LMFDB - Embedded newform 230.6.b.a.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.b (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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.3
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -17.9630i q^{3} -16.0000 q^{4} +(-33.0651 + 45.0744i) q^{5} -71.8519 q^{6} +13.4457i q^{7} +64.0000i q^{8} -79.6687 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -17.9630i q^{3} -16.0000 q^{4} +(-33.0651 + 45.0744i) q^{5} -71.8519 q^{6} +13.4457i q^{7} +64.0000i q^{8} -79.6687 q^{9} +(180.297 + 132.260i) q^{10} +554.717 q^{11} +287.408i q^{12} -117.992i q^{13} +53.7828 q^{14} +(809.670 + 593.948i) q^{15} +256.000 q^{16} +288.229i q^{17} +318.675i q^{18} +515.720 q^{19} +(529.042 - 721.190i) q^{20} +241.525 q^{21} -2218.87i q^{22} -529.000i q^{23} +1149.63 q^{24} +(-938.396 - 2980.78i) q^{25} -471.968 q^{26} -2933.92i q^{27} -215.131i q^{28} +8067.93 q^{29} +(2375.79 - 3238.68i) q^{30} -6691.55 q^{31} -1024.00i q^{32} -9964.37i q^{33} +1152.91 q^{34} +(-606.056 - 444.583i) q^{35} +1274.70 q^{36} -3918.67i q^{37} -2062.88i q^{38} -2119.49 q^{39} +(-2884.76 - 2116.17i) q^{40} +4434.88 q^{41} -966.099i q^{42} +14328.1i q^{43} -8875.47 q^{44} +(2634.25 - 3591.02i) q^{45} -2116.00 q^{46} -21285.5i q^{47} -4598.52i q^{48} +16626.2 q^{49} +(-11923.1 + 3753.58i) q^{50} +5177.44 q^{51} +1887.87i q^{52} +5760.59i q^{53} -11735.7 q^{54} +(-18341.8 + 25003.5i) q^{55} -860.524 q^{56} -9263.86i q^{57} -32271.7i q^{58} -48625.6 q^{59} +(-12954.7 - 9503.17i) q^{60} -2624.64 q^{61} +26766.2i q^{62} -1071.20i q^{63} -4096.00 q^{64} +(5318.42 + 3901.42i) q^{65} -39857.5 q^{66} -1384.02i q^{67} -4611.66i q^{68} -9502.42 q^{69} +(-1778.33 + 2424.22i) q^{70} +40118.8 q^{71} -5098.80i q^{72} -30189.0i q^{73} -15674.7 q^{74} +(-53543.7 + 16856.4i) q^{75} -8251.51 q^{76} +7458.55i q^{77} +8477.95i q^{78} +33289.3 q^{79} +(-8464.67 + 11539.0i) q^{80} -72061.4 q^{81} -17739.5i q^{82} -69040.5i q^{83} -3864.40 q^{84} +(-12991.7 - 9530.31i) q^{85} +57312.3 q^{86} -144924. i q^{87} +35501.9i q^{88} +100052. q^{89} +(-14364.1 - 10537.0i) q^{90} +1586.48 q^{91} +8464.00i q^{92} +120200. i q^{93} -85142.1 q^{94} +(-17052.3 + 23245.7i) q^{95} -18394.1 q^{96} -104025. i q^{97} -66504.9i q^{98} -44193.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	17.9630i		−	1.15233i	−0.817335	−	0.576163i	$-0.804549\pi$
$3$		−	17.9630i		−	1.15233i	0.817335	−	0.576163i	$-0.195451\pi$
$4$	−16.0000			−0.500000
$5$	−33.0651	+	45.0744i	−0.591487	+	0.806315i
$5$	−33.0651	+	45.0744i	−0.591487	+	0.806315i
$6$	−71.8519			−0.814817
$7$			13.4457i			0.103714i	0.998655	+	0.0518571i	$0.0165140\pi$
$7$			13.4457i			0.103714i	−0.998655	+	0.0518571i	$0.983486\pi$
$8$			64.0000i			0.353553i
$9$	−79.6687			−0.327855
$10$	180.297	+	132.260i	0.570151	+	0.418244i
$11$	554.717			1.38226			0.691130	−	0.722730i	$-0.257113\pi$
$11$	554.717			1.38226			0.691130	+	0.722730i	$0.257113\pi$
$12$			287.408i			0.576163i
$13$		−	117.992i		−	0.193640i	−0.995302	−	0.0968198i	$-0.969133\pi$
$13$		−	117.992i		−	0.193640i	0.995302	−	0.0968198i	$-0.0308671\pi$
$14$	53.7828			0.0733370
$15$	809.670	+	593.948i	0.929137	+	0.681585i
$16$	256.000			0.250000
$17$			288.229i			0.241888i	0.992659	+	0.120944i	$0.0385922\pi$
$17$			288.229i			0.241888i	−0.992659	+	0.120944i	$0.961408\pi$
$18$			318.675i			0.231828i
$19$	515.720			0.327740			0.163870	−	0.986482i	$-0.447602\pi$
$19$	515.720			0.327740			0.163870	+	0.986482i	$0.447602\pi$
$20$	529.042	−	721.190i	0.295743	−	0.403157i
$21$	241.525			0.119513
$22$		−	2218.87i		−	0.977405i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	1149.63			0.407409
$25$	−938.396	−	2980.78i	−0.300287	−	0.953849i
$26$	−471.968			−0.136924
$27$		−	2933.92i		−	0.774530i
$28$		−	215.131i		−	0.0518571i
$29$	8067.93			1.78142			0.890712	−	0.454568i	$-0.150206\pi$
$29$	8067.93			1.78142			0.890712	+	0.454568i	$0.150206\pi$
$30$	2375.79	−	3238.68i	0.481954	−	0.656999i
$31$	−6691.55			−1.25061			−0.625306	−	0.780379i	$-0.715026\pi$
$31$	−6691.55			−1.25061			−0.625306	+	0.780379i	$0.715026\pi$
$32$		−	1024.00i		−	0.176777i
$33$		−	9964.37i		−	1.59281i
$34$	1152.91			0.171041
$35$	−606.056	−	444.583i	−0.0836263	−	0.0613456i
$36$	1274.70			0.163927
$37$		−	3918.67i		−	0.470581i	−0.971925	−	0.235290i	$-0.924396\pi$
$37$		−	3918.67i		−	0.470581i	0.971925	−	0.235290i	$-0.0756041\pi$
$38$		−	2062.88i		−	0.231747i
$39$	−2119.49			−0.223136
$40$	−2884.76	−	2116.17i	−0.285075	−	0.209122i
$41$	4434.88			0.412024			0.206012	−	0.978549i	$-0.433951\pi$
$41$	4434.88			0.412024			0.206012	+	0.978549i	$0.433951\pi$
$42$		−	966.099i		−	0.0845081i
$43$			14328.1i			1.18173i	0.806772	+	0.590863i	$0.201212\pi$
$43$			14328.1i			1.18173i	−0.806772	+	0.590863i	$0.798788\pi$
$44$	−8875.47			−0.691130
$45$	2634.25	−	3591.02i	0.193922	−	0.264354i
$46$	−2116.00			−0.147442
$47$		−	21285.5i		−	1.40553i	−0.711423	−	0.702765i	$-0.751949\pi$
$47$		−	21285.5i		−	1.40553i	0.711423	−	0.702765i	$-0.248051\pi$
$48$		−	4598.52i		−	0.288081i
$49$	16626.2			0.989243
$50$	−11923.1	+	3753.58i	−0.674473	+	0.212335i
$51$	5177.44			0.278734
$52$			1887.87i			0.0968198i
$53$			5760.59i			0.281694i	0.990031	+	0.140847i	$0.0449825\pi$
$53$			5760.59i			0.281694i	−0.990031	+	0.140847i	$0.955017\pi$
$54$	−11735.7			−0.547676
$55$	−18341.8	+	25003.5i	−0.817589	+	1.11454i
$56$	−860.524			−0.0366685
$57$		−	9263.86i		−	0.377663i
$58$		−	32271.7i		−	1.25966i
$59$	−48625.6			−1.81859			−0.909295	−	0.416152i	$-0.863379\pi$
$59$	−48625.6			−1.81859			−0.909295	+	0.416152i	$0.863379\pi$
$60$	−12954.7	−	9503.17i	−0.464569	−	0.340793i
$61$	−2624.64			−0.0903119			−0.0451560	−	0.998980i	$-0.514378\pi$
$61$	−2624.64			−0.0903119			−0.0451560	+	0.998980i	$0.514378\pi$
$62$			26766.2i			0.884317i
$63$		−	1071.20i		−	0.0340032i
$64$	−4096.00			−0.125000
$65$	5318.42	+	3901.42i	0.156134	+	0.114535i
$66$	−39857.5			−1.12629
$67$		−	1384.02i		−	0.0376664i	−0.999823	−	0.0188332i	$-0.994005\pi$
$67$		−	1384.02i		−	0.0376664i	0.999823	−	0.0188332i	$-0.00599514\pi$
$68$		−	4611.66i		−	0.120944i
$69$	−9502.42			−0.240277
$70$	−1778.33	+	2424.22i	−0.0433779	+	0.0591327i
$71$	40118.8			0.944500			0.472250	−	0.881465i	$-0.343442\pi$
$71$	40118.8			0.944500			0.472250	+	0.881465i	$0.343442\pi$
$72$		−	5098.80i		−	0.115914i
$73$		−	30189.0i		−	0.663043i	−0.943448	−	0.331522i	$-0.892438\pi$
$73$		−	30189.0i		−	0.663043i	0.943448	−	0.331522i	$-0.107562\pi$
$74$	−15674.7			−0.332751
$75$	−53543.7	+	16856.4i	−1.09914	+	0.346028i
$76$	−8251.51			−0.163870
$77$			7458.55i			0.143360i
$78$			8477.95i			0.157781i
$79$	33289.3			0.600119			0.300060	−	0.953920i	$-0.402993\pi$
$79$	33289.3			0.600119			0.300060	+	0.953920i	$0.402993\pi$
$80$	−8464.67	+	11539.0i	−0.147872	+	0.201579i
$81$	−72061.4			−1.22037
$82$		−	17739.5i		−	0.291345i
$83$		−	69040.5i		−	1.10004i	−0.835151	−	0.550020i	$-0.814620\pi$
$83$		−	69040.5i		−	1.10004i	0.835151	−	0.550020i	$-0.185380\pi$
$84$	−3864.40			−0.0597563
$85$	−12991.7	−	9530.31i	−0.195038	−	0.143074i
$86$	57312.3			0.835606
$87$		−	144924.i		−	2.05278i
$88$			35501.9i			0.488703i
$89$	100052.			1.33891			0.669457	−	0.742851i	$-0.266527\pi$
$89$	100052.			1.33891			0.669457	+	0.742851i	$0.266527\pi$
$90$	−14364.1	−	10537.0i	−0.186927	−	0.137123i
$91$	1586.48			0.0200832
$92$			8464.00i			0.104257i
$93$			120200.i			1.44111i
$94$	−85142.1			−0.993859
$95$	−17052.3	+	23245.7i	−0.193854	+	0.264262i
$96$	−18394.1			−0.203704
$97$		−	104025.i		−	1.12256i	−0.827625	−	0.561281i	$-0.810309\pi$
$97$		−	104025.i		−	1.12256i	0.827625	−	0.561281i	$-0.189691\pi$
$98$		−	66504.9i		−	0.699501i
$99$	−44193.6			−0.453180
$100$	15014.3	+	47692.4i	0.150143	+	0.476924i
$101$	43359.0			0.422937			0.211468	−	0.977385i	$-0.432175\pi$
$101$	43359.0			0.422937			0.211468	+	0.977385i	$0.432175\pi$
$102$		−	20709.8i		−	0.197095i
$103$		−	148963.i		−	1.38352i	−0.722126	−	0.691761i	$-0.756835\pi$
$103$		−	148963.i		−	1.38352i	0.722126	−	0.691761i	$-0.243165\pi$
$104$	7551.49			0.0684620
$105$	−7986.04	+	10886.6i	−0.0706901	+	0.0963647i
$106$	23042.3			0.199187
$107$		−	212921.i		−	1.79787i	−0.438079	−	0.898936i	$-0.644341\pi$
$107$		−	212921.i		−	1.79787i	0.438079	−	0.898936i	$-0.355659\pi$
$108$			46942.7i			0.387265i
$109$	−11660.6			−0.0940060			−0.0470030	−	0.998895i	$-0.514967\pi$
$109$	−11660.6			−0.0940060			−0.0470030	+	0.998895i	$0.514967\pi$
$110$	100014.	+	73367.1i	0.788096	+	0.578122i
$111$	−70390.9			−0.542262
$112$			3442.10i			0.0259285i
$113$		−	75504.3i		−	0.556257i	−0.960544	−	0.278128i	$-0.910286\pi$
$113$		−	75504.3i		−	0.556257i	0.960544	−	0.278128i	$-0.0897141\pi$
$114$	−37055.5			−0.267048
$115$	23844.3	+	17491.4i	0.168128	+	0.123334i
$116$	−129087.			−0.890712
$117$			9400.27i			0.0634857i
$118$			194502.i			1.28594i
$119$	−3875.43			−0.0250872
$120$	−38012.7	+	51818.9i	−0.240977	+	0.328500i
$121$	146660.			0.910643
$122$			10498.6i			0.0638602i
$123$		−	79663.7i		−	0.474786i
$124$	107065.			0.625306
$125$	165385.	+	56262.2i	0.946718	+	0.322064i
$126$	−4284.80			−0.0240439
$127$			180177.i			0.991266i	0.868532	+	0.495633i	$0.165064\pi$
$127$			180177.i			0.991266i	−0.868532	+	0.495633i	$0.834936\pi$
$128$			16384.0i			0.0883883i
$129$	257375.			1.36173
$130$	15605.7	−	21273.7i	0.0809887	−	0.110404i
$131$	−294975.			−1.50178			−0.750891	−	0.660427i	$-0.770376\pi$
$131$	−294975.			−1.50178			−0.750891	+	0.660427i	$0.770376\pi$
$132$			159430.i			0.796407i
$133$			6934.21i			0.0339913i
$134$	−5536.06			−0.0266341
$135$	132244.	+	97010.3i	0.624515	+	0.458124i
$136$	−18446.6			−0.0855204
$137$			35039.1i			0.159496i	0.996815	+	0.0797482i	$0.0254116\pi$
$137$			35039.1i			0.159496i	−0.996815	+	0.0797482i	$0.974588\pi$
$138$			38009.7i			0.169901i
$139$	139847.			0.613925			0.306963	−	0.951722i	$-0.400687\pi$
$139$	139847.			0.613925			0.306963	+	0.951722i	$0.400687\pi$
$140$	9696.90	+	7113.34i	0.0418131	+	0.0306728i
$141$	−382352.			−1.61963
$142$		−	160475.i		−	0.667862i
$143$		−	65452.2i		−	0.267660i
$144$	−20395.2			−0.0819637
$145$	−266767.	+	363657.i	−1.05369	+	1.43639i
$146$	−120756.			−0.468842
$147$		−	298656.i		−	1.13993i
$148$			62698.7i			0.235290i
$149$	158567.			0.585122			0.292561	−	0.956247i	$-0.405492\pi$
$149$	158567.			0.585122			0.292561	+	0.956247i	$0.405492\pi$
$150$	67425.6	+	214175.i	0.244679	+	0.777213i
$151$	−8880.93			−0.0316968			−0.0158484	−	0.999874i	$-0.505045\pi$
$151$	−8880.93			−0.0316968			−0.0158484	+	0.999874i	$0.505045\pi$
$152$			33006.1i			0.115874i
$153$		−	22962.8i		−	0.0793042i
$154$	29834.2			0.101371
$155$	221257.	−	301618.i	0.739721	−	1.00839i
$156$	33911.8			0.111568
$157$		−	247148.i		−	0.800218i	−0.916468	−	0.400109i	$-0.868972\pi$
$157$		−	247148.i		−	0.800218i	0.916468	−	0.400109i	$-0.131028\pi$
$158$		−	133157.i		−	0.424348i
$159$	103477.			0.324603
$160$	46156.1	+	33858.7i	0.142538	+	0.104561i
$161$	7112.77			0.0216259
$162$			288246.i			0.862929i
$163$			259492.i			0.764989i	0.923958	+	0.382494i	$0.124935\pi$
$163$			259492.i			0.764989i	−0.923958	+	0.382494i	$0.875065\pi$
$164$	−70958.1			−0.206012
$165$	449138.	+	329473.i	1.28431	+	0.942128i
$166$	−276162.			−0.777846
$167$			92473.6i			0.256582i	0.991737	+	0.128291i	$0.0409492\pi$
$167$			92473.6i			0.256582i	−0.991737	+	0.128291i	$0.959051\pi$
$168$			15457.6i			0.0422541i
$169$	357371.			0.962504
$170$	−38121.3	+	51966.9i	−0.101168	+	0.137913i
$171$	−41086.7			−0.107451
$172$		−	229249.i		−	0.590863i
$173$		−	141323.i		−	0.359002i	−0.983758	−	0.179501i	$-0.942552\pi$
$173$		−	141323.i		−	0.359002i	0.983758	−	0.179501i	$-0.0574483\pi$
$174$	−579697.			−1.45154
$175$	40078.6	−	12617.4i	0.0989277	−	0.0311440i
$176$	142008.			0.345565
$177$			873461.i			2.09561i
$178$		−	400210.i		−	0.946755i
$179$	426547.			0.995026			0.497513	−	0.867456i	$-0.334247\pi$
$179$	426547.			0.995026			0.497513	+	0.867456i	$0.334247\pi$
$180$	−42148.1	+	57456.2i	−0.0969609	+	0.132177i
$181$	814323.			1.84757			0.923783	−	0.382916i	$-0.125080\pi$
$181$	814323.			1.84757			0.923783	+	0.382916i	$0.125080\pi$
$182$		−	6345.94i		−	0.0142010i
$183$			47146.4i			0.104069i
$184$	33856.0			0.0737210
$185$	176631.	+	129571.i	0.379436	+	0.278342i
$186$	480801.			1.01902
$187$			159885.i			0.334352i
$188$			340568.i			0.702765i
$189$	39448.6			0.0803298
$190$	92982.9	+	68209.3i	0.186861	+	0.137075i
$191$	337131.			0.668676			0.334338	−	0.942453i	$-0.391487\pi$
$191$	337131.			0.668676			0.334338	+	0.942453i	$0.391487\pi$
$192$			73576.4i			0.144041i
$193$		−	71246.1i		−	0.137679i	−0.997628	−	0.0688395i	$-0.978070\pi$
$193$		−	71246.1i		−	0.137679i	0.997628	−	0.0688395i	$-0.0219296\pi$
$194$	−416102.			−0.793771
$195$	70081.1	−	95534.6i	0.131982	−	0.179918i
$196$	−266019.			−0.494622
$197$			486469.i			0.893079i	0.894764	+	0.446540i	$0.147344\pi$
$197$			486469.i			0.893079i	−0.894764	+	0.446540i	$0.852656\pi$
$198$			176774.i			0.320447i
$199$	870591.			1.55841			0.779205	−	0.626769i	$-0.215623\pi$
$199$	870591.			1.55841			0.779205	+	0.626769i	$0.215623\pi$
$200$	190770.	−	60057.3i	0.337237	−	0.106167i
$201$	−24861.0			−0.0434039
$202$		−	173436.i		−	0.299062i
$203$			108479.i			0.184759i
$204$	−82839.1			−0.139367
$205$	−146640.	+	199899.i	−0.243707	+	0.332221i
$206$	−595853.			−0.978298
$207$			42144.7i			0.0683624i
$208$		−	30206.0i		−	0.0484099i
$209$	286078.			0.453022
$210$	43546.3	+	31944.2i	0.0681401	+	0.0499854i
$211$	−966426.			−1.49439			−0.747193	−	0.664608i	$-0.768599\pi$
$211$	−966426.			−1.49439			−0.747193	+	0.664608i	$0.768599\pi$
$212$		−	92169.4i		−	0.140847i
$213$		−	720653.i		−	1.08837i
$214$	−851684.			−1.27129
$215$	−645829.	−	473759.i	−0.952842	−	0.698975i
$216$	187771.			0.273838
$217$		−	89972.6i		−	0.129706i
$218$			46642.5i			0.0664723i
$219$	−542285.			−0.764042
$220$	293469.	−	400056.i	0.408794	−	0.557268i
$221$	34008.7			0.0468392
$222$			281564.i			0.383437i
$223$		−	1.36254e6i		−	1.83479i	−0.397978	−	0.917395i	$-0.630288\pi$
$223$		−	1.36254e6i		−	1.83479i	0.397978	−	0.917395i	$-0.369712\pi$
$224$	13768.4			0.0183342
$225$	74760.8	+	237475.i	0.0984504	+	0.312724i
$226$	−302017.			−0.393333
$227$			693338.i			0.893059i	0.894769	+	0.446530i	$0.147340\pi$
$227$			693338.i			0.893059i	−0.894769	+	0.446530i	$0.852660\pi$
$228$			148222.i			0.188832i
$229$	590581.			0.744202			0.372101	−	0.928192i	$-0.378638\pi$
$229$	590581.			0.744202			0.372101	+	0.928192i	$0.378638\pi$
$230$	69965.8	−	95377.3i	0.0872100	−	0.118885i
$231$	133978.			0.165197
$232$			516348.i			0.629829i
$233$			446245.i			0.538497i	0.963071	+	0.269248i	$0.0867753\pi$
$233$			446245.i			0.538497i	−0.963071	+	0.269248i	$0.913225\pi$
$234$	37601.1			0.0448911
$235$	959432.	+	703809.i	1.13330	+	0.831352i
$236$	778010.			0.909295
$237$		−	597976.i		−	0.691533i
$238$			15501.7i			0.0177394i
$239$	−696255.			−0.788449			−0.394225	−	0.919014i	$-0.628987\pi$
$239$	−696255.			−0.788449			−0.394225	+	0.919014i	$0.628987\pi$
$240$	207275.	+	152051.i	0.232284	+	0.170396i
$241$	−360641.			−0.399975			−0.199987	−	0.979798i	$-0.564090\pi$
$241$	−360641.			−0.399975			−0.199987	+	0.979798i	$0.564090\pi$
$242$		−	586640.i		−	0.643922i
$243$			581496.i			0.631729i
$244$	41994.2			0.0451560
$245$	−549748.	+	749416.i	−0.585124	+	0.797641i
$246$	−318655.			−0.335724
$247$		−	60850.8i		−	0.0634635i
$248$		−	428260.i		−	0.442158i
$249$	−1.24017e6			−1.26760
$250$	225049.	−	661539.i	0.227733	−	0.669431i
$251$	−129143.			−0.129385			−0.0646927	−	0.997905i	$-0.520607\pi$
$251$	−129143.			−0.129385			−0.0646927	+	0.997905i	$0.520607\pi$
$252$			17139.2i			0.0170016i
$253$		−	293445.i		−	0.288221i
$254$	720708.			0.700931
$255$	−171193.	+	233370.i	−0.164868	+	0.224747i
$256$	65536.0			0.0625000
$257$			137421.i			0.129784i	0.997892	+	0.0648921i	$0.0206703\pi$
$257$			137421.i			0.129784i	−0.997892	+	0.0648921i	$0.979330\pi$
$258$		−	1.02950e6i		−	0.962890i
$259$	52689.2			0.0488059
$260$	−85094.6	−	62422.7i	−0.0780672	−	0.0572677i
$261$	−642762.			−0.584048
$262$			1.17990e6i			1.06192i
$263$			1.20091e6i			1.07059i	0.844666	+	0.535294i	$0.179799\pi$
$263$			1.20091e6i			1.07059i	−0.844666	+	0.535294i	$0.820201\pi$
$264$	637720.			0.563145
$265$	−259655.	−	190474.i	−0.227134	−	0.166618i
$266$	27736.8			0.0240355
$267$		−	1.79724e6i		−	1.54286i
$268$			22144.2i			0.0188332i
$269$	−728310.			−0.613671			−0.306836	−	0.951763i	$-0.599270\pi$
$269$	−728310.			−0.613671			−0.306836	+	0.951763i	$0.599270\pi$
$270$	388041.	−	528978.i	0.323943	−	0.441599i
$271$	−388277.			−0.321158			−0.160579	−	0.987023i	$-0.551336\pi$
$271$	−388277.			−0.321158			−0.160579	+	0.987023i	$0.551336\pi$
$272$			73786.5i			0.0604721i
$273$		−	28498.0i		−	0.0231424i
$274$	140156.			0.112781
$275$	−520544.	−	1.65349e6i	−0.415074	−	1.31847i
$276$	152039.			0.120138
$277$			1.47922e6i			1.15834i	0.815208	+	0.579168i	$0.196623\pi$
$277$			1.47922e6i			1.15834i	−0.815208	+	0.579168i	$0.803377\pi$
$278$		−	559387.i		−	0.434111i
$279$	533107.			0.410019
$280$	28453.3	−	38787.6i	0.0216889	−	0.0295663i
$281$	−2.35153e6			−1.77658			−0.888289	−	0.459285i	$-0.848106\pi$
$281$	−2.35153e6			−1.77658			−0.888289	+	0.459285i	$0.848106\pi$
$282$			1.52941e6i			1.14525i
$283$		−	525460.i		−	0.390008i	−0.980802	−	0.195004i	$-0.937528\pi$
$283$		−	525460.i		−	0.390008i	0.980802	−	0.195004i	$-0.0624720\pi$
$284$	−641901.			−0.472250
$285$	417563.	+	306311.i	0.304516	+	0.223383i
$286$	−261809.			−0.189264
$287$			59630.1i			0.0427327i
$288$			81580.7i			0.0579571i
$289$	1.33678e6			0.941490
$290$	1.45463e6	+	1.06707e6i	1.01568	+	0.745071i
$291$	−1.86861e6			−1.29356
$292$			483024.i			0.331522i
$293$		−	263970.i		−	0.179633i	−0.995958	−	0.0898165i	$-0.971372\pi$
$293$		−	263970.i		−	0.179633i	0.995958	−	0.0898165i	$-0.0286281\pi$
$294$	−1.19463e6			−0.806053
$295$	1.60781e6	−	2.19177e6i	1.07567	−	1.46636i
$296$	250795.			0.166375
$297$		−	1.62749e6i		−	1.07060i
$298$		−	634267.i		−	0.413744i
$299$	−62417.8			−0.0403767
$300$	856699.	−	269702.i	0.549572	−	0.173014i
$301$	−192651.			−0.122562
$302$			35523.7i			0.0224131i
$303$		−	778856.i		−	0.487361i
$304$	132024.			0.0819350
$305$	86784.0	−	118304.i	0.0534183	−	0.0728198i
$306$	−91851.2			−0.0560765
$307$		−	877869.i		−	0.531599i	−0.964028	−	0.265799i	$-0.914364\pi$
$307$		−	877869.i		−	0.531599i	0.964028	−	0.265799i	$-0.0856359\pi$
$308$		−	119337.i		−	0.0716800i
$309$	−2.67583e6			−1.59427
$310$	−1.20647e6	−	885028.i	−0.713038	−	0.523062i
$311$	−1.66929e6			−0.978660			−0.489330	−	0.872099i	$-0.662759\pi$
$311$	−1.66929e6			−0.978660			−0.489330	+	0.872099i	$0.662759\pi$
$312$		−	135647.i		−	0.0788905i
$313$		−	210436.i		−	0.121411i	−0.998156	−	0.0607057i	$-0.980665\pi$
$313$		−	210436.i		−	0.121411i	0.998156	−	0.0607057i	$-0.0193351\pi$
$314$	−988593.			−0.565839
$315$	48283.7	+	35419.4i	0.0274173	+	0.0201124i
$316$	−532629.			−0.300060
$317$			1.27366e6i			0.711876i	0.934510	+	0.355938i	$0.115839\pi$
$317$			1.27366e6i			0.711876i	−0.934510	+	0.355938i	$0.884161\pi$
$318$		−	413909.i		−	0.229529i
$319$	4.47542e6			2.46239
$320$	135435.	−	184625.i	0.0739359	−	0.100789i
$321$	−3.82469e6			−2.07173
$322$		−	28451.1i		−	0.0152918i
$323$			148645.i			0.0792765i
$324$	1.15298e6			0.610183
$325$	−351708.	+	110723.i	−0.184703	+	0.0581474i
$326$	1.03797e6			0.540929
$327$			209460.i			0.108326i
$328$			283832.i			0.145672i
$329$	286199.			0.145773
$330$	1.31789e6	−	1.79655e6i	0.666185	−	0.908144i
$331$	1.57328e6			0.789289			0.394644	−	0.918834i	$-0.370868\pi$
$331$	1.57328e6			0.789289			0.394644	+	0.918834i	$0.370868\pi$
$332$			1.10465e6i			0.550020i
$333$			312195.i			0.154282i
$334$	369894.			0.181431
$335$	62383.6	+	45762.6i	0.0303709	+	0.0222792i
$336$	61830.3			0.0298781
$337$		−	2.33665e6i		−	1.12078i	−0.828230	−	0.560388i	$-0.810652\pi$
$337$		−	2.33665e6i		−	1.12078i	0.828230	−	0.560388i	$-0.189348\pi$
$338$		−	1.42948e6i		−	0.680593i
$339$	−1.35628e6			−0.640989
$340$	207868.	+	152485.i	0.0975190	+	0.0715369i
$341$	−3.71192e6			−1.72867
$342$			164347.i			0.0759794i
$343$			449533.i			0.206313i
$344$	−916996.			−0.417803
$345$	314199.	−	428315.i	0.142120	−	0.193738i
$346$	−565291.			−0.253853
$347$		−	255230.i		−	0.113791i	−0.998380	−	0.0568955i	$-0.981880\pi$
$347$		−	255230.i		−	0.113791i	0.998380	−	0.0568955i	$-0.0181202\pi$
$348$			2.31879e6i			1.02639i
$349$	3.29099e6			1.44631			0.723157	−	0.690684i	$-0.242690\pi$
$349$	3.29099e6			1.44631			0.723157	+	0.690684i	$0.242690\pi$
$350$	−50469.5	−	160315.i	−0.0220221	−	0.0699524i
$351$	−346179.			−0.149980
$352$		−	568030.i		−	0.244351i
$353$		−	2.58446e6i		−	1.10391i	−0.833874	−	0.551955i	$-0.813882\pi$
$353$		−	2.58446e6i		−	1.10391i	0.833874	−	0.551955i	$-0.186118\pi$
$354$	3.49384e6			1.48182
$355$	−1.32653e6	+	1.80833e6i	−0.558659	+	0.761564i
$356$	−1.60084e6			−0.669457
$357$			69614.3i			0.0289087i
$358$		−	1.70619e6i		−	0.703590i
$359$	2.22651e6			0.911775			0.455888	−	0.890037i	$-0.349322\pi$
$359$	2.22651e6			0.911775			0.455888	+	0.890037i	$0.349322\pi$
$360$	229825.	+	168592.i	0.0934633	+	0.0685617i
$361$	−2.21013e6			−0.892586
$362$		−	3.25729e6i		−	1.30643i
$363$		−	2.63445e6i		−	1.04936i
$364$	−25383.8			−0.0100416
$365$	1.36075e6	+	998203.i	0.534621	+	0.392181i
$366$	188585.			0.0735877
$367$			4.31435e6i			1.67205i	0.548689	+	0.836027i	$0.315127\pi$
$367$			4.31435e6i			1.67205i	−0.548689	+	0.836027i	$0.684873\pi$
$368$		−	135424.i		−	0.0521286i
$369$	−353321.			−0.135084
$370$	518285.	−	706526.i	0.196818	−	0.268302i
$371$	−77455.1			−0.0292156
$372$		−	1.92320e6i		−	0.720557i
$373$			497296.i			0.185073i	0.995709	+	0.0925366i	$0.0294975\pi$
$373$			497296.i			0.185073i	−0.995709	+	0.0925366i	$0.970502\pi$
$374$	639541.			0.236423
$375$	1.01064e6	−	2.97080e6i	0.371122	−	1.09093i
$376$	1.36227e6			0.496930
$377$		−	951952.i		−	0.344954i
$378$		−	157794.i		−	0.0568017i
$379$	1.59344e6			0.569819			0.284909	−	0.958554i	$-0.408036\pi$
$379$	1.59344e6			0.569819			0.284909	+	0.958554i	$0.408036\pi$
$380$	272837.	−	371932.i	0.0969270	−	0.132131i
$381$	3.23652e6			1.14226
$382$		−	1.34853e6i		−	0.472825i
$383$			3.26513e6i			1.13738i	0.822554	+	0.568688i	$0.192549\pi$
$383$			3.26513e6i			1.13738i	−0.822554	+	0.568688i	$0.807451\pi$
$384$	294305.			0.101852
$385$	−336190.	−	246618.i	−0.115593	−	0.0847955i
$386$	−284984.			−0.0973538
$387$		−	1.14150e6i		−	0.387434i
$388$			1.66441e6i			0.561281i
$389$	−1.58350e6			−0.530572			−0.265286	−	0.964170i	$-0.585466\pi$
$389$	−1.58350e6			−0.530572			−0.265286	+	0.964170i	$0.585466\pi$
$390$	−382138.	−	280325.i	−0.127221	−	0.0933254i
$391$	152473.			0.0504372
$392$			1.06408e6i			0.349750i
$393$			5.29863e6i			1.73054i
$394$	1.94588e6			0.631502
$395$	−1.10072e6	+	1.50050e6i	−0.354963	+	0.483885i
$396$	707097.			0.226590
$397$			5.80120e6i			1.84732i	0.383216	+	0.923659i	$0.374817\pi$
$397$			5.80120e6i			1.84732i	−0.383216	+	0.923659i	$0.625183\pi$
$398$		−	3.48237e6i		−	1.10196i
$399$	124559.			0.0391691
$400$	−240229.	−	763079.i	−0.0750717	−	0.238462i
$401$	−1.32234e6			−0.410659			−0.205330	−	0.978693i	$-0.565827\pi$
$401$	−1.32234e6			−0.410659			−0.205330	+	0.978693i	$0.565827\pi$
$402$			99444.1i			0.0306912i
$403$			789550.i			0.242168i
$404$	−693744.			−0.211468
$405$	2.38272e6	−	3.24812e6i	0.721830	−	0.983999i
$406$	433916.			0.130644
$407$		−	2.17375e6i		−	0.650465i
$408$			331356.i			0.0985474i
$409$	−3.99481e6			−1.18083			−0.590415	−	0.807100i	$-0.701036\pi$
$409$	−3.99481e6			−1.18083			−0.590415	+	0.807100i	$0.701036\pi$
$410$	799598.	+	586560.i	0.234916	+	0.172327i
$411$	629406.			0.183792
$412$			2.38341e6i			0.691761i
$413$		−	653805.i		−	0.188614i
$414$	168579.			0.0483395
$415$	3.11196e6	+	2.28283e6i	0.886979	+	0.650659i
$416$	−120824.			−0.0342310
$417$		−	2.51207e6i		−	0.707442i
$418$		−	1.14431e6i		−	0.320335i
$419$	897918.			0.249863			0.124931	−	0.992165i	$-0.460129\pi$
$419$	897918.			0.249863			0.124931	+	0.992165i	$0.460129\pi$
$420$	127777.	−	174185.i	0.0353450	−	0.0481823i
$421$	−3.43731e6			−0.945177			−0.472589	−	0.881283i	$-0.656680\pi$
$421$	−3.43731e6			−0.945177			−0.472589	+	0.881283i	$0.656680\pi$
$422$			3.86570e6i			1.05669i
$423$			1.69579e6i			0.460809i
$424$	−368678.			−0.0995937
$425$	859145.	−	270473.i	0.230725	−	0.0726358i
$426$	−2.88261e6			−0.769595
$427$		−	35290.1i		−	0.00936663i
$428$			3.40673e6i			0.898936i
$429$	−1.17572e6			−0.308432
$430$	−1.89504e6	+	2.58331e6i	−0.494250	+	0.673761i
$431$	−5.92933e6			−1.53749			−0.768746	−	0.639555i	$-0.779119\pi$
$431$	−5.92933e6			−1.53749			−0.768746	+	0.639555i	$0.779119\pi$
$432$		−	751083.i		−	0.193633i
$433$			6.04974e6i			1.55066i	0.631556	+	0.775331i	$0.282417\pi$
$433$			6.04974e6i			1.55066i	−0.631556	+	0.775331i	$0.717583\pi$
$434$	−359890.			−0.0917162
$435$	6.53236e6	+	4.79193e6i	1.65519	+	1.21419i
$436$	186570.			0.0470030
$437$		−	272816.i		−	0.0683386i
$438$			2.16914e6i			0.540259i
$439$	6.08978e6			1.50813			0.754067	−	0.656797i	$-0.228089\pi$
$439$	6.08978e6			1.50813			0.754067	+	0.656797i	$0.228089\pi$
$440$	−1.60022e6	−	1.17387e6i	−0.394048	−	0.289061i
$441$	−1.32459e6			−0.324328
$442$		−	136035.i		−	0.0331203i
$443$			5.07192e6i			1.22790i	0.789345	+	0.613951i	$0.210421\pi$
$443$			5.07192e6i			1.22790i	−0.789345	+	0.613951i	$0.789579\pi$
$444$	1.12626e6			0.271131
$445$	−3.30824e6	+	4.50980e6i	−0.791950	+	1.07959i
$446$	−5.45015e6			−1.29739
$447$		−	2.84833e6i		−	0.674252i
$448$		−	55073.6i		−	0.0129643i
$449$	−2.07018e6			−0.484609			−0.242305	−	0.970200i	$-0.577903\pi$
$449$	−2.07018e6			−0.484609			−0.242305	+	0.970200i	$0.577903\pi$
$450$	949899.	−	299043.i	0.221129	−	0.0696150i
$451$	2.46010e6			0.569524
$452$			1.20807e6i			0.278128i
$453$			159528.i			0.0365251i
$454$	2.77335e6			0.631488
$455$	−52457.3	+	71509.8i	−0.0118789	+	0.0161934i
$456$	592887.			0.133524
$457$			5.35086e6i			1.19849i	0.800567	+	0.599243i	$0.204532\pi$
$457$			5.35086e6i			1.19849i	−0.800567	+	0.599243i	$0.795468\pi$
$458$		−	2.36232e6i		−	0.526230i
$459$	845639.			0.187350
$460$	−381509.	−	279863.i	−0.0840641	−	0.0616668i
$461$	3.24380e6			0.710889			0.355445	−	0.934697i	$-0.384329\pi$
$461$	3.24380e6			0.710889			0.355445	+	0.934697i	$0.384329\pi$
$462$		−	535912.i		−	0.116812i
$463$			2.99458e6i			0.649207i	0.945850	+	0.324603i	$0.105231\pi$
$463$			2.99458e6i			0.649207i	−0.945850	+	0.324603i	$0.894769\pi$
$464$	2.06539e6			0.445356
$465$	−5.41795e6	−	3.97444e6i	−1.16199	−	0.852399i
$466$	1.78498e6			0.380775
$467$		−	7.56734e6i		−	1.60565i	−0.596214	−	0.802825i	$-0.703329\pi$
$467$		−	7.56734e6i		−	1.60565i	0.596214	−	0.802825i	$-0.296671\pi$
$468$		−	150404.i		−	0.0317428i
$469$	18609.0			0.00390654
$470$	2.81523e6	−	3.83773e6i	0.587855	−	0.801363i
$471$	−4.43952e6			−0.922112
$472$		−	3.11204e6i		−	0.642969i
$473$			7.94802e6i			1.63345i
$474$	−2.39190e6			−0.488987
$475$	−483949.	−	1.53725e6i	−0.0984160	−	0.312615i
$476$	62006.9			0.0125436
$477$		−	458938.i		−	0.0923546i
$478$			2.78502e6i			0.557518i
$479$	−4.87074e6			−0.969965			−0.484983	−	0.874524i	$-0.661174\pi$
$479$	−4.87074e6			−0.969965			−0.484983	+	0.874524i	$0.661174\pi$
$480$	608203.	−	829102.i	0.120488	−	0.164250i
$481$	−462372.			−0.0911231
$482$			1.44256e6i			0.282825i
$483$		−	127767.i		−	0.0249201i
$484$	−2.34656e6			−0.455321
$485$	4.68888e6	+	3.43961e6i	0.905138	+	0.663980i
$486$	2.32598e6			0.446700
$487$			3.75548e6i			0.717534i	0.933427	+	0.358767i	$0.116803\pi$
$487$			3.75548e6i			0.717534i	−0.933427	+	0.358767i	$0.883197\pi$
$488$		−	167977.i		−	0.0319301i
$489$	4.66125e6			0.881516
$490$	2.99766e6	+	2.19899e6i	0.564018	+	0.413745i
$491$	−6.96357e6			−1.30355			−0.651776	−	0.758412i	$-0.725976\pi$
$491$	−6.96357e6			−1.30355			−0.651776	+	0.758412i	$0.725976\pi$
$492$			1.27462e6i			0.237393i
$493$			2.32541e6i			0.430906i
$494$	−243403.			−0.0448755
$495$	1.46127e6	−	1.99200e6i	0.268050	−	0.365406i
$496$	−1.71304e6			−0.312653
$497$			539425.i			0.0979580i
$498$			4.96069e6i			0.896332i
$499$	−1.15075e6			−0.206885			−0.103443	−	0.994635i	$-0.532986\pi$
$499$	−1.15075e6			−0.206885			−0.103443	+	0.994635i	$0.532986\pi$
$500$	−2.64616e6	−	900195.i	−0.473359	−	0.161032i
$501$	1.66110e6			0.295666
$502$			516570.i			0.0914892i
$503$			8.94444e6i			1.57628i	0.615497	+	0.788139i	$0.288955\pi$
$503$			8.94444e6i			1.57628i	−0.615497	+	0.788139i	$0.711045\pi$
$504$	68556.9			0.0120219
$505$	−1.43367e6	+	1.95438e6i	−0.250162	+	0.341020i
$506$	−1.17378e6			−0.203803
$507$		−	6.41945e6i		−	1.10912i
$508$		−	2.88283e6i		−	0.495633i
$509$	1.93083e6			0.330332			0.165166	−	0.986266i	$-0.447184\pi$
$509$	1.93083e6			0.330332			0.165166	+	0.986266i	$0.447184\pi$
$510$	933480.	+	684771.i	0.158920	+	0.116579i
$511$	405912.			0.0687670
$512$		−	262144.i		−	0.0441942i
$513$		−	1.51308e6i		−	0.253845i
$514$	549686.			0.0917713
$515$	6.71443e6	+	4.92549e6i	1.11555	+	0.818335i
$516$	−4.11800e6			−0.680866
$517$		−	1.18074e7i		−	1.94281i
$518$		−	210757.i		−	0.0345110i
$519$	−2.53858e6			−0.413687
$520$	−249691.	+	340379.i	−0.0404943	+	0.0552019i
$521$	2.22757e6			0.359531			0.179766	−	0.983709i	$-0.442466\pi$
$521$	2.22757e6			0.359531			0.179766	+	0.983709i	$0.442466\pi$
$522$			2.57105e6i			0.412985i
$523$		−	3.80243e6i		−	0.607865i	−0.952694	−	0.303932i	$-0.901700\pi$
$523$		−	3.80243e6i		−	0.607865i	0.952694	−	0.303932i	$-0.0982997\pi$
$524$	4.71960e6			0.750891
$525$	−226646.	−	719932.i	−0.0358880	−	0.113997i
$526$	4.80365e6			0.757020
$527$		−	1.92870e6i		−	0.302508i
$528$		−	2.55088e6i		−	0.398203i
$529$	−279841.			−0.0434783
$530$	−761898.	+	1.03862e6i	−0.117817	+	0.160608i
$531$	3.87394e6			0.596233
$532$		−	110947.i		−	0.0169957i
$533$		−	523281.i		−	0.0797842i
$534$	−7.18896e6			−1.09097
$535$	9.59728e6	+	7.04026e6i	1.44965	+	1.06342i
$536$	88577.0			0.0133171
$537$		−	7.66206e6i		−	1.14659i
$538$			2.91324e6i			0.433931i
$539$	9.22284e6			1.36739
$540$	−2.11591e6	−	1.55217e6i	−0.312258	−	0.229062i
$541$	1.08700e7			1.59675			0.798374	−	0.602162i	$-0.205694\pi$
$541$	1.08700e7			1.59675			0.798374	+	0.602162i	$0.205694\pi$
$542$			1.55311e6i			0.227093i
$543$		−	1.46277e7i		−	2.12900i
$544$	295146.			0.0427602
$545$	385560.	−	525595.i	0.0556033	−	0.0757984i
$546$	−113992.			−0.0163641
$547$		−	3.70921e6i		−	0.530046i	−0.964242	−	0.265023i	$-0.914621\pi$
$547$		−	3.70921e6i		−	0.530046i	0.964242	−	0.265023i	$-0.0853795\pi$
$548$		−	560625.i		−	0.0797482i
$549$	209102.			0.0296092
$550$	−6.61395e6	+	2.08218e6i	−0.932297	+	0.293502i
$551$	4.16079e6			0.583844
$552$		−	608155.i		−	0.0849506i
$553$			447598.i			0.0622409i
$554$	5.91690e6			0.819068
$555$	2.32748e6	−	3.17283e6i	0.320741	−	0.437234i
$556$	−2.23755e6			−0.306963
$557$		−	8.95316e6i		−	1.22275i	−0.791340	−	0.611376i	$-0.790616\pi$
$557$		−	8.95316e6i		−	1.22275i	0.791340	−	0.611376i	$-0.209384\pi$
$558$		−	2.13243e6i		−	0.289927i
$559$	1.69060e6			0.228829
$560$	−155150.	−	113813.i	−0.0209066	−	0.0153364i
$561$	2.87202e6			0.385283
$562$			9.40611e6i			1.25623i
$563$		−	8.66187e6i		−	1.15170i	−0.817554	−	0.575852i	$-0.804671\pi$
$563$		−	8.66187e6i		−	1.15170i	0.817554	−	0.575852i	$-0.195329\pi$
$564$	6.11763e6			0.809814
$565$	3.40331e6	+	2.49656e6i	0.448518	+	0.329019i
$566$	−2.10184e6			−0.275778
$567$		−	968915.i		−	0.126569i
$568$			2.56760e6i			0.333931i
$569$	−1.26588e7			−1.63912			−0.819561	−	0.572991i	$-0.805783\pi$
$569$	−1.26588e7			−1.63912			−0.819561	+	0.572991i	$0.805783\pi$
$570$	1.22524e6	−	1.67025e6i	0.157956	−	0.215325i
$571$	7.09314e6			0.910434			0.455217	−	0.890381i	$-0.349562\pi$
$571$	7.09314e6			0.910434			0.455217	+	0.890381i	$0.349562\pi$
$572$			1.04723e6i			0.133830i
$573$		−	6.05588e6i		−	0.770533i
$574$	238520.			0.0302166
$575$	−1.57683e6	+	496411.i	−0.198891	+	0.0626141i
$576$	326323.			0.0409818
$577$			4.84634e6i			0.606003i	0.952990	+	0.303001i	$0.0979887\pi$
$577$			4.84634e6i			0.606003i	−0.952990	+	0.303001i	$0.902011\pi$
$578$		−	5.34713e6i		−	0.665734i
$579$	−1.27979e6			−0.158651
$580$	4.26828e6	−	5.81851e6i	0.526844	−	0.718194i
$581$	928297.			0.114090
$582$			7.47443e6i			0.914683i
$583$			3.19550e6i			0.389374i
$584$	1.93210e6			0.234421
$585$	−423711.	−	310821.i	−0.0511894	−	0.0375509i
$586$	−1.05588e6			−0.127020
$587$		−	1.34791e7i		−	1.61460i	−0.590140	−	0.807301i	$-0.700927\pi$
$587$		−	1.34791e7i		−	1.61460i	0.590140	−	0.807301i	$-0.299073\pi$
$588$			4.77850e6i			0.569965i
$589$	−3.45097e6			−0.409876
$590$	−8.76707e6	−	6.43124e6i	−1.03687	−	0.760615i
$591$	8.73844e6			1.02912
$592$		−	1.00318e6i		−	0.117645i
$593$		−	1.46171e7i		−	1.70697i	−0.521119	−	0.853484i	$-0.674485\pi$
$593$		−	1.46171e7i		−	1.70697i	0.521119	−	0.853484i	$-0.325515\pi$
$594$	−6.50997e6			−0.757030
$595$	128142.	−	174683.i	0.0148388	−	0.0202282i
$596$	−2.53707e6			−0.292561
$597$		−	1.56384e7i		−	1.79580i
$598$			249671.i			0.0285506i
$599$	921750.			0.104965			0.0524827	−	0.998622i	$-0.483287\pi$
$599$	921750.			0.104965			0.0524827	+	0.998622i	$0.483287\pi$
$600$	−1.07881e6	−	3.42679e6i	−0.122339	−	0.388606i
$601$	−1.17035e7			−1.32169			−0.660845	−	0.750522i	$-0.729802\pi$
$601$	−1.17035e7			−1.32169			−0.660845	+	0.750522i	$0.729802\pi$
$602$			770603.i			0.0866642i
$603$			110263.i			0.0123491i
$604$	142095.			0.0158484
$605$	−4.84933e6	+	6.61060e6i	−0.538633	+	0.734265i
$606$	−3.11543e6			−0.344616
$607$			1.18871e7i			1.30950i	0.755847	+	0.654748i	$0.227225\pi$
$607$			1.18871e7i			1.30950i	−0.755847	+	0.654748i	$0.772775\pi$
$608$		−	528097.i		−	0.0579368i
$609$	1.94861e6			0.212903
$610$	−473216.	−	347136.i	−0.0514914	−	0.0377725i
$611$	−2.51152e6			−0.272166
$612$			367405.i			0.0396521i
$613$			1.08099e7i			1.16190i	0.813938	+	0.580951i	$0.197319\pi$
$613$			1.08099e7i			1.16190i	−0.813938	+	0.580951i	$0.802681\pi$
$614$	−3.51148e6			−0.375897
$615$	3.59079e6	+	2.63409e6i	0.382827	+	0.280830i
$616$	−477348.			−0.0506854
$617$		−	1.05828e7i		−	1.11915i	−0.828781	−	0.559573i	$-0.810965\pi$
$617$		−	1.05828e7i		−	1.11915i	0.828781	−	0.559573i	$-0.189035\pi$
$618$			1.07033e7i			1.12732i
$619$	−4.88318e6			−0.512244			−0.256122	−	0.966645i	$-0.582445\pi$
$619$	−4.88318e6			−0.512244			−0.256122	+	0.966645i	$0.582445\pi$
$620$	−3.54011e6	+	4.82588e6i	−0.369860	+	0.504194i
$621$	−1.55204e6			−0.161501
$622$			6.67717e6i			0.692017i
$623$			1.34527e6i			0.138864i
$624$	−542589.			−0.0557840
$625$	−8.00445e6	+	5.59430e6i	−0.819656	+	0.572856i
$626$	−841744.			−0.0858508
$627$		−	5.13882e6i		−	0.522029i
$628$			3.95437e6i			0.400109i
$629$	1.12947e6			0.113828
$630$	141678.	−	193135.i	0.0142216	−	0.0193869i
$631$	9.50470e6			0.950309			0.475155	−	0.879902i	$-0.342392\pi$
$631$	9.50470e6			0.950309			0.475155	+	0.879902i	$0.342392\pi$
$632$			2.13052e6i			0.212174i
$633$			1.73599e7i			1.72202i
$634$	5.09463e6			0.503373
$635$	−8.12136e6	−	5.95757e6i	−0.799272	−	0.586321i
$636$	−1.65564e6			−0.162301
$637$		−	1.96176e6i		−	0.191557i
$638$		−	1.79017e7i		−	1.74117i
$639$	−3.19621e6			−0.309659
$640$	−738498.	−	541739.i	−0.0712688	−	0.0522805i
$641$	−2.49152e6			−0.239507			−0.119754	−	0.992804i	$-0.538210\pi$
$641$	−2.49152e6			−0.239507			−0.119754	+	0.992804i	$0.538210\pi$
$642$			1.52988e7i			1.46494i
$643$		−	1.80357e7i		−	1.72030i	−0.510037	−	0.860152i	$-0.670368\pi$
$643$		−	1.80357e7i		−	1.72030i	0.510037	−	0.860152i	$-0.329632\pi$
$644$	−113804.			−0.0108130
$645$	−8.51013e6	+	1.16010e7i	−0.805447	+	1.09798i
$646$	594581.			0.0560570
$647$			5.81304e6i			0.545937i	0.962023	+	0.272969i	$0.0880055\pi$
$647$			5.81304e6i			0.545937i	−0.962023	+	0.272969i	$0.911994\pi$
$648$		−	4.61193e6i		−	0.431465i
$649$	−2.69734e7			−2.51376
$650$	442893.	+	1.40683e6i	0.0411164	+	0.130605i
$651$	−1.61618e6			−0.149464
$652$		−	4.15187e6i		−	0.382494i
$653$			8.27182e6i			0.759133i	0.925164	+	0.379567i	$0.123927\pi$
$653$			8.27182e6i			0.759133i	−0.925164	+	0.379567i	$0.876073\pi$
$654$	837838.			0.0765977
$655$	9.75338e6	−	1.32958e7i	0.888284	−	1.21091i
$656$	1.13533e6			0.103006
$657$			2.40512e6i			0.217382i
$658$		−	1.14479e6i		−	0.103077i
$659$	−1.33200e6			−0.119479			−0.0597396	−	0.998214i	$-0.519027\pi$
$659$	−1.33200e6			−0.119479			−0.0597396	+	0.998214i	$0.519027\pi$
$660$	−7.18620e6	−	5.27157e6i	−0.642155	−	0.471064i
$661$	2.84345e6			0.253129			0.126564	−	0.991958i	$-0.459605\pi$
$661$	2.84345e6			0.253129			0.126564	+	0.991958i	$0.459605\pi$
$662$		−	6.29312e6i		−	0.558111i
$663$		−	610897.i		−	0.0539740i
$664$	4.41859e6			0.388923
$665$	−312555.	−	229280.i	−0.0274077	−	0.0201054i
$666$	1.24878e6			0.109094
$667$		−	4.26794e6i		−	0.371453i
$668$		−	1.47958e6i		−	0.128291i
$669$	−2.44752e7			−2.11428
$670$	183050.	−	249534.i	0.0157537	−	0.0214755i
$671$	−1.45593e6			−0.124835
$672$		−	247321.i		−	0.0211270i
$673$			7.32605e6i			0.623494i	0.950165	+	0.311747i	$0.100914\pi$
$673$			7.32605e6i			0.623494i	−0.950165	+	0.311747i	$0.899086\pi$
$674$	−9.34660e6			−0.792509
$675$	−8.74536e6	+	2.75318e6i	−0.738785	+	0.232581i
$676$	−5.71793e6			−0.481252
$677$			1.45267e7i			1.21813i	0.793119	+	0.609066i	$0.208456\pi$
$677$			1.45267e7i			1.21813i	−0.793119	+	0.609066i	$0.791544\pi$
$678$			5.42513e6i			0.453248i
$679$	1.39869e6			0.116426
$680$	609940.	−	831470.i	0.0505842	−	0.0689564i
$681$	1.24544e7			1.02909
$682$			1.48477e7i			1.22236i
$683$		−	2.25360e7i		−	1.84852i	−0.381762	−	0.924261i	$-0.624683\pi$
$683$		−	2.25360e7i		−	1.84852i	0.381762	−	0.924261i	$-0.375317\pi$
$684$	657387.			0.0537256
$685$	−1.57936e6	−	1.15857e6i	−0.128604	−	0.0943400i
$686$	1.79813e6			0.145885
$687$		−	1.06086e7i		−	0.857563i
$688$			3.66799e6i			0.295431i
$689$	679703.			0.0545471
$690$	−1.71326e6	−	1.25679e6i	−0.136994	−	0.100494i
$691$	−1.49984e7			−1.19495			−0.597477	−	0.801886i	$-0.703830\pi$
$691$	−1.49984e7			−1.19495			−0.597477	+	0.801886i	$0.703830\pi$
$692$			2.26117e6i			0.179501i
$693$		−	594213.i		−	0.0470012i
$694$	−1.02092e6			−0.0804624
$695$	−4.62405e6	+	6.30351e6i	−0.363129	+	0.495017i
$696$	9.27515e6			0.725768
$697$			1.27826e6i			0.0996637i
$698$		−	1.31639e7i		−	1.02270i
$699$	8.01588e6			0.620524
$700$	−641258.	+	201878.i	−0.0494638	+	0.0155720i
$701$	−3.60539e6			−0.277113			−0.138557	−	0.990355i	$-0.544246\pi$
$701$	−3.60539e6			−0.277113			−0.138557	+	0.990355i	$0.544246\pi$
$702$			1.38472e6i			0.106052i
$703$		−	2.02093e6i		−	0.154228i
$704$	−2.27212e6			−0.172782
$705$	1.26425e7	−	1.72343e7i	0.957988	−	1.30593i
$706$	−1.03379e7			−0.780582
$707$			582992.i			0.0438646i
$708$		−	1.39754e7i		−	1.04780i
$709$	7.76819e6			0.580369			0.290184	−	0.956971i	$-0.406283\pi$
$709$	7.76819e6			0.580369			0.290184	+	0.956971i	$0.406283\pi$
$710$	7.23332e6	+	5.30613e6i	0.538507	+	0.395032i
$711$	−2.65212e6			−0.196752
$712$			6.40335e6i			0.473377i
$713$			3.53983e6i			0.260771i
$714$	278457.			0.0204415
$715$	2.95022e6	+	2.16418e6i	0.215818	+	0.158318i
$716$	−6.82475e6			−0.497513
$717$			1.25068e7i			0.908550i
$718$		−	8.90603e6i		−	0.644723i
$719$	2.07513e7			1.49700			0.748501	−	0.663134i	$-0.230774\pi$
$719$	2.07513e7			1.49700			0.748501	+	0.663134i	$0.230774\pi$
$720$	674369.	−	919300.i	0.0484804	−	0.0660885i
$721$	2.00292e6			0.143491
$722$			8.84053e6i			0.631154i
$723$			6.47819e6i			0.460901i
$724$	−1.30292e7			−0.923783
$725$	−7.57092e6	−	2.40487e7i	−0.534938	−	1.69921i
$726$	−1.05378e7			−0.742007
$727$			458253.i			0.0321565i	0.999871	+	0.0160783i	$0.00511809\pi$
$727$			458253.i			0.0321565i	−0.999871	+	0.0160783i	$0.994882\pi$
$728$			101535.i			0.00710048i
$729$	−7.06552e6			−0.492409
$730$	3.99281e6	−	5.44300e6i	0.277314	−	0.378034i
$731$	−4.12976e6			−0.285845
$732$		−	754342.i		−	0.0520344i
$733$		−	1.07977e7i		−	0.742289i	−0.928575	−	0.371145i	$-0.878965\pi$
$733$		−	1.07977e7i		−	0.742289i	0.928575	−	0.371145i	$-0.121035\pi$
$734$	1.72574e7			1.18232
$735$	1.34617e7	+	9.87511e6i	0.919143	+	0.674254i
$736$	−541696.			−0.0368605
$737$		−	767737.i		−	0.0520647i
$738$			1.41328e6i			0.0955188i
$739$	1.33659e7			0.900301			0.450150	−	0.892953i	$-0.351370\pi$
$739$	1.33659e7			0.900301			0.450150	+	0.892953i	$0.351370\pi$
$740$	−2.82610e6	−	2.07314e6i	−0.189718	−	0.139171i
$741$	−1.09306e6			−0.0731306
$742$			309820.i			0.0206586i
$743$			5.51156e6i			0.366271i	0.983088	+	0.183135i	$0.0586247\pi$
$743$			5.51156e6i			0.366271i	−0.983088	+	0.183135i	$0.941375\pi$
$744$	−7.69282e6			−0.509510
$745$	−5.24303e6	+	7.14730e6i	−0.346092	+	0.471793i
$746$	1.98919e6			0.130866
$747$			5.50036e6i			0.360653i
$748$		−	2.55816e6i		−	0.167176i
$749$	2.86287e6			0.186465
$750$	−1.18832e7	−	4.04255e6i	−0.771402	−	0.262423i
$751$	−6.85470e6			−0.443495			−0.221747	−	0.975104i	$-0.571176\pi$
$751$	−6.85470e6			−0.443495			−0.221747	+	0.975104i	$0.571176\pi$
$752$		−	5.44910e6i		−	0.351382i
$753$			2.31978e6i			0.149094i
$754$	−3.80781e6			−0.243920
$755$	293649.	−	400302.i	0.0187483	−	0.0255576i
$756$	−631177.			−0.0401649
$757$			1.24703e7i			0.790927i	0.918482	+	0.395464i	$0.129416\pi$
$757$			1.24703e7i			0.790927i	−0.918482	+	0.395464i	$0.870584\pi$
$758$		−	6.37375e6i		−	0.402923i
$759$	−5.27115e6			−0.332125
$760$	−1.48773e6	−	1.09135e6i	−0.0934306	−	0.0685377i
$761$	1.76878e6			0.110717			0.0553583	−	0.998467i	$-0.482370\pi$
$761$	1.76878e6			0.110717			0.0553583	+	0.998467i	$0.482370\pi$
$762$		−	1.29461e7i		−	0.807701i
$763$		−	156785.i		−	0.00974975i
$764$	−5.39410e6			−0.334338
$765$	1.03503e6	+	759268.i	0.0639441	+	0.0469074i
$766$	1.30605e7			0.804246
$767$			5.73743e6i			0.352151i
$768$		−	1.17722e6i		−	0.0720204i
$769$	5.49668e6			0.335185			0.167592	−	0.985856i	$-0.446401\pi$
$769$	5.49668e6			0.335185			0.167592	+	0.985856i	$0.446401\pi$
$770$	−986472.	+	1.34476e6i	−0.0599595	+	0.0817368i
$771$	2.46850e6			0.149554
$772$			1.13994e6i			0.0688395i
$773$		−	1.74991e6i		−	0.105334i	−0.998612	−	0.0526668i	$-0.983228\pi$
$773$		−	1.74991e6i		−	0.105334i	0.998612	−	0.0526668i	$-0.0167721\pi$
$774$	−4.56599e6			−0.273957
$775$	6.27933e6	+	1.99460e7i	0.375542	+	1.19290i
$776$	6.65763e6			0.396885
$777$		−	946455.i		−	0.0562403i
$778$			6.33400e6i			0.375171i
$779$	2.28716e6			0.135037
$780$	−1.12130e6	+	1.52855e6i	−0.0659910	+	0.0899589i
$781$	2.22546e7			1.30554
$782$		−	609892.i		−	0.0356645i
$783$		−	2.36707e7i		−	1.37977i
$784$	4.25631e6			0.247311
$785$	1.11400e7	+	8.17198e6i	0.645227	+	0.473318i
$786$	2.11945e7			1.22368
$787$		−	3.21947e6i		−	0.185288i	−0.995699	−	0.0926440i	$-0.970468\pi$
$787$		−	3.21947e6i		−	0.185288i	0.995699	−	0.0926440i	$-0.0295319\pi$
$788$		−	7.78351e6i		−	0.446540i
$789$	2.15720e7			1.23367
$790$	6.00198e6	+	4.40286e6i	0.342158	+	0.250996i
$791$	1.01521e6			0.0576917
$792$		−	2.82839e6i		−	0.160223i
$793$			309687.i			0.0174880i
$794$	2.32048e7			1.30625
$795$	−3.42149e6	+	4.66417e6i	−0.191998	+	0.261732i
$796$	−1.39295e7			−0.779205
$797$			6.79148e6i			0.378721i	0.981908	+	0.189360i	$0.0606414\pi$
$797$			6.79148e6i			0.378721i	−0.981908	+	0.189360i	$0.939359\pi$
$798$		−	498236.i		−	0.0276967i
$799$	6.13510e6			0.339981
$800$	−3.05232e6	+	960917.i	−0.168618	+	0.0530837i
$801$	−7.97104e6			−0.438969
$802$			5.28935e6i			0.290380i
$803$		−	1.67464e7i		−	0.916498i
$804$	397777.			0.0217020
$805$	−235185.	+	320604.i	−0.0127914	+	0.0174373i
$806$	3.15820e6			0.171239
$807$			1.30826e7i			0.707149i
$808$			2.77497e6i			0.149531i
$809$	−8.26979e6			−0.444246			−0.222123	−	0.975019i	$-0.571299\pi$
$809$	−8.26979e6			−0.444246			−0.222123	+	0.975019i	$0.571299\pi$
$810$	−1.29925e7	−	9.53087e6i	−0.695792	−	0.510411i
$811$	3.67263e7			1.96076			0.980380	−	0.197115i	$-0.0631572\pi$
$811$	3.67263e7			1.96076			0.980380	+	0.197115i	$0.0631572\pi$
$812$		−	1.73566e6i		−	0.0923795i
$813$			6.97462e6i			0.370079i
$814$	−8.69501e6			−0.459948
$815$	−1.16964e7	−	8.58013e6i	−0.616822	−	0.452481i
$816$	1.32543e6			0.0696835
$817$			7.38927e6i			0.387299i
$818$			1.59792e7i			0.834973i
$819$	−126393.			−0.00658436
$820$	2.34624e6	−	3.19839e6i	0.121853	−	0.166110i
$821$	4.17830e6			0.216342			0.108171	−	0.994132i	$-0.465501\pi$
$821$	4.17830e6			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$822$		−	2.51762e6i		−	0.129960i
$823$		−	1.90225e7i		−	0.978966i	−0.872013	−	0.489483i	$-0.837185\pi$
$823$		−	1.90225e7i		−	0.978966i	0.872013	−	0.489483i	$-0.162815\pi$
$824$	9.53365e6			0.489149
$825$	−2.97016e7	+	9.35053e6i	−1.51930	+	0.478301i
$826$	−2.61522e6			−0.133370
$827$			728260.i			0.0370274i	0.999829	+	0.0185137i	$0.00589342\pi$
$827$			728260.i			0.0370274i	−0.999829	+	0.0185137i	$0.994107\pi$
$828$		−	674316.i		−	0.0341812i
$829$	2.67325e6			0.135099			0.0675497	−	0.997716i	$-0.478482\pi$
$829$	2.67325e6			0.135099			0.0675497	+	0.997716i	$0.478482\pi$
$830$	9.13133e6	−	1.24478e7i	0.460086	−	0.627189i
$831$	2.65713e7			1.33478
$832$			483295.i			0.0242050i
$833$			4.79215e6i			0.239286i
$834$	−1.00483e7			−0.500237
$835$	−4.16819e6	−	3.05765e6i	−0.206886	−	0.151765i
$836$	−4.57726e6			−0.226511
$837$			1.96325e7i			0.968637i
$838$		−	3.59167e6i		−	0.176680i
$839$	1.24558e7			0.610893			0.305447	−	0.952209i	$-0.401194\pi$
$839$	1.24558e7			0.610893			0.305447	+	0.952209i	$0.401194\pi$
$840$	−696741.	−	511107.i	−0.0340701	−	0.0249927i
$841$	4.45804e7			2.17347
$842$			1.37492e7i			0.668341i
$843$			4.22404e7i			2.04720i
$844$	1.54628e7			0.747193
$845$	−1.18165e7	+	1.61083e7i	−0.569308	+	0.776081i
$846$	6.78316e6			0.325841
$847$			1.97194e6i			0.0944466i
$848$			1.47471e6i			0.0704234i
$849$	−9.43883e6			−0.449417
$850$	−1.08189e6	−	3.43658e6i	−0.0513613	−	0.163147i
$851$	−2.07297e6			−0.0981229
$852$			1.15304e7i			0.544186i
$853$			1.60756e7i			0.756473i	0.925709	+	0.378237i	$0.123469\pi$
$853$			1.60756e7i			0.756473i	−0.925709	+	0.378237i	$0.876531\pi$
$854$	−141160.			−0.00662321
$855$	1.35854e6	−	1.85196e6i	0.0635559	−	0.0866394i
$856$	1.36269e7			0.635644
$857$			3.53258e7i			1.64301i	0.570203	+	0.821504i	$0.306864\pi$
$857$			3.53258e7i			1.64301i	−0.570203	+	0.821504i	$0.693136\pi$
$858$			4.70287e6i			0.218094i
$859$	−2.54826e7			−1.17832			−0.589158	−	0.808018i	$-0.700540\pi$
$859$	−2.54826e7			−1.17832			−0.589158	+	0.808018i	$0.700540\pi$
$860$	1.03333e7	+	7.58015e6i	0.476421	+	0.349487i
$861$	1.07113e6			0.0492420
$862$			2.37173e7i			1.08717i
$863$			6.28831e6i			0.287413i	0.989620	+	0.143707i	$0.0459022\pi$
$863$			6.28831e6i			0.287413i	−0.989620	+	0.143707i	$0.954098\pi$
$864$	−3.00433e6			−0.136919
$865$	6.37004e6	+	4.67286e6i	0.289469	+	0.212345i
$866$	2.41990e7			1.09648
$867$		−	2.40126e7i		−	1.08490i
$868$			1.43956e6i			0.0648531i
$869$	1.84662e7			0.829521
$870$	1.91677e7	−	2.61295e7i	0.858564	−	1.17039i
$871$	−163303.			−0.00729370
$872$		−	746280.i		−	0.0332361i
$873$			8.28757e6i			0.368037i
$874$	−1.09126e6			−0.0483227
$875$	−756484.	+	2.22371e6i	−0.0334026	+	0.0981881i
$876$	8.67655e6			0.382021
$877$		−	2.11703e7i		−	0.929456i	−0.885453	−	0.464728i	$-0.846152\pi$
$877$		−	2.11703e7i		−	0.929456i	0.885453	−	0.464728i	$-0.153848\pi$
$878$		−	2.43591e7i		−	1.06641i
$879$	−4.74170e6			−0.206996
$880$	−4.69550e6	+	6.40090e6i	−0.204397	+	0.278634i
$881$	3.89745e7			1.69177			0.845883	−	0.533369i	$-0.179074\pi$
$881$	3.89745e7			1.69177			0.845883	+	0.533369i	$0.179074\pi$
$882$			5.29835e6i			0.229335i
$883$		−	1.66916e6i		−	0.0720439i	−0.999351	−	0.0360219i	$-0.988531\pi$
$883$		−	1.66916e6i		−	0.0720439i	0.999351	−	0.0360219i	$-0.0114686\pi$
$884$	−544139.			−0.0234196
$885$	−3.93707e7	−	2.88811e7i	−1.68972	−	1.23952i
$886$	2.02877e7			0.868257
$887$		−	2.52663e7i		−	1.07828i	−0.842215	−	0.539142i	$-0.818749\pi$
$887$		−	2.52663e7i		−	1.07828i	0.842215	−	0.539142i	$-0.181251\pi$
$888$		−	4.50502e6i		−	0.191719i
$889$	−2.42261e6			−0.102808
$890$	1.80392e7	+	1.32330e7i	0.763382	+	0.559993i
$891$	−3.99737e7			−1.68686
$892$			2.18006e7i			0.917395i
$893$		−	1.09774e7i		−	0.460648i
$894$	−1.13933e7			−0.476768
$895$	−1.41038e7	+	1.92263e7i	−0.588545	+	0.802304i
$896$	−220294.			−0.00916712
$897$			1.12121e6i			0.0465271i
$898$			8.28071e6i			0.342670i
$899$	−5.39870e7			−2.22787
$900$	−1.19617e6	−	3.79960e6i	−0.0492252	−	0.156362i
$901$	−1.66037e6			−0.0681384
$902$		−	9.84042e6i		−	0.402714i
$903$			3.46058e6i			0.141231i
$904$	4.83227e6			0.196666
$905$	−2.69257e7	+	3.67051e7i	−1.09281	+	1.48972i
$906$	638112.			0.0258271
$907$		−	2.64654e6i		−	0.106822i	−0.998573	−	0.0534110i	$-0.982991\pi$
$907$		−	2.64654e6i		−	0.106822i	0.998573	−	0.0534110i	$-0.0170094\pi$
$908$		−	1.10934e7i		−	0.446530i
$909$	−3.45435e6			−0.138662
$910$	286039.	+	209829.i	0.0114504	+	0.00839968i
$911$	4.65685e6			0.185907			0.0929536	−	0.995670i	$-0.470369\pi$
$911$	4.65685e6			0.185907			0.0929536	+	0.995670i	$0.470369\pi$
$912$		−	2.37155e6i		−	0.0944159i
$913$		−	3.82979e7i		−	1.52054i
$914$	2.14034e7			0.847457
$915$	−2.12509e6	−	1.55890e6i	−0.0839122	−	0.0615553i
$916$	−9.44930e6			−0.372101
$917$		−	3.96614e6i		−	0.155756i
$918$		−	3.38256e6i		−	0.132476i
$919$	−9.69381e6			−0.378622			−0.189311	−	0.981917i	$-0.560625\pi$
$919$	−9.69381e6			−0.378622			−0.189311	+	0.981917i	$0.560625\pi$
$920$	−1.11945e6	+	1.52604e6i	−0.0436050	+	0.0594423i
$921$	−1.57691e7			−0.612575
$922$		−	1.29752e7i		−	0.502675i
$923$		−	4.73370e6i		−	0.182893i
$924$	−2.14365e6			−0.0825987
$925$	−1.16807e7	+	3.67726e6i	−0.448863	+	0.141309i
$926$	1.19783e7			0.459058
$927$			1.18677e7i			0.453594i
$928$		−	8.26156e6i		−	0.314914i
$929$	375746.			0.0142842			0.00714208	−	0.999974i	$-0.497727\pi$
$929$	375746.			0.0142842			0.00714208	+	0.999974i	$0.497727\pi$
$930$	−1.58977e7	+	2.16718e7i	−0.602737	+	0.821652i
$931$	8.57447e6			0.324215
$932$		−	7.13991e6i		−	0.269248i
$933$			2.99855e7i			1.12773i
$934$	−3.02694e7			−1.13537
$935$	−7.20673e6	−	5.28663e6i	−0.269593	−	0.197765i
$936$	−601617.			−0.0224456
$937$			4.37705e6i			0.162867i	0.996679	+	0.0814335i	$0.0259498\pi$
$937$			4.37705e6i			0.162867i	−0.996679	+	0.0814335i	$0.974050\pi$
$938$		−	74436.2i		−	0.00276234i
$939$	−3.78006e6			−0.139905
$940$	−1.53509e7	−	1.12609e7i	−0.566649	−	0.415676i
$941$	−6.80986e6			−0.250706			−0.125353	−	0.992112i	$-0.540006\pi$
$941$	−6.80986e6			−0.250706			−0.125353	+	0.992112i	$0.540006\pi$
$942$			1.77581e7i			0.652031i
$943$		−	2.34605e6i		−	0.0859129i
$944$	−1.24482e7			−0.454648
$945$	−1.30437e6	+	1.77812e6i	−0.0475140	+	0.0647711i
$946$	3.17921e7			1.15502
$947$		−	3.56248e7i		−	1.29086i	−0.763821	−	0.645428i	$-0.776679\pi$
$947$		−	3.56248e7i		−	1.29086i	0.763821	−	0.645428i	$-0.223321\pi$
$948$			9.56761e6i			0.345766i
$949$	−3.56206e6			−0.128391
$950$	−6.14898e6	+	1.93580e6i	−0.221052	+	0.0695906i
$951$	2.28787e7			0.820313
$952$		−	248028.i		−	0.00886968i
$953$			3.13360e7i			1.11766i	0.829281	+	0.558832i	$0.188750\pi$
$953$			3.13360e7i			1.11766i	−0.829281	+	0.558832i	$0.811250\pi$
$954$	−1.83575e6			−0.0653046
$955$	−1.11473e7	+	1.51960e7i	−0.395513	+	0.539163i
$956$	1.11401e7			0.394225
$957$		−	8.03919e7i		−	2.83748i
$958$			1.94830e7i			0.685869i
$959$	−471124.			−0.0165420
$960$	−3.31641e6	−	2.43281e6i	−0.116142	−	0.0851982i
$961$	1.61478e7			0.564032
$962$			1.84949e6i			0.0644337i
$963$			1.69631e7i			0.589441i
$964$	5.77026e6			0.199987
$965$	3.21137e6	+	2.35576e6i	0.111013	+	0.0814353i
$966$	−511066.			−0.0176212
$967$			1.69027e7i			0.581284i	0.956832	+	0.290642i	$0.0938689\pi$
$967$			1.69027e7i			0.581284i	−0.956832	+	0.290642i	$0.906131\pi$
$968$			9.38623e6i			0.321961i
$969$	2.67011e6			0.0913524
$970$	1.37585e7	−	1.87555e7i	0.469505	−	0.640029i
$971$	−3.07791e7			−1.04763			−0.523816	−	0.851832i	$-0.675492\pi$
$971$	−3.07791e7			−1.04763			−0.523816	+	0.851832i	$0.675492\pi$
$972$		−	9.30393e6i		−	0.315864i
$973$			1.88034e6i			0.0636728i
$974$	1.50219e7			0.507373
$975$	1.98892e6	+	6.31773e6i	0.0670048	+	0.212838i
$976$	−671908.			−0.0225780
$977$		−	1.49299e7i		−	0.500404i	−0.968194	−	0.250202i	$-0.919503\pi$
$977$		−	1.49299e7i		−	0.500404i	0.968194	−	0.250202i	$-0.0804971\pi$
$978$		−	1.86450e7i		−	0.623326i
$979$	5.55008e7			1.85073
$980$	8.79596e6	−	1.19907e7i	0.292562	−	0.398821i
$981$	928987.			0.0308203
$982$			2.78543e7i			0.921750i
$983$			2.04300e7i			0.674350i	0.941442	+	0.337175i	$0.109471\pi$
$983$			2.04300e7i			0.674350i	−0.941442	+	0.337175i	$0.890529\pi$
$984$	5.09848e6			0.167862
$985$	−2.19273e7	−	1.60852e7i	−0.720103	−	0.528244i
$986$	9.30164e6			0.304696
$987$		−	5.14098e6i		−	0.167978i
$988$			973613.i			0.0317317i
$989$	7.57955e6			0.246407
$990$	−7.96799e6	−	5.84506e6i	−0.258381	−	0.189540i
$991$	−4.24636e7			−1.37351			−0.686757	−	0.726887i	$-0.740966\pi$
$991$	−4.24636e7			−1.37351			−0.686757	+	0.726887i	$0.740966\pi$
$992$			6.85215e6i			0.221079i
$993$		−	2.82608e7i		−	0.909518i
$994$	2.15770e6			0.0692668
$995$	−2.87862e7	+	3.92414e7i	−0.921779	+	1.25657i
$996$	1.98428e7			0.633802
$997$			5.67184e7i			1.80712i	0.428465	+	0.903558i	$0.359054\pi$
$997$			5.67184e7i			1.80712i	−0.428465	+	0.903558i	$0.640946\pi$
$998$			4.60300e6i			0.146290i
$999$	−1.14970e7			−0.364479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.3	✓	26
5.4	even	2	inner	230.6.b.a.139.24	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.3	✓	26	1.1	even	1	trivial
230.6.b.a.139.24	yes	26	5.4	even	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -17.9630i q^{3} -16.0000 q^{4} +(-33.0651 + 45.0744i) q^{5} -71.8519 q^{6} +13.4457i q^{7} +64.0000i q^{8} -79.6687 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -17.9630i q^{3} -16.0000 q^{4} +(-33.0651 + 45.0744i) q^{5} -71.8519 q^{6} +13.4457i q^{7} +64.0000i q^{8} -79.6687 q^{9} +(180.297 + 132.260i) q^{10} +554.717 q^{11} +287.408i q^{12} -117.992i q^{13} +53.7828 q^{14} +(809.670 + 593.948i) q^{15} +256.000 q^{16} +288.229i q^{17} +318.675i q^{18} +515.720 q^{19} +(529.042 - 721.190i) q^{20} +241.525 q^{21} -2218.87i q^{22} -529.000i q^{23} +1149.63 q^{24} +(-938.396 - 2980.78i) q^{25} -471.968 q^{26} -2933.92i q^{27} -215.131i q^{28} +8067.93 q^{29} +(2375.79 - 3238.68i) q^{30} -6691.55 q^{31} -1024.00i q^{32} -9964.37i q^{33} +1152.91 q^{34} +(-606.056 - 444.583i) q^{35} +1274.70 q^{36} -3918.67i q^{37} -2062.88i q^{38} -2119.49 q^{39} +(-2884.76 - 2116.17i) q^{40} +4434.88 q^{41} -966.099i q^{42} +14328.1i q^{43} -8875.47 q^{44} +(2634.25 - 3591.02i) q^{45} -2116.00 q^{46} -21285.5i q^{47} -4598.52i q^{48} +16626.2 q^{49} +(-11923.1 + 3753.58i) q^{50} +5177.44 q^{51} +1887.87i q^{52} +5760.59i q^{53} -11735.7 q^{54} +(-18341.8 + 25003.5i) q^{55} -860.524 q^{56} -9263.86i q^{57} -32271.7i q^{58} -48625.6 q^{59} +(-12954.7 - 9503.17i) q^{60} -2624.64 q^{61} +26766.2i q^{62} -1071.20i q^{63} -4096.00 q^{64} +(5318.42 + 3901.42i) q^{65} -39857.5 q^{66} -1384.02i q^{67} -4611.66i q^{68} -9502.42 q^{69} +(-1778.33 + 2424.22i) q^{70} +40118.8 q^{71} -5098.80i q^{72} -30189.0i q^{73} -15674.7 q^{74} +(-53543.7 + 16856.4i) q^{75} -8251.51 q^{76} +7458.55i q^{77} +8477.95i q^{78} +33289.3 q^{79} +(-8464.67 + 11539.0i) q^{80} -72061.4 q^{81} -17739.5i q^{82} -69040.5i q^{83} -3864.40 q^{84} +(-12991.7 - 9530.31i) q^{85} +57312.3 q^{86} -144924. i q^{87} +35501.9i q^{88} +100052. q^{89} +(-14364.1 - 10537.0i) q^{90} +1586.48 q^{91} +8464.00i q^{92} +120200. i q^{93} -85142.1 q^{94} +(-17052.3 + 23245.7i) q^{95} -18394.1 q^{96} -104025. i q^{97} -66504.9i q^{98} -44193.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Introduction

L-functions

Modular forms

Varieties

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