i
$357$	2.69623e6			1.11966
$358$	−1.00429e6	+	633102.i	−0.414145	+	0.261075i
$359$	1.97109e6			0.807179			0.403590	−	0.914940i	$-0.367762\pi$
$359$	1.97109e6			0.807179			0.403590	+	0.914940i	$0.367762\pi$
$360$		0			0
$361$	−1.49328e6			−0.603077
$362$	−1.01923e6	+	642520.i	−0.408792	+	0.257701i
$363$	−2.36336e6			−0.941377
$364$	−1.17540e6	−	561790.i	−0.464979	−	0.222239i
$365$		0			0
$366$	5.41887e6	−	3.41603e6i	2.11449	−	1.33297i
$367$			1.04179e6i			0.403754i	0.979411	+	0.201877i	$0.0647041\pi$
$367$			1.04179e6i			0.403754i	−0.979411	+	0.201877i	$0.935296\pi$
$368$	−2.04807e6	+	1.65309e6i	−0.788363	+	0.636324i
$369$	6.05022e6			2.31316
$370$		0			0
$371$			90712.4i			0.0342162i
$372$	−2.71470e6	+	5.67982e6i	−1.01710	+	2.12803i
$373$	1.58767e6			0.590866			0.295433	−	0.955363i	$-0.404536\pi$
$373$	1.58767e6			0.590866			0.295433	+	0.955363i	$0.404536\pi$
$374$	−1.47753e6	−	2.34381e6i	−0.546205	−	0.866449i
$375$		0			0
$376$	45093.2	+	384936.i	0.0164491	+	0.140417i
$377$		−	1.22519e6i		−	0.443965i
$378$	1.10638e6	−	697456.i	0.398267	−	0.251066i
$379$			995922.i			0.356145i	0.984017	+	0.178073i	$0.0569862\pi$
$379$			995922.i			0.356145i	−0.984017	+	0.178073i	$0.943014\pi$
$380$		0			0
$381$		−	6.04892e6i		−	2.13484i
$382$	534692.	+	848186.i	0.187476	+	0.297394i
$383$		−	1.53418e6i		−	0.534415i	−0.963639	−	0.267208i	$-0.913899\pi$
$383$		−	1.53418e6i		−	0.534415i	0.963639	−	0.267208i	$-0.0861009\pi$
$384$	3.36788e6	+	3.29922e6i	1.16554	+	1.14178i
$385$		0			0
$386$	−3.62786e6	+	2.28699e6i	−1.23932	+	0.781260i
$387$	−7.31629e6			−2.48321
$388$	1.13211e6	+	541099.i	0.381777	+	0.182472i
$389$		−	4.70941e6i		−	1.57795i	−0.614428	−	0.788973i	$-0.710613\pi$
$389$		−	4.70941e6i		−	1.57795i	0.614428	−	0.788973i	$-0.289387\pi$
$390$		0			0
$391$	−4.82301e6			−1.59542
$392$	2.44792e6	−	286760.i	0.804604	−	0.0942549i
$393$			3.84599e6i			1.25611i
$394$	1.06642e6	+	1.69167e6i	0.346089	+	0.549002i
$395$		0			0
$396$	−3.04385e6	−	1.45482e6i	−0.975405	−	0.466200i
$397$	485420.			0.154576			0.0772879	−	0.997009i	$-0.475374\pi$
$397$	485420.			0.154576			0.0772879	+	0.997009i	$0.475374\pi$
$398$	702966.	+	1.11512e6i	0.222447	+	0.352869i
$399$	2.86274e6			0.900223
$400$		0			0
$401$	1.73402e6			0.538508			0.269254	−	0.963069i	$-0.413223\pi$
$401$	1.73402e6			0.538508			0.269254	+	0.963069i	$0.413223\pi$
$402$	−958010.	−	1.51970e6i	−0.295669	−	0.469021i
$403$	5.57385e6			1.70959
$404$	−1.20952e6	−	578098.i	−0.368690	−	0.176217i
$405$		0			0
$406$	−289746.	−	459626.i	−0.0872374	−	0.138385i
$407$			3.19177e6i			0.955092i
$408$	1.00518e6	+	8.58066e6i	0.298946	+	2.55194i
$409$	853587.			0.252313			0.126156	−	0.992010i	$-0.459736\pi$
$409$	853587.			0.252313			0.126156	+	0.992010i	$0.459736\pi$
$410$		0			0
$411$		−	4.15129e6i		−	1.21221i
$412$	−3.41720e6	−	1.63327e6i	−0.991807	−	0.474039i
$413$	151454.			0.0436925
$414$	−4.96794e6	+	3.13177e6i	−1.42454	+	0.898025i
$415$		0			0
$416$	1.34968e6	−	3.95012e6i	0.382382	−	1.11912i
$417$			190511.i			0.0536514i
$418$	−1.56878e6	−	2.48856e6i	−0.439157	−	0.696638i
$419$		−	3.86903e6i		−	1.07663i	−0.842743	−	0.538316i	$-0.819061\pi$
$419$		−	3.86903e6i		−	1.07663i	0.842743	−	0.538316i	$-0.180939\pi$
$420$		0			0
$421$		−	1.15014e6i		−	0.316260i	−0.987418	−	0.158130i	$-0.949454\pi$
$421$		−	1.15014e6i		−	0.316260i	0.987418	−	0.158130i	$-0.0505464\pi$
$422$	1.91999e6	−	1.21036e6i	0.524830	−	0.330851i
$423$			864773.i			0.234991i
$424$	−288690.	+	33818.4i	−0.0779860	+	0.00913563i
$425$		0			0
$426$	628346.	+	996749.i	0.167755	+	0.266110i
$427$	−2.51522e6			−0.667583
$428$	2.04201e6	−	4.27239e6i	0.538826	−	1.12736i
$429$			4.78415e6i			1.25505i
$430$		0			0
$431$	−3.09078e6			−0.801448			−0.400724	−	0.916199i	$-0.631241\pi$
$431$	−3.09078e6			−0.801448			−0.400724	+	0.916199i	$0.631241\pi$
$432$	2.63210e6	+	3.26100e6i	0.678567	+	0.840700i
$433$		−	2.47892e6i		−	0.635394i	−0.948192	−	0.317697i	$-0.897090\pi$
$433$		−	2.47892e6i		−	0.635394i	0.948192	−	0.317697i	$-0.102910\pi$
$434$	2.09102e6	−	1.31817e6i	0.532885	−	0.335928i
$435$		0			0
$436$	−3.65338e6	−	1.74615e6i	−0.920405	−	0.439913i
$437$	−5.12087e6			−1.28275
$438$	−5.00028e6	+	3.15215e6i	−1.24540	+	0.785094i
$439$	−997159.			−0.246947			−0.123473	−	0.992348i	$-0.539403\pi$
$439$	−997159.			−0.246947			−0.123473	+	0.992348i	$0.539403\pi$
$440$		0			0
$441$	5.49934e6			1.34652
$442$	6.47088e6	−	4.07921e6i	1.57546	−	0.993163i
$443$	−2.10966e6			−0.510744			−0.255372	−	0.966843i	$-0.582198\pi$
$443$	−2.10966e6			−0.510744			−0.255372	+	0.966843i	$0.582198\pi$
$444$	4.29180e6	−	8.97951e6i	1.03319	−	2.16170i
$445$		0			0
$446$	2.27620e6	−	1.43491e6i	0.541843	−	0.341575i
$447$		−	904020.i		−	0.213998i
$448$	−427842.	−	1.80107e6i	−0.100714	−	0.423971i
$449$	−6.24963e6			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−6.24963e6			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$450$		0			0
$451$			3.90989e6i			0.905156i
$452$	−6.40659e6	−	3.06206e6i	−1.47496	−	0.704966i
$453$	−1.39838e7			−3.20170
$454$	86153.0	+	136665.i	0.0196169	+	0.0311184i
$455$		0			0
$456$	1.06726e6	+	9.11059e6i	0.240357	+	2.05180i
$457$			1.87669e6i			0.420340i	0.977665	+	0.210170i	$0.0674018\pi$
$457$			1.87669e6i			0.420340i	−0.977665	+	0.210170i	$0.932598\pi$
$458$	4.64054e6	−	2.92537e6i	1.03372	−	0.651655i
$459$			7.67933e6i			1.70134i
$460$		0			0
$461$			8.54777e6i			1.87327i	0.350307	+	0.936635i	$0.386077\pi$
$461$			8.54777e6i			1.87327i	−0.350307	+	0.936635i	$0.613923\pi$
$462$	1.13141e6	+	1.79477e6i	0.246613	+	0.391204i
$463$			7.55869e6i			1.63868i	0.573308	+	0.819340i	$0.305660\pi$
$463$			7.55869e6i			1.63868i	−0.573308	+	0.819340i	$0.694340\pi$
$464$	1.35473e6	−	1.09346e6i	0.292117	−	0.235781i
$465$		0			0
$466$	76593.1	−	48283.9i	0.0163390	−	0.0103000i
$467$	3.29127e6			0.698346			0.349173	−	0.937058i	$-0.386462\pi$
$467$	3.29127e6			0.698346			0.349173	+	0.937058i	$0.386462\pi$
$468$	4.01653e6	−	8.40358e6i	0.847689	−	1.77358i
$469$			705380.i			0.148078i
$470$		0			0
$471$	6.42013e6			1.33349
$472$	56463.6	+	481999.i	0.0116658	+	0.0995844i
$473$		−	4.72807e6i		−	0.971698i
$474$	−3.55445e6	−	5.63844e6i	−0.726651	−	1.15269i
$475$		0			0
$476$	1.46284e6	−	3.06062e6i	0.295923	−	0.619144i
$477$	−648551.			−0.130511
$478$	3.81905e6	+	6.05817e6i	0.764513	+	1.21275i
$479$	−4.95610e6			−0.986965			−0.493482	−	0.869756i	$-0.664276\pi$
$479$	−4.95610e6			−0.986965			−0.493482	+	0.869756i	$0.664276\pi$
$480$		0			0
$481$	−8.81196e6			−1.73664
$482$	−1.25068e6	−	1.98396e6i	−0.245205	−	0.388970i
$483$	3.69321e6			0.720338
$484$	−1.28224e6	+	2.68277e6i	−0.248804	+	0.520559i
$485$		0			0
$486$	−2.54417e6	−	4.03584e6i	−0.488603	−	0.775074i
$487$		−	7.56942e6i		−	1.44624i	−0.690723	−	0.723120i	$-0.742707\pi$
$487$		−	7.56942e6i		−	1.44624i	0.690723	−	0.723120i	$-0.257293\pi$
$488$	−937695.	−	8.00460e6i	−0.178243	−	1.52156i
$489$	−9.74688e6			−1.84329
$490$		0			0
$491$		−	1.25015e6i		−	0.234023i	−0.993131	−	0.117012i	$-0.962668\pi$
$491$		−	1.25015e6i		−	0.234023i	0.993131	−	0.117012i	$-0.0373315\pi$
$492$	5.25742e6	−	1.09998e7i	0.979175	−	2.04867i
$493$	3.19025e6			0.591163
$494$	6.87051e6	−	4.33114e6i	1.26669	−	0.798518i
$495$		0			0
$496$	4.97458e6	+	6.16318e6i	0.907930	+	1.12487i
$497$		−	462649.i		−	0.0840158i
$498$	−4.73063e6	−	7.50423e6i	−0.854763	−	1.35592i
$499$			5.59295e6i			1.00552i	0.864427	+	0.502758i	$0.167681\pi$
$499$			5.59295e6i			1.00552i	−0.864427	+	0.502758i	$0.832319\pi$
$500$		0			0
$501$		−	2.75753e6i		−	0.490824i
$502$	−881223.	+	555519.i	−0.156073	+	0.0983874i
$503$		−	9.76813e6i		−	1.72144i	−0.509080	−	0.860719i	$-0.670014\pi$
$503$		−	9.76813e6i		−	1.72144i	0.509080	−	0.860719i	$-0.329986\pi$
$504$	−480581.	−	4.10247e6i	−0.0842734	−	0.719397i
$505$		0			0
$506$	−2.02387e6	−	3.21048e6i	−0.351404	−	0.557434i
$507$	−3.76469e6			−0.650443
$508$	−6.86642e6	−	3.28184e6i	−1.18051	−	0.564233i
$509$			9.05091e6i			1.54845i	0.632909	+	0.774226i	$0.281861\pi$
$509$			9.05091e6i			1.54845i	−0.632909	+	0.774226i	$0.718139\pi$
$510$		0			0
$511$	2.32092e6			0.393195
$512$	5.57235e6	−	2.03305e6i	0.939428	−	0.342747i
$513$			8.15359e6i			1.36790i
$514$	−4.04970e6	+	2.55291e6i	−0.676106	+	0.426214i
$515$		0			0
$516$	−6.35759e6	+	1.33016e7i	−1.05116	+	2.19928i
$517$	−558850.			−0.0919536
$518$	−3.30579e6	+	2.08396e6i	−0.541316	+	0.341243i
$519$	7.78116e6			1.26802
$520$		0			0
$521$	−7.68287e6			−1.24002			−0.620011	−	0.784593i	$-0.712872\pi$
$521$	−7.68287e6			−1.24002			−0.620011	+	0.784593i	$0.712872\pi$
$522$	3.28611e6	−	2.07155e6i	0.527845	−	0.332751i
$523$	8.45353e6			1.35140			0.675700	−	0.737177i	$-0.263841\pi$
$523$	8.45353e6			1.35140			0.675700	+	0.737177i	$0.263841\pi$
$524$	4.36577e6	+	2.08664e6i	0.694596	+	0.331986i
$525$		0			0
$526$	7.34004e6	−	4.62713e6i	1.15674	−	0.729201i
$527$			1.45137e7i			2.27641i
$528$	−5.28999e6	+	4.26979e6i	−0.825790	+	0.666533i
$529$	−170070.			−0.0264234
$530$		0			0
$531$			1.08283e6i			0.166657i
$532$	1.55318e6	−	3.24964e6i	0.237927	−	0.497801i
$533$	−1.07946e7			−1.64584
$534$	−4.08229e6	−	6.47576e6i	−0.619513	−	0.982737i
$535$		0			0
$536$	−2.24485e6	+	262972.i	−0.337501	+	0.0395365i
$537$			5.33784e6i			0.798785i
$538$	3.09476e6	−	1.95092e6i	0.460969	−	0.290592i
$539$			3.55389e6i			0.526904i
$540$		0			0
$541$			4.67406e6i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$541$			4.67406e6i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$542$	4.77593e6	+	7.57609e6i	0.698329	+	1.10776i
$543$			5.41725e6i			0.788459i
$544$	1.02857e7	+	3.51441e6i	1.49017	+	0.509162i
$545$		0			0
$546$	−4.95506e6	+	3.12365e6i	−0.711324	+	0.448415i
$547$	−1.86478e6			−0.266477			−0.133238	−	0.991084i	$-0.542538\pi$
$547$	−1.86478e6			−0.266477			−0.133238	+	0.991084i	$0.542538\pi$
$548$	−4.71233e6	−	2.25228e6i	−0.670324	−	0.320385i
$549$		−	1.79826e7i		−	2.54637i
$550$		0			0
$551$	3.38727e6			0.475304
$552$	1.37686e6	+	1.17535e7i	0.192328	+	1.64180i
$553$			2.61713e6i			0.363925i
$554$	−4.90134e6	−	7.77503e6i	−0.678486	−	1.07629i
$555$		0			0
$556$	216259.	+	103362.i	0.0296679	+	0.0141799i
$557$	−9.40472e6			−1.28442			−0.642211	−	0.766528i	$-0.721983\pi$
$557$	−9.40472e6			−1.28442			−0.642211	+	0.766528i	$0.721983\pi$
$558$	9.42429e6	+	1.49498e7i	1.28134	+	2.03259i
$559$	1.30535e7			1.76683
$560$		0			0
$561$	−1.24574e7			−1.67117
$562$	4.47599e6	+	7.10029e6i	0.597790	+	0.948277i
$563$	849619.			0.112967			0.0564837	−	0.998404i	$-0.482011\pi$
$563$	849619.			0.112967			0.0564837	+	0.998404i	$0.482011\pi$
$564$	1.57223e6	+	751456.i	0.208122	+	0.0994731i
$565$		0			0
$566$	3.56703e6	+	5.65841e6i	0.468022	+	0.742426i
$567$		−	335627.i		−	0.0438429i
$568$	1.47237e6	−	172480.i	0.191490	−	0.0224320i
$569$	5.41948e6			0.701741			0.350870	−	0.936424i	$-0.385886\pi$
$569$	5.41948e6			0.701741			0.350870	+	0.936424i	$0.385886\pi$
$570$		0			0
$571$		−	331372.i		−	0.0425329i	−0.999774	−	0.0212664i	$-0.993230\pi$
$571$		−	331372.i		−	0.0425329i	0.999774	−	0.0212664i	$-0.00676983\pi$
$572$	5.43072e6	+	2.59564e6i	0.694013	+	0.331707i
$573$	4.50813e6			0.573601
$574$	−4.04957e6	+	2.55283e6i	−0.513014	+	0.323402i
$575$		0			0
$576$	1.28768e7	−	3.05887e6i	1.61716	−	0.384154i
$577$		−	1.51001e7i		−	1.88817i	−0.329701	−	0.944086i	$-0.606948\pi$
$577$		−	1.51001e7i		−	1.88817i	0.329701	−	0.944086i	$-0.393052\pi$
$578$	6.33857e6	+	1.00549e7i	0.789173	+	1.25187i
$579$			1.92822e7i			2.39034i
$580$		0			0
$581$			3.48315e6i			0.428087i
$582$	4.77256e6	−	3.00860e6i	0.584042	−	0.368177i
$583$		−	419119.i		−	0.0510700i
$584$	865260.	+	7.38626e6i	0.104982	+	0.896174i
$585$		0			0
$586$	−2.67875e6	−	4.24931e6i	−0.322246	−	0.511181i
$587$	1.51509e7			1.81486			0.907432	−	0.420199i	$-0.138040\pi$
$587$	1.51509e7			1.81486			0.907432	+	0.420199i	$0.138040\pi$
$588$	4.77872e6	−	9.99827e6i	0.569992	−	1.19256i
$589$			1.54100e7i			1.83027i
$590$		0			0
$591$	8.99125e6			1.05889
$592$	−7.86456e6	−	9.74367e6i	−0.922295	−	1.14266i
$593$			1.46568e7i			1.71160i	0.517307	+	0.855800i	$0.326934\pi$
$593$			1.46568e7i			1.71160i	−0.517307	+	0.855800i	$0.673066\pi$
$594$	−5.11181e6	+	3.22246e6i	−0.594440	+	0.374732i
$595$		0			0
$596$	−1.02620e6	−	490476.i	−0.118336	−	0.0565591i
$597$	5.92688e6			0.680597
$598$	8.86361e6	−	5.58758e6i	1.01358	−	0.638956i
$599$	5.14552e6			0.585952			0.292976	−	0.956120i	$-0.405354\pi$
$599$	5.14552e6			0.585952			0.292976	+	0.956120i	$0.405354\pi$
$600$		0			0
$601$	9.03954e6			1.02085			0.510423	−	0.859923i	$-0.329489\pi$
$601$	9.03954e6			1.02085			0.510423	+	0.859923i	$0.329489\pi$
$602$	4.89698e6	−	3.08703e6i	0.550728	−	0.347176i
$603$	−5.04314e6			−0.564817
$604$	−7.58694e6	+	1.58737e7i	−0.846202	+	1.77046i
$605$		0			0
$606$	−5.09890e6	+	3.21432e6i	−0.564021	+	0.355556i
$607$			1.25949e7i			1.38747i	0.720232	+	0.693733i	$0.244035\pi$
$607$			1.25949e7i			1.38747i	−0.720232	+	0.693733i	$0.755965\pi$
$608$	1.09209e7	+	3.73146e6i	1.19812	+	0.409373i
$609$	−2.44292e6			−0.266911
$610$		0			0
$611$		−	1.54290e6i		−	0.167199i
$612$	2.18820e7	+	1.04586e7i	2.36161	+	1.12874i
$613$	−8.66424e6			−0.931278			−0.465639	−	0.884975i	$-0.654175\pi$
$613$	−8.66424e6			−0.931278			−0.465639	+	0.884975i	$0.654175\pi$
$614$	−4.45533e6	−	7.06751e6i	−0.476934	−	0.756564i
$615$		0			0
$616$	2.65117e6	−	310570.i	0.281505	−	0.0329768i
$617$			6.86089e6i			0.725551i	0.931877	+	0.362775i	$0.118171\pi$
$617$			6.86089e6i			0.725551i	−0.931877	+	0.362775i	$0.881829\pi$
$618$	−1.44056e7	+	9.08124e6i	−1.51726	+	0.956476i
$619$		−	3.44552e6i		−	0.361434i	−0.983535	−	0.180717i	$-0.942158\pi$
$619$		−	3.44552e6i		−	0.361434i	0.983535	−	0.180717i	$-0.0578417\pi$
$620$		0			0
$621$			1.05189e7i			1.09457i
$622$	−1.09964e6	−	1.74436e6i	−0.113966	−	0.180785i
$623$			3.00578e6i			0.310268i
$624$	−1.17882e7	−	1.46048e7i	−1.21195	−	1.50153i
$625$		0			0
$626$	−1.55164e6	+	978144.i	−0.158254	+	0.0997624i
$627$	−1.32267e7			−1.34364
$628$	3.48324e6	−	7.28780e6i	0.352439	−	0.737390i
$629$		−	2.29454e7i		−	2.31243i
$630$		0			0
$631$	−7.79725e6			−0.779593			−0.389797	−	0.920901i	$-0.627455\pi$
$631$	−7.79725e6			−0.779593			−0.389797	+	0.920901i	$0.627455\pi$
$632$	−8.32893e6	+	975689.i	−0.829462	+	0.0971670i
$633$		−	1.02048e7i		−	1.01227i
$634$	4.69604e6	+	7.44936e6i	0.463990	+	0.736031i
$635$		0			0
$636$	−563567.	+	1.17912e6i	−0.0552463	+	0.115589i
$637$	−9.81171e6			−0.958068
$638$	1.33872e6	+	2.12361e6i	0.130208	+	0.206549i
$639$	3.30773e6			0.320463
$640$		0			0
$641$	7.82134e6			0.751859			0.375929	−	0.926648i	$-0.377324\pi$
$641$	7.82134e6			0.751859			0.375929	+	0.926648i	$0.377324\pi$
$642$	−1.13539e7	−	1.80108e7i	−1.08720	−	1.72463i
$643$	1.35325e7			1.29078			0.645389	−	0.763854i	$-0.276695\pi$
$643$	1.35325e7			1.29078			0.645389	+	0.763854i	$0.276695\pi$
$644$	2.00375e6	−	4.19234e6i	0.190383	−	0.398329i
$645$		0			0
$646$	1.12778e7	+	1.78900e7i	1.06327	+	1.68667i
$647$		−	1.34237e6i		−	0.126070i	−0.998011	−	0.0630352i	$-0.979922\pi$
$647$		−	1.34237e6i		−	0.126070i	0.998011	−	0.0630352i	$-0.0200780\pi$
$648$	1.06812e6	−	125125.i	0.0999273	−	0.0117059i
$649$	−699766.			−0.0652140
$650$		0			0
$651$		−	1.11138e7i		−	1.02780i
$652$	−5.28817e6	+	1.10642e7i	−0.487177	+	1.01929i
$653$	−5.36490e6			−0.492355			−0.246178	−	0.969225i	$-0.579175\pi$
$653$	−5.36490e6			−0.492355			−0.246178	+	0.969225i	$0.579175\pi$
$654$	−1.54013e7	+	9.70891e6i	−1.40803	+	0.887618i
$655$		0			0
$656$	−9.63402e6	−	1.19359e7i	−0.874074	−	1.08292i
$657$			1.65935e7i			1.49977i
$658$	−364882.	−	578815.i	−0.0328540	−	0.0521164i
$659$		−	8.49067e6i		−	0.761603i	−0.924657	−	0.380801i	$-0.875648\pi$
$659$		−	8.49067e6i		−	0.761603i	0.924657	−	0.380801i	$-0.124352\pi$
$660$		0			0
$661$		−	9.80254e6i		−	0.872640i	−0.899792	−	0.436320i	$-0.856282\pi$
$661$		−	9.80254e6i		−	0.872640i	0.899792	−	0.436320i	$-0.143718\pi$
$662$	2.67391e6	−	1.68562e6i	0.237139	−	0.149491i
$663$		−	3.43929e7i		−	3.03868i
$664$	−1.10850e7	+	1.29855e6i	−0.975700	+	0.114298i
$665$		0			0
$666$	−1.48993e7	−	2.36349e7i	−1.30161	−	2.06475i
$667$	4.36990e6			0.380327
$668$	−3.13020e6	−	1.49610e6i	−0.271413	−	0.129723i
$669$		−	1.20981e7i		−	1.04508i
$670$		0			0
$671$	1.16211e7			0.996413
$672$	−7.87624e6	−	2.69115e6i	−0.672815	−	0.229888i
$673$		−	7.99241e6i		−	0.680205i	−0.940388	−	0.340103i	$-0.889538\pi$
$673$		−	7.99241e6i		−	0.680205i	0.940388	−	0.340103i	$-0.110462\pi$
$674$	1.04474e7	−	6.58600e6i	0.885848	−	0.558434i
$675$		0			0
$676$	−2.04253e6	+	4.27348e6i	−0.171910	+	0.359679i
$677$	8.50891e6			0.713514			0.356757	−	0.934197i	$-0.383882\pi$
$677$	8.50891e6			0.713514			0.356757	+	0.934197i	$0.383882\pi$
$678$	−2.70078e7	+	1.70256e7i	−2.25639	+	1.42242i
$679$	−2.21522e6			−0.184392
$680$		0			0
$681$	726378.			0.0600198
$682$	−9.66115e6	+	6.09034e6i	−0.795367	+	0.501396i
$683$	−1.39302e7			−1.14263			−0.571314	−	0.820732i	$-0.693566\pi$
$683$	−1.39302e7			−1.14263			−0.571314	+	0.820732i	$0.693566\pi$
$684$	2.32334e7	+	1.11045e7i	1.89877	+	0.907527i
$685$		0			0
$686$	−8.22451e6	+	5.18469e6i	−0.667267	+	0.420642i
$687$		−	2.46646e7i		−	1.99380i
$688$	1.16500e7	+	1.44336e7i	0.938331	+	1.16253i
$689$	1.15712e6			0.0928604
$690$		0			0
$691$			1.79579e6i			0.143074i	0.997438	+	0.0715371i	$0.0227904\pi$
$691$			1.79579e6i			0.143074i	−0.997438	+	0.0715371i	$0.977210\pi$
$692$	4.22167e6	−	8.83277e6i	0.335134	−	0.701184i
$693$	5.95595e6			0.471106
$694$	−7.66005e6	−	1.21512e7i	−0.603716	−	0.957678i
$695$		0			0
$696$	−910744.	−	7.77453e6i	−0.0712645	−	0.608347i
$697$		−	2.81079e7i		−	2.19152i
$698$	1.23678e7	−	7.79664e6i	0.960850	−	0.605716i
$699$		−	407094.i		−	0.0315139i
$700$		0			0
$701$		−	1.76628e7i		−	1.35758i	−0.734334	−	0.678789i	$-0.762505\pi$
$701$		−	1.76628e7i		−	1.35758i	0.734334	−	0.678789i	$-0.237495\pi$
$702$	−8.89669e6	−	1.41129e7i	−0.681374	−	1.08087i
$703$		−	2.43624e7i		−	1.85923i
$704$	1.97676e6	+	8.32150e6i	0.150322	+	0.632805i
$705$		0			0
$706$	−1.36066e6	+	857753.i	−0.102740	+	0.0647665i
$707$	2.36670e6			0.178071
$708$	1.96867e6	+	940938.i	0.147601	+	0.0705469i
$709$			1.67397e7i			1.25064i	0.780369	+	0.625319i	$0.215031\pi$
$709$			1.67397e7i			1.25064i	−0.780369	+	0.625319i	$0.784969\pi$
$710$		0			0
$711$	−1.87112e7			−1.38812
$712$	−9.56579e6	+	1.12058e6i	−0.707165	+	0.0828405i
$713$			1.98804e7i			1.46454i
$714$	−8.13363e6	−	1.29024e7i	−0.597089	−	0.947165i
$715$		0			0
$716$	6.05924e6	+	2.89605e6i	0.441709	+	0.211117i
$717$	3.21993e7			2.33910
$718$	−5.94613e6	−	9.43238e6i	−0.430450	−	0.682826i
$719$	1.41699e7			1.02222			0.511111	−	0.859515i	$-0.329234\pi$
$719$	1.41699e7			1.02222			0.511111	+	0.859515i	$0.329234\pi$
$720$		0			0
$721$	6.68649e6			0.479027
$722$	4.50473e6	+	7.14588e6i	0.321607	+	0.510167i
$723$	−1.05448e7			−0.750227
$724$	6.14938e6	+	2.93913e6i	0.435999	+	0.208388i
$725$		0			0
$726$	7.12948e6	+	1.13095e7i	0.502015	+	0.796349i
$727$			3.78412e6i			0.265539i	0.991147	+	0.132770i	$0.0423871\pi$
$727$			3.78412e6i			0.265539i	−0.991147	+	0.132770i	$0.957613\pi$
$728$	857435.	+	7.31947e6i	0.0599616	+	0.511860i
$729$	−2.28942e7			−1.59554
$730$		0			0
$731$			3.39897e7i			2.35263i
$732$	−3.26939e7	−	1.56262e7i	−2.25522	−	1.07790i
$733$	2.58722e7			1.77858			0.889290	−	0.457345i	$-0.151199\pi$
$733$	2.58722e7			1.77858			0.889290	+	0.457345i	$0.151199\pi$
$734$	4.98536e6	−	3.14275e6i	0.341552	−	0.215313i
$735$		0			0
$736$	1.40890e7	+	4.81394e6i	0.958708	+	0.327571i
$737$		−	3.25907e6i		−	0.221017i
$738$	−1.82515e7	−	2.89525e7i	−1.23355	−	1.95680i
$739$		−	5.89215e6i		−	0.396883i	−0.980113	−	0.198441i	$-0.936412\pi$
$739$		−	5.89215e6i		−	0.396883i	0.980113	−	0.198441i	$-0.0635880\pi$
$740$		0			0
$741$		−	3.65169e7i		−	2.44314i
$742$	434092.	−	273650.i	0.0289449	−	0.0182467i
$743$			2.47551e7i			1.64510i	0.568692	+	0.822551i	$0.307450\pi$
$743$			2.47551e7i			1.64510i	−0.568692	+	0.822551i	$0.692550\pi$
$744$	3.53694e7	−	4.14333e6i	2.34258	−	0.274421i
$745$		0			0
$746$	−4.78949e6	−	7.59759e6i	−0.315095	−	0.499838i
$747$	−2.49029e7			−1.63286
$748$	−6.75876e6	+	1.41410e7i	−0.441685	+	0.924115i
$749$			8.35986e6i			0.544496i
$750$		0			0
$751$	1.98371e6			0.128345			0.0641724	−	0.997939i	$-0.479559\pi$
$751$	1.98371e6			0.128345			0.0641724	+	0.997939i	$0.479559\pi$
$752$	1.70603e6	−	1.37701e6i	0.110012	−	0.0887960i
$753$			4.68372e6i			0.301026i
$754$	−5.86296e6	+	3.69598e6i	−0.375568	+	0.236756i
$755$		0			0
$756$	−6.67516e6	−	3.19043e6i	−0.424773	−	0.203023i
$757$	−1.85647e7			−1.17746			−0.588732	−	0.808328i	$-0.700373\pi$
$757$	−1.85647e7			−1.17746			−0.588732	+	0.808328i	$0.700373\pi$
$758$	4.76585e6	−	3.00437e6i	0.301278	−	0.189924i
$759$	−1.70638e7			−1.07515
$760$		0			0
$761$	−5.16348e6			−0.323207			−0.161603	−	0.986856i	$-0.551667\pi$
$761$	−5.16348e6			−0.323207			−0.161603	+	0.986856i	$0.551667\pi$
$762$	−2.89463e7	+	1.82476e7i	−1.80595	+	1.13846i
$763$	7.14864e6			0.444542
$764$	2.44589e6	−	5.11739e6i	0.151601	−	0.317187i
$765$		0			0
$766$	−7.34160e6	+	4.62811e6i	−0.452083	+	0.284991i
$767$		−	1.93194e6i		−	0.118578i
$768$	5.62818e6	−	2.60692e7i	0.344322	−	1.59487i
$769$	−3.01408e7			−1.83797			−0.918985	−	0.394293i	$-0.870989\pi$
$769$	−3.01408e7			−1.83797			−0.918985	+	0.394293i	$0.870989\pi$
$770$		0			0
$771$			2.15242e7i			1.30404i
$772$	2.18881e7	+	1.04615e7i	1.32180	+	0.631761i
$773$	−1.51718e7			−0.913246			−0.456623	−	0.889660i	$-0.650941\pi$
$773$	−1.51718e7			−0.913246			−0.456623	+	0.889660i	$0.650941\pi$
$774$	2.20708e7	+	3.50111e7i	1.32424	+	2.10065i
$775$		0			0
$776$	−825855.	−	7.04988e6i	−0.0492322	−	0.420269i
$777$			1.75704e7i			1.04407i
$778$	−2.25362e7	+	1.42067e7i	−1.33485	+	0.841483i
$779$		−	2.98438e7i		−	1.76202i
$780$		0			0
$781$			2.13758e6i			0.125399i
$782$	1.45494e7	+	2.30799e7i	0.850804	+	1.34963i
$783$		−	6.95788e6i		−	0.405576i
$784$	−8.75682e6	−	1.08491e7i	−0.508811	−	0.630383i
$785$		0			0
$786$	1.84044e7	−	1.16021e7i	1.06259	−	0.669853i
$787$	1.46106e7			0.840874			0.420437	−	0.907322i	$-0.361877\pi$
$787$	1.46106e7			0.840874			0.420437	+	0.907322i	$0.361877\pi$
$788$	4.87820e6	−	1.02064e7i	0.279862	−	0.585541i
$789$		−	3.90125e7i		−	2.23106i
$790$		0			0
$791$	1.25359e7			0.712384
$792$	2.22043e6	+	1.89546e7i	0.125784	+	1.07375i
$793$			3.20839e7i			1.81177i
$794$	−1.46435e6	−	2.32291e6i	−0.0824318	−	0.130762i
$795$		0			0
$796$	3.21563e6	−	6.72789e6i	0.179880	−	0.376354i
$797$	−4.81785e6			−0.268663			−0.134331	−	0.990936i	$-0.542889\pi$
$797$	−4.81785e6			−0.268663			−0.134331	+	0.990936i	$0.542889\pi$
$798$	−8.63595e6	−	1.36993e7i	−0.480068	−	0.761535i
$799$	4.01753e6			0.222634
$800$		0			0
$801$	−2.14899e7			−1.18346
$802$	−5.23096e6	−	8.29790e6i	−0.287174	−	0.455546i
$803$	−1.07234e7			−0.586870
$804$	−4.38230e6	+	9.16886e6i	−0.239090	+	0.500236i
$805$		0			0
$806$	−1.68145e7	−	2.66729e7i	−0.911686	−	1.44621i
$807$		−	1.64487e7i		−	0.889095i
$808$	882326.	+	7.53194e6i	0.0475445	+	0.405862i
$809$	267715.			0.0143814			0.00719072	−	0.999974i	$-0.497711\pi$
$809$	267715.			0.0143814			0.00719072	+	0.999974i	$0.497711\pi$
$810$		0			0
$811$		−	1.10232e7i		−	0.588514i	−0.955726	−	0.294257i	$-0.904928\pi$
$811$		−	1.10232e7i		−	0.588514i	0.955726	−	0.294257i	$-0.0950722\pi$
$812$	−1.32541e6	+	2.77308e6i	−0.0705440	+	0.147595i
$813$	4.02671e7			2.13660
$814$	1.52738e7	−	9.62851e6i	0.807951	−	0.509329i
$815$		0			0
$816$	3.80293e7	−	3.06952e7i	1.99937	−	1.61378i
$817$			3.60889e7i			1.89155i
$818$	−2.57499e6	−	4.08472e6i	−0.134553	−	0.213442i
$819$			1.64434e7i			0.856609i
$820$		0			0
$821$			7.52183e6i			0.389462i	0.980857	+	0.194731i	$0.0623834\pi$
$821$			7.52183e6i			0.389462i	−0.980857	+	0.194731i	$0.937617\pi$
$822$	−1.98654e7	+	1.25231e7i	−1.02546	+	0.646445i
$823$			2.86933e7i			1.47666i	0.674439	+	0.738331i	$0.264386\pi$
$823$			2.86933e7i			1.47666i	−0.674439	+	0.738331i	$0.735614\pi$
$824$	2.49278e6	+	2.12796e7i	0.127899	+	1.09180i
$825$		0			0
$826$	−456888.	−	724764.i	−0.0233002	−	0.0369613i
$827$	−1.90830e7			−0.970248			−0.485124	−	0.874445i	$-0.661226\pi$
$827$	−1.90830e7			−0.970248			−0.485124	+	0.874445i	$0.661226\pi$
$828$	2.99733e7	+	1.43259e7i	1.51935	+	0.726182i
$829$			2.31916e7i			1.17205i	0.810295	+	0.586023i	$0.199307\pi$
$829$			2.31916e7i			1.17205i	−0.810295	+	0.586023i	$0.800693\pi$
$830$		0			0
$831$	−4.13245e7			−2.07589
$832$	−2.29743e7	+	5.45752e6i	−1.15063	+	0.273330i
$833$		−	2.55486e7i		−	1.27572i
$834$	911666.	−	574710.i	0.0453859	−	0.0286111i
$835$		0			0
$836$	−7.17617e6	+	1.50143e7i	−0.355122	+	0.743002i
$837$	3.16541e7			1.56177
$838$	−1.85147e7	+	1.16716e7i	−0.910766	+	0.574143i
$839$	887580.			0.0435314			0.0217657	−	0.999763i	$-0.493071\pi$
$839$	887580.			0.0435314			0.0217657	+	0.999763i	$0.493071\pi$
$840$		0			0
$841$	1.76206e7			0.859075
$842$	−5.50382e6	+	3.46958e6i	−0.267537	+	0.168654i
$843$	3.77382e7			1.82899
$844$	−1.15840e7	−	5.53663e6i	−0.559760	−	0.267540i
$845$		0			0
$846$	4.13825e6	−	2.60873e6i	0.198788	−	0.125315i
$847$		−	5.24942e6i		−	0.251422i
$848$	1.03271e6	+	1.27947e6i	0.0493163	+	0.0610997i
$849$	3.00746e7			1.43196
$850$		0			0
$851$		−	3.14299e7i		−	1.48771i
$852$	2.87429e6	−	6.01373e6i	0.135654	−	0.283821i
$853$	−1.39449e7			−0.656208			−0.328104	−	0.944642i	$-0.606410\pi$
$853$	−1.39449e7			−0.656208			−0.328104	+	0.944642i	$0.606410\pi$
$854$	7.58758e6	+	1.20362e7i	0.356007	+	0.564736i
$855$		0			0
$856$	−2.66050e7	+	3.11663e6i	−1.24102	+	0.145379i
$857$		−	3.58423e7i		−	1.66703i	−0.552495	−	0.833516i	$-0.686324\pi$
$857$		−	3.58423e7i		−	1.66703i	0.552495	−	0.833516i	$-0.313676\pi$
$858$	2.28939e7	−	1.44322e7i	1.06170	−	0.669290i
$859$		−	767053.i		−	0.0354685i	−0.999843	−	0.0177342i	$-0.994355\pi$
$859$		−	767053.i		−	0.0354685i	0.999843	−	0.0177342i	$-0.00564528\pi$
$860$		0			0
$861$			2.15236e7i			0.989478i
$862$	9.32387e6	+	1.47905e7i	0.427394	+	0.677977i
$863$			2.90420e7i			1.32739i	0.748002	+	0.663697i	$0.231013\pi$
$863$			2.90420e7i			1.32739i	−0.748002	+	0.663697i	$0.768987\pi$
$864$	7.66488e6	−	2.24329e7i	0.349318	−	1.02235i
$865$		0			0
$866$	−1.18625e7	+	7.47809e6i	−0.537506	+	0.338841i
$867$	5.34421e7			2.41455
$868$	−1.26158e7	−	6.02980e6i	−0.568351	−	0.271646i
$869$		−	1.20919e7i		−	0.543183i
$870$		0			0
$871$	8.99778e6			0.401874
$872$	2.66508e6	+	2.27503e7i	0.118691	+	1.01320i
$873$		−	1.58378e7i		−	0.703330i
$874$	1.54480e7	+	2.45052e7i	0.684059	+	1.08513i
$875$		0			0
$876$	3.01684e7	+	1.44191e7i	1.32829	+	0.634861i
$877$	9.62715e6			0.422667			0.211334	−	0.977414i	$-0.432219\pi$
$877$	9.62715e6			0.422667			0.211334	+	0.977414i	$0.432219\pi$
$878$	3.00810e6	+	4.77177e6i	0.131691	+	0.208902i
$879$	−2.25852e7			−0.985942
$880$		0			0
$881$	3.88627e7			1.68691			0.843457	−	0.537196i	$-0.180517\pi$
$881$	3.88627e7			1.68691			0.843457	+	0.537196i	$0.180517\pi$
$882$	−1.65897e7	−	2.63163e7i	−0.718070	−	1.13908i
$883$	4.29023e6			0.185173			0.0925867	−	0.995705i	$-0.470486\pi$
$883$	4.29023e6			0.185173			0.0925867	+	0.995705i	$0.470486\pi$
$884$	−3.90410e7	−	1.86599e7i	−1.68031	−	0.803115i
$885$		0			0
$886$	6.36416e6	+	1.00955e7i	0.272368	+	0.432059i
$887$		−	1.30883e7i		−	0.558564i	−0.960209	−	0.279282i	$-0.909904\pi$
$887$		−	1.30883e7i		−	0.558564i	0.960209	−	0.279282i	$-0.0900964\pi$
$888$	−5.59171e7	+	6.55039e6i	−2.37965	+	0.278763i
$889$	1.34356e7			0.570170
$890$		0			0
$891$			1.55070e6i			0.0654386i
$892$	−1.37331e7	−	6.56380e6i	−0.577905	−	0.276212i
$893$	4.26564e6			0.179001
$894$	−4.32606e6	+	2.72713e6i	−0.181029	+	0.114120i
$895$		0			0
$896$	−7.32812e6	+	7.48062e6i	−0.304946	+	0.311292i
$897$		−	4.71103e7i		−	1.95495i
$898$	1.88531e7	+	2.99068e7i	0.780174	+	1.23760i
$899$		−	1.31502e7i		−	0.542665i
$900$		0			0
$901$			3.01301e6i			0.123649i
$902$	1.87102e7	−	1.17949e7i	0.765708	−	0.482699i
$903$		−	2.60276e7i		−	1.06222i
$904$	4.67349e6	+	3.98951e7i	0.190204	+	1.62367i
$905$		0			0
$906$	4.21846e7	+	6.69178e7i	1.70739	+	2.70845i
$907$	2.36895e7			0.956175			0.478087	−	0.878312i	$-0.341330\pi$
$907$	2.36895e7			0.956175			0.478087	+	0.878312i	$0.341330\pi$
$908$	394096.	−	824547.i	0.0158631	−	0.0331895i
$909$			1.69208e7i			0.679220i
$910$		0			0
$911$	1.27323e7			0.508289			0.254144	−	0.967166i	$-0.418206\pi$
$911$	1.27323e7			0.508289			0.254144	+	0.967166i	$0.418206\pi$
$912$	4.03779e7	−	3.25909e7i	1.60752	−	1.29750i
$913$		−	1.60932e7i		−	0.638948i
$914$	8.98062e6	−	5.66135e6i	0.355583	−	0.224158i
$915$		0			0
$916$	−2.79980e7	−	1.33818e7i	−1.10252	−	0.526957i
$917$	−8.54258e6			−0.335479
$918$	3.67484e7	−	2.31660e7i	1.43923	−	0.907286i
$919$	−3.36064e7			−1.31260			−0.656302	−	0.754499i	$-0.727880\pi$
$919$	−3.36064e7			−1.31260			−0.656302	+	0.754499i	$0.727880\pi$
$920$		0			0
$921$	−3.75640e7			−1.45923
$922$	4.09042e7	−	2.57858e7i	1.58467	−	0.998972i
$923$	−5.90152e6			−0.228013
$924$	5.17551e6	−	1.08284e7i	0.199422	−	0.417240i
$925$		0			0
$926$	3.61711e7	−	2.28021e7i	1.38623	−	0.873871i
$927$			4.78053e7i			1.82716i
$928$	−9.31938e6	−	3.18425e6i	−0.355236	−	0.121377i
$929$	−2.44326e7			−0.928816			−0.464408	−	0.885621i	$-0.653733\pi$
$929$	−2.44326e7			−0.928816			−0.464408	+	0.885621i	$0.653733\pi$
$930$		0			0
$931$		−	2.71265e7i		−	1.02570i
$932$	−462112.	−	220869.i	−0.0174264	−	0.00832904i
$933$	−9.27134e6			−0.348689
$934$	−9.92867e6	−	1.57499e7i	−0.372412	−	0.590760i
$935$		0			0
$936$	−5.23307e7	+	6.13026e6i	−1.95239	+	0.228712i
$937$		−	2.46226e7i		−	0.916188i	−0.888904	−	0.458094i	$-0.848532\pi$
$937$		−	2.46226e7i		−	0.916188i	0.888904	−	0.458094i	$-0.151468\pi$
$938$	3.37550e6	−	2.12790e6i	0.125265	−	0.0789667i
$939$			8.24698e6i			0.305233i
$940$		0			0
$941$			3.64578e7i			1.34220i	0.741368	+	0.671098i	$0.234177\pi$
$941$			3.64578e7i			1.34220i	−0.741368	+	0.671098i	$0.765823\pi$
$942$	−1.93674e7	−	3.07226e7i	−0.711122	−	1.12806i
$943$		−	3.85013e7i		−	1.40993i
$944$	2.13621e6	−	1.72423e6i	0.0780214	−	0.0629746i
$945$		0			0
$946$	−2.26255e7	+	1.42630e7i	−0.821999	+	0.518184i
$947$	−1.49302e7			−0.540992			−0.270496	−	0.962721i	$-0.587188\pi$
$947$	−1.49302e7			−0.540992			−0.270496	+	0.962721i	$0.587188\pi$
$948$	−1.62594e7	+	3.40186e7i	−0.587602	+	1.22941i
$949$		−	2.96055e7i		−	1.06710i
$950$		0			0
$951$	3.95935e7			1.41962
$952$	−1.90591e7	+	2.23267e6i	−0.681568	+	0.0798420i
$953$		−	2.82853e7i		−	1.00885i	−0.863455	−	0.504426i	$-0.831704\pi$
$953$		−	2.82853e7i		−	1.00885i	0.863455	−	0.504426i	$-0.168296\pi$
$954$	1.95647e6	+	3.10355e6i	0.0695987	+	0.110405i
$955$		0			0
$956$	1.74698e7	−	3.65510e7i	0.618219	−	1.29347i
$957$	1.12871e7			0.398383
$958$	1.49509e7	+	2.37168e7i	0.526326	+	0.834914i
$959$	9.22071e6			0.323756
$960$		0			0
$961$	3.11960e7			1.08966
$962$	2.65828e7	+	4.21684e7i	0.926110	+	1.46909i
$963$	−5.97691e7			−2.07688
$964$	−5.72109e6	+	1.19699e7i	−0.198283	+	0.414857i
$965$		0			0
$966$	−1.11412e7	−	1.76733e7i	−0.384140	−	0.609363i
$967$			3.47503e7i			1.19507i	0.801844	+	0.597533i	$0.203852\pi$
$967$			3.47503e7i			1.19507i	−0.801844	+	0.597533i	$0.796148\pi$
$968$	1.67061e7	−	1.95703e6i	0.573043	−	0.0671288i
$969$	9.50860e7			3.25317
$970$		0			0
$971$			4.65499e7i			1.58442i	0.610247	+	0.792211i	$0.291070\pi$
$971$			4.65499e7i			1.58442i	−0.610247	+	0.792211i	$0.708930\pi$
$972$	−1.16380e7	+	2.43496e7i	−0.395106	+	0.826658i
$973$	−423158.			−0.0143291
$974$	−3.62224e7	+	2.28345e7i	−1.22343	+	0.771247i
$975$		0			0
$976$	−3.54762e7	+	2.86344e7i	−1.19210	+	0.962198i
$977$			4.15712e7i			1.39334i	0.717394	+	0.696668i	$0.245335\pi$
$977$			4.15712e7i			1.39334i	−0.717394	+	0.696668i	$0.754665\pi$
$978$	2.94031e7	+	4.66424e7i	0.982984	+	1.55931i
$979$		−	1.38876e7i		−	0.463096i
$980$		0			0
$981$			5.11094e7i			1.69562i
$982$	−5.98243e6	+	3.77130e6i	−0.197970	+	0.124799i
$983$			2.55186e7i			0.842313i	0.906988	+	0.421157i	$0.138376\pi$
$983$			2.55186e7i			0.842313i	−0.906988	+	0.421157i	$0.861624\pi$
$984$	−6.84981e7	+	8.02417e6i	−2.25523	+	0.264188i
$985$		0			0
$986$	−9.62393e6	−	1.52665e7i	−0.315254	−	0.500089i
$987$	−3.07641e6			−0.100520
$988$	−4.14521e7	−	1.98123e7i	−1.35100	−	0.645716i
$989$			4.65581e7i			1.51358i
$990$		0			0
$991$	−3.10296e7			−1.00367			−0.501836	−	0.864963i	$-0.667342\pi$
$991$	−3.10296e7			−1.00367			−0.501836	+	0.864963i	$0.667342\pi$
$992$	1.44864e7	−	4.23975e7i	0.467391	−	1.36792i
$993$		−	1.42119e7i		−	0.457382i
$994$	−2.21395e6	+	1.39566e6i	−0.0710724	+	0.0448037i
$995$		0			0
$996$	−2.16397e7	+	4.52756e7i	−0.691198	+	1.44616i
$997$	−1.66036e7			−0.529011			−0.264505	−	0.964384i	$-0.585209\pi$
$997$	−1.66036e7			−0.529011			−0.264505	+	0.964384i	$0.585209\pi$
$998$	2.67643e7	−	1.68721e7i	0.850607	−	0.536219i
$999$	−5.00435e7			−1.58648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.c.149.7		20
4.3	odd	2		800.6.f.b.49.20		20
5.2	odd	4		200.6.d.b.101.17		20
5.3	odd	4		40.6.d.a.21.4	yes	20
5.4	even	2		200.6.f.b.149.14		20
8.3	odd	2		800.6.f.c.49.2		20
8.5	even	2		200.6.f.b.149.13		20
15.8	even	4		360.6.k.b.181.17		20
20.3	even	4		160.6.d.a.81.19		20
20.7	even	4		800.6.d.c.401.2		20
20.19	odd	2		800.6.f.c.49.1		20
40.3	even	4		160.6.d.a.81.2		20
40.13	odd	4		40.6.d.a.21.3	✓	20
40.19	odd	2		800.6.f.b.49.19		20
40.27	even	4		800.6.d.c.401.19		20
40.29	even	2	inner	200.6.f.c.149.8		20
40.37	odd	4		200.6.d.b.101.18		20
120.53	even	4		360.6.k.b.181.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.3	✓	20	40.13	odd	4
40.6.d.a.21.4	yes	20	5.3	odd	4
160.6.d.a.81.2		20	40.3	even	4
160.6.d.a.81.19		20	20.3	even	4
200.6.d.b.101.17		20	5.2	odd	4
200.6.d.b.101.18		20	40.37	odd	4
200.6.f.b.149.13		20	8.5	even	2
200.6.f.b.149.14		20	5.4	even	2
200.6.f.c.149.7		20	1.1	even	1	trivial
200.6.f.c.149.8		20	40.29	even	2	inner
360.6.k.b.181.17		20	15.8	even	4
360.6.k.b.181.18		20	120.53	even	4
800.6.d.c.401.2		20	20.7	even	4
800.6.d.c.401.19		20	40.27	even	4
800.6.f.b.49.19		20	40.19	odd	2
800.6.f.b.49.20		20	4.3	odd	2
800.6.f.c.49.1		20	20.19	odd	2
800.6.f.c.49.2		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.01667 - 4.78536i) q^{2} -25.4343 q^{3} +(-13.7994 + 28.8717i) q^{4} +(76.7270 + 121.712i) q^{6} -56.4938i q^{7} +(179.790 - 21.0614i) q^{8} +403.904 q^{9} +O(q^{10})\)	\(q+(-3.01667 - 4.78536i) q^{2} -25.4343 q^{3} +(-13.7994 + 28.8717i) q^{4} +(76.7270 + 121.712i) q^{6} -56.4938i q^{7} +(179.790 - 21.0614i) q^{8} +403.904 q^{9} +261.019i q^{11} +(350.978 - 734.333i) q^{12} -720.631 q^{13} +(-270.343 + 170.423i) q^{14} +(-643.154 - 796.825i) q^{16} -1876.44i q^{17} +(-1218.45 - 1932.83i) q^{18} -1992.33i q^{19} +1436.88i q^{21} +(1249.07 - 787.408i) q^{22} -2570.29i q^{23} +(-4572.83 + 535.682i) q^{24} +(2173.91 + 3448.48i) q^{26} -4092.49 q^{27} +(1631.07 + 779.581i) q^{28} +1700.16i q^{29} -7734.68 q^{31} +(-1872.91 + 5481.48i) q^{32} -6638.83i q^{33} +(-8979.46 + 5660.61i) q^{34} +(-5573.63 + 11661.4i) q^{36} +12228.1 q^{37} +(-9534.02 + 6010.20i) q^{38} +18328.8 q^{39} +14979.3 q^{41} +(6876.00 - 4334.60i) q^{42} -18113.9 q^{43} +(-7536.06 - 3601.90i) q^{44} +(-12299.8 + 7753.73i) q^{46} +2141.03i q^{47} +(16358.2 + 20266.7i) q^{48} +13615.4 q^{49} +47726.0i q^{51} +(9944.27 - 20805.9i) q^{52} -1605.71 q^{53} +(12345.7 + 19584.1i) q^{54} +(-1189.84 - 10157.0i) q^{56} +50673.5i q^{57} +(8135.87 - 5128.81i) q^{58} +2680.90i q^{59} -44521.9i q^{61} +(23333.0 + 37013.2i) q^{62} -22818.1i q^{63} +(31880.8 - 7573.26i) q^{64} +(-31769.2 + 20027.2i) q^{66} -12486.0 q^{67} +(54176.2 + 25893.8i) q^{68} +65373.7i q^{69} +8189.38 q^{71} +(72617.9 - 8506.79i) q^{72} +41082.7i q^{73} +(-36888.2 - 58516.0i) q^{74} +(57522.0 + 27492.9i) q^{76} +14746.0 q^{77} +(-55291.8 - 87709.7i) q^{78} -46325.9 q^{79} +5940.95 q^{81} +(-45187.8 - 71681.6i) q^{82} -61655.4 q^{83} +(-41485.3 - 19828.1i) q^{84} +(54643.7 + 86681.7i) q^{86} -43242.3i q^{87} +(5497.42 + 46928.5i) q^{88} -53205.4 q^{89} +40711.2i q^{91} +(74208.8 + 35468.5i) q^{92} +196726. q^{93} +(10245.6 - 6458.79i) q^{94} +(47636.2 - 139418. i) q^{96} -39211.8i q^{97} +(-41073.3 - 65154.8i) q^{98} +105427. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28} + 7160 q^{31} + 14792 q^{32} - 21132 q^{34} + 18344 q^{36} - 3608 q^{37} - 16884 q^{38} + 44904 q^{39} + 11608 q^{41} - 49444 q^{42} - 51772 q^{43} - 72296 q^{44} - 28516 q^{46} - 85048 q^{48} - 18756 q^{49} - 111624 q^{52} + 928 q^{53} + 100584 q^{54} - 53624 q^{56} + 152344 q^{58} + 228648 q^{62} + 11264 q^{64} - 56688 q^{66} - 161604 q^{67} + 359040 q^{68} - 200312 q^{71} + 563448 q^{72} - 78876 q^{74} - 153872 q^{76} + 26008 q^{77} - 624640 q^{78} - 282080 q^{79} + 65172 q^{81} - 410576 q^{82} - 99092 q^{83} + 297128 q^{84} + 27452 q^{86} - 464496 q^{88} + 3160 q^{89} - 519244 q^{92} + 293472 q^{93} - 148820 q^{94} + 395168 q^{96} + 663674 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

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